LMFDB - Embedded newform 36.5.f.a.31.5

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			31.5
Character	$\chi$	$=$	36.31
Dual form			36.5.f.a.7.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.05951 - 2.57671i) q^{2} +(-5.87916 + 6.81436i) q^{3} +(2.72116 + 15.7669i) q^{4} +(14.3046 - 24.7763i) q^{5} +(35.5459 - 5.69969i) q^{6} +(22.2124 - 12.8243i) q^{7} +(32.3013 - 55.2506i) q^{8} +(-11.8710 - 80.1254i) q^{9} +O(q^{10})$	\(q+(-3.05951 - 2.57671i) q^{2} +(-5.87916 + 6.81436i) q^{3} +(2.72116 + 15.7669i) q^{4} +(14.3046 - 24.7763i) q^{5} +(35.5459 - 5.69969i) 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} +(-123.439 - 74.1532i) q^{12} +(44.2246 - 76.5993i) q^{13} +(-101.004 - 17.9987i) q^{14} +(84.7356 + 243.141i) q^{15} +(-241.191 + 85.8084i) q^{16} +504.169 q^{17} +(-170.140 + 275.732i) q^{18} +191.405i q^{19} +(429.571 + 158.119i) q^{20} +(-43.2006 + 226.760i) q^{21} +(-427.287 - 76.1421i) q^{22} +(-831.897 - 480.296i) q^{23} +(186.593 + 544.940i) 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} +(367.254 - 962.230i) q^{30} +(-285.428 - 164.792i) q^{31} +(959.027 + 358.946i) q^{32} +(-182.757 + 959.288i) q^{33} +(-1542.51 - 1299.10i) q^{34} -733.789i q^{35} +(1231.03 - 405.202i) q^{36} +209.943 q^{37} +(493.194 - 585.604i) q^{38} +(261.971 + 751.702i) q^{39} +(-906.848 - 1590.65i) q^{40} +(-528.200 + 914.869i) q^{41} +(716.466 - 582.457i) 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} +(833.269 - 2148.04i) q^{48} +(-871.573 + 1509.61i) q^{49} +(-135.779 + 761.951i) q^{50} +(-2964.09 + 3435.59i) q^{51} +(1328.08 + 488.847i) q^{52} +1138.62 q^{53} +(-878.655 - 2780.47i) q^{54} -3104.23i q^{55} +(8.93796 - 1641.49i) q^{56} +(-1304.30 - 1125.30i) q^{57} +(-556.720 + 3124.15i) q^{58} +(-4037.49 - 2331.05i) q^{59} +(-3603.00 + 1997.64i) 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} +(3030.95 - 2464.04i) q^{66} +(6127.74 + 3537.85i) q^{67} +(1371.92 + 7949.19i) q^{68} +(8163.76 - 2845.11i) q^{69} +(-1890.76 + 2245.03i) q^{70} +4433.42i q^{71} +(-4810.42 - 1932.28i) q^{72} -1953.21 q^{73} +(-642.322 - 540.962i) q^{74} +(1710.63 + 325.897i) q^{75} +(-3017.86 + 520.842i) q^{76} +(1391.50 - 2410.15i) q^{77} +(1135.41 - 2974.86i) 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} +(-3692.85 - 64.0924i) q^{84} +(7211.95 - 12491.5i) q^{85} +(-13129.7 - 2339.71i) q^{86} +(7013.92 + 1336.24i) q^{87} +(37.8113 - 6944.19i) q^{88} -559.336 q^{89} +(4397.84 + 8159.70i) q^{90} -2268.61i q^{91} +(5309.06 - 14423.4i) q^{92} +(2801.03 - 976.170i) q^{93} +(4443.42 + 791.814i) q^{94} +(4742.31 + 2737.97i) q^{95} +(-8084.26 + 4424.85i) 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 $

$2$	−3.05951	−	2.57671i	−0.764877	−	0.644177i
$2$	−3.05951	−	2.57671i	−0.764877	−	0.644177i
$3$	−5.87916	+	6.81436i	−0.653240	+	0.757151i
$3$	−5.87916	+	6.81436i	−0.653240	+	0.757151i
$4$	2.72116	+	15.7669i	0.170072	+	0.985432i
$5$	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	$-0.0272373\pi$
$6$	35.5459	−	5.69969i	0.987387	−	0.158325i
$7$	22.2124	−	12.8243i	0.453314	−	0.261721i	−0.255915	−	0.966699i	$-0.582377\pi$
$7$	22.2124	−	12.8243i	0.453314	−	0.261721i	0.709229	+	0.704978i	$0.249043\pi$
$8$	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	$-0.518673\pi$
$11$	93.9677	−	54.2523i	0.776593	−	0.448366i	0.835221	+	0.549914i	$0.185339\pi$
$12$	−123.439	−	74.1532i	−0.857218	−	0.514953i
$13$	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	$0.0823888\pi$
$14$	−101.004	−	17.9987i	−0.515324	−	0.0918302i
$15$	84.7356	+	243.141i	0.376603	+	1.08063i
$16$	−241.191	+	85.8084i	−0.942151	+	0.335189i
$17$	504.169			1.74453			0.872265	−	0.489034i	$-0.162651\pi$
$17$	504.169			1.74453			0.872265	+	0.489034i	$0.162651\pi$
$18$	−170.140	+	275.732i	−0.525125	+	0.851025i
$19$			191.405i			0.530207i	0.964220	+	0.265104i	$0.0854062\pi$
$19$			191.405i			0.530207i	−0.964220	+	0.265104i	$0.914594\pi$
$20$	429.571	+	158.119i	1.07393	+	0.395298i
$21$	−43.2006	+	226.760i	−0.0979606	+	0.514194i
$22$	−427.287	−	76.1421i	−0.882825	−	0.157318i
$23$	−831.897	−	480.296i	−1.57258	−	0.907932i	−0.995851	−	0.0909988i	$-0.970994\pi$
$23$	−831.897	−	480.296i	−1.57258	−	0.907932i	−0.576733	−	0.816933i	$-0.695673\pi$
$24$	186.593	+	544.940i	0.323945	+	0.946076i
$25$	−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	$0.989680\pi$
$30$	367.254	−	962.230i	0.408060	−	1.06914i
$31$	−285.428	−	164.792i	−0.297011	−	0.171480i	0.344088	−	0.938937i	$-0.388188\pi$
$31$	−285.428	−	164.792i	−0.297011	−	0.171480i	−0.641099	+	0.767458i	$0.721521\pi$
$32$	959.027	+	358.946i	0.936550	+	0.350534i
$33$	−182.757	+	959.288i	−0.167821	+	0.880888i
$34$	−1542.51	−	1299.10i	−1.33435	−	1.12379i
$35$		−	733.789i		−	0.599011i
$36$	1231.03	−	405.202i	0.949866	−	0.312656i
$37$	209.943			0.153355			0.0766775	−	0.997056i	$-0.475569\pi$
$37$	209.943			0.153355			0.0766775	+	0.997056i	$0.475569\pi$
$38$	493.194	−	585.604i	0.341547	−	0.405543i
$39$	261.971	+	751.702i	0.172236	+	0.494216i
$40$	−906.848	−	1590.65i	−0.566780	−	0.994154i
$41$	−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	$0.268409\pi$
$42$	716.466	−	582.457i	0.406160	−	0.330191i
$43$	2887.45	−	1667.07i	1.56163	−	0.901608i	0.564537	−	0.825407i	$-0.309055\pi$
$43$	2887.45	−	1667.07i	1.56163	−	0.901608i	0.997093	−	0.0762001i	$-0.0242788\pi$
$44$	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	$-0.748874\pi$
$47$	−977.185	+	564.178i	−0.442365	+	0.255400i	0.262235	+	0.965004i	$0.415540\pi$
$48$	833.269	−	2148.04i	0.361662	−	0.932309i
$49$	−871.573	+	1509.61i	−0.363004	+	0.628742i
$50$	−135.779	+	761.951i	−0.0543116	+	0.304780i
$51$	−2964.09	+	3435.59i	−1.13960	+	1.32087i
$52$	1328.08	+	488.847i	0.491152	+	0.180787i
$53$	1138.62			0.405346			0.202673	−	0.979247i	$-0.435037\pi$
$53$	1138.62			0.405346			0.202673	+	0.979247i	$0.435037\pi$
$54$	−878.655	−	2780.47i	−0.301322	−	0.953522i
$55$		−	3104.23i		−	1.02619i
$56$	8.93796	−	1641.49i	0.00285011	−	0.523434i
$57$	−1304.30	−	1125.30i	−0.401447	−	0.346353i
$58$	−556.720	+	3124.15i	−0.165493	+	0.928700i
$59$	−4037.49	−	2331.05i	−1.15987	−	0.669648i	−0.208593	−	0.978002i	$-0.566889\pi$
$59$	−4037.49	−	2331.05i	−1.15987	−	0.669648i	−0.951272	+	0.308354i	$0.900222\pi$
$60$	−3603.00	+	1997.64i	−1.00083	+	0.554901i
$61$	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
$66$	3030.95	−	2464.04i	0.695810	−	0.565665i
$67$	6127.74	+	3537.85i	1.36506	+	0.788116i	0.990292	−	0.139004i	$-0.0443902\pi$
$67$	6127.74	+	3537.85i	1.36506	+	0.788116i	0.374764	+	0.927120i	$0.377724\pi$
$68$	1371.92	+	7949.19i	0.296696	+	1.71911i
$69$	8163.76	−	2845.11i	1.71472	−	0.597586i
$70$	−1890.76	+	2245.03i	−0.385869	+	0.458170i
$71$			4433.42i			0.879472i	0.898127	+	0.439736i	$0.144928\pi$
$71$			4433.42i			0.879472i	−0.898127	+	0.439736i	$0.855072\pi$
$72$	−4810.42	−	1932.28i	−0.927936	−	0.372739i
$73$	−1953.21			−0.366524			−0.183262	−	0.983064i	$-0.558666\pi$
