LMFDB - Embedded newform 36.5.f.a.7.10

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			7.10
Character	$\chi$	$=$	36.7
Dual form			36.5.f.a.31.10

$q$-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 $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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	0.996341	+	0.0854642i	$0.0272373\pi$
$5$	14.3046	+	24.7763i	0.572185	+	0.991053i	−0.424156	+	0.905589i	$0.639429\pi$
$6$	−30.9603	+	18.3700i	−0.860010	+	0.510278i
$7$	−22.2124	−	12.8243i	−0.453314	−	0.261721i	0.255915	−	0.966699i	$-0.417623\pi$
$7$	−22.2124	−	12.8243i	−0.453314	−	0.261721i	−0.709229	+	0.704978i	$0.750957\pi$
$8$	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	0.0586287	−	0.998280i	$-0.481327\pi$
$11$	−93.9677	−	54.2523i	−0.776593	−	0.448366i	−0.835221	+	0.549914i	$0.814661\pi$
$12$	−50.6143	−	134.812i	−0.351488	−	0.936192i
$13$	44.2246	+	76.5993i	0.261684	+	0.453250i	0.966690	−	0.255952i	$-0.0823888\pi$
$13$	44.2246	+	76.5993i	0.261684	+	0.453250i	−0.705005	+	0.709202i	$0.749055\pi$
$14$	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	$0.0854062\pi$
$19$			191.405i			0.530207i	−0.964220	+	0.265104i	$0.914594\pi$
$20$	−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	0.576733	−	0.816933i	$-0.304327\pi$
$23$	831.897	−	480.296i	1.57258	−	0.907932i	0.995851	−	0.0909988i	$-0.0290059\pi$
$24$	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	−0.999475	−	0.0324147i	$-0.989680\pi$
$29$	−396.671	+	687.053i	−0.471665	+	0.816948i	0.527809	+	0.849363i	$0.323014\pi$
$30$	−898.017	−	504.308i	−0.997797	−	0.560342i
$31$	285.428	−	164.792i	0.297011	−	0.171480i	−0.344088	−	0.938937i	$-0.611812\pi$
$31$	285.428	−	164.792i	0.297011	−	0.171480i	0.641099	+	0.767458i	$0.278479\pi$
$32$	−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	0.665053	−	0.746796i	$-0.268409\pi$
$41$	−528.200	−	914.869i	−0.314218	−	0.544241i	−0.979271	+	0.202555i	$0.935076\pi$
$42$	923.286	−	10.9960i	0.523405	−	0.00623356i
$43$	−2887.45	−	1667.07i	−1.56163	−	0.901608i	−0.997093	−	0.0762001i	$-0.975721\pi$
$43$	−2887.45	−	1667.07i	−1.56163	−	0.901608i	−0.564537	−	0.825407i	$-0.690945\pi$
$44$	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	0.704600	−	0.709604i	$-0.251126\pi$
$47$	977.185	+	564.178i	0.442365	+	0.255400i	−0.262235	+	0.965004i	$0.584460\pi$
$48$	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	0.208593	−	0.978002i	$-0.433111\pi$
$59$	4037.49	−	2331.05i	1.15987	−	0.669648i	0.951272	+	0.308354i	$0.0997781\pi$
$60$	2616.12	−	3182.47i	0.726700	−	0.884018i
$61$	2799.84	−	4849.46i	0.752442	−	1.30327i	−0.194193	−	0.980963i	$-0.562209\pi$
$61$	2799.84	−	4849.46i	0.752442	−	1.30327i	0.946636	−	0.322305i	$-0.104458\pi$
$62$	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	−0.990292	−	0.139004i	$-0.955610\pi$
$67$	−6127.74	+	3537.85i	−1.36506	+	0.788116i	−0.374764	+	0.927120i	$0.622276\pi$
$68$	−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	$0.144928\pi$
$71$			4433.42i			0.879472i	−0.898127	+	0.439736i	$0.855072\pi$
$72$	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	0.617095	−	0.786889i	$-0.288310\pi$
$79$	1523.90	+	879.826i	0.244176	+	0.140975i	−0.372918	+	0.927864i	$0.621643\pi$
