LMFDB - Embedded newform 80.6.l.a.61.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(21,80)]

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, 1, 0]))

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

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.17
Character	$\chi$	$=$	80.61
Dual form			80.6.l.a.21.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86060 + 5.34211i) q^{2} +(-6.56300 - 6.56300i) q^{3} +(-25.0763 - 19.8791i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(47.2714 - 22.8492i) q^{6} -42.0449i q^{7} +(152.853 - 96.9737i) q^{8} -156.854i q^{9} +O(q^{10})$	\(q+(-1.86060 + 5.34211i) q^{2} +(-6.56300 - 6.56300i) q^{3} +(-25.0763 - 19.8791i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(47.2714 - 22.8492i) q^{6} -42.0449i q^{7} +(152.853 - 96.9737i) q^{8} -156.854i q^{9} +(-61.5451 - 127.327i) q^{10} +(-158.224 + 158.224i) q^{11} +(34.1098 + 295.042i) q^{12} +(429.302 + 429.302i) q^{13} +(224.608 + 78.2286i) q^{14} +232.037 q^{15} +(233.646 + 996.988i) q^{16} +204.434 q^{17} +(837.932 + 291.842i) q^{18} +(1004.23 + 1004.23i) q^{19} +(794.707 - 91.8760i) q^{20} +(-275.940 + 275.940i) q^{21} +(-550.858 - 1139.64i) q^{22} +2077.49i q^{23} +(-1639.61 - 366.737i) q^{24} -625.000i q^{25} +(-3092.14 + 1494.62i) q^{26} +(-2624.24 + 2624.24i) q^{27} +(-835.812 + 1054.33i) q^{28} +(4690.38 + 4690.38i) q^{29} +(-431.728 + 1239.57i) q^{30} -1806.19 q^{31} +(-5760.75 - 606.829i) q^{32} +2076.84 q^{33} +(-380.369 + 1092.11i) q^{34} +(743.255 + 743.255i) q^{35} +(-3118.11 + 3933.33i) q^{36} +(7482.02 - 7482.02i) q^{37} +(-7233.15 + 3496.23i) q^{38} -5635.02i q^{39} +(-987.818 + 4416.36i) q^{40} +12876.9i q^{41} +(-960.691 - 1987.52i) q^{42} +(9285.39 - 9285.39i) q^{43} +(7113.01 - 822.335i) q^{44} +(2772.81 + 2772.81i) q^{45} +(-11098.2 - 3865.37i) q^{46} +5125.48 q^{47} +(5009.81 - 8076.66i) q^{48} +15039.2 q^{49} +(3338.82 + 1162.87i) q^{50} +(-1341.70 - 1341.70i) q^{51} +(-2231.21 - 19299.4i) q^{52} +(13272.8 - 13272.8i) q^{53} +(-9136.34 - 18901.7i) q^{54} -5594.05i q^{55} +(-4077.25 - 6426.69i) q^{56} -13181.5i q^{57} +(-33783.4 + 16329.6i) q^{58} +(6865.06 - 6865.06i) q^{59} +(-5818.64 - 4612.68i) q^{60} +(27935.8 + 27935.8i) q^{61} +(3360.59 - 9648.85i) q^{62} -6594.91 q^{63} +(13960.2 - 29645.5i) q^{64} -15178.1 q^{65} +(-3864.17 + 11094.7i) q^{66} +(-22450.3 - 22450.3i) q^{67} +(-5126.45 - 4063.95i) q^{68} +(13634.5 - 13634.5i) q^{69} +(-5353.45 + 2587.65i) q^{70} +31718.5i q^{71} +(-15210.7 - 23975.6i) q^{72} +6119.87i q^{73} +(26048.8 + 53890.8i) q^{74} +(-4101.88 + 4101.88i) q^{75} +(-5219.26 - 45145.4i) q^{76} +(6652.49 + 6652.49i) q^{77} +(30102.9 + 10484.5i) q^{78} -45826.3 q^{79} +(-21754.8 - 13494.1i) q^{80} -3669.72 q^{81} +(-68790.1 - 23958.8i) q^{82} +(-11401.6 - 11401.6i) q^{83} +(12405.0 - 1434.14i) q^{84} +(-3613.91 + 3613.91i) q^{85} +(32327.2 + 66880.0i) q^{86} -61565.9i q^{87} +(-8841.45 + 39528.5i) q^{88} +105399. i q^{89} +(-19971.8 + 9653.59i) q^{90} +(18049.9 - 18049.9i) q^{91} +(41298.5 - 52095.8i) q^{92} +(11854.0 + 11854.0i) q^{93} +(-9536.46 + 27380.9i) q^{94} -35504.8 q^{95} +(33825.2 + 41790.4i) q^{96} -49125.2 q^{97} +(-27982.0 + 80341.3i) q^{98} +(24818.0 + 24818.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) $ 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * 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 $

$2$	−1.86060	+	5.34211i	−0.328910	+	0.944361i
$2$	−1.86060	+	5.34211i	−0.328910	+	0.944361i
$3$	−6.56300	−	6.56300i	−0.421017	−	0.421017i	0.464537	−	0.885554i	$-0.346221\pi$
$3$	−6.56300	−	6.56300i	−0.421017	−	0.421017i	−0.885554	+	0.464537i	$0.846221\pi$
$4$	−25.0763	−	19.8791i	−0.783636	−	0.621220i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$5$	−17.6777	+	17.6777i	−0.316228	+	0.316228i
$6$	47.2714	−	22.8492i	0.536069	−	0.259115i
$7$		−	42.0449i		−	0.324316i	−0.986765	−	0.162158i	$-0.948155\pi$
$7$		−	42.0449i		−	0.324316i	0.986765	−	0.162158i	$-0.0518454\pi$
$8$	152.853	−	96.9737i	0.844402	−	0.535709i
$9$		−	156.854i		−	0.645490i
$10$	−61.5451	−	127.327i	−0.194623	−	0.402644i
$11$	−158.224	+	158.224i	−0.394266	+	0.394266i	−0.876205	−	0.481939i	$-0.839933\pi$
$11$	−158.224	+	158.224i	−0.394266	+	0.394266i	0.481939	+	0.876205i	$0.339933\pi$
$12$	34.1098	+	295.042i	0.0683796	+	0.591468i
$13$	429.302	+	429.302i	0.704538	+	0.704538i	0.965381	−	0.260843i	$-0.0840005\pi$
$13$	429.302	+	429.302i	0.704538	+	0.704538i	−0.260843	+	0.965381i	$0.584000\pi$
$14$	224.608	+	78.2286i	0.306271	+	0.106671i
$15$	232.037			0.266274
$16$	233.646	+	996.988i	0.228170	+	0.973621i
$17$	204.434			0.171566			0.0857828	−	0.996314i	$-0.472661\pi$
$17$	204.434			0.171566			0.0857828	+	0.996314i	$0.472661\pi$
$18$	837.932	+	291.842i	0.609576	+	0.212308i
$19$	1004.23	+	1004.23i	0.638186	+	0.638186i	0.950108	−	0.311922i	$-0.100973\pi$
$19$	1004.23	+	1004.23i	0.638186	+	0.638186i	−0.311922	+	0.950108i	$0.600973\pi$
$20$	794.707	−	91.8760i	0.444255	−	0.0513603i
$21$	−275.940	+	275.940i	−0.136542	+	0.136542i
$22$	−550.858	−	1139.64i	−0.242652	−	0.502008i
$23$			2077.49i			0.818877i	0.912338	+	0.409438i	$0.134275\pi$
$23$			2077.49i			0.818877i	−0.912338	+	0.409438i	$0.865725\pi$
$24$	−1639.61	−	366.737i	−0.581050	−	0.129965i
$25$		−	625.000i		−	0.200000i
$26$	−3092.14	+	1494.62i	−0.897069	+	0.433609i
$27$	−2624.24	+	2624.24i	−0.692779	+	0.692779i
$28$	−835.812	+	1054.33i	−0.201471	+	0.254145i
$29$	4690.38	+	4690.38i	1.03565	+	1.03565i	0.999341	+	0.0363085i	$0.0115599\pi$
$29$	4690.38	+	4690.38i	1.03565	+	1.03565i	0.0363085	+	0.999341i	$0.488440\pi$
$30$	−431.728	+	1239.57i	−0.0875804	+	0.251459i
$31$	−1806.19			−0.337566			−0.168783	−	0.985653i	$-0.553984\pi$
$31$	−1806.19			−0.337566			−0.168783	+	0.985653i	$0.553984\pi$
$32$	−5760.75	−	606.829i	−0.994498	−	0.104759i
$33$	2076.84			0.331986
$34$	−380.369	+	1092.11i	−0.0564297	+	0.162020i
$35$	743.255	+	743.255i	0.102558	+	0.102558i
$36$	−3118.11	+	3933.33i	−0.400992	+	0.505829i
$37$	7482.02	−	7482.02i	0.898492	−	0.898492i	−0.0968105	−	0.995303i	$-0.530864\pi$
$37$	7482.02	−	7482.02i	0.898492	−	0.898492i	0.995303	+	0.0968105i	$0.0308641\pi$
$38$	−7233.15	+	3496.23i	−0.812584	+	0.392772i
$39$		−	5635.02i		−	0.593245i
$40$	−987.818	+	4416.36i	−0.0976173	+	0.436430i
$41$			12876.9i			1.19634i	0.801371	+	0.598168i	$0.204104\pi$
$41$			12876.9i			1.19634i	−0.801371	+	0.598168i	$0.795896\pi$
$42$	−960.691	−	1987.52i	−0.0840350	−	0.173855i
$43$	9285.39	−	9285.39i	0.765824	−	0.765824i	−0.211544	−	0.977368i	$-0.567849\pi$
$43$	9285.39	−	9285.39i	0.765824	−	0.765824i	0.977368	+	0.211544i	$0.0678492\pi$
$44$	7113.01	−	822.335i	0.553888	−	0.0640349i
$45$	2772.81	+	2772.81i	0.204122	+	0.204122i
$46$	−11098.2	−	3865.37i	−0.773315	−	0.269337i
$47$	5125.48			0.338446			0.169223	−	0.985578i	$-0.445874\pi$
$47$	5125.48			0.338446			0.169223	+	0.985578i	$0.445874\pi$
$48$	5009.81	−	8076.66i	0.313847	−	0.505974i
$49$	15039.2			0.894819
$50$	3338.82	+	1162.87i	0.188872	+	0.0657821i
$51$	−1341.70	−	1341.70i	−0.0722320	−	0.0722320i
$52$	−2231.21	−	19299.4i	−0.114428	−	0.989775i
$53$	13272.8	−	13272.8i	0.649040	−	0.649040i	−0.303721	−	0.952761i	$-0.598229\pi$
$53$	13272.8	−	13272.8i	0.649040	−	0.649040i	0.952761	+	0.303721i	$0.0982290\pi$
$54$	−9136.34	−	18901.7i	−0.426371	−	0.882095i
$55$		−	5594.05i		−	0.249356i
$56$	−4077.25	−	6426.69i	−0.173739	−	0.273853i
$57$		−	13181.5i		−	0.537374i
$58$	−33783.4	+	16329.6i	−1.31866	+	0.637391i
$59$	6865.06	−	6865.06i	0.256752	−	0.256752i	−0.566980	−	0.823732i	$-0.691888\pi$
$59$	6865.06	−	6865.06i	0.256752	−	0.256752i	0.823732	+	0.566980i	$0.191888\pi$
$60$	−5818.64	−	4612.68i	−0.208662	−	0.165415i
$61$	27935.8	+	27935.8i	0.961251	+	0.961251i	0.999277	−	0.0380253i	$-0.0121067\pi$
$61$	27935.8	+	27935.8i	0.961251	+	0.961251i	−0.0380253	+	0.999277i	$0.512107\pi$
$62$	3360.59	−	9648.85i	0.111029	−	0.318784i
$63$	−6594.91			−0.209342
$64$	13960.2	−	29645.5i	0.426031	−	0.904709i
$65$	−15178.1			−0.445589
$66$	−3864.17	+	11094.7i	−0.109193	+	0.313514i
$67$	−22450.3	−	22450.3i	−0.610993	−	0.610993i	0.332212	−	0.943205i	$-0.392205\pi$
$67$	−22450.3	−	22450.3i	−0.610993	−	0.610993i	−0.943205	+	0.332212i	$0.892205\pi$
$68$	−5126.45	−	4063.95i	−0.134445	−	0.106580i
$69$	13634.5	−	13634.5i	0.344761	−	0.344761i
$70$	−5353.45	+	2587.65i	−0.130584	+	0.0631191i
$71$			31718.5i			0.746736i	0.927683	+	0.373368i	$0.121797\pi$
$71$			31718.5i			0.746736i	−0.927683	+	0.373368i	$0.878203\pi$
$72$	−15210.7	−	23975.6i	−0.345795	−	0.545053i
$73$			6119.87i			0.134411i	0.997739	+	0.0672056i	$0.0214083\pi$
$73$			6119.87i			0.134411i	−0.997739	+	0.0672056i	$0.978592\pi$
$74$	26048.8	+	53890.8i	0.552978	+	1.14402i
$75$	−4101.88	+	4101.88i	−0.0842033	+	0.0842033i
$76$	−5219.26	−	45145.4i	−0.103651	−	0.896560i
