LMFDB - Embedded newform 60.6.e.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,6,Mod(11,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("60.11");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	60.e (of order $2$, degree $1$, 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:	$9.62302918878$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.4
Character	$\chi$	$=$	60.11
Dual form			60.6.e.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.54388 + 1.12492i) q^{2} +(15.2205 + 3.36711i) q^{3} +(29.4691 - 12.4728i) q^{4} -25.0000i q^{5} +(-88.1681 - 1.54508i) q^{6} -209.419i q^{7} +(-149.342 + 102.298i) q^{8} +(220.325 + 102.498i) q^{9} +O(q^{10})$	\(q+(-5.54388 + 1.12492i) q^{2} +(15.2205 + 3.36711i) q^{3} +(29.4691 - 12.4728i) q^{4} -25.0000i q^{5} +(-88.1681 - 1.54508i) q^{6} -209.419i q^{7} +(-149.342 + 102.298i) q^{8} +(220.325 + 102.498i) q^{9} +(28.1229 + 138.597i) q^{10} -618.662 q^{11} +(490.531 - 90.6161i) q^{12} -94.2663 q^{13} +(235.579 + 1160.99i) q^{14} +(84.1778 - 380.512i) q^{15} +(712.858 - 735.125i) q^{16} -333.164i q^{17} +(-1336.76 - 320.388i) q^{18} -3064.76i q^{19} +(-311.820 - 736.728i) q^{20} +(705.136 - 3187.45i) q^{21} +(3429.78 - 695.943i) q^{22} +1828.91 q^{23} +(-2617.51 + 1054.17i) q^{24} -625.000 q^{25} +(522.601 - 106.042i) q^{26} +(3008.33 + 2301.93i) q^{27} +(-2612.04 - 6171.38i) q^{28} -5163.61i q^{29} +(-38.6269 + 2204.20i) q^{30} +5764.58i q^{31} +(-3125.04 + 4877.35i) q^{32} +(-9416.32 - 2083.10i) q^{33} +(374.781 + 1847.02i) q^{34} -5235.47 q^{35} +(7771.23 + 272.453i) q^{36} +9393.47 q^{37} +(3447.60 + 16990.7i) q^{38} +(-1434.78 - 317.405i) q^{39} +(2557.45 + 3733.56i) q^{40} -2280.24i q^{41} +(-323.568 + 18464.0i) q^{42} +2578.73i q^{43} +(-18231.4 + 7716.45i) q^{44} +(2562.45 - 5508.13i) q^{45} +(-10139.2 + 2057.37i) q^{46} +16293.0 q^{47} +(13325.3 - 8788.67i) q^{48} -27049.2 q^{49} +(3464.92 - 703.073i) q^{50} +(1121.80 - 5070.90i) q^{51} +(-2777.95 + 1175.77i) q^{52} +8566.21i q^{53} +(-19267.3 - 9377.47i) q^{54} +15466.5i q^{55} +(21423.1 + 31275.1i) q^{56} +(10319.4 - 46647.1i) q^{57} +(5808.64 + 28626.4i) q^{58} -17849.1 q^{59} +(-2265.40 - 12263.3i) q^{60} -3268.13 q^{61} +(-6484.68 - 31958.1i) q^{62} +(21465.0 - 46140.2i) q^{63} +(11838.2 - 30554.8i) q^{64} +2356.66i q^{65} +(54546.2 + 955.879i) q^{66} +8190.33i q^{67} +(-4155.48 - 9818.04i) q^{68} +(27836.8 + 6158.13i) q^{69} +(29024.8 - 5889.47i) q^{70} -49026.2 q^{71} +(-43389.2 + 7231.54i) q^{72} +9210.58 q^{73} +(-52076.2 + 10566.9i) q^{74} +(-9512.79 - 2104.44i) q^{75} +(-38226.2 - 90315.8i) q^{76} +129559. i q^{77} +(8311.28 + 145.649i) q^{78} +54240.3i q^{79} +(-18378.1 - 17821.5i) q^{80} +(38037.3 + 45165.8i) q^{81} +(2565.09 + 12641.4i) q^{82} +72243.1 q^{83} +(-18976.7 - 102726. i) q^{84} -8329.09 q^{85} +(-2900.86 - 14296.2i) q^{86} +(17386.5 - 78592.6i) q^{87} +(92392.3 - 63287.9i) q^{88} -40424.7i q^{89} +(-8009.71 + 33418.9i) q^{90} +19741.1i q^{91} +(53896.3 - 22811.6i) q^{92} +(-19410.0 + 87739.6i) q^{93} +(-90326.2 + 18328.2i) q^{94} -76619.0 q^{95} +(-63987.2 + 63713.2i) q^{96} -11768.2 q^{97} +(149957. - 30428.1i) q^{98} +(-136307. - 63411.6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 10 q^{4} - 114 q^{6} + 44 q^{9}+O(q^{10}) $ 40 * q - 10 * q^4 - 114 * q^6 + 44 * q^9	$ 40 q - 10 q^{4} - 114 q^{6} + 44 q^{9} + 50 q^{10} + 1876 q^{12} - 232 q^{13} - 2734 q^{16} - 3536 q^{18} + 820 q^{21} + 13684 q^{22} + 9550 q^{24} - 25000 q^{25} - 23188 q^{28} - 5800 q^{30} - 9424 q^{33} + 38972 q^{34} + 53754 q^{36} + 2152 q^{37} - 10850 q^{40} - 62868 q^{42} + 5900 q^{45} + 78748 q^{46} + 100956 q^{48} - 52144 q^{49} - 82528 q^{52} - 120862 q^{54} - 44424 q^{57} + 97476 q^{58} + 3850 q^{60} + 2072 q^{61} - 91234 q^{64} - 45784 q^{66} + 52764 q^{69} - 3300 q^{70} - 10344 q^{72} + 264960 q^{73} + 73356 q^{76} + 176440 q^{78} - 165120 q^{81} - 170920 q^{82} - 250544 q^{84} - 132400 q^{85} + 359116 q^{88} + 35550 q^{90} + 510368 q^{93} - 623100 q^{94} - 379254 q^{96} + 453648 q^{97}+O(q^{100}) $ 40 * q - 10 * q^4 - 114 * q^6 + 44 * q^9 + 50 * q^10 + 1876 * q^12 - 232 * q^13 - 2734 * q^16 - 3536 * q^18 + 820 * q^21 + 13684 * q^22 + 9550 * q^24 - 25000 * q^25 - 23188 * q^28 - 5800 * q^30 - 9424 * q^33 + 38972 * q^34 + 53754 * q^36 + 2152 * q^37 - 10850 * q^40 - 62868 * q^42 + 5900 * q^45 + 78748 * q^46 + 100956 * q^48 - 52144 * q^49 - 82528 * q^52 - 120862 * q^54 - 44424 * q^57 + 97476 * q^58 + 3850 * q^60 + 2072 * q^61 - 91234 * q^64 - 45784 * q^66 + 52764 * q^69 - 3300 * q^70 - 10344 * q^72 + 264960 * q^73 + 73356 * q^76 + 176440 * q^78 - 165120 * q^81 - 170920 * q^82 - 250544 * q^84 - 132400 * q^85 + 359116 * q^88 + 35550 * q^90 + 510368 * q^93 - 623100 * q^94 - 379254 * q^96 + 453648 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−5.54388	+	1.12492i	−0.980028	+	0.198859i
$2$	−5.54388	+	1.12492i	−0.980028	+	0.198859i
$3$	15.2205	+	3.36711i	0.976393	+	0.216000i
$3$	15.2205	+	3.36711i	0.976393	+	0.216000i
$4$	29.4691	−	12.4728i	0.920910	−	0.389775i
$5$		−	25.0000i		−	0.447214i
$5$		−	25.0000i		−	0.447214i
$6$	−88.1681	−	1.54508i	−0.999846	−	0.0175215i
$7$		−	209.419i		−	1.61536i	−0.589619	−	0.807682i	$-0.700722\pi$
$7$		−	209.419i		−	1.61536i	0.589619	−	0.807682i	$-0.299278\pi$
$8$	−149.342	+	102.298i	−0.825007	+	0.565122i
$9$	220.325	+	102.498i	0.906688	+	0.421802i
$10$	28.1229	+	138.597i	0.0889325	+	0.438282i
$11$	−618.662			−1.54160			−0.770800	−	0.637078i	$-0.780143\pi$
$11$	−618.662			−1.54160			−0.770800	+	0.637078i	$0.780143\pi$
$12$	490.531	−	90.6161i	0.983362	−	0.181657i
$13$	−94.2663			−0.154703			−0.0773514	−	0.997004i	$-0.524646\pi$
$13$	−94.2663			−0.154703			−0.0773514	+	0.997004i	$0.524646\pi$
$14$	235.579	+	1160.99i	0.321230	+	1.58310i
$15$	84.1778	−	380.512i	0.0965982	−	0.436656i
$16$	712.858	−	735.125i	0.696151	−	0.717896i
$17$		−	333.164i		−	0.279599i	−0.990180	−	0.139799i	$-0.955354\pi$
$17$		−	333.164i		−	0.279599i	0.990180	−	0.139799i	$-0.0446458\pi$
$18$	−1336.76	−	320.388i	−0.972459	−	0.233075i
$19$		−	3064.76i		−	1.94766i	−0.227282	−	0.973829i	$-0.572984\pi$
$19$		−	3064.76i		−	1.94766i	0.227282	−	0.973829i	$-0.427016\pi$
$20$	−311.820	−	736.728i	−0.174313	−	0.411844i
$21$	705.136	−	3187.45i	0.348919	−	1.57723i
$22$	3429.78	−	695.943i	1.51081	−	0.306561i
$23$	1828.91			0.720895			0.360448	−	0.932779i	$-0.382624\pi$
$23$	1828.91			0.720895			0.360448	+	0.932779i	$0.382624\pi$
$24$	−2617.51	+	1054.17i	−0.927598	+	0.373580i
$25$	−625.000			−0.200000
$26$	522.601	−	106.042i	0.151613	−	0.0307641i
$27$	3008.33	+	2301.93i	0.794175	+	0.607690i
$28$	−2612.04	−	6171.38i	−0.629628	−	1.48760i
$29$		−	5163.61i		−	1.14014i	−0.821596	−	0.570071i	$-0.806916\pi$
$29$		−	5163.61i		−	1.14014i	0.821596	−	0.570071i	$-0.193084\pi$
$30$	−38.6269	+	2204.20i	−0.00783586	+	0.447145i
$31$			5764.58i			1.07737i	0.842508	+	0.538683i	$0.181078\pi$
$31$			5764.58i			1.07737i	−0.842508	+	0.538683i	$0.818922\pi$
$32$	−3125.04	+	4877.35i	−0.539487	+	0.841994i
$33$	−9416.32	−	2083.10i	−1.50521	−	0.332986i
$34$	374.781	+	1847.02i	0.0556008	+	0.274015i
$35$	−5235.47			−0.722412
$36$	7771.23	+	272.453i	0.999386	+	0.0350377i
$37$	9393.47			1.12803			0.564016	−	0.825764i	$-0.309255\pi$
$37$	9393.47			1.12803			0.564016	+	0.825764i	$0.309255\pi$
$38$	3447.60	+	16990.7i	0.387310	+	1.90876i
$39$	−1434.78	−	317.405i	−0.151051	−	0.0334158i
$40$	2557.45	+	3733.56i	0.252730	+	0.368955i
$41$		−	2280.24i		−	0.211847i	−0.994374	−	0.105923i	$-0.966220\pi$
$41$		−	2280.24i		−	0.211847i	0.994374	−	0.105923i	$-0.0337798\pi$
$42$	−323.568	+	18464.0i	−0.0283036	+	1.61512i
$43$			2578.73i			0.212684i	0.994330	+	0.106342i	$0.0339139\pi$
$43$			2578.73i			0.212684i	−0.994330	+	0.106342i	$0.966086\pi$
$44$	−18231.4	+	7716.45i	−1.41967	+	0.600877i
$45$	2562.45	−	5508.13i	0.188636	−	0.405483i
$46$	−10139.2	+	2057.37i	−0.706498	+	0.143357i
$47$	16293.0			1.07586			0.537930	−	0.842990i	$-0.319207\pi$
$47$	16293.0			1.07586			0.537930	+	0.842990i	$0.319207\pi$
$48$	13325.3	−	8788.67i	0.834783	−	0.550580i
$49$	−27049.2			−1.60940
$50$	3464.92	−	703.073i	0.196006	−	0.0397718i
$51$	1121.80	−	5070.90i	0.0603934	−	0.272998i
$52$	−2777.95	+	1175.77i	−0.142467	+	0.0602993i
$53$			8566.21i			0.418889i	0.977821	+	0.209444i	$0.0671656\pi$
$53$			8566.21i			0.418889i	−0.977821	+	0.209444i	$0.932834\pi$
$54$	−19267.3	−	9377.47i	−0.899158	−	0.437624i
$55$			15466.5i			0.689424i
$56$	21423.1	+	31275.1i	0.912877	+	1.33269i
$57$	10319.4	−	46647.1i	0.420695	−	1.90168i
$58$	5808.64	+	28626.4i	0.226728	+	1.11737i
$59$	−17849.1			−0.667553			−0.333776	−	0.942652i	$-0.608323\pi$
$59$	−17849.1			−0.667553			−0.333776	+	0.942652i	$0.608323\pi$
$60$	−2265.40	−	12263.3i	−0.0812395	−	0.439773i
