LMFDB - Embedded newform 60.7.l.a.23.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(23,60)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 3]))

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

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

chi := DirichletCharacter("60.23");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.l (of order $4$, degree $2$, 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:	$136$
Relative dimension:	$68$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	60.23
Dual form			60.7.l.a.47.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.21208 + 3.46207i) q^{2} +(16.1580 + 21.6314i) q^{3} +(40.0282 - 49.9374i) q^{4} +(17.7152 + 123.738i) q^{5} +(-191.422 - 100.068i) q^{6} +(0.599925 + 0.599925i) q^{7} +(-115.800 + 498.733i) q^{8} +(-206.838 + 699.041i) q^{9} +O(q^{10})$	\(q+(-7.21208 + 3.46207i) q^{2} +(16.1580 + 21.6314i) q^{3} +(40.0282 - 49.9374i) q^{4} +(17.7152 + 123.738i) q^{5} +(-191.422 - 100.068i) q^{6} +(0.599925 + 0.599925i) q^{7} +(-115.800 + 498.733i) q^{8} +(-206.838 + 699.041i) q^{9} +(-556.154 - 831.079i) q^{10} +1615.65 q^{11} +(1726.99 + 58.9787i) q^{12} +(1196.02 + 1196.02i) q^{13} +(-6.40369 - 2.24973i) q^{14} +(-2390.40 + 2382.57i) q^{15} +(-891.489 - 3997.81i) q^{16} +(1486.33 + 1486.33i) q^{17} +(-928.395 - 5757.63i) q^{18} -8056.57 q^{19} +(6888.28 + 4068.37i) q^{20} +(-3.28365 + 22.6708i) q^{21} +(-11652.2 + 5593.50i) q^{22} +(2785.22 + 2785.22i) q^{23} +(-12659.4 + 5553.61i) q^{24} +(-14997.3 + 4384.11i) q^{25} +(-12766.5 - 4485.10i) q^{26} +(-18463.4 + 6820.90i) q^{27} +(53.9726 - 5.94479i) q^{28} -44199.1 q^{29} +(8991.11 - 25459.0i) q^{30} -14738.2i q^{31} +(20270.2 + 25746.1i) q^{32} +(26105.7 + 34948.9i) q^{33} +(-15865.3 - 5573.75i) q^{34} +(-63.6059 + 84.8615i) q^{35} +(26629.0 + 38310.3i) q^{36} +(-22271.5 + 22271.5i) q^{37} +(58104.6 - 27892.4i) q^{38} +(-6546.36 + 45197.1i) q^{39} +(-63763.8 - 5493.71i) q^{40} +71100.1i q^{41} +(-54.8059 - 174.872i) q^{42} +(77064.1 - 77064.1i) q^{43} +(64671.7 - 80681.5i) q^{44} +(-90162.4 - 13210.1i) q^{45} +(-29729.9 - 10444.6i) q^{46} +(103056. - 103056. i) q^{47} +(72073.6 - 83880.7i) q^{48} -117648. i q^{49} +(92984.0 - 83540.3i) q^{50} +(-8135.32 + 56167.5i) q^{51} +(107601. - 11851.7i) q^{52} +(-115283. + 115283. i) q^{53} +(109545. - 113114. i) q^{54} +(28621.7 + 199918. i) q^{55} +(-368.673 + 229.731i) q^{56} +(-130178. - 174275. i) q^{57} +(318768. - 153020. i) q^{58} +324963. i q^{59} +(23296.2 + 214740. i) q^{60} +172561. q^{61} +(51024.7 + 106293. i) q^{62} +(-543.460 + 295.285i) q^{63} +(-235325. - 115506. i) q^{64} +(-126806. + 169182. i) q^{65} +(-309272. - 161675. i) q^{66} +(99096.4 + 99096.4i) q^{67} +(133718. - 14728.3i) q^{68} +(-15244.8 + 105252. i) q^{69} +(164.935 - 832.236i) q^{70} +114765. q^{71} +(-324683. - 184106. i) q^{72} +(93737.6 + 93737.6i) q^{73} +(83518.3 - 237729. i) q^{74} +(-337162. - 253576. i) q^{75} +(-322490. + 402324. i) q^{76} +(969.271 + 969.271i) q^{77} +(-109262. - 348629. i) q^{78} +95504.0 q^{79} +(478889. - 181133. i) q^{80} +(-445877. - 289177. i) q^{81} +(-246153. - 512779. i) q^{82} +(80011.9 + 80011.9i) q^{83} +(1000.68 + 1071.45i) q^{84} +(-157585. + 210246. i) q^{85} +(-288991. + 822594. i) q^{86} +(-714169. - 956091. i) q^{87} +(-187092. + 805779. i) q^{88} +1.00047e6 q^{89} +(695993. - 216876. i) q^{90} +1435.05i q^{91} +(250574. - 27599.4i) q^{92} +(318809. - 238140. i) q^{93} +(-386462. + 1.10004e6i) q^{94} +(-142724. - 996907. i) q^{95} +(-229400. + 854478. i) q^{96} +(-7526.89 + 7526.89i) q^{97} +(407306. + 848489. i) q^{98} +(-334179. + 1.12941e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 4 q^{6}+O(q^{10}) $ 136 * q - 4 * q^6	$ 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) $ 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−7.21208	+	3.46207i	−0.901510	+	0.432758i
$2$	−7.21208	+	3.46207i	−0.901510	+	0.432758i
$3$	16.1580	+	21.6314i	0.598444	+	0.801164i
$3$	16.1580	+	21.6314i	0.598444	+	0.801164i
$4$	40.0282	−	49.9374i	0.625440	−	0.780272i
$5$	17.7152	+	123.738i	0.141722	+	0.989907i
$5$	17.7152	+	123.738i	0.141722	+	0.989907i
$6$	−191.422	−	100.068i	−0.886214	−	0.463276i
$7$	0.599925	+	0.599925i	0.00174905	+	0.00174905i	0.707981	−	0.706232i	$-0.249606\pi$
$7$	0.599925	+	0.599925i	0.00174905	+	0.00174905i	−0.706232	+	0.707981i	$0.749606\pi$
$8$	−115.800	+	498.733i	−0.226172	+	0.974087i
$9$	−206.838	+	699.041i	−0.283729	+	0.958905i
$10$	−556.154	−	831.079i	−0.556154	−	0.831079i
$11$	1615.65			1.21386			0.606932	−	0.794754i	$-0.292400\pi$
$11$	1615.65			1.21386			0.606932	+	0.794754i	$0.292400\pi$
$12$	1726.99	+	58.9787i	0.999417	+	0.0341312i
$13$	1196.02	+	1196.02i	0.544390	+	0.544390i	0.924813	−	0.380423i	$-0.124222\pi$
$13$	1196.02	+	1196.02i	0.544390	+	0.544390i	−0.380423	+	0.924813i	$0.624222\pi$
$14$	−6.40369	−	2.24973i	−0.00233371	−	0.000819871i
$15$	−2390.40	+	2382.57i	−0.708265	+	0.705946i
$16$	−891.489	−	3997.81i	−0.217649	−	0.976027i
$17$	1486.33	+	1486.33i	0.302529	+	0.302529i	0.842003	−	0.539473i	$-0.181377\pi$
$17$	1486.33	+	1486.33i	0.302529	+	0.302529i	−0.539473	+	0.842003i	$0.681377\pi$
$18$	−928.395	−	5757.63i	−0.159190	−	0.987248i
$19$	−8056.57			−1.17460			−0.587299	−	0.809370i	$-0.699809\pi$
$19$	−8056.57			−1.17460			−0.587299	+	0.809370i	$0.699809\pi$
$20$	6888.28	+	4068.37i	0.861035	+	0.508546i
$21$	−3.28365	+	22.6708i	−0.000354568	+	0.00244799i
$22$	−11652.2	+	5593.50i	−1.09431	+	0.525310i
$23$	2785.22	+	2785.22i	0.228916	+	0.228916i	0.812240	−	0.583324i	$-0.198248\pi$
$23$	2785.22	+	2785.22i	0.228916	+	0.228916i	−0.583324	+	0.812240i	$0.698248\pi$
$24$	−12659.4	+	5553.61i	−0.915755	+	0.401737i
$25$	−14997.3	+	4384.11i	−0.959830	+	0.280583i
$26$	−12766.5	−	4485.10i	−0.726362	−	0.255183i
$27$	−18463.4	+	6820.90i	−0.938036	+	0.346538i
$28$	53.9726	−	5.94479i	0.00245866	−	0.000270808i
$29$	−44199.1			−1.81226			−0.906128	−	0.423003i	$-0.860976\pi$
$29$	−44199.1			−1.81226			−0.906128	+	0.423003i	$0.860976\pi$
$30$	8991.11	−	25459.0i	0.333004	−	0.942925i
$31$		−	14738.2i		−	0.494721i	−0.968924	−	0.247360i	$-0.920437\pi$
$31$		−	14738.2i		−	0.494721i	0.968924	−	0.247360i	$-0.0795632\pi$
$32$	20270.2	+	25746.1i	0.618596	+	0.785709i
$33$	26105.7	+	34948.9i	0.726430	+	0.972505i
$34$	−15865.3	−	5573.75i	−0.403656	−	0.141811i
$35$	−63.6059	+	84.8615i	−0.00148352	+	0.00197928i
$36$	26629.0	+	38310.3i	0.570751	+	0.821123i
$37$	−22271.5	+	22271.5i	−0.439687	+	0.439687i	−0.891907	−	0.452220i	$-0.850632\pi$
$37$	−22271.5	+	22271.5i	−0.439687	+	0.439687i	0.452220	+	0.891907i	$0.350632\pi$
$38$	58104.6	−	27892.4i	1.05891	−	0.508317i
$39$	−6546.36	+	45197.1i	−0.110359	+	0.761932i
$40$	−63763.8	−	5493.71i	−0.996309	−	0.0858392i
$41$			71100.1i			1.03162i	0.856704	+	0.515808i	$0.172508\pi$
$41$			71100.1i			1.03162i	−0.856704	+	0.515808i	$0.827492\pi$
$42$	−54.8059	−	174.872i	−0.000739741	−	0.00236033i
$43$	77064.1	−	77064.1i	0.969275	−	0.969275i	−0.0302671	−	0.999542i	$-0.509636\pi$
$43$	77064.1	−	77064.1i	0.969275	−	0.969275i	0.999542	+	0.0302671i	$0.00963579\pi$
$44$	64671.7	−	80681.5i	0.759200	−	0.947144i
$45$	−90162.4	−	13210.1i	−0.989436	−	0.144967i
$46$	−29729.9	−	10444.6i	−0.305436	−	0.107305i
$47$	103056.	−	103056.i	0.992614	−	0.992614i	−0.00735901	−	0.999973i	$-0.502342\pi$
$47$	103056.	−	103056.i	0.992614	−	0.992614i	0.999973	+	0.00735901i	$0.00234247\pi$
$48$	72073.6	−	83880.7i	0.651708	−	0.758470i
$49$		−	117648.i		−	0.999994i
$50$	92984.0	−	83540.3i	0.743872	−	0.668323i
$51$	−8135.32	+	56167.5i	−0.0613288	+	0.423423i
$52$	107601.	−	11851.7i	0.765255	−	0.0842887i
$53$	−115283.	+	115283.i	−0.774351	+	0.774351i	−0.978864	−	0.204513i	$-0.934439\pi$
$53$	−115283.	+	115283.i	−0.774351	+	0.774351i	0.204513	+	0.978864i	$0.434439\pi$
$54$	109545.	−	113114.i	0.695682	−	0.718350i
$55$	28621.7	+	199918.i	0.172031	+	1.20161i
$56$	−368.673	+	229.731i	−0.00209932	+	0.00130814i
$57$	−130178.	−	174275.i	−0.702932	−	0.941047i
$58$	318768.	−	153020.i	1.63377	−	0.784269i
$59$			324963.i			1.58226i	0.611647	+	0.791131i	$0.290507\pi$
$59$			324963.i			1.58226i	−0.611647	+	0.791131i	$0.709493\pi$
$60$	23296.2	+	214740.i	0.107853	+	0.994167i
$61$	172561.			0.760243			0.380121	−	0.924937i	$-0.375882\pi$
$61$	172561.			0.760243			0.380121	+	0.924937i	$0.375882\pi$
$62$	51024.7	+	106293.i	0.214095	+	0.445996i
$63$	−543.460	+	295.285i	−0.00217343	+	0.00118092i
$64$	−235325.	−	115506.i	−0.897693	−	0.440622i
$65$	−126806.	+	169182.i	−0.461743	+	0.616047i
$66$	−309272.	−	161675.i	−1.07574	−	0.562354i
$67$	99096.4	+	99096.4i	0.329483	+	0.329483i	0.852390	−	0.522907i	$-0.175152\pi$
$67$	99096.4	+	99096.4i	0.329483	+	0.329483i	−0.522907	+	0.852390i	$0.675152\pi$
$68$	133718.	−	14728.3i	0.425269	−	0.0468411i
$69$	−15244.8	+	105252.i	−0.0464059	+	0.320393i
$70$	164.935	−	832.236i	0.000480859	−	0.00242634i
$71$	114765.			0.320651			0.160326	−	0.987064i	$-0.448746\pi$
$71$	114765.			0.320651			0.160326	+	0.987064i	$0.448746\pi$
$72$	−324683.	−	184106.i	−0.869886	−	0.493254i
$73$	93737.6	+	93737.6i	0.240960	+	0.240960i	0.817247	−	0.576287i	$-0.195499\pi$
$73$	93737.6	+	93737.6i	0.240960	+	0.240960i	−0.576287	+	0.817247i	$0.695499\pi$
$74$	83518.3	−	237729.i	0.206104	−	0.586660i
$75$	−337162.	−	253576.i	−0.799198	−	0.601068i
$76$	−322490.	+	402324.i	−0.734641	+	0.916506i
$77$	969.271	+	969.271i	0.00212311	+	0.00212311i
$78$	−109262.	−	348629.i	−0.230243	−	0.734648i
$79$	95504.0			0.193705			0.0968524	−	0.995299i	$-0.469123\pi$
