LMFDB - Embedded newform 60.7.c.a.31.4

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			31.4
Character	$\chi$	$=$	60.31
Dual form			60.7.c.a.31.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.61106 + 4.50487i) q^{2} -15.5885i q^{3} +(23.4123 - 59.5639i) q^{4} -55.9017 q^{5} +(70.2239 + 103.056i) q^{6} +489.339i q^{7} +(113.547 + 499.250i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(-6.61106 + 4.50487i) q^{2} -15.5885i q^{3} +(23.4123 - 59.5639i) q^{4} -55.9017 q^{5} +(70.2239 + 103.056i) q^{6} +489.339i q^{7} +(113.547 + 499.250i) q^{8} -243.000 q^{9} +(369.570 - 251.830i) q^{10} -1671.97i q^{11} +(-928.510 - 364.962i) q^{12} -528.612 q^{13} +(-2204.41 - 3235.05i) q^{14} +871.421i q^{15} +(-2999.73 - 2789.06i) q^{16} +8236.70 q^{17} +(1606.49 - 1094.68i) q^{18} +3892.37i q^{19} +(-1308.79 + 3329.73i) q^{20} +7628.03 q^{21} +(7532.02 + 11053.5i) q^{22} -23107.8i q^{23} +(7782.54 - 1770.03i) q^{24} +3125.00 q^{25} +(3494.69 - 2381.33i) q^{26} +3788.00i q^{27} +(29146.9 + 11456.6i) q^{28} +43960.2 q^{29} +(-3925.64 - 5761.02i) q^{30} -18298.7i q^{31} +(32395.7 + 4925.29i) q^{32} -26063.5 q^{33} +(-54453.3 + 37105.2i) q^{34} -27354.9i q^{35} +(-5689.20 + 14474.0i) q^{36} +76080.2 q^{37} +(-17534.6 - 25732.7i) q^{38} +8240.25i q^{39} +(-6347.49 - 27908.9i) q^{40} -77333.8 q^{41} +(-50429.4 + 34363.3i) q^{42} -45051.5i q^{43} +(-99589.3 - 39144.8i) q^{44} +13584.1 q^{45} +(104098. + 152767. i) q^{46} -79645.0i q^{47} +(-43477.2 + 46761.1i) q^{48} -121803. q^{49} +(-20659.6 + 14077.7i) q^{50} -128397. i q^{51} +(-12376.0 + 31486.2i) q^{52} +46149.0 q^{53} +(-17064.4 - 25042.7i) q^{54} +93466.2i q^{55} +(-244302. + 55563.1i) q^{56} +60676.0 q^{57} +(-290623. + 198035. i) q^{58} -122143. i q^{59} +(51905.3 + 20402.0i) q^{60} +173832. q^{61} +(82433.2 + 120974. i) q^{62} -118909. i q^{63} +(-236358. + 113377. i) q^{64} +29550.3 q^{65} +(172307. - 117413. i) q^{66} +354754. i q^{67} +(192840. - 490610. i) q^{68} -360215. q^{69} +(123230. + 180845. i) q^{70} +37307.9i q^{71} +(-27592.0 - 121318. i) q^{72} +366139. q^{73} +(-502971. + 342731. i) q^{74} -48713.9i q^{75} +(231845. + 91129.4i) q^{76} +818161. q^{77} +(-37121.2 - 54476.8i) q^{78} -110073. i q^{79} +(167690. + 155913. i) q^{80} +59049.0 q^{81} +(511259. - 348379. i) q^{82} +353049. i q^{83} +(178590. - 454356. i) q^{84} -460445. q^{85} +(202951. + 297838. i) q^{86} -685271. i q^{87} +(834733. - 189848. i) q^{88} -965332. q^{89} +(-89805.4 + 61194.6i) q^{90} -258670. i q^{91} +(-1.37639e6 - 541008. i) q^{92} -285248. q^{93} +(358790. + 526538. i) q^{94} -217590. i q^{95} +(76777.6 - 504999. i) q^{96} -368862. q^{97} +(805249. - 548707. i) q^{98} +406290. i 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 $

$2$	−6.61106	+	4.50487i	−0.826383	+	0.563109i
$2$	−6.61106	+	4.50487i	−0.826383	+	0.563109i
$3$		−	15.5885i		−	0.577350i
$3$		−	15.5885i		−	0.577350i
$4$	23.4123	−	59.5639i	0.365818	−	0.930687i
$5$	−55.9017			−0.447214
$5$	−55.9017			−0.447214
$6$	70.2239	+	103.056i	0.325111	+	0.477112i
$7$			489.339i			1.42664i	0.700837	+	0.713321i	$0.252810\pi$
$7$			489.339i			1.42664i	−0.700837	+	0.713321i	$0.747190\pi$
$8$	113.547	+	499.250i	0.221772	+	0.975099i
$9$	−243.000			−0.333333
$10$	369.570	−	251.830i	0.369570	−	0.251830i
$11$		−	1671.97i		−	1.25618i	−0.778141	−	0.628089i	$-0.783837\pi$
$11$		−	1671.97i		−	1.25618i	0.778141	−	0.628089i	$-0.216163\pi$
$12$	−928.510	−	364.962i	−0.537332	−	0.211205i
$13$	−528.612			−0.240606			−0.120303	−	0.992737i	$-0.538387\pi$
$13$	−528.612			−0.240606			−0.120303	+	0.992737i	$0.538387\pi$
$14$	−2204.41	−	3235.05i	−0.803355	−	1.17895i
$15$			871.421i			0.258199i
$16$	−2999.73	−	2789.06i	−0.732355	−	0.680923i
$17$	8236.70			1.67651			0.838255	−	0.545278i	$-0.183576\pi$
$17$	8236.70			1.67651			0.838255	+	0.545278i	$0.183576\pi$
$18$	1606.49	−	1094.68i	0.275461	−	0.187703i
$19$			3892.37i			0.567483i	0.958901	+	0.283742i	$0.0915758\pi$
$19$			3892.37i			0.567483i	−0.958901	+	0.283742i	$0.908424\pi$
$20$	−1308.79	+	3329.73i	−0.163599	+	0.416216i
$21$	7628.03			0.823673
$22$	7532.02	+	11053.5i	0.707365	+	1.03808i
$23$		−	23107.8i		−	1.89922i	−0.313432	−	0.949611i	$-0.601479\pi$
$23$		−	23107.8i		−	1.89922i	0.313432	−	0.949611i	$-0.398521\pi$
$24$	7782.54	−	1770.03i	0.562973	−	0.128040i
$25$	3125.00			0.200000
$26$	3494.69	−	2381.33i	0.198833	−	0.135488i
$27$			3788.00i			0.192450i
$28$	29146.9	+	11456.6i	1.32776	+	0.521891i
$29$	43960.2			1.80246			0.901229	−	0.433343i	$-0.142666\pi$
$29$	43960.2			1.80246			0.901229	+	0.433343i	$0.142666\pi$
$30$	−3925.64	−	5761.02i	−0.145394	−	0.213371i
$31$		−	18298.7i		−	0.614236i	−0.951672	−	0.307118i	$-0.900635\pi$
$31$		−	18298.7i		−	0.614236i	0.951672	−	0.307118i	$-0.0993646\pi$
$32$	32395.7	+	4925.29i	0.988639	+	0.150308i
$33$	−26063.5			−0.725255
$34$	−54453.3	+	37105.2i	−1.38544	+	0.944058i
$35$		−	27354.9i		−	0.638014i
$36$	−5689.20	+	14474.0i	−0.121939	+	0.310229i
$37$	76080.2			1.50199			0.750994	−	0.660309i	$-0.229575\pi$
$37$	76080.2			1.50199			0.750994	+	0.660309i	$0.229575\pi$
$38$	−17534.6	−	25732.7i	−0.319555	−	0.468958i
$39$			8240.25i			0.138914i
$40$	−6347.49	−	27908.9i	−0.0991795	−	0.436077i
$41$	−77333.8			−1.12206			−0.561032	−	0.827794i	$-0.689596\pi$
$41$	−77333.8			−1.12206			−0.561032	+	0.827794i	$0.689596\pi$
$42$	−50429.4	+	34363.3i	−0.680669	+	0.463817i
$43$		−	45051.5i		−	0.566636i	−0.959026	−	0.283318i	$-0.908565\pi$
$43$		−	45051.5i		−	0.566636i	0.959026	−	0.283318i	$-0.0914352\pi$
$44$	−99589.3	−	39144.8i	−1.16911	−	0.459532i
$45$	13584.1			0.149071
$46$	104098.	+	152767.i	1.06947	+	1.56948i
$47$		−	79645.0i		−	0.767123i	−0.923515	−	0.383562i	$-0.874697\pi$
$47$		−	79645.0i		−	0.767123i	0.923515	−	0.383562i	$-0.125303\pi$
$48$	−43477.2	+	46761.1i	−0.393131	+	0.422825i
$49$	−121803.			−1.03531
$50$	−20659.6	+	14077.7i	−0.165277	+	0.112622i
$51$		−	128397.i		−	0.967934i
$52$	−12376.0	+	31486.2i	−0.0880181	+	0.223929i
$53$	46149.0			0.309980			0.154990	−	0.987916i	$-0.450465\pi$
$53$	46149.0			0.309980			0.154990	+	0.987916i	$0.450465\pi$
$54$	−17064.4	−	25042.7i	−0.108370	−	0.159037i
$55$			93466.2i			0.561780i
$56$	−244302.	+	55563.1i	−1.39112	+	0.316390i
$57$	60676.0			0.327637
$58$	−290623.	+	198035.i	−1.48952	+	1.01498i
$59$		−	122143.i		−	0.594718i	−0.954766	−	0.297359i	$-0.903894\pi$
$59$		−	122143.i		−	0.594718i	0.954766	−	0.297359i	$-0.0961058\pi$
$60$	51905.3	+	20402.0i	0.240302	+	0.0944537i
$61$	173832.			0.765843			0.382922	−	0.923781i	$-0.374918\pi$
$61$	173832.			0.765843			0.382922	+	0.923781i	$0.374918\pi$
$62$	82433.2	+	120974.i	0.345881	+	0.507594i
$63$		−	118909.i		−	0.475548i
$64$	−236358.	+	113377.i	−0.901634	+	0.432499i
$65$	29550.3			0.107602
$66$	172307.	−	117413.i	0.599338	−	0.408397i
$67$			354754.i			1.17951i	0.807581	+	0.589757i	$0.200776\pi$
$67$			354754.i			1.17951i	−0.807581	+	0.589757i	$0.799224\pi$
$68$	192840.	−	490610.i	0.613297	−	1.56031i
$69$	−360215.			−1.09652
$70$	123230.	+	180845.i	0.359271	+	0.527244i
$71$			37307.9i			0.104238i	0.998641	+	0.0521189i	$0.0165975\pi$
$71$			37307.9i			0.104238i	−0.998641	+	0.0521189i	$0.983403\pi$
$72$	−27592.0	−	121318.i	−0.0739240	−	0.325033i
$73$	366139.			0.941190			0.470595	−	0.882349i	$-0.344039\pi$
$73$	366139.			0.941190			0.470595	+	0.882349i	$0.344039\pi$
$74$	−502971.	+	342731.i	−1.24122	+	0.845782i
$75$		−	48713.9i		−	0.115470i
$76$	231845.	+	91129.4i	0.528149	+	0.207595i
$77$	818161.			1.79212
$78$	−37121.2	−	54476.8i	−0.0782238	−	0.114796i
$79$		−	110073.i		−	0.223253i	−0.993750	−	0.111627i	$-0.964394\pi$
$79$		−	110073.i		−	0.223253i	0.993750	−	0.111627i	$-0.0356061\pi$
$80$	167690.	+	155913.i	0.327519	+	0.304518i
$81$	59049.0			0.111111
$82$	511259.	−	348379.i	0.927255	−	0.631844i
$83$			353049.i			0.617449i	0.951151	+	0.308725i	$0.0999021\pi$
$83$			353049.i			0.617449i	−0.951151	+	0.308725i	$0.900098\pi$
$84$	178590.	−	454356.i	0.301314	−	0.766581i
