LMFDB - Embedded newform 950.2.w.a.113.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(37,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([9, 10]))

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

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

chi := DirichletCharacter("950.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.w (of order $20$, degree $8$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$50$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.18
Character	$\chi$	$=$	950.113
Dual form			950.2.w.a.227.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 - 0.987688i) q^{2} +(1.36837 + 0.697221i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.20636 - 1.88274i) q^{5} +(0.474577 - 1.46060i) q^{6} +(0.0898753 - 0.0898753i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-0.377026 - 0.518932i) q^{9} +O(q^{10})$	\(q+(-0.156434 - 0.987688i) q^{2} +(1.36837 + 0.697221i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.20636 - 1.88274i) q^{5} +(0.474577 - 1.46060i) q^{6} +(0.0898753 - 0.0898753i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-0.377026 - 0.518932i) q^{9} +(-2.04827 - 0.896980i) q^{10} +(-1.78395 - 1.29611i) q^{11} +(-1.51685 - 0.240246i) q^{12} +(0.155214 - 0.979980i) q^{13} +(-0.102828 - 0.0747092i) q^{14} +(2.96343 - 1.73519i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-2.08636 - 4.09471i) q^{17} +(-0.453563 + 0.453563i) q^{18} +(-0.201461 - 4.35424i) q^{19} +(-0.565516 + 2.16337i) q^{20} +(0.185646 - 0.0603200i) q^{21} +(-1.00108 + 1.96474i) q^{22} +(1.11150 + 7.01776i) q^{23} +1.53576i q^{24} +(-2.08940 - 4.54251i) q^{25} -0.992195 q^{26} +(-0.874841 - 5.52353i) q^{27} +(-0.0577035 + 0.113249i) q^{28} +(-1.80251 - 5.54754i) q^{29} +(-2.17741 - 2.65550i) q^{30} +(7.35207 + 2.38883i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.53743 - 3.01737i) q^{33} +(-3.71792 + 2.70122i) q^{34} +(-0.0607898 - 0.277633i) q^{35} +(0.518932 + 0.377026i) q^{36} +(2.13005 + 0.337367i) q^{37} +(-4.26912 + 0.880134i) q^{38} +(0.895653 - 1.23276i) q^{39} +(2.22521 + 0.220128i) q^{40} +(2.88904 + 3.97642i) q^{41} +(-0.0886188 - 0.173924i) q^{42} +(-4.67876 - 4.67876i) q^{43} +(2.09715 + 0.681406i) q^{44} +(-1.43184 + 0.0838237i) q^{45} +(6.75748 - 2.19564i) q^{46} +(4.71972 + 2.40482i) q^{47} +(1.51685 - 0.240246i) q^{48} +6.98384i q^{49} +(-4.15973 + 2.77428i) q^{50} -7.05774i q^{51} +(0.155214 + 0.979980i) q^{52} +(8.91875 + 4.54433i) q^{53} +(-5.31867 + 1.72814i) q^{54} +(-4.59231 + 1.79513i) q^{55} +(0.120882 + 0.0392769i) q^{56} +(2.76020 - 6.09869i) q^{57} +(-5.19727 + 2.64814i) q^{58} +(3.12435 - 2.26997i) q^{59} +(-2.28219 + 2.56602i) q^{60} +(-12.4317 - 9.03213i) q^{61} +(1.20931 - 7.63525i) q^{62} +(-0.0805245 - 0.0127538i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-1.65780 - 1.47443i) q^{65} +(-2.73972 + 1.99052i) q^{66} +(-8.43686 + 4.29879i) q^{67} +(3.24958 + 3.24958i) q^{68} +(-3.37198 + 10.3779i) q^{69} +(-0.264706 + 0.103473i) q^{70} +(10.0798 - 3.27514i) q^{71} +(0.291205 - 0.571523i) q^{72} +(-0.0492189 - 0.310756i) q^{73} -2.15660i q^{74} +(0.308052 - 7.67263i) q^{75} +(1.53714 + 4.07887i) q^{76} +(-0.276821 + 0.0438441i) q^{77} +(-1.35769 - 0.691780i) q^{78} +(1.96929 + 6.06085i) q^{79} +(-0.130682 - 2.23225i) q^{80} +(2.05937 - 6.33808i) q^{81} +(3.47552 - 3.47552i) q^{82} +(11.6769 - 5.94966i) q^{83} +(-0.157920 + 0.114735i) q^{84} +(-10.2262 - 1.01162i) q^{85} +(-3.88924 + 5.35307i) q^{86} +(1.40136 - 8.84786i) q^{87} +(0.344950 - 2.17793i) q^{88} +(1.08249 + 0.786473i) q^{89} +(0.306781 + 1.40110i) q^{90} +(-0.0741261 - 0.102026i) q^{91} +(-3.22571 - 6.33081i) q^{92} +(8.39484 + 8.39484i) q^{93} +(1.63688 - 5.03781i) q^{94} +(-8.44093 - 4.87347i) q^{95} +(-0.474577 - 1.46060i) q^{96} +(4.17353 - 8.19102i) q^{97} +(6.89786 - 1.09251i) q^{98} +1.41441i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) $ 400 * q + 4 * q^5 - 4 * q^7	$ 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) $ 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{19}{20}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$3$	1.36837	+	0.697221i	0.790031	+	0.402541i	0.801952	−	0.597388i	$-0.203795\pi$
$3$	1.36837	+	0.697221i	0.790031	+	0.402541i	−0.0119213	+	0.999929i	$0.503795\pi$
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	1.20636	−	1.88274i	0.539500	−	0.841986i
$5$	1.20636	−	1.88274i	0.539500	−	0.841986i
$6$	0.474577	−	1.46060i	0.193745	−	0.596286i
$7$	0.0898753	−	0.0898753i	0.0339697	−	0.0339697i	−0.689918	−	0.723888i	$-0.742353\pi$
$7$	0.0898753	−	0.0898753i	0.0339697	−	0.0339697i	0.723888	+	0.689918i	$0.242353\pi$
$8$	0.453990	+	0.891007i	0.160510	+	0.315018i
$9$	−0.377026	−	0.518932i	−0.125675	−	0.172977i
$10$	−2.04827	−	0.896980i	−0.647721	−	0.283650i
$11$	−1.78395	−	1.29611i	−0.537880	−	0.390792i	0.285417	−	0.958403i	$-0.407868\pi$
$11$	−1.78395	−	1.29611i	−0.537880	−	0.390792i	−0.823297	+	0.567611i	$0.807868\pi$
$12$	−1.51685	−	0.240246i	−0.437878	−	0.0693531i
$13$	0.155214	−	0.979980i	0.0430485	−	0.271797i	−0.956770	−	0.290845i	$-0.906063\pi$
$13$	0.155214	−	0.979980i	0.0430485	−	0.271797i	0.999819	+	0.0190479i	$0.00606349\pi$
$14$	−0.102828	−	0.0747092i	−0.0274820	−	0.0199669i
$15$	2.96343	−	1.73519i	0.765155	−	0.448024i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−2.08636	−	4.09471i	−0.506016	−	0.993112i	−0.992822	−	0.119602i	$-0.961838\pi$
$17$	−2.08636	−	4.09471i	−0.506016	−	0.993112i	0.486806	−	0.873510i	$-0.338162\pi$
$18$	−0.453563	+	0.453563i	−0.106906	+	0.106906i
$19$	−0.201461	−	4.35424i	−0.0462183	−	0.998931i
$19$	−0.201461	−	4.35424i	−0.0462183	−	0.998931i
$20$	−0.565516	+	2.16337i	−0.126453	+	0.483745i
$21$	0.185646	−	0.0603200i	0.0405113	−	0.0131629i
$22$	−1.00108	+	1.96474i	−0.213432	+	0.418884i
$23$	1.11150	+	7.01776i	0.231765	+	1.46330i	0.779368	+	0.626566i	$0.215540\pi$
$23$	1.11150	+	7.01776i	0.231765	+	1.46330i	−0.547604	+	0.836738i	$0.684460\pi$
$24$			1.53576i			0.313486i
$25$	−2.08940	−	4.54251i	−0.417880	−	0.908502i
$26$	−0.992195			−0.194585
$27$	−0.874841	−	5.52353i	−0.168363	−	1.06300i
$28$	−0.0577035	+	0.113249i	−0.0109049	+	0.0214021i
$29$	−1.80251	−	5.54754i	−0.334717	−	1.03015i	−0.966861	−	0.255302i	$-0.917825\pi$
$29$	−1.80251	−	5.54754i	−0.334717	−	1.03015i	0.632144	−	0.774851i	$-0.282175\pi$
$30$	−2.17741	−	2.65550i	−0.397539	−	0.484827i
$31$	7.35207	+	2.38883i	1.32047	+	0.429047i	0.882657	−	0.470018i	$-0.155753\pi$
$31$	7.35207	+	2.38883i	1.32047	+	0.429047i	0.437814	+	0.899065i	$0.355753\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−1.53743	−	3.01737i	−0.267632	−	0.525257i
$34$	−3.71792	+	2.70122i	−0.637617	+	0.463256i
$35$	−0.0607898	−	0.277633i	−0.0102754	−	0.0469286i
$36$	0.518932	+	0.377026i	0.0864887	+	0.0628377i
$37$	2.13005	+	0.337367i	0.350178	+	0.0554628i	0.329046	−	0.944314i	$-0.393273\pi$
$37$	2.13005	+	0.337367i	0.350178	+	0.0554628i	0.0211322	+	0.999777i	$0.493273\pi$
$38$	−4.26912	+	0.880134i	−0.692542	+	0.142777i
$39$	0.895653	−	1.23276i	0.143419	−	0.197400i
$40$	2.22521	+	0.220128i	0.351836	+	0.0348052i
$41$	2.88904	+	3.97642i	0.451193	+	0.621013i	0.972653	−	0.232262i	$-0.0746127\pi$
$41$	2.88904	+	3.97642i	0.451193	+	0.621013i	−0.521461	+	0.853275i	$0.674613\pi$
$42$	−0.0886188	−	0.173924i	−0.0136742	−	0.0268371i
$43$	−4.67876	−	4.67876i	−0.713504	−	0.713504i	0.253763	−	0.967266i	$-0.418332\pi$
$43$	−4.67876	−	4.67876i	−0.713504	−	0.713504i	−0.967266	+	0.253763i	$0.918332\pi$
$44$	2.09715	+	0.681406i	0.316158	+	0.102726i
$45$	−1.43184	+	0.0838237i	−0.213446	+	0.0124957i
$46$	6.75748	−	2.19564i	0.996336	−	0.323729i
$47$	4.71972	+	2.40482i	0.688442	+	0.350779i	0.762964	−	0.646440i	$-0.223743\pi$
$47$	4.71972	+	2.40482i	0.688442	+	0.350779i	−0.0745221	+	0.997219i	$0.523743\pi$
$48$	1.51685	−	0.240246i	0.218939	−	0.0346765i
$49$			6.98384i			0.997692i
$50$	−4.15973	+	2.77428i	−0.588275	+	0.392343i
$51$		−	7.05774i		−	0.988282i
$52$	0.155214	+	0.979980i	0.0215242	+	0.135899i
$53$	8.91875	+	4.54433i	1.22508	+	0.624212i	0.942235	−	0.334952i	$-0.108720\pi$
$53$	8.91875	+	4.54433i	1.22508	+	0.624212i	0.282850	+	0.959164i	$0.408720\pi$
$54$	−5.31867	+	1.72814i	−0.723779	+	0.235170i
$55$	−4.59231	+	1.79513i	−0.619228	+	0.242055i
$56$	0.120882	+	0.0392769i	0.0161535	+	0.00524860i
$57$	2.76020	−	6.09869i	0.365597	−	0.807792i
$58$	−5.19727	+	2.64814i	−0.682435	+	0.347718i
$59$	3.12435	−	2.26997i	0.406755	−	0.295525i	−0.365532	−	0.930799i	$-0.619113\pi$
$59$	3.12435	−	2.26997i	0.406755	−	0.295525i	0.772287	+	0.635274i	$0.219113\pi$
$60$	−2.28219	+	2.56602i	−0.294629	+	0.331271i
$61$	−12.4317	−	9.03213i	−1.59171	−	1.15645i	−0.901448	−	0.432887i	$-0.857495\pi$
$61$	−12.4317	−	9.03213i	−1.59171	−	1.15645i	−0.690263	−	0.723559i	$-0.742505\pi$
$62$	1.20931	−	7.63525i	0.153582	−	0.969678i
$63$	−0.0805245	−	0.0127538i	−0.0101451	−	0.00160683i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	−1.65780	−	1.47443i	−0.205625	−	0.182881i
$66$	−2.73972	+	1.99052i	−0.337236	+	0.245016i
$67$	−8.43686	+	4.29879i	−1.03073	+	0.525181i	−0.885706	−	0.464248i	$-0.846325\pi$
$67$	−8.43686	+	4.29879i	−1.03073	+	0.525181i	−0.145020	+	0.989429i	$0.546325\pi$
$68$	3.24958	+	3.24958i	0.394069	+	0.394069i
$69$	−3.37198	+	10.3779i	−0.405938	+	1.24935i
$70$	−0.264706	+	0.103473i	−0.0316384	+	0.0123674i
$71$	10.0798	−	3.27514i	1.19626	−	0.388687i	0.357874	−	0.933770i	$-0.383502\pi$
$71$	10.0798	−	3.27514i	1.19626	−	0.388687i	0.838382	+	0.545082i	$0.183502\pi$