$79$	95504.0			0.193705			0.0968524	+	0.995299i	$0.469123\pi$
$80$	478889.	−	181133.i	0.935330	−	0.353776i
$81$	−445877.	−	289177.i	−0.838996	−	0.544138i
$82$	−246153.	−	512779.i	−0.446441	−	0.930013i
$83$	80011.9	+	80011.9i	0.139933	+	0.139933i	0.773603	−	0.633670i	$-0.218452\pi$
$83$	80011.9	+	80011.9i	0.139933	+	0.139933i	−0.633670	+	0.773603i	$0.718452\pi$
$84$	1000.68	+	1071.45i	0.00168834	+	0.00180773i
$85$	−157585.	+	210246.i	−0.256601	+	0.342351i
$86$	−288991.	+	822594.i	−0.454349	+	1.29327i
$87$	−714169.	−	956091.i	−1.08453	−	1.45192i
$88$	−187092.	+	805779.i	−0.274542	+	1.18241i
$89$	1.00047e6			1.41917			0.709584	−	0.704621i	$-0.248883\pi$
$89$	1.00047e6			1.41917			0.709584	+	0.704621i	$0.248883\pi$
$90$	695993.	−	216876.i	0.954723	−	0.297498i
$91$			1435.05i			0.00190433i
$92$	250574.	−	27599.4i	0.321790	−	0.0354435i
$93$	318809.	−	238140.i	0.396353	−	0.296063i
$94$	−386462.	+	1.10004e6i	−0.465289	+	1.32441i
$95$	−142724.	−	996907.i	−0.166466	−	1.16274i
$96$	−229400.	+	854478.i	−0.259287	+	0.965800i
$97$	−7526.89	+	7526.89i	−0.00824709	+	0.00824709i	−0.711218	−	0.702971i	$-0.751856\pi$
$97$	−7526.89	+	7526.89i	−0.00824709	+	0.00824709i	0.702971	+	0.711218i	$0.251856\pi$
$98$	407306.	+	848489.i	0.432756	+	0.901504i
$99$	−334179.	+	1.12941e6i	−0.344408	+	1.16398i
$100$	−381386.	+	924416.i	−0.381386	+	0.924416i
$101$			1.16386e6i			1.12963i	0.825216	+	0.564817i	$0.191053\pi$
$101$			1.16386e6i			1.12963i	−0.825216	+	0.564817i	$0.808947\pi$
$102$	−135783.	−	433249.i	−0.127951	−	0.408261i
$103$	374863.	−	374863.i	0.343053	−	0.343053i	−0.514461	−	0.857514i	$-0.672008\pi$
$103$	374863.	−	374863.i	0.343053	−	0.343053i	0.857514	+	0.514461i	$0.172008\pi$
$104$	−734996.	+	457997.i	−0.653408	+	0.407158i
$105$	−2863.42	−	4.69486i	−0.00247353	−	4.05560e-6i
$106$	432313.	−	1.23055e6i	0.362978	−	1.03319i
$107$	843146.	−	843146.i	0.688258	−	0.688258i	−0.273589	−	0.961847i	$-0.588211\pi$
$107$	843146.	−	843146.i	0.688258	−	0.688258i	0.961847	+	0.273589i	$0.0882106\pi$
$108$	−398437.	+	1.19504e6i	−0.316292	+	0.948662i
$109$		−	1.04553e6i		−	0.807340i	−0.914905	−	0.403670i	$-0.867734\pi$
$109$		−	1.04553e6i		−	0.807340i	0.914905	−	0.403670i	$-0.132266\pi$
$110$	−898552.	−	1.34274e6i	−0.675095	−	1.00882i
$111$	−841626.	−	121902.i	−0.615390	−	0.0891334i
$112$	1863.56	−	2933.21i	0.00132644	−	0.00208780i
$113$	1.98519e6	−	1.98519e6i	1.37583	−	1.37583i	0.524298	−	0.851535i	$-0.324328\pi$
$113$	1.98519e6	−	1.98519e6i	1.37583	−	1.37583i	0.851535	−	0.524298i	$-0.175672\pi$
$114$	1.54221e6	+	806202.i	1.04095	+	0.544163i
$115$	−295298.	+	393980.i	−0.194163	+	0.259048i
$116$	−1.76921e6	+	2.20719e6i	−1.13346	+	1.41405i
$117$	−1.08345e6	+	588687.i	−0.676477	+	0.367559i
$118$	−1.12505e6	−	2.34366e6i	−0.684737	−	1.42643i
$119$			1783.37i			0.00105828i
$120$	−911458.	−	1.46807e6i	−0.527464	−	0.849577i
$121$	838775.			0.473467
$122$	−1.24452e6	+	597417.i	−0.685366	+	0.329001i
$123$	−1.53800e6	+	1.14883e6i	−0.826495	+	0.617365i
$124$	−735989.	−	589944.i	−0.386017	−	0.309418i
$125$	−808163.	−	1.77808e6i	−0.413780	−	0.910377i
$126$	2897.18	−	4011.11i	0.00144832	−	0.00200518i
$127$	2.51301e6	+	2.51301e6i	1.22682	+	1.22682i	0.965158	+	0.261667i	$0.0842721\pi$
$127$	2.51301e6	+	2.51301e6i	1.22682	+	1.22682i	0.261667	+	0.965158i	$0.415728\pi$
$128$	2.09707e6	+	18330.7i	0.999962	+	0.00874075i
$129$	2.91221e6	+	421806.i	1.35661	+	0.196491i
$130$	328817.	−	1.65916e6i	0.149666	−	0.755195i
$131$	−3.13077e6			−1.39263			−0.696317	−	0.717734i	$-0.745179\pi$
$131$	−3.13077e6			−1.39263			−0.696317	+	0.717734i	$0.745179\pi$
$132$	2.79022e6	+	95289.2i	1.21316	+	0.0414307i
$133$	−4833.34	−	4833.34i	−0.00205443	−	0.00205443i
$134$	−1.05777e6	−	371613.i	−0.439619	−	0.154446i
$135$	−1.17109e6	−	2.16379e6i	−0.475980	−	0.879456i
$136$	−913397.	+	569164.i	−0.363114	+	0.226267i
$137$	772836.	+	772836.i	0.300556	+	0.300556i	0.841231	−	0.540675i	$-0.181831\pi$
$137$	772836.	+	772836.i	0.300556	+	0.300556i	−0.540675	+	0.841231i	$0.681831\pi$
$138$	−254443.	−	811864.i	−0.0968174	−	0.308920i
$139$	4.23049e6			1.57524			0.787620	−	0.616162i	$-0.211313\pi$
$139$	4.23049e6			1.57524			0.787620	+	0.616162i	$0.211313\pi$
$140$	1691.74	+	6573.17i	0.000616522	+	0.00239547i
$141$	3.89443e6	+	564072.i	1.38927	+	0.201223i
$142$	−827692.	+	397323.i	−0.289070	+	0.138765i
$143$	1.93236e6	+	1.93236e6i	0.660815	+	0.660815i
$144$	2.97903e6	+	203712.i	0.997670	+	0.0682227i
$145$	−782998.	−	5.46913e6i	−0.256836	−	1.79396i
$146$	−1.00057e6	−	351517.i	−0.321506	−	0.112950i
$147$	2.54490e6	−	1.90096e6i	0.801159	−	0.598441i
$148$	220693.	+	2.00367e6i	0.0680774	+	0.618073i
$149$	−3.44585e6			−1.04169			−0.520844	−	0.853652i	$-0.674383\pi$
$149$	−3.44585e6			−1.04169			−0.520844	+	0.853652i	$0.674383\pi$
$150$	3.30953e6	+	661532.i	0.980602	+	0.196010i
$151$			8492.50i			0.00246663i	0.999999	+	0.00123332i	$0.000392577\pi$
$151$			8492.50i			0.00246663i	−0.999999	+	0.00123332i	$0.999607\pi$
$152$	932950.	−	4.01808e6i	0.265661	−	1.14416i
$153$	−1.34643e6	+	731575.i	−0.375933	+	0.204261i
$154$	−10346.1	−	3634.78i	−0.00283280	−	0.000995212i
$155$	1.82368e6	−	261091.i	0.489727	−	0.0701127i
$156$	1.99498e6	+	2.13606e6i	0.525492	+	0.562653i
$157$	−3.21055e6	+	3.21055e6i	−0.829623	+	0.829623i	−0.987464	−	0.157842i	$-0.949546\pi$
$157$	−3.21055e6	+	3.21055e6i	−0.829623	+	0.829623i	0.157842	+	0.987464i	$0.449546\pi$
$158$	−688783.	+	330641.i	−0.174627	+	0.0838274i
$159$	−4.35648e6	−	630995.i	−1.08379	−	0.156976i
$160$	−2.82669e6	+	2.96429e6i	−0.690110	+	0.723705i
$161$			3341.85i			0.000800773i
$162$	4.21685e6	+	541912.i	0.991843	+	0.127463i
$163$	2.64827e6	−	2.64827e6i	0.611505	−	0.611505i	−0.331833	−	0.943338i	$-0.607667\pi$
$163$	2.64827e6	−	2.64827e6i	0.611505	−	0.611505i	0.943338	+	0.331833i	$0.107667\pi$
$164$	3.55055e6	+	2.84601e6i	0.804942	+	0.645215i
$165$	−3.86205e6	+	3.84941e6i	−0.859738	+	0.856923i
$166$	−854059.	−	300046.i	−0.186708	−	0.0655938i
$167$	−4.80902e6	+	4.80902e6i	−1.03254	+	1.03254i	−0.0330880	+	0.999452i	$0.510534\pi$
$167$	−4.80902e6	+	4.80902e6i	−1.03254	+	1.03254i	−0.999452	+	0.0330880i	$0.989466\pi$
$168$	−10926.4	−	4262.94i	−0.00230436	−	0.000899046i
$169$		−	1.96586e6i		−	0.407280i
$170$	408629.	−	2.06188e6i	0.0831730	−	0.419679i
$171$	1.66641e6	−	5.63188e6i	0.333267	−	1.12633i
$172$	−763645.	−	6.93312e6i	−0.150074	−	1.36252i
$173$	−1.65427e6	+	1.65427e6i	−0.319499	+	0.319499i	−0.848575	−	0.529076i	$-0.822539\pi$
$173$	−1.65427e6	+	1.65427e6i	−0.319499	+	0.319499i	0.529076	+	0.848575i	$0.322539\pi$
$174$	8.46070e6	+	4.42290e6i	1.60605	+	0.839575i
$175$	−11627.4	−	6367.14i	−0.00216955	−	0.00118804i
$176$	−1.44034e6	−	6.45907e6i	−0.264196	−	1.18476i
$177$	−7.02943e6	+	5.25076e6i	−1.26765	+	0.946896i
$178$	−7.21547e6	+	3.46369e6i	−1.27939	+	0.614157i
$179$		−	1.57611e6i		−	0.274806i	−0.990515	−	0.137403i	$-0.956124\pi$
$179$		−	1.57611e6i		−	0.274806i	0.990515	−	0.137403i	$-0.0438756\pi$
$180$	−4.26872e6	+	3.97370e6i	−0.731947	+	0.681361i
$181$	4.78416e6			0.806807			0.403404	−	0.915022i	$-0.367827\pi$
$181$	4.78416e6			0.806807			0.403404	+	0.915022i	$0.367827\pi$
$182$	−4968.24	−	10349.7i	−0.000824115	−	0.00171677i
$183$	2.78823e6	+	3.73274e6i	0.454963	+	0.609079i
$184$	−1.71161e6	+	1.06655e6i	−0.274759	+	0.171210i
$185$	−3.15038e6	−	2.36129e6i	−0.497562	−	0.372936i
$186$	−1.47482e6	+	2.82122e6i	−0.229192	+	0.438429i
$187$	2.40139e6	+	2.40139e6i	0.367230	+	0.367230i
$188$	−1.02121e6	−	9.27151e6i	−0.153688	−	1.39533i
$189$	−15168.7	−	6984.60i	−0.00224679	−	0.00103456i
$190$	4.48069e6	+	6.69565e6i	0.653258	+	0.976185i
$191$	−6.12773e6			−0.879426			−0.439713	−	0.898138i	$-0.644920\pi$
$191$	−6.12773e6			−0.879426			−0.439713	+	0.898138i	$0.644920\pi$
$192$	−1.30381e6	−	6.95677e6i	−0.184209	−	0.982887i
$193$	9.47378e6	+	9.47378e6i	1.31781	+	1.31781i	0.915510	+	0.402295i	$0.131787\pi$
$193$	9.47378e6	+	9.47378e6i	1.31781	+	1.31781i	0.402295	+	0.915510i	$0.368213\pi$
$194$	28225.9	−	80343.2i	0.00386584	−	0.0110038i
$195$	−5.70858e6	−	9359.78i	−0.769882	−	0.00126230i
$196$	−5.87505e6	−	4.70925e6i	−0.780267	−	0.625437i
$197$	−578366.	−	578366.i	−0.0756492	−	0.0756492i	0.668270	−	0.743919i	$-0.267035\pi$
$197$	−578366.	−	578366.i	−0.0756492	−	0.0756492i	−0.743919	+	0.668270i	$0.767035\pi$
$198$	−1.49996e6	−	9.30233e6i	−0.193235	−	1.19839i
$199$	−7.73224e6			−0.981174			−0.490587	−	0.871392i	$-0.663218\pi$
$199$	−7.73224e6			−0.981174			−0.490587	+	0.871392i	$0.663218\pi$
$200$	−449808.	−	7.98734e6i	−0.0562260	−	0.998418i
$201$	−542398.	+	3.74480e6i	−0.0667929	+	0.461148i
$202$	−4.02937e6	−	8.39387e6i	−0.488859	−	1.01838i
$203$	−26516.2	−	26516.2i	−0.00316973	−	0.00316973i
$204$	2.47922e6	+	2.65454e6i	0.292028	+	0.312679i
$205$	−8.79780e6	+	1.25955e6i	−1.02120	+	0.146203i
$206$	−1.40574e6	+	4.00134e6i	−0.160806	+	0.457724i
$207$	−2.52308e6	+	1.37090e6i	−0.284459	+	0.154559i
$208$	3.71523e6	−	5.84771e6i	0.412853	−	0.649825i
$209$	−1.30166e7			−1.42580
$210$	20667.5	−	9879.49i	0.00223167	−	0.00106678i
$211$			9.43925e6i			1.00482i	0.864628	+	0.502412i	$0.167554\pi$
$211$			9.43925e6i			1.00482i	−0.864628	+	0.502412i	$0.832446\pi$
$212$	1.14237e6	+	1.03715e7i	0.119894	+	1.08851i
$213$	1.85437e6	+	2.48252e6i	0.191892	+	0.256894i
$214$	−3.16181e6	+	8.99986e6i	−0.322622	+	0.918321i
$215$	1.09010e7	+	8.17058e6i	1.09686	+	0.822124i
$216$	−1.26375e6	−	9.99814e6i	−0.125401	−	0.992106i
$217$	8841.83	−	8841.83i	0.000865292	−	0.000865292i
$218$	3.61969e6	+	7.54044e6i	0.349383	+	0.727825i
$219$	−513067.	+	3.54229e6i	−0.0488475	+	0.337250i
