LMFDB - Embedded newform 63.6.i.a.5.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,6,Mod(5,63)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("63.5"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 5])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	63.5
Dual form			63.6.i.a.38.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.10258i q^{2} +(-6.99587 - 13.9305i) q^{3} +5.96367 q^{4} +(-37.1817 - 64.4006i) q^{5} +(-71.0813 + 35.6970i) q^{6} +(111.893 - 65.4751i) q^{7} -193.713i q^{8} +(-145.116 + 194.911i) q^{9} +(-328.609 + 189.723i) q^{10} +(-180.338 - 104.118i) q^{11} +(-41.7210 - 83.0767i) q^{12} +(262.655 + 151.644i) q^{13} +(-334.092 - 570.942i) q^{14} +(-637.012 + 968.496i) q^{15} -797.597 q^{16} +(345.748 + 598.853i) q^{17} +(994.551 + 740.465i) q^{18} +(1481.25 + 855.200i) q^{19} +(-221.739 - 384.064i) q^{20} +(-1694.89 - 1100.66i) q^{21} +(-531.271 + 920.189i) q^{22} +(-4006.04 + 2312.89i) q^{23} +(-2698.51 + 1355.19i) q^{24} +(-1202.46 + 2082.72i) q^{25} +(773.774 - 1340.22i) q^{26} +(3730.42 + 657.956i) q^{27} +(667.292 - 390.472i) q^{28} +(2240.10 - 1293.32i) q^{29} +(4941.83 + 3250.41i) q^{30} -6685.49i q^{31} -2129.00i q^{32} +(-188.794 + 3240.59i) q^{33} +(3055.70 - 1764.21i) q^{34} +(-8377.00 - 4771.49i) q^{35} +(-865.422 + 1162.39i) q^{36} +(-2419.44 + 4190.59i) q^{37} +(4363.73 - 7558.20i) q^{38} +(274.971 - 4719.78i) q^{39} +(-12475.2 + 7202.57i) q^{40} +(9882.05 - 17116.2i) q^{41} +(-5616.23 + 8648.29i) q^{42} +(-3595.27 - 6227.20i) q^{43} +(-1075.48 - 620.927i) q^{44} +(17948.1 + 2098.40i) q^{45} +(11801.7 + 20441.2i) q^{46} -10341.3 q^{47} +(5579.88 + 11110.9i) q^{48} +(8233.02 - 14652.4i) q^{49} +(10627.2 + 6135.64i) q^{50} +(5923.50 - 9005.93i) q^{51} +(1566.38 + 904.353i) q^{52} +(6723.70 - 3881.93i) q^{53} +(3357.27 - 19034.7i) q^{54} +15485.2i q^{55} +(-12683.4 - 21675.1i) q^{56} +(1550.71 - 26617.4i) q^{57} +(-6599.27 - 11430.3i) q^{58} +42670.7 q^{59} +(-3798.93 + 5775.79i) q^{60} -4181.30i q^{61} -34113.2 q^{62} +(-3475.56 + 31310.7i) q^{63} -36386.5 q^{64} -22553.5i q^{65} +(16535.4 + 963.338i) q^{66} -12219.8 q^{67} +(2061.93 + 3571.36i) q^{68} +(60245.4 + 39625.4i) q^{69} +(-24346.9 + 42744.3i) q^{70} -7009.61i q^{71} +(37756.8 + 28110.8i) q^{72} +(-73466.6 + 42416.0i) q^{73} +(21382.8 + 12345.4i) q^{74} +(37425.5 + 2180.38i) q^{75} +(8833.69 + 5100.13i) q^{76} +(-26995.7 + 157.574i) q^{77} +(-24083.0 - 1403.06i) q^{78} -49797.6 q^{79} +(29656.0 + 51365.7i) q^{80} +(-16931.9 - 56569.4i) q^{81} +(-87336.9 - 50424.0i) q^{82} +(20121.1 + 34850.7i) q^{83} +(-10107.7 - 6564.00i) q^{84} +(25711.0 - 44532.8i) q^{85} +(-31774.8 + 18345.2i) q^{86} +(-33688.0 - 22157.7i) q^{87} +(-20169.0 + 34933.8i) q^{88} +(-22608.2 + 39158.5i) q^{89} +(10707.3 - 91581.4i) q^{90} +(39318.0 - 229.499i) q^{91} +(-23890.7 + 13793.3i) q^{92} +(-93131.9 + 46770.8i) q^{93} +52767.5i q^{94} -127191. i q^{95} +(-29658.0 + 14894.2i) q^{96} +(54936.0 - 31717.3i) q^{97} +(-74765.0 - 42009.6i) q^{98} +(46463.7 - 20040.7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 3 q^{3} - 1154 q^{4} - 3 q^{5} + 96 q^{6} - 30 q^{7} + 489 q^{9} - 6 q^{10} + 567 q^{11} - 1542 q^{12} + 543 q^{13} - 1638 q^{14} + 234 q^{15} + 16446 q^{16} - 801 q^{17} - 2022 q^{18} - 6 q^{19}+ \cdots - 144540 q^{99}+O(q^{100}) $ 76 * q - 3 * q^3 - 1154 * q^4 - 3 * q^5 + 96 * q^6 - 30 * q^7 + 489 * q^9 - 6 * q^10 + 567 * q^11 - 1542 * q^12 + 543 * q^13 - 1638 * q^14 + 234 * q^15 + 16446 * q^16 - 801 * q^17 - 2022 * q^18 - 6 * q^19 + 96 * q^20 - 4119 * q^21 + 62 * q^22 + 7806 * q^23 - 2346 * q^24 - 18749 * q^25 + 10128 * q^26 - 1539 * q^27 + 860 * q^28 + 17904 * q^29 + 11457 * q^30 - 3 * q^33 + 96 * q^34 + 3960 * q^35 - 57846 * q^36 + 2577 * q^37 + 14967 * q^38 - 16269 * q^39 + 9564 * q^40 + 28230 * q^41 + 15606 * q^42 - 9246 * q^43 - 69885 * q^44 - 23649 * q^45 - 9418 * q^46 - 56562 * q^47 + 48615 * q^48 + 7948 * q^49 - 67509 * q^50 - 103722 * q^51 - 40899 * q^52 + 25296 * q^53 + 176211 * q^54 + 104754 * q^56 + 33399 * q^57 - 4951 * q^58 - 59076 * q^59 + 33729 * q^60 + 79536 * q^62 - 95871 * q^63 - 198600 * q^64 + 114900 * q^66 + 1244 * q^67 + 191496 * q^68 + 3702 * q^69 - 127197 * q^70 + 183582 * q^72 - 6 * q^73 - 45681 * q^74 - 240486 * q^75 - 2880 * q^76 + 13854 * q^77 + 184431 * q^78 + 59984 * q^79 + 243225 * q^80 + 177117 * q^81 + 90 * q^82 - 246930 * q^83 + 56085 * q^84 + 11973 * q^85 + 291801 * q^86 + 205125 * q^87 - 34751 * q^88 - 6345 * q^89 - 269187 * q^90 - 120111 * q^91 - 463488 * q^92 + 200946 * q^93 - 382521 * q^96 - 104037 * q^97 - 646797 * q^98 - 144540 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$		−	5.10258i		−	0.902017i	−0.892520	−	0.451009i	$-0.851064\pi$
$2$		−	5.10258i		−	0.902017i	0.892520	−	0.451009i	$-0.148936\pi$
$3$	−6.99587	−	13.9305i	−0.448785	−	0.893640i
$3$	−6.99587	−	13.9305i	−0.448785	−	0.893640i
$4$	5.96367			0.186365
$5$	−37.1817	−	64.4006i	−0.665127	−	1.15203i	−0.979251	−	0.202651i	$-0.935044\pi$
$5$	−37.1817	−	64.4006i	−0.665127	−	1.15203i	0.314124	−	0.949382i	$-0.398289\pi$
$6$	−71.0813	+	35.6970i	−0.806079	+	0.404812i
$7$	111.893	−	65.4751i	0.863092	−	0.505046i
$7$	111.893	−	65.4751i	0.863092	−	0.505046i
$8$		−	193.713i		−	1.07012i
$9$	−145.116	+	194.911i	−0.597184	+	0.802104i
$10$	−328.609	+	189.723i	−1.03915	+	0.599956i
$11$	−180.338	−	104.118i	−0.449372	−	0.259445i	0.258193	−	0.966093i	$-0.416873\pi$
$11$	−180.338	−	104.118i	−0.449372	−	0.259445i	−0.707565	+	0.706649i	$0.750206\pi$
$12$	−41.7210	−	83.0767i	−0.0836377	−	0.166543i
$13$	262.655	+	151.644i	0.431049	+	0.248866i	0.699793	−	0.714345i	$-0.253275\pi$
$13$	262.655	+	151.644i	0.431049	+	0.248866i	−0.268745	+	0.963211i	$0.586609\pi$
$14$	−334.092	−	570.942i	−0.455561	−	0.778524i
$15$	−637.012	+	968.496i	−0.731004	+	1.11140i
$16$	−797.597			−0.778904
$17$	345.748	+	598.853i	0.290160	+	0.502572i	0.973847	−	0.227203i	$-0.0729582\pi$
$17$	345.748	+	598.853i	0.290160	+	0.502572i	−0.683687	+	0.729775i	$0.739625\pi$
$18$	994.551	+	740.465i	0.723512	+	0.538670i
$19$	1481.25	+	855.200i	0.941335	+	0.543480i	0.890379	−	0.455221i	$-0.150440\pi$
$19$	1481.25	+	855.200i	0.941335	+	0.543480i	0.0509566	+	0.998701i	$0.483773\pi$
$20$	−221.739	−	384.064i	−0.123956	−	0.214698i
$21$	−1694.89	−	1100.66i	−0.838672	−	0.544636i
$22$	−531.271	+	920.189i	−0.234024	+	0.405341i
$23$	−4006.04	+	2312.89i	−1.57905	+	0.911665i	−0.584058	+	0.811712i	$0.698536\pi$
$23$	−4006.04	+	2312.89i	−1.57905	+	0.911665i	−0.994992	+	0.0999528i	$0.968131\pi$
$24$	−2698.51	+	1355.19i	−0.956303	+	0.480255i
$25$	−1202.46	+	2082.72i	−0.384787	+	0.666470i
$26$	773.774	−	1340.22i	0.224482	−	0.388814i
$27$	3730.42	+	657.956i	0.984800	+	0.173695i
$28$	667.292	−	390.472i	0.160850	−	0.0941228i
$29$	2240.10	−	1293.32i	0.494620	−	0.285569i	−0.231869	−	0.972747i	$-0.574484\pi$
$29$	2240.10	−	1293.32i	0.494620	−	0.285569i	0.726489	+	0.687178i	$0.241151\pi$
$30$	4941.83	+	3250.41i	1.00250	+	0.659378i
$31$		−	6685.49i		−	1.24948i	−0.780834	−	0.624739i	$-0.785205\pi$
$31$		−	6685.49i		−	1.24948i	0.780834	−	0.624739i	$-0.214795\pi$
$32$		−	2129.00i		−	0.367537i
$33$	−188.794	+	3240.59i	−0.0301789	+	0.518011i
$34$	3055.70	−	1764.21i	0.453328	−	0.261729i
$35$	−8377.00	−	4771.49i	−1.15590	−	0.658391i
$36$	−865.422	+	1162.39i	−0.111294	+	0.149484i
$37$	−2419.44	+	4190.59i	−0.290543	+	0.503235i	−0.973938	−	0.226814i	$-0.927169\pi$
$37$	−2419.44	+	4190.59i	−0.290543	+	0.503235i	0.683395	+	0.730048i	$0.260503\pi$
$38$	4363.73	−	7558.20i	0.490229	−	0.849101i
$39$	274.971	−	4719.78i	0.0289484	−	0.496890i
$40$	−12475.2	+	7202.57i	−1.23282	+	0.711766i
$41$	9882.05	−	17116.2i	0.918095	−	1.59019i	0.115788	−	0.993274i	$-0.463061\pi$
$41$	9882.05	−	17116.2i	0.918095	−	1.59019i	0.802306	−	0.596913i	$-0.203606\pi$
$42$	−5616.23	+	8648.29i	−0.491271	+	0.756497i
$43$	−3595.27	−	6227.20i	−0.296525	−	0.513596i	0.678814	−	0.734310i	$-0.262494\pi$
$43$	−3595.27	−	6227.20i	−0.296525	−	0.513596i	−0.975338	+	0.220715i	$0.929161\pi$
$44$	−1075.48	−	620.927i	−0.0837470	−	0.0483513i
$45$	17948.1	+	2098.40i	1.32125	+	0.154475i
$46$	11801.7	+	20441.2i	0.822338	+	1.42433i
$47$	−10341.3			−0.682860			−0.341430	−	0.939907i	$-0.610911\pi$
$47$	−10341.3			−0.682860			−0.341430	+	0.939907i	$0.610911\pi$
$48$	5579.88	+	11110.9i	0.349560	+	0.696059i
$49$	8233.02	−	14652.4i	0.489856	−	0.871803i
$50$	10627.2	+	6135.64i	0.601168	+	0.347084i
$51$	5923.50	−	9005.93i	0.318899	−	0.484845i
$52$	1566.38	+	904.353i	0.0803323	+	0.0463799i
$53$	6723.70	−	3881.93i	0.328790	−	0.189827i	−0.326514	−	0.945192i	$-0.605874\pi$
$53$	6723.70	−	3881.93i	0.328790	−	0.189827i	0.655304	+	0.755366i	$0.272541\pi$
$54$	3357.27	−	19034.7i	0.156676	−	0.888306i
$55$			15485.2i			0.690254i
$56$	−12683.4	−	21675.1i	−0.540461	−	0.923614i
$57$	1550.71	−	26617.4i	0.0632183	−	1.08512i
$58$	−6599.27	−	11430.3i	−0.257588	−	0.446156i
$59$	42670.7			1.59588			0.797938	−	0.602739i	$-0.205924\pi$
$59$	42670.7			1.59588			0.797938	+	0.602739i	$0.205924\pi$
$60$	−3798.93	+	5775.79i	−0.136233	+	0.207125i
$61$		−	4181.30i		−	0.143876i	−0.997409	−	0.0719378i	$-0.977082\pi$
$61$		−	4181.30i		−	0.143876i	0.997409	−	0.0719378i	$-0.0229183\pi$
$62$	−34113.2			−1.12705
$63$	−3475.56	+	31310.7i	−0.110325	+	0.993896i
$64$	−36386.5			−1.11043
$65$		−	22553.5i		−	0.662110i
$66$	16535.4	+	963.338i	0.467255	+	0.0272219i
$67$	−12219.8			−0.332566			−0.166283	−	0.986078i	$-0.553177\pi$
