LMFDB - Embedded newform 60.6.e.a.11.7

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			11.7
Character	$\chi$	$=$	60.11
Dual form			60.6.e.a.11.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.53291 - 3.38418i) q^{2} +(12.7254 - 9.00363i) q^{3} +(9.09463 + 30.6804i) q^{4} -25.0000i q^{5} +(-88.1529 - 2.25224i) q^{6} -20.4870i q^{7} +(62.6029 - 169.850i) q^{8} +(80.8694 - 229.149i) q^{9} +O(q^{10})$	\(q+(-4.53291 - 3.38418i) q^{2} +(12.7254 - 9.00363i) q^{3} +(9.09463 + 30.6804i) q^{4} -25.0000i q^{5} +(-88.1529 - 2.25224i) q^{6} -20.4870i q^{7} +(62.6029 - 169.850i) q^{8} +(80.8694 - 229.149i) q^{9} +(-84.6045 + 113.323i) q^{10} +681.335 q^{11} +(391.967 + 308.534i) q^{12} -767.277 q^{13} +(-69.3316 + 92.8656i) q^{14} +(-225.091 - 318.134i) q^{15} +(-858.575 + 558.054i) q^{16} -2038.21i q^{17} +(-1142.05 + 765.035i) q^{18} -321.846i q^{19} +(767.010 - 227.366i) q^{20} +(-184.457 - 260.704i) q^{21} +(-3088.43 - 2305.76i) q^{22} -3927.07 q^{23} +(-732.618 - 2725.05i) q^{24} -625.000 q^{25} +(3478.00 + 2596.60i) q^{26} +(-1034.08 - 3644.12i) q^{27} +(628.548 - 186.321i) q^{28} +1211.31i q^{29} +(-56.3060 + 2203.82i) q^{30} -2332.43i q^{31} +(5780.41 + 375.962i) q^{32} +(8670.23 - 6134.48i) q^{33} +(-6897.67 + 9239.03i) q^{34} -512.174 q^{35} +(7765.85 + 397.083i) q^{36} +8116.61 q^{37} +(-1089.19 + 1458.90i) q^{38} +(-9763.87 + 6908.27i) q^{39} +(-4246.24 - 1565.07i) q^{40} -442.133i q^{41} +(-46.1415 + 1805.98i) q^{42} +11058.4i q^{43} +(6196.49 + 20903.6i) q^{44} +(-5728.72 - 2021.74i) q^{45} +(17801.1 + 13289.9i) q^{46} +19519.2 q^{47} +(-5901.16 + 14831.7i) q^{48} +16387.3 q^{49} +(2833.07 + 2115.11i) q^{50} +(-18351.3 - 25936.9i) q^{51} +(-6978.10 - 23540.4i) q^{52} -16369.3i q^{53} +(-7644.97 + 20018.0i) q^{54} -17033.4i q^{55} +(-3479.70 - 1282.54i) q^{56} +(-2897.78 - 4095.60i) q^{57} +(4099.29 - 5490.76i) q^{58} -2494.16 q^{59} +(7713.36 - 9799.19i) q^{60} +14438.4 q^{61} +(-7893.38 + 10572.7i) q^{62} +(-4694.56 - 1656.77i) q^{63} +(-24929.8 - 21266.1i) q^{64} +19181.9i q^{65} +(-60061.6 - 1534.53i) q^{66} +23655.1i q^{67} +(62533.1 - 18536.8i) q^{68} +(-49973.4 + 35357.9i) q^{69} +(2321.64 + 1733.29i) q^{70} +20086.3 q^{71} +(-33858.2 - 28081.0i) q^{72} -7207.09 q^{73} +(-36791.9 - 27468.1i) q^{74} +(-7953.35 + 5627.27i) q^{75} +(9874.37 - 2927.07i) q^{76} -13958.5i q^{77} +(67637.6 + 1728.09i) q^{78} +51621.7i q^{79} +(13951.4 + 21464.4i) q^{80} +(-45969.3 - 37062.2i) q^{81} +(-1496.26 + 2004.15i) q^{82} +61999.4 q^{83} +(6320.93 - 8030.22i) q^{84} -50955.2 q^{85} +(37423.8 - 50126.9i) q^{86} +(10906.2 + 15414.3i) q^{87} +(42653.5 - 115724. i) q^{88} +97726.8i q^{89} +(19125.9 + 28551.4i) q^{90} +15719.2i q^{91} +(-35715.3 - 120484. i) q^{92} +(-21000.4 - 29681.0i) q^{93} +(-88478.9 - 66056.5i) q^{94} -8046.15 q^{95} +(76942.7 - 47260.4i) q^{96} +106672. q^{97} +(-74282.2 - 55457.5i) q^{98} +(55099.2 - 156127. i) 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 $

$2$	−4.53291	−	3.38418i	−0.801314	−	0.598244i
$2$	−4.53291	−	3.38418i	−0.801314	−	0.598244i
$3$	12.7254	−	9.00363i	0.816332	−	0.577583i
$3$	12.7254	−	9.00363i	0.816332	−	0.577583i
$4$	9.09463	+	30.6804i	0.284207	+	0.958763i
$5$		−	25.0000i		−	0.447214i
$5$		−	25.0000i		−	0.447214i
$6$	−88.1529	−	2.25224i	−0.999674	−	0.0255409i
$7$		−	20.4870i		−	0.158027i	−0.996874	−	0.0790137i	$-0.974823\pi$
$7$		−	20.4870i		−	0.158027i	0.996874	−	0.0790137i	$-0.0251771\pi$
$8$	62.6029	−	169.850i	0.345835	−	0.938295i
$9$	80.8694	−	229.149i	0.332796	−	0.942999i
$10$	−84.6045	+	113.323i	−0.267543	+	0.358358i
$11$	681.335			1.69777			0.848885	−	0.528577i	$-0.177274\pi$
$11$	681.335			1.69777			0.848885	+	0.528577i	$0.177274\pi$
$12$	391.967	+	308.534i	0.785773	+	0.618516i
$13$	−767.277			−1.25920			−0.629598	−	0.776921i	$-0.716781\pi$
$13$	−767.277			−1.25920			−0.629598	+	0.776921i	$0.716781\pi$
$14$	−69.3316	+	92.8656i	−0.0945390	+	0.126629i
$15$	−225.091	−	318.134i	−0.258303	−	0.365075i
$16$	−858.575	+	558.054i	−0.838452	+	0.544975i
$17$		−	2038.21i		−	1.71051i	−0.518205	−	0.855257i	$-0.673399\pi$
$17$		−	2038.21i		−	1.71051i	0.518205	−	0.855257i	$-0.326601\pi$
$18$	−1142.05	+	765.035i	−0.830818	+	0.556545i
$19$		−	321.846i		−	0.204533i	−0.994757	−	0.102267i	$-0.967390\pi$
$19$		−	321.846i		−	0.204533i	0.994757	−	0.102267i	$-0.0326095\pi$
$20$	767.010	−	227.366i	0.428772	−	0.127101i
$21$	−184.457	−	260.704i	−0.0912739	−	0.129003i
$22$	−3088.43	−	2305.76i	−1.36045	−	1.01568i
$23$	−3927.07			−1.54792			−0.773962	−	0.633232i	$-0.781728\pi$
$23$	−3927.07			−1.54792			−0.773962	+	0.633232i	$0.781728\pi$
$24$	−732.618	−	2725.05i	−0.259627	−	0.965709i
$25$	−625.000			−0.200000
$26$	3478.00	+	2596.60i	1.00901	+	0.753307i
$27$	−1034.08	−	3644.12i	−0.272988	−	0.962017i
$28$	628.548	−	186.321i	0.151511	−	0.0449125i
$29$			1211.31i			0.267461i	0.991018	+	0.133730i	$0.0426956\pi$
$29$			1211.31i			0.267461i	−0.991018	+	0.133730i	$0.957304\pi$
$30$	−56.3060	+	2203.82i	−0.0114222	+	0.447068i
$31$		−	2332.43i		−	0.435918i	−0.975958	−	0.217959i	$-0.930060\pi$
$31$		−	2332.43i		−	0.435918i	0.975958	−	0.217959i	$-0.0699399\pi$
$32$	5780.41	+	375.962i	0.997892	+	0.0649036i
$33$	8670.23	−	6134.48i	1.38594	−	0.980603i
$34$	−6897.67	+	9239.03i	−1.02330	+	1.37066i
$35$	−512.174			−0.0706720
$36$	7765.85	+	397.083i	0.998695	+	0.0510652i
$37$	8116.61			0.974698			0.487349	−	0.873207i	$-0.337964\pi$
$37$	8116.61			0.974698			0.487349	+	0.873207i	$0.337964\pi$
$38$	−1089.19	+	1458.90i	−0.122361	+	0.163895i
$39$	−9763.87	+	6908.27i	−1.02792	+	0.727291i
$40$	−4246.24	−	1565.07i	−0.419618	−	0.154662i
$41$		−	442.133i		−	0.0410765i	−0.999789	−	0.0205382i	$-0.993462\pi$
$41$		−	442.133i		−	0.0410765i	0.999789	−	0.0205382i	$-0.00653798\pi$
$42$	−46.1415	+	1805.98i	−0.00403616	+	0.157976i
$43$			11058.4i			0.912058i	0.889965	+	0.456029i	$0.150729\pi$
$43$			11058.4i			0.912058i	−0.889965	+	0.456029i	$0.849271\pi$
$44$	6196.49	+	20903.6i	0.482519	+	1.62776i
$45$	−5728.72	−	2021.74i	−0.421722	−	0.148831i
$46$	17801.1	+	13289.9i	1.24037	+	0.926037i
$47$	19519.2			1.28889			0.644447	−	0.764649i	$-0.277088\pi$
$47$	19519.2			1.28889			0.644447	+	0.764649i	$0.277088\pi$
$48$	−5901.16	+	14831.7i	−0.369687	+	0.929156i
$49$	16387.3			0.975027
$50$	2833.07	+	2115.11i	0.160263	+	0.119649i
$51$	−18351.3	−	25936.9i	−0.987963	−	1.39635i
$52$	−6978.10	−	23540.4i	−0.357873	−	1.20727i
$53$		−	16369.3i		−	0.800460i	−0.916415	−	0.400230i	$-0.868930\pi$
$53$		−	16369.3i		−	0.800460i	0.916415	−	0.400230i	$-0.131070\pi$
$54$	−7644.97	+	20018.0i	−0.356772	+	0.934191i
$55$		−	17033.4i		−	0.759266i
$56$	−3479.70	−	1282.54i	−0.148276	−	0.0546514i
$57$	−2897.78	−	4095.60i	−0.118135	−	0.166967i
$58$	4099.29	−	5490.76i	0.160007	−	0.214320i
$59$	−2494.16			−0.0932814			−0.0466407	−	0.998912i	$-0.514852\pi$
$59$	−2494.16			−0.0932814			−0.0466407	+	0.998912i	$0.514852\pi$
$60$	7713.36	−	9799.19i	0.276609	−	0.351408i
$61$	14438.4			0.496816			0.248408	−	0.968655i	$-0.420093\pi$
$61$	14438.4			0.496816			0.248408	+	0.968655i	$0.420093\pi$
$62$	−7893.38	+	10572.7i	−0.260786	+	0.349307i
$63$	−4694.56	−	1656.77i	−0.149020	−	0.0525909i
$64$	−24929.8	−	21266.1i	−0.760796	−	0.648991i
$65$			19181.9i			0.563130i
$66$	−60061.6	−	1534.53i	−1.69722	−	0.0433626i
$67$			23655.1i			0.643779i	0.946777	+	0.321890i	$0.104318\pi$
$67$			23655.1i			0.643779i	−0.946777	+	0.321890i	$0.895682\pi$
$68$	62533.1	−	18536.8i	1.63998	−	0.486140i
$69$	−49973.4	+	35357.9i	−1.26362	+	0.894054i
$70$	2321.64	+	1733.29i	0.0566304	+	0.0422791i
$71$	20086.3			0.472884			0.236442	−	0.971646i	$-0.424019\pi$
$71$	20086.3			0.472884			0.236442	+	0.971646i	$0.424019\pi$
$72$	−33858.2	−	28081.0i	−0.769719	−	0.638383i
$73$	−7207.09			−0.158290			−0.0791449	−	0.996863i	$-0.525219\pi$
$73$	−7207.09			−0.158290			−0.0791449	+	0.996863i	$0.525219\pi$
$74$	−36791.9	−	27468.1i	−0.781039	−	0.583108i
$75$	−7953.35	+	5627.27i	−0.163266	+	0.115517i
$76$	9874.37	−	2927.07i	0.196099	−	0.0581299i
$77$		−	13958.5i		−	0.268294i
$78$	67637.6	+	1728.09i	1.25879	+	0.0321610i
$79$			51621.7i			0.930604i	0.885152	+	0.465302i	$0.154054\pi$
$79$			51621.7i			0.930604i	−0.885152	+	0.465302i	$0.845946\pi$
$80$	13951.4	+	21464.4i	0.243720	+	0.374967i
$81$	−45969.3	−	37062.2i	−0.778494	−	0.627652i
$82$	−1496.26	+	2004.15i	−0.0245738	+	0.0329151i