$72$	0.291205	−	0.571523i	0.0343189	−	0.0673546i
$73$	−0.0492189	−	0.310756i	−0.00576063	−	0.0363712i	0.984641	−	0.174594i	$-0.0558611\pi$
$73$	−0.0492189	−	0.310756i	−0.00576063	−	0.0363712i	−0.990401	+	0.138222i	$0.955861\pi$
$74$		−	2.15660i		−	0.250700i
$75$	0.308052	−	7.67263i	0.0355707	−	0.885959i
$76$	1.53714	+	4.07887i	0.176321	+	0.467879i
$77$	−0.276821	+	0.0438441i	−0.0315467	+	0.00499650i
$78$	−1.35769	−	0.691780i	−0.153729	−	0.0783286i
$79$	1.96929	+	6.06085i	0.221562	+	0.681899i	0.998622	+	0.0524724i	$0.0167102\pi$
$79$	1.96929	+	6.06085i	0.221562	+	0.681899i	−0.777060	+	0.629427i	$0.783290\pi$
$80$	−0.130682	−	2.23225i	−0.0146106	−	0.249573i
$81$	2.05937	−	6.33808i	0.228819	−	0.704232i
$82$	3.47552	−	3.47552i	0.383807	−	0.383807i
$83$	11.6769	−	5.94966i	1.28170	−	0.653060i	0.325438	−	0.945563i	$-0.394488\pi$
$83$	11.6769	−	5.94966i	1.28170	−	0.653060i	0.956265	+	0.292503i	$0.0944882\pi$
$84$	−0.157920	+	0.114735i	−0.0172305	+	0.0125187i
$85$	−10.2262	−	1.01162i	−1.10918	−	0.109725i
$86$	−3.88924	+	5.35307i	−0.419387	+	0.577237i
$87$	1.40136	−	8.84786i	0.150242	−	0.948590i
$88$	0.344950	−	2.17793i	0.0367718	−	0.232168i
$89$	1.08249	+	0.786473i	0.114743	+	0.0833660i	0.643677	−	0.765297i	$-0.277408\pi$
$89$	1.08249	+	0.786473i	0.114743	+	0.0833660i	−0.528934	+	0.848663i	$0.677408\pi$
$90$	0.306781	+	1.40110i	0.0323376	+	0.147689i
$91$	−0.0741261	−	0.102026i	−0.00777052	−	0.0106952i
$92$	−3.22571	−	6.33081i	−0.336303	−	0.660033i
$93$	8.39484	+	8.39484i	0.870504	+	0.870504i
$94$	1.63688	−	5.03781i	0.168832	−	0.519611i
$95$	−8.44093	−	4.87347i	−0.866021	−	0.500008i
$96$	−0.474577	−	1.46060i	−0.0484363	−	0.149072i
$97$	4.17353	−	8.19102i	0.423758	−	0.831672i	−0.576139	−	0.817352i	$-0.695441\pi$
$97$	4.17353	−	8.19102i	0.423758	−	0.831672i	0.999897	−	0.0143208i	$-0.00455861\pi$
$98$	6.89786	−	1.09251i	0.696789	−	0.110361i
$99$			1.41441i			0.142154i
$100$	3.39085	+	3.67452i	0.339085	+	0.367452i
$101$	−1.90250			−0.189306			−0.0946528	−	0.995510i	$-0.530174\pi$
$101$	−1.90250			−0.189306			−0.0946528	+	0.995510i	$0.530174\pi$
$102$	−6.97085	+	1.10407i	−0.690217	+	0.109320i
$103$	−1.52710	−	0.778097i	−0.150470	−	0.0766682i	0.377134	−	0.926159i	$-0.376910\pi$
$103$	−1.52710	−	0.778097i	−0.150470	−	0.0766682i	−0.527604	+	0.849490i	$0.676910\pi$
$104$	0.943634	−	0.306605i	0.0925309	−	0.0300651i
$105$	0.110389	−	0.422290i	0.0107728	−	0.0412113i
$106$	3.09318	−	9.51984i	0.300436	−	0.924648i
$107$	−3.23124	−	3.23124i	−0.312375	−	0.312375i	0.533454	−	0.845829i	$-0.320894\pi$
$107$	−3.23124	−	3.23124i	−0.312375	−	0.312375i	−0.845829	+	0.533454i	$0.820894\pi$
$108$	2.53889	+	4.98284i	0.244304	+	0.479474i
$109$	−2.47215	+	1.79612i	−0.236789	+	0.172037i	−0.699851	−	0.714288i	$-0.746751\pi$
$109$	−2.47215	+	1.79612i	−0.236789	+	0.172037i	0.463063	+	0.886326i	$0.346751\pi$
$110$	2.49142	+	4.25496i	0.237548	+	0.405694i
$111$	2.67949	+	1.94676i	0.254326	+	0.184778i
$112$	0.0198833	−	0.125538i	0.00187879	−	0.0118622i
$113$	−2.59942	+	16.4121i	−0.244533	+	1.54392i	0.493854	+	0.869545i	$0.335588\pi$
$113$	−2.59942	+	16.4121i	−0.244533	+	1.54392i	−0.738387	+	0.674377i	$0.764412\pi$
$114$	−6.45540	−	1.77217i	−0.604603	−	0.165979i
$115$	14.5535	+	6.37326i	1.35712	+	0.594309i
$116$	3.42857	+	4.71902i	0.318335	+	0.438150i
$117$	−0.567062	+	0.288933i	−0.0524249	+	0.0267118i
$118$	−2.73078	−	2.73078i	−0.251389	−	0.251389i
$119$	−0.555525	−	0.180501i	−0.0509249	−	0.0165465i
$120$	2.89144	+	1.85268i	0.263951	+	0.169126i
$121$	−1.89663	−	5.83724i	−0.172421	−	0.530658i
$122$	−6.97619	+	13.6915i	−0.631595	+	1.23957i
$123$	1.18084	+	7.45554i	0.106473	+	0.672243i
$124$	−7.73043			−0.694213
$125$	−11.0729	−	1.54610i	−0.990392	−	0.138287i
$126$			0.0815282i			0.00726311i
$127$	−0.149836	−	0.946029i	−0.0132958	−	0.0839465i	0.980148	−	0.198266i	$-0.0635311\pi$
$127$	−0.149836	−	0.946029i	−0.0132958	−	0.0839465i	−0.993444	+	0.114320i	$0.963531\pi$
$128$	0.891007	+	0.453990i	0.0787546	+	0.0401275i
$129$	−3.14016	−	9.66442i	−0.276476	−	0.850905i
$130$	−1.19694	+	1.86804i	−0.104979	+	0.163838i
$131$	−4.73979	+	14.5876i	−0.414117	+	1.27452i	0.498921	+	0.866647i	$0.333730\pi$
$131$	−4.73979	+	14.5876i	−0.414117	+	1.27452i	−0.913038	+	0.407874i	$0.866270\pi$
$132$	2.39460	+	2.39460i	0.208423	+	0.208423i
$133$	−0.409445	−	0.373232i	−0.0355034	−	0.0323633i
$134$	5.56568	+	7.66050i	0.480802	+	0.661767i
$135$	−11.4547	−	5.01625i	−0.985865	−	0.431730i
$136$	2.70122	−	3.71792i	0.231628	−	0.318809i
$137$	−1.72357	+	10.8822i	−0.147255	+	0.929731i	0.797824	+	0.602890i	$0.205984\pi$
$137$	−1.72357	+	10.8822i	−0.147255	+	0.929731i	−0.945079	+	0.326841i	$0.894016\pi$
$138$	10.7776	+	1.70700i	0.917451	+	0.145310i
$139$	−8.25462	+	11.3615i	−0.700147	+	0.963670i	0.299806	+	0.954000i	$0.403078\pi$
$139$	−8.25462	+	11.3615i	−0.700147	+	0.963670i	−0.999953	+	0.00966994i	$0.996922\pi$
$140$	0.143608	+	0.245260i	0.0121371	+	0.0207282i
$141$	4.78165	+	6.58138i	0.402688	+	0.554252i
$142$	−4.81165	−	9.44339i	−0.403785	−	0.792472i
$143$	−1.54706	+	1.54706i	−0.129371	+	0.129371i
$144$	−0.610041	−	0.198214i	−0.0508368	−	0.0165179i
$145$	−12.6190	−	3.29867i	−1.04795	−	0.273940i
$146$	−0.299230	+	0.0972258i	−0.0247645	+	0.00804647i
$147$	−4.86929	+	9.55651i	−0.401612	+	0.788208i
$148$	−2.13005	+	0.337367i	−0.175089	+	0.0277314i
$149$			2.25014i			0.184338i	0.995743	+	0.0921692i	$0.0293801\pi$
$149$			2.25014i			0.184338i	−0.995743	+	0.0921692i	$0.970620\pi$
$150$	−7.62636	+	0.896005i	−0.622689	+	0.0731585i
$151$			12.7507i			1.03763i	0.854886	+	0.518817i	$0.173627\pi$
$151$			12.7507i			1.03763i	−0.854886	+	0.518817i	$0.826373\pi$
$152$	3.78820	−	2.15629i	0.307263	−	0.174898i
$153$	−1.33826	+	2.62649i	−0.108192	+	0.212339i
$154$	0.0866087	+	0.266554i	0.00697913	+	0.0214795i
$155$	13.3668	−	10.9602i	1.07365	−	0.880347i
$156$	−0.470873	+	1.44920i	−0.0377000	+	0.116029i
$157$	16.7880	−	16.7880i	1.33983	−	1.33983i	0.443602	−	0.896224i	$-0.353700\pi$
$157$	16.7880	−	16.7880i	1.33983	−	1.33983i	0.896224	−	0.443602i	$-0.146300\pi$
$158$	5.67817	−	2.89317i	0.451731	−	0.230168i
$159$	9.03578	+	12.4367i	0.716584	+	0.986293i
$160$	−2.18432	+	0.478273i	−0.172686	+	0.0378108i
$161$	0.730619	+	0.530826i	0.0575809	+	0.0418350i
$162$	−6.58221	−	1.04252i	−0.517147	−	0.0819080i
$163$	17.3436	+	2.74696i	1.35846	+	0.215159i	0.792801	−	0.609481i	$-0.208622\pi$
$163$	17.3436	+	2.74696i	1.35846	+	0.215159i	0.565659	+	0.824640i	$0.308622\pi$
$164$	−3.97642	−	2.88904i	−0.310507	−	0.225596i
$165$	−7.53560	−	0.745456i	−0.586646	−	0.0580337i
$166$	−7.70308	−	10.6024i	−0.597875	−	0.822904i
$167$	18.4362	−	9.39369i	1.42663	−	0.726906i	0.441270	−	0.897375i	$-0.354528\pi$
$167$	18.4362	−	9.39369i	1.42663	−	0.726906i	0.985363	+	0.170469i	$0.0545282\pi$
$168$	0.138027	+	0.138027i	0.0106490	+	0.0106490i
$169$	11.4275	+	3.71301i	0.879036	+	0.285616i
$170$	0.600560	+	10.2585i	0.0460608	+	0.786791i
$171$	−2.18360	+	1.74621i	−0.166984	+	0.133536i
$172$	5.89558	+	3.00395i	0.449534	+	0.229049i
$173$	1.27328	−	0.201668i	0.0968059	−	0.0153326i	−0.107844	−	0.994168i	$-0.534395\pi$
$173$	1.27328	−	0.201668i	0.0968059	−	0.0153326i	0.204649	+	0.978835i	$0.434395\pi$
$174$	−8.95815			−0.679115
$175$	−0.596045	−	0.220474i	−0.0450568	−	0.0166662i
$176$	−2.20508			−0.166214
$177$	5.85794	−	0.927807i	0.440310	−	0.0697383i
$178$	0.607452	−	1.19219i	0.0455305	−	0.0893586i
$179$	5.94168	+	18.2866i	0.444102	+	1.36680i	0.883466	+	0.468495i	$0.155204\pi$
$179$	5.94168	+	18.2866i	0.444102	+	1.36680i	−0.439364	+	0.898309i	$0.644796\pi$
$180$	1.33586	−	0.522184i	0.0995690	−	0.0389213i
$181$	−19.6628	−	6.38883i	−1.46152	−	0.474878i	−0.532989	−	0.846122i	$-0.678931\pi$
$181$	−19.6628	−	6.38883i	−1.46152	−	0.474878i	−0.928535	+	0.371244i	$0.878931\pi$
$182$	−0.0891738	+	0.0891738i	−0.00661000	+	0.00661000i
$183$	−10.7138	−	21.0270i	−0.791984	−	1.55436i
$184$	−5.74826	+	4.17635i	−0.423767	+	0.307885i
$185$	3.20478	−	3.60334i	0.235620	−	0.264923i
$186$	6.97824	−	9.60473i	0.511670	−	0.704253i
$187$	−1.58525	+	10.0089i	−0.115925	+	0.731922i
$188$	−5.23185	−	0.828644i	−0.381572	−	0.0604351i
$189$	−0.575055	−	0.417802i	−0.0418291	−	0.0303906i
$190$	−3.49302	+	9.09938i	−0.253410	+	0.660139i
$191$	−15.5128	+	11.2707i	−1.12247	+	0.815519i	−0.984581	−	0.174929i	$-0.944030\pi$
$191$	−15.5128	+	11.2707i	−1.12247	+	0.815519i	−0.137884	+	0.990448i	$0.544030\pi$
$192$	−1.36837	+	0.697221i	−0.0987539	+	0.0503176i
$193$	−11.9585	+	11.9585i	−0.860791	+	0.860791i	−0.991430	−	0.130639i	$-0.958297\pi$
$193$	−11.9585	+	11.9585i	−0.860791	+	0.860791i	0.130639	+	0.991430i	$0.458297\pi$
$194$	−8.74306	−	2.84079i	−0.627715	−	0.203957i
$195$	−1.24049	−	3.17343i	−0.0888331	−	0.227254i
$196$	−2.15813	−	6.64203i	−0.154152	−	0.474431i
$197$	13.9453	+	7.10550i	0.993563	+	0.506246i	0.873659	−	0.486540i	$-0.161741\pi$
$197$	13.9453	+	7.10550i	0.993563	+	0.506246i	0.119905	+	0.992785i	$0.461741\pi$
$198$	1.39700	−	0.221263i	0.0992805	−	0.0157245i
$199$		−	4.49058i		−	0.318329i	−0.987252	−	0.159165i	$-0.949120\pi$
$199$		−	4.49058i		−	0.318329i	0.987252	−	0.159165i	$-0.0508800\pi$
$200$	3.09884	−	3.92393i	0.219121	−	0.277464i
$201$	−14.5420			−1.02571
$202$	0.297616	+	1.87907i	0.0209402	+	0.132211i
$203$	−0.660587	−	0.336586i	−0.0463642	−	0.0236237i
$204$	2.18096	+	6.71231i	0.152698	+	0.469956i
$205$	10.9718	−	0.642317i	0.766303	−	0.0448614i
$206$	−0.529626	+	1.63002i	−0.0369008	+	0.113569i
$207$	3.22267	−	3.22267i	0.223991	−	0.223991i
