LMFDB - Embedded newform 36.5.f.a.7.5

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			7.5
Character	$\chi$	$=$	36.7
Dual form			36.5.f.a.31.5

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

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

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 $

$2$	−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	0.996341	+	0.0854642i	$0.0272373\pi$
$5$	14.3046	+	24.7763i	0.572185	+	0.991053i	−0.424156	+	0.905589i	$0.639429\pi$
$6$	35.5459	+	5.69969i	0.987387	+	0.158325i
$7$	22.2124	+	12.8243i	0.453314	+	0.261721i	0.709229	−	0.704978i	$-0.249043\pi$
$7$	22.2124	+	12.8243i	0.453314	+	0.261721i	−0.255915	+	0.966699i	$0.582377\pi$
$8$	32.3013	+	55.2506i	0.504708	+	0.863290i
$9$	−11.8710	+	80.1254i	−0.146555	+	0.989203i
$10$	−107.606	−	38.9445i	−1.07606	−	0.389445i
$11$	93.9677	+	54.2523i	0.776593	+	0.448366i	0.835221	−	0.549914i	$-0.185339\pi$
$11$	93.9677	+	54.2523i	0.776593	+	0.448366i	−0.0586287	+	0.998280i	$0.518673\pi$
$12$	−123.439	+	74.1532i	−0.857218	+	0.514953i
$13$	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	$0.749055\pi$
$14$	−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	$-0.914594\pi$
$19$		−	191.405i		−	0.530207i	0.964220	−	0.265104i	$-0.0854062\pi$
$20$	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	−0.576733	+	0.816933i	$0.695673\pi$
$23$	−831.897	+	480.296i	−1.57258	+	0.907932i	−0.995851	+	0.0909988i	$0.970994\pi$
$24$	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	−0.999475	−	0.0324147i	$-0.989680\pi$
$29$	−396.671	+	687.053i	−0.471665	+	0.816948i	0.527809	+	0.849363i	$0.323014\pi$
$30$	367.254	+	962.230i	0.408060	+	1.06914i
$31$	−285.428	+	164.792i	−0.297011	+	0.171480i	−0.641099	−	0.767458i	$-0.721521\pi$
$31$	−285.428	+	164.792i	−0.297011	+	0.171480i	0.344088	+	0.938937i	$0.388188\pi$
$32$	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	0.665053	−	0.746796i	$-0.268409\pi$
$41$	−528.200	−	914.869i	−0.314218	−	0.544241i	−0.979271	+	0.202555i	$0.935076\pi$
$42$	716.466	+	582.457i	0.406160	+	0.330191i
$43$	2887.45	+	1667.07i	1.56163	+	0.901608i	0.997093	+	0.0762001i	$0.0242788\pi$
$43$	2887.45	+	1667.07i	1.56163	+	0.901608i	0.564537	+	0.825407i	$0.309055\pi$
$44$	1111.09	−	1333.95i	0.573911	−	0.689024i
$45$	−2155.02	+	852.045i	−1.06421	+	0.420763i
$46$	1307.61	−	3613.02i	0.617964	−	1.70748i
$47$	−977.185	−	564.178i	−0.442365	−	0.255400i	0.262235	−	0.965004i	$-0.415540\pi$
$47$	−977.185	−	564.178i	−0.442365	−	0.255400i	−0.704600	+	0.709604i	$0.748874\pi$
$48$	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	−0.951272	−	0.308354i	$-0.900222\pi$
$59$	−4037.49	+	2331.05i	−1.15987	+	0.669648i	−0.208593	+	0.978002i	$0.566889\pi$
$60$	−3603.00	−	1997.64i	−1.00083	−	0.554901i
$61$	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
$66$	3030.95	+	2464.04i	0.695810	+	0.565665i
$67$	6127.74	−	3537.85i	1.36506	−	0.788116i	0.374764	−	0.927120i	$-0.377724\pi$
$67$	6127.74	−	3537.85i	1.36506	−	0.788116i	0.990292	+	0.139004i	$0.0443902\pi$
$68$	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	$-0.855072\pi$
$71$		−	4433.42i		−	0.879472i	0.898127	−	0.439736i	$-0.144928\pi$
$72$	−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	0.372918	−	0.927864i	$-0.378357\pi$
$79$	−1523.90	−	879.826i	−0.244176	−	0.140975i	−0.617095	+	0.786889i	$0.711690\pi$
$80$	−1324.12	−	7203.27i	−0.206894	−	1.12551i
$81$	−6279.16	−	1902.33i	−0.957043	−	0.289945i