$77$	6652.49	+	6652.49i	0.127867	+	0.127867i
$78$	30102.9	+	10484.5i	0.560237	+	0.195124i
$79$	−45826.3			−0.826128			−0.413064	−	0.910702i	$-0.635541\pi$
$79$	−45826.3			−0.826128			−0.413064	+	0.910702i	$0.635541\pi$
$80$	−21754.8	−	13494.1i	−0.380040	−	0.235732i
$81$	−3669.72			−0.0621471
$82$	−68790.1	−	23958.8i	−1.12977	−	0.393487i
$83$	−11401.6	−	11401.6i	−0.181665	−	0.181665i	0.610416	−	0.792081i	$-0.291002\pi$
$83$	−11401.6	−	11401.6i	−0.181665	−	0.181665i	−0.792081	+	0.610416i	$0.791002\pi$
$84$	12405.0	−	1434.14i	0.191822	−	0.0221766i
$85$	−3613.91	+	3613.91i	−0.0542538	+	0.0542538i
$86$	32327.2	+	66880.0i	0.471327	+	0.975102i
$87$		−	61565.9i		−	0.872051i
$88$	−8841.45	+	39528.5i	−0.121707	+	0.544132i
$89$			105399.i			1.41046i	0.708979	+	0.705230i	$0.249156\pi$
$89$			105399.i			1.41046i	−0.708979	+	0.705230i	$0.750844\pi$
$90$	−19971.8	+	9653.59i	−0.259903	+	0.125627i
$91$	18049.9	−	18049.9i	0.228493	−	0.228493i
$92$	41298.5	−	52095.8i	0.508703	−	0.641701i
$93$	11854.0	+	11854.0i	0.142121	+	0.142121i
$94$	−9536.46	+	27380.9i	−0.111319	+	0.319616i
$95$	−35504.8			−0.403624
$96$	33825.2	+	41790.4i	0.374595	+	0.462805i
$97$	−49125.2			−0.530121			−0.265060	−	0.964232i	$-0.585392\pi$
$97$	−49125.2			−0.530121			−0.265060	+	0.964232i	$0.585392\pi$
$98$	−27982.0	+	80341.3i	−0.294315	+	0.845033i
$99$	24818.0	+	24818.0i	0.254495	+	0.254495i
$100$	−12424.4	+	15672.7i	−0.124244	+	0.156727i
$101$	14743.7	−	14743.7i	0.143814	−	0.143814i	−0.631534	−	0.775348i	$-0.717574\pi$
$101$	14743.7	−	14743.7i	0.143814	−	0.143814i	0.775348	+	0.631534i	$0.217574\pi$
$102$	9663.87	−	4671.15i	0.0919710	−	0.0444552i
$103$		−	56155.2i		−	0.521551i	−0.965399	−	0.260776i	$-0.916022\pi$
$103$		−	56155.2i		−	0.521551i	0.965399	−	0.260776i	$-0.0839783\pi$
$104$	107251.	+	23989.2i	0.972342	+	0.217486i
$105$		−	9755.97i		−	0.0863569i
$106$	46209.3	+	95599.9i	0.399452	+	0.826404i
$107$	−83704.1	+	83704.1i	−0.706785	+	0.706785i	−0.965858	−	0.259073i	$-0.916583\pi$
$107$	−83704.1	+	83704.1i	−0.706785	+	0.706785i	0.259073	+	0.965858i	$0.416583\pi$
$108$	117974.	−	13639.0i	0.973255	−	0.112518i
$109$	58434.0	+	58434.0i	0.471085	+	0.471085i	0.902266	−	0.431181i	$-0.141903\pi$
$109$	58434.0	+	58434.0i	0.471085	+	0.471085i	−0.431181	+	0.902266i	$0.641903\pi$
$110$	29884.1	+	10408.3i	0.235482	+	0.0820158i
$111$	−98209.0			−0.756561
$112$	41918.2	−	9823.63i	0.315761	−	0.0739992i
$113$	162812.			1.19947			0.599737	−	0.800197i	$-0.295272\pi$
$113$	162812.			1.19947			0.599737	+	0.800197i	$0.295272\pi$
$114$	70416.9	+	24525.4i	0.507475	+	0.176748i
$115$	−36725.1	−	36725.1i	−0.258952	−	0.258952i
$116$	−24377.3	−	210858.i	−0.168205	−	1.45494i
$117$	67337.8	−	67337.8i	0.454772	−	0.454772i
$118$	23900.8	+	49447.1i	0.158018	+	0.326915i
$119$		−	8595.39i		−	0.0556414i
$120$	35467.6	−	22501.5i	0.224843	−	0.142646i
$121$			110982.i			0.689108i
$122$	−201214.	+	97259.0i	−1.22393	+	0.591603i
$123$	84511.4	−	84511.4i	0.503677	−	0.503677i
$124$	45292.6	+	35905.3i	0.264529	+	0.209703i
$125$	11048.5	+	11048.5i	0.0632456	+	0.0632456i
$126$	12270.5	−	35230.7i	0.0688549	−	0.197695i
$127$	−291766.			−1.60519			−0.802594	−	0.596525i	$-0.796547\pi$
$127$	−291766.			−1.60519			−0.802594	+	0.596525i	$0.796547\pi$
$128$	132395.	+	129735.i	0.714246	+	0.699895i
$129$	−121880.			−0.644850
$130$	28240.4	−	81083.2i	0.146559	−	0.420797i
$131$	−15696.3	−	15696.3i	−0.0799134	−	0.0799134i	0.666020	−	0.745934i	$-0.267996\pi$
$131$	−15696.3	−	15696.3i	−0.0799134	−	0.0799134i	−0.745934	+	0.666020i	$0.767996\pi$
$132$	−52079.7	−	41285.7i	−0.260156	−	0.206236i
$133$	42222.5	−	42222.5i	0.206974	−	0.206974i
$134$	161703.	−	78161.2i	0.777959	−	0.376036i
$135$		−	92781.0i		−	0.438152i
$136$	31248.4	−	19824.7i	0.144870	−	0.0919093i
$137$			105185.i			0.478800i	0.970921	+	0.239400i	$0.0769507\pi$
$137$			105185.i			0.478800i	−0.970921	+	0.239400i	$0.923049\pi$
$138$	47468.9	+	98205.7i	0.212183	+	0.438974i
$139$	−310110.	+	310110.i	−1.36138	+	1.36138i	−0.489210	+	0.872166i	$0.662715\pi$
$139$	−310110.	+	310110.i	−1.36138	+	1.36138i	−0.872166	+	0.489210i	$0.837285\pi$
$140$	−3862.91	−	33413.3i	−0.0166569	−	0.144079i
$141$	−33638.5	−	33638.5i	−0.142492	−	0.142492i
$142$	−169444.	−	59015.4i	−0.705188	−	0.245609i
$143$	−135852.			−0.555552
$144$	156382.	−	36648.4i	0.628463	−	0.147282i
$145$	−165830.			−0.655002
$146$	−32693.0	−	11386.6i	−0.126933	−	0.0442092i
$147$	−98702.5	−	98702.5i	−0.376734	−	0.376734i
$148$	−336357.	+	38886.2i	−1.26225	+	0.145929i
$149$	84960.2	−	84960.2i	0.313509	−	0.313509i	−0.532758	−	0.846267i	$-0.678845\pi$
$149$	84960.2	−	84960.2i	0.313509	−	0.313509i	0.846267	+	0.532758i	$0.178845\pi$
$150$	−14280.7	−	29544.6i	−0.0518230	−	0.107214i
$151$		−	534460.i		−	1.90754i	−0.300543	−	0.953768i	$-0.597168\pi$
$151$		−	534460.i		−	1.90754i	0.300543	−	0.953768i	$-0.402832\pi$
$152$	250883.	+	56115.6i	0.880768	+	0.197004i
$153$		−	32066.3i		−	0.110744i
$154$	−47916.0	+	23160.8i	−0.162809	+	0.0786957i
$155$	31929.2	−	31929.2i	0.106748	−	0.106748i
$156$	−112019.	+	141306.i	−0.368536	+	0.464888i
$157$	−192703.	−	192703.i	−0.623934	−	0.623934i	0.322601	−	0.946535i	$-0.395443\pi$
$157$	−192703.	−	192703.i	−0.623934	−	0.623934i	−0.946535	+	0.322601i	$0.895443\pi$
$158$	85264.4	−	244809.i	0.271722	−	0.780163i
$159$	−174218.			−0.546513
$160$	112564.	−	91109.2i	0.347615	−	0.281360i
$161$	87347.6			0.265574
$162$	6827.88	−	19604.1i	0.0204408	−	0.0586893i
$163$	390541.	+	390541.i	1.15132	+	1.15132i	0.986288	+	0.165036i	$0.0527741\pi$
$163$	390541.	+	390541.i	1.15132	+	1.15132i	0.165036	+	0.986288i	$0.447226\pi$
$164$	255981.	−	322907.i	0.743188	−	0.937492i
$165$	−36713.8	+	36713.8i	−0.104983	+	0.104983i
$166$	82122.6	−	39694.9i	0.231309	−	0.111806i
$167$			10987.0i			0.0304850i	0.999884	+	0.0152425i	$0.00485203\pi$
$167$			10987.0i			0.0304850i	−0.999884	+	0.0152425i	$0.995148\pi$
$168$	−15419.4	+	68937.3i	−0.0421497	+	0.188444i
$169$		−	2692.45i		−	0.00725155i
$170$	−12581.9	−	26030.0i	−0.0333906	−	0.0690799i
$171$	157517.	−	157517.i	0.411943	−	0.411943i
$172$	−417429.	+	48258.9i	−1.07587	+	0.124382i
$173$	119839.	+	119839.i	0.304427	+	0.304427i	0.842743	−	0.538316i	$-0.180939\pi$
$173$	119839.	+	119839.i	0.304427	+	0.304427i	−0.538316	+	0.842743i	$0.680939\pi$
$174$	328892.	+	114549.i	0.823531	+	0.286827i
$175$	−26278.0			−0.0648631
$176$	−194716.	−	120779.i	−0.473826	−	0.293906i
$177$	−90110.8			−0.216194
$178$	−563052.	−	196105.i	−1.33198	−	0.463915i
$179$	549667.	+	549667.i	1.28223	+	1.28223i	0.939394	+	0.342838i	$0.111388\pi$
$179$	549667.	+	549667.i	1.28223	+	1.28223i	0.342838	+	0.939394i	$0.388612\pi$
$180$	−14411.1	−	124653.i	−0.0331525	−	0.286762i
$181$	361738.	−	361738.i	0.820725	−	0.820725i	−0.165487	−	0.986212i	$-0.552920\pi$
$181$	361738.	−	361738.i	0.820725	−	0.820725i	0.986212	+	0.165487i	$0.0529196\pi$
$182$	62841.2	+	130009.i	0.140626	+	0.290933i
$183$		−	366686.i		−	0.809406i
$184$	201462.	+	317550.i	0.438680	+	0.691462i
$185$			264529.i			0.568256i
$186$	−85381.0	+	41269.9i	−0.180958	+	0.0874683i
$187$	−32346.3	+	32346.3i	−0.0676426	+	0.0676426i
$188$	−128528.	−	101890.i	−0.265219	−	0.210250i
$189$	110336.	+	110336.i	0.224679	+	0.224679i
$190$	66060.1	−	189670.i	0.132756	−	0.381167i
$191$	320924.			0.636529			0.318265	−	0.948002i	$-0.396900\pi$
$191$	320924.			0.636529			0.318265	+	0.948002i	$0.396900\pi$
$192$	−286184.	+	102943.i	−0.560264	+	0.201531i
$193$	−552018.			−1.06674			−0.533372	−	0.845881i	$-0.679075\pi$
$193$	−552018.			−1.06674			−0.533372	+	0.845881i	$0.679075\pi$
$194$	91402.2	−	262432.i	0.174362	−	0.500625i
$195$	99614.0	+	99614.0i	0.187600	+	0.187600i
$196$	−377129.	−	298966.i	−0.701213	−	0.555880i
$197$	643476.	−	643476.i	1.18132	−	1.18132i	0.201916	−	0.979403i	$-0.435283\pi$
$197$	643476.	−	643476.i	1.18132	−	1.18132i	0.979403	−	0.201916i	$-0.0647167\pi$
$198$	−178757.	+	86404.3i	−0.324041	+	0.156629i
$199$		−	90986.0i		−	0.162870i	−0.996679	−	0.0814352i	$-0.974050\pi$
$199$		−	90986.0i		−	0.162870i	0.996679	−	0.0814352i	$-0.0259504\pi$
$200$	−60608.6	−	95533.2i	−0.107142	−	0.168880i
$201$			294683.i			0.514476i
$202$	51330.3	+	106194.i	0.0885107	+	0.183115i
$203$	197206.	−	197206.i	0.335877	−	0.335877i
$204$	6973.20	+	60316.6i	0.0117316	+	0.101476i
$205$	−227634.	−	227634.i	−0.378315	−	0.378315i
$206$	299988.	+	104482.i	0.492533	+	0.171544i
$207$	325862.			0.528577
$208$	−327704.	+	528314.i	−0.525199	+	0.846708i
$209$	−317785.			−0.503231
$210$	52117.5	+	18151.9i	0.0815521	+	0.0284037i
$211$	442406.	+	442406.i	0.684092	+	0.684092i	0.960920	−	0.276827i	$-0.0892830\pi$
$211$	442406.	+	442406.i	0.684092	+	0.684092i	−0.276827	+	0.960920i	$0.589283\pi$
$212$	−596682.	+	68982.4i	−0.911808	+	0.105414i
$213$	208169.	−	208169.i	0.314388	−	0.314388i
$214$	−291417.	−	602896.i	−0.434991	−	0.899929i
