LMFDB - Embedded newform 36.5.f.a.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,5,Mod(7,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("36.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	36.f (of order $6$, degree $2$, 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:	$3.72131867102$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	36.31
Dual form			36.5.f.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.86509 - 1.03009i) q^{2} +(7.79916 - 4.49144i) q^{3} +(13.8778 + 7.96277i) q^{4} +(-5.89438 + 10.2094i) q^{5} +(-34.7711 + 9.32599i) q^{6} +(50.5548 - 29.1878i) q^{7} +(-45.4367 - 45.0722i) q^{8} +(40.6539 - 70.0590i) q^{9} +O(q^{10})$	\(q+(-3.86509 - 1.03009i) q^{2} +(7.79916 - 4.49144i) q^{3} +(13.8778 + 7.96277i) q^{4} +(-5.89438 + 10.2094i) q^{5} +(-34.7711 + 9.32599i) q^{6} +(50.5548 - 29.1878i) q^{7} +(-45.4367 - 45.0722i) q^{8} +(40.6539 - 70.0590i) q^{9} +(33.2988 - 33.3884i) q^{10} +(86.9742 - 50.2146i) q^{11} +(144.000 - 0.228531i) q^{12} +(85.3178 - 147.775i) q^{13} +(-225.465 + 60.7377i) q^{14} +(-0.116489 + 106.099i) q^{15} +(129.189 + 221.012i) q^{16} -398.571 q^{17} +(-229.298 + 228.907i) q^{18} +404.608i q^{19} +(-163.096 + 94.7483i) q^{20} +(263.190 - 454.704i) q^{21} +(-387.889 + 104.493i) q^{22} +(291.091 + 168.062i) q^{23} +(-556.808 - 147.449i) q^{24} +(243.013 + 420.910i) q^{25} +(-481.982 + 483.278i) q^{26} +(2.40116 - 728.996i) q^{27} +(934.007 - 2.50777i) q^{28} +(327.671 + 567.543i) q^{29} +(109.741 - 409.961i) q^{30} +(-550.166 - 317.638i) q^{31} +(-271.664 - 987.307i) q^{32} +(452.791 - 782.271i) q^{33} +(1540.51 + 410.563i) q^{34} +688.176i q^{35} +(1122.05 - 648.549i) q^{36} -1599.91 q^{37} +(416.782 - 1563.85i) q^{38} +(1.68611 - 1535.72i) q^{39} +(727.980 - 198.207i) q^{40} +(-1231.63 + 2133.25i) q^{41} +(-1485.64 + 1486.36i) q^{42} +(-1933.38 + 1116.24i) q^{43} +(1606.86 - 4.31435i) q^{44} +(475.628 + 828.005i) q^{45} +(-951.976 - 949.423i) q^{46} +(2514.55 - 1451.78i) q^{47} +(2000.23 + 1143.47i) q^{48} +(503.358 - 871.842i) q^{49} +(-505.691 - 1877.18i) q^{50} +(-3108.52 + 1790.16i) q^{51} +(2360.72 - 1371.43i) q^{52} +1291.73 q^{53} +(-760.211 + 2815.16i) q^{54} +1183.94i q^{55} +(-3612.60 - 952.417i) q^{56} +(1817.27 + 3155.61i) q^{57} +(-681.858 - 2531.13i) q^{58} +(-1002.24 - 578.642i) q^{59} +(-846.456 + 1471.49i) q^{60} +(-2960.81 - 5128.28i) q^{61} +(1799.24 + 1794.42i) q^{62} +(10.3829 - 4728.42i) q^{63} +(32.9923 + 4095.87i) q^{64} +(1005.79 + 1742.08i) q^{65} +(-2555.88 + 2557.14i) q^{66} +(3085.87 + 1781.63i) q^{67} +(-5531.30 - 3173.73i) q^{68} +(3025.11 + 3.32134i) q^{69} +(708.882 - 2659.86i) q^{70} +5639.73i q^{71} +(-5004.89 + 1350.89i) q^{72} -5496.39 q^{73} +(6183.80 + 1648.05i) q^{74} +(3785.79 + 2191.27i) q^{75} +(-3221.80 + 5615.09i) q^{76} +(2931.31 - 5077.18i) q^{77} +(-1588.44 + 5933.96i) q^{78} +(-2788.94 + 1610.20i) q^{79} +(-3017.88 + 16.2058i) q^{80} +(-3255.51 - 5696.34i) q^{81} +(6957.81 - 6976.52i) q^{82} +(7063.92 - 4078.36i) q^{83} +(7273.21 - 4214.59i) q^{84} +(2349.33 - 4069.15i) q^{85} +(8622.53 - 2322.81i) q^{86} +(5104.64 + 2954.64i) q^{87} +(-6215.11 - 1638.53i) q^{88} +910.873 q^{89} +(-985.425 - 3690.25i) q^{90} -9960.97i q^{91} +(2701.48 + 4650.22i) q^{92} +(-5717.49 - 6.27738i) q^{93} +(-11214.4 + 3021.04i) q^{94} +(-4130.79 - 2384.91i) q^{95} +(-6553.18 - 6480.01i) q^{96} +(8804.44 + 15249.7i) q^{97} +(-2843.60 + 2851.24i) q^{98} +(17.8627 - 8134.75i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	$ 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) $ 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−3.86509	−	1.03009i	−0.966272	−	0.257522i
$2$	−3.86509	−	1.03009i	−0.966272	−	0.257522i
$3$	7.79916	−	4.49144i	0.866574	−	0.499049i
$3$	7.79916	−	4.49144i	0.866574	−	0.499049i
$4$	13.8778	+	7.96277i	0.867365	+	0.497673i
$5$	−5.89438	+	10.2094i	−0.235775	+	0.408374i	−0.959498	−	0.281717i	$-0.909096\pi$
$5$	−5.89438	+	10.2094i	−0.235775	+	0.408374i	0.723723	+	0.690091i	$0.242430\pi$
$6$	−34.7711	+	9.32599i	−0.965863	+	0.259055i
$7$	50.5548	−	29.1878i	1.03173	−	0.595670i	0.114251	−	0.993452i	$-0.463553\pi$
$7$	50.5548	−	29.1878i	1.03173	−	0.595670i	0.917480	+	0.397782i	$0.130220\pi$
$8$	−45.4367	−	45.0722i	−0.709949	−	0.704253i
$9$	40.6539	−	70.0590i	0.501900	−	0.864925i
$10$	33.2988	−	33.3884i	0.332988	−	0.333884i
$11$	86.9742	−	50.2146i	0.718795	−	0.414997i	−0.0955138	−	0.995428i	$-0.530449\pi$
$11$	86.9742	−	50.2146i	0.718795	−	0.414997i	0.814309	+	0.580431i	$0.197116\pi$
$12$	144.000	−	0.228531i	0.999999	−	0.00158702i
$13$	85.3178	−	147.775i	0.504839	−	0.874407i	−0.495145	−	0.868810i	$-0.664885\pi$
$13$	85.3178	−	147.775i	0.504839	−	0.874407i	0.999984	−	0.00559684i	$-0.00178154\pi$
$14$	−225.465	+	60.7377i	−1.15033	+	0.309886i
$15$	−0.116489	+	106.099i	−0.000517727	+	0.471550i
$16$	129.189	+	221.012i	0.504643	+	0.863328i
$17$	−398.571			−1.37914			−0.689569	−	0.724220i	$-0.742200\pi$
$17$	−398.571			−1.37914			−0.689569	+	0.724220i	$0.742200\pi$
$18$	−229.298	+	228.907i	−0.707710	+	0.706503i
$19$			404.608i			1.12080i	0.828223	+	0.560399i	$0.189352\pi$
$19$			404.608i			1.12080i	−0.828223	+	0.560399i	$0.810648\pi$
$20$	−163.096	+	94.7483i	−0.407740	+	0.236871i
$21$	263.190	−	454.704i	0.596802	−	1.03108i
$22$	−387.889	+	104.493i	−0.801423	+	0.215894i
$23$	291.091	+	168.062i	0.550267	+	0.317697i	0.749230	−	0.662310i	$-0.230424\pi$
$23$	291.091	+	168.062i	0.550267	+	0.317697i	−0.198963	+	0.980007i	$0.563757\pi$
$24$	−556.808	−	147.449i	−0.966680	−	0.255988i
$25$	243.013	+	420.910i	0.388820	+	0.673456i
$26$	−481.982	+	483.278i	−0.712991	+	0.714908i
$27$	2.40116	−	728.996i	0.00329377	−	0.999995i
$28$	934.007	−	2.50777i	1.19134	−	0.00319868i
$29$	327.671	+	567.543i	0.389621	+	0.674843i	0.992398	−	0.123066i	$-0.0392728\pi$
$29$	327.671	+	567.543i	0.389621	+	0.674843i	−0.602778	+	0.797909i	$0.705939\pi$
$30$	109.741	−	409.961i	0.121935	−	0.455512i
$31$	−550.166	−	317.638i	−0.572493	−	0.330529i	0.185651	−	0.982616i	$-0.440560\pi$
$31$	−550.166	−	317.638i	−0.572493	−	0.330529i	−0.758144	+	0.652087i	$0.773894\pi$
$32$	−271.664	−	987.307i	−0.265297	−	0.964167i
$33$	452.791	−	782.271i	0.415786	−	0.718339i
$34$	1540.51	+	410.563i	1.33262	+	0.355158i
$35$			688.176i			0.561776i
$36$	1122.05	−	648.549i	0.865781	−	0.500424i
$37$	−1599.91			−1.16867			−0.584336	−	0.811512i	$-0.698645\pi$
$37$	−1599.91			−1.16867			−0.584336	+	0.811512i	$0.698645\pi$
$38$	416.782	−	1563.85i	0.288630	−	1.08300i
$39$	1.68611	−	1535.72i	0.00110855	−	1.00968i
$40$	727.980	−	198.207i	0.454987	−	0.123880i
$41$	−1231.63	+	2133.25i	−0.732679	+	1.26904i	0.223055	+	0.974806i	$0.428397\pi$
$41$	−1231.63	+	2133.25i	−0.732679	+	1.26904i	−0.955734	+	0.294232i	$0.904936\pi$
$42$	−1485.64	+	1486.36i	−0.842198	+	0.842610i
$43$	−1933.38	+	1116.24i	−1.04564	+	0.603699i	−0.921425	−	0.388557i	$-0.872974\pi$
$43$	−1933.38	+	1116.24i	−1.04564	+	0.603699i	−0.124212	+	0.992256i	$0.539640\pi$
$44$	1606.86	−	4.31435i	0.829990	−	0.00222849i
$45$	475.628	+	828.005i	0.234878	+	0.408891i
$46$	−951.976	−	949.423i	−0.449894	−	0.448688i
$47$	2514.55	−	1451.78i	1.13832	−	0.657211i	0.192308	−	0.981335i	$-0.438403\pi$
$47$	2514.55	−	1451.78i	1.13832	−	0.657211i	0.946015	+	0.324124i	$0.105069\pi$
$48$	2000.23	+	1143.47i	0.868153	+	0.496296i
$49$	503.358	−	871.842i	0.209645	−	0.363116i
$50$	−505.691	−	1877.18i	−0.202276	−	0.750872i
$51$	−3108.52	+	1790.16i	−1.19512	+	0.688257i
$52$	2360.72	−	1371.43i	0.873048	−	0.507185i
$53$	1291.73			0.459852			0.229926	−	0.973208i	$-0.426152\pi$
$53$	1291.73			0.459852			0.229926	+	0.973208i	$0.426152\pi$
$54$	−760.211	+	2815.16i	−0.260703	+	0.965419i
$55$			1183.94i			0.391384i
$56$	−3612.60	−	952.417i	−1.15198	−	0.303704i
$57$	1817.27	+	3155.61i	0.559333	+	0.971254i
$58$	−681.858	−	2531.13i	−0.202693	−	0.752418i
$59$	−1002.24	−	578.642i	−0.287917	−	0.166229i	0.349085	−	0.937091i	$-0.386492\pi$
$59$	−1002.24	−	578.642i	−0.287917	−	0.166229i	−0.637002	+	0.770862i	$0.719826\pi$
$60$	−846.456	+	1471.49i	−0.235127	+	0.408748i
$61$	−2960.81	−	5128.28i	−0.795703	−	1.37820i	−0.922392	−	0.386256i	$-0.873768\pi$
$61$	−2960.81	−	5128.28i	−0.795703	−	1.37820i	0.126688	−	0.991943i	$-0.459565\pi$
$62$	1799.24	+	1794.42i	0.468066	+	0.466811i
$63$	10.3829	−	4728.42i	0.00261600	−	1.19134i
$64$	32.9923	+	4095.87i	0.00805476	+	0.999968i
$65$	1005.79	+	1742.08i	0.238057	+	0.412327i
$66$	−2555.88	+	2557.14i	−0.586750	+	0.587037i
$67$	3085.87	+	1781.63i	0.687430	+	0.396888i	0.802648	−	0.596452i	$-0.203424\pi$
$67$	3085.87	+	1781.63i	0.687430	+	0.396888i	−0.115219	+	0.993340i	$0.536757\pi$
$68$	−5531.30	−	3173.73i	−1.19622	−	0.686360i
$69$	3025.11	+	3.32134i	0.635393	+	0.000697615i
$70$	708.882	−	2659.86i	0.144670	−	0.542829i
$71$			5639.73i			1.11877i	0.828907	+	0.559386i	$0.188963\pi$
$71$			5639.73i			1.11877i	−0.828907	+	0.559386i	$0.811037\pi$
$72$	−5004.89	+	1350.89i	−0.965450	+	0.260588i
$73$	−5496.39			−1.03141			−0.515705	−	0.856766i	$-0.672470\pi$
$73$	−5496.39			−1.03141			−0.515705	+	0.856766i	$0.672470\pi$
$74$	6183.80	+	1648.05i	1.12926	+	0.300959i
$75$	3785.79	+	2191.27i	0.673029	+	0.389559i
$76$	−3221.80	+	5615.09i	−0.557791	+	0.972141i
$77$	2931.31	−	5077.18i	0.494402	−	0.856329i
$78$	−1588.44	+	5933.96i	−0.261085	+	0.975338i
