LMFDB - Embedded newform 60.6.e.a.11.10

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			11.10
Character	$\chi$	$=$	60.11
Dual form			60.6.e.a.11.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.48243 + 3.45077i) q^{2} +(-10.3661 + 11.6423i) q^{3} +(8.18436 - 30.9357i) q^{4} +25.0000i q^{5} +(6.29061 - 87.9570i) q^{6} -180.345i q^{7} +(70.0661 + 166.909i) q^{8} +(-28.0862 - 241.371i) q^{9} +O(q^{10})$	\(q+(-4.48243 + 3.45077i) q^{2} +(-10.3661 + 11.6423i) q^{3} +(8.18436 - 30.9357i) q^{4} +25.0000i q^{5} +(6.29061 - 87.9570i) q^{6} -180.345i q^{7} +(70.0661 + 166.909i) q^{8} +(-28.0862 - 241.371i) q^{9} +(-86.2693 - 112.061i) q^{10} -274.021 q^{11} +(275.322 + 415.968i) q^{12} +983.273 q^{13} +(622.331 + 808.386i) q^{14} +(-291.057 - 259.154i) q^{15} +(-890.032 - 506.378i) q^{16} +225.673i q^{17} +(958.812 + 985.012i) q^{18} +2117.01i q^{19} +(773.392 + 204.609i) q^{20} +(2099.63 + 1869.49i) q^{21} +(1228.28 - 945.585i) q^{22} +3888.71 q^{23} +(-2669.52 - 914.476i) q^{24} -625.000 q^{25} +(-4407.45 + 3393.05i) q^{26} +(3101.26 + 2175.10i) q^{27} +(-5579.11 - 1476.01i) q^{28} -2819.30i q^{29} +(2198.92 + 157.265i) q^{30} -4999.75i q^{31} +(5736.90 - 801.494i) q^{32} +(2840.55 - 3190.24i) q^{33} +(-778.747 - 1011.57i) q^{34} +4508.63 q^{35} +(-7696.86 - 1106.61i) q^{36} +6760.11 q^{37} +(-7305.33 - 9489.36i) q^{38} +(-10192.7 + 11447.6i) q^{39} +(-4172.73 + 1751.65i) q^{40} -14715.6i q^{41} +(-15862.6 - 1134.48i) q^{42} +8630.48i q^{43} +(-2242.69 + 8477.04i) q^{44} +(6034.29 - 702.155i) q^{45} +(-17430.9 + 13419.0i) q^{46} +5286.62 q^{47} +(15121.6 - 5112.84i) q^{48} -15717.5 q^{49} +(2801.52 - 2156.73i) q^{50} +(-2627.36 - 2339.36i) q^{51} +(8047.46 - 30418.2i) q^{52} -14138.4i q^{53} +(-21407.0 + 952.004i) q^{54} -6850.54i q^{55} +(30101.3 - 12636.1i) q^{56} +(-24646.9 - 21945.3i) q^{57} +(9728.75 + 12637.3i) q^{58} +22909.5 q^{59} +(-10399.2 + 6883.05i) q^{60} +50668.1 q^{61} +(17253.0 + 22411.0i) q^{62} +(-43530.2 + 5065.22i) q^{63} +(-22949.5 + 23389.4i) q^{64} +24581.8i q^{65} +(-1723.76 + 24102.1i) q^{66} -642.717i q^{67} +(6981.36 + 1846.99i) q^{68} +(-40310.9 + 45273.5i) q^{69} +(-20209.6 + 15558.3i) q^{70} +38530.9 q^{71} +(38319.3 - 21599.8i) q^{72} +42005.1 q^{73} +(-30301.7 + 23327.6i) q^{74} +(6478.84 - 7276.44i) q^{75} +(65491.2 + 17326.4i) q^{76} +49418.5i q^{77} +(6185.38 - 86485.7i) q^{78} -19047.8i q^{79} +(12659.4 - 22250.8i) q^{80} +(-57471.3 + 13558.4i) q^{81} +(50780.2 + 65961.7i) q^{82} -48036.9 q^{83} +(75018.0 - 49653.1i) q^{84} -5641.84 q^{85} +(-29781.8 - 38685.5i) q^{86} +(32823.1 + 29225.2i) q^{87} +(-19199.6 - 45736.8i) q^{88} +63513.7i q^{89} +(-24625.3 + 23970.3i) q^{90} -177329. i q^{91} +(31826.6 - 120300. i) q^{92} +(58208.5 + 51828.1i) q^{93} +(-23696.9 + 18242.9i) q^{94} -52925.3 q^{95} +(-50138.3 + 75099.1i) q^{96} -47892.4 q^{97} +(70452.4 - 54237.3i) q^{98} +(7696.22 + 66140.9i) 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 $

$2$	−4.48243	+	3.45077i	−0.792389	+	0.610016i
$2$	−4.48243	+	3.45077i	−0.792389	+	0.610016i
$3$	−10.3661	+	11.6423i	−0.664988	+	0.746854i
$3$	−10.3661	+	11.6423i	−0.664988	+	0.746854i
$4$	8.18436	−	30.9357i	0.255761	−	0.966740i
$5$			25.0000i			0.447214i
$5$			25.0000i			0.447214i
$6$	6.29061	−	87.9570i	0.0713370	−	0.997452i
$7$		−	180.345i		−	1.39110i	−0.718475	−	0.695552i	$-0.755160\pi$
$7$		−	180.345i		−	1.39110i	0.718475	−	0.695552i	$-0.244840\pi$
$8$	70.0661	+	166.909i	0.387064	+	0.922053i
$9$	−28.0862	−	241.371i	−0.115581	−	0.993298i
$10$	−86.2693	−	112.061i	−0.272807	−	0.354367i
$11$	−274.021			−0.682815			−0.341407	−	0.939915i	$-0.610904\pi$
$11$	−274.021			−0.682815			−0.341407	+	0.939915i	$0.610904\pi$
$12$	275.322	+	415.968i	0.551935	+	0.833887i
$13$	983.273			1.61367			0.806836	−	0.590775i	$-0.201178\pi$
$13$	983.273			1.61367			0.806836	+	0.590775i	$0.201178\pi$
$14$	622.331	+	808.386i	0.848596	+	1.10230i
$15$	−291.057	−	259.154i	−0.334003	−	0.297392i
$16$	−890.032	−	506.378i	−0.869172	−	0.494510i
$17$			225.673i			0.189391i	0.995506	+	0.0946953i	$0.0301877\pi$
$17$			225.673i			0.189391i	−0.995506	+	0.0946953i	$0.969812\pi$
$18$	958.812	+	985.012i	0.697513	+	0.716572i
$19$			2117.01i			1.34536i	0.739932	+	0.672682i	$0.234858\pi$
$19$			2117.01i			1.34536i	−0.739932	+	0.672682i	$0.765142\pi$
$20$	773.392	+	204.609i	0.432339	+	0.114380i
$21$	2099.63	+	1869.49i	1.03895	+	0.925069i
$22$	1228.28	−	945.585i	0.541055	−	0.416528i
$23$	3888.71			1.53280			0.766400	−	0.642364i	$-0.222046\pi$
$23$	3888.71			1.53280			0.766400	+	0.642364i	$0.222046\pi$
$24$	−2669.52	−	914.476i	−0.946032	−	0.324074i
$25$	−625.000			−0.200000
$26$	−4407.45	+	3393.05i	−1.27866	+	0.984366i
$27$	3101.26	+	2175.10i	0.818708	+	0.574209i
$28$	−5579.11	−	1476.01i	−1.34484	−	0.355791i
$29$		−	2819.30i		−	0.622510i	−0.950327	−	0.311255i	$-0.899251\pi$
$29$		−	2819.30i		−	0.622510i	0.950327	−	0.311255i	$-0.100749\pi$
$30$	2198.92	+	157.265i	0.446074	+	0.0319029i
$31$		−	4999.75i		−	0.934424i	−0.884145	−	0.467212i	$-0.845259\pi$
$31$		−	4999.75i		−	0.934424i	0.884145	−	0.467212i	$-0.154741\pi$
$32$	5736.90	−	801.494i	0.990381	−	0.138365i
$33$	2840.55	−	3190.24i	0.454064	−	0.509963i
$34$	−778.747	−	1011.57i	−0.115531	−	0.150071i
$35$	4508.63			0.622121
$36$	−7696.86	−	1106.61i	−0.989822	−	0.142310i
$37$	6760.11			0.811800			0.405900	−	0.913917i	$-0.366958\pi$
$37$	6760.11			0.811800			0.405900	+	0.913917i	$0.366958\pi$
$38$	−7305.33	−	9489.36i	−0.820693	−	1.06605i
$39$	−10192.7	+	11447.6i	−1.07307	+	1.20518i
$40$	−4172.73	+	1751.65i	−0.412355	+	0.173100i
$41$		−	14715.6i		−	1.36716i	−0.729877	−	0.683579i	$-0.760423\pi$
$41$		−	14715.6i		−	1.36716i	0.729877	−	0.683579i	$-0.239577\pi$
$42$	−15862.6	−	1134.48i	−1.38756	−	0.0992372i
$43$			8630.48i			0.711810i	0.934522	+	0.355905i	$0.115827\pi$
$43$			8630.48i			0.711810i	−0.934522	+	0.355905i	$0.884173\pi$
$44$	−2242.69	+	8477.04i	−0.174638	+	0.660104i
$45$	6034.29	−	702.155i	0.444216	−	0.0516894i
$46$	−17430.9	+	13419.0i	−1.21457	+	0.935032i
$47$	5286.62			0.349087			0.174543	−	0.984650i	$-0.444155\pi$
$47$	5286.62			0.349087			0.174543	+	0.984650i	$0.444155\pi$
$48$	15121.6	−	5112.84i	0.947316	−	0.320301i
$49$	−15717.5			−0.935173
$50$	2801.52	−	2156.73i	0.158478	−	0.122003i
$51$	−2627.36	−	2339.36i	−0.141447	−	0.125942i
$52$	8047.46	−	30418.2i	0.412715	−	1.56000i
$53$		−	14138.4i		−	0.691371i	−0.938350	−	0.345686i	$-0.887646\pi$
$53$		−	14138.4i		−	0.691371i	0.938350	−	0.345686i	$-0.112354\pi$
$54$	−21407.0	+	952.004i	−0.999013	+	0.0444278i
$55$		−	6850.54i		−	0.305364i
$56$	30101.3	−	12636.1i	1.28267	−	0.538447i
$57$	−24646.9	−	21945.3i	−1.00479	−	0.894651i
$58$	9728.75	+	12637.3i	0.379741	+	0.493270i
$59$	22909.5			0.856812			0.428406	−	0.903586i	$-0.359075\pi$
$59$	22909.5			0.856812			0.428406	+	0.903586i	$0.359075\pi$
$60$	−10399.2	+	6883.05i	−0.372926	+	0.246833i
$61$	50668.1			1.74345			0.871726	−	0.489994i	$-0.163001\pi$
$61$	50668.1			1.74345			0.871726	+	0.489994i	$0.163001\pi$
$62$	17253.0	+	22411.0i	0.570013	+	0.740427i
$63$	−43530.2	+	5065.22i	−1.38178	+	0.160785i
$64$	−22949.5	+	23389.4i	−0.700363	+	0.713787i
$65$			24581.8i			0.721656i
$66$	−1723.76	+	24102.1i	−0.0487099	+	0.681075i
$67$		−	642.717i		−	0.0174917i	−0.999962	−	0.00874586i	$-0.997216\pi$
$67$		−	642.717i		−	0.0174917i	0.999962	−	0.00874586i	$-0.00278393\pi$
$68$	6981.36	+	1846.99i	0.183091	+	0.0484388i
$69$	−40310.9	+	45273.5i	−1.01929	+	1.14478i
$70$	−20209.6	+	15558.3i	−0.492962	+	0.379504i
$71$	38530.9			0.907117			0.453559	−	0.891227i	$-0.350154\pi$
$71$	38530.9			0.907117			0.453559	+	0.891227i	$0.350154\pi$
$72$	38319.3	−	21599.8i	0.871136	−	0.491042i
$73$	42005.1			0.922561			0.461280	−	0.887254i	$-0.347390\pi$
$73$	42005.1			0.922561			0.461280	+	0.887254i	$0.347390\pi$
$74$	−30301.7	+	23327.6i	−0.643262	+	0.495211i
$75$	6478.84	−	7276.44i	0.132998	−	0.149371i
$76$	65491.2	+	17326.4i	1.30062	+	0.344092i
$77$			49418.5i			0.949867i
$78$	6185.38	−	86485.7i	0.115115	−	1.60956i
$79$		−	19047.8i		−	0.343381i	−0.985151	−	0.171691i	$-0.945077\pi$
$79$		−	19047.8i		−	0.343381i	0.985151	−	0.171691i	$-0.0549229\pi$
$80$	12659.4	−	22250.8i	0.221151	−	0.388706i
$81$	−57471.3	+	13558.4i	−0.973282	+	0.229613i
$82$	50780.2	+	65961.7i	0.833988	+	1.08332i