$73$	−1953.21			−0.366524			−0.183262	+	0.983064i	$0.558666\pi$
$74$	−642.322	−	540.962i	−0.117298	−	0.0987878i
$75$	1710.63	+	325.897i	0.304112	+	0.0579373i
$76$	−3017.86	+	520.842i	−0.522483	+	0.0901735i
$77$	1391.50	−	2410.15i	0.234694	−	0.406501i
$78$	1135.41	−	2974.86i	0.186623	−	0.488965i
$79$	−1523.90	+	879.826i	−0.244176	+	0.140975i	−0.617095	−	0.786889i	$-0.711690\pi$
$79$	−1523.90	+	879.826i	−0.244176	+	0.140975i	0.372918	+	0.927864i	$0.378357\pi$
$80$	−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	$-0.596154\pi$
$83$	2621.64	−	1513.61i	0.380555	−	0.219714i	0.678060	+	0.735007i	$0.262821\pi$
$84$	−3692.85	−	64.0924i	−0.523363	−	0.00908338i
$85$	7211.95	−	12491.5i	0.998193	−	1.72892i
$86$	−13129.7	−	2339.71i	−1.77525	−	0.316348i
$87$	7013.92	+	1336.24i	0.926664	+	0.176541i
$88$	37.8113	−	6944.19i	0.00488266	−	0.896719i
$89$	−559.336			−0.0706144			−0.0353072	−	0.999377i	$-0.511241\pi$
$89$	−559.336			−0.0706144			−0.0353072	+	0.999377i	$0.511241\pi$
$90$	4397.84	+	8159.70i	0.542943	+	1.00737i
$91$		−	2268.61i		−	0.273953i
$92$	5309.06	−	14423.4i	0.627252	−	1.70409i
$93$	2801.03	−	976.170i	0.323855	−	0.112865i
$94$	4443.42	+	791.814i	0.502877	+	0.0896122i
$95$	4742.31	+	2737.97i	0.525463	+	0.303376i
$96$	−8084.26	+	4424.85i	−0.877199	+	0.480127i
$97$	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	$0.821915\pi$
$102$	17921.2	−	2873.61i	1.72253	−	0.276202i
$103$	−8533.78	−	4926.98i	−0.804391	−	0.464415i	0.0406134	−	0.999175i	$-0.487069\pi$
$103$	−8533.78	−	4926.98i	−0.804391	−	0.464415i	−0.845004	+	0.534760i	$0.820402\pi$
$104$	−2803.64	−	4917.69i	−0.259212	−	0.454668i
$105$	5000.30	+	4314.06i	0.453542	+	0.391298i
$106$	−3483.60	−	2933.88i	−0.310039	−	0.261114i
$107$			804.642i			0.0702806i	0.999382	+	0.0351403i	$0.0111878\pi$
$107$			804.642i			0.0702806i	−0.999382	+	0.0351403i	$0.988812\pi$
$108$	−4476.21	+	10770.9i	−0.383763	+	0.923432i
$109$	−17324.9			−1.45820			−0.729102	−	0.684405i	$-0.760062\pi$
$109$	−17324.9			−1.45820			−0.729102	+	0.684405i	$0.760062\pi$
$110$	−7998.70	+	9497.42i	−0.661050	+	0.784911i
$111$	−1234.29	+	1430.63i	−0.100178	+	0.116113i
$112$	−4256.99	+	4999.12i	−0.339364	+	0.398527i
$113$	−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	$0.932332\pi$
$114$	1090.95	+	6803.66i	0.0839450	+	0.523520i
$115$	−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
$120$	16170.7	+	3172.08i	1.12297	+	0.220283i
$121$	−1433.88	+	2483.55i	−0.0979359	+	0.169630i
$122$	3929.52	−	22051.3i	0.264010	−	1.48155i
$123$	−3128.87	−	8978.01i	−0.206813	−	0.593430i
$124$	1821.56	−	4948.74i	0.118468	−	0.321848i
$125$	12345.2			0.790094
$126$	−243.147	+	8306.61i	−0.0153154	+	0.523218i
$127$			9591.51i			0.594675i	0.954772	+	0.297337i	$0.0960986\pi$
$127$			9591.51i			0.594675i	−0.954772	+	0.297337i	$0.903901\pi$
$128$	−3049.81	+	16097.6i	−0.186146	+	0.982522i
$129$	−5615.78	+	29477.1i	−0.337466	+	1.77136i
$130$	−1775.73	+	9964.88i	−0.105073	+	0.589638i
$131$	3933.27	+	2270.88i	0.229198	+	0.132328i	0.610202	−	0.792246i	$-0.291088\pi$
$131$	3933.27	+	2270.88i	0.229198	+	0.132328i	−0.381004	+	0.924573i	$0.624422\pi$
$132$	−15622.3	−	271.138i	−0.896597	−	0.0155612i
$133$	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	$0.791650\pi$
$138$	−32308.1	−	12331.0i	−1.69650	−	0.647501i
$139$	7491.80	+	4325.39i	0.387754	+	0.223870i	0.681187	−	0.732110i	$-0.261464\pi$
$139$	7491.80	+	4325.39i	0.387754	+	0.223870i	−0.293432	+	0.955980i	$0.594798\pi$
$140$	11569.6	−	1996.75i	0.590285	−	0.101875i
$141$	1900.52	−	9975.78i	0.0955946	−	0.501775i
$142$	11423.6	−	13564.1i	0.566535	−	0.672687i
$143$		−	9597.15i		−	0.469321i
$144$	9738.60	+	18306.9i	0.469647	+	0.882854i
$145$	−22696.9			−1.07952
$146$	5975.85	+	5032.84i	0.280346	+	0.236106i
$147$	−5162.90	−	14814.4i	−0.238923	−	0.685568i
$148$	571.288	+	3310.15i	0.0260814	+	0.151121i
$149$	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	$0.0743863\pi$
$150$	−4393.94	−	5404.88i	−0.195286	−	0.240217i
$151$	−11055.3	+	6382.78i	−0.484860	+	0.279934i	−0.722440	−	0.691434i	$-0.756979\pi$
$151$	−11055.3	+	6382.78i	−0.484860	+	0.279934i	0.237579	+	0.971368i	$0.423646\pi$
$152$	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
$156$	−11139.1	+	6175.98i	−0.457723	+	0.253779i
$157$	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	$-0.140963\pi$
$158$	6929.45	+	1234.82i	0.277578	+	0.0494641i
$159$	−6694.10	+	7758.93i	−0.264788	+	0.306908i
$160$	22611.9	−	18626.6i	0.883277	−	0.727601i
$161$	−24637.9			−0.950499
$162$	24112.9	+	10359.4i	0.918796	+	0.394733i
$163$		−	6872.98i		−	0.258684i	−0.991600	−	0.129342i	$-0.958713\pi$
$163$		−	6872.98i		−	0.258684i	0.991600	−	0.129342i	$-0.0412865\pi$
$164$	−15862.0	−	5838.58i	−0.589752	−	0.217080i
$165$	21153.4	+	18250.3i	0.776983	+	0.670350i
$166$	−11921.1	−	2124.32i	−0.432612	−	0.0770910i
$167$	30405.5	+	17554.6i	1.09023	+	0.629447i	0.933639	−	0.358216i	$-0.116615\pi$
$167$	30405.5	+	17554.6i	1.09023	+	0.629447i	0.156595	+	0.987663i	$0.449948\pi$
$168$	11133.2	+	9711.49i	0.394457	+	0.344086i
$169$	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	$0.849205\pi$
$174$	−18016.0	−	22161.1i	−0.595059	−	0.731968i
$175$	−4297.84	−	2481.36i	−0.140338	−	0.0810240i
$176$	−18008.8	+	21148.4i	−0.581380	+	0.682734i
$177$	39621.6	−	13808.3i	1.26470	−	0.440752i
$178$	1711.29	+	1441.25i	0.0540113	+	0.0454881i
$179$			45199.3i			1.41067i	0.708874	+	0.705335i	$0.249203\pi$
$179$			45199.3i			1.41067i	−0.708874	+	0.705335i	$0.750797\pi$
$180$	7569.96	−	36296.6i	0.233641	−	1.12027i
$181$	27600.9			0.842492			0.421246	−	0.906946i	$-0.361593\pi$
$181$	27600.9			0.842492			0.421246	+	0.906946i	$0.361593\pi$
$182$	−5845.53	+	6940.81i	−0.176474	+	0.209540i
$183$	−49506.7	−	9431.66i	−1.47830	−	0.281635i
$184$	−53408.0	+	30448.6i	−1.57750	+	0.899356i
$185$	3003.16	−	5201.62i	0.0877474	−	0.151983i
$186$	−11085.1	−	4230.83i	−0.320415	−	0.122292i
$187$	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	$-0.749723\pi$
$191$	−16300.9	+	9411.33i	−0.446833	+	0.257979i	0.259659	+	0.965700i	$0.416390\pi$
$192$	36135.4	+	7292.92i	0.980236	+	0.197833i
$193$	−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	$0.207171\pi$
$194$	1545.08	−	8670.52i	0.0410532	−	0.230378i
$195$	22371.8	+	4262.12i	0.588345	+	0.112087i
$196$	−26173.5	−	9634.13i	−0.681319	−	0.250784i
$197$	−21650.0			−0.557860			−0.278930	−	0.960311i	$-0.589980\pi$
$197$	−21650.0			−0.557860			−0.278930	+	0.960311i	$0.589980\pi$
$198$	−1028.61	+	35140.4i	−0.0262374	+	0.896348i
$199$		−	25261.4i		−	0.637898i	−0.947772	−	0.318949i	$-0.896670\pi$
$199$		−	25261.4i		−	0.637898i	0.947772	−	0.318949i	$-0.103330\pi$
$200$	−12383.1	−	67.4262i	−0.309577	−	0.00168566i
$201$	−60134.1	+	20957.0i	−1.48843	+	0.518725i
$202$	513.451	−	2881.34i	0.0125834	−	0.0706141i
$203$	−17622.0	−	10174.1i	−0.427625	−	0.246889i
$204$	−62234.4	−	37385.8i	−1.49544	−	0.898351i