$82$	3973.38	+	1438.03i	0.590925	+	0.213865i
$83$	2621.64	+	1513.61i	0.380555	+	0.219714i	0.678060	−	0.735007i	$-0.262821\pi$
$83$	2621.64	+	1513.61i	0.380555	+	0.219714i	−0.297505	+	0.954720i	$0.596154\pi$
$84$	−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	−0.801575	−	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	$0.155249\pi$
$102$	17921.2	+	2873.61i	1.72253	+	0.276202i
$103$	−8533.78	+	4926.98i	−0.804391	+	0.464415i	−0.845004	−	0.534760i	$-0.820402\pi$
$103$	−8533.78	+	4926.98i	−0.804391	+	0.464415i	0.0406134	+	0.999175i	$0.487069\pi$
$104$	−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	$-0.988812\pi$
$107$		−	804.642i		−	0.0702806i	0.999382	−	0.0351403i	$-0.0111878\pi$
$108$	−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	−0.977489	−	0.210988i	$-0.932332\pi$
$113$	−8573.94	−	14850.5i	−0.671465	−	1.16301i	0.306024	−	0.952024i	$-0.401001\pi$
$114$	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	$-0.903901\pi$
$127$		−	9591.51i		−	0.594675i	0.954772	−	0.297337i	$-0.0960986\pi$
$128$	−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	−0.381004	−	0.924573i	$-0.624422\pi$
$131$	3933.27	−	2270.88i	0.229198	−	0.132328i	0.610202	+	0.792246i	$0.291088\pi$
$132$	−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	−0.793321	−	0.608803i	$-0.791650\pi$
$137$	2450.82	−	4244.95i	0.130578	−	0.226168i	0.923900	+	0.382635i	$0.124983\pi$
$138$	−32308.1	+	12331.0i	−1.69650	+	0.647501i
$139$	7491.80	−	4325.39i	0.387754	−	0.223870i	−0.293432	−	0.955980i	$-0.594798\pi$
$139$	7491.80	−	4325.39i	0.387754	−	0.223870i	0.681187	+	0.732110i	$0.261464\pi$
$140$	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	0.972818	−	0.231570i	$-0.0743863\pi$
$149$	6346.46	+	10992.4i	0.285863	+	0.495130i	−0.686955	+	0.726700i	$0.741053\pi$
$150$	−4393.94	+	5404.88i	−0.195286	+	0.240217i
$151$	−11055.3	−	6382.78i	−0.484860	−	0.279934i	0.237579	−	0.971368i	$-0.423646\pi$
$151$	−11055.3	−	6382.78i	−0.484860	−	0.279934i	−0.722440	+	0.691434i	$0.756979\pi$
$152$	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	0.903534	+	0.428516i	$0.140963\pi$
$157$	20283.0	+	35131.2i	0.822873	+	1.42526i	−0.0806612	+	0.996742i	$0.525703\pi$
$158$	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	$0.0412865\pi$
$163$			6872.98i			0.258684i	−0.991600	+	0.129342i	$0.958713\pi$
$164$	−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	0.156595	−	0.987663i	$-0.449948\pi$
$167$	30405.5	−	17554.6i	1.09023	−	0.629447i	0.933639	+	0.358216i	$0.116615\pi$
$168$	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	−0.889870	−	0.456214i	$-0.849205\pi$
$173$	−1491.72	+	2583.74i	−0.0498420	+	0.0863290i	0.840028	+	0.542543i	$0.182538\pi$
$174$	−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	$-0.750797\pi$
$179$		−	45199.3i		−	1.41067i	0.708874	−	0.705335i	$-0.249203\pi$
$180$	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	0.259659	−	0.965700i	$-0.416390\pi$
$191$	−16300.9	−	9411.33i	−0.446833	−	0.257979i	−0.706492	+	0.707721i	$0.749723\pi$
$192$	36135.4	−	7292.92i	0.980236	−	0.197833i
$193$	−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	$0.873838\pi$
$194$	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	$0.103330\pi$
$199$			25261.4i			0.637898i	−0.947772	+	0.318949i	$0.896670\pi$
$200$	−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	−0.275396	−	0.961331i	$-0.588809\pi$
$211$	18674.0	−	10781.5i	0.419443	−	0.242166i	0.694839	+	0.719165i	$0.255476\pi$
