LMFDB - Embedded newform 36.5.f.a.31.10

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			31.10
Character	$\chi$	$=$	36.31
Dual form			36.5.f.a.7.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.701741 - 3.93796i) q^{2} +(5.87916 - 6.81436i) q^{3} +(-15.0151 + 5.52686i) q^{4} +(14.3046 - 24.7763i) q^{5} +(-30.9603 - 18.3700i) q^{6} +(-22.2124 + 12.8243i) q^{7} +(32.3013 + 55.2506i) q^{8} +(-11.8710 - 80.1254i) q^{9} +O(q^{10})$	\(q+(-0.701741 - 3.93796i) q^{2} +(5.87916 - 6.81436i) q^{3} +(-15.0151 + 5.52686i) q^{4} +(14.3046 - 24.7763i) q^{5} +(-30.9603 - 18.3700i) q^{6} +(-22.2124 + 12.8243i) q^{7} +(32.3013 + 55.2506i) q^{8} +(-11.8710 - 80.1254i) q^{9} +(-107.606 - 38.9445i) q^{10} +(-93.9677 + 54.2523i) q^{11} +(-50.6143 + 134.812i) q^{12} +(44.2246 - 76.5993i) q^{13} +(66.0891 + 78.4722i) q^{14} +(-84.7356 - 243.141i) q^{15} +(194.908 - 165.973i) q^{16} +504.169 q^{17} +(-307.201 + 102.975i) q^{18} -191.405i q^{19} +(-77.8502 + 451.079i) q^{20} +(-43.2006 + 226.760i) q^{21} +(279.585 + 331.970i) q^{22} +(831.897 + 480.296i) q^{23} +(566.402 + 104.714i) q^{24} +(-96.7443 - 167.566i) q^{25} +(-332.680 - 120.402i) q^{26} +(-615.794 - 390.177i) q^{27} +(262.643 - 315.324i) q^{28} +(-396.671 - 687.053i) q^{29} +(-898.017 + 504.308i) q^{30} +(285.428 + 164.792i) q^{31} +(-790.370 - 651.069i) q^{32} +(-182.757 + 959.288i) q^{33} +(-353.796 - 1985.40i) q^{34} +733.789i q^{35} +(621.086 + 1137.48i) q^{36} +209.943 q^{37} +(-753.745 + 134.317i) q^{38} +(-261.971 - 751.702i) q^{39} +(1830.96 - 9.96965i) q^{40} +(-528.200 + 914.869i) q^{41} +(923.286 + 10.9960i) q^{42} +(-2887.45 + 1667.07i) q^{43} +(1111.09 - 1333.95i) q^{44} +(-2155.02 - 852.045i) q^{45} +(1307.61 - 3613.02i) q^{46} +(977.185 - 564.178i) q^{47} +(14.8932 - 2303.95i) q^{48} +(-871.573 + 1509.61i) q^{49} +(-591.979 + 498.563i) q^{50} +(2964.09 - 3435.59i) q^{51} +(-240.684 + 1394.57i) q^{52} +1138.62 q^{53} +(-1104.37 + 2698.78i) q^{54} +3104.23i q^{55} +(-1426.04 - 813.005i) q^{56} +(-1304.30 - 1125.30i) q^{57} +(-2427.23 + 2044.21i) q^{58} +(4037.49 + 2331.05i) q^{59} +(2616.12 + 3182.47i) q^{60} +(2799.84 + 4849.46i) q^{61} +(448.648 - 1239.65i) q^{62} +(1291.24 + 1627.54i) q^{63} +(-2009.25 + 3569.33i) q^{64} +(-1265.23 - 2191.45i) q^{65} +(3905.89 + 46.5177i) q^{66} +(-6127.74 - 3537.85i) q^{67} +(-7570.16 + 2786.47i) q^{68} +(8163.76 - 2845.11i) q^{69} +(2889.63 - 514.930i) q^{70} -4433.42i q^{71} +(4043.53 - 3244.03i) q^{72} -1953.21 q^{73} +(-147.326 - 826.748i) q^{74} +(-1710.63 - 325.897i) q^{75} +(1057.87 + 2873.97i) q^{76} +(1391.50 - 2410.15i) q^{77} +(-2776.34 + 1559.13i) q^{78} +(1523.90 - 879.826i) q^{79} +(-1324.12 - 7203.27i) q^{80} +(-6279.16 + 1902.33i) q^{81} +(3973.38 + 1438.03i) q^{82} +(-2621.64 + 1513.61i) q^{83} +(-604.606 - 3643.58i) q^{84} +(7211.95 - 12491.5i) q^{85} +(8591.12 + 10200.8i) q^{86} +(-7013.92 - 1336.24i) q^{87} +(-6032.75 - 3439.35i) q^{88} -559.336 q^{89} +(-1843.05 + 9084.32i) q^{90} +2268.61i q^{91} +(-15145.6 - 2613.92i) q^{92} +(2801.03 - 976.170i) q^{93} +(-2907.44 - 3452.21i) q^{94} +(-4742.31 - 2737.97i) q^{95} +(-9083.33 + 1558.13i) q^{96} +(1100.89 + 1906.79i) q^{97} +(6556.40 + 2372.87i) q^{98} +(5462.47 + 6885.17i) 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 $

$2$	−0.701741	−	3.93796i	−0.175435	−	0.984491i
$2$	−0.701741	−	3.93796i	−0.175435	−	0.984491i
$3$	5.87916	−	6.81436i	0.653240	−	0.757151i
$3$	5.87916	−	6.81436i	0.653240	−	0.757151i
$4$	−15.0151	+	5.52686i	−0.938445	+	0.345429i
$5$	14.3046	−	24.7763i	0.572185	−	0.991053i	−0.424156	−	0.905589i	$-0.639429\pi$
$5$	14.3046	−	24.7763i	0.572185	−	0.991053i	0.996341	−	0.0854642i	$-0.0272373\pi$
$6$	−30.9603	−	18.3700i	−0.860010	−	0.510278i
$7$	−22.2124	+	12.8243i	−0.453314	+	0.261721i	−0.709229	−	0.704978i	$-0.750957\pi$
$7$	−22.2124	+	12.8243i	−0.453314	+	0.261721i	0.255915	+	0.966699i	$0.417623\pi$
$8$	32.3013	+	55.2506i	0.504708	+	0.863290i
$9$	−11.8710	−	80.1254i	−0.146555	−	0.989203i
$10$	−107.606	−	38.9445i	−1.07606	−	0.389445i
$11$	−93.9677	+	54.2523i	−0.776593	+	0.448366i	−0.835221	−	0.549914i	$-0.814661\pi$
$11$	−93.9677	+	54.2523i	−0.776593	+	0.448366i	0.0586287	+	0.998280i	$0.481327\pi$
$12$	−50.6143	+	134.812i	−0.351488	+	0.936192i
$13$	44.2246	−	76.5993i	0.261684	−	0.453250i	−0.705005	−	0.709202i	$-0.749055\pi$
$13$	44.2246	−	76.5993i	0.261684	−	0.453250i	0.966690	+	0.255952i	$0.0823888\pi$
$14$	66.0891	+	78.4722i	0.337189	+	0.400369i
$15$	−84.7356	−	243.141i	−0.376603	−	1.08063i
$16$	194.908	−	165.973i	0.761358	−	0.648332i
$17$	504.169			1.74453			0.872265	−	0.489034i	$-0.162651\pi$
$17$	504.169			1.74453			0.872265	+	0.489034i	$0.162651\pi$
$18$	−307.201	+	102.975i	−0.948150	+	0.317823i
$19$		−	191.405i		−	0.530207i	−0.964220	−	0.265104i	$-0.914594\pi$
$19$		−	191.405i		−	0.530207i	0.964220	−	0.265104i	$-0.0854062\pi$
$20$	−77.8502	+	451.079i	−0.194625	+	1.12770i
$21$	−43.2006	+	226.760i	−0.0979606	+	0.514194i
$22$	279.585	+	331.970i	0.577654	+	0.685889i
$23$	831.897	+	480.296i	1.57258	+	0.907932i	0.995851	+	0.0909988i	$0.0290059\pi$
$23$	831.897	+	480.296i	1.57258	+	0.907932i	0.576733	+	0.816933i	$0.304327\pi$
$24$	566.402	+	104.714i	0.983336	+	0.181795i
$25$	−96.7443	−	167.566i	−0.154791	−	0.268106i
$26$	−332.680	−	120.402i	−0.492129	−	0.178110i
$27$	−615.794	−	390.177i	−0.844711	−	0.535222i
$28$	262.643	−	315.324i	0.335004	−	0.402199i
$29$	−396.671	−	687.053i	−0.471665	−	0.816948i	0.527809	−	0.849363i	$-0.323014\pi$
$29$	−396.671	−	687.053i	−0.471665	−	0.816948i	−0.999475	+	0.0324147i	$0.989680\pi$
$30$	−898.017	+	504.308i	−0.997797	+	0.560342i
$31$	285.428	+	164.792i	0.297011	+	0.171480i	0.641099	−	0.767458i	$-0.278479\pi$
$31$	285.428	+	164.792i	0.297011	+	0.171480i	−0.344088	+	0.938937i	$0.611812\pi$
$32$	−790.370	−	651.069i	−0.771846	−	0.635809i
$33$	−182.757	+	959.288i	−0.167821	+	0.880888i
$34$	−353.796	−	1985.40i	−0.306052	−	1.71747i
$35$			733.789i			0.599011i
$36$	621.086	+	1137.48i	0.479233	+	0.877688i
$37$	209.943			0.153355			0.0766775	−	0.997056i	$-0.475569\pi$
$37$	209.943			0.153355			0.0766775	+	0.997056i	$0.475569\pi$
$38$	−753.745	+	134.317i	−0.521984	+	0.0930171i
$39$	−261.971	−	751.702i	−0.172236	−	0.494216i
$40$	1830.96	−	9.96965i	1.14435	−	0.00623103i
$41$	−528.200	+	914.869i	−0.314218	+	0.544241i	−0.979271	−	0.202555i	$-0.935076\pi$
$41$	−528.200	+	914.869i	−0.314218	+	0.544241i	0.665053	+	0.746796i	$0.268409\pi$
$42$	923.286	+	10.9960i	0.523405	+	0.00623356i
$43$	−2887.45	+	1667.07i	−1.56163	+	0.901608i	−0.564537	+	0.825407i	$0.690945\pi$
$43$	−2887.45	+	1667.07i	−1.56163	+	0.901608i	−0.997093	+	0.0762001i	$0.975721\pi$
$44$	1111.09	−	1333.95i	0.573911	−	0.689024i
$45$	−2155.02	−	852.045i	−1.06421	−	0.420763i
$46$	1307.61	−	3613.02i	0.617964	−	1.70748i
$47$	977.185	−	564.178i	0.442365	−	0.255400i	−0.262235	−	0.965004i	$-0.584460\pi$
$47$	977.185	−	564.178i	0.442365	−	0.255400i	0.704600	+	0.709604i	$0.251126\pi$
$48$	14.8932	−	2303.95i	0.00646406	−	0.999979i
$49$	−871.573	+	1509.61i	−0.363004	+	0.628742i
$50$	−591.979	+	498.563i	−0.236792	+	0.199425i
$51$	2964.09	−	3435.59i	1.13960	−	1.32087i
$52$	−240.684	+	1394.57i	−0.0890104	+	0.515744i
$53$	1138.62			0.405346			0.202673	−	0.979247i	$-0.435037\pi$
$53$	1138.62			0.405346			0.202673	+	0.979247i	$0.435037\pi$
$54$	−1104.37	+	2698.78i	−0.378729	+	0.925507i
$55$			3104.23i			1.02619i
$56$	−1426.04	−	813.005i	−0.454732	−	0.259249i
$57$	−1304.30	−	1125.30i	−0.401447	−	0.346353i
$58$	−2427.23	+	2044.21i	−0.721531	+	0.607672i
$59$	4037.49	+	2331.05i	1.15987	+	0.669648i	0.951272	−	0.308354i	$-0.0997781\pi$
$59$	4037.49	+	2331.05i	1.15987	+	0.669648i	0.208593	+	0.978002i	$0.433111\pi$
$60$	2616.12	+	3182.47i	0.726700	+	0.884018i
$61$	2799.84	+	4849.46i	0.752442	+	1.30327i	0.946636	+	0.322305i	$0.104458\pi$
$61$	2799.84	+	4849.46i	0.752442	+	1.30327i	−0.194193	+	0.980963i	$0.562209\pi$
$62$	448.648	−	1239.65i	0.116714	−	0.322488i
$63$	1291.24	+	1627.54i	0.325331	+	0.410063i
$64$	−2009.25	+	3569.33i	−0.490540	+	0.871419i
$65$	−1265.23	−	2191.45i	−0.299463	−	0.518686i
$66$	3905.89	+	46.5177i	0.896668	+	0.0106790i
$67$	−6127.74	−	3537.85i	−1.36506	−	0.788116i	−0.374764	−	0.927120i	$-0.622276\pi$
$67$	−6127.74	−	3537.85i	−1.36506	−	0.788116i	−0.990292	+	0.139004i	$0.955610\pi$
$68$	−7570.16	+	2786.47i	−1.63715	+	0.602611i
$69$	8163.76	−	2845.11i	1.71472	−	0.597586i
$70$	2889.63	−	514.930i	0.589721	−	0.105088i
$71$		−	4433.42i		−	0.879472i	−0.898127	−	0.439736i	$-0.855072\pi$
$71$		−	4433.42i		−	0.879472i	0.898127	−	0.439736i	$-0.144928\pi$
$72$	4043.53	−	3244.03i	0.780001	−	0.625778i
$73$	−1953.21			−0.366524			−0.183262	−	0.983064i	$-0.558666\pi$
$73$	−1953.21			−0.366524			−0.183262	+	0.983064i	$0.558666\pi$
$74$	−147.326	−	826.748i	−0.0269039	−	0.150977i
$75$	−1710.63	−	325.897i	−0.304112	−	0.0579373i
$76$	1057.87	+	2873.97i	0.183149	+	0.497570i
$77$	1391.50	−	2410.15i	0.234694	−	0.406501i
$78$	−2776.34	+	1559.13i	−0.456334	+	0.256268i