$83$	61999.4			0.987853			0.493927	−	0.869504i	$-0.335561\pi$
$83$	61999.4			0.987853			0.493927	+	0.869504i	$0.335561\pi$
$84$	6320.93	−	8030.22i	0.0977424	−	0.124174i
$85$	−50955.2			−0.764965
$86$	37423.8	−	50126.9i	0.545634	−	0.730845i
$87$	10906.2	+	15414.3i	0.154481	+	0.218337i
$88$	42653.5	−	115724.i	0.587149	−	1.59301i
$89$			97726.8i			1.30779i	0.756585	+	0.653896i	$0.226867\pi$
$89$			97726.8i			1.30779i	−0.756585	+	0.653896i	$0.773133\pi$
$90$	19125.9	+	28551.4i	0.248894	+	0.371553i
$91$			15719.2i			0.198988i
$92$	−35715.3	−	120484.i	−0.439931	−	1.48409i
$93$	−21000.4	−	29681.0i	−0.251779	−	0.355854i
$94$	−88478.9	−	66056.5i	−1.03281	−	0.771074i
$95$	−8046.15			−0.0914701
$96$	76942.7	−	47260.4i	0.852098	−	0.523382i
$97$	106672.			1.15112			0.575562	−	0.817758i	$-0.304783\pi$
$97$	106672.			1.15112			0.575562	+	0.817758i	$0.304783\pi$
$98$	−74282.2	−	55457.5i	−0.781303	−	0.583305i
$99$	55099.2	−	156127.i	0.565011	−	1.60100i
$100$	−5684.15	−	19175.3i	−0.0568415	−	0.191753i
$101$			150535.i			1.46837i	0.678950	+	0.734185i	$0.262435\pi$
$101$			150535.i			1.46837i	−0.678950	+	0.734185i	$0.737565\pi$
$102$	−4590.54	+	179674.i	−0.0436881	+	1.70996i
$103$			135952.i			1.26268i	0.775506	+	0.631340i	$0.217495\pi$
$103$			135952.i			1.26268i	−0.775506	+	0.631340i	$0.782505\pi$
$104$	−48033.7	+	130322.i	−0.435475	+	1.18150i
$105$	−6517.59	+	4611.42i	−0.0576918	+	0.0408189i
$106$	−55396.6	+	74200.5i	−0.478871	+	0.641420i
$107$	−76179.0			−0.643244			−0.321622	−	0.946868i	$-0.604228\pi$
$107$	−76179.0			−0.643244			−0.321622	+	0.946868i	$0.604228\pi$
$108$	102398.	−	64867.8i	0.844761	−	0.535143i
$109$	−162539.			−1.31036			−0.655180	−	0.755473i	$-0.727407\pi$
$109$	−162539.			−1.31036			−0.655180	+	0.755473i	$0.727407\pi$
$110$	−57644.0	+	77210.8i	−0.454227	+	0.608410i
$111$	103287.	−	73078.9i	0.795677	−	0.562969i
$112$	11432.8	+	17589.6i	0.0861209	+	0.132498i
$113$		−	240171.i		−	1.76940i	−0.466164	−	0.884698i	$-0.654364\pi$
$113$		−	240171.i		−	1.76940i	0.466164	−	0.884698i	$-0.345636\pi$
$114$	−724.874	+	28371.6i	−0.00522397	+	0.204467i
$115$			98176.9i			0.692253i
$116$	−37163.4	+	11016.4i	−0.256431	+	0.0760142i
$117$	−62049.2	+	175820.i	−0.419056	+	1.18742i
$118$	11305.8	+	8440.70i	0.0747477	+	0.0558051i
$119$	−41756.7			−0.270308
$120$	−68126.2	+	18315.5i	−0.431878	+	0.116109i
$121$	303166.			1.88242
$122$	−65448.2	−	48862.3i	−0.398106	−	0.297218i
$123$	−3980.80	−	5626.30i	−0.0237251	−	0.0335320i
$124$	71560.0	−	21212.6i	0.417942	−	0.123891i
$125$			15625.0i			0.0894427i
$126$	15673.2	+	23397.2i	0.0879493	+	0.131292i
$127$			1150.90i			0.00633181i	0.999995	+	0.00316591i	$0.00100774\pi$
$127$			1150.90i			0.00633181i	−0.999995	+	0.00316591i	$0.998992\pi$
$128$	41036.0	+	180764.i	0.221381	+	0.975187i
$129$	99566.0	+	140723.i	0.526789	+	0.744542i
$130$	64915.1	−	86950.0i	0.336889	−	0.451244i
$131$	138937.			0.707358			0.353679	−	0.935367i	$-0.384930\pi$
$131$	138937.			0.707358			0.353679	+	0.935367i	$0.384930\pi$
$132$	267061.	+	210215.i	1.33406	+	1.05010i
$133$	−6593.64			−0.0323219
$134$	80053.0	−	107226.i	0.385137	−	0.515869i
$135$	−91102.9	+	25851.9i	−0.430227	+	0.122084i
$136$	−346189.	−	127598.i	−1.60497	−	0.591556i
$137$		−	47378.6i		−	0.215665i	−0.994169	−	0.107833i	$-0.965609\pi$
$137$		−	47378.6i		−	0.215665i	0.994169	−	0.107833i	$-0.0343911\pi$
$138$	346183.	+	8844.72i	1.54742	+	0.0395354i
$139$		−	29701.3i		−	0.130388i	−0.997873	−	0.0651941i	$-0.979233\pi$
$139$		−	29701.3i		−	0.130388i	0.997873	−	0.0651941i	$-0.0207666\pi$
$140$	−4658.03	−	15713.7i	−0.0200855	−	0.0677577i
$141$	248389.	−	175744.i	1.05217	−	0.744443i
$142$	−91049.6	−	67975.8i	−0.378929	−	0.282900i
$143$	−522772.			−2.13783
$144$	58444.9	+	241871.i	0.234877	+	0.972025i
$145$	30282.7			0.119612
$146$	32669.1	+	24390.1i	0.126840	+	0.0946960i
$147$	208534.	−	147545.i	0.795946	−	0.563159i
$148$	73817.6	+	249021.i	0.277016	+	0.934505i
$149$		−	263191.i		−	0.971194i	−0.874183	−	0.485597i	$-0.838602\pi$
$149$		−	263191.i		−	0.971194i	0.874183	−	0.485597i	$-0.161398\pi$
$150$	55095.5	+	1407.65i	0.199935	+	0.00510818i
$151$		−	29711.9i		−	0.106044i	−0.998593	−	0.0530222i	$-0.983115\pi$
$151$		−	29711.9i		−	0.106044i	0.998593	−	0.0530222i	$-0.0168854\pi$
$152$	−54665.4	−	20148.5i	−0.191913	−	0.0707348i
$153$	−467053.	−	164829.i	−1.61301	−	0.569252i
$154$	−47238.0	+	63272.6i	−0.160505	+	0.214988i
$155$	−58310.8			−0.194949
$156$	−300747.	−	236731.i	−0.989442	−	0.778833i
$157$	109319.			0.353953			0.176977	−	0.984215i	$-0.443368\pi$
$157$	109319.			0.353953			0.176977	+	0.984215i	$0.443368\pi$
$158$	174697.	−	233997.i	0.556729	−	0.745706i
$159$	−147383.	−	208305.i	−0.462332	−	0.653441i
$160$	9399.04	−	144510.i	0.0290258	−	0.446271i
$161$			80453.8i			0.244614i
$162$	82949.5	+	323568.i	0.248328	+	0.968676i
$163$			310037.i			0.913997i	0.889467	+	0.456999i	$0.151076\pi$
$163$			310037.i			0.913997i	−0.889467	+	0.456999i	$0.848924\pi$
$164$	13564.8	−	4021.04i	0.0393826	−	0.0116742i
$165$	−153362.	−	216756.i	−0.438539	−	0.619813i
$166$	−281038.	−	209817.i	−0.791580	−	0.590978i
$167$	−114004.			−0.316321			−0.158160	−	0.987413i	$-0.550556\pi$
$167$	−114004.			−0.316321			−0.158160	+	0.987413i	$0.550556\pi$
$168$	−55828.0	+	15009.1i	−0.152608	+	0.0410282i
$169$	217421.			0.585577
$170$	230976.	+	172442.i	0.612977	+	0.457636i
$171$	−73750.6	−	26027.5i	−0.192875	−	0.0680679i
$172$	−339277.	+	100572.i	−0.874448	+	0.259214i
$173$		−	124139.i		−	0.315350i	−0.987491	−	0.157675i	$-0.949600\pi$
$173$		−	124139.i		−	0.315350i	0.987491	−	0.157675i	$-0.0503998\pi$
$174$	2728.16	−	106780.i	0.00683119	−	0.267373i
$175$			12804.3i			0.0316055i
$176$	−584977.	+	380222.i	−1.42350	+	0.925242i
$177$	−31739.1	+	22456.5i	−0.0761486	+	0.0538777i
$178$	330725.	−	442987.i	0.782379	−	1.04795i
$179$	99467.4			0.232032			0.116016	−	0.993247i	$-0.462988\pi$
$179$	99467.4			0.232032			0.116016	+	0.993247i	$0.462988\pi$
$180$	9927.07	−	194146.i	0.0228370	−	0.446630i
$181$	301984.			0.685152			0.342576	−	0.939490i	$-0.388701\pi$
$181$	301984.			0.685152			0.342576	+	0.939490i	$0.388701\pi$
$182$	53196.5	−	71253.6i	0.119043	−	0.159451i
$183$	183734.	−	129998.i	0.405567	−	0.286953i
$184$	−245846.	+	667012.i	−0.535327	+	1.45241i
$185$		−	202915.i		−	0.435898i
$186$	−5253.20	+	205611.i	−0.0111338	+	0.435776i
$187$		−	1.38870e6i		−	2.90406i
$188$	177520.	+	598857.i	0.366313	+	1.23574i
$189$	−74656.9	+	21185.1i	−0.152025	+	0.0431396i
$190$	36472.5	+	27229.6i	0.0732962	+	0.0547215i
$191$	153353.			0.304164			0.152082	−	0.988368i	$-0.451402\pi$
$191$	153353.			0.304164			0.152082	+	0.988368i	$0.451402\pi$
$192$	−508713.	−	46161.0i	−0.995908	−	0.0903695i
$193$	−705142.			−1.36265			−0.681323	−	0.731983i	$-0.738595\pi$
$193$	−705142.			−1.36265			−0.681323	+	0.731983i	$0.738595\pi$
$194$	−483536.	−	360998.i	−0.922412	−	0.688654i
$195$	172707.	+	244097.i	0.325254	+	0.459701i
$196$	149036.	+	502769.i	0.277110	+	0.934820i
$197$		−	210132.i		−	0.385768i	−0.981222	−	0.192884i	$-0.938216\pi$
$197$		−	210132.i		−	0.385768i	0.981222	−	0.192884i	$-0.0617840\pi$
$198$	−778122.	+	521245.i	−1.41054	+	0.944885i
$199$			747889.i			1.33876i	0.742918	+	0.669382i	$0.233441\pi$
$199$			747889.i			1.33876i	−0.742918	+	0.669382i	$0.766559\pi$
$200$	−39126.8	+	106156.i	−0.0691670	+	0.187659i
$201$	212981.	+	301019.i	0.371836	+	0.525538i
$202$	509439.	−	682364.i	0.878444	−	1.17662i
$203$	24816.0			0.0422661
$204$	628858.	−	798912.i	1.05798	−	1.34407i
$205$	−11053.3			−0.0183699
$206$	460087.	−	616260.i	0.755391	−	1.01180i
$207$	−317580.	+	899884.i	−0.515143	+	1.45969i
$208$	658765.	−	428182.i	1.05578	−	0.686231i
$209$		−	219285.i		−	0.347251i
$210$	45149.6	+	1153.54i	0.0706489	+	0.00180503i
$211$		−	466221.i		−	0.720917i	−0.932775	−	0.360459i	$-0.882620\pi$
$211$		−	466221.i		−	0.720917i	0.932775	−	0.360459i	$-0.117380\pi$
$212$	502216.	−	148873.i	0.767451	−	0.227497i
$213$	255606.	−	180850.i	0.386030	−	0.273130i
$214$	345313.	+	257804.i	0.515441	+	0.384817i
$215$	276461.			0.407885
$216$	−683688.	−	52494.6i	−0.997065	−	0.0765561i
$217$	−47784.4			−0.0688870
$218$	736774.	+	550061.i	1.05001	+	0.783915i
$219$	−91712.8	+	64890.0i	−0.129217	+	0.0914255i
$220$	522591.	−	154912.i	0.727956	−	0.215789i
$221$			1.56387e6i			2.15387i