$212$	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	0.658507	−	0.752575i	$-0.271188\pi$
$223$	16709.5	+	9647.22i	0.336011	+	0.193996i	−0.322496	+	0.946571i	$0.604522\pi$
$224$	25905.5	+	4325.83i	0.516293	+	0.0862130i
$225$	−12277.8	−	9740.84i	−0.242525	−	0.192412i
$226$	64497.4	+	23342.7i	1.26277	+	0.457018i
$227$	−56144.4	−	32415.0i	−1.08957	−	0.629063i	−0.156107	−	0.987740i	$-0.549895\pi$
$227$	−56144.4	−	32415.0i	−1.08957	−	0.629063i	−0.933462	+	0.358677i	$0.883228\pi$
$228$	14193.3	+	23626.9i	0.273032	+	0.454503i
$229$	−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	$0.955102\pi$
$230$	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	−0.950206	−	0.311623i	$-0.899128\pi$
$239$	−65999.7	+	38104.9i	−1.15544	+	0.667091i	−0.205230	+	0.978714i	$0.565794\pi$
$240$	−41301.0	+	51372.3i	−0.717031	+	0.891879i
$241$	−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
$246$	−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	$0.0865334\pi$
$251$			33833.6i			0.537033i	−0.963275	+	0.268517i	$0.913467\pi$
$252$	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	0.997347	−	0.0727940i	$-0.0231916\pi$
$257$	28773.1	+	49836.4i	0.435632	+	0.754537i	−0.561715	+	0.827331i	$0.689858\pi$
$258$	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	0.903288	−	0.429034i	$-0.141146\pi$
$263$	68019.2	+	39270.9i	0.983378	+	0.567753i	0.0800895	+	0.996788i	$0.474479\pi$
$264$	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	$0.263312\pi$
$271$			108113.i			1.47211i	−0.676924	+	0.736053i	$0.736688\pi$
$272$	−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	−0.686588	−	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	$0.271065\pi$
$282$	−31519.3	−	25623.9i	−0.396350	−	0.322216i
$283$	22858.8	−	13197.5i	0.285418	−	0.164786i	−0.350456	−	0.936579i	$-0.613973\pi$
$283$	22858.8	−	13197.5i	0.285418	−	0.164786i	0.635873	+	0.771793i	$0.280640\pi$
$284$	−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	−0.941949	−	0.335757i	$-0.891008\pi$
$293$	−65395.3	−	113268.i	−0.761748	−	1.31939i	0.180201	−	0.983630i	$-0.442325\pi$
$294$	−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	$-0.907116\pi$
$307$		−	54227.3i		−	0.575362i	0.957726	−	0.287681i	$-0.0928843\pi$
$308$	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	0.253013	−	0.967463i	$-0.418578\pi$
$311$	117745.	−	67980.1i	1.21737	−	0.702847i	0.964354	+	0.264616i	$0.0852451\pi$
$312$	49994.0	−	9806.89i	0.513581	−	0.100745i
$313$	−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	$0.961770\pi$
$318$	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	0.881848	−	0.471534i	$-0.156299\pi$
$331$	100184.	+	57841.2i	0.914412	+	0.527936i	0.0325639	+	0.999470i	$0.489633\pi$
$332$	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	−0.900746	−	0.434347i	$-0.856979\pi$
$337$	−93868.0	−	162584.i	−0.826528	−	1.43159i	0.0742175	−	0.997242i	$-0.476354\pi$
$338$	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	−0.900065	−	0.435756i	$-0.856481\pi$
$347$	−117124.	+	67621.8i	−0.972721	+	0.561601i	−0.0726566	+	0.997357i	$0.523148\pi$
$348$	−1982.45	−	114224.i	−0.0163698	−	0.943189i
$349$	−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	$0.221517\pi$
$354$	−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	$-0.761072\pi$
$359$		−	175816.i		−	1.36418i	0.731270	−	0.682088i	$-0.238928\pi$
$360$	−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	0.525277	−	0.850932i	$-0.323962\pi$
