LMFDB - Embedded newform 60.7.c.a.31.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(31,60)]

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, 0]))

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

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

chi := DirichletCharacter("60.31");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.c (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:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			31.14
Character	$\chi$	$=$	60.31
Dual form			60.7.c.a.31.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.59351 + 7.56794i) q^{2} +15.5885i q^{3} +(-50.5474 + 39.2551i) q^{4} -55.9017 q^{5} +(-117.972 + 40.4289i) q^{6} -671.100i q^{7} +(-428.176 - 280.731i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(2.59351 + 7.56794i) q^{2} +15.5885i q^{3} +(-50.5474 + 39.2551i) q^{4} -55.9017 q^{5} +(-117.972 + 40.4289i) q^{6} -671.100i q^{7} +(-428.176 - 280.731i) q^{8} -243.000 q^{9} +(-144.982 - 423.061i) q^{10} +199.628i q^{11} +(-611.927 - 787.955i) q^{12} +2041.73 q^{13} +(5078.84 - 1740.51i) q^{14} -871.421i q^{15} +(1014.07 - 3968.49i) q^{16} -8219.18 q^{17} +(-630.224 - 1839.01i) q^{18} +5147.13i q^{19} +(2825.68 - 2194.43i) q^{20} +10461.4 q^{21} +(-1510.77 + 517.738i) q^{22} -14631.4i q^{23} +(4376.16 - 6674.60i) q^{24} +3125.00 q^{25} +(5295.27 + 15451.7i) q^{26} -3788.00i q^{27} +(26344.1 + 33922.3i) q^{28} -12573.4 q^{29} +(6594.86 - 2260.04i) q^{30} -54422.8i q^{31} +(32663.3 - 2617.90i) q^{32} -3111.89 q^{33} +(-21316.6 - 62202.2i) q^{34} +37515.6i q^{35} +(12283.0 - 9538.99i) q^{36} -11.6361 q^{37} +(-38953.1 + 13349.2i) q^{38} +31827.5i q^{39} +(23935.7 + 15693.3i) q^{40} -67862.4 q^{41} +(27131.8 + 79171.3i) q^{42} -105037. i q^{43} +(-7836.42 - 10090.7i) q^{44} +13584.1 q^{45} +(110729. - 37946.7i) q^{46} +89660.8i q^{47} +(61862.6 + 15807.8i) q^{48} -332726. q^{49} +(8104.73 + 23649.8i) q^{50} -128124. i q^{51} +(-103204. + 80148.5i) q^{52} -1369.17 q^{53} +(28667.3 - 9824.22i) q^{54} -11159.5i q^{55} +(-188398. + 287349. i) q^{56} -80235.8 q^{57} +(-32609.2 - 95154.5i) q^{58} -5601.86i q^{59} +(34207.7 + 44048.0i) q^{60} -132681. q^{61} +(411868. - 141146. i) q^{62} +163077. i q^{63} +(104525. + 240404. i) q^{64} -114136. q^{65} +(-8070.74 - 23550.6i) q^{66} +325492. i q^{67} +(415458. - 322645. i) q^{68} +228081. q^{69} +(-283916. + 97297.4i) q^{70} +303340. i q^{71} +(104047. + 68217.5i) q^{72} -247561. q^{73} +(-30.1783 - 88.0611i) q^{74} +48713.9i q^{75} +(-202051. - 260174. i) q^{76} +133970. q^{77} +(-240868. + 82545.0i) q^{78} -389964. i q^{79} +(-56688.3 + 221845. i) q^{80} +59049.0 q^{81} +(-176002. - 513578. i) q^{82} -215366. i q^{83} +(-528797. + 410664. i) q^{84} +459466. q^{85} +(794916. - 272416. i) q^{86} -195999. i q^{87} +(56041.7 - 85475.8i) q^{88} +46200.5 q^{89} +(35230.6 + 102804. i) q^{90} -1.37021e6i q^{91} +(574357. + 739578. i) q^{92} +848367. q^{93} +(-678547. + 232537. i) q^{94} -287733. i q^{95} +(40809.0 + 509170. i) q^{96} +800223. q^{97} +(-862931. - 2.51805e6i) q^{98} -48509.6i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9}+O(q^{10}) $ 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9} - 750 q^{10} + 5040 q^{13} - 2596 q^{14} + 4194 q^{16} - 4860 q^{18} + 7000 q^{20} + 19440 q^{21} + 45780 q^{22} + 24786 q^{24} + 75000 q^{25} + 75852 q^{26} + 54300 q^{28} + 132800 q^{29} - 10700 q^{32} - 173484 q^{34} + 59778 q^{36} - 69840 q^{37} + 215800 q^{38} - 14250 q^{40} - 70448 q^{41} - 189540 q^{42} - 395668 q^{44} - 158760 q^{46} + 252720 q^{48} - 642984 q^{49} + 62500 q^{50} - 210240 q^{52} - 644320 q^{53} - 39366 q^{54} - 917708 q^{56} + 408240 q^{57} - 1345020 q^{58} + 222750 q^{60} - 222864 q^{61} + 1948520 q^{62} + 935922 q^{64} + 266000 q^{65} - 640548 q^{66} + 572680 q^{68} - 541728 q^{69} + 220500 q^{70} + 82620 q^{72} + 771120 q^{73} - 589164 q^{74} - 191544 q^{76} + 1383840 q^{77} - 693360 q^{78} - 946000 q^{80} + 1417176 q^{81} + 2672520 q^{82} + 1256796 q^{84} - 372000 q^{85} + 1781528 q^{86} + 956940 q^{88} - 1566224 q^{89} + 182250 q^{90} - 3040560 q^{92} + 1496880 q^{93} - 3788352 q^{94} - 413262 q^{96} - 1666800 q^{97} - 2709660 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9 - 750 * q^10 + 5040 * q^13 - 2596 * q^14 + 4194 * q^16 - 4860 * q^18 + 7000 * q^20 + 19440 * q^21 + 45780 * q^22 + 24786 * q^24 + 75000 * q^25 + 75852 * q^26 + 54300 * q^28 + 132800 * q^29 - 10700 * q^32 - 173484 * q^34 + 59778 * q^36 - 69840 * q^37 + 215800 * q^38 - 14250 * q^40 - 70448 * q^41 - 189540 * q^42 - 395668 * q^44 - 158760 * q^46 + 252720 * q^48 - 642984 * q^49 + 62500 * q^50 - 210240 * q^52 - 644320 * q^53 - 39366 * q^54 - 917708 * q^56 + 408240 * q^57 - 1345020 * q^58 + 222750 * q^60 - 222864 * q^61 + 1948520 * q^62 + 935922 * q^64 + 266000 * q^65 - 640548 * q^66 + 572680 * q^68 - 541728 * q^69 + 220500 * q^70 + 82620 * q^72 + 771120 * q^73 - 589164 * q^74 - 191544 * q^76 + 1383840 * q^77 - 693360 * q^78 - 946000 * q^80 + 1417176 * q^81 + 2672520 * q^82 + 1256796 * q^84 - 372000 * q^85 + 1781528 * q^86 + 956940 * q^88 - 1566224 * q^89 + 182250 * q^90 - 3040560 * q^92 + 1496880 * q^93 - 3788352 * q^94 - 413262 * q^96 - 1666800 * q^97 - 2709660 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	2.59351	+	7.56794i	0.324189	+	0.945992i
$2$	2.59351	+	7.56794i	0.324189	+	0.945992i
$3$			15.5885i			0.577350i
$3$			15.5885i			0.577350i
$4$	−50.5474	+	39.2551i	−0.789803	+	0.613361i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$	−117.972	+	40.4289i	−0.546169	+	0.187171i
$7$		−	671.100i		−	1.95656i	−0.207288	−	0.978280i	$-0.566464\pi$
$7$		−	671.100i		−	1.95656i	0.207288	−	0.978280i	$-0.433536\pi$
$8$	−428.176	−	280.731i	−0.836281	−	0.548302i
$9$	−243.000			−0.333333
$10$	−144.982	−	423.061i	−0.144982	−	0.423061i
$11$			199.628i			0.149983i	0.997184	+	0.0749917i	$0.0238930\pi$
$11$			199.628i			0.149983i	−0.997184	+	0.0749917i	$0.976107\pi$
$12$	−611.927	−	787.955i	−0.354124	−	0.455993i
$13$	2041.73			0.929328			0.464664	−	0.885487i	$-0.346175\pi$
$13$	2041.73			0.929328			0.464664	+	0.885487i	$0.346175\pi$
$14$	5078.84	−	1740.51i	1.85089	−	0.634296i
$15$		−	871.421i		−	0.258199i
$16$	1014.07	−	3968.49i	0.247576	−	0.968868i
$17$	−8219.18			−1.67294			−0.836472	−	0.548009i	$-0.815386\pi$
$17$	−8219.18			−1.67294			−0.836472	+	0.548009i	$0.815386\pi$
$18$	−630.224	−	1839.01i	−0.108063	−	0.315331i
$19$			5147.13i			0.750420i	0.926940	+	0.375210i	$0.122429\pi$
$19$			5147.13i			0.750420i	−0.926940	+	0.375210i	$0.877571\pi$
$20$	2825.68	−	2194.43i	0.353210	−	0.274303i
$21$	10461.4			1.12962
$22$	−1510.77	+	517.738i	−0.141883	+	0.0486230i
$23$		−	14631.4i		−	1.20255i	−0.799044	−	0.601273i	$-0.794660\pi$
$23$		−	14631.4i		−	1.20255i	0.799044	−	0.601273i	$-0.205340\pi$
$24$	4376.16	−	6674.60i	0.316562	−	0.482827i
$25$	3125.00			0.200000
$26$	5295.27	+	15451.7i	0.301278	+	0.879137i
$27$		−	3788.00i		−	0.192450i
$28$	26344.1	+	33922.3i	1.20008	+	1.54530i
$29$	−12573.4			−0.515534			−0.257767	−	0.966207i	$-0.582987\pi$
$29$	−12573.4			−0.515534			−0.257767	+	0.966207i	$0.582987\pi$
$30$	6594.86	−	2260.04i	0.244254	−	0.0837053i
$31$		−	54422.8i		−	1.82682i	−0.407041	−	0.913410i	$-0.633439\pi$
$31$		−	54422.8i		−	1.82682i	0.407041	−	0.913410i	$-0.366561\pi$
$32$	32663.3	−	2617.90i	0.996804	−	0.0798919i
$33$	−3111.89			−0.0865930
$34$	−21316.6	−	62202.2i	−0.542351	−	1.58259i
$35$			37515.6i			0.875000i
$36$	12283.0	−	9538.99i	0.263268	−	0.204454i
$37$	−11.6361			−0.000229721			−0.000114861	−	1.00000i	$-0.500037\pi$
$37$	−11.6361			−0.000229721			−0.000114861		1.00000i	$0.500037\pi$
$38$	−38953.1	+	13349.2i	−0.709891	+	0.243278i
$39$			31827.5i			0.536548i
$40$	23935.7	+	15693.3i	0.373996	+	0.245208i
$41$	−67862.4			−0.984640			−0.492320	−	0.870414i	$-0.663851\pi$
$41$	−67862.4			−0.984640			−0.492320	+	0.870414i	$0.663851\pi$
$42$	27131.8	+	79171.3i	0.366211	+	1.06861i
$43$		−	105037.i		−	1.32111i	−0.750778	−	0.660554i	$-0.770321\pi$
$43$		−	105037.i		−	1.32111i	0.750778	−	0.660554i	$-0.229679\pi$
$44$	−7836.42	−	10090.7i	−0.0919940	−	0.118457i
$45$	13584.1			0.149071
$46$	110729.	−	37946.7i	1.13760	−	0.389853i
$47$			89660.8i			0.863592i	0.901971	+	0.431796i	$0.142120\pi$
$47$			89660.8i			0.863592i	−0.901971	+	0.431796i	$0.857880\pi$
$48$	61862.6	+	15807.8i	0.559376	+	0.142938i
$49$	−332726.			−2.82813
$50$	8104.73	+	23649.8i	0.0648379	+	0.189198i
$51$		−	128124.i		−	0.965875i
$52$	−103204.	+	80148.5i	−0.733985	+	0.570014i
$53$	−1369.17			−0.00919668			−0.00459834	−	0.999989i	$-0.501464\pi$
