LMFDB - Embedded newform 80.6.q.a.29.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(29,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.q (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$116$
Relative dimension:	$58$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			29.12
Character	$\chi$	$=$	80.29
Dual form			80.6.q.a.69.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.71172 - 3.13045i) q^{2} +(-21.0051 + 21.0051i) q^{3} +(12.4006 + 29.4996i) q^{4} +(9.85062 - 55.0270i) q^{5} +(164.725 - 33.2148i) q^{6} -32.3244 q^{7} +(33.9186 - 177.813i) q^{8} -639.428i q^{9} +O(q^{10})$	\(q+(-4.71172 - 3.13045i) q^{2} +(-21.0051 + 21.0051i) q^{3} +(12.4006 + 29.4996i) q^{4} +(9.85062 - 55.0270i) q^{5} +(164.725 - 33.2148i) q^{6} -32.3244 q^{7} +(33.9186 - 177.813i) q^{8} -639.428i q^{9} +(-218.672 + 228.435i) q^{10} +(-230.870 + 230.870i) q^{11} +(-880.117 - 359.165i) q^{12} +(651.055 - 651.055i) q^{13} +(152.304 + 101.190i) q^{14} +(948.933 + 1362.76i) q^{15} +(-716.450 + 731.626i) q^{16} +1176.45i q^{17} +(-2001.69 + 3012.81i) q^{18} +(-242.298 - 242.298i) q^{19} +(1745.43 - 391.779i) q^{20} +(678.977 - 678.977i) q^{21} +(1810.52 - 365.068i) q^{22} -48.1530 q^{23} +(3022.52 + 4447.45i) q^{24} +(-2930.93 - 1084.10i) q^{25} +(-5105.68 + 1029.50i) q^{26} +(8327.01 + 8327.01i) q^{27} +(-400.843 - 953.557i) q^{28} +(5171.60 + 5171.60i) q^{29} +(-205.062 - 9391.53i) q^{30} -3323.92 q^{31} +(5666.02 - 1204.41i) q^{32} -9698.88i q^{33} +(3682.82 - 5543.11i) q^{34} +(-318.415 + 1778.71i) q^{35} +(18862.9 - 7929.30i) q^{36} +(-1791.92 - 1791.92i) q^{37} +(383.140 + 1900.14i) q^{38} +27350.9i q^{39} +(-9450.40 - 3618.01i) q^{40} +9797.06i q^{41} +(-5324.65 + 1073.65i) q^{42} +(-2561.27 - 2561.27i) q^{43} +(-9673.48 - 3947.63i) q^{44} +(-35185.8 - 6298.76i) q^{45} +(226.884 + 150.740i) q^{46} +20236.8i q^{47} +(-318.775 - 30417.0i) q^{48} -15762.1 q^{49} +(10416.0 + 14283.1i) q^{50} +(-24711.5 - 24711.5i) q^{51} +(27279.3 + 11132.4i) q^{52} +(17293.9 + 17293.9i) q^{53} +(-13167.3 - 65301.8i) q^{54} +(10429.8 + 14978.3i) q^{55} +(-1096.40 + 5747.71i) q^{56} +10179.0 q^{57} +(-8177.71 - 40556.5i) q^{58} +(15290.8 - 15290.8i) q^{59} +(-28433.5 + 44892.2i) q^{60} +(19966.9 + 19966.9i) q^{61} +(15661.4 + 10405.4i) q^{62} +20669.1i q^{63} +(-30467.1 - 12062.3i) q^{64} +(-29412.3 - 42238.8i) q^{65} +(-30361.8 + 45698.4i) q^{66} +(41363.5 - 41363.5i) q^{67} +(-34704.8 + 14588.7i) q^{68} +(1011.46 - 1011.46i) q^{69} +(7068.45 - 7384.02i) q^{70} -19336.1i q^{71} +(-113699. - 21688.5i) q^{72} +39755.2 q^{73} +(2833.51 + 14052.5i) q^{74} +(84336.1 - 38792.9i) q^{75} +(4143.05 - 10152.3i) q^{76} +(7462.73 - 7462.73i) q^{77} +(85620.6 - 128870. i) q^{78} +86421.1 q^{79} +(33201.7 + 46631.0i) q^{80} -194438. q^{81} +(30669.2 - 46161.0i) q^{82} +(-14279.7 + 14279.7i) q^{83} +(28449.3 + 11609.8i) q^{84} +(64736.5 + 11588.8i) q^{85} +(4050.07 + 20085.9i) q^{86} -217260. q^{87} +(33220.9 + 48882.4i) q^{88} +80993.3i q^{89} +(146068. + 139825. i) q^{90} +(-21045.0 + 21045.0i) q^{91} +(-597.127 - 1420.49i) q^{92} +(69819.3 - 69819.3i) q^{93} +(63350.3 - 95350.3i) q^{94} +(-15719.7 + 10946.1i) q^{95} +(-93716.7 + 144314. i) q^{96} +88094.6i q^{97} +(74266.8 + 49342.5i) q^{98} +(147625. + 147625. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−4.71172	−	3.13045i	−0.832922	−	0.553390i
$2$	−4.71172	−	3.13045i	−0.832922	−	0.553390i
$3$	−21.0051	+	21.0051i	−1.34748	+	1.34748i	−0.459085	+	0.888392i	$0.651823\pi$
$3$	−21.0051	+	21.0051i	−1.34748	+	1.34748i	−0.888392	+	0.459085i	$0.848177\pi$
$4$	12.4006	+	29.4996i	0.387519	+	0.921862i
$5$	9.85062	−	55.0270i	0.176213	−	0.984352i
$5$	9.85062	−	55.0270i	0.176213	−	0.984352i
$6$	164.725	−	33.2148i	1.86802	−	0.376664i
$7$	−32.3244			−0.249336			−0.124668	−	0.992198i	$-0.539787\pi$
$7$	−32.3244			−0.249336			−0.124668	+	0.992198i	$0.539787\pi$
$8$	33.9186	−	177.813i	0.187376	−	0.982288i
$9$		−	639.428i		−	2.63139i
$10$	−218.672	+	228.435i	−0.691502	+	0.722374i
$11$	−230.870	+	230.870i	−0.575288	+	0.575288i	−0.933601	−	0.358314i	$-0.883352\pi$
$11$	−230.870	+	230.870i	−0.575288	+	0.575288i	0.358314	+	0.933601i	$0.383352\pi$
$12$	−880.117	−	359.165i	−1.76436	−	0.720014i
$13$	651.055	−	651.055i	1.06846	−	1.06846i	0.0709847	−	0.997477i	$-0.477386\pi$
$13$	651.055	−	651.055i	1.06846	−	1.06846i	0.997477	−	0.0709847i	$-0.0226141\pi$
$14$	152.304	+	101.190i	0.207678	+	0.137980i
$15$	948.933	+	1362.76i	1.08895	+	1.56384i
$16$	−716.450	+	731.626i	−0.699658	+	0.714478i
$17$			1176.45i			0.987305i	0.869659	+	0.493653i	$0.164339\pi$
$17$			1176.45i			0.987305i	−0.869659	+	0.493653i	$0.835661\pi$
$18$	−2001.69	+	3012.81i	−1.45619	+	2.19174i
$19$	−242.298	−	242.298i	−0.153981	−	0.153981i	0.625913	−	0.779893i	$-0.284727\pi$
$19$	−242.298	−	242.298i	−0.153981	−	0.153981i	−0.779893	+	0.625913i	$0.784727\pi$
$20$	1745.43	−	391.779i	0.975722	−	0.219011i
$21$	678.977	−	678.977i	0.335975	−	0.335975i
$22$	1810.52	−	365.068i	0.797528	−	0.160812i
$23$	−48.1530			−0.0189803			−0.00949017	−	0.999955i	$-0.503021\pi$
$23$	−48.1530			−0.0189803			−0.00949017	+	0.999955i	$0.503021\pi$
$24$	3022.52	+	4447.45i	1.07113	+	1.57610i
$25$	−2930.93	−	1084.10i	−0.937898	−	0.346912i
$26$	−5105.68	+	1029.50i	−1.48122	+	0.298670i
$27$	8327.01	+	8327.01i	2.19826	+	2.19826i
$28$	−400.843	−	953.557i	−0.0966226	−	0.229854i
$29$	5171.60	+	5171.60i	1.14190	+	1.14190i	0.988102	+	0.153802i	$0.0491518\pi$
$29$	5171.60	+	5171.60i	1.14190	+	1.14190i	0.153802	+	0.988102i	$0.450848\pi$
$30$	−205.062	−	9391.53i	−0.0415990	−	1.90517i
$31$	−3323.92			−0.621222			−0.310611	−	0.950537i	$-0.600534\pi$
$31$	−3323.92			−0.621222			−0.310611	+	0.950537i	$0.600534\pi$
$32$	5666.02	−	1204.41i	0.978146	−	0.207921i
$33$		−	9698.88i		−	1.55037i
$34$	3682.82	−	5543.11i	0.546365	−	0.822349i
$35$	−318.415	+	1778.71i	−0.0439364	+	0.245435i
$36$	18862.9	−	7929.30i	2.42578	−	1.01971i
$37$	−1791.92	−	1791.92i	−0.215186	−	0.215186i	0.591280	−	0.806466i	$-0.298623\pi$
$37$	−1791.92	−	1791.92i	−0.215186	−	0.215186i	−0.806466	+	0.591280i	$0.798623\pi$
$38$	383.140	+	1900.14i	0.0430426	+	0.213465i
$39$			27350.9i			2.87946i
$40$	−9450.40	−	3618.01i	−0.933899	−	0.357536i
$41$			9797.06i			0.910198i	0.890441	+	0.455099i	$0.150396\pi$
$41$			9797.06i			0.910198i	−0.890441	+	0.455099i	$0.849604\pi$
$42$	−5324.65	+	1073.65i	−0.465766	+	0.0939159i
$43$	−2561.27	−	2561.27i	−0.211244	−	0.211244i	0.593552	−	0.804796i	$-0.297725\pi$
$43$	−2561.27	−	2561.27i	−0.211244	−	0.211244i	−0.804796	+	0.593552i	$0.797725\pi$
$44$	−9673.48	−	3947.63i	−0.753271	−	0.307401i
$45$	−35185.8	−	6298.76i	−2.59021	−	0.463686i
$46$	226.884	+	150.740i	0.0158091	+	0.0105035i
$47$			20236.8i			1.33628i	0.744035	+	0.668141i	$0.232910\pi$
$47$			20236.8i			1.33628i	−0.744035	+	0.668141i	$0.767090\pi$
$48$	−318.775	−	30417.0i	−0.0199701	−	1.90552i
$49$	−15762.1			−0.937831
$50$	10416.0	+	14283.1i	0.589219	+	0.807974i
$51$	−24711.5	−	24711.5i	−1.33037	−	1.33037i
$52$	27279.3	+	11132.4i	1.39902	+	0.570925i
$53$	17293.9	+	17293.9i	0.845673	+	0.845673i	0.989590	−	0.143917i	$-0.0459697\pi$
$53$	17293.9	+	17293.9i	0.845673	+	0.845673i	−0.143917	+	0.989590i	$0.545970\pi$
$54$	−13167.3	−	65301.8i	−0.614485	−	3.04748i
$55$	10429.8	+	14978.3i	0.464912	+	0.667659i
$56$	−1096.40	+	5747.71i	−0.0467195	+	0.244920i
$57$	10179.0			0.414971
$58$	−8177.71	−	40556.5i	−0.319199	−	1.58304i
$59$	15290.8	−	15290.8i	0.571874	−	0.571874i	−0.360778	−	0.932652i	$-0.617489\pi$
$59$	15290.8	−	15290.8i	0.571874	−	0.571874i	0.932652	+	0.360778i	$0.117489\pi$
$60$	−28433.5	+	44892.2i	−1.01965	+	1.60988i
$61$	19966.9	+	19966.9i	0.687045	+	0.687045i	0.961578	−	0.274533i	$-0.0885232\pi$
$61$	19966.9	+	19966.9i	0.687045	+	0.687045i	−0.274533	+	0.961578i	$0.588523\pi$
$62$	15661.4	+	10405.4i	0.517430	+	0.343778i
$63$			20669.1i			0.656101i
$64$	−30467.1	−	12062.3i	−0.929781	−	0.368114i
$65$	−29412.3	−	42238.8i	−0.863466	−	1.24002i
$66$	−30361.8	+	45698.4i	−0.857962	+	1.29134i
$67$	41363.5	−	41363.5i	1.12572	−	1.12572i	0.134853	−	0.990866i	$-0.456944\pi$
$67$	41363.5	−	41363.5i	1.12572	−	1.12572i	0.990866	−	0.134853i	$-0.0430563\pi$
$68$	−34704.8	+	14588.7i	−0.910159	+	0.382600i
$69$	1011.46	−	1011.46i	0.0255756	−	0.0255756i
$70$	7068.45	−	7384.02i	0.172417	−	0.180114i
$71$		−	19336.1i		−	0.455222i	−0.973752	−	0.227611i	$-0.926909\pi$
$71$		−	19336.1i		−	0.455222i	0.973752	−	0.227611i	$-0.0730914\pi$
$72$	−113699.	−	21688.5i	−2.58478	−	0.493058i
$73$	39755.2			0.873146			0.436573	−	0.899669i	$-0.356192\pi$
$73$	39755.2			0.873146			0.436573	+	0.899669i	$0.356192\pi$
$74$	2833.51	+	14052.5i	0.0601514	+	0.298314i
$75$	84336.1	−	38792.9i	1.73125	−	0.796341i
$76$	4143.05	−	10152.3i	0.0822784	−	0.201619i
$77$	7462.73	−	7462.73i	0.143440	−	0.143440i
$78$	85620.6	−	128870.i	1.59346	−	2.39836i
$79$	86421.1			1.55794			0.778972	−	0.627059i	$-0.215741\pi$