$220$	1.11291e7	+	6.57307e6i	1.04518	+	0.617306i
$221$			3.55537e6i			0.329388i
$222$	6.49191e6	−	2.03460e6i	0.593353	−	0.185960i
$223$	4.11544e6	−	4.11544e6i	0.371109	−	0.371109i	−0.496772	−	0.867881i	$-0.665482\pi$
$223$	4.11544e6	−	4.11544e6i	0.371109	−	0.371109i	0.867881	+	0.496772i	$0.165482\pi$
$224$	−3285.16	+	27606.3i	−0.000292289	+	0.00245620i
$225$	37352.0	−	1.13906e7i	0.00327919	−	0.999995i
$226$	−7.44447e6	+	2.11902e7i	−0.644924	+	1.83573i
$227$	1.65247e6	−	1.65247e6i	0.141272	−	0.141272i	−0.632934	−	0.774206i	$-0.718150\pi$
$227$	1.65247e6	−	1.65247e6i	0.141272	−	0.141272i	0.774206	+	0.632934i	$0.218150\pi$
$228$	−1.39136e7	−	475167.i	−1.17391	−	0.0400905i
$229$		−	1.53321e7i		−	1.27672i	−0.769737	−	0.638361i	$-0.779613\pi$
$229$		−	1.53321e7i		−	1.27672i	0.769737	−	0.638361i	$-0.220387\pi$
$230$	765729.	−	3.86376e6i	0.0629349	−	0.317560i
$231$	−5305.25	+	36628.2i	−0.000430397	+	0.00297153i
$232$	5.11825e6	−	2.20436e7i	0.409881	−	1.76530i
$233$	2.39606e6	−	2.39606e6i	0.189421	−	0.189421i	−0.606025	−	0.795446i	$-0.707237\pi$
$233$	2.39606e6	−	2.39606e6i	0.189421	−	0.189421i	0.795446	+	0.606025i	$0.207237\pi$
$234$	5.77588e6	−	7.99664e6i	0.450786	−	0.624109i
$235$	1.45777e7	+	1.09263e7i	1.12327	+	0.841920i
$236$	1.62278e7	+	1.30077e7i	1.23459	+	0.989611i
$237$	1.54315e6	+	2.06589e6i	0.115922	+	0.155189i
$238$	−6174.15	−	12861.8i	−0.000457979	−	0.000954050i
$239$		−	1.71764e7i		−	1.25817i	−0.777338	−	0.629083i	$-0.783431\pi$
$239$		−	1.71764e7i		−	1.25817i	0.777338	−	0.629083i	$-0.216569\pi$
$240$	1.16561e7	+	7.43231e6i	0.843176	+	0.537638i
$241$	9.85684e6			0.704185			0.352092	−	0.935965i	$-0.385470\pi$
$241$	9.85684e6			0.704185			0.352092	+	0.935965i	$0.385470\pi$
$242$	−6.04931e6	+	2.90389e6i	−0.426835	+	0.204897i
$243$	−949164.	−	1.43175e7i	−0.0661488	−	0.997810i
$244$	6.90729e6	−	8.61723e6i	0.475487	−	0.593196i
$245$	1.45576e7	−	2.08417e6i	0.989900	−	0.141721i
$246$	7.11481e6	−	1.36101e7i	0.477923	−	0.914233i
$247$	−9.63585e6	−	9.63585e6i	−0.639439	−	0.639439i
$248$	7.35044e6	+	1.70668e6i	0.481901	+	0.111892i
$249$	−437940.	+	3.02360e6i	−0.0283672	+	0.195851i
$250$	1.19844e7	+	1.00257e7i	0.767000	+	0.641647i
$251$	2.07654e7			1.31316			0.656581	−	0.754255i	$-0.272002\pi$
$251$	2.07654e7			1.31316			0.656581	+	0.754255i	$0.272002\pi$
$252$	−7007.94	+	38958.7i	−0.000437914	+	0.00243446i
$253$	4.49996e6	+	4.49996e6i	0.277873	+	0.277873i
$254$	−2.68242e7	−	9.42381e6i	−1.63691	−	0.575076i
$255$	−7.09419e6	−	11631.6i	−0.427841	−	0.000701487i
$256$	−1.51877e7	+	7.12800e6i	−0.905258	+	0.424862i
$257$	1.55440e7	+	1.55440e7i	0.915719	+	0.915719i	0.996714	−	0.0809953i	$-0.0258099\pi$
$257$	1.55440e7	+	1.55440e7i	0.915719	+	0.915719i	−0.0809953	+	0.996714i	$0.525810\pi$
$258$	−2.24634e7	+	7.04017e6i	−1.30803	+	0.409943i
$259$	−26722.4			−0.00153807
$260$	3.37268e6	+	1.31044e7i	0.191891	+	0.745585i
$261$	9.14207e6	−	3.08970e7i	0.514189	−	1.73778i
$262$	2.25794e7	−	1.08389e7i	1.25547	−	0.602674i
$263$	−1.26544e7	−	1.26544e7i	−0.695626	−	0.695626i	0.267838	−	0.963464i	$-0.413691\pi$
$263$	−1.26544e7	−	1.26544e7i	−0.695626	−	0.695626i	−0.963464	+	0.267838i	$0.913691\pi$
$264$	−2.04532e7	+	8.97270e6i	−1.11160	+	0.487654i
$265$	−1.63072e7	−	1.22227e7i	−0.876278	−	0.656793i
$266$	51591.8	+	18125.1i	0.00274117	+	0.000963019i
$267$	1.61656e7	+	2.16416e7i	0.849293	+	1.13699i
$268$	8.91527e6	−	981968.i	0.463159	−	0.0510144i
$269$	1.66962e7			0.857750			0.428875	−	0.903364i	$-0.358910\pi$
$269$	1.66962e7			0.857750			0.428875	+	0.903364i	$0.358910\pi$
$270$	1.59372e7	+	1.15510e7i	0.809693	+	0.586854i
$271$		−	2.41519e7i		−	1.21351i	−0.794888	−	0.606756i	$-0.792471\pi$
$271$		−	2.41519e7i		−	1.21351i	0.794888	−	0.606756i	$-0.207529\pi$
$272$	4.61701e6	−	7.26709e6i	0.229432	−	0.361122i
$273$	−31042.2	+	23187.5i	−0.00152568	+	0.00113964i
$274$	−8.24936e6	−	2.89814e6i	−0.401022	−	0.140886i
$275$	−2.42305e7	+	7.08319e6i	−1.16510	+	0.340589i
$276$	4.64579e6	+	4.97433e6i	0.220970	+	0.236596i
$277$	−2.17898e7	+	2.17898e7i	−1.02521	+	1.02521i	−0.0255392	+	0.999674i	$0.508130\pi$
$277$	−2.17898e7	+	2.17898e7i	−1.02521	+	1.02521i	−0.999674	+	0.0255392i	$0.991870\pi$
$278$	−3.05107e7	+	1.46462e7i	−1.42009	+	0.681698i
$279$	1.03026e7	+	3.04843e6i	0.474390	+	0.140366i
$280$	−34957.7	−	41549.3i	−0.00159246	−	0.00189273i
$281$		−	1.94502e7i		−	0.876606i	−0.898827	−	0.438303i	$-0.855580\pi$
$281$		−	1.94502e7i		−	0.876606i	0.898827	−	0.438303i	$-0.144420\pi$
$282$	−3.00398e7	+	9.41466e6i	−1.33952	+	0.419814i
$283$	6.69520e6	−	6.69520e6i	0.295396	−	0.295396i	−0.543812	−	0.839207i	$-0.683019\pi$
$283$	6.69520e6	−	6.69520e6i	0.295396	−	0.295396i	0.839207	+	0.543812i	$0.183019\pi$
$284$	4.59382e6	−	5.73105e6i	0.200548	−	0.250195i
$285$	1.92584e7	−	1.91953e7i	0.831927	−	0.829204i
$286$	−2.06263e7	−	7.24637e6i	−0.881705	−	0.309758i
$287$	−42654.7	+	42654.7i	−0.00180435	+	0.00180435i
$288$	−2.21902e7	+	8.84441e6i	−0.928933	+	0.370247i
$289$		−	1.97192e7i		−	0.816952i
$290$	2.45815e7	+	3.67330e7i	1.00789	+	1.50613i
$291$	−284437.	−	41198.0i	−0.0115427	−	0.00167185i
$292$	8.43316e6	−	928867.i	0.338721	−	0.0373082i
$293$	5.52664e6	−	5.52664e6i	0.219714	−	0.219714i	−0.588664	−	0.808378i	$-0.700346\pi$
$293$	5.52664e6	−	5.52664e6i	0.219714	−	0.219714i	0.808378	+	0.588664i	$0.200346\pi$
$294$	−1.17728e7	+	2.25205e7i	−0.463273	+	0.886209i
$295$	−4.02104e7	+	5.75680e6i	−1.56629	+	0.224241i
$296$	−8.52848e6	−	1.36865e7i	−0.328849	−	0.527738i
$297$	−2.98304e7	+	1.10202e7i	−1.13865	+	0.420650i
$298$	2.48518e7	−	1.19298e7i	0.939093	−	0.450799i
$299$			6.66239e6i			0.249239i
$300$	−2.61589e7	+	6.68680e6i	−0.968847	+	0.247659i
$301$	92465.4			0.00339062
$302$	−29401.6	−	61248.6i	−0.00106746	−	0.00222369i
$303$	−2.51760e7	+	1.88057e7i	−0.905022	+	0.676023i
$304$	7.18234e6	+	3.22086e7i	0.255650	+	1.14644i
$305$	3.05695e6	+	2.13524e7i	0.107743	+	0.752569i
$306$	7.17783e6	−	9.93762e6i	0.250512	−	0.346831i
$307$	8.36640e6	+	8.36640e6i	0.289150	+	0.289150i	0.836744	−	0.547594i	$-0.184456\pi$
$307$	8.36640e6	+	8.36640e6i	0.289150	+	0.289150i	−0.547594	+	0.836744i	$0.684456\pi$
$308$	87201.0	−	9604.72i	0.00298448	−	0.000328725i
$309$	1.41659e7	+	2.05179e6i	0.480139	+	0.0695436i
$310$	−1.22486e7	+	8.19672e6i	−0.411152	+	0.275141i
$311$	4.44318e7			1.47711			0.738555	−	0.674194i	$-0.235509\pi$
$311$	4.44318e7			1.47711			0.738555	+	0.674194i	$0.235509\pi$
$312$	−2.17832e7	−	8.49870e6i	−0.717229	−	0.279826i
$313$	3.42027e7	+	3.42027e7i	1.11539	+	1.11539i	0.992409	+	0.122982i	$0.0392456\pi$
$313$	3.42027e7	+	3.42027e7i	1.11539	+	1.11539i	0.122982	+	0.992409i	$0.460754\pi$
$314$	1.20396e7	−	3.42699e7i	0.388887	−	1.10694i
$315$	−46165.6	−	62015.8i	−0.00147702	−	0.00198413i
$316$	3.82285e6	−	4.76922e6i	0.121151	−	0.151142i
$317$	1.14784e7	+	1.14784e7i	0.360333	+	0.360333i	0.863935	−	0.503603i	$-0.167992\pi$
$317$	1.14784e7	+	1.14784e7i	0.360333	+	0.360333i	−0.503603	+	0.863935i	$0.667992\pi$
$318$	3.36038e7	−	1.05316e7i	1.04498	−	0.327503i
$319$	−7.14105e7			−2.19983
$320$	1.01237e7	−	3.11649e7i	0.308952	−	0.951078i
$321$	3.18620e7	+	4.61491e6i	0.963292	+	0.139524i
$322$	−11569.7	−	24101.7i	−0.000346541	−	0.000721905i
$323$	−1.19747e7	−	1.19747e7i	−0.355351	−	0.355351i
$324$	−3.22884e7	+	1.06907e7i	−0.949317	+	0.314319i
$325$	−2.31807e7	−	1.26937e7i	−0.675268	−	0.369775i
$326$	−9.93106e6	+	2.82681e7i	−0.286644	+	0.815912i
$327$	2.26163e7	−	1.68936e7i	0.646812	−	0.483148i
$328$	−3.54599e7	−	8.23338e6i	−1.00489	−	0.233322i
$329$	123652.			0.00347227
$330$	1.45265e7	−	4.11329e7i	0.404222	−	1.14458i
$331$		−	1.74095e7i		−	0.480067i	−0.970765	−	0.240033i	$-0.922842\pi$
$331$		−	1.74095e7i		−	0.480067i	0.970765	−	0.240033i	$-0.0771584\pi$
$332$	7.19832e6	−	792855.i	0.196706	−	0.0216660i
$333$	−1.09621e7	−	2.01753e7i	−0.296866	−	0.546370i
$334$	1.80339e7	−	5.13322e7i	0.484005	−	1.37769i
$335$	−1.05065e7	+	1.40175e7i	−0.279463	+	0.372853i
$336$	93560.9	−	7083.37i	0.00246647	−	0.000186733i
$337$	−2.80540e7	+	2.80540e7i	−0.733002	+	0.733002i	−0.971213	−	0.238211i	$-0.923439\pi$
$337$	−2.80540e7	+	2.80540e7i	−0.733002	+	0.733002i	0.238211	+	0.971213i	$0.423439\pi$
$338$	6.80595e6	+	1.41780e7i	0.176254	+	0.367167i
$339$	7.50190e7	+	1.08658e7i	1.92563	+	0.278909i
$340$	4.19131e6	+	1.62852e7i	0.106638	+	0.414339i
$341$		−	2.38119e7i		−	0.600524i
$342$	7.47968e6	+	4.63868e7i	0.186984	+	1.15962i
$343$	141161.	−	141161.i	0.00349809	−	0.00349809i
$344$	2.95104e7	+	4.73584e7i	0.724936	+	1.16338i
$345$	−1.32938e7	−	21796.5i	−0.323736	−	0.000530797i
$346$	6.20355e6	−	1.76580e7i	0.149766	−	0.426297i
$347$	1.14893e7	−	1.14893e7i	0.274981	−	0.274981i	−0.556120	−	0.831102i	$-0.687711\pi$
$347$	1.14893e7	−	1.14893e7i	0.274981	−	0.274981i	0.831102	+	0.556120i	$0.187711\pi$
$348$	−7.63316e7	−	2.60681e6i	−1.81120	−	0.0618545i
$349$			1.47481e7i			0.346944i	0.984839	+	0.173472i	$0.0554987\pi$
$349$			1.47481e7i			0.346944i	−0.984839	+	0.173472i	$0.944501\pi$
$350$	105901.	+	5665.47i	0.00247000	+	0.000132139i
$351$	−3.02406e7	−	1.39247e7i	−0.699308	−	0.322005i
$352$	3.27496e7	+	4.15968e7i	0.750892	+	0.953744i
$353$	−4.75457e7	+	4.75457e7i	−1.08090	+	1.08090i	−0.0844789	+	0.996425i	$0.526923\pi$
$353$	−4.75457e7	+	4.75457e7i	−1.08090	+	1.08090i	−0.996425	+	0.0844789i	$0.973077\pi$
$354$	3.25183e7	−	6.22052e7i	0.733024	−	1.40222i
$355$	2.03308e6	+	1.42008e7i	0.0454433	+	0.317415i
$356$	4.00470e7	−	4.99609e7i	0.887605	−	1.10734i
$357$	−38576.9	+	28815.7i	−0.000847856	+	0.000633322i
$358$	5.45659e6	+	1.13670e7i	0.118925	+	0.247740i