$222$	−715502.	−	18280.5i	−0.974380	−	0.0248947i
$223$			1.31947e6i			1.77679i	0.459078	+	0.888396i	$0.348180\pi$
$223$			1.31947e6i			1.77679i	−0.459078	+	0.888396i	$0.651820\pi$
$224$	7702.31	−	118423.i	0.0102565	−	0.157694i
$225$	−50543.4	+	143218.i	−0.0665592	+	0.188600i
$226$	−812784.	+	1.08868e6i	−1.05853	+	1.41784i
$227$	865232.			1.11447			0.557235	−	0.830355i	$-0.311862\pi$
$227$	865232.			1.11447			0.557235	+	0.830355i	$0.311862\pi$
$228$	99300.6	−	126153.i	0.126507	−	0.160717i
$229$	1.01891e6			1.28394			0.641972	−	0.766728i	$-0.278116\pi$
$229$	1.01891e6			1.28394			0.641972	+	0.766728i	$0.278116\pi$
$230$	332248.	−	445027.i	0.414136	−	0.554711i
$231$	−125677.	−	177627.i	−0.154962	−	0.219017i
$232$	205740.	+	75831.4i	0.250957	+	0.0924973i
$233$			1.23087e6i			1.48533i	0.669665	+	0.742664i	$0.266438\pi$
$233$			1.23087e6i			1.48533i	−0.669665	+	0.742664i	$0.733562\pi$
$234$	876272.	−	586993.i	1.04616	−	0.700799i
$235$		−	487980.i		−	0.576411i
$236$	−22683.5	−	76522.0i	−0.0265113	−	0.0894347i
$237$	464783.	+	656905.i	0.537501	+	0.759682i
$238$	189280.	+	141312.i	0.216601	+	0.161710i
$239$	593081.			0.671613			0.335806	−	0.941931i	$-0.390991\pi$
$239$	593081.			0.671613			0.335806	+	0.941931i	$0.390991\pi$
$240$	370793.	+	147529.i	0.415531	+	0.165329i
$241$	−872289.			−0.967426			−0.483713	−	0.875227i	$-0.660712\pi$
$241$	−872289.			−0.967426			−0.483713	+	0.875227i	$0.660712\pi$
$242$	−1.37423e6	−	1.02597e6i	−1.50841	−	1.12615i
$243$	−918670.	−	57740.1i	−0.998031	−	0.0627281i
$244$	131312.	+	442977.i	0.141199	+	0.476329i
$245$		−	409682.i		−	0.436045i
$246$	−995.789	+	38975.3i	−0.00104913	+	0.0410631i
$247$			246945.i			0.257548i
$248$	−396163.	−	146017.i	−0.409020	−	0.150756i
$249$	788965.	−	558220.i	0.806416	−	0.570567i
$250$	52877.8	−	70826.8i	0.0535086	−	0.0716717i
$251$	581747.			0.582841			0.291421	−	0.956595i	$-0.405872\pi$
$251$	581747.			0.582841			0.291421	+	0.956595i	$0.405872\pi$
$252$	8135.02	−	159099.i	0.00806969	−	0.157821i
$253$	−2.67565e6			−2.62802
$254$	3894.85	−	5216.93i	0.00378797	−	0.00507377i
$255$	−648423.	+	458782.i	−0.624465	+	0.441831i
$256$	425727.	−	958263.i	0.406005	−	0.913871i
$257$			1.32605e6i			1.25236i	0.779680	+	0.626178i	$0.215382\pi$
$257$			1.32605e6i			1.25236i	−0.779680	+	0.626178i	$0.784618\pi$
$258$	24906.3	−	974833.i	0.0232948	−	0.911761i
$259$		−	166285.i		−	0.154029i
$260$	−588509.	+	174453.i	−0.539908	+	0.160046i
$261$	277570.	+	97957.8i	0.252215	+	0.0890098i
$262$	−629789.	−	470188.i	−0.566816	−	0.423173i
$263$	−696552.			−0.620961			−0.310480	−	0.950580i	$-0.600490\pi$
$263$	−696552.			−0.620961			−0.310480	+	0.950580i	$0.600490\pi$
$264$	−499159.	−	1.85667e6i	−0.440787	−	1.63955i
$265$	−409232.			−0.357977
$266$	29888.4	+	22314.1i	0.0258999	+	0.0193364i
$267$	879895.	+	1.24361e6i	0.755358	+	1.06759i
$268$	−725747.	+	215134.i	−0.617232	+	0.182967i
$269$		−	948575.i		−	0.799265i	−0.916675	−	0.399633i	$-0.869138\pi$
$269$		−	948575.i		−	0.799265i	0.916675	−	0.399633i	$-0.130862\pi$
$270$	500449.	+	191124.i	0.417783	+	0.159553i
$271$		−	1.15631e6i		−	0.956422i	−0.878245	−	0.478211i	$-0.841285\pi$
$271$		−	1.15631e6i		−	0.956422i	0.878245	−	0.478211i	$-0.158715\pi$
$272$	1.13743e6	+	1.74996e6i	0.932187	+	1.43418i
$273$	141529.	+	200032.i	0.114932	+	0.162440i
$274$	−160338.	+	214763.i	−0.129021	+	0.172816i
$275$	−425834.			−0.339554
$276$	−1.53929e6	−	1.21164e6i	−1.21632	−	0.957415i
$277$	922162.			0.722118			0.361059	−	0.932543i	$-0.382415\pi$
$277$	922162.			0.722118			0.361059	+	0.932543i	$0.382415\pi$
$278$	−100514.	+	134633.i	−0.0780040	+	0.104482i
$279$	−534474.	−	188622.i	−0.411070	−	0.145072i
$280$	−32063.5	+	86992.5i	−0.0244409	+	0.0663112i
$281$		−	895607.i		−	0.676631i	−0.941033	−	0.338315i	$-0.890143\pi$
$281$		−	895607.i		−	0.676631i	0.941033	−	0.338315i	$-0.109857\pi$
$282$	−1.72067e6	−	43961.9i	−1.28847	−	0.0329196i
$283$		−	1.89178e6i		−	1.40412i	−0.712119	−	0.702059i	$-0.752264\pi$
$283$		−	1.89178e6i		−	1.40412i	0.712119	−	0.702059i	$-0.247736\pi$
$284$	182678.	+	616257.i	0.134397	+	0.453384i
$285$	−102390.	+	72444.5i	−0.0746700	+	0.0528316i
$286$	2.36968e6	+	1.76916e6i	1.71307	+	1.27894i
$287$	−9057.95			−0.00649120
$288$	553609.	−	1.29417e6i	0.393298	−	0.919411i
$289$	−2.73444e6			−1.92586
$290$	−137269.	−	102482.i	−0.0958467	−	0.0715572i
$291$	1.35744e6	−	960437.i	0.939700	−	0.664870i
$292$	−65545.9	−	221117.i	−0.0449871	−	0.151762i
$293$		−	2.03913e6i		−	1.38764i	−0.720151	−	0.693818i	$-0.755927\pi$
$293$		−	2.03913e6i		−	1.38764i	0.720151	−	0.693818i	$-0.244073\pi$
$294$	−1.44459e6	−	36908.1i	−0.974709	−	0.0249031i
$295$			62354.1i			0.0417167i
$296$	508123.	−	1.37860e6i	0.337085	−	0.914555i
$297$	−704553.	−	2.48286e6i	−0.463471	−	1.63328i
$298$	−890687.	+	1.19302e6i	−0.581011	+	0.778231i
$299$	3.01315e6			1.94914
$300$	−244980.	−	192834.i	−0.157155	−	0.123703i
$301$	226554.			0.144130
$302$	−100550.	+	134681.i	−0.0634405	+	0.0849748i
$303$	1.35537e6	+	1.91562e6i	0.848105	+	1.19868i
$304$	179608.	+	276329.i	0.111466	+	0.171491i
$305$		−	360961.i		−	0.222183i
$306$	1.55930e6	+	2.32775e6i	0.951977	+	1.42112i
$307$		−	464992.i		−	0.281579i	−0.990040	−	0.140789i	$-0.955036\pi$
$307$		−	464992.i		−	0.281579i	0.990040	−	0.140789i	$-0.0449640\pi$
$308$	428252.	−	126947.i	0.257230	−	0.0762512i
$309$	1.22406e6	+	1.73004e6i	0.729302	+	1.03077i
$310$	264318.	+	197334.i	0.156215	+	0.116627i
$311$	−2.89861e6			−1.69937			−0.849686	−	0.527289i	$-0.823208\pi$
$311$	−2.89861e6			−1.69937			−0.849686	+	0.527289i	$0.823208\pi$
$312$	562121.	+	2.09087e6i	0.326921	+	1.21602i
$313$	2.70104e6			1.55837			0.779186	−	0.626793i	$-0.215633\pi$
$313$	2.70104e6			1.55837			0.779186	+	0.626793i	$0.215633\pi$
$314$	−495533.	−	369955.i	−0.283628	−	0.211751i
$315$	−41419.2	+	117364.i	−0.0235193	+	0.0666436i
$316$	−1.58378e6	+	469481.i	−0.892229	+	0.264485i
$317$			130346.i			0.0728532i	0.999336	+	0.0364266i	$0.0115975\pi$
$317$			130346.i			0.0728532i	−0.999336	+	0.0364266i	$0.988402\pi$
$318$	−36867.5	+	1.44300e6i	−0.0204445	+	0.800199i
$319$			825307.i			0.454087i
$320$	−531654.	+	623244.i	−0.290238	+	0.340238i
$321$	−969406.	+	685888.i	−0.525101	+	0.371527i
$322$	272270.	−	364690.i	0.146339	−	0.196013i
$323$	−655989.			−0.349857
$324$	719011.	−	1.74742e6i	0.380516	−	0.924774i
$325$	479548.			0.251839
$326$	1.04922e6	−	1.40537e6i	0.546794	−	0.732399i
$327$	−2.06836e6	+	1.46344e6i	−1.06969	+	0.756842i
$328$	−75096.0	−	27678.8i	−0.0385418	−	0.0142057i
$329$		−	399889.i		−	0.203681i
$330$	−38363.2	+	1.50154e6i	−0.0193924	+	0.759018i
$331$		−	547886.i		−	0.274866i	−0.990511	−	0.137433i	$-0.956115\pi$
$331$		−	547886.i		−	0.274866i	0.990511	−	0.137433i	$-0.0438851\pi$
$332$	563862.	+	1.90217e6i	0.280755	+	0.947117i
$333$	656385.	−	1.85991e6i	0.324376	−	0.919139i
$334$	516769.	+	385809.i	0.253472	+	0.189237i
$335$	591376.			0.287907
$336$	303857.	+	120897.i	0.146832	+	0.0584207i
$337$	1.63196e6			0.782772			0.391386	−	0.920226i	$-0.371996\pi$
$337$	1.63196e6			0.782772			0.391386	+	0.920226i	$0.371996\pi$
$338$	−985549.	−	735790.i	−0.469231	−	0.350318i
$339$	−2.16241e6	−	3.05627e6i	−1.02197	−	1.44442i
$340$	−463419.	−	1.56333e6i	−0.217409	−	0.733420i
$341$		−	1.58917e6i		−	0.740089i
$342$	246223.	+	367566.i	0.113832	+	0.169930i
$343$		−	680050.i		−	0.312108i
$344$	1.87827e6	+	692290.i	0.855780	+	0.315422i
$345$	883948.	+	1.24934e6i	0.399833	+	0.565108i
$346$	−420108.	+	562711.i	−0.188656	+	0.252694i
$347$	−3.73409e6			−1.66479			−0.832397	−	0.554180i	$-0.813032\pi$
$347$	−3.73409e6			−1.66479			−0.832397	+	0.554180i	$0.813032\pi$
$348$	−373730.	+	474793.i	−0.165428	+	0.210163i
$349$	489164.			0.214976			0.107488	−	0.994206i	$-0.465719\pi$
$349$	489164.			0.214976			0.107488	+	0.994206i	$0.465719\pi$
$350$	43332.2	−	58041.0i	0.0189078	−	0.0253259i
$351$	793424.	+	2.79605e6i	0.343746	+	1.21137i
$352$	3.93839e6	+	256156.i	1.69419	+	0.110191i
$353$			3.46900e6i			1.48172i	0.671658	+	0.740861i	$0.265582\pi$
$353$			3.46900e6i			1.48172i	−0.671658	+	0.740861i	$0.734418\pi$
$354$	219868.	+	5617.46i	0.0932510	+	0.00238249i
$355$		−	502158.i		−	0.211480i
$356$	−2.99830e6	+	888789.i	−1.25386	+	0.371684i
$357$	−531369.	+	375962.i	−0.220661	+	0.156125i
$358$	−450877.	−	336616.i	−0.185931	−	0.138812i
$359$	−4.42901e6			−1.81372			−0.906862	−	0.421429i	$-0.861529\pi$