$85$	−460445.			−0.749759
$86$	202951.	+	297838.i	0.319078	+	0.468258i
$87$		−	685271.i		−	1.04065i
$88$	834733.	−	189848.i	1.22490	−	0.278585i
$89$	−965332.			−1.36933			−0.684663	−	0.728860i	$-0.740050\pi$
$89$	−965332.			−1.36933			−0.684663	+	0.728860i	$0.740050\pi$
$90$	−89805.4	+	61194.6i	−0.123190	+	0.0839433i
$91$		−	258670.i		−	0.343259i
$92$	−1.37639e6	−	541008.i	−1.76758	−	0.694768i
$93$	−285248.			−0.354629
$94$	358790.	+	526538.i	0.431974	+	0.633938i
$95$		−	217590.i		−	0.253786i
$96$	76777.6	−	504999.i	0.0867803	−	0.570791i
$97$	−368862.			−0.404155			−0.202078	−	0.979370i	$-0.564769\pi$
$97$	−368862.			−0.404155			−0.202078	+	0.979370i	$0.564769\pi$
$98$	805249.	−	548707.i	0.855562	−	0.582992i
$99$			406290.i			0.418726i
$100$	73163.5	−	186137.i	0.0731635	−	0.186137i
$101$	270425.			0.262472			0.131236	−	0.991351i	$-0.458105\pi$
$101$	270425.			0.262472			0.131236	+	0.991351i	$0.458105\pi$
$102$	578413.	+	848844.i	0.545052	+	0.799884i
$103$			528514.i			0.483666i	0.970318	+	0.241833i	$0.0777485\pi$
$103$			528514.i			0.483666i	−0.970318	+	0.241833i	$0.922251\pi$
$104$	−60022.5	−	263910.i	−0.0533598	−	0.234615i
$105$	−426420.			−0.368358
$106$	−305094.	+	207895.i	−0.256163	+	0.174553i
$107$			1.09673e6i			0.895255i	0.894220	+	0.447628i	$0.147731\pi$
$107$			1.09673e6i			0.895255i	−0.894220	+	0.447628i	$0.852269\pi$
$108$	225628.	+	88685.8i	0.179111	+	0.0704016i
$109$	33665.5			0.0259959			0.0129980	−	0.999916i	$-0.495863\pi$
$109$	33665.5			0.0259959			0.0129980	+	0.999916i	$0.495863\pi$
$110$	−421053.	−	617911.i	−0.316343	−	0.464245i
$111$		−	1.18597e6i		−	0.867173i
$112$	1.36479e6	−	1.46788e6i	0.971434	−	1.04481i
$113$	2.26998e6			1.57321			0.786607	−	0.617455i	$-0.211836\pi$
$113$	2.26998e6			1.57321			0.786607	+	0.617455i	$0.211836\pi$
$114$	−401133.	+	273337.i	−0.270753	+	0.184495i
$115$			1.29177e6i			0.849357i
$116$	1.02921e6	−	2.61844e6i	0.659371	−	1.67752i
$117$	128453.			0.0802022
$118$	550236.	+	807492.i	0.334891	+	0.491465i
$119$			4.03053e6i			2.39178i
$120$	−435057.	+	98947.5i	−0.251769	+	0.0572613i
$121$	−1.02393e6			−0.577984
$122$	−1.14921e6	+	783090.i	−0.632880	+	0.431253i
$123$			1.20552e6i			0.647824i
$124$	−1.08994e6	−	428415.i	−0.571661	−	0.224698i
$125$	−174693.			−0.0894427
$126$	535671.	+	786117.i	0.267785	+	0.392984i
$127$		−	753363.i		−	0.367784i	−0.982946	−	0.183892i	$-0.941130\pi$
$127$		−	753363.i		−	0.367784i	0.982946	−	0.183892i	$-0.0588697\pi$
$128$	1.05183e6	−	1.81430e6i	0.501551	−	0.865128i
$129$	−702284.			−0.327147
$130$	−195359.	+	133120.i	−0.0889209	+	0.0605919i
$131$		−	1.18839e6i		−	0.528623i	−0.964437	−	0.264311i	$-0.914855\pi$
$131$		−	1.18839e6i		−	0.528623i	0.964437	−	0.264311i	$-0.0851447\pi$
$132$	−610207.	+	1.55244e6i	−0.265311	+	0.674985i
$133$	−1.90469e6			−0.809596
$134$	−1.59812e6	−	2.34530e6i	−0.664194	−	0.974730i
$135$		−	211755.i		−	0.0860663i
$136$	935255.	+	4.11218e6i	0.371803	+	1.63476i
$137$	−2.07235e6			−0.805938			−0.402969	−	0.915214i	$-0.632022\pi$
$137$	−2.07235e6			−0.805938			−0.402969	+	0.915214i	$0.632022\pi$
$138$	2.38141e6	−	1.62272e6i	0.906142	−	0.617457i
$139$		−	2.53703e6i		−	0.944673i	−0.881418	−	0.472336i	$-0.843411\pi$
$139$		−	2.53703e6i		−	0.944673i	0.881418	−	0.472336i	$-0.156589\pi$
$140$	−1.62936e6	−	640441.i	−0.593791	−	0.233397i
$141$	−1.24154e6			−0.442899
$142$	−168067.	−	246645.i	−0.0586972	−	0.0861404i
$143$			883826.i			0.302245i
$144$	728933.	+	677742.i	0.244118	+	0.226974i
$145$	−2.45745e6			−0.806084
$146$	−2.42057e6	+	1.64941e6i	−0.777783	+	0.529992i
$147$			1.89872e6i			0.597736i
$148$	1.78121e6	−	4.53163e6i	0.549453	−	1.39788i
$149$	2.04152e6			0.617156			0.308578	−	0.951199i	$-0.400147\pi$
$149$	2.04152e6			0.617156			0.308578	+	0.951199i	$0.400147\pi$
$150$	219450.	+	322051.i	0.0650222	+	0.0954225i
$151$			1.03197e6i			0.299735i	0.988706	+	0.149868i	$0.0478848\pi$
$151$			1.03197e6i			0.299735i	−0.988706	+	0.149868i	$0.952115\pi$
$152$	−1.94327e6	+	441968.i	−0.553352	+	0.125852i
$153$	−2.00152e6			−0.558837
$154$	−5.40891e6	+	3.68571e6i	−1.48098	+	1.00916i
$155$			1.02293e6i			0.274694i
$156$	490822.	+	192923.i	0.129286	+	0.0508173i
$157$	−1.65351e6			−0.427275			−0.213637	−	0.976913i	$-0.568531\pi$
$157$	−1.65351e6			−0.427275			−0.213637	+	0.976913i	$0.568531\pi$
$158$	495862.	+	727696.i	0.125716	+	0.184493i
$159$		−	719391.i		−	0.178967i
$160$	−1.81098e6	−	275332.i	−0.442133	−	0.0672197i
$161$	1.13075e7			2.70951
$162$	−390377.	+	266008.i	−0.0918203	+	0.0625676i
$163$		−	3.72806e6i		−	0.860836i	−0.902630	−	0.430418i	$-0.858366\pi$
$163$		−	3.72806e6i		−	0.860836i	0.902630	−	0.430418i	$-0.141634\pi$
$164$	−1.81056e6	+	4.60631e6i	−0.410471	+	1.04429i
$165$	1.45699e6			0.324344
$166$	−1.59044e6	−	2.33403e6i	−0.347691	−	0.510249i
$167$		−	5.98513e6i		−	1.28506i	−0.766259	−	0.642531i	$-0.777884\pi$
$167$		−	5.98513e6i		−	1.28506i	0.766259	−	0.642531i	$-0.222116\pi$
$168$	866143.	+	3.80830e6i	0.182668	+	0.803162i
$169$	−4.54738e6			−0.942109
$170$	3.04403e6	−	2.07425e6i	0.619588	−	0.422195i
$171$		−	945845.i		−	0.189161i
$172$	−2.68345e6	−	1.05476e6i	−0.527360	−	0.207285i
$173$	1.24240e6			0.239950			0.119975	−	0.992777i	$-0.461718\pi$
$173$	1.24240e6			0.239950			0.119975	+	0.992777i	$0.461718\pi$
$174$	3.08706e6	+	4.53037e6i	0.585999	+	0.859975i
$175$			1.52918e6i			0.285329i
$176$	−4.66324e6	+	5.01546e6i	−0.855361	+	0.919968i
$177$	−1.90401e6			−0.343361
$178$	6.38187e6	−	4.34869e6i	1.13159	−	0.771079i
$179$			4.24325e6i			0.739842i	0.929063	+	0.369921i	$0.120615\pi$
$179$			4.24325e6i			0.739842i	−0.929063	+	0.369921i	$0.879385\pi$
$180$	318036.	−	809123.i	0.0545329	−	0.138739i
$181$	7.51866e6			1.26796			0.633979	−	0.773350i	$-0.281421\pi$
$181$	7.51866e6			1.26796			0.633979	+	0.773350i	$0.281421\pi$
$182$	1.16528e6	+	1.71009e6i	0.193292	+	0.283664i
$183$		−	2.70977e6i		−	0.442160i
$184$	1.15366e7	−	2.62383e6i	1.85193	−	0.421194i
$185$	−4.25301e6			−0.671709
$186$	1.88580e6	−	1.28501e6i	0.293059	−	0.199695i
$187$		−	1.37715e7i		−	2.10600i
$188$	−4.74397e6	−	1.86468e6i	−0.713951	−	0.280627i
$189$	−1.85361e6			−0.274558
$190$	980214.	+	1.43850e6i	0.142909	+	0.209725i
$191$		−	6.32700e6i		−	0.908025i	−0.890995	−	0.454013i	$-0.849992\pi$
$191$		−	6.32700e6i		−	0.908025i	0.890995	−	0.454013i	$-0.150008\pi$
$192$	1.76737e6	+	3.68446e6i	0.249704	+	0.520559i
$193$	3.86775e6			0.538005			0.269002	−	0.963140i	$-0.413306\pi$
$193$	3.86775e6			0.538005			0.269002	+	0.963140i	$0.413306\pi$
$194$	2.43857e6	−	1.66167e6i	0.333987	−	0.227583i
$195$		−	460644.i		−	0.0621243i
$196$	−2.85170e6	+	7.25508e6i	−0.378735	+	0.963549i
$197$	1.29512e7			1.69399			0.846996	−	0.531600i	$-0.178409\pi$
$197$	1.29512e7			1.69399			0.846996	+	0.531600i	$0.178409\pi$
$198$	−1.83028e6	−	2.68601e6i	−0.235788	−	0.346028i
$199$		−	1.47597e7i		−	1.87291i	−0.350783	−	0.936457i	$-0.614085\pi$
$199$		−	1.47597e7i		−	1.87291i	0.350783	−	0.936457i	$-0.385915\pi$
$200$	354835.	+	1.56016e6i	0.0443544	+	0.195020i
$201$	5.53007e6			0.680992
$202$	−1.78780e6	+	1.21823e6i	−0.216902	+	0.147800i
$203$			2.15114e7i			2.57146i
$204$	−7.64786e6	−	3.00608e6i	−0.900843	−	0.354087i
$205$	4.32309e6			0.501803
$206$	−2.38089e6	−	3.49404e6i	−0.272356	−	0.399693i
$207$			5.61520e6i			0.633074i
$208$	1.58569e6	+	1.47433e6i	0.176209	+	0.163834i
$209$	6.50793e6			0.712860
$210$	2.81909e6	−	1.92097e6i	0.304404	−	0.207425i
$211$		−	4.46144e6i		−	0.474928i	−0.971396	−	0.237464i	$-0.923684\pi$
$211$		−	4.46144e6i		−	0.474928i	0.971396	−	0.237464i	$-0.0763161\pi$
$212$	1.08045e6	−	2.74881e6i	0.113396	−	0.288495i
$213$	581572.			0.0601818
$214$	−4.94061e6	−	7.25053e6i	−0.504126	−	0.739824i
$215$			2.51846e6i			0.253407i
$216$	−1.89116e6	+	430117.i	−0.187658	+	0.0426801i
$217$	8.95425e6			0.876295
$218$	−222565.	+	151659.i	−0.0214826	+	0.0146385i
$219$		−	5.70754e6i		−	0.543396i
$220$	5.56721e6	+	2.18826e6i	0.522841	+	0.205509i
