LMFDB - Embedded newform 80.6.j.a.43.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(43,80)]

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([2, 1, 3]))

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

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

chi := DirichletCharacter("80.43");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.j (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			43.13
Character	$\chi$	$=$	80.43
Dual form			80.6.j.a.67.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.35770 - 3.60700i) q^{2} +8.79961i q^{3} +(5.97913 + 31.4364i) q^{4} +(-29.5991 - 47.4225i) q^{5} +(31.7402 - 38.3461i) q^{6} +(-6.66435 + 6.66435i) q^{7} +(87.3359 - 158.557i) q^{8} +165.567 q^{9} +O(q^{10})$	\(q+(-4.35770 - 3.60700i) q^{2} +8.79961i q^{3} +(5.97913 + 31.4364i) q^{4} +(-29.5991 - 47.4225i) q^{5} +(31.7402 - 38.3461i) q^{6} +(-6.66435 + 6.66435i) q^{7} +(87.3359 - 158.557i) q^{8} +165.567 q^{9} +(-42.0688 + 313.417i) q^{10} +(90.0969 - 90.0969i) q^{11} +(-276.628 + 52.6140i) q^{12} -441.808 q^{13} +(53.0795 - 5.00295i) q^{14} +(417.300 - 260.461i) q^{15} +(-952.500 + 375.925i) q^{16} +(-1193.08 + 1193.08i) q^{17} +(-721.491 - 597.199i) q^{18} +(-690.532 + 690.532i) q^{19} +(1313.82 - 1214.04i) q^{20} +(-58.6437 - 58.6437i) q^{21} +(-717.595 + 67.6361i) q^{22} +(2731.55 + 2731.55i) q^{23} +(1395.24 + 768.522i) q^{24} +(-1372.79 + 2807.33i) q^{25} +(1925.27 + 1593.60i) q^{26} +3595.23i q^{27} +(-249.350 - 169.656i) q^{28} +(2169.09 + 2169.09i) q^{29} +(-2757.95 - 370.189i) q^{30} +1246.87i q^{31} +(5506.67 + 1797.50i) q^{32} +(792.818 + 792.818i) q^{33} +(9502.54 - 895.652i) q^{34} +(513.299 + 118.781i) q^{35} +(989.946 + 5204.83i) q^{36} -9836.99 q^{37} +(5499.88 - 518.385i) q^{38} -3887.74i q^{39} +(-10104.3 + 551.467i) q^{40} +8773.06i q^{41} +(44.0240 + 467.079i) q^{42} -7908.26 q^{43} +(3371.03 + 2293.63i) q^{44} +(-4900.63 - 7851.59i) q^{45} +(-2050.59 - 21756.0i) q^{46} +(-17098.7 - 17098.7i) q^{47} +(-3308.00 - 8381.63i) q^{48} +16718.2i q^{49} +(16108.2 - 7281.85i) q^{50} +(-10498.7 - 10498.7i) q^{51} +(-2641.63 - 13888.9i) q^{52} +21623.1i q^{53} +(12968.0 - 15666.9i) q^{54} +(-6939.41 - 1605.83i) q^{55} +(474.644 + 1638.72i) q^{56} +(-6076.41 - 6076.41i) q^{57} +(-1628.34 - 17276.1i) q^{58} +(12633.6 + 12633.6i) q^{59} +(10683.0 + 11561.1i) q^{60} +(32609.2 - 32609.2i) q^{61} +(4497.45 - 5433.48i) q^{62} +(-1103.39 + 1103.39i) q^{63} +(-17512.9 - 27695.5i) q^{64} +(13077.1 + 20951.7i) q^{65} +(-595.172 - 6314.56i) q^{66} +2779.13 q^{67} +(-44639.9 - 30372.7i) q^{68} +(-24036.6 + 24036.6i) q^{69} +(-1808.36 - 2369.08i) q^{70} +11341.6 q^{71} +(14459.9 - 26251.8i) q^{72} +(-37909.6 + 37909.6i) q^{73} +(42866.7 + 35482.0i) q^{74} +(-24703.4 - 12080.0i) q^{75} +(-25836.6 - 17579.1i) q^{76} +1200.87i q^{77} +(-14023.1 + 16941.6i) q^{78} +10521.9 q^{79} +(46020.5 + 34042.9i) q^{80} +8596.12 q^{81} +(31644.4 - 38230.4i) q^{82} -74906.8i q^{83} +(1492.91 - 2194.19i) q^{84} +(91893.1 + 21264.8i) q^{85} +(34461.9 + 28525.1i) q^{86} +(-19087.1 + 19087.1i) q^{87} +(-6416.83 - 22154.2i) q^{88} +18693.6 q^{89} +(-6965.20 + 51891.5i) q^{90} +(2944.36 - 2944.36i) q^{91} +(-69537.9 + 102203. i) q^{92} -10972.0 q^{93} +(12836.1 + 136186. i) q^{94} +(53185.9 + 12307.6i) q^{95} +(-15817.3 + 48456.6i) q^{96} +(-53039.7 + 53039.7i) q^{97} +(60302.4 - 72852.8i) q^{98} +(14917.1 - 14917.1i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 2 q^{2} - 20 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 248 q^{8} - 8748 q^{9}+O(q^{10}) $ 116 * q - 2 * q^2 - 20 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 248 * q^8 - 8748 * q^9	\( 116 q - 2 q^{2} - 20 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 248 q^{8} - 8748 q^{9} - 66 q^{10} - 4 q^{11} - 308 q^{12} - 4 q^{13} + 972 q^{15} - 1224 q^{16} - 4 q^{17} + 4214 q^{18} - 2360 q^{19} - 836 q^{20} - 4 q^{21} - 2440 q^{22} - 4 q^{23} + 972 q^{24} - 884 q^{26} - 12416 q^{28} + 15336 q^{30} - 17612 q^{32} - 4 q^{33} - 12520 q^{34} - 8640 q^{35} + 2380 q^{36} - 4 q^{37} + 15108 q^{38} + 11864 q^{40} - 41092 q^{42} - 1316 q^{43} + 8200 q^{44} - 5766 q^{45} - 35924 q^{46} + 65256 q^{47} + 5180 q^{48} - 44378 q^{50} + 10436 q^{51} + 63080 q^{52} + 33820 q^{54} - 4 q^{55} - 64684 q^{56} + 972 q^{57} - 66940 q^{58} - 14480 q^{59} + 136260 q^{60} + 48076 q^{61} + 109524 q^{62} + 972 q^{63} + 71920 q^{64} - 4 q^{65} + 72436 q^{66} - 89260 q^{67} + 36360 q^{68} - 21348 q^{69} + 59552 q^{70} - 143848 q^{71} + 179728 q^{72} - 10072 q^{73} - 82508 q^{74} - 32272 q^{75} - 128004 q^{76} + 111388 q^{78} + 313732 q^{80} + 551116 q^{81} - 282876 q^{82} - 80928 q^{84} - 6252 q^{85} - 85324 q^{86} - 282188 q^{87} + 80224 q^{88} + 115550 q^{90} - 164724 q^{91} + 474536 q^{92} + 968 q^{93} - 106060 q^{94} + 204760 q^{95} - 62264 q^{96} - 4 q^{97} + 50214 q^{98} - 168788 q^{99}+O(q^{100}) \) 116 * q - 2 * q^2 - 20 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 248 * q^8 - 8748 * q^9 - 66 * q^10 - 4 * q^11 - 308 * q^12 - 4 * q^13 + 972 * q^15 - 1224 * q^16 - 4 * q^17 + 4214 * q^18 - 2360 * q^19 - 836 * q^20 - 4 * q^21 - 2440 * q^22 - 4 * q^23 + 972 * q^24 - 884 * q^26 - 12416 * q^28 + 15336 * q^30 - 17612 * q^32 - 4 * q^33 - 12520 * q^34 - 8640 * q^35 + 2380 * q^36 - 4 * q^37 + 15108 * q^38 + 11864 * q^40 - 41092 * q^42 - 1316 * q^43 + 8200 * q^44 - 5766 * q^45 - 35924 * q^46 + 65256 * q^47 + 5180 * q^48 - 44378 * q^50 + 10436 * q^51 + 63080 * q^52 + 33820 * q^54 - 4 * q^55 - 64684 * q^56 + 972 * q^57 - 66940 * q^58 - 14480 * q^59 + 136260 * q^60 + 48076 * q^61 + 109524 * q^62 + 972 * q^63 + 71920 * q^64 - 4 * q^65 + 72436 * q^66 - 89260 * q^67 + 36360 * q^68 - 21348 * q^69 + 59552 * q^70 - 143848 * q^71 + 179728 * q^72 - 10072 * q^73 - 82508 * q^74 - 32272 * q^75 - 128004 * q^76 + 111388 * q^78 + 313732 * q^80 + 551116 * q^81 - 282876 * q^82 - 80928 * q^84 - 6252 * q^85 - 85324 * q^86 - 282188 * q^87 + 80224 * q^88 + 115550 * q^90 - 164724 * q^91 + 474536 * q^92 + 968 * q^93 - 106060 * q^94 + 204760 * q^95 - 62264 * q^96 - 4 * q^97 + 50214 * q^98 - 168788 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−4.35770	−	3.60700i	−0.770340	−	0.637633i
$2$	−4.35770	−	3.60700i	−0.770340	−	0.637633i
$3$			8.79961i			0.564495i	0.959342	+	0.282248i	$0.0910800\pi$
$3$			8.79961i			0.564495i	−0.959342	+	0.282248i	$0.908920\pi$
$4$	5.97913	+	31.4364i	0.186848	+	0.982389i
$5$	−29.5991	−	47.4225i	−0.529485	−	0.848319i
$5$	−29.5991	−	47.4225i	−0.529485	−	0.848319i
$6$	31.7402	−	38.3461i	0.359941	−	0.434853i
$7$	−6.66435	+	6.66435i	−0.0514059	+	0.0514059i	−0.732342	−	0.680937i	$-0.761573\pi$
$7$	−6.66435	+	6.66435i	−0.0514059	+	0.0514059i	0.680937	+	0.732342i	$0.261573\pi$
$8$	87.3359	−	158.557i	0.482467	−	0.875914i
$9$	165.567			0.681345
$10$	−42.0688	+	313.417i	−0.133033	+	0.991112i