$83$	−48036.9			−0.765385			−0.382692	−	0.923876i	$-0.625003\pi$
$83$	−48036.9			−0.765385			−0.382692	+	0.923876i	$0.625003\pi$
$84$	75018.0	−	49653.1i	1.16002	−	0.767800i
$85$	−5641.84			−0.0846980
$86$	−29781.8	−	38685.5i	−0.434215	−	0.564030i
$87$	32823.1	+	29225.2i	0.464924	+	0.413962i
$88$	−19199.6	−	45736.8i	−0.264293	−	0.629591i
$89$			63513.7i			0.849948i	0.905205	+	0.424974i	$0.139717\pi$
$89$			63513.7i			0.849948i	−0.905205	+	0.424974i	$0.860283\pi$
$90$	−24625.3	+	23970.3i	−0.320461	+	0.311937i
$91$		−	177329.i		−	2.24479i
$92$	31826.6	−	120300.i	0.392031	−	1.48182i
$93$	58208.5	+	51828.1i	0.697878	+	0.621381i
$94$	−23696.9	+	18242.9i	−0.276612	+	0.212948i
$95$	−52925.3			−0.601665
$96$	−50138.3	+	75099.1i	−0.555254	+	0.831681i
$97$	−47892.4			−0.516817			−0.258409	−	0.966036i	$-0.583198\pi$
$97$	−47892.4			−0.516817			−0.258409	+	0.966036i	$0.583198\pi$
$98$	70452.4	−	54237.3i	0.741021	−	0.570470i
$99$	7696.22	+	66140.9i	0.0789205	+	0.678238i
$100$	−5115.23	+	19334.8i	−0.0511523	+	0.193348i
$101$		−	123131.i		−	1.20106i	−0.799603	−	0.600529i	$-0.794957\pi$
$101$		−	123131.i		−	1.20106i	0.799603	−	0.600529i	$-0.205043\pi$
$102$	19849.6	+	1419.62i	0.188908	+	0.0135105i
$103$		−	88789.9i		−	0.824652i	−0.911036	−	0.412326i	$-0.864717\pi$
$103$		−	88789.9i		−	0.824652i	0.911036	−	0.412326i	$-0.135283\pi$
$104$	68894.1	+	164117.i	0.624595	+	1.48789i
$105$	−46737.1	+	52490.9i	−0.413703	+	0.464633i
$106$	48788.5	+	63374.5i	0.421747	+	0.547835i
$107$	−143700.			−1.21339			−0.606693	−	0.794936i	$-0.707504\pi$
$107$	−143700.			−1.21339			−0.606693	+	0.794936i	$0.707504\pi$
$108$	92670.1	−	78137.9i	0.764505	−	0.644618i
$109$	−121207.			−0.977150			−0.488575	−	0.872522i	$-0.662483\pi$
$109$	−121207.			−0.977150			−0.488575	+	0.872522i	$0.662483\pi$
$110$	23639.6	+	30707.1i	0.186277	+	0.241967i
$111$	−70076.2	+	78703.2i	−0.539838	+	0.606296i
$112$	−91322.9	+	160513.i	−0.687915	+	1.20911i
$113$			22287.1i			0.164194i	0.996624	+	0.0820971i	$0.0261618\pi$
$113$			22287.1i			0.164194i	−0.996624	+	0.0820971i	$0.973838\pi$
$114$	186206.	+	13317.3i	1.34194	+	0.0959741i
$115$			97217.7i			0.685489i
$116$	−87216.9	−	23074.2i	−0.601805	−	0.159214i
$117$	−27616.4	−	237334.i	−0.186510	−	1.60286i
$118$	−102690.	+	79055.5i	−0.678929	+	0.522669i
$119$	40699.2			0.263462
$120$	22861.9	−	66738.1i	0.144930	−	0.423078i
$121$	−85963.2			−0.533764
$122$	−227116.	+	174844.i	−1.38149	+	1.06353i
$123$	171323.	+	152544.i	1.02107	+	0.909144i
$124$	−154671.	−	40919.8i	−0.903345	−	0.238989i
$125$		−	15625.0i		−	0.0894427i
$126$	177642.	−	172917.i	0.996827	−	0.970313i
$127$		−	47041.1i		−	0.258802i	−0.991592	−	0.129401i	$-0.958695\pi$
$127$		−	47041.1i		−	0.258802i	0.991592	−	0.129401i	$-0.0413055\pi$
$128$	22158.1	−	184035.i	0.119539	−	0.992830i
$129$	−100479.	−	89464.8i	−0.531618	−	0.473345i
$130$	−84826.2	−	110186.i	−0.440222	−	0.571833i
$131$	116078.			0.590976			0.295488	−	0.955346i	$-0.404518\pi$
$131$	116078.			0.590976			0.295488	+	0.955346i	$0.404518\pi$
$132$	−75444.2	−	113984.i	−0.376869	−	0.569390i
$133$	381794.			1.87154
$134$	2217.87	+	2880.93i	0.0106702	+	0.0138603i
$135$	−54377.6	+	77531.6i	−0.256794	+	0.366138i
$136$	−37667.0	+	15812.1i	−0.174628	+	0.0733063i
$137$			36890.3i			0.167923i	0.996469	+	0.0839616i	$0.0267573\pi$
$137$			36890.3i			0.167923i	−0.996469	+	0.0839616i	$0.973243\pi$
$138$	24462.3	−	342039.i	0.109345	−	1.52890i
$139$		−	300891.i		−	1.32090i	−0.750868	−	0.660452i	$-0.770364\pi$
$139$		−	300891.i		−	1.32090i	0.750868	−	0.660452i	$-0.229636\pi$
$140$	36900.3	−	139478.i	0.159115	−	0.601429i
$141$	−54801.8	+	61548.4i	−0.232138	+	0.260717i
$142$	−172712.	+	132961.i	−0.718790	+	0.553356i
$143$	−269438.			−1.10184
$144$	−97227.5	+	229051.i	−0.390735	+	0.920503i
$145$	70482.5			0.278395
$146$	−188285.	+	144950.i	−0.731027	+	0.562777i
$147$	162929.	−	182987.i	0.621879	−	0.698437i
$148$	55327.2	−	209128.i	0.207627	−	0.784800i
$149$			214071.i			0.789937i	0.918695	+	0.394968i	$0.129244\pi$
$149$			214071.i			0.789937i	−0.918695	+	0.394968i	$0.870756\pi$
$150$	−3931.63	+	54973.1i	−0.0142674	+	0.199490i
$151$			296235.i			1.05729i	0.848844	+	0.528644i	$0.177299\pi$
$151$			296235.i			1.05729i	−0.848844	+	0.528644i	$0.822701\pi$
$152$	−353349.	+	148331.i	−1.24050	+	0.520742i
$153$	54471.1	−	6338.31i	0.188121	−	0.0218900i
$154$	−170532.	−	221515.i	−0.579434	−	0.752664i
$155$	124994.			0.417887
$156$	270717.	+	409010.i	0.890643	+	1.34562i
$157$	409202.			1.32492			0.662458	−	0.749099i	$-0.269513\pi$
$157$	409202.			1.32492			0.662458	+	0.749099i	$0.269513\pi$
$158$	65729.5	+	85380.3i	0.209468	+	0.272091i
$159$	164604.	+	146561.i	0.516353	+	0.459754i
$160$	20037.4	+	143423.i	0.0618786	+	0.442912i
$161$		−	701310.i		−	2.13229i
$162$	210824.	−	259095.i	0.631151	−	0.775660i
$163$			159919.i			0.471446i	0.971820	+	0.235723i	$0.0757459\pi$
$163$			159919.i			0.471446i	−0.971820	+	0.235723i	$0.924254\pi$
$164$	−455237.	−	120438.i	−1.32169	−	0.349666i
$165$	79756.0	+	71013.6i	0.228062	+	0.203063i
$166$	215322.	−	165764.i	0.606482	−	0.466897i
$167$	289689.			0.803786			0.401893	−	0.915687i	$-0.368352\pi$
$167$	289689.			0.803786			0.401893	+	0.915687i	$0.368352\pi$
$168$	−164922.	+	481436.i	−0.450821	+	1.31603i
$169$	595532.			1.60394
$170$	25289.1	−	19468.7i	0.0671138	−	0.0516671i
$171$	510986.	−	59458.9i	1.33635	−	0.155499i
$172$	266990.	+	70635.0i	0.688135	+	0.182053i
$173$			595658.i			1.51315i	0.653908	+	0.756574i	$0.273128\pi$
$173$			595658.i			1.51315i	−0.653908	+	0.756574i	$0.726872\pi$
$174$	−247977.	−	17735.1i	−0.620924	−	0.0444079i
$175$			112716.i			0.278221i
$176$	243888.	+	138758.i	0.593484	+	0.337658i
$177$	−237483.	+	266719.i	−0.569770	+	0.639914i
$178$	−219171.	−	284696.i	−0.518482	−	0.673490i
$179$	−30553.2			−0.0712729			−0.0356365	−	0.999365i	$-0.511346\pi$
$179$	−30553.2			−0.0712729			−0.0356365	+	0.999365i	$0.511346\pi$
$180$	27665.1	−	192421.i	0.0636432	−	0.442662i
$181$	−836174.			−1.89714			−0.948572	−	0.316561i	$-0.897472\pi$
$181$	−836174.			−1.89714			−0.948572	+	0.316561i	$0.897472\pi$
$182$	611920.	+	794863.i	1.36936	+	1.77875i
$183$	−525232.	+	589893.i	−1.15937	+	1.30210i
$184$	272466.	+	649062.i	0.593292	+	1.41332i
$185$			169003.i			0.363048i
$186$	−439763.	−	31451.5i	−0.932043	−	0.0666589i
$187$		−	61839.4i		−	0.129319i
$188$	43267.6	−	163545.i	0.0892829	−	0.337476i
$189$	392270.	−	559299.i	0.798786	−	1.13891i
$190$	237234.	−	182633.i	0.476753	−	0.367025i
$191$	53781.1			0.106671			0.0533355	−	0.998577i	$-0.483015\pi$
$191$	53781.1			0.106671			0.0533355	+	0.998577i	$0.483015\pi$
$192$	−34408.4	−	509642.i	−0.0673615	−	0.997729i
$193$	230872.			0.446147			0.223073	−	0.974802i	$-0.428391\pi$
$193$	230872.			0.446147			0.223073	+	0.974802i	$0.428391\pi$
$194$	214674.	−	165266.i	0.409520	−	0.315267i
$195$	−286189.	−	254819.i	−0.538972	−	0.479893i
$196$	−128637.	+	486230.i	−0.239181	+	0.904069i
$197$		−	583827.i		−	1.07181i	−0.844278	−	0.535906i	$-0.819970\pi$
$197$		−	583827.i		−	1.07181i	0.844278	−	0.535906i	$-0.180030\pi$
$198$	−262735.	−	269914.i	−0.476272	−	0.489286i
$199$		−	35376.3i		−	0.0633257i	−0.999499	−	0.0316628i	$-0.989920\pi$
$199$		−	35376.3i		−	0.0633257i	0.999499	−	0.0316628i	$-0.0100803\pi$
$200$	−43791.3	−	104318.i	−0.0774128	−	0.184411i
$201$	7482.70	+	6662.49i	0.0130638	+	0.0116318i
$202$	424897.	+	551926.i	0.732665	+	0.951706i
$203$	−508447.			−0.865976
$204$	−93873.0	+	62132.9i	−0.157930	+	0.104531i
$205$	367890.			0.611411
$206$	306394.	+	397995.i	0.503051	+	0.653445i
$207$	−109219.	−	938623.i	−0.177163	−	1.52253i
$208$	−875144.	−	497907.i	−1.40256	−	0.797977i
$209$		−	580107.i		−	0.918634i
$210$	28362.1	−	396566.i	0.0443802	−	0.620536i
$211$		−	756704.i		−	1.17009i	−0.811000	−	0.585046i	$-0.801076\pi$
$211$		−	756704.i		−	1.17009i	0.811000	−	0.585046i	$-0.198924\pi$
$212$	−437382.	−	115714.i	−0.668376	−	0.176826i
$213$	−399417.	+	448588.i	−0.603222	+	0.677484i
$214$	644127.	−	495877.i	0.961474	−	0.740184i
$215$	−215762.			−0.318331
$216$	−145752.	+	670031.i	−0.212559	+	0.977148i
$217$	−901681.			−1.29988
$218$	543301.	−	418257.i	0.774283	−	0.596077i
$219$	−435431.	+	489036.i	−0.613492	+	0.689018i
$220$	−211926.	−	56067.3i	−0.295208	−	0.0781003i
$221$			221899.i			0.305614i
$222$	42525.2	−	594599.i	0.0579114	−	0.809732i
