LMFDB - Embedded newform 60.7.f.a.19.27

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(19,60)]

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, 0, 1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.f (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:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.27
Character	$\chi$	$=$	60.19
Dual form			60.7.f.a.19.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.26743 - 6.02115i) q^{2} +15.5885 q^{3} +(-8.50840 - 63.4319i) q^{4} +(-13.2381 - 124.297i) q^{5} +(82.1111 - 93.8604i) q^{6} -380.004 q^{7} +(-426.750 - 282.893i) q^{8} +243.000 q^{9} +O(q^{10})$	\(q+(5.26743 - 6.02115i) q^{2} +15.5885 q^{3} +(-8.50840 - 63.4319i) q^{4} +(-13.2381 - 124.297i) q^{5} +(82.1111 - 93.8604i) q^{6} -380.004 q^{7} +(-426.750 - 282.893i) q^{8} +243.000 q^{9} +(-818.142 - 575.017i) q^{10} +847.255i q^{11} +(-132.633 - 988.806i) q^{12} -311.394i q^{13} +(-2001.64 + 2288.06i) q^{14} +(-206.362 - 1937.60i) q^{15} +(-3951.21 + 1079.41i) q^{16} -4506.17i q^{17} +(1279.99 - 1463.14i) q^{18} -5561.11i q^{19} +(-7771.76 + 1897.29i) q^{20} -5923.67 q^{21} +(5101.45 + 4462.86i) q^{22} +15489.8 q^{23} +(-6652.38 - 4409.86i) q^{24} +(-15274.5 + 3290.92i) q^{25} +(-1874.95 - 1640.24i) q^{26} +3788.00 q^{27} +(3233.22 + 24104.4i) q^{28} -18883.3 q^{29} +(-12753.6 - 8963.63i) q^{30} +460.340i q^{31} +(-14313.5 + 29476.5i) q^{32} +13207.4i q^{33} +(-27132.3 - 23735.9i) q^{34} +(5030.54 + 47233.3i) q^{35} +(-2067.54 - 15414.0i) q^{36} -98574.7i q^{37} +(-33484.2 - 29292.7i) q^{38} -4854.15i q^{39} +(-29513.3 + 56788.8i) q^{40} +69606.4 q^{41} +(-31202.5 + 35667.3i) q^{42} +145883. q^{43} +(53743.0 - 7208.79i) q^{44} +(-3216.87 - 30204.2i) q^{45} +(81591.6 - 93266.5i) q^{46} -33666.1 q^{47} +(-61593.3 + 16826.3i) q^{48} +26753.8 q^{49} +(-60642.2 + 109305. i) q^{50} -70244.2i q^{51} +(-19752.3 + 2649.46i) q^{52} -128136. i q^{53} +(19953.0 - 22808.1i) q^{54} +(105311. - 11216.1i) q^{55} +(162167. + 107500. i) q^{56} -86689.1i q^{57} +(-99466.2 + 113699. i) q^{58} +114967. i q^{59} +(-121150. + 29575.8i) q^{60} +254794. q^{61} +(2771.78 + 2424.81i) q^{62} -92340.9 q^{63} +(102087. + 241449. i) q^{64} +(-38705.3 + 4122.27i) q^{65} +(79523.7 + 69569.0i) q^{66} +523410. q^{67} +(-285835. + 38340.3i) q^{68} +241463. q^{69} +(310897. + 218509. i) q^{70} -165291. i q^{71} +(-103700. - 68742.9i) q^{72} +508290. i q^{73} +(-593533. - 519235. i) q^{74} +(-238106. + 51300.4i) q^{75} +(-352752. + 47316.1i) q^{76} -321960. i q^{77} +(-29227.5 - 25568.9i) q^{78} +101497. i q^{79} +(186474. + 476835. i) q^{80} +59049.0 q^{81} +(366647. - 419110. i) q^{82} +38887.4 q^{83} +(50401.0 + 375750. i) q^{84} +(-560103. + 59653.3i) q^{85} +(768430. - 878385. i) q^{86} -294361. q^{87} +(239682. - 361566. i) q^{88} -1.05953e6 q^{89} +(-198808. - 139729. i) q^{90} +118331. i q^{91} +(-131794. - 982550. i) q^{92} +7176.00i q^{93} +(-177334. + 202708. i) q^{94} +(-691229. + 73618.7i) q^{95} +(-223125. + 459494. i) q^{96} -631894. i q^{97} +(140924. - 161088. i) q^{98} +205883. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	5.26743	−	6.02115i	0.658429	−	0.752643i
$2$	5.26743	−	6.02115i	0.658429	−	0.752643i
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	−8.50840	−	63.4319i	−0.132944	−	0.991124i
$5$	−13.2381	−	124.297i	−0.105905	−	0.994376i
$5$	−13.2381	−	124.297i	−0.105905	−	0.994376i
$6$	82.1111	−	93.8604i	0.380144	−	0.434539i
$7$	−380.004			−1.10788			−0.553941	−	0.832556i	$-0.686877\pi$
$7$	−380.004			−1.10788			−0.553941	+	0.832556i	$0.686877\pi$
$8$	−426.750	−	282.893i	−0.833496	−	0.552525i
$9$	243.000			0.333333
$10$	−818.142	−	575.017i	−0.818142	−	0.575017i
$11$			847.255i			0.636555i	0.947998	+	0.318278i	$0.103104\pi$
$11$			847.255i			0.636555i	−0.947998	+	0.318278i	$0.896896\pi$
$12$	−132.633	−	988.806i	−0.0767551	−	0.572225i
$13$		−	311.394i		−	0.141736i	−0.997486	−	0.0708679i	$-0.977423\pi$
$13$		−	311.394i		−	0.141736i	0.997486	−	0.0708679i	$-0.0225769\pi$
$14$	−2001.64	+	2288.06i	−0.729461	+	0.833840i
$15$	−206.362	−	1937.60i	−0.0611444	−	0.574103i
$16$	−3951.21	+	1079.41i	−0.964652	+	0.263527i
$17$		−	4506.17i		−	0.917192i	−0.888645	−	0.458596i	$-0.848352\pi$
$17$		−	4506.17i		−	0.917192i	0.888645	−	0.458596i	$-0.151648\pi$
$18$	1279.99	−	1463.14i	0.219476	−	0.250881i
$19$		−	5561.11i		−	0.810775i	−0.914145	−	0.405387i	$-0.867137\pi$
$19$		−	5561.11i		−	0.810775i	0.914145	−	0.405387i	$-0.132863\pi$
$20$	−7771.76	+	1897.29i	−0.971470	+	0.237161i
$21$	−5923.67			−0.639636
$22$	5101.45	+	4462.86i	0.479099	+	0.419126i
$23$	15489.8			1.27310			0.636551	−	0.771235i	$-0.280360\pi$
$23$	15489.8			1.27310			0.636551	+	0.771235i	$0.280360\pi$
$24$	−6652.38	−	4409.86i	−0.481219	−	0.319000i
$25$	−15274.5	+	3290.92i	−0.977568	+	0.210619i
$26$	−1874.95	−	1640.24i	−0.106677	−	0.0933229i
$27$	3788.00			0.192450
$28$	3233.22	+	24104.4i	0.147286	+	1.09805i
$29$	−18883.3			−0.774253			−0.387127	−	0.922027i	$-0.626532\pi$
$29$	−18883.3			−0.774253			−0.387127	+	0.922027i	$0.626532\pi$
$30$	−12753.6	−	8963.63i	−0.472354	−	0.331986i
$31$			460.340i			0.0154523i	0.999970	+	0.00772616i	$0.00245934\pi$
$31$			460.340i			0.0154523i	−0.999970	+	0.00772616i	$0.997541\pi$
$32$	−14313.5	+	29476.5i	−0.436812	+	0.899553i
$33$			13207.4i			0.367515i
$34$	−27132.3	−	23735.9i	−0.690319	−	0.603906i
$35$	5030.54	+	47233.3i	0.117330	+	1.10165i
$36$	−2067.54	−	15414.0i	−0.0443146	−	0.330375i
$37$		−	98574.7i		−	1.94608i	−0.230640	−	0.973039i	$-0.574082\pi$
$37$		−	98574.7i		−	1.94608i	0.230640	−	0.973039i	$-0.425918\pi$
$38$	−33484.2	−	29292.7i	−0.610224	−	0.533837i
$39$		−	4854.15i		−	0.0818312i
$40$	−29513.3	+	56788.8i	−0.461146	+	0.887324i
$41$	69606.4			1.00995			0.504973	−	0.863135i	$-0.331503\pi$
$41$	69606.4			1.00995			0.504973	+	0.863135i	$0.331503\pi$
$42$	−31202.5	+	35667.3i	−0.421155	+	0.481418i
$43$	145883.			1.83485			0.917425	−	0.397910i	$-0.130264\pi$
$43$	145883.			1.83485			0.917425	+	0.397910i	$0.130264\pi$
$44$	53743.0	−	7208.79i	0.630905	−	0.0846261i
$45$	−3216.87	−	30204.2i	−0.0353017	−	0.331459i
$46$	81591.6	−	93266.5i	0.838247	−	0.958192i
$47$	−33666.1			−0.324264			−0.162132	−	0.986769i	$-0.551837\pi$
$47$	−33666.1			−0.324264			−0.162132	+	0.986769i	$0.551837\pi$
$48$	−61593.3	+	16826.3i	−0.556942	+	0.152148i
$49$	26753.8			0.227403
$50$	−60642.2	+	109305.i	−0.485138	+	0.874438i
$51$		−	70244.2i		−	0.529541i
$52$	−19752.3	+	2649.46i	−0.140478	+	0.0188429i
$53$		−	128136.i		−	0.860681i	−0.902667	−	0.430341i	$-0.858393\pi$
$53$		−	128136.i		−	0.860681i	0.902667	−	0.430341i	$-0.141607\pi$
$54$	19953.0	−	22808.1i	0.126715	−	0.144846i
$55$	105311.	−	11216.1i	0.632976	−	0.0674145i
$56$	162167.	+	107500.i	0.923416	+	0.612133i
$57$		−	86689.1i		−	0.468101i
$58$	−99466.2	+	113699.i	−0.509790	+	0.582737i
$59$			114967.i			0.559781i	0.960032	+	0.279891i	$0.0902982\pi$
$59$			114967.i			0.559781i	−0.960032	+	0.279891i	$0.909702\pi$
$60$	−121150.	+	29575.8i	−0.560879	+	0.136925i
$61$	254794.			1.12253			0.561266	−	0.827635i	$-0.310314\pi$
$61$	254794.			1.12253			0.561266	+	0.827635i	$0.310314\pi$
$62$	2771.78	+	2424.81i	0.0116301	+	0.0101743i
$63$	−92340.9			−0.369294
$64$	102087.	+	241449.i	0.389433	+	0.921055i
$65$	−38705.3	+	4122.27i	−0.140939	+	0.0150106i
$66$	79523.7	+	69569.0i	0.276608	+	0.241983i
$67$	523410.			1.74028			0.870138	−	0.492809i	$-0.164030\pi$
$67$	523410.			1.74028			0.870138	+	0.492809i	$0.164030\pi$
$68$	−285835.	+	38340.3i	−0.909051	+	0.121935i
$69$	241463.			0.735026
$70$	310897.	+	218509.i	0.906405	+	0.637051i
$71$		−	165291.i		−	0.461822i	−0.972975	−	0.230911i	$-0.925829\pi$
$71$		−	165291.i		−	0.461822i	0.972975	−	0.230911i	$-0.0741706\pi$
$72$	−103700.	−	68742.9i	−0.277832	−	0.184175i
$73$			508290.i			1.30660i	0.757098	+	0.653301i	$0.226616\pi$
$73$			508290.i			1.30660i	−0.757098	+	0.653301i	$0.773384\pi$
$74$	−593533.	−	519235.i	−1.46470	−	1.28135i
$75$	−238106.	+	51300.4i	−0.564399	+	0.121601i
$76$	−352752.	+	47316.1i	−0.803578	+	0.107787i
$77$		−	321960.i		−	0.705229i
$78$	−29227.5	−	25568.9i	−0.0615897	−	0.0538800i
$79$			101497.i			0.205859i	0.994689	+	0.102930i	$0.0328216\pi$
$79$			101497.i			0.205859i	−0.994689	+	0.102930i	$0.967178\pi$
$80$	186474.	+	476835.i	0.364207	+	0.931318i
$81$	59049.0			0.111111
