LMFDB - Embedded newform 60.6.e.a.11.16

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			11.16
Character	$\chi$	$=$	60.11
Dual form			60.6.e.a.11.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.24299 + 5.19317i) q^{2} +(15.5136 - 1.52631i) q^{3} +(-21.9379 - 23.2965i) q^{4} -25.0000i q^{5} +(-26.8704 + 83.9880i) q^{6} +85.2589i q^{7} +(170.189 - 61.6735i) q^{8} +(238.341 - 47.3571i) q^{9} +O(q^{10})$	\(q+(-2.24299 + 5.19317i) q^{2} +(15.5136 - 1.52631i) q^{3} +(-21.9379 - 23.2965i) q^{4} -25.0000i q^{5} +(-26.8704 + 83.9880i) q^{6} +85.2589i q^{7} +(170.189 - 61.6735i) q^{8} +(238.341 - 47.3571i) q^{9} +(129.829 + 56.0749i) q^{10} +246.014 q^{11} +(-375.893 - 327.927i) q^{12} +940.853 q^{13} +(-442.764 - 191.235i) q^{14} +(-38.1578 - 387.839i) q^{15} +(-61.4527 + 1022.15i) q^{16} -639.874i q^{17} +(-288.664 + 1343.96i) q^{18} +2058.59i q^{19} +(-582.412 + 548.449i) q^{20} +(130.132 + 1322.67i) q^{21} +(-551.809 + 1277.59i) q^{22} +1540.06 q^{23} +(2546.11 - 1216.54i) q^{24} -625.000 q^{25} +(-2110.33 + 4886.01i) q^{26} +(3625.23 - 1098.46i) q^{27} +(1986.23 - 1870.41i) q^{28} -2380.79i q^{29} +(2099.70 + 671.760i) q^{30} +5331.21i q^{31} +(-5170.38 - 2611.82i) q^{32} +(3816.55 - 375.495i) q^{33} +(3322.97 + 1435.23i) q^{34} +2131.47 q^{35} +(-6331.96 - 4513.58i) q^{36} -13791.3 q^{37} +(-10690.6 - 4617.40i) q^{38} +(14596.0 - 1436.04i) q^{39} +(-1541.84 - 4254.73i) q^{40} -19258.7i q^{41} +(-7160.73 - 2290.94i) q^{42} -12690.9i q^{43} +(-5397.05 - 5731.27i) q^{44} +(-1183.93 - 5958.52i) q^{45} +(-3454.34 + 7997.77i) q^{46} +5176.73 q^{47} +(606.778 + 15951.0i) q^{48} +9537.91 q^{49} +(1401.87 - 3245.73i) q^{50} +(-976.648 - 9926.72i) q^{51} +(-20640.4 - 21918.6i) q^{52} +18009.7i q^{53} +(-2426.89 + 21290.3i) q^{54} -6150.36i q^{55} +(5258.22 + 14510.2i) q^{56} +(3142.05 + 31936.0i) q^{57} +(12363.8 + 5340.10i) q^{58} +9349.54 q^{59} +(-8198.18 + 9397.33i) q^{60} +4688.33 q^{61} +(-27685.9 - 11957.9i) q^{62} +(4037.62 + 20320.7i) q^{63} +(25160.8 - 20992.3i) q^{64} -23521.3i q^{65} +(-6610.51 + 20662.2i) q^{66} +19618.1i q^{67} +(-14906.8 + 14037.5i) q^{68} +(23891.7 - 2350.61i) q^{69} +(-4780.88 + 11069.1i) q^{70} -46147.6 q^{71} +(37642.3 - 22759.0i) q^{72} -54402.2 q^{73} +(30933.9 - 71620.8i) q^{74} +(-9695.97 + 953.946i) q^{75} +(47957.8 - 45161.2i) q^{76} +20974.9i q^{77} +(-25281.1 + 79020.3i) q^{78} +28196.1i q^{79} +(25553.9 + 1536.32i) q^{80} +(54563.6 - 22574.3i) q^{81} +(100013. + 43197.1i) q^{82} -117828. q^{83} +(27958.7 - 32048.3i) q^{84} -15996.8 q^{85} +(65905.9 + 28465.6i) q^{86} +(-3633.83 - 36934.5i) q^{87} +(41869.0 - 15172.6i) q^{88} -67203.4i q^{89} +(33599.1 + 7216.59i) q^{90} +80216.1i q^{91} +(-33785.7 - 35877.9i) q^{92} +(8137.10 + 82706.1i) q^{93} +(-11611.4 + 26883.6i) q^{94} +51464.6 q^{95} +(-84197.4 - 32627.0i) q^{96} +1534.77 q^{97} +(-21393.5 + 49532.0i) q^{98} +(58635.2 - 11650.5i) 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 $

$2$	−2.24299	+	5.19317i	−0.396509	+	0.918031i
$2$	−2.24299	+	5.19317i	−0.396509	+	0.918031i
$3$	15.5136	−	1.52631i	0.995195	−	0.0979131i
$3$	15.5136	−	1.52631i	0.995195	−	0.0979131i
$4$	−21.9379	−	23.2965i	−0.685561	−	0.728015i
$5$		−	25.0000i		−	0.447214i
$5$		−	25.0000i		−	0.447214i
$6$	−26.8704	+	83.9880i	−0.304717	+	0.952443i
$7$			85.2589i			0.657650i	0.944391	+	0.328825i	$0.106653\pi$
$7$			85.2589i			0.657650i	−0.944391	+	0.328825i	$0.893347\pi$
$8$	170.189	−	61.6735i	0.940172	−	0.340701i
$9$	238.341	−	47.3571i	0.980826	−	0.194885i
$10$	129.829	+	56.0749i	0.410556	+	0.177324i
$11$	246.014			0.613025			0.306513	−	0.951867i	$-0.400838\pi$
$11$	246.014			0.613025			0.306513	+	0.951867i	$0.400838\pi$
$12$	−375.893	−	327.927i	−0.753549	−	0.657392i
$13$	940.853			1.54406			0.772029	−	0.635588i	$-0.219242\pi$
$13$	940.853			1.54406			0.772029	+	0.635588i	$0.219242\pi$
$14$	−442.764	−	191.235i	−0.603743	−	0.260764i
$15$	−38.1578	−	387.839i	−0.0437881	−	0.445065i
$16$	−61.4527	+	1022.15i	−0.0600124	+	0.998198i
$17$		−	639.874i		−	0.536997i	−0.963280	−	0.268499i	$-0.913473\pi$
$17$		−	639.874i		−	0.536997i	0.963280	−	0.268499i	$-0.0865275\pi$
$18$	−288.664	+	1343.96i	−0.209996	+	0.977702i
$19$			2058.59i			1.30823i	0.756394	+	0.654116i	$0.226959\pi$
$19$			2058.59i			1.30823i	−0.756394	+	0.654116i	$0.773041\pi$
$20$	−582.412	+	548.449i	−0.325578	+	0.306592i
$21$	130.132	+	1322.67i	0.0643925	+	0.654490i
$22$	−551.809	+	1277.59i	−0.243070	+	0.562776i
$23$	1540.06			0.607039			0.303520	−	0.952825i	$-0.401838\pi$
$23$	1540.06			0.607039			0.303520	+	0.952825i	$0.401838\pi$
$24$	2546.11	−	1216.54i	0.902295	−	0.431119i
$25$	−625.000			−0.200000
$26$	−2110.33	+	4886.01i	−0.612233	+	1.41749i
$27$	3625.23	−	1098.46i	0.957031	−	0.289984i
$28$	1986.23	−	1870.41i	0.478779	−	0.450859i
$29$		−	2380.79i		−	0.525685i	−0.964839	−	0.262843i	$-0.915340\pi$
$29$		−	2380.79i		−	0.525685i	0.964839	−	0.262843i	$-0.0846600\pi$
$30$	2099.70	+	671.760i	0.425945	+	0.136273i
$31$			5331.21i			0.996373i	0.867070	+	0.498186i	$0.166000\pi$
$31$			5331.21i			0.996373i	−0.867070	+	0.498186i	$0.834000\pi$
$32$	−5170.38	−	2611.82i	−0.892581	−	0.450888i
$33$	3816.55	−	375.495i	0.610080	−	0.0600232i
$34$	3322.97	+	1435.23i	0.492980	+	0.212924i
$35$	2131.47			0.294110
$36$	−6331.96	−	4513.58i	−0.814295	−	0.580451i
$37$	−13791.3			−1.65616			−0.828080	−	0.560609i	$-0.810567\pi$
$37$	−13791.3			−1.65616			−0.828080	+	0.560609i	$0.810567\pi$
$38$	−10690.6	−	4617.40i	−1.20100	−	0.518726i
$39$	14596.0	−	1436.04i	1.53664	−	0.151183i
$40$	−1541.84	−	4254.73i	−0.152366	−	0.420458i
$41$		−	19258.7i		−	1.78923i	−0.446837	−	0.894615i	$-0.647450\pi$
$41$		−	19258.7i		−	1.78923i	0.446837	−	0.894615i	$-0.352550\pi$
$42$	−7160.73	−	2290.94i	−0.626374	−	0.200397i
$43$		−	12690.9i		−	1.04670i	−0.852119	−	0.523348i	$-0.824683\pi$
$43$		−	12690.9i		−	1.04670i	0.852119	−	0.523348i	$-0.175317\pi$
$44$	−5397.05	−	5731.27i	−0.420266	−	0.446292i
$45$	−1183.93	−	5958.52i	−0.0871553	−	0.438639i
$46$	−3454.34	+	7997.77i	−0.240697	+	0.557281i
$47$	5176.73			0.341831			0.170915	−	0.985286i	$-0.445328\pi$
$47$	5176.73			0.341831			0.170915	+	0.985286i	$0.445328\pi$
$48$	606.778	+	15951.0i	0.0380125	+	0.999277i
$49$	9537.91			0.567496
$50$	1401.87	−	3245.73i	0.0793018	−	0.183606i
$51$	−976.648	−	9926.72i	−0.0525790	−	0.534417i
$52$	−20640.4	−	21918.6i	−1.05855	−	1.12410i
$53$			18009.7i			0.880679i	0.897831	+	0.440340i	$0.145142\pi$
$53$			18009.7i			0.880679i	−0.897831	+	0.440340i	$0.854858\pi$
$54$	−2426.89	+	21290.3i	−0.113257	+	0.993566i
$55$		−	6150.36i		−	0.274153i
$56$	5258.22	+	14510.2i	0.224062	+	0.618304i
$57$	3142.05	+	31936.0i	0.128093	+	1.30195i
$58$	12363.8	+	5340.10i	0.482595	+	0.208439i
$59$	9349.54			0.349671			0.174836	−	0.984598i	$-0.444061\pi$
$59$	9349.54			0.349671			0.174836	+	0.984598i	$0.444061\pi$
$60$	−8198.18	+	9397.33i	−0.293995	+	0.336997i
$61$	4688.33			0.161322			0.0806610	−	0.996742i	$-0.474297\pi$
$61$	4688.33			0.161322			0.0806610	+	0.996742i	$0.474297\pi$
$62$	−27685.9	−	11957.9i	−0.914701	−	0.395071i
$63$	4037.62	+	20320.7i	0.128166	+	0.645040i
$64$	25160.8	−	20992.3i	0.767845	−	0.640635i
$65$		−	23521.3i		−	0.690523i
$66$	−6610.51	+	20662.2i	−0.186799	+	0.583872i
$67$			19618.1i			0.533913i	0.963709	+	0.266956i	$0.0860180\pi$
$67$			19618.1i			0.533913i	−0.963709	+	0.266956i	$0.913982\pi$
$68$	−14906.8	+	14037.5i	−0.390942	+	0.368144i
$69$	23891.7	−	2350.61i	0.604122	−	0.0594371i
$70$	−4780.88	+	11069.1i	−0.116617	+	0.270002i
$71$	−46147.6			−1.08643			−0.543217	−	0.839593i	$-0.682794\pi$
$71$	−46147.6			−1.08643			−0.543217	+	0.839593i	$0.682794\pi$
$72$	37642.3	−	22759.0i	0.855747	−	0.517394i
$73$	−54402.2			−1.19484			−0.597419	−	0.801929i	$-0.703807\pi$
$73$	−54402.2			−1.19484			−0.597419	+	0.801929i	$0.703807\pi$
$74$	30933.9	−	71620.8i	0.656683	−	1.52041i
$75$	−9695.97	+	953.946i	−0.199039	+	0.0195826i
$76$	47957.8	−	45161.2i	0.952413	−	0.896873i
$77$			20974.9i			0.403156i
$78$	−25281.1	+	79020.3i	−0.470500	+	1.47063i
$79$			28196.1i			0.508302i	0.967165	+	0.254151i	$0.0817960\pi$
$79$			28196.1i			0.508302i	−0.967165	+	0.254151i	$0.918204\pi$
$80$	25553.9	+	1536.32i	0.446408	+	0.0268384i
$81$	54563.6	−	22574.3i	0.924040	−	0.382297i
$82$	100013.	+	43197.1i	1.64257	+	0.709446i
$83$	−117828.			−1.87738			−0.938689	−	0.344765i	$-0.887959\pi$