$53$	−1369.17			−0.00919668			−0.00459834	+	0.999989i	$0.501464\pi$
$54$	28667.3	−	9824.22i	0.182056	−	0.0623903i
$55$		−	11159.5i		−	0.0670746i
$56$	−188398.	+	287349.i	−1.07279	+	1.63623i
$57$	−80235.8			−0.433255
$58$	−32609.2	−	95154.5i	−0.167131	−	0.487691i
$59$		−	5601.86i		−	0.0272757i	−0.999907	−	0.0136379i	$-0.995659\pi$
$59$		−	5601.86i		−	0.0272757i	0.999907	−	0.0136379i	$-0.00434120\pi$
$60$	34207.7	+	44048.0i	0.158369	+	0.203926i
$61$	−132681.			−0.584548			−0.292274	−	0.956335i	$-0.594412\pi$
$61$	−132681.			−0.584548			−0.292274	+	0.956335i	$0.594412\pi$
$62$	411868.	−	141146.i	1.72816	−	0.592235i
$63$			163077.i			0.652187i
$64$	104525.	+	240404.i	0.398730	+	0.917068i
$65$	−114136.			−0.415608
$66$	−8070.74	−	23550.6i	−0.0280725	−	0.0819163i
$67$			325492.i			1.08222i	0.840951	+	0.541111i	$0.181996\pi$
$67$			325492.i			1.08222i	−0.840951	+	0.541111i	$0.818004\pi$
$68$	415458.	−	322645.i	1.32130	−	1.02612i
$69$	228081.			0.694290
$70$	−283916.	+	97297.4i	−0.827743	+	0.283666i
$71$			303340.i			0.847529i	0.905772	+	0.423764i	$0.139292\pi$
$71$			303340.i			0.847529i	−0.905772	+	0.423764i	$0.860708\pi$
$72$	104047.	+	68217.5i	0.278760	+	0.182767i
$73$	−247561.			−0.636376			−0.318188	−	0.948028i	$-0.603074\pi$
$73$	−247561.			−0.636376			−0.318188	+	0.948028i	$0.603074\pi$
$74$	−30.1783	−	88.0611i	−7.44732e−5	−	0.000217315i
$75$			48713.9i			0.115470i
$76$	−202051.	−	260174.i	−0.460278	−	0.592683i
$77$	133970.			0.293452
$78$	−240868.	+	82545.0i	−0.507570	+	0.173943i
$79$		−	389964.i		−	0.790939i	−0.918479	−	0.395470i	$-0.870582\pi$
$79$		−	389964.i		−	0.790939i	0.918479	−	0.395470i	$-0.129418\pi$
$80$	−56688.3	+	221845.i	−0.110719	+	0.433291i
$81$	59049.0			0.111111
$82$	−176002.	−	513578.i	−0.319210	−	0.931462i
$83$		−	215366.i		−	0.376654i	−0.982106	−	0.188327i	$-0.939694\pi$
$83$		−	215366.i		−	0.376654i	0.982106	−	0.188327i	$-0.0603065\pi$
$84$	−528797.	+	410664.i	−0.892177	+	0.692865i
$85$	459466.			0.748164
$86$	794916.	−	272416.i	1.24976	−	0.428289i
$87$		−	195999.i		−	0.297644i
$88$	56041.7	−	85475.8i	0.0822362	−	0.125428i
$89$	46200.5			0.0655355			0.0327677	−	0.999463i	$-0.489568\pi$
$89$	46200.5			0.0655355			0.0327677	+	0.999463i	$0.489568\pi$
$90$	35230.6	+	102804.i	0.0483273	+	0.141020i
$91$		−	1.37021e6i		−	1.81829i
$92$	574357.	+	739578.i	0.737595	+	0.949774i
$93$	848367.			1.05471
$94$	−678547.	+	232537.i	−0.816952	+	0.279968i
$95$		−	287733.i		−	0.335598i
$96$	40809.0	+	509170.i	0.0461256	+	0.575505i
$97$	800223.			0.876791			0.438396	−	0.898782i	$-0.355547\pi$
$97$	800223.			0.876791			0.438396	+	0.898782i	$0.355547\pi$
$98$	−862931.	−	2.51805e6i	−0.916849	−	2.67539i
$99$		−	48509.6i		−	0.0499945i
$100$	−157961.	+	122672.i	−0.157961	+	0.122672i
$101$	850500.			0.825487			0.412743	−	0.910847i	$-0.364571\pi$
$101$	850500.			0.825487			0.412743	+	0.910847i	$0.364571\pi$
$102$	969637.	−	332292.i	0.913710	−	0.313126i
$103$		−	591093.i		−	0.540934i	−0.962729	−	0.270467i	$-0.912822\pi$
$103$		−	591093.i		−	0.540934i	0.962729	−	0.270467i	$-0.0871781\pi$
$104$	−874220.	−	573177.i	−0.777179	−	0.509552i
$105$	−584811.			−0.505182
$106$	−3550.97	−	10361.8i	−0.00298147	−	0.00869999i
$107$			1.02379e6i			0.835718i	0.908512	+	0.417859i	$0.137219\pi$
$107$			1.02379e6i			0.835718i	−0.908512	+	0.417859i	$0.862781\pi$
$108$	148698.	+	191473.i	0.118041	+	0.151998i
$109$	−1.78875e6			−1.38125			−0.690623	−	0.723215i	$-0.742663\pi$
$109$	−1.78875e6			−1.38125			−0.690623	+	0.723215i	$0.742663\pi$
$110$	84454.7	−	28942.4i	0.0634521	−	0.0217449i
$111$		−	181.389i		−	0.000132630i
$112$	−2.66325e6	−	680543.i	−1.89565	−	0.484397i
$113$	2.22824e6			1.54428			0.772142	−	0.635450i	$-0.219186\pi$
$113$	2.22824e6			1.54428			0.772142	+	0.635450i	$0.219186\pi$
$114$	−208093.	−	607219.i	−0.140457	−	0.409856i
$115$			817919.i			0.537795i
$116$	635551.	−	493569.i	0.407170	−	0.316209i
$117$	−496141.			−0.309776
$118$	42394.5	−	14528.5i	0.0258026	−	0.00884250i
$119$			5.51589e6i			3.27322i
$120$	−244635.	+	373121.i	−0.141571	+	0.215927i
$121$	1.73171e6			0.977505
$122$	−344111.	−	1.00412e6i	−0.189504	−	0.552978i
$123$		−	1.05787e6i		−	0.568482i
$124$	2.13637e6	+	2.75093e6i	1.12050	+	1.44283i
$125$	−174693.			−0.0894427
$126$	−1.23416e6	+	422943.i	−0.616964	+	0.211432i
$127$		−	1.20836e6i		−	0.589908i	−0.955511	−	0.294954i	$-0.904696\pi$
$127$		−	1.20836e6i		−	0.589908i	0.955511	−	0.294954i	$-0.0953043\pi$
$128$	−1.54828e6	+	1.41453e6i	−0.738275	+	0.674499i
$129$	1.63737e6			0.762742
$130$	−296014.	−	863777.i	−0.134736	−	0.393162i
$131$			283537.i			0.126123i	0.998010	+	0.0630616i	$0.0200865\pi$
$131$			283537.i			0.126123i	−0.998010	+	0.0630616i	$0.979914\pi$
$132$	157298.	−	122158.i	0.0683914	−	0.0531128i
$133$	3.45424e6			1.46824
$134$	−2.46331e6	+	844169.i	−1.02377	+	0.350845i
$135$			211755.i			0.0860663i
$136$	3.51925e6	+	2.30737e6i	1.39905	+	0.917279i
$137$	−4.15204e6			−1.61473			−0.807364	−	0.590053i	$-0.799107\pi$
$137$	−4.15204e6			−1.61473			−0.807364	+	0.590053i	$0.799107\pi$
$138$	591531.	+	1.72610e6i	0.225082	+	0.656793i
$139$			3.85092e6i			1.43391i	0.697122	+	0.716953i	$0.254464\pi$
$139$			3.85092e6i			1.43391i	−0.697122	+	0.716953i	$0.745536\pi$
$140$	−1.47268e6	−	1.89632e6i	−0.536691	−	0.691077i
$141$	−1.39767e6			−0.498595
$142$	−2.29566e6	+	786716.i	−0.801756	+	0.274760i
$143$			407587.i			0.139384i
$144$	−246419.	+	964342.i	−0.0825253	+	0.322956i
$145$	702873.			0.230554
$146$	−642054.	−	1.87353e6i	−0.206306	−	0.602007i
$147$		−	5.18669e6i		−	1.63282i
$148$	588.173	−	456.776i	0.000181435	−	0.000140902i
$149$	−3.30508e6			−0.999132			−0.499566	−	0.866276i	$-0.666507\pi$
$149$	−3.30508e6			−0.999132			−0.499566	+	0.866276i	$0.666507\pi$
$150$	−368664.	+	126340.i	−0.109234	+	0.0374342i
$151$		−	2.96350e6i		−	0.860743i	−0.902652	−	0.430371i	$-0.858383\pi$
$151$		−	2.96350e6i		−	0.860743i	0.902652	−	0.430371i	$-0.141617\pi$
$152$	1.44496e6	−	2.20387e6i	0.411456	−	0.627561i
$153$	1.99726e6			0.557648
$154$	347454.	+	1.01388e6i	0.0951339	+	0.277603i
$155$			3.04233e6i			0.816979i
$156$	−1.24939e6	−	1.60879e6i	−0.329098	−	0.423767i
$157$	3010.29			0.000777874			0.000388937	−	1.00000i	$-0.499876\pi$
$157$	3010.29			0.000777874			0.000388937		1.00000i	$0.499876\pi$
$158$	2.95122e6	−	1.01138e6i	0.748222	−	0.256414i
$159$		−	21343.3i		−	0.00530971i
$160$	−1.82593e6	+	146345.i	−0.445784	+	0.0357287i
$161$	−9.81912e6			−2.35285
$162$	153144.	+	446879.i	0.0360210	+	0.105110i
$163$			1.03461e6i			0.238899i	0.992840	+	0.119449i	$0.0381129\pi$
$163$			1.03461e6i			0.238899i	−0.992840	+	0.119449i	$0.961887\pi$
$164$	3.43026e6	−	2.66395e6i	0.777671	−	0.603940i
$165$	173960.			0.0387256
$166$	1.62988e6	−	558555.i	0.356312	−	0.122107i
$167$		−	593738.i		−	0.127481i	−0.997967	−	0.0637405i	$-0.979697\pi$
$167$		−	593738.i		−	0.127481i	0.997967	−	0.0637405i	$-0.0203030\pi$
$168$	−4.47932e6	−	2.93684e6i	−0.944680	−	0.619373i
$169$	−658135.			−0.136350
$170$	1.19163e6	+	3.47721e6i	0.242547	+	0.707757i
$171$		−	1.25075e6i		−	0.250140i
$172$	4.12325e6	+	5.30936e6i	0.810317	+	1.04341i
$173$	1.01324e6			0.195692			0.0978458	−	0.995202i	$-0.468805\pi$
$173$	1.01324e6			0.195692			0.0978458	+	0.995202i	$0.468805\pi$
$174$	1.48331e6	−	508327.i	0.281569	−	0.0964930i
$175$		−	2.09719e6i		−	0.391312i
$176$	792221.	+	202437.i	0.145314	+	0.0371323i
$177$	87324.3			0.0157476
$178$	119822.	+	349642.i	0.0212459	+	0.0619960i
$179$		−	1.05856e7i		−	1.84569i	−0.385176	−	0.922843i	$-0.625859\pi$
$179$		−	1.05856e7i		−	1.84569i	0.385176	−	0.922843i	$-0.374141\pi$
$180$	−686641.	+	533246.i	−0.117737	+	0.0914345i
$181$	−2.44921e6			−0.413038			−0.206519	−	0.978443i	$-0.566214\pi$
$181$	−2.44921e6			−0.413038			−0.206519	+	0.978443i	$0.566214\pi$
$182$	1.03696e7	−	3.55365e6i	1.72008	−	0.589469i
$183$		−	2.06830e6i		−	0.337489i
$184$	−4.10748e6	+	6.26480e6i	−0.659358	+	1.00567i
$185$	650.477			0.000102735
$186$	2.20025e6	+	6.42039e6i	0.341927	+	0.997752i
$187$		−	1.64078e6i		−	0.250914i
$188$	−3.51964e6	−	4.53212e6i	−0.529694	−	0.682068i
$189$	−2.54212e6			−0.376540
$190$	2.17755e6	−	746240.i	0.317473	−	0.108797i
$191$			5.41860e6i			0.777655i	0.921311	+	0.388827i	$0.127120\pi$
$191$			5.41860e6i			0.777655i	−0.921311	+	0.388827i	$0.872880\pi$
$192$	−3.74753e6	+	1.62938e6i	−0.529470	+	0.230207i
$193$	9.97092e6			1.38696			0.693479	−	0.720477i	$-0.256077\pi$
$193$	9.97092e6			1.38696			0.693479	+	0.720477i	$0.256077\pi$
$194$	2.07539e6	+	6.05604e6i	0.284246	+	0.829437i
$195$		−	1.77921e6i		−	0.239951i