$79$	1523.90	−	879.826i	0.244176	−	0.140975i	−0.372918	−	0.927864i	$-0.621643\pi$
$79$	1523.90	−	879.826i	0.244176	−	0.140975i	0.617095	+	0.786889i	$0.288310\pi$
$80$	−1324.12	−	7203.27i	−0.206894	−	1.12551i
$81$	−6279.16	+	1902.33i	−0.957043	+	0.289945i
$82$	3973.38	+	1438.03i	0.590925	+	0.213865i
$83$	−2621.64	+	1513.61i	−0.380555	+	0.219714i	−0.678060	−	0.735007i	$-0.737179\pi$
$83$	−2621.64	+	1513.61i	−0.380555	+	0.219714i	0.297505	+	0.954720i	$0.403846\pi$
$84$	−604.606	−	3643.58i	−0.0856868	−	0.516381i
$85$	7211.95	−	12491.5i	0.998193	−	1.72892i
$86$	8591.12	+	10200.8i	1.16159	+	1.37924i
$87$	−7013.92	−	1336.24i	−0.926664	−	0.176541i
$88$	−6032.75	−	3439.35i	−0.779023	−	0.444131i
$89$	−559.336			−0.0706144			−0.0353072	−	0.999377i	$-0.511241\pi$
$89$	−559.336			−0.0706144			−0.0353072	+	0.999377i	$0.511241\pi$
$90$	−1843.05	+	9084.32i	−0.227537	+	1.12152i
$91$			2268.61i			0.273953i
$92$	−15145.6	−	2613.92i	−1.78941	−	0.308828i
$93$	2801.03	−	976.170i	0.323855	−	0.112865i
$94$	−2907.44	−	3452.21i	−0.329045	−	0.390698i
$95$	−4742.31	−	2737.97i	−0.525463	−	0.303376i
$96$	−9083.33	+	1558.13i	−0.985604	+	0.169068i
$97$	1100.89	+	1906.79i	0.117004	+	0.202656i	0.918579	−	0.395238i	$-0.129338\pi$
$97$	1100.89	+	1906.79i	0.117004	+	0.202656i	−0.801575	+	0.597894i	$0.796004\pi$
$98$	6556.40	+	2372.87i	0.682674	+	0.247071i
$99$	5462.47	+	6885.17i	0.557338	+	0.702497i
$100$	2378.74	+	1981.33i	0.237874	+	0.198133i
$101$	365.841	+	633.655i	0.0358632	+	0.0621170i	0.883400	−	0.468620i	$-0.155249\pi$
$101$	365.841	+	633.655i	0.0358632	+	0.0621170i	−0.847537	+	0.530737i	$0.821915\pi$
$102$	−15609.2	−	9261.59i	−1.50031	−	0.890195i
$103$	8533.78	+	4926.98i	0.804391	+	0.464415i	0.845004	−	0.534760i	$-0.179598\pi$
$103$	8533.78	+	4926.98i	0.804391	+	0.464415i	−0.0406134	+	0.999175i	$0.512931\pi$
$104$	5660.67	−	30.8225i	0.523361	−	0.00284971i
$105$	5000.30	+	4314.06i	0.453542	+	0.391298i
$106$	−799.013	−	4483.83i	−0.0711119	−	0.399059i
$107$		−	804.642i		−	0.0702806i	−0.999382	−	0.0351403i	$-0.988812\pi$
$107$		−	804.642i		−	0.0702806i	0.999382	−	0.0351403i	$-0.0111878\pi$
$108$	11402.7	+	2455.14i	0.977596	+	0.210489i
$109$	−17324.9			−1.45820			−0.729102	−	0.684405i	$-0.760062\pi$
$109$	−17324.9			−1.45820			−0.729102	+	0.684405i	$0.760062\pi$
$110$	12224.4	−	2178.37i	1.01028	−	0.180030i
$111$	1234.29	−	1430.63i	0.100178	−	0.116113i
$112$	−2200.87	+	6186.22i	−0.175452	+	0.493161i
$113$	−8573.94	+	14850.5i	−0.671465	+	1.16301i	0.306024	+	0.952024i	$0.401001\pi$
$113$	−8573.94	+	14850.5i	−0.671465	+	1.16301i	−0.977489	+	0.210988i	$0.932332\pi$
$114$	−3516.11	+	5925.96i	−0.270553	+	0.455983i
$115$	23799.9	−	13740.9i	1.79962	−	1.03901i
$116$	9753.31	+	8123.85i	0.724829	+	0.603734i
$117$	−6662.54	−	2634.21i	−0.486707	−	0.192433i
$118$	6346.30	−	17535.3i	0.455782	−	1.25936i
$119$	−11198.8	+	6465.63i	−0.790820	+	0.456580i
$120$	10696.6	−	12535.5i	0.742819	−	0.870518i
$121$	−1433.88	+	2483.55i	−0.0979359	+	0.169630i
$122$	17132.2	−	14428.7i	1.15105	−	0.969412i
$123$	3128.87	+	8978.01i	0.206813	+	0.593430i
$124$	−5196.51	−	896.848i	−0.337963	−	0.0583278i
$125$	12345.2			0.790094
$126$	5503.08	−	6226.96i	0.346629	−	0.392225i
$127$		−	9591.51i		−	0.594675i	−0.954772	−	0.297337i	$-0.903901\pi$
$127$		−	9591.51i		−	0.594675i	0.954772	−	0.297337i	$-0.0960986\pi$
$128$	15465.9	+	5407.61i	0.943962	+	0.330054i
$129$	−5615.78	+	29477.1i	−0.337466	+	1.77136i
$130$	−7741.98	+	6520.27i	−0.458105	+	0.385815i
$131$	−3933.27	−	2270.88i	−0.229198	−	0.132328i	0.381004	−	0.924573i	$-0.375578\pi$
$131$	−3933.27	−	2270.88i	−0.229198	−	0.132328i	−0.610202	+	0.792246i	$0.708912\pi$
$132$	−2557.74	−	15413.9i	−0.146794	−	0.884635i
$133$	2454.64	+	4251.56i	0.138766	+	0.240350i
$134$	−9631.84	+	26613.5i	−0.536414	+	1.48215i
$135$	−18475.9	+	9675.79i	−1.01376	+	0.530908i
$136$	16285.3	+	27855.6i	0.880478	+	1.50604i
$137$	2450.82	+	4244.95i	0.130578	+	0.226168i	0.923900	−	0.382635i	$-0.124983\pi$
$137$	2450.82	+	4244.95i	0.130578	+	0.226168i	−0.793321	+	0.608803i	$0.791650\pi$
$138$	−16932.8	−	30152.1i	−0.889140	−	1.58328i
$139$	−7491.80	−	4325.39i	−0.387754	−	0.223870i	0.293432	−	0.955980i	$-0.405202\pi$
$139$	−7491.80	−	4325.39i	−0.387754	−	0.223870i	−0.681187	+	0.732110i	$0.738536\pi$
$140$	−4055.55	−	11017.9i	−0.206916	−	0.562139i
$141$	1900.52	−	9975.78i	0.0955946	−	0.501775i
$142$	−17458.6	+	3111.11i	−0.865832	+	0.154290i
$143$			9597.15i			0.469321i
$144$	−15612.4	−	13646.8i	−0.752913	−	0.658121i
$145$	−22696.9			−1.07952
$146$	1370.65	+	7691.66i	0.0643013	+	0.360840i
$147$	5162.90	+	14814.4i	0.238923	+	0.685568i
$148$	−3152.32	+	1160.33i	−0.143915	+	0.0529733i
$149$	6346.46	−	10992.4i	0.285863	−	0.495130i	−0.686955	−	0.726700i	$-0.741053\pi$
$149$	6346.46	−	10992.4i	0.285863	−	0.495130i	0.972818	+	0.231570i	$0.0743863\pi$
$150$	−82.9518	+	6965.09i	−0.00368674	+	0.309560i
$151$	11055.3	−	6382.78i	0.484860	−	0.279934i	−0.237579	−	0.971368i	$-0.576354\pi$
$151$	11055.3	−	6382.78i	0.484860	−	0.279934i	0.722440	+	0.691434i	$0.243021\pi$
$152$	10575.2	−	6182.63i	0.457723	−	0.267600i
$153$	−5984.97	−	40396.8i	−0.255670	−	1.72569i
$154$	−10467.5	−	3788.37i	−0.441370	−	0.159739i
$155$	8165.87	−	4714.57i	0.339891	−	0.196236i
$156$	8088.09	+	9839.01i	0.332351	+	0.404299i
$157$	20283.0	−	35131.2i	0.822873	−	1.42526i	−0.0806612	−	0.996742i	$-0.525703\pi$
$157$	20283.0	−	35131.2i	0.822873	−	1.42526i	0.903534	−	0.428516i	$-0.140963\pi$
$158$	−4534.11	−	5383.67i	−0.181626	−	0.215657i
$159$	6694.10	−	7758.93i	0.264788	−	0.306908i
$160$	−27437.0	+	10269.2i	−1.07176	+	0.401140i
$161$	−24637.9			−0.950499
$162$	11897.7	+	23392.2i	0.453348	+	0.891334i
$163$			6872.98i			0.258684i	0.991600	+	0.129342i	$0.0412865\pi$
$163$			6872.98i			0.258684i	−0.991600	+	0.129342i	$0.958713\pi$
$164$	2874.63	−	16656.2i	0.106879	−	0.619280i
$165$	21153.4	+	18250.3i	0.776983	+	0.670350i
$166$	7800.24	+	9261.78i	0.283069	+	0.336108i
$167$	−30405.5	−	17554.6i	−1.09023	−	0.629447i	−0.156595	−	0.987663i	$-0.550052\pi$
$167$	−30405.5	−	17554.6i	−1.09023	−	0.629447i	−0.933639	+	0.358216i	$0.883385\pi$
$168$	−13924.0	+	4937.77i	−0.493340	+	0.174949i
$169$	10368.9	+	17959.4i	0.363043	+	0.628809i
$170$	−54251.8	−	19634.6i	−1.87723	−	0.679398i
$171$	−15336.4	+	2272.16i	−0.524482	+	0.0777045i
$172$	34141.8	−	40989.9i	1.15406	−	1.38554i
$173$	−1491.72	−	2583.74i	−0.0498420	−	0.0863290i	0.840028	−	0.542543i	$-0.182538\pi$
$173$	−1491.72	−	2583.74i	−0.0498420	−	0.0863290i	−0.889870	+	0.456214i	$0.849205\pi$
$174$	−340.118	+	28558.3i	−0.0112339	+	0.943264i
$175$	4297.84	+	2481.36i	0.140338	+	0.0810240i
$176$	−9310.60	+	26170.3i	−0.300575	+	0.844857i
$177$	39621.6	−	13808.3i	1.26470	−	0.440752i
$178$	392.509	+	2202.65i	0.0123883	+	0.0695192i
$179$		−	45199.3i		−	1.41067i	−0.708874	−	0.705335i	$-0.750797\pi$
$179$		−	45199.3i		−	1.41067i	0.708874	−	0.705335i	$-0.249203\pi$
$180$	37067.1	+	883.036i	1.14404	+	0.0272542i
$181$	27600.9			0.842492			0.421246	−	0.906946i	$-0.361593\pi$
$181$	27600.9			0.842492			0.421246	+	0.906946i	$0.361593\pi$
$182$	8933.68	−	1591.97i	0.269704	−	0.0480610i
$183$	49506.7	+	9431.66i	1.47830	+	0.281635i
$184$	334.744	+	61477.0i	0.00988728	+	1.81584i
$185$	3003.16	−	5201.62i	0.0877474	−	0.151983i
$186$	−5809.72	−	10345.3i	−0.167930	−	0.299032i
$187$	−47375.6	+	27352.3i	−1.35479	+	0.782188i
$188$	−11554.4	+	13872.0i	−0.326913	+	0.392484i
$189$	18682.0	+	769.615i	0.522999	+	0.0215452i
$190$	−7454.16	+	20596.4i	−0.206487	+	0.570537i
$191$	16300.9	−	9411.33i	0.446833	−	0.257979i	−0.259659	−	0.965700i	$-0.583610\pi$
$191$	16300.9	−	9411.33i	0.446833	−	0.257979i	0.706492	+	0.707721i	$0.250277\pi$
$192$	12510.0	+	34676.4i	0.339356	+	0.940658i
$193$	−4727.11	+	8187.59i	−0.126906	+	0.219807i	−0.922476	−	0.386054i	$-0.873838\pi$
$193$	−4727.11	+	8187.59i	−0.126906	+	0.219807i	0.795571	+	0.605861i	$0.207171\pi$
$194$	6736.35	−	5673.33i	0.178987	−	0.150742i
$195$	−22371.8	−	4262.12i	−0.588345	−	0.112087i
$196$	4743.37	−	27484.0i	0.123474	−	0.715432i
$197$	−21650.0			−0.557860			−0.278930	−	0.960311i	$-0.589980\pi$
$197$	−21650.0			−0.557860			−0.278930	+	0.960311i	$0.589980\pi$
$198$	23280.3	−	26342.6i	0.593825	−	0.671937i
$199$			25261.4i			0.637898i	0.947772	+	0.318949i	$0.103330\pi$
$199$			25261.4i			0.637898i	−0.947772	+	0.318949i	$0.896670\pi$
$200$	6133.15	−	10757.8i	0.153329	−	0.268944i
$201$	−60134.1	+	20957.0i	−1.48843	+	0.518725i
$202$	2238.58	−	1885.33i	0.0548619	−	0.0462045i
$203$	17622.0	+	10174.1i	0.427625	+	0.246889i
$204$	−25518.1	+	67967.9i	−0.613181	+	1.63322i
$205$	15111.4	+	26173.7i	0.359581	+	0.622813i
$206$	13413.8	−	37063.2i	0.316094	−	0.873390i
$207$	28608.5	−	72357.6i	0.667658	−	1.68867i
$208$	−4093.70	−	22269.9i	−0.0946214	−	0.514744i
$209$	10384.1	+	17985.9i	0.237727	+	0.411755i
$210$	13479.7	−	22718.4i	0.305662	−	0.515155i
$211$	−18674.0	−	10781.5i	−0.419443	−	0.242166i	0.275396	−	0.961331i	$-0.411191\pi$
$211$	−18674.0	−	10781.5i	−0.419443	−	0.242166i	−0.694839	+	0.719165i	$0.744524\pi$