$79$	86421.1			1.55794			0.778972	+	0.627059i	$0.215741\pi$
$80$	33201.7	+	46631.0i	0.580009	+	0.814610i
$81$	−194438.			−3.29283
$82$	30669.2	−	46161.0i	0.503694	−	0.758124i
$83$	−14279.7	+	14279.7i	−0.227522	+	0.227522i	−0.811657	−	0.584135i	$-0.801434\pi$
$83$	−14279.7	+	14279.7i	−0.227522	+	0.227522i	0.584135	+	0.811657i	$0.301434\pi$
$84$	28449.3	+	11609.8i	0.439919	+	0.179526i
$85$	64736.5	+	11588.8i	0.971856	+	0.173976i
$86$	4050.07	+	20085.9i	0.0590495	+	0.292850i
$87$	−217260.			−3.07738
$88$	33220.9	+	48882.4i	0.457304	+	0.672893i
$89$			80993.3i			1.08386i	0.840423	+	0.541931i	$0.182307\pi$
$89$			80993.3i			1.08386i	−0.840423	+	0.541931i	$0.817693\pi$
$90$	146068.	+	139825.i	1.90085	+	1.81961i
$91$	−21045.0	+	21045.0i	−0.266406	+	0.266406i
$92$	−597.127	−	1420.49i	−0.00735524	−	0.0174972i
$93$	69819.3	−	69819.3i	0.837083	−	0.837083i
$94$	63350.3	−	95350.3i	0.739485	−	1.11302i
$95$	−15719.7	+	10946.1i	−0.178705	+	0.124438i
$96$	−93716.7	+	144314.i	−1.03786	+	1.59820i
$97$			88094.6i			0.950649i	0.879811	+	0.475324i	$0.157669\pi$
$97$			88094.6i			0.950649i	−0.879811	+	0.475324i	$0.842331\pi$
$98$	74266.8	+	49342.5i	0.781141	+	0.518986i
$99$	147625.	+	147625.i	1.51381	+	1.51381i
$100$	−4364.89	−	99904.7i	−0.0436489	−	0.999047i
$101$	29479.5	−	29479.5i	0.287552	−	0.287552i	−0.548560	−	0.836111i	$-0.684824\pi$
$101$	29479.5	−	29479.5i	0.287552	−	0.287552i	0.836111	+	0.548560i	$0.184824\pi$
$102$	39075.6	+	193791.i	0.371882	+	1.84431i
$103$	−42415.4			−0.393940			−0.196970	−	0.980409i	$-0.563110\pi$
$103$	−42415.4			−0.393940			−0.196970	+	0.980409i	$0.563110\pi$
$104$	−93683.3	−	137849.i	−0.849334	−	1.24974i
$105$	−30673.7	−	44050.4i	−0.271515	−	0.389921i
$106$	−27346.3	−	135621.i	−0.236393	−	1.17237i
$107$	90713.9	+	90713.9i	0.765975	+	0.765975i	0.977395	−	0.211420i	$-0.0678089\pi$
$107$	90713.9	+	90713.9i	0.765975	+	0.765975i	−0.211420	+	0.977395i	$0.567809\pi$
$108$	−142383.	+	348903.i	−1.17462	+	2.87836i
$109$	33393.9	+	33393.9i	0.269216	+	0.269216i	0.828784	−	0.559568i	$-0.189033\pi$
$109$	33393.9	+	33393.9i	0.269216	+	0.269216i	−0.559568	+	0.828784i	$0.689033\pi$
$110$	−2253.87	−	103223.i	−0.0177601	−	0.813386i
$111$	75278.7			0.579916
$112$	23158.8	−	23649.4i	0.174450	−	0.178145i
$113$		−	70480.8i		−	0.519248i	−0.965710	−	0.259624i	$-0.916401\pi$
$113$		−	70480.8i		−	0.519248i	0.965710	−	0.259624i	$-0.0835986\pi$
$114$	−47960.6	−	31864.8i	−0.345639	−	0.229641i
$115$	−474.337	+	2649.71i	−0.00334459	+	0.0186833i
$116$	−88428.9	+	216691.i	−0.610168	+	1.49519i
$117$	−416303.	−	416303.i	−2.81154	−	2.81154i
$118$	−119913.	+	24178.9i	−0.792796	+	0.159857i
$119$		−	38028.1i		−	0.246171i
$120$	274503.	−	122510.i	1.74018	−	0.776637i
$121$			54449.4i			0.338088i
$122$	−31573.1	−	156583.i	−0.192051	−	0.952459i
$123$	−205788.	−	205788.i	−1.22647	−	1.22647i
$124$	−41218.7	−	98054.3i	−0.240735	−	0.572681i
$125$	−88526.1	+	150601.i	−0.506753	+	0.862091i
$126$	64703.6	−	97387.2i	0.363080	−	0.546482i
$127$			143001.i			0.786736i	0.919381	+	0.393368i	$0.128690\pi$
$127$			143001.i			0.786736i	−0.919381	+	0.393368i	$0.871310\pi$
$128$	105792.	+	152210.i	0.570725	+	0.821141i
$129$	107599.			0.569293
$130$	6355.93	+	291091.i	0.0329853	+	1.51067i
$131$	137562.	+	137562.i	0.700357	+	0.700357i	0.964487	−	0.264130i	$-0.0850847\pi$
$131$	137562.	+	137562.i	0.700357	+	0.700357i	−0.264130	+	0.964487i	$0.585085\pi$
$132$	286113.	−	120272.i	1.42923	−	0.600800i
$133$	7832.15	+	7832.15i	0.0383930	+	0.0383930i
$134$	−324379.	+	65407.0i	−1.56060	+	0.314675i
$135$	540236.	−	376184.i	2.55123	−	1.77650i
$136$	209188.	+	39903.6i	0.969818	+	0.184997i
$137$	−162986.			−0.741905			−0.370952	−	0.928652i	$-0.620969\pi$
$137$	−162986.			−0.741905			−0.370952	+	0.928652i	$0.620969\pi$
$138$	−7932.03	+	1599.39i	−0.0354557	+	0.00714920i
$139$	141219.	−	141219.i	0.619950	−	0.619950i	−0.325568	−	0.945518i	$-0.605556\pi$
$139$	141219.	−	141219.i	0.619950	−	0.619950i	0.945518	+	0.325568i	$0.105556\pi$
$140$	−56419.9	+	12664.0i	−0.243283	+	0.0546074i
$141$	−425077.	−	425077.i	−1.80061	−	1.80061i
$142$	−60530.6	+	91106.3i	−0.251915	+	0.379164i
$143$			300618.i			1.22935i
$144$	467822.	+	458118.i	1.88007	+	1.84107i
$145$	335521.	−	233634.i	1.32525	−	0.922817i
$146$	−187315.	−	124452.i	−0.727263	−	0.483190i
$147$	331085.	−	331085.i	1.26371	−	1.26371i
$148$	30639.9	−	75081.6i	0.114983	−	0.281760i
$149$	38714.4	−	38714.4i	0.142859	−	0.142859i	−0.632060	−	0.774919i	$-0.717791\pi$
$149$	38714.4	−	38714.4i	0.142859	−	0.142859i	0.774919	+	0.632060i	$0.217791\pi$
$150$	−518807.	−	81228.4i	−1.88268	−	0.294767i
$151$			186695.i			0.666333i	0.942868	+	0.333166i	$0.108117\pi$
$151$			186695.i			0.666333i	−0.942868	+	0.333166i	$0.891883\pi$
$152$	−51302.2	+	34865.4i	−0.180106	+	0.122401i
$153$	752255.			2.59799
$154$	−58524.0	+	11800.6i	−0.198853	+	0.0400962i
$155$	−32742.7	+	182905.i	−0.109468	+	0.611501i
$156$	−806841.	+	339168.i	−2.65446	+	1.11584i
$157$	85417.1	−	85417.1i	0.276564	−	0.276564i	−0.555172	−	0.831736i	$-0.687347\pi$
$157$	85417.1	−	85417.1i	0.276564	−	0.276564i	0.831736	+	0.555172i	$0.187347\pi$
$158$	−407192.	−	270536.i	−1.29765	−	0.862151i
$159$	−726519.			−2.27905
$160$	−10461.1	−	323648.i	−0.0323055	−	0.999478i
$161$	1556.52			0.00473249
$162$	916138.	+	608678.i	2.74267	+	1.82222i
$163$	−413981.	+	413981.i	−1.22043	+	1.22043i	−0.252945	+	0.967481i	$0.581399\pi$
$163$	−413981.	+	413981.i	−1.22043	+	1.22043i	−0.967481	+	0.252945i	$0.918601\pi$
$164$	−289009.	+	121489.i	−0.839077	+	0.352719i
$165$	−533700.	−	95539.9i	−1.52611	−	0.273196i
$166$	111984.	−	22580.1i	0.315417	−	0.0635998i
$167$	85966.2			0.238527			0.119263	−	0.992863i	$-0.461947\pi$
$167$	85966.2			0.238527			0.119263	+	0.992863i	$0.461947\pi$
$168$	−97701.2	−	143761.i	−0.267071	−	0.392978i
$169$		−	476452.i		−	1.28322i
$170$	−268742.	−	257257.i	−0.713204	−	0.682724i
$171$	−154932.	+	154932.i	−0.405183	+	0.405183i
$172$	43795.0	−	107318.i	0.112877	−	0.276599i
$173$	150249.	−	150249.i	0.381677	−	0.381677i	−0.490029	−	0.871706i	$-0.663014\pi$
$173$	150249.	−	150249.i	0.381677	−	0.381677i	0.871706	+	0.490029i	$0.163014\pi$
$174$	1.02367e6	+	680120.i	2.56322	+	1.70299i
$175$	94740.6	+	35042.9i	0.233852	+	0.0864977i
$176$	−3503.70	−	334317.i	−0.00852599	−	0.813535i
$177$			642369.i			1.54117i
$178$	253545.	−	381618.i	0.599798	−	0.902773i
$179$	112055.	+	112055.i	0.261396	+	0.261396i	0.825621	−	0.564225i	$-0.190825\pi$
$179$	112055.	+	112055.i	0.261396	+	0.261396i	−0.564225	+	0.825621i	$0.690825\pi$
$180$	−250514.	−	1.11607e6i	−0.576304	−	2.56751i
$181$	37719.5	−	37719.5i	0.0855794	−	0.0855794i	−0.663021	−	0.748601i	$-0.730726\pi$
$181$	37719.5	−	37719.5i	0.0855794	−	0.0855794i	0.748601	+	0.663021i	$0.230726\pi$
$182$	165038.	−	33277.9i	0.369323	−	0.0744692i
$183$	−838811.			−1.85155
$184$	−1633.28	+	8562.24i	−0.00355645	+	0.0186442i
$185$	−116255.	+	80952.2i	−0.249737	+	0.173900i
$186$	−547535.	+	110403.i	−1.16046	+	0.233992i
$187$	−271607.	−	271607.i	−0.567985	−	0.567985i
$188$	−596978.	+	250949.i	−1.23187	+	0.517835i
$189$	−269166.	−	269166.i	−0.548107	−	0.548107i
$190$	108333.	−	2365.44i	0.217710	−	0.00475365i
$191$	22570.2			0.0447664			0.0223832	−	0.999749i	$-0.492875\pi$
$191$	22570.2			0.0447664			0.0223832	+	0.999749i	$0.492875\pi$
$192$	893334.	−	386593.i	1.74888	−	0.756834i
$193$			847216.i			1.63720i	0.574366	+	0.818598i	$0.305248\pi$
$193$			847216.i			1.63720i	−0.574366	+	0.818598i	$0.694752\pi$
$194$	275775.	−	415077.i	0.526079	−	0.791816i
$195$	1.50504e6	+	269424.i	2.83440	+	0.507398i
$196$	−195460.	−	464976.i	−0.363428	−	0.864551i
$197$	−161774.	−	161774.i	−0.296991	−	0.296991i	0.542843	−	0.839834i	$-0.317348\pi$
$197$	−161774.	−	161774.i	−0.296991	−	0.296991i	−0.839834	+	0.542843i	$0.817348\pi$
$198$	−233435.	−	1.15770e6i	−0.423158	−	2.09861i
$199$		−	1.06516e6i		−	1.90669i	−0.301877	−	0.953347i	$-0.597613\pi$
$199$		−	1.06516e6i		−	1.90669i	0.301877	−	0.953347i	$-0.402387\pi$
$200$	−292180.	+	484387.i	−0.516506	+	0.856283i
$201$			1.73769e6i			3.03376i
$202$	−231183.	+	46615.1i	−0.398636	+	0.0803800i
$203$	−167169.	−	167169.i	−0.284718	−	0.284718i
$204$	422540.	−	1.03541e6i	0.710874	−	1.74196i
$205$	539102.	+	96507.0i	0.895955	+	0.160389i
$206$	199850.	+	132779.i	0.328122	+	0.218003i
$207$			30790.4i			0.0499447i
$208$	9880.46	+	942776.i	0.0158350	+	1.51095i
$209$	111879.			0.177166
$210$	6628.52	+	303576.i	0.0103721	+	0.475027i
$211$	−829752.	−	829752.i	−1.28305	−	1.28305i	−0.938926	−	0.344120i	$-0.888177\pi$
$211$	−829752.	−	829752.i	−1.28305	−	1.28305i	−0.344120	−	0.938926i	$-0.611823\pi$
$212$	−295707.	+	724616.i	−0.451879	+	1.10731i
$213$	406157.	+	406157.i	0.613401	+	0.613401i
$214$	−143444.	−	711394.i	−0.214115	−	1.06188i
$215$	−166169.	+	115709.i	−0.245162	+	0.170714i
$216$	1.76309e6	−	1.19821e6i	2.57123	−	1.74743i
$217$	107444.			0.154893
$218$	−52805.0	−	261881.i	−0.0752547	−	0.373218i
$219$	−835062.	+	835062.i	−1.17654	+	1.17654i