$196$	1.68184e7	−	1.30612e7i	2.23366	−	1.73466i
$197$	1.33406e7			1.74492			0.872459	−	0.488687i	$-0.162524\pi$
$197$	1.33406e7			1.74492			0.872459	+	0.488687i	$0.162524\pi$
$198$	367118.	−	125810.i	0.0472944	−	0.0162077i
$199$		−	6.57996e6i		−	0.834957i	−0.908687	−	0.417479i	$-0.862914\pi$
$199$		−	6.57996e6i		−	0.834957i	0.908687	−	0.417479i	$-0.137086\pi$
$200$	−1.33805e6	−	877283.i	−0.167256	−	0.109660i
$201$	−5.07392e6			−0.624821
$202$	2.20578e6	+	6.43653e6i	0.267614	+	0.780904i
$203$			8.43799e6i			1.00867i
$204$	5.02953e6	+	6.47634e6i	0.592430	+	0.762851i
$205$	3.79362e6			0.440344
$206$	4.47336e6	−	1.53301e6i	0.511719	−	0.175365i
$207$			3.55543e6i			0.400849i
$208$	2.07046e6	−	8.10259e6i	0.230079	−	0.900396i
$209$	−1.02751e6			−0.112551
$210$	−1.51672e6	−	4.42581e6i	−0.163775	−	0.477898i
$211$			870512.i			0.0926675i	0.998926	+	0.0463337i	$0.0147538\pi$
$211$			870512.i			0.0926675i	−0.998926	+	0.0463337i	$0.985246\pi$
$212$	69208.1	−	53747.1i	0.00726356	−	0.00564089i
$213$	−4.72860e6			−0.489321
$214$	−7.74798e6	+	2.65521e6i	−0.790582	+	0.270931i
$215$			5.87177e6i			0.590818i
$216$	−1.06341e6	+	1.62193e6i	−0.105521	+	0.160942i
$217$	−3.65231e7			−3.57428
$218$	−4.63916e6	−	1.35372e7i	−0.447785	−	1.30665i
$219$		−	3.85910e6i		−	0.367412i
$220$	438069.	+	564086.i	0.0411410	+	0.0529757i
$221$	−1.67814e7			−1.55471
$222$	1372.74	−	470.434i	0.000125467	−	4.29971e-5i
$223$			5.16242e6i			0.465521i	0.972534	+	0.232760i	$0.0747758\pi$
$223$			5.16242e6i			0.465521i	−0.972534	+	0.232760i	$0.925224\pi$
$224$	−1.75687e6	−	2.19203e7i	−0.156313	−	1.95031i
$225$	−759375.			−0.0666667
$226$	5.77898e6	+	1.68632e7i	0.500640	+	1.46088i
$227$		−	3.88936e6i		−	0.332506i	−0.986083	−	0.166253i	$-0.946833\pi$
$227$		−	3.88936e6i		−	0.332506i	0.986083	−	0.166253i	$-0.0531669\pi$
$228$	4.05571e6	−	3.14967e6i	0.342186	−	0.265742i
$229$	1.00633e7			0.837978			0.418989	−	0.907991i	$-0.362385\pi$
$229$	1.00633e7			0.837978			0.418989	+	0.907991i	$0.362385\pi$
$230$	−6.18996e6	+	2.12129e6i	−0.508750	+	0.174347i
$231$			2.08839e6i			0.169424i
$232$	5.38361e6	+	3.52973e6i	0.431131	+	0.282668i
$233$	6.03617e6			0.477192			0.238596	−	0.971119i	$-0.423313\pi$
$233$	6.03617e6			0.477192			0.238596	+	0.971119i	$0.423313\pi$
$234$	−1.28675e6	−	3.75477e6i	−0.100426	−	0.293046i
$235$		−	5.01219e6i		−	0.386210i
$236$	219902.	+	283159.i	0.0167299	+	0.0215424i
$237$	6.07894e6			0.456649
$238$	−4.17439e7	+	1.43055e7i	−3.09644	+	1.06114i
$239$		−	1.34966e6i		−	0.0988621i	−0.998778	−	0.0494311i	$-0.984259\pi$
$239$		−	1.34966e6i		−	0.0988621i	0.998778	−	0.0494311i	$-0.0157408\pi$
$240$	−3.45822e6	−	883683.i	−0.250161	−	0.0639239i
$241$	7.74261e6			0.553141			0.276571	−	0.960994i	$-0.410802\pi$
$241$	7.74261e6			0.553141			0.276571	+	0.960994i	$0.410802\pi$
$242$	4.49121e6	+	1.31055e7i	0.316897	+	0.924712i
$243$			920483.i			0.0641500i
$244$	6.70669e6	−	5.20842e6i	0.461677	−	0.358539i
$245$	1.86000e7			1.26478
$246$	8.00589e6	−	2.74360e6i	0.537780	−	0.184296i
$247$			1.05091e7i			0.697386i
$248$	−1.52781e7	+	2.33025e7i	−1.00165	+	1.52773i
$249$	3.35722e6			0.217461
$250$	−453068.	−	1.32206e6i	−0.0289964	−	0.0846121i
$251$		−	1.64750e7i		−	1.04185i	−0.853603	−	0.520924i	$-0.825587\pi$
$251$		−	1.64750e7i		−	1.04185i	0.853603	−	0.520924i	$-0.174413\pi$
$252$	−6.40162e6	−	8.24313e6i	−0.400026	−	0.515099i
$253$	2.92083e6			0.180362
$254$	9.14477e6	−	3.13389e6i	0.558048	−	0.191242i
$255$			7.16237e6i			0.431952i
$256$	−1.47205e7	−	8.04865e6i	−0.877412	−	0.479737i
$257$	1.38542e7			0.816175			0.408088	−	0.912943i	$-0.366196\pi$
$257$	1.38542e7			0.816175			0.408088	+	0.912943i	$0.366196\pi$
$258$	4.24655e6	+	1.23915e7i	0.247273	+	0.721548i
$259$			7808.97i			0.000449464i
$260$	5.76929e6	−	4.48044e6i	0.328248	−	0.254918i
$261$	3.05533e6			0.171845
$262$	−2.14579e6	+	735356.i	−0.119312	+	0.0408878i
$263$			7.65702e6i			0.420913i	0.977603	+	0.210457i	$0.0674950\pi$
$263$			7.65702e6i			0.420913i	−0.977603	+	0.210457i	$0.932505\pi$
$264$	1.33244e6	+	873603.i	0.0724160	+	0.0474791i
$265$	76539.2			0.00411288
$266$	8.95862e6	+	2.61415e7i	0.475988	+	1.38894i
$267$			720194.i			0.0378369i
$268$	−1.27772e7	−	1.64528e7i	−0.663793	−	0.854742i
$269$	−3.63062e7			−1.86520			−0.932598	−	0.360917i	$-0.882464\pi$
$269$	−3.63062e7			−1.86520			−0.932598	+	0.360917i	$0.882464\pi$
$270$	−1.60255e6	+	549191.i	−0.0814180	+	0.0279018i
$271$		−	144294.i		−	0.00725002i	−0.999993	−	0.00362501i	$-0.998846\pi$
$271$		−	144294.i		−	0.00725002i	0.999993	−	0.00362501i	$-0.00115388\pi$
$272$	−8.33483e6	+	3.26177e7i	−0.414181	+	1.62086i
$273$	2.13594e7			1.04979
$274$	−1.07684e7	−	3.14224e7i	−0.523478	−	1.52752i
$275$			623838.i			0.0299967i
$276$	−1.15289e7	+	8.95333e6i	−0.548352	+	0.425851i
$277$	4.74727e6			0.223360			0.111680	−	0.993744i	$-0.464377\pi$
$277$	4.74727e6			0.223360			0.111680	+	0.993744i	$0.464377\pi$
$278$	−2.91436e7	+	9.98743e6i	−1.35646	+	0.464857i
$279$			1.32247e7i			0.608940i
$280$	1.05318e7	−	1.60633e7i	0.479764	−	0.731746i
$281$	4.52651e6			0.204007			0.102003	−	0.994784i	$-0.467475\pi$
$281$	4.52651e6			0.204007			0.102003	+	0.994784i	$0.467475\pi$
$282$	−3.62489e6	−	1.05775e7i	−0.161639	−	0.471667i
$283$			1.07319e7i			0.473497i	0.971571	+	0.236749i	$0.0760818\pi$
$283$			1.07319e7i			0.473497i	−0.971571	+	0.236749i	$0.923918\pi$
$284$	−1.19076e7	−	1.53330e7i	−0.519841	−	0.669380i
$285$	4.48532e6			0.193758
$286$	−3.08459e6	+	1.05708e6i	−0.131856	+	0.0451867i
$287$			4.55424e7i			1.92651i
$288$	−7.93717e6	+	636149.i	−0.332268	+	0.0266306i
$289$	4.34173e7			1.79874
$290$	1.82291e6	+	5.31930e6i	0.0747431	+	0.218102i
$291$			1.24742e7i			0.506216i
$292$	1.25136e7	−	9.71804e6i	0.502612	−	0.390328i
$293$	2.88844e7			1.14831			0.574157	−	0.818745i	$-0.305330\pi$
$293$	2.88844e7			1.14831			0.574157	+	0.818745i	$0.305330\pi$
$294$	3.92525e7	−	1.34518e7i	1.54463	−	0.529343i
$295$			313153.i			0.0121981i
$296$	4982.29	+	3266.60i	0.000192112	+	0.000125957i
$297$	756190.			0.0288643
$298$	−8.57177e6	−	2.50126e7i	−0.323908	−	0.945171i
$299$		−	2.98734e7i		−	1.11756i
$300$	−1.91227e6	−	2.46236e6i	−0.0708249	−	0.0911985i
$301$	−7.04906e7			−2.58483
$302$	2.24275e7	−	7.68587e6i	0.814256	−	0.279044i
$303$			1.32580e7i			0.476595i
$304$	2.04263e7	+	5.21956e6i	0.727058	+	0.185786i
$305$	7.41711e6			0.261418
$306$	5.17992e6	+	1.51151e7i	0.180784	+	0.527531i
$307$		−	4.55936e7i		−	1.57575i	−0.615833	−	0.787877i	$-0.711180\pi$
$307$		−	4.55936e7i		−	1.57575i	0.615833	−	0.787877i	$-0.288820\pi$
$308$	−6.77185e6	+	5.25902e6i	−0.231769	+	0.179992i
$309$	9.21423e6			0.312308
$310$	−2.30241e7	+	7.89032e6i	−0.772855	+	0.264856i
$311$		−	2.33624e7i		−	0.776670i	−0.921518	−	0.388335i	$-0.873050\pi$
$311$		−	2.33624e7i		−	0.776670i	0.921518	−	0.388335i	$-0.126950\pi$
$312$	8.93494e6	−	1.36277e7i	0.294190	−	0.448704i
$313$	2.77900e7			0.906266			0.453133	−	0.891443i	$-0.350306\pi$
$313$	2.77900e7			0.906266			0.453133	+	0.891443i	$0.350306\pi$
$314$	7807.23	+	22781.7i	0.000252179	+	0.000735863i
$315$		−	9.11630e6i		−	0.291667i
$316$	1.53081e7	+	1.97116e7i	0.485131	+	0.624686i
$317$	7.68469e6			0.241239			0.120620	−	0.992699i	$-0.461512\pi$
$317$	7.68469e6			0.241239			0.120620	+	0.992699i	$0.461512\pi$
$318$	161525.	−	55354.2i	0.00502294	−	0.00172135i
$319$		−	2.51000e6i		−	0.0773216i
$320$	−5.84311e6	−	1.34390e7i	−0.178318	−	0.410125i
$321$	−1.59593e7			−0.482502
$322$	−2.54660e7	−	7.43105e7i	−0.762770	−	2.22578i
$323$		−	4.23052e7i		−	1.25541i
$324$	−2.98477e6	+	2.31798e6i	−0.0877558	+	0.0681512i
$325$	6.38042e6			0.185866
$326$	−7.82987e6	+	2.68328e6i	−0.225996	+	0.0774484i
$327$		−	2.78839e7i		−	0.797462i
$328$	2.90570e7	+	1.90510e7i	0.823435	+	0.539880i
$329$	6.01713e7			1.68967
$330$	451168.	+	1.31652e6i	0.0125544	+	0.0366341i
$331$		−	2.26621e7i		−	0.624907i	−0.949933	−	0.312453i	$-0.898849\pi$
$331$		−	2.26621e7i		−	0.624907i	0.949933	−	0.312453i	$-0.101151\pi$
$332$	8.45421e6	+	1.08862e7i	0.231025	+	0.297482i
$333$	2827.57			7.65738e−5
$334$	4.49338e6	−	1.53987e6i	0.120596	−	0.0413280i
$335$		−	1.81956e7i		−	0.483984i
$336$	1.06086e7	−	4.15160e7i	0.279667	−	1.09445i
$337$	−5.15429e7			−1.34673			−0.673363	−	0.739312i	$-0.735151\pi$
$337$	−5.15429e7			−1.34673			−0.673363	+	0.739312i	$0.735151\pi$
$338$	−1.70688e6	−	4.98073e6i	−0.0442032	−	0.128986i
$339$			3.47349e7i			0.891593i
$340$	−2.32248e7	+	1.80364e7i	−0.590901	+	0.458895i
$341$	1.08643e7			0.273993
$342$	9.46561e6	−	3.24384e6i	0.236630	−	0.0810927i
$343$			1.44338e8i			3.57684i