$61$	−3268.13			−0.112454			−0.0562269	−	0.998418i	$-0.517907\pi$
$61$	−3268.13			−0.112454			−0.0562269	+	0.998418i	$0.517907\pi$
$62$	−6484.68	−	31958.1i	−0.214244	−	1.05585i
$63$	21465.0	−	46140.2i	0.681364	−	1.46463i
$64$	11838.2	−	30554.8i	0.361274	−	0.932460i
$65$			2356.66i			0.0691852i
$66$	54546.2	+	955.879i	1.54136	+	0.0270112i
$67$			8190.33i			0.222902i	0.993770	+	0.111451i	$0.0355499\pi$
$67$			8190.33i			0.222902i	−0.993770	+	0.111451i	$0.964450\pi$
$68$	−4155.48	−	9818.04i	−0.108981	−	0.257485i
$69$	27836.8	+	6158.13i	0.703877	+	0.155714i
$70$	29024.8	−	5889.47i	0.707984	−	0.143658i
$71$	−49026.2			−1.15420			−0.577101	−	0.816673i	$-0.695816\pi$
$71$	−49026.2			−1.15420			−0.577101	+	0.816673i	$0.695816\pi$
$72$	−43389.2	+	7231.54i	−0.986394	+	0.164399i
$73$	9210.58			0.202292			0.101146	−	0.994872i	$-0.467749\pi$
$73$	9210.58			0.202292			0.101146	+	0.994872i	$0.467749\pi$
$74$	−52076.2	+	10566.9i	−1.10550	+	0.224320i
$75$	−9512.79	−	2104.44i	−0.195279	−	0.0432000i
$76$	−38226.2	−	90315.8i	−0.759149	−	1.79362i
$77$			129559.i			2.49024i
$78$	8311.28	+	145.649i	0.154679	+	0.00271063i
$79$			54240.3i			0.977810i	0.872337	+	0.488905i	$0.162603\pi$
$79$			54240.3i			0.977810i	−0.872337	+	0.488905i	$0.837397\pi$
$80$	−18378.1	−	17821.5i	−0.321053	−	0.311328i
$81$	38037.3	+	45165.8i	0.644166	+	0.764886i
$82$	2565.09	+	12641.4i	0.0421277	+	0.207616i
$83$	72243.1			1.15107			0.575534	−	0.817778i	$-0.304794\pi$
$83$	72243.1			1.15107			0.575534	+	0.817778i	$0.304794\pi$
$84$	−18976.7	−	102726.i	−0.293442	−	1.58849i
$85$	−8329.09			−0.125040
$86$	−2900.86	−	14296.2i	−0.0422942	−	0.208436i
$87$	17386.5	−	78592.6i	0.246271	−	1.11323i
$88$	92392.3	−	63287.9i	1.27183	−	0.871192i
$89$		−	40424.7i		−	0.540969i	−0.962724	−	0.270484i	$-0.912816\pi$
$89$		−	40424.7i		−	0.540969i	0.962724	−	0.270484i	$-0.0871839\pi$
$90$	−8009.71	+	33418.9i	−0.104234	+	0.434897i
$91$			19741.1i			0.249901i
$92$	53896.3	−	22811.6i	0.663880	−	0.280987i
$93$	−19410.0	+	87739.6i	−0.232711	+	1.05193i
$94$	−90326.2	+	18328.2i	−1.05437	+	0.213945i
$95$	−76619.0			−0.871019
$96$	−63987.2	+	63713.2i	−0.708622	+	0.705588i
$97$	−11768.2			−0.126993			−0.0634967	−	0.997982i	$-0.520225\pi$
$97$	−11768.2			−0.126993			−0.0634967	+	0.997982i	$0.520225\pi$
$98$	149957.	−	30428.1i	1.57726	−	0.320044i
$99$	−136307.	−	63411.6i	−1.39775	−	0.650250i
$100$	−18418.2	+	7795.50i	−0.184182	+	0.0779550i
$101$		−	38687.0i		−	0.377365i	−0.982038	−	0.188682i	$-0.939578\pi$
$101$		−	38687.0i		−	0.377365i	0.982038	−	0.188682i	$-0.0604216\pi$
$102$	−514.763	+	29374.4i	−0.00489899	+	0.279556i
$103$			87011.2i			0.808132i	0.914730	+	0.404066i	$0.132403\pi$
$103$			87011.2i			0.808132i	−0.914730	+	0.404066i	$0.867597\pi$
$104$	14078.0	−	9643.26i	0.127631	−	0.0874260i
$105$	−79686.2	−	17628.4i	−0.705359	−	0.156041i
$106$	−9636.28	−	47490.0i	−0.0832999	−	0.410523i
$107$	40902.2			0.345372			0.172686	−	0.984977i	$-0.444755\pi$
$107$	40902.2			0.345372			0.172686	+	0.984977i	$0.444755\pi$
$108$	117364.	+	30313.4i	0.968226	+	0.250078i
$109$	110590.			0.891557			0.445778	−	0.895143i	$-0.352927\pi$
$109$	110590.			0.891557			0.445778	+	0.895143i	$0.352927\pi$
$110$	−17398.6	−	85744.6i	−0.137098	−	0.675655i
$111$	142973.	+	31628.9i	1.10140	+	0.243655i
$112$	−153949.	−	149286.i	−1.15966	−	1.12454i
$113$			76627.3i			0.564530i	0.959336	+	0.282265i	$0.0910858\pi$
$113$			76627.3i			0.564530i	−0.959336	+	0.282265i	$0.908914\pi$
$114$	−4735.29	+	270214.i	−0.0341259	+	1.94736i
$115$		−	45722.7i		−	0.322394i
$116$	−64404.8	−	152167.i	−0.444399	−	1.04997i
$117$	−20769.2	−	9662.11i	−0.140267	−	0.0652540i
$118$	98953.1	−	20078.7i	0.654221	−	0.132749i
$119$	−69770.7			−0.451653
$120$	26354.3	+	65437.7i	0.167070	+	0.414835i
$121$	221691.			1.37653
$122$	18118.1	−	3676.37i	0.110208	−	0.0223625i
$123$	7677.83	−	34706.4i	0.0457589	−	0.206846i
$124$	71900.5	+	169877.i	0.419931	+	0.992158i
$125$			15625.0i			0.0894427i
$126$	−67095.3	+	279942.i	−0.376501	+	1.57087i
$127$			197435.i			1.08621i	0.839665	+	0.543105i	$0.182751\pi$
$127$			197435.i			1.08621i	−0.839665	+	0.543105i	$0.817249\pi$
$128$	−31258.0	+	182709.i	−0.168631	+	0.985679i
$129$	−8682.88	+	39249.5i	−0.0459398	+	0.207663i
$130$	−2651.05	−	13065.0i	−0.0137581	−	0.0678034i
$131$	151070.			0.769132			0.384566	−	0.923098i	$-0.374351\pi$
$131$	151070.			0.769132			0.384566	+	0.923098i	$0.374351\pi$
$132$	−303473.	+	56060.7i	−1.51595	+	0.280042i
$133$	−641818.			−3.14618
$134$	−9213.45	−	45406.2i	−0.0443262	−	0.218451i
$135$	57548.1	−	75208.2i	0.271767	−	0.355166i
$136$	34082.0	+	49755.4i	0.158007	+	0.230671i
$137$		−	299015.i		−	1.36111i	−0.732699	−	0.680553i	$-0.761740\pi$
$137$		−	299015.i		−	1.36111i	0.732699	−	0.680553i	$-0.238260\pi$
$138$	−161251.	−	2825.80i	−0.720785	−	0.0126312i
$139$			151182.i			0.663689i	0.943334	+	0.331844i	$0.107671\pi$
$139$			151182.i			0.663689i	−0.943334	+	0.331844i	$0.892329\pi$
$140$	−154285.	+	65300.9i	−0.665277	+	0.281578i
$141$	247987.	+	54860.2i	1.05046	+	0.232386i
$142$	271795.	−	55150.4i	1.13115	−	0.229524i
$143$	58319.0			0.238490
$144$	232409.	−	88900.0i	0.934001	−	0.357269i
$145$	−129090.			−0.509887
$146$	−51062.3	+	10361.1i	−0.198252	+	0.0402277i
$147$	−411701.	−	91077.5i	−1.57141	−	0.347631i
$148$	276817.	−	117163.i	1.03882	−	0.439679i
$149$		−	259029.i		−	0.955834i	−0.878405	−	0.477917i	$-0.841392\pi$
$149$		−	259029.i		−	0.955834i	0.878405	−	0.477917i	$-0.158608\pi$
$150$	55105.1	+	965.673i	0.199969	+	0.00350430i
$151$			216927.i			0.774233i	0.922031	+	0.387117i	$0.126529\pi$
$151$			216927.i			0.774233i	−0.922031	+	0.387117i	$0.873471\pi$
$152$	313519.	+	457699.i	1.10066	+	1.60683i
$153$	34148.6	−	73404.3i	0.117935	−	0.253509i
$154$	−145743.	−	718261.i	−0.495208	−	2.44051i
$155$	144115.			0.481813
$156$	−46240.6	+	8542.05i	−0.152129	+	0.0281029i
$157$	500164.			1.61943			0.809717	−	0.586821i	$-0.199621\pi$
$157$	500164.			1.61943			0.809717	+	0.586821i	$0.199621\pi$
$158$	−61015.8	−	300701.i	−0.194446	−	0.958281i
$159$	−28843.4	+	130382.i	−0.0904801	+	0.409000i
$160$	121934.	+	78126.1i	0.376551	+	0.241266i
$161$		−	383007.i		−	1.16451i
$162$	−261682.	−	207605.i	−0.783405	−	0.621512i
$163$		−	518201.i		−	1.52767i	−0.645412	−	0.763834i	$-0.723314\pi$
$163$		−	518201.i		−	1.52767i	0.645412	−	0.763834i	$-0.276686\pi$
$164$	−28441.0	−	67196.8i	−0.0825726	−	0.195092i
$165$	−52077.5	+	235408.i	−0.148916	+	0.673149i
$166$	−400507.	+	81267.5i	−1.12808	+	0.228900i
$167$	48783.1			0.135356			0.0676781	−	0.997707i	$-0.478441\pi$
$167$	48783.1			0.135356			0.0676781	+	0.997707i	$0.478441\pi$
$168$	220763.	+	548155.i	0.603467	+	1.49841i
$169$	−362407.			−0.976067
$170$	46175.4	−	9369.54i	0.122543	−	0.0248654i
$171$	314132.	−	675244.i	0.821527	−	1.76592i
$172$	32164.0	+	75993.0i	0.0828990	+	0.195863i
$173$		−	98044.7i		−	0.249063i	−0.992216	−	0.124531i	$-0.960257\pi$
$173$		−	98044.7i		−	0.249063i	0.992216	−	0.124531i	$-0.0397428\pi$
$174$	−7978.18	+	455266.i	−0.0199770	+	1.13997i
$175$			130887.i			0.323073i
$176$	−441018.	+	454794.i	−1.07319	+	1.10671i
$177$	−271671.	−	60099.8i	−0.651794	−	0.144192i
$178$	45474.5	+	224110.i	0.107577	+	0.530165i
$179$	313369.			0.731009			0.365505	−	0.930810i	$-0.380896\pi$
$179$	313369.			0.731009			0.365505	+	0.930810i	$0.380896\pi$
$180$	6811.32	−	194281.i	0.0156693	−	0.446939i
$181$	486897.			1.10469			0.552345	−	0.833616i	$-0.313733\pi$
$181$	486897.			1.10469			0.552345	+	0.833616i	$0.313733\pi$
$182$	−22207.1	−	109442.i	−0.0496952	−	0.244910i
$183$	−49742.4	−	11004.1i	−0.109799	−	0.0242900i
$184$	−273133.	+	187094.i	−0.594744	+	0.407394i
$185$		−	234837.i		−	0.504472i
$186$	8906.72	−	508252.i	0.0188771	−	1.07720i
$187$			206115.i			0.431029i
$188$	480140.	−	203219.i	0.990770	−	0.419343i
$189$	482066.	−	630000.i	0.981640	−	1.28288i
$190$	424766.	−	86190.1i	0.853623	−	0.173210i
$191$	−384344.			−0.762318			−0.381159	−	0.924509i	$-0.624475\pi$
$191$	−384344.			−0.762318			−0.381159	+	0.924509i	$0.624475\pi$
$192$	283065.	−	425198.i	0.554157	−	0.832412i
$193$	−532428.			−1.02889			−0.514444	−	0.857524i	$-0.672002\pi$
$193$	−532428.			−1.02889			−0.514444	+	0.857524i	$0.672002\pi$
$194$	65241.5	−	13238.3i	0.124457	−	0.0252538i
$195$	−7935.13	+	35869.4i	−0.0149440	+	0.0675520i
$196$	−797115.	+	337379.i	−1.48211	+	0.627304i
$197$			18328.9i			0.0336489i	0.999858	+	0.0168245i	$0.00535565\pi$
$197$			18328.9i			0.0336489i	−0.999858	+	0.0168245i	$0.994644\pi$
$198$	827000.	+	198212.i	1.49914	+	0.359308i
$199$		−	471424.i		−	0.843876i	−0.906625	−	0.421938i	$-0.861350\pi$
$199$		−	471424.i		−	0.843876i	0.906625	−	0.421938i	$-0.138650\pi$
$200$	93338.9	−	63936.3i	0.165001	−	0.113024i
$201$	−27577.8	+	124661.i	−0.0481469	+	0.217640i