$212$	−17096.4	+	6292.97i	−0.380394	+	0.140018i
$213$	−30210.9	−	26064.8i	−0.665893	−	0.574506i
$214$	−3168.65	+	564.650i	−0.0691906	+	0.0123297i
$215$			95387.3i			2.06354i
$216$	1666.53	−	46626.2i	0.0357196	−	0.999362i
$217$	−8453.38			−0.179519
$218$	12157.6	+	68224.9i	0.255821	+	1.43559i
$219$	−11483.2	+	13309.8i	−0.239428	+	0.277514i
$220$	−17156.7	−	46610.4i	−0.354477	−	0.963025i
$221$	22296.7	−	38619.0i	0.456516	−	0.790709i
$222$	−6499.91	−	3856.65i	−0.131887	−	0.0782537i
$223$	−16709.5	+	9647.22i	−0.336011	+	0.193996i	−0.658507	−	0.752575i	$-0.728812\pi$
$223$	−16709.5	+	9647.22i	−0.336011	+	0.193996i	0.322496	+	0.946571i	$0.395478\pi$
$224$	25905.5	+	4325.83i	0.516293	+	0.0862130i
$225$	−12277.8	+	9740.84i	−0.242525	+	0.192412i
$226$	64497.4	+	23342.7i	1.26277	+	0.457018i
$227$	56144.4	−	32415.0i	1.08957	−	0.629063i	0.156107	−	0.987740i	$-0.450105\pi$
$227$	56144.4	−	32415.0i	1.08957	−	0.629063i	0.933462	+	0.358677i	$0.116772\pi$
$228$	25803.6	+	9687.81i	0.496376	+	0.186361i
$229$	−19575.4	+	33905.7i	−0.373285	+	0.646549i	−0.990069	−	0.140584i	$-0.955102\pi$
$229$	−19575.4	+	33905.7i	−0.373285	+	0.646549i	0.616784	+	0.787133i	$0.288435\pi$
$230$	−70812.6	−	84080.7i	−1.33861	−	1.58943i
$231$	−8242.76	−	23651.8i	−0.154472	−	0.443241i
$232$	25147.1	−	44109.0i	0.467210	−	0.819504i
$233$	−2307.53			−0.0425045			−0.0212522	−	0.999774i	$-0.506765\pi$
$233$	−2307.53			−0.0425045			−0.0212522	+	0.999774i	$0.506765\pi$
$234$	−5698.04	+	28085.4i	−0.104062	+	0.512919i
$235$		−	32281.4i		−	0.584543i
$236$	−73506.8	−	12686.3i	−1.31979	−	0.227777i
$237$	2963.82	−	15557.1i	0.0527662	−	0.276969i
$238$	33320.1	+	39563.3i	0.588237	+	0.698455i
$239$	65999.7	+	38104.9i	1.15544	+	0.667091i	0.950206	−	0.311623i	$-0.100872\pi$
$239$	65999.7	+	38104.9i	1.15544	+	0.667091i	0.205230	+	0.978714i	$0.434206\pi$
$240$	−56870.4	−	33326.2i	−0.987334	−	0.578579i
$241$	−8157.12	−	14128.5i	−0.140444	−	0.243256i	0.787220	−	0.616672i	$-0.211520\pi$
$241$	−8157.12	−	14128.5i	−0.140444	−	0.243256i	−0.927664	+	0.373416i	$0.878186\pi$
$242$	10786.3	+	3903.75i	0.184180	+	0.0666579i
$243$	−23953.0	+	53972.6i	−0.405647	+	0.914030i
$244$	−68842.2	−	57340.9i	−1.15631	−	0.963130i
$245$	24935.0	+	43188.8i	0.415411	+	0.719513i
$246$	33159.4	−	18621.6i	0.547944	−	0.307714i
$247$	−14661.5	−	8464.81i	−0.240317	−	0.138747i
$248$	114.852	+	21093.0i	0.00186739	+	0.342954i
$249$	−5098.80	+	26763.6i	−0.0822375	+	0.431663i
$250$	−8663.15	−	48615.0i	−0.138610	−	0.777840i
$251$			33833.6i			0.537033i	0.963275	+	0.268517i	$0.0865334\pi$
$251$			33833.6i			0.537033i	−0.963275	+	0.268517i	$0.913467\pi$
$252$	−28383.3	−	17301.2i	−0.446952	−	0.272443i
$253$	−104229.			−1.62834
$254$	−37771.0	+	6730.76i	−0.585452	+	0.104327i
$255$	−42721.1	−	122584.i	−0.656995	−	1.88518i
$256$	10441.9	−	64698.8i	0.159331	−	0.987225i
$257$	28773.1	−	49836.4i	0.435632	−	0.754537i	−0.561715	−	0.827331i	$-0.689858\pi$
$257$	28773.1	−	49836.4i	0.435632	−	0.754537i	0.997347	+	0.0727940i	$0.0231916\pi$
$258$	120021.	+	1429.40i	1.80309	+	0.0214741i
$259$	−4663.34	+	2692.38i	−0.0695180	+	0.0401362i
$260$	31109.5	+	25912.1i	0.460199	+	0.383315i
$261$	−50341.6	+	39939.4i	−0.739002	+	0.586300i
$262$	−6182.49	+	17082.6i	−0.0900659	+	0.248859i
$263$	−68019.2	+	39270.9i	−0.983378	+	0.567753i	−0.903288	−	0.429034i	$-0.858854\pi$
$263$	−68019.2	+	39270.9i	−0.983378	+	0.567753i	−0.0800895	+	0.996788i	$0.525521\pi$
$264$	−58904.5	+	20888.8i	−0.845163	+	0.299714i
$265$	16287.5	−	28210.7i	0.231933	−	0.401719i
$266$	15020.0	−	12649.8i	0.212278	−	0.178780i
$267$	−3288.43	+	3811.52i	−0.0461281	+	0.0534657i
$268$	111562.	+	19254.1i	1.55327	+	0.268073i
$269$	−5376.96			−0.0743074			−0.0371537	−	0.999310i	$-0.511829\pi$
$269$	−5376.96			−0.0743074			−0.0371537	+	0.999310i	$0.511829\pi$
$270$	51068.2	+	65967.4i	0.700524	+	0.904902i
$271$			108113.i			1.47211i	0.676924	+	0.736053i	$0.263312\pi$
$271$			108113.i			1.47211i	−0.676924	+	0.736053i	$0.736688\pi$
$272$	98266.4	−	83678.5i	1.32821	−	1.13103i
$273$	15459.1	+	13337.5i	0.207424	+	0.178957i
$274$	14996.6	−	12630.1i	0.199752	−	0.168231i
$275$	18181.7	+	10497.2i	0.240419	+	0.138806i
$276$	−106855.	+	87839.6i	−1.40274	+	1.15311i
$277$	21971.1	+	38055.1i	0.286347	+	0.495968i	0.972935	−	0.231079i	$-0.0742255\pi$
$277$	21971.1	+	38055.1i	0.286347	+	0.495968i	−0.686588	+	0.727047i	$0.740892\pi$
$278$	−11775.9	+	32537.8i	−0.152372	+	0.421015i
$279$	9815.71	−	24826.3i	0.126099	−	0.318935i
$280$	−40542.2	+	23702.3i	−0.517120	+	0.302326i
$281$	−25435.7	−	44055.9i	−0.322130	−	0.557945i	0.658798	−	0.752320i	$-0.271065\pi$
$281$	−25435.7	−	44055.9i	−0.322130	−	0.557945i	−0.980927	+	0.194375i	$0.937732\pi$
$282$	−40617.9	−	483.745i	−0.510763	−	0.00608300i
$283$	−22858.8	−	13197.5i	−0.285418	−	0.164786i	0.350456	−	0.936579i	$-0.386027\pi$
$283$	−22858.8	−	13197.5i	−0.285418	−	0.164786i	−0.635873	+	0.771793i	$0.719360\pi$
$284$	24502.9	+	66568.3i	0.303795	+	0.825336i
$285$	−46538.3	+	16218.8i	−0.572956	+	0.199678i
$286$	37793.2	−	6734.71i	0.462042	−	0.0823355i
$287$		−	27095.2i		−	0.328950i
$288$	−42784.7	+	71057.6i	−0.515826	+	0.856693i
$289$	170665.			2.04338
$290$	15927.3	+	89379.5i	0.189386	+	1.06278i
$291$	19465.9	+	3708.50i	0.229873	+	0.0437938i
$292$	29327.6	−	10795.1i	0.343963	−	0.126608i
$293$	−65395.3	+	113268.i	−0.761748	+	1.31939i	0.180201	+	0.983630i	$0.442325\pi$
$293$	−65395.3	+	113268.i	−0.761748	+	1.31939i	−0.941949	+	0.335757i	$0.891008\pi$
$294$	54715.7	−	30727.2i	0.633020	−	0.355491i
$295$	115510.	−	66689.5i	1.32731	−	0.766325i
$296$	6781.44	+	11599.5i	0.0773995	+	0.132390i
$297$	79032.8	+	3255.79i	0.895972	+	0.0369100i
$298$	−47741.2	−	17278.3i	−0.537602	−	0.194567i
$299$	73580.7	−	42481.8i	0.823041	−	0.475183i
$300$	27486.5	−	4561.03i	0.305406	−	0.0506781i
$301$	42758.2	−	74059.3i	0.471939	−	0.817423i
$302$	−32893.1	−	39056.3i	−0.360654	−	0.428230i
$303$	6468.79	+	1232.39i	0.0704592	+	0.0134234i
$304$	−31768.0	−	37306.2i	−0.343750	−	0.403677i
$305$	160202.			1.72214
$306$	−154881.	+	51916.7i	−1.65408	+	0.554452i
$307$		−	54227.3i		−	0.575362i	−0.957726	−	0.287681i	$-0.907116\pi$
$307$		−	54227.3i		−	0.575362i	0.957726	−	0.287681i	$-0.0928843\pi$
$308$	−7572.97	+	43879.3i	−0.0798297	+	0.462549i
$309$	83745.7	−	29185.7i	0.877093	−	0.305671i
$310$	−24296.1	−	28848.5i	−0.252821	−	0.300193i
$311$	−117745.	−	67980.1i	−1.21737	−	0.702847i	−0.253013	−	0.967463i	$-0.581422\pi$
$311$	−117745.	−	67980.1i	−1.21737	−	0.702847i	−0.964354	+	0.264616i	$0.914755\pi$
$312$	33069.9	−	38755.0i	0.339722	−	0.398125i
$313$	−82194.2	−	142364.i	−0.838981	−	1.45316i	−0.890747	−	0.454499i	$-0.849818\pi$
$313$	−82194.2	−	142364.i	−0.838981	−	1.45316i	0.0517658	−	0.998659i	$-0.483515\pi$
$314$	−152579.	−	55220.7i	−1.54751	−	0.560070i
$315$	58795.1	−	8710.77i	0.592543	−	0.0877881i
$316$	−18018.9	+	21633.1i	−0.180449	+	0.216643i
$317$	−60309.5	−	104459.i	−0.600160	−	1.03951i	−0.992796	−	0.119814i	$-0.961770\pi$
$317$	−60309.5	−	104459.i	−0.600160	−	1.03951i	0.392637	−	0.919694i	$-0.371563\pi$
$318$	−35251.9	−	20916.4i	−0.348601	−	0.206839i
$319$	74548.4	+	43040.6i	0.732584	+	0.422957i
$320$	59693.4	+	100840.i	0.582943	+	0.984763i
$321$	−5483.12	−	4730.62i	−0.0532130	−	0.0459101i
$322$	17289.4	+	97023.1i	0.166751	+	0.935758i
$323$		−	96500.4i		−	0.924962i
$324$	83768.4	−	63267.8i	0.797977	−	0.602688i
$325$	−17113.9			−0.162025
$326$	27065.5	−	4823.05i	0.254672	−	0.0453823i
$327$	−101856.	+	118058.i	−0.952557	+	1.10408i
$328$	−67608.6	+	368.131i	−0.628426	+	0.00342180i
$329$	−14470.4	+	25063.5i	−0.133687	+	0.231553i
$330$	57024.8	−	96108.1i	0.523643	−	0.882536i
$331$	−100184.	+	57841.2i	−0.914412	+	0.527936i	−0.881848	−	0.471534i	$-0.843701\pi$
$331$	−100184.	+	57841.2i	−0.914412	+	0.527936i	−0.0325639	+	0.999470i	$0.510367\pi$
$332$	30998.8	−	37216.5i	0.281235	−	0.337644i
$333$	−2492.23	−	16821.8i	−0.0224750	−	0.151699i
$334$	−47792.7	+	132055.i	−0.428419	+	1.18375i
$335$	−175310.	+	101215.i	−1.56213	+	0.901895i
$336$	29215.8	+	51367.3i	0.258785	+	0.454996i
$337$	−93868.0	+	162584.i	−0.826528	+	1.43159i	0.0742175	+	0.997242i	$0.476354\pi$
$337$	−93868.0	+	162584.i	−0.826528	+	1.43159i	−0.900746	+	0.434347i	$0.856979\pi$
$338$	63447.2	−	53435.1i	0.555366	−	0.467728i
$339$	50789.1	+	145734.i	0.441948	+	1.26813i
$340$	−39249.7	+	227420.i	−0.339530	+	1.96730i
$341$	−35761.3			−0.307542
$342$	19709.9	+	58799.7i	0.168512	+	0.502716i
$343$		−	106292.i		−	0.903465i
$344$	−185375.	−	105685.i	−1.56652	−	0.893091i
$345$	46288.2	−	242966.i	0.388895	−	2.04130i
$346$	−9127.87	+	7687.47i	−0.0762460	+	0.0642142i
$347$	117124.	+	67621.8i	0.972721	+	0.561601i	0.900065	−	0.435756i	$-0.143519\pi$
$347$	117124.	+	67621.8i	0.972721	+	0.561601i	0.0726566	+	0.997357i	$0.476852\pi$
$348$	112700.	−	18701.1i	0.930605	−	0.154422i
$349$	−1651.44	−	2860.38i	−0.0135585	−	0.0234841i	0.859167	−	0.511696i	$-0.170983\pi$
$349$	−1651.44	−	2860.38i	−0.0135585	−	0.0234841i	−0.872725	+	0.488212i	$0.837649\pi$
