LMFDB - Embedded newform 60.7.f.a.19.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(19,60)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.22
Character	$\chi$	$=$	60.19
Dual form			60.7.f.a.19.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63894 + 7.83032i) q^{2} +15.5885 q^{3} +(-58.6278 + 25.6668i) q^{4} +(-44.2074 - 116.922i) q^{5} +(25.5485 + 122.063i) q^{6} -42.6864 q^{7} +(-297.066 - 417.008i) q^{8} +243.000 q^{9} +O(q^{10})$	\(q+(1.63894 + 7.83032i) q^{2} +15.5885 q^{3} +(-58.6278 + 25.6668i) q^{4} +(-44.2074 - 116.922i) q^{5} +(25.5485 + 122.063i) q^{6} -42.6864 q^{7} +(-297.066 - 417.008i) q^{8} +243.000 q^{9} +(843.082 - 537.785i) q^{10} -1842.57i q^{11} +(-913.917 + 400.106i) q^{12} -887.003i q^{13} +(-69.9602 - 334.248i) q^{14} +(-689.125 - 1822.63i) q^{15} +(2778.43 - 3009.57i) q^{16} -798.396i q^{17} +(398.262 + 1902.77i) q^{18} -2308.89i q^{19} +(5592.79 + 5720.20i) q^{20} -665.414 q^{21} +(14427.9 - 3019.86i) q^{22} -7162.68 q^{23} +(-4630.81 - 6500.51i) q^{24} +(-11716.4 + 10337.6i) q^{25} +(6945.51 - 1453.74i) q^{26} +3788.00 q^{27} +(2502.61 - 1095.62i) q^{28} +37170.9 q^{29} +(13142.3 - 8383.25i) q^{30} -47643.5i q^{31} +(28119.6 + 16823.5i) q^{32} -28722.9i q^{33} +(6251.69 - 1308.52i) q^{34} +(1887.05 + 4990.96i) q^{35} +(-14246.5 + 6237.03i) q^{36} +30635.5i q^{37} +(18079.4 - 3784.13i) q^{38} -13827.0i q^{39} +(-35624.8 + 53168.4i) q^{40} +51219.0 q^{41} +(-1090.57 - 5210.41i) q^{42} -135337. q^{43} +(47292.9 + 108026. i) q^{44} +(-10742.4 - 28412.0i) q^{45} +(-11739.2 - 56086.0i) q^{46} -157494. q^{47} +(43311.5 - 46914.6i) q^{48} -115827. q^{49} +(-100149. - 74800.5i) q^{50} -12445.8i q^{51} +(22766.5 + 52003.0i) q^{52} -140651. i q^{53} +(6208.28 + 29661.2i) q^{54} +(-215437. + 81455.3i) q^{55} +(12680.7 + 17800.5i) q^{56} -35992.1i q^{57} +(60920.8 + 291060. i) q^{58} +150330. i q^{59} +(87182.9 + 89169.1i) q^{60} +39704.1 q^{61} +(373064. - 78084.7i) q^{62} -10372.8 q^{63} +(-85647.2 + 247758. i) q^{64} +(-103710. + 39212.1i) q^{65} +(224909. - 47074.9i) q^{66} +188483. q^{67} +(20492.3 + 46808.2i) q^{68} -111655. q^{69} +(-35988.1 + 22956.1i) q^{70} -300445. i q^{71} +(-72187.1 - 101333. i) q^{72} +137469. i q^{73} +(-239886. + 50209.7i) q^{74} +(-182641. + 161148. i) q^{75} +(59261.9 + 135365. i) q^{76} +78652.7i q^{77} +(108270. - 22661.6i) q^{78} -392225. i q^{79} +(-474712. - 191814. i) q^{80} +59049.0 q^{81} +(83944.7 + 401061. i) q^{82} +261510. q^{83} +(39011.8 - 17079.1i) q^{84} +(-93349.8 + 35295.0i) q^{85} +(-221808. - 1.05973e6i) q^{86} +579437. q^{87} +(-768367. + 547366. i) q^{88} +944102. q^{89} +(204869. - 130682. i) q^{90} +37862.9i q^{91} +(419932. - 183843. i) q^{92} -742689. i q^{93} +(-258122. - 1.23322e6i) q^{94} +(-269960. + 102070. i) q^{95} +(438341. + 262253. i) q^{96} +1.18506e6i q^{97} +(-189833. - 906961. i) q^{98} -447745. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.63894	+	7.83032i	0.204867	+	0.978790i
$2$	1.63894	+	7.83032i	0.204867	+	0.978790i
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	−58.6278	+	25.6668i	−0.916059	+	0.401044i
$5$	−44.2074	−	116.922i	−0.353659	−	0.935374i
$5$	−44.2074	−	116.922i	−0.353659	−	0.935374i
$6$	25.5485	+	122.063i	0.118280	+	0.565105i
$7$	−42.6864			−0.124450			−0.0622250	−	0.998062i	$-0.519820\pi$
$7$	−42.6864			−0.124450			−0.0622250	+	0.998062i	$0.519820\pi$
$8$	−297.066	−	417.008i	−0.580208	−	0.814469i
$9$	243.000			0.333333
$10$	843.082	−	537.785i	0.843082	−	0.537785i
$11$		−	1842.57i		−	1.38435i	−0.721729	−	0.692176i	$-0.756652\pi$
$11$		−	1842.57i		−	1.38435i	0.721729	−	0.692176i	$-0.243348\pi$
$12$	−913.917	+	400.106i	−0.528887	+	0.231543i
$13$		−	887.003i		−	0.403734i	−0.979413	−	0.201867i	$-0.935299\pi$
$13$		−	887.003i		−	0.403734i	0.979413	−	0.201867i	$-0.0647008\pi$
$14$	−69.9602	−	334.248i	−0.0254957	−	0.121810i
$15$	−689.125	−	1822.63i	−0.204185	−	0.540039i
$16$	2778.43	−	3009.57i	0.678328	−	0.734759i
$17$		−	798.396i		−	0.162507i	−0.996693	−	0.0812534i	$-0.974108\pi$
$17$		−	798.396i		−	0.162507i	0.996693	−	0.0812534i	$-0.0258923\pi$
$18$	398.262	+	1902.77i	0.0682890	+	0.326263i
$19$		−	2308.89i		−	0.336622i	−0.985734	−	0.168311i	$-0.946169\pi$
$19$		−	2308.89i		−	0.336622i	0.985734	−	0.168311i	$-0.0538314\pi$
$20$	5592.79	+	5720.20i	0.699099	+	0.715025i
$21$	−665.414			−0.0718512
$22$	14427.9	−	3019.86i	1.35499	−	0.283608i
$23$	−7162.68			−0.588697			−0.294348	−	0.955698i	$-0.595103\pi$
$23$	−7162.68			−0.588697			−0.294348	+	0.955698i	$0.595103\pi$
$24$	−4630.81	−	6500.51i	−0.334983	−	0.470234i
$25$	−11716.4	+	10337.6i	−0.749850	+	0.661608i
$26$	6945.51	−	1453.74i	0.395170	−	0.0827117i
$27$	3788.00			0.192450
$28$	2502.61	−	1095.62i	0.114004	−	0.0499099i
$29$	37170.9			1.52408			0.762042	−	0.647527i	$-0.224197\pi$
$29$	37170.9			1.52408			0.762042	+	0.647527i	$0.224197\pi$
$30$	13142.3	−	8383.25i	0.486753	−	0.310491i
$31$		−	47643.5i		−	1.59926i	−0.600494	−	0.799629i	$-0.705029\pi$
$31$		−	47643.5i		−	1.59926i	0.600494	−	0.799629i	$-0.294971\pi$
$32$	28119.6	+	16823.5i	0.858142	+	0.513413i
$33$		−	28722.9i		−	0.799256i
$34$	6251.69	−	1308.52i	0.159060	−	0.0332923i
$35$	1887.05	+	4990.96i	0.0440129	+	0.116407i
$36$	−14246.5	+	6237.03i	−0.305353	+	0.133681i
$37$			30635.5i			0.604812i	0.953179	+	0.302406i	$0.0977899\pi$
$37$			30635.5i			0.604812i	−0.953179	+	0.302406i	$0.902210\pi$
$38$	18079.4	−	3784.13i	0.329483	−	0.0689629i
$39$		−	13827.0i		−	0.233096i
$40$	−35624.8	+	53168.4i	−0.556637	+	0.830756i
$41$	51219.0			0.743156			0.371578	−	0.928402i	$-0.378817\pi$
$41$	51219.0			0.743156			0.371578	+	0.928402i	$0.378817\pi$
$42$	−1090.57	−	5210.41i	−0.0147200	−	0.0703273i
$43$	−135337.			−1.70220			−0.851099	−	0.525005i	$-0.824063\pi$
$43$	−135337.			−1.70220			−0.851099	+	0.525005i	$0.824063\pi$
$44$	47292.9	+	108026.i	0.555185	+	1.26815i
$45$	−10742.4	−	28412.0i	−0.117886	−	0.311791i
$46$	−11739.2	−	56086.0i	−0.120605	−	0.576211i
$47$	−157494.			−1.51694			−0.758471	−	0.651706i	$-0.774053\pi$
$47$	−157494.			−1.51694			−0.758471	+	0.651706i	$0.774053\pi$
$48$	43311.5	−	46914.6i	0.391633	−	0.424213i
$49$	−115827.			−0.984512
$50$	−100149.	−	74800.5i	−0.801194	−	0.598404i
$51$		−	12445.8i		−	0.0938233i
$52$	22766.5	+	52003.0i	0.161915	+	0.369844i
$53$		−	140651.i		−	0.944743i	−0.881400	−	0.472372i	$-0.843398\pi$
$53$		−	140651.i		−	0.944743i	0.881400	−	0.472372i	$-0.156602\pi$
$54$	6208.28	+	29661.2i	0.0394267	+	0.188368i
$55$	−215437.	+	81455.3i	−1.29489	+	0.489589i
$56$	12680.7	+	17800.5i	0.0722068	+	0.101361i
$57$		−	35992.1i		−	0.194349i
$58$	60920.8	+	291060.i	0.312235	+	1.49176i
$59$			150330.i			0.731965i	0.930622	+	0.365983i	$0.119267\pi$
$59$			150330.i			0.731965i	−0.930622	+	0.365983i	$0.880733\pi$
$60$	87182.9	+	89169.1i	0.403625	+	0.412820i
$61$	39704.1			0.174923			0.0874613	−	0.996168i	$-0.472125\pi$
$61$	39704.1			0.174923			0.0874613	+	0.996168i	$0.472125\pi$
$62$	373064.	−	78084.7i	1.56534	−	0.327635i
$63$	−10372.8			−0.0414833
$64$	−85647.2	+	247758.i	−0.326718	+	0.945122i
$65$	−103710.	+	39212.1i	−0.377642	+	0.142784i
$66$	224909.	−	47074.9i	0.782303	−	0.163741i
$67$	188483.			0.626683			0.313342	−	0.949640i	$-0.398552\pi$
$67$	188483.			0.626683			0.313342	+	0.949640i	$0.398552\pi$
$68$	20492.3	+	46808.2i	0.0651723	+	0.148866i
$69$	−111655.			−0.339884
$70$	−35988.1	+	22956.1i	−0.104922	+	0.0669274i
$71$		−	300445.i		−	0.839440i	−0.907654	−	0.419720i	$-0.862128\pi$
$71$		−	300445.i		−	0.839440i	0.907654	−	0.419720i	$-0.137872\pi$
$72$	−72187.1	−	101333.i	−0.193403	−	0.271490i
$73$			137469.i			0.353376i	0.984267	+	0.176688i	$0.0565383\pi$
$73$			137469.i			0.353376i	−0.984267	+	0.176688i	$0.943462\pi$
$74$	−239886.	+	50209.7i	−0.591984	+	0.123906i
$75$	−182641.	+	161148.i	−0.432926	+	0.381979i
$76$	59261.9	+	135365.i	0.135000	+	0.308366i
$77$			78652.7i			0.172283i
$78$	108270.	−	22661.6i	0.228152	−	0.0477536i
$79$		−	392225.i		−	0.795526i	−0.917488	−	0.397763i	$-0.869787\pi$
$79$		−	392225.i		−	0.795526i	0.917488	−	0.397763i	$-0.130213\pi$
$80$	−474712.	−	191814.i	−0.927172	−	0.374636i
$81$	59049.0			0.111111
$82$	83944.7	+	401061.i	0.152248	+	0.727393i
$83$	261510.			0.457356			0.228678	−	0.973502i	$-0.426560\pi$
$83$	261510.			0.457356			0.228678	+	0.973502i	$0.426560\pi$