$208$	−0.450447	−	0.884052i	−0.0312329	−	0.0612980i
$209$	−5.28419	+	8.02884i	−0.365515	+	0.555367i
$210$	−0.434360	−	0.0429688i	−0.0299737	−	0.00296513i
$211$	2.49541	−	3.43464i	0.171791	−	0.236450i	−0.714436	−	0.699700i	$-0.753317\pi$
$211$	2.49541	−	3.43464i	0.171791	−	0.236450i	0.886228	+	0.463250i	$0.153317\pi$
$212$	−9.88651	−	1.56587i	−0.679008	−	0.107544i
$213$	16.0765	+	2.54627i	1.10154	+	0.174467i
$214$	−2.68598	+	3.69693i	−0.183610	+	0.252717i
$215$	−14.4531	+	3.16462i	−0.985695	+	0.215825i
$216$	4.52433	−	3.28712i	0.307842	−	0.223660i
$217$	0.875466	−	0.446072i	0.0594305	−	0.0302814i
$218$	2.16074	+	2.16074i	0.146344	+	0.146344i
$219$	0.149316	−	0.459547i	0.0100898	−	0.0310533i
$220$	3.81283	−	3.12637i	0.257061	−	0.210780i
$221$	−4.33656	+	1.40903i	−0.291709	+	0.0947819i
$222$	1.50363	−	2.95104i	0.100917	−	0.198061i
$223$	22.4994	−	3.56356i	1.50667	−	0.238634i	0.652167	−	0.758075i	$-0.273860\pi$
$223$	22.4994	−	3.56356i	1.50667	−	0.238634i	0.854506	+	0.519442i	$0.173860\pi$
$224$	−0.127103			−0.00849241
$225$	−1.56949	+	2.79690i	−0.104633	+	0.186460i
$226$	16.6167			1.10533
$227$	−2.24625	−	14.1822i	−0.149089	−	0.941308i	−0.942883	−	0.333123i	$-0.891898\pi$
$227$	−2.24625	−	14.1822i	−0.149089	−	0.941308i	0.793795	−	0.608186i	$-0.208102\pi$
$228$	−0.740503	+	6.65315i	−0.0490410	+	0.440616i
$229$	−20.6671	+	6.71515i	−1.36572	+	0.443750i	−0.897949	−	0.440100i	$-0.854943\pi$
$229$	−20.6671	+	6.71515i	−1.36572	+	0.443750i	−0.467772	+	0.883849i	$0.654943\pi$
$230$	4.01813	−	15.3713i	0.264947	−	1.01355i
$231$	−0.409364	−	0.133010i	−0.0269342	−	0.00875144i
$232$	4.12458	−	4.12458i	0.270792	−	0.270792i
$233$	−1.38471	+	0.705547i	−0.0907156	+	0.0462219i	−0.498760	−	0.866740i	$-0.666211\pi$
$233$	−1.38471	+	0.705547i	−0.0907156	+	0.0462219i	0.408044	+	0.912962i	$0.366211\pi$
$234$	0.374083	+	0.514882i	0.0244546	+	0.0336589i
$235$	10.2213	−	5.98493i	0.666765	−	0.390414i
$236$	−2.26997	+	3.12435i	−0.147762	+	0.203378i
$237$	−1.53103	+	9.66654i	−0.0994511	+	0.627909i
$238$	−0.0913754	+	0.576922i	−0.00592299	+	0.0373963i
$239$	12.0099	−	16.5303i	0.776858	−	1.06925i	−0.218763	−	0.975778i	$-0.570202\pi$
$239$	12.0099	−	16.5303i	0.776858	−	1.06925i	0.995622	−	0.0934758i	$-0.0297978\pi$
$240$	1.37755	−	3.14566i	0.0889204	−	0.203052i
$241$	12.5709	+	17.3024i	0.809763	+	1.11454i	0.991360	+	0.131170i	$0.0418735\pi$
$241$	12.5709	+	17.3024i	0.809763	+	1.11454i	−0.181597	+	0.983373i	$0.558126\pi$
$242$	−5.46867	+	2.78643i	−0.351540	+	0.179118i
$243$	−4.62619	+	4.62619i	−0.296770	+	0.296770i
$244$	14.6143	+	4.74847i	0.935584	+	0.303990i
$245$	13.1487	+	8.42502i	0.840043	+	0.538254i
$246$	7.17902	−	2.33261i	0.457718	−	0.148722i
$247$	−4.29834	−	0.478410i	−0.273497	−	0.0304405i
$248$	1.20931	+	7.63525i	0.0767909	+	0.484839i
$249$	20.1266			1.27547
$250$	0.205125	+	11.1785i	0.0129733	+	0.706988i
$251$	9.99039			0.630588			0.315294	−	0.948994i	$-0.397897\pi$
$251$	9.99039			0.630588			0.315294	+	0.948994i	$0.397897\pi$
$252$	0.0805245	−	0.0127538i	0.00507256	−	0.000803415i
$253$	7.11294	−	13.9599i	0.447187	−	0.877653i
$254$	−0.910942	+	0.295983i	−0.0571576	+	0.0185716i
$255$	−13.2879	−	8.51416i	−0.832119	−	0.533177i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	18.6429	+	18.6429i	1.16291	+	1.16291i	0.983835	+	0.179079i	$0.0573118\pi$
$257$	18.6429	+	18.6429i	1.16291	+	1.16291i	0.179079	+	0.983835i	$0.442688\pi$
$258$	−9.05420	+	4.61335i	−0.563690	+	0.287214i
$259$	0.221760	−	0.161118i	0.0137795	−	0.0100114i
$260$	2.03229	+	0.889980i	0.126037	+	0.0551942i
$261$	−2.19920	+	3.02695i	−0.136127	+	0.187363i
$262$	15.1494	+	2.39943i	0.935935	+	0.148238i
$263$	14.8801	+	2.35678i	0.917548	+	0.145325i	0.597309	−	0.802011i	$-0.296237\pi$
$263$	14.8801	+	2.35678i	0.917548	+	0.145325i	0.320239	+	0.947337i	$0.396237\pi$
$264$	1.99052	−	2.73972i	0.122508	−	0.168618i
$265$	19.3150	−	11.3096i	1.18651	−	0.694742i
$266$	−0.304586	+	0.462790i	−0.0186754	+	0.0283755i
$267$	0.932902	+	1.83092i	0.0570927	+	0.112051i
$268$	6.69553	−	6.69553i	0.408994	−	0.408994i
$269$	−0.687897	+	2.11713i	−0.0419418	+	0.129084i	−0.969835	−	0.243763i	$-0.921618\pi$
$269$	−0.687897	+	2.11713i	−0.0419418	+	0.129084i	0.927893	+	0.372846i	$0.121618\pi$
$270$	−3.16258	+	12.0984i	−0.192469	+	0.736286i
$271$	−5.36706	−	16.5181i	−0.326026	−	1.00340i	−0.970975	−	0.239179i	$-0.923122\pi$
$271$	−5.36706	−	16.5181i	−0.326026	−	1.00340i	0.644950	−	0.764225i	$-0.276878\pi$
$272$	−4.09471	−	2.08636i	−0.248278	−	0.126504i
$273$	−0.0302976	−	0.191292i	−0.00183370	−	0.0115775i
$274$	11.0179			0.665614
$275$	−2.16022	+	10.8117i	−0.130266	+	0.651969i
$276$		−	10.9119i		−	0.656822i
$277$	9.62292	−	1.52412i	0.578185	−	0.0915756i	0.139509	−	0.990221i	$-0.455448\pi$
$277$	9.62292	−	1.52412i	0.578185	−	0.0915756i	0.438676	+	0.898645i	$0.355448\pi$
$278$	12.5129	+	6.37566i	0.750476	+	0.382386i
$279$	−1.53228	−	4.71588i	−0.0917353	−	0.282332i
$280$	0.219775	−	0.180207i	0.0131341	−	0.0107694i
$281$	17.2886	+	5.61741i	1.03135	+	0.335107i	0.775325	−	0.631563i	$-0.217586\pi$
$281$	17.2886	+	5.61741i	1.03135	+	0.335107i	0.256028	+	0.966669i	$0.417586\pi$
$282$	5.75234	−	5.75234i	0.342547	−	0.342547i
$283$	3.06237	−	1.56036i	0.182039	−	0.0927536i	−0.360596	−	0.932722i	$-0.617427\pi$
$283$	3.06237	−	1.56036i	0.182039	−	0.0927536i	0.542635	+	0.839969i	$0.317427\pi$
$284$	−8.57442	+	6.22968i	−0.508798	+	0.369664i
$285$	−8.15245	−	12.5539i	−0.482910	−	0.743631i
$286$	1.77002	+	1.28600i	0.104664	+	0.0760425i
$287$	0.617036	+	0.0977289i	0.0364225	+	0.00576875i
$288$	−0.100343	+	0.633538i	−0.00591274	+	0.0373316i
$289$	−2.42138	+	3.33275i	−0.142434	+	0.196044i
$290$	−1.28401	+	12.9797i	−0.0753997	+	0.762194i
$291$	11.4219	−	8.29851i	0.669564	−	0.486467i
$292$	0.142839	+	0.280337i	0.00835901	+	0.0164055i
$293$	−13.8704	+	13.8704i	−0.810315	+	0.810315i	−0.984681	−	0.174366i	$-0.944212\pi$
$293$	−13.8704	+	13.8704i	−0.810315	+	0.810315i	0.174366	+	0.984681i	$0.444212\pi$
$294$	10.2006	+	3.31437i	0.594910	+	0.193298i
$295$	−0.504680	−	8.62072i	−0.0293836	−	0.501918i
$296$	0.666426	+	2.05105i	0.0387352	+	0.119215i
$297$	−5.59844	+	10.9876i	−0.324854	+	0.637563i
$298$	2.22244	−	0.351999i	0.128742	−	0.0203908i
$299$	7.04978			0.407699
$300$	2.07800	+	7.39230i	0.119973	+	0.426794i
$301$	−0.841009			−0.0484750
$302$	12.5937	−	1.99464i	0.724684	−	0.114779i
$303$	−2.60333	−	1.32646i	−0.149557	−	0.0762032i
$304$	−2.72234	−	3.40424i	−0.156137	−	0.195247i
$305$	−32.0022	+	12.5096i	−1.83244	+	0.716296i
$306$	2.80350	+	0.910913i	0.160266	+	0.0520734i
$307$	4.28551	+	4.28551i	0.244587	+	0.244587i	0.818745	−	0.574158i	$-0.194670\pi$
$307$	4.28551	+	4.28551i	0.244587	+	0.244587i	−0.574158	+	0.818745i	$0.694670\pi$
$308$	0.249724	−	0.127241i	0.0142293	−	0.00725021i
$309$	−1.54714	−	2.12945i	−0.0880137	−	0.121140i
$310$	−12.9163	−	11.4876i	−0.733598	−	0.652455i
$311$	−14.4819	−	10.5217i	−0.821191	−	0.596630i	0.0958627	−	0.995395i	$-0.469439\pi$
$311$	−14.4819	−	10.5217i	−0.821191	−	0.596630i	−0.917053	+	0.398765i	$0.869439\pi$
$312$	1.50502	+	0.238371i	0.0852047	+	0.0134951i
$313$	5.24742	+	0.831110i	0.296602	+	0.0469771i	0.302962	−	0.953003i	$-0.402024\pi$
$313$	5.24742	+	0.831110i	0.296602	+	0.0469771i	−0.00636010	+	0.999980i	$0.502024\pi$
$314$	−19.2075	−	13.9551i	−1.08394	−	0.787530i
$315$	−0.121153	+	0.136221i	−0.00682622	+	0.00767517i
$316$	−3.74581	−	5.15567i	−0.210718	−	0.290029i
$317$	−0.149789	+	0.0763213i	−0.00841299	+	0.00428663i	−0.458192	−	0.888853i	$-0.651503\pi$
$317$	−0.149789	+	0.0763213i	−0.00841299	+	0.00428663i	0.449779	+	0.893140i	$0.351503\pi$
$318$	10.8701	−	10.8701i	0.609563	−	0.609563i
$319$	−3.97466	+	12.2328i	−0.222538	+	0.684903i
$320$	0.814087	+	2.08261i	0.0455089	+	0.116421i
$321$	−2.16865	−	6.67443i	−0.121042	−	0.372530i
$322$	0.409997	−	0.804664i	0.0228482	−	0.0448422i
$323$	−17.4090	+	9.90942i	−0.968664	+	0.551375i
$324$			6.66426i			0.370236i
$325$	−4.77587	+	1.34251i	−0.264918	+	0.0744692i
$326$		−	17.5598i		−	0.972550i
$327$	−4.63512	+	0.734131i	−0.256323	+	0.0405975i
$328$	−2.23142	+	4.37941i	−0.123210	+	0.241813i
$329$	0.640320	−	0.208053i	0.0353020	−	0.0114703i
$330$	0.442550	+	7.55944i	0.0243616	+	0.416134i
$331$	−16.4299	−	5.33840i	−0.903069	−	0.293425i	−0.179566	−	0.983746i	$-0.557469\pi$
$331$	−16.4299	−	5.33840i	−0.903069	−	0.293425i	−0.723503	+	0.690321i	$0.757469\pi$
$332$	−9.26681	+	9.26681i	−0.508583	+	0.508583i
$333$	−0.628014	−	1.23255i	−0.0344150	−	0.0675432i
$334$	−12.1621	−	16.7397i	−0.665480	−	0.915955i
$335$	−2.08437	+	21.0703i	−0.113881	+	1.15119i
$336$	0.114735	−	0.157920i	0.00625933	−	0.00861523i
$337$	24.7354	+	3.91770i	1.34742	+	0.213411i	0.788104	−	0.615542i	$-0.211063\pi$
$337$	24.7354	+	3.91770i	1.34742	+	0.213411i	0.559319	+	0.828953i	$0.311063\pi$
$338$	1.87965	−	11.8676i	0.102239	−	0.645513i
$339$	−14.9999	+	20.6455i	−0.814681	+	1.12131i
$340$	10.0383	−	2.19795i	0.544401	−	0.119201i
$341$	−10.0195	−	13.7907i	−0.542586	−	0.746806i
$342$	2.06630	+	1.88355i	0.111733	+	0.101851i
$343$	1.25680	+	1.25680i	0.0678609	+	0.0678609i
$344$	2.04469	−	6.29291i	0.110242	−	0.339291i
$345$	15.4710	+	18.8680i	0.832931	+	1.01582i
$346$	−0.398371	−	1.22606i	−0.0214165	−	0.0659133i
$347$	20.1166	+	10.2499i	1.07991	+	0.550244i	0.901088	−	0.433637i	$-0.142770\pi$
$347$	20.1166	+	10.2499i	1.07991	+	0.550244i	0.178826	+	0.983881i	$0.442770\pi$
$348$	1.40136	+	8.84786i	0.0751209	+	0.474295i
$349$		−	11.8154i		−	0.632466i	−0.948682	−	0.316233i	$-0.897582\pi$