$83$	−117828.			−1.87738			−0.938689	+	0.344765i	$0.887959\pi$
$84$	27958.7	−	32048.3i	0.432334	−	0.495572i
$85$	−15996.8			−0.240152
$86$	65905.9	+	28465.6i	0.960899	+	0.415025i
$87$	−3633.83	−	36934.5i	−0.0514715	−	0.523159i
$88$	41869.0	−	15172.6i	0.576349	−	0.208859i
$89$		−	67203.4i		−	0.899324i	−0.893199	−	0.449662i	$-0.851544\pi$
$89$		−	67203.4i		−	0.899324i	0.893199	−	0.449662i	$-0.148456\pi$
$90$	33599.1	+	7216.59i	0.437242	+	0.0939130i
$91$			80216.1i			1.01545i
$92$	−33785.7	−	35877.9i	−0.416162	−	0.441934i
$93$	8137.10	+	82706.1i	0.0975579	+	0.991585i
$94$	−11611.4	+	26883.6i	−0.135539	+	0.313811i
$95$	51464.6			0.585059
$96$	−84197.4	−	32627.0i	−0.932440	−	0.361326i
$97$	1534.77			0.0165620			0.00828102	−	0.999966i	$-0.497364\pi$
$97$	1534.77			0.0165620			0.00828102	+	0.999966i	$0.497364\pi$
$98$	−21393.5	+	49532.0i	−0.225018	+	0.520979i
$99$	58635.2	−	11650.5i	0.601271	−	0.119470i
$100$	13711.2	+	14560.3i	0.137112	+	0.145603i
$101$			146857.i			1.43249i	0.697851	+	0.716243i	$0.254140\pi$
$101$			146857.i			1.43249i	−0.697851	+	0.716243i	$0.745860\pi$
$102$	53741.7	+	17193.7i	0.511459	+	0.163632i
$103$		−	140519.i		−	1.30509i	−0.757748	−	0.652547i	$-0.773700\pi$
$103$		−	140519.i		−	1.30509i	0.757748	−	0.652547i	$-0.226300\pi$
$104$	160123.	−	58025.7i	1.45168	−	0.526062i
$105$	33066.7	−	3253.30i	0.292697	−	0.0287972i
$106$	−93527.6	−	40395.7i	−0.808491	−	0.349197i
$107$	−105916.			−0.894338			−0.447169	−	0.894450i	$-0.647568\pi$
$107$	−105916.			−0.894338			−0.447169	+	0.894450i	$0.647568\pi$
$108$	−105120.	−	60357.2i	−0.867216	−	0.497931i
$109$	−152027.			−1.22562			−0.612808	−	0.790232i	$-0.709960\pi$
$109$	−152027.			−1.22562			−0.612808	+	0.790232i	$0.709960\pi$
$110$	31939.8	+	13795.2i	0.251681	+	0.108704i
$111$	−213953.	+	21049.9i	−1.64820	+	0.162160i
$112$	−87147.8	−	5239.39i	−0.656465	−	0.0394672i
$113$			48087.5i			0.354271i	0.984186	+	0.177136i	$0.0566832\pi$
$113$			48087.5i			0.354271i	−0.984186	+	0.177136i	$0.943317\pi$
$114$	−172896.	−	55315.1i	−1.24602	−	0.398640i
$115$		−	38501.4i		−	0.271476i
$116$	−55464.0	+	52229.6i	−0.382707	+	0.360389i
$117$	224244.	−	44556.1i	1.51445	−	0.300914i
$118$	−20971.0	+	48553.7i	−0.138648	+	0.321009i
$119$	54555.0			0.353156
$120$	−30413.4	−	63652.7i	−0.192802	−	0.403519i
$121$	−100528.			−0.624200
$122$	−10515.9	+	24347.3i	−0.0639656	+	0.148098i
$123$	−29394.8	−	298770.i	−0.175189	−	1.78063i
$124$	124199.	−	116956.i	0.725375	−	0.683074i
$125$			15625.0i			0.0894427i
$126$	−114585.	−	24611.2i	−0.642986	−	0.138104i
$127$			334258.i			1.83896i	0.393134	+	0.919481i	$0.371391\pi$
$127$			334258.i			1.83896i	−0.393134	+	0.919481i	$0.628609\pi$
$128$	52581.3	+	177750.i	0.283665	+	0.958923i
$129$	−19370.3	−	196881.i	−0.102485	−	1.04167i
$130$	122150.	+	52758.2i	0.633922	+	0.273799i
$131$	358018.			1.82275			0.911373	−	0.411581i	$-0.135023\pi$
$131$	358018.			1.82275			0.911373	+	0.411581i	$0.135023\pi$
$132$	−92475.1	−	80674.7i	−0.461945	−	0.402998i
$133$	−175513.			−0.860359
$134$	−101880.	−	44003.3i	−0.490148	−	0.211701i
$135$	−27461.5	−	90630.8i	−0.129685	−	0.427997i
$136$	−39463.3	−	108900.i	−0.182956	−	0.504869i
$137$		−	96906.1i		−	0.441113i	−0.975374	−	0.220556i	$-0.929213\pi$
$137$		−	96906.1i		−	0.441113i	0.975374	−	0.220556i	$-0.0707873\pi$
$138$	−41381.9	+	129346.i	−0.184975	+	0.578170i
$139$		−	126881.i		−	0.557005i	−0.960435	−	0.278503i	$-0.910162\pi$
$139$		−	126881.i		−	0.557005i	0.960435	−	0.278503i	$-0.0898381\pi$
$140$	−46760.2	−	49655.9i	−0.201630	−	0.214117i
$141$	80309.6	−	7901.32i	0.340188	−	0.0334697i
$142$	103509.	−	239652.i	0.430781	−	0.997379i
$143$	231463.			0.946546
$144$	33759.6	+	246531.i	0.135672	+	0.990754i
$145$	−59519.7			−0.235094
$146$	122024.	−	282520.i	0.473765	−	1.09690i
$147$	147967.	−	14557.8i	0.564770	−	0.0555653i
$148$	302554.	+	321290.i	1.13540	+	1.20571i
$149$		−	4664.35i		−	0.0172118i	−0.999963	−	0.00860589i	$-0.997261\pi$
$149$		−	4664.35i		−	0.0172118i	0.999963	−	0.00860589i	$-0.00273937\pi$
$150$	16794.0	−	52492.5i	0.0609433	−	0.190489i
$151$			473902.i			1.69140i	0.533659	+	0.845700i	$0.320817\pi$
$151$			473902.i			1.69140i	−0.533659	+	0.845700i	$0.679183\pi$
$152$	126960.	+	350349.i	0.445717	+	1.22996i
$153$	−30302.6	−	152508.i	−0.104653	−	0.526701i
$154$	−108926.	−	47046.6i	−0.370110	−	0.159855i
$155$	133280.			0.445591
$156$	−353660.	−	308531.i	−1.16352	−	1.01505i
$157$	−187503.			−0.607098			−0.303549	−	0.952816i	$-0.598172\pi$
$157$	−187503.			−0.607098			−0.303549	+	0.952816i	$0.598172\pi$
$158$	−146427.	−	63243.7i	−0.466637	−	0.201546i
$159$	27488.5	+	279395.i	0.0862300	+	0.876447i
$160$	−65295.5	+	129259.i	−0.201643	+	0.399174i
$161$			131304.i			0.399219i
$162$	−5154.05	+	333992.i	−0.0154298	+	0.999881i
$163$		−	381898.i		−	1.12585i	−0.826509	−	0.562923i	$-0.809677\pi$
$163$		−	381898.i		−	1.12585i	0.826509	−	0.562923i	$-0.190323\pi$
$164$	−448659.	+	422495.i	−1.30259	+	1.22663i
$165$	−9387.37	−	95413.9i	−0.0268432	−	0.272836i
$166$	264287.	−	611898.i	0.744398	−	1.72349i
$167$	−78923.2			−0.218985			−0.109492	−	0.993988i	$-0.534923\pi$
$167$	−78923.2			−0.218985			−0.109492	+	0.993988i	$0.534923\pi$
$168$	103721.	+	217078.i	0.283526	+	0.593394i
$169$	513911.			1.38411
$170$	35880.8	−	83074.3i	0.0952226	−	0.220467i
$171$	97488.6	+	490645.i	0.254955	+	1.28315i
$172$	−295653.	+	278412.i	−0.762011	+	0.717574i
$173$		−	222573.i		−	0.565401i	−0.959208	−	0.282700i	$-0.908770\pi$
$173$		−	222573.i		−	0.565401i	0.959208	−	0.282700i	$-0.0912302\pi$
$174$	199958.	+	63972.8i	0.500685	+	0.160185i
$175$		−	53286.8i		−	0.131530i
$176$	−15118.2	+	251465.i	−0.0367891	+	0.611921i
$177$	145045.	−	14270.3i	0.347991	−	0.0342374i
$178$	348998.	+	150737.i	0.825607	+	0.356590i
$179$	−48241.4			−0.112535			−0.0562675	−	0.998416i	$-0.517920\pi$
$179$	−48241.4			−0.112535			−0.0562675	+	0.998416i	$0.517920\pi$
$180$	−112840.	+	158299.i	−0.259585	+	0.364164i
$181$	552758.			1.25412			0.627059	−	0.778972i	$-0.284258\pi$
$181$	552758.			1.25412			0.627059	+	0.778972i	$0.284258\pi$
$182$	−416576.	−	179924.i	−0.932214	−	0.402635i
$183$	72732.6	−	7155.86i	0.160547	−	0.0157955i
$184$	262101.	−	94980.7i	0.570721	−	0.206819i
$185$			344784.i			0.740658i
$186$	−447758.	−	143252.i	−0.948988	−	0.303611i
$187$		−	157418.i		−	0.329193i
$188$	−113567.	−	120600.i	−0.234346	−	0.248858i
$189$	93653.5	+	309083.i	0.190708	+	0.629392i
$190$	−115435.	+	267264.i	−0.231981	+	0.537103i
$191$	−41930.3			−0.0831657			−0.0415829	−	0.999135i	$-0.513240\pi$
$191$	−41930.3			−0.0831657			−0.0415829	+	0.999135i	$0.513240\pi$
$192$	358292.	−	364069.i	0.701429	−	0.712739i
$193$	−86456.1			−0.167072			−0.0835358	−	0.996505i	$-0.526621\pi$
$193$	−86456.1			−0.167072			−0.0835358	+	0.996505i	$0.526621\pi$
$194$	−3442.48	+	7970.31i	−0.00656700	+	0.0152045i
$195$	−35900.9	−	364899.i	−0.0676113	−	0.687205i
$196$	−209242.	−	222200.i	−0.389053	−	0.413146i
$197$		−	552462.i		−	1.01423i	−0.861878	−	0.507115i	$-0.830712\pi$
$197$		−	552462.i		−	1.01423i	0.861878	−	0.507115i	$-0.169288\pi$
$198$	−71015.4	+	330634.i	−0.128733	+	0.599356i
$199$			126729.i			0.226852i	0.993546	+	0.113426i	$0.0361824\pi$
$199$			126729.i			0.226852i	−0.993546	+	0.113426i	$0.963818\pi$
$200$	−106368.	+	38546.0i	−0.188034	+	0.0681403i
$201$	29943.4	+	304347.i	0.0522770	+	0.531347i
$202$	−762651.	−	329399.i	−1.31507	−	0.567994i
$203$	202984.			0.345717
$204$	−209832.	+	240524.i	−0.353017	+	0.404654i
$205$	−481466.			−0.800168
$206$	729739.	+	315183.i	1.19812	+	0.517482i
$207$	367058.	−	72932.6i	0.595400	−	0.118303i
$208$	−57818.0	+	961697.i	−0.0926626	+	1.54127i
$209$			506441.i			0.801980i
$210$	−57273.6	+	179018.i	−0.0896203	+	0.280123i
$211$		−	274834.i		−	0.424977i	−0.977164	−	0.212488i	$-0.931843\pi$
$211$		−	274834.i		−	0.424977i	0.977164	−	0.212488i	$-0.0681567\pi$
$212$	419564.	−	395097.i	0.641148	−	0.603759i
$213$	−715913.	+	70435.7i	−1.08121	+	0.106376i
$214$	237569.	−	550039.i	0.354613	−	0.821030i
$215$	−317272.			−0.468097
$216$	549229.	−	410527.i	0.800976	−	0.598697i
$217$	−454534.			−0.655265
$218$	340996.	−	789502.i	0.485968	−	1.12515i
$219$	−843971.	+	83034.8i	−1.18910	+	0.116990i
$220$	−143282.	+	134926.i	−0.199588	+	0.187949i
$221$		−	602027.i		−	0.829154i
$222$	370579.	−	1.15831e6i	0.504660	−	1.57740i