$220$	−312516.	+	493416.i	−0.435327	+	0.687316i
$221$	765934.	+	765934.i	1.05490	+	1.05490i
$222$	−354692.	−	235656.i	−0.483025	−	0.320919i
$223$		−	123222.i		−	0.165930i	−0.996552	−	0.0829652i	$-0.973561\pi$
$223$		−	123222.i		−	0.165930i	0.996552	−	0.0829652i	$-0.0264390\pi$
$224$	−183151.	+	38931.8i	−0.243887	+	0.0518423i
$225$	−693203.	+	1.87412e6i	−0.912860	+	2.46798i
$226$	−220636.	+	332086.i	−0.287347	+	0.432493i
$227$	−567370.	+	567370.i	−0.730805	+	0.730805i	−0.970779	−	0.239974i	$-0.922861\pi$
$227$	−567370.	+	567370.i	−0.730805	+	0.730805i	0.239974	+	0.970779i	$0.422861\pi$
$228$	126226.	+	300276.i	0.160809	+	0.382546i
$229$	397217.	−	397217.i	0.500541	−	0.500541i	−0.411065	−	0.911606i	$-0.634843\pi$
$229$	397217.	−	397217.i	0.500541	−	0.500541i	0.911606	+	0.411065i	$0.134843\pi$
$230$	10529.7	−	10999.8i	0.0131249	−	0.0137109i
$231$			313511.i			0.386565i
$232$	1.09499e6	−	744165.i	1.33564	−	0.907714i
$233$	1.54172e6			1.86044			0.930221	−	0.367000i	$-0.119615\pi$
$233$	1.54172e6			1.86044			0.930221	+	0.367000i	$0.119615\pi$
$234$	658288.	+	3.26471e6i	0.785917	+	3.89767i
$235$	1.11357e6	+	199345.i	1.31537	+	0.235470i
$236$	640687.	+	261457.i	0.748801	+	0.305576i
$237$	−1.81528e6	+	1.81528e6i	−2.09929	+	2.09929i
$238$	−119045.	+	179178.i	−0.136229	+	0.205041i
$239$	−804561.			−0.911096			−0.455548	−	0.890211i	$-0.650557\pi$
$239$	−804561.			−0.911096			−0.455548	+	0.890211i	$0.650557\pi$
$240$	−1.67689e6	−	282085.i	−1.87922	−	0.316119i
$241$	−368334.			−0.408506			−0.204253	−	0.978918i	$-0.565477\pi$
$241$	−368334.			−0.408506			−0.204253	+	0.978918i	$0.565477\pi$
$242$	170451.	−	256550.i	0.187094	−	0.281601i
$243$	2.06073e6	−	2.06073e6i	2.23875	−	2.23875i
$244$	−341412.	+	836615.i	−0.367117	+	0.899603i
$245$	−155267.	+	867342.i	−0.165258	+	0.923156i
$246$	325407.	+	1.61382e6i	0.342838	+	1.70027i
$247$	−315499.			−0.329045
$248$	−112743.	+	591037.i	−0.116402	+	0.610219i
$249$		−	599893.i		−	0.613162i
$250$	888559.	−	432464.i	0.899159	−	0.437623i
$251$	705831.	−	705831.i	0.707158	−	0.707158i	−0.258779	−	0.965937i	$-0.583320\pi$
$251$	705831.	−	705831.i	0.707158	−	0.707158i	0.965937	+	0.258779i	$0.0833201\pi$
$252$	−609731.	+	256310.i	−0.604835	+	0.254252i
$253$	11117.1	−	11117.1i	0.0109192	−	0.0109192i
$254$	447656.	−	673779.i	0.435372	−	0.655290i
$255$	−1.60322e6	+	1.11637e6i	−1.54398	+	1.07512i
$256$	−21976.1	−	1.04835e6i	−0.0209580	−	0.999780i
$257$		−	1.97850e6i		−	1.86854i	−0.356560	−	0.934272i	$-0.616050\pi$
$257$		−	1.97850e6i		−	1.86854i	0.356560	−	0.934272i	$-0.383950\pi$
$258$	−506978.	−	336834.i	−0.474176	−	0.315041i
$259$	57922.6	+	57922.6i	0.0536536	+	0.0536536i
$260$	881298.	−	1.39144e6i	0.808517	−	1.27653i
$261$	3.30686e6	−	3.30686e6i	3.00480	−	3.00480i
$262$	−217523.	−	1.07878e6i	−0.195773	−	0.970914i
$263$	−288233.			−0.256954			−0.128477	−	0.991713i	$-0.541009\pi$
$263$	−288233.			−0.256954			−0.128477	+	0.991713i	$0.541009\pi$
$264$	−1.72459e6	−	328972.i	−1.52291	−	0.290502i
$265$	1.12198e6	−	781274.i	0.981459	−	0.683421i
$266$	−12384.8	−	61421.0i	−0.0107321	−	0.0532247i
$267$	−1.70127e6	−	1.70127e6i	−1.46048	−	1.46048i
$268$	1.73314e6	+	707272.i	1.47399	+	0.601519i
$269$	370575.	+	370575.i	0.312245	+	0.312245i	0.845779	−	0.533534i	$-0.179136\pi$
$269$	370575.	+	370575.i	0.312245	+	0.312245i	−0.533534	+	0.845779i	$0.679136\pi$
$270$	−3.72306e6	+	81292.5i	−3.10807	+	0.0678642i
$271$	607902.			0.502817			0.251409	−	0.967881i	$-0.419106\pi$
$271$	607902.			0.502817			0.251409	+	0.967881i	$0.419106\pi$
$272$	−860721.	−	842868.i	−0.705408	−	0.690776i
$273$		−	884103.i		−	0.717953i
$274$	767943.	+	510218.i	0.617949	+	0.410563i
$275$	926948.	−	426377.i	0.739135	−	0.339987i
$276$	42380.3	+	17294.9i	0.0334882	+	0.0136661i
$277$	142700.	+	142700.i	0.111744	+	0.111744i	0.760768	−	0.649024i	$-0.224822\pi$
$277$	142700.	+	142700.i	0.111744	+	0.111744i	−0.649024	+	0.760768i	$0.724822\pi$
$278$	−1.10746e6	+	223306.i	−0.859444	+	0.173296i
$279$			2.12541e6i			1.63468i
$280$	305479.	+	116950.i	0.232855	+	0.0891467i
$281$			1.75177e6i			1.32346i	0.749742	+	0.661730i	$0.230178\pi$
$281$			1.75177e6i			1.32346i	−0.749742	+	0.661730i	$0.769822\pi$
$282$	672163.	+	3.33352e6i	0.503329	+	2.49621i
$283$	1.02051e6	+	1.02051e6i	0.757446	+	0.757446i	0.975857	−	0.218411i	$-0.0700872\pi$
$283$	1.02051e6	+	1.02051e6i	0.757446	+	0.757446i	−0.218411	+	0.975857i	$0.570087\pi$
$284$	570407.	−	239779.i	0.419651	−	0.176407i
$285$	100269.	−	560119.i	0.0731233	−	0.408477i
$286$	941067.	−	1.41643e6i	0.680308	−	1.02395i
$287$		−	316684.i		−	0.226945i
$288$	−770132.	−	3.62301e6i	−0.547122	−	2.57388i
$289$	35820.9			0.0252285
$290$	−2.31226e6	+	50487.7i	−1.61451	+	0.0352526i
$291$	−1.85044e6	−	1.85044e6i	−1.28098	−	1.28098i
$292$	492989.	+	1.17276e6i	0.338361	+	0.804920i
$293$	−1.57455e6	−	1.57455e6i	−1.07149	−	1.07149i	−0.997240	−	0.0742474i	$-0.976345\pi$
$293$	−1.57455e6	−	1.57455e6i	−1.07149	−	1.07149i	−0.0742474	−	0.997240i	$-0.523655\pi$
$294$	−2.59642e6	+	523536.i	−1.75189	+	0.353247i
$295$	−690782.	−	992030.i	−0.462153	−	0.663697i
$296$	−379406.	+	257847.i	−0.251695	+	0.171054i
$297$	−3.84491e6			−2.52927
$298$	−303605.	+	61218.1i	−0.198047	+	0.0399337i
$299$	−31350.2	+	31350.2i	−0.0202798	+	0.0202798i
$300$	2.19019e6	+	2.00682e6i	1.40501	+	1.28738i
$301$	82791.5	+	82791.5i	0.0526708	+	0.0526708i
$302$	584440.	−	879656.i	0.368742	−	0.555003i
$303$			1.23844e6i			0.774939i
$304$	350866.	−	3677.14i	0.217750	−	0.00228205i
$305$	1.29540e6	−	902029.i	0.797360	−	0.555228i
$306$	−3.54442e6	−	2.35489e6i	−2.16392	−	1.43770i
$307$	−547229.	+	547229.i	−0.331378	+	0.331378i	−0.853110	−	0.521732i	$-0.825286\pi$
$307$	−547229.	+	547229.i	−0.331378	+	0.331378i	0.521732	+	0.853110i	$0.325286\pi$
$308$	312690.	+	127605.i	0.187818	+	0.0766462i
$309$	890940.	−	890940.i	0.530826	−	0.530826i
$310$	726850.	−	759300.i	0.429576	−	0.448755i
$311$			995943.i			0.583893i	0.956435	+	0.291947i	$0.0943030\pi$
$311$			995943.i			0.583893i	−0.956435	+	0.291947i	$0.905697\pi$
$312$	4.86336e6	+	927705.i	2.82846	+	0.539540i
$313$	−529411.			−0.305444			−0.152722	−	0.988269i	$-0.548804\pi$
$313$	−529411.			−0.305444			−0.152722	+	0.988269i	$0.548804\pi$
$314$	−669855.	+	135068.i	−0.383404	+	0.0773086i
$315$	1.13736e6	+	203604.i	0.645835	+	0.115614i
$316$	1.07167e6	+	2.54938e6i	0.603733	+	1.43621i
$317$	1.49497e6	−	1.49497e6i	0.835574	−	0.835574i	−0.152699	−	0.988273i	$-0.548797\pi$
$317$	1.49497e6	−	1.49497e6i	0.835574	−	0.835574i	0.988273	+	0.152699i	$0.0487965\pi$
$318$	3.42315e6	+	2.27433e6i	1.89827	+	1.26120i
$319$	−2.38793e6			−1.31385
$320$	−963874.	+	1.55769e6i	−0.526193	+	0.850365i
$321$	−3.81091e6			−2.06427
$322$	−7333.88	−	4872.60i	−0.00394180	−	0.00261891i
$323$	285052.	−	285052.i	0.152026	−	0.152026i
$324$	−2.41115e6	−	5.73584e6i	−1.27603	−	3.03553i
$325$	−2.61400e6	+	1.20239e6i	−1.37277	+	0.631446i
$326$	3.24651e6	−	654617.i	1.69189	−	0.341149i
$327$	−1.40289e6			−0.725526
$328$	1.74205e6	+	332302.i	0.894077	+	0.170549i
$329$		−	654144.i		−	0.333184i
$330$	2.21556e6	+	2.12088e6i	1.11995	+	1.07209i
$331$	−1.29537e6	+	1.29537e6i	−0.649866	+	0.649866i	−0.952960	−	0.303095i	$-0.901980\pi$
$331$	−1.29537e6	+	1.29537e6i	−0.649866	+	0.649866i	0.303095	+	0.952960i	$0.401980\pi$
$332$	−598322.	−	244168.i	−0.297913	−	0.121575i
$333$	−1.14580e6	+	1.14580e6i	−0.566237	+	0.566237i
$334$	−405049.	−	269113.i	−0.198674	−	0.131998i
$335$	−1.86865e6	−	2.68356e6i	−0.909737	−	1.30647i
$336$	10304.2	+	983210.i	0.00497928	+	0.475114i
$337$		−	1.63734e6i		−	0.785350i	−0.919677	−	0.392675i	$-0.871550\pi$
$337$		−	1.63734e6i		−	0.785350i	0.919677	−	0.392675i	$-0.128450\pi$
$338$	−1.49151e6	+	2.24491e6i	−0.710122	+	1.06882i
$339$	1.48046e6	+	1.48046e6i	0.699675	+	0.699675i
$340$	460909.	+	2.05341e6i	0.216231	+	0.963336i
$341$	767393.	−	767393.i	0.357381	−	0.357381i
$342$	1.21500e6	−	244990.i	0.561710	−	0.113262i
$343$	1.05278e6			0.483172
$344$	−542302.	+	368553.i	−0.247084	+	0.167920i
$345$	−45694.0	−	65621.0i	−0.0206686	−	0.0296821i
$346$	−1.17828e6	+	237584.i	−0.529123	+	0.106691i
$347$	1.30577e6	+	1.30577e6i	0.582159	+	0.582159i	0.935496	−	0.353337i	$-0.114953\pi$
$347$	1.30577e6	+	1.30577e6i	0.582159	+	0.582159i	−0.353337	+	0.935496i	$0.614953\pi$
$348$	−2.69415e6	−	6.40907e6i	−1.19254	−	2.83692i
$349$	2.24617e6	+	2.24617e6i	0.987143	+	0.987143i	0.999918	−	0.0127756i	$-0.00406671\pi$
$349$	2.24617e6	+	2.24617e6i	0.987143	+	0.987143i	−0.0127756	+	0.999918i	$0.504067\pi$
$350$	−336692.	−	461693.i	−0.146914	−	0.201457i
$351$	1.08427e7			4.69752
$352$	−1.03005e6	+	1.58617e6i	−0.443101	+	0.682330i
$353$			1.98152e6i			0.846371i	0.906043	+	0.423186i	$0.139088\pi$
$353$			1.98152e6i			0.846371i	−0.906043	+	0.423186i	$0.860912\pi$
$354$	2.01090e6	−	3.02667e6i	0.852870	−	1.28368i
$355$	−1.06401e6	−	190472.i	−0.448098	−	0.0802161i
$356$	−2.38927e6	+	1.00437e6i	−0.999171	+	0.420017i