$11$	90.0969	−	90.0969i	0.224506	−	0.224506i	−0.585887	−	0.810393i	$-0.699254\pi$
$11$	90.0969	−	90.0969i	0.224506	−	0.224506i	0.810393	+	0.585887i	$0.199254\pi$
$12$	−276.628	+	52.6140i	−0.554554	+	0.105475i
$13$	−441.808			−0.725063			−0.362531	−	0.931972i	$-0.618087\pi$
$13$	−441.808			−0.725063			−0.362531	+	0.931972i	$0.618087\pi$
$14$	53.0795	−	5.00295i	0.0723781	−	0.00682191i
$15$	417.300	−	260.461i	0.478872	−	0.298892i
$16$	−952.500	+	375.925i	−0.930176	+	0.367115i
$17$	−1193.08	+	1193.08i	−1.00126	+	1.00126i	−0.00126360	+	0.999999i	$0.500402\pi$
$17$	−1193.08	+	1193.08i	−1.00126	+	1.00126i	−0.999999	+	0.00126360i	$0.999598\pi$
$18$	−721.491	−	597.199i	−0.524867	−	0.434448i
$19$	−690.532	+	690.532i	−0.438833	+	0.438833i	−0.891619	−	0.452786i	$-0.850430\pi$
$19$	−690.532	+	690.532i	−0.438833	+	0.438833i	0.452786	+	0.891619i	$0.350430\pi$
$20$	1313.82	−	1214.04i	0.734447	−	0.678667i
$21$	−58.6437	−	58.6437i	−0.0290184	−	0.0290184i
$22$	−717.595	+	67.6361i	−0.316099	+	0.0297935i
$23$	2731.55	+	2731.55i	1.07669	+	1.07669i	0.996804	+	0.0798830i	$0.0254547\pi$
$23$	2731.55	+	2731.55i	1.07669	+	1.07669i	0.0798830	+	0.996804i	$0.474545\pi$
$24$	1395.24	+	768.522i	0.494449	+	0.272351i
$25$	−1372.79	+	2807.33i	−0.439292	+	0.898344i
$26$	1925.27	+	1593.60i	0.558545	+	0.462324i
$27$			3595.23i			0.949111i
$28$	−249.350	−	169.656i	−0.0601056	−	0.0408955i
$29$	2169.09	+	2169.09i	0.478941	+	0.478941i	0.904793	−	0.425852i	$-0.140026\pi$
$29$	2169.09	+	2169.09i	0.478941	+	0.478941i	−0.425852	+	0.904793i	$0.640026\pi$
$30$	−2757.95	−	370.189i	−0.559478	−	0.0750967i
$31$			1246.87i			0.233033i	0.993189	+	0.116516i	$0.0371727\pi$
$31$			1246.87i			0.233033i	−0.993189	+	0.116516i	$0.962827\pi$
$32$	5506.67	+	1797.50i	0.950636	+	0.310308i
$33$	792.818	+	792.818i	0.126733	+	0.126733i
$34$	9502.54	−	895.652i	1.40975	−	0.132875i
$35$	513.299	+	118.781i	0.0708272	+	0.0163900i
$36$	989.946	+	5204.83i	0.127308	+	0.669346i
$37$	−9836.99			−1.18129			−0.590647	−	0.806930i	$-0.701127\pi$
$37$	−9836.99			−1.18129			−0.590647	+	0.806930i	$0.701127\pi$
$38$	5499.88	−	518.385i	0.617866	−	0.0582363i
$39$		−	3887.74i		−	0.409295i
$40$	−10104.3	+	551.467i	−0.998514	+	0.0544966i
$41$			8773.06i			0.815064i	0.913191	+	0.407532i	$0.133610\pi$
$41$			8773.06i			0.815064i	−0.913191	+	0.407532i	$0.866390\pi$
$42$	44.0240	+	467.079i	0.00385094	+	0.0408571i
$43$	−7908.26			−0.652244			−0.326122	−	0.945328i	$-0.605742\pi$
$43$	−7908.26			−0.652244			−0.326122	+	0.945328i	$0.605742\pi$
$44$	3371.03	+	2293.63i	0.262501	+	0.178604i
$45$	−4900.63	−	7851.59i	−0.360762	−	0.577998i
$46$	−2050.59	−	21756.0i	−0.142884	−	1.51595i
$47$	−17098.7	−	17098.7i	−1.12907	−	1.12907i	−0.990329	−	0.138736i	$-0.955696\pi$
$47$	−17098.7	−	17098.7i	−1.12907	−	1.12907i	−0.138736	−	0.990329i	$-0.544304\pi$
$48$	−3308.00	−	8381.63i	−0.207234	−	0.525080i
$49$			16718.2i			0.994715i
$50$	16108.2	−	7281.85i	0.911218	−	0.411924i
$51$	−10498.7	−	10498.7i	−0.565208	−	0.565208i
$52$	−2641.63	−	13888.9i	−0.135476	−	0.712294i
$53$			21623.1i			1.05738i	0.848816	+	0.528688i	$0.177316\pi$
$53$			21623.1i			1.05738i	−0.848816	+	0.528688i	$0.822684\pi$
$54$	12968.0	−	15666.9i	0.605185	−	0.731139i
$55$	−6939.41	−	1605.83i	−0.309326	−	0.0715804i
$56$	474.644	+	1638.72i	0.0202255	+	0.0698287i
$57$	−6076.41	−	6076.41i	−0.247719	−	0.247719i
$58$	−1628.34	−	17276.1i	−0.0635588	−	0.674336i
$59$	12633.6	+	12633.6i	0.472496	+	0.472496i	0.902722	−	0.430225i	$-0.141566\pi$
$59$	12633.6	+	12633.6i	0.472496	+	0.472496i	−0.430225	+	0.902722i	$0.641566\pi$
$60$	10683.0	+	11561.1i	0.383104	+	0.414592i
$61$	32609.2	−	32609.2i	1.12206	−	1.12206i	0.130629	−	0.991431i	$-0.458300\pi$
$61$	32609.2	−	32609.2i	1.12206	−	1.12206i	0.991431	−	0.130629i	$-0.0416997\pi$
$62$	4497.45	−	5433.48i	0.148589	−	0.179514i
$63$	−1103.39	+	1103.39i	−0.0350251	+	0.0350251i
$64$	−17512.9	−	27695.5i	−0.534451	−	0.845200i
$65$	13077.1	+	20951.7i	0.383910	+	0.615085i
$66$	−595.172	−	6314.56i	−0.0168183	−	0.178436i
$67$	2779.13			0.0756348			0.0378174	−	0.999285i	$-0.487959\pi$
$67$	2779.13			0.0756348			0.0378174	+	0.999285i	$0.487959\pi$
$68$	−44639.9	−	30372.7i	−1.17071	−	0.796546i
$69$	−24036.6	+	24036.6i	−0.607785	+	0.607785i
$70$	−1808.36	−	2369.08i	−0.0441102	−	0.0577876i
$71$	11341.6			0.267010			0.133505	−	0.991048i	$-0.457377\pi$
$71$	11341.6			0.267010			0.133505	+	0.991048i	$0.457377\pi$
$72$	14459.9	−	26251.8i	0.328727	−	0.596800i
$73$	−37909.6	+	37909.6i	−0.832611	+	0.832611i	−0.987873	−	0.155262i	$-0.950378\pi$
$73$	−37909.6	+	37909.6i	−0.832611	+	0.832611i	0.155262	+	0.987873i	$0.450378\pi$
$74$	42866.7	+	35482.0i	0.909998	+	0.753232i
$75$	−24703.4	−	12080.0i	−0.507111	−	0.247978i
$76$	−25836.6	−	17579.1i	−0.513100	−	0.349110i
$77$			1200.87i			0.0230819i
$78$	−14023.1	+	16941.6i	−0.260980	+	0.315296i
$79$	10521.9			0.189683			0.0948413	−	0.995492i	$-0.469766\pi$
$79$	10521.9			0.189683			0.0948413	+	0.995492i	$0.469766\pi$
$80$	46020.5	+	34042.9i	0.803944	+	0.594705i
$81$	8596.12			0.145576
$82$	31644.4	−	38230.4i	0.519712	−	0.627876i
$83$		−	74906.8i		−	1.19351i	−0.802424	−	0.596755i	$-0.796457\pi$
$83$		−	74906.8i		−	1.19351i	0.802424	−	0.596755i	$-0.203543\pi$
$84$	1492.91	−	2194.19i	0.0230853	−	0.0339293i
$85$	91893.1	+	21264.8i	1.37954	+	0.319237i
$86$	34461.9	+	28525.1i	0.502450	+	0.415892i
$87$	−19087.1	+	19087.1i	−0.270360	+	0.270360i
$88$	−6416.83	−	22154.2i	−0.0883312	−	0.304965i
$89$	18693.6			0.250160			0.125080	−	0.992147i	$-0.460081\pi$
$89$	18693.6			0.250160			0.125080	+	0.992147i	$0.460081\pi$
$90$	−6965.20	+	51891.5i	−0.0906416	+	0.675289i
$91$	2944.36	−	2944.36i	0.0372725	−	0.0372725i
$92$	−69537.9	+	102203.i	−0.856549	+	1.25890i
$93$	−10972.0			−0.131546
$94$	12836.1	+	136186.i	0.149835	+	1.58969i
$95$	53185.9	+	12307.6i	0.604627	+	0.139915i
$96$	−15817.3	+	48456.6i	−0.175167	+	0.536630i
$97$	−53039.7	+	53039.7i	−0.572363	+	0.572363i	−0.932788	−	0.360425i	$-0.882632\pi$
$97$	−53039.7	+	53039.7i	−0.572363	+	0.572363i	0.360425	+	0.932788i	$0.382632\pi$
$98$	60302.4	−	72852.8i	0.634263	−	0.766269i
$99$	14917.1	−	14917.1i	0.152966	−	0.152966i
$100$	−96460.4	−	26370.2i	−0.964604	−	0.263702i
$101$	29085.3	+	29085.3i	0.283707	+	0.283707i	0.834585	−	0.550879i	$-0.185707\pi$
$101$	29085.3	+	29085.3i	0.283707	+	0.283707i	−0.550879	+	0.834585i	$0.685707\pi$
$102$	7881.39	+	83618.7i	0.0750071	+	0.795798i
$103$	−121008.	−	121008.i	−1.12389	−	1.12389i	−0.991152	−	0.132735i	$-0.957624\pi$
$103$	−121008.	−	121008.i	−1.12389	−	1.12389i	−0.132735	−	0.991152i	$-0.542376\pi$
$104$	−38585.7	+	70052.0i	−0.349819	+	0.635093i
$105$	−1045.23	+	4516.83i	−0.00925206	+	0.0399816i
$106$	77994.7	−	94227.2i	0.674218	−	0.814539i
$107$			30256.1i			0.255478i	0.991808	+	0.127739i	$0.0407720\pi$
$107$			30256.1i			0.255478i	−0.991808	+	0.127739i	$0.959228\pi$
$108$	−113021.	+	21496.3i	−0.932396	+	0.177339i