$215$			328288.i			0.484350i
$216$	−146641.	+	655606.i	−0.213856	+	0.956112i
$217$			75940.9i			0.109478i
$218$	−420883.	+	203439.i	−0.599819	+	0.289930i
$219$	40164.7	−	40164.7i	0.0565893	−	0.0565893i
$220$	−111204.	+	140278.i	−0.154905	+	0.195404i
$221$	87763.9	+	87763.9i	0.120875	+	0.120875i
$222$	182727.	−	524643.i	0.248841	−	0.714466i
$223$	1.23616e6			1.66462			0.832308	−	0.554313i	$-0.187019\pi$
$223$	1.23616e6			1.66462			0.832308	+	0.554313i	$0.187019\pi$
$224$	−25514.0	+	242210.i	−0.0339750	+	0.322531i
$225$	−98033.8			−0.129098
$226$	−302928.	+	869761.i	−0.394519	+	1.13274i
$227$	645061.	+	645061.i	0.830876	+	0.830876i	0.987637	−	0.156760i	$-0.0501051\pi$
$227$	645061.	+	645061.i	0.830876	+	0.830876i	−0.156760	+	0.987637i	$0.550105\pi$
$228$	−262035.	+	330543.i	−0.333828	+	0.421106i
$229$	−805818.	+	805818.i	−1.01543	+	1.01543i	−0.0155463	+	0.999879i	$0.504949\pi$
$229$	−805818.	+	805818.i	−1.01543	+	1.01543i	−0.999879	+	0.0155463i	$0.995051\pi$
$230$	264520.	−	127859.i	0.329716	−	0.159372i
$231$		−	87320.6i		−	0.107668i
$232$	1.17178e6	+	262095.i	1.42931	+	0.319698i
$233$			139317.i			0.168119i	0.996461	+	0.0840593i	$0.0267885\pi$
$233$			139317.i			0.168119i	−0.996461	+	0.0840593i	$0.973211\pi$
$234$	234437.	+	485015.i	0.279890	+	0.579049i
$235$	−90606.6	+	90606.6i	−0.107026	+	0.107026i
$236$	−308622.	+	35679.7i	−0.360700	+	0.0417005i
$237$	300758.	+	300758.i	0.347814	+	0.347814i
$238$	45917.5	+	15992.6i	0.0525456	+	0.0183010i
$239$	−1.14083e6			−1.29189			−0.645944	−	0.763385i	$-0.723536\pi$
$239$	−1.14083e6			−1.29189			−0.645944	+	0.763385i	$0.723536\pi$
$240$	54214.6	+	231338.i	0.0607559	+	0.259250i
$241$	−325740.			−0.361267			−0.180633	−	0.983550i	$-0.557815\pi$
$241$	−325740.			−0.361267			−0.180633	+	0.983550i	$0.557815\pi$
$242$	−592876.	−	206492.i	−0.650767	−	0.226655i
$243$	661775.	+	661775.i	0.718944	+	0.718944i
$244$	−145191.	−	1.25587e6i	−0.156122	−	1.35042i
$245$	−265859.	+	265859.i	−0.282967	+	0.282967i
$246$	294228.	+	608711.i	0.309989	+	0.641318i
$247$			862233.i			0.899253i
$248$	−276081.	+	175153.i	−0.285041	+	0.180837i
$249$			149658.i			0.152968i
$250$	−79579.5	+	38465.7i	−0.0805288	+	0.0389245i
$251$	−190040.	+	190040.i	−0.190397	+	0.190397i	−0.795868	−	0.605470i	$-0.792985\pi$
$251$	−190040.	+	190040.i	−0.190397	+	0.190397i	0.605470	+	0.795868i	$0.292985\pi$
$252$	165376.	+	131100.i	0.164048	+	0.130048i
$253$	−328708.	−	328708.i	−0.322856	−	0.322856i
$254$	542860.	−	1.55865e6i	0.527963	−	1.51588i
$255$	47436.2			0.0456835
$256$	−939395.	+	465885.i	−0.895877	+	0.444303i
$257$	−671224.			−0.633920			−0.316960	−	0.948439i	$-0.602662\pi$
$257$	−671224.			−0.633920			−0.316960	+	0.948439i	$0.602662\pi$
$258$	226770.	−	651097.i	0.212098	−	0.608971i
$259$	−314580.	−	314580.i	−0.291395	−	0.291395i
$260$	380612.	+	301727.i	0.349180	+	0.276809i
$261$	735704.	−	735704.i	0.668501	−	0.668501i
$262$	113056.	−	54647.0i	0.101751	−	0.0491828i
$263$		−	902574.i		−	0.804625i	−0.915502	−	0.402312i	$-0.868207\pi$
$263$		−	902574.i		−	0.804625i	0.915502	−	0.402312i	$-0.131793\pi$
$264$	317452.	−	201399.i	0.280329	−	0.177848i
$265$			469263.i			0.410489i
$266$	146998.	+	304117.i	0.127382	+	0.263534i
$267$	691732.	−	691732.i	0.593827	−	0.593827i
$268$	116681.	+	1.00926e6i	0.0992346	+	0.858357i
$269$	−1.21609e6	−	1.21609e6i	−1.02467	−	1.02467i	−0.999688	−	0.0249826i	$-0.992047\pi$
$269$	−1.21609e6	−	1.21609e6i	−1.02467	−	1.02467i	−0.0249826	−	0.999688i	$-0.507953\pi$
$270$	495646.	+	172628.i	0.413773	+	0.144113i
$271$	−1.26970e6			−1.05021			−0.525107	−	0.851036i	$-0.675975\pi$
$271$	−1.26970e6			−1.05021			−0.525107	+	0.851036i	$0.675975\pi$
$272$	47765.2	+	203818.i	0.0391462	+	0.167040i
$273$	−236924.			−0.192399
$274$	−561912.	−	195708.i	−0.452160	−	0.157482i
$275$	98889.8	+	98889.8i	0.0788533	+	0.0788533i
$276$	−612946.	+	70862.7i	−0.484339	+	0.0559945i
$277$	640108.	−	640108.i	0.501249	−	0.501249i	−0.410577	−	0.911826i	$-0.634673\pi$
$277$	640108.	−	640108.i	0.501249	−	0.501249i	0.911826	+	0.410577i	$0.134673\pi$
$278$	−1.07965e6	−	2.23363e6i	−0.837860	−	1.73340i
$279$			283308.i			0.217895i
$280$	185685.	+	41532.7i	0.141541	+	0.0316588i
$281$		−	355397.i		−	0.268502i	−0.990947	−	0.134251i	$-0.957137\pi$
$281$		−	355397.i		−	0.268502i	0.990947	−	0.134251i	$-0.0428629\pi$
$282$	242289.	−	117113.i	0.181431	−	0.0876966i
$283$	1.27404e6	−	1.27404e6i	0.945624	−	0.945624i	−0.0529717	−	0.998596i	$-0.516869\pi$
$283$	1.27404e6	−	1.27404e6i	0.945624	−	0.945624i	0.998596	+	0.0529717i	$0.0168693\pi$
$284$	630534.	−	795384.i	0.463888	−	0.585169i
$285$	233018.	+	233018.i	0.169933	+	0.169933i
$286$	252765.	−	725734.i	0.182727	−	0.524641i
$287$	541409.			0.387990
$288$	−95183.6	+	903596.i	−0.0676209	+	0.641938i
$289$	−1.37806e6			−0.970565
$290$	308543.	−	885882.i	0.215437	−	0.618558i
$291$	322409.	+	322409.i	0.223190	+	0.223190i
$292$	121657.	−	153464.i	0.0834989	−	0.105329i
$293$	665933.	−	665933.i	0.453170	−	0.453170i	−0.443235	−	0.896405i	$-0.646169\pi$
$293$	665933.	−	665933.i	0.453170	−	0.453170i	0.896405	+	0.443235i	$0.146169\pi$
$294$	710925.	−	343634.i	0.479685	−	0.231861i
$295$			242717.i			0.162384i
$296$	418091.	−	1.86921e6i	0.277358	−	1.24002i
$297$		−	830435.i		−	0.546279i
$298$	295790.	+	611944.i	0.192949	+	0.399182i
$299$	−891869.	+	891869.i	−0.576930	+	0.576930i
$300$	184401.	−	21318.6i	0.118294	−	0.0136759i
$301$	−390403.	−	390403.i	−0.248369	−	0.248369i
$302$	2.85515e6	+	994415.i	1.80140	+	0.627409i
$303$	−193526.			−0.121097
$304$	−766568.	+	1.23584e6i	−0.475737	+	0.766967i
$305$	−987681.			−0.607949
$306$	171302.	+	59662.4i	0.104582	+	0.0364248i
$307$	−1.13156e6	−	1.13156e6i	−0.685220	−	0.685220i	0.275951	−	0.961172i	$-0.411007\pi$
$307$	−1.13156e6	−	1.13156e6i	−0.685220	−	0.685220i	−0.961172	+	0.275951i	$0.911007\pi$
$308$	−34575.0	−	299065.i	−0.0207675	−	0.179634i
$309$	−368547.	+	368547.i	−0.219582	+	0.219582i
$310$	111162.	+	229977.i	0.0656979	+	0.135919i
$311$			704918.i			0.413273i	0.978418	+	0.206637i	$0.0662518\pi$
$311$			704918.i			0.413273i	−0.978418	+	0.206637i	$0.933748\pi$
$312$	−546449.	−	861331.i	−0.317807	−	0.500937i
$313$		−	1.04625e6i		−	0.603635i	−0.953366	−	0.301818i	$-0.902407\pi$
$313$		−	1.04625e6i		−	0.603635i	0.953366	−	0.301818i	$-0.0975934\pi$
$314$	1.38798e6	−	670898.i	0.794438	−	0.384001i
$315$	116583.	−	116583.i	0.0661999	−	0.0661999i
$316$	1.14916e6	+	910984.i	0.647384	+	0.513208i
$317$	1.15885e6	+	1.15885e6i	0.647705	+	0.647705i	0.952438	−	0.304733i	$-0.0985671\pi$
$317$	1.15885e6	+	1.15885e6i	0.647705	+	0.647705i	−0.304733	+	0.952438i	$0.598567\pi$
$318$	324150.	−	930694.i	0.179754	−	0.516106i
$319$	−1.48426e6			−0.816643
$320$	277280.	+	770847.i	0.151371	+	0.420817i
$321$	1.09870e6			0.595136
$322$	−162519.	+	466621.i	−0.0873502	+	0.250798i
$323$	205298.	+	205298.i	0.109491	+	0.109491i
$324$	92023.2	+	72950.6i	0.0487007	+	0.0386070i
$325$	268314.	−	268314.i	0.140908	−	0.140908i
$326$	−2.81295e6	+	1.35967e6i	−1.46595	+	0.708583i
$327$		−	767004.i		−	0.396669i
$328$	1.24873e6	+	1.96828e6i	0.640888	+	1.01019i
$329$		−	215500.i		−	0.109763i
$330$	−127820.	−	264439.i	−0.0646119	−	0.133672i
$331$	−671715.	+	671715.i	−0.336988	+	0.336988i	−0.855233	−	0.518244i	$-0.826586\pi$
$331$	−671715.	+	671715.i	−0.336988	+	0.336988i	0.518244	+	0.855233i	$0.326586\pi$
$332$	59257.6	+	512565.i	0.0295052	+	0.255213i
$333$	−1.17358e6	−	1.17358e6i	−0.579968	−	0.579968i
$334$	−58693.6	−	20442.3i	−0.0287889	−	0.0100268i
$335$	793739.			0.386426
$336$	−339582.	−	210637.i	−0.164095	−	0.101786i
$337$	178410.			0.0855747			0.0427873	−	0.999084i	$-0.486376\pi$
$337$	178410.			0.0855747			0.0427873	+	0.999084i	$0.486376\pi$
$338$	14383.4	+	5009.57i	0.00684808	+	0.00238511i
$339$	−1.06854e6	−	1.06854e6i	−0.504998	−	0.504998i
$340$	162465.	−	18782.6i	0.0762188	−	0.00881166i
$341$	285781.	−	285781.i	0.133091	−	0.133091i
$342$	548397.	+	1.13455e6i	0.253530	+	0.524515i
$343$		−	1.33897e6i		−	0.614519i
$344$	518863.	−	2.31974e6i	0.236405	−	1.05692i
$345$			482054.i			0.218046i
$346$	−863167.	+	417222.i	−0.387618	+	0.187360i
$347$	−2.93043e6	+	2.93043e6i	−1.30649	+	1.30649i	−0.382566	+	0.923928i	$0.624959\pi$
$347$	−2.93043e6	+	2.93043e6i	−1.30649	+	1.30649i	−0.923928	+	0.382566i	$0.875041\pi$
$348$	−1.22387e6	+	1.54385e6i	−0.541736	+	0.683371i
$349$	561233.	+	561233.i	0.246649	+	0.246649i	0.819594	−	0.572945i	$-0.194199\pi$
$349$	561233.	+	561233.i	0.246649	+	0.246649i	−0.572945	+	0.819594i	$0.694199\pi$
$350$	48892.9	−	140380.i	0.0213342	−	0.0612542i
$351$	−2.25319e6			−0.976178
$352$	1.00750e6	−	815472.i	0.433400	−	0.350794i
$353$	−2.28009e6			−0.973904			−0.486952	−	0.873429i	$-0.661891\pi$
$353$	−2.28009e6			−0.973904			−0.486952	+	0.873429i	$0.661891\pi$
$354$	167660.	−	481382.i	0.0711085	−	0.204165i