$344$	−2.94872e7	+	4.49744e7i	−0.724366	+	1.10482i
$345$	−1.27501e7			−0.310496
$346$	2.62784e6	+	7.66811e6i	0.0634411	+	0.185123i
$347$		−	2.69989e7i		−	0.646186i	−0.946367	−	0.323093i	$-0.895277\pi$
$347$		−	2.69989e7i		−	0.646186i	0.946367	−	0.323093i	$-0.104723\pi$
$348$	7.69398e6	+	9.90725e6i	0.182563	+	0.235080i
$349$	−3.98391e7			−0.937201			−0.468601	−	0.883410i	$-0.655242\pi$
$349$	−3.98391e7			−0.937201			−0.468601	+	0.883410i	$0.655242\pi$
$350$	1.58714e7	−	5.43909e6i	0.370178	−	0.126859i
$351$		−	7.73407e6i		−	0.178849i
$352$	522605.	+	6.52050e6i	0.0119825	+	0.149504i
$353$	−3.70984e7			−0.843395			−0.421697	−	0.906737i	$-0.638566\pi$
$353$	−3.70984e7			−0.843395			−0.421697	+	0.906737i	$0.638566\pi$
$354$	226477.	+	660865.i	0.00510522	+	0.0148971i
$355$		−	1.69572e7i		−	0.379026i
$356$	−2.33531e6	+	1.81360e6i	−0.0517601	+	0.0401969i
$357$	−8.59842e7			−1.88979
$358$	8.01114e7	−	2.74540e7i	1.74600	−	0.598352i
$359$		−	3.23502e7i		−	0.699186i	−0.936902	−	0.349593i	$-0.886320\pi$
$359$		−	3.23502e7i		−	0.699186i	0.936902	−	0.349593i	$-0.113680\pi$
$360$	−5.81639e6	−	3.81348e6i	−0.124665	−	0.0817360i
$361$	2.05530e7			0.436870
$362$	−6.35206e6	−	1.85355e7i	−0.133903	−	0.390731i
$363$			2.69947e7i			0.564363i
$364$	5.37876e7	+	6.92604e7i	1.11527	+	1.43609i
$365$	1.38391e7			0.284596
$366$	1.56527e7	−	5.36416e6i	0.319262	−	0.109410i
$367$			5.83482e6i			0.118040i	0.998257	+	0.0590200i	$0.0187976\pi$
$367$			5.83482e6i			0.118040i	−0.998257	+	0.0590200i	$0.981202\pi$
$368$	−5.80644e7	−	1.48373e7i	−1.16511	−	0.297722i
$369$	1.64906e7			0.328213
$370$	1687.02	+	4922.77i	3.33054e−5	+	9.71861e-5i
$371$			918853.i			0.0179939i
$372$	−4.28827e7	+	3.33028e7i	−0.833016	+	0.646921i
$373$	−1.63274e7			−0.314623			−0.157311	−	0.987549i	$-0.550283\pi$
$373$	−1.63274e7			−0.314623			−0.157311	+	0.987549i	$0.550283\pi$
$374$	1.24173e7	−	4.25538e6i	0.237363	−	0.0813437i
$375$		−	2.72319e6i		−	0.0516398i
$376$	2.51705e7	−	3.83906e7i	0.473509	−	0.722206i
$377$	−2.56715e7			−0.479100
$378$	−6.59304e6	−	1.92386e7i	−0.122070	−	0.356204i
$379$		−	6.49860e7i		−	1.19372i	−0.802346	−	0.596859i	$-0.796415\pi$
$379$		−	6.49860e7i		−	1.19372i	0.802346	−	0.596859i	$-0.203585\pi$
$380$	1.12950e7	+	1.45442e7i	0.205843	+	0.265056i
$381$	1.88364e7			0.340583
$382$	−4.10076e7	+	1.40532e7i	−0.735656	+	0.252107i
$383$		−	5.64474e7i		−	1.00473i	−0.864657	−	0.502363i	$-0.832464\pi$
$383$		−	5.64474e7i		−	1.00473i	0.864657	−	0.502363i	$-0.167536\pi$
$384$	−2.20503e7	−	2.41352e7i	−0.389422	−	0.426243i
$385$	−7.48917e6			−0.131236
$386$	2.58597e7	+	7.54593e7i	0.449637	+	1.31205i
$387$			2.55241e7i			0.440370i
$388$	−4.04492e7	+	3.14129e7i	−0.692492	+	0.537790i
$389$	−8.66539e7			−1.47211			−0.736053	−	0.676924i	$-0.763313\pi$
$389$	−8.66539e7			−1.47211			−0.736053	+	0.676924i	$0.763313\pi$
$390$	1.34649e7	−	4.61441e6i	0.226992	−	0.0777897i
$391$			1.20258e8i			2.01179i
$392$	1.42465e8	+	9.34064e7i	2.36511	+	1.55067i
$393$	−4.41990e6			−0.0728173
$394$	3.45989e7	+	1.00960e8i	0.565684	+	1.65068i
$395$			2.17996e7i			0.353719i
$396$	1.90425e6	+	2.45203e6i	0.0306647	+	0.0394858i
$397$	1.11044e8			1.77469			0.887346	−	0.461105i	$-0.152547\pi$
$397$	1.11044e8			1.77469			0.887346	+	0.461105i	$0.152547\pi$
$398$	4.97968e7	−	1.70652e7i	0.789863	−	0.270684i
$399$			5.38462e7i			0.847689i
$400$	3.16897e6	−	1.24015e7i	0.0495152	−	0.193774i
$401$	−5.61325e7			−0.870525			−0.435262	−	0.900304i	$-0.643344\pi$
$401$	−5.61325e7			−0.870525			−0.435262	+	0.900304i	$0.643344\pi$
$402$	−1.31593e7	−	3.83991e7i	−0.202560	−	0.591076i
$403$		−	1.11117e8i		−	1.69771i
$404$	−4.29905e7	+	3.33865e7i	−0.651971	+	0.506321i
$405$	−3.30094e6			−0.0496904
$406$	−6.38582e7	+	2.18840e7i	−0.954198	+	0.327001i
$407$		−	2322.89i		−	3.44544e-5i
$408$	−3.59684e7	+	5.48597e7i	−0.529591	+	0.807742i
$409$	−5.17276e7			−0.756053			−0.378026	−	0.925795i	$-0.623397\pi$
$409$	−5.17276e7			−0.756053			−0.378026	+	0.925795i	$0.623397\pi$
$410$	9.83881e6	+	2.87099e7i	0.142755	+	0.416562i
$411$		−	6.47238e7i		−	0.932264i
$412$	2.32034e7	+	2.98782e7i	0.331788	+	0.427231i
$413$	−3.75941e6			−0.0533666
$414$	−2.69072e7	+	9.22105e6i	−0.379200	+	0.129951i
$415$			1.20393e7i			0.168445i
$416$	6.66897e7	−	5.34505e6i	0.926357	−	0.0742457i
$417$	−6.00300e7			−0.827866
$418$	−2.66486e6	−	7.77614e6i	−0.0364877	−	0.106472i
$419$			2.85658e7i			0.388333i	0.980969	+	0.194167i	$0.0622002\pi$
$419$			2.85658e7i			0.388333i	−0.980969	+	0.194167i	$0.937800\pi$
$420$	2.95606e7	−	2.29568e7i	0.398994	−	0.309859i
$421$	−1.03346e7			−0.138499			−0.0692496	−	0.997599i	$-0.522060\pi$
$421$	−1.03346e7			−0.138499			−0.0692496	+	0.997599i	$0.522060\pi$
$422$	−6.58798e6	+	2.25769e6i	−0.0876627	+	0.0300418i
$423$		−	2.17876e7i		−	0.287864i
$424$	586247.	+	384369.i	0.00769101	+	0.00504256i
$425$	−2.56849e7			−0.334589
$426$	−1.22637e7	−	3.57858e7i	−0.158633	−	0.462894i
$427$			8.90424e7i			1.14370i
$428$	−4.01890e7	−	5.17499e7i	−0.512597	−	0.660052i
$429$	−6.35365e6			−0.0804733
$430$	−4.44372e7	+	1.52285e7i	−0.558909	+	0.191537i
$431$		−	3.74717e7i		−	0.468027i	−0.972233	−	0.234014i	$-0.924814\pi$
$431$		−	3.74717e7i		−	0.468027i	0.972233	−	0.234014i	$-0.0751860\pi$
$432$	−1.50326e7	−	3.84130e6i	−0.186459	−	0.0476460i
$433$	−7.74967e7			−0.954595			−0.477298	−	0.878742i	$-0.658384\pi$
$433$	−7.74967e7			−0.954595			−0.477298	+	0.878742i	$0.658384\pi$
$434$	−9.47233e7	−	2.76405e8i	−1.15874	−	3.38124i
$435$			1.09567e7i			0.133110i
$436$	9.04167e7	−	7.02177e7i	1.09091	−	0.847202i
$437$	7.53096e7			0.902414
$438$	2.92054e7	−	1.00086e7i	0.347569	−	0.119111i
$439$			1.06961e8i			1.26425i	0.774868	+	0.632124i	$0.217817\pi$
$439$			1.06961e8i			1.26425i	−0.774868	+	0.632124i	$0.782183\pi$
$440$	−3.13283e6	+	4.77824e6i	−0.0367772	+	0.0560932i
$441$	8.08525e7			0.942709
$442$	−4.35227e7	−	1.27000e8i	−0.504022	−	1.47075i
$443$		−	6.93528e7i		−	0.797724i	−0.917011	−	0.398862i	$-0.869405\pi$
$443$		−	6.93528e7i		−	0.797724i	0.917011	−	0.398862i	$-0.130595\pi$
$444$	7120.43	+	9168.71i	8.13499e−5	+	0.000104751i
$445$	−2.58268e6			−0.0293083
$446$	−3.90689e7	+	1.33888e7i	−0.440379	+	0.150917i
$447$		−	5.15211e7i		−	0.576849i
$448$	1.61335e8	−	7.01466e7i	1.79430	−	0.780140i
$449$	−1.10854e8			−1.22465			−0.612327	−	0.790605i	$-0.709766\pi$
$449$	−1.10854e8			−1.22465			−0.612327	+	0.790605i	$0.709766\pi$
$450$	−1.96945e6	−	5.74690e6i	−0.0216126	−	0.0630661i
$451$		−	1.35472e7i		−	0.147680i
$452$	−1.12632e8	+	8.74699e7i	−1.21968	+	0.947204i
$453$	4.61963e7			0.496950
$454$	2.94344e7	−	1.00871e7i	0.314548	−	0.107795i
$455$			7.65969e7i			0.813162i
$456$	3.43550e7	+	2.25246e7i	0.362323	+	0.237554i
$457$	1.12207e8			1.17564			0.587818	−	0.808993i	$-0.299987\pi$
$457$	1.12207e8			1.17564			0.587818	+	0.808993i	$0.299987\pi$
$458$	2.60992e7	+	7.61582e7i	0.271664	+	0.792721i
$459$			3.11342e7i			0.321958i
$460$	−3.21075e7	−	4.13436e7i	−0.329863	−	0.424752i
$461$	1.44607e8			1.47600			0.737998	−	0.674803i	$-0.235771\pi$
$461$	1.44607e8			1.47600			0.737998	+	0.674803i	$0.235771\pi$
$462$	−1.58048e7	+	5.41627e6i	−0.160274	+	0.0549256i
$463$		−	9.36261e7i		−	0.943309i	−0.881783	−	0.471655i	$-0.843657\pi$
$463$		−	9.36261e7i		−	0.943309i	0.881783	−	0.471655i	$-0.156343\pi$
$464$	−1.27503e7	+	4.98972e7i	−0.127634	+	0.499485i
$465$	−4.74252e7			−0.471683
$466$	1.56549e7	+	4.56813e7i	0.154701	+	0.451420i
$467$		−	5.11897e7i		−	0.502611i	−0.967908	−	0.251305i	$-0.919140\pi$
$467$		−	5.11897e7i		−	0.502611i	0.967908	−	0.251305i	$-0.0808598\pi$
$468$	2.50786e7	−	1.94761e7i	0.244662	−	0.190005i
$469$	2.18438e8			2.11743
$470$	3.79319e7	−	1.29992e7i	0.365352	−	0.125205i
$471$			46925.8i			0.000449106i
$472$	−1.57261e6	+	2.39858e6i	−0.0149553	+	0.0228101i
$473$	2.09684e7			0.198144
$474$	1.57658e7	+	4.60050e7i	0.148041	+	0.431986i
$475$			1.60848e7i			0.150084i
$476$	−2.16527e8	−	2.78814e8i	−2.00766	−	2.58519i
$477$	332709.			0.00306556
$478$	1.02141e7	−	3.50036e6i	0.0935228	−	0.0320500i
$479$			1.88871e8i			1.71854i	0.511525	+	0.859269i	$0.329081\pi$
$479$			1.88871e8i			1.71854i	−0.511525	+	0.859269i	$0.670919\pi$
$480$	−2.28129e6	−	2.84635e7i	−0.0206280	−	0.257374i
$481$	−23757.8			−0.000213487
$482$	2.00806e7	+	5.85956e7i	0.179323	+	0.523267i
$483$		−	1.53065e8i		−	1.35842i
$484$	−8.75334e7	+	6.79785e7i	−0.772036	+	0.599564i
$485$	−4.47339e7			−0.392113
$486$	−6.96616e6	+	2.38729e6i	−0.0606854	+	0.0207968i
$487$		−	1.41791e8i		−	1.22761i	−0.789456	−	0.613807i	$-0.789637\pi$
$487$		−	1.41791e8i		−	1.22761i	0.789456	−	0.613807i	$-0.210363\pi$