$223$			545767.i			0.734929i	0.930038	+	0.367465i	$0.119774\pi$
$223$			545767.i			0.734929i	−0.930038	+	0.367465i	$0.880226\pi$
$224$	−144546.	−	1.03462e6i	−0.192480	−	1.37772i
$225$	17553.9	+	150857.i	0.0231162	+	0.198660i
$226$	−76907.7	−	99900.5i	−0.100161	−	0.130106i
$227$	1.10556e6			1.42403			0.712013	−	0.702166i	$-0.247784\pi$
$227$	1.10556e6			1.42403			0.712013	+	0.702166i	$0.247784\pi$
$228$	−880611.	+	582860.i	−1.12188	+	0.742553i
$229$	−1.47505e6			−1.85873			−0.929367	−	0.369157i	$-0.879646\pi$
$229$	−1.47505e6			−1.85873			−0.929367	+	0.369157i	$0.879646\pi$
$230$	−335476.	−	435771.i	−0.418159	−	0.543174i
$231$	−575345.	−	512279.i	−0.709412	−	0.631650i
$232$	470567.	−	197537.i	0.573987	−	0.240951i
$233$			1.25996e6i			1.52043i	0.649669	+	0.760217i	$0.274907\pi$
$233$			1.25996e6i			1.52043i	−0.649669	+	0.760217i	$0.725093\pi$
$234$	942773.	+	968535.i	1.12556	+	1.15631i
$235$			132165.i			0.156116i
$236$	187500.	−	708721.i	0.219140	−	0.828315i
$237$	221760.	+	197452.i	0.256455	+	0.228344i
$238$	−182431.	+	140443.i	−0.208765	+	0.160716i
$239$	−628669.			−0.711913			−0.355957	−	0.934502i	$-0.615845\pi$
$239$	−628669.			−0.711913			−0.355957	+	0.934502i	$0.615845\pi$
$240$	127821.	+	378040.i	0.143243	+	0.423652i
$241$	−115053.			−0.127601			−0.0638006	−	0.997963i	$-0.520322\pi$
$241$	−115053.			−0.127601			−0.0638006	+	0.997963i	$0.520322\pi$
$242$	385324.	−	296639.i	0.422949	−	0.325605i
$243$	437905.	−	809647.i	0.475734	−	0.879589i
$244$	414686.	−	1.56745e6i	0.445908	−	1.68546i
$245$		−	392936.i		−	0.418222i
$246$	−1.29434e6	−	92570.1i	−1.36367	−	0.0975289i
$247$			2.08160e6i			2.17098i
$248$	834505.	−	350313.i	0.861588	−	0.361682i
$249$	497957.	−	559260.i	0.508972	−	0.571630i
$250$	53918.3	+	70038.0i	0.0545615	+	0.0708734i
$251$	1.39319e6			1.39580			0.697902	−	0.716193i	$-0.254117\pi$
$251$	1.39319e6			1.39580			0.697902	+	0.716193i	$0.254117\pi$
$252$	−199571.	+	1.38809e6i	−0.197969	+	1.37695i
$253$	−1.06559e6			−1.04662
$254$	162328.	+	210858.i	0.157873	+	0.205072i
$255$	58484.1	−	65683.9i	0.0563232	−	0.0632570i
$256$	535739.	+	901385.i	0.510921	+	0.859628i
$257$			254260.i			0.240130i	0.992766	+	0.120065i	$0.0383102\pi$
$257$			254260.i			0.240130i	−0.992766	+	0.120065i	$0.961690\pi$
$258$	759111.	+	54291.0i	0.709996	+	0.0507783i
$259$		−	1.21915e6i		−	1.12930i
$260$	760455.	+	201187.i	0.697654	+	0.184572i
$261$	−680498.	+	79183.4i	−0.618338	+	0.0719503i
$262$	−520309.	+	400557.i	−0.468283	+	0.360505i
$263$	−227287.			−0.202621			−0.101310	−	0.994855i	$-0.532304\pi$
$263$	−227287.			−0.202621			−0.101310	+	0.994855i	$0.532304\pi$
$264$	731507.	+	250586.i	0.645964	+	0.221283i
$265$	353461.			0.309191
$266$	−1.71136e6	+	1.31748e6i	−1.48299	+	1.14167i
$267$	−739446.	−	658392.i	−0.634787	−	0.565206i
$268$	−19882.9	−	5260.23i	−0.0169099	−	0.00447371i
$269$			804326.i			0.677722i	0.940836	+	0.338861i	$0.110042\pi$
$269$			804326.i			0.677722i	−0.940836	+	0.338861i	$0.889958\pi$
$270$	−23800.1	−	535174.i	−0.0198687	−	0.446772i
$271$		−	707187.i		−	0.584939i	−0.956275	−	0.292470i	$-0.905523\pi$
$271$		−	707187.i		−	0.584939i	0.956275	−	0.292470i	$-0.0944770\pi$
$272$	114276.	−	200857.i	0.0936554	−	0.164613i
$273$	2.06451e6	+	1.83821e6i	1.67653	+	1.49276i
$274$	−127300.	−	165358.i	−0.102436	−	0.133060i
$275$	171263.			0.136563
$276$	1.07065e6	+	1.61758e6i	0.846006	+	1.27818i
$277$	−931374.			−0.729331			−0.364665	−	0.931139i	$-0.618817\pi$
$277$	−931374.			−0.729331			−0.364665	+	0.931139i	$0.618817\pi$
$278$	1.03830e6	+	1.34872e6i	0.805773	+	1.04667i
$279$	−1.20680e6	+	140424.i	−0.928161	+	0.108002i
$280$	315902.	+	752533.i	0.240801	+	0.573628i
$281$			38307.0i			0.0289409i	0.999895	+	0.0144705i	$0.00460626\pi$
$281$			38307.0i			0.0289409i	−0.999895	+	0.0144705i	$0.995394\pi$
$282$	33256.0	−	464995.i	0.0249028	−	0.348197i
$283$			45699.2i			0.0339189i	0.999856	+	0.0169595i	$0.00539862\pi$
$283$			45699.2i			0.0339189i	−0.999856	+	0.0169595i	$0.994601\pi$
$284$	315351.	−	1.19198e6i	0.232006	−	0.876946i
$285$	548631.	−	616172.i	0.400100	−	0.449356i
$286$	1.20774e6	−	929768.i	0.873086	−	0.672140i
$287$	−2.65389e6			−1.90186
$288$	−354586.	−	1.36221e6i	−0.251907	−	0.967751i
$289$	1.36893e6			0.964131
$290$	−315933.	+	243219.i	−0.220597	+	0.169825i
$291$	496459.	−	557577.i	0.343677	−	0.385987i
$292$	343785.	−	1.29946e6i	0.235955	−	0.891876i
$293$		−	2.26203e6i		−	1.53932i	−0.638451	−	0.769662i	$-0.720425\pi$
$293$		−	2.26203e6i		−	1.53932i	0.638451	−	0.769662i	$-0.279575\pi$
$294$	−98872.4	+	1.38246e6i	−0.0667124	+	0.932790i
$295$			572738.i			0.383178i
$296$	473654.	+	1.12833e6i	0.314219	+	0.748523i
$297$	−849813.	−	596025.i	−0.559026	−	0.392079i
$298$	−738710.	−	959559.i	−0.481874	−	0.625937i
$299$	3.82366e6			2.47344
$300$	−172076.	−	259980.i	−0.110387	−	0.166777i
$301$	1.55647e6			0.990202
$302$	−1.02224e6	−	1.32785e6i	−0.644962	−	0.837784i
$303$	1.43353e6	+	1.27639e6i	0.897015	+	0.798690i
$304$	1.07201e6	−	1.88421e6i	0.665295	−	1.16935i
$305$			1.26670e6i			0.779695i
$306$	−222291.	+	216378.i	−0.135712	+	0.132102i
$307$			1.23751e6i			0.749384i	0.927149	+	0.374692i	$0.122252\pi$
$307$			1.23751e6i			0.749384i	−0.927149	+	0.374692i	$0.877748\pi$
$308$	1.52879e6	+	404459.i	0.918274	+	0.242939i
$309$	1.03372e6	+	920409.i	0.615894	+	0.548384i
$310$	−560275.	+	431324.i	−0.331129	+	0.254918i
$311$	−2.58236e6			−1.51397			−0.756984	−	0.653434i	$-0.773328\pi$
$311$	−2.58236e6			−1.51397			−0.756984	+	0.653434i	$0.773328\pi$
$312$	−2.62487e6	−	899179.i	−1.52659	−	0.522950i
$313$	−1.41687e6			−0.817465			−0.408733	−	0.912654i	$-0.634029\pi$
$313$	−1.41687e6			−0.817465			−0.408733	+	0.912654i	$0.634029\pi$
$314$	−1.83422e6	+	1.41206e6i	−1.04985	+	0.808219i
$315$	−126630.	−	1.08826e6i	−0.0719054	−	0.617952i
$316$	−589256.	−	155894.i	−0.331960	−	0.0878236i
$317$		−	201964.i		−	0.112882i	−0.998406	−	0.0564410i	$-0.982025\pi$
$317$		−	201964.i		−	0.112882i	0.998406	−	0.0564410i	$-0.0179753\pi$
$318$	−1.24357e6	−	88939.3i	−0.689610	−	0.0493203i
$319$			772548.i			0.425059i
$320$	−584734.	−	573737.i	−0.319215	−	0.313212i
$321$	1.48962e6	−	1.67300e6i	0.806887	−	0.906221i
$322$	2.42006e6	+	3.14357e6i	1.30073	+	1.68960i
$323$	−477754.			−0.254799
$324$	−50927.6	+	1.88888e6i	−0.0269520	+	0.999637i
$325$	−614545.			−0.322735
$326$	−551845.	−	716828.i	−0.287590	−	0.373569i
$327$	1.25645e6	−	1.41113e6i	0.649793	−	0.729788i
$328$	2.45617e6	−	1.03106e6i	1.26059	−	0.529178i
$329$		−	953417.i		−	0.485616i
$330$	−602552.	−	43094.1i	−0.304586	−	0.0217837i
$331$			1.60093e6i			0.803161i	0.915824	+	0.401580i	$0.131539\pi$
$331$			1.60093e6i			0.803161i	−0.915824	+	0.401580i	$0.868461\pi$
$332$	−393151.	+	1.48605e6i	−0.195756	+	0.739928i
$333$	−189866.	−	1.63170e6i	−0.0938288	−	0.806360i
$334$	−1.29851e6	+	999649.i	−0.636911	+	0.490322i
$335$	16067.9			0.00782254
$336$	−922077.	−	2.72711e6i	−0.445573	−	1.31782i
$337$	2.68941e6			1.28998			0.644990	−	0.764191i	$-0.276862\pi$
$337$	2.68941e6			1.28998			0.644990	+	0.764191i	$0.276862\pi$
$338$	−2.66943e6	+	2.05504e6i	−1.27095	+	0.978429i
$339$	−259473.	−	231031.i	−0.122629	−	0.109187i
$340$	−46174.9	+	174534.i	−0.0216625	+	0.0818809i
$341$			1.37004e6i			0.638038i
$342$	−2.08528e6	+	2.02982e6i	−0.964050	+	0.938408i
$343$		−	196495.i		−	0.0901811i
$344$	−1.44051e6	+	604704.i	−0.656326	+	0.275516i
$345$	−1.13184e6	−	1.00777e6i	−0.511960	−	0.455842i
$346$	−2.05548e6	−	2.66999e6i	−0.923044	−	1.19900i
$347$	1.59631e6			0.711693			0.355846	−	0.934544i	$-0.384193\pi$
$347$	1.59631e6			0.711693			0.355846	+	0.934544i	$0.384193\pi$
$348$	1.17274e6	−	776215.i	0.519103	−	0.343585i
$349$	−497024.			−0.218431			−0.109215	−	0.994018i	$-0.534834\pi$
$349$	−497024.			−0.218431			−0.109215	+	0.994018i	$0.534834\pi$
$350$	−388957.	−	505241.i	−0.169719	−	0.220459i
$351$	3.04939e6	+	2.13872e6i	1.32113	+	0.926586i
$352$	−1.57203e6	+	219627.i	−0.676247	+	0.0944775i
$353$		−	2.57075e6i		−	1.09805i	−0.835805	−	0.549026i	$-0.814999\pi$
$353$		−	2.57075e6i		−	1.09805i	0.835805	−	0.549026i	$-0.185001\pi$
$354$	144115.	−	2.01505e6i	0.0611224	−	0.854629i
$355$			963273.i			0.405675i
$356$	1.96484e6	+	519820.i	0.821679	+	0.217384i
$357$	−421893.	+	473832.i	−0.175199	+	0.196768i
$358$	136953.	−	105432.i	0.0564759	−	0.0434776i
$359$	1.73590e6			0.710868			0.355434	−	0.934701i	$-0.384333\pi$