$355$	−560709.	−	560709.i	−0.236139	−	0.236139i
$356$	2.09523e6	−	2.64302e6i	0.876206	−	1.10529i
$357$	−56411.6	+	56411.6i	−0.0234260	+	0.0234260i
$358$	−3.95909e6	+	1.91367e6i	−1.63263	+	0.789151i
$359$			249426.i			0.102142i	0.998695	+	0.0510711i	$0.0162635\pi$
$359$			249426.i			0.102142i	−0.998695	+	0.0510711i	$0.983737\pi$
$360$	692724.	+	154943.i	0.281711	+	0.0630110i
$361$		−	459159.i		−	0.185437i
$362$	1.25940e6	+	2.60549e6i	0.505116	+	1.04501i
$363$	728372.	−	728372.i	0.290126	−	0.290126i
$364$	−811443.	+	93810.8i	−0.320999	+	0.0371107i
$365$	−108185.	−	108185.i	−0.0425045	−	0.0425045i
$366$	1.95888e6	+	682255.i	0.764371	+	0.266222i
$367$	2.54893e6			0.987854			0.493927	−	0.869504i	$-0.335561\pi$
$367$	2.54893e6			0.987854			0.493927	+	0.869504i	$0.335561\pi$
$368$	−2.07123e6	+	485397.i	−0.797276	+	0.186843i
$369$	2.01980e6			0.772223
$370$	−1.41315e6	−	492183.i	−0.536639	−	0.186905i
$371$	−558051.	−	558051.i	−0.210494	−	0.210494i
$372$	−61608.7	−	532901.i	−0.0230826	−	0.199659i
$373$	−3.29571e6	+	3.29571e6i	−1.22652	+	1.22652i	−0.261255	+	0.965270i	$0.584136\pi$
$373$	−3.29571e6	+	3.29571e6i	−1.22652	+	1.22652i	−0.965270	+	0.261255i	$0.915864\pi$
$374$	−112614.	−	232981.i	−0.0416307	−	0.0861274i
$375$		−	145023.i		−	0.0532549i
$376$	783446.	−	497037.i	0.285785	−	0.181309i
$377$			4.02718e6i			1.45931i
$378$	−794718.	+	384136.i	−0.286077	+	0.138279i
$379$	−101204.	+	101204.i	−0.0361909	+	0.0361909i	−0.724971	−	0.688780i	$-0.758147\pi$
$379$	−101204.	+	101204.i	−0.0361909	+	0.0361909i	0.688780	+	0.724971i	$0.258147\pi$
$380$	890329.	+	705801.i	0.316295	+	0.250740i
$381$	1.91486e6	+	1.91486e6i	0.675811	+	0.675811i
$382$	−597110.	+	1.71441e6i	−0.209361	+	0.601114i
$383$	2.95243e6			1.02845			0.514224	−	0.857656i	$-0.328080\pi$
$383$	2.95243e6			1.02845			0.514224	+	0.857656i	$0.328080\pi$
$384$	−17457.8	−	1.72036e6i	−0.00604172	−	0.595377i
$385$	−235201.			−0.0808700
$386$	1.02708e6	−	2.94894e6i	0.350863	−	1.00739i
$387$	−1.45645e6	−	1.45645e6i	−0.494332	−	0.494332i
$388$	1.23188e6	+	976562.i	0.415422	+	0.329322i
$389$	−2.14600e6	+	2.14600e6i	−0.719046	+	0.719046i	−0.968410	−	0.249364i	$-0.919778\pi$
$389$	−2.14600e6	+	2.14600e6i	−0.719046	+	0.719046i	0.249364	+	0.968410i	$0.419778\pi$
$390$	−717491.	+	346808.i	−0.238866	+	0.115459i
$391$			424708.i			0.140491i
$392$	2.29879e6	−	1.45841e6i	0.755588	−	0.479363i
$393$			206030.i			0.0672898i
$394$	2.24027e6	+	4.63478e6i	0.727043	+	1.50414i
$395$	810103.	−	810103.i	0.261245	−	0.261245i
$396$	−128987.	−	1.11570e6i	−0.0413339	−	0.357529i
$397$	2.09299e6	+	2.09299e6i	0.666486	+	0.666486i	0.956901	−	0.290415i	$-0.0937934\pi$
$397$	2.09299e6	+	2.09299e6i	0.666486	+	0.666486i	−0.290415	+	0.956901i	$0.593793\pi$
$398$	486058.	+	169288.i	0.153808	+	0.0535697i
$399$	−554213.			−0.174279
$400$	623118.	−	146029.i	0.194724	−	0.0456341i
$401$	4.94183e6			1.53471			0.767357	−	0.641220i	$-0.221572\pi$
$401$	4.94183e6			1.53471			0.767357	+	0.641220i	$0.221572\pi$
$402$	−1.57423e6	−	548287.i	−0.485851	−	0.169217i
$403$	−775400.	−	775400.i	−0.237828	−	0.237828i
$404$	−662808.	+	76627.2i	−0.202039	+	0.0233577i
$405$	64872.1	−	64872.1i	0.0196526	−	0.0196526i
$406$	686576.	+	1.42042e6i	0.206716	+	0.427663i
$407$			2.36766e6i			0.708491i
$408$	−335193.	−	74973.4i	−0.0996883	−	0.0222975i
$409$		−	647728.i		−	0.191463i	−0.995407	−	0.0957313i	$-0.969481\pi$
$409$		−	647728.i		−	0.191463i	0.995407	−	0.0957313i	$-0.0305190\pi$
$410$	1.63958e6	−	792512.i	0.481697	−	0.232834i
$411$	690332.	−	690332.i	0.201583	−	0.201583i
$412$	−1.11631e6	+	1.40817e6i	−0.323998	+	0.408706i
$413$	−288641.	−	288641.i	−0.0832688	−	0.0832688i
$414$	−606298.	+	1.74079e6i	−0.173854	+	0.499167i
$415$	403108.			0.114895
$416$	−2.21259e6	−	2.73361e6i	−0.626855	−	0.774468i
$417$	4.07050e6			1.14632
$418$	591270.	−	1.69764e6i	0.165518	−	0.475232i
$419$	2.29457e6	+	2.29457e6i	0.638507	+	0.638507i	0.950187	−	0.311680i	$-0.100892\pi$
$419$	2.29457e6	+	2.29457e6i	0.638507	+	0.638507i	−0.311680	+	0.950187i	$0.600892\pi$
$420$	−193939.	+	244644.i	−0.0536467	+	0.0676724i
$421$	3.97175e6	−	3.97175e6i	1.09214	−	1.09214i	0.0968369	−	0.995300i	$-0.469127\pi$
$421$	3.97175e6	−	3.97175e6i	1.09214	−	1.09214i	0.995300	−	0.0968369i	$-0.0308725\pi$
$422$	−3.18652e6	+	1.54024e6i	−0.871035	+	0.421025i
$423$		−	803952.i		−	0.218464i
$424$	741674.	−	3.31589e6i	0.200354	−	0.895748i
$425$		−	127771.i		−	0.0343131i
$426$	724742.	+	1.49938e6i	0.193490	+	0.400302i
$427$	1.17456e6	−	1.17456e6i	0.311749	−	0.311749i
$428$	3.76295e6	−	435034.i	0.992931	−	0.114793i
$429$	891594.	+	891594.i	0.233897	+	0.233897i
$430$	−1.75375e6	−	610813.i	−0.457401	−	0.159308i
$431$	−6.80546e6			−1.76467			−0.882336	−	0.470620i	$-0.844030\pi$
$431$	−6.80546e6			−1.76467			−0.882336	+	0.470620i	$0.844030\pi$
$432$	−3.22948e6	−	2.00319e6i	−0.832576	−	0.516433i
$433$	4.23928e6			1.08661			0.543303	−	0.839537i	$-0.317173\pi$
$433$	4.23928e6			1.08661			0.543303	+	0.839537i	$0.317173\pi$
$434$	−405685.	−	141295.i	−0.103387	−	0.0360084i
$435$	1.08834e6	+	1.08834e6i	0.275767	+	0.275767i
$436$	−303698.	−	2.62692e6i	−0.0765114	−	0.661807i
$437$	−2.08627e6	+	2.08627e6i	−0.522596	+	0.522596i
$438$	139834.	+	289295.i	0.0348279	+	0.0720536i
$439$		−	2.92903e6i		−	0.725374i	−0.931911	−	0.362687i	$-0.881859\pi$
$439$		−	2.92903e6i		−	0.725374i	0.931911	−	0.362687i	$-0.118141\pi$
$440$	−542476.	−	855069.i	−0.133582	−	0.210557i
$441$		−	2.35896e6i		−	0.577597i
$442$	−632138.	+	305551.i	−0.153906	+	0.0743923i
$443$	947047.	−	947047.i	0.229278	−	0.229278i	−0.583113	−	0.812391i	$-0.698166\pi$
$443$	947047.	−	947047.i	0.229278	−	0.229278i	0.812391	+	0.583113i	$0.198166\pi$
$444$	2.46272e6	+	1.95230e6i	0.592868	+	0.469991i
$445$	−1.86320e6	−	1.86320e6i	−0.446026	−	0.446026i
$446$	−2.30001e6	+	6.60373e6i	−0.547510	+	1.57200i
$447$	−1.11519e6			−0.263985
$448$	−1.24644e6	−	586954.i	−0.293411	−	0.138168i
$449$	5.43200e6			1.27158			0.635790	−	0.771862i	$-0.280674\pi$
$449$	5.43200e6			1.27158			0.635790	+	0.771862i	$0.280674\pi$
$450$	182401.	−	523708.i	0.0424617	−	0.121915i
$451$	−2.03744e6	−	2.03744e6i	−0.471675	−	0.471675i
$452$	−4.08273e6	−	3.23655e6i	−0.939950	−	0.745137i
$453$	−3.50766e6	+	3.50766e6i	−0.803105	+	0.803105i
$454$	−4.64619e6	+	2.24579e6i	−1.05793	+	0.511363i
$455$			638162.i			0.144511i
$456$	−1.27826e6	−	2.01483e6i	−0.287876	−	0.453760i
$457$		−	5.09132e6i		−	1.14035i	−0.821522	−	0.570177i	$-0.806874\pi$
$457$		−	5.09132e6i		−	1.14035i	0.821522	−	0.570177i	$-0.193126\pi$
$458$	−2.80547e6	−	5.80407e6i	−0.624944	−	1.29291i
$459$	−536484.	+	536484.i	−0.118857	+	0.118857i
$460$	190871.	+	1.65099e6i	0.0420577	+	0.363790i
$461$	−676336.	−	676336.i	−0.148221	−	0.148221i	0.629102	−	0.777323i	$-0.283423\pi$
$461$	−676336.	−	676336.i	−0.148221	−	0.148221i	−0.777323	+	0.629102i	$0.783423\pi$
$462$	466477.	+	162469.i	0.101678	+	0.0354132i
$463$	7.98501e6			1.73110			0.865552	−	0.500820i	$-0.166968\pi$
$463$	7.98501e6			1.73110			0.865552	+	0.500820i	$0.166968\pi$
$464$	−3.58036e6	+	5.77214e6i	−0.772026	+	1.24463i
$465$	−419102.			−0.0898851
$466$	−744249.	−	259214.i	−0.158765	−	0.0552959i
$467$	−6.09338e6	−	6.09338e6i	−1.29290	−	1.29290i	−0.932983	−	0.359921i	$-0.882804\pi$
$467$	−6.09338e6	−	6.09338e6i	−1.29290	−	1.29290i	−0.359921	−	0.932983i	$-0.617196\pi$
$468$	−3.02720e6	+	349974.i	−0.638890	+	0.0738620i
$469$	−943921.	+	943921.i	−0.198154	+	0.198154i
$470$	−315448.	−	652613.i	−0.0658693	−	0.136273i
$471$			2.52942e6i			0.525373i
$472$	383616.	−	1.71508e6i	0.0792577	−	0.354347i
$473$			2.93834e6i			0.603878i
$474$	−2.16628e6	+	1.04709e6i	−0.442861	+	0.214062i
$475$	627641.	−	627641.i	0.127637	−	0.127637i
$476$	−170868.	+	215541.i	−0.0345656	+	0.0436026i
$477$	−2.08189e6	−	2.08189e6i	−0.418949	−	0.418949i
$478$	2.12262e6	−	6.09443e6i	0.424915	−	1.22001i
$479$	6.80295e6			1.35475			0.677374	−	0.735639i	$-0.263118\pi$
$479$	6.80295e6			1.35475			0.677374	+	0.735639i	$0.263118\pi$
$480$	−1.33671e6	−	140807.i	−0.264809	−	0.0278946i
$481$	6.42409e6			1.26604
$482$	606071.	−	1.74014e6i	0.118824	−	0.341166i
$483$	−573262.	−	573262.i	−0.111811	−	0.111811i
$484$	2.20621e6	−	2.78301e6i	0.428088	−	0.540010i
$485$	868419.	−	868419.i	0.167639	−	0.167639i
$486$	−4.76658e6	+	2.30398e6i	−0.915411	+	0.442474i
$487$			1.23561e6i			0.236080i	0.993009	+	0.118040i	$0.0376611\pi$
$487$			1.23561e6i			0.236080i	−0.993009	+	0.118040i	$0.962339\pi$
$488$	6.97912e6	+	1.56104e6i	1.32663	+	0.296732i
$489$		−	5.12624e6i		−	0.969453i
$490$	−925590.	−	1.91490e6i	−0.174152	−	0.360294i
$491$	−4.77833e6	+	4.77833e6i	−0.894484	+	0.894484i	−0.994941	−	0.100457i	$-0.967969\pi$
$491$	−4.77833e6	+	4.77833e6i	−0.894484	+	0.894484i	0.100457	+	0.994941i	$0.467969\pi$
$492$	−3.79924e6	+	439230.i	−0.707594	+	0.0818049i
$493$	958871.	+	958871.i	0.177682	+	0.177682i
