LMFDB - Embedded newform 60.7.c.a.31.2

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			31.2
Character	$\chi$	$=$	60.31
Dual form			60.7.c.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.80071 + 1.77450i) q^{2} +15.5885i q^{3} +(57.7023 - 27.6847i) q^{4} +55.9017 q^{5} +(-27.6617 - 121.601i) q^{6} -264.480i q^{7} +(-400.993 + 318.353i) q^{8} -243.000 q^{9} +O(q^{10})$	\(q+(-7.80071 + 1.77450i) q^{2} +15.5885i q^{3} +(57.7023 - 27.6847i) q^{4} +55.9017 q^{5} +(-27.6617 - 121.601i) q^{6} -264.480i q^{7} +(-400.993 + 318.353i) q^{8} -243.000 q^{9} +(-436.073 + 99.1975i) q^{10} +29.4629i q^{11} +(431.562 + 899.490i) q^{12} -2759.92 q^{13} +(469.319 + 2063.13i) q^{14} +871.421i q^{15} +(2563.11 - 3194.95i) q^{16} +1562.12 q^{17} +(1895.57 - 431.203i) q^{18} -7299.42i q^{19} +(3225.66 - 1547.62i) q^{20} +4122.83 q^{21} +(-52.2820 - 229.832i) q^{22} -16832.0i q^{23} +(-4962.64 - 6250.86i) q^{24} +3125.00 q^{25} +(21529.4 - 4897.48i) q^{26} -3788.00i q^{27} +(-7322.05 - 15261.1i) q^{28} +36225.1 q^{29} +(-1546.34 - 6797.71i) q^{30} -45432.8i q^{31} +(-14324.7 + 29471.1i) q^{32} -459.282 q^{33} +(-12185.6 + 2771.97i) q^{34} -14784.9i q^{35} +(-14021.7 + 6727.39i) q^{36} -40535.5 q^{37} +(12952.8 + 56940.7i) q^{38} -43023.0i q^{39} +(-22416.2 + 17796.5i) q^{40} +54626.1 q^{41} +(-32161.1 + 7315.97i) q^{42} -53952.0i q^{43} +(815.673 + 1700.08i) q^{44} -13584.1 q^{45} +(29868.3 + 131301. i) q^{46} +112919. i q^{47} +(49804.3 + 39955.0i) q^{48} +47699.4 q^{49} +(-24377.2 + 5545.31i) q^{50} +24351.0i q^{51} +(-159254. + 76407.7i) q^{52} -78155.8 q^{53} +(6721.79 + 29549.1i) q^{54} +1647.03i q^{55} +(84198.1 + 106055. i) q^{56} +113787. q^{57} +(-282582. + 64281.5i) q^{58} -267725. i q^{59} +(24125.1 + 50283.0i) q^{60} -353443. q^{61} +(80620.4 + 354408. i) q^{62} +64268.6i q^{63} +(59446.3 - 255315. i) q^{64} -154284. q^{65} +(3582.73 - 814.995i) q^{66} -203409. i q^{67} +(90137.6 - 43246.7i) q^{68} +262385. q^{69} +(26235.8 + 115333. i) q^{70} +51657.2i q^{71} +(97441.2 - 77359.9i) q^{72} +221763. q^{73} +(316206. - 71930.2i) q^{74} +48713.9i q^{75} +(-202083. - 421193. i) q^{76} +7792.35 q^{77} +(76344.2 + 335610. i) q^{78} -540997. i q^{79} +(143282. - 178603. i) q^{80} +59049.0 q^{81} +(-426123. + 96934.0i) q^{82} -264246. i q^{83} +(237897. - 114140. i) q^{84} +87324.9 q^{85} +(95737.8 + 420864. i) q^{86} +564694. i q^{87} +(-9379.62 - 11814.4i) q^{88} +314597. q^{89} +(105966. - 24105.0i) q^{90} +729945. i q^{91} +(-465989. - 971244. i) q^{92} +708227. q^{93} +(-200374. - 880846. i) q^{94} -408050. i q^{95} +(-459409. - 223300. i) q^{96} -155146. q^{97} +(-372089. + 84642.5i) q^{98} -7159.49i 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 $

$2$	−7.80071	+	1.77450i	−0.975089	+	0.221812i
$2$	−7.80071	+	1.77450i	−0.975089	+	0.221812i
$3$			15.5885i			0.577350i
$3$			15.5885i			0.577350i
$4$	57.7023	−	27.6847i	0.901599	−	0.432574i
$5$	55.9017			0.447214
$5$	55.9017			0.447214
$6$	−27.6617	−	121.601i	−0.128063	−	0.562968i
$7$		−	264.480i		−	0.771079i	−0.922691	−	0.385539i	$-0.874015\pi$
$7$		−	264.480i		−	0.771079i	0.922691	−	0.385539i	$-0.125985\pi$
$8$	−400.993	+	318.353i	−0.783189	+	0.621784i
$9$	−243.000			−0.333333
$10$	−436.073	+	99.1975i	−0.436073	+	0.0991975i
$11$			29.4629i			0.0221359i	0.999939	+	0.0110680i	$0.00352312\pi$
$11$			29.4629i			0.0221359i	−0.999939	+	0.0110680i	$0.996477\pi$
$12$	431.562	+	899.490i	0.249747	+	0.520538i
$13$	−2759.92			−1.25622			−0.628112	−	0.778123i	$-0.716172\pi$
$13$	−2759.92			−1.25622			−0.628112	+	0.778123i	$0.716172\pi$
$14$	469.319	+	2063.13i	0.171035	+	0.751870i
$15$			871.421i			0.258199i
$16$	2563.11	−	3194.95i	0.625760	−	0.780016i
$17$	1562.12			0.317955			0.158978	−	0.987282i	$-0.449180\pi$
$17$	1562.12			0.317955			0.158978	+	0.987282i	$0.449180\pi$
$18$	1895.57	−	431.203i	0.325030	−	0.0739375i
$19$		−	7299.42i		−	1.06421i	−0.846678	−	0.532105i	$-0.821401\pi$
$19$		−	7299.42i		−	1.06421i	0.846678	−	0.532105i	$-0.178599\pi$
$20$	3225.66	−	1547.62i	0.403207	−	0.193453i
$21$	4122.83			0.445182
$22$	−52.2820	−	229.832i	−0.00491003	−	0.0215845i
$23$		−	16832.0i		−	1.38341i	−0.722179	−	0.691706i	$-0.756859\pi$
$23$		−	16832.0i		−	1.38341i	0.722179	−	0.691706i	$-0.243141\pi$
$24$	−4962.64	−	6250.86i	−0.358987	−	0.452174i
$25$	3125.00			0.200000
$26$	21529.4	−	4897.48i	1.22493	−	0.278646i
$27$		−	3788.00i		−	0.192450i
$28$	−7322.05	−	15261.1i	−0.333548	−	0.695203i
$29$	36225.1			1.48531			0.742653	−	0.669676i	$-0.233567\pi$
$29$	36225.1			1.48531			0.742653	+	0.669676i	$0.233567\pi$
$30$	−1546.34	−	6797.71i	−0.0572717	−	0.251767i
$31$		−	45432.8i		−	1.52505i	−0.646959	−	0.762525i	$-0.723959\pi$
$31$		−	45432.8i		−	1.52505i	0.646959	−	0.762525i	$-0.276041\pi$
$32$	−14324.7	+	29471.1i	−0.437154	+	0.899386i
$33$	−459.282			−0.0127802
$34$	−12185.6	+	2771.97i	−0.310035	+	0.0705265i
$35$		−	14784.9i		−	0.344837i
$36$	−14021.7	+	6727.39i	−0.300533	+	0.144191i
$37$	−40535.5			−0.800258			−0.400129	−	0.916459i	$-0.631035\pi$
$37$	−40535.5			−0.800258			−0.400129	+	0.916459i	$0.631035\pi$
$38$	12952.8	+	56940.7i	0.236055	+	1.03770i
$39$		−	43023.0i		−	0.725281i
$40$	−22416.2	+	17796.5i	−0.350253	+	0.278070i
$41$	54626.1			0.792590			0.396295	−	0.918123i	$-0.370296\pi$
$41$	54626.1			0.792590			0.396295	+	0.918123i	$0.370296\pi$
$42$	−32161.1	+	7315.97i	−0.434093	+	0.0987470i
$43$		−	53952.0i		−	0.678582i	−0.940681	−	0.339291i	$-0.889813\pi$
$43$		−	53952.0i		−	0.678582i	0.940681	−	0.339291i	$-0.110187\pi$
$44$	815.673	+	1700.08i	0.00957543	+	0.0199577i
$45$	−13584.1			−0.149071
$46$	29868.3	+	131301.i	0.306858	+	1.34895i
$47$			112919.i			1.08761i	0.839213	+	0.543803i	$0.183016\pi$
$47$			112919.i			1.08761i	−0.839213	+	0.543803i	$0.816984\pi$
$48$	49804.3	+	39955.0i	0.450342	+	0.361283i
$49$	47699.4			0.405438
$50$	−24377.2	+	5545.31i	−0.195018	+	0.0443625i
$51$			24351.0i			0.183572i
$52$	−159254.	+	76407.7i	−1.13261	+	0.543410i
$53$	−78155.8			−0.524969			−0.262484	−	0.964936i	$-0.584542\pi$
$53$	−78155.8			−0.524969			−0.262484	+	0.964936i	$0.584542\pi$
$54$	6721.79	+	29549.1i	0.0426878	+	0.187656i
$55$			1647.03i			0.00989949i
$56$	84198.1	+	106055.i	0.479444	+	0.603900i
$57$	113787.			0.614422
$58$	−282582.	+	64281.5i	−1.44831	+	0.329459i
$59$		−	267725.i		−	1.30357i	−0.758406	−	0.651783i	$-0.774021\pi$
$59$		−	267725.i		−	1.30357i	0.758406	−	0.651783i	$-0.225979\pi$
$60$	24125.1	+	50283.0i	0.111690	+	0.232792i
$61$	−353443.			−1.55715			−0.778575	−	0.627552i	$-0.784057\pi$
$61$	−353443.			−1.55715			−0.778575	+	0.627552i	$0.784057\pi$
$62$	80620.4	+	354408.i	0.338275	+	1.48706i
$63$			64268.6i			0.257026i
$64$	59446.3	−	255315.i	0.226770	−	0.973948i
$65$	−154284.			−0.561800
$66$	3582.73	−	814.995i	0.0124618	−	0.00283480i
$67$		−	203409.i		−	0.676310i	−0.941090	−	0.338155i	$-0.890197\pi$
$67$		−	203409.i		−	0.676310i	0.941090	−	0.338155i	$-0.109803\pi$
$68$	90137.6	−	43246.7i	0.286668	−	0.137539i
$69$	262385.			0.798713
$70$	26235.8	+	115333.i	0.0764891	+	0.336247i
$71$			51657.2i			0.144330i	0.997393	+	0.0721649i	$0.0229908\pi$
$71$			51657.2i			0.144330i	−0.997393	+	0.0721649i	$0.977009\pi$
$72$	97441.2	−	77359.9i	0.261063	−	0.207261i
$73$	221763.			0.570059			0.285030	−	0.958519i	$-0.407997\pi$
$73$	221763.			0.570059			0.285030	+	0.958519i	$0.407997\pi$
$74$	316206.	−	71930.2i	0.780323	−	0.177507i
$75$			48713.9i			0.115470i
$76$	−202083.	−	421193.i	−0.460350	−	0.959491i
$77$	7792.35			0.0170685
$78$	76344.2	+	335610.i	0.160876	+	0.707214i
$79$		−	540997.i		−	1.09727i	−0.836062	−	0.548635i	$-0.815148\pi$
$79$		−	540997.i		−	1.09727i	0.836062	−	0.548635i	$-0.184852\pi$
$80$	143282.	−	178603.i	0.279848	−	0.348834i
$81$	59049.0			0.111111
$82$	−426123.	+	96934.0i	−0.772846	+	0.175806i
$83$		−	264246.i		−	0.462141i	−0.972937	−	0.231070i	$-0.925777\pi$
$83$		−	264246.i		−	0.462141i	0.972937	−	0.231070i	$-0.0742228\pi$
$84$	237897.	−	114140.i	0.401376	−	0.192574i