$80$	−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	0.297505	−	0.954720i	$-0.403846\pi$
$83$	−2621.64	−	1513.61i	−0.380555	−	0.219714i	−0.678060	+	0.735007i	$0.737179\pi$
$84$	−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	−0.801575	−	0.597894i	$-0.796004\pi$
$97$	1100.89	−	1906.79i	0.117004	−	0.202656i	0.918579	+	0.395238i	$0.129338\pi$
$98$	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	−0.847537	−	0.530737i	$-0.821915\pi$
$101$	365.841	−	633.655i	0.0358632	−	0.0621170i	0.883400	+	0.468620i	$0.155249\pi$
$102$	−15609.2	+	9261.59i	−1.50031	+	0.890195i
$103$	8533.78	−	4926.98i	0.804391	−	0.464415i	−0.0406134	−	0.999175i	$-0.512931\pi$
$103$	8533.78	−	4926.98i	0.804391	−	0.464415i	0.845004	+	0.534760i	$0.179598\pi$
$104$	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	$0.0111878\pi$
$107$			804.642i			0.0702806i	−0.999382	+	0.0351403i	$0.988812\pi$
$108$	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	−0.977489	−	0.210988i	$-0.932332\pi$
$113$	−8573.94	−	14850.5i	−0.671465	−	1.16301i	0.306024	−	0.952024i	$-0.401001\pi$
$114$	−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	$0.0960986\pi$
$127$			9591.51i			0.594675i	−0.954772	+	0.297337i	$0.903901\pi$
$128$	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	−0.610202	−	0.792246i	$-0.708912\pi$
$131$	−3933.27	+	2270.88i	−0.229198	+	0.132328i	0.381004	+	0.924573i	$0.375578\pi$
$132$	−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	−0.793321	−	0.608803i	$-0.791650\pi$
$137$	2450.82	−	4244.95i	0.130578	−	0.226168i	0.923900	+	0.382635i	$0.124983\pi$
$138$	−16932.8	+	30152.1i	−0.889140	+	1.58328i
$139$	−7491.80	+	4325.39i	−0.387754	+	0.223870i	−0.681187	−	0.732110i	$-0.738536\pi$
$139$	−7491.80	+	4325.39i	−0.387754	+	0.223870i	0.293432	+	0.955980i	$0.405202\pi$
$140$	−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	0.972818	−	0.231570i	$-0.0743863\pi$
$149$	6346.46	+	10992.4i	0.285863	+	0.495130i	−0.686955	+	0.726700i	$0.741053\pi$
$150$	−82.9518	−	6965.09i	−0.00368674	−	0.309560i
$151$	11055.3	+	6382.78i	0.484860	+	0.279934i	0.722440	−	0.691434i	$-0.243021\pi$
$151$	11055.3	+	6382.78i	0.484860	+	0.279934i	−0.237579	+	0.971368i	$0.576354\pi$
$152$	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	0.903534	+	0.428516i	$0.140963\pi$
$157$	20283.0	+	35131.2i	0.822873	+	1.42526i	−0.0806612	+	0.996742i	$0.525703\pi$
$158$	−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	$-0.958713\pi$
$163$		−	6872.98i		−	0.258684i	0.991600	−	0.129342i	$-0.0412865\pi$
$164$	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	−0.933639	−	0.358216i	$-0.883385\pi$
$167$	−30405.5	+	17554.6i	−1.09023	+	0.629447i	−0.156595	+	0.987663i	$0.550052\pi$
$168$	−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	−0.889870	−	0.456214i	$-0.849205\pi$
$173$	−1491.72	+	2583.74i	−0.0498420	+	0.0863290i	0.840028	+	0.542543i	$0.182538\pi$
$174$	−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	$0.249203\pi$
$179$			45199.3i			1.41067i	−0.708874	+	0.705335i	$0.750797\pi$
$180$	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	0.706492	−	0.707721i	$-0.250277\pi$
$191$	16300.9	+	9411.33i	0.446833	+	0.257979i	−0.259659	+	0.965700i	$0.583610\pi$
$192$	12510.0	−	34676.4i	0.339356	−	0.940658i