$494$	−4.60614e6	−	1.60427e6i	−0.849220	−	0.295774i
$495$	−877450.			−0.160957
$496$	−422009.	−	1.80075e6i	−0.0770225	−	0.328661i
$497$	1.33360e6			0.242178
$498$	−799488.	−	278453.i	−0.144457	−	0.0503128i
$499$	−4.84517e6	−	4.84517e6i	−0.871079	−	0.871079i	0.121511	−	0.992590i	$-0.461226\pi$
$499$	−4.84517e6	−	4.84517e6i	−0.871079	−	0.871079i	−0.992590	+	0.121511i	$0.961226\pi$
$500$	−57422.5	−	496692.i	−0.0102721	−	0.0888509i
$501$	72107.4	−	72107.4i	0.0128347	−	0.0128347i
$502$	−661628.	−	1.36880e6i	−0.117180	−	0.242428i
$503$			5.52120e6i			0.973001i	0.873680	+	0.486500i	$0.161727\pi$
$503$			5.52120e6i			0.973001i	−0.873680	+	0.486500i	$0.838273\pi$
$504$	−1.00805e6	+	639533.i	−0.176769	+	0.112147i
$505$			521268.i			0.0909562i
$506$	2.36759e6	−	1.14440e6i	0.411083	−	0.198702i
$507$	−17670.6	+	17670.6i	−0.00305302	+	0.00305302i
$508$	7.31644e6	+	5.80004e6i	1.25788	+	0.997176i
$509$	6.98285e6	+	6.98285e6i	1.19464	+	1.19464i	0.975748	+	0.218896i	$0.0702455\pi$
$509$	6.98285e6	+	6.98285e6i	1.19464	+	1.19464i	0.218896	+	0.975748i	$0.429754\pi$
$510$	−88259.8	+	253410.i	−0.0150258	+	0.0431418i
$511$	257309.			0.0435916
$512$	−740976.	−	5.88518e6i	−0.124919	−	0.992167i
$513$	−5.27067e6			−0.884244
$514$	1.24888e6	−	3.58575e6i	0.208503	−	0.598650i
$515$	992693.	+	992693.i	0.164929	+	0.164929i
$516$	3.05631e6	+	2.42286e6i	0.505327	+	0.400594i
$517$	−810973.	+	810973.i	−0.133438	+	0.133438i
$518$	2.26583e6	−	1.09522e6i	0.371025	−	0.179339i
$519$		−	1.57301e6i		−	0.256338i
$520$	−2.32002e6	+	1.47188e6i	−0.376257	+	0.238706i
$521$			3.12578e6i			0.504504i	0.967662	+	0.252252i	$0.0811711\pi$
$521$			3.12578e6i			0.504504i	−0.967662	+	0.252252i	$0.918829\pi$
$522$	2.56137e6	+	5.29907e6i	0.411429	+	0.851183i
$523$	3.72190e6	−	3.72190e6i	0.594991	−	0.594991i	−0.343984	−	0.938976i	$-0.611777\pi$
$523$	3.72190e6	−	3.72190e6i	0.594991	−	0.594991i	0.938976	+	0.343984i	$0.111777\pi$
$524$	81578.4	+	705635.i	0.0129792	+	0.112267i
$525$	172463.	+	172463.i	0.0273085	+	0.0273085i
$526$	4.82165e6	+	1.67933e6i	0.759856	+	0.264649i
$527$	−369246.			−0.0579147
$528$	485247.	+	2.07059e6i	0.0757492	+	0.323228i
$529$	2.12039e6			0.329441
$530$	−2.50686e6	−	873110.i	−0.387650	−	0.135014i
$531$	−1.07681e6	−	1.07681e6i	−0.165731	−	0.165731i
$532$	−1.89813e6	+	219443.i	−0.290768	+	0.0336157i
$533$	−5.52810e6	+	5.52810e6i	−0.842864	+	0.842864i
$534$	2.40828e6	+	4.98235e6i	0.365471	+	0.756103i
$535$		−	2.95939e6i		−	0.447010i
$536$	−5.60870e6	−	1.25451e6i	−0.843238	−	0.188609i
$537$		−	7.21493e6i		−	1.07968i
$538$	8.75913e6	−	4.23383e6i	1.30468	−	0.630634i
$539$	−2.37956e6	+	2.37956e6i	−0.352797	+	0.352797i
$540$	−1.84440e6	+	2.32661e6i	−0.272189	+	0.343351i
$541$	−2.59180e6	−	2.59180e6i	−0.380722	−	0.380722i	0.490640	−	0.871362i	$-0.336763\pi$
$541$	−2.59180e6	−	2.59180e6i	−0.380722	−	0.380722i	−0.871362	+	0.490640i	$0.836763\pi$
$542$	2.36240e6	−	6.78288e6i	0.345426	−	0.991781i
$543$	−4.74817e6			−0.691078
$544$	−1.17769e6	−	124056.i	−0.170622	−	0.0179731i
$545$	−2.06595e6			−0.297940
$546$	440820.	−	1.26567e6i	0.0632819	−	0.181694i
$547$	−4.93878e6	−	4.93878e6i	−0.705750	−	0.705750i	0.259889	−	0.965639i	$-0.416314\pi$
$547$	−4.93878e6	−	4.93878e6i	−0.705750	−	0.705750i	−0.965639	+	0.259889i	$0.916314\pi$
$548$	2.09099e6	−	2.63767e6i	0.297440	−	0.375205i
$549$	4.38185e6	−	4.38185e6i	0.620478	−	0.620478i
$550$	−712275.	+	344286.i	−0.100402	+	0.0485303i
$551$			9.42039e6i			1.32187i
$552$	761890.	−	3.40628e6i	0.106425	−	0.475808i
$553$			1.92676e6i			0.267926i
$554$	2.22855e6	+	4.61051e6i	0.308494	+	0.638227i
$555$	1.73611e6	−	1.73611e6i	0.239245	−	0.239245i
$556$	1.39411e7	−	1.61173e6i	1.91254	−	0.221108i
$557$	−1.83759e6	−	1.83759e6i	−0.250963	−	0.250963i	0.570402	−	0.821365i	$-0.306787\pi$
$557$	−1.83759e6	−	1.83759e6i	−0.250963	−	0.250963i	−0.821365	+	0.570402i	$0.806787\pi$
$558$	−1.51346e6	−	527122.i	−0.205772	−	0.0716680i
$559$	7.97248e6			1.07911
$560$	−567358.	+	914675.i	−0.0764517	+	0.123253i
$561$	424577.			0.0569573
$562$	1.89857e6	+	661251.i	0.253563	+	0.0883131i
$563$	1.11206e6	+	1.11206e6i	0.147862	+	0.147862i	0.777162	−	0.629300i	$-0.216658\pi$
$563$	1.11206e6	+	1.11206e6i	0.147862	+	0.147862i	−0.629300	+	0.777162i	$0.716658\pi$
$564$	174829.	+	1.51223e6i	0.0231428	+	0.200180i
$565$	−2.87814e6	+	2.87814e6i	−0.379307	+	0.379307i
$566$	4.43561e6	+	9.17658e6i	0.581985	+	1.20404i
$567$			154293.i			0.0201553i
$568$	3.07586e6	+	4.84828e6i	0.400033	+	0.630546i
$569$		−	6.57708e6i		−	0.851633i	−0.904809	−	0.425817i	$-0.859987\pi$
$569$		−	6.57708e6i		−	0.851633i	0.904809	−	0.425817i	$-0.140013\pi$
$570$	−1.67836e6	+	811255.i	−0.216370	+	0.104585i
$571$	1.65771e6	−	1.65771e6i	0.212774	−	0.212774i	−0.592671	−	0.805445i	$-0.701927\pi$
$571$	1.65771e6	−	1.65771e6i	0.212774	−	0.212774i	0.805445	+	0.592671i	$0.201927\pi$
$572$	3.40666e6	+	2.70060e6i	0.435350	+	0.345120i
$573$	−2.10622e6	−	2.10622e6i	−0.267990	−	0.267990i
$574$	−1.00735e6	+	2.89227e6i	−0.127614	+	0.366403i
$575$	1.29843e6			0.163775
$576$	−4.65001e6	−	2.18971e6i	−0.583980	−	0.274999i
$577$	−4.52363e6			−0.565649			−0.282825	−	0.959172i	$-0.591271\pi$
$577$	−4.52363e6			−0.565649			−0.282825	+	0.959172i	$0.591271\pi$
$578$	2.56402e6	−	7.36177e6i	0.319229	−	0.916564i
$579$	3.62289e6	+	3.62289e6i	0.449117	+	0.449117i
$580$	4.15841e6	+	3.29654e6i	0.513283	+	0.406901i
$581$	−479380.	+	479380.i	−0.0589168	+	0.0589168i
$582$	−2.32222e6	+	1.12247e6i	−0.284181	+	0.137362i
$583$			4.20013e6i			0.511789i
$584$	593467.	+	935442.i	0.0720053	+	0.113497i
$585$			2.38075e6i			0.287623i
$586$	2.31845e6	+	4.79652e6i	0.278904	+	0.577009i
$587$	−5.25994e6	+	5.25994e6i	−0.630065	+	0.630065i	−0.948084	−	0.318019i	$-0.896982\pi$
$587$	−5.25994e6	+	5.25994e6i	−0.630065	+	0.630065i	0.318019	+	0.948084i	$0.396982\pi$
$588$	512986.	+	4.43721e6i	0.0611874	+	0.529257i
$589$	−1.81382e6	−	1.81382e6i	−0.215430	−	0.215430i
$590$	−1.29662e6	−	451598.i	−0.153350	−	0.0534099i
$591$	−8.44627e6			−0.994710
$592$	9.20763e6	+	5.71134e6i	1.07980	+	0.669782i
$593$	−1.38857e7			−1.62155			−0.810774	−	0.585360i	$-0.800953\pi$
$593$	−1.38857e7			−1.62155			−0.810774	+	0.585360i	$0.800953\pi$
$594$	4.43628e6	+	1.54511e6i	0.515884	+	0.179677i
$595$	151946.	+	151946.i	0.0175954	+	0.0175954i
$596$	−3.81942e6	+	441563.i	−0.440435	+	0.0509187i
$597$	−597141.	+	597141.i	−0.0685711	+	0.0685711i
$598$	−3.10506e6	−	6.42388e6i	−0.355072	−	0.734589i
$599$			8.38212e6i			0.954524i	0.878761	+	0.477262i	$0.158371\pi$
$599$			8.38212e6i			0.954524i	−0.878761	+	0.477262i	$0.841629\pi$
$600$	−229210.	+	1.02476e6i	−0.0259930	+	0.116210i
$601$			1.75269e7i			1.97934i	0.143371	+	0.989669i	$0.454206\pi$
$601$			1.75269e7i			1.97934i	−0.143371	+	0.989669i	$0.545794\pi$
$602$	2.81196e6	−	1.35919e6i	0.316241	−	0.152859i
$603$	−3.52143e6	+	3.52143e6i	−0.394390	+	0.394390i
$604$	−1.06246e7	+	1.34023e7i	−1.18500	+	1.49481i
$605$	−1.96189e6	−	1.96189e6i	−0.217915	−	0.217915i
$606$	360073.	−	1.03384e6i	0.0398299	−	0.114359i
$607$	2.09360e6			0.230633			0.115317	−	0.993329i	$-0.463212\pi$
$607$	2.09360e6			0.230633			0.115317	+	0.993329i	$0.463212\pi$
$608$	−5.17570e6	−	6.39448e6i	−0.567819	−	0.701531i
$609$	−2.58853e6			−0.282820
$610$	1.83768e6	−	5.27630e6i	0.199961	−	0.574123i
$611$	2.20038e6	+	2.20038e6i	0.238448	+	0.238448i
$612$	−637447.	+	804105.i	−0.0687964	+	0.0867829i
$613$	−1.12371e7	+	1.12371e7i	−1.20782	+	1.20782i	−0.236094	+	0.971730i	$0.575867\pi$
$613$	−1.12371e7	+	1.12371e7i	−1.20782	+	1.20782i	−0.971730	+	0.236094i	$0.924133\pi$
$614$	8.15027e6	−	3.93953e6i	0.872472	−	0.421719i
$615$			2.98793e6i			0.318553i
$616$	1.66197e6	+	371737.i	0.176470	+	0.0394716i
$617$		−	1.65368e7i		−	1.74880i	−0.485208	−	0.874399i	$-0.661256\pi$
$617$		−	1.65368e7i		−	1.74880i	0.485208	−	0.874399i	$-0.338744\pi$
$618$	−1.28310e6	−	2.65454e6i	−0.135142	−	0.279587i
$619$	1.21691e7	−	1.21691e7i	1.27654	−	1.27654i	0.333942	−	0.942594i	$-0.391621\pi$
$619$	1.21691e7	−	1.21691e7i	1.27654	−	1.27654i	0.942594	−	0.333942i	$-0.108379\pi$
$620$	−1.43539e6	+	165945.i	−0.149965	+	0.0173375i
$621$	−5.45183e6	−	5.45183e6i	−0.567300	−	0.567300i
$622$	−3.76575e6	−	1.31157e6i	−0.390279	−	0.135930i
$623$	4.43148e6			0.457434
$624$	5.61805e6	−	1.31660e6i	0.577596	−	0.135361i
$625$	−390625.			−0.0400000
$626$	5.58919e6	+	1.94665e6i	0.570050	+	0.198542i
$627$	2.08562e6	+	2.08562e6i	0.211869	+	0.211869i
$628$	1.00153e6	+	8.66303e6i	0.101337	+	0.876538i
$629$	1.52958e6	−	1.52958e6i	0.154150	−	0.154150i
$630$	405884.	+	839711.i	0.0407428	+	0.0842904i
$631$		−	1.33765e7i		−	1.33743i	−0.743520	−	0.668713i	$-0.766845\pi$
$631$		−	1.33765e7i		−	1.33743i	0.743520	−	0.668713i	$-0.233155\pi$
$632$	−7.00470e6	+	4.44395e6i	−0.697585	+	0.442565i
$633$		−	5.80702e6i		−	0.576028i
$634$	−8.34683e6	+	4.03454e6i	−0.824705	+	0.398631i