$205$	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
$210$	−4182.37	−	26083.2i	−0.0948384	−	0.591456i
$211$	18674.0	+	10781.5i	0.419443	+	0.242166i	0.694839	−	0.719165i	$-0.255476\pi$
$211$	18674.0	+	10781.5i	0.419443	+	0.242166i	−0.275396	+	0.961331i	$0.588809\pi$
$212$	3098.35	+	17952.4i	0.0689380	+	0.399440i
$213$	−30210.9	−	26064.8i	−0.665893	−	0.574506i
$214$	2073.33	−	2461.81i	0.0452731	−	0.0537559i
$215$		−	95387.3i		−	2.06354i
$216$	41448.5	−	21419.8i	0.888385	−	0.459100i
$217$	−8453.38			−0.179519
$218$	53005.7	+	44641.3i	1.11535	+	0.939342i
$219$	11483.2	−	13309.8i	0.239428	−	0.277514i
$220$	48944.2	−	8447.10i	1.01124	−	0.174527i
$221$	22296.7	−	38619.0i	0.456516	−	0.790709i
$222$	7462.62	−	1196.61i	0.151421	−	0.0242799i
$223$	16709.5	−	9647.22i	0.336011	−	0.193996i	−0.322496	−	0.946571i	$-0.604522\pi$
$223$	16709.5	−	9647.22i	0.336011	−	0.193996i	0.658507	+	0.752575i	$0.271188\pi$
$224$	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	$-0.883228\pi$
$227$	−56144.4	+	32415.0i	−1.08957	+	0.629063i	−0.156107	+	0.987740i	$0.549895\pi$
$228$	14193.3	−	23626.9i	0.273032	−	0.454503i
$229$	−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	$0.288435\pi$
$230$	108222.	+	19285.1i	2.04579	+	0.364558i
$231$	8242.76	+	23651.8i	0.154472	+	0.443241i
$232$	−50773.1	−	276.461i	−0.943317	−	0.00513639i
$233$	−2307.53			−0.0425045			−0.0212522	−	0.999774i	$-0.506765\pi$
$233$	−2307.53			−0.0425045			−0.0212522	+	0.999774i	$0.506765\pi$
$234$	13596.5	+	25226.8i	0.248311	+	0.460713i
$235$			32281.4i			0.584543i
$236$	25766.7	−	70001.9i	0.462632	−	1.25686i
$237$	2963.82	−	15557.1i	0.0527662	−	0.276969i
$238$	−50922.8	−	9074.40i	−0.898998	−	0.160201i
$239$	−65999.7	−	38104.9i	−1.15544	−	0.667091i	−0.205230	−	0.978714i	$-0.565794\pi$
$239$	−65999.7	−	38104.9i	−1.15544	−	0.667091i	−0.950206	+	0.311623i	$0.899128\pi$
$240$	−41301.0	−	51372.3i	−0.717031	−	0.891879i
$241$	−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
$246$	−13560.9	+	35530.5i	−0.224088	+	0.587125i
$247$	14661.5	+	8464.81i	0.240317	+	0.138747i
$248$	−18324.5	+	10447.1i	−0.297941	+	0.169860i
$249$	−5098.80	+	26763.6i	−0.0822375	+	0.431663i
$250$	−37770.3	−	31810.0i	−0.604324	−	0.508960i
$251$		−	33833.6i		−	0.537033i	−0.963275	−	0.268517i	$-0.913467\pi$
$251$		−	33833.6i		−	0.537033i	0.963275	−	0.268517i	$-0.0865334\pi$
$252$	22147.6	−	24787.6i	0.348759	−	0.390331i
$253$	−104229.			−1.62834
$254$	24714.5	−	29345.3i	0.383076	−	0.454853i
$255$	42721.1	+	122584.i	0.656995	+	1.88518i
$256$	50809.8	−	41392.4i	0.775297	−	0.631597i
$257$	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	$0.0231916\pi$
$258$	93135.4	−	75715.2i	1.39919	−	1.13748i
$259$	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	$-0.474479\pi$
$263$	68019.2	−	39270.9i	0.983378	−	0.567753i	0.903288	+	0.429034i	$0.141146\pi$
$264$	47097.9	+	41083.7i	0.675762	+	0.589469i
$265$	16287.5	−	28210.7i	0.231933	−	0.401719i
$266$	3445.04	−	19332.6i	0.0486890	−	0.273229i
$267$	3288.43	−	3811.52i	0.0461281	−	0.0534657i
$268$	−39106.4	+	106242.i	−0.544476	+	1.47921i
$269$	−5376.96			−0.0743074			−0.0371537	−	0.999310i	$-0.511829\pi$
$269$	−5376.96			−0.0743074			−0.0371537	+	0.999310i	$0.511829\pi$
$270$	−81458.7	−	18003.8i	−1.11740	−	0.246965i
$271$		−	108113.i		−	1.47211i	−0.676924	−	0.736053i	$-0.736688\pi$
$271$		−	108113.i		−	1.47211i	0.676924	−	0.736053i	$-0.263312\pi$
$272$	−121601.	+	43261.9i	−1.64361	+	0.584747i
$273$	15459.1	+	13337.5i	0.207424	+	0.178957i
$274$	3439.68	−	19302.5i	0.0458160	−	0.257106i
$275$	−18181.7	−	10497.2i	−0.240419	−	0.138806i
$276$	67073.4	+	120975.i	0.880506	+	1.58810i
$277$	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	$0.937732\pi$
$282$	−31519.3	+	25623.9i	−0.396350	+	0.322216i
$283$	22858.8	+	13197.5i	0.285418	+	0.164786i	0.635873	−	0.771793i	$-0.280640\pi$
$283$	22858.8	+	13197.5i	0.285418	+	0.164786i	−0.350456	+	0.936579i	$0.613973\pi$
$284$	−69901.3	+	12064.0i	−0.866659	+	0.149574i
$285$	−46538.3	+	16218.8i	−0.572956	+	0.199678i
$286$	−24729.0	+	29362.5i	−0.302326	+	0.358973i
$287$			27095.2i			0.328950i
$288$	17376.2	−	81103.5i	0.209493	−	0.977810i
$289$	170665.			2.04338
$290$	69441.2	+	58483.2i	0.825699	+	0.695401i
$291$	−19465.9	−	3708.50i	−0.229873	−	0.0437938i
$292$	−5314.98	−	30796.0i	−0.0623356	−	0.361184i
$293$	−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	$0.891008\pi$
$294$	−22376.6	+	58628.2i	−0.258880	+	0.678284i
$295$	−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
$300$	−483.500	+	27858.2i	−0.00537223	+	0.309535i
$301$	42758.2	−	74059.3i	0.471939	−	0.817423i
$302$	50270.3	+	8958.12i	0.551186	+	0.0982207i
$303$	−6468.79	−	1232.39i	−0.0704592	−	0.0134234i
$304$	−16424.1	−	46165.0i	−0.177720	−	0.499535i
$305$	160202.			1.72214
$306$	−85779.6	+	139016.i	−0.916096	+	1.48464i
$307$			54227.3i			0.575362i	0.957726	+	0.287681i	$0.0928843\pi$
$307$			54227.3i			0.575362i	−0.957726	+	0.287681i	$0.907116\pi$
$308$	41787.0	+	15381.2i	0.440494	+	0.162140i
$309$	83745.7	−	29185.7i	0.877093	−	0.305671i
$310$	37131.6	+	6616.81i	0.386385	+	0.0688534i
$311$	117745.	+	67980.1i	1.21737	+	0.702847i	0.964354	−	0.264616i	$-0.0852451\pi$
$311$	117745.	+	67980.1i	1.21737	+	0.702847i	0.253013	+	0.967463i	$0.418578\pi$
$312$	49994.0	+	9806.89i	0.513581	+	0.100745i
$313$	−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	$-0.371563\pi$
$318$	40473.2	−	6489.76i	0.400233	−	0.0641763i
$319$	−74548.4	−	43040.6i	−0.732584	−	0.422957i
$320$	−117176.	−	1276.10i	−1.14430	−	0.0124619i
$321$	−5483.12	−	4730.62i	−0.0532130	−	0.0459101i
$322$	75379.8	+	63484.6i	0.727015	+	0.612290i
$323$			96500.4i			0.924962i
$324$	−47080.4	−	93826.4i	−0.448488	−	0.893789i
$325$	−17113.9			−0.162025
$326$	−17709.6	+	21027.9i	−0.166638	+	0.197861i
$327$	101856.	−	118058.i	0.952557	−	1.10408i
$328$	33485.5	+	58734.8i	0.311250	+	0.545944i
$329$	−14470.4	+	25063.5i	−0.133687	+	0.231553i
$330$	−17693.2	−	110343.i	−0.162472	−	1.01325i
$331$	100184.	−	57841.2i	0.914412	−	0.527936i	0.0325639	−	0.999470i	$-0.489633\pi$
$331$	100184.	−	57841.2i	0.914412	−	0.527936i	0.881848	+	0.471534i	$0.156299\pi$
$332$	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
$336$	−9038.28	−	58399.2i	−0.0800585	−	0.517284i
$337$	−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	$0.856979\pi$
$338$	14552.5	−	81664.4i	0.127381	−	0.714825i
$339$	−50789.1	−	145734.i	−0.441948	−	1.26813i
$340$	216576.	+	79718.9i	1.87350	+	0.689610i
$341$	−35761.3			−0.307542
$342$	−52776.5	−	32565.7i	−0.451220	−	0.278425i
$343$			106292.i			0.903465i
$344$	1161.87	−	213382.i	0.00981841	−	1.80319i
$345$	46288.2	−	242966.i	0.388895	−	2.04130i
$346$	−2093.61	+	11748.7i	−0.0174881	+	0.0981381i
$347$	−117124.	−	67621.8i	−0.972721	−	0.561601i	−0.0726566	−	0.997357i	$-0.523148\pi$
$347$	−117124.	−	67621.8i	−0.972721	−	0.561601i	−0.900065	+	0.435756i	$0.856481\pi$
$348$	−1982.45	+	114224.i	−0.0163698	+	0.943189i
