LMFDB - Embedded newform 40.6.k.a.3.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.k (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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.12
Character	$\chi$	$=$	40.3
Dual form			40.6.k.a.27.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.949067 + 5.57667i) q^{2} +(-3.12794 - 3.12794i) q^{3} +(-30.1985 - 10.5853i) q^{4} +(34.4559 - 44.0204i) q^{5} +(20.4121 - 14.4749i) q^{6} +(19.1929 + 19.1929i) q^{7} +(87.6910 - 158.361i) q^{8} -223.432i q^{9} +O(q^{10})$	\(q+(-0.949067 + 5.57667i) q^{2} +(-3.12794 - 3.12794i) q^{3} +(-30.1985 - 10.5853i) q^{4} +(34.4559 - 44.0204i) q^{5} +(20.4121 - 14.4749i) q^{6} +(19.1929 + 19.1929i) q^{7} +(87.6910 - 158.361i) q^{8} -223.432i q^{9} +(212.786 + 233.927i) q^{10} +648.221 q^{11} +(61.3491 + 127.569i) q^{12} +(-392.250 + 392.250i) q^{13} +(-125.248 + 88.8172i) q^{14} +(-245.469 + 29.9171i) q^{15} +(799.904 + 639.320i) q^{16} +(739.873 - 739.873i) q^{17} +(1246.01 + 212.052i) q^{18} -1806.23i q^{19} +(-1506.49 + 964.626i) q^{20} -120.068i q^{21} +(-615.206 + 3614.92i) q^{22} +(1662.57 - 1662.57i) q^{23} +(-769.636 + 221.052i) q^{24} +(-750.584 - 3033.52i) q^{25} +(-1815.18 - 2559.72i) q^{26} +(-1458.97 + 1458.97i) q^{27} +(-376.436 - 782.760i) q^{28} -7682.01 q^{29} +(66.1286 - 1397.29i) q^{30} -2500.39i q^{31} +(-4324.44 + 3854.04i) q^{32} +(-2027.59 - 2027.59i) q^{33} +(3423.84 + 4828.22i) q^{34} +(1506.19 - 183.570i) q^{35} +(-2365.09 + 6747.32i) q^{36} +(4619.77 + 4619.77i) q^{37} +(10072.8 + 1714.23i) q^{38} +2453.86 q^{39} +(-3949.65 - 9316.67i) q^{40} -1664.65 q^{41} +(669.582 + 113.953i) q^{42} +(11387.6 + 11387.6i) q^{43} +(-19575.3 - 6861.60i) q^{44} +(-9835.56 - 7698.55i) q^{45} +(7693.72 + 10849.5i) q^{46} +(12902.6 + 12902.6i) q^{47} +(-502.298 - 4501.80i) q^{48} -16070.3i q^{49} +(17629.3 - 1306.75i) q^{50} -4628.55 q^{51} +(15997.4 - 7693.30i) q^{52} +(-12615.7 + 12615.7i) q^{53} +(-6751.54 - 9520.86i) q^{54} +(22335.0 - 28534.9i) q^{55} +(4722.46 - 1356.37i) q^{56} +(-5649.78 + 5649.78i) q^{57} +(7290.75 - 42840.1i) q^{58} +30075.1i q^{59} +(7729.48 + 1694.90i) q^{60} +22710.0i q^{61} +(13943.8 + 2373.04i) q^{62} +(4288.31 - 4288.31i) q^{63} +(-17388.6 - 27773.7i) q^{64} +(3751.66 + 30782.3i) q^{65} +(13231.6 - 9382.91i) q^{66} +(-6337.59 + 6337.59i) q^{67} +(-30174.8 + 14511.3i) q^{68} -10400.8 q^{69} +(-405.763 + 8573.73i) q^{70} +2950.81i q^{71} +(-35383.0 - 19593.0i) q^{72} +(-10777.2 - 10777.2i) q^{73} +(-30147.4 + 21378.5i) q^{74} +(-7140.88 + 11836.4i) q^{75} +(-19119.5 + 54545.6i) q^{76} +(12441.2 + 12441.2i) q^{77} +(-2328.88 + 13684.4i) q^{78} +7474.95 q^{79} +(55704.5 - 13183.7i) q^{80} -45166.9 q^{81} +(1579.86 - 9283.19i) q^{82} +(9875.91 + 9875.91i) q^{83} +(-1270.96 + 3625.89i) q^{84} +(-7076.50 - 58062.5i) q^{85} +(-74312.6 + 52697.4i) q^{86} +(24028.8 + 24028.8i) q^{87} +(56843.2 - 102653. i) q^{88} +226.889i q^{89} +(52266.9 - 47543.2i) q^{90} -15056.8 q^{91} +(-67806.0 + 32608.5i) q^{92} +(-7821.06 + 7821.06i) q^{93} +(-84199.2 + 59708.2i) q^{94} +(-79511.0 - 62235.3i) q^{95} +(25581.8 + 1471.36i) q^{96} +(69631.7 - 69631.7i) q^{97} +(89618.6 + 15251.8i) q^{98} -144833. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.949067	+	5.57667i	−0.167773	+	0.985826i
$2$	−0.949067	+	5.57667i	−0.167773	+	0.985826i
$3$	−3.12794	−	3.12794i	−0.200657	−	0.200657i	0.599624	−	0.800282i	$-0.295317\pi$
$3$	−3.12794	−	3.12794i	−0.200657	−	0.200657i	−0.800282	+	0.599624i	$0.795317\pi$
$4$	−30.1985	−	10.5853i	−0.943704	−	0.330790i
$5$	34.4559	−	44.0204i	0.616366	−	0.787460i
$5$	34.4559	−	44.0204i	0.616366	−	0.787460i
$6$	20.4121	−	14.4749i	0.231478	−	0.164148i
$7$	19.1929	+	19.1929i	0.148046	+	0.148046i	0.777244	−	0.629199i	$-0.216617\pi$
$7$	19.1929	+	19.1929i	0.148046	+	0.148046i	−0.629199	+	0.777244i	$0.716617\pi$
$8$	87.6910	−	158.361i	0.484429	−	0.874830i
$9$		−	223.432i		−	0.919473i
$10$	212.786	+	233.927i	0.672889	+	0.739744i
$11$	648.221			1.61526			0.807628	−	0.589692i	$-0.200751\pi$
$11$	648.221			1.61526			0.807628	+	0.589692i	$0.200751\pi$
$12$	61.3491	+	127.569i	0.122986	+	0.255736i
$13$	−392.250	+	392.250i	−0.643731	+	0.643731i	−0.951471	−	0.307740i	$-0.900427\pi$
$13$	−392.250	+	392.250i	−0.643731	+	0.643731i	0.307740	+	0.951471i	$0.400427\pi$
$14$	−125.248	+	88.8172i	−0.170785	+	0.121109i
$15$	−245.469	+	29.9171i	−0.281688	+	0.0343313i
$16$	799.904	+	639.320i	0.781156	+	0.624336i
$17$	739.873	−	739.873i	0.620919	−	0.620919i	−0.324847	−	0.945766i	$-0.605313\pi$
$17$	739.873	−	739.873i	0.620919	−	0.620919i	0.945766	+	0.324847i	$0.105313\pi$
$18$	1246.01	+	212.052i	0.906440	+	0.154263i
$19$		−	1806.23i		−	1.14786i	−0.818904	−	0.573931i	$-0.805418\pi$
$19$		−	1806.23i		−	1.14786i	0.818904	−	0.573931i	$-0.194582\pi$
$20$	−1506.49	+	964.626i	−0.842151	+	0.539242i
$21$		−	120.068i		−	0.0594128i
$22$	−615.206	+	3614.92i	−0.270996	+	1.59236i
$23$	1662.57	−	1662.57i	0.655331	−	0.655331i	−0.298941	−	0.954272i	$-0.596633\pi$
$23$	1662.57	−	1662.57i	0.655331	−	0.655331i	0.954272	+	0.298941i	$0.0966333\pi$
$24$	−769.636	+	221.052i	−0.272745	+	0.0783368i
$25$	−750.584	−	3033.52i	−0.240187	−	0.970727i
$26$	−1815.18	−	2559.72i	−0.526606	−	0.742607i
$27$	−1458.97	+	1458.97i	−0.385156	+	0.385156i
$28$	−376.436	−	782.760i	−0.0907393	−	0.188683i
$29$	−7682.01			−1.69621			−0.848106	−	0.529827i	$-0.822257\pi$
$29$	−7682.01			−1.69621			−0.848106	+	0.529827i	$0.822257\pi$
$30$	66.1286	−	1397.29i	0.0134149	−	0.283455i
$31$		−	2500.39i		−	0.467308i	−0.972320	−	0.233654i	$-0.924932\pi$
$31$		−	2500.39i		−	0.467308i	0.972320	−	0.233654i	$-0.0750683\pi$
$32$	−4324.44	+	3854.04i	−0.746543	+	0.665337i
$33$	−2027.59	−	2027.59i	−0.324113	−	0.324113i
$34$	3423.84	+	4828.22i	0.507944	+	0.716291i
$35$	1506.19	−	183.570i	0.207830	−	0.0253298i
$36$	−2365.09	+	6747.32i	−0.304152	+	0.867711i
$37$	4619.77	+	4619.77i	0.554774	+	0.554774i	0.927815	−	0.373041i	$-0.121685\pi$
$37$	4619.77	+	4619.77i	0.554774	+	0.554774i	−0.373041	+	0.927815i	$0.621685\pi$
$38$	10072.8	+	1714.23i	1.13159	+	0.192580i
$39$	2453.86			0.258338
$40$	−3949.65	−	9316.67i	−0.390309	−	0.920684i
$41$	−1664.65			−0.154654			−0.0773272	−	0.997006i	$-0.524639\pi$
$41$	−1664.65			−0.154654			−0.0773272	+	0.997006i	$0.524639\pi$
$42$	669.582	+	113.953i	0.0585707	+	0.00996787i
$43$	11387.6	+	11387.6i	0.939208	+	0.939208i	0.998255	−	0.0590474i	$-0.0188063\pi$
$43$	11387.6	+	11387.6i	0.939208	+	0.939208i	−0.0590474	+	0.998255i	$0.518806\pi$
$44$	−19575.3	−	6861.60i	−1.52432	−	0.534310i
$45$	−9835.56	−	7698.55i	−0.724049	−	0.566732i
$46$	7693.72	+	10849.5i	0.536095	+	0.755989i
$47$	12902.6	+	12902.6i	0.851988	+	0.851988i	0.990378	−	0.138390i	$-0.0441927\pi$
$47$	12902.6	+	12902.6i	0.851988	+	0.851988i	−0.138390	+	0.990378i	$0.544193\pi$
$48$	−502.298	−	4501.80i	−0.0314672	−	0.282022i
$49$		−	16070.3i		−	0.956165i
$50$	17629.3	−	1306.75i	0.997264	−	0.0739207i
$51$	−4628.55			−0.249184
$52$	15997.4	−	7693.30i	0.820431	−	0.394552i
$53$	−12615.7	+	12615.7i	−0.616908	+	0.616908i	−0.944737	−	0.327829i	$-0.893683\pi$
$53$	−12615.7	+	12615.7i	−0.616908	+	0.616908i	0.327829	+	0.944737i	$0.393683\pi$
$54$	−6751.54	−	9520.86i	−0.315078	−	0.444316i
$55$	22335.0	−	28534.9i	0.995589	−	1.27195i
$56$	4722.46	−	1356.37i	0.201232	−	0.0577972i
$57$	−5649.78	+	5649.78i	−0.230327	+	0.230327i
$58$	7290.75	−	42840.1i	0.284578	−	1.67217i
$59$			30075.1i			1.12481i	0.826863	+	0.562403i	$0.190123\pi$
$59$			30075.1i			1.12481i	−0.826863	+	0.562403i	$0.809877\pi$
$60$	7729.48	+	1694.90i	0.277186	+	0.0607808i
$61$			22710.0i			0.781435i	0.920511	+	0.390717i	$0.127773\pi$
$61$			22710.0i			0.781435i	−0.920511	+	0.390717i	$0.872227\pi$
$62$	13943.8	+	2373.04i	0.460684	+	0.0784016i
$63$	4288.31	−	4288.31i	0.136124	−	0.136124i
$64$	−17388.6	−	27773.7i	−0.530657	−	0.847587i
$65$	3751.66	+	30782.3i	0.110139	+	0.903686i
$66$	13231.6	−	9382.91i	0.373896	−	0.265141i
$67$	−6337.59	+	6337.59i	−0.172479	+	0.172479i	−0.788068	−	0.615588i	$-0.788918\pi$
$67$	−6337.59	+	6337.59i	−0.172479	+	0.172479i	0.615588	+	0.788068i	$0.288918\pi$
$68$	−30174.8	+	14511.3i	−0.791358	+	0.380570i
$69$	−10400.8			−0.262994
$70$	−405.763	+	8573.73i	−0.00989754	+	0.209134i
$71$			2950.81i			0.0694696i	0.999397	+	0.0347348i	$0.0110587\pi$
$71$			2950.81i			0.0694696i	−0.999397	+	0.0347348i	$0.988941\pi$
$72$	−35383.0	−	19593.0i	−0.804383	−	0.445420i
$73$	−10777.2	−	10777.2i	−0.236700	−	0.236700i	0.578782	−	0.815482i	$-0.303528\pi$
$73$	−10777.2	−	10777.2i	−0.236700	−	0.236700i	−0.815482	+	0.578782i	$0.803528\pi$
$74$	−30147.4	+	21378.5i	−0.639987	+	0.453835i
$75$	−7140.88	+	11836.4i	−0.146588	+	0.242979i
$76$	−19119.5	+	54545.6i	−0.379701	+	1.08324i
$77$	12441.2	+	12441.2i	0.239132	+	0.239132i
$78$	−2328.88	+	13684.4i	−0.0433422	+	0.254677i
$79$	7474.95			0.134754			0.0673768	−	0.997728i	$-0.478537\pi$
$79$	7474.95			0.134754			0.0673768	+	0.997728i	$0.478537\pi$
$80$	55704.5	−	13183.7i	0.973117	−	0.230310i