$635$	5.15775e6	−	5.15775e6i	0.507605	−	0.507605i
$636$	4.36876e6	+	3.46329e6i	0.428268	+	0.339505i
$637$	6.45637e6	+	6.45637e6i	0.630435	+	0.630435i
$638$	2.76161e6	−	7.92907e6i	0.268603	−	0.771206i
$639$	4.97518e6			0.482010
$640$	−4.63386e6	+	47023.1i	−0.447191	+	0.00453797i
$641$	−1.05200e7			−1.01128			−0.505641	−	0.862744i	$-0.668744\pi$
$641$	−1.05200e7			−1.01128			−0.505641	+	0.862744i	$0.668744\pi$
$642$	−2.04424e6	+	5.86938e6i	−0.195747	+	0.562024i
$643$	5.97274e6	+	5.97274e6i	0.569700	+	0.569700i	0.932044	−	0.362345i	$-0.118024\pi$
$643$	5.97274e6	+	5.97274e6i	0.569700	+	0.569700i	−0.362345	+	0.932044i	$0.618024\pi$
$644$	−2.19036e6	−	1.73639e6i	−0.208114	−	0.164980i
$645$	2.15456e6	−	2.15456e6i	0.203919	−	0.203919i
$646$	−1.47870e6	+	714747.i	−0.139412	+	0.0673862i
$647$			6.68641e6i			0.627960i	0.949430	+	0.313980i	$0.101662\pi$
$647$			6.68641e6i			0.627960i	−0.949430	+	0.313980i	$0.898338\pi$
$648$	−560929.	+	355867.i	−0.0524771	+	0.0332928i
$649$			2.17243e6i			0.202458i
$650$	934138.	+	1.93259e6i	0.0867217	+	0.179414i
$651$	498400.	−	498400.i	0.0460920	−	0.0460920i
$652$	−2.02976e6	−	1.75569e7i	−0.186993	−	1.61744i
$653$	−4.85058e6	−	4.85058e6i	−0.445155	−	0.445155i	0.448585	−	0.893740i	$-0.351928\pi$
$653$	−4.85058e6	−	4.85058e6i	−0.445155	−	0.445155i	−0.893740	+	0.448585i	$0.851928\pi$
$654$	4.09742e6	+	1.42709e6i	0.374599	+	0.130469i
$655$	554949.			0.0505417
$656$	−1.28382e7	+	3.00865e6i	−1.16478	+	0.272968i
$657$	959927.			0.0867610
$658$	1.15123e6	+	400959.i	0.103656	+	0.0361023i
$659$	−5.91567e6	−	5.91567e6i	−0.530629	−	0.530629i	0.390131	−	0.920759i	$-0.372430\pi$
$659$	−5.91567e6	−	5.91567e6i	−0.530629	−	0.530629i	−0.920759	+	0.390131i	$0.872430\pi$
$660$	1.65048e6	−	190812.i	0.147486	−	0.0170509i
$661$	9.64450e6	−	9.64450e6i	0.858571	−	0.858571i	−0.132599	−	0.991170i	$-0.542332\pi$
$661$	9.64450e6	−	9.64450e6i	0.858571	−	0.858571i	0.991170	+	0.132599i	$0.0423322\pi$
$662$	−2.33858e6	−	4.83817e6i	−0.207400	−	0.429078i
$663$		−	1.15199e6i		−	0.101780i
$664$	−2.84843e6	−	637116.i	−0.250718	−	0.0560788i
$665$			1.49279e6i			0.130902i
$666$	8.45299e6	−	4.08585e6i	0.738456	−	0.356942i
$667$	−9.74419e6	+	9.74419e6i	−0.848069	+	0.848069i
$668$	218410.	−	275513.i	0.0189379	−	0.0238892i
$669$	−8.11295e6	−	8.11295e6i	−0.700831	−	0.700831i
$670$	−1.47683e6	+	4.24025e6i	−0.127099	+	0.364925i
$671$	−8.84022e6			−0.757978
$672$	1.75707e6	−	1.42217e6i	0.150095	−	0.121487i
$673$	−1.32602e7			−1.12853			−0.564265	−	0.825594i	$-0.690840\pi$
$673$	−1.32602e7			−1.12853			−0.564265	+	0.825594i	$0.690840\pi$
$674$	−331950.	+	953088.i	−0.0281464	+	0.0808134i
$675$	1.64015e6	+	1.64015e6i	0.138556	+	0.138556i
$676$	−53523.4	+	67516.8i	−0.00450481	+	0.00568258i
$677$	−4.03747e6	+	4.03747e6i	−0.338561	+	0.338561i	−0.855826	−	0.517264i	$-0.826950\pi$
$677$	−4.03747e6	+	4.03747e6i	−0.338561	+	0.338561i	0.517264	+	0.855826i	$0.326950\pi$
$678$	7.69636e6	−	3.72012e6i	0.643000	−	0.310802i
$679$			2.06546e6i			0.171926i
$680$	−201943.	+	902853.i	−0.0167478	+	0.0748763i
$681$		−	8.46708e6i		−	0.699626i
$682$	994952.	+	2.05840e6i	0.0819108	+	0.169461i
$683$	581314.	−	581314.i	0.0476825	−	0.0476825i	−0.682863	−	0.730546i	$-0.739266\pi$
$683$	581314.	−	581314.i	0.0476825	−	0.0476825i	0.730546	+	0.682863i	$0.239266\pi$
$684$	−7.08124e6	+	818661.i	−0.578720	+	0.0669058i
$685$	−1.85943e6	−	1.85943e6i	−0.151410	−	0.151410i
$686$	7.15293e6	+	2.49129e6i	0.580328	+	0.202122i
$687$	1.05772e7			0.855022
$688$	1.14269e7	+	7.08793e6i	0.920361	+	0.570885i
$689$	1.13960e7			0.914547
$690$	−2.57519e6	−	896909.i	−0.205914	−	0.0717176i
$691$	9.75086e6	+	9.75086e6i	0.776869	+	0.776869i	0.979297	−	0.202428i	$-0.0648832\pi$
$691$	9.75086e6	+	9.75086e6i	0.776869	+	0.776869i	−0.202428	+	0.979297i	$0.564883\pi$
$692$	−622839.	−	5.38742e6i	−0.0494436	−	0.427676i
$693$	1.04347e6	−	1.04347e6i	0.0825367	−	0.0825367i
$694$	−1.02023e7	−	2.11070e7i	−0.804083	−	1.66352i
$695$		−	1.09640e7i		−	0.861010i
$696$	−5.97027e6	−	9.41054e6i	−0.467166	−	0.736362i
$697$			2.63248e6i			0.205250i
$698$	−4.04240e6	+	1.95394e6i	−0.314051	+	0.151800i
$699$	914340.	−	914340.i	0.0707807	−	0.0707807i
$700$	658957.	+	522383.i	0.0508291	+	0.0402943i
$701$	474503.	+	474503.i	0.0364707	+	0.0364707i	0.725107	−	0.688636i	$-0.241790\pi$
$701$	474503.	+	474503.i	0.0364707	+	0.0364707i	−0.688636	+	0.725107i	$0.741790\pi$
$702$	4.19227e6	−	1.20368e7i	0.321075	−	0.921865i
$703$	1.50273e7			1.14681
$704$	2.48179e6	+	6.89945e6i	0.188726	+	0.524666i
$705$	1.18930e6			0.0901196
$706$	4.24234e6	−	1.21805e7i	0.320327	−	0.919717i
$707$	−619896.	−	619896.i	−0.0466413	−	0.0466413i
$708$	2.25965e6	+	1.79132e6i	0.169417	+	0.134304i
$709$	6.33212e6	−	6.33212e6i	0.473079	−	0.473079i	−0.429831	−	0.902909i	$-0.641427\pi$
$709$	6.33212e6	−	6.33212e6i	0.473079	−	0.473079i	0.902909	+	0.429831i	$0.141427\pi$
$710$	4.03863e6	−	1.95212e6i	0.300669	−	0.145332i
$711$			7.18805e6i			0.533257i
$712$	1.02209e7	+	1.61105e7i	0.755596	+	1.19100i
$713$		−	3.75233e6i		−	0.276425i
$714$	−196398.	−	406316.i	−0.0144175	−	0.0298276i
$715$	2.40154e6	−	2.40154e6i	0.175681	−	0.175681i
$716$	−2.85678e6	−	2.47105e7i	−0.208254	−	1.80135i
$717$	7.48725e6	+	7.48725e6i	0.543906	+	0.543906i
$718$	−1.33246e6	−	464081.i	−0.0964590	−	0.0335956i
$719$	393042.			0.0283542			0.0141771	−	0.999900i	$-0.495487\pi$
$719$	393042.			0.0283542			0.0141771	+	0.999900i	$0.495487\pi$
$720$	−2.11660e6	+	3.41232e6i	−0.152163	+	0.245312i
$721$	−2.36104e6			−0.169147
$722$	2.45288e6	+	854311.i	0.175119	+	0.0609920i
$723$	2.13783e6	+	2.13783e6i	0.152099	+	0.152099i
$724$	−1.62621e7	+	1.88006e6i	−1.15300	+	0.133298i
$725$	2.93148e6	−	2.93148e6i	0.207130	−	0.207130i
$726$	2.53584e6	+	5.24625e6i	0.178558	+	0.369409i
$727$		−	1.63831e7i		−	1.14964i	−0.818281	−	0.574818i	$-0.805073\pi$
$727$		−	1.63831e7i		−	1.14964i	0.818281	−	0.574818i	$-0.194927\pi$
$728$	1.00862e6	−	4.50936e6i	0.0705341	−	0.315346i
$729$		−	7.79472e6i		−	0.543228i
$730$	779226.	−	376648.i	0.0541198	−	0.0261594i
$731$	1.89825e6	−	1.89825e6i	0.131389	−	0.131389i
$732$	−7.28937e6	+	9.19514e6i	−0.502819	+	0.634279i
$733$	−3.71303e6	−	3.71303e6i	−0.255252	−	0.255252i	0.567868	−	0.823120i	$-0.307768\pi$
$733$	−3.71303e6	−	3.71303e6i	−0.255252	−	0.255252i	−0.823120	+	0.567868i	$0.807768\pi$
$734$	−4.74253e6	+	1.36167e7i	−0.324915	+	0.932890i
$735$	3.48966e6			0.238267
$736$	1.26068e6	−	1.19679e7i	0.0857847	−	0.814371i
$737$	7.10435e6			0.481788
$738$	−3.75804e6	+	1.07900e7i	−0.253992	+	0.729257i
$739$	−1.96304e6	−	1.96304e6i	−0.132226	−	0.132226i	0.637896	−	0.770122i	$-0.279805\pi$
$739$	−1.96304e6	−	1.96304e6i	−0.132226	−	0.132226i	−0.770122	+	0.637896i	$0.779805\pi$
$740$	5.25859e6	−	6.63343e6i	0.353013	−	0.445306i
$741$	5.65883e6	−	5.65883e6i	0.378601	−	0.378601i
$742$	4.01948e6	−	1.94286e6i	0.268016	−	0.129549i
$743$		−	1.13191e7i		−	0.752209i	−0.926577	−	0.376105i	$-0.877263\pi$
$743$		−	1.13191e7i		−	0.752209i	0.926577	−	0.376105i	$-0.122737\pi$
$744$	2.96145e6	+	662395.i	0.196143	+	0.0438717i
$745$			3.00380e6i			0.198280i
$746$	−1.14740e7	−	2.37380e7i	−0.754865	−	1.56170i
$747$	−1.78839e6	+	1.78839e6i	−0.117263	+	0.117263i
$748$	1.45414e6	−	168113.i	0.0950281	−	0.0109862i
$749$	3.51933e6	+	3.51933e6i	0.229221	+	0.229221i
$750$	774730.	+	269830.i	0.0502918	+	0.0175161i
$751$	−2.47594e7			−1.60192			−0.800959	−	0.598720i	$-0.795676\pi$
$751$	−2.47594e7			−1.60192			−0.800959	+	0.598720i	$0.795676\pi$
$752$	1.19755e6	+	5.11004e6i	0.0772234	+	0.329519i
$753$	2.49447e6			0.160321
$754$	−2.15136e7	−	7.49296e6i	−1.37811	−	0.479982i
$755$	9.44801e6	+	9.44801e6i	0.603216	+	0.603216i
$756$	−573448.	−	4.96019e6i	−0.0364913	−	0.315642i
$757$	−1.12072e7	+	1.12072e7i	−0.710815	+	0.710815i	−0.966706	−	0.255891i	$-0.917631\pi$
$757$	−1.12072e7	+	1.12072e7i	−0.710815	+	0.710815i	0.255891	+	0.966706i	$0.417631\pi$
$758$	−352343.	−	728942.i	−0.0222737	−	0.0460808i
$759$			4.31462e6i			0.271855i
$760$	−5.42701e6	+	3.44303e6i	−0.340821	+	0.216225i
$761$			3.13327e7i			1.96126i	0.195859	+	0.980632i	$0.437251\pi$
$761$			3.13327e7i			1.96126i	−0.195859	+	0.980632i	$0.562749\pi$
$762$	−1.37922e7	+	6.66662e6i	−0.860491	+	0.415928i
$763$	2.45685e6	−	2.45685e6i	0.152780	−	0.152780i
$764$	−8.04760e6	−	6.37966e6i	−0.498807	−	0.395425i
$765$	566857.	+	566857.i	0.0350203	+	0.0350203i
$766$	−5.49328e6	+	1.57722e7i	−0.338267	+	0.971226i
$767$	5.89437e6			0.361784
$768$	9.22285e6	+	3.10764e6i	0.564238	+	0.190120i
$769$	−7.69730e6			−0.469378			−0.234689	−	0.972071i	$-0.575407\pi$
$769$	−7.69730e6			−0.469378			−0.234689	+	0.972071i	$0.575407\pi$
$770$	437615.	−	1.25647e6i	0.0265990	−	0.0763705i
$771$	4.40524e6	+	4.40524e6i	0.266891	+	0.266891i
$772$	1.38426e7	+	1.09736e7i	0.835938	+	0.662683i