$349$	−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	$0.888184\pi$
$354$	−156803.	−	59846.8i	−1.25126	−	0.477567i
$355$	109844.	+	63418.4i	0.871603	+	0.503220i
$356$	−1522.04	−	8819.00i	−0.0120095	−	0.0695856i
$357$	−21780.4	+	114325.i	−0.170895	+	0.897027i
$358$	116465.	−	138287.i	0.908721	−	1.07899i
$359$			175816.i			1.36418i	0.731270	+	0.682088i	$0.238928\pi$
$359$			175816.i			1.36418i	−0.731270	+	0.682088i	$0.761072\pi$
$360$	−116686.	+	91544.1i	−0.900355	+	0.706359i
$361$	93685.2			0.718880
$362$	−84445.1	−	71119.4i	−0.644402	−	0.542714i
$363$	−8493.80	−	24372.2i	−0.0644598	−	0.184961i
$364$	35768.9	−	6173.23i	0.269962	−	0.0465918i
$365$	−27939.9	+	48393.3i	−0.209719	+	0.363245i
$366$	127163.	+	156420.i	0.949292	+	1.16770i
$367$	6867.31	−	3964.84i	0.0509864	−	0.0294370i	−0.474290	−	0.880369i	$-0.657295\pi$
$367$	6867.31	−	3964.84i	0.0509864	−	0.0294370i	0.525277	+	0.850932i	$0.323962\pi$
$368$	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
$372$	23013.2	+	41507.2i	0.166300	+	0.299942i
$373$	−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	$0.819806\pi$
$374$	−215425.	−	38388.5i	−1.54011	−	0.274447i
$375$	−72579.5	+	84124.7i	−0.516121	+	0.598220i
$376$	−393.206	+	72213.7i	−0.00278128	+	0.510792i
$377$	−70170.4			−0.493709
$378$	−55174.7	−	50492.8i	−0.386150	−	0.353383i
$379$			147423.i			1.02633i	0.858291	+	0.513163i	$0.171526\pi$
$379$			147423.i			1.02633i	−0.858291	+	0.513163i	$0.828474\pi$
$380$	−30264.8	+	82222.0i	−0.209590	+	0.569404i
$381$	−65360.0	−	56390.0i	−0.450258	−	0.388465i
$382$	74123.0	+	13208.6i	0.507956	+	0.0905172i
$383$	105968.	+	61180.9i	0.722402	+	0.417079i	0.815636	−	0.578565i	$-0.196387\pi$
$383$	105968.	+	61180.9i	0.722402	+	0.417079i	−0.0932341	+	0.995644i	$0.529720\pi$
$384$	−91764.8	−	115423.i	−0.622320	−	0.782763i
$385$	−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	$0.626034\pi$
$390$	−57464.5	−	70685.6i	−0.377807	−	0.464731i
$391$	−419417.	−	242150.i	−2.74342	−	1.58391i
$392$	55253.8	+	96917.3i	0.359575	+	0.630709i
$393$	−38598.9	+	13451.9i	−0.249914	+	0.0870959i
$394$	66238.3	+	55785.7i	0.426694	+	0.359361i
$395$			50342.3i			0.322656i
$396$	93693.7	−	104862.i	0.597475	−	0.668694i
$397$	81466.1			0.516887			0.258444	−	0.966026i	$-0.416790\pi$
$397$	81466.1			0.516887			0.258444	+	0.966026i	$0.416790\pi$
$398$	−65091.2	+	77287.4i	−0.410919	+	0.487913i
$399$	−43402.9	−	8268.81i	−0.272629	−	0.0519394i
$400$	37712.4	+	32113.9i	0.235702	+	0.200712i
$401$	−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	$0.951554\pi$
$402$	237981.	+	90830.0i	1.47262	+	0.562053i
$403$	−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
$408$	94074.2	+	274742.i	0.565132	+	1.65046i
$409$	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	$0.0285666\pi$
$410$	21208.6	−	119016.i	0.126166	−	0.708009i
$411$	−43335.4	−	8255.95i	−0.256542	−	0.0488746i
$412$	54461.5	−	147958.i	0.320845	−	0.871656i
$413$	−119576.			−0.701044
$414$	273972.	−	147663.i	1.59848	−	0.861531i
$415$		−	86606.3i		−	0.502867i
$416$	69907.7	−	57586.6i	0.403960	−	0.332763i
$417$	−73520.3	+	25622.1i	−0.422800	+	0.147348i
$418$	14574.0	−	81784.8i	0.0834114	−	0.468080i
$419$	133102.	+	76846.6i	0.758154	+	0.437720i	0.828633	−	0.559793i	$-0.189119\pi$
$419$	133102.	+	76846.6i	0.758154	+	0.437720i	−0.0704785	+	0.997513i	$0.522453\pi$
$420$	−54412.8	+	90578.5i	−0.308463	+	0.513483i
$421$	−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
$426$	25269.1	+	157590.i	0.139242	+	0.868379i
$427$	124382.	+	71812.1i	0.682186	+	0.393860i
$428$	−12686.7	+	2189.56i	−0.0692567	+	0.0119528i
$429$	65398.4	+	56423.2i	0.355347	+	0.306579i
$430$	−245785.	+	291838.i	−1.32929	+	1.57836i
$431$		−	191579.i		−	1.03132i	−0.856793	−	0.515660i	$-0.827547\pi$
$431$		−	191579.i		−	1.03132i	0.856793	−	0.515660i	$-0.172453\pi$
$432$	−182004.	−	41266.7i	−0.975246	−	0.221122i
$433$	−53963.8			−0.287824			−0.143912	−	0.989591i	$-0.545968\pi$
$433$	−53963.8			−0.287824			−0.143912	+	0.989591i	$0.545968\pi$
$434$	25863.2	+	21781.9i	0.137310	+	0.115642i
$435$	133439.	−	154665.i	0.705185	−	0.817359i
$436$	−47143.8	−	273160.i	−0.248000	−	1.43696i
$437$	91930.9	−	159229.i	0.481392	−	0.833795i
$438$	−69428.6	+	11132.7i	−0.361901	+	0.0580299i
$439$	−14586.4	+	8421.44i	−0.0756864	+	0.0436976i	−0.537366	−	0.843349i	$-0.680580\pi$
$439$	−14586.4	+	8421.44i	−0.0756864	+	0.0436976i	0.461679	+	0.887047i	$0.347247\pi$
$440$	−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	$-0.801905\pi$
$443$	−140111.	+	80892.9i	−0.713943	+	0.412195i	0.0985761	+	0.995130i	$0.468571\pi$
$444$	−25915.3	−	15568.0i	−0.131459	−	0.0789706i
$445$	−8001.09	+	13858.3i	−0.0404045	+	0.0699826i
$446$	−75980.8	−	13539.7i	−0.381974	−	0.0680674i
$447$	37594.2	+	107873.i	0.188151	+	0.539881i
$448$	−90404.5	−	53516.1i	−0.450437	−	0.266642i
$449$	127200.			0.630949			0.315475	−	0.948934i	$-0.397836\pi$
$449$	127200.			0.630949			0.315475	+	0.948934i	$0.397836\pi$
$450$	62663.4	+	1834.25i	0.309449	+	0.00905804i
$451$			114624.i			0.563538i
$452$	−257477.	−	94774.0i	−1.26027	−	0.463887i
$453$	21501.3	−	112860.i	0.104778	−	0.549977i
$454$	255298.	+	45493.9i	1.23861	+	0.220720i
$455$	−56207.7	−	32451.5i	−0.271502	−	0.156752i
$456$	−104304.	+	35714.7i	−0.501616	+	0.171758i
$457$	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	$0.789254\pi$
$462$	35725.0	−	93602.0i	0.167374	−	0.438532i
$463$	41167.7	+	23768.2i	0.192041	+	0.110875i	0.592938	−	0.805248i	$-0.297968\pi$
$463$	41167.7	+	23768.2i	0.192041	+	0.110875i	−0.400897	+	0.916123i	$0.631301\pi$
$464$	154628.	+	131673.i	0.718212	+	0.611591i
$465$	15881.7	−	83362.9i	0.0734499	−	0.385538i
$466$	7059.89	+	5945.82i	0.0325107	+	0.0273804i
$467$		−	150686.i		−	0.690936i	−0.938431	−	0.345468i	$-0.887720\pi$
$467$		−	150686.i		−	0.690936i	0.938431	−	0.345468i	$-0.112280\pi$
$468$	23403.5	−	112216.i	0.106854	−	0.512344i
$469$	181482.			0.825066
$470$	83179.7	−	98765.1i	0.376549	−	0.447103i
$471$	120149.	+	344757.i	0.541602	+	1.55407i
$472$	−259208.	+	147778.i	−1.16349	+	0.663323i
$473$	180885.	−	313302.i	0.808500	−	1.40036i
$474$	−49153.9	+	39960.0i	−0.218777	+	0.177856i
$475$	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	$-0.628263\pi$
$479$	47830.3	−	27614.8i	0.208464	−	0.120357i	0.600598	+	0.799551i	$0.294929\pi$
$480$	−6010.73	+	263594.i	−0.0260883	+	1.14407i
$481$	9284.65	−	16081.5i	0.0401306	−	0.0695082i
$482$	−11448.4	+	64244.9i	−0.0492776	+	0.276531i
$483$	144850.	−	167891.i	0.620904	−	0.719671i
$484$	−43059.7	−	15849.7i	−0.183815	−	0.0676598i
$485$	62991.1			0.267791
$486$	−212356.	+	103409.i	−0.899067	+	0.437812i
$487$		−	2975.59i		−	0.0125463i	−0.999980	−	0.00627313i	$-0.998003\pi$
$487$		−	2975.59i		−	0.0125463i	0.999980	−	0.00627313i	$-0.00199681\pi$
$488$	358374.	+	1951.36i	1.50486	+	0.00819402i
$489$	46834.9	+	40407.3i	0.195863	+	0.168983i
$490$	34995.9	−	196387.i	0.145755	−	0.817937i