$349$		−	11.8154i		−	0.632466i	0.948682	−	0.316233i	$-0.102418\pi$
$350$	−0.124517	+	0.623196i	−0.00665573	+	0.0333112i
$351$	−5.54873			−0.296169
$352$	0.344950	+	2.17793i	0.0183859	+	0.116084i
$353$	3.75162	−	7.36298i	0.199679	−	0.391892i	−0.769354	−	0.638822i	$-0.779422\pi$
$353$	3.75162	−	7.36298i	0.199679	−	0.391892i	0.969033	+	0.246930i	$0.0794219\pi$
$354$	−1.83277	−	5.64068i	−0.0974106	−	0.299799i
$355$	5.99367	−	22.9287i	0.318111	−	1.21693i
$356$	−1.27254	−	0.413473i	−0.0674445	−	0.0219140i
$357$	−0.634316	−	0.634316i	−0.0335716	−	0.0335716i
$358$	17.1320	−	8.72918i	0.905453	−	0.461351i
$359$	7.05511	+	9.71052i	0.372354	+	0.512502i	0.953539	−	0.301270i	$-0.0974106\pi$
$359$	7.05511	+	9.71052i	0.372354	+	0.512502i	−0.581185	+	0.813772i	$0.697411\pi$
$360$	−0.724730	−	1.23772i	−0.0381966	−	0.0652338i
$361$	−18.9188	+	1.75442i	−0.995728	+	0.0923378i
$362$	−3.23423	+	20.4201i	−0.169988	+	1.07326i
$363$	1.47454	−	9.30989i	0.0773934	−	0.488643i
$364$	0.102026	+	0.0741261i	0.00534760	+	0.00388526i
$365$	−0.644447	−	0.282216i	−0.0337319	−	0.0147719i
$366$	−19.0921	+	13.8712i	−0.997959	+	0.725059i
$367$	−11.9163	−	23.3871i	−0.622028	−	1.22080i	−0.960094	−	0.279676i	$-0.909773\pi$
$367$	−11.9163	−	23.3871i	−0.622028	−	1.22080i	0.338066	−	0.941122i	$-0.390227\pi$
$368$	5.02416	+	5.02416i	0.261902	+	0.261902i
$369$	0.974250	−	2.99843i	0.0507174	−	0.156092i
$370$	−4.06031	−	2.60163i	−0.211086	−	0.135252i
$371$	1.21000	−	0.393152i	0.0628200	−	0.0204114i
$372$	−10.5781	−	5.38982i	−0.548450	−	0.279449i
$373$	−21.6451	+	3.42825i	−1.12074	+	0.177508i	−0.689190	−	0.724581i	$-0.742033\pi$
$373$	−21.6451	+	3.42825i	−1.12074	+	0.177508i	−0.431551	+	0.902089i	$0.642033\pi$
$374$	10.1336			0.523998
$375$	−14.0739	−	9.83591i	−0.726774	−	0.507924i
$376$			5.29707i			0.273175i
$377$	−5.71625	+	0.905365i	−0.294402	+	0.0466287i
$378$	−0.322700	+	0.633334i	−0.0165979	+	0.0325752i
$379$	1.92675	+	5.92991i	0.0989703	+	0.304599i	0.988268	−	0.152729i	$-0.0488063\pi$
$379$	1.92675	+	5.92991i	0.0989703	+	0.304599i	−0.889298	+	0.457329i	$0.848806\pi$
$380$	9.53379	+	2.02656i	0.489073	+	0.103960i
$381$	0.454560	−	1.39899i	0.0232878	−	0.0716725i
$382$	13.5587	+	13.5587i	0.693722	+	0.693722i
$383$	−2.97856	−	5.84575i	−0.152197	−	0.298704i	0.802301	−	0.596919i	$-0.203609\pi$
$383$	−2.97856	−	5.84575i	−0.152197	−	0.298704i	−0.954499	+	0.298215i	$0.903609\pi$
$384$	0.902698	+	1.24246i	0.0460656	+	0.0634039i
$385$	−0.251398	+	0.574073i	−0.0128124	+	0.0292575i
$386$	13.6820	+	9.94054i	0.696394	+	0.505960i
$387$	−0.663943	+	4.19197i	−0.0337501	+	0.213090i
$388$	−1.43810	+	9.07982i	−0.0730086	+	0.460958i
$389$	−20.8756	+	28.7328i	−1.05843	+	1.45681i	−0.177174	+	0.984180i	$0.556695\pi$
$389$	−20.8756	+	28.7328i	−1.05843	+	1.45681i	−0.881261	+	0.472631i	$0.843305\pi$
$390$	−2.94030	+	1.72165i	−0.148888	+	0.0871790i
$391$	26.4167	−	19.1928i	1.33595	−	0.970623i
$392$	−6.22265	+	3.17060i	−0.314291	+	0.160139i
$393$	−16.6566	+	16.6566i	−0.840212	+	0.840212i
$394$	4.83649	−	14.8852i	0.243659	−	0.749905i
$395$	13.7867	+	3.60390i	0.693682	+	0.181332i
$396$	−0.437078	−	1.34519i	−0.0219640	−	0.0675982i
$397$	−11.4898	−	5.85435i	−0.576657	−	0.293822i	0.141235	−	0.989976i	$-0.454893\pi$
$397$	−11.4898	−	5.85435i	−0.576657	−	0.293822i	−0.717892	+	0.696155i	$0.754893\pi$
$398$	−4.43530	+	0.702482i	−0.222321	+	0.0352122i
$399$	−0.300048	−	0.796195i	−0.0150212	−	0.0398596i
$400$	−4.36038	−	2.44685i	−0.218019	−	0.122342i
$401$		−	3.60920i		−	0.180235i	−0.995931	−	0.0901173i	$-0.971276\pi$
$401$		−	3.60920i		−	0.180235i	0.995931	−	0.0901173i	$-0.0287242\pi$
$402$	2.27487	+	14.3629i	0.113460	+	0.716359i
$403$	3.48215	−	6.83410i	0.173458	−	0.340431i
$404$	1.80938	−	0.587904i	0.0900201	−	0.0292493i
$405$	−9.44861	−	11.5232i	−0.469505	−	0.572595i
$406$	−0.229104	+	0.705108i	−0.0113702	+	0.0349939i
$407$	−3.36263	−	3.36263i	−0.166679	−	0.166679i
$408$	6.28849	−	3.20415i	0.311327	−	0.158629i
$409$	−6.78847	+	4.93211i	−0.335668	+	0.243877i	−0.742832	−	0.669478i	$-0.766518\pi$
$409$	−6.78847	+	4.93211i	−0.335668	+	0.243877i	0.407164	+	0.913355i	$0.366518\pi$
$410$	−2.35077	−	10.7362i	−0.116096	−	0.530224i
$411$	−9.94581	+	13.6892i	−0.490591	+	0.675240i
$412$	1.69280	+	0.268114i	0.0833985	+	0.0132090i
$413$	0.0767872	−	0.484816i	0.00377845	−	0.0238562i
$414$	−3.68713	−	2.67886i	−0.181213	−	0.131659i
$415$	2.88483	−	29.1619i	0.141611	−	1.43150i
$416$	−0.802703	+	0.583198i	−0.0393557	+	0.0285936i
$417$	−19.2169	+	9.79149i	−0.941055	+	0.479491i
$418$	8.75662	+	3.96314i	0.428300	+	0.193844i
$419$	17.8299	+	5.79329i	0.871048	+	0.283021i	0.710236	−	0.703964i	$-0.248588\pi$
$419$	17.8299	+	5.79329i	0.871048	+	0.283021i	0.160813	+	0.986985i	$0.448588\pi$
$420$	0.0255090	+	0.435734i	0.00124471	+	0.0212616i
$421$	−20.3836	+	6.62304i	−0.993437	+	0.322787i	−0.760240	−	0.649642i	$-0.774919\pi$
$421$	−20.3836	+	6.62304i	−0.993437	+	0.322787i	−0.233197	+	0.972430i	$0.574919\pi$
$422$	−3.78272	−	1.92739i	−0.184140	−	0.0938240i
$423$	−0.531521	−	3.35589i	−0.0258435	−	0.163169i
$424$			10.0097i			0.486116i
$425$	−14.2410	+	18.0328i	−0.690790	+	0.874719i
$426$		−	16.2769i		−	0.788617i
$427$	−1.92906	+	0.305534i	−0.0933539	+	0.0147858i
$428$	4.07160	+	2.07458i	0.196808	+	0.100279i
$429$	−3.19559	+	1.03831i	−0.154285	+	0.0501301i
$430$	5.38662	+	13.7801i	0.259766	+	0.664537i
$431$	−22.4950	−	7.30908i	−1.08355	−	0.352066i	−0.287797	−	0.957691i	$-0.592923\pi$
$431$	−22.4950	−	7.30908i	−1.08355	−	0.352066i	−0.795750	+	0.605625i	$0.792923\pi$
$432$	−3.95441	−	3.95441i	−0.190257	−	0.190257i
$433$	−11.9428	−	23.4391i	−0.573934	−	1.12641i	−0.977397	−	0.211413i	$-0.932193\pi$
$433$	−11.9428	−	23.4391i	−0.573934	−	1.12641i	0.403463	−	0.914996i	$-0.367807\pi$
$434$	−0.577534	−	0.794907i	−0.0277225	−	0.0381568i
$435$	−14.9676	−	13.3121i	−0.717644	−	0.638265i
$436$	1.79612	−	2.47215i	0.0860186	−	0.118394i
$437$	30.3331	−	6.25356i	1.45103	−	0.299148i
$438$	−0.477247	−	0.0755885i	−0.0228037	−	0.00361176i
$439$	−1.14672	−	0.833139i	−0.0547298	−	0.0397635i	0.560084	−	0.828436i	$-0.310769\pi$
$439$	−1.14672	−	0.833139i	−0.0547298	−	0.0397635i	−0.614814	+	0.788672i	$0.710769\pi$
$440$	−3.68434	−	3.27681i	−0.175644	−	0.156216i
$441$	3.62414	−	2.63309i	0.172578	−	0.125385i
$442$	2.07007	+	4.06275i	0.0984634	+	0.193245i
$443$	−17.1900	−	17.1900i	−0.816722	−	0.816722i	0.168909	−	0.985632i	$-0.445975\pi$
$443$	−17.1900	−	17.1900i	−0.816722	−	0.816722i	−0.985632	+	0.168909i	$0.945975\pi$
$444$	−3.14992	−	1.02347i	−0.149489	−	0.0485719i
$445$	2.78659	−	1.08927i	0.132097	−	0.0516364i
$446$	−7.03937	−	21.6650i	−0.333324	−	1.02587i
$447$	−1.56884	+	3.07903i	−0.0742038	+	0.145633i
$448$	0.0198833	+	0.125538i	0.000939396	+	0.00593111i
$449$	−11.0067			−0.519439			−0.259720	−	0.965684i	$-0.583630\pi$
$449$	−11.0067			−0.519439			−0.259720	+	0.965684i	$0.583630\pi$
$450$	3.00799	+	1.11264i	0.141798	+	0.0524503i
$451$		−	10.8382i		−	0.510353i
$452$	−2.59942	−	16.4121i	−0.122267	−	0.771961i
$453$	−8.89003	+	17.4477i	−0.417690	+	0.819763i
$454$	−13.6562	+	4.43718i	−0.640919	+	0.208247i
$455$	−0.281510	+	0.0164804i	−0.0131974	+	0.000772611i
$456$	6.68708	−	0.309396i	0.313151	−	0.0144888i
$457$	19.7542	−	19.7542i	0.924064	−	0.924064i	−0.0732492	−	0.997314i	$-0.523337\pi$
$457$	19.7542	−	19.7542i	0.924064	−	0.924064i	0.997314	+	0.0732492i	$0.0233369\pi$
$458$	9.86552	+	19.3622i	0.460986	+	0.904735i
$459$	−20.7920	+	15.1063i	−0.970487	+	0.705100i
$460$	−15.8106	−	1.56406i	−0.737174	−	0.0729246i
$461$	−27.0153	−	19.6278i	−1.25823	−	0.914157i	−0.259560	−	0.965727i	$-0.583578\pi$
$461$	−27.0153	−	19.6278i	−1.25823	−	0.914157i	−0.998669	+	0.0515694i	$0.983578\pi$
$462$	−0.0673342	+	0.425131i	−0.00313267	+	0.0197789i
$463$	−20.2492	−	3.20715i	−0.941058	−	0.149049i	−0.332987	−	0.942931i	$-0.608057\pi$
$463$	−20.2492	−	3.20715i	−0.941058	−	0.149049i	−0.608071	+	0.793882i	$0.708057\pi$
$464$	−4.71902	−	3.42857i	−0.219075	−	0.159167i
$465$	25.9325	−	5.67810i	1.20259	−	0.263316i
$466$	0.913478	+	1.25729i	0.0423160	+	0.0582430i
$467$	−6.86845	−	13.4801i	−0.317834	−	0.623785i	0.675718	−	0.737160i	$-0.263834\pi$
$467$	−6.86845	−	13.4801i	−0.317834	−	0.623785i	−0.993552	+	0.113375i	$0.963834\pi$
$468$	0.450023	−	0.450023i	0.0208023	−	0.0208023i
$469$	−0.371910	+	1.14462i	−0.0171732	+	0.0528536i
$470$	−7.51021	−	9.15923i	−0.346420	−	0.422484i
$471$	34.6772	−	11.2673i	1.59784	−	0.519169i
$472$	3.44098	+	1.75327i	0.158384	+	0.0807007i
$473$	2.28245	+	14.4108i	0.104947	+	0.662611i
$474$	9.78704			0.449533
$475$	−19.3583	+	10.0129i	−0.888217	+	0.459423i
$476$	0.584113			0.0267728
$477$	−1.00440	−	6.34156i	−0.0459885	−	0.290360i
$478$	−18.2055	−	9.27617i	−0.832701	−	0.424282i
$479$	−22.2423	+	7.22696i	−1.01628	+	0.330208i	−0.769351	−	0.638826i	$-0.779420\pi$
$479$	−22.2423	+	7.22696i	−1.01628	+	0.330208i	−0.246926	+	0.969034i	$0.579420\pi$
$480$	−3.32243	−	0.868499i	−0.151647	−	0.0396414i
$481$	0.661225	−	2.03504i	0.0301493	−	0.0927899i
$482$	15.1228	−	15.1228i	0.688826	−	0.688826i
$483$	0.629657	+	1.23577i	0.0286504	+	0.0562296i
$484$	3.60761	+	4.96545i	0.163982	+	0.225702i
$485$	−10.3868	−	17.7390i	−0.471639	−	0.805485i
$486$	5.29293	+	3.84554i	0.240092	+	0.174437i
$487$	31.2019	+	4.94189i	1.41389	+	0.223938i	0.816192	−	0.577781i	$-0.196081\pi$
$487$	31.2019	+	4.94189i	1.41389	+	0.223938i	0.597700	+	0.801720i	$0.296081\pi$
$488$	2.40383	−	15.1772i	0.108816	−	0.687039i
$489$	21.8174	+	15.8512i	0.986615	+	0.716818i