$82$	366647.	−	419110.i	0.664977	−	0.760128i
$83$	38887.4			0.0680103			0.0340051	−	0.999422i	$-0.489174\pi$
$83$	38887.4			0.0680103			0.0340051	+	0.999422i	$0.489174\pi$
$84$	50401.0	+	375750.i	0.0850356	+	0.633959i
$85$	−560103.	+	59653.3i	−0.912034	+	0.0971354i
$86$	768430.	−	878385.i	1.20812	−	1.38099i
$87$	−294361.			−0.447015
$88$	239682.	−	361566.i	0.351713	−	0.530567i
$89$	−1.05953e6			−1.50295			−0.751475	−	0.659761i	$-0.770657\pi$
$89$	−1.05953e6			−1.50295			−0.751475	+	0.659761i	$0.770657\pi$
$90$	−198808.	−	139729.i	−0.272714	−	0.191672i
$91$			118331.i			0.157027i
$92$	−131794.	−	982550.i	−0.169251	−	1.26180i
$93$			7176.00i			0.00892141i
$94$	−177334.	+	202708.i	−0.213505	+	0.244055i
$95$	−691229.	+	73618.7i	−0.806215	+	0.0858652i
$96$	−223125.	+	459494.i	−0.252194	+	0.519357i
$97$		−	631894.i		−	0.692355i	−0.938169	−	0.346178i	$-0.887479\pi$
$97$		−	631894.i		−	0.692355i	0.938169	−	0.346178i	$-0.112521\pi$
$98$	140924.	−	161088.i	0.149729	−	0.171154i
$99$			205883.i			0.212185i
$100$	338711.	+	940890.i	0.338711	+	0.940890i
$101$	−1.49061e6			−1.44677			−0.723385	−	0.690445i	$-0.757415\pi$
$101$	−1.49061e6			−1.44677			−0.723385	+	0.690445i	$0.757415\pi$
$102$	−422950.	−	370006.i	−0.398556	−	0.348665i
$103$	−498876.			−0.456543			−0.228271	−	0.973598i	$-0.573307\pi$
$103$	−498876.			−0.456543			−0.228271	+	0.973598i	$0.573307\pi$
$104$	−88091.0	+	132887.i	−0.0783126	+	0.118136i
$105$	78418.4	+	736295.i	0.0677408	+	0.636039i
$106$	−771523.	−	674945.i	−0.647786	−	0.566697i
$107$	−1.17394e6			−0.958286			−0.479143	−	0.877737i	$-0.659052\pi$
$107$	−1.17394e6			−0.958286			−0.479143	+	0.877737i	$0.659052\pi$
$108$	−32229.8	−	240280.i	−0.0255850	−	0.190742i
$109$	1.24446e6			0.960953			0.480476	−	0.877008i	$-0.340464\pi$
$109$	1.24446e6			0.960953			0.480476	+	0.877008i	$0.340464\pi$
$110$	487186.	−	693175.i	0.366030	−	0.520792i
$111$		−	1.53663e6i		−	1.12357i
$112$	1.50148e6	−	410179.i	1.06872	−	0.291957i
$113$			2.28429e6i			1.58313i	0.611087	+	0.791564i	$0.290733\pi$
$113$			2.28429e6i			1.58313i	−0.611087	+	0.791564i	$0.709267\pi$
$114$	−521967.	−	456628.i	−0.352313	−	0.308211i
$115$	−205057.	−	1.92534e6i	−0.134828	−	1.26594i
$116$	160666.	+	1.19780e6i	0.102932	+	0.767381i
$117$		−	75668.7i		−	0.0472453i
$118$	692235.	+	605582.i	0.421316	+	0.368576i
$119$			1.71236e6i			1.01614i
$120$	−460068.	+	885249.i	−0.266243	+	0.512297i
$121$	1.05372e6			0.594797
$122$	1.34211e6	−	1.53415e6i	0.739108	−	0.844867i
$123$	1.08506e6			0.583092
$124$	29200.3	−	3916.76i	0.0153152	−	0.00205429i
$125$	611258.	+	1.85501e6i	0.312964	+	0.949765i
$126$	−486399.	+	555998.i	−0.243154	+	0.277947i
$127$	−1.33841e6			−0.653396			−0.326698	−	0.945129i	$-0.605936\pi$
$127$	−1.33841e6			−0.653396			−0.326698	+	0.945129i	$0.605936\pi$
$128$	1.99154e6	+	657132.i	0.949639	+	0.313345i
$129$	2.27410e6			1.05935
$130$	−179057.	+	254764.i	−0.0815005	+	0.115960i
$131$			3.50060e6i			1.55714i	0.627556	+	0.778572i	$0.284055\pi$
$131$			3.50060e6i			1.55714i	−0.627556	+	0.778572i	$0.715945\pi$
$132$	837771.	−	112374.i	0.364253	−	0.0488589i
$133$			2.11324e6i			0.898243i
$134$	2.75703e6	−	3.15153e6i	1.14585	−	1.30981i
$135$	−50146.0	−	470837.i	−0.0203815	−	0.191368i
$136$	−1.27476e6	+	1.92301e6i	−0.506772	+	0.764476i
$137$		−	3.77105e6i		−	1.46656i	−0.679926	−	0.733281i	$-0.737988\pi$
$137$		−	3.77105e6i		−	1.46656i	0.679926	−	0.733281i	$-0.262012\pi$
$138$	1.27189e6	−	1.45388e6i	0.483962	−	0.553212i
$139$		−	593087.i		−	0.220838i	−0.993885	−	0.110419i	$-0.964781\pi$
$139$		−	593087.i		−	0.220838i	0.993885	−	0.110419i	$-0.0352193\pi$
$140$	2.95330e6	−	720977.i	1.07627	−	0.262747i
$141$	−524802.			−0.187214
$142$	−995242.	−	870659.i	−0.347587	−	0.304077i
$143$	263830.			0.0902227
$144$	−960145.	+	262296.i	−0.321551	+	0.0878424i
$145$	249979.	+	2.34713e6i	0.0819974	+	0.769899i
$146$	3.06049e6	+	2.67738e6i	0.983405	+	0.860304i
$147$	417050.			0.131291
$148$	−6.25278e6	+	838713.i	−1.92880	+	0.258719i
$149$	1.48276e6			0.448240			0.224120	−	0.974562i	$-0.428049\pi$
$149$	1.48276e6			0.448240			0.224120	+	0.974562i	$0.428049\pi$
$150$	−945319.	+	1.70389e6i	−0.280094	+	0.504857i
$151$		−	1.46213e6i		−	0.424672i	−0.977197	−	0.212336i	$-0.931893\pi$
$151$		−	1.46213e6i		−	0.424672i	0.977197	−	0.212336i	$-0.0681072\pi$
$152$	−1.57320e6	+	2.37320e6i	−0.447973	+	0.675778i
$153$		−	1.09500e6i		−	0.305731i
$154$	−1.93857e6	−	1.69590e6i	−0.530786	−	0.464343i
$155$	57218.9	−	6094.05i	0.0153654	−	0.00163648i
$156$	−307908.	+	41301.0i	−0.0811049	+	0.0108789i
$157$		−	4.68323e6i		−	1.21017i	−0.796161	−	0.605085i	$-0.793139\pi$
$157$		−	4.68323e6i		−	1.21017i	0.796161	−	0.605085i	$-0.206861\pi$
$158$	611126.	+	534626.i	0.154939	+	0.135544i
$159$		−	1.99744e6i		−	0.496915i
$160$	3.85333e6	+	1.38891e6i	0.940754	+	0.339088i
$161$	−5.88619e6			−1.41045
$162$	311036.	−	355543.i	0.0731587	−	0.0836270i
$163$	−6.78005e6			−1.56556			−0.782781	−	0.622298i	$-0.786199\pi$
$163$	−6.78005e6			−1.56556			−0.782781	+	0.622298i	$0.786199\pi$
$164$	−592239.	−	4.41527e6i	−0.134266	−	1.00098i
$165$	1.64164e6	−	174841.i	0.365449	−	0.0389218i
$166$	204837.	−	234147.i	0.0447799	−	0.0511875i
$167$	6.63886e6			1.42542			0.712712	−	0.701457i	$-0.247467\pi$
$167$	6.63886e6			1.42542			0.712712	+	0.701457i	$0.247467\pi$
$168$	2.52793e6	+	1.67576e6i	0.533134	+	0.353415i
$169$	4.72984e6			0.979911
$170$	−2.59112e6	+	3.68668e6i	−0.527401	+	0.750393i
$171$		−	1.35135e6i		−	0.270258i
$172$	−1.24123e6	−	9.25366e6i	−0.243932	−	1.81856i
$173$		−	8.64108e6i		−	1.66890i	−0.551085	−	0.834449i	$-0.685786\pi$
$173$		−	8.64108e6i		−	1.66890i	0.551085	−	0.834449i	$-0.314214\pi$
$174$	−1.55053e6	+	1.77239e6i	−0.294328	+	0.336443i
$175$	5.80437e6	−	1.25056e6i	1.08303	−	0.233341i
$176$	−914534.	−	3.34769e6i	−0.167750	−	0.614054i
$177$			1.79216e6i			0.323190i
$178$	−5.58102e6	+	6.37961e6i	−0.989586	+	1.13119i
$179$			9.09605e6i			1.58596i	0.609244	+	0.792982i	$0.291473\pi$
$179$			9.09605e6i			1.58596i	−0.609244	+	0.792982i	$0.708527\pi$
$180$	−1.88854e6	+	461041.i	−0.323823	+	0.0790537i
$181$	−3.61021e6			−0.608831			−0.304416	−	0.952539i	$-0.598461\pi$
$181$	−3.61021e6			−0.608831			−0.304416	+	0.952539i	$0.598461\pi$
$182$	712487.	+	623299.i	0.118185	+	0.103391i
$183$	3.97184e6			0.648095
$184$	−6.61029e6	−	4.38196e6i	−1.06113	−	0.703421i
$185$	−1.22525e7	+	1.30495e6i	−1.93513	+	0.206100i
$186$	43207.7	+	37799.0i	0.00671464	+	0.00587411i
$187$	3.81787e6			0.583844
$188$	286444.	+	2.13550e6i	0.0431089	+	0.321386i
$189$	−1.43945e6			−0.213212
$190$	−3.19773e6	+	4.54977e6i	−0.466209	+	0.663329i
$191$			770722.i			0.110611i	0.998469	+	0.0553054i	$0.0176133\pi$
$191$			770722.i			0.110611i	−0.998469	+	0.0553054i	$0.982387\pi$
$192$	1.59139e6	+	3.76382e6i	0.224839	+	0.531771i
$193$		−	856832.i		−	0.119186i	−0.998223	−	0.0595928i	$-0.981020\pi$
$193$		−	856832.i		−	0.119186i	0.998223	−	0.0595928i	$-0.0189802\pi$
$194$	−3.80473e6	−	3.32846e6i	−0.521096	−	0.455866i
$195$	−603356.	+	64259.9i	−0.0813710	+	0.00866635i
$196$	−227632.	−	1.69704e6i	−0.0302319	−	0.225385i
$197$			6.40644e6i			0.837950i	0.907998	+	0.418975i	$0.137610\pi$
$197$			6.40644e6i			0.837950i	−0.907998	+	0.418975i	$0.862390\pi$
$198$	1.23965e6	+	1.08447e6i	0.159700	+	0.139709i
$199$			7.76623e6i			0.985487i	0.870175	+	0.492743i	$0.164006\pi$
$199$			7.76623e6i			0.985487i	−0.870175	+	0.492743i	$0.835994\pi$
$200$	7.44938e6	+	2.91664e6i	0.931172	+	0.364580i
$201$	8.15916e6			1.00475
$202$	−7.85168e6	+	8.97517e6i	−0.952595	+	1.08890i
$203$	7.17571e6			0.857782
$204$	−4.45572e6	+	597665.i	−0.524841	+	0.0703992i
$205$	−921460.	−	8.65187e6i	−0.106958	−	1.00427i
$206$	−2.62780e6	+	3.00381e6i	−0.300601	+	0.343614i
$207$	3.76403e6			0.424367
$208$	336121.	+	1.23038e6i	0.0373513	+	0.136726i
$209$	4.71168e6			0.516103
$210$	4.84640e6	+	3.40621e6i	0.523313	+	0.367802i
$211$		−	1.37248e7i		−	1.46103i	−0.682898	−	0.730514i	$-0.739281\pi$
$211$		−	1.37248e7i		−	1.46103i	0.682898	−	0.730514i	$-0.260719\pi$
$212$	−8.12789e6	+	1.09023e6i	−0.853041	+	0.114422i
$213$		−	2.57663e6i		−	0.266633i
$214$	−6.18365e6	+	7.06847e6i	−0.630963	+	0.721247i
$215$	−1.93122e6	−	1.81329e7i	−0.194320	−	1.82453i
$216$	−1.61653e6	−	1.07160e6i	−0.160406	−	0.106333i
$217$		−	174931.i		−	0.0171194i
$218$	6.55511e6	−	7.49309e6i	0.632719	−	0.723255i