$491$	−234443.	−	135356.i	−0.972467	−	0.561454i	−0.0724794	−	0.997370i	$-0.523091\pi$
$491$	−234443.	−	135356.i	−0.972467	−	0.561454i	−0.899987	+	0.435916i	$0.856424\pi$
$492$	133041.	−	73763.2i	0.549612	−	0.304726i
$493$	−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
$498$	84561.7	−	68745.1i	0.340969	−	0.277194i
$499$	226339.	+	130677.i	0.908988	+	0.524805i	0.880105	−	0.474778i	$-0.157472\pi$
$499$	226339.	+	130677.i	0.908988	+	0.524805i	0.0288827	+	0.999583i	$0.490805\pi$
$500$	33593.2	+	194646.i	0.134373	+	0.778583i
$501$	−298383.	+	103988.i	−1.18877	+	0.414292i
$502$	−87179.4	+	103514.i	−0.345944	+	0.410764i
$503$		−	283008.i		−	1.11857i	−0.828976	−	0.559284i	$-0.811076\pi$
$503$		−	283008.i		−	1.11857i	0.828976	−	0.559284i	$-0.188924\pi$
$504$	−131631.	+	18769.9i	−0.518200	+	0.0738926i
$505$	20932.9			0.0820816
$506$	318888.	+	268567.i	1.24548	+	1.04894i
$507$	−183342.	−	34929.0i	−0.713257	−	0.135885i
$508$	−151228.	+	26100.0i	−0.586011	+	0.101138i
$509$	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	$0.0313651\pi$
$510$	185158.	−	485126.i	0.711872	−	1.86515i
$511$	−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
$516$	−480045.	−	8331.55i	−1.80294	−	0.0312915i
$517$	−61215.9	+	106029.i	−0.229025	+	0.396683i
$518$	−21205.0	−	3778.71i	−0.0790275	−	0.0140826i
$519$	26376.6	+	5025.08i	0.0979229	+	0.0186556i
$520$	−161947.	−	881.808i	−0.598918	−	0.00326113i
$521$	168525.			0.620854			0.310427	−	0.950597i	$-0.399528\pi$
$521$	168525.			0.620854			0.310427	+	0.950597i	$0.399528\pi$
$522$	256932.	+	7520.79i	0.942927	+	0.0276009i
$523$		−	231592.i		−	0.846681i	−0.905971	−	0.423340i	$-0.860857\pi$
$523$		−	231592.i		−	0.846681i	0.905971	−	0.423340i	$-0.139143\pi$
$524$	−25101.6	+	68194.9i	−0.0914196	+	0.248364i
$525$	42176.6	−	14698.7i	0.153022	−	0.0533287i
$526$	−309295.	−	55116.1i	−1.11790	−	0.199208i
$527$	−143904.	−	83082.9i	−0.518145	−	0.299151i
$528$	−38235.7	−	247053.i	−0.137152	−	0.886182i
$529$	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
$534$	−19882.1	+	3188.05i	−0.0697237	+	0.0111800i
$535$	19936.1	+	11510.1i	0.0696518	+	0.0402135i
$536$	393402.	−	224284.i	1.36933	−	0.780671i
$537$	−308004.	−	265734.i	−1.06809	−	0.921506i
$538$	16450.8	+	13854.8i	0.0568360	+	0.0478671i
$539$			189139.i			0.651035i
$540$	202833.	+	264978.i	0.695586	+	0.908703i
$541$	−3552.06			−0.0121363			−0.00606815	−	0.999982i	$-0.501932\pi$
$541$	−3552.06			−0.0121363			−0.00606815	+	0.999982i	$0.501932\pi$
$542$	−278575.	+	330772.i	−0.948296	+	1.12598i
$543$	−162270.	+	188082.i	−0.550350	+	0.637894i
$544$	483512.	+	180970.i	1.63384	+	0.611516i
$545$	−247826.	+	429248.i	−0.834362	+	1.44516i
$546$	−12930.4	−	80639.7i	−0.0433736	−	0.270498i
$547$	444293.	−	256513.i	1.48489	−	0.857302i	0.485039	−	0.874493i	$-0.338805\pi$
$547$	444293.	−	256513.i	1.48489	−	0.857302i	0.999852	+	0.0171904i	$0.00547213\pi$
$548$	−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
$552$	106507.	−	542953.i	0.349541	−	1.78190i
$553$	−22566.4	+	39086.1i	−0.0737924	+	0.127812i
$554$	30836.1	−	173043.i	0.100471	−	0.563813i
$555$	17789.7	+	51045.7i	0.0577539	+	0.165719i
$556$	−47811.7	+	129893.i	−0.154662	+	0.420180i
$557$	−269383.			−0.868281			−0.434141	−	0.900845i	$-0.642948\pi$
$557$	−269383.			−0.868281			−0.434141	+	0.900845i	$0.642948\pi$
$558$	94001.2	−	50663.9i	0.301901	−	0.162716i
$559$		−	294903.i		−	0.943746i
$560$	62965.2	+	176983.i	0.200782	+	0.564359i
$561$	−92140.3	+	483643.i	−0.292768	+	1.53674i
$562$	−35698.5	+	200330.i	−0.113026	+	0.634267i
$563$	48439.2	+	27966.4i	0.152820	+	0.0882307i	0.574460	−	0.818533i	$-0.305212\pi$
$563$	48439.2	+	27966.4i	0.152820	+	0.0882307i	−0.421640	+	0.906763i	$0.638545\pi$
$564$	162459.	+	2819.60i	0.510722	+	0.00886399i
$565$	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	$-0.394262\pi$
$570$	184175.	+	70294.1i	0.566868	+	0.216356i
$571$	25297.4	+	14605.5i	0.0775897	+	0.0447964i	0.538293	−	0.842758i	$-0.319069\pi$
$571$	25297.4	+	14605.5i	0.0775897	+	0.0447964i	−0.460703	+	0.887554i	$0.652403\pi$
$572$	151317.	−	26115.3i	0.462484	−	0.0798185i
$573$	31703.4	−	166411.i	0.0965600	−	0.506842i
$574$	69816.5	−	82898.1i	0.211902	−	0.251606i
$575$			185863.i			0.562158i
$576$	−262142.	+	203363.i	−0.790119	+	0.612954i
$577$	−494524.			−1.48537			−0.742687	−	0.669639i	$-0.766449\pi$
$577$	−494524.			−1.48537			−0.742687	+	0.669639i	$0.766449\pi$
$578$	−522152.	−	439755.i	−1.56294	−	1.31630i
$579$	−28001.8	−	80348.4i	−0.0835272	−	0.239673i
$580$	−61761.7	−	357860.i	−0.183596	−	1.06379i
$581$	38822.0	−	67241.7i	0.115007	−	0.199199i
$582$	50000.2	+	61504.1i	0.147614	+	0.181576i
$583$	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	$-0.780099\pi$
$587$	−208206.	+	120208.i	−0.604251	+	0.348865i	0.166461	+	0.986048i	$0.446766\pi$
$588$	219529.	−	121715.i	0.634946	−	0.352039i
$589$	31541.9	−	54632.2i	0.0909197	−	0.157477i
$590$	525241.	+	93597.5i	1.50888	+	0.268881i
$591$	127284.	−	147531.i	0.364417	−	0.422384i
$592$	−50636.3	+	18014.9i	−0.144484	+	0.0514029i
$593$	−470902.			−1.33912			−0.669562	−	0.742756i	$-0.733518\pi$
$593$	−470902.			−1.33912			−0.669562	+	0.742756i	$0.733518\pi$
$594$	−233412.	−	213606.i	−0.661531	−	0.605396i
$595$		−	369954.i		−	1.04499i
$596$	190586.	+	70152.0i	0.536534	+	0.197491i
$597$	172140.	+	148516.i	0.482985	+	0.416701i
$598$	334584.	+	59622.5i	0.935626	+	0.166728i
$599$	8669.92	+	5005.58i	0.0241636	+	0.0139509i	0.512033	−	0.858966i	$-0.328892\pi$
$599$	8669.92	+	5005.58i	0.0241636	+	0.0139509i	−0.487870	+	0.872917i	$0.662226\pi$
$600$	73261.6	−	83986.4i	0.203504	−	0.233295i
$601$	−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
$606$	16615.8	+	20438.7i	0.0452456	+	0.0556554i
$607$	375426.	+	216752.i	1.01894	+	0.588283i	0.913796	−	0.406174i	$-0.133137\pi$
$607$	375426.	+	216752.i	1.01894	+	0.588283i	0.105141	+	0.994457i	$0.466471\pi$
$608$	−68704.1	+	183562.i	−0.185855	+	0.496566i
$609$	172932.	−	60267.7i	0.466274	−	0.162499i
$610$	−490140.	−	412795.i	−1.31723	−	1.10937i
$611$			99802.2i			0.267336i
$612$	620646.	−	204290.i	1.65707	−	0.545437i
$613$	301951.			0.803555			0.401778	−	0.915737i	$-0.368393\pi$
$613$	301951.			0.803555			0.401778	+	0.915737i	$0.368393\pi$
$614$	139728.	−	165909.i	0.370635	−	0.440081i
$615$	−267199.	−	50904.9i	−0.706456	−	0.134589i
$616$	−88214.7	−	154732.i	−0.232477	−	0.407773i
$617$	−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	$0.249865\pi$
$618$	−331424.	−	126494.i	−0.867774	−	0.331203i
$619$	−536199.	+	309575.i	−1.39941	+	0.807949i	−0.994331	−	0.106333i	$-0.966089\pi$
$619$	−536199.	+	309575.i	−1.39941	+	0.807949i	−0.405078	+	0.914282i	$0.632756\pi$
$620$	−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
$624$	−127687.	−	158824.i	−0.327928	−	0.407894i
$625$	237059.	−	410598.i	0.606870	−	1.05113i
$626$	−115358.	+	647355.i	−0.294374	+	1.65194i
$627$	−183612.	−	34980.5i	−0.467053	−	0.0889797i