$85$	87324.9			0.142194
$86$	95737.8	+	420864.i	0.150518	+	0.661678i
$87$			564694.i			0.857542i
$88$	−9379.62	−	11814.4i	−0.0137638	−	0.0173366i
$89$	314597.			0.446257			0.223128	−	0.974789i	$-0.428373\pi$
$89$	314597.			0.446257			0.223128	+	0.974789i	$0.428373\pi$
$90$	105966.	−	24105.0i	0.145358	−	0.0330658i
$91$			729945.i			0.968647i
$92$	−465989.	−	971244.i	−0.598428	−	1.24728i
$93$	708227.			0.880488
$94$	−200374.	−	880846.i	−0.241245	−	1.06051i
$95$		−	408050.i		−	0.475930i
$96$	−459409.	−	223300.i	−0.519261	−	0.252391i
$97$	−155146.			−0.169990			−0.0849952	−	0.996381i	$-0.527087\pi$
$97$	−155146.			−0.169990			−0.0849952	+	0.996381i	$0.527087\pi$
$98$	−372089.	+	84642.5i	−0.395338	+	0.0899312i
$99$		−	7159.49i		−	0.00737865i
$100$	180320.	−	86514.8i	0.180320	−	0.0865148i
$101$	−1.55143e6			−1.50580			−0.752902	−	0.658133i	$-0.771347\pi$
$101$	−1.55143e6			−1.50580			−0.752902	+	0.658133i	$0.771347\pi$
$102$	−43210.8	−	189955.i	−0.0407185	−	0.178999i
$103$			1.69380e6i			1.55007i	0.631920	+	0.775033i	$0.282267\pi$
$103$			1.69380e6i			1.55007i	−0.631920	+	0.775033i	$0.717733\pi$
$104$	1.10671e6	−	878631.i	0.983861	−	0.781100i
$105$	230473.			0.199092
$106$	609671.	−	138687.i	0.511892	−	0.116445i
$107$			1.31304e6i			1.07183i	0.844271	+	0.535916i	$0.180034\pi$
$107$			1.31304e6i			1.07183i	−0.844271	+	0.535916i	$0.819966\pi$
$108$	−104870.	−	218576.i	−0.0832489	−	0.173513i
$109$	−150713.			−0.116378			−0.0581889	−	0.998306i	$-0.518533\pi$
$109$	−150713.			−0.116378			−0.0581889	+	0.998306i	$0.518533\pi$
$110$	−2922.65	−	12848.0i	−0.00219583	−	0.00965289i
$111$		−	631885.i		−	0.462029i
$112$	−844999.	−	677892.i	−0.601454	−	0.482510i
$113$	−1.70784e6			−1.18362			−0.591811	−	0.806077i	$-0.701587\pi$
$113$	−1.70784e6			−1.18362			−0.591811	+	0.806077i	$0.701587\pi$
$114$	−887618.	+	201914.i	−0.599117	+	0.136287i
$115$		−	940936.i		−	0.618681i
$116$	2.09027e6	−	1.00288e6i	1.33915	−	0.642505i
$117$	670662.			0.418741
$118$	475078.	+	2.08845e6i	0.289147	+	1.27109i
$119$		−	413148.i		−	0.245169i
$120$	−277420.	−	349434.i	−0.160544	−	0.202218i
$121$	1.77069e6			0.999510
$122$	2.75711e6	−	627185.i	1.51836	−	0.345395i
$123$			851536.i			0.457602i
$124$	−1.25779e6	−	2.62158e6i	−0.659697	−	1.37498i
$125$	174693.			0.0894427
$126$	−114045.	−	501341.i	−0.0570116	−	0.250623i
$127$		−	471582.i		−	0.230222i	−0.993353	−	0.115111i	$-0.963278\pi$
$127$		−	471582.i		−	0.230222i	0.993353	−	0.115111i	$-0.0367223\pi$
$128$	−10667.6	+	2.09712e6i	−0.00508672	+	0.999987i
$129$	841029.			0.391779
$130$	1.20353e6	−	273778.i	0.547806	−	0.124614i
$131$			3.66693e6i			1.63113i	0.578666	+	0.815565i	$0.303574\pi$
$131$			3.66693e6i			1.63113i	−0.578666	+	0.815565i	$0.696426\pi$
$132$	−26501.6	+	12715.1i	−0.0115226	+	0.00552838i
$133$	−1.93055e6			−0.820590
$134$	360949.	+	1.58674e6i	0.150014	+	0.659463i
$135$		−	211755.i		−	0.0860663i
$136$	−626397.	+	497305.i	−0.249019	+	0.197700i
$137$	−1.97967e6			−0.769893			−0.384947	−	0.922939i	$-0.625780\pi$
$137$	−1.97967e6			−0.769893			−0.384947	+	0.922939i	$0.625780\pi$
$138$	−2.04679e6	+	465601.i	−0.778817	+	0.177165i
$139$			1.30893e6i			0.487383i	0.969853	+	0.243692i	$0.0783585\pi$
$139$			1.30893e6i			0.487383i	−0.969853	+	0.243692i	$0.921642\pi$
$140$	−409315.	−	853122.i	−0.149167	−	0.310904i
$141$	−1.76023e6			−0.627930
$142$	−91665.7	−	402963.i	−0.0320141	−	0.140734i
$143$		−	81315.5i		−	0.0278077i
$144$	−622836.	+	776372.i	−0.208587	+	0.260005i
$145$	2.02505e6			0.664249
$146$	−1.72991e6	+	393518.i	−0.555859	+	0.126446i
$147$			743559.i			0.234080i
$148$	−2.33899e6	+	1.12221e6i	−0.721511	+	0.346171i
$149$	−1.19790e6			−0.362126			−0.181063	−	0.983471i	$-0.557954\pi$
$149$	−1.19790e6			−0.362126			−0.181063	+	0.983471i	$0.557954\pi$
$150$	−86442.8	−	380003.i	−0.0256127	−	0.112594i
$151$			5.97408e6i			1.73516i	0.497296	+	0.867581i	$0.334326\pi$
$151$			5.97408e6i			1.73516i	−0.497296	+	0.867581i	$0.665674\pi$
$152$	2.32380e6	+	2.92701e6i	0.661709	+	0.833478i
$153$	−379594.			−0.105985
$154$	−60785.9	+	13827.5i	−0.0166434	+	0.00378602i
$155$		−	2.53977e6i		−	0.682023i
$156$	−1.19108e6	−	2.48252e6i	−0.313738	−	0.653912i
$157$	2.98776e6			0.772053			0.386026	−	0.922488i	$-0.373847\pi$
$157$	2.98776e6			0.772053			0.386026	+	0.922488i	$0.373847\pi$
$158$	959998.	+	4.22016e6i	0.243388	+	1.06994i
$159$		−	1.21833e6i		−	0.303091i
$160$	−800774.	+	1.64748e6i	−0.195501	+	0.402218i
$161$	−4.45172e6			−1.06672
$162$	−460624.	+	104782.i	−0.108343	+	0.0246458i
$163$		−	5.21249e6i		−	1.20360i	−0.798646	−	0.601801i	$-0.794450\pi$
$163$		−	5.21249e6i		−	1.20360i	0.798646	−	0.601801i	$-0.205550\pi$
$164$	3.15205e6	−	1.51231e6i	0.714598	−	0.342854i
$165$	−25674.6			−0.00571547
$166$	468905.	+	2.06131e6i	0.102509	+	0.450629i
$167$		−	4.71791e6i		−	1.01298i	−0.862246	−	0.506490i	$-0.830943\pi$
$167$		−	4.71791e6i		−	1.01298i	0.862246	−	0.506490i	$-0.169057\pi$
$168$	−1.65323e6	+	1.31252e6i	−0.348662	+	0.276807i
$169$	2.79037e6			0.578099
$170$	−681197.	+	154958.i	−0.138652	+	0.0315404i
$171$			1.77376e6i			0.354737i
$172$	−1.49365e6	−	3.11315e6i	−0.293537	−	0.611808i
$173$	−898914.			−0.173612			−0.0868060	−	0.996225i	$-0.527666\pi$
$173$	−898914.			−0.173612			−0.0868060	+	0.996225i	$0.527666\pi$
$174$	−1.00205e6	−	4.40502e6i	−0.190213	−	0.836180i
$175$		−	826500.i		−	0.154216i
$176$	94132.5	+	75516.8i	0.0172664	+	0.0138518i
$177$	4.17342e6			0.752614
$178$	−2.45408e6	+	558252.i	−0.435140	+	0.0989853i
$179$		−	3.75535e6i		−	0.654774i	−0.944890	−	0.327387i	$-0.893832\pi$
$179$		−	3.75535e6i		−	0.654774i	0.944890	−	0.327387i	$-0.106168\pi$
$180$	−783835.	+	376072.i	−0.134402	+	0.0644843i
$181$	1.00688e7			1.69802			0.849008	−	0.528380i	$-0.177200\pi$
$181$	1.00688e7			1.69802			0.849008	+	0.528380i	$0.177200\pi$
$182$	−1.29529e6	−	5.69409e6i	−0.214858	−	0.944518i
$183$		−	5.50964e6i		−	0.899021i
$184$	5.35852e6	+	6.74950e6i	0.860183	+	1.08347i
$185$	−2.26600e6			−0.357886
$186$	−5.52467e6	+	1.25675e6i	−0.858554	+	0.195303i
$187$			46024.5i			0.00703824i
$188$	3.12612e6	+	6.51566e6i	0.470470	+	0.980585i
$189$	−1.00185e6			−0.148394
$190$	724085.	+	3.18308e6i	0.105567	+	0.464074i
$191$		−	9.44334e6i		−	1.35527i	−0.735399	−	0.677634i	$-0.763005\pi$
$191$		−	9.44334e6i		−	1.35527i	0.735399	−	0.677634i	$-0.236995\pi$
$192$	3.97996e6	+	926676.i	0.562309	+	0.130925i
$193$	1.09450e7			1.52246			0.761228	−	0.648485i	$-0.224597\pi$
$193$	1.09450e7			1.52246			0.761228	+	0.648485i	$0.224597\pi$
$194$	1.21025e6	−	275306.i	0.165756	−	0.0377060i
$195$		−	2.40506e6i		−	0.324356i
$196$	2.75236e6	−	1.32054e6i	0.365542	−	0.175382i
$197$	−1.05084e7			−1.37448			−0.687242	−	0.726428i	$-0.741179\pi$
$197$	−1.05084e7			−1.37448			−0.687242	+	0.726428i	$0.741179\pi$
$198$	12704.5	+	55849.2i	0.00163668	+	0.00719484i
$199$		−	1.04841e7i		−	1.33037i	−0.746679	−	0.665184i	$-0.768353\pi$
$199$		−	1.04841e7i		−	1.33037i	0.746679	−	0.665184i	$-0.231647\pi$
$200$	−1.25310e6	+	994854.i	−0.156638	+	0.124357i
$201$	3.17083e6			0.390468
$202$	1.21023e7	−	2.75301e6i	1.46829	−	0.334006i
$203$		−	9.58082e6i		−	1.14529i
$204$	674150.	+	1.40511e6i	0.0794083	+	0.165508i
$205$	3.05369e6			0.354457
$206$	−3.00565e6	−	1.32128e7i	−0.343824	−	1.51145i
$207$			4.09017e6i			0.461137i
$208$	−7.07399e6	+	8.81781e6i	−0.786094	+	0.979875i
$209$	215062.			0.0235573
$210$	−1.79786e6	+	408975.i	−0.194132	+	0.0441610i
$211$			1.36416e7i			1.45217i	0.687602	+	0.726087i	$0.258663\pi$
$211$			1.36416e7i			1.45217i	−0.687602	+	0.726087i	$0.741337\pi$
$212$	−4.50977e6	+	2.16372e6i	−0.473311	+	0.227088i
$213$	−805256.			−0.0833288
$214$	−2.32999e6	−	1.02427e7i	−0.237746	−	1.04513i
$215$		−	3.01601e6i		−	0.303471i
$216$	1.20592e6	+	1.51896e6i	0.119662	+	0.150725i
$217$	−1.20161e7			−1.17593
$218$	1.17567e6	−	267439.i	0.113479	−	0.0258140i
$219$			3.45694e6i			0.329124i
$220$	45597.5	+	95037.3i	0.00428226	+	0.00892537i
$221$	−4.31132e6			−0.399423