$202$	43519.6	+	214476.i	0.0750424	+	0.369828i
$203$	−1.08136e6			−1.84174
$204$	−30190.0	−	163427.i	−0.0507911	−	0.274947i
$205$	−57006.1			−0.0947407
$206$	−97880.4	−	482379.i	−0.160704	−	0.791992i
$207$	402954.	+	187459.i	0.653627	+	0.304075i
$208$	−67198.5	+	69297.6i	−0.107696	+	0.111060i
$209$			1.89605e6i			3.00251i
$210$	461601.	+	8089.19i	0.722302	+	0.0126578i
$211$			112221.i			0.173527i	0.996229	+	0.0867634i	$0.0276524\pi$
$211$			112221.i			0.173527i	−0.996229	+	0.0867634i	$0.972348\pi$
$212$	106845.	+	252439.i	0.163273	+	0.385759i
$213$	−746201.	−	165076.i	−1.12696	−	0.249308i
$214$	−226757.	+	46011.6i	−0.338475	+	0.0686804i
$215$	64468.3			0.0951153
$216$	−684753.	−	36028.8i	−0.998619	−	0.0525430i
$217$	1.20721e6			1.74034
$218$	−613096.	+	124404.i	−0.873750	+	0.177294i
$219$	140189.	+	31013.0i	0.197517	+	0.0436952i
$220$	192911.	+	455785.i	0.268720	+	0.634898i
$221$			31406.1i			0.0432547i
$222$	−828204.	−	14513.6i	−1.12786	−	0.0197649i
$223$			558284.i			0.751783i	0.926664	+	0.375892i	$0.122664\pi$
$223$			558284.i			0.751783i	−0.926664	+	0.375892i	$0.877336\pi$
$224$	1.02141e6	+	654442.i	1.36013	+	0.871468i
$225$	−137703.	−	64061.2i	−0.181338	−	0.0843605i
$226$	−86199.4	−	424812.i	−0.112262	−	0.553256i
$227$	177751.			0.228954			0.114477	−	0.993426i	$-0.463481\pi$
$227$	177751.			0.228954			0.114477	+	0.993426i	$0.463481\pi$
$228$	−277717.	−	1.50336e6i	−0.353806	−	1.91525i
$229$	−884502.			−1.11458			−0.557288	−	0.830319i	$-0.688158\pi$
$229$	−884502.			−1.11458			−0.557288	+	0.830319i	$0.688158\pi$
$230$	51434.3	+	253481.i	0.0641110	+	0.315955i
$231$	−436240.	+	1.97195e6i	−0.537893	+	2.43146i
$232$	528228.	+	771146.i	0.644319	+	0.940625i
$233$			898586.i			1.08435i	0.840265	+	0.542175i	$0.182399\pi$
$233$			898586.i			1.08435i	−0.840265	+	0.542175i	$0.817601\pi$
$234$	126011.	+	30201.8i	0.150442	+	0.0360574i
$235$		−	407324.i		−	0.481139i
$236$	−525997.	+	222628.i	−0.614756	+	0.260196i
$237$	−182633.	+	825562.i	−0.211207	+	0.954727i
$238$	386800.	−	78486.2i	0.442633	−	0.0898154i
$239$	1.66002e6			1.87983			0.939913	−	0.341415i	$-0.110906\pi$
$239$	1.66002e6			1.87983			0.939913	+	0.341415i	$0.110906\pi$
$240$	−219717.	−	333132.i	−0.246227	−	0.373326i
$241$	692446.			0.767968			0.383984	−	0.923340i	$-0.374552\pi$
$241$	692446.			0.767968			0.383984	+	0.923340i	$0.374552\pi$
$242$	−1.22903e6	+	249384.i	−1.34904	+	0.273735i
$243$	426868.	+	815520.i	0.463743	+	0.885970i
$244$	−96308.8	+	40762.7i	−0.103560	+	0.0438317i
$245$			676229.i			0.719745i
$246$	−3523.15	+	201045.i	−0.00371188	+	0.211814i
$247$			288904.i			0.301308i
$248$	−589705.	−	860896.i	−0.608844	−	0.888835i
$249$	1.09957e6	+	243250.i	1.12390	+	0.248631i
$250$	−17576.8	−	86623.1i	−0.0177865	−	0.0876564i
$251$	−1.49702e6			−1.49984			−0.749919	−	0.661529i	$-0.769908\pi$
$251$	−1.49702e6			−1.49984			−0.749919	+	0.661529i	$0.769908\pi$
$252$	57056.7	−	1.62744e6i	0.0565986	−	1.61437i
$253$	−1.13148e6			−1.11133
$254$	−222098.	−	1.09455e6i	−0.216003	−	1.06452i
$255$	−126773.	−	28045.0i	−0.122089	−	0.0270087i
$256$	−32242.1	−	1.04808e6i	−0.0307484	−	0.999527i
$257$		−	260541.i		−	0.246061i	−0.992403	−	0.123031i	$-0.960739\pi$
$257$		−	260541.i		−	0.246061i	0.992403	−	0.123031i	$-0.0392613\pi$
$258$	3984.34	−	227362.i	0.00372655	−	0.212652i
$259$		−	1.96717e6i		−	1.82218i
$260$	29394.1	+	69448.7i	0.0269667	+	0.0637134i
$261$	529260.	−	1.13767e6i	0.480914	−	1.03375i
$262$	−837515.	+	169942.i	−0.753770	+	0.152949i
$263$	−382772.			−0.341233			−0.170616	−	0.985338i	$-0.554576\pi$
$263$	−382772.			−0.341233			−0.170616	+	0.985338i	$0.554576\pi$
$264$	1.61935e6	−	652175.i	1.42998	−	0.575910i
$265$	214155.			0.187333
$266$	3.55816e6	−	721992.i	3.08334	−	0.625646i
$267$	136115.	−	615283.i	0.116849	−	0.528198i
$268$	102156.	+	241362.i	0.0868818	+	0.205273i
$269$		−	908465.i		−	0.765469i	−0.923858	−	0.382734i	$-0.874982\pi$
$269$		−	908465.i		−	0.765469i	0.923858	−	0.382734i	$-0.125018\pi$
$270$	−234437.	+	481682.i	−0.195711	+	0.402116i
$271$		−	1.05504e6i		−	0.872664i	−0.899786	−	0.436332i	$-0.856277\pi$
$271$		−	1.05504e6i		−	0.872664i	0.899786	−	0.436332i	$-0.143723\pi$
$272$	−244917.	−	237498.i	−0.200723	−	0.194643i
$273$	−66470.6	+	300469.i	−0.0539787	+	0.244002i
$274$	336368.	+	1.65770e6i	0.270668	+	1.33392i
$275$	386664.			0.308320
$276$	897136.	−	165729.i	0.708901	−	0.130956i
$277$	729637.			0.571357			0.285679	−	0.958326i	$-0.407781\pi$
$277$	729637.			0.571357			0.285679	+	0.958326i	$0.407781\pi$
$278$	−170068.	−	838137.i	−0.131981	−	0.650434i
$279$	−590858.	+	1.27008e6i	−0.454436	+	0.976835i
$280$	781876.	−	535578.i	0.595996	−	0.408251i
$281$			1.25930e6i			0.951400i	0.879608	+	0.475700i	$0.157805\pi$
$281$			1.25930e6i			0.951400i	−0.879608	+	0.475700i	$0.842195\pi$
$282$	−1.43652e6	−	25173.9i	−1.07569	−	0.0188507i
$283$		−	2.18394e6i		−	1.62097i	−0.585758	−	0.810486i	$-0.699203\pi$
$283$		−	2.18394e6i		−	1.62097i	0.585758	−	0.810486i	$-0.300797\pi$
$284$	−1.44476e6	+	611494.i	−1.06292	+	0.449879i
$285$	−1.16618e6	−	257985.i	−0.850457	−	0.188140i
$286$	−323313.	+	65604.0i	−0.233727	+	0.0474259i
$287$	−477526.			−0.342209
$288$	−1.18844e6	+	754292.i	−0.844301	+	0.535869i
$289$	1.30886e6			0.921825
$290$	715661.	−	145216.i	0.499703	−	0.101396i
$291$	−179118.	−	39624.9i	−0.123995	−	0.0274306i
$292$	271428.	−	114882.i	0.186293	−	0.0788486i
$293$		−	970292.i		−	0.660288i	−0.943931	−	0.330144i	$-0.892903\pi$
$293$		−	970292.i		−	0.660288i	0.943931	−	0.330144i	$-0.107097\pi$
$294$	2.38487e6	+	41793.0i	1.60915	+	0.0281991i
$295$			446227.i			0.298539i
$296$	−1.40284e6	+	960933.i	−0.930635	+	0.637476i
$297$	−1.86114e6	−	1.42411e6i	−1.22430	−	0.936814i
$298$	291386.	+	1.43602e6i	0.190076	+	0.936744i
$299$	−172404.			−0.111525
$300$	−306582.	+	56635.1i	−0.196672	+	0.0363314i
$301$	540035.			0.343562
$302$	−244025.	−	1.20262e6i	−0.153963	−	0.758770i
$303$	130263.	−	588834.i	0.0815108	−	0.368456i
$304$	−2.25298e6	−	2.18474e6i	−1.39822	−	1.35586i
$305$			81703.1i			0.0502909i
$306$	−106742.	+	445359.i	−0.0651675	+	0.271898i
$307$		−	2.42156e6i		−	1.46639i	−0.680017	−	0.733196i	$-0.738028\pi$
$307$		−	2.42156e6i		−	1.46639i	0.680017	−	0.733196i	$-0.261972\pi$
$308$	1.61597e6	+	3.81800e6i	0.970635	+	2.29329i
$309$	−292976.	+	1.32435e6i	−0.174557	+	0.789054i
$310$	−798953.	+	162117.i	−0.472190	+	0.0958129i
$311$	1.78844e6			1.04851			0.524255	−	0.851561i	$-0.324344\pi$
$311$	1.78844e6			1.04851			0.524255	+	0.851561i	$0.324344\pi$
$312$	246743.	−	99372.9i	0.143502	−	0.0577938i
$313$	656157.			0.378571			0.189285	−	0.981922i	$-0.439383\pi$
$313$	656157.			0.378571			0.189285	+	0.981922i	$0.439383\pi$
$314$	−2.77285e6	+	562643.i	−1.58709	+	0.322039i
$315$	−1.15350e6	−	536625.i	−0.655003	−	0.304715i
$316$	676529.	+	1.59841e6i	0.381126	+	0.900475i
$317$			944573.i			0.527944i	0.964530	+	0.263972i	$0.0850326\pi$
$317$			944573.i			0.527944i	−0.964530	+	0.263972i	$0.914967\pi$
$318$	13235.4	−	755266.i	0.00733957	−	0.418825i
$319$			3.19453e6i			1.75764i
$320$	−763871.	−	295956.i	−0.417009	−	0.161567i
$321$	622551.	+	137722.i	0.337219	+	0.0746005i
$322$	430852.	+	2.12335e6i	0.231573	+	1.14125i
$323$	−1.02107e6			−0.544563
$324$	1.68427e6	+	856563.i	0.891352	+	0.453312i
$325$	58916.5			0.0309406
$326$	582933.	+	2.87284e6i	0.303791	+	1.49716i
$327$	1.68323e6	+	372368.i	0.870510	+	0.192576i
$328$	233264.	+	340537.i	0.119719	+	0.174775i
$329$		−	3.41205e6i		−	1.73790i
$330$	23897.0	−	1.36366e6i	0.0120798	−	0.689318i
$331$			36914.9i			0.0185196i	0.999957	+	0.00925981i	$0.00294753\pi$
$331$			36914.9i			0.0185196i	−0.999957	+	0.00925981i	$0.997052\pi$
$332$	2.12894e6	−	901074.i	1.06003	−	0.448658i
$333$	2.06962e6	+	962812.i	1.02277	+	0.475807i
$334$	−270447.	+	54876.9i	−0.132653	+	0.0269168i
$335$	204758.			0.0996849
$336$	−1.84051e6	−	2.79056e6i	−0.889387	−	1.34848i
$337$	−1.53845e6			−0.737918			−0.368959	−	0.929446i	$-0.620286\pi$
$337$	−1.53845e6			−0.737918			−0.368959	+	0.929446i	$0.620286\pi$
$338$	2.00914e6	−	407678.i	0.956573	−	0.194100i
$339$	−258013.	+	1.16630e6i	−0.121939	+	0.551204i
$340$	−245451.	+	103887.i	−0.115151	+	0.0487376i
$341$		−	3.56633e6i		−	1.66087i
$342$	−981914.	+	4.09684e6i	−0.453950	+	1.89402i
$343$			2.14490e6i			0.984401i
$344$	−263799.	−	385114.i	−0.120193	−	0.175466i
$345$	153953.	−	695921.i	0.0696372	−	0.314784i
$346$	110292.	+	543548.i	0.0495284	+	0.244089i
$347$	−427686.			−0.190678			−0.0953392	−	0.995445i	$-0.530394\pi$
$347$	−427686.			−0.190678			−0.0953392	+	0.995445i	$0.530394\pi$
$348$	−467907.	−	2.53291e6i	−0.207115	−	1.12117i
$349$	−1.62335e6			−0.713427			−0.356714	−	0.934214i	$-0.616103\pi$
$349$	−1.62335e6			−0.713427			−0.356714	+	0.934214i	$0.616103\pi$