$367$	6867.31	+	3964.84i	0.0509864	+	0.0294370i	−0.474290	+	0.880369i	$0.657295\pi$
$368$	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	−0.844001	−	0.536342i	$-0.819806\pi$
$373$	−123336.	−	213624.i	−0.886486	−	1.53544i	−0.0424851	−	0.999097i	$-0.513527\pi$
$374$	−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	$-0.828474\pi$
$379$		−	147423.i		−	1.02633i	0.858291	−	0.513163i	$-0.171526\pi$
$380$	−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	−0.0932341	−	0.995644i	$-0.529720\pi$
$383$	105968.	−	61180.9i	0.722402	−	0.417079i	0.815636	+	0.578565i	$0.196387\pi$
$384$	−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	−0.385682	−	0.922632i	$-0.626034\pi$
$389$	91728.1	−	158878.i	0.606182	−	1.04994i	0.991863	−	0.127306i	$-0.0406330\pi$
$390$	−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	−0.988440	−	0.151610i	$-0.951554\pi$
$401$	−100584.	−	174217.i	−0.625518	−	1.08343i	0.362922	−	0.931820i	$-0.381779\pi$
$402$	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	0.995976	−	0.0896241i	$-0.0285666\pi$
$409$	70320.1	+	121798.i	0.420371	+	0.728104i	−0.575605	+	0.817728i	$0.695233\pi$
$410$	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	−0.0704785	−	0.997513i	$-0.522453\pi$
$419$	133102.	−	76846.6i	0.758154	−	0.437720i	0.828633	+	0.559793i	$0.189119\pi$
$420$	−54412.8	−	90578.5i	−0.308463	−	0.513483i
$421$	−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
$426$	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	$0.172453\pi$
$431$			191579.i			1.03132i	−0.856793	+	0.515660i	$0.827547\pi$
$432$	−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	0.461679	−	0.887047i	$-0.347247\pi$
$439$	−14586.4	−	8421.44i	−0.0756864	−	0.0436976i	−0.537366	+	0.843349i	$0.680580\pi$
$440$	−171511.	+	100271.i	−0.885902	+	0.517928i
$441$	131304.	−	51914.6i	0.675153	−	0.266939i
$442$	−167727.	−	60703.0i	−0.858534	−	0.310718i
$443$	−140111.	−	80892.9i	−0.713943	−	0.412195i	0.0985761	−	0.995130i	$-0.468571\pi$
$443$	−140111.	−	80892.9i	−0.713943	−	0.412195i	−0.812519	+	0.582934i	$0.801905\pi$
$444$	−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	−0.842582	−	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	$0.122587\pi$
$462$	35725.0	+	93602.0i	0.167374	+	0.438532i
$463$	41167.7	−	23768.2i	0.192041	−	0.110875i	−0.400897	−	0.916123i	$-0.631301\pi$
$463$	41167.7	−	23768.2i	0.192041	−	0.110875i	0.592938	+	0.805248i	$0.297968\pi$
$464$	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	$0.112280\pi$
$467$			150686.i			0.690936i	−0.938431	+	0.345468i	$0.887720\pi$
$468$	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	0.600598	−	0.799551i	$-0.294929\pi$
$479$	47830.3	+	27614.8i	0.208464	+	0.120357i	−0.392133	+	0.919908i	$0.628263\pi$
$480$	−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	$0.00199681\pi$
$487$			2975.59i			0.0125463i	−0.999980	+	0.00627313i	$0.998003\pi$
$488$	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	−0.899987	−	0.435916i	$-0.856424\pi$
$491$	−234443.	+	135356.i	−0.972467	+	0.561454i	−0.0724794	+	0.997370i	$0.523091\pi$
$492$	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	0.0288827	−	0.999583i	$-0.490805\pi$
$499$	226339.	−	130677.i	0.908988	−	0.524805i	0.880105	+	0.474778i	$0.157472\pi$
$500$	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	$0.188924\pi$
$503$			283008.i			1.11857i	−0.828976	+	0.559284i	$0.811076\pi$
$504$	−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	0.995149	−	0.0983769i	$-0.0313651\pi$