$79$	−2788.94	+	1610.20i	−0.446874	+	0.258003i	−0.706509	−	0.707704i	$-0.749731\pi$
$79$	−2788.94	+	1610.20i	−0.446874	+	0.258003i	0.259635	+	0.965707i	$0.416398\pi$
$80$	−3017.88	+	16.2058i	−0.471543	+	0.00253216i
$81$	−3255.51	−	5696.34i	−0.496192	−	0.868213i
$82$	6957.81	−	6976.52i	1.03477	−	1.03755i
$83$	7063.92	−	4078.36i	1.02539	−	0.592010i	0.109730	−	0.993961i	$-0.465001\pi$
$83$	7063.92	−	4078.36i	1.02539	−	0.592010i	0.915661	+	0.401951i	$0.131668\pi$
$84$	7273.21	−	4214.59i	1.03078	−	0.597306i
$85$	2349.33	−	4069.15i	0.325166	−	0.563205i
$86$	8622.53	−	2322.81i	1.16584	−	0.314063i
$87$	5104.64	+	2954.64i	0.674415	+	0.390361i
$88$	−6215.11	−	1638.53i	−0.802571	−	0.211588i
$89$	910.873			0.114995			0.0574974	−	0.998346i	$-0.481688\pi$
$89$	910.873			0.114995			0.0574974	+	0.998346i	$0.481688\pi$
$90$	−985.425	−	3690.25i	−0.121657	−	0.455587i
$91$		−	9960.97i		−	1.20287i
$92$	2701.48	+	4650.22i	0.319173	+	0.549412i
$93$	−5717.49	−	6.27738i	−0.661057	−	0.000725792i
$94$	−11214.4	+	3021.04i	−1.26918	+	0.341902i
$95$	−4130.79	−	2384.91i	−0.457705	−	0.264256i
$96$	−6553.18	−	6480.01i	−0.711066	−	0.703126i
$97$	8804.44	+	15249.7i	0.935747	+	1.62076i	0.773297	+	0.634044i	$0.218606\pi$
$97$	8804.44	+	15249.7i	0.935747	+	1.62076i	0.162450	+	0.986717i	$0.448060\pi$
$98$	−2843.60	+	2851.24i	−0.296085	+	0.296881i
$99$	17.8627	−	8134.75i	0.00182254	−	0.829991i
$100$	20.8792	+	7776.38i	0.00208792	+	0.777638i
$101$	−3330.41	−	5768.44i	−0.326479	−	0.565478i	0.655332	−	0.755341i	$-0.272529\pi$
$101$	−3330.41	−	5768.44i	−0.326479	−	0.565478i	−0.981810	+	0.189863i	$0.939195\pi$
$102$	13858.7	−	3717.07i	1.33206	−	0.357273i
$103$	5848.70	+	3376.75i	0.551296	+	0.318291i	0.749645	−	0.661841i	$-0.230224\pi$
$103$	5848.70	+	3376.75i	0.551296	+	0.318291i	−0.198348	+	0.980132i	$0.563558\pi$
$104$	−10537.1	+	2868.94i	−0.974214	+	0.265250i
$105$	3090.90	+	5367.20i	0.280354	+	0.486821i
$106$	−4992.64	−	1330.59i	−0.444343	−	0.118422i
$107$			30.7569i			0.00268643i	0.999999	+	0.00134321i	$0.000427558\pi$
$107$			30.7569i			0.00268643i	−0.999999	+	0.00134321i	$0.999572\pi$
$108$	5838.15	−	10097.8i	0.500527	−	0.865721i
$109$	10691.4			0.899872			0.449936	−	0.893061i	$-0.351447\pi$
$109$	10691.4			0.899872			0.449936	+	0.893061i	$0.351447\pi$
$110$	1219.56	−	4576.02i	0.100790	−	0.378183i
$111$	−12478.0	+	7185.91i	−1.01274	+	0.583225i
$112$	12982.0	+	7402.48i	1.03491	+	0.590121i
$113$	−5008.09	+	8674.27i	−0.392207	+	0.679322i	−0.992740	−	0.120277i	$-0.961622\pi$
$113$	−5008.09	+	8674.27i	−0.392207	+	0.679322i	0.600533	+	0.799600i	$0.294955\pi$
$114$	−3773.37	−	14068.6i	−0.290349	−	1.08254i
$115$	−3431.60	+	1981.24i	−0.259479	+	0.149810i
$116$	28.1529	+	10485.4i	0.00209222	+	0.779238i
$117$	−6884.44	−	11984.9i	−0.502918	−	0.875514i
$118$	3277.69	+	3268.90i	0.235398	+	0.234767i
$119$	−20149.7	+	11633.4i	−1.42290	+	0.821511i
$120$	4787.40	−	4815.53i	0.332458	−	0.334412i
$121$	−2277.49	+	3944.73i	−0.155556	+	0.269430i
$122$	6161.23	+	22871.1i	0.413950	+	1.53663i
$123$	−24.3403	+	22169.4i	−0.00160885	+	1.46536i
$124$	−5105.83	−	8788.97i	−0.332065	−	0.571603i
$125$	−13097.6			−0.838247
$126$	−4910.82	+	18265.1i	−0.309323	+	1.15048i
$127$		−	16087.8i		−	0.997444i	−0.866762	−	0.498722i	$-0.833803\pi$
$127$		−	16087.8i		−	0.997444i	0.866762	−	0.498722i	$-0.166197\pi$
$128$	4091.59	−	15864.9i	0.249731	−	0.968315i
$129$	−10065.3	+	17389.4i	−0.604847	+	1.04497i
$130$	−2092.97	−	7769.35i	−0.123845	−	0.459725i
$131$	−18105.5	−	10453.2i	−1.05504	−	0.609127i	−0.130983	−	0.991385i	$-0.541813\pi$
$131$	−18105.5	−	10453.2i	−1.05504	−	0.609127i	−0.924056	+	0.382257i	$0.875147\pi$
$132$	12512.8	−	7250.77i	0.718136	−	0.416137i
$133$	11809.6	+	20454.9i	0.667626	+	1.15636i
$134$	−10091.9	−	10064.9i	−0.562037	−	0.560530i
$135$	7428.43	+	4321.49i	0.407596	+	0.237119i
$136$	18109.8	+	17964.5i	0.979117	+	0.971262i
$137$	−2338.02	−	4049.57i	−0.124568	−	0.215759i	0.796996	−	0.603985i	$-0.206421\pi$
$137$	−2338.02	−	4049.57i	−0.124568	−	0.215759i	−0.921564	+	0.388226i	$0.873088\pi$
$138$	−11688.9	−	3128.97i	−0.613783	−	0.164302i
$139$	8058.42	+	4652.53i	0.417081	+	0.240802i	0.693828	−	0.720141i	$-0.255923\pi$
$139$	8058.42	+	4652.53i	0.417081	+	0.240802i	−0.276747	+	0.960943i	$0.589256\pi$
$140$	−5479.79	+	9550.40i	−0.279581	+	0.487265i
$141$	13090.8	−	22616.6i	0.658460	−	1.13760i
$142$	5809.42	−	21798.0i	0.288108	−	1.08104i
$143$		−	17136.8i		−	0.838026i
$144$	20735.9	−	65.8169i	0.999995	−	0.00317404i
$145$	−7725.67			−0.367451
$146$	21244.0	+	5661.77i	0.996624	+	0.265611i
$147$	9.94769	−	9060.44i	0.000460349	−	0.419290i
$148$	−22203.3	−	12739.7i	−1.01367	−	0.581617i
$149$	12385.8	−	21452.8i	0.557893	−	0.966299i	−0.439779	−	0.898106i	$-0.644943\pi$
$149$	12385.8	−	21452.8i	0.557893	−	0.966299i	0.997672	−	0.0681928i	$-0.0217233\pi$
$150$	−12375.2	−	12369.2i	−0.550009	−	0.549740i
$151$	8841.72	−	5104.77i	0.387778	−	0.223884i	−0.293419	−	0.955984i	$-0.594793\pi$
$151$	8841.72	−	5104.77i	0.387778	−	0.223884i	0.681197	+	0.732100i	$0.261460\pi$
$152$	18236.6	−	18384.1i	0.789326	−	0.795709i
$153$	−16203.5	+	27923.5i	−0.692190	+	1.19285i
$154$	−16559.7	+	16604.2i	−0.698251	+	0.700128i
$155$	6485.77	−	3744.56i	0.269959	−	0.155861i
$156$	12252.0	−	21299.0i	0.503451	−	0.875207i
$157$	14486.5	−	25091.4i	0.587712	−	1.01795i	−0.406819	−	0.913509i	$-0.633362\pi$
$157$	14486.5	−	25091.4i	0.587712	−	1.01795i	0.994531	−	0.104439i	$-0.0333046\pi$
$158$	12438.2	−	3350.70i	0.498244	−	0.134221i
$159$	10074.4	−	5801.71i	0.398496	−	0.229489i
$160$	11681.1	+	3046.04i	0.456291	+	0.118986i
$161$	19621.4			0.756970
$162$	6715.12	+	25370.4i	0.255873	+	0.966711i
$163$		−	17736.4i		−	0.667560i	−0.942651	−	0.333780i	$-0.891676\pi$
$163$		−	17736.4i		−	0.667560i	0.942651	−	0.333780i	$-0.108324\pi$
$164$	−34079.0	+	19797.7i	−1.26707	+	0.736084i
$165$	5317.57	+	9233.71i	0.195320	+	0.339163i
$166$	−31503.8	+	8486.75i	−1.14326	+	0.307982i
$167$	35562.1	+	20531.8i	1.27513	+	0.736197i	0.975949	−	0.217999i	$-0.0699530\pi$
$167$	35562.1	+	20531.8i	1.27513	+	0.736197i	0.299182	+	0.954196i	$0.403286\pi$
$168$	−32453.0	+	8797.74i	−1.14984	+	0.311711i
$169$	−277.761	−	481.096i	−0.00972518	−	0.0168445i
$170$	−13271.9	+	13307.6i	−0.459237	+	0.460472i
$171$	28346.4	+	16448.9i	0.969407	+	0.562529i
$172$	−35719.5	+	95.9053i	−1.20739	+	0.00324180i
$173$	−3477.87	−	6023.84i	−0.116204	−	0.201271i	0.802056	−	0.597248i	$-0.203739\pi$
$173$	−3477.87	−	6023.84i	−0.116204	−	0.201271i	−0.918260	+	0.395977i	$0.870406\pi$
$174$	−16686.4	−	16678.2i	−0.551142	−	0.550872i
$175$	24570.9	+	14186.0i	0.802315	+	0.463217i
$176$	22334.1	+	12735.2i	0.721013	+	0.411131i
$177$	−10415.6	−	11.4355i	−0.332457	−	0.000365013i
$178$	−3520.61	−	938.280i	−0.111116	−	0.0296137i
$179$			1754.50i			0.0547580i	0.999625	+	0.0273790i	$0.00871609\pi$
$179$			1754.50i			0.0547580i	−0.999625	+	0.0273790i	$0.991284\pi$
$180$	7.47253	+	15278.2i	0.000230634	+	0.471550i
$181$	−43787.9			−1.33659			−0.668293	−	0.743898i	$-0.732975\pi$
$181$	−43787.9			−1.33659			−0.668293	+	0.743898i	$0.732975\pi$
$182$	−10260.7	+	38500.0i	−0.309766	+	1.16230i
$183$	−46125.2	−	26698.0i	−1.37732	−	0.797216i
$184$	−5651.33	−	20756.3i	−0.166922	−	0.613076i
$185$	9430.49	−	16334.1i	0.275544	−	0.477256i
$186$	22092.1	+	5913.78i	0.638575	+	0.170938i
$187$	−34665.4	+	20014.1i	−0.991318	+	0.572338i
$188$	46456.8	−	124.734i	1.31442	−	0.00352915i
$189$	−21156.4	−	36924.3i	−0.592268	−	1.03369i
$190$	13509.2	+	13473.0i	0.374216	+	0.373213i
$191$	−34403.1	+	19862.7i	−0.943042	+	0.544466i	−0.890913	−	0.454174i	$-0.849934\pi$
$191$	−34403.1	+	19862.7i	−0.943042	+	0.544466i	−0.0521297	+	0.998640i	$0.516601\pi$
$192$	18653.7	+	31796.2i	0.506013	+	0.862526i
$193$	10547.2	−	18268.3i	0.283154	−	0.490437i	−0.689006	−	0.724756i	$-0.741953\pi$
$193$	10547.2	−	18268.3i	0.283154	−	0.490437i	0.972160	+	0.234319i	$0.0752859\pi$
$194$	−18321.4	−	68011.0i	−0.486805	−	1.80707i
$195$	15668.8	+	9069.33i	0.412065	+	0.238510i
$196$	13927.8	−	8091.15i	0.362552	−	0.210619i
$197$	28256.1			0.728080			0.364040	−	0.931383i	$-0.381397\pi$
$197$	28256.1			0.728080			0.364040	+	0.931383i	$0.381397\pi$
$198$	−8448.55	+	31423.1i	−0.215502	+	0.801528i
$199$			24063.5i			0.607650i	0.952728	+	0.303825i	$0.0982638\pi$
$199$			24063.5i			0.607650i	−0.952728	+	0.303825i	$0.901736\pi$
$200$	7929.65	−	30077.9i	0.198241	−	0.751947i
$201$	32069.3	+	35.2097i	0.793775	+	0.000871506i
$202$	6930.33	+	25726.1i	0.169844	+	0.630481i
$203$	33130.7	+	19128.0i	0.803967	+	0.464171i
$204$	−57394.1	+	91.0858i	−1.37914	+	0.00218872i
$205$	−14519.4	−	25148.4i	−0.345495	−	0.598415i
$206$	−19127.4	−	19076.1i	−0.450735	−	0.449527i
$207$	23608.2	−	13561.2i	0.550963	−	0.316488i
$208$	43682.1	−	234.571i	1.00966	−	0.00542184i
$209$	20317.2	+	35190.5i	0.465127	+	0.805624i
$210$	−6417.92	−	23928.6i	−0.145531	−	0.542599i
$211$	−50298.6	−	29039.9i	−1.12977	−	0.652274i	−0.185895	−	0.982570i	$-0.559518\pi$
$211$	−50298.6	−	29039.9i	−1.12977	−	0.652274i	−0.943878	+	0.330295i	$0.892852\pi$
$212$	17926.4	+	10285.7i	0.398860	+	0.228856i
$213$	25330.5	+	43985.2i	0.558322	+	0.969498i
$214$	31.6823	−	118.878i	0.000691814	−	0.00259582i
$215$		−	26318.1i		−	0.569349i
$216$	−32966.6	+	33015.0i	−0.706588	+	0.707625i
$217$	−37084.7			−0.787545
$218$	−41323.1	−	11013.1i	−0.869522	−	0.231737i