$350$	−147237.	−	725619.i	−0.0642460	−	0.316620i
$351$	−283584.	−	216994.i	−0.122861	−	0.0940113i
$352$	1.93334e6	−	3.01743e6i	0.831673	−	1.29802i
$353$		−	3.48144e6i		−	1.48704i	−0.668714	−	0.743519i	$-0.733155\pi$
$353$		−	3.48144e6i		−	1.48704i	0.668714	−	0.743519i	$-0.266845\pi$
$354$	1.57372e6	+	27578.2i	0.667450	+	0.0116965i
$355$			1.22565e6i			0.516175i
$356$	−504210.	−	1.19128e6i	−0.210856	−	0.498184i
$357$	−1.06194e6	−	234925.i	−0.440991	−	0.0975573i
$358$	−1.73728e6	+	352514.i	−0.716410	+	0.145368i
$359$	1.16051e6			0.475240			0.237620	−	0.971358i	$-0.423633\pi$
$359$	1.16051e6			0.475240			0.237620	+	0.971358i	$0.423633\pi$
$360$	180789.	+	1.08473e6i	0.0735215	+	0.441129i
$361$	−6.91667e6			−2.79337
$362$	−2.69929e6	+	547718.i	−1.08263	+	0.219678i
$363$	3.37424e6	+	746459.i	1.34403	+	0.297330i
$364$	246227.	+	581754.i	0.0974053	+	0.230137i
$365$		−	230264.i		−	0.0904679i
$366$	288144.	+	5049.50i	0.112437	+	0.00197036i
$367$			3.42971e6i			1.32920i	0.747197	+	0.664602i	$0.231399\pi$
$367$			3.42971e6i			1.32920i	−0.747197	+	0.664602i	$0.768601\pi$
$368$	1.30375e6	−	1.34448e6i	0.501852	−	0.517528i
$369$	233720.	−	502395.i	0.0893574	−	0.192079i
$370$	264172.	+	1.30191e6i	0.100319	+	0.494396i
$371$	1.79392e6			0.676658
$372$	522364.	+	2.82771e6i	0.195711	+	1.05944i
$373$	1.15190e6			0.428690			0.214345	−	0.976758i	$-0.431238\pi$
$373$	1.15190e6			0.428690			0.214345	+	0.976758i	$0.431238\pi$
$374$	−231863.	−	1.14268e6i	−0.0857141	−	0.422421i
$375$	−52611.1	+	237820.i	−0.0193196	+	0.0873313i
$376$	−2.43323e6	+	1.66674e6i	−0.887592	+	0.607992i
$377$			486755.i			0.176383i
$378$	−1.96382e6	+	4.03493e6i	−0.706922	+	1.45247i
$379$		−	3.91478e6i		−	1.39994i	−0.714173	−	0.699969i	$-0.753197\pi$
$379$		−	3.91478e6i		−	1.39994i	0.714173	−	0.699969i	$-0.246803\pi$
$380$	−2.25790e6	+	955654.i	−0.802130	+	0.339502i
$381$	−664784.	+	3.00505e6i	−0.234622	+	1.06057i
$382$	2.13075e6	−	432355.i	0.747093	−	0.151594i
$383$	2.48791e6			0.866639			0.433320	−	0.901240i	$-0.357342\pi$
$383$	2.48791e6			0.866639			0.433320	+	0.901240i	$0.357342\pi$
$384$	−1.09096e6	+	2.67567e6i	−0.377557	+	0.925986i
$385$	3.23898e6			1.11367
$386$	2.95172e6	−	598938.i	1.00834	−	0.204604i
$387$	−264315.	+	568160.i	−0.0897107	+	0.192838i
$388$	−346799.	+	146783.i	−0.116949	+	0.0494989i
$389$			703487.i			0.235712i	0.993031	+	0.117856i	$0.0376022\pi$
$389$			703487.i			0.235712i	−0.993031	+	0.117856i	$0.962398\pi$
$390$	3641.22	−	207782.i	0.00121223	−	0.0691746i
$391$		−	609325.i		−	0.201561i
$392$	4.03958e6	−	2.76708e6i	1.32777	−	0.909507i
$393$	2.29936e6	+	508670.i	0.750975	+	0.166133i
$394$	−20618.5	−	101613.i	−0.00669140	−	0.0329769i
$395$	1.35601e6			0.437290
$396$	−4.80776e6	−	168556.i	−1.54065	−	0.0540140i
$397$	3.98929e6			1.27034			0.635169	−	0.772373i	$-0.280931\pi$
$397$	3.98929e6			1.27034			0.635169	+	0.772373i	$0.280931\pi$
$398$	530313.	+	2.61351e6i	0.167813	+	0.827022i
$399$	−9.76877e6	−	2.16107e6i	−3.07190	−	0.679575i
$400$	−445536.	+	459453.i	−0.139230	+	0.143579i
$401$			4.67544e6i			1.45198i	0.687703	+	0.725992i	$0.258619\pi$
$401$			4.67544e6i			1.45198i	−0.687703	+	0.725992i	$0.741381\pi$
$402$	12654.7	−	722126.i	0.00390559	−	0.222868i
$403$		−	543406.i		−	0.166672i
$404$	−482535.	−	1.14007e6i	−0.147087	−	0.347519i
$405$	1.12914e6	−	950933.i	0.342067	−	0.288080i
$406$	5.99491e6	−	1.21644e6i	1.80496	−	0.366248i
$407$	−5.81138e6			−1.73897
$408$	351211.	+	872058.i	0.104452	+	0.259355i
$409$	−4.61147e6			−1.36311			−0.681556	−	0.731766i	$-0.738696\pi$
$409$	−4.61147e6			−1.36311			−0.681556	+	0.731766i	$0.738696\pi$
$410$	316035.	−	64127.2i	0.0928486	−	0.0188401i
$411$	1.00682e6	−	4.55115e6i	0.293999	−	1.32898i
$412$	1.08527e6	+	2.56414e6i	0.314990	+	0.744216i
$413$			3.73793e6i			1.07834i
$414$	−2.44481e6	−	585961.i	−0.701041	−	0.168023i
$415$		−	1.80608e6i		−	0.514773i
$416$	294586.	−	459770.i	0.0834602	−	0.130259i
$417$	−509048.	+	2.30107e6i	−0.143357	+	0.648021i
$418$	−2.13290e6	−	1.05115e7i	−0.597076	−	2.94254i
$419$	−2.38168e6			−0.662748			−0.331374	−	0.943500i	$-0.607512\pi$
$419$	−2.38168e6			−0.662748			−0.331374	+	0.943500i	$0.607512\pi$
$420$	−2.56816e6	+	474418.i	−0.710393	+	0.131231i
$421$	3.36839e6			0.926227			0.463114	−	0.886299i	$-0.346732\pi$
$421$	3.36839e6			0.926227			0.463114	+	0.886299i	$0.346732\pi$
$422$	−126239.	−	622137.i	−0.0345074	−	0.170061i
$423$	3.58975e6	+	1.67000e6i	0.975469	+	0.453800i
$424$	−876306.	−	1.27930e6i	−0.236723	−	0.345586i
$425$			208227.i			0.0559197i
$426$	4.32254e6	+	75749.2i	1.15403	+	0.0202234i
$427$			684406.i			0.181654i
$428$	1.20535e6	−	510165.i	0.318057	−	0.134618i
$429$	887642.	+	196366.i	0.232860	+	0.0515138i
$430$	−357404.	+	72521.5i	−0.0932156	+	0.0189145i
$431$	2.62157e6			0.679779			0.339890	−	0.940465i	$-0.389610\pi$
$431$	2.62157e6			0.679779			0.339890	+	0.940465i	$0.389610\pi$
$432$	3.83672e6	−	570552.i	0.989123	−	0.147091i
$433$	6.84367e6			1.75416			0.877080	−	0.480344i	$-0.159488\pi$
$433$	6.84367e6			1.75416			0.877080	+	0.480344i	$0.159488\pi$
$434$	−6.69263e6	+	1.35801e6i	−1.70558	+	0.346082i
$435$	−1.96482e6	−	434662.i	−0.497850	−	0.110136i
$436$	3.25898e6	−	1.37937e6i	0.821043	−	0.347507i
$437$		−	5.60517e6i		−	1.40406i
$438$	−812079.	−	14231.0i	−0.202261	−	0.00354447i
$439$			669261.i			0.165743i	0.996560	+	0.0828713i	$0.0264090\pi$
$439$			669261.i			0.165743i	−0.996560	+	0.0828713i	$0.973591\pi$
$440$	−1.58220e6	−	2.30981e6i	−0.389609	−	0.568780i
$441$	−5.95961e6	−	2.77248e6i	−1.45922	−	0.678848i
$442$	−35329.3	−	174112.i	−0.00860160	−	0.0423908i
$443$	−4.74205e6			−1.14804			−0.574020	−	0.818841i	$-0.694617\pi$
$443$	−4.74205e6			−1.14804			−0.574020	+	0.818841i	$0.694617\pi$
$444$	4.60779e6	−	851200.i	1.10926	−	0.204915i
$445$	−1.01062e6			−0.241929
$446$	−628023.	−	3.09505e6i	−0.149499	−	0.736769i
$447$	872179.	−	3.94254e6i	0.206460	−	0.933270i
$448$	−6.39875e6	−	2.47915e6i	−1.50626	−	0.583589i
$449$			3.61616e6i			0.846510i	0.906011	+	0.423255i	$0.139113\pi$
$449$			3.61616e6i			0.846510i	−0.906011	+	0.423255i	$0.860887\pi$
$450$	835473.	+	200243.i	0.194492	+	0.0466150i
$451$			1.41070e6i			0.326583i
$452$	955757.	+	2.25814e6i	0.220040	+	0.519882i
$453$	−730418.	+	3.30173e6i	−0.167235	+	0.755956i
$454$	−985431.	+	199956.i	−0.224381	+	0.0455296i
$455$	493528.			0.111759
$456$	3.23078e6	+	8.02204e6i	0.727605	+	1.80664i
$457$	−1.70440e6			−0.381751			−0.190875	−	0.981614i	$-0.561133\pi$
$457$	−1.70440e6			−0.381751			−0.190875	+	0.981614i	$0.561133\pi$
$458$	4.90357e6	−	994991.i	1.09232	−	0.221644i
$459$	766918.	−	1.00227e6i	0.169909	−	0.222050i
$460$	−570290.	−	1.34741e6i	−0.125661	−	0.296896i
$461$			7.02487e6i			1.53952i	0.638332	+	0.769761i	$0.279625\pi$
$461$			7.02487e6i			1.53952i	−0.638332	+	0.769761i	$0.720375\pi$
$462$	200179.	−	1.14230e7i	0.0436328	−	2.48986i
$463$			285734.i			0.0619453i	0.999520	+	0.0309727i	$0.00986049\pi$
$463$			285734.i			0.0619453i	−0.999520	+	0.0309727i	$0.990140\pi$
$464$	−3.79590e6	−	3.68093e6i	−0.818503	−	0.793710i
$465$	2.19349e6	+	485250.i	0.470439	+	0.104072i
$466$	−1.01083e6	−	4.98165e6i	−0.215633	−	1.06269i
$467$	5.80136e6			1.23094			0.615471	−	0.788159i	$-0.288966\pi$
$467$	5.80136e6			1.23094			0.615471	+	0.788159i	$0.288966\pi$
$468$	−732565.	−	25683.1i	−0.154608	−	0.00542043i
$469$	1.71521e6			0.360068
$470$	458206.	+	2.25816e6i	0.0956789	+	0.471530i
$471$	7.61272e6	+	1.68411e6i	1.58120	+	0.349798i
$472$	2.66562e6	−	1.82592e6i	0.550736	−	0.377249i
$473$		−	1.59536e6i		−	0.327874i
$474$	83805.4	−	4.78226e6i	0.0171327	−	0.977659i
$475$			1.91548e6i			0.389532i
$476$	−2.05608e6	+	870236.i	−0.415932	+	0.176043i
$477$	−878019.	+	1.88735e6i	−0.176688	+	0.379802i
$478$	−9.20292e6	+	1.86738e6i	−1.84228	+	0.373820i
$479$	4.05192e6			0.806905			0.403452	−	0.915001i	$-0.367810\pi$
$479$	4.05192e6			0.806905			0.403452	+	0.915001i	$0.367810\pi$
$480$	1.59283e6	+	1.59968e6i	0.315548	+	0.316906i
$481$	−885488.			−0.174510
$482$	−3.83883e6	+	778944.i	−0.752630	+	0.152718i
$483$	1.28963e6	−	5.82955e6i	0.251534	−	1.13702i
$484$	6.53305e6	−	2.76511e6i	1.26766	−	0.536536i
$485$			294205.i			0.0567932i
$486$	−3.28389e6	−	4.04095e6i	−0.630665	−	0.776055i
$487$			6.12613e6i			1.17048i	0.810860	+	0.585240i	$0.199000\pi$
$487$			6.12613e6i			1.17048i	−0.810860	+	0.585240i	$0.801000\pi$
$488$	488069.	−	334323.i	0.0927752	−	0.0635501i
$489$	1.74484e6	−	7.88726e6i	0.329977	−	1.49161i
$490$	−760702.	−	3.74893e6i	−0.143128	−	0.705370i
$491$	−8.55402e6			−1.60128			−0.800639	−	0.599147i	$-0.795506\pi$
$491$	−8.55402e6			−1.60128			−0.800639	+	0.599147i	$0.795506\pi$
$492$	−206627.	−	1.11853e6i	−0.0384834	−	0.208322i
$493$	−1.72033e6			−0.318782
$494$	−324993.	−	1.60165e6i	−0.0599179	−	0.295291i
