LMFDB - Embedded newform 930.2.z.d.109.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			109.17
Character	$\chi$	$=$	930.109
Dual form			930.2.z.d.529.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.06791 - 0.850729i) q^{5} +1.00000 q^{6} +(4.57919 + 1.48787i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})$	\(q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.06791 - 0.850729i) q^{5} +1.00000 q^{6} +(4.57919 + 1.48787i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.90374 + 1.17293i) q^{10} +(-0.756539 + 2.32839i) q^{11} +(0.587785 + 0.809017i) q^{12} +(-2.05560 + 2.82930i) q^{13} +(1.48787 + 4.57919i) q^{14} +(0.527234 - 2.17302i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.166785 + 0.0541918i) q^{17} +(0.587785 - 0.809017i) q^{18} +(4.18203 - 3.03842i) q^{19} +(0.170071 + 2.22959i) q^{20} +(3.89529 - 2.83010i) q^{21} +(-2.32839 + 0.756539i) q^{22} +(-7.34995 + 2.38814i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(3.55252 - 3.51846i) q^{25} -3.49720 q^{26} +(-0.951057 - 0.309017i) q^{27} +(-2.83010 + 3.89529i) q^{28} +(1.16639 - 0.847433i) q^{29} +(2.06791 - 0.850729i) q^{30} +(-3.48777 + 4.33998i) q^{31} -1.00000i q^{32} +(1.43902 + 1.98064i) q^{33} +(-0.141876 - 0.103079i) q^{34} +(10.7351 - 0.818866i) q^{35} +1.00000 q^{36} -7.01829i q^{37} +(4.91627 + 1.59739i) q^{38} +(1.08070 + 3.32604i) q^{39} +(-1.70381 + 1.44811i) q^{40} +(2.53632 - 1.84275i) q^{41} +(4.57919 + 1.48787i) q^{42} +(-6.95127 - 9.56761i) q^{43} +(-1.98064 - 1.43902i) q^{44} +(-1.44811 - 1.70381i) q^{45} +(-6.25224 - 4.54252i) q^{46} +(5.11096 - 7.03463i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(13.0921 + 9.51199i) q^{49} +(4.93462 + 0.805949i) q^{50} +(-0.0541918 + 0.166785i) q^{51} +(-2.05560 - 2.82930i) q^{52} +(-12.6164 + 4.09933i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(0.416370 + 5.45851i) q^{55} -4.81485 q^{56} -5.16928i q^{57} +(1.37118 + 0.445522i) q^{58} +(0.313586 + 0.227834i) q^{59} +(1.90374 + 1.17293i) q^{60} +8.48817 q^{61} +(-5.56118 - 0.270686i) q^{62} -4.81485i q^{63} +(0.809017 - 0.587785i) q^{64} +(-1.84385 + 7.59950i) q^{65} +(-0.756539 + 2.32839i) q^{66} +7.67240i q^{67} -0.175368i q^{68} +(-2.38814 + 7.34995i) q^{69} +(6.97243 + 8.20359i) q^{70} +(1.23262 + 3.79361i) q^{71} +(0.587785 + 0.809017i) q^{72} +(8.55266 + 2.77893i) q^{73} +(5.67792 - 4.12525i) q^{74} +(-0.758377 - 4.94215i) q^{75} +(1.59739 + 4.91627i) q^{76} +(-6.92867 + 9.53650i) q^{77} +(-2.05560 + 2.82930i) q^{78} +(-0.366066 - 1.12663i) q^{79} +(-2.17302 - 0.527234i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(2.98162 + 0.968788i) q^{82} +(4.23864 + 5.83399i) q^{83} +(1.48787 + 4.57919i) q^{84} +(-0.298795 + 0.253953i) q^{85} +(3.65450 - 11.2474i) q^{86} -1.44174i q^{87} -2.44821i q^{88} +(2.13360 - 6.56655i) q^{89} +(0.527234 - 2.17302i) q^{90} +(-13.6226 + 9.89742i) q^{91} -7.72820i q^{92} +(1.46106 + 5.37264i) q^{93} +8.69528 q^{94} +(6.06320 - 9.84097i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-13.8684 - 4.50610i) q^{97} +16.1828i q^{98} +2.44821 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$2$	0.587785	+	0.809017i	0.415627	+	0.572061i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$3$	0.587785	−	0.809017i	0.339358	−	0.467086i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	2.06791	−	0.850729i	0.924798	−	0.380457i
$5$	2.06791	−	0.850729i	0.924798	−	0.380457i
$6$	1.00000			0.408248
$7$	4.57919	+	1.48787i	1.73077	+	0.562362i	0.993561	−	0.113300i	$-0.0361422\pi$
$7$	4.57919	+	1.48787i	1.73077	+	0.562362i	0.737211	+	0.675662i	$0.236142\pi$
$8$	−0.951057	+	0.309017i	−0.336249	+	0.109254i
$9$	−0.309017	−	0.951057i	−0.103006	−	0.317019i
$10$	1.90374	+	1.17293i	0.602016	+	0.370913i
$11$	−0.756539	+	2.32839i	−0.228105	+	0.702035i	0.769856	+	0.638217i	$0.220328\pi$
$11$	−0.756539	+	2.32839i	−0.228105	+	0.702035i	−0.997962	+	0.0638181i	$0.979672\pi$
$12$	0.587785	+	0.809017i	0.169679	+	0.233543i
$13$	−2.05560	+	2.82930i	−0.570122	+	0.784706i	−0.992569	−	0.121682i	$-0.961171\pi$
$13$	−2.05560	+	2.82930i	−0.570122	+	0.784706i	0.422447	+	0.906388i	$0.361171\pi$
$14$	1.48787	+	4.57919i	0.397650	+	1.22384i
$15$	0.527234	−	2.17302i	0.136131	−	0.561072i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.166785	+	0.0541918i	−0.0404514	+	0.0131435i	−0.329173	−	0.944270i	$-0.606770\pi$
$17$	−0.166785	+	0.0541918i	−0.0404514	+	0.0131435i	0.288721	+	0.957413i	$0.406770\pi$
$18$	0.587785	−	0.809017i	0.138542	−	0.190687i
$19$	4.18203	−	3.03842i	0.959424	−	0.697062i	0.00640706	−	0.999979i	$-0.497961\pi$
$19$	4.18203	−	3.03842i	0.959424	−	0.697062i	0.953017	+	0.302917i	$0.0979606\pi$
$20$	0.170071	+	2.22959i	0.0380290	+	0.498552i
$21$	3.89529	−	2.83010i	0.850023	−	0.617578i
$22$	−2.32839	+	0.756539i	−0.496414	+	0.161295i
$23$	−7.34995	+	2.38814i	−1.53257	+	0.497962i	−0.949315	−	0.314326i	$-0.898221\pi$
$23$	−7.34995	+	2.38814i	−1.53257	+	0.497962i	−0.583256	+	0.812289i	$0.698221\pi$
$24$	−0.309017	+	0.951057i	−0.0630778	+	0.194134i
$25$	3.55252	−	3.51846i	0.710504	−	0.703693i
$26$	−3.49720			−0.685858
$27$	−0.951057	−	0.309017i	−0.183031	−	0.0594703i
$28$	−2.83010	+	3.89529i	−0.534838	+	0.736141i
$29$	1.16639	−	0.847433i	0.216593	−	0.157364i	−0.474198	−	0.880418i	$-0.657262\pi$
$29$	1.16639	−	0.847433i	0.216593	−	0.157364i	0.690792	+	0.723054i	$0.257262\pi$
$30$	2.06791	−	0.850729i	0.377547	−	0.155321i
$31$	−3.48777	+	4.33998i	−0.626422	+	0.779484i
$31$	−3.48777	+	4.33998i	−0.626422	+	0.779484i
$32$		−	1.00000i		−	0.176777i
$33$	1.43902	+	1.98064i	0.250502	+	0.344786i
$34$	−0.141876	−	0.103079i	−0.0243315	−	0.0176779i
$35$	10.7351	−	0.818866i	1.81457	−	0.138414i
$36$	1.00000			0.166667
$37$		−	7.01829i		−	1.15380i	−0.816815	−	0.576900i	$-0.804262\pi$
$37$		−	7.01829i		−	1.15380i	0.816815	−	0.576900i	$-0.195738\pi$
$38$	4.91627	+	1.59739i	0.797525	+	0.259132i
$39$	1.08070	+	3.32604i	0.173050	+	0.532592i
$40$	−1.70381	+	1.44811i	−0.269396	+	0.228966i
$41$	2.53632	−	1.84275i	0.396107	−	0.287788i	−0.371847	−	0.928294i	$-0.621275\pi$
$41$	2.53632	−	1.84275i	0.396107	−	0.287788i	0.767953	+	0.640506i	$0.221275\pi$
$42$	4.57919	+	1.48787i	0.706585	+	0.229583i
$43$	−6.95127	−	9.56761i	−1.06006	−	1.45905i	−0.879750	−	0.475436i	$-0.842290\pi$
$43$	−6.95127	−	9.56761i	−1.06006	−	1.45905i	−0.180309	−	0.983610i	$-0.557710\pi$
$44$	−1.98064	−	1.43902i	−0.298593	−	0.216941i
$45$	−1.44811	−	1.70381i	−0.215872	−	0.253989i
$46$	−6.25224	−	4.54252i	−0.921843	−	0.669758i
$47$	5.11096	−	7.03463i	0.745510	−	1.02611i	−0.252773	−	0.967526i	$-0.581343\pi$
$47$	5.11096	−	7.03463i	0.745510	−	1.02611i	0.998283	−	0.0585806i	$-0.0186575\pi$
$48$	−0.951057	+	0.309017i	−0.137273	+	0.0446028i
$49$	13.0921	+	9.51199i	1.87030	+	1.35886i
$50$	4.93462	+	0.805949i	0.697860	+	0.113978i
$51$	−0.0541918	+	0.166785i	−0.00758838	+	0.0233546i
$52$	−2.05560	−	2.82930i	−0.285061	−	0.392353i
$53$	−12.6164	+	4.09933i	−1.73300	+	0.563087i	−0.993878	−	0.110482i	$-0.964760\pi$
$53$	−12.6164	+	4.09933i	−1.73300	+	0.563087i	−0.739124	+	0.673569i	$0.764760\pi$
$54$	−0.309017	−	0.951057i	−0.0420519	−	0.129422i
$55$	0.416370	+	5.45851i	0.0561433	+	0.736025i
$56$	−4.81485			−0.643411
$57$		−	5.16928i		−	0.684687i
$58$	1.37118	+	0.445522i	0.180044	+	0.0584999i
$59$	0.313586	+	0.227834i	0.0408254	+	0.0296614i	0.608011	−	0.793929i	$-0.291968\pi$
$59$	0.313586	+	0.227834i	0.0408254	+	0.0296614i	−0.567185	+	0.823590i	$0.691968\pi$
$60$	1.90374	+	1.17293i	0.245772	+	0.151425i
$61$	8.48817			1.08680			0.543400	−	0.839474i	$-0.317137\pi$
$61$	8.48817			1.08680			0.543400	+	0.839474i	$0.317137\pi$
$62$	−5.56118	−	0.270686i	−0.706271	−	0.0343772i
$63$		−	4.81485i		−	0.606614i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$	−1.84385	+	7.59950i	−0.228701	+	0.942602i
$66$	−0.756539	+	2.32839i	−0.0931235	+	0.286605i
$67$			7.67240i			0.937333i	0.883375	+	0.468666i	$0.155265\pi$
$67$			7.67240i			0.937333i	−0.883375	+	0.468666i	$0.844735\pi$
$68$		−	0.175368i		−	0.0212666i
$69$	−2.38814	+	7.34995i	−0.287499	+	0.884830i
$70$	6.97243	+	8.20359i	0.833365	+	0.980517i
$71$	1.23262	+	3.79361i	0.146285	+	0.450219i	0.997174	−	0.0751265i	$-0.0239361\pi$
$71$	1.23262	+	3.79361i	0.146285	+	0.450219i	−0.850889	+	0.525346i	$0.823936\pi$
$72$	0.587785	+	0.809017i	0.0692712	+	0.0953436i
$73$	8.55266	+	2.77893i	1.00101	+	0.325249i	0.763271	−	0.646079i	$-0.223592\pi$
$73$	8.55266	+	2.77893i	1.00101	+	0.325249i	0.237743	+	0.971328i	$0.423592\pi$
$74$	5.67792	−	4.12525i	0.660044	−	0.479550i
$75$	−0.758377	−	4.94215i	−0.0875699	−	0.570671i
$76$	1.59739	+	4.91627i	0.183234	+	0.563935i
$77$	−6.92867	+	9.53650i	−0.789596	+	1.08679i
$78$	−2.05560	+	2.82930i	−0.232751	+	0.320355i
$79$	−0.366066	−	1.12663i	−0.0411856	−	0.126756i	0.928350	−	0.371708i	$-0.121228\pi$
$79$	−0.366066	−	1.12663i	−0.0411856	−	0.126756i	−0.969535	+	0.244952i	$0.921228\pi$