$357$	798783.	+	798783.i	0.331710	+	0.331710i
$358$	−177190.	−	878756.i	−0.0730688	−	0.362377i
$359$			2.59048e6i			1.06082i	0.847740	+	0.530412i	$0.177963\pi$
$359$			2.59048e6i			1.06082i	−0.847740	+	0.530412i	$0.822037\pi$
$360$	−2.31345e6	+	6.04285e6i	−0.940816	+	2.45745i
$361$		−	2.35868e6i		−	0.952580i
$362$	−295802.	+	59644.8i	−0.118640	+	0.0239222i
$363$	−1.14371e6	−	1.14371e6i	−0.455566	−	0.455566i
$364$	−881788.	−	359847.i	−0.348828	−	0.142352i
$365$	391613.	−	2.18761e6i	0.153860	−	0.859483i
$366$	3.95224e6	+	2.62585e6i	1.54220	+	1.02463i
$367$		−	1.73093e6i		−	0.670832i	−0.942070	−	0.335416i	$-0.891123\pi$
$367$		−	1.73093e6i		−	0.670832i	0.942070	−	0.335416i	$-0.108877\pi$
$368$	34499.2	−	35230.0i	0.0132797	−	0.0135610i
$369$	6.26451e6			2.39509
$370$	801178.	−	17493.6i	0.304246	−	0.00664316i
$371$	−559014.	−	559014.i	−0.210857	−	0.210857i
$372$	2.92544e6	+	1.19384e6i	1.09606	+	0.447289i
$373$	404589.	+	404589.i	0.150571	+	0.150571i	0.778373	−	0.627802i	$-0.216045\pi$
$373$	404589.	+	404589.i	0.150571	+	0.150571i	−0.627802	+	0.778373i	$0.716045\pi$
$374$	429485.	+	2.12999e6i	0.158770	+	0.787404i
$375$	−1.30389e6	−	5.02289e6i	−0.478810	−	1.84449i
$376$	3.59838e6	+	686405.i	1.31261	+	0.250387i
$377$	6.73398e6			2.44016
$378$	425625.	+	2.11084e6i	0.153214	+	0.759847i
$379$	71522.8	−	71522.8i	0.0255768	−	0.0255768i	−0.694203	−	0.719780i	$-0.744243\pi$
$379$	71522.8	−	71522.8i	0.0255768	−	0.0255768i	0.719780	+	0.694203i	$0.244243\pi$
$380$	−517841.	−	327986.i	−0.183966	−	0.116519i
$381$	−3.00374e6	−	3.00374e6i	−1.06011	−	1.06011i
$382$	−106345.	−	70654.8i	−0.0372869	−	0.0247733i
$383$			804828.i			0.280354i	0.990126	+	0.140177i	$0.0447671\pi$
$383$			804828.i			0.280354i	−0.990126	+	0.140177i	$0.955233\pi$
$384$	−5.41935e6	−	975018.i	−1.87551	−	0.337431i
$385$	−337139.	−	484164.i	−0.115920	−	0.166472i
$386$	2.65216e6	−	3.99184e6i	0.906008	−	1.36366i
$387$	−1.63775e6	+	1.63775e6i	−0.555865	+	0.555865i
$388$	−2.59875e6	+	1.09243e6i	−0.876366	+	0.368395i
$389$	−2.13995e6	+	2.13995e6i	−0.717016	+	0.717016i	−0.967993	−	0.250977i	$-0.919248\pi$
$389$	−2.13995e6	+	2.13995e6i	−0.717016	+	0.717016i	0.250977	+	0.967993i	$0.419248\pi$
$390$	−6.24790e6	−	5.98089e6i	−2.08005	−	1.99115i
$391$		−	56649.6i		−	0.0187394i
$392$	−534629.	+	2.80271e6i	−0.175727	+	0.921221i
$393$	−5.77900e6			−1.88743
$394$	255809.	+	1.26866e6i	0.0830185	+	0.411722i
$395$	851301.	−	4.75549e6i	0.274530	−	1.53357i
$396$	−2.52423e6	+	6.18549e6i	−0.808891	+	1.98215i
$397$	−728887.	+	728887.i	−0.232105	+	0.232105i	−0.813571	−	0.581466i	$-0.802479\pi$
$397$	−728887.	+	728887.i	−0.232105	+	0.232105i	0.581466	+	0.813571i	$0.302479\pi$
$398$	−3.33442e6	+	5.01872e6i	−1.05515	+	1.58813i
$399$	−329030.			−0.103467
$400$	2.89302e6	−	1.36764e6i	0.904068	−	0.427388i
$401$	−1.26052e6			−0.391461			−0.195730	−	0.980658i	$-0.562708\pi$
$401$	−1.26052e6			−0.391461			−0.195730	+	0.980658i	$0.562708\pi$
$402$	5.43974e6	−	8.18749e6i	1.67885	−	2.52689i
$403$	−2.16406e6	+	2.16406e6i	−0.663752	+	0.663752i
$404$	1.23519e6	+	504068.i	0.376515	+	0.153651i
$405$	−1.91534e6	+	1.06993e7i	−0.580239	+	3.24130i
$406$	264340.	+	1.31097e6i	0.0795880	+	0.394708i
$407$	827398.			0.247587
$408$	−5.23220e6	+	3.55584e6i	−1.55609	+	1.05753i
$409$			102667.i			0.0303476i	0.999885	+	0.0151738i	$0.00483016\pi$
$409$			102667.i			0.0303476i	−0.999885	+	0.0151738i	$0.995170\pi$
$410$	−2.23799e6	−	2.14234e6i	−0.657504	−	0.629404i
$411$	3.42353e6	−	3.42353e6i	0.999700	−	0.999700i
$412$	−525977.	−	1.25124e6i	−0.152659	−	0.363159i
$413$	−494266.	+	494266.i	−0.142589	+	0.142589i
$414$	96387.6	−	145076.i	0.0276389	−	0.0416000i
$415$	645104.	+	926432.i	0.183869	+	0.264054i
$416$	2.90476e6	−	4.47303e6i	0.822955	−	1.26727i
$417$			5.93264e6i			1.67074i
$418$	−527141.	−	350230.i	−0.147566	−	0.0980421i
$419$	1.91510e6	+	1.91510e6i	0.532914	+	0.532914i	0.921438	−	0.388524i	$-0.127015\pi$
$419$	1.91510e6	+	1.91510e6i	0.532914	+	0.532914i	−0.388524	+	0.921438i	$0.627015\pi$
$420$	919095.	−	1.45111e6i	0.254236	−	0.401401i
$421$	−3.26358e6	+	3.26358e6i	−0.897407	+	0.897407i	−0.995206	−	0.0977990i	$-0.968820\pi$
$421$	−3.26358e6	+	3.26358e6i	−0.897407	+	0.897407i	0.0977990	+	0.995206i	$0.468820\pi$
$422$	1.31207e6	+	6.50705e6i	0.358653	+	1.77870i
$423$	1.29400e7			3.51628
$424$	3.66166e6	−	2.48849e6i	0.989153	−	0.672236i
$425$	1.27539e6	−	3.44810e6i	0.342508	−	0.925991i
$426$	−642245.	−	3.18515e6i	−0.171465	−	0.850365i
$427$	−645417.	−	645417.i	−0.171305	−	0.171305i
$428$	−1.55111e6	+	3.80093e6i	−0.409293	+	1.00295i
$429$	−6.31450e6	−	6.31450e6i	−1.65652	−	1.65652i
$430$	1.14516e6	−	25004.4i	0.298673	−	0.00652147i
$431$	−3.84016e6			−0.995764			−0.497882	−	0.867245i	$-0.665889\pi$
$431$	−3.84016e6			−0.995764			−0.497882	+	0.867245i	$0.665889\pi$
$432$	−1.20581e7	+	126371.i	−3.10864	+	0.0325791i
$433$		−	3.70855e6i		−	0.950572i	−0.879831	−	0.475286i	$-0.842345\pi$
$433$		−	3.70855e6i		−	0.950572i	0.879831	−	0.475286i	$-0.157655\pi$
$434$	−506246.	−	336347.i	−0.129014	−	0.0857164i
$435$	−2.14014e6	+	1.19551e7i	−0.542275	+	3.02922i
$436$	−571001.	+	1.39921e6i	−0.143854	+	0.352507i
$437$	11667.4	+	11667.4i	0.00292260	+	0.00292260i
$438$	6.54869e6	−	1.32046e6i	1.63106	−	0.328882i
$439$		−	5.33655e6i		−	1.32160i	−0.750563	−	0.660799i	$-0.770218\pi$
$439$		−	5.33655e6i		−	1.32160i	0.750563	−	0.660799i	$-0.229782\pi$
$440$	3.01710e6	−	1.34652e6i	0.742947	−	0.331575i
$441$			1.00787e7i			2.46780i
$442$	−1.21115e6	−	6.00658e6i	−0.294878	−	1.46242i
$443$	296026.	+	296026.i	0.0716673	+	0.0716673i	0.742032	−	0.670365i	$-0.233862\pi$
$443$	296026.	+	296026.i	0.0716673	+	0.0716673i	−0.670365	+	0.742032i	$0.733862\pi$
$444$	933502.	+	2.22069e6i	0.224728	+	0.534602i
$445$	4.45681e6	+	797834.i	1.06690	+	0.190991i
$446$	−385740.	+	580587.i	−0.0918242	+	0.138207i
$447$			1.62640e6i			0.384998i
$448$	984830.	+	389908.i	0.231828	+	0.0917841i
$449$	2.99123e6			0.700219			0.350110	−	0.936709i	$-0.386144\pi$
$449$	2.99123e6			0.700219			0.350110	+	0.936709i	$0.386144\pi$
$450$	9.13301e6	−	6.66029e6i	2.12609	−	1.55046i
$451$	−2.26184e6	−	2.26184e6i	−0.523626	−	0.523626i
$452$	2.07915e6	−	874005.i	0.478675	−	0.201219i
$453$	−3.92155e6	−	3.92155e6i	−0.897868	−	0.897868i
$454$	4.44941e6	−	897167.i	1.01312	−	0.204284i
$455$	950734.	+	1.36535e6i	0.215293	+	0.309182i
$456$	345257.	−	1.80996e6i	0.0777554	−	0.407621i
$457$	−4.94502e6			−1.10759			−0.553793	−	0.832654i	$-0.686820\pi$
$457$	−4.94502e6			−1.10759			−0.553793	+	0.832654i	$0.686820\pi$
$458$	−3.11504e6	+	628109.i	−0.693906	+	0.139917i
$459$	−9.79631e6	+	9.79631e6i	−2.17036	+	2.17036i
$460$	−84047.5	+	18865.3i	−0.0185195	+	0.00415690i
$461$	−773879.	−	773879.i	−0.169598	−	0.169598i	0.617205	−	0.786803i	$-0.288265\pi$
$461$	−773879.	−	773879.i	−0.169598	−	0.169598i	−0.786803	+	0.617205i	$0.788265\pi$
$462$	981428.	−	1.47717e6i	0.213921	−	0.321978i
$463$			989094.i			0.214430i	0.994236	+	0.107215i	$0.0341933\pi$
$463$			989094.i			0.214430i	−0.994236	+	0.107215i	$0.965807\pi$
$464$	−7.48886e6	+	78484.6i	−1.61481	+	0.0169235i
$465$	−3.15418e6	−	4.52971e6i	−0.676479	−	0.971489i
$466$	−7.26416e6	−	4.82628e6i	−1.54960	−	1.02955i
$467$	−176655.	+	176655.i	−0.0374829	+	0.0374829i	−0.725600	−	0.688117i	$-0.758438\pi$
$467$	−176655.	+	176655.i	−0.0374829	+	0.0374829i	0.688117	+	0.725600i	$0.258438\pi$
$468$	7.11834e6	−	1.74432e7i	1.50233	−	3.68138i
$469$	−1.33705e6	+	1.33705e6i	−0.280683	+	0.280683i
$470$	−4.62280e6	−	4.42523e6i	−0.965295	−	0.924042i
$471$			3.58839e6i			0.745327i
$472$	−2.20026e6	−	3.23755e6i	−0.454590	−	0.668900i
$473$	1.18264e6			0.243052
$474$	1.42357e7	−	2.87046e6i	2.91028	−	0.586821i
$475$	447484.	+	972834.i	0.0910004	+	0.197836i
$476$	1.12181e6	−	471572.i	0.226936	−	0.0953960i
$477$	1.10582e7	−	1.10582e7i	2.22530	−	2.22530i
$478$	3.79086e6	+	2.51863e6i	0.758872	+	0.504191i
$479$	239770.			0.0477481			0.0238741	−	0.999715i	$-0.492400\pi$
$479$	239770.			0.0477481			0.0238741	+	0.999715i	$0.492400\pi$
$480$	7.01800e6	+	6.57852e6i	1.39031	+	1.30324i
$481$	−2.33327e6			−0.459835
$482$	1.73548e6	+	1.15305e6i	0.340254	+	0.226063i
$483$	−32694.8	+	32694.8i	−0.00637692	+	0.00637692i
$484$	−1.60623e6	+	675206.i	−0.311670	+	0.131016i
$485$	4.84758e6	+	867786.i	0.935773	+	0.167517i
$486$	−1.61606e7	+	3.25858e6i	−3.10360	+	0.625802i
$487$	−6.61335e6			−1.26357			−0.631784	−	0.775144i	$-0.717677\pi$
$487$	−6.61335e6			−1.26357			−0.631784	+	0.775144i	$0.717677\pi$
$488$	4.22762e6	−	2.87312e6i	0.803612	−	0.546141i
$489$		−	1.73914e7i		−	3.28899i
$490$	3.44674e6	−	3.60062e6i	0.648513	−	0.677465i
$491$	−4.31317e6	+	4.31317e6i	−0.807408	+	0.807408i	−0.984241	−	0.176833i	$-0.943415\pi$
$491$	−4.31317e6	+	4.31317e6i	−0.807408	+	0.807408i	0.176833	+	0.984241i	$0.443415\pi$
$492$	3.51876e6	−	8.62256e6i	0.655356	−	1.60592i
$493$	−6.08413e6	+	6.08413e6i	−1.12741	+	1.12741i
$494$	1.48654e6	+	987652.i	0.274069	+	0.182090i