$219$	−42867.2	+	24686.7i	−0.893794	+	0.514724i
$220$	−9427.40	+	16430.5i	−0.194781	+	0.339472i
$221$	−34005.2	+	58898.7i	−0.696243	+	1.20593i
$222$	55630.6	−	14920.8i	1.12878	−	0.302751i
$223$	14429.6	−	8330.91i	0.290164	−	0.167526i	−0.347852	−	0.937550i	$-0.613089\pi$
$223$	14429.6	−	8330.91i	0.290164	−	0.167526i	0.638016	+	0.770023i	$0.279755\pi$
$224$	−42551.3	−	41983.8i	−0.848040	−	0.836731i
$225$	39368.0	+	86.4463i	0.777639	+	0.00170758i
$226$	28292.0	−	28368.0i	0.553919	−	0.555409i
$227$	48721.5	−	28129.4i	0.945515	−	0.545894i	0.0538304	−	0.998550i	$-0.482857\pi$
$227$	48721.5	−	28129.4i	0.945515	−	0.545894i	0.891685	+	0.452657i	$0.149524\pi$
$228$	92.4655	+	58263.5i	0.00177873	+	1.12080i
$229$	−1223.91	+	2119.87i	−0.0233388	+	0.0404239i	−0.877459	−	0.479652i	$-0.840763\pi$
$229$	−1223.91	+	2119.87i	−0.0233388	+	0.0404239i	0.854120	+	0.520076i	$0.174096\pi$
$230$	15304.3	−	4122.81i	0.289306	−	0.0779358i
$231$	57.9305	−	52763.5i	0.00108563	−	0.988803i
$232$	10692.1	−	40556.1i	0.198649	−	0.753495i
$233$	−76971.2			−1.41781			−0.708903	−	0.705306i	$-0.750809\pi$
$233$	−76971.2			−1.41781			−0.708903	+	0.705306i	$0.750809\pi$
$234$	14263.5	+	53414.3i	0.260492	+	0.975497i
$235$			34229.3i			0.619816i
$236$	−9301.30	−	16010.9i	−0.167001	−	0.287469i
$237$	−14519.3	+	25084.6i	−0.258494	+	0.446591i
$238$	89863.7	−	24208.3i	1.58646	−	0.427375i
$239$	−22567.5	−	13029.4i	−0.395083	−	0.228101i	0.289277	−	0.957245i	$-0.406585\pi$
$239$	−22567.5	−	13029.4i	−0.395083	−	0.228101i	−0.684360	+	0.729144i	$0.739918\pi$
$240$	−23464.1	+	13681.0i	−0.407364	+	0.237518i
$241$	13999.8	+	24248.4i	0.241039	+	0.417492i	0.961011	−	0.276512i	$-0.0891784\pi$
$241$	13999.8	+	24248.4i	0.241039	+	0.417492i	−0.719971	+	0.694004i	$0.755845\pi$
$242$	12866.1	−	12900.7i	0.219693	−	0.220284i
$243$	−50975.1	−	29804.8i	−0.863268	−	0.504747i
$244$	−254.388	−	94745.6i	−0.00427284	−	1.59140i
$245$	5933.96	+	10277.9i	0.0988582	+	0.171227i
$246$	22930.5	−	85661.6i	0.378916	−	1.41552i
$247$	59790.9	+	34520.3i	0.980034	+	0.565823i
$248$	10681.1	+	39229.6i	0.173665	+	0.637839i
$249$	36775.0	−	63535.0i	0.593135	−	1.02474i
$250$	50623.4	+	13491.7i	0.809975	+	0.215867i
$251$		−	19782.5i		−	0.314003i	−0.987598	−	0.157001i	$-0.949817\pi$
$251$		−	19782.5i		−	0.314003i	0.987598	−	0.157001i	$-0.0501827\pi$
$252$	37795.4	−	65537.5i	0.595165	−	1.03202i
$253$	33756.6			0.527373
$254$	−16571.8	+	62180.7i	−0.256864	+	0.963803i
$255$	46.4289	−	42287.9i	0.000714017	−	0.650332i
$256$	−32156.6	+	57104.5i	−0.490670	+	0.871345i
$257$	−38636.9	+	66921.1i	−0.584974	+	1.01320i	0.409905	+	0.912128i	$0.365562\pi$
$257$	−38636.9	+	66921.1i	−0.584974	+	1.01320i	−0.994879	+	0.101076i	$0.967771\pi$
$258$	56815.7	−	56843.5i	0.853550	−	0.853968i
$259$	−80883.2	+	46698.0i	−1.20575	+	0.696143i
$260$	86.4158	+	32185.2i	0.00127834	+	0.476112i
$261$	53082.6	+	116.562i	0.779239	+	0.00171110i
$262$	59211.7	+	59053.0i	0.862592	+	0.860279i
$263$	−18370.5	+	10606.2i	−0.265588	+	0.153337i	−0.626881	−	0.779115i	$-0.715669\pi$
$263$	−18370.5	+	10606.2i	−0.265588	+	0.153337i	0.361293	+	0.932452i	$0.382335\pi$
$264$	−55832.0	+	15135.6i	−0.801079	+	0.217166i
$265$	−7613.92	+	13187.7i	−0.108422	+	0.187792i
$266$	−24574.9	−	91224.9i	−0.347320	−	1.28929i
$267$	7104.05	−	4091.13i	0.0996514	−	0.0573880i
$268$	28638.5	+	49297.2i	0.398732	+	0.686361i
$269$	1106.24			0.0152878			0.00764389	−	0.999971i	$-0.497567\pi$
$269$	1106.24			0.0152878			0.00764389	+	0.999971i	$0.497567\pi$
$270$	−24260.0	−	24354.9i	−0.332785	−	0.334086i
$271$		−	33038.3i		−	0.449861i	−0.974375	−	0.224931i	$-0.927784\pi$
$271$		−	33038.3i		−	0.449861i	0.974375	−	0.224931i	$-0.0722155\pi$
$272$	−51490.8	−	88088.9i	−0.695972	−	1.19065i
$273$	−44739.1	−	77687.2i	−0.600291	−	1.04238i
$274$	4865.25	+	18060.3i	0.0648043	+	0.240561i
$275$	42271.7	+	24405.6i	0.558964	+	0.322718i
$276$	41955.5	+	24134.3i	0.550771	+	0.316823i
$277$	−14421.3	−	24978.4i	−0.187951	−	0.325540i	0.756616	−	0.653859i	$-0.226851\pi$
$277$	−14421.3	−	24978.4i	−0.187951	−	0.325540i	−0.944567	+	0.328319i	$0.893518\pi$
$278$	−26354.0	−	26283.3i	−0.341002	−	0.340088i
$279$	−44619.8	+	25630.8i	−0.573217	+	0.329271i
$280$	31017.6	−	31268.5i	0.395633	−	0.398833i
$281$	−16062.9	−	27821.8i	−0.203428	−	0.352348i	0.746203	−	0.665719i	$-0.231875\pi$
$281$	−16062.9	−	27821.8i	−0.203428	−	0.352348i	−0.949631	+	0.313371i	$0.898542\pi$
$282$	−73894.4	+	73930.6i	−0.929209	+	0.929664i
$283$	−61782.5	−	35670.2i	−0.771424	−	0.445382i	0.0619586	−	0.998079i	$-0.480265\pi$
$283$	−61782.5	−	35670.2i	−0.771424	−	0.445382i	−0.833382	+	0.552697i	$0.813599\pi$
$284$	−44907.8	+	78267.2i	−0.556782	+	0.970383i
$285$	−42928.4	−	47.1322i	−0.528512	−	0.000580267i
$286$	−17652.4	+	66235.3i	−0.215810	+	0.809762i
$287$			143795.i			1.74574i
$288$	−80213.9	−	21105.4i	−0.967085	−	0.254454i
$289$	75337.7			0.902021
$290$	29860.4	+	7958.12i	0.355058	+	0.0946268i
$291$	137161.	+	79390.6i	1.61973	+	0.937526i
$292$	−76278.0	−	43766.5i	−0.894609	−	0.513305i
$293$	18320.8	−	31732.5i	0.213407	−	0.369631i	−0.739372	−	0.673297i	$-0.764877\pi$
$293$	18320.8	−	31732.5i	0.213407	−	0.369631i	0.952779	+	0.303666i	$0.0982107\pi$
$294$	−9371.50	+	35009.2i	−0.108421	+	0.405030i
$295$	11815.1	−	6821.47i	0.135767	−	0.0783852i
$296$	72694.8	+	72111.6i	0.829698	+	0.823041i
$297$	−36397.4	−	63524.4i	−0.412627	−	0.720158i
$298$	−69970.4	+	70158.5i	−0.787920	+	0.790038i
$299$	49670.5	−	28677.3i	0.555593	−	0.320772i
$300$	35090.0	+	60555.5i	0.389889	+	0.672838i
$301$	−65161.2	+	112863.i	−0.719211	+	1.24571i
$302$	−39432.4	+	10622.6i	−0.432354	+	0.116471i
$303$	−51883.0	−	30030.7i	−0.565119	−	0.327099i
$304$	−89423.2	+	52270.8i	−0.967616	+	0.565603i
$305$	69808.6			0.750428
$306$	91391.5	−	91235.6i	0.976029	−	0.974365i
$307$		−	11668.1i		−	0.123801i	−0.998082	−	0.0619005i	$-0.980284\pi$
$307$		−	11668.1i		−	0.123801i	0.998082	−	0.0619005i	$-0.0197161\pi$
$308$	81108.6	−	47118.9i	0.854999	−	0.496699i
$309$	60781.5	+	66.7335i	0.636582	+	0.000698919i
$310$	−28925.3	+	7792.15i	−0.300992	+	0.0810837i
$311$	−3755.11	−	2168.01i	−0.0388242	−	0.0224151i	0.480462	−	0.877015i	$-0.340469\pi$
$311$	−3755.11	−	2168.01i	−0.0388242	−	0.0224151i	−0.519286	+	0.854600i	$0.673802\pi$
$312$	−69294.9	+	69702.1i	−0.711856	+	0.716039i
$313$	−43249.3	−	74909.9i	−0.441459	−	0.764629i	0.556339	−	0.830955i	$-0.312206\pi$
$313$	−43249.3	−	74909.9i	−0.441459	−	0.764629i	−0.997798	+	0.0663262i	$0.978872\pi$
$314$	−81838.0	+	82058.1i	−0.830034	+	0.832266i
$315$	48212.9	+	27977.1i	0.485895	+	0.281956i
$316$	−51526.1	+	138.345i	−0.516004	+	0.00138545i
$317$	12316.1	+	21332.1i	0.122562	+	0.212283i	0.920777	−	0.390089i	$-0.127556\pi$
$317$	12316.1	+	21332.1i	0.122562	+	0.212283i	−0.798215	+	0.602372i	$0.794222\pi$
$318$	−44914.7	+	12046.6i	−0.444154	+	0.119127i
$319$	56997.9	+	32907.7i	0.560115	+	0.323383i
$320$	−42010.7	−	23805.8i	−0.410260	−	0.232478i
$321$	138.143	+	239.878i	0.00134066	+	0.00232799i
$322$	−75838.5	−	20211.8i	−0.731439	−	0.194936i
$323$		−	161265.i		−	1.54573i
$324$	179.168	−	104976.i	0.00170675	−	0.999999i
$325$	82933.2			0.785167
$326$	−18270.0	+	68552.7i	−0.171911	+	0.645044i
$327$	83383.8	−	48019.7i	0.779806	−	0.449080i
$328$	152112.	−	41415.5i	1.41389	−	0.384960i
$329$	84748.5	−	146789.i	0.782961	−	1.35613i
$330$	−11041.4	−	41166.7i	−0.101390	−	0.378023i
$331$	162176.	−	93632.3i	1.48023	−	0.854614i	0.480485	−	0.877003i	$-0.340461\pi$
$331$	162176.	−	93632.3i	1.48023	−	0.854614i	0.999749	+	0.0223896i	$0.00712742\pi$
$332$	130507.	−	350.405i	1.18402	−	0.00317903i
$333$	−65042.7	+	112088.i	−0.586557	+	1.01081i
$334$	−116301.	−	115989.i	−1.04254	−	1.03974i
$335$	−36378.6	+	21003.2i	−0.324158	+	0.187152i
$336$	134496.	−	574.568i	1.19133	−	0.00508935i
$337$	50479.6	−	87433.2i	0.444484	−	0.769868i	−0.553532	−	0.832828i	$-0.686720\pi$
$337$	50479.6	−	87433.2i	0.444484	−	0.769868i	0.998016	+	0.0629592i	$0.0200538\pi$
$338$	577.999	+	2145.60i	0.00505934	+	0.0187808i
$339$	−98.9732	+	90145.6i	−0.000861228	+	0.784414i
$340$	65005.3	−	37763.9i	0.562330	−	0.326677i
$341$	−63800.3			−0.548674
$342$	−92617.6	−	92775.8i	−0.791847	−	0.793200i
$343$			81392.2i			0.691823i
$344$	138158.	+	36423.6i	1.16751	+	0.307798i
$345$	−17865.0	+	30864.8i	−0.150095	+	0.259314i
$346$	7237.18	+	26865.2i	0.0604529	+	0.224408i
$347$	−151470.	−	87451.5i	−1.25797	−	0.726287i	−0.285287	−	0.958442i	$-0.592089\pi$
$347$	−151470.	−	87451.5i	−1.25797	−	0.726287i	−0.972679	+	0.232155i	$0.925422\pi$
$348$	47314.3	+	81651.2i	0.390691	+	0.674224i
$349$	−21948.5	−	38015.9i	−0.180199	−	0.312114i	0.761749	−	0.647872i	$-0.224341\pi$
$349$	−21948.5	−	38015.9i	−0.180199	−	0.312114i	−0.941948	+	0.335758i	$0.891008\pi$
$350$	−80355.9	−	80140.4i	−0.655967	−	0.654208i
$351$	−107522.	−	62551.2i	−0.872740	−	0.507717i
$352$	−73205.0	−	72228.8i	−0.590820	−	0.582941i
$353$	−77789.6	−	134736.i	−0.624270	−	1.08127i	−0.988682	−	0.150029i	$-0.952063\pi$
$353$	−77789.6	−	134736.i	−0.624270	−	1.08127i	0.364412	−	0.931238i	$-0.381270\pi$
$354$	40245.3	+	10773.1i	0.321150	+	0.0859678i
$355$	−57578.0	−	33242.7i	−0.456878	−	0.263778i
$356$	12641.0	+	7253.07i	0.0997424	+	0.0572298i
$357$	−104900.	+	181232.i	−0.823072	+	1.42200i
$358$	1807.29	−	6781.30i	0.0141014	−	0.0529111i
$359$			184004.i			1.42771i	0.700295	+	0.713853i	$0.253052\pi$