$773$	2.07601e7	−	2.07601e7i	1.24963	−	1.24963i	0.293745	−	0.955884i	$-0.405098\pi$
$773$	2.07601e7	−	2.07601e7i	1.24963	−	1.24963i	0.955884	−	0.293745i	$-0.0949017\pi$
$774$	1.04904e7	−	5.07066e6i	0.629419	−	0.304237i
$775$			1.12887e6i			0.0675131i
$776$	−7.50894e6	+	4.76385e6i	−0.447635	+	0.283991i
$777$			4.12918e6i			0.245364i
$778$	−7.47134e6	−	1.54570e7i	−0.442537	−	0.915540i
$779$	−1.29314e7	+	1.29314e7i	−0.763485	+	0.763485i
$780$	−517723.	−	4.47819e6i	−0.0304692	−	0.263552i
$781$	−5.01862e6	−	5.01862e6i	−0.294413	−	0.294413i
$782$	−2.26884e6	−	790212.i	−0.132674	−	0.0462090i
$783$	−2.46174e7			−1.43495
$784$	3.51386e6	+	1.49939e7i	0.204171	+	0.871215i
$785$	6.81307e6			0.394611
$786$	−1.10064e6	−	383339.i	−0.0635458	−	0.0221323i
$787$	1.53754e7	+	1.53754e7i	0.884889	+	0.884889i	0.994027	−	0.109138i	$-0.0348090\pi$
$787$	1.53754e7	+	1.53754e7i	0.884889	+	0.884889i	−0.109138	+	0.994027i	$0.534809\pi$
$788$	−2.89277e7	+	3.34434e6i	−1.65958	+	0.191864i
$789$	−5.92359e6	+	5.92359e6i	−0.338760	+	0.338760i
$790$	2.82038e6	+	5.83494e6i	0.160783	+	0.332635i
$791$		−	6.84541e6i		−	0.389008i
$792$	6.20021e6	+	1.38682e6i	0.351232	+	0.0785609i
$793$			2.39858e7i			1.35448i
$794$	−1.50752e7	+	7.28677e6i	−0.848617	+	0.410189i
$795$	3.07977e6	−	3.07977e6i	0.172823	−	0.172823i
$796$	−1.80872e6	+	2.28160e6i	−0.101178	+	0.127631i
$797$	1.59398e7	+	1.59398e7i	0.888865	+	0.888865i	0.994414	−	0.105549i	$-0.0336600\pi$
$797$	1.59398e7	+	1.59398e7i	0.888865	+	0.888865i	−0.105549	+	0.994414i	$0.533660\pi$
$798$	1.03117e6	−	2.96067e6i	0.0573221	−	0.164582i
$799$	1.04782e6			0.0580658
$800$	−379268.	+	3.60047e6i	−0.0209518	+	0.198900i
$801$	1.65322e7			0.910437
$802$	−9.19477e6	+	2.63998e7i	−0.504783	+	1.44932i
$803$	−968309.	−	968309.i	−0.0529938	−	0.0529938i
$804$	5.85802e6	−	7.38958e6i	0.319603	−	0.403162i
$805$	−1.54410e6	+	1.54410e6i	−0.0839820	+	0.0839820i
$806$	5.58498e6	−	2.69957e6i	0.302820	−	0.146371i
$807$			1.59624e7i			0.862807i
$808$	823868.	−	3.68337e6i	0.0443945	−	0.198480i
$809$			2.35208e6i			0.126352i	0.998002	+	0.0631758i	$0.0201229\pi$
$809$			2.35208e6i			0.126352i	−0.998002	+	0.0631758i	$0.979877\pi$
$810$	225853.	+	467255.i	0.0120952	+	0.0250231i
$811$	2.42377e7	−	2.42377e7i	1.29402	−	1.29402i	0.361734	−	0.932281i	$-0.382185\pi$
$811$	2.42377e7	−	2.42377e7i	1.29402	−	1.29402i	0.932281	−	0.361734i	$-0.117815\pi$
$812$	−8.86548e6	+	1.02494e6i	−0.471859	+	0.0545516i
$813$	8.33303e6	+	8.33303e6i	0.442157	+	0.442157i
$814$	−1.26483e7	−	4.40527e6i	−0.669071	−	0.233030i
$815$	−1.38077e7			−0.728161
$816$	1.02418e6	−	1.65114e6i	0.0538454	−	0.0868078i
$817$	1.86493e7			0.977477
$818$	3.46023e6	+	1.20516e6i	0.180810	+	0.0629741i
$819$	−2.83121e6	−	2.83121e6i	−0.147490	−	0.147490i
$820$	1.18308e6	+	1.02334e7i	0.0614441	+	0.531478i
$821$	1.85342e7	−	1.85342e7i	0.959659	−	0.959659i	−0.0395583	−	0.999217i	$-0.512595\pi$
$821$	1.85342e7	−	1.85342e7i	0.959659	−	0.959659i	0.999217	+	0.0395583i	$0.0125951\pi$
$822$	2.40340e6	+	4.97226e6i	0.124064	+	0.256670i
$823$		−	5.26273e6i		−	0.270839i	−0.990788	−	0.135420i	$-0.956762\pi$
$823$		−	5.26273e6i		−	0.270839i	0.990788	−	0.135420i	$-0.0432383\pi$
$824$	−5.44558e6	−	8.58350e6i	−0.279400	−	0.440399i
$825$		−	1.29803e6i		−	0.0663971i
$826$	2.07899e6	−	1.00491e6i	0.106024	−	0.0512478i
$827$	−2.36453e7	+	2.36453e7i	−1.20221	+	1.20221i	−0.228718	+	0.973493i	$0.573453\pi$
$827$	−2.36453e7	+	2.36453e7i	−1.20221	+	1.20221i	−0.973493	+	0.228718i	$0.926547\pi$
$828$	−8.17143e6	−	6.47783e6i	−0.414212	−	0.328363i
$829$	7.00369e6	+	7.00369e6i	0.353949	+	0.353949i	0.861577	−	0.507628i	$-0.169477\pi$
$829$	7.00369e6	+	7.00369e6i	0.353949	+	0.353949i	−0.507628	+	0.861577i	$0.669477\pi$
$830$	−750023.	+	2.15345e6i	−0.0377902	+	0.108502i
$831$	−8.40206e6			−0.422069
$832$	1.87200e7	−	6.73373e6i	0.937557	−	0.337247i
$833$	3.07453e6			0.153520
$834$	−7.57356e6	+	2.17451e7i	−0.377038	+	1.08254i
$835$	−194224.	−	194224.i	−0.00964021	−	0.00964021i
$836$	7.96888e6	+	6.31726e6i	0.394350	+	0.312617i
$837$	4.73987e6	−	4.73987e6i	0.233858	−	0.233858i
$838$	−1.65271e7	+	7.98857e6i	−0.812993	+	0.392970i
$839$		−	2.64826e7i		−	1.29884i	−0.760429	−	0.649421i	$-0.775011\pi$
$839$		−	2.64826e7i		−	1.29884i	0.760429	−	0.649421i	$-0.224989\pi$
$840$	−946073.	−	1.49123e6i	−0.0462622	−	0.0729200i
$841$			2.34881e7i			1.14514i
$842$	1.38277e7	+	2.86074e7i	0.672157	+	1.39059i
$843$	−2.33247e6	+	2.33247e6i	−0.113044	+	0.113044i
$844$	−2.29931e6	−	1.98885e7i	−0.111107	−	0.961051i
$845$	47596.2	+	47596.2i	0.00229314	+	0.00229314i
$846$	4.29480e6	+	1.49583e6i	0.206309	+	0.0718550i
$847$	4.66620e6			0.223488
$848$	1.63339e7	+	1.01317e7i	0.780011	+	0.483828i
$849$	−1.67231e7			−0.796247
$850$	682568.	+	237731.i	0.0324040	+	0.0112859i
$851$	1.55438e7	+	1.55438e7i	0.735755	+	0.735755i
$852$	−9.35830e6	+	1.08191e6i	−0.441670	+	0.0510615i
$853$	−829478.	+	829478.i	−0.0390330	+	0.0390330i	−0.726354	−	0.687321i	$-0.758787\pi$
$853$	−829478.	+	829478.i	−0.0390330	+	0.0390330i	0.687321	+	0.726354i	$0.258787\pi$
$854$	4.08924e6	+	8.46000e6i	0.191866	+	0.396941i
$855$			5.56906e6i			0.260535i
$856$	−4.67733e6	+	2.09115e7i	−0.218180	+	0.975442i
$857$		−	4.10414e7i		−	1.90884i	−0.298463	−	0.954421i	$-0.596474\pi$
$857$		−	4.10414e7i		−	1.90884i	0.298463	−	0.954421i	$-0.403526\pi$
$858$	−6.42189e6	+	3.10410e6i	−0.297814	+	0.143952i
$859$	−1.37014e7	+	1.37014e7i	−0.633551	+	0.633551i	−0.948957	−	0.315406i	$-0.897859\pi$
$859$	−1.37014e7	+	1.37014e7i	−0.633551	+	0.633551i	0.315406	+	0.948957i	$0.397859\pi$
$860$	6.52606e6	−	8.23227e6i	0.300888	−	0.379554i
$861$	−3.55327e6	−	3.55327e6i	−0.163350	−	0.163350i
$862$	1.26622e7	−	3.63555e7i	0.580419	−	1.66649i
$863$	1.84490e7			0.843230			0.421615	−	0.906775i	$-0.361463\pi$
$863$	1.84490e7			0.843230			0.421615	+	0.906775i	$0.361463\pi$
$864$	1.67101e7	−	1.35251e7i	0.761542	−	0.616392i
$865$	−4.23695e6			−0.192537
$866$	−7.88759e6	+	2.26467e7i	−0.357396	+	1.02615i
$867$	9.04423e6	+	9.04423e6i	0.408624	+	0.408624i
$868$	1.50963e6	−	1.90432e6i	0.0680099	−	0.0857907i
$869$	7.25081e6	−	7.25081e6i	0.325715	−	0.325715i
$870$	−7.83901e6	+	3.78908e6i	−0.351126	+	0.169721i
$871$		−	1.92760e7i		−	0.860935i
$872$	1.45984e7	+	3.26526e6i	0.650150	+	0.145421i
$873$			7.70548e6i			0.342188i
$874$	−7.26336e6	−	1.50268e7i	−0.321632	−	0.665407i
$875$	464534.	−	464534.i	0.0205115	−	0.0205115i
$876$	−1.80562e6	+	208748.i	−0.0794999	+	0.00919098i
$877$	−9.58937e6	−	9.58937e6i	−0.421009	−	0.421009i	0.464542	−	0.885551i	$-0.346219\pi$
$877$	−9.58937e6	−	9.58937e6i	−0.421009	−	0.421009i	−0.885551	+	0.464542i	$0.846219\pi$
$878$	1.56472e7	+	5.44974e6i	0.685015	+	0.238583i
$879$	−8.74103e6			−0.381584
$880$	5.57720e6	−	1.30703e6i	0.242778	−	0.0568956i
$881$	−2.81821e7			−1.22330			−0.611650	−	0.791129i	$-0.709494\pi$
$881$	−2.81821e7			−1.22330			−0.611650	+	0.791129i	$0.709494\pi$
$882$	1.26019e7	+	4.38908e6i	0.545460	+	0.189978i
$883$	−2.69238e7	−	2.69238e7i	−1.16208	−	1.16208i	−0.984020	−	0.178057i	$-0.943019\pi$
$883$	−2.69238e7	−	2.69238e7i	−1.16208	−	1.16208i	−0.178057	−	0.984020i	$-0.556981\pi$
$884$	−456134.	−	3.94546e6i	−0.0196319	−	0.169811i
$885$	1.59295e6	−	1.59295e6i	0.0683666	−	0.0683666i
$886$	3.29716e6	+	6.82131e6i	0.141109	+	0.291933i
$887$		−	1.95508e7i		−	0.834363i	−0.908823	−	0.417181i	$-0.863018\pi$
$887$		−	1.95508e7i		−	0.834363i	0.908823	−	0.417181i	$-0.136982\pi$
$888$	−1.50116e7	+	9.52369e6i	−0.638842	+	0.405297i
$889$			1.22673e7i			0.520588i
$890$	1.34201e7	−	6.48677e6i	0.567913	−	0.274507i
$891$	580637.	−	580637.i	0.0245025	−	0.0245025i
$892$	−3.09985e7	−	2.45738e7i	−1.30445	−	1.03409i
$893$	5.14714e6	+	5.14714e6i	0.215992	+	0.215992i
$894$	2.07492e6	−	5.95746e6i	0.0868274	−	0.249297i
$895$	−1.94337e7			−0.810955
$896$	5.45470e6	−	5.56654e6i	0.226987	−	0.231641i
$897$	1.17067e7			0.485794
$898$	−1.01068e7	+	2.90184e7i	−0.418236	+	1.20083i
$899$	−8.47169e6	−	8.47169e6i	−0.349600	−	0.349600i
$900$	2.45833e6	+	1.94882e6i	0.101166	+	0.0801983i
$901$	2.71340e6	−	2.71340e6i	0.111353	−	0.111353i
$902$	1.46751e7	−	7.09337e6i	0.600570	−	0.290293i
$903$			5.12443e6i			0.209135i
$904$	2.48863e7	−	1.57885e7i	1.01284	−	0.642569i
$905$			1.27894e7i			0.519072i
$906$	−1.22120e7	−	2.52647e7i	−0.494271	−	1.02257i
$907$	2.19797e7	−	2.19797e7i	0.887162	−	0.887162i	−0.107088	−	0.994250i	$-0.534153\pi$
$907$	2.19797e7	−	2.19797e7i	0.887162	−	0.887162i	0.994250	+	0.107088i	$0.0341525\pi$
$908$	−3.35257e6	−	2.89990e7i	−0.134947	−	1.16726i
$909$	−2.31261e6	−	2.31261e6i	−0.0928307	−	0.0928307i
$910$	−3.40913e6	−	1.18736e6i	−0.136471	−	0.0475313i
$911$	−2.26971e7			−0.906098			−0.453049	−	0.891486i	$-0.649664\pi$
$911$	−2.26971e7			−0.906098			−0.453049	+	0.891486i	$0.649664\pi$
$912$	1.31418e7	−	3.07980e6i	0.523199	−	0.122613i
$913$	3.60801e6			0.143249
