LMFDB - Embedded newform 5.5.c.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,5,Mod(2,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("5.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	5.c (of order $4$, 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:	$0.516849815419$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	5.2
Dual form			5.5.c.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +(-6.00000 + 6.00000i) q^{3} -14.0000i q^{4} +(20.0000 + 15.0000i) q^{5} +12.0000 q^{6} +(-26.0000 - 26.0000i) q^{7} +(-30.0000 + 30.0000i) q^{8} +9.00000i q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +(-6.00000 + 6.00000i) q^{3} -14.0000i q^{4} +(20.0000 + 15.0000i) q^{5} +12.0000 q^{6} +(-26.0000 - 26.0000i) q^{7} +(-30.0000 + 30.0000i) q^{8} +9.00000i q^{9} +(-5.00000 - 35.0000i) q^{10} -8.00000 q^{11} +(84.0000 + 84.0000i) q^{12} +(139.000 - 139.000i) q^{13} +52.0000i q^{14} +(-210.000 + 30.0000i) q^{15} -164.000 q^{16} +(-1.00000 - 1.00000i) q^{17} +(9.00000 - 9.00000i) q^{18} +180.000i q^{19} +(210.000 - 280.000i) q^{20} +312.000 q^{21} +(8.00000 + 8.00000i) q^{22} +(-166.000 + 166.000i) q^{23} -360.000i q^{24} +(175.000 + 600.000i) q^{25} -278.000 q^{26} +(-540.000 - 540.000i) q^{27} +(-364.000 + 364.000i) q^{28} -480.000i q^{29} +(240.000 + 180.000i) q^{30} +572.000 q^{31} +(644.000 + 644.000i) q^{32} +(48.0000 - 48.0000i) q^{33} +2.00000i q^{34} +(-130.000 - 910.000i) q^{35} +126.000 q^{36} +(-251.000 - 251.000i) q^{37} +(180.000 - 180.000i) q^{38} +1668.00i q^{39} +(-1050.00 + 150.000i) q^{40} -1688.00 q^{41} +(-312.000 - 312.000i) q^{42} +(1474.00 - 1474.00i) q^{43} +112.000i q^{44} +(-135.000 + 180.000i) q^{45} +332.000 q^{46} +(2474.00 + 2474.00i) q^{47} +(984.000 - 984.000i) q^{48} -1049.00i q^{49} +(425.000 - 775.000i) q^{50} +12.0000 q^{51} +(-1946.00 - 1946.00i) q^{52} +(-3331.00 + 3331.00i) q^{53} +1080.00i q^{54} +(-160.000 - 120.000i) q^{55} +1560.00 q^{56} +(-1080.00 - 1080.00i) q^{57} +(-480.000 + 480.000i) q^{58} -3660.00i q^{59} +(420.000 + 2940.00i) q^{60} +1592.00 q^{61} +(-572.000 - 572.000i) q^{62} +(234.000 - 234.000i) q^{63} +1336.00i q^{64} +(4865.00 - 695.000i) q^{65} -96.0000 q^{66} +(874.000 + 874.000i) q^{67} +(-14.0000 + 14.0000i) q^{68} -1992.00i q^{69} +(-780.000 + 1040.00i) q^{70} -6068.00 q^{71} +(-270.000 - 270.000i) q^{72} +(-791.000 + 791.000i) q^{73} +502.000i q^{74} +(-4650.00 - 2550.00i) q^{75} +2520.00 q^{76} +(208.000 + 208.000i) q^{77} +(1668.00 - 1668.00i) q^{78} +9120.00i q^{79} +(-3280.00 - 2460.00i) q^{80} +5751.00 q^{81} +(1688.00 + 1688.00i) q^{82} +(5654.00 - 5654.00i) q^{83} -4368.00i q^{84} +(-5.00000 - 35.0000i) q^{85} -2948.00 q^{86} +(2880.00 + 2880.00i) q^{87} +(240.000 - 240.000i) q^{88} +2160.00i q^{89} +(315.000 - 45.0000i) q^{90} -7228.00 q^{91} +(2324.00 + 2324.00i) q^{92} +(-3432.00 + 3432.00i) q^{93} -4948.00i q^{94} +(-2700.00 + 3600.00i) q^{95} -7728.00 q^{96} +(-6551.00 - 6551.00i) q^{97} +(-1049.00 + 1049.00i) q^{98} -72.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 12 q^{3} + 40 q^{5} + 24 q^{6} - 52 q^{7} - 60 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 12 * q^3 + 40 * q^5 + 24 * q^6 - 52 * q^7 - 60 * q^8	\( 2 q - 2 q^{2} - 12 q^{3} + 40 q^{5} + 24 q^{6} - 52 q^{7} - 60 q^{8} - 10 q^{10} - 16 q^{11} + 168 q^{12} + 278 q^{13} - 420 q^{15} - 328 q^{16} - 2 q^{17} + 18 q^{18} + 420 q^{20} + 624 q^{21} + 16 q^{22} - 332 q^{23} + 350 q^{25} - 556 q^{26} - 1080 q^{27} - 728 q^{28} + 480 q^{30} + 1144 q^{31} + 1288 q^{32} + 96 q^{33} - 260 q^{35} + 252 q^{36} - 502 q^{37} + 360 q^{38} - 2100 q^{40} - 3376 q^{41} - 624 q^{42} + 2948 q^{43} - 270 q^{45} + 664 q^{46} + 4948 q^{47} + 1968 q^{48} + 850 q^{50} + 24 q^{51} - 3892 q^{52} - 6662 q^{53} - 320 q^{55} + 3120 q^{56} - 2160 q^{57} - 960 q^{58} + 840 q^{60} + 3184 q^{61} - 1144 q^{62} + 468 q^{63} + 9730 q^{65} - 192 q^{66} + 1748 q^{67} - 28 q^{68} - 1560 q^{70} - 12136 q^{71} - 540 q^{72} - 1582 q^{73} - 9300 q^{75} + 5040 q^{76} + 416 q^{77} + 3336 q^{78} - 6560 q^{80} + 11502 q^{81} + 3376 q^{82} + 11308 q^{83} - 10 q^{85} - 5896 q^{86} + 5760 q^{87} + 480 q^{88} + 630 q^{90} - 14456 q^{91} + 4648 q^{92} - 6864 q^{93} - 5400 q^{95} - 15456 q^{96} - 13102 q^{97} - 2098 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 12 * q^3 + 40 * q^5 + 24 * q^6 - 52 * q^7 - 60 * q^8 - 10 * q^10 - 16 * q^11 + 168 * q^12 + 278 * q^13 - 420 * q^15 - 328 * q^16 - 2 * q^17 + 18 * q^18 + 420 * q^20 + 624 * q^21 + 16 * q^22 - 332 * q^23 + 350 * q^25 - 556 * q^26 - 1080 * q^27 - 728 * q^28 + 480 * q^30 + 1144 * q^31 + 1288 * q^32 + 96 * q^33 - 260 * q^35 + 252 * q^36 - 502 * q^37 + 360 * q^38 - 2100 * q^40 - 3376 * q^41 - 624 * q^42 + 2948 * q^43 - 270 * q^45 + 664 * q^46 + 4948 * q^47 + 1968 * q^48 + 850 * q^50 + 24 * q^51 - 3892 * q^52 - 6662 * q^53 - 320 * q^55 + 3120 * q^56 - 2160 * q^57 - 960 * q^58 + 840 * q^60 + 3184 * q^61 - 1144 * q^62 + 468 * q^63 + 9730 * q^65 - 192 * q^66 + 1748 * q^67 - 28 * q^68 - 1560 * q^70 - 12136 * q^71 - 540 * q^72 - 1582 * q^73 - 9300 * q^75 + 5040 * q^76 + 416 * q^77 + 3336 * q^78 - 6560 * q^80 + 11502 * q^81 + 3376 * q^82 + 11308 * q^83 - 10 * q^85 - 5896 * q^86 + 5760 * q^87 + 480 * q^88 + 630 * q^90 - 14456 * q^91 + 4648 * q^92 - 6864 * q^93 - 5400 * q^95 - 15456 * q^96 - 13102 * q^97 - 2098 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.00000	−	1.00000i	−0.250000	−	0.250000i	0.570971	−	0.820971i	$-0.306567\pi$
$2$	−1.00000	−	1.00000i	−0.250000	−	0.250000i	−0.820971	+	0.570971i	$0.806567\pi$
$3$	−6.00000	+	6.00000i	−0.666667	+	0.666667i	−0.956943	−	0.290276i	$-0.906253\pi$
$3$	−6.00000	+	6.00000i	−0.666667	+	0.666667i	0.290276	+	0.956943i	$0.406253\pi$
$4$		−	14.0000i		−	0.875000i
$5$	20.0000	+	15.0000i	0.800000	+	0.600000i
$5$	20.0000	+	15.0000i	0.800000	+	0.600000i
$6$	12.0000			0.333333
$7$	−26.0000	−	26.0000i	−0.530612	−	0.530612i	0.390142	−	0.920755i	$-0.372426\pi$
$7$	−26.0000	−	26.0000i	−0.530612	−	0.530612i	−0.920755	+	0.390142i	$0.872426\pi$
$8$	−30.0000	+	30.0000i	−0.468750	+	0.468750i
$9$			9.00000i			0.111111i
$10$	−5.00000	−	35.0000i	−0.0500000	−	0.350000i
$11$	−8.00000			−0.0661157			−0.0330579	−	0.999453i	$-0.510525\pi$
$11$	−8.00000			−0.0661157			−0.0330579	+	0.999453i	$0.510525\pi$
$12$	84.0000	+	84.0000i	0.583333	+	0.583333i
$13$	139.000	−	139.000i	0.822485	−	0.822485i	−0.163979	−	0.986464i	$-0.552433\pi$
$13$	139.000	−	139.000i	0.822485	−	0.822485i	0.986464	+	0.163979i	$0.0524328\pi$
$14$			52.0000i			0.265306i
$15$	−210.000	+	30.0000i	−0.933333	+	0.133333i
$16$	−164.000			−0.640625
$17$	−1.00000	−	1.00000i	−0.00346021	−	0.00346021i	0.705375	−	0.708835i	$-0.250779\pi$
$17$	−1.00000	−	1.00000i	−0.00346021	−	0.00346021i	−0.708835	+	0.705375i	$0.750779\pi$
$18$	9.00000	−	9.00000i	0.0277778	−	0.0277778i
$19$			180.000i			0.498615i	0.968424	+	0.249307i	$0.0802030\pi$
$19$			180.000i			0.498615i	−0.968424	+	0.249307i	$0.919797\pi$
$20$	210.000	−	280.000i	0.525000	−	0.700000i
$21$	312.000			0.707483
$22$	8.00000	+	8.00000i	0.0165289	+	0.0165289i
$23$	−166.000	+	166.000i	−0.313800	+	0.313800i	−0.846380	−	0.532580i	$-0.821223\pi$
$23$	−166.000	+	166.000i	−0.313800	+	0.313800i	0.532580	+	0.846380i	$0.321223\pi$
$24$		−	360.000i		−	0.625000i
$25$	175.000	+	600.000i	0.280000	+	0.960000i
$26$	−278.000			−0.411243
$27$	−540.000	−	540.000i	−0.740741	−	0.740741i
$28$	−364.000	+	364.000i	−0.464286	+	0.464286i
$29$		−	480.000i		−	0.570749i	−0.958416	−	0.285375i	$-0.907882\pi$
$29$		−	480.000i		−	0.570749i	0.958416	−	0.285375i	$-0.0921180\pi$
$30$	240.000	+	180.000i	0.266667	+	0.200000i
$31$	572.000			0.595213			0.297607	−	0.954689i	$-0.403812\pi$
$31$	572.000			0.595213			0.297607	+	0.954689i	$0.403812\pi$
$32$	644.000	+	644.000i	0.628906	+	0.628906i
$33$	48.0000	−	48.0000i	0.0440771	−	0.0440771i
$34$			2.00000i			0.00173010i
$35$	−130.000	−	910.000i	−0.106122	−	0.742857i
$36$	126.000			0.0972222
$37$	−251.000	−	251.000i	−0.183346	−	0.183346i	0.609466	−	0.792812i	$-0.291384\pi$
$37$	−251.000	−	251.000i	−0.183346	−	0.183346i	−0.792812	+	0.609466i	$0.791384\pi$
$38$	180.000	−	180.000i	0.124654	−	0.124654i
$39$			1668.00i			1.09665i
$40$	−1050.00	+	150.000i	−0.656250	+	0.0937500i
$41$	−1688.00			−1.00416			−0.502082	−	0.864820i	$-0.667432\pi$
$41$	−1688.00			−1.00416			−0.502082	+	0.864820i	$0.667432\pi$
$42$	−312.000	−	312.000i	−0.176871	−	0.176871i
$43$	1474.00	−	1474.00i	0.797188	−	0.797188i	−0.185463	−	0.982651i	$-0.559379\pi$
$43$	1474.00	−	1474.00i	0.797188	−	0.797188i	0.982651	+	0.185463i	$0.0593786\pi$
$44$			112.000i			0.0578512i
$45$	−135.000	+	180.000i	−0.0666667	+	0.0888889i
$46$	332.000			0.156900
$47$	2474.00	+	2474.00i	1.11996	+	1.11996i	0.991746	+	0.128218i	$0.0409256\pi$
$47$	2474.00	+	2474.00i	1.11996	+	1.11996i	0.128218	+	0.991746i	$0.459074\pi$