$84$	39011.8	−	17079.1i	0.0658200	−	0.0288155i
$85$	−93349.8	+	35295.0i	−0.152005	+	0.0574720i
$86$	−221808.	−	1.05973e6i	−0.348724	−	1.66609i
$87$	579437.			0.879931
$88$	−768367.	+	547366.i	−1.12751	+	0.803211i
$89$	944102.			1.33921			0.669605	−	0.742717i	$-0.266463\pi$
$89$	944102.			1.33921			0.669605	+	0.742717i	$0.266463\pi$
$90$	204869.	−	130682.i	0.281027	−	0.179262i
$91$			37862.9i			0.0502446i
$92$	419932.	−	183843.i	0.539281	−	0.236093i
$93$		−	742689.i		−	0.923332i
$94$	−258122.	−	1.23322e6i	−0.310772	−	1.48477i
$95$	−269960.	+	102070.i	−0.314868	+	0.119050i
$96$	438341.	+	262253.i	0.495448	+	0.296419i
$97$			1.18506e6i			1.29845i	0.760596	+	0.649225i	$0.224907\pi$
$97$			1.18506e6i			1.29845i	−0.760596	+	0.649225i	$0.775093\pi$
$98$	−189833.	−	906961.i	−0.201694	−	0.963631i
$99$		−	447745.i		−	0.461451i
$100$	421574.	−	906794.i	0.421574	−	0.906794i
$101$	713405.			0.692424			0.346212	−	0.938156i	$-0.387468\pi$
$101$	713405.			0.692424			0.346212	+	0.938156i	$0.387468\pi$
$102$	97454.2	−	20397.8i	0.0918333	−	0.0192213i
$103$	−261895.			−0.239671			−0.119836	−	0.992794i	$-0.538237\pi$
$103$	−261895.			−0.239671			−0.119836	+	0.992794i	$0.538237\pi$
$104$	−369887.	+	263499.i	−0.328828	+	0.234249i
$105$	29416.2	+	77801.4i	0.0254109	+	0.0672078i
$106$	1.10134e6	−	230517.i	0.924705	−	0.193547i
$107$	2.24212e6			1.83024			0.915118	−	0.403185i	$-0.132097\pi$
$107$	2.24212e6			1.83024			0.915118	+	0.403185i	$0.132097\pi$
$108$	−222082.	+	97225.7i	−0.176296	+	0.0771809i
$109$	−1.25787e6			−0.971307			−0.485654	−	0.874151i	$-0.661418\pi$
$109$	−1.25787e6			−0.971307			−0.485654	+	0.874151i	$0.661418\pi$
$110$	−990908.	−	1.55344e6i	−0.744484	−	1.16712i
$111$			477561.i			0.349188i
$112$	−118601.	+	128468.i	−0.0844179	+	0.0914408i
$113$		−	687372.i		−	0.476383i	−0.971218	−	0.238192i	$-0.923445\pi$
$113$		−	687372.i		−	0.476383i	0.971218	−	0.238192i	$-0.0765546\pi$
$114$	281830.	−	58988.7i	0.190227	−	0.0398157i
$115$	316643.	+	837473.i	0.208198	+	0.550652i
$116$	−2.17925e6	+	954058.i	−1.39615	+	0.611224i
$117$		−	215542.i		−	0.134578i
$118$	−1.17713e6	+	246382.i	−0.716440	+	0.149956i
$119$			34080.6i			0.0202240i
$120$	−555335.	+	828813.i	−0.321375	+	0.479637i
$121$	−1.62351e6			−0.916430
$122$	65072.5	+	310896.i	0.0358359	+	0.171212i
$123$	798426.			0.429061
$124$	1.22286e6	+	2.79323e6i	0.641372	+	1.46502i
$125$	1.72664e6	+	912905.i	0.884042	+	0.467407i
$126$	−17000.3	−	81222.2i	−0.00849857	−	0.0406035i
$127$	3.19336e6			1.55897			0.779484	−	0.626422i	$-0.215481\pi$
$127$	3.19336e6			1.55897			0.779484	+	0.626422i	$0.215481\pi$
$128$	−2.08039e6	−	264585.i	−0.992009	−	0.126164i
$129$	−2.10969e6			−0.982764
$130$	−477017.	−	747816.i	−0.217122	−	0.340380i
$131$			3.71407e6i			1.65210i	0.563596	+	0.826051i	$0.309418\pi$
$131$			3.71407e6i			1.65210i	−0.563596	+	0.826051i	$0.690582\pi$
$132$	737224.	+	1.68396e6i	0.320536	+	0.732165i
$133$			98558.2i			0.0418927i
$134$	308912.	+	1.47588e6i	0.128387	+	0.613391i
$135$	−167457.	−	442899.i	−0.0680617	−	0.180013i
$136$	−332937.	+	237176.i	−0.132357	+	0.0942876i
$137$			4.29631e6i			1.67084i	0.549614	+	0.835419i	$0.314775\pi$
$137$			4.29631e6i			1.67084i	−0.549614	+	0.835419i	$0.685225\pi$
$138$	−182996.	−	874295.i	−0.0696311	−	0.332675i
$139$		−	2.19309e6i		−	0.816605i	−0.912847	−	0.408302i	$-0.866121\pi$
$139$		−	2.19309e6i		−	0.816605i	0.912847	−	0.408302i	$-0.133879\pi$
$140$	−238736.	−	244175.i	−0.0870028	−	0.0889849i
$141$	−2.45508e6			−0.875807
$142$	2.35258e6	−	492410.i	0.821636	−	0.171974i
$143$	−1.63437e6			−0.558909
$144$	675159.	−	731326.i	0.226109	−	0.244920i
$145$	−1.64323e6	−	4.34609e6i	−0.539007	−	1.42559i
$146$	−1.07643e6	+	225303.i	−0.345881	+	0.0723951i
$147$	−1.80556e6			−0.568408
$148$	−786316.	−	1.79609e6i	−0.242556	−	0.554044i
$149$	6.37636e6			1.92759			0.963793	−	0.266651i	$-0.0859170\pi$
$149$	6.37636e6			1.92759			0.963793	+	0.266651i	$0.0859170\pi$
$150$	−1.56117e6	−	1.16602e6i	−0.462570	−	0.345489i
$151$			2.84487e6i			0.826289i	0.910665	+	0.413145i	$0.135570\pi$
$151$			2.84487e6i			0.826289i	−0.910665	+	0.413145i	$0.864430\pi$
$152$	−962827.	+	685895.i	−0.274168	+	0.195311i
$153$		−	194010.i		−	0.0541689i
$154$	−615876.	+	128907.i	−0.168628	+	0.0352950i
$155$	−5.57056e6	+	2.10620e6i	−1.49591	+	0.565593i
$156$	354895.	+	810646.i	0.0934815	+	0.213529i
$157$		−	6.80838e6i		−	1.75932i	−0.475604	−	0.879660i	$-0.657770\pi$
$157$		−	6.80838e6i		−	1.75932i	0.475604	−	0.879660i	$-0.342230\pi$
$158$	3.07125e6	−	642832.i	0.778653	−	0.162977i
$159$		−	2.19252e6i		−	0.545448i
$160$	723940.	−	4.03152e6i	0.176743	−	0.984257i
$161$	305748.			0.0732633
$162$	96777.6	+	462372.i	0.0227630	+	0.108754i
$163$	−3.53027e6			−0.815164			−0.407582	−	0.913169i	$-0.633628\pi$
$163$	−3.53027e6			−0.815164			−0.407582	+	0.913169i	$0.633628\pi$
$164$	−3.00286e6	+	1.31463e6i	−0.680774	+	0.298038i
$165$	−3.35833e6	+	1.26976e6i	−0.747603	+	0.282664i
$166$	428599.	+	2.04771e6i	0.0936972	+	0.447656i
$167$	558205.			0.119852			0.0599258	−	0.998203i	$-0.480914\pi$
$167$	558205.			0.119852			0.0599258	+	0.998203i	$0.480914\pi$
$168$	197672.	+	277483.i	0.0416886	+	0.0585206i
$169$	4.04004e6			0.836999
$170$	−429365.	−	673113.i	−0.0873937	−	0.137006i
$171$		−	561061.i		−	0.112207i
$172$	7.93449e6	−	3.47366e6i	1.55931	−	0.682656i
$173$			4.94875e6i			0.955778i	0.878420	+	0.477889i	$0.158598\pi$
$173$			4.94875e6i			0.955778i	−0.878420	+	0.477889i	$0.841402\pi$
$174$	949661.	+	4.53718e6i	0.180269	+	0.861267i
$175$	500131.	−	441275.i	0.0933189	−	0.0823371i
$176$	−5.54536e6	−	5.11946e6i	−1.01717	−	0.939045i
$177$			2.34342e6i			0.422600i
$178$	1.54732e6	+	7.39262e6i	0.274360	+	1.31081i
$179$		−	8.92645e6i		−	1.55639i	−0.628020	−	0.778197i	$-0.716135\pi$
$179$		−	8.92645e6i		−	1.55639i	0.628020	−	0.778197i	$-0.283865\pi$
$180$	1.35905e6	+	1.39001e6i	0.233033	+	0.238342i
$181$	489115.			0.0824850			0.0412425	−	0.999149i	$-0.486868\pi$
$181$	489115.			0.0824850			0.0412425	+	0.999149i	$0.486868\pi$
$182$	−296479.	+	62054.9i	−0.0491789	+	0.0102935i
$183$	618925.			0.100992
$184$	2.12779e6	+	2.98689e6i	0.341566	+	0.479475i
$185$	3.58196e6	−	1.35432e6i	0.565726	−	0.213897i
$186$	5.81549e6	−	1.21722e6i	0.903748	−	0.189160i
$187$	−1.47110e6			−0.224966
$188$	9.23350e6	−	4.04235e6i	1.38961	−	0.608360i
$189$	−161696.			−0.0239504
$190$	−1.24169e6	−	1.94659e6i	−0.181031	−	0.283800i
$191$		−	6.73881e6i		−	0.967126i	−0.875310	−	0.483563i	$-0.839342\pi$
$191$		−	6.73881e6i		−	0.967126i	0.875310	−	0.483563i	$-0.160658\pi$
$192$	−1.33511e6	+	3.86217e6i	−0.188631	+	0.545666i
$193$			4.71075e6i			0.655267i	0.944805	+	0.327634i	$0.106251\pi$
$193$			4.71075e6i			0.655267i	−0.944805	+	0.327634i	$0.893749\pi$
$194$	−9.27940e6	+	1.94224e6i	−1.27091	+	0.266010i
$195$	−1.61668e6	+	611256.i	−0.218032	+	0.0824364i
$196$	6.79067e6	−	2.97290e6i	0.901871	−	0.394832i
$197$		−	1.51577e6i		−	0.198260i	−0.995075	−	0.0991299i	$-0.968394\pi$
$197$		−	1.51577e6i		−	0.198260i	0.995075	−	0.0991299i	$-0.0316059\pi$
$198$	3.50599e6	−	733826.i	0.451663	−	0.0945360i
$199$		−	1.23590e7i		−	1.56828i	−0.620586	−	0.784139i	$-0.713105\pi$
$199$		−	1.23590e7i		−	1.56828i	0.620586	−	0.784139i	$-0.286895\pi$
$200$	7.79142e6	+	1.81488e6i	0.973927	+	0.226860i
$201$	2.93816e6			0.361816
$202$	1.16923e6	+	5.58619e6i	0.141855	+	0.677738i
$203$	−1.58669e6			−0.189672
$204$	319443.	+	729667.i	0.0376272	+	0.0859477i
$205$	−2.26426e6	−	5.98862e6i	−0.262824	−	0.695129i
$206$	−429230.	−	2.05072e6i	−0.0491007	−	0.234588i
$207$	−1.74053e6			−0.196232
$208$	−2.66950e6	−	2.46448e6i	−0.296647	−	0.273864i
$209$	−4.25430e6			−0.466004
$210$	−560999.	+	357850.i	−0.0605765	+	0.0386406i
$211$			989173.i			0.105299i	0.998613	+	0.0526496i	$0.0167666\pi$
$211$			989173.i			0.105299i	−0.998613	+	0.0526496i	$0.983233\pi$
$212$	3.61005e6	+	8.24603e6i	0.378883	+	0.865440i
$213$		−	4.68347e6i		−	0.484651i
$214$	3.67469e6	+	1.75565e7i	0.374955	+	1.79142i
$215$	5.98288e6	+	1.58238e7i	0.601998	+	1.59219i
$216$	−1.12529e6	−	1.57962e6i	−0.111661	−	0.156745i
$217$			2.03373e6i			0.199028i
$218$	−2.06157e6	−	9.84953e6i	−0.198989	−	0.950706i
$219$			2.14293e6i			0.204022i
$220$	1.05399e7	−	1.03051e7i	0.989846	−	0.967798i
$221$	−708179.			−0.0656094
$222$	−3.73945e6	+	782692.i	−0.341782	+	0.0715372i
