LMFDB - Embedded newform 930.2.y.a.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(29,930)]

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([5, 5, 3]))

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

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

chi := DirichletCharacter("930.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.y (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:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	930.29
Dual form			930.2.y.a.449.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{2} +(-1.61743 - 0.619623i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.184552 - 2.22844i) q^{5} +(0.944320 + 1.45198i) q^{6} +(2.03784 - 0.662134i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.23213 + 2.00439i) q^{9} +O(q^{10})$	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.61743 - 0.619623i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.184552 - 2.22844i) q^{5} +(0.944320 + 1.45198i) q^{6} +(2.03784 - 0.662134i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.23213 + 2.00439i) q^{9} +(-1.16054 + 1.91132i) q^{10} +(0.778518 + 2.39603i) q^{11} +(0.0894846 - 1.72974i) q^{12} +(-5.75657 + 4.18239i) q^{13} +(-2.03784 - 0.662134i) q^{14} +(-1.08229 + 3.71869i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.0713422 - 0.0231805i) q^{17} +(-0.627684 - 2.93360i) q^{18} +(1.93781 + 1.40790i) q^{19} +(2.06234 - 0.864145i) q^{20} +(-3.70633 - 0.191740i) q^{21} +(0.778518 - 2.39603i) q^{22} +(-6.57902 - 2.13765i) q^{23} +(-1.08911 + 1.34679i) q^{24} +(-4.93188 + 0.822528i) q^{25} +7.11551 q^{26} +(-2.36835 - 4.62503i) q^{27} +(1.25945 + 1.73349i) q^{28} +(1.57706 + 1.14580i) q^{29} +(3.06138 - 2.37233i) q^{30} +(-4.53562 + 3.22926i) q^{31} +1.00000 q^{32} +(0.225442 - 4.35779i) q^{33} +(0.0440919 + 0.0606873i) q^{34} +(-1.85161 - 4.41900i) q^{35} +(-1.21652 + 2.74228i) q^{36} +7.16065 q^{37} +(-0.740178 - 2.27803i) q^{38} +(11.9023 - 3.19781i) q^{39} +(-2.17640 - 0.513106i) q^{40} +(-1.49478 + 2.05739i) q^{41} +(2.88578 + 2.33364i) q^{42} +(5.74329 + 4.17274i) q^{43} +(-2.03819 + 1.48083i) q^{44} +(4.05471 - 5.34409i) q^{45} +(4.06606 + 5.59645i) q^{46} +(-10.5015 + 7.62979i) q^{47} +(1.67273 - 0.449413i) q^{48} +(-1.94876 + 1.41585i) q^{49} +(4.47345 + 2.23345i) q^{50} +(0.101028 + 0.0816980i) q^{51} +(-5.75657 - 4.18239i) q^{52} +(6.25666 + 2.03291i) q^{53} +(-0.802496 + 5.13381i) q^{54} +(5.19573 - 2.17707i) q^{55} -2.14271i q^{56} +(-2.26190 - 3.47789i) q^{57} +(-0.602383 - 1.85395i) q^{58} +(2.59424 + 3.57067i) q^{59} +(-3.87113 + 0.119816i) q^{60} -0.765884i q^{61} +(5.56751 + 0.0534406i) q^{62} +(5.87590 + 2.60665i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(10.3826 + 12.0563i) q^{65} +(-2.74383 + 3.39302i) q^{66} +11.3965i q^{67} -0.0750136i q^{68} +(9.31654 + 7.53401i) q^{69} +(-1.09944 + 4.66340i) q^{70} +(3.34743 + 1.08765i) q^{71} +(2.59606 - 1.50350i) q^{72} +(3.28865 + 10.1214i) q^{73} +(-5.79309 - 4.20892i) q^{74} +(8.48661 + 1.72553i) q^{75} +(-0.740178 + 2.27803i) q^{76} +(3.17299 + 4.36724i) q^{77} +(-11.5088 - 4.40894i) q^{78} +(-11.4514 - 3.72079i) q^{79} +(1.45915 + 1.69437i) q^{80} +(0.964844 + 8.94813i) q^{81} +(2.41861 - 0.785854i) q^{82} +(-3.04370 + 4.18929i) q^{83} +(-0.962963 - 3.58418i) q^{84} +(-0.0384899 + 0.163260i) q^{85} +(-2.19374 - 6.75164i) q^{86} +(-1.84081 - 2.83043i) q^{87} +2.51934 q^{88} +(-1.97299 - 6.07224i) q^{89} +(-6.42151 + 1.94016i) q^{90} +(-8.96165 + 12.3347i) q^{91} -6.91759i q^{92} +(9.33696 - 2.41272i) q^{93} +12.9806 q^{94} +(2.77980 - 4.57813i) q^{95} +(-1.61743 - 0.619623i) q^{96} +(17.7212 - 5.75796i) q^{97} +2.40879 q^{98} +(-3.06483 + 6.90872i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	$ 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) $ 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$2$	−0.809017	−	0.587785i	−0.572061	−	0.415627i
$3$	−1.61743	−	0.619623i	−0.933821	−	0.357740i
$3$	−1.61743	−	0.619623i	−0.933821	−	0.357740i
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.184552	−	2.22844i	−0.0825344	−	0.996588i
$5$	−0.184552	−	2.22844i	−0.0825344	−	0.996588i
$6$	0.944320	+	1.45198i	0.385517	+	0.592770i
$7$	2.03784	−	0.662134i	0.770230	−	0.250263i	0.102567	−	0.994726i	$-0.467294\pi$
$7$	2.03784	−	0.662134i	0.770230	−	0.250263i	0.667664	+	0.744463i	$0.267294\pi$
$8$	0.309017	−	0.951057i	0.109254	−	0.336249i
$9$	2.23213	+	2.00439i	0.744045	+	0.668130i
$10$	−1.16054	+	1.91132i	−0.366994	+	0.604413i
$11$	0.778518	+	2.39603i	0.234732	+	0.722431i	0.997157	+	0.0753541i	$0.0240087\pi$
$11$	0.778518	+	2.39603i	0.234732	+	0.722431i	−0.762425	+	0.647077i	$0.775991\pi$
$12$	0.0894846	−	1.72974i	0.0258320	−	0.499332i
$13$	−5.75657	+	4.18239i	−1.59659	+	1.15999i	−0.702903	+	0.711285i	$0.748113\pi$
$13$	−5.75657	+	4.18239i	−1.59659	+	1.15999i	−0.893682	+	0.448702i	$0.851887\pi$
$14$	−2.03784	−	0.662134i	−0.544635	−	0.176963i
$15$	−1.08229	+	3.71869i	−0.279447	+	0.960161i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.0713422	−	0.0231805i	−0.0173030	−	0.00562209i	0.300353	−	0.953828i	$-0.402896\pi$
$17$	−0.0713422	−	0.0231805i	−0.0173030	−	0.00562209i	−0.317656	+	0.948206i	$0.602896\pi$
$18$	−0.627684	−	2.93360i	−0.147946	−	0.691456i
$19$	1.93781	+	1.40790i	0.444565	+	0.322995i	0.787446	−	0.616384i	$-0.211403\pi$
$19$	1.93781	+	1.40790i	0.444565	+	0.322995i	−0.342881	+	0.939379i	$0.611403\pi$
$20$	2.06234	−	0.864145i	0.461154	−	0.193229i
$21$	−3.70633	−	0.191740i	−0.808787	−	0.0418410i
$22$	0.778518	−	2.39603i	0.165981	−	0.510836i
$23$	−6.57902	−	2.13765i	−1.37182	−	0.445731i	−0.471848	−	0.881680i	$-0.656413\pi$
$23$	−6.57902	−	2.13765i	−1.37182	−	0.445731i	−0.899972	+	0.435948i	$0.856413\pi$
$24$	−1.08911	+	1.34679i	−0.222313	+	0.274912i
$25$	−4.93188	+	0.822528i	−0.986376	+	0.164506i
$26$	7.11551			1.39547
$27$	−2.36835	−	4.62503i	−0.455788	−	0.890088i
$28$	1.25945	+	1.73349i	0.238014	+	0.327599i
$29$	1.57706	+	1.14580i	0.292853	+	0.212770i	0.724504	−	0.689271i	$-0.242069\pi$
$29$	1.57706	+	1.14580i	0.292853	+	0.212770i	−0.431651	+	0.902041i	$0.642069\pi$
$30$	3.06138	−	2.37233i	0.558930	−	0.433126i
$31$	−4.53562	+	3.22926i	−0.814621	+	0.579993i
$31$	−4.53562	+	3.22926i	−0.814621	+	0.579993i
$32$	1.00000			0.176777
$33$	0.225442	−	4.35779i	0.0392444	−	0.758594i
$34$	0.0440919	+	0.0606873i	0.00756170	+	0.0104078i
$35$	−1.85161	−	4.41900i	−0.312980	−	0.746947i
$36$	−1.21652	+	2.74228i	−0.202753	+	0.457046i
$37$	7.16065			1.17720			0.588602	−	0.808423i	$-0.299679\pi$
$37$	7.16065			1.17720			0.588602	+	0.808423i	$0.299679\pi$
$38$	−0.740178	−	2.27803i	−0.120073	−	0.369546i
$39$	11.9023	−	3.19781i	1.90590	−	0.512059i
$40$	−2.17640	−	0.513106i	−0.344119	−	0.0811291i
$41$	−1.49478	+	2.05739i	−0.233446	+	0.321311i	−0.909628	−	0.415424i	$-0.863633\pi$
$41$	−1.49478	+	2.05739i	−0.233446	+	0.321311i	0.676182	+	0.736735i	$0.263633\pi$
$42$	2.88578	+	2.33364i	0.445285	+	0.360089i
$43$	5.74329	+	4.17274i	0.875843	+	0.636337i	0.932149	−	0.362076i	$-0.117932\pi$
$43$	5.74329	+	4.17274i	0.875843	+	0.636337i	−0.0563051	+	0.998414i	$0.517932\pi$
$44$	−2.03819	+	1.48083i	−0.307268	+	0.223243i
$45$	4.05471	−	5.34409i	0.604441	−	0.796650i
$46$	4.06606	+	5.59645i	0.599507	+	0.825151i
$47$	−10.5015	+	7.62979i	−1.53180	+	1.11292i	−0.576574	+	0.817045i	$0.695611\pi$
$47$	−10.5015	+	7.62979i	−1.53180	+	1.11292i	−0.955227	+	0.295874i	$0.904389\pi$
$48$	1.67273	−	0.449413i	0.241438	−	0.0648672i
$49$	−1.94876	+	1.41585i	−0.278394	+	0.202265i
$50$	4.47345	+	2.23345i	0.632641	+	0.315857i
$51$	0.101028	+	0.0816980i	0.0141467	+	0.0114400i
$52$	−5.75657	−	4.18239i	−0.798293	−	0.579993i
$53$	6.25666	+	2.03291i	0.859419	+	0.279242i	0.705386	−	0.708824i	$-0.250774\pi$
$53$	6.25666	+	2.03291i	0.859419	+	0.279242i	0.154033	+	0.988066i	$0.450774\pi$
$54$	−0.802496	+	5.13381i	−0.109206	+	0.698623i
$55$	5.19573	−	2.17707i	0.700593	−	0.293557i
$56$		−	2.14271i		−	0.286332i
$57$	−2.26190	−	3.47789i	−0.299596	−	0.460658i
$58$	−0.602383	−	1.85395i	−0.0790968	−	0.243435i
$59$	2.59424	+	3.57067i	0.337742	+	0.464862i	0.943780	−	0.330574i	$-0.107242\pi$
$59$	2.59424	+	3.57067i	0.337742	+	0.464862i	−0.606038	+	0.795435i	$0.707242\pi$
$60$	−3.87113	+	0.119816i	−0.499761	+	0.0154682i
$61$		−	0.765884i		−	0.0980614i	−0.998797	−	0.0490307i	$-0.984387\pi$
$61$		−	0.765884i		−	0.0980614i	0.998797	−	0.0490307i	$-0.0156132\pi$
$62$	5.56751	+	0.0534406i	0.707074	+	0.00678696i
$63$	5.87590	+	2.60665i	0.740294	+	0.328407i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	10.3826	+	12.0563i	1.28780	+	1.49540i
$66$	−2.74383	+	3.39302i	−0.337742	+	0.417652i
$67$			11.3965i			1.39231i	0.717892	+	0.696154i	$0.245107\pi$
$67$			11.3965i			1.39231i	−0.717892	+	0.696154i	$0.754893\pi$
$68$		−	0.0750136i		−	0.00909674i
$69$	9.31654	+	7.53401i	1.12158	+	0.906988i
$70$	−1.09944	+	4.66340i	−0.131408	+	0.557382i
$71$	3.34743	+	1.08765i	0.397267	+	0.129080i	0.500836	−	0.865542i	$-0.333026\pi$
$71$	3.34743	+	1.08765i	0.397267	+	0.129080i	−0.103569	+	0.994622i	$0.533026\pi$
$72$	2.59606	−	1.50350i	0.305948	−	0.177189i
$73$	3.28865	+	10.1214i	0.384907	+	1.18462i	0.936548	+	0.350540i	$0.114002\pi$
$73$	3.28865	+	10.1214i	0.384907	+	1.18462i	−0.551641	+	0.834082i	$0.685998\pi$
$74$	−5.79309	−	4.20892i	−0.673433	−	0.489278i
$75$	8.48661	+	1.72553i	0.979949	+	0.199247i