$109$	5299.40	+	5299.40i	0.0427228	+	0.0427228i	0.728145	−	0.685423i	$-0.240383\pi$
$109$	5299.40	+	5299.40i	0.0427228	+	0.0427228i	−0.685423	+	0.728145i	$0.740383\pi$
$110$	24447.6	+	32028.2i	0.192644	+	0.252377i
$111$		−	86561.7i		−	0.666835i
$112$	3842.49	−	8853.09i	0.0289446	−	0.0666883i
$113$	33097.6	+	33097.6i	0.243838	+	0.243838i	0.818436	−	0.574598i	$-0.194842\pi$
$113$	33097.6	+	33097.6i	0.243838	+	0.243838i	−0.574598	+	0.818436i	$0.694842\pi$
$114$	4561.59	+	48396.8i	0.0328741	+	0.348782i
$115$	48685.5	−	210388.i	0.343285	−	1.48346i
$116$	−55219.1	+	81157.6i	−0.381017	+	0.559995i
$117$	−73148.8			−0.494018
$118$	−9484.12	−	100623.i	−0.0627036	−	0.665262i
$119$		−	15902.2i		−	0.102942i
$120$	−4852.70	−	88913.5i	−0.0307631	−	0.563656i
$121$			144816.i			0.899194i
$122$	−259723.	+	24479.9i	−1.57983	+	0.148905i
$123$	−77199.5			−0.460100
$124$	−39197.1	+	7455.19i	−0.228929	+	0.0435416i
$125$	173764.	−	17993.3i	0.994681	−	0.103000i
$126$	8788.21	−	828.323i	0.0493144	−	0.00464808i
$127$	212339.	+	212339.i	1.16821	+	1.16821i	0.982630	+	0.185576i	$0.0594151\pi$
$127$	212339.	+	212339.i	1.16821	+	1.16821i	0.185576	+	0.982630i	$0.440585\pi$
$128$	−23581.7	+	183858.i	−0.127219	+	0.991875i
$129$		−	69589.6i		−	0.368189i
$130$	18586.4	−	138470.i	0.0964575	−	0.718618i
$131$	−155377.	−	155377.i	−0.791058	−	0.791058i	0.190608	−	0.981666i	$-0.438954\pi$
$131$	−155377.	−	155377.i	−0.791058	−	0.791058i	−0.981666	+	0.190608i	$0.938954\pi$
$132$	−20183.0	+	29663.7i	−0.100821	+	0.148181i
$133$		−	9203.89i		−	0.0451172i
$134$	−12110.6	−	10024.3i	−0.0582646	−	0.0482273i
$135$	170495.	−	106416.i	0.805150	−	0.502540i
$136$	84973.0	+	293371.i	0.393943	+	1.36010i
$137$	138729.	+	138729.i	0.631490	+	0.631490i	0.948442	−	0.316952i	$-0.102659\pi$
$137$	138729.	+	138729.i	0.631490	+	0.631490i	−0.316952	+	0.948442i	$0.602659\pi$
$138$	191444.	−	18044.4i	0.855745	−	0.0806573i
$139$	−33907.9	−	33907.9i	−0.148855	−	0.148855i	0.628751	−	0.777607i	$-0.283566\pi$
$139$	−33907.9	−	33907.9i	−0.148855	−	0.148855i	−0.777607	+	0.628751i	$0.783566\pi$
$140$	−664.983	+	16846.5i	−0.00286742	+	0.0726423i
$141$	150462.	−	150462.i	0.637352	−	0.637352i
$142$	−49423.1	−	40909.0i	−0.205688	−	0.170254i
$143$	−39805.6	+	39805.6i	−0.162781	+	0.162781i
$144$	−157702.	+	62240.8i	−0.633771	+	0.250132i
$145$	38660.5	−	167067.i	0.152703	−	0.659887i
$146$	301939.	−	28458.9i	1.17229	−	0.110493i
$147$	−147113.			−0.561512
$148$	−58816.6	−	309240.i	−0.220722	−	1.16049i
$149$	−68930.7	+	68930.7i	−0.254359	+	0.254359i	−0.822755	−	0.568396i	$-0.807564\pi$
$149$	−68930.7	+	68930.7i	−0.254359	+	0.254359i	0.568396	+	0.822755i	$0.307564\pi$
$150$	64077.5	+	141746.i	0.232529	+	0.514379i
$151$	463361.			1.65378			0.826888	−	0.562366i	$-0.190109\pi$
$151$	463361.			1.65378			0.826888	+	0.562366i	$0.190109\pi$
$152$	49180.7	+	169797.i	0.172658	+	0.596103i
$153$	−197535.	+	197535.i	−0.682205	+	0.682205i
$154$	4331.55	−	5233.05i	0.0147178	−	0.0177809i
$155$	59129.6	−	36906.2i	0.197686	−	0.123387i
$156$	122217.	−	23245.3i	0.402086	−	0.0764758i
$157$		−	168011.i		−	0.543986i	−0.962299	−	0.271993i	$-0.912317\pi$
$157$		−	168011.i		−	0.543986i	0.962299	−	0.271993i	$-0.0876828\pi$
$158$	−45851.4	−	37952.6i	−0.146120	−	0.120948i
$159$	−190275.			−0.596884
$160$	−77750.8	−	314344.i	−0.240107	−	0.970746i
$161$	−36408.0			−0.110696
$162$	−37459.3	−	31006.2i	−0.112143	−	0.0928241i
$163$		−	475876.i		−	1.40289i	−0.712721	−	0.701447i	$-0.752538\pi$
$163$		−	475876.i		−	1.40289i	0.712721	−	0.701447i	$-0.247462\pi$
$164$	−275794.	+	52455.3i	−0.800710	+	0.152293i
$165$	14130.7	−	61064.1i	0.0404068	−	0.174613i
$166$	−270189.	+	326421.i	−0.761021	+	0.919408i
$167$	291550.	−	291550.i	0.808950	−	0.808950i	−0.175525	−	0.984475i	$-0.556162\pi$
$167$	291550.	−	291550.i	0.808950	−	0.808950i	0.984475	+	0.175525i	$0.0561623\pi$
$168$	−14420.1	+	4176.69i	−0.0394180	+	0.0114172i
$169$	−176098.			−0.474284
$170$	−323741.	−	424124.i	−0.859162	−	1.12556i
$171$	−114329.	+	114329.i	−0.298997	+	0.298997i
$172$	−47284.5	−	248608.i	−0.121870	−	0.640757i
$173$	51775.9			0.131526			0.0657631	−	0.997835i	$-0.479052\pi$
$173$	51775.9			0.131526			0.0657631	+	0.997835i	$0.479052\pi$
$174$	152023.	−	14328.8i	0.380660	−	0.0358786i
$175$	−9560.27	−	27857.7i	−0.0235980	−	0.0687623i
$176$	−51947.6	+	119687.i	−0.126411	+	0.291250i
$177$	−111171.	+	111171.i	−0.266722	+	0.266722i
$178$	−81461.3	−	67427.9i	−0.192709	−	0.159511i
$179$	−591050.	+	591050.i	−1.37877	+	1.37877i	−0.532070	+	0.846700i	$0.678586\pi$
$179$	−591050.	+	591050.i	−1.37877	+	1.37877i	−0.846700	+	0.532070i	$0.821414\pi$
$180$	217525.	−	201004.i	0.500411	−	0.462406i
$181$	−552594.	−	552594.i	−1.25375	−	1.25375i	−0.954028	−	0.299719i	$-0.903107\pi$
$181$	−552594.	−	552594.i	−1.25375	−	1.25375i	−0.299719	−	0.954028i	$-0.596893\pi$
$182$	−23451.0	+	2210.35i	−0.0524786	+	0.00494632i
$183$	286949.	+	286949.i	0.633398	+	0.633398i
$184$	671670.	−	194545.i	1.46255	−	0.423619i
$185$	291166.	+	466495.i	0.625477	+	1.00211i
$186$	47812.5	+	39575.8i	0.101335	+	0.0838780i
$187$			214986.i			0.449579i
$188$	435288.	−	639759.i	0.898218	−	1.32014i
$189$	−23959.9	−	23959.9i	−0.0487899	−	0.0487899i
$190$	−187375.	−	245474.i	−0.376553	−	0.493312i
$191$			95678.5i			0.189771i	0.995488	+	0.0948857i	$0.0302486\pi$
$191$			95678.5i			0.189771i	−0.995488	+	0.0948857i	$0.969751\pi$
$192$	243710.	−	154107.i	0.477111	−	0.301695i
$193$	−274042.	−	274042.i	−0.529571	−	0.529571i	0.390874	−	0.920444i	$-0.372173\pi$
$193$	−274042.	−	274042.i	−0.529571	−	0.529571i	−0.920444	+	0.390874i	$0.872173\pi$
$194$	422445.	−	39817.1i	0.805872	−	0.0759566i
$195$	−184366.	+	115074.i	−0.347213	+	0.216715i
$196$	−525560.	+	99960.2i	−0.977197	+	0.185860i
$197$	−160971.			−0.295517			−0.147758	−	0.989023i	$-0.547206\pi$
$197$	−160971.			−0.295517			−0.147758	+	0.989023i	$0.547206\pi$
$198$	−118810.	+	11198.3i	−0.215372	+	0.0202997i
$199$			665536.i			1.19135i	0.803226	+	0.595674i	$0.203115\pi$
$199$			665536.i			1.19135i	−0.803226	+	0.595674i	$0.796885\pi$
$200$	325229.	+	462846.i	0.574928	+	0.818204i
$201$			24455.3i			0.0426955i
$202$	−21834.4	−	231656.i	−0.0376499	−	0.399452i
$203$	−28911.1			−0.0492407
$204$	267268.	−	392813.i	0.449646	−	0.660862i
$205$	416041.	−	259675.i	0.691434	−	0.431564i
$206$	90841.5	+	963795.i	0.149148	+	1.58240i
$207$	452254.	+	452254.i	0.733595	+	0.733595i
$208$	420822.	−	166087.i	0.674436	−	0.266181i
$209$			124430.i			0.197042i
$210$	20847.0	−	15912.9i	0.0326208	−	0.0249000i
$211$	−597357.	−	597357.i	−0.923694	−	0.923694i	0.0735943	−	0.997288i	$-0.476553\pi$
$211$	−597357.	−	597357.i	−0.923694	−	0.923694i	−0.997288	+	0.0735943i	$0.976553\pi$
$212$	−679755.	+	129288.i	−1.03875	+	0.197568i
$213$			99801.3i			0.150726i
$214$	109134.	−	131847.i	0.162901	−	0.196805i
$215$	234077.	+	375030.i	0.345353	+	0.553311i