$67$	−12219.8			−0.332566			−0.166283	+	0.986078i	$0.553177\pi$
$68$	2061.93	+	3571.36i	0.0540756	+	0.0936616i
$69$	60245.4	+	39625.4i	1.52335	+	1.00196i
$70$	−24346.9	+	42744.3i	−0.593880	+	1.04264i
$71$		−	7009.61i		−	0.165024i	−0.996590	−	0.0825121i	$-0.973706\pi$
$71$		−	7009.61i		−	0.165024i	0.996590	−	0.0825121i	$-0.0262943\pi$
$72$	37756.8	+	28110.8i	0.858349	+	0.639059i
$73$	−73466.6	+	42416.0i	−1.61355	+	0.931584i	−0.625013	+	0.780614i	$0.714906\pi$
$73$	−73466.6	+	42416.0i	−1.61355	+	0.931584i	−0.988538	+	0.150970i	$0.951760\pi$
$74$	21382.8	+	12345.4i	0.453927	+	0.262075i
$75$	37425.5	+	2180.38i	0.768271	+	0.0447589i
$76$	8833.69	+	5100.13i	0.175432	+	0.101286i
$77$	−26995.7	+	157.574i	−0.518881	+	0.00302870i
$78$	−24083.0	−	1403.06i	−0.448203	−	0.0261120i
$79$	−49797.6			−0.897720			−0.448860	−	0.893602i	$-0.648170\pi$
$79$	−49797.6			−0.897720			−0.448860	+	0.893602i	$0.648170\pi$
$80$	29656.0	+	51365.7i	0.518069	+	0.897323i
$81$	−16931.9	−	56569.4i	−0.286743	−	0.958008i
$82$	−87336.9	−	50424.0i	−1.43438	−	0.828137i
$83$	20121.1	+	34850.7i	0.320595	+	0.555286i	0.980611	−	0.195965i	$-0.0627840\pi$
$83$	20121.1	+	34850.7i	0.320595	+	0.555286i	−0.660016	+	0.751251i	$0.729451\pi$
$84$	−10107.7	−	6564.00i	−0.156299	−	0.101501i
$85$	25711.0	−	44532.8i	0.385986	−	0.668548i
$86$	−31774.8	+	18345.2i	−0.463272	+	0.267470i
$87$	−33688.0	−	22157.7i	−0.477174	−	0.313853i
$88$	−20169.0	+	34933.8i	−0.277637	+	0.480882i
$89$	−22608.2	+	39158.5i	−0.302545	+	0.524024i	−0.976712	−	0.214555i	$-0.931170\pi$
$89$	−22608.2	+	39158.5i	−0.302545	+	0.524024i	0.674166	+	0.738580i	$0.264503\pi$
$90$	10707.3	−	91581.4i	0.139339	−	1.19179i
$91$	39318.0	−	229.499i	0.497724	−	0.00290521i
$92$	−23890.7	+	13793.3i	−0.294279	+	0.169902i
$93$	−93131.9	+	46770.8i	−1.11658	+	0.560747i
$94$			52767.5i			0.615952i
$95$		−	127191.i		−	1.44593i
$96$	−29658.0	+	14894.2i	−0.328446	+	0.164945i
$97$	54936.0	−	31717.3i	0.592827	−	0.342269i	−0.173388	−	0.984854i	$-0.555471\pi$
$97$	54936.0	−	31717.3i	0.592827	−	0.342269i	0.766214	+	0.642585i	$0.222138\pi$
$98$	−74765.0	−	42009.6i	−0.786382	−	0.441859i
$99$	46463.7	−	20040.7i	0.476459	−	0.205507i
$100$	−7171.06	+	12420.6i	−0.0717106	+	0.124206i
$101$	−4001.98	+	6931.64i	−0.0390366	+	0.0676134i	−0.884884	−	0.465812i	$-0.845762\pi$
$101$	−4001.98	+	6931.64i	−0.0390366	+	0.0676134i	0.845847	+	0.533426i	$0.179096\pi$
$102$	−45953.5	−	30225.1i	−0.437339	−	0.287652i
$103$	177185.	−	102298.i	1.64564	−	0.950110i	0.666862	−	0.745181i	$-0.267637\pi$
$103$	177185.	−	102298.i	1.64564	−	0.950110i	0.978777	−	0.204929i	$-0.0656964\pi$
$104$	29375.3	−	50879.5i	0.266317	−	0.461275i
$105$	−7864.66	+	150076.i	−0.0696157	+	1.32843i
$106$	−19807.8	−	34308.2i	−0.171227	−	0.296574i
$107$	−56809.5	−	32799.0i	−0.479691	−	0.276949i	0.240597	−	0.970625i	$-0.422657\pi$
$107$	−56809.5	−	32799.0i	−0.479691	−	0.276949i	−0.720288	+	0.693676i	$0.755990\pi$
$108$	22247.0	+	3923.83i	0.183532	+	0.0323706i
$109$	76256.8	+	132081.i	0.614770	+	1.06481i	0.990425	+	0.138053i	$0.0440845\pi$
$109$	76256.8	+	132081.i	0.614770	+	1.06481i	−0.375655	+	0.926760i	$0.622582\pi$
$110$	79014.3			0.622621
$111$	75302.9	+	4387.09i	0.580102	+	0.0337963i
$112$	−89245.4	+	52222.8i	−0.672266	+	0.393382i
$113$	77481.4	+	44733.9i	0.570823	+	0.329565i	0.757478	−	0.652861i	$-0.226431\pi$
$113$	77481.4	+	44733.9i	0.570823	+	0.329565i	−0.186655	+	0.982425i	$0.559765\pi$
$114$	−135817.	−	7912.61i	−0.978797	−	0.0570240i
$115$	297903.	+	171994.i	2.10054	+	1.21275i
$116$	13359.2	−	7712.93i	0.0921797	−	0.0532200i
$117$	−67672.4	+	29188.5i	−0.457032	+	0.197127i
$118$		−	217730.i		−	1.43951i
$119$	77896.7	+	44369.5i	0.504257	+	0.287221i
$120$	187610.	+	123397.i	1.18933	+	0.782263i
$121$	−58844.3	−	101921.i	−0.365377	−	0.632851i
$122$	−21335.4			−0.129778
$123$	−307570.	−	17918.8i	−1.83308	−	0.106794i
$124$		−	39870.0i		−	0.232859i
$125$	−53547.9			−0.306526
$126$	159765.	+	17734.3i	0.896511	+	0.0995151i
$127$	261822.			1.44044			0.720221	−	0.693744i	$-0.244040\pi$
$127$	261822.			1.44044			0.720221	+	0.693744i	$0.244040\pi$
$128$			117537.i			0.634089i
$129$	−61595.7	+	93648.5i	−0.325894	+	0.495480i
$130$	−115081.			−0.597235
$131$	−111091.	−	192415.i	−0.565587	−	0.979626i	−0.996995	−	0.0774686i	$-0.975316\pi$
$131$	−111091.	−	192415.i	−0.565587	−	0.979626i	0.431408	−	0.902157i	$-0.358017\pi$
$132$	−1125.91	+	19325.8i	−0.00562429	+	0.0965390i
$133$	221736.	−	1294.27i	1.08694	−	0.00634447i
$134$			62352.6i			0.299980i
$135$	−96330.5	−	264705.i	−0.454914	−	1.25005i
$136$	116005.	−	66975.8i	0.537813	−	0.310506i
$137$	214626.	+	123915.i	0.976971	+	0.564054i	0.901354	−	0.433082i	$-0.142574\pi$
$137$	214626.	+	123915.i	0.976971	+	0.564054i	0.0756167	+	0.997137i	$0.475907\pi$
$138$	202192.	−	307407.i	0.903786	−	1.37409i
$139$	−166668.	−	96225.7i	−0.731669	−	0.422429i	0.0873635	−	0.996176i	$-0.472156\pi$
$139$	−166668.	−	96225.7i	−0.731669	−	0.422429i	−0.819032	+	0.573747i	$0.805489\pi$
$140$	−49957.7	−	28455.6i	−0.215418	−	0.122701i
$141$	72346.5	+	144060.i	0.306457	+	0.610231i
$142$	−35767.1			−0.148855
$143$	−31577.7	−	54694.2i	−0.129134	−	0.223667i
$144$	115744.	−	155461.i	0.465149	−	0.624762i
$145$	−166581.	−	96175.7i	−0.657970	−	0.379879i
$146$	216431.	+	374869.i	0.840305	+	1.45545i
$147$	−261712.	−	12183.5i	−0.998918	−	0.0465029i
$148$	−14428.7	+	24991.3i	−0.0541469	+	0.0937852i
$149$	−157839.	+	91128.5i	−0.582437	+	0.336270i	−0.762101	−	0.647458i	$-0.775832\pi$
$149$	−157839.	+	91128.5i	−0.582437	+	0.336270i	0.179664	+	0.983728i	$0.442499\pi$
$150$	11125.6	−	190967.i	0.0403733	−	0.692993i
$151$	199293.	−	345186.i	0.711295	−	1.23200i	−0.253076	−	0.967446i	$-0.581442\pi$
$151$	199293.	−	345186.i	0.711295	−	1.23200i	0.964371	−	0.264553i	$-0.0852245\pi$
$152$	165663.	−	286937.i	0.581590	−	1.00734i
$153$	−166897.	−	19512.8i	−0.576394	−	0.0673893i
$154$	804.032	+	137748.i	0.00273194	+	0.468039i
$155$	−430549.	+	248578.i	−1.43944	+	0.831061i
$156$	1639.83	−	28147.2i	0.00539496	−	0.0926027i
$157$			55937.2i			0.181114i	0.995891	+	0.0905570i	$0.0288647\pi$
$157$			55937.2i			0.181114i	−0.995891	+	0.0905570i	$0.971135\pi$
$158$			254096.i			0.809759i
$159$	−101115.	−	66506.8i	−0.317193	−	0.208628i
$160$	−137109.	+	79159.9i	−0.423415	+	0.244459i
$161$	−296811.	+	521092.i	−0.902433	+	1.58434i
$162$	−288650.	+	86396.2i	−0.864140	+	0.258647i
$163$	83312.6	−	144302.i	0.245608	−	0.425405i	−0.716695	−	0.697387i	$-0.754346\pi$
$163$	83312.6	−	144302.i	0.245608	−	0.425405i	0.962302	+	0.271982i	$0.0876792\pi$
$164$	58933.3	−	102075.i	0.171100	−	0.296355i
$165$	215716.	−	108332.i	0.616839	−	0.309776i
$166$	177829.	−	102669.i	0.500878	−	0.289182i
$167$	218053.	−	377678.i	0.605020	−	1.04793i	−0.387028	−	0.922068i	$-0.626498\pi$
$167$	218053.	−	377678.i	0.605020	−	1.04793i	0.992048	−	0.125858i	$-0.0401684\pi$
$168$	−213213.	+	328321.i	−0.582827	+	0.897481i
$169$	−139655.	−	241889.i	−0.376131	−	0.651478i
$170$	−227232.	−	131192.i	−0.603041	−	0.348166i
$171$	−381641.	+	164609.i	−0.998078	+	0.430491i
$172$	−21441.0	−	37136.9i	−0.0552617	−	0.0957161i
$173$	−47742.7			−0.121281			−0.0606403	−	0.998160i	$-0.519314\pi$
$173$	−47742.7			−0.121281			−0.0606403	+	0.998160i	$0.519314\pi$
$174$	−113061.	+	171896.i	−0.283101	+	0.430419i
$175$	1819.81	+	311772.i	0.00449191	+	0.769560i
$176$	143837.	+	83044.4i	0.350017	+	0.202082i
$177$	−298518.	−	594422.i	−0.716205	−	1.42614i
$178$	199810.	+	115360.i	0.472679	+	0.272901i
$179$	143517.	−	82859.4i	0.334788	−	0.193290i	−0.323177	−	0.946339i	$-0.604751\pi$
$179$	143517.	−	82859.4i	0.334788	−	0.193290i	0.657965	+	0.753049i	$0.271418\pi$
$180$	107036.	+	12514.2i	0.246235	+	0.0287886i
$181$			505612.i			1.14715i	0.819153	+	0.573575i	$0.194444\pi$
$181$			505612.i			1.14715i	−0.819153	+	0.573575i	$0.805556\pi$
$182$	−1171.04	−	200624.i	−0.00262055	−	0.448956i
$183$	−58247.5	+	29251.8i	−0.128573	+	0.0645692i
$184$	448036.	+	776021.i	0.975592	+	1.68978i
$185$	359835.			0.772991
$186$	238652.	+	475213.i	0.505804	+	1.00718i
$187$		−	143995.i		−	0.301122i
$188$	−61672.3			−0.127261
$189$	460487.	−	170629.i	0.937697	−	0.347455i
$190$	−649003.			−1.30426
$191$			1.00698e6i			1.99728i	0.0521379	+	0.998640i	$0.483396\pi$
$191$			1.00698e6i			1.99728i	−0.0521379	+	0.998640i	$0.516604\pi$
$192$	254555.	+	506881.i	0.498344	+	0.992323i
$193$	−507202.			−0.980139			−0.490070	−	0.871683i	$-0.663029\pi$
$193$	−507202.			−0.980139			−0.490070	+	0.871683i	$0.663029\pi$
$194$	−161840.	−	280315.i	−0.308732	−	0.534740i
$195$	−314180.	+	157781.i	−0.591688	+	0.297145i
$196$	49099.0	−	87382.0i	0.0912919	−	0.162473i
$197$			1.01655e6i			1.86622i	0.359597	+	0.933108i	$0.382914\pi$
$197$			1.01655e6i			1.86622i	−0.359597	+	0.933108i	$0.617086\pi$
$198$	−102259.	−	237085.i	−0.185370	−	0.429774i
$199$	680636.	−	392965.i	1.21838	−	0.703431i	0.253808	−	0.967255i	$-0.418317\pi$
$199$	680636.	−	392965.i	1.21838	−	0.703431i	0.964571	+	0.263823i	$0.0849836\pi$
$200$	403449.	+	232931.i	0.713204	+	0.411768i
$201$	85488.3	+	170228.i	0.149251	+	0.297194i
$202$	35369.2	+	20420.4i	0.0609884	+	0.0352117i
$203$	165970.	−	291384.i	0.282677	−	0.496278i
$204$	35325.8	−	53708.4i	0.0594314	−	0.0903580i
$205$	−1.46973e6			−2.44260
$206$	−521984.	−	904102.i	−0.857016	−	1.48440i
$207$	130531.	−	1.11646e6i	0.211733	−	1.81099i
$208$	−209493.	−	120951.i	−0.335745	−	0.193843i