$219$			7.92346e6i			0.754367i
$220$	−1.60749e6	−	6.58467e6i	−0.150966	−	0.618395i
$221$	−1.40319e6			−0.129999
$222$	−9.25226e6	−	8.09408e6i	−0.845647	−	0.739790i
$223$	−6.24824e6			−0.563434			−0.281717	−	0.959498i	$-0.590904\pi$
$223$	−6.24824e6			−0.563434			−0.281717	+	0.959498i	$0.590904\pi$
$224$	5.43917e6	−	1.12012e7i	0.483937	−	0.996599i
$225$	−3.71170e6	+	799695.i	−0.325856	+	0.0702064i
$226$	1.37540e7	+	1.20323e7i	1.19153	+	1.04238i
$227$	−9.00061e6			−0.769475			−0.384738	−	0.923026i	$-0.625708\pi$
$227$	−9.00061e6			−0.769475			−0.384738	+	0.923026i	$0.625708\pi$
$228$	−5.49885e6	+	737585.i	−0.463946	+	0.0622311i
$229$	7.98446e6			0.664873			0.332437	−	0.943126i	$-0.392129\pi$
$229$	7.98446e6			0.664873			0.332437	+	0.943126i	$0.392129\pi$
$230$	−1.26729e7	−	8.90692e6i	−1.04158	−	0.732055i
$231$		−	5.01886e6i		−	0.407164i
$232$	8.05844e6	+	5.34194e6i	0.645337	+	0.427794i
$233$		−	5.18086e6i		−	0.409575i	−0.978806	−	0.204788i	$-0.934350\pi$
$233$		−	5.18086e6i		−	0.409575i	0.978806	−	0.204788i	$-0.0656504\pi$
$234$	−455612.	−	398579.i	−0.0355588	−	0.0311076i
$235$	445676.	+	4.18459e6i	0.0343412	+	0.322440i
$236$	7.29260e6	−	978188.i	0.554812	−	0.0744194i
$237$			1.58218e6i			0.118853i
$238$	1.03104e7	+	9.01973e6i	0.764792	+	0.669056i
$239$			2.14971e6i			0.157466i	0.996896	+	0.0787330i	$0.0250874\pi$
$239$			2.14971e6i			0.157466i	−0.996896	+	0.0787330i	$0.974913\pi$
$240$	2.90684e6	+	7.43312e6i	0.210275	+	0.537697i
$241$	9.40539e6			0.671933			0.335966	−	0.941874i	$-0.390937\pi$
$241$	9.40539e6			0.671933			0.335966	+	0.941874i	$0.390937\pi$
$242$	5.55039e6	−	6.34460e6i	0.391631	−	0.447670i
$243$	920483.			0.0641500
$244$	−2.16789e6	−	1.61620e7i	−0.149234	−	1.11257i
$245$	−354170.	−	3.32542e6i	−0.0240832	−	0.226125i
$246$	5.71546e6	−	6.53329e6i	0.383924	−	0.438860i
$247$	−1.73169e6			−0.114916
$248$	130227.	−	196450.i	0.00853780	−	0.0128795i
$249$	606195.			0.0392658
$250$	1.43890e7	+	6.09066e6i	0.920899	+	0.389802i
$251$			1.65833e7i			1.04870i	0.851504	+	0.524349i	$0.175691\pi$
$251$			1.65833e7i			1.04870i	−0.851504	+	0.524349i	$0.824309\pi$
$252$	785673.	+	5.85736e6i	0.0490953	+	0.366016i
$253$			1.31238e7i			0.810400i
$254$	−7.04995e6	+	8.05873e6i	−0.430215	+	0.491774i
$255$	−8.73114e6	+	929902.i	−0.526563	+	0.0560811i
$256$	1.44470e7	−	8.52994e6i	0.861107	−	0.508424i
$257$			1.55714e7i			0.917335i	0.888608	+	0.458667i	$0.151673\pi$
$257$			1.55714e7i			0.917335i	−0.888608	+	0.458667i	$0.848327\pi$
$258$	1.19786e7	−	1.36927e7i	0.697507	−	0.797313i
$259$			3.74588e7i			2.15603i
$260$	590804.	+	2.42008e6i	0.0336142	+	0.137692i
$261$	−4.58863e6			−0.258084
$262$	2.10776e7	+	1.84392e7i	1.17197	+	1.02527i
$263$	−6.62596e6			−0.364235			−0.182117	−	0.983277i	$-0.558295\pi$
$263$	−6.62596e6			−0.364235			−0.182117	+	0.983277i	$0.558295\pi$
$264$	3.73628e6	−	5.63626e6i	0.203061	−	0.306323i
$265$	−1.59269e7	+	1.69628e6i	−0.855841	+	0.0911506i
$266$	1.27241e7	+	1.11313e7i	0.676057	+	0.591429i
$267$	−1.65165e7			−0.867729
$268$	−4.45339e6	−	3.32009e7i	−0.231359	−	1.72483i
$269$	3.17423e7			1.63073			0.815363	−	0.578950i	$-0.196538\pi$
$269$	3.17423e7			1.63073			0.815363	+	0.578950i	$0.196538\pi$
$270$	−3.09912e6	−	2.17816e6i	−0.157451	−	0.110662i
$271$		−	3.46140e7i		−	1.73918i	−0.493778	−	0.869588i	$-0.664384\pi$
$271$		−	3.46140e7i		−	1.73918i	0.493778	−	0.869588i	$-0.335616\pi$
$272$	4.86399e6	+	1.78048e7i	0.241705	+	0.884771i
$273$			1.84459e6i			0.0906594i
$274$	−2.27060e7	−	1.98637e7i	−1.10380	−	0.965626i
$275$	−2.78825e6	−	1.29414e7i	−0.134071	−	0.622276i
$276$	−2.05446e6	−	1.53164e7i	−0.0977171	−	0.728501i
$277$			2.60617e7i			1.22620i	0.790004	+	0.613102i	$0.210079\pi$
$277$			2.60617e7i			1.22620i	−0.790004	+	0.613102i	$0.789921\pi$
$278$	−3.57107e6	−	3.12405e6i	−0.166212	−	0.145406i
$279$			111863.i			0.00515078i
$280$	1.12152e7	−	2.15799e7i	0.510896	−	0.983051i
$281$	1.09611e7			0.494008			0.247004	−	0.969014i	$-0.420554\pi$
$281$	1.09611e7			0.494008			0.247004	+	0.969014i	$0.420554\pi$
$282$	−2.76436e6	+	3.15991e6i	−0.123267	+	0.140905i
$283$	1.99923e7			0.882071			0.441035	−	0.897490i	$-0.354611\pi$
$283$	1.99923e7			0.882071			0.441035	+	0.897490i	$0.354611\pi$
$284$	−1.04847e7	+	1.40636e6i	−0.457722	+	0.0613963i
$285$	−1.07752e7	+	1.14760e6i	−0.465469	+	0.0495743i
$286$	1.38971e6	−	1.58856e6i	0.0594052	−	0.0679055i
$287$	−2.64507e7			−1.11890
$288$	−3.47817e6	+	7.16280e6i	−0.145604	+	0.299851i
$289$	3.83204e6			0.158758
$290$	1.54492e7	+	1.08582e7i	0.633449	+	0.445209i
$291$		−	9.85025e6i		−	0.399731i
$292$	3.22418e7	−	4.32474e6i	1.29500	−	0.173705i
$293$			2.67017e7i			1.06154i	0.847516	+	0.530770i	$0.178097\pi$
$293$			2.67017e7i			1.06154i	−0.847516	+	0.530770i	$0.821903\pi$
$294$	2.19678e6	−	2.51112e6i	0.0864460	−	0.0988156i
$295$	1.42901e7	−	1.52195e6i	0.556633	−	0.0592837i
$296$	−2.78861e7	+	4.20668e7i	−1.07526	+	1.62205i
$297$			3.20940e6i			0.122505i
$298$	7.81031e6	−	8.92789e6i	0.295134	−	0.337365i
$299$		−	4.82344e6i		−	0.180444i
$300$	5.27998e6	+	1.46670e7i	0.195555	+	0.543223i
$301$	−5.54362e7			−2.03280
$302$	−8.80368e6	−	7.70165e6i	−0.319627	−	0.279616i
$303$	−2.32363e7			−0.835293
$304$	6.00270e6	+	2.19731e7i	0.213661	+	0.782116i
$305$	−3.37299e6	−	3.16701e7i	−0.118882	−	1.11622i
$306$	−6.59314e6	−	5.76782e6i	−0.230106	−	0.201302i
$307$	−2.87808e6			−0.0994689			−0.0497344	−	0.998762i	$-0.515837\pi$
$307$	−2.87808e6			−0.0994689			−0.0497344	+	0.998762i	$0.515837\pi$
$308$	−2.04225e7	+	2.73936e6i	−0.698969	+	0.0937557i
$309$	−7.77671e6			−0.263585
$310$	264703.	−	376624.i	0.00888535	−	0.0126422i
$311$		−	3.85699e6i		−	0.128223i	−0.997943	−	0.0641117i	$-0.979579\pi$
$311$		−	3.85699e6i		−	0.128223i	0.997943	−	0.0641117i	$-0.0204214\pi$
$312$	−1.37320e6	+	2.07151e6i	−0.0452138	+	0.0682060i
$313$		−	1.83655e7i		−	0.598922i	−0.954109	−	0.299461i	$-0.903193\pi$
$313$		−	1.83655e7i		−	0.598922i	0.954109	−	0.299461i	$-0.0968068\pi$
$314$	−2.81984e7	−	2.46686e7i	−0.910826	−	0.796811i
$315$	1.22242e6	+	1.14777e7i	0.0391102	+	0.367217i
$316$	6.43812e6	−	863574.i	0.204032	−	0.0273677i
$317$			1.47905e7i			0.464305i	0.972679	+	0.232153i	$0.0745769\pi$
$317$			1.47905e7i			0.464305i	−0.972679	+	0.232153i	$0.925423\pi$
$318$	−1.20269e7	−	1.05214e7i	−0.373999	−	0.327183i
$319$		−	1.59989e7i		−	0.492855i
$320$	2.86599e7	−	1.58855e7i	0.874632	−	0.484787i
$321$	−1.82999e7			−0.553267
$322$	−3.10051e7	+	3.54416e7i	−0.928679	+	1.06156i
$323$	−2.50593e7			−0.743637
$324$	−502412.	−	3.74559e6i	−0.0147715	−	0.110125i
$325$	1.02477e6	+	4.75638e6i	0.0298523	+	0.138556i
$326$	−3.57134e7	+	4.08237e7i	−1.03081	+	1.17831i
$327$	1.93992e7			0.554806
$328$	−2.97046e7	−	1.96912e7i	−0.841786	−	0.558020i
$329$	1.27932e7			0.359246
$330$	7.59448e6	−	1.08055e7i	0.211328	−	0.300680i
$331$			5.72550e7i			1.57881i	0.613873	+	0.789404i	$0.289610\pi$
$331$			5.72550e7i			1.57881i	−0.613873	+	0.789404i	$0.710390\pi$
$332$	−330869.	−	2.46670e6i	−0.00904154	−	0.0674066i
$333$		−	2.39537e7i		−	0.648693i
$334$	3.49697e7	−	3.99735e7i	0.938540	−	1.07284i
$335$	−6.92898e6	−	6.50584e7i	−0.184304	−	1.73049i
$336$	2.34057e7	−	6.39406e6i	0.617026	−	0.168562i
$337$		−	1.73651e7i		−	0.453719i	−0.973928	−	0.226859i	$-0.927154\pi$
$337$		−	1.73651e7i		−	0.453719i	0.973928	−	0.226859i	$-0.0728458\pi$
$338$	2.49141e7	−	2.84791e7i	0.645201	−	0.737523i
$339$			3.56085e7i			0.914019i
$340$	8.54950e6	+	3.50208e7i	0.217522	+	0.891025i
$341$	−390026.			−0.00983626
$342$	−8.13667e6	−	7.11813e6i	−0.203408	−	0.177946i
$343$	3.45405e7			0.855946
$344$	−6.22557e7	−	4.12693e7i	−1.52934	−	1.01380i
$345$	−3.19652e6	−	3.00131e7i	−0.0778430	−	0.730892i
$346$	−5.20292e7	−	4.55163e7i	−1.25608	−	1.09885i
$347$	6.56313e7			1.57081			0.785403	−	0.618985i	$-0.212456\pi$
$347$	6.56313e7			1.57081			0.785403	+	0.618985i	$0.212456\pi$
$348$	2.50454e6	+	1.86719e7i	0.0594279	+	0.443047i
$349$	1.61690e7			0.380370			0.190185	−	0.981748i	$-0.439091\pi$
$349$	1.61690e7			0.380370			0.190185	+	0.981748i	$0.439091\pi$
$350$	2.30443e7	−	4.15362e7i	0.537476	−	0.968774i
$351$		−	1.17956e6i		−	0.0272771i
$352$	−2.49742e7	−	1.21272e7i	−0.572615	−	0.278055i
$353$		−	2.08055e7i		−	0.472993i	−0.971632	−	0.236497i	$-0.924001\pi$
$353$		−	2.08055e7i		−	0.472993i	0.971632	−	0.236497i	$-0.0759992\pi$
$354$	1.07909e7	+	9.44009e6i	0.243247	+	0.212797i