$359$			184004.i			1.42771i	−0.700295	+	0.713853i	$0.746948\pi$
$360$	15709.0	−	59059.4i	0.121212	−	0.455705i
$361$	−33386.7			−0.256188
$362$	169244.	+	45105.4i	1.29151	+	0.344200i
$363$	−45.0092	+	40994.8i	−0.000341577	+	0.311111i
$364$	79316.9	−	138237.i	0.598636	−	1.04333i
$365$	32397.8	−	56114.6i	0.243181	−	0.421202i
$366$	150777.	+	150703.i	1.12557	+	1.12502i
$367$	143674.	−	82950.4i	1.06671	−	0.615866i	0.139430	−	0.990232i	$-0.455473\pi$
$367$	143674.	−	82950.4i	1.06671	−	0.615866i	0.927281	+	0.374366i	$0.122140\pi$
$368$	462.064	+	86046.3i	0.00341198	+	0.635385i
$369$	99382.7	+	173012.i	0.729891	+	1.27064i
$370$	−53275.2	+	53418.5i	−0.389154	+	0.390201i
$371$	65302.9	−	37702.7i	0.474444	−	0.273920i
$372$	−79296.4	−	45614.1i	−0.573017	−	0.329620i
$373$	−65160.0	+	112861.i	−0.468343	+	0.811193i	−0.999345	−	0.0361768i	$-0.988482\pi$
$373$	−65160.0	+	112861.i	−0.468343	+	0.811193i	0.531003	+	0.847370i	$0.321815\pi$
$374$	154601.	−	41647.8i	1.10527	−	0.297748i
$375$	−102150.	+	58827.1i	−0.726403	+	0.418326i
$376$	−179688.	−	47372.4i	−1.27099	−	0.335081i
$377$	111825.			0.786783
$378$	43736.1	+	164509.i	0.306095	+	1.15135i
$379$		−	43645.6i		−	0.303852i	−0.988392	−	0.151926i	$-0.951453\pi$
$379$		−	43645.6i		−	0.303852i	0.988392	−	0.151926i	$-0.0485475\pi$
$380$	−38335.9	−	65990.0i	−0.265484	−	0.456994i
$381$	−72257.3	−	125471.i	−0.497773	−	0.864359i
$382$	153431.	−	41332.7i	1.05145	−	0.283248i
$383$	−237186.	−	136939.i	−1.61693	−	0.933535i	−0.987708	−	0.156310i	$-0.950040\pi$
$383$	−237186.	−	136939.i	−1.61693	−	0.933535i	−0.629223	−	0.777225i	$-0.716627\pi$
$384$	−39345.2	−	142110.i	−0.266827	−	0.963745i
$385$	34556.5	+	59853.6i	0.233135	+	0.403802i
$386$	−59583.9	+	59744.1i	−0.399902	+	0.400978i
$387$	−397.077	+	180830.i	−0.00265126	+	1.20740i
$388$	756.462	+	281741.i	0.00502486	+	1.87149i
$389$	122594.	+	212339.i	0.810159	+	1.40324i	0.912753	+	0.408513i	$0.133952\pi$
$389$	122594.	+	212339.i	0.810159	+	1.40324i	−0.102594	+	0.994723i	$0.532714\pi$
$390$	−51219.0	−	51194.0i	−0.336746	−	0.336581i
$391$	−116020.	−	66984.5i	−0.758894	−	0.438148i
$392$	−62166.8	+	16926.2i	−0.404563	+	0.110151i
$393$	−188158.	−	206.584i	−1.21825	−	0.00133755i
$394$	−109212.	−	29106.2i	−0.703524	−	0.187497i
$395$		−	37964.4i		−	0.243323i
$396$	65023.0	−	112750.i	0.414645	−	0.718998i
$397$	−4252.39			−0.0269806			−0.0134903	−	0.999909i	$-0.504294\pi$
$397$	−4252.39			−0.0269806			−0.0134903	+	0.999909i	$0.504294\pi$
$398$	24787.6	−	93007.8i	0.156483	−	0.587155i
$399$	183977.	+	106489.i	1.15563	+	0.668895i
$400$	−61631.7	+	108086.i	−0.385198	+	0.675535i
$401$	−3665.61	+	6349.02i	−0.0227959	+	0.0394837i	−0.877198	−	0.480128i	$-0.840590\pi$
$401$	−3665.61	+	6349.02i	−0.0227959	+	0.0394837i	0.854402	+	0.519612i	$0.173923\pi$
$402$	−123914.	−	33170.3i	−0.766778	−	0.205257i
$403$	−93877.9	+	54200.4i	−0.578034	+	0.333728i
$404$	−286.143	−	106573.i	−0.00175315	−	0.652955i
$405$	77345.3	+	339.680i	0.471546	+	0.00207090i
$406$	−108349.	−	108059.i	−0.657317	−	0.655554i
$407$	−139151.	+	80339.0i	−0.840036	+	0.484995i
$408$	221927.	+	58769.0i	1.33318	+	0.353043i
$409$	14207.0	−	24607.2i	0.0849289	−	0.147101i	−0.820432	−	0.571744i	$-0.806267\pi$
$409$	14207.0	−	24607.2i	0.0849289	−	0.147101i	0.905361	+	0.424643i	$0.139600\pi$
$410$	30213.8	+	112157.i	0.179737	+	0.667204i
$411$	−36423.0	−	21082.2i	−0.215622	−	0.124805i
$412$	54279.1	+	93433.8i	0.319770	+	0.550440i
$413$	−67557.2			−0.396070
$414$	−105217.	+	28096.6i	−0.613883	+	0.163928i
$415$			96157.5i			0.558325i
$416$	−169077.	−	44089.8i	−0.977007	−	0.254772i
$417$	83745.5	+	91.9464i	0.481603	+	0.000528765i
$418$	−42278.6	−	156943.i	−0.241974	−	0.898233i
$419$	137256.	+	79245.0i	0.781816	+	0.451382i	0.837073	−	0.547091i	$-0.184265\pi$
$419$	137256.	+	79245.0i	0.781816	+	0.451382i	−0.0552577	+	0.998472i	$0.517598\pi$
$420$	157.270	+	99097.2i	0.000891551	+	0.561776i
$421$	142796.	+	247330.i	0.805659	+	1.39544i	0.915845	+	0.401532i	$0.131522\pi$
$421$	142796.	+	247330.i	0.805659	+	1.39544i	−0.110186	+	0.993911i	$0.535145\pi$
$422$	164495.	+	164054.i	0.923693	+	0.921216i
$423$	516.438	−	235188.i	0.00288627	−	1.31442i
$424$	−58691.8	−	58220.9i	−0.326472	−	0.323853i
$425$	−96857.7	−	167763.i	−0.536237	−	0.928789i
$426$	−52596.0	−	196099.i	−0.289824	−	1.08058i
$427$	−299366.	−	172839.i	−1.64190	−	0.947953i
$428$	−244.910	+	426.839i	−0.00133696	+	0.00233011i
$429$	−76968.9	−	133653.i	−0.418216	−	0.726212i
$430$	−27110.0	+	101722.i	−0.146620	+	0.550146i
$431$			115124.i			0.619741i	0.950779	+	0.309870i	$0.100286\pi$
$431$			115124.i			0.619741i	−0.950779	+	0.309870i	$0.899714\pi$
$432$	161427.	−	93647.3i	0.864985	−	0.501797i
$433$	95600.5			0.509899			0.254950	−	0.966954i	$-0.417941\pi$
$433$	95600.5			0.509899			0.254950	+	0.966954i	$0.417941\pi$
$434$	143336.	+	38200.5i	0.760983	+	0.202810i
$435$	−60253.7	+	34699.4i	−0.318424	+	0.183376i
$436$	148373.	+	85133.0i	0.780517	+	0.447842i
$437$	−67999.1	+	117778.i	−0.356074	+	0.616738i
$438$	191115.	−	51259.3i	0.996201	−	0.267192i
$439$	321749.	−	185762.i	1.66951	−	0.963890i	0.701603	−	0.712568i	$-0.252468\pi$
$439$	321749.	−	185762.i	1.66951	−	0.963890i	0.967903	−	0.251322i	$-0.0808654\pi$
$440$	53362.6	−	53794.1i	0.275633	−	0.277862i
$441$	−40616.8	−	70708.5i	−0.208847	−	0.363576i
$442$	192104.	−	192620.i	0.983313	−	0.985957i
$443$	119741.	−	69132.2i	0.610146	−	0.352268i	−0.162877	−	0.986646i	$-0.552077\pi$
$443$	119741.	−	69132.2i	0.610146	−	0.352268i	0.773023	+	0.634379i	$0.218744\pi$
$444$	−230387.	+	365.630i	−1.16867	+	0.00185471i
$445$	−5369.03	+	9299.44i	−0.0271129	+	0.0469609i
$446$	−64353.2	+	17336.0i	−0.323519	+	0.0871524i
$447$	244.776	−	222944.i	0.00122505	−	1.11578i
$448$	121217.	+	206103.i	0.603961	+	1.02690i
$449$	128427.			0.637035			0.318518	−	0.947917i	$-0.396815\pi$
$449$	128427.			0.637035			0.318518	+	0.947917i	$0.396815\pi$
$450$	−152072.	−	40886.6i	−0.750971	−	0.201909i
$451$			247384.i			1.21624i
$452$	−138573.	+	80501.8i	−0.678267	+	0.394030i
$453$	46030.3	−	79525.0i	0.224309	−	0.387532i
$454$	−217289.	+	58535.0i	−1.05421	+	0.283991i
$455$	101695.	+	58713.7i	0.491221	+	0.283607i
$456$	59659.2	−	225289.i	0.286911	−	1.08345i
$457$	−146543.	−	253819.i	−0.701668	−	1.21532i	−0.967881	−	0.251410i	$-0.919106\pi$
$457$	−146543.	−	253819.i	−0.701668	−	1.21532i	0.266213	−	0.963914i	$-0.414227\pi$
$458$	6914.17	−	6932.76i	0.0329617	−	0.0330503i
$459$	−957.032	+	290557.i	−0.00454256	+	1.37913i
$460$	−63399.4	+	170.224i	−0.299619	+	0.000804463i
$461$	−148067.	−	256460.i	−0.696717	−	1.20675i	−0.969598	−	0.244702i	$-0.921310\pi$
$461$	−148067.	−	256460.i	−0.696717	−	1.20675i	0.272881	−	0.962048i	$-0.412023\pi$
$462$	−54575.0	+	203876.i	−0.255688	+	0.955174i
$463$	307165.	+	177342.i	1.43288	+	0.827273i	0.997339	−	0.0728974i	$-0.0232246\pi$
$463$	307165.	+	177342.i	1.43288	+	0.827273i	0.435539	+	0.900170i	$0.356558\pi$
$464$	−83102.4	+	145739.i	−0.385991	+	0.676925i
$465$	33765.1	−	58334.9i	0.156157	−	0.269788i
$466$	297501.	+	79287.2i	1.36999	+	0.365116i
$467$		−	116644.i		−	0.534848i	−0.963579	−	0.267424i	$-0.913828\pi$
$467$		−	116644.i		−	0.534848i	0.963579	−	0.267424i	$-0.0861724\pi$
$468$	−108.161	−	221144.i	−0.000493831	−	1.00968i
$469$	208007.			0.945656
$470$	35259.2	−	132299.i	0.159616	−	0.598911i
$471$	286.292	−	260757.i	0.00129053	−	1.17542i
$472$	19457.7	+	71464.7i	0.0873389	+	0.320780i
$473$	−112103.	+	194168.i	−0.501066	+	0.867872i
$474$	81957.8	−	81997.9i	0.364782	−	0.364961i
$475$	−170304.	+	98324.9i	−0.754809	+	0.435789i
$476$	−372268.	+	999.522i	−1.64302	+	0.00441142i
$477$	52513.7	−	90496.9i	0.230800	−	0.397738i
$478$	73804.1	+	73606.2i	0.323017	+	0.322151i
$479$	90134.6	−	52039.3i	0.392845	−	0.226809i	−0.290547	−	0.956861i	$-0.593837\pi$
$479$	90134.6	−	52039.3i	0.392845	−	0.226809i	0.683392	+	0.730052i	$0.260504\pi$
$480$	104784.	−	28708.2i	0.454790	−	0.124602i
$481$	−136501.	+	236427.i	−0.589992	+	1.02190i
$482$	−29132.5	−	108143.i	−0.125396	−	0.465484i
$483$	153031.	−	88128.4i	0.655970	−	0.377765i
$484$	−63017.5	+	36609.1i	−0.269011	+	0.156278i
$485$	−207587.			−0.882503
$486$	166322.	+	167707.i	0.704168	+	0.710033i
$487$		−	101284.i		−	0.427055i	−0.976937	−	0.213527i	$-0.931505\pi$
$487$		−	101284.i		−	0.427055i	0.976937	−	0.213527i	$-0.0684953\pi$
$488$	−96613.2	+	366462.i	−0.405692	+	1.53883i
$489$	−79661.9	−	138329.i	−0.333145	−	0.578490i
$490$	−12348.1	−	45837.6i	−0.0514291	−	0.190911i
$491$	151749.	+	87612.6i	0.629454	+	0.363416i	0.780541	−	0.625105i	$-0.214944\pi$
$491$	151749.	+	87612.6i	0.629454	+	0.363416i	−0.151086	+	0.988521i	$0.548277\pi$
$492$	−176867.	+	307469.i	−0.730664	+	1.27020i
$493$	−130600.	−	226206.i	−0.537341	−	0.930701i
$494$	−195538.	−	195014.i	−0.801268	−	0.799119i
$495$	82945.3	+	48131.6i	0.338518	+	0.196436i
$496$	−873.306	−	162628.i	−0.00354979	−	0.661048i
$497$	164611.	+	285115.i	0.666418	+	1.15427i
$498$	−207585.	+	207687.i	−0.837024	+	0.837433i
$499$	83227.2	+	48051.2i	0.334244	+	0.192976i	0.657724	−	0.753259i	$-0.271519\pi$
$499$	83227.2	+	48051.2i	0.334244	+	0.192976i	−0.323480	+	0.946235i	$0.604853\pi$
$500$	−181766.	−	104293.i	−0.727066	−	0.417173i
$501$	369572.	+	405.763i	1.47239	+	0.00161658i
$502$	−20377.7	+	76461.1i	−0.0808627	+	0.303412i
$503$		−	164729.i		−	0.651080i	−0.945528	−	0.325540i	$-0.894454\pi$