$359$	−4.42901e6			−1.81372			−0.906862	+	0.421429i	$0.861529\pi$
$360$	−702025.	+	846454.i	−0.285494	+	0.344229i
$361$	2.37251e6			0.958166
$362$	−1.36887e6	−	1.02197e6i	−0.549022	−	0.409888i
$363$	3.85790e6	−	2.72960e6i	1.53668	−	1.08726i
$364$	−482270.	+	142960.i	−0.190782	+	0.0565537i
$365$			180177.i			0.0707894i
$366$	−1.27279e6	−	32518.9i	−0.496654	−	0.0126891i
$367$		−	4.11688e6i		−	1.59552i	−0.602974	−	0.797761i	$-0.706018\pi$
$367$		−	4.11688e6i		−	1.59552i	0.602974	−	0.797761i	$-0.293982\pi$
$368$	3.37169e6	−	2.19152e6i	1.29786	−	0.843580i
$369$	−101314.	−	35755.0i	−0.0387351	−	0.0136701i
$370$	−686702.	+	919797.i	−0.260774	+	0.349291i
$371$	−335356.			−0.126495
$372$	719636.	−	914238.i	0.269622	−	0.342533i
$373$	1.73214e6			0.644630			0.322315	−	0.946632i	$-0.395539\pi$
$373$	1.73214e6			0.644630			0.322315	+	0.946632i	$0.395539\pi$
$374$	−4.69962e6	+	6.29487e6i	−1.73734	+	2.32706i
$375$	140682.	+	198834.i	0.0516606	+	0.0730150i
$376$	1.22196e6	−	3.31533e6i	0.445745	−	1.20936i
$377$		−	929409.i		−	0.336785i
$378$	410107.	+	156622.i	0.147628	+	0.0563798i
$379$			1.16291e6i			0.415863i	0.978143	+	0.207931i	$0.0666730\pi$
$379$			1.16291e6i			0.415863i	−0.978143	+	0.207931i	$0.933327\pi$
$380$	−73176.8	−	246859.i	−0.0259965	−	0.0876981i
$381$	10362.3	+	14645.6i	0.00365715	+	0.00516886i
$382$	−695135.	−	518973.i	−0.243731	−	0.181964i
$383$	−1.86840e6			−0.650837			−0.325419	−	0.945570i	$-0.605505\pi$
$383$	−1.86840e6			−0.650837			−0.325419	+	0.945570i	$0.605505\pi$
$384$	2.14973e6	+	1.93082e6i	0.743972	+	0.668211i
$385$	−348962.			−0.119985
$386$	3.19635e6	+	2.38633e6i	1.09191	+	0.815196i
$387$	2.53403e6	+	894289.i	0.860070	+	0.303529i
$388$	970145.	+	3.27275e6i	0.327158	+	1.10366i
$389$			2.03347e6i			0.681341i	0.940183	+	0.340670i	$0.110654\pi$
$389$			2.03347e6i			0.681341i	−0.940183	+	0.340670i	$0.889346\pi$
$390$	43202.3	−	1.69094e6i	0.0143829	−	0.562946i
$391$			8.00420e6i			2.64774i
$392$	1.02589e6	−	2.78337e6i	0.337199	−	0.914864i
$393$	1.76802e6	−	1.25094e6i	0.577439	−	0.408558i
$394$	−711123.	+	952509.i	−0.230783	+	0.309121i
$395$	1.29054e6			0.416179
$396$	5.29115e6	+	270546.i	1.69556	+	0.0866969i
$397$	−4.85163e6			−1.54494			−0.772469	−	0.635052i	$-0.780979\pi$
$397$	−4.85163e6			−1.54494			−0.772469	+	0.635052i	$0.780979\pi$
$398$	2.53099e6	−	3.39012e6i	0.800909	−	1.07277i
$399$	−83906.5	+	59366.7i	−0.0263854	+	0.0186686i
$400$	536610.	−	348784.i	0.167690	−	0.108995i
$401$		−	5.92095e6i		−	1.83878i	−0.393343	−	0.919392i	$-0.628681\pi$
$401$		−	5.92095e6i		−	1.83878i	0.393343	−	0.919392i	$-0.371319\pi$
$402$	53276.9	−	2.08526e6i	0.0164427	−	0.643569i
$403$			1.78962e6i			0.548907i
$404$	−4.61849e6	+	1.36907e6i	−1.40782	+	0.417321i
$405$	−926556.	+	1.14923e6i	−0.280695	+	0.348153i
$406$	−112489.	−	83981.9i	−0.0338684	−	0.0252854i
$407$	5.53013e6			1.65481
$408$	−5.55422e6	+	1.49323e6i	−1.65186	+	0.444095i
$409$	−2.42874e6			−0.717913			−0.358957	−	0.933354i	$-0.616867\pi$
$409$	−2.42874e6			−0.717913			−0.358957	+	0.933354i	$0.616867\pi$
$410$	50103.7	+	37406.4i	0.0147201	+	0.0109897i
$411$	−426579.	−	602909.i	−0.124565	−	0.176055i
$412$	−4.17107e6	+	1.23644e6i	−1.21061	+	0.358863i
$413$			51097.8i			0.0147410i
$414$	4.48494e6	−	3.00435e6i	1.28604	−	0.861489i
$415$		−	1.54999e6i		−	0.441781i
$416$	−4.43517e6	−	288467.i	−1.25654	−	0.0817264i
$417$	−267419.	−	377959.i	−0.0753100	−	0.106440i
$418$	−742100.	+	994000.i	−0.207741	+	0.278257i
$419$	5.14163e6			1.43076			0.715378	−	0.698738i	$-0.246255\pi$
$419$	5.14163e6			1.43076			0.715378	+	0.698738i	$0.246255\pi$
$420$	−200755.	−	158023.i	−0.0555321	−	0.0437117i
$421$	−4.22462e6			−1.16167			−0.580834	−	0.814022i	$-0.697273\pi$
$421$	−4.22462e6			−1.16167			−0.580834	+	0.814022i	$0.697273\pi$
$422$	−1.57778e6	+	2.11334e6i	−0.431285	+	0.577681i
$423$	1.57851e6	−	4.47280e6i	0.428939	−	1.21543i
$424$	−2.78031e6	−	1.02476e6i	−0.751068	−	0.276827i
$425$			1.27388e6i			0.342103i
$426$	−1.77067e6	−	45239.2i	−0.472730	−	0.0120779i
$427$		−	295800.i		−	0.0785106i
$428$	−692821.	−	2.33720e6i	−0.182815	−	0.616719i
$429$	−6.65247e6	+	4.70685e6i	−1.74518	+	1.23477i
$430$	−1.25317e6	−	935594.i	−0.326844	−	0.244015i
$431$	−85977.8			−0.0222943			−0.0111471	−	0.999938i	$-0.503548\pi$
$431$	−85977.8			−0.0222943			−0.0111471	+	0.999938i	$0.503548\pi$
$432$	2.92145e6	+	2.55168e6i	0.753163	+	0.657834i
$433$	5.57531e6			1.42906			0.714528	−	0.699607i	$-0.246641\pi$
$433$	5.57531e6			1.42906			0.714528	+	0.699607i	$0.246641\pi$
$434$	216603.	+	161711.i	0.0552001	+	0.0412112i
$435$	385358.	−	272654.i	0.0976431	−	0.0690858i
$436$	−1.47823e6	−	4.98676e6i	−0.372414	−	1.25632i
$437$			1.26391e6i			0.316602i
$438$	635326.	+	16232.1i	0.158238	+	0.00404287i
$439$			1.26655e6i			0.313662i	0.987625	+	0.156831i	$0.0501277\pi$
$439$			1.26655e6i			0.313662i	−0.987625	+	0.156831i	$0.949872\pi$
$440$	−2.89311e6	−	1.06634e6i	−0.712416	−	0.262581i
$441$	1.32523e6	−	3.75513e6i	0.324485	−	0.919450i
$442$	5.29242e6	−	7.08889e6i	1.28854	−	1.72593i
$443$	2.43716e6			0.590030			0.295015	−	0.955493i	$-0.404675\pi$
$443$	2.43716e6			0.590030			0.295015	+	0.955493i	$0.404675\pi$
$444$	3.18145e6	+	2.50425e6i	0.765891	+	0.602866i
$445$	2.44317e6			0.584862
$446$	4.46532e6	−	5.98103e6i	1.06296	−	1.42377i
$447$	−2.36968e6	−	3.34920e6i	−0.560945	−	0.792817i
$448$	−435678.	+	510735.i	−0.102558	+	0.120227i
$449$			290528.i			0.0680098i	0.999422	+	0.0340049i	$0.0108262\pi$
$449$			290528.i			0.0680098i	−0.999422	+	0.0340049i	$0.989174\pi$
$450$	713784.	−	478147.i	0.166164	−	0.111309i
$451$		−	301240.i		−	0.0697384i
$452$	7.36856e6	−	2.18427e6i	1.69643	−	0.502876i
$453$	−267515.	−	378094.i	−0.0612494	−	0.0865674i
$454$	−3.92202e6	−	2.92810e6i	−0.893040	−	0.666725i
$455$	392979.			0.0889899
$456$	−877046.	+	235790.i	−0.197520	+	0.0531024i
$457$	−4.43702e6			−0.993803			−0.496902	−	0.867807i	$-0.665529\pi$
$457$	−4.43702e6			−0.993803			−0.496902	+	0.867807i	$0.665529\pi$
$458$	−4.61862e6	−	3.44817e6i	−1.02884	−	0.768112i
$459$	−7.42747e6	+	2.10767e6i	−1.64554	+	0.466950i
$460$	−3.01211e6	+	892883.i	−0.663706	+	0.196743i
$461$			4.88335e6i			1.07020i	0.844788	+	0.535101i	$0.179727\pi$
$461$			4.88335e6i			1.07020i	−0.844788	+	0.535101i	$0.820273\pi$
$462$	−31437.8	+	1.23048e6i	−0.00685248	+	0.268207i
$463$			3.30428e6i			0.716348i	0.933655	+	0.358174i	$0.116601\pi$
$463$			3.30428e6i			0.716348i	−0.933655	+	0.358174i	$0.883399\pi$
$464$	−675976.	−	1.04000e6i	−0.145759	−	0.224253i
$465$	−742026.	+	525009.i	−0.159143	+	0.112599i
$466$	4.16548e6	−	5.57943e6i	0.888589	−	1.19021i
$467$	−2.42435e6			−0.514403			−0.257202	−	0.966358i	$-0.582800\pi$
$467$	−2.42435e6			−0.514403			−0.257202	+	0.966358i	$0.582800\pi$
$468$	−5.95856e6	−	304672.i	−1.25755	−	0.0643011i
$469$	484620.			0.101735
$470$	−1.65141e6	+	2.21197e6i	−0.344835	+	0.461886i
$471$	1.39112e6	−	984266.i	0.288943	−	0.204437i
$472$	−156142.	+	423633.i	−0.0322600	+	0.0875255i
$473$			7.53450e6i			1.54847i
$474$	116265.	−	4.55060e6i	0.0237685	−	0.930300i
$475$			201154.i			0.0409067i
$476$	−379762.	−	1.28111e6i	−0.0768235	−	0.259161i
$477$	−3.75100e6	−	1.32377e6i	−0.754833	−	0.266390i
$478$	−2.68838e6	−	2.00709e6i	−0.538173	−	0.401789i
$479$	3.29323e6			0.655818			0.327909	−	0.944709i	$-0.393656\pi$
$479$	3.29323e6			0.655818			0.327909	+	0.944709i	$0.393656\pi$
$480$	−1.18151e6	−	1.92357e6i	−0.234064	−	0.381070i
$481$	−6.22768e6			−1.22734
$482$	3.95401e6	+	2.95198e6i	0.775212	+	0.578757i
$483$	724376.	+	1.02380e6i	0.141285	+	0.199686i
$484$	2.75719e6	+	9.30126e6i	0.534999	+	1.80480i
$485$		−	2.66681e6i		−	0.514798i
$486$	3.96885e6	+	3.37068e6i	0.762209	+	0.647331i
$487$			9.58600e6i			1.83153i	0.401710	+	0.915767i	$0.368416\pi$
$487$			9.58600e6i			1.83153i	−0.401710	+	0.915767i	$0.631584\pi$
$488$	903888.	−	2.45236e6i	0.171817	−	0.466160i
$489$	2.79146e6	+	3.94534e6i	0.527909	+	0.746125i
$490$	−1.38644e6	+	1.85705e6i	−0.260862	+	0.349409i
$491$	−3.42101e6			−0.640400			−0.320200	−	0.947350i	$-0.603750\pi$
$491$	−3.42101e6			−0.640400			−0.320200	+	0.947350i	$0.603750\pi$
$492$	136413.	−	173302.i	0.0254064	−	0.0322768i
$493$	2.46890e6			0.457495
$494$	835706.	−	1.11938e6i	0.154076	−	0.206377i
$495$	−3.90318e6	−	1.37748e6i	−0.715987	−	0.252681i