$221$	−4.35402e6			−0.403379
$222$	5.34265e6	+	7.84054e6i	0.488312	+	0.716617i
$223$			1.76802e7i			1.59431i	0.603777	+	0.797153i	$0.293662\pi$
$223$			1.76802e7i			1.59431i	−0.603777	+	0.797153i	$0.706338\pi$
$224$	−2.41013e6	+	1.58525e7i	−0.214436	+	1.41044i
$225$	−759375.			−0.0666667
$226$	−1.50070e7	+	1.02260e7i	−1.30008	+	0.885890i
$227$			5.13872e6i			0.439316i	0.975577	+	0.219658i	$0.0704942\pi$
$227$			5.13872e6i			0.439316i	−0.975577	+	0.219658i	$0.929506\pi$
$228$	1.42057e6	−	3.61410e6i	0.119855	−	0.304927i
$229$	−1.04734e7			−0.872133			−0.436067	−	0.899914i	$-0.643629\pi$
$229$	−1.04734e7			−0.872133			−0.436067	+	0.899914i	$0.643629\pi$
$230$	−5.81924e6	−	8.53995e6i	−0.478280	−	0.701895i
$231$		−	1.27539e7i		−	1.03468i
$232$	4.99156e6	+	2.19471e7i	0.399735	+	1.75757i
$233$	−2.36952e7			−1.87324			−0.936619	−	0.350351i	$-0.886062\pi$
$233$	−2.36952e7			−1.87324			−0.936619	+	0.350351i	$0.886062\pi$
$234$	−849210.	+	578663.i	−0.0662777	+	0.0451625i
$235$			4.45229e6i			0.343068i
$236$	−7.27529e6	−	2.85964e6i	−0.553496	−	0.217558i
$237$	−1.71586e6			−0.128895
$238$	−1.81570e7	−	2.66461e7i	−1.34683	−	1.97653i
$239$		−	1.12351e7i		−	0.822971i	−0.911416	−	0.411486i	$-0.865010\pi$
$239$		−	1.12351e7i		−	0.822971i	0.911416	−	0.411486i	$-0.134990\pi$
$240$	2.43045e6	−	2.61402e6i	0.175814	−	0.189093i
$241$	−1.18227e7			−0.844632			−0.422316	−	0.906449i	$-0.638783\pi$
$241$	−1.18227e7			−0.844632			−0.422316	+	0.906449i	$0.638783\pi$
$242$	6.76929e6	−	4.61269e6i	0.477636	−	0.325468i
$243$		−	920483.i		−	0.0641500i
$244$	4.06981e6	−	1.03541e7i	0.280159	−	0.712760i
$245$	6.80900e6			0.463005
$246$	−5.43069e6	−	7.96974e6i	−0.364795	−	0.535351i
$247$		−	2.05755e6i		−	0.136540i
$248$	9.13563e6	−	2.07777e6i	0.598940	−	0.136220i
$249$	5.50349e6			0.356484
$250$	1.15491e6	−	786968.i	0.0739139	−	0.0503660i
$251$		−	1.35403e7i		−	0.856263i	−0.903716	−	0.428132i	$-0.859172\pi$
$251$		−	1.35403e7i		−	0.856263i	0.903716	−	0.428132i	$-0.140828\pi$
$252$	−7.08270e6	−	2.78394e6i	−0.442586	−	0.173964i
$253$	−3.86357e7			−2.38576
$254$	3.39380e6	+	4.98053e6i	0.207103	+	0.303931i
$255$			7.17763e6i			0.432873i
$256$	1.21950e6	+	1.67328e7i	0.0726876	+	0.997355i
$257$	−2.13424e7			−1.25731			−0.628657	−	0.777682i	$-0.716395\pi$
$257$	−2.13424e7			−1.25731			−0.628657	+	0.777682i	$0.716395\pi$
$258$	4.64284e6	−	3.16370e6i	0.270349	−	0.184219i
$259$			3.72290e7i			2.14280i
$260$	691842.	−	1.76013e6i	0.0393629	−	0.100144i
$261$	−1.06823e7			−0.600819
$262$	5.35355e6	+	7.85654e6i	0.297672	+	0.436845i
$263$			3.34374e6i			0.183808i	0.995768	+	0.0919042i	$0.0292954\pi$
$263$			3.34374e6i			0.183808i	−0.995768	+	0.0919042i	$0.970705\pi$
$264$	−2.95944e6	−	1.30122e7i	−0.160841	−	0.707195i
$265$	−2.57980e6			−0.138627
$266$	1.25920e7	−	8.58036e6i	0.669036	−	0.455890i
$267$			1.50480e7i			0.790580i
$268$	2.11305e7	+	8.30562e6i	1.09776	+	0.431487i
$269$	1.17373e7			0.602991			0.301496	−	0.953468i	$-0.402514\pi$
$269$	1.17373e7			0.602991			0.301496	+	0.953468i	$0.402514\pi$
$270$	953930.	+	1.39993e6i	0.0484647	+	0.0711237i
$271$			7.60965e6i			0.382346i	0.981556	+	0.191173i	$0.0612292\pi$
$271$			7.60965e6i			0.382346i	−0.981556	+	0.191173i	$0.938771\pi$
$272$	−2.47078e7	−	2.29727e7i	−1.22780	−	1.14157i
$273$	−4.03227e6			−0.198181
$274$	1.37005e7	−	9.33567e6i	0.666014	−	0.453831i
$275$		−	5.22492e6i		−	0.251236i
$276$	−8.43348e6	+	2.14558e7i	−0.401125	+	1.02051i
$277$	3.37880e7			1.58973			0.794864	−	0.606788i	$-0.207542\pi$
$277$	3.37880e7			1.58973			0.794864	+	0.606788i	$0.207542\pi$
$278$	1.14290e7	+	1.67725e7i	0.531953	+	0.780662i
$279$			4.44658e6i			0.204745i
$280$	1.36569e7	−	3.10607e6i	0.622127	−	0.141494i
$281$	3.45425e6			0.155681			0.0778404	−	0.996966i	$-0.475198\pi$
$281$	3.45425e6			0.155681			0.0778404	+	0.996966i	$0.475198\pi$
$282$	8.20792e6	−	5.59299e6i	0.366004	−	0.249400i
$283$			3.62562e7i			1.59964i	0.600238	+	0.799822i	$0.295073\pi$
$283$			3.62562e7i			1.59964i	−0.600238	+	0.799822i	$0.704927\pi$
$284$	2.22220e6	+	873464.i	0.0970128	+	0.0381320i
$285$	−3.39189e6			−0.146524
$286$	−3.98152e6	−	5.84303e6i	−0.170197	−	0.249770i
$287$		−	3.78424e7i		−	1.60079i
$288$	−7.87216e6	−	1.19685e6i	−0.329546	−	0.0501026i
$289$	4.37056e7			1.81069
$290$	1.62463e7	−	1.10705e7i	0.666134	−	0.453913i
$291$			5.74998e6i			0.233339i
$292$	8.57216e6	−	2.18087e7i	0.344304	−	0.875953i
$293$	−3.73544e7			−1.48504			−0.742521	−	0.669823i	$-0.766370\pi$
$293$	−3.73544e7			−1.48504			−0.742521	+	0.669823i	$0.766370\pi$
$294$	−8.55350e6	−	1.25526e7i	−0.336590	−	0.493959i
$295$			6.82798e6i			0.265966i
$296$	8.63870e6	+	3.79831e7i	0.333099	+	1.46459i
$297$	6.33343e6			0.241752
$298$	−1.34966e7	+	9.19678e6i	−0.510007	+	0.347526i
$299$			1.22151e7i			0.456965i
$300$	−2.90159e6	−	1.14051e6i	−0.107466	−	0.0422410i
$301$	2.20454e7			0.808387
$302$	−4.64891e6	−	6.82245e6i	−0.168784	−	0.247696i
$303$		−	4.21551e6i		−	0.151538i
$304$	1.08560e7	−	1.16760e7i	0.386412	−	0.415599i
$305$	−9.71750e6			−0.342496
$306$	1.32322e7	−	9.01657e6i	0.461813	−	0.314686i
$307$			3.42634e7i			1.18417i	0.805874	+	0.592087i	$0.201696\pi$
$307$			3.42634e7i			1.18417i	−0.805874	+	0.592087i	$0.798304\pi$
$308$	1.91551e7	−	4.87329e7i	0.655588	−	1.66790i
$309$	8.23872e6			0.279244
$310$	−4.60816e6	−	6.76264e6i	−0.154683	−	0.227003i
$311$		−	2.53880e7i		−	0.844008i	−0.906594	−	0.422004i	$-0.861327\pi$
$311$		−	2.53880e7i		−	0.844008i	0.906594	−	0.422004i	$-0.138673\pi$
$312$	−4.11395e6	+	935659.i	−0.135455	+	0.0308073i
$313$	1.21539e7			0.396354			0.198177	−	0.980166i	$-0.436498\pi$
$313$	1.21539e7			0.396354			0.198177	+	0.980166i	$0.436498\pi$
$314$	1.09314e7	−	7.44883e6i	0.353093	−	0.240602i
$315$			6.64723e6i			0.212671i
$316$	−6.55635e6	−	2.57705e6i	−0.207779	−	0.0816699i
$317$	−3.66896e7			−1.15177			−0.575884	−	0.817532i	$-0.695342\pi$
$317$	−3.66896e7			−1.15177			−0.575884	+	0.817532i	$0.695342\pi$
$318$	3.24076e6	+	4.75594e6i	0.100778	+	0.147896i
$319$		−	7.35002e7i		−	2.26421i
$320$	1.32128e7	−	6.33797e6i	0.403223	−	0.193420i
$321$	1.70963e7			0.516876
$322$	−7.47549e7	+	5.09390e7i	−2.23909	+	1.52575i
$323$			3.20603e7i			0.951392i
$324$	1.38247e6	−	3.51719e6i	0.0406464	−	0.103410i
$325$	−1.65191e6			−0.0481213
$326$	1.67944e7	+	2.46465e7i	0.484744	+	0.711380i
$327$		−	524793.i		−	0.0150088i
$328$	−8.78105e6	−	3.86090e7i	−0.248843	−	1.09412i
$329$	3.89734e7			1.09441
$330$	−9.63227e6	+	6.56356e6i	−0.268032	+	0.182641i
$331$			1.02423e7i			0.282432i	0.989979	+	0.141216i	$0.0451012\pi$
$331$			1.02423e7i			0.282432i	−0.989979	+	0.141216i	$0.954899\pi$
$332$	2.10290e7	+	8.26571e6i	0.574652	+	0.225874i
$333$	−1.84875e7			−0.500662
$334$	2.69622e7	+	3.95681e7i	0.723630	+	1.06195i
$335$		−	1.98314e7i		−	0.527494i
$336$	−2.28820e7	−	2.12750e7i	−0.603221	−	0.560858i
$337$	−1.49174e7			−0.389766			−0.194883	−	0.980826i	$-0.562433\pi$
$337$	−1.49174e7			−0.389766			−0.194883	+	0.980826i	$0.562433\pi$
$338$	3.00630e7	−	2.04853e7i	0.778542	−	0.530509i
$339$		−	3.53856e7i		−	0.908295i
$340$	−1.07801e7	+	2.74259e7i	−0.274275	+	0.697790i
$341$	−3.05949e7			−0.771589
$342$	4.26091e6	+	6.25304e6i	0.106518	+	0.156319i
$343$		−	2.03280e6i		−	0.0503746i
$344$	2.24920e7	−	5.11548e6i	0.552526	−	0.125664i
$345$	2.01366e7			0.490377
$346$	−8.21355e6	+	5.59683e6i	−0.198291	+	0.135118i
$347$		−	6.50530e7i		−	1.55697i	−0.627666	−	0.778483i	$-0.715990\pi$
$347$		−	6.50530e7i		−	1.55697i	0.627666	−	0.778483i	$-0.284010\pi$
$348$	−4.08174e7	−	1.60438e7i	−0.968519	−	0.380688i
$349$	−4.79094e7			−1.12705			−0.563527	−	0.826098i	$-0.690556\pi$
$349$	−4.79094e7			−1.12705			−0.563527	+	0.826098i	$0.690556\pi$
$350$	−6.88877e6	−	1.01095e7i	−0.160671	−	0.235791i
$351$		−	2.00238e6i		−	0.0463047i
$352$	8.23495e6	−	5.41648e7i	0.188813	−	1.24191i
$353$	2.86619e7			0.651599			0.325800	−	0.945439i	$-0.394367\pi$
$353$	2.86619e7			0.651599			0.325800	+	0.945439i	$0.394367\pi$