$495$	9.57752e6	−	6.66913e6i	1.75687	−	1.22337i
$496$	2.38142e6	−	2.43187e6i	0.434643	−	0.443850i
$497$			625028.i			0.113503i
$498$	−1.87793e6	+	2.82653e6i	−0.339318	+	0.510716i
$499$	870474.	+	870474.i	0.156496	+	0.156496i	0.781012	−	0.624516i	$-0.214704\pi$
$499$	870474.	+	870474.i	0.156496	+	0.156496i	−0.624516	+	0.781012i	$0.714704\pi$
$500$	−5.54045e6	−	743937.i	−0.991105	−	0.133079i
$501$	−1.80573e6	+	1.80573e6i	−0.321409	+	0.321409i
$502$	−5.53524e6	+	1.11611e6i	−0.980342	+	0.197674i
$503$	−1.49845e6			−0.264072			−0.132036	−	0.991245i	$-0.542151\pi$
$503$	−1.49845e6			−0.264072			−0.132036	+	0.991245i	$0.542151\pi$
$504$	3.67525e6	+	701068.i	0.644481	+	0.122937i
$505$	−1.33177e6	−	1.91256e6i	−0.232382	−	0.333723i
$506$	−87181.9	+	17579.1i	−0.0151374	+	0.00305226i
$507$	1.00079e7	+	1.00079e7i	1.72911	+	1.72911i
$508$	−4.21846e6	+	1.77330e6i	−0.725261	+	0.304875i
$509$	5.26182e6	+	5.26182e6i	0.900206	+	0.900206i	0.995454	−	0.0952477i	$-0.0303643\pi$
$509$	5.26182e6	+	5.26182e6i	0.900206	+	0.900206i	−0.0952477	+	0.995454i	$0.530364\pi$
$510$	1.10487e7	−	241246.i	1.88098	−	0.0410709i
$511$	−1.28506e6			−0.217707
$512$	−3.17824e6	+	5.00831e6i	−0.535812	+	0.844337i
$513$		−	4.03524e6i		−	0.676980i
$514$	−6.19359e6	+	9.32215e6i	−1.03403	+	1.55635i
$515$	−417818.	+	2.33399e6i	−0.0694175	+	0.387776i
$516$	1.33430e6	+	3.17414e6i	0.220612	+	0.524809i
$517$	−4.67207e6	−	4.67207e6i	−0.768746	−	0.768746i
$518$	−91591.6	−	454239.i	−0.0149979	−	0.0743806i
$519$			6.31198e6i			1.02860i
$520$	−8.50825e6	+	3.79721e6i	−1.37985	+	0.615823i
$521$			1.86604e6i			0.301181i	0.988596	+	0.150590i	$0.0481174\pi$
$521$			1.86604e6i			0.301181i	−0.988596	+	0.150590i	$0.951883\pi$
$522$	−2.59330e7	+	5.22906e6i	−4.16558	+	0.839938i
$523$	5.54562e6	+	5.54562e6i	0.886535	+	0.886535i	0.994188	−	0.107654i	$-0.0343338\pi$
$523$	5.54562e6	+	5.54562e6i	0.886535	+	0.886535i	−0.107654	+	0.994188i	$0.534334\pi$
$524$	−2.35216e6	+	5.76387e6i	−0.374231	+	0.917034i
$525$	−2.72611e6	+	1.25396e6i	−0.431664	+	0.198557i
$526$	1.35807e6	+	902298.i	0.214022	+	0.142196i
$527$		−	3.91043e6i		−	0.613336i
$528$	7.09595e6	+	6.94876e6i	1.10771	+	1.08473i
$529$	−6.43402e6			−0.999640
$530$	−7.73221e6	+	168832.i	−1.19568	+	0.0261074i
$531$	−9.77737e6	−	9.77737e6i	−1.50482	−	1.50482i
$532$	−133922.	+	328168.i	−0.0205150	+	0.0502710i
$533$	6.37842e6	+	6.37842e6i	0.972512	+	0.972512i
$534$	2.69018e6	+	1.33417e7i	0.408251	+	2.02468i
$535$	5.88530e6	−	4.09812e6i	0.888964	−	0.619014i
$536$	−5.95198e6	−	8.75796e6i	−0.894848	−	1.31671i
$537$	−4.70746e6			−0.704452
$538$	−585981.	−	2.90611e6i	−0.0872826	−	0.432869i
$539$	3.63900e6	−	3.63900e6i	0.539523	−	0.539523i
$540$	1.77965e7	+	1.12718e7i	2.62634	+	1.66345i
$541$	4.79861e6	+	4.79861e6i	0.704891	+	0.704891i	0.965456	−	0.260565i	$-0.0839089\pi$
$541$	4.79861e6	+	4.79861e6i	0.704891	+	0.704891i	−0.260565	+	0.965456i	$0.583909\pi$
$542$	−2.86426e6	−	1.90300e6i	−0.418808	−	0.278254i
$543$			1.58460e6i			0.230632i
$544$	1.41693e6	+	6.66580e6i	0.205282	+	0.965728i
$545$	2.16652e6	−	1.50862e6i	0.312443	−	0.217564i
$546$	−2.76764e6	+	4.16565e6i	−0.397308	+	0.597999i
$547$	3.85519e6	−	3.85519e6i	0.550907	−	0.550907i	−0.375796	−	0.926702i	$-0.622631\pi$
$547$	3.85519e6	−	3.85519e6i	0.550907	−	0.550907i	0.926702	+	0.375796i	$0.122631\pi$
$548$	−2.02112e6	−	4.80801e6i	−0.287502	−	0.683934i
$549$	1.27674e7	−	1.27674e7i	1.80788	−	1.80788i
$550$	−5.70227e6	−	892791.i	−0.803788	−	0.125847i
$551$		−	2.50614e6i		−	0.351662i
$552$	−145543.	−	214158.i	−0.0203304	−	0.0299148i
$553$	−2.79351e6			−0.388452
$554$	−225648.	−	1.11908e6i	−0.0312361	−	0.154912i
$555$	741542.	−	4.14236e6i	0.102189	−	0.570841i
$556$	5.91711e6	+	2.41470e6i	0.811751	+	0.331266i
$557$	−3.62819e6	+	3.62819e6i	−0.495510	+	0.495510i	−0.910037	−	0.414527i	$-0.863947\pi$
$557$	−3.62819e6	+	3.62819e6i	−0.495510	+	0.495510i	0.414527	+	0.910037i	$0.363947\pi$
$558$	6.65348e6	−	1.00143e7i	0.904614	−	1.36156i
$559$	−3.33505e6			−0.451412
$560$	−1.07322e6	−	1.50732e6i	−0.144617	−	0.203112i
$561$	1.14103e7			1.53069
$562$	5.48382e6	−	8.25384e6i	0.732390	−	1.10234i
$563$	2.24066e6	−	2.24066e6i	0.297924	−	0.297924i	−0.542276	−	0.840200i	$-0.682437\pi$
$563$	2.24066e6	−	2.24066e6i	0.297924	−	0.297924i	0.840200	+	0.542276i	$0.182437\pi$
$564$	7.26837e6	−	1.78108e7i	0.962142	−	2.35768i
$565$	−3.87834e6	−	694280.i	−0.511123	−	0.0914984i
$566$	−1.61371e6	−	8.00302e6i	−0.211731	−	1.05006i
$567$	6.28510e6			0.821021
$568$	−3.43821e6	−	655853.i	−0.447159	−	0.0852974i
$569$		−	5.97280e6i		−	0.773388i	−0.922208	−	0.386694i	$-0.873617\pi$
$569$		−	5.97280e6i		−	0.773388i	0.922208	−	0.386694i	$-0.126383\pi$
$570$	−2.22586e6	+	2.32524e6i	−0.286953	+	0.299764i
$571$	5.35890e6	−	5.35890e6i	0.687837	−	0.687837i	−0.273917	−	0.961753i	$-0.588319\pi$
$571$	5.35890e6	−	5.35890e6i	0.687837	−	0.687837i	0.961753	+	0.273917i	$0.0883193\pi$
$572$	−8.86809e6	+	3.72784e6i	−1.13329	+	0.476395i
$573$	−474089.	+	474089.i	−0.0603217	+	0.0603217i
$574$	−991363.	+	1.49213e6i	−0.125589	+	0.189028i
$575$	141133.	+	52202.6i	0.0178016	+	0.00658450i
$576$	−7.71300e6	+	1.94815e7i	−0.968651	+	2.44662i
$577$			4.14173e6i			0.517895i	0.965891	+	0.258948i	$0.0833757\pi$
$577$			4.14173e6i			0.517895i	−0.965891	+	0.258948i	$0.916624\pi$
$578$	−168778.	−	112135.i	−0.0210134	−	0.0139612i
$579$	−1.77959e7	−	1.77959e7i	−2.20609	−	2.20609i
$580$	1.10528e7	+	7.00051e6i	1.36427	+	0.864091i
$581$	461583.	−	461583.i	0.0567295	−	0.0567295i
$582$	2.92605e6	+	1.45114e7i	0.358075	+	1.77583i
$583$	−7.98526e6			−0.973011
$584$	1.34844e6	−	7.06900e6i	0.163606	−	0.857681i
$585$	−2.70087e7	+	1.88070e7i	−3.26298	+	2.27212i
$586$	2.48979e6	+	1.23479e7i	0.299515	+	1.48542i
$587$	−2.42607e6	−	2.42607e6i	−0.290608	−	0.290608i	0.546712	−	0.837320i	$-0.315879\pi$
$587$	−2.42607e6	−	2.42607e6i	−0.290608	−	0.290608i	−0.837320	+	0.546712i	$0.815879\pi$
$588$	1.38725e7	+	5.66121e6i	1.65467	+	0.675252i
$589$	805381.	+	805381.i	0.0956562	+	0.0956562i
$590$	149277.	+	6.83663e6i	0.0176548	+	0.808559i
$591$	6.79615e6			0.800376
$592$	2.59483e6	−	27194.3i	0.304302	−	0.00318914i
$593$		−	1.36433e7i		−	1.59325i	−0.604474	−	0.796625i	$-0.706617\pi$
$593$		−	1.36433e7i		−	1.59325i	0.604474	−	0.796625i	$-0.293383\pi$
$594$	1.81161e7	+	1.20363e7i	2.10668	+	1.39967i
$595$	−2.09257e6	−	374600.i	−0.242319	−	0.0433786i
$596$	1.62214e6	+	661976.i	0.187057	+	0.0763355i
$597$	2.23737e7	+	2.23737e7i	2.56923	+	2.56923i
$598$	245854.	−	49573.3i	0.0281141	−	0.00566885i
$599$			1.42092e7i			1.61809i	0.587748	+	0.809044i	$0.300015\pi$
$599$			1.42092e7i			1.61809i	−0.587748	+	0.809044i	$0.699985\pi$
$600$	−4.03732e6	−	1.63119e7i	−0.457842	−	1.84980i
$601$		−	2.15726e6i		−	0.243622i	−0.992553	−	0.121811i	$-0.961130\pi$
$601$		−	2.15726e6i		−	0.243622i	0.992553	−	0.121811i	$-0.0388702\pi$
$602$	−130916.	−	649265.i	−0.0147232	−	0.0730181i
$603$	−2.64490e7	−	2.64490e7i	−2.96221	−	2.96221i
$604$	−5.50743e6	+	2.31514e6i	−0.614267	+	0.258217i
$605$	2.99618e6	+	536360.i	0.332798	+	0.0595756i
$606$	3.87686e6	−	5.83517e6i	0.428843	−	0.645464i
$607$		−	1.21033e7i		−	1.33332i	−0.745363	−	0.666659i	$-0.767724\pi$
$607$		−	1.21033e7i		−	1.33332i	0.745363	−	0.666659i	$-0.232276\pi$
$608$	−1.66469e6	−	1.08104e6i	−0.182631	−	0.118600i
$609$	7.02279e6			0.767303
$610$	−8.92732e6	+	194927.i	−0.971397	+	0.0212103i
$611$	1.31753e7	+	1.31753e7i	1.42777	+	1.42777i
$612$	9.32843e6	+	2.21912e7i	1.00677	+	2.39498i
$613$	−2.11836e6	−	2.11836e6i	−0.227693	−	0.227693i	0.584036	−	0.811728i	$-0.301473\pi$
$613$	−2.11836e6	−	2.11836e6i	−0.227693	−	0.227693i	−0.811728	+	0.584036i	$0.801473\pi$
$614$	4.29146e6	−	865319.i	0.459393	−	0.0926308i
$615$	−1.33510e7	+	9.29675e6i	−1.42340	+	0.991159i
$616$	−1.07385e6	−	1.58010e6i	−0.114022	−	0.167777i
$617$	9.90588e6			1.04756			0.523782	−	0.851853i	$-0.324521\pi$
$617$	9.90588e6			1.04756			0.523782	+	0.851853i	$0.324521\pi$
$618$	−6.98690e6	+	1.40882e6i	−0.735890	+	0.148383i
$619$	9.72084e6	−	9.72084e6i	1.01971	−	1.01971i	0.0199096	−	0.999802i	$-0.493662\pi$
$619$	9.72084e6	−	9.72084e6i	1.01971	−	1.01971i	0.999802	−	0.0199096i	$-0.00633785\pi$
$620$	−5.80166e6	+	1.30224e6i	−0.606140	+	0.136055i
$621$	−400970.	−	400970.i	−0.0417238	−	0.0417238i
$622$	3.11775e6	−	4.69261e6i	0.323121	−	0.486338i
$623$		−	2.61806e6i		−	0.270246i
$624$	−2.00106e7	−	1.95956e7i	−2.05731	−	2.01463i
$625$	7.41508e6	+	6.35484e6i	0.759305	+	0.650735i
$626$	2.49444e6	+	1.65729e6i	0.254411	+	0.169030i
$627$	−2.35002e6	+	2.35002e6i	−0.238728	+	0.238728i
$628$	3.57899e6	+	1.46054e6i	0.362128	+	0.147780i
$629$	2.10810e6	−	2.10810e6i	0.212454	−	0.212454i
$630$	−4.72155e6	−	4.51977e6i	−0.473951	−	0.453696i
$631$			1.78843e7i			1.78813i	0.447938	+	0.894065i	$0.352158\pi$
$631$			1.78843e7i			1.78813i	−0.447938	+	0.894065i	$0.647842\pi$
$632$	2.93128e6	−	1.53668e7i	0.291921	−	1.53035i
$633$	3.48580e7			3.45775