$216$	570050.	+	313993.i	0.831340	+	0.457915i
$217$	−8309.57	−	8309.57i	−0.0119792	−	0.0119792i
$218$	−3978.28	−	42208.1i	−0.00566962	−	0.0601526i
$219$	−333590.	−	333590.i	−0.470005	−	0.470005i
$220$	8990.07	−	227752.i	0.0125229	−	0.317253i
$221$	527114.	−	527114.i	0.725978	−	0.725978i
$222$	−312228.	+	377210.i	−0.425196	+	0.513690i
$223$	−851894.	+	851894.i	−1.14716	+	1.14716i	−0.160049	+	0.987109i	$0.551165\pi$
$223$	−851894.	+	851894.i	−1.14716	+	1.14716i	−0.987109	+	0.160049i	$0.948835\pi$
$224$	−48677.5	+	24719.2i	−0.0648199	+	0.0329166i
$225$	−227288.	+	464800.i	−0.299309	+	0.612082i
$226$	−24846.5	−	263613.i	−0.0323590	−	0.343317i
$227$	109248.			0.140718			0.0703589	−	0.997522i	$-0.477586\pi$
$227$	109248.			0.140718			0.0703589	+	0.997522i	$0.477586\pi$
$228$	154689.	−	227352.i	0.197071	−	0.289643i
$229$	82251.3	−	82251.3i	0.103646	−	0.103646i	−0.653382	−	0.757028i	$-0.726650\pi$
$229$	82251.3	−	82251.3i	0.103646	−	0.103646i	0.757028	+	0.653382i	$0.226650\pi$
$230$	−971027.	+	741201.i	−1.21035	+	0.923882i
$231$	−10567.2			−0.0130296
$232$	533364.	−	154486.i	0.650584	−	0.188438i
$233$	−708552.	+	708552.i	−0.855031	+	0.855031i	−0.990748	−	0.135716i	$-0.956666\pi$
$233$	−708552.	+	708552.i	−0.855031	+	0.855031i	0.135716	+	0.990748i	$0.456666\pi$
$234$	318761.	+	263848.i	0.380562	+	0.315002i
$235$	−304757.	+	1.31697e6i	−0.359985	+	1.55563i
$236$	−321618.	+	472695.i	−0.375890	+	0.552460i
$237$			92588.9i			0.107075i
$238$	−57359.3	+	69297.2i	−0.0656389	+	0.0793000i
$239$	−300673.			−0.340487			−0.170243	−	0.985402i	$-0.554455\pi$
$239$	−300673.			−0.340487			−0.170243	+	0.985402i	$0.554455\pi$
$240$	−299564.	+	404962.i	−0.335708	+	0.453823i
$241$	−1.31134e6			−1.45436			−0.727180	−	0.686447i	$-0.759170\pi$
$241$	−1.31134e6			−1.45436			−0.727180	+	0.686447i	$0.759170\pi$
$242$	522351.	−	631065.i	0.573356	−	0.692685i
$243$			949283.i			1.03129i
$244$	1.22009e6	+	830144.i	1.31195	+	0.892645i
$245$	792818.	−	494843.i	0.843836	−	0.526686i
$246$	336413.	+	278459.i	0.354433	+	0.293375i
$247$	305083.	−	305083.i	0.318182	−	0.318182i
$248$	197700.	+	108896.i	0.204116	+	0.112431i
$249$	659150.			0.673730
$250$	−822112.	−	548356.i	−0.831919	−	0.554897i
$251$	836025.	−	836025.i	0.837596	−	0.837596i	−0.150946	−	0.988542i	$-0.548232\pi$
$251$	836025.	−	836025.i	0.837596	−	0.837596i	0.988542	+	0.150946i	$0.0482319\pi$
$252$	−41284.2	−	28089.5i	−0.0409527	−	0.0278639i
$253$	492209.			0.483446
$254$	−159403.	−	1.69121e6i	−0.155029	−	1.64480i
$255$	−187122.	+	808624.i	−0.180208	+	0.778746i
$256$	765936.	−	716138.i	0.730454	−	0.682962i
$257$	200800.	−	200800.i	0.189640	−	0.189640i	−0.605900	−	0.795541i	$-0.707187\pi$
$257$	200800.	−	200800.i	0.189640	−	0.189640i	0.795541	+	0.605900i	$0.207187\pi$
$258$	−251010.	+	303251.i	−0.234769	+	0.283630i
$259$	65557.1	−	65557.1i	0.0607254	−	0.0607254i
$260$	−580456.	+	536371.i	−0.532520	+	0.492076i
$261$	359129.	+	359129.i	0.326324	+	0.326324i
$262$	116642.	+	1.23753e6i	0.104979	+	1.11379i
$263$	774869.	+	774869.i	0.690779	+	0.690779i	0.962403	−	0.271625i	$-0.0875609\pi$
$263$	774869.	+	774869.i	0.690779	+	0.690779i	−0.271625	+	0.962403i	$0.587561\pi$
$264$	194949.	−	56465.6i	0.172151	−	0.0498625i
$265$	1.02542e6	−	640026.i	0.896992	−	0.559864i
$266$	−33198.4	+	40107.8i	−0.0287682	+	0.0347556i
$267$			164497.i			0.141214i
$268$	16616.8	+	87366.0i	0.0141322	+	0.0743028i
$269$	−677530.	−	677530.i	−0.570884	−	0.570884i	0.361491	−	0.932375i	$-0.382268\pi$
$269$	−677530.	−	677530.i	−0.570884	−	0.570884i	−0.932375	+	0.361491i	$0.882268\pi$
$270$	−1.12681e6	−	151247.i	−0.940675	−	0.126263i
$271$		−	1.47043e6i		−	1.21625i	−0.793843	−	0.608123i	$-0.791923\pi$
$271$		−	1.47043e6i		−	1.21625i	0.793843	−	0.608123i	$-0.208077\pi$
$272$	687901.	−	1.58492e6i	0.563772	−	1.29893i
$273$	25909.3	+	25909.3i	0.0210401	+	0.0210401i
$274$	−104145.	−	1.10494e6i	−0.0838031	−	0.889121i
$275$	129248.	+	376615.i	0.103060	+	0.300308i
$276$	−899342.	−	611907.i	−0.710644	−	0.483518i
$277$	−1.28911e6			−1.00947			−0.504733	−	0.863275i	$-0.668409\pi$
$277$	−1.28911e6			−1.00947			−0.504733	+	0.863275i	$0.668409\pi$
$278$	25454.8	+	270067.i	0.0197541	+	0.209584i
$279$			206440.i			0.158776i
$280$	63663.1	−	71013.4i	0.0485280	−	0.0541309i
$281$		−	1.08356e6i		−	0.818632i	−0.912393	−	0.409316i	$-0.865767\pi$
$281$		−	1.08356e6i		−	0.818632i	0.912393	−	0.409316i	$-0.134233\pi$
$282$	−1.19839e6	+	112952.i	−0.897375	+	0.0845811i
$283$	1.30800e6			0.970825			0.485413	−	0.874285i	$-0.338669\pi$
$283$	1.30800e6			0.970825			0.485413	+	0.874285i	$0.338669\pi$
$284$	67812.7	+	356538.i	0.0498902	+	0.262307i
$285$	−108302.	+	468015.i	−0.0789816	+	0.341309i
$286$	317039.	−	29882.2i	0.229191	−	0.0216022i
$287$	−58466.7	−	58466.7i	−0.0418990	−	0.0418990i
$288$	911722.	+	297606.i	0.647711	+	0.211427i
$289$		−	1.42703e6i		−	1.00505i
$290$	−771080.	+	588578.i	−0.538399	+	0.410969i
$291$	−466729.	−	466729.i	−0.323096	−	0.323096i
$292$	−1.41841e6	−	965077.i	−0.973519	−	0.662376i
$293$		−	1.12485e6i		−	0.765464i	−0.923860	−	0.382732i	$-0.874983\pi$
$293$		−	1.12485e6i		−	0.765464i	0.923860	−	0.382732i	$-0.125017\pi$
$294$	641076.	+	530638.i	0.432555	+	0.358039i
$295$	225174.	−	973063.i	0.150648	−	0.651007i
$296$	−859122.	+	1.55973e6i	−0.569936	+	1.03471i
$297$	323919.	+	323919.i	0.213081	+	0.213081i
$298$	549012.	−	51746.5i	0.358130	−	0.0337552i
$299$	−1.20682e6	−	1.20682e6i	−0.780666	−	0.780666i
$300$	232047.	−	848814.i	0.148858	−	0.544515i
$301$	52703.4	−	52703.4i	0.0335292	−	0.0335292i
$302$	−2.01919e6	−	1.67134e6i	−1.27397	−	1.05450i
$303$	−255939.	+	255939.i	−0.160151	+	0.160151i
$304$	398143.	−	917320.i	0.247090	−	0.569294i
$305$	−2.51162e6	−	581208.i	−1.54598	−	0.357752i
$306$	1.57331e6	−	148290.i	0.960527	−	0.0905334i
$307$	2.43667e6			1.47554			0.737770	−	0.675052i	$-0.235879\pi$
$307$	2.43667e6			1.47554			0.737770	+	0.675052i	$0.235879\pi$
$308$	−37751.2	+	7180.19i	−0.0226754	+	0.00431280i
$309$	1.06483e6	−	1.06483e6i	0.634429	−	0.634429i
$310$	−390790.	−	52454.3i	−0.230961	−	0.0310011i
$311$	1.11224e6			0.652073			0.326037	−	0.945357i	$-0.394287\pi$
$311$	1.11224e6			0.652073			0.326037	+	0.945357i	$0.394287\pi$
$312$	−616430.	−	339540.i	−0.358507	−	0.197471i
$313$	−1.68385e6	+	1.68385e6i	−0.971499	+	0.971499i	−0.999605	−	0.0281061i	$-0.991052\pi$
$313$	−1.68385e6	+	1.68385e6i	−0.971499	+	0.971499i	0.0281061	+	0.999605i	$0.491052\pi$
$314$	−606015.	+	732141.i	−0.346864	+	0.419055i
$315$	84985.2	+	19666.3i	0.0482578	+	0.0111672i
$316$	62912.0	+	330772.i	0.0354418	+	0.186342i
$317$		−	2.25800e6i		−	1.26205i	−0.775764	−	0.631023i	$-0.782635\pi$
$317$		−	2.25800e6i		−	1.26205i	0.775764	−	0.631023i	$-0.217365\pi$
$318$	829163.	+	686323.i	0.459803	+	0.380593i
$319$	390856.			0.215050
$320$	−795025.	+	1.65027e6i	−0.434016	+	0.900905i
$321$	−266242.			−0.144216
$322$	158655.	+	131324.i	0.0852736	+	0.0705835i