$490$	6.26437	−	14.3048i	0.282995	−	0.646226i
$491$	−19.9677	+	14.5074i	−0.901130	+	0.654710i	−0.938756	−	0.344582i	$-0.888021\pi$
$491$	−19.9677	+	14.5074i	−0.901130	+	0.654710i	0.0376257	+	0.999292i	$0.488021\pi$
$492$	−3.42693	−	6.72574i	−0.154498	−	0.303220i
$493$	−18.9549	+	18.9549i	−0.853685	+	0.853685i
$494$	0.199888	+	4.32026i	0.00899341	+	0.194378i
$495$	2.66297	+	1.70629i	0.119692	+	0.0766920i
$496$	7.35207	−	2.38883i	0.330118	−	0.107262i
$497$	0.611574	−	1.20028i	0.0274329	−	0.0538400i
$498$	−3.14849	−	19.8788i	−0.141087	−	0.890789i
$499$		−	41.3260i		−	1.85000i	−0.379963	−	0.925002i	$-0.624063\pi$
$499$		−	41.3260i		−	1.85000i	0.379963	−	0.925002i	$-0.375937\pi$
$500$	11.0087	−	1.95130i	0.492326	−	0.0872646i
$501$	31.7770			1.41969
$502$	−1.56284	−	9.86739i	−0.0697530	−	0.440403i
$503$	7.57109	−	14.8591i	0.337578	−	0.662535i	−0.658347	−	0.752714i	$-0.728744\pi$
$503$	7.57109	−	14.8591i	0.337578	−	0.662535i	0.995926	+	0.0901795i	$0.0287441\pi$
$504$	−0.0251936	−	0.0775379i	−0.00112221	−	0.00345381i
$505$	−2.29509	+	3.58190i	−0.102130	+	0.159393i
$506$	−14.9008	−	4.84155i	−0.662420	−	0.215233i
$507$	13.0483	+	13.0483i	0.579493	+	0.579493i
$508$	0.434842	+	0.853425i	0.0192930	+	0.0378646i
$509$	11.7500	−	8.53686i	0.520809	−	0.378390i	−0.296100	−	0.955157i	$-0.595686\pi$
$509$	11.7500	−	8.53686i	0.520809	−	0.378390i	0.816908	+	0.576767i	$0.195686\pi$
$510$	−6.33066	+	14.4562i	−0.280326	+	0.640131i
$511$	−0.0323528	−	0.0235057i	−0.00143120	−	0.00103983i
$512$	−0.987688	−	0.156434i	−0.0436501	−	0.00691349i
$513$	−23.8745	+	4.92204i	−1.05409	+	0.217313i
$514$	15.4970	−	21.3298i	0.683544	−	0.940817i
$515$	−3.30718	+	1.93647i	−0.145732	+	0.0853310i
$516$	5.97294	+	8.22105i	0.262944	+	0.361911i
$517$	−5.30281	−	10.4074i	−0.233217	−	0.457715i
$518$	−0.193825	−	0.193825i	−0.00851619	−	0.00851619i
$519$	1.88293	+	0.611803i	0.0826517	+	0.0268552i
$520$	0.561103	−	2.14649i	0.0246060	−	0.0941298i
$521$	−36.6920	+	11.9220i	−1.60751	+	0.522311i	−0.968949	−	0.247262i	$-0.920469\pi$
$521$	−36.6920	+	11.9220i	−1.60751	+	0.522311i	−0.638559	+	0.769573i	$0.720469\pi$
$522$	3.33371	+	1.69861i	0.145913	+	0.0743462i
$523$	34.1745	−	5.41270i	1.49435	−	0.236681i	0.644863	−	0.764298i	$-0.276914\pi$
$523$	34.1745	−	5.41270i	1.49435	−	0.236681i	0.849482	+	0.527617i	$0.176914\pi$
$524$		−	15.3383i		−	0.670055i
$525$	−0.661893	−	0.717266i	−0.0288874	−	0.0313040i
$526$		−	15.0656i		−	0.656892i
$527$	−5.55748	−	35.0885i	−0.242088	−	1.52848i
$528$	−3.01737	−	1.53743i	−0.131314	−	0.0669079i
$529$	−26.1392	+	8.49313i	−1.13649	+	0.369267i
$530$	−14.1919	−	17.3080i	−0.616455	−	0.751811i
$531$	−2.35592	−	0.765485i	−0.102238	−	0.0332192i
$532$	0.504740	+	0.228440i	0.0218833	+	0.00990411i
$533$	4.34523	−	2.21401i	0.188213	−	0.0958993i
$534$	1.66244	−	1.20784i	0.0719410	−	0.0522682i
$535$	−9.98160	+	2.18554i	−0.431542	+	0.0944893i
$536$	−7.66050	−	5.56568i	−0.330883	−	0.240401i
$537$	−4.61937	+	29.1656i	−0.199341	+	1.25859i
$538$	2.19867	+	0.348236i	0.0947916	+	0.0150135i
$539$	9.05185	−	12.4588i	0.389891	−	0.536638i
$540$	12.4442	+	1.23104i	0.535513	+	0.0529754i
$541$	21.3349	−	15.5007i	0.917259	−	0.666427i	−0.0255815	−	0.999673i	$-0.508144\pi$
$541$	21.3349	−	15.5007i	0.917259	−	0.666427i	0.942840	+	0.333245i	$0.108144\pi$
$542$	−15.4752	+	7.88499i	−0.664715	+	0.338689i
$543$	−22.4516	−	22.4516i	−0.963492	−	0.963492i
$544$	−1.42012	+	4.37067i	−0.0608870	+	0.187391i
$545$	0.399329	+	6.82117i	0.0171054	+	0.292187i
$546$	−0.184197	+	0.0598492i	−0.00788290	+	0.00256131i
$547$	−0.789887	+	1.55024i	−0.0337731	+	0.0662835i	−0.907277	−	0.420535i	$-0.861843\pi$
$547$	−0.789887	+	1.55024i	−0.0337731	+	0.0662835i	0.873503	+	0.486818i	$0.161843\pi$
$548$	−1.72357	−	10.8822i	−0.0736275	−	0.464865i
$549$			9.85653i			0.420667i
$550$	11.0165	+	0.442307i	0.469746	+	0.0188600i
$551$	−23.7922	+	8.96616i	−1.01358	+	0.381971i
$552$	−10.7776	+	1.70700i	−0.458725	+	0.0726550i
$553$	0.721711	+	0.367730i	0.0306903	+	0.0156375i
$554$	−3.01071	−	9.26602i	−0.127913	−	0.393676i
$555$	6.89766	−	2.69628i	0.292789	−	0.114451i
$556$	4.33971	−	13.3562i	0.184045	−	0.566431i
$557$	−27.2847	+	27.2847i	−1.15609	+	1.15609i	−0.170781	+	0.985309i	$0.554629\pi$
$557$	−27.2847	+	27.2847i	−1.15609	+	1.15609i	−0.985309	+	0.170781i	$0.945371\pi$
$558$	−4.41812	+	2.25114i	−0.187034	+	0.0952984i
$559$	−5.31129	+	3.85888i	−0.224644	+	0.163213i
$560$	−0.212369	−	0.188879i	−0.00897422	−	0.00798158i
$561$	−9.14762	+	12.5906i	−0.386213	+	0.531577i
$562$	2.84372	−	17.9545i	0.119955	−	0.757366i
$563$	1.73273	−	10.9400i	0.0730260	−	0.461068i	−0.923894	−	0.382648i	$-0.875012\pi$
$563$	1.73273	−	10.9400i	0.0730260	−	0.461068i	0.996920	−	0.0784203i	$-0.0249876\pi$
$564$	−6.58138	−	4.78165i	−0.277126	−	0.201344i
$565$	27.7639	+	24.6929i	1.16804	+	1.03884i
$566$	−2.02021	−	2.78058i	−0.0849156	−	0.116876i
$567$	−0.384551	−	0.754723i	−0.0161496	−	0.0316954i
$568$	7.49432	+	7.49432i	0.314455	+	0.314455i
$569$	6.29441	−	19.3722i	0.263875	−	0.812125i	−0.728075	−	0.685498i	$-0.759585\pi$
$569$	6.29441	−	19.3722i	0.263875	−	0.812125i	0.991950	−	0.126627i	$-0.0404153\pi$
$570$	−11.1240	+	10.0160i	−0.465935	+	0.419522i
$571$	0.724076	+	2.22848i	0.0303017	+	0.0932589i	0.965064	−	0.262016i	$-0.0843873\pi$
$571$	0.724076	+	2.22848i	0.0303017	+	0.0932589i	−0.934762	+	0.355275i	$0.884387\pi$
$572$	0.993271	−	1.94940i	0.0415307	−	0.0815087i
$573$	−29.0855	+	4.60668i	−1.21506	+	0.192447i
$574$		−	0.624727i		−	0.0260756i
$575$	29.5559	−	19.7119i	1.23256	−	0.822044i
$576$	0.641435			0.0267265
$577$	8.12066	−	1.28619i	0.338068	−	0.0535446i	0.0149073	−	0.999889i	$-0.495255\pi$
$577$	8.12066	−	1.28619i	0.338068	−	0.0535446i	0.323160	+	0.946344i	$0.395255\pi$
$578$	3.67051	+	1.87022i	0.152673	+	0.0777907i
$579$	−24.7014	+	8.02597i	−1.02656	+	0.333548i
$580$	13.0208	−	0.762269i	0.540658	−	0.0316515i
$581$	0.514734	−	1.58419i	0.0213548	−	0.0657232i
$582$	−9.98312	−	9.98312i	−0.413814	−	0.413814i
$583$	−10.0206	−	19.6665i	−0.415011	−	0.814505i
$584$	0.254541	−	0.184935i	0.0105330	−	0.00765264i
$585$	−0.140096	+	1.41619i	−0.00579224	+	0.0585521i
$586$	15.8694	+	11.5298i	0.655558	+	0.476291i
$587$	−1.98091	+	12.5070i	−0.0817611	+	0.516219i	0.912486	+	0.409108i	$0.134160\pi$
$587$	−1.98091	+	12.5070i	−0.0817611	+	0.516219i	−0.994247	+	0.107111i	$0.965840\pi$
$588$	1.67784	−	10.5935i	0.0691930	−	0.436868i
$589$	8.92040	−	32.4939i	0.367559	−	1.33889i
$590$	−8.43563	+	1.84704i	−0.347290	+	0.0760416i
$591$	14.1283	+	19.4460i	0.581161	+	0.799900i
$592$	1.92155	−	0.979076i	0.0789750	−	0.0402398i
$593$	−9.53591	−	9.53591i	−0.391593	−	0.391593i	0.483662	−	0.875255i	$-0.339306\pi$
$593$	−9.53591	−	9.53591i	−0.391593	−	0.391593i	−0.875255	+	0.483662i	$0.839306\pi$
$594$	11.7281	+	3.81068i	0.481209	+	0.156354i
$595$	−1.01000	+	0.828159i	−0.0414059	+	0.0339512i
$596$	−0.695331	−	2.14001i	−0.0284819	−	0.0876582i
$597$	3.13093	−	6.14480i	0.128140	−	0.251490i
$598$	−1.10283	−	6.96298i	−0.0450980	−	0.284738i
$599$	47.4944			1.94057			0.970284	−	0.241971i	$-0.0777938\pi$
$599$	47.4944			1.94057			0.970284	+	0.241971i	$0.0777938\pi$
$600$	6.97621	−	3.20882i	0.284803	−	0.131000i
$601$			24.1963i			0.986988i	0.869749	+	0.493494i	$0.164281\pi$
$601$			24.1963i			0.986988i	−0.869749	+	0.493494i	$0.835719\pi$
$602$	0.131563	+	0.830655i	0.00536210	+	0.0338550i
$603$	5.41170	+	2.75740i	0.220381	+	0.112290i
$604$	−3.94017	−	12.1266i	−0.160323	−	0.493424i
$605$	−13.2780	−	3.47093i	−0.539828	−	0.141113i
$606$	−0.902881	+	2.77878i	−0.0366770	+	0.112880i
$607$	7.83336	+	7.83336i	0.317946	+	0.317946i	0.847978	−	0.530032i	$-0.177820\pi$
$607$	7.83336	+	7.83336i	0.317946	+	0.317946i	−0.530032	+	0.847978i	$0.677820\pi$
$608$	−2.93646	+	3.22137i	−0.119089	+	0.130644i
$609$	−0.669256	−	0.921151i	−0.0271196	−	0.0373269i
$610$	17.3618	+	29.6512i	0.702959	+	1.20054i
$611$	3.08924	−	4.25197i	0.124977	−	0.172016i
$612$	0.461134	−	2.91148i	0.0186402	−	0.117690i
$613$	−12.8474	−	2.03484i	−0.518904	−	0.0821862i	−0.108511	−	0.994095i	$-0.534608\pi$
$613$	−12.8474	−	2.03484i	−0.518904	−	0.0821862i	−0.410392	+	0.911909i	$0.634608\pi$
$614$	3.56235	−	4.90315i	0.143765	−	0.197875i
$615$	15.4613	+	6.77083i	0.623461	+	0.273026i
$616$	−0.164740	−	0.226744i	−0.00663754	−	0.00913580i
$617$	0.995607	+	1.95399i	0.0400816	+	0.0786646i	0.910179	−	0.414216i	$-0.135944\pi$
$617$	0.995607	+	1.95399i	0.0400816	+	0.0786646i	−0.870097	+	0.492880i	$0.835944\pi$
$618$	−1.86121	+	1.86121i	−0.0748689	+	0.0748689i
$619$	−0.537661	−	0.174697i	−0.0216104	−	0.00702165i	0.298192	−	0.954506i	$-0.403616\pi$
$619$	−0.537661	−	0.174697i	−0.0216104	−	0.00702165i	−0.319802	+	0.947484i	$0.603616\pi$
$620$	−9.32566	+	14.5544i	−0.374527	+	0.584517i
$621$	37.7904	−	12.2788i	1.51648	−	0.492733i
$622$	−8.12668	+	15.9495i	−0.325850	+	0.639517i
$623$	0.167973	−	0.0266044i	0.00672971	−	0.00106588i
$624$		−	1.52378i		−	0.0609998i
$625$	−16.2688	+	18.9823i	−0.650752	+	0.759290i
$626$		−	5.31283i		−	0.212343i
$627$	−12.8286	+	7.30221i	−0.512326	+	0.291622i
$628$	−10.7785	+	21.1541i	−0.430111	+	0.844140i
$629$	−3.06263	−	9.42580i	−0.122115	−	0.375831i
$630$	0.153496	+	0.0983522i	0.00611544	+	0.00391845i
$631$	0.135285	−	0.416364i	0.00538561	−	0.0165752i	−0.948328	−	0.317293i	$-0.897226\pi$
$631$	0.135285	−	0.416364i	0.00538561	−	0.0165752i	0.953713	+	0.300718i	$0.0972262\pi$
$632$	−4.50622	+	4.50622i	−0.179248	+	0.179248i
$633$	5.80936	−	2.96002i	0.230901	−	0.117650i