$355$	−2.05452e7	+	2.18815e6i	−0.459225	+	0.0489093i
$356$	9.01493e6	+	6.72082e7i	0.199808	+	1.48961i
$357$			2.66930e7i			0.586669i
$358$	5.47686e7	+	4.79128e7i	1.19367	+	1.04424i
$359$		−	6.24674e7i		−	1.35011i	−0.737766	−	0.675057i	$-0.764119\pi$
$359$		−	6.24674e7i		−	1.35011i	0.737766	−	0.675057i	$-0.235881\pi$
$360$	−7.17174e6	+	1.37997e7i	−0.153715	+	0.295775i
$361$	1.61200e7			0.342644
$362$	−1.90165e7	+	2.17376e7i	−0.400872	+	0.458233i
$363$	1.64259e7			0.343406
$364$	7.50594e6	−	1.00681e6i	0.155633	−	0.0208757i
$365$	6.31790e7	−	6.72882e6i	1.29925	−	0.138376i
$366$	2.09214e7	−	2.39150e7i	0.426724	−	0.487784i
$367$	−4.84042e7			−0.979230			−0.489615	−	0.871939i	$-0.662863\pi$
$367$	−4.84042e7			−0.979230			−0.489615	+	0.871939i	$0.662863\pi$
$368$	−6.12037e7	+	1.67198e7i	−1.22810	+	0.335497i
$369$	1.69144e7			0.336648
$370$	−5.66821e7	+	8.06481e7i	−1.11903	+	1.59217i
$371$			4.86920e7i			0.953534i
$372$	455187.	−	61056.2i	0.00884222	−	0.00118604i
$373$			591779.i			0.0114034i	0.999984	+	0.00570168i	$0.00181491\pi$
$373$			591779.i			0.0114034i	−0.999984	+	0.00570168i	$0.998185\pi$
$374$	2.01104e7	−	2.29880e7i	0.384419	−	0.439426i
$375$	9.52857e6	+	2.89167e7i	0.180690	+	0.548347i
$376$	1.43670e7	+	9.52388e6i	0.270273	+	0.179164i
$377$			5.88013e6i			0.109739i
$378$	−7.58221e6	+	8.66715e6i	−0.140385	+	0.160473i
$379$			8.70799e7i			1.59956i	0.600294	+	0.799779i	$0.295050\pi$
$379$			8.70799e7i			1.59956i	−0.600294	+	0.799779i	$0.704950\pi$
$380$	1.05510e7	+	4.32196e7i	0.192284	+	0.787644i
$381$	−2.08637e7			−0.377238
$382$	4.64063e6	+	4.05972e6i	0.0832505	+	0.0728293i
$383$	7.55854e7			1.34537			0.672685	−	0.739929i	$-0.265141\pi$
$383$	7.55854e7			1.34537			0.672685	+	0.739929i	$0.265141\pi$
$384$	3.10450e7	+	1.02437e7i	0.548275	+	0.180910i
$385$	−4.00187e7	+	4.26215e6i	−0.701263	+	0.0746873i
$386$	−5.15911e6	−	4.51330e6i	−0.0897043	−	0.0784752i
$387$	3.54497e7			0.611616
$388$	−4.00822e7	+	5.37641e6i	−0.686210	+	0.0920443i
$389$	−3.84170e6			−0.0652641			−0.0326320	−	0.999467i	$-0.510389\pi$
$389$	−3.84170e6			−0.0652641			−0.0326320	+	0.999467i	$0.510389\pi$
$390$	−2.79122e6	+	3.97138e6i	−0.0470543	+	0.0669495i
$391$		−	6.97998e7i		−	1.16768i
$392$	−1.14172e7	−	7.56845e6i	−0.189540	−	0.125646i
$393$			5.45689e7i			0.899017i
$394$	3.85741e7	+	3.37454e7i	0.630677	+	0.551730i
$395$	1.26157e7	−	1.34363e6i	0.204701	−	0.0218015i
$396$	1.30596e7	−	1.75173e6i	0.210302	−	0.0282087i
$397$		−	1.13247e8i		−	1.80990i	−0.425521	−	0.904949i	$-0.639909\pi$
$397$		−	1.13247e8i		−	1.80990i	0.425521	−	0.904949i	$-0.360091\pi$
$398$	4.67616e7	+	4.09080e7i	0.741720	+	0.648873i
$399$			3.29422e7i			0.518601i
$400$	5.68006e7	−	2.94906e7i	0.887509	−	0.460790i
$401$	5.79807e6			0.0899188			0.0449594	−	0.998989i	$-0.485684\pi$
$401$	5.79807e6			0.0899188			0.0449594	+	0.998989i	$0.485684\pi$
$402$	4.29778e7	−	4.91275e7i	0.661555	−	0.756217i
$403$	143347.			0.00219015
$404$	1.26827e7	+	9.45522e7i	0.192339	+	1.43393i
$405$	−781699.	−	7.33962e6i	−0.0117672	−	0.110486i
$406$	3.77975e7	−	4.32060e7i	0.564788	−	0.645604i
$407$	8.35179e7			1.23879
$408$	−1.98716e7	+	2.99767e7i	−0.292585	+	0.441371i
$409$	384767.			0.00562378			0.00281189	−	0.999996i	$-0.499105\pi$
$409$	384767.			0.00562378			0.00281189	+	0.999996i	$0.499105\pi$
$410$	−5.69479e7	−	4.00249e7i	−0.826278	−	0.580736i
$411$		−	5.87848e7i		−	0.846720i
$412$	4.24464e6	+	3.16447e7i	0.0606945	+	0.452490i
$413$		−	4.36880e7i		−	0.620172i
$414$	1.98268e7	−	2.26638e7i	0.279416	−	0.319397i
$415$	−514797.	−	4.83359e6i	−0.00720264	−	0.0676278i
$416$	9.17881e6	+	4.45712e6i	0.127499	+	0.0619120i
$417$		−	9.24532e6i		−	0.127501i
$418$	2.48184e7	−	2.83697e7i	0.339817	−	0.388442i
$419$		−	1.49355e7i		−	0.203039i	−0.994834	−	0.101519i	$-0.967630\pi$
$419$		−	1.49355e7i		−	0.203039i	0.994834	−	0.101519i	$-0.0323704\pi$
$420$	4.60374e7	−	1.12389e7i	0.621388	−	0.151697i
$421$	9.49221e7			1.27210			0.636049	−	0.771648i	$-0.280567\pi$
$421$	9.49221e7			1.27210			0.636049	+	0.771648i	$0.280567\pi$
$422$	−8.26390e7	−	7.22944e7i	−1.09963	−	0.961982i
$423$	−8.18085e6			−0.108088
$424$	−3.62486e7	+	5.46819e7i	−0.475548	+	0.717375i
$425$	1.48294e7	+	6.88294e7i	0.193178	+	0.896618i
$426$	−1.55143e7	−	1.35722e7i	−0.200679	−	0.175559i
$427$	−9.68225e7			−1.24363
$428$	9.98836e6	+	7.44653e7i	0.127398	+	0.949780i
$429$	4.11270e6			0.0520901
$430$	−1.19353e8	−	8.38854e7i	−1.50117	−	1.05507i
$431$			1.79875e7i			0.224667i	0.993671	+	0.112333i	$0.0358325\pi$
$431$			1.79875e7i			0.224667i	−0.993671	+	0.112333i	$0.964168\pi$
$432$	−1.49672e7	+	4.08879e6i	−0.185647	+	0.0507159i
$433$		−	2.17575e7i		−	0.268006i	−0.990981	−	0.134003i	$-0.957217\pi$
$433$		−	2.17575e7i		−	0.268006i	0.990981	−	0.134003i	$-0.0427833\pi$
$434$	−1.05329e6	−	921436.i	−0.0128848	−	0.0112719i
$435$	3.89679e6	+	3.65882e7i	0.0473412	+	0.444501i
$436$	−1.05884e7	−	7.89386e7i	−0.127753	−	0.952423i
$437$		−	8.61406e7i		−	1.03220i
$438$	4.77083e7	+	4.17363e7i	0.567769	+	0.496697i
$439$		−	9.99238e7i		−	1.18107i	−0.807012	−	0.590534i	$-0.798917\pi$
$439$		−	9.99238e7i		−	1.18107i	0.807012	−	0.590534i	$-0.201083\pi$
$440$	−4.81146e7	−	2.50053e7i	−0.564831	−	0.293545i
$441$	6.50117e6			0.0758011
$442$	−7.39121e6	+	8.44882e6i	−0.0855951	+	0.0978429i
$443$	−1.05070e8			−1.20856			−0.604278	−	0.796773i	$-0.706538\pi$
$443$	−1.05070e8			−1.20856			−0.604278	+	0.796773i	$0.706538\pi$
$444$	−9.74712e7	+	1.30742e7i	−1.11360	+	0.149371i
$445$	1.40263e7	+	1.31697e8i	0.159170	+	1.49450i
$446$	−3.29122e7	+	3.76216e7i	−0.370981	+	0.424065i
$447$	2.31139e7			0.258792
$448$	−3.87936e7	−	9.17515e7i	−0.431446	−	1.02042i
$449$	1.88095e7			0.207796			0.103898	−	0.994588i	$-0.466868\pi$
$449$	1.88095e7			0.207796			0.103898	+	0.994588i	$0.466868\pi$
$450$	−1.47361e7	+	2.65610e7i	−0.161713	+	0.291479i
$451$			5.89744e7i			0.642886i
$452$	1.44897e8	−	1.94356e7i	1.56907	−	0.210467i
$453$		−	2.27923e7i		−	0.245185i
$454$	−4.74101e7	+	5.41940e7i	−0.506644	+	0.579140i
$455$	1.47082e7	−	1.56648e6i	0.156144	−	0.0166299i
$456$	−2.45237e7	+	3.69946e7i	−0.258638	+	0.390161i
$457$		−	3.09010e7i		−	0.323761i	−0.986810	−	0.161880i	$-0.948244\pi$
$457$		−	3.09010e7i		−	0.323761i	0.986810	−	0.161880i	$-0.0517559\pi$
$458$	4.20576e7	−	4.80756e7i	0.437772	−	0.500412i
$459$		−	1.70693e7i		−	0.176514i
$460$	−1.20383e8	+	2.93887e7i	−1.23678	+	0.301930i
$461$	−3.31900e7			−0.338769			−0.169385	−	0.985550i	$-0.554178\pi$
$461$	−3.31900e7			−0.338769			−0.169385	+	0.985550i	$0.554178\pi$
$462$	−3.02193e7	−	2.64365e7i	−0.306449	−	0.268088i
$463$	1.33317e7			0.134321			0.0671603	−	0.997742i	$-0.478606\pi$
$463$	1.33317e7			0.134321			0.0671603	+	0.997742i	$0.478606\pi$
$464$	7.46118e7	−	2.03827e7i	0.746885	−	0.204037i
$465$	891955.	−	94996.9i	0.00887123	−	0.000944823i
$466$	−3.11947e7	−	2.72898e7i	−0.308264	−	0.269676i
$467$	−8.54793e7			−0.839287			−0.419643	−	0.907689i	$-0.637845\pi$
$467$	−8.54793e7			−0.839287			−0.419643	+	0.907689i	$0.637845\pi$
$468$	−4.79981e6	+	643819.i	−0.0468259	+	0.00628096i
$469$	−1.98898e8			−1.92802
$470$	2.75436e7	+	1.93586e7i	0.265294	+	0.186457i
$471$		−	7.30043e7i		−	0.698692i
$472$	3.25234e7	−	4.90623e7i	0.309293	−	0.466576i
$473$			1.23600e8i			1.16798i
$474$	9.52651e6	+	8.33400e6i	0.0894538	+	0.0782561i
$475$	1.83012e7	+	8.49431e7i	0.170765	+	0.792588i
$476$	1.08618e8	−	1.45694e7i	1.00712	−	0.135090i
$477$		−	3.11370e7i		−	0.286894i
$478$	1.29437e7	+	1.13235e7i	0.118516	+	0.103680i
$479$		−	1.27765e7i		−	0.116254i	−0.998309	−	0.0581268i	$-0.981487\pi$
$479$		−	1.27765e7i		−	0.116254i	0.998309	−	0.0581268i	$-0.0185128\pi$
$480$	6.00675e7	+	2.16509e7i	0.543145	+	0.195773i
$481$	−3.06955e7			−0.275829
$482$	4.95422e7	−	5.66312e7i	0.442420	−	0.505725i
$483$	−9.17567e7			−0.814322
$484$	−8.96547e6	−	6.68394e7i	−0.0790746	−	0.589518i
$485$	−7.85425e7	+	8.36510e6i	−0.688462	+	0.0733240i
$486$	4.84858e6	−	5.54236e6i	0.0422382	−	0.0482821i
$487$	−3.20267e7			−0.277285			−0.138642	−	0.990343i	$-0.544274\pi$
$487$	−3.20267e7			−0.277285			−0.138642	+	0.990343i	$0.544274\pi$
$488$	−1.08733e8	−	7.20793e7i	−0.935627	−	0.620227i
$489$	−1.05691e8			−0.903877
$490$	−2.18884e7	−	1.53839e7i	−0.186048	−	0.130761i
$491$			1.89567e8i			1.60147i	0.599022	+	0.800733i	$0.295556\pi$