$76$	−0.740178	+	2.27803i	−0.0849043	+	0.261309i
$77$	3.17299	+	4.36724i	0.361596	+	0.497694i
$78$	−11.5088	−	4.40894i	−1.30312	−	0.499214i
$79$	−11.4514	−	3.72079i	−1.28838	−	0.418621i	−0.416859	−	0.908971i	$-0.636869\pi$
$79$	−11.4514	−	3.72079i	−1.28838	−	0.418621i	−0.871526	+	0.490350i	$0.836869\pi$
$80$	1.45915	+	1.69437i	0.163138	+	0.189436i
$81$	0.964844	+	8.94813i	0.107205	+	0.994237i
$82$	2.41861	−	0.785854i	0.267091	−	0.0867830i
$83$	−3.04370	+	4.18929i	−0.334089	+	0.459834i	−0.942703	−	0.333632i	$-0.891726\pi$
$83$	−3.04370	+	4.18929i	−0.334089	+	0.459834i	0.608614	+	0.793466i	$0.291726\pi$
$84$	−0.962963	−	3.58418i	−0.105068	−	0.391066i
$85$	−0.0384899	+	0.163260i	−0.00417482	+	0.0177080i
$86$	−2.19374	−	6.75164i	−0.236557	−	0.728048i
$87$	−1.84081	−	2.83043i	−0.197356	−	0.303454i
$88$	2.51934			0.268562
$89$	−1.97299	−	6.07224i	−0.209136	−	0.643656i	−0.999518	−	0.0310410i	$-0.990118\pi$
$89$	−1.97299	−	6.07224i	−0.209136	−	0.643656i	0.790382	−	0.612615i	$-0.209882\pi$
$90$	−6.42151	+	1.94016i	−0.676887	+	0.204511i
$91$	−8.96165	+	12.3347i	−0.939437	+	1.29302i
$92$		−	6.91759i		−	0.721209i
$93$	9.33696	−	2.41272i	0.968197	−	0.250188i
$94$	12.9806			1.33884
$95$	2.77980	−	4.57813i	0.285201	−	0.469706i
$96$	−1.61743	−	0.619623i	−0.165078	−	0.0632400i
$97$	17.7212	−	5.75796i	1.79931	−	0.584633i	0.799444	−	0.600740i	$-0.205127\pi$
$97$	17.7212	−	5.75796i	1.79931	−	0.584633i	0.999870	+	0.0161074i	$0.00512735\pi$
$98$	2.40879			0.243325
$99$	−3.06483	+	6.90872i	−0.308027	+	0.694352i
$100$	−2.30631	−	4.43632i	−0.230631	−	0.443632i
$101$	−8.52132	−	2.76875i	−0.847903	−	0.275500i	−0.147336	−	0.989087i	$-0.547070\pi$
$101$	−8.52132	−	2.76875i	−0.847903	−	0.275500i	−0.700568	+	0.713586i	$0.747070\pi$
$102$	−0.0337121	−	0.125478i	−0.00333800	−	0.0124241i
$103$	5.87666	−	8.08853i	0.579045	−	0.796987i	−0.414545	−	0.910029i	$-0.636059\pi$
$103$	5.87666	−	8.08853i	0.579045	−	0.796987i	0.993590	+	0.113042i	$0.0360594\pi$
$104$	2.19881	+	6.76725i	0.215611	+	0.663584i
$105$	0.256732	+	8.29471i	0.0250544	+	0.809481i
$106$	−3.86683	−	5.32224i	−0.375580	−	0.516941i
$107$	4.87322	−	14.9982i	0.471112	−	1.44993i	−0.380019	−	0.924979i	$-0.624083\pi$
$107$	4.87322	−	14.9982i	0.471112	−	1.44993i	0.851131	−	0.524954i	$-0.175917\pi$
$108$	3.66681	−	3.68164i	0.352839	−	0.354266i
$109$	13.7192	−	9.96758i	1.31406	−	0.954721i	0.314075	−	0.949398i	$-0.398306\pi$
$109$	13.7192	−	9.96758i	1.31406	−	0.954721i	0.999986	−	0.00532285i	$-0.00169433\pi$
$110$	−5.48309	−	1.29269i	−0.522792	−	0.123253i
$111$	−11.5818	−	4.43691i	−1.09930	−	0.421132i
$112$	−1.25945	+	1.73349i	−0.119007	+	0.163799i
$113$	−3.43919	−	10.5848i	−0.323532	−	0.995730i	−0.972099	−	0.234572i	$-0.924631\pi$
$113$	−3.43919	−	10.5848i	−0.323532	−	0.995730i	0.648567	−	0.761158i	$-0.275369\pi$
$114$	−0.214340	+	4.14318i	−0.0200747	+	0.388045i
$115$	−3.54945	+	15.0554i	−0.330988	+	1.40393i
$116$	−0.602383	+	1.85395i	−0.0559299	+	0.172134i
$117$	−21.2326	−	2.20275i	−1.96295	−	0.203644i
$118$		−	4.41359i		−	0.406304i
$119$	−0.160732			−0.0147343
$120$	3.20224	+	2.17846i	0.292323	+	0.198865i
$121$	3.76431	−	2.73493i	0.342210	−	0.248630i
$122$	−0.450175	+	0.619613i	−0.0407570	+	0.0560971i
$123$	3.69251	−	2.40148i	0.332942	−	0.216534i
$124$	−4.47280	−	3.31573i	−0.401669	−	0.297762i
$125$	2.74314	+	10.8386i	0.245354	+	0.969433i
$126$	−3.22155	−	5.56259i	−0.286999	−	0.495555i
$127$	−12.1867	+	8.85417i	−1.08140	+	0.785681i	−0.977926	−	0.208952i	$-0.932995\pi$
$127$	−12.1867	+	8.85417i	−1.08140	+	0.785681i	−0.103471	+	0.994633i	$0.532995\pi$
$128$	0.309017	+	0.951057i	0.0273135	+	0.0840623i
$129$	−6.70382	−	10.3078i	−0.590238	−	0.907549i
$130$	−1.31319	−	15.8565i	−0.115174	−	1.39071i
$131$	−12.0358	+	3.91067i	−1.05157	+	0.341677i	−0.783286	−	0.621662i	$-0.786458\pi$
$131$	−12.0358	+	3.91067i	−1.05157	+	0.341677i	−0.268288	+	0.963339i	$0.586458\pi$
$132$	4.21417	−	1.13222i	0.366797	−	0.0985474i
$133$	4.88117	+	1.58599i	0.423251	+	0.137523i
$134$	6.69872	−	9.21999i	0.578681	−	0.796486i
$135$	−9.86952	+	6.13127i	−0.849433	+	0.527696i
$136$	−0.0440919	+	0.0606873i	−0.00378085	+	0.00520389i
$137$	10.9475	+	15.0680i	0.935311	+	1.28734i	0.957752	+	0.287596i	$0.0928562\pi$
$137$	10.9475	+	15.0680i	0.935311	+	1.28734i	−0.0224412	+	0.999748i	$0.507144\pi$
$138$	−3.10886	−	11.5713i	−0.264643	−	0.985011i
$139$	9.01520	+	12.4084i	0.764659	+	1.05246i	0.996812	+	0.0797840i	$0.0254230\pi$
$139$	9.01520	+	12.4084i	0.764659	+	1.05246i	−0.232153	+	0.972679i	$0.574577\pi$
$140$	3.63054	−	3.12653i	0.306837	−	0.264240i
$141$	21.7130	−	5.83364i	1.82856	−	0.491281i
$142$	−2.06883	−	2.84749i	−0.173612	−	0.238956i
$143$	−14.5027	−	10.5369i	−1.21278	−	0.881136i
$144$	−2.98398	−	0.309570i	−0.248665	−	0.0257975i
$145$	2.26230	−	3.72584i	0.187874	−	0.309414i
$146$	3.28865	−	10.1214i	0.272170	−	0.837654i
$147$	4.02926	−	1.08254i	0.332328	−	0.0892868i
$148$	2.21276	+	6.81018i	0.181888	+	0.559794i
$149$			4.25021i			0.348191i	0.984729	+	0.174096i	$0.0557002\pi$
$149$			4.25021i			0.348191i	−0.984729	+	0.174096i	$0.944300\pi$
$150$	−5.85157	−	6.38429i	−0.477779	−	0.521275i
$151$	−14.8715	+	4.83206i	−1.21023	+	0.393227i	−0.843515	−	0.537106i	$-0.819517\pi$
$151$	−14.8715	+	4.83206i	−1.21023	+	0.393227i	−0.366714	+	0.930334i	$0.619517\pi$
$152$	1.93781	−	1.40790i	0.157177	−	0.114196i
$153$	−0.112783	−	0.194739i	−0.00911793	−	0.0157438i
$154$		−	5.39821i		−	0.435000i
$155$	8.03328	+	9.51138i	0.645249	+	0.763973i
$156$	6.71932	+	10.3316i	0.537976	+	0.827191i
$157$	−0.652659	+	0.898308i	−0.0520879	+	0.0716928i	−0.834266	−	0.551362i	$-0.814108\pi$
$157$	−0.652659	+	0.898308i	−0.0520879	+	0.0716928i	0.782179	+	0.623054i	$0.214108\pi$
$158$	7.07736	+	9.74115i	0.563045	+	0.774964i
$159$	−8.86005	−	7.16486i	−0.702648	−	0.568210i
$160$	−0.184552	−	2.22844i	−0.0145902	−	0.176174i
$161$	−14.8224			−1.16817
$162$	4.47901	−	7.80631i	0.351904	−	0.613322i
$163$	7.05838	+	2.29341i	0.552855	+	0.179633i	0.572104	−	0.820181i	$-0.306127\pi$
$163$	7.05838	+	2.29341i	0.552855	+	0.179633i	−0.0192489	+	0.999815i	$0.506127\pi$
$164$	−2.41861	−	0.785854i	−0.188862	−	0.0613649i
$165$	−9.75268	+	0.301858i	−0.759245	+	0.0234996i
$166$	4.92481	−	1.60017i	0.382239	−	0.124197i
$167$	−5.33101	+	7.33751i	−0.412526	+	0.567793i	−0.963832	−	0.266510i	$-0.914130\pi$
$167$	−5.33101	+	7.33751i	−0.412526	+	0.567793i	0.551306	+	0.834303i	$0.314130\pi$
$168$	−1.32767	+	3.46567i	−0.102432	+	0.267383i
$169$	11.6285	−	35.7887i	0.894497	−	2.75298i
$170$	0.127101	−	0.109456i	0.00974817	−	0.00839490i
$171$	1.50347	+	7.02676i	0.114973	+	0.537350i
$172$	−2.19374	+	6.75164i	−0.167271	+	0.514808i
$173$	−2.21912	+	1.61229i	−0.168717	+	0.122580i	−0.668939	−	0.743317i	$-0.733251\pi$
$173$	−2.21912	+	1.61229i	−0.168717	+	0.122580i	0.500223	+	0.865897i	$0.333251\pi$
$174$	−0.174437	+	3.37187i	−0.0132240	+	0.255621i
$175$	−9.50575	+	4.94174i	−0.718567	+	0.373561i
$176$	−2.03819	−	1.48083i	−0.153634	−	0.111622i
$177$	−1.98353	−	7.38275i	−0.149091	−	0.554921i
$178$	−1.97299	+	6.07224i	−0.147882	+	0.455133i
$179$	0.00971135	+	0.0298885i	0.000725860	+	0.00223397i	0.951419	−	0.307900i	$-0.0996262\pi$
$179$	0.00971135	+	0.0298885i	0.000725860	+	0.00223397i	−0.950693	+	0.310134i	$0.899626\pi$
$180$	6.33551	+	2.20485i	0.472221	+	0.164340i
$181$			23.5531i			1.75069i	0.483499	+	0.875345i	$0.339366\pi$
$181$			23.5531i			1.75069i	−0.483499	+	0.875345i	$0.660634\pi$
$182$	14.5003	−	4.71142i	1.07483	−	0.349234i
$183$	−0.474560	+	1.23876i	−0.0350805	+	0.0915718i
$184$	−4.06606	+	5.59645i	−0.299754	+	0.412576i
$185$	−1.32152	−	15.9571i	−0.0971598	−	1.17319i
$186$	−8.97192	−	3.53619i	−0.657853	−	0.259286i
$187$		−	0.188985i		−	0.0138199i
$188$	−10.5015	−	7.62979i	−0.765901	−	0.556459i
$189$	−7.88870	−	7.85691i	−0.573818	−	0.571506i
$190$	−4.93986	+	2.06986i	−0.358375	+	0.150163i
$191$		−	15.1585i		−	1.09683i	−0.836207	−	0.548414i	$-0.815232\pi$
$191$		−	15.1585i		−	1.09683i	0.836207	−	0.548414i	$-0.184768\pi$
$192$	0.944320	+	1.45198i	0.0681504	+	0.104788i
$193$	−4.30403	+	1.39846i	−0.309811	+	0.100664i	−0.459796	−	0.888025i	$-0.652077\pi$
$193$	−4.30403	+	1.39846i	−0.309811	+	0.100664i	0.149985	+	0.988688i	$0.452077\pi$
$194$	−17.7212	−	5.75796i	−1.27231	−	0.413398i
$195$	−9.32272	−	25.9335i	−0.667614	−	1.85713i
$196$	−1.94876	−	1.41585i	−0.139197	−	0.101132i
$197$	−4.49801	+	1.46149i	−0.320470	+	0.104127i	−0.464834	−	0.885398i	$-0.653886\pi$
$197$	−4.49801	+	1.46149i	−0.320470	+	0.104127i	0.144365	+	0.989525i	$0.453886\pi$
$198$	6.54034	−	3.78781i	0.464802	−	0.269188i
$199$	−5.04893	−	6.94925i	−0.357909	−	0.492620i	0.591656	−	0.806191i	$-0.298475\pi$
$199$	−5.04893	−	6.94925i	−0.357909	−	0.492620i	−0.949565	+	0.313571i	$0.898475\pi$
$200$	−0.741765	+	4.94467i	−0.0524507	+	0.349641i
$201$	7.06156	−	18.4331i	0.498084	−	1.30017i
$202$	5.26647	+	7.24867i	0.370547	+	0.510015i
$203$	3.97247	+	1.29073i	0.278812	+	0.0905917i
$204$	−0.0464802	+	0.121329i	−0.00325426	+	0.00849473i
$205$	4.86064	+	2.95134i	0.339482	+	0.206130i
$206$	−9.50864	+	3.08954i	−0.662498	+	0.215259i
$207$	−10.4006	−	17.9584i	−0.722889	−	1.24820i
$208$	2.19881	−	6.76725i	0.152460	−	0.469225i
$209$	−1.86476	+	5.73914i	−0.128988	+	0.396985i
$210$	4.66781	−	6.86146i	0.322109	−	0.473486i
$211$	−7.05032			−0.485364			−0.242682	−	0.970106i	$-0.578027\pi$