$223$	−6.80020e6			−0.613207			−0.306604	−	0.951837i	$-0.599193\pi$
$223$	−6.80020e6			−0.613207			−0.306604	+	0.951837i	$0.599193\pi$
$224$	−1.20032e6	−	718134.i	−0.106796	−	0.0638942i
$225$	−2.84709e6	+	2.51204e6i	−0.249950	+	0.220536i
$226$	5.38234e6	−	1.12656e6i	0.466279	−	0.0975953i
$227$	−1.40557e7			−1.20164			−0.600821	−	0.799384i	$-0.705160\pi$
$227$	−1.40557e7			−1.20164			−0.600821	+	0.799384i	$0.705160\pi$
$228$	923801.	+	2.11014e6i	0.0779424	+	0.178035i
$229$	−1.18694e7			−0.988375			−0.494188	−	0.869355i	$-0.664534\pi$
$229$	−1.18694e7			−0.988375			−0.494188	+	0.869355i	$0.664534\pi$
$230$	−6.03872e6	+	3.85198e6i	−0.496320	+	0.316593i
$231$			1.22607e6i			0.0994674i
$232$	−1.10422e7	−	1.55006e7i	−0.884286	−	1.24132i
$233$		−	1.00854e7i		−	0.797310i	−0.917101	−	0.398655i	$-0.869477\pi$
$233$		−	1.00854e7i		−	0.797310i	0.917101	−	0.398655i	$-0.130523\pi$
$234$	1.68776e6	−	353259.i	0.131723	−	0.0275706i
$235$	6.96238e6	+	1.84144e7i	0.536481	+	1.41891i
$236$	−3.85850e6	−	8.81353e6i	−0.293550	−	0.670523i
$237$		−	6.11419e6i		−	0.459297i
$238$	−266862.	+	55855.9i	−0.0197950	+	0.00414322i
$239$		−	1.83092e7i		−	1.34114i	−0.741845	−	0.670571i	$-0.766049\pi$
$239$		−	1.83092e7i		−	1.34114i	0.741845	−	0.670571i	$-0.233951\pi$
$240$	−7.40003e6	−	2.99008e6i	−0.535303	−	0.216296i
$241$	9.34514e6			0.667629			0.333814	−	0.942639i	$-0.391664\pi$
$241$	9.34514e6			0.667629			0.333814	+	0.942639i	$0.391664\pi$
$242$	−2.66083e6	−	1.27126e7i	−0.187746	−	0.896992i
$243$	920483.			0.0641500
$244$	−2.32776e6	+	1.01908e6i	−0.160239	+	0.0701515i
$245$	5.12041e6	+	1.35427e7i	0.348182	+	0.920887i
$246$	1.30857e6	+	6.25193e6i	0.0879005	+	0.419961i
$247$	−2.04799e6			−0.135906
$248$	−1.98677e7	+	1.41533e7i	−1.30255	+	0.927902i
$249$	4.07654e6			0.264055
$250$	−4.31847e6	+	1.50164e7i	−0.276382	+	0.961048i
$251$			1.63531e7i			1.03414i	0.855943	+	0.517070i	$0.172977\pi$
$251$			1.63531e7i			1.03414i	−0.855943	+	0.517070i	$0.827023\pi$
$252$	608133.	−	266236.i	0.0380012	−	0.0166366i
$253$			1.31977e7i			0.814964i
$254$	5.23372e6	+	2.50051e7i	0.319381	+	1.52590i
$255$	−1.45518e6	+	550194.i	−0.0877599	+	0.0331815i
$256$	−1.33785e6	−	1.67238e7i	−0.0797420	−	0.996816i
$257$		−	1.43214e7i		−	0.843694i	−0.906667	−	0.421847i	$-0.861382\pi$
$257$		−	1.43214e7i		−	0.843694i	0.906667	−	0.421847i	$-0.138618\pi$
$258$	−3.45765e6	−	1.65195e7i	−0.201336	−	0.961920i
$259$		−	1.30772e6i		−	0.0752689i
$260$	5.07383e6	−	4.96082e6i	0.288680	−	0.282250i
$261$	9.03253e6			0.508028
$262$	−2.90824e7	+	6.08713e6i	−1.61706	+	0.338461i
$263$	2.73591e7			1.50396			0.751978	−	0.659188i	$-0.229100\pi$
$263$	2.73591e7			1.50396			0.751978	+	0.659188i	$0.229100\pi$
$264$	−1.19777e7	+	8.53259e6i	−0.650969	+	0.463734i
$265$	−1.64451e7	+	6.21779e6i	−0.883688	+	0.334117i
$266$	−771742.	+	161531.i	−0.0410041	+	0.00858243i
$267$	1.47171e7			0.773194
$268$	−1.10503e7	+	4.83776e6i	−0.574079	+	0.251327i
$269$	1.18794e7			0.610294			0.305147	−	0.952305i	$-0.401294\pi$
$269$	1.18794e7			0.610294			0.305147	+	0.952305i	$0.401294\pi$
$270$	3.19359e6	−	2.03713e6i	0.162251	−	0.103497i
$271$			8.03680e6i			0.403809i	0.979405	+	0.201904i	$0.0647130\pi$
$271$			8.03680e6i			0.403809i	−0.979405	+	0.201904i	$0.935287\pi$
$272$	−2.40283e6	−	2.21829e6i	−0.119403	−	0.110233i
$273$			590224.i			0.0290088i
$274$	−3.36415e7	+	7.04138e6i	−1.63540	+	0.342300i
$275$	1.90478e7	+	2.15883e7i	0.915897	+	1.03806i
$276$	6.54609e6	−	2.86583e6i	0.311354	−	0.136308i
$277$			2.36287e7i			1.11173i	0.831271	+	0.555867i	$0.187614\pi$
$277$			2.36287e7i			1.11173i	−0.831271	+	0.555867i	$0.812386\pi$
$278$	1.71726e7	−	3.59433e6i	0.799285	−	0.167295i
$279$		−	1.15774e7i		−	0.533086i
$280$	1.52069e6	−	2.26956e6i	0.0692735	−	0.103388i
$281$	−4.00913e7			−1.80689			−0.903444	−	0.428707i	$-0.858969\pi$
$281$	−4.00913e7			−1.80689			−0.903444	+	0.428707i	$0.858969\pi$
$282$	−4.02372e6	−	1.92241e7i	−0.179424	−	0.857231i
$283$	2.00039e7			0.882584			0.441292	−	0.897364i	$-0.354520\pi$
$283$	2.00039e7			0.882584			0.441292	+	0.897364i	$0.354520\pi$
$284$	7.71146e6	+	1.76144e7i	0.336652	+	0.768977i
$285$	−4.20826e6	+	1.59112e6i	−0.181789	+	0.0687333i
$286$	−2.67862e6	−	1.27976e7i	−0.114502	−	0.547055i
$287$	−2.18635e6			−0.0924857
$288$	6.83306e6	+	4.08811e6i	0.286047	+	0.171138i
$289$	2.35001e7			0.973592
$290$	3.13381e7	−	1.99900e7i	1.28493	−	0.819631i
$291$			1.84733e7i			0.749661i
$292$	−3.52839e6	−	8.05952e6i	−0.141719	−	0.323713i
$293$		−	1.18746e6i		−	0.0472080i	−0.999721	−	0.0236040i	$-0.992486\pi$
$293$		−	1.18746e6i		−	0.0472080i	0.999721	−	0.0236040i	$-0.00751408\pi$
$294$	−2.95920e6	−	1.41381e7i	−0.116448	−	0.556352i
$295$	1.75769e7	−	6.64571e6i	0.684661	−	0.258866i
$296$	1.27753e7	−	9.10079e6i	0.492600	−	0.350917i
$297$		−	6.97965e6i		−	0.266419i
$298$	1.04504e7	+	4.99289e7i	0.394899	+	1.88670i
$299$			6.35331e6i			0.237677i
$300$	6.57168e6	−	1.41355e7i	0.243396	−	0.523538i
$301$	5.77703e6			0.211839
$302$	−2.22763e7	+	4.66257e6i	−0.808764	+	0.169279i
$303$	1.11209e7			0.399771
$304$	−6.94878e6	−	6.41510e6i	−0.247336	−	0.228340i
$305$	−1.75521e6	−	4.64227e6i	−0.0618630	−	0.163618i
$306$	1.51916e6	−	317970.i	0.0530200	−	0.0110974i
$307$	−3.06814e7			−1.06038			−0.530188	−	0.847880i	$-0.677879\pi$
$307$	−3.06814e7			−1.06038			−0.530188	+	0.847880i	$0.677879\pi$
$308$	−2.01876e6	−	4.61123e6i	−0.0690928	−	0.157821i
$309$	−4.08254e6			−0.138374
$310$	−2.56220e7	−	4.01674e7i	−0.860058	−	1.34831i
$311$		−	3.32935e7i		−	1.10682i	−0.832908	−	0.553412i	$-0.813326\pi$
$311$		−	3.32935e7i		−	1.10682i	0.832908	−	0.553412i	$-0.186674\pi$
$312$	−5.76597e6	+	4.10754e6i	−0.189849	+	0.135244i
$313$		−	1.22049e7i		−	0.398018i	−0.979998	−	0.199009i	$-0.936228\pi$
$313$		−	1.22049e7i		−	0.398018i	0.979998	−	0.199009i	$-0.0637722\pi$
$314$	5.33118e7	−	1.11585e7i	1.72200	−	0.360427i
$315$	458554.	+	1.21280e6i	0.0146710	+	0.0388024i
$316$	1.00672e7	+	2.29953e7i	0.319041	+	0.728749i
$317$		−	1.63806e7i		−	0.514225i	−0.966382	−	0.257112i	$-0.917229\pi$
$317$		−	1.63806e7i		−	0.514225i	0.966382	−	0.257112i	$-0.0827710\pi$
$318$	1.71682e7	−	3.59341e6i	0.533879	−	0.111744i
$319$		−	6.84901e7i		−	2.10987i
$320$	3.27546e7	−	938716.i	0.999590	−	0.0286474i
$321$	3.49512e7			1.05669
$322$	501102.	+	2.39411e6i	0.0150092	+	0.0717094i
$323$	−1.84341e6			−0.0547034
$324$	−3.46191e6	+	1.51560e6i	−0.101784	+	0.0445604i
$325$	9.16949e6	+	1.03925e7i	0.267113	+	0.302740i
$326$	−5.78588e6	−	2.76431e7i	−0.167000	−	0.797874i
$327$	−1.96083e7			−0.560785
$328$	−1.52154e7	−	2.13587e7i	−0.431185	−	0.605277i
$329$	6.72282e6			0.188784
$330$	−1.54467e7	−	2.42157e7i	−0.429828	−	0.673838i
$331$			4.78385e7i			1.31915i	0.751639	+	0.659574i	$0.229263\pi$
$331$			4.78385e7i			1.31915i	−0.751639	+	0.659574i	$0.770737\pi$
$332$	−1.53318e7	+	6.71213e6i	−0.418965	+	0.183420i
$333$			7.44444e6i			0.201604i
$334$	914862.	+	4.37092e6i	0.0245537	+	0.117310i
$335$	−8.33235e6	−	2.20378e7i	−0.221632	−	0.586183i
$336$	−1.84881e6	+	2.00261e6i	−0.0487387	+	0.0527934i
$337$			6.77117e6i			0.176919i	0.996080	+	0.0884593i	$0.0281943\pi$
$337$			6.77117e6i			0.176919i	−0.996080	+	0.0884593i	$0.971806\pi$
$338$	6.62136e6	+	3.16348e7i	0.171474	+	0.819246i
$339$		−	1.07151e7i		−	0.275040i
$340$	4.56698e6	−	4.46526e6i	0.116196	−	0.113608i
$341$	−8.77866e7			−2.21394
$342$	4.39329e6	−	919544.i	0.109828	−	0.0229876i
$343$	9.96623e6			0.246973
$344$	4.02040e7	+	5.64365e7i	0.987628	+	1.38639i
$345$	4.93598e6	+	1.30549e7i	0.120203	+	0.317919i
$346$	−3.87503e7	+	8.11069e6i	−0.935506	+	0.195808i
$347$	−1.75962e6			−0.0421145			−0.0210572	−	0.999778i	$-0.506703\pi$
$347$	−1.75962e6			−0.0421145			−0.0210572	+	0.999778i	$0.506703\pi$
$348$	−3.39711e7	+	1.48723e7i	−0.806069	+	0.352891i
$349$	8.41394e6			0.197935			0.0989677	−	0.995091i	$-0.468446\pi$
$349$	8.41394e6			0.197935			0.0989677	+	0.995091i	$0.468446\pi$
$350$	4.27501e6	+	3.19296e6i	0.0997086	+	0.0744714i
$351$		−	3.35996e6i		−	0.0776985i
$352$	3.09985e7	−	5.18124e7i	0.710744	−	1.18797i
$353$		−	4.18620e6i		−	0.0951691i	−0.998867	−	0.0475846i	$-0.984848\pi$
$353$		−	4.18620e6i		−	0.0951691i	0.998867	−	0.0475846i	$-0.0151524\pi$
$354$	−1.83497e7	+	3.84071e6i	−0.413637	+	0.0865769i
$355$	−3.51286e7	+	1.32819e7i	−0.785191	+	0.296876i
$356$	−5.53506e7	+	2.42321e7i	−1.22680	+	0.537082i