$81$	−45166.9			−0.764905
$82$	1579.86	−	9283.19i	0.0259468	−	0.152462i
$83$	9875.91	+	9875.91i	0.157356	+	0.157356i	0.781394	−	0.624038i	$-0.214509\pi$
$83$	9875.91	+	9875.91i	0.157356	+	0.157356i	−0.624038	+	0.781394i	$0.714509\pi$
$84$	−1270.96	+	3625.89i	−0.0196532	+	0.0560682i
$85$	−7076.50	−	58062.5i	−0.106236	−	0.871662i
$86$	−74312.6	+	52697.4i	−1.08347	+	0.768321i
$87$	24028.8	+	24028.8i	0.340357	+	0.340357i
$88$	56843.2	−	102653.i	0.782477	−	1.41308i
$89$			226.889i			0.00303626i	0.999999	+	0.00151813i	$0.000483236\pi$
$89$			226.889i			0.00303626i	−0.999999	+	0.00151813i	$0.999517\pi$
$90$	52266.9	−	47543.2i	0.680174	−	0.618703i
$91$	−15056.8			−0.190603
$92$	−67806.0	+	32608.5i	−0.835216	+	0.401662i
$93$	−7821.06	+	7821.06i	−0.0937687	+	0.0937687i
$94$	−84199.2	+	59708.2i	−0.982852	+	0.696971i
$95$	−79511.0	−	62235.3i	−0.903895	−	0.707502i
$96$	25581.8	+	1471.36i	0.283304	+	0.0162945i
$97$	69631.7	−	69631.7i	0.751411	−	0.751411i	−0.223331	−	0.974743i	$-0.571693\pi$
$97$	69631.7	−	69631.7i	0.751411	−	0.751411i	0.974743	+	0.223331i	$0.0716931\pi$
$98$	89618.6	+	15251.8i	0.942612	+	0.160419i
$99$		−	144833.i		−	1.48519i
$100$	−9444.11	+	99553.0i	−0.0944411	+	0.995530i
$101$		−	62934.7i		−	0.613884i	−0.951728	−	0.306942i	$-0.900694\pi$
$101$		−	62934.7i		−	0.613884i	0.951728	−	0.306942i	$-0.0993058\pi$
$102$	4392.81	−	25811.9i	0.0418063	−	0.245652i
$103$	−141817.	+	141817.i	−1.31715	+	1.31715i	−0.401131	+	0.916021i	$0.631383\pi$
$103$	−141817.	+	141817.i	−1.31715	+	1.31715i	−0.916021	+	0.401131i	$0.868617\pi$
$104$	27720.4	+	96514.0i	0.251313	+	0.874997i
$105$	−5285.45	−	4137.06i	−0.0467852	−	0.0366200i
$106$	−58380.3	−	82326.6i	−0.504664	−	0.711665i
$107$	69303.7	−	69303.7i	0.585190	−	0.585190i	−0.351135	−	0.936325i	$-0.614204\pi$
$107$	69303.7	−	69303.7i	0.585190	−	0.585190i	0.936325	+	0.351135i	$0.114204\pi$
$108$	59502.4	−	28615.2i	0.490879	−	0.236068i
$109$	162445.			1.30961			0.654804	−	0.755799i	$-0.272751\pi$
$109$	162445.			1.30961			0.654804	+	0.755799i	$0.272751\pi$
$110$	137933.	+	151637.i	1.08689	+	1.19488i
$111$		−	28900.7i		−	0.222639i
$112$	3082.08	+	27622.9i	0.0232166	+	0.208077i
$113$	72741.9	+	72741.9i	0.535906	+	0.535906i	0.922324	−	0.386418i	$-0.126288\pi$
$113$	72741.9	+	72741.9i	0.535906	+	0.535906i	−0.386418	+	0.922324i	$0.626288\pi$
$114$	−26144.9	−	36869.0i	−0.188419	−	0.265704i
$115$	−15901.6	−	130472.i	−0.112124	−	0.919970i
$116$	231986.	+	81316.2i	1.60072	+	0.561090i
$117$	87641.2	+	87641.2i	0.591893	+	0.591893i
$118$	−167719.	−	28543.3i	−1.10886	−	0.188712i
$119$	28400.6			0.183849
$120$	−16787.7	+	41496.2i	−0.106424	+	0.263060i
$121$	259140.			1.60905
$122$	−126646.	−	21553.3i	−0.770358	−	0.131104i
$123$	5206.91	+	5206.91i	0.0310325	+	0.0310325i
$124$	−26467.3	+	75508.1i	−0.154581	+	0.441001i
$125$	−159399.	−	71481.7i	−0.912451	−	0.409185i
$126$	19844.6	+	27984.4i	0.111357	+	0.157032i
$127$	−46439.3	−	46439.3i	−0.255492	−	0.255492i	0.567726	−	0.823218i	$-0.307823\pi$
$127$	−46439.3	−	46439.3i	−0.255492	−	0.255492i	−0.823218	+	0.567726i	$0.807823\pi$
$128$	171388.	−	70611.2i	0.924603	−	0.380933i
$129$		−	71239.5i		−	0.376918i
$130$	−175223.	−	8292.67i	−0.909355	−	0.0430364i
$131$	−154464.			−0.786408			−0.393204	−	0.919451i	$-0.628633\pi$
$131$	−154464.			−0.786408			−0.393204	+	0.919451i	$0.628633\pi$
$132$	39767.8	+	82693.1i	0.198654	+	0.413080i
$133$	34666.8	−	34666.8i	0.169936	−	0.169936i
$134$	−29327.9	−	41357.5i	−0.141097	−	0.198972i
$135$	13954.3	+	114494.i	0.0658981	+	0.540692i
$136$	−52287.0	−	182047.i	−0.242408	−	0.843990i
$137$	−209839.	+	209839.i	−0.955180	+	0.955180i	−0.999038	−	0.0438575i	$-0.986035\pi$
$137$	−209839.	+	209839.i	−0.955180	+	0.955180i	0.0438575	+	0.999038i	$0.486035\pi$
$138$	9871.09	−	58002.0i	0.0441232	−	0.259266i
$139$			138092.i			0.606222i	0.952955	+	0.303111i	$0.0980253\pi$
$139$			138092.i			0.606222i	−0.952955	+	0.303111i	$0.901975\pi$
$140$	−47427.8	−	10399.9i	−0.204509	−	0.0448443i
$141$		−	80717.2i		−	0.341915i
$142$	−16455.7	−	2800.51i	−0.0684849	−	0.0116551i
$143$	−254265.	+	254265.i	−1.03979	+	1.03979i
$144$	142844.	−	178724.i	0.574060	−	0.718252i
$145$	−264691.	+	338165.i	−1.04549	+	1.33570i
$146$	70329.0	−	49872.5i	0.273056	−	0.193633i
$147$	−50266.8	+	50266.8i	−0.191861	+	0.191861i
$148$	−90608.8	−	188412.i	−0.340029	−	0.707056i
$149$	493486.			1.82100			0.910498	−	0.413514i	$-0.135699\pi$
$149$	493486.			1.82100			0.910498	+	0.413514i	$0.135699\pi$
$150$	−59230.8	−	51055.9i	−0.214941	−	0.185276i
$151$		−	490809.i		−	1.75174i	−0.482545	−	0.875871i	$-0.660288\pi$
$151$		−	490809.i		−	1.75174i	0.482545	−	0.875871i	$-0.339712\pi$
$152$	−286037.	−	158390.i	−1.00418	−	0.556057i
$153$	−165311.	−	165311.i	−0.570918	−	0.570918i
$154$	−81188.3	+	57573.2i	−0.275862	+	0.195622i
$155$	−110068.	−	86153.1i	−0.367986	−	0.288033i
$156$	−74103.1	−	25974.8i	−0.243795	−	0.0854557i
$157$	−71767.6	−	71767.6i	−0.232369	−	0.232369i	0.581312	−	0.813681i	$-0.302540\pi$
$157$	−71767.6	−	71767.6i	−0.232369	−	0.232369i	−0.813681	+	0.581312i	$0.802540\pi$
$158$	−7094.23	+	41685.3i	−0.0226080	+	0.132844i
$159$	78922.0			0.247574
$160$	20654.1	+	323158.i	0.0637831	+	0.997964i
$161$	63819.1			0.194038
$162$	42866.4	−	251881.i	0.128330	−	0.754063i
$163$	345655.	+	345655.i	1.01900	+	1.01900i	0.999816	+	0.0191825i	$0.00610636\pi$
$163$	345655.	+	345655.i	1.01900	+	1.01900i	0.0191825	+	0.999816i	$0.493894\pi$
$164$	50269.9	+	17620.7i	0.145948	+	0.0511581i
$165$	−159118.	+	19392.9i	−0.454998	+	0.0554539i
$166$	−64447.6	+	45701.8i	−0.181525	+	0.128725i
$167$	371161.	+	371161.i	1.02984	+	1.02984i	0.999541	+	0.0303018i	$0.00964683\pi$
$167$	371161.	+	371161.i	1.02984	+	1.02984i	0.0303018	+	0.999541i	$0.490353\pi$
$168$	−19014.2	−	10528.9i	−0.0519762	−	0.0287813i
$169$			63573.2i			0.171221i
$170$	330511.	+	15641.9i	0.877130	+	0.0415113i
$171$	−403570.			−1.05543
$172$	−223348.	−	464430.i	−0.575654	−	1.19701i
$173$	−289958.	+	289958.i	−0.736579	+	0.736579i	−0.971914	−	0.235335i	$-0.924381\pi$
$173$	−289958.	+	289958.i	−0.736579	+	0.736579i	0.235335	+	0.971914i	$0.424381\pi$
$174$	−156806.	+	111196.i	−0.392636	+	0.278430i
$175$	43816.2	−	72627.9i	0.108153	−	0.179270i
$176$	518515.	+	414421.i	1.26177	+	1.00846i
$177$	94073.1	−	94073.1i	0.225700	−	0.225700i
$178$	−1265.29	−	215.333i	−0.00299322	−	0.000509402i
$179$			546325.i			1.27444i	0.770683	+	0.637218i	$0.219915\pi$
$179$			546325.i			1.27444i	−0.770683	+	0.637218i	$0.780085\pi$
$180$	215528.	+	336597.i	0.495819	+	0.774335i
$181$			272124.i			0.617406i	0.951158	+	0.308703i	$0.0998949\pi$
$181$			272124.i			0.617406i	−0.951158	+	0.308703i	$0.900105\pi$
$182$	14289.9	−	83967.0i	0.0319780	−	0.187901i
$183$	71035.5	−	71035.5i	0.156800	−	0.156800i
$184$	−117494.	−	409079.i	−0.255842	−	0.890765i
$185$	362542.	−	44185.7i	0.778806	−	0.0949188i
$186$	−36192.8	−	51038.2i	−0.0767078	−	0.108171i
$187$	479601.	−	479601.i	1.00294	−	1.00294i
$188$	−253063.	−	526218.i	−0.522196	−	1.08585i
$189$	−56003.7			−0.114041
$190$	422527.	−	384341.i	0.849123	−	0.772383i
$191$		−	83461.3i		−	0.165539i	−0.996569	−	0.0827697i	$-0.973623\pi$
$191$		−	83461.3i		−	0.165539i	0.996569	−	0.0827697i	$-0.0263766\pi$
$192$	−32484.1	+	141265.i	−0.0635943	+	0.276555i
$193$	38883.2	+	38883.2i	0.0751397	+	0.0751397i	0.743678	−	0.668538i	$-0.233080\pi$
$193$	38883.2	+	38883.2i	0.0751397	+	0.0751397i	−0.668538	+	0.743678i	$0.733080\pi$
$194$	322228.	+	454398.i	0.614694	+	0.866827i
$195$	84550.1	−	108020.i	0.159231	−	0.203431i
$196$	−170108.	+	485299.i	−0.316290	+	0.902337i
$197$	−386340.	−	386340.i	−0.709257	−	0.709257i	0.257122	−	0.966379i	$-0.417226\pi$
$197$	−386340.	−	386340.i	−0.709257	−	0.709257i	−0.966379	+	0.257122i	$0.917226\pi$
$198$	807688.	+	137457.i	1.46413	+	0.249174i
$199$	297969.			0.533382			0.266691	−	0.963782i	$-0.414070\pi$
$199$	297969.			0.533382			0.266691	+	0.963782i	$0.414070\pi$
$200$	−546212.	−	147149.i	−0.965575	−	0.260126i
$201$	39647.2			0.0692184
$202$	350966.	+	59729.2i	0.605183	+	0.102993i
$203$	−147440.	−	147440.i	−0.251117	−	0.251117i
$204$	139776.	+	48994.5i	0.235156	+	0.0824274i
$205$	−57356.9	+	73278.3i	−0.0953237	+	0.121784i
$206$	−656274.	−	925462.i	−1.07750	−	1.51946i
$207$	−371472.	−	371472.i	−0.602559	−	0.602559i
$208$	−564535.	+	62989.2i	−0.904758	+	0.100950i
$209$		−	1.17084e6i		−	1.85409i
$210$	28087.3	−	25548.9i	0.0439503	−	0.0399782i
$211$	132172.			0.204377			0.102189	−	0.994765i	$-0.467416\pi$
$211$	132172.			0.204377			0.102189	+	0.994765i	$0.467416\pi$
$212$	514515.	−	247435.i	0.786246	−	0.378112i
$213$	9229.93	−	9229.93i	0.0139396	−	0.0139396i
$214$	320710.	+	452258.i	0.478717	+	0.675075i
$215$	893657.	−	108917.i	1.31848	−	0.160693i
$216$	103106.	+	358983.i	0.150365	+	0.523527i
$217$	47989.7	−	47989.7i	0.0691829	−	0.0691829i
$218$	−154172.	+	905905.i	−0.219717	+	1.29105i
$219$			67420.6i			0.0949910i
$220$	−976536.	+	625291.i	−1.36029	+	0.871015i