$209$	−178084.	−	308450.i	−0.282006	−	0.488449i
$210$	765776.	+	40130.1i	1.19827	+	0.0627945i
$211$	131050.	−	226985.i	0.202642	−	0.350986i	−0.746737	−	0.665120i	$-0.768381\pi$
$211$	131050.	−	226985.i	0.202642	−	0.350986i	0.949379	+	0.314133i	$0.101714\pi$
$212$	40097.9	−	23150.5i	0.0612748	−	0.0353770i
$213$	−97647.1	+	49038.3i	−0.147472	+	0.0740604i
$214$	−167359.	+	289875.i	−0.249813	+	0.432689i
$215$	−267357.	+	463076.i	−0.394453	+	0.683212i
$216$	127454.	−	722629.i	0.185875	−	1.05386i
$217$	−437733.	−	748058.i	−0.631044	−	1.07841i
$218$	673953.	−	389107.i	0.960480	−	0.554533i
$219$	1.10484e6	+	726687.i	1.55664	+	1.02385i
$220$			92348.4i			0.128639i
$221$			209722.i			0.288844i
$222$	22385.5	−	384239.i	0.0304849	−	0.523262i
$223$	−800834.	+	462362.i	−1.07840	+	0.622615i	−0.930465	−	0.366382i	$-0.880596\pi$
$223$	−800834.	+	462362.i	−1.07840	+	0.622615i	−0.147937	+	0.988997i	$0.547263\pi$
$224$	−139397.	−	238220.i	−0.185623	−	0.317218i
$225$	−231450.	−	536608.i	−0.304790	−	0.706644i
$226$	228258.	−	395355.i	0.297273	−	0.514892i
$227$	418812.	−	725404.i	0.539455	−	0.934363i	−0.459479	−	0.888189i	$-0.651964\pi$
$227$	418812.	−	725404.i	0.539455	−	0.934363i	0.998933	−	0.0461740i	$-0.0147029\pi$
$228$	9247.91	−	158737.i	0.0117817	−	0.202228i
$229$	473896.	−	273604.i	0.597165	−	0.344773i	−0.170760	−	0.985313i	$-0.554622\pi$
$229$	473896.	−	273604.i	0.597165	−	0.344773i	0.767926	+	0.640539i	$0.221289\pi$
$230$	877615.	−	1.52007e6i	1.09392	−	1.89472i
$231$	191053.	+	374960.i	0.235572	+	0.462333i
$232$	−250533.	−	433935.i	−0.305594	−	0.529304i
$233$	−578196.	−	333821.i	−0.697726	−	0.402832i	0.108774	−	0.994067i	$-0.465308\pi$
$233$	−578196.	−	333821.i	−0.697726	−	0.402832i	−0.806500	+	0.591234i	$0.798641\pi$
$234$	148937.	+	345304.i	0.177812	+	0.412251i
$235$	384508.	+	665988.i	0.454188	+	0.786677i
$236$	254474.			0.297415
$237$	348378.	+	693704.i	0.402883	+	0.802238i
$238$	226399.	−	397474.i	0.259079	−	0.454848i
$239$	441296.	+	254782.i	0.499730	+	0.288519i	0.728602	−	0.684937i	$-0.240170\pi$
$239$	441296.	+	254782.i	0.499730	+	0.288519i	−0.228872	+	0.973456i	$0.573504\pi$
$240$	508079.	−	772470.i	0.569381	−	0.865672i
$241$	933206.	+	538787.i	1.03499	+	0.597550i	0.918409	−	0.395632i	$-0.129474\pi$
$241$	933206.	+	538787.i	1.03499	+	0.597550i	0.116577	+	0.993182i	$0.462808\pi$
$242$	−520062.	+	300258.i	−0.570843	+	0.329576i
$243$	−669585.	+	631621.i	−0.727428	+	0.686184i
$244$		−	24935.9i		−	0.0268133i
$245$	−1.24974e6	+	14589.9i	−1.33016	+	0.0155288i
$246$	−91432.2	+	1.56940e6i	−0.0963300	+	1.65347i
$247$	259371.	+	449244.i	0.270508	+	0.468533i
$248$	−1.29506e6			−1.33709
$249$	344723.	−	524107.i	0.352348	−	0.535700i
$250$			273232.i			0.276492i
$251$	855998.			0.857607			0.428803	−	0.903398i	$-0.358935\pi$
$251$	855998.			0.857607			0.428803	+	0.903398i	$0.358935\pi$
$252$	−20727.1	+	186726.i	−0.0205607	+	0.185227i
$253$	963255.			0.946107
$254$		−	1.33597e6i		−	1.29930i
$255$	−800233.	−	46621.0i	−0.770665	−	0.0448984i
$256$	−564626.			−0.538469
$257$	292270.	+	506226.i	0.276027	+	0.478092i	0.970394	−	0.241529i	$-0.0776489\pi$
$257$	292270.	+	506226.i	0.276027	+	0.478092i	−0.694367	+	0.719621i	$0.744316\pi$
$258$	477849.	+	314297.i	0.446932	+	0.293962i
$259$	3661.60	+	627310.i	0.00339173	+	0.581076i
$260$		−	134501.i		−	0.123394i
$261$	−72990.4	+	624301.i	−0.0663230	+	0.567274i
$262$	−981812.	+	566849.i	−0.883639	+	0.510169i
$263$	614222.	+	354621.i	0.547565	+	0.316137i	0.748139	−	0.663542i	$-0.230947\pi$
$263$	614222.	+	354621.i	0.547565	+	0.316137i	−0.200574	+	0.979679i	$0.564281\pi$
$264$	627743.	+	36571.9i	0.554335	+	0.0322951i
$265$	−499997.	−	288673.i	−0.437374	−	0.252518i
$266$	−6604.11	−	1.13142e6i	−0.00572282	−	0.980440i
$267$	703660.	+	40994.7i	0.604067	+	0.0351925i
$268$	−72875.0			−0.0619786
$269$	−299666.	−	519036.i	−0.252497	−	0.437338i	0.711716	−	0.702468i	$-0.247918\pi$
$269$	−299666.	−	519036.i	−0.252497	−	0.437338i	−0.964213	+	0.265130i	$0.914585\pi$
$270$	−1.35068e6	+	491534.i	−1.12757	+	0.410340i
$271$	1.09631e6	+	632957.i	0.906800	+	0.523541i	0.879400	−	0.476083i	$-0.157944\pi$
$271$	1.09631e6	+	632957.i	0.906800	+	0.523541i	0.0273998	+	0.999625i	$0.491277\pi$
$272$	−275768.	−	477644.i	−0.226007	−	0.391455i
$273$	−278261.	−	546113.i	−0.225967	−	0.443482i
$274$	632284.	−	1.09515e6i	0.508787	−	0.881245i
$275$	433698.	−	250396.i	0.345824	−	0.199662i
$276$	359283.	+	236313.i	0.283899	+	0.186730i
$277$	191750.	−	332121.i	0.150154	−	0.260074i	−0.781130	−	0.624368i	$-0.785356\pi$
$277$	191750.	−	332121.i	0.150154	−	0.260074i	0.931284	+	0.364294i	$0.118690\pi$
$278$	−490999.	+	850436.i	−0.381038	+	0.659978i
$279$	1.30308e6	+	970169.i	1.00221	+	0.746168i
$280$	−924298.	+	1.62273e6i	−0.704558	+	1.23695i
$281$	1.22655e6	−	708146.i	0.926654	−	0.535004i	0.0409025	−	0.999163i	$-0.486977\pi$
$281$	1.22655e6	−	708146.i	0.926654	−	0.535004i	0.885752	+	0.464159i	$0.153643\pi$
$282$	735075.	−	369154.i	0.550439	−	0.276430i
$283$			1.27393e6i			0.945540i	0.881186	+	0.472770i	$0.156746\pi$
$283$			1.27393e6i			0.945540i	−0.881186	+	0.472770i	$0.843254\pi$
$284$		−	41803.0i		−	0.0307547i
$285$	−1.77183e6	+	889812.i	−1.29214	+	0.648913i
$286$	−279082.	+	161128.i	−0.201751	+	0.116481i
$287$	−14955.6	−	2.56221e6i	−0.0107176	−	1.83616i
$288$	414967.	+	308952.i	0.294803	+	0.219487i
$289$	470845.	−	815528.i	0.331614	−	0.574373i
$290$	−490744.	+	849994.i	−0.342657	+	0.593500i
$291$	−826162.	−	543394.i	−0.571917	−	0.376168i
$292$	−438130.	+	252955.i	−0.300709	+	0.173614i
$293$	−545071.	+	944090.i	−0.370923	+	0.642458i	−0.989708	−	0.143103i	$-0.954292\pi$
$293$	−545071.	+	944090.i	−0.370923	+	0.642458i	0.618785	+	0.785561i	$0.287625\pi$
$294$	−62167.4	+	1.33541e6i	−0.0419464	+	0.901042i
$295$	−1.58657e6	−	2.74802e6i	−1.06146	−	1.83850i
$296$	811770.	+	468676.i	0.538522	+	0.310916i
$297$	−604231.	−	507059.i	−0.397477	−	0.333555i
$298$	464990.	+	805387.i	0.303322	+	0.525368i
$299$	−1.40294e6			−0.907530
$300$	223193.	+	13003.1i	0.143178	+	0.00834147i
$301$	−810012.	−	461378.i	−0.515318	−	0.293522i
$302$	−1.76134e6	−	1.01691e6i	−1.11129	−	0.641601i
$303$	124558.	+	7256.67i	0.0779410	+	0.00454079i
$304$	−1.18144e6	−	682105.i	−0.733209	−	0.423319i
$305$	−269278.	+	155468.i	−0.165749	+	0.0956954i
$306$	−99565.6	+	851604.i	−0.0607863	+	0.519917i
$307$			224808.i			0.136134i	0.997681	+	0.0680670i	$0.0216832\pi$
$307$			224808.i			0.136134i	−0.997681	+	0.0680670i	$0.978317\pi$
$308$	−160993.	+	939.716i	−0.0967010	+	0.000564443i
$309$	−2.66462e6	−	1.75261e6i	−1.58759	−	1.04421i
$310$	1.26839e6	+	2.19691e6i	0.749632	+	1.29840i
$311$	1.20840e6			0.708449			0.354225	−	0.935160i	$-0.384745\pi$
$311$	1.20840e6			0.708449			0.354225	+	0.935160i	$0.384745\pi$
$312$	−914281.	−	53265.3i	−0.531732	−	0.0309783i
$313$			436880.i			0.252059i	0.992027	+	0.126029i	$0.0402233\pi$
$313$			436880.i			0.252059i	−0.992027	+	0.126029i	$0.959777\pi$
$314$	285424.			0.163368
$315$	2.14565e6	−	940355.i	1.21838	−	0.533968i
$316$	−296977.			−0.167303
$317$			2.38131e6i			1.33097i	0.746412	+	0.665484i	$0.231775\pi$
$317$			2.38131e6i			1.33097i	−0.746412	+	0.665484i	$0.768225\pi$
$318$	−339356.	+	515948.i	−0.188186	+	0.286113i
$319$	−538633.			−0.296358
$320$	1.35291e6	+	2.34331e6i	0.738575	+	1.27925i
$321$	−59473.3	+	1.02084e6i	−0.0322151	+	0.552961i
$322$	2.65891e6	+	1.51450e6i	1.42911	+	0.814010i
$323$			1.18273e6i			0.630785i
$324$	−100976.	−	337361.i	−0.0534387	−	0.178539i
$325$	−631662.	+	364690.i	−0.331724	+	0.191521i
$326$	−736311.	−	425109.i	−0.383723	−	0.221542i
$327$	1.30646e6	−	1.98631e6i	0.675659	−	1.02725i
$328$	−3.31563e6	−	1.91428e6i	−1.70169	−	0.982473i
$329$	−1.15712e6	+	677100.i	−0.589371	+	0.344876i
$330$	−552774.	−	1.10071e6i	−0.279423	−	0.556399i
$331$	3.65382e6			1.83306			0.916531	−	0.399964i	$-0.130978\pi$
$331$	3.65382e6			1.83306			0.916531	+	0.399964i	$0.130978\pi$
$332$	119995.	+	207838.i	0.0597475	+	0.103486i
$333$	−465695.	−	1.07970e6i	−0.230139	−	0.533569i
$334$	−1.92713e6	−	1.11263e6i	−0.945248	−	0.545739i
$335$	454354.	+	786964.i	0.221199	+	0.383127i
$336$	1.35184e6	+	877887.i	0.653245	+	0.424219i
$337$	1.23728e6	−	2.14303e6i	0.593462	−	1.02791i	−0.400300	−	0.916384i	$-0.631094\pi$
$337$	1.23728e6	−	2.14303e6i	0.593462	−	1.02791i	0.993762	−	0.111522i	$-0.0355725\pi$
$338$	−1.23426e6	+	712600.i	−0.587645	+	0.339277i
$339$	81114.6	−	1.39230e6i	0.0383354	−	0.658013i
$340$	153332.	−	265579.i	0.0719342	−	0.124594i
$341$	−696081.	+	1.20565e6i	−0.324171	+	0.561480i
$342$	839933.	+	1.94735e6i	0.388311	+	0.900284i
$343$	−38152.1	−	2.17856e6i	−0.0175099	−	0.999847i
$344$	−1.20629e6	+	696450.i	−0.549610	+	0.317317i
$345$	311872.	−	5.35318e6i	0.141068	−	2.42138i
$346$			243611.i			0.109397i
$347$		−	685946.i		−	0.305820i	−0.988240	−	0.152910i	$-0.951136\pi$
$347$		−	685946.i		−	0.305820i	0.988240	−	0.152910i	$-0.0488645\pi$
$348$	−200904.	−	132141.i	−0.0889284	−	0.0584911i
$349$	−145771.	+	84161.1i	−0.0640632	+	0.0369869i	−0.531689	−	0.846939i	$-0.678443\pi$
$349$	−145771.	+	84161.1i	−0.0640632	+	0.0369869i	0.467626	+	0.883926i	$0.345109\pi$
$350$	1.59084e6	−	9285.74i	0.694157	−	0.00405178i
$351$	880036.	+	738509.i	0.381270	+	0.319954i
$352$	−221668.	+	383940.i	−0.0953556	+	0.165161i
$353$	−189290.	+	327859.i	−0.0808518	+	0.140039i	−0.903616	−	0.428343i	$-0.859097\pi$
$353$	−189290.	+	327859.i	−0.0808518	+	0.140039i	0.822764	+	0.568383i	$0.192431\pi$