$323$		−	1.64772e6i		−	0.878775i
$324$	51397.3	+	270231.i	0.0272006	+	0.143012i
$325$	606509.	−	1.24030e6i	0.318514	−	0.651356i
$326$	−1.71649e6	+	2.07373e6i	−0.894532	+	1.08071i
$327$	−46632.6	+	46632.6i	−0.0241168	+	0.0241168i
$328$	1.39103e6	+	766203.i	0.713926	+	0.393242i
$329$	227904.			0.116081
$330$	−281836.	+	215130.i	−0.142466	+	0.108747i
$331$	−559094.	+	559094.i	−0.280488	+	0.280488i	−0.833304	−	0.552815i	$-0.813553\pi$
$331$	−559094.	+	559094.i	−0.280488	+	0.280488i	0.552815	+	0.833304i	$0.313553\pi$
$332$	2.35480e6	−	447877.i	1.17249	−	0.223005i
$333$	−1.62868e6			−0.804869
$334$	−2.32211e6	+	218868.i	−1.13898	+	0.107353i
$335$	−82259.7	−	131793.i	−0.0400475	−	0.0641625i
$336$	77903.7	+	33812.5i	0.0376452	+	0.0163391i
$337$	1.16391e6	−	1.16391e6i	0.558272	−	0.558272i	−0.370543	−	0.928815i	$-0.620828\pi$
$337$	1.16391e6	−	1.16391e6i	0.558272	−	0.558272i	0.928815	+	0.370543i	$0.120828\pi$
$338$	767384.	+	635186.i	0.365360	+	0.302419i
$339$	−291246.	+	291246.i	−0.137645	+	0.137645i
$340$	−119048.	+	3.01594e6i	−0.0558504	+	1.41490i
$341$	112339.	+	112339.i	0.0523172	+	0.0523172i
$342$	910598.	−	85827.4i	0.420980	−	0.0396790i
$343$	−223423.	−	223423.i	−0.102540	−	0.102540i
$344$	−690675.	+	1.25391e6i	−0.314686	+	0.571310i
$345$	1.85134e6	+	428414.i	0.837409	+	0.193783i
$346$	−225624.	−	186756.i	−0.101320	−	0.0838655i
$347$			941557.i			0.419781i	0.977725	+	0.209891i	$0.0673108\pi$
$347$			941557.i			0.419781i	−0.977725	+	0.209891i	$0.932689\pi$
$348$	−714156.	−	485907.i	−0.316115	−	0.215082i
$349$	713365.	+	713365.i	0.313508	+	0.313508i	0.846267	−	0.532759i	$-0.178845\pi$
$349$	713365.	+	713365.i	0.313508	+	0.313508i	−0.532759	+	0.846267i	$0.678845\pi$
$350$	−58822.0	+	155880.i	−0.0256667	+	0.0680172i
$351$		−	1.58840e6i		−	0.688165i
$352$	658083.	−	334185.i	0.283090	−	0.143758i
$353$	3.15469e6	+	3.15469e6i	1.34747	+	1.34747i	0.888397	+	0.459076i	$0.151819\pi$
$353$	3.15469e6	+	3.15469e6i	1.34747	+	1.34747i	0.459076	+	0.888397i	$0.348181\pi$
$354$	885445.	−	83456.6i	0.375537	−	0.0353959i
$355$	−335700.	−	537845.i	−0.141377	−	0.226509i
$356$	111772.	+	587661.i	0.0467419	+	0.245755i
$357$	139933.			0.0581100
$358$	4.70754e6	−	443704.i	1.94127	−	0.182972i
$359$		−	3.18444e6i		−	1.30406i	−0.758194	−	0.652029i	$-0.773918\pi$
$359$		−	3.18444e6i		−	1.30406i	0.758194	−	0.652029i	$-0.226082\pi$
$360$	−1.67293e6	+	91304.7i	−0.680333	+	0.0371310i
$361$			1.52243e6i			0.614850i
$362$	414834.	+	4.40124e6i	0.166381	+	1.76524i
$363$	−1.27433e6			−0.507591
$364$	110165.	+	74955.6i	0.0435803	+	0.0296518i
$365$	2.91986e6	+	675678.i	1.14717	+	0.265465i
$366$	−215414.	−	2.28546e6i	−0.0840563	−	0.891807i
$367$	2.54062e6	+	2.54062e6i	0.984634	+	0.984634i	0.999884	−	0.0152493i	$-0.00485420\pi$
$367$	2.54062e6	+	2.54062e6i	0.984634	+	0.984634i	−0.0152493	+	0.999884i	$0.504854\pi$
$368$	−3.62866e6	−	1.57494e6i	−1.39678	−	0.606241i
$369$			1.45253e6i			0.555340i
$370$	413831.	−	3.08308e6i	0.157151	−	1.17079i
$371$	−144104.	−	144104.i	−0.0543553	−	0.0543553i
$372$	−65602.8	−	344919.i	−0.0245790	−	0.129229i
$373$			3.28147e6i			1.22123i	0.791930	+	0.610613i	$0.209077\pi$
$373$			3.28147e6i			1.22123i	−0.791930	+	0.610613i	$0.790923\pi$
$374$	775454.	−	936845.i	0.286667	−	0.346329i
$375$	158334.	+	1.52905e6i	0.0581429	+	0.561493i
$376$	−4.20446e6	+	1.21780e6i	−1.53370	+	0.444227i
$377$	−958321.	−	958321.i	−0.347262	−	0.347262i
$378$	17986.8	+	190833.i	0.00647476	+	0.0686948i
$379$	653381.	+	653381.i	0.233651	+	0.233651i	0.814215	−	0.580563i	$-0.197168\pi$
$379$	653381.	+	653381.i	0.233651	+	0.233651i	−0.580563	+	0.814215i	$0.697168\pi$
$380$	−68902.8	+	1.74556e6i	−0.0244781	+	0.620121i
$381$	−1.86850e6	+	1.86850e6i	−0.659447	+	0.659447i
$382$	345112.	−	416938.i	0.121005	−	0.146189i
$383$	2.15838e6	−	2.15838e6i	0.751851	−	0.751851i	−0.222974	−	0.974824i	$-0.571576\pi$
$383$	2.15838e6	−	2.15838e6i	0.751851	−	0.751851i	0.974824	+	0.222974i	$0.0715765\pi$
$384$	−1.61788e6	−	207510.i	−0.559909	−	0.0718144i
$385$	56948.5	−	35544.8i	0.0195808	−	0.0122215i
$386$	205724.	+	2.18266e6i	0.0702777	+	0.745621i
$387$	−1.30935e6			−0.444403
$388$	−1.98451e6	−	1.35025e6i	−0.669228	−	0.455339i
$389$	−2.93854e6	+	2.93854e6i	−0.984595	+	0.984595i	−0.999883	−	0.0152882i	$-0.995133\pi$
$389$	−2.93854e6	+	2.93854e6i	−0.984595	+	0.984595i	0.0152882	+	0.999883i	$0.495133\pi$
$390$	1.21848e6	+	163553.i	0.405657	+	0.0544498i
$391$	−6.51793e6			−2.15609
$392$	2.65079e6	+	1.46010e6i	0.871285	+	0.479917i
$393$	1.36726e6	−	1.36726e6i	0.446549	−	0.446549i
$394$	701464.	+	580622.i	0.227648	+	0.188431i
$395$	−311440.	−	498976.i	−0.100434	−	0.160912i
$396$	558131.	+	379748.i	0.178854	+	0.121691i
$397$			3.03119e6i			0.965244i	0.875829	+	0.482622i	$0.160315\pi$
$397$			3.03119e6i			0.965244i	−0.875829	+	0.482622i	$0.839685\pi$
$398$	2.40059e6	−	2.90021e6i	0.759644	−	0.917744i
$399$	80990.7			0.0254685
$400$	252235.	−	3.19004e6i	0.0788234	−	0.996889i
$401$	5.68838e6			1.76656			0.883278	−	0.468850i	$-0.155331\pi$
$401$	5.68838e6			1.76656			0.883278	+	0.468850i	$0.155331\pi$
$402$	88210.1	−	106569.i	0.0272241	−	0.0328901i
$403$		−	550877.i		−	0.168963i
$404$	−740433.	+	1.08824e6i	−0.225700	+	0.331721i
$405$	−254437.	−	407649.i	−0.0770803	−	0.123495i
$406$	125986.	+	104282.i	0.0379321	+	0.0313975i
$407$	−886282.	+	886282.i	−0.265208	+	0.265208i
$408$	−2.58155e6	+	747730.i	−0.767768	+	0.222379i
$409$	−1.86016e6			−0.549847			−0.274923	−	0.961466i	$-0.588652\pi$
$409$	−1.86016e6			−0.549847			−0.274923	+	0.961466i	$0.588652\pi$
$410$	−2.74963e6	−	369072.i	−0.807819	−	0.108431i
$411$	−1.22076e6	+	1.22076e6i	−0.356473	+	0.356473i
$412$	3.08055e6	−	4.52760e6i	0.894098	−	1.31409i
$413$	−168390.			−0.0485782
$414$	−339509.	−	3.60207e6i	−0.0973532	−	1.03288i
$415$	−3.55227e6	+	2.21717e6i	−1.01248	+	0.631945i
$416$	−2.43289e6	−	794148.i	−0.689271	−	0.224993i
$417$	298377.	−	298377.i	0.0840281	−	0.0840281i
$418$	448817.	−	542227.i	0.125640	−	0.151789i
$419$	−871573.	+	871573.i	−0.242532	+	0.242532i	−0.817897	−	0.575365i	$-0.804860\pi$
$419$	−871573.	+	871573.i	−0.242532	+	0.242532i	0.575365	+	0.817897i	$0.304860\pi$
$420$	−148243.	−	5851.60i	−0.0410062	−	0.00161864i
$421$	3.23556e6	+	3.23556e6i	0.889702	+	0.889702i	0.994494	−	0.104792i	$-0.0334177\pi$
$421$	3.23556e6	+	3.23556e6i	0.889702	+	0.889702i	−0.104792	+	0.994494i	$0.533418\pi$
$422$	448439.	+	4.75777e6i	0.122581	+	1.30054i
$423$	−2.83098e6	−	2.83098e6i	−0.769283	−	0.769283i
$424$	3.42851e6	+	1.88848e6i	0.926170	+	0.510149i
$425$	−1.71152e6	−	4.98722e6i	−0.459632	−	1.33933i
$426$	359983.	−	434904.i	0.0961077	−	0.116110i
$427$			434639.i			0.115361i
$428$	−951144.	+	180905.i	−0.250979	+	0.0477355i
$429$	−350274.	−	350274.i	−0.0918891	−	0.0918891i
$430$	332691.	−	2.47858e6i	0.0867702	−	0.646446i
$431$		−	6.55892e6i		−	1.70074i	−0.526182	−	0.850372i	$-0.676377\pi$