$359$	1.73590e6			0.710868			0.355434	+	0.934701i	$0.384333\pi$
$360$	539995.	+	957982.i	0.219601	+	0.389584i
$361$	−2.00565e6			−0.810002
$362$	3.74809e6	−	2.88545e6i	1.50328	−	1.15729i
$363$	891107.	−	1.00081e6i	0.354947	−	0.398644i
$364$	−5.48578e6	−	1.45132e6i	−2.17013	−	0.574130i
$365$			1.05013e6i			0.412582i
$366$	318733.	−	4.45661e6i	0.124373	−	1.73901i
$367$			2.56027e6i			0.992249i	0.868251	+	0.496125i	$0.165244\pi$
$367$			2.56027e6i			0.992249i	−0.868251	+	0.496125i	$0.834756\pi$
$368$	−3.46107e6	−	1.96915e6i	−1.33227	−	0.757984i
$369$	−3.55193e6	+	413306.i	−1.35799	+	0.158018i
$370$	−583189.	−	757543.i	−0.221465	−	0.287675i
$371$	−2.54980e6			−0.961770
$372$	2.07974e6	−	1.37654e6i	0.779204	−	0.515741i
$373$	4.04455e6			1.50521			0.752607	−	0.658470i	$-0.228796\pi$
$373$	4.04455e6			1.50521			0.752607	+	0.658470i	$0.228796\pi$
$374$	213393.	+	277191.i	0.0788864	+	0.102471i
$375$	181911.	+	161971.i	0.0668006	+	0.0594784i
$376$	370412.	+	882386.i	0.135119	+	0.321876i
$377$		−	2.77214e6i		−	1.00453i
$378$	171690.	+	3.86065e6i	0.0618037	+	1.38973i
$379$		−	1.75871e6i		−	0.628921i	−0.949271	−	0.314460i	$-0.898176\pi$
$379$		−	1.75871e6i		−	0.628921i	0.949271	−	0.314460i	$-0.101824\pi$
$380$	−433160.	+	1.63728e6i	−0.153883	+	0.581653i
$381$	547666.	+	487635.i	0.193287	+	0.172100i
$382$	−241070.	+	185586.i	−0.0845249	+	0.0650710i
$383$	−2.71855e6			−0.946979			−0.473490	−	0.880799i	$-0.657006\pi$
$383$	−2.71855e6			−0.946979			−0.473490	+	0.880799i	$0.657006\pi$
$384$	1.91289e6	+	2.16570e6i	0.662007	+	0.749498i
$385$	−1.23546e6			−0.424793
$386$	−1.03487e6	+	796686.i	−0.353522	+	0.272157i
$387$	2.08315e6	−	242397.i	0.707039	−	0.0822717i
$388$	−391969.	+	1.48158e6i	−0.132182	+	0.499628i
$389$			3.34555e6i			1.12097i	0.828165	+	0.560485i	$0.189385\pi$
$389$			3.34555e6i			1.12097i	−0.828165	+	0.560485i	$0.810615\pi$
$390$	2.16214e6	+	154635.i	0.719818	+	0.0514808i
$391$			877578.i			0.290298i
$392$	−1.10126e6	−	2.62339e6i	−0.361972	−	0.862279i
$393$	−1.20328e6	+	1.35141e6i	−0.392992	+	0.441373i
$394$	2.01465e6	+	2.61696e6i	0.653822	+	0.849292i
$395$	476194.			0.153565
$396$	2.10910e6	+	303234.i	0.675865	+	0.0971717i
$397$	3.68294e6			1.17278			0.586392	−	0.810027i	$-0.300548\pi$
$397$	3.68294e6			1.17278			0.586392	+	0.810027i	$0.300548\pi$
$398$	122076.	+	158572.i	0.0386297	+	0.0501786i
$399$	−3.95773e6	+	4.44495e6i	−1.24455	+	1.39777i
$400$	556270.	+	316486.i	0.173834	+	0.0989019i
$401$		−	1.17820e6i		−	0.365895i	−0.983123	−	0.182947i	$-0.941436\pi$
$401$		−	1.17820e6i		−	0.365895i	0.983123	−	0.182947i	$-0.0585638\pi$
$402$	−56531.4	−	4043.08i	−0.0174472	−	0.00124781i
$403$		−	4.91611e6i		−	1.50785i
$404$	−3.80914e6	−	1.00775e6i	−1.16111	−	0.307184i
$405$	−338960.	−	1.43678e6i	−0.102686	−	0.435265i
$406$	2.27908e6	−	1.75454e6i	0.686190	−	0.528259i
$407$	−1.85241e6			−0.554309
$408$	206373.	−	602441.i	0.0613766	−	0.179169i
$409$	−4.26843e6			−1.26171			−0.630856	−	0.775900i	$-0.717296\pi$
$409$	−4.26843e6			−1.26171			−0.630856	+	0.775900i	$0.717296\pi$
$410$	−1.64904e6	+	1.26950e6i	−0.484476	+	0.372971i
$411$	−429488.	−	382410.i	−0.125414	−	0.111667i
$412$	−2.74678e6	−	726689.i	−0.797224	−	0.210914i
$413$		−	4.13162e6i		−	1.19192i
$414$	3.72854e6	+	3.83042e6i	1.06915	+	1.09836i
$415$		−	1.20092e6i		−	0.342290i
$416$	5.64094e6	−	788087.i	1.59815	−	0.223276i
$417$	3.50306e6	+	3.11907e6i	0.986523	+	0.878386i
$418$	2.00182e6	+	2.60029e6i	0.560381	+	0.727916i
$419$	−4.64997e6			−1.29394			−0.646972	−	0.762514i	$-0.723965\pi$
$419$	−4.64997e6			−1.29394			−0.646972	+	0.762514i	$0.723965\pi$
$420$	1.24133e6	+	1.87545e6i	0.343370	+	0.518779i
$421$	1.99597e6			0.548845			0.274422	−	0.961609i	$-0.411513\pi$
$421$	1.99597e6			0.548845			0.274422	+	0.961609i	$0.411513\pi$
$422$	2.61121e6	+	3.39187e6i	0.713775	+	0.927168i
$423$	−148481.	−	1.27604e6i	−0.0403478	−	0.346747i
$424$	2.35984e6	−	990624.i	0.637481	−	0.267605i
$425$		−	141046.i		−	0.0378781i
$426$	242383.	−	3.38906e6i	0.0647110	−	0.904806i
$427$		−	9.13775e6i		−	2.42532i
$428$	−1.17610e6	+	4.44547e6i	−0.310337	+	1.17303i
$429$	2.79303e6	−	3.13687e6i	0.732710	−	0.822913i
$430$	967138.	−	744545.i	0.252242	−	0.194187i
$431$	−1.42879e6			−0.370489			−0.185244	−	0.982693i	$-0.559308\pi$
$431$	−1.42879e6			−0.370489			−0.185244	+	0.982693i	$0.559308\pi$
$432$	−1.65880e6	−	3.50632e6i	−0.427647	−	0.903946i
$433$	−3.86587e6			−0.990895			−0.495448	−	0.868638i	$-0.664996\pi$
$433$	−3.86587e6			−0.990895			−0.495448	+	0.868638i	$0.664996\pi$
$434$	4.04172e6	−	3.11150e6i	1.03001	−	0.792948i
$435$	−730631.	+	820578.i	−0.185129	+	0.207920i
$436$	−992001.	+	3.74962e6i	−0.249917	+	0.944650i
$437$			8.23244e6i			2.06217i
$438$	264238.	−	3.69464e6i	0.0658127	−	0.920210i
$439$		−	46376.1i		−	0.0114851i	−0.999984	−	0.00574253i	$-0.998172\pi$
$439$		−	46376.1i		−	0.0114851i	0.999984	−	0.00574253i	$-0.00182791\pi$
$440$	1.14342e6	−	479990.i	0.281562	−	0.118195i
$441$	441444.	+	3.79374e6i	0.108088	+	0.928906i
$442$	−765721.	−	994645.i	−0.186430	−	0.242166i
$443$	6.35812e6			1.53929			0.769643	−	0.638475i	$-0.220434\pi$
$443$	6.35812e6			1.53929			0.769643	+	0.638475i	$0.220434\pi$
$444$	1.86121e6	+	2.81199e6i	0.448061	+	0.676950i
$445$	−1.58784e6			−0.380108
$446$	−1.88332e6	−	2.44636e6i	−0.448318	−	0.582350i
$447$	−2.49228e6	−	2.21909e6i	−0.589967	−	0.525299i
$448$	4.21817e6	+	4.13883e6i	0.992953	+	0.974278i
$449$			6.94765e6i			1.62638i	0.581999	+	0.813190i	$0.302271\pi$
$449$			6.94765e6i			1.62638i	−0.581999	+	0.813190i	$0.697729\pi$
$450$	−599257.	−	615632.i	−0.139503	−	0.143314i
$451$			4.03239e6i			0.933515i
$452$	689467.	+	182406.i	0.158733	+	0.0419945i
$453$	−3.44885e6	−	3.07081e6i	−0.789640	−	0.703084i
$454$	−4.95560e6	+	3.81504e6i	−1.12838	+	0.868678i
$455$	4.43322e6			1.00390
$456$	1.93596e6	−	5.65142e6i	0.435997	−	1.27276i
$457$	−3.11144e6			−0.696900			−0.348450	−	0.937327i	$-0.613292\pi$
$457$	−3.11144e6			−0.696900			−0.348450	+	0.937327i	$0.613292\pi$
$458$	6.61180e6	−	5.09005e6i	1.47284	−	1.13386i
$459$	−490863.	+	699873.i	−0.108750	+	0.155056i
$460$	3.00749e6	+	795665.i	0.662690	+	0.175322i
$461$			6.03298e6i			1.32215i	0.750322	+	0.661073i	$0.229899\pi$
$461$			6.03298e6i			1.32215i	−0.750322	+	0.661073i	$0.770101\pi$
$462$	4.34670e6	+	310873.i	0.947447	+	0.0677606i
$463$		−	5.49917e6i		−	1.19219i	−0.802915	−	0.596093i	$-0.796719\pi$
$463$		−	5.49917e6i		−	1.19219i	0.802915	−	0.596093i	$-0.203281\pi$
$464$	−1.42763e6	+	2.50927e6i	−0.307837	+	0.541068i
$465$	−1.29570e6	+	1.45521e6i	−0.277890	+	0.312100i
$466$	−4.34784e6	−	5.64769e6i	−0.927489	−	1.20478i
$467$	508896.			0.107978			0.0539892	−	0.998542i	$-0.482806\pi$
$467$	508896.			0.107978			0.0539892	+	0.998542i	$0.482806\pi$
$468$	−7.56811e6	−	1.08810e6i	−1.59725	−	0.229643i
$469$	−115911.			−0.0243328
$470$	−456072.	−	592422.i	−0.0952334	−	0.123705i
$471$	−4.24184e6	+	4.76405e6i	−0.881053	+	0.989518i
$472$	1.60518e6	+	3.82381e6i	0.331641	+	0.790026i
$473$		−	2.36494e6i		−	0.486034i
$474$	−1.67538e6	−	119822.i	−0.342506	−	0.0244958i
$475$		−	1.32313e6i		−	0.269073i
$476$	333097.	−	1.25906e6i	0.0673834	−	0.254699i
$477$	−3.41261e6	+	397095.i	−0.686738	+	0.0799094i
$478$	2.81796e6	−	2.16939e6i	0.564113	−	0.434278i
$479$	9.77229e6			1.94607			0.973033	−	0.230667i	$-0.0740908\pi$
$479$	9.77229e6			1.94607			0.973033	+	0.230667i	$0.0740908\pi$
$480$	−1.87748e6	−	1.25346e6i	−0.371939	−	0.248317i
$481$	6.64703e6			1.30998
$482$	515716.	−	397021.i	0.101110	−	0.0778388i
$483$	8.16486e6	+	7.26988e6i	1.59251	+	1.41795i
$484$	−703555.	+	2.65933e6i	−0.136516	+	0.516011i
$485$		−	1.19731e6i		−	0.231128i
$486$	831027.	+	5.14029e6i	0.159597	+	0.987182i
$487$			4.48663e6i			0.857232i	0.903487	+	0.428616i	$0.140999\pi$
$487$			4.48663e6i			0.857232i	−0.903487	+	0.428616i	$0.859001\pi$
$488$	3.55011e6	+	8.45698e6i	0.674827	+	1.60755i
$489$	−1.86183e6	−	1.65775e6i	−0.352102	−	0.313506i
$490$	1.35593e6	+	1.76131e6i	0.255122	+	0.331395i
$491$	−5.69329e6			−1.06576			−0.532880	−	0.846191i	$-0.678890\pi$
$491$	−5.69329e6			−1.06576			−0.532880	+	0.846191i	$0.678890\pi$
$492$	6.12123e6	−	4.05153e6i	1.14005	−	0.754582i
$493$	636241.			0.117897
$494$	−7.18313e6	−	9.33063e6i	−1.32433	−	1.72026i
$495$	−1.65352e6	+	192406.i	−0.303317	+	0.0352943i
$496$	−2.53176e6	+	4.44994e6i	−0.462081	+	0.812175i