$357$			531264.i			0.0116763i
$358$	6.98969e7	−	1.46299e7i	1.52338	−	0.318854i
$359$		−	3.66938e7i		−	0.793065i	−0.918021	−	0.396532i	$-0.870213\pi$
$359$		−	3.66938e7i		−	0.793065i	0.918021	−	0.396532i	$-0.129787\pi$
$360$	−8.65682e6	+	1.29199e7i	−0.185546	+	0.276919i
$361$	4.17149e7			0.886685
$362$	801628.	+	3.82992e6i	0.0168985	+	0.0807354i
$363$	−2.53080e7			−0.529101
$364$	−971819.	−	2.21982e6i	−0.0201503	−	0.0460271i
$365$	1.60731e7	−	6.07716e6i	0.330539	−	0.124975i
$366$	1.01438e6	+	4.84638e6i	0.0206898	+	0.0988495i
$367$	−9.45536e6			−0.191285			−0.0956423	−	0.995416i	$-0.530491\pi$
$367$	−9.45536e6			−0.191285			−0.0956423	+	0.995416i	$0.530491\pi$
$368$	−1.99010e7	+	2.15566e7i	−0.399330	+	0.432550i
$369$	1.24462e7			0.247719
$370$	1.64754e7	+	2.58283e7i	0.325259	+	0.509906i
$371$			6.00386e6i			0.117573i
$372$	1.90624e7	+	4.35422e7i	0.370297	+	0.845827i
$373$		−	5.35560e7i		−	1.03200i	−0.856587	−	0.516002i	$-0.827420\pi$
$373$		−	5.35560e7i		−	1.03200i	0.856587	−	0.516002i	$-0.172580\pi$
$374$	−2.41104e6	−	1.15192e7i	−0.0460882	−	0.220195i
$375$	2.69157e7	+	1.42308e7i	0.510402	+	0.269858i
$376$	4.67860e7	+	6.56760e7i	0.880142	+	1.23550i
$377$		−	3.29707e7i		−	0.615324i
$378$	−265009.	−	1.26613e6i	−0.00490665	−	0.0234424i
$379$			5.05485e7i			0.928518i	0.885699	+	0.464259i	$0.153679\pi$
$379$			5.05485e7i			0.928518i	−0.885699	+	0.464259i	$0.846321\pi$
$380$	1.32073e7	−	1.29132e7i	0.240694	−	0.235332i
$381$	4.97796e7			0.900071
$382$	5.27670e7	−	1.10445e7i	0.946613	−	0.198132i
$383$	−7.44208e7			−1.32464			−0.662320	−	0.749221i	$-0.730428\pi$
$383$	−7.44208e7			−1.32464			−0.662320	+	0.749221i	$0.730428\pi$
$384$	−3.24301e7	−	4.12447e6i	−0.572737	−	0.0728408i
$385$	9.19621e6	−	3.47703e6i	0.161149	−	0.0609293i
$386$	−3.68867e7	+	7.72063e6i	−0.641369	+	0.134243i
$387$	−3.28868e7			−0.567399
$388$	−3.04167e7	−	6.94775e7i	−0.520735	−	1.18946i
$389$	−3.91704e7			−0.665441			−0.332721	−	0.943025i	$-0.607967\pi$
$389$	−3.91704e7			−0.665441			−0.332721	+	0.943025i	$0.607967\pi$
$390$	−7.43596e6	−	1.16573e7i	−0.125355	−	0.196519i
$391$			5.71865e6i			0.0956672i
$392$	3.44083e7	+	4.83007e7i	0.571222	+	0.801854i
$393$			5.78967e7i			0.953841i
$394$	1.18690e7	−	2.48425e6i	0.194055	−	0.0406169i
$395$	−4.58597e7	+	1.73393e7i	−0.744114	+	0.281345i
$396$	1.14922e7	+	2.62503e7i	0.185062	+	0.422716i
$397$			6.48990e7i			1.03721i	0.855014	+	0.518604i	$0.173548\pi$
$397$			6.48990e7i			1.03721i	−0.855014	+	0.518604i	$0.826452\pi$
$398$	9.67746e7	−	2.02556e7i	1.53501	−	0.321288i
$399$			1.53637e6i			0.0241867i
$400$	−1.44143e6	+	6.39838e7i	−0.0225223	+	0.999746i
$401$	−9.69420e7			−1.50341			−0.751707	−	0.659497i	$-0.770769\pi$
$401$	−9.69420e7			−1.50341			−0.751707	+	0.659497i	$0.770769\pi$
$402$	4.81546e6	+	2.30067e7i	0.0741241	+	0.354142i
$403$	−4.22599e7			−0.645674
$404$	−4.18254e7	+	1.83108e7i	−0.634301	+	0.277692i
$405$	−2.61040e6	−	6.90411e6i	−0.0392955	−	0.103930i
$406$	−2.60048e6	−	1.24243e7i	−0.0388576	−	0.185649i
$407$	5.64482e7			0.837273
$408$	−5.18998e6	+	3.69721e6i	−0.0764161	+	0.0544370i
$409$	−3.78803e7			−0.553660			−0.276830	−	0.960919i	$-0.589284\pi$
$409$	−3.78803e7			−0.553660			−0.276830	+	0.960919i	$0.589284\pi$
$410$	4.31818e7	−	2.75448e7i	0.626541	−	0.399658i
$411$			6.69729e7i			0.964658i
$412$	1.53543e7	−	6.72201e6i	0.219553	−	0.0961186i
$413$		−	6.41705e6i		−	0.0910931i
$414$	−2.85262e6	−	1.36289e7i	−0.0402015	−	0.192070i
$415$	−1.15607e7	−	3.05763e7i	−0.161748	−	0.427799i
$416$	1.49225e7	−	2.49421e7i	0.207282	−	0.346461i
$417$		−	3.41869e7i		−	0.471467i
$418$	−6.97253e6	−	3.33125e7i	−0.0954688	−	0.456120i
$419$			5.92341e7i			0.805248i	0.915365	+	0.402624i	$0.131902\pi$
$419$			5.92341e7i			0.805248i	−0.915365	+	0.402624i	$0.868098\pi$
$420$	−3.72152e6	−	3.80630e6i	−0.0502311	−	0.0513755i
$421$	7.02355e7			0.941262			0.470631	−	0.882330i	$-0.344026\pi$
$421$	7.02355e7			0.941262			0.470631	+	0.882330i	$0.344026\pi$
$422$	−7.74554e6	+	1.62119e6i	−0.103066	+	0.0215723i
$423$	−3.82709e7			−0.505648
$424$	−5.86524e7	+	4.17825e7i	−0.769464	+	0.548147i
$425$	8.25351e6	+	9.35433e6i	0.107516	+	0.121856i
$426$	3.66731e7	−	7.67592e6i	0.474372	−	0.0992891i
$427$	−1.69482e6			−0.0217691
$428$	−1.31450e8	+	5.75480e7i	−1.67660	+	0.734005i
$429$	−2.54772e7			−0.322686
$430$	−1.14100e8	+	7.27821e7i	−1.43509	+	0.915417i
$431$		−	9.18112e7i		−	1.14674i	−0.819298	−	0.573368i	$-0.805636\pi$
$431$		−	9.18112e7i		−	1.14674i	0.819298	−	0.573368i	$-0.194364\pi$
$432$	1.05247e7	−	1.14002e7i	0.130544	−	0.141404i
$433$		−	1.07675e8i		−	1.32632i	−0.748476	−	0.663162i	$-0.769214\pi$
$433$		−	1.07675e8i		−	1.32632i	0.748476	−	0.663162i	$-0.230786\pi$
$434$	−1.59247e7	+	3.33315e6i	−0.194806	+	0.0407742i
$435$	−2.56154e7	−	6.77488e7i	−0.311196	−	0.823065i
$436$	7.37462e7	−	3.22855e7i	0.889775	−	0.389537i
$437$			1.65379e7i			0.198169i
$438$	−1.67799e7	+	3.51213e6i	−0.199694	+	0.0417973i
$439$		−	6.90483e6i		−	0.0816130i	−0.999167	−	0.0408065i	$-0.987007\pi$
$439$		−	6.90483e6i		−	0.0816130i	0.999167	−	0.0408065i	$-0.0129927\pi$
$440$	9.79665e7	+	6.56412e7i	1.15006	+	0.770582i
$441$	−2.81459e7			−0.328171
$442$	−1.16066e6	−	5.54527e6i	−0.0134412	−	0.0642178i
$443$	−5.25821e7			−0.604821			−0.302410	−	0.953178i	$-0.597791\pi$
$443$	−5.25821e7			−0.604821			−0.302410	+	0.953178i	$0.597791\pi$
$444$	−1.22575e7	−	2.79983e7i	−0.140040	−	0.319877i
$445$	−4.17363e7	−	1.10386e8i	−0.473624	−	1.25266i
$446$	−1.11451e7	−	5.32477e7i	−0.125626	−	0.600201i
$447$	9.93976e7			1.11289
$448$	3.65597e6	−	1.05759e7i	0.0406601	−	0.117620i
$449$	9.75225e7			1.07737			0.538686	−	0.842506i	$-0.318921\pi$
$449$	9.75225e7			1.07737			0.538686	+	0.842506i	$0.318921\pi$
$450$	−2.43363e7	−	1.81765e7i	−0.267065	−	0.199468i
$451$		−	9.43747e7i		−	1.02879i
$452$	1.76426e7	+	4.02991e7i	0.191050	+	0.436395i
$453$			4.43472e7i			0.477058i
$454$	−2.30364e7	−	1.10061e8i	−0.246177	−	1.17615i
$455$	4.42700e6	−	1.67382e6i	0.0469975	−	0.0177695i
$456$	−1.50090e7	+	1.06920e7i	−0.158291	+	0.112763i
$457$			3.78570e7i			0.396641i	0.980137	+	0.198320i	$0.0635486\pi$
$457$			3.78570e7i			0.396641i	−0.980137	+	0.198320i	$0.936451\pi$
$458$	−1.94532e7	−	9.29411e7i	−0.202485	−	0.967411i
$459$		−	3.02432e6i		−	0.0312744i
$460$	−4.00593e7	−	4.09720e7i	−0.411557	−	0.420933i
$461$	7.34284e7			0.749483			0.374741	−	0.927129i	$-0.377732\pi$
$461$	7.34284e7			0.749483			0.374741	+	0.927129i	$0.377732\pi$
$462$	−9.60055e6	+	2.00946e6i	−0.0973577	+	0.0203776i
$463$	1.84010e8			1.85395			0.926977	−	0.375118i	$-0.122398\pi$
$463$	1.84010e8			1.85395			0.926977	+	0.375118i	$0.122398\pi$
$464$	1.03277e8	−	1.11869e8i	1.03383	−	1.11984i
$465$	−8.68365e7	+	3.28323e7i	−0.863661	+	0.326545i
$466$	7.89722e7	−	1.65294e7i	0.780398	−	0.163342i
$467$	9.86693e7			0.968794			0.484397	−	0.874848i	$-0.339039\pi$
$467$	9.86693e7			0.968794			0.484397	+	0.874848i	$0.339039\pi$
$468$	5.53226e6	+	1.26367e7i	0.0539716	+	0.123281i
$469$	−8.04566e6			−0.0779907
$470$	−1.32780e8	+	8.46977e7i	−1.27891	+	0.815790i
$471$		−	1.06132e8i		−	1.01574i
$472$	6.26889e7	−	4.46581e7i	0.596163	−	0.424692i
$473$			2.49368e8i			2.35644i
$474$	4.78760e7	−	1.00208e7i	0.449555	−	0.0940948i
$475$	2.38685e7	+	2.70519e7i	0.222712	+	0.252416i
$476$	−874739.	−	1.99807e6i	−0.00811069	−	0.0185263i
$477$		−	3.41781e7i		−	0.314914i
$478$	1.43367e8	−	3.00076e7i	1.31270	−	0.274756i
$479$			8.02038e7i			0.729774i	0.931052	+	0.364887i	$0.118892\pi$
$479$			8.02038e7i			0.729774i	−0.931052	+	0.364887i	$0.881108\pi$
$480$	1.12851e7	−	6.28451e7i	0.102043	−	0.568261i
$481$	2.71738e7			0.244183
$482$	1.53161e7	+	7.31755e7i	0.136775	+	0.653468i
$483$	4.76615e6			0.0422986
$484$	9.51828e7	−	4.16703e7i	0.839504	−	0.367528i
$485$	1.38559e8	−	5.23885e7i	1.21454	−	0.459209i
$486$	1.50861e6	+	7.20767e6i	0.0131422	+	0.0627894i
$487$	1.13713e8			0.984516			0.492258	−	0.870449i	$-0.336172\pi$
$487$	1.13713e8			0.984516			0.492258	+	0.870449i	$0.336172\pi$
$488$	−1.17947e7	−	1.65569e7i	−0.101491	−	0.142469i
$489$	−5.50314e7			−0.470635
$490$	−9.76515e7	+	6.22900e7i	−0.830024	+	0.529456i
$491$			9.37372e6i			0.0791895i	0.999216	+	0.0395947i	$0.0126067\pi$
$491$			9.37372e6i			0.0791895i	−0.999216	+	0.0395947i	$0.987393\pi$
$492$	−4.68099e7	+	2.04930e7i	−0.393045	+	0.172072i