$354$	1.25876e7	−	8.57733e6i	0.283747	−	0.193349i
$355$		−	2.08557e6i		−	0.0466166i
$356$	−2.26007e7	+	5.74990e7i	−0.500923	+	1.27441i
$357$	6.28298e7			1.38090
$358$	−1.91153e7	−	2.80524e7i	−0.416611	−	0.611393i
$359$			6.83927e7i			1.47818i	0.673609	+	0.739088i	$0.264743\pi$
$359$			6.83927e7i			1.47818i	−0.673609	+	0.739088i	$0.735257\pi$
$360$	1.54244e6	+	6.78187e6i	0.0330598	+	0.145359i
$361$	3.18954e7			0.677963
$362$	−4.97063e7	+	3.38706e7i	−1.04782	+	0.713998i
$363$			1.59616e7i			0.333699i
$364$	−1.54074e7	−	6.05608e6i	−0.319467	−	0.125570i
$365$	−2.04678e7			−0.420913
$366$	1.22072e7	+	1.79145e7i	0.248984	+	0.365393i
$367$			4.76260e7i			0.963488i	0.876312	+	0.481744i	$0.159996\pi$
$367$			4.76260e7i			0.963488i	−0.876312	+	0.481744i	$0.840004\pi$
$368$	−6.44491e7	+	6.93171e7i	−1.29322	+	1.39090i
$369$	1.87921e7			0.374022
$370$	2.81169e7	−	1.91593e7i	0.555089	−	0.378245i
$371$			2.25825e7i			0.442231i
$372$	−6.67833e6	+	1.69905e7i	−0.129730	+	0.330048i
$373$	8.65965e7			1.66868			0.834341	−	0.551248i	$-0.185848\pi$
$373$	8.65965e7			1.66868			0.834341	+	0.551248i	$0.185848\pi$
$374$	6.20390e7	+	9.10445e7i	1.18590	+	1.74036i
$375$			2.72319e6i			0.0516398i
$376$	3.97628e7	−	9.04348e6i	0.748021	−	0.170127i
$377$	−2.32379e7			−0.433683
$378$	1.22543e7	−	8.35028e6i	0.226890	−	0.154606i
$379$		−	3.25539e7i		−	0.597979i	−0.954256	−	0.298989i	$-0.903350\pi$
$379$		−	3.25539e7i		−	0.597979i	0.954256	−	0.298989i	$-0.0966495\pi$
$380$	−1.29605e7	−	5.09429e6i	−0.236195	−	0.0928395i
$381$	−1.17438e7			−0.212340
$382$	2.85023e7	+	4.18282e7i	0.511317	+	0.750376i
$383$		−	5.20471e7i		−	0.926404i	−0.886253	−	0.463202i	$-0.846700\pi$
$383$		−	5.20471e7i		−	0.926404i	0.886253	−	0.463202i	$-0.153300\pi$
$384$	−2.82822e7	−	1.63964e7i	−0.499482	−	0.289571i
$385$	−4.57366e7			−0.801460
$386$	−2.55699e7	+	1.74237e7i	−0.444598	+	0.302955i
$387$			1.09475e7i			0.188879i
$388$	−8.63591e6	+	2.19709e7i	−0.147847	+	0.376142i
$389$	−3.96590e7			−0.673741			−0.336871	−	0.941551i	$-0.609368\pi$
$389$	−3.96590e7			−0.673741			−0.336871	+	0.941551i	$0.609368\pi$
$390$	2.07514e6	+	3.04535e6i	0.0349827	+	0.0513385i
$391$		−	1.90332e8i		−	3.18406i
$392$	−1.38304e7	−	6.08103e7i	−0.229603	−	1.00953i
$393$	−1.85252e7			−0.305201
$394$	−8.56212e7	+	5.83434e7i	−1.39989	+	0.953901i
$395$			6.15324e6i			0.0998419i
$396$	2.42002e7	+	9.51218e6i	0.389703	+	0.153177i
$397$	−3.49965e7			−0.559310			−0.279655	−	0.960101i	$-0.590220\pi$
$397$	−3.49965e7			−0.559310			−0.279655	+	0.960101i	$0.590220\pi$
$398$	6.64904e7	+	9.75772e7i	1.05465	+	1.54774i
$399$			2.96911e7i			0.467420i
$400$	−9.37414e6	−	8.71581e6i	−0.146471	−	0.136185i
$401$	−3.61187e7			−0.560143			−0.280072	−	0.959979i	$-0.590358\pi$
$401$	−3.61187e7			−0.560143			−0.280072	+	0.959979i	$0.590358\pi$
$402$	−3.65596e7	+	2.49122e7i	−0.562761	+	0.383473i
$403$			9.67291e6i			0.147789i
$404$	6.33128e6	−	1.61076e7i	0.0960168	−	0.244279i
$405$	−3.30094e6			−0.0496904
$406$	−9.69060e7	−	1.42213e8i	−1.44801	−	2.12501i
$407$		−	1.27204e8i		−	1.88676i
$408$	6.41025e7	−	1.45792e7i	0.943831	−	0.214661i
$409$	−1.44295e7			−0.210903			−0.105451	−	0.994424i	$-0.533629\pi$
$409$	−1.44295e7			−0.210903			−0.105451	+	0.994424i	$0.533629\pi$
$410$	−2.85802e7	+	1.94750e7i	−0.414681	+	0.282569i
$411$			3.23048e7i			0.465309i
$412$	3.14804e7	+	1.23738e7i	0.450141	+	0.176933i
$413$	5.97691e7			0.848450
$414$	−2.52957e7	−	3.71225e7i	−0.356489	−	0.523161i
$415$		−	1.97361e7i		−	0.276132i
$416$	−1.71248e7	−	2.60357e6i	−0.237873	−	0.0361650i
$417$	−3.95484e7			−0.545407
$418$	−4.30244e7	+	2.93174e7i	−0.589095	+	0.401418i
$419$			6.90024e7i			0.938041i	0.883187	+	0.469021i	$0.155393\pi$
$419$			6.90024e7i			0.938041i	−0.883187	+	0.469021i	$0.844607\pi$
$420$	−9.98348e6	+	2.53993e7i	−0.134752	+	0.342825i
$421$	6.10435e7			0.818075			0.409037	−	0.912518i	$-0.365865\pi$
$421$	6.10435e7			0.818075			0.409037	+	0.912518i	$0.365865\pi$
$422$	2.00982e7	+	2.94949e7i	0.267436	+	0.392472i
$423$			1.93537e7i			0.255708i
$424$	5.24009e6	+	2.30399e7i	0.0687450	+	0.302261i
$425$	2.57397e7			0.335302
$426$	−3.84481e6	+	2.61991e6i	−0.0497332	+	0.0338889i
$427$			8.50626e7i			1.09258i
$428$	6.53253e7	+	2.56769e7i	0.833202	+	0.327500i
$429$	1.37775e7			0.174501
$430$	−1.13453e7	−	1.66497e7i	−0.142696	−	0.209411i
$431$			1.07830e8i			1.34682i	0.739270	+	0.673409i	$0.235171\pi$
$431$			1.07830e8i			1.34682i	−0.739270	+	0.673409i	$0.764829\pi$
$432$	1.05649e7	−	1.13629e7i	0.131044	−	0.140942i
$433$	−9.10528e7			−1.12158			−0.560789	−	0.827958i	$-0.689502\pi$
$433$	−9.10528e7			−1.12158			−0.560789	+	0.827958i	$0.689502\pi$
$434$	−5.91971e7	+	4.03377e7i	−0.724155	+	0.493449i
$435$			3.83078e7i			0.465393i
$436$	788187.	−	2.00525e6i	0.00950977	−	0.0241941i
$437$	8.99441e7			1.07778
$438$	2.57117e7	+	3.77329e7i	0.305991	+	0.449053i
$439$		−	7.88744e7i		−	0.932272i	−0.884713	−	0.466136i	$-0.845646\pi$
$439$		−	7.88744e7i		−	0.932272i	0.884713	−	0.466136i	$-0.154354\pi$
$440$	−4.66630e7	+	1.06128e7i	−0.547791	+	0.124587i
$441$	2.95982e7			0.345103
$442$	2.87847e7	−	1.96143e7i	0.333346	−	0.227146i
$443$		−	6.25122e7i		−	0.719041i	−0.933137	−	0.359520i	$-0.882940\pi$
$443$		−	6.25122e7i		−	0.719041i	0.933137	−	0.359520i	$-0.117060\pi$
$444$	−7.06412e7	−	2.77664e7i	−0.807066	−	0.317227i
$445$	5.39637e7			0.612381
$446$	−7.96468e7	−	1.16885e8i	−0.897768	−	1.31751i
$447$		−	3.18241e7i		−	0.356315i
$448$	−5.54798e7	−	1.15659e8i	−0.617022	−	1.28631i
$449$	−1.83745e7			−0.202990			−0.101495	−	0.994836i	$-0.532363\pi$
$449$	−1.83745e7			−0.202990			−0.101495	+	0.994836i	$0.532363\pi$
$450$	5.02028e6	−	3.42088e6i	0.0550922	−	0.0375406i
$451$			1.29300e8i			1.40951i
$452$	5.31456e7	−	1.35209e8i	0.575509	−	1.46417i
$453$	1.60869e7			0.173052
$454$	−2.31492e7	−	3.39724e7i	−0.247383	−	0.363043i
$455$			1.44601e7i			0.153510i
$456$	6.88960e6	+	3.02925e7i	0.0726607	+	0.319478i
$457$	3.53983e7			0.370880			0.185440	−	0.982656i	$-0.440629\pi$
$457$	3.53983e7			0.370880			0.185440	+	0.982656i	$0.440629\pi$
$458$	6.92406e7	−	4.71815e7i	0.720716	−	0.491106i
$459$			3.12006e7i			0.322645i
$460$	7.69427e7	+	3.02433e7i	0.790486	+	0.310710i
$461$	1.10748e7			0.113040			0.0565199	−	0.998401i	$-0.482000\pi$
$461$	1.10748e7			0.113040			0.0565199	+	0.998401i	$0.482000\pi$
$462$	5.74545e7	+	8.43166e7i	0.582637	+	0.855042i
$463$		−	1.34336e8i		−	1.35347i	−0.736225	−	0.676737i	$-0.763394\pi$
$463$		−	1.34336e8i		−	1.35347i	0.736225	−	0.676737i	$-0.236606\pi$
$464$	−1.31868e8	−	1.22608e8i	−1.32004	−	1.22734i
$465$	1.59459e7			0.158595
$466$	1.56651e8	−	1.06744e8i	1.54801	−	1.05484i
$467$			9.60280e7i			0.942860i	0.881903	+	0.471430i	$0.156262\pi$
$467$			9.60280e7i			0.942860i	−0.881903	+	0.471430i	$0.843738\pi$
$468$	3.00738e6	−	7.65116e6i	0.0293394	−	0.0746431i
$469$	−1.73595e8			−1.68274
$470$	−2.00570e7	−	2.94344e7i	−0.193184	−	0.283505i
$471$			2.57756e7i			0.246687i
$472$	6.09797e7	−	1.38690e7i	0.579909	−	0.131892i
$473$	−7.53249e7			−0.711796
$474$	1.13437e7	−	7.72973e6i	0.106517	−	0.0725820i
$475$			1.21636e7i			0.113497i
$476$	2.40074e8	+	9.43642e7i	2.22600	+	0.874956i
$477$	−1.12142e7			−0.103327
$478$	5.06128e7	+	7.42762e7i	0.463422	+	0.680089i
$479$			1.53193e7i			0.139390i	0.997568	+	0.0696951i	$0.0222026\pi$
$479$			1.53193e7i			0.139390i	−0.997568	+	0.0696951i	$0.977797\pi$
$480$	−4.29200e6	+	2.82303e7i	−0.0388093	+	0.255266i
$481$	−4.02169e7			−0.361388
$482$	7.81609e7	−	5.32599e7i	0.697989	−	0.475619i
$483$		−	1.76267e8i		−	1.56434i
$484$	−2.39727e7	+	6.09896e7i	−0.211437	+	0.537922i
$485$	2.06200e7			0.180744
$486$	4.14665e6	+	6.08537e6i	0.0361234	+	0.0530125i
$487$			9.26753e7i			0.802375i	0.915996	+	0.401187i	$0.131402\pi$
$487$			9.26753e7i			0.802375i	−0.915996	+	0.401187i	$0.868598\pi$
$488$	1.97381e7	+	8.67856e7i	0.169843	+	0.746773i
$489$	−5.81148e7			−0.497004
$490$	−4.50148e7	+	3.06737e7i	−0.382619	+	0.260722i