$48$	984.000	−	984.000i	0.427083	−	0.427083i
$49$		−	1049.00i		−	0.436901i
$50$	425.000	−	775.000i	0.170000	−	0.310000i
$51$	12.0000			0.00461361
$52$	−1946.00	−	1946.00i	−0.719675	−	0.719675i
$53$	−3331.00	+	3331.00i	−1.18583	+	1.18583i	−0.207622	+	0.978209i	$0.566572\pi$
$53$	−3331.00	+	3331.00i	−1.18583	+	1.18583i	−0.978209	+	0.207622i	$0.933428\pi$
$54$			1080.00i			0.370370i
$55$	−160.000	−	120.000i	−0.0528926	−	0.0396694i
$56$	1560.00			0.497449
$57$	−1080.00	−	1080.00i	−0.332410	−	0.332410i
$58$	−480.000	+	480.000i	−0.142687	+	0.142687i
$59$		−	3660.00i		−	1.05142i	−0.850663	−	0.525711i	$-0.823799\pi$
$59$		−	3660.00i		−	1.05142i	0.850663	−	0.525711i	$-0.176201\pi$
$60$	420.000	+	2940.00i	0.116667	+	0.816667i
$61$	1592.00			0.427842			0.213921	−	0.976851i	$-0.431376\pi$
$61$	1592.00			0.427842			0.213921	+	0.976851i	$0.431376\pi$
$62$	−572.000	−	572.000i	−0.148803	−	0.148803i
$63$	234.000	−	234.000i	0.0589569	−	0.0589569i
$64$			1336.00i			0.326172i
$65$	4865.00	−	695.000i	1.15148	−	0.164497i
$66$	−96.0000			−0.0220386
$67$	874.000	+	874.000i	0.194698	+	0.194698i	0.797723	−	0.603025i	$-0.206038\pi$
$67$	874.000	+	874.000i	0.194698	+	0.194698i	−0.603025	+	0.797723i	$0.706038\pi$
$68$	−14.0000	+	14.0000i	−0.00302768	+	0.00302768i
$69$		−	1992.00i		−	0.418399i
$70$	−780.000	+	1040.00i	−0.159184	+	0.212245i
$71$	−6068.00			−1.20373			−0.601865	−	0.798598i	$-0.705575\pi$
$71$	−6068.00			−1.20373			−0.601865	+	0.798598i	$0.705575\pi$
$72$	−270.000	−	270.000i	−0.0520833	−	0.0520833i
$73$	−791.000	+	791.000i	−0.148433	+	0.148433i	−0.777418	−	0.628985i	$-0.783471\pi$
$73$	−791.000	+	791.000i	−0.148433	+	0.148433i	0.628985	+	0.777418i	$0.283471\pi$
$74$			502.000i			0.0916728i
$75$	−4650.00	−	2550.00i	−0.826667	−	0.453333i
$76$	2520.00			0.436288
$77$	208.000	+	208.000i	0.0350818	+	0.0350818i
$78$	1668.00	−	1668.00i	0.274162	−	0.274162i
$79$			9120.00i			1.46130i	0.682750	+	0.730652i	$0.260784\pi$
$79$			9120.00i			1.46130i	−0.682750	+	0.730652i	$0.739216\pi$
$80$	−3280.00	−	2460.00i	−0.512500	−	0.384375i
$81$	5751.00			0.876543
$82$	1688.00	+	1688.00i	0.251041	+	0.251041i
$83$	5654.00	−	5654.00i	0.820729	−	0.820729i	−0.165484	−	0.986213i	$-0.552919\pi$
$83$	5654.00	−	5654.00i	0.820729	−	0.820729i	0.986213	+	0.165484i	$0.0529186\pi$
$84$		−	4368.00i		−	0.619048i
$85$	−5.00000	−	35.0000i	−0.000692042	−	0.00484429i
$86$	−2948.00			−0.398594
$87$	2880.00	+	2880.00i	0.380499	+	0.380499i
$88$	240.000	−	240.000i	0.0309917	−	0.0309917i
$89$			2160.00i			0.272693i	0.990661	+	0.136346i	$0.0435360\pi$
$89$			2160.00i			0.272693i	−0.990661	+	0.136346i	$0.956464\pi$
$90$	315.000	−	45.0000i	0.0388889	−	0.00555556i
$91$	−7228.00			−0.872841
$92$	2324.00	+	2324.00i	0.274575	+	0.274575i
$93$	−3432.00	+	3432.00i	−0.396809	+	0.396809i
$94$		−	4948.00i		−	0.559982i
$95$	−2700.00	+	3600.00i	−0.299169	+	0.398892i
$96$	−7728.00			−0.838542
$97$	−6551.00	−	6551.00i	−0.696248	−	0.696248i	0.267351	−	0.963599i	$-0.413852\pi$
$97$	−6551.00	−	6551.00i	−0.696248	−	0.696248i	−0.963599	+	0.267351i	$0.913852\pi$
$98$	−1049.00	+	1049.00i	−0.109225	+	0.109225i
$99$		−	72.0000i		−	0.00734619i
$100$	8400.00	−	2450.00i	0.840000	−	0.245000i
$101$	16102.0			1.57847			0.789236	−	0.614090i	$-0.210477\pi$
$101$	16102.0			1.57847			0.789236	+	0.614090i	$0.210477\pi$
$102$	−12.0000	−	12.0000i	−0.00115340	−	0.00115340i
$103$	994.000	−	994.000i	0.0936940	−	0.0936940i	−0.658706	−	0.752400i	$-0.728896\pi$
$103$	994.000	−	994.000i	0.0936940	−	0.0936940i	0.752400	+	0.658706i	$0.228896\pi$
$104$			8340.00i			0.771080i
$105$	6240.00	+	4680.00i	0.565986	+	0.424490i
$106$	6662.00			0.592916
$107$	−8326.00	−	8326.00i	−0.727225	−	0.727225i	0.242841	−	0.970066i	$-0.421921\pi$
$107$	−8326.00	−	8326.00i	−0.727225	−	0.727225i	−0.970066	+	0.242841i	$0.921921\pi$
$108$	−7560.00	+	7560.00i	−0.648148	+	0.648148i
$109$		−	17010.0i		−	1.43170i	−0.698255	−	0.715849i	$-0.746040\pi$
$109$		−	17010.0i		−	1.43170i	0.698255	−	0.715849i	$-0.253960\pi$
$110$	40.0000	+	280.000i	0.00330579	+	0.0231405i
$111$	3012.00			0.244461
$112$	4264.00	+	4264.00i	0.339923	+	0.339923i
$113$	−5161.00	+	5161.00i	−0.404182	+	0.404182i	−0.879704	−	0.475522i	$-0.842259\pi$
$113$	−5161.00	+	5161.00i	−0.404182	+	0.404182i	0.475522	+	0.879704i	$0.342259\pi$
$114$			2160.00i			0.166205i
$115$	−5810.00	+	830.000i	−0.439319	+	0.0627599i
$116$	−6720.00			−0.499405
$117$	1251.00	+	1251.00i	0.0913872	+	0.0913872i
$118$	−3660.00	+	3660.00i	−0.262856	+	0.262856i
$119$			52.0000i			0.00367206i
$120$	5400.00	−	7200.00i	0.375000	−	0.500000i
$121$	−14577.0			−0.995629
$122$	−1592.00	−	1592.00i	−0.106960	−	0.106960i
$123$	10128.0	−	10128.0i	0.669443	−	0.669443i
$124$		−	8008.00i		−	0.520812i
$125$	−5500.00	+	14625.0i	−0.352000	+	0.936000i
$126$	−468.000			−0.0294785
$127$	12574.0	+	12574.0i	0.779590	+	0.779590i	0.979761	−	0.200171i	$-0.0641499\pi$
$127$	12574.0	+	12574.0i	0.779590	+	0.779590i	−0.200171	+	0.979761i	$0.564150\pi$
$128$	11640.0	−	11640.0i	0.710449	−	0.710449i
$129$			17688.0i			1.06292i
$130$	−5560.00	−	4170.00i	−0.328994	−	0.246746i
$131$	20272.0			1.18128			0.590642	−	0.806934i	$-0.298875\pi$
$131$	20272.0			1.18128			0.590642	+	0.806934i	$0.298875\pi$
$132$	−672.000	−	672.000i	−0.0385675	−	0.0385675i
$133$	4680.00	−	4680.00i	0.264571	−	0.264571i
$134$		−	1748.00i		−	0.0973491i
$135$	−2700.00	−	18900.0i	−0.148148	−	1.03704i
$136$	60.0000			0.00324394
$137$	−10351.0	−	10351.0i	−0.551494	−	0.551494i	0.375378	−	0.926872i	$-0.377513\pi$
$137$	−10351.0	−	10351.0i	−0.551494	−	0.551494i	−0.926872	+	0.375378i	$0.877513\pi$
$138$	−1992.00	+	1992.00i	−0.104600	+	0.104600i
$139$			27060.0i			1.40055i	0.713874	+	0.700274i	$0.246939\pi$
$139$			27060.0i			1.40055i	−0.713874	+	0.700274i	$0.753061\pi$
$140$	−12740.0	+	1820.00i	−0.650000	+	0.0928571i
$141$	−29688.0			−1.49329
$142$	6068.00	+	6068.00i	0.300932	+	0.300932i
$143$	−1112.00	+	1112.00i	−0.0543792	+	0.0543792i
$144$		−	1476.00i		−	0.0711806i
$145$	7200.00	−	9600.00i	0.342449	−	0.456599i
$146$	1582.00			0.0742166
$147$	6294.00	+	6294.00i	0.291268	+	0.291268i
$148$	−3514.00	+	3514.00i	−0.160427	+	0.160427i
$149$		−	16350.0i		−	0.736453i	−0.929736	−	0.368227i	$-0.879965\pi$
$149$		−	16350.0i		−	0.736453i	0.929736	−	0.368227i	$-0.120035\pi$
$150$	2100.00	+	7200.00i	0.0933333	+	0.320000i
$151$	1052.00			0.0461383			0.0230692	−	0.999734i	$-0.492656\pi$
$151$	1052.00			0.0461383			0.0230692	+	0.999734i	$0.492656\pi$
$152$	−5400.00	−	5400.00i	−0.233726	−	0.233726i
$153$	9.00000	−	9.00000i	0.000384468	−	0.000384468i
$154$		−	416.000i		−	0.0175409i
$155$	11440.0	+	8580.00i	0.476171	+	0.357128i
$156$	23352.0			0.959566
$157$	6499.00	+	6499.00i	0.263662	+	0.263662i	0.826540	−	0.562878i	$-0.190306\pi$
$157$	6499.00	+	6499.00i	0.263662	+	0.263662i	−0.562878	+	0.826540i	$0.690306\pi$
$158$	9120.00	−	9120.00i	0.365326	−	0.365326i
$159$		−	39972.0i		−	1.58111i
$160$	3220.00	+	22540.0i	0.125781	+	0.880469i
$161$	8632.00			0.333012
$162$	−5751.00	−	5751.00i	−0.219136	−	0.219136i
$163$	−19286.0	+	19286.0i	−0.725884	+	0.725884i	−0.969797	−	0.243913i	$-0.921569\pi$
$163$	−19286.0	+	19286.0i	−0.725884	+	0.725884i	0.243913	+	0.969797i	$0.421569\pi$
$164$			23632.0i			0.878644i
$165$	1680.00	−	240.000i	0.0617080	−	0.00881543i
$166$	−11308.0			−0.410364
$167$	−15526.0	−	15526.0i	−0.556707	−	0.556707i	0.371661	−	0.928368i	$-0.378788\pi$
$167$	−15526.0	−	15526.0i	−0.556707	−	0.556707i	−0.928368	+	0.371661i	$0.878788\pi$
$168$	−9360.00	+	9360.00i	−0.331633	+	0.331633i
$169$		−	10081.0i		−	0.352964i
$170$	−30.0000	+	40.0000i	−0.00103806	+	0.00138408i
$171$	−1620.00			−0.0554017
$172$	−20636.0	−	20636.0i	−0.697539	−	0.697539i
$173$	−16891.0	+	16891.0i	−0.564369	+	0.564369i	−0.930545	−	0.366176i	$-0.880667\pi$
$173$	−16891.0	+	16891.0i	−0.564369	+	0.564369i	0.366176	+	0.930545i	$0.380667\pi$
$174$		−	5760.00i		−	0.190250i
$175$	11050.0	−	20150.0i	0.360816	−	0.657959i
$176$	1312.00			0.0423554
$177$	21960.0	+	21960.0i	0.700948	+	0.700948i
$178$	2160.00	−	2160.00i	0.0681732	−	0.0681732i
$179$			10620.0i			0.331450i	0.986172	+	0.165725i	$0.0529965\pi$
$179$			10620.0i			0.331450i	−0.986172	+	0.165725i	$0.947004\pi$
$180$	2520.00	+	1890.00i	0.0777778	+	0.0583333i
$181$	24122.0			0.736302			0.368151	−	0.929766i	$-0.379991\pi$
$181$	24122.0			0.736302			0.368151	+	0.929766i	$0.379991\pi$
$182$	7228.00	+	7228.00i	0.218210	+	0.218210i
$183$	−9552.00	+	9552.00i	−0.285228	+	0.285228i
$184$		−	9960.00i		−	0.294187i
$185$	−1255.00	−	8785.00i	−0.0366691	−	0.256684i
$186$	6864.00			0.198404
$187$	8.00000	+	8.00000i	0.000228774	+	0.000228774i
$188$	34636.0	−	34636.0i	0.979968	−	0.979968i
$189$			28080.0i			0.786092i
$190$	6300.00	−	900.000i	0.174515	−	0.0249307i
$191$	−45188.0			−1.23867			−0.619336	−	0.785126i	$-0.712598\pi$