$914$	2.71984e7	+	9.47290e6i	1.07691	+	0.375075i
$915$	6.48215e6	+	6.48215e6i	0.255957	+	0.255957i
$916$	3.62259e7	−	4.18807e6i	1.42653	−	0.164921i
$917$	−659950.	+	659950.i	−0.0259172	+	0.0259172i
$918$	−1.86778e6	−	3.86414e6i	−0.0731506	−	0.151337i
$919$		−	9.37523e6i		−	0.366179i	−0.983096	−	0.183089i	$-0.941390\pi$
$919$		−	9.37523e6i		−	0.366179i	0.983096	−	0.183089i	$-0.0586098\pi$
$920$	−9.17492e6	−	2.05218e6i	−0.357382	−	0.0799366i
$921$			1.48528e7i			0.576978i
$922$	4.87145e6	−	2.35467e6i	0.188726	−	0.0912228i
$923$	−1.36168e7	+	1.36168e7i	−0.526104	+	0.526104i
$924$	−1.73585e6	+	2.18968e6i	−0.0668856	+	0.0843726i
$925$	−4.67626e6	−	4.67626e6i	−0.179698	−	0.179698i
$926$	−1.48569e7	+	4.26568e7i	−0.569378	+	1.63479i
$927$	−8.80817e6			−0.336656
$928$	−2.41738e7	−	2.98663e7i	−0.921457	−	1.13844i
$929$	−1.09940e7			−0.417942			−0.208971	−	0.977922i	$-0.567011\pi$
$929$	−1.09940e7			−0.417942			−0.208971	+	0.977922i	$0.567011\pi$
$930$	779781.	−	2.23889e6i	0.0295641	−	0.0848840i
$931$	1.51028e7	+	1.51028e7i	0.571061	+	0.571061i
$932$	2.76950e6	−	3.49357e6i	0.104439	−	0.131744i
$933$	4.62638e6	−	4.62638e6i	0.173995	−	0.173995i
$934$	4.38889e7	−	2.12142e7i	1.64622	−	0.795718i
$935$		−	1.14361e6i		−	0.0427809i
$936$	3.76280e6	−	1.68228e7i	0.140385	−	0.627637i
$937$			1.98431e7i			0.738346i	0.929361	+	0.369173i	$0.120359\pi$
$937$			1.98431e7i			0.738346i	−0.929361	+	0.369173i	$0.879641\pi$
$938$	−3.28628e6	−	6.79879e6i	−0.121954	−	0.252304i
$939$	−6.86654e6	+	6.86654e6i	−0.254141	+	0.254141i
$940$	4.07325e6	−	470909.i	0.150356	−	0.0173827i
$941$	−675505.	−	675505.i	−0.0248688	−	0.0248688i	0.694563	−	0.719432i	$-0.255598\pi$
$941$	−675505.	−	675505.i	−0.0248688	−	0.0248688i	−0.719432	+	0.694563i	$0.755598\pi$
$942$	−1.35124e7	−	4.70623e6i	−0.496142	−	0.172801i
$943$	−2.67517e7			−0.979651
$944$	8.44838e6	+	5.24039e6i	0.308563	+	0.191396i
$945$	−3.90096e6			−0.142099
$946$	−1.56969e7	−	5.46707e6i	−0.570279	−	0.198622i
$947$	−2.78122e7	−	2.78122e7i	−1.00777	−	1.00777i	−0.999970	−	0.00779749i	$-0.997518\pi$
$947$	−2.78122e7	−	2.78122e7i	−1.00777	−	1.00777i	−0.00779749	−	0.999970i	$-0.502482\pi$
$948$	−1.56313e6	−	1.35207e7i	−0.0564903	−	0.488628i
$949$	−2.62727e6	+	2.62727e6i	−0.0946978	+	0.0946978i
$950$	2.18514e6	+	4.52072e6i	0.0785544	+	0.162517i
$951$		−	1.52110e7i		−	0.545389i
$952$	−833527.	−	1.31383e6i	−0.0298076	−	0.0469837i
$953$		−	3.53971e7i		−	1.26251i	−0.775574	−	0.631256i	$-0.782540\pi$
$953$		−	3.53971e7i		−	1.26251i	0.775574	−	0.631256i	$-0.217460\pi$
$954$	1.49952e7	−	7.24812e6i	0.533436	−	0.257842i
$955$	−5.67319e6	+	5.67319e6i	−0.201288	+	0.201288i
$956$	2.86078e7	+	2.26786e7i	1.01237	+	0.802547i
$957$	9.74118e6	+	9.74118e6i	0.343820	+	0.343820i
$958$	−1.26576e7	+	3.63421e7i	−0.445591	+	1.27937i
$959$	4.42250e6			0.155282
$960$	3.23928e6	−	6.87885e6i	0.113441	−	0.240901i
$961$	−2.53668e7			−0.886049
$962$	−1.19527e7	+	3.43182e7i	−0.416415	+	1.19560i
$963$	1.31293e7	+	1.31293e7i	0.456222	+	0.456222i
$964$	8.16836e6	+	6.47540e6i	0.283102	+	0.224426i
$965$	9.75839e6	−	9.75839e6i	0.337334	−	0.337334i
$966$	4.12904e6	−	1.99582e6i	0.142366	−	0.0688143i
$967$		−	2.63332e7i		−	0.905602i	−0.891612	−	0.452801i	$-0.850425\pi$
$967$		−	2.63332e7i		−	0.905602i	0.891612	−	0.452801i	$-0.149575\pi$
$968$	1.07623e7	+	1.69639e7i	0.369162	+	0.581884i
$969$		−	2.69474e6i		−	0.0921950i
$970$	3.02341e6	+	6.25497e6i	0.103173	+	0.213450i
$971$	3.80165e6	−	3.80165e6i	0.129397	−	0.129397i	−0.639442	−	0.768839i	$-0.720835\pi$
$971$	3.80165e6	−	3.80165e6i	0.129397	−	0.129397i	0.768839	+	0.639442i	$0.220835\pi$
$972$	−3.43944e6	−	2.97504e7i	−0.116768	−	1.01001i
$973$	1.30385e7	+	1.30385e7i	0.441515	+	0.441515i
$974$	−6.60077e6	−	2.29898e6i	−0.222945	−	0.0776492i
$975$	−3.52189e6			−0.118649
$976$	−2.13246e7	+	3.43788e7i	−0.716566	+	1.15522i
$977$	−3.04728e7			−1.02135			−0.510676	−	0.859773i	$-0.670605\pi$
$977$	−3.04728e7			−1.02135			−0.510676	+	0.859773i	$0.670605\pi$
$978$	2.73850e7	+	9.53787e6i	0.915514	+	0.318863i
$979$	−1.66766e7	−	1.66766e7i	−0.556097	−	0.556097i
$980$	1.19518e7	−	1.38174e6i	0.397528	−	0.0459582i
$981$	9.16560e6	−	9.16560e6i	0.304081	−	0.304081i
$982$	−1.66358e7	−	3.44169e7i	−0.550511	−	1.13892i
$983$		−	3.80748e7i		−	1.25676i	−0.777905	−	0.628382i	$-0.783718\pi$
$983$		−	3.80748e7i		−	1.25676i	0.777905	−	0.628382i	$-0.216282\pi$
$984$	4.72245e6	−	2.11132e7i	0.155482	−	0.695131i
$985$			2.27503e7i			0.747132i
$986$	−6.90647e6	+	3.33832e6i	−0.226237	+	0.109354i
$987$	−1.41433e6	+	1.41433e6i	−0.0462122	+	0.0462122i
$988$	1.71404e7	−	2.16216e7i	0.558635	−	0.704687i
$989$	1.92903e7	+	1.92903e7i	0.627116	+	0.627116i
$990$	1.63258e6	−	4.68744e6i	0.0529404	−	0.152001i
$991$	−3.48133e7			−1.12606			−0.563030	−	0.826437i	$-0.690364\pi$
$991$	−3.48133e7			−1.12606			−0.563030	+	0.826437i	$0.690364\pi$
$992$	1.04050e7	+	1.09605e6i	0.335708	+	0.0353631i
$993$	8.81693e6			0.283755
$994$	−2.48129e6	+	7.12424e6i	−0.0796549	+	0.228704i
$995$	1.60842e6	+	1.60842e6i	0.0515041	+	0.0515041i
$996$	2.97505e6	−	3.75287e6i	0.0950269	−	0.119871i
$997$	−3.92368e7	+	3.92368e7i	−1.25013	+	1.25013i	−0.294471	+	0.955660i	$0.595143\pi$
$997$	−3.92368e7	+	3.92368e7i	−1.25013	+	1.25013i	−0.955660	+	0.294471i	$0.904857\pi$
$998$	3.48984e7	−	1.68685e7i	1.10912	−	0.536106i
$999$			3.92693e7i			1.24491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.61.17	yes	80
4.3	odd	2		320.6.l.a.81.25		80
16.5	even	4	inner	80.6.l.a.21.17	✓	80
16.11	odd	4		320.6.l.a.241.25		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.17	✓	80	16.5	even	4	inner
80.6.l.a.61.17	yes	80	1.1	even	1	trivial
320.6.l.a.81.25		80	4.3	odd	2
320.6.l.a.241.25		80	16.11	odd	4

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.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86060 + 5.34211i) q^{2} +(-6.56300 - 6.56300i) q^{3} +(-25.0763 - 19.8791i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(47.2714 - 22.8492i) q^{6} -42.0449i q^{7} +(152.853 - 96.9737i) q^{8} -156.854i q^{9} +O(q^{10})\)	\(q+(-1.86060 + 5.34211i) q^{2} +(-6.56300 - 6.56300i) q^{3} +(-25.0763 - 19.8791i) q^{4} +(-17.6777 + 17.6777i) q^{5} +(47.2714 - 22.8492i) q^{6} -42.0449i q^{7} +(152.853 - 96.9737i) q^{8} -156.854i q^{9} +(-61.5451 - 127.327i) q^{10} +(-158.224 + 158.224i) q^{11} +(34.1098 + 295.042i) q^{12} +(429.302 + 429.302i) q^{13} +(224.608 + 78.2286i) q^{14} +232.037 q^{15} +(233.646 + 996.988i) q^{16} +204.434 q^{17} +(837.932 + 291.842i) q^{18} +(1004.23 + 1004.23i) q^{19} +(794.707 - 91.8760i) q^{20} +(-275.940 + 275.940i) q^{21} +(-550.858 - 1139.64i) q^{22} +2077.49i q^{23} +(-1639.61 - 366.737i) q^{24} -625.000i q^{25} +(-3092.14 + 1494.62i) q^{26} +(-2624.24 + 2624.24i) q^{27} +(-835.812 + 1054.33i) q^{28} +(4690.38 + 4690.38i) q^{29} +(-431.728 + 1239.57i) q^{30} -1806.19 q^{31} +(-5760.75 - 606.829i) q^{32} +2076.84 q^{33} +(-380.369 + 1092.11i) q^{34} +(743.255 + 743.255i) q^{35} +(-3118.11 + 3933.33i) q^{36} +(7482.02 - 7482.02i) q^{37} +(-7233.15 + 3496.23i) q^{38} -5635.02i q^{39} +(-987.818 + 4416.36i) q^{40} +12876.9i q^{41} +(-960.691 - 1987.52i) q^{42} +(9285.39 - 9285.39i) q^{43} +(7113.01 - 822.335i) q^{44} +(2772.81 + 2772.81i) q^{45} +(-11098.2 - 3865.37i) q^{46} +5125.48 q^{47} +(5009.81 - 8076.66i) q^{48} +15039.2 q^{49} +(3338.82 + 1162.87i) q^{50} +(-1341.70 - 1341.70i) q^{51} +(-2231.21 - 19299.4i) q^{52} +(13272.8 - 13272.8i) q^{53} +(-9136.34 - 18901.7i) q^{54} -5594.05i q^{55} +(-4077.25 - 6426.69i) q^{56} -13181.5i q^{57} +(-33783.4 + 16329.6i) q^{58} +(6865.06 - 6865.06i) q^{59} +(-5818.64 - 4612.68i) q^{60} +(27935.8 + 27935.8i) q^{61} +(3360.59 - 9648.85i) q^{62} -6594.91 q^{63} +(13960.2 - 29645.5i) q^{64} -15178.1 q^{65} +(-3864.17 + 11094.7i) q^{66} +(-22450.3 - 22450.3i) q^{67} +(-5126.45 - 4063.95i) q^{68} +(13634.5 - 13634.5i) q^{69} +(-5353.45 + 2587.65i) q^{70} +31718.5i q^{71} +(-15210.7 - 23975.6i) q^{72} +6119.87i q^{73} +(26048.8 + 53890.8i) q^{74} +(-4101.88 + 4101.88i) q^{75} +(-5219.26 - 45145.4i) q^{76} +(6652.49 + 6652.49i) q^{77} +(30102.9 + 10484.5i) q^{78} -45826.3 q^{79} +(-21754.8 - 13494.1i) q^{80} -3669.72 q^{81} +(-68790.1 - 23958.8i) q^{82} +(-11401.6 - 11401.6i) q^{83} +(12405.0 - 1434.14i) q^{84} +(-3613.91 + 3613.91i) q^{85} +(32327.2 + 66880.0i) q^{86} -61565.9i q^{87} +(-8841.45 + 39528.5i) q^{88} +105399. i q^{89} +(-19971.8 + 9653.59i) q^{90} +(18049.9 - 18049.9i) q^{91} +(41298.5 - 52095.8i) q^{92} +(11854.0 + 11854.0i) q^{93} +(-9536.46 + 27380.9i) q^{94} -35504.8 q^{95} +(33825.2 + 41790.4i) q^{96} -49125.2 q^{97} +(-27982.0 + 80341.3i) q^{98} +(24818.0 + 24818.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) \) 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

Introduction

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