$634$	0.0988138	+	0.136006i	0.00392440	+	0.00540147i
$635$	−1.96188	−	0.859147i	−0.0778549	−	0.0340942i
$636$	−12.4367	−	9.03578i	−0.493147	−	0.358292i
$637$	6.84403	+	1.08399i	0.271170	+	0.0429491i
$638$	12.7039	+	2.01210i	0.502953	+	0.0796600i
$639$	−5.49994	−	3.99594i	−0.217574	−	0.158077i
$640$	1.92962	−	1.12986i	0.0762748	−	0.0446615i
$641$	−6.15880	−	8.47686i	−0.243258	−	0.334816i	0.669878	−	0.742471i	$-0.266346\pi$
$641$	−6.15880	−	8.47686i	−0.243258	−	0.334816i	−0.913136	+	0.407655i	$0.866346\pi$
$642$	−6.25300	+	3.18606i	−0.246786	+	0.125744i
$643$	−12.6359	−	12.6359i	−0.498312	−	0.498312i	0.412600	−	0.910912i	$-0.364621\pi$
$643$	−12.6359	−	12.6359i	−0.498312	−	0.498312i	−0.910912	+	0.412600i	$0.864621\pi$
$644$	−0.858895	−	0.279072i	−0.0338452	−	0.0109970i
$645$	−21.9837	−	5.74665i	−0.865608	−	0.226274i
$646$	12.5108	+	15.6445i	0.492231	+	0.615525i
$647$	11.0589	+	5.63480i	0.434771	+	0.221527i	0.657657	−	0.753318i	$-0.271548\pi$
$647$	11.0589	+	5.63480i	0.434771	+	0.221527i	−0.222886	+	0.974845i	$0.571548\pi$
$648$	6.58221	−	1.04252i	0.258574	−	0.0409540i
$649$	−8.51580			−0.334274
$650$	2.07309	+	4.50706i	0.0813135	+	0.176781i
$651$	1.50898			0.0591415
$652$	−17.3436	+	2.74696i	−0.679230	+	0.107579i
$653$	−6.82019	+	13.3854i	−0.266895	+	0.523810i	−0.985092	−	0.172029i	$-0.944968\pi$
$653$	−6.82019	+	13.3854i	−0.266895	+	0.523810i	0.718197	+	0.695840i	$0.244968\pi$
$654$	1.45018	+	4.46321i	0.0567067	+	0.174525i
$655$	21.7467	+	26.5216i	0.849713	+	1.03628i
$656$	4.67457	+	1.51886i	0.182511	+	0.0593015i
$657$	−0.142704	+	0.142704i	−0.00556742	+	0.00556742i
$658$	−0.305659	−	0.599890i	−0.0119158	−	0.0233862i
$659$	24.6493	−	17.9087i	0.960199	−	0.697625i	0.00700197	−	0.999975i	$-0.497771\pi$
$659$	24.6493	−	17.9087i	0.960199	−	0.697625i	0.953197	+	0.302350i	$0.0977712\pi$
$660$	7.39714	−	1.61966i	0.287933	−	0.0630451i
$661$	11.4418	−	15.7482i	0.445033	−	0.612535i	−0.526288	−	0.850306i	$-0.676417\pi$
$661$	11.4418	−	15.7482i	0.445033	−	0.612535i	0.971321	+	0.237771i	$0.0764168\pi$
$662$	−2.70247	+	17.0627i	−0.105035	+	0.663162i
$663$	−6.91644	−	1.09546i	−0.268612	−	0.0425440i
$664$	10.6024	+	7.70308i	0.411452	+	0.298937i
$665$	−1.19664	+	0.320626i	−0.0464035	+	0.0124333i
$666$	−1.11913	+	0.813095i	−0.0433654	+	0.0315068i
$667$	36.9278	−	18.8157i	1.42985	−	0.728545i
$668$	−14.6310	+	14.6310i	−0.566091	+	0.566091i
$669$	33.2722	+	10.8108i	1.28638	+	0.417970i
$670$	21.1369	−	1.23741i	0.816591	−	0.0478054i
$671$	10.4707	+	32.2256i	0.404219	+	1.24406i
$672$	−0.173924	−	0.0886188i	−0.00670927	−	0.00341854i
$673$	−8.14976	+	1.29080i	−0.314150	+	0.0497565i	−0.311519	−	0.950240i	$-0.600838\pi$
$673$	−8.14976	+	1.29080i	−0.314150	+	0.0497565i	−0.00263155	+	0.999997i	$0.500838\pi$
$674$		−	25.0437i		−	0.964648i
$675$	−23.2628	+	15.5148i	−0.895385	+	0.597166i
$676$	−12.0155			−0.462136
$677$	−5.97936	−	37.7522i	−0.229805	−	1.45093i	−0.785146	−	0.619311i	$-0.787412\pi$
$677$	−5.97936	−	37.7522i	−0.229805	−	1.45093i	0.555341	−	0.831623i	$-0.312588\pi$
$678$	22.7379	+	11.5855i	0.873242	+	0.444939i
$679$	−0.361073	−	1.11127i	−0.0138567	−	0.0426466i
$680$	−3.74122	−	9.57083i	−0.143469	−	0.367025i
$681$	6.81446	−	20.9727i	0.261131	−	0.803677i
$682$	−12.0535	+	12.0535i	−0.461551	+	0.461551i
$683$	−4.96489	−	9.74415i	−0.189976	−	0.372849i	0.776297	−	0.630367i	$-0.217096\pi$
$683$	−4.96489	−	9.74415i	−0.189976	−	0.372849i	−0.966274	+	0.257517i	$0.917096\pi$
$684$	1.53712	−	2.33551i	0.0587732	−	0.0893005i
$685$	18.4091	+	16.3729i	0.703376	+	0.625576i
$686$	1.04472	−	1.43794i	0.0398876	−	0.0549006i
$687$	−32.9623	−	5.22071i	−1.25759	−	0.199183i
$688$	−6.53530	−	1.03509i	−0.249156	−	0.0394624i
$689$	5.83766	−	8.03485i	0.222397	−	0.306103i
$690$	16.2155	−	18.2321i	0.617313	−	0.694086i
$691$	−1.03808	+	0.754209i	−0.0394904	+	0.0286915i	−0.607355	−	0.794430i	$-0.707770\pi$
$691$	−1.03808	+	0.754209i	−0.0394904	+	0.0286915i	0.567865	+	0.823122i	$0.307770\pi$
$692$	−1.14865	+	0.585264i	−0.0436649	+	0.0222484i
$693$	0.127121	+	0.127121i	0.00482892	+	0.00482892i
$694$	6.97679	−	21.4723i	0.264835	−	0.815079i
$695$	11.4327	+	29.2473i	0.433667	+	1.10941i
$696$	8.51970	−	2.76822i	0.322939	−	0.104929i
$697$	10.2547	−	20.1260i	0.388425	−	0.762327i
$698$	−11.6700	+	1.84834i	−0.441715	+	0.0699608i
$699$	−2.38673			−0.0902744
$700$	0.635003	+	0.0254950i	0.0240008	+	0.000963620i
$701$	40.2917			1.52180			0.760899	−	0.648870i	$-0.224758\pi$
$701$	40.2917			1.52180			0.760899	+	0.648870i	$0.224758\pi$
$702$	0.868013	+	5.48042i	0.0327610	+	0.206845i
$703$	1.03985	−	9.34272i	0.0392189	−	0.352367i
$704$	2.09715	−	0.681406i	0.0790394	−	0.0256815i
$705$	18.1594	−	1.06310i	0.683923	−	0.0400386i
$706$	−7.85921	−	2.55361i	−0.295785	−	0.0961065i
$707$	−0.170987	+	0.170987i	−0.00643065	+	0.00643065i
$708$	−5.28453	+	2.69260i	−0.198605	+	0.101194i
$709$	24.0730	+	33.1336i	0.904080	+	1.24436i	0.969148	+	0.246479i	$0.0792735\pi$
$709$	24.0730	+	33.1336i	0.904080	+	1.24436i	−0.0650682	+	0.997881i	$0.520726\pi$
$710$	−23.5840	−	2.33304i	−0.885092	−	0.0875573i
$711$	2.40270	−	3.30703i	0.0901081	−	0.124023i
$712$	−0.209314	+	1.32155i	−0.00784436	+	0.0495274i
$713$	−8.59240	+	54.2503i	−0.321788	+	2.03169i
$714$	−0.527278	+	0.725736i	−0.0197329	+	0.0271600i
$715$	1.04640	+	4.77900i	0.0391330	+	0.178725i
$716$	−11.3017	−	15.5555i	−0.422366	−	0.581337i
$717$	27.9593	−	14.2460i	1.04416	−	0.532026i
$718$	8.48730	−	8.48730i	0.316743	−	0.316743i
$719$	20.1026	+	6.53174i	0.749702	+	0.243593i	0.658853	−	0.752272i	$-0.271042\pi$
$719$	20.1026	+	6.53174i	0.749702	+	0.243593i	0.0908490	+	0.995865i	$0.471042\pi$
$720$	−1.10911	+	0.909430i	−0.0413342	+	0.0338924i
$721$	−0.207180	+	0.0673170i	−0.00771580	+	0.00250701i
$722$	4.69237	+	18.4115i	0.174632	+	0.685203i
$723$	5.13812	+	32.4408i	0.191089	+	1.20649i
$724$	20.6747			0.768369
$725$	−21.4336	+	19.7789i	−0.796024	+	0.734572i
$726$	−9.42594			−0.349830
$727$	−23.5829	+	3.73516i	−0.874640	+	0.138529i	−0.577585	−	0.816331i	$-0.696005\pi$
$727$	−23.5829	+	3.73516i	−0.874640	+	0.138529i	−0.297056	+	0.954860i	$0.596005\pi$
$728$	0.0572531	−	0.112366i	0.00212194	−	0.00416454i
$729$	−28.5701	+	9.28299i	−1.05815	+	0.343814i
$730$	−0.177928	+	0.680661i	−0.00658541	+	0.0251924i
$731$	−9.39658	+	28.9197i	−0.347545	+	1.06963i
$732$	16.6871	+	16.6871i	0.616772	+	0.616772i
$733$	−29.6923	+	15.1290i	−1.09671	+	0.558801i	−0.906185	−	0.422881i	$-0.861019\pi$
$733$	−29.6923	+	15.1290i	−1.09671	+	0.558801i	−0.190524	+	0.981683i	$0.561019\pi$
$734$	−21.2351	+	15.4282i	−0.783801	+	0.569465i
$735$	12.1183	+	20.6962i	0.446990	+	0.763389i
$736$	4.17635	−	5.74826i	0.153942	−	0.211883i
$737$	20.6226	+	3.26630i	0.759643	+	0.120316i
$738$	−3.11392	−	0.493197i	−0.114625	−	0.0181548i
$739$	−1.12764	+	1.55207i	−0.0414810	+	0.0570937i	−0.829254	−	0.558872i	$-0.811234\pi$
$739$	−1.12764	+	1.55207i	−0.0414810	+	0.0570937i	0.787773	+	0.615966i	$0.211234\pi$
$740$	−1.93443	+	4.41731i	−0.0711110	+	0.162384i
$741$	−5.54817	−	3.65154i	−0.203817	−	0.134143i
$742$	−0.577597	−	1.13360i	−0.0212043	−	0.0416157i
$743$	23.2750	−	23.2750i	0.853876	−	0.853876i	−0.136732	−	0.990608i	$-0.543660\pi$
$743$	23.2750	−	23.2750i	0.853876	−	0.853876i	0.990608	+	0.136732i	$0.0436600\pi$
$744$	−3.66868	+	11.2910i	−0.134500	+	0.413949i
$745$	4.23642	+	2.71447i	0.155210	+	0.0994505i
$746$	6.77208	+	20.8423i	0.247943	+	0.763091i
$747$	−7.48995	−	3.81632i	−0.274043	−	0.139632i
$748$	−1.58525	−	10.0089i	−0.0579625	−	0.365961i
$749$	−0.580817			−0.0212226
$750$	−7.51317	+	15.4393i	−0.274342	+	0.563765i
$751$			15.2799i			0.557571i	0.960353	+	0.278786i	$0.0899319\pi$
$751$			15.2799i			0.557571i	−0.960353	+	0.278786i	$0.910068\pi$
$752$	5.23185	−	0.828644i	0.190786	−	0.0302175i
$753$	13.6706	+	6.96551i	0.498184	+	0.253837i
$754$	1.78844	+	5.50424i	0.0651310	+	0.200453i
$755$	24.0061	+	15.3818i	0.873673	+	0.559803i
$756$	0.676018	+	0.219651i	0.0245865	+	0.00798865i
$757$	−8.57296	+	8.57296i	−0.311590	+	0.311590i	−0.845525	−	0.533936i	$-0.820713\pi$
$757$	−8.57296	+	8.57296i	−0.311590	+	0.311590i	0.533936	+	0.845525i	$0.320713\pi$
$758$	5.55550	−	2.83067i	0.201785	−	0.102814i
$759$	19.4663	−	14.1431i	0.706583	−	0.513362i
$760$	0.510197	−	9.73343i	0.0185068	−	0.353069i
$761$	7.85048	+	5.70371i	0.284580	+	0.206759i	0.720912	−	0.693026i	$-0.243723\pi$
$761$	7.85048	+	5.70371i	0.284580	+	0.206759i	−0.436333	+	0.899785i	$0.643723\pi$
$762$	−1.45288	−	0.230113i	−0.0526321	−	0.00833611i
$763$	−0.0607582	+	0.383612i	−0.00219959	+	0.0138877i
$764$	11.2707	−	15.5128i	0.407759	−	0.561233i
$765$	3.33057	+	5.68808i	0.120417	+	0.205653i
$766$	−5.30783	+	3.85637i	−0.191780	+	0.139336i
$767$	−1.73958	−	3.41413i	−0.0628127	−	0.123277i
$768$	1.08595	−	1.08595i	0.0391858	−	0.0391858i
$769$	−16.8256	−	5.46697i	−0.606747	−	0.197144i	−0.0104997	−	0.999945i	$-0.503342\pi$
$769$	−16.8256	−	5.46697i	−0.606747	−	0.197144i	−0.596247	+	0.802801i	$0.703342\pi$
$770$	0.606333	+	0.158498i	0.0218507	+	0.00571188i
$771$	12.5122	+	38.5087i	0.450618	+	1.38686i
$772$	7.67782	−	15.0686i	0.276331	−	0.542330i
$773$	37.2465	−	5.89927i	1.33966	−	0.212182i	0.554870	−	0.831937i	$-0.312768\pi$
$773$	37.2465	−	5.89927i	1.33966	−	0.212182i	0.784795	+	0.619755i	$0.212768\pi$
$774$	4.24422			0.152555
$775$	−4.51014	−	38.3881i	−0.162009	−	1.37894i
$776$	9.19300			0.330009
$777$	0.415785	−	0.0658539i	0.0149162	−	0.00236250i
$778$	31.6447	+	16.1238i	1.13452	+	0.578066i
$779$	16.7323	−	13.3807i	0.599496	−	0.479413i