$431$		−	6.55892e6i		−	1.70074i	0.526182	−	0.850372i	$-0.323623\pi$
$432$	−1.35154e6	−	3.42446e6i	−0.348433	−	0.882840i
$433$	−821279.	−	821279.i	−0.210509	−	0.210509i	0.593975	−	0.804484i	$-0.297558\pi$
$433$	−821279.	−	821279.i	−0.210509	−	0.210509i	−0.804484	+	0.593975i	$0.797558\pi$
$434$	6238.03	+	66183.2i	0.00158973	+	0.0168664i
$435$	1.47012e6	+	340197.i	0.372503	+	0.0862001i
$436$	−134908.	+	198280.i	−0.0339878	+	0.0499531i
$437$	−3.77245e6			−0.944973
$438$	250427.	+	2.65694e6i	0.0623729	+	0.661755i
$439$			1.42533e6i			0.352982i	0.984302	+	0.176491i	$0.0564747\pi$
$439$			1.42533e6i			0.352982i	−0.984302	+	0.176491i	$0.943525\pi$
$440$	−860676.	+	960047.i	−0.211938	+	0.236407i
$441$			2.76798e6i			0.677744i
$442$	−4.19830e6	+	395706.i	−1.02216	+	0.0963424i
$443$	6.39043e6			1.54711			0.773554	−	0.633730i	$-0.218477\pi$
$443$	6.39043e6			1.54711			0.773554	+	0.633730i	$0.218477\pi$
$444$	2.72119e6	−	517564.i	0.655091	−	0.124597i
$445$	−553314.	−	886499.i	−0.132456	−	0.212216i
$446$	6.78508e6	−	639520.i	1.61517	−	0.152236i
$447$	−606563.	−	606563.i	−0.143584	−	0.143584i
$448$	301284.	+	67860.6i	0.0709221	+	0.0159743i
$449$			1.84122e6i			0.431013i	0.976502	+	0.215506i	$0.0691402\pi$
$449$			1.84122e6i			0.431013i	−0.976502	+	0.215506i	$0.930860\pi$
$450$	2.66699e6	−	1.20563e6i	0.620854	−	0.280662i
$451$	790426.	+	790426.i	0.182987	+	0.182987i
$452$	−842577.	+	1.23837e6i	−0.193983	+	0.285104i
$453$			4.07739e6i			0.933549i
$454$	−476070.	−	394057.i	−0.108401	−	0.0897263i
$455$	−226780.	−	52478.6i	−0.0513542	−	0.0118838i
$456$	−1.49415e6	+	432771.i	−0.336497	+	0.0974644i
$457$	−6.15716e6	−	6.15716e6i	−1.37908	−	1.37908i	−0.846173	−	0.532908i	$-0.821099\pi$
$457$	−6.15716e6	−	6.15716e6i	−1.37908	−	1.37908i	−0.532908	−	0.846173i	$-0.678901\pi$
$458$	−655107.	+	61746.4i	−0.145931	+	0.0137546i
$459$	−4.28940e6	−	4.28940e6i	−0.950310	−	0.950310i
$460$	6.90496e6	+	272560.i	1.52148	+	0.0600576i
$461$	−4.76816e6	+	4.76816e6i	−1.04496	+	1.04496i	−0.0460163	+	0.998941i	$0.514653\pi$
$461$	−4.76816e6	+	4.76816e6i	−1.04496	+	1.04496i	−0.998941	+	0.0460163i	$0.985347\pi$
$462$	46048.8	+	38116.0i	0.0100372	+	0.00830811i
$463$	−1.51769e6	+	1.51769e6i	−0.329026	+	0.329026i	−0.852216	−	0.523190i	$-0.824742\pi$
$463$	−1.51769e6	+	1.51769e6i	−0.329026	+	0.329026i	0.523190	+	0.852216i	$0.324742\pi$
$464$	−2.88147e6	−	1.25064e6i	−0.621325	−	0.269673i
$465$	324760.	+	520318.i	0.0696515	+	0.111593i
$466$	5.64340e6	−	531913.i	1.20386	−	0.113469i
$467$	6.64656e6			1.41028			0.705139	−	0.709070i	$-0.250885\pi$
$467$	6.64656e6			1.41028			0.705139	+	0.709070i	$0.250885\pi$
$468$	−437366.	−	2.29954e6i	−0.0923062	−	0.485318i
$469$	−18521.1	+	18521.1i	−0.00388807	+	0.00388807i
$470$	6.07835e6	−	4.63971e6i	1.26923	−	0.968826i
$471$	1.47843e6			0.307078
$472$	3.10653e6	−	899786.i	0.641830	−	0.185902i
$473$	−712510.	+	712510.i	−0.146433	+	0.146433i
$474$	333968.	−	403475.i	0.0682746	−	0.0824842i
$475$	−990595.	−	2.88650e6i	−0.201448	−	0.587000i
$476$	499910.	−	95081.5i	0.101129	−	0.0192344i
$477$			3.58008e6i			0.720438i
$478$	1.31025e6	+	1.08453e6i	0.262291	+	0.217106i
$479$	4.91969e6			0.979713			0.489856	−	0.871803i	$-0.337049\pi$
$479$	4.91969e6			0.979713			0.489856	+	0.871803i	$0.337049\pi$
$480$	2.76611e6	−	684177.i	0.547982	−	0.135539i
$481$	4.34606e6			0.856512
$482$	5.71442e6	+	4.72999e6i	1.12035	+	0.927349i
$483$		−	320376.i		−	0.0624874i
$484$	−4.55250e6	+	865874.i	−0.883358	+	0.168012i
$485$	4.08520e6	+	945348.i	0.788605	+	0.182489i
$486$	3.42406e6	−	4.13669e6i	0.657584	−	0.794443i
$487$	−5.12923e6	+	5.12923e6i	−0.980009	+	0.980009i	−0.999804	−	0.0197954i	$-0.993699\pi$
$487$	−5.12923e6	+	5.12923e6i	−0.980009	+	0.980009i	0.0197954	+	0.999804i	$0.493699\pi$
$488$	−2.32248e6	−	8.01840e6i	−0.441471	−	1.52419i
$489$	4.18753e6			0.791928
$490$	−5.23976e6	−	703314.i	−0.985873	−	0.132330i
$491$	5.62176e6	−	5.62176e6i	1.05237	−	1.05237i	0.0538192	−	0.998551i	$-0.482861\pi$
$491$	5.62176e6	−	5.62176e6i	1.05237	−	1.05237i	0.998551	−	0.0538192i	$-0.0171395\pi$
$492$	−461586.	−	2.42688e6i	−0.0859686	−	0.451997i
$493$	−5.17580e6			−0.959091
$494$	−2.42989e6	+	229027.i	−0.447991	+	0.0422249i
$495$	−1.14894e6	−	265873.i	−0.210757	−	0.0487709i
$496$	−468730.	−	1.18764e6i	−0.0855496	−	0.216761i
$497$	−75584.1	+	75584.1i	−0.0137259	+	0.0137259i
$498$	−2.87238e6	−	2.37755e6i	−0.519002	−	0.429593i
$499$	−4.78274e6	+	4.78274e6i	−0.859856	+	0.859856i	−0.991321	−	0.131465i	$-0.958032\pi$
$499$	−4.78274e6	+	4.78274e6i	−0.859856	+	0.859856i	0.131465	+	0.991321i	$0.458032\pi$
$500$	1.60460e6	+	5.35493e6i	0.287040	+	0.957919i
$501$	2.56553e6	+	2.56553e6i	0.456649	+	0.456649i
$502$	−6.65869e6	+	627607.i	−1.17931	+	0.111155i
$503$	−5.50336e6	−	5.50336e6i	−0.969857	−	0.969857i	0.0297017	−	0.999559i	$-0.490544\pi$
$503$	−5.50336e6	−	5.50336e6i	−0.969857	−	0.969857i	−0.999559	+	0.0297017i	$0.990544\pi$
$504$	78585.4	+	271317.i	0.0137805	+	0.0475775i
$505$	518399.	−	2.24019e6i	0.0904556	−	0.390893i
$506$	−2.14490e6	−	1.77540e6i	−0.372418	−	0.308261i
$507$		−	1.54960e6i		−	0.267731i
$508$	−5.40557e6	+	7.94477e6i	−0.929356	+	1.36591i
$509$	92430.7	+	92430.7i	0.0158133	+	0.0158133i	0.714969	−	0.699156i	$-0.246441\pi$
$509$	92430.7	+	92430.7i	0.0158133	+	0.0158133i	−0.699156	+	0.714969i	$0.746441\pi$
$510$	3.73212e6	−	2.84879e6i	0.635376	−	0.484993i
$511$		−	505286.i		−	0.0856022i
$512$	−5.92083e6	+	357983.i	−0.998177	+	0.0603514i
$513$	−2.48262e6	−	2.48262e6i	−0.416502	−	0.416502i
$514$	−1.59931e6	+	150741.i	−0.267009	+	0.0251666i
$515$	−2.15678e6	+	9.32026e6i	−0.358334	+	1.54850i
$516$	2.18765e6	−	416086.i	0.361704	−	0.0687953i
$517$	−3.08108e6			−0.506964
$518$	−522143.	+	49214.0i	−0.0854997	+	0.00805868i
$519$			455608.i			0.0742459i
$520$	4.46414e6	−	243643.i	0.723985	−	0.0395135i
$521$		−	4.46944e6i		−	0.721371i	−0.932687	−	0.360686i	$-0.882543\pi$
$521$		−	4.46944e6i		−	0.721371i	0.932687	−	0.360686i	$-0.117457\pi$
$522$	−269599.	−	2.86035e6i	−0.0433055	−	0.459455i
$523$	3.03387e6			0.485000			0.242500	−	0.970151i	$-0.422032\pi$
$523$	3.03387e6			0.485000			0.242500	+	0.970151i	$0.422032\pi$
$524$	3.95548e6	−	5.81352e6i	0.629319	−	0.924934i
$525$	245137.	−	84126.6i	0.0388160	−	0.0133210i
$526$	−581697.	−	6.17160e6i	−0.0916711	−	0.972598i
$527$	−1.48762e6	−	1.48762e6i	−0.233327	−	0.233327i
$528$	−1.05320e6	−	457119.i	−0.164409	−	0.0713583i
$529$			8.48639e6i			1.31851i
$530$	−6.77706e6	−	909661.i	−1.04798	−	0.140666i
$531$	2.09171e6	+	2.09171e6i	0.321933	+	0.321933i
$532$	289338.	−	55031.3i	0.0443227	−	0.00843006i
$533$		−	3.87601e6i		−	0.590972i
$534$	593339.	−	716827.i	0.0900430	−	0.108783i
$535$	1.43482e6	−	895553.i	0.216727	−	0.135272i
$536$	242718.	−	440652.i	0.0364913	−	0.0662496i
$537$	−5.20101e6	−	5.20101e6i	−0.778310	−	0.778310i
$538$	508624.	+	5.39632e6i	0.0757603	+	0.803789i