$359$			3.78272e7i			0.817563i	0.912632	+	0.408782i	$0.134046\pi$
$359$			3.78272e7i			0.817563i	−0.912632	+	0.408782i	$0.865954\pi$
$360$	1.70291e7	−	4.34372e7i	0.364993	−	0.931010i
$361$	1.78625e7			0.379682
$362$	−3.45037e7	+	1.65631e7i	−0.727345	+	0.349153i
$363$	1.35529e7	+	1.81439e7i	0.283343	+	0.379325i
$364$	71662.6	+	57442.4i	0.00148590	+	0.00119105i
$365$	−9.93835e6	+	1.32595e7i	−0.204379	+	0.272677i
$366$	−3.30320e7	−	1.72677e7i	−0.673738	−	0.352202i
$367$	−2.91579e7	−	2.91579e7i	−0.589873	−	0.589873i	0.347724	−	0.937597i	$-0.386955\pi$
$367$	−2.91579e7	−	2.91579e7i	−0.589873	−	0.589873i	−0.937597	+	0.347724i	$0.886955\pi$
$368$	8.65179e6	−	1.36178e7i	0.173605	−	0.273252i
$369$	−4.97019e7	−	1.47062e7i	−0.989222	−	0.292699i
$370$	3.08957e7	+	6.12299e6i	0.609948	+	0.120881i
$371$	−138322.			−0.00270876
$372$	869242.	−	2.54528e7i	0.0168854	−	0.494433i
$373$	2.55995e7	+	2.55995e7i	0.493293	+	0.493293i	0.909342	−	0.416049i	$-0.136586\pi$
$373$	2.55995e7	+	2.55995e7i	0.493293	+	0.493293i	−0.416049	+	0.909342i	$0.636586\pi$
$374$	−2.56328e7	−	9.00524e6i	−0.489983	−	0.172140i
$375$	2.54041e7	−	4.62119e7i	0.481738	−	0.876315i
$376$	3.94636e7	+	6.33314e7i	0.742392	+	1.19139i
$377$	−5.28632e7	−	5.28632e7i	−0.986574	−	0.986574i
$378$	133579.	−	2141.41i	0.00247322	−	3.96482e-5i
$379$	4.59270e7			0.843626			0.421813	−	0.906683i	$-0.361394\pi$
$379$	4.59270e7			0.843626			0.421813	+	0.906683i	$0.361394\pi$
$380$	−5.54959e7	−	3.27771e7i	−1.01137	−	0.597337i
$381$	−1.37548e7	+	9.49651e7i	−0.248702	+	1.71707i
$382$	4.41937e7	−	2.12146e7i	0.792812	−	0.380579i
$383$	−1.32825e7	−	1.32825e7i	−0.236419	−	0.236419i	0.578946	−	0.815366i	$-0.303464\pi$
$383$	−1.32825e7	−	1.32825e7i	−0.236419	−	0.236419i	−0.815366	+	0.578946i	$0.803464\pi$
$384$	3.34880e7	+	4.56589e7i	0.591419	+	0.806365i
$385$	−102765.	+	137107.i	−0.00180079	+	0.00240257i
$386$	−1.01124e8	−	3.55268e7i	−1.75831	−	0.617723i
$387$	3.79312e7	+	6.98108e7i	0.654431	+	1.20445i
$388$	74585.6	+	677161.i	0.00127691	+	0.0115930i
$389$	−6.35778e7			−1.08008			−0.540041	−	0.841639i	$-0.681591\pi$
$389$	−6.35778e7			−1.08008			−0.540041	+	0.841639i	$0.681591\pi$
$390$	4.12031e7	−	1.96960e7i	0.694603	−	0.332035i
$391$			8.27951e6i			0.138508i
$392$	5.86751e7	+	1.36236e7i	0.974082	+	0.226170i
$393$	−5.05870e7	−	6.77230e7i	−0.833414	−	1.11573i
$394$	6.17357e6	+	2.16888e6i	0.100936	+	0.0354607i
$395$	1.69188e6	+	1.18175e7i	0.0274522	+	0.191750i
$396$	4.30232e7	+	6.18962e7i	0.692814	+	0.996732i
$397$	8.14220e7	−	8.14220e7i	1.30128	−	1.30128i	0.373747	−	0.927531i	$-0.378073\pi$
$397$	8.14220e7	−	8.14220e7i	1.30128	−	1.30128i	0.927531	−	0.373747i	$-0.121927\pi$
$398$	5.57655e7	−	2.67695e7i	0.884538	−	0.424611i
$399$	26455.0	−	182649.i	0.000416475	−	0.00287540i
$400$	3.08968e7	+	5.60481e7i	0.482762	+	0.875752i
$401$		−	1.74587e7i		−	0.270757i	−0.990794	−	0.135378i	$-0.956775\pi$
$401$		−	1.74587e7i		−	0.270757i	0.990794	−	0.135378i	$-0.0432250\pi$
$402$	−9.05292e6	−	2.88856e7i	−0.139351	−	0.444635i
$403$	1.76273e7	−	1.76273e7i	0.269321	−	0.269321i
$404$	5.81203e7	+	4.65873e7i	0.881422	+	0.706519i
$405$	2.78835e7	−	6.02949e7i	0.419741	−	0.907644i
$406$	283037.	+	99435.9i	0.00422927	+	0.00148582i
$407$	−3.59830e7	+	3.59830e7i	−0.533720	+	0.533720i
$408$	−2.70705e7	−	1.05615e7i	−0.398580	−	0.155506i
$409$		−	1.20214e7i		−	0.175706i	−0.996133	−	0.0878529i	$-0.971999\pi$
$409$		−	1.20214e7i		−	0.175706i	0.996133	−	0.0878529i	$-0.0280006\pi$
$410$	5.90898e7	−	3.95426e7i	0.857355	−	0.573738i
$411$	−4.23007e6	+	2.92050e7i	−0.0609287	+	0.420661i
$412$	−3.71460e6	−	3.37248e7i	−0.0531154	−	0.482233i
$413$	−194954.	+	194954.i	−0.00276746	+	0.00276746i
$414$	1.34505e7	−	1.86221e7i	0.189556	−	0.262438i
$415$	−8.48311e6	+	1.13180e7i	−0.118689	+	0.158352i
$416$	−6.54936e6	+	5.50366e7i	−0.0909744	+	0.764489i
$417$	6.83563e7	+	9.15116e7i	0.942693	+	1.26203i
$418$	9.38770e7	−	4.50644e7i	1.28538	−	0.617028i
$419$		−	8.74629e7i		−	1.18900i	−0.804096	−	0.594500i	$-0.797350\pi$
$419$		−	8.74629e7i		−	1.18900i	0.804096	−	0.594500i	$-0.202650\pi$
$420$	−114852.	+	142804.i	−0.00155021	+	0.00192749i
$421$	−9.89861e7			−1.32656			−0.663282	−	0.748370i	$-0.730837\pi$
$421$	−9.89861e7			−1.32656			−0.663282	+	0.748370i	$0.730837\pi$
$422$	−3.26793e7	−	6.80766e7i	−0.434846	−	0.905859i
$423$	5.07246e7	+	9.33565e7i	0.670189	+	1.23346i
$424$	−4.41457e7	−	7.08452e7i	−0.579150	−	0.929422i
$425$	−2.88072e7	−	1.57747e7i	−0.375261	−	0.205492i
$426$	−2.19685e7	−	1.14842e7i	−0.284166	−	0.148550i
$427$	103523.	+	103523.i	0.00132970	+	0.00132970i
$428$	−8.35492e6	−	7.58541e7i	−0.106564	−	0.967493i
$429$	−1.05767e7	+	7.30228e7i	−0.133960	+	0.924882i
$430$	−1.06906e8	−	2.11869e7i	−1.34461	−	0.266478i
$431$	−4.28205e7			−0.534836			−0.267418	−	0.963581i	$-0.586170\pi$
$431$	−4.28205e7			−0.534836			−0.267418	+	0.963581i	$0.586170\pi$
$432$	4.37285e7	+	6.77322e7i	0.542392	+	0.840125i
$433$	−4.69603e6	−	4.69603e6i	−0.0578452	−	0.0578452i	0.677592	−	0.735438i	$-0.263023\pi$
$433$	−4.69603e6	−	4.69603e6i	−0.0578452	−	0.0578452i	−0.735438	+	0.677592i	$0.763023\pi$
$434$	−33157.0	+	94379.0i	−0.000405607	+	0.00115453i
$435$	1.05653e8	−	1.05307e8i	1.28356	−	1.27936i
$436$	−5.22110e7	−	4.18506e7i	−0.629945	−	0.504943i
$437$	−2.24394e7	−	2.24394e7i	−0.268885	−	0.268885i
$438$	−8.56337e6	−	2.73236e7i	−0.101911	−	0.325173i
$439$	−8.97200e7			−1.06046			−0.530232	−	0.847853i	$-0.677895\pi$
$439$	−8.97200e7			−1.06046			−0.530232	+	0.847853i	$0.677895\pi$
$440$	−1.03020e8	−	8.87593e6i	−1.20938	−	0.104197i
$441$	8.22410e7	+	2.43342e7i	0.958899	+	0.283727i
$442$	−1.23089e7	−	2.56416e7i	−0.142545	−	0.296946i
$443$	5.66785e7	+	5.66785e7i	0.651940	+	0.651940i	0.953460	−	0.301520i	$-0.0974941\pi$
$443$	5.66785e7	+	5.66785e7i	0.651940	+	0.651940i	−0.301520	+	0.953460i	$0.597494\pi$
$444$	−3.97762e7	+	3.71491e7i	−0.454438	+	0.424424i
$445$	1.77235e7	+	1.23796e8i	0.201127	+	1.40484i
$446$	−1.54329e7	+	4.39288e7i	−0.173958	+	0.495159i
$447$	−5.56781e7	−	7.45388e7i	−0.623393	−	0.834564i
$448$	−71882.1	−	210472.i	−0.000799441	−	0.00234078i
$449$	1.34733e8			1.48845			0.744225	−	0.667929i	$-0.232819\pi$
$449$	1.34733e8			1.48845			0.744225	+	0.667929i	$0.232819\pi$
$450$	3.91655e7	+	8.22790e7i	0.429800	+	0.902924i
$451$			1.14873e8i			1.25224i
$452$	−1.96716e7	−	1.78598e8i	−0.213022	−	1.93403i
$453$	−183705.	+	137222.i	−0.00197618	+	0.00147614i
$454$	−6.19677e6	+	1.76387e7i	−0.0662213	+	0.188494i
$455$	−177571.	+	25422.2i	−0.00188511	+	0.000269885i
$456$	1.01991e8	−	4.47430e7i	1.07564	−	0.471879i
$457$	2.34970e6	−	2.34970e6i	0.0246186	−	0.0246186i	−0.694690	−	0.719309i	$-0.744459\pi$
$457$	2.34970e6	−	2.34970e6i	0.0246186	−	0.0246186i	0.719309	+	0.694690i	$0.244459\pi$
$458$	5.30809e7	+	1.10577e8i	0.552512	+	1.15098i
$459$	−3.75807e7	−	1.73045e7i	−0.388621	−	0.178946i
$460$	7.85408e6	+	3.05167e7i	0.0806904	+	0.313519i
$461$			7.44385e7i			0.759792i	0.925029	+	0.379896i	$0.124040\pi$
$461$			7.44385e7i			0.759792i	−0.925029	+	0.379896i	$0.875960\pi$
$462$	−88547.4	−	282533.i	−0.000897945	−	0.00286512i
$463$	2.48945e7	−	2.48945e7i	0.250819	−	0.250819i	−0.570488	−	0.821306i	$-0.693246\pi$
$463$	2.48945e7	−	2.48945e7i	0.250819	−	0.250819i	0.821306	+	0.570488i	$0.193246\pi$
$464$	3.94030e7	+	1.76700e8i	0.394435	+	1.76881i
$465$	3.51148e7	+	3.52302e7i	0.349246	+	0.350394i
$466$	−8.98524e6	+	2.55759e7i	−0.0887916	+	0.252739i
$467$	−9.02595e6	+	9.02595e6i	−0.0886221	+	0.0886221i	−0.750028	−	0.661406i	$-0.769960\pi$
$467$	−9.02595e6	+	9.02595e6i	−0.0886221	+	0.0886221i	0.661406	+	0.750028i	$0.269960\pi$
$468$	−1.39712e7	+	7.76689e7i	−0.136300	+	0.757722i
$469$			118901.i			0.00115257i
$470$	−1.42963e8	−	2.83327e7i	−1.37699	−	0.272895i
$471$	−1.21325e8	−	1.75728e7i	−1.16115	−	0.168181i
$472$	−1.62070e8	−	3.76307e7i	−1.54126	−	0.357863i
$473$	1.24509e8	−	1.24509e8i	1.17657	−	1.17657i
$474$	−1.82816e7	−	9.55686e6i	−0.171664	−	0.0897388i
$475$	1.20827e8	−	3.53209e7i	1.12741	−	0.329572i
$476$	89056.9	+	71385.1i	0.000825746	+	0.000661891i
$477$	−5.67427e7	−	1.04433e8i	−0.522823	−	0.962234i
$478$	5.94657e7	+	1.23877e8i	0.544482	+	1.13425i
$479$			1.01281e8i			0.921555i	0.887516	+	0.460777i	$0.152429\pi$
$479$			1.01281e8i			0.921555i	−0.887516	+	0.460777i	$0.847571\pi$
$480$	−1.09796e8	−	1.32483e7i	−0.992799	−	0.119794i
$481$	−5.32744e7			−0.478722
$482$	−7.10883e7	+	3.41250e7i	−0.634829	+	0.304742i
$483$	−72289.0	+	53997.6i	−0.000641551	+	0.000479218i
$484$	3.35746e7	−	4.18862e7i	0.296125	−	0.369433i
$485$	−1.06471e6	−	798025.i	−0.00933264	−	0.00699505i
$486$	5.64135e7	+	9.99727e7i	0.491444	+	0.870909i
$487$	−1.13209e8	−	1.13209e8i	−0.980155	−	0.980155i	0.0196516	−	0.999807i	$-0.493744\pi$
$487$	−1.13209e8	−	1.13209e8i	−0.980155	−	0.980155i	−0.999807	+	0.0196516i	$0.993744\pi$
$488$	−1.99825e7	+	8.60617e7i	−0.171945	+	0.740543i
$489$	1.00077e8	+	1.44952e7i	0.855868	+	0.123964i
$490$	−9.77750e7	+	6.54306e7i	−0.831074	+	0.556151i
$491$	−7.27558e7			−0.614643			−0.307322	−	0.951606i	$-0.599433\pi$
$491$	−7.27558e7			−0.614643			−0.307322	+	0.951606i	$0.599433\pi$
$492$	−4.19339e6	+	1.22789e8i	−0.0352103	+	1.03102i
$493$	−6.56944e7	−	6.56944e7i	−0.548261	−	0.548261i
$494$	1.02854e8	+	3.61346e7i	0.853183	+	0.299738i
$495$	−1.45671e8	−	2.13430e7i	−1.20104	−	0.175970i
$496$	−5.89206e7	+	1.31390e7i	−0.482861	+	0.107675i
$497$	68850.2	+	68850.2i	0.000560836	+	0.000560836i
$498$	−7.30946e6	−	2.33226e7i	−0.0591830	−	0.188838i
$499$	4.27956e7			0.344427			0.172213	−	0.985060i	$-0.444908\pi$
$499$	4.27956e7			0.344427			0.172213	+	0.985060i	$0.444908\pi$