$193$	−4727.11	−	8187.59i	−0.126906	−	0.219807i	0.795571	−	0.605861i	$-0.207171\pi$
$193$	−4727.11	−	8187.59i	−0.126906	−	0.219807i	−0.922476	+	0.386054i	$0.873838\pi$
$194$	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	$-0.896670\pi$
$199$		−	25261.4i		−	0.637898i	0.947772	−	0.318949i	$-0.103330\pi$
$200$	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	−0.694839	−	0.719165i	$-0.744524\pi$
$211$	−18674.0	+	10781.5i	−0.419443	+	0.242166i	0.275396	+	0.961331i	$0.411191\pi$
$212$	−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	0.322496	−	0.946571i	$-0.395478\pi$
$223$	−16709.5	−	9647.22i	−0.336011	−	0.193996i	−0.658507	+	0.752575i	$0.728812\pi$
$224$	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	0.933462	−	0.358677i	$-0.116772\pi$
$227$	56144.4	+	32415.0i	1.08957	+	0.629063i	0.156107	+	0.987740i	$0.450105\pi$
$228$	25803.6	−	9687.81i	0.496376	−	0.186361i
$229$	−19575.4	−	33905.7i	−0.373285	−	0.646549i	0.616784	−	0.787133i	$-0.288435\pi$
$229$	−19575.4	−	33905.7i	−0.373285	−	0.646549i	−0.990069	+	0.140584i	$0.955102\pi$
$230$	−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	0.205230	−	0.978714i	$-0.434206\pi$
$239$	65999.7	−	38104.9i	1.15544	−	0.667091i	0.950206	+	0.311623i	$0.100872\pi$
$240$	−56870.4	+	33326.2i	−0.987334	+	0.578579i
$241$	−8157.12	+	14128.5i	−0.140444	+	0.243256i	−0.927664	−	0.373416i	$-0.878186\pi$
$241$	−8157.12	+	14128.5i	−0.140444	+	0.243256i	0.787220	+	0.616672i	$0.211520\pi$
$242$	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	$-0.913467\pi$
$251$		−	33833.6i		−	0.537033i	0.963275	−	0.268517i	$-0.0865334\pi$
$252$	−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	0.997347	−	0.0727940i	$-0.0231916\pi$
$257$	28773.1	+	49836.4i	0.435632	+	0.754537i	−0.561715	+	0.827331i	$0.689858\pi$
$258$	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	−0.0800895	−	0.996788i	$-0.525521\pi$
$263$	−68019.2	−	39270.9i	−0.983378	−	0.567753i	−0.903288	+	0.429034i	$0.858854\pi$
$264$	−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	$-0.736688\pi$
$271$		−	108113.i		−	1.47211i	0.676924	−	0.736053i	$-0.263312\pi$
$272$	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	−0.686588	−	0.727047i	$-0.740892\pi$
$277$	21971.1	−	38055.1i	0.286347	−	0.495968i	0.972935	+	0.231079i	$0.0742255\pi$
$278$	−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	−0.980927	−	0.194375i	$-0.937732\pi$
$281$	−25435.7	+	44055.9i	−0.322130	+	0.557945i	0.658798	+	0.752320i	$0.271065\pi$
$282$	−40617.9	+	483.745i	−0.510763	+	0.00608300i
$283$	−22858.8	+	13197.5i	−0.285418	+	0.164786i	−0.635873	−	0.771793i	$-0.719360\pi$
$283$	−22858.8	+	13197.5i	−0.285418	+	0.164786i	0.350456	+	0.936579i	$0.386027\pi$
$284$	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	−0.941949	−	0.335757i	$-0.891008\pi$
$293$	−65395.3	−	113268.i	−0.761748	−	1.31939i	0.180201	−	0.983630i	$-0.442325\pi$
$294$	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	$0.0928843\pi$
$307$			54227.3i			0.575362i	−0.957726	+	0.287681i	$0.907116\pi$
$308$	−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	−0.964354	−	0.264616i	$-0.914755\pi$
$311$	−117745.	+	67980.1i	−1.21737	+	0.702847i	−0.253013	+	0.967463i	$0.581422\pi$
$312$	33069.9	+	38755.0i	0.339722	+	0.398125i