$221$			580430.i			0.799409i
$222$	161170.	+	27428.7i	0.219483	+	0.0373528i
$223$	143338.	−	143338.i	0.193018	−	0.193018i	−0.603981	−	0.796999i	$-0.706420\pi$
$223$	143338.	−	143338.i	0.193018	−	0.193018i	0.796999	+	0.603981i	$0.206420\pi$
$224$	−156969.	−	9028.22i	−0.209023	−	0.0120221i
$225$	−677786.	+	167704.i	−0.892557	+	0.220845i
$226$	−474695.	+	336621.i	−0.618221	+	0.438400i
$227$	−160750.	+	160750.i	−0.207055	+	0.207055i	−0.803015	−	0.595959i	$-0.796772\pi$
$227$	−160750.	+	160750.i	−0.207055	+	0.207055i	0.595959	+	0.803015i	$0.296772\pi$
$228$	230419.	−	110811.i	0.293550	−	0.141171i
$229$	−1.00602e6			−1.26771			−0.633854	−	0.773453i	$-0.718528\pi$
$229$	−1.00602e6			−1.26771			−0.633854	+	0.773453i	$0.718528\pi$
$230$	742693.	+	35148.9i	0.925742	+	0.0438119i
$231$		−	77830.8i		−	0.0959670i
$232$	−673644.	+	1.21653e6i	−0.821694	+	1.48390i
$233$	−1.09508e6	−	1.09508e6i	−1.32147	−	1.32147i	−0.912589	−	0.408879i	$-0.865920\pi$
$233$	−1.09508e6	−	1.09508e6i	−1.32147	−	1.32147i	−0.408879	−	0.912589i	$-0.634080\pi$
$234$	−571923.	+	405569.i	−0.682807	+	0.484200i
$235$	1.01255e6	−	123407.i	1.19604	−	0.145770i
$236$	318353.	−	908225.i	0.372074	−	1.06148i
$237$	−23381.2	−	23381.2i	−0.0270393	−	0.0270393i
$238$	−26954.1	+	158381.i	−0.0308448	+	0.181243i
$239$	−1.17736e6			−1.33326			−0.666628	−	0.745390i	$-0.732263\pi$
$239$	−1.17736e6			−1.33326			−0.666628	+	0.745390i	$0.732263\pi$
$240$	−215478.	−	133002.i	−0.241476	−	0.149050i
$241$	1.26027e6			1.39772			0.698859	−	0.715259i	$-0.253691\pi$
$241$	1.26027e6			1.39772			0.698859	+	0.715259i	$0.253691\pi$
$242$	−245941.	+	1.44514e6i	−0.269956	+	1.58625i
$243$	495809.	+	495809.i	0.538640	+	0.538640i
$244$	240392.	−	685809.i	0.258491	−	0.737443i
$245$	−707419.	−	553715.i	−0.752942	−	0.589347i
$246$	−33978.9	+	24095.5i	−0.0357991	+	0.0253862i
$247$	708494.	+	708494.i	0.738914	+	0.738914i
$248$	−395965.	−	219262.i	−0.408815	−	0.226378i
$249$		−	61782.4i		−	0.0631490i
$250$	549910.	−	821073.i	0.556470	−	0.830868i
$251$	−1.54897e6			−1.55188			−0.775942	−	0.630804i	$-0.782725\pi$
$251$	−1.54897e6			−1.55188			−0.775942	+	0.630804i	$0.782725\pi$
$252$	−174894.	+	84107.7i	−0.173489	+	0.0834324i
$253$	1.07771e6	−	1.07771e6i	1.05853	−	1.05853i
$254$	303051.	−	214903.i	0.294735	−	0.209006i
$255$	−159481.	+	203751.i	−0.153588	+	0.196222i
$256$	231117.	+	1.02279e6i	0.220410	+	0.975407i
$257$	−678258.	+	678258.i	−0.640564	+	0.640564i	−0.950694	−	0.310130i	$-0.899627\pi$
$257$	−678258.	+	678258.i	−0.640564	+	0.640564i	0.310130	+	0.950694i	$0.399627\pi$
$258$	397279.	+	67611.1i	0.371575	+	0.0632366i
$259$			177334.i			0.164264i
$260$	212544.	−	969293.i	0.194992	−	0.889245i
$261$			1.71641e6i			1.55962i
$262$	146596.	−	861393.i	0.131938	−	0.775262i
$263$	280837.	−	280837.i	0.250360	−	0.250360i	−0.570758	−	0.821118i	$-0.693351\pi$
$263$	280837.	−	280837.i	0.250360	−	0.250360i	0.821118	+	0.570758i	$0.193351\pi$
$264$	−498894.	+	143291.i	−0.440554	+	0.126534i
$265$	120662.	+	990031.i	0.105550	+	0.866032i
$266$	160424.	+	226227.i	0.139016	+	0.196038i
$267$	709.695	−	709.695i	0.000609247	−	0.000609247i
$268$	258471.	−	124301.i	0.219824	−	0.105715i
$269$	135326.			0.114025			0.0570124	−	0.998373i	$-0.481843\pi$
$269$	135326.			0.114025			0.0570124	+	0.998373i	$0.481843\pi$
$270$	−651742.	−	30844.5i	−0.544084	−	0.0257495i
$271$		−	1.40272e6i		−	1.16024i	−0.814532	−	0.580119i	$-0.803006\pi$
$271$		−	1.40272e6i		−	1.16024i	0.814532	−	0.580119i	$-0.196994\pi$
$272$	1.06484e6	−	118812.i	0.872696	−	0.0973729i
$273$	47096.8	+	47096.8i	0.0382459	+	0.0382459i
$274$	−971053.	−	1.36936e6i	−0.781388	−	1.10189i
$275$	−486544.	−	1.96639e6i	−0.387963	−	1.56797i
$276$	314090.	+	110096.i	0.248188	+	0.0869957i
$277$	306749.	+	306749.i	0.240206	+	0.240206i	0.816935	−	0.576729i	$-0.195671\pi$
$277$	306749.	+	306749.i	0.240206	+	0.240206i	−0.576729	+	0.816935i	$0.695671\pi$
$278$	−770094.	−	131059.i	−0.597629	−	0.101708i
$279$	−558667.			−0.429677
$280$	103009.	−	254619.i	0.0785197	−	0.194087i
$281$	1.42850e6			1.07923			0.539615	−	0.841912i	$-0.318570\pi$
$281$	1.42850e6			1.07923			0.539615	+	0.841912i	$0.318570\pi$
$282$	450133.	+	76606.0i	0.337069	+	0.0573641i
$283$	948370.	+	948370.i	0.703901	+	0.703901i	0.965246	−	0.261344i	$-0.0841658\pi$
$283$	948370.	+	948370.i	0.703901	+	0.703901i	−0.261344	+	0.965246i	$0.584166\pi$
$284$	31235.1	−	89110.0i	0.0229798	−	0.0655588i
$285$	54037.1	+	443373.i	0.0394076	+	0.323338i
$286$	−1.17664e6	−	1.65926e6i	−0.850603	−	1.19950i
$287$	−31949.4	−	31949.4i	−0.0228959	−	0.0228959i
$288$	861117.	+	966218.i	0.611760	+	0.686426i
$289$			325033.i			0.228919i
$290$	−1.63463e6	−	1.79703e6i	−1.14136	−	1.25476i
$291$	−435607.			−0.301552
$292$	211376.	+	439534.i	0.145077	+	0.301672i
$293$	1.76289e6	−	1.76289e6i	1.19966	−	1.19966i	0.225387	−	0.974269i	$-0.427635\pi$
$293$	1.76289e6	−	1.76289e6i	1.19966	−	1.19966i	0.974269	−	0.225387i	$-0.0723646\pi$
$294$	−232615.	−	328028.i	−0.156953	−	0.221331i
$295$	1.32392e6	+	1.03626e6i	0.885739	+	0.693291i
$296$	1.13671e6	−	326480.i	0.754082	−	0.216585i
$297$	−945735.	+	945735.i	−0.622126	+	0.622126i
$298$	−468351.	+	2.75201e6i	−0.305514	+	1.79518i
$299$			1.30429e6i			0.843714i
$300$	340936.	−	281855.i	0.218711	−	0.180810i
$301$			437123.i			0.278091i
$302$	2.73708e6	+	465811.i	1.72691	+	0.293895i
$303$	−196856.	+	196856.i	−0.123180	+	0.123180i
$304$	1.15476e6	−	1.44481e6i	0.716651	−	0.896659i
$305$	999703.	+	782493.i	0.615349	+	0.481649i
$306$	1.07878e6	−	764996.i	0.658611	−	0.467041i
$307$	−123298.	+	123298.i	−0.0746635	+	0.0746635i	−0.743452	−	0.668789i	$-0.766813\pi$
$307$	−123298.	+	123298.i	−0.0746635	+	0.0746635i	0.668789	+	0.743452i	$0.266813\pi$
$308$	−244013.	−	507401.i	−0.146567	−	0.304772i
$309$	887190.			0.528592
$310$	584909.	−	532048.i	0.345688	−	0.314446i
$311$			3.16561e6i			1.85591i	0.372693	+	0.927955i	$0.378435\pi$
$311$			3.16561e6i			1.85591i	−0.372693	+	0.927955i	$0.621565\pi$
$312$	215182.	−	388597.i	0.125147	−	0.226002i
$313$	531452.	+	531452.i	0.306622	+	0.306622i	0.843598	−	0.536976i	$-0.180433\pi$
$313$	531452.	+	531452.i	0.306622	+	0.306622i	−0.536976	+	0.843598i	$0.680433\pi$
$314$	468336.	−	332112.i	0.268061	−	0.190090i
$315$	−41015.4	−	336530.i	−0.0232901	−	0.191094i
$316$	−225732.	−	79124.3i	−0.127168	−	0.0445751i
$317$	−1.06483e6	−	1.06483e6i	−0.595159	−	0.595159i	0.343862	−	0.939020i	$-0.388265\pi$
$317$	−1.06483e6	−	1.06483e6i	−0.595159	−	0.595159i	−0.939020	+	0.343862i	$0.888265\pi$
$318$	−74902.3	+	440122.i	−0.0415363	+	0.244065i
$319$	−4.97964e6			−2.73982
$320$	−1.82175e6	−	191518.i	−0.994519	−	0.104552i
$321$	−433555.			−0.234845
$322$	−60568.6	+	355898.i	−0.0325543	+	0.191287i
$323$	−1.33638e6	−	1.33638e6i	−0.712729	−	0.712729i
$324$	1.36397e6	+	478103.i	0.721844	+	0.253023i
$325$	1.48431e6	+	895482.i	0.779502	+	0.470271i
$326$	−2.25565e6	+	1.59955e6i	−1.17552	+	0.833594i
$327$	−508119.	−	508119.i	−0.262782	−	0.262782i
$328$	−145975.	+	263616.i	−0.0749191	+	0.135296i
$329$			495278.i			0.252266i
$330$	42866.0	−	905754.i	0.0216685	−	0.457852i
$331$	99178.8			0.0497564			0.0248782	−	0.999690i	$-0.492080\pi$
$331$	99178.8			0.0497564			0.0248782	+	0.999690i	$0.492080\pi$
$332$	−193699.	−	402777.i	−0.0964455	−	0.200549i
$333$	1.03221e6	−	1.03221e6i	0.510100	−	0.510100i
$334$	−2.42210e6	+	1.71759e6i	−1.18802	+	0.842465i
$335$	60615.7	+	497350.i	0.0295103	+	0.242131i
$336$	76762.0	−	96043.1i	0.0370935	−	0.0464107i
$337$	−615804.	+	615804.i	−0.295371	+	0.295371i	−0.839198	−	0.543827i	$-0.816975\pi$
$337$	−615804.	+	615804.i	−0.295371	+	0.295371i	0.543827	+	0.839198i	$0.316975\pi$
$338$	−354527.	−	60335.2i	−0.168794	−	0.0287263i
$339$		−	455064.i		−	0.215067i
$340$	−400907.	+	1.82831e6i	−0.188082	+	0.857733i
$341$		−	1.62080e6i		−	0.754822i
$342$	383015.	−	2.25058e6i	0.177072	−	1.04047i
$343$	631010.	−	631010.i	0.289602	−	0.289602i
$344$	2.80195e6	−	804765.i	1.27663	−	0.366668i
$345$	−358370.	+	457848.i	−0.162100	+	0.207097i
$346$	−1.34181e6	−	1.89219e6i	−0.602561	−	0.849717i
$347$	−162825.	+	162825.i	−0.0725937	+	0.0725937i	−0.742471	−	0.669878i	$-0.766346\pi$
$347$	−162825.	+	162825.i	−0.0725937	+	0.0725937i	0.669878	+	0.742471i	$0.266346\pi$
$348$	−471284.	−	979988.i	−0.208610	−	0.433783i
$349$	926819.			0.407316			0.203658	−	0.979042i	$-0.434717\pi$
$349$	926819.			0.407316			0.203658	+	0.979042i	$0.434717\pi$
$350$	363438.	+	313277.i	0.158584	+	0.136697i
$351$		−	1.14456e6i		−	0.495874i
$352$	−2.80319e6	+	2.49827e6i	−1.20586	+	1.07469i
$353$	−1.42444e6	−	1.42444e6i	−0.608427	−	0.608427i	0.334108	−	0.942535i	$-0.391565\pi$
$353$	−1.42444e6	−	1.42444e6i	−0.608427	−	0.608427i	−0.942535	+	0.334108i	$0.891565\pi$
$354$	435333.	+	613896.i	0.184635	+	0.260368i
$355$	129896.	+	101673.i	0.0547045	+	0.0428187i
$356$	2401.68	−	6851.72i	0.00100436	−	0.00286533i
$357$	−88835.3	−	88835.3i	−0.0368906	−	0.0368906i
$358$	−3.04667e6	−	518499.i	−1.25637	−	0.213816i
$359$	4.66887e6			1.91195			0.955974	−	0.293452i	$-0.0948042\pi$