$509$	106839.	+	185051.i	0.412378	+	0.714259i	−0.582772	+	0.812636i	$0.698032\pi$
$510$	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	$0.139143\pi$
$523$			231592.i			0.846681i	−0.905971	+	0.423340i	$0.860857\pi$
$524$	−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	0.999852	−	0.0171904i	$-0.00547213\pi$
$547$	444293.	+	256513.i	1.48489	+	0.857302i	0.485039	+	0.874493i	$0.338805\pi$
$548$	−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	−0.421640	−	0.906763i	$-0.638545\pi$
$563$	48439.2	−	27966.4i	0.152820	−	0.0882307i	0.574460	+	0.818533i	$0.305212\pi$
$564$	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	0.326111	+	0.945331i	$0.394262\pi$
$569$	−212266.	+	367655.i	−0.655625	+	1.13558i	−0.981737	+	0.190245i	$0.939072\pi$
$570$	184175.	−	70294.1i	0.566868	−	0.216356i
$571$	25297.4	−	14605.5i	0.0775897	−	0.0447964i	−0.460703	−	0.887554i	$-0.652403\pi$
$571$	25297.4	−	14605.5i	0.0775897	−	0.0447964i	0.538293	+	0.842758i	$0.319069\pi$
$572$	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	0.166461	−	0.986048i	$-0.446766\pi$
$587$	−208206.	−	120208.i	−0.604251	−	0.348865i	−0.770712	+	0.637183i	$0.780099\pi$
$588$	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	−0.487870	−	0.872917i	$-0.662226\pi$
$599$	8669.92	−	5005.58i	0.0241636	−	0.0139509i	0.512033	+	0.858966i	$0.328892\pi$
$600$	73261.6	+	83986.4i	0.203504	+	0.233295i
$601$	−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
$606$	16615.8	−	20438.7i	0.0452456	−	0.0556554i
$607$	375426.	−	216752.i	1.01894	−	0.588283i	0.105141	−	0.994457i	$-0.466471\pi$
$607$	375426.	−	216752.i	1.01894	−	0.588283i	0.913796	+	0.406174i	$0.133137\pi$
$608$	−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	0.707407	−	0.706806i	$-0.249865\pi$
$617$	−98373.3	−	170388.i	−0.258409	−	0.447577i	−0.965816	+	0.259229i	$0.916531\pi$
$618$	−331424.	+	126494.i	−0.867774	+	0.331203i
$619$	−536199.	−	309575.i	−1.39941	−	0.807949i	−0.405078	−	0.914282i	$-0.632756\pi$
$619$	−536199.	−	309575.i	−1.39941	−	0.807949i	−0.994331	+	0.106333i	$0.966089\pi$
$620$	−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	$-0.873256\pi$
$631$		−	308766.i		−	0.775479i	0.921769	−	0.387740i	$-0.126744\pi$
$632$	−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	−0.578935	−	0.815373i	$-0.696532\pi$
$641$	171200.	−	296528.i	0.416666	−	0.721687i	0.995602	+	0.0936860i	$0.0298650\pi$
$642$	4586.21	−	28601.8i	0.0111272	−	0.0693941i
$643$	−478867.	+	276474.i	−1.15823	+	0.668702i	−0.950878	−	0.309566i	$-0.899816\pi$
$643$	−478867.	+	276474.i	−1.15823	+	0.668702i	−0.207347	+	0.978267i	$0.566483\pi$
$644$	−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	$0.241935\pi$
$647$			576814.i			1.37793i	−0.724794	+	0.688965i	$0.758065\pi$
$648$	−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	0.977169	+	0.212463i	$0.0681484\pi$
$653$	286795.	+	496744.i	0.672583	+	1.16495i	−0.304586	+	0.952485i	$0.598518\pi$
$654$	−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	0.114125	−	0.993466i	$-0.463594\pi$
$659$	−299298.	−	172800.i	−0.689180	−	0.397899i	−0.803305	+	0.595568i	$0.796927\pi$
$660$	−230189.	−	383185.i	−0.528441	−	0.879671i
$661$	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	$0.692083\pi$
$662$	−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	−0.353503	−	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	$0.157089\pi$
$678$	−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	$-0.999646\pi$