$80$	−2.17302	−	0.527234i	−0.242951	−	0.0589466i
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$	2.98162	+	0.968788i	0.329265	+	0.106985i
$83$	4.23864	+	5.83399i	0.465251	+	0.640364i	0.975587	−	0.219612i	$-0.0704790\pi$
$83$	4.23864	+	5.83399i	0.465251	+	0.640364i	−0.510336	+	0.859975i	$0.670479\pi$
$84$	1.48787	+	4.57919i	0.162340	+	0.499631i
$85$	−0.298795	+	0.253953i	−0.0324089	+	0.0275451i
$86$	3.65450	−	11.2474i	0.394075	−	1.21284i
$87$		−	1.44174i		−	0.154571i
$88$		−	2.44821i		−	0.260980i
$89$	2.13360	−	6.56655i	0.226161	−	0.696053i	−0.772010	−	0.635610i	$-0.780749\pi$
$89$	2.13360	−	6.56655i	0.226161	−	0.696053i	0.998172	−	0.0604432i	$-0.0192514\pi$
$90$	0.527234	−	2.17302i	0.0555754	−	0.229057i
$91$	−13.6226	+	9.89742i	−1.42804	+	1.03753i
$92$		−	7.72820i		−	0.805720i
$93$	1.46106	+	5.37264i	0.151505	+	0.557117i
$94$	8.69528			0.896850
$95$	6.06320	−	9.84097i	0.622071	−	1.00966i
$96$	−0.809017	−	0.587785i	−0.0825700	−	0.0599906i
$97$	−13.8684	−	4.50610i	−1.40812	−	0.457525i	−0.496311	−	0.868145i	$-0.665312\pi$
$97$	−13.8684	−	4.50610i	−1.40812	−	0.457525i	−0.911807	+	0.410620i	$0.865312\pi$
$98$			16.1828i			1.63471i
$99$	2.44821			0.246054
$100$	2.24847	+	4.46591i	0.224847	+	0.446591i
$101$	−5.43706	−	16.7335i	−0.541007	−	1.66505i	−0.730299	−	0.683128i	$-0.760619\pi$
$101$	−5.43706	−	16.7335i	−0.541007	−	1.66505i	0.189291	−	0.981921i	$-0.439381\pi$
$102$	−0.166785	+	0.0541918i	−0.0165142	+	0.00536579i
$103$	6.50016	+	8.94670i	0.640480	+	0.881545i	0.998641	−	0.0521150i	$-0.0165962\pi$
$103$	6.50016	+	8.94670i	0.640480	+	0.881545i	−0.358161	+	0.933660i	$0.616596\pi$
$104$	1.08070	−	3.32604i	0.105971	−	0.326145i
$105$	5.64748	−	9.16623i	0.551138	−	0.894532i
$106$	−10.7322	−	7.79739i	−1.04240	−	0.757350i
$107$	0.275616	−	0.0895531i	0.0266448	−	0.00865743i	−0.295664	−	0.955292i	$-0.595541\pi$
$107$	0.275616	−	0.0895531i	0.0266448	−	0.00865743i	0.322309	+	0.946634i	$0.395541\pi$
$108$	0.587785	−	0.809017i	0.0565597	−	0.0778477i
$109$	−6.38713	−	4.64052i	−0.611776	−	0.444481i	0.238263	−	0.971201i	$-0.423422\pi$
$109$	−6.38713	−	4.64052i	−0.611776	−	0.444481i	−0.850039	+	0.526719i	$0.823422\pi$
$110$	−4.17129	+	3.54528i	−0.397717	+	0.338029i
$111$	−5.67792	−	4.12525i	−0.538924	−	0.391551i
$112$	−2.83010	−	3.89529i	−0.267419	−	0.368071i
$113$	−18.9712	−	6.16412i	−1.78466	−	0.579872i	−0.785425	−	0.618957i	$-0.787556\pi$
$113$	−18.9712	−	6.16412i	−1.78466	−	0.579872i	−0.999236	+	0.0390850i	$0.987556\pi$
$114$	4.18203	−	3.03842i	0.391683	−	0.284574i
$115$	−13.1674	+	11.1913i	−1.22787	+	1.04359i
$116$	0.445522	+	1.37118i	0.0413657	+	0.127310i
$117$	3.32604	+	1.08070i	0.307492	+	0.0999103i
$118$			0.387614i			0.0356827i
$119$	−0.844373			−0.0774035
$120$	0.170071	+	2.22959i	0.0155253	+	0.203533i
$121$	4.05015	+	2.94261i	0.368196	+	0.267510i
$122$	4.98922	+	6.86708i	0.451703	+	0.621716i
$123$		−	3.13507i		−	0.282679i
$124$	−3.04979	−	4.65819i	−0.273879	−	0.418318i
$125$	4.35305	−	10.2981i	0.389348	−	0.921091i
$126$	3.89529	−	2.83010i	0.347020	−	0.252125i
$127$	6.01431	−	8.27799i	0.533684	−	0.734553i	−0.454002	−	0.891001i	$-0.650004\pi$
$127$	6.01431	−	8.27799i	0.533684	−	0.734553i	0.987686	+	0.156448i	$0.0500042\pi$
$128$	0.951057	+	0.309017i	0.0840623	+	0.0273135i
$129$	−11.8262			−1.04124
$130$	−7.23191	+	2.97517i	−0.634280	+	0.260940i
$131$	2.07736	−	6.39346i	0.181500	−	0.558599i	−0.818371	−	0.574691i	$-0.805122\pi$
$131$	2.07736	−	6.39346i	0.181500	−	0.558599i	0.999871	+	0.0160916i	$0.00512234\pi$
$132$	−2.32839	+	0.756539i	−0.202660	+	0.0658483i
$133$	23.6711	−	7.69121i	2.05255	−	0.666912i
$134$	−6.20710	+	4.50972i	−0.536212	+	0.389581i
$135$	−2.22959	+	0.170071i	−0.191893	+	0.0146374i
$136$	0.141876	−	0.103079i	0.0121658	−	0.00883895i
$137$	−7.93486	+	10.9214i	−0.677921	+	0.933078i	−0.999907	−	0.0136664i	$-0.995650\pi$
$137$	−7.93486	+	10.9214i	−0.677921	+	0.933078i	0.321986	+	0.946745i	$0.395650\pi$
$138$	−7.34995	+	2.38814i	−0.625669	+	0.203292i
$139$	7.63815	+	5.54944i	0.647859	+	0.470697i	0.862541	−	0.505987i	$-0.168872\pi$
$139$	7.63815	+	5.54944i	0.647859	+	0.470697i	−0.214682	+	0.976684i	$0.568872\pi$
$140$	−2.53855	+	10.4628i	−0.214547	+	0.884265i
$141$	−2.68699	−	8.26970i	−0.226285	−	0.696435i
$142$	−2.34458	+	3.22704i	−0.196753	+	0.270807i
$143$	−5.03255	−	6.92672i	−0.420843	−	0.579241i
$144$	−0.309017	+	0.951057i	−0.0257514	+	0.0792547i
$145$	1.69106	−	2.74470i	0.140435	−	0.227935i
$146$	2.77893	+	8.55266i	0.229986	+	0.707824i
$147$	15.3907	−	5.00075i	1.26941	−	0.412455i
$148$	6.67479	+	2.16877i	0.548664	+	0.178272i
$149$	−21.6687			−1.77517			−0.887585	−	0.460644i	$-0.847619\pi$
$149$	−21.6687			−1.77517			−0.887585	+	0.460644i	$0.847619\pi$
$150$	3.55252	−	3.51846i	0.290062	−	0.287281i
$151$	3.93661	−	12.1156i	0.320357	−	0.985957i	−0.653136	−	0.757240i	$-0.726547\pi$
$151$	3.93661	−	12.1156i	0.320357	−	0.985957i	0.973493	−	0.228716i	$-0.0734528\pi$
$152$	−3.03842	+	4.18203i	−0.246449	+	0.339208i
$153$	0.103079	+	0.141876i	0.00833344	+	0.0114700i
$154$	−11.7878			−0.949885
$155$	−3.52025	+	11.9419i	−0.282753	+	0.959193i
$156$	−3.49720			−0.280000
$157$	−8.94957	−	12.3180i	−0.714253	−	0.983085i	−0.999695	−	0.0246893i	$-0.992140\pi$
$157$	−8.94957	−	12.3180i	−0.714253	−	0.983085i	0.285442	−	0.958396i	$-0.407860\pi$
$158$	0.696299	−	0.958373i	0.0553945	−	0.0762440i
$159$	−4.09933	+	12.6164i	−0.325098	+	1.00055i
$160$	−0.850729	−	2.06791i	−0.0672560	−	0.163483i
$161$	−37.2101			−2.93257
$162$	−0.951057	−	0.309017i	−0.0747221	−	0.0242787i
$163$	2.00514	−	0.651509i	0.157055	−	0.0510301i	−0.229435	−	0.973324i	$-0.573688\pi$
$163$	2.00514	−	0.651509i	0.157055	−	0.0510301i	0.386489	+	0.922294i	$0.373688\pi$
$164$	0.968788	+	2.98162i	0.0756497	+	0.232826i
$165$	4.66076	+	2.87158i	0.362840	+	0.223552i
$166$	−2.22839	+	6.85827i	−0.172956	+	0.532305i
$167$	−2.60031	−	3.57902i	−0.201218	−	0.276953i	0.696469	−	0.717587i	$-0.254753\pi$
$167$	−2.60031	−	3.57902i	−0.201218	−	0.276953i	−0.897687	+	0.440635i	$0.854753\pi$
$168$	−2.83010	+	3.89529i	−0.218347	+	0.300528i
$169$	0.237811	+	0.731907i	0.0182931	+	0.0563005i
$170$	−0.381080	−	0.0924603i	−0.0292275	−	0.00709138i
$171$	−4.18203	−	3.03842i	−0.319808	−	0.232354i
$172$	11.2474	−	3.65450i	0.857606	−	0.278653i
$173$	−3.74228	+	5.15081i	−0.284521	+	0.391609i	−0.927225	−	0.374505i	$-0.877812\pi$
$173$	−3.74228	+	5.15081i	−0.284521	+	0.391609i	0.642704	+	0.766115i	$0.277812\pi$
$174$	1.16639	−	0.847433i	0.0884239	−	0.0642437i
$175$	21.5027	−	10.8260i	1.62545	−	0.818371i
$176$	1.98064	−	1.43902i	0.149297	−	0.108470i
$177$	0.368642	−	0.119779i	0.0277089	−	0.00900316i
$178$	6.56655	−	2.13360i	0.492184	−	0.159920i
$179$	1.58702	−	4.88435i	0.118620	−	0.365073i	−0.874065	−	0.485809i	$-0.838525\pi$
$179$	1.58702	−	4.88435i	0.118620	−	0.365073i	0.992685	+	0.120735i	$0.0385252\pi$
$180$	2.06791	−	0.850729i	0.154133	−	0.0634096i
$181$	−8.28986			−0.616180			−0.308090	−	0.951357i	$-0.599690\pi$
$181$	−8.28986			−0.616180			−0.308090	+	0.951357i	$0.599690\pi$
$182$	−16.0144	−	5.20338i	−1.18706	−	0.385700i
$183$	4.98922	−	6.86708i	0.368814	−	0.507629i
$184$	6.25224	−	4.54252i	0.460921	−	0.334879i
$185$	−5.97066	−	14.5132i	−0.438972	−	1.06703i
$186$	−3.48777	+	4.33998i	−0.255736	+	0.318223i
$187$		−	0.429339i		−	0.0313964i
$188$	5.11096	+	7.03463i	0.372755	+	0.513053i
$189$	−3.89529	−	2.83010i	−0.283341	−	0.205859i
$190$	11.5254	−	0.879144i	0.836138	−	0.0637798i
$191$	−11.6955			−0.846259			−0.423129	−	0.906069i	$-0.639068\pi$
$191$	−11.6955			−0.846259			−0.423129	+	0.906069i	$0.639068\pi$
$192$		−	1.00000i		−	0.0721688i
$193$	−3.65044	−	1.18610i	−0.262764	−	0.0853772i	0.174672	−	0.984627i	$-0.444113\pi$
$193$	−3.65044	−	1.18610i	−0.262764	−	0.0853772i	−0.437436	+	0.899249i	$0.644113\pi$
$194$	−4.50610	−	13.8684i	−0.323519	−	0.995690i
$195$	5.06434	+	5.95858i	0.362665	+	0.426702i
$196$	−13.0921	+	9.51199i	−0.935152	+	0.679428i
$197$	10.1655	+	3.30298i	0.724263	+	0.235327i	0.647871	−	0.761750i	$-0.275660\pi$
$197$	10.1655	+	3.30298i	0.724263	+	0.235327i	0.0763926	+	0.997078i	$0.475660\pi$
$198$	1.43902	+	1.98064i	0.102267	+	0.140758i
$199$	8.76618	+	6.36900i	0.621418	+	0.451486i	0.853416	−	0.521230i	$-0.174526\pi$
$199$	8.76618	+	6.36900i	0.621418	+	0.451486i	−0.231999	+	0.972716i	$0.574526\pi$
$200$	−2.29138	+	4.44405i	−0.162025	+	0.314242i
$201$	6.20710	+	4.50972i	0.437815	+	0.318091i
$202$	10.3419	−	14.2344i	0.727653	−	1.00153i
$203$	6.60200	−	2.14512i	0.463370	−	0.150558i
$204$	−0.141876	−	0.103079i	−0.00993331	−	0.00721697i
$205$	3.67721	−	5.96836i	0.256828	−	0.416848i
$206$	−3.41734	+	10.5175i	−0.238097	+	0.732787i
$207$	4.54252	+	6.25224i	0.315727	+	0.434561i
$208$	3.32604	−	1.08070i	0.230619	−	0.0749327i
$209$	3.91076	+	12.0361i	0.270513	+	0.832553i
$210$	10.7351	−	0.818866i	0.740795	−	0.0565071i
$211$	12.0095			0.826765			0.413383	−	0.910557i	$-0.364347\pi$