$780$	2.16042	+	2.63478i	0.0773553	+	0.0943402i
$781$	−22.2268	−	7.22193i	−0.795338	−	0.258421i
$782$	−23.0890	−	23.0890i	−0.825661	−	0.825661i
$783$	−29.0651	+	14.8094i	−1.03870	+	0.529245i
$784$	4.10500	+	5.65005i	0.146607	+	0.201787i
$785$	−11.3550	−	51.8596i	−0.405279	−	1.85095i
$786$	19.0571	+	13.8458i	0.679746	+	0.493864i
$787$	−42.0599	−	6.66164i	−1.49927	−	0.237462i	−0.647781	−	0.761827i	$-0.724303\pi$
$787$	−42.0599	−	6.66164i	−1.49927	−	0.237462i	−0.851493	+	0.524365i	$0.824303\pi$
$788$	−15.4585	−	2.44839i	−0.550687	−	0.0872202i
$789$	18.7184	+	13.5997i	0.666392	+	0.484162i
$790$	1.40282	−	14.1807i	0.0499101	−	0.504527i
$791$	1.24142	+	1.70867i	0.0441398	+	0.0607532i
$792$	−1.26025	+	0.642131i	−0.0447811	+	0.0228171i
$793$	−10.7809	+	10.7809i	−0.382840	+	0.382840i
$794$	−3.98487	+	12.2642i	−0.141418	+	0.435239i
$795$	34.3154	−	2.00891i	1.21704	−	0.0712488i
$796$	1.38767	+	4.27080i	0.0491845	+	0.151374i
$797$	−24.2701	+	47.6327i	−0.859690	+	1.68724i	−0.143137	+	0.989703i	$0.545719\pi$
$797$	−24.2701	+	47.6327i	−0.859690	+	1.68724i	−0.716552	+	0.697533i	$0.754281\pi$
$798$	−0.739455	+	0.420907i	−0.0261764	+	0.0148999i
$799$		−	24.3432i		−	0.861200i
$800$	−1.73461	+	4.68947i	−0.0613277	+	0.165798i
$801$		−	0.858258i		−	0.0303251i
$802$	−3.56476	+	0.564603i	−0.125876	+	0.0199368i
$803$	−0.314970	+	0.618164i	−0.0111151	+	0.0218145i
$804$	13.8302	−	4.49372i	0.487755	−	0.158481i
$805$	1.88079	−	0.735199i	0.0662893	−	0.0259123i
$806$	−7.29469	−	2.37019i	−0.256945	−	0.0834863i
$807$	−2.41741	+	2.41741i	−0.0850968	+	0.0850968i
$808$	−0.863716	−	1.69514i	−0.0303854	−	0.0596347i
$809$	25.6500	+	35.3041i	0.901805	+	1.24123i	0.969889	+	0.243548i	$0.0783113\pi$
$809$	25.6500	+	35.3041i	0.901805	+	1.24123i	−0.0680843	+	0.997680i	$0.521689\pi$
$810$	−9.90329	+	11.1349i	−0.347966	+	0.391241i
$811$	−21.9834	+	30.2576i	−0.771942	+	1.06249i	0.224184	+	0.974547i	$0.428028\pi$
$811$	−21.9834	+	30.2576i	−0.771942	+	1.06249i	−0.996126	+	0.0879399i	$0.971972\pi$
$812$	0.732267	+	0.115980i	0.0256975	+	0.00407009i
$813$	4.17264	−	26.3450i	0.146341	−	0.923959i
$814$	−2.79520	+	3.84726i	−0.0979716	+	0.134846i
$815$	26.0945	−	29.3397i	0.914049	−	1.02773i
$816$	−4.14844	−	5.70983i	−0.145224	−	0.199884i
$817$	−19.4298	+	21.3150i	−0.679764	+	0.745718i
$818$	5.93334	+	5.93334i	0.207454	+	0.207454i
$819$	−0.0249970	+	0.0769328i	−0.000873465	+	0.00268825i
$820$	−10.2363	+	4.00135i	−0.357467	+	0.139733i
$821$	2.54942	+	7.84632i	0.0889755	+	0.273839i	0.985637	−	0.168879i	$-0.0540146\pi$
$821$	2.54942	+	7.84632i	0.0889755	+	0.273839i	−0.896661	+	0.442717i	$0.854015\pi$
$822$	15.0766	+	7.68189i	0.525856	+	0.267937i
$823$	−5.85424	−	36.9622i	−0.204066	−	1.28842i	−0.850712	−	0.525632i	$-0.823829\pi$
$823$	−5.85424	−	36.9622i	−0.204066	−	1.28842i	0.646646	−	0.762790i	$-0.276171\pi$
$824$		−	1.71391i		−	0.0597067i
$825$	−10.4941	+	13.2883i	−0.365359	+	0.462638i
$826$	−0.490859			−0.0170792
$827$	3.10392	+	19.5974i	0.107934	+	0.681468i	0.981021	+	0.193903i	$0.0621147\pi$
$827$	3.10392	+	19.5974i	0.107934	+	0.681468i	−0.873087	+	0.487565i	$0.837885\pi$
$828$	−2.06908	+	4.06080i	−0.0719056	+	0.141123i
$829$	−7.33633	−	22.5789i	−0.254801	−	0.784198i	−0.993869	−	0.110566i	$-0.964734\pi$
$829$	−7.33633	−	22.5789i	−0.254801	−	0.784198i	0.739068	−	0.673631i	$-0.235266\pi$
$830$	−29.2542	+	1.71261i	−1.01543	+	0.0594457i
$831$	14.2304	+	4.62374i	0.493647	+	0.160396i
$832$	0.701588	+	0.701588i	0.0243232	+	0.0243232i
$833$	28.5968	−	14.5708i	0.990820	−	0.504848i
$834$	12.6771	+	17.4486i	0.438973	+	0.604194i
$835$	4.55474	−	46.0426i	0.157623	−	1.59337i
$836$	2.54451	−	9.26879i	0.0880038	−	0.320568i
$837$	6.76289	−	42.6992i	0.233760	−	1.47590i
$838$	2.93275	−	18.5167i	0.101310	−	0.639648i
$839$	−4.60582	−	3.34632i	−0.159010	−	0.115528i	0.505435	−	0.862865i	$-0.331332\pi$
$839$	−4.60582	−	3.34632i	−0.159010	−	0.115528i	−0.664445	+	0.747337i	$0.731332\pi$
$840$	0.426379	−	0.0933587i	0.0147115	−	0.00322118i
$841$	−4.06470	+	2.95318i	−0.140162	+	0.101834i
$842$	9.73020	+	19.0966i	0.335325	+	0.658112i
$843$	19.7407	+	19.7407i	0.679906	+	0.679906i
$844$	−1.31192	+	4.03766i	−0.0451580	+	0.138982i
$845$	20.7762	−	17.0357i	0.714724	−	0.586046i
$846$	−3.23143	+	1.04995i	−0.111099	+	0.0360982i
$847$	−0.695084	−	0.354163i	−0.0238834	−	0.0121692i
$848$	9.88651	−	1.56587i	0.339504	−	0.0537722i
$849$	5.27839			0.181154
$850$	20.0386	+	11.2447i	0.687317	+	0.385691i
$851$			15.3232i			0.525271i
$852$	−16.0765	+	2.54627i	−0.550771	+	0.0872336i
$853$	0.792661	−	1.55568i	0.0271402	−	0.0532656i	−0.877038	−	0.480420i	$-0.840484\pi$
$853$	0.792661	−	1.55568i	0.0271402	−	0.0532656i	0.904178	+	0.427155i	$0.140484\pi$
$854$	0.603544	+	1.85752i	0.0206529	+	0.0635630i
$855$	0.653449	+	6.21769i	0.0223475	+	0.212641i
$856$	1.41210	−	4.34600i	0.0482647	−	0.148543i
$857$	−15.3423	−	15.3423i	−0.524084	−	0.524084i	0.394719	−	0.918802i	$-0.370842\pi$
$857$	−15.3423	−	15.3423i	−0.524084	−	0.524084i	−0.918802	+	0.394719i	$0.870842\pi$
$858$	1.52543	+	2.99382i	0.0520772	+	0.102207i
$859$	2.73929	+	3.77031i	0.0934635	+	0.128641i	0.853188	−	0.521604i	$-0.174666\pi$
$859$	2.73929	+	3.77031i	0.0934635	+	0.128641i	−0.759724	+	0.650245i	$0.774666\pi$
$860$	12.7678	−	7.47599i	0.435379	−	0.254929i
$861$	0.776197	+	0.563940i	0.0264527	+	0.0192190i
$862$	−3.70009	+	23.3615i	−0.126026	+	0.795695i
$863$	−2.82616	+	17.8437i	−0.0962037	+	0.607406i	0.891735	+	0.452559i	$0.149489\pi$
$863$	−2.82616	+	17.8437i	−0.0962037	+	0.607406i	−0.987938	+	0.154848i	$0.950511\pi$
$864$	−3.28712	+	4.52433i	−0.111830	+	0.153921i
$865$	1.15635	−	2.64054i	0.0393170	−	0.0897811i
$866$	−21.2822	+	15.4624i	−0.723199	+	0.525435i
$867$	−5.63702	+	2.87221i	−0.191443	+	0.0975453i
$868$	−0.694774	+	0.694774i	−0.0235822	+	0.0235822i
$869$	4.34244	−	13.3646i	0.147307	−	0.453365i
$870$	−10.8067	+	16.8658i	−0.366382	+	0.571806i
$871$	2.90322	+	8.93518i	0.0983717	+	0.302757i
$872$	−2.72269	−	1.38728i	−0.0922018	−	0.0469792i
$873$	−5.82411	+	0.922449i	−0.197116	+	0.0312202i
$874$	−10.9217	−	28.9814i	−0.369432	−	0.980309i
$875$	−1.13414	+	0.856226i	−0.0383408	+	0.0289457i
$876$			0.483196i			0.0163257i
$877$	−6.06650	−	38.3024i	−0.204851	−	1.29338i	−0.848965	−	0.528449i	$-0.822774\pi$
$877$	−6.06650	−	38.3024i	−0.204851	−	1.29338i	0.644114	−	0.764930i	$-0.277226\pi$
$878$	−0.643495	+	1.26293i	−0.0217169	+	0.0426218i
$879$	−28.6505	+	9.30912i	−0.966359	+	0.313989i
$880$	−2.66011	+	4.15158i	−0.0896724	+	0.139950i
$881$	−7.64422	+	23.5265i	−0.257540	+	0.792628i	0.735778	+	0.677223i	$0.236817\pi$
$881$	−7.64422	+	23.5265i	−0.257540	+	0.792628i	−0.993318	+	0.115405i	$0.963183\pi$
$882$	−3.16761	−	3.16761i	−0.106659	−	0.106659i
$883$	23.6528	−	12.0517i	0.795981	−	0.405573i	−0.00819298	−	0.999966i	$-0.502608\pi$
$883$	23.6528	−	12.0517i	0.795981	−	0.405573i	0.804174	+	0.594394i	$0.202608\pi$
$884$	3.68890	−	2.68014i	0.124071	−	0.0901429i
$885$	5.31996	−	12.1482i	0.178828	−	0.408359i
$886$	−14.2893	+	19.6675i	−0.480057	+	0.660742i
$887$	−30.7032	−	4.86291i	−1.03091	−	0.163280i	−0.382014	−	0.924156i	$-0.624770\pi$
$887$	−30.7032	−	4.86291i	−1.03091	−	0.163280i	−0.648897	+	0.760876i	$0.724770\pi$
$888$	−0.518115	+	3.27125i	−0.0173868	+	0.109776i
$889$	−0.0984912	−	0.0715580i	−0.00330329	−	0.00239998i
$890$	−1.51178	−	2.58188i	−0.0506750	−	0.0865449i
$891$	−11.8887	+	8.63762i	−0.398285	+	0.289371i
$892$	−20.2970	+	10.3419i	−0.679595	+	0.346271i
$893$	9.52032	−	21.0353i	0.318585	−	0.703919i
$894$	3.28654	+	1.06786i	0.109918	+	0.0357147i
$895$	41.5966	+	10.8736i	1.39042	+	0.363463i
$896$	0.120882	−	0.0392769i	0.00403838	−	0.00131215i
$897$	9.64673	+	4.91526i	0.322095	+	0.164116i
$898$	1.72183	+	10.8712i	0.0574582	+	0.362777i
$899$		−	45.0918i		−	1.50390i
$900$	0.628387	−	3.14501i	0.0209462	−	0.104834i
$901$		−	46.0008i		−	1.53251i
$902$	−10.7048	+	1.69548i	−0.356431	+	0.0564531i
$903$	−1.15081	−	0.586370i	−0.0382967	−	0.0195132i
$904$	−15.8034	+	5.13484i	−0.525614	+	0.170782i
$905$	−35.7489	+	29.3127i	−1.18833	+	0.974386i
$906$	18.6236	+	6.05116i	0.618726	+	0.201036i
$907$	−18.5470	−	18.5470i	−0.615842	−	0.615842i	0.328620	−	0.944462i	$-0.393416\pi$
$907$	−18.5470	−	18.5470i	−0.615842	−	0.615842i	−0.944462	+	0.328620i	$0.893416\pi$
$908$	6.51886	+	12.7940i	0.216336	+	0.424583i
$909$	0.717291	+	0.987267i	0.0237910	+	0.0327456i
$910$	0.0603154	+	0.275466i	0.00199944	+	0.00913162i
$911$	20.4380	−	28.1304i	0.677140	−	0.932003i	−0.322755	−	0.946482i	$-0.604609\pi$
$911$	20.4380	−	28.1304i	0.677140	−	0.932003i	0.999895	+	0.0144795i	$0.00460912\pi$
$912$	−1.35168	−	6.55635i	−0.0447585	−	0.217102i
$913$	−28.5423	−	4.52066i	−0.944613	−	0.149612i
$914$	−22.6013	−	16.4208i	−0.747584	−	0.543151i
$915$	−52.5129	−	5.19481i	−1.73602	−	0.171735i
$916$	17.5805	−	12.7730i	0.580876	−	0.422031i
$917$	0.885071	+	1.73705i	0.0292276	+	0.0573625i
$918$	18.1729	+	18.1729i	0.599794	+	0.599794i
$919$	38.8166	+	12.6123i	1.28044	+	0.416041i	0.868736	−	0.495275i	$-0.164933\pi$
$919$	38.8166	+	12.6123i	1.28044	+	0.416041i	0.411707	+	0.911316i	$0.364933\pi$
$920$	0.928523	+	15.8606i	0.0306125	+	0.522910i
$921$	2.87623	+	8.85213i	0.0947751	+	0.291688i
$922$	−15.1600	+	29.7532i	−0.499268	+	0.979869i
$923$	−1.64504	−	10.3864i	−0.0541472	−	0.341872i
$924$	0.430430			0.0141601
$925$	−2.91804	−	10.3807i	−0.0959445	−	0.341314i
$926$			20.5016i			0.673723i
$927$	0.171978	+	1.08582i	0.00564849	+	0.0356631i
$928$	−2.64814	+	5.19727i	−0.0869295	+	0.170609i