$539$	1.50626e6	+	1.50626e6i	0.223320	+	0.223320i
$540$	4.36474e6	+	4.72348e6i	0.644130	+	0.697072i
$541$	−395841.	+	395841.i	−0.0581470	+	0.0581470i	−0.735582	−	0.677435i	$-0.763091\pi$
$541$	−395841.	+	395841.i	−0.0581470	+	0.0581470i	0.677435	+	0.735582i	$0.263091\pi$
$542$	−5.30384e6	+	6.40770e6i	−0.775519	+	0.936923i
$543$	4.86261e6	−	4.86261e6i	0.707734	−	0.707734i
$544$	−8.71447e6	+	4.42535e6i	−1.26254	+	0.641137i
$545$	94453.3	−	408168.i	0.0136215	−	0.0588637i
$546$	−19450.2	−	206360.i	−0.00279217	−	0.0296239i
$547$	1.26202e7			1.80343			0.901715	−	0.432332i	$-0.142309\pi$
$547$	1.26202e7			1.80343			0.901715	+	0.432332i	$0.142309\pi$
$548$	−3.53167e6	+	5.19063e6i	−0.502376	+	0.738361i
$549$	5.39901e6	−	5.39901e6i	0.764510	−	0.764510i
$550$	795229.	−	2.10737e6i	0.112095	−	0.297054i
$551$	−2.99565e6			−0.420351
$552$	1.71192e6	+	5.91043e6i	0.239131	+	0.825604i
$553$	−70121.8	+	70121.8i	−0.00975080	+	0.00975080i
$554$	5.61758e6	+	4.64983e6i	0.777633	+	0.643670i
$555$	−4.10497e6	+	2.56215e6i	−0.565689	+	0.353079i
$556$	863205.	−	1.26869e6i	0.118421	−	0.174047i
$557$			1.07726e6i			0.147123i	0.997291	+	0.0735616i	$0.0234366\pi$
$557$			1.07726e6i			0.147123i	−0.997291	+	0.0735616i	$0.976563\pi$
$558$	744629.	−	899605.i	0.101241	−	0.122311i
$559$	3.49394e6			0.472918
$560$	−533570.	+	79822.7i	−0.0718987	+	0.0107561i
$561$	−1.89179e6			−0.253785
$562$	−3.90841e6	+	4.72185e6i	−0.521987	+	0.630625i
$563$		−	1.09678e7i		−	1.45831i	−0.684349	−	0.729155i	$-0.739913\pi$
$563$		−	1.09678e7i		−	1.45831i	0.684349	−	0.729155i	$-0.260087\pi$
$564$	5.62963e6	+	3.83036e6i	0.745215	+	0.507040i
$565$	589912.	−	2.54923e6i	0.0777439	−	0.335961i
$566$	−5.69987e6	−	4.71795e6i	−0.747866	−	0.619030i
$567$	−57287.5	+	57287.5i	−0.00748346	+	0.00748346i
$568$	990525.	−	1.79829e6i	0.128823	−	0.233877i
$569$	1.41101e7			1.82705			0.913526	−	0.406780i	$-0.133348\pi$
$569$	1.41101e7			1.82705			0.913526	+	0.406780i	$0.133348\pi$
$570$	2.16008e6	−	1.64882e6i	0.278473	−	0.212563i
$571$	−7.43654e6	+	7.43654e6i	−0.954510	+	0.954510i	−0.999009	−	0.0444991i	$-0.985831\pi$
$571$	−7.43654e6	+	7.43654e6i	−0.954510	+	0.954510i	0.0444991	+	0.999009i	$0.485831\pi$
$572$	−1.48935e6	−	1.01334e6i	−0.190330	−	0.129499i
$573$	−841933.			−0.107125
$574$	43891.2	+	465670.i	0.00556029	+	0.0589927i
$575$	−1.14182e7	+	3.91852e6i	−1.44022	+	0.494256i
$576$	−2.89955e6	−	4.58546e6i	−0.364145	−	0.575873i
$577$	6.54418e6	−	6.54418e6i	0.818306	−	0.818306i	−0.167556	−	0.985862i	$-0.553588\pi$
$577$	6.54418e6	−	6.54418e6i	0.818306	−	0.818306i	0.985862	+	0.167556i	$0.0535876\pi$
$578$	−5.14731e6	+	6.21859e6i	−0.640856	+	0.774234i
$579$	2.41146e6	−	2.41146e6i	0.298940	−	0.298940i
$580$	5.48313e6	+	216436.i	0.676798	+	0.0267153i
$581$	499205.	+	499205.i	0.0613534	+	0.0613534i
$582$	350375.	+	3.71736e6i	0.0428771	+	0.454911i
$583$	1.94818e6	+	1.94818e6i	0.237387	+	0.237387i
$584$	2.69998e6	+	9.32172e6i	0.327588	+	1.13100i
$585$	2.16514e6	+	3.46890e6i	0.261575	+	0.419085i
$586$	−4.05732e6	+	4.90175e6i	−0.488085	+	0.589667i
$587$			8.09259e6i			0.969376i	0.874687	+	0.484688i	$0.161067\pi$
$587$			8.09259e6i			0.969376i	−0.874687	+	0.484688i	$0.838933\pi$
$588$	−879611.	−	4.62472e6i	−0.104917	−	0.551623i
$589$	−861003.	−	861003.i	−0.102262	−	0.102262i
$590$	−4.49108e6	+	3.42811e6i	−0.531154	+	0.405439i
$591$		−	1.41648e6i		−	0.166818i
$592$	9.36973e6	−	3.69797e6i	1.09881	−	0.433670i
$593$	−6.75337e6	−	6.75337e6i	−0.788649	−	0.788649i	0.192624	−	0.981273i	$-0.438300\pi$
$593$	−6.75337e6	−	6.75337e6i	−0.788649	−	0.788649i	−0.981273	+	0.192624i	$0.938300\pi$
$594$	−243167.	−	2.57992e6i	−0.0282774	−	0.300013i
$595$	−754124.	+	470692.i	−0.0873273	+	0.0545060i
$596$	−2.57908e6	−	1.75479e6i	−0.297406	−	0.202353i
$597$	−5.85646e6			−0.672511
$598$	905966.	+	9.61197e6i	0.103600	+	1.09916i
$599$			2.05890e6i			0.234460i	0.993105	+	0.117230i	$0.0374015\pi$
$599$			2.05890e6i			0.234460i	−0.993105	+	0.117230i	$0.962599\pi$
$600$	−4.07286e6	+	2.86189e6i	−0.461872	+	0.324544i
$601$			7.72194e6i			0.872048i	0.899935	+	0.436024i	$0.143614\pi$
$601$			7.72194e6i			0.872048i	−0.899935	+	0.436024i	$0.856386\pi$
$602$	−419767.	+	39564.7i	−0.0472082	+	0.00444955i
$603$	460132.			0.0515334
$604$	2.77049e6	+	1.45664e7i	0.309005	+	1.62465i
$605$	6.86754e6	−	4.28643e6i	0.762804	−	0.476109i
$606$	2.03848e6	−	192135.i	0.225489	−	0.0212532i
$607$	−1.89090e6	−	1.89090e6i	−0.208304	−	0.208304i	0.595242	−	0.803546i	$-0.297056\pi$
$607$	−1.89090e6	−	1.89090e6i	−0.208304	−	0.208304i	−0.803546	+	0.595242i	$0.797056\pi$
$608$	−5.04376e6	+	2.56131e6i	−0.553344	+	0.280997i
$609$		−	254406.i		−	0.0277962i
$610$	8.84846e6	+	1.15921e7i	0.962816	+	1.26136i
$611$	7.55436e6	+	7.55436e6i	0.818643	+	0.818643i
$612$	−7.39088e6	−	5.02871e6i	−0.797660	−	0.542722i
$613$		−	3.90015e6i		−	0.419209i	−0.977786	−	0.209604i	$-0.932782\pi$
$613$		−	3.90015e6i		−	0.419209i	0.977786	−	0.209604i	$-0.0672176\pi$
$614$	−1.06183e7	−	8.78907e6i	−1.13667	−	0.940854i
$615$	2.28504e6	+	3.66100e6i	0.243616	+	0.390312i
$616$	190407.	+	104879.i	0.0202177	+	0.0111362i
$617$	909212.	+	909212.i	0.0961507	+	0.0961507i	0.753546	−	0.657395i	$-0.228342\pi$
$617$	909212.	+	909212.i	0.0961507	+	0.0961507i	−0.657395	+	0.753546i	$0.728342\pi$
$618$	−8.48102e6	+	799370.i	−0.893258	+	0.0841931i
$619$	5.50130e6	+	5.50130e6i	0.577083	+	0.577083i	0.934099	−	0.357015i	$-0.116206\pi$
$619$	5.50130e6	+	5.50130e6i	0.577083	+	0.577083i	−0.357015	+	0.934099i	$0.616206\pi$
$620$	1.51374e6	+	1.63816e6i	0.158151	+	0.171150i
$621$	−9.82055e6	+	9.82055e6i	−1.02190	+	1.02190i
$622$	−4.84680e6	−	4.01184e6i	−0.502318	−	0.415784i
$623$	−124581.	+	124581.i	−0.0128597	+	0.0128597i
$624$	1.46150e6	+	3.70307e6i	0.150258	+	0.380716i
$625$	−5.99654e6	−	7.70772e6i	−0.614045	−	0.789271i
$626$	1.34114e7	−	1.26407e6i	1.36784	−	0.128925i
$627$	−1.09493e6			−0.111229
$628$	5.28166e6	−	1.00456e6i	0.534406	−	0.101643i
$629$	1.17363e7	−	1.17363e7i	1.18279	−	1.18279i
$630$	−299404.	−	392241.i	−0.0300543	−	0.0393733i
$631$	1.67113e6			0.167085			0.0835423	−	0.996504i	$-0.473377\pi$
$631$	1.67113e6			0.167085			0.0835423	+	0.996504i	$0.473377\pi$
$632$	918942.	−	1.66833e6i	0.0915157	−	0.166146i
$633$	5.25651e6	−	5.25651e6i	0.521421	−	0.521421i
$634$	−8.14460e6	+	9.83968e6i	−0.804723	+	0.972205i
$635$	3.78460e6	−	1.63547e7i	0.372465	−	1.60956i
$636$	−1.13768e6	−	5.98158e6i	−0.111526	−	0.586372i
$637$		−	7.38623e6i		−	0.721231i
$638$	−1.70323e6	−	1.40982e6i	−0.165662	−	0.137123i
$639$	1.87779e6			0.181926
$640$	9.41699e6	−	4.32372e6i	0.908787	−	0.417260i
$641$	3.80691e6			0.365955			0.182978	−	0.983117i	$-0.441426\pi$
$641$	3.80691e6			0.365955			0.182978	+	0.983117i	$0.441426\pi$
$642$	1.16020e6	+	960334.i	0.111095	+	0.0919570i
$643$			6.14251e6i			0.585894i	0.956129	+	0.292947i	$0.0946359\pi$
$643$			6.14251e6i			0.585894i	−0.956129	+	0.292947i	$0.905364\pi$