$211$	−7.05032			−0.485364			−0.242682	+	0.970106i	$0.578027\pi$
$212$			6.57865i			0.451823i
$213$	−4.74029	−	3.83333i	−0.324799	−	0.262656i
$214$	−12.7582	+	9.26941i	−0.872136	+	0.633644i
$215$	8.23877	−	13.5687i	0.561879	−	0.925375i
$216$	−5.13053	+	0.823216i	−0.349088	+	0.0560127i
$217$	−7.10465	+	9.58391i	−0.482295	+	0.650598i
$218$	−16.9579			−1.14853
$219$	0.952321	−	18.4084i	0.0643519	−	1.24392i
$220$	3.67609	+	4.26868i	0.247842	+	0.287795i
$221$	0.507636	−	0.164941i	0.0341473	−	0.0110951i
$222$	6.76194	+	10.3972i	0.453832	+	0.697811i
$223$	−11.7748			−0.788499			−0.394250	−	0.919003i	$-0.628995\pi$
$223$	−11.7748			−0.788499			−0.394250	+	0.919003i	$0.628995\pi$
$224$	2.03784	−	0.662134i	0.136159	−	0.0442407i
$225$	−12.6573	−	8.04942i	−0.843819	−	0.536628i
$226$	−3.43919	+	10.5848i	−0.228772	+	0.704087i
$227$	−9.81115	−	7.12822i	−0.651189	−	0.473116i	0.212487	−	0.977164i	$-0.431844\pi$
$227$	−9.81115	−	7.12822i	−0.651189	−	0.473116i	−0.863676	+	0.504048i	$0.831844\pi$
$228$	2.60871	−	3.22592i	0.172766	−	0.213642i
$229$	−0.273083	+	0.375866i	−0.0180458	+	0.0248379i	−0.817945	−	0.575297i	$-0.804886\pi$
$229$	−0.273083	+	0.375866i	−0.0180458	+	0.0248379i	0.799899	+	0.600135i	$0.204886\pi$
$230$	11.7209	−	10.0938i	0.772856	−	0.665565i
$231$	−2.42603	−	9.02975i	−0.159621	−	0.594114i
$232$	1.57706	−	1.14580i	0.103539	−	0.0752255i
$233$	−6.24139	+	4.53464i	−0.408887	+	0.297074i	−0.773151	−	0.634222i	$-0.781321\pi$
$233$	−6.24139	+	4.53464i	−0.408887	+	0.297074i	0.364264	+	0.931296i	$0.381321\pi$
$234$	15.8828	+	14.2623i	1.03829	+	0.932353i
$235$	18.9406	+	21.9939i	1.23555	+	1.43472i
$236$	−2.59424	+	3.57067i	−0.168871	+	0.232431i
$237$	16.2163	+	13.1137i	1.05336	+	0.851824i
$238$	0.130035	+	0.0944761i	0.00842893	+	0.00612398i
$239$	−5.73494	+	17.6503i	−0.370962	+	1.14170i	0.575200	+	0.818013i	$0.304924\pi$
$239$	−5.73494	+	17.6503i	−0.370962	+	1.14170i	−0.946163	+	0.323692i	$0.895076\pi$
$240$	−1.31020	−	3.64464i	−0.0845728	−	0.235260i
$241$	−3.55905	+	1.15641i	−0.229259	+	0.0744907i	−0.421394	−	0.906878i	$-0.638459\pi$
$241$	−3.55905	+	1.15641i	−0.229259	+	0.0744907i	0.192135	+	0.981369i	$0.438459\pi$
$242$	−4.65294			−0.299102
$243$	3.98391	−	15.0708i	0.255568	−	0.966791i
$244$	0.728399	−	0.236671i	0.0466310	−	0.0151513i
$245$	3.51479	+	4.08138i	0.224552	+	0.260750i
$246$	−4.39886	−	0.227566i	−0.280461	−	0.0145091i
$247$	−17.0436			−1.08446
$248$	1.66963	+	5.31153i	0.106022	+	0.337282i
$249$	7.51874	−	4.88992i	0.476481	−	0.309886i
$250$	4.15152	−	10.3810i	0.262565	−	0.656551i
$251$	−18.9503	+	13.7682i	−1.19613	+	0.869041i	−0.993899	−	0.110296i	$-0.964820\pi$
$251$	−18.9503	+	13.7682i	−1.19613	+	0.869041i	−0.202233	+	0.979337i	$0.564820\pi$
$252$	−0.663318	+	6.39381i	−0.0417851	+	0.402772i
$253$		−	17.4277i		−	1.09567i
$254$	15.0636			0.945175
$255$	0.163414	−	0.240211i	0.0102334	−	0.0150426i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−0.830220	+	2.55516i	−0.0517877	+	0.159386i	−0.973606	−	0.228237i	$-0.926704\pi$
$257$	−0.830220	+	2.55516i	−0.0517877	+	0.159386i	0.921818	+	0.387623i	$0.126704\pi$
$258$	−0.635260	+	12.2796i	−0.0395496	+	0.764493i
$259$	14.5922	−	4.74131i	0.906718	−	0.294611i
$260$	−8.25782	+	13.6000i	−0.512128	+	0.843438i
$261$	1.22358	+	5.71862i	0.0757375	+	0.353974i
$262$	12.0358	+	3.91067i	0.743575	+	0.241602i
$263$	7.61283	+	10.4782i	0.469427	+	0.646111i	0.976430	−	0.215833i	$-0.0692467\pi$
$263$	7.61283	+	10.4782i	0.469427	+	0.646111i	−0.507003	+	0.861944i	$0.669247\pi$
$264$	−4.07484	−	1.56104i	−0.250789	−	0.0960754i
$265$	3.37554	−	14.3178i	0.207358	−	0.879534i
$266$	−3.01673	−	4.15217i	−0.184967	−	0.254586i
$267$	−0.571335	+	11.0439i	−0.0349651	+	0.675876i
$268$	−10.8388	+	3.52172i	−0.662082	+	0.215124i
$269$	−3.26971	−	2.37559i	−0.199358	−	0.144842i	0.483628	−	0.875274i	$-0.339319\pi$
$269$	−3.26971	−	2.37559i	−0.199358	−	0.144842i	−0.682986	+	0.730432i	$0.739319\pi$
$270$	11.5885	+	0.840855i	0.705253	+	0.0511728i
$271$	10.2377	+	3.32644i	0.621897	+	0.202067i	0.602982	−	0.797755i	$-0.293979\pi$
$271$	10.2377	+	3.32644i	0.621897	+	0.202067i	0.0189146	+	0.999821i	$0.493979\pi$
$272$	0.0713422	−	0.0231805i	0.00432576	−	0.00140552i
$273$	22.1377	−	14.3975i	1.33983	−	0.871379i
$274$		−	18.6250i		−	1.12518i
$275$	−5.81036	−	11.1766i	−0.350378	−	0.673974i
$276$	−4.28630	+	11.1887i	−0.258005	+	0.673480i
$277$	−1.10044	−	0.799514i	−0.0661188	−	0.0480381i	0.554235	−	0.832360i	$-0.313011\pi$
$277$	−1.10044	−	0.799514i	−0.0661188	−	0.0480381i	−0.620354	+	0.784322i	$0.713011\pi$
$278$		−	15.3376i		−	0.919887i
$279$	−16.5968	−	1.88300i	−0.993625	−	0.112732i
$280$	−4.77490	+	0.395442i	−0.285355	+	0.0236322i
$281$	−8.06170	+	11.0960i	−0.480921	+	0.661930i	−0.978681	−	0.205384i	$-0.934156\pi$
$281$	−8.06170	+	11.0960i	−0.480921	+	0.661930i	0.497761	+	0.867314i	$0.334156\pi$
$282$	−20.9951	−	8.04306i	−1.25024	−	0.478957i
$283$	−3.10314	+	1.00827i	−0.184463	+	0.0599356i	−0.399792	−	0.916606i	$-0.630918\pi$
$283$	−3.10314	+	1.00827i	−0.184463	+	0.0599356i	0.215329	+	0.976542i	$0.430918\pi$
$284$			3.51970i			0.208856i
$285$	−7.33283	+	5.68236i	−0.434359	+	0.336594i
$286$	5.53955	+	17.0490i	0.327561	+	1.00813i
$287$	−1.68386	+	5.18238i	−0.0993949	+	0.305906i
$288$	2.23213	+	2.00439i	0.131530	+	0.118110i
$289$	−13.7487	−	9.98904i	−0.808749	−	0.587591i
$290$	−4.02023	+	1.68452i	−0.236076	+	0.0989187i
$291$	−32.2305	−	1.66738i	−1.88938	−	0.0977437i
$292$	−8.60979	+	6.25538i	−0.503850	+	0.366068i
$293$	5.05171	−	15.5476i	0.295124	−	0.908299i	−0.688055	−	0.725658i	$-0.741535\pi$
$293$	5.05171	−	15.5476i	0.295124	−	0.908299i	0.983180	−	0.182641i	$-0.0584646\pi$
$294$	−3.89605	−	1.49255i	−0.227222	−	0.0870470i
$295$	7.47825	−	6.44009i	0.435400	−	0.374957i
$296$	2.21276	−	6.81018i	0.128614	−	0.395834i
$297$	9.23793	−	9.27530i	0.536039	−	0.538208i
$298$	2.49821	−	3.43850i	0.144718	−	0.199187i
$299$	46.8131	−	15.2105i	2.70727	−	0.879645i
$300$	0.981430	+	8.60446i	0.0566629	+	0.496779i
$301$	14.4668	+	4.70055i	0.833853	+	0.270935i
$302$	14.8715	+	4.83206i	0.855761	+	0.278054i
$303$	12.0670	+	9.75825i	0.693233	+	0.560597i
$304$	−2.39527			−0.137378
$305$	−1.70673	+	0.141346i	−0.0977268	+	0.00809344i
$306$	−0.0232220	+	0.223839i	−0.00132751	+	0.0127961i
$307$	0.408013	+	0.561581i	0.0232865	+	0.0320511i	0.820502	−	0.571644i	$-0.193694\pi$
$307$	0.408013	+	0.561581i	0.0232865	+	0.0320511i	−0.797215	+	0.603695i	$0.793694\pi$
$308$	−3.17299	+	4.36724i	−0.180798	+	0.248847i
$309$	−14.5169	+	9.44129i	−0.825838	+	0.537096i
$310$	−0.908408	−	12.4167i	−0.0515941	−	0.705222i
$311$		−	9.42275i		−	0.534315i	−0.963653	−	0.267157i	$-0.913916\pi$
$311$		−	9.42275i		−	0.534315i	0.963653	−	0.267157i	$-0.0860844\pi$
$312$	0.636729	−	12.3080i	0.0360477	−	0.696801i
$313$	10.3042	−	7.48642i	0.582427	−	0.423158i	−0.257171	−	0.966366i	$-0.582791\pi$
$313$	10.3042	−	7.48642i	0.582427	−	0.423158i	0.839598	+	0.543208i	$0.182791\pi$
$314$	1.05602	−	0.343123i	0.0595949	−	0.0193636i
$315$	4.72435	−	13.5752i	0.266187	−	0.764873i
$316$		−	12.0407i		−	0.677344i
$317$	−0.745683	−	2.29498i	−0.0418817	−	0.128899i	0.927929	−	0.372756i	$-0.121587\pi$
$317$	−0.745683	−	2.29498i	−0.0418817	−	0.128899i	−0.969811	+	0.243857i	$0.921587\pi$
$318$	2.95653	+	11.0043i	0.165794	+	0.617091i
$319$	−1.51761	+	4.67071i	−0.0849697	+	0.261510i
$320$	−1.16054	+	1.91132i	−0.0648760	+	0.106846i
$321$	−17.1753	+	21.2390i	−0.958633	+	1.18544i
$322$	11.9916	+	8.71238i	0.668264	+	0.485522i
$323$	−0.105612	−	0.145362i	−0.00587640	−	0.00808817i
$324$	−8.21203	+	3.68275i	−0.456224	+	0.204597i
$325$	24.9506	−	25.3620i	1.38401	−	1.40683i
$326$	−4.36232	−	6.00422i	−0.241606	−	0.332543i
$327$	−28.3659	+	7.62109i	−1.56864	+	0.421447i
$328$	1.49478	+	2.05739i	0.0825356	+	0.113600i
$329$	−16.3484	+	22.5017i	−0.901317	+	1.24056i
$330$	8.06751	+	5.48827i	0.444102	+	0.302120i
$331$	−0.124011	+	0.170686i	−0.00681625	+	0.00938176i	−0.812412	−	0.583084i	$-0.801846\pi$
$331$	−0.124011	+	0.170686i	−0.00681625	+	0.00938176i	0.805595	+	0.592466i	$0.201846\pi$
$332$	−4.92481	−	1.60017i	−0.270284	−	0.0878205i
$333$	15.9835	+	14.3527i	0.875892	+	0.786525i
$334$	8.62576	−	2.80268i	0.471980	−	0.153356i
$335$	25.3965	−	2.10326i	1.38756	−	0.114913i
$336$	3.11118	−	2.02340i	0.169729	−	0.110386i
$337$	−6.80218	−	20.9350i	−0.370538	−	1.14040i	−0.946440	−	0.322881i	$-0.895349\pi$
$337$	−6.80218	−	20.9350i	−0.370538	−	1.14040i	0.575901	−	0.817519i	$-0.304651\pi$
$338$	−30.4437	+	22.1187i	−1.65592	+	1.20310i
$339$	−0.995916	+	19.2511i	−0.0540908	+	1.04557i
$340$	−0.167163	+	0.0138439i	−0.00906570	+	0.000750793i
$341$	−11.2685	−	8.35345i	−0.610223	−	0.452365i
$342$	2.91389	−	6.56848i	0.157565	−	0.355183i
$343$	−11.8499	+	16.3100i	−0.639836	+	0.880659i
$344$	5.74329	−	4.17274i	0.309657	−	0.224979i
$345$	15.0697	−	22.1518i	0.811325	−	1.19261i
$346$	2.74298			0.147464
$347$			7.42055i			0.398356i	0.979963	+	0.199178i	$0.0638272\pi$
$347$			7.42055i			0.398356i	−0.979963	+	0.199178i	$0.936173\pi$
$348$	2.12306	−	2.62537i	0.113808	−	0.140735i
$349$	−5.77954	+	17.7876i	−0.309372	+	0.952148i	0.668638	+	0.743588i	$0.266878\pi$
$349$	−5.77954	+	17.7876i	−0.309372	+	0.952148i	−0.978010	+	0.208560i	$0.933122\pi$
$350$	10.5950	+	1.58939i	0.566326	+	0.0849563i
$351$	32.9773	+	16.7190i	1.76020	+	0.892393i
$352$	0.778518	+	2.39603i	0.0414952	+	0.127709i