$223$		−	968194.i		−	1.30377i	−0.758319	−	0.651884i	$-0.773979\pi$
$223$		−	968194.i		−	1.30377i	0.758319	−	0.651884i	$-0.226021\pi$
$224$	222681.	−	440821.i	0.296526	−	0.587006i
$225$	−148963.	+	29598.2i	−0.196165	+	0.0389770i
$226$	−249726.	−	107860.i	−0.325232	−	0.140472i
$227$	−792976.			−1.02140			−0.510699	−	0.859759i	$-0.670613\pi$
$227$	−792976.			−1.02140			−0.510699	+	0.859759i	$0.670613\pi$
$228$	675066.	−	773809.i	0.860021	−	0.985817i
$229$	349110.			0.439920			0.219960	−	0.975509i	$-0.429407\pi$
$229$	349110.			0.439920			0.219960	+	0.975509i	$0.429407\pi$
$230$	199944.	+	86358.4i	0.249224	+	0.107643i
$231$	32014.3	+	325395.i	0.0394743	+	0.401219i
$232$	−146832.	−	405185.i	−0.179102	−	0.494234i
$233$		−	835005.i		−	1.00763i	−0.863813	−	0.503813i	$-0.831930\pi$
$233$		−	835005.i		−	1.00763i	0.863813	−	0.503813i	$-0.168070\pi$
$234$	−271590.	+	1.26447e6i	−0.324246	+	1.50963i
$235$		−	129418.i		−	0.152871i
$236$	−205110.	−	217811.i	−0.239721	−	0.254566i
$237$	43036.1	+	437422.i	0.0497694	+	0.505859i
$238$	−122366.	+	283313.i	−0.140030	+	0.324208i
$239$	−947388.			−1.07284			−0.536418	−	0.843952i	$-0.680223\pi$
$239$	−947388.			−1.07284			−0.536418	+	0.843952i	$0.680223\pi$
$240$	398776.	−	15169.5i	0.446890	−	0.0169997i
$241$	325696.			0.361218			0.180609	−	0.983555i	$-0.442193\pi$
$241$	325696.			0.361218			0.180609	+	0.983555i	$0.442193\pi$
$242$	225484.	−	522059.i	0.247501	−	0.573035i
$243$	812020.	−	433488.i	0.882168	−	0.470936i
$244$	−102852.	−	109222.i	−0.110596	−	0.117445i
$245$		−	238448.i		−	0.253792i
$246$	1.61750e6	+	517488.i	1.70414	+	0.545209i
$247$			1.93683e6i			2.01999i
$248$	328795.	+	907315.i	0.339465	+	0.936761i
$249$	−1.82792e6	+	179842.i	−1.86836	+	0.183820i
$250$	−81143.2	−	35046.8i	−0.0821112	−	0.0354649i
$251$	−949963.			−0.951749			−0.475874	−	0.879513i	$-0.657868\pi$
$251$	−949963.			−0.951749			−0.475874	+	0.879513i	$0.657868\pi$
$252$	384823.	−	539856.i	0.381733	−	0.535521i
$253$	378876.			0.372131
$254$	−1.73586e6	−	749739.i	−1.68822	−	0.729165i
$255$	−248168.	+	24416.2i	−0.238998	+	0.0235141i
$256$	−1.04102e6	−	125628.i	−0.992797	−	0.119809i
$257$			1.95333e6i			1.84477i	0.386266	+	0.922387i	$0.373765\pi$
$257$			1.95333e6i			1.84477i	−0.386266	+	0.922387i	$0.626235\pi$
$258$	1.06588e6	+	341009.i	0.996919	+	0.318946i
$259$		−	1.17584e6i		−	1.08917i
$260$	−547964.	+	516010.i	−0.502712	+	0.473396i
$261$	−112747.	−	567439.i	−0.102448	−	0.515606i
$262$	−803032.	+	1.85925e6i	−0.722736	+	1.67334i
$263$	−738426.			−0.658290			−0.329145	−	0.944279i	$-0.606761\pi$
$263$	−738426.			−0.658290			−0.329145	+	0.944279i	$0.606761\pi$
$264$	626378.	−	299286.i	0.553130	−	0.264287i
$265$	450243.			0.393852
$266$	393674.	−	911467.i	0.341140	−	0.789836i
$267$	−102573.	−	1.04256e6i	−0.0880556	−	0.895003i
$268$	457033.	−	430381.i	0.388697	−	0.366030i
$269$			1.89387e6i			1.59577i	0.602809	+	0.797885i	$0.294048\pi$
$269$			1.89387e6i			1.59577i	−0.602809	+	0.797885i	$0.705952\pi$
$270$	532257.	+	60672.2i	0.444336	+	0.0506501i
$271$			2.05304e6i			1.69814i	0.528280	+	0.849070i	$0.322837\pi$
$271$			2.05304e6i			1.69814i	−0.528280	+	0.849070i	$0.677163\pi$
$272$	654050.	+	39322.0i	0.536029	+	0.0322265i
$273$	122435.	+	1.24444e6i	0.0994257	+	1.01057i
$274$	503250.	+	217360.i	0.404955	+	0.174905i
$275$	−153759.			−0.122605
$276$	−578897.	−	505026.i	−0.457434	−	0.399063i
$277$	1.03338e6			0.809206			0.404603	−	0.914493i	$-0.367410\pi$
$277$	1.03338e6			0.809206			0.404603	+	0.914493i	$0.367410\pi$
$278$	658913.	+	284593.i	0.511348	+	0.220858i
$279$	252471.	+	1.27065e6i	0.194178	+	0.977268i
$280$	362754.	−	131455.i	0.276514	−	0.100204i
$281$		−	1.70084e6i		−	1.28498i	−0.766293	−	0.642491i	$-0.777901\pi$
$281$		−	1.70084e6i		−	1.28498i	0.766293	−	0.642491i	$-0.222099\pi$
$282$	−139101.	+	434784.i	−0.104162	+	0.325574i
$283$		−	2.22846e6i		−	1.65401i	−0.562192	−	0.827007i	$-0.690042\pi$
$283$		−	2.22846e6i		−	1.65401i	0.562192	−	0.827007i	$-0.309958\pi$
$284$	1.01238e6	+	1.07508e6i	0.744816	+	0.790940i
$285$	798400.	−	78551.2i	0.582248	−	0.0572850i
$286$	−519171.	+	1.20203e6i	−0.375314	+	0.868959i
$287$	1.64197e6			1.17669
$288$	−1.35600e6	−	377649.i	−0.963338	−	0.268292i
$289$	1.01042e6			0.711634
$290$	133502.	−	309096.i	0.0932168	−	0.215823i
$291$	23809.7	−	2342.54i	0.0164825	−	0.00162164i
$292$	1.19347e6	+	1.26738e6i	0.819135	+	0.869861i
$293$		−	1.42528e6i		−	0.969908i	−0.874540	−	0.484954i	$-0.838836\pi$
$293$		−	1.42528e6i		−	0.969908i	0.874540	−	0.484954i	$-0.161164\pi$
$294$	−256288.	+	801070.i	−0.172926	+	0.540508i
$295$		−	233738.i		−	0.156378i
$296$	−2.34714e6	+	850561.i	−1.55708	+	0.564256i
$297$	891858.	−	270237.i	0.586685	−	0.177768i
$298$	24222.8	+	10462.1i	0.0158009	+	0.00682463i
$299$	1.44897e6			0.937303
$300$	234933.	+	204954.i	0.150710	+	0.131478i
$301$	1.08201e6			0.688360
$302$	−2.46105e6	−	1.06296e6i	−1.55276	−	0.670655i
$303$	224149.	+	2.27827e6i	0.140259	+	1.42560i
$304$	−2.10419e6	−	126506.i	−1.30587	−	0.0785102i
$305$		−	117208.i		−	0.0721454i
$306$	859968.	+	184708.i	0.525023	+	0.112767i
$307$			441427.i			0.267309i	0.991028	+	0.133654i	$0.0426712\pi$
$307$			441427.i			0.267309i	−0.991028	+	0.133654i	$0.957329\pi$
$308$	488642.	−	460147.i	0.293504	−	0.276388i
$309$	−214476.	−	2.17995e6i	−0.127786	−	1.29882i
$310$	−298947.	+	692147.i	−0.176681	+	0.409067i
$311$	35679.1			0.0209177			0.0104588	−	0.999945i	$-0.496671\pi$
$311$	35679.1			0.0209177			0.0104588	+	0.999945i	$0.496671\pi$
$312$	2.39551e6	−	1.14458e6i	1.39319	−	0.665673i
$313$	1.28298e6			0.740218			0.370109	−	0.928988i	$-0.379320\pi$
$313$	1.28298e6			0.740218			0.370109	+	0.928988i	$0.379320\pi$
$314$	420568.	−	973733.i	0.240720	−	0.557334i
$315$	508017.	−	100940.i	0.288471	−	0.0573177i
$316$	656870.	−	618565.i	0.370051	−	0.348472i
$317$		−	1.34414e6i		−	0.751268i	−0.926768	−	0.375634i	$-0.877425\pi$
$317$		−	1.34414e6i		−	0.751268i	0.926768	−	0.375634i	$-0.122575\pi$
$318$	−1.51260e6	−	483929.i	−0.838797	−	0.268358i
$319$		−	585708.i		−	0.322258i
$320$	−524808.	−	629019.i	−0.286501	−	0.343391i
$321$	−1.64313e6	+	161661.i	−0.890040	+	0.0875673i
$322$	−681881.	−	294513.i	−0.366496	−	0.158294i
$323$	1.31723e6			0.702517
$324$	−1.72291e6	−	775908.i	−0.911803	−	0.410627i
$325$	−588033.			−0.308811
$326$	1.98326e6	+	856596.i	1.03356	+	0.446408i
$327$	−2.35848e6	+	232041.i	−1.21973	+	0.120004i
$328$	−1.18775e6	−	3.27762e6i	−0.609593	−	1.68218i
$329$			441363.i			0.224805i
$330$	516556.	+	165263.i	0.261115	+	0.0835391i
$331$		−	2.99912e6i		−	1.50461i	−0.658816	−	0.752304i	$-0.728942\pi$
$331$		−	2.99912e6i		−	1.50461i	0.658816	−	0.752304i	$-0.271058\pi$
$332$	2.58490e6	+	2.74497e6i	1.28706	+	1.36676i
$333$	−3.28704e6	+	653118.i	−1.62441	+	0.322761i
$334$	177024.	−	409861.i	0.0868294	−	0.201035i
$335$	490453.			0.238773
$336$	−1.35997e6	+	51733.3i	−0.657175	+	0.0249989i
$337$	−1.59579e6			−0.765421			−0.382710	−	0.923868i	$-0.625009\pi$
$337$	−1.59579e6			−0.765421			−0.382710	+	0.923868i	$0.625009\pi$
$338$	−1.15270e6	+	2.66883e6i	−0.548813	+	1.27066i
$339$	73396.6	+	746008.i	0.0346878	+	0.352569i
$340$	350938.	+	372670.i	0.164639	+	0.174835i
$341$			1.31155e6i			0.610802i
$342$	−2.76667e6	−	594239.i	−1.27906	−	0.274724i
$343$			2.24614e6i			1.03086i
$344$	−782691.	−	2.15985e6i	−0.356611	−	0.984074i
$345$	−58765.2	−	597293.i	−0.0265811	−	0.270172i
$346$	1.15586e6	+	499229.i	0.519055	+	0.224187i
$347$	3.17322e6			1.41474			0.707369	−	0.706844i	$-0.249882\pi$
$347$	3.17322e6			1.41474			0.707369	+	0.706844i	$0.249882\pi$
$348$	−780725.	+	894923.i	−0.345581	+	0.396130i
$349$	24719.7			0.0108637			0.00543187	−	0.999985i	$-0.498271\pi$
$349$	24719.7			0.0108637			0.00543187	+	0.999985i	$0.498271\pi$
$350$	276727.	+	119522.i	0.120749	+	0.0521529i
$351$	3.41081e6	−	1.03349e6i	1.47771	−	0.447753i
$352$	−1.27199e6	−	642545.i	−0.547175	−	0.276406i
$353$			1.43084e6i			0.611160i	0.952166	+	0.305580i	$0.0988504\pi$
$353$			1.43084e6i			0.611160i	−0.952166	+	0.305580i	$0.901150\pi$
$354$	−251226.	+	785249.i	−0.106551	+	0.333042i
$355$			1.15369e6i			0.485868i
$356$	−1.56560e6	+	1.47430e6i	−0.654722	+	0.616541i
$357$	846341.	−	83268.0i	0.351459	−	0.0345786i
$358$	108205.	−	250526.i	0.0446211	−	0.103311i
$359$	2.53954e6			1.03996			0.519982	−	0.854177i	$-0.325939\pi$