$503$		−	164729.i		−	0.651080i	0.945528	−	0.325540i	$-0.105546\pi$
$504$	−213592.	+	214376.i	−0.840860	+	0.843946i
$505$	78522.7			0.307902
$506$	−130472.	−	34772.3i	−0.509586	−	0.135810i
$507$	−4327.12	−	2504.60i	−0.0168338	−	0.00974367i
$508$	128103.	−	223264.i	0.496401	−	0.865148i
$509$	42970.1	−	74426.4i	0.165856	−	0.287271i	−0.771103	−	0.636710i	$-0.780295\pi$
$509$	42970.1	−	74426.4i	0.165856	−	0.287271i	0.936959	+	0.349440i	$0.113628\pi$
$510$	−43739.7	+	163399.i	−0.168165	+	0.628214i
$511$	−277869.	+	160428.i	−1.06414	+	0.614380i
$512$	183111.	−	187590.i	0.698512	−	0.715598i
$513$	294958.	+	971.528i	1.12079	+	0.00369165i
$514$	218270.	−	218857.i	0.826166	−	0.828388i
$515$	−68948.9	+	39807.7i	−0.259964	+	0.150090i
$516$	−278152.	+	161180.i	−1.04468	+	0.605358i
$517$	145801.	−	252535.i	0.545481	−	0.944800i
$518$	360724.	−	97174.9i	1.34436	−	0.362155i
$519$	−54180.2	−	31360.3i	−0.201143	−	0.116425i
$520$	32819.6	−	124488.i	0.121374	−	0.460383i
$521$	−173047.			−0.637514			−0.318757	−	0.947836i	$-0.603265\pi$
$521$	−173047.			−0.637514			−0.318757	+	0.947836i	$0.603265\pi$
$522$	−205049.	−	55130.3i	−0.752517	−	0.202325i
$523$		−	252188.i		−	0.921978i	−0.887406	−	0.460989i	$-0.847495\pi$
$523$		−	252188.i		−	0.921978i	0.887406	−	0.460989i	$-0.152505\pi$
$524$	−168029.	−	289238.i	−0.611958	−	1.05340i
$525$	255348.	+	280.353i	0.926433	+	0.00101716i
$526$	81928.8	−	22070.7i	0.296118	−	0.0797709i
$527$	219280.	+	126601.i	0.789547	+	0.455845i
$528$	231387.	−	988.483i	0.829986	−	0.00354570i
$529$	−83431.1	−	144507.i	−0.298137	−	0.516389i
$530$	43013.0	−	43128.6i	0.153126	−	0.153537i
$531$	−81284.0	+	46691.6i	−0.288281	+	0.165596i
$532$	1014.66	+	377907.i	0.00358508	+	1.33525i
$533$	210161.	+	364009.i	0.739770	+	1.28132i
$534$	−31672.0	+	8494.80i	−0.111069	+	0.0297900i
$535$	−314.008	−	181.293i	−0.00109707	−	0.000633393i
$536$	−59910.0	−	220038.i	−0.208530	−	0.765894i
$537$	7880.23	+	13683.6i	0.0273269	+	0.0474518i
$538$	−4275.71	−	1139.52i	−0.0147722	−	0.00393694i
$539$		−	101104.i		−	0.348008i
$540$	68679.5	+	119124.i	0.235526	+	0.408518i
$541$	−472358.			−1.61390			−0.806950	−	0.590620i	$-0.798883\pi$
$541$	−472358.			−1.61390			−0.806950	+	0.590620i	$0.798883\pi$
$542$	−34032.3	+	127696.i	−0.115849	+	0.434688i
$543$	−341509.	+	196671.i	−1.15825	+	0.667022i
$544$	108277.	+	393512.i	0.365881	+	1.32972i
$545$	−63019.0	+	109152.i	−0.212167	+	0.367485i
$546$	92895.9	+	346353.i	0.311610	+	1.16181i
$547$	−332881.	+	192189.i	−1.11254	+	0.642323i	−0.939485	−	0.342590i	$-0.888696\pi$
$547$	−332881.	+	192189.i	−1.11254	+	0.642323i	−0.173051	+	0.984913i	$0.555362\pi$
$548$	−200.879	−	74816.5i	−0.000668918	−	0.249136i
$549$	−479650.	−	1053.24i	−1.59140	−	0.00349449i
$550$	−138244.	−	137873.i	−0.457005	−	0.455779i
$551$	−229632.	+	132578.i	−0.756362	+	0.436686i
$552$	−137301.	−	136499.i	−0.450605	−	0.447973i
$553$	−93996.3	+	162806.i	−0.307369	+	0.532379i
$554$	30009.5	+	111399.i	0.0977777	+	0.362962i
$555$	186.371	−	169749.i	0.000605053	−	0.551087i
$556$	74786.4	+	128734.i	0.241921	+	0.416433i
$557$	−19803.1			−0.0638297			−0.0319148	−	0.999491i	$-0.510161\pi$
$557$	−19803.1			−0.0638297			−0.0319148	+	0.999491i	$0.510161\pi$
$558$	198862.	−	53102.9i	0.638679	−	0.170549i
$559$			380940.i			1.21908i
$560$	−152095.	+	88904.6i	−0.484997	+	0.283497i
$561$	−180469.	+	311791.i	−0.573426	+	0.990689i
$562$	33425.7	+	124080.i	0.105830	+	0.392851i
$563$	132566.	+	76536.8i	0.418229	+	0.241465i	0.694319	−	0.719667i	$-0.255706\pi$
$563$	132566.	+	76536.8i	0.418229	+	0.241465i	−0.276090	+	0.961132i	$0.589039\pi$
$564$	361764.	−	209631.i	1.13728	−	0.659017i
$565$	−59039.2	−	102259.i	−0.184945	−	0.320335i
$566$	202052.	+	201510.i	0.630710	+	0.629019i
$567$	−330846.	−	192956.i	−1.02910	−	0.600195i
$568$	254195.	−	256251.i	0.787898	−	0.794271i
$569$	25955.5	+	44956.2i	0.0801687	+	0.138856i	0.903322	−	0.428963i	$-0.141121\pi$
$569$	25955.5	+	44956.2i	0.0801687	+	0.138856i	−0.823154	+	0.567819i	$0.807787\pi$
$570$	165874.	+	44402.2i	0.510537	+	0.136664i
$571$	92961.9	+	53671.6i	0.285123	+	0.164616i	0.635741	−	0.771903i	$-0.280695\pi$
$571$	92961.9	+	53671.6i	0.285123	+	0.164616i	−0.350617	+	0.936519i	$0.614028\pi$
$572$	136456.	−	237822.i	0.417063	−	0.726874i
$573$	−179104.	+	309432.i	−0.545501	+	0.942444i
$574$	148121.	−	555780.i	0.449566	−	1.68686i
$575$			163364.i			0.494108i
$576$	288293.	+	164202.i	0.868940	+	0.494917i
$577$	−114098.			−0.342710			−0.171355	−	0.985209i	$-0.554814\pi$
$577$	−114098.			−0.342710			−0.171355	+	0.985209i	$0.554814\pi$
$578$	−291187.	−	77604.5i	−0.871598	−	0.232290i
$579$	208.441	−	189850.i	0.000621764	−	0.566308i
$580$	−107216.	−	61517.7i	−0.318714	−	0.182871i
$581$	238077.	−	412361.i	0.705285	−	1.22159i
$582$	−448359.	−	448139.i	−1.32367	−	1.32302i
$583$	112347.	−	64863.5i	0.330540	−	0.190837i
$584$	249738.	+	247734.i	0.732249	+	0.726374i
$585$	162938.	+	357.788i	0.476113	+	0.00104547i
$586$	−103499.	+	103777.i	−0.301397	+	0.302208i
$587$	45237.1	−	26117.7i	0.131286	−	0.0757980i	−0.432919	−	0.901433i	$-0.642516\pi$
$587$	45237.1	−	26117.7i	0.131286	−	0.0757980i	0.564205	+	0.825635i	$0.309183\pi$
$588$	72284.2	−	125660.i	0.209069	−	0.363448i
$589$	128519.	−	222602.i	0.370456	−	0.641649i
$590$	−52693.3	+	14195.0i	−0.151374	+	0.0407784i
$591$	220374.	−	126910.i	0.630935	−	0.363348i
$592$	−206691.	−	353600.i	−0.589763	−	1.00895i
$593$	277354.			0.788724			0.394362	−	0.918955i	$-0.370966\pi$
$593$	277354.			0.788724			0.394362	+	0.918955i	$0.370966\pi$
$594$	75243.4	+	283020.i	0.213253	+	0.802130i
$595$		−	274287.i		−	0.774767i
$596$	342711.	−	199093.i	0.964797	−	0.560485i
$597$	108080.	+	187676.i	0.303247	+	0.526574i
$598$	−221521.	+	59675.3i	−0.619460	+	0.166875i
$599$	−16547.3	−	9553.58i	−0.0461183	−	0.0266264i	0.476764	−	0.879032i	$-0.341810\pi$
$599$	−16547.3	−	9553.58i	−0.0461183	−	0.0266264i	−0.522882	+	0.852405i	$0.675143\pi$
$600$	−73248.4	−	270198.i	−0.203468	−	0.750550i
$601$	209446.	+	362771.i	0.579861	+	1.00435i	0.995495	+	0.0948161i	$0.0302263\pi$
$601$	209446.	+	362771.i	0.579861	+	1.00435i	−0.415634	+	0.909532i	$0.636440\pi$
$602$	368112.	−	369102.i	1.01575	−	1.01848i
$603$	250272.	−	143763.i	0.688299	−	0.395377i
$604$	163352.	−	438.593i	0.447765	−	0.00120223i
$605$	−26848.8	−	46503.4i	−0.0733522	−	0.127050i
$606$	169598.	+	169515.i	0.461823	+	0.461598i
$607$	−331153.	−	191191.i	−0.898776	−	0.518909i	−0.0219735	−	0.999759i	$-0.506995\pi$
$607$	−331153.	−	191191.i	−0.898776	−	0.518909i	−0.876803	+	0.480850i	$0.840328\pi$
$608$	399472.	−	109917.i	1.08064	−	0.297344i
$609$	344304.	+	378.020i	0.928341	+	0.00101925i
$610$	−269816.	−	71909.0i	−0.725118	−	0.193252i
$611$		−	495450.i		−	1.32714i
$612$	−447217.	+	258493.i	−1.19403	+	0.690153i
$613$	−210852.			−0.561121			−0.280560	−	0.959836i	$-0.590520\pi$
$613$	−210852.			−0.561121			−0.280560	+	0.959836i	$0.590520\pi$
$614$	−12019.2	+	45098.3i	−0.0318815	+	0.119625i
$615$	−226192.	−	130923.i	−0.598035	−	0.346152i
$616$	−362029.	+	98569.7i	−0.954073	+	0.259766i
$617$	−313290.	+	542634.i	−0.822955	+	1.42540i	0.0805170	+	0.996753i	$0.474343\pi$
$617$	−313290.	+	542634.i	−0.822955	+	1.42540i	−0.903472	+	0.428647i	$0.858990\pi$
$618$	−234857.	−	62868.2i	−0.614931	−	0.164609i
$619$	−35684.5	+	20602.5i	−0.0931319	+	0.0537697i	−0.545843	−	0.837888i	$-0.683790\pi$
$619$	−35684.5	+	20602.5i	−0.0931319	+	0.0537697i	0.452711	+	0.891657i	$0.350457\pi$
$620$	119825.	−	321.726i	0.311721	−	0.000836956i
$621$	123215.	−	211801.i	0.319508	−	0.549218i
$622$	12280.6	+	12247.7i	0.0317423	+	0.0316572i
$623$	46049.0	−	26586.4i	0.118644	−	0.0684989i
$624$	339630.	−	198025.i	0.872242	−	0.508570i
$625$	−74680.7	+	129351.i	−0.191183	+	0.331138i
$626$	89998.5	+	334084.i	0.229661	+	0.852525i
$627$	316513.	+	183203.i	0.805113	+	0.466012i
$628$	400838.	−	232861.i	1.01637	−	0.590443i
$629$	637678.			1.61176
$630$	−157528.	−	157797.i	−0.396897	−	0.397575i
$631$		−	150814.i		−	0.378777i	−0.981902	−	0.189389i	$-0.939349\pi$
$631$		−	150814.i		−	0.378777i	0.981902	−	0.189389i	$-0.0606506\pi$
$632$	199296.	+	52541.7i	0.498958	+	0.131544i
$633$	−522718.	−	573.906i	−1.30455	−	0.00143230i
$634$	−25628.9	−	95137.3i	−0.0637605	−	0.236686i
$635$	164246.	+	94827.4i	0.407331	+	0.235172i
$636$	186008.	−	295.200i	0.459852	−	0.000729796i
$637$	−85890.8	−	148767.i	−0.211674	−	0.366630i
$638$	−186404.	−	185904.i	−0.457946	−	0.456718i
$639$	395113.	+	229277.i	0.967654	+	0.561512i
$640$	137853.	+	135286.i	0.336555	+	0.330288i
$641$	−214189.	−	370987.i	−0.521293	−	0.902906i	−0.999693	−	0.0247640i	$-0.992117\pi$
$641$	−214189.	−	370987.i	−0.521293	−	0.902906i	0.478400	−	0.878142i	$-0.341217\pi$
$642$	−286.839	−	1069.45i	−0.000695933	−	0.00259472i
$643$	−74279.9	−	42885.5i	−0.179659	−	0.103726i	0.407473	−	0.913217i	$-0.366410\pi$
$643$	−74279.9	−	42885.5i	−0.179659	−	0.103726i	−0.587133	+	0.809491i	$0.699743\pi$
$644$	272303.	+	156241.i	0.656569	+	0.376723i
$645$	−118206.	−	205260.i	−0.284133	−	0.493383i
$646$	−166117.	+	623304.i	−0.398061	+	1.49360i
$647$			128368.i			0.306653i	0.988176	+	0.153327i	$0.0489986\pi$
$647$			128368.i			0.306653i	−0.988176	+	0.153327i	$0.951001\pi$
$648$	−108827.	+	405557.i	−0.259171	+	0.965831i
$649$	−116225.			−0.275937
$650$	−320544.	−	85428.6i	−0.758685	−	0.202198i