$495$	−1.58529e6	+	3.40767e6i	−0.290801	+	0.625092i
$496$	4.23769e6	+	4.10933e6i	0.773437	+	0.750010i
$497$			1.02670e7i			1.86446i
$498$	−6.36954e6	−	111621.i	−1.15089	−	0.0201685i
$499$			9.91103e6i			1.78183i	0.454166	+	0.890917i	$0.349937\pi$
$499$			9.91103e6i			1.78183i	−0.454166	+	0.890917i	$0.650063\pi$
$500$	194888.	+	460455.i	0.0348625	+	0.0823687i
$501$	742501.	+	164258.i	0.132161	+	0.0292370i
$502$	8.29932e6	−	1.68403e6i	1.46988	−	0.298257i
$503$	−7.53601e6			−1.32807			−0.664036	−	0.747700i	$-0.731158\pi$
$503$	−7.53601e6			−1.32807			−0.664036	+	0.747700i	$0.731158\pi$
$504$	1.51442e6	+	9.08651e6i	0.265564	+	1.59338i
$505$	−967174.			−0.168763
$506$	6.27276e6	−	1.27282e6i	1.08914	−	0.220999i
$507$	−5.51600e6	−	1.22026e6i	−0.953025	−	0.210831i
$508$	2.46256e6	+	5.81822e6i	0.423378	+	1.00030i
$509$			5.68648e6i			0.972858i	0.873720	+	0.486429i	$0.161701\pi$
$509$			5.68648e6i			0.972858i	−0.873720	+	0.486429i	$0.838299\pi$
$510$	734360.	+	12869.1i	0.125021	+	0.00219090i
$511$		−	1.92887e6i		−	0.326776i
$512$	1.35775e6	+	5.77416e6i	0.228899	+	0.973450i
$513$	7.05485e6	−	9.21981e6i	1.18357	−	1.54678i
$514$	293087.	+	1.44441e6i	0.0489315	+	0.241147i
$515$	2.17528e6			0.361407
$516$	233675.	+	1.26495e6i	0.0386356	+	0.209146i
$517$	−1.00798e7			−1.65854
$518$	2.21290e6	+	1.09057e7i	0.362358	+	1.78579i
$519$	330127.	−	1.49229e6i	0.0537976	−	0.243183i
$520$	−241081.	−	351949.i	−0.0390981	−	0.0570783i
$521$		−	9.06654e6i		−	1.46335i	−0.681656	−	0.731673i	$-0.738740\pi$
$521$		−	9.06654e6i		−	1.46335i	0.681656	−	0.731673i	$-0.261260\pi$
$522$	−1.65436e6	+	6.90250e6i	−0.265738	+	1.10874i
$523$			6.87128e6i			1.09846i	0.835672	+	0.549229i	$0.185078\pi$
$523$			6.87128e6i			1.09846i	−0.835672	+	0.549229i	$0.814922\pi$
$524$	4.45191e6	−	1.88427e6i	0.708301	−	0.299788i
$525$	−440710.	+	1.99216e6i	−0.0697838	+	0.315446i
$526$	2.12204e6	−	430586.i	0.334417	−	0.0678572i
$527$	1.92055e6			0.301230
$528$	−8.24384e6	+	5.43722e6i	−1.28690	+	0.848773i
$529$	−3.09144e6			−0.480310
$530$	−1.18725e6	+	240907.i	−0.183591	+	0.0372529i
$531$	−3.93260e6	−	1.82949e6i	−0.605262	−	0.281575i
$532$	−1.89138e7	+	8.00527e6i	−2.89734	+	1.22630i
$533$			214950.i			0.0327733i
$534$	−62459.3	+	3.56417e6i	−0.00947860	+	0.540886i
$535$		−	1.02256e6i		−	0.154455i
$536$	−837855.	−	1.22316e6i	−0.125967	−	0.183896i
$537$	4.76962e6	+	1.05515e6i	0.713753	+	0.157898i
$538$	1.02195e6	+	5.03642e6i	0.152220	+	0.750181i
$539$	1.67343e7			2.48105
$540$	757836.	−	2.93411e6i	0.111838	−	0.433004i
$541$	−9.89026e6			−1.45283			−0.726415	−	0.687256i	$-0.758815\pi$
$541$	−9.89026e6			−1.45283			−0.726415	+	0.687256i	$0.758815\pi$
$542$	1.18684e6	+	5.84903e6i	0.173537	+	0.855235i
$543$	7.41079e6	+	1.63943e6i	1.07861	+	0.238613i
$544$	1.62495e6	+	1.04115e6i	0.235420	+	0.150840i
$545$		−	2.76475e6i		−	0.398716i
$546$	30501.5	−	1.74054e6i	0.00437865	−	0.249863i
$547$		−	9.22378e6i		−	1.31808i	−0.752109	−	0.659038i	$-0.770964\pi$
$547$		−	9.22378e6i		−	1.31808i	0.752109	−	0.659038i	$-0.229036\pi$
$548$	−3.72956e6	−	8.81172e6i	−0.530525	−	1.25346i
$549$	−720050.	−	334976.i	−0.101960	−	0.0474333i
$550$	−2.14361e6	+	434965.i	−0.302162	+	0.0613122i
$551$	−1.58252e7			−2.22061
$552$	−4.78718e6	+	1.92798e6i	−0.668701	+	0.269312i
$553$	1.13589e7			1.57952
$554$	−4.04502e6	+	820782.i	−0.559946	+	0.113620i
$555$	790721.	−	3.57432e6i	0.108966	−	0.492563i
$556$	1.88567e6	+	4.45521e6i	0.258689	+	0.611198i
$557$		−	1.21914e7i		−	1.66501i	−0.554021	−	0.832503i	$-0.686907\pi$
$557$		−	1.21914e7i		−	1.66501i	0.554021	−	0.832503i	$-0.313093\pi$
$558$	1.84691e6	−	7.70584e6i	0.251107	−	1.04769i
$559$		−	243088.i		−	0.0329028i
$560$	−3.73215e6	+	3.84872e6i	−0.502908	+	0.518617i
$561$	−694014.	+	3.13717e6i	−0.0931024	+	0.420854i
$562$	−1.41661e6	−	6.98140e6i	−0.189195	−	0.932399i
$563$	−1.89063e6			−0.251383			−0.125692	−	0.992069i	$-0.540115\pi$
$563$	−1.89063e6			−0.251383			−0.125692	+	0.992069i	$0.540115\pi$
$564$	7.99221e6	−	1.47641e6i	1.05796	−	0.195438i
$565$	1.91568e6			0.252466
$566$	2.45676e6	+	1.21075e7i	0.322345	+	1.58860i
$567$	9.45855e6	−	7.96573e6i	1.23557	−	1.04056i
$568$	7.32168e6	−	5.01528e6i	0.952226	−	0.652265i
$569$			4.75313e6i			0.615459i	0.951474	+	0.307730i	$0.0995692\pi$
$569$			4.75313e6i			0.615459i	−0.951474	+	0.307730i	$0.900431\pi$
$570$	6.75536e6	+	118382.i	0.870885	+	0.0152616i
$571$			1.17132e7i			1.50344i	0.659483	+	0.751720i	$0.270775\pi$
$571$			1.17132e7i			1.50344i	−0.659483	+	0.751720i	$0.729225\pi$
$572$	1.71861e6	−	727401.i	0.219628	−	0.0929574i
$573$	−5.84989e6	−	1.29413e6i	−0.744322	−	0.164661i
$574$	2.64734e6	−	537177.i	0.335375	−	0.0680515i
$575$	−1.14307e6			−0.144179
$576$	5.74007e6	−	5.51860e6i	0.720877	−	0.693063i
$577$	−6.54419e6			−0.818307			−0.409153	−	0.912466i	$-0.634176\pi$
$577$	−6.54419e6			−0.818307			−0.409153	+	0.912466i	$0.634176\pi$
$578$	−7.25615e6	+	1.47236e6i	−0.903414	+	0.183313i
$579$	−8.10381e6	−	1.79275e6i	−1.00460	−	0.222240i
$580$	−3.80418e6	+	1.61012e6i	−0.469560	+	0.198741i
$581$		−	1.51290e7i		−	1.85939i
$582$	1.03758e6	+	18182.8i	0.126974	+	0.00222512i
$583$		−	5.29958e6i		−	0.645759i
$584$	−1.37553e6	+	942224.i	−0.166893	+	0.114320i
$585$	−241553.	+	519231.i	−0.0291825	+	0.0627294i
$586$	1.09150e6	+	5.37918e6i	0.131304	+	0.647101i
$587$	3.20782e6			0.384250			0.192125	−	0.981370i	$-0.438462\pi$
$587$	3.20782e6			0.384250			0.192125	+	0.981370i	$0.438462\pi$
$588$	−1.32685e7	+	2.45109e6i	−1.58262	+	0.292359i
$589$	1.76671e7			2.09834
$590$	−501968.	−	2.47383e6i	−0.0593672	−	0.292576i
$591$	−61715.5	+	278975.i	−0.00726818	+	0.0328546i
$592$	6.69621e6	−	6.90538e6i	0.785281	−	0.809810i
$593$		−	2.44422e6i		−	0.285433i	−0.989764	−	0.142716i	$-0.954416\pi$
$593$		−	2.44422e6i		−	0.285433i	0.989764	−	0.142716i	$-0.0455837\pi$
$594$	1.19199e7	+	5.80148e6i	1.38614	+	0.674641i
$595$			1.74427e6i			0.201986i
$596$	−3.23082e6	−	7.63335e6i	−0.372560	−	0.880237i
$597$	1.58734e6	−	7.17529e6i	0.182277	−	0.823955i
$598$	955789.	−	193941.i	0.109297	−	0.0221777i
$599$	1.13909e7			1.29715			0.648575	−	0.761151i	$-0.275365\pi$
$599$	1.13909e7			1.29715			0.648575	+	0.761151i	$0.275365\pi$
$600$	1.63594e6	−	658857.i	0.185520	−	0.0747159i
$601$	−4.68968e6			−0.529611			−0.264806	−	0.964302i	$-0.585308\pi$
$601$	−4.68968e6			−0.529611			−0.264806	+	0.964302i	$0.585308\pi$
$602$	−2.99389e6	+	607494.i	−0.336701	+	0.0683205i
$603$	−839492.	+	1.80454e6i	−0.0940207	+	0.202103i
$604$	2.70569e6	+	6.39266e6i	0.301777	+	0.712999i
$605$		−	5.54228e6i		−	0.615602i
$606$	−59774.3	+	3.41096e6i	−0.00661200	+	0.377307i
$607$		−	9.31780e6i		−	1.02646i	−0.858251	−	0.513230i	$-0.828449\pi$
$607$		−	9.31780e6i		−	1.02646i	0.858251	−	0.513230i	$-0.171551\pi$
$608$	1.49479e7	+	9.57751e6i	1.63992	+	1.05074i
$609$	−1.64588e7	−	3.64105e6i	−1.79827	−	0.397817i
$610$	−91909.3	−	452952.i	−0.0100008	−	0.0492865i
$611$	−1.53588e6			−0.166439
$612$	90771.4	−	2.58909e6i	0.00979648	−	0.279427i
$613$	−3.74517e6			−0.402551			−0.201275	−	0.979535i	$-0.564509\pi$
$613$	−3.74517e6			−0.402551			−0.201275	+	0.979535i	$0.564509\pi$
$614$	2.72406e6	+	1.34249e7i	0.291606	+	1.43711i
$615$	−867659.	−	191946.i	−0.0925042	−	0.0204640i
$616$	−1.32537e7	−	1.93487e7i	−1.40729	−	2.05447i
$617$			6.66510e6i			0.704845i	0.935841	+	0.352423i	$0.114642\pi$
$617$			6.66510e6i			0.704845i	−0.935841	+	0.352423i	$0.885358\pi$
$618$	134439.	−	7.67161e6i	0.0141597	−	0.808007i
$619$		−	1.70069e7i		−	1.78402i	−0.452019	−	0.892008i	$-0.649296\pi$
$619$		−	1.70069e7i		−	1.78402i	0.452019	−	0.892008i	$-0.350704\pi$
$620$	4.24693e6	−	1.79751e6i	0.443706	−	0.187799i
$621$	5.50196e6	+	4.21001e6i	0.572517	+	0.438081i
$622$	−9.91487e6	+	2.01184e6i	−1.02757	+	0.208506i
$623$	−8.46569e6			−0.873861
$624$	−1.25613e6	+	828476.i	−0.129143	+	0.0851763i
$625$	390625.			0.0400000
$626$	−3.63766e6	+	738123.i	−0.371010	+	0.0752823i
$627$	−6.38421e6	+	2.88588e7i	−0.648542	+	2.93163i
$628$	1.47394e7	−	6.23844e6i	1.49135	−	0.631215i
$629$		−	3.12956e6i		−	0.315397i
$630$	6.99855e6	+	1.67738e6i	0.702516	+	0.168376i
$631$		−	1.10528e7i		−	1.10509i	−0.833482	−	0.552547i	$-0.813656\pi$
$631$		−	1.10528e7i		−	1.10509i	0.833482	−	0.552547i	$-0.186344\pi$
$632$	−5.54867e6	−	8.10037e6i	−0.552582	−	0.806700i
$633$	−377859.	+	1.70805e6i	−0.0374818	+	0.169430i
$634$	−1.06257e6	−	5.23660e6i	−0.104986	−	0.517400i
$635$	4.93586e6			0.485768
$636$	776236.	+	4.20199e6i	0.0760941	+	0.411919i
$637$	2.54983e6			0.248979
$638$	−3.59358e6	−	1.77101e7i	−0.349523	−	1.72254i
$639$	−1.08017e7	−	5.02508e6i	−1.04650	−	0.486845i
$640$	4.56773e6	+	781451.i	0.440809	+	0.0754140i
$641$			1.68019e7i			1.61515i	0.589766	+	0.807574i	$0.299220\pi$
$641$			1.68019e7i			1.61515i	−0.589766	+	0.807574i	$0.700780\pi$