$353$	−11.8805	+	16.3521i	−0.632335	+	0.870334i	−0.998178	−	0.0603424i	$-0.980781\pi$
$353$	−11.8805	+	16.3521i	−0.632335	+	0.870334i	0.365843	+	0.930677i	$0.380781\pi$
$354$	−2.73476	+	7.13866i	−0.145351	+	0.379415i
$355$	1.80598	−	7.66027i	0.0958513	−	0.406565i
$356$	5.16535	−	3.75285i	0.273763	−	0.198901i
$357$	0.259973	+	0.0995935i	0.0137592	+	0.00527105i
$358$	0.00971135	−	0.0298885i	0.000513261	−	0.00157965i
$359$	14.1038	+	19.4123i	0.744372	+	1.02454i	0.998355	+	0.0573318i	$0.0182593\pi$
$359$	14.1038	+	19.4123i	0.744372	+	1.02454i	−0.253983	+	0.967209i	$0.581741\pi$
$360$	−3.82956	−	5.50768i	−0.201835	−	0.290280i
$361$	−4.09840	−	12.6136i	−0.215705	−	0.663872i
$362$	13.8442	−	19.0549i	0.727634	−	1.00150i
$363$	−7.78311	+	2.09109i	−0.408508	+	0.109754i
$364$	−14.5003	−	4.71142i	−0.760020	−	0.246946i
$365$	21.9480	−	9.19648i	1.14881	−	0.481366i
$366$	1.11205	−	0.723239i	0.0581279	−	0.0378043i
$367$	−28.3098			−1.47776			−0.738881	−	0.673836i	$-0.764645\pi$
$367$	−28.3098			−1.47776			−0.738881	+	0.673836i	$0.764645\pi$
$368$	6.57902	−	2.13765i	0.342955	−	0.111433i
$369$	−7.46037	+	1.59625i	−0.388371	+	0.0830973i
$370$	−8.31020	+	13.6863i	−0.432027	+	0.711517i
$371$	14.0961			0.731834
$372$	5.17991	+	8.13440i	0.268566	+	0.421749i
$373$			14.1273i			0.731482i	0.930717	+	0.365741i	$0.119184\pi$
$373$			14.1273i			0.731482i	−0.930717	+	0.365741i	$0.880816\pi$
$374$	−0.111082	+	0.152892i	−0.00574393	+	0.00790584i
$375$	2.27901	−	19.2303i	0.117688	−	0.993051i
$376$	4.01122	+	12.3453i	0.206863	+	0.636658i
$377$	−13.8706			−0.714375
$378$	1.76391	+	10.9932i	0.0907259	+	0.565431i
$379$	−6.43359	−	19.8006i	−0.330472	−	1.01709i	−0.968910	−	0.247414i	$-0.920419\pi$
$379$	−6.43359	−	19.8006i	−0.330472	−	1.01709i	0.638438	−	0.769673i	$-0.279581\pi$
$380$	5.21306	+	1.22903i	0.267425	+	0.0630477i
$381$	25.1974	−	6.76979i	1.29090	−	0.346827i
$382$	−8.90992	+	12.2635i	−0.455871	+	0.627453i
$383$	−21.4872	+	6.98162i	−1.09795	+	0.356744i	−0.801311	−	0.598247i	$-0.795864\pi$
$383$	−21.4872	+	6.98162i	−1.09795	+	0.356744i	−0.296634	+	0.954991i	$0.595864\pi$
$384$	0.0894846	−	1.72974i	0.00456649	−	0.0882703i
$385$	9.14655	−	7.87679i	0.466151	−	0.401439i
$386$	4.30403	+	1.39846i	0.219069	+	0.0711799i
$387$	4.45599	+	20.8259i	0.226510	+	1.05864i
$388$	10.9523	+	15.0745i	0.556019	+	0.765294i
$389$	7.27619	−	22.3938i	0.368917	−	1.13541i	−0.578574	−	0.815630i	$-0.696391\pi$
$389$	7.27619	−	22.3938i	0.368917	−	1.13541i	0.947492	−	0.319781i	$-0.103609\pi$
$390$	−7.70107	+	26.4604i	−0.389959	+	1.33987i
$391$	0.419810	+	0.305010i	0.0212307	+	0.0154250i
$392$	0.744358	+	2.29090i	0.0375958	+	0.115708i
$393$	21.8902	+	1.13245i	1.10421	+	0.0571243i
$394$	4.49801	+	1.46149i	0.226606	+	0.0736289i
$395$	−6.17816	+	26.2054i	−0.310857	+	1.31854i
$396$	−7.51767	−	0.779911i	−0.377777	−	0.0391920i
$397$		−	5.11131i		−	0.256529i	−0.991740	−	0.128265i	$-0.959059\pi$
$397$		−	5.11131i		−	0.256529i	0.991740	−	0.128265i	$-0.0409407\pi$
$398$			8.58975i			0.430565i
$399$	−6.91221	−	5.58970i	−0.346043	−	0.279835i
$400$	3.50651	−	3.56433i	0.175325	−	0.178216i
$401$	13.5172	+	9.82082i	0.675017	+	0.490428i	0.871701	−	0.490039i	$-0.163017\pi$
$401$	13.5172	+	9.82082i	0.675017	+	0.490428i	−0.196684	+	0.980467i	$0.563017\pi$
$402$	−16.5476	+	10.7620i	−0.825319	+	0.536759i
$403$	12.6036	−	37.5592i	0.627828	−	1.87096i
$404$		−	8.95985i		−	0.445769i
$405$	19.7623	−	3.80150i	0.981997	−	0.188898i
$406$	−2.45512	−	3.37918i	−0.121846	−	0.167706i
$407$	5.57470	+	17.1571i	0.276327	+	0.850448i
$408$	0.108919	−	0.0708368i	0.00539228	−	0.00350695i
$409$		−	19.6189i		−	0.970093i	−0.874488	−	0.485046i	$-0.838803\pi$
$409$		−	19.6189i		−	0.970093i	0.874488	−	0.485046i	$-0.161197\pi$
$410$	−2.19759	−	5.24469i	−0.108531	−	0.259017i
$411$	−8.37035	−	31.1547i	−0.412879	−	1.53675i
$412$	9.50864	+	3.08954i	0.468457	+	0.152211i
$413$	7.65091	+	5.55871i	0.376477	+	0.273526i
$414$	−2.14148	+	20.6420i	−0.105248	+	1.01450i
$415$	9.89730	+	6.00955i	0.485839	+	0.294997i
$416$	−5.75657	+	4.18239i	−0.282239	+	0.205059i
$417$	−6.89291	−	25.6556i	−0.337547	−	1.25636i
$418$	4.88200	−	3.54698i	0.238787	−	0.173489i
$419$	2.54660	+	3.50509i	0.124409	+	0.171235i	0.866679	−	0.498867i	$-0.166250\pi$
$419$	2.54660	+	3.50509i	0.124409	+	0.171235i	−0.742269	+	0.670102i	$0.766250\pi$
$420$	−7.80940	+	2.80737i	−0.381060	+	0.136986i
$421$	−5.14328	+	3.73681i	−0.250668	+	0.182121i	−0.706023	−	0.708189i	$-0.749512\pi$
$421$	−5.14328	+	3.73681i	−0.250668	+	0.182121i	0.455355	+	0.890310i	$0.349512\pi$
$422$	5.70383	+	4.14407i	0.277658	+	0.201730i
$423$	−38.7338	−	4.01839i	−1.88330	−	0.195381i
$424$	3.86683	−	5.32224i	0.187790	−	0.258471i
$425$	0.370918	+	0.0556424i	0.0179922	+	0.00269905i
$426$	1.58180	+	5.88750i	0.0766384	+	0.285250i
$427$	−0.507118	−	1.56075i	−0.0245411	−	0.0755299i
$428$	15.7701			0.762275
$429$	16.9282	+	26.0288i	0.817303	+	1.25668i
$430$	−14.6408	+	6.13465i	−0.706040	+	0.295839i
$431$	3.13227	+	4.31120i	0.150876	+	0.207663i	0.877764	−	0.479093i	$-0.159034\pi$
$431$	3.13227	+	4.31120i	0.150876	+	0.207663i	−0.726888	+	0.686756i	$0.759034\pi$
$432$	4.63456	+	2.34965i	0.222980	+	0.113048i
$433$	−10.6241			−0.510564			−0.255282	−	0.966867i	$-0.582168\pi$
$433$	−10.6241			−0.510564			−0.255282	+	0.966867i	$0.582168\pi$
$434$	11.3811	−	3.57753i	0.546309	−	0.171727i
$435$	−5.96772	+	4.62450i	−0.286130	+	0.221728i
$436$	13.7192	+	9.96758i	0.657030	+	0.477361i
$437$	−9.73929	−	13.4050i	−0.465894	−	0.641248i
$438$	−11.5906	+	14.3329i	−0.553820	+	0.684853i
$439$	37.3127			1.78084			0.890418	−	0.455143i	$-0.150412\pi$
$439$	37.3127			1.78084			0.890418	+	0.455143i	$0.150412\pi$
$440$	−0.464950	−	5.61419i	−0.0221656	−	0.267646i
$441$	−7.18781	−	0.745690i	−0.342277	−	0.0355091i
$442$	−0.507636	−	0.164941i	−0.0241458	−	0.00784544i
$443$	3.51800	−	10.8273i	0.167145	−	0.514421i	−0.832043	−	0.554712i	$-0.812829\pi$
$443$	3.51800	−	10.8273i	0.167145	−	0.514421i	0.999188	+	0.0402911i	$0.0128285\pi$
$444$	0.640768	−	12.3860i	0.0304095	−	0.587816i
$445$	−13.1675	+	5.51733i	−0.624199	+	0.261547i
$446$	9.52602	+	6.92106i	0.451070	+	0.327722i
$447$	2.63353	−	6.87441i	0.124562	−	0.325148i
$448$	−2.03784	−	0.662134i	−0.0962788	−	0.0312829i
$449$	28.9439	−	21.0290i	1.36595	−	0.992419i	0.367906	−	0.929863i	$-0.380075\pi$
$449$	28.9439	−	21.0290i	1.36595	−	0.992419i	0.998041	−	0.0625559i	$-0.0199252\pi$
$450$	5.50863	+	13.9519i	0.259679	+	0.657698i
$451$	−6.09329	−	1.97983i	−0.286922	−	0.0932266i
$452$	9.00393	−	6.54174i	0.423509	−	0.307697i
$453$	27.0477	+	1.39926i	1.27081	+	0.0657429i
$454$	3.74752	+	11.5337i	0.175880	+	0.541303i
$455$	29.1409	+	17.6941i	1.36615	+	0.829513i
$456$	−4.00664	+	1.07647i	−0.187628	+	0.0504101i
$457$	4.28719	−	13.1946i	0.200546	−	0.617218i	−0.799321	−	0.600905i	$-0.794807\pi$
$457$	4.28719	−	13.1946i	0.200546	−	0.617218i	0.999867	−	0.0163130i	$-0.00519283\pi$
$458$	0.441857	−	0.143568i	0.0206466	−	0.00670850i
$459$	0.0617524	+	0.384859i	0.00288235	+	0.0179637i
$460$	−15.4154	+	1.27666i	−0.718748	+	0.0595245i
$461$	9.96410	+	30.6663i	0.464074	+	1.42827i	0.860143	+	0.510053i	$0.170374\pi$
$461$	9.96410	+	30.6663i	0.464074	+	1.42827i	−0.396069	+	0.918221i	$0.629626\pi$
$462$	−3.34486	+	8.73120i	−0.155617	+	0.406212i
$463$	−2.44347	−	1.77529i	−0.113558	−	0.0825046i	0.529557	−	0.848274i	$-0.322358\pi$
$463$	−2.44347	−	1.77529i	−0.113558	−	0.0825046i	−0.643115	+	0.765770i	$0.722358\pi$
$464$	−1.94935			−0.0904965
$465$	−7.09976	−	20.3616i	−0.329243	−	0.944245i
$466$	7.71479			0.357381
$467$	14.9161	+	10.8372i	0.690236	+	0.501486i	0.876738	−	0.480969i	$-0.159715\pi$
$467$	14.9161	+	10.8372i	0.690236	+	0.501486i	−0.186502	+	0.982455i	$0.559715\pi$
$468$	−4.46629	−	20.8741i	−0.206454	−	0.964904i
$469$	7.54603	+	23.2243i	0.348443	+	1.07240i
$470$	−2.39560	−	28.9264i	−0.110501	−	1.33428i
$471$	1.61224	−	1.04854i	0.0742881	−	0.0483144i
$472$	4.19758	−	1.36387i	0.193209	−	0.0627774i
$473$	−5.52677	+	17.0097i	−0.254121	+	0.782105i
$474$	−5.41126	−	20.1409i	−0.248548	−	0.925102i
$475$	−10.7151	−	5.34971i	−0.491642	−	0.245461i
$476$	−0.0496690	−	0.152866i	−0.00227658	−	0.00700658i
$477$	9.89096	+	17.0785i	0.452876	+	0.781972i
$478$	15.0143	−	10.9085i	0.686736	−	0.498943i
$479$	−28.6698	−	9.31538i	−1.30996	−	0.425630i	−0.430922	−	0.902389i	$-0.641811\pi$
$479$	−28.6698	−	9.31538i	−1.30996	−	0.425630i	−0.879034	+	0.476759i	$0.841811\pi$
$480$	−1.08229	+	3.71869i	−0.0493997	+	0.169734i
$481$	−41.2208	+	29.9486i	−1.87951	+	1.36554i
$482$	3.55905	+	1.15641i	0.162110	+	0.0526729i
$483$	23.9741	+	9.18430i	1.09086	+	0.417900i
$484$	3.76431	+	2.73493i	0.171105	+	0.124315i
$485$	−16.1018	−	38.4280i	−0.731143	−	1.74492i
$486$	−12.0814	+	9.85084i	−0.548025	+	0.446843i
$487$	6.19216	−	19.0575i	0.280594	−	0.863579i	−0.707091	−	0.707122i	$-0.749993\pi$
$487$	6.19216	−	19.0575i	0.280594	−	0.863579i	0.987685	−	0.156456i	$-0.0500071\pi$
$488$	−0.728399	−	0.236671i	−0.0329731	−	0.0107136i
$489$	−9.99536	−	8.08295i	−0.452006	−	0.365524i
$490$	−0.444549	−	5.36785i	−0.0200827	−	0.242495i
$491$	21.2534			0.959154			0.479577	−	0.877500i	$-0.340790\pi$
$491$	21.2534			0.959154			0.479577	+	0.877500i	$0.340790\pi$
$492$	3.42499	+	2.76969i	0.154410	+	0.124867i
$493$	−0.0859507	−	0.118301i	−0.00387102	−	0.00532801i
$494$	13.7885	+	10.0179i	0.620375	+	0.450729i