$493$		−	2.96771e7i		−	0.247674i
$494$	−3.35653e6	−	1.60364e7i	−0.0278426	−	0.133023i
$495$	−5.23512e7	+	1.97936e7i	−0.431629	+	0.163196i
$496$	−1.43387e8	−	1.32374e8i	−1.17507	−	1.08482i
$497$			1.28249e7i			0.104468i
$498$	6.68120e6	+	3.19206e7i	0.0540961	+	0.258454i
$499$			1.95311e8i			1.57190i	0.618289	+	0.785951i	$0.287826\pi$
$499$			1.95311e8i			1.57190i	−0.618289	+	0.785951i	$0.712174\pi$
$500$	−1.24661e8	−	9.20413e6i	−0.997285	−	0.0736331i
$501$	8.70155e6			0.0691964
$502$	−1.28050e8	+	2.68017e7i	−1.01220	+	0.211861i
$503$	1.57813e8			1.24005			0.620024	−	0.784583i	$-0.287123\pi$
$503$	1.57813e8			1.24005			0.620024	+	0.784583i	$0.287123\pi$
$504$	3.08140e6	+	4.32553e6i	0.0240689	+	0.0337869i
$505$	−3.15378e7	−	8.34126e7i	−0.244882	−	0.647676i
$506$	−1.03343e8	+	2.16303e7i	−0.797678	+	0.166959i
$507$	6.29779e7			0.483242
$508$	−1.87220e8	+	8.19634e7i	−1.42811	+	0.625214i
$509$	−7.46265e7			−0.565900			−0.282950	−	0.959135i	$-0.591313\pi$
$509$	−7.46265e7			−0.565900			−0.282950	+	0.959135i	$0.591313\pi$
$510$	−6.69315e6	−	1.04928e7i	−0.0504568	−	0.0791007i
$511$		−	5.86806e6i		−	0.0439776i
$512$	1.28760e8	−	3.78850e7i	0.959336	−	0.282265i
$513$		−	8.74608e6i		−	0.0647830i
$514$	1.12141e8	−	2.34718e7i	0.825799	−	0.172845i
$515$	1.15777e7	+	3.06213e7i	0.0847619	+	0.224182i
$516$	1.23686e8	−	5.41490e7i	0.900270	−	0.394131i
$517$			2.90193e8i			2.09998i
$518$	1.02399e7	−	2.14327e6i	0.0736724	−	0.0154201i
$519$			7.71434e7i			0.551819i
$520$	4.71605e7	+	3.15993e7i	0.335404	+	0.224733i
$521$	1.33012e8			0.940543			0.470272	−	0.882522i	$-0.344156\pi$
$521$	1.33012e8			0.940543			0.470272	+	0.882522i	$0.344156\pi$
$522$	1.48037e7	+	7.07276e7i	0.104078	+	0.497253i
$523$	−8.07772e7			−0.564656			−0.282328	−	0.959318i	$-0.591107\pi$
$523$	−8.07772e7			−0.564656			−0.282328	+	0.959318i	$0.591107\pi$
$524$	−9.53284e7	−	2.17748e8i	−0.662565	−	1.51342i
$525$	7.79627e6	−	6.87880e6i	0.0538777	−	0.0475373i
$526$	4.48399e7	+	2.14231e8i	0.308111	+	1.47206i
$527$	−3.80384e7			−0.259890
$528$	−8.64435e7	−	7.98045e7i	−0.587261	−	0.542158i
$529$	−9.67320e7			−0.653436
$530$	−7.56398e7	−	1.18580e8i	−0.508069	−	0.796496i
$531$			3.65303e7i			0.243988i
$532$	−2.52967e6	−	5.77825e6i	−0.0168008	−	0.0383762i
$533$		−	4.54314e7i		−	0.300037i
$534$	2.41204e7	+	1.15240e8i	0.158402	+	0.756794i
$535$	−9.91182e7	−	2.62153e8i	−0.647280	−	1.71196i
$536$	−5.59920e7	−	7.85989e7i	−0.363606	−	0.510414i
$537$		−	1.39150e8i		−	0.898584i
$538$	1.94696e7	+	9.30198e7i	0.125029	+	0.597349i
$539$			2.13419e8i			1.36291i
$540$	2.11855e7	+	2.16681e7i	0.134542	+	0.137607i
$541$	−1.30546e8			−0.824465			−0.412232	−	0.911079i	$-0.635251\pi$
$541$	−1.30546e8			−0.824465			−0.412232	+	0.911079i	$0.635251\pi$
$542$	−6.29307e7	+	1.31718e7i	−0.395244	+	0.0827271i
$543$	7.62454e6			0.0476227
$544$	1.34318e7	−	2.24506e7i	0.0834330	−	0.139454i
$545$	5.56072e7	+	1.47073e8i	0.343512	+	0.908536i
$546$	−4.62164e6	+	967340.i	−0.0283935	+	0.00594294i
$547$	9.69022e7			0.592068			0.296034	−	0.955177i	$-0.404336\pi$
$547$	9.69022e7			0.592068			0.296034	+	0.955177i	$0.404336\pi$
$548$	−1.10273e8	−	2.51883e8i	−0.670079	−	1.53059i
$549$	9.64809e6			0.0583075
$550$	−1.37825e8	+	1.84532e8i	−0.828402	+	1.10913i
$551$		−	8.58237e7i		−	0.513041i
$552$	3.31690e7	+	4.65610e7i	0.197203	+	0.276825i
$553$			1.67427e7i			0.0990032i
$554$	−1.85021e8	+	3.87260e7i	−1.08815	+	0.227758i
$555$	5.58373e7	−	2.11117e7i	0.326622	−	0.123494i
$556$	5.62896e7	+	1.28576e8i	0.327494	+	0.748058i
$557$		−	3.21040e8i		−	1.85778i	−0.370356	−	0.928890i	$-0.620764\pi$
$557$		−	3.21040e8i		−	1.85778i	0.370356	−	0.928890i	$-0.379236\pi$
$558$	9.06545e7	−	1.89746e7i	0.521779	−	0.109212i
$559$			1.20044e8i			0.687234i
$560$	2.02637e7	+	8.18783e6i	0.115387	+	0.0466235i
$561$	−2.29322e7			−0.129884
$562$	−6.57071e7	−	3.13928e8i	−0.370172	−	1.76856i
$563$	−1.10496e8			−0.619186			−0.309593	−	0.950869i	$-0.600193\pi$
$563$	−1.10496e8			−0.619186			−0.309593	+	0.950869i	$0.600193\pi$
$564$	1.43936e8	−	6.30141e7i	0.802291	−	0.351237i
$565$	−8.03688e7	+	3.03869e7i	−0.445597	+	0.168477i
$566$	3.27852e7	+	1.56637e8i	0.180812	+	0.863864i
$567$	−2.52059e6			−0.0138278
$568$	−1.25288e8	+	8.92521e7i	−0.683698	+	0.487050i
$569$	1.78862e8			0.970913			0.485457	−	0.874261i	$-0.338653\pi$
$569$	1.78862e8			0.970913			0.485457	+	0.874261i	$0.338653\pi$
$570$	−1.93560e7	−	3.03443e7i	−0.104518	−	0.163852i
$571$			4.65669e6i			0.0250132i	0.999922	+	0.0125066i	$0.00398108\pi$
$571$			4.65669e6i			0.0250132i	−0.999922	+	0.0125066i	$0.996019\pi$
$572$	9.58192e7	−	4.19489e7i	0.511994	−	0.224147i
$573$		−	1.05048e8i		−	0.558371i
$574$	−3.58329e6	−	1.71198e7i	−0.0189473	−	0.0905241i
$575$	8.39208e7	−	7.40450e7i	0.441435	−	0.389486i
$576$	−2.08123e7	+	6.02052e7i	−0.108906	+	0.315041i
$577$			1.91916e8i			0.999041i	0.866302	+	0.499521i	$0.166490\pi$
$577$			1.91916e8i			0.999041i	−0.866302	+	0.499521i	$0.833510\pi$
$578$	3.85152e7	+	1.84014e8i	0.199457	+	0.952942i
$579$			7.34334e7i			0.378319i
$580$	2.07889e8	+	2.12625e8i	1.06549	+	1.08976i
$581$	−1.11629e7			−0.0569180
$582$	−1.44652e8	+	3.02765e7i	−0.733760	+	0.153581i
$583$	−2.59159e8			−1.30786
$584$	5.73258e7	−	4.08375e7i	0.287814	−	0.205031i
$585$	−2.52015e7	+	9.52853e6i	−0.125881	+	0.0475947i
$586$	9.29818e6	−	1.94617e6i	0.0462067	−	0.00967136i
$587$	−8.23978e7			−0.407382			−0.203691	−	0.979035i	$-0.565294\pi$
$587$	−8.23978e7			−0.407382			−0.203691	+	0.979035i	$0.565294\pi$
$588$	1.05856e8	−	4.63430e7i	0.520696	−	0.227957i
$589$	−1.10004e8			−0.538346
$590$	8.08454e7	+	1.26741e8i	0.393640	+	0.617106i
$591$		−	2.36285e7i		−	0.114465i
$592$	9.21999e7	+	8.51188e7i	0.444391	+	0.410261i
$593$		−	3.25768e8i		−	1.56223i	−0.624388	−	0.781114i	$-0.714652\pi$
$593$		−	3.25768e8i		−	1.56223i	0.624388	−	0.781114i	$-0.285348\pi$
$594$	5.46529e7	−	1.14392e7i	0.260768	−	0.0545804i
$595$	3.98476e6	−	1.50661e6i	0.0189170	−	0.00715239i
$596$	−3.73832e8	+	1.63661e8i	−1.76578	+	0.773046i
$597$		−	1.92657e8i		−	0.905445i
$598$	−4.97484e7	+	1.04127e7i	−0.232635	+	0.0486921i
$599$			2.65951e7i			0.123743i	0.998084	+	0.0618716i	$0.0197069\pi$
$599$			2.65951e7i			0.123743i	−0.998084	+	0.0618716i	$0.980293\pi$
$600$	1.21456e8	+	2.82911e7i	0.562297	+	0.130978i
$601$	−2.51378e8			−1.15799			−0.578994	−	0.815332i	$-0.696555\pi$
$601$	−2.51378e8			−1.15799			−0.578994	+	0.815332i	$0.696555\pi$
$602$	9.46818e6	+	4.52360e7i	0.0433987	+	0.207345i
$603$	4.58014e7			0.208894
$604$	−7.30188e7	−	1.66789e8i	−0.331378	−	0.756930i
$605$	7.17712e7	+	1.89824e8i	0.324104	+	0.857205i
$606$	1.82264e7	+	8.70801e7i	0.0819000	+	0.391292i
$607$	−4.32296e8			−1.93293			−0.966463	−	0.256805i	$-0.917330\pi$
$607$	−4.32296e8			−1.93293			−0.966463	+	0.256805i	$0.917330\pi$
$608$	3.88437e7	−	6.49251e7i	0.172826	−	0.288870i
$609$	−2.47341e7			−0.109507
$610$	3.34738e7	−	2.13523e7i	0.147474	−	0.0940708i
$611$			1.39697e8i			0.612441i
$612$	4.97962e6	+	1.13744e7i	0.0217241	+	0.0496219i
$613$			8.56795e7i			0.371959i	0.982554	+	0.185980i	$0.0595458\pi$
$613$			8.56795e7i			0.371959i	−0.982554	+	0.185980i	$0.940454\pi$
$614$	−5.02849e7	−	2.40245e8i	−0.217236	−	1.03789i
$615$	−3.52963e7	−	9.33533e7i	−0.151741	−	0.401333i
$616$	3.27988e7	−	2.33651e7i	0.140319	−	0.0999597i
$617$			2.77104e8i			1.17974i	0.807497	+	0.589871i	$0.200821\pi$
$617$			2.77104e8i			1.17974i	−0.807497	+	0.589871i	$0.799179\pi$
$618$	−6.69103e6	−	3.19676e7i	−0.0283483	−	0.135439i
$619$			1.95819e6i			0.00825625i	0.999991	+	0.00412813i	$0.00131403\pi$
$619$			1.95819e6i			0.00825625i	−0.999991	+	0.00412813i	$0.998686\pi$
$620$	2.72531e8	−	2.66460e8i	1.14351	−	1.11804i
$621$	−2.71322e7			−0.113295
$622$	2.60699e8	−	5.45660e7i	1.08335	−	0.226752i
$623$	−4.03003e7			−0.166665
$624$	−4.16134e7	−	3.84174e7i	−0.171269	−	0.158115i
$625$	3.04080e7	−	2.42240e8i	0.124551	−	0.992213i
$626$	9.55685e7	−	2.00031e7i	0.389576	−	0.0815407i
$627$	−6.63180e7			−0.269047
$628$	1.74749e8	+	3.99160e8i	0.705564	+	1.61164i
$629$	2.44593e7			0.0982860
$630$	−8.74510e6	+	5.57833e6i	−0.0349738	+	0.0223091i
$631$		−	7.22111e6i		−	0.0287419i	−0.999897	−	0.0143710i	$-0.995425\pi$
$631$		−	7.22111e6i		−	0.0287419i	0.999897	−	0.0143710i	$-0.00457458\pi$
$632$	−1.63561e8	+	1.16517e8i	−0.647931	+	0.461570i
$633$			1.54197e7i			0.0607945i