$222$	1.12128e6	+	4.92916e6i	0.102484	+	0.450520i
$223$		−	2.02736e7i		−	1.82817i	−0.405523	−	0.914085i	$-0.632911\pi$
$223$		−	2.02736e7i		−	1.82817i	0.405523	−	0.914085i	$-0.367089\pi$
$224$	7.79451e6	+	3.78859e6i	0.693498	+	0.337080i
$225$	−759375.			−0.0666667
$226$	1.33224e7	−	3.03057e6i	1.15414	−	0.262542i
$227$			1.36821e7i			1.16970i	0.811140	+	0.584852i	$0.198848\pi$
$227$			1.36821e7i			1.16970i	−0.811140	+	0.584852i	$0.801152\pi$
$228$	6.56576e6	−	3.15015e6i	0.553962	−	0.265783i
$229$	−1.72378e7			−1.43541			−0.717705	−	0.696347i	$-0.754808\pi$
$229$	−1.72378e7			−1.43541			−0.717705	+	0.696347i	$0.754808\pi$
$230$	1.66969e6	+	7.33997e6i	0.137231	+	0.603269i
$231$			121471.i			0.00985453i
$232$	−1.45260e7	+	1.15324e7i	−1.16328	+	0.923540i
$233$	1.24552e7			0.984656			0.492328	−	0.870410i	$-0.336146\pi$
$233$	1.24552e7			0.984656			0.492328	+	0.870410i	$0.336146\pi$
$234$	−5.23164e6	+	1.19009e6i	−0.408310	+	0.0928820i
$235$			6.31234e6i			0.486393i
$236$	−7.41189e6	−	1.54484e7i	−0.563888	−	1.17529i
$237$	8.43330e6			0.633509
$238$	733131.	+	3.22285e6i	0.0543814	+	0.239061i
$239$			2.17394e7i			1.59241i	0.605028	+	0.796204i	$0.293162\pi$
$239$			2.17394e7i			1.59241i	−0.605028	+	0.796204i	$0.706838\pi$
$240$	2.78414e6	+	2.23355e6i	0.201399	+	0.161570i
$241$	−7.91913e6			−0.565752			−0.282876	−	0.959156i	$-0.591289\pi$
$241$	−7.91913e6			−0.565752			−0.282876	+	0.959156i	$0.591289\pi$
$242$	−1.38127e7	+	3.14209e6i	−0.974612	+	0.221704i
$243$			920483.i			0.0641500i
$244$	−2.03945e7	+	9.78498e6i	−1.40392	+	0.673582i
$245$	2.66648e6			0.181317
$246$	−1.51105e6	−	6.64259e6i	−0.101502	−	0.446203i
$247$			2.01458e7i			1.33689i
$248$	1.44637e7	+	1.82182e7i	0.948252	+	1.19440i
$249$	4.11919e6			0.266817
$250$	−1.36273e6	+	309992.i	−0.0872146	+	0.0198395i
$251$			2.60051e7i			1.64451i	0.569118	+	0.822256i	$0.307285\pi$
$251$			2.60051e7i			1.64451i	−0.569118	+	0.822256i	$0.692715\pi$
$252$	1.77926e6	+	3.70845e6i	0.111183	+	0.231734i
$253$	495919.			0.0306231
$254$	836822.	+	3.67868e6i	0.0510660	+	0.224487i
$255$			1.36126e6i			0.0820957i
$256$	−3.63813e6	−	1.63780e7i	−0.216850	−	0.976205i
$257$	−1.09623e7			−0.645807			−0.322903	−	0.946432i	$-0.604659\pi$
$257$	−1.09623e7			−0.645807			−0.322903	+	0.946432i	$0.604659\pi$
$258$	−6.56062e6	+	1.49240e6i	−0.382020	+	0.0869015i
$259$			1.07208e7i			0.617062i
$260$	−8.90257e6	+	4.27132e6i	−0.506518	+	0.243020i
$261$	−8.80271e6			−0.495102
$262$	−6.50696e6	−	2.86047e7i	−0.361805	−	1.59050i
$263$		−	1.86567e7i		−	1.02558i	−0.858515	−	0.512788i	$-0.828613\pi$
$263$		−	1.86567e7i		−	1.02558i	0.858515	−	0.512788i	$-0.171387\pi$
$264$	184169.	−	146214.i	0.0100093	−	0.00794652i
$265$	−4.36904e6			−0.234773
$266$	1.50597e7	−	3.42576e6i	0.800149	−	0.182017i
$267$			4.90408e6i			0.257646i
$268$	−5.63133e6	−	1.17372e7i	−0.292554	−	0.609760i
$269$	3.29387e7			1.69219			0.846095	−	0.533033i	$-0.178948\pi$
$269$	3.29387e7			1.69219			0.846095	+	0.533033i	$0.178948\pi$
$270$	375760.	+	1.65184e6i	0.0190906	+	0.0839223i
$271$			4.83316e6i			0.242842i	0.992601	+	0.121421i	$0.0387450\pi$
$271$			4.83316e6i			0.242842i	−0.992601	+	0.121421i	$0.961255\pi$
$272$	4.00388e6	−	4.99087e6i	0.198964	−	0.248010i
$273$	−1.13787e7			−0.559249
$274$	1.54428e7	−	3.51292e6i	0.750714	−	0.170772i
$275$			92071.7i			0.00442719i
$276$	1.51402e7	−	7.26404e6i	0.720119	−	0.345503i
$277$	−951737.			−0.0447793			−0.0223897	−	0.999749i	$-0.507127\pi$
$277$	−951737.			−0.0447793			−0.0223897	+	0.999749i	$0.507127\pi$
$278$	−2.32269e6	−	1.02106e7i	−0.108108	−	0.475242i
$279$			1.10402e7i			0.508350i
$280$	4.70682e6	+	5.92863e6i	0.214414	+	0.270072i
$281$	1.05420e7			0.475121			0.237560	−	0.971373i	$-0.423652\pi$
$281$	1.05420e7			0.475121			0.237560	+	0.971373i	$0.423652\pi$
$282$	1.37310e7	−	3.12352e6i	0.612288	−	0.139283i
$283$		−	2.15466e7i		−	0.950648i	−0.879811	−	0.475324i	$-0.842331\pi$
$283$		−	2.15466e7i		−	0.950648i	0.879811	−	0.475324i	$-0.157669\pi$
$284$	1.43012e6	+	2.98074e6i	0.0624333	+	0.130127i
$285$	6.36087e6			0.274778
$286$	144294.	+	634319.i	0.00616809	+	0.0271150i
$287$		−	1.44475e7i		−	0.611149i
$288$	3.48090e6	−	7.16148e6i	0.145718	−	0.299795i
$289$	−2.16974e7			−0.898904
$290$	−1.57968e7	+	3.59344e6i	−0.647702	+	0.147339i
$291$		−	2.41848e6i		−	0.0981440i
$292$	1.27962e7	−	6.13944e6i	0.513965	−	0.246593i
$293$	2.97274e7			1.18183			0.590915	−	0.806734i	$-0.298767\pi$
$293$	2.97274e7			1.18183			0.590915	+	0.806734i	$0.298767\pi$
$294$	−1.31945e6	−	5.80030e6i	−0.0519218	−	0.228249i
$295$		−	1.49663e7i		−	0.582972i
$296$	1.62544e7	−	1.29046e7i	0.626753	−	0.497587i
$297$	111605.			0.00426006
$298$	9.34444e6	−	2.12566e6i	0.353105	−	0.0803241i
$299$			4.64550e7i			1.73788i
$300$	1.34863e6	+	2.81091e6i	0.0499493	+	0.104108i
$301$	−1.42692e7			−0.523240
$302$	−1.06010e7	−	4.66021e7i	−0.384880	−	1.69194i
$303$		−	2.41844e7i		−	0.869376i
$304$	−2.33213e7	−	1.87092e7i	−0.830101	−	0.665940i
$305$	−1.97581e7			−0.696379
$306$	2.96110e6	−	673589.i	0.103345	−	0.0235088i
$307$			1.66951e7i			0.576999i	0.957480	+	0.288499i	$0.0931563\pi$
$307$			1.66951e7i			0.576999i	−0.957480	+	0.288499i	$0.906844\pi$
$308$	449637.	−	215729.i	0.0153890	−	0.00738341i
$309$	−2.64037e7			−0.894931
$310$	4.50682e6	+	1.98120e7i	0.151281	+	0.665033i
$311$			2.09869e7i			0.697699i	0.937179	+	0.348849i	$0.113428\pi$
$311$			2.09869e7i			0.697699i	−0.937179	+	0.348849i	$0.886572\pi$
$312$	1.36965e7	+	1.72519e7i	0.450968	+	0.568032i
$313$	−2.69018e7			−0.877299			−0.438650	−	0.898658i	$-0.644543\pi$
$313$	−2.69018e7			−0.877299			−0.438650	+	0.898658i	$0.644543\pi$
$314$	−2.33067e7	+	5.30178e6i	−0.752820	+	0.171251i
$315$			3.59273e6i			0.114946i
$316$	−1.49773e7	−	3.12168e7i	−0.474650	−	0.989297i
$317$	3.75955e7			1.18021			0.590104	−	0.807327i	$-0.299087\pi$
$317$	3.75955e7			1.18021			0.590104	+	0.807327i	$0.299087\pi$
$318$	2.16192e6	+	9.50383e6i	0.0672293	+	0.295541i
$319$			1.06730e6i			0.0328787i
$320$	3.32315e6	−	1.42725e7i	0.101414	−	0.435563i
$321$	−2.04683e7			−0.618823
$322$	3.47266e7	−	7.89957e6i	1.04015	−	0.236612i
$323$		−	1.14025e7i		−	0.338372i
$324$	3.40726e6	−	1.63476e6i	0.100178	−	0.0480638i
$325$	−8.62476e6			−0.251245
$326$	9.24957e6	+	4.06612e7i	0.266974	+	1.17362i
$327$		−	2.34938e6i		−	0.0671908i
$328$	−2.19047e7	+	1.73904e7i	−0.620748	+	0.492820i
$329$	2.98647e7			0.838630
$330$	200280.	−	45559.6i	0.00557310	−	0.00126776i
$331$		−	9.30712e6i		−	0.256644i	−0.991733	−	0.128322i	$-0.959041\pi$
$331$		−	9.30712e6i		−	0.256644i	0.991733	−	0.128322i	$-0.0409591\pi$
$332$	−7.31558e6	−	1.52476e7i	−0.199910	−	0.416665i
$333$	9.85012e6			0.266753
$334$	8.37194e6	+	3.68031e7i	0.224691	+	0.987745i
$335$		−	1.13709e7i		−	0.302455i
$336$	1.05673e7	−	1.31722e7i	0.278577	−	0.347249i
$337$	6.20337e7			1.62083			0.810417	−	0.585854i	$-0.199241\pi$
$337$	6.20337e7			1.62083			0.810417	+	0.585854i	$0.199241\pi$
$338$	−2.17669e7	+	4.95151e6i	−0.563698	+	0.128229i
$339$		−	2.66226e7i		−	0.683364i
$340$	5.03885e6	−	2.41757e6i	0.128202	−	0.0615094i
$341$	1.33858e6			0.0337584
$342$	−3.14754e6	−	1.38366e7i	−0.0786851	−	0.345900i
$343$		−	4.37313e7i		−	1.08370i
$344$	1.71758e7	+	2.16344e7i	0.421931	+	0.531458i
$345$	1.46677e7			0.357195
$346$	7.01217e6	−	1.59512e6i	0.169287	−	0.0385093i
$347$		−	2.00609e7i		−	0.480132i	−0.970757	−	0.240066i	$-0.922831\pi$
$347$		−	2.00609e7i		−	0.480132i	0.970757	−	0.240066i	$-0.0771692\pi$
$348$	1.56334e7	+	3.25841e7i	0.370950	+	0.773159i
$349$	−7.17249e7			−1.68731			−0.843653	−	0.536889i	$-0.819599\pi$
$349$	−7.17249e7			−1.68731			−0.843653	+	0.536889i	$0.819599\pi$
$350$	1.46662e6	+	6.44729e6i	0.0342070	+	0.150374i
$351$			1.04546e7i			0.241760i
$352$	−868305.	−	422047.i	−0.0199088	−	0.00967682i
$353$	1.66396e7			0.378284			0.189142	−	0.981950i	$-0.439429\pi$
$353$	1.66396e7			0.378284			0.189142	+	0.981950i	$0.439429\pi$
$354$	−3.25557e7	+	7.40573e6i	−0.733866	+	0.166939i
$355$			2.88773e6i			0.0645462i