$491$			1.89567e8i			1.60147i	−0.599022	+	0.800733i	$0.704444\pi$
$492$	−9.23210e6	−	6.88272e7i	−0.0775184	−	0.577916i
$493$			8.50911e7i			0.710139i
$494$	−9.12157e6	+	1.04268e7i	−0.0756639	+	0.0864907i
$495$	2.55906e7	−	2.72551e6i	0.210992	−	0.0224715i
$496$	−496895.	−	1.81890e6i	−0.00407211	−	0.0149061i
$497$			6.28112e7i			0.511644i
$498$	3.19309e6	−	3.64999e6i	0.0258537	−	0.0295531i
$499$		−	1.21997e8i		−	0.981855i	−0.871200	−	0.490928i	$-0.836658\pi$
$499$		−	1.21997e8i		−	0.981855i	0.871200	−	0.490928i	$-0.163342\pi$
$500$	1.12466e8	−	5.45564e7i	0.899728	−	0.436451i
$501$	1.03490e8			0.822969
$502$	9.98505e7	+	8.73514e7i	0.789295	+	0.690492i
$503$	−1.54905e8			−1.21720			−0.608599	−	0.793478i	$-0.708268\pi$
$503$	−1.54905e8			−1.21720			−0.608599	+	0.793478i	$0.708268\pi$
$504$	3.94065e7	+	2.61226e7i	0.307805	+	0.204044i
$505$	1.97329e7	+	1.85278e8i	0.153220	+	1.43863i
$506$	7.90206e7	+	6.91289e7i	0.609942	+	0.533591i
$507$	7.37310e7			0.565752
$508$	1.13877e7	+	8.48976e7i	0.0868649	+	0.647596i
$509$	−2.04699e8			−1.55225			−0.776127	−	0.630576i	$-0.782819\pi$
$509$	−2.04699e8			−1.55225			−0.776127	+	0.630576i	$0.782819\pi$
$510$	−4.03916e7	+	5.74697e7i	−0.304495	+	0.433240i
$511$		−	1.93152e8i		−	1.44756i
$512$	2.47384e7	−	1.31918e8i	0.184315	−	0.982867i
$513$		−	2.10654e7i		−	0.156034i
$514$	9.37576e7	+	8.20212e7i	0.690426	+	0.604000i
$515$	6.60420e6	+	6.20089e7i	0.0483502	+	0.453975i
$516$	−1.93489e7	−	1.44250e8i	−0.140834	−	1.04995i
$517$		−	2.85237e7i		−	0.206412i
$518$	2.25545e8	+	1.97311e8i	1.62272	+	1.41959i
$519$		−	1.34701e8i		−	0.963539i
$520$	1.76837e7	+	9.19027e6i	0.125766	+	0.0653609i
$521$	−1.10279e6			−0.00779792			−0.00389896	−	0.999992i	$-0.501241\pi$
$521$	−1.10279e6			−0.00779792			−0.00389896	+	0.999992i	$0.501241\pi$
$522$	−2.41703e7	+	2.76288e7i	−0.169930	+	0.194246i
$523$	7.01848e7			0.490612			0.245306	−	0.969446i	$-0.421112\pi$
$523$	7.01848e7			0.490612			0.245306	+	0.969446i	$0.421112\pi$
$524$	2.22050e8	−	2.97845e7i	1.54332	−	0.207012i
$525$	9.04811e7	−	1.94944e7i	0.625288	−	0.134720i
$526$	−3.49018e7	+	3.98959e7i	−0.239823	+	0.274139i
$527$	2.07437e6			0.0141728
$528$	−1.42562e7	−	5.21853e7i	−0.0968504	−	0.354524i
$529$	9.18990e7			0.620789
$530$	−7.36802e7	+	1.04833e8i	−0.494906	+	0.704159i
$531$			2.79371e7i			0.186594i
$532$	1.34047e8	−	1.79803e7i	0.890270	−	0.119416i
$533$		−	2.16750e7i		−	0.143145i
$534$	−8.69994e7	+	9.94482e7i	−0.571337	+	0.653090i
$535$	1.55408e7	+	1.45917e8i	0.101487	+	0.952897i
$536$	−2.23366e8	−	1.48069e8i	−1.45051	−	0.961545i
$537$			1.41793e8i			0.915657i
$538$	1.67200e8	−	1.91125e8i	1.07372	−	1.22735i
$539$			2.26673e7i			0.144755i
$540$	−2.94394e7	+	7.18692e6i	−0.186960	+	0.0456417i
$541$	1.96474e8			1.24083			0.620417	−	0.784272i	$-0.286963\pi$
$541$	1.96474e8			1.24083			0.620417	+	0.784272i	$0.286963\pi$
$542$	−2.08416e8	−	1.82327e8i	−1.30898	−	1.14512i
$543$	−5.62776e7			−0.351509
$544$	1.32826e8	+	6.44988e7i	0.825063	+	0.400641i
$545$	−1.64744e7	−	1.54683e8i	−0.101770	−	0.955549i
$546$	1.11066e7	+	9.71626e6i	0.0682342	+	0.0596927i
$547$	−4.61576e7			−0.282021			−0.141010	−	0.990008i	$-0.545035\pi$
$547$	−4.61576e7			−0.282021			−0.141010	+	0.990008i	$0.545035\pi$
$548$	−2.39205e8	+	3.20856e7i	−1.45354	+	0.194970i
$549$	6.19148e7			0.374178
$550$	−9.26090e7	−	5.13794e7i	−0.556628	−	0.308817i
$551$			1.05012e8i			0.627745i
$552$	−1.03044e8	−	6.83080e7i	−0.612641	−	0.406120i
$553$		−	3.85691e7i		−	0.228068i
$554$	1.56921e8	+	1.37278e8i	0.922894	+	0.807368i
$555$	−1.90998e8	+	2.03421e7i	−1.11725	+	0.118992i
$556$	−3.76207e7	+	5.04622e6i	−0.218878	+	0.0293591i
$557$			9.17119e7i			0.530714i	0.964150	+	0.265357i	$0.0854898\pi$
$557$			9.17119e7i			0.530714i	−0.964150	+	0.265357i	$0.914510\pi$
$558$	673542.	+	589229.i	0.00387670	+	0.00339142i
$559$		−	4.54271e7i		−	0.260064i
$560$	−7.08608e7	−	1.81199e8i	−0.403498	−	1.03179i
$561$	5.95147e7			0.337082
$562$	5.77367e7	−	6.59983e7i	0.325269	−	0.371812i
$563$	2.08056e7			0.116588			0.0582941	−	0.998299i	$-0.481434\pi$
$563$	2.08056e7			0.116588			0.0582941	+	0.998299i	$0.481434\pi$
$564$	4.46522e6	+	3.32892e7i	0.0248889	+	0.185552i
$565$	2.83930e8	−	3.02398e7i	1.57422	−	0.167661i
$566$	1.05308e8	−	1.20377e8i	0.580780	−	0.663885i
$567$	−2.24388e7			−0.123098
$568$	−4.67596e7	+	7.05380e7i	−0.255168	+	0.384927i
$569$	2.96314e7			0.160848			0.0804239	−	0.996761i	$-0.474373\pi$
$569$	2.96314e7			0.160848			0.0804239	+	0.996761i	$0.474373\pi$
$570$	−4.98477e7	+	7.09239e7i	−0.269166	+	0.382973i
$571$			8.21130e7i			0.441066i	0.975380	+	0.220533i	$0.0707797\pi$
$571$			8.21130e7i			0.441066i	−0.975380	+	0.220533i	$0.929220\pi$
$572$	−2.24477e6	−	1.67352e7i	−0.0119945	−	0.0894219i
$573$			1.20144e7i			0.0638612i
$574$	−1.39327e8	+	1.59264e8i	−0.736716	+	0.842133i
$575$	−2.36600e8	+	5.09759e7i	−1.24454	+	0.268140i
$576$	2.48072e7	+	5.86721e7i	0.129811	+	0.307018i
$577$		−	3.79151e8i		−	1.97372i	−0.161582	−	0.986859i	$-0.551660\pi$
$577$		−	3.79151e8i		−	1.97372i	0.161582	−	0.986859i	$-0.448340\pi$
$578$	2.01850e7	−	2.30733e7i	0.104531	−	0.119488i
$579$		−	1.33567e7i		−	0.0688119i
$580$	1.46756e8	−	3.58270e7i	0.752164	−	0.183623i
$581$	−1.47774e7			−0.0753474
$582$	−5.93098e7	−	5.18855e7i	−0.300855	−	0.263195i
$583$	1.08564e8			0.547871
$584$	1.43792e8	−	2.16913e8i	0.721930	−	1.08905i
$585$	−9.40539e6	+	1.00171e6i	−0.0469796	+	0.00500352i
$586$	1.60775e8	+	1.40649e8i	0.798961	+	0.698948i
$587$	2.59598e8			1.28347			0.641737	−	0.766925i	$-0.278214\pi$
$587$	2.59598e8			1.28347			0.641737	+	0.766925i	$0.278214\pi$
$588$	−3.54843e6	−	2.64543e7i	−0.0174544	−	0.130126i
$589$	2.56000e6			0.0125284
$590$	6.61081e7	−	9.40595e7i	0.321884	−	0.457980i
$591$			9.98665e7i			0.483790i
$592$	1.06402e8	+	3.89490e8i	0.512845	+	1.87729i
$593$		−	7.63709e7i		−	0.366238i	−0.983091	−	0.183119i	$-0.941381\pi$
$593$		−	7.63709e7i		−	0.366238i	0.983091	−	0.183119i	$-0.0586194\pi$
$594$	1.93243e7	+	1.69053e7i	0.0922027	+	0.0806609i
$595$	2.12841e8	−	2.26685e7i	1.01043	−	0.107615i
$596$	−1.26159e7	−	9.40541e7i	−0.0595907	−	0.444262i
$597$			1.21063e8i			0.568971i
$598$	−2.90426e7	−	2.54071e7i	−0.135810	−	0.118810i
$599$		−	3.48124e8i		−	1.61977i	−0.586587	−	0.809886i	$-0.699529\pi$
$599$		−	3.48124e8i		−	1.61977i	0.586587	−	0.809886i	$-0.300471\pi$
$600$	1.16124e8	+	4.54660e7i	0.537612	+	0.210491i
$601$	−2.40011e8			−1.10562			−0.552811	−	0.833306i	$-0.686445\pi$
$601$	−2.40011e8			−1.10562			−0.552811	+	0.833306i	$0.686445\pi$
$602$	−2.92006e8	+	3.33789e8i	−1.33845	+	1.52997i
$603$	1.27189e8			0.580092
$604$	−9.27455e7	+	1.24404e7i	−0.420903	+	0.0564575i
$605$	−1.39493e7	−	1.30974e8i	−0.0629921	−	0.591452i
$606$	−1.22396e8	+	1.39909e8i	−0.549981	+	0.628678i
$607$	9.26126e6			0.0414099			0.0207049	−	0.999786i	$-0.493409\pi$
$607$	9.26126e6			0.0414099			0.0207049	+	0.999786i	$0.493409\pi$
$608$	1.63922e8	+	7.95987e7i	0.729335	+	0.354156i
$609$	1.11858e8			0.495240
$610$	−2.08457e8	−	1.46511e8i	−0.918391	−	0.645475i
$611$			1.04834e7i			0.0459598i
$612$	−6.94578e7	+	9.31668e6i	−0.303017	+	0.0406450i
$613$			3.01920e8i			1.31072i	0.755316	+	0.655361i	$0.227483\pi$
$613$			3.01920e8i			1.31072i	−0.755316	+	0.655361i	$0.772517\pi$
$614$	−1.51601e7	+	1.73293e7i	−0.0654931	+	0.0748646i
$615$	−1.43641e7	−	1.34869e8i	−0.0617525	−	0.579813i
$616$	−9.10802e7	+	1.37397e8i	−0.389656	+	0.587805i
$617$			1.47492e8i			0.627933i	0.949434	+	0.313966i	$0.101658\pi$
$617$			1.47492e8i			0.627933i	−0.949434	+	0.313966i	$0.898342\pi$
$618$	−4.09633e7	+	4.68247e7i	−0.173552	+	0.198385i
$619$		−	1.93464e8i		−	0.815697i	−0.913050	−	0.407849i	$-0.866279\pi$
$619$		−	1.93464e8i		−	0.815697i	0.913050	−	0.407849i	$-0.133721\pi$
$620$	−873399.	−	3.57766e6i	−0.00366469	−	0.0150115i
$621$	5.86754e7			0.245009
$622$	−2.32235e7	−	2.03164e7i	−0.0965065	−	0.0844260i
$623$	4.02627e8			1.66509
$624$	5.23960e6	+	1.91798e7i	0.0215648	+	0.0789387i
$625$	2.22480e8	−	1.00534e8i	0.911279	−	0.411789i
$626$	−1.10581e8	−	9.67390e7i	−0.450774	−	0.394347i
$627$	7.34478e7			0.297972
$628$	−2.97066e8	+	3.98468e7i	−1.19943	+	0.160885i
$629$	−4.44194e8			−1.78493
$630$	7.55479e7	+	5.30976e7i	0.302135	+	0.212350i
$631$			1.92567e8i			0.766468i	0.923651	+	0.383234i	$0.125190\pi$
$631$			1.92567e8i			0.766468i	−0.923651	+	0.383234i	$0.874810\pi$