$354$	−3.03309e6	+	1.52321e6i	−1.28640	+	0.646030i
$355$	−451423.	+	260629.i	−0.190113	+	0.109762i
$356$	−134828.	+	233529.i	−0.0563838	+	0.0976596i
$357$	73132.5	−	1.39554e6i	0.0303697	−	0.579525i
$358$	−422797.	−	732305.i	−0.174351	−	0.301984i
$359$	122992.	+	71009.6i	0.0503665	+	0.0290791i	0.524972	−	0.851120i	$-0.324076\pi$
$359$	122992.	+	71009.6i	0.0503665	+	0.0290791i	−0.474605	+	0.880199i	$0.657409\pi$
$360$	406487.	−	3.47677e6i	0.165307	−	1.41390i
$361$	224685.	+	389165.i	0.0907414	+	0.157169i
$362$	2.57992e6			1.03475
$363$	−1.00814e6	+	1.53276e6i	−0.401565	+	0.610529i
$364$	234480.	−	1368.66i	0.0927581	−	0.000541428i
$365$	5.46323e6	+	3.15420e6i	2.14643	+	1.23924i
$366$	149260.	+	297212.i	0.0582425	+	0.115975i
$367$	−1.10847e6	−	639975.i	−0.429594	−	0.248026i	0.269580	−	0.962978i	$-0.413115\pi$
$367$	−1.10847e6	−	639975.i	−0.429594	−	0.248026i	−0.699174	+	0.714952i	$0.746449\pi$
$368$	3.19521e6	−	1.84475e6i	1.22993	−	0.710099i
$369$	1.90210e6	+	4.40996e6i	0.727224	+	1.68604i
$370$		−	1.83609e6i		−	0.697251i
$371$	498164.	−	874595.i	0.187905	−	0.329892i
$372$	−555408.	+	278925.i	−0.208092	+	0.104503i
$373$	1.01829e6	+	1.76372e6i	0.378964	+	0.656384i	0.990912	−	0.134514i	$-0.0429472\pi$
$373$	1.01829e6	+	1.76372e6i	0.378964	+	0.656384i	−0.611948	+	0.790898i	$0.709614\pi$
$374$	−734744.			−0.271617
$375$	374614.	+	745947.i	0.137564	+	0.273924i
$376$			2.00325e6i			0.730743i
$377$	784495.			0.284274
$378$	−870648.	−	2.34967e6i	−0.313410	−	0.845819i
$379$	−807467.			−0.288753			−0.144377	−	0.989523i	$-0.546118\pi$
$379$	−807467.			−0.288753			−0.144377	+	0.989523i	$0.546118\pi$
$380$		−	758526.i		−	0.269471i
$381$	−1.83167e6	−	3.64730e6i	−0.646449	−	1.28724i
$382$	5.13821e6			1.80158
$383$	−1.28802e6	−	2.23092e6i	−0.448669	−	0.777118i	0.549631	−	0.835408i	$-0.314768\pi$
$383$	−1.28802e6	−	2.23092e6i	−0.448669	−	0.777118i	−0.998300	+	0.0582902i	$0.981435\pi$
$384$	1.63735e6	−	822274.i	0.566647	−	0.284569i
$385$	1.01389e6	+	1.73268e6i	0.348610	+	0.595753i
$386$			2.58804e6i			0.884103i
$387$	1.73548e6	+	202904.i	0.589037	+	0.0688675i
$388$	327620.	−	189152.i	0.110482	−	0.0637868i
$389$	−726630.	−	419520.i	−0.243466	−	0.140565i	0.373302	−	0.927710i	$-0.378225\pi$
$389$	−726630.	−	419520.i	−0.243466	−	0.140565i	−0.616769	+	0.787144i	$0.711559\pi$
$390$	805091.	+	1.60313e6i	0.268030	+	0.533713i
$391$	−2.77016e6	−	1.59935e6i	−0.916354	−	0.529057i
$392$	−2.83836e6	−	1.59484e6i	−0.932935	−	0.524206i
$393$	−1.90325e6	+	2.89365e6i	−0.621605	+	0.945073i
$394$	5.18701e6			1.68336
$395$	1.85156e6	+	3.20700e6i	0.597097	+	1.03420i
$396$	277094.	−	119516.i	0.0887952	−	0.0382992i
$397$	2.13404e6	+	1.23209e6i	0.679559	+	0.392344i	0.799689	−	0.600415i	$-0.204998\pi$
$397$	2.13404e6	+	1.23209e6i	0.679559	+	0.392344i	−0.120130	+	0.992758i	$0.538331\pi$
$398$	−2.00514e6	−	3.47300e6i	−0.634507	−	1.09900i
$399$	−1.56926e6	−	3.07983e6i	−0.493473	−	0.968487i
$400$	959077.	−	1.66117e6i	0.299712	−	0.519116i
$401$	−3.84155e6	+	2.21792e6i	−1.19302	+	0.688788i	−0.958989	−	0.283443i	$-0.908523\pi$
$401$	−3.84155e6	+	2.21792e6i	−1.19302	+	0.688788i	−0.234026	+	0.972230i	$0.575190\pi$
$402$	868601.	−	436211.i	0.268074	−	0.134627i
$403$	1.01381e6	−	1.75597e6i	0.310953	−	0.538586i
$404$	−23866.5	+	41338.0i	−0.00727504	+	0.0126007i
$405$	−3.01355e6	+	3.19377e6i	−0.912936	+	0.967533i
$406$	−1.48681e6	−	846877.i	−0.447652	−	0.254980i
$407$	872633.	−	503815.i	0.261123	−	0.150760i
$408$	−1.74456e6	−	1.14746e6i	−0.518843	−	0.341260i
$409$		−	1.50062e6i		−	0.443569i	−0.975096	−	0.221785i	$-0.928812\pi$
$409$		−	1.50062e6i		−	0.443569i	0.975096	−	0.221785i	$-0.0711882\pi$
$410$			7.49940e6i			2.20326i
$411$	224691.	−	3.85674e6i	0.0656115	−	1.12620i
$412$	1.05667e6	−	610071.i	0.306689	−	0.177067i
$413$	4.77454e6	−	2.79387e6i	1.37739	−	0.805992i
$414$	−5.69682e6	−	666046.i	−1.63355	−	0.190987i
$415$	1.49627e6	−	2.59162e6i	0.426472	−	0.738671i
$416$	322850.	−	559192.i	0.0914675	−	0.158426i
$417$	−174483.	+	2.99494e6i	−0.0491375	+	0.843428i
$418$	−1.57389e6	+	908687.i	−0.440590	+	0.254374i
$419$	1.30169e6	−	2.25460e6i	0.362221	−	0.627385i	−0.626105	−	0.779738i	$-0.715352\pi$
$419$	1.30169e6	−	2.25460e6i	0.362221	−	0.627385i	0.988326	+	0.152354i	$0.0486854\pi$
$420$	−46902.3	+	895005.i	−0.0129739	+	0.247572i
$421$	2.21517e6	+	3.83679e6i	0.609120	+	1.05503i	0.991386	+	0.130974i	$0.0418104\pi$
$421$	2.21517e6	+	3.83679e6i	0.609120	+	1.05503i	−0.382266	+	0.924052i	$0.624856\pi$
$422$	−1.15821e6	−	668691.i	−0.316596	−	0.182787i
$423$	1.50069e6	−	2.01564e6i	0.407793	−	0.547725i
$424$	−751979.	−	1.30247e6i	−0.203138	−	0.351845i
$425$	−1.66299e6			−0.446599
$426$	250222.	+	498252.i	0.0668038	+	0.133023i
$427$	−273771.	−	467858.i	−0.0726638	−	0.124178i
$428$	−338793.	−	195602.i	−0.0893974	−	0.0516136i
$429$	−541002.	+	822526.i	−0.141924	+	0.215778i
$430$	2.36288e6	+	1.36421e6i	0.616269	+	0.355803i
$431$	−3.12312e6	+	1.80313e6i	−0.809832	+	0.467557i	−0.846898	−	0.531756i	$-0.821532\pi$
$431$	−3.12312e6	+	1.80313e6i	−0.809832	+	0.467557i	0.0370654	+	0.999313i	$0.488199\pi$
$432$	−2.97537e6	−	524784.i	−0.767064	−	0.135292i
$433$			3.26141e6i			0.835960i	0.908456	+	0.417980i	$0.137262\pi$
$433$			3.26141e6i			0.835960i	−0.908456	+	0.417980i	$0.862738\pi$
$434$	−3.81703e6	+	2.23357e6i	−0.972749	+	0.569213i
$435$	−174392.	+	2.99339e6i	−0.0441880	+	0.758472i
$436$	454771.	+	787686.i	0.114571	+	0.198443i
$437$	−7.91193e6			−1.98189
$438$	3.70798e6	−	5.63752e6i	0.923533	−	1.40411i
$439$		−	6.66779e6i		−	1.65128i	−0.564198	−	0.825639i	$-0.690815\pi$
$439$		−	6.66779e6i		−	1.65128i	0.564198	−	0.825639i	$-0.309185\pi$
$440$	2.99967e6			0.738656
$441$	1.66118e6	+	3.73100e6i	0.406743	+	0.913543i
$442$	1.07012e6			0.260542
$443$			2.71496e6i			0.657287i	0.944454	+	0.328643i	$0.106591\pi$
$443$			2.71496e6i			0.657287i	−0.944454	+	0.328643i	$0.893409\pi$
$444$	449082.	+	26163.2i	0.108111	+	0.00629844i
$445$	3.36244e6			0.804924
$446$	2.35924e6	+	4.08632e6i	0.561610	+	0.972737i
$447$	2.37368e6	+	1.56125e6i	0.561893	+	0.369576i
$448$	−4.07139e6	+	2.38241e6i	−0.958402	+	0.560818i
$449$		−	3.48056e6i		−	0.814767i	−0.913257	−	0.407384i	$-0.866441\pi$
$449$		−	3.48056e6i		−	0.814767i	0.913257	−	0.407384i	$-0.133559\pi$
$450$	−2.73809e6	+	1.18099e6i	−0.637405	+	0.274926i
$451$	−3.56422e6	+	2.05780e6i	−0.825131	+	0.476390i
$452$	462073.	+	266778.i	0.106381	+	0.0614192i
$453$	−6.20283e6	−	361372.i	−1.42018	−	0.0827388i
$454$	−3.70143e6	−	2.13702e6i	−0.842811	−	0.486597i
$455$	−1.47669e6	−	2.52357e6i	−0.334396	−	0.571462i
$456$	−5.15612e6	−	300392.i	−1.16121	−	0.0676513i
$457$	−5.63553e6			−1.26225			−0.631123	−	0.775682i	$-0.717406\pi$
$457$	−5.63553e6			−1.26225			−0.631123	+	0.775682i	$0.717406\pi$
$458$	−1.39609e6	−	2.41809e6i	−0.310992	−	0.538653i
$459$	895765.	+	2.46146e6i	0.198455	+	0.545332i
$460$	1.77659e6	+	1.02572e6i	0.391466	+	0.226013i
$461$	−884339.	−	1.53172e6i	−0.193806	−	0.335681i	0.752703	−	0.658361i	$-0.228750\pi$
$461$	−884339.	−	1.53172e6i	−0.193806	−	0.335681i	−0.946508	+	0.322679i	$0.895416\pi$
$462$	1.91326e6	−	974865.i	0.417033	−	0.212490i
$463$	−1.63522e6	+	2.83229e6i	−0.354507	+	0.614024i	−0.987033	−	0.160515i	$-0.948685\pi$
$463$	−1.63522e6	+	2.83229e6i	−0.354507	+	0.614024i	0.632527	+	0.774539i	$0.282018\pi$
$464$	−1.78669e6	+	1.03155e6i	−0.385261	+	0.222431i
$465$	6.47487e6	+	4.25874e6i	1.38867	+	0.913373i
$466$	−1.70335e6	+	2.95029e6i	−0.363362	+	0.629361i
$467$	3.95618e6	−	6.85231e6i	0.839429	−	1.45393i	−0.0509430	−	0.998702i	$-0.516223\pi$
$467$	3.95618e6	−	6.85231e6i	0.839429	−	1.45393i	0.890372	−	0.455233i	$-0.150444\pi$
$468$	−403576.	+	174070.i	−0.0851746	+	0.0367376i
$469$	−1.36731e6	+	800095.i	−0.287035	+	0.167961i
$470$	3.39826e6	−	1.96198e6i	0.709597	−	0.409686i
$471$	779232.	−	391329.i	0.161851	−	0.0812812i
$472$		−	8.26585e6i		−	1.70778i
$473$			1.49733e6i			0.307727i
$474$	3.53968e6	−	1.77762e6i	0.723633	−	0.363408i
$475$	−3.56228e6	+	2.05668e6i	−0.724427	+	0.418248i
$476$	464550.	+	264605.i	0.0939756	+	0.0535279i
$477$	−219082.	+	1.87385e6i	−0.0440871	+	0.377085i
$478$	1.30005e6	−	2.25175e6i	0.260249	−	0.450765i
$479$	−926652.	+	1.60501e6i	−0.184535	+	0.319623i	−0.943420	−	0.331601i	$-0.892411\pi$
$479$	−926652.	+	1.60501e6i	−0.184535	+	0.319623i	0.758885	+	0.651225i	$0.225744\pi$
$480$	2.06193e6	+	1.35620e6i	0.408480	+	0.268671i
$481$	−1.27095e6	+	733785.i	−0.250476	+	0.144613i
$482$	2.74920e6	−	4.76176e6i	0.539000	−	0.933576i
$483$	9.33550e6	+	489222.i	1.82083	+	0.0954197i
$484$	−350928.	−	607825.i	−0.0680933	−	0.117941i
$485$	−4.08523e6	−	2.35861e6i	−0.788610	−	0.455304i
$486$	3.22290e6	+	3.41661e6i	0.618950	+	0.656153i
$487$	−2.42402e6	−	4.19852e6i	−0.463141	−	0.802184i	0.535974	−	0.844234i	$-0.319944\pi$
$487$	−2.42402e6	−	4.19852e6i	−0.463141	−	0.802184i	−0.999115	+	0.0420504i	$0.986611\pi$
$488$	−809971.			−0.153964
$489$	−2.59303e6	−	151068.i	−0.490384	−	0.0285694i
$490$	74446.4	+	6.37690e6i	0.0140073	+	1.19983i
$491$	6.77492e6	+	3.91150e6i	1.26824	+	0.732217i	0.974654	−	0.223716i	$-0.0718190\pi$
$491$	6.77492e6	+	3.91150e6i	1.26824	+	0.732217i	0.293583	+	0.955934i	$0.405152\pi$
$492$	−1.83425e6	−	106862.i	−0.341622	−	0.0199026i
$493$	1.54902e6	+	894326.i	0.287038	+	0.165721i
$494$	2.29231e6	−	1.32346e6i	0.422625	−	0.244003i
$495$	−3.01823e6	−	2.24714e6i	−0.553656	−	0.412209i
$496$			5.33232e6i			0.973223i