$634$	1.28266e8	−	2.68468e7i	0.503318	−	0.105348i
$635$	−1.41170e8	−	3.73374e8i	−0.551343	−	1.45822i
$636$	5.62751e7	+	1.28543e8i	0.218748	+	0.499662i
$637$			1.02739e8i			0.397481i
$638$	5.36299e8	−	1.12251e8i	2.06512	−	0.432243i
$639$		−	7.30081e7i		−	0.279813i
$640$	6.10331e7	+	2.54940e8i	0.232823	+	0.972519i
$641$	1.00144e8			0.380232			0.190116	−	0.981762i	$-0.439114\pi$
$641$	1.00144e8			0.380232			0.190116	+	0.981762i	$0.439114\pi$
$642$	5.72828e7	+	2.73679e8i	0.216480	+	1.03428i
$643$	2.09841e8			0.789328			0.394664	−	0.918825i	$-0.370861\pi$
$643$	2.09841e8			0.789328			0.394664	+	0.918825i	$0.370861\pi$
$644$	−1.79254e7	+	7.84758e6i	−0.0671135	+	0.0293818i
$645$	9.32639e7	+	2.46669e8i	0.347564	+	0.919253i
$646$	−3.02123e6	−	1.44345e7i	−0.0112069	−	0.0535431i
$647$	−1.00473e8			−0.370967			−0.185484	−	0.982647i	$-0.559385\pi$
$647$	−1.00473e8			−0.370967			−0.185484	+	0.982647i	$0.559385\pi$
$648$	−1.75415e7	−	2.46239e7i	−0.0644675	−	0.0904965i
$649$	2.76994e8			1.01330
$650$	−6.63483e7	+	8.88327e7i	−0.241596	+	0.323469i
$651$			3.17027e7i			0.114909i
$652$	2.06972e8	−	9.06106e7i	0.746738	−	0.326916i
$653$			2.46927e8i			0.886808i	0.896322	+	0.443404i	$0.146229\pi$
$653$			2.46927e8i			0.886808i	−0.896322	+	0.443404i	$0.853771\pi$
$654$	−3.21367e7	−	1.53539e8i	−0.114886	−	0.548890i
$655$	4.34256e8	−	1.64190e8i	1.54533	−	0.584281i
$656$	1.42309e8	−	1.54147e8i	0.504103	−	0.546040i
$657$			3.34050e7i			0.117792i
$658$	1.10183e7	+	5.26419e7i	0.0386755	+	0.184779i
$659$		−	1.58874e8i		−	0.555133i	−0.960706	−	0.277566i	$-0.910472\pi$
$659$		−	1.58874e8i		−	0.555133i	0.960706	−	0.277566i	$-0.0895279\pi$
$660$	1.64301e8	−	1.60641e8i	0.571488	−	0.558759i
$661$	3.01264e8			1.04314			0.521571	−	0.853208i	$-0.325346\pi$
$661$	3.01264e8			1.04314			0.521571	+	0.853208i	$0.325346\pi$
$662$	−3.74591e8	+	7.84043e7i	−1.29117	+	0.270250i
$663$	−1.10394e7			−0.0378796
$664$	−7.76859e7	−	1.09052e8i	−0.265362	−	0.372502i
$665$	1.15236e7	−	4.35700e6i	0.0391853	−	0.0148157i
$666$	−5.82923e7	+	1.22010e7i	−0.197328	+	0.0413020i
$667$	−2.66243e8			−0.897224
$668$	−3.27263e7	+	1.43273e7i	−0.109791	+	0.0480658i
$669$	−1.06005e8			−0.354035
$670$	1.58907e8	−	1.01363e8i	0.528345	−	0.337021i
$671$		−	7.31576e7i		−	0.242154i
$672$	−1.87112e7	−	1.11946e7i	−0.0616586	−	0.0368893i
$673$		−	4.48612e8i		−	1.47172i	−0.677133	−	0.735861i	$-0.736778\pi$
$673$		−	4.48612e8i		−	1.47172i	0.677133	−	0.735861i	$-0.263222\pi$
$674$	−5.30204e7	+	1.10975e7i	−0.173166	+	0.0362448i
$675$	−4.43817e7	+	3.91588e7i	−0.144309	+	0.127326i
$676$	−2.36858e8	+	1.03695e8i	−0.766741	+	0.335673i
$677$		−	3.71161e8i		−	1.19618i	−0.801429	−	0.598089i	$-0.795927\pi$
$677$		−	3.71161e8i		−	1.19618i	0.801429	−	0.598089i	$-0.204073\pi$
$678$	8.39024e7	−	1.75613e7i	0.269206	−	0.0563467i
$679$		−	5.05859e7i		−	0.161592i
$680$	4.24494e7	+	2.84427e7i	0.135003	+	0.0904573i
$681$	−2.19107e8			−0.693768
$682$	−1.43877e8	−	6.87397e8i	−0.453563	−	2.16698i
$683$	1.22266e8			0.383745			0.191872	−	0.981420i	$-0.438544\pi$
$683$	1.22266e8			0.383745			0.191872	+	0.981420i	$0.438544\pi$
$684$	1.44006e7	+	3.28938e7i	0.0450001	+	0.102789i
$685$	5.02333e8	−	1.89929e8i	1.56286	−	0.590907i
$686$	1.63340e7	+	7.80388e7i	0.0505965	+	0.241734i
$687$	−1.85025e8			−0.570639
$688$	−3.76024e8	+	4.07306e8i	−1.15465	+	1.25071i
$689$	−1.24757e8			−0.381424
$690$	−9.41343e7	+	6.00465e7i	−0.286550	+	0.182785i
$691$		−	4.44528e8i		−	1.34730i	−0.739049	−	0.673652i	$-0.764725\pi$
$691$		−	4.44528e8i		−	1.34730i	0.739049	−	0.673652i	$-0.235275\pi$
$692$	−1.27019e8	−	2.90134e8i	−0.383309	−	0.875549i
$693$			1.91126e7i			0.0574275i
$694$	−2.88391e6	−	1.37784e7i	−0.00862787	−	0.0412212i
$695$	−2.56420e8	+	9.69508e7i	−0.763831	+	0.288800i
$696$	−1.72131e8	−	2.41630e8i	−0.510543	−	0.716676i
$697$		−	4.08930e7i		−	0.120768i
$698$	1.37899e7	+	6.58839e7i	0.0405504	+	0.193737i
$699$		−	1.57216e8i		−	0.460327i
$700$	−1.79954e7	+	3.87077e7i	−0.0524648	+	0.112851i
$701$	3.22331e8			0.935724			0.467862	−	0.883801i	$-0.345024\pi$
$701$	3.22331e8			0.935724			0.467862	+	0.883801i	$0.345024\pi$
$702$	2.63096e7	−	5.50676e6i	0.0760505	−	0.0159179i
$703$	7.07342e7			0.203593
$704$	4.56512e8	+	1.57811e8i	1.30838	+	0.452293i
$705$	1.08533e8	+	2.87052e8i	0.309737	+	0.819208i
$706$	3.27793e7	−	6.86092e6i	0.0931506	−	0.0194970i
$707$	−3.04527e7			−0.0861722
$708$	−6.01480e7	−	1.37389e8i	−0.169481	−	0.387127i
$709$	−6.64544e8			−1.86460			−0.932299	−	0.361689i	$-0.882200\pi$
$709$	−6.64544e8			−1.86460			−0.932299	+	0.361689i	$0.882200\pi$
$710$	−1.61575e8	−	2.53300e8i	−0.451439	−	0.707717i
$711$		−	9.53107e7i		−	0.265175i
$712$	−2.80461e8	−	3.93698e8i	−0.777020	−	1.09075i
$713$			3.41255e8i			0.941479i
$714$	−4.15997e6	+	870708.i	−0.0114287	+	0.00239209i
$715$	7.22511e7	+	1.91093e8i	0.197663	+	0.522789i
$716$	2.29113e8	+	5.23338e8i	0.624182	+	1.42575i
$717$		−	2.85412e8i		−	0.774309i
$718$	2.87324e8	−	6.01387e7i	0.776244	−	0.162473i
$719$			5.57077e8i			1.49875i	0.662148	+	0.749373i	$0.269645\pi$
$719$			5.57077e8i			1.49875i	−0.662148	+	0.749373i	$0.730355\pi$
$720$	−1.15355e8	−	4.66108e7i	−0.309057	−	0.124879i
$721$	1.11793e7			0.0298271
$722$	6.83681e7	+	3.26641e8i	0.181653	+	0.867879i
$723$	1.45676e8			0.385456
$724$	−2.86757e7	+	1.25540e7i	−0.0755611	+	0.0330801i
$725$	−4.35510e8	+	3.84259e8i	−1.14284	+	1.00835i
$726$	−4.14783e7	−	1.98170e8i	−0.108395	−	0.517879i
$727$	−7.39877e7			−0.192556			−0.0962779	−	0.995354i	$-0.530694\pi$
$727$	−7.39877e7			−0.192556			−0.0962779	+	0.995354i	$0.530694\pi$
$728$	1.57891e7	−	1.12478e7i	0.0409227	−	0.0291523i
$729$	1.43489e7			0.0370370
$730$	7.39290e7	+	1.15898e8i	0.190040	+	0.297925i
$731$			1.08052e8i			0.276619i
$732$	−3.62862e7	+	1.58858e7i	−0.0925142	+	0.0405020i
$733$			3.30711e8i			0.839725i	0.907588	+	0.419862i	$0.137922\pi$
$733$			3.30711e8i			0.839725i	−0.907588	+	0.419862i	$0.862078\pi$
$734$	−1.54967e7	−	7.40385e7i	−0.0391879	−	0.187227i
$735$	7.98192e7	+	2.11110e8i	0.201023	+	0.531675i
$736$	−2.01412e8	−	1.20501e8i	−0.505185	−	0.302244i
$737$		−	3.47294e8i		−	0.867550i
$738$	2.03986e7	+	9.74579e7i	0.0507494	+	0.242464i
$739$			3.13996e7i			0.0778020i	0.999243	+	0.0389010i	$0.0123857\pi$
$739$			3.13996e7i			0.0778020i	−0.999243	+	0.0389010i	$0.987614\pi$
$740$	−1.75242e8	+	1.71338e8i	−0.432456	+	0.422823i
$741$	−3.19251e7			−0.0784652
$742$	−4.70121e7	+	9.83994e6i	−0.115080	+	0.0240869i
$743$	1.07991e8			0.263283			0.131642	−	0.991297i	$-0.457975\pi$
$743$	1.07991e8			0.263283			0.131642	+	0.991297i	$0.457975\pi$
$744$	−3.09707e8	+	2.20628e8i	−0.752025	+	0.535725i
$745$	−2.81882e8	−	7.45535e8i	−0.681709	−	1.80301i
$746$	4.19361e8	−	8.77749e7i	1.01012	−	0.211424i
$747$	6.35470e7			0.152452
$748$	8.62474e7	−	3.77584e7i	0.206083	−	0.0902214i
$749$	−9.57079e7			−0.227773
$750$	−6.73183e7	+	2.34082e8i	−0.159569	+	0.554861i
$751$			7.98972e8i			1.88631i	0.332360	+	0.943153i	$0.392155\pi$
$751$			7.98972e8i			1.88631i	−0.332360	+	0.943153i	$0.607845\pi$
$752$	−4.37585e8	+	4.73988e8i	−1.02898	+	1.11459i
$753$			2.54920e8i			0.597061i
$754$	2.58171e8	−	5.40369e7i	0.602273	−	0.126060i
$755$	3.32628e8	−	1.25764e8i	0.772890	−	0.292225i
$756$	9.47986e6	−	4.15021e6i	0.0219400	−	0.00960516i
$757$			5.82545e8i			1.34290i	0.741052	+	0.671448i	$0.234327\pi$
$757$			5.82545e8i			1.34290i	−0.741052	+	0.671448i	$0.765673\pi$
$758$	−3.95811e8	+	8.28458e7i	−0.908824	+	0.190223i
$759$			2.05732e8i			0.470519i
$760$	1.22760e8	+	8.22538e7i	0.279651	+	0.187377i
$761$	−1.80005e8			−0.408443			−0.204221	−	0.978925i	$-0.565466\pi$
$761$	−1.80005e8			−0.408443			−0.204221	+	0.978925i	$0.565466\pi$
$762$	8.15856e7	+	3.89790e8i	0.184395	+	0.880980i
$763$	5.36939e7			0.120879
$764$	1.72964e8	+	3.95081e8i	0.387860	+	0.885945i
$765$	−2.26840e7	+	8.57668e6i	−0.0506682	+	0.0191573i
$766$	−1.21971e8	−	5.82739e8i	−0.271375	−	1.29654i
$767$	1.33343e8			0.295519
$768$	−2.08550e7	−	2.60698e8i	−0.0460391	−	0.575512i
$769$	8.51283e8			1.87195			0.935976	−	0.352063i	$-0.114520\pi$
$769$	8.51283e8			1.87195			0.935976	+	0.352063i	$0.114520\pi$
$770$	4.22983e7	+	6.63106e7i	0.0926511	+	0.145248i
$771$		−	2.23248e8i		−	0.487107i
$772$	−1.20910e8	−	2.76181e8i	−0.262791	−	0.600263i
$773$		−	4.28461e8i		−	0.927626i	−0.885933	−	0.463813i	$-0.846481\pi$