$500$	−1.21142e8	−	3.08158e7i	−0.969136	−	0.246526i
$501$	−1.81730e8	−	2.63219e7i	−1.44515	−	0.209317i
$502$	−1.49762e8	+	7.18911e7i	−1.18383	+	0.568282i
$503$	−1.22024e8	−	1.22024e8i	−0.958828	−	0.958828i	0.0403569	−	0.999185i	$-0.487151\pi$
$503$	−1.22024e8	−	1.22024e8i	−0.958828	−	0.958828i	−0.999185	+	0.0403569i	$0.987151\pi$
$504$	−84335.8	−	305235.i	−0.000658749	−	0.00238420i
$505$	−1.44014e8	+	2.06181e7i	−1.11823	+	0.160094i
$506$	−4.80332e7	−	1.68749e7i	−0.370757	−	0.130254i
$507$	4.25245e7	−	3.17644e7i	0.326298	−	0.243734i
$508$	2.26084e8	−	2.49019e7i	1.72456	−	0.189951i
$509$	1.29997e8			0.985784			0.492892	−	0.870091i	$-0.335940\pi$
$509$	1.29997e8			0.985784			0.492892	+	0.870091i	$0.335940\pi$
$510$	5.12041e7	−	2.44767e7i	0.386006	−	0.184519i
$511$			112471.i			0.000842904i
$512$	8.48574e7	−	1.03989e8i	0.632237	−	0.774775i
$513$	1.48751e8	−	5.49531e7i	1.10182	−	0.407043i
$514$	−1.65919e8	−	5.82901e7i	−1.22182	−	0.429245i
$515$	5.30257e7	+	3.97441e7i	0.388208	+	0.290972i
$516$	1.37634e8	−	1.28544e8i	1.00179	−	0.935627i
$517$	1.66503e8	−	1.66503e8i	1.20490	−	1.20490i
$518$	192724.	−	92514.8i	0.00138659	−	0.000665613i
$519$	−6.25141e7	−	9.05457e6i	−0.447173	−	0.0647688i
$520$	−6.96924e7	−	8.28336e7i	−0.495650	−	0.589110i
$521$		−	4.60919e7i		−	0.325920i	−0.986633	−	0.162960i	$-0.947896\pi$
$521$		−	4.60919e7i		−	0.325920i	0.986633	−	0.162960i	$-0.0521042\pi$
$522$	4.10342e7	+	2.54482e8i	0.288493	+	1.78915i
$523$	9.73126e7	−	9.73126e7i	0.680243	−	0.680243i	−0.279812	−	0.960055i	$-0.590272\pi$
$523$	9.73126e7	−	9.73126e7i	0.680243	−	0.680243i	0.960055	+	0.279812i	$0.0902722\pi$
$524$	−1.25319e8	+	1.56343e8i	−0.871010	+	1.08663i
$525$	−50145.2	−	354398.i	−0.000346539	−	0.00244914i
$526$	1.35075e8	+	4.74543e7i	0.928151	+	0.326076i
$527$	2.19058e7	−	2.19058e7i	0.149668	−	0.149668i
$528$	1.16446e8	−	1.35522e8i	0.791085	−	0.920680i
$529$		−	1.32521e8i		−	0.895195i
$530$	1.59924e8	+	3.16942e7i	1.07421	+	0.212889i
$531$	−2.27163e8	−	6.72149e7i	−1.51724	−	0.448933i
$532$	−434834.	+	47894.6i	−0.00288794	+	0.000318091i
$533$	−8.50374e7	+	8.50374e7i	−0.561601	+	0.561601i
$534$	−1.91512e8	−	1.00115e8i	−1.25769	−	0.657466i
$535$	1.19266e8	+	8.93929e7i	0.778853	+	0.583770i
$536$	−6.08980e7	+	3.79473e7i	−0.395465	+	0.246426i
$537$	3.40934e7	−	2.54667e7i	0.220165	−	0.164456i
$538$	−1.20414e8	+	5.78034e7i	−0.773270	+	0.371198i
$539$		−	1.90079e8i		−	1.21386i
$540$	−1.54931e8	−	2.81315e7i	−0.983912	−	0.178653i
$541$	5.95072e7			0.375818			0.187909	−	0.982186i	$-0.439829\pi$
$541$	5.95072e7			0.375818			0.187909	+	0.982186i	$0.439829\pi$
$542$	8.36156e7	+	1.74186e8i	0.525157	+	1.09399i
$543$	7.73024e7	+	1.03488e8i	0.482829	+	0.646385i
$544$	−8.13905e6	+	6.83952e7i	−0.0505565	+	0.424844i
$545$	1.29372e8	−	1.85218e7i	0.799191	−	0.114418i
$546$	143602.	−	274700.i	0.000882231	−	0.00168765i
$547$	1.50616e8	+	1.50616e8i	0.920258	+	0.920258i	0.997047	−	0.0767892i	$-0.0244668\pi$
$547$	1.50616e8	+	1.50616e8i	0.920258	+	0.920258i	−0.0767892	+	0.997047i	$0.524467\pi$
$548$	6.95286e7	−	7.65820e6i	0.422495	−	0.0465356i
$549$	−3.56921e7	+	1.20627e8i	−0.215703	+	0.729000i
$550$	1.50230e8	−	1.34972e8i	0.902959	−	0.811253i
$551$	3.56094e8			2.12867
$552$	−5.07273e7	−	1.97912e7i	−0.301595	−	0.117667i
$553$	57295.3	+	57295.3i	0.000338800	+	0.000338800i
$554$	8.17121e7	−	2.32588e8i	0.480570	−	1.36791i
$555$	174291.	−	1.06301e8i	0.00101952	−	0.621811i
$556$	1.69339e8	−	2.11260e8i	0.985218	−	1.22912i
$557$	1.09796e8	+	1.09796e8i	0.635362	+	0.635362i	0.949408	−	0.314046i	$-0.101685\pi$
$557$	1.09796e8	+	1.09796e8i	0.635362	+	0.635362i	−0.314046	+	0.949408i	$0.601685\pi$
$558$	−8.48573e7	+	1.36829e7i	−0.488412	+	0.0787545i
$559$	1.84341e8			1.05533
$560$	395964.	+	178631.i	0.00225471	+	0.00101717i
$561$	−1.31439e7	+	9.07472e7i	−0.0744448	+	0.513978i
$562$	6.73378e7	+	1.40276e8i	0.379359	+	0.790269i
$563$	4.64687e6	+	4.64687e6i	0.0260397	+	0.0260397i	0.720007	−	0.693967i	$-0.244139\pi$
$563$	4.64687e6	+	4.64687e6i	0.0260397	+	0.0260397i	−0.693967	+	0.720007i	$0.744139\pi$
$564$	1.84055e8	−	1.71899e8i	1.02591	−	0.958156i
$565$	2.80811e8	+	2.10475e8i	1.55693	+	1.16696i
$566$	−2.51071e7	+	7.14655e7i	−0.138467	+	0.394137i
$567$	−94008.2	−	440977.i	−0.000515723	−	0.00241917i
$568$	−1.32897e7	+	5.72369e7i	−0.0725222	+	0.312342i
$569$	−2.74410e8			−1.48958			−0.744789	−	0.667300i	$-0.767450\pi$
$569$	−2.74410e8			−1.48958			−0.744789	+	0.667300i	$0.767450\pi$
$570$	−7.24375e7	+	2.05112e8i	−0.391146	+	1.10756i
$571$			1.79718e8i			0.965349i	0.875800	+	0.482675i	$0.160335\pi$
$571$			1.79718e8i			0.965349i	−0.875800	+	0.482675i	$0.839665\pi$
$572$	1.73846e8	−	1.91482e7i	0.928916	−	0.102315i
$573$	−9.90118e7	−	1.32552e8i	−0.526288	−	0.704565i
$574$	159956.	−	455303.i	0.000845793	−	0.00240749i
$575$	−5.39817e7	−	2.95602e7i	−0.283951	−	0.155491i
$576$	1.29418e8	−	1.40611e8i	0.677215	−	0.735785i
$577$	6.25809e7	−	6.25809e7i	0.325773	−	0.325773i	−0.525204	−	0.850976i	$-0.676011\pi$
$577$	6.25809e7	−	6.25809e7i	0.325773	−	0.325773i	0.850976	+	0.525204i	$0.176011\pi$
$578$	6.82693e7	+	1.42217e8i	0.353543	+	0.736490i
$579$	−5.18542e7	+	3.58009e8i	−0.267145	+	1.84441i
$580$	−3.04456e8	−	1.79818e8i	−1.56042	−	0.921616i
$581$			96002.2i			0.000489500i
$582$	2.19401e6	−	687617.i	0.0111294	−	0.00348801i
$583$	−1.86257e8	+	1.86257e8i	−0.939957	+	0.939957i
$584$	−5.76048e7	+	3.58952e7i	−0.289215	+	0.180218i
$585$	−9.20367e7	−	1.23636e8i	−0.459720	−	0.617557i
$586$	−2.07250e7	+	5.89921e7i	−0.102991	+	0.293158i
$587$	−1.43681e7	+	1.43681e7i	−0.0710369	+	0.0710369i	−0.741733	−	0.670696i	$-0.765996\pi$
$587$	−1.43681e7	+	1.43681e7i	−0.0710369	+	0.0710369i	0.670696	+	0.741733i	$0.265996\pi$
$588$	6.93875e6	−	2.03178e8i	0.0341310	−	0.999411i
$589$			1.18740e8i			0.581098i
$590$	2.70070e8	−	1.80730e8i	1.31499	−	0.879981i
$591$	3.16565e6	−	2.18561e7i	0.0153356	−	0.105879i
$592$	1.08892e8	+	6.91823e7i	0.524844	+	0.333449i
$593$	−1.23655e8	+	1.23655e8i	−0.592993	+	0.592993i	−0.938439	−	0.345446i	$-0.887728\pi$
$593$	−1.23655e8	+	1.23655e8i	−0.592993	+	0.592993i	0.345446	+	0.938439i	$0.387728\pi$
$594$	1.76986e8	−	1.82753e8i	0.844463	−	0.871980i
$595$	−220671.	+	31592.8i	−0.00104760	+	0.000149981i
$596$	−1.37931e8	+	1.72077e8i	−0.651514	+	0.812800i
$597$	−1.24937e8	−	1.67259e8i	−0.587178	−	0.786082i
$598$	−2.30656e7	−	4.80497e7i	−0.107860	−	0.224692i
$599$		−	1.48145e8i		−	0.689298i	−0.938732	−	0.344649i	$-0.887998\pi$
$599$		−	1.48145e8i		−	0.689298i	0.938732	−	0.344649i	$-0.112002\pi$
$600$	1.65510e8	−	1.38789e8i	0.766249	−	0.642544i
$601$	−1.49935e8			−0.690686			−0.345343	−	0.938477i	$-0.612237\pi$
$601$	−1.49935e8			−0.690686			−0.345343	+	0.938477i	$0.612237\pi$
$602$	−666868.	+	320121.i	−0.00305668	+	0.00146732i
$603$	−8.97694e7	+	4.87756e7i	−0.409427	+	0.222459i
$604$	424093.	+	339939.i	0.00192464	+	0.00154273i
$605$	1.48591e7	+	1.03789e8i	0.0671005	+	0.468688i
$606$	1.16465e8	−	2.22789e8i	0.523332	−	1.00110i
$607$	1.09513e7	+	1.09513e7i	0.0489666	+	0.0489666i	0.731166	−	0.682199i	$-0.238976\pi$
$607$	1.09513e7	+	1.09513e7i	0.0489666	+	0.0489666i	−0.682199	+	0.731166i	$0.738976\pi$
$608$	−1.63308e8	−	2.07425e8i	−0.726602	−	0.922893i
$609$	145135.	−	1.00203e6i	0.000642568	−	0.00443638i
$610$	−9.59703e7	−	1.43412e8i	−0.422812	−	0.631822i
$611$	2.46515e8			1.08074
$612$	−1.73623e7	+	9.65210e7i	−0.0757450	+	0.421083i
$613$	−2.35252e8	−	2.35252e8i	−1.02130	−	1.02130i	−0.999768	−	0.0215269i	$-0.993147\pi$
$613$	−2.35252e8	−	2.35252e8i	−1.02130	−	1.02130i	−0.0215269	−	0.999768i	$-0.506853\pi$
$614$	−8.93042e7	−	3.13741e7i	−0.385804	−	0.135540i
$615$	−1.69401e8	−	1.69957e8i	−0.728266	−	0.730658i
$616$	−595648.	+	371166.i	−0.00254828	+	0.00158791i
$617$	1.78754e7	+	1.78754e7i	0.0761027	+	0.0761027i	0.744134	−	0.668031i	$-0.232863\pi$
$617$	1.78754e7	+	1.78754e7i	0.0761027	+	0.0761027i	−0.668031	+	0.744134i	$0.732863\pi$
$618$	−1.09269e8	+	3.42455e7i	−0.462946	+	0.145090i
$619$	2.88843e8			1.21784			0.608919	−	0.793232i	$-0.291603\pi$
$619$	2.88843e8			1.21784			0.608919	+	0.793232i	$0.291603\pi$
$620$	5.99605e7	−	1.01521e8i	0.251588	−	0.425972i
$621$	−7.04223e7	−	3.24269e7i	−0.294060	−	0.135404i
$622$	−3.20446e8	+	1.53826e8i	−1.33163	+	0.639231i
$623$	600207.	+	600207.i	0.00248220	+	0.00248220i
$624$	1.86525e8	−	1.41216e7i	0.767686	−	0.0581205i
$625$	2.05700e8	−	1.31500e8i	0.842547	−	0.538623i
$626$	−3.65084e8	−	1.28260e8i	−1.48823	−	0.522841i
$627$	−2.10323e8	−	2.81568e8i	−0.853264	−	1.14230i
$628$	3.18141e7	+	2.88839e8i	0.128452	+	1.16621i
$629$	−6.62054e7			−0.266037
$630$	547653.	+	287434.i	0.00219020	+	0.00114952i
$631$		−	1.04472e8i		−	0.415826i	−0.978147	−	0.207913i	$-0.933333\pi$
$631$		−	1.04472e8i		−	0.415826i	0.978147	−	0.207913i	$-0.0666670\pi$
$632$	−1.10594e7	+	4.76310e7i	−0.0438105	+	0.188685i
$633$	−2.04185e8	+	1.52519e8i	−0.805030	+	0.601332i
$634$	−1.22522e8	−	4.30441e7i	−0.480780	−	0.168906i
$635$	−2.66437e8	+	3.55474e8i	−1.04057	+	1.38831i
$636$	−2.05892e8	+	1.92294e8i	−0.800329	+	0.747470i
$637$	1.40710e8	−	1.40710e8i	0.544386	−	0.544386i
$638$	5.15018e8	−	2.47228e8i	1.98317	−	0.951996i
$639$	−2.37377e7	+	8.02252e7i	−0.0909780	+	0.307474i
$640$	3.48819e7	+	2.59813e8i	0.133064	+	0.991107i
$641$		−	6.82680e7i		−	0.259205i	−0.991566	−	0.129602i	$-0.958630\pi$
$641$		−	6.82680e7i		−	0.259205i	0.991566	−	0.129602i	$-0.0413701\pi$
$642$	−2.45768e8	+	7.70253e7i	−0.928798	+	0.291091i
$643$	−1.44567e8	+	1.44567e8i	−0.543797	+	0.543797i	−0.924640	−	0.380843i	$-0.875634\pi$