$495$	15.9613	+	5.55476i	0.717406	+	0.249668i
$496$	1.77128	−	5.27850i	0.0795328	−	0.237012i
$497$	7.54169			0.338291
$498$	−8.95701	−	0.463374i	−0.401373	−	0.0207643i
$499$	14.5305	+	19.9995i	0.650474	+	0.895300i	0.999120	−	0.0419544i	$-0.0133584\pi$
$499$	14.5305	+	19.9995i	0.650474	+	0.895300i	−0.348646	+	0.937255i	$0.613358\pi$
$500$	−9.46044	+	5.95820i	−0.423084	+	0.266459i
$501$	13.1690	−	8.56466i	0.588348	−	0.382641i
$502$	23.4239			1.04546
$503$	0.288073	+	0.886597i	0.0128445	+	0.0395314i	0.957273	−	0.289185i	$-0.0933841\pi$
$503$	0.288073	+	0.886597i	0.0128445	+	0.0395314i	−0.944429	+	0.328716i	$0.893384\pi$
$504$	4.29483	−	4.78282i	0.191307	−	0.213044i
$505$	−4.59735	+	19.5002i	−0.204579	+	0.867749i
$506$	−10.2438	+	14.0993i	−0.455391	+	0.626792i
$507$	−40.9837	+	50.6804i	−1.82015	+	2.25079i
$508$	−12.1867	−	8.85417i	−0.540698	−	0.392840i
$509$	−9.09173	+	6.60553i	−0.402984	+	0.292785i	−0.770755	−	0.637131i	$-0.780121\pi$
$509$	−9.09173	+	6.60553i	−0.402984	+	0.292785i	0.367771	+	0.929916i	$0.380121\pi$
$510$	−0.273397	+	0.0982826i	−0.0121062	+	0.00435203i
$511$	13.4035	+	18.4483i	0.592934	+	0.816103i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	1.92219	−	12.2968i	0.0848668	−	0.542919i
$514$	2.17355	−	1.57917i	0.0958710	−	0.0696543i
$515$	−19.1094	−	11.6030i	−0.842059	−	0.511290i
$516$	7.73169	−	9.56099i	0.340369	−	0.420899i
$517$	−26.4568	−	19.2220i	−1.16357	−	0.845383i
$518$	−14.5922	−	4.74131i	−0.641146	−	0.208321i
$519$	4.58827	−	1.23273i	0.201403	−	0.0541110i
$520$	14.6746	−	6.14884i	0.643524	−	0.269644i
$521$			17.2138i			0.754151i	0.926183	+	0.377075i	$0.123070\pi$
$521$			17.2138i			0.754151i	−0.926183	+	0.377075i	$0.876930\pi$
$522$	2.37143	−	5.34566i	0.103795	−	0.233973i
$523$	−1.56602	−	4.81971i	−0.0684773	−	0.210751i	0.910962	−	0.412490i	$-0.135341\pi$
$523$	−1.56602	−	4.81971i	−0.0684773	−	0.210751i	−0.979439	+	0.201739i	$0.935341\pi$
$524$	−7.43854	−	10.2383i	−0.324954	−	0.447261i
$525$	18.4369	−	2.10292i	0.804651	−	0.0917789i
$526$		−	12.9517i		−	0.564722i
$527$	0.398437	−	0.125245i	0.0173562	−	0.00545576i
$528$	2.37906	+	3.65804i	0.103535	+	0.159196i
$529$	20.1065	+	14.6082i	0.874197	+	0.635141i
$530$	−11.1466	+	9.59923i	−0.484179	+	0.416964i
$531$	−1.36632	+	13.1701i	−0.0592930	+	0.571533i
$532$			5.13236i			0.222516i
$533$		−	18.0953i		−	0.783794i
$534$	6.95366	−	8.59888i	0.300914	−	0.372110i
$535$	−34.3220	−	8.09171i	−1.48387	−	0.349835i
$536$	10.8388	+	3.52172i	0.468163	+	0.152115i
$537$	0.00281220	−	0.0543598i	0.000121355	−	0.00234580i
$538$	1.24892	+	3.84378i	0.0538447	+	0.165717i
$539$	−4.90957	−	3.56701i	−0.211470	−	0.153642i
$540$	−8.88104	−	7.49181i	−0.382179	−	0.322396i
$541$	−0.932301	+	2.86933i	−0.0400828	+	0.123362i	−0.969096	−	0.246685i	$-0.920659\pi$
$541$	−0.932301	+	2.86933i	−0.0400828	+	0.123362i	0.929013	+	0.370047i	$0.120659\pi$
$542$	−6.32726	−	8.70872i	−0.271779	−	0.374072i
$543$	14.5941	−	38.0954i	0.626291	−	1.63483i
$544$	−0.0713422	−	0.0231805i	−0.00305877	−	0.000993855i
$545$	−24.7441	−	28.7329i	−1.05992	−	1.23078i
$546$	−26.3724	−	1.36433i	−1.12863	−	0.0583877i
$547$	28.1174	−	9.13590i	1.20221	−	0.390623i	0.361639	−	0.932318i	$-0.382217\pi$
$547$	28.1174	−	9.13590i	1.20221	−	0.390623i	0.840575	+	0.541695i	$0.182217\pi$
$548$	−10.9475	+	15.0680i	−0.467655	+	0.643672i
$549$	1.53513	−	1.70956i	0.0655178	−	0.0729621i
$550$	−1.86876	+	12.4573i	−0.0796840	+	0.531181i
$551$	1.44287	+	4.44069i	0.0614683	+	0.189180i
$552$	10.0442	−	6.53242i	0.427511	−	0.278038i
$553$	−25.7998			−1.09712
$554$	0.420329	+	1.29364i	0.0178581	+	0.0549615i
$555$	−7.74992	+	26.6282i	−0.328966	+	1.13031i
$556$	−9.01520	+	12.4084i	−0.382330	+	0.526232i
$557$			2.52025i			0.106787i	0.998574	+	0.0533933i	$0.0170037\pi$
$557$			2.52025i			0.106787i	−0.998574	+	0.0533933i	$0.982996\pi$
$558$	12.3203	+	11.2787i	0.521560	+	0.477467i
$559$	−50.5137			−2.13650
$560$	4.09541	+	2.48670i	0.173063	+	0.105082i
$561$	−0.117099	+	0.305669i	−0.00494393	+	0.0129053i
$562$	13.0441	−	4.23828i	0.550232	−	0.178781i
$563$	−40.3785			−1.70175			−0.850875	−	0.525368i	$-0.823928\pi$
$563$	−40.3785			−1.70175			−0.850875	+	0.525368i	$0.823928\pi$
$564$	12.2578	+	18.8476i	0.516147	+	0.793627i
$565$	−22.9528	+	9.61748i	−0.965630	+	0.404610i
$566$	3.10314	+	1.00827i	0.130435	+	0.0423809i
$567$	7.89106	+	17.5960i	0.331393	+	0.738962i
$568$	2.06883	−	2.84749i	0.0868060	−	0.119478i
$569$	4.44051	+	13.6665i	0.186156	+	0.572929i	0.999966	−	0.00820156i	$-0.00261067\pi$
$569$	4.44051	+	13.6665i	0.186156	+	0.572929i	−0.813811	+	0.581130i	$0.802611\pi$
$570$	9.27239	−	0.286992i	0.388378	−	0.0120208i
$571$	−10.0179	−	13.7884i	−0.419235	−	0.577027i	0.546206	−	0.837651i	$-0.316072\pi$
$571$	−10.0179	−	13.7884i	−0.419235	−	0.577027i	−0.965440	+	0.260624i	$0.916072\pi$
$572$	5.53955	−	17.0490i	0.231620	−	0.712854i
$573$	−9.39254	+	24.5177i	−0.392379	+	1.02424i
$574$	4.40839	−	3.20289i	0.184003	−	0.133686i
$575$	34.2052	+	5.13122i	1.42646	+	0.213987i
$576$	−0.627684	−	2.93360i	−0.0261535	−	0.122233i
$577$	7.13488	−	9.82032i	0.297029	−	0.408825i	−0.634252	−	0.773126i	$-0.718692\pi$
$577$	7.13488	−	9.82032i	0.297029	−	0.408825i	0.931281	+	0.364301i	$0.118692\pi$
$578$	5.25155	+	16.1626i	0.218436	+	0.672276i
$579$	7.82797	+	0.404965i	0.325319	+	0.0168298i
$580$	4.24257	+	1.00022i	0.176163	+	0.0415321i
$581$	−3.42869	+	10.5524i	−0.142246	+	0.437789i
$582$	25.0950	+	20.2935i	1.04022	+	0.841195i
$583$			16.5738i			0.686418i
$584$	10.6423			0.440381
$585$	−0.990165	+	47.7220i	−0.0409383	+	1.97306i
$586$	−13.2256	+	9.60893i	−0.546343	+	0.396941i
$587$	20.4661	−	28.1692i	0.844726	−	1.16267i	−0.140274	−	0.990113i	$-0.544798\pi$
$587$	20.4661	−	28.1692i	0.844726	−	1.16267i	0.985000	−	0.172553i	$-0.0552017\pi$
$588$	2.27467	+	3.49753i	0.0938059	+	0.144236i
$589$	−13.3357	−	0.128005i	−0.549487	−	0.00527434i
$590$	−9.83542	+	0.814539i	−0.404918	+	0.0335341i
$591$	8.18077	+	0.423216i	0.336512	+	0.0174088i
$592$	−5.79309	+	4.20892i	−0.238094	+	0.172986i
$593$	14.7851	+	45.5038i	0.607151	+	1.86862i	0.481267	+	0.876574i	$0.340177\pi$
$593$	14.7851	+	45.5038i	0.607151	+	1.86862i	0.125884	+	0.992045i	$0.459823\pi$
$594$	−12.9255	+	2.07396i	−0.530341	+	0.0850955i
$595$	0.0296636	+	0.358182i	0.00121609	+	0.0146840i
$596$	−4.04219	+	1.31339i	−0.165575	+	0.0537985i
$597$	3.86035	+	14.3683i	0.157994	+	0.588057i
$598$	−46.8131	−	15.2105i	−1.91433	−	0.622003i
$599$	−18.0233	+	24.8070i	−0.736414	+	1.01359i	0.262403	+	0.964958i	$0.415485\pi$
$599$	−18.0233	+	24.8070i	−0.736414	+	1.01359i	−0.998817	+	0.0486281i	$0.984515\pi$
$600$	4.26358	−	7.53803i	0.174060	−	0.307739i
$601$	3.19149	−	4.39271i	0.130184	−	0.179183i	−0.738949	−	0.673761i	$-0.764678\pi$
$601$	3.19149	−	4.39271i	0.130184	−	0.179183i	0.869133	+	0.494579i	$0.164678\pi$
$602$	−8.94098	−	12.3062i	−0.364407	−	0.501563i
$603$	−22.8431	+	25.4386i	−0.930243	+	1.03594i
$604$	−9.19112	−	12.6505i	−0.373981	−	0.514741i
$605$	−6.78933	−	7.88379i	−0.276026	−	0.320522i
$606$	−4.02668	−	14.9874i	−0.163573	−	0.608822i
$607$	−9.53510	−	13.1239i	−0.387018	−	0.532684i	0.570409	−	0.821361i	$-0.306785\pi$
$607$	−9.53510	−	13.1239i	−0.387018	−	0.532684i	−0.957427	+	0.288677i	$0.906785\pi$
$608$	1.93781	+	1.40790i	0.0785887	+	0.0570980i
$609$	−5.62540	−	4.54910i	−0.227953	−	0.184339i
$610$	1.46385	+	0.888837i	0.0592696	+	0.0359880i
$611$	28.5418	−	87.8428i	1.15468	−	3.55374i
$612$	0.150357	−	0.167440i	0.00607780	−	0.00676838i
$613$	−6.33860	−	19.5082i	−0.256014	−	0.787930i	−0.993628	−	0.112707i	$-0.964048\pi$
$613$	−6.33860	−	19.5082i	−0.256014	−	0.787930i	0.737614	−	0.675222i	$-0.235952\pi$
$614$		−	0.694153i		−	0.0280137i
$615$	−6.03301	−	7.78533i	−0.243274	−	0.313935i
$616$	5.13400	−	1.66814i	0.206855	−	0.0672112i
$617$	4.74513	−	3.44754i	0.191032	−	0.138793i	−0.488158	−	0.872755i	$-0.662331\pi$
$617$	4.74513	−	3.44754i	0.191032	−	0.138793i	0.679190	+	0.733962i	$0.262331\pi$
$618$	17.2939	+	0.894665i	0.695662	+	0.0359887i
$619$		−	1.30523i		−	0.0524615i	−0.999656	−	0.0262307i	$-0.991650\pi$
$619$		−	1.30523i		−	0.0524615i	0.999656	−	0.0262307i	$-0.00835046\pi$
$620$	−6.56344	+	10.5793i	−0.263594	+	0.424874i
$621$	5.69467	+	35.4909i	0.228519	+	1.42420i
$622$	−5.53855	+	7.62316i	−0.222076	+	0.305661i
$623$	−8.04126	−	11.0679i	−0.322166	−	0.443424i
$624$	−7.74957	+	9.58310i	−0.310231	+	0.383631i
$625$	23.6469	−	8.11322i	0.945876	−	0.324529i
$626$	−12.7367			−0.509060
$627$	6.57221	−	8.12718i	0.262469	−	0.324568i
$628$	−1.05602	−	0.343123i	−0.0421400	−	0.0136921i
$629$	−0.510856	−	0.165987i	−0.0203692	−	0.00661835i
$630$	−11.8014	+	8.20563i	−0.470177	+	0.326920i
$631$	−11.5024	+	3.73735i	−0.457903	+	0.148782i	−0.528881	−	0.848696i	$-0.677388\pi$
$631$	−11.5024	+	3.73735i	−0.457903	+	0.148782i	0.0709776	+	0.997478i	$0.477388\pi$
$632$	−7.07736	+	9.74115i	−0.281522	+	0.387482i
$633$	11.4034	+	4.36854i	0.453243	+	0.173634i
$634$	−0.745683	+	2.29498i	−0.0296149	+	0.0911451i
$635$	21.9801	+	25.5233i	0.872252	+	1.01286i
$636$	4.07628	−	10.6405i	0.161635	−	0.421922i
$637$	5.29649	−	16.3009i	0.209855	−	0.645866i
$638$	3.97315	−	2.88666i	0.157298	−	0.114284i
$639$	5.29185	+	9.13733i	0.209342	+	0.361467i
$640$	2.06234	−	0.864145i	0.0815212	−	0.0341583i
$641$	23.5840	+	17.1348i	0.931514	+	0.676784i	0.946363	−	0.323105i	$-0.104727\pi$
$641$	23.5840	+	17.1348i	0.931514	+	0.676784i	−0.0148491	+	0.999890i	$0.504727\pi$