$350$	6755.54	−	18666.0i	0.0551472	−	0.152376i
$351$	−57120.6	+	29914.0i	−0.463637	+	0.242806i
$352$	109591.	+	18300.1i	0.884485	+	0.147695i
$353$	−21366.4	−	37007.7i	−0.171467	−	0.296990i	0.767466	−	0.641090i	$-0.221517\pi$
$353$	−21366.4	−	37007.7i	−0.171467	−	0.296990i	−0.938933	+	0.344100i	$0.888184\pi$
$354$	−82180.8	−	146339.i	−0.655788	−	1.16776i
$355$	−109844.	−	63418.4i	−0.871603	−	0.503220i
$356$	8398.50	−	3091.38i	0.0662677	−	0.0243922i
$357$	−21780.4	+	114325.i	−0.170895	+	0.897027i
$358$	−177993.	+	31718.2i	−1.38879	+	0.247481i
$359$		−	175816.i		−	1.36418i	−0.731270	−	0.682088i	$-0.761072\pi$
$359$		−	175816.i		−	1.36418i	0.731270	−	0.682088i	$-0.238928\pi$
$360$	−22534.1	−	146588.i	−0.173874	−	1.13108i
$361$	93685.2			0.718880
$362$	−19368.7	−	108691.i	−0.147803	−	0.829426i
$363$	8493.80	+	24372.2i	0.0644598	+	0.184961i
$364$	−12538.3	−	34063.4i	−0.0946313	−	0.257090i
$365$	−27939.9	+	48393.3i	−0.209719	+	0.363245i
$366$	2400.67	−	201574.i	0.0179214	−	1.50478i
$367$	−6867.31	+	3964.84i	−0.0509864	+	0.0294370i	−0.525277	−	0.850932i	$-0.676038\pi$
$367$	−6867.31	+	3964.84i	−0.0509864	+	0.0294370i	0.474290	+	0.880369i	$0.342705\pi$
$368$	241859.	−	44459.1i	1.78594	−	0.328296i
$369$	79574.5	+	31461.9i	0.584415	+	0.231064i
$370$	−22591.2	−	8176.13i	−0.165020	−	0.0597234i
$371$	−25291.4	+	14602.0i	−0.183749	+	0.106087i
$372$	−36662.6	+	30138.2i	−0.264934	+	0.217787i
$373$	−123336.	+	213624.i	−0.886486	+	1.53544i	−0.0424851	+	0.999097i	$0.513527\pi$
$373$	−123336.	+	213624.i	−0.886486	+	1.53544i	−0.844001	+	0.536342i	$0.819806\pi$
$374$	140958.	+	167369.i	1.00773	+	1.19655i
$375$	72579.5	−	84124.7i	0.516121	−	0.598220i
$376$	62735.5	+	35766.3i	0.443749	+	0.252987i
$377$	−70170.4			−0.493709
$378$	−10079.2	−	74109.2i	−0.0705414	−	0.518667i
$379$		−	147423.i		−	1.02633i	−0.858291	−	0.513163i	$-0.828474\pi$
$379$		−	147423.i		−	1.02633i	0.858291	−	0.513163i	$-0.171526\pi$
$380$	86338.7	+	14900.9i	0.597914	+	0.103192i
$381$	−65360.0	−	56390.0i	−0.450258	−	0.388465i
$382$	−48500.5	−	57588.0i	−0.332368	−	0.394644i
$383$	−105968.	−	61180.9i	−0.722402	−	0.417079i	0.0932341	−	0.995644i	$-0.470280\pi$
$383$	−105968.	−	61180.9i	−0.722402	−	0.417079i	−0.815636	+	0.578565i	$0.803613\pi$
$384$	127776.	−	73597.8i	0.866535	−	0.499117i
$385$	−39809.7	−	68952.5i	−0.268576	−	0.465188i
$386$	35559.6	+	12869.6i	0.238662	+	0.0863755i
$387$	167852.	+	211569.i	1.12074	+	1.41263i
$388$	−27068.6	−	22546.3i	−0.179805	−	0.149765i
$389$	91728.1	+	158878.i	0.606182	+	1.04994i	0.991863	+	0.127306i	$0.0406330\pi$
$389$	91728.1	+	158878.i	0.606182	+	1.04994i	−0.385682	+	0.922632i	$0.626034\pi$
$390$	−1084.85	+	91090.3i	−0.00713250	+	0.598884i
$391$	419417.	+	242150.i	2.74342	+	1.58391i
$392$	−111560.	+	607.446i	−0.725998	+	0.00395308i
$393$	−38598.9	+	13451.9i	−0.249914	+	0.0870959i
$394$	15192.7	+	85256.9i	0.0978684	+	0.549208i
$395$		−	50342.3i		−	0.322656i
$396$	−120073.	−	73191.4i	−0.765694	−	0.466734i
$397$	81466.1			0.516887			0.258444	−	0.966026i	$-0.416790\pi$
$397$	81466.1			0.516887			0.258444	+	0.966026i	$0.416790\pi$
$398$	99478.5	−	17727.0i	0.628005	−	0.111910i
$399$	43402.9	+	8268.81i	0.272629	+	0.0519394i
$400$	−46667.6	−	16602.9i	−0.291673	−	0.103768i
$401$	−100584.	+	174217.i	−0.625518	+	1.08343i	0.362922	+	0.931820i	$0.381779\pi$
$401$	−100584.	+	174217.i	−0.625518	+	1.08343i	−0.988440	+	0.151610i	$0.951554\pi$
$402$	124727.	+	222100.i	0.771804	+	1.37434i
$403$	25245.9	−	14575.7i	0.155446	−	0.0897469i
$404$	−8995.27	−	7492.45i	−0.0551127	−	0.0459051i
$405$	−42688.2	+	182787.i	−0.260254	+	1.11438i
$406$	27699.0	−	76534.4i	0.168040	−	0.464306i
$407$	−19727.9	+	11389.9i	−0.119094	+	0.0687592i
$408$	285562.	+	52793.7i	1.71546	+	0.317148i
$409$	70320.1	−	121798.i	0.420371	−	0.728104i	−0.575605	−	0.817728i	$-0.695233\pi$
$409$	70320.1	−	121798.i	0.420371	−	0.728104i	0.995976	+	0.0896241i	$0.0285666\pi$
$410$	92466.8	−	77875.3i	0.550070	−	0.463268i
$411$	43335.4	+	8255.95i	0.256542	+	0.0488746i
$412$	−155367.	−	26814.2i	−0.915299	−	0.157968i
$413$	−119576.			−0.701044
$414$	−305018.	−	61882.8i	−1.77961	−	0.361052i
$415$			86606.3i			0.502867i
$416$	−84825.3	+	31748.5i	−0.490161	+	0.183458i
$417$	−73520.3	+	25622.1i	−0.422800	+	0.147348i
$418$	63540.7	−	53513.8i	0.363663	−	0.306276i
$419$	−133102.	−	76846.6i	−0.758154	−	0.437720i	0.0704785	−	0.997513i	$-0.477547\pi$
$419$	−133102.	−	76846.6i	−0.758154	−	0.437720i	−0.828633	+	0.559793i	$0.810881\pi$
$420$	−98923.3	−	37140.2i	−0.560790	−	0.210545i
$421$	−77206.0	−	133725.i	−0.435599	−	0.754479i	0.561746	−	0.827310i	$-0.310130\pi$
$421$	−77206.0	−	133725.i	−0.435599	−	0.754479i	−0.997344	+	0.0728309i	$0.976797\pi$
$422$	−29352.6	+	81103.5i	−0.164825	+	0.455422i
$423$	−56805.1	−	71600.0i	−0.317473	−	0.400159i
$424$	36778.8	+	62909.2i	0.204581	+	0.349931i
$425$	−48775.5	−	84481.6i	−0.270037	−	0.467718i
$426$	−81441.9	+	137260.i	−0.448775	+	0.756354i
$427$	−124382.	−	71812.1i	−0.682186	−	0.393860i
$428$	4447.15	+	12081.8i	0.0242769	+	0.0659544i
$429$	65398.4	+	56423.2i	0.355347	+	0.306579i
$430$	375632.	−	66937.2i	2.03154	−	0.362019i
$431$			191579.i			1.03132i	0.856793	+	0.515660i	$0.172453\pi$
$431$			191579.i			1.03132i	−0.856793	+	0.515660i	$0.827547\pi$
$432$	−184782.	+	26156.8i	−0.990129	+	0.140158i
$433$	−53963.8			−0.287824			−0.143912	−	0.989591i	$-0.545968\pi$
$433$	−53963.8			−0.287824			−0.143912	+	0.989591i	$0.545968\pi$
$434$	5932.08	+	33289.1i	0.0314940	+	0.176735i
$435$	−133439.	+	154665.i	−0.705185	+	0.817359i
$436$	260136.	−	95752.5i	1.36844	−	0.503706i
$437$	91930.9	−	159229.i	0.481392	−	0.833795i
$438$	60472.0	+	35880.4i	0.315214	+	0.187029i
$439$	14586.4	−	8421.44i	0.0756864	−	0.0436976i	−0.461679	−	0.887047i	$-0.652753\pi$
$439$	14586.4	−	8421.44i	0.0756864	−	0.0436976i	0.537366	+	0.843349i	$0.319420\pi$
$440$	−171511.	+	100271.i	−0.885902	+	0.517928i
$441$	131304.	+	51914.6i	0.675153	+	0.266939i
$442$	−167727.	−	60703.0i	−0.858534	−	0.310718i
$443$	140111.	−	80892.9i	0.713943	−	0.412195i	−0.0985761	−	0.995130i	$-0.531429\pi$
$443$	140111.	−	80892.9i	0.713943	−	0.412195i	0.812519	+	0.582934i	$0.198095\pi$
$444$	−10626.1	+	28302.8i	−0.0539024	+	0.143570i
$445$	−8001.09	+	13858.3i	−0.0404045	+	0.0699826i
$446$	49716.1	+	59031.5i	0.249935	+	0.296766i
$447$	−37594.2	−	107873.i	−0.188151	−	0.539881i
$448$	−1144.04	−	105051.i	−0.00570015	−	0.523411i
$449$	127200.			0.630949			0.315475	−	0.948934i	$-0.397836\pi$
$449$	127200.			0.630949			0.315475	+	0.948934i	$0.397836\pi$
$450$	46975.0	+	41514.2i	0.231975	+	0.205008i
$451$		−	114624.i		−	0.563538i
$452$	46662.0	−	270369.i	0.228395	−	1.32337i
$453$	21501.3	−	112860.i	0.104778	−	0.549977i
$454$	−167048.	−	198348.i	−0.810456	−	0.962311i
$455$	56207.7	+	32451.5i	0.271502	+	0.156752i
$456$	20042.8	−	108412.i	0.0963893	−	0.521372i
$457$	9423.93	+	16322.7i	0.0451232	+	0.0781556i	0.887705	−	0.460413i	$-0.152299\pi$
$457$	9423.93	+	16322.7i	0.0451232	+	0.0781556i	−0.842582	+	0.538569i	$0.818965\pi$
$458$	147256.	+	53294.4i	0.702009	+	0.254068i
$459$	−310465.	−	196715.i	−1.47362	−	0.933711i
$460$	−281415.	+	337860.i	−1.32994	+	1.59669i
$461$	29335.9	+	50811.3i	0.138038	+	0.239088i	0.926754	−	0.375669i	$-0.122587\pi$
$461$	29335.9	+	50811.3i	0.138038	+	0.239088i	−0.788716	+	0.614758i	$0.789254\pi$
$462$	−87355.7	+	49057.1i	−0.409267	+	0.229836i
$463$	−41167.7	−	23768.2i	−0.192041	−	0.110875i	0.400897	−	0.916123i	$-0.368699\pi$
$463$	−41167.7	−	23768.2i	−0.192041	−	0.110875i	−0.592938	+	0.805248i	$0.702032\pi$
$464$	−191346.	−	68075.3i	−0.888760	−	0.316194i
$465$	15881.7	−	83362.9i	0.0734499	−	0.385538i
$466$	1619.29	+	9086.96i	0.00745679	+	0.0418453i
$467$			150686.i			0.690936i	0.938431	+	0.345468i	$0.112280\pi$
$467$			150686.i			0.690936i	−0.938431	+	0.345468i	$0.887720\pi$
$468$	114598.	+	2730.02i	0.523220	+	0.0124645i
$469$	181482.			0.825066
$470$	−127123.	+	22653.2i	−0.575478	+	0.102550i
$471$	−120149.	−	344757.i	−0.541602	−	1.55407i
$472$	1624.63	+	298370.i	0.00729240	+	1.33928i
$473$	180885.	−	313302.i	0.808500	−	1.40036i
$474$	−63343.0	−	754.392i	−0.281930	−	0.00335769i
$475$	−32072.9	+	18517.3i	−0.142152	+	0.0820712i
$476$	132417.	−	158976.i	0.584425	−	0.701647i
$477$	−13516.5	−	91232.0i	−0.0594054	−	0.400969i
$478$	103741.	−	286644.i	0.454041	−	1.25455i
$479$	−47830.3	+	27614.8i	−0.208464	+	0.120357i	−0.600598	−	0.799551i	$-0.705071\pi$
$479$	−47830.3	+	27614.8i	−0.208464	+	0.120357i	0.392133	+	0.919908i	$0.371737\pi$
$480$	−91328.9	+	247340.i	−0.396393	+	1.07352i
$481$	9284.65	−	16081.5i	0.0401306	−	0.0695082i
$482$	−49913.5	+	42037.0i	−0.214844	+	0.180941i
$483$	−144850.	+	167891.i	−0.620904	+	0.719671i
$484$	7803.61	−	45215.7i	0.0333123	−	0.193018i
$485$	62991.1			0.267791
$486$	229351.	+	56451.4i	0.971019	+	0.239002i
$487$			2975.59i			0.0125463i	0.999980	+	0.00627313i	$0.00199681\pi$
$487$			2975.59i			0.0125463i	−0.999980	+	0.00627313i	$0.998003\pi$
$488$	−177497.	+	311337.i	−0.745335	+	1.30735i
$489$	46834.9	+	40407.3i	0.195863	+	0.168983i