$359$	2.53954e6			1.03996			0.519982	+	0.854177i	$0.325939\pi$
$360$	−568975.	−	941059.i	−0.231386	−	0.382702i
$361$	−1.76168e6			−0.711473
$362$	−1.23983e6	+	2.87056e6i	−0.497269	+	1.15132i
$363$	−1.55955e6	+	153437.i	−0.621201	+	0.0611173i
$364$	1.86875e6	−	1.75978e6i	0.739263	−	0.696152i
$365$			1.36005e6i			0.534348i
$366$	−125977.	+	393763.i	−0.0491575	+	0.153650i
$367$		−	1.61626e6i		−	0.626393i	−0.949688	−	0.313196i	$-0.898600\pi$
$367$		−	1.61626e6i		−	0.626393i	0.949688	−	0.313196i	$-0.101400\pi$
$368$	−94640.6	+	1.57417e6i	−0.0364299	+	0.605945i
$369$	−912034.	−	4.59012e6i	−0.348695	−	1.75492i
$370$	−1.79052e6	−	773348.i	−0.679946	−	0.293678i
$371$	−1.53549e6			−0.579179
$372$	1.74825e6	−	2.00397e6i	0.655007	−	0.750816i
$373$	−1.03216e6			−0.384127			−0.192064	−	0.981382i	$-0.561518\pi$
$373$	−1.03216e6			−0.384127			−0.192064	+	0.981382i	$0.561518\pi$
$374$	817498.	+	353088.i	0.302209	+	0.130528i
$375$	23848.6	+	242399.i	0.00875761	+	0.0890129i
$376$	881025.	−	319267.i	0.321380	−	0.116462i
$377$		−	2.23997e6i		−	0.811688i
$378$	−1.81519e6	−	206914.i	−0.653419	−	0.0744835i
$379$		−	2.48176e6i		−	0.887485i	−0.896154	−	0.443742i	$-0.853651\pi$
$379$		−	2.48176e6i		−	0.887485i	0.896154	−	0.443742i	$-0.146349\pi$
$380$	−1.12903e6	−	1.19895e6i	−0.401094	−	0.425932i
$381$	510183.	+	5.18553e6i	0.180058	+	1.83013i
$382$	94049.4	−	217751.i	0.0329760	−	0.0763487i
$383$	−2.69677e6			−0.939393			−0.469696	−	0.882828i	$-0.655637\pi$
$383$	−2.69677e6			−0.939393			−0.469696	+	0.882828i	$0.655637\pi$
$384$	1.08702e6	+	2.67727e6i	0.376193	+	0.926541i
$385$	524373.			0.180297
$386$	193921.	−	448981.i	0.0662454	−	0.153377i
$387$	−601003.	−	3.02475e6i	−0.203986	−	1.02663i
$388$	−33669.7	−	35754.7i	−0.0113543	−	0.0120574i
$389$		−	1.89961e6i		−	0.636490i	−0.948009	−	0.318245i	$-0.896907\pi$
$389$		−	1.89961e6i		−	0.636490i	0.948009	−	0.318245i	$-0.103093\pi$
$390$	1.97551e6	+	632028.i	0.657684	+	0.210414i
$391$		−	985441.i		−	0.325978i
$392$	1.62325e6	−	588237.i	0.533544	−	0.193347i
$393$	5.55413e6	−	546447.i	1.81399	−	0.178471i
$394$	2.86902e6	+	1.23917e6i	0.931095	+	0.402152i
$395$	704903.			0.227319
$396$	−1.55775e6	−	1.11041e6i	−0.499184	−	0.355831i
$397$	−1.70078e6			−0.541592			−0.270796	−	0.962637i	$-0.587287\pi$
$397$	−1.70078e6			−0.541592			−0.270796	+	0.962637i	$0.587287\pi$
$398$	−658122.	−	284251.i	−0.208257	−	0.0899487i
$399$	−2.72283e6	+	267888.i	−0.856225	+	0.0842404i
$400$	38407.9	−	638846.i	0.0120025	−	0.199640i
$401$			1.71580e6i			0.532851i	0.963856	+	0.266426i	$0.0858426\pi$
$401$			1.71580e6i			0.532851i	−0.963856	+	0.266426i	$0.914157\pi$
$402$	−1.64769e6	−	527147.i	−0.508521	−	0.162692i
$403$			5.01589e6i			1.53846i
$404$	3.42125e6	−	3.22173e6i	1.04287	−	0.982056i
$405$	−564356.	−	1.36409e6i	−0.170968	−	0.413243i
$406$	−455291.	+	1.05413e6i	−0.137080	+	0.317379i
$407$	−3.39287e6			−1.01527
$408$	−778430.	−	1.62919e6i	−0.231510	−	0.484530i
$409$	1.33593e6			0.394891			0.197445	−	0.980314i	$-0.436736\pi$
$409$	1.33593e6			0.394891			0.197445	+	0.980314i	$0.436736\pi$
$410$	1.07993e6	−	2.50034e6i	0.317274	−	0.734579i
$411$	−147909.	−	1.50336e6i	−0.0431907	−	0.438993i
$412$	−3.27360e6	+	3.08270e6i	−0.950129	+	0.894722i
$413$			797132.i			0.229961i
$414$	−444558.	+	2.06978e6i	−0.127476	+	0.593504i
$415$			2.94569e6i			0.839589i
$416$	−4.86457e6	−	2.45734e6i	−1.37820	−	0.696196i
$417$	−193660.	−	1.96837e6i	−0.0545381	−	0.554329i
$418$	−2.63003e6	−	1.13595e6i	−0.736242	−	0.317992i
$419$	4.80050e6			1.33583			0.667915	−	0.744237i	$-0.267187\pi$
$419$	4.80050e6			1.33583			0.667915	+	0.744237i	$0.267187\pi$
$420$	−801207.	−	698968.i	−0.221626	−	0.193346i
$421$	377265.			0.103739			0.0518694	−	0.998654i	$-0.483482\pi$
$421$	377265.			0.103739			0.0518694	+	0.998654i	$0.483482\pi$
$422$	1.42726e6	+	616452.i	0.390142	+	0.168507i
$423$	1.23383e6	−	245155.i	0.335277	−	0.0666178i
$424$	1.11072e6	+	3.06506e6i	0.300049	+	0.827989i
$425$			399921.i			0.107399i
$426$	1.24000e6	−	3.87584e6i	0.331054	−	1.03477i
$427$			399722.i			0.106093i
$428$	2.32358e6	+	2.46747e6i	0.613123	+	0.651091i
$429$	3.59082e6	−	353285.i	0.941998	−	0.0926792i
$430$	711640.	−	1.64765e6i	0.185605	−	0.429727i
$431$	−1.74750e6			−0.453131			−0.226566	−	0.973996i	$-0.572750\pi$
$431$	−1.74750e6			−0.453131			−0.226566	+	0.973996i	$0.572750\pi$
$432$	900015.	+	3.77305e6i	0.232028	+	0.972709i
$433$	4.06122e6			1.04097			0.520483	−	0.853872i	$-0.325752\pi$
$433$	4.06122e6			1.04097			0.520483	+	0.853872i	$0.325752\pi$
$434$	1.01952e6	−	2.36047e6i	0.259818	−	0.601553i
$435$	−923362.	+	90845.7i	−0.233964	+	0.0230187i
$436$	3.33516e6	+	3.54170e6i	0.840235	+	0.892268i
$437$			3.17034e6i			0.794149i
$438$	1.46181e6	−	4.56913e6i	0.364087	−	1.13802i
$439$			4.74926e6i			1.17616i	0.808805	+	0.588078i	$0.200115\pi$
$439$			4.74926e6i			1.17616i	−0.808805	+	0.588078i	$0.799885\pi$
$440$	−379314.	−	1.04672e6i	−0.0934044	−	0.257751i
$441$	2.27327e6	−	451688.i	0.556615	−	0.110597i
$442$	3.12643e6	+	1.35034e6i	0.761189	+	0.328767i
$443$	−7.78294e6			−1.88423			−0.942116	−	0.335287i	$-0.891167\pi$
$443$	−7.78294e6			−1.88423			−0.942116	+	0.335287i	$0.891167\pi$
$444$	5.18408e6	+	4.52256e6i	1.24800	+	1.08875i
$445$	−1.68008e6			−0.402190
$446$	5.02799e6	+	2.17165e6i	1.19690	+	0.516956i
$447$	−7119.27	−	72360.7i	−0.00168526	−	0.0171291i
$448$	1.78978e6	+	2.14518e6i	0.421314	+	0.504974i
$449$			5.65655e6i			1.32415i	0.749439	+	0.662073i	$0.230323\pi$
$449$			5.65655e6i			1.32415i	−0.749439	+	0.662073i	$0.769677\pi$
$450$	180415.	−	839978.i	0.0419992	−	0.195540i
$451$		−	4.73790e6i		−	1.09684i
$452$	1.12027e6	−	1.05494e6i	0.257915	−	0.242875i
$453$	723323.	+	7.35190e6i	0.165610	+	1.68327i
$454$	1.77864e6	−	4.11805e6i	0.404994	−	0.937675i
$455$	2.00540e6			0.454123
$456$	2.50435e6	+	5.24138e6i	0.564004	+	1.18041i
$457$	−5.23957e6			−1.17356			−0.586780	−	0.809747i	$-0.699605\pi$
$457$	−5.23957e6			−1.17356			−0.586780	+	0.809747i	$0.699605\pi$
$458$	−783052.	+	1.81299e6i	−0.174432	+	0.403860i
$459$	−702875.	−	2.31969e6i	−0.155721	−	0.513923i
$460$	−896947.	+	844642.i	−0.197639	+	0.186114i
$461$		−	4.22462e6i		−	0.925840i	−0.886400	−	0.462920i	$-0.846802\pi$
$461$		−	4.22462e6i		−	0.925840i	0.886400	−	0.462920i	$-0.153198\pi$
$462$	−1.76164e6	−	563605.i	−0.383983	−	0.122848i
$463$			5.87238e6i			1.27310i	0.771236	+	0.636549i	$0.219639\pi$
$463$			5.87238e6i			1.27310i	−0.771236	+	0.636549i	$0.780361\pi$
$464$	2.43353e6	+	146306.i	0.524738	+	0.0315476i
$465$	2.06765e6	−	203428.i	0.443450	−	0.0436292i
$466$	4.33632e6	+	1.87291e6i	0.925031	+	0.399533i
$467$	−4.85194e6			−1.02949			−0.514746	−	0.857343i	$-0.672114\pi$
$467$	−4.85194e6			−1.02949			−0.514746	+	0.857343i	$0.672114\pi$
$468$	−5.95744e6	−	4.24662e6i	−1.25732	−	0.896249i
$469$	−1.67262e6			−0.351128
$470$	672091.	+	290285.i	0.140341	+	0.0606149i
$471$	−2.90883e6	+	286188.i	−0.604181	+	0.0594428i
$472$	1.59119e6	−	576619.i	0.328751	−	0.119133i
$473$		−	3.12214e6i		−	0.641651i
$474$	−2.36813e6	−	757641.i	−0.484128	−	0.154888i
$475$		−	1.28662e6i		−	0.261647i
$476$	−1.19682e6	−	1.27094e6i	−0.242110	−	0.257103i
$477$	852889.	+	4.29245e6i	0.171631	+	0.863793i
$478$	2.12499e6	−	4.91995e6i	0.425389	−	0.984896i
$479$	−5.46784e6			−1.08887			−0.544437	−	0.838802i	$-0.683257\pi$
$479$	−5.46784e6			−1.08887			−0.544437	+	0.838802i	$0.683257\pi$
$480$	−815675.	+	2.10494e6i	−0.161590	+	0.417000i
$481$	−1.29756e7			−2.55721
$482$	−730534.	+	1.69139e6i	−0.143226	+	0.331609i
$483$	200410.	+	2.03698e6i	0.0390888	+	0.397301i
$484$	2.20538e6	+	2.34195e6i	0.427927	+	0.454427i
$485$		−	38369.2i		−	0.00740677i
$486$	429819.	+	5.18927e6i	0.0825457	+	0.996587i
$487$		−	4.16014e6i		−	0.794851i	−0.917634	−	0.397425i	$-0.869904\pi$
$487$		−	4.16014e6i		−	0.794851i	0.917634	−	0.397425i	$-0.130096\pi$
$488$	797903.	−	289146.i	0.151670	−	0.0549626i
$489$	−582897.	−	5.92460e6i	−0.110235	−	1.12044i
$490$	1.23830e6	+	534837.i	0.232989	+	0.100631i
$491$	637672.			0.119370			0.0596848	−	0.998217i	$-0.480990\pi$
$491$	637672.			0.119370			0.0596848	+	0.998217i	$0.480990\pi$
$492$	−6.31544e6	+	7.23920e6i	−1.17623	+	1.34827i
$493$	−1.52340e6			−0.282291
$494$	−1.00583e7	−	4.34429e6i	−1.85441	−	0.800943i
$495$	−291263.	−	1.46588e6i	−0.0534284	−	0.268897i
$496$	−5.44932e6	−	327618.i	−0.994577	−	0.0597947i