$313$	−82194.2	+	142364.i	−0.838981	+	1.45316i	0.0517658	+	0.998659i	$0.483515\pi$
$313$	−82194.2	+	142364.i	−0.838981	+	1.45316i	−0.890747	+	0.454499i	$0.849818\pi$
$314$	−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	0.392637	+	0.919694i	$0.371563\pi$
$317$	−60309.5	+	104459.i	−0.600160	+	1.03951i	−0.992796	+	0.119814i	$0.961770\pi$
$318$	−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	−0.0325639	−	0.999470i	$-0.510367\pi$
$331$	−100184.	−	57841.2i	−0.914412	−	0.527936i	−0.881848	+	0.471534i	$0.843701\pi$
$332$	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	−0.900746	−	0.434347i	$-0.856979\pi$
$337$	−93868.0	−	162584.i	−0.826528	−	1.43159i	0.0742175	−	0.997242i	$-0.476354\pi$
$338$	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	0.0726566	−	0.997357i	$-0.476852\pi$
$347$	117124.	−	67621.8i	0.972721	−	0.561601i	0.900065	+	0.435756i	$0.143519\pi$
$348$	112700.	+	18701.1i	0.930605	+	0.154422i
$349$	−1651.44	+	2860.38i	−0.0135585	+	0.0234841i	−0.872725	−	0.488212i	$-0.837649\pi$
$349$	−1651.44	+	2860.38i	−0.0135585	+	0.0234841i	0.859167	+	0.511696i	$0.170983\pi$
$350$	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	−0.938933	−	0.344100i	$-0.888184\pi$
$353$	−21366.4	+	37007.7i	−0.171467	+	0.296990i	0.767466	+	0.641090i	$0.221517\pi$
$354$	−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	$0.238928\pi$
$359$			175816.i			1.36418i	−0.731270	+	0.682088i	$0.761072\pi$
$360$	−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	0.474290	−	0.880369i	$-0.342705\pi$
$367$	−6867.31	−	3964.84i	−0.0509864	−	0.0294370i	−0.525277	+	0.850932i	$0.676038\pi$
$368$	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	−0.844001	−	0.536342i	$-0.819806\pi$
$373$	−123336.	−	213624.i	−0.886486	−	1.53544i	−0.0424851	−	0.999097i	$-0.513527\pi$
$374$	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	$0.171526\pi$
$379$			147423.i			1.02633i	−0.858291	+	0.513163i	$0.828474\pi$
$380$	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	−0.815636	−	0.578565i	$-0.803613\pi$
$383$	−105968.	+	61180.9i	−0.722402	+	0.417079i	0.0932341	+	0.995644i	$0.470280\pi$
$384$	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	−0.385682	−	0.922632i	$-0.626034\pi$
$389$	91728.1	−	158878.i	0.606182	−	1.04994i	0.991863	−	0.127306i	$-0.0406330\pi$
$390$	−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	−0.988440	−	0.151610i	$-0.951554\pi$
$401$	−100584.	−	174217.i	−0.625518	−	1.08343i	0.362922	−	0.931820i	$-0.381779\pi$
$402$	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	0.995976	−	0.0896241i	$-0.0285666\pi$
$409$	70320.1	+	121798.i	0.420371	+	0.728104i	−0.575605	+	0.817728i	$0.695233\pi$
$410$	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	−0.828633	−	0.559793i	$-0.810881\pi$
$419$	−133102.	+	76846.6i	−0.758154	+	0.437720i	0.0704785	+	0.997513i	$0.477547\pi$
$420$	−98923.3	+	37140.2i	−0.560790	+	0.210545i
$421$	−77206.0	+	133725.i	−0.435599	+	0.754479i	−0.997344	−	0.0728309i	$-0.976797\pi$
$421$	−77206.0	+	133725.i	−0.435599	+	0.754479i	0.561746	+	0.827310i	$0.310130\pi$
$422$	−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	$-0.827547\pi$
$431$		−	191579.i		−	1.03132i	0.856793	−	0.515660i	$-0.172453\pi$
$432$	−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	0.537366	−	0.843349i	$-0.319420\pi$