$642$	−3.60627e6	−	63197.1i	−0.345319	−	0.00605145i
$643$			2.02200e7i			1.92865i	0.264724	+	0.964324i	$0.414719\pi$
$643$			2.02200e7i			1.92865i	−0.264724	+	0.964324i	$0.585281\pi$
$644$	−4.77718e6	−	1.12869e7i	−0.453896	−	1.07241i
$645$	981238.	+	217072.i	0.0928699	+	0.0205449i
$646$	5.66067e6	−	1.14862e6i	0.533687	−	0.108291i
$647$	−156118.			−0.0146620			−0.00733099	−	0.999973i	$-0.502334\pi$
$647$	−156118.			−0.0146620			−0.00733099	+	0.999973i	$0.502334\pi$
$648$	−1.03009e7	−	2.85401e6i	−0.963695	−	0.267005i
$649$	1.10425e7			1.02910
$650$	−326626.	+	66276.1i	−0.0303226	+	0.00615282i
$651$	1.83743e7	+	4.06481e6i	1.69926	+	0.375914i
$652$	−6.46342e6	−	1.52709e7i	−0.595447	−	1.40685i
$653$		−	1.89317e7i		−	1.73743i	−0.495313	−	0.868714i	$-0.664947\pi$
$653$		−	1.89317e7i		−	1.73743i	0.495313	−	0.868714i	$-0.335053\pi$
$654$	−9.75049e6	−	170870.i	−0.891420	−	0.0156214i
$655$		−	3.77676e6i		−	0.343966i
$656$	−1.67626e6	−	1.62549e6i	−0.152084	−	0.147477i
$657$	2.02932e6	+	944065.i	0.183416	+	0.0853274i
$658$	3.83828e6	+	1.89160e7i	0.345598	+	1.70320i
$659$	1.76992e7			1.58760			0.793800	−	0.608179i	$-0.208100\pi$
$659$	1.76992e7			1.58760			0.793800	+	0.608179i	$0.208100\pi$
$660$	1.40152e6	+	7.58682e6i	0.125239	+	0.677953i
$661$	1.23422e7			1.09872			0.549361	−	0.835585i	$-0.314871\pi$
$661$	1.23422e7			1.09872			0.549361	+	0.835585i	$0.314871\pi$
$662$	−41526.3	−	204652.i	−0.00368280	−	0.0181498i
$663$	−105748.	+	478016.i	−0.00934303	+	0.0422336i
$664$	−1.07889e7	+	7.39032e6i	−0.949640	+	0.650494i
$665$			1.60455e7i			1.40701i
$666$	−1.25568e7	−	3.00956e6i	−1.09697	−	0.262916i
$667$		−	9.44378e6i		−	0.821923i
$668$	1.43760e6	−	608462.i	0.124651	−	0.0527585i
$669$	−1.87980e6	+	8.49734e6i	−0.162385	+	0.734036i
$670$	−1.13515e6	+	230336.i	−0.0976940	+	0.0198233i
$671$	2.02186e6			0.173359
$672$	1.33427e7	+	1.34001e7i	1.13978	+	1.14468i
$673$	−6.18664e6			−0.526523			−0.263262	−	0.964724i	$-0.584798\pi$
$673$	−6.18664e6			−0.526523			−0.263262	+	0.964724i	$0.584798\pi$
$674$	8.52896e6	−	1.73063e6i	0.723180	−	0.146742i
$675$	−1.88021e6	−	1.43870e6i	−0.158835	−	0.121538i
$676$	−1.06798e7	+	4.52023e6i	−0.898870	+	0.380447i
$677$			6.71680e6i			0.563236i	0.959527	+	0.281618i	$0.0908711\pi$
$677$			6.71680e6i			0.563236i	−0.959527	+	0.281618i	$0.909129\pi$
$678$	118395.	−	6.75608e6i	0.00989143	−	0.564444i
$679$			2.46448e6i			0.205140i
$680$	1.24389e6	−	852049.i	0.103159	−	0.0706630i
$681$	2.70546e6	+	598508.i	0.223549	+	0.0494541i
$682$	4.01182e6	+	1.97713e7i	0.330279	+	1.62770i
$683$	−2.15433e7			−1.76710			−0.883549	−	0.468338i	$-0.844853\pi$
$683$	−2.15433e7			−1.76710			−0.883549	+	0.468338i	$0.844853\pi$
$684$	835003.	−	2.38170e7i	0.0682414	−	1.94646i
$685$	−7.47538e6			−0.608705
$686$	−2.41284e6	−	1.18911e7i	−0.195757	−	0.964740i
$687$	−1.34625e7	−	2.97822e6i	−1.08827	−	0.240749i
$688$	1.89569e6	+	1.83827e6i	0.152685	+	0.148060i
$689$		−	807505.i		−	0.0648033i
$690$	−70645.1	+	4.03128e6i	−0.00564884	+	0.322345i
$691$		−	2.16821e6i		−	0.172745i	−0.996263	−	0.0863727i	$-0.972472\pi$
$691$		−	2.16821e6i		−	0.172745i	0.996263	−	0.0863727i	$-0.0275276\pi$
$692$	−1.22289e6	−	2.88929e6i	−0.0970785	−	0.229364i
$693$	−1.32796e7	+	2.85452e7i	−1.05039	+	2.25787i
$694$	2.37104e6	−	481112.i	0.186870	−	0.0379182i
$695$	3.77956e6			0.296811
$696$	5.44333e6	+	1.35158e7i	0.425934	+	1.05759i
$697$	−759694.			−0.0592321
$698$	8.99967e6	−	1.82614e6i	0.699179	−	0.141872i
$699$	−3.02564e6	+	1.36769e7i	−0.234220	+	1.05875i
$700$	1.63252e6	+	3.85711e6i	0.125926	+	0.297521i
$701$		−	1.47654e7i		−	1.13488i	−0.823416	−	0.567439i	$-0.807934\pi$
$701$		−	1.47654e7i		−	1.13488i	0.823416	−	0.567439i	$-0.192066\pi$
$702$	1.81626e6	+	883980.i	0.139102	+	0.0677017i
$703$		−	2.87888e7i		−	2.19702i
$704$	−7.32386e6	+	1.89031e7i	−0.556940	+	1.43748i
$705$	1.37151e6	−	6.19967e6i	0.103926	−	0.469781i
$706$	3.91633e6	+	1.93007e7i	0.295711	+	1.45734i
$707$	−8.10177e6			−0.609581
$708$	−8.75553e6	+	1.61741e6i	−0.656446	+	0.121266i
$709$	−1.30426e7			−0.974427			−0.487213	−	0.873283i	$-0.661987\pi$
$709$	−1.30426e7			−0.974427			−0.487213	+	0.873283i	$0.661987\pi$
$710$	−1.37876e6	−	6.79487e6i	−0.102646	−	0.505866i
$711$	−5.55952e6	+	1.19505e7i	−0.412442	+	0.886568i
$712$	4.13537e6	+	6.03712e6i	0.305713	+	0.446303i
$713$			1.05429e7i			0.776669i
$714$	6.15155e6	+	107801.i	0.451584	+	0.00791366i
$715$		−	1.45797e6i		−	0.106656i
$716$	9.23470e6	−	3.90858e6i	0.673194	−	0.284929i
$717$	2.52662e7	+	5.58946e6i	1.83545	+	0.406043i
$718$	−6.43372e6	+	1.30548e6i	−0.465748	+	0.0945058i
$719$	−8.36863e6			−0.603715			−0.301858	−	0.953353i	$-0.597607\pi$
$719$	−8.36863e6			−0.603715			−0.301858	+	0.953353i	$0.597607\pi$
$720$	−2.22250e6	−	5.81024e6i	−0.159776	−	0.417698i
$721$	1.82218e7			1.30543
$722$	3.83451e7	−	7.78068e6i	2.73758	−	0.555488i
$723$	1.05393e7	+	2.33154e6i	0.749839	+	0.165881i
$724$	1.43484e7	−	6.07297e6i	1.01732	−	0.430581i
$725$			3.22726e6i			0.228028i
$726$	−1.95461e7	−	342530.i	−1.37632	−	0.0241189i
$727$			1.78461e7i			1.25229i	0.779705	+	0.626147i	$0.215369\pi$
$727$			1.78461e7i			1.25229i	−0.779705	+	0.626147i	$0.784631\pi$
$728$	−2.01948e6	−	2.94819e6i	−0.141225	−	0.206170i
$729$	3.75118e6	+	1.38499e7i	0.261426	+	0.965223i
$730$	259028.	+	1.27656e6i	0.0179904	+	0.0886611i
$731$	859140.			0.0594662
$732$	−1.60312e6	+	296145.i	−0.110583	+	0.0204280i
$733$	−2.07942e7			−1.42949			−0.714746	−	0.699384i	$-0.753458\pi$
$733$	−2.07942e7			−1.42949			−0.714746	+	0.699384i	$0.753458\pi$
$734$	−3.85814e6	−	1.90139e7i	−0.264325	−	1.30266i
$735$	−2.27694e6	+	1.02925e7i	−0.155465	+	0.702754i
$736$	−5.71542e6	+	8.92022e6i	−0.388914	+	0.606989i
$737$		−	5.06704e6i		−	0.343626i
$738$	−730564.	+	3.04813e6i	−0.0493762	+	0.206012i
$739$			1.94256e7i			1.30847i	0.756293	+	0.654233i	$0.227009\pi$
$739$			1.94256e7i			1.30847i	−0.756293	+	0.654233i	$0.772991\pi$
$740$	−2.92907e6	−	6.92043e6i	−0.196631	−	0.464573i
$741$	−972771.	+	4.39725e6i	−0.0650826	+	0.294195i
$742$	−9.94529e6	+	2.01802e6i	−0.663144	+	0.134560i
$743$	1.73283e7			1.15155			0.575776	−	0.817608i	$-0.304700\pi$
$743$	1.73283e7			1.15155			0.575776	+	0.817608i	$0.304700\pi$
$744$	−6.07686e6	−	1.50888e7i	−0.402482	−	0.999363i
$745$	−6.47572e6			−0.427462
$746$	−6.38600e6	+	1.29579e6i	−0.420128	+	0.0852490i
$747$	1.59170e7	+	7.40477e6i	1.04366	+	0.485523i
$748$	2.57084e6	+	6.07404e6i	0.168004	+	0.396939i
$749$		−	8.56569e6i		−	0.557902i
$750$	24141.8	−	1.37763e6i	0.00156717	−	0.0894290i
$751$		−	1.06334e7i		−	0.687972i	−0.938975	−	0.343986i	$-0.888223\pi$
$751$		−	1.06334e7i		−	0.687972i	0.938975	−	0.343986i	$-0.111777\pi$
$752$	1.16146e7	−	1.19774e7i	0.748960	−	0.772355i
$753$	−2.27854e7	−	5.04065e6i	−1.46443	−	0.323965i
$754$	−547559.	−	2.69851e6i	−0.0350754	−	0.172860i
$755$	5.42318e6			0.346248
$756$	6.34820e6	−	2.45783e7i	0.403967	−	1.56404i
$757$	7.28072e6			0.461780			0.230890	−	0.972980i	$-0.425836\pi$
$757$	7.28072e6			0.461780			0.230890	+	0.972980i	$0.425836\pi$
$758$	4.40380e6	+	2.17030e7i	0.278391	+	1.37198i
$759$	−1.72216e7	−	3.80980e6i	−1.08510	−	0.240048i
$760$	1.14425e7	−	7.83798e6i	0.718597	−	0.492232i
$761$			6.45785e6i			0.404228i	0.979362	+	0.202114i	$0.0647812\pi$
$761$			6.45785e6i			0.404228i	−0.979362	+	0.202114i	$0.935219\pi$
$762$	305051.	−	1.74074e7i	0.0190320	−	1.08604i
$763$		−	2.31596e7i		−	1.44019i
$764$	−1.13263e7	+	4.79384e6i	−0.702026	+	0.297133i
$765$	−1.83511e6	−	853715.i	−0.113373	−	0.0527423i
$766$	−1.37927e7	+	2.79870e6i	−0.849331	+	0.172339i
$767$	1.68257e6			0.103272
$768$	3.03826e6	−	1.60608e7i	0.185876	−	0.982573i
$769$	1.39199e6			0.0848831			0.0424416	−	0.999099i	$-0.486486\pi$
$769$	1.39199e6			0.0848831			0.0424416	+	0.999099i	$0.486486\pi$
$770$	−1.79565e7	+	3.64359e6i	−1.09143	+	0.221464i
$771$	877270.	−	3.96556e6i	0.0531493	−	0.240253i
$772$	−1.56902e7	+	6.64088e6i	−0.947513	+	0.401035i
$773$			2.39151e7i			1.43954i	0.694214	+	0.719769i	$0.255752\pi$
$773$			2.39151e7i			1.43954i	−0.694214	+	0.719769i	$0.744248\pi$
$774$	826196.	−	3.44714e6i	0.0495714	−	0.206827i
$775$		−	3.60286e6i		−	0.215473i
$776$	1.75749e6	−	1.20386e6i	0.104770	−	0.0717667i
$777$	6.62367e6	−	2.99412e7i	0.393592	−	1.77917i
$778$	−791365.	−	3.90005e6i	−0.0468735	−	0.231005i
$779$	−6.98841e6			−0.412605
$780$	213551.	+	1.15601e6i	0.0125680	+	0.0680341i
$781$	3.03306e7			1.77932
$782$	685441.	+	3.37802e6i	0.0400823	+	0.197536i
$783$	1.18863e7	−	1.55339e7i	0.692852	−	0.905472i
$784$	−1.92822e7	+	1.98845e7i	−1.12038	+	1.15538i
$785$		−	1.25041e7i		−	0.724233i
$786$	−1.33196e7	−	233415.i	−0.769013	−	0.0134764i
$787$			2.03963e7i			1.17385i	0.809640	+	0.586926i	$0.199662\pi$