$211$	12.0095			0.826765			0.413383	+	0.910557i	$0.364347\pi$
$212$		−	13.2657i		−	0.911093i
$213$	3.79361	+	1.23262i	0.259934	+	0.0844577i
$214$	0.234453	+	0.170340i	0.0160269	+	0.0116442i
$215$	−22.5141	−	13.8713i	−1.53545	−	0.946016i
$216$	1.00000			0.0680414
$217$	−22.4285	+	14.6843i	−1.52255	+	0.996834i
$218$		−	7.89492i		−	0.534712i
$219$	7.27533	−	5.28584i	0.491621	−	0.357184i
$220$	−5.32002	−	1.29078i	−0.358675	−	0.0870245i
$221$	0.189520	−	0.583282i	0.0127485	−	0.0392358i
$222$		−	7.01829i		−	0.471037i
$223$		−	13.3404i		−	0.893336i	−0.894700	−	0.446668i	$-0.852611\pi$
$223$		−	13.3404i		−	0.893336i	0.894700	−	0.446668i	$-0.147389\pi$
$224$	1.48787	−	4.57919i	0.0994125	−	0.305960i
$225$	−4.44405	−	2.29138i	−0.296270	−	0.152759i
$226$	−6.16412	−	18.9712i	−0.410031	−	1.26195i
$227$	14.9764	+	20.6133i	0.994020	+	1.36815i	0.928923	+	0.370272i	$0.120736\pi$
$227$	14.9764	+	20.6133i	0.994020	+	1.36815i	0.0650966	+	0.997879i	$0.479264\pi$
$228$	4.91627	+	1.59739i	0.325588	+	0.105790i
$229$	−0.787756	+	0.572338i	−0.0520564	+	0.0378212i	−0.613509	−	0.789688i	$-0.710243\pi$
$229$	−0.787756	+	0.572338i	−0.0520564	+	0.0378212i	0.561453	+	0.827509i	$0.310243\pi$
$230$	−16.7935	−	4.07457i	−1.10733	−	0.268669i
$231$	3.64262	+	11.2108i	0.239667	+	0.737618i
$232$	−0.847433	+	1.16639i	−0.0556367	+	0.0765773i
$233$	3.94529	−	5.43022i	0.258464	−	0.355745i	−0.659989	−	0.751275i	$-0.729439\pi$
$233$	3.94529	−	5.43022i	0.258464	−	0.355745i	0.918453	+	0.395530i	$0.129439\pi$
$234$	1.08070	+	3.32604i	0.0706472	+	0.217430i
$235$	4.58445	−	18.8950i	0.299057	−	1.23258i
$236$	−0.313586	+	0.227834i	−0.0204127	+	0.0148307i
$237$	−1.12663	−	0.366066i	−0.0731828	−	0.0237785i
$238$	−0.496310	−	0.683112i	−0.0321710	−	0.0442796i
$239$	−1.27679	−	3.92955i	−0.0825886	−	0.254181i	0.901232	−	0.433336i	$-0.142664\pi$
$239$	−1.27679	−	3.92955i	−0.0825886	−	0.254181i	−0.983821	+	0.179155i	$0.942664\pi$
$240$	−1.70381	+	1.44811i	−0.109981	+	0.0934752i
$241$	−7.44065	+	22.9000i	−0.479294	+	1.47512i	0.360783	+	0.932650i	$0.382510\pi$
$241$	−7.44065	+	22.9000i	−0.479294	+	1.47512i	−0.840077	+	0.542467i	$0.817490\pi$
$242$			5.00626i			0.321815i
$243$			1.00000i			0.0641500i
$244$	−2.62299	+	8.07273i	−0.167920	+	0.516804i
$245$	35.1655	+	8.53211i	2.24664	+	0.545096i
$246$	2.53632	−	1.84275i	0.161710	−	0.117489i
$247$			18.0780i			1.15028i
$248$	1.97594	−	5.20535i	0.125472	−	0.330540i
$249$	7.21121			0.456992
$250$	10.8900	−	2.53139i	0.688744	−	0.160099i
$251$	−6.90194	−	5.01455i	−0.435646	−	0.316516i	0.348256	−	0.937399i	$-0.386774\pi$
$251$	−6.90194	−	5.01455i	−0.435646	−	0.316516i	−0.783903	+	0.620884i	$0.786774\pi$
$252$	4.57919	+	1.48787i	0.288462	+	0.0937270i
$253$		−	18.9203i		−	1.18951i
$254$	10.2322			0.642023
$255$	0.0298251	+	0.391000i	0.00186772	+	0.0244854i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	7.73068	−	2.51185i	0.482226	−	0.156685i	−0.0578082	−	0.998328i	$-0.518411\pi$
$257$	7.73068	−	2.51185i	0.482226	−	0.156685i	0.540035	+	0.841643i	$0.318411\pi$
$258$	−6.95127	−	9.56761i	−0.432767	−	0.595653i
$259$	10.4423	−	32.1381i	0.648853	−	1.99696i
$260$	−6.65777	−	4.10198i	−0.412898	−	0.254394i
$261$	−1.16639	−	0.847433i	−0.0721978	−	0.0524548i
$262$	6.39346	−	2.07736i	0.394989	−	0.128340i
$263$	−7.99967	+	11.0106i	−0.493280	+	0.678942i	−0.980989	−	0.194064i	$-0.937833\pi$
$263$	−7.99967	+	11.0106i	−0.493280	+	0.678942i	0.487708	+	0.873007i	$0.337833\pi$
$264$	−1.98064	−	1.43902i	−0.121900	−	0.0885657i
$265$	−22.6023	+	19.2102i	−1.38845	+	1.18008i
$266$	20.1358	+	14.6295i	1.23461	+	0.896995i
$267$	−4.05835	−	5.58585i	−0.248367	−	0.341848i
$268$	−7.29689	−	2.37090i	−0.445728	−	0.144826i
$269$	−13.7559	+	9.99422i	−0.838710	+	0.609358i	−0.922010	−	0.387166i	$-0.873454\pi$
$269$	−13.7559	+	9.99422i	−0.838710	+	0.609358i	0.0833002	+	0.996525i	$0.473454\pi$
$270$	−1.44811	−	1.70381i	−0.0881292	−	0.103691i
$271$	−1.79717	−	5.53114i	−0.109171	−	0.335993i	0.881516	−	0.472154i	$-0.156523\pi$
$271$	−1.79717	−	5.53114i	−0.109171	−	0.335993i	−0.990687	+	0.136162i	$0.956523\pi$
$272$	0.166785	+	0.0541918i	0.0101128	+	0.00328586i
$273$			16.8385i			1.01911i
$274$	−13.4996			−0.815540
$275$	5.50473	+	10.9335i	0.331947	+	0.659315i
$276$	−6.25224	−	4.54252i	−0.376341	−	0.273428i
$277$	14.4576	+	19.8991i	0.868671	+	1.19562i	0.979432	+	0.201776i	$0.0646712\pi$
$277$	14.4576	+	19.8991i	0.868671	+	1.19562i	−0.110761	+	0.993847i	$0.535329\pi$
$278$			9.44127i			0.566250i
$279$	5.20535	+	1.97594i	0.311636	+	0.118296i
$280$	−9.95668	+	4.09613i	−0.595026	+	0.244791i
$281$	−18.2190	+	13.2369i	−1.08685	+	0.789646i	−0.978865	−	0.204506i	$-0.934441\pi$
$281$	−18.2190	+	13.2369i	−1.08685	+	0.789646i	−0.107989	+	0.994152i	$0.534441\pi$
$282$	5.11096	−	7.03463i	0.304353	−	0.418906i
$283$	−1.94336	−	0.631437i	−0.115521	−	0.0375350i	0.250686	−	0.968068i	$-0.419344\pi$
$283$	−1.94336	−	0.631437i	−0.115521	−	0.0375350i	−0.366207	+	0.930533i	$0.619344\pi$
$284$	−3.98884			−0.236694
$285$	−4.39765	−	10.6896i	−0.260494	−	0.633198i
$286$	2.64577	−	8.14284i	0.156448	−	0.481496i
$287$	14.3561	−	4.66457i	0.847412	−	0.275341i
$288$	−0.951057	+	0.309017i	−0.0560415	+	0.0182090i
$289$	−13.7284	+	9.97427i	−0.807553	+	0.586722i
$290$	3.21449	−	0.245198i	0.188761	−	0.0143985i
$291$	−11.7971	+	8.57111i	−0.691560	+	0.502447i
$292$	−5.28584	+	7.27533i	−0.309330	+	0.425757i
$293$	−27.2810	+	8.86414i	−1.59377	+	0.517849i	−0.965558	−	0.260189i	$-0.916215\pi$
$293$	−27.2810	+	8.86414i	−1.59377	+	0.517849i	−0.628217	+	0.778038i	$0.716215\pi$
$294$	13.0921	+	9.51199i	0.763548	+	0.554750i
$295$	0.842293	+	0.204363i	0.0490402	+	0.0118985i
$296$	2.16877	+	6.67479i	0.126057	+	0.387964i
$297$	1.43902	−	1.98064i	0.0835006	−	0.114929i
$298$	−12.7366	−	17.5304i	−0.737809	−	1.01551i
$299$	8.35182	−	25.7043i	0.482998	−	1.48652i
$300$	4.93462	+	0.805949i	0.284900	+	0.0465315i
$301$	−17.5959	−	54.1545i	−1.01421	−	3.12141i
$302$	12.1156	−	3.93661i	0.697177	−	0.226526i
$303$	−16.7335	−	5.43706i	−0.961317	−	0.312351i
$304$	−5.16928			−0.296478
$305$	17.5528	−	7.22113i	1.00507	−	0.413481i
$306$	−0.0541918	+	0.166785i	−0.00309794	+	0.00953448i
$307$	−3.64973	+	5.02342i	−0.208301	+	0.286702i	−0.900366	−	0.435133i	$-0.856701\pi$
$307$	−3.64973	+	5.02342i	−0.208301	+	0.286702i	0.692065	+	0.721835i	$0.256701\pi$
$308$	−6.92867	−	9.53650i	−0.394798	−	0.543393i
$309$	11.0587			0.629109
$310$	−11.7303	+	4.17130i	−0.666237	+	0.236914i
$311$	7.90841			0.448445			0.224222	−	0.974538i	$-0.428016\pi$
$311$	7.90841			0.448445			0.224222	+	0.974538i	$0.428016\pi$
$312$	−2.05560	−	2.82930i	−0.116376	−	0.160177i
$313$	6.69013	−	9.20817i	0.378148	−	0.520477i	−0.576944	−	0.816783i	$-0.695755\pi$
$313$	6.69013	−	9.20817i	0.378148	−	0.520477i	0.955093	+	0.296307i	$0.0957551\pi$
$314$	4.70507	−	14.4807i	0.265522	−	0.817194i
$315$	−4.09613	−	9.95668i	−0.230791	−	0.560996i
$316$	1.18461			0.0666397
$317$	8.00095	+	2.59967i	0.449378	+	0.146012i	0.524958	−	0.851128i	$-0.324081\pi$
$317$	8.00095	+	2.59967i	0.449378	+	0.146012i	−0.0755803	+	0.997140i	$0.524081\pi$
$318$	−12.6164	+	4.09933i	−0.707495	+	0.229879i
$319$	1.09073	+	3.35693i	0.0610692	+	0.187952i
$320$	1.17293	−	1.90374i	0.0655688	−	0.106422i
$321$	0.0895531	−	0.275616i	0.00499837	−	0.0153834i
$322$	−21.8715	−	30.1036i	−1.21885	−	1.67761i
$323$	−0.532844	+	0.733397i	−0.0296482	+	0.0408073i
$324$	−0.309017	−	0.951057i	−0.0171676	−	0.0528365i
$325$	2.65220	+	17.2837i	0.147118	+	0.958728i
$326$	1.70567	+	1.23924i	0.0944685	+	0.0686354i
$327$	−7.50852	+	2.43967i	−0.415222	+	0.134914i
$328$	−1.84275	+	2.53632i	−0.101749	+	0.140045i
$329$	33.8707	−	24.6085i	1.86735	−	1.35671i
$330$	0.416370	+	5.45851i	0.0229204	+	0.300481i
$331$	7.97151	−	5.79164i	0.438154	−	0.318337i	−0.346747	−	0.937959i	$-0.612714\pi$
$331$	7.97151	−	5.79164i	0.438154	−	0.318337i	0.784901	+	0.619621i	$0.212714\pi$
$332$	−6.85827	+	2.22839i	−0.376396	+	0.122299i
$333$	−6.67479	+	2.16877i	−0.365776	+	0.118848i
$334$	1.36706	−	4.20739i	0.0748023	−	0.230218i
$335$	6.52713	+	15.8658i	0.356615	+	0.866844i
$336$	−4.81485			−0.262671
$337$	18.9132	+	6.14526i	1.03027	+	0.334754i	0.774895	−	0.632089i	$-0.217802\pi$
$337$	18.9132	+	6.14526i	1.03027	+	0.334754i	0.255371	+	0.966843i	$0.417802\pi$
$338$	−0.452343	+	0.622597i	−0.0246042	+	0.0338648i
$339$	−16.1379	+	11.7249i	−0.876489	+	0.636807i
$340$	−0.149191	−	0.362647i	−0.00809102	−	0.0196673i
$341$	−7.46653	−	11.4042i	−0.404335	−	0.617574i
$342$		−	5.16928i		−	0.279522i
$343$	25.9881	+	35.7695i	1.40323	+	1.93137i
$344$	9.56761	+	6.95127i	0.515851	+	0.374788i
$345$	1.31434	+	17.2307i	0.0707618	+	0.927671i
$346$	−6.36676			−0.342279
$347$		−	14.7759i		−	0.793211i	−0.917989	−	0.396605i	$-0.870188\pi$
$347$		−	14.7759i		−	0.793211i	0.917989	−	0.396605i	$-0.129812\pi$
$348$	1.37118	+	0.445522i	0.0735027	+	0.0238825i