$651$	−289230.	+	166564.i	−0.682465	+	0.393023i
$652$	141231.	−	246143.i	0.332226	−	0.579018i
$653$	232940.	−	403463.i	0.546282	−	0.946189i	−0.452243	−	0.891895i	$-0.649376\pi$
$653$	232940.	−	403463.i	0.546282	−	0.946189i	0.998525	−	0.0542939i	$-0.0172908\pi$
$654$	−371751.	+	99707.7i	−0.869153	+	0.233117i
$655$	213442.	−	123231.i	0.497504	−	0.287234i
$656$	−630587.	+	3386.22i	−1.46534	+	0.00786878i
$657$	−223450.	+	385071.i	−0.517666	+	0.892094i
$658$	−478766.	+	480053.i	−1.10579	+	1.10876i
$659$	−303989.	+	175508.i	−0.699983	+	0.404135i	−0.807341	−	0.590085i	$-0.799094\pi$
$659$	−303989.	+	175508.i	−0.699983	+	0.404135i	0.107358	+	0.994220i	$0.465761\pi$
$660$	270.566	+	170486.i	0.000621134	+	0.391383i
$661$	141131.	−	244446.i	0.323013	−	0.559475i	−0.658095	−	0.752935i	$-0.728638\pi$
$661$	141131.	−	244446.i	0.323013	−	0.559475i	0.981108	+	0.193460i	$0.0619709\pi$
$662$	−723274.	+	194842.i	−1.65039	+	0.444597i
$663$	−672.033	+	612093.i	−0.00152884	+	1.39248i
$664$	−504782.	−	133079.i	−1.14490	−	0.301838i
$665$	−278442.			−0.629638
$666$	366857.	−	366231.i	0.827081	−	0.825671i
$667$			220276.i			0.495125i
$668$	330035.	+	568110.i	0.739618	+	1.27315i
$669$	75120.8	−	129784.i	0.167845	−	0.289980i
$670$	162242.	−	43706.0i	0.361420	−	0.0973625i
$671$	−515029.	−	297352.i	−1.14390	−	0.660428i
$672$	−520432.	−	136322.i	−1.15246	−	0.301876i
$673$	398590.	+	690378.i	0.880028	+	1.52425i	0.851309	+	0.524665i	$0.175809\pi$
$673$	398590.	+	690378.i	0.880028	+	1.52425i	0.0287190	+	0.999588i	$0.490857\pi$
$674$	−285172.	+	285939.i	−0.627751	+	0.629438i
$675$	307425.	−	176145.i	0.674733	−	0.386600i
$676$	−23.8647	−	8888.32i	−5.22231e−5	−	0.0194503i
$677$	−140673.	−	243653.i	−0.306926	−	0.531612i	0.670762	−	0.741673i	$-0.265967\pi$
$677$	−140673.	−	243653.i	−0.306926	−	0.531612i	−0.977688	+	0.210061i	$0.932634\pi$
$678$	93240.5	−	348319.i	0.202836	−	0.757735i
$679$	890213.	+	513965.i	1.93088	+	1.11479i
$680$	−290151.	+	78999.7i	−0.627490	+	0.170847i
$681$	253645.	−	438215.i	0.546931	−	0.944915i
$682$	246594.	+	65720.0i	0.530168	+	0.141296i
$683$			687094.i			1.47291i	0.676489	+	0.736453i	$0.263501\pi$
$683$			687094.i			1.47291i	−0.676489	+	0.736453i	$0.736499\pi$
$684$	262408.	+	453991.i	0.560874	+	0.970365i
$685$	55124.8			0.117480
$686$	83841.2	−	314588.i	0.178160	−	0.668489i
$687$	−24.1877	+	22030.3i	−5.12484e−5	+	0.0466775i
$688$	−496473.	−	283095.i	−1.04886	−	0.598075i
$689$	110207.	−	190884.i	0.232152	−	0.402098i
$690$	100843.	−	100893.i	0.211812	−	0.211915i
$691$	284957.	−	164520.i	0.596792	−	0.344558i	−0.170986	−	0.985273i	$-0.554695\pi$
$691$	284957.	−	164520.i	0.596792	−	0.344558i	0.767779	+	0.640715i	$0.221362\pi$
$692$	−298.812	−	111291.i	−0.000624002	−	0.232407i
$693$	−236532.	−	411772.i	−0.492520	−	0.857413i
$694$	495364.	+	494036.i	1.02850	+	1.02574i
$695$	−94998.8	+	54847.6i	−0.196675	+	0.113550i
$696$	−98765.9	−	364327.i	−0.203887	−	0.752095i
$697$	490893.	−	850252.i	1.01047	−	1.75018i
$698$	45673.1	+	169544.i	0.0937453	+	0.347993i
$699$	−600311.	+	345712.i	−1.22863	+	0.707554i
$700$	228031.	+	392524.i	0.465369	+	0.801069i
$701$	−961471.			−1.95659			−0.978296	−	0.207214i	$-0.933560\pi$
$701$	−961471.			−1.95659			−0.978296	+	0.207214i	$0.933560\pi$
$702$	351150.	+	352523.i	0.712556	+	0.715342i
$703$		−	647338.i		−	1.30985i
$704$	208542.	+	354578.i	0.420773	+	0.715429i
$705$	153739.	+	266960.i	0.309318	+	0.537116i
$706$	161874.	+	600895.i	0.324764	+	1.20556i
$707$	−336736.	−	194415.i	−0.673676	−	0.388947i
$708$	−144454.	−	83095.3i	−0.288180	−	0.165772i
$709$	299138.	+	518122.i	0.595085	+	1.03072i	0.993535	+	0.113528i	$0.0362151\pi$
$709$	299138.	+	518122.i	0.595085	+	1.03072i	−0.398450	+	0.917190i	$0.630452\pi$
$710$	188301.	+	187796.i	0.373540	+	0.372538i
$711$	−572.792	+	260851.i	−0.00113307	+	0.516005i
$712$	−41387.1	−	41055.1i	−0.0816404	−	0.0809854i
$713$	−106766.	−	184923.i	−0.210016	−	0.363758i
$714$	592132.	−	592422.i	1.16151	−	1.16208i
$715$	174956.	+	101011.i	0.342229	+	0.197586i
$716$	−13970.7	+	24348.7i	−0.0272516	+	0.0474951i
$717$	−234529.	−	257.495i	−0.456202	−	0.000500876i
$718$	189541.	−	711193.i	0.367666	−	1.37955i
$719$		−	608601.i		−	1.17727i	−0.808400	−	0.588633i	$-0.799666\pi$
$719$		−	608601.i		−	1.17727i	0.808400	−	0.588633i	$-0.200334\pi$
$720$	−121553.	+	212088.i	−0.234478	+	0.409121i
$721$	394240.			0.758385
$722$	129043.	+	34391.3i	0.247548	+	0.0659742i
$723$	218097.	+	126238.i	0.417227	+	0.241498i
$724$	−607681.	−	348673.i	−1.15931	−	0.665183i
$725$	−159256.	+	275840.i	−0.302985	+	0.524785i
$726$	42402.2	−	158402.i	0.0804480	−	0.300530i
$727$	−396978.	+	229195.i	−0.751100	+	0.433648i	−0.826091	−	0.563536i	$-0.809440\pi$
$727$	−396978.	+	229195.i	−0.751100	+	0.433648i	0.0749911	+	0.997184i	$0.476107\pi$
$728$	−448963.	+	452594.i	−0.847125	+	0.853976i
$729$	−531429.	−	3500.87i	−0.999978	−	0.00658750i
$730$	−183023.	+	183515.i	−0.343448	+	0.344371i
$731$	770590.	−	444900.i	1.44208	−	0.832584i
$732$	−427528.	−	737794.i	−0.797890	−	1.37693i
$733$	−35347.8	+	61224.2i	−0.0657892	+	0.113950i	−0.897044	−	0.441942i	$-0.854290\pi$
$733$	−35347.8	+	61224.2i	−0.0657892	+	0.113950i	0.831255	+	0.555892i	$0.187623\pi$
$734$	−640760.	+	172614.i	−1.18933	+	0.320393i
$735$	92442.7	+	53507.2i	0.171119	+	0.0990462i
$736$	86849.4	−	333053.i	0.160329	−	0.614833i
$737$	357855.			0.658828
$738$	−205905.	−	771080.i	−0.378055	−	1.41575i
$739$		−	476430.i		−	0.872390i	−0.899852	−	0.436195i	$-0.856326\pi$
$739$		−	476430.i		−	0.872390i	0.899852	−	0.436195i	$-0.143674\pi$
$740$	260939.	−	151589.i	0.476514	−	0.276824i
$741$	621365.	+	682.212i	1.13164	+	0.00124246i
$742$	−291239.	+	78456.4i	−0.528982	+	0.142502i
$743$	109137.	+	63010.2i	0.197694	+	0.114139i	0.595579	−	0.803296i	$-0.296922\pi$
$743$	109137.	+	63010.2i	0.197694	+	0.114139i	−0.397885	+	0.917435i	$0.630256\pi$
$744$	259501.	+	257985.i	0.468806	+	0.466067i
$745$	146013.	+	252902.i	0.263074	+	0.455658i
$746$	368106.	−	369095.i	0.661447	−	0.663225i
$747$	1450.78	−	660692.i	0.00259993	−	1.18402i
$748$	−640448.	+	1719.57i	−1.14467	+	0.00307339i
$749$	897.727	+	1554.91i	0.00160022	+	0.00277167i
$750$	455417.	−	122148.i	0.809631	−	0.217152i
$751$	−176908.	−	102138.i	−0.313667	−	0.181096i	0.334899	−	0.942254i	$-0.391298\pi$
$751$	−176908.	−	102138.i	−0.313667	−	0.181096i	−0.648566	+	0.761158i	$0.724631\pi$
$752$	645712.	+	368193.i	1.14184	+	0.651089i
$753$	−88851.9	−	154287.i	−0.156703	−	0.272107i
$754$	−432212.	−	115189.i	−0.760247	−	0.202614i
$755$			120358.i			0.211145i
$756$	414.547	−	680893.i	0.000725321	−	1.19134i
$757$	588244.			1.02652			0.513258	−	0.858235i	$-0.328438\pi$
$757$	588244.			1.02652			0.513258	+	0.858235i	$0.328438\pi$
$758$	−44958.8	+	168694.i	−0.0782485	+	0.293603i
$759$	263273.	−	151616.i	0.457007	−	0.263185i
$760$	80196.3	+	294546.i	0.138844	+	0.509949i
$761$	25368.8	−	43940.0i	0.0438056	−	0.0758736i	−0.843291	−	0.537457i	$-0.819385\pi$
$761$	25368.8	−	43940.0i	0.0438056	−	0.0758736i	0.887097	+	0.461583i	$0.152718\pi$
$762$	150034.	+	559389.i	0.258393	+	0.963394i
$763$	540501.	−	312058.i	0.928426	−	0.536027i
$764$	−635603.	+	1706.56i	−1.08893	+	0.00292372i
$765$	−189571.	−	330018.i	−0.323929	−	0.563917i
$766$	775685.	+	773605.i	1.32199	+	1.31844i
$767$	−171017.	+	98737.0i	−0.290703	+	0.167838i
$768$	5686.92	+	589797.i	0.00964172	+	0.999954i
$769$	−441340.	+	764423.i	−0.746312	+	1.29265i	0.203268	+	0.979123i	$0.434844\pi$
$769$	−441340.	+	764423.i	−0.746312	+	1.29265i	−0.949579	+	0.313526i	$0.898490\pi$
$770$	−71909.4	−	266936.i	−0.121284	−	0.450221i
$771$	−763.568	+	695464.i	−0.00128451	+	1.16995i
$772$	291839.	−	169540.i	0.489675	−	0.284470i
$773$	−100820.			−0.168728			−0.0843642	−	0.996435i	$-0.526886\pi$
$773$	−100820.			−0.168728			−0.0843642	+	0.996435i	$0.526886\pi$
$774$	187806.	−	698517.i	0.313493	−	1.16599i
$775$		−	308760.i		−	0.514065i
$776$	287294.	−	1.08973e6i	0.477094	−	1.80966i
$777$	−421081.	+	727487.i	−0.697466	+	1.20499i
$778$	−255109.	−	946992.i	−0.421470	−	1.56454i
$779$	−863131.	−	498329.i	−1.42233	−	0.821185i
$780$	145232.	+	250629.i	0.238711	+	0.411949i
$781$	283197.	+	490511.i	0.464286	+	0.804168i
$782$	379430.	+	378412.i	0.620466	+	0.618802i
$783$	414523.	−	237508.i	0.676122	−	0.387396i
$784$	257716.	−	1383.92i	0.419284	−	0.00225153i
$785$	170778.	+	295796.i	0.277136	+	0.480013i
$786$	727035.	+	194618.i	1.17682	+	0.315020i
$787$	98569.7	+	56909.2i	0.159145	+	0.0918826i	0.577458	−	0.816421i	$-0.304045\pi$
$787$	98569.7	+	56909.2i	0.159145	+	0.0918826i	−0.418312	+	0.908303i	$0.637378\pi$
$788$	392133.	+	224996.i	0.631511	+	0.362346i
$789$	−95637.2	+	165229.i	−0.153629	+	0.265420i
$790$	−39106.7	+	146736.i	−0.0626610	+	0.235116i
$791$			584701.i			0.934504i
$792$	−367463.	+	368811.i	−0.585818	+	0.587968i
$793$	−1.01044e6			−1.60681
$794$	16435.9	+	4380.34i	0.0260707	+	0.00694811i
$795$	−150.471	+	137050.i	−0.000238078	+	0.216843i
$796$	−191612.	+	333950.i	−0.302411	+	0.527054i
$797$	350591.	−	607241.i	0.551930	−	0.955971i	−0.446205	−	0.894931i	$-0.647225\pi$
$797$	350591.	−	607241.i	0.551930	−	0.955971i	0.998135	−	0.0610403i	$-0.0194418\pi$
$798$	−601395.	−	601101.i	−0.944396	−	0.943934i
$799$	−1.00223e6	+	578637.i	−1.56990	+	0.906384i
$800$	349550.	−	354274.i	0.546171	−	0.553553i
$801$	37030.6	−	63814.8i	0.0577159	−	0.0994619i