$491$		−	4.66588e7i		−	0.394175i	−0.980386	−	0.197088i	$-0.936852\pi$
$491$		−	4.66588e7i		−	0.394175i	0.980386	−	0.197088i	$-0.0631483\pi$
$492$	7.18052e7	+	2.82239e7i	0.602922	+	0.236986i
$493$	3.62087e8			3.02184
$494$	9.26901e6	+	1.36026e7i	0.0768869	+	0.112834i
$495$		−	2.27123e7i		−	0.187260i
$496$	−5.10362e7	+	5.48911e7i	−0.418247	+	0.449838i
$497$	−1.82562e7			−0.148710
$498$	−3.63840e7	+	2.47925e7i	−0.294593	+	0.200739i
$499$			5.88986e7i			0.474027i	0.971506	+	0.237014i	$0.0761686\pi$
$499$			5.88986e7i			0.474027i	−0.971506	+	0.237014i	$0.923831\pi$
$500$	−4.08997e6	+	1.04054e7i	−0.0327197	+	0.0832431i
$501$	−9.32990e7			−0.741931
$502$	6.09973e7	+	8.95158e7i	0.482169	+	0.707601i
$503$			9.59290e7i			0.753782i	0.926258	+	0.376891i	$0.123007\pi$
$503$			9.59290e7i			0.753782i	−0.926258	+	0.376891i	$0.876993\pi$
$504$	5.93655e7	−	1.35018e7i	0.463706	−	0.105463i
$505$	−1.51172e7			−0.117381
$506$	2.55423e8	−	1.74049e8i	1.97155	−	1.34344i
$507$			7.08866e7i			0.543927i
$508$	−4.48733e7	−	1.76380e7i	−0.342292	−	0.134542i
$509$	4.35652e7			0.330359			0.165179	−	0.986264i	$-0.447180\pi$
$509$	4.35652e7			0.330359			0.165179	+	0.986264i	$0.447180\pi$
$510$	−3.23343e7	−	4.74518e7i	−0.243755	−	0.357719i
$511$			1.79166e8i			1.34274i
$512$	−8.34414e7	−	1.05128e8i	−0.621687	−	0.783266i
$513$	−1.47443e7			−0.109212
$514$	1.41096e8	−	9.61447e7i	1.03902	−	0.708005i
$515$		−	2.95449e7i		−	0.216302i
$516$	−1.64421e7	+	4.18308e7i	−0.119676	+	0.304472i
$517$	−1.33164e8			−0.963644
$518$	−1.67712e8	−	2.46123e8i	−1.20663	−	1.77077i
$519$		−	1.93670e7i		−	0.138535i
$520$	3.35536e6	+	1.47530e7i	0.0238632	+	0.104923i
$521$	1.99431e8			1.41020			0.705099	−	0.709108i	$-0.250902\pi$
$521$	1.99431e8			1.41020			0.705099	+	0.709108i	$0.250902\pi$
$522$	7.06215e7	−	4.81224e7i	0.496507	−	0.338327i
$523$			3.33251e7i			0.232952i	0.993194	+	0.116476i	$0.0371598\pi$
$523$			3.33251e7i			0.232952i	−0.993194	+	0.116476i	$0.962840\pi$
$524$	−7.07853e7	−	2.78230e7i	−0.491982	−	0.193380i
$525$	2.38376e7			0.164735
$526$	−1.50631e7	−	2.21057e7i	−0.103504	−	0.151896i
$527$		−	1.50721e8i		−	1.02977i
$528$	7.81833e7	+	7.26926e7i	0.531144	+	0.493843i
$529$	−3.85936e8			−2.60704
$530$	1.70553e7	−	1.16217e7i	0.114559	−	0.0780623i
$531$			2.96807e7i			0.198239i
$532$	−4.45931e7	+	1.13451e8i	−0.296164	+	0.753480i
$533$	4.08796e7			0.269976
$534$	−6.77894e7	−	9.94835e7i	−0.445183	−	0.653322i
$535$		−	6.13089e7i		−	0.400370i
$536$	−1.77111e8	+	4.02814e7i	−1.15014	+	0.261583i
$537$	6.61457e7			0.427148
$538$	−7.75960e7	+	5.28749e7i	−0.498302	+	0.339549i
$539$			2.03652e8i			1.30053i
$540$	−1.26130e7	−	4.95769e6i	−0.0801007	−	0.0314846i
$541$	−1.29602e8			−0.818500			−0.409250	−	0.912422i	$-0.634210\pi$
$541$	−1.29602e8			−0.818500			−0.409250	+	0.912422i	$0.634210\pi$
$542$	−3.42805e7	−	5.03079e7i	−0.215302	−	0.315964i
$543$		−	1.17204e8i		−	0.732056i
$544$	2.66834e8	+	4.05681e7i	1.65746	+	0.251993i
$545$	−1.88196e6			−0.0116257
$546$	2.66576e7	−	1.81649e7i	0.163773	−	0.111597i
$547$		−	9.98146e7i		−	0.609862i	−0.952374	−	0.304931i	$-0.901367\pi$
$547$		−	9.98146e7i		−	0.609862i	0.952374	−	0.304931i	$-0.0986335\pi$
$548$	−4.85186e7	+	1.23437e8i	−0.294826	+	0.750076i
$549$	−4.22411e7			−0.255281
$550$	2.35376e7	+	3.45423e7i	0.141473	+	0.207617i
$551$			1.71109e8i			1.02286i
$552$	−4.09015e7	−	1.79838e8i	−0.243177	−	1.06921i
$553$	5.38627e7			0.318503
$554$	−2.23374e8	+	1.52210e8i	−1.31372	+	0.895189i
$555$			6.62979e7i			0.387811i
$556$	−1.51116e8	−	5.93978e7i	−0.879194	−	0.345578i
$557$	−2.67691e8			−1.54906			−0.774529	−	0.632538i	$-0.782013\pi$
$557$	−2.67691e8			−1.54906			−0.774529	+	0.632538i	$0.782013\pi$
$558$	−2.00313e7	−	2.93966e7i	−0.115294	−	0.169198i
$559$			2.38148e7i			0.136336i
$560$	−7.62943e7	+	8.20571e7i	−0.434438	+	0.467253i
$561$	−2.14677e8			−1.21590
$562$	−2.28363e7	+	1.55610e7i	−0.128652	+	0.0876652i
$563$		−	1.44353e7i		−	0.0808912i	−0.999182	−	0.0404456i	$-0.987122\pi$
$563$		−	1.44353e7i		−	0.0808912i	0.999182	−	0.0404456i	$-0.0128777\pi$
$564$	−2.90674e7	+	7.39512e7i	−0.162020	+	0.412200i
$565$	−1.26896e8			−0.703562
$566$	−1.63329e8	−	2.39692e8i	−0.900773	−	1.32192i
$567$			2.88949e7i			0.158516i
$568$	−1.86260e7	+	4.23621e6i	−0.101642	+	0.0231171i
$569$	1.61516e8			0.876755			0.438378	−	0.898791i	$-0.355553\pi$
$569$	1.61516e8			0.876755			0.438378	+	0.898791i	$0.355553\pi$
$570$	2.24240e7	−	1.52800e7i	0.121085	−	0.0825086i
$571$			1.12052e8i			0.601882i	0.953643	+	0.300941i	$0.0973007\pi$
$571$			1.12052e8i			0.601882i	−0.953643	+	0.300941i	$0.902699\pi$
$572$	5.26442e7	+	2.06924e7i	0.281295	+	0.110566i
$573$	−9.86282e7			−0.524249
$574$	1.70475e8	+	2.50179e8i	0.901416	+	1.32286i
$575$		−	7.22119e7i		−	0.379844i
$576$	5.74350e7	−	2.75506e7i	0.300545	−	0.144166i
$577$	3.07042e8			1.59835			0.799173	−	0.601102i	$-0.205271\pi$
$577$	3.07042e8			1.59835			0.799173	+	0.601102i	$0.205271\pi$
$578$	−2.88941e8	+	1.96888e8i	−1.49632	+	1.01961i
$579$		−	6.02922e7i		−	0.310617i
$580$	−5.75346e7	+	1.46375e8i	−0.294880	+	0.750211i
$581$	−1.72761e8			−0.880879
$582$	−2.59029e7	−	3.80135e7i	−0.131395	−	0.192828i
$583$		−	7.71598e7i		−	0.389391i
$584$	4.15741e7	+	1.82795e8i	0.208730	+	0.917753i
$585$	−7.18073e6			−0.0358675
$586$	2.46952e8	−	1.68276e8i	1.22721	−	0.836239i
$587$			3.65313e8i			1.80614i	0.429498	+	0.903068i	$0.358691\pi$
$587$			3.65313e8i			1.80614i	−0.429498	+	0.903068i	$0.641309\pi$
$588$	1.13095e8	+	4.44535e7i	0.556305	+	0.218663i
$589$	7.12252e7			0.348568
$590$	−3.07591e7	−	4.51402e7i	−0.149768	−	0.219790i
$591$		−	2.01889e8i		−	0.978026i
$592$	−2.28220e8	−	2.12192e8i	−1.09999	−	1.02274i
$593$	2.24772e8			1.07790			0.538949	−	0.842338i	$-0.318821\pi$
$593$	2.24772e8			1.07790			0.538949	+	0.842338i	$0.318821\pi$
$594$	−4.18707e7	+	2.85313e7i	−0.199779	+	0.136132i
$595$		−	2.25314e8i		−	1.06964i
$596$	4.77967e7	−	1.21601e8i	0.225766	−	0.574379i
$597$	−2.30081e8			−1.08133
$598$	−5.50273e7	−	8.07547e7i	−0.257321	−	0.377628i
$599$		−	1.94995e8i		−	0.907284i	−0.891184	−	0.453642i	$-0.850125\pi$
$599$		−	1.94995e8i		−	0.907284i	0.891184	−	0.453642i	$-0.149875\pi$
$600$	2.43205e7	−	5.53134e6i	0.112595	−	0.0256080i
$601$	6.04496e7			0.278465			0.139232	−	0.990260i	$-0.455537\pi$
$601$	6.04496e7			0.278465			0.139232	+	0.990260i	$0.455537\pi$
$602$	−1.45744e8	+	9.93118e7i	−0.668037	+	0.455210i
$603$		−	8.62052e7i		−	0.393171i
$604$	6.14684e7	+	2.41609e7i	0.278960	+	0.109648i
$605$	5.72397e7			0.258482
$606$	1.89903e7	+	2.78690e7i	0.0853324	+	0.125229i
$607$			2.42035e8i			1.08221i	0.840954	+	0.541107i	$0.181995\pi$
$607$			2.42035e8i			1.08221i	−0.840954	+	0.541107i	$0.818005\pi$
$608$	−1.91710e7	+	1.26096e8i	−0.0852972	+	0.561036i
$609$	3.35330e8			1.48464
$610$	6.42430e7	−	4.37760e7i	0.283032	−	0.192862i
$611$			4.21014e7i			0.184575i
$612$	−4.68602e7	+	1.19218e8i	−0.204432	+	0.520102i
$613$	1.06610e8			0.462826			0.231413	−	0.972856i	$-0.425665\pi$
$613$	1.06610e8			0.462826			0.231413	+	0.972856i	$0.425665\pi$
$614$	−1.54352e8	−	2.26518e8i	−0.666818	−	0.978581i
$615$		−	6.73903e7i		−	0.289716i
$616$	9.29000e7	+	4.08467e8i	0.397442	+	1.74749i
$617$	1.94002e8			0.825945			0.412972	−	0.910744i	$-0.364491\pi$
$617$	1.94002e8			0.825945			0.412972	+	0.910744i	$0.364491\pi$
$618$	−5.44667e7	+	3.71144e7i	−0.230763	+	0.157245i
$619$		−	2.34375e8i		−	0.988188i	−0.869409	−	0.494094i	$-0.835500\pi$
$619$		−	2.34375e8i		−	0.988188i	0.869409	−	0.494094i	$-0.164500\pi$
$620$	6.09296e7	+	2.39491e7i	0.255654	+	0.100488i
$621$	8.75323e7			0.365505
$622$	1.14369e8	+	1.67841e8i	0.475268	+	0.697474i
$623$		−	4.72374e8i		−	1.95354i
$624$	2.29826e7	−	2.47185e7i	0.0945899	−	0.101735i
$625$	9.76562e6			0.0400000
$626$	−8.03504e7	+	5.47518e7i	−0.327540	+	0.223190i
$627$		−	1.01449e8i		−	0.411570i
$628$	−3.87125e7	+	9.84894e7i	−0.156305	+	0.397659i
$629$	6.26649e8			2.51810
$630$	−2.99449e7	−	4.39453e7i	−0.119757	−	0.175748i