$349$	6.39100	+	19.6695i	0.342102	+	1.05288i	0.963117	+	0.269084i	$0.0867209\pi$
$349$	6.39100	+	19.6695i	0.342102	+	1.05288i	−0.621014	+	0.783799i	$0.713279\pi$
$350$	21.3974	+	11.0327i	1.14374	+	0.589721i
$351$	2.82930	−	2.05560i	0.151017	−	0.109720i
$352$	2.32839	+	0.756539i	0.124103	+	0.0403237i
$353$	−4.93483	−	6.79221i	−0.262654	−	0.361513i	0.657238	−	0.753683i	$-0.271725\pi$
$353$	−4.93483	−	6.79221i	−0.262654	−	0.361513i	−0.919893	+	0.392170i	$0.871725\pi$
$354$	0.313586	+	0.227834i	0.0166669	+	0.0121092i
$355$	5.77628	+	6.79623i	0.306573	+	0.360707i
$356$	5.58585	+	4.05835i	0.296049	+	0.215092i
$357$	−0.496310	+	0.683112i	−0.0262675	+	0.0361541i
$358$	4.88435	−	1.58702i	0.258146	−	0.0838767i
$359$	3.13813	+	2.27998i	0.165624	+	0.120333i	0.667510	−	0.744601i	$-0.267360\pi$
$359$	3.13813	+	2.27998i	0.165624	+	0.120333i	−0.501886	+	0.864934i	$0.667360\pi$
$360$	1.90374	+	1.17293i	0.100336	+	0.0618189i
$361$	2.38605	−	7.34350i	0.125581	−	0.386500i
$362$	−4.87266	−	6.70664i	−0.256101	−	0.352493i
$363$	4.76124	−	1.54702i	0.249900	−	0.0811975i
$364$	−5.20338	−	16.0144i	−0.272731	−	0.839381i
$365$	20.0503	−	1.52941i	1.04948	−	0.0800532i
$366$	8.48817			0.443684
$367$			24.1966i			1.26305i	0.775355	+	0.631526i	$0.217571\pi$
$367$			24.1966i			1.26305i	−0.775355	+	0.631526i	$0.782429\pi$
$368$	7.34995	+	2.38814i	0.383143	+	0.124491i
$369$	−2.53632	−	1.84275i	−0.132036	−	0.0959295i
$370$	8.23197	−	13.3610i	0.427959	−	0.694606i
$371$	−63.8724			−3.31609
$372$	−5.56118	−	0.270686i	−0.288334	−	0.0140344i
$373$		−	24.1608i		−	1.25100i	−0.780224	−	0.625500i	$-0.784895\pi$
$373$		−	24.1608i		−	1.25100i	0.780224	−	0.625500i	$-0.215105\pi$
$374$	0.347343	−	0.252359i	0.0179607	−	0.0130492i
$375$	−5.77269	−	9.57476i	−0.298100	−	0.494439i
$376$	−2.68699	+	8.26970i	−0.138571	+	0.426477i
$377$			5.04205i			0.259679i
$378$		−	4.81485i		−	0.247649i
$379$	−6.56450	+	20.2034i	−0.337195	+	1.03778i	0.628435	+	0.777862i	$0.283696\pi$
$379$	−6.56450	+	20.2034i	−0.337195	+	1.03778i	−0.965630	+	0.259919i	$0.916304\pi$
$380$	7.48569	+	8.80747i	0.384008	+	0.451814i
$381$	−3.16191	−	9.73136i	−0.161990	−	0.498553i
$382$	−6.87446	−	9.46188i	−0.351728	−	0.484112i
$383$	14.7590	+	4.79549i	0.754150	+	0.245038i	0.660766	−	0.750592i	$-0.270232\pi$
$383$	14.7590	+	4.79549i	0.754150	+	0.245038i	0.0933840	+	0.995630i	$0.470232\pi$
$384$	0.809017	−	0.587785i	0.0412850	−	0.0299953i
$385$	−6.21492	+	25.6151i	−0.316741	+	1.30546i
$386$	−1.18610	−	3.65044i	−0.0603708	−	0.185802i
$387$	−6.95127	+	9.56761i	−0.353353	+	0.486349i
$388$	8.57111	−	11.7971i	0.435132	−	0.598908i
$389$	−6.49811	−	19.9991i	−0.329467	−	1.01400i	−0.969384	−	0.245551i	$-0.921031\pi$
$389$	−6.49811	−	19.9991i	−0.329467	−	1.01400i	0.639916	−	0.768445i	$-0.278969\pi$
$390$	−1.84385	+	7.59950i	−0.0933668	+	0.384816i
$391$	1.09645	−	0.796615i	0.0554497	−	0.0402865i
$392$	−15.3907	−	5.00075i	−0.777349	−	0.252576i
$393$	−3.95138	−	5.43860i	−0.199321	−	0.274341i
$394$	3.30298	+	10.1655i	0.166402	+	0.512131i
$395$	−1.71545	−	2.01836i	−0.0863138	−	0.101555i
$396$	−0.756539	+	2.32839i	−0.0380175	+	0.117006i
$397$		−	13.5138i		−	0.678239i	−0.940743	−	0.339119i	$-0.889871\pi$
$397$		−	13.5138i		−	0.678239i	0.940743	−	0.339119i	$-0.110129\pi$
$398$			10.8356i			0.543139i
$399$	7.69121	−	23.6711i	0.385042	−	1.18504i
$400$	−4.94215	+	0.758377i	−0.247108	+	0.0379189i
$401$	8.35703	−	6.07174i	0.417330	−	0.303208i	−0.359232	−	0.933248i	$-0.616961\pi$
$401$	8.35703	−	6.07174i	0.417330	−	0.303208i	0.776563	+	0.630040i	$0.216961\pi$
$402$			7.67240i			0.382664i
$403$	−5.10963	−	18.7892i	−0.254529	−	0.935958i
$404$	17.5947			0.875368
$405$	−1.17293	+	1.90374i	−0.0582834	+	0.0945977i
$406$	5.61600	+	4.08026i	0.278717	+	0.202500i
$407$	16.3413	+	5.30961i	0.810008	+	0.263188i
$408$		−	0.175368i		−	0.00868203i
$409$	−21.7330			−1.07463			−0.537314	−	0.843382i	$-0.680561\pi$
$409$	−21.7330			−1.07463			−0.537314	+	0.843382i	$0.680561\pi$
$410$	6.98991	−	0.533183i	0.345207	−	0.0263321i
$411$	4.17160	+	12.8389i	0.205770	+	0.633295i
$412$	−10.5175	+	3.41734i	−0.518159	+	0.168360i
$413$	1.09698	+	1.50987i	0.0539791	+	0.0742958i
$414$	−2.38814	+	7.34995i	−0.117371	+	0.361230i
$415$	13.7283	+	8.45824i	0.673895	+	0.415199i
$416$	2.82930	+	2.05560i	0.138718	+	0.100784i
$417$	8.97918	−	2.91751i	0.439712	−	0.142871i
$418$	−7.43870	+	10.2385i	−0.363839	+	0.500781i
$419$	31.6173	+	22.9713i	1.54461	+	1.12222i	0.947364	+	0.320160i	$0.103737\pi$
$419$	31.6173	+	22.9713i	1.54461	+	1.12222i	0.597241	+	0.802061i	$0.296263\pi$
$420$	6.97243	+	8.20359i	0.340220	+	0.400294i
$421$	−10.1046	−	7.34143i	−0.492469	−	0.357799i	0.313664	−	0.949534i	$-0.398443\pi$
$421$	−10.1046	−	7.34143i	−0.492469	−	0.357799i	−0.806133	+	0.591735i	$0.798443\pi$
$422$	7.05898	+	9.71586i	0.343626	+	0.472961i
$423$	−8.26970	−	2.68699i	−0.402087	−	0.130646i
$424$	10.7322	−	7.79739i	0.521201	−	0.378675i
$425$	−0.401837	+	0.779346i	−0.0194919	+	0.0378038i
$426$	1.23262	+	3.79361i	0.0597206	+	0.183801i
$427$	38.8690	+	12.6293i	1.88100	+	0.611174i
$428$			0.289800i			0.0140080i
$429$	−8.56189			−0.413372
$430$	−2.01130	−	26.3676i	−0.0969933	−	1.27156i
$431$	21.1650	+	15.3773i	1.01948	+	0.740699i	0.966177	−	0.257879i	$-0.0830237\pi$
$431$	21.1650	+	15.3773i	1.01948	+	0.740699i	0.0533072	+	0.998578i	$0.483024\pi$
$432$	0.587785	+	0.809017i	0.0282798	+	0.0389238i
$433$			14.8389i			0.713112i	0.934274	+	0.356556i	$0.116049\pi$
$433$			14.8389i			0.713112i	−0.934274	+	0.356556i	$0.883951\pi$
$434$	−25.0630	−	9.51384i	−1.20306	−	0.456679i
$435$	−1.22653	−	2.98139i	−0.0588075	−	0.142947i
$436$	6.38713	−	4.64052i	0.305888	−	0.222241i
$437$	−23.4815	+	32.3196i	−1.12327	+	1.54605i
$438$	8.55266	+	2.77893i	0.408662	+	0.132782i
$439$	−16.2437			−0.775272			−0.387636	−	0.921813i	$-0.626708\pi$
$439$	−16.2437			−0.775272			−0.387636	+	0.921813i	$0.626708\pi$
$440$	−2.08276	−	5.06269i	−0.0992918	−	0.241354i
$441$	5.00075	−	15.3907i	0.238131	−	0.732891i
$442$	0.583282	−	0.189520i	0.0277439	−	0.00901454i
$443$	8.23355	−	2.67524i	0.391188	−	0.127105i	−0.106817	−	0.994279i	$-0.534066\pi$
$443$	8.23355	−	2.67524i	0.391188	−	0.127105i	0.498005	+	0.867174i	$0.334066\pi$
$444$	5.67792	−	4.12525i	0.269462	−	0.195776i
$445$	−1.17425	−	15.3942i	−0.0556649	−	0.729754i
$446$	10.7926	−	7.84126i	0.511043	−	0.371294i
$447$	−12.7366	+	17.5304i	−0.602418	+	0.829158i
$448$	4.57919	−	1.48787i	0.216347	−	0.0702952i
$449$	6.84978	+	4.97666i	0.323261	+	0.234863i	0.737566	−	0.675275i	$-0.235975\pi$
$449$	6.84978	+	4.97666i	0.323261	+	0.234863i	−0.414305	+	0.910138i	$0.635975\pi$
$450$	−0.758377	−	4.94215i	−0.0357502	−	0.232975i
$451$	2.37180	+	7.29965i	0.111684	+	0.343727i
$452$	11.7249	−	16.1379i	0.551491	−	0.759062i
$453$	−7.48788	−	10.3062i	−0.351811	−	0.484226i
$454$	−7.87357	+	24.2324i	−0.369525	+	1.13728i
$455$	−19.7504	+	32.0562i	−0.925912	+	1.50282i
$456$	1.59739	+	4.91627i	0.0748048	+	0.230226i
$457$	−23.7757	+	7.72521i	−1.11218	+	0.361370i	−0.806779	−	0.590853i	$-0.798791\pi$
$457$	−23.7757	+	7.72521i	−1.11218	+	0.361370i	−0.305403	+	0.952223i	$0.598791\pi$
$458$	−0.926062	−	0.300896i	−0.0432721	−	0.0140599i
$459$	0.175368			0.00818550
$460$	−6.57460	−	15.9812i	−0.306542	−	0.745129i
$461$	−2.55326	+	7.85813i	−0.118917	+	0.365990i	−0.992744	−	0.120248i	$-0.961631\pi$
$461$	−2.55326	+	7.85813i	−0.118917	+	0.365990i	0.873827	+	0.486238i	$0.161631\pi$
$462$	−6.92867	+	9.53650i	−0.322351	+	0.443678i
$463$	10.3363	+	14.2267i	0.480368	+	0.661170i	0.978576	−	0.205888i	$-0.0660082\pi$
$463$	10.3363	+	14.2267i	0.480368	+	0.661170i	−0.498208	+	0.867058i	$0.666008\pi$
$464$	−1.44174			−0.0669310
$465$	7.59201	+	9.86719i	0.352071	+	0.457580i
$466$	6.71212			0.310933
$467$	−7.84273	−	10.7946i	−0.362918	−	0.499514i	0.588041	−	0.808831i	$-0.299900\pi$
$467$	−7.84273	−	10.7946i	−0.362918	−	0.499514i	−0.950959	+	0.309317i	$0.899900\pi$
$468$	−2.05560	+	2.82930i	−0.0950203	+	0.130784i
$469$	−11.4155	+	35.1334i	−0.527120	+	1.62231i
$470$	17.9811	−	7.39732i	0.829405	−	0.341213i
$471$	−15.2259			−0.701573
$472$	−0.368642	−	0.119779i	−0.0169681	−	0.00551328i
$473$	27.5360	−	8.94699i	1.26611	−	0.411383i
$474$	−0.366066	−	1.12663i	−0.0168140	−	0.0517481i
$475$	4.16617	−	25.5084i	0.191157	−	1.17041i
$476$	0.260925	−	0.803046i	0.0119595	−	0.0368076i
$477$	7.79739	+	10.7322i	0.357018	+	0.491393i
$478$	2.42860	−	3.34267i	0.111081	−	0.152890i
$479$	−1.77523	−	5.46358i	−0.0811121	−	0.249637i	0.902274	−	0.431163i	$-0.141897\pi$
$479$	−1.77523	−	5.46358i	−0.0811121	−	0.249637i	−0.983386	+	0.181525i	$0.941897\pi$
$480$	−2.17302	−	0.527234i	−0.0991844	−	0.0240648i
$481$	19.8568	+	14.4268i	0.905393	+	0.657807i
$482$	−22.9000	+	7.44065i	−1.04306	+	0.338912i
$483$	−21.8715	+	30.1036i	−0.995190	+	1.36976i
$484$	−4.05015	+	2.94261i	−0.184098	+	0.133755i
$485$	−32.5120	+	2.47998i	−1.47629	+	0.112610i