$359$	4.66887e6			1.91195			0.955974	+	0.293452i	$0.0948042\pi$
$360$	−2.08164e6	+	882477.i	−0.846544	+	0.358878i
$361$	−786373.			−0.317585
$362$	−1.51755e6	−	258264.i	−0.608655	−	0.103584i
$363$	−810573.	−	810573.i	−0.322868	−	0.322868i
$364$	454694.	+	159381.i	0.179873	+	0.0630495i
$365$	−845752.	+	103078.i	−0.332285	+	0.0404980i
$366$	328724.	+	463559.i	0.128271	+	0.180885i
$367$	−3.11370e6	−	3.11370e6i	−1.20673	−	1.20673i	−0.972079	−	0.234655i	$-0.924604\pi$
$367$	−3.11370e6	−	3.11370e6i	−1.20673	−	1.20673i	−0.234655	−	0.972079i	$-0.575396\pi$
$368$	2.39281e6	−	266983.i	0.921062	−	0.102769i
$369$			371935.i			0.142201i
$370$	−97668.0	+	2.06372e6i	−0.0370892	+	0.783692i
$371$	−484263.			−0.182661
$372$	318973.	−	153396.i	0.119508	−	0.0574722i
$373$	−1.67420e6	+	1.67420e6i	−0.623070	+	0.623070i	−0.946315	−	0.323246i	$-0.895226\pi$
$373$	−1.67420e6	+	1.67420e6i	−0.623070	+	0.623070i	0.323246	+	0.946315i	$0.395226\pi$
$374$	2.21941e6	+	3.12975e6i	0.820461	+	1.15699i
$375$	274999.	+	722179.i	0.100984	+	0.265196i
$376$	3.17472e6	−	911831.i	1.15807	−	0.332617i
$377$	3.01327e6	−	3.01327e6i	1.09190	−	1.09190i
$378$	53151.3	−	312314.i	0.0191331	−	0.112425i
$379$		−	1.27799e6i		−	0.457013i	−0.973542	−	0.228506i	$-0.926616\pi$
$379$		−	1.27799e6i		−	0.457013i	0.973542	−	0.228506i	$-0.0733842\pi$
$380$	1.74234e6	+	2.72106e6i	0.618975	+	0.966672i
$381$			290519.i			0.102532i
$382$	465436.	+	79210.3i	0.163193	+	0.0277730i
$383$	−3.07991e6	+	3.07991e6i	−1.07285	+	1.07285i	−0.0757254	+	0.997129i	$0.524127\pi$
$383$	−3.07991e6	+	3.07991e6i	−1.07285	+	1.07285i	−0.997129	+	0.0757254i	$0.975873\pi$
$384$	−756958.	−	315223.i	−0.261965	−	0.109091i
$385$	976342.	−	118994.i	0.335699	−	0.0409141i
$386$	−253742.	+	179936.i	−0.0866810	+	0.0614682i
$387$	2.54436e6	−	2.54436e6i	0.863577	−	0.863577i
$388$	−2.83985e6	+	1.36571e6i	−0.957670	+	0.460551i
$389$	−1.71604e6			−0.574980			−0.287490	−	0.957784i	$-0.592821\pi$
$389$	−1.71604e6			−0.574980			−0.287490	+	0.957784i	$0.592821\pi$
$390$	522148.	+	574026.i	0.173833	+	0.191104i
$391$		−	2.46018e6i		−	0.813815i
$392$	−2.54491e6	−	1.40922e6i	−0.836482	−	0.463194i
$393$	483153.	+	483153.i	0.157799	+	0.157799i
$394$	2.52115e6	−	1.78783e6i	0.818198	−	0.580210i
$395$	257556.	−	329050.i	0.0830575	−	0.106113i
$396$	−1.53310e6	+	4.37376e6i	−0.491284	+	1.40158i
$397$	65868.8	+	65868.8i	0.0209751	+	0.0209751i	0.717517	−	0.696541i	$-0.245279\pi$
$397$	65868.8	+	65868.8i	0.0209751	+	0.0209751i	−0.696541	+	0.717517i	$0.745279\pi$
$398$	−282792.	+	1.66167e6i	−0.0894870	+	0.525821i
$399$	−216871.			−0.0681977
$400$	1.33899e6	−	2.90639e6i	0.418436	−	0.908246i
$401$	3.68346e6			1.14392			0.571959	−	0.820282i	$-0.306184\pi$
$401$	3.68346e6			1.14392			0.571959	+	0.820282i	$0.306184\pi$
$402$	−37627.8	+	221099.i	−0.0116130	+	0.0682373i
$403$	980777.	+	980777.i	0.300821	+	0.300821i
$404$	−666181.	+	1.90054e6i	−0.203067	+	0.579326i
$405$	−1.55626e6	+	1.98826e6i	−0.471461	+	0.602332i
$406$	962156.	−	682295.i	0.289688	−	0.205427i
$407$	2.99463e6	+	2.99463e6i	0.896103	+	0.896103i
$408$	−405883.	+	732983.i	−0.120712	+	0.217994i
$409$		−	2.74141e6i		−	0.810337i	−0.914242	−	0.405168i	$-0.867213\pi$
$409$		−	2.74141e6i		−	0.810337i	0.914242	−	0.405168i	$-0.132787\pi$
$410$	−354214.	−	389407.i	−0.104065	−	0.114405i
$411$	1.31273e6			0.383328
$412$	5.78385e6	−	2.78150e6i	1.67870	−	0.807302i
$413$	−577229.	+	577229.i	−0.166522	+	0.166522i
$414$	2.42413e6	−	1.71902e6i	0.695112	−	0.492925i
$415$	775024.	−	94457.9i	0.220900	−	0.0269227i
$416$	184512.	−	3.20801e6i	0.0522746	−	0.908871i
$417$	431943.	−	431943.i	0.121643	−	0.121643i
$418$	6.52938e6	+	1.11120e6i	1.82781	+	0.311066i
$419$			2.43743e6i			0.678263i	0.940739	+	0.339131i	$0.110133\pi$
$419$			2.43743e6i			0.678263i	−0.940739	+	0.339131i	$0.889867\pi$
$420$	115821.	+	180881.i	0.0320379	+	0.0500346i
$421$			695447.i			0.191231i	0.995418	+	0.0956155i	$0.0304819\pi$
$421$			695447.i			0.191231i	−0.995418	+	0.0956155i	$0.969518\pi$
$422$	−125440.	+	737078.i	−0.0342889	+	0.201480i
$423$	2.88286e6	−	2.88286e6i	0.783380	−	0.783380i
$424$	891552.	+	3.10412e6i	0.240842	+	0.838539i
$425$	−2.79976e6	−	1.68908e6i	−0.751879	−	0.453606i
$426$	42712.5	+	60232.1i	0.0114033	+	0.0160807i
$427$	−435871.	+	435871.i	−0.115688	+	0.115688i
$428$	−2.82647e6	+	1.35927e6i	−0.745822	+	0.358672i
$429$	1.59065e6			0.417283
$430$	−240749.	+	5.08700e6i	−0.0627904	+	1.32676i
$431$		−	1.52454e6i		−	0.395316i	−0.980271	−	0.197658i	$-0.936666\pi$
$431$		−	1.52454e6i		−	0.395316i	0.980271	−	0.197658i	$-0.0633336\pi$
$432$	−2.09978e6	+	234288.i	−0.541334	+	0.0604004i
$433$	−4.56566e6	−	4.56566e6i	−1.17026	−	1.17026i	−0.982147	−	0.188117i	$-0.939762\pi$
$433$	−4.56566e6	−	4.56566e6i	−1.17026	−	1.17026i	−0.188117	−	0.982147i	$-0.560238\pi$
$434$	222077.	+	313168.i	0.0565953	+	0.0798093i
$435$	1.88569e6	−	229823.i	0.477802	−	0.0582332i
$436$	−4.90562e6	−	1.71953e6i	−1.23588	−	0.433205i
$437$	−3.00299e6	−	3.00299e6i	−0.752229	−	0.752229i
$438$	−375983.	−	63986.7i	−0.0936446	−	0.0159369i
$439$	4.66021e6			1.15410			0.577051	−	0.816708i	$-0.304204\pi$
$439$	4.66021e6			1.15410			0.577051	+	0.816708i	$0.304204\pi$
$440$	−2.56024e6	−	6.03926e6i	−0.630449	−	1.48714i
$441$	−3.59061e6			−0.879168
$442$	−3.23687e6	−	550867.i	−0.788078	−	0.134119i
$443$	3.39264e6	+	3.39264e6i	0.821350	+	0.821350i	0.986302	−	0.164951i	$-0.0527468\pi$
$443$	3.39264e6	+	3.39264e6i	0.821350	+	0.821350i	−0.164951	+	0.986302i	$0.552747\pi$
$444$	−305922.	+	872759.i	−0.0736467	+	0.210105i
$445$	9987.75	+	7817.67i	0.00239093	+	0.00187145i
$446$	663311.	+	935385.i	0.157899	+	0.222666i
$447$	−1.54359e6	−	1.54359e6i	−0.365396	−	0.365396i
$448$	199321.	−	866795.i	0.0469201	−	0.204043i
$449$			3.02340e6i			0.707749i	0.935293	+	0.353874i	$0.115136\pi$
$449$			3.02340e6i			0.707749i	−0.935293	+	0.353874i	$0.884864\pi$
$450$	−291969.	−	3.93895e6i	−0.0679681	−	0.916958i
$451$	−1.07906e6			−0.249807
$452$	−1.42671e6	−	2.96669e6i	−0.328465	−	0.683009i
$453$	−1.53522e6	+	1.53522e6i	−0.351500	+	0.351500i
$454$	−743887.	−	1.04901e6i	−0.169382	−	0.238858i
$455$	−518796.	+	662807.i	−0.117481	+	0.150092i
$456$	399271.	+	1.39014e6i	0.0899198	+	0.313074i
$457$	−2.25695e6	+	2.25695e6i	−0.505512	+	0.505512i	−0.913146	−	0.407633i	$-0.866354\pi$
$457$	−2.25695e6	+	2.25695e6i	−0.505512	+	0.505512i	0.407633	+	0.913146i	$0.366354\pi$
$458$	954783.	−	5.61026e6i	0.212687	−	1.24974i
$459$			2.15890e6i			0.478302i
$460$	−900880.	+	4.10840e6i	−0.198505	+	0.905270i
$461$		−	149750.i		−	0.0328181i	−0.999865	−	0.0164090i	$-0.994777\pi$
$461$		−	149750.i		−	0.0328181i	0.999865	−	0.0164090i	$-0.00522340\pi$
$462$	434037.	+	73866.7i	0.0946067	+	0.0161007i
$463$	−504994.	+	504994.i	−0.109480	+	0.109480i	−0.759725	−	0.650245i	$-0.774666\pi$
$463$	−504994.	+	504994.i	−0.109480	+	0.109480i	0.650245	+	0.759725i	$0.274666\pi$
$464$	−6.14487e6	−	4.91126e6i	−1.32501	−	1.05901i
$465$	74804.3	+	613767.i	0.0160433	+	0.131635i
$466$	7.14621e6	−	5.06760e6i	1.52444	−	1.08103i
$467$	−6.16159e6	+	6.16159e6i	−1.30738	+	1.30738i	−0.384076	+	0.923302i	$0.625480\pi$
$467$	−6.16159e6	+	6.16159e6i	−1.30738	+	1.30738i	−0.923302	+	0.384076i	$0.874520\pi$
$468$	−1.71893e6	−	3.57434e6i	−0.362780	−	0.754365i
$469$	−243273.			−0.0510696
$470$	−272778.	+	5.76378e6i	−0.0569594	+	1.20355i
$471$			448969.i			0.0932532i
$472$	4.76273e6	+	2.63732e6i	0.984014	+	0.544889i
$473$	7.38169e6	+	7.38169e6i	1.51706	+	1.51706i
$474$	152579.	−	108199.i	0.0311925	−	0.0221196i
$475$	−5.47924e6	+	1.35573e6i	−1.11426	+	0.275701i
$476$	−857657.	−	300628.i	−0.173499	−	0.0608152i
$477$	2.81875e6	+	2.81875e6i	0.567231	+	0.567231i
$478$	1.11739e6	−	6.56574e6i	0.223684	−	1.31436i
$479$	3.27963e6			0.653110			0.326555	−	0.945178i	$-0.394112\pi$
$479$	3.27963e6			0.653110			0.326555	+	0.945178i	$0.394112\pi$
$480$	946213.	−	1.07542e6i	0.187450	−	0.213047i
$481$	−3.62421e6			−0.714251
$482$	−1.19608e6	+	7.02809e6i	−0.234499	+	1.37791i
$483$	−199622.	−	199622.i	−0.0389351	−	0.0389351i
$484$	−7.82564e6	−	2.74307e6i	−1.51847	−	0.532259i
$485$	−665991.	−	5.46444e6i	−0.128562	−	1.05485i
$486$	−3.23552e6	+	2.29441e6i	−0.621374	+	0.440636i
$487$	6.00351e6	+	6.00351e6i	1.14705	+	1.14705i	0.987130	+	0.159922i	$0.0511241\pi$
$487$	6.00351e6	+	6.00351e6i	1.14705	+	1.14705i	0.159922	+	0.987130i	$0.448876\pi$
$488$	3.59638e6	+	1.99146e6i	0.683623	+	0.378550i
$489$		−	2.16237e6i		−	0.408939i
$490$	3.75928e6	−	3.41953e6i	0.707317	−	0.643393i
$491$	2.80758e6			0.525568			0.262784	−	0.964855i	$-0.415359\pi$
$491$	2.80758e6			0.525568			0.262784	+	0.964855i	$0.415359\pi$
$492$	−102125.	−	212358.i	−0.0190203	−	0.0395508i
$493$	−5.68371e6	+	5.68371e6i	−1.05321	+	1.05321i
$494$	−4.62345e6	+	3.27863e6i	−0.852410	+	0.604470i
$495$	−6.37562e6	−	4.99036e6i	−1.16952	−	0.915417i
$496$	1.59855e6	−	2.00007e6i	0.291757	−	0.365041i
$497$	−56634.5	+	56634.5i	−0.0102847	+	0.0102847i
$498$	344540.	+	58635.7i	0.0622539	+	0.0105947i