$490$	152578.	−	128501.i	0.635476	−	0.535196i
$491$	234443.	+	135356.i	0.972467	+	0.561454i	0.899987	−	0.435916i	$-0.143576\pi$
$491$	234443.	+	135356.i	0.972467	+	0.561454i	0.0724794	+	0.997370i	$0.476909\pi$
$492$	−96600.6	−	117513.i	−0.399071	−	0.485462i
$493$	−199989.	−	346391.i	−0.822834	−	1.42519i
$494$	−23045.5	+	63676.5i	−0.0944350	+	0.260931i
$495$	248728.	−	36850.2i	1.01511	−	0.150394i
$496$	82983.0	−	15254.1i	0.337307	−	0.0620047i
$497$	56855.6	+	98476.8i	0.230176	+	0.398677i
$498$	108972.	+	1297.82i	0.439396	+	0.00523305i
$499$	−226339.	−	130677.i	−0.908988	−	0.524805i	−0.0288827	−	0.999583i	$-0.509195\pi$
$499$	−226339.	−	130677.i	−0.908988	−	0.524805i	−0.880105	+	0.474778i	$0.842528\pi$
$500$	−185365.	+	68230.3i	−0.741459	+	0.272921i
$501$	−298383.	+	103988.i	−1.18877	+	0.414292i
$502$	133236.	−	23742.5i	0.528704	−	0.0942146i
$503$			283008.i			1.11857i	0.828976	+	0.559284i	$0.188924\pi$
$503$			283008.i			1.11857i	−0.828976	+	0.559284i	$0.811076\pi$
$504$	−48213.8	+	123913.i	−0.189806	+	0.487817i
$505$	20932.9			0.0820816
$506$	73141.5	+	410448.i	0.285669	+	1.60309i
$507$	183342.	+	34929.0i	0.713257	+	0.135885i
$508$	53010.9	+	144018.i	0.205418	+	0.558069i
$509$	106839.	−	185051.i	0.412378	−	0.714259i	−0.582772	−	0.812636i	$-0.698032\pi$
$509$	106839.	−	185051.i	0.412378	−	0.714259i	0.995149	+	0.0983769i	$0.0313651\pi$
$510$	−452753.	+	254256.i	−1.74069	+	0.977533i
$511$	43385.4	−	25048.6i	0.166151	−	0.0959271i
$512$	−262109.	+	4281.91i	−0.999867	+	0.0163342i
$513$	−74681.8	+	117866.i	−0.283779	+	0.447872i
$514$	−216445.	−	78335.0i	−0.819260	−	0.296503i
$515$	244145.	−	140957.i	0.920520	−	0.531463i
$516$	−78594.5	−	473640.i	−0.295184	−	1.77889i
$517$	−61215.9	+	106029.i	−0.229025	+	0.396683i
$518$	13874.9	+	16474.7i	0.0517097	+	0.0613985i
$519$	−26376.6	−	5025.08i	−0.0979229	−	0.0186556i
$520$	80210.0	−	140691.i	0.296635	−	0.520309i
$521$	168525.			0.620854			0.310427	−	0.950597i	$-0.399528\pi$
$521$	168525.			0.620854			0.310427	+	0.950597i	$0.399528\pi$
$522$	192607.	+	170216.i	0.706855	+	0.624683i
$523$			231592.i			0.846681i	0.905971	+	0.423340i	$0.139143\pi$
$523$			231592.i			0.846681i	−0.905971	+	0.423340i	$0.860857\pi$
$524$	71609.4	+	12358.8i	0.260800	+	0.0450105i
$525$	42176.6	−	14698.7i	0.153022	−	0.0533287i
$526$	202379.	+	240299.i	0.731467	+	0.868522i
$527$	143904.	+	83082.9i	0.518145	+	0.299151i
$528$	123595.	+	217305.i	0.443337	+	0.779475i
$529$	321448.	+	556764.i	1.14868	+	1.98957i
$530$	−122522.	−	44342.8i	−0.436178	−	0.157860i
$531$	138847.	−	351177.i	0.492434	−	1.24548i
$532$	−60354.5	−	50271.2i	−0.213249	−	0.177622i
$533$	46718.9	+	80919.5i	0.164452	+	0.284839i
$534$	17317.2	+	10275.0i	0.0607290	+	0.0360329i
$535$	−19936.1	−	11510.1i	−0.0696518	−	0.0402135i
$536$	−2465.72	−	452838.i	−0.00858250	−	1.57621i
$537$	−308004.	−	265734.i	−1.06809	−	0.921506i
$538$	3773.23	+	21174.3i	0.0130361	+	0.0731550i
$539$		−	189139.i		−	0.651035i
$540$	223940.	−	247397.i	0.767971	−	0.848411i
$541$	−3552.06			−0.0121363			−0.00606815	−	0.999982i	$-0.501932\pi$
$541$	−3552.06			−0.0121363			−0.00606815	+	0.999982i	$0.501932\pi$
$542$	425745.	−	75867.3i	1.44927	−	0.258259i
$543$	162270.	−	188082.i	0.550350	−	0.637894i
$544$	−398480.	−	328249.i	−1.34651	−	1.10919i
$545$	−247826.	+	429248.i	−0.834362	+	1.44516i
$546$	41674.3	−	70236.8i	0.139792	−	0.235602i
$547$	−444293.	+	256513.i	−1.48489	+	0.857302i	−0.999852	−	0.0171904i	$-0.994528\pi$
$547$	−444293.	+	256513.i	−1.48489	+	0.857302i	−0.485039	+	0.874493i	$0.661195\pi$
$548$	−60260.6	−	50193.0i	−0.200665	−	0.167141i
$549$	355328.	−	281906.i	1.17892	−	0.935319i
$550$	28578.7	−	78965.1i	0.0944752	−	0.261042i
$551$	−131505.	+	75924.6i	−0.433152	+	0.250080i
$552$	420894.	+	359152.i	1.38132	+	1.17869i
$553$	−22566.4	+	39086.1i	−0.0737924	+	0.127812i
$554$	134442.	−	113226.i	0.438041	−	0.368917i
$555$	−17789.7	−	51045.7i	−0.0577539	−	0.165719i
$556$	136396.	+	23540.1i	0.441217	+	0.0761482i
$557$	−269383.			−0.868281			−0.434141	−	0.900845i	$-0.642948\pi$
$557$	−269383.			−0.868281			−0.434141	+	0.900845i	$0.642948\pi$
$558$	−104653.	−	21232.3i	−0.336111	−	0.0681913i
$559$			294903.i			0.943746i
$560$	121789.	+	143021.i	0.388358	+	0.456062i
$561$	−92140.3	+	483643.i	−0.292768	+	1.53674i
$562$	−155641.	+	131081.i	−0.492779	+	0.415017i
$563$	−48439.2	−	27966.4i	−0.152820	−	0.0882307i	0.421640	−	0.906763i	$-0.361455\pi$
$563$	−48439.2	−	27966.4i	−0.152820	−	0.0882307i	−0.574460	+	0.818533i	$0.694788\pi$
$564$	26598.3	+	160291.i	0.0836172	+	0.503909i
$565$	245294.	+	424861.i	0.768404	+	1.33092i
$566$	−35930.5	+	99278.4i	−0.112158	+	0.309900i
$567$	115079.	−	122781.i	0.357956	−	0.381915i
$568$	244949.	−	143205.i	0.759239	−	0.443877i
$569$	−212266.	−	367655.i	−0.655625	−	1.13558i	−0.981737	−	0.190245i	$-0.939072\pi$
$569$	−212266.	−	367655.i	−0.655625	−	1.13558i	0.326111	−	0.945331i	$-0.394262\pi$
$570$	96526.9	+	171885.i	0.297097	+	0.529039i
$571$	−25297.4	−	14605.5i	−0.0775897	−	0.0447964i	0.460703	−	0.887554i	$-0.347597\pi$
$571$	−25297.4	−	14605.5i	−0.0775897	−	0.0447964i	−0.538293	+	0.842758i	$0.680931\pi$
$572$	−53042.1	−	144102.i	−0.162117	−	0.440432i
$573$	31703.4	−	166411.i	0.0965600	−	0.506842i
$574$	−106700.	+	19013.9i	−0.323848	+	0.0577094i
$575$		−	185863.i		−	0.562158i
$576$	309846.	+	118621.i	0.933901	+	0.357532i
$577$	−494524.			−1.48537			−0.742687	−	0.669639i	$-0.766449\pi$
$577$	−494524.			−1.48537			−0.742687	+	0.669639i	$0.766449\pi$
$578$	−119763.	−	672074.i	−0.358482	−	2.01169i
$579$	28001.8	+	80348.4i	0.0835272	+	0.239673i
$580$	340796.	−	125443.i	1.01307	−	0.372897i
$581$	38822.0	−	67241.7i	0.115007	−	0.199199i
$582$	943.938	−	79258.3i	0.00278675	−	0.233991i
$583$	−106993.	+	61772.5i	−0.314788	+	0.181743i
$584$	−63091.1	−	107916.i	−0.184988	−	0.316417i
$585$	−160571.	+	127392.i	−0.469197	+	0.372246i
$586$	491936.	+	178040.i	1.43256	+	0.518467i
$587$	208206.	−	120208.i	0.604251	−	0.348865i	−0.166461	−	0.986048i	$-0.553234\pi$
$587$	208206.	−	120208.i	0.604251	−	0.348865i	0.770712	+	0.637183i	$0.219901\pi$
$588$	−159399.	−	193906.i	−0.461032	−	0.560837i
$589$	31541.9	−	54632.2i	0.0909197	−	0.157477i
$590$	−343678.	−	408074.i	−0.987298	−	1.17229i
$591$	−127284.	+	147531.i	−0.364417	+	0.422384i
$592$	40919.5	−	34844.9i	0.116758	−	0.0994250i
$593$	−470902.			−1.33912			−0.669562	−	0.742756i	$-0.733518\pi$
$593$	−470902.			−1.33912			−0.669562	+	0.742756i	$0.733518\pi$
$594$	−42639.4	−	313513.i	−0.120848	−	0.888552i
$595$			369954.i			1.04499i
$596$	−34539.4	+	200128.i	−0.0972349	+	0.563398i
$597$	172140.	+	148516.i	0.482985	+	0.416701i
$598$	−218926.	−	259947.i	−0.612203	−	0.726912i
$599$	−8669.92	−	5005.58i	−0.0241636	−	0.0139509i	0.487870	−	0.872917i	$-0.337774\pi$
$599$	−8669.92	−	5005.58i	−0.0241636	−	0.0139509i	−0.512033	+	0.858966i	$0.671108\pi$
$600$	−37249.6	−	105040.i	−0.103471	−	0.291778i
$601$	−196449.	−	340259.i	−0.543876	−	0.942021i	−0.998677	−	0.0514280i	$-0.983623\pi$
$601$	−196449.	−	340259.i	−0.543876	−	0.942021i	0.454800	−	0.890593i	$-0.349711\pi$
$602$	−321648.	−	116410.i	−0.887540	−	0.321215i
$603$	−210730.	+	532985.i	−0.579550	+	1.46582i
$604$	−130720.	+	156939.i	−0.358317	+	0.430188i
$605$	41022.2	+	71052.5i	0.112075	+	0.194119i
$606$	313.684	−	26338.7i	0.000854176	−	0.0717214i
$607$	−375426.	−	216752.i	−1.01894	−	0.588283i	−0.105141	−	0.994457i	$-0.533529\pi$
$607$	−375426.	−	216752.i	−1.01894	−	0.588283i	−0.913796	+	0.406174i	$0.866863\pi$
$608$	−124618.	+	151281.i	−0.337111	+	0.409238i
$609$	172932.	−	60267.7i	0.466274	−	0.162499i
$610$	−112421.	−	630872.i	−0.302125	−	1.69544i
$611$		−	99802.2i		−	0.267336i
$612$	313132.	+	573484.i	0.836036	+	1.53115i
$613$	301951.			0.803555			0.401778	−	0.915737i	$-0.368393\pi$
$613$	301951.			0.803555			0.401778	+	0.915737i	$0.368393\pi$
$614$	−213545.	+	38053.5i	−0.566439	+	0.100939i
$615$	267199.	+	50904.9i	0.706456	+	0.134589i
$616$	178109.	−	969.810i	0.469380	−	0.00255579i
$617$	−98373.3	+	170388.i	−0.258409	+	0.447577i	−0.965816	−	0.259229i	$-0.916531\pi$
$617$	−98373.3	+	170388.i	−0.258409	+	0.447577i	0.707407	+	0.706806i	$0.249865\pi$
$618$	−173700.	−	309307.i	−0.454803	−	0.809864i
$619$	536199.	−	309575.i	1.39941	−	0.807949i	0.405078	−	0.914282i	$-0.367244\pi$
$619$	536199.	−	309575.i	1.39941	−	0.807949i	0.994331	+	0.106333i	$0.0339110\pi$
$620$	−96554.8	+	115921.i	−0.251183	+	0.301565i
$621$	−324877.	−	620351.i	−0.842434	−	1.60862i
$622$	−185077.	+	511380.i	−0.478378	+	1.32179i
$623$	12424.2	−	7173.12i	0.0320105	−	0.0184813i
$624$	−175822.	−	103032.i	−0.451549	−	0.264609i
$625$	237059.	−	410598.i	0.606870	−	1.05113i
$626$	−502947.	+	423581.i	−1.28343	+	1.08090i
$627$	183612.	+	34980.5i	0.467053	+	0.0889797i
$628$	−110386.	+	639600.i	−0.279896	+	1.62177i
$629$	105847.			0.267532
$630$	−75561.7	−	225420.i	−0.190380	−	0.567952i
$631$		−	308766.i		−	0.775479i	−0.921769	−	0.387740i	$-0.873256\pi$
$631$		−	308766.i		−	0.775479i	0.921769	−	0.387740i	$-0.126744\pi$