$496$	1.30162e6	+	2.00257e6i	0.237564	+	0.365497i
$497$		−	411508.i		−	0.0747286i
$498$	−5.46543e6	−	139638.i	−0.987531	−	0.0252307i
$499$			670965.i			0.120628i	0.998179	+	0.0603140i	$0.0192102\pi$
$499$			670965.i			0.120628i	−0.998179	+	0.0603140i	$0.980790\pi$
$500$	−479381.	+	142104.i	−0.0857544	+	0.0254203i
$501$	−1.45074e6	+	1.02645e6i	−0.258223	+	0.182702i
$502$	−2.63701e6	−	1.96874e6i	−0.467039	−	0.348681i
$503$	74144.9			0.0130666			0.00653328	−	0.999979i	$-0.497920\pi$
$503$	74144.9			0.0130666			0.00653328	+	0.999979i	$0.497920\pi$
$504$	−575294.	+	693650.i	−0.100882	+	0.121637i
$505$	3.76339e6			0.656675
$506$	1.21285e7	+	9.05489e6i	2.10587	+	1.57220i
$507$	2.76675e6	−	1.95757e6i	0.478025	−	0.338219i
$508$	−35310.1	+	10467.0i	−0.00607071	+	0.00179955i
$509$		−	8.22309e6i		−	1.40683i	−0.710781	−	0.703414i	$-0.751658\pi$
$509$		−	8.22309e6i		−	1.40683i	0.710781	−	0.703414i	$-0.248342\pi$
$510$	4.49185e6	+	114763.i	0.764715	+	0.0195379i
$511$			147651.i			0.0250141i
$512$	−5.17272e6	+	2.90299e6i	−0.872055	+	0.489407i
$513$	−1.17284e6	+	332814.i	−0.196765	+	0.0558352i
$514$	4.48760e6	−	6.01089e6i	0.749215	−	1.00353i
$515$	3.39881e6			0.564688
$516$	−3.41191e6	+	4.33455e6i	−0.564122	+	0.716670i
$517$	1.32991e7			2.18825
$518$	−562737.	+	753754.i	−0.0921470	+	0.123426i
$519$	−1.11770e6	−	1.57971e6i	−0.182141	−	0.257430i
$520$	3.25804e6	+	1.20084e6i	0.528382	+	0.194750i
$521$			6.39310e6i			1.03185i	0.856633	+	0.515925i	$0.172552\pi$
$521$			6.39310e6i			1.03185i	−0.856633	+	0.515925i	$0.827448\pi$
$522$	−926693.	−	1.38338e6i	−0.148854	−	0.222211i
$523$		−	7.33325e6i		−	1.17231i	−0.810199	−	0.586155i	$-0.800641\pi$
$523$		−	7.33325e6i		−	1.17231i	0.810199	−	0.586155i	$-0.199359\pi$
$524$	1.26358e6	+	4.26264e6i	0.201036	+	0.678189i
$525$	115286.	+	162940.i	0.0182548	+	0.0258006i
$526$	3.15741e6	+	2.35726e6i	0.497584	+	0.371486i
$527$	−4.75399e6			−0.745644
$528$	−4.02067e6	+	1.01054e7i	−0.627644	+	1.57749i
$529$	8.98557e6			1.39607
$530$	1.85501e6	+	1.38491e6i	0.286852	+	0.214157i
$531$	−201702.	+	571535.i	−0.0310437	+	0.0879642i
$532$	−59966.8	−	202296.i	−0.00918611	−	0.0309890i
$533$			339238.i			0.0517233i
$534$	220104.	−	8.61489e6i	0.0334022	−	1.30736i
$535$			1.90448e6i			0.287668i
$536$	4.01780e6	+	1.48087e6i	0.604055	+	0.222642i
$537$	1.26576e6	−	895567.i	0.189415	−	0.134018i
$538$	−3.21015e6	+	4.29981e6i	−0.478156	+	0.640462i
$539$	1.11652e7			1.65537
$540$	−1.62170e6	−	2.55996e6i	−0.239323	−	0.377789i
$541$	4.28651e6			0.629666			0.314833	−	0.949147i	$-0.398051\pi$
$541$	4.28651e6			0.629666			0.314833	+	0.949147i	$0.398051\pi$
$542$	−3.91315e6	+	5.24144e6i	−0.572174	+	0.766394i
$543$	3.84285e6	−	2.71895e6i	0.559312	−	0.395732i
$544$	766289.	−	1.17817e7i	0.111018	−	1.70691i
$545$			4.06347e6i			0.586011i
$546$	35403.3	−	1.38569e6i	0.00508233	−	0.198923i
$547$			6.19383e6i			0.885097i	0.896744	+	0.442549i	$0.145926\pi$
$547$			6.19383e6i			0.885097i	−0.896744	+	0.442549i	$0.854074\pi$
$548$	1.45359e6	−	430891.i	0.206772	−	0.0612937i
$549$	1.16763e6	−	3.30855e6i	0.165338	−	0.468497i
$550$	1.93027e6	+	1.44110e6i	0.272089	+	0.203136i
$551$	389855.			0.0547046
$552$	2.87705e6	+	1.07015e7i	0.401883	+	1.49484i
$553$	1.05757e6			0.147061
$554$	−4.18008e6	−	3.12076e6i	−0.578643	−	0.432003i
$555$	−1.82697e6	−	2.58217e6i	−0.251767	−	0.355838i
$556$	911247.	−	270122.i	0.125011	−	0.0370573i
$557$		−	4.77647e6i		−	0.652333i	−0.945312	−	0.326166i	$-0.894243\pi$
$557$		−	4.77647e6i		−	0.652333i	0.945312	−	0.326166i	$-0.105757\pi$
$558$	1.78439e6	+	2.66377e6i	0.242608	+	0.362168i
$559$		−	8.48488e6i		−	1.14846i
$560$	439740.	−	285821.i	0.0592551	−	0.0385145i
$561$	−1.25034e7	−	1.76717e7i	−1.67733	−	2.37068i
$562$	−3.03090e6	+	4.05971e6i	−0.404791	+	0.542194i
$563$	−1.00423e7			−1.33525			−0.667626	−	0.744497i	$-0.732689\pi$
$563$	−1.00423e7			−1.33525			−0.667626	+	0.744497i	$0.732689\pi$
$564$	7.65089e6	+	6.02235e6i	1.01278	+	0.797201i
$565$	−6.00429e6			−0.791298
$566$	−6.40211e6	+	8.57526e6i	−0.840006	+	1.12514i
$567$	−759292.	+	941770.i	−0.0991862	+	0.123023i
$568$	1.25746e6	−	3.41166e6i	0.163540	−	0.443705i
$569$		−	1.20533e7i		−	1.56072i	−0.625329	−	0.780362i	$-0.715035\pi$
$569$		−	1.20533e7i		−	1.56072i	0.625329	−	0.780362i	$-0.284965\pi$
$570$	709291.	+	18121.9i	0.0914402	+	0.00233623i
$571$		−	1.09626e6i		−	0.140709i	−0.997522	−	0.0703547i	$-0.977587\pi$
$571$		−	1.09626e6i		−	0.140709i	0.997522	−	0.0703547i	$-0.0224131\pi$
$572$	−4.75442e6	−	1.60389e7i	−0.607586	−	2.04967i
$573$	1.95147e6	−	1.38073e6i	0.248299	−	0.175680i
$574$	41058.9	+	30653.7i	0.00520149	+	0.00388333i
$575$	2.45442e6			0.309585
$576$	−6.88916e6	+	3.99284e6i	−0.865188	+	0.501448i
$577$	−2.65691e6			−0.332228			−0.166114	−	0.986107i	$-0.553122\pi$
$577$	−2.65691e6			−0.332228			−0.166114	+	0.986107i	$0.553122\pi$
$578$	1.23950e7	+	9.25384e6i	1.54321	+	1.15213i
$579$	−8.97318e6	+	6.34883e6i	−1.11237	+	0.787041i
$580$	275410.	+	929086.i	0.0339946	+	0.114680i
$581$		−	1.27018e6i		−	0.156108i
$582$	−9.40347e6	−	240252.i	−1.15075	−	0.0294008i
$583$		−	1.11530e7i		−	1.35900i
$584$	−451185.	+	1.22412e6i	−0.0547422	+	0.148523i
$585$	4.39551e6	+	1.55123e6i	0.531031	+	0.187407i
$586$	−6.90078e6	+	9.24319e6i	−0.830145	+	1.11193i
$587$	−4.31304e6			−0.516640			−0.258320	−	0.966059i	$-0.583169\pi$
$587$	−4.31304e6			−0.516640			−0.258320	+	0.966059i	$0.583169\pi$
$588$	6.42328e6	+	5.05604e6i	0.766150	+	0.603070i
$589$	−750684.			−0.0891598
$590$	211018.	−	282646.i	0.0249568	−	0.0334282i
$591$	−1.89195e6	−	2.67400e6i	−0.222813	−	0.314914i
$592$	−6.96872e6	+	4.52951e6i	−0.817238	+	0.531186i
$593$			1.26476e7i			1.47697i	0.674268	+	0.738487i	$0.264459\pi$
$593$			1.26476e7i			1.47697i	−0.674268	+	0.738487i	$0.735541\pi$
$594$	−5.20878e6	+	1.36389e7i	−0.605718	+	1.58604i
$595$			1.04392e6i			0.120885i
$596$	8.07482e6	−	2.39363e6i	0.931145	−	0.276020i
$597$	6.73371e6	+	9.51715e6i	0.773248	+	1.09288i
$598$	−1.36584e7	−	1.01971e7i	−1.56187	−	1.16606i
$599$	940927.			0.107149			0.0535746	−	0.998564i	$-0.482939\pi$
$599$	940927.			0.107149			0.0535746	+	0.998564i	$0.482939\pi$
$600$	457887.	+	1.70316e6i	0.0519254	+	0.193142i
$601$	−4.15378e6			−0.469092			−0.234546	−	0.972105i	$-0.575360\pi$
$601$	−4.15378e6			−0.469092			−0.234546	+	0.972105i	$0.575360\pi$
$602$	−1.02695e6	−	766699.i	−0.115493	−	0.0862250i
$603$	5.42053e6	+	1.91297e6i	0.607083	+	0.214247i
$604$	911573.	−	270219.i	0.101671	−	0.0301386i
$605$		−	7.57916e6i		−	0.841845i
$606$	339042.	−	1.32701e7i	0.0375035	−	1.46789i
$607$			6.76513e6i			0.745254i	0.927981	+	0.372627i	$0.121543\pi$
$607$			6.76513e6i			0.745254i	−0.927981	+	0.372627i	$0.878457\pi$
$608$	121002.	−	1.86040e6i	0.0132749	−	0.204102i
$609$	315793.	−	223434.i	0.0345032	−	0.0244122i
$610$	−1.22156e6	+	1.63621e6i	−0.132920	+	0.178038i
$611$	−1.49766e7			−1.62297
$612$	809338.	−	1.58284e7i	0.0873477	−	1.70828i
$613$	−3.55719e6			−0.382346			−0.191173	−	0.981556i	$-0.561229\pi$
$613$	−3.55719e6			−0.382346			−0.191173	+	0.981556i	$0.561229\pi$
$614$	−1.57362e6	+	2.10777e6i	−0.168453	+	0.225633i
$615$	−140657.	+	99519.9i	−0.0149960	+	0.0106102i
$616$	−2.37084e6	−	873841.i	−0.251739	−	0.0927856i
$617$		−	9.04265e6i		−	0.956275i	−0.878285	−	0.478138i	$-0.841312\pi$
$617$		−	9.04265e6i		−	0.956275i	0.878285	−	0.478138i	$-0.158688\pi$
$618$	306197.	−	1.19846e7i	0.0322500	−	1.26227i
$619$			5.32981e6i			0.559094i	0.960132	+	0.279547i	$0.0901843\pi$
$619$			5.32981e6i			0.559094i	−0.960132	+	0.279547i	$0.909816\pi$
$620$	−530316.	−	1.78900e6i	−0.0554058	−	0.186909i
$621$	4.06090e6	+	1.43107e7i	0.422565	+	1.48913i
$622$	1.31391e7	+	9.80941e6i	1.36173	+	1.01664i
$623$	2.00212e6			0.206667
$624$	4.52783e6	−	1.13800e7i	0.465509	−	1.16999i
$625$	390625.			0.0400000
$626$	−1.22436e7	−	9.14082e6i	−1.24874	−	0.932287i
$627$	−1.97436e6	−	2.79048e6i	−0.200566	−	0.283472i
$628$	994215.	+	3.35395e6i	0.100596	+	0.339357i
$629$		−	1.65433e7i		−	1.66723i
$630$	584931.	−	391831.i	0.0587155	−	0.0393321i
$631$		−	1.65389e7i		−	1.65361i	−0.562486	−	0.826807i	$-0.690155\pi$
$631$		−	1.65389e7i		−	1.65361i	0.562486	−	0.826807i	$-0.309845\pi$
$632$	8.76793e6	+	3.23167e6i	0.873181	+	0.321836i
$633$	−4.19768e6	−	5.93283e6i	−0.416390	−	0.588508i
$634$	441114.	−	590846.i	0.0435840	−	0.0583783i
$635$	28772.5			0.00283167