$488$	5.68109e7	+	3.72477e7i	0.488846	+	0.320509i
$489$	−1.61280e7			−0.137928
$490$	4.82393e7	+	1.40763e8i	0.410027	+	1.19647i
$491$			1.73081e7i			0.146219i	0.997324	+	0.0731095i	$0.0232923\pi$
$491$			1.73081e7i			0.146219i	−0.997324	+	0.0731095i	$0.976708\pi$
$492$	4.15268e7	+	5.34725e7i	0.348685	+	0.448989i
$493$	1.03343e8			0.862460
$494$	−7.95319e7	+	2.72554e7i	−0.659721	+	0.226085i
$495$			2.71177e6i			0.0223582i
$496$	−2.15976e8	−	5.51886e7i	−1.76995	−	0.452277i
$497$	2.03571e8			1.65824
$498$	8.70701e6	+	2.54073e7i	0.0704987	+	0.205717i
$499$		−	2.37084e8i		−	1.90810i	−0.299655	−	0.954048i	$-0.596872\pi$
$499$		−	2.37084e8i		−	1.90810i	0.299655	−	0.954048i	$-0.403128\pi$
$500$	8.83026e6	−	6.85759e6i	0.0706421	−	0.0548607i
$501$	9.25547e6			0.0736012
$502$	1.24682e8	−	4.27282e7i	0.985580	−	0.337756i
$503$		−	2.25165e7i		−	0.176928i	−0.996079	−	0.0884640i	$-0.971804\pi$
$503$		−	2.25165e7i		−	0.176928i	0.996079	−	0.0884640i	$-0.0281958\pi$
$504$	4.57808e7	−	6.98257e7i	0.357595	−	0.545411i
$505$	−4.75444e7			−0.369169
$506$	7.57522e6	+	2.21047e7i	0.0584715	+	0.170621i
$507$		−	1.02593e7i		−	0.0787217i
$508$	4.74342e7	+	6.10793e7i	0.361827	+	0.465911i
$509$	−9.38014e7			−0.711305			−0.355653	−	0.934618i	$-0.615741\pi$
$509$	−9.38014e7			−0.711305			−0.355653	+	0.934618i	$0.615741\pi$
$510$	−5.42043e7	+	1.85757e7i	−0.408624	+	0.140034i
$511$			1.66138e8i			1.24511i
$512$	2.27338e7	−	1.32278e8i	0.169380	−	0.985551i
$513$	1.94973e7			0.144418
$514$	3.59312e7	+	1.04848e8i	0.264595	+	0.772095i
$515$			3.30431e7i			0.241913i
$516$	−8.27648e7	+	6.42752e7i	−0.602416	+	0.467837i
$517$	−1.78988e7			−0.129525
$518$	−59097.8	+	20252.7i	−0.000425189	+	0.000145711i
$519$			1.57948e7i			0.112983i
$520$	4.88704e7	+	3.20416e7i	0.347565	+	0.227879i
$521$	1.78407e8			1.26153			0.630765	−	0.775974i	$-0.282741\pi$
$521$	1.78407e8			1.26153			0.630765	+	0.775974i	$0.282741\pi$
$522$	7.92404e6	+	2.31225e7i	0.0557102	+	0.162564i
$523$			2.26348e8i			1.58224i	0.611662	+	0.791119i	$0.290501\pi$
$523$			2.26348e8i			1.58224i	−0.611662	+	0.791119i	$0.709499\pi$
$524$	−1.11303e7	−	1.43320e7i	−0.0773591	−	0.0996125i
$525$	3.26919e7			0.225924
$526$	−5.79478e7	+	1.98586e7i	−0.398180	+	0.136456i
$527$			4.47310e8i			3.05617i
$528$	−3.15568e6	+	1.23495e7i	−0.0214384	+	0.0838972i
$529$	−6.60414e7			−0.446118
$530$	198505.	+	579244.i	0.00133335	+	0.00389075i
$531$			1.36125e6i			0.00909190i
$532$	−1.74603e8	+	1.35597e8i	−1.15962	+	0.900562i
$533$	−1.38557e8			−0.915053
$534$	−5.45038e6	+	1.86783e6i	−0.0357934	+	0.0122663i
$535$		−	5.72316e7i		−	0.373744i
$536$	9.13757e7	−	1.39368e8i	0.593384	−	0.905041i
$537$	1.65014e8			1.06561
$538$	−9.41608e7	−	2.74763e8i	−0.604677	−	1.76446i
$539$		−	6.64215e7i		−	0.424172i
$540$	−8.31248e6	−	1.07037e7i	−0.0527897	−	0.0679754i
$541$	5.52591e7			0.348990			0.174495	−	0.984658i	$-0.444171\pi$
$541$	5.52591e7			0.348990			0.174495	+	0.984658i	$0.444171\pi$
$542$	1.09201e6	−	374228.i	0.00685847	−	0.00235038i
$543$		−	3.81794e7i		−	0.238468i
$544$	−2.68465e8	+	2.15170e7i	−1.66760	+	0.133655i
$545$	9.99943e7			0.617712
$546$	5.53960e7	+	1.61647e8i	0.340330	+	0.993091i
$547$		−	5.20328e7i		−	0.317918i	−0.987285	−	0.158959i	$-0.949186\pi$
$547$		−	5.20328e7i		−	0.317918i	0.987285	−	0.158959i	$-0.0508137\pi$
$548$	2.09875e8	−	1.62989e8i	1.27532	−	0.990412i
$549$	3.22416e7			0.194849
$550$	−4.72116e6	+	1.61793e6i	−0.0283766	+	0.00972461i
$551$		−	6.47167e7i		−	0.386867i
$552$	−9.76586e7	−	6.40292e7i	−0.580622	−	0.380681i
$553$	−2.61705e8			−1.54752
$554$	1.23121e7	+	3.59271e7i	0.0724109	+	0.211297i
$555$			10139.9i			5.93138e-5i
$556$	−1.51168e8	−	1.94654e8i	−0.879502	−	1.13250i
$557$	−2.24751e8			−1.30058			−0.650289	−	0.759687i	$-0.725352\pi$
$557$	−2.24751e8			−1.30058			−0.650289	+	0.759687i	$0.725352\pi$
$558$	−1.00084e8	+	3.42986e7i	−0.576052	+	0.197412i
$559$		−	2.14458e8i		−	1.22774i
$560$	1.48880e8	+	3.80435e7i	0.847760	+	0.216629i
$561$	2.55772e7			0.144865
$562$	1.17396e7	+	3.42563e7i	0.0661367	+	0.192989i
$563$			1.16024e8i			0.650165i	0.945686	+	0.325083i	$0.105392\pi$
$563$			1.16024e8i			0.650165i	−0.945686	+	0.325083i	$0.894608\pi$
$564$	7.06487e7	−	5.48658e7i	0.393792	−	0.305819i
$565$	−1.24563e8			−0.690625
$566$	−8.12184e7	+	2.78334e7i	−0.447925	+	0.153503i
$567$		−	3.96278e7i		−	0.217396i
$568$	8.51568e7	−	1.29883e8i	0.464702	−	0.708772i
$569$	6.45365e7			0.350323			0.175161	−	0.984540i	$-0.443955\pi$
$569$	6.45365e7			0.350323			0.175161	+	0.984540i	$0.443955\pi$
$570$	1.16327e7	+	3.39446e7i	0.0628141	+	0.183293i
$571$		−	5.29903e7i		−	0.284635i	−0.989821	−	0.142317i	$-0.954545\pi$
$571$		−	5.29903e7i		−	0.284635i	0.989821	−	0.142317i	$-0.0454553\pi$
$572$	−1.59999e7	−	2.06025e7i	−0.0854926	−	0.110086i
$573$	−8.44676e7			−0.448979
$574$	−3.44662e8	+	1.18115e8i	−1.82246	+	0.624553i
$575$		−	4.57231e7i		−	0.240509i
$576$	−2.53995e7	−	5.84182e7i	−0.132910	−	0.305689i
$577$	−1.97923e8			−1.03031			−0.515155	−	0.857097i	$-0.672266\pi$
$577$	−1.97923e8			−1.03031			−0.515155	+	0.857097i	$0.672266\pi$
$578$	1.12603e8	+	3.28579e8i	0.583134	+	1.70160i
$579$			1.55431e8i			0.800760i
$580$	−3.55284e7	+	2.75913e7i	−0.182092	+	0.141413i
$581$	−1.44532e8			−0.736946
$582$	−9.44043e7	+	3.23522e7i	−0.478876	+	0.164110i
$583$		−	273326.i		−	0.00137935i
$584$	1.06000e8	+	6.94980e7i	0.532189	+	0.348926i
$585$	2.77351e7			0.138536
$586$	7.49122e7	+	2.18596e8i	0.372271	+	1.08630i
$587$		−	6.20004e7i		−	0.306535i	−0.988185	−	0.153268i	$-0.951020\pi$
$587$		−	6.20004e7i		−	0.306535i	0.988185	−	0.153268i	$-0.0489796\pi$
$588$	2.03604e8	+	2.62174e8i	1.00151	+	1.28961i
$589$	2.80121e8			1.37088
$590$	−2.36993e6	+	812168.i	−0.0115393	+	0.00395448i
$591$			2.07959e8i			1.00743i
$592$	−11799.8	+	46177.6i	−5.68735e−5	+	0.000222570i
$593$	−3.48324e8			−1.67039			−0.835197	−	0.549950i	$-0.814647\pi$
$593$	−3.48324e8			−1.67039			−0.835197	+	0.549950i	$0.814647\pi$
$594$	1.96119e6	+	5.72280e6i	0.00935751	+	0.0273054i
$595$		−	3.08348e8i		−	1.46383i
$596$	1.67063e8	−	1.29741e8i	0.789117	−	0.612829i
$597$	1.02571e8			0.482063
$598$	2.26080e8	−	7.74770e7i	1.05720	−	0.362301i
$599$			2.16010e8i			1.00506i	0.864559	+	0.502531i	$0.167598\pi$
$599$			2.16010e8i			1.00506i	−0.864559	+	0.502531i	$0.832402\pi$
$600$	1.36755e7	−	2.08581e7i	0.0633124	−	0.0965654i
$601$	2.07109e8			0.954058			0.477029	−	0.878888i	$-0.341714\pi$
$601$	2.07109e8			0.954058			0.477029	+	0.878888i	$0.341714\pi$
$602$	−1.82818e8	−	5.33468e8i	−0.837974	−	2.44523i
$603$		−	7.90946e7i		−	0.360741i
$604$	1.16332e8	+	1.49797e8i	0.527946	+	0.679817i
$605$	−9.68055e7			−0.437154
$606$	−1.00336e8	+	3.43848e7i	−0.450855	+	0.154507i
$607$		−	7.87805e7i		−	0.352251i	−0.984368	−	0.176126i	$-0.943644\pi$
$607$		−	7.87805e7i		−	0.352251i	0.984368	−	0.176126i	$-0.0563565\pi$
$608$	1.34746e7	+	1.68122e8i	0.0599524	+	0.748021i
$609$	−1.31535e8			−0.582358
$610$	1.92364e7	+	5.61322e7i	0.0847489	+	0.247299i
$611$			1.83063e8i			0.802560i
$612$	−1.00956e8	+	7.84027e7i	−0.440432	+	0.342040i
$613$	−2.49628e8			−1.08371			−0.541853	−	0.840473i	$-0.682277\pi$
$613$	−2.49628e8			−1.08371			−0.541853	+	0.840473i	$0.682277\pi$
$614$	3.45049e8	−	1.18248e8i	1.49065	−	0.510843i
$615$			5.91367e7i			0.254233i
$616$	−5.73628e7	−	3.76096e7i	−0.245408	−	0.160900i
$617$	2.37350e8			1.01049			0.505247	−	0.862975i	$-0.331401\pi$
$617$	2.37350e8			1.01049			0.505247	+	0.862975i	$0.331401\pi$
$618$	2.38972e7	+	6.97327e7i	0.101247	+	0.295441i
$619$			5.81494e7i			0.245173i	0.992458	+	0.122587i	$0.0391190\pi$
$619$			5.81494e7i			0.245173i	−0.992458	+	0.122587i	$0.960881\pi$
$620$	−1.19427e8	−	1.53782e8i	−0.501103	−	0.645252i
$621$	−5.54236e7			−0.231430
$622$	1.76805e8	−	6.05908e7i	0.734724	−	0.251788i
$623$		−	3.10051e7i		−	0.128224i
$624$	1.26307e8	+	3.22753e7i	0.519844	+	0.132836i
$625$	9.76562e6			0.0400000
$626$	7.20738e7	+	2.10313e8i	0.293802	+	0.857320i
$627$		−	1.60173e7i		−	0.0649811i
$628$	−152162.	+	118169.i	−0.000614367	+	0.000477118i
$629$	95639.0			0.000384311
$630$	6.89916e7	−	2.36433e7i	0.275914	−	0.0945553i
$631$		−	1.07588e8i		−	0.428227i	−0.976809	−	0.214114i	$-0.931314\pi$
$631$		−	1.07588e8i		−	0.428227i	0.976809	−	0.214114i	$-0.0686863\pi$
$632$	−1.09475e8	+	1.66973e8i	−0.433673	+	0.661447i
$633$	−1.35699e7			−0.0535016
$634$	1.99304e7	+	5.81572e7i	0.0782073	+	0.228211i
$635$			6.75492e7i			0.263815i
$636$	837834.	+	1.07885e6i	0.00325677	+	0.00419362i
$637$	−6.79338e8			−2.62826
$638$	1.89955e7	−	6.50971e6i	0.0731457	−	0.0250668i
$639$		−	7.37116e7i		−	0.282510i