$497$		−	6.94887e6i		−	1.26190i
$498$	−302181.	+	4.22518e6i	−0.0546002	+	0.763435i
$499$		−	3.25184e6i		−	0.584626i	−0.956323	−	0.292313i	$-0.905575\pi$
$499$		−	3.25184e6i		−	0.584626i	0.956323	−	0.292313i	$-0.0944250\pi$
$500$	−483370.	−	127881.i	−0.0864678	−	0.0228760i
$501$	−3.00295e6	+	3.37264e6i	−0.534508	+	0.600310i
$502$	−6.24486e6	+	4.80756e6i	−1.10602	+	0.851463i
$503$	−8.06485e6			−1.42127			−0.710635	−	0.703561i	$-0.751592\pi$
$503$	−8.06485e6			−1.42127			−0.710635	+	0.703561i	$0.751592\pi$
$504$	−3.89542e6	−	6.91070e6i	−0.683091	−	1.21184i
$505$	3.07828e6			0.537130
$506$	4.77643e6	−	3.67710e6i	0.829329	−	0.638454i
$507$	−6.17337e6	+	6.93336e6i	−1.06660	+	1.19791i
$508$	−1.45525e6	−	385001.i	−0.250194	−	0.0661916i
$509$			1.00799e6i			0.172450i	0.996276	+	0.0862248i	$0.0274803\pi$
$509$			1.00799e6i			0.172450i	−0.996276	+	0.0862248i	$0.972520\pi$
$510$	−35490.6	+	496239.i	−0.00604210	+	0.0844822i
$511$		−	7.57543e6i		−	1.28338i
$512$	−5.51189e6	−	2.19168e6i	−0.929235	−	0.369490i
$513$	−4.60472e6	+	6.56542e6i	−0.772520	+	1.10146i
$514$	−877394.	−	1.13970e6i	−0.146483	−	0.190276i
$515$	2.21975e6			0.368795
$516$	−3.59001e6	+	2.37616e6i	−0.593569	+	0.392873i
$517$	−1.44865e6			−0.238361
$518$	4.20702e6	+	5.46477e6i	0.688891	+	0.894845i
$519$	−6.93482e6	−	6.17467e6i	−1.13010	−	1.00623i
$520$	−4.10294e6	+	1.72235e6i	−0.665405	+	0.279327i
$521$		−	8.62583e6i		−	1.39222i	−0.717937	−	0.696108i	$-0.754914\pi$
$521$		−	8.62583e6i		−	1.39222i	0.717937	−	0.696108i	$-0.245086\pi$
$522$	2.77704e6	−	2.70318e6i	0.446073	−	0.434208i
$523$			4.27946e6i			0.684124i	0.939677	+	0.342062i	$0.111125\pi$
$523$			4.27946e6i			0.684124i	−0.939677	+	0.342062i	$0.888875\pi$
$524$	950021.	−	3.59094e6i	0.151149	−	0.571320i
$525$	−1.31227e6	−	1.16843e6i	−0.207790	−	0.185014i
$526$	1.01880e6	−	784314.i	0.160555	−	0.123602i
$527$	1.12831e6			0.176971
$528$	−4.14364e6	+	1.40103e6i	−0.646841	+	0.218707i
$529$	8.68569e6			1.34948
$530$	−1.58436e6	+	1.21971e6i	−0.244999	+	0.188611i
$531$	−643441.	−	5.52970e6i	−0.0990313	−	0.851070i
$532$	3.12474e6	−	1.18110e7i	0.478668	−	1.80929i
$533$		−	1.44695e7i		−	2.20614i
$534$	5.58647e6	+	399540.i	0.847783	+	0.0606327i
$535$		−	3.59251e6i		−	0.542642i
$536$	107275.	−	45032.6i	0.0161283	−	0.00677042i
$537$	316719.	−	355710.i	0.0473957	−	0.0532304i
$538$	−2.77554e6	−	3.60534e6i	−0.413421	−	0.537019i
$539$	4.30692e6			0.638550
$540$	1.95345e6	+	2.31675e6i	0.288282	+	0.341897i
$541$	1.59237e6			0.233911			0.116956	−	0.993137i	$-0.462686\pi$
$541$	1.59237e6			0.233911			0.116956	+	0.993137i	$0.462686\pi$
$542$	2.44034e6	+	3.16991e6i	0.356822	+	0.463500i
$543$	8.66790e6	−	9.73499e6i	1.26158	−	1.41689i
$544$	180876.	+	1.29467e6i	0.0262050	+	0.187569i
$545$		−	3.03017e6i		−	0.436995i
$546$	−1.55973e7	−	1.11551e6i	−2.23907	−	0.160136i
$547$			8.81639e6i			1.25986i	0.776652	+	0.629930i	$0.216916\pi$
$547$			8.81639e6i			1.25986i	−0.776652	+	0.629930i	$0.783084\pi$
$548$	1.14123e6	+	301923.i	0.162338	+	0.0429482i
$549$	−1.42307e6	−	1.22298e7i	−0.201510	−	1.73177i
$550$	−767676.	+	590991.i	−0.108211	+	0.0833056i
$551$	5.96849e6			0.837501
$552$	−1.03810e7	−	3.55613e6i	−1.45008	−	0.496741i
$553$	−3.43518e6			−0.477679
$554$	4.17482e6	−	3.21396e6i	0.577914	−	0.444903i
$555$	−1.96758e6	−	1.75191e6i	−0.271144	−	0.241423i
$556$	−9.30825e6	−	2.46260e6i	−1.27697	−	0.337837i
$557$		−	834236.i		−	0.113933i	−0.998376	−	0.0569667i	$-0.981857\pi$
$557$		−	834236.i		−	0.113933i	0.998376	−	0.0569667i	$-0.0181429\pi$
$558$	4.92481e6	−	4.79382e6i	0.669582	−	0.651772i
$559$			8.48611e6i			1.14863i
$560$	−4.01283e6	−	2.28307e6i	−0.540730	−	0.307645i
$561$	719952.	+	641036.i	0.0965821	+	0.0859954i
$562$	−132189.	−	171709.i	−0.0176544	−	0.0229325i
$563$	−7.17682e6			−0.954248			−0.477124	−	0.878836i	$-0.658321\pi$
$563$	−7.17682e6			−0.954248			−0.477124	+	0.878836i	$0.658321\pi$
$564$	1.45552e6	+	2.19907e6i	0.192673	+	0.291099i
$565$	−557178.			−0.0734299
$566$	−157697.	−	204843.i	−0.0206911	−	0.0268770i
$567$	2.44520e6	+	1.03647e7i	0.319416	+	1.35394i
$568$	2.69971e6	+	6.43117e6i	0.351112	+	0.836410i
$569$			3.64849e6i			0.472425i	0.971701	+	0.236213i	$0.0759062\pi$
$569$			3.64849e6i			0.472425i	−0.971701	+	0.236213i	$0.924094\pi$
$570$	−332933.	+	4.65515e6i	−0.0429209	+	0.600132i
$571$			3.06655e6i			0.393604i	0.980443	+	0.196802i	$0.0630556\pi$
$571$			3.06655e6i			0.393604i	−0.980443	+	0.196802i	$0.936944\pi$
$572$	−2.20518e6	+	8.33524e6i	−0.281808	+	1.06519i
$573$	−557502.	+	626135.i	−0.0709349	+	0.0796676i
$574$	1.18959e7	−	9.15797e6i	1.50701	−	1.16016i
$575$	−2.43044e6			−0.306560
$576$	6.29009e6	+	4.88243e6i	0.789952	+	0.613169i
$577$	7.32892e6			0.916432			0.458216	−	0.888841i	$-0.348489\pi$
$577$	7.32892e6			0.916432			0.458216	+	0.888841i	$0.348489\pi$
$578$	−6.13613e6	+	4.72386e6i	−0.763967	+	0.588135i
$579$	−2.39325e6	+	2.68788e6i	−0.296682	+	0.333206i
$580$	576854.	−	2.18042e6i	0.0712026	−	0.269135i
$581$			8.66323e6i			1.06473i
$582$	−301272.	+	4.21247e6i	−0.0368682	+	0.515501i
$583$			3.87423e6i			0.472078i
$584$	2.94313e6	+	7.01105e6i	0.357090	+	0.850650i
$585$	5.93335e6	−	690410.i	0.716820	−	0.0834098i
$586$	7.80576e6	+	1.01394e7i	0.939012	+	1.21974i
$587$	−2.66084e6			−0.318731			−0.159365	−	0.987220i	$-0.550945\pi$
$587$	−2.66084e6			−0.318731			−0.159365	+	0.987220i	$0.550945\pi$
$588$	−4.32736e6	−	6.53796e6i	−0.516155	−	0.779829i
$589$	1.05845e7			1.25714
$590$	−1.97639e6	−	2.56726e6i	−0.233745	−	0.303626i
$591$	6.79709e6	+	6.05203e6i	0.800487	+	0.712742i
$592$	−6.01671e6	−	3.42317e6i	−0.705594	−	0.401443i
$593$			1.50490e7i			1.75740i	0.477378	+	0.878698i	$0.341587\pi$
$593$			1.50490e7i			1.75740i	−0.477378	+	0.878698i	$0.658413\pi$
$594$	5.86597e6	−	260870.i	0.682140	−	0.0303359i
$595$			1.01748e6i			0.117824i
$596$	6.62243e6	+	1.75204e6i	0.763664	+	0.202035i
$597$	411862.	+	366716.i	0.0472950	+	0.0421108i
$598$	−1.71393e7	+	1.31946e7i	−1.95993	+	1.50884i
$599$	8.67824e6			0.988245			0.494122	−	0.869392i	$-0.335489\pi$
$599$	8.67824e6			0.988245			0.494122	+	0.869392i	$0.335489\pi$
$600$	1.66845e6	+	571548.i	0.189206	+	0.0648148i
$601$	474775.			0.0536169			0.0268085	−	0.999641i	$-0.491466\pi$
$601$	474775.			0.0536169			0.0268085	+	0.999641i	$0.491466\pi$
$602$	−6.97676e6	+	5.37101e6i	−0.784625	+	0.604039i
$603$	−155133.	+	18051.5i	−0.0173745	+	0.00202171i
$604$	9.16422e6	+	2.42449e6i	1.02212	+	0.270413i
$605$		−	2.14908e6i		−	0.238707i
$606$	−1.08302e7	−	774569.i	−1.19800	−	0.0856799i
$607$		−	1.18550e7i		−	1.30596i	−0.757375	−	0.652981i	$-0.773518\pi$
$607$		−	1.18550e7i		−	1.30596i	0.757375	−	0.652981i	$-0.226482\pi$
$608$	1.69677e6	+	1.21451e7i	0.186151	+	1.33242i
$609$	5.27064e6	−	5.91950e6i	0.575864	−	0.646758i
$610$	−4.37110e6	−	5.67790e6i	−0.475626	−	0.617822i
$611$	5.19818e6			0.563311
$612$	249732.	−	1.73698e6i	0.0269522	−	0.187463i
$613$	−5.93825e6			−0.638274			−0.319137	−	0.947709i	$-0.603393\pi$
$613$	−5.93825e6			−0.638274			−0.319137	+	0.947709i	$0.603393\pi$
$614$	−4.27038e6	−	5.54707e6i	−0.457136	−	0.593804i
$615$	−3.81360e6	+	4.28309e6i	−0.406581	+	0.456635i
$616$	−8.24841e6	+	3.46256e6i	−0.875827	+	0.367659i
$617$		−	1.11613e6i		−	0.118032i	−0.998257	−	0.0590161i	$-0.981204\pi$
$617$		−	1.11613e6i		−	0.118032i	0.998257	−	0.0590161i	$-0.0187963\pi$
$618$	−7.80969e6	−	558543.i	−0.822551	−	0.0588281i
$619$			886041.i			0.0929453i	0.998920	+	0.0464726i	$0.0147980\pi$
$619$			886041.i			0.0929453i	−0.998920	+	0.0464726i	$0.985202\pi$
$620$	1.02299e6	−	3.86676e6i	0.106879	−	0.403988i
$621$	1.20599e7	+	8.45833e6i	1.25492	+	0.880148i
$622$	1.15753e7	−	8.91115e6i	1.19965	−	0.923544i
$623$	1.14544e7			1.18237
$624$	1.48687e7	−	5.02731e6i	1.52866	−	0.516862i
$625$	390625.			0.0400000
$626$	6.35102e6	−	4.88930e6i	0.647751	−	0.498667i
$627$	6.75378e6	+	6.01347e6i	0.686085	+	0.610881i
$628$	3.34906e6	−	1.26589e7i	0.338862	−	1.28085i
$629$			1.52558e6i			0.153747i
$630$	4.32293e6	+	4.44106e6i	0.433937	+	0.445795i
$631$		−	7.80122e6i		−	0.779990i	−0.920817	−	0.389995i	$-0.872477\pi$
$631$		−	7.80122e6i		−	0.779990i	0.920817	−	0.389995i	$-0.127523\pi$
$632$	3.17925e6	−	1.33460e6i	0.316615	−	0.132910i
$633$	8.80977e6	+	7.84410e6i	0.873887	+	0.778097i
$634$	696930.	+	905288.i	0.0688598	+	0.0894465i
$635$	1.17603e6			0.115740