$439$	14586.4	+	8421.44i	0.0756864	+	0.0436976i	−0.461679	+	0.887047i	$0.652753\pi$
$440$	−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	0.812519	−	0.582934i	$-0.198095\pi$
$443$	140111.	+	80892.9i	0.713943	+	0.412195i	−0.0985761	+	0.995130i	$0.531429\pi$
$444$	−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	−0.842582	−	0.538569i	$-0.818965\pi$
$457$	9423.93	−	16322.7i	0.0451232	−	0.0781556i	0.887705	+	0.460413i	$0.152299\pi$
$458$	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	−0.788716	−	0.614758i	$-0.789254\pi$
$461$	29335.9	−	50811.3i	0.138038	−	0.239088i	0.926754	+	0.375669i	$0.122587\pi$
$462$	−87355.7	−	49057.1i	−0.409267	−	0.229836i
$463$	−41167.7	+	23768.2i	−0.192041	+	0.110875i	−0.592938	−	0.805248i	$-0.702032\pi$
$463$	−41167.7	+	23768.2i	−0.192041	+	0.110875i	0.400897	+	0.916123i	$0.368699\pi$
$464$	−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	$-0.887720\pi$
$467$		−	150686.i		−	0.690936i	0.938431	−	0.345468i	$-0.112280\pi$
$468$	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	0.392133	−	0.919908i	$-0.371737\pi$
$479$	−47830.3	−	27614.8i	−0.208464	−	0.120357i	−0.600598	+	0.799551i	$0.705071\pi$
$480$	−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	$-0.998003\pi$
$487$		−	2975.59i		−	0.0125463i	0.999980	−	0.00627313i	$-0.00199681\pi$
$488$	−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	0.0724794	−	0.997370i	$-0.476909\pi$
$491$	234443.	−	135356.i	0.972467	−	0.561454i	0.899987	+	0.435916i	$0.143576\pi$
$492$	−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	−0.880105	−	0.474778i	$-0.842528\pi$
$499$	−226339.	+	130677.i	−0.908988	+	0.524805i	−0.0288827	+	0.999583i	$0.509195\pi$
$500$	−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	$-0.811076\pi$
$503$		−	283008.i		−	1.11857i	0.828976	−	0.559284i	$-0.188924\pi$
$504$	−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	0.995149	−	0.0983769i	$-0.0313651\pi$
$509$	106839.	+	185051.i	0.412378	+	0.714259i	−0.582772	+	0.812636i	$0.698032\pi$
$510$	−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	$-0.860857\pi$
$523$		−	231592.i		−	0.846681i	0.905971	−	0.423340i	$-0.139143\pi$
$524$	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	−0.485039	−	0.874493i	$-0.661195\pi$
$547$	−444293.	−	256513.i	−1.48489	−	0.857302i	−0.999852	+	0.0171904i	$0.994528\pi$
$548$	−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	−0.574460	−	0.818533i	$-0.694788\pi$
$563$	−48439.2	+	27966.4i	−0.152820	+	0.0882307i	0.421640	+	0.906763i	$0.361455\pi$
$564$	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	0.326111	+	0.945331i	$0.394262\pi$
$569$	−212266.	+	367655.i	−0.655625	+	1.13558i	−0.981737	+	0.190245i	$0.939072\pi$
$570$	96526.9	−	171885.i	0.297097	−	0.529039i
$571$	−25297.4	+	14605.5i	−0.0775897	+	0.0447964i	−0.538293	−	0.842758i	$-0.680931\pi$
$571$	−25297.4	+	14605.5i	−0.0775897	+	0.0447964i	0.460703	+	0.887554i	$0.347597\pi$
$572$	−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	0.770712	−	0.637183i	$-0.219901\pi$
$587$	208206.	+	120208.i	0.604251	+	0.348865i	−0.166461	+	0.986048i	$0.553234\pi$
$588$	−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	−0.512033	−	0.858966i	$-0.671108\pi$