$773$		−	4.28461e8i		−	0.927626i	0.885933	−	0.463813i	$-0.153519\pi$
$774$	−5.38994e7	−	2.57514e8i	−0.116241	−	0.555365i
$775$	4.92520e8	+	5.58211e8i	1.05808	+	1.19920i
$776$	4.94180e8	−	3.52042e8i	1.05755	−	0.753371i
$777$		−	2.03853e7i		−	0.0434565i
$778$	−6.41979e7	−	3.06717e8i	−0.136327	−	0.651327i
$779$		−	1.18259e8i		−	0.250163i
$780$	7.90932e7	−	7.73315e7i	0.166669	−	0.162957i
$781$	−5.53592e8			−1.16208
$782$	−4.47788e7	+	9.37250e6i	−0.0936381	+	0.0195991i
$783$	1.40803e8			0.293310
$784$	−3.21817e8	+	3.48589e8i	−0.667822	+	0.723379i
$785$	−7.96048e8	+	3.00981e8i	−1.64562	+	0.622199i
$786$	−4.53350e8	+	9.48890e7i	−0.933610	+	0.195411i
$787$	3.33224e8			0.683615			0.341808	−	0.939770i	$-0.388961\pi$
$787$	3.33224e8			0.683615			0.341808	+	0.939770i	$0.388961\pi$
$788$	3.89049e7	+	8.88662e7i	0.0795108	+	0.181618i
$789$	4.26487e8			0.868309
$790$	−2.10933e8	−	3.30678e8i	−0.427822	−	0.670693i
$791$			2.93414e7i			0.0592859i
$792$	−1.86713e8	+	1.33010e8i	−0.375837	+	0.267737i
$793$		−	3.52176e7i		−	0.0706221i
$794$	−5.08179e8	+	1.06365e8i	−1.01521	+	0.212490i
$795$	−2.56354e8	+	9.69258e7i	−0.510198	+	0.192903i
$796$	3.17215e8	+	7.24578e8i	0.628947	+	1.43663i
$797$			2.03165e7i			0.0401305i	0.999799	+	0.0200653i	$0.00638740\pi$
$797$			2.03165e7i			0.0401305i	−0.999799	+	0.0200653i	$0.993613\pi$
$798$	−1.20303e7	+	2.51801e6i	−0.0236737	+	0.00495507i
$799$			1.25742e8i			0.246513i
$800$	−5.03376e8	+	9.35785e7i	−0.983156	+	0.182770i
$801$	2.29417e8			0.446404
$802$	−1.58882e8	−	7.59086e8i	−0.308000	−	1.47153i
$803$	2.53297e8			0.489197
$804$	−1.72258e8	+	7.54132e7i	−0.331445	+	0.145104i
$805$	−1.35163e7	−	3.57487e7i	−0.0259103	−	0.0685286i
$806$	−6.92613e7	−	3.30909e8i	−0.132277	−	0.631979i
$807$	1.85182e8			0.352353
$808$	−2.11929e8	−	2.97496e8i	−0.401750	−	0.563958i
$809$	−4.55083e8			−0.859499			−0.429749	−	0.902948i	$-0.641398\pi$
$809$	−4.55083e8			−0.859499			−0.429749	+	0.902948i	$0.641398\pi$
$810$	4.97831e7	−	3.17557e7i	0.0936757	−	0.0597539i
$811$		−	5.22513e8i		−	0.979567i	−0.871844	−	0.489784i	$-0.837076\pi$
$811$		−	5.22513e8i		−	0.979567i	0.871844	−	0.489784i	$-0.162924\pi$
$812$	9.30241e7	−	4.07252e7i	0.173751	−	0.0760669i
$813$			1.25281e8i			0.233139i
$814$	9.25150e7	+	4.42007e8i	0.171530	+	0.819514i
$815$	1.56064e8	+	4.12765e8i	0.288290	+	0.762483i
$816$	−3.74564e7	−	3.45797e7i	−0.0689375	−	0.0636430i
$817$			3.12478e8i			0.572998i
$818$	−6.20834e7	−	2.96615e8i	−0.113427	−	0.541917i
$819$			9.20068e6i			0.0167482i
$820$	2.86457e8	+	2.92983e8i	0.519539	+	0.531375i
$821$	5.58769e7			0.100972			0.0504862	−	0.998725i	$-0.483923\pi$
$821$	5.58769e7			0.100972			0.0504862	+	0.998725i	$0.483923\pi$
$822$	−5.24419e8	+	1.09764e8i	−0.944198	+	0.197627i
$823$	6.67182e7			0.119686			0.0598432	−	0.998208i	$-0.480940\pi$
$823$	6.67182e7			0.119686			0.0598432	+	0.998208i	$0.480940\pi$
$824$	7.78002e7	+	1.09212e8i	0.139059	+	0.195205i
$825$	2.96926e8	+	3.36529e8i	0.528794	+	0.599322i
$826$	5.02476e7	−	1.05171e7i	0.0891610	−	0.0186620i
$827$	3.12256e8			0.552070			0.276035	−	0.961148i	$-0.410979\pi$
$827$	3.12256e8			0.552070			0.276035	+	0.961148i	$0.410979\pi$
$828$	1.02043e8	−	4.46738e7i	0.179760	−	0.0786977i
$829$	5.05526e8			0.887319			0.443660	−	0.896195i	$-0.353680\pi$
$829$	5.05526e8			0.887319			0.443660	+	0.896195i	$0.353680\pi$
$830$	2.20475e8	−	1.40636e8i	0.385589	−	0.245960i
$831$			3.68336e8i			0.641860i
$832$	2.19762e8	+	7.59693e7i	0.381577	+	0.131907i
$833$			9.24757e7i			0.159990i
$834$	2.67694e8	−	5.60301e7i	0.461467	−	0.0965881i
$835$	−2.46768e7	−	6.52663e7i	−0.0423867	−	0.112106i
$836$	2.49420e8	−	1.09194e8i	0.426887	−	0.186888i
$837$		−	1.80473e8i		−	0.307777i
$838$	−4.63822e8	+	9.70809e7i	−0.788169	+	0.164969i
$839$		−	9.40483e8i		−	1.59245i	−0.605003	−	0.796223i	$-0.706828\pi$
$839$		−	9.40483e8i		−	1.59245i	0.605003	−	0.796223i	$-0.293172\pi$
$840$	2.37052e7	−	3.53790e7i	0.0399951	−	0.0596908i
$841$	7.86853e8			1.32283
$842$	1.15112e8	+	5.49966e8i	0.192834	+	0.921298i
$843$	−6.24961e8			−1.04321
$844$	−2.53889e7	−	5.79930e7i	−0.0422295	−	0.0964602i
$845$	−1.78599e8	−	4.72368e8i	−0.296013	−	0.782908i
$846$	−6.27236e7	−	2.99674e8i	−0.103591	−	0.494923i
$847$	6.93018e7			0.114050
$848$	−4.23298e8	−	3.90788e8i	−0.694159	−	0.640846i
$849$	3.11830e8			0.509560
$850$	−5.97204e7	+	7.99587e7i	−0.0972447	+	0.130199i
$851$		−	2.19432e8i		−	0.356051i
$852$	1.20210e8	+	2.74582e8i	0.194366	+	0.443969i
$853$		−	3.83843e7i		−	0.0618453i	−0.999522	−	0.0309226i	$-0.990155\pi$
$853$		−	3.83843e7i		−	0.0618453i	0.999522	−	0.0309226i	$-0.00984455\pi$
$854$	−2.77771e6	−	1.32710e7i	−0.00445977	−	0.0213074i
$855$	−6.56003e7	+	2.48031e7i	−0.104956	+	0.0396832i
$856$	−6.66058e8	−	9.34981e8i	−1.06192	−	1.49067i
$857$		−	7.80244e8i		−	1.23962i	−0.784753	−	0.619809i	$-0.787210\pi$
$857$		−	7.80244e8i		−	1.23962i	0.784753	−	0.619809i	$-0.212790\pi$
$858$	−4.17556e7	−	1.99495e8i	−0.0661078	−	0.315842i
$859$		−	5.41399e8i		−	0.854157i	−0.904214	−	0.427079i	$-0.859543\pi$
$859$		−	5.41399e8i		−	0.854157i	0.904214	−	0.427079i	$-0.140457\pi$
$860$	−7.56909e8	−	7.74153e8i	−1.19000	−	1.21711i
$861$	−3.40819e7			−0.0533967
$862$	7.18911e8	−	1.50473e8i	1.12241	−	0.234929i
$863$	−1.87897e8			−0.292339			−0.146170	−	0.989260i	$-0.546695\pi$
$863$	−1.87897e8			−0.292339			−0.146170	+	0.989260i	$0.546695\pi$
$864$	1.06517e8	+	6.37274e7i	0.165149	+	0.0988063i
$865$	5.78617e8	−	2.18771e8i	0.894011	−	0.338020i
$866$	8.43126e8	−	1.76472e8i	1.29819	−	0.271720i
$867$	3.66331e8			0.562103
$868$	−5.21993e7	−	1.19233e8i	−0.0798188	−	0.182321i
$869$	−7.22703e8			−1.10129
$870$	4.88513e8	−	3.11613e8i	0.741854	−	0.473214i
$871$		−	1.67185e8i		−	0.253013i
$872$	3.73671e8	+	5.24542e8i	0.563560	+	0.791099i
$873$			2.87970e8i			0.432817i
$874$	−1.29497e8	+	2.71045e7i	−0.193965	+	0.0405982i
$875$	−7.37042e7	−	3.89686e7i	−0.110019	−	0.0581688i
$876$	−5.50022e7	−	1.25635e8i	−0.0818216	−	0.186896i
$877$			9.77817e8i			1.44964i	0.688941	+	0.724818i	$0.258076\pi$
$877$			9.77817e8i			1.44964i	−0.688941	+	0.724818i	$0.741924\pi$
$878$	5.40670e7	−	1.13166e7i	0.0798820	−	0.0167198i
$879$		−	1.85106e7i		−	0.0272555i
$880$	−3.53431e8	+	8.74691e8i	−0.518628	+	1.28353i
$881$	−1.01906e8			−0.149029			−0.0745147	−	0.997220i	$-0.523741\pi$
$881$	−1.01906e8			−0.149029			−0.0745147	+	0.997220i	$0.523741\pi$
$882$	−4.61294e7	−	2.20392e8i	−0.0672314	−	0.321210i
$883$	−3.87166e8			−0.562361			−0.281180	−	0.959655i	$-0.590726\pi$
$883$	−3.87166e8			−0.562361			−0.281180	+	0.959655i	$0.590726\pi$
$884$	4.15189e7	−	1.81767e7i	0.0601021	−	0.0263122i
$885$	2.73997e8	−	1.03596e8i	0.395289	−	0.149456i
$886$	−8.61787e7	−	4.11735e8i	−0.123908	−	0.591992i
$887$	−6.78239e8			−0.971878			−0.485939	−	0.873993i	$-0.661522\pi$
$887$	−6.78239e8			−0.971878			−0.485939	+	0.873993i	$0.661522\pi$
$888$	1.99147e8	−	1.41867e8i	0.284403	−	0.202602i
$889$	−1.36313e8			−0.194014
$890$	7.95955e8	−	5.07724e8i	1.12906	−	0.720208i
$891$		−	1.08802e8i		−	0.153817i
$892$	3.98681e8	−	1.74539e8i	0.561734	−	0.245923i
$893$			3.63636e8i			0.510637i
$894$	1.62906e8	+	7.78315e8i	0.227995	+	1.08929i
$895$	−1.04370e9	+	3.94615e8i	−1.45581	+	0.550433i
$896$	8.88045e7	+	1.12942e7i	0.123456	+	0.0157011i
$897$			9.90383e7i			0.137223i
$898$	1.59833e8	+	7.63633e8i	0.220718	+	1.05452i
$899$		−	1.77095e9i		−	2.43741i
$900$	1.02442e8	−	2.20351e8i	0.140525	−	0.302265i
$901$	−1.12295e8			−0.153527
$902$	7.38984e8	−	1.54674e8i	1.00697	−	0.210765i
$903$	9.00550e7			0.122305
$904$	−2.86640e8	+	2.04195e8i	−0.387999	+	0.276401i
$905$	−2.16225e7	−	5.71881e7i	−0.0291716	−	0.0771543i
$906$	−3.47253e8	+	7.26822e7i	−0.466940	+	0.0977336i
$907$	3.95120e8			0.529551			0.264775	−	0.964310i	$-0.414702\pi$
$907$	3.95120e8			0.529551			0.264775	+	0.964310i	$0.414702\pi$
$908$	8.24055e8	−	3.60765e8i	1.10077	−	0.481911i
$909$	1.73357e8			0.230808
$910$	2.03621e7	+	3.19215e7i	0.0270208	+	0.0423603i
$911$			1.40048e9i			1.85234i	0.377107	+	0.926170i	$0.376919\pi$
$911$			1.40048e9i			1.85234i	−0.377107	+	0.926170i	$0.623081\pi$
$912$	−1.08321e8	−	1.00002e8i	−0.142800	−	0.131832i
$913$		−	4.81852e8i		−	0.633142i
$914$	−2.96432e8	+	6.20452e7i	−0.388228	+	0.0812586i
$915$	−2.73611e7	−	7.23659e7i	−0.0357166	−	0.0944649i
$916$	6.95876e8	−	3.04649e8i	0.905410	−	0.396381i