$632$	2.87127e7	−	4.33137e7i	0.113742	−	0.171583i
$633$		−	2.13948e8i		−	0.843525i
$634$	8.90555e7	+	7.79077e7i	0.349456	+	0.305712i
$635$	1.77180e7	+	1.66360e8i	0.0691980	+	0.649722i
$636$	−1.26701e8	+	1.69950e7i	−0.492504	+	0.0660617i
$637$		−	8.33096e6i		−	0.0322312i
$638$	−9.63320e7	−	8.42733e7i	−0.370944	−	0.324510i
$639$		−	4.01657e7i		−	0.153941i
$640$	5.53153e7	−	2.56241e8i	0.211011	−	0.977484i
$641$	−2.82910e8			−1.07417			−0.537086	−	0.843528i	$-0.680475\pi$
$641$	−2.82910e8			−1.07417			−0.537086	+	0.843528i	$0.680475\pi$
$642$	−9.63936e7	+	1.10187e8i	−0.364287	+	0.416412i
$643$	3.08979e8			1.16224			0.581120	−	0.813818i	$-0.302615\pi$
$643$	3.08979e8			1.16224			0.581120	+	0.813818i	$0.302615\pi$
$644$	5.00821e7	+	3.73372e8i	0.187510	+	1.39793i
$645$	−3.01048e7	−	2.82663e8i	−0.112191	−	1.05339i
$646$	−1.31998e8	+	1.50885e8i	−0.489632	+	0.559693i
$647$	−3.15317e8			−1.16422			−0.582109	−	0.813111i	$-0.697772\pi$
$647$	−3.15317e8			−1.16422			−0.582109	+	0.813111i	$0.697772\pi$
$648$	−2.51992e7	−	1.67045e7i	−0.0926107	−	0.0613916i
$649$	−9.74066e7			−0.356332
$650$	3.40368e7	+	1.88836e7i	0.123939	+	0.0687614i
$651$		−	2.72690e6i		−	0.00988387i
$652$	5.76874e7	+	4.30072e8i	0.208132	+	1.55166i
$653$		−	3.98350e8i		−	1.43062i	−0.698805	−	0.715312i	$-0.746284\pi$
$653$		−	3.98350e8i		−	1.43062i	0.698805	−	0.715312i	$-0.253716\pi$
$654$	1.02184e8	−	1.16806e8i	0.365300	−	0.417571i
$655$	4.35114e8	−	4.63414e7i	1.54839	−	0.164909i
$656$	−2.75030e8	+	7.51337e7i	−0.974246	+	0.266148i
$657$			1.23515e8i			0.435534i
$658$	6.73874e7	−	7.70299e7i	0.236538	−	0.270384i
$659$			2.49936e8i			0.873317i	0.899627	+	0.436659i	$0.143838\pi$
$659$			2.49936e8i			0.873317i	−0.899627	+	0.436659i	$0.856162\pi$
$660$	−2.50583e7	−	1.02645e8i	−0.0871604	−	0.357030i
$661$	−8.36472e7			−0.289632			−0.144816	−	0.989459i	$-0.546259\pi$
$661$	−8.36472e7			−0.289632			−0.144816	+	0.989459i	$0.546259\pi$
$662$	3.44741e8	+	3.01587e8i	1.18828	+	1.03953i
$663$	−2.18736e7			−0.0750550
$664$	−1.65952e7	−	1.10010e7i	−0.0566863	−	0.0375774i
$665$	2.62670e8	−	2.79754e7i	0.893192	−	0.0951286i
$666$	−1.44228e8	−	1.26174e8i	−0.488234	−	0.427118i
$667$	−2.92499e8			−0.985704
$668$	−5.64861e7	−	4.21116e8i	−0.189501	−	1.41277i
$669$	−9.74004e7			−0.325299
$670$	−4.28224e8	−	3.00970e8i	−1.42379	−	1.00069i
$671$			2.15875e8i			0.714554i
$672$	8.47883e7	−	1.74609e8i	0.279401	−	0.575386i
$673$			1.44164e8i			0.472945i	0.971638	+	0.236473i	$0.0759913\pi$
$673$			1.44164e8i			0.472945i	−0.971638	+	0.236473i	$0.924009\pi$
$674$	−1.04558e8	−	9.14693e7i	−0.341488	−	0.298741i
$675$	−5.78597e7	+	1.24660e7i	−0.188133	+	0.0405337i
$676$	−4.02434e7	−	3.00023e8i	−0.130273	−	0.971213i
$677$			9.93179e7i			0.320082i	0.987110	+	0.160041i	$0.0511627\pi$
$677$			9.93179e7i			0.320082i	−0.987110	+	0.160041i	$0.948837\pi$
$678$	2.14404e8	+	1.87565e8i	0.687930	+	0.601816i
$679$			2.40122e8i			0.767048i
$680$	2.55900e8	+	1.32992e8i	0.813847	+	0.422960i
$681$	−1.40306e8			−0.444257
$682$	−2.05443e6	+	2.34840e6i	−0.00647648	+	0.00740320i
$683$	−3.90996e8			−1.22719			−0.613593	−	0.789623i	$-0.710276\pi$
$683$	−3.90996e8			−1.22719			−0.613593	+	0.789623i	$0.710276\pi$
$684$	−8.57186e7	+	1.14978e7i	−0.267859	+	0.0359291i
$685$	−4.68730e8	+	4.99217e7i	−1.45831	+	0.155316i
$686$	1.81940e8	−	2.07973e8i	0.563579	−	0.644222i
$687$	1.24465e8			0.383865
$688$	−5.76416e8	+	1.57468e8i	−1.76999	+	0.483533i
$689$	−3.99006e7			−0.121989
$690$	−1.97551e8	−	1.38845e8i	−0.601355	−	0.422652i
$691$		−	3.51198e8i		−	1.06443i	−0.846608	−	0.532217i	$-0.821359\pi$
$691$		−	3.51198e8i		−	1.06443i	0.846608	−	0.532217i	$-0.178641\pi$
$692$	−5.48120e8	+	7.35218e7i	−1.65408	+	0.221870i
$693$		−	7.82363e7i		−	0.235076i
$694$	3.45708e8	−	3.95176e8i	1.03426	−	1.18226i
$695$	−7.37190e7	+	7.85138e6i	−0.219596	+	0.0233879i
$696$	1.25619e8	+	8.32726e7i	0.372586	+	0.246987i
$697$		−	3.13658e8i		−	0.926314i
$698$	8.51690e7	−	9.73559e7i	0.250447	−	0.286283i
$699$		−	8.07616e7i		−	0.236469i
$700$	−1.28711e8	−	3.57542e8i	−0.375252	−	1.04240i
$701$	3.99331e8			1.15925			0.579627	−	0.814882i	$-0.303198\pi$
$701$	3.99331e8			1.15925			0.579627	+	0.814882i	$0.303198\pi$
$702$	−7.10229e6	−	6.21324e6i	−0.0205299	−	0.0179600i
$703$	−5.48184e8			−1.57783
$704$	−2.04569e8	+	8.64941e7i	−0.586303	+	0.247895i
$705$	6.94740e6	+	6.52313e7i	0.0198269	+	0.186161i
$706$	−1.25273e8	−	1.09592e8i	−0.355995	−	0.311432i
$707$	5.66437e8			1.60285
$708$	1.13680e8	−	1.52484e7i	0.320321	−	0.0429661i
$709$	9.18319e6			0.0257665			0.0128832	−	0.999917i	$-0.495899\pi$
$709$	9.18319e6			0.0257665			0.0128832	+	0.999917i	$0.495899\pi$
$710$	−9.50452e7	+	1.35232e8i	−0.265555	+	0.377836i
$711$			2.46637e7i			0.0686197i
$712$	4.52156e8	+	2.99734e8i	1.25270	+	0.830418i
$713$			7.13059e6i			0.0196724i
$714$	1.60723e8	+	1.40604e8i	0.441553	+	0.386280i
$715$	−3.49262e6	−	3.27933e7i	−0.00955505	−	0.0897153i
$716$	5.76980e8	−	7.73928e7i	1.57189	−	0.210844i
$717$			3.35107e7i			0.0909130i
$718$	−3.76126e8	−	3.29043e8i	−1.01615	−	0.888953i
$719$			2.20660e8i			0.593658i	0.954931	+	0.296829i	$0.0959292\pi$
$719$			2.20660e8i			0.593658i	−0.954931	+	0.296829i	$0.904071\pi$
$720$	4.53132e7	+	1.15871e8i	0.121402	+	0.310439i
$721$	1.89575e8			0.505796
$722$	8.49109e7	−	9.70608e7i	0.225607	−	0.257889i
$723$	1.46616e8			0.387940
$724$	3.07171e7	+	2.29003e8i	0.0809403	+	0.603427i
$725$	2.88432e8	−	6.21434e7i	0.756885	−	0.163073i
$726$	8.65220e7	−	9.89025e7i	0.226109	−	0.258462i
$727$	−4.38080e8			−1.14012			−0.570059	−	0.821604i	$-0.693080\pi$
$727$	−4.38080e8			−1.14012			−0.570059	+	0.821604i	$0.693080\pi$
$728$	3.34749e7	−	5.04977e7i	0.0867611	−	0.130881i
$729$	1.43489e7			0.0370370
$730$	2.92276e8	−	4.15853e8i	0.751318	−	1.06899i
$731$		−	6.57375e8i		−	1.68291i
$732$	−3.37940e7	−	2.51941e8i	−0.0861601	−	0.642342i
$733$			3.17227e7i			0.0805487i	0.999189	+	0.0402744i	$0.0128232\pi$
$733$			3.17227e7i			0.0805487i	−0.999189	+	0.0402744i	$0.987177\pi$
$734$	−2.54966e8	+	2.91449e8i	−0.644753	+	0.737011i
$735$	−5.52097e6	−	5.18381e7i	−0.0139044	−	0.130553i
$736$	−2.21713e8	+	4.56587e8i	−0.556107	+	1.14522i
$737$			4.43462e8i			1.10778i
$738$	8.90952e7	−	1.01844e8i	0.221659	−	0.253376i
$739$		−	4.13892e8i		−	1.02554i	−0.858526	−	0.512771i	$-0.828619\pi$
$739$		−	4.13892e8i		−	1.02554i	0.858526	−	0.512771i	$-0.171381\pi$
$740$	1.87025e8	+	7.66099e8i	0.461534	+	1.89056i
$741$	−2.69944e7			−0.0663467
$742$	2.93182e8	+	2.56482e8i	0.717671	+	0.627834i
$743$	4.45636e8			1.08646			0.543230	−	0.839584i	$-0.317201\pi$
$743$	4.45636e8			1.08646			0.543230	+	0.839584i	$0.317201\pi$
$744$	2.03004e6	−	3.06236e6i	0.00492930	−	0.00743596i
$745$	−1.96289e7	−	1.84302e8i	−0.0474710	−	0.445720i
$746$	3.56319e6	+	3.11715e6i	0.00858266	+	0.00750830i
$747$	9.44964e6			0.0226701
$748$	−3.24840e7	−	2.42175e8i	−0.0776184	−	0.578661i
$749$	4.46102e8			1.06167
$750$	2.24303e8	+	9.49439e7i	0.531681	+	0.225052i
$751$			5.33301e8i			1.25908i	0.776969	+	0.629539i	$0.216756\pi$
$751$			5.33301e8i			1.25908i	−0.776969	+	0.629539i	$0.783244\pi$
$752$	1.33022e8	−	3.63394e7i	0.312802	−	0.0854524i
$753$			2.58508e8i			0.605466i
$754$	3.54051e7	+	3.09732e7i	0.0825947	+	0.0722556i
$755$	−1.81738e8	+	1.93558e7i	−0.422284	+	0.0449750i
$756$	1.22474e7	+	9.13072e7i	0.0283452	+	0.211320i
$757$			4.21379e8i			0.971371i	0.874134	+	0.485685i	$0.161430\pi$
$757$			4.21379e8i			0.971371i	−0.874134	+	0.485685i	$0.838570\pi$
$758$	5.24321e8	+	4.58687e8i	1.20390	+	1.05320i
$759$			2.04580e8i			0.467885i
$760$	3.15808e8	+	1.64127e8i	0.719420	+	0.373886i
$761$	3.86731e8			0.877517			0.438758	−	0.898605i	$-0.355418\pi$
$761$	3.86731e8			0.877517			0.438758	+	0.898605i	$0.355418\pi$
$762$	−1.09898e8	+	1.25623e8i	−0.248385	+	0.283926i
$763$	−4.72900e8			−1.06462
$764$	4.88884e7	−	6.55761e6i	0.109629	−	0.0147050i
$765$	−1.36105e8	+	1.44957e7i	−0.304011	+	0.0323785i
$766$	3.98141e8	−	4.55111e8i	0.885830	−	1.01258i
$767$	3.58001e7			0.0793411
$768$	2.25206e8	−	1.32969e8i	0.497160	−	0.293539i
$769$	2.56434e8			0.563894			0.281947	−	0.959430i	$-0.409020\pi$
$769$	2.56434e8			0.563894			0.281947	+	0.959430i	$0.409020\pi$
$770$	−1.85133e8	+	2.63409e8i	−0.405518	+	0.576977i
$771$			2.42734e8i			0.529624i
$772$	−5.43505e7	+	7.29027e6i	−0.118128	+	0.0158450i
$773$			1.49302e8i			0.323241i	0.986853	+	0.161620i	$0.0516720\pi$