$191$	−45188.0			−1.23867			−0.619336	+	0.785126i	$0.712598\pi$
$192$	−8016.00	−	8016.00i	−0.217448	−	0.217448i
$193$	39199.0	−	39199.0i	1.05235	−	1.05235i	0.0537986	−	0.998552i	$-0.482867\pi$
$193$	39199.0	−	39199.0i	1.05235	−	1.05235i	0.998552	−	0.0537986i	$-0.0171329\pi$
$194$			13102.0i			0.348124i
$195$	−25020.0	+	33360.0i	−0.657988	+	0.877318i
$196$	−14686.0			−0.382289
$197$	28349.0	+	28349.0i	0.730475	+	0.730475i	0.970714	−	0.240239i	$-0.0772258\pi$
$197$	28349.0	+	28349.0i	0.730475	+	0.730475i	−0.240239	+	0.970714i	$0.577226\pi$
$198$	−72.0000	+	72.0000i	−0.00183655	+	0.00183655i
$199$		−	1800.00i		−	0.0454534i	−0.999742	−	0.0227267i	$-0.992765\pi$
$199$		−	1800.00i		−	0.0454534i	0.999742	−	0.0227267i	$-0.00723476\pi$
$200$	−23250.0	−	12750.0i	−0.581250	−	0.318750i
$201$	−10488.0			−0.259598
$202$	−16102.0	−	16102.0i	−0.394618	−	0.394618i
$203$	−12480.0	+	12480.0i	−0.302846	+	0.302846i
$204$		−	168.000i		−	0.00403691i
$205$	−33760.0	−	25320.0i	−0.803331	−	0.602499i
$206$	−1988.00			−0.0468470
$207$	−1494.00	−	1494.00i	−0.0348666	−	0.0348666i
$208$	−22796.0	+	22796.0i	−0.526905	+	0.526905i
$209$		−	1440.00i		−	0.0329663i
$210$	−1560.00	−	10920.0i	−0.0353741	−	0.247619i
$211$	18392.0			0.413108			0.206554	−	0.978435i	$-0.433775\pi$
$211$	18392.0			0.413108			0.206554	+	0.978435i	$0.433775\pi$
$212$	46634.0	+	46634.0i	1.03760	+	1.03760i
$213$	36408.0	−	36408.0i	0.802486	−	0.802486i
$214$			16652.0i			0.363613i
$215$	51590.0	−	7370.00i	1.11606	−	0.159438i
$216$	32400.0			0.694444
$217$	−14872.0	−	14872.0i	−0.315827	−	0.315827i
$218$	−17010.0	+	17010.0i	−0.357924	+	0.357924i
$219$		−	9492.00i		−	0.197911i
$220$	−1680.00	+	2240.00i	−0.0347107	+	0.0462810i
$221$	−278.000			−0.00569194
$222$	−3012.00	−	3012.00i	−0.0611152	−	0.0611152i
$223$	−866.000	+	866.000i	−0.0174144	+	0.0174144i	−0.715760	−	0.698346i	$-0.753920\pi$
$223$	−866.000	+	866.000i	−0.0174144	+	0.0174144i	0.698346	+	0.715760i	$0.253920\pi$
$224$		−	33488.0i		−	0.667411i
$225$	−5400.00	+	1575.00i	−0.106667	+	0.0311111i
$226$	10322.0			0.202091
$227$	−45226.0	−	45226.0i	−0.877681	−	0.877681i	0.115614	−	0.993294i	$-0.463117\pi$
$227$	−45226.0	−	45226.0i	−0.877681	−	0.877681i	−0.993294	+	0.115614i	$0.963117\pi$
$228$	−15120.0	+	15120.0i	−0.290859	+	0.290859i
$229$			39120.0i			0.745981i	0.927835	+	0.372991i	$0.121668\pi$
$229$			39120.0i			0.745981i	−0.927835	+	0.372991i	$0.878332\pi$
$230$	6640.00	+	4980.00i	0.125520	+	0.0941399i
$231$	−2496.00			−0.0467757
$232$	14400.0	+	14400.0i	0.267539	+	0.267539i
$233$	−33121.0	+	33121.0i	−0.610087	+	0.610087i	−0.942969	−	0.332882i	$-0.891979\pi$
$233$	−33121.0	+	33121.0i	−0.610087	+	0.610087i	0.332882	+	0.942969i	$0.391979\pi$
$234$		−	2502.00i		−	0.0456936i
$235$	12370.0	+	86590.0i	0.223993	+	1.56795i
$236$	−51240.0			−0.919994
$237$	−54720.0	−	54720.0i	−0.974203	−	0.974203i
$238$	52.0000	−	52.0000i	0.000918014	−	0.000918014i
$239$		−	88440.0i		−	1.54829i	−0.633007	−	0.774146i	$-0.718180\pi$
$239$		−	88440.0i		−	1.54829i	0.633007	−	0.774146i	$-0.281820\pi$
$240$	34440.0	−	4920.00i	0.597917	−	0.0854167i
$241$	20312.0			0.349718			0.174859	−	0.984593i	$-0.444053\pi$
$241$	20312.0			0.349718			0.174859	+	0.984593i	$0.444053\pi$
$242$	14577.0	+	14577.0i	0.248907	+	0.248907i
$243$	9234.00	−	9234.00i	0.156379	−	0.156379i
$244$		−	22288.0i		−	0.374362i
$245$	15735.0	−	20980.0i	0.262141	−	0.349521i
$246$	−20256.0			−0.334721
$247$	25020.0	+	25020.0i	0.410103	+	0.410103i
$248$	−17160.0	+	17160.0i	−0.279006	+	0.279006i
$249$			67848.0i			1.09430i
$250$	20125.0	−	9125.00i	0.322000	−	0.146000i
$251$	74752.0			1.18652			0.593260	−	0.805011i	$-0.297840\pi$
$251$	74752.0			1.18652			0.593260	+	0.805011i	$0.297840\pi$
$252$	−3276.00	−	3276.00i	−0.0515873	−	0.0515873i
$253$	1328.00	−	1328.00i	0.0207471	−	0.0207471i
$254$		−	25148.0i		−	0.389795i
$255$	240.000	+	180.000i	0.00369089	+	0.00276817i
$256$	−1904.00			−0.0290527
$257$	37799.0	+	37799.0i	0.572287	+	0.572287i	0.932767	−	0.360480i	$-0.117387\pi$
$257$	37799.0	+	37799.0i	0.572287	+	0.572287i	−0.360480	+	0.932767i	$0.617387\pi$
$258$	17688.0	−	17688.0i	0.265729	−	0.265729i
$259$			13052.0i			0.194571i
$260$	−9730.00	−	68110.0i	−0.143935	−	1.00754i
$261$	4320.00			0.0634166
$262$	−20272.0	−	20272.0i	−0.295321	−	0.295321i
$263$	−33586.0	+	33586.0i	−0.485564	+	0.485564i	−0.906903	−	0.421339i	$-0.861560\pi$
$263$	−33586.0	+	33586.0i	−0.485564	+	0.485564i	0.421339	+	0.906903i	$0.361560\pi$
$264$			2880.00i			0.0413223i
$265$	−116585.	+	16655.0i	−1.66016	+	0.237166i
$266$	−9360.00			−0.132286
$267$	−12960.0	−	12960.0i	−0.181795	−	0.181795i
$268$	12236.0	−	12236.0i	0.170361	−	0.170361i
$269$			28530.0i			0.394273i	0.980376	+	0.197137i	$0.0631642\pi$
$269$			28530.0i			0.394273i	−0.980376	+	0.197137i	$0.936836\pi$
$270$	−16200.0	+	21600.0i	−0.222222	+	0.296296i
$271$	−7468.00			−0.101687			−0.0508435	−	0.998707i	$-0.516191\pi$
$271$	−7468.00			−0.101687			−0.0508435	+	0.998707i	$0.516191\pi$
$272$	164.000	+	164.000i	0.00221670	+	0.00221670i
$273$	43368.0	−	43368.0i	0.581894	−	0.581894i
$274$			20702.0i			0.275747i
$275$	−1400.00	−	4800.00i	−0.0185124	−	0.0634711i
$276$	−27888.0			−0.366100
$277$	6499.00	+	6499.00i	0.0847007	+	0.0847007i	0.748188	−	0.663487i	$-0.230924\pi$
$277$	6499.00	+	6499.00i	0.0847007	+	0.0847007i	−0.663487	+	0.748188i	$0.730924\pi$
$278$	27060.0	−	27060.0i	0.350137	−	0.350137i
$279$			5148.00i			0.0661348i
$280$	31200.0	+	23400.0i	0.397959	+	0.298469i
$281$	−97928.0			−1.24021			−0.620104	−	0.784520i	$-0.712909\pi$
$281$	−97928.0			−1.24021			−0.620104	+	0.784520i	$0.712909\pi$
$282$	29688.0	+	29688.0i	0.373321	+	0.373321i
$283$	59854.0	−	59854.0i	0.747344	−	0.747344i	−0.226636	−	0.973980i	$-0.572773\pi$
$283$	59854.0	−	59854.0i	0.747344	−	0.747344i	0.973980	+	0.226636i	$0.0727728\pi$
$284$			84952.0i			1.05326i
$285$	−5400.00	−	37800.0i	−0.0664820	−	0.465374i
$286$	2224.00			0.0271896
$287$	43888.0	+	43888.0i	0.532822	+	0.532822i
$288$	−5796.00	+	5796.00i	−0.0698785	+	0.0698785i
$289$		−	83519.0i		−	0.999976i
$290$	−16800.0	+	2400.00i	−0.199762	+	0.0285375i
$291$	78612.0			0.928331
$292$	11074.0	+	11074.0i	0.129879	+	0.129879i
$293$	28499.0	−	28499.0i	0.331967	−	0.331967i	−0.521366	−	0.853333i	$-0.674577\pi$
$293$	28499.0	−	28499.0i	0.331967	−	0.331967i	0.853333	+	0.521366i	$0.174577\pi$
$294$		−	12588.0i		−	0.145634i
$295$	54900.0	−	73200.0i	0.630853	−	0.841138i
$296$	15060.0			0.171886
$297$	4320.00	+	4320.00i	0.0489746	+	0.0489746i
$298$	−16350.0	+	16350.0i	−0.184113	+	0.184113i
$299$			46148.0i			0.516191i
$300$	−35700.0	+	65100.0i	−0.396667	+	0.723333i
$301$	−76648.0			−0.845995
$302$	−1052.00	−	1052.00i	−0.0115346	−	0.0115346i
$303$	−96612.0	+	96612.0i	−1.05232	+	1.05232i
$304$		−	29520.0i		−	0.319425i
$305$	31840.0	+	23880.0i	0.342274	+	0.256705i
$306$	−18.0000			−0.000192234
$307$	−117926.	−	117926.i	−1.25122	−	1.25122i	−0.955175	−	0.296043i	$-0.904333\pi$
$307$	−117926.	−	117926.i	−1.25122	−	1.25122i	−0.296043	−	0.955175i	$-0.595667\pi$
$308$	2912.00	−	2912.00i	0.0306966	−	0.0306966i
$309$			11928.0i			0.124925i
$310$	−2860.00	−	20020.0i	−0.0297607	−	0.208325i
$311$	3892.00			0.0402395			0.0201197	−	0.999798i	$-0.493595\pi$
$311$	3892.00			0.0402395			0.0201197	+	0.999798i	$0.493595\pi$
$312$	−50040.0	−	50040.0i	−0.514053	−	0.514053i
$313$	−49961.0	+	49961.0i	−0.509967	+	0.509967i	−0.914516	−	0.404549i	$-0.867429\pi$
$313$	−49961.0	+	49961.0i	−0.509967	+	0.509967i	0.404549	+	0.914516i	$0.367429\pi$
$314$		−	12998.0i		−	0.131831i
$315$	8190.00	−	1170.00i	0.0825397	−	0.0117914i
$316$	127680.			1.27864
$317$	17099.0	+	17099.0i	0.170158	+	0.170158i	0.787049	−	0.616891i	$-0.211608\pi$
$317$	17099.0	+	17099.0i	0.170158	+	0.170158i	−0.616891	+	0.787049i	$0.711608\pi$
$318$	−39972.0	+	39972.0i	−0.395277	+	0.395277i
$319$			3840.00i			0.0377355i
$320$	−20040.0	+	26720.0i	−0.195703	+	0.260937i
$321$	99912.0			0.969633
$322$	−8632.00	−	8632.00i	−0.0832530	−	0.0832530i
$323$	180.000	−	180.000i	0.00172531	−	0.00172531i
$324$		−	80514.0i		−	0.766975i
$325$	107725.	+	59075.0i	1.01988	+	0.559290i
$326$	38572.0			0.362942
$327$	102060.	+	102060.i	0.954465	+	0.954465i
$328$	50640.0	−	50640.0i	0.470702	−	0.470702i
$329$		−	128648.i		−	1.18853i
$330$	−1920.00	−	1440.00i	−0.0176309	−	0.0132231i
$331$	−143128.			−1.30638			−0.653189	−	0.757195i	$-0.726569\pi$
$331$	−143128.			−1.30638			−0.653189	+	0.757195i	$0.726569\pi$
$332$	−79156.0	−	79156.0i	−0.718138	−	0.718138i
$333$	2259.00	−	2259.00i	0.0203717	−	0.0203717i
$334$			31052.0i			0.278353i
$335$	4370.00	+	30590.0i	0.0389396	+	0.272577i
$336$	−51168.0			−0.453231
$337$	103249.	+	103249.i	0.909130	+	0.909130i	0.996202	−	0.0870719i	$-0.0277510\pi$
$337$	103249.	+	103249.i	0.909130	+	0.909130i	−0.0870719	+	0.996202i	$0.527751\pi$
$338$	−10081.0	+	10081.0i	−0.0882410	+	0.0882410i