$642$	26.3791	−	7.08728i	1.04110	−	0.279713i
$643$	−4.61237	+	14.1954i	−0.181894	+	0.559813i	−0.999881	−	0.0154243i	$-0.995090\pi$
$643$	−4.61237	+	14.1954i	−0.181894	+	0.559813i	0.817987	+	0.575237i	$0.195090\pi$
$644$	−4.58037	−	14.0969i	−0.180492	−	0.555497i
$645$	−21.7331	+	16.8414i	−0.855738	+	0.663128i
$646$			0.179678i			0.00706932i
$647$	25.1119	−	8.15936i	0.987252	−	0.320777i	0.229491	−	0.973311i	$-0.426294\pi$
$647$	25.1119	−	8.15936i	0.987252	−	0.320777i	0.757760	+	0.652533i	$0.226294\pi$
$648$	8.80833	+	1.84750i	0.346024	+	0.0725768i
$649$	−6.53578	+	8.99572i	−0.256552	+	0.353113i
$650$	−35.0929	+	5.85271i	−1.37645	+	0.229562i
$651$	17.4297	−	11.0990i	0.683122	−	0.435006i
$652$			7.42162i			0.290653i
$653$	26.5659	+	19.3013i	1.03961	+	0.755318i	0.970209	−	0.242271i	$-0.0778924\pi$
$653$	26.5659	+	19.3013i	1.03961	+	0.755318i	0.0693973	+	0.997589i	$0.477892\pi$
$654$	27.4281	+	10.5075i	1.07252	+	0.410875i
$655$	10.9359	+	26.0993i	0.427302	+	1.01979i
$656$		−	2.54308i		−	0.0992905i
$657$	−12.9466	+	29.1841i	−0.505093	+	1.13858i
$658$	26.4523	−	8.59487i	1.03122	−	0.335063i
$659$	3.17011	+	1.03003i	0.123490	+	0.0401243i	0.370110	−	0.928988i	$-0.379320\pi$
$659$	3.17011	+	1.03003i	0.123490	+	0.0401243i	−0.246620	+	0.969112i	$0.579320\pi$
$660$	−3.30083	−	9.18207i	−0.128485	−	0.357412i
$661$	−29.0102	−	21.0772i	−1.12837	−	0.819807i	−0.142911	−	0.989736i	$-0.545646\pi$
$661$	−29.0102	−	21.0772i	−1.12837	−	0.819807i	−0.985456	+	0.169929i	$0.945646\pi$
$662$	0.200654	−	0.0651963i	0.00779863	−	0.00253393i
$663$	−0.923265	−	0.0477633i	−0.0358566	−	0.00185497i
$664$	3.04370	+	4.18929i	0.118118	+	0.162576i
$665$	2.63344	−	11.1701i	0.102121	−	0.433157i
$666$	−4.49462	−	21.0065i	−0.174163	−	0.813985i
$667$	−7.92618	−	10.9095i	−0.306903	−	0.422416i
$668$	−8.62576	−	2.80268i	−0.333741	−	0.108439i
$669$	19.0449	+	7.29594i	0.736318	+	0.282078i
$670$	−21.7825	−	13.2261i	−0.841530	−	0.510969i
$671$	1.83508	−	0.596255i	0.0708426	−	0.0230182i
$672$	−3.70633	−	0.191740i	−0.142975	−	0.00739652i
$673$	−4.69943	+	14.4634i	−0.181150	+	0.557522i	−0.999861	−	0.0166839i	$-0.994689\pi$
$673$	−4.69943	+	14.4634i	−0.181150	+	0.557522i	0.818711	+	0.574206i	$0.194689\pi$
$674$	−6.80218	+	20.9350i	−0.262010	+	0.806385i
$675$	15.4846	+	20.8621i	0.596003	+	0.802982i
$676$	37.6305			1.44733
$677$		−	19.1901i		−	0.737534i	−0.929522	−	0.368767i	$-0.879780\pi$
$677$		−	19.1901i		−	0.737534i	0.929522	−	0.368767i	$-0.120220\pi$
$678$	12.1212	−	14.9891i	0.465512	−	0.575651i
$679$	32.3004	−	23.4676i	1.23957	−	0.900604i
$680$	0.143375	+	0.0870561i	0.00549819	+	0.00333845i
$681$	11.4520	+	17.6086i	0.438841	+	0.674762i
$682$	4.20636	+	13.3815i	0.161070	+	0.512405i
$683$	−16.3973			−0.627425			−0.313713	−	0.949518i	$-0.601573\pi$
$683$	−16.3973			−0.627425			−0.313713	+	0.949518i	$0.601573\pi$
$684$	−6.21825	+	3.60127i	−0.237761	+	0.137698i
$685$	31.5577	−	27.1767i	1.20576	−	1.03837i
$686$	19.1736	−	6.22988i	0.732051	−	0.237858i
$687$	0.674587	−	0.438727i	0.0257371	−	0.0167385i
$688$	−7.09910			−0.270650
$689$	−44.5194	+	14.4652i	−1.69605	+	0.551081i
$690$	−25.2121	+	9.06340i	−0.959808	+	0.345038i
$691$	11.3762	−	35.0124i	0.432771	−	1.33193i	−0.462582	−	0.886576i	$-0.653077\pi$
$691$	11.3762	−	35.0124i	0.432771	−	1.33193i	0.895353	−	0.445356i	$-0.146923\pi$
$692$	−2.21912	−	1.61229i	−0.0843583	−	0.0612899i
$693$	−1.67112	+	16.1082i	−0.0634807	+	0.611899i
$694$	4.36169	−	6.00335i	0.165567	−	0.227884i
$695$	25.9875	−	22.3798i	0.985762	−	0.848915i
$696$	−3.26074	+	0.876065i	−0.123598	+	0.0332072i
$697$	0.154332	−	0.112129i	0.00584576	−	0.00424719i
$698$	15.1310	−	10.9933i	0.572718	−	0.416104i
$699$	12.9048	−	3.46713i	0.488103	−	0.131139i
$700$	−7.63732	−	7.51342i	−0.288663	−	0.283981i
$701$	12.2564	−	16.8694i	0.462917	−	0.637150i	−0.512194	−	0.858870i	$-0.671167\pi$
$701$	12.2564	−	16.8694i	0.462917	−	0.637150i	0.975110	+	0.221720i	$0.0711671\pi$
$702$	−16.8520	−	32.9095i	−0.636037	−	1.24209i
$703$	13.8760	+	10.0815i	0.523343	+	0.380231i
$704$	0.778518	−	2.39603i	0.0293415	−	0.0903039i
$705$	−17.0071	−	47.3095i	−0.640524	−	1.78178i
$706$	19.2230	−	6.24594i	0.723469	−	0.235069i
$707$	−19.1984			−0.722029
$708$	6.40847	−	4.16784i	0.240845	−	0.156637i
$709$	2.22544	−	0.723088i	0.0835780	−	0.0271561i	−0.266930	−	0.963716i	$-0.586009\pi$
$709$	2.22544	−	0.723088i	0.0835780	−	0.0271561i	0.350508	+	0.936560i	$0.386009\pi$
$710$	−5.96366	+	5.13576i	−0.223812	+	0.192742i
$711$	−18.1032	−	31.2584i	−0.678922	−	1.17228i
$712$	−6.38473			−0.239278
$713$	36.7430	−	11.5498i	1.37604	−	0.432544i
$714$	−0.151783	−	0.233381i	−0.00568033	−	0.00873407i
$715$	−20.8042	+	34.2631i	−0.778034	+	1.28137i
$716$	−0.0254246	+	0.0184721i	−0.000950164	+	0.000690334i
$717$	20.2124	−	24.9946i	0.754846	−	0.933440i
$718$		−	23.9949i		−	0.895481i
$719$	−32.0159			−1.19399			−0.596995	−	0.802245i	$-0.703639\pi$
$719$	−32.0159			−1.19399			−0.596995	+	0.802245i	$0.703639\pi$
$720$	−0.139156	+	6.70676i	−0.00518603	+	0.249946i
$721$	6.62000	−	20.3743i	0.246542	−	0.758777i
$722$	−4.09840	+	12.6136i	−0.152527	+	0.469428i
$723$	6.47304	+	0.334870i	0.240735	+	0.0124540i
$724$	−22.4004	+	7.27832i	−0.832503	+	0.270496i
$725$	−8.72032	−	4.35378i	−0.323865	−	0.161695i
$726$	7.52578	+	2.88307i	0.279308	+	0.107001i
$727$	−26.4463	−	8.59294i	−0.980841	−	0.318694i	−0.225656	−	0.974207i	$-0.572453\pi$
$727$	−26.4463	−	8.59294i	−0.980841	−	0.318694i	−0.755184	+	0.655513i	$0.772453\pi$
$728$	8.96165	+	12.3347i	0.332141	+	0.457153i
$729$	−15.7819	+	21.9074i	−0.584514	+	0.811383i
$730$	−23.1619	−	5.46061i	−0.857259	−	0.202106i
$731$	−0.313013	−	0.430825i	−0.0115772	−	0.0159346i
$732$	−1.32478	−	0.0685349i	−0.0489652	−	0.00253312i
$733$	−15.1662	+	4.92781i	−0.560178	+	0.182013i	−0.575401	−	0.817871i	$-0.695154\pi$
$733$	−15.1662	+	4.92781i	−0.560178	+	0.182013i	0.0152234	+	0.999884i	$0.495154\pi$
$734$	22.9031	+	16.6401i	0.845370	+	0.614198i
$735$	−3.15600	−	8.77918i	−0.116411	−	0.323825i
$736$	−6.57902	−	2.13765i	−0.242506	−	0.0787949i
$737$	−27.3065	+	8.87241i	−1.00585	+	0.326819i
$738$	6.97382	+	3.09371i	0.256710	+	0.113881i
$739$			17.5548i			0.645763i	0.946439	+	0.322881i	$0.104652\pi$
$739$			17.5548i			0.645763i	−0.946439	+	0.322881i	$0.895348\pi$
$740$	14.7677	−	6.18784i	0.542872	−	0.227470i
$741$	27.5667	+	10.5606i	1.01269	+	0.387953i
$742$	−11.4040	−	8.28550i	−0.418654	−	0.304170i
$743$		−	21.1218i		−	0.774884i	−0.921894	−	0.387442i	$-0.873359\pi$
$743$		−	21.1218i		−	0.774884i	0.921894	−	0.387442i	$-0.126641\pi$
$744$	0.590645	−	9.62555i	0.0216541	−	0.352890i
$745$	9.47134	−	0.784387i	0.347003	−	0.0287377i
$746$	8.30380	−	11.4292i	0.304024	−	0.418453i
$747$	−15.1909	+	3.25030i	−0.555806	+	0.118922i
$748$	0.179735	−	0.0583995i	0.00657176	−	0.00213530i
$749$		−	33.7907i		−	1.23468i
$750$	−13.1471	+	14.2181i	−0.480063	+	0.519172i
$751$	−6.57766	−	20.2439i	−0.240022	−	0.738712i	−0.996415	−	0.0845949i	$-0.973040\pi$
$751$	−6.57766	−	20.2439i	−0.240022	−	0.738712i	0.756393	−	0.654117i	$-0.226960\pi$
$752$	4.01122	−	12.3453i	0.146274	−	0.450185i
$753$	39.1818	−	10.5270i	1.42786	−	0.383625i
$754$	11.2216	+	8.15296i	0.408666	+	0.296913i
$755$	13.5125	+	32.2486i	0.491771	+	1.17365i
$756$	5.03462	−	9.93051i	0.183108	−	0.361169i
$757$	−7.18579	+	5.22078i	−0.261172	+	0.189753i	−0.710664	−	0.703532i	$-0.751605\pi$
$757$	−7.18579	+	5.22078i	−0.261172	+	0.189753i	0.449492	+	0.893285i	$0.351605\pi$
$758$	−6.43359	+	19.8006i	−0.233679	+	0.719189i
$759$	−10.7986	+	28.1881i	−0.391966	+	1.02316i
$760$	−3.49505	−	4.05846i	−0.126779	−	0.147216i
$761$	−1.05211	+	3.23806i	−0.0381389	+	0.117380i	−0.968313	−	0.249738i	$-0.919655\pi$
$761$	−1.05211	+	3.23806i	−0.0381389	+	0.117380i	0.930174	+	0.367118i	$0.119655\pi$
$762$	−24.3643	−	9.33377i	−0.882625	−	0.338127i
$763$	21.3576	−	29.3963i	0.773198	−	1.06422i
$764$	14.4166	−	4.68422i	0.521573	−	0.169469i
$765$	−0.413151	+	0.287269i	−0.0149375	+	0.0103862i
$766$	21.4872	+	6.98162i	0.776364	+	0.252256i
$767$	−29.8679	−	9.70467i	−1.07847	−	0.350415i
$768$	−1.08911	+	1.34679i	−0.0392998	+	0.0485981i
$769$	9.88349			0.356408			0.178204	−	0.983994i	$-0.442971\pi$
$769$	9.88349			0.356408			0.178204	+	0.983994i	$0.442971\pi$
$770$	−12.0296	+	0.996253i	−0.433516	+	0.0359025i
$771$	2.92605	−	3.61835i	0.105379	−	0.130312i
$772$	−2.66004	−	3.66122i	−0.0957368	−	0.131770i
$773$	−26.6271	+	36.6490i	−0.957709	+	1.31817i	−0.00969176	+	0.999953i	$0.503085\pi$
$773$	−26.6271	+	36.6490i	−0.957709	+	1.31817i	−0.948017	+	0.318220i	$0.896915\pi$
$774$	8.63620	−	19.4677i	0.310422	−	0.699751i
$775$	19.7130	−	19.6570i	0.708111	−	0.706101i
$776$		−	18.6332i		−	0.668892i
$777$	−26.5397	−	1.37298i	−0.952107	−	0.0492554i
$778$	−19.0493	+	13.8401i	−0.682950	+	0.496193i
$779$	−5.79322	+	1.88233i	−0.207564	+	0.0674415i
$780$	21.7833	−	16.8803i	0.779968	−	0.604412i
$781$			8.86730i			0.317297i
$782$	−0.160353	−	0.493516i	−0.00573421	−	0.0176481i
$783$	1.56435	−	10.0076i	0.0559052	−	0.357643i
$784$	0.744358	−	2.29090i	0.0265842	−	0.0818178i
$785$	2.12227	+	1.28863i	0.0757472	+	0.0459930i
$786$	−17.0439	−	13.7829i	−0.607935	−	0.491619i
$787$	−0.592899	−	0.430766i	−0.0211346	−	0.0153552i	0.577168	−	0.816626i	$-0.304158\pi$
$787$	−0.592899	−	0.430766i	−0.0211346	−	0.0153552i	−0.598302	+	0.801270i	$0.704158\pi$