$636$	5.05048e6	−	6.41622e6i	0.495097	−	0.628980i
$637$	−1.25736e7			−1.22775
$638$	2.79299e6	−	3.74104e6i	0.271655	−	0.363866i
$639$	1.62437e6	−	4.60276e6i	0.157374	−	0.445929i
$640$	4.51911e6	−	1.02590e6i	0.436117	−	0.0990046i
$641$			1.16495e7i			1.11985i	0.828542	+	0.559927i	$0.189171\pi$
$641$			1.16495e7i			1.11985i	−0.828542	+	0.559927i	$0.810829\pi$
$642$	6.71540e6	+	171574.i	0.643035	+	0.0164291i
$643$			5.98124e6i			0.570511i	0.958452	+	0.285255i	$0.0920784\pi$
$643$			5.98124e6i			0.570511i	−0.958452	+	0.285255i	$0.907922\pi$
$644$	−2.46836e6	+	731698.i	−0.234527	+	0.0695212i
$645$	3.51806e6	−	2.48915e6i	0.332969	−	0.235587i
$646$	2.97354e6	+	2.21999e6i	0.280345	+	0.209300i
$647$	3.64629e6			0.342444			0.171222	−	0.985232i	$-0.445228\pi$
$647$	3.64629e6			0.342444			0.171222	+	0.985232i	$0.445228\pi$
$648$	−9.17282e6	+	5.48766e6i	−0.858154	+	0.513393i
$649$	−1.69936e6			−0.158370
$650$	−2.17375e6	−	1.62288e6i	−0.201802	−	0.150661i
$651$	−608074.	+	430233.i	−0.0562346	+	0.0397879i
$652$	−9.51207e6	+	2.81968e6i	−0.876307	+	0.259765i
$653$		−	4.43691e6i		−	0.407190i	−0.979055	−	0.203595i	$-0.934737\pi$
$653$		−	4.43691e6i		−	0.407190i	0.979055	−	0.203595i	$-0.0652626\pi$
$654$	1.43283e7	+	366076.i	1.30993	+	0.0334678i
$655$		−	3.47342e6i		−	0.316340i
$656$	246734.	+	379604.i	0.0223856	+	0.0344407i
$657$	−582833.	+	1.65150e6i	−0.0526782	+	0.149267i
$658$	−1.35330e6	+	1.81266e6i	−0.121851	+	0.163212i
$659$	2.98319e6			0.267589			0.133794	−	0.991009i	$-0.457284\pi$
$659$	2.98319e6			0.267589			0.133794	+	0.991009i	$0.457284\pi$
$660$	5.25538e6	−	6.67653e6i	0.469618	−	0.596610i
$661$	7.43256e6			0.661660			0.330830	−	0.943690i	$-0.392671\pi$
$661$	7.43256e6			0.661660			0.330830	+	0.943690i	$0.392671\pi$
$662$	−1.85415e6	+	2.48352e6i	−0.164437	+	0.220254i
$663$	1.40805e7	+	1.99008e7i	1.24404	+	1.75828i
$664$	3.88134e6	−	1.05306e7i	0.341634	−	0.926898i
$665$			164841.i			0.0144548i
$666$	−9.26961e6	+	6.20949e6i	−0.809797	+	0.542463i
$667$		−	4.75690e6i		−	0.414009i
$668$	−1.03682e6	−	3.49768e6i	−0.0899007	−	0.303277i
$669$	1.18800e7	+	1.67907e7i	1.02624	+	1.45045i
$670$	−2.68066e6	−	2.00132e6i	−0.230704	−	0.172239i
$671$	9.83742e6			0.843480
$672$	−968221.	−	1.57632e6i	−0.0827087	−	0.134655i
$673$	−1.68280e7			−1.43217			−0.716085	−	0.698013i	$-0.754068\pi$
$673$	−1.68280e7			−1.43217			−0.716085	+	0.698013i	$0.754068\pi$
$674$	−7.39755e6	−	5.52286e6i	−0.627246	−	0.468289i
$675$	646298.	+	2.27757e6i	0.0545976	+	0.192403i
$676$	1.97736e6	+	6.67055e6i	0.166425	+	0.561429i
$677$			9.53318e6i			0.799404i	0.916645	+	0.399702i	$0.130886\pi$
$677$			9.53318e6i			0.799404i	−0.916645	+	0.399702i	$0.869114\pi$
$678$	−540924.	+	2.11718e7i	−0.0451920	+	1.76882i
$679$		−	2.18539e6i		−	0.181909i
$680$	−3.18994e6	+	8.65472e6i	−0.264552	+	0.717763i
$681$	1.10104e7	−	7.79023e6i	0.909777	−	0.643698i
$682$	−5.37803e6	+	7.20356e6i	−0.442754	+	0.593043i
$683$	−2.22827e7			−1.82774			−0.913872	−	0.406002i	$-0.866923\pi$
$683$	−2.22827e7			−1.82774			−0.913872	+	0.406002i	$0.866923\pi$
$684$	127800.	−	2.49941e6i	0.0104445	−	0.204266i
$685$	−1.18446e6			−0.0964485
$686$	−2.30141e6	+	3.08261e6i	−0.186717	+	0.250097i
$687$	1.29660e7	−	9.17386e6i	1.04812	−	0.741584i
$688$	−6.17121e6	−	9.49450e6i	−0.497049	−	0.764717i
$689$			1.25598e7i			1.00794i
$690$	221118.	−	8.65457e6i	0.0176808	−	0.692027i
$691$			1.73408e7i			1.38158i	0.723058	+	0.690788i	$0.242736\pi$
$691$			1.73408e7i			1.38158i	−0.723058	+	0.690788i	$0.757264\pi$
$692$	3.80863e6	−	1.12900e6i	0.302345	−	0.0896247i
$693$	−3.19857e6	−	1.12881e6i	−0.253001	−	0.0892872i
$694$	1.69263e7	+	1.26368e7i	1.33402	+	0.995954i
$695$	−742532.			−0.0583113
$696$	3.30088e6	−	887427.i	0.258289	−	0.0694400i
$697$	−901159.			−0.0702618
$698$	−2.21734e6	−	1.65542e6i	−0.172264	−	0.128608i
$699$	1.10823e7	+	1.56633e7i	0.857900	+	1.21252i
$700$	−392843.	+	116451.i	−0.0303021	+	0.00898251i
$701$			3.41026e6i			0.262115i	0.991375	+	0.131058i	$0.0418373\pi$
$701$			3.41026e6i			0.262115i	−0.991375	+	0.131058i	$0.958163\pi$
$702$	5.86581e6	−	1.53593e7i	0.449247	−	1.17633i
$703$		−	2.61230e6i		−	0.199358i
$704$	−1.69855e7	−	1.44894e7i	−1.29166	−	1.10184i
$705$	−4.39359e6	−	6.20972e6i	−0.332925	−	0.470543i
$706$	1.17397e7	−	1.57247e7i	0.886432	−	1.18732i
$707$	3.08401e6			0.232043
$708$	−977631.	−	769536.i	−0.0732980	−	0.0576960i
$709$	−1.52586e6			−0.113999			−0.0569994	−	0.998374i	$-0.518153\pi$
$709$	−1.52586e6			−0.113999			−0.0569994	+	0.998374i	$0.518153\pi$
$710$	−1.69939e6	+	2.27624e6i	−0.126517	+	0.169462i
$711$	1.18291e7	+	4.17462e6i	0.877559	+	0.309701i
$712$	1.65989e7	+	6.11798e6i	1.22709	+	0.452280i
$713$			9.15964e6i			0.674768i
$714$	3.68097e6	+	94046.1i	0.270220	+	0.00690391i
$715$			1.30693e7i			0.956065i
$716$	904620.	+	3.05170e6i	0.0659453	+	0.222464i
$717$	7.54716e6	−	5.33988e6i	0.548259	−	0.387912i
$718$	2.00763e7	+	1.49886e7i	1.45336	+	1.08505i
$719$	1.49038e6			0.107517			0.0537583	−	0.998554i	$-0.482880\pi$
$719$	1.49038e6			0.107517			0.0537583	+	0.998554i	$0.482880\pi$
$720$	6.04677e6	−	1.46112e6i	0.434703	−	0.105040i
$721$	2.78525e6			0.199538
$722$	−1.07544e7	−	8.02902e6i	−0.767792	−	0.573217i
$723$	−1.11002e7	+	7.85376e6i	−0.789741	+	0.558769i
$724$	2.74643e6	+	9.26498e6i	0.194725	+	0.656898i
$725$		−	757068.i		−	0.0534921i
$726$	−2.67250e7	−	682803.i	−1.88181	−	0.0480788i
$727$		−	2.01845e7i		−	1.41639i	−0.706017	−	0.708194i	$-0.749510\pi$
$727$		−	2.01845e7i		−	1.41639i	0.706017	−	0.708194i	$-0.250490\pi$
$728$	2.66989e6	+	984064.i	0.186709	+	0.0688169i
$729$	−1.22103e7	+	7.53660e6i	−0.850955	+	0.525239i
$730$	609753.	−	816729.i	0.0423493	−	0.0567245i
$731$	2.25394e7			1.56009
$732$	5.65940e6	+	4.45476e6i	0.390385	+	0.307289i
$733$	−6.38127e6			−0.438679			−0.219340	−	0.975649i	$-0.570390\pi$
$733$	−6.38127e6			−0.438679			−0.219340	+	0.975649i	$0.570390\pi$
$734$	−1.39323e7	+	1.86614e7i	−0.954512	+	1.27851i
$735$	−3.68862e6	−	5.21335e6i	−0.251852	−	0.355958i
$736$	−2.27001e7	−	1.47643e6i	−1.54466	−	0.100466i
$737$			1.61170e7i			1.09299i
$738$	338247.	+	504940.i	0.0228609	+	0.0341270i
$739$		−	1.62657e7i		−	1.09562i	−0.836602	−	0.547812i	$-0.815461\pi$
$739$		−	1.62657e7i		−	1.09562i	0.836602	−	0.547812i	$-0.184539\pi$
$740$	6.22552e6	−	1.84544e6i	0.417923	−	0.123886i
$741$	2.22340e6	+	3.14246e6i	0.148755	+	0.210244i
$742$	1.52014e6	+	1.13491e6i	0.101362	+	0.0756747i
$743$	−1.19714e7			−0.795557			−0.397778	−	0.917481i	$-0.630219\pi$
$743$	−1.19714e7			−0.795557			−0.397778	+	0.917481i	$0.630219\pi$
$744$	−6.35599e6	+	1.70878e6i	−0.420970	+	0.113176i
$745$	−6.57978e6			−0.434331
$746$	−7.85164e6	−	5.86187e6i	−0.516551	−	0.385646i
$747$	5.01386e6	−	1.42071e7i	0.328754	−	0.931545i
$748$	4.26060e7	−	1.26297e7i	2.78430	−	0.825355i
$749$			1.56068e6i			0.101650i
$750$	35191.3	−	1.37739e6i	0.00228445	−	0.0894135i
$751$		−	9.93487e6i		−	0.642780i	−0.946947	−	0.321390i	$-0.895850\pi$
$751$		−	9.93487e6i		−	0.642780i	0.946947	−	0.321390i	$-0.104150\pi$
$752$	−1.67587e7	+	1.08928e7i	−1.08068	+	0.702415i
$753$	7.40294e6	−	5.23784e6i	0.475792	−	0.336639i
$754$	−3.14529e6	+	4.21293e6i	−0.201480	+	0.269871i
$755$	−742797.			−0.0474245
$756$	−1.32894e6	−	2.09783e6i	−0.0845673	−	0.133495i
$757$	−2.53967e6			−0.161079			−0.0805393	−	0.996751i	$-0.525664\pi$
$757$	−2.53967e6			−0.161079			−0.0805393	+	0.996751i	$0.525664\pi$
$758$	3.93551e6	−	5.27139e6i	0.248787	−	0.333236i
$759$	−3.40486e7	+	2.40906e7i	−2.14534	+	1.51790i
$760$	−503712.	+	1.36664e6i	−0.0316336	+	0.0858259i
$761$			1.19650e7i			0.748950i	0.927237	+	0.374475i	$0.122177\pi$
$761$			1.19650e7i			0.748950i	−0.927237	+	0.374475i	$0.877823\pi$
$762$	2592.10	−	101455.i	0.000161720	−	0.00632975i
$763$			3.32992e6i			0.207073i
$764$	1.39469e6	+	4.70492e6i	0.0864457	+	0.291621i
$765$	−4.12072e6	+	1.16763e7i	−0.254577	+	0.721361i
$766$	8.46929e6	+	6.32300e6i	0.521525	+	0.389360i
$767$	1.91371e6			0.117460
$768$	−3.21032e6	−	1.60273e7i	−0.196402	−	0.980524i
$769$	7.59430e6			0.463097			0.231548	−	0.972823i	$-0.425621\pi$
$769$	7.59430e6			0.463097			0.231548	+	0.972823i	$0.425621\pi$
$770$	1.58181e6	+	1.18095e6i	0.0961454	+	0.0717802i
$771$	1.19393e7	+	1.68745e7i	0.723340	+	1.02234i
$772$	−6.41301e6	−	2.16340e7i	−0.387274	−	1.30645i
$773$		−	1.90915e7i		−	1.14919i	−0.818439	−	0.574593i	$-0.805160\pi$