$486$	−0.809017	+	0.587785i	−0.0366978	+	0.0266625i
$487$	−14.2068	+	4.61607i	−0.643772	+	0.209174i	−0.612666	−	0.790342i	$-0.709903\pi$
$487$	−14.2068	+	4.61607i	−0.643772	+	0.209174i	−0.0311060	+	0.999516i	$0.509903\pi$
$488$	−8.07273	+	2.62299i	−0.365435	+	0.118737i
$489$	0.651509	−	2.00514i	0.0294623	−	0.0906755i
$490$	13.7671	+	33.4645i	0.621936	+	1.51177i
$491$	40.0043			1.80537			0.902685	−	0.430301i	$-0.141593\pi$
$491$	40.0043			1.80537			0.902685	+	0.430301i	$0.141593\pi$
$492$	2.98162	+	0.968788i	0.134422	+	0.0436764i
$493$	−0.148613	+	0.204548i	−0.00669319	+	0.00921239i
$494$	−14.6254	+	10.6260i	−0.658028	+	0.478086i
$495$	5.06269	−	2.08276i	0.227551	−	0.0936132i
$496$	5.37264	−	1.46106i	0.241239	−	0.0656036i
$497$			19.2057i			0.861492i
$498$	4.23864	+	5.83399i	0.189938	+	0.261427i
$499$	21.1419	+	15.3605i	0.946443	+	0.687631i	0.949963	−	0.312363i	$-0.101120\pi$
$499$	21.1419	+	15.3605i	0.946443	+	0.687631i	−0.00351980	+	0.999994i	$0.501120\pi$
$500$	8.44892	+	7.32228i	0.377847	+	0.327462i
$501$	−4.42391			−0.197646
$502$		−	8.53126i		−	0.380769i
$503$	−29.0244	−	9.43060i	−1.29413	−	0.420490i	−0.420597	−	0.907248i	$-0.638179\pi$
$503$	−29.0244	−	9.43060i	−1.29413	−	0.420490i	−0.873537	+	0.486758i	$0.838179\pi$
$504$	1.48787	+	4.57919i	0.0662750	+	0.203973i
$505$	−25.4791	−	29.9780i	−1.13380	−	1.33400i
$506$	15.3068	−	11.1210i	0.680471	−	0.494391i
$507$	0.731907	+	0.237811i	0.0325051	+	0.0105616i
$508$	6.01431	+	8.27799i	0.266842	+	0.367276i
$509$	9.54738	+	6.93658i	0.423180	+	0.307458i	0.778916	−	0.627128i	$-0.215770\pi$
$509$	9.54738	+	6.93658i	0.423180	+	0.307458i	−0.355736	+	0.934587i	$0.615770\pi$
$510$	−0.298795	+	0.253953i	−0.0132309	+	0.0112452i
$511$	35.0296	+	25.4505i	1.54962	+	1.12586i
$512$	−0.587785	+	0.809017i	−0.0259767	+	0.0357538i
$513$	−4.91627	+	1.59739i	−0.217059	+	0.0705267i
$514$	6.57611	+	4.77782i	0.290060	+	0.210741i
$515$	21.0530	+	12.9711i	0.927705	+	0.571576i
$516$	3.65450	−	11.2474i	0.160880	−	0.495139i
$517$	12.5127	+	17.2223i	0.550308	+	0.757434i
$518$	32.1381	−	10.4423i	1.41207	−	0.458808i
$519$	1.96744	+	6.05514i	0.0863608	+	0.265791i
$520$	−0.594773	−	7.79733i	−0.0260825	−	0.341936i
$521$	9.93015			0.435048			0.217524	−	0.976055i	$-0.430202\pi$
$521$	9.93015			0.435048			0.217524	+	0.976055i	$0.430202\pi$
$522$		−	1.44174i		−	0.0631032i
$523$	−2.61834	−	0.850751i	−0.114492	−	0.0372007i	0.251211	−	0.967932i	$-0.419171\pi$
$523$	−2.61834	−	0.850751i	−0.114492	−	0.0372007i	−0.365703	+	0.930732i	$0.619171\pi$
$524$	5.43860	+	3.95138i	0.237586	+	0.172617i
$525$	3.88052	−	23.7594i	0.169360	−	1.03695i
$526$	−13.6098			−0.593417
$527$	0.346517	−	0.912854i	0.0150945	−	0.0397646i
$528$		−	2.44821i		−	0.106545i
$529$	29.7112	−	21.5864i	1.29179	−	0.938540i
$530$	−28.8267	−	6.99414i	−1.25215	−	0.303806i
$531$	0.119779	−	0.368642i	0.00519797	−	0.0159977i
$532$			24.8893i			1.07909i
$533$			10.9640i			0.474902i
$534$	2.13360	−	6.56655i	0.0923300	−	0.284163i
$535$	0.493765	−	0.419663i	0.0213473	−	0.0181436i
$536$	−2.37090	−	7.29689i	−0.102407	−	0.315177i
$537$	−3.01869	−	4.15488i	−0.130266	−	0.179296i
$538$	−16.1710	−	5.25427i	−0.697181	−	0.226528i
$539$	−32.0523	+	23.2874i	−1.38059	+	1.00306i
$540$	0.527234	−	2.17302i	0.0226886	−	0.0935120i
$541$	−2.62481	−	8.07834i	−0.112849	−	0.347315i	0.878643	−	0.477479i	$-0.158449\pi$
$541$	−2.62481	−	8.07834i	−0.112849	−	0.347315i	−0.991492	+	0.130164i	$0.958449\pi$
$542$	3.41843	−	4.70506i	0.146834	−	0.202100i
$543$	−4.87266	+	6.70664i	−0.209106	+	0.287809i
$544$	0.0541918	+	0.166785i	0.00232346	+	0.00715086i
$545$	−17.1558	−	4.16248i	−0.734875	−	0.178301i
$546$	−13.6226	+	9.89742i	−0.582995	+	0.423571i
$547$	−20.3220	−	6.60302i	−0.868906	−	0.282325i	−0.159562	−	0.987188i	$-0.551008\pi$
$547$	−20.3220	−	6.60302i	−0.868906	−	0.282325i	−0.709343	+	0.704863i	$0.751008\pi$
$548$	−7.93486	−	10.9214i	−0.338960	−	0.466539i
$549$	−2.62299	−	8.07273i	−0.111946	−	0.344536i
$550$	−5.60979	+	10.8800i	−0.239202	+	0.463923i
$551$	2.30303	−	7.08798i	0.0981122	−	0.301958i
$552$		−	7.72820i		−	0.328934i
$553$		−	5.70374i		−	0.242548i
$554$	−7.60079	+	23.3928i	−0.322927	+	0.993866i
$555$	−15.2509	−	3.70028i	−0.647364	−	0.157068i
$556$	−7.63815	+	5.54944i	−0.323930	+	0.235349i
$557$		−	39.7434i		−	1.68398i	−0.539490	−	0.841992i	$-0.681383\pi$
$557$		−	39.7434i		−	1.68398i	0.539490	−	0.841992i	$-0.318617\pi$
$558$	1.46106	+	5.37264i	0.0618517	+	0.227442i
$559$	41.3587			1.74929
$560$	−9.16623	−	5.64748i	−0.387344	−	0.238650i
$561$	−0.347343	−	0.252359i	−0.0146648	−	0.0106546i
$562$	−21.4177	−	6.95904i	−0.903452	−	0.293549i
$563$			3.51501i			0.148140i	0.997253	+	0.0740700i	$0.0235988\pi$
$563$			3.51501i			0.148140i	−0.997253	+	0.0740700i	$0.976401\pi$
$564$	8.69528			0.366137
$565$	−44.4748	+	3.39249i	−1.87107	+	0.142723i
$566$	−0.631437	−	1.94336i	−0.0265413	−	0.0816856i
$567$	−4.57919	+	1.48787i	−0.192308	+	0.0624847i
$568$	−2.34458	−	3.22704i	−0.0983765	−	0.135404i
$569$	9.90811	−	30.4940i	0.415370	−	1.27838i	−0.496550	−	0.868008i	$-0.665400\pi$
$569$	9.90811	−	30.4940i	0.415370	−	1.27838i	0.911920	−	0.410368i	$-0.134600\pi$
$570$	6.06320	−	9.84097i	0.253960	−	0.412193i
$571$	−11.4995	−	8.35488i	−0.481240	−	0.349641i	0.320566	−	0.947226i	$-0.396127\pi$
$571$	−11.4995	−	8.35488i	−0.481240	−	0.349641i	−0.801805	+	0.597585i	$0.796127\pi$
$572$	8.14284	−	2.64577i	0.340469	−	0.110625i
$573$	−6.87446	+	9.46188i	−0.287185	+	0.395276i
$574$	12.2120	+	8.87254i	0.509719	+	0.370333i
$575$	−17.7083	+	34.3445i	−0.738486	+	1.43226i
$576$	−0.809017	−	0.587785i	−0.0337090	−	0.0244911i
$577$	25.3539	+	34.8967i	1.05550	+	1.45277i	0.883944	+	0.467592i	$0.154879\pi$
$577$	25.3539	+	34.8967i	1.05550	+	1.45277i	0.171553	+	0.985175i	$0.445121\pi$
$578$	−16.1387	−	5.24379i	−0.671282	−	0.218113i
$579$	−3.10525	+	2.25609i	−0.129050	+	0.0937600i
$580$	2.08780	+	2.45645i	0.0866911	+	0.101999i
$581$	10.7293	+	33.0215i	0.445128	+	1.36996i
$582$	−13.8684	−	4.50610i	−0.574862	−	0.186784i
$583$		−	32.4773i		−	1.34507i
$584$	−8.99280			−0.372125
$585$	7.79733	−	0.594773i	0.322380	−	0.0245908i
$586$	−23.2066	−	16.8606i	−0.958657	−	0.696505i
$587$	−10.1211	−	13.9304i	−0.417741	−	0.574971i	0.547344	−	0.836908i	$-0.315639\pi$
$587$	−10.1211	−	13.9304i	−0.417741	−	0.574971i	−0.965085	+	0.261937i	$0.915639\pi$
$588$			16.1828i			0.667366i
$589$	−1.39925	+	28.7473i	−0.0576551	+	1.18451i
$590$	0.329754	+	0.801551i	0.0135758	+	0.0329993i
$591$	8.64731	−	6.28264i	0.355703	−	0.258433i
$592$	−4.12525	+	5.67792i	−0.169547	+	0.233361i
$593$	39.9623	+	12.9845i	1.64105	+	0.533211i	0.976774	−	0.214272i	$-0.0687380\pi$
$593$	39.9623	+	12.9845i	1.64105	+	0.533211i	0.664281	+	0.747483i	$0.268738\pi$
$594$	2.44821			0.100451
$595$	−1.74609	+	0.718332i	−0.0715826	+	0.0294487i
$596$	6.69600	−	20.6082i	0.274279	−	0.844144i
$597$	10.3053	−	3.34838i	0.421766	−	0.137040i
$598$	25.7043	−	8.35182i	1.05113	−	0.341531i
$599$	−9.74864	+	7.08280i	−0.398319	+	0.289395i	−0.768856	−	0.639422i	$-0.779174\pi$
$599$	−9.74864	+	7.08280i	−0.398319	+	0.289395i	0.370537	+	0.928818i	$0.379174\pi$
$600$	2.24847	+	4.46591i	0.0917933	+	0.182320i
$601$	7.45501	−	5.41638i	0.304096	−	0.220939i	−0.425263	−	0.905070i	$-0.639818\pi$
$601$	7.45501	−	5.41638i	0.304096	−	0.220939i	0.729359	+	0.684131i	$0.239818\pi$
$602$	33.4693	−	46.0666i	1.36411	−	1.87753i
$603$	7.29689	−	2.37090i	0.297152	−	0.0965506i
$604$	10.3062	+	7.48788i	0.419352	+	0.304677i
$605$	10.8787	+	2.63947i	0.442283	+	0.107310i
$606$	−5.43706	−	16.7335i	−0.220865	−	0.679753i
$607$	−12.7591	+	17.5614i	−0.517877	+	0.712796i	−0.985223	−	0.171279i	$-0.945210\pi$
$607$	−12.7591	+	17.5614i	−0.517877	+	0.712796i	0.467346	+	0.884074i	$0.345210\pi$
$608$	−3.03842	−	4.18203i	−0.123224	−	0.169604i
$609$	2.14512	−	6.60200i	0.0869246	−	0.267527i
$610$	16.1593	+	9.95603i	0.654271	+	0.403108i
$611$	9.39695	+	28.9208i	0.380160	+	1.17001i
$612$	−0.166785	+	0.0541918i	−0.00674190	+	0.00219058i
$613$	26.5226	+	8.61773i	1.07124	+	0.348067i	0.790970	−	0.611855i	$-0.209576\pi$
$613$	26.5226	+	8.61773i	1.07124	+	0.348067i	0.280269	+	0.959921i	$0.409576\pi$
$614$	−6.20929			−0.250587
$615$	−2.66709	−	6.48304i	−0.107547	−	0.261421i
$616$	3.64262	−	11.2108i	0.146765	−	0.451697i
$617$	−10.3273	+	14.2143i	−0.415760	+	0.572245i	−0.964612	−	0.263675i	$-0.915065\pi$
$617$	−10.3273	+	14.2143i	−0.415760	+	0.572245i	0.548851	+	0.835920i	$0.315065\pi$
$618$	6.50016	+	8.94670i	0.261475	+	0.359889i
$619$	−20.6346			−0.829376			−0.414688	−	0.909964i	$-0.636109\pi$
$619$	−20.6346			−0.829376			−0.414688	+	0.909964i	$0.636109\pi$
$620$	−10.2696	−	7.03819i	−0.412435	−	0.282661i
$621$	7.72820			0.310122
$622$	4.64845	+	6.39804i	0.186386	+	0.256538i
$623$	19.5404	−	26.8950i	0.782868	−	1.07753i
$624$	1.08070	−	3.32604i	0.0432624	−	0.133148i
$625$	0.240822	−	24.9988i	0.00963287	−	0.999954i
$626$	11.3819			0.454913