$788$	−2.77992	−	3.82623i	−0.0990306	−	0.136304i
$789$	−5.82068	−	21.6647i	−0.207222	−	0.771285i
$790$	20.4014	−	17.5692i	0.725850	−	0.625085i
$791$	−14.0170	−	19.2928i	−0.498389	−	0.685973i
$792$	5.62350	+	5.04973i	0.199822	+	0.179434i
$793$	3.20323	+	4.40887i	0.113750	+	0.156563i
$794$	−3.00435	+	4.13514i	−0.106621	+	0.146751i
$795$	−14.3313	+	21.0664i	−0.508279	+	0.747147i
$796$	5.04893	−	6.94925i	0.178955	−	0.246310i
$797$	32.0414	+	10.4109i	1.13496	+	0.368772i	0.815461	−	0.578813i	$-0.196484\pi$
$797$	32.0414	+	10.4109i	1.13496	+	0.368772i	0.319504	+	0.947585i	$0.396484\pi$
$798$	2.30655	+	8.58506i	0.0816511	+	0.303908i
$799$	0.926062	−	0.300896i	0.0327617	−	0.0106449i
$800$	−4.93188	+	0.822528i	−0.174368	+	0.0290808i
$801$	7.76715	−	17.5087i	0.274439	−	0.618639i
$802$	−5.16311	−	15.8904i	−0.182316	−	0.561110i
$803$	−21.6910	+	15.7594i	−0.765457	+	0.556137i
$804$	19.7130	+	1.01982i	0.695225	+	0.0359661i
$805$	2.73551	+	33.0308i	0.0964140	+	1.16418i
$806$	−32.2733	+	22.9779i	−1.13678	+	0.809361i
$807$	3.81655	+	5.86832i	0.134349	+	0.206575i
$808$	−5.26647	+	7.24867i	−0.185274	+	0.255007i
$809$	−37.2593	+	27.0705i	−1.30997	+	0.951747i	−0.309968	+	0.950747i	$0.600318\pi$
$809$	−37.2593	+	27.0705i	−1.30997	+	0.951747i	−0.999999	+	0.00100027i	$0.999682\pi$
$810$	−18.2225	−	8.54052i	−0.640273	−	0.300083i
$811$	46.4545			1.63124			0.815619	−	0.578589i	$-0.196396\pi$
$811$	46.4545			1.63124			0.815619	+	0.578589i	$0.196396\pi$
$812$			4.17690i			0.146580i
$813$	−14.4976	−	11.7238i	−0.508453	−	0.411171i
$814$	5.57470	−	17.1571i	0.195393	−	0.601358i
$815$	3.80807	−	16.1524i	0.133391	−	0.565795i
$816$	−0.129754	−	0.00671257i	−0.00454229	−	0.000234987i
$817$	5.25460	+	16.1720i	0.183835	+	0.565786i
$818$	−11.5317	+	15.8720i	−0.403197	+	0.554952i
$819$	−44.7271	+	9.56996i	−1.56289	+	0.334402i
$820$	−1.30487	+	5.53476i	−0.0455679	+	0.193282i
$821$	9.05360	−	6.57783i	0.315973	−	0.229568i	−0.418482	−	0.908225i	$-0.637438\pi$
$821$	9.05360	−	6.57783i	0.315973	−	0.229568i	0.734455	+	0.678657i	$0.237438\pi$
$822$	−11.5405	+	30.1246i	−0.402522	+	1.05072i
$823$	−0.0289787	+	0.0891874i	−0.00101014	+	0.00310888i	−0.951560	−	0.307462i	$-0.900520\pi$
$823$	−0.0289787	+	0.0891874i	−0.00101014	+	0.00310888i	0.950550	+	0.310571i	$0.100520\pi$
$824$	−5.87666	−	8.08853i	−0.204723	−	0.281777i
$825$	2.47255	+	21.6775i	0.0860832	+	0.754715i
$826$	−2.92239	−	8.99419i	−0.101683	−	0.312948i
$827$	11.6660	−	16.0569i	0.405666	−	0.558352i	−0.556489	−	0.830855i	$-0.687852\pi$
$827$	11.6660	−	16.0569i	0.405666	−	0.558352i	0.962155	+	0.272504i	$0.0878517\pi$
$828$	13.8655	−	15.4410i	0.481861	−	0.536611i
$829$	9.25555	+	3.00731i	0.321459	+	0.104448i	0.465301	−	0.885152i	$-0.345946\pi$
$829$	9.25555	+	3.00731i	0.321459	+	0.104448i	−0.143843	+	0.989601i	$0.545946\pi$
$830$	−4.47476	−	10.6793i	−0.155321	−	0.370684i
$831$	1.28448	+	1.97501i	0.0445580	+	0.0685123i
$832$	7.11551			0.246686
$833$	0.171849	−	0.0558370i	0.00595420	−	0.00193464i
$834$	−9.50352	+	24.8074i	−0.329080	+	0.859010i
$835$	17.3350	+	10.5257i	0.599904	+	0.364256i
$836$	−6.03449			−0.208707
$837$	25.6774	+	13.3294i	0.887540	+	0.460731i
$838$		−	4.33253i		−	0.149665i
$839$	27.1452	−	37.3622i	0.937157	−	1.28989i	−0.0198450	−	0.999803i	$-0.506317\pi$
$839$	27.1452	−	37.3622i	0.937157	−	1.28989i	0.957002	−	0.290082i	$-0.0936827\pi$
$840$	7.96807	+	2.31904i	0.274925	+	0.0800145i
$841$	−7.78724	−	23.9666i	−0.268525	−	0.826436i
$842$	6.35745			0.219092
$843$	19.9145	−	12.9517i	0.685893	−	0.446080i
$844$	−2.17867	−	6.70525i	−0.0749929	−	0.230804i
$845$	−81.8991	−	19.3084i	−2.81741	−	0.664230i
$846$	28.9744	+	26.0181i	0.996159	+	0.894521i
$847$	5.86016	−	8.06582i	0.201357	−	0.277145i
$848$	−6.25666	+	2.03291i	−0.214855	+	0.0698105i
$849$	5.64385	+	0.291974i	0.193697	+	0.0100205i
$850$	−0.267373	−	0.263036i	−0.00917082	−	0.00902205i
$851$	−47.1100	−	15.3070i	−1.61491	−	0.524717i
$852$	2.18089	−	5.69285i	0.0747159	−	0.195034i
$853$	18.5424	+	25.5215i	0.634881	+	0.873839i	0.998330	−	0.0577754i	$-0.0184007\pi$
$853$	18.5424	+	25.5215i	0.634881	+	0.873839i	−0.363449	+	0.931614i	$0.618401\pi$
$854$	−0.507118	+	1.56075i	−0.0173532	+	0.0534077i
$855$	15.3812	−	4.64720i	0.526027	−	0.158931i
$856$	−12.7582	−	9.26941i	−0.436068	−	0.316822i
$857$	−10.8124	−	33.2771i	−0.369344	−	1.13672i	−0.947216	−	0.320597i	$-0.896117\pi$
$857$	−10.8124	−	33.2771i	−0.369344	−	1.13672i	0.577872	−	0.816128i	$-0.303883\pi$
$858$	1.60414	−	31.0079i	0.0547643	−	1.05859i
$859$	4.50594	+	1.46407i	0.153741	+	0.0499534i	0.384876	−	0.922968i	$-0.374244\pi$
$859$	4.50594	+	1.46407i	0.153741	+	0.0499534i	−0.231136	+	0.972922i	$0.574244\pi$
$860$	15.4505	+	3.64259i	0.526857	+	0.124211i
$861$	5.93464	−	7.33876i	0.202252	−	0.250104i
$862$		−	5.32893i		−	0.181504i
$863$		−	23.3684i		−	0.795470i	−0.917500	−	0.397735i	$-0.869796\pi$
$863$		−	23.3684i		−	0.795470i	0.917500	−	0.397735i	$-0.130204\pi$
$864$	−2.36835	−	4.62503i	−0.0805727	−	0.157347i
$865$	4.00243	+	4.64763i	0.136087	+	0.158024i
$866$	8.59511	+	6.24471i	0.292074	+	0.212204i
$867$	16.0481	+	24.6756i	0.545023	+	0.838026i
$868$	−11.3103	−	3.79534i	−0.383896	−	0.128822i
$869$		−	30.3346i		−	1.02903i
$870$	7.54620	−	0.233564i	0.255840	−	0.00791857i
$871$	−47.6648	−	65.6050i	−1.61506	−	2.22294i
$872$	−5.24027	−	16.1279i	−0.177458	−	0.546159i
$873$	51.0973	+	22.6676i	1.72938	+	0.767183i
$874$			16.5695i			0.560471i
$875$	12.7667	+	20.2710i	0.431593	+	0.685284i
$876$	17.8017	−	4.78278i	0.601463	−	0.161595i
$877$	−8.98572	−	2.91964i	−0.303426	−	0.0985891i	0.153347	−	0.988172i	$-0.450995\pi$
$877$	−8.98572	−	2.91964i	−0.303426	−	0.0985891i	−0.456773	+	0.889583i	$0.650995\pi$
$878$	−30.1866	−	21.9318i	−1.01875	−	0.740164i
$879$	−17.8044	+	22.0169i	−0.600528	+	0.742611i
$880$	−2.92379	+	4.81527i	−0.0985608	+	0.162323i
$881$	−37.8000	+	27.4633i	−1.27351	+	0.925262i	−0.999337	−	0.0364175i	$-0.988405\pi$
$881$	−37.8000	+	27.4633i	−1.27351	+	0.925262i	−0.274177	+	0.961679i	$0.588405\pi$
$882$	5.37675	+	4.82816i	0.181045	+	0.162573i
$883$	−14.4829	+	10.5224i	−0.487387	+	0.354107i	−0.804178	−	0.594388i	$-0.797394\pi$
$883$	−14.4829	+	10.5224i	−0.487387	+	0.354107i	0.316792	+	0.948495i	$0.397394\pi$
$884$	0.313736	+	0.431821i	0.0105521	+	0.0145237i
$885$	−16.0859	+	5.78267i	−0.540723	+	0.194382i
$886$	−9.21025	+	6.69164i	−0.309425	+	0.224810i
$887$	−7.83672	−	5.69371i	−0.263131	−	0.191176i	0.448395	−	0.893835i	$-0.351996\pi$
$887$	−7.83672	−	5.69371i	−0.263131	−	0.191176i	−0.711526	+	0.702659i	$0.751996\pi$
$888$	−7.79873	+	9.64389i	−0.261708	+	0.323628i
$889$	−18.9719	+	26.1126i	−0.636298	+	0.875789i
$890$	13.8957	+	3.27604i	0.465786	+	0.109813i
$891$	−20.6889	+	9.27808i	−0.693103	+	0.310827i
$892$	−3.63862	−	11.1985i	−0.121830	−	0.374954i
$893$	−31.0919			−1.04045
$894$	−6.17125	+	4.01356i	−0.206397	+	0.134234i
$895$	0.0648124	−	0.0271571i	0.00216644	−	0.000907763i
$896$	1.25945	+	1.73349i	0.0420754	+	0.0579118i
$897$	−85.1415	−	4.40463i	−2.84279	−	0.147066i
$898$	−35.7766			−1.19388
$899$	−10.8530	−	0.104175i	−0.361969	−	0.00347442i
$900$	3.74414	−	14.5252i	0.124805	−	0.484173i
$901$	−0.399240	−	0.290065i	−0.0133006	−	0.00966346i
$902$	3.76586	+	5.18327i	0.125390	+	0.172584i
$903$	−20.4864	−	16.5668i	−0.681745	−	0.551307i
$904$	−11.1295			−0.370161
$905$	52.4867	−	4.34679i	1.74472	−	0.144492i
$906$	−21.0596	−	17.0302i	−0.699657	−	0.565792i
$907$	43.0817	+	13.9981i	1.43050	+	0.464799i	0.918923	−	0.394436i	$-0.129060\pi$
$907$	43.0817	+	13.9981i	1.43050	+	0.464799i	0.511581	+	0.859235i	$0.329060\pi$
$908$	3.74752	−	11.5337i	0.124366	−	0.382759i
$909$	−13.4711	−	23.2603i	−0.446808	−	0.771494i
$910$	−13.1752	−	31.4434i	−0.436753	−	1.04234i
$911$	28.1623	+	20.4611i	0.933057	+	0.677906i	0.946739	−	0.322001i	$-0.104355\pi$
$911$	28.1623	+	20.4611i	0.933057	+	0.677906i	−0.0136822	+	0.999906i	$0.504355\pi$
$912$	3.87417	+	1.48416i	0.128287	+	0.0491456i
$913$	−12.4072	−	4.03136i	−0.410620	−	0.133419i
$914$	−11.2240	+	8.15471i	−0.371257	+	0.269734i
$915$	2.84808	+	0.828911i	0.0941548	+	0.0274029i
$916$	−0.441857	−	0.143568i	−0.0145994	−	0.00474362i
$917$	−21.9376	+	15.9386i	−0.724445	+	0.526340i
$918$	0.176256	−	0.347655i	0.00581731	−	0.0114743i
$919$	13.6086	+	41.8829i	0.448905	+	1.38159i	0.878143	+	0.478397i	$0.158782\pi$
$919$	13.6086	+	41.8829i	0.448905	+	1.38159i	−0.429238	+	0.903191i	$0.641218\pi$
$920$	13.2217	+	8.02812i	0.435908	+	0.264679i
$921$	−0.311962	−	1.16113i	−0.0102795	−	0.0382606i
$922$	9.96410	−	30.6663i	0.328150	−	1.00994i
$923$	−23.8187	+	7.73916i	−0.784001	+	0.254737i
$924$	7.83812	−	5.09764i	0.257855	−	0.167700i
$925$	−35.3155	+	5.88983i	−1.16117	+	0.193657i
$926$	0.933323	+	2.87247i	0.0306709	+	0.0943953i
$927$	29.3301	−	6.27557i	0.963326	−	0.206117i
$928$	1.57706	+	1.14580i	0.0517695	+	0.0376128i
$929$	−45.6156			−1.49660			−0.748299	−	0.663362i	$-0.769129\pi$
$929$	−45.6156			−1.49660			−0.748299	+	0.663362i	$0.769129\pi$
$930$	−6.22440	+	20.6460i	−0.204106	+	0.677009i
$931$	−5.76971			−0.189095
$932$	−6.24139	−	4.53464i	−0.204444	−	0.148537i
$933$	−5.83855	+	15.2406i	−0.191146	+	0.498955i
$934$	−5.69745	−	17.5350i	−0.186426	−	0.573761i
$935$	−0.421141	+	0.0348776i	−0.0137728	+	0.00114062i
$936$	−8.65617	+	19.5127i	−0.282936	+	0.637792i
$937$	37.9317	−	12.3248i	1.23917	−	0.402632i	0.385145	−	0.922856i	$-0.374152\pi$