$640$	8.65512e7	−	7.90745e7i	0.330167	−	0.301645i
$641$	2.45332e8			0.931492			0.465746	−	0.884918i	$-0.345786\pi$
$641$	2.45332e8			0.931492			0.465746	+	0.884918i	$0.345786\pi$
$642$	−4.13907e7	−	1.20779e8i	−0.156422	−	0.456443i
$643$			3.42151e8i			1.28702i	0.765439	+	0.643509i	$0.222522\pi$
$643$			3.42151e8i			1.28702i	−0.765439	+	0.643509i	$0.777478\pi$
$644$	4.96331e8	−	3.85451e8i	1.85829	−	1.44315i
$645$	−9.15318e7			−0.341109
$646$	3.20163e8	−	1.09719e8i	1.18761	−	0.406991i
$647$		−	2.08510e8i		−	0.769862i	−0.922945	−	0.384931i	$-0.874225\pi$
$647$		−	2.08510e8i		−	0.769862i	0.922945	−	0.384931i	$-0.125775\pi$
$648$	−2.52833e7	−	1.65769e7i	−0.0929201	−	0.0609224i
$649$	1.11829e6			0.00409091
$650$	1.65477e7	+	4.82866e7i	0.0602556	+	0.175827i
$651$		−	5.69339e8i		−	2.06361i
$652$	−4.06137e7	−	5.22968e7i	−0.146531	−	0.188683i
$653$	4.76031e8			1.70960			0.854802	−	0.518954i	$-0.173678\pi$
$653$	4.76031e8			1.70960			0.854802	+	0.518954i	$0.173678\pi$
$654$	2.11024e8	−	7.23173e7i	0.754393	−	0.258529i
$655$		−	1.58502e7i		−	0.0564040i
$656$	−6.88173e7	+	2.69311e8i	−0.243773	+	0.953987i
$657$	6.01574e7			0.212125
$658$	1.56055e8	+	4.55373e8i	0.547773	+	1.59842i
$659$			1.75876e8i			0.614540i	0.951622	+	0.307270i	$0.0994155\pi$
$659$			1.75876e8i			0.614540i	−0.951622	+	0.307270i	$0.900584\pi$
$660$	−8.79322e6	+	6.82882e6i	−0.0305855	+	0.0237528i
$661$	3.80396e8			1.31714			0.658570	−	0.752520i	$-0.271162\pi$
$661$	3.80396e8			1.31714			0.658570	+	0.752520i	$0.271162\pi$
$662$	1.71505e8	−	5.87744e7i	0.591157	−	0.202588i
$663$		−	2.61596e8i		−	0.897614i
$664$	−6.04598e7	+	9.22144e7i	−0.206520	+	0.314988i
$665$	−1.93098e8			−0.656617
$666$	7333.34	+	21398.9i	2.48244e−5	+	7.24382e-5i
$667$			1.83966e8i			0.619954i
$668$	2.33073e7	+	3.00119e7i	0.0781920	+	0.100685i
$669$	−8.04742e7			−0.268769
$670$	1.37703e8	−	4.71905e7i	0.457846	−	0.156903i
$671$		−	2.64869e7i		−	0.0876725i
$672$	3.41704e8	−	2.73869e7i	1.12601	−	0.0902475i
$673$	−3.67932e8			−1.20704			−0.603521	−	0.797347i	$-0.706236\pi$
$673$	−3.67932e8			−1.20704			−0.603521	+	0.797347i	$0.706236\pi$
$674$	−1.33677e8	−	3.90074e8i	−0.436594	−	1.27399i
$675$		−	1.18375e7i		−	0.0384900i
$676$	3.32670e7	−	2.58352e7i	0.107690	−	0.0836318i
$677$	4.64821e7			0.149803			0.0749014	−	0.997191i	$-0.476136\pi$
$677$	4.64821e7			0.149803			0.0749014	+	0.997191i	$0.476136\pi$
$678$	−2.62871e8	+	9.00854e7i	−0.843440	+	0.289045i
$679$		−	5.37030e8i		−	1.71549i
$680$	−1.96732e8	−	1.28986e8i	−0.625675	−	0.410219i
$681$	6.06290e7			0.191973
$682$	2.81768e7	+	8.22204e7i	0.0888255	+	0.259195i
$683$		−	6.18385e8i		−	1.94087i	−0.241361	−	0.970435i	$-0.577594\pi$
$683$		−	6.18385e8i		−	1.94087i	0.241361	−	0.970435i	$-0.422406\pi$
$684$	4.90984e7	+	6.32222e7i	0.153426	+	0.197561i
$685$	2.32106e8			0.722129
$686$	−1.09234e9	+	3.74344e8i	−3.38366	+	1.15957i
$687$			1.56871e8i			0.483807i
$688$	−4.16839e8	−	1.06515e8i	−1.27998	−	0.327075i
$689$	−2.79549e6			−0.00854673
$690$	−3.30676e7	−	9.64919e7i	−0.100660	−	0.293727i
$691$			5.57874e7i			0.169084i	0.996420	+	0.0845419i	$0.0269427\pi$
$691$			5.57874e7i			0.169084i	−0.996420	+	0.0845419i	$0.973057\pi$
$692$	−5.12164e7	+	3.97747e7i	−0.154558	+	0.120030i
$693$	−3.25548e7			−0.0978172
$694$	2.04326e8	−	7.00221e7i	0.611287	−	0.209487i
$695$		−	2.15273e8i		−	0.641262i
$696$	−5.50230e7	+	8.39222e7i	−0.163199	+	0.248914i
$697$	5.57773e8			1.64725
$698$	−1.03323e8	−	3.01500e8i	−0.303831	−	0.886585i
$699$			9.40946e7i			0.275507i
$700$	8.23254e7	+	1.06007e8i	0.240016	+	0.309059i
$701$	−5.45837e8			−1.58456			−0.792280	−	0.610158i	$-0.791106\pi$
$701$	−5.45837e8			−1.58456			−0.792280	+	0.610158i	$0.791106\pi$
$702$	5.85310e7	−	2.00584e7i	0.169190	−	0.0579810i
$703$		−	59892.4i		−	0.000172387i
$704$	−4.79914e7	+	2.08661e7i	−0.137545	+	0.0598029i
$705$	7.81323e7			0.222979
$706$	−9.62152e7	−	2.80758e8i	−0.273420	−	0.797845i
$707$		−	5.70770e8i		−	1.61511i
$708$	−4.41401e6	+	3.42793e6i	−0.0124375	+	0.00965899i
$709$	2.11110e8			0.592339			0.296170	−	0.955135i	$-0.404291\pi$
$709$	2.11110e8			0.592339			0.296170	+	0.955135i	$0.404291\pi$
$710$	1.28331e8	−	4.39788e7i	0.358556	−	0.122876i
$711$			9.47612e7i			0.263646i
$712$	−1.97819e7	−	1.29699e7i	−0.0548060	−	0.0359332i
$713$	−7.96280e8			−2.19684
$714$	−2.23001e8	−	6.50723e8i	−0.612651	−	1.78773i
$715$		−	2.27848e7i		−	0.0623343i
$716$	4.15540e8	+	5.35076e8i	1.13207	+	1.45773i
$717$	2.10391e7			0.0570781
$718$	2.44824e8	−	8.39006e7i	0.661425	−	0.226669i
$719$			2.73670e8i			0.736276i	0.929771	+	0.368138i	$0.120005\pi$
$719$			2.73670e8i			0.736276i	−0.929771	+	0.368138i	$0.879995\pi$
$720$	1.37753e7	−	5.39084e7i	0.0369065	−	0.144430i
$721$	−3.96683e8			−1.05837
$722$	5.33044e7	+	1.55543e8i	0.141629	+	0.413276i
$723$			1.20695e8i			0.319356i
$724$	1.23801e8	−	9.61440e7i	0.326219	−	0.253342i
$725$	−3.92918e7			−0.103107
$726$	−2.04294e8	+	7.00111e7i	−0.533883	+	0.182960i
$727$			6.77998e8i			1.76451i	0.470768	+	0.882257i	$0.343977\pi$
$727$			6.77998e8i			1.76451i	−0.470768	+	0.882257i	$0.656023\pi$
$728$	−3.84659e8	+	5.86689e8i	−0.996969	+	1.52060i
$729$	−1.43489e7			−0.0370370
$730$	3.58919e7	+	1.04733e8i	0.0922630	+	0.269226i
$731$			8.63321e8i			2.21014i
$732$	8.11912e7	+	1.04547e8i	0.207003	+	0.266550i
$733$	4.75863e8			1.20829			0.604143	−	0.796876i	$-0.293516\pi$
$733$	4.75863e8			1.20829			0.604143	+	0.796876i	$0.293516\pi$
$734$	−4.41575e7	+	1.51327e7i	−0.111665	+	0.0382673i
$735$			2.89945e8i			0.730219i
$736$	−3.83034e7	−	4.77909e8i	−0.0960737	−	1.19870i
$737$	−6.49774e7			−0.162315
$738$	4.27685e7	+	1.24800e8i	0.106403	+	0.310487i
$739$		−	4.04862e8i		−	1.00317i	−0.865109	−	0.501584i	$-0.832751\pi$
$739$		−	4.04862e8i		−	1.00317i	0.865109	−	0.501584i	$-0.167249\pi$
$740$	−32879.9	+	25534.5i	−8.11400e−5	+	6.30134e-5i
$741$	−1.63820e8			−0.402636
$742$	−6.95382e6	+	2.38306e6i	−0.0170221	+	0.00583342i
$743$			3.57127e8i			0.870676i	0.900267	+	0.435338i	$0.143371\pi$
$743$			3.57127e8i			0.870676i	−0.900267	+	0.435338i	$0.856629\pi$
$744$	−3.63250e8	−	2.38163e8i	−0.882037	−	0.578302i
$745$	1.84759e8			0.446825
$746$	−4.23453e7	−	1.23565e8i	−0.101997	−	0.297631i
$747$			5.23339e7i			0.125551i
$748$	6.44089e7	+	8.29370e7i	0.153901	+	0.198173i
$749$	6.87066e8			1.63513
$750$	2.06089e7	−	7.06264e6i	0.0488508	−	0.0167411i
$751$			1.02196e8i			0.241275i	0.992697	+	0.120637i	$0.0384938\pi$
$751$			1.02196e8i			0.241275i	−0.992697	+	0.120637i	$0.961506\pi$
$752$	3.55817e8	+	9.09224e7i	0.836708	+	0.213805i
$753$	2.56820e8			0.601511
$754$	−6.65793e7	−	1.94280e8i	−0.155319	−	0.453225i
$755$			1.65664e8i			0.384936i
$756$	1.28498e8	−	9.97914e7i	0.297392	−	0.230955i
$757$	4.38046e8			1.00979			0.504896	−	0.863180i	$-0.331531\pi$
$757$	4.38046e8			1.00979			0.504896	+	0.863180i	$0.331531\pi$
$758$	4.91810e8	−	1.68542e8i	1.12925	−	0.386991i
$759$			4.55313e7i			0.104132i
$760$	−8.07755e7	+	1.23200e8i	−0.184009	+	0.280654i
$761$	1.40458e8			0.318708			0.159354	−	0.987222i	$-0.449059\pi$
$761$	1.40458e8			0.318708			0.159354	+	0.987222i	$0.449059\pi$
$762$	4.88525e7	+	1.42553e8i	0.110414	+	0.322189i
$763$			1.20043e9i			2.70249i
$764$	−2.12708e8	−	2.73896e8i	−0.476983	−	0.614194i
$765$	−1.11650e8			−0.249388
$766$	4.27191e8	−	1.46397e8i	0.950464	−	0.325722i
$767$		−	1.14375e7i		−	0.0253481i
$768$	1.25466e8	−	2.29470e8i	0.276976	−	0.506574i
$769$	2.32792e7			0.0511905			0.0255952	−	0.999672i	$-0.491852\pi$
$769$	2.32792e7			0.0511905			0.0255952	+	0.999672i	$0.491852\pi$
$770$	−1.94233e7	−	5.66776e7i	−0.0425452	−	0.124148i
$771$			2.15966e8i			0.471219i
$772$	−5.04004e8	+	3.91410e8i	−1.09542	+	0.850706i
$773$	1.98042e8			0.428763			0.214382	−	0.976750i	$-0.431226\pi$
$773$	1.98042e8			0.428763			0.214382	+	0.976750i	$0.431226\pi$
$774$	−1.93165e8	+	6.61971e7i	−0.416586	+	0.142763i
$775$		−	1.70071e8i		−	0.365364i
$776$	−3.42636e8	−	2.24647e8i	−0.733243	−	0.480746i
$777$	−121730.			−0.000259498
$778$	−2.24738e8	−	6.55791e8i	−0.477241	−	1.39260i
$779$		−	3.49296e8i		−	0.738893i
$780$	6.98431e7	+	8.99343e7i	0.147177	+	0.189514i
$781$	−6.05551e7			−0.127115
$782$	−9.10104e8	+	3.11891e8i	−1.90314	+	0.652202i
$783$			4.76279e7i			0.0992146i
$784$	−3.37408e8	+	1.32042e9i	−0.700176	+	2.74008i
$785$	−168280.			−0.000347876
$786$	−1.14631e7	−	3.34495e7i	−0.0236066	−	0.0688846i
$787$			8.67740e8i			1.78019i	0.455778	+	0.890093i	$0.349361\pi$
$787$			8.67740e8i			1.78019i	−0.455778	+	0.890093i	$0.650639\pi$
$788$	−6.74330e8	+	5.23685e8i	−1.37814	+	1.07027i
$789$	−1.19361e8			−0.243014