$628$	609103.	+	224203.i	1.54444	+	0.568488i
$629$	105847.			0.267532
$630$	202329.	+	124847.i	0.509774	+	0.314556i
$631$			308766.i			0.775479i	0.921769	+	0.387740i	$0.126744\pi$
$631$			308766.i			0.775479i	−0.921769	+	0.387740i	$0.873256\pi$
$632$	−613.198	+	112616.i	−0.00153521	+	0.281946i
$633$	−183256.	+	63865.6i	−0.457353	+	0.159390i
$634$	−84643.3	+	474993.i	−0.210578	+	1.18170i
$635$	237642.	+	137203.i	0.589354	+	0.340264i
$636$	−140550.	−	84432.0i	−0.347470	−	0.208734i
$637$	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	$0.696532\pi$
$642$	4586.21	+	28601.8i	0.0111272	+	0.0693941i
$643$	−478867.	−	276474.i	−1.15823	−	0.668702i	−0.207347	−	0.978267i	$-0.566483\pi$
$643$	−478867.	−	276474.i	−1.15823	−	0.668702i	−0.950878	+	0.309566i	$0.899816\pi$
$644$	−67043.5	−	388463.i	−0.161654	−	0.936652i
$645$	650003.	+	560797.i	1.56241	+	1.34799i
$646$	248653.	−	295244.i	0.595839	−	0.707482i
$647$		−	576814.i		−	1.37793i	−0.724794	−	0.688965i	$-0.758065\pi$
$647$		−	576814.i		−	1.37793i	0.724794	−	0.688965i	$-0.241935\pi$
$648$	−97720.3	+	408375.i	−0.232721	+	0.972544i
$649$	−505858.			−1.20099
$650$	52360.1	+	44097.6i	0.123929	+	0.104373i
$651$	49698.8	−	57604.4i	0.117269	−	0.135923i
$652$	108366.	−	18702.4i	0.254915	−	0.0439950i
$653$	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	$-0.0681484\pi$
$654$	−615831.	+	98746.8i	−1.43981	+	0.230870i
$655$	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	$-0.796927\pi$
$659$	−299298.	+	172800.i	−0.689180	+	0.397899i	0.114125	+	0.993466i	$0.463594\pi$
$660$	−230189.	+	383185.i	−0.528441	+	0.879671i
$661$	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	$0.0254163\pi$
$662$	−455553.	−	81179.1i	−1.03950	−	0.185237i
$663$	132078.	+	378985.i	0.300471	+	0.862174i
$664$	1054.91	−	193739.i	0.00239266	−	0.439421i
$665$	140451.			0.317600
$666$	−35719.8	+	57888.1i	−0.0805306	+	0.130509i
$667$			762077.i			1.71296i
$668$	−194044.	+	527170.i	−0.434858	+	1.18140i
$669$	−32498.1	+	170582.i	−0.0726115	+	0.381137i
$670$	−797164.	−	142054.i	−1.77582	−	0.316449i
$671$	526189.	+	303795.i	1.16868	+	0.674739i
$672$	−122825.	+	201962.i	−0.271987	+	0.447230i
$673$	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	$0.823755\pi$
$678$	−220125.	+	576744.i	−0.478862	+	1.25465i
$679$	48906.7	+	28236.3i	0.106079	+	0.0612447i
$680$	−457205.	−	801955.i	−0.988765	−	1.73433i
$681$	109195.	−	573161.i	0.235454	−	1.23590i
$682$	109412.	+	92146.5i	0.235232	+	0.198112i
$683$			1038.30i			0.00222578i	0.999999	+	0.00111289i	$0.000354244\pi$
$683$			1038.30i			0.00222578i	−0.999999	+	0.00111289i	$0.999646\pi$
$684$	77557.6	+	235624.i	0.165772	+	0.503626i
$685$	140232.			0.298859
$686$	273883.	−	325200.i	0.581992	−	0.691040i
$687$	−115958.	−	332731.i	−0.245690	−	0.704985i
$688$	−553378.	+	649850.i	−1.16908	+	1.37289i
$689$	50354.8	−	87217.2i	0.106073	−	0.183723i
$690$	−767672.	+	624085.i	−1.61242	+	1.31083i
$691$	−289343.	+	167052.i	−0.605978	+	0.349862i	−0.771390	−	0.636363i	$-0.780438\pi$
$691$	−289343.	+	167052.i	−0.605978	+	0.349862i	0.165411	+	0.986225i	$0.447105\pi$
$692$	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
$696$	300387.	−	344361.i	0.620101	−	0.710878i
$697$	−266302.	+	461249.i	−0.548162	+	0.949445i
$698$	−2317.77	+	13006.6i	−0.00475729	+	0.0266965i
$699$	13566.3	−	15724.3i	0.0277656	−	0.0321823i
$700$	27428.3	−	74515.9i	0.0559761	−	0.152073i
$701$	177927.			0.362082			0.181041	−	0.983476i	$-0.442053\pi$
$701$	177927.			0.362082			0.181041	+	0.983476i	$0.442053\pi$
$702$	−251840.	−	55661.0i	−0.511036	−	0.112948i
$703$			40184.1i			0.0813100i
$704$	−382449.	−	226396.i	−0.771664	−	0.456796i
$705$	−219977.	−	189788.i	−0.442587	−	0.381847i
$706$	−29987.3	+	168280.i	−0.0601629	+	0.337616i
$707$	16252.4	+	9383.33i	0.0325146	+	0.0187723i
$708$	325531.	+	587136.i	0.649420	+	1.17131i
$709$	−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
$714$	361220.	−	293657.i	0.708557	−	0.576028i
$715$	−237782.	−	137284.i	−0.465122	−	0.268538i
$716$	−712652.	+	122994.i	−1.39012	+	0.239916i
$717$	647683.	−	225720.i	1.25987	−	0.439069i
$718$	453027.	−	537911.i	0.878770	−	1.04343i
$719$			536436.i			1.03767i	0.854874	+	0.518836i	$0.173634\pi$
$719$			536436.i			1.03767i	−0.854874	+	0.518836i	$0.826366\pi$
$720$	592884.	+	20586.1i	1.14368	+	0.0397109i
$721$	−252741.			−0.486189
$722$	−286630.	−	241399.i	−0.549855	−	0.463086i
$723$	144234.	+	27478.4i	0.275925	+	0.0525673i
$724$	75106.3	+	435181.i	0.143284	+	0.830218i
$725$	−76751.2	+	132937.i	−0.146019	+	0.252912i
$726$	−36813.1	+	96452.8i	−0.0698440	+	0.182996i
$727$	−375814.	+	216977.i	−0.711057	+	0.410529i	−0.811452	−	0.584418i	$-0.801323\pi$
$727$	−375814.	+	216977.i	−0.711057	+	0.410529i	0.100395	+	0.994948i	$0.467989\pi$
$728$	−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
$732$	13992.8	−	806232.i	0.0261145	−	1.50466i
$733$	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	$-0.0920735\pi$
$734$	−31226.8	−	5564.59i	−0.0579610	−	0.0103286i
$735$	−440901.	−	83997.3i	−0.816143	−	0.155486i
$736$	−625411.	−	759223.i	−1.15454	−	1.40157i
$737$	767746.			1.41346
$738$	−162391.	−	301298.i	−0.298159	−	0.553202i
$739$		−	215142.i		−	0.393947i	−0.980409	−	0.196973i	$-0.936889\pi$
$739$		−	215142.i		−	0.393947i	0.980409	−	0.196973i	$-0.0631112\pi$
$740$	90185.5	+	33196.1i	0.164692	+	0.0606210i
$741$	−143879.	+	50142.6i	−0.262037	+	0.0913209i
$742$	−115004.	−	20493.6i	−0.208884	−	0.0372230i
$743$	−250360.	−	144546.i	−0.453511	−	0.261835i	0.255801	−	0.966730i	$-0.417661\pi$
$743$	−250360.	−	144546.i	−0.453511	−	0.261835i	−0.709312	+	0.704895i	$0.750994\pi$
$744$	36542.9	−	186290.i	0.0660172	−	0.336545i
$745$	−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
$750$	438822.	−	70363.9i	0.780128	−	0.125091i
$751$	−593117.	−	342436.i	−1.05162	−	0.607156i	−0.128521	−	0.991707i	$-0.541023\pi$
$751$	−593117.	−	342436.i	−1.05162	−	0.607156i	−0.923104	+	0.384551i	$0.874356\pi$
$752$	187277.	−	219925.i	0.331168	−	0.388901i
$753$	230554.	+	198913.i	0.406615	+	0.350812i
$754$	214687.	+	180809.i	0.377627	+	0.318036i
$755$			365213.i			0.640697i
$756$	38702.3	+	296652.i	0.0677162	+	0.519043i
$757$	−646906.			−1.12888			−0.564442	−	0.825472i	$-0.690909\pi$
$757$	−646906.			−1.12888			−0.564442	+	0.825472i	$0.690909\pi$
$758$	379865.	−	451040.i	0.661136	−	0.785013i
$759$	612777.	−	710251.i	1.06370	−	1.23290i
$760$	304457.	−	173575.i	0.527108	−	0.300511i
$761$	−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	$0.936350\pi$
$762$	54668.7	+	340939.i	0.0941518	+	0.587174i
$763$	−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
$768$	−16656.8	+	589589.i	−0.0282402	+	0.999601i
$769$	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	$0.00360135\pi$
$770$	−55872.2	+	313538.i	−0.0942355	+	0.528822i
$771$	170442.	+	489066.i	0.286726	+	0.822733i
$772$	−141956.	−	52252.2i	−0.238188	−	0.0876738i