$802$	20708.0	−	20763.6i	0.0321950	−	0.0322816i
$803$	−478044.	+	275999.i	−0.741373	+	0.428032i
$804$	444772.	+	255849.i	0.688059	+	0.395796i
$805$	−115656.	+	200322.i	−0.178475	+	0.309127i
$806$	418678.	−	112787.i	0.644480	−	0.173616i
$807$	8627.74	−	4968.60i	0.0132480	−	0.00762935i
$808$	−108673.	+	412208.i	−0.166456	+	0.631384i
$809$	514560.			0.786211			0.393105	−	0.919493i	$-0.371401\pi$
$809$	514560.			0.786211			0.393105	+	0.919493i	$0.371401\pi$
$810$	−298597.	−	80985.4i	−0.455108	−	0.123434i
$811$			36669.2i			0.0557519i	0.999611	+	0.0278759i	$0.00887434\pi$
$811$			36669.2i			0.0557519i	−0.999611	+	0.0278759i	$0.991126\pi$
$812$	307470.	+	529267.i	0.466327	+	0.802718i
$813$	−148389.	−	257671.i	−0.224503	−	0.389838i
$814$	620588.	−	167179.i	0.936601	−	0.252310i
$815$	181077.	+	104545.i	0.272614	+	0.157394i
$816$	−797231.	−	455752.i	−1.19730	−	0.684460i
$817$	−451640.	−	782263.i	−0.676625	−	1.17195i
$818$	−80258.9	+	80474.7i	−0.119946	+	0.120269i
$819$	−697855.	−	404952.i	−1.04039	−	0.603721i
$820$	−1247.48	−	464620.i	−0.00185527	−	0.690987i
$821$	239492.	+	414812.i	0.355307	+	0.615410i	0.987170	−	0.159670i	$-0.0510430\pi$
$821$	239492.	+	414812.i	0.355307	+	0.615410i	−0.631863	+	0.775080i	$0.717710\pi$
$822$	119062.	+	119004.i	0.176209	+	0.176123i
$823$	−679126.	−	392093.i	−1.00265	−	0.578882i	−0.0936206	−	0.995608i	$-0.529844\pi$
$823$	−679126.	−	392093.i	−1.00265	−	0.578882i	−0.909032	+	0.416726i	$0.863177\pi$
$824$	−113548.	−	417042.i	−0.167235	−	0.614222i
$825$	439300.	+	482.319i	0.645436	+	0.000708641i
$826$	261115.	+	69589.9i	0.382711	+	0.101997i
$827$			1.21724e6i			1.77978i	0.456175	+	0.889890i	$0.349219\pi$
$827$			1.21724e6i			1.77978i	−0.456175	+	0.889890i	$0.650781\pi$
$828$	435616.	−	213.058i	0.635394	−	0.000310769i
$829$	−335235.			−0.487799			−0.243900	−	0.969801i	$-0.578427\pi$
$829$	−335235.			−0.487799			−0.243900	+	0.969801i	$0.578427\pi$
$830$	99050.7	−	371657.i	0.143781	−	0.539494i
$831$	−224663.	−	130038.i	−0.325333	−	0.188308i
$832$	608081.	+	344575.i	0.878445	+	0.497780i
$833$	−200624.	+	347491.i	−0.289130	+	0.500787i
$834$	−323589.	−	86620.7i	−0.465224	−	0.124534i
$835$	−419233.	+	242044.i	−0.601288	+	0.347154i
$836$	1745.62	+	650149.i	0.00249768	+	0.930252i
$837$	−232878.	+	400306.i	−0.332413	+	0.571401i
$838$	−448879.	−	447675.i	−0.639206	−	0.637492i
$839$	808477.	−	466775.i	1.14853	−	0.663107i	0.200005	−	0.979795i	$-0.435904\pi$
$839$	808477.	−	466775.i	1.14853	−	0.663107i	0.948530	+	0.316688i	$0.102571\pi$
$840$	101471.	−	383182.i	0.143808	−	0.543058i
$841$	138904.	−	240589.i	0.196391	−	0.340160i
$842$	−297147.	−	1.10304e6i	−0.419129	−	1.55585i
$843$	−250237.	−	144841.i	−0.352124	−	0.203815i
$844$	−466798.	−	803527.i	−0.655305	−	1.12802i
$845$	6548.91			0.00917182
$846$	−244260.	+	908489.i	−0.341281	+	1.26934i
$847$			265900.i			0.370639i
$848$	166876.	+	285487.i	0.232061	+	0.397004i
$849$	−642063.	−	704.937i	−0.890763	−	0.000977991i
$850$	201554.	+	748189.i	0.278967	+	1.03556i
$851$	−465721.	−	268884.i	−0.643082	−	0.371284i
$852$	1288.85	+	812120.i	0.00177551	+	1.11877i
$853$	−124910.	−	216350.i	−0.171672	−	0.297344i	0.767333	−	0.641249i	$-0.221583\pi$
$853$	−124910.	−	216350.i	−0.171672	−	0.297344i	−0.939004	+	0.343905i	$0.888250\pi$
$854$	979039.	+	976413.i	1.34241	+	1.33881i
$855$	−335017.	+	192443.i	−0.458284	+	0.263251i
$856$	1386.28	−	1397.49i	0.00189193	−	0.00190723i
$857$	−330493.	−	572431.i	−0.449988	−	0.779402i	0.548397	−	0.836218i	$-0.315238\pi$
$857$	−330493.	−	572431.i	−0.449988	−	0.779402i	−0.998385	+	0.0568162i	$0.981905\pi$
$858$	159818.	+	595865.i	0.217095	+	0.809418i
$859$	716685.	+	413779.i	0.971275	+	0.560766i	0.899625	−	0.436664i	$-0.143840\pi$
$859$	716685.	+	413779.i	0.971275	+	0.560766i	0.0716503	+	0.997430i	$0.477173\pi$
$860$	209565.	−	365239.i	0.283349	−	0.493833i
$861$	645846.	+	1.12148e6i	0.871209	+	1.51281i
$862$	118588.	−	444963.i	0.159597	−	0.598838i
$863$		−	1.22724e6i		−	1.64781i	−0.566728	−	0.823905i	$-0.691791\pi$
$863$		−	1.22724e6i		−	1.64781i	0.566728	−	0.823905i	$-0.308209\pi$
$864$	−720395.	+	195671.i	−0.965035	+	0.262120i
$865$	81999.4			0.109592
$866$	−369505.	−	98477.0i	−0.492702	−	0.131310i
$867$	587571.	−	338375.i	0.781668	−	0.450152i
$868$	−514655.	−	295297.i	−0.683088	−	0.391940i
$869$	−161711.	+	280091.i	−0.214141	+	0.370903i
$870$	268630.	−	72049.5i	0.354908	−	0.0951902i
$871$	526560.	−	304009.i	0.694083	−	0.400729i
$872$	−485781.	−	481884.i	−0.638863	−	0.633738i
$873$	1.42632e6	+	3131.98i	1.87149	+	0.00410952i
$874$	384144.	−	385177.i	0.502888	−	0.504240i
$875$	−662147.	+	382291.i	−0.864845	+	0.499318i
$876$	−791479.	+	1256.10i	−1.03141	+	0.00163687i
$877$	313105.	−	542314.i	0.407091	−	0.705102i	−0.587472	−	0.809245i	$-0.699877\pi$
$877$	313105.	−	542314.i	0.407091	−	0.705102i	0.994562	+	0.104143i	$0.0332099\pi$
$878$	−1.43494e6	+	386556.i	−1.86142	+	0.501446i
$879$	362.067	−	329773.i	0.000468609	−	0.426813i
$880$	−261664.	+	152951.i	−0.337892	+	0.197509i
$881$	447853.			0.577011			0.288505	−	0.957478i	$-0.406842\pi$
$881$	447853.			0.577011			0.288505	+	0.957478i	$0.406842\pi$
$882$	84151.7	+	315134.i	0.108175	+	0.405096i
$883$			1.38655e6i			1.77833i	0.457582	+	0.889167i	$0.348715\pi$
$883$			1.38655e6i			1.77833i	−0.457582	+	0.889167i	$0.651285\pi$
$884$	−940915.	+	546611.i	−1.20405	+	0.699478i
$885$	61509.9	−	106269.i	0.0785342	−	0.135681i
$886$	−534020.	+	143859.i	−0.680284	+	0.183261i
$887$	1.32667e6	+	765956.i	1.68623	+	0.973546i	0.957361	+	0.288895i	$0.0932877\pi$
$887$	1.32667e6	+	765956.i	1.68623	+	0.973546i	0.728870	+	0.684652i	$0.240046\pi$
$888$	890843.	+	235906.i	1.12973	+	0.299166i
$889$	−469567.	−	813314.i	−0.594147	−	1.02909i
$890$	30331.0	−	30412.6i	0.0382919	−	0.0383949i
$891$	−569186.	−	331961.i	−0.716966	−	0.418149i
$892$	266588.	−	715.777i	0.335051	−	0.000899598i
$893$	587401.	+	1.01741e6i	0.736601	+	1.27583i
$894$	−230598.	+	861446.i	−0.288523	+	1.07784i
$895$	−17912.3	−	10341.7i	−0.0223618	−	0.0129106i
$896$	−256212.	−	921470.i	−0.319142	−	1.14780i
$897$	258586.	−	446751.i	0.321381	−	0.555240i
$898$	−496382.	−	132291.i	−0.615550	−	0.164051i
$899$		−	416323.i		−	0.515124i
$900$	545654.	+	314678.i	0.673646	+	0.388491i
$901$	−514844.			−0.634200
$902$	254827.	−	956161.i	0.313208	−	1.17522i
$903$	−1287.76	+	1.17290e6i	−0.00157928	+	1.43842i
$904$	618520.	−	168405.i	0.756862	−	0.206071i
$905$	258102.	−	447047.i	0.315134	−	0.545828i
$906$	−259829.	+	259956.i	−0.316542	+	0.316697i
$907$	282696.	−	163214.i	0.343641	−	0.198401i	−0.318240	−	0.948010i	$-0.603092\pi$
$907$	282696.	−	163214.i	0.343641	−	0.198401i	0.661881	+	0.749609i	$0.269758\pi$
$908$	900136.	−	2416.82i	1.09178	−	0.00293139i
$909$	−539525.	−	1184.72i	−0.652956	−	0.00143380i
$910$	−332580.	−	331689.i	−0.401619	−	0.400542i
$911$	1.11746e6	−	645168.i	1.34647	−	0.777384i	0.358722	−	0.933445i	$-0.383213\pi$
$911$	1.11746e6	−	645168.i	1.34647	−	0.777384i	0.987748	+	0.156060i	$0.0498793\pi$
$912$	−462655.	+	809308.i	−0.556247	+	0.973025i
$913$	409586.	−	709424.i	0.491364	−	0.851068i
$914$	304944.	+	1.13199e6i	0.365029	+	1.35503i
$915$	544449.	−	313541.i	0.650301	−	0.374500i
$916$	−33865.2	+	19673.5i	−0.0403611	+	0.0234472i
$917$	−1.22043e6			−1.45135
$918$	302998.	−	1.12204e6i	0.359546	−	1.33145i
$919$		−	844321.i		−	0.999715i	−0.866108	−	0.499858i	$-0.833386\pi$
$919$		−	844321.i		−	0.999715i	0.866108	−	0.499858i	$-0.166614\pi$
$920$	245220.	+	64649.0i	0.289721	+	0.0763812i
$921$	−52406.6	−	91001.6i	−0.0617827	−	0.107283i
$922$	308116.	+	1.14376e6i	0.362454	+	1.34547i
$923$	833409.	+	481169.i	0.978262	+	0.564800i
$924$	420948.	−	731782.i	0.493042	−	0.857113i
$925$	−388799.	−	673419.i	−0.454403	−	0.787050i
$926$	−1.00454e6	−	1.00185e6i	−1.17151	−	1.16837i
$927$	474344.	−	272476.i	0.551994	−	0.317080i
$928$	471322.	−	477693.i	0.547296	−	0.554693i
$929$	−301633.	−	522445.i	−0.349501	−	0.605353i	0.636660	−	0.771145i	$-0.280315\pi$
$929$	−301633.	−	522445.i	−0.349501	−	0.605353i	−0.986161	+	0.165792i	$0.946982\pi$
$930$	−190595.	+	190689.i	−0.220367	+	0.220475i
$931$	352754.	+	203663.i	0.406980	+	0.234970i
$932$	−1.06819e6	−	612904.i	−1.22975	−	0.705603i
$933$	−39024.2	−	42.8457i	−0.0448303	−	4.92203e-5i
$934$	−120154.	+	450841.i	−0.137735	+	0.516809i
$935$		−	471882.i		−	0.539772i
$936$	−227380.	+	854852.i	−0.259537	+	0.975751i
$937$	−109044.			−0.124200			−0.0621002	−	0.998070i	$-0.519780\pi$
$937$	−109044.			−0.124200			−0.0621002	+	0.998070i	$0.519780\pi$
$938$	−803967.	−	214266.i	−0.913761	−	0.243527i
$939$	−673762.	−	389983.i	−0.764144	−	0.442298i
$940$	−272560.	+	475029.i	−0.308466	+	0.537606i
$941$	−345476.	+	598382.i	−0.390156	+	0.675770i	−0.992470	−	0.122489i	$-0.960912\pi$
$941$	−345476.	+	598382.i	−0.390156	+	0.675770i	0.602314	+	0.798259i	$0.294246\pi$
$942$	−269709.	+	1.00755e6i	−0.303945	+	1.13545i
$943$	−717036.	+	413981.i	−0.806338	+	0.465540i
$944$	−1590.90	−	296261.i	−0.00178525	−	0.332453i
$945$	501678.	+	1652.42i	0.561773	+	0.00185036i
$946$	633299.	−	635001.i	0.707663	−	0.709565i
$947$	1.04225e6	−	601745.i	1.16218	−	0.670984i	0.210354	−	0.977625i	$-0.432538\pi$
$947$	1.04225e6	−	601745.i	1.16218	−	0.670984i	0.951825	+	0.306641i	$0.0992051\pi$
$948$	−401239.	+	232505.i	−0.446464	+	0.258712i
$949$	−468940.	+	812228.i	−0.520697	+	0.901873i