$497$		−	3.93449e6i		−	0.714493i
$498$	3.16608e6	−	9.89610e6i	0.572068	−	1.78810i
$499$			2.03320e6i			0.365536i	0.983156	+	0.182768i	$0.0585057\pi$
$499$			2.03320e6i			0.365536i	−0.983156	+	0.182768i	$0.941494\pi$
$500$	364008.	−	342780.i	0.0651157	−	0.0613184i
$501$	−1.22438e6	+	120462.i	−0.217932	+	0.0214415i
$502$	2.13076e6	−	4.93332e6i	0.377377	−	0.873735i
$503$	4.70441e6			0.829059			0.414529	−	0.910036i	$-0.363946\pi$
$503$	4.70441e6			0.829059			0.414529	+	0.910036i	$0.363946\pi$
$504$	1.94041e6	+	3.20935e6i	0.340264	+	0.562782i
$505$	3.67142e6			0.640627
$506$	−849816.	+	1.96756e6i	−0.147553	+	0.341627i
$507$	7.97259e6	−	784390.i	1.37746	−	0.135523i
$508$	7.78704e6	−	7.33294e6i	1.33879	−	1.26072i
$509$			3.12453e6i			0.534553i	0.963620	+	0.267276i	$0.0861236\pi$
$509$			3.12453e6i			0.534553i	−0.963620	+	0.267276i	$0.913876\pi$
$510$	429842.	−	1.34354e6i	0.0731785	−	0.228731i
$511$		−	4.63827e6i		−	0.785786i
$512$	2.98742e6	−	5.12442e6i	0.503641	−	0.863913i
$513$	2.26127e6	+	7.46285e6i	0.379367	+	1.25202i
$514$	−1.01440e7	−	4.38131e6i	−1.69356	−	0.731470i
$515$	−3.51297e6			−0.583656
$516$	−4.16168e6	+	4.77042e6i	−0.688089	+	0.788737i
$517$	1.27355e6			0.209551
$518$	6.10631e6	+	2.63739e6i	0.999895	+	0.431868i
$519$	−339716.	−	3.45289e6i	−0.0553601	−	0.562684i
$520$	−1.45064e6	−	4.00308e6i	−0.235262	−	0.649210i
$521$		−	1.18677e6i		−	0.191546i	−0.995403	−	0.0957732i	$-0.969468\pi$
$521$		−	1.18677e6i		−	0.191546i	0.995403	−	0.0957732i	$-0.0305324\pi$
$522$	3.19970e6	+	687247.i	0.513964	+	0.110392i
$523$			759390.i			0.121398i	0.998156	+	0.0606989i	$0.0193329\pi$
$523$			759390.i			0.121398i	−0.998156	+	0.0606989i	$0.980667\pi$
$524$	−7.85417e6	−	8.34055e6i	−1.24960	−	1.32699i
$525$	−81332.4	−	826668.i	−0.0128785	−	0.130898i
$526$	1.65629e6	−	3.83477e6i	0.261018	−	0.604331i
$527$	3.41130e6			0.535049
$528$	149276.	+	3.92418e6i	0.0233026	+	0.612582i
$529$	−4.06457e6			−0.631503
$530$	−1.00989e6	+	2.33819e6i	−0.156166	+	0.361568i
$531$	2.22838e6	−	442767.i	0.342967	−	0.0681458i
$532$	3.85039e6	+	4.08883e6i	0.589829	+	0.626355i
$533$		−	1.81196e7i		−	2.76267i
$534$	5.64428e6	+	1.80578e6i	0.856555	+	0.274039i
$535$			2.64790e6i			0.399960i
$536$	1.20992e6	+	3.33879e6i	0.181905	+	0.501970i
$537$	−748396.	+	73631.5i	−0.111994	+	0.0110186i
$538$	−9.83520e6	−	4.24795e6i	−1.46497	−	0.632738i
$539$	2.34646e6			0.347890
$540$	−1.50893e6	+	2.62801e6i	−0.222682	+	0.387831i
$541$	9.05042e6			1.32946			0.664731	−	0.747083i	$-0.268546\pi$
$541$	9.05042e6			1.32946			0.664731	+	0.747083i	$0.268546\pi$
$542$	−1.06618e7	−	4.60495e6i	−1.55895	−	0.673328i
$543$	8.57524e6	−	843682.i	1.24809	−	0.122795i
$544$	−1.67124e6	+	3.30839e6i	−0.242125	+	0.479313i
$545$			3.80068e6i			0.548112i
$546$	−6.73719e6	−	2.15544e6i	−0.967158	−	0.309424i
$547$		−	410405.i		−	0.0586469i	−0.999570	−	0.0293234i	$-0.990665\pi$
$547$		−	410405.i		−	0.0586469i	0.999570	−	0.0293234i	$-0.00933528\pi$
$548$	−2.25757e6	+	2.12592e6i	−0.321137	+	0.302410i
$549$	1.11742e6	−	222026.i	0.158229	−	0.0314393i
$550$	344880.	−	798495.i	0.0486140	−	0.112555i
$551$	4.90106e6			0.687719
$552$	3.92115e6	−	1.87354e6i	0.547729	−	0.261706i
$553$	−2.40397e6			−0.334285
$554$	−2.31786e6	+	5.36649e6i	−0.320857	+	0.742876i
$555$	526248.	+	5.34882e6i	0.0725200	+	0.737099i
$556$	−2.95588e6	+	2.78351e6i	−0.405508	+	0.381861i
$557$			1.65626e6i			0.226200i	0.993584	+	0.113100i	$0.0360780\pi$
$557$			1.65626e6i			0.226200i	−0.993584	+	0.113100i	$0.963922\pi$
$558$	−7.16496e6	−	1.53893e6i	−0.974156	−	0.209234i
$559$		−	1.19403e7i		−	1.61616i
$560$	−130985.	+	2.17870e6i	−0.0176503	+	0.293580i
$561$	−240269.	−	2.44211e6i	−0.0322323	−	0.327611i
$562$	8.83273e6	+	3.81497e6i	1.17965	+	0.509507i
$563$	−152000.			−0.0202103			−0.0101052	−	0.999949i	$-0.503217\pi$
$563$	−152000.			−0.0202103			−0.0101052	+	0.999949i	$0.503217\pi$
$564$	−1.94590e6	−	1.69759e6i	−0.257586	−	0.224717i
$565$	1.20219e6			0.158435
$566$	1.15728e7	+	4.99843e6i	1.51843	+	0.655831i
$567$	1.92466e6	+	4.65204e6i	0.251418	+	0.607695i
$568$	−7.85382e6	+	2.84608e6i	−1.02143	+	0.370149i
$569$			1.18722e7i			1.53727i	0.639686	+	0.768636i	$0.279064\pi$
$569$			1.18722e7i			1.53727i	−0.639686	+	0.768636i	$0.720936\pi$
$570$	−1.38288e6	+	4.32241e6i	−0.178277	+	0.557236i
$571$			3.84275e6i			0.493233i	0.969113	+	0.246617i	$0.0793189\pi$
$571$			3.84275e6i			0.493233i	−0.969113	+	0.246617i	$0.920681\pi$
$572$	−5.07783e6	−	5.39228e6i	−0.648915	−	0.689100i
$573$	−650488.	+	63998.8i	−0.0827661	+	0.00814301i
$574$	−3.68294e6	+	8.52704e6i	−0.466568	+	1.08024i
$575$	−962535.			−0.121408
$576$	5.00270e6	−	6.19487e6i	0.628272	−	0.777994i
$577$	1.13094e7			1.41417			0.707083	−	0.707131i	$-0.250011\pi$
$577$	1.13094e7			1.41417			0.707083	+	0.707131i	$0.250011\pi$
$578$	−2.26636e6	+	5.24727e6i	−0.282169	+	0.653302i
$579$	−1.34124e6	+	131959.i	−0.166269	+	0.0163585i
$580$	1.30574e6	+	1.38660e6i	0.161171	+	0.171152i
$581$		−	1.00459e7i		−	1.23466i
$582$	−41239.9	+	128902.i	−0.00504673	+	0.0157744i
$583$			4.43065e6i			0.539879i
$584$	−9.25867e6	+	3.35517e6i	−1.12335	+	0.407083i
$585$	−1.11390e6	−	5.60609e6i	−0.134573	−	0.677283i
$586$	7.40171e6	+	3.19689e6i	0.890406	+	0.384578i
$587$	−517378.			−0.0619745			−0.0309872	−	0.999520i	$-0.509865\pi$
$587$	−517378.			−0.0619745			−0.0309872	+	0.999520i	$0.509865\pi$
$588$	−3.58524e6	−	3.12774e6i	−0.427636	−	0.373067i
$589$	−1.09748e7			−1.30349
$590$	1.21384e6	+	524274.i	0.143560	+	0.0620052i
$591$	−843230.	−	8.57064e6i	−0.0993064	−	1.00936i
$592$	847516.	−	1.40969e7i	0.0993902	−	1.65318i
$593$		−	1.18455e6i		−	0.138330i	−0.997605	−	0.0691650i	$-0.977967\pi$
$593$		−	1.18455e6i		−	0.138330i	0.997605	−	0.0691650i	$-0.0220335\pi$
$594$	−597049.	+	5.23771e6i	−0.0694295	+	0.609081i
$595$		−	1.36387e6i		−	0.157936i
$596$	−108663.	+	102326.i	−0.0125304	+	0.0117997i
$597$	193427.	+	1.96601e6i	0.0222117	+	0.225761i
$598$	−3.25002e6	+	7.52472e6i	−0.371649	+	0.860473i
$599$	6.77244e6			0.771220			0.385610	−	0.922662i	$-0.373991\pi$
$599$	6.77244e6			0.771220			0.385610	+	0.922662i	$0.373991\pi$
$600$	−1.59132e6	+	760336.i	−0.180459	+	0.0862239i
$601$	2.08341e6			0.235281			0.117641	−	0.993056i	$-0.462467\pi$
$601$	2.08341e6			0.235281			0.117641	+	0.993056i	$0.462467\pi$
$602$	−2.42695e6	+	5.61906e6i	−0.272941	+	0.631936i
$603$	929057.	+	4.67580e6i	0.104052	+	0.523676i
$604$	1.10403e7	−	1.03964e7i	1.23136	−	1.15956i
$605$			2.51320e6i			0.279151i
$606$	−1.23342e7	−	3.94610e6i	−1.36436	−	0.436502i
$607$			113505.i			0.0125038i	0.999980	+	0.00625191i	$0.00199006\pi$
$607$			113505.i			0.0125038i	−0.999980	+	0.00625191i	$0.998010\pi$
$608$	5.37666e6	−	1.06437e7i	0.589866	−	1.16770i
$609$	3.14900e6	−	309817.i	0.344056	−	0.0338502i
$610$	608682.	+	262897.i	0.0662317	+	0.0286063i
$611$	4.87055e6			0.527806
$612$	−2.88812e6	+	4.05166e6i	−0.311700	+	0.437274i
$613$	−6.04738e6			−0.650005			−0.325002	−	0.945713i	$-0.605365\pi$
$613$	−6.04738e6			−0.650005			−0.325002	+	0.945713i	$0.605365\pi$
$614$	−2.29240e6	−	990119.i	−0.245398	−	0.105990i
$615$	−7.46926e6	+	734869.i	−0.796324	+	0.0783469i
$616$	1.29360e6	+	3.56970e6i	0.137356	+	0.379036i
$617$			5.26294e6i			0.556564i	0.960499	+	0.278282i	$0.0897650\pi$
$617$			5.26294e6i			0.556564i	−0.960499	+	0.278282i	$0.910235\pi$
$618$	1.18019e7	+	3.77580e6i	1.24303	+	0.397684i
$619$			1.67176e7i			1.75367i	0.480789	+	0.876836i	$0.340350\pi$
$619$			1.67176e7i			1.75367i	−0.480789	+	0.876836i	$0.659650\pi$
$620$	−2.92390e6	−	3.10496e6i	−0.305480	−	0.324397i
$621$	5.58306e6	−	1.69169e6i	0.580956	−	0.176032i
$622$	−80028.0	+	185288.i	−0.00829404	+	0.0192031i
$623$	5.72969e6			0.591440
$624$	570889.	+	1.50076e7i	0.0586935	+	1.54294i
$625$	390625.			0.0400000
$626$	−2.87772e6	+	6.66274e6i	−0.293503	+	0.679543i
$627$	772988.	+	7.85671e6i	0.0785243	+	0.798126i
$628$	4.11343e6	+	4.36816e6i	0.416202	+	0.441976i
$629$			8.82472e6i			0.889354i
$630$	−615279.	+	2.86463e6i	−0.0617619	+	0.287552i
$631$			2.72195e6i			0.272149i	0.990699	+	0.136074i	$0.0434486\pi$
$631$			2.72195e6i			0.272149i	−0.990699	+	0.136074i	$0.956551\pi$
$632$	1.73895e6	+	4.79867e6i	0.173179	+	0.477891i
$633$	−419484.	−	4.26366e6i	−0.0416108	−	0.422935i
$634$	6.98032e6	+	3.01489e6i	0.689687	+	0.297885i
$635$	8.35645e6			0.822409
$636$	5.90588e6	−	6.76974e6i	0.578951	−	0.663635i