$787$			2.03963e7i			1.17385i	−0.809640	+	0.586926i	$0.800338\pi$
$788$	228613.	+	540137.i	0.0131155	+	0.0309876i
$789$	−5.82596e6	−	1.28883e6i	−0.333177	−	0.0737063i
$790$	−7.51754e6	+	1.52540e6i	−0.428556	+	0.0869591i
$791$	1.60472e7			0.911922
$792$	2.68432e7	−	4.47388e6i	1.52062	−	0.253438i
$793$	308074.			0.0173969
$794$	−2.21161e7	+	4.48762e6i	−1.24497	+	0.252618i
$795$	3.25954e6	+	721084.i	0.182911	+	0.0404639i
$796$	−5.87998e6	−	1.38924e7i	−0.328922	−	0.777134i
$797$			1.63026e7i			0.909098i	0.890722	+	0.454549i	$0.150200\pi$
$797$			1.63026e7i			0.909098i	−0.890722	+	0.454549i	$0.849800\pi$
$798$	5.65879e7	+	991658.i	3.14569	+	0.0551258i
$799$		−	5.42822e6i		−	0.300809i
$800$	1.95315e6	−	3.04834e6i	0.107897	−	0.168399i
$801$	4.14345e6	−	8.90659e6i	0.228182	−	0.490490i
$802$	−5.25949e6	−	2.59201e7i	−0.288740	−	1.42299i
$803$	−5.69823e6			−0.311854
$804$	742176.	+	4.01761e6i	0.0404918	+	0.219194i
$805$	−9.57518e6			−0.520784
$806$	611287.	+	3.01258e6i	0.0331442	+	0.163343i
$807$	3.05890e6	−	1.38273e7i	0.165341	−	0.747398i
$808$	3.95760e6	+	5.77760e6i	0.213257	+	0.311329i
$809$			4.91162e6i			0.263848i	0.991260	+	0.131924i	$0.0421155\pi$
$809$			4.91162e6i			0.263848i	−0.991260	+	0.131924i	$0.957885\pi$
$810$	−5.19011e6	+	6.54205e6i	−0.277948	+	0.350349i
$811$			1.67734e6i			0.0895505i	0.998997	+	0.0447752i	$0.0142572\pi$
$811$			1.67734e6i			0.0895505i	−0.998997	+	0.0447752i	$0.985743\pi$
$812$	−3.18666e7	+	1.34876e7i	−1.69608	+	0.717866i
$813$	3.55245e6	−	1.60582e7i	0.188496	−	0.852063i
$814$	3.22176e7	−	6.53732e6i	1.70424	−	0.345811i
$815$	−1.29550e7			−0.683194
$816$	−2.92807e6	−	4.43950e6i	−0.153941	−	0.233404i
$817$	7.90320e6			0.414236
$818$	2.55654e7	−	5.18753e6i	1.33589	−	0.271067i
$819$	−2.02343e6	+	4.34947e6i	−0.105409	+	0.226582i
$820$	−1.67992e6	+	711026.i	−0.0872477	+	0.0369276i
$821$		−	1.50894e6i		−	0.0781295i	−0.999237	−	0.0390647i	$-0.987562\pi$
$821$		−	1.50894e6i		−	0.0781295i	0.999237	−	0.0390647i	$-0.0124379\pi$
$822$	−462001.	+	2.63636e7i	−0.0238487	+	1.36090i
$823$			2.83062e7i			1.45674i	0.685183	+	0.728371i	$0.259722\pi$
$823$			2.83062e7i			1.45674i	−0.685183	+	0.728371i	$0.740278\pi$
$824$	−8.90107e6	−	1.29945e7i	−0.456693	−	0.666714i
$825$	5.88520e6	+	1.30194e6i	0.301041	+	0.0665972i
$826$	−4.20486e6	−	2.07226e7i	−0.214438	−	1.05680i
$827$	−3.09276e7			−1.57247			−0.786234	−	0.617928i	$-0.787972\pi$
$827$	−3.09276e7			−1.57247			−0.786234	+	0.617928i	$0.787972\pi$
$828$	1.42129e7	+	498291.i	0.720453	+	0.0252585i
$829$	−8.54403e6			−0.431794			−0.215897	−	0.976416i	$-0.569267\pi$
$829$	−8.54403e6			−0.431794			−0.215897	+	0.976416i	$0.569267\pi$
$830$	2.03169e6	+	1.00127e7i	0.102367	+	0.504492i
$831$	1.11054e7	+	2.45677e6i	0.557869	+	0.123413i
$832$	−1.11595e6	+	2.88029e6i	−0.0558902	+	0.144254i
$833$			9.01180e6i			0.449986i
$834$	233588.	−	1.33295e7i	0.0116288	−	0.663587i
$835$		−	1.21958e6i		−	0.0605331i
$836$	2.36491e7	+	5.58749e7i	1.17030	+	2.76504i
$837$	−1.32696e7	+	1.73418e7i	−0.654705	+	0.855617i
$838$	1.32037e7	−	2.67919e6i	0.649511	−	0.131793i
$839$	−2.86348e7			−1.40439			−0.702197	−	0.711982i	$-0.747798\pi$
$839$	−2.86348e7			−1.40439			−0.702197	+	0.711982i	$0.747798\pi$
$840$	1.37039e7	−	5.51908e6i	0.670108	−	0.269879i
$841$	−6.15177e6			−0.299923
$842$	−1.86740e7	+	3.78916e6i	−0.907729	+	0.184189i
$843$	−4.24020e6	+	1.91671e7i	−0.205503	+	0.928941i
$844$	1.39971e6	+	3.30704e6i	0.0676364	+	0.159803i
$845$			9.06017e6i			0.436510i
$846$	−2.17797e7	−	5.22008e6i	−1.04623	−	0.250756i
$847$		−	4.64263e7i		−	2.22359i
$848$	6.29724e6	+	6.10649e6i	0.300719	+	0.291610i
$849$	7.35358e6	−	3.32407e7i	0.350130	−	1.58271i
$850$	−234238.	−	1.15439e6i	−0.0111202	−	0.0548029i
$851$	1.71798e7			0.813194
$852$	−2.40489e7	+	4.44256e6i	−1.13500	+	0.209669i
$853$	727499.			0.0342342			0.0171171	−	0.999853i	$-0.494551\pi$
$853$	727499.			0.0342342			0.0171171	+	0.999853i	$0.494551\pi$
$854$	−769901.	−	3.79426e6i	−0.0361235	−	0.178026i
$855$	−1.68811e7	−	7.85330e6i	−0.789742	−	0.367398i
$856$	−6.10843e6	+	4.18422e6i	−0.284935	+	0.195177i
$857$		−	1.41838e7i		−	0.659693i	−0.944035	−	0.329846i	$-0.893003\pi$
$857$		−	1.41838e7i		−	0.659693i	0.944035	−	0.329846i	$-0.106997\pi$
$858$	−5.14187e6	−	90107.3i	−0.238453	−	0.00417870i
$859$		−	9.85846e6i		−	0.455854i	−0.973678	−	0.227927i	$-0.926805\pi$
$859$		−	9.85846e6i		−	0.455854i	0.973678	−	0.227927i	$-0.0731948\pi$
$860$	1.89982e6	−	804101.i	0.0875926	−	0.0370736i
$861$	−7.26816e6	−	1.60788e6i	−0.334131	−	0.0739173i
$862$	−1.45336e7	+	2.94905e6i	−0.666203	+	0.135180i
$863$	1.76189e7			0.805289			0.402645	−	0.915356i	$-0.368091\pi$
$863$	1.76189e7			0.805289			0.402645	+	0.915356i	$0.368091\pi$
$864$	−2.06285e7	+	7.47906e6i	−0.940118	+	0.340849i
$865$	−2.45112e6			−0.111384
$866$	−3.79405e7	+	7.69856e6i	−1.71913	+	0.348831i
$867$	1.99214e7	+	4.40707e6i	0.900063	+	0.199114i
$868$	3.55754e7	−	1.50573e7i	1.60270	−	0.678341i
$869$		−	3.35564e7i		−	1.50739i
$870$	1.13817e7	+	199454.i	0.509809	+	0.00893399i
$871$		−	772073.i		−	0.0344836i
$872$	−1.65157e7	+	1.13131e7i	−0.735541	+	0.503838i
$873$	−2.59283e6	−	1.20622e6i	−0.115143	−	0.0535661i
$874$	6.30535e6	+	3.10744e7i	0.279210	+	1.37602i
$875$	3.27217e6			0.144482
$876$	4.51807e6	−	834627.i	0.198927	−	0.0367479i
$877$	−1.80138e7			−0.790874			−0.395437	−	0.918493i	$-0.629407\pi$
$877$	−1.80138e7			−0.790874			−0.395437	+	0.918493i	$0.629407\pi$
$878$	−752863.	−	3.71030e6i	−0.0329594	−	0.162432i
$879$	3.26708e6	−	1.47683e7i	0.142622	−	0.644701i
$880$	1.13698e7	+	1.10255e7i	0.494935	+	0.479943i
$881$		−	658406.i		−	0.0285795i	−0.999898	−	0.0142897i	$-0.995451\pi$
$881$		−	658406.i		−	0.0285795i	0.999898	−	0.0142897i	$-0.00454872\pi$
$882$	3.61582e7	+	8.66624e6i	1.56507	+	0.375111i
$883$		−	5.40523e6i		−	0.233299i	−0.993173	−	0.116649i	$-0.962785\pi$
$883$		−	5.40523e6i		−	0.233299i	0.993173	−	0.116649i	$-0.0372154\pi$
$884$	391722.	+	925510.i	0.0168596	+	0.0398337i
$885$	−1.50250e6	+	6.79178e6i	−0.0644844	+	0.291491i
$886$	2.62894e7	−	5.33442e6i	1.12511	−	0.228298i
$887$	2.25591e7			0.962746			0.481373	−	0.876516i	$-0.340138\pi$
$887$	2.25591e7			0.962746			0.481373	+	0.876516i	$0.340138\pi$
$888$	−2.45875e7	+	9.90233e6i	−1.04636	+	0.421410i
$889$	4.13465e7			1.75462
$890$	5.60274e6	−	1.13686e6i	0.237097	−	0.0481097i
$891$	−2.35322e7	−	2.79423e7i	−0.993045	−	1.17915i
$892$	6.96336e6	+	1.64521e7i	0.293026	+	0.692325i
$893$		−	4.99341e7i		−	2.09541i
$894$	−400219.	+	2.28381e7i	−0.0167477	+	0.955687i
$895$		−	7.83421e6i		−	0.326917i
$896$	3.82627e7	+	6.54602e6i	1.59223	+	0.272400i
$897$	−2.62408e6	−	580505.i	−0.108892	−	0.0240893i
$898$	−4.06788e6	−	2.00476e7i	−0.168336	−	0.829604i
$899$	2.97661e7			1.22835
$900$	−4.85702e6	−	170283.i	−0.199877	−	0.00700753i
$901$	2.85395e6			0.117121
$902$	−1.58692e6	−	7.82074e6i	−0.0649440	−	0.320060i
$903$	8.21958e6	+	1.81836e6i	0.335452	+	0.0742095i
$904$	−7.83882e6	−	1.14437e7i	−0.319029	−	0.465742i
$905$		−	1.21724e7i		−	0.494032i
$906$	335169.	−	1.91261e7i	0.0135657	−	0.774115i
$907$		−	6.90234e6i		−	0.278598i	−0.990250	−	0.139299i	$-0.955515\pi$
$907$		−	6.90234e6i		−	0.278598i	0.990250	−	0.139299i	$-0.0444849\pi$
$908$	5.23817e6	−	2.21706e6i	0.210846	−	0.0892406i
$909$	3.96534e6	−	8.52371e6i	0.159173	−	0.342152i
$910$	−2.73606e6	+	555178.i	−0.109527	+	0.0222244i
$911$	5.06083e6			0.202035			0.101017	−	0.994885i	$-0.467790\pi$
$911$	5.06083e6			0.202035			0.101017	+	0.994885i	$0.467790\pi$
$912$	−2.69352e7	−	4.08388e7i	−1.07234	−	1.62587i
$913$	−4.46940e7			−1.77449
$914$	9.44896e6	−	1.91730e6i	0.374126	−	0.0759146i
$915$	−275103.	+	1.24356e6i	−0.0108628	+	0.0491037i
$916$	−2.60655e7	+	1.10322e7i	−1.02643	+	0.434434i
$917$		−	3.16369e7i		−	1.24243i
$918$	−3.12423e6	+	6.41915e6i	−0.122359	+	0.251403i
$919$			5.18197e6i			0.202398i	0.994866	+	0.101199i	$0.0322679\pi$
$919$			5.18197e6i			0.202398i	−0.994866	+	0.101199i	$0.967732\pi$
$920$	4.67734e6	+	6.82833e6i	0.182192	+	0.265978i
$921$	8.15368e6	−	3.68573e7i	0.316741	−	1.43178i
$922$	−7.90240e6	−	3.89450e7i	−0.306148	−	1.50878i
$923$	4.62152e6			0.178558
$924$	1.17402e7	+	6.35529e7i	0.452370	+	2.44881i
$925$	−5.87092e6			−0.225607
$926$	−321427.	−	1.58407e6i	−0.0123184	−	0.0607082i
$927$	−8.91847e6	+	1.91708e7i	−0.340872	+	0.732723i
$928$	2.51848e7	+	1.61365e7i	0.959992	+	0.615092i
$929$			3.96165e7i			1.50604i	0.657996	+	0.753021i	$0.271404\pi$
$929$			3.96165e7i			1.50604i	−0.657996	+	0.753021i	$0.728596\pi$
$930$	−1.27063e7	−	222668.i	−0.481739	−	0.00844210i
$931$			8.28993e7i			3.13456i
$932$	1.12079e7	+	2.64805e7i	0.422653	+	0.998590i
$933$	2.72208e7	+	6.02186e6i	1.02376	+	0.226478i
$934$	−3.21620e7	+	6.52605e6i	−1.20636	+	0.244784i
$935$	5.15289e6			0.192762
$936$	4.09014e6	−	681691.i	0.152598	−	0.0254330i