$643$	−1.44567e8	+	1.44567e8i	−0.543797	+	0.543797i	0.380843	+	0.924640i	$0.375634\pi$
$644$	166883.	+	133768.i	0.000624821	+	0.000500836i
$645$	−603084.	+	3.67824e8i	−0.00224750	+	1.37076i
$646$	1.27820e8	+	4.49053e7i	0.474133	+	0.166571i
$647$	−1.86821e8	+	1.86821e8i	−0.689782	+	0.689782i	−0.962184	−	0.272401i	$-0.912182\pi$
$647$	−1.86821e8	+	1.86821e8i	−0.689782	+	0.689782i	0.272401	+	0.962184i	$0.412182\pi$
$648$	1.95855e8	−	1.88887e8i	0.719795	−	0.694187i
$649$			5.25028e8i			1.92065i
$650$	2.11127e8	+	1.12948e7i	0.768784	+	0.0411281i
$651$	334128.	+	48395.2i	0.00121107	+	0.000175412i
$652$	−2.62423e7	−	2.38253e8i	−0.0946802	−	0.859600i
$653$	−2.23527e8	+	2.23527e8i	−0.802770	+	0.802770i	−0.983528	−	0.180758i	$-0.942145\pi$
$653$	−2.23527e8	+	2.23527e8i	−0.802770	+	0.802770i	0.180758	+	0.983528i	$0.442145\pi$
$654$	−1.04624e8	+	2.00137e8i	−0.374021	+	0.715476i
$655$	−5.54623e7	−	3.87396e8i	−0.197367	−	1.37858i
$656$	2.84244e8	−	6.33849e7i	1.00689	−	0.224530i
$657$	−8.49150e7	+	4.61380e7i	−0.299425	+	0.162691i
$658$	−891787.	+	428091.i	−0.00313028	+	0.00150265i
$659$			1.60969e8i			0.562453i	0.959641	+	0.281227i	$0.0907412\pi$
$659$			1.60969e8i			0.562453i	−0.959641	+	0.281227i	$0.909259\pi$
$660$	3.76385e7	+	3.46945e8i	0.130918	+	1.20678i
$661$	−2.32348e8			−0.804516			−0.402258	−	0.915526i	$-0.631774\pi$
$661$	−2.32348e8			−0.804516			−0.402258	+	0.915526i	$0.631774\pi$
$662$	6.02728e7	+	1.25559e8i	0.207753	+	0.432785i
$663$	−7.69077e7	+	5.74476e7i	−0.263894	+	0.197120i
$664$	−4.91699e7	+	3.06392e7i	−0.167956	+	0.104658i
$665$	512445.	−	683693.i	0.00174254	−	0.00232486i
$666$	1.48908e8	+	1.07554e8i	0.504074	+	0.364086i
$667$	−1.23104e8	−	1.23104e8i	−0.414855	−	0.414855i
$668$	4.76536e7	+	4.32646e8i	0.159870	+	1.45145i
$669$	1.55520e8	+	2.25256e7i	0.519407	+	0.0752312i
$670$	2.72441e7	−	1.37470e8i	0.0905833	−	0.457070i
$671$	2.78798e8			0.922832
$672$	−650246.	+	375000.i	−0.00214274	+	0.00123573i
$673$	4.34522e7	+	4.34522e7i	0.142550	+	0.142550i	0.774780	−	0.632231i	$-0.217860\pi$
$673$	4.34522e7	+	4.34522e7i	0.142550	+	0.142550i	−0.632231	+	0.774780i	$0.717860\pi$
$674$	1.05203e8	−	2.99453e8i	0.343596	−	0.978021i
$675$	2.46998e8	−	1.83241e8i	0.803122	−	0.595814i
$676$	−9.81701e7	−	7.86899e7i	−0.317789	−	0.254729i
$677$	−1.35891e8	−	1.35891e8i	−0.437951	−	0.437951i	0.453371	−	0.891322i	$-0.350221\pi$
$677$	−1.35891e8	−	1.35891e8i	−0.437951	−	0.437951i	−0.891322	+	0.453371i	$0.850221\pi$
$678$	−5.78661e8	+	1.81356e8i	−1.85667	+	0.581892i
$679$	−9031.14			−2.88492e−5
$680$	−8.66084e7	−	1.02939e8i	−0.275444	−	0.327382i
$681$	6.24457e7	+	9.04467e6i	0.197725	+	0.0286386i
$682$	8.24383e7	+	1.71733e8i	0.259882	+	0.541378i
$683$	−2.42525e8	−	2.42525e8i	−0.761192	−	0.761192i	0.215346	−	0.976538i	$-0.430912\pi$
$683$	−2.42525e8	−	2.42525e8i	−0.761192	−	0.761192i	−0.976538	+	0.215346i	$0.930912\pi$
$684$	−2.14538e8	−	3.08650e8i	−0.670403	−	0.964490i
$685$	−8.19384e7	+	1.09320e8i	−0.254927	+	0.340118i
$686$	−529354.	+	1.50677e6i	−0.00163974	+	0.00466740i
$687$	3.31656e8	−	2.47737e8i	1.02286	−	0.764047i
$688$	−3.76789e8	−	2.39386e8i	−1.15700	−	0.735077i
$689$	−2.75763e8			−0.843097
$690$	9.59512e7	−	4.58667e7i	0.292081	−	0.139621i
$691$		−	3.27526e8i		−	0.992685i	−0.868127	−	0.496343i	$-0.834676\pi$
$691$		−	3.27526e8i		−	0.992685i	0.868127	−	0.496343i	$-0.165324\pi$
$692$	1.63926e7	+	1.48828e8i	0.0494685	+	0.449124i
$693$	−878043.	+	477078.i	−0.00263825	+	0.00143347i
$694$	−4.30848e7	+	1.22638e8i	−0.128898	+	0.366899i
$695$	7.49442e7	+	5.23474e8i	0.223246	+	1.55934i
$696$	5.59535e8	−	2.45465e8i	1.65958	−	0.728050i
$697$	−1.05678e8	+	1.05678e8i	−0.312095	+	0.312095i
$698$	−5.10589e7	−	1.06365e8i	−0.150143	−	0.312774i
$699$	9.05456e7	+	1.31147e7i	0.265116	+	0.0383995i
$700$	−783383.	+	325778.i	−0.00228392	+	0.000949789i
$701$		−	3.53061e7i		−	0.102493i	−0.998686	−	0.0512466i	$-0.983681\pi$
$701$		−	3.53061e7i		−	0.102493i	0.998686	−	0.0512466i	$-0.0163195\pi$
$702$	2.66306e8	−	4.26916e6i	0.769784	−	0.0123404i
$703$	1.79432e8	−	1.79432e8i	0.516456	−	0.516456i
$704$	−3.80203e8	−	1.86618e8i	−1.08968	−	0.534855i
$705$	−806491.	+	4.91883e8i	−0.00230161	+	1.40377i
$706$	1.78297e8	−	5.07510e8i	0.506676	−	1.44222i
$707$	−698230.	+	698230.i	−0.00197579	+	0.00197579i
$708$	−1.91659e7	+	5.61210e8i	−0.0540045	+	1.58134i
$709$		−	2.01980e8i		−	0.566720i	−0.959014	−	0.283360i	$-0.908551\pi$
$709$		−	2.01980e8i		−	0.566720i	0.959014	−	0.283360i	$-0.0914492\pi$
$710$	−6.38268e7	−	9.53785e7i	−0.178331	−	0.266487i
$711$	−1.97539e7	+	6.67613e7i	−0.0549596	+	0.185744i
$712$	−1.15854e8	+	4.98967e8i	−0.320975	+	1.38239i
$713$	4.10493e7	−	4.10493e7i	0.113250	−	0.113250i
$714$	178457.	−	341377.i	0.000490275	−	0.000937862i
$715$	−2.04875e8	+	2.73339e8i	−0.560493	+	0.747797i
$716$	−7.87067e7	−	6.30887e7i	−0.214424	−	0.171875i
$717$	3.71550e8	−	2.77536e8i	1.00800	−	0.752942i
$718$	−1.30960e8	−	2.72813e8i	−0.353807	−	0.737041i
$719$		−	4.20913e8i		−	1.13242i	−0.824263	−	0.566208i	$-0.808410\pi$
$719$		−	4.20913e8i		−	1.13242i	0.824263	−	0.566208i	$-0.191590\pi$
$720$	2.75672e7	+	3.72229e8i	0.0738576	+	0.997269i
$721$	449779.			0.00120003
$722$	−1.28826e8	+	6.18411e7i	−0.342287	+	0.164311i
$723$	1.59267e8	+	2.13218e8i	0.421415	+	0.564168i
$724$	1.91501e8	−	2.38908e8i	0.504610	−	0.629529i
$725$	6.62869e8	−	1.93774e8i	1.73946	−	0.508488i
$726$	−1.60560e8	−	8.39342e7i	−0.419593	−	0.219346i
$727$	2.56565e8	+	2.56565e8i	0.667719	+	0.667719i	0.957188	−	0.289468i	$-0.0934785\pi$
$727$	2.56565e8	+	2.56565e8i	0.667719	+	0.667719i	−0.289468	+	0.957188i	$0.593478\pi$
$728$	−715706.	−	166178.i	−0.00185499	−	0.000430706i
$729$	2.94371e8	−	2.51874e8i	0.759823	−	0.650130i
$730$	2.57708e7	−	1.30036e8i	0.0662461	−	0.334268i
$731$	2.29085e8			0.586468
$732$	2.98011e8	+	1.01774e7i	0.759800	+	0.0259480i
$733$	−1.66873e7	−	1.66873e7i	−0.0423715	−	0.0423715i	0.685604	−	0.727975i	$-0.259538\pi$
$733$	−1.66873e7	−	1.66873e7i	−0.0423715	−	0.0423715i	−0.727975	+	0.685604i	$0.759538\pi$
$734$	3.11236e8	+	1.09343e8i	0.787049	+	0.276504i
$735$	2.80305e8	+	2.81226e8i	0.705942	+	0.708261i
$736$	−1.52517e7	+	1.28166e8i	−0.0382548	+	0.321468i
$737$	1.60105e8	+	1.60105e8i	0.399948	+	0.399948i
$738$	4.09368e8	−	6.60089e7i	1.01846	−	0.164223i
$739$	−6.02113e8			−1.49192			−0.745958	−	0.665993i	$-0.768008\pi$
$739$	−6.02113e8			−1.49192			−0.745958	+	0.665993i	$0.768008\pi$
$740$	−2.44021e8	+	6.28036e7i	−0.602187	+	0.154985i
$741$	5.27413e7	−	3.64133e8i	0.129627	−	0.894965i
$742$	997592.	−	478881.i	0.00244198	−	0.00117224i
$743$	−5.52974e8	−	5.52974e8i	−1.34815	−	1.34815i	−0.887670	−	0.460480i	$-0.847677\pi$
$743$	−5.52974e8	−	5.52974e8i	−1.34815	−	1.34815i	−0.460480	−	0.887670i	$-0.652323\pi$
$744$	8.18503e7	+	1.86577e8i	0.198747	+	0.453043i
$745$	−6.10441e7	−	4.26384e8i	−0.147630	−	1.03117i
$746$	−2.73253e8	−	9.59984e7i	−0.658185	−	0.231232i
$747$	−7.24811e7	+	3.93821e7i	−0.173885	+	0.0944794i
$748$	2.16042e8	−	2.37959e7i	0.516219	−	0.0568588i
$749$	1.01165e6			0.00240760
$750$	−2.32278e7	+	4.21235e8i	−0.0550585	+	0.998483i
$751$			4.06077e8i			0.958714i	0.877620	+	0.479357i	$0.159130\pi$
$751$			4.06077e8i			0.958714i	−0.877620	+	0.479357i	$0.840870\pi$
$752$	−5.03872e8	−	3.20125e8i	−1.18486	−	0.752777i
$753$	3.35527e8	+	4.49185e8i	0.785855	+	1.05206i
$754$	5.64270e8	+	1.98238e8i	1.31635	+	0.462458i
$755$	−1.05085e6	+	150447.i	−0.00244174	+	0.000349576i
$756$	−955967.	+	477903.i	−0.00221247	+	0.00110605i
$757$	−1.23737e8	+	1.23737e8i	−0.285242	+	0.285242i	−0.835195	−	0.549953i	$-0.814645\pi$
$757$	−1.23737e8	+	1.23737e8i	−0.285242	+	0.285242i	0.549953	+	0.835195i	$0.314645\pi$
$758$	−3.31229e8	+	1.59002e8i	−0.760537	+	0.365086i
$759$	−2.46302e7	+	1.70051e8i	−0.0563305	+	0.388914i
$760$	5.13717e8	+	4.42605e7i	1.17026	+	0.100827i
$761$		−	8.16299e8i		−	1.85223i	−0.377240	−	0.926116i	$-0.623127\pi$
$761$		−	8.16299e8i		−	1.85223i	0.377240	−	0.926116i	$-0.376873\pi$
$762$	−2.29575e8	−	7.32516e8i	−0.518871	−	1.65559i
$763$	627239.	−	627239.i	0.00141208	−	0.00141208i
$764$	−2.45282e8	+	3.06003e8i	−0.550029	+	0.686192i
$765$	−1.14376e8	−	1.53645e8i	−0.255477	−	0.343191i
$766$	1.41779e8	+	4.98094e7i	0.315447	+	0.110822i
$767$	−3.88664e8	+	3.88664e8i	−0.861367	+	0.861367i
$768$	−3.99592e8	−	2.13358e8i	−0.882131	−	0.471004i
$769$		−	4.76696e8i		−	1.04824i	−0.851643	−	0.524122i	$-0.824394\pi$
$769$		−	4.76696e8i		−	1.04824i	0.851643	−	0.524122i	$-0.175606\pi$
$770$	266477.	−	1.34460e6i	0.000583697	−	0.00294525i
$771$	−8.50789e7	+	5.87398e8i	−0.185635	+	1.28165i
$772$	8.52314e8	−	9.38777e7i	1.85245	−	0.204038i
$773$	4.52739e8	−	4.52739e8i	0.980189	−	0.980189i	−0.0196184	−	0.999808i	$-0.506245\pi$
$773$	4.52739e8	−	4.52739e8i	0.980189	−	0.980189i	0.999808	+	0.0196184i	$0.00624513\pi$
$774$	−5.15253e8	−	3.72161e8i	−1.11121	−	0.802616i
$775$	6.46139e7	+	2.21034e8i	0.138810	+	0.474848i
$776$	−2.88230e6	−	4.62552e6i	−0.00616813	−	0.00989864i
$777$	−431781.	−	578044.i	−0.000920450	−	0.00123225i
$778$	4.58528e8	−	2.20111e8i	0.973705	−	0.467415i
$779$		−	5.72823e8i		−	1.21174i
$780$	−2.28971e8	+	2.84697e8i	−0.482500	+	0.599928i
$781$	1.85420e8			0.389227
$782$	−2.86642e7	−	5.97125e7i	−0.0599404	−	0.124866i
$783$	8.16065e8	−	3.01478e8i	1.69996	−	0.628015i
$784$	−4.70335e8	+	1.04882e8i	−0.976021	+	0.217647i
$785$	−4.54144e8	−	3.40393e8i	−0.938825	−	0.703673i
$786$	5.99299e8	+	3.13289e8i	1.23417	+	0.645174i
$787$	−1.15220e8	−	1.15220e8i	−0.236377	−	0.236377i	0.578971	−	0.815348i	$-0.303454\pi$
$787$	−1.15220e8	−	1.15220e8i	−0.236377	−	0.236377i	−0.815348	+	0.578971i	$0.803454\pi$