$627$	12.0361	+	3.91076i	0.480675	+	0.156181i
$628$	14.4807	−	4.70507i	0.577843	−	0.187753i
$629$	0.380334	+	1.17055i	0.0151649	+	0.0466728i
$630$	5.64748	−	9.16623i	0.225001	−	0.365191i
$631$	−11.2607	+	34.6569i	−0.448282	+	1.37967i	0.430562	+	0.902561i	$0.358315\pi$
$631$	−11.2607	+	34.6569i	−0.448282	+	1.37967i	−0.878844	+	0.477109i	$0.841685\pi$
$632$	0.696299	+	0.958373i	0.0276973	+	0.0381220i
$633$	7.05898	−	9.71586i	0.280569	−	0.386171i
$634$	2.59967	+	8.00095i	0.103246	+	0.317758i
$635$	5.39475	−	22.2347i	0.214084	−	0.882357i
$636$	−10.7322	−	7.79739i	−0.425559	−	0.309187i
$637$	−53.8245	+	17.4886i	−2.13260	+	0.692925i
$638$	−2.07469	+	2.85557i	−0.0821379	+	0.113053i
$639$	3.22704	−	2.34458i	0.127660	−	0.0927502i
$640$	2.22959	−	0.170071i	0.0881323	−	0.00672264i
$641$	17.9946	−	13.0738i	0.710743	−	0.516385i	−0.172670	−	0.984980i	$-0.555240\pi$
$641$	17.9946	−	13.0738i	0.710743	−	0.516385i	0.883413	+	0.468595i	$0.155240\pi$
$642$	0.275616	−	0.0895531i	0.0108777	−	0.00353438i
$643$	47.4157	−	15.4063i	1.86989	−	0.607565i	0.878311	−	0.478090i	$-0.158671\pi$
$643$	47.4157	−	15.4063i	1.86989	−	0.607565i	0.991583	−	0.129476i	$-0.0413294\pi$
$644$	11.4985	−	35.3889i	0.453106	−	1.39452i
$645$	−24.4556	+	10.0609i	−0.962937	+	0.396147i
$646$	−0.906528			−0.0356669
$647$	33.0629	+	10.7428i	1.29984	+	0.422342i	0.875525	−	0.483174i	$-0.160516\pi$
$647$	33.0629	+	10.7428i	1.29984	+	0.422342i	0.424312	+	0.905516i	$0.360516\pi$
$648$	0.587785	−	0.809017i	0.0230904	−	0.0317812i
$649$	−0.767725	+	0.557785i	−0.0301358	+	0.0218950i
$650$	−12.4239	+	12.3048i	−0.487305	+	0.482633i
$651$	−1.30331	+	26.7762i	−0.0510808	+	1.04944i
$652$			2.10833i			0.0825685i
$653$	5.58063	+	7.68108i	0.218387	+	0.300584i	0.904128	−	0.427262i	$-0.140522\pi$
$653$	5.58063	+	7.68108i	0.218387	+	0.300584i	−0.685741	+	0.727846i	$0.740522\pi$
$654$	−6.38713	−	4.64052i	−0.249756	−	0.181459i
$655$	−1.14330	−	14.9884i	−0.0446724	−	0.585645i
$656$	−3.13507			−0.122404
$657$		−	8.99280i		−	0.350843i
$658$	39.8174	+	12.9374i	1.55224	+	0.504354i
$659$	9.03636	+	27.8110i	0.352006	+	1.08336i	0.957725	+	0.287686i	$0.0928858\pi$
$659$	9.03636	+	27.8110i	0.352006	+	1.08336i	−0.605718	+	0.795679i	$0.707114\pi$
$660$	−4.17129	+	3.54528i	−0.162367	+	0.138000i
$661$	5.57122	−	4.04773i	0.216695	−	0.157438i	−0.474142	−	0.880448i	$-0.657242\pi$
$661$	5.57122	−	4.04773i	0.216695	−	0.157438i	0.690838	+	0.723010i	$0.257242\pi$
$662$	9.37107	+	3.04485i	0.364217	+	0.118341i
$663$	−0.360488	−	0.496169i	−0.0140002	−	0.0192696i
$664$	−5.83399	−	4.23864i	−0.226403	−	0.164491i
$665$	42.4066	−	36.0424i	1.64446	−	1.39767i
$666$	−5.67792	−	4.12525i	−0.220015	−	0.159850i
$667$	−6.54913	+	9.01410i	−0.253583	+	0.349027i
$668$	4.20739	−	1.36706i	0.162789	−	0.0528932i
$669$	−10.7926	−	7.84126i	−0.417265	−	0.303161i
$670$	−8.99919	+	14.6063i	−0.347669	+	0.564289i
$671$	−6.42163	+	19.7638i	−0.247904	+	0.762971i
$672$	−2.83010	−	3.89529i	−0.109173	−	0.150264i
$673$	43.6101	−	14.1698i	1.68105	−	0.546205i	0.695933	−	0.718106i	$-0.254991\pi$
$673$	43.6101	−	14.1698i	1.68105	−	0.546205i	0.985114	+	0.171901i	$0.0549909\pi$
$674$	6.14526	+	18.9132i	0.236707	+	0.728508i
$675$	−4.46591	+	2.24847i	−0.171893	+	0.0865436i
$676$	−0.769572			−0.0295989
$677$			5.82311i			0.223800i	0.993719	+	0.111900i	$0.0356937\pi$
$677$			5.82311i			0.223800i	−0.993719	+	0.111900i	$0.964306\pi$
$678$	−18.9712	−	6.16412i	−0.728585	−	0.236732i
$679$	−56.8014	−	41.2686i	−2.17984	−	1.58374i
$680$	0.205695	−	0.333856i	0.00788804	−	0.0128028i
$681$	25.4794			0.976373
$682$	4.83751	−	12.7438i	0.185238	−	0.487985i
$683$		−	4.39796i		−	0.168283i	−0.996454	−	0.0841416i	$-0.973185\pi$
$683$		−	4.39796i		−	0.168283i	0.996454	−	0.0841416i	$-0.0268148\pi$
$684$	4.18203	−	3.03842i	0.159904	−	0.116177i
$685$	−7.11745	+	29.3349i	−0.271944	+	1.12083i
$686$	−13.6628	+	42.0496i	−0.521646	+	1.60546i
$687$			0.973720i			0.0371497i
$688$			11.8262i			0.450870i
$689$	14.3362	−	44.1223i	0.546166	−	1.68092i
$690$	−13.1674	+	11.1913i	−0.501274	+	0.426045i
$691$	−14.2417	−	43.8316i	−0.541781	−	1.66743i	−0.728522	−	0.685023i	$-0.759792\pi$
$691$	−14.2417	−	43.8316i	−0.541781	−	1.66743i	0.186740	−	0.982409i	$-0.440208\pi$
$692$	−3.74228	−	5.15081i	−0.142260	−	0.195805i
$693$	11.2108	+	3.64262i	0.425864	+	0.138372i
$694$	11.9539	−	8.68504i	0.453765	−	0.329680i
$695$	20.5161	+	4.97776i	0.778219	+	0.188817i
$696$	0.445522	+	1.37118i	0.0168875	+	0.0519743i
$697$	−0.323159	+	0.444791i	−0.0122405	+	0.0168477i
$698$	−12.1564	+	16.7319i	−0.460127	+	0.633310i
$699$	−2.07416	−	6.38361i	−0.0784519	−	0.241450i
$700$	3.65147	+	23.7957i	0.138013	+	0.899393i
$701$	18.3661	−	13.3438i	0.693679	−	0.503987i	−0.184188	−	0.982891i	$-0.558966\pi$
$701$	18.3661	−	13.3438i	0.693679	−	0.503987i	0.877868	+	0.478903i	$0.158966\pi$
$702$	3.32604	+	1.08070i	0.125533	+	0.0407882i
$703$	−21.3245	−	29.3507i	−0.804270	−	1.10698i
$704$	0.756539	+	2.32839i	0.0285131	+	0.0877544i
$705$	−12.5917	−	14.8151i	−0.474232	−	0.557970i
$706$	2.59439	−	7.98472i	0.0976413	−	0.300509i
$707$		−	84.7157i		−	3.18606i
$708$			0.387614i			0.0145674i
$709$	−2.90438	+	8.93875i	−0.109076	+	0.335702i	−0.990666	−	0.136315i	$-0.956474\pi$
$709$	−2.90438	+	8.93875i	−0.109076	+	0.335702i	0.881589	+	0.472017i	$0.156474\pi$
$710$	−2.10305	+	8.66784i	−0.0789262	+	0.325298i
$711$	−0.958373	+	0.696299i	−0.0359418	+	0.0261132i
$712$			6.90448i			0.258756i
$713$	15.2704	−	40.2280i	0.571882	−	1.50655i
$714$	−0.844373			−0.0315999
$715$	−16.2996	−	10.0425i	−0.609572	−	0.375568i
$716$	4.15488	+	3.01869i	0.155275	+	0.112814i
$717$	−3.92955	−	1.27679i	−0.146752	−	0.0476825i
$718$			3.87894i			0.144761i
$719$	−12.4778			−0.465345			−0.232673	−	0.972555i	$-0.574747\pi$
$719$	−12.4778			−0.465345			−0.232673	+	0.972555i	$0.574747\pi$
$720$	0.170071	+	2.22959i	0.00633817	+	0.0830919i
$721$	16.4540	+	50.6401i	0.612777	+	1.88593i
$722$	7.34350	−	2.38605i	0.273297	−	0.0887995i
$723$	14.1530	+	19.4799i	0.526354	+	0.724464i
$724$	2.56171	−	7.88412i	0.0952051	−	0.293011i
$725$	1.16197	−	7.11443i	0.0431544	−	0.264223i
$726$	4.05015	+	2.94261i	0.150315	+	0.109210i
$727$	47.4275	−	15.4101i	1.75899	−	0.571529i	0.761892	−	0.647704i	$-0.224271\pi$
$727$	47.4275	−	15.4101i	1.75899	−	0.571529i	0.997095	+	0.0761744i	$0.0242706\pi$
$728$	9.89742	−	13.6226i	0.366823	−	0.504888i
$729$	0.809017	+	0.587785i	0.0299636	+	0.0217698i
$730$	13.0226	+	15.3220i	0.481987	+	0.567094i
$731$	1.67786	+	1.21903i	0.0620578	+	0.0450876i
$732$	4.98922	+	6.86708i	0.184407	+	0.253814i
$733$	−37.6062	−	12.2190i	−1.38902	−	0.451318i	−0.483393	−	0.875404i	$-0.660596\pi$
$733$	−37.6062	−	12.2190i	−1.38902	−	0.451318i	−0.905622	+	0.424085i	$0.860596\pi$
$734$	−19.5754	+	14.2224i	−0.722543	+	0.524958i
$735$	27.5724	−	23.4344i	1.01702	−	0.864392i
$736$	2.38814	+	7.34995i	0.0880282	+	0.270923i
$737$	−17.8643	−	5.80447i	−0.658041	−	0.213810i
$738$		−	3.13507i		−	0.115403i
$739$	15.0974			0.555368			0.277684	−	0.960673i	$-0.410433\pi$
$739$	15.0974			0.555368			0.277684	+	0.960673i	$0.410433\pi$
$740$	15.6479	−	1.19361i	0.575229	−	0.0438779i
$741$	14.6254	+	10.6260i	0.537278	+	0.390355i
$742$	−37.5433	−	51.6739i	−1.37826	−	1.89701i
$743$			19.9264i			0.731029i	0.930806	+	0.365514i	$0.119107\pi$
$743$			19.9264i			0.731029i	−0.930806	+	0.365514i	$0.880893\pi$
$744$	−3.04979	−	4.65819i	−0.111811	−	0.170778i
$745$	−44.8090	+	18.4342i	−1.64167	+	0.675377i
$746$	19.5465	−	14.2014i	0.715649	−	0.519949i
$747$	4.23864	−	5.83399i	0.155084	−	0.213455i
$748$	0.408326	+	0.132673i	0.0149299	+	0.00485101i
$749$	1.39534			0.0509847
$750$	4.35305	−	10.2981i	0.158951	−	0.376034i
$751$	0.127048	−	0.391012i	0.00463603	−	0.0142682i	−0.948712	−	0.316142i	$-0.897612\pi$
$751$	0.127048	−	0.391012i	0.00463603	−	0.0142682i	0.953348	+	0.301874i	$0.0976123\pi$
$752$	−8.26970	+	2.68699i	−0.301565	+	0.0979844i
$753$	−8.11371	+	2.63630i	−0.295680	+	0.0960723i
$754$	−4.07911	+	2.96364i	−0.148552	+	0.107930i
$755$	−2.16656	−	28.4031i	−0.0788491	−	1.03369i
$756$	3.89529	−	2.83010i	0.141670	−	0.102930i
$757$	17.6378	−	24.2764i	0.641057	−	0.882339i	−0.357614	−	0.933869i	$-0.616410\pi$
$757$	17.6378	−	24.2764i	0.641057	−	0.882339i	0.998671	+	0.0515300i	$0.0164098\pi$
$758$	−20.2034	+	6.56450i	−0.733822	+	0.238433i
$759$	−15.3068	−	11.1210i	−0.555602	−	0.403668i
$760$	−2.72542	+	11.2329i	−0.0988614	+	0.407462i
$761$	8.75481	+	26.9445i	0.317362	+	0.976739i	0.974771	+	0.223206i	$0.0716521\pi$
$761$	8.75481	+	26.9445i	0.317362	+	0.976739i	−0.657410	+	0.753533i	$0.728348\pi$
$762$	6.01431	−	8.27799i	0.217876	−	0.299880i
$763$	−22.3434	−	30.7530i	−0.808885	−	1.11333i
$764$	3.61412	−	11.1231i	0.130754	−	0.402420i
$765$	0.333856	+	0.205695i	0.0120706	+	0.00743692i
$766$	4.79549	+	14.7590i	0.173268	+	0.533265i
$767$	−1.28922	+	0.418892i	−0.0465509	+	0.0151253i
$768$	0.951057	+	0.309017i	0.0343183	+	0.0111507i