$773$	−885783.			−1.48241			−0.741205	−	0.671279i	$-0.765745\pi$
$773$	−885783.			−1.48241			−0.741205	+	0.671279i	$0.765745\pi$
$774$	−31607.4	+	1.07980e6i	−0.0527602	+	1.80244i
$775$			63770.7i			0.106174i
$776$	140912.	+	767.268i	0.234004	+	0.00127416i
$777$	−9069.67	+	47606.6i	−0.0150228	+	0.0788542i
$778$	128739.	−	722444.i	0.212691	−	1.19356i
$779$	−175110.	−	101100.i	−0.288561	−	0.166601i
$780$	−6323.27	+	364332.i	−0.0103933	+	0.598837i
$781$	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
$786$	152755.	+	58301.9i	0.247258	+	0.0943709i
$787$	910515.	+	525686.i	1.47007	+	0.848744i	0.999436	−	0.0335849i	$-0.0106924\pi$
$787$	910515.	+	525686.i	1.47007	+	0.848744i	0.470633	+	0.882329i	$0.344026\pi$
$788$	−58913.0	−	341353.i	−0.0948765	−	0.549733i
$789$	−132290.	+	694388.i	−0.212507	+	1.11544i
$790$	129717.	−	154023.i	0.207847	−	0.246792i
$791$			439820.i			0.702946i
$792$	−556855.	+	79404.5i	−0.887752	+	0.126589i
$793$	495287.			0.787609
$794$	−249246.	−	209914.i	−0.395355	−	0.332967i
$795$	96481.3	+	276844.i	0.152654	+	0.438027i
$796$	398294.	−	68740.2i	0.628605	−	0.108489i
$797$	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	$0.142887\pi$
$798$	111485.	+	137135.i	0.175070	+	0.215349i
$799$	−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
$804$	−494061.	−	891102.i	−0.764309	−	1.37853i
$805$	−352436.	+	610436.i	−0.543861	+	0.941995i
$806$	114797.	+	20456.8i	0.176710	+	0.0314896i
$807$	31612.0	−	36640.5i	0.0485406	−	0.0562619i
$808$	46826.9	+	254.974i	0.0717254	+	0.000390547i
$809$	−209085.			−0.319467			−0.159734	−	0.987160i	$-0.551063\pi$
$809$	−209085.			−0.319467			−0.159734	+	0.987160i	$0.551063\pi$
$810$	601593.	−	449242.i	0.916922	−	0.684715i
$811$		−	577209.i		−	0.877589i	−0.898587	−	0.438794i	$-0.855406\pi$
$811$		−	577209.i		−	0.877589i	0.898587	−	0.438794i	$-0.144594\pi$
$812$	112461.	−	305530.i	0.170566	−	0.463384i
$813$	736720.	+	635613.i	1.11461	+	0.961638i
$814$	−89706.0	−	15985.5i	−0.135386	−	0.0241256i
$815$	−170287.	−	98315.3i	−0.256370	−	0.148015i
$816$	420109.	−	1.08298e6i	0.630930	−	1.62644i
$817$	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	$0.649541\pi$
$822$	111312.	+	136922.i	0.164739	+	0.202642i
$823$	148172.	+	85547.4i	0.218760	+	0.126301i	0.605376	−	0.795940i	$-0.293023\pi$
$823$	148172.	+	85547.4i	0.218760	+	0.126301i	−0.386616	+	0.922241i	$0.626356\pi$
$824$	−547871.	+	312348.i	−0.806908	+	0.460029i
$825$	178425.	−	62181.8i	0.262148	−	0.0913598i
$826$	365845.	+	308114.i	0.536212	+	0.451597i
$827$		−	1.03882e6i		−	1.51890i	−0.650563	−	0.759452i	$-0.725467\pi$
$827$		−	1.03882e6i		−	1.51890i	0.650563	−	0.759452i	$-0.274533\pi$
$828$	−1.21870e6	−	254171.i	−1.77761	−	0.370736i
$829$	−802150.			−1.16720			−0.583601	−	0.812040i	$-0.698357\pi$
$829$	−802150.			−1.16720			−0.583601	+	0.812040i	$0.698357\pi$
$830$	−223159.	+	264972.i	−0.323935	+	0.384631i
$831$	−388493.	−	74013.0i	−0.562576	−	0.107178i
$832$	−362267.	−	3945.22i	−0.523337	−	0.00569934i
$833$	−439420.	+	761098.i	−0.633272	+	1.09686i
$834$	290957.	+	111049.i	0.418308	+	0.159655i
$835$	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	$-0.797615\pi$
$839$	−487546.	+	281485.i	−0.692615	+	0.399881i	0.111976	+	0.993711i	$0.464282\pi$
$840$	399871.	−	136920.i	0.566710	−	0.194047i
$841$	38945.5	−	67455.6i	0.0550637	−	0.0953732i
$842$	−108357.	+	608069.i	−0.152839	+	0.857686i
$843$	449753.	+	85683.8i	0.632876	+	0.120571i
$844$	−119175.	+	323770.i	−0.167302	+	0.454518i
$845$	593291.			0.830910
$846$	10696.7	−	365431.i	0.0149455	−	0.510581i
$847$			73554.1i			0.102527i
$848$	−274623.	+	97702.8i	−0.381897	+	0.135867i
$849$	−224323.	+	78177.7i	−0.311214	+	0.108459i
$850$	−68455.5	+	384152.i	−0.0947481	+	0.531698i
$851$	−174651.	−	100835.i	−0.241164	−	0.139236i
$852$	328752.	−	547259.i	0.452887	−	0.753899i
$853$	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	$-0.447143\pi$
$858$	−54700.8	−	341140.i	−0.0743052	−	0.463402i
$859$	−347489.	−	200623.i	−0.470928	−	0.271890i	0.245700	−	0.969346i	$-0.420982\pi$
$859$	−347489.	−	200623.i	−0.470928	−	0.271890i	−0.716628	+	0.697456i	$0.754315\pi$
$860$	1.50396e6	−	259564.i	2.03348	−	0.350952i
$861$	−184637.	−	159297.i	−0.249064	−	0.214883i
$862$	−493643.	+	586137.i	−0.664352	+	0.788832i
$863$			1.22445e6i			1.64407i	0.569437	+	0.822035i	$0.307161\pi$
$863$			1.22445e6i			1.64407i	−0.569437	+	0.822035i	$0.692839\pi$
$864$	450511.	+	595228.i	0.603501	+	0.797362i
$865$	−85354.1			−0.114075
$866$	165103.	+	139049.i	0.220150	+	0.185409i
$867$	−1.00337e6	+	1.16298e6i	−1.33482	+	1.54715i
$868$	−23003.0	−	133284.i	−0.0305312	−	0.176904i
$869$	−95465.2	+	165351.i	−0.126417	+	0.218961i
$870$	−806782.	+	129365.i	−1.06590	+	0.170915i
$871$	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
$876$	241103.	+	144837.i	0.314191	+	0.188743i
$877$	−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	$0.193986\pi$
$878$	66326.6	+	11819.3i	0.0860397	+	0.0153322i
$879$	−387379.	−	1.11155e6i	−0.501370	−	1.43863i
$880$	266369.	+	748712.i	0.343969	+	0.966828i
$881$	510450.			0.657660			0.328830	−	0.944389i	$-0.393346\pi$
$881$	510450.			0.657660			0.328830	+	0.944389i	$0.393346\pi$
$882$	−267958.	−	497166.i	−0.344452	−	0.639094i
$883$		−	233561.i		−	0.299557i	−0.988720	−	0.149778i	$-0.952144\pi$
$883$		−	233561.i		−	0.299557i	0.988720	−	0.149778i	$-0.0478560\pi$
$884$	669575.	+	246462.i	0.856830	+	0.315388i
$885$	224653.	−	1.17920e6i	0.286831	−	1.50557i
$886$	637107.	+	113532.i	0.811605	+	0.144627i
$887$	−554282.	−	320015.i	−0.704504	−	0.406746i	0.104519	−	0.994523i	$-0.466670\pi$
$887$	−554282.	−	320015.i	−0.704504	−	0.406746i	−0.809023	+	0.587777i	$0.800003\pi$
$888$	39173.8	+	114406.i	0.0496787	+	0.145085i
$889$	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
$894$	162937.	−	426907.i	0.203867	−	0.534144i
$895$	1.11987e6	+	646558.i	1.39805	+	0.807164i
$896$	138698.	+	396679.i	0.172764	+	0.494109i
$897$	143106.	−	751162.i	0.177858	−	0.933574i
$898$	−389169.	−	327757.i	−0.482598	−	0.406443i
$899$			261472.i			0.323524i
$900$	−186993.	−	167077.i	−0.230855	−	0.206268i
$901$	574055.			0.707137
$902$	295353.	−	350694.i	0.363018	−	0.431037i
$903$	253285.	+	726776.i	0.310623	+	0.891303i
$904$	543549.	+	953406.i	0.665123	+	1.16665i
$905$	394820.	−	683849.i	0.482061	−	0.834954i
$906$	−356591.	+	289894.i	−0.434424	+	0.353169i
$907$	379256.	−	218964.i	0.461018	−	0.266169i	−0.251454	−	0.967869i	$-0.580909\pi$
$907$	379256.	−	218964.i	0.461018	−	0.266169i	0.712472	+	0.701700i	$0.247575\pi$
$908$	−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	$-0.820029\pi$
$911$	−666090.	+	384567.i	−0.802594	+	0.463378i	0.0417834	+	0.999127i	$0.486696\pi$
$912$	411145.	+	159492.i	0.494317	+	0.191756i
$913$	164233.	−	284460.i	0.197024	−	0.341256i
$914$	13226.3	−	74222.2i	0.0158324	−	0.0888467i
$915$	−941856.	+	1.09168e6i	−1.12497	+	1.30392i
$916$	−587855.	−	216382.i	−0.700615	−	0.257887i