$339$		−	61932.0i		−	0.538909i
$340$	−490.000	+	70.0000i	−0.00423875	+	0.000605536i
$341$	−4576.00			−0.0393529
$342$	1620.00	+	1620.00i	0.0138504	+	0.0138504i
$343$	−89700.0	+	89700.0i	−0.762437	+	0.762437i
$344$			88440.0i			0.747363i
$345$	29880.0	−	39840.0i	0.251040	−	0.334720i
$346$	33782.0			0.282185
$347$	−104626.	−	104626.i	−0.868922	−	0.868922i	0.123431	−	0.992353i	$-0.460610\pi$
$347$	−104626.	−	104626.i	−0.868922	−	0.868922i	−0.992353	+	0.123431i	$0.960610\pi$
$348$	40320.0	−	40320.0i	0.332937	−	0.332937i
$349$			94800.0i			0.778319i	0.921170	+	0.389159i	$0.127234\pi$
$349$			94800.0i			0.778319i	−0.921170	+	0.389159i	$0.872766\pi$
$350$	−31200.0	+	9100.00i	−0.254694	+	0.0742857i
$351$	−150120.			−1.21850
$352$	−5152.00	−	5152.00i	−0.0415806	−	0.0415806i
$353$	63569.0	−	63569.0i	0.510148	−	0.510148i	−0.404424	−	0.914572i	$-0.632528\pi$
$353$	63569.0	−	63569.0i	0.510148	−	0.510148i	0.914572	+	0.404424i	$0.132528\pi$
$354$		−	43920.0i		−	0.350474i
$355$	−121360.	−	91020.0i	−0.962984	−	0.722238i
$356$	30240.0			0.238606
$357$	−312.000	−	312.000i	−0.00244804	−	0.00244804i
$358$	10620.0	−	10620.0i	0.0828626	−	0.0828626i
$359$			141840.i			1.10055i	0.834983	+	0.550275i	$0.185477\pi$
$359$			141840.i			1.10055i	−0.834983	+	0.550275i	$0.814523\pi$
$360$	−1350.00	−	9450.00i	−0.0104167	−	0.0729167i
$361$	97921.0			0.751383
$362$	−24122.0	−	24122.0i	−0.184076	−	0.184076i
$363$	87462.0	−	87462.0i	0.663752	−	0.663752i
$364$			101192.i			0.763736i
$365$	−27685.0	+	3955.00i	−0.207806	+	0.0296866i
$366$	19104.0			0.142614
$367$	142174.	+	142174.i	1.05557	+	1.05557i	0.998362	+	0.0572103i	$0.0182206\pi$
$367$	142174.	+	142174.i	1.05557	+	1.05557i	0.0572103	+	0.998362i	$0.481779\pi$
$368$	27224.0	−	27224.0i	0.201028	−	0.201028i
$369$		−	15192.0i		−	0.111574i
$370$	−7530.00	+	10040.0i	−0.0550037	+	0.0733382i
$371$	173212.			1.25843
$372$	48048.0	+	48048.0i	0.347208	+	0.347208i
$373$	10309.0	−	10309.0i	0.0740967	−	0.0740967i	−0.669087	−	0.743184i	$-0.733315\pi$
$373$	10309.0	−	10309.0i	0.0740967	−	0.0740967i	0.743184	+	0.669087i	$0.233315\pi$
$374$		−	16.0000i		−	0.000114387i
$375$	−54750.0	−	120750.i	−0.389333	−	0.858667i
$376$	−148440.			−1.04997
$377$	−66720.0	−	66720.0i	−0.469433	−	0.469433i
$378$	28080.0	−	28080.0i	0.196523	−	0.196523i
$379$		−	115380.i		−	0.803253i	−0.915804	−	0.401626i	$-0.868445\pi$
$379$		−	115380.i		−	0.803253i	0.915804	−	0.401626i	$-0.131555\pi$
$380$	50400.0	+	37800.0i	0.349030	+	0.261773i
$381$	−150888.			−1.03945
$382$	45188.0	+	45188.0i	0.309668	+	0.309668i
$383$	62654.0	−	62654.0i	0.427121	−	0.427121i	−0.460525	−	0.887647i	$-0.652339\pi$
$383$	62654.0	−	62654.0i	0.427121	−	0.427121i	0.887647	+	0.460525i	$0.152339\pi$
$384$			139680.i			0.947266i
$385$	1040.00	+	7280.00i	0.00701636	+	0.0491145i
$386$	−78398.0			−0.526175
$387$	13266.0	+	13266.0i	0.0885764	+	0.0885764i
$388$	−91714.0	+	91714.0i	−0.609217	+	0.609217i
$389$		−	132690.i		−	0.876878i	−0.898761	−	0.438439i	$-0.855532\pi$
$389$		−	132690.i		−	0.876878i	0.898761	−	0.438439i	$-0.144468\pi$
$390$	58380.0	−	8340.00i	0.383826	−	0.0548323i
$391$	332.000			0.00217162
$392$	31470.0	+	31470.0i	0.204797	+	0.204797i
$393$	−121632.	+	121632.i	−0.787522	+	0.787522i
$394$		−	56698.0i		−	0.365237i
$395$	−136800.	+	182400.i	−0.876783	+	1.16904i
$396$	−1008.00			−0.00642792
$397$	−88451.0	−	88451.0i	−0.561205	−	0.561205i	0.368444	−	0.929650i	$-0.379890\pi$
$397$	−88451.0	−	88451.0i	−0.561205	−	0.561205i	−0.929650	+	0.368444i	$0.879890\pi$
$398$	−1800.00	+	1800.00i	−0.0113633	+	0.0113633i
$399$			56160.0i			0.352762i
$400$	−28700.0	−	98400.0i	−0.179375	−	0.615000i
$401$	63202.0			0.393045			0.196522	−	0.980499i	$-0.437035\pi$
$401$	63202.0			0.393045			0.196522	+	0.980499i	$0.437035\pi$
$402$	10488.0	+	10488.0i	0.0648994	+	0.0648994i
$403$	79508.0	−	79508.0i	0.489554	−	0.489554i
$404$		−	225428.i		−	1.38116i
$405$	115020.	+	86265.0i	0.701235	+	0.525926i
$406$	24960.0			0.151423
$407$	2008.00	+	2008.00i	0.0121220	+	0.0121220i
$408$	−360.000	+	360.000i	−0.00216263	+	0.00216263i
$409$			52890.0i			0.316175i	0.987425	+	0.158087i	$0.0505327\pi$
$409$			52890.0i			0.316175i	−0.987425	+	0.158087i	$0.949467\pi$
$410$	8440.00	+	59080.0i	0.0502082	+	0.351457i
$411$	124212.			0.735326
$412$	−13916.0	−	13916.0i	−0.0819823	−	0.0819823i
$413$	−95160.0	+	95160.0i	−0.557897	+	0.557897i
$414$			2988.00i			0.0174333i
$415$	197890.	−	28270.0i	1.14902	−	0.164146i
$416$	179032.			1.03453
$417$	−162360.	−	162360.i	−0.933699	−	0.933699i
$418$	−1440.00	+	1440.00i	−0.00824157	+	0.00824157i
$419$			256980.i			1.46376i	0.681431	+	0.731882i	$0.261358\pi$
$419$			256980.i			1.46376i	−0.681431	+	0.731882i	$0.738642\pi$
$420$	65520.0	−	87360.0i	0.371429	−	0.495238i
$421$	186632.			1.05298			0.526492	−	0.850180i	$-0.323507\pi$
$421$	186632.			1.05298			0.526492	+	0.850180i	$0.323507\pi$
$422$	−18392.0	−	18392.0i	−0.103277	−	0.103277i
$423$	−22266.0	+	22266.0i	−0.124440	+	0.124440i
$424$		−	199860.i		−	1.11172i
$425$	425.000	−	775.000i	0.00235294	−	0.00429066i
$426$	−72816.0			−0.401243
$427$	−41392.0	−	41392.0i	−0.227018	−	0.227018i
$428$	−116564.	+	116564.i	−0.636322	+	0.636322i
$429$		−	13344.0i		−	0.0725056i
$430$	−58960.0	−	44220.0i	−0.318875	−	0.239156i
$431$	−208028.			−1.11987			−0.559935	−	0.828537i	$-0.689174\pi$
$431$	−208028.			−1.11987			−0.559935	+	0.828537i	$0.689174\pi$
$432$	88560.0	+	88560.0i	0.474537	+	0.474537i
$433$	−151271.	+	151271.i	−0.806826	+	0.806826i	−0.984152	−	0.177326i	$-0.943255\pi$
$433$	−151271.	+	151271.i	−0.806826	+	0.806826i	0.177326	+	0.984152i	$0.443255\pi$
$434$			29744.0i			0.157914i
$435$	14400.0	+	100800.i	0.0760999	+	0.532699i
$436$	−238140.			−1.25274
$437$	−29880.0	−	29880.0i	−0.156465	−	0.156465i
$438$	−9492.00	+	9492.00i	−0.0494777	+	0.0494777i
$439$		−	158640.i		−	0.823159i	−0.911374	−	0.411579i	$-0.864977\pi$
$439$		−	158640.i		−	0.823159i	0.911374	−	0.411579i	$-0.135023\pi$
$440$	8400.00	−	1200.00i	0.0433884	−	0.00619835i
$441$	9441.00			0.0485446
$442$	278.000	+	278.000i	0.00142298	+	0.00142298i
$443$	252974.	−	252974.i	1.28905	−	1.28905i	0.353679	−	0.935367i	$-0.384930\pi$
$443$	252974.	−	252974.i	1.28905	−	1.28905i	0.935367	−	0.353679i	$-0.115070\pi$
$444$		−	42168.0i		−	0.213903i
$445$	−32400.0	+	43200.0i	−0.163616	+	0.218154i
$446$	1732.00			0.00870719
$447$	98100.0	+	98100.0i	0.490969	+	0.490969i
$448$	34736.0	−	34736.0i	0.173071	−	0.173071i
$449$			123750.i			0.613836i	0.951736	+	0.306918i	$0.0992978\pi$
$449$			123750.i			0.613836i	−0.951736	+	0.306918i	$0.900702\pi$
$450$	6975.00	+	3825.00i	0.0344444	+	0.0188889i
$451$	13504.0			0.0663910
$452$	72254.0	+	72254.0i	0.353659	+	0.353659i
$453$	−6312.00	+	6312.00i	−0.0307589	+	0.0307589i
$454$			90452.0i			0.438840i
$455$	−144560.	−	108420.i	−0.698273	−	0.523705i
$456$	64800.0			0.311634
$457$	−32201.0	−	32201.0i	−0.154183	−	0.154183i	0.625800	−	0.779983i	$-0.284773\pi$
$457$	−32201.0	−	32201.0i	−0.154183	−	0.154183i	−0.779983	+	0.625800i	$0.784773\pi$
$458$	39120.0	−	39120.0i	0.186495	−	0.186495i
$459$			1080.00i			0.00512623i
$460$	11620.0	+	81340.0i	0.0549149	+	0.384405i
$461$	75142.0			0.353574			0.176787	−	0.984249i	$-0.443430\pi$
$461$	75142.0			0.353574			0.176787	+	0.984249i	$0.443430\pi$
$462$	2496.00	+	2496.00i	0.0116939	+	0.0116939i
$463$	235714.	−	235714.i	1.09957	−	1.09957i	0.105111	−	0.994461i	$-0.466480\pi$
$463$	235714.	−	235714.i	1.09957	−	1.09957i	0.994461	−	0.105111i	$-0.0335197\pi$
$464$			78720.0i			0.365636i
$465$	−120120.	+	17160.0i	−0.555532	+	0.0793618i
$466$	66242.0			0.305043
$467$	28574.0	+	28574.0i	0.131020	+	0.131020i	0.769576	−	0.638556i	$-0.220468\pi$
$467$	28574.0	+	28574.0i	0.131020	+	0.131020i	−0.638556	+	0.769576i	$0.720468\pi$
$468$	17514.0	−	17514.0i	0.0799638	−	0.0799638i
$469$		−	45448.0i		−	0.206618i
$470$	74220.0	−	98960.0i	0.335989	−	0.447986i
$471$	−77988.0			−0.351549
$472$	109800.	+	109800.i	0.492854	+	0.492854i
$473$	−11792.0	+	11792.0i	−0.0527066	+	0.0527066i
$474$			109440.i			0.487101i
$475$	−108000.	+	31500.0i	−0.478670	+	0.139612i
$476$	728.000			0.00321305
$477$	−29979.0	−	29979.0i	−0.131759	−	0.131759i
$478$	−88440.0	+	88440.0i	−0.387073	+	0.387073i
$479$			26520.0i			0.115585i	0.998329	+	0.0577926i	$0.0184062\pi$
$479$			26520.0i			0.115585i	−0.998329	+	0.0577926i	$0.981594\pi$
$480$	−154560.	−	115920.i	−0.670833	−	0.503125i
$481$	−69778.0			−0.301598
$482$	−20312.0	−	20312.0i	−0.0874296	−	0.0874296i
$483$	−51792.0	+	51792.0i	−0.222008	+	0.222008i
$484$			204078.i			0.871175i
$485$	−32755.0	−	229285.i	−0.139250	−	0.974748i
$486$	−18468.0			−0.0781893
$487$	41374.0	+	41374.0i	0.174449	+	0.174449i	0.788931	−	0.614482i	$-0.210635\pi$
$487$	41374.0	+	41374.0i	0.174449	+	0.174449i	−0.614482	+	0.788931i	$0.710635\pi$
$488$	−47760.0	+	47760.0i	−0.200551	+	0.200551i