$950$	759522.	−	204607.i	0.841576	−	0.226711i
$951$	191867.	+	111056.i	0.212149	+	0.122795i
$952$	1.43988e6	+	379606.i	1.58874	+	0.418850i
$953$	1.58732e6			1.74775			0.873873	−	0.486154i	$-0.161600\pi$
$953$	1.58732e6			1.74775			0.873873	+	0.486154i	$0.161600\pi$
$954$	−296190.	+	295685.i	−0.325442	+	0.324887i
$955$		−	468312.i		−	0.513486i
$956$	−209439.	−	360519.i	−0.229161	−	0.394469i
$957$	592339.	+	650.344i	0.646765	+	0.000710100i
$958$	−401984.	+	108290.i	−0.438003	+	0.117993i
$959$	−236397.	−	136484.i	−0.257042	−	0.148403i
$960$	−434570.	+	3023.32i	−0.471539	+	0.00328051i
$961$	−259972.	−	450285.i	−0.281501	−	0.487574i
$962$	771129.	−	773202.i	0.833253	−	0.835493i
$963$	2154.80	+	1250.39i	0.00232356	+	0.00134832i
$964$	1202.84	+	447992.i	0.00129435	+	0.482077i
$965$	124338.	+	215361.i	0.133521	+	0.231266i
$966$	−682257.	+	182989.i	−0.731129	+	0.196097i
$967$	−854421.	−	493300.i	−0.913732	−	0.527544i	−0.0321023	−	0.999485i	$-0.510220\pi$
$967$	−854421.	−	493300.i	−0.913732	−	0.527544i	−0.881630	+	0.471941i	$0.843554\pi$
$968$	281279.	−	76584.0i	0.300183	−	0.0817311i
$969$	−724312.	−	1.25773e6i	−0.771397	−	1.33949i
$970$	802342.	+	213833.i	0.852738	+	0.227264i
$971$			1.42706e6i			1.51358i	0.653658	+	0.756790i	$0.273233\pi$
$971$			1.42706e6i			1.51358i	−0.653658	+	0.756790i	$0.726767\pi$
$972$	−470095.	−	819529.i	−0.497569	−	0.867424i
$973$	543189.			0.573754
$974$	−104332.	+	391472.i	−0.109976	+	0.412651i
$975$	646810.	−	372490.i	0.680405	−	0.391837i
$976$	750907.	−	1.31689e6i	0.788291	−	1.38245i
$977$	−801658.	+	1.38851e6i	−0.839847	+	1.45466i	0.0501755	+	0.998740i	$0.484022\pi$
$977$	−801658.	+	1.38851e6i	−0.839847	+	1.45466i	−0.890022	+	0.455917i	$0.849311\pi$
$978$	165409.	+	616713.i	0.172935	+	0.644771i
$979$	79222.5	−	45739.1i	0.0826577	−	0.0477224i
$980$	509.836	+	189886.i	0.000530858	+	0.197716i
$981$	434647.	−	749027.i	0.451646	−	0.778322i
$982$	−496277.	−	494946.i	−0.514637	−	0.513257i
$983$	−1.27188e6	+	734318.i	−1.31625	+	0.759936i	−0.983123	−	0.182946i	$-0.941437\pi$
$983$	−1.27188e6	+	734318.i	−1.31625	+	0.759936i	−0.333126	+	0.942882i	$0.608103\pi$
$984$	1.00033e6	−	1.00621e6i	1.03312	−	1.03920i
$985$	−166552.	+	288476.i	−0.171663	+	0.297329i
$986$	271769.	+	1.00884e6i	0.279541	+	1.03769i
$987$	1674.86	−	1.52547e6i	0.00171927	−	1.56592i
$988$	554891.	+	955168.i	0.568452	+	0.978511i
$989$	−750388.			−0.767173
$990$	−271011.	−	271474.i	−0.276514	−	0.276986i
$991$			1.48147e6i			1.50850i	0.656585	+	0.754252i	$0.272000\pi$
$991$			1.48147e6i			1.50850i	−0.656585	+	0.754252i	$0.728000\pi$
$992$	−164146.	+	629473.i	−0.166804	+	0.639667i
$993$	844293.	−	1.45866e6i	0.856238	−	1.47929i
$994$	−342544.	−	1.27156e6i	−0.346692	−	1.28696i
$995$	−245673.	−	141840.i	−0.248149	−	0.143269i
$996$	1.01627e6	−	588897.i	1.02445	−	0.593637i
$997$	23467.9	+	40647.6i	0.0236093	+	0.0408926i	0.877589	−	0.479414i	$-0.159151\pi$
$997$	23467.9	+	40647.6i	0.0236093	+	0.0408926i	−0.853979	+	0.520307i	$0.825818\pi$
$998$	−272184.	−	271454.i	−0.273276	−	0.272543i
$999$	−3841.64	+	1.16633e6i	−0.00384934	+	1.16867i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.31.3	yes	44
3.2	odd	2		108.5.f.a.91.20		44
4.3	odd	2	inner	36.5.f.a.31.13	yes	44
9.2	odd	6		108.5.f.a.19.10		44
9.4	even	3		324.5.d.f.163.17		22
9.5	odd	6		324.5.d.e.163.6		22
9.7	even	3	inner	36.5.f.a.7.13	yes	44
12.11	even	2		108.5.f.a.91.10		44
36.7	odd	6	inner	36.5.f.a.7.3	✓	44
36.11	even	6		108.5.f.a.19.20		44
36.23	even	6		324.5.d.e.163.5		22
36.31	odd	6		324.5.d.f.163.18		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.3	✓	44	36.7	odd	6	inner
36.5.f.a.7.13	yes	44	9.7	even	3	inner
36.5.f.a.31.3	yes	44	1.1	even	1	trivial
36.5.f.a.31.13	yes	44	4.3	odd	2	inner
108.5.f.a.19.10		44	9.2	odd	6
108.5.f.a.19.20		44	36.11	even	6
108.5.f.a.91.10		44	12.11	even	2
108.5.f.a.91.20		44	3.2	odd	2
324.5.d.e.163.5		22	36.23	even	6
324.5.d.e.163.6		22	9.5	odd	6
324.5.d.f.163.17		22	9.4	even	3
324.5.d.f.163.18		22	36.31	odd	6

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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.86509 - 1.03009i) q^{2} +(7.79916 - 4.49144i) q^{3} +(13.8778 + 7.96277i) q^{4} +(-5.89438 + 10.2094i) q^{5} +(-34.7711 + 9.32599i) q^{6} +(50.5548 - 29.1878i) q^{7} +(-45.4367 - 45.0722i) q^{8} +(40.6539 - 70.0590i) q^{9} +O(q^{10})\)	\(q+(-3.86509 - 1.03009i) q^{2} +(7.79916 - 4.49144i) q^{3} +(13.8778 + 7.96277i) q^{4} +(-5.89438 + 10.2094i) q^{5} +(-34.7711 + 9.32599i) q^{6} +(50.5548 - 29.1878i) q^{7} +(-45.4367 - 45.0722i) q^{8} +(40.6539 - 70.0590i) q^{9} +(33.2988 - 33.3884i) q^{10} +(86.9742 - 50.2146i) q^{11} +(144.000 - 0.228531i) q^{12} +(85.3178 - 147.775i) q^{13} +(-225.465 + 60.7377i) q^{14} +(-0.116489 + 106.099i) q^{15} +(129.189 + 221.012i) q^{16} -398.571 q^{17} +(-229.298 + 228.907i) q^{18} +404.608i q^{19} +(-163.096 + 94.7483i) q^{20} +(263.190 - 454.704i) q^{21} +(-387.889 + 104.493i) q^{22} +(291.091 + 168.062i) q^{23} +(-556.808 - 147.449i) q^{24} +(243.013 + 420.910i) q^{25} +(-481.982 + 483.278i) q^{26} +(2.40116 - 728.996i) q^{27} +(934.007 - 2.50777i) q^{28} +(327.671 + 567.543i) q^{29} +(109.741 - 409.961i) q^{30} +(-550.166 - 317.638i) q^{31} +(-271.664 - 987.307i) q^{32} +(452.791 - 782.271i) q^{33} +(1540.51 + 410.563i) q^{34} +688.176i q^{35} +(1122.05 - 648.549i) q^{36} -1599.91 q^{37} +(416.782 - 1563.85i) q^{38} +(1.68611 - 1535.72i) q^{39} +(727.980 - 198.207i) q^{40} +(-1231.63 + 2133.25i) q^{41} +(-1485.64 + 1486.36i) q^{42} +(-1933.38 + 1116.24i) q^{43} +(1606.86 - 4.31435i) q^{44} +(475.628 + 828.005i) q^{45} +(-951.976 - 949.423i) q^{46} +(2514.55 - 1451.78i) q^{47} +(2000.23 + 1143.47i) q^{48} +(503.358 - 871.842i) q^{49} +(-505.691 - 1877.18i) q^{50} +(-3108.52 + 1790.16i) q^{51} +(2360.72 - 1371.43i) q^{52} +1291.73 q^{53} +(-760.211 + 2815.16i) q^{54} +1183.94i q^{55} +(-3612.60 - 952.417i) q^{56} +(1817.27 + 3155.61i) q^{57} +(-681.858 - 2531.13i) q^{58} +(-1002.24 - 578.642i) q^{59} +(-846.456 + 1471.49i) q^{60} +(-2960.81 - 5128.28i) q^{61} +(1799.24 + 1794.42i) q^{62} +(10.3829 - 4728.42i) q^{63} +(32.9923 + 4095.87i) q^{64} +(1005.79 + 1742.08i) q^{65} +(-2555.88 + 2557.14i) q^{66} +(3085.87 + 1781.63i) q^{67} +(-5531.30 - 3173.73i) q^{68} +(3025.11 + 3.32134i) q^{69} +(708.882 - 2659.86i) q^{70} +5639.73i q^{71} +(-5004.89 + 1350.89i) q^{72} -5496.39 q^{73} +(6183.80 + 1648.05i) q^{74} +(3785.79 + 2191.27i) q^{75} +(-3221.80 + 5615.09i) q^{76} +(2931.31 - 5077.18i) q^{77} +(-1588.44 + 5933.96i) q^{78} +(-2788.94 + 1610.20i) q^{79} +(-3017.88 + 16.2058i) q^{80} +(-3255.51 - 5696.34i) q^{81} +(6957.81 - 6976.52i) q^{82} +(7063.92 - 4078.36i) q^{83} +(7273.21 - 4214.59i) q^{84} +(2349.33 - 4069.15i) q^{85} +(8622.53 - 2322.81i) q^{86} +(5104.64 + 2954.64i) q^{87} +(-6215.11 - 1638.53i) q^{88} +910.873 q^{89} +(-985.425 - 3690.25i) q^{90} -9960.97i q^{91} +(2701.48 + 4650.22i) q^{92} +(-5717.49 - 6.27738i) q^{93} +(-11214.4 + 3021.04i) q^{94} +(-4130.79 - 2384.91i) q^{95} +(-6553.18 - 6480.01i) q^{96} +(8804.44 + 15249.7i) q^{97} +(-2843.60 + 2851.24i) q^{98} +(17.8627 - 8134.75i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9}+O(q^{10}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9	\( 44 q - q^{2} - q^{4} - 2 q^{5} + 15 q^{6} + 122 q^{8} - 60 q^{9} + 28 q^{10} - 228 q^{12} - 2 q^{13} + 252 q^{14} - q^{16} - 56 q^{17} + 72 q^{18} - 140 q^{20} + 138 q^{21} - 33 q^{22} - 951 q^{24} - 1752 q^{25} + 1096 q^{26} - 516 q^{28} + 526 q^{29} - 1980 q^{30} - 121 q^{32} + 2994 q^{33} + 385 q^{34} - 1005 q^{36} - 8 q^{37} + 1395 q^{38} - 2276 q^{40} - 2762 q^{41} + 3330 q^{42} + 6714 q^{44} + 4110 q^{45} + 3576 q^{46} + 2163 q^{48} + 3428 q^{49} + 6375 q^{50} + 1438 q^{52} - 10088 q^{53} - 4983 q^{54} - 7506 q^{56} + 1752 q^{57} - 4064 q^{58} - 16392 q^{60} - 2 q^{61} - 18324 q^{62} + 9026 q^{64} - 2014 q^{65} - 17358 q^{66} - 11405 q^{68} + 3354 q^{69} + 3666 q^{70} + 4083 q^{72} - 3416 q^{73} + 14620 q^{74} + 1581 q^{76} - 3942 q^{77} + 34566 q^{78} + 45520 q^{80} - 1164 q^{81} - 8486 q^{82} + 51078 q^{84} - 1252 q^{85} + 22113 q^{86} + 1995 q^{88} + 13048 q^{89} - 4692 q^{90} - 30294 q^{92} + 12090 q^{93} + 7524 q^{94} - 76164 q^{96} + 5638 q^{97} - 92938 q^{98}+O(q^{100}) \) 44 * q - q^2 - q^4 - 2 * q^5 + 15 * q^6 + 122 * q^8 - 60 * q^9 + 28 * q^10 - 228 * q^12 - 2 * q^13 + 252 * q^14 - q^16 - 56 * q^17 + 72 * q^18 - 140 * q^20 + 138 * q^21 - 33 * q^22 - 951 * q^24 - 1752 * q^25 + 1096 * q^26 - 516 * q^28 + 526 * q^29 - 1980 * q^30 - 121 * q^32 + 2994 * q^33 + 385 * q^34 - 1005 * q^36 - 8 * q^37 + 1395 * q^38 - 2276 * q^40 - 2762 * q^41 + 3330 * q^42 + 6714 * q^44 + 4110 * q^45 + 3576 * q^46 + 2163 * q^48 + 3428 * q^49 + 6375 * q^50 + 1438 * q^52 - 10088 * q^53 - 4983 * q^54 - 7506 * q^56 + 1752 * q^57 - 4064 * q^58 - 16392 * q^60 - 2 * q^61 - 18324 * q^62 + 9026 * q^64 - 2014 * q^65 - 17358 * q^66 - 11405 * q^68 + 3354 * q^69 + 3666 * q^70 + 4083 * q^72 - 3416 * q^73 + 14620 * q^74 + 1581 * q^76 - 3942 * q^77 + 34566 * q^78 + 45520 * q^80 - 1164 * q^81 - 8486 * q^82 + 51078 * q^84 - 1252 * q^85 + 22113 * q^86 + 1995 * q^88 + 13048 * q^89 - 4692 * q^90 - 30294 * q^92 + 12090 * q^93 + 7524 * q^94 - 76164 * q^96 + 5638 * q^97 - 92938 * q^98

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