$769$	−34.3227			−1.23771			−0.618853	−	0.785506i	$-0.712403\pi$
$769$	−34.3227			−1.23771			−0.618853	+	0.785506i	$0.712403\pi$
$770$	−24.3761	+	10.0282i	−0.878452	+	0.361391i
$771$	2.51185	−	7.73068i	0.0904620	−	0.278414i
$772$	2.25609	−	3.10525i	0.0811986	−	0.111760i
$773$	4.78947	+	6.59214i	0.172265	+	0.237103i	0.886416	−	0.462889i	$-0.153187\pi$
$773$	4.78947	+	6.59214i	0.172265	+	0.237103i	−0.714151	+	0.699992i	$0.753187\pi$
$774$	−11.8262			−0.425084
$775$	2.87970	+	27.6895i	0.103442	+	0.994635i
$776$	14.5820			0.523465
$777$	−19.8624	−	27.3383i	−0.712561	−	0.980756i
$778$	12.3601	−	17.0123i	0.443133	−	0.609920i
$779$	5.00793	−	15.4128i	0.179428	−	0.552222i
$780$	−7.23191	+	2.97517i	−0.258944	+	0.106528i
$781$	−9.76553			−0.349438
$782$	1.28895	+	0.418805i	0.0460928	+	0.0149764i
$783$	−1.37118	+	0.445522i	−0.0490018	+	0.0159216i
$784$	−5.00075	−	15.3907i	−0.178598	−	0.549669i
$785$	−28.9862	−	17.8589i	−1.03456	−	0.637413i
$786$	2.07736	−	6.39346i	0.0740970	−	0.228047i
$787$	−23.6781	−	32.5901i	−0.844033	−	1.16171i	−0.985146	−	0.171718i	$-0.945068\pi$
$787$	−23.6781	−	32.5901i	−0.844033	−	1.16171i	0.141113	−	0.989993i	$-0.454932\pi$
$788$	−6.28264	+	8.64731i	−0.223810	+	0.308048i
$789$	4.20567	+	12.9437i	0.149726	+	0.460809i
$790$	0.624569	−	2.57419i	0.0222212	−	0.0915856i
$791$	−77.7014	−	56.4534i	−2.76274	−	2.00725i
$792$	−2.32839	+	0.756539i	−0.0827356	+	0.0268824i
$793$	−17.4483	+	24.0156i	−0.619608	+	0.852817i
$794$	10.9329	−	7.94322i	0.387994	−	0.281894i
$795$	2.25611	+	29.5771i	0.0800161	+	1.04899i
$796$	−8.76618	+	6.36900i	−0.310709	+	0.225743i
$797$	−4.99418	+	1.62271i	−0.176903	+	0.0574793i	−0.396129	−	0.918195i	$-0.629647\pi$
$797$	−4.99418	+	1.62271i	−0.176903	+	0.0574793i	0.219226	+	0.975674i	$0.429647\pi$
$798$	23.6711	−	7.69121i	0.837948	−	0.272266i
$799$	−0.471213	+	1.45025i	−0.0166703	+	0.0513060i
$800$	−3.51846	−	3.55252i	−0.124396	−	0.125601i
$801$	−6.90448			−0.243958
$802$	9.82428	+	3.19210i	0.346907	+	0.112717i
$803$	−12.9408	+	17.8115i	−0.456673	+	0.628556i
$804$	−6.20710	+	4.50972i	−0.218908	+	0.159046i
$805$	−76.9472	+	31.6557i	−2.71203	+	1.11572i
$806$	12.1974	−	15.1778i	0.429636	−	0.534615i
$807$			17.0032i			0.598540i
$808$	10.3419	+	14.2344i	0.363827	+	0.500764i
$809$	−26.8343	−	19.4963i	−0.943444	−	0.685452i	0.00580308	−	0.999983i	$-0.498153\pi$
$809$	−26.8343	−	19.4963i	−0.943444	−	0.685452i	−0.949247	+	0.314531i	$0.898153\pi$
$810$	−2.22959	+	0.170071i	−0.0783398	+	0.00597568i
$811$	54.0032			1.89631			0.948155	−	0.317808i	$-0.102947\pi$
$811$	54.0032			1.89631			0.948155	+	0.317808i	$0.102947\pi$
$812$			6.94175i			0.243608i
$813$	−5.53114	−	1.79717i	−0.193985	−	0.0630297i
$814$	5.30961	+	16.3413i	0.186102	+	0.572762i
$815$	3.59219	−	3.05309i	0.125829	−	0.106945i
$816$	0.141876	−	0.103079i	0.00496666	−	0.00360849i
$817$	−58.1409	−	18.8911i	−2.03409	−	0.660917i
$818$	−12.7743	−	17.5824i	−0.446644	−	0.614753i
$819$	13.6226	+	9.89742i	0.476013	+	0.345844i
$820$	4.53992	+	5.34156i	0.158541	+	0.186535i
$821$	−13.9046	−	10.1023i	−0.485275	−	0.352573i	0.318089	−	0.948061i	$-0.396959\pi$
$821$	−13.9046	−	10.1023i	−0.485275	−	0.352573i	−0.803364	+	0.595488i	$0.796959\pi$
$822$	−7.93486	+	10.9214i	−0.276760	+	0.380928i
$823$	−14.8587	+	4.82789i	−0.517943	+	0.168290i	−0.556312	−	0.830974i	$-0.687784\pi$
$823$	−14.8587	+	4.82789i	−0.517943	+	0.168290i	0.0383687	+	0.999264i	$0.487784\pi$
$824$	−8.94670	−	6.50016i	−0.311673	−	0.226444i
$825$	12.0810	+	1.97313i	0.420606	+	0.0686957i
$826$	−0.576719	+	1.77496i	−0.0200666	+	0.0617587i
$827$	6.82085	+	9.38809i	0.237184	+	0.326456i	0.910971	−	0.412469i	$-0.135334\pi$
$827$	6.82085	+	9.38809i	0.237184	+	0.326456i	−0.673787	+	0.738925i	$0.735334\pi$
$828$	−7.34995	+	2.38814i	−0.255428	+	0.0829937i
$829$	−11.7286	−	36.0969i	−0.407351	−	1.25370i	−0.918916	−	0.394453i	$-0.870934\pi$
$829$	−11.7286	−	36.0969i	−0.407351	−	1.25370i	0.511565	−	0.859245i	$-0.329066\pi$
$830$	1.22642	+	16.0780i	0.0425696	+	0.558077i
$831$	24.5967			0.853249
$832$			3.49720i			0.121244i
$833$	−2.69905	−	0.876974i	−0.0935164	−	0.0303853i
$834$	7.63815	+	5.54944i	0.264487	+	0.192161i
$835$	−8.42198	−	5.18894i	−0.291455	−	0.179571i
$836$	−12.6555			−0.437699
$837$	4.65819	−	3.04979i	0.161011	−	0.105416i
$838$			39.0811i			1.35003i
$839$	14.7359	−	10.7063i	0.508739	−	0.369621i	−0.303606	−	0.952798i	$-0.598191\pi$
$839$	14.7359	−	10.7063i	0.508739	−	0.369621i	0.812345	+	0.583177i	$0.198191\pi$
$840$	−2.53855	+	10.4628i	−0.0875884	+	0.361000i
$841$	−8.31917	+	25.6038i	−0.286868	+	0.882888i
$842$		−	12.4900i		−	0.430433i
$843$			22.5199i			0.775627i
$844$	−3.71113	+	11.4217i	−0.127742	+	0.393150i
$845$	1.11443	+	1.31121i	0.0383374	+	0.0451069i
$846$	−2.68699	−	8.26970i	−0.0923806	−	0.284318i
$847$	14.1682	+	19.5009i	0.486825	+	0.670057i
$848$	12.6164	+	4.09933i	0.433251	+	0.140772i
$849$	−1.65312	+	1.20106i	−0.0567350	+	0.0412204i
$850$	−0.866698	+	0.132995i	−0.0297275	+	0.00456171i
$851$	16.7607	+	51.5841i	0.574549	+	1.76828i
$852$	−2.34458	+	3.22704i	−0.0803240	+	0.110557i
$853$	−3.20756	+	4.41482i	−0.109825	+	0.151161i	−0.860391	−	0.509634i	$-0.829781\pi$
$853$	−3.20756	+	4.41482i	−0.109825	+	0.151161i	0.750566	+	0.660795i	$0.229781\pi$
$854$	12.6293	+	38.8690i	0.432166	+	1.33007i
$855$	−11.2329	−	2.72542i	−0.384159	−	0.0932074i
$856$	−0.234453	+	0.170340i	−0.00801344	+	0.00582211i
$857$	16.7758	+	5.45080i	0.573051	+	0.186196i	0.581185	−	0.813771i	$-0.302589\pi$
$857$	16.7758	+	5.45080i	0.573051	+	0.186196i	−0.00813404	+	0.999967i	$0.502589\pi$
$858$	−5.03255	−	6.92672i	−0.171809	−	0.236474i
$859$	−15.2971	−	47.0795i	−0.521929	−	1.60633i	−0.770310	−	0.637670i	$-0.779899\pi$
$859$	−15.2971	−	47.0795i	−0.521929	−	1.60633i	0.248381	−	0.968662i	$-0.420101\pi$
$860$	20.1496	−	17.1257i	0.687097	−	0.583980i
$861$	4.66457	−	14.3561i	0.158968	−	0.489253i
$862$			26.1614i			0.891062i
$863$			42.1318i			1.43418i	0.696979	+	0.717091i	$0.254527\pi$
$863$			42.1318i			1.43418i	−0.696979	+	0.717091i	$0.745473\pi$
$864$	−0.309017	+	0.951057i	−0.0105130	+	0.0323556i
$865$	−3.35677	+	13.8351i	−0.114134	+	0.470407i
$866$	−12.0049	+	8.72209i	−0.407944	+	0.296389i
$867$			16.9692i			0.576306i
$868$	−7.03479	−	25.8685i	−0.238776	−	0.878033i
$869$	2.90019			0.0983820
$870$	1.69106	−	2.74470i	0.0573323	−	0.0930540i
$871$	−21.7075	−	15.7714i	−0.735530	−	0.534394i
$872$	7.50852	+	2.43967i	0.254270	+	0.0826175i
$873$			14.5820i			0.493528i
$874$	−39.9492			−1.35130
$875$	35.2557	−	40.6802i	1.19186	−	1.37524i
$876$	2.77893	+	8.55266i	0.0938913	+	0.288968i
$877$	−15.6751	+	5.09316i	−0.529312	+	0.171984i	−0.561467	−	0.827499i	$-0.689763\pi$
$877$	−15.6751	+	5.09316i	−0.529312	+	0.171984i	0.0321553	+	0.999483i	$0.489763\pi$
$878$	−9.54784	−	13.1415i	−0.322224	−	0.443503i
$879$	−8.86414	+	27.2810i	−0.298980	+	0.920166i
$880$	2.87158	−	4.66076i	0.0968010	−	0.157114i
$881$	−5.24365	−	3.80973i	−0.176663	−	0.128353i	0.495940	−	0.868357i	$-0.334824\pi$
$881$	−5.24365	−	3.80973i	−0.176663	−	0.128353i	−0.672603	+	0.740004i	$0.734824\pi$
$882$	15.3907	−	5.00075i	0.518232	−	0.168384i
$883$	9.60393	−	13.2187i	0.323198	−	0.444844i	−0.616242	−	0.787557i	$-0.711346\pi$
$883$	9.60393	−	13.2187i	0.323198	−	0.444844i	0.939440	+	0.342713i	$0.111346\pi$
$884$	0.496169	+	0.360488i	0.0166880	+	0.0121245i
$885$	0.660421	−	0.561308i	0.0221998	−	0.0188681i
$886$	7.00388	+	5.08862i	0.235300	+	0.170955i
$887$	27.5962	+	37.9829i	0.926588	+	1.27534i	0.961176	+	0.275938i	$0.0889883\pi$
$887$	27.5962	+	37.9829i	0.926588	+	1.27534i	−0.0345873	+	0.999402i	$0.511012\pi$
$888$	6.67479	+	2.16877i	0.223991	+	0.0727792i
$889$	39.8573	−	28.9580i	1.33677	−	0.971220i
$890$	11.7639	−	9.99846i	0.394328	−	0.335149i
$891$	−0.756539	−	2.32839i	−0.0253450	−	0.0780039i
$892$	12.6874	+	4.12240i	0.424806	+	0.138028i
$893$		−	44.9483i		−	1.50414i
$894$	−21.6687			−0.724710
$895$	−0.873435	−	11.4505i	−0.0291957	−	0.382749i
$896$	3.89529	+	2.83010i	0.130133	+	0.0945469i
$897$	−15.8861	−	21.8654i	−0.530422	−	0.730063i
$898$			8.46680i			0.282541i
$899$	−0.390259	+	8.01777i	−0.0130159	+	0.267408i
$900$	3.55252	−	3.51846i	0.118417	−	0.117282i
$901$	1.88209	−	1.36742i	0.0627015	−	0.0455553i
$902$	−4.51143	+	6.20945i	−0.150214	+	0.206752i
$903$	−54.1545	−	17.5959i	−1.80215	−	0.585554i
$904$	19.9475			0.663444
$905$	−17.1427	+	7.05242i	−0.569843	+	0.234430i
$906$	3.93661	−	12.1156i	0.130785	−	0.402515i
$907$	2.35467	−	0.765078i	0.0781855	−	0.0254040i	−0.269663	−	0.962955i	$-0.586912\pi$
$907$	2.35467	−	0.765078i	0.0781855	−	0.0254040i	0.347849	+	0.937551i	$0.386912\pi$
$908$	−24.2324	+	7.87357i	−0.804179	+	0.261294i
$909$	−14.2344	+	10.3419i	−0.472125	+	0.343019i
$910$	−37.5430	+	2.86374i	−1.24454	+	0.0949320i
$911$	18.6791	−	13.5712i	0.618866	−	0.449632i	−0.233659	−	0.972319i	$-0.575070\pi$
$911$	18.6791	−	13.5712i	0.618866	−	0.449632i	0.852525	+	0.522686i	$0.175070\pi$