$632$	97835.0	+	55777.0i	0.244940	+	0.139644i
$633$	−183256.	+	63865.6i	−0.457353	+	0.159390i
$634$	−369034.	+	310800.i	−0.918096	+	0.773218i
$635$	−237642.	−	137203.i	−0.589354	−	0.340264i
$636$	−57630.2	+	153499.i	−0.142474	+	0.379481i
$637$	77090.0	+	133524.i	0.189985	+	0.329064i
$638$	117178.	−	323772.i	0.287877	−	0.795424i
$639$	−355229.	+	52628.9i	−0.869976	+	0.128891i
$640$	355214.	−	305834.i	0.867222	−	0.746665i
$641$	171200.	+	296528.i	0.416666	+	0.721687i	0.995602	−	0.0936860i	$-0.0298650\pi$
$641$	171200.	+	296528.i	0.416666	+	0.721687i	−0.578935	+	0.815373i	$0.696532\pi$
$642$	−14781.3	+	24912.0i	−0.0358626	+	0.0604419i
$643$	478867.	+	276474.i	1.15823	+	0.668702i	0.950878	−	0.309566i	$-0.100184\pi$
$643$	478867.	+	276474.i	1.15823	+	0.668702i	0.207347	+	0.978267i	$0.433517\pi$
$644$	369941.	−	136170.i	0.891991	−	0.328330i
$645$	650003.	+	560797.i	1.56241	+	1.34799i
$646$	−380015.	+	67718.3i	−0.910617	+	0.162271i
$647$			576814.i			1.37793i	0.724794	+	0.688965i	$0.241935\pi$
$647$			576814.i			1.37793i	−0.724794	+	0.688965i	$0.758065\pi$
$648$	−307930.	−	285479.i	−0.733334	−	0.679868i
$649$	−505858.			−1.20099
$650$	12009.5	+	67394.0i	0.0284250	+	0.159512i
$651$	−49698.8	+	57604.4i	−0.117269	+	0.135923i
$652$	−37986.0	−	103199.i	−0.0893569	−	0.242761i
$653$	286795.	−	496744.i	0.672583	−	1.16495i	−0.304586	−	0.952485i	$-0.598518\pi$
$653$	286795.	−	496744.i	0.672583	−	1.16495i	0.977169	−	0.212463i	$-0.0681484\pi$
$654$	536386.	+	318259.i	1.25407	+	0.744089i
$655$	−112528.	+	64968.0i	−0.262288	+	0.151432i
$656$	48893.4	+	265982.i	0.113617	+	0.618080i
$657$	23186.4	+	156501.i	0.0537159	+	0.362567i
$658$	108854.	+	39395.9i	0.251415	+	0.0909911i
$659$	299298.	−	172800.i	0.689180	−	0.397899i	−0.114125	−	0.993466i	$-0.536406\pi$
$659$	299298.	−	172800.i	0.689180	−	0.397899i	0.803305	+	0.595568i	$0.203073\pi$
$660$	−418487.	−	157118.i	−0.960714	−	0.360694i
$661$	187583.	−	324904.i	0.429330	−	0.743622i	−0.567484	−	0.823385i	$-0.692083\pi$
$661$	187583.	−	324904.i	0.429330	−	0.743622i	0.996814	+	0.0797628i	$0.0254163\pi$
$662$	298080.	+	353931.i	0.680168	+	0.807612i
$663$	−132078.	−	378985.i	−0.300471	−	0.862174i
$664$	−168310.	−	95955.8i	−0.381746	−	0.217638i
$665$	140451.			0.317600
$666$	−64494.6	+	21618.8i	−0.145404	+	0.0487398i
$667$		−	762077.i		−	1.71296i
$668$	553565.	+	95537.8i	1.24055	+	0.214103i
$669$	−32498.1	+	170582.i	−0.0726115	+	0.381137i
$670$	521604.	+	619337.i	1.16196	+	1.37968i
$671$	−526189.	−	303795.i	−1.16868	−	0.674739i
$672$	181781.	−	151097.i	0.402540	−	0.334594i
$673$	286866.	+	496866.i	0.633358	+	1.09701i	0.986861	+	0.161574i	$0.0516571\pi$
$673$	286866.	+	496866.i	0.633358	+	1.09701i	−0.353503	+	0.935433i	$0.615010\pi$
$674$	706121.	+	255557.i	1.55439	+	0.562558i
$675$	−5805.83	+	140934.i	−0.0127426	+	0.309319i
$676$	−254949.	−	212355.i	−0.557904	−	0.464697i
$677$	13789.2	+	23883.6i	0.0300859	+	0.0521103i	0.880676	−	0.473719i	$-0.157089\pi$
$677$	13789.2	+	23883.6i	0.0300859	+	0.0521103i	−0.850590	+	0.525829i	$0.823755\pi$
$678$	538256.	−	302273.i	1.17093	−	0.657567i
$679$	−48906.7	−	28236.3i	−0.106079	−	0.0612447i
$680$	923116.	−	5026.39i	1.99636	−	0.0108702i
$681$	109195.	−	573161.i	0.235454	−	1.23590i
$682$	25095.2	+	140827.i	0.0539538	+	0.302773i
$683$		−	1038.30i		−	0.00222578i	−0.999999	−	0.00111289i	$-0.999646\pi$
$683$		−	1038.30i		−	0.00222578i	0.999999	−	0.00111289i	$-0.000354244\pi$
$684$	217720.	−	118879.i	0.465356	−	0.254093i
$685$	140232.			0.298859
$686$	−418573.	+	74589.3i	−0.889454	+	0.158500i
$687$	115958.	+	332731.i	0.245690	+	0.704985i
$688$	−286098.	+	804164.i	−0.604418	+	1.69890i
$689$	50354.8	−	87217.2i	0.106073	−	0.183723i
$690$	−989275.	−	11781.9i	−2.07787	−	0.0247467i
$691$	289343.	−	167052.i	0.605978	−	0.349862i	−0.165411	−	0.986225i	$-0.552895\pi$
$691$	289343.	−	167052.i	0.605978	−	0.349862i	0.771390	+	0.636363i	$0.219562\pi$
$692$	36678.4	+	30550.6i	0.0765945	+	0.0637981i
$693$	−209632.	−	82883.6i	−0.436508	−	0.172585i
$694$	184101.	−	508685.i	0.382241	−	1.05616i
$695$	−214335.	+	123746.i	−0.443734	+	0.256190i
$696$	−152731.	−	430685.i	−0.315288	−	0.889082i
$697$	−266302.	+	461249.i	−0.548162	+	0.949445i
$698$	−10105.2	+	8510.57i	−0.0207412	+	0.0174682i
$699$	−13566.3	+	15724.3i	−0.0277656	+	0.0321823i
$700$	−78246.8	−	13504.3i	−0.159687	−	0.0275599i
$701$	177927.			0.362082			0.181041	−	0.983476i	$-0.442053\pi$
$701$	177927.			0.362082			0.181041	+	0.983476i	$0.442053\pi$
$702$	157884.	+	203947.i	0.320379	+	0.413850i
$703$		−	40184.1i		−	0.0813100i
$704$	−4839.78	−	444408.i	−0.00976517	−	0.896679i
$705$	−219977.	−	189788.i	−0.442587	−	0.381847i
$706$	−130741.	+	110110.i	−0.262303	+	0.220911i
$707$	−16252.4	−	9383.33i	−0.0325146	−	0.0187723i
$708$	−518607.	+	426317.i	−1.03460	+	0.850484i
$709$	−362484.	−	627841.i	−0.721102	−	1.24899i	−0.960558	−	0.278079i	$-0.910302\pi$
$709$	−362484.	−	627841.i	−0.721102	−	1.24899i	0.239456	−	0.970907i	$-0.423031\pi$
$710$	−172657.	+	477064.i	−0.342506	+	0.946368i
$711$	−88586.6	−	111659.i	−0.175238	−	0.220879i
$712$	−18067.3	−	30903.7i	−0.0356396	−	0.0609607i
$713$	158298.	+	274180.i	0.311383	+	0.539332i
$714$	465492.	+	5543.85i	0.913096	+	0.0108746i
$715$	237782.	+	137284.i	0.465122	+	0.268538i
$716$	249810.	+	678672.i	0.487286	+	1.32384i
$717$	647683.	−	225720.i	1.25987	−	0.439069i
$718$	−692358.	+	123378.i	−1.34302	+	0.239325i
$719$		−	536436.i		−	1.03767i	−0.854874	−	0.518836i	$-0.826366\pi$
$719$		−	536436.i		−	1.03767i	0.854874	−	0.518836i	$-0.173634\pi$
$720$	−561447.	+	191606.i	−1.08304	+	0.369610i
$721$	−252741.			−0.486189
$722$	−65742.8	−	368929.i	−0.126117	−	0.707731i
$723$	−144234.	−	27478.4i	−0.275925	−	0.0525673i
$724$	−414431.	+	152546.i	−0.790632	+	0.291021i
$725$	−76751.2	+	132937.i	−0.146019	+	0.252912i
$726$	90016.2	−	50551.2i	0.170784	−	0.0959088i
$727$	375814.	−	216977.i	0.711057	−	0.410529i	−0.100395	−	0.994948i	$-0.532011\pi$
$727$	375814.	−	216977.i	0.711057	−	0.410529i	0.811452	+	0.584418i	$0.198677\pi$
$728$	−125342.	+	73278.9i	−0.236501	+	0.138266i
$729$	226965.	+	480538.i	0.427074	+	0.904217i
$730$	210178.	+	76066.7i	0.394403	+	0.142741i
$731$	−1.45577e6	+	840486.i	−2.72431	+	1.57288i
$732$	−795476.	+	131999.i	−1.48458	+	0.246348i
$733$	390208.	−	675860.i	0.726254	−	1.25791i	−0.232202	−	0.972667i	$-0.574593\pi$
$733$	390208.	−	675860.i	0.726254	−	1.25791i	0.958456	−	0.285241i	$-0.0920735\pi$
$734$	20432.5	+	24260.9i	0.0379253	+	0.0450314i
$735$	440901.	+	83997.3i	0.816143	+	0.155486i
$736$	−344801.	−	921234.i	−0.636521	−	1.70065i
$737$	767746.			1.41346
$738$	68055.0	−	335440.i	0.124953	−	0.615888i
$739$			215142.i			0.393947i	0.980409	+	0.196973i	$0.0631112\pi$
$739$			215142.i			0.393947i	−0.980409	+	0.196973i	$0.936889\pi$
$740$	−16344.1	+	94700.9i	−0.0298468	+	0.172938i
$741$	−143879.	+	50142.6i	−0.262037	+	0.0913209i
$742$	75250.1	+	89349.7i	0.136678	+	0.162288i
$743$	250360.	+	144546.i	0.453511	+	0.261835i	0.709312	−	0.704895i	$-0.249006\pi$
$743$	250360.	+	144546.i	0.453511	+	0.261835i	−0.255801	+	0.966730i	$0.582339\pi$
$744$	144411.	+	123227.i	0.260888	+	0.222617i
$745$	−181567.	−	314484.i	−0.327133	−	0.566612i
$746$	927794.	+	335784.i	1.66715	+	0.603367i
$747$	152400.	+	192092.i	0.273113	+	0.344246i
$748$	560178.	−	672537.i	1.00120	−	1.20202i
$749$	10319.0	+	17873.0i	0.0183939	+	0.0318592i
$750$	−382212.	−	226782.i	−0.679488	−	0.403167i
$751$	593117.	+	342436.i	1.05162	+	0.607156i	0.923104	−	0.384551i	$-0.125644\pi$
$751$	593117.	+	342436.i	1.05162	+	0.607156i	0.128521	+	0.991707i	$0.458977\pi$
$752$	96822.4	−	272149.i	0.171214	−	0.481250i
$753$	230554.	+	198913.i	0.406615	+	0.350812i
$754$	49241.5	+	276329.i	0.0866141	+	0.486052i
$755$		−	365213.i		−	0.640697i
$756$	−284766.	+	91697.2i	−0.498248	+	0.160440i
$757$	−646906.			−1.12888			−0.564442	−	0.825472i	$-0.690909\pi$
$757$	−646906.			−1.12888			−0.564442	+	0.825472i	$0.690909\pi$
$758$	−580545.	+	103452.i	−1.01041	+	0.180054i
$759$	−612777.	+	710251.i	−1.06370	+	1.23290i
$760$	−1908.24	−	350455.i	−0.00330374	−	0.606744i
$761$	−383411.	+	664087.i	−0.662057	+	1.14672i	0.318018	+	0.948085i	$0.396983\pi$
$761$	−383411.	+	664087.i	−0.662057	+	1.14672i	−0.980074	+	0.198631i	$0.936350\pi$
$762$	−176196.	+	296956.i	−0.303449	+	0.511426i
$763$	384828.	−	222181.i	0.661025	−	0.381643i
$764$	−192745.	+	231405.i	−0.330214	+	0.396448i
$765$	−1.08650e6	−	429575.i	−1.85654	−	0.734033i
$766$	−166566.	+	460233.i	−0.283876	+	0.784369i
$767$	357113.	−	206179.i	0.607037	−	0.350473i
$768$	−379491.	−	451530.i	−0.643397	−	0.765533i
$769$	289867.	−	502065.i	0.490170	−	0.848999i	−0.509766	−	0.860313i	$-0.670268\pi$
$769$	289867.	−	502065.i	0.490170	−	0.848999i	0.999936	+	0.0113137i	$0.00360135\pi$
$770$	−243596.	+	205156.i	−0.410855	+	0.346021i
$771$	−170442.	−	489066.i	−0.286726	−	0.822733i
$772$	25726.4	−	149064.i	0.0431662	−	0.250114i
$773$	−885783.			−1.48241			−0.741205	−	0.671279i	$-0.765745\pi$
$773$	−885783.			−1.48241			−0.741205	+	0.671279i	$0.765745\pi$