$356$	1.81530e7	−	8.70954e6i	0.402344	−	0.193039i
$357$	6.44034e6			0.141548
$358$	6.66387e6	+	2.92944e7i	0.145237	+	0.638463i
$359$		−	2.91649e7i		−	0.630344i	−0.949035	−	0.315172i	$-0.897938\pi$
$359$		−	2.91649e7i		−	0.630344i	0.949035	−	0.315172i	$-0.102062\pi$
$360$	5.44713e6	−	4.32455e6i	0.116751	−	0.0926901i
$361$	−6.23568e6			−0.132545
$362$	−7.85438e7	+	1.78671e7i	−1.65572	+	0.376641i
$363$			2.76024e7i			0.577067i
$364$	2.02083e7	+	4.21195e7i	0.419012	+	0.873331i
$365$	1.23969e7			0.254938
$366$	9.77685e6	+	4.29791e7i	0.199414	+	0.876626i
$367$		−	6.15826e7i		−	1.24583i	−0.782288	−	0.622917i	$-0.785948\pi$
$367$		−	6.15826e7i		−	1.24583i	0.782288	−	0.622917i	$-0.214052\pi$
$368$	−5.37772e7	−	4.31422e7i	−1.07908	−	0.865684i
$369$	−1.32741e7			−0.264197
$370$	1.76764e7	−	4.02102e6i	0.348971	−	0.0793836i
$371$			2.06706e7i			0.404792i
$372$	4.08663e7	−	1.96071e7i	0.793847	−	0.380876i
$373$	6.41180e7			1.23553			0.617765	−	0.786363i	$-0.288038\pi$
$373$	6.41180e7			1.23553			0.617765	+	0.786363i	$0.288038\pi$
$374$	−81670.4	−	359024.i	−0.00156117	−	0.00686291i
$375$			2.72319e6i			0.0516398i
$376$	−3.59480e7	−	4.52795e7i	−0.676256	−	0.851801i
$377$	−9.99786e7			−1.86588
$378$	7.81514e6	−	1.77778e6i	0.144698	−	0.0329157i
$379$			4.31205e7i			0.792075i	0.918234	+	0.396038i	$0.129615\pi$
$379$			4.31205e7i			0.792075i	−0.918234	+	0.396038i	$0.870385\pi$
$380$	−1.12968e7	−	2.35454e7i	−0.205875	−	0.429097i
$381$	7.35124e6			0.132918
$382$	1.67572e7	+	7.36648e7i	0.300615	+	1.32151i
$383$		−	4.47938e7i		−	0.797299i	−0.917103	−	0.398650i	$-0.869479\pi$
$383$		−	4.47938e7i		−	0.797299i	0.917103	−	0.398650i	$-0.130521\pi$
$384$	−3.26909e7	−	166292.i	−0.577343	−	0.00293682i
$385$	435606.			0.00763329
$386$	−8.53790e7	+	1.94219e7i	−1.48453	+	0.337699i
$387$			1.31103e7i			0.226194i
$388$	−8.95226e6	+	4.29516e6i	−0.153263	+	0.0735334i
$389$	6.70778e7			1.13954			0.569770	−	0.821804i	$-0.307032\pi$
$389$	6.70778e7			1.13954			0.569770	+	0.821804i	$0.307032\pi$
$390$	4.26777e6	+	1.87612e7i	0.0719461	+	0.316276i
$391$		−	2.62935e7i		−	0.439863i
$392$	−1.91271e7	+	1.51853e7i	−0.317534	+	0.252095i
$393$	−5.71617e7			−0.941733
$394$	8.19734e7	−	1.86472e7i	1.34025	−	0.304878i
$395$		−	3.02426e7i		−	0.490714i
$396$	−198209.	−	413119.i	−0.00319181	−	0.00665258i
$397$	3.89648e7			0.622731			0.311366	−	0.950290i	$-0.399214\pi$
$397$	3.89648e7			0.622731			0.311366	+	0.950290i	$0.399214\pi$
$398$	1.86040e7	+	8.17835e7i	0.295092	+	1.29723i
$399$		−	3.00943e7i		−	0.473768i
$400$	8.00972e6	−	9.98420e6i	0.125152	−	0.156003i
$401$	9.85306e7			1.52805			0.764026	−	0.645186i	$-0.223220\pi$
$401$	9.85306e7			1.52805			0.764026	+	0.645186i	$0.223220\pi$
$402$	−2.47348e7	+	5.62664e6i	−0.380741	+	0.0866107i
$403$			1.25391e8i			1.91580i
$404$	−8.95212e7	+	4.29510e7i	−1.35763	+	0.651372i
$405$	3.30094e6			0.0496904
$406$	1.70012e7	+	7.47373e7i	0.254039	+	1.11676i
$407$		−	1.19429e6i		−	0.0177145i
$408$	−7.75221e6	−	9.76456e6i	−0.114142	−	0.143771i
$409$	2.55058e7			0.372794			0.186397	−	0.982475i	$-0.440319\pi$
$409$	2.55058e7			0.372794			0.186397	+	0.982475i	$0.440319\pi$
$410$	−2.38210e7	+	5.41877e6i	−0.345627	+	0.0786230i
$411$		−	3.08600e7i		−	0.444498i
$412$	4.68924e7	+	9.77361e7i	0.670518	+	1.39754i
$413$	−7.08079e7			−1.00515
$414$	−7.25800e6	−	3.19063e7i	−0.102286	−	0.449650i
$415$		−	1.47718e7i		−	0.206676i
$416$	3.95350e7	−	8.13380e7i	0.549164	−	1.12983i
$417$	−2.04041e7			−0.281391
$418$	−1.67764e6	+	381628.i	−0.0229705	+	0.00522530i
$419$			4.64583e6i			0.0631569i	0.999501	+	0.0315785i	$0.0100534\pi$
$419$			4.64583e6i			0.0631569i	−0.999501	+	0.0315785i	$0.989947\pi$
$420$	1.32988e7	−	6.38059e6i	0.179501	−	0.0861218i
$421$	−6.21970e7			−0.833534			−0.416767	−	0.909013i	$-0.636837\pi$
$421$	−6.21970e7			−0.833534			−0.416767	+	0.909013i	$0.636837\pi$
$422$	−2.42071e7	−	1.06414e8i	−0.322110	−	1.41600i
$423$		−	2.74392e7i		−	0.362536i
$424$	3.13399e7	−	2.48812e7i	0.411150	−	0.326417i
$425$	4.88161e6			0.0635911
$426$	6.28157e6	−	1.42893e6i	0.0812530	−	0.0184834i
$427$			9.34787e7i			1.20068i
$428$	3.63512e7	+	7.57655e7i	0.463647	+	0.966363i
$429$	1.26758e6			0.0160548
$430$	5.35191e6	+	2.35270e7i	0.0673136	+	0.295911i
$431$		−	8.54691e7i		−	1.06752i	−0.845635	−	0.533761i	$-0.820778\pi$
$431$		−	8.54691e7i		−	1.06752i	0.845635	−	0.533761i	$-0.179222\pi$
$432$	−1.21024e7	−	9.70906e6i	−0.150114	−	0.120428i
$433$	4.86765e7			0.599591			0.299796	−	0.954003i	$-0.403081\pi$
$433$	4.86765e7			0.599591			0.299796	+	0.954003i	$0.403081\pi$
$434$	9.37338e7	−	2.13225e7i	1.14664	−	0.260837i
$435$			3.15674e7i			0.383505i
$436$	−8.69647e6	+	4.17244e6i	−0.104926	+	0.0503420i
$437$	−1.22864e8			−1.47224
$438$	−6.13434e6	−	2.69666e7i	−0.0730038	−	0.320925i
$439$		−	1.38585e8i		−	1.63804i	−0.573768	−	0.819018i	$-0.694519\pi$
$439$		−	1.38585e8i		−	1.63804i	0.573768	−	0.819018i	$-0.305481\pi$
$440$	−524337.	−	660446.i	−0.00615534	−	0.00775317i
$441$	−1.15909e7			−0.135146
$442$	3.36314e7	−	7.65043e6i	0.389473	−	0.0885970i
$443$			1.24746e8i			1.43488i	0.696619	+	0.717442i	$0.254687\pi$
$443$			1.24746e8i			1.43488i	−0.696619	+	0.717442i	$0.745313\pi$
$444$	−1.74936e7	−	3.64612e7i	−0.199862	−	0.416565i
$445$	1.75865e7			0.199572
$446$	3.59755e7	+	1.58149e8i	0.405511	+	1.78263i
$447$		−	1.86733e7i		−	0.209074i
$448$	−6.75256e7	−	1.57223e7i	−0.750991	−	0.174857i
$449$	4.35883e7			0.481539			0.240769	−	0.970582i	$-0.422600\pi$
$449$	4.35883e7			0.481539			0.240769	+	0.970582i	$0.422600\pi$
$450$	5.92367e6	−	1.34751e6i	0.0650060	−	0.0147875i
$451$			1.60944e6i			0.0175447i
$452$	−9.85465e7	+	4.72812e7i	−1.06715	+	0.512004i
$453$	−9.31266e7			−1.00180
$454$	−2.42789e7	−	1.06730e8i	−0.259455	−	1.14057i
$455$			4.08051e7i			0.433192i
$456$	−4.56276e7	+	3.62244e7i	−0.481209	+	0.382038i
$457$	3.43555e7			0.359954			0.179977	−	0.983671i	$-0.442398\pi$
$457$	3.43555e7			0.359954			0.179977	+	0.983671i	$0.442398\pi$
$458$	1.34467e8	−	3.05885e7i	1.39965	−	0.318392i
$459$		−	5.91728e6i		−	0.0611906i
$460$	−2.60496e7	−	5.42942e7i	−0.267625	−	0.557802i
$461$	−6.32112e7			−0.645195			−0.322598	−	0.946536i	$-0.604556\pi$
$461$	−6.32112e7			−0.645195			−0.322598	+	0.946536i	$0.604556\pi$
$462$	−215550.	−	947559.i	−0.00218586	−	0.00960905i
$463$			7.88603e7i			0.794539i	0.917702	+	0.397270i	$0.130042\pi$
$463$			7.88603e7i			0.794539i	−0.917702	+	0.397270i	$0.869958\pi$
$464$	9.28491e7	−	1.15737e8i	0.929445	−	1.15856i
$465$	3.95911e7			0.393766
$466$	−9.71598e7	+	2.21018e7i	−0.960128	+	0.218409i
$467$		−	5.22025e7i		−	0.512556i	−0.966603	−	0.256278i	$-0.917504\pi$
$467$		−	5.22025e7i		−	0.512556i	0.966603	−	0.256278i	$-0.0824962\pi$
$468$	3.86987e7	−	1.85671e7i	0.377537	−	0.181137i
$469$	−5.37976e7			−0.521488
$470$	−1.12012e7	−	4.92408e7i	−0.107888	−	0.474276i
$471$			4.65746e7i			0.445745i
$472$	8.52312e7	+	1.07356e8i	0.810536	+	1.02094i
$473$	1.58958e6			0.0150210
$474$	−6.57858e7	+	1.49649e7i	−0.617728	+	0.140520i
$475$		−	2.28107e7i		−	0.212842i
$476$	−1.14379e7	−	2.38396e7i	−0.106054	−	0.221044i
$477$	1.89919e7			0.174990
$478$	−3.85766e7	−	1.69583e8i	−0.353216	−	1.55274i
$479$		−	8.50400e7i		−	0.773778i	−0.922126	−	0.386889i	$-0.873550\pi$
$479$		−	8.50400e7i		−	0.773778i	0.922126	−	0.386889i	$-0.126450\pi$
$480$	−2.56817e7	−	1.24828e7i	−0.232221	−	0.112873i
$481$	1.11875e8			1.00530
$482$	6.17748e7	−	1.40525e7i	0.551659	−	0.125491i
$483$		−	6.93954e7i		−	0.615871i
$484$	1.02173e8	−	4.90211e7i	0.901157	−	0.432362i
$485$	−8.67290e6			−0.0760220
$486$	−1.63340e6	−	7.18042e6i	−0.0142293	−	0.0625520i
$487$			6.20201e6i			0.0536964i	0.999640	+	0.0268482i	$0.00854708\pi$
$487$			6.20201e6i			0.0536964i	−0.999640	+	0.0268482i	$0.991453\pi$
$488$	1.41728e8	−	1.12520e8i	1.21954	−	0.968211i
$489$	8.12547e7			0.694900
$490$	−2.08004e7	+	4.73166e6i	−0.176801	+	0.0402184i
$491$			1.34450e8i			1.13584i	0.823083	+	0.567921i	$0.192252\pi$