$790$	−1.64978e8	+	5.65377e7i	−0.334615	+	0.114672i
$791$		−	1.49537e9i		−	3.02148i
$792$	−1.36181e7	+	2.07706e7i	−0.0274121	+	0.0418094i
$793$	−2.70900e8			−0.543237
$794$	2.87994e8	+	8.40372e8i	0.575336	+	1.67884i
$795$			1.19313e6i			0.00237457i
$796$	2.58297e8	+	3.32600e8i	0.512130	+	0.659451i
$797$	−9.81006e8			−1.93775			−0.968873	−	0.247558i	$-0.920372\pi$
$797$	−9.81006e8			−1.93775			−0.968873	+	0.247558i	$0.920372\pi$
$798$	−4.07505e8	+	1.39651e8i	−0.801908	+	0.274812i
$799$		−	7.36938e8i		−	1.44474i
$800$	1.02073e8	−	8.18093e6i	0.199361	−	0.0159784i
$801$	−1.12267e7			−0.0218452
$802$	−1.45580e8	−	4.24807e8i	−0.282215	−	0.823509i
$803$		−	4.94201e7i		−	0.0954459i
$804$	2.56473e8	−	1.99177e8i	0.493485	−	0.383241i
$805$	5.48906e8			1.05223
$806$	8.40925e8	−	2.88183e8i	1.60602	−	0.550381i
$807$		−	5.65958e8i		−	1.07687i
$808$	−3.64163e8	−	2.38761e8i	−0.690338	−	0.452616i
$809$	1.28177e8			0.242084			0.121042	−	0.992647i	$-0.461376\pi$
$809$	1.28177e8			0.242084			0.121042	+	0.992647i	$0.461376\pi$
$810$	−8.56104e6	−	2.49813e7i	−0.0161091	−	0.0470067i
$811$			7.64793e8i			1.43378i	0.697189	+	0.716888i	$0.254434\pi$
$811$			7.64793e8i			1.43378i	−0.697189	+	0.716888i	$0.745566\pi$
$812$	−3.31234e8	−	4.26518e8i	−0.618681	−	0.796653i
$813$	2.24932e6			0.00418580
$814$	17579.5	−	6024.44i	3.25936e−5	−	1.11698e-5i
$815$		−	5.78365e7i		−	0.106839i
$816$	−5.08459e8	−	1.29927e8i	−0.935806	−	0.239128i
$817$	5.40641e8			0.991386
$818$	−1.34156e8	−	3.91471e8i	−0.245104	−	0.715220i
$819$			3.32960e8i			0.606095i
$820$	−1.91758e8	+	1.48919e8i	−0.347785	+	0.270090i
$821$	5.85652e8			1.05830			0.529152	−	0.848527i	$-0.322510\pi$
$821$	5.85652e8			1.05830			0.529152	+	0.848527i	$0.322510\pi$
$822$	4.89826e8	−	1.67862e8i	0.881914	−	0.302230i
$823$			2.85566e8i			0.512280i	0.966640	+	0.256140i	$0.0824508\pi$
$823$			2.85566e8i			0.512280i	−0.966640	+	0.256140i	$0.917549\pi$
$824$	−1.65938e8	+	2.53092e8i	−0.296595	+	0.452372i
$825$	−9.72466e6			−0.0173186
$826$	−9.75008e6	−	2.84510e7i	−0.0173009	−	0.0504844i
$827$			8.74738e7i			0.154654i	0.997006	+	0.0773271i	$0.0246386\pi$
$827$			8.74738e7i			0.154654i	−0.997006	+	0.0773271i	$0.975361\pi$
$828$	−1.39569e8	−	1.79717e8i	−0.245865	−	0.316591i
$829$	−6.72359e8			−1.18015			−0.590076	−	0.807348i	$-0.700902\pi$
$829$	−6.72359e8			−1.18015			−0.590076	+	0.807348i	$0.700902\pi$
$830$	−9.11128e7	+	3.12242e7i	−0.159348	+	0.0546080i
$831$			7.40027e7i			0.128957i
$832$	2.13412e8	+	4.90841e8i	0.370551	+	0.852257i
$833$	2.73474e9			4.73130
$834$	−1.55689e8	−	4.54303e8i	−0.268385	−	0.783155i
$835$			3.31910e7i			0.0570113i
$836$	5.19380e7	−	4.03351e7i	0.0888927	−	0.0690341i
$837$	−2.06153e8			−0.351572
$838$	−2.16184e8	+	7.40859e7i	−0.367360	+	0.125893i
$839$		−	1.71003e8i		−	0.289547i	−0.989465	−	0.144773i	$-0.953755\pi$
$839$		−	1.71003e8i		−	0.289547i	0.989465	−	0.144773i	$-0.0462453\pi$
$840$	2.50402e8	+	1.64174e8i	0.422474	+	0.276992i
$841$	−4.36734e8			−0.734224
$842$	−2.68029e7	−	7.82116e7i	−0.0449000	−	0.131019i
$843$			7.05612e7i			0.117783i
$844$	−3.41720e7	−	4.40021e7i	−0.0568386	−	0.0731890i
$845$	3.67909e7			0.0609775
$846$	1.64887e8	−	5.65064e7i	0.272317	−	0.0933225i
$847$		−	1.16215e9i		−	1.91255i
$848$	−1.38844e6	+	5.43355e6i	−0.00227688	+	0.00891037i
$849$	−1.67294e8			−0.273374
$850$	−6.66142e7	−	1.94382e8i	−0.108470	−	0.316519i
$851$			170252.i			0.000276251i
$852$	2.39018e8	−	1.85622e8i	0.386467	−	0.300130i
$853$	−4.85282e8			−0.781892			−0.390946	−	0.920414i	$-0.627852\pi$
$853$	−4.85282e8			−0.781892			−0.390946	+	0.920414i	$0.627852\pi$
$854$	−6.73867e8	+	2.30933e8i	−1.08193	+	0.370776i
$855$			6.99192e7i			0.111866i
$856$	2.87409e8	−	4.38362e8i	0.458226	−	0.698894i
$857$	−3.49086e8			−0.554612			−0.277306	−	0.960782i	$-0.589442\pi$
$857$	−3.49086e8			−0.554612			−0.277306	+	0.960782i	$0.589442\pi$
$858$	−1.64783e7	−	4.80841e7i	−0.0260886	−	0.0761271i
$859$		−	7.34854e8i		−	1.15937i	−0.814841	−	0.579684i	$-0.803176\pi$
$859$		−	7.34854e8i		−	1.15937i	0.814841	−	0.579684i	$-0.196824\pi$
$860$	−2.30497e8	−	2.96802e8i	−0.362385	−	0.466629i
$861$	−7.09936e8			−1.11227
$862$	2.83583e8	−	9.71833e7i	0.442750	−	0.151729i
$863$		−	8.76714e8i		−	1.36403i	−0.731336	−	0.682017i	$-0.761103\pi$
$863$		−	8.76714e8i		−	1.36403i	0.731336	−	0.682017i	$-0.238897\pi$
$864$	−9.91658e6	−	1.23728e8i	−0.0153752	−	0.191835i
$865$	−5.66416e7			−0.0875160
$866$	−2.00989e8	−	5.86490e8i	−0.309470	−	0.903040i
$867$			6.76809e8i			1.03851i
$868$	1.84615e9	−	1.43372e9i	2.82298	−	2.19233i
$869$	7.78477e7			0.118628
$870$	−8.29196e7	+	2.84164e7i	−0.125921	+	0.0431530i
$871$			6.64569e8i			1.00574i
$872$	7.65900e8	+	5.02158e8i	1.15511	+	0.757339i
$873$	−1.94454e8			−0.292264
$874$	1.95317e8	+	5.69938e8i	0.292553	+	0.853677i
$875$			1.17236e8i			0.175000i
$876$	1.51489e8	+	1.95067e8i	0.225356	+	0.290183i
$877$	4.38615e8			0.650256			0.325128	−	0.945670i	$-0.394593\pi$
$877$	4.38615e8			0.650256			0.325128	+	0.945670i	$0.394593\pi$
$878$	−8.09474e8	+	2.77405e8i	−1.19597	+	0.409856i
$879$			4.50264e8i			0.662980i
$880$	−4.42865e7	−	1.13166e7i	−0.0649865	−	0.0166061i
$881$	−9.05059e7			−0.132358			−0.0661788	−	0.997808i	$-0.521081\pi$
$881$	−9.05059e7			−0.132358			−0.0661788	+	0.997808i	$0.521081\pi$
$882$	2.09692e8	+	6.11887e8i	0.305616	+	0.891795i
$883$		−	8.35267e8i		−	1.21323i	−0.794995	−	0.606615i	$-0.792527\pi$
$883$		−	8.35267e8i		−	1.21323i	0.794995	−	0.606615i	$-0.207473\pi$
$884$	8.48254e8	−	6.58754e8i	1.22792	−	0.953601i
$885$	−4.88158e6			−0.00704256
$886$	5.24858e8	−	1.79868e8i	0.754641	−	0.258614i
$887$		−	9.00078e8i		−	1.28976i	−0.764283	−	0.644881i	$-0.776907\pi$
$887$		−	9.00078e8i		−	1.28976i	0.764283	−	0.644881i	$-0.223093\pi$
$888$	−50921.3	+	77666.2i	−7.27211e−5	+	0.000110916i
$889$	−8.10928e8			−1.15419
$890$	−6.69823e6	−	1.95456e7i	−0.00950145	−	0.0277255i
$891$			1.17878e7i			0.0166648i
$892$	−2.02652e8	−	2.60947e8i	−0.285532	−	0.367669i
$893$	−4.61495e8			−0.648057
$894$	3.89908e8	−	1.33621e8i	0.545695	−	0.187008i
$895$			5.91755e8i			0.825416i
$896$	9.49290e8	+	1.03905e9i	1.31970	+	1.44448i
$897$	4.65680e8			0.645223
$898$	−2.87502e8	−	8.38938e8i	−0.397020	−	1.15851i
$899$			6.84278e8i			0.941788i
$900$	3.83844e7	−	2.98094e7i	0.0526535	−	0.0408907i
$901$	1.12535e7			0.0153855
$902$	1.02525e8	−	3.51349e7i	0.139704	−	0.0478762i
$903$		−	1.09884e9i		−	1.49235i
$904$	−9.54079e8	−	6.25536e8i	−1.29145	−	0.846733i
$905$	1.36915e8			0.184716
$906$	1.19811e8	+	3.49611e8i	0.161106	+	0.470111i
$907$			5.63841e8i			0.755675i	0.925872	+	0.377838i	$0.123332\pi$
$907$			5.63841e8i			0.755675i	−0.925872	+	0.377838i	$0.876668\pi$
$908$	1.52677e8	+	1.96597e8i	0.203947	+	0.262614i
$909$	−2.06671e8			−0.275162
$910$	−5.79681e8	+	1.98655e8i	−0.769245	+	0.263618i
$911$		−	1.25733e9i		−	1.66301i	−0.555517	−	0.831505i	$-0.687480\pi$
$911$		−	1.25733e9i		−	1.66301i	0.555517	−	0.831505i	$-0.312520\pi$
$912$	−8.13648e7	+	3.18415e8i	−0.107264	+	0.419767i
$913$	4.29931e7			0.0564919
$914$	2.91012e8	+	8.49178e8i	0.381129	+	1.11214i
$915$			1.15621e8i			0.150930i
$916$	−5.08672e8	+	3.95035e8i	−0.661837	+	0.513983i
$917$	1.90281e8			0.246768
$918$	−2.35622e8	+	8.07470e7i	−0.304570	+	0.104375i
$919$			6.09120e8i			0.784796i	0.919796	+	0.392398i	$0.128354\pi$
$919$			6.09120e8i			0.784796i	−0.919796	+	0.392398i	$0.871646\pi$
$920$	2.29615e8	−	3.50213e8i	0.294874	−	0.449748i
$921$	7.10733e8			0.909762
$922$	3.75039e8	+	1.09437e9i	0.478502	+	1.39628i
$923$			6.19339e8i			0.787632i
$924$	−8.19801e7	−	1.05563e8i	−0.103918	−	0.133812i
$925$	−36362.8			−4.59443e−5
$926$	7.08557e8	−	2.42821e8i	0.892363	−	0.305811i
$927$			1.43636e8i			0.180311i
$928$	−4.10687e8	+	3.29158e7i	−0.513886	+	0.0411870i
$929$	1.98668e8			0.247788			0.123894	−	0.992295i	$-0.460462\pi$
$929$	1.98668e8			0.247788			0.123894	+	0.992295i	$0.460462\pi$
$930$	−1.22998e8	−	3.58911e8i	−0.152915	−	0.446208i
$931$		−	1.71259e9i		−	2.12228i
$932$	−3.05112e8	+	2.36951e8i	−0.376888	+	0.292691i
$933$	3.64184e8			0.448411
$934$	3.87400e8	−	1.32761e8i	0.475466	−	0.162941i
$935$			9.17223e7i			0.112212i
$936$	2.12436e8	+	1.39282e8i	0.259060	+	0.169851i
$937$	−1.36957e9			−1.66481			−0.832404	−	0.554169i	$-0.813036\pi$
$937$	−1.36957e9			−1.66481			−0.832404	+	0.554169i	$0.813036\pi$
$938$	5.66522e8	+	1.65312e9i	0.686449	+	2.00307i
$939$			4.33203e8i			0.523233i
$940$	1.96754e8	+	2.53353e8i	0.236886	+	0.305030i
$941$	−1.54960e9			−1.85974			−0.929869	−	0.367890i	$-0.880080\pi$
$941$	−1.54960e9			−1.85974			−0.929869	+	0.367890i	$0.880080\pi$