$774$	715361.	−	809460.i	1.19411	−	1.35118i
$775$		−	63770.7i		−	0.106174i
$776$	−69791.3	+	122417.i	−0.115899	+	0.203291i
$777$	−9069.67	+	47606.6i	−0.0150228	+	0.0788542i
$778$	561285.	−	472713.i	0.927309	−	0.780977i
$779$	175110.	+	101100.i	0.288561	+	0.166601i
$780$	359472.	−	59649.7i	0.590848	−	0.0980436i
$781$	240523.	+	416598.i	0.394325	+	0.682991i
$782$	659257.	−	1.82157e6i	1.07806	−	2.97875i
$783$	−23805.0	+	577855.i	−0.0388280	+	0.942531i
$784$	80678.1	+	438892.i	0.131257	+	0.714045i
$785$	−580281.	−	1.00508e6i	−0.941671	−	1.63102i
$786$	80059.5	+	142561.i	0.129589	+	0.230758i
$787$	−910515.	−	525686.i	−1.47007	−	0.848744i	−0.470633	−	0.882329i	$-0.655974\pi$
$787$	−910515.	−	525686.i	−1.47007	−	0.848744i	−0.999436	+	0.0335849i	$0.989308\pi$
$788$	325077.	−	119657.i	0.523521	−	0.192701i
$789$	−132290.	+	694388.i	−0.212507	+	1.11544i
$790$	−198246.	+	35327.3i	−0.317651	+	0.0566052i
$791$		−	439820.i		−	0.702946i
$792$	−203965.	+	524205.i	−0.325166	+	0.835701i
$793$	495287.			0.787609
$794$	−57168.1	−	320811.i	−0.0906803	−	0.508871i
$795$	−96481.3	−	276844.i	−0.152654	−	0.438027i
$796$	−139616.	−	379303.i	−0.220348	−	0.598632i
$797$	47409.2	−	82115.1i	0.0746356	−	0.129273i	−0.826292	−	0.563242i	$-0.809554\pi$
$797$	47409.2	−	82115.1i	0.0746356	−	0.129273i	0.900928	+	0.433969i	$0.142887\pi$
$798$	2104.69	−	176721.i	0.00330508	−	0.277513i
$799$	492666.	−	284441.i	0.771719	−	0.445552i
$800$	−32633.2	+	195426.i	−0.0509894	+	0.305354i
$801$	6639.86	+	44817.1i	0.0103489	+	0.0698519i
$802$	756643.	+	273841.i	1.17636	+	0.425745i
$803$	183538.	−	105966.i	0.284640	−	0.164337i
$804$	787095.	−	647025.i	1.21763	−	1.00094i
$805$	−352436.	+	610436.i	−0.543861	+	0.941995i
$806$	−75114.7	−	89189.0i	−0.115626	−	0.137291i
$807$	−31612.0	+	36640.5i	−0.0485406	+	0.0562619i
$808$	−23192.7	+	40680.8i	−0.0355245	+	0.0623113i
$809$	−209085.			−0.319467			−0.159734	−	0.987160i	$-0.551063\pi$
$809$	−209085.			−0.319467			−0.159734	+	0.987160i	$0.551063\pi$
$810$	749763.	+	39835.8i	1.14276	+	0.0607161i
$811$			577209.i			0.877589i	0.898587	+	0.438794i	$0.144594\pi$
$811$			577209.i			0.877589i	−0.898587	+	0.438794i	$0.855406\pi$
$812$	−320827.	−	55370.4i	−0.486585	−	0.0839781i
$813$	736720.	+	635613.i	1.11461	+	0.961638i
$814$	58696.8	+	69694.9i	0.0885862	+	0.105185i
$815$	170287.	+	98315.3i	0.256370	+	0.148015i
$816$	7508.68	−	1.16158e6i	0.0112767	−	1.74449i
$817$	319086.	+	552673.i	0.478039	+	0.827987i
$818$	−528983.	−	191447.i	−0.790560	−	0.286116i
$819$	181773.	−	26930.5i	0.270995	−	0.0401492i
$820$	−371558.	−	309483.i	−0.552585	−	0.460266i
$821$	367923.	+	637262.i	0.545847	+	0.945435i	0.998553	+	0.0537749i	$0.0171253\pi$
$821$	367923.	+	637262.i	0.545847	+	0.945435i	−0.452706	+	0.891660i	$0.649541\pi$
$822$	2101.42	−	176447.i	0.00311006	−	0.261138i
$823$	−148172.	−	85547.4i	−0.218760	−	0.126301i	0.386616	−	0.922241i	$-0.373644\pi$
$823$	−148172.	−	85547.4i	−0.218760	−	0.126301i	−0.605376	+	0.795940i	$0.706977\pi$
$824$	3433.88	+	630644.i	0.00505743	+	0.928817i
$825$	178425.	−	62181.8i	0.262148	−	0.0913598i
$826$	83911.7	+	470888.i	0.122988	+	0.690172i
$827$			1.03882e6i			1.51890i	0.650563	+	0.759452i	$0.274533\pi$
$827$			1.03882e6i			1.51890i	−0.650563	+	0.759452i	$0.725467\pi$
$828$	−29649.1	+	1.24457e6i	−0.0432464	+	1.81535i
$829$	−802150.			−1.16720			−0.583601	−	0.812040i	$-0.698357\pi$
$829$	−802150.			−1.16720			−0.583601	+	0.812040i	$0.698357\pi$
$830$	341052.	−	60775.2i	0.495068	−	0.0882206i
$831$	388493.	+	74013.0i	0.562576	+	0.107178i
$832$	184550.	+	311760.i	0.266604	+	0.450374i
$833$	−439420.	+	761098.i	−0.633272	+	1.09686i
$834$	152491.	+	271540.i	0.219237	+	0.390393i
$835$	−869879.	+	502225.i	−1.24763	+	0.720320i
$836$	−255325.	−	212668.i	−0.365326	−	0.304292i
$837$	−111467.	−	212845.i	−0.159109	−	0.303818i
$838$	−209216.	+	578078.i	−0.297925	+	0.823187i
$839$	487546.	−	281485.i	0.692615	−	0.399881i	−0.111976	−	0.993711i	$-0.535718\pi$
$839$	487546.	−	281485.i	0.692615	−	0.399881i	0.804591	+	0.593830i	$0.202385\pi$
$840$	−76838.1	+	415619.i	−0.108898	+	0.589029i
$841$	38945.5	−	67455.6i	0.0550637	−	0.0953732i
$842$	−472424.	+	397874.i	−0.666358	+	0.561205i
$843$	−449753.	−	85683.8i	−0.632876	−	0.120571i
$844$	339980.	+	58676.0i	0.477275	+	0.0823713i
$845$	593291.			0.830910
$846$	−242096.	+	273941.i	−0.338257	+	0.382751i
$847$		−	73554.1i		−	0.102527i
$848$	221925.	−	188979.i	0.308613	−	0.262798i
$849$	−224323.	+	78177.7i	−0.311214	+	0.108459i
$850$	−298458.	+	251360.i	−0.413090	+	0.347903i
$851$	174651.	+	100835.i	0.241164	+	0.139236i
$852$	597677.	+	224394.i	0.823355	+	0.309124i
$853$	331406.	+	574011.i	0.455472	+	0.788901i	0.998715	−	0.0506745i	$-0.0161371\pi$
$853$	331406.	+	574011.i	0.455472	+	0.788901i	−0.543243	+	0.839575i	$0.682804\pi$
$854$	−195509.	+	540206.i	−0.268072	+	0.740703i
$855$	−163085.	+	412482.i	−0.223091	+	0.564251i
$856$	44456.9	−	25991.0i	0.0606725	−	0.0354712i
$857$	−566602.	−	981383.i	−0.771465	−	1.33622i	−0.936760	−	0.349973i	$-0.886191\pi$
$857$	−566602.	−	981383.i	−0.771465	−	1.33622i	0.165294	−	0.986244i	$-0.447143\pi$
$858$	176300.	−	297131.i	0.239484	−	0.403621i
$859$	347489.	+	200623.i	0.470928	+	0.271890i	0.716628	−	0.697456i	$-0.245685\pi$
$859$	347489.	+	200623.i	0.470928	+	0.271890i	−0.245700	+	0.969346i	$0.579018\pi$
$860$	−527193.	−	1.43225e6i	−0.712808	−	1.93652i
$861$	−184637.	−	159297.i	−0.249064	−	0.214883i
$862$	754431.	−	134439.i	1.01532	−	0.180930i
$863$		−	1.22445e6i		−	1.64407i	−0.569437	−	0.822035i	$-0.692839\pi$
$863$		−	1.22445e6i		−	1.64407i	0.569437	−	0.822035i	$-0.307161\pi$
$864$	232674.	+	709309.i	0.311688	+	0.950185i
$865$	−85354.1			−0.114075
$866$	37868.6	+	212508.i	0.0504945	+	0.283360i
$867$	1.00337e6	−	1.16298e6i	1.33482	−	1.54715i
$868$	126928.	−	46720.7i	0.168469	−	0.0620111i
$869$	−95465.2	+	165351.i	−0.126417	+	0.218961i
$870$	702703.	+	416942.i	0.928397	+	0.550855i
$871$	−541994.	+	312920.i	−0.714427	+	0.412475i
$872$	−559618.	−	957212.i	−0.735967	−	1.25885i
$873$	139714.	−	110845.i	0.183321	−	0.145441i
$874$	−691550.	−	250283.i	−0.905317	−	0.327649i
$875$	−274217.	+	158319.i	−0.358161	+	0.206784i
$876$	98860.1	−	263315.i	0.128829	−	0.343137i
$877$	−65931.0	+	114196.i	−0.0857216	+	0.148474i	−0.905698	−	0.423922i	$-0.860653\pi$
$877$	−65931.0	+	114196.i	−0.0857216	+	0.148474i	0.819977	+	0.572397i	$0.193986\pi$
$878$	−43399.2	−	51530.9i	−0.0562979	−	0.0668465i
$879$	387379.	+	1.11155e6i	0.501370	+	1.43863i
$880$	515219.	+	605039.i	0.665314	+	0.781300i
$881$	510450.			0.657660			0.328830	−	0.944389i	$-0.393346\pi$
$881$	510450.			0.657660			0.328830	+	0.944389i	$0.393346\pi$
$882$	112296.	−	553503.i	0.144354	−	0.711513i
$883$			233561.i			0.299557i	0.988720	+	0.149778i	$0.0478560\pi$
$883$			233561.i			0.299557i	−0.988720	+	0.149778i	$0.952144\pi$
$884$	−121346.	+	703100.i	−0.155281	+	0.899730i
$885$	224653.	−	1.17920e6i	0.286831	−	1.50557i
$886$	−416875.	−	494985.i	−0.531053	−	0.630557i
$887$	554282.	+	320015.i	0.704504	+	0.406746i	0.809023	−	0.587777i	$-0.199997\pi$
$887$	554282.	+	320015.i	0.704504	+	0.406746i	−0.104519	+	0.994523i	$0.533330\pi$
$888$	118912.	+	21984.0i	0.150800	+	0.0278792i
$889$	123005.	+	213050.i	0.155639	+	0.269574i
$890$	60188.2	+	21783.1i	0.0759856	+	0.0275004i
$891$	486833.	−	519416.i	0.613231	−	0.654275i
$892$	197576.	−	237205.i	0.248316	−	0.298122i
$893$	−107986.	−	187038.i	−0.135415	−	0.234545i
$894$	−398419.	+	223744.i	−0.498499	+	0.279947i
$895$	−1.11987e6	−	646558.i	−1.39805	−	0.807164i
$896$	−412883.	+	78223.6i	−0.514293	+	0.0974365i
$897$	143106.	−	751162.i	0.177858	−	0.933574i
$898$	−89261.5	−	500909.i	−0.110691	−	0.621164i
$899$		−	261472.i		−	0.323524i
$900$	130517.	−	214118.i	0.161132	−	0.264343i
$901$	574055.			0.707137
$902$	−451386.	+	80436.5i	−0.554798	+	0.0988645i
$903$	−253285.	−	726776.i	−0.310623	−	0.891303i
$904$	−1.09745e6	+	5975.64i	−1.34291	+	0.00731219i
$905$	394820.	−	683849.i	0.482061	−	0.834954i
$906$	−459528.	−	5472.81i	−0.559829	−	0.00666736i
$907$	−379256.	+	218964.i	−0.461018	+	0.266169i	−0.712472	−	0.701700i	$-0.752425\pi$
$907$	−379256.	+	218964.i	−0.461018	+	0.266169i	0.251454	+	0.967869i	$0.419091\pi$
$908$	−663862.	+	797017.i	−0.805204	+	0.966710i
$909$	46429.0	−	36835.2i	0.0561903	−	0.0445796i
$910$	88349.7	−	244116.i	0.106690	−	0.294791i
$911$	666090.	−	384567.i	0.802594	−	0.463378i	−0.0417834	−	0.999127i	$-0.513304\pi$
$911$	666090.	−	384567.i	0.802594	−	0.463378i	0.844377	+	0.535749i	$0.179971\pi$
$912$	−440987.	−	2850.63i	−0.530196	−	0.00342729i
$913$	164233.	−	284460.i	0.197024	−	0.341256i
$914$	57665.1	−	48565.4i	0.0690273	−	0.0581346i
$915$	941856.	−	1.09168e6i	1.12497	−	1.30392i
$916$	106536.	−	617288.i	0.126971	−	0.735694i
$917$	116490.			0.138532
$918$	−556792.	+	1.36064e6i	−0.660705	+	1.61458i
$919$			1.37883e6i			1.63260i	0.577626	+	0.816301i	$0.303979\pi$
$919$			1.37883e6i			1.63260i	−0.577626	+	0.816301i	$0.696021\pi$
$920$	1.52796e6	+	871111.i	1.80525	+	1.02920i