$773$		−	1.90915e7i		−	1.14919i	0.818439	−	0.574593i	$-0.194840\pi$
$774$	−8.46009e6	−	1.26293e7i	−0.507601	−	0.757754i
$775$			1.45777e6i			0.0871836i
$776$	6.67799e6	−	1.81182e7i	0.398099	−	1.08009i
$777$	−1.49716e6	−	2.11603e6i	−0.0889645	−	0.125739i
$778$	6.88164e6	−	9.21756e6i	0.407608	−	0.545968i
$779$	−142299.			−0.00840150
$780$	−5.91828e6	+	7.51869e6i	−0.348305	+	0.442492i
$781$	1.36855e7			0.802849
$782$	2.70877e7	−	3.62824e7i	1.58400	−	2.12167i
$783$	4.41415e6	−	1.25259e6i	0.257302	−	0.0730135i
$784$	−1.40697e7	+	9.14499e6i	−0.817514	+	0.531365i
$785$		−	2.73297e6i		−	0.158293i
$786$	−1.22477e7	−	312919.i	−0.707127	−	0.0180666i
$787$			2.01262e7i			1.15831i	0.815218	+	0.579155i	$0.196617\pi$
$787$			2.01262e7i			1.15831i	−0.815218	+	0.579155i	$0.803383\pi$
$788$	6.44692e6	−	1.91107e6i	0.369860	−	0.109638i
$789$	−8.86387e6	+	6.27149e6i	−0.506910	+	0.358656i
$790$	−5.84992e6	−	4.36743e6i	−0.333490	−	0.248977i
$791$	−4.92038e6			−0.279613
$792$	−2.30687e7	−	1.91326e7i	−1.30681	−	1.08383i
$793$	−1.10783e7			−0.625590
$794$	2.19920e7	+	1.64188e7i	1.23798	+	0.924251i
$795$	−5.20762e6	+	3.68457e6i	−0.292228	+	0.206761i
$796$	−2.29455e7	+	6.80177e6i	−1.28356	+	0.380487i
$797$		−	5.17898e6i		−	0.288801i	−0.989519	−	0.144400i	$-0.953875\pi$
$797$		−	5.17898e6i		−	0.288801i	0.989519	−	0.144400i	$-0.0461253\pi$
$798$	581249.	+	14850.5i	0.0323113	+	0.000825530i
$799$		−	3.97842e7i		−	2.20467i
$800$	−3.61275e6	−	234976.i	−0.199578	−	0.0129807i
$801$	2.23940e7	+	7.90311e6i	1.23325	+	0.435228i
$802$	−2.00376e7	+	2.68392e7i	−1.10004	+	1.47344i
$803$	−4.91044e6			−0.268740
$804$	−7.29840e6	+	9.27201e6i	−0.398187	+	0.505864i
$805$	2.01134e6			0.109395
$806$	6.05640e6	−	8.11220e6i	0.328380	−	0.439846i
$807$	−8.54062e6	−	1.20710e7i	−0.461642	−	0.652466i
$808$	2.55684e7	+	9.42395e6i	1.37776	+	0.507814i
$809$		−	359839.i		−	0.0193302i	−0.999953	−	0.00966511i	$-0.996923\pi$
$809$		−	359839.i		−	0.0193302i	0.999953	−	0.00966511i	$-0.00307655\pi$
$810$	8.08921e6	−	2.07374e6i	0.433205	−	0.111056i
$811$		−	1.11026e7i		−	0.592750i	−0.955072	−	0.296375i	$-0.904222\pi$
$811$		−	1.11026e7i		−	0.592750i	0.955072	−	0.296375i	$-0.0957778\pi$
$812$	225693.	+	761366.i	0.0120123	+	0.0405231i
$813$	−1.04109e7	−	1.47144e7i	−0.552413	−	0.780758i
$814$	−2.50676e7	−	1.87150e7i	−1.32602	−	0.989983i
$815$	7.75093e6			0.408752
$816$	3.02302e7	+	1.20278e7i	1.58933	+	0.632355i
$817$	3.55911e6			0.186546
$818$	1.10092e7	+	8.21928e6i	0.575274	+	0.429487i
$819$	3.60203e6	+	1.27120e6i	0.187645	+	0.0662222i
$820$	−100526.	−	339120.i	−0.00522087	−	0.0176124i
$821$		−	2.09829e7i		−	1.08644i	−0.839589	−	0.543222i	$-0.817204\pi$
$821$		−	2.09829e7i		−	1.08644i	0.839589	−	0.543222i	$-0.182796\pi$
$822$	−106708.	+	4.17656e6i	−0.00550829	+	0.215595i
$823$			3.50985e7i			1.80630i	0.429330	+	0.903148i	$0.358750\pi$
$823$			3.50985e7i			1.80630i	−0.429330	+	0.903148i	$0.641250\pi$
$824$	2.30914e7	+	8.51100e6i	1.18477	+	0.436679i
$825$	−5.41889e6	+	3.83405e6i	−0.277189	+	0.196121i
$826$	172924.	−	231622.i	0.00881873	−	0.0118122i
$827$	4.52044e6			0.229836			0.114918	−	0.993375i	$-0.463340\pi$
$827$	4.52044e6			0.229836			0.114918	+	0.993375i	$0.463340\pi$
$828$	−3.04971e7	−	1.55937e6i	−1.54590	−	0.0790450i
$829$	−1.51914e7			−0.767735			−0.383867	−	0.923388i	$-0.625408\pi$
$829$	−1.51914e7			−0.767735			−0.383867	+	0.923388i	$0.625408\pi$
$830$	−5.24543e6	+	7.02595e6i	−0.264293	+	0.354006i
$831$	1.17348e7	−	8.30281e6i	0.589488	−	0.417083i
$832$	1.91280e7	+	1.63170e7i	0.957992	+	0.817208i
$833$		−	3.34007e7i		−	1.66780i
$834$	−66894.4	+	2.61825e6i	−0.00333023	+	0.130346i
$835$			2.85009e6i			0.141463i
$836$	6.72775e6	−	1.99432e6i	0.332931	−	0.0986912i
$837$	−8.49966e6	+	2.41192e6i	−0.419361	+	0.119000i
$838$	−2.33065e7	−	1.74002e7i	−1.14648	−	0.855941i
$839$	1.66391e7			0.816068			0.408034	−	0.912967i	$-0.366215\pi$
$839$	1.66391e7			0.816068			0.408034	+	0.912967i	$0.366215\pi$
$840$	375228.	+	1.39570e6i	0.0183483	+	0.0682486i
$841$	1.90439e7			0.928465
$842$	1.91498e7	+	1.42969e7i	0.930860	+	0.694961i
$843$	−8.06371e6	−	1.13969e7i	−0.390810	−	0.552355i
$844$	1.43038e7	−	4.24011e6i	0.691189	−	0.204890i
$845$		−	5.43551e6i		−	0.261878i
$846$	−2.22920e7	+	1.49329e7i	−1.07084	+	0.717327i
$847$		−	6.21095e6i		−	0.297474i
$848$	9.13494e6	+	1.40543e7i	0.436231	+	0.671148i
$849$	−1.70328e7	−	2.40735e7i	−0.810995	−	1.14623i
$850$	4.31104e6	−	5.77439e6i	0.204661	−	0.274132i
$851$	−3.18745e7			−1.50876
$852$	7.87319e6	+	6.19733e6i	0.371579	+	0.292486i
$853$	−757984.			−0.0356687			−0.0178344	−	0.999841i	$-0.505677\pi$
$853$	−757984.			−0.0356687			−0.0178344	+	0.999841i	$0.505677\pi$
$854$	−1.00104e6	+	1.34084e6i	−0.0469685	+	0.0629116i
$855$	−650687.	+	1.84376e6i	−0.0304409	+	0.0862562i
$856$	−4.76903e6	+	1.29390e7i	−0.222457	+	0.603553i
$857$			6.79216e6i			0.315905i	0.987447	+	0.157952i	$0.0504892\pi$
$857$			6.79216e6i			0.315905i	−0.987447	+	0.157952i	$0.949511\pi$
$858$	4.60839e7	+	1.17741e6i	2.13713	+	0.0546021i
$859$			1.34595e7i			0.622367i	0.950350	+	0.311184i	$0.100725\pi$
$859$			1.34595e7i			0.622367i	−0.950350	+	0.311184i	$0.899275\pi$
$860$	2.51431e6	+	8.48193e6i	0.115924	+	0.391065i
$861$	−115266.	+	81554.4i	−0.00529898	+	0.00374921i
$862$	389730.	+	290964.i	0.0178647	+	0.0133374i
$863$	4.32536e7			1.97695			0.988474	−	0.151390i	$-0.0483751\pi$
$863$	4.32536e7			1.97695			0.988474	+	0.151390i	$0.0483751\pi$
$864$	−4.60734e6	−	2.14532e7i	−0.209974	−	0.977707i
$865$	−3.10347e6			−0.141029
$866$	−2.52724e7	−	1.88679e7i	−1.14512	−	0.854925i
$867$	−3.47967e7	+	2.46199e7i	−1.57214	+	1.11234i
$868$	−434582.	−	1.46605e6i	−0.0195782	−	0.0660463i
$869$			3.51717e7i			1.57995i
$870$	−2.66951e6	−	68203.9i	−0.119573	−	0.00305500i
$871$		−	1.81500e7i		−	0.810645i
$872$	−1.01754e7	+	2.76071e7i	−0.453169	+	1.22950i
$873$	8.62652e6	−	2.44438e7i	0.383089	−	1.08551i
$874$	4.27731e6	−	5.72921e6i	0.189405	−	0.253698i
$875$	320109.			0.0141344
$876$	−2.82495e6	−	2.22364e6i	−0.124380	−	0.0979047i
$877$	1.00835e7			0.442703			0.221351	−	0.975194i	$-0.428953\pi$
$877$	1.00835e7			0.442703			0.221351	+	0.975194i	$0.428953\pi$
$878$	4.28624e6	−	5.74117e6i	0.187646	−	0.251341i
$879$	−1.83595e7	−	2.59486e7i	−0.801474	−	1.13277i
$880$	9.50555e6	+	1.46244e7i	0.413781	+	0.636608i
$881$		−	5.34970e6i		−	0.232215i	−0.993237	−	0.116107i	$-0.962958\pi$
$881$		−	5.34970e6i		−	0.232215i	0.993237	−	0.116107i	$-0.0370416\pi$
$882$	−1.87152e7	+	1.25368e7i	−0.810070	+	0.542646i
$883$		−	1.63008e7i		−	0.703572i	−0.936080	−	0.351786i	$-0.885574\pi$
$883$		−	1.63008e7i		−	0.703572i	0.936080	−	0.351786i	$-0.114426\pi$
$884$	−4.79802e7	+	1.42228e7i	−2.06505	+	0.612146i
$885$	561413.	+	793478.i	0.0240949	+	0.0340547i
$886$	−1.10474e7	−	8.24778e6i	−0.472799	−	0.352982i
$887$	690733.			0.0294782			0.0147391	−	0.999891i	$-0.495308\pi$
$887$	690733.			0.0294782			0.0147391	+	0.999891i	$0.495308\pi$
$888$	−5.94638e6	−	2.21182e7i	−0.253058	−	0.941275i
$889$	23578.4			0.00100060
$890$	−1.10747e7	−	8.26813e6i	−0.468658	−	0.349891i
$891$	−3.13205e7	−	2.52518e7i	−1.32170	−	1.06561i
$892$	−4.04818e7	+	1.20001e7i	−1.70352	+	0.504977i
$893$		−	6.28218e6i		−	0.263622i
$894$	−592770.	+	2.32011e7i	−0.0248052	+	0.970877i
$895$		−	2.48669e6i		−	0.103768i
$896$	3.70331e6	−	840703.i	0.154106	−	0.0349842i
$897$	3.83434e7	−	2.71293e7i	1.59115	−	1.12579i
$898$	983198.	−	1.31694e6i	0.0406865	−	0.0544972i
$899$	2.82530e6			0.116591
$900$	−4.85366e6	−	248177.i	−0.199739	−	0.0102130i
$901$	−3.33640e7			−1.36920
$902$	−1.01945e6	+	1.36550e6i	−0.0417206	+	0.0558823i
$903$	2.88298e6	−	2.03980e6i	0.117658	−	0.0832471i
$904$	−4.07930e7	−	1.50354e7i	−1.66022	−	0.611920i
$905$		−	7.54959e6i		−	0.306409i
$906$	−66918.3	+	2.61919e6i	−0.00270847	+	0.106010i
$907$			552634.i			0.0223059i	0.999938	+	0.0111529i	$0.00355017\pi$
$907$			552634.i			0.0223059i	−0.999938	+	0.0111529i	$0.996450\pi$
$908$	7.86897e6	+	2.65457e7i	0.316740	+	1.06851i
$909$	3.44950e7	+	1.21737e7i	1.38467	+	0.488667i
$910$	−1.78134e6	−	1.32991e6i	−0.0713088	−	0.0532377i
$911$	7.62450e6			0.304380			0.152190	−	0.988351i	$-0.451367\pi$
$911$	7.62450e6			0.304380			0.152190	+	0.988351i	$0.451367\pi$
$912$	4.77353e6	+	1.89927e6i	0.190043	+	0.0756134i
$913$	4.22424e7			1.67715
$914$	2.01126e7	+	1.50157e7i	0.796348	+	0.594537i