$599$	−8669.92	+	5005.58i	−0.0241636	+	0.0139509i	0.487870	+	0.872917i	$0.337774\pi$
$600$	−37249.6	+	105040.i	−0.103471	+	0.291778i
$601$	−196449.	+	340259.i	−0.543876	+	0.942021i	0.454800	+	0.890593i	$0.349711\pi$
$601$	−196449.	+	340259.i	−0.543876	+	0.942021i	−0.998677	+	0.0514280i	$0.983623\pi$
$602$	−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	−0.913796	−	0.406174i	$-0.866863\pi$
$607$	−375426.	+	216752.i	−1.01894	+	0.588283i	−0.105141	+	0.994457i	$0.533529\pi$
$608$	−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	0.707407	−	0.706806i	$-0.249865\pi$
$617$	−98373.3	−	170388.i	−0.258409	−	0.447577i	−0.965816	+	0.259229i	$0.916531\pi$
$618$	−173700.	+	309307.i	−0.454803	+	0.809864i
$619$	536199.	+	309575.i	1.39941	+	0.807949i	0.994331	−	0.106333i	$-0.0339110\pi$
$619$	536199.	+	309575.i	1.39941	+	0.807949i	0.405078	+	0.914282i	$0.367244\pi$
$620$	−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	$0.126744\pi$
$631$			308766.i			0.775479i	−0.921769	+	0.387740i	$0.873256\pi$
$632$	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	−0.578935	−	0.815373i	$-0.696532\pi$
$641$	171200.	−	296528.i	0.416666	−	0.721687i	0.995602	+	0.0936860i	$0.0298650\pi$
$642$	−14781.3	−	24912.0i	−0.0358626	−	0.0604419i
$643$	478867.	−	276474.i	1.15823	−	0.668702i	0.207347	−	0.978267i	$-0.433517\pi$
$643$	478867.	−	276474.i	1.15823	−	0.668702i	0.950878	+	0.309566i	$0.100184\pi$
$644$	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	$-0.758065\pi$
$647$		−	576814.i		−	1.37793i	0.724794	−	0.688965i	$-0.241935\pi$
$648$	−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	0.977169	+	0.212463i	$0.0681484\pi$
$653$	286795.	+	496744.i	0.672583	+	1.16495i	−0.304586	+	0.952485i	$0.598518\pi$
$654$	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	0.803305	−	0.595568i	$-0.203073\pi$
$659$	299298.	+	172800.i	0.689180	+	0.397899i	−0.114125	+	0.993466i	$0.536406\pi$
$660$	−418487.	+	157118.i	−0.960714	+	0.360694i
$661$	187583.	+	324904.i	0.429330	+	0.743622i	0.996814	−	0.0797628i	$-0.0254163\pi$
$661$	187583.	+	324904.i	0.429330	+	0.743622i	−0.567484	+	0.823385i	$0.692083\pi$
$662$	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	−0.353503	−	0.935433i	$-0.615010\pi$
$673$	286866.	−	496866.i	0.633358	−	1.09701i	0.986861	−	0.161574i	$-0.0516571\pi$
$674$	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	−0.850590	−	0.525829i	$-0.823755\pi$
$677$	13789.2	−	23883.6i	0.0300859	−	0.0521103i	0.880676	+	0.473719i	$0.157089\pi$
$678$	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	$0.000354244\pi$
$683$			1038.30i			0.00222578i	−0.999999	+	0.00111289i	$0.999646\pi$
$684$	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	0.771390	−	0.636363i	$-0.219562\pi$
$691$	289343.	+	167052.i	0.605978	+	0.349862i	−0.165411	+	0.986225i	$0.552895\pi$
$692$	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	0.239456	+	0.970907i	$0.423031\pi$
$709$	−362484.	+	627841.i	−0.721102	+	1.24899i	−0.960558	+	0.278079i	$0.910302\pi$
$710$	−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	$0.173634\pi$
$719$			536436.i			1.03767i	−0.854874	+	0.518836i	$0.826366\pi$
$720$	−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	0.811452	−	0.584418i	$-0.198677\pi$