$683$		−	1038.30i		−	0.00222578i	0.999999	−	0.00111289i	$-0.000354244\pi$
$684$	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	0.165411	−	0.986225i	$-0.447105\pi$
$691$	−289343.	−	167052.i	−0.605978	−	0.349862i	−0.771390	+	0.636363i	$0.780438\pi$
$692$	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	0.239456	+	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
$714$	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	$-0.826366\pi$
$719$		−	536436.i		−	1.03767i	0.854874	−	0.518836i	$-0.173634\pi$
$720$	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	0.100395	−	0.994948i	$-0.467989\pi$
$727$	−375814.	−	216977.i	−0.711057	−	0.410529i	−0.811452	+	0.584418i	$0.801323\pi$
$728$	−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	0.958456	+	0.285241i	$0.0920735\pi$
$733$	390208.	+	675860.i	0.726254	+	1.25791i	−0.232202	+	0.972667i	$0.574593\pi$
$734$	−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	$0.0631112\pi$
$739$			215142.i			0.393947i	−0.980409	+	0.196973i	$0.936889\pi$
$740$	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	−0.709312	−	0.704895i	$-0.750994\pi$
$743$	−250360.	+	144546.i	−0.453511	+	0.261835i	0.255801	+	0.966730i	$0.417661\pi$
$744$	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	−0.923104	−	0.384551i	$-0.874356\pi$
$751$	−593117.	+	342436.i	−1.05162	+	0.607156i	−0.128521	+	0.991707i	$0.541023\pi$
$752$	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	−0.980074	−	0.198631i	$-0.936350\pi$
$761$	−383411.	−	664087.i	−0.662057	−	1.14672i	0.318018	−	0.948085i	$-0.396983\pi$
$762$	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	0.999936	−	0.0113137i	$-0.00360135\pi$
$769$	289867.	+	502065.i	0.490170	+	0.848999i	−0.509766	+	0.860313i	$0.670268\pi$
$770$	−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	0.470633	−	0.882329i	$-0.344026\pi$
$787$	910515.	−	525686.i	1.47007	−	0.848744i	0.999436	+	0.0335849i	$0.0106924\pi$
$788$	−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	0.900928	−	0.433969i	$-0.142887\pi$
$797$	47409.2	+	82115.1i	0.0746356	+	0.129273i	−0.826292	+	0.563242i	$0.809554\pi$
$798$	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	$0.144594\pi$
$811$			577209.i			0.877589i	−0.898587	+	0.438794i	$0.855406\pi$
$812$	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	−0.452706	−	0.891660i	$-0.649541\pi$
$821$	367923.	−	637262.i	0.545847	−	0.945435i	0.998553	−	0.0537749i	$-0.0171253\pi$
$822$	111312.	−	136922.i	0.164739	−	0.202642i
$823$	148172.	−	85547.4i	0.218760	−	0.126301i	−0.386616	−	0.922241i	$-0.626356\pi$
$823$	148172.	−	85547.4i	0.218760	−	0.126301i	0.605376	+	0.795940i	$0.293023\pi$
$824$	−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	$0.274533\pi$
$827$			1.03882e6i			1.51890i	−0.650563	+	0.759452i	$0.725467\pi$
$828$	−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	0.111976	−	0.993711i	$-0.464282\pi$
$839$	−487546.	−	281485.i	−0.692615	−	0.399881i	−0.804591	+	0.593830i	$0.797615\pi$
$840$	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	−0.543243	−	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	$0.886191\pi$
$858$	−54700.8	+	341140.i	−0.0743052	+	0.463402i
$859$	−347489.	+	200623.i	−0.470928	+	0.271890i	−0.716628	−	0.697456i	$-0.754315\pi$
$859$	−347489.	+	200623.i	−0.470928	+	0.271890i	0.245700	+	0.969346i	$0.420982\pi$
$860$	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	$-0.692839\pi$
$863$		−	1.22445e6i		−	1.64407i	0.569437	−	0.822035i	$-0.307161\pi$