$497$	−458955.	−	784325.i	−0.0833449	−	0.142431i
$498$	−2.67430e6	−	1.75897e6i	−0.483211	−	0.317824i
$499$	3.83892e6	+	6.64921e6i	0.690173	+	1.19541i	0.971781	+	0.235885i	$0.0757989\pi$
$499$	3.83892e6	+	6.64921e6i	0.690173	+	1.19541i	−0.281608	+	0.959529i	$0.590868\pi$
$500$	−319342.			−0.0571256
$501$	−6.78670e6	−	395388.i	−1.20799	−	0.0703768i
$502$		−	4.36780e6i		−	0.773576i
$503$	−2.55761e6			−0.450727			−0.225363	−	0.974275i	$-0.572357\pi$
$503$	−2.55761e6			−0.450727			−0.225363	+	0.974275i	$0.572357\pi$
$504$	6.06527e6	+	673261.i	1.06359	+	0.118061i
$505$	595202.			0.103857
$506$		−	4.91509e6i		−	0.853405i
$507$	−2.39262e6	+	3.63768e6i	−0.413385	+	0.628500i
$508$	1.56142e6			0.268448
$509$	−550752.	−	953931.i	−0.0942241	−	0.163201i	0.815060	−	0.579376i	$-0.196704\pi$
$509$	−550752.	−	953931.i	−0.0942241	−	0.163201i	−0.909285	+	0.416175i	$0.863370\pi$
$510$	−237887.	+	4.08325e6i	−0.0404991	+	0.695154i
$511$	−5.44320e6	+	9.55628e6i	−0.922150	+	1.61896i
$512$			6.64224e6i			1.11980i
$513$	4.96299e6	+	4.16485e6i	0.832627	+	0.698724i
$514$	2.58306e6	−	1.49133e6i	0.431247	−	0.248981i
$515$	−1.31761e7	−	7.60723e6i	−2.18912	−	1.26389i
$516$	−367336.	+	558488.i	−0.0607351	+	0.0923400i
$517$	1.86493e6	+	1.07672e6i	0.306858	+	0.177164i
$518$	3.20090e6	−	18683.6i	0.524140	−	0.00305940i
$519$	334001.	+	665078.i	0.0544289	+	0.108381i
$520$	−4.36889e6			−0.708538
$521$	1.54794e6	+	2.68110e6i	0.249838	+	0.432732i	0.963481	−	0.267778i	$-0.0862893\pi$
$521$	1.54794e6	+	2.68110e6i	0.249838	+	0.432732i	−0.713643	+	0.700510i	$0.752956\pi$
$522$	3.18555e6	+	372439.i	0.511691	+	0.0598245i
$523$	7.51491e6	+	4.33873e6i	1.20135	+	0.693599i	0.960855	−	0.277051i	$-0.0893572\pi$
$523$	7.51491e6	+	4.33873e6i	1.20135	+	0.693599i	0.240494	+	0.970651i	$0.422691\pi$
$524$	−662508.	−	1.14750e6i	−0.105405	−	0.182568i
$525$	4.33040e6	−	2.20647e6i	0.685694	−	0.349381i
$526$	1.80948e6	−	3.13412e6i	0.285161	−	0.493913i
$527$	4.00362e6	−	2.31149e6i	0.627952	−	0.362548i
$528$	150582.	−	2.58468e6i	0.0235065	−	0.403481i
$529$	7.48074e6	−	1.29570e7i	1.16227	−	2.01310i
$530$	−1.47298e6	+	2.55127e6i	−0.227775	+	0.394519i
$531$	−6.19218e6	+	8.31699e6i	−0.953032	+	1.28006i
$532$	1.32236e6	−	7718.59i	0.202568	−	0.00118238i
$533$	5.19113e6	−	2.99710e6i	0.791487	−	0.456965i
$534$	209179.	−	3.59048e6i	0.0317442	−	0.544879i
$535$			4.87808e6i			0.736826i
$536$			2.36714e6i			0.355886i
$537$	−2.15829e6	−	1.41958e6i	−0.322979	−	0.212434i
$538$	−2.64842e6	+	1.52907e6i	−0.394486	+	0.227757i
$539$	−3.01031e6	+	1.78518e6i	−0.446312	+	0.264673i
$540$	−574483.	−	1.57861e6i	−0.0847799	−	0.232965i
$541$	−3.53504e6	+	6.12287e6i	−0.519280	+	0.899419i	0.480469	+	0.877012i	$0.340466\pi$
$541$	−3.53504e6	+	6.12287e6i	−0.519280	+	0.899419i	−0.999749	+	0.0224074i	$0.992867\pi$
$542$	3.22971e6	−	5.59403e6i	0.472243	−	0.817949i
$543$	7.04340e6	−	3.53719e6i	1.02514	−	0.514824i
$544$	1.27496e6	−	736098.i	0.184714	−	0.106645i
$545$	5.67072e6	−	9.82197e6i	0.817800	−	1.41647i
$546$	−2.78659e6	+	1.41985e6i	−0.400028	+	0.203826i
$547$	−1.92948e6	−	3.34196e6i	−0.275723	−	0.477566i	0.694594	−	0.719402i	$-0.255584\pi$
$547$	−1.92948e6	−	3.34196e6i	−0.275723	−	0.477566i	−0.970317	+	0.241836i	$0.922251\pi$
$548$	1.27996e6	+	738986.i	0.182073	+	0.105120i
$549$	814983.	+	606773.i	0.115403	+	0.0859202i
$550$	−1.27766e6	−	2.21298e6i	−0.180098	−	0.311940i
$551$	4.42419e6			0.620804
$552$	7.67593e6	−	1.16703e7i	1.07222	−	1.63017i
$553$	−5.57200e6	+	3.26051e6i	−0.774815	+	0.453390i
$554$	−1.69467e6	−	978420.i	−0.234591	−	0.135441i
$555$	−2.51736e6	−	5.01267e6i	−0.346907	−	0.690775i
$556$	−993951.	−	573858.i	−0.136357	−	0.0787259i
$557$	−7.63910e6	+	4.41043e6i	−1.04329	+	0.602342i	−0.920763	−	0.390123i	$-0.872432\pi$
$557$	−7.63910e6	+	4.41043e6i	−1.04329	+	0.602342i	−0.122525	+	0.992465i	$0.539099\pi$
$558$	4.95037e6	−	6.64906e6i	0.673057	−	0.904013i
$559$		−	2.18080e6i		−	0.295180i
$560$	6.68148e6	+	3.80573e6i	0.900331	+	0.512823i
$561$	−2.00591e6	+	1.00737e6i	−0.269094	+	0.135139i
$562$	−3.61337e6	−	6.25855e6i	−0.482583	−	0.835858i
$563$	−1.59058e6			−0.211487			−0.105743	−	0.994393i	$-0.533722\pi$
$563$	−1.59058e6			−0.211487			−0.105743	+	0.994393i	$0.533722\pi$
$564$	431451.	+	859123.i	0.0571128	+	0.113725i
$565$		−	6.65313e6i		−	0.876808i
$566$	6.50034e6			0.852893
$567$	−5.59844e6	−	5.22109e6i	−0.731324	−	0.682031i
$568$	−1.35785e6			−0.176596
$569$		−	1.03476e7i		−	1.33986i	−0.742423	−	0.669932i	$-0.766323\pi$
$569$		−	1.03476e7i		−	1.33986i	0.742423	−	0.669932i	$-0.233677\pi$
$570$	4.54034e6	+	9.04092e6i	0.585331	+	1.16554i
$571$	−1.01238e7			−1.29943			−0.649717	−	0.760176i	$-0.725113\pi$
$571$	−1.01238e7			−1.29943			−0.649717	+	0.760176i	$0.725113\pi$
$572$	−188319.	−	326178.i	−0.0240660	−	0.0416836i
$573$	1.40277e7	−	7.04472e6i	1.78485	−	0.896349i
$574$	−1.30739e7	+	76312.1i	−1.65625	+	0.00966749i
$575$		−	1.11246e7i		−	1.40319i
$576$	5.28025e6	−	7.09214e6i	0.663130	−	0.890679i
$577$	−9.11784e6	+	5.26419e6i	−1.14012	+	0.658251i	−0.946461	−	0.322817i	$-0.895370\pi$
$577$	−9.11784e6	+	5.26419e6i	−1.14012	+	0.658251i	−0.193663	+	0.981068i	$0.562037\pi$
$578$	−4.16130e6	−	2.40253e6i	−0.518095	−	0.299122i
$579$	3.54832e6	+	7.06556e6i	0.439872	+	0.875891i
$580$	−993435.	−	573560.i	−0.122622	−	0.0707960i
$581$	4.53326e6	+	2.58212e6i	0.557148	+	0.317348i
$582$	−2.77271e6	+	4.21556e6i	−0.339311	+	0.515879i
$583$	−1.61672e6			−0.196998
$584$	8.21651e6	+	1.42314e7i	0.996908	+	1.72670i
$585$	4.39593e6	+	3.27286e6i	0.531081	+	0.395401i
$586$	4.81730e6	+	2.78127e6i	0.579508	+	0.334579i
$587$	1.90428e6	+	3.29830e6i	0.228105	+	0.395090i	0.957246	−	0.289273i	$-0.0934137\pi$
$587$	1.90428e6	+	3.29830e6i	0.228105	+	0.395090i	−0.729141	+	0.684363i	$0.760080\pi$
$588$	−1.56076e6	−	72658.5i	−0.186163	−	0.00866649i
$589$	5.71743e6	−	9.90288e6i	0.679067	−	1.17618i
$590$	−1.40220e7	+	8.09559e6i	−1.65836	+	0.957455i
$591$	1.41610e7	−	7.11162e6i	1.66772	−	0.837529i
$592$	1.92974e6	−	3.34240e6i	0.226305	−	0.391971i
$593$	3.93145e6	−	6.80947e6i	0.459109	−	0.795200i	−0.539805	−	0.841790i	$-0.681502\pi$
$593$	3.93145e6	−	6.80947e6i	0.459109	−	0.795200i	0.998914	+	0.0465899i	$0.0148354\pi$
$594$	−2.58731e6	+	3.08314e6i	−0.300872	+	0.358531i
$595$	−38911.3	−	6.66633e6i	−0.00450592	−	0.771959i
$596$	−941300.	+	543460.i	−0.108546	+	0.0626689i
$597$	−1.02358e7	−	6.73244e6i	−1.17540	−	0.773102i
$598$			7.15861e6i			0.818608i
$599$			9.46995e6i			1.07840i	0.842177	+	0.539201i	$0.181274\pi$
$599$			9.46995e6i			1.07840i	−0.842177	+	0.539201i	$0.818726\pi$
$600$	422367.	−	7.24979e6i	0.0478974	−	0.822143i
$601$	−3.29432e6	+	1.90198e6i	−0.372031	+	0.214792i	−0.674346	−	0.738416i	$-0.735574\pi$
$601$	−3.29432e6	+	1.90198e6i	−0.372031	+	0.214792i	0.302314	+	0.953208i	$0.402241\pi$
$602$	−2.35422e6	+	4.13315e6i	−0.264762	+	0.464826i
$603$	1.77329e6	−	2.38178e6i	0.198603	−	0.266753i
$604$	1.18852e6	−	2.05857e6i	0.132560	−	0.229601i
$605$	−4.37586e6	+	7.57922e6i	−0.486044	+	0.841852i
$606$	37027.8	−	635569.i	0.00409587	−	0.0703042i
$607$	−1.45111e7	+	8.37798e6i	−1.59856	+	0.922927i	−0.606791	+	0.794861i	$0.707544\pi$
$607$	−1.45111e7	+	8.37798e6i	−1.59856	+	0.922927i	−0.991766	+	0.128066i	$0.959123\pi$
$608$	1.82072e6	−	3.15358e6i	0.199749	−	0.345976i
$609$	−5.22022e6	−	273563.i	−0.570355	−	0.0298892i
$610$	793288.	+	1.37401e6i	0.0863189	+	0.149509i
$611$	−2.71620e6	−	1.56820e6i	−0.294346	−	0.169941i
$612$	−995317.	−	116368.i	−0.107419	−	0.0125590i
$613$	2.03098e6	+	3.51777e6i	0.218301	+	0.378108i	0.954289	−	0.298887i	$-0.0966152\pi$
$613$	2.03098e6	+	3.51777e6i	0.218301	+	0.378108i	−0.735988	+	0.676995i	$0.763282\pi$
$614$	1.14710e6			0.122795
$615$	1.02820e7	+	2.04740e7i	1.09620	+	2.18280i
$616$	30524.0	+	5.22941e6i	0.00324108	+	0.555265i
$617$	7.78164e6	+	4.49273e6i	0.822921	+	0.475114i	0.851423	−	0.524480i	$-0.175740\pi$
$617$	7.78164e6	+	4.49273e6i	0.822921	+	0.475114i	−0.0285019	+	0.999594i	$0.509074\pi$
$618$	−8.94284e6	+	1.35965e7i	−0.941899	+	1.43204i
$619$	6.71117e6	+	3.87469e6i	0.703998	+	0.406453i	0.808835	−	0.588036i	$-0.200099\pi$
$619$	6.71117e6	+	3.87469e6i	0.703998	+	0.406453i	−0.104837	+	0.994489i	$0.533432\pi$
$620$	−2.56765e6	+	1.48244e6i	−0.268261	+	0.154880i
$621$	−1.64660e7	+	5.99224e6i	−1.71340	+	0.623534i
$622$		−	6.16595e6i		−	0.639034i
$623$	34215.5	+	5.86183e6i	0.00353185	+	0.605081i
$624$	−219316.	+	3.76448e6i	−0.0225480	+	0.387029i
$625$	5.74868e6	+	9.95701e6i	0.588665	+	1.01960i
$626$	2.22922e6			0.227361
$627$	−3.05100e6	+	4.63867e6i	−0.309937	+	0.471221i
$628$			333591.i			0.0337532i
$629$	−3.34606e6			−0.337215
$630$	−4.79824e6	−	1.09484e7i	−0.481649	−	1.09900i
$631$	5.16857e6			0.516770			0.258385	−	0.966042i	$-0.416810\pi$
$631$	5.16857e6			0.516770			0.258385	+	0.966042i	$0.416810\pi$
$632$			9.64643e6i			0.960670i
$633$	−4.07881e6	−	237628.i	−0.404598	−	0.0235716i
$634$	1.21508e7			1.20056
$635$	−9.73497e6	−	1.68615e7i	−0.958077	−	1.65944i
$636$	−603017.	−	396624.i	−0.0591135	−	0.0388809i
$637$	4.38438e6	−	2.60003e6i	0.428114	−	0.253881i
$638$			2.74842e6i			0.267320i
$639$	1.36625e6	+	1.01720e6i	0.132367	+	0.0985498i
$640$	7.56946e6	−	4.37023e6i	0.730491	−	0.421749i
$641$	9.36522e6	+	5.40701e6i	0.900270	+	0.519771i	0.877288	−	0.479965i	$-0.159351\pi$
$641$	9.36522e6	+	5.40701e6i	0.900270	+	0.519771i	0.0229823	+	0.999736i	$0.492684\pi$
$642$	5.20891e6	+	303468.i	0.498781	+	0.0290586i