$636$	5.88114e6	−	3.89262e6i	0.576526	−	0.381592i
$637$	−1.54545e7			−1.50906
$638$	−2.66589e6	−	3.46289e6i	−0.259293	−	0.336812i
$639$	−1.08219e6	−	9.30026e6i	−0.104846	−	0.901038i
$640$	4.60087e6	+	553953.i	0.444007	+	0.0534593i
$641$		−	1.73319e7i		−	1.66610i	−0.553198	−	0.833050i	$-0.686593\pi$
$641$		−	1.73319e7i		−	1.66610i	0.553198	−	0.833050i	$-0.313407\pi$
$642$	−903964.	+	1.26395e7i	−0.0865592	+	1.21029i
$643$			2.10425e6i			0.200710i	0.994952	+	0.100355i	$0.0319979\pi$
$643$			2.10425e6i			0.200710i	−0.994952	+	0.100355i	$0.968002\pi$
$644$	−2.16955e7	−	5.73978e6i	−2.06137	−	0.545356i
$645$	2.23662e6	−	2.51197e6i	0.211686	−	0.237747i
$646$	2.14150e6	−	1.64862e6i	0.201900	−	0.155431i
$647$	−1.74447e6			−0.163834			−0.0819169	−	0.996639i	$-0.526104\pi$
$647$	−1.74447e6			−0.163834			−0.0819169	+	0.996639i	$0.526104\pi$
$648$	−6.28982e6	−	8.64252e6i	−0.588438	−	0.808543i
$649$	−6.27770e6			−0.585044
$650$	2.75466e6	−	2.12065e6i	0.255731	−	0.196873i
$651$	9.34696e6	−	1.04976e7i	0.864406	−	0.970821i
$652$	4.94722e6	+	1.30884e6i	0.455766	+	0.120578i
$653$			1.25294e7i			1.14986i	0.818202	+	0.574932i	$0.194971\pi$
$653$			1.25294e7i			1.14986i	−0.818202	+	0.574932i	$0.805029\pi$
$654$	−762465.	+	1.06610e7i	−0.0697069	+	0.974660i
$655$			2.90194e6i			0.264293i
$656$	−7.45166e6	+	1.30974e7i	−0.676072	+	1.18830i
$657$	−1.17976e6	−	1.01388e7i	−0.106631	−	0.916378i
$658$	3.29002e6	+	4.27362e6i	0.296233	+	0.384797i
$659$	−1.58091e7			−1.41806			−0.709030	−	0.705178i	$-0.750867\pi$
$659$	−1.58091e7			−1.41806			−0.709030	+	0.705178i	$0.750867\pi$
$660$	2.84961e6	−	1.88610e6i	0.254639	−	0.168541i
$661$	−9.72088e6			−0.865370			−0.432685	−	0.901545i	$-0.642434\pi$
$661$	−9.72088e6			−0.865370			−0.432685	+	0.901545i	$0.642434\pi$
$662$	−5.52444e6	−	7.17606e6i	−0.489941	−	0.636416i
$663$	−2.58341e6	−	2.30023e6i	−0.228249	−	0.203230i
$664$	−3.36576e6	−	8.01781e6i	−0.296253	−	0.705725i
$665$			9.54484e6i			0.836979i
$666$	6.48167e6	+	6.65878e6i	0.566241	+	0.581714i
$667$		−	1.09634e7i		−	0.954183i
$668$	2.37092e6	−	8.96171e6i	0.205577	−	0.777052i
$669$	−6.35399e6	−	5.65750e6i	−0.548884	−	0.488719i
$670$	−72023.3	+	55446.7i	−0.00619849	+	0.00477187i
$671$	−1.38841e7			−1.19045
$672$	1.35438e7	+	9.04221e6i	1.15696	+	0.772416i
$673$	−3.53077e6			−0.300492			−0.150246	−	0.988649i	$-0.548006\pi$
$673$	−3.53077e6			−0.300492			−0.150246	+	0.988649i	$0.548006\pi$
$674$	−1.20551e7	+	9.28055e6i	−1.02217	+	0.786908i
$675$	−1.93829e6	−	1.35944e6i	−0.163742	−	0.114842i
$676$	4.87405e6	−	1.84232e7i	0.410226	−	1.55059i
$677$			2.20778e7i			1.85133i	0.378343	+	0.925666i	$0.376494\pi$
$677$			2.20778e7i			1.85133i	−0.378343	+	0.925666i	$0.623506\pi$
$678$	1.96031e6	+	140200.i	0.163776	+	0.0117131i
$679$			8.63717e6i			0.718947i
$680$	−395301.	−	941676.i	−0.0327836	−	0.0780960i
$681$	−1.14604e7	+	1.28713e7i	−0.946961	+	1.06354i
$682$	−4.72769e6	−	6.14110e6i	−0.389213	−	0.505575i
$683$	−1.88920e7			−1.54962			−0.774811	−	0.632193i	$-0.782155\pi$
$683$	−1.88920e7			−1.54962			−0.774811	+	0.632193i	$0.782155\pi$
$684$	2.34270e6	−	1.62943e7i	0.191459	−	1.33167i
$685$	−922257.			−0.0750975
$686$	678058.	+	880774.i	0.0550119	+	0.0714585i
$687$	1.52905e7	−	1.71729e7i	1.23604	−	1.38820i
$688$	4.37028e6	−	7.68141e6i	0.351997	−	0.618685i
$689$		−	1.39019e7i		−	1.11565i
$690$	8.55097e6	+	611558.i	0.683743	+	0.0489007i
$691$			2.47324e7i			1.97048i	0.171187	+	0.985239i	$0.445240\pi$
$691$			2.47324e7i			1.97048i	−0.171187	+	0.985239i	$0.554760\pi$
$692$	1.84271e7	+	4.87508e6i	1.46282	+	0.387005i
$693$	1.19282e7	−	1.38798e6i	0.943501	−	0.109787i
$694$	−7.15533e6	+	5.50849e6i	−0.563938	+	0.434144i
$695$	7.52226e6			0.590727
$696$	−2.57818e6	+	7.52618e6i	−0.201739	+	0.588914i
$697$	3.32092e6			0.258927
$698$	2.22787e6	−	1.71511e6i	0.173082	−	0.133246i
$699$	−1.46689e7	−	1.30609e7i	−1.13554	−	1.01107i
$700$	3.48694e6	+	922508.i	0.268967	+	0.0711582i
$701$		−	1.47732e7i		−	1.13548i	−0.823208	−	0.567740i	$-0.807818\pi$
$701$		−	1.47732e7i		−	1.13548i	0.823208	−	0.567740i	$-0.192182\pi$
$702$	−2.10489e7	+	936079.i	−1.61208	+	0.0716919i
$703$			1.43112e7i			1.09217i
$704$	6.28865e6	−	6.40919e6i	0.478218	−	0.487384i
$705$	−1.53871e6	−	1.37005e6i	−0.116596	−	0.103815i
$706$	8.87106e6	+	1.15232e7i	0.669829	+	0.870084i
$707$	−2.22061e7			−1.67080
$708$	6.30749e6	+	9.52963e6i	0.472905	+	0.714485i
$709$	−4.88482e6			−0.364949			−0.182475	−	0.983211i	$-0.558411\pi$
$709$	−4.88482e6			−0.364949			−0.182475	+	0.983211i	$0.558411\pi$
$710$	−3.32403e6	−	4.31780e6i	−0.247468	−	0.321453i
$711$	−4.59759e6	+	534980.i	−0.341080	+	0.0396884i
$712$	−1.06010e7	+	4.45016e6i	−0.783697	+	0.328985i
$713$		−	1.94425e7i		−	1.43228i
$714$	256023.	−	3.57978e6i	0.0187946	−	0.262791i
$715$		−	6.73594e6i		−	0.492758i
$716$	−250059.	+	945185.i	−0.0182289	+	0.0689024i
$717$	6.51687e6	−	7.31915e6i	0.473414	−	0.531695i
$718$	−7.78105e6	+	5.99019e6i	−0.563284	+	0.433640i
$719$	8.39607e6			0.605695			0.302847	−	0.953039i	$-0.402063\pi$
$719$	8.39607e6			0.605695			0.302847	+	0.953039i	$0.402063\pi$
$720$	−5.72627e6	−	2.43069e6i	−0.411661	−	0.174742i
$721$	−1.60128e7			−1.14718
$722$	8.99017e6	−	6.92102e6i	0.641837	−	0.494114i
$723$	1.19265e6	−	1.33948e6i	0.0848533	−	0.0952994i
$724$	−6.84356e6	+	2.58676e7i	−0.485216	+	1.83405i
$725$			1.76206e6i			0.124502i
$726$	−540761.	+	7.56107e6i	−0.0380771	+	0.532404i
$727$		−	1.62270e7i		−	1.13868i	−0.822102	−	0.569340i	$-0.807199\pi$
$727$		−	1.62270e7i		−	1.13868i	0.822102	−	0.569340i	$-0.192801\pi$
$728$	2.95978e7	−	1.24247e7i	2.06981	−	0.868877i
$729$	4.88677e6	+	1.34911e7i	0.340567	+	0.940220i
$730$	−3.62375e6	−	4.70712e6i	−0.251681	−	0.326925i
$731$	−1.94767e6			−0.134810
$732$	1.39500e7	+	2.10763e7i	0.962272	+	1.45384i
$733$	−2.97083e6			−0.204229			−0.102115	−	0.994773i	$-0.532561\pi$
$733$	−2.97083e6			−0.204229			−0.102115	+	0.994773i	$0.532561\pi$
$734$	−8.83491e6	−	1.14762e7i	−0.605288	−	0.786248i
$735$	4.57468e6	+	4.07323e6i	0.312351	+	0.278113i
$736$	2.23091e7	−	3.11678e6i	1.51806	−	0.212086i
$737$			176118.i			0.0119436i
$738$	1.44950e7	−	1.41095e7i	0.979667	−	0.953610i
$739$			1.25180e7i			0.843188i	0.906785	+	0.421594i	$0.138529\pi$
$739$			1.25180e7i			0.843188i	−0.906785	+	0.421594i	$0.861471\pi$
$740$	5.22821e6	+	1.38318e6i	0.350973	+	0.0928537i
$741$	−2.42346e7	−	2.15782e7i	−1.62140	−	1.44367i
$742$	1.14293e7	−	8.79877e6i	0.762096	−	0.586695i
$743$	−1.53119e7			−1.01755			−0.508775	−	0.860899i	$-0.669902\pi$
$743$	−1.53119e7			−1.01755			−0.508775	+	0.860899i	$0.669902\pi$
$744$	−4.57215e6	+	1.33469e7i	−0.302822	+	0.883994i
$745$	−5.35178e6			−0.353271
$746$	−1.81294e7	+	1.39568e7i	−1.19271	+	0.918204i
$747$	1.34917e6	+	1.15947e7i	0.0884640	+	0.760255i
$748$	−1.91304e6	−	506116.i	−0.125017	−	0.0330747i
$749$			2.59157e7i			1.68795i
$750$	−1.37433e6	−	98290.8i	−0.0892148	−	0.00638057i
$751$		−	2.14018e7i		−	1.38469i	−0.721568	−	0.692343i	$-0.756578\pi$
$751$		−	2.14018e7i		−	1.38469i	0.721568	−	0.692343i	$-0.243422\pi$
$752$	−4.70526e6	−	2.67702e6i	−0.303416	−	0.172627i
$753$	−1.44420e7	+	1.62199e7i	−0.928193	+	1.04246i
$754$	9.56601e6	+	1.24259e7i	0.612777	+	0.795976i
$755$	−7.40586e6			−0.472834
$756$	−1.40918e7	−	1.67126e7i	−0.896731	−	1.06351i
$757$	−5.65467e6			−0.358647			−0.179324	−	0.983790i	$-0.557391\pi$
$757$	−5.65467e6			−0.358647			−0.179324	+	0.983790i	$0.557391\pi$
$758$	6.06890e6	+	7.88329e6i	0.383652	+	0.498350i
$759$	1.10460e7	−	1.24059e7i	0.695989	−	0.781671i
$760$	−3.70827e6	−	8.83373e6i	−0.232883	−	0.554767i
$761$			2.88782e6i			0.180763i	0.995907	+	0.0903814i	$0.0288086\pi$
$761$			2.88782e6i			0.180763i	−0.995907	+	0.0903814i	$0.971191\pi$
$762$	−4.13759e6	−	295917.i	−0.258143	−	0.0184622i
$763$			2.18591e7i			1.35932i
$764$	440164.	−	1.66375e6i	0.0272823	−	0.103123i
$765$	158458.	+	1.36178e6i	0.00978949	+	0.0841304i
$766$	1.21857e7	−	9.38109e6i	0.750376	−	0.577672i
$767$	2.25263e7			1.38261
$768$	−1.60477e7	−	3.10665e6i	−0.981773	−	0.190059i
$769$	−5.05859e6			−0.308470			−0.154235	−	0.988034i	$-0.549291\pi$
$769$	−5.05859e6			−0.308470			−0.154235	+	0.988034i	$0.549291\pi$
$770$	5.53787e6	−	4.26330e6i	0.336602	−	0.259131i
$771$	−2.96017e6	−	2.63570e6i	−0.179342	−	0.159683i
$772$	1.88954e6	−	7.14218e6i	0.114107	−	0.431308i
$773$			3.85109e6i			0.231812i	0.993260	+	0.115906i	$0.0369771\pi$