$631$			9.78994e6i			0.0389665i	0.999810	+	0.0194833i	$0.00620211\pi$
$631$			9.78994e6i			0.0389665i	−0.999810	+	0.0194833i	$0.993798\pi$
$632$	5.49538e7	−	1.24984e7i	0.217694	−	0.0495113i
$633$	−6.95470e7			−0.274200
$634$	2.42557e8	−	1.65282e8i	0.951801	−	0.648570i
$635$			4.21143e7i			0.164478i
$636$	−4.28498e7	−	1.68426e7i	−0.166562	−	0.0654694i
$637$	6.43867e7			0.249102
$638$	3.31109e8	+	4.85915e8i	1.27500	+	1.87110i
$639$		−	9.06582e6i		−	0.0347460i
$640$	−5.87990e7	+	1.01423e8i	−0.224300	+	0.386897i
$641$	−2.62400e8			−0.996297			−0.498149	−	0.867092i	$-0.665987\pi$
$641$	−2.62400e8			−0.996297			−0.498149	+	0.867092i	$0.665987\pi$
$642$	−1.13025e8	+	7.70165e7i	−0.427138	+	0.291057i
$643$			2.58694e8i			0.973090i	0.873655	+	0.486545i	$0.161743\pi$
$643$			2.58694e8i			0.973090i	−0.873655	+	0.486545i	$0.838257\pi$
$644$	2.64736e8	−	6.73522e8i	0.991186	−	2.52170i
$645$	3.92589e7			0.146305
$646$	−1.44427e8	−	2.11952e8i	−0.535737	−	0.786214i
$647$			1.56584e8i			0.578141i	0.957308	+	0.289070i	$0.0933462\pi$
$647$			1.56584e8i			0.578141i	−0.957308	+	0.289070i	$0.906654\pi$
$648$	6.70486e6	+	2.94802e7i	0.0246413	+	0.108344i
$649$	−2.04219e8			−0.747072
$650$	1.09209e7	−	7.44165e6i	0.0397666	−	0.0270975i
$651$		−	1.39583e8i		−	0.505929i
$652$	−2.22058e8	−	8.72826e7i	−0.801169	−	0.314909i
$653$	−2.72428e7			−0.0978391			−0.0489195	−	0.998803i	$-0.515578\pi$
$653$	−2.72428e7			−0.0978391			−0.0489195	+	0.998803i	$0.515578\pi$
$654$	2.36412e6	+	3.46944e6i	0.00845156	+	0.0124030i
$655$			6.64332e7i			0.236407i
$656$	2.31980e8	+	2.15689e8i	0.821750	+	0.764040i
$657$	−8.89718e7			−0.313730
$658$	−2.57656e8	+	1.75570e8i	−0.904402	+	0.616272i
$659$			2.14808e8i			0.750575i	0.926909	+	0.375287i	$0.122456\pi$
$659$			2.14808e8i			0.750575i	−0.926909	+	0.375287i	$0.877544\pi$
$660$	3.41116e7	−	8.67843e7i	0.118651	−	0.301862i
$661$	1.02802e8			0.355958			0.177979	−	0.984034i	$-0.443044\pi$
$661$	1.02802e8			0.355958			0.177979	+	0.984034i	$0.443044\pi$
$662$	−4.61403e7	−	6.77126e7i	−0.159040	−	0.233397i
$663$			6.78725e7i			0.232891i
$664$	−1.76260e8	+	4.00878e7i	−0.602074	+	0.136933i
$665$	1.06475e8			0.362062
$666$	1.22222e8	−	8.32837e7i	0.413739	−	0.281927i
$667$		−	1.01582e9i		−	3.42327i
$668$	−3.56498e8	−	1.40126e8i	−1.19599	−	0.470099i
$669$	2.75607e8			0.920473
$670$	8.93376e7	+	1.31106e8i	0.297037	+	0.435912i
$671$		−	2.90642e8i		−	0.962036i
$672$	2.47116e8	+	3.75703e7i	0.814315	+	0.123804i
$673$	2.06604e8			0.677786			0.338893	−	0.940825i	$-0.389948\pi$
$673$	2.06604e8			0.677786			0.338893	+	0.940825i	$0.389948\pi$
$674$	9.86201e7	−	6.72011e7i	0.322096	−	0.219481i
$675$			1.18375e7i			0.0384900i
$676$	−1.06465e8	+	2.70860e8i	−0.344640	+	0.876808i
$677$	−4.17968e7			−0.134703			−0.0673515	−	0.997729i	$-0.521455\pi$
$677$	−4.17968e7			−0.134703			−0.0673515	+	0.997729i	$0.521455\pi$
$678$	1.59407e8	+	2.33936e8i	0.511469	+	0.750600i
$679$		−	1.80498e8i		−	0.576585i
$680$	−5.22823e7	−	2.29878e8i	−0.166276	−	0.731088i
$681$	8.01047e7			0.253639
$682$	2.02265e8	−	1.37826e8i	0.637628	−	0.434489i
$683$		−	3.82961e8i		−	1.20197i	−0.799261	−	0.600983i	$-0.794776\pi$
$683$		−	3.82961e8i		−	1.20197i	0.799261	−	0.600983i	$-0.205224\pi$
$684$	−5.63383e7	−	2.21444e7i	−0.176050	−	0.0691984i
$685$	1.15848e8			0.360427
$686$	9.15748e6	+	1.34389e7i	0.0283664	+	0.0416287i
$687$			1.63265e8i			0.503526i
$688$	−1.25651e8	+	1.35142e8i	−0.385835	+	0.414979i
$689$	−2.43949e7			−0.0745833
$690$	−1.33125e8	+	9.07129e7i	−0.405239	+	0.276135i
$691$			3.85201e8i			1.16749i	0.811937	+	0.583744i	$0.198413\pi$
$691$			3.85201e8i			1.16749i	−0.811937	+	0.583744i	$0.801587\pi$
$692$	2.90874e7	−	7.40020e7i	0.0877781	−	0.223319i
$693$	−1.98813e8			−0.597373
$694$	2.93055e8	+	4.30070e8i	0.876740	+	1.28665i
$695$			1.41824e8i			0.422471i
$696$	3.42122e8	−	7.78107e7i	1.01474	−	0.230787i
$697$	−6.36975e8			−1.88115
$698$	3.16732e8	−	2.15826e8i	0.931378	−	0.634654i
$699$			3.69372e8i			1.08151i
$700$	9.10842e7	+	3.58017e7i	0.265551	+	0.104378i
$701$	−4.74929e8			−1.37872			−0.689358	−	0.724420i	$-0.742107\pi$
$701$	−4.74929e8			−1.37872			−0.689358	+	0.724420i	$0.742107\pi$
$702$	9.02046e6	+	1.32379e7i	0.0260746	+	0.0382654i
$703$			2.96132e8i			0.852353i
$704$	1.89564e8	+	3.95184e8i	0.543296	+	1.13261i
$705$	6.94044e7			0.198070
$706$	−1.89485e8	+	1.29118e8i	−0.538470	+	0.366921i
$707$			1.32329e8i			0.374453i
$708$	−4.45774e7	+	1.13411e8i	−0.125607	+	0.319561i
$709$	6.32167e8			1.77375			0.886877	−	0.462006i	$-0.152870\pi$
$709$	6.32167e8			1.77375			0.886877	+	0.462006i	$0.152870\pi$
$710$	9.39524e6	+	1.37879e7i	0.0262502	+	0.0385232i
$711$			2.67476e7i			0.0744177i
$712$	−1.09611e8	−	4.81942e8i	−0.303678	−	1.33523i
$713$	−4.22843e8			−1.16657
$714$	−4.15372e8	+	2.83040e8i	−1.14115	+	0.777594i
$715$		−	4.94074e7i		−	0.135168i
$716$	2.52744e8	+	9.93443e7i	0.688561	+	0.270647i
$717$	−1.75138e8			−0.475143
$718$	−3.08100e8	−	4.52148e8i	−0.832374	−	1.22154i
$719$		−	6.43480e7i		−	0.173120i	−0.996247	−	0.0865602i	$-0.972413\pi$
$719$		−	6.43480e7i		−	0.173120i	0.996247	−	0.0865602i	$-0.0275875\pi$
$720$	−4.07486e7	−	3.78869e7i	−0.109173	−	0.101506i
$721$	−2.58622e8			−0.690018
$722$	−2.10862e8	+	1.43684e8i	−0.560257	+	0.381767i
$723$			1.84298e8i			0.487648i
$724$	1.76029e8	−	4.47841e8i	0.463841	−	1.18007i
$725$	1.37375e8			0.360492
$726$	−7.19047e7	−	1.05523e8i	−0.187909	−	0.275763i
$727$			2.63761e8i			0.686448i	0.939254	+	0.343224i	$0.111519\pi$
$727$			2.63761e8i			0.686448i	−0.939254	+	0.343224i	$0.888481\pi$
$728$	1.29141e8	−	2.93713e7i	0.334712	−	0.0761254i
$729$	−1.43489e7			−0.0370370
$730$	1.35314e8	−	9.22047e7i	0.347835	−	0.237020i
$731$		−	3.71076e8i		−	0.949971i
$732$	−1.61405e8	−	6.34420e7i	−0.411512	−	0.161750i
$733$	−7.94382e7			−0.201705			−0.100853	−	0.994901i	$-0.532157\pi$
$733$	−7.94382e7			−0.201705			−0.100853	+	0.994901i	$0.532157\pi$
$734$	−2.14549e8	−	3.14859e8i	−0.542548	−	0.796210i
$735$		−	1.06142e8i		−	0.267316i
$736$	1.13813e8	−	7.48595e8i	0.285468	−	1.87764i
$737$	5.93139e8			1.48168
$738$	−1.24236e8	+	8.46560e7i	−0.309085	+	0.210615i
$739$		−	3.58605e8i		−	0.888552i	−0.895890	−	0.444276i	$-0.853461\pi$
$739$		−	3.58605e8i		−	0.888552i	0.895890	−	0.444276i	$-0.146539\pi$
$740$	−9.95729e7	+	2.53326e8i	−0.245723	+	0.625151i
$741$	−3.20741e7			−0.0788315
$742$	−1.01731e8	−	1.49294e8i	−0.249024	−	0.365452i
$743$			4.60265e8i			1.12213i	0.827773	+	0.561063i	$0.189607\pi$
$743$			4.60265e8i			1.12213i	−0.827773	+	0.561063i	$0.810393\pi$
$744$	−3.23892e7	−	1.42410e8i	−0.0786468	−	0.345798i
$745$	−1.14124e8			−0.276000
$746$	−5.72495e8	+	3.90106e8i	−1.37897	+	0.939650i
$747$		−	8.57910e7i		−	0.205816i
$748$	−8.20287e8	−	3.22424e8i	−1.96002	−	0.770411i
$749$	−5.36670e8			−1.27721
$750$	−1.22676e7	−	1.80032e7i	−0.0290788	−	0.0426742i
$751$			4.03140e8i			0.951779i	0.879505	+	0.475889i	$0.157874\pi$
$751$			4.03140e8i			0.951779i	−0.879505	+	0.475889i	$0.842126\pi$
$752$	−2.22135e8	+	2.38913e8i	−0.522352	+	0.561807i
$753$	−2.11072e8			−0.494364
$754$	1.53627e8	−	1.04684e8i	0.358388	−	0.244211i
$755$		−	5.76891e7i		−	0.134046i
$756$	−4.33974e7	+	1.10408e8i	−0.100438	+	0.255527i
$757$	3.68817e8			0.850204			0.425102	−	0.905145i	$-0.360238\pi$
$757$	3.68817e8			0.850204			0.425102	+	0.905145i	$0.360238\pi$
$758$	1.46651e8	+	2.15216e8i	0.336727	+	0.494160i
$759$			6.02270e8i			1.37742i
$760$	1.08632e8	−	2.47068e7i	0.247467	−	0.0562827i
$761$	4.74390e8			1.07642			0.538210	−	0.842811i	$-0.319101\pi$
$761$	4.74390e8			1.07642			0.538210	+	0.842811i	$0.319101\pi$
$762$	7.76388e7	−	5.29042e7i	0.175475	−	0.119571i
$763$			1.64738e7i			0.0370869i
$764$	−3.76861e8	−	1.48130e8i	−0.845087	−	0.332172i
$765$	1.11888e8			0.249920
$766$	2.34465e8	+	3.44087e8i	0.521666	+	0.765564i
$767$			6.45661e7i			0.143093i
$768$	2.60839e8	−	1.90101e7i	0.575823	−	0.0419662i
$769$	−7.61175e8			−1.67381			−0.836904	−	0.547349i	$-0.815637\pi$
$769$	−7.61175e8			−1.67381			−0.836904	+	0.547349i	$0.815637\pi$