$637$	8.97377e6			0.876247
$638$	3.04168e6	+	1.31374e6i	0.295843	+	0.127778i
$639$	−1.09988e7	+	2.18542e6i	−1.06560	+	0.211730i
$640$	4.44374e6	−	1.31453e6i	0.428844	−	0.126859i
$641$		−	3.61898e6i		−	0.347889i	−0.984755	−	0.173944i	$-0.944349\pi$
$641$		−	3.61898e6i		−	0.347889i	0.984755	−	0.173944i	$-0.0556513\pi$
$642$	2.84600e6	−	8.89566e6i	0.272520	−	0.851806i
$643$		−	1.25937e6i		−	0.120123i	−0.998195	−	0.0600617i	$-0.980870\pi$
$643$		−	1.25937e6i		−	0.120123i	0.998195	−	0.0600617i	$-0.0191297\pi$
$644$	3.05891e6	−	2.88053e6i	0.290638	−	0.273689i
$645$	−4.92202e6	+	484257.i	−0.465848	+	0.0458328i
$646$	−2.95455e6	+	6.84062e6i	−0.278555	+	0.644932i
$647$	−133273.			−0.0125165			−0.00625824	−	0.999980i	$-0.501992\pi$
$647$	−133273.			−0.0125165			−0.00625824	+	0.999980i	$0.501992\pi$
$648$	7.89391e6	−	7.20702e6i	0.738507	−	0.674246i
$649$	2.30012e6			0.214357
$650$	1.31896e6	−	3.05375e6i	0.122447	−	0.283498i
$651$	−7.05143e6	+	693761.i	−0.652116	+	0.0641590i
$652$	−8.89689e6	+	8.37807e6i	−0.819633	+	0.771836i
$653$		−	1.23659e6i		−	0.113486i	−0.998389	−	0.0567429i	$-0.981928\pi$
$653$		−	1.23659e6i		−	0.113486i	0.998389	−	0.0567429i	$-0.0180715\pi$
$654$	4.08503e6	−	1.27684e7i	0.373466	−	1.16733i
$655$		−	8.95044e6i		−	0.815157i
$656$	1.96853e7	+	1.18350e6i	1.78601	+	0.107376i
$657$	−1.29663e7	+	2.57633e6i	−1.17193	+	0.232856i
$658$	−2.29207e6	−	989975.i	−0.206378	−	0.0891373i
$659$	−7.95805e6			−0.713827			−0.356913	−	0.934137i	$-0.616171\pi$
$659$	−7.95805e6			−0.713827			−0.356913	+	0.934137i	$0.616171\pi$
$660$	−2.01687e6	+	2.31188e6i	−0.180226	+	0.206588i
$661$	1.46238e6			0.130184			0.0650918	−	0.997879i	$-0.479266\pi$
$661$	1.46238e6			0.130184			0.0650918	+	0.997879i	$0.479266\pi$
$662$	1.55749e7	+	6.72700e6i	1.38128	+	0.596591i
$663$	−918882.	−	9.33958e6i	−0.0811850	−	0.825170i
$664$	−2.00530e7	+	7.26684e6i	−1.76506	+	0.639625i
$665$			4.38782e6i			0.384764i
$666$	3.98106e6	−	1.85351e7i	0.347787	−	1.61923i
$667$		−	3.66655e6i		−	0.319112i
$668$	1.73141e6	+	1.83863e6i	0.150127	+	0.159424i
$669$	−1.47777e6	−	1.50201e7i	−0.127656	−	1.29750i
$670$	−1.10008e6	+	2.54700e6i	−0.0946757	+	0.219201i
$671$	1.15340e6			0.0988944
$672$	2.78174e6	−	7.17858e6i	0.237626	−	0.613219i
$673$	1.49927e7			1.27598			0.637989	−	0.770046i	$-0.279767\pi$
$673$	1.49927e7			1.27598			0.637989	+	0.770046i	$0.279767\pi$
$674$	3.57934e6	−	8.28719e6i	0.303496	−	0.702680i
$675$	−2.26577e6	+	686537.i	−0.191406	+	0.0579969i
$676$	−1.12742e7	−	1.19723e7i	−0.948893	−	1.00765i
$677$		−	1.44430e7i		−	1.21111i	−0.795802	−	0.605557i	$-0.792950\pi$
$677$		−	1.44430e7i		−	1.21111i	0.795802	−	0.605557i	$-0.207050\pi$
$678$	−4.03877e6	−	1.29213e6i	−0.337423	−	0.107952i
$679$			130853.i			0.0108920i
$680$	−2.72249e6	+	986582.i	−0.225784	+	0.0818202i
$681$	−1.23019e7	+	1.21033e6i	−1.01649	+	0.100008i
$682$	−6.81112e6	−	2.94181e6i	−0.560735	−	0.242189i
$683$	−855827.			−0.0701996			−0.0350998	−	0.999384i	$-0.511175\pi$
$683$	−855827.			−0.0701996			−0.0350998	+	0.999384i	$0.511175\pi$
$684$	9.29160e6	−	1.30349e7i	0.759365	−	1.06529i
$685$	−2.42265e6			−0.197272
$686$	−1.16646e7	−	5.03808e6i	−0.946365	−	0.408747i
$687$	5.41594e6	−	532851.i	0.437806	−	0.0430739i
$688$	1.29720e7	+	779889.i	1.04481	+	0.0628148i
$689$			1.69445e7i			1.35982i
$690$	3.23365e6	+	1.03455e6i	0.258566	+	0.0827234i
$691$			2.05338e7i			1.63597i	0.575243	+	0.817983i	$0.304908\pi$
$691$			2.05338e7i			1.63597i	−0.575243	+	0.817983i	$0.695092\pi$
$692$	−5.18516e6	+	4.88279e6i	−0.411620	+	0.387617i
$693$	993311.	+	4.99918e6i	0.0785692	+	0.395426i
$694$	−7.11751e6	+	1.64790e7i	−0.560957	+	1.29877i
$695$	−3.17202e6			−0.249100
$696$	−2.89632e6	−	6.06174e6i	−0.226633	−	0.474323i
$697$	−1.23231e7			−0.960812
$698$	−55446.2	+	128373.i	−0.00430757	+	0.00997325i
$699$	−1.27448e6	−	1.29539e7i	−0.0986597	−	1.00278i
$700$	−1.24140e6	+	1.16900e6i	−0.0957559	+	0.0901718i
$701$			5.43841e6i			0.418000i	0.977916	+	0.209000i	$0.0670209\pi$
$701$			5.43841e6i			0.418000i	−0.977916	+	0.209000i	$0.932979\pi$
$702$	−2.28335e6	+	2.00310e7i	−0.174875	+	1.53412i
$703$		−	2.83907e7i		−	2.16664i
$704$	6.18990e6	−	5.16441e6i	0.470709	−	0.392726i
$705$	−197533.	−	2.00774e6i	−0.0149681	−	0.152137i
$706$	−7.43060e6	−	3.20937e6i	−0.561064	−	0.242331i
$707$	−1.25208e7			−0.942074
$708$	−3.51443e6	−	3.06597e6i	−0.263494	−	0.229871i
$709$	1.97668e7			1.47680			0.738399	−	0.674364i	$-0.235582\pi$
$709$	1.97668e7			1.47680			0.738399	+	0.674364i	$0.235582\pi$
$710$	−5.99130e6	−	2.58772e6i	−0.446041	−	0.192651i
$711$	1.33529e6	+	6.72028e6i	0.0990605	+	0.498555i
$712$	−4.14467e6	−	1.14373e7i	−0.306401	−	0.845519i
$713$			8.21037e6i			0.604837i
$714$	−1.46591e6	+	4.58196e6i	−0.107613	+	0.336361i
$715$		−	5.78658e6i		−	0.423308i
$716$	1.05832e6	+	1.12386e6i	0.0771496	+	0.0819272i
$717$	−1.46974e7	+	1.44601e6i	−1.06768	+	0.105045i
$718$	−5.69617e6	+	1.31882e7i	−0.412355	+	0.954719i
$719$	−1.76948e7			−1.27651			−0.638255	−	0.769825i	$-0.720344\pi$
$719$	−1.76948e7			−1.27651			−0.638255	+	0.769825i	$0.720344\pi$
$720$	6.16328e6	−	843989.i	0.443079	−	0.0606744i
$721$	1.19805e7			0.858296
$722$	3.95143e6	−	9.14868e6i	0.282105	−	0.653154i
$723$	5.05270e6	−	497114.i	0.359483	−	0.0353680i
$724$	−1.21264e7	−	1.28773e7i	−0.859774	−	0.913017i
$725$			1.48799e6i			0.105137i
$726$	2.70123e6	−	8.44314e6i	0.190204	−	0.594515i
$727$		−	2.26643e7i		−	1.59040i	−0.606349	−	0.795199i	$-0.707366\pi$
$727$		−	2.26643e7i		−	1.59040i	0.606349	−	0.795199i	$-0.292634\pi$
$728$	4.94721e6	+	1.36519e7i	0.345965	+	0.954697i
$729$	1.19357e7	−	7.96434e6i	0.831818	−	0.555048i
$730$	−7.06299e6	−	3.05060e6i	−0.490548	−	0.211874i
$731$	−8.12056e6			−0.562073
$732$	−1.76231e6	−	1.53743e6i	−0.121564	−	0.106052i
$733$	−1.62487e7			−1.11701			−0.558506	−	0.829501i	$-0.688625\pi$
$733$	−1.62487e7			−1.11701			−0.558506	+	0.829501i	$0.688625\pi$
$734$	8.39352e6	+	3.62527e6i	0.575048	+	0.248370i
$735$	−363946.	−	3.69917e6i	−0.0248496	−	0.252573i
$736$	−7.96267e6	−	4.02235e6i	−0.541832	−	0.273707i
$737$			4.82634e6i			0.327302i
$738$	2.58830e7	+	5.55928e6i	1.74934	+	0.375731i
$739$			8.26820e6i			0.556929i	0.960447	+	0.278464i	$0.0898254\pi$
$739$			8.26820e6i			0.556929i	−0.960447	+	0.278464i	$0.910175\pi$
$740$	8.03225e6	−	7.56385e6i	0.539210	−	0.507766i
$741$	2.95620e6	+	3.00471e7i	0.197783	+	2.01028i
$742$	3.44410e6	−	7.97406e6i	0.229650	−	0.531704i
$743$	−1.96813e7			−1.30792			−0.653961	−	0.756528i	$-0.726894\pi$
$743$	−1.96813e7			−1.30792			−0.653961	+	0.756528i	$0.726894\pi$
$744$	6.48562e6	+	1.35738e7i	0.429556	+	0.899022i
$745$	−116609.			−0.00769734
$746$	2.31513e6	−	5.36018e6i	0.152310	−	0.352640i
$747$	−2.80831e7	+	5.57997e6i	−1.84138	+	0.365873i
$748$	−3.66729e6	+	3.45343e6i	−0.239657	+	0.225682i
$749$		−	9.03027e6i		−	0.588161i
$750$	−1.31231e6	−	419850.i	−0.0851891	−	0.0272547i
$751$			1.67203e6i			0.108180i	0.998536	+	0.0540898i	$0.0172257\pi$
$751$			1.67203e6i			0.108180i	−0.998536	+	0.0540898i	$0.982774\pi$
$752$	−318124.	+	5.29142e6i	−0.0205141	+	0.341215i
$753$	−1.47373e7	+	1.44994e6i	−0.947176	+	0.0931886i
$754$	1.16325e7	+	5.02424e6i	0.745155	+	0.321842i
$755$	1.18476e7			0.756417
$756$	5.14599e6	−	8.96245e6i	0.327465	−	0.570325i
$757$	1.75039e7			1.11019			0.555093	−	0.831788i	$-0.312683\pi$
$757$	1.75039e7			1.11019			0.555093	+	0.831788i	$0.312683\pi$
$758$	1.28882e7	+	5.56656e6i	0.814738	+	0.351896i
$759$	5.87771e6	−	578283.i	0.370342	−	0.0364364i
$760$	8.75873e6	−	3.17401e6i	0.550056	−	0.199330i
$761$			2.39002e7i			1.49603i	0.663681	+	0.748015i	$0.268993\pi$
$761$			2.39002e7i			1.49603i	−0.663681	+	0.748015i	$0.731007\pi$
$762$	−2.80737e7	−	8.98166e6i	−1.75151	−	0.560363i
$763$		−	1.29617e7i		−	0.806027i
$764$	919864.	+	976828.i	0.0570152	+	0.0605459i
$765$	−3.81270e6	+	757564.i	−0.235548	+	0.0468021i
$766$	6.04884e6	−	1.40048e7i	0.372478	−	0.862392i
$767$	8.79654e6			0.539913
$768$	−1.63417e7	−	360014.i	−0.999757	−	0.0220250i
$769$	−1.22860e7			−0.749192			−0.374596	−	0.927188i	$-0.622219\pi$
$769$	−1.22860e7			−0.749192			−0.374596	+	0.927188i	$0.622219\pi$
$770$	−1.17617e6	+	2.72316e6i	−0.0714894	+	0.165518i
$771$	2.98140e6	+	3.03031e7i	0.180628	+	1.83591i
$772$	1.89667e6	+	2.01412e6i	0.114538	+	0.121631i
$773$		−	1.77382e7i		−	1.06773i	−0.845571	−	0.533863i	$-0.820740\pi$