$773$			1.49302e8i			0.323241i	−0.986853	+	0.161620i	$0.948328\pi$
$774$	1.86729e8	−	2.13448e8i	0.402706	−	0.460329i
$775$	−1.51494e6	−	7.03147e6i	−0.00325456	−	0.0151057i
$776$	−1.78758e8	+	2.69661e8i	−0.382543	+	0.577076i
$777$			5.83924e8i			1.24478i
$778$	−2.02359e7	+	2.31314e7i	−0.0429717	+	0.0491206i
$779$		−	3.87089e8i		−	0.818838i
$780$	9.20972e6	+	3.77253e7i	0.0194072	+	0.0794966i
$781$	1.40044e8			0.293975
$782$	−4.20275e8	−	3.67665e8i	−0.878846	−	0.768833i
$783$	−7.15297e7			−0.149005
$784$	−1.05710e8	+	2.88782e7i	−0.219365	+	0.0599270i
$785$	−5.82111e8	+	6.19973e7i	−1.20336	+	0.128163i
$786$	3.28568e8	+	2.87438e8i	0.676639	+	0.591938i
$787$	−5.82854e8			−1.19574			−0.597869	−	0.801594i	$-0.703986\pi$
$787$	−5.82854e8			−1.19574			−0.597869	+	0.801594i	$0.703986\pi$
$788$	4.06373e8	−	5.45085e7i	0.830512	−	0.111400i
$789$	−1.03288e8			−0.210291
$790$	5.83623e7	−	8.30386e7i	0.118373	−	0.168422i
$791$		−	8.68038e8i		−	1.75392i
$792$	5.82428e7	−	8.78606e7i	0.117238	−	0.176856i
$793$		−	7.93411e7i		−	0.159103i
$794$	−6.81875e8	−	5.96519e8i	−1.36221	−	1.19169i
$795$	−2.48275e8	+	2.64424e7i	−0.494120	+	0.0526258i
$796$	4.92627e8	−	6.60782e7i	0.976739	−	0.131014i
$797$			7.32923e8i			1.44772i	0.689949	+	0.723858i	$0.257633\pi$
$797$			7.32923e8i			1.44772i	−0.689949	+	0.723858i	$0.742367\pi$
$798$	1.98350e8	+	1.73520e8i	0.390322	+	0.341462i
$799$			1.51705e8i			0.297412i
$800$	1.21626e8	−	4.97344e8i	0.237551	−	0.971375i
$801$	−2.57467e8			−0.500984
$802$	3.05409e7	−	3.49110e7i	0.0592051	−	0.0676767i
$803$	−4.30652e8			−0.831725
$804$	−6.94214e7	−	5.17551e8i	−0.133575	−	0.995830i
$805$	7.79223e7	+	7.31636e8i	0.149374	+	1.40252i
$806$	755070.	−	863113.i	0.00144206	−	0.00164840i
$807$	4.94813e8			0.941500
$808$	6.36118e8	+	4.21682e8i	1.20588	+	0.799377i
$809$	3.74521e8			0.707343			0.353672	−	0.935370i	$-0.384933\pi$
$809$	3.74521e8			0.707343			0.353672	+	0.935370i	$0.384933\pi$
$810$	−4.83104e7	−	3.39542e7i	−0.0909046	−	0.0638908i
$811$			7.54657e8i			1.41477i	0.706826	+	0.707387i	$0.250126\pi$
$811$			7.54657e8i			1.41477i	−0.706826	+	0.707387i	$0.749874\pi$
$812$	−6.10538e7	−	4.55169e8i	−0.114037	−	0.850168i
$813$		−	5.39579e8i		−	1.00411i
$814$	4.39925e8	−	5.02874e8i	0.815653	−	0.932365i
$815$	8.97553e7	+	8.42740e8i	0.165801	+	1.55676i
$816$	7.58221e7	+	2.77550e8i	0.139549	+	0.510823i
$817$		−	8.11273e8i		−	1.48765i
$818$	2.02673e6	−	2.31674e6i	0.00370286	−	0.00423270i
$819$			2.87544e7i			0.0523422i
$820$	−5.40965e8	+	1.32064e8i	−0.981132	+	0.239520i
$821$	4.19834e8			0.758661			0.379330	−	0.925261i	$-0.376154\pi$
$821$	4.19834e8			0.758661			0.379330	+	0.925261i	$0.376154\pi$
$822$	−3.53952e8	−	3.09645e8i	−0.637278	−	0.557504i
$823$	−5.49205e7			−0.0985224			−0.0492612	−	0.998786i	$-0.515687\pi$
$823$	−5.49205e7			−0.0985224			−0.0492612	+	0.998786i	$0.515687\pi$
$824$	2.12896e8	+	1.41129e8i	0.380527	+	0.252251i
$825$	−4.34646e7	−	2.01737e8i	−0.0774058	−	0.359271i
$826$	−2.63052e8	−	2.30123e8i	−0.466768	−	0.408339i
$827$	−1.20010e8			−0.212178			−0.106089	−	0.994357i	$-0.533833\pi$
$827$	−1.20010e8			−0.212178			−0.106089	+	0.994357i	$0.533833\pi$
$828$	−3.20259e7	−	2.38760e8i	−0.0564170	−	0.420601i
$829$	−5.25236e8			−0.921915			−0.460957	−	0.887422i	$-0.652494\pi$
$829$	−5.25236e8			−0.921915			−0.460957	+	0.887422i	$0.652494\pi$
$830$	−3.18154e7	−	2.23609e7i	−0.0556420	−	0.0391071i
$831$			4.06261e8i			0.707949i
$832$	7.51857e7	−	3.17894e7i	0.130547	−	0.0551966i
$833$		−	1.20557e8i		−	0.208573i
$834$	−5.56674e7	−	4.86990e7i	−0.0959628	−	0.0839503i
$835$	−8.78862e7	−	8.25191e8i	−0.150960	−	1.41741i
$836$	−4.00888e7	−	2.98871e8i	−0.0686127	−	0.511522i
$837$			1.74377e6i			0.00297380i
$838$	−8.99290e7	−	7.86719e7i	−0.152816	−	0.133686i
$839$			5.84293e8i			0.989338i	0.869081	+	0.494669i	$0.164711\pi$
$839$			5.84293e8i			0.989338i	−0.869081	+	0.494669i	$0.835289\pi$
$840$	1.74827e8	−	3.36398e8i	0.294966	−	0.567565i
$841$	−2.38246e8			−0.400532
$842$	4.99995e8	−	5.71540e8i	0.837586	−	0.957437i
$843$	1.70866e8			0.285216
$844$	−8.70590e8	+	1.16776e8i	−1.44806	+	0.194234i
$845$	−6.26143e7	−	5.87905e8i	−0.103778	−	0.974400i
$846$	−4.30921e7	+	4.92581e7i	−0.0711682	+	0.0813517i
$847$	−4.00417e8			−0.658965
$848$	1.38311e8	+	5.06291e8i	0.226813	+	0.830258i
$849$	3.11649e8			0.509264
$850$	4.92545e8	+	2.73264e8i	0.802028	+	0.444965i
$851$		−	1.52691e9i		−	2.47756i
$852$	−1.63441e8	+	2.19230e7i	−0.264266	+	0.0354472i
$853$			4.23065e8i			0.681647i	0.940127	+	0.340824i	$0.110706\pi$
$853$			4.23065e8i			0.681647i	−0.940127	+	0.340824i	$0.889294\pi$
$854$	−5.10006e8	+	5.82982e8i	−0.818844	+	0.936013i
$855$	−1.67969e8	+	1.78893e7i	−0.268738	+	0.0286217i
$856$	5.00980e8	+	3.32099e8i	0.798728	+	0.529477i
$857$		−	5.82340e6i		−	0.00925197i	−0.999989	−	0.00462599i	$-0.998527\pi$
$857$		−	5.82340e6i		−	0.00925197i	0.999989	−	0.00462599i	$-0.00147250\pi$
$858$	2.16634e7	−	2.47632e7i	0.0342976	−	0.0392053i
$859$			7.80303e8i			1.23107i	0.788108	+	0.615537i	$0.211061\pi$
$859$			7.80303e8i			1.23107i	−0.788108	+	0.615537i	$0.788939\pi$
$860$	−1.13377e9	+	2.76783e8i	−1.78250	+	0.435155i
$861$	−4.12326e8			−0.645997
$862$	1.08305e8	+	9.47479e7i	0.169094	+	0.147927i
$863$	−1.24930e8			−0.194373			−0.0971863	−	0.995266i	$-0.530984\pi$
$863$	−1.24930e8			−0.194373			−0.0971863	+	0.995266i	$0.530984\pi$
$864$	−5.42193e7	+	1.11657e8i	−0.0840646	+	0.173119i
$865$	−1.07406e9	+	1.14392e8i	−1.65951	+	0.176745i
$866$	−1.31005e8	−	1.14606e8i	−0.201713	−	0.176463i
$867$	5.97356e7			0.0916591
$868$	−1.10962e7	+	1.48838e6i	−0.0169674	+	0.00227591i
$869$	−8.59935e7			−0.131041
$870$	2.40829e8	+	1.69263e8i	0.365722	+	0.257041i
$871$		−	1.62987e8i		−	0.246659i
$872$	−5.31074e8	−	3.52049e8i	−0.800951	−	0.530950i
$873$		−	1.53550e8i		−	0.230785i
$874$	−5.18665e8	−	4.53739e8i	−0.776878	−	0.679629i
$875$	−2.32280e8	−	7.04910e8i	−0.346727	−	1.05223i
$876$	5.02600e8	−	6.74160e7i	0.747671	−	0.100288i
$877$		−	7.92920e8i		−	1.17552i	−0.809035	−	0.587761i	$-0.800010\pi$
$877$		−	7.92920e8i		−	1.17552i	0.809035	−	0.587761i	$-0.199990\pi$
$878$	−6.01656e8	−	5.26341e8i	−0.888924	−	0.777649i
$879$			4.16239e8i			0.612880i
$880$	−4.04001e8	+	1.57991e8i	−0.592836	+	0.231838i
$881$	−7.45465e8			−1.09018			−0.545092	−	0.838377i	$-0.683505\pi$
$881$	−7.45465e8			−1.09018			−0.545092	+	0.838377i	$0.683505\pi$
$882$	3.42444e7	−	3.91445e7i	0.0499096	−	0.0570512i
$883$	9.67235e8			1.40492			0.702458	−	0.711726i	$-0.252086\pi$
$883$	9.67235e8			1.40492			0.702458	+	0.711726i	$0.252086\pi$
$884$	1.19389e7	+	8.90071e7i	0.0172826	+	0.128845i
$885$	2.22761e8	−	2.37249e7i	0.321372	−	0.0342275i
$886$	−5.53448e8	+	6.32641e8i	−0.795748	+	0.909612i
$887$	2.50813e8			0.359400			0.179700	−	0.983721i	$-0.442487\pi$
$887$	2.50813e8			0.359400			0.179700	+	0.983721i	$0.442487\pi$
$888$	−4.34701e8	+	6.55756e8i	−0.620800	+	0.936491i
$889$	5.08599e8			0.723886
$890$	8.66848e8	+	6.09250e8i	1.22963	+	0.864222i
$891$			5.00296e7i			0.0707284i
$892$	5.31625e7	+	3.96338e8i	0.0749050	+	0.558433i
$893$			1.87221e8i			0.262905i
$894$	1.21751e8	−	1.39172e8i	0.170396	−	0.194778i
$895$	1.13061e9	−	1.20415e8i	1.57705	−	0.167962i
$896$	−7.56792e8	−	2.49713e8i	−1.05209	−	0.347149i
$897$		−	7.51899e7i		−	0.104180i
$898$	9.90777e7	−	1.13255e8i	0.136819	−	0.156397i
$899$		−	8.69273e6i		−	0.0119640i
$900$	8.23068e7	+	2.28636e8i	0.112904	+	0.313630i
$901$	−5.77400e8			−0.789410
$902$	3.55094e8	+	3.10643e8i	0.483864	+	0.423295i
$903$	−8.64165e8			−1.17364
$904$	6.46209e8	−	9.74821e8i	0.874717	−	1.31953i
$905$	4.77925e7	+	4.48738e8i	0.0644783	+	0.605407i
$906$	−1.37236e8	−	1.20057e8i	−0.184537	−	0.161437i
$907$	1.03612e9			1.38863			0.694315	−	0.719672i	$-0.255708\pi$
$907$	1.03612e9			1.38863			0.694315	+	0.719672i	$0.255708\pi$
$908$	7.65808e7	+	5.70926e8i	0.102297	+	0.762645i
$909$	−3.62218e8			−0.482257
$910$	6.80422e7	−	9.68113e7i	0.0902930	−	0.128470i
$911$		−	2.02292e8i		−	0.267562i	−0.991011	−	0.133781i	$-0.957288\pi$
$911$		−	2.02292e8i		−	0.267562i	0.991011	−	0.133781i	$-0.0427118\pi$
$912$	9.35729e7	+	3.42527e8i	0.123357	+	0.451555i
$913$			3.29476e7i			0.0432923i
$914$	−1.86060e8	−	1.62769e8i	−0.243676	−	0.213173i
$915$	−5.25798e7	−	4.93688e8i	−0.0686366	−	0.644450i
$916$	−6.79349e7	−	5.06469e8i	−0.0883908	−	0.658972i