$489$		−	231432.i		−	0.967845i
$490$	−36715.0	+	5245.00i	−0.152915	+	0.0218451i
$491$	−149288.			−0.619244			−0.309622	−	0.950860i	$-0.600203\pi$
$491$	−149288.			−0.619244			−0.309622	+	0.950860i	$0.600203\pi$
$492$	−141792.	−	141792.i	−0.585762	−	0.585762i
$493$	−480.000	+	480.000i	−0.00197491	+	0.00197491i
$494$		−	50040.0i		−	0.205052i
$495$	1080.00	−	1440.00i	0.00440771	−	0.00587695i
$496$	−93808.0			−0.381309
$497$	157768.	+	157768.i	0.638714	+	0.638714i
$498$	67848.0	−	67848.0i	0.273576	−	0.273576i
$499$			284100.i			1.14096i	0.821312	+	0.570480i	$0.193243\pi$
$499$			284100.i			1.14096i	−0.821312	+	0.570480i	$0.806757\pi$
$500$	204750.	+	77000.0i	0.819000	+	0.308000i
$501$	186312.			0.742276
$502$	−74752.0	−	74752.0i	−0.296630	−	0.296630i
$503$	−117406.	+	117406.i	−0.464039	+	0.464039i	−0.899977	−	0.435938i	$-0.856417\pi$
$503$	−117406.	+	117406.i	−0.464039	+	0.464039i	0.435938	+	0.899977i	$0.356417\pi$
$504$			14040.0i			0.0552721i
$505$	322040.	+	241530.i	1.26278	+	0.947084i
$506$	−2656.00			−0.0103735
$507$	60486.0	+	60486.0i	0.235309	+	0.235309i
$508$	176036.	−	176036.i	0.682141	−	0.682141i
$509$		−	234960.i		−	0.906898i	−0.891282	−	0.453449i	$-0.850193\pi$
$509$		−	234960.i		−	0.906898i	0.891282	−	0.453449i	$-0.149807\pi$
$510$	−60.0000	−	420.000i	−0.000230681	−	0.00161476i
$511$	41132.0			0.157521
$512$	−184336.	−	184336.i	−0.703186	−	0.703186i
$513$	97200.0	−	97200.0i	0.369344	−	0.369344i
$514$		−	75598.0i		−	0.286144i
$515$	34790.0	−	4970.00i	0.131172	−	0.0187388i
$516$	247632.			0.930052
$517$	−19792.0	−	19792.0i	−0.0740472	−	0.0740472i
$518$	13052.0	−	13052.0i	0.0486427	−	0.0486427i
$519$		−	202692.i		−	0.752492i
$520$	−125100.	+	166800.i	−0.462648	+	0.616864i
$521$	−171218.			−0.630774			−0.315387	−	0.948963i	$-0.602134\pi$
$521$	−171218.			−0.630774			−0.315387	+	0.948963i	$0.602134\pi$
$522$	−4320.00	−	4320.00i	−0.0158541	−	0.0158541i
$523$	−332666.	+	332666.i	−1.21620	+	1.21620i	−0.247248	+	0.968952i	$0.579526\pi$
$523$	−332666.	+	332666.i	−1.21620	+	1.21620i	−0.968952	+	0.247248i	$0.920474\pi$
$524$		−	283808.i		−	1.03362i
$525$	54600.0	+	187200.i	0.198095	+	0.679184i
$526$	67172.0			0.242782
$527$	−572.000	−	572.000i	−0.00205956	−	0.00205956i
$528$	−7872.00	+	7872.00i	−0.0282369	+	0.0282369i
$529$			224729.i			0.803060i
$530$	133240.	+	99930.0i	0.474333	+	0.355749i
$531$	32940.0			0.116825
$532$	−65520.0	−	65520.0i	−0.231500	−	0.231500i
$533$	−234632.	+	234632.i	−0.825910	+	0.825910i
$534$			25920.0i			0.0908976i
$535$	−41630.0	−	291410.i	−0.145445	−	1.01812i
$536$	−52440.0			−0.182530
$537$	−63720.0	−	63720.0i	−0.220967	−	0.220967i
$538$	28530.0	−	28530.0i	0.0985683	−	0.0985683i
$539$			8392.00i			0.0288860i
$540$	−264600.	+	37800.0i	−0.907407	+	0.129630i
$541$	13862.0			0.0473621			0.0236811	−	0.999720i	$-0.492461\pi$
$541$	13862.0			0.0473621			0.0236811	+	0.999720i	$0.492461\pi$
$542$	7468.00	+	7468.00i	0.0254218	+	0.0254218i
$543$	−144732.	+	144732.i	−0.490868	+	0.490868i
$544$		−	1288.00i		−	0.00435229i
$545$	255150.	−	340200.i	0.859019	−	1.14536i
$546$	−86736.0			−0.290947
$547$	−180026.	−	180026.i	−0.601673	−	0.601673i	0.339083	−	0.940756i	$-0.389883\pi$
$547$	−180026.	−	180026.i	−0.601673	−	0.601673i	−0.940756	+	0.339083i	$0.889883\pi$
$548$	−144914.	+	144914.i	−0.482558	+	0.482558i
$549$			14328.0i			0.0475380i
$550$	−3400.00	+	6200.00i	−0.0112397	+	0.0204959i
$551$	86400.0			0.284584
$552$	59760.0	+	59760.0i	0.196125	+	0.196125i
$553$	237120.	−	237120.i	0.775386	−	0.775386i
$554$		−	12998.0i		−	0.0423503i
$555$	60240.0	+	45180.0i	0.195569	+	0.146676i
$556$	378840.			1.22548
$557$	422549.	+	422549.i	1.36197	+	1.36197i	0.871408	+	0.490560i	$0.163208\pi$
$557$	422549.	+	422549.i	1.36197	+	1.36197i	0.490560	+	0.871408i	$0.336792\pi$
$558$	5148.00	−	5148.00i	0.0165337	−	0.0165337i
$559$		−	409772.i		−	1.31135i
$560$	21320.0	+	149240.i	0.0679847	+	0.475893i
$561$	−96.0000			−0.000305032
$562$	97928.0	+	97928.0i	0.310052	+	0.310052i
$563$	105314.	−	105314.i	0.332253	−	0.332253i	−0.521188	−	0.853442i	$-0.674511\pi$
$563$	105314.	−	105314.i	0.332253	−	0.332253i	0.853442	+	0.521188i	$0.174511\pi$
$564$			415632.i			1.30662i
$565$	−180635.	+	25805.0i	−0.565855	+	0.0808364i
$566$	−119708.			−0.373672
$567$	−149526.	−	149526.i	−0.465105	−	0.465105i
$568$	182040.	−	182040.i	0.564248	−	0.564248i
$569$			85830.0i			0.265103i	0.991176	+	0.132551i	$0.0423170\pi$
$569$			85830.0i			0.265103i	−0.991176	+	0.132551i	$0.957683\pi$
$570$	−32400.0	+	43200.0i	−0.0997230	+	0.132964i
$571$	−142168.			−0.436043			−0.218022	−	0.975944i	$-0.569960\pi$
$571$	−142168.			−0.436043			−0.218022	+	0.975944i	$0.569960\pi$
$572$	15568.0	+	15568.0i	0.0475818	+	0.0475818i
$573$	271128.	−	271128.i	0.825781	−	0.825781i
$574$		−	87776.0i		−	0.266411i
$575$	−128650.	−	70550.0i	−0.389112	−	0.213384i
$576$	−12024.0			−0.0362413
$577$	−154601.	−	154601.i	−0.464366	−	0.464366i	0.435717	−	0.900084i	$-0.356495\pi$
$577$	−154601.	−	154601.i	−0.464366	−	0.464366i	−0.900084	+	0.435717i	$0.856495\pi$
$578$	−83519.0	+	83519.0i	−0.249994	+	0.249994i
$579$			470388.i			1.40313i
$580$	−134400.	−	100800.i	−0.399524	−	0.299643i
$581$	−294008.			−0.870977
$582$	−78612.0	−	78612.0i	−0.232083	−	0.232083i
$583$	26648.0	−	26648.0i	0.0784021	−	0.0784021i
$584$		−	47460.0i		−	0.139156i
$585$	6255.00	+	43785.0i	0.0182774	+	0.127942i
$586$	−56998.0			−0.165983
$587$	222974.	+	222974.i	0.647110	+	0.647110i	0.952294	−	0.305184i	$-0.0987178\pi$
$587$	222974.	+	222974.i	0.647110	+	0.647110i	−0.305184	+	0.952294i	$0.598718\pi$
$588$	88116.0	−	88116.0i	0.254859	−	0.254859i
$589$			102960.i			0.296782i
$590$	−128100.	+	18300.0i	−0.367998	+	0.0525711i
$591$	−340188.			−0.973967
$592$	41164.0	+	41164.0i	0.117456	+	0.117456i
$593$	148049.	−	148049.i	0.421014	−	0.421014i	−0.464539	−	0.885553i	$-0.653780\pi$
$593$	148049.	−	148049.i	0.421014	−	0.421014i	0.885553	+	0.464539i	$0.153780\pi$
$594$		−	8640.00i		−	0.0244873i
$595$	−780.000	+	1040.00i	−0.00220323	+	0.00293765i
$596$	−228900.			−0.644397
$597$	10800.0	+	10800.0i	0.0303023	+	0.0303023i
$598$	46148.0	−	46148.0i	0.129048	−	0.129048i
$599$			31800.0i			0.0886285i	0.999018	+	0.0443143i	$0.0141103\pi$
$599$			31800.0i			0.0886285i	−0.999018	+	0.0443143i	$0.985890\pi$
$600$	216000.	−	63000.0i	0.600000	−	0.175000i
$601$	−71848.0			−0.198914			−0.0994571	−	0.995042i	$-0.531711\pi$
$601$	−71848.0			−0.198914			−0.0994571	+	0.995042i	$0.531711\pi$
$602$	76648.0	+	76648.0i	0.211499	+	0.211499i
$603$	−7866.00	+	7866.00i	−0.0216331	+	0.0216331i
$604$		−	14728.0i		−	0.0403710i
$605$	−291540.	−	218655.i	−0.796503	−	0.597377i
$606$	193224.			0.526158
$607$	−13526.0	−	13526.0i	−0.0367106	−	0.0367106i	0.688513	−	0.725224i	$-0.258264\pi$
$607$	−13526.0	−	13526.0i	−0.0367106	−	0.0367106i	−0.725224	+	0.688513i	$0.758264\pi$
$608$	−115920.	+	115920.i	−0.313582	+	0.313582i
$609$		−	149760.i		−	0.403795i
$610$	−7960.00	−	55720.0i	−0.0213921	−	0.149745i
$611$	687772.			1.84231
$612$	−126.000	−	126.000i	−0.000336409	−	0.000336409i
$613$	−303461.	+	303461.i	−0.807573	+	0.807573i	−0.984266	−	0.176693i	$-0.943460\pi$
$613$	−303461.	+	303461.i	−0.807573	+	0.807573i	0.176693	+	0.984266i	$0.443460\pi$
$614$			235852.i			0.625609i
$615$	354480.	−	50640.0i	0.937220	−	0.133889i
$616$	−12480.0			−0.0328892
$617$	122399.	+	122399.i	0.321520	+	0.321520i	0.849350	−	0.527830i	$-0.176994\pi$
$617$	122399.	+	122399.i	0.321520	+	0.321520i	−0.527830	+	0.849350i	$0.676994\pi$
$618$	11928.0	−	11928.0i	0.0312313	−	0.0312313i
$619$		−	110220.i		−	0.287660i	−0.989602	−	0.143830i	$-0.954058\pi$
$619$		−	110220.i		−	0.287660i	0.989602	−	0.143830i	$-0.0459418\pi$
$620$	120120.	−	160160.i	0.312487	−	0.416649i
$621$	179280.			0.464888
$622$	−3892.00	−	3892.00i	−0.0100599	−	0.0100599i
$623$	56160.0	−	56160.0i	0.144694	−	0.144694i
$624$		−	273552.i		−	0.702539i
$625$	−329375.	+	210000.i	−0.843200	+	0.537600i
$626$	99922.0			0.254984
$627$	8640.00	+	8640.00i	0.0219775	+	0.0219775i
$628$	90986.0	−	90986.0i	0.230704	−	0.230704i
$629$			502.000i			0.00126883i
$630$	−9360.00	−	7020.00i	−0.0235828	−	0.0176871i
$631$	620372.			1.55809			0.779047	−	0.626966i	$-0.215703\pi$
$631$	620372.			1.55809			0.779047	+	0.626966i	$0.215703\pi$
$632$	−273600.	−	273600.i	−0.684986	−	0.684986i
$633$	−110352.	+	110352.i	−0.275406	+	0.275406i
$634$		−	34198.0i		−	0.0850790i
$635$	62870.0	+	440090.i	0.155918	+	1.09143i
$636$	−559608.			−1.38347
$637$	−145811.	−	145811.i	−0.359345	−	0.359345i
$638$	3840.00	−	3840.00i	0.00943387	−	0.00943387i
$639$		−	54612.0i		−	0.133748i
$640$	407400.	−	58200.0i	0.994629	−	0.142090i
$641$	−722888.			−1.75936			−0.879680	−	0.475565i	$-0.842244\pi$
$641$	−722888.			−1.75936			−0.879680	+	0.475565i	$0.842244\pi$
$642$	−99912.0	−	99912.0i	−0.242408	−	0.242408i