$773$		−	1.77382e7i		−	1.06773i	0.845571	−	0.533863i	$-0.179260\pi$
$774$	1.70561e7	+	3.66340e6i	1.02336	+	0.219802i
$775$		−	3.33201e6i		−	0.199275i
$776$	261201.	−	94654.6i	0.0155712	−	0.00564271i
$777$	−1.79469e6	−	1.82414e7i	−0.106644	−	1.08394i
$778$	9.86501e6	+	4.26082e6i	0.584317	+	0.252374i
$779$	3.96456e7			2.34073
$780$	−7.71328e6	+	8.84151e6i	−0.453944	+	0.520343i
$781$	−1.13530e7			−0.666011
$782$	5.11756e6	+	2.21034e6i	0.299258	+	0.129253i
$783$	−2.61520e6	−	8.63091e6i	−0.152441	−	0.503097i
$784$	−586131.	+	9.74922e6i	−0.0340568	+	0.566474i
$785$			4.68757e6i			0.271502i
$786$	−9.62008e6	+	3.00692e7i	−0.555421	+	1.73606i
$787$			3.16548e7i			1.82181i	0.412616	+	0.910905i	$0.364615\pi$
$787$			3.16548e7i			1.82181i	−0.412616	+	0.910905i	$0.635385\pi$
$788$	−1.28704e7	+	1.21199e7i	−0.738375	+	0.695317i
$789$	−1.14556e7	+	1.12707e6i	−0.655127	+	0.0644552i
$790$	−1.58109e6	+	3.66068e6i	−0.0901342	+	0.208686i
$791$	−4.09989e6			−0.232987
$792$	9.26055e6	−	5.59903e6i	0.524595	−	0.317176i
$793$	4.41103e6			0.249090
$794$	3.81484e6	−	8.83244e6i	0.214746	−	0.497198i
$795$	6.98488e6	−	687213.i	0.391959	−	0.0385632i
$796$	2.95233e6	−	2.78016e6i	0.165151	−	0.155521i
$797$		−	2.37179e7i		−	1.32261i	−0.750119	−	0.661303i	$-0.770004\pi$
$797$		−	2.37179e7i		−	1.32261i	0.750119	−	0.661303i	$-0.229996\pi$
$798$	4.71610e6	−	1.47410e7i	0.262166	−	0.819443i
$799$		−	3.31246e6i		−	0.183562i
$800$	3.23149e6	+	1.63239e6i	0.178516	+	0.0901776i
$801$	−3.18256e6	−	1.60173e7i	−0.175265	−	0.882080i
$802$	−8.91044e6	−	3.84853e6i	−0.489174	−	0.211280i
$803$	−1.33837e7			−0.732467
$804$	6.43331e6	−	7.37432e6i	0.350990	−	0.402329i
$805$	3.28259e6			0.178536
$806$	−2.60483e7	−	1.12506e7i	−1.41235	−	0.610012i
$807$	2.89065e6	+	2.93807e7i	0.156247	+	1.58810i
$808$	9.05717e6	+	2.49934e7i	0.488050	+	1.34678i
$809$		−	2.13390e7i		−	1.14631i	−0.819447	−	0.573155i	$-0.805719\pi$
$809$		−	2.13390e7i		−	1.14631i	0.819447	−	0.573155i	$-0.194281\pi$
$810$	8.34980e6	+	128851.i	0.447160	+	0.00690043i
$811$		−	1.29765e7i		−	0.692795i	−0.938088	−	0.346398i	$-0.887405\pi$
$811$		−	1.29765e7i		−	0.692795i	0.938088	−	0.346398i	$-0.112595\pi$
$812$	−4.45304e6	−	4.72880e6i	−0.237010	−	0.251687i
$813$	3.13358e6	+	3.18499e7i	0.166270	+	1.68998i
$814$	7.61018e6	−	1.76197e7i	0.402563	−	0.932048i
$815$	−9.54746e6			−0.503494
$816$	1.02067e7	−	388261.i	0.536609	−	0.0204126i
$817$	2.61253e7			1.36932
$818$	−2.99649e6	+	6.93773e6i	−0.156578	+	0.362522i
$819$	3.79880e6	+	1.91188e7i	0.197896	+	0.995979i
$820$	1.05624e7	+	1.12165e7i	0.548564	+	0.582535i
$821$		−	1.95871e6i		−	0.101417i	−0.998713	−	0.0507087i	$-0.983852\pi$
$821$		−	1.95871e6i		−	0.101417i	0.998713	−	0.0507087i	$-0.0161480\pi$
$822$	8.13895e6	+	2.60391e6i	0.420135	+	0.134414i
$823$		−	377230.i		−	0.0194136i	−0.999953	−	0.00970680i	$-0.996910\pi$
$823$		−	377230.i		−	0.0194136i	0.999953	−	0.00970680i	$-0.00308982\pi$
$824$	−8.66630e6	−	2.39148e7i	−0.444647	−	1.22701i
$825$	−2.38535e6	+	234684.i	−0.122016	+	0.0120046i
$826$	−4.13964e6	−	1.78796e6i	−0.211112	−	0.0911818i
$827$	7.53272e6			0.382991			0.191495	−	0.981494i	$-0.438666\pi$
$827$	7.53272e6			0.382991			0.191495	+	0.981494i	$0.438666\pi$
$828$	−9.75157e6	−	6.95117e6i	−0.494309	−	0.352356i
$829$	2.04509e7			1.03354			0.516769	−	0.856125i	$-0.327135\pi$
$829$	2.04509e7			1.03354			0.516769	+	0.856125i	$0.327135\pi$
$830$	−1.52975e7	−	6.60717e6i	−0.770768	−	0.332905i
$831$	1.60313e7	−	1.57726e6i	0.805317	−	0.0792318i
$832$	2.36726e7	−	1.97507e7i	1.18560	−	0.989178i
$833$		−	6.10306e6i		−	0.304744i
$834$	1.06565e7	+	3.40934e6i	0.530516	+	0.169729i
$835$			1.97308e6i			0.0979329i
$836$	1.17983e7	−	1.11103e7i	0.583854	−	0.549806i
$837$	5.85612e6	+	1.93269e7i	0.288933	+	0.953560i
$838$	−1.07675e7	+	2.49298e7i	−0.529669	+	1.22633i
$839$	1.51336e6			0.0742230			0.0371115	−	0.999311i	$-0.488184\pi$
$839$	1.51336e6			0.0742230			0.0371115	+	0.999311i	$0.488184\pi$
$840$	5.42696e6	−	2.59302e6i	0.265374	−	0.126797i
$841$	1.48430e7			0.723655
$842$	−846203.	+	1.95920e6i	−0.0411334	+	0.0952354i
$843$	−2.59601e6	−	2.63860e7i	−0.125817	−	1.27881i
$844$	−6.40268e6	+	6.02930e6i	−0.309389	+	0.291347i
$845$		−	1.28478e7i		−	0.618994i
$846$	−1.49434e6	+	6.95735e6i	−0.0717831	+	0.334209i
$847$		−	8.57091e6i		−	0.410505i
$848$	−1.84087e7	−	1.10675e6i	−0.879092	−	0.0528517i
$849$	−3.40133e6	−	3.45713e7i	−0.161949	−	1.64607i
$850$	−2.07686e6	−	897021.i	−0.0985960	−	0.0425849i
$851$	−2.12394e7			−1.00535
$852$	1.73466e7	+	1.51330e7i	0.818681	+	0.714212i
$853$	−1.61023e7			−0.757733			−0.378866	−	0.925451i	$-0.623686\pi$
$853$	−1.61023e7			−0.757733			−0.378866	+	0.925451i	$0.623686\pi$
$854$	−2.07582e6	−	896574.i	−0.0973970	−	0.0420670i
$855$	1.22661e7	−	2.43722e6i	0.573842	−	0.114019i
$856$	−1.80257e7	+	6.53220e6i	−0.840831	+	0.304702i
$857$			2.47010e7i			1.14885i	0.818558	+	0.574424i	$0.194774\pi$
$857$			2.47010e7i			1.14885i	−0.818558	+	0.574424i	$0.805226\pi$
$858$	−6.21951e6	+	1.94401e7i	−0.288429	+	0.901531i
$859$			1.32679e6i			0.0613505i	0.999529	+	0.0306753i	$0.00976577\pi$
$859$			1.32679e6i			0.0613505i	−0.999529	+	0.0306753i	$0.990234\pi$
$860$	6.96030e6	+	7.39132e6i	0.320909	+	0.340782i
$861$	2.54728e7	−	2.50617e6i	1.17103	−	0.115213i
$862$	3.91963e6	−	9.07505e6i	0.179671	−	0.415988i
$863$	3.86184e7			1.76509			0.882545	−	0.470228i	$-0.155828\pi$
$863$	3.86184e7			1.76509			0.882545	+	0.470228i	$0.155828\pi$
$864$	−2.16128e7	−	3.78900e6i	−0.984978	−	0.172679i
$865$	−5.56431e6			−0.252855
$866$	−9.10928e6	+	2.10906e7i	−0.412752	+	0.955638i
$867$	1.56752e7	−	1.54222e6i	0.708215	−	0.0696783i
$868$	9.97154e6	+	1.05890e7i	0.449224	+	0.477043i
$869$			6.93664e6i			0.311602i
$870$	1.59932e6	−	4.99894e6i	0.0716370	−	0.223913i
$871$			1.84578e7i			0.824392i
$872$	−2.58734e7	+	9.37604e6i	−1.15229	+	0.417569i
$873$	365798.	−	72682.2i	0.0162445	−	0.00322769i
$874$	−1.64641e7	−	7.11105e6i	−0.729053	−	0.314887i
$875$	−1.33217e6			−0.0588220
$876$	2.04494e7	+	1.78400e7i	0.900369	+	0.785477i
$877$	−9.70480e6			−0.426077			−0.213038	−	0.977044i	$-0.568336\pi$
$877$	−9.70480e6			−0.426077			−0.213038	+	0.977044i	$0.568336\pi$
$878$	−2.46637e7	−	1.06526e7i	−1.07975	−	0.466356i
$879$	−2.17542e6	−	2.21111e7i	−0.0949667	−	0.965248i
$880$	6.28661e6	+	377956.i	0.273659	+	0.0164526i
$881$		−	1.93812e7i		−	0.841282i	−0.907227	−	0.420641i	$-0.861805\pi$
$881$		−	1.93812e7i		−	0.841282i	0.907227	−	0.420641i	$-0.138195\pi$
$882$	−2.75325e6	+	1.28186e7i	−0.119172	+	0.554842i
$883$			2.18123e7i			0.941455i	0.882279	+	0.470727i	$0.156008\pi$
$883$			2.18123e7i			0.941455i	−0.882279	+	0.470727i	$0.843992\pi$
$884$	−1.40251e7	+	1.32072e7i	−0.603637	+	0.568436i
$885$	−356758.	−	3.62611e6i	−0.0153114	−	0.155626i
$886$	1.74571e7	−	4.04181e7i	0.747115	−	1.72978i
$887$	4.80070e6			0.204878			0.102439	−	0.994739i	$-0.467335\pi$
$887$	4.80070e6			0.204878			0.102439	+	0.994739i	$0.467335\pi$
$888$	−3.51142e7	+	1.67777e7i	−1.49435	+	0.714003i
$889$	−2.84985e7			−1.20939
$890$	3.76842e6	−	8.72496e6i	0.159472	−	0.369223i
$891$	1.34234e7	−	5.55359e6i	0.566460	−	0.234358i
$892$	−2.25555e7	+	2.12402e7i	−0.949163	+	0.893813i
$893$			1.06568e7i			0.447194i
$894$	391750.	+	125333.i	0.0163932	+	0.00524472i
$895$			1.20604e6i			0.0503272i
$896$	−1.51548e7	+	4.48302e6i	−0.630636	+	0.186552i
$897$	2.24786e7	−	2.21158e6i	0.932800	−	0.0917742i
$898$	−2.93754e7	−	1.26876e7i	−1.21561	−	0.525036i
$899$	1.26925e7			0.523779
$900$	3.95748e6	+	2.82099e6i	0.162859	+	0.116090i
$901$	1.15240e7			0.472922
$902$	2.46047e7	+	1.06271e7i	1.00694	+	0.434909i
$903$	1.67858e7	−	1.65149e6i	0.685052	−	0.0673994i
$904$	2.96573e6	+	8.18398e6i	0.120701	+	0.333076i
$905$		−	1.38189e7i		−	0.560859i
$906$	−3.98021e7	−	1.27339e7i	−1.61096	−	0.515398i
$907$		−	1.57716e7i		−	0.636588i	−0.947992	−	0.318294i	$-0.896890\pi$
$907$		−	1.57716e7i		−	0.636588i	0.947992	−	0.318294i	$-0.103110\pi$
$908$	1.73963e7	+	1.84735e7i	0.700231	+	0.743594i
$909$	6.95471e6	+	3.50019e7i	0.279170	+	1.40502i
$910$	−4.49811e6	+	1.04144e7i	−0.180064	+	0.416899i
$911$	3.52751e6			0.140823			0.0704113	−	0.997518i	$-0.477569\pi$
$911$	3.52751e6			0.140823			0.0704113	+	0.997518i	$0.477569\pi$
$912$	−3.28366e7	+	1.24910e6i	−1.30729	+	0.0497292i
$913$	−2.89873e7			−1.15088
$914$	1.17523e7	−	2.72100e7i	0.465327	−	1.07736i