$788$	−5.20331e7	+	5.73116e6i	−0.106341	+	0.0117129i
$789$	6.92633e7	−	4.78204e8i	0.141017	−	0.973604i
$790$	−5.31150e7	−	7.93714e7i	−0.107730	−	0.160984i
$791$	2.38192e6			0.00481281
$792$	−5.24575e8	−	2.97451e8i	−1.05592	−	0.598743i
$793$	2.06387e8	+	2.06387e8i	0.413868	+	0.413868i
$794$	−3.05333e8	+	8.69110e8i	−0.609976	+	1.73625i
$795$	902176.	−	5.50242e8i	0.00179552	−	1.09510i
$796$	−3.09507e8	+	3.86128e8i	−0.613666	+	0.765583i
$797$	4.16401e8	+	4.16401e8i	0.822501	+	0.822501i	0.986466	−	0.163965i	$-0.0524284\pi$
$797$	4.16401e8	+	4.16401e8i	0.822501	+	0.822501i	−0.163965	+	0.986466i	$0.552428\pi$
$798$	441548.	+	1.40887e6i	0.000868899	+	0.00277244i
$799$	3.06350e8			0.600590
$800$	−4.16872e8	−	2.97257e8i	−0.814204	−	0.580579i
$801$	−2.06935e8	+	6.99370e8i	−0.402659	+	1.36085i
$802$	6.04433e7	+	1.25914e8i	0.117172	+	0.244090i
$803$	1.51448e8	+	1.51448e8i	0.292493	+	0.292493i
$804$	1.65294e8	+	1.76983e8i	0.318046	+	0.340537i
$805$	−413515.	+	59201.7i	−0.000792690	+	0.000113487i
$806$	−6.61025e7	+	1.88156e8i	−0.126245	+	0.359346i
$807$	2.69777e8	+	3.61163e8i	0.513316	+	0.687199i
$808$	−5.80457e8	−	1.34775e8i	−1.10036	−	0.255491i
$809$	−3.09643e8			−0.584811			−0.292405	−	0.956294i	$-0.594456\pi$
$809$	−3.09643e8			−0.584811			−0.292405	+	0.956294i	$0.594456\pi$
$810$	7.64721e6	+	5.31386e8i	0.0143896	+	0.999896i
$811$		−	1.01478e9i		−	1.90243i	−0.308527	−	0.951216i	$-0.599836\pi$
$811$		−	1.01478e9i		−	1.90243i	0.308527	−	0.951216i	$-0.400164\pi$
$812$	−2.38554e6	+	262754.i	−0.00445573	+	0.000490775i
$813$	5.22441e8	−	3.90247e8i	0.972223	−	0.726219i
$814$	1.34937e8	−	3.84088e8i	0.250182	−	0.712126i
$815$	3.74608e8	+	2.80778e8i	0.691996	+	0.518669i
$816$	2.31799e8	−	1.75492e7i	0.426620	−	0.0322989i
$817$	−6.20873e8	+	6.20873e8i	−1.13851	+	1.13851i
$818$	4.16190e7	+	8.66995e7i	0.0760382	+	0.158401i
$819$	−1.00316e6	−	296823.i	−0.00182607	−	0.000540314i
$820$	−2.89261e8	+	4.89757e8i	−0.524625	+	0.888258i
$821$			6.14432e8i			1.11031i	0.831747	+	0.555155i	$0.187341\pi$
$821$			6.14432e8i			1.11031i	−0.831747	+	0.555155i	$0.812659\pi$
$822$	−7.06022e7	−	2.25274e8i	−0.127117	−	0.405597i
$823$	−1.58201e8	+	1.58201e8i	−0.283799	+	0.283799i	−0.834622	−	0.550823i	$-0.814314\pi$
$823$	−1.58201e8	+	1.58201e8i	−0.283799	+	0.283799i	0.550823	+	0.834622i	$0.314314\pi$
$824$	1.43547e8	+	2.30365e8i	0.256574	+	0.411752i
$825$	−5.44736e8	−	4.09690e8i	−0.970117	−	0.729615i
$826$	731079.	−	2.08096e6i	0.00129725	−	0.00369253i
$827$	−1.04327e8	+	1.04327e8i	−0.184450	+	0.184450i	−0.793292	−	0.608842i	$-0.791634\pi$
$827$	−1.04327e8	+	1.04327e8i	−0.184450	+	0.184450i	0.608842	+	0.793292i	$0.291634\pi$
$828$	−3.25352e7	+	1.80870e8i	−0.0573143	+	0.318623i
$829$			6.92513e8i			1.21553i	0.794119	+	0.607763i	$0.207933\pi$
$829$			6.92513e8i			1.21553i	−0.794119	+	0.607763i	$0.792067\pi$
$830$	2.19973e7	−	1.10995e8i	0.0384711	−	0.194120i
$831$	−8.23425e8	−	1.19265e8i	−1.43490	−	0.207831i
$832$	−1.43306e8	−	4.19602e8i	−0.248825	−	0.728564i
$833$	1.74864e8	−	1.74864e8i	0.302528	−	0.302528i
$834$	−8.09810e8	−	4.23335e8i	−1.39600	−	0.729770i
$835$	−6.80253e8	−	5.09867e8i	−1.16845	−	0.875785i
$836$	−5.21032e8	+	6.50017e8i	−0.891755	+	1.11251i
$837$	1.00528e8	+	2.72117e8i	0.171439	+	0.464066i
$838$	3.02802e8	+	6.30789e8i	0.514550	+	1.07189i
$839$		−	5.74500e8i		−	0.972756i	−0.873749	−	0.486378i	$-0.838318\pi$
$839$		−	5.74500e8i		−	0.972756i	0.873749	−	0.486378i	$-0.161682\pi$
$840$	333925.	−	1.42754e6i	0.000563393	−	0.00240852i
$841$	1.35874e9			2.28427
$842$	7.13896e8	−	3.42697e8i	1.19591	−	0.574081i
$843$	4.20735e8	−	3.14276e8i	0.702306	−	0.524600i
$844$	4.71372e8	+	3.77836e8i	0.784036	+	0.628458i
$845$	2.43253e8	−	3.48257e7i	0.403169	−	0.0577205i
$846$	−6.89036e8	−	4.97682e8i	−1.13797	−	0.821942i
$847$	503202.	+	503202.i	0.000828118	+	0.000828118i
$848$	5.63653e8	+	3.58106e8i	0.924324	+	0.587251i
$849$	2.53008e8	+	3.66458e7i	0.413438	+	0.0598826i
$850$	2.62373e8	+	1.40363e7i	0.427230	+	0.0228558i
$851$	−1.24062e8			−0.201303
$852$	1.98198e8	+	6.76867e6i	0.320464	+	0.0109442i
$853$	−2.66733e8	−	2.66733e8i	−0.429763	−	0.429763i	0.458785	−	0.888548i	$-0.348285\pi$
$853$	−2.66733e8	−	2.66733e8i	−0.429763	−	0.429763i	−0.888548	+	0.458785i	$0.848285\pi$
$854$	−1.10502e6	−	388214.i	−0.00177418	−	0.000623301i
$855$	7.26400e8	+	1.06428e8i	1.16219	+	0.170278i
$856$	3.22868e8	+	5.18141e8i	0.514759	+	0.826088i
$857$	−1.85267e8	−	1.85267e8i	−0.294344	−	0.294344i	0.544450	−	0.838793i	$-0.316738\pi$
$857$	−1.85267e8	−	1.85267e8i	−0.294344	−	0.294344i	−0.838793	+	0.544450i	$0.816738\pi$
$858$	−1.76530e8	−	5.63263e8i	−0.279484	−	0.891763i
$859$	−1.25379e9			−1.97808			−0.989041	−	0.147642i	$-0.952832\pi$
$859$	−1.25379e9			−1.97808			−0.989041	+	0.147642i	$0.952832\pi$
$860$	8.44364e8	−	2.17314e8i	1.32750	−	0.341659i
$861$	−1.61190e6	−	233468.i	−0.00252539	−	0.000365778i
$862$	3.08825e8	−	1.48248e8i	0.482160	−	0.231455i
$863$	2.59672e8	+	2.59672e8i	0.404011	+	0.404011i	0.879644	−	0.475633i	$-0.157781\pi$
$863$	2.59672e8	+	2.59672e8i	0.404011	+	0.404011i	−0.475633	+	0.879644i	$0.657781\pi$
$864$	−5.49867e8	−	3.37099e8i	−0.852543	−	0.522656i
$865$	−2.34003e8	−	1.75391e8i	−0.361554	−	0.270994i
$866$	5.01261e7	+	1.76102e7i	0.0771810	+	0.0271150i
$867$	4.26555e8	−	3.18623e8i	0.654513	−	0.488900i
$868$	−87615.6	−	795460.i	−0.000133975	−	0.00121635i
$869$	1.54301e8			0.235131
$870$	−3.97399e8	+	1.12527e9i	−0.603489	+	1.70882i
$871$			2.37043e8i			0.358735i
$872$	5.21439e8	+	1.21072e8i	0.786420	+	0.182597i
$873$	−3.70476e6	−	6.81846e6i	−0.00556823	−	0.0102481i
$874$	2.39521e8	+	8.41479e7i	0.358764	+	0.126040i
$875$	581877.	−	1.55155e6i	0.000868575	−	0.00231602i
$876$	1.56356e8	+	1.67413e8i	0.232596	+	0.249044i
$877$	−3.25860e8	+	3.25860e8i	−0.483095	+	0.483095i	−0.906119	−	0.423023i	$-0.860969\pi$
$877$	−3.25860e8	+	3.25860e8i	−0.483095	+	0.483095i	0.423023	+	0.906119i	$0.360969\pi$
$878$	6.47068e8	−	3.10617e8i	0.956018	−	0.458924i
$879$	2.08848e8	+	3.02497e7i	0.307514	+	0.0445405i
$880$	7.73719e8	−	2.92649e8i	1.13536	−	0.429436i
$881$		−	6.98463e7i		−	0.102145i	−0.998695	−	0.0510723i	$-0.983736\pi$
$881$		−	6.98463e7i		−	0.102145i	0.998695	−	0.0510723i	$-0.0162639\pi$
$882$	−6.77375e8	+	1.09224e8i	−0.987242	+	0.159189i
$883$	−2.87140e8	+	2.87140e8i	−0.417072	+	0.417072i	−0.884193	−	0.467121i	$-0.845291\pi$
$883$	−2.87140e8	+	2.87140e8i	−0.417072	+	0.417072i	0.467121	+	0.884193i	$0.345291\pi$
$884$	1.77546e8	+	1.42315e8i	0.257012	+	0.206012i
$885$	−7.74248e8	−	7.76791e8i	−1.11699	−	1.12066i
$886$	−6.04995e8	−	2.12545e8i	−0.869862	−	0.305598i
$887$	−1.29164e7	+	1.29164e7i	−0.0185084	+	0.0185084i	−0.716300	−	0.697792i	$-0.754166\pi$
$887$	−1.29164e7	+	1.29164e7i	−0.0185084	+	0.0185084i	0.697792	+	0.716300i	$0.254166\pi$
$888$	1.58256e8	−	4.05630e8i	0.226007	−	0.579284i
$889$			3.01523e6i			0.00429156i
$890$	−5.56415e8	−	8.31469e8i	−0.789276	−	1.17944i
$891$	−7.20383e8	−	4.67210e8i	−1.01843	−	0.660509i
$892$	−4.07808e7	−	3.70248e8i	−0.0574594	−	0.521672i
$893$	−8.30279e8	+	8.30279e8i	−1.16592	+	1.16592i
$894$	6.59613e8	+	3.44818e8i	0.923159	+	0.482589i
$895$	1.95025e8	−	2.79211e7i	0.272032	−	0.0389460i
$896$	1.24709e6	+	1.26908e6i	0.00173370	+	0.00176427i
$897$	−1.44117e8	+	1.07651e8i	−0.199682	+	0.149156i
$898$	−9.71704e8	+	4.66454e8i	−1.34185	+	0.644139i
$899$			6.51417e8i			0.896561i
$900$	−5.67320e8	−	4.57809e8i	−0.778217	−	0.627996i
$901$	−3.42697e8			−0.468528
$902$	−3.97698e8	−	8.28474e8i	−0.541919	−	1.12891i
$903$	1.49406e6	+	2.00016e6i	0.00202910	+	0.00271645i
$904$	7.60193e8	+	1.21996e9i	1.02901	+	1.65136i
$905$	8.47525e7	+	5.91984e8i	0.114342	+	0.798664i
$906$	849824.	−	1.62565e6i	0.00114273	−	0.00218596i
$907$	−5.33423e8	−	5.33423e8i	−0.714908	−	0.714908i	0.252650	−	0.967558i	$-0.418698\pi$
$907$	−5.33423e8	−	5.33423e8i	−0.714908	−	0.714908i	−0.967558	+	0.252650i	$0.918698\pi$
$908$	−1.63746e7	−	1.48665e8i	−0.0218733	−	0.198587i
$909$	−8.13588e8	−	2.40731e8i	−1.08321	−	0.320510i
$910$	1.19264e6	−	798108.i	0.00158265	−	0.00105910i
$911$	2.86012e8			0.378294			0.189147	−	0.981949i	$-0.439428\pi$
$911$	2.86012e8			0.378294			0.189147	+	0.981949i	$0.439428\pi$
$912$	−5.80667e8	+	6.75791e8i	−0.765495	+	0.890898i
$913$	1.29271e8	+	1.29271e8i	0.169860	+	0.169860i
$914$	−8.81140e6	+	2.50810e7i	−0.0115400	+	0.0328478i
$915$	−4.12488e8	+	4.11138e8i	−0.538453	+	0.536691i
$916$	−7.65647e8	−	6.13718e8i	−0.996190	−	0.798513i
$917$	−1.87823e6	−	1.87823e6i	−0.00243579	−	0.00243579i
$918$	3.30944e8	−	5.30538e6i	0.427786	−	0.00685786i
$919$	5.10519e8			0.657757			0.328879	−	0.944372i	$-0.393329\pi$
$919$	5.10519e8			0.657757			0.328879	+	0.944372i	$0.393329\pi$
$920$	−1.62295e8	−	1.92898e8i	−0.208421	−	0.247721i
$921$	−4.57930e7	+	3.16162e8i	−0.0586166	+	0.404697i
$922$	−2.57711e8	−	5.36856e8i	−0.328806	−	0.684960i
$923$	1.37261e8	+	1.37261e8i	0.174559	+	0.174559i
$924$	1.61676e6	+	1.73109e6i	0.00204941	+	0.00219434i
$925$	2.36372e8	−	4.31653e8i	0.298656	−	0.545393i
$926$	−9.33545e7	+	2.65727e8i	−0.117572	+	0.334659i
$927$	1.84509e8	+	3.39581e8i	0.231621	+	0.426289i
$928$	−8.95924e8	−	1.13796e9i	−1.12106	−	1.42391i
$929$	5.17336e7			0.0645246			0.0322623	−	0.999479i	$-0.489729\pi$
$929$	5.17336e7			0.0645246			0.0322623	+	0.999479i	$0.489729\pi$
$930$	−3.75220e8	−	1.32513e8i	−0.466485	−	0.164744i
$931$			9.47842e8i			1.17459i
$932$	−2.37430e7	−	2.15563e8i	−0.0293284	−	0.266272i
$933$	7.17929e8	+	9.61124e8i	0.883968	+	1.18341i
$934$	3.38474e7	−	9.63443e7i	0.0415418	−	0.118246i
$935$	−2.54603e8	+	3.39685e8i	−0.311479	+	0.415568i