$643$	−393026.	+	393026.i	−0.950603	+	0.950603i	−0.998836	−	0.0482328i	$-0.984641\pi$
$643$	−393026.	+	393026.i	−0.950603	+	0.950603i	0.0482328	+	0.998836i	$0.484641\pi$
$644$		−	120848.i		−	0.291385i
$645$	−265320.	+	353760.i	−0.637750	+	0.850334i
$646$	−360.000			−0.000862656
$647$	−338626.	−	338626.i	−0.808931	−	0.808931i	0.175541	−	0.984472i	$-0.443833\pi$
$647$	−338626.	−	338626.i	−0.808931	−	0.808931i	−0.984472	+	0.175541i	$0.943833\pi$
$648$	−172530.	+	172530.i	−0.410880	+	0.410880i
$649$			29280.0i			0.0695155i
$650$	−48650.0	−	166800.i	−0.115148	−	0.394793i
$651$	178464.			0.421103
$652$	270004.	+	270004.i	0.635148	+	0.635148i
$653$	254669.	−	254669.i	0.597241	−	0.597241i	−0.342336	−	0.939577i	$-0.611218\pi$
$653$	254669.	−	254669.i	0.597241	−	0.597241i	0.939577	+	0.342336i	$0.111218\pi$
$654$		−	204120.i		−	0.477233i
$655$	405440.	+	304080.i	0.945027	+	0.708770i
$656$	276832.			0.643293
$657$	−7119.00	−	7119.00i	−0.0164926	−	0.0164926i
$658$	−128648.	+	128648.i	−0.297133	+	0.297133i
$659$		−	603660.i		−	1.39002i	−0.718999	−	0.695011i	$-0.755400\pi$
$659$		−	603660.i		−	1.39002i	0.718999	−	0.695011i	$-0.244600\pi$
$660$	−3360.00	−	23520.0i	−0.00771350	−	0.0539945i
$661$	14792.0			0.0338551			0.0169275	−	0.999857i	$-0.494612\pi$
$661$	14792.0			0.0338551			0.0169275	+	0.999857i	$0.494612\pi$
$662$	143128.	+	143128.i	0.326594	+	0.326594i
$663$	1668.00	−	1668.00i	0.00379463	−	0.00379463i
$664$			339240.i			0.769433i
$665$	163800.	−	23400.0i	0.370400	−	0.0529142i
$666$	−4518.00			−0.0101859
$667$	79680.0	+	79680.0i	0.179101	+	0.179101i
$668$	−217364.	+	217364.i	−0.487119	+	0.487119i
$669$		−	10392.0i		−	0.0232192i
$670$	26220.0	−	34960.0i	0.0584094	−	0.0778793i
$671$	−12736.0			−0.0282871
$672$	200928.	+	200928.i	0.444940	+	0.444940i
$673$	300409.	−	300409.i	0.663258	−	0.663258i	−0.292888	−	0.956147i	$-0.594616\pi$
$673$	300409.	−	300409.i	0.663258	−	0.663258i	0.956147	+	0.292888i	$0.0946164\pi$
$674$		−	206498.i		−	0.454565i
$675$	229500.	−	418500.i	0.503704	−	0.918519i
$676$	−141134.			−0.308843
$677$	−256051.	−	256051.i	−0.558662	−	0.558662i	0.370264	−	0.928926i	$-0.379267\pi$
$677$	−256051.	−	256051.i	−0.558662	−	0.558662i	−0.928926	+	0.370264i	$0.879267\pi$
$678$	−61932.0	+	61932.0i	−0.134727	+	0.134727i
$679$			340652.i			0.738876i
$680$	1200.00	+	900.000i	0.00259516	+	0.00194637i
$681$	542712.			1.17024
$682$	4576.00	+	4576.00i	0.00983824	+	0.00983824i
$683$	341954.	−	341954.i	0.733038	−	0.733038i	−0.238183	−	0.971220i	$-0.576552\pi$
$683$	341954.	−	341954.i	0.733038	−	0.733038i	0.971220	+	0.238183i	$0.0765517\pi$
$684$			22680.0i			0.0484765i
$685$	−51755.0	−	362285.i	−0.110299	−	0.772092i
$686$	179400.			0.381219
$687$	−234720.	−	234720.i	−0.497321	−	0.497321i
$688$	−241736.	+	241736.i	−0.510698	+	0.510698i
$689$			926018.i			1.95066i
$690$	−69720.0	+	9960.00i	−0.146440	+	0.0209200i
$691$	−717688.			−1.50307			−0.751536	−	0.659692i	$-0.770687\pi$
$691$	−717688.			−1.50307			−0.751536	+	0.659692i	$0.770687\pi$
$692$	236474.	+	236474.i	0.493823	+	0.493823i
$693$	−1872.00	+	1872.00i	−0.00389798	+	0.00389798i
$694$			209252.i			0.434461i
$695$	−405900.	+	541200.i	−0.840329	+	1.12044i
$696$	−172800.			−0.356718
$697$	1688.00	+	1688.00i	0.00347462	+	0.00347462i
$698$	94800.0	−	94800.0i	0.194580	−	0.194580i
$699$		−	397452.i		−	0.813449i
$700$	−282100.	−	154700.i	−0.575714	−	0.315714i
$701$	267352.			0.544061			0.272030	−	0.962289i	$-0.412305\pi$
$701$	267352.			0.544061			0.272030	+	0.962289i	$0.412305\pi$
$702$	150120.	+	150120.i	0.304624	+	0.304624i
$703$	45180.0	−	45180.0i	0.0914188	−	0.0914188i
$704$		−	10688.0i		−	0.0215651i
$705$	−593760.	−	445320.i	−1.19463	−	0.895971i
$706$	−127138.			−0.255074
$707$	−418652.	−	418652.i	−0.837557	−	0.837557i
$708$	307440.	−	307440.i	0.613330	−	0.613330i
$709$		−	159360.i		−	0.317020i	−0.987357	−	0.158510i	$-0.949331\pi$
$709$		−	159360.i		−	0.317020i	0.987357	−	0.158510i	$-0.0506690\pi$
$710$	30340.0	+	212380.i	0.0601865	+	0.421305i
$711$	−82080.0			−0.162367
$712$	−64800.0	−	64800.0i	−0.127825	−	0.127825i
$713$	−94952.0	+	94952.0i	−0.186778	+	0.186778i
$714$			624.000i			0.00122402i
$715$	−38920.0	+	5560.00i	−0.0761309	+	0.0108758i
$716$	148680.			0.290019
$717$	530640.	+	530640.i	1.03219	+	1.03219i
$718$	141840.	−	141840.i	0.275138	−	0.275138i
$719$			364680.i			0.705430i	0.935731	+	0.352715i	$0.114742\pi$
$719$			364680.i			0.705430i	−0.935731	+	0.352715i	$0.885258\pi$
$720$	22140.0	−	29520.0i	0.0427083	−	0.0569444i
$721$	−51688.0			−0.0994304
$722$	−97921.0	−	97921.0i	−0.187846	−	0.187846i
$723$	−121872.	+	121872.i	−0.233146	+	0.233146i
$724$		−	337708.i		−	0.644265i
$725$	288000.	−	84000.0i	0.547919	−	0.159810i
$726$	−174924.			−0.331876
$727$	716374.	+	716374.i	1.35541	+	1.35541i	0.879486	+	0.475925i	$0.157887\pi$
$727$	716374.	+	716374.i	1.35541	+	1.35541i	0.475925	+	0.879486i	$0.342113\pi$
$728$	216840.	−	216840.i	0.409144	−	0.409144i
$729$			576639.i			1.08505i
$730$	31640.0	+	23730.0i	0.0593732	+	0.0445299i
$731$	−2948.00			−0.00551687
$732$	133728.	+	133728.i	0.249574	+	0.249574i
$733$	641029.	−	641029.i	1.19308	−	1.19308i	0.216883	−	0.976198i	$-0.430411\pi$
$733$	641029.	−	641029.i	1.19308	−	1.19308i	0.976198	−	0.216883i	$-0.0695889\pi$
$734$		−	284348.i		−	0.527786i
$735$	31470.0	+	220290.i	0.0582535	+	0.407775i
$736$	−213808.			−0.394701
$737$	−6992.00	−	6992.00i	−0.0128726	−	0.0128726i
$738$	−15192.0	+	15192.0i	−0.0278934	+	0.0278934i
$739$		−	607140.i		−	1.11173i	−0.831272	−	0.555866i	$-0.812387\pi$
$739$		−	607140.i		−	1.11173i	0.831272	−	0.555866i	$-0.187613\pi$
$740$	−122990.	+	17570.0i	−0.224598	+	0.0320855i
$741$	−300240.			−0.546805
$742$	−173212.	−	173212.i	−0.314608	−	0.314608i
$743$	−248026.	+	248026.i	−0.449283	+	0.449283i	−0.895116	−	0.445833i	$-0.852907\pi$
$743$	−248026.	+	248026.i	−0.449283	+	0.449283i	0.445833	+	0.895116i	$0.352907\pi$
$744$		−	205920.i		−	0.372008i
$745$	245250.	−	327000.i	0.441872	−	0.589163i
$746$	−20618.0			−0.0370484
$747$	50886.0	+	50886.0i	0.0911921	+	0.0911921i
$748$	112.000	−	112.000i	0.000200177	−	0.000200177i
$749$			432952.i			0.771749i
$750$	−66000.0	+	175500.i	−0.117333	+	0.312000i
$751$	169052.			0.299737			0.149869	−	0.988706i	$-0.452115\pi$
$751$	169052.			0.299737			0.149869	+	0.988706i	$0.452115\pi$
$752$	−405736.	−	405736.i	−0.717477	−	0.717477i
$753$	−448512.	+	448512.i	−0.791014	+	0.791014i
$754$			133440.i			0.234716i
$755$	21040.0	+	15780.0i	0.0369107	+	0.0276830i
$756$	393120.			0.687831
$757$	−166301.	−	166301.i	−0.290204	−	0.290204i	0.546957	−	0.837161i	$-0.315786\pi$
$757$	−166301.	−	166301.i	−0.290204	−	0.290204i	−0.837161	+	0.546957i	$0.815786\pi$
$758$	−115380.	+	115380.i	−0.200813	+	0.200813i
$759$			15936.0i			0.0276628i
$760$	−27000.0	−	189000.i	−0.0467452	−	0.327216i
$761$	557842.			0.963256			0.481628	−	0.876376i	$-0.340046\pi$
$761$	557842.			0.963256			0.481628	+	0.876376i	$0.340046\pi$
$762$	150888.	+	150888.i	0.259863	+	0.259863i
$763$	−442260.	+	442260.i	−0.759676	+	0.759676i
$764$			632632.i			1.08384i
$765$	315.000	−	45.0000i	0.000538255	−	7.68935e-5i
$766$	−125308.			−0.213561
$767$	−508740.	−	508740.i	−0.864779	−	0.864779i
$768$	11424.0	−	11424.0i	0.0193685	−	0.0193685i
$769$		−	678720.i		−	1.14773i	−0.818952	−	0.573863i	$-0.805444\pi$
$769$		−	678720.i		−	1.14773i	0.818952	−	0.573863i	$-0.194556\pi$
$770$	6240.00	−	8320.00i	0.0105245	−	0.0140327i
$771$	−453588.			−0.763050
$772$	−548786.	−	548786.i	−0.920807	−	0.920807i
$773$	−164341.	+	164341.i	−0.275034	+	0.275034i	−0.831123	−	0.556089i	$-0.812301\pi$
$773$	−164341.	+	164341.i	−0.275034	+	0.275034i	0.556089	+	0.831123i	$0.312301\pi$
$774$		−	26532.0i		−	0.0442882i
$775$	100100.	+	343200.i	0.166660	+	0.571405i
$776$	393060.			0.652733
$777$	−78312.0	−	78312.0i	−0.129714	−	0.129714i
$778$	−132690.	+	132690.i	−0.219219	+	0.219219i
$779$		−	303840.i		−	0.500691i
$780$	467040.	+	350280.i	0.767653	+	0.575740i
$781$	48544.0			0.0795854
$782$	−332.000	−	332.000i	−0.000542906	−	0.000542906i
$783$	−259200.	+	259200.i	−0.422777	+	0.422777i
$784$			172036.i			0.279890i
$785$	32495.0	+	227465.i	0.0527324	+	0.369127i
$786$	243264.			0.393761
$787$	323074.	+	323074.i	0.521618	+	0.521618i	0.918060	−	0.396442i	$-0.129755\pi$
$787$	323074.	+	323074.i	0.521618	+	0.521618i	−0.396442	+	0.918060i	$0.629755\pi$
$788$	396886.	−	396886.i	0.639166	−	0.639166i
$789$		−	403032.i		−	0.647419i
$790$	319200.	−	45600.0i	0.511456	−	0.0730652i
$791$	268372.			0.428928
$792$	2160.00	+	2160.00i	0.00344353	+	0.00344353i
$793$	221288.	−	221288.i	0.351894	−	0.351894i
$794$			176902.i			0.280603i
$795$	599580.	−	799440.i	0.948665	−	1.26489i
$796$	−25200.0			−0.0397717
$797$	510299.	+	510299.i	0.803356	+	0.803356i	0.983619	−	0.180262i	$-0.0576947\pi$
$797$	510299.	+	510299.i	0.803356	+	0.803356i	−0.180262	+	0.983619i	$0.557695\pi$