$915$	−178896.	−	1.81832e6i	−0.00706397	−	0.0717987i
$916$	−7.65876e6	−	8.13304e6i	−0.301592	−	0.320268i
$917$			3.05242e7i			1.19873i
$918$	1.36231e7	+	1.55290e6i	0.533542	+	0.0608187i
$919$			1.78356e7i			0.696624i	0.937379	+	0.348312i	$0.113245\pi$
$919$			1.78356e7i			0.696624i	−0.937379	+	0.348312i	$0.886755\pi$
$920$	−2.37452e6	−	6.55252e6i	−0.0924923	−	0.255234i
$921$	673756.	+	6.84810e6i	0.0261730	+	0.266024i
$922$	2.19392e7	+	9.47581e6i	0.849949	+	0.367104i
$923$	−4.34181e7			−1.67751
$924$	6.87824e6	−	7.88433e6i	0.265032	−	0.303798i
$925$	8.61959e6			0.331232
$926$	−3.04963e7	−	1.31717e7i	−1.16874	−	0.504795i
$927$	−6.65457e6	−	3.34914e7i	−0.254344	−	1.28007i
$928$	−6.21819e6	+	1.23096e7i	−0.237025	+	0.469217i
$929$		−	4.15329e6i		−	0.157889i	−0.996879	−	0.0789447i	$-0.974845\pi$
$929$		−	4.15329e6i		−	0.157889i	0.996879	−	0.0789447i	$-0.0251551\pi$
$930$	−3.58130e6	+	1.11939e7i	−0.135779	+	0.424400i
$931$			1.96346e7i			0.742417i
$932$	−1.94527e7	+	1.83183e7i	−0.733567	+	0.690789i
$933$	553510.	−	54457.5i	0.0208171	−	0.00204811i
$934$	1.08829e7	−	2.51969e7i	0.408203	−	0.945105i
$935$	−3.93545e6			−0.147220
$936$	3.54159e7	−	2.14129e7i	1.32132	−	0.798886i
$937$	−3.81453e6			−0.141936			−0.0709679	−	0.997479i	$-0.522609\pi$
$937$	−3.81453e6			−0.141936			−0.0709679	+	0.997479i	$0.522609\pi$
$938$	3.75168e6	−	8.68619e6i	0.139225	−	0.322346i
$939$	1.99036e7	−	1.95823e6i	0.736661	−	0.0724770i
$940$	−3.01499e6	+	2.83917e6i	−0.111293	+	0.104803i
$941$		−	4.84987e7i		−	1.78549i	−0.450566	−	0.892743i	$-0.648778\pi$
$941$		−	4.84987e7i		−	1.78549i	0.450566	−	0.892743i	$-0.351222\pi$
$942$	5.03828e6	−	1.57480e7i	0.184993	−	0.578226i
$943$		−	2.96594e7i		−	1.08613i
$944$	−574554.	+	9.55667e6i	−0.0209846	+	0.349041i
$945$	7.72708e6	−	2.34134e6i	0.281473	−	0.0852873i
$946$	1.62138e7	+	7.00294e6i	0.589056	+	0.254421i
$947$	2.05097e7			0.743164			0.371582	−	0.928400i	$-0.378816\pi$
$947$	2.05097e7			0.743164			0.371582	+	0.928400i	$0.378816\pi$
$948$	9.24627e6	−	1.05987e7i	0.334153	−	0.383030i
$949$	−5.11845e7			−1.84490
$950$	6.68161e6	+	2.88587e6i	0.240200	+	0.103745i
$951$	−2.05157e6	−	2.08523e7i	−0.0735590	−	0.747658i
$952$	9.28467e6	−	3.36460e6i	0.332027	−	0.120321i
$953$			7.22870e6i			0.257827i	0.991656	+	0.128913i	$0.0411489\pi$
$953$			7.22870e6i			0.257827i	−0.991656	+	0.128913i	$0.958851\pi$
$954$	−2.42045e7	−	5.19876e6i	−0.861042	−	0.184939i
$955$			1.04826e6i			0.0371928i
$956$	2.07838e7	+	2.20708e7i	0.735494	+	0.781041i
$957$	−893974.	−	9.08641e6i	−0.0315533	−	0.320710i
$958$	1.22643e7	−	2.83954e7i	0.431748	−	0.999619i
$959$	8.26211e6			0.290098
$960$	−9.10172e6	−	8.95730e6i	−0.318747	−	0.313689i
$961$	207312.			0.00724129
$962$	2.91043e7	−	6.73846e7i	1.01396	−	2.34759i
$963$	−2.52441e7	+	5.01587e6i	−0.877190	+	0.174293i
$964$	−7.14510e6	−	7.58757e6i	−0.247637	−	0.262972i
$965$			2.16140e6i			0.0747167i
$966$	−1.10279e7	−	3.52818e6i	−0.380234	−	0.121649i
$967$			3.40168e7i			1.16984i	0.811091	+	0.584920i	$0.198874\pi$
$967$			3.40168e7i			1.16984i	−0.811091	+	0.584920i	$0.801126\pi$
$968$	−1.71088e7	+	6.19992e6i	−0.586855	+	0.212666i
$969$	2.04350e7	−	2.01051e6i	0.699142	−	0.0687856i
$970$	199258.	+	86062.0i	0.00679964	+	0.00293685i
$971$	−2.53035e7			−0.861258			−0.430629	−	0.902529i	$-0.641708\pi$
$971$	−2.53035e7			−0.861258			−0.430629	+	0.902529i	$0.641708\pi$
$972$	−2.79128e7	−	9.40738e6i	−0.947628	−	0.319377i
$973$	1.08177e7			0.366314
$974$	2.16043e7	+	9.33117e6i	0.729698	+	0.315166i
$975$	−9.12248e6	+	897523.i	−0.307328	+	0.0302367i
$976$	−288110.	+	4.79219e6i	−0.00968132	+	0.161031i
$977$		−	8.29785e6i		−	0.278118i	−0.990284	−	0.139059i	$-0.955592\pi$
$977$		−	8.29785e6i		−	0.278118i	0.990284	−	0.139059i	$-0.0444078\pi$
$978$	3.20749e7	+	1.02618e7i	1.07230	+	0.343064i
$979$		−	1.65330e7i		−	0.551308i
$980$	−5.55500e6	+	5.23106e6i	−0.184765	+	0.173990i
$981$	−3.62342e7	+	7.19956e6i	−1.20212	+	0.238855i
$982$	−1.43030e6	+	3.31154e6i	−0.0473312	+	0.109585i
$983$	2.89037e7			0.954046			0.477023	−	0.878891i	$-0.341716\pi$
$983$	2.89037e7			0.954046			0.477023	+	0.878891i	$0.341716\pi$
$984$	−2.34289e7	−	4.90346e7i	−0.771372	−	1.61441i
$985$	−1.38115e7			−0.453578
$986$	3.41699e6	−	7.91129e6i	0.111931	−	0.259152i
$987$	673658.	+	6.84711e6i	0.0220114	+	0.223725i
$988$	4.51213e7	−	4.24900e7i	1.47058	−	1.38482i
$989$		−	1.95447e7i		−	0.635386i
$990$	8.26586e6	+	1.77538e6i	0.268040	+	0.0575711i
$991$		−	3.67021e6i		−	0.118715i	−0.998237	−	0.0593576i	$-0.981095\pi$
$991$		−	3.67021e6i		−	0.118715i	0.998237	−	0.0593576i	$-0.0189052\pi$
$992$	1.39242e7	−	2.75644e7i	0.449252	−	0.889343i
$993$	−4.57759e6	−	4.65270e7i	−0.147321	−	1.49738i
$994$	2.04325e7	+	8.82505e6i	0.655926	+	0.283303i
$995$	3.16821e6			0.101451
$996$	4.42906e7	+	3.86389e7i	1.41470	+	1.23417i
$997$	−3.56516e7			−1.13590			−0.567951	−	0.823062i	$-0.692264\pi$
$997$	−3.56516e7			−1.13590			−0.567951	+	0.823062i	$0.692264\pi$
$998$	−1.05588e7	−	4.56047e6i	−0.335573	−	0.144938i
$999$	−4.99968e7	+	1.51492e7i	−1.58500	+	0.480261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.6.e.a.11.16	yes	40
3.2	odd	2	inner	60.6.e.a.11.25	yes	40
4.3	odd	2	inner	60.6.e.a.11.26	yes	40
12.11	even	2	inner	60.6.e.a.11.15	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.6.e.a.11.15	✓	40	12.11	even	2	inner
60.6.e.a.11.16	yes	40	1.1	even	1	trivial
60.6.e.a.11.25	yes	40	3.2	odd	2	inner
60.6.e.a.11.26	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)

\(f(q)\)	\(=\)	\(q+(-2.24299 + 5.19317i) q^{2} +(15.5136 - 1.52631i) q^{3} +(-21.9379 - 23.2965i) q^{4} -25.0000i q^{5} +(-26.8704 + 83.9880i) q^{6} +85.2589i q^{7} +(170.189 - 61.6735i) q^{8} +(238.341 - 47.3571i) q^{9} +O(q^{10})\)	\(q+(-2.24299 + 5.19317i) q^{2} +(15.5136 - 1.52631i) q^{3} +(-21.9379 - 23.2965i) q^{4} -25.0000i q^{5} +(-26.8704 + 83.9880i) q^{6} +85.2589i q^{7} +(170.189 - 61.6735i) q^{8} +(238.341 - 47.3571i) q^{9} +(129.829 + 56.0749i) q^{10} +246.014 q^{11} +(-375.893 - 327.927i) q^{12} +940.853 q^{13} +(-442.764 - 191.235i) q^{14} +(-38.1578 - 387.839i) q^{15} +(-61.4527 + 1022.15i) q^{16} -639.874i q^{17} +(-288.664 + 1343.96i) q^{18} +2058.59i q^{19} +(-582.412 + 548.449i) q^{20} +(130.132 + 1322.67i) q^{21} +(-551.809 + 1277.59i) q^{22} +1540.06 q^{23} +(2546.11 - 1216.54i) q^{24} -625.000 q^{25} +(-2110.33 + 4886.01i) q^{26} +(3625.23 - 1098.46i) q^{27} +(1986.23 - 1870.41i) q^{28} -2380.79i q^{29} +(2099.70 + 671.760i) q^{30} +5331.21i q^{31} +(-5170.38 - 2611.82i) q^{32} +(3816.55 - 375.495i) q^{33} +(3322.97 + 1435.23i) q^{34} +2131.47 q^{35} +(-6331.96 - 4513.58i) q^{36} -13791.3 q^{37} +(-10690.6 - 4617.40i) q^{38} +(14596.0 - 1436.04i) q^{39} +(-1541.84 - 4254.73i) q^{40} -19258.7i q^{41} +(-7160.73 - 2290.94i) q^{42} -12690.9i q^{43} +(-5397.05 - 5731.27i) q^{44} +(-1183.93 - 5958.52i) q^{45} +(-3454.34 + 7997.77i) q^{46} +5176.73 q^{47} +(606.778 + 15951.0i) q^{48} +9537.91 q^{49} +(1401.87 - 3245.73i) q^{50} +(-976.648 - 9926.72i) q^{51} +(-20640.4 - 21918.6i) q^{52} +18009.7i q^{53} +(-2426.89 + 21290.3i) q^{54} -6150.36i q^{55} +(5258.22 + 14510.2i) q^{56} +(3142.05 + 31936.0i) q^{57} +(12363.8 + 5340.10i) q^{58} +9349.54 q^{59} +(-8198.18 + 9397.33i) q^{60} +4688.33 q^{61} +(-27685.9 - 11957.9i) q^{62} +(4037.62 + 20320.7i) q^{63} +(25160.8 - 20992.3i) q^{64} -23521.3i q^{65} +(-6610.51 + 20662.2i) q^{66} +19618.1i q^{67} +(-14906.8 + 14037.5i) q^{68} +(23891.7 - 2350.61i) q^{69} +(-4780.88 + 11069.1i) q^{70} -46147.6 q^{71} +(37642.3 - 22759.0i) q^{72} -54402.2 q^{73} +(30933.9 - 71620.8i) q^{74} +(-9695.97 + 953.946i) q^{75} +(47957.8 - 45161.2i) q^{76} +20974.9i q^{77} +(-25281.1 + 79020.3i) q^{78} +28196.1i q^{79} +(25553.9 + 1536.32i) q^{80} +(54563.6 - 22574.3i) q^{81} +(100013. + 43197.1i) q^{82} -117828. q^{83} +(27958.7 - 32048.3i) q^{84} -15996.8 q^{85} +(65905.9 + 28465.6i) q^{86} +(-3633.83 - 36934.5i) q^{87} +(41869.0 - 15172.6i) q^{88} -67203.4i q^{89} +(33599.1 + 7216.59i) q^{90} +80216.1i q^{91} +(-33785.7 - 35877.9i) q^{92} +(8137.10 + 82706.1i) q^{93} +(-11611.4 + 26883.6i) q^{94} +51464.6 q^{95} +(-84197.4 - 32627.0i) q^{96} +1534.77 q^{97} +(-21393.5 + 49532.0i) q^{98} +(58635.2 - 11650.5i) 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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