$770$	3.02368e8	−	2.06037e8i	0.662312	−	0.451309i
$771$			3.32695e8i			0.725911i
$772$	9.05530e7	−	2.30378e8i	0.196812	−	0.500714i
$773$	−4.57650e8			−0.990820			−0.495410	−	0.868659i	$-0.664982\pi$
$773$	−4.57650e8			−0.990820			−0.495410	+	0.868659i	$0.664982\pi$
$774$	−4.93171e7	−	7.23747e7i	−0.106359	−	0.156086i
$775$		−	5.71834e7i		−	0.122847i
$776$	−4.18832e7	−	1.84154e8i	−0.0896304	−	0.394091i
$777$	5.80342e8			1.23715
$778$	2.62188e8	−	1.78659e8i	0.556768	−	0.379389i
$779$		−	3.01012e8i		−	0.636753i
$780$	−2.74378e7	−	1.07847e7i	−0.0578183	−	0.0227262i
$781$	6.23778e7			0.130941
$782$	8.57421e8	+	1.25830e9i	1.79297	+	2.63126i
$783$			1.66521e8i			0.346883i
$784$	3.65376e8	+	3.39716e8i	0.758214	+	0.704966i
$785$	9.24339e7			0.191083
$786$	1.22471e8	−	8.34536e7i	0.252213	−	0.171861i
$787$			6.27317e8i			1.28695i	0.765465	+	0.643477i	$0.222509\pi$
$787$			6.27317e8i			1.28695i	−0.765465	+	0.643477i	$0.777491\pi$
$788$	3.03218e8	−	7.71424e8i	0.619692	−	1.57657i
$789$	5.21238e7			0.106122
$790$	−2.77195e7	−	4.06795e7i	−0.0562218	−	0.0825076i
$791$			1.11079e9i			2.24441i
$792$	−2.02840e8	+	4.61331e7i	−0.408299	+	0.0928618i
$793$	−9.18897e7			−0.184267
$794$	2.31364e8	−	1.57654e8i	0.462204	−	0.314952i
$795$			4.02152e7i			0.0800366i
$796$	−8.79145e8	−	3.45558e8i	−1.74310	−	0.685145i
$797$	−8.30910e8			−1.64127			−0.820633	−	0.571455i	$-0.806379\pi$
$797$	−8.30910e8			−1.64127			−0.820633	+	0.571455i	$0.806379\pi$
$798$	−1.33755e8	−	1.96290e8i	−0.263208	−	0.386268i
$799$		−	6.56012e8i		−	1.28609i
$800$	1.01237e8	+	1.53915e7i	0.197728	+	0.0300616i
$801$	2.34576e8			0.456442
$802$	2.38783e8	−	1.62710e8i	0.462893	−	0.315422i
$803$		−	6.12175e8i		−	1.18230i
$804$	1.29472e8	−	3.29393e8i	0.249119	−	0.633790i
$805$	−6.32111e8			−1.21173
$806$	−4.35752e7	−	6.39483e7i	−0.0832213	−	0.122130i
$807$		−	1.82966e8i		−	0.348137i
$808$	3.07060e7	+	1.35010e8i	0.0582089	+	0.255936i
$809$	−2.49696e8			−0.471592			−0.235796	−	0.971803i	$-0.575770\pi$
$809$	−2.49696e8			−0.471592			−0.235796	+	0.971803i	$0.575770\pi$
$810$	2.18227e7	−	1.48703e7i	0.0410633	−	0.0279811i
$811$		−	2.43488e8i		−	0.456472i	−0.973606	−	0.228236i	$-0.926704\pi$
$811$		−	2.43488e8i		−	0.456472i	0.973606	−	0.228236i	$-0.0732958\pi$
$812$	1.28130e9	+	5.03632e8i	2.39323	+	0.940687i
$813$	1.18623e8			0.220748
$814$	5.73037e8	+	8.40954e8i	1.06245	+	1.55919i
$815$			2.08405e8i			0.384978i
$816$	−3.58108e8	+	3.85157e8i	−0.659089	+	0.708871i
$817$	1.75357e8			0.321556
$818$	9.53946e7	−	6.50031e7i	0.174286	−	0.118761i
$819$			6.28569e7i			0.114420i
$820$	1.01214e8	−	2.57500e8i	0.183568	−	0.467021i
$821$	−7.86656e7			−0.142153			−0.0710764	−	0.997471i	$-0.522643\pi$
$821$	−7.86656e7			−0.142153			−0.0710764	+	0.997471i	$0.522643\pi$
$822$	−1.45529e8	−	2.13569e8i	−0.262019	−	0.384523i
$823$			6.03034e8i			1.08179i	0.841091	+	0.540894i	$0.181914\pi$
$823$			6.03034e8i			1.08179i	−0.841091	+	0.540894i	$0.818086\pi$
$824$	−2.63861e8	+	6.00114e7i	−0.471622	+	0.107264i
$825$	−8.14484e7			−0.145051
$826$	−3.95137e8	+	2.69252e8i	−0.701145	+	0.477770i
$827$			8.14490e8i			1.44002i	0.693963	+	0.720011i	$0.255863\pi$
$827$			8.14490e8i			1.44002i	−0.693963	+	0.720011i	$0.744137\pi$
$828$	3.34463e8	+	1.31465e8i	0.589193	+	0.231589i
$829$	−1.00075e9			−1.75655			−0.878277	−	0.478152i	$-0.841307\pi$
$829$	−1.00075e9			−1.75655			−0.878277	+	0.478152i	$0.841307\pi$
$830$	8.89083e7	+	1.30476e8i	0.155492	+	0.228190i
$831$		−	5.26702e8i		−	0.917830i
$832$	1.24942e8	−	5.99325e7i	0.216939	−	0.104062i
$833$	−1.00326e9			−1.73571
$834$	2.61457e8	−	1.78160e8i	0.450715	−	0.307123i
$835$			3.34579e8i			0.574698i
$836$	1.52366e8	−	3.87638e8i	0.260777	−	0.663449i
$837$	6.93154e7			0.118210
$838$	−3.10847e8	−	4.56179e8i	−0.528219	−	0.775181i
$839$			2.18074e8i			0.369248i	0.982809	+	0.184624i	$0.0591067\pi$
$839$			2.18074e8i			0.369248i	−0.982809	+	0.184624i	$0.940893\pi$
$840$	−4.84188e7	−	2.12890e8i	−0.0816914	−	0.359185i
$841$	1.33767e9			2.24886
$842$	−4.03562e8	+	2.74993e8i	−0.676043	+	0.460665i
$843$		−	5.38465e7i		−	0.0898824i
$844$	−2.65741e8	−	1.04453e8i	−0.442009	−	0.173737i
$845$	2.54206e8			0.421324
$846$	−8.71861e7	−	1.27949e8i	−0.143991	−	0.211313i
$847$		−	5.01050e8i		−	0.824577i
$848$	−1.38434e8	−	1.28712e8i	−0.227016	−	0.211073i
$849$	5.65179e8			0.923555
$850$	−1.70167e8	+	1.15954e8i	−0.277088	+	0.188812i
$851$		−	1.75805e9i		−	2.85261i
$852$	1.36160e7	−	3.46407e7i	0.0220155	−	0.0560104i
$853$	1.06491e9			1.71579			0.857895	−	0.513824i	$-0.171772\pi$
$853$	1.06491e9			1.71579			0.857895	+	0.513824i	$0.171772\pi$
$854$	−3.83196e8	−	5.62354e8i	−0.615244	−	0.902893i
$855$			5.28744e7i			0.0845954i
$856$	−5.47541e8	+	1.24530e8i	−0.872962	+	0.198543i
$857$	−6.69486e7			−0.106365			−0.0531825	−	0.998585i	$-0.516937\pi$
$857$	−6.69486e7			−0.106365			−0.0531825	+	0.998585i	$0.516937\pi$
$858$	−9.10838e7	+	6.20657e7i	−0.144205	+	0.0982630i
$859$		−	5.63953e7i		−	0.0889740i	−0.999010	−	0.0444870i	$-0.985835\pi$
$859$		−	5.63953e7i		−	0.0889740i	0.999010	−	0.0444870i	$-0.0141653\pi$
$860$	1.50009e8	+	5.89629e7i	0.235843	+	0.0927008i
$861$	−5.89905e8			−0.924214
$862$	−4.85761e8	−	7.12873e8i	−0.758405	−	1.11299i
$863$			9.96757e8i			1.55080i	0.631468	+	0.775402i	$0.282453\pi$
$863$			9.96757e8i			1.55080i	−0.631468	+	0.775402i	$0.717547\pi$
$864$	−1.86570e7	+	1.22715e8i	−0.0289268	+	0.190264i
$865$	−6.94520e7			−0.107309
$866$	6.01956e8	−	4.10181e8i	0.926854	−	0.631571i
$867$		−	6.81303e8i		−	1.04540i
$868$	2.09640e8	−	5.33351e8i	0.320564	−	0.815556i
$869$	−1.84038e8			−0.280446
$870$	−1.72572e8	−	2.53255e8i	−0.262067	−	0.384593i
$871$		−	1.87527e8i		−	0.283799i
$872$	3.82263e6	+	1.68075e7i	0.00576517	+	0.0253486i
$873$	8.96334e7			0.134718
$874$	−5.94626e8	+	4.05186e8i	−0.890656	+	0.606905i
$875$		−	8.54839e7i		−	0.127603i
$876$	−3.39964e8	−	1.33627e8i	−0.505732	−	0.198784i
$877$	6.59113e8			0.977150			0.488575	−	0.872522i	$-0.337517\pi$
$877$	6.59113e8			0.977150			0.488575	+	0.872522i	$0.337517\pi$
$878$	3.55319e8	+	5.21444e8i	0.524970	+	0.770414i
$879$			5.82297e8i			0.857389i
$880$	2.60683e8	−	2.80373e8i	0.382529	−	0.411422i
$881$	−3.81472e8			−0.557873			−0.278937	−	0.960310i	$-0.589982\pi$
$881$	−3.81472e8			−0.557873			−0.278937	+	0.960310i	$0.589982\pi$
$882$	−1.95675e8	+	1.33336e8i	−0.285187	+	0.194331i
$883$			5.17519e7i			0.0751700i	0.999293	+	0.0375850i	$0.0119665\pi$
$883$			5.17519e7i			0.0751700i	−0.999293	+	0.0375850i	$0.988034\pi$
$884$	−1.01938e8	+	2.59343e8i	−0.147563	+	0.375420i
$885$	1.06438e8			0.153556
$886$	2.81609e8	+	4.13272e8i	0.404898	+	0.594203i
$887$		−	9.12476e8i		−	1.30753i	−0.756699	−	0.653764i	$-0.773189\pi$
$887$		−	9.12476e8i		−	1.30753i	0.756699	−	0.653764i	$-0.226811\pi$
$888$	5.92097e8	−	1.34664e8i	0.845579	−	0.192315i
$889$	3.68650e8			0.524697
$890$	−3.56757e8	+	2.43099e8i	−0.506061	+	0.344837i
$891$		−	9.87284e7i		−	0.139575i
$892$	1.05310e9	+	4.13934e8i	1.48380	+	0.583225i
$893$	3.10008e8			0.435330
$894$	1.43364e8	+	2.10391e8i	0.200644	+	0.294453i
$895$		−	2.37205e8i		−	0.330868i
$896$	8.87809e8	+	5.14700e8i	1.23423	+	0.715534i
$897$	1.90414e8			0.263829
$898$	1.21475e8	−	8.27745e7i	0.167748	−	0.114306i
$899$		−	8.04413e8i		−	1.10713i
$900$	−1.77787e7	+	4.52314e7i	−0.0243878	+	0.0620458i
$901$	3.80115e8			0.519686
$902$	−5.82480e8	−	8.54811e8i	−0.793709	−	1.16480i
$903$		−	3.43654e8i		−	0.466722i
$904$	2.57751e8	+	1.13329e9i	0.348895	+	1.53404i
$905$	−4.20306e8			−0.567048
$906$	−1.06351e8	+	7.24693e7i	−0.143007	+	0.0974472i
$907$		−	5.39098e8i		−	0.722514i	−0.932466	−	0.361257i	$-0.882348\pi$
$907$		−	5.39098e8i		−	0.722514i	0.932466	−	0.361257i	$-0.117652\pi$
$908$	3.06082e8	+	1.20309e8i	0.408866	+	0.160710i
$909$	−6.57133e7			−0.0874906
$910$	−6.51409e7	−	9.55967e7i	−0.0864430	−	0.126858i
$911$		−	9.85634e6i		−	0.0130365i	−0.999979	−	0.00651824i	$-0.997925\pi$