$727$	375814.	+	216977.i	0.711057	+	0.410529i	−0.100395	+	0.994948i	$0.532011\pi$
$728$	−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	0.958456	+	0.285241i	$0.0920735\pi$
$733$	390208.	+	675860.i	0.726254	+	1.25791i	−0.232202	+	0.972667i	$0.574593\pi$
$734$	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	$-0.936889\pi$
$739$		−	215142.i		−	0.393947i	0.980409	−	0.196973i	$-0.0631112\pi$
$740$	−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	−0.255801	−	0.966730i	$-0.582339\pi$
$743$	250360.	−	144546.i	0.453511	−	0.261835i	0.709312	+	0.704895i	$0.249006\pi$
$744$	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	0.128521	−	0.991707i	$-0.458977\pi$
$751$	593117.	−	342436.i	1.05162	−	0.607156i	0.923104	+	0.384551i	$0.125644\pi$
$752$	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	−0.980074	−	0.198631i	$-0.936350\pi$
$761$	−383411.	−	664087.i	−0.662057	−	1.14672i	0.318018	−	0.948085i	$-0.396983\pi$
$762$	−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	0.999936	−	0.0113137i	$-0.00360135\pi$
$769$	289867.	+	502065.i	0.490170	+	0.848999i	−0.509766	+	0.860313i	$0.670268\pi$
$770$	−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	−0.999436	−	0.0335849i	$-0.989308\pi$
$787$	−910515.	+	525686.i	−1.47007	+	0.848744i	−0.470633	+	0.882329i	$0.655974\pi$
$788$	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	0.900928	−	0.433969i	$-0.142887\pi$
$797$	47409.2	+	82115.1i	0.0746356	+	0.129273i	−0.826292	+	0.563242i	$0.809554\pi$
$798$	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	$-0.855406\pi$
$811$		−	577209.i		−	0.877589i	0.898587	−	0.438794i	$-0.144594\pi$
$812$	−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	−0.452706	−	0.891660i	$-0.649541\pi$
$821$	367923.	−	637262.i	0.545847	−	0.945435i	0.998553	−	0.0537749i	$-0.0171253\pi$
$822$	2101.42	+	176447.i	0.00311006	+	0.261138i
$823$	−148172.	+	85547.4i	−0.218760	+	0.126301i	−0.605376	−	0.795940i	$-0.706977\pi$
$823$	−148172.	+	85547.4i	−0.218760	+	0.126301i	0.386616	+	0.922241i	$0.373644\pi$
$824$	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	$-0.725467\pi$
$827$		−	1.03882e6i		−	1.51890i	0.650563	−	0.759452i	$-0.274533\pi$
$828$	−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	0.804591	−	0.593830i	$-0.202385\pi$
$839$	487546.	+	281485.i	0.692615	+	0.399881i	−0.111976	+	0.993711i	$0.535718\pi$
$840$	−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	−0.543243	−	0.839575i	$-0.682804\pi$
$853$	331406.	−	574011.i	0.455472	−	0.788901i	0.998715	+	0.0506745i	$0.0161371\pi$
$854$	−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	0.165294	+	0.986244i	$0.447143\pi$
$857$	−566602.	+	981383.i	−0.771465	+	1.33622i	−0.936760	+	0.349973i	$0.886191\pi$
$858$	176300.	+	297131.i	0.239484	+	0.403621i
$859$	347489.	−	200623.i	0.470928	−	0.271890i	−0.245700	−	0.969346i	$-0.579018\pi$
$859$	347489.	−	200623.i	0.470928	−	0.271890i	0.716628	+	0.697456i	$0.245685\pi$
$860$	−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	$0.307161\pi$
$863$			1.22445e6i			1.64407i	−0.569437	+	0.822035i	$0.692839\pi$
$864$	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	0.819977	−	0.572397i	$-0.193986\pi$
$877$	−65931.0	−	114196.i	−0.0857216	−	0.148474i	−0.905698	+	0.423922i	$0.860653\pi$