$499$		−	2.83578e6i		−	0.509826i	−0.966964	−	0.254913i	$-0.917953\pi$
$499$		−	2.83578e6i		−	0.509826i	0.966964	−	0.254913i	$-0.0820468\pi$
$500$	4.05696e6	+	3.84592e6i	0.725730	+	0.687979i
$501$		−	2.32193e6i		−	0.413291i
$502$	1.47008e6	−	8.63811e6i	0.260364	−	1.52989i
$503$	1.49851e6	−	1.49851e6i	0.264083	−	0.264083i	−0.562628	−	0.826710i	$-0.690209\pi$
$503$	1.49851e6	−	1.49851e6i	0.264083	−	0.264083i	0.826710	+	0.562628i	$0.190209\pi$
$504$	−303056.	−	1.05515e6i	−0.0531430	−	0.185028i
$505$	−2.77041e6	−	2.16847e6i	−0.483410	−	0.378377i
$506$	4.98723e6	+	7.03288e6i	0.865931	+	1.22112i
$507$	198853.	−	198853.i	0.0343568	−	0.0343568i
$508$	910827.	+	1.89397e6i	0.156595	+	0.325623i
$509$	−3.58529e6			−0.613380			−0.306690	−	0.951809i	$-0.599222\pi$
$509$	−3.58529e6			−0.613380			−0.306690	+	0.951809i	$0.599222\pi$
$510$	−984892.	−	1.08275e6i	−0.167673	−	0.184332i
$511$		−	413690.i		−	0.0700847i
$512$	−5.92310e6	+	318167.i	−0.998560	+	0.0536390i
$513$	2.63524e6	+	2.63524e6i	0.442106	+	0.442106i
$514$	−3.13871e6	−	4.42614e6i	−0.524015	−	0.738953i
$515$	1.35641e6	+	1.11293e7i	0.225357	+	1.84905i
$516$	−754089.	+	2.15133e6i	−0.124681	+	0.355699i
$517$	8.36376e6	+	8.36376e6i	1.37618	+	1.37618i
$518$	−988932.	−	168302.i	−0.161935	−	0.0275590i
$519$	1.81394e6			0.295600
$520$	5.20371e6	+	2.10521e6i	0.843926	+	0.341419i
$521$	−1.82322e6			−0.294269			−0.147135	−	0.989116i	$-0.547005\pi$
$521$	−1.82322e6			−0.294269			−0.147135	+	0.989116i	$0.547005\pi$
$522$	−9.57184e6	−	1.62899e6i	−1.53751	−	0.261662i
$523$	−5.80194e6	−	5.80194e6i	−0.927511	−	0.927511i	0.0700335	−	0.997545i	$-0.477689\pi$
$523$	−5.80194e6	−	5.80194e6i	−0.927511	−	0.927511i	−0.997545	+	0.0700335i	$0.977689\pi$
$524$	4.66458e6	+	1.63504e6i	0.742137	+	0.260136i
$525$	−364230.	+	90121.4i	−0.0576736	+	0.0142702i
$526$	1.29960e6	+	1.83267e6i	0.204808	+	0.288815i
$527$	−1.84997e6	−	1.84997e6i	−0.290160	−	0.290160i
$528$	−325600.	−	2.91816e6i	−0.0508276	−	0.455538i
$529$			908056.i			0.141083i
$530$	−5.63559e6	−	266712.i	−0.871465	−	0.0412432i
$531$	6.71975e6			1.03423
$532$	−1.41385e6	+	679930.i	−0.216582	+	0.104156i
$533$	652957.	−	652957.i	0.0995558	−	0.0995558i
$534$	3284.19	+	4631.29i	0.000498396	+	0.000702827i
$535$	−662854.	−	5.43870e6i	−0.100123	−	0.821505i
$536$	447879.	+	1.55938e6i	0.0673362	+	0.234444i
$537$	1.70887e6	−	1.70887e6i	0.255725	−	0.255725i
$538$	−128433.	+	754667.i	−0.0191303	+	0.112409i
$539$		−	1.04171e7i		−	1.54445i
$540$	790556.	−	3.60528e6i	0.116667	−	0.532052i
$541$		−	9.16864e6i		−	1.34683i	−0.739266	−	0.673414i	$-0.764827\pi$
$541$		−	9.16864e6i		−	1.34683i	0.739266	−	0.673414i	$-0.235173\pi$
$542$	7.82250e6	+	1.33127e6i	1.14379	+	0.194657i
$543$	851188.	−	851188.i	0.123887	−	0.123887i
$544$	−348032.	+	6.05104e6i	−0.0504222	+	0.876663i
$545$	5.59720e6	−	7.15091e6i	0.807197	−	1.03126i
$546$	−307341.	+	217945.i	−0.0441204	+	0.0312871i
$547$	6.83419e6	−	6.83419e6i	0.976605	−	0.976605i	−0.0231275	−	0.999733i	$-0.507362\pi$
$547$	6.83419e6	−	6.83419e6i	0.976605	−	0.976605i	0.999733	+	0.0231275i	$0.00736237\pi$
$548$	8.55805e6	−	4.11563e6i	1.21737	−	0.585444i
$549$	5.07414e6			0.718508
$550$	1.14277e7	−	847060.i	1.61084	−	0.119401i
$551$			1.38755e7i			1.94702i
$552$	−912060.	+	1.64709e6i	−0.127402	+	0.230075i
$553$	143466.	+	143466.i	0.0199497	+	0.0199497i
$554$	−2.00176e6	+	1.41951e6i	−0.277101	+	0.196501i
$555$	−1.27222e6	−	995799.i	−0.175319	−	0.137227i
$556$	1.46174e6	−	4.17018e6i	0.200532	−	0.572095i
$557$	−1.90300e6	−	1.90300e6i	−0.259897	−	0.259897i	0.565115	−	0.825012i	$-0.308832\pi$
$557$	−1.90300e6	−	1.90300e6i	−0.259897	−	0.259897i	−0.825012	+	0.565115i	$0.808832\pi$
$558$	530212.	−	3.11550e6i	0.0720882	−	0.423587i
$559$	−8.93358e6			−1.20919
$560$	1.32216e6	+	816096.i	0.178162	+	0.109969i
$561$	−3.00033e6			−0.402496
$562$	−1.35574e6	+	7.96626e6i	−0.181065	+	1.06393i
$563$	−2.90513e6	−	2.90513e6i	−0.386273	−	0.386273i	0.487083	−	0.873356i	$-0.338061\pi$
$563$	−2.90513e6	−	2.90513e6i	−0.386273	−	0.386273i	−0.873356	+	0.487083i	$0.838061\pi$
$564$	−854413.	+	2.43754e6i	−0.113102	+	0.322667i
$565$	5.70851e6	−	695738.i	0.752319	−	0.0916906i
$566$	−6.18882e6	+	4.38868e6i	−0.812020	+	0.575828i
$567$	−866883.	−	866883.i	−0.113241	−	0.113241i
$568$	467293.	+	258759.i	0.0607741	+	0.0336531i
$569$			1.63994e6i			0.212348i	0.994348	+	0.106174i	$0.0338601\pi$
$569$			1.63994e6i			0.212348i	−0.994348	+	0.106174i	$0.966140\pi$
$570$	−2.52383e6	−	119444.i	−0.325367	−	0.0153984i
$571$	3.51371e6			0.450999			0.225500	−	0.974243i	$-0.427599\pi$
$571$	3.51371e6			0.450999			0.225500	+	0.974243i	$0.427599\pi$
$572$	1.03699e7	−	4.98696e6i	1.32521	−	0.637303i
$573$	−261062.	+	261062.i	−0.0332167	+	0.0332167i
$574$	208493.	−	147849.i	0.0264127	−	0.0187301i
$575$	−6.29134e6	−	3.79555e6i	−0.793549	−	0.478745i
$576$	−6.20554e6	+	3.88516e6i	−0.779333	+	0.487925i
$577$	1.30066e6	−	1.30066e6i	0.162639	−	0.162639i	−0.621096	−	0.783735i	$-0.713312\pi$
$577$	1.30066e6	−	1.30066e6i	0.162639	−	0.162639i	0.783735	+	0.621096i	$0.213312\pi$
$578$	−1.81260e6	−	308478.i	−0.225675	−	0.0384065i
$579$		−	243249.i		−	0.0301546i
$580$	1.15728e7	−	7.41027e6i	1.42847	−	0.914669i
$581$			379095.i			0.0465916i
$582$	413421.	−	2.42924e6i	0.0505923	−	0.297278i
$583$	−8.17775e6	+	8.17775e6i	−0.996466	+	0.996466i
$584$	−2.65175e6	+	761625.i	−0.321736	+	0.0924079i
$585$	6.87775e6	−	838242.i	0.830915	−	0.101270i
$586$	8.15797e6	+	1.15042e7i	0.981382	+	1.38392i
$587$	2.17744e6	−	2.17744e6i	0.260826	−	0.260826i	−0.564563	−	0.825390i	$-0.690955\pi$
$587$	2.17744e6	−	2.17744e6i	0.260826	−	0.260826i	0.825390	+	0.564563i	$0.190955\pi$
$588$	2.05007e6	−	985896.i	0.244526	−	0.117595i
$589$	−4.51628e6			−0.536405
$590$	−7.03540e6	+	6.39957e6i	−0.832068	+	0.756869i
$591$			2.41689e6i			0.284635i
$592$	741863.	+	6.64889e6i	0.0870000	+	0.779731i
$593$	6.39982e6	+	6.39982e6i	0.747362	+	0.747362i	0.973983	−	0.226621i	$-0.0727680\pi$
$593$	6.39982e6	+	6.39982e6i	0.747362	+	0.747362i	−0.226621	+	0.973983i	$0.572768\pi$
$594$	−4.37649e6	−	6.17162e6i	−0.508932	−	0.717684i
$595$	978568.	−	1.25021e6i	0.113318	−	0.144773i
$596$	−1.49025e7	−	5.22368e6i	−1.71848	−	0.602367i
$597$	−932028.	−	932028.i	−0.107027	−	0.107027i
$598$	−7.27358e6	−	1.23786e6i	−0.831754	−	0.141552i
$599$	1.52076e6			0.173178			0.0865890	−	0.996244i	$-0.472403\pi$
$599$	1.52076e6			0.173178			0.0865890	+	0.996244i	$0.472403\pi$
$600$	1.24824e6	+	2.16879e6i	0.141553	+	0.245946i
$601$	−8.93347e6			−1.00887			−0.504434	−	0.863450i	$-0.668299\pi$
$601$	−8.93347e6			−1.00887			−0.504434	+	0.863450i	$0.668299\pi$
$602$	−2.43769e6	−	414859.i	−0.274149	−	0.0466562i
$603$	1.41602e6	+	1.41602e6i	0.158590	+	0.158590i
$604$	−5.19535e6	+	1.48217e7i	−0.579458	+	1.65313i
$605$	8.92889e6	−	1.14074e7i	0.991766	−	1.26707i
$606$	−910970.	−	1.28463e6i	−0.100768	−	0.142101i
$607$	1.52331e6	+	1.52331e6i	0.167810	+	0.167810i	0.786016	−	0.618206i	$-0.212140\pi$
$607$	1.52331e6	+	1.52331e6i	0.167810	+	0.167810i	−0.618206	+	0.786016i	$0.712140\pi$
$608$	6.96130e6	+	7.81094e6i	0.763715	+	0.856928i
$609$			922367.i			0.100777i
$610$	−5.31249e6	+	4.83237e6i	−0.578061	+	0.525819i
$611$	−1.01221e7			−1.09690
$612$	3.24230e6	+	6.74203e6i	0.349924	+	0.727632i
$613$	−2.44300e6	+	2.44300e6i	−0.262587	+	0.262587i	−0.826104	−	0.563518i	$-0.809448\pi$
$613$	−2.44300e6	+	2.44300e6i	−0.262587	+	0.262587i	0.563518	+	0.826104i	$0.309448\pi$
$614$	−570572.	−	804608.i	−0.0610787	−	0.0861317i
$615$	408619.	−	49801.3i	0.0435643	−	0.00530950i
$616$	3.06120e6	−	879225.i	0.325042	−	0.0933573i
$617$	6.66745e6	−	6.66745e6i	0.705093	−	0.705093i	−0.260406	−	0.965499i	$-0.583856\pi$
$617$	6.66745e6	−	6.66745e6i	0.705093	−	0.705093i	0.965499	+	0.260406i	$0.0838564\pi$
$618$	−842003.	+	4.94757e6i	−0.0886834	+	0.521100i
$619$		−	7.26158e6i		−	0.761736i	−0.924629	−	0.380868i	$-0.875625\pi$
$619$		−	7.26158e6i		−	0.761736i	0.924629	−	0.380868i	$-0.124375\pi$
$620$	2.41194e6	+	3.76680e6i	0.251992	+	0.393544i
$621$			4.85128e6i			0.504810i
$622$	−1.76536e7	−	3.00438e6i	−1.82960	−	0.311371i
$623$	−4354.66	+	4354.66i	−0.000449505	+	0.000449505i
$624$	1.96286e6	+	1.56880e6i	0.201803	+	0.161290i
$625$	−8.63887e6	+	4.55382e6i	−0.884621	+	0.466312i
$626$	−3.46812e6	+	2.45935e6i	−0.353719	+	0.250833i
$627$	−3.66231e6	+	3.66231e6i	−0.372037	+	0.372037i
$628$	1.40760e6	+	2.92696e6i	0.142423	+	0.296154i
$629$	6.83609e6			0.688940
$630$	1.91565e6	+	90660.4i	0.192293	+	0.00910052i
$631$		−	1.27725e7i		−	1.27704i	−0.769606	−	0.638519i	$-0.779548\pi$
$631$		−	1.27725e7i		−	1.27704i	0.769606	−	0.638519i	$-0.220452\pi$
$632$	655486.	−	1.18374e6i	0.0652786	−	0.117887i
$633$	−413424.	−	413424.i	−0.0410097	−	0.0410097i
$634$	6.94881e6	−	4.92762e6i	0.686574	−	0.486871i
$635$	−3.64438e6	+	444168.i	−0.358666	+	0.0437132i
$636$	−2.38333e6	−	835411.i	−0.233637	−	0.0818950i
$637$	6.30356e6	+	6.30356e6i	0.615513	+	0.615513i
$638$	4.72602e6	−	2.77698e7i	0.459667	−	2.70098i