$912$	−3.03842	+	4.18203i	−0.100612	+	0.138481i
$913$	−16.7905	+	5.45556i	−0.555684	+	0.180553i
$914$	−20.2249	−	14.6942i	−0.668979	−	0.486042i
$915$	4.47526	−	18.4450i	0.147947	−	0.609772i
$916$	−0.300896	−	0.926062i	−0.00994188	−	0.0305980i
$917$	19.0253	−	26.1860i	0.628270	−	0.864739i
$918$	0.103079	+	0.141876i	0.00340211	+	0.00468261i
$919$	−8.18386	+	25.1873i	−0.269961	+	0.830853i	0.720548	+	0.693405i	$0.243890\pi$
$919$	−8.18386	+	25.1873i	−0.269961	+	0.830853i	−0.990509	+	0.137449i	$0.956110\pi$
$920$	9.06464	−	14.7125i	0.298852	−	0.485057i
$921$	1.91878	+	5.90539i	0.0632259	+	0.194589i
$922$	−7.85813	+	2.55326i	−0.258794	+	0.0840872i
$923$	−13.2670	−	4.31072i	−0.436690	−	0.141889i
$924$	−11.7878			−0.387789
$925$	−24.6936	−	24.9326i	−0.811921	−	0.819780i
$926$	−5.43411	+	16.7245i	−0.178576	+	0.549600i
$927$	6.50016	−	8.94670i	0.213493	−	0.293848i
$928$	−0.847433	−	1.16639i	−0.0278183	−	0.0382887i
$929$	−7.34128			−0.240860			−0.120430	−	0.992722i	$-0.538427\pi$
$929$	−7.34128			−0.240860			−0.120430	+	0.992722i	$0.538427\pi$
$930$	−3.52025	+	11.9419i	−0.115434	+	0.391589i
$931$	83.6531			2.74162
$932$	3.94529	+	5.43022i	0.129232	+	0.177873i
$933$	4.64845	−	6.39804i	0.152183	−	0.209462i
$934$	4.12317	−	12.6898i	0.134914	−	0.415223i
$935$	−0.365251	−	0.887836i	−0.0119450	−	0.0290353i
$936$	−3.49720			−0.114310
$937$	5.27205	+	1.71299i	0.172230	+	0.0559611i	0.393863	−	0.919169i	$-0.371138\pi$
$937$	5.27205	+	1.71299i	0.172230	+	0.0559611i	−0.221632	+	0.975130i	$0.571138\pi$
$938$	−35.1334	+	11.4155i	−1.14715	+	0.372730i
$939$	−3.51721	−	10.8249i	−0.114780	−	0.353256i
$940$	16.5536	+	10.1990i	0.539918	+	0.332653i
$941$	7.89507	−	24.2985i	0.257372	−	0.792110i	−0.735981	−	0.677002i	$-0.763279\pi$
$941$	7.89507	−	24.2985i	0.257372	−	0.792110i	0.993353	−	0.115108i	$-0.0367213\pi$
$942$	−8.94957	−	12.3180i	−0.291593	−	0.401343i
$943$	−14.2411	+	19.6012i	−0.463754	+	0.638302i
$944$	−0.119779	−	0.368642i	−0.00389848	−	0.0119983i
$945$	−10.4628	−	2.53855i	−0.340354	−	0.0825792i
$946$	23.4235	+	17.0182i	0.761564	+	0.553309i
$947$	33.5141	−	10.8894i	1.08906	−	0.353857i	0.291177	−	0.956669i	$-0.405953\pi$
$947$	33.5141	−	10.8894i	1.08906	−	0.353857i	0.797883	+	0.602812i	$0.205953\pi$
$948$	0.696299	−	0.958373i	0.0226147	−	0.0311265i
$949$	−25.4433	+	18.4856i	−0.825925	+	0.600069i
$950$	23.0855	−	11.6230i	0.748994	−	0.377098i
$951$	6.80601	−	4.94486i	0.220700	−	0.160348i
$952$	0.803046	−	0.260925i	0.0260269	−	0.00845664i
$953$	53.7925	−	17.4783i	1.74251	−	0.566176i	0.747350	−	0.664431i	$-0.231326\pi$
$953$	53.7925	−	17.4783i	1.74251	−	0.566176i	0.995161	+	0.0982550i	$0.0313261\pi$
$954$	−4.09933	+	12.6164i	−0.132721	+	0.408473i
$955$	−24.1853	+	9.94972i	−0.782619	+	0.321965i
$956$	4.13177			0.133631
$957$	3.35693	+	1.09073i	0.108514	+	0.0352583i
$958$	3.37668	−	4.64760i	0.109096	−	0.150157i
$959$	−52.5849	+	38.2052i	−1.69805	+	1.23371i
$960$	−0.850729	−	2.06791i	−0.0274571	−	0.0667416i
$961$	−6.67093	−	30.2737i	−0.215191	−	0.976572i
$962$			24.5444i			0.791343i
$963$	−0.170340	−	0.234453i	−0.00548913	−	0.00755515i
$964$	−19.4799	−	14.1530i	−0.627405	−	0.455836i
$965$	−8.55783	+	0.652782i	−0.275486	+	0.0210138i
$966$	−37.2101			−1.19721
$967$			26.3271i			0.846624i	0.905984	+	0.423312i	$0.139132\pi$
$967$			26.3271i			0.846624i	−0.905984	+	0.423312i	$0.860868\pi$
$968$	−4.76124	−	1.54702i	−0.153032	−	0.0497231i
$969$	0.280133	+	0.862159i	0.00899916	+	0.0276966i
$970$	−21.1164	−	24.8451i	−0.678007	−	0.797727i
$971$	17.4629	−	12.6875i	0.560410	−	0.407161i	−0.271199	−	0.962523i	$-0.587420\pi$
$971$	17.4629	−	12.6875i	0.560410	−	0.407161i	0.831609	+	0.555362i	$0.187420\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	26.7197	+	36.7765i	0.856594	+	1.17900i
$974$	−12.0850	−	8.78029i	−0.387230	−	0.281339i
$975$	15.5417	+	8.01343i	0.497734	+	0.256635i
$976$	−6.86708	−	4.98922i	−0.219810	−	0.159701i
$977$	0.587020	−	0.807964i	0.0187804	−	0.0258490i	−0.799524	−	0.600635i	$-0.794915\pi$
$977$	0.587020	−	0.807964i	0.0187804	−	0.0258490i	0.818304	+	0.574786i	$0.194915\pi$
$978$	2.00514	−	0.651509i	0.0641173	−	0.0208330i
$979$	13.6753	+	9.93571i	0.437065	+	0.317547i
$980$	−18.9813	+	30.8078i	−0.606334	+	0.984119i
$981$	−2.43967	+	7.50852i	−0.0778925	+	0.239729i
$982$	23.5140	+	32.3642i	0.750361	+	1.03278i
$983$	2.19169	−	0.712122i	0.0699040	−	0.0227132i	−0.273856	−	0.961771i	$-0.588299\pi$
$983$	2.19169	−	0.712122i	0.0699040	−	0.0227132i	0.343760	+	0.939057i	$0.388299\pi$
$984$	0.968788	+	2.98162i	0.0308838	+	0.0950507i
$985$	23.8313	−	1.81783i	0.759329	−	0.0579209i
$986$	−0.252836			−0.00805192
$987$		−	41.8665i		−	1.33262i
$988$	−17.1932	−	5.58641i	−0.546989	−	0.177727i
$989$	73.9403	+	53.7208i	2.35117	+	1.70822i
$990$	4.66076	+	2.87158i	0.148129	+	0.0912648i
$991$	−9.99366			−0.317459			−0.158730	−	0.987322i	$-0.550740\pi$
$991$	−9.99366			−0.317459			−0.158730	+	0.987322i	$0.550740\pi$
$992$	4.33998	+	3.48777i	0.137795	+	0.110737i
$993$		−	9.85333i		−	0.312686i
$994$	−15.5377	+	11.2888i	−0.492826	+	0.358059i
$995$	23.5460	+	5.71290i	0.746458	+	0.181111i
$996$	−2.22839	+	6.85827i	−0.0706091	+	0.217312i
$997$		−	42.6270i		−	1.35001i	−0.737813	−	0.675005i	$-0.764141\pi$
$997$		−	42.6270i		−	1.35001i	0.737813	−	0.675005i	$-0.235859\pi$
$998$			26.1329i			0.827222i
$999$	−2.16877	+	6.67479i	−0.0686169	+	0.211181i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.d.109.17	yes	72
5.4	even	2	inner	930.2.z.d.109.8	✓	72
31.2	even	5	inner	930.2.z.d.529.8	yes	72
155.64	even	10	inner	930.2.z.d.529.17	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.d.109.8	✓	72	5.4	even	2	inner
930.2.z.d.109.17	yes	72	1.1	even	1	trivial
930.2.z.d.529.8	yes	72	31.2	even	5	inner
930.2.z.d.529.17	yes	72	155.64	even	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.06791 - 0.850729i) q^{5} +1.00000 q^{6} +(4.57919 + 1.48787i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.587785 + 0.809017i) q^{2} +(0.587785 - 0.809017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(2.06791 - 0.850729i) q^{5} +1.00000 q^{6} +(4.57919 + 1.48787i) q^{7} +(-0.951057 + 0.309017i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(1.90374 + 1.17293i) q^{10} +(-0.756539 + 2.32839i) q^{11} +(0.587785 + 0.809017i) q^{12} +(-2.05560 + 2.82930i) q^{13} +(1.48787 + 4.57919i) q^{14} +(0.527234 - 2.17302i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.166785 + 0.0541918i) q^{17} +(0.587785 - 0.809017i) q^{18} +(4.18203 - 3.03842i) q^{19} +(0.170071 + 2.22959i) q^{20} +(3.89529 - 2.83010i) q^{21} +(-2.32839 + 0.756539i) q^{22} +(-7.34995 + 2.38814i) q^{23} +(-0.309017 + 0.951057i) q^{24} +(3.55252 - 3.51846i) q^{25} -3.49720 q^{26} +(-0.951057 - 0.309017i) q^{27} +(-2.83010 + 3.89529i) q^{28} +(1.16639 - 0.847433i) q^{29} +(2.06791 - 0.850729i) q^{30} +(-3.48777 + 4.33998i) q^{31} -1.00000i q^{32} +(1.43902 + 1.98064i) q^{33} +(-0.141876 - 0.103079i) q^{34} +(10.7351 - 0.818866i) q^{35} +1.00000 q^{36} -7.01829i q^{37} +(4.91627 + 1.59739i) q^{38} +(1.08070 + 3.32604i) q^{39} +(-1.70381 + 1.44811i) q^{40} +(2.53632 - 1.84275i) q^{41} +(4.57919 + 1.48787i) q^{42} +(-6.95127 - 9.56761i) q^{43} +(-1.98064 - 1.43902i) q^{44} +(-1.44811 - 1.70381i) q^{45} +(-6.25224 - 4.54252i) q^{46} +(5.11096 - 7.03463i) q^{47} +(-0.951057 + 0.309017i) q^{48} +(13.0921 + 9.51199i) q^{49} +(4.93462 + 0.805949i) q^{50} +(-0.0541918 + 0.166785i) q^{51} +(-2.05560 - 2.82930i) q^{52} +(-12.6164 + 4.09933i) q^{53} +(-0.309017 - 0.951057i) q^{54} +(0.416370 + 5.45851i) q^{55} -4.81485 q^{56} -5.16928i q^{57} +(1.37118 + 0.445522i) q^{58} +(0.313586 + 0.227834i) q^{59} +(1.90374 + 1.17293i) q^{60} +8.48817 q^{61} +(-5.56118 - 0.270686i) q^{62} -4.81485i q^{63} +(0.809017 - 0.587785i) q^{64} +(-1.84385 + 7.59950i) q^{65} +(-0.756539 + 2.32839i) q^{66} +7.67240i q^{67} -0.175368i q^{68} +(-2.38814 + 7.34995i) q^{69} +(6.97243 + 8.20359i) q^{70} +(1.23262 + 3.79361i) q^{71} +(0.587785 + 0.809017i) q^{72} +(8.55266 + 2.77893i) q^{73} +(5.67792 - 4.12525i) q^{74} +(-0.758377 - 4.94215i) q^{75} +(1.59739 + 4.91627i) q^{76} +(-6.92867 + 9.53650i) q^{77} +(-2.05560 + 2.82930i) q^{78} +(-0.366066 - 1.12663i) q^{79} +(-2.17302 - 0.527234i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(2.98162 + 0.968788i) q^{82} +(4.23864 + 5.83399i) q^{83} +(1.48787 + 4.57919i) q^{84} +(-0.298795 + 0.253953i) q^{85} +(3.65450 - 11.2474i) q^{86} -1.44174i q^{87} -2.44821i q^{88} +(2.13360 - 6.56655i) q^{89} +(0.527234 - 2.17302i) q^{90} +(-13.6226 + 9.89742i) q^{91} -7.72820i q^{92} +(1.46106 + 5.37264i) q^{93} +8.69528 q^{94} +(6.06320 - 9.84097i) q^{95} +(-0.809017 - 0.587785i) q^{96} +(-13.8684 - 4.50610i) q^{97} +16.1828i q^{98} +2.44821 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

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