$937$	37.9317	−	12.3248i	1.23917	−	0.402632i	0.854030	+	0.520224i	$0.174152\pi$
$938$	7.54603	−	23.2243i	0.246387	−	0.758300i
$939$	−21.3050	+	5.72403i	−0.695263	+	0.186797i
$940$	−15.0644	+	24.8100i	−0.491348	+	0.809214i
$941$	−5.64702	−	17.3797i	−0.184088	−	0.566563i	0.815844	−	0.578272i	$-0.196273\pi$
$941$	−5.64702	−	17.3797i	−0.184088	−	0.566563i	−0.999931	+	0.0117089i	$0.996273\pi$
$942$	−1.92065	−	0.0993611i	−0.0625781	−	0.00323736i
$943$	14.2322	−	10.3403i	0.463464	−	0.336726i
$944$	−4.19758	−	1.36387i	−0.136619	−	0.0443903i
$945$	−16.0528	+	19.0295i	−0.522197	+	0.619029i
$946$	14.4693	−	10.5125i	0.470437	−	0.341792i
$947$	−28.0939	−	9.12825i	−0.912928	−	0.296628i	−0.185365	−	0.982670i	$-0.559347\pi$
$947$	−28.0939	−	9.12825i	−0.912928	−	0.296628i	−0.727562	+	0.686041i	$0.759347\pi$
$948$	−7.46071	+	19.4750i	−0.242313	+	0.632518i
$949$	−61.2630	−	44.5102i	−1.98868	−	1.44486i
$950$	5.52422	+	10.6262i	0.179229	+	0.344759i
$951$	−0.215934	+	4.17400i	−0.00700213	+	0.135351i
$952$	−0.0496690	+	0.152866i	−0.00160978	+	0.00495440i
$953$	−5.93597	−	1.92871i	−0.192285	−	0.0624771i	0.211292	−	0.977423i	$-0.432233\pi$
$953$	−5.93597	−	1.92871i	−0.192285	−	0.0624771i	−0.403576	+	0.914946i	$0.632233\pi$
$954$	2.03655	−	19.6306i	0.0659358	−	0.635563i
$955$	−33.7797	+	2.79753i	−1.09309	+	0.0905260i
$956$	−18.5587			−0.600230
$957$	5.34870	−	6.61419i	0.172899	−	0.213806i
$958$	17.7189	+	24.3880i	0.572472	+	0.787940i
$959$	32.2863	+	23.4574i	1.04258	+	0.757478i
$960$	3.06138	−	2.37233i	0.0988057	−	0.0765665i
$961$	10.1437	−	29.2934i	0.327216	−	0.944950i
$962$	50.9517			1.64275
$963$	40.9400	−	23.7102i	1.31927	−	0.764051i
$964$	−2.19962	−	3.02751i	−0.0708449	−	0.0975096i
$965$	3.91071	+	9.33317i	0.125890	+	0.300445i
$966$	−13.9971	−	21.5219i	−0.450348	−	0.692455i
$967$	−10.4419			−0.335790			−0.167895	−	0.985805i	$-0.553697\pi$
$967$	−10.4419			−0.335790			−0.167895	+	0.985805i	$0.553697\pi$
$968$	−1.43784	−	4.42521i	−0.0462138	−	0.142232i
$969$	0.0807496	+	0.300552i	0.00259405	+	0.00965513i
$970$	−9.56078	+	40.5532i	−0.306978	+	1.30209i
$971$	−6.41379	+	8.82782i	−0.205828	+	0.283298i	−0.899434	−	0.437056i	$-0.856021\pi$
$971$	−6.41379	+	8.82782i	−0.205828	+	0.283298i	0.693606	+	0.720355i	$0.256021\pi$
$972$	15.5643	−	0.868206i	0.499224	−	0.0278477i
$973$	26.5875	+	19.3170i	0.852357	+	0.619273i
$974$	−16.2113	+	11.7782i	−0.519443	+	0.377398i
$975$	−56.0706	+	25.5612i	−1.79570	+	0.818613i
$976$	0.450175	+	0.619613i	0.0144098	+	0.0198333i
$977$	1.46663	−	1.06557i	0.0469218	−	0.0340907i	−0.564077	−	0.825722i	$-0.690768\pi$
$977$	1.46663	−	1.06557i	0.0469218	−	0.0340907i	0.610999	+	0.791631i	$0.290768\pi$
$978$	3.33537	+	12.4144i	0.106654	+	0.396968i
$979$	13.0133	−	9.45469i	0.415906	−	0.302173i
$980$	−2.79550	+	4.60398i	−0.0892989	+	0.147069i
$981$	50.6020	+	5.24964i	1.61560	+	0.167608i
$982$	−17.1944	−	12.4925i	−0.548695	−	0.398650i
$983$	−23.6036	−	7.66928i	−0.752838	−	0.244612i	−0.0926361	−	0.995700i	$-0.529529\pi$
$983$	−23.6036	−	7.66928i	−0.752838	−	0.244612i	−0.660202	+	0.751088i	$0.729529\pi$
$984$	−1.14289	−	4.25388i	−0.0364341	−	0.135609i
$985$	4.08696	+	9.75381i	0.130221	+	0.310782i
$986$			0.146228i			0.00465685i
$987$	40.3849	−	26.2649i	1.28547	−	0.836022i
$988$	−5.26675	−	16.2094i	−0.167558	−	0.515689i
$989$	−28.8653	−	39.7297i	−0.917864	−	1.26333i
$990$	−9.64794	−	13.8757i	−0.306632	−	0.440999i
$991$		−	12.7841i		−	0.406099i	−0.979168	−	0.203049i	$-0.934915\pi$
$991$		−	12.7841i		−	0.406099i	0.979168	−	0.203049i	$-0.0650852\pi$
$992$	−4.53562	+	3.22926i	−0.144006	+	0.102529i
$993$	0.306339	−	0.199232i	0.00972139	−	0.00632245i
$994$	−6.10135	−	4.43289i	−0.193523	−	0.140603i
$995$	−14.5542	+	12.5337i	−0.461399	+	0.397346i
$996$	6.97401	+	5.63968i	0.220980	+	0.178700i
$997$			50.8730i			1.61116i	0.592484	+	0.805582i	$0.298147\pi$
$997$			50.8730i			1.61116i	−0.592484	+	0.805582i	$0.701853\pi$
$998$		−	24.7207i		−	0.782521i
$999$	−16.9589	−	33.1183i	−0.536556	−	1.04782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.y.a.29.4	✓	128
3.2	odd	2		930.2.y.b.29.18	yes	128
5.4	even	2		930.2.y.b.29.29	yes	128
15.14	odd	2	inner	930.2.y.a.29.15	yes	128
31.15	odd	10	inner	930.2.y.a.449.15	yes	128
93.77	even	10		930.2.y.b.449.29	yes	128
155.139	odd	10		930.2.y.b.449.18	yes	128
465.449	even	10	inner	930.2.y.a.449.4	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.y.a.29.4	✓	128	1.1	even	1	trivial
930.2.y.a.29.15	yes	128	15.14	odd	2	inner
930.2.y.a.449.4	yes	128	465.449	even	10	inner
930.2.y.a.449.15	yes	128	31.15	odd	10	inner
930.2.y.b.29.18	yes	128	3.2	odd	2
930.2.y.b.29.29	yes	128	5.4	even	2
930.2.y.b.449.18	yes	128	155.139	odd	10
930.2.y.b.449.29	yes	128	93.77	even	10

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.y (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.61743 - 0.619623i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.184552 - 2.22844i) q^{5} +(0.944320 + 1.45198i) q^{6} +(2.03784 - 0.662134i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.23213 + 2.00439i) q^{9} +O(q^{10})\)	\(q+(-0.809017 - 0.587785i) q^{2} +(-1.61743 - 0.619623i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.184552 - 2.22844i) q^{5} +(0.944320 + 1.45198i) q^{6} +(2.03784 - 0.662134i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.23213 + 2.00439i) q^{9} +(-1.16054 + 1.91132i) q^{10} +(0.778518 + 2.39603i) q^{11} +(0.0894846 - 1.72974i) q^{12} +(-5.75657 + 4.18239i) q^{13} +(-2.03784 - 0.662134i) q^{14} +(-1.08229 + 3.71869i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.0713422 - 0.0231805i) q^{17} +(-0.627684 - 2.93360i) q^{18} +(1.93781 + 1.40790i) q^{19} +(2.06234 - 0.864145i) q^{20} +(-3.70633 - 0.191740i) q^{21} +(0.778518 - 2.39603i) q^{22} +(-6.57902 - 2.13765i) q^{23} +(-1.08911 + 1.34679i) q^{24} +(-4.93188 + 0.822528i) q^{25} +7.11551 q^{26} +(-2.36835 - 4.62503i) q^{27} +(1.25945 + 1.73349i) q^{28} +(1.57706 + 1.14580i) q^{29} +(3.06138 - 2.37233i) q^{30} +(-4.53562 + 3.22926i) q^{31} +1.00000 q^{32} +(0.225442 - 4.35779i) q^{33} +(0.0440919 + 0.0606873i) q^{34} +(-1.85161 - 4.41900i) q^{35} +(-1.21652 + 2.74228i) q^{36} +7.16065 q^{37} +(-0.740178 - 2.27803i) q^{38} +(11.9023 - 3.19781i) q^{39} +(-2.17640 - 0.513106i) q^{40} +(-1.49478 + 2.05739i) q^{41} +(2.88578 + 2.33364i) q^{42} +(5.74329 + 4.17274i) q^{43} +(-2.03819 + 1.48083i) q^{44} +(4.05471 - 5.34409i) q^{45} +(4.06606 + 5.59645i) q^{46} +(-10.5015 + 7.62979i) q^{47} +(1.67273 - 0.449413i) q^{48} +(-1.94876 + 1.41585i) q^{49} +(4.47345 + 2.23345i) q^{50} +(0.101028 + 0.0816980i) q^{51} +(-5.75657 - 4.18239i) q^{52} +(6.25666 + 2.03291i) q^{53} +(-0.802496 + 5.13381i) q^{54} +(5.19573 - 2.17707i) q^{55} -2.14271i q^{56} +(-2.26190 - 3.47789i) q^{57} +(-0.602383 - 1.85395i) q^{58} +(2.59424 + 3.57067i) q^{59} +(-3.87113 + 0.119816i) q^{60} -0.765884i q^{61} +(5.56751 + 0.0534406i) q^{62} +(5.87590 + 2.60665i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(10.3826 + 12.0563i) q^{65} +(-2.74383 + 3.39302i) q^{66} +11.3965i q^{67} -0.0750136i q^{68} +(9.31654 + 7.53401i) q^{69} +(-1.09944 + 4.66340i) q^{70} +(3.34743 + 1.08765i) q^{71} +(2.59606 - 1.50350i) q^{72} +(3.28865 + 10.1214i) q^{73} +(-5.79309 - 4.20892i) q^{74} +(8.48661 + 1.72553i) q^{75} +(-0.740178 + 2.27803i) q^{76} +(3.17299 + 4.36724i) q^{77} +(-11.5088 - 4.40894i) q^{78} +(-11.4514 - 3.72079i) q^{79} +(1.45915 + 1.69437i) q^{80} +(0.964844 + 8.94813i) q^{81} +(2.41861 - 0.785854i) q^{82} +(-3.04370 + 4.18929i) q^{83} +(-0.962963 - 3.58418i) q^{84} +(-0.0384899 + 0.163260i) q^{85} +(-2.19374 - 6.75164i) q^{86} +(-1.84081 - 2.83043i) q^{87} +2.51934 q^{88} +(-1.97299 - 6.07224i) q^{89} +(-6.42151 + 1.94016i) q^{90} +(-8.96165 + 12.3347i) q^{91} -6.91759i q^{92} +(9.33696 - 2.41272i) q^{93} +12.9806 q^{94} +(2.77980 - 4.57813i) q^{95} +(-1.61743 - 0.619623i) q^{96} +(17.7212 - 5.75796i) q^{97} +2.40879 q^{98} +(-3.06483 + 6.90872i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9	\( 128 q - 32 q^{2} - 32 q^{4} + 2 q^{5} - 32 q^{8} - 4 q^{9} + 2 q^{10} + 25 q^{15} - 32 q^{16} + 6 q^{18} - 8 q^{19} - 3 q^{20} - 20 q^{23} - 10 q^{25} - 48 q^{31} + 128 q^{32} - 8 q^{33} + 10 q^{34} + 16 q^{35} - 4 q^{36} + 12 q^{38} + 4 q^{39} - 3 q^{40} + 37 q^{45} + 10 q^{46} + 6 q^{47} + 46 q^{49} - 5 q^{50} + 34 q^{51} - 20 q^{53} - 25 q^{60} - 8 q^{62} + 36 q^{63} - 32 q^{64} - 8 q^{66} + 8 q^{69} + 16 q^{70} + 6 q^{72} + 5 q^{75} + 12 q^{76} + 50 q^{77} + 4 q^{78} - 10 q^{79} + 2 q^{80} - 24 q^{81} - 40 q^{83} - 30 q^{85} - 4 q^{87} - 53 q^{90} + 20 q^{91} - 26 q^{93} - 4 q^{94} - 26 q^{95} - 124 q^{98}+O(q^{100}) \) 128 * q - 32 * q^2 - 32 * q^4 + 2 * q^5 - 32 * q^8 - 4 * q^9 + 2 * q^10 + 25 * q^15 - 32 * q^16 + 6 * q^18 - 8 * q^19 - 3 * q^20 - 20 * q^23 - 10 * q^25 - 48 * q^31 + 128 * q^32 - 8 * q^33 + 10 * q^34 + 16 * q^35 - 4 * q^36 + 12 * q^38 + 4 * q^39 - 3 * q^40 + 37 * q^45 + 10 * q^46 + 6 * q^47 + 46 * q^49 - 5 * q^50 + 34 * q^51 - 20 * q^53 - 25 * q^60 - 8 * q^62 + 36 * q^63 - 32 * q^64 - 8 * q^66 + 8 * q^69 + 16 * q^70 + 6 * q^72 + 5 * q^75 + 12 * q^76 + 50 * q^77 + 4 * q^78 - 10 * q^79 + 2 * q^80 - 24 * q^81 - 40 * q^83 - 30 * q^85 - 4 * q^87 - 53 * q^90 + 20 * q^91 - 26 * q^93 - 4 * q^94 - 26 * q^95 - 124 * q^98

Introduction

L-functions

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