$911$		−	9.85634e6i		−	0.0130365i	0.999979	−	0.00651824i	$-0.00207484\pi$
$912$	−1.82011e8	−	1.69229e8i	−0.239946	−	0.223095i
$913$	5.90289e8			0.775626
$914$	−2.34020e8	+	1.59465e8i	−0.306489	+	0.208846i
$915$			1.51481e8i			0.197740i
$916$	−2.45208e8	+	6.23839e8i	−0.319042	+	0.811683i
$917$	5.81526e8			0.754156
$918$	−1.40554e8	−	2.06269e8i	−0.181684	−	0.266628i
$919$			7.24302e8i			0.933196i	0.884469	+	0.466598i	$0.154521\pi$
$919$			7.24302e8i			0.933196i	−0.884469	+	0.466598i	$0.845479\pi$
$920$	−6.44915e8	+	1.46677e8i	−0.828207	+	0.188364i
$921$	5.34114e8			0.683683
$922$	−7.32160e7	+	4.98904e7i	−0.0934142	+	0.0636537i
$923$		−	1.97214e7i		−	0.0250803i
$924$	−7.59671e8	−	2.98598e8i	−0.962963	−	0.378504i
$925$	2.37751e8			0.300397
$926$	6.05166e8	+	8.88104e8i	0.762152	+	1.11849i
$927$		−	1.28429e8i		−	0.161222i
$928$	1.42412e9	+	2.16516e8i	1.78198	+	0.270924i
$929$	1.27987e9			1.59632			0.798160	−	0.602446i	$-0.205807\pi$
$929$	1.27987e9			1.59632			0.798160	+	0.602446i	$0.205807\pi$
$930$	−1.05419e8	+	7.18340e7i	−0.131060	+	0.0893062i
$931$		−	4.74103e8i		−	0.587521i
$932$	−5.54760e8	+	1.41138e9i	−0.685263	+	1.74340i
$933$	−3.95759e8			−0.487288
$934$	−4.32594e8	−	6.34847e8i	−0.530933	−	0.779164i
$935$			7.69853e8i			0.941830i
$936$	1.45855e7	+	6.41301e7i	0.0177866	+	0.0782050i
$937$	−1.36364e9			−1.65760			−0.828801	−	0.559543i	$-0.810977\pi$
$937$	−1.36364e9			−1.65760			−0.828801	+	0.559543i	$0.810977\pi$
$938$	1.14765e9	−	7.82022e8i	1.39059	−	0.947568i
$939$		−	1.89461e8i		−	0.228835i
$940$	2.65196e8	+	1.04239e8i	0.319289	+	0.125500i
$941$	1.28040e9			1.53666			0.768331	−	0.640053i	$-0.221088\pi$
$941$	1.28040e9			1.53666			0.768331	+	0.640053i	$0.221088\pi$
$942$	−1.16116e8	−	1.70404e8i	−0.138912	−	0.203858i
$943$			1.78702e9i			2.13105i
$944$	−3.40663e8	+	3.66394e8i	−0.404957	+	0.435545i
$945$	1.03620e8			0.122786
$946$	4.97978e8	−	3.39329e8i	0.588216	−	0.400818i
$947$		−	7.70468e8i		−	0.907203i	−0.891205	−	0.453602i	$-0.850139\pi$
$947$		−	7.70468e8i		−	0.907203i	0.891205	−	0.453602i	$-0.149861\pi$
$948$	−4.01723e7	+	1.02203e8i	−0.0471522	+	0.119961i
$949$	−1.93546e8			−0.226456
$950$	−5.47956e7	−	8.04146e7i	−0.0639109	−	0.0937917i
$951$			5.71934e8i			0.664973i
$952$	−2.01225e9	+	4.57656e8i	−2.33222	+	0.530431i
$953$	−6.08010e8			−0.702476			−0.351238	−	0.936286i	$-0.614239\pi$
$953$	−6.08010e8			−0.702476			−0.351238	+	0.936286i	$0.614239\pi$
$954$	7.41378e7	−	5.05185e7i	0.0853875	−	0.0581842i
$955$			3.53690e8i			0.406081i
$956$	−6.69209e8	−	2.63041e8i	−0.765928	−	0.301057i
$957$	−1.14576e9			−1.30724
$958$	−6.90114e7	−	1.01277e8i	−0.0784918	−	0.115190i
$959$		−	1.01408e9i		−	1.14979i
$960$	−9.87992e7	−	2.05967e8i	−0.111671	−	0.232801i
$961$	5.52662e8			0.622715
$962$	2.65877e8	−	1.81172e8i	0.298645	−	0.203501i
$963$		−	2.66505e8i		−	0.298418i
$964$	−2.76798e8	+	7.04209e8i	−0.308981	+	0.786087i
$965$	−2.16214e8			−0.240603
$966$	7.94061e8	+	1.16531e9i	0.880891	+	1.29274i
$967$			4.87548e8i			0.539185i	0.962974	+	0.269593i	$0.0868890\pi$
$967$			4.87548e8i			0.539185i	−0.962974	+	0.269593i	$0.913111\pi$
$968$	−1.16265e8	−	5.11200e8i	−0.128181	−	0.563591i
$969$	4.99770e8			0.549286
$970$	−1.36320e8	+	9.28903e7i	−0.149364	+	0.101778i
$971$		−	1.52219e9i		−	1.66269i	−0.555757	−	0.831345i	$-0.687571\pi$
$971$		−	1.52219e9i		−	1.66269i	0.555757	−	0.831345i	$-0.312429\pi$
$972$	−5.48276e7	−	2.15506e7i	−0.0597036	−	0.0234672i
$973$	1.24147e9			1.34771
$974$	−4.17490e8	−	6.12683e8i	−0.451824	−	0.663069i
$975$			2.57508e7i			0.0277828i
$976$	−5.21448e8	−	4.84828e8i	−0.560869	−	0.521480i
$977$	3.14908e8			0.337676			0.168838	−	0.985644i	$-0.445998\pi$
$977$	3.14908e8			0.337676			0.168838	+	0.985644i	$0.445998\pi$
$978$	3.84200e8	−	2.61799e8i	0.410716	−	0.279867i
$979$			1.61401e9i			1.72012i
$980$	1.59415e8	−	4.05571e8i	0.169375	−	0.430912i
$981$	−8.18071e6			−0.00866531
$982$	2.10192e8	+	3.08464e8i	0.221963	+	0.325740i
$983$		−	1.47682e9i		−	1.55478i	−0.629020	−	0.777389i	$-0.716544\pi$
$983$		−	1.47682e9i		−	1.55478i	0.629020	−	0.777389i	$-0.283456\pi$
$984$	−6.01854e8	+	1.36883e8i	−0.631693	+	0.143669i
$985$	−7.23994e8			−0.757576
$986$	−2.39378e9	+	1.63115e9i	−2.49720	+	1.70162i
$987$		−	6.07535e8i		−	0.631858i
$988$	−1.22556e8	−	4.81721e7i	−0.127076	−	0.0499488i
$989$	−1.04104e9			−1.07617
$990$	1.02316e8	+	1.50152e8i	0.105448	+	0.154748i
$991$		−	7.56155e8i		−	0.776944i	−0.921461	−	0.388472i	$-0.873003\pi$
$991$		−	7.56155e8i		−	0.776944i	0.921461	−	0.388472i	$-0.126997\pi$
$992$	9.01263e7	−	5.92799e8i	0.0923244	−	0.607257i
$993$	1.59662e8			0.163062
$994$	1.20693e8	−	8.22417e7i	0.122892	−	0.0837400i
$995$			8.25091e8i			0.837592i
$996$	1.28850e8	−	3.27810e8i	0.130408	−	0.331775i
$997$	8.97707e8			0.905835			0.452918	−	0.891552i	$-0.350383\pi$
$997$	8.97707e8			0.905835			0.452918	+	0.891552i	$0.350383\pi$
$998$	−2.65330e8	−	3.89382e8i	−0.266929	−	0.391728i
$999$			2.88191e8i			0.289058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.c.a.31.4	yes	24
3.2	odd	2		180.7.c.b.91.21		24
4.3	odd	2	inner	60.7.c.a.31.3	✓	24
12.11	even	2		180.7.c.b.91.22		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.3	✓	24	4.3	odd	2	inner
60.7.c.a.31.4	yes	24	1.1	even	1	trivial
180.7.c.b.91.21		24	3.2	odd	2
180.7.c.b.91.22		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)

\(f(q)\)	\(=\)	\(q+(-6.61106 + 4.50487i) q^{2} -15.5885i q^{3} +(23.4123 - 59.5639i) q^{4} -55.9017 q^{5} +(70.2239 + 103.056i) q^{6} +489.339i q^{7} +(113.547 + 499.250i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(-6.61106 + 4.50487i) q^{2} -15.5885i q^{3} +(23.4123 - 59.5639i) q^{4} -55.9017 q^{5} +(70.2239 + 103.056i) q^{6} +489.339i q^{7} +(113.547 + 499.250i) q^{8} -243.000 q^{9} +(369.570 - 251.830i) q^{10} -1671.97i q^{11} +(-928.510 - 364.962i) q^{12} -528.612 q^{13} +(-2204.41 - 3235.05i) q^{14} +871.421i q^{15} +(-2999.73 - 2789.06i) q^{16} +8236.70 q^{17} +(1606.49 - 1094.68i) q^{18} +3892.37i q^{19} +(-1308.79 + 3329.73i) q^{20} +7628.03 q^{21} +(7532.02 + 11053.5i) q^{22} -23107.8i q^{23} +(7782.54 - 1770.03i) q^{24} +3125.00 q^{25} +(3494.69 - 2381.33i) q^{26} +3788.00i q^{27} +(29146.9 + 11456.6i) q^{28} +43960.2 q^{29} +(-3925.64 - 5761.02i) q^{30} -18298.7i q^{31} +(32395.7 + 4925.29i) q^{32} -26063.5 q^{33} +(-54453.3 + 37105.2i) q^{34} -27354.9i q^{35} +(-5689.20 + 14474.0i) q^{36} +76080.2 q^{37} +(-17534.6 - 25732.7i) q^{38} +8240.25i q^{39} +(-6347.49 - 27908.9i) q^{40} -77333.8 q^{41} +(-50429.4 + 34363.3i) q^{42} -45051.5i q^{43} +(-99589.3 - 39144.8i) q^{44} +13584.1 q^{45} +(104098. + 152767. i) q^{46} -79645.0i q^{47} +(-43477.2 + 46761.1i) q^{48} -121803. q^{49} +(-20659.6 + 14077.7i) q^{50} -128397. i q^{51} +(-12376.0 + 31486.2i) q^{52} +46149.0 q^{53} +(-17064.4 - 25042.7i) q^{54} +93466.2i q^{55} +(-244302. + 55563.1i) q^{56} +60676.0 q^{57} +(-290623. + 198035. i) q^{58} -122143. i q^{59} +(51905.3 + 20402.0i) q^{60} +173832. q^{61} +(82433.2 + 120974. i) q^{62} -118909. i q^{63} +(-236358. + 113377. i) q^{64} +29550.3 q^{65} +(172307. - 117413. i) q^{66} +354754. i q^{67} +(192840. - 490610. i) q^{68} -360215. q^{69} +(123230. + 180845. i) q^{70} +37307.9i q^{71} +(-27592.0 - 121318. i) q^{72} +366139. q^{73} +(-502971. + 342731. i) q^{74} -48713.9i q^{75} +(231845. + 91129.4i) q^{76} +818161. q^{77} +(-37121.2 - 54476.8i) q^{78} -110073. i q^{79} +(167690. + 155913. i) q^{80} +59049.0 q^{81} +(511259. - 348379. i) q^{82} +353049. i q^{83} +(178590. - 454356. i) q^{84} -460445. q^{85} +(202951. + 297838. i) q^{86} -685271. i q^{87} +(834733. - 189848. i) q^{88} -965332. q^{89} +(-89805.4 + 61194.6i) q^{90} -258670. i q^{91} +(-1.37639e6 - 541008. i) q^{92} -285248. q^{93} +(358790. + 526538. i) q^{94} -217590. i q^{95} +(76777.6 - 504999. i) q^{96} -368862. q^{97} +(805249. - 548707. i) q^{98} +406290. i 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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