$929$	9.30740	−	3.02416i	0.305366	−	0.0992194i	−0.152326	−	0.988330i	$-0.548676\pi$
$929$	9.30740	−	3.02416i	0.305366	−	0.0992194i	0.457692	+	0.889111i	$0.348676\pi$
$930$	−9.66492	−	24.7249i	−0.316925	−	0.810763i
$931$	30.4093	−	1.40697i	0.996626	−	0.0461116i
$932$	1.09892	−	1.09892i	0.0359962	−	0.0359962i
$933$	−12.4807	−	24.4947i	−0.408598	−	0.801919i
$934$	−12.2397	+	8.89265i	−0.400494	+	0.290976i
$935$	16.9317	+	15.0589i	0.553727	+	0.492479i
$936$	−0.514882	−	0.374083i	−0.0168294	−	0.0122273i
$937$	1.38454	−	8.74165i	0.0452310	−	0.285577i	−0.954697	−	0.297580i	$-0.903821\pi$
$937$	1.38454	−	8.74165i	0.0452310	−	0.285577i	0.999928	+	0.0120024i	$0.00382058\pi$
$938$	1.18871	+	0.188273i	0.0388127	+	0.00614732i
$939$	6.60097	+	4.79588i	0.215414	+	0.156508i
$940$	−7.87161	+	8.85057i	−0.256743	+	0.288674i
$941$	7.75531	+	10.6743i	0.252816	+	0.347971i	0.916495	−	0.400046i	$-0.131006\pi$
$941$	7.75531	+	10.6743i	0.252816	+	0.347971i	−0.663679	+	0.748017i	$0.731006\pi$
$942$	−16.5533	−	32.4876i	−0.539335	−	1.05850i
$943$	−24.6944	+	24.6944i	−0.804160	+	0.804160i
$944$	1.19339	−	3.67289i	0.0388417	−	0.119542i
$945$	−1.48033	+	0.578659i	−0.0481552	+	0.0188238i
$946$	13.8764	−	4.50870i	0.451160	−	0.146591i
$947$	−20.5338	−	10.4625i	−0.667260	−	0.339986i	0.0873329	−	0.996179i	$-0.472166\pi$
$947$	−20.5338	−	10.4625i	−0.667260	−	0.339986i	−0.754593	+	0.656193i	$0.772166\pi$
$948$	−1.53103	−	9.66654i	−0.0497255	−	0.313955i
$949$	−0.312174			−0.0101336
$950$	12.9179	+	17.5536i	0.419113	+	0.569513i
$951$	−0.258180			−0.00837207
$952$	−0.0913754	−	0.576922i	−0.00296150	−	0.0186981i
$953$	−13.5605	−	6.90943i	−0.439268	−	0.223818i	0.220347	−	0.975421i	$-0.429281\pi$
$953$	−13.5605	−	6.90943i	−0.439268	−	0.223818i	−0.659616	+	0.751603i	$0.729281\pi$
$954$	−6.10636	+	1.98408i	−0.197701	+	0.0642368i
$955$	2.50580	+	42.8030i	0.0810858	+	1.38507i
$956$	−6.31400	+	19.4325i	−0.204209	+	0.628492i
$957$	−13.9678	+	13.9678i	−0.451514	+	0.451514i
$958$	10.6174	+	20.8379i	0.343034	+	0.673242i
$959$	0.823136	+	1.13295i	0.0265804	+	0.0365848i
$960$	−0.338064	+	3.41739i	−0.0109110	+	0.110296i
$961$	23.2669	+	16.9044i	0.750546	+	0.545303i
$962$	−2.11343	−	0.334734i	−0.0681396	−	0.0107922i
$963$	−0.458531	+	2.89505i	−0.0147760	+	0.0932918i
$964$	−17.3024	−	12.5709i	−0.557272	−	0.404882i
$965$	8.08848	+	36.9409i	0.260377	+	1.18917i
$966$	1.12206	−	0.815223i	0.0361016	−	0.0262294i
$967$	−6.05480	−	11.8832i	−0.194709	−	0.382138i	0.772924	−	0.634498i	$-0.218793\pi$
$967$	−6.05480	−	11.8832i	−0.194709	−	0.382138i	−0.967633	+	0.252360i	$0.918793\pi$
$968$	4.33996	−	4.33996i	0.139492	−	0.139492i
$969$	−30.7311	+	1.42186i	−0.987225	+	0.0456767i
$970$	−15.8957	+	13.0339i	−0.510381	+	0.418493i
$971$	33.5629	−	10.9052i	1.07708	−	0.349966i	0.283842	−	0.958871i	$-0.408391\pi$
$971$	33.5629	−	10.9052i	1.07708	−	0.349966i	0.793243	+	0.608905i	$0.208391\pi$
$972$	2.97020	−	5.82934i	0.0952691	−	0.186976i
$973$	0.279232	+	1.76300i	0.00895178	+	0.0565193i
$974$		−	31.5908i		−	1.01223i
$975$	−7.47121	−	1.49278i	−0.239270	−	0.0478072i
$976$	−15.3664			−0.491866
$977$	−0.548200	−	3.46120i	−0.0175385	−	0.110734i	0.977366	−	0.211555i	$-0.0678528\pi$
$977$	−0.548200	−	3.46120i	−0.0175385	−	0.110734i	−0.994905	+	0.100822i	$0.967853\pi$
$978$	12.2431	−	24.0284i	0.391491	−	0.768344i
$979$	−0.911741	−	2.80605i	−0.0291394	−	0.0896818i
$980$	−15.1087	−	3.94948i	−0.482629	−	0.126161i
$981$	1.86413	+	0.605692i	0.0595171	+	0.0193383i
$982$	17.4524	+	17.4524i	0.556929	+	0.556929i
$983$	13.7414	+	26.9690i	0.438282	+	0.860177i	0.999472	+	0.0324897i	$0.0103436\pi$
$983$	13.7414	+	26.9690i	0.438282	+	0.860177i	−0.561190	+	0.827687i	$0.689656\pi$
$984$	−6.10684	+	4.43688i	−0.194679	+	0.141443i
$985$	30.2008	−	17.6836i	0.962279	−	0.563447i
$986$	21.6867	+	15.7563i	0.690646	+	0.501783i
$987$	1.02126	+	0.161751i	0.0325069	+	0.00514859i
$988$	4.23580	−	0.873265i	0.134759	−	0.0277822i
$989$	27.6339	−	38.0348i	0.878708	−	1.20944i
$990$	1.26870	−	2.89711i	0.0403220	−	0.0920761i
$991$	21.3215	+	29.3465i	0.677300	+	0.932224i	0.999898	−	0.0143127i	$-0.00455603\pi$
$991$	21.3215	+	29.3465i	0.677300	+	0.932224i	−0.322598	+	0.946536i	$0.604556\pi$
$992$	−3.50954	−	6.88786i	−0.111428	−	0.218690i
$993$	−18.7602	−	18.7602i	−0.595337	−	0.595337i
$994$	−1.28118	−	0.416279i	−0.0406364	−	0.0132036i
$995$	−8.45459	−	5.41725i	−0.268029	−	0.171738i
$996$	−19.1415	+	6.21945i	−0.606521	+	0.197071i
$997$	40.3287	+	20.5485i	1.27722	+	0.650777i	0.955202	−	0.295956i	$-0.0956380\pi$
$997$	40.3287	+	20.5485i	1.27722	+	0.650777i	0.322020	+	0.946733i	$0.395638\pi$
$998$	−40.8172	+	6.46480i	−1.29204	+	0.204640i
$999$		−	12.0605i		−	0.381578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.w.a.113.18	✓	400
19.18	odd	2	inner	950.2.w.a.113.33	yes	400
25.2	odd	20	inner	950.2.w.a.227.33	yes	400
475.227	even	20	inner	950.2.w.a.227.18	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.w.a.113.18	✓	400	1.1	even	1	trivial
950.2.w.a.113.33	yes	400	19.18	odd	2	inner
950.2.w.a.227.18	yes	400	475.227	even	20	inner
950.2.w.a.227.33	yes	400	25.2	odd	20	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 - 0.987688i) q^{2} +(1.36837 + 0.697221i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.20636 - 1.88274i) q^{5} +(0.474577 - 1.46060i) q^{6} +(0.0898753 - 0.0898753i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-0.377026 - 0.518932i) q^{9} +O(q^{10})\)	\(q+(-0.156434 - 0.987688i) q^{2} +(1.36837 + 0.697221i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(1.20636 - 1.88274i) q^{5} +(0.474577 - 1.46060i) q^{6} +(0.0898753 - 0.0898753i) q^{7} +(0.453990 + 0.891007i) q^{8} +(-0.377026 - 0.518932i) q^{9} +(-2.04827 - 0.896980i) q^{10} +(-1.78395 - 1.29611i) q^{11} +(-1.51685 - 0.240246i) q^{12} +(0.155214 - 0.979980i) q^{13} +(-0.102828 - 0.0747092i) q^{14} +(2.96343 - 1.73519i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-2.08636 - 4.09471i) q^{17} +(-0.453563 + 0.453563i) q^{18} +(-0.201461 - 4.35424i) q^{19} +(-0.565516 + 2.16337i) q^{20} +(0.185646 - 0.0603200i) q^{21} +(-1.00108 + 1.96474i) q^{22} +(1.11150 + 7.01776i) q^{23} +1.53576i q^{24} +(-2.08940 - 4.54251i) q^{25} -0.992195 q^{26} +(-0.874841 - 5.52353i) q^{27} +(-0.0577035 + 0.113249i) q^{28} +(-1.80251 - 5.54754i) q^{29} +(-2.17741 - 2.65550i) q^{30} +(7.35207 + 2.38883i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-1.53743 - 3.01737i) q^{33} +(-3.71792 + 2.70122i) q^{34} +(-0.0607898 - 0.277633i) q^{35} +(0.518932 + 0.377026i) q^{36} +(2.13005 + 0.337367i) q^{37} +(-4.26912 + 0.880134i) q^{38} +(0.895653 - 1.23276i) q^{39} +(2.22521 + 0.220128i) q^{40} +(2.88904 + 3.97642i) q^{41} +(-0.0886188 - 0.173924i) q^{42} +(-4.67876 - 4.67876i) q^{43} +(2.09715 + 0.681406i) q^{44} +(-1.43184 + 0.0838237i) q^{45} +(6.75748 - 2.19564i) q^{46} +(4.71972 + 2.40482i) q^{47} +(1.51685 - 0.240246i) q^{48} +6.98384i q^{49} +(-4.15973 + 2.77428i) q^{50} -7.05774i q^{51} +(0.155214 + 0.979980i) q^{52} +(8.91875 + 4.54433i) q^{53} +(-5.31867 + 1.72814i) q^{54} +(-4.59231 + 1.79513i) q^{55} +(0.120882 + 0.0392769i) q^{56} +(2.76020 - 6.09869i) q^{57} +(-5.19727 + 2.64814i) q^{58} +(3.12435 - 2.26997i) q^{59} +(-2.28219 + 2.56602i) q^{60} +(-12.4317 - 9.03213i) q^{61} +(1.20931 - 7.63525i) q^{62} +(-0.0805245 - 0.0127538i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-1.65780 - 1.47443i) q^{65} +(-2.73972 + 1.99052i) q^{66} +(-8.43686 + 4.29879i) q^{67} +(3.24958 + 3.24958i) q^{68} +(-3.37198 + 10.3779i) q^{69} +(-0.264706 + 0.103473i) q^{70} +(10.0798 - 3.27514i) q^{71} +(0.291205 - 0.571523i) q^{72} +(-0.0492189 - 0.310756i) q^{73} -2.15660i q^{74} +(0.308052 - 7.67263i) q^{75} +(1.53714 + 4.07887i) q^{76} +(-0.276821 + 0.0438441i) q^{77} +(-1.35769 - 0.691780i) q^{78} +(1.96929 + 6.06085i) q^{79} +(-0.130682 - 2.23225i) q^{80} +(2.05937 - 6.33808i) q^{81} +(3.47552 - 3.47552i) q^{82} +(11.6769 - 5.94966i) q^{83} +(-0.157920 + 0.114735i) q^{84} +(-10.2262 - 1.01162i) q^{85} +(-3.88924 + 5.35307i) q^{86} +(1.40136 - 8.84786i) q^{87} +(0.344950 - 2.17793i) q^{88} +(1.08249 + 0.786473i) q^{89} +(0.306781 + 1.40110i) q^{90} +(-0.0741261 - 0.102026i) q^{91} +(-3.22571 - 6.33081i) q^{92} +(8.39484 + 8.39484i) q^{93} +(1.63688 - 5.03781i) q^{94} +(-8.44093 - 4.87347i) q^{95} +(-0.474577 - 1.46060i) q^{96} +(4.17353 - 8.19102i) q^{97} +(6.89786 - 1.09251i) q^{98} +1.41441i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q + 4 q^{5} - 4 q^{7}+O(q^{10}) \) 400 * q + 4 * q^5 - 4 * q^7	\( 400 q + 4 q^{5} - 4 q^{7} + 100 q^{16} + 40 q^{17} - 40 q^{19} - 76 q^{23} - 20 q^{25} - 4 q^{28} + 64 q^{30} + 8 q^{35} - 100 q^{36} + 4 q^{38} + 80 q^{39} + 32 q^{42} - 84 q^{43} - 144 q^{45} + 20 q^{47} - 16 q^{55} - 32 q^{57} - 16 q^{62} + 108 q^{63} - 100 q^{68} - 12 q^{73} + 256 q^{77} - 4 q^{80} + 100 q^{81} - 16 q^{82} + 116 q^{85} - 272 q^{87} - 4 q^{92} - 24 q^{93} - 56 q^{95}+O(q^{100}) \) 400 * q + 4 * q^5 - 4 * q^7 + 100 * q^16 + 40 * q^17 - 40 * q^19 - 76 * q^23 - 20 * q^25 - 4 * q^28 + 64 * q^30 + 8 * q^35 - 100 * q^36 + 4 * q^38 + 80 * q^39 + 32 * q^42 - 84 * q^43 - 144 * q^45 + 20 * q^47 - 16 * q^55 - 32 * q^57 - 16 * q^62 + 108 * q^63 - 100 * q^68 - 12 * q^73 + 256 * q^77 - 4 * q^80 + 100 * q^81 - 16 * q^82 + 116 * q^85 - 272 * q^87 - 4 * q^92 - 24 * q^93 - 56 * q^95

Introduction

L-functions

Modular forms

Varieties

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Database

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