$921$	−369524.	−	318811.i	−0.435636	−	0.375849i
$922$	179507.	−	151180.i	0.211164	−	0.177841i
$923$	−339597.	−	196066.i	−0.398621	−	0.230144i
$924$	254486.	+	309578.i	0.298071	+	0.362599i
$925$	−20310.8	−	35179.3i	−0.0237380	−	0.0411153i
$926$	−64709.1	+	178796.i	−0.0754646	+	0.208514i
$927$	293472.	−	742261.i	0.341513	−	0.863768i
$928$	−133802.	+	801287.i	−0.155370	+	0.930448i
$929$	130885.	+	226699.i	0.151656	+	0.262675i	0.931836	−	0.362879i	$-0.118206\pi$
$929$	130885.	+	226699.i	0.151656	+	0.262675i	−0.780181	+	0.625554i	$0.784873\pi$
$930$	−339425.	−	4042.43i	−0.392444	−	0.00467387i
$931$	288946.	+	166823.i	0.333363	+	0.192467i
$932$	34647.8	−	12753.4i	0.0398881	−	0.0146823i
$933$	−1.15548e6	+	402691.i	−1.32739	+	0.462603i
$934$	593394.	−	105742.i	0.680220	−	0.121215i
$935$			1.56506e6i			1.79022i
$936$	−69667.2	−	453197.i	−0.0795201	−	0.517292i
$937$	1.29656e6			1.47677			0.738384	−	0.674380i	$-0.235589\pi$
$937$	1.29656e6			1.47677			0.738384	+	0.674380i	$0.235589\pi$
$938$	−127354.	−	714671.i	−0.144746	−	0.812270i
$939$	−1.45336e6	−	276883.i	−1.64832	−	0.314026i
$940$	178415.	+	484709.i	0.201918	+	0.548562i
$941$	211160.	−	365741.i	0.238470	−	0.413042i	−0.721806	−	0.692096i	$-0.756688\pi$
$941$	211160.	−	365741.i	0.238470	−	0.413042i	0.960275	+	0.279054i	$0.0900209\pi$
$942$	−1.27333e6	+	715075.i	−1.43496	+	0.805841i
$943$	−878816.	+	507385.i	−0.988267	+	0.570576i
$944$	1.17383e6	−	215776.i	1.31723	−	0.242136i
$945$	286308.	−	451863.i	0.320604	−	0.505991i
$946$	−1.36071e6	−	492462.i	−1.52048	−	0.550288i
$947$	−844845.	+	487772.i	−0.942057	+	0.543897i	−0.890605	−	0.454779i	$-0.849718\pi$
$947$	−844845.	+	487772.i	−0.942057	+	0.543897i	−0.0514525	+	0.998675i	$0.516385\pi$
$948$	41479.6	+	249972.i	0.0461549	+	0.278147i
$949$	−86379.8	+	149614.i	−0.0959135	+	0.166127i
$950$	95427.4	+	113308.i	0.105737	+	0.125549i
$951$	−1.06639e6	−	203161.i	−1.17911	−	0.224636i
$952$	−718966.	−	409892.i	−0.793294	−	0.452267i
$953$	1.52194e6			1.67576			0.837878	−	0.545857i	$-0.183796\pi$
$953$	1.52194e6			1.67576			0.837878	+	0.545857i	$0.183796\pi$
$954$	−349783.	+	117249.i	−0.384328	+	0.128828i
$955$		−	538502.i		−	0.590447i
$956$	−1.20159e6	−	207379.i	−1.31475	−	0.226907i
$957$	731576.	−	254957.i	0.798795	−	0.278384i
$958$	142311.	+	168976.i	0.155062	+	0.184117i
$959$	−108877.	−	62860.3i	−0.118386	−	0.0683501i
$960$	1.03811e6	+	186081.i	1.12642	+	0.201911i
$961$	−407448.	−	705720.i	−0.441190	−	0.764163i
$962$	−69843.8	−	25277.6i	−0.0754705	−	0.0273140i
$963$	−64472.3	+	9551.87i	−0.0695217	+	0.0103000i
$964$	200567.	+	167058.i	0.215826	+	0.179769i
$965$	135239.	+	234241.i	0.145227	+	0.251540i
$966$	762798.	+	452598.i	0.817439	+	0.485019i
$967$	−1.31627e6	−	759947.i	−1.40764	−	0.812700i	−0.412478	−	0.910967i	$-0.635337\pi$
$967$	−1.31627e6	−	759947.i	−1.40764	−	0.812700i	−0.995160	+	0.0982670i	$0.968670\pi$
$968$	−183534.	+	999.347i	−0.195869	+	0.00106651i
$969$	−657588.	−	567341.i	−0.700336	−	0.604222i
$970$	−44203.5	−	248057.i	−0.0469800	−	0.263638i
$971$			606895.i			0.643687i	0.946793	+	0.321844i	$0.104303\pi$
$971$			606895.i			0.643687i	−0.946793	+	0.321844i	$0.895697\pi$
$972$	61358.6	−	942789.i	0.0649446	−	0.997889i
$973$	221881.			0.234366
$974$	11717.7	−	2088.09i	0.0123517	−	0.00220106i
$975$	−100615.	+	116620.i	−0.105841	+	0.122678i
$976$	1.35059e6	+	480499.i	1.41783	+	0.504421i
$977$	440254.	−	762542.i	0.461226	−	0.798867i	−0.537796	−	0.843075i	$-0.680743\pi$
$977$	440254.	−	762542.i	0.461226	−	0.798867i	0.999022	+	0.0442080i	$0.0140764\pi$
$978$	126257.	−	212790.i	0.132001	−	0.222471i
$979$	52559.6	−	30345.3i	0.0548386	−	0.0316611i
$980$	−613101.	−	510672.i	−0.638381	−	0.531728i
$981$	205663.	+	1.38817e6i	0.213707	+	1.44246i
$982$	368508.	−	1.01821e6i	0.382141	−	1.05588i
$983$	1.55074e6	−	895318.i	1.60484	−	0.926553i	0.614336	−	0.789044i	$-0.289424\pi$
$983$	1.55074e6	−	895318.i	1.60484	−	0.926553i	0.990501	−	0.137509i	$-0.0439095\pi$
$984$	−394973.	+	462874.i	−0.407922	+	0.478049i
$985$	−309695.	+	536407.i	−0.319199	+	0.552869i
$986$	−1.22374e6	+	1.03063e6i	−1.25873	+	1.06010i
$987$	85717.7	+	245959.i	0.0879906	+	0.252481i
$988$	266928.	+	46068.1i	0.273451	+	0.0471940i
$989$	−3.20275e6			−3.27439
$990$	−319657.	−	953622.i	−0.326148	−	0.972985i
$991$		−	1.12180e6i		−	1.14227i	−0.820858	−	0.571133i	$-0.806504\pi$
$991$		−	1.12180e6i		−	1.14227i	0.820858	−	0.571133i	$-0.193496\pi$
$992$	−118303.	−	316080.i	−0.120219	−	0.321198i
$993$	−194846.	+	1.02275e6i	−0.197603	+	1.03722i
$994$	347900.	−	293001.i	0.352113	−	0.296549i
$995$	625885.	+	361355.i	0.632191	+	0.364996i
$996$	−71359.4	−	430038.i	−0.0719337	−	0.433499i
$997$	−420584.	−	728473.i	−0.423119	−	0.732864i	0.573124	−	0.819469i	$-0.305731\pi$
$997$	−420584.	−	728473.i	−0.423119	−	0.732864i	−0.996243	+	0.0866051i	$0.972398\pi$
$998$	−355769.	+	983016.i	−0.357197	+	0.986960i
$999$	−129282.	−	81915.0i	−0.129541	−	0.0820791i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.5.f.a.31.10	yes	44
3.2	odd	2		108.5.f.a.91.13		44
4.3	odd	2	inner	36.5.f.a.31.5	yes	44
9.2	odd	6		108.5.f.a.19.18		44
9.4	even	3		324.5.d.f.163.20		22
9.5	odd	6		324.5.d.e.163.3		22
9.7	even	3	inner	36.5.f.a.7.5	✓	44
12.11	even	2		108.5.f.a.91.18		44
36.7	odd	6	inner	36.5.f.a.7.10	yes	44
36.11	even	6		108.5.f.a.19.13		44
36.23	even	6		324.5.d.e.163.4		22
36.31	odd	6		324.5.d.f.163.19		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.5.f.a.7.5	✓	44	9.7	even	3	inner
36.5.f.a.7.10	yes	44	36.7	odd	6	inner
36.5.f.a.31.5	yes	44	4.3	odd	2	inner
36.5.f.a.31.10	yes	44	1.1	even	1	trivial
108.5.f.a.19.13		44	36.11	even	6
108.5.f.a.19.18		44	9.2	odd	6
108.5.f.a.91.13		44	3.2	odd	2
108.5.f.a.91.18		44	12.11	even	2
324.5.d.e.163.3		22	9.5	odd	6
324.5.d.e.163.4		22	36.23	even	6
324.5.d.f.163.19		22	36.31	odd	6
324.5.d.f.163.20		22	9.4	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.701741 - 3.93796i) q^{2} +(5.87916 - 6.81436i) q^{3} +(-15.0151 + 5.52686i) q^{4} +(14.3046 - 24.7763i) q^{5} +(-30.9603 - 18.3700i) q^{6} +(-22.2124 + 12.8243i) q^{7} +(32.3013 + 55.2506i) q^{8} +(-11.8710 - 80.1254i) q^{9} +O(q^{10})\)	\(q+(-0.701741 - 3.93796i) q^{2} +(5.87916 - 6.81436i) q^{3} +(-15.0151 + 5.52686i) q^{4} +(14.3046 - 24.7763i) q^{5} +(-30.9603 - 18.3700i) q^{6} +(-22.2124 + 12.8243i) q^{7} +(32.3013 + 55.2506i) q^{8} +(-11.8710 - 80.1254i) q^{9} +(-107.606 - 38.9445i) q^{10} +(-93.9677 + 54.2523i) q^{11} +(-50.6143 + 134.812i) q^{12} +(44.2246 - 76.5993i) q^{13} +(66.0891 + 78.4722i) q^{14} +(-84.7356 - 243.141i) q^{15} +(194.908 - 165.973i) q^{16} +504.169 q^{17} +(-307.201 + 102.975i) q^{18} -191.405i q^{19} +(-77.8502 + 451.079i) q^{20} +(-43.2006 + 226.760i) q^{21} +(279.585 + 331.970i) q^{22} +(831.897 + 480.296i) q^{23} +(566.402 + 104.714i) q^{24} +(-96.7443 - 167.566i) q^{25} +(-332.680 - 120.402i) q^{26} +(-615.794 - 390.177i) q^{27} +(262.643 - 315.324i) q^{28} +(-396.671 - 687.053i) q^{29} +(-898.017 + 504.308i) q^{30} +(285.428 + 164.792i) q^{31} +(-790.370 - 651.069i) q^{32} +(-182.757 + 959.288i) q^{33} +(-353.796 - 1985.40i) q^{34} +733.789i q^{35} +(621.086 + 1137.48i) q^{36} +209.943 q^{37} +(-753.745 + 134.317i) q^{38} +(-261.971 - 751.702i) q^{39} +(1830.96 - 9.96965i) q^{40} +(-528.200 + 914.869i) q^{41} +(923.286 + 10.9960i) q^{42} +(-2887.45 + 1667.07i) q^{43} +(1111.09 - 1333.95i) q^{44} +(-2155.02 - 852.045i) q^{45} +(1307.61 - 3613.02i) q^{46} +(977.185 - 564.178i) q^{47} +(14.8932 - 2303.95i) q^{48} +(-871.573 + 1509.61i) q^{49} +(-591.979 + 498.563i) q^{50} +(2964.09 - 3435.59i) q^{51} +(-240.684 + 1394.57i) q^{52} +1138.62 q^{53} +(-1104.37 + 2698.78i) q^{54} +3104.23i q^{55} +(-1426.04 - 813.005i) q^{56} +(-1304.30 - 1125.30i) q^{57} +(-2427.23 + 2044.21i) q^{58} +(4037.49 + 2331.05i) q^{59} +(2616.12 + 3182.47i) q^{60} +(2799.84 + 4849.46i) q^{61} +(448.648 - 1239.65i) q^{62} +(1291.24 + 1627.54i) q^{63} +(-2009.25 + 3569.33i) q^{64} +(-1265.23 - 2191.45i) q^{65} +(3905.89 + 46.5177i) q^{66} +(-6127.74 - 3537.85i) q^{67} +(-7570.16 + 2786.47i) q^{68} +(8163.76 - 2845.11i) q^{69} +(2889.63 - 514.930i) q^{70} -4433.42i q^{71} +(4043.53 - 3244.03i) q^{72} -1953.21 q^{73} +(-147.326 - 826.748i) q^{74} +(-1710.63 - 325.897i) q^{75} +(1057.87 + 2873.97i) q^{76} +(1391.50 - 2410.15i) q^{77} +(-2776.34 + 1559.13i) q^{78} +(1523.90 - 879.826i) q^{79} +(-1324.12 - 7203.27i) q^{80} +(-6279.16 + 1902.33i) q^{81} +(3973.38 + 1438.03i) q^{82} +(-2621.64 + 1513.61i) q^{83} +(-604.606 - 3643.58i) q^{84} +(7211.95 - 12491.5i) q^{85} +(8591.12 + 10200.8i) q^{86} +(-7013.92 - 1336.24i) q^{87} +(-6032.75 - 3439.35i) q^{88} -559.336 q^{89} +(-1843.05 + 9084.32i) q^{90} +2268.61i q^{91} +(-15145.6 - 2613.92i) q^{92} +(2801.03 - 976.170i) q^{93} +(-2907.44 - 3452.21i) q^{94} +(-4742.31 - 2737.97i) q^{95} +(-9083.33 + 1558.13i) q^{96} +(1100.89 + 1906.79i) q^{97} +(6556.40 + 2372.87i) q^{98} +(5462.47 + 6885.17i) 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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