$937$	−2.71511e7			−1.01027			−0.505137	−	0.863039i	$-0.668558\pi$
$937$	−2.71511e7			−1.01027			−0.505137	+	0.863039i	$0.668558\pi$
$938$	−9.50890e6	+	1.92947e6i	−0.352877	+	0.0716029i
$939$	9.98702e6	+	2.20935e6i	0.369634	+	0.0817714i
$940$	−5.08048e6	−	1.20035e7i	−0.187536	−	0.443086i
$941$			3.78758e7i			1.39440i	0.716876	+	0.697201i	$0.245571\pi$
$941$			3.78758e7i			1.39440i	−0.716876	+	0.697201i	$0.754429\pi$
$942$	−4.40985e7	−	772791.i	−1.61918	−	0.0283749i
$943$		−	4.17036e6i		−	0.152719i
$944$	−1.27239e7	+	1.31213e7i	−0.464717	+	0.479233i
$945$	−1.57500e7	−	1.20517e7i	−0.573722	−	0.439003i
$946$	1.79465e6	+	8.84450e6i	0.0652007	+	0.321326i
$947$	2.90252e6			0.105172			0.0525861	−	0.998616i	$-0.483254\pi$
$947$	2.90252e6			0.105172			0.0525861	+	0.998616i	$0.483254\pi$
$948$	4.91504e6	+	2.66065e7i	0.177626	+	0.961541i
$949$	−868247.			−0.0312952
$950$	−2.15475e6	−	1.06192e7i	−0.0774619	−	0.381752i
$951$	−3.18048e6	+	1.43768e7i	−0.114036	+	0.515481i
$952$	1.04197e7	−	7.13740e6i	0.372617	−	0.255239i
$953$			4.84150e7i			1.72682i	0.504502	+	0.863411i	$0.331676\pi$
$953$			4.84150e7i			1.72682i	−0.504502	+	0.863411i	$0.668324\pi$
$954$	2.74451e6	−	1.14509e7i	0.0976325	−	0.407352i
$955$			9.60859e6i			0.340919i
$956$	4.89192e7	−	2.07051e7i	1.73115	−	0.732709i
$957$	−1.07563e7	+	4.86222e7i	−0.379651	+	1.71615i
$958$	−2.24634e7	+	4.55808e6i	−0.790789	+	0.160460i
$959$	−6.26194e7			−2.19868
$960$	−1.06300e7	−	7.07662e6i	−0.372266	−	0.247827i
$961$	−4.60125e6			−0.160719
$962$	4.90904e6	−	996101.i	0.171025	−	0.0347029i
$963$	9.01179e6	+	4.19240e6i	0.313145	+	0.145679i
$964$	2.04058e7	−	8.63674e6i	0.707230	−	0.299335i
$965$			1.33107e7i			0.460133i
$966$	−591776.	+	3.37690e7i	−0.0204040	+	1.16433i
$967$			3.96883e7i			1.36489i	0.730939	+	0.682443i	$0.239083\pi$
$967$			3.96883e7i			1.36489i	−0.730939	+	0.682443i	$0.760917\pi$
$968$	−3.31079e7	+	2.26786e7i	−1.13565	+	0.777906i
$969$	−1.55411e7	−	3.43804e6i	−0.531707	−	0.117626i
$970$	−330957.	−	1.63104e6i	−0.0112938	−	0.0556589i
$971$	−5.31554e7			−1.80925			−0.904626	−	0.426207i	$-0.859850\pi$
$971$	−5.31554e7			−1.80925			−0.904626	+	0.426207i	$0.859850\pi$
$972$	2.27512e7	+	1.87084e7i	0.772395	+	0.635143i
$973$	3.16604e7			1.07210
$974$	−6.89139e6	−	3.39625e7i	−0.232761	−	1.14710i
$975$	896736.	+	198378.i	0.0302102	+	0.00668317i
$976$	−2.32971e6	+	2.40248e6i	−0.0782848	+	0.0807301i
$977$		−	1.26835e7i		−	0.425112i	−0.977149	−	0.212556i	$-0.931821\pi$
$977$		−	1.26835e7i		−	0.425112i	0.977149	−	0.212556i	$-0.0681788\pi$
$978$	−800660.	+	4.56888e7i	−0.0267671	+	1.52743i
$979$			2.50092e7i			0.833957i
$980$	8.43447e6	+	1.99279e7i	0.280539	+	0.662820i
$981$	2.43657e7	+	1.13352e7i	0.808363	+	0.376061i
$982$	4.74224e7	−	9.62257e6i	1.56930	−	0.318429i
$983$	7.47024e6			0.246576			0.123288	−	0.992371i	$-0.460656\pi$
$983$	7.47024e6			0.246576			0.123288	+	0.992371i	$0.460656\pi$
$984$	2.40377e6	+	5.96856e6i	0.0791416	+	0.196509i
$985$	458223.			0.0150483
$986$	9.53729e6	−	1.93523e6i	0.312415	−	0.0633928i
$987$	1.14888e7	−	5.19330e7i	0.375388	−	1.69688i
$988$	3.60344e6	+	8.51374e6i	0.117442	+	0.277478i
$989$			4.71627e6i			0.153323i
$990$	4.95530e6	−	2.06750e7i	0.160688	−	0.670437i
$991$		−	4.55608e7i		−	1.47369i	−0.676060	−	0.736847i	$-0.736314\pi$
$991$		−	4.55608e7i		−	1.47369i	0.676060	−	0.736847i	$-0.263686\pi$
$992$	−2.81159e7	−	1.80146e7i	−0.907136	−	0.581225i
$993$	−124297.	+	561863.i	−0.00400024	+	0.0180824i
$994$	−1.15495e7	−	5.69189e7i	−0.370764	−	1.82722i
$995$	−1.17856e7			−0.377393
$996$	3.54375e7	−	6.54639e6i	1.13192	−	0.209100i
$997$	5.91294e7			1.88393			0.941967	−	0.335706i	$-0.108975\pi$
$997$	5.91294e7			1.88393			0.941967	+	0.335706i	$0.108975\pi$
$998$	−1.11491e7	−	5.49455e7i	−0.354334	−	1.74625i
$999$	2.82587e7	+	2.16231e7i	0.895855	+	0.685494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.6.e.a.11.4	yes	40
3.2	odd	2	inner	60.6.e.a.11.37	yes	40
4.3	odd	2	inner	60.6.e.a.11.38	yes	40
12.11	even	2	inner	60.6.e.a.11.3	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.6.e.a.11.3	✓	40	12.11	even	2	inner
60.6.e.a.11.4	yes	40	1.1	even	1	trivial
60.6.e.a.11.37	yes	40	3.2	odd	2	inner
60.6.e.a.11.38	yes	40	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	60.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.54388 + 1.12492i) q^{2} +(15.2205 + 3.36711i) q^{3} +(29.4691 - 12.4728i) q^{4} -25.0000i q^{5} +(-88.1681 - 1.54508i) q^{6} -209.419i q^{7} +(-149.342 + 102.298i) q^{8} +(220.325 + 102.498i) q^{9} +O(q^{10})\)	\(q+(-5.54388 + 1.12492i) q^{2} +(15.2205 + 3.36711i) q^{3} +(29.4691 - 12.4728i) q^{4} -25.0000i q^{5} +(-88.1681 - 1.54508i) q^{6} -209.419i q^{7} +(-149.342 + 102.298i) q^{8} +(220.325 + 102.498i) q^{9} +(28.1229 + 138.597i) q^{10} -618.662 q^{11} +(490.531 - 90.6161i) q^{12} -94.2663 q^{13} +(235.579 + 1160.99i) q^{14} +(84.1778 - 380.512i) q^{15} +(712.858 - 735.125i) q^{16} -333.164i q^{17} +(-1336.76 - 320.388i) q^{18} -3064.76i q^{19} +(-311.820 - 736.728i) q^{20} +(705.136 - 3187.45i) q^{21} +(3429.78 - 695.943i) q^{22} +1828.91 q^{23} +(-2617.51 + 1054.17i) q^{24} -625.000 q^{25} +(522.601 - 106.042i) q^{26} +(3008.33 + 2301.93i) q^{27} +(-2612.04 - 6171.38i) q^{28} -5163.61i q^{29} +(-38.6269 + 2204.20i) q^{30} +5764.58i q^{31} +(-3125.04 + 4877.35i) q^{32} +(-9416.32 - 2083.10i) q^{33} +(374.781 + 1847.02i) q^{34} -5235.47 q^{35} +(7771.23 + 272.453i) q^{36} +9393.47 q^{37} +(3447.60 + 16990.7i) q^{38} +(-1434.78 - 317.405i) q^{39} +(2557.45 + 3733.56i) q^{40} -2280.24i q^{41} +(-323.568 + 18464.0i) q^{42} +2578.73i q^{43} +(-18231.4 + 7716.45i) q^{44} +(2562.45 - 5508.13i) q^{45} +(-10139.2 + 2057.37i) q^{46} +16293.0 q^{47} +(13325.3 - 8788.67i) q^{48} -27049.2 q^{49} +(3464.92 - 703.073i) q^{50} +(1121.80 - 5070.90i) q^{51} +(-2777.95 + 1175.77i) q^{52} +8566.21i q^{53} +(-19267.3 - 9377.47i) q^{54} +15466.5i q^{55} +(21423.1 + 31275.1i) q^{56} +(10319.4 - 46647.1i) q^{57} +(5808.64 + 28626.4i) q^{58} -17849.1 q^{59} +(-2265.40 - 12263.3i) q^{60} -3268.13 q^{61} +(-6484.68 - 31958.1i) q^{62} +(21465.0 - 46140.2i) q^{63} +(11838.2 - 30554.8i) q^{64} +2356.66i q^{65} +(54546.2 + 955.879i) q^{66} +8190.33i q^{67} +(-4155.48 - 9818.04i) q^{68} +(27836.8 + 6158.13i) q^{69} +(29024.8 - 5889.47i) q^{70} -49026.2 q^{71} +(-43389.2 + 7231.54i) q^{72} +9210.58 q^{73} +(-52076.2 + 10566.9i) q^{74} +(-9512.79 - 2104.44i) q^{75} +(-38226.2 - 90315.8i) q^{76} +129559. i q^{77} +(8311.28 + 145.649i) q^{78} +54240.3i q^{79} +(-18378.1 - 17821.5i) q^{80} +(38037.3 + 45165.8i) q^{81} +(2565.09 + 12641.4i) q^{82} +72243.1 q^{83} +(-18976.7 - 102726. i) q^{84} -8329.09 q^{85} +(-2900.86 - 14296.2i) q^{86} +(17386.5 - 78592.6i) q^{87} +(92392.3 - 63287.9i) q^{88} -40424.7i q^{89} +(-8009.71 + 33418.9i) q^{90} +19741.1i q^{91} +(53896.3 - 22811.6i) q^{92} +(-19410.0 + 87739.6i) q^{93} +(-90326.2 + 18328.2i) q^{94} -76619.0 q^{95} +(-63987.2 + 63713.2i) q^{96} -11768.2 q^{97} +(149957. - 30428.1i) q^{98} +(-136307. - 63411.6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 10 q^{4} - 114 q^{6} + 44 q^{9}+O(q^{10}) \) 40 * q - 10 * q^4 - 114 * q^6 + 44 * q^9	\( 40 q - 10 q^{4} - 114 q^{6} + 44 q^{9} + 50 q^{10} + 1876 q^{12} - 232 q^{13} - 2734 q^{16} - 3536 q^{18} + 820 q^{21} + 13684 q^{22} + 9550 q^{24} - 25000 q^{25} - 23188 q^{28} - 5800 q^{30} - 9424 q^{33} + 38972 q^{34} + 53754 q^{36} + 2152 q^{37} - 10850 q^{40} - 62868 q^{42} + 5900 q^{45} + 78748 q^{46} + 100956 q^{48} - 52144 q^{49} - 82528 q^{52} - 120862 q^{54} - 44424 q^{57} + 97476 q^{58} + 3850 q^{60} + 2072 q^{61} - 91234 q^{64} - 45784 q^{66} + 52764 q^{69} - 3300 q^{70} - 10344 q^{72} + 264960 q^{73} + 73356 q^{76} + 176440 q^{78} - 165120 q^{81} - 170920 q^{82} - 250544 q^{84} - 132400 q^{85} + 359116 q^{88} + 35550 q^{90} + 510368 q^{93} - 623100 q^{94} - 379254 q^{96} + 453648 q^{97}+O(q^{100}) \) 40 * q - 10 * q^4 - 114 * q^6 + 44 * q^9 + 50 * q^10 + 1876 * q^12 - 232 * q^13 - 2734 * q^16 - 3536 * q^18 + 820 * q^21 + 13684 * q^22 + 9550 * q^24 - 25000 * q^25 - 23188 * q^28 - 5800 * q^30 - 9424 * q^33 + 38972 * q^34 + 53754 * q^36 + 2152 * q^37 - 10850 * q^40 - 62868 * q^42 + 5900 * q^45 + 78748 * q^46 + 100956 * q^48 - 52144 * q^49 - 82528 * q^52 - 120862 * q^54 - 44424 * q^57 + 97476 * q^58 + 3850 * q^60 + 2072 * q^61 - 91234 * q^64 - 45784 * q^66 + 52764 * q^69 - 3300 * q^70 - 10344 * q^72 + 264960 * q^73 + 73356 * q^76 + 176440 * q^78 - 165120 * q^81 - 170920 * q^82 - 250544 * q^84 - 132400 * q^85 + 359116 * q^88 + 35550 * q^90 + 510368 * q^93 - 623100 * q^94 - 379254 * q^96 + 453648 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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