$634$	−1.17238e7	+	2.36396e6i	−1.15837	+	0.233570i
$635$	7.86889e6	+	1.40864e6i	0.774425	+	0.138633i
$636$	−9.00928e6	−	2.14320e7i	−0.883176	−	2.10097i
$637$	−1.02620e7	+	1.02620e7i	−1.00204	+	1.00204i
$638$	1.12513e7	+	7.47528e6i	1.09433	+	0.727069i
$639$	−1.23640e7			−1.19787
$640$	9.41776e6	−	4.32203e6i	0.908861	−	0.417098i
$641$	−1.89860e7			−1.82511			−0.912553	−	0.408959i	$-0.865892\pi$
$641$	−1.89860e7			−1.82511			−0.912553	+	0.408959i	$0.865892\pi$
$642$	1.79559e7	+	1.19298e7i	1.71937	+	1.14235i
$643$	1.29713e6	−	1.29713e6i	0.123724	−	0.123724i	−0.642533	−	0.766258i	$-0.722117\pi$
$643$	1.29713e6	−	1.29713e6i	0.123724	−	0.123724i	0.766258	+	0.642533i	$0.222117\pi$
$644$	19301.8	+	45916.6i	0.00183393	+	0.00436270i
$645$	1.05992e6	−	5.92087e6i	0.100317	−	0.560384i
$646$	−2.23542e6	+	450745.i	−0.210755	+	0.0424962i
$647$	2.03269e7			1.90902			0.954510	−	0.298177i	$-0.0963787\pi$
$647$	2.03269e7			1.90902			0.954510	+	0.298177i	$0.0963787\pi$
$648$	−6.59507e6	+	3.45737e7i	−0.616995	+	3.23450i
$649$			7.06036e6i			0.657984i
$650$	1.60805e7	+	2.51768e6i	1.49285	+	0.233731i
$651$	−2.25687e6	+	2.25687e6i	−0.208715	+	0.208715i
$652$	−1.73459e7	−	7.07864e6i	−1.59800	−	0.652125i
$653$	−3.53649e6	+	3.53649e6i	−0.324556	+	0.324556i	−0.850512	−	0.525956i	$-0.823708\pi$
$653$	−3.53649e6	+	3.53649e6i	−0.324556	+	0.324556i	0.525956	+	0.850512i	$0.323708\pi$
$654$	6.61000e6	+	4.39166e6i	0.604307	+	0.401499i
$655$	8.92468e6	−	6.21454e6i	0.812810	−	0.565986i
$656$	−7.16778e6	−	7.01910e6i	−0.650317	−	0.636827i
$657$		−	2.54206e7i		−	2.29759i
$658$	−2.04776e6	+	3.08214e6i	−0.184380	+	0.277516i
$659$	4.69975e6	+	4.69975e6i	0.421562	+	0.421562i	0.885741	−	0.464180i	$-0.153651\pi$
$659$	4.69975e6	+	4.69975e6i	0.421562	+	0.421562i	−0.464180	+	0.885741i	$0.653651\pi$
$660$	−3.79982e6	−	1.69287e7i	−0.339549	−	1.51274i
$661$	−1.25667e7	+	1.25667e7i	−1.11871	+	1.11871i	−0.126781	+	0.991931i	$0.540465\pi$
$661$	−1.25667e7	+	1.25667e7i	−1.11871	+	1.11871i	−0.991931	+	0.126781i	$0.959535\pi$
$662$	1.01585e7	−	2.04833e6i	0.900917	−	0.181659i
$663$	−3.21770e7			−2.84290
$664$	2.05477e6	+	3.02346e6i	0.180860	+	0.266124i
$665$	508131.	−	353828.i	0.0445576	−	0.0310269i
$666$	8.98556e6	−	1.81183e6i	0.784982	−	0.158282i
$667$	−249028.	−	249028.i	−0.0216737	−	0.0216737i
$668$	1.06603e6	+	2.53597e6i	0.0924336	+	0.219888i
$669$	2.58829e6	+	2.58829e6i	0.223587	+	0.223587i
$670$	403811.	+	1.84939e7i	0.0347529	+	1.59163i
$671$	−9.21948e6			−0.790497
$672$	3.02934e6	−	4.66487e6i	0.258776	−	0.398489i
$673$			1.57984e7i			1.34455i	0.740302	+	0.672274i	$0.234682\pi$
$673$			1.57984e7i			1.34455i	−0.740302	+	0.672274i	$0.765318\pi$
$674$	−5.12560e6	+	7.71468e6i	−0.434605	+	0.654136i
$675$	−1.53786e7	−	3.34332e7i	−1.29914	−	2.82435i
$676$	1.40551e7	−	5.90829e6i	1.18295	−	0.497273i
$677$	2.49220e6	+	2.49220e6i	0.208983	+	0.208983i	0.803835	−	0.594852i	$-0.202789\pi$
$677$	2.49220e6	+	2.49220e6i	0.208983	+	0.208983i	−0.594852	+	0.803835i	$0.702789\pi$
$678$	−2.34101e6	−	1.16100e7i	−0.195582	−	0.969968i
$679$		−	2.84761e6i		−	0.237031i
$680$	4.25641e6	−	1.11179e7i	0.352997	−	0.922044i
$681$		−	2.38353e7i		−	1.96949i
$682$	−6.01802e6	+	1.21346e6i	−0.495442	+	0.0998997i
$683$	2.47570e6	+	2.47570e6i	0.203070	+	0.203070i	0.801314	−	0.598244i	$-0.204135\pi$
$683$	2.47570e6	+	2.47570e6i	0.203070	+	0.203070i	−0.598244	+	0.801314i	$0.704135\pi$
$684$	−6.49169e6	−	2.64918e6i	−0.530539	−	0.216507i
$685$	−1.60551e6	+	8.96861e6i	−0.130733	+	0.730296i
$686$	−4.96040e6	−	3.29567e6i	−0.402445	−	0.267382i
$687$			1.66872e7i			1.34893i
$688$	3.70891e6	−	38870.0i	0.298727	−	0.00313072i
$689$	2.25185e7			1.80714
$690$	9874.37	+	452230.i	0.000789563	+	0.0361607i
$691$	−448193.	−	448193.i	−0.0357084	−	0.0357084i	0.689027	−	0.724736i	$-0.258038\pi$
$691$	−448193.	−	448193.i	−0.0357084	−	0.0357084i	−0.724736	+	0.689027i	$0.758038\pi$
$692$	6.29545e6	+	2.56910e6i	0.499760	+	0.203946i
$693$	−4.77188e6	−	4.77188e6i	−0.377447	−	0.377447i
$694$	−2.06477e6	−	1.02400e7i	−0.162732	−	0.807054i
$695$	−6.37977e6	−	9.16196e6i	−0.501006	−	0.719493i
$696$	−7.36914e6	+	3.86316e7i	−0.576626	+	3.02287i
$697$	−1.15258e7			−0.898643
$698$	−3.55182e6	−	1.76149e7i	−0.275938	−	1.36849i
$699$	−3.23840e7	+	3.23840e7i	−2.50690	+	2.50690i
$700$	141092.	+	3.22936e6i	0.0108832	+	0.249099i
$701$	1.06992e6	+	1.06992e6i	0.0822350	+	0.0822350i	0.747028	−	0.664793i	$-0.231480\pi$
$701$	1.06992e6	+	1.06992e6i	0.0822350	+	0.0822350i	−0.664793	+	0.747028i	$0.731480\pi$
$702$	−5.10876e7	−	3.39424e7i	−3.91267	−	2.59956i
$703$			868356.i			0.0662688i
$704$	9.81875e6	−	4.24909e6i	0.746663	−	0.323120i
$705$	−2.75779e7	+	1.92034e7i	−2.08972	+	1.45514i
$706$	6.20303e6	−	9.33635e6i	0.468373	−	0.704961i
$707$	−952906.	+	952906.i	−0.0716971	+	0.0716971i
$708$	−1.89496e7	+	7.96578e6i	−1.42075	+	0.597235i
$709$	7.74192e6	−	7.74192e6i	0.578406	−	0.578406i	−0.356058	−	0.934464i	$-0.615879\pi$
$709$	7.74192e6	−	7.74192e6i	0.578406	−	0.578406i	0.934464	+	0.356058i	$0.115879\pi$
$710$	4.41704e6	+	4.22827e6i	0.328840	+	0.314787i
$711$		−	5.52600e7i		−	4.09956i
$712$	1.44017e7	+	2.74718e6i	1.06467	+	0.203089i
$713$	160057.			0.0117910
$714$	−1.26310e6	−	6.26419e6i	−0.0927237	−	0.459854i
$715$	1.65421e7	+	2.96127e6i	1.21011	+	0.216627i
$716$	−1.91603e6	+	4.69514e6i	−0.139675	+	0.342267i
$717$	1.68999e7	−	1.68999e7i	1.22768	−	1.22768i
$718$	8.10935e6	−	1.22056e7i	0.587050	−	0.883585i
$719$	9.82491e6			0.708771			0.354386	−	0.935099i	$-0.384690\pi$
$719$	9.82491e6			0.708771			0.354386	+	0.935099i	$0.384690\pi$
$720$	2.98172e7	−	2.12301e7i	2.14356	−	1.52623i
$721$	1.37105e6			0.0982237
$722$	−7.38373e6	+	1.11135e7i	−0.527148	+	0.793425i
$723$	7.73688e6	−	7.73688e6i	0.550453	−	0.550453i
$724$	1.58045e6	+	644963.i	0.112056	+	0.0457287i
$725$	−9.55107e6	−	2.07641e7i	−0.674849	−	1.46713i
$726$	1.80853e6	+	8.96920e6i	0.127345	+	0.631557i
$727$	2.32735e7			1.63315			0.816573	−	0.577242i	$-0.195871\pi$
$727$	2.32735e7			1.63315			0.816573	+	0.577242i	$0.195871\pi$
$728$	3.02826e6	+	4.45589e6i	0.211770	+	0.311606i
$729$			3.93231e7i			2.74050i
$730$	−8.69336e6	+	9.08147e6i	−0.603782	+	0.630738i
$731$	3.01321e6	−	3.01321e6i	0.208562	−	0.208562i
$732$	−1.04018e7	−	2.47446e7i	−0.717513	−	1.70688i
$733$	1.79665e6	−	1.79665e6i	0.123510	−	0.123510i	−0.642650	−	0.766160i	$-0.722165\pi$
$733$	1.79665e6	−	1.79665e6i	0.123510	−	0.123510i	0.766160	+	0.642650i	$0.222165\pi$
$734$	−5.41858e6	+	8.15565e6i	−0.371232	+	0.558751i
$735$	−1.49572e7	−	2.14800e7i	−1.02125	−	1.46661i
$736$	−272836.	+	57995.9i	−0.0185655	+	0.00394642i
$737$			1.90991e7i			1.29522i
$738$	−2.95166e7	−	1.96107e7i	−1.99492	−	1.32542i
$739$	1.19099e7	+	1.19099e7i	0.802228	+	0.802228i	0.983443	−	0.181215i	$-0.0580031\pi$
$739$	1.19099e7	+	1.19099e7i	0.802228	+	0.802228i	−0.181215	+	0.983443i	$0.558003\pi$
$740$	−3.82969e6	−	2.42562e6i	−0.257089	−	0.162833i
$741$	6.62708e6	−	6.62708e6i	0.443381	−	0.443381i
$742$	883955.	+	4.38388e6i	0.0589414	+	0.292314i
$743$	1.11616e7			0.741742			0.370871	−	0.928684i	$-0.379059\pi$
$743$	1.11616e7			0.741742			0.370871	+	0.928684i	$0.379059\pi$
$744$	−1.00466e7	−	1.47830e7i	−0.665408	−	0.979105i
$745$	−1.74897e6	−	2.51170e6i	−0.115450	−	0.165797i
$746$	−639767.	−	3.17286e6i	−0.0420896	−	0.208739i
$747$	9.13083e6	+	9.13083e6i	0.598700	+	0.598700i
$748$	4.64419e6	−	1.13804e7i	0.303498	−	0.743708i
$749$	−2.93228e6	−	2.93228e6i	−0.190985	−	0.190985i
$750$	−9.58032e6	+	2.77482e7i	−0.621909	+	1.80128i
$751$	−2.48590e7			−1.60836			−0.804179	−	0.594387i	$-0.797395\pi$
$751$	−2.48590e7			−1.60836			−0.804179	+	0.594387i	$0.797395\pi$
$752$	−1.48058e7	−	1.44987e7i	−0.954744	−	0.934940i
$753$			2.96521e7i			1.90576i
$754$	−3.17286e7	−	2.10804e7i	−2.03247	−	1.35036i
$755$	1.02733e7	+	1.83906e6i	0.655906	+	0.117417i
$756$	4.60245e6	−	1.12781e7i	0.292877	−	0.717680i
$757$	−3.41514e6	−	3.41514e6i	−0.216605	−	0.216605i	0.590461	−	0.807066i	$-0.298946\pi$
$757$	−3.41514e6	−	3.41514e6i	−0.216605	−	0.216605i	−0.807066	+	0.590461i	$0.798946\pi$
$758$	−560893.	+	113097.i	−0.0354574	+	0.00714955i
$759$			467030.i			0.0294266i
$760$	1.41318e6	+	3.16645e6i	0.0887489	+	0.198856i
$761$		−	2.60605e7i		−	1.63125i	−0.578580	−	0.815626i	$-0.696393\pi$
$761$		−	2.60605e7i		−	1.63125i	0.578580	−	0.815626i	$-0.303607\pi$
$762$	4.74974e6	+	2.35558e7i	0.296335	+	1.46964i
$763$	−1.07944e6	−	1.07944e6i	−0.0671254	−	0.0671254i
$764$	279884.	+	665812.i	0.0173478	+	0.0412684i
$765$	7.41018e6	−	4.13943e7i	0.457799	−	2.55733i
$766$	2.51947e6	−	3.79213e6i	0.155145	−	0.233513i
$767$		−	1.99103e7i		−	1.22205i
$768$	2.24822e7	+	2.15590e7i	1.37542	+	1.31894i
$769$	−7.47869e6			−0.456047			−0.228023	−	0.973656i	$-0.573226\pi$
$769$	−7.47869e6			−0.456047			−0.228023	+	0.973656i	$0.573226\pi$
$770$	72854.9	+	3.33664e6i	0.00442825	+	0.202807i
$771$	4.15586e7	+	4.15586e7i	2.51782	+	2.51782i
$772$	−2.49925e7	+	1.05060e7i	−1.50927	+	0.634445i