$878$	−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	$-0.952144\pi$
$883$		−	233561.i		−	0.299557i	0.988720	−	0.149778i	$-0.0478560\pi$
$884$	−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	−0.104519	−	0.994523i	$-0.533330\pi$
$887$	554282.	−	320015.i	0.704504	−	0.406746i	0.809023	+	0.587777i	$0.199997\pi$
$888$	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	0.251454	−	0.967869i	$-0.419091\pi$
$907$	−379256.	−	218964.i	−0.461018	−	0.266169i	−0.712472	+	0.701700i	$0.752425\pi$
$908$	−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	0.844377	−	0.535749i	$-0.179971\pi$
$911$	666090.	+	384567.i	0.802594	+	0.463378i	−0.0417834	+	0.999127i	$0.513304\pi$
$912$	−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	$-0.696021\pi$
$919$		−	1.37883e6i		−	1.63260i	0.577626	−	0.816301i	$-0.303979\pi$
$920$	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	−0.780181	−	0.625554i	$-0.784873\pi$
$929$	130885.	−	226699.i	0.151656	−	0.262675i	0.931836	+	0.362879i	$0.118206\pi$
$930$	−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	0.960275	−	0.279054i	$-0.0900209\pi$
$941$	211160.	+	365741.i	0.238470	+	0.413042i	−0.721806	+	0.692096i	$0.756688\pi$
$942$	−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	−0.0514525	−	0.998675i	$-0.516385\pi$
$947$	−844845.	−	487772.i	−0.942057	−	0.543897i	−0.890605	+	0.454779i	$0.849718\pi$
$948$	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	−0.995160	−	0.0982670i	$-0.968670\pi$
$967$	−1.31627e6	+	759947.i	−1.40764	+	0.812700i	−0.412478	+	0.910967i	$0.635337\pi$
$968$	−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	$-0.895697\pi$
$971$		−	606895.i		−	0.643687i	0.946793	−	0.321844i	$-0.104303\pi$
$972$	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	0.999022	−	0.0442080i	$-0.0140764\pi$
$977$	440254.	+	762542.i	0.461226	+	0.798867i	−0.537796	+	0.843075i	$0.680743\pi$
$978$	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	0.990501	+	0.137509i	$0.0439095\pi$
$983$	1.55074e6	+	895318.i	1.60484	+	0.926553i	0.614336	+	0.789044i	$0.289424\pi$
$984$	−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	$0.193496\pi$
$991$			1.12180e6i			1.14227i	−0.820858	+	0.571133i	$0.806504\pi$
$992$	−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	−0.996243	−	0.0866051i	$-0.972398\pi$
$997$	−420584.	+	728473.i	−0.423119	+	0.732864i	0.573124	+	0.819469i	$0.305731\pi$
$998$	−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.7.10	yes	44
3.2	odd	2		108.5.f.a.19.13		44
4.3	odd	2	inner	36.5.f.a.7.5	✓	44
9.2	odd	6		324.5.d.e.163.4		22
9.4	even	3	inner	36.5.f.a.31.5	yes	44
9.5	odd	6		108.5.f.a.91.18		44
9.7	even	3		324.5.d.f.163.19		22
12.11	even	2		108.5.f.a.19.18		44
36.7	odd	6		324.5.d.f.163.20		22
36.11	even	6		324.5.d.e.163.3		22
36.23	even	6		108.5.f.a.91.13		44
36.31	odd	6	inner	36.5.f.a.31.10	yes	44

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

\(f(q)\)	\(=\)	\(q+(-0.701741 + 3.93796i) q^{2} +(5.87916 + 6.81436i) q^{3} +(-15.0151 - 5.52686i) q^{4} +(14.3046 + 24.7763i) q^{5} +(-30.9603 + 18.3700i) q^{6} +(-22.2124 - 12.8243i) q^{7} +(32.3013 - 55.2506i) q^{8} +(-11.8710 + 80.1254i) q^{9} +O(q^{10})\)	\(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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