$936$	−1.68134e8	−	6.08524e8i	−0.205035	−	0.742079i
$937$	−6.28310e8	+	6.28310e8i	−0.763757	+	0.763757i	−0.976999	−	0.213242i	$-0.931598\pi$
$937$	−6.28310e8	+	6.28310e8i	−0.763757	+	0.763757i	0.213242	+	0.976999i	$0.431598\pi$
$938$	−411643.	−	857522.i	−0.000498783	−	0.00103905i
$939$	−1.87206e8	+	1.29250e9i	−0.226112	+	1.56111i
$940$	1.12915e9	−	2.90609e8i	1.35946	−	0.349885i
$941$			1.22844e8i			0.147430i	0.997279	+	0.0737149i	$0.0234855\pi$
$941$			1.22844e8i			0.147430i	−0.997279	+	0.0737149i	$0.976515\pi$
$942$	9.35843e8	−	2.93299e8i	1.11957	−	0.350879i
$943$	−1.98030e8	+	1.98030e8i	−0.236154	+	0.236154i
$944$	1.29914e9	−	2.89701e8i	1.54433	−	0.344377i
$945$	595547.	−	2.00068e6i	0.000705700	−	0.00237073i
$946$	−4.66910e8	+	1.32903e9i	−0.551518	+	1.56986i
$947$	9.83660e7	−	9.83660e7i	0.115823	−	0.115823i	−0.646820	−	0.762643i	$-0.723901\pi$
$947$	9.83660e7	−	9.83660e7i	0.115823	−	0.115823i	0.762643	+	0.646820i	$0.223901\pi$
$948$	1.64935e8	+	5.63271e6i	0.193592	+	0.00661138i
$949$			2.24225e8i			0.262352i
$950$	−7.49132e8	+	6.73049e8i	−0.873751	+	0.785011i
$951$	−6.28263e7	+	4.33762e8i	−0.0730466	+	0.504325i
$952$	−889425.	−	206514.i	−0.00103086	−	0.000239353i
$953$	7.03254e7	−	7.03254e7i	0.0812519	−	0.0812519i	−0.665313	−	0.746565i	$-0.731702\pi$
$953$	7.03254e7	−	7.03254e7i	0.0812519	−	0.0812519i	0.746565	+	0.665313i	$0.231702\pi$
$954$	7.70785e8	+	5.56729e8i	0.887745	+	0.641208i
$955$	−1.08554e8	−	7.58235e8i	−0.124634	−	0.870550i
$956$	−8.57743e8	−	6.87539e8i	−0.981711	−	0.786907i
$957$	−1.15385e9	−	1.54471e9i	−1.31648	−	1.76243i
$958$	−3.50641e8	−	7.30446e8i	−0.398810	−	0.830791i
$959$			927287.i			0.00105138i
$960$	8.37721e8	−	2.84572e8i	0.946860	−	0.321646i
$961$	6.70288e8			0.755251
$962$	3.84219e8	−	1.84440e8i	0.431573	−	0.207171i
$963$	4.14999e8	+	7.63789e8i	0.464695	+	0.855253i
$964$	3.94551e8	−	4.92225e8i	0.440425	−	0.549455i
$965$	−1.00444e9	+	1.34010e9i	−1.11774	+	1.49127i
$966$	334411.	−	639705.i	0.000370979	−	0.000709656i
$967$	9.44500e8	+	9.44500e8i	1.04453	+	1.04453i	0.998961	+	0.0455730i	$0.0145114\pi$
$967$	9.44500e8	+	9.44500e8i	1.04453	+	1.04453i	0.0455730	+	0.998961i	$0.485489\pi$
$968$	−9.71300e7	+	4.18325e8i	−0.107085	+	0.461198i
$969$	6.55428e7	−	4.52517e8i	0.0720367	−	0.497352i
$970$	1.04416e7	+	2.06933e6i	0.0114406	+	0.00226733i
$971$	1.54062e8			0.168283			0.0841413	−	0.996454i	$-0.473185\pi$
$971$	1.54062e8			0.168283			0.0841413	+	0.996454i	$0.473185\pi$
$972$	−7.52971e8	−	5.25704e8i	−0.819935	−	0.572456i
$973$	2.53798e6	+	2.53798e6i	0.00275518	+	0.00275518i
$974$	1.20841e9	+	4.24536e8i	1.30779	+	0.459449i
$975$	−9.99706e7	−	7.06536e8i	−0.107860	−	0.762290i
$976$	−1.53836e8	−	6.89864e8i	−0.165466	−	0.742018i
$977$	−3.77190e8	−	3.77190e8i	−0.404461	−	0.404461i	0.475341	−	0.879802i	$-0.342325\pi$
$977$	−3.77190e8	−	3.77190e8i	−0.404461	−	0.404461i	−0.879802	+	0.475341i	$0.842325\pi$
$978$	−7.71945e8	+	2.41932e8i	−0.825220	+	0.258629i
$979$	1.61641e9			1.72268
$980$	4.78636e8	−	8.10394e8i	0.508543	−	0.861030i
$981$	7.30868e8	+	2.16255e8i	0.774162	+	0.229066i
$982$	5.24721e8	−	2.51885e8i	0.554107	−	0.265992i
$983$	−1.79866e8	−	1.79866e8i	−0.189360	−	0.189360i	0.606059	−	0.795419i	$-0.292749\pi$
$983$	−1.79866e8	−	1.79866e8i	−0.189360	−	0.189360i	−0.795419	+	0.606059i	$0.792749\pi$
$984$	−3.94862e8	−	9.00084e8i	−0.414438	−	0.944709i
$985$	6.13202e7	−	8.18120e7i	0.0641645	−	0.0856068i
$986$	7.01231e8	+	2.46355e8i	0.731527	+	0.256998i
$987$	1.99797e6	+	2.67477e6i	0.00207796	+	0.00278186i
$988$	−8.66895e8	+	9.54838e7i	−0.898868	+	0.0990054i
$989$	4.29282e8			0.443765
$990$	1.12448e9	−	3.50396e8i	1.15890	−	0.361122i
$991$		−	1.49878e9i		−	1.53999i	−0.638050	−	0.769995i	$-0.720259\pi$
$991$		−	1.49878e9i		−	1.53999i	0.638050	−	0.769995i	$-0.279741\pi$
$992$	3.79452e8	−	2.98746e8i	0.388707	−	0.306032i
$993$	3.76592e8	−	2.81302e8i	0.384613	−	0.287293i
$994$	−734917.	−	258189.i	−0.000748305	−	0.000262893i
$995$	−1.36978e8	−	9.56774e8i	−0.139054	−	0.971271i
$996$	1.33461e8	+	1.42899e8i	0.135075	+	0.144628i
$997$	−1.86990e8	+	1.86990e8i	−0.188683	+	0.188683i	−0.795126	−	0.606444i	$-0.792596\pi$
$997$	−1.86990e8	+	1.86990e8i	−0.188683	+	0.188683i	0.606444	+	0.795126i	$0.292596\pi$
$998$	−3.08645e8	+	1.48161e8i	−0.310504	+	0.149054i
$999$	2.59295e8	−	5.63118e8i	0.260074	−	0.564810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.l.a.23.9	✓	136
3.2	odd	2	inner	60.7.l.a.23.60	yes	136
4.3	odd	2	inner	60.7.l.a.23.43	yes	136
5.2	odd	4	inner	60.7.l.a.47.26	yes	136
12.11	even	2	inner	60.7.l.a.23.26	yes	136
15.2	even	4	inner	60.7.l.a.47.43	yes	136
20.7	even	4	inner	60.7.l.a.47.60	yes	136
60.47	odd	4	inner	60.7.l.a.47.9	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.l.a.23.9	✓	136	1.1	even	1	trivial
60.7.l.a.23.26	yes	136	12.11	even	2	inner
60.7.l.a.23.43	yes	136	4.3	odd	2	inner
60.7.l.a.23.60	yes	136	3.2	odd	2	inner
60.7.l.a.47.9	yes	136	60.47	odd	4	inner
60.7.l.a.47.26	yes	136	5.2	odd	4	inner
60.7.l.a.47.43	yes	136	15.2	even	4	inner
60.7.l.a.47.60	yes	136	20.7	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.21208 + 3.46207i) q^{2} +(16.1580 + 21.6314i) q^{3} +(40.0282 - 49.9374i) q^{4} +(17.7152 + 123.738i) q^{5} +(-191.422 - 100.068i) q^{6} +(0.599925 + 0.599925i) q^{7} +(-115.800 + 498.733i) q^{8} +(-206.838 + 699.041i) q^{9} +O(q^{10})\)	\(q+(-7.21208 + 3.46207i) q^{2} +(16.1580 + 21.6314i) q^{3} +(40.0282 - 49.9374i) q^{4} +(17.7152 + 123.738i) q^{5} +(-191.422 - 100.068i) q^{6} +(0.599925 + 0.599925i) q^{7} +(-115.800 + 498.733i) q^{8} +(-206.838 + 699.041i) q^{9} +(-556.154 - 831.079i) q^{10} +1615.65 q^{11} +(1726.99 + 58.9787i) q^{12} +(1196.02 + 1196.02i) q^{13} +(-6.40369 - 2.24973i) q^{14} +(-2390.40 + 2382.57i) q^{15} +(-891.489 - 3997.81i) q^{16} +(1486.33 + 1486.33i) q^{17} +(-928.395 - 5757.63i) q^{18} -8056.57 q^{19} +(6888.28 + 4068.37i) q^{20} +(-3.28365 + 22.6708i) q^{21} +(-11652.2 + 5593.50i) q^{22} +(2785.22 + 2785.22i) q^{23} +(-12659.4 + 5553.61i) q^{24} +(-14997.3 + 4384.11i) q^{25} +(-12766.5 - 4485.10i) q^{26} +(-18463.4 + 6820.90i) q^{27} +(53.9726 - 5.94479i) q^{28} -44199.1 q^{29} +(8991.11 - 25459.0i) q^{30} -14738.2i q^{31} +(20270.2 + 25746.1i) q^{32} +(26105.7 + 34948.9i) q^{33} +(-15865.3 - 5573.75i) q^{34} +(-63.6059 + 84.8615i) q^{35} +(26629.0 + 38310.3i) q^{36} +(-22271.5 + 22271.5i) q^{37} +(58104.6 - 27892.4i) q^{38} +(-6546.36 + 45197.1i) q^{39} +(-63763.8 - 5493.71i) q^{40} +71100.1i q^{41} +(-54.8059 - 174.872i) q^{42} +(77064.1 - 77064.1i) q^{43} +(64671.7 - 80681.5i) q^{44} +(-90162.4 - 13210.1i) q^{45} +(-29729.9 - 10444.6i) q^{46} +(103056. - 103056. i) q^{47} +(72073.6 - 83880.7i) q^{48} -117648. i q^{49} +(92984.0 - 83540.3i) q^{50} +(-8135.32 + 56167.5i) q^{51} +(107601. - 11851.7i) q^{52} +(-115283. + 115283. i) q^{53} +(109545. - 113114. i) q^{54} +(28621.7 + 199918. i) q^{55} +(-368.673 + 229.731i) q^{56} +(-130178. - 174275. i) q^{57} +(318768. - 153020. i) q^{58} +324963. i q^{59} +(23296.2 + 214740. i) q^{60} +172561. q^{61} +(51024.7 + 106293. i) q^{62} +(-543.460 + 295.285i) q^{63} +(-235325. - 115506. i) q^{64} +(-126806. + 169182. i) q^{65} +(-309272. - 161675. i) q^{66} +(99096.4 + 99096.4i) q^{67} +(133718. - 14728.3i) q^{68} +(-15244.8 + 105252. i) q^{69} +(164.935 - 832.236i) q^{70} +114765. q^{71} +(-324683. - 184106. i) q^{72} +(93737.6 + 93737.6i) q^{73} +(83518.3 - 237729. i) q^{74} +(-337162. - 253576. i) q^{75} +(-322490. + 402324. i) q^{76} +(969.271 + 969.271i) q^{77} +(-109262. - 348629. i) q^{78} +95504.0 q^{79} +(478889. - 181133. i) q^{80} +(-445877. - 289177. i) q^{81} +(-246153. - 512779. i) q^{82} +(80011.9 + 80011.9i) q^{83} +(1000.68 + 1071.45i) q^{84} +(-157585. + 210246. i) q^{85} +(-288991. + 822594. i) q^{86} +(-714169. - 956091. i) q^{87} +(-187092. + 805779. i) q^{88} +1.00047e6 q^{89} +(695993. - 216876. i) q^{90} +1435.05i q^{91} +(250574. - 27599.4i) q^{92} +(318809. - 238140. i) q^{93} +(-386462. + 1.10004e6i) q^{94} +(-142724. - 996907. i) q^{95} +(-229400. + 854478. i) q^{96} +(-7526.89 + 7526.89i) q^{97} +(407306. + 848489. i) q^{98} +(-334179. + 1.12941e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 4 q^{6}+O(q^{10}) \) 136 * q - 4 * q^6	\( 136 q - 4 q^{6} - 2092 q^{10} - 1460 q^{12} - 8 q^{13} - 932 q^{16} - 12744 q^{18} - 16056 q^{21} + 25444 q^{22} - 8 q^{25} - 52244 q^{28} + 82868 q^{30} - 2920 q^{33} - 69524 q^{36} - 113000 q^{37} + 99944 q^{40} + 19436 q^{42} - 62504 q^{45} + 145936 q^{46} - 82364 q^{48} + 219504 q^{52} - 286152 q^{57} - 351260 q^{58} + 466756 q^{60} + 652976 q^{61} - 61800 q^{66} + 243868 q^{70} - 145560 q^{72} - 316856 q^{73} + 269024 q^{76} + 613272 q^{78} + 1472232 q^{81} - 1652880 q^{82} - 1466984 q^{85} - 1084100 q^{88} + 448368 q^{90} - 2869552 q^{93} - 278860 q^{96} + 2135272 q^{97}+O(q^{100}) \) 136 * q - 4 * q^6 - 2092 * q^10 - 1460 * q^12 - 8 * q^13 - 932 * q^16 - 12744 * q^18 - 16056 * q^21 + 25444 * q^22 - 8 * q^25 - 52244 * q^28 + 82868 * q^30 - 2920 * q^33 - 69524 * q^36 - 113000 * q^37 + 99944 * q^40 + 19436 * q^42 - 62504 * q^45 + 145936 * q^46 - 82364 * q^48 + 219504 * q^52 - 286152 * q^57 - 351260 * q^58 + 466756 * q^60 + 652976 * q^61 - 61800 * q^66 + 243868 * q^70 - 145560 * q^72 - 316856 * q^73 + 269024 * q^76 + 613272 * q^78 + 1472232 * q^81 - 1652880 * q^82 - 1466984 * q^85 - 1084100 * q^88 + 448368 * q^90 - 2869552 * q^93 - 278860 * q^96 + 2135272 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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