$917$		−	1.58540e8i		−	0.205604i
$918$	2.36814e7	−	4.95667e6i	0.0306111	−	0.00640710i
$919$		−	1.65383e8i		−	0.213081i	−0.994308	−	0.106540i	$-0.966023\pi$
$919$		−	1.65383e8i		−	0.213081i	0.994308	−	0.106540i	$-0.0339774\pi$
$920$	2.55169e8	−	3.80828e8i	0.327691	−	0.489063i
$921$	−4.78276e8			−0.612208
$922$	1.20345e8	+	5.74968e8i	0.153544	+	0.733586i
$923$	−2.66495e8			−0.338910
$924$	−3.14694e7	−	7.18820e7i	−0.0398908	−	0.0911180i
$925$	−3.16699e8	−	3.58939e8i	−0.400148	−	0.453519i
$926$	3.01581e8	+	1.44086e9i	0.379814	+	1.81463i
$927$	−6.36405e7			−0.0798904
$928$	1.04523e9	+	6.25345e8i	1.30788	+	0.782485i
$929$	−7.21234e8			−0.899557			−0.449779	−	0.893140i	$-0.648497\pi$
$929$	−7.21234e8			−0.899557			−0.449779	+	0.893140i	$0.648497\pi$
$930$	−3.99407e8	−	6.26147e8i	−0.496555	−	0.778445i
$931$			2.67432e8i			0.331409i
$932$	2.58861e8	+	5.91287e8i	0.319756	+	0.730383i
$933$		−	5.18995e8i		−	0.639025i
$934$	1.61713e8	+	7.72612e8i	0.198474	+	0.948246i
$935$	6.50336e7	+	1.72004e8i	0.0795615	+	0.210428i
$936$	−8.98826e7	+	6.40302e7i	−0.109609	+	0.0780831i
$937$			6.16936e8i			0.749931i	0.927039	+	0.374966i	$0.122346\pi$
$937$			6.16936e8i			0.749931i	−0.927039	+	0.374966i	$0.877654\pi$
$938$	−1.31863e7	−	6.30001e7i	−0.0159777	−	0.0763365i
$939$		−	1.90256e8i		−	0.229796i
$940$	−8.80828e8	−	9.00895e8i	−1.06049	−	1.08465i
$941$	1.02280e9			1.22750			0.613748	−	0.789502i	$-0.289661\pi$
$941$	1.02280e9			1.22750			0.613748	+	0.789502i	$0.289661\pi$
$942$	8.31048e8	−	1.73944e8i	0.994199	−	0.208092i
$943$	−3.66865e8			−0.437493
$944$	4.52430e8	+	4.17682e8i	0.537818	+	0.496513i
$945$	7.14815e6	+	1.89058e7i	0.00847028	+	0.0224026i
$946$	−1.95263e9	+	4.08698e8i	−2.30646	+	0.482757i
$947$	1.01174e9			1.19130			0.595648	−	0.803246i	$-0.296895\pi$
$947$	1.01174e9			1.19130			0.595648	+	0.803246i	$0.296895\pi$
$948$	1.56932e8	+	3.58461e8i	0.184198	+	0.420743i
$949$	1.21936e8			0.142670
$950$	−1.72706e8	+	2.31234e8i	−0.201436	+	0.269700i
$951$		−	2.55349e8i		−	0.296888i
$952$	1.42119e7	−	1.01242e7i	0.0164718	−	0.0117341i
$953$			2.58951e8i			0.299184i	0.988748	+	0.149592i	$0.0477961\pi$
$953$			2.58951e8i			0.299184i	−0.988748	+	0.149592i	$0.952204\pi$
$954$	2.67625e8	−	5.60157e7i	0.308235	−	0.0645156i
$955$	−7.87914e8	+	2.97905e8i	−0.904625	+	0.342033i
$956$	4.69937e8	+	1.07343e9i	0.537856	+	1.22857i
$957$		−	1.06765e9i		−	1.21813i
$958$	−6.28022e8	+	1.31449e8i	−0.714296	+	0.149507i
$959$		−	1.83394e8i		−	0.207936i
$960$	5.10593e8	−	1.46331e7i	0.577113	−	0.0165396i
$961$	−1.38240e9			−1.55763
$962$	4.45361e7	+	2.12780e8i	0.0500250	+	0.239004i
$963$	5.44835e8			0.610079
$964$	−5.47885e8	+	2.39860e8i	−0.611587	+	0.267748i
$965$	5.50790e8	−	2.08250e8i	0.612920	−	0.231741i
$966$	7.81141e6	+	3.73204e7i	0.00866559	+	0.0414014i
$967$	−6.55319e8			−0.724725			−0.362362	−	0.932037i	$-0.618030\pi$
$967$	−6.55319e8			−0.724725			−0.362362	+	0.932037i	$0.618030\pi$
$968$	4.82290e8	+	6.77017e8i	0.531720	+	0.746403i
$969$	−2.87359e7			−0.0315830
$970$	6.37308e8	+	9.99103e8i	0.698288	+	1.09470i
$971$			3.60583e8i			0.393865i	0.980417	+	0.196933i	$0.0630980\pi$
$971$			3.60583e8i			0.393865i	−0.980417	+	0.196933i	$0.936902\pi$
$972$	−5.39659e7	+	2.36258e7i	−0.0587652	+	0.0257270i
$973$			9.36150e7i			0.101626i
$974$	1.86368e8	+	8.90408e8i	0.201695	+	0.963634i
$975$	1.42938e8	+	1.62003e8i	0.154218	+	0.174787i
$976$	1.10315e8	−	1.19492e8i	0.118655	−	0.128526i
$977$		−	2.40742e8i		−	0.258147i	−0.991635	−	0.129074i	$-0.958800\pi$
$977$		−	2.40742e8i		−	0.258147i	0.991635	−	0.129074i	$-0.0412003\pi$
$978$	−9.01930e7	−	4.30914e8i	−0.0964176	−	0.460653i
$979$		−	1.73958e9i		−	1.85394i
$980$	−6.47795e8	−	6.62553e8i	−0.688271	−	0.703951i
$981$	−3.05663e8			−0.323769
$982$	−7.33992e7	+	1.53629e7i	−0.0775098	+	0.0162233i
$983$	−9.35058e8			−0.984415			−0.492207	−	0.870478i	$-0.663810\pi$
$983$	−9.35058e8			−0.984415			−0.492207	+	0.870478i	$0.663810\pi$
$984$	−2.37185e8	−	3.32950e8i	−0.248945	−	0.349457i
$985$	−1.77227e8	+	6.70082e7i	−0.185447	+	0.0701164i
$986$	2.32381e8	−	4.86389e7i	0.242421	−	0.0507403i
$987$	1.04798e8			0.108994
$988$	1.20069e8	−	5.25654e7i	0.124498	−	0.0545041i
$989$	9.69372e8			1.00208
$990$	−2.40791e8	−	3.77486e8i	−0.248161	−	0.389041i
$991$			5.34695e7i			0.0549396i	0.999623	+	0.0274698i	$0.00874500\pi$
$991$			5.34695e7i			0.0549396i	−0.999623	+	0.0274698i	$0.991255\pi$
$992$	8.01531e8	−	1.33972e9i	0.821080	−	1.37239i
$993$			7.45729e8i			0.761611i
$994$	−1.00423e8	+	2.10192e7i	−0.102253	+	0.0214021i
$995$	−1.44503e9	+	5.46358e8i	−1.46693	+	0.554636i
$996$	−2.38999e8	+	1.04632e8i	−0.241890	+	0.105897i
$997$			1.60576e9i			1.62030i	0.586222	+	0.810150i	$0.300614\pi$
$997$			1.60576e9i			1.62030i	−0.586222	+	0.810150i	$0.699386\pi$
$998$	−1.52935e9	+	3.20102e8i	−1.53856	+	0.322031i
$999$			1.16047e8i			0.116396i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.f.a.19.22	yes	36
3.2	odd	2		180.7.f.g.19.15		36
4.3	odd	2	inner	60.7.f.a.19.16	yes	36
5.4	even	2	inner	60.7.f.a.19.15	✓	36
12.11	even	2		180.7.f.g.19.21		36
15.14	odd	2		180.7.f.g.19.22		36
20.19	odd	2	inner	60.7.f.a.19.21	yes	36
60.59	even	2		180.7.f.g.19.16		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.f.a.19.15	✓	36	5.4	even	2	inner
60.7.f.a.19.16	yes	36	4.3	odd	2	inner
60.7.f.a.19.21	yes	36	20.19	odd	2	inner
60.7.f.a.19.22	yes	36	1.1	even	1	trivial
180.7.f.g.19.15		36	3.2	odd	2
180.7.f.g.19.16		36	60.59	even	2
180.7.f.g.19.21		36	12.11	even	2
180.7.f.g.19.22		36	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63894 + 7.83032i) q^{2} +15.5885 q^{3} +(-58.6278 + 25.6668i) q^{4} +(-44.2074 - 116.922i) q^{5} +(25.5485 + 122.063i) q^{6} -42.6864 q^{7} +(-297.066 - 417.008i) q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+(1.63894 + 7.83032i) q^{2} +15.5885 q^{3} +(-58.6278 + 25.6668i) q^{4} +(-44.2074 - 116.922i) q^{5} +(25.5485 + 122.063i) q^{6} -42.6864 q^{7} +(-297.066 - 417.008i) q^{8} +243.000 q^{9} +(843.082 - 537.785i) q^{10} -1842.57i q^{11} +(-913.917 + 400.106i) q^{12} -887.003i q^{13} +(-69.9602 - 334.248i) q^{14} +(-689.125 - 1822.63i) q^{15} +(2778.43 - 3009.57i) q^{16} -798.396i q^{17} +(398.262 + 1902.77i) q^{18} -2308.89i q^{19} +(5592.79 + 5720.20i) q^{20} -665.414 q^{21} +(14427.9 - 3019.86i) q^{22} -7162.68 q^{23} +(-4630.81 - 6500.51i) q^{24} +(-11716.4 + 10337.6i) q^{25} +(6945.51 - 1453.74i) q^{26} +3788.00 q^{27} +(2502.61 - 1095.62i) q^{28} +37170.9 q^{29} +(13142.3 - 8383.25i) q^{30} -47643.5i q^{31} +(28119.6 + 16823.5i) q^{32} -28722.9i q^{33} +(6251.69 - 1308.52i) q^{34} +(1887.05 + 4990.96i) q^{35} +(-14246.5 + 6237.03i) q^{36} +30635.5i q^{37} +(18079.4 - 3784.13i) q^{38} -13827.0i q^{39} +(-35624.8 + 53168.4i) q^{40} +51219.0 q^{41} +(-1090.57 - 5210.41i) q^{42} -135337. q^{43} +(47292.9 + 108026. i) q^{44} +(-10742.4 - 28412.0i) q^{45} +(-11739.2 - 56086.0i) q^{46} -157494. q^{47} +(43311.5 - 46914.6i) q^{48} -115827. q^{49} +(-100149. - 74800.5i) q^{50} -12445.8i q^{51} +(22766.5 + 52003.0i) q^{52} -140651. i q^{53} +(6208.28 + 29661.2i) q^{54} +(-215437. + 81455.3i) q^{55} +(12680.7 + 17800.5i) q^{56} -35992.1i q^{57} +(60920.8 + 291060. i) q^{58} +150330. i q^{59} +(87182.9 + 89169.1i) q^{60} +39704.1 q^{61} +(373064. - 78084.7i) q^{62} -10372.8 q^{63} +(-85647.2 + 247758. i) q^{64} +(-103710. + 39212.1i) q^{65} +(224909. - 47074.9i) q^{66} +188483. q^{67} +(20492.3 + 46808.2i) q^{68} -111655. q^{69} +(-35988.1 + 22956.1i) q^{70} -300445. i q^{71} +(-72187.1 - 101333. i) q^{72} +137469. i q^{73} +(-239886. + 50209.7i) q^{74} +(-182641. + 161148. i) q^{75} +(59261.9 + 135365. i) q^{76} +78652.7i q^{77} +(108270. - 22661.6i) q^{78} -392225. i q^{79} +(-474712. - 191814. i) q^{80} +59049.0 q^{81} +(83944.7 + 401061. i) q^{82} +261510. q^{83} +(39011.8 - 17079.1i) q^{84} +(-93349.8 + 35295.0i) q^{85} +(-221808. - 1.05973e6i) q^{86} +579437. q^{87} +(-768367. + 547366. i) q^{88} +944102. q^{89} +(204869. - 130682. i) q^{90} +37862.9i q^{91} +(419932. - 183843. i) q^{92} -742689. i q^{93} +(-258122. - 1.23322e6i) q^{94} +(-269960. + 102070. i) q^{95} +(438341. + 262253. i) q^{96} +1.18506e6i q^{97} +(-189833. - 906961. i) q^{98} -447745. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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