$491$			1.34450e8i			1.13584i	−0.823083	+	0.567921i	$0.807748\pi$
$492$	2.35746e7	+	4.91356e7i	0.197947	+	0.412573i
$493$	5.65878e7			0.472261
$494$	−3.57488e7	−	1.57152e8i	−0.296538	−	1.30358i
$495$		−	400228.i		−	0.00329983i
$496$	−1.45155e8	−	1.16449e8i	−1.18956	−	0.954315i
$497$	1.36623e7			0.111290
$498$	−3.21326e7	+	7.30950e6i	−0.260171	+	0.0591833i
$499$		−	1.21185e8i		−	0.975321i	−0.873033	−	0.487660i	$-0.837850\pi$
$499$		−	1.21185e8i		−	0.975321i	0.873033	−	0.487660i	$-0.162150\pi$
$500$	1.00802e7	−	4.83632e6i	0.0806414	−	0.0386906i
$501$	7.35450e7			0.584844
$502$	−4.61460e7	−	2.02858e8i	−0.364773	−	1.60355i
$503$			2.01030e8i			1.57964i	0.613342	+	0.789818i	$0.289825\pi$
$503$			2.01030e8i			1.57964i	−0.613342	+	0.789818i	$0.710175\pi$
$504$	−2.04601e7	−	2.57712e7i	−0.159815	−	0.201300i
$505$	−8.67277e7			−0.673416
$506$	−3.86853e6	+	880009.i	−0.0298603	+	0.00679259i
$507$			4.34976e7i			0.333765i
$508$	−1.30556e7	−	2.72114e7i	−0.0995878	−	0.207567i
$509$	2.09283e8			1.58701			0.793507	−	0.608562i	$-0.208253\pi$
$509$	2.09283e8			1.58701			0.793507	+	0.608562i	$0.208253\pi$
$510$	−2.41556e6	−	1.06188e7i	−0.0182099	−	0.0800507i
$511$		−	5.86518e7i		−	0.439560i
$512$	5.74428e7	+	1.21304e8i	0.427982	+	0.903787i
$513$	−2.76502e7			−0.204807
$514$	8.55138e7	−	1.94526e7i	0.629719	−	0.143248i
$515$			9.46863e7i			0.693211i
$516$	4.85293e7	−	2.32836e7i	0.353228	−	0.169474i
$517$	−3.32691e6			−0.0240752
$518$	−1.90241e7	−	8.36300e7i	−0.136872	−	0.601690i
$519$		−	1.40127e7i		−	0.100235i
$520$	6.18669e7	−	4.91170e7i	0.439996	−	0.349318i
$521$	−1.09676e8			−0.775531			−0.387766	−	0.921758i	$-0.626753\pi$
$521$	−1.09676e8			−0.775531			−0.387766	+	0.921758i	$0.626753\pi$
$522$	6.86674e7	−	1.56204e7i	0.482769	−	0.109820i
$523$			1.53121e8i			1.07036i	0.844738	+	0.535180i	$0.179756\pi$
$523$			1.53121e8i			1.07036i	−0.844738	+	0.535180i	$0.820244\pi$
$524$	1.01518e8	+	2.11590e8i	0.705584	+	1.47062i
$525$	1.28839e7			0.0890365
$526$	3.31063e7	+	1.45536e8i	0.227485	+	1.00003i
$527$		−	7.09712e7i		−	0.484898i
$528$	−1.17719e6	+	1.46738e6i	−0.00799733	+	0.00996875i
$529$	−1.35280e8			−0.913829
$530$	3.40817e7	−	7.75286e6i	0.228925	−	0.0520756i
$531$			6.50572e7i			0.434522i
$532$	−1.11397e8	+	5.34468e7i	−0.739843	+	0.354966i
$533$	−1.50764e8			−0.995670
$534$	−8.70229e6	−	3.82554e7i	−0.0571492	−	0.251228i
$535$			7.34013e7i			0.479338i
$536$	6.47560e7	+	8.15656e7i	0.420519	+	0.529679i
$537$	5.85401e7			0.378034
$538$	−2.56945e8	+	5.84496e7i	−1.65004	+	0.375349i
$539$			1.40536e6i			0.00897475i
$540$	−5.86239e6	−	1.22188e7i	−0.0372300	−	0.0775972i
$541$	1.17596e8			0.742676			0.371338	−	0.928498i	$-0.378899\pi$
$541$	1.17596e8			0.742676			0.371338	+	0.928498i	$0.378899\pi$
$542$	−8.57643e6	−	3.77021e7i	−0.0538653	−	0.236792i
$543$			1.56957e8i			0.980350i
$544$	−2.23768e7	+	4.60372e7i	−0.138996	+	0.285965i
$545$	−8.42509e6			−0.0520457
$546$	8.87621e7	−	2.01915e7i	0.545318	−	0.124048i
$547$			1.63945e8i			1.00170i	0.865535	+	0.500848i	$0.166979\pi$
$547$			1.63945e8i			1.00170i	−0.865535	+	0.500848i	$0.833021\pi$
$548$	−1.14231e8	+	5.48065e7i	−0.694134	+	0.333036i
$549$	8.58867e7			0.519050
$550$	−163381.	−	718225.i	−0.000982005	−	0.00431690i
$551$		−	2.64423e8i		−	1.58068i
$552$	−1.05214e8	+	8.35310e7i	−0.625543	+	0.496627i
$553$	−1.43083e8			−0.846081
$554$	7.42423e6	−	1.68886e6i	0.0436639	−	0.00993262i
$555$		−	3.53235e7i		−	0.206626i
$556$	3.62373e7	+	7.55280e7i	0.210829	+	0.439424i
$557$	−2.93846e8			−1.70041			−0.850206	−	0.526450i	$-0.823523\pi$
$557$	−2.93846e8			−1.70041			−0.850206	+	0.526450i	$0.823523\pi$
$558$	−1.95908e7	−	8.61212e7i	−0.112758	−	0.495687i
$559$			1.48903e8i			0.852451i
$560$	−4.72369e7	−	3.78953e7i	−0.268978	−	0.215785i
$561$	−717451.			−0.00406353
$562$	−8.22352e7	+	1.87068e7i	−0.463285	+	0.105388i
$563$			1.32511e8i			0.742554i	0.928522	+	0.371277i	$0.121080\pi$
$563$			1.32511e8i			0.742554i	−0.928522	+	0.371277i	$0.878920\pi$
$564$	−1.01569e8	+	4.87314e7i	−0.566141	+	0.271626i
$565$	−9.54713e7			−0.529331
$566$	3.82344e7	+	1.68079e8i	0.210865	+	0.926967i
$567$		−	1.56173e7i		−	0.0856754i
$568$	−1.64452e7	−	2.07142e7i	−0.0897419	−	0.113037i
$569$	−1.92681e8			−1.04593			−0.522964	−	0.852354i	$-0.675174\pi$
$569$	−1.92681e8			−1.04593			−0.522964	+	0.852354i	$0.675174\pi$
$570$	−4.96193e7	+	1.12874e7i	−0.267933	+	0.0609492i
$571$		−	7.65822e7i		−	0.411357i	−0.978620	−	0.205679i	$-0.934060\pi$
$571$		−	7.65822e7i		−	0.411357i	0.978620	−	0.205679i	$-0.0659402\pi$
$572$	−2.25120e6	−	4.69209e6i	−0.0120289	−	0.0250714i
$573$	1.47207e8			0.782465
$574$	2.56371e7	+	1.12701e8i	0.135560	+	0.595925i
$575$		−	5.25999e7i		−	0.276682i
$576$	−1.44454e7	+	6.20415e7i	−0.0755899	+	0.324649i
$577$	1.71942e8			0.895066			0.447533	−	0.894268i	$-0.352303\pi$
$577$	1.71942e8			0.895066			0.447533	+	0.894268i	$0.352303\pi$
$578$	1.69255e8	−	3.85020e7i	0.876512	−	0.199388i
$579$			1.70616e8i			0.878990i
$580$	1.16850e8	−	5.60629e7i	0.598886	−	0.287337i
$581$	−6.98878e7			−0.356347
$582$	4.29159e6	+	1.88659e7i	0.0217695	+	0.0956991i
$583$		−	2.30270e6i		−	0.0116207i
$584$	−8.89252e7	+	7.05989e7i	−0.446464	+	0.354454i
$585$	3.74911e7			0.187267
$586$	−2.31895e8	+	5.27513e7i	−1.15239	+	0.262144i
$587$		−	1.75375e8i		−	0.867068i	−0.901137	−	0.433534i	$-0.857266\pi$
$587$		−	1.75375e8i		−	0.867068i	0.901137	−	0.433534i	$-0.142734\pi$
$588$	2.05852e7	+	4.29051e7i	0.101257	+	0.211046i
$589$	−3.31633e8			−1.62297
$590$	2.65577e7	+	1.16748e8i	0.129310	+	0.568450i
$591$		−	1.63810e8i		−	0.793559i
$592$	−1.03897e8	+	1.29509e8i	−0.500769	+	0.624214i
$593$	−1.46804e8			−0.704003			−0.352001	−	0.935999i	$-0.614499\pi$
$593$	−1.46804e8			−0.704003			−0.352001	+	0.935999i	$0.614499\pi$
$594$	−870602.	+	198044.i	−0.00415394	+	0.000944935i
$595$		−	2.30957e7i		−	0.109643i
$596$	−6.91213e7	+	3.31634e7i	−0.326492	+	0.156646i
$597$	1.63431e8			0.768088
$598$	−8.24343e7	−	3.62382e8i	−0.385482	−	1.69458i
$599$			1.52954e8i			0.711672i	0.934548	+	0.355836i	$0.115804\pi$
$599$			1.52954e8i			0.711672i	−0.934548	+	0.355836i	$0.884196\pi$
$600$	−1.55082e7	−	1.95339e7i	−0.0717974	−	0.0904349i
$601$	1.98847e8			0.916003			0.458001	−	0.888952i	$-0.348565\pi$
$601$	1.98847e8			0.916003			0.458001	+	0.888952i	$0.348565\pi$
$602$	1.11310e8	−	2.53207e7i	0.510206	−	0.116061i
$603$			4.94284e7i			0.225437i
$604$	1.65391e8	+	3.44718e8i	0.750586	+	1.56442i
$605$	9.89847e7			0.446994
$606$	4.29152e7	+	1.88656e8i	0.192838	+	0.847720i
$607$		−	2.62997e8i		−	1.17594i	−0.808883	−	0.587970i	$-0.799927\pi$
$607$		−	2.62997e8i		−	1.17594i	0.808883	−	0.587970i	$-0.200073\pi$
$608$	2.15122e8	+	1.04562e8i	0.957137	+	0.465224i
$609$	1.49350e8			0.661232
$610$	1.54127e8	−	3.50607e7i	0.679031	−	0.154465i
$611$		−	3.11647e8i		−	1.36628i
$612$	−2.19034e7	+	1.05090e7i	−0.0955561	+	0.0458464i
$613$	3.30925e8			1.43664			0.718321	−	0.695712i	$-0.244911\pi$
$613$	3.30925e8			1.43664			0.718321	+	0.695712i	$0.244911\pi$
$614$	−2.96255e7	−	1.30234e8i	−0.127986	−	0.562625i
$615$			4.76023e7i			0.204646i
$616$	−3.12468e6	+	2.48072e6i	−0.0133679	+	0.0106129i
$617$	3.38754e8			1.44221			0.721106	−	0.692824i	$-0.243634\pi$
$617$	3.38754e8			1.44221			0.721106	+	0.692824i	$0.243634\pi$
$618$	2.05968e8	−	4.68534e7i	0.872638	−	0.198507i
$619$		−	2.66432e8i		−	1.12335i	−0.827358	−	0.561675i	$-0.810157\pi$
$619$		−	2.66432e8i		−	1.12335i	0.827358	−	0.561675i	$-0.189843\pi$
$620$	−7.03128e7	−	1.46551e8i	−0.295025	−	0.614911i
$621$	−6.37594e7			−0.266238
$622$	−3.72413e7	−	1.63713e8i	−0.154758	−	0.680319i
$623$		−	8.32046e7i		−	0.344099i
$624$	−1.37456e8	−	1.10273e8i	−0.565731	−	0.453852i
$625$	9.76562e6			0.0400000
$626$	2.09853e8	−	4.77372e7i	0.855445	−	0.194596i
$627$			3.35249e6i			0.0136008i
$628$	1.72401e8	−	8.27153e7i	0.696081	−	0.333970i
$629$	−6.33211e7			−0.254446
$630$	−6.37529e6	−	2.80258e7i	−0.0254964	−	0.112082i
$631$		−	1.51752e8i		−	0.604013i	−0.953306	−	0.302007i	$-0.902343\pi$