$942$	−355131.	+	121703.i	−0.000424851	+	0.000145595i
$943$			9.92920e8i			1.18408i
$944$	−2.22309e7	−	5.68068e6i	−0.0264266	−	0.00675281i
$945$	1.42109e8			0.168394
$946$	5.43819e7	+	1.58688e8i	0.0642363	+	0.187443i
$947$		−	1.24286e9i		−	1.46343i	−0.681613	−	0.731713i	$-0.738721\pi$
$947$		−	1.24286e9i		−	1.46343i	0.681613	−	0.731713i	$-0.261279\pi$
$948$	−3.07274e8	+	2.38629e8i	−0.360663	+	0.280091i
$949$	−5.05454e8			−0.591402
$950$	−1.21729e8	+	4.17161e7i	−0.141978	+	0.0486556i
$951$			1.19792e8i			0.139280i
$952$	1.54848e9	−	2.36177e9i	1.79471	−	2.73733i
$953$	1.19499e8			0.138066			0.0690331	−	0.997614i	$-0.478009\pi$
$953$	1.19499e8			0.138066			0.0690331	+	0.997614i	$0.478009\pi$
$954$	862887.	+	2.51792e6i	0.000993822	+	0.00290000i
$955$		−	3.02909e8i		−	0.347778i
$956$	5.29810e7	+	6.82216e7i	0.0606382	+	0.0780815i
$957$	3.91270e7			0.0446417
$958$	−1.42936e9	+	4.89840e8i	−1.62572	+	0.557131i
$959$			2.78643e9i			3.15931i
$960$	2.09493e8	−	9.10851e7i	0.236786	−	0.102952i
$961$	−2.07434e9			−2.33727
$962$	−61616.1	−	179797.i	−6.92101e−5	−	0.000201957i
$963$		−	2.48781e8i		−	0.278573i
$964$	−3.91368e8	+	3.03937e8i	−0.436872	+	0.339276i
$965$	−5.57391e8			−0.620266
$966$	1.15839e9	−	3.96976e8i	1.28506	−	0.440386i
$967$		−	5.80070e8i		−	0.641506i	−0.947163	−	0.320753i	$-0.896064\pi$
$967$		−	5.80070e8i		−	0.641506i	0.947163	−	0.320753i	$-0.103936\pi$
$968$	−7.41476e8	−	4.86144e8i	−0.817468	−	0.535968i
$969$	6.59472e8			0.724812
$970$	−1.16018e8	−	3.38543e8i	−0.127119	−	0.370936i
$971$			1.33064e9i			1.45346i	0.686925	+	0.726729i	$0.258960\pi$
$971$			1.33064e9i			1.45346i	−0.686925	+	0.726729i	$0.741040\pi$
$972$	−3.61337e7	−	4.65280e7i	−0.0393471	−	0.0506659i
$973$	2.58436e9			2.80552
$974$	1.07306e9	−	3.67737e8i	1.16131	−	0.397979i
$975$			9.94608e7i			0.107310i
$976$	−1.34548e8	+	5.26544e8i	−0.144720	+	0.566350i
$977$	−1.81751e9			−1.94891			−0.974456	−	0.224577i	$-0.927900\pi$
$977$	−1.81751e9			−1.94891			−0.974456	+	0.224577i	$0.927900\pi$
$978$	−4.18281e7	−	1.22056e8i	−0.0447149	−	0.130479i
$979$			9.22291e6i			0.00982923i
$980$	−9.40179e8	+	7.30144e8i	−0.998924	+	0.775765i
$981$	4.34667e8			0.460415
$982$	−1.30986e8	+	4.48887e7i	−0.138322	+	0.0474027i
$983$		−	9.05360e8i		−	0.953149i	−0.879134	−	0.476575i	$-0.841878\pi$
$983$		−	9.05360e8i		−	0.953149i	0.879134	−	0.476575i	$-0.158122\pi$
$984$	−2.96976e8	+	4.52954e8i	−0.311700	+	0.475411i
$985$	−7.45760e8			−0.780351
$986$	2.68021e8	+	7.82091e8i	0.279600	+	0.815881i
$987$			9.37978e8i			0.975532i
$988$	−4.12534e8	−	5.31205e8i	−0.427749	−	0.550797i
$989$	−1.53684e9			−1.58869
$990$	−2.05225e7	+	7.03301e6i	−0.0211507	+	0.00724830i
$991$			1.75428e6i			0.00180251i	1.00000		0.000901257i	$0.000286879\pi$
$991$			1.75428e6i			0.00180251i	−1.00000		0.000901257i	$0.999713\pi$
$992$	−1.42473e8	−	1.77763e9i	−0.145948	−	1.82098i
$993$	3.53266e8			0.360790
$994$	5.27965e8	+	1.54062e9i	0.537584	+	1.56868i
$995$			3.67831e8i			0.373404i
$996$	−1.69699e8	+	1.31788e8i	−0.171752	+	0.133382i
$997$	2.07639e8			0.209519			0.104759	−	0.994498i	$-0.466593\pi$
$997$	2.07639e8			0.209519			0.104759	+	0.994498i	$0.466593\pi$
$998$	1.79423e9	−	6.14880e8i	1.80504	−	0.618584i
$999$			44077.4i			4.42099e-5i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.c.a.31.14	yes	24
3.2	odd	2		180.7.c.b.91.11		24
4.3	odd	2	inner	60.7.c.a.31.13	✓	24
12.11	even	2		180.7.c.b.91.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.13	✓	24	4.3	odd	2	inner
60.7.c.a.31.14	yes	24	1.1	even	1	trivial
180.7.c.b.91.11		24	3.2	odd	2
180.7.c.b.91.12		24	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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.59351 + 7.56794i) q^{2} +15.5885i q^{3} +(-50.5474 + 39.2551i) q^{4} -55.9017 q^{5} +(-117.972 + 40.4289i) q^{6} -671.100i q^{7} +(-428.176 - 280.731i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(2.59351 + 7.56794i) q^{2} +15.5885i q^{3} +(-50.5474 + 39.2551i) q^{4} -55.9017 q^{5} +(-117.972 + 40.4289i) q^{6} -671.100i q^{7} +(-428.176 - 280.731i) q^{8} -243.000 q^{9} +(-144.982 - 423.061i) q^{10} +199.628i q^{11} +(-611.927 - 787.955i) q^{12} +2041.73 q^{13} +(5078.84 - 1740.51i) q^{14} -871.421i q^{15} +(1014.07 - 3968.49i) q^{16} -8219.18 q^{17} +(-630.224 - 1839.01i) q^{18} +5147.13i q^{19} +(2825.68 - 2194.43i) q^{20} +10461.4 q^{21} +(-1510.77 + 517.738i) q^{22} -14631.4i q^{23} +(4376.16 - 6674.60i) q^{24} +3125.00 q^{25} +(5295.27 + 15451.7i) q^{26} -3788.00i q^{27} +(26344.1 + 33922.3i) q^{28} -12573.4 q^{29} +(6594.86 - 2260.04i) q^{30} -54422.8i q^{31} +(32663.3 - 2617.90i) q^{32} -3111.89 q^{33} +(-21316.6 - 62202.2i) q^{34} +37515.6i q^{35} +(12283.0 - 9538.99i) q^{36} -11.6361 q^{37} +(-38953.1 + 13349.2i) q^{38} +31827.5i q^{39} +(23935.7 + 15693.3i) q^{40} -67862.4 q^{41} +(27131.8 + 79171.3i) q^{42} -105037. i q^{43} +(-7836.42 - 10090.7i) q^{44} +13584.1 q^{45} +(110729. - 37946.7i) q^{46} +89660.8i q^{47} +(61862.6 + 15807.8i) q^{48} -332726. q^{49} +(8104.73 + 23649.8i) q^{50} -128124. i q^{51} +(-103204. + 80148.5i) q^{52} -1369.17 q^{53} +(28667.3 - 9824.22i) q^{54} -11159.5i q^{55} +(-188398. + 287349. i) q^{56} -80235.8 q^{57} +(-32609.2 - 95154.5i) q^{58} -5601.86i q^{59} +(34207.7 + 44048.0i) q^{60} -132681. q^{61} +(411868. - 141146. i) q^{62} +163077. i q^{63} +(104525. + 240404. i) q^{64} -114136. q^{65} +(-8070.74 - 23550.6i) q^{66} +325492. i q^{67} +(415458. - 322645. i) q^{68} +228081. q^{69} +(-283916. + 97297.4i) q^{70} +303340. i q^{71} +(104047. + 68217.5i) q^{72} -247561. q^{73} +(-30.1783 - 88.0611i) q^{74} +48713.9i q^{75} +(-202051. - 260174. i) q^{76} +133970. q^{77} +(-240868. + 82545.0i) q^{78} -389964. i q^{79} +(-56688.3 + 221845. i) q^{80} +59049.0 q^{81} +(-176002. - 513578. i) q^{82} -215366. i q^{83} +(-528797. + 410664. i) q^{84} +459466. q^{85} +(794916. - 272416. i) q^{86} -195999. i q^{87} +(56041.7 - 85475.8i) q^{88} +46200.5 q^{89} +(35230.6 + 102804. i) q^{90} -1.37021e6i q^{91} +(574357. + 739578. i) q^{92} +848367. q^{93} +(-678547. + 232537. i) q^{94} -287733. i q^{95} +(40809.0 + 509170. i) q^{96} +800223. q^{97} +(-862931. - 2.51805e6i) q^{98} -48509.6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9}+O(q^{10}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9	\( 24 q + 20 q^{2} - 246 q^{4} + 162 q^{6} - 340 q^{8} - 5832 q^{9} - 750 q^{10} + 5040 q^{13} - 2596 q^{14} + 4194 q^{16} - 4860 q^{18} + 7000 q^{20} + 19440 q^{21} + 45780 q^{22} + 24786 q^{24} + 75000 q^{25} + 75852 q^{26} + 54300 q^{28} + 132800 q^{29} - 10700 q^{32} - 173484 q^{34} + 59778 q^{36} - 69840 q^{37} + 215800 q^{38} - 14250 q^{40} - 70448 q^{41} - 189540 q^{42} - 395668 q^{44} - 158760 q^{46} + 252720 q^{48} - 642984 q^{49} + 62500 q^{50} - 210240 q^{52} - 644320 q^{53} - 39366 q^{54} - 917708 q^{56} + 408240 q^{57} - 1345020 q^{58} + 222750 q^{60} - 222864 q^{61} + 1948520 q^{62} + 935922 q^{64} + 266000 q^{65} - 640548 q^{66} + 572680 q^{68} - 541728 q^{69} + 220500 q^{70} + 82620 q^{72} + 771120 q^{73} - 589164 q^{74} - 191544 q^{76} + 1383840 q^{77} - 693360 q^{78} - 946000 q^{80} + 1417176 q^{81} + 2672520 q^{82} + 1256796 q^{84} - 372000 q^{85} + 1781528 q^{86} + 956940 q^{88} - 1566224 q^{89} + 182250 q^{90} - 3040560 q^{92} + 1496880 q^{93} - 3788352 q^{94} - 413262 q^{96} - 1666800 q^{97} - 2709660 q^{98}+O(q^{100}) \) 24 * q + 20 * q^2 - 246 * q^4 + 162 * q^6 - 340 * q^8 - 5832 * q^9 - 750 * q^10 + 5040 * q^13 - 2596 * q^14 + 4194 * q^16 - 4860 * q^18 + 7000 * q^20 + 19440 * q^21 + 45780 * q^22 + 24786 * q^24 + 75000 * q^25 + 75852 * q^26 + 54300 * q^28 + 132800 * q^29 - 10700 * q^32 - 173484 * q^34 + 59778 * q^36 - 69840 * q^37 + 215800 * q^38 - 14250 * q^40 - 70448 * q^41 - 189540 * q^42 - 395668 * q^44 - 158760 * q^46 + 252720 * q^48 - 642984 * q^49 + 62500 * q^50 - 210240 * q^52 - 644320 * q^53 - 39366 * q^54 - 917708 * q^56 + 408240 * q^57 - 1345020 * q^58 + 222750 * q^60 - 222864 * q^61 + 1948520 * q^62 + 935922 * q^64 + 266000 * q^65 - 640548 * q^66 + 572680 * q^68 - 541728 * q^69 + 220500 * q^70 + 82620 * q^72 + 771120 * q^73 - 589164 * q^74 - 191544 * q^76 + 1383840 * q^77 - 693360 * q^78 - 946000 * q^80 + 1417176 * q^81 + 2672520 * q^82 + 1256796 * q^84 - 372000 * q^85 + 1781528 * q^86 + 956940 * q^88 - 1566224 * q^89 + 182250 * q^90 - 3040560 * q^92 + 1496880 * q^93 - 3788352 * q^94 - 413262 * q^96 - 1666800 * q^97 - 2709660 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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