$798$	56160.0	−	56160.0i	0.0881904	−	0.0881904i
$799$		−	4948.00i		−	0.00775061i
$800$	−273700.	+	499100.i	−0.427656	+	0.779844i
$801$	−19440.0			−0.0302992
$802$	−63202.0	−	63202.0i	−0.0982612	−	0.0982612i
$803$	6328.00	−	6328.00i	0.00981376	−	0.00981376i
$804$			146832.i			0.227148i
$805$	172640.	+	129480.i	0.266409	+	0.199807i
$806$	−159016.			−0.244777
$807$	−171180.	−	171180.i	−0.262849	−	0.262849i
$808$	−483060.	+	483060.i	−0.739909	+	0.739909i
$809$		−	1.18656e6i		−	1.81298i	−0.422229	−	0.906489i	$-0.638752\pi$
$809$		−	1.18656e6i		−	1.81298i	0.422229	−	0.906489i	$-0.361248\pi$
$810$	−28755.0	−	201285.i	−0.0438272	−	0.306790i
$811$	−431008.			−0.655305			−0.327653	−	0.944798i	$-0.606258\pi$
$811$	−431008.			−0.655305			−0.327653	+	0.944798i	$0.606258\pi$
$812$	174720.	+	174720.i	0.264991	+	0.264991i
$813$	44808.0	−	44808.0i	0.0677914	−	0.0677914i
$814$		−	4016.00i		−	0.00606101i
$815$	−675010.	+	96430.0i	−1.01624	+	0.145177i
$816$	−1968.00			−0.00295559
$817$	265320.	+	265320.i	0.397490	+	0.397490i
$818$	52890.0	−	52890.0i	0.0790436	−	0.0790436i
$819$		−	65052.0i		−	0.0969824i
$820$	−354480.	+	472640.i	−0.527186	+	0.702915i
$821$	−639368.			−0.948560			−0.474280	−	0.880374i	$-0.657291\pi$
$821$	−639368.			−0.948560			−0.474280	+	0.880374i	$0.657291\pi$
$822$	−124212.	−	124212.i	−0.183831	−	0.183831i
$823$	−74966.0	+	74966.0i	−0.110679	+	0.110679i	−0.760277	−	0.649599i	$-0.774937\pi$
$823$	−74966.0	+	74966.0i	−0.110679	+	0.110679i	0.649599	+	0.760277i	$0.274937\pi$
$824$			59640.0i			0.0878382i
$825$	37200.0	+	20400.0i	0.0546556	+	0.0299725i
$826$	190320.			0.278949
$827$	−144226.	−	144226.i	−0.210879	−	0.210879i	0.593762	−	0.804641i	$-0.297642\pi$
$827$	−144226.	−	144226.i	−0.210879	−	0.210879i	−0.804641	+	0.593762i	$0.797642\pi$
$828$	−20916.0	+	20916.0i	−0.0305083	+	0.0305083i
$829$			685170.i			0.996987i	0.866894	+	0.498493i	$0.166113\pi$
$829$			685170.i			0.996987i	−0.866894	+	0.498493i	$0.833887\pi$
$830$	−226160.	−	169620.i	−0.328291	−	0.246219i
$831$	−77988.0			−0.112934
$832$	185704.	+	185704.i	0.268272	+	0.268272i
$833$	−1049.00	+	1049.00i	−0.00151177	+	0.00151177i
$834$			324720.i			0.466850i
$835$	−77630.0	−	543410.i	−0.111341	−	0.779390i
$836$	−20160.0			−0.0288455
$837$	−308880.	−	308880.i	−0.440899	−	0.440899i
$838$	256980.	−	256980.i	0.365941	−	0.365941i
$839$			445560.i			0.632969i	0.948598	+	0.316484i	$0.102502\pi$
$839$			445560.i			0.632969i	−0.948598	+	0.316484i	$0.897498\pi$
$840$	−327600.	+	46800.0i	−0.464286	+	0.0663265i
$841$	476881.			0.674245
$842$	−186632.	−	186632.i	−0.263246	−	0.263246i
$843$	587568.	−	587568.i	0.826805	−	0.826805i
$844$		−	257488.i		−	0.361470i
$845$	151215.	−	201620.i	0.211778	−	0.282371i
$846$	44532.0			0.0622202
$847$	379002.	+	379002.i	0.528293	+	0.528293i
$848$	546284.	−	546284.i	0.759673	−	0.759673i
$849$			718248.i			0.996458i
$850$	−1200.00	+	350.000i	−0.00166090	+	0.000484429i
$851$	83332.0			0.115068
$852$	−509712.	−	509712.i	−0.702175	−	0.702175i
$853$	−319781.	+	319781.i	−0.439496	+	0.439496i	−0.891842	−	0.452347i	$-0.850587\pi$
$853$	−319781.	+	319781.i	−0.439496	+	0.439496i	0.452347	+	0.891842i	$0.350587\pi$
$854$			82784.0i			0.113509i
$855$	−32400.0	−	24300.0i	−0.0443213	−	0.0332410i
$856$	499560.			0.681774
$857$	576449.	+	576449.i	0.784873	+	0.784873i	0.980649	−	0.195776i	$-0.0627225\pi$
$857$	576449.	+	576449.i	0.784873	+	0.784873i	−0.195776	+	0.980649i	$0.562723\pi$
$858$	−13344.0	+	13344.0i	−0.0181264	+	0.0181264i
$859$			807540.i			1.09440i	0.837001	+	0.547202i	$0.184307\pi$
$859$			807540.i			1.09440i	−0.837001	+	0.547202i	$0.815693\pi$
$860$	−103180.	−	722260.i	−0.139508	−	0.976555i
$861$	−526656.			−0.710429
$862$	208028.	+	208028.i	0.279967	+	0.279967i
$863$	507914.	−	507914.i	0.681975	−	0.681975i	−0.278470	−	0.960445i	$-0.589827\pi$
$863$	507914.	−	507914.i	0.681975	−	0.681975i	0.960445	+	0.278470i	$0.0898272\pi$
$864$		−	695520.i		−	0.931713i
$865$	−591185.	+	84455.0i	−0.790117	+	0.112874i
$866$	302542.			0.403413
$867$	501114.	+	501114.i	0.666651	+	0.666651i
$868$	−208208.	+	208208.i	−0.276349	+	0.276349i
$869$		−	72960.0i		−	0.0966152i
$870$	86400.0	−	115200.i	0.114150	−	0.152200i
$871$	242972.			0.320273
$872$	510300.	+	510300.i	0.671108	+	0.671108i
$873$	58959.0	−	58959.0i	0.0773609	−	0.0773609i
$874$			59760.0i			0.0782326i
$875$	523250.	−	237250.i	0.683429	−	0.309878i
$876$	−132888.			−0.173172
$877$	−673901.	−	673901.i	−0.876187	−	0.876187i	0.116951	−	0.993138i	$-0.462688\pi$
$877$	−673901.	−	673901.i	−0.876187	−	0.876187i	−0.993138	+	0.116951i	$0.962688\pi$
$878$	−158640.	+	158640.i	−0.205790	+	0.205790i
$879$			341988.i			0.442622i
$880$	26240.0	+	19680.0i	0.0338843	+	0.0254132i
$881$	−1.33753e6			−1.72326			−0.861631	−	0.507536i	$-0.830556\pi$
$881$	−1.33753e6			−1.72326			−0.861631	+	0.507536i	$0.830556\pi$
$882$	−9441.00	−	9441.00i	−0.0121361	−	0.0121361i
$883$	131554.	−	131554.i	0.168726	−	0.168726i	−0.617693	−	0.786419i	$-0.711933\pi$
$883$	131554.	−	131554.i	0.168726	−	0.168726i	0.786419	+	0.617693i	$0.211933\pi$
$884$			3892.00i			0.00498045i
$885$	109800.	+	768600.i	0.140190	+	0.981327i
$886$	−505948.			−0.644523
$887$	−327826.	−	327826.i	−0.416674	−	0.416674i	0.467382	−	0.884056i	$-0.345197\pi$
$887$	−327826.	−	327826.i	−0.416674	−	0.416674i	−0.884056	+	0.467382i	$0.845197\pi$
$888$	−90360.0	+	90360.0i	−0.114591	+	0.114591i
$889$		−	653848.i		−	0.827320i
$890$	75600.0	−	10800.0i	0.0954425	−	0.0136346i
$891$	−46008.0			−0.0579533
$892$	12124.0	+	12124.0i	0.0152376	+	0.0152376i
$893$	−445320.	+	445320.i	−0.558431	+	0.558431i
$894$		−	196200.i		−	0.245484i
$895$	−159300.	+	212400.i	−0.198870	+	0.265160i
$896$	−605280.			−0.753946
$897$	−276888.	−	276888.i	−0.344127	−	0.344127i
$898$	123750.	−	123750.i	0.153459	−	0.153459i
$899$		−	274560.i		−	0.339717i
$900$	22050.0	+	75600.0i	0.0272222	+	0.0933333i
$901$	6662.00			0.00820644
$902$	−13504.0	−	13504.0i	−0.0165978	−	0.0165978i
$903$	459888.	−	459888.i	0.563997	−	0.563997i
$904$		−	309660.i		−	0.378921i
$905$	482440.	+	361830.i	0.589042	+	0.441781i
$906$	12624.0			0.0153794
$907$	105274.	+	105274.i	0.127970	+	0.127970i	0.768191	−	0.640221i	$-0.221157\pi$
$907$	105274.	+	105274.i	0.127970	+	0.127970i	−0.640221	+	0.768191i	$0.721157\pi$
$908$	−633164.	+	633164.i	−0.767970	+	0.767970i
$909$			144918.i			0.175386i
$910$	36140.0	+	252980.i	0.0436421	+	0.305495i
$911$	1.59209e6			1.91837			0.959183	−	0.282787i	$-0.0912588\pi$
$911$	1.59209e6			1.91837			0.959183	+	0.282787i	$0.0912588\pi$
$912$	177120.	+	177120.i	0.212950	+	0.212950i
$913$	−45232.0	+	45232.0i	−0.0542631	+	0.0542631i
$914$			64402.0i			0.0770916i
$915$	−334320.	+	47760.0i	−0.399319	+	0.0570456i
$916$	547680.			0.652734
$917$	−527072.	−	527072.i	−0.626803	−	0.626803i
$918$	1080.00	−	1080.00i	0.00128156	−	0.00128156i
$919$			515880.i			0.610826i	0.952220	+	0.305413i	$0.0987946\pi$
$919$			515880.i			0.610826i	−0.952220	+	0.305413i	$0.901205\pi$
$920$	149400.	−	199200.i	0.176512	−	0.235350i
$921$	1.41511e6			1.66829
$922$	−75142.0	−	75142.0i	−0.0883936	−	0.0883936i
$923$	−843452.	+	843452.i	−0.990050	+	0.990050i
$924$			34944.0i			0.0409288i
$925$	106675.	−	194525.i	0.124675	−	0.227348i
$926$	−471428.			−0.549786
$927$	8946.00	+	8946.00i	0.0104104	+	0.0104104i
$928$	309120.	−	309120.i	0.358948	−	0.358948i
$929$		−	1.60023e6i		−	1.85418i	−0.374844	−	0.927088i	$-0.622304\pi$
$929$		−	1.60023e6i		−	1.85418i	0.374844	−	0.927088i	$-0.377696\pi$
$930$	137280.	+	102960.i	0.158724	+	0.119043i
$931$	188820.			0.217846
$932$	463694.	+	463694.i	0.533826	+	0.533826i
$933$	−23352.0	+	23352.0i	−0.0268263	+	0.0268263i
$934$		−	57148.0i		−	0.0655100i
$935$	40.0000	+	280.000i	4.57548e−5	+	0.000320284i
$936$	−75060.0			−0.0856755
$937$	−908801.	−	908801.i	−1.03512	−	1.03512i	−0.999361	−	0.0357569i	$-0.988616\pi$
$937$	−908801.	−	908801.i	−1.03512	−	1.03512i	−0.0357569	−	0.999361i	$-0.511384\pi$
$938$	−45448.0	+	45448.0i	−0.0516546	+	0.0516546i
$939$		−	599532.i		−	0.679957i
$940$	1.21226e6	−	173180.i	1.37196	−	0.195994i
$941$	455962.			0.514931			0.257466	−	0.966287i	$-0.417113\pi$
$941$	455962.			0.514931			0.257466	+	0.966287i	$0.417113\pi$
$942$	77988.0	+	77988.0i	0.0878873	+	0.0878873i
$943$	280208.	−	280208.i	0.315106	−	0.315106i
$944$			600240.i			0.673567i
$945$	−421200.	+	561600.i	−0.471655	+	0.628874i
$946$	23584.0			0.0263533
$947$	463274.	+	463274.i	0.516580	+	0.516580i	0.916535	−	0.399955i	$-0.130974\pi$
$947$	463274.	+	463274.i	0.516580	+	0.516580i	−0.399955	+	0.916535i	$0.630974\pi$
$948$	−766080.	+	766080.i	−0.852427	+	0.852427i
$949$			219898.i			0.244168i
$950$	139500.	+	76500.0i	0.154571	+	0.0847645i
$951$	−205188.			−0.226877
$952$	−1560.00	−	1560.00i	−0.00172128	−	0.00172128i
$953$	−1.03428e6	+	1.03428e6i	−1.13881	+	1.13881i	−0.150151	+	0.988663i	$0.547976\pi$