$631$		−	1.51752e8i		−	0.604013i	0.953306	−	0.302007i	$-0.0976565\pi$
$632$	1.72228e8	+	2.16936e8i	0.682265	+	0.859369i
$633$	−2.12652e8			−0.838413
$634$	−2.93272e8	+	6.67133e7i	−1.15081	+	0.261785i
$635$		−	2.63622e7i		−	0.102958i
$636$	−3.37291e7	−	7.03004e7i	−0.131109	−	0.273266i
$637$	−1.31647e8			−0.509321
$638$	−1.89392e6	−	8.32569e6i	−0.00729289	−	0.0320596i
$639$		−	1.25527e7i		−	0.0481099i
$640$	−596339.	+	1.17233e8i	−0.00227485	+	0.447208i
$641$	−1.47284e8			−0.559219			−0.279610	−	0.960114i	$-0.590205\pi$
$641$	−1.47284e8			−0.559219			−0.279610	+	0.960114i	$0.590205\pi$
$642$	1.59667e8	−	3.63210e7i	0.603408	−	0.137263i
$643$		−	5.45081e7i		−	0.205035i	−0.994731	−	0.102518i	$-0.967310\pi$
$643$		−	5.45081e7i		−	0.205035i	0.994731	−	0.102518i	$-0.0326898\pi$
$644$	−2.56874e8	+	1.23245e8i	−0.961753	+	0.461435i
$645$	4.70149e7			0.175209
$646$	2.02338e7	+	8.89479e7i	0.0750550	+	0.329943i
$647$		−	1.13471e8i		−	0.418960i	−0.977813	−	0.209480i	$-0.932823\pi$
$647$		−	1.13471e8i		−	0.418960i	0.977813	−	0.209480i	$-0.0671771\pi$
$648$	−2.36782e7	+	1.87984e7i	−0.0870210	+	0.0690871i
$649$	7.88796e6			0.0288556
$650$	6.72793e7	−	1.53046e7i	0.244986	−	0.0557292i
$651$		−	1.87312e8i		−	0.678925i
$652$	−1.44306e8	−	3.00773e8i	−0.520647	−	1.08517i
$653$	1.43973e8			0.517060			0.258530	−	0.966003i	$-0.416762\pi$
$653$	1.43973e8			0.517060			0.258530	+	0.966003i	$0.416762\pi$
$654$	4.16897e6	+	1.83268e7i	0.0149037	+	0.0655170i
$655$			2.04988e8i			0.729463i
$656$	1.40013e8	−	1.74527e8i	0.495971	−	0.618233i
$657$	−5.38883e7			−0.190020
$658$	−2.32966e8	+	5.29949e7i	−0.817739	+	0.186019i
$659$			8.17629e7i			0.285693i	0.989745	+	0.142847i	$0.0456256\pi$
$659$			8.17629e7i			0.285693i	−0.989745	+	0.142847i	$0.954374\pi$
$660$	−1.48149e6	+	710795.i	−0.00515306	+	0.00247236i
$661$	−1.06717e7			−0.0369512			−0.0184756	−	0.999829i	$-0.505881\pi$
$661$	−1.06717e7			−0.0369512			−0.0184756	+	0.999829i	$0.505881\pi$
$662$	1.65155e7	+	7.26022e7i	0.0569268	+	0.250251i
$663$		−	6.72068e7i		−	0.230607i
$664$	8.41236e7	+	1.05961e8i	0.287352	+	0.361944i
$665$	−1.07921e8			−0.366979
$666$	−7.68380e7	+	1.74790e7i	−0.260108	+	0.0591690i
$667$		−	6.09741e8i		−	2.05479i
$668$	−1.30614e8	−	2.72235e8i	−0.438188	−	0.913301i
$669$	3.16034e8			1.05549
$670$	2.01777e7	+	8.87013e7i	0.0670883	+	0.294921i
$671$		−	1.04135e7i		−	0.0344690i
$672$	−5.90583e7	+	1.21504e8i	−0.194613	+	0.400391i
$673$	4.04111e8			1.32573			0.662865	−	0.748739i	$-0.269340\pi$
$673$	4.04111e8			1.32573			0.662865	+	0.748739i	$0.269340\pi$
$674$	−4.83908e8	+	1.10079e8i	−1.58046	+	0.359521i
$675$		−	1.18375e7i		−	0.0384900i
$676$	1.61011e8	−	7.72507e7i	0.521213	−	0.250070i
$677$	4.71145e8			1.51841			0.759204	−	0.650853i	$-0.225589\pi$
$677$	4.71145e8			1.51841			0.759204	+	0.650853i	$0.225589\pi$
$678$	4.72419e7	+	2.07676e8i	0.151579	+	0.666341i
$679$			4.10329e7i			0.131076i
$680$	−3.50166e7	+	2.78002e7i	−0.111365	+	0.0884139i
$681$	−2.13283e8			−0.675329
$682$	−1.04419e7	+	2.37531e6i	−0.0329175	+	0.00748803i
$683$		−	3.10535e8i		−	0.974649i	−0.873221	−	0.487325i	$-0.837973\pi$
$683$		−	3.10535e8i		−	0.974649i	0.873221	−	0.487325i	$-0.162027\pi$
$684$	4.91060e7	+	1.02350e8i	0.153450	+	0.319830i
$685$	−1.10667e8			−0.344307
$686$	7.76012e7	+	3.41136e8i	0.240379	+	1.05671i
$687$		−	2.68711e8i		−	0.828735i
$688$	−1.72374e8	−	1.38285e8i	−0.529305	−	0.424629i
$689$	2.15704e8			0.659479
$690$	−1.14419e8	+	2.60279e7i	−0.348298	+	0.0792304i
$691$			6.84679e7i			0.207517i	0.994603	+	0.103758i	$0.0330869\pi$
$691$			6.84679e7i			0.207517i	−0.994603	+	0.103758i	$0.966913\pi$
$692$	−5.18694e7	+	2.48862e7i	−0.156528	+	0.0751000i
$693$	−1.89354e6			−0.00568952
$694$	3.55980e7	+	1.56489e8i	0.106499	+	0.468172i
$695$			7.31712e7i			0.217964i
$696$	−1.79772e8	−	2.26438e8i	−0.533206	−	0.671617i
$697$	8.53322e7			0.252008
$698$	5.59505e8	−	1.27276e8i	1.64527	−	0.374265i
$699$			1.94158e8i			0.568492i
$700$	−2.28814e7	−	4.76909e7i	−0.0667097	−	0.139041i
$701$	−1.82766e8			−0.530569			−0.265285	−	0.964170i	$-0.585466\pi$
$701$	−1.82766e8			−0.530569			−0.265285	+	0.964170i	$0.585466\pi$
$702$	−1.85516e7	−	8.15532e7i	−0.0536255	−	0.235738i
$703$			2.95885e8i			0.851643i
$704$	7.52232e6	+	1.75146e6i	0.0215593	+	0.00501976i
$705$	−9.83997e7			−0.280819
$706$	−1.29801e8	+	2.95269e7i	−0.368861	+	0.0839081i
$707$			4.10323e8i			1.16109i
$708$	2.40816e8	−	1.15540e8i	0.678556	−	0.325561i
$709$	−4.30437e8			−1.20773			−0.603867	−	0.797085i	$-0.706374\pi$
$709$	−4.30437e8			−1.20773			−0.603867	+	0.797085i	$0.706374\pi$
$710$	−5.12427e6	−	2.25263e7i	−0.0143172	−	0.0629383i
$711$			1.31462e8i			0.365757i
$712$	−1.26151e8	+	1.00153e8i	−0.349503	+	0.277475i
$713$	−7.64723e8			−2.10977
$714$	−5.02393e7	+	1.14284e7i	−0.138022	+	0.0313971i
$715$		−	4.54567e6i		−	0.0124360i
$716$	−1.03966e8	−	2.16692e8i	−0.283238	−	0.590343i
$717$	−3.38884e8			−0.919378
$718$	5.17532e7	+	2.27507e8i	0.139818	+	0.614642i
$719$			3.35482e8i			0.902573i	0.892379	+	0.451287i	$0.149035\pi$
$719$			3.35482e8i			0.902573i	−0.892379	+	0.451287i	$0.850965\pi$
$720$	−3.48176e7	+	4.34005e7i	−0.0932828	+	0.116278i
$721$	4.47976e8			1.19522
$722$	4.86428e7	−	1.10652e7i	0.129243	−	0.0294001i
$723$		−	1.23447e8i		−	0.326637i
$724$	5.80993e8	−	2.78752e8i	1.53093	−	0.734517i
$725$	1.13204e8			0.297061
$726$	−4.89804e7	−	2.15318e8i	−0.128001	−	0.562692i
$727$			3.91654e8i			1.01929i	0.860383	+	0.509647i	$0.170224\pi$
$727$			3.91654e8i			1.01929i	−0.860383	+	0.509647i	$0.829776\pi$
$728$	−2.32380e8	−	2.92702e8i	−0.602289	−	0.758634i
$729$	−1.43489e7			−0.0370370
$730$	−9.67048e7	+	2.19983e7i	−0.248588	+	0.0565485i
$731$		−	8.42792e7i		−	0.215759i
$732$	−1.52533e8	−	3.17919e8i	−0.388893	−	0.810556i
$733$	4.73042e8			1.20112			0.600562	−	0.799578i	$-0.294944\pi$
$733$	4.73042e8			1.20112			0.600562	+	0.799578i	$0.294944\pi$
$734$	1.09278e8	+	4.80389e8i	0.276341	+	1.21480i
$735$			4.15662e7i			0.104684i
$736$	4.96057e8	+	2.41113e8i	1.24422	+	0.604765i
$737$	5.99303e6			0.0149708
$738$	1.03548e8	−	2.35550e7i	0.257615	−	0.0586021i
$739$			3.38422e8i			0.838543i	0.907861	+	0.419272i	$0.137715\pi$
$739$			3.38422e8i			0.838543i	−0.907861	+	0.419272i	$0.862285\pi$
$740$	−1.30753e8	+	6.27336e7i	−0.322670	+	0.154812i
$741$	−3.14043e8			−0.771852
$742$	−3.66800e7	−	1.61246e8i	−0.0897880	−	0.394709i
$743$		−	3.10086e8i		−	0.755990i	−0.925808	−	0.377995i	$-0.876614\pi$
$743$		−	3.10086e8i		−	0.755990i	0.925808	−	0.377995i	$-0.123386\pi$
$744$	−2.83994e8	+	2.25466e8i	−0.689588	+	0.547473i
$745$	−6.69644e7			−0.161948
$746$	−5.00166e8	+	1.13777e8i	−1.20475	+	0.274056i
$747$			6.42118e7i			0.154047i
$748$	1.27418e6	+	2.65572e6i	0.00304456	+	0.00634567i
$749$	3.47273e8			0.826467
$750$	−4.83230e6	−	2.12428e7i	−0.0114543	−	0.0503534i
$751$			3.62391e8i			0.855575i	0.903879	+	0.427787i	$0.140707\pi$
$751$			3.62391e8i			0.855575i	−0.903879	+	0.427787i	$0.859293\pi$
$752$	3.60769e8	+	2.89423e8i	0.848351	+	0.680580i
$753$	−4.05379e8			−0.949460
$754$	7.79905e8	−	1.77412e8i	1.81940	−	0.413875i
$755$			3.33961e8i			0.775988i
$756$	−5.78090e7	+	2.77359e7i	−0.133792	+	0.0641914i
$757$	−6.63275e8			−1.52900			−0.764498	−	0.644627i	$-0.777013\pi$
$757$	−6.63275e8			−1.52900			−0.764498	+	0.644627i	$0.777013\pi$
$758$	−7.65174e7	−	3.36371e8i	−0.175692	−	0.772344i
$759$			7.73062e6i			0.0176803i
$760$	1.29904e8	+	1.63625e8i	0.295925	+	0.372743i
$761$	3.91992e8			0.889453			0.444726	−	0.895666i	$-0.353301\pi$
$761$	3.91992e8			0.889453			0.444726	+	0.895666i	$0.353301\pi$
$762$	−5.73449e7	+	1.30448e7i	−0.129607	+	0.0294830i
$763$			3.98605e7i			0.0897364i
$764$	−2.61436e8	−	5.44902e8i	−0.586254	−	1.22191i
$765$	−2.12199e7			−0.0473980
$766$	7.94865e7	+	3.49423e8i	0.176851	+	0.777438i
$767$			7.38901e8i			1.63757i
$768$	2.55308e8	−	5.67129e7i	0.563612	−	0.125198i
$769$	−8.33190e8			−1.83217			−0.916084	−	0.400988i	$-0.868667\pi$
$769$	−8.33190e8			−1.83217			−0.916084	+	0.400988i	$0.868667\pi$