$639$	659304.			0.0638754
$640$	2.79699e6	−	9.97753e6i	0.269924	−	0.962882i
$641$	2.59483e6			0.249439			0.124719	−	0.992192i	$-0.460197\pi$
$641$	2.59483e6			0.249439			0.124719	+	0.992192i	$0.460197\pi$
$642$	411473.	−	2.41780e6i	0.0394007	−	0.231517i
$643$	−9.83511e6	−	9.83511e6i	−0.938106	−	0.938106i	0.0600871	−	0.998193i	$-0.480862\pi$
$643$	−9.83511e6	−	9.83511e6i	−0.938106	−	0.938106i	−0.998193	+	0.0600871i	$0.980862\pi$
$644$	−1.92724e6	−	675543.i	−0.183114	−	0.0641857i
$645$	−3.13599e6	−	2.45462e6i	−0.296808	−	0.232319i
$646$	8.72088e6	−	6.18425e6i	0.822203	−	0.583050i
$647$	−6.28343e6	−	6.28343e6i	−0.590114	−	0.590114i	0.347548	−	0.937662i	$-0.387014\pi$
$647$	−6.28343e6	−	6.28343e6i	−0.590114	−	0.590114i	−0.937662	+	0.347548i	$0.887014\pi$
$648$	−3.96073e6	+	7.15268e6i	−0.370542	+	0.669162i
$649$			1.94953e7i			1.81685i
$650$	−6.40252e6	+	7.42766e6i	−0.594385	+	0.689555i
$651$	−300217.			−0.0277641
$652$	−6.77942e6	−	1.40971e7i	−0.624559	−	1.29871i
$653$	532425.	−	532425.i	0.0488625	−	0.0488625i	−0.682253	−	0.731116i	$-0.739000\pi$
$653$	532425.	−	532425.i	0.0488625	−	0.0488625i	0.731116	+	0.682253i	$0.239000\pi$
$654$	3.31585e6	−	2.35137e6i	0.303145	−	0.214970i
$655$	−5.32218e6	+	6.79955e6i	−0.484715	+	0.619265i
$656$	−1.33156e6	−	1.06424e6i	−0.120809	−	0.0965563i
$657$	−2.40797e6	+	2.40797e6i	−0.217639	+	0.217639i
$658$	−2.76200e6	−	470052.i	−0.248690	−	0.0423234i
$659$		−	3.54164e6i		−	0.317681i	−0.987304	−	0.158841i	$-0.949224\pi$
$659$		−	3.54164e6i		−	0.317681i	0.987304	−	0.158841i	$-0.0507756\pi$
$660$	5.01041e6	+	1.09867e6i	0.447727	+	0.0981766i
$661$		−	1.14846e7i		−	1.02238i	−0.859468	−	0.511189i	$-0.829205\pi$
$661$		−	1.14846e7i		−	1.02238i	0.859468	−	0.511189i	$-0.170795\pi$
$662$	−94127.3	+	553087.i	−0.00834777	+	0.0490511i
$663$	1.81555e6	−	1.81555e6i	0.160407	−	0.160407i
$664$	2.42999e6	−	697933.i	0.213887	−	0.0614318i
$665$	−331570.	−	2.72052e6i	−0.0290751	−	0.238560i
$666$	4.77664e6	+	6.73590e6i	0.417289	+	0.588451i
$667$	−1.27719e7	+	1.27719e7i	−1.11158	+	1.11158i
$668$	−7.27968e6	−	1.51374e7i	−0.631206	−	1.31253i
$669$	−896703.			−0.0774610
$670$	−2.83109e6	−	133985.i	−0.243650	−	0.0115310i
$671$			1.47211e7i			1.26222i
$672$	462749.	+	519228.i	0.0395296	+	0.0443542i
$673$	2.64129e6	+	2.64129e6i	0.224790	+	0.224790i	0.810512	−	0.585722i	$-0.199189\pi$
$673$	2.64129e6	+	2.64129e6i	0.224790	+	0.224790i	−0.585722	+	0.810512i	$0.699189\pi$
$674$	−2.84970e6	−	4.01858e6i	−0.241629	−	0.340740i
$675$	5.52089e6	+	3.33074e6i	0.466391	+	0.281372i
$676$	672940.	−	1.91982e6i	0.0566382	−	0.161582i
$677$	−4.45791e6	−	4.45791e6i	−0.373817	−	0.373817i	0.495048	−	0.868866i	$-0.335150\pi$
$677$	−4.45791e6	−	4.45791e6i	−0.373817	−	0.373817i	−0.868866	+	0.495048i	$0.835150\pi$
$678$	2.53774e6	+	431887.i	0.212018	+	0.0360824i
$679$	2.67287e6			0.222486
$680$	−9.81539e6	−	3.97091e6i	−0.814020	−	0.329320i
$681$	1.00563e6			0.0830942
$682$	9.03870e6	+	1.53825e6i	0.744123	+	0.126639i
$683$	8.50766e6	+	8.50766e6i	0.697844	+	0.697844i	0.963945	−	0.266101i	$-0.0857354\pi$
$683$	8.50766e6	+	8.50766e6i	0.697844	+	0.697844i	−0.266101	+	0.963945i	$0.585735\pi$
$684$	1.21872e7	+	4.27190e6i	0.996012	+	0.349125i
$685$	2.00700e6	+	1.64674e7i	0.163426	+	1.34091i
$686$	2.92007e6	+	4.11781e6i	0.236909	+	0.334084i
$687$	3.14677e6	+	3.14677e6i	0.254375	+	0.254375i
$688$	1.82867e6	+	1.63893e7i	0.147287	+	1.32005i
$689$		−	9.89699e6i		−	0.794246i
$690$	−2.21315e6	−	2.43304e6i	−0.176966	−	0.194548i
$691$	1.94961e7			1.55329			0.776643	−	0.629940i	$-0.216921\pi$
$691$	1.94961e7			1.55329			0.776643	+	0.629940i	$0.216921\pi$
$692$	1.18256e7	−	5.68702e6i	0.938766	−	0.451460i
$693$	2.77977e6	−	2.77977e6i	0.219875	−	0.219875i
$694$	−753492.	−	1.06256e6i	−0.0593854	−	0.0837439i
$695$	6.07886e6	+	4.75809e6i	0.477376	+	0.373655i
$696$	5.91235e6	−	1.69812e6i	0.462634	−	0.132876i
$697$	−1.23163e6	+	1.23163e6i	−0.0960279	+	0.0960279i
$698$	−879614.	+	5.16857e6i	−0.0683366	+	0.401543i
$699$			6.85069e6i			0.530324i
$700$	−2.09197e6	+	1.72945e6i	−0.161365	+	0.133402i
$701$		−	2.02740e6i		−	0.155828i	−0.996960	−	0.0779139i	$-0.975174\pi$
$701$		−	2.02740e6i		−	0.155828i	0.996960	−	0.0779139i	$-0.0248259\pi$
$702$	6.38284e6	+	1.08627e6i	0.488845	+	0.0831942i
$703$	8.34438e6	−	8.34438e6i	0.636804	−	0.636804i
$704$	−1.12716e7	−	1.80035e7i	−0.857147	−	1.36907i
$705$	−3.55320e6	−	2.78118e6i	−0.269244	−	0.210745i
$706$	9.29555e6	−	6.59176e6i	0.701881	−	0.497725i
$707$	1.20790e6	−	1.20790e6i	0.0908829	−	0.0908829i
$708$	−3.83666e6	+	1.84508e6i	−0.287654	+	0.138335i
$709$	−2.16543e7			−1.61781			−0.808907	−	0.587937i	$-0.799940\pi$
$709$	−2.16543e7			−1.61781			−0.808907	+	0.587937i	$0.799940\pi$
$710$	−690274.	+	627891.i	−0.0513897	+	0.0467453i
$711$		−	1.67014e6i		−	0.123902i
$712$	35930.5	+	19896.2i	0.00265621	+	0.00147085i
$713$	−4.15707e6	−	4.15707e6i	−0.306241	−	0.306241i
$714$	579716.	−	411095.i	0.0425569	−	0.0301784i
$715$	2.43191e6	+	1.99537e7i	0.177902	+	1.45968i
$716$	5.78300e6	−	1.64982e7i	0.421571	−	1.20269i
$717$	3.68270e6	+	3.68270e6i	0.267528	+	0.267528i
$718$	−4.43107e6	+	2.60368e7i	−0.320773	+	1.88485i
$719$	1.85327e7			1.33695			0.668477	−	0.743733i	$-0.266947\pi$
$719$	1.85327e7			1.33695			0.668477	+	0.743733i	$0.266947\pi$
$720$	−2.94567e6	−	1.24462e7i	−0.211764	−	0.894755i
$721$	−5.44377e6			−0.389997
$722$	746320.	−	4.38534e6i	0.0532822	−	0.313084i
$723$	−3.94203e6	−	3.94203e6i	−0.280462	−	0.280462i
$724$	2.88051e6	−	8.21776e6i	0.204232	−	0.582649i
$725$	5.76600e6	+	2.33035e7i	0.407408	+	1.64656i
$726$	5.28959e6	−	3.75101e6i	0.372460	−	0.264123i
$727$	−4.14363e6	−	4.14363e6i	−0.290767	−	0.290767i	0.546616	−	0.837383i	$-0.315916\pi$
$727$	−4.14363e6	−	4.14363e6i	−0.290767	−	0.290767i	−0.837383	+	0.546616i	$0.815916\pi$
$728$	−1.32035e6	+	2.38442e6i	−0.0923337	+	0.166745i
$729$			7.87383e6i			0.548741i
$730$	227843.	−	4.81431e6i	0.0158245	−	0.334370i
$731$	1.68508e7			1.16634
$732$	−2.89710e6	+	1.39324e6i	−0.199841	+	0.0961053i
$733$	4.63493e6	−	4.63493e6i	0.318628	−	0.318628i	−0.529612	−	0.848240i	$-0.677663\pi$
$733$	4.63493e6	−	4.63493e6i	0.318628	−	0.318628i	0.848240	+	0.529612i	$0.177663\pi$
$734$	2.03192e7	−	1.44090e7i	1.39209	−	0.987172i
$735$	480775.	+	3.94475e6i	0.0328264	+	0.269340i
$736$	−782063.	+	1.35973e7i	−0.0532166	+	0.925249i
$737$	−4.10816e6	+	4.10816e6i	−0.278598	+	0.278598i
$738$	−2.07416e6	−	352992.i	−0.140185	−	0.0238574i
$739$			9.51962e6i			0.641222i	0.947211	+	0.320611i	$0.103888\pi$
$739$			9.51962e6i			0.641222i	−0.947211	+	0.320611i	$0.896112\pi$
$740$	−1.14160e7	−	2.50327e6i	−0.766361	−	0.168046i
$741$		−	4.43225e6i		−	0.296537i
$742$	459598.	−	2.70057e6i	0.0306456	−	0.180072i
$743$	1.19265e7	−	1.19265e7i	0.792579	−	0.792579i	−0.189333	−	0.981913i	$-0.560633\pi$
$743$	1.19265e7	−	1.19265e7i	0.792579	−	0.792579i	0.981913	+	0.189333i	$0.0606327\pi$
$744$	552716.	+	1.92439e6i	0.0366074	+	0.127456i
$745$	1.70035e7	−	2.17234e7i	1.12240	−	1.43396i
$746$	−7.74756e6	−	1.09254e7i	−0.509704	−	0.718772i
$747$	2.20659e6	−	2.20659e6i	0.144684	−	0.144684i
$748$	−1.95600e7	+	9.40655e6i	−1.27825	+	0.614719i
$749$	2.66028e6			0.173270
$750$	−4.28835e6	+	848182.i	−0.278379	+	0.0550600i
$751$			619101.i			0.0400555i	0.999799	+	0.0200277i	$0.00637545\pi$
$751$			619101.i			0.0400555i	−0.999799	+	0.0200277i	$0.993625\pi$
$752$	2.07196e6	+	1.85698e7i	0.133609	+	1.19746i
$753$	4.84509e6	+	4.84509e6i	0.311397	+	0.311397i
$754$	1.39442e7	+	1.96638e7i	0.893235	+	1.25962i
$755$	−2.16056e7	−	1.69113e7i	−1.37943	−	1.07971i
$756$	1.69123e6	+	592815.i	0.107621	+	0.0377237i
$757$	−5.29958e6	−	5.29958e6i	−0.336126	−	0.336126i	0.518781	−	0.854907i	$-0.326386\pi$
$757$	−5.29958e6	−	5.29958e6i	−0.336126	−	0.336126i	−0.854907	+	0.518781i	$0.826386\pi$
$758$	7.12692e6	+	1.21290e6i	0.450535	+	0.0766744i
$759$	−6.74204e6			−0.424802
$760$	−1.68281e7	+	7.13397e6i	−1.05682	+	0.448020i
$761$	−1.89611e7			−1.18686			−0.593432	−	0.804884i	$-0.702227\pi$
$761$	−1.89611e7			−1.18686			−0.593432	+	0.804884i	$0.702227\pi$
$762$	−1.62013e6	−	275722.i	−0.101079	−	0.0172022i
$763$	3.11780e6	+	3.11780e6i	0.193882	+	0.193882i
$764$	−883460.	+	2.52041e6i	−0.0547588	+	0.156220i
$765$	−1.29730e7	+	1.58112e6i	−0.801470	+	0.0976810i
$766$	−1.42526e7	−	2.00987e7i	−0.877651	−	1.23764i
$767$	−1.17970e7	−	1.17970e7i	−0.724072	−	0.724072i
$768$	2.47630e6	−	3.92214e6i	0.151496	−	0.239949i
$769$		−	5.44231e6i		−	0.331869i	−0.986137	−	0.165935i	$-0.946936\pi$
$769$		−	5.44231e6i		−	0.331869i	0.986137	−	0.165935i	$-0.0530641\pi$
$770$	−263024.	+	5.55767e6i	−0.0159871	+	0.337805i
$771$	4.24310e6			0.257067
$772$	−762628.	−	1.58581e6i	−0.0460542	−	0.0957651i
$773$	−1.35362e7	+	1.35362e7i	−0.814792	+	0.814792i	−0.985348	−	0.170556i	$-0.945444\pi$
$773$	−1.35362e7	+	1.35362e7i	−0.814792	+	0.814792i	0.170556	+	0.985348i	$0.445444\pi$
$774$	1.17743e7	+	1.66038e7i	0.706451	+	0.996221i
$775$	−7.58498e6	+	1.87675e6i	−0.453628	+	0.112241i