$917$	116490.			0.138532
$918$	−442990.	−	1.40183e6i	−0.525665	−	1.66345i
$919$		−	1.37883e6i		−	1.63260i	−0.577626	−	0.816301i	$-0.696021\pi$
$919$		−	1.37883e6i		−	1.63260i	0.577626	−	0.816301i	$-0.303979\pi$
$920$	−9576.76	+	1.75881e6i	−0.0113147	+	2.07799i
$921$	−369524.	−	318811.i	−0.435636	−	0.375849i
$922$	41172.4	−	231048.i	0.0484334	−	0.271794i
$923$	339597.	+	196066.i	0.398621	+	0.230144i
$924$	−350486.	+	194323.i	−0.410513	+	0.227604i
$925$	−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	$0.784873\pi$
$930$	−263392.	+	214127.i	−0.304535	+	0.247574i
$931$	−288946.	−	166823.i	−0.333363	−	0.192467i
$932$	−6279.14	−	36382.6i	−0.00722883	−	0.0418853i
$933$	−1.15548e6	+	402691.i	−1.32739	+	0.462603i
$934$	−388273.	+	461023.i	−0.445085	+	0.528481i
$935$		−	1.56506e6i		−	1.79022i
$936$	−360750.	+	283021.i	−0.411770	+	0.323047i
$937$	1.29656e6			1.47677			0.738384	−	0.674380i	$-0.235589\pi$
$937$	1.29656e6			1.47677			0.738384	+	0.674380i	$0.235589\pi$
$938$	−555246.	−	467627.i	−0.631073	−	0.531488i
$939$	1.45336e6	+	276883.i	1.64832	+	0.314026i
$940$	−508978.	+	87842.7i	−0.576027	+	0.0994146i
$941$	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	$0.0900209\pi$
$942$	520741.	−	1.36438e6i	0.586840	−	1.53756i
$943$	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	$-0.483615\pi$
$947$	844845.	−	487772.i	0.942057	−	0.543897i	0.890605	+	0.454779i	$0.150282\pi$
$948$	253352.	+	4397.12i	0.281908	+	0.00489274i
$949$	−86379.8	+	149614.i	−0.0959135	+	0.166127i
$950$	−145841.	−	25988.7i	−0.161597	−	0.0287964i
$951$	1.06639e6	+	203161.i	1.17911	+	0.224636i
$952$	4506.24	−	827589.i	0.00497211	−	0.913147i
$953$	1.52194e6			1.67576			0.837878	−	0.545857i	$-0.183796\pi$
$953$	1.52194e6			1.67576			0.837878	+	0.545857i	$0.183796\pi$
$954$	−193725.	+	313953.i	−0.212857	+	0.344959i
$955$			538502.i			0.590447i
$956$	421201.	−	1.14430e6i	0.460865	−	1.25206i
$957$	731576.	−	254957.i	0.798795	−	0.278384i
$958$	−217492.	−	38756.9i	−0.236981	−	0.0422297i
$959$	108877.	+	62860.3i	0.118386	+	0.0683501i
$960$	697595.	−	790980.i	0.756939	−	0.858268i
$961$	−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
$966$	−875777.	+	140428.i	−0.938511	+	0.150488i
$967$	1.31627e6	+	759947.i	1.40764	+	0.812700i	0.995160	−	0.0982670i	$-0.0313299\pi$
$967$	1.31627e6	+	759947.i	1.40764	+	0.812700i	0.412478	+	0.910967i	$0.364663\pi$
$968$	90901.4	+	159445.i	0.0970108	+	0.170161i
$969$	−657588.	−	567341.i	−0.700336	−	0.604222i
$970$	−192722.	−	162310.i	−0.204827	−	0.172505i
$971$		−	606895.i		−	0.643687i	−0.946793	−	0.321844i	$-0.895697\pi$
$971$		−	606895.i		−	0.643687i	0.946793	−	0.321844i	$-0.104303\pi$
$972$	916160.	+	230797.i	0.969703	+	0.244286i
$973$	221881.			0.234366
$974$	−7667.21	+	9103.82i	−0.00808201	+	0.00959634i
$975$	100615.	−	116620.i	0.105841	−	0.122678i
$976$	−1.09142e6	−	929395.i	−1.14576	−	0.975665i
$977$	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	$0.0140764\pi$
$978$	−39173.9	−	244306.i	−0.0409561	−	0.255421i
$979$	−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	$0.710576\pi$
$983$	−1.55074e6	+	895318.i	−1.60484	+	0.926553i	−0.990501	+	0.137509i	$0.956091\pi$
$984$	−597107.	−	117129.i	−0.616683	−	0.120969i
$985$	−309695.	+	536407.i	−0.319199	+	0.552869i
$986$	−280681.	+	1.57510e6i	−0.288708	+	1.62015i
$987$	−85717.7	−	245959.i	−0.0879906	−	0.252481i
$988$	−93567.6	+	254200.i	−0.0958543	+	0.260413i
$989$	−3.20275e6			−3.27439
$990$	855937.	+	528156.i	0.873316	+	0.538879i
$991$			1.12180e6i			1.14227i	0.820858	+	0.571133i	$0.193496\pi$
$991$			1.12180e6i			1.14227i	−0.820858	+	0.571133i	$0.806504\pi$
$992$	−214582.	−	260493.i	−0.218057	−	0.264712i
$993$	−194846.	+	1.02275e6i	−0.197603	+	1.03722i
$994$	79795.9	−	447791.i	0.0807621	−	0.453213i
$995$	−625885.	−	361355.i	−0.632191	−	0.364996i
$996$	−435853.	−	7564.58i	−0.439361	−	0.00762546i
$997$	−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.31.5	yes	44
3.2	odd	2		108.5.f.a.91.18		44
4.3	odd	2	inner	36.5.f.a.31.10	yes	44
9.2	odd	6		108.5.f.a.19.13		44
9.4	even	3		324.5.d.f.163.19		22
9.5	odd	6		324.5.d.e.163.4		22
9.7	even	3	inner	36.5.f.a.7.10	yes	44
12.11	even	2		108.5.f.a.91.13		44
36.7	odd	6	inner	36.5.f.a.7.5	✓	44
36.11	even	6		108.5.f.a.19.18		44
36.23	even	6		324.5.d.e.163.3		22
36.31	odd	6		324.5.d.f.163.20		22

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-3.05951 - 2.57671i) q^{2} +(-5.87916 + 6.81436i) q^{3} +(2.72116 + 15.7669i) q^{4} +(14.3046 - 24.7763i) q^{5} +(35.5459 - 5.69969i) q^{6} +(22.2124 - 12.8243i) q^{7} +(32.3013 - 55.2506i) q^{8} +(-11.8710 - 80.1254i) q^{9} +O(q^{10})\)	\(q+(-3.05951 - 2.57671i) q^{2} +(-5.87916 + 6.81436i) q^{3} +(2.72116 + 15.7669i) q^{4} +(14.3046 - 24.7763i) q^{5} +(35.5459 - 5.69969i) 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} +(-123.439 - 74.1532i) q^{12} +(44.2246 - 76.5993i) q^{13} +(-101.004 - 17.9987i) q^{14} +(84.7356 + 243.141i) q^{15} +(-241.191 + 85.8084i) q^{16} +504.169 q^{17} +(-170.140 + 275.732i) q^{18} +191.405i q^{19} +(429.571 + 158.119i) q^{20} +(-43.2006 + 226.760i) q^{21} +(-427.287 - 76.1421i) q^{22} +(-831.897 - 480.296i) q^{23} +(186.593 + 544.940i) 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} +(367.254 - 962.230i) q^{30} +(-285.428 - 164.792i) q^{31} +(959.027 + 358.946i) q^{32} +(-182.757 + 959.288i) q^{33} +(-1542.51 - 1299.10i) q^{34} -733.789i q^{35} +(1231.03 - 405.202i) q^{36} +209.943 q^{37} +(493.194 - 585.604i) q^{38} +(261.971 + 751.702i) q^{39} +(-906.848 - 1590.65i) q^{40} +(-528.200 + 914.869i) q^{41} +(716.466 - 582.457i) 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} +(833.269 - 2148.04i) q^{48} +(-871.573 + 1509.61i) q^{49} +(-135.779 + 761.951i) q^{50} +(-2964.09 + 3435.59i) q^{51} +(1328.08 + 488.847i) q^{52} +1138.62 q^{53} +(-878.655 - 2780.47i) q^{54} -3104.23i q^{55} +(8.93796 - 1641.49i) q^{56} +(-1304.30 - 1125.30i) q^{57} +(-556.720 + 3124.15i) q^{58} +(-4037.49 - 2331.05i) q^{59} +(-3603.00 + 1997.64i) 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} +(3030.95 - 2464.04i) q^{66} +(6127.74 + 3537.85i) q^{67} +(1371.92 + 7949.19i) q^{68} +(8163.76 - 2845.11i) q^{69} +(-1890.76 + 2245.03i) q^{70} +4433.42i q^{71} +(-4810.42 - 1932.28i) q^{72} -1953.21 q^{73} +(-642.322 - 540.962i) q^{74} +(1710.63 + 325.897i) q^{75} +(-3017.86 + 520.842i) q^{76} +(1391.50 - 2410.15i) q^{77} +(1135.41 - 2974.86i) 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} +(-3692.85 - 64.0924i) q^{84} +(7211.95 - 12491.5i) q^{85} +(-13129.7 - 2339.71i) q^{86} +(7013.92 + 1336.24i) q^{87} +(37.8113 - 6944.19i) q^{88} -559.336 q^{89} +(4397.84 + 8159.70i) q^{90} -2268.61i q^{91} +(5309.06 - 14423.4i) q^{92} +(2801.03 - 976.170i) q^{93} +(4443.42 + 791.814i) q^{94} +(4742.31 + 2737.97i) q^{95} +(-8084.26 + 4424.85i) 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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