$773$	−1.01856e7	−	1.01856e7i	−0.613111	−	0.613111i	0.330644	−	0.943756i	$-0.392734\pi$
$773$	−1.01856e7	−	1.01856e7i	−0.613111	−	0.613111i	−0.943756	+	0.330644i	$0.892734\pi$
$774$	1.28435e7	−	2.58973e6i	0.770602	−	0.155382i
$775$	9.74219e6	+	3.60346e6i	0.582643	+	0.215509i
$776$	1.56644e7	+	2.98805e6i	0.933811	+	0.178128i
$777$	−2.43334e6			−0.144594
$778$	1.67818e7	−	3.38384e6i	0.994008	−	0.200429i
$779$	2.37381e6	−	2.37381e6i	0.140153	−	0.140153i
$780$	1.07155e7	+	4.77390e7i	0.630633	+	2.80955i
$781$	4.46412e6	+	4.46412e6i	0.261883	+	0.261883i
$782$	−177339.	+	266917.i	−0.0103702	+	0.0156085i
$783$			8.61278e7i			5.02041i
$784$	1.12928e7	−	1.15320e7i	0.656161	−	0.670060i
$785$	−3.85883e6	−	5.54165e6i	−0.223502	−	0.320971i
$786$	2.72290e7	+	1.80908e7i	1.57208	+	1.04449i
$787$	−3.32524e6	+	3.32524e6i	−0.191375	+	0.191375i	−0.796290	−	0.604915i	$-0.793207\pi$
$787$	−3.32524e6	+	3.32524e6i	−0.191375	+	0.191375i	0.604915	+	0.796290i	$0.293207\pi$
$788$	2.76616e6	−	6.77836e6i	0.158695	−	0.388874i
$789$	6.05437e6	−	6.05437e6i	0.346239	−	0.346239i
$790$	−1.88979e7	+	1.97416e7i	−1.07732	+	1.12542i
$791$			2.27825e6i			0.129467i
$792$	3.12568e7	−	2.12424e7i	1.77065	−	1.20334i
$793$	2.59990e7			1.46816
$794$	5.71605e6	−	1.15257e6i	0.321769	−	0.0648807i
$795$	−7.15666e6	+	3.99781e7i	−0.401599	+	2.24339i
$796$	3.14217e7	−	1.32086e7i	1.75771	−	0.738881i
$797$	−1.52746e7	+	1.52746e7i	−0.851772	+	0.851772i	−0.990351	−	0.138580i	$-0.955746\pi$
$797$	−1.52746e7	+	1.52746e7i	−0.851772	+	0.851772i	0.138580	+	0.990351i	$0.455746\pi$
$798$	1.55030e6	+	1.03001e6i	0.0861803	+	0.0572578i
$799$	−2.38076e7			−1.31932
$800$	−1.79124e7	−	2.61249e6i	−0.989531	−	0.144321i
$801$	5.17894e7			2.85207
$802$	5.93921e6	+	3.94599e6i	0.326056	+	0.216630i
$803$	−9.17827e6	+	9.17827e6i	−0.502310	+	0.502310i
$804$	−5.12610e7	+	2.15484e7i	−2.79671	+	1.17564i
$805$	15332.7	−	85650.5i	0.000833927	−	0.00465843i
$806$	1.69709e7	−	3.42197e6i	0.920168	−	0.185540i
$807$	−1.55679e7			−0.841486
$808$	−4.24193e6	−	6.24174e6i	−0.228579	−	0.336339i
$809$		−	1.30780e7i		−	0.702539i	−0.936274	−	0.351269i	$-0.885750\pi$
$809$		−	1.30780e7i		−	0.702539i	0.936274	−	0.351269i	$-0.114250\pi$
$810$	4.25182e7	−	4.44164e7i	2.27700	−	2.37865i
$811$	−7.18053e6	+	7.18053e6i	−0.383358	+	0.383358i	−0.872310	−	0.488952i	$-0.837379\pi$
$811$	−7.18053e6	+	7.18053e6i	−0.383358	+	0.383358i	0.488952	+	0.872310i	$0.337379\pi$
$812$	2.85841e6	−	7.00440e6i	0.152137	−	0.372805i
$813$	−1.27690e7	+	1.27690e7i	−0.677535	+	0.677535i
$814$	−3.89847e6	−	2.59012e6i	−0.206221	−	0.137012i
$815$	1.87021e7	+	2.68581e7i	0.986274	+	1.41638i
$816$	3.57840e7	−	375023.i	1.88133	−	0.0197166i
$817$			1.24118e6i			0.0650549i
$818$	321395.	−	483740.i	0.0167941	−	0.0252772i
$819$	1.34567e7	+	1.34567e7i	0.701019	+	0.701019i
$820$	3.83828e6	+	1.71000e7i	0.199343	+	0.888101i
$821$	−2.25985e7	+	2.25985e7i	−1.17010	+	1.17010i	−0.187911	+	0.982186i	$0.560172\pi$
$821$	−2.25985e7	+	2.25985e7i	−1.17010	+	1.17010i	−0.982186	+	0.187911i	$0.939828\pi$
$822$	−2.68479e7	+	5.41354e6i	−1.38590	+	0.279449i
$823$	1.42305e7			0.732355			0.366178	−	0.930545i	$-0.380666\pi$
$823$	1.42305e7			0.732355			0.366178	+	0.930545i	$0.380666\pi$
$824$	−1.43867e6	+	7.54202e6i	−0.0738148	+	0.386963i
$825$	−1.05145e7	+	2.84267e7i	−0.537843	+	1.45409i
$826$	3.87612e6	−	781571.i	0.197673	−	0.0398582i
$827$	−6.92671e6	−	6.92671e6i	−0.352179	−	0.352179i	0.508741	−	0.860920i	$-0.330111\pi$
$827$	−6.92671e6	−	6.92671e6i	−0.352179	−	0.352179i	−0.860920	+	0.508741i	$0.830111\pi$
$828$	−908303.	+	381820.i	−0.0460421	+	0.0193545i
$829$	−1.67826e6	−	1.67826e6i	−0.0848151	−	0.0848151i	0.663426	−	0.748242i	$-0.269102\pi$
$829$	−1.67826e6	−	1.67826e6i	−0.0848151	−	0.0848151i	−0.748242	+	0.663426i	$0.769102\pi$
$830$	−139406.	−	6.38455e6i	−0.00702401	−	0.321688i
$831$	−5.99486e6			−0.301145
$832$	−2.76890e7	+	1.19825e7i	−1.38675	+	0.600120i
$833$		−	1.85434e7i		−	0.925926i
$834$	1.85718e7	−	2.79530e7i	0.924569	−	1.39159i
$835$	846820.	−	4.73046e6i	0.0420315	−	0.234794i
$836$	1.38736e6	+	3.30037e6i	0.0686554	+	0.163323i
$837$	−2.76783e7	−	2.76783e7i	−1.36561	−	1.36561i
$838$	−3.02830e6	−	1.50186e7i	−0.148967	−	0.738785i
$839$			2.52468e7i			1.23823i	0.785300	+	0.619116i	$0.212509\pi$
$839$			2.52468e7i			1.23823i	−0.785300	+	0.619116i	$0.787491\pi$
$840$	−8.87315e6	+	3.96006e6i	−0.433890	+	0.193644i
$841$			3.29796e7i			1.60789i
$842$	2.55936e7	−	5.16062e6i	1.24409	−	0.250854i
$843$	−3.67961e7	−	3.67961e7i	−1.78333	−	1.78333i
$844$	1.41879e7	−	3.47668e7i	0.685586	−	1.68000i
$845$	−2.62177e7	−	4.69334e6i	−1.26314	−	0.226121i
$846$	−6.09697e7	−	4.05080e7i	−2.92879	−	1.94587i
$847$		−	1.76005e6i		−	0.0842976i
$848$	−2.50428e7	+	262453.i	−1.19590	+	0.0125332i
$849$	−4.28719e7			−2.04128
$850$	−1.68034e7	+	1.22539e7i	−0.797717	+	0.581739i
$851$	86286.1	+	86286.1i	0.00408430	+	0.00408430i
$852$	−6.94485e6	+	1.70180e7i	−0.327766	+	0.803175i
$853$	−1.68154e7	−	1.68154e7i	−0.791289	−	0.791289i	0.190415	−	0.981704i	$-0.439017\pi$
$853$	−1.68154e7	−	1.68154e7i	−0.791289	−	0.791289i	−0.981704	+	0.190415i	$0.939017\pi$
$854$	1.02058e6	+	5.06147e6i	0.0478854	+	0.237483i
$855$	6.99927e6	+	1.00516e7i	0.327444	+	0.470242i
$856$	1.92070e7	−	1.30532e7i	0.895933	−	0.608883i
$857$	103716.			0.00482384			0.00241192	−	0.999997i	$-0.499232\pi$
$857$	103716.			0.00482384			0.00241192	+	0.999997i	$0.499232\pi$
$858$	9.98495e6	+	4.95194e7i	0.463050	+	2.29645i
$859$	2.09672e7	−	2.09672e7i	0.969520	−	0.969520i	−0.0300286	−	0.999549i	$-0.509560\pi$
$859$	2.09672e7	−	2.09672e7i	0.969520	−	0.969520i	0.999549	+	0.0300286i	$0.00955984\pi$
$860$	−5.47395e6	−	3.46705e6i	−0.252380	−	0.159851i
$861$	6.65198e6	+	6.65198e6i	0.305804	+	0.305804i
$862$	1.80938e7	+	1.20214e7i	0.829394	+	0.551046i
$863$		−	1.28717e7i		−	0.588313i	−0.955757	−	0.294157i	$-0.904961\pi$
$863$		−	1.28717e7i		−	0.588313i	0.955757	−	0.294157i	$-0.0950388\pi$
$864$	5.72101e7	+	3.71519e7i	2.60729	+	1.69315i
$865$	−6.78769e6	−	9.74778e6i	−0.308448	−	0.442961i
$866$	−1.16094e7	+	1.74737e7i	−0.526037	+	0.791752i
$867$	−752421.	+	752421.i	−0.0339949	+	0.0339949i
$868$	1.33237e6	+	3.16955e6i	0.0600241	+	0.142790i
$869$	−1.99520e7	+	1.99520e7i	−0.896266	+	0.896266i
$870$	4.75087e7	−	4.96297e7i	2.12802	−	2.22302i
$871$		−	5.38598e7i		−	2.40558i
$872$	7.07056e6	−	4.80521e6i	0.314893	−	0.214003i
$873$	5.63302e7			2.50153
$874$	−18449.3	−	91497.6i	−0.000816963	−	0.00405164i
$875$	2.86156e6	−	4.86809e6i	0.126352	−	0.214951i
$876$	−3.49892e7	−	1.42787e7i	−1.54054	−	0.628678i
$877$	−2.36696e6	+	2.36696e6i	−0.103918	+	0.103918i	−0.757154	−	0.653236i	$-0.773411\pi$
$877$	−2.36696e6	+	2.36696e6i	−0.103918	+	0.103918i	0.653236	+	0.757154i	$0.273411\pi$
$878$	−1.67058e7	+	2.51443e7i	−0.731359	+	1.10079i
$879$	6.61471e7			2.88761
$880$	−1.84309e7	−	3.10043e6i	−0.802307	−	0.134963i
$881$	1.91249e7			0.830157			0.415079	−	0.909785i	$-0.363754\pi$
$881$	1.91249e7			0.830157			0.415079	+	0.909785i	$0.363754\pi$
$882$	3.15510e7	−	4.74882e7i	1.36566	−	2.05549i
$883$	1.44658e7	−	1.44658e7i	0.624368	−	0.624368i	−0.322277	−	0.946645i	$-0.604448\pi$
$883$	1.44658e7	−	1.44658e7i	0.624368	−	0.624368i	0.946645	+	0.322277i	$0.104448\pi$
$884$	−1.30967e7	+	3.20928e7i	−0.563677	+	1.38126i
$885$	3.53476e7	+	6.32774e6i	1.51706	+	0.271575i
$886$	−468099.	−	2.32149e6i	−0.0200333	−	0.0993533i
$887$	−3.63988e7			−1.55338			−0.776691	−	0.629882i	$-0.783103\pi$
$887$	−3.63988e7			−1.55338			−0.776691	+	0.629882i	$0.783103\pi$
$888$	2.55335e6	−	1.33855e7i	0.108662	−	0.569644i
$889$		−	4.62241e6i		−	0.196162i
$890$	−1.85017e7	−	1.77110e7i	−0.782954	−	0.749493i
$891$	4.48899e7	−	4.48899e7i	1.89432	−	1.89432i
$892$	3.63499e6	−	1.52803e6i	0.152965	−	0.0643012i
$893$	4.90335e6	−	4.90335e6i	0.205761	−	0.205761i
$894$	5.09136e6	−	7.66314e6i	0.213054	−	0.320673i
$895$	7.26987e6	−	5.06225e6i	0.303368	−	0.211245i
$896$	−3.41966e6	−	4.92010e6i	−0.142302	−	0.204740i
$897$		−	1.31703e6i		−	0.0546531i
$898$	−1.40938e7	−	9.36389e6i	−0.583228	−	0.387494i
$899$	−1.71900e7	−	1.71900e7i	−0.709376	−	0.709376i
$900$	−6.38819e7	+	2.79103e6i	−2.62888	+	0.114857i
$901$	−2.03454e7	+	2.03454e7i	−0.834937	+	0.834937i
$902$	3.57659e6	+	1.77377e7i	0.146370	+	0.725909i
$903$	−3.47809e6			−0.141945
$904$	−1.25324e7	−	2.39061e6i	−0.510051	−	0.0972944i
$905$	−1.70403e6	−	2.44715e6i	−0.0691600	−	0.0993204i
$906$	6.20105e6	+	3.07535e7i	0.250983	+	1.24473i
$907$	9.18418e6	+	9.18418e6i	0.370700	+	0.370700i	0.867732	−	0.497032i	$-0.165577\pi$
$907$	9.18418e6	+	9.18418e6i	0.370700	+	0.370700i	−0.497032	+	0.867732i	$0.665577\pi$
$908$	−2.37729e7	−	9.70143e6i	−0.956902	−	0.390500i
$909$	−1.88500e7	−	1.88500e7i	−0.756661	−	0.756661i
$910$	−205452.	−	9.40935e6i	−0.00822444	−	0.376666i
$911$	−4.55245e7			−1.81739			−0.908697	−	0.417456i	$-0.862922\pi$
$911$	−4.55245e7			−1.81739			−0.908697	+	0.417456i	$0.862922\pi$