$776$	−4.92089e6	−	1.71330e7i	−0.293352	−	1.02136i
$777$	554688.	−	554688.i	0.0329607	−	0.0329607i
$778$	1.62864e6	−	9.56979e6i	0.0964662	−	0.566830i
$779$			3.00674e6i			0.177522i
$780$	−3.69671e6	+	2.36706e6i	−0.217560	+	0.139307i
$781$			1.91277e6i			0.112211i
$782$	1.37196e7	+	2.33488e6i	0.802280	+	0.136536i
$783$	1.12078e7	−	1.12078e7i	0.653306	−	0.653306i
$784$	1.02740e7	−	1.28547e7i	0.596968	−	0.746914i
$785$	−5.63205e6	+	686419.i	−0.326206	+	0.0397571i
$786$	−3.15293e6	+	2.23584e6i	−0.182036	+	0.129088i
$787$	−1.00190e7	+	1.00190e7i	−0.576615	+	0.576615i	−0.933969	−	0.357354i	$-0.883679\pi$
$787$	−1.00190e7	+	1.00190e7i	−0.576615	+	0.576615i	0.357354	+	0.933969i	$0.383679\pi$
$788$	7.57738e6	+	1.57564e7i	0.434714	+	0.903944i
$789$	−1.75688e6			−0.100473
$790$	1.59056e6	+	1.74859e6i	0.0906742	+	0.0996831i
$791$			2.79226e6i			0.158677i
$792$	−2.29360e7	−	1.27006e7i	−1.29929	−	0.719467i
$793$	−8.90799e6	−	8.90799e6i	−0.503034	−	0.503034i
$794$	−429843.	+	304815.i	−0.0241968	+	0.0171587i
$795$	2.71933e6	−	3.47418e6i	0.152596	−	0.194955i
$796$	−8.99822e6	−	3.15408e6i	−0.503355	−	0.176437i
$797$	−2.38772e7	−	2.38772e7i	−1.33149	−	1.33149i	−0.904038	−	0.427453i	$-0.859411\pi$
$797$	−2.38772e7	−	2.38772e7i	−1.33149	−	1.33149i	−0.427453	−	0.904038i	$-0.640589\pi$
$798$	205825.	−	1.20942e6i	0.0114417	−	0.0672310i
$799$	1.90926e7			1.05803
$800$	1.49372e7	+	1.02255e7i	0.825170	+	0.564884i
$801$	50694.3			0.00279176
$802$	−3.49585e6	+	2.05414e7i	−0.191918	+	1.12770i
$803$	−6.98599e6	−	6.98599e6i	−0.382331	−	0.382331i
$804$	−1.19729e6	−	419676.i	−0.0653218	−	0.0228968i
$805$	2.19894e6	−	2.80934e6i	0.119598	−	0.152797i
$806$	−6.40029e6	+	4.53865e6i	−0.347026	+	0.246087i
$807$	−423290.	−	423290.i	−0.0228799	−	0.0228799i
$808$	−9.96641e6	−	5.51881e6i	−0.537045	−	0.297384i
$809$		−	6.68830e6i		−	0.359290i	−0.983732	−	0.179645i	$-0.942505\pi$
$809$		−	6.68830e6i		−	0.359290i	0.983732	−	0.179645i	$-0.0574948\pi$
$810$	−9.61088e6	−	1.05658e7i	−0.514696	−	0.565833i
$811$	−2.06080e7			−1.10023			−0.550115	−	0.835089i	$-0.685416\pi$
$811$	−2.06080e7			−1.10023			−0.550115	+	0.835089i	$0.685416\pi$
$812$	2.89178e6	+	6.01317e6i	0.153913	+	0.320047i
$813$	−4.38761e6	+	4.38761e6i	−0.232810	+	0.232810i
$814$	−1.95422e7	+	1.38580e7i	−1.03374	+	0.733059i
$815$	2.71257e7	−	3.30601e6i	1.43050	−	0.174345i
$816$	−3.70240e6	−	2.95912e6i	−0.194651	−	0.155574i
$817$	2.05687e7	−	2.05687e7i	1.07808	−	1.07808i
$818$	1.52879e7	+	2.60178e6i	0.798851	+	0.135953i
$819$			3.36418e6i			0.175254i
$820$	2.50777e6	−	1.60576e6i	0.130242	−	0.0833962i
$821$			1.74397e7i			0.902985i	0.892275	+	0.451492i	$0.149108\pi$
$821$			1.74397e7i			0.902985i	−0.892275	+	0.451492i	$0.850892\pi$
$822$	−1.24587e6	+	7.32065e6i	−0.0643120	+	0.377894i
$823$	−4.29034e6	+	4.29034e6i	−0.220797	+	0.220797i	−0.808834	−	0.588037i	$-0.799901\pi$
$823$	−4.29034e6	+	4.29034e6i	−0.220797	+	0.220797i	0.588037	+	0.808834i	$0.299901\pi$
$824$	1.00222e7	+	3.48944e7i	0.514218	+	1.79035i
$825$	−4.62887e6	+	7.67263e6i	−0.236777	+	0.392473i
$826$	−2.67119e6	−	3.76684e6i	−0.136224	−	0.192100i
$827$	1.22618e7	−	1.22618e7i	0.623434	−	0.623434i	−0.322974	−	0.946408i	$-0.604683\pi$
$827$	1.22618e7	−	1.22618e7i	0.623434	−	0.623434i	0.946408	+	0.322974i	$0.104683\pi$
$828$	7.28577e6	+	1.51500e7i	0.369317	+	0.767958i
$829$	−1.66613e6			−0.0842021			−0.0421010	−	0.999113i	$-0.513405\pi$
$829$	−1.66613e6			−0.0842021			−0.0421010	+	0.999113i	$0.513405\pi$
$830$	−208790.	+	4.41170e6i	−0.0105199	+	0.222285i
$831$		−	1.91898e6i		−	0.0963980i
$832$	1.77149e7	+	4.07358e6i	0.887218	+	0.204018i
$833$	−1.18900e7	−	1.18900e7i	−0.593701	−	0.593701i
$834$	1.99886e6	+	2.81875e6i	0.0995103	+	0.140327i
$835$	2.91273e7	−	3.54996e6i	1.44572	−	0.176200i
$836$	−1.23936e7	+	3.53576e7i	−0.613314	+	1.74971i
$837$	3.64799e6	+	3.64799e6i	0.179987	+	0.179987i
$838$	−1.35928e7	−	2.31329e6i	−0.668649	−	0.113794i
$839$	−3.44947e7			−1.69179			−0.845896	−	0.533348i	$-0.820934\pi$
$839$	−3.44947e7			−1.69179			−0.845896	+	0.533348i	$0.820934\pi$
$840$	−1.11864e6	+	474227.i	−0.0547005	+	0.0231893i
$841$	3.85022e7			1.87713
$842$	−3.87828e6	−	660025.i	−0.188521	−	0.0320834i
$843$	−4.46825e6	−	4.46825e6i	−0.216555	−	0.216555i
$844$	−3.99139e6	−	1.39907e6i	−0.192872	−	0.0676058i
$845$	2.79852e6	+	2.19047e6i	0.134830	+	0.105535i
$846$	1.33407e7	+	1.88128e7i	0.640846	+	0.903706i
$847$	4.97364e6	+	4.97364e6i	0.238213	+	0.238213i
$848$	−1.81568e7	+	2.02588e6i	−0.867060	+	0.0967440i
$849$		−	5.93288e6i		−	0.282486i
$850$	1.20766e7	−	1.40103e7i	0.573321	−	0.665119i
$851$	1.53614e7			0.727121
$852$	−376432.	+	181029.i	−0.0177659	+	0.00854377i
$853$	2.02443e7	−	2.02443e7i	0.952642	−	0.952642i	−0.0462866	−	0.998928i	$-0.514739\pi$
$853$	2.02443e7	−	2.02443e7i	0.952642	−	0.952642i	0.998928	+	0.0462866i	$0.0147387\pi$
$854$	−2.01704e6	−	2.84438e6i	−0.0946388	−	0.133457i
$855$	−1.39054e7	+	1.77653e7i	−0.650529	+	0.831107i
$856$	−4.89771e6	−	1.70523e7i	−0.228459	−	0.795426i
$857$	−1.43088e7	+	1.43088e7i	−0.665505	+	0.665505i	−0.956672	−	0.291167i	$-0.905957\pi$
$857$	−1.43088e7	+	1.43088e7i	−0.665505	+	0.665505i	0.291167	+	0.956672i	$0.405957\pi$
$858$	−1.50963e6	+	8.87052e6i	−0.0700088	+	0.411368i
$859$		−	1.60807e7i		−	0.743571i	−0.928319	−	0.371785i	$-0.878746\pi$
$859$		−	1.60807e7i		−	0.743571i	0.928319	−	0.371785i	$-0.121254\pi$
$860$	−2.81401e7	−	6.17049e6i	−1.29741	−	0.284494i
$861$			199871.i			0.00918846i
$862$	8.50184e6	+	1.44689e6i	0.389713	+	0.0663234i
$863$	−6.83472e6	+	6.83472e6i	−0.312387	+	0.312387i	−0.845834	−	0.533446i	$-0.820897\pi$
$863$	−6.83472e6	+	6.83472e6i	−0.312387	+	0.312387i	0.533446	+	0.845834i	$0.320897\pi$
$864$	686290.	−	1.19322e7i	0.0312769	−	0.543794i
$865$	2.77329e6	+	2.27548e7i	0.126025	+	1.03403i
$866$	2.97943e7	−	2.11281e7i	1.35001	−	0.957337i
$867$	1.01668e6	−	1.01668e6i	0.0459343	−	0.0459343i
$868$	−1.95720e6	+	941235.i	−0.0881732	+	0.0424032i
$869$	4.84542e6			0.217662
$870$	−508001.	+	1.07340e7i	−0.0227545	+	0.480800i
$871$		−	4.97184e6i		−	0.222061i
$872$	1.42450e7	−	2.57251e7i	0.634412	−	1.14568i
$873$	−1.55580e7	−	1.55580e7i	−0.690903	−	0.690903i
$874$	1.95967e7	−	1.38966e7i	0.867770	−	0.615363i
$875$	−1.68738e6	−	4.43126e6i	−0.0745064	−	0.195662i
$876$	713666.	−	2.03600e6i	0.0314221	−	0.0896434i
$877$	5.82980e6	+	5.82980e6i	0.255950	+	0.255950i	0.823405	−	0.567455i	$-0.192072\pi$
$877$	5.82980e6	+	5.82980e6i	0.255950	+	0.255950i	−0.567455	+	0.823405i	$0.692072\pi$
$878$	−4.42285e6	+	2.59884e7i	−0.193627	+	1.13774i
$879$	−1.10284e7			−0.481439
$880$	3.61088e7	−	8.54598e6i	1.57183	−	0.372010i
$881$	979191.			0.0425038			0.0212519	−	0.999774i	$-0.493235\pi$
$881$	979191.			0.0425038			0.0212519	+	0.999774i	$0.493235\pi$
$882$	3.40773e6	−	2.00237e7i	0.147501	−	0.866707i
$883$	1.83879e7	+	1.83879e7i	0.793653	+	0.793653i	0.982086	−	0.188433i	$-0.0603410\pi$
$883$	1.83879e7	+	1.83879e7i	0.793653	+	0.793653i	−0.188433	+	0.982086i	$0.560341\pi$
$884$	6.14401e6	−	1.75281e7i	0.264436	−	0.754406i
$885$	−899759.	−	7.38250e6i	−0.0386161	−	0.316844i
$886$	−2.21395e7	+	1.56998e7i	−0.947508	+	0.671908i
$887$	−1.72529e7	−	1.72529e7i	−0.736297	−	0.736297i	0.235562	−	0.971859i	$-0.424307\pi$
$887$	−1.72529e7	−	1.72529e7i	−0.736297	−	0.736297i	−0.971859	+	0.235562i	$0.924307\pi$
$888$	−4.57675e6	−	2.53433e6i	−0.194771	−	0.107853i
$889$		−	1.78261e6i		−	0.0756488i
$890$	−53075.6	+	48278.9i	−0.00224605	+	0.00204307i
$891$	−2.92781e7			−1.23552
$892$	−5.84586e6	+	2.81132e6i	−0.246001	+	0.118304i
$893$	2.33051e7	−	2.33051e7i	0.977964	−	0.977964i
$894$	1.00731e7	−	7.14313e6i	0.421520	−	0.298913i
$895$	2.40494e7	+	1.88241e7i	1.00357	+	0.785519i
$896$	4.64466e6	+	1.93420e6i	0.193279	+	0.0804879i
$897$	4.07973e6	−	4.07973e6i	0.169297	−	0.169297i
$898$	−1.68605e7	−	2.86941e6i	−0.697717	−	0.118741i
$899$			1.92080e7i			0.792653i
$900$	2.22433e7	+	2.11012e6i	0.915364	+	0.0868360i
$901$			1.86680e7i			0.766100i
$902$	1.02410e6	−	6.01756e6i	0.0419108	−	0.246266i
$903$	1.36729e6	−	1.36729e6i	0.0558010	−	0.0558010i
$904$	1.78983e7	−	5.14069e6i	0.728436	−	0.209219i
$905$	1.19790e7	+	9.37629e6i	0.486183	+	0.380548i
$906$	−7.10439e6	−	1.00184e7i	−0.287545	−	0.405490i
$907$	1.97949e7	−	1.97949e7i	0.798980	−	0.798980i	−0.183955	−	0.982935i	$-0.558890\pi$
$907$	1.97949e7	−	1.97949e7i	0.798980	−	0.798980i	0.982935	+	0.183955i	$0.0588901\pi$
$908$	6.55599e6	−	3.15283e6i	0.263890	−	0.126907i
$909$	−1.40616e7			−0.564450
$910$	−3.20388e6	−	3.52220e6i	−0.128255	−	0.140997i
$911$			3.84298e6i			0.153416i	0.997054	+	0.0767082i	$0.0244410\pi$
$911$			3.84298e6i			0.153416i	−0.997054	+	0.0767082i	$0.975559\pi$
$912$	−8.13129e6	+	907266.i	−0.323722	+	0.0361200i
$913$	6.40178e6	+	6.40178e6i	0.254170	+	0.254170i
$914$	−1.04443e7	−	1.47283e7i	−0.413536	−	0.583158i
$915$	−679417.	−	5.57460e6i	−0.0268277	−	0.220121i
$916$	3.03804e7	+	1.06490e7i	1.19634	+	0.419345i
$917$	−2.96461e6	−	2.96461e6i	−0.116424	−	0.116424i