$770$	−3.39804e6	+	772982.i	−0.00744314	+	0.00169316i
$771$		−	1.70885e8i		−	0.372857i
$772$	6.31553e8	−	3.03010e8i	1.37264	−	0.658574i
$773$	1.73029e7			0.0374612			0.0187306	−	0.999825i	$-0.494038\pi$
$773$	1.73029e7			0.0374612			0.0187306	+	0.999825i	$0.494038\pi$
$774$	−2.32643e7	−	1.02270e8i	−0.0501726	−	0.220559i
$775$		−	1.41977e8i		−	0.305010i
$776$	6.22122e7	−	4.93911e7i	0.133135	−	0.105697i
$777$	−1.67121e8			−0.356261
$778$	−5.23254e8	+	1.19029e8i	−1.11115	+	0.252764i
$779$		−	3.98739e8i		−	0.843483i
$780$	−6.65833e7	−	1.38777e8i	−0.140308	−	0.292439i
$781$	−1.52197e6			−0.00319487
$782$	4.66578e7	+	2.05108e8i	0.0975672	+	0.428906i
$783$		−	1.37221e8i		−	0.285847i
$784$	1.22259e8	−	1.52397e8i	0.253707	−	0.316248i
$785$	1.67021e8			0.345272
$786$	4.45903e8	−	1.01433e8i	0.918274	−	0.208888i
$787$			4.60899e8i			0.945544i	0.881185	+	0.472772i	$0.156747\pi$
$787$			4.60899e8i			0.945544i	−0.881185	+	0.472772i	$0.843253\pi$
$788$	−6.06362e8	+	2.90924e8i	−1.23923	+	0.594566i
$789$	2.90829e8			0.592116
$790$	5.36655e7	+	2.35914e8i	0.108846	+	0.478490i
$791$			4.51690e8i			0.912665i
$792$	2.27925e6	+	2.87090e6i	0.00458792	+	0.00577887i
$793$	9.75477e8			1.95613
$794$	−3.03953e8	+	6.91430e7i	−0.607219	+	0.138130i
$795$		−	6.81066e7i		−	0.135546i
$796$	−2.90249e8	−	6.04957e8i	−0.575482	−	1.19946i
$797$	3.41609e8			0.674768			0.337384	−	0.941367i	$-0.390458\pi$
$797$	3.41609e8			0.674768			0.337384	+	0.941367i	$0.390458\pi$
$798$	5.34023e7	+	2.34757e8i	0.105088	+	0.461966i
$799$			1.76392e8i			0.345810i
$800$	−4.47646e7	+	9.20972e7i	−0.0874309	+	0.179877i
$801$	−7.64471e7			−0.148752
$802$	−7.68609e8	+	1.74843e8i	−1.48999	+	0.338941i
$803$			6.53378e6i			0.0126188i
$804$	1.82964e8	−	8.77837e7i	0.352045	−	0.168906i
$805$	−2.48859e8			−0.477051
$806$	−2.22506e8	−	9.78139e8i	−0.424949	−	1.86808i
$807$			5.13463e8i			0.976986i
$808$	6.22113e8	−	4.93903e8i	1.17933	−	0.936285i
$809$	−3.89991e8			−0.736562			−0.368281	−	0.929714i	$-0.620054\pi$
$809$	−3.89991e8			−0.736562			−0.368281	+	0.929714i	$0.620054\pi$
$810$	−2.57497e7	+	5.85751e6i	−0.0484526	+	0.0110219i
$811$			3.29858e8i			0.618394i	0.950998	+	0.309197i	$0.100060\pi$
$811$			3.29858e8i			0.618394i	−0.950998	+	0.309197i	$0.899940\pi$
$812$	−2.65242e8	−	5.52836e8i	−0.495422	−	1.03259i
$813$	−7.53414e7			−0.140205
$814$	2.11927e6	+	9.31634e6i	0.00392929	+	0.0172732i
$815$		−	2.91387e8i		−	0.538267i
$816$	7.78000e7	+	6.24142e7i	0.143189	+	0.114872i
$817$	−3.93818e8			−0.722154
$818$	−1.98963e8	+	4.52600e7i	−0.363507	+	0.0826903i
$819$		−	1.77377e8i		−	0.322882i
$820$	1.76205e8	−	8.45406e7i	0.319578	−	0.153329i
$821$	3.48609e8			0.629955			0.314978	−	0.949099i	$-0.398003\pi$
$821$	3.48609e8			0.629955			0.314978	+	0.949099i	$0.398003\pi$
$822$	5.47610e7	+	2.40730e8i	0.0985952	+	0.433425i
$823$		−	2.21129e8i		−	0.396685i	−0.980133	−	0.198343i	$-0.936444\pi$
$823$		−	2.21129e8i		−	0.396685i	0.980133	−	0.198343i	$-0.0635559\pi$
$824$	−5.39227e8	−	6.79201e8i	−0.963806	−	1.21399i
$825$	−1.43526e6			−0.00255604
$826$	5.52352e8	−	1.25649e8i	0.980113	−	0.222955i
$827$		−	2.45088e8i		−	0.433317i	−0.976247	−	0.216659i	$-0.930484\pi$
$827$		−	2.45088e8i		−	0.433317i	0.976247	−	0.216659i	$-0.0695158\pi$
$828$	1.13235e8	+	2.36012e8i	0.199476	+	0.415761i
$829$	7.32697e7			0.128606			0.0643029	−	0.997930i	$-0.479518\pi$
$829$	7.32697e7			0.128606			0.0643029	+	0.997930i	$0.479518\pi$
$830$	2.62126e7	+	1.15231e8i	0.0458432	+	0.201527i
$831$		−	1.48361e7i		−	0.0258534i
$832$	−1.64067e8	+	7.04649e8i	−0.284873	+	1.22350i
$833$	7.45119e7			0.128911
$834$	1.59167e8	−	3.62071e7i	0.274381	−	0.0624160i
$835$		−	2.63739e8i		−	0.453018i
$836$	1.24096e7	−	5.95394e6i	0.0212392	−	0.0101903i
$837$	−1.72099e8			−0.293496
$838$	−8.24402e6	−	3.62408e7i	−0.0140090	−	0.0615837i
$839$			3.17675e8i			0.537895i	0.963155	+	0.268948i	$0.0866759\pi$
$839$			3.17675e8i			0.537895i	−0.963155	+	0.268948i	$0.913324\pi$
$840$	−9.24182e7	+	7.33720e7i	−0.155926	+	0.123792i
$841$	7.17438e8			1.20614
$842$	4.85181e8	−	1.10369e8i	0.812770	−	0.184888i
$843$			1.64334e8i			0.274311i
$844$	3.77665e8	+	7.87153e8i	0.628173	+	1.30928i
$845$	1.55986e8			0.258534
$846$	4.86909e7	+	2.14046e8i	0.0804149	+	0.353505i
$847$		−	4.68313e8i		−	0.770701i
$848$	−2.00322e8	+	2.49704e8i	−0.328504	+	0.409484i
$849$	3.35878e8			0.548857
$850$	−3.80800e7	+	8.66241e6i	−0.0620070	+	0.0141053i
$851$			6.82292e8i			1.10709i
$852$	−4.64651e7	+	2.22933e7i	−0.0751291	+	0.0360459i
$853$	−8.91387e8			−1.43621			−0.718107	−	0.695933i	$-0.754991\pi$
$853$	−8.91387e8			−1.43621			−0.718107	+	0.695933i	$0.754991\pi$
$854$	−1.65878e8	−	7.29201e8i	−0.266327	−	1.17077i
$855$			9.91562e7i			0.158643i
$856$	−4.18011e8	−	5.26520e8i	−0.666448	−	0.839448i
$857$	−1.67921e8			−0.266786			−0.133393	−	0.991063i	$-0.542587\pi$
$857$	−1.67921e8			−0.266786			−0.133393	+	0.991063i	$0.542587\pi$
$858$	−9.88805e6	+	2.24932e6i	−0.0156548	+	0.00356115i
$859$		−	7.27537e8i		−	1.14782i	−0.818917	−	0.573912i	$-0.805425\pi$
$859$		−	7.27537e8i		−	1.14782i	0.818917	−	0.573912i	$-0.194575\pi$
$860$	−8.34974e7	−	1.74031e8i	−0.131274	−	0.273609i
$861$	2.25214e8			0.352847
$862$	1.51665e8	+	6.66720e8i	0.236790	+	1.04093i
$863$		−	6.52206e8i		−	1.01474i	−0.861730	−	0.507368i	$-0.830619\pi$
$863$		−	6.52206e8i		−	1.01474i	0.861730	−	0.507368i	$-0.169381\pi$
$864$	1.11636e8	+	5.42618e7i	0.173087	+	0.0841304i
$865$	−5.02508e7			−0.0776416
$866$	−3.79711e8	+	8.63764e7i	−0.584655	+	0.132997i
$867$		−	3.38228e8i		−	0.518983i
$868$	−6.93354e8	+	3.32661e8i	−1.06022	+	0.508678i
$869$	1.59393e7			0.0242891
$870$	−5.60163e7	−	2.46248e8i	−0.0850661	−	0.373951i
$871$			5.61394e8i			0.849597i
$872$	6.04347e7	−	4.79799e7i	0.0911458	−	0.0723618i
$873$	3.77004e7			0.0566634
$874$	9.58425e8	−	2.18022e8i	1.43557	−	0.326562i
$875$		−	4.62027e7i		−	0.0689674i
$876$	9.57044e7	+	1.99473e8i	0.142370	+	0.296738i
$877$	9.00052e7			0.133435			0.0667174	−	0.997772i	$-0.478747\pi$
$877$	9.00052e7			0.133435			0.0667174	+	0.997772i	$0.478747\pi$
$878$	2.45919e8	+	1.08106e9i	0.363337	+	1.59723i
$879$			4.63405e8i			0.682329i
$880$	5.26216e6	+	4.22152e6i	0.00772176	+	0.00619470i
$881$	−6.72192e8			−0.983027			−0.491514	−	0.870870i	$-0.663556\pi$
$881$	−6.72192e8			−0.983027			−0.491514	+	0.870870i	$0.663556\pi$
$882$	9.04177e7	−	2.05681e7i	0.131779	−	0.0299771i
$883$		−	1.80609e8i		−	0.262336i	−0.991360	−	0.131168i	$-0.958127\pi$
$883$		−	1.80609e8i		−	0.262336i	0.991360	−	0.131168i	$-0.0418727\pi$
$884$	−2.48773e8	+	1.19358e8i	−0.360119	+	0.172780i
$885$	2.33301e8			0.336579
$886$	−2.21362e8	−	9.73111e8i	−0.318275	−	1.39914i
$887$			1.00620e9i			1.44183i	0.693022	+	0.720916i	$0.256279\pi$
$887$			1.00620e9i			1.44183i	−0.693022	+	0.720916i	$0.743721\pi$
$888$	2.01163e8	+	2.53381e8i	0.287282	+	0.361856i
$889$	−1.24724e8			−0.177519
$890$	−1.37187e8	+	3.12073e7i	−0.194601	+	0.0442676i
$891$			1.73976e6i			0.00245955i
$892$	−5.61269e8	−	1.16983e9i	−0.790818	−	1.64828i
$893$	8.24240e8			1.15744
$894$	3.31358e7	+	1.45665e8i	0.0463751	+	0.203866i
$895$		−	2.09930e8i		−	0.292824i
$896$	5.54647e8	+	2.82137e6i	0.771069	+	0.00392226i
$897$	−7.24161e8			−1.00336
$898$	−3.40020e8	+	7.73474e7i	−0.469543	+	0.106811i
$899$		−	1.64581e9i		−	2.26517i
$900$	−4.38177e7	+	2.10231e7i	−0.0601066	+	0.0288383i
$901$	−1.22088e8			−0.166917
$902$	−2.85596e6	−	1.25548e7i	−0.00389164	−	0.0171077i
$903$		−	2.22435e8i		−	0.302093i
$904$	6.84833e8	−	5.43698e8i	0.926999	−	0.735957i
$905$	5.62863e8			0.759376
$906$	7.26454e8	−	1.65253e8i	0.976841	−	0.222211i
$907$		−	8.47891e8i		−	1.13637i	−0.822903	−	0.568183i	$-0.807647\pi$
$907$		−	8.47891e8i		−	1.13637i	0.822903	−	0.568183i	$-0.192353\pi$
$908$	3.78786e8	+	7.89490e8i	0.505984	+	1.05460i
$909$	3.76998e8			0.501935
$910$	−7.24087e7	−	3.18309e8i	−0.0960874	−	0.422401i
$911$		−	3.23382e8i		−	0.427722i	−0.976864	−	0.213861i	$-0.931396\pi$