$643$	5.06450e6	+	2.92399e6i	0.483069	+	0.278900i	0.721694	−	0.692212i	$-0.243364\pi$
$643$	5.06450e6	+	2.92399e6i	0.483069	+	0.278900i	−0.238626	+	0.971112i	$0.576697\pi$
$644$	−1.77008e6	+	3.10762e6i	−0.168182	+	0.295266i
$645$	8.32125e6	+	484790.i	0.787570	+	0.0458833i
$646$	6.03500e6			0.568979
$647$	−4.41785e6	−	7.65193e6i	−0.414906	−	0.718639i	0.580512	−	0.814251i	$-0.302852\pi$
$647$	−4.41785e6	−	7.65193e6i	−0.414906	−	0.718639i	−0.995419	+	0.0956129i	$0.969519\pi$
$648$	−1.09582e7	+	3.27992e6i	−1.02518	+	0.306849i
$649$	−7.69514e6	−	4.44279e6i	−0.717141	−	0.414042i
$650$	1.86086e6	+	3.22311e6i	0.172755	+	0.299221i
$651$	−7.35847e6	+	1.13311e7i	−0.680511	+	1.04790i
$652$	496849.	−	860568.i	0.0457726	−	0.0792805i
$653$	1.73281e6	−	1.00044e6i	0.159026	−	0.0918138i	−0.418375	−	0.908274i	$-0.637400\pi$
$653$	1.73281e6	−	1.00044e6i	0.159026	−	0.0918138i	0.577401	+	0.816461i	$0.304067\pi$
$654$	−1.01353e7	−	6.66633e6i	−0.926602	−	0.609457i
$655$	−8.26109e6	+	1.43086e7i	−0.752374	+	1.30315i
$656$	−7.88190e6	+	1.36518e7i	−0.715107	+	1.23860i
$657$	2.39381e6	−	2.04747e7i	0.216359	−	1.85056i
$658$	3.45496e6	+	5.90430e6i	0.311084	+	0.531623i
$659$	−6.44246e6	+	3.71956e6i	−0.577881	+	0.333640i	−0.760291	−	0.649583i	$-0.774944\pi$
$659$	−6.44246e6	+	3.71956e6i	−0.577881	+	0.333640i	0.182410	+	0.983223i	$0.441610\pi$
$660$	1.28646e6	−	646057.i	0.114957	−	0.0577313i
$661$		−	2.02751e7i		−	1.80493i	−0.430764	−	0.902464i	$-0.641756\pi$
$661$		−	2.02751e7i		−	1.80493i	0.430764	−	0.902464i	$-0.358244\pi$
$662$		−	1.86439e7i		−	1.65345i
$663$	2.92152e6	−	1.46719e6i	0.258122	−	0.129629i
$664$	6.75103e6	−	3.89771e6i	0.594223	−	0.343075i
$665$	−8.32786e6	−	1.42318e7i	−0.730263	−	1.24797i
$666$	−5.50924e6	+	2.37625e6i	−0.481289	+	0.207590i
$667$	−5.98261e6	+	1.03622e7i	−0.520686	+	0.901855i
$668$	1.30039e6	−	2.25235e6i	0.112754	−	0.195296i
$669$	1.20434e7	+	7.92137e6i	1.04036	+	0.684282i
$670$	4.01555e6	−	2.31838e6i	0.345587	−	0.199525i
$671$	−435350.	+	754048.i	−0.0373277	+	0.0646536i
$672$	−2.34332e6	+	3.60842e6i	−0.200174	+	0.308243i
$673$	3.37184e6	+	5.84020e6i	0.286965	+	0.497039i	0.973084	−	0.230451i	$-0.0740202\pi$
$673$	3.37184e6	+	5.84020e6i	0.286965	+	0.497039i	−0.686118	+	0.727490i	$0.740687\pi$
$674$	−1.09350e7	−	6.31331e6i	−0.927189	−	0.535313i
$675$	−5.85601e6	+	6.97824e6i	−0.494700	+	0.589504i
$676$	−832856.	−	1.44255e6i	−0.0700976	−	0.121413i
$677$	308651.			0.0258819			0.0129409	−	0.999916i	$-0.495881\pi$
$677$	308651.			0.0258819			0.0129409	+	0.999916i	$0.495881\pi$
$678$	−7.10434e6	−	413894.i	−0.593539	−	0.0345792i
$679$	4.07025e6	−	7.14588e6i	0.338803	−	0.594814i
$680$	−8.62656e6	−	4.98055e6i	−0.715427	−	0.413052i
$681$	−1.30352e7	−	759420.i	−1.07708	−	0.0627500i
$682$	6.15191e6	+	3.55181e6i	0.506465	+	0.292408i
$683$	2.01748e7	−	1.16479e7i	1.65485	−	0.955427i	0.679810	−	0.733388i	$-0.262062\pi$
$683$	2.01748e7	−	1.16479e7i	1.65485	−	0.955427i	0.975038	−	0.222039i	$-0.0712711\pi$
$684$	−2.27598e6	+	981676.i	−0.186007	+	0.0802284i
$685$		−	1.84294e7i		−	1.50067i
$686$	−1.11163e7	+	194674.i	−0.901879	+	0.0157942i
$687$	−7.12674e6	−	4.68750e6i	−0.576102	−	0.378921i
$688$	2.86758e6	+	4.96679e6i	0.230964	+	0.400042i
$689$	2.35468e6			0.188966
$690$	−2.73150e7	−	1.59135e6i	−2.18413	−	0.127246i
$691$		−	9.65654e6i		−	0.769354i	−0.923051	−	0.384677i	$-0.874313\pi$
$691$		−	9.65654e6i		−	0.769354i	0.923051	−	0.384677i	$-0.125687\pi$
$692$	−284722.			−0.0226024
$693$	3.88678e6	−	5.28463e6i	0.307438	−	0.418005i
$694$	−3.50009e6			−0.275855
$695$			1.43113e7i			1.12388i
$696$	−4.29223e6	+	6.52579e6i	−0.335861	+	0.510634i
$697$	1.36668e7			1.06558
$698$	429439.	+	743810.i	0.0333628	+	0.0577861i
$699$	−605308.	+	1.03899e7i	−0.0468580	+	0.804301i
$700$	10852.8	+	1.85931e6i	0.000837134	+	0.143419i
$701$			6.54280e6i			0.502885i	0.967872	+	0.251442i	$0.0809049\pi$
$701$			6.54280e6i			0.502885i	−0.967872	+	0.251442i	$0.919095\pi$
$702$	3.76830e6	−	4.49045e6i	0.288604	−	0.343912i
$703$	−7.16758e6	+	4.13821e6i	−0.546996	+	0.315808i
$704$	6.56187e6	+	3.78850e6i	0.498995	+	0.288095i
$705$	6.58755e6	−	1.00155e7i	0.499173	−	0.758930i
$706$	1.67293e6	+	965865.i	0.126318	+	0.0729298i
$707$	6056.64	+	1.03763e6i	0.000455705	+	0.0780719i
$708$	−1.78026e6	−	3.54494e6i	−0.133475	−	0.265782i
$709$	4.80386e6			0.358901			0.179451	−	0.983767i	$-0.442568\pi$
$709$	4.80386e6			0.358901			0.179451	+	0.983767i	$0.442568\pi$
$710$	1.32988e6	+	2.30342e6i	0.0990072	+	0.171486i
$711$	7.22642e6	−	9.70612e6i	0.536104	−	0.720065i
$712$	7.58550e6	+	4.37949e6i	0.560770	+	0.323760i
$713$	1.54628e7	+	2.67823e7i	1.13911	+	1.97299i
$714$	−7.12086e6	−	373165.i	−0.522741	−	0.0273940i
$715$	−2.34823e6	+	4.06725e6i	−0.171781	+	0.297533i
$716$	855886.	−	494146.i	0.0623926	−	0.0360224i
$717$	461989.	−	7.92988e6i	0.0335609	−	0.576061i
$718$	362332.	−	627578.i	0.0262299	−	0.0454314i
$719$	−1.33542e6	+	2.31301e6i	−0.0963374	+	0.166861i	−0.910166	−	0.414244i	$-0.864046\pi$
$719$	−1.33542e6	+	2.31301e6i	−0.0963374	+	0.166861i	0.813829	+	0.581105i	$0.197379\pi$
$720$	−1.43153e7	−	1.67368e6i	−1.02913	−	0.120321i
$721$	1.31278e7	−	2.30476e7i	0.940489	−	1.65116i
$722$	1.98575e6	−	1.14647e6i	0.141769	−	0.0818503i
$723$	976965.	−	1.67693e7i	0.0695078	−	1.19308i
$724$			3.01530e6i			0.213788i
$725$			6.22065e6i			0.439533i
$726$	7.82101e6	+	5.14414e6i	0.550708	+	0.362219i
$727$	−920558.	+	531484.i	−0.0645974	+	0.0372953i	−0.531951	−	0.846775i	$-0.678541\pi$
$727$	−920558.	+	531484.i	−0.0645974	+	0.0372953i	0.467353	+	0.884071i	$0.345208\pi$
$728$	−44456.9	−	7.61640e6i	−0.00310893	−	0.532625i
$729$	1.34831e7	+	4.90890e6i	0.939660	+	0.342109i
$730$	1.60945e7	−	2.78766e7i	1.11782	−	1.93612i
$731$	2.48612e6	−	4.30608e6i	0.172079	−	0.298050i
$732$	−347369.	+	174448.i	−0.0239614	+	0.0120334i
$733$	−4.05844e6	+	2.34314e6i	−0.278997	+	0.161079i	−0.632969	−	0.774177i	$-0.718164\pi$
$733$	−4.05844e6	+	2.34314e6i	−0.278997	+	0.161079i	0.353973	+	0.935256i	$0.384831\pi$
$734$	−3.26552e6	+	5.65605e6i	−0.223724	+	0.387501i
$735$	8.94626e6	+	1.73074e7i	0.610834	+	1.18172i
$736$	4.92415e6	+	8.52887e6i	0.335071	+	0.580359i
$737$	2.20370e6	+	1.27231e6i	0.149446	+	0.0862825i
$738$	2.25022e7	−	9.70564e6i	1.52084	−	0.655969i
$739$	1.55866e6	+	2.69967e6i	0.104988	+	0.181844i	0.913733	−	0.406315i	$-0.133186\pi$
$739$	1.55866e6	+	2.69967e6i	0.104988	+	0.181844i	−0.808745	+	0.588159i	$0.799853\pi$
$740$	2.14594e6			0.144058
$741$	4.44365e6	−	6.75602e6i	0.297300	−	0.452007i
$742$	−4.46269e6	−	2.54192e6i	−0.297569	−	0.169493i
$743$	−1.39080e7	−	8.02980e6i	−0.924258	−	0.533620i	−0.0392668	−	0.999229i	$-0.512502\pi$
$743$	−1.39080e7	−	8.02980e6i	−0.924258	−	0.533620i	−0.884991	+	0.465608i	$0.845836\pi$
$744$	9.06009e6	+	1.80408e7i	0.600068	+	1.19488i
$745$	1.17375e7	+	6.77662e6i	0.774789	+	0.447324i
$746$	8.99953e6	−	5.19588e6i	0.592070	−	0.341832i
$747$	−9.71269e6	−	1.13556e6i	−0.636851	−	0.0744577i
$748$		−	858736.i		−	0.0561185i
$749$	−8.50409e6	+	49638.3i	−0.553890	+	0.00323305i
$750$	3.80625e6	−	1.91150e6i	0.247084	−	0.124085i
$751$	−1.13839e7	−	1.97174e7i	−0.736529	−	1.27571i	−0.954049	−	0.299650i	$-0.903130\pi$
$751$	−1.13839e7	−	1.97174e7i	−0.736529	−	1.27571i	0.217520	−	0.976056i	$-0.430203\pi$
$752$	8.24821e6			0.531882
$753$	−5.98844e6	−	1.19244e7i	−0.384881	−	0.766392i
$754$		−	4.00295e6i		−	0.256420i
$755$	−2.96402e7			−1.89241
$756$	2.74619e6	−	1.01757e6i	0.174754	−	0.0647533i
$757$	−2.31425e7			−1.46781			−0.733905	−	0.679252i	$-0.762304\pi$
$757$	−2.31425e7			−1.46781			−0.733905	+	0.679252i	$0.762304\pi$
$758$			4.12016e6i			0.260460i
$759$	−6.73881e6	−	1.34186e7i	−0.424599	−	0.845479i
$760$	−2.46385e7			−1.54732
$761$	1.31119e7	+	2.27105e7i	0.820736	+	1.42156i	0.905135	+	0.425125i	$0.139770\pi$
$761$	1.31119e7	+	2.27105e7i	0.820736	+	1.42156i	−0.0843982	+	0.996432i	$0.526897\pi$
$762$	−1.86106e7	+	9.34624e6i	−1.16111	+	0.583108i
$763$	1.71806e7	+	9.78596e6i	1.06838	+	0.608544i
$764$			6.00532e6i			0.372222i
$765$	4.94887e6	+	1.14738e7i	0.305740	+	0.708847i
$766$	−1.13834e7	+	6.57223e6i	−0.700973	+	0.404707i
$767$	1.12076e7	+	6.47073e6i	0.687901	+	0.397160i
$768$	3.95005e6	+	7.86550e6i	0.241657	+	0.481198i
$769$	4.50512e6	+	2.60103e6i	0.274720	+	0.158610i	0.631031	−	0.775758i	$-0.282632\pi$
$769$	4.50512e6	+	2.60103e6i	0.274720	+	0.158610i	−0.356311	+	0.934368i	$0.615966\pi$
$770$	8.84114e6	−	5.17347e6i	0.537380	−	0.314453i
$771$	5.00728e6	−	7.61294e6i	0.303365	−	0.461229i
$772$	−3.02479e6			−0.182663
$773$	2.52020e6	+	4.36512e6i	0.151700	+	0.262753i	0.931853	−	0.362837i	$-0.118192\pi$
$773$	2.52020e6	+	4.36512e6i	0.151700	+	0.262753i	−0.780152	+	0.625590i	$0.784858\pi$
$774$	1.03534e6	−	8.85544e6i	0.0621197	−	0.531322i
$775$	1.39240e7	+	8.03902e6i	0.832740	+	0.480783i
$776$	−6.14405e6	−	1.06418e7i	−0.366269	−	0.634397i
$777$	8.71310e6	−	4.43958e6i	0.517750	−	0.263809i
$778$	−2.14063e6	+	3.70769e6i	−0.126792	+	0.219611i
$779$	2.92756e7	−	1.69023e7i	1.72847	−	0.997933i
$780$	−1.87367e6	+	940954.i	−0.110270	+	0.0553773i
$781$	−729828.	+	1.26410e6i	−0.0428147	+	0.0741572i
$782$	−8.16083e6	+	1.41350e7i	−0.477219	+	0.826567i
$783$	9.20744e6	−	3.35074e6i	0.536703	−	0.195315i
$784$	−6.56663e6	+	1.16867e7i	−0.381551	+	0.679051i
$785$	3.60239e6	−	2.07984e6i	0.208649	−	0.120464i
$786$	1.47651e7	+	9.71149e6i	0.852472	+	0.560699i