$773$			3.85109e6i			0.231812i	−0.993260	+	0.115906i	$0.963023\pi$
$774$	−8.50112e6	+	8.27501e6i	−0.510063	+	0.496496i
$775$			3.12484e6i			0.186885i
$776$	−3.35563e6	−	7.99369e6i	−0.200041	−	0.476533i
$777$	1.41938e7	+	1.26379e7i	0.843422	+	0.750971i
$778$	−1.15447e7	−	1.49962e7i	−0.683809	−	0.888245i
$779$	3.11531e7			1.83932
$780$	−1.02253e7	+	6.76792e6i	−0.601780	+	0.398307i
$781$	−1.05583e7			−0.619393
$782$	−3.02832e6	−	3.93368e6i	−0.177086	−	0.230029i
$783$	6.13226e6	−	8.74339e6i	0.357451	−	0.509654i
$784$	1.39890e7	+	7.95897e6i	0.812826	+	0.462452i
$785$			1.02300e7i			0.592520i
$786$	730199.	−	1.02098e7i	0.0421584	−	0.589471i
$787$		−	6.59163e6i		−	0.379364i	−0.981846	−	0.189682i	$-0.939254\pi$
$787$		−	6.59163e6i		−	0.379364i	0.981846	−	0.189682i	$-0.0607457\pi$
$788$	−1.80611e7	−	4.77825e6i	−1.03616	−	0.274128i
$789$	2.35608e6	−	2.64614e6i	0.134741	−	0.151328i
$790$	−2.13451e6	+	1.64324e6i	−0.121683	+	0.0936769i
$791$	4.01938e6			0.228411
$792$	−1.05003e7	+	5.91881e6i	−0.594824	+	0.335291i
$793$	4.98205e7			2.81336
$794$	−1.65085e7	+	1.27090e7i	−0.929302	+	0.715417i
$795$	−3.66402e6	+	4.11509e6i	−0.205608	+	0.230920i
$796$	−1.09439e6	−	289533.i	−0.0612195	−	0.0161963i
$797$		−	2.46009e7i		−	1.37184i	−0.727676	−	0.685922i	$-0.759399\pi$
$797$		−	2.46009e7i		−	1.37184i	0.727676	−	0.685922i	$-0.240601\pi$
$798$	2.40171e6	−	3.35814e7i	0.133510	−	1.86677i
$799$			1.19305e6i			0.0661137i
$800$	−3.58556e6	+	500934.i	−0.198076	+	0.0276730i
$801$	1.53304e7	−	1.78386e6i	0.844252	−	0.0982380i
$802$	4.06568e6	+	5.28118e6i	0.223202	+	0.289931i
$803$	−1.15103e7			−0.629938
$804$	267350.	−	176954.i	0.0145861	−	0.00965429i
$805$	1.75328e7			0.953587
$806$	1.69644e7	+	2.20361e7i	0.919815	+	1.19481i
$807$	−9.36420e6	−	8.33776e6i	−0.506159	−	0.450677i
$808$	2.05517e7	−	8.62731e6i	1.10744	−	0.464887i
$809$			450469.i			0.0241988i	0.999927	+	0.0120994i	$0.00385145\pi$
$809$			450469.i			0.0241988i	−0.999927	+	0.0120994i	$0.996149\pi$
$810$	6.47738e6	+	5.27061e6i	0.346886	+	0.282259i
$811$			1.49741e7i			0.799443i	0.916637	+	0.399721i	$0.130893\pi$
$811$			1.49741e7i			0.799443i	−0.916637	+	0.399721i	$0.869107\pi$
$812$	−4.16132e6	+	1.57292e7i	−0.221483	+	0.837174i
$813$	8.23328e6	+	7.33080e6i	0.436864	+	0.388978i
$814$	8.30332e6	−	6.39226e6i	0.439229	−	0.338137i
$815$	−3.99799e6			−0.210837
$816$	1.15383e6	+	3.41254e6i	0.0606621	+	0.179413i
$817$	−1.82708e7			−0.957642
$818$	1.91329e7	−	1.47294e7i	0.999766	−	0.769664i
$819$	−4.28021e7	+	4.98049e6i	−2.22974	+	0.259455i
$820$	3.01095e6	−	1.13809e7i	0.156375	−	0.591076i
$821$			1.70086e7i			0.880663i	0.897835	+	0.440331i	$0.145139\pi$
$821$			1.70086e7i			0.880663i	−0.897835	+	0.440331i	$0.854861\pi$
$822$	3.24476e6	+	232062.i	0.167495	+	0.0119791i
$823$		−	1.57580e7i		−	0.810963i	−0.914103	−	0.405481i	$-0.867104\pi$
$823$		−	1.57580e7i		−	0.810963i	0.914103	−	0.405481i	$-0.132896\pi$
$824$	1.48199e7	−	6.22116e6i	0.760372	−	0.319193i
$825$	−1.77534e6	+	1.99390e6i	−0.0908128	+	0.101993i
$826$	1.42573e7	+	1.85197e7i	0.727088	+	0.944461i
$827$	3.12174e7			1.58721			0.793603	−	0.608436i	$-0.208203\pi$
$827$	3.12174e7			1.58721			0.793603	+	0.608436i	$0.208203\pi$
$828$	−2.99308e7	−	4.30327e6i	−1.51720	−	0.218133i
$829$	−2.01398e7			−1.01781			−0.508907	−	0.860821i	$-0.669950\pi$
$829$	−2.01398e7			−1.01781			−0.508907	+	0.860821i	$0.669950\pi$
$830$	4.14411e6	+	5.38305e6i	0.208803	+	0.271227i
$831$	9.65475e6	−	1.08433e7i	0.484997	−	0.544704i
$832$	−2.25656e7	+	2.29981e7i	−1.13016	+	1.15182i
$833$		−	3.54701e6i		−	0.177113i
$834$	−2.64654e7	−	1.89279e6i	−1.31754	−	0.0942294i
$835$			7.24221e6i			0.359464i
$836$	−1.79460e7	−	4.74781e6i	−0.888080	−	0.234951i
$837$	1.08750e7	−	1.55055e7i	0.536555	−	0.765020i
$838$	2.08432e7	−	1.60460e7i	1.02531	−	0.789326i
$839$	1.43792e7			0.705229			0.352614	−	0.935769i	$-0.385293\pi$
$839$	1.43792e7			0.705229			0.352614	+	0.935769i	$0.385293\pi$
$840$	−1.20359e7	−	4.12304e6i	−0.588546	−	0.201613i
$841$	1.25627e7			0.612482
$842$	−8.94682e6	+	6.88765e6i	−0.434899	+	0.334804i
$843$	−445982.	−	397096.i	−0.0216147	−	0.0192454i
$844$	−2.34092e7	−	6.19314e6i	−1.13117	−	0.299264i
$845$			1.48883e7i			0.717304i
$846$	5.06887e6	+	5.20738e6i	0.243492	+	0.250146i
$847$			1.55031e7i			0.742522i
$848$	−7.15938e6	+	1.25837e7i	−0.341890	+	0.600921i
$849$	−532043.	−	473724.i	−0.0253325	−	0.0225557i
$850$	486717.	+	632229.i	0.0231062	+	0.0300142i
$851$	2.62881e7			1.24433
$852$	1.06084e7	+	1.60276e7i	0.500670	+	0.756433i
$853$	2.49242e7			1.17286			0.586432	−	0.809998i	$-0.300532\pi$
$853$	2.49242e7			1.17286			0.586432	+	0.809998i	$0.300532\pi$
$854$	3.15323e7	+	4.09593e7i	1.47949	+	1.92180i
$855$	1.48647e6	+	1.27747e7i	0.0695411	+	0.597632i
$856$	−1.00685e7	−	2.39850e7i	−0.469658	−	1.11881i
$857$		−	2.19311e7i		−	1.02002i	−0.860169	−	0.510009i	$-0.829642\pi$
$857$		−	2.19311e7i		−	1.02002i	0.860169	−	0.510009i	$-0.170358\pi$
$858$	−1.69493e6	+	2.36989e7i	−0.0786019	+	1.09903i
$859$		−	2.27005e7i		−	1.04967i	−0.851204	−	0.524835i	$-0.824127\pi$
$859$		−	2.27005e7i		−	1.04967i	0.851204	−	0.524835i	$-0.175873\pi$
$860$	−1.76587e6	+	6.67474e6i	−0.0814168	+	0.307743i
$861$	2.75106e7	−	3.08974e7i	1.26471	−	1.42041i
$862$	6.40444e6	−	4.93042e6i	0.293571	−	0.226004i
$863$	−1.62322e7			−0.741908			−0.370954	−	0.928651i	$-0.620969\pi$
$863$	−1.62322e7			−0.741908			−0.370954	+	0.928651i	$0.620969\pi$
$864$	1.95350e7	+	9.99270e6i	0.890284	+	0.455406i
$865$	−1.48914e7			−0.676700
$866$	1.73285e7	−	1.33402e7i	0.785175	−	0.604462i
$867$	−1.41905e7	+	1.59375e7i	−0.641136	+	0.720065i
$868$	−7.37969e6	+	2.78941e7i	−0.332459	+	1.25665i
$869$			5.21950e6i			0.234466i
$870$	443378.	−	6.19942e6i	0.0198598	−	0.277685i
$871$		−	631966.i		−	0.0282259i
$872$	−8.49249e6	−	2.02306e7i	−0.378220	−	0.900984i
$873$	1.34512e6	+	1.15598e7i	0.0597343	+	0.513354i
$874$	−2.84083e7	−	3.69013e7i	−1.25796	−	1.63404i
$875$	−2.81790e6			−0.124424
$876$	1.15649e7	+	1.74728e7i	0.509194	+	0.769311i
$877$	4.03067e7			1.76961			0.884806	−	0.465960i	$-0.154291\pi$
$877$	4.03067e7			1.76961			0.884806	+	0.465960i	$0.154291\pi$
$878$	160033.	+	207878.i	0.00700606	+	0.00910063i
$879$	2.63353e7	+	2.34486e7i	1.14965	+	1.02363i
$880$	−3.46896e6	+	6.09720e6i	−0.151005	+	0.265414i
$881$		−	3.59170e7i		−	1.55905i	−0.626371	−	0.779525i	$-0.715461\pi$
$881$		−	3.59170e7i		−	1.55905i	0.626371	−	0.779525i	$-0.284539\pi$
$882$	−1.50701e7	−	1.54819e7i	−0.652295	−	0.670119i
$883$			2.07134e7i			0.894024i	0.894528	+	0.447012i	$0.147512\pi$
$883$			2.07134e7i			0.894024i	−0.894528	+	0.447012i	$0.852488\pi$
$884$	6.86458e6	+	1.81610e6i	0.295450	+	0.0781644i
$885$	−6.66798e6	−	5.93708e6i	−0.286178	−	0.254809i
$886$	−2.84998e7	+	2.19404e7i	−1.21971	+	0.938989i
$887$	−1.42179e7			−0.606774			−0.303387	−	0.952867i	$-0.598117\pi$
$887$	−1.42179e7			−0.606774			−0.303387	+	0.952867i	$0.598117\pi$
$888$	−1.80463e7	−	6.18196e6i	−0.767989	−	0.263083i
$889$	−8.48364e6			−0.360021
$890$	7.11740e6	−	5.47928e6i	0.301194	−	0.231872i
$891$	1.57484e7	−	3.71530e6i	0.664571	−	0.156783i
$892$	1.68837e7	+	4.46676e6i	0.710485	+	0.187966i
$893$			1.11918e7i			0.469648i
$894$	1.88290e7	+	1.34664e6i	0.787924	+	0.0563517i
$895$		−	763831.i		−	0.0318742i
$896$	−3.31898e7	−	3.99611e6i	−1.38113	−	0.166291i
$897$	−3.96366e7	+	4.45162e7i	−1.64481	+	1.84730i
$898$	−2.39747e7	−	3.11423e7i	−0.992117	−	1.28873i
$899$	−1.40958e7			−0.581688
$900$	4.81054e6	+	691629.i	0.197964	+	0.0284621i
$901$	3.19067e6			0.130939
$902$	−1.39149e7	−	1.80749e7i	−0.569459	−	0.739707i
$903$	−1.61346e7	+	1.81209e7i	−0.658473	+	0.739536i
$904$	−3.71993e6	+	1.56157e6i	−0.151396	+	0.0635537i
$905$		−	2.09044e7i		−	0.848429i
$906$	2.60559e7	+	1.86350e6i	1.05459	+	0.0754237i
$907$			5.22546e6i			0.210914i	0.994424	+	0.105457i	$0.0336306\pi$
$907$			5.22546e6i			0.210914i	−0.994424	+	0.105457i	$0.966369\pi$
$908$	9.04831e6	−	3.42013e7i	0.364211	−	1.37666i
$909$	−2.97203e7	+	3.45828e6i	−1.19301	+	0.138820i
$910$	−1.98716e7	+	1.52980e7i	−0.795480	+	0.612395i
$911$	1.61365e7			0.644188			0.322094	−	0.946708i	$-0.395613\pi$
$911$	1.61365e7			0.644188			0.322094	+	0.946708i	$0.395613\pi$
$912$	1.08239e7	+	3.20126e7i	0.430922	+	1.27448i
$913$	1.31631e7			0.522616
$914$	1.39468e7	−	1.07369e7i	0.552216	−	0.425120i