$912$	−7.29273e6	+	7.44721e6i	−0.290338	+	0.296488i
$913$		−	6.59350e6i		−	0.261781i
$914$	2.32996e7	+	1.54801e7i	0.922534	+	0.612927i
$915$	−8.26281e6	+	4.61572e7i	−0.326268	+	1.82258i
$916$	1.66435e7	+	6.79200e6i	0.655399	+	0.267460i
$917$	−4.44661e6	−	4.44661e6i	−0.174625	−	0.174625i
$918$	7.68243e7	−	1.54907e7i	3.00879	−	0.606685i
$919$		−	4.49920e7i		−	1.75730i	−0.477466	−	0.878650i	$-0.658445\pi$
$919$		−	4.49920e7i		−	1.75730i	0.477466	−	0.878650i	$-0.341555\pi$
$920$	455065.	+	174218.i	0.0177257	+	0.00678615i
$921$		−	2.29892e7i		−	0.893048i
$922$	1.22372e6	+	6.06889e6i	0.0474082	+	0.235116i
$923$	−1.25889e7	−	1.25889e7i	−0.486387	−	0.486387i
$924$	−9.24843e6	+	3.88772e6i	−0.356359	+	0.149801i
$925$	3.30937e6	+	7.19459e6i	0.127172	+	0.276473i
$926$	3.09631e6	−	4.66033e6i	0.118663	−	0.178603i
$927$			2.71216e7i			1.03661i
$928$	3.55311e7	+	2.30737e7i	1.35437	+	0.879522i
$929$	−3.15862e7			−1.20077			−0.600383	−	0.799713i	$-0.704985\pi$
$929$	−3.15862e7			−1.20077			−0.600383	+	0.799713i	$0.704985\pi$
$930$	681612.	+	3.12167e7i	0.0258422	+	1.18353i
$931$	3.81914e6	+	3.81914e6i	0.144408	+	0.144408i
$932$	1.91183e7	+	4.54801e7i	0.720957	+	1.71507i
$933$	−2.09199e7	−	2.09199e7i	−0.786783	−	0.786783i
$934$	1.38536e6	−	279340.i	0.0519630	−	0.0104777i
$935$	−1.76212e7	+	1.22702e7i	−0.659183	+	0.459010i
$936$	−8.81445e7	+	5.99037e7i	−3.28856	+	2.23493i
$937$	6.95610e6			0.258831			0.129416	−	0.991590i	$-0.458690\pi$
$937$	6.95610e6			0.258831			0.129416	+	0.991590i	$0.458690\pi$
$938$	1.04854e7	−	2.11424e6i	0.389114	−	0.0784599i
$939$	1.11203e7	−	1.11203e7i	0.411579	−	0.411579i
$940$	7.92837e6	+	3.53219e7i	0.292661	+	1.30384i
$941$	−2.64805e7	−	2.64805e7i	−0.974883	−	0.974883i	0.0248094	−	0.999692i	$-0.492102\pi$
$941$	−2.64805e7	−	2.64805e7i	−0.974883	−	0.974883i	−0.999692	+	0.0248094i	$0.992102\pi$
$942$	1.12333e7	−	1.69075e7i	0.412457	−	0.620800i
$943$		−	471758.i		−	0.0172759i
$944$	232054.	+	2.21422e7i	0.00847540	+	0.808707i
$945$	−1.74628e7	+	1.21599e7i	−0.636114	+	0.442946i
$946$	−5.57226e6	−	3.70219e6i	−0.202443	−	0.134503i
$947$	1.34223e6	−	1.34223e6i	0.0486352	−	0.0486352i	−0.682371	−	0.731006i	$-0.739051\pi$
$947$	1.34223e6	−	1.34223e6i	0.0486352	−	0.0486352i	0.731006	+	0.682371i	$0.239051\pi$
$948$	−7.60607e7	−	3.10394e7i	−2.74878	−	1.12174i
$949$	2.58828e7	−	2.58828e7i	0.932923	−	0.932923i
$950$	936986.	−	5.98455e6i	0.0336840	−	0.215141i
$951$			6.28040e7i			2.25183i
$952$	−6.76189e6	−	1.28986e6i	−0.241811	−	0.0461264i
$953$	2.84920e6			0.101623			0.0508114	−	0.998708i	$-0.483819\pi$
$953$	2.84920e6			0.101623			0.0508114	+	0.998708i	$0.483819\pi$
$954$	−8.67201e7	+	1.74860e7i	−3.08496	+	0.622042i
$955$	222330.	−	1.24197e6i	0.00788843	−	0.0440659i
$956$	−9.97705e6	−	2.37342e7i	−0.353067	−	0.839904i
$957$	5.01587e7	−	5.01587e7i	1.77038	−	1.77038i
$958$	−1.12973e6	−	750588.i	−0.0397705	−	0.0264233i
$959$	5.26842e6			0.184984
$960$	−1.24731e7	−	5.29656e7i	−0.436815	−	1.85488i
$961$	−1.75807e7			−0.614083
$962$	1.09937e7	+	7.30418e6i	0.383007	+	0.254468i
$963$	5.80050e7	−	5.80050e7i	2.01558	−	2.01558i
$964$	−4.56756e6	−	1.08657e7i	−0.158304	−	0.376586i
$965$	4.66197e7	+	8.34560e6i	1.61158	+	0.288496i
$966$	256398.	−	51699.5i	0.00884040	−	0.00178256i
$967$	−3.30779e7			−1.13755			−0.568776	−	0.822492i	$-0.692583\pi$
$967$	−3.30779e7			−1.13755			−0.568776	+	0.822492i	$0.692583\pi$
$968$	9.68182e6	+	1.84685e6i	0.332100	+	0.0633494i
$969$			1.19751e7i			0.409703i
$970$	−2.01239e7	−	1.92638e7i	−0.686724	−	0.657376i
$971$	−1.05993e7	+	1.05993e7i	−0.360769	+	0.360769i	−0.864096	−	0.503327i	$-0.832109\pi$
$971$	−1.05993e7	+	1.05993e7i	−0.360769	+	0.360769i	0.503327	+	0.864096i	$0.332109\pi$
$972$	8.63449e7	+	3.52363e7i	2.93137	+	1.19626i
$973$	−4.56483e6	+	4.56483e6i	−0.154576	+	0.154576i
$974$	3.11602e7	+	2.07027e7i	1.05245	+	0.699246i
$975$	2.96511e7	−	8.01637e7i	0.998917	−	2.70064i
$976$	−2.89135e7	+	303019.i	−0.971575	+	0.0101823i
$977$			4.23235e7i			1.41855i	0.704931	+	0.709276i	$0.250978\pi$
$977$			4.23235e7i			1.41855i	−0.704931	+	0.709276i	$0.749022\pi$
$978$	−5.44429e7	+	8.19435e7i	−1.82010	+	2.73948i
$979$	−1.86989e7	−	1.86989e7i	−0.623533	−	0.623533i
$980$	−2.75116e7	+	6.17527e6i	−0.915063	+	0.205395i
$981$	2.13530e7	−	2.13530e7i	0.708413	−	0.708413i
$982$	3.38246e7	−	6.82031e6i	1.11932	−	0.225697i
$983$	1.63609e7			0.540035			0.270018	−	0.962855i	$-0.412970\pi$
$983$	1.63609e7			0.540035			0.270018	+	0.962855i	$0.412970\pi$
$984$	−4.35719e7	+	2.96118e7i	−1.43456	+	0.974938i
$985$	−1.04955e7	+	7.30835e6i	−0.344677	+	0.240010i
$986$	4.77127e7	−	9.62067e6i	1.56294	−	0.315147i
$987$	1.37404e7	+	1.37404e7i	0.448957	+	0.448957i
$988$	−3.91238e6	−	9.30708e6i	−0.127511	−	0.303334i
$989$	123333.	+	123333.i	0.00400948	+	0.00400948i
$990$	−6.60040e7	+	1.44119e6i	−2.14034	+	0.0467339i
$991$	3.27836e7			1.06041			0.530203	−	0.847871i	$-0.322116\pi$
$991$	3.27836e7			1.06041			0.530203	+	0.847871i	$0.322116\pi$
$992$	−1.88334e7	+	4.00336e6i	−0.607646	+	0.129165i
$993$		−	5.44187e7i		−	1.75136i
$994$	1.95662e6	−	2.94496e6i	0.0628116	−	0.0945394i
$995$	−5.86124e7	−	1.04925e7i	−1.87686	−	0.335985i
$996$	1.76966e7	−	7.43904e6i	0.565250	−	0.237612i
$997$	1.55548e7	+	1.55548e7i	0.495594	+	0.495594i	0.910063	−	0.414469i	$-0.136033\pi$
$997$	1.55548e7	+	1.55548e7i	0.495594	+	0.495594i	−0.414469	+	0.910063i	$0.636033\pi$
$998$	−1.37646e6	−	6.82640e6i	−0.0437458	−	0.216953i
$999$		−	2.98426e7i		−	0.946069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.29.12	✓	116
5.4	even	2	inner	80.6.q.a.29.47	yes	116
16.5	even	4	inner	80.6.q.a.69.47	yes	116
80.69	even	4	inner	80.6.q.a.69.12	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.12	✓	116	1.1	even	1	trivial
80.6.q.a.29.47	yes	116	5.4	even	2	inner
80.6.q.a.69.12	yes	116	80.69	even	4	inner
80.6.q.a.69.47	yes	116	16.5	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.q (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.71172 - 3.13045i) q^{2} +(-21.0051 + 21.0051i) q^{3} +(12.4006 + 29.4996i) q^{4} +(9.85062 - 55.0270i) q^{5} +(164.725 - 33.2148i) q^{6} -32.3244 q^{7} +(33.9186 - 177.813i) q^{8} -639.428i q^{9} +O(q^{10})\)	\(q+(-4.71172 - 3.13045i) q^{2} +(-21.0051 + 21.0051i) q^{3} +(12.4006 + 29.4996i) q^{4} +(9.85062 - 55.0270i) q^{5} +(164.725 - 33.2148i) q^{6} -32.3244 q^{7} +(33.9186 - 177.813i) q^{8} -639.428i q^{9} +(-218.672 + 228.435i) q^{10} +(-230.870 + 230.870i) q^{11} +(-880.117 - 359.165i) q^{12} +(651.055 - 651.055i) q^{13} +(152.304 + 101.190i) q^{14} +(948.933 + 1362.76i) q^{15} +(-716.450 + 731.626i) q^{16} +1176.45i q^{17} +(-2001.69 + 3012.81i) q^{18} +(-242.298 - 242.298i) q^{19} +(1745.43 - 391.779i) q^{20} +(678.977 - 678.977i) q^{21} +(1810.52 - 365.068i) q^{22} -48.1530 q^{23} +(3022.52 + 4447.45i) q^{24} +(-2930.93 - 1084.10i) q^{25} +(-5105.68 + 1029.50i) q^{26} +(8327.01 + 8327.01i) q^{27} +(-400.843 - 953.557i) q^{28} +(5171.60 + 5171.60i) q^{29} +(-205.062 - 9391.53i) q^{30} -3323.92 q^{31} +(5666.02 - 1204.41i) q^{32} -9698.88i q^{33} +(3682.82 - 5543.11i) q^{34} +(-318.415 + 1778.71i) q^{35} +(18862.9 - 7929.30i) q^{36} +(-1791.92 - 1791.92i) q^{37} +(383.140 + 1900.14i) q^{38} +27350.9i q^{39} +(-9450.40 - 3618.01i) q^{40} +9797.06i q^{41} +(-5324.65 + 1073.65i) q^{42} +(-2561.27 - 2561.27i) q^{43} +(-9673.48 - 3947.63i) q^{44} +(-35185.8 - 6298.76i) q^{45} +(226.884 + 150.740i) q^{46} +20236.8i q^{47} +(-318.775 - 30417.0i) q^{48} -15762.1 q^{49} +(10416.0 + 14283.1i) q^{50} +(-24711.5 - 24711.5i) q^{51} +(27279.3 + 11132.4i) q^{52} +(17293.9 + 17293.9i) q^{53} +(-13167.3 - 65301.8i) q^{54} +(10429.8 + 14978.3i) q^{55} +(-1096.40 + 5747.71i) q^{56} +10179.0 q^{57} +(-8177.71 - 40556.5i) q^{58} +(15290.8 - 15290.8i) q^{59} +(-28433.5 + 44892.2i) q^{60} +(19966.9 + 19966.9i) q^{61} +(15661.4 + 10405.4i) q^{62} +20669.1i q^{63} +(-30467.1 - 12062.3i) q^{64} +(-29412.3 - 42238.8i) q^{65} +(-30361.8 + 45698.4i) q^{66} +(41363.5 - 41363.5i) q^{67} +(-34704.8 + 14588.7i) q^{68} +(1011.46 - 1011.46i) q^{69} +(7068.45 - 7384.02i) q^{70} -19336.1i q^{71} +(-113699. - 21688.5i) q^{72} +39755.2 q^{73} +(2833.51 + 14052.5i) q^{74} +(84336.1 - 38792.9i) q^{75} +(4143.05 - 10152.3i) q^{76} +(7462.73 - 7462.73i) q^{77} +(85620.6 - 128870. i) q^{78} +86421.1 q^{79} +(33201.7 + 46631.0i) q^{80} -194438. q^{81} +(30669.2 - 46161.0i) q^{82} +(-14279.7 + 14279.7i) q^{83} +(28449.3 + 11609.8i) q^{84} +(64736.5 + 11588.8i) q^{85} +(4050.07 + 20085.9i) q^{86} -217260. q^{87} +(33220.9 + 48882.4i) q^{88} +80993.3i q^{89} +(146068. + 139825. i) q^{90} +(-21045.0 + 21045.0i) q^{91} +(-597.127 - 1420.49i) q^{92} +(69819.3 - 69819.3i) q^{93} +(63350.3 - 95350.3i) q^{94} +(-15719.7 + 10946.1i) q^{95} +(-93716.7 + 144314. i) q^{96} +88094.6i q^{97} +(74266.8 + 49342.5i) q^{98} +(147625. + 147625. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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