$787$		−	1.21097e7i		−	0.696941i	−0.937320	−	0.348470i	$-0.886701\pi$
$787$		−	1.21097e7i		−	0.696941i	0.937320	−	0.348470i	$-0.113299\pi$
$788$			6.06235e6i			0.347797i
$789$	643024.	−	1.10373e7i	0.0367735	−	0.631204i
$790$	1.63640e7	−	9.44774e6i	0.932869	−	0.538592i
$791$	1.15986e7	−	67700.7i	0.659118	−	0.00384726i
$792$	−3.88214e6	−	9.00061e6i	−0.219917	−	0.509869i
$793$	634068.	−	1.09824e6i	0.0358057	−	0.0620174i
$794$	6.28684e6	−	1.08891e7i	0.353901	−	0.612974i
$795$	−523443.	+	8.98471e6i	−0.0293732	+	0.504181i
$796$	4.05909e6	−	2.34352e6i	0.227063	−	0.131095i
$797$	−4.55148e6	+	7.88339e6i	−0.253809	+	0.439609i	−0.964571	−	0.263822i	$-0.915017\pi$
$797$	−4.55148e6	+	7.88339e6i	−0.253809	+	0.439609i	0.710763	+	0.703432i	$0.248350\pi$
$798$	−1.57151e7	+	8.00729e6i	−0.873592	+	0.445121i
$799$	−3.57549e6	−	6.19294e6i	−0.198139	−	0.343186i
$800$	4.43411e6	+	2.56004e6i	0.244952	+	0.141423i
$801$	−4.35164e6	−	1.00891e7i	−0.239647	−	0.555612i
$802$	1.13171e7	+	1.96018e7i	0.621299	+	1.07612i
$803$	1.76651e7			0.966779
$804$	509824.	+	1.01518e6i	0.0278151	+	0.0553865i
$805$	4.45946e7	−	260298.i	2.42545	−	0.0141573i
$806$	−8.95999e6	−	5.17305e6i	−0.485814	−	0.280485i
$807$	−5.13399e6	+	7.80559e6i	−0.277505	+	0.421912i
$808$	1.34275e6	+	775235.i	0.0723545	+	0.0417739i
$809$	−1.17864e7	+	6.80490e6i	−0.633157	+	0.365553i	−0.781974	−	0.623312i	$-0.785787\pi$
$809$	−1.17864e7	+	6.80490e6i	−0.633157	+	0.365553i	0.148817	+	0.988865i	$0.452453\pi$
$810$	1.62965e7	+	1.53769e7i	0.872732	+	0.823484i
$811$			2.44311e7i			1.30434i	0.758073	+	0.652170i	$0.226141\pi$
$811$			2.44311e7i			1.30434i	−0.758073	+	0.652170i	$0.773859\pi$
$812$	989793.	−	1.73772e6i	0.0526810	−	0.0924888i
$813$	1.14772e6	−	1.97002e7i	0.0608990	−	1.04531i
$814$	−2.57076e6	−	4.45268e6i	−0.135988	−	0.235538i
$815$	−1.23908e7			−0.653441
$816$	−4.72456e6	+	7.18310e6i	−0.248391	+	0.377648i
$817$		−	1.22987e7i		−	0.644621i
$818$	−7.65702e6			−0.400107
$819$	−5.66093e6	+	7.69684e6i	−0.294902	+	0.400961i
$820$	−8.76496e6			−0.455214
$821$			2.07768e7i			1.07577i	0.843017	+	0.537887i	$0.180777\pi$
$821$			2.07768e7i			1.07577i	−0.843017	+	0.537887i	$0.819223\pi$
$822$	−1.96793e7	−	1.14650e6i	−1.01585	−	0.0591827i
$823$	−2.79854e7			−1.44023			−0.720114	−	0.693855i	$-0.755911\pi$
$823$	−2.79854e7			−1.44023			−0.720114	+	0.693855i	$0.755911\pi$
$824$	−1.98164e7	−	3.43230e7i	−1.01673	−	1.76103i
$825$	−6.52222e6	−	4.28988e6i	−0.333626	−	0.219437i
$826$	−1.42559e7	−	2.43625e7i	−0.727018	−	1.24243i
$827$			1.87131e7i			0.951443i	0.879596	+	0.475722i	$0.157813\pi$
$827$			1.87131e7i			0.951443i	−0.879596	+	0.475722i	$0.842187\pi$
$828$	778445.	−	6.65820e6i	0.0394596	−	0.337505i
$829$	−1.73622e7	+	1.00241e7i	−0.877441	+	0.506591i	−0.869814	−	0.493380i	$-0.835761\pi$
$829$	−1.73622e7	+	1.00241e7i	−0.877441	+	0.506591i	−0.00762723	+	0.999971i	$0.502428\pi$
$830$	−1.32239e7	−	7.63485e6i	−0.666294	−	0.384685i
$831$	−5.96806e6	−	347694.i	−0.299799	−	0.0174661i
$832$	−9.55708e6	−	5.51778e6i	−0.478649	−	0.276348i
$833$	1.16212e7	−	135670.i	0.580280	−	0.00677441i
$834$	1.52819e7	+	890314.i	0.760787	+	0.0443229i
$835$	−3.24303e7			−1.60966
$836$	−1.06203e6	−	1.83949e6i	−0.0525560	−	0.0910296i
$837$	4.39875e6	−	2.49396e7i	0.217028	−	1.23049i
$838$	−1.15043e7	−	6.64199e6i	−0.565912	−	0.326729i
$839$	−9.21454e6	−	1.59601e7i	−0.451928	−	0.782761i	0.546578	−	0.837408i	$-0.315930\pi$
$839$	−9.21454e6	−	1.59601e7i	−0.451928	−	0.782761i	−0.998506	+	0.0546466i	$0.982597\pi$
$840$	2.90717e7	+	1.52349e6i	1.42158	+	0.0744972i
$841$	−6.91022e6	+	1.19689e7i	−0.336901	+	0.583529i
$842$	1.95776e7	−	1.13031e7i	0.951652	−	0.549437i
$843$	−1.84456e7	−	1.21322e7i	−0.893970	−	0.587993i
$844$	781537.	−	1.35366e6i	0.0377653	−	0.0654115i
$845$	−1.03852e7	+	1.79877e7i	−0.500350	+	0.866631i
$846$	−1.02850e7	−	7.65739e6i	−0.494057	−	0.367836i
$847$	−1.32576e7	−	7.55143e6i	−0.634973	−	0.361677i
$848$	−5.36280e6	+	3.09621e6i	−0.256096	+	0.147857i
$849$	1.77465e7	−	8.91225e6i	0.844972	−	0.424344i
$850$			8.48554e6i			0.402840i
$851$		−	2.23836e7i		−	1.05951i
$852$	−582335.	+	292448.i	−0.0274836	+	0.0138022i
$853$	−2.80525e6	+	1.61961e6i	−0.132008	+	0.0762146i	−0.564550	−	0.825399i	$-0.690950\pi$
$853$	−2.80525e6	+	1.61961e6i	−0.132008	+	0.0762146i	0.432542	+	0.901614i	$0.357617\pi$
$854$	−2.38728e6	+	1.39694e6i	−0.112011	+	0.0655440i
$855$	2.47910e7	+	1.84574e7i	1.15979	+	0.863488i
$856$	−6.35357e6	+	1.10047e7i	−0.296370	+	0.513327i
$857$	1.09571e6	−	1.89783e6i	0.0509618	−	0.0882684i	−0.839419	−	0.543485i	$-0.817105\pi$
$857$	1.09571e6	−	1.89783e6i	0.0509618	−	0.0882684i	0.890381	+	0.455216i	$0.150438\pi$
$858$	4.19700e6	+	2.76051e6i	0.194635	+	0.128018i
$859$	−2.62166e7	+	1.51361e7i	−1.21225	+	0.699894i	−0.963249	−	0.268609i	$-0.913436\pi$
$859$	−2.62166e7	+	1.51361e7i	−1.21225	+	0.699894i	−0.249003	+	0.968503i	$0.580103\pi$
$860$	−1.59443e6	+	2.76163e6i	−0.0735121	+	0.127327i
$861$	−3.55882e7	+	1.81332e7i	−1.63605	+	0.833618i
$862$	9.20063e6	+	1.59360e7i	0.421744	+	0.730483i
$863$	−4.37590e6	−	2.52643e6i	−0.200005	−	0.115473i	0.396653	−	0.917969i	$-0.370172\pi$
$863$	−4.37590e6	−	2.52643e6i	−0.200005	−	0.115473i	−0.596658	+	0.802496i	$0.703505\pi$
$864$	1.40079e6	−	7.94206e6i	0.0638393	−	0.361950i
$865$	1.77515e6	+	3.07466e6i	0.0806670	+	0.139719i
$866$	1.66416e7			0.754051
$867$	−1.46546e7	−	853769.i	−0.662106	−	0.0385738i
$868$	−2.61050e6	−	4.46117e6i	−0.117604	−	0.200978i
$869$	8.98041e6	+	5.18484e6i	0.403410	+	0.232909i
$870$	1.52740e7	+	889851.i	0.684155	+	0.0398584i
$871$	−3.20959e6	−	1.85306e6i	−0.143352	−	0.0827645i
$872$	2.55857e7	−	1.47719e7i	1.13948	−	0.657879i
$873$	−1.79001e6	+	1.53103e7i	−0.0794915	+	0.679906i
$874$			4.03713e7i			1.78770i
$875$	−5.99162e6	+	3.50605e6i	−0.264560	+	0.154810i
$876$	6.58888e6	+	4.33372e6i	0.290102	+	0.190810i
$877$	4.79373e6	+	8.30299e6i	0.210462	+	0.364532i	0.951859	−	0.306535i	$-0.0991697\pi$
$877$	4.79373e6	+	8.30299e6i	0.210462	+	0.364532i	−0.741397	+	0.671067i	$0.765836\pi$
$878$	−3.40229e7			−1.48948
$879$	1.69649e7	+	988360.i	0.740590	+	0.0431462i
$880$		−	1.23509e7i		−	0.537642i
$881$	−8.45162e6			−0.366860			−0.183430	−	0.983033i	$-0.558720\pi$
$881$	−8.45162e6			−0.366860			−0.183430	+	0.983033i	$0.558720\pi$
$882$	1.90377e7	−	8.47630e6i	0.824031	−	0.366889i
$883$	−1.84651e6			−0.0796987			−0.0398493	−	0.999206i	$-0.512688\pi$
$883$	−1.84651e6			−0.0796987			−0.0398493	+	0.999206i	$0.512688\pi$
$884$			1.25071e6i			0.0538303i
$885$	−2.71817e7	+	4.13264e7i	−1.16659	+	1.77365i
$886$	1.38533e7			0.592884
$887$	−1.71500e6	−	2.97046e6i	−0.0731905	−	0.126770i	0.827107	−	0.562044i	$-0.189985\pi$
$887$	−1.71500e6	−	2.97046e6i	−0.0731905	−	0.126770i	−0.900298	+	0.435274i	$0.856651\pi$
$888$	849835.	−	1.45871e7i	0.0361662	−	0.620780i
$889$	2.92960e7	−	1.71428e7i	1.24324	−	0.727490i
$890$		−	1.71571e7i		−	0.726056i
$891$	−2.83645e6	+	1.19645e7i	−0.119696	+	0.504895i
$892$	−4.77591e6	+	2.75737e6i	−0.200976	+	0.116033i
$893$	−1.53181e7	−	8.84390e6i	−0.642800	−	0.371121i
$894$	7.96640e6	−	1.21119e7i	0.333364	−	0.506838i
$895$	−1.06724e7	−	6.16171e6i	−0.445353	−	0.257124i
$896$	7.69575e6	+	1.31516e7i	0.320244	+	0.547277i
$897$	9.81478e6	+	1.95436e7i	0.407286	+	0.811005i
$898$	−1.77598e7			−0.734934
$899$	−8.64647e6	−	1.49761e7i	−0.356812	−	0.618017i
$900$	−1.38029e6	−	3.20015e6i	−0.0568021	−	0.131694i
$901$	4.64941e6	+	2.68434e6i	0.190803	+	0.110160i
$902$	1.05001e7	+	1.81867e7i	0.429712	+	0.744283i
$903$	−760471.	+	1.45116e7i	−0.0310358	+	0.592237i
$904$	8.66552e6	−	1.50091e7i	0.352674	−	0.610849i
$905$	3.25617e7	−	1.87995e7i	1.32156	−	0.763001i
$906$	−1.84393e6	+	3.16504e7i	−0.0746318	+	1.28103i
$907$	−1.86525e7	+	3.23071e7i	−0.752869	+	1.30401i	0.193558	+	0.981089i	$0.437997\pi$
$907$	−1.86525e7	+	3.23071e7i	−0.752869	+	1.30401i	−0.946427	+	0.322918i	$0.895336\pi$
$908$	2.49766e6	−	4.32607e6i	0.100535	−	0.174132i
$909$	−770304.	−	1.78592e6i	−0.0309209	−	0.0716890i
$910$	−1.28767e7	+	7.53494e6i	−0.515469	+	0.301631i
$911$	−1.16681e7	+	6.73656e6i	−0.465804	+	0.268932i	−0.714481	−	0.699654i	$-0.753337\pi$
$911$	−1.16681e7	+	6.73656e6i	−0.465804	+	0.268932i	0.248678	+	0.968586i	$0.420004\pi$
$912$	−1.23684e6	+	2.12299e7i	−0.0492410	+	0.845204i
$913$		−	8.37988e6i		−	0.332706i
$914$			2.87557e7i			1.13857i
$915$	4.04958e6	+	2.66354e6i	0.159903	+	0.105174i
$916$	2.82616e6	−	1.63168e6i	0.111290	−	0.0642536i
$917$	−2.50286e7	−	1.42562e7i	−0.982910	−	0.559860i
$918$	1.25598e7	−	4.57071e6i	0.491899	−	0.179010i
$919$	2.73522e6	−	4.73755e6i	0.106833	−	0.185040i	−0.807653	−	0.589658i	$-0.799262\pi$
$919$	2.73522e6	−	4.73755e6i	0.106833	−	0.185040i	0.914485	+	0.404619i	$0.132596\pi$
$920$	3.33175e7	−	5.77076e7i	1.29778	−	2.24783i
$921$	3.13168e6	−	1.57273e6i	0.121655	−	0.0610949i
$922$	−7.81573e6	+	4.51241e6i	−0.302790	+	0.174816i
$923$	1.06296e6	−	1.84110e6i	0.0410690	−	0.0711335i
$924$	1.13938e6	+	2.23614e6i	0.0439024	+	0.0861626i
$925$	−5.81854e6	−	1.00780e7i	−0.223594	−	0.387276i
$926$	1.44520e7	+	8.34386e6i	0.553860	+	0.319771i
$927$	−5.77333e6	+	4.93805e7i	−0.220662	+	1.88736i
$928$	−2.75348e6	−	4.76917e6i	−0.104957	−	0.181791i
$929$	−2.62166e7			−0.996638			−0.498319	−	0.866994i	$-0.666049\pi$
$929$	−2.62166e7			−0.996638			−0.498319	+	0.866994i	$0.666049\pi$
$930$	2.17305e7	−	3.30385e7i	0.823878	−	1.25260i
$931$	2.47259e7	−	1.46630e7i	0.934927	−	0.554432i
$932$	−3.44817e6	−	1.99080e6i	−0.130032	−	0.0750737i