$918$	−1.20395e7	−	2.04895e6i	−0.471522	−	0.0802461i
$919$	−2.06477e7			−0.806459			−0.403229	−	0.915099i	$-0.632112\pi$
$919$	−2.06477e7			−0.806459			−0.403229	+	0.915099i	$0.632112\pi$
$920$	−2.20562e7	−	8.92306e6i	−0.859134	−	0.347571i
$921$	771334.			0.0299635
$922$	835104.	+	142122.i	0.0323529	+	0.00550599i
$923$	−1.15745e6	−	1.15745e6i	−0.0447197	−	0.0447197i
$924$	−823861.	+	2.35038e6i	−0.0317449	+	0.0905645i
$925$	1.05466e7	−	1.74817e7i	0.405285	−	0.671784i
$926$	−2.33691e6	−	3.29546e6i	−0.0895601	−	0.126296i
$927$	3.16865e7	+	3.16865e7i	1.21109	+	1.21109i
$928$	3.32204e7	−	2.96068e7i	1.26629	−	1.12855i
$929$			1.55025e7i			0.589335i	0.955600	+	0.294668i	$0.0952089\pi$
$929$			1.55025e7i			0.589335i	−0.955600	+	0.294668i	$0.904791\pi$
$930$	−3.49377e6	−	165347.i	−0.132461	−	0.00626888i
$931$	−2.90266e7			−1.09754
$932$	2.14781e7	+	4.46616e7i	0.809947	+	1.68420i
$933$	9.90184e6	−	9.90184e6i	0.372402	−	0.372402i
$934$	−2.85134e7	−	4.02090e7i	−1.06950	−	1.50819i
$935$	−4.58713e6	−	3.76373e7i	−0.171598	−	1.40796i
$936$	2.15643e7	−	6.19362e6i	0.804537	−	0.231076i
$937$	−1.92742e7	+	1.92742e7i	−0.717177	+	0.717177i	−0.968026	−	0.250849i	$-0.919290\pi$
$937$	−1.92742e7	+	1.92742e7i	−0.717177	+	0.717177i	0.250849	+	0.968026i	$0.419290\pi$
$938$	230883.	−	1.35666e6i	0.00856810	−	0.0503457i
$939$		−	3.32470e6i		−	0.123052i
$940$	−3.18838e7	−	6.99141e6i	−1.17693	−	0.258074i
$941$			3.56736e7i			1.31333i	0.754183	+	0.656664i	$0.228033\pi$
$941$			3.56736e7i			1.31333i	−0.754183	+	0.656664i	$0.771967\pi$
$942$	−2.50375e6	−	426102.i	−0.0919314	−	0.0156454i
$943$	−2.76759e6	+	2.76759e6i	−0.101350	+	0.101350i
$944$	−1.92276e7	+	2.40572e7i	−0.702256	+	0.878649i
$945$	−1.92966e6	+	2.46530e6i	−0.0702912	+	0.0898030i
$946$	−4.81710e7	+	3.41596e7i	−1.75008	+	1.24104i
$947$	−2.34596e7	+	2.34596e7i	−0.850052	+	0.850052i	−0.990139	−	0.140087i	$-0.955262\pi$
$947$	−2.34596e7	+	2.34596e7i	−0.850052	+	0.850052i	0.140087	+	0.990139i	$0.455262\pi$
$948$	458581.	+	953573.i	0.0165728	+	0.0344614i
$949$	8.45469e6			0.304742
$950$	−2.36028e6	−	3.18426e7i	−0.0848507	−	1.14472i
$951$			6.66145e6i			0.238846i
$952$	2.49048e6	−	4.49756e6i	0.0890616	−	0.160836i
$953$	2.67137e7	+	2.67137e7i	0.952798	+	0.952798i	0.998935	−	0.0461367i	$-0.0146910\pi$
$953$	2.67137e7	+	2.67137e7i	0.952798	+	0.952798i	−0.0461367	+	0.998935i	$0.514691\pi$
$954$	−1.83944e7	+	1.30440e7i	−0.654357	+	0.464025i
$955$	−3.67399e6	−	2.87573e6i	−0.130356	−	0.102033i
$956$	3.55545e7	+	1.24627e7i	1.25820	+	0.441028i
$957$	1.55760e7	+	1.55760e7i	0.549764	+	0.549764i
$958$	−3.11259e6	+	1.82894e7i	−0.109574	+	0.643852i
$959$	−8.05485e6			−0.282820
$960$	5.09926e6	+	6.29737e6i	0.178578	+	0.220537i
$961$	2.23772e7			0.781623
$962$	3.43962e6	−	2.02110e7i	0.119832	−	0.704126i
$963$	−1.54847e7	−	1.54847e7i	−0.538067	−	0.538067i
$964$	−3.80582e7	−	1.33403e7i	−1.31903	−	0.462351i
$965$	3.05141e6	−	371898.i	0.105483	−	0.0128560i
$966$	1.30268e6	−	923773.i	0.0449154	−	0.0318509i
$967$	−1.09161e7	−	1.09161e7i	−0.375407	−	0.375407i	0.494035	−	0.869442i	$-0.335521\pi$
$967$	−1.09161e7	−	1.09161e7i	−0.375407	−	0.375407i	−0.869442	+	0.494035i	$0.835521\pi$
$968$	2.27242e7	−	4.10377e7i	0.779473	−	1.40765i
$969$			8.36024e6i			0.286028i
$970$	3.11054e7	+	1.47210e6i	1.06147	+	0.0502354i
$971$	−1.97557e7			−0.672427			−0.336214	−	0.941786i	$-0.609146\pi$
$971$	−1.97557e7			−0.672427			−0.336214	+	0.941786i	$0.609146\pi$
$972$	−9.72443e6	−	2.02210e7i	−0.330140	−	0.686493i
$973$	−2.65039e6	+	2.65039e6i	−0.0897485	+	0.0897485i
$974$	−3.91773e7	+	2.77819e7i	−1.32324	+	0.938348i
$975$	−1.84183e6	−	7.44385e6i	−0.0620495	−	0.250776i
$976$	−1.45190e7	+	1.81658e7i	−0.487877	+	0.610423i
$977$	−3.50337e7	+	3.50337e7i	−1.17422	+	1.17422i	−0.193025	+	0.981194i	$0.561830\pi$
$977$	−3.50337e7	+	3.50337e7i	−1.17422	+	1.17422i	−0.981194	+	0.193025i	$0.938170\pi$
$978$	1.20588e7	+	2.05224e6i	0.403142	+	0.0686089i
$979$			147074.i			0.00490434i
$980$	1.55018e7	+	2.42096e7i	0.515604	+	0.805235i
$981$		−	3.62955e7i		−	1.20415i
$982$	−2.66458e6	+	1.56570e7i	−0.0881761	+	0.518118i
$983$	−3.24328e7	+	3.24328e7i	−1.07054	+	1.07054i	−0.0732202	+	0.997316i	$0.523328\pi$
$983$	−3.24328e7	+	3.24328e7i	−1.07054	+	1.07054i	−0.997316	+	0.0732202i	$0.976672\pi$
$984$	1.28117e6	−	367973.i	0.0421813	−	0.0121151i
$985$	−3.03185e7	+	3.69513e6i	−0.995673	+	0.121350i
$986$	−2.63020e7	−	3.70904e7i	−0.861581	−	1.21498i
$987$	1.54920e6	−	1.54920e6i	0.0506190	−	0.0506190i
$988$	−1.38959e7	−	2.88951e7i	−0.452891	−	0.941741i
$989$	3.78654e7			1.23098
$990$	3.38805e7	−	3.08185e7i	1.09866	−	0.999365i
$991$		−	1.17192e7i		−	0.379066i	−0.981874	−	0.189533i	$-0.939303\pi$
$991$		−	1.17192e7i		−	0.379066i	0.981874	−	0.189533i	$-0.0606974\pi$
$992$	9.63661e6	+	1.08128e7i	0.310917	+	0.348865i
$993$	−310225.	−	310225.i	−0.00998398	−	0.00998398i
$994$	−262082.	−	369582.i	−0.00841340	−	0.0118644i
$995$	1.02668e7	−	1.31167e7i	0.328758	−	0.420017i
$996$	−653984.	+	1.86574e6i	−0.0208891	+	0.0595940i
$997$	6.91501e6	+	6.91501e6i	0.220320	+	0.220320i	0.808633	−	0.588313i	$-0.200208\pi$
$997$	6.91501e6	+	6.91501e6i	0.220320	+	0.220320i	−0.588313	+	0.808633i	$0.700208\pi$
$998$	1.58142e7	+	2.69135e6i	0.502599	+	0.0855350i
$999$	−1.34802e7			−0.427349

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.k.a.3.12	yes	56
4.3	odd	2		160.6.o.a.143.15		56
5.2	odd	4	inner	40.6.k.a.27.3	yes	56
8.3	odd	2	inner	40.6.k.a.3.3	✓	56
8.5	even	2		160.6.o.a.143.16		56
20.7	even	4		160.6.o.a.47.16		56
40.27	even	4	inner	40.6.k.a.27.12	yes	56
40.37	odd	4		160.6.o.a.47.15		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.3	✓	56	8.3	odd	2	inner
40.6.k.a.3.12	yes	56	1.1	even	1	trivial
40.6.k.a.27.3	yes	56	5.2	odd	4	inner
40.6.k.a.27.12	yes	56	40.27	even	4	inner
160.6.o.a.47.15		56	40.37	odd	4
160.6.o.a.47.16		56	20.7	even	4
160.6.o.a.143.15		56	4.3	odd	2
160.6.o.a.143.16		56	8.5	even	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.949067 + 5.57667i) q^{2} +(-3.12794 - 3.12794i) q^{3} +(-30.1985 - 10.5853i) q^{4} +(34.4559 - 44.0204i) q^{5} +(20.4121 - 14.4749i) q^{6} +(19.1929 + 19.1929i) q^{7} +(87.6910 - 158.361i) q^{8} -223.432i q^{9} +O(q^{10})\)	\(q+(-0.949067 + 5.57667i) q^{2} +(-3.12794 - 3.12794i) q^{3} +(-30.1985 - 10.5853i) q^{4} +(34.4559 - 44.0204i) q^{5} +(20.4121 - 14.4749i) q^{6} +(19.1929 + 19.1929i) q^{7} +(87.6910 - 158.361i) q^{8} -223.432i q^{9} +(212.786 + 233.927i) q^{10} +648.221 q^{11} +(61.3491 + 127.569i) q^{12} +(-392.250 + 392.250i) q^{13} +(-125.248 + 88.8172i) q^{14} +(-245.469 + 29.9171i) q^{15} +(799.904 + 639.320i) q^{16} +(739.873 - 739.873i) q^{17} +(1246.01 + 212.052i) q^{18} -1806.23i q^{19} +(-1506.49 + 964.626i) q^{20} -120.068i q^{21} +(-615.206 + 3614.92i) q^{22} +(1662.57 - 1662.57i) q^{23} +(-769.636 + 221.052i) q^{24} +(-750.584 - 3033.52i) q^{25} +(-1815.18 - 2559.72i) q^{26} +(-1458.97 + 1458.97i) q^{27} +(-376.436 - 782.760i) q^{28} -7682.01 q^{29} +(66.1286 - 1397.29i) q^{30} -2500.39i q^{31} +(-4324.44 + 3854.04i) q^{32} +(-2027.59 - 2027.59i) q^{33} +(3423.84 + 4828.22i) q^{34} +(1506.19 - 183.570i) q^{35} +(-2365.09 + 6747.32i) q^{36} +(4619.77 + 4619.77i) q^{37} +(10072.8 + 1714.23i) q^{38} +2453.86 q^{39} +(-3949.65 - 9316.67i) q^{40} -1664.65 q^{41} +(669.582 + 113.953i) q^{42} +(11387.6 + 11387.6i) q^{43} +(-19575.3 - 6861.60i) q^{44} +(-9835.56 - 7698.55i) q^{45} +(7693.72 + 10849.5i) q^{46} +(12902.6 + 12902.6i) q^{47} +(-502.298 - 4501.80i) q^{48} -16070.3i q^{49} +(17629.3 - 1306.75i) q^{50} -4628.55 q^{51} +(15997.4 - 7693.30i) q^{52} +(-12615.7 + 12615.7i) q^{53} +(-6751.54 - 9520.86i) q^{54} +(22335.0 - 28534.9i) q^{55} +(4722.46 - 1356.37i) q^{56} +(-5649.78 + 5649.78i) q^{57} +(7290.75 - 42840.1i) q^{58} +30075.1i q^{59} +(7729.48 + 1694.90i) q^{60} +22710.0i q^{61} +(13943.8 + 2373.04i) q^{62} +(4288.31 - 4288.31i) q^{63} +(-17388.6 - 27773.7i) q^{64} +(3751.66 + 30782.3i) q^{65} +(13231.6 - 9382.91i) q^{66} +(-6337.59 + 6337.59i) q^{67} +(-30174.8 + 14511.3i) q^{68} -10400.8 q^{69} +(-405.763 + 8573.73i) q^{70} +2950.81i q^{71} +(-35383.0 - 19593.0i) q^{72} +(-10777.2 - 10777.2i) q^{73} +(-30147.4 + 21378.5i) q^{74} +(-7140.88 + 11836.4i) q^{75} +(-19119.5 + 54545.6i) q^{76} +(12441.2 + 12441.2i) q^{77} +(-2328.88 + 13684.4i) q^{78} +7474.95 q^{79} +(55704.5 - 13183.7i) q^{80} -45166.9 q^{81} +(1579.86 - 9283.19i) q^{82} +(9875.91 + 9875.91i) q^{83} +(-1270.96 + 3625.89i) q^{84} +(-7076.50 - 58062.5i) q^{85} +(-74312.6 + 52697.4i) q^{86} +(24028.8 + 24028.8i) q^{87} +(56843.2 - 102653. i) q^{88} +226.889i q^{89} +(52266.9 - 47543.2i) q^{90} -15056.8 q^{91} +(-67806.0 + 32608.5i) q^{92} +(-7821.06 + 7821.06i) q^{93} +(-84199.2 + 59708.2i) q^{94} +(-79511.0 - 62235.3i) q^{95} +(25581.8 + 1471.36i) q^{96} +(69631.7 - 69631.7i) q^{97} +(89618.6 + 15251.8i) q^{98} -144833. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

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