$915$	−3.24996e6	−	4.59336e6i	−0.128329	−	0.181375i
$916$	9.26659e6	+	3.12605e7i	0.364906	+	1.23100i
$917$		−	2.84639e6i		−	0.111782i
$918$	4.08008e7	+	1.55820e7i	1.59795	+	0.610264i
$919$			9.45535e6i			0.369308i	0.982804	+	0.184654i	$0.0591165\pi$
$919$			9.45535e6i			0.369308i	−0.982804	+	0.184654i	$0.940884\pi$
$920$	1.66753e7	+	6.14615e6i	0.649537	+	0.239405i
$921$	−4.18662e6	−	5.91719e6i	−0.162635	−	0.229862i
$922$	1.65262e7	−	2.21358e7i	0.640243	−	0.857568i
$923$	−1.54118e7			−0.595454
$924$	4.30667e6	−	5.47127e6i	0.165944	−	0.210818i
$925$	−5.07288e6			−0.194940
$926$	1.11823e7	−	1.49780e7i	0.428551	−	0.574020i
$927$	3.11533e7	+	1.09944e7i	1.19071	+	0.420215i
$928$	−455406.	+	7.00185e6i	−0.0173591	+	0.266897i
$929$		−	172428.i		−	0.00655493i	−0.999995	−	0.00327746i	$-0.998957\pi$
$929$		−	172428.i		−	0.00655493i	0.999995	−	0.00327746i	$-0.00104325\pi$
$930$	5.14027e6	+	131330.i	0.194885	+	0.00497916i
$931$		−	5.27418e6i		−	0.199426i
$932$	−3.77636e7	+	1.11943e7i	−1.42408	+	0.422141i
$933$	−3.68858e7	+	2.60980e7i	−1.38725	+	0.981528i
$934$	1.09894e7	+	8.20445e6i	0.412198	+	0.307739i
$935$	−3.47176e7			−1.29873
$936$	2.59786e7	+	2.15459e7i	0.969227	+	0.803850i
$937$	1.83653e7			0.683360			0.341680	−	0.939816i	$-0.389004\pi$
$937$	1.83653e7			0.683360			0.341680	+	0.939816i	$0.389004\pi$
$938$	−2.19674e6	−	1.64004e6i	−0.0815214	−	0.0608622i
$939$	3.43718e7	−	2.43192e7i	1.27215	−	0.900089i
$940$	1.49714e7	−	4.43800e6i	0.552642	−	0.163820i
$941$		−	1.27692e7i		−	0.470100i	−0.971983	−	0.235050i	$-0.924475\pi$
$941$		−	1.27692e7i		−	0.470100i	0.971983	−	0.235050i	$-0.0755253\pi$
$942$	−9.63677e6	−	246212.i	−0.353838	−	0.00904029i
$943$			1.73629e6i			0.0635832i
$944$	2.14143e6	−	1.39188e6i	0.0782120	−	0.0508360i
$945$	529627.	+	1.86642e6i	0.0192926	+	0.0679877i
$946$	2.54981e7	−	3.41532e7i	0.926361	−	1.24081i
$947$	−6.19053e6			−0.224312			−0.112156	−	0.993691i	$-0.535776\pi$
$947$	−6.19053e6			−0.224312			−0.112156	+	0.993691i	$0.535776\pi$
$948$	−1.59271e7	+	2.02340e7i	−0.575593	+	0.731243i
$949$	5.52984e6			0.199318
$950$	680741.	−	911813.i	0.0244722	−	0.0327791i
$951$	1.17358e6	+	1.65870e6i	0.0420788	+	0.0594724i
$952$	−2.61409e6	+	7.09236e6i	−0.0934820	+	0.253629i
$953$			4.37797e7i			1.56149i	0.624847	+	0.780747i	$0.285161\pi$
$953$			4.37797e7i			1.56149i	−0.624847	+	0.780747i	$0.714839\pi$
$954$	1.25231e7	+	1.86946e7i	0.445492	+	0.665036i
$955$		−	3.83382e6i		−	0.136026i
$956$	5.39385e6	+	1.81960e7i	0.190877	+	0.643918i
$957$	7.43075e6	+	1.05023e7i	0.262273	+	0.370685i
$958$	−1.49279e7	−	1.11449e7i	−0.525516	−	0.392339i
$959$	−970643.			−0.0340810
$960$	−1.15402e6	+	1.27178e7i	−0.0404145	+	0.445384i
$961$	2.31889e7			0.809975
$962$	2.82296e7	+	2.10756e7i	0.983482	+	0.734247i
$963$	−6.16055e6	+	1.74563e7i	−0.214069	+	0.606579i
$964$	−7.93315e6	−	2.67622e7i	−0.274950	−	0.927532i
$965$			1.76285e7i			0.609394i
$966$	181201.	−	7.09223e6i	0.00624767	−	0.244534i
$967$			5.06463e7i			1.74173i	0.491521	+	0.870866i	$0.336441\pi$
$967$			5.06463e7i			1.74173i	−0.491521	+	0.870866i	$0.663559\pi$
$968$	1.89791e7	−	5.14927e7i	0.651008	−	1.76627i
$969$	−8.34770e6	+	5.90628e6i	−0.285599	+	0.202071i
$970$	−9.02496e6	+	1.20884e7i	−0.307975	+	0.412515i
$971$	2.44809e7			0.833257			0.416628	−	0.909077i	$-0.363212\pi$
$971$	2.44809e7			0.833257			0.416628	+	0.909077i	$0.363212\pi$
$972$	−6.58348e6	−	2.87103e7i	−0.223506	−	0.974702i
$973$	−608489.			−0.0206049
$974$	3.24408e7	−	4.34525e7i	1.09570	−	1.46763i
$975$	6.10242e6	−	4.31767e6i	0.205585	−	0.145458i
$976$	−1.23965e7	+	8.05744e6i	−0.416557	+	0.270752i
$977$			3.11204e7i			1.04306i	0.853233	+	0.521529i	$0.174638\pi$
$977$			3.11204e7i			1.04306i	−0.853233	+	0.521529i	$0.825362\pi$
$978$	698278.	−	2.73307e7i	0.0233443	−	0.913699i
$979$			6.65847e7i			2.22033i
$980$	1.25692e7	−	3.72591e6i	0.418064	−	0.123927i
$981$	−1.31444e7	+	3.72455e7i	−0.436082	+	1.23567i
$982$	1.55072e7	+	1.15773e7i	0.513161	+	0.383116i
$983$	−1.97896e7			−0.653209			−0.326605	−	0.945161i	$-0.605905\pi$
$983$	−1.97896e7			−0.653209			−0.326605	+	0.945161i	$0.605905\pi$
$984$	−1.20483e6	+	323915.i	−0.0396679	+	0.0106646i
$985$	−5.25329e6			−0.172521
$986$	−1.11913e7	−	8.35520e6i	−0.366597	−	0.273694i
$987$	−3.60045e6	−	5.08873e6i	−0.117642	−	0.166271i
$988$	−7.57637e6	+	2.24587e6i	−0.246927	+	0.0731970i
$989$		−	4.34273e7i		−	1.41180i
$990$	1.30311e7	+	1.94530e7i	0.422565	+	0.630812i
$991$			4.81206e7i			1.55649i	0.627960	+	0.778246i	$0.283890\pi$
$991$			4.81206e7i			1.55649i	−0.627960	+	0.778246i	$0.716110\pi$
$992$	876905.	−	1.34824e7i	0.0282926	−	0.434999i
$993$	−4.93296e6	−	6.97205e6i	−0.158758	−	0.224382i
$994$	−1.39262e6	+	1.86533e6i	−0.0447060	+	0.0598811i
$995$	1.86972e7			0.598714
$996$	2.43018e7	+	1.91290e7i	0.776228	+	0.611003i
$997$	2.32964e6			0.0742250			0.0371125	−	0.999311i	$-0.488184\pi$
$997$	2.32964e6			0.0742250			0.0371125	+	0.999311i	$0.488184\pi$
$998$	2.27067e6	−	3.04143e6i	0.0721650	−	0.0966609i
$999$	−8.39320e6	−	2.95779e7i	−0.266081	−	0.937677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.6.e.a.11.7	✓	40
3.2	odd	2	inner	60.6.e.a.11.34	yes	40
4.3	odd	2	inner	60.6.e.a.11.33	yes	40
12.11	even	2	inner	60.6.e.a.11.8	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.6.e.a.11.7	✓	40	1.1	even	1	trivial
60.6.e.a.11.8	yes	40	12.11	even	2	inner
60.6.e.a.11.33	yes	40	4.3	odd	2	inner
60.6.e.a.11.34	yes	40	3.2	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)

\(f(q)\)	\(=\)	\(q+(-4.53291 - 3.38418i) q^{2} +(12.7254 - 9.00363i) q^{3} +(9.09463 + 30.6804i) q^{4} -25.0000i q^{5} +(-88.1529 - 2.25224i) q^{6} -20.4870i q^{7} +(62.6029 - 169.850i) q^{8} +(80.8694 - 229.149i) q^{9} +O(q^{10})\)	\(q+(-4.53291 - 3.38418i) q^{2} +(12.7254 - 9.00363i) q^{3} +(9.09463 + 30.6804i) q^{4} -25.0000i q^{5} +(-88.1529 - 2.25224i) q^{6} -20.4870i q^{7} +(62.6029 - 169.850i) q^{8} +(80.8694 - 229.149i) q^{9} +(-84.6045 + 113.323i) q^{10} +681.335 q^{11} +(391.967 + 308.534i) q^{12} -767.277 q^{13} +(-69.3316 + 92.8656i) q^{14} +(-225.091 - 318.134i) q^{15} +(-858.575 + 558.054i) q^{16} -2038.21i q^{17} +(-1142.05 + 765.035i) q^{18} -321.846i q^{19} +(767.010 - 227.366i) q^{20} +(-184.457 - 260.704i) q^{21} +(-3088.43 - 2305.76i) q^{22} -3927.07 q^{23} +(-732.618 - 2725.05i) q^{24} -625.000 q^{25} +(3478.00 + 2596.60i) q^{26} +(-1034.08 - 3644.12i) q^{27} +(628.548 - 186.321i) q^{28} +1211.31i q^{29} +(-56.3060 + 2203.82i) q^{30} -2332.43i q^{31} +(5780.41 + 375.962i) q^{32} +(8670.23 - 6134.48i) q^{33} +(-6897.67 + 9239.03i) q^{34} -512.174 q^{35} +(7765.85 + 397.083i) q^{36} +8116.61 q^{37} +(-1089.19 + 1458.90i) q^{38} +(-9763.87 + 6908.27i) q^{39} +(-4246.24 - 1565.07i) q^{40} -442.133i q^{41} +(-46.1415 + 1805.98i) q^{42} +11058.4i q^{43} +(6196.49 + 20903.6i) q^{44} +(-5728.72 - 2021.74i) q^{45} +(17801.1 + 13289.9i) q^{46} +19519.2 q^{47} +(-5901.16 + 14831.7i) q^{48} +16387.3 q^{49} +(2833.07 + 2115.11i) q^{50} +(-18351.3 - 25936.9i) q^{51} +(-6978.10 - 23540.4i) q^{52} -16369.3i q^{53} +(-7644.97 + 20018.0i) q^{54} -17033.4i q^{55} +(-3479.70 - 1282.54i) q^{56} +(-2897.78 - 4095.60i) q^{57} +(4099.29 - 5490.76i) q^{58} -2494.16 q^{59} +(7713.36 - 9799.19i) q^{60} +14438.4 q^{61} +(-7893.38 + 10572.7i) q^{62} +(-4694.56 - 1656.77i) q^{63} +(-24929.8 - 21266.1i) q^{64} +19181.9i q^{65} +(-60061.6 - 1534.53i) q^{66} +23655.1i q^{67} +(62533.1 - 18536.8i) q^{68} +(-49973.4 + 35357.9i) q^{69} +(2321.64 + 1733.29i) q^{70} +20086.3 q^{71} +(-33858.2 - 28081.0i) q^{72} -7207.09 q^{73} +(-36791.9 - 27468.1i) q^{74} +(-7953.35 + 5627.27i) q^{75} +(9874.37 - 2927.07i) q^{76} -13958.5i q^{77} +(67637.6 + 1728.09i) q^{78} +51621.7i q^{79} +(13951.4 + 21464.4i) q^{80} +(-45969.3 - 37062.2i) q^{81} +(-1496.26 + 2004.15i) q^{82} +61999.4 q^{83} +(6320.93 - 8030.22i) q^{84} -50955.2 q^{85} +(37423.8 - 50126.9i) q^{86} +(10906.2 + 15414.3i) q^{87} +(42653.5 - 115724. i) q^{88} +97726.8i q^{89} +(19125.9 + 28551.4i) q^{90} +15719.2i q^{91} +(-35715.3 - 120484. i) q^{92} +(-21000.4 - 29681.0i) q^{93} +(-88478.9 - 66056.5i) q^{94} -8046.15 q^{95} +(76942.7 - 47260.4i) q^{96} +106672. q^{97} +(-74282.2 - 55457.5i) q^{98} +(55099.2 - 156127. i) 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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