$933$	−8.45379e6	−	1.68335e7i	−0.317942	−	0.633099i
$934$	−3.49645e7	−	2.01867e7i	−1.31147	−	0.757180i
$935$	−9.27334e6	+	5.35397e6i	−0.346902	+	0.200284i
$936$	5.65418e6	+	1.31090e7i	0.210950	+	0.489080i
$937$		−	1.23069e7i		−	0.457932i	−0.973434	−	0.228966i	$-0.926465\pi$
$937$		−	1.23069e7i		−	0.457932i	0.973434	−	0.228966i	$-0.0735345\pi$
$938$	4.08255e6	+	6.97681e6i	0.151504	+	0.258911i
$939$	6.08594e6	−	3.05636e6i	0.225250	−	0.113120i
$940$	2.29308e6	+	3.97173e6i	0.0846447	+	0.146609i
$941$	−5.62428e6			−0.207058			−0.103529	−	0.994626i	$-0.533014\pi$
$941$	−5.62428e6			−0.207058			−0.103529	+	0.994626i	$0.533014\pi$
$942$	−1.99679e6	−	3.97609e6i	−0.0733171	−	0.145992i
$943$			9.14244e7i			3.34798i
$944$	−3.40340e7			−1.24303
$945$	−2.81103e7	−	2.33113e7i	−1.02397	−	0.849156i
$946$	7.64027e6			0.277575
$947$		−	4.32527e7i		−	1.56725i	−0.621233	−	0.783626i	$-0.713368\pi$
$947$		−	4.32527e7i		−	1.56725i	0.621233	−	0.783626i	$-0.286632\pi$
$948$	2.07761e6	+	4.13702e6i	0.0750832	+	0.149509i
$949$	−2.57284e7			−0.927359
$950$	1.04944e7	+	1.81768e7i	0.377267	+	0.653445i
$951$	3.31728e7	−	1.66593e7i	1.18941	−	0.597319i
$952$	8.59493e6	−	1.50896e7i	0.307362	−	0.539616i
$953$		−	1.18322e7i		−	0.422020i	−0.977484	−	0.211010i	$-0.932325\pi$
$953$		−	1.18322e7i		−	0.422020i	0.977484	−	0.211010i	$-0.0676752\pi$
$954$	9.56149e6	+	1.11788e6i	0.340138	+	0.0397673i
$955$	6.48503e7	−	3.74414e7i	2.30093	−	1.32844i
$956$	2.63174e6	+	1.51944e6i	0.0931320	+	0.0537698i
$957$	3.76820e6	+	7.50340e6i	0.133001	+	0.264837i
$958$	8.18969e6	+	4.72832e6i	0.288306	+	0.166453i
$959$	3.21285e7	−	187534.i	1.12809	−	0.00658465i
$960$	2.31786e7	−	3.52402e7i	0.811727	−	1.23413i
$961$	−1.60666e7			−0.561196
$962$	3.74420e6	+	6.48514e6i	0.130443	+	0.225934i
$963$	1.46368e7	−	6.31316e6i	0.508606	−	0.219372i
$964$	5.56533e6	+	3.21314e6i	0.192885	+	0.111362i
$965$	1.88586e7	+	3.26641e7i	0.651917	+	1.12915i
$966$	2.49629e6	−	4.76351e7i	0.0860702	−	1.64242i
$967$	9.14008e6	−	1.58311e7i	0.314329	−	0.544433i	−0.664966	−	0.746874i	$-0.731554\pi$
$967$	9.14008e6	−	1.58311e7i	0.314329	−	0.544433i	0.979295	+	0.202440i	$0.0648873\pi$
$968$	−1.97435e7	+	1.13989e7i	−0.677228	+	0.390998i
$969$	1.64760e7	−	8.27425e6i	0.563694	−	0.283087i
$970$	−1.20350e7	+	2.08452e7i	−0.410692	+	0.711340i
$971$	1.36023e7	−	2.35598e7i	0.462981	−	0.801906i	−0.536127	−	0.844137i	$-0.680113\pi$
$971$	1.36023e7	−	2.35598e7i	0.462981	−	0.801906i	0.999108	+	0.0422311i	$0.0134466\pi$
$972$	−3.99318e6	+	3.76678e6i	−0.135567	+	0.127880i
$973$	−2.49493e7	+	145629.i	−0.844844	+	0.00493135i
$974$	−2.14233e7	+	1.23687e7i	−0.723584	+	0.417761i
$975$	9.49933e6	+	6.24802e6i	0.320023	+	0.210490i
$976$			3.33499e6i			0.112065i
$977$			1.25018e7i			0.419023i	0.977806	+	0.209511i	$0.0671874\pi$
$977$			1.25018e7i			0.419023i	−0.977806	+	0.209511i	$0.932813\pi$
$978$	−770838.	+	1.32312e7i	−0.0257701	+	0.442335i
$979$	8.15423e6	−	4.70785e6i	0.271911	−	0.156988i
$980$	−7.45304e6	+	87009.6i	−0.247895	+	0.00289402i
$981$	−3.68101e7	−	4.30367e6i	−1.22122	−	0.142780i
$982$	1.99588e7	−	3.45696e7i	0.660473	−	1.14397i
$983$	4.69851e6	−	8.13806e6i	0.155087	−	0.268619i	−0.778003	−	0.628260i	$-0.783767\pi$
$983$	4.69851e6	−	8.13806e6i	0.155087	−	0.268619i	0.933091	+	0.359641i	$0.117101\pi$
$984$	−3.47110e6	+	5.95803e7i	−0.114282	+	1.96162i
$985$	6.54662e7	−	3.77969e7i	2.14994	−	1.24127i
$986$	4.56337e6	−	7.90399e6i	0.149484	−	0.258913i
$987$	1.75274e7	+	1.13823e7i	0.572696	+	0.371910i
$988$	1.54680e6	+	2.67914e6i	0.0504131	+	0.0873180i
$989$	2.88056e7	+	1.66309e7i	0.936454	+	0.540662i
$990$	−1.14662e7	+	1.54008e7i	−0.371820	+	0.499407i
$991$	−1.77070e7	−	3.06694e7i	−0.572745	−	0.992023i	−0.996283	−	0.0861447i	$-0.972545\pi$
$991$	−1.77070e7	−	3.06694e7i	−0.572745	−	0.992023i	0.423538	−	0.905878i	$-0.360788\pi$
$992$	−1.42334e7			−0.459230
$993$	−2.55616e7	−	5.08994e7i	−0.822650	−	1.63810i
$994$	−4.00208e6	+	2.34185e6i	−0.128475	+	0.0751785i
$995$	−5.06144e7	−	2.92223e7i	−1.62075	−	0.935742i
$996$	2.05581e6	−	3.12560e6i	0.0656651	−	0.0998356i
$997$	1.07678e7	+	6.21678e6i	0.343074	+	0.198074i	0.661631	−	0.749830i	$-0.269865\pi$
$997$	1.07678e7	+	6.21678e6i	0.343074	+	0.198074i	−0.318556	+	0.947904i	$0.603198\pi$
$998$	3.39281e7	−	1.95884e7i	1.07828	−	0.622548i
$999$	−1.17827e7	+	1.40408e7i	−0.373536	+	0.445120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.i.a.5.13	✓	76
3.2	odd	2		189.6.i.a.152.26		76
7.3	odd	6		63.6.s.a.59.26	yes	76
9.2	odd	6		63.6.s.a.47.26	yes	76
9.7	even	3		189.6.s.a.89.13		76
21.17	even	6		189.6.s.a.17.13		76
63.38	even	6	inner	63.6.i.a.38.26	yes	76
63.52	odd	6		189.6.i.a.143.13		76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.i.a.5.13	✓	76	1.1	even	1	trivial
63.6.i.a.38.26	yes	76	63.38	even	6	inner
63.6.s.a.47.26	yes	76	9.2	odd	6
63.6.s.a.59.26	yes	76	7.3	odd	6
189.6.i.a.143.13		76	63.52	odd	6
189.6.i.a.152.26		76	3.2	odd	2
189.6.s.a.17.13		76	21.17	even	6
189.6.s.a.89.13		76	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-5.10258i q^{2} +(-6.99587 - 13.9305i) q^{3} +5.96367 q^{4} +(-37.1817 - 64.4006i) q^{5} +(-71.0813 + 35.6970i) q^{6} +(111.893 - 65.4751i) q^{7} -193.713i q^{8} +(-145.116 + 194.911i) q^{9} +(-328.609 + 189.723i) q^{10} +(-180.338 - 104.118i) q^{11} +(-41.7210 - 83.0767i) q^{12} +(262.655 + 151.644i) q^{13} +(-334.092 - 570.942i) q^{14} +(-637.012 + 968.496i) q^{15} -797.597 q^{16} +(345.748 + 598.853i) q^{17} +(994.551 + 740.465i) q^{18} +(1481.25 + 855.200i) q^{19} +(-221.739 - 384.064i) q^{20} +(-1694.89 - 1100.66i) q^{21} +(-531.271 + 920.189i) q^{22} +(-4006.04 + 2312.89i) q^{23} +(-2698.51 + 1355.19i) q^{24} +(-1202.46 + 2082.72i) q^{25} +(773.774 - 1340.22i) q^{26} +(3730.42 + 657.956i) q^{27} +(667.292 - 390.472i) q^{28} +(2240.10 - 1293.32i) q^{29} +(4941.83 + 3250.41i) q^{30} -6685.49i q^{31} -2129.00i q^{32} +(-188.794 + 3240.59i) q^{33} +(3055.70 - 1764.21i) q^{34} +(-8377.00 - 4771.49i) q^{35} +(-865.422 + 1162.39i) q^{36} +(-2419.44 + 4190.59i) q^{37} +(4363.73 - 7558.20i) q^{38} +(274.971 - 4719.78i) q^{39} +(-12475.2 + 7202.57i) q^{40} +(9882.05 - 17116.2i) q^{41} +(-5616.23 + 8648.29i) q^{42} +(-3595.27 - 6227.20i) q^{43} +(-1075.48 - 620.927i) q^{44} +(17948.1 + 2098.40i) q^{45} +(11801.7 + 20441.2i) q^{46} -10341.3 q^{47} +(5579.88 + 11110.9i) q^{48} +(8233.02 - 14652.4i) q^{49} +(10627.2 + 6135.64i) q^{50} +(5923.50 - 9005.93i) q^{51} +(1566.38 + 904.353i) q^{52} +(6723.70 - 3881.93i) q^{53} +(3357.27 - 19034.7i) q^{54} +15485.2i q^{55} +(-12683.4 - 21675.1i) q^{56} +(1550.71 - 26617.4i) q^{57} +(-6599.27 - 11430.3i) q^{58} +42670.7 q^{59} +(-3798.93 + 5775.79i) q^{60} -4181.30i q^{61} -34113.2 q^{62} +(-3475.56 + 31310.7i) q^{63} -36386.5 q^{64} -22553.5i q^{65} +(16535.4 + 963.338i) q^{66} -12219.8 q^{67} +(2061.93 + 3571.36i) q^{68} +(60245.4 + 39625.4i) q^{69} +(-24346.9 + 42744.3i) q^{70} -7009.61i q^{71} +(37756.8 + 28110.8i) q^{72} +(-73466.6 + 42416.0i) q^{73} +(21382.8 + 12345.4i) q^{74} +(37425.5 + 2180.38i) q^{75} +(8833.69 + 5100.13i) q^{76} +(-26995.7 + 157.574i) q^{77} +(-24083.0 - 1403.06i) q^{78} -49797.6 q^{79} +(29656.0 + 51365.7i) q^{80} +(-16931.9 - 56569.4i) q^{81} +(-87336.9 - 50424.0i) q^{82} +(20121.1 + 34850.7i) q^{83} +(-10107.7 - 6564.00i) q^{84} +(25711.0 - 44532.8i) q^{85} +(-31774.8 + 18345.2i) q^{86} +(-33688.0 - 22157.7i) q^{87} +(-20169.0 + 34933.8i) q^{88} +(-22608.2 + 39158.5i) q^{89} +(10707.3 - 91581.4i) q^{90} +(39318.0 - 229.499i) q^{91} +(-23890.7 + 13793.3i) q^{92} +(-93131.9 + 46770.8i) q^{93} +52767.5i q^{94} -127191. i q^{95} +(-29658.0 + 14894.2i) q^{96} +(54936.0 - 31717.3i) q^{97} +(-74765.0 - 42009.6i) q^{98} +(46463.7 - 20040.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 3 q^{3} - 1154 q^{4} - 3 q^{5} + 96 q^{6} - 30 q^{7} + 489 q^{9} - 6 q^{10} + 567 q^{11} - 1542 q^{12} + 543 q^{13} - 1638 q^{14} + 234 q^{15} + 16446 q^{16} - 801 q^{17} - 2022 q^{18} - 6 q^{19}+ \cdots - 144540 q^{99}+O(q^{100}) \) 76 * q - 3 * q^3 - 1154 * q^4 - 3 * q^5 + 96 * q^6 - 30 * q^7 + 489 * q^9 - 6 * q^10 + 567 * q^11 - 1542 * q^12 + 543 * q^13 - 1638 * q^14 + 234 * q^15 + 16446 * q^16 - 801 * q^17 - 2022 * q^18 - 6 * q^19 + 96 * q^20 - 4119 * q^21 + 62 * q^22 + 7806 * q^23 - 2346 * q^24 - 18749 * q^25 + 10128 * q^26 - 1539 * q^27 + 860 * q^28 + 17904 * q^29 + 11457 * q^30 - 3 * q^33 + 96 * q^34 + 3960 * q^35 - 57846 * q^36 + 2577 * q^37 + 14967 * q^38 - 16269 * q^39 + 9564 * q^40 + 28230 * q^41 + 15606 * q^42 - 9246 * q^43 - 69885 * q^44 - 23649 * q^45 - 9418 * q^46 - 56562 * q^47 + 48615 * q^48 + 7948 * q^49 - 67509 * q^50 - 103722 * q^51 - 40899 * q^52 + 25296 * q^53 + 176211 * q^54 + 104754 * q^56 + 33399 * q^57 - 4951 * q^58 - 59076 * q^59 + 33729 * q^60 + 79536 * q^62 - 95871 * q^63 - 198600 * q^64 + 114900 * q^66 + 1244 * q^67 + 191496 * q^68 + 3702 * q^69 - 127197 * q^70 + 183582 * q^72 - 6 * q^73 - 45681 * q^74 - 240486 * q^75 - 2880 * q^76 + 13854 * q^77 + 184431 * q^78 + 59984 * q^79 + 243225 * q^80 + 177117 * q^81 + 90 * q^82 - 246930 * q^83 + 56085 * q^84 + 11973 * q^85 + 291801 * q^86 + 205125 * q^87 - 34751 * q^88 - 6345 * q^89 - 269187 * q^90 - 120111 * q^91 - 463488 * q^92 + 200946 * q^93 - 382521 * q^96 - 104037 * q^97 - 646797 * q^98 - 144540 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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