$915$	−1.47473e7	−	1.31308e7i	−0.582318	−	0.518488i
$916$	−1.20723e7	+	4.56316e7i	−0.475392	+	1.79691i
$917$		−	2.09340e7i		−	0.822110i
$918$	−214842.	−	4.83099e6i	−0.00841420	−	0.189204i
$919$			3.84259e7i			1.50084i	0.660960	+	0.750421i	$0.270149\pi$
$919$			3.84259e7i			1.50084i	−0.660960	+	0.750421i	$0.729851\pi$
$920$	−1.62265e7	+	6.81166e6i	−0.632057	+	0.265328i
$921$	−1.44075e7	−	1.28282e7i	−0.559680	−	0.498331i
$922$	−2.08184e7	−	2.70424e7i	−0.806530	−	1.04765i
$923$	3.78864e7			1.46379
$924$	−2.05565e7	+	1.36060e7i	−0.792082	+	0.524265i
$925$	−4.22507e6			−0.162360
$926$	1.89764e7	+	2.46496e7i	0.727253	+	0.944676i
$927$	−2.14313e7	+	2.49377e6i	−0.819125	+	0.0953141i
$928$	−2.25965e6	−	1.61740e7i	−0.0861334	−	0.616522i
$929$		−	2.19799e7i		−	0.835576i	−0.908545	−	0.417788i	$-0.862805\pi$
$929$		−	2.19799e7i		−	0.835576i	0.908545	−	0.417788i	$-0.137195\pi$
$930$	786286.	−	1.09941e7i	0.0298108	−	0.416822i
$931$		−	3.32741e7i		−	1.25815i
$932$	3.89778e7	+	1.03120e7i	1.46986	+	0.388868i
$933$	2.67692e7	−	3.00647e7i	1.00677	−	1.13071i
$934$	−2.28109e6	+	1.75608e6i	−0.0855609	+	0.0658685i
$935$	1.54598e6			0.0578330
$936$	3.76783e7	−	2.12385e7i	1.40573	−	0.792381i
$937$	−5.17423e7			−1.92529			−0.962647	−	0.270760i	$-0.912725\pi$
$937$	−5.17423e7			−1.92529			−0.962647	+	0.270760i	$0.912725\pi$
$938$	519563.	−	399982.i	0.0192811	−	0.0148434i
$939$	1.46875e7	−	1.64956e7i	0.543605	−	0.610527i
$940$	4.08863e6	+	1.08169e6i	0.150924	+	0.0399285i
$941$			6.69208e6i			0.246370i	0.992384	+	0.123185i	$0.0393108\pi$
$941$			6.69208e6i			0.246370i	−0.992384	+	0.123185i	$0.960689\pi$
$942$	2.57413e6	−	3.59921e7i	0.0945155	−	1.32154i
$943$		−	5.72247e7i		−	2.09558i
$944$	−2.03902e7	−	1.16009e7i	−0.744718	−	0.423702i
$945$	1.39825e7	+	9.80674e6i	0.509336	+	0.357228i
$946$	8.16085e6	+	1.06007e7i	0.296488	+	0.385128i
$947$	−2.15813e7			−0.781994			−0.390997	−	0.920392i	$-0.627870\pi$
$947$	−2.15813e7			−0.781994			−0.390997	+	0.920392i	$0.627870\pi$
$948$	7.92327e6	−	5.24427e6i	0.286341	−	0.189524i
$949$	4.13025e7			1.48871
$950$	4.56583e6	+	5.93085e6i	0.164139	+	0.213210i
$951$	2.35132e6	+	2.09358e6i	0.0843064	+	0.0750653i
$952$	2.85163e6	+	6.79307e6i	0.101977	+	0.242926i
$953$		−	1.61367e7i		−	0.575550i	−0.957698	−	0.287775i	$-0.907084\pi$
$953$		−	1.61367e7i		−	0.575550i	0.957698	−	0.287775i	$-0.0929156\pi$
$954$	1.39265e7	−	1.35561e7i	0.495418	−	0.482240i
$955$			1.34453e6i			0.0477047i
$956$	−5.14526e6	+	1.94483e7i	−0.182080	+	0.688235i
$957$	−8.99424e6	−	8.00834e6i	−0.317457	−	0.282659i
$958$	−4.38036e7	+	3.37219e7i	−1.54204	+	1.18713i
$959$	6.65299e6			0.233599
$960$	1.27411e7	−	860210.i	0.446198	−	0.0301250i
$961$	3.63168e6			0.126853
$962$	−2.97948e7	+	2.29374e7i	−1.03801	+	0.799109i
$963$	4.03600e6	+	3.46852e7i	0.140244	+	1.20525i
$964$	−941634.	+	3.55924e6i	−0.0326355	+	0.123357i
$965$			5.77180e6i			0.199523i
$966$	−6.16851e7	−	4.41167e6i	−2.12685	−	0.152111i
$967$			1.42102e7i			0.488691i	0.969688	+	0.244346i	$0.0785732\pi$
$967$			1.42102e7i			0.488691i	−0.969688	+	0.244346i	$0.921427\pi$
$968$	−6.02311e6	−	1.43481e7i	−0.206601	−	0.492159i
$969$	4.95246e6	−	5.56215e6i	0.169438	−	0.190298i
$970$	4.13164e6	+	5.36686e6i	0.140992	+	0.183143i
$971$	−2.49846e7			−0.850401			−0.425201	−	0.905099i	$-0.639796\pi$
$971$	−2.49846e7			−0.850401			−0.425201	+	0.905099i	$0.639796\pi$
$972$	−2.14630e7	−	2.01733e7i	−0.728660	−	0.684876i
$973$	−5.42642e7			−1.83752
$974$	−1.54823e7	−	2.01110e7i	−0.522925	−	0.679261i
$975$	6.37046e6	−	7.15472e6i	0.214615	−	0.241036i
$976$	−4.50962e7	−	2.56572e7i	−1.51536	−	0.862153i
$977$			1.58369e6i			0.0530802i	0.999648	+	0.0265401i	$0.00844897\pi$
$977$			1.58369e6i			0.0530802i	−0.999648	+	0.0265401i	$0.991551\pi$
$978$	1.40660e7	+	1.00599e6i	0.470245	+	0.0336316i
$979$		−	1.74041e7i		−	0.580357i
$980$	−1.21558e7	−	3.21593e6i	−0.404312	−	0.106965i
$981$	3.40424e6	+	2.92559e7i	0.112940	+	0.970601i
$982$	2.55198e7	−	1.96462e7i	0.844497	−	0.650131i
$983$	−1.62045e7			−0.534873			−0.267436	−	0.963575i	$-0.586177\pi$
$983$	−1.62045e7			−0.534873			−0.267436	+	0.963575i	$0.586177\pi$
$984$	−1.34571e7	+	3.92837e7i	−0.443060	+	1.29337i
$985$	1.45957e7			0.479329
$986$	−2.85191e6	+	2.19552e6i	−0.0934206	+	0.0719193i
$987$	1.11000e7	+	9.88325e6i	0.362684	+	0.322929i
$988$	6.43957e7	+	1.70366e7i	2.09877	+	0.555252i
$989$			3.35614e7i			1.09106i
$990$	6.74786e6	−	6.56838e6i	0.218815	−	0.212995i
$991$		−	2.33489e7i		−	0.755234i	−0.925962	−	0.377617i	$-0.876744\pi$
$991$		−	2.33489e7i		−	0.755234i	0.925962	−	0.377617i	$-0.123256\pi$
$992$	−4.00727e6	−	2.86831e7i	−0.129291	−	0.925436i
$993$	−1.86385e7	−	1.65955e7i	−0.599844	−	0.534092i
$994$	2.39790e7	+	3.11478e7i	0.769776	+	0.999912i
$995$	884408.			0.0283201
$996$	−1.32256e7	−	1.99818e7i	−0.422443	−	0.638244i
$997$	1.51396e7			0.482364			0.241182	−	0.970480i	$-0.422465\pi$
$997$	1.51396e7			0.482364			0.241182	+	0.970480i	$0.422465\pi$
$998$	1.12214e7	+	1.45762e7i	0.356631	+	0.463252i
$999$	2.09649e7	+	1.47039e7i	0.664628	+	0.466143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.6.e.a.11.10	yes	40
3.2	odd	2	inner	60.6.e.a.11.31	yes	40
4.3	odd	2	inner	60.6.e.a.11.32	yes	40
12.11	even	2	inner	60.6.e.a.11.9	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.6.e.a.11.9	✓	40	12.11	even	2	inner
60.6.e.a.11.10	yes	40	1.1	even	1	trivial
60.6.e.a.11.31	yes	40	3.2	odd	2	inner
60.6.e.a.11.32	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)

\(f(q)\)	\(=\)	\(q+(-4.48243 + 3.45077i) q^{2} +(-10.3661 + 11.6423i) q^{3} +(8.18436 - 30.9357i) q^{4} +25.0000i q^{5} +(6.29061 - 87.9570i) q^{6} -180.345i q^{7} +(70.0661 + 166.909i) q^{8} +(-28.0862 - 241.371i) q^{9} +O(q^{10})\)	\(q+(-4.48243 + 3.45077i) q^{2} +(-10.3661 + 11.6423i) q^{3} +(8.18436 - 30.9357i) q^{4} +25.0000i q^{5} +(6.29061 - 87.9570i) q^{6} -180.345i q^{7} +(70.0661 + 166.909i) q^{8} +(-28.0862 - 241.371i) q^{9} +(-86.2693 - 112.061i) q^{10} -274.021 q^{11} +(275.322 + 415.968i) q^{12} +983.273 q^{13} +(622.331 + 808.386i) q^{14} +(-291.057 - 259.154i) q^{15} +(-890.032 - 506.378i) q^{16} +225.673i q^{17} +(958.812 + 985.012i) q^{18} +2117.01i q^{19} +(773.392 + 204.609i) q^{20} +(2099.63 + 1869.49i) q^{21} +(1228.28 - 945.585i) q^{22} +3888.71 q^{23} +(-2669.52 - 914.476i) q^{24} -625.000 q^{25} +(-4407.45 + 3393.05i) q^{26} +(3101.26 + 2175.10i) q^{27} +(-5579.11 - 1476.01i) q^{28} -2819.30i q^{29} +(2198.92 + 157.265i) q^{30} -4999.75i q^{31} +(5736.90 - 801.494i) q^{32} +(2840.55 - 3190.24i) q^{33} +(-778.747 - 1011.57i) q^{34} +4508.63 q^{35} +(-7696.86 - 1106.61i) q^{36} +6760.11 q^{37} +(-7305.33 - 9489.36i) q^{38} +(-10192.7 + 11447.6i) q^{39} +(-4172.73 + 1751.65i) q^{40} -14715.6i q^{41} +(-15862.6 - 1134.48i) q^{42} +8630.48i q^{43} +(-2242.69 + 8477.04i) q^{44} +(6034.29 - 702.155i) q^{45} +(-17430.9 + 13419.0i) q^{46} +5286.62 q^{47} +(15121.6 - 5112.84i) q^{48} -15717.5 q^{49} +(2801.52 - 2156.73i) q^{50} +(-2627.36 - 2339.36i) q^{51} +(8047.46 - 30418.2i) q^{52} -14138.4i q^{53} +(-21407.0 + 952.004i) q^{54} -6850.54i q^{55} +(30101.3 - 12636.1i) q^{56} +(-24646.9 - 21945.3i) q^{57} +(9728.75 + 12637.3i) q^{58} +22909.5 q^{59} +(-10399.2 + 6883.05i) q^{60} +50668.1 q^{61} +(17253.0 + 22411.0i) q^{62} +(-43530.2 + 5065.22i) q^{63} +(-22949.5 + 23389.4i) q^{64} +24581.8i q^{65} +(-1723.76 + 24102.1i) q^{66} -642.717i q^{67} +(6981.36 + 1846.99i) q^{68} +(-40310.9 + 45273.5i) q^{69} +(-20209.6 + 15558.3i) q^{70} +38530.9 q^{71} +(38319.3 - 21599.8i) q^{72} +42005.1 q^{73} +(-30301.7 + 23327.6i) q^{74} +(6478.84 - 7276.44i) q^{75} +(65491.2 + 17326.4i) q^{76} +49418.5i q^{77} +(6185.38 - 86485.7i) q^{78} -19047.8i q^{79} +(12659.4 - 22250.8i) q^{80} +(-57471.3 + 13558.4i) q^{81} +(50780.2 + 65961.7i) q^{82} -48036.9 q^{83} +(75018.0 - 49653.1i) q^{84} -5641.84 q^{85} +(-29781.8 - 38685.5i) q^{86} +(32823.1 + 29225.2i) q^{87} +(-19199.6 - 45736.8i) q^{88} +63513.7i q^{89} +(-24625.3 + 23970.3i) q^{90} -177329. i q^{91} +(31826.6 - 120300. i) q^{92} +(58208.5 + 51828.1i) q^{93} +(-23696.9 + 18242.9i) q^{94} -52925.3 q^{95} +(-50138.3 + 75099.1i) q^{96} -47892.4 q^{97} +(70452.4 - 54237.3i) q^{98} +(7696.22 + 66140.9i) 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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