$953$	−1.03428e6	+	1.03428e6i	−1.13881	+	1.13881i	−0.988663	+	0.150151i	$0.952024\pi$
$954$			59958.0i			0.0658795i
$955$	−903760.	−	677820.i	−0.990938	−	0.743203i
$956$	−1.23816e6			−1.35476
$957$	−23040.0	−	23040.0i	−0.0251570	−	0.0251570i
$958$	26520.0	−	26520.0i	0.0288963	−	0.0288963i
$959$			538252.i			0.585259i
$960$	−40080.0	−	280560.i	−0.0434896	−	0.304427i
$961$	−596337.			−0.645721
$962$	69778.0	+	69778.0i	0.0753995	+	0.0753995i
$963$	74934.0	−	74934.0i	0.0808028	−	0.0808028i
$964$		−	284368.i		−	0.306004i
$965$	1.37196e6	−	195995.i	1.47329	−	0.210470i
$966$	103584.			0.111004
$967$	−1.10253e6	−	1.10253e6i	−1.17906	−	1.17906i	−0.979984	−	0.199076i	$-0.936206\pi$
$967$	−1.10253e6	−	1.10253e6i	−1.17906	−	1.17906i	−0.199076	−	0.979984i	$-0.563794\pi$
$968$	437310.	−	437310.i	0.466701	−	0.466701i
$969$			2160.00i			0.00230042i
$970$	−196530.	+	262040.i	−0.208874	+	0.278499i
$971$	−264368.			−0.280395			−0.140198	−	0.990124i	$-0.544774\pi$
$971$	−264368.			−0.280395			−0.140198	+	0.990124i	$0.544774\pi$
$972$	−129276.	−	129276.i	−0.136831	−	0.136831i
$973$	703560.	−	703560.i	0.743148	−	0.743148i
$974$		−	82748.0i		−	0.0872247i
$975$	−1.00080e6	+	291900.i	−1.05278	+	0.307061i
$976$	−261088.			−0.274086
$977$	866249.	+	866249.i	0.907515	+	0.907515i	0.996071	−	0.0885566i	$-0.0282254\pi$
$977$	866249.	+	866249.i	0.907515	+	0.907515i	−0.0885566	+	0.996071i	$0.528225\pi$
$978$	−231432.	+	231432.i	−0.241961	+	0.241961i
$979$		−	17280.0i		−	0.0180293i
$980$	−293720.	−	220290.i	−0.305831	−	0.229373i
$981$	153090.			0.159078
$982$	149288.	+	149288.i	0.154811	+	0.154811i
$983$	1.08205e6	−	1.08205e6i	1.11980	−	1.11980i	0.128034	−	0.991770i	$-0.459133\pi$
$983$	1.08205e6	−	1.08205e6i	1.11980	−	1.11980i	0.991770	−	0.128034i	$-0.0408666\pi$
$984$			607680.i			0.627603i
$985$	141745.	+	992215.i	0.146095	+	1.02266i
$986$	960.000			0.000987455
$987$	771888.	+	771888.i	0.792355	+	0.792355i
$988$	350280.	−	350280.i	0.358840	−	0.358840i
$989$			489368.i			0.500314i
$990$	−2520.00	+	360.000i	−0.00257117	+	0.000367309i
$991$	−54988.0			−0.0559913			−0.0279957	−	0.999608i	$-0.508912\pi$
$991$	−54988.0			−0.0559913			−0.0279957	+	0.999608i	$0.508912\pi$
$992$	368368.	+	368368.i	0.374333	+	0.374333i
$993$	858768.	−	858768.i	0.870918	−	0.870918i
$994$		−	315536.i		−	0.319357i
$995$	27000.0	−	36000.0i	0.0272720	−	0.0363627i
$996$	949872.			0.957517
$997$	73099.0	+	73099.0i	0.0735396	+	0.0735396i	0.742920	−	0.669380i	$-0.233440\pi$
$997$	73099.0	+	73099.0i	0.0735396	+	0.0735396i	−0.669380	+	0.742920i	$0.733440\pi$
$998$	284100.	−	284100.i	0.285240	−	0.285240i
$999$			271080.i			0.271623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.5.c.a.2.1	✓	2
3.2	odd	2		45.5.g.b.37.1		2
4.3	odd	2		80.5.p.d.17.1		2
5.2	odd	4		25.5.c.a.18.1		2
5.3	odd	4	inner	5.5.c.a.3.1	yes	2
5.4	even	2		25.5.c.a.7.1		2
8.3	odd	2		320.5.p.c.257.1		2
8.5	even	2		320.5.p.h.257.1		2
15.2	even	4		225.5.g.b.118.1		2
15.8	even	4		45.5.g.b.28.1		2
15.14	odd	2		225.5.g.b.82.1		2
20.3	even	4		80.5.p.d.33.1		2
20.7	even	4		400.5.p.a.193.1		2
20.19	odd	2		400.5.p.a.257.1		2
40.3	even	4		320.5.p.c.193.1		2
40.13	odd	4		320.5.p.h.193.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.5.c.a.2.1	✓	2	1.1	even	1	trivial
5.5.c.a.3.1	yes	2	5.3	odd	4	inner
25.5.c.a.7.1		2	5.4	even	2
25.5.c.a.18.1		2	5.2	odd	4
45.5.g.b.28.1		2	15.8	even	4
45.5.g.b.37.1		2	3.2	odd	2
80.5.p.d.17.1		2	4.3	odd	2
80.5.p.d.33.1		2	20.3	even	4
225.5.g.b.82.1		2	15.14	odd	2
225.5.g.b.118.1		2	15.2	even	4
320.5.p.c.193.1		2	40.3	even	4
320.5.p.c.257.1		2	8.3	odd	2
320.5.p.h.193.1		2	40.13	odd	4
320.5.p.h.257.1		2	8.5	even	2
400.5.p.a.193.1		2	20.7	even	4
400.5.p.a.257.1		2	20.19	odd	2

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-6.00000 + 6.00000i) q^{3} -14.0000i q^{4} +(20.0000 + 15.0000i) q^{5} +12.0000 q^{6} +(-26.0000 - 26.0000i) q^{7} +(-30.0000 + 30.0000i) q^{8} +9.00000i q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +(-6.00000 + 6.00000i) q^{3} -14.0000i q^{4} +(20.0000 + 15.0000i) q^{5} +12.0000 q^{6} +(-26.0000 - 26.0000i) q^{7} +(-30.0000 + 30.0000i) q^{8} +9.00000i q^{9} +(-5.00000 - 35.0000i) q^{10} -8.00000 q^{11} +(84.0000 + 84.0000i) q^{12} +(139.000 - 139.000i) q^{13} +52.0000i q^{14} +(-210.000 + 30.0000i) q^{15} -164.000 q^{16} +(-1.00000 - 1.00000i) q^{17} +(9.00000 - 9.00000i) q^{18} +180.000i q^{19} +(210.000 - 280.000i) q^{20} +312.000 q^{21} +(8.00000 + 8.00000i) q^{22} +(-166.000 + 166.000i) q^{23} -360.000i q^{24} +(175.000 + 600.000i) q^{25} -278.000 q^{26} +(-540.000 - 540.000i) q^{27} +(-364.000 + 364.000i) q^{28} -480.000i q^{29} +(240.000 + 180.000i) q^{30} +572.000 q^{31} +(644.000 + 644.000i) q^{32} +(48.0000 - 48.0000i) q^{33} +2.00000i q^{34} +(-130.000 - 910.000i) q^{35} +126.000 q^{36} +(-251.000 - 251.000i) q^{37} +(180.000 - 180.000i) q^{38} +1668.00i q^{39} +(-1050.00 + 150.000i) q^{40} -1688.00 q^{41} +(-312.000 - 312.000i) q^{42} +(1474.00 - 1474.00i) q^{43} +112.000i q^{44} +(-135.000 + 180.000i) q^{45} +332.000 q^{46} +(2474.00 + 2474.00i) q^{47} +(984.000 - 984.000i) q^{48} -1049.00i q^{49} +(425.000 - 775.000i) q^{50} +12.0000 q^{51} +(-1946.00 - 1946.00i) q^{52} +(-3331.00 + 3331.00i) q^{53} +1080.00i q^{54} +(-160.000 - 120.000i) q^{55} +1560.00 q^{56} +(-1080.00 - 1080.00i) q^{57} +(-480.000 + 480.000i) q^{58} -3660.00i q^{59} +(420.000 + 2940.00i) q^{60} +1592.00 q^{61} +(-572.000 - 572.000i) q^{62} +(234.000 - 234.000i) q^{63} +1336.00i q^{64} +(4865.00 - 695.000i) q^{65} -96.0000 q^{66} +(874.000 + 874.000i) q^{67} +(-14.0000 + 14.0000i) q^{68} -1992.00i q^{69} +(-780.000 + 1040.00i) q^{70} -6068.00 q^{71} +(-270.000 - 270.000i) q^{72} +(-791.000 + 791.000i) q^{73} +502.000i q^{74} +(-4650.00 - 2550.00i) q^{75} +2520.00 q^{76} +(208.000 + 208.000i) q^{77} +(1668.00 - 1668.00i) q^{78} +9120.00i q^{79} +(-3280.00 - 2460.00i) q^{80} +5751.00 q^{81} +(1688.00 + 1688.00i) q^{82} +(5654.00 - 5654.00i) q^{83} -4368.00i q^{84} +(-5.00000 - 35.0000i) q^{85} -2948.00 q^{86} +(2880.00 + 2880.00i) q^{87} +(240.000 - 240.000i) q^{88} +2160.00i q^{89} +(315.000 - 45.0000i) q^{90} -7228.00 q^{91} +(2324.00 + 2324.00i) q^{92} +(-3432.00 + 3432.00i) q^{93} -4948.00i q^{94} +(-2700.00 + 3600.00i) q^{95} -7728.00 q^{96} +(-6551.00 - 6551.00i) q^{97} +(-1049.00 + 1049.00i) q^{98} -72.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 12 q^{3} + 40 q^{5} + 24 q^{6} - 52 q^{7} - 60 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 12 * q^3 + 40 * q^5 + 24 * q^6 - 52 * q^7 - 60 * q^8	\( 2 q - 2 q^{2} - 12 q^{3} + 40 q^{5} + 24 q^{6} - 52 q^{7} - 60 q^{8} - 10 q^{10} - 16 q^{11} + 168 q^{12} + 278 q^{13} - 420 q^{15} - 328 q^{16} - 2 q^{17} + 18 q^{18} + 420 q^{20} + 624 q^{21} + 16 q^{22} - 332 q^{23} + 350 q^{25} - 556 q^{26} - 1080 q^{27} - 728 q^{28} + 480 q^{30} + 1144 q^{31} + 1288 q^{32} + 96 q^{33} - 260 q^{35} + 252 q^{36} - 502 q^{37} + 360 q^{38} - 2100 q^{40} - 3376 q^{41} - 624 q^{42} + 2948 q^{43} - 270 q^{45} + 664 q^{46} + 4948 q^{47} + 1968 q^{48} + 850 q^{50} + 24 q^{51} - 3892 q^{52} - 6662 q^{53} - 320 q^{55} + 3120 q^{56} - 2160 q^{57} - 960 q^{58} + 840 q^{60} + 3184 q^{61} - 1144 q^{62} + 468 q^{63} + 9730 q^{65} - 192 q^{66} + 1748 q^{67} - 28 q^{68} - 1560 q^{70} - 12136 q^{71} - 540 q^{72} - 1582 q^{73} - 9300 q^{75} + 5040 q^{76} + 416 q^{77} + 3336 q^{78} - 6560 q^{80} + 11502 q^{81} + 3376 q^{82} + 11308 q^{83} - 10 q^{85} - 5896 q^{86} + 5760 q^{87} + 480 q^{88} + 630 q^{90} - 14456 q^{91} + 4648 q^{92} - 6864 q^{93} - 5400 q^{95} - 15456 q^{96} - 13102 q^{97} - 2098 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 12 * q^3 + 40 * q^5 + 24 * q^6 - 52 * q^7 - 60 * q^8 - 10 * q^10 - 16 * q^11 + 168 * q^12 + 278 * q^13 - 420 * q^15 - 328 * q^16 - 2 * q^17 + 18 * q^18 + 420 * q^20 + 624 * q^21 + 16 * q^22 - 332 * q^23 + 350 * q^25 - 556 * q^26 - 1080 * q^27 - 728 * q^28 + 480 * q^30 + 1144 * q^31 + 1288 * q^32 + 96 * q^33 - 260 * q^35 + 252 * q^36 - 502 * q^37 + 360 * q^38 - 2100 * q^40 - 3376 * q^41 - 624 * q^42 + 2948 * q^43 - 270 * q^45 + 664 * q^46 + 4948 * q^47 + 1968 * q^48 + 850 * q^50 + 24 * q^51 - 3892 * q^52 - 6662 * q^53 - 320 * q^55 + 3120 * q^56 - 2160 * q^57 - 960 * q^58 + 840 * q^60 + 3184 * q^61 - 1144 * q^62 + 468 * q^63 + 9730 * q^65 - 192 * q^66 + 1748 * q^67 - 28 * q^68 - 1560 * q^70 - 12136 * q^71 - 540 * q^72 - 1582 * q^73 - 9300 * q^75 + 5040 * q^76 + 416 * q^77 + 3336 * q^78 - 6560 * q^80 + 11502 * q^81 + 3376 * q^82 + 11308 * q^83 - 10 * q^85 - 5896 * q^86 + 5760 * q^87 + 480 * q^88 + 630 * q^90 - 14456 * q^91 + 4648 * q^92 - 6864 * q^93 - 5400 * q^95 - 15456 * q^96 - 13102 * q^97 - 2098 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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