$911$		−	3.23382e8i		−	0.427722i	0.976864	−	0.213861i	$-0.0686039\pi$
$912$	2.91648e8	−	3.63542e8i	0.384481	−	0.479259i
$913$	7.78547e6			0.0102299
$914$	−2.67997e8	+	6.09638e7i	−0.350988	+	0.0798423i
$915$		−	3.07998e8i		−	0.402054i
$916$	−9.94663e8	+	4.77225e8i	−1.29416	+	0.620921i
$917$	9.69829e8			1.25773
$918$	1.05002e7	+	4.61590e7i	0.0135728	+	0.0596663i
$919$			1.03492e8i			0.133340i	0.997775	+	0.0666699i	$0.0212374\pi$
$919$			1.03492e8i			0.133340i	−0.997775	+	0.0666699i	$0.978763\pi$
$920$	2.99550e8	+	3.77308e8i	0.384686	+	0.484544i
$921$	−2.60251e8			−0.333130
$922$	4.93092e8	−	1.12168e8i	0.629123	−	0.143112i
$923$		−	1.42570e8i		−	0.181310i
$924$	3.36289e6	+	7.00914e6i	0.00426281	+	0.00888483i
$925$	−1.26673e8			−0.160052
$926$	−1.39938e8	−	6.15167e8i	−0.176239	−	0.774747i
$927$		−	4.11593e8i		−	0.516689i
$928$	−5.18913e8	+	1.06759e9i	−0.649308	+	1.33586i
$929$	1.31287e9			1.63747			0.818735	−	0.574172i	$-0.194676\pi$
$929$	1.31287e9			1.63747			0.818735	+	0.574172i	$0.194676\pi$
$930$	−3.08839e8	+	7.02543e7i	−0.383957	+	0.0873422i
$931$		−	3.48178e8i		−	0.431471i
$932$	7.18697e8	−	3.44820e8i	0.887765	−	0.425937i
$933$	−3.27154e8			−0.402817
$934$	9.26334e7	+	4.07217e8i	0.113691	+	0.499788i
$935$			2.57285e6i			0.00314760i
$936$	−2.68930e8	+	2.13507e8i	−0.327954	+	0.260367i
$937$	4.13735e8			0.502926			0.251463	−	0.967867i	$-0.419088\pi$
$937$	4.13735e8			0.502926			0.251463	+	0.967867i	$0.419088\pi$
$938$	4.19660e8	−	9.54639e7i	0.508498	−	0.115673i
$939$		−	4.19357e8i		−	0.506509i
$940$	1.74755e8	+	3.64237e8i	0.210401	+	0.438531i
$941$	−7.06411e8			−0.847791			−0.423895	−	0.905711i	$-0.639338\pi$
$941$	−7.06411e8			−0.847791			−0.423895	+	0.905711i	$0.639338\pi$
$942$	−8.26466e7	−	3.63315e8i	−0.0988717	−	0.434641i
$943$		−	9.19465e8i		−	1.09648i
$944$	−8.55367e8	−	6.86209e8i	−1.01680	−	0.815719i
$945$	−5.60050e7			−0.0663639
$946$	−1.23999e7	+	2.82072e6i	−0.0146469	+	0.00333185i
$947$		−	1.19548e9i		−	1.40764i	−0.710377	−	0.703822i	$-0.751475\pi$
$947$		−	1.19548e9i		−	1.40764i	0.710377	−	0.703822i	$-0.248525\pi$
$948$	4.86621e8	−	2.33474e8i	0.571171	−	0.274039i
$949$	−6.12048e8			−0.716122
$950$	4.04776e7	+	1.77940e8i	0.0472110	+	0.207540i
$951$			5.86056e8i			0.681393i
$952$	1.31527e8	+	1.65669e8i	0.152442	+	0.192013i
$953$	−6.95229e8			−0.803247			−0.401623	−	0.915805i	$-0.631554\pi$
$953$	−6.95229e8			−0.803247			−0.401623	+	0.915805i	$0.631554\pi$
$954$	−1.48150e8	+	3.37010e7i	−0.170631	+	0.0388149i
$955$		−	5.27899e8i		−	0.606094i
$956$	6.01850e8	+	1.25442e9i	0.688834	+	1.43571i
$957$	−1.66375e7			−0.0189825
$958$	1.50903e8	+	6.63372e8i	0.171634	+	0.754503i
$959$			5.23582e8i			0.593648i
$960$	2.22487e8	+	5.18028e7i	0.251472	+	0.0585516i
$961$	−1.17663e9			−1.32578
$962$	−8.72703e8	+	1.98522e8i	−0.980260	+	0.222989i
$963$		−	3.19069e8i		−	0.357278i
$964$	−4.56952e8	+	2.19239e8i	−0.510081	+	0.244730i
$965$	6.11845e8			0.680863
$966$	1.23142e8	+	5.41334e8i	0.136608	+	0.600529i
$967$			8.16482e8i			0.902958i	0.892282	+	0.451479i	$0.149103\pi$
$967$			8.16482e8i			0.902958i	−0.892282	+	0.451479i	$0.850897\pi$
$968$	−7.10035e8	+	5.63706e8i	−0.782805	+	0.621479i
$969$	1.77748e8			0.195359
$970$	6.76548e7	−	1.53901e7i	0.0741282	−	0.0168626i
$971$			3.34681e8i			0.365572i	0.983153	+	0.182786i	$0.0585115\pi$
$971$			3.34681e8i			0.365572i	−0.983153	+	0.182786i	$0.941488\pi$
$972$	2.54833e7	+	5.31140e7i	0.0277496	+	0.0578376i
$973$	3.46185e8			0.375811
$974$	−1.10055e7	−	4.83801e7i	−0.0119105	−	0.0523588i
$975$		−	1.34447e8i		−	0.145056i
$976$	−9.05915e8	+	1.12923e9i	−0.974402	+	1.21460i
$977$	4.91550e8			0.527089			0.263545	−	0.964647i	$-0.415108\pi$
$977$	4.91550e8			0.527089			0.263545	+	0.964647i	$0.415108\pi$
$978$	−6.33845e8	+	1.44186e8i	−0.677589	+	0.154137i
$979$			9.26896e6i			0.00987831i
$980$	1.53862e8	−	7.38206e7i	0.163475	−	0.0784331i
$981$	3.66232e7			0.0387926
$982$	−2.38582e8	−	1.04881e9i	−0.251944	−	1.10755i
$983$			8.15838e8i			0.858902i	0.903090	+	0.429451i	$0.141293\pi$
$983$			8.15838e8i			0.858902i	−0.903090	+	0.429451i	$0.858707\pi$
$984$	−2.71089e8	−	3.41460e8i	−0.284530	−	0.358389i
$985$	−5.87440e8			−0.614688
$986$	−4.41426e8	+	1.00415e8i	−0.460497	+	0.104753i
$987$			4.65545e8i			0.484183i
$988$	5.57732e8	+	1.16246e9i	0.578302	+	1.20534i
$989$	−9.08119e8			−0.938758
$990$	710204.	+	3.12206e6i	0.000731943	+	0.00321763i
$991$			1.09131e9i			1.12132i	0.828047	+	0.560659i	$0.189452\pi$
$991$			1.09131e9i			1.12132i	−0.828047	+	0.560659i	$0.810548\pi$
$992$	1.33895e9	+	6.50810e8i	1.37161	+	0.666682i
$993$	1.45084e8			0.148173
$994$	−1.06576e8	+	2.42437e7i	−0.108517	+	0.0246854i
$995$		−	5.86079e8i		−	0.594959i
$996$	2.37687e8	−	1.14039e8i	0.240562	−	0.115418i
$997$	−4.66809e8			−0.471035			−0.235518	−	0.971870i	$-0.575679\pi$
$997$	−4.66809e8			−0.471035			−0.235518	+	0.971870i	$0.575679\pi$
$998$	2.15043e8	+	9.45330e8i	0.216338	+	0.951025i
$999$			1.53548e8i			0.154010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.c.a.31.2	yes	24
3.2	odd	2		180.7.c.b.91.23		24
4.3	odd	2	inner	60.7.c.a.31.1	✓	24
12.11	even	2		180.7.c.b.91.24		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.c.a.31.1	✓	24	4.3	odd	2	inner
60.7.c.a.31.2	yes	24	1.1	even	1	trivial
180.7.c.b.91.23		24	3.2	odd	2
180.7.c.b.91.24		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)

\(f(q)\)	\(=\)	\(q+(-7.80071 + 1.77450i) q^{2} +15.5885i q^{3} +(57.7023 - 27.6847i) q^{4} +55.9017 q^{5} +(-27.6617 - 121.601i) q^{6} -264.480i q^{7} +(-400.993 + 318.353i) q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+(-7.80071 + 1.77450i) q^{2} +15.5885i q^{3} +(57.7023 - 27.6847i) q^{4} +55.9017 q^{5} +(-27.6617 - 121.601i) q^{6} -264.480i q^{7} +(-400.993 + 318.353i) q^{8} -243.000 q^{9} +(-436.073 + 99.1975i) q^{10} +29.4629i q^{11} +(431.562 + 899.490i) q^{12} -2759.92 q^{13} +(469.319 + 2063.13i) q^{14} +871.421i q^{15} +(2563.11 - 3194.95i) q^{16} +1562.12 q^{17} +(1895.57 - 431.203i) q^{18} -7299.42i q^{19} +(3225.66 - 1547.62i) q^{20} +4122.83 q^{21} +(-52.2820 - 229.832i) q^{22} -16832.0i q^{23} +(-4962.64 - 6250.86i) q^{24} +3125.00 q^{25} +(21529.4 - 4897.48i) q^{26} -3788.00i q^{27} +(-7322.05 - 15261.1i) q^{28} +36225.1 q^{29} +(-1546.34 - 6797.71i) q^{30} -45432.8i q^{31} +(-14324.7 + 29471.1i) q^{32} -459.282 q^{33} +(-12185.6 + 2771.97i) q^{34} -14784.9i q^{35} +(-14021.7 + 6727.39i) q^{36} -40535.5 q^{37} +(12952.8 + 56940.7i) q^{38} -43023.0i q^{39} +(-22416.2 + 17796.5i) q^{40} +54626.1 q^{41} +(-32161.1 + 7315.97i) q^{42} -53952.0i q^{43} +(815.673 + 1700.08i) q^{44} -13584.1 q^{45} +(29868.3 + 131301. i) q^{46} +112919. i q^{47} +(49804.3 + 39955.0i) q^{48} +47699.4 q^{49} +(-24377.2 + 5545.31i) q^{50} +24351.0i q^{51} +(-159254. + 76407.7i) q^{52} -78155.8 q^{53} +(6721.79 + 29549.1i) q^{54} +1647.03i q^{55} +(84198.1 + 106055. i) q^{56} +113787. q^{57} +(-282582. + 64281.5i) q^{58} -267725. i q^{59} +(24125.1 + 50283.0i) q^{60} -353443. q^{61} +(80620.4 + 354408. i) q^{62} +64268.6i q^{63} +(59446.3 - 255315. i) q^{64} -154284. q^{65} +(3582.73 - 814.995i) q^{66} -203409. i q^{67} +(90137.6 - 43246.7i) q^{68} +262385. q^{69} +(26235.8 + 115333. i) q^{70} +51657.2i q^{71} +(97441.2 - 77359.9i) q^{72} +221763. q^{73} +(316206. - 71930.2i) q^{74} +48713.9i q^{75} +(-202083. - 421193. i) q^{76} +7792.35 q^{77} +(76344.2 + 335610. i) q^{78} -540997. i q^{79} +(143282. - 178603. i) q^{80} +59049.0 q^{81} +(-426123. + 96934.0i) q^{82} -264246. i q^{83} +(237897. - 114140. i) q^{84} +87324.9 q^{85} +(95737.8 + 420864. i) q^{86} +564694. i q^{87} +(-9379.62 - 11814.4i) q^{88} +314597. q^{89} +(105966. - 24105.0i) q^{90} +729945. i q^{91} +(-465989. - 971244. i) q^{92} +708227. q^{93} +(-200374. - 880846. i) q^{94} -408050. i q^{95} +(-459409. - 223300. i) q^{96} -155146. q^{97} +(-372089. + 84642.5i) q^{98} -7159.49i 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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