$864$	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	0.819977	−	0.572397i	$-0.193986\pi$
$877$	−65931.0	−	114196.i	−0.0857216	−	0.148474i	−0.905698	+	0.423922i	$0.860653\pi$
$878$	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	$0.0478560\pi$
$883$			233561.i			0.299557i	−0.988720	+	0.149778i	$0.952144\pi$
$884$	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	−0.809023	−	0.587777i	$-0.800003\pi$
$887$	−554282.	+	320015.i	−0.704504	+	0.406746i	0.104519	+	0.994523i	$0.466670\pi$
$888$	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	0.712472	−	0.701700i	$-0.247575\pi$
$907$	379256.	+	218964.i	0.461018	+	0.266169i	−0.251454	+	0.967869i	$0.580909\pi$
$908$	−663862.	+	797017.i	−0.805204	+	0.966710i
$909$	46429.0	+	36835.2i	0.0561903	+	0.0445796i
$910$	88349.7	−	244116.i	0.106690	−	0.294791i
$911$	−666090.	−	384567.i	−0.802594	−	0.463378i	0.0417834	−	0.999127i	$-0.486696\pi$
$911$	−666090.	−	384567.i	−0.802594	−	0.463378i	−0.844377	+	0.535749i	$0.820029\pi$
$912$	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	$0.303979\pi$
$919$			1.37883e6i			1.63260i	−0.577626	+	0.816301i	$0.696021\pi$
$920$	−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	−0.780181	−	0.625554i	$-0.784873\pi$
$929$	130885.	−	226699.i	0.151656	−	0.262675i	0.931836	+	0.362879i	$0.118206\pi$
$930$	−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	0.960275	−	0.279054i	$-0.0900209\pi$
$941$	211160.	+	365741.i	0.238470	+	0.413042i	−0.721806	+	0.692096i	$0.756688\pi$
$942$	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	0.890605	−	0.454779i	$-0.150282\pi$
$947$	844845.	+	487772.i	0.942057	+	0.543897i	0.0514525	+	0.998675i	$0.483615\pi$
$948$	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	0.412478	−	0.910967i	$-0.364663\pi$
$967$	1.31627e6	−	759947.i	1.40764	−	0.812700i	0.995160	+	0.0982670i	$0.0313299\pi$
$968$	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	$0.104303\pi$
$971$			606895.i			0.643687i	−0.946793	+	0.321844i	$0.895697\pi$
$972$	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	0.999022	−	0.0442080i	$-0.0140764\pi$
$977$	440254.	+	762542.i	0.461226	+	0.798867i	−0.537796	+	0.843075i	$0.680743\pi$
$978$	−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	−0.990501	−	0.137509i	$-0.956091\pi$
$983$	−1.55074e6	−	895318.i	−1.60484	−	0.926553i	−0.614336	−	0.789044i	$-0.710576\pi$
$984$	−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	$-0.806504\pi$
$991$		−	1.12180e6i		−	1.14227i	0.820858	−	0.571133i	$-0.193496\pi$
$992$	−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	−0.996243	−	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.7.5	✓	44
3.2	odd	2		108.5.f.a.19.18		44
4.3	odd	2	inner	36.5.f.a.7.10	yes	44
9.2	odd	6		324.5.d.e.163.3		22
9.4	even	3	inner	36.5.f.a.31.10	yes	44
9.5	odd	6		108.5.f.a.91.13		44
9.7	even	3		324.5.d.f.163.20		22
12.11	even	2		108.5.f.a.19.13		44
36.7	odd	6		324.5.d.f.163.19		22
36.11	even	6		324.5.d.e.163.4		22
36.23	even	6		108.5.f.a.91.18		44
36.31	odd	6	inner	36.5.f.a.31.5	yes	44

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-3.05951 + 2.57671i) q^{2} +(-5.87916 - 6.81436i) q^{3} +(2.72116 - 15.7669i) q^{4} +(14.3046 + 24.7763i) q^{5} +(35.5459 + 5.69969i) q^{6} +(22.2124 + 12.8243i) q^{7} +(32.3013 + 55.2506i) q^{8} +(-11.8710 + 80.1254i) q^{9} +O(q^{10})\)	\(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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more