$917$		−	1.33024e9i		−	1.72513i
$918$	−1.02777e8	−	8.99115e7i	−0.132852	−	0.116222i
$919$			8.53644e8i			1.09984i	0.835217	+	0.549921i	$0.185342\pi$
$919$			8.53644e8i			1.09984i	−0.835217	+	0.549921i	$0.814658\pi$
$920$	−4.57157e8	+	8.79648e8i	−0.587086	+	1.12965i
$921$	−4.48648e7			−0.0574284
$922$	−1.74826e8	+	1.99842e8i	−0.223055	+	0.254972i
$923$	−5.14706e7			−0.0654567
$924$	−3.18356e8	+	4.27025e7i	−0.403550	+	0.0541299i
$925$	3.24402e8	+	1.50568e9i	0.409881	+	1.90242i
$926$	7.02238e7	−	8.02721e7i	0.0884405	−	0.101096i
$927$	−1.21227e8			−0.152181
$928$	2.70285e8	−	5.56613e8i	0.338203	−	0.696482i
$929$	1.26523e9			1.57805			0.789027	−	0.614358i	$-0.210585\pi$
$929$	1.26523e9			1.57805			0.789027	+	0.614358i	$0.210585\pi$
$930$	4.12632e6	−	5.87098e6i	0.00512996	−	0.00729897i
$931$		−	1.48781e8i		−	0.184373i
$932$	−3.28632e8	+	4.40808e7i	−0.405940	+	0.0544505i
$933$		−	6.01246e7i		−	0.0740299i
$934$	−4.50256e8	+	5.14683e8i	−0.552610	+	0.631683i
$935$	−5.05415e7	−	4.74550e8i	−0.0618321	−	0.580560i
$936$	−2.14061e7	+	3.22916e7i	−0.0261042	+	0.0393788i
$937$		−	1.48128e9i		−	1.80060i	−0.435265	−	0.900302i	$-0.643345\pi$
$937$		−	1.48128e9i		−	1.80060i	0.435265	−	0.900302i	$-0.356655\pi$
$938$	−1.04768e9	+	1.19759e9i	−1.26946	+	1.45111i
$939$		−	2.86290e8i		−	0.345788i
$940$	2.61645e8	−	6.38743e7i	0.315013	−	0.0769028i
$941$	−5.87649e7			−0.0705259			−0.0352630	−	0.999378i	$-0.511227\pi$
$941$	−5.87649e7			−0.0705259			−0.0352630	+	0.999378i	$0.511227\pi$
$942$	−4.39570e8	−	3.84545e8i	−0.525866	−	0.460039i
$943$	1.07819e9			1.28576
$944$	−1.24097e8	−	4.54260e8i	−0.147518	−	0.539994i
$945$	1.90557e7	+	1.78920e8i	0.0225803	+	0.212013i
$946$	7.44216e8	+	6.51056e8i	0.879075	+	0.769033i
$947$	8.51061e8			1.00210			0.501050	−	0.865419i	$-0.332947\pi$
$947$	8.51061e8			1.00210			0.501050	+	0.865419i	$0.332947\pi$
$948$	1.00360e8	−	1.34618e7i	0.117798	−	0.0158007i
$949$	1.58278e8			0.185192
$950$	6.07855e8	+	3.37238e8i	0.708972	+	0.393338i
$951$			2.30560e8i			0.268067i
$952$	4.84414e8	−	7.30750e8i	0.561443	−	0.846950i
$953$		−	4.68464e8i		−	0.541250i	−0.962685	−	0.270625i	$-0.912770\pi$
$953$		−	4.68464e8i		−	0.541250i	0.962685	−	0.270625i	$-0.0872303\pi$
$954$	−1.87480e8	−	1.64012e8i	−0.215929	−	0.188899i
$955$	9.57985e7	−	1.02029e7i	0.109989	−	0.0117143i
$956$	1.36360e8	−	1.82906e7i	0.156068	−	0.0209341i
$957$		−	2.49399e8i		−	0.284550i
$958$	−7.69294e7	−	6.72995e7i	−0.0874975	−	0.0765447i
$959$			1.43301e9i			1.62478i
$960$	4.46764e8	−	2.47630e8i	0.504969	−	0.279892i
$961$	8.87292e8			0.999761
$962$	−1.61687e8	+	1.84822e8i	−0.181614	+	0.207601i
$963$	−2.85268e8			−0.319429
$964$	−8.00248e7	−	5.96602e8i	−0.0893292	−	0.665968i
$965$	−1.06502e8	+	1.13429e7i	−0.118515	+	0.0126224i
$966$	−4.83322e8	+	5.52480e8i	−0.536173	+	0.612894i
$967$	−5.93383e8			−0.656229			−0.328114	−	0.944638i	$-0.606413\pi$
$967$	−5.93383e8			−0.656229			−0.328114	+	0.944638i	$0.606413\pi$
$968$	−4.49675e8	−	2.98090e8i	−0.495761	−	0.328640i
$969$	−3.90635e8			−0.429339
$970$	−3.63350e8	+	5.16979e8i	−0.398116	+	0.566445i
$971$			4.83882e8i			0.528544i	0.964448	+	0.264272i	$0.0851317\pi$
$971$			4.83882e8i			0.528544i	−0.964448	+	0.264272i	$0.914868\pi$
$972$	−7.83183e6	−	5.83880e7i	−0.00852834	−	0.0635806i
$973$			2.25375e8i			0.244663i
$974$	−1.68699e8	+	1.92838e8i	−0.182572	+	0.208696i
$975$	1.59746e7	+	7.41447e7i	0.0172352	+	0.0799956i
$976$	−1.00674e9	+	2.75026e8i	−1.08285	+	0.295818i
$977$			2.25662e8i			0.241977i	0.992654	+	0.120989i	$0.0386064\pi$
$977$			2.25662e8i			0.241977i	−0.992654	+	0.120989i	$0.961394\pi$
$978$	−5.56717e8	+	6.36378e8i	−0.595139	+	0.680297i
$979$		−	8.97695e8i		−	0.956711i
$980$	−2.07924e8	+	5.07597e7i	−0.220916	+	0.0539313i
$981$	3.02404e8			0.320318
$982$	1.14141e9	+	9.98529e8i	1.20533	+	1.05445i
$983$	−2.00052e8			−0.210611			−0.105306	−	0.994440i	$-0.533582\pi$
$983$	−2.00052e8			−0.210611			−0.105306	+	0.994440i	$0.533582\pi$
$984$	−4.63048e8	−	3.06955e8i	−0.486005	−	0.322173i
$985$	7.96301e8	−	8.48093e7i	0.833237	−	0.0887432i
$986$	5.12346e8	+	4.48211e8i	0.534481	+	0.467576i
$987$	1.99427e8			0.207411
$988$	1.47339e7	+	1.09845e8i	0.0152773	+	0.113896i
$989$	2.25971e9			2.33595
$990$	1.18386e8	−	1.68441e8i	0.122010	−	0.173597i
$991$			9.52073e8i			0.978249i	0.872214	+	0.489125i	$0.162684\pi$
$991$			9.52073e8i			0.978249i	−0.872214	+	0.489125i	$0.837316\pi$
$992$	−1.35692e7	−	6.58906e6i	−0.0139002	−	0.00674977i
$993$			8.92517e8i			0.911526i
$994$	3.78196e8	+	3.30854e8i	0.385086	+	0.336881i
$995$	9.65319e8	−	1.02810e8i	0.979945	−	0.104368i
$996$	−5.15775e6	−	3.84521e7i	−0.00522014	−	0.0389172i
$997$		−	2.94735e8i		−	0.297404i	−0.988882	−	0.148702i	$-0.952491\pi$
$997$		−	2.94735e8i		−	0.297404i	0.988882	−	0.148702i	$-0.0475094\pi$
$998$	−7.34561e8	−	6.42610e8i	−0.738987	−	0.646481i
$999$		−	3.73401e8i		−	0.374523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.f.a.19.27	yes	36
3.2	odd	2		180.7.f.g.19.10		36
4.3	odd	2	inner	60.7.f.a.19.9	✓	36
5.4	even	2	inner	60.7.f.a.19.10	yes	36
12.11	even	2		180.7.f.g.19.28		36
15.14	odd	2		180.7.f.g.19.27		36
20.19	odd	2	inner	60.7.f.a.19.28	yes	36
60.59	even	2		180.7.f.g.19.9		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.f.a.19.9	✓	36	4.3	odd	2	inner
60.7.f.a.19.10	yes	36	5.4	even	2	inner
60.7.f.a.19.27	yes	36	1.1	even	1	trivial
60.7.f.a.19.28	yes	36	20.19	odd	2	inner
180.7.f.g.19.9		36	60.59	even	2
180.7.f.g.19.10		36	3.2	odd	2
180.7.f.g.19.27		36	15.14	odd	2
180.7.f.g.19.28		36	12.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(5.26743 - 6.02115i) q^{2} +15.5885 q^{3} +(-8.50840 - 63.4319i) q^{4} +(-13.2381 - 124.297i) q^{5} +(82.1111 - 93.8604i) q^{6} -380.004 q^{7} +(-426.750 - 282.893i) q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+(5.26743 - 6.02115i) q^{2} +15.5885 q^{3} +(-8.50840 - 63.4319i) q^{4} +(-13.2381 - 124.297i) q^{5} +(82.1111 - 93.8604i) q^{6} -380.004 q^{7} +(-426.750 - 282.893i) q^{8} +243.000 q^{9} +(-818.142 - 575.017i) q^{10} +847.255i q^{11} +(-132.633 - 988.806i) q^{12} -311.394i q^{13} +(-2001.64 + 2288.06i) q^{14} +(-206.362 - 1937.60i) q^{15} +(-3951.21 + 1079.41i) q^{16} -4506.17i q^{17} +(1279.99 - 1463.14i) q^{18} -5561.11i q^{19} +(-7771.76 + 1897.29i) q^{20} -5923.67 q^{21} +(5101.45 + 4462.86i) q^{22} +15489.8 q^{23} +(-6652.38 - 4409.86i) q^{24} +(-15274.5 + 3290.92i) q^{25} +(-1874.95 - 1640.24i) q^{26} +3788.00 q^{27} +(3233.22 + 24104.4i) q^{28} -18883.3 q^{29} +(-12753.6 - 8963.63i) q^{30} +460.340i q^{31} +(-14313.5 + 29476.5i) q^{32} +13207.4i q^{33} +(-27132.3 - 23735.9i) q^{34} +(5030.54 + 47233.3i) q^{35} +(-2067.54 - 15414.0i) q^{36} -98574.7i q^{37} +(-33484.2 - 29292.7i) q^{38} -4854.15i q^{39} +(-29513.3 + 56788.8i) q^{40} +69606.4 q^{41} +(-31202.5 + 35667.3i) q^{42} +145883. q^{43} +(53743.0 - 7208.79i) q^{44} +(-3216.87 - 30204.2i) q^{45} +(81591.6 - 93266.5i) q^{46} -33666.1 q^{47} +(-61593.3 + 16826.3i) q^{48} +26753.8 q^{49} +(-60642.2 + 109305. i) q^{50} -70244.2i q^{51} +(-19752.3 + 2649.46i) q^{52} -128136. i q^{53} +(19953.0 - 22808.1i) q^{54} +(105311. - 11216.1i) q^{55} +(162167. + 107500. i) q^{56} -86689.1i q^{57} +(-99466.2 + 113699. i) q^{58} +114967. i q^{59} +(-121150. + 29575.8i) q^{60} +254794. q^{61} +(2771.78 + 2424.81i) q^{62} -92340.9 q^{63} +(102087. + 241449. i) q^{64} +(-38705.3 + 4122.27i) q^{65} +(79523.7 + 69569.0i) q^{66} +523410. q^{67} +(-285835. + 38340.3i) q^{68} +241463. q^{69} +(310897. + 218509. i) q^{70} -165291. i q^{71} +(-103700. - 68742.9i) q^{72} +508290. i q^{73} +(-593533. - 519235. i) q^{74} +(-238106. + 51300.4i) q^{75} +(-352752. + 47316.1i) q^{76} -321960. i q^{77} +(-29227.5 - 25568.9i) q^{78} +101497. i q^{79} +(186474. + 476835. i) q^{80} +59049.0 q^{81} +(366647. - 419110. i) q^{82} +38887.4 q^{83} +(50401.0 + 375750. i) q^{84} +(-560103. + 59653.3i) q^{85} +(768430. - 878385. i) q^{86} -294361. q^{87} +(239682. - 361566. i) q^{88} -1.05953e6 q^{89} +(-198808. - 139729. i) q^{90} +118331. i q^{91} +(-131794. - 982550. i) q^{92} +7176.00i q^{93} +(-177334. + 202708. i) q^{94} +(-691229. + 73618.7i) q^{95} +(-223125. + 459494. i) q^{96} -631894. i q^{97} +(140924. - 161088. i) q^{98} +205883. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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