$644$	−217688.	−	1.14454e6i	−0.0206833	−	0.108747i
$645$	−3.30012e6	+	2.05979e6i	−0.312342	+	0.194950i
$646$	−5.94333e6	+	7.18028e6i	−0.560336	+	0.676956i
$647$	9.95858e6	−	9.95858e6i	0.935269	−	0.935269i	−0.0627597	−	0.998029i	$-0.519990\pi$
$647$	9.95858e6	−	9.95858e6i	0.935269	−	0.935269i	0.998029	+	0.0627597i	$0.0199902\pi$
$648$	750750.	−	1.36298e6i	0.0702357	−	0.127512i
$649$	2.27650e6			0.212157
$650$	−7.11675e6	+	3.21718e6i	−0.660690	+	0.298670i
$651$	73121.0	−	73121.0i	0.00676222	−	0.00676222i
$652$	1.49599e7	−	2.84533e6i	1.37819	−	0.262128i
$653$	7.46098e6			0.684720			0.342360	−	0.939569i	$-0.388774\pi$
$653$	7.46098e6			0.684720			0.342360	+	0.939569i	$0.388774\pi$
$654$	371415.	−	35007.3i	0.0339559	−	0.00320047i
$655$	−2.76935e6	+	1.19674e7i	−0.252217	+	1.08992i
$656$	−3.29802e6	−	8.35634e6i	−0.299222	−	0.758153i
$657$	−6.27657e6	+	6.27657e6i	−0.567295	+	0.567295i
$658$	−993136.	−	822048.i	−0.0894219	−	0.0740172i
$659$	−8.02890e6	+	8.02890e6i	−0.720183	+	0.720183i	−0.968642	−	0.248460i	$-0.920076\pi$
$659$	−8.02890e6	+	8.02890e6i	−0.720183	+	0.720183i	0.248460	+	0.968642i	$0.420076\pi$
$660$	2.00413e6	+	79109.1i	0.179088	+	0.00706914i
$661$	−3.33689e6	−	3.33689e6i	−0.297056	−	0.297056i	0.542804	−	0.839860i	$-0.317363\pi$
$661$	−3.33689e6	−	3.33689e6i	−0.297056	−	0.297056i	−0.839860	+	0.542804i	$0.817363\pi$
$662$	4.45302e6	−	419714.i	0.394920	−	0.0372228i
$663$	4.63840e6	+	4.63840e6i	0.409811	+	0.409811i
$664$	−1.18770e7	−	6.54205e6i	−1.04541	−	0.575829i
$665$	−436471.	+	272427.i	−0.0382738	+	0.0238889i
$666$	7.09730e6	+	5.87464e6i	0.620023	+	0.513211i
$667$			1.18499e7i			1.03134i
$668$	1.09085e7	+	7.42208e6i	0.945854	+	0.643553i
$669$	−7.49634e6	−	7.49634e6i	−0.647566	−	0.647566i
$670$	−116915.	+	871027.i	−0.0100620	+	0.0749626i
$671$		−	5.87599e6i		−	0.503819i
$672$	−217520.	−	428343.i	−0.0185813	−	0.0365905i
$673$	1.89807e6	+	1.89807e6i	0.161538	+	0.161538i	0.783248	−	0.621710i	$-0.213562\pi$
$673$	1.89807e6	+	1.89807e6i	0.161538	+	0.161538i	−0.621710	+	0.783248i	$0.713562\pi$
$674$	−9.27022e6	+	873754.i	−0.786032	+	0.0740866i
$675$	−1.00930e7	−	4.93548e6i	−0.852629	−	0.416937i
$676$	−1.05292e6	−	5.53591e6i	−0.0886190	−	0.465931i
$677$	−5.73042e6			−0.480523			−0.240262	−	0.970708i	$-0.577233\pi$
$677$	−5.73042e6			−0.480523			−0.240262	+	0.970708i	$0.577233\pi$
$678$	2.31969e6	−	218640.i	0.193801	−	0.0182665i
$679$		−	706950.i		−	0.0588457i
$680$	1.13973e7	−	1.27131e7i	0.945209	−	1.05434i
$681$			961340.i			0.0794345i
$682$	−84333.4	−	894747.i	−0.00694286	−	0.0736613i
$683$	−5.24472e6			−0.430200			−0.215100	−	0.976592i	$-0.569008\pi$
$683$	−5.24472e6			−0.430200			−0.215100	+	0.976592i	$0.569008\pi$
$684$	−4.27769e6	−	2.91051e6i	−0.349598	−	0.237864i
$685$	2.47263e6	−	1.06851e7i	0.201341	−	0.870070i
$686$	167725.	+	1.77950e6i	0.0136078	+	0.144374i
$687$	723780.	+	723780.i	0.0585079	+	0.0585079i
$688$	7.53262e6	−	2.97292e6i	0.606701	−	0.239448i
$689$		−	9.55329e6i		−	0.766664i
$690$	−6.52228e6	−	8.54466e6i	−0.521527	−	0.683238i
$691$	5.79792e6	+	5.79792e6i	0.461931	+	0.461931i	0.899288	−	0.437357i	$-0.144085\pi$
$691$	5.79792e6	+	5.79792e6i	0.461931	+	0.461931i	−0.437357	+	0.899288i	$0.644085\pi$
$692$	309575.	+	1.62765e6i	0.0245754	+	0.129210i
$693$			198825.i			0.0157267i
$694$	3.39619e6	−	4.10302e6i	0.267666	−	0.323374i
$695$	−604355.	+	2.61164e6i	−0.0474603	+	0.205094i
$696$	1.35941e6	+	4.69339e6i	0.106372	+	0.367252i
$697$	−1.04670e7	−	1.04670e7i	−0.816093	−	0.816093i
$698$	−535526.	−	5.68174e6i	−0.0416047	−	0.441411i
$699$	−6.23498e6	−	6.23498e6i	−0.482661	−	0.482661i
$700$	818586.	−	467106.i	0.0631421	−	0.0360305i
$701$	−3.43875e6	+	3.43875e6i	−0.264305	+	0.264305i	−0.826801	−	0.562495i	$-0.809842\pi$
$701$	−3.43875e6	+	3.43875e6i	−0.264305	+	0.264305i	0.562495	+	0.826801i	$0.309842\pi$
$702$	−5.72936e6	+	6.92178e6i	−0.438797	+	0.530121i
$703$	6.79275e6	−	6.79275e6i	0.518391	−	0.518391i
$704$	−4.07314e6	−	917424.i	−0.309740	−	0.0697651i
$705$	−1.15888e7	−	2.68175e6i	−0.878146	−	0.203210i
$706$	−2.36824e6	−	2.51262e7i	−0.178819	−	1.89721i
$707$	−387669.			−0.0291684
$708$	−4.15953e6	−	2.83012e6i	−0.311861	−	0.212188i
$709$	9.38043e6	−	9.38043e6i	0.700821	−	0.700821i	−0.263766	−	0.964587i	$-0.584965\pi$
$709$	9.38043e6	−	9.38043e6i	0.700821	−	0.700821i	0.964587	+	0.263766i	$0.0849645\pi$
$710$	−477126.	+	3.55464e6i	−0.0355212	+	0.264636i
$711$	1.74208e6			0.129239
$712$	1.63263e6	−	2.96401e6i	0.120694	−	0.219119i
$713$	−3.40588e6	+	3.40588e6i	−0.250903	+	0.250903i
$714$	−609788.	−	504740.i	−0.0447645	−	0.0370529i
$715$	3.06589e6	+	709471.i	0.224280	+	0.0519003i
$716$	−2.21145e7	−	1.50466e7i	−1.61211	−	1.09687i
$717$		−	2.64581e6i		−	0.192203i
$718$	−1.14863e7	+	1.38768e7i	−0.831510	+	1.00457i
$719$	−1.54976e7			−1.11800			−0.559000	−	0.829168i	$-0.688815\pi$
$719$	−1.54976e7			−1.11800			−0.559000	+	0.829168i	$0.688815\pi$
$720$	7.61946e6	+	5.63637e6i	0.547763	+	0.405199i
$721$	1.61288e6			0.115549
$722$	5.49140e6	−	6.63430e6i	0.392049	−	0.473644i
$723$		−	1.15393e7i		−	0.820980i
$724$	1.40676e7	−	2.06756e7i	0.997407	−	1.46593i
$725$	−9.06703e6	+	3.11164e6i	−0.640649	+	0.219859i
$726$	5.55313e6	+	4.59649e6i	0.391018	+	0.323657i
$727$	−4.73399e6	+	4.73399e6i	−0.332194	+	0.332194i	−0.853419	−	0.521225i	$-0.825475\pi$
$727$	−4.73399e6	+	4.73399e6i	−0.332194	+	0.332194i	0.521225	+	0.853419i	$0.325475\pi$
$728$	−209702.	−	723999.i	−0.0146647	−	0.0506302i
$729$	−6.26447e6			−0.436581
$730$	−1.02867e7	−	1.34763e7i	−0.714445	−	0.935975i
$731$	9.43521e6	−	9.43521e6i	0.653068	−	0.653068i
$732$	−7.30494e6	+	1.07364e7i	−0.503894	+	0.740592i
$733$	1.33926e7			0.920670			0.460335	−	0.887745i	$-0.347729\pi$
$733$	1.33926e7			0.920670			0.460335	+	0.887745i	$0.347729\pi$
$734$	−1.90726e6	−	2.02353e7i	−0.130668	−	1.38634i
$735$	4.35442e6	+	6.97649e6i	0.297312	+	0.476341i
$736$	1.01318e7	+	1.99517e7i	0.689433	+	1.35764i
$737$	250391.	−	250391.i	0.0169805	−	0.0169805i
$738$	5.23927e6	−	6.32968e6i	0.354103	−	0.427800i
$739$	−1.26554e7	+	1.26554e7i	−0.852443	+	0.852443i	−0.990434	−	0.137991i	$-0.955936\pi$
$739$	−1.26554e7	+	1.26554e7i	−0.852443	+	0.852443i	0.137991	+	0.990434i	$0.455936\pi$
$740$	−1.29240e7	+	1.19425e7i	−0.867597	+	0.801704i
$741$	2.68461e6	+	2.68461e6i	0.179612	+	0.179612i
$742$	108180.	+	1.14775e6i	0.00721333	+	0.0765308i
$743$	1.47669e7	+	1.47669e7i	0.981337	+	0.981337i	0.999829	−	0.0184916i	$-0.00588639\pi$
$743$	1.47669e7	+	1.47669e7i	0.981337	+	0.981337i	−0.0184916	+	0.999829i	$0.505886\pi$
$744$	−958246.	+	1.73969e6i	−0.0634665	+	0.115223i
$745$	5.30915e6	+	1.22858e6i	0.350457	+	0.0810984i
$746$	1.18362e7	−	1.42996e7i	0.778694	−	0.940759i
$747$		−	1.24021e7i		−	0.813191i
$748$	−6.75840e6	+	1.28543e6i	−0.441662	+	0.0840029i
$749$	−201637.	−	201637.i	−0.0131331	−	0.0131331i
$750$	4.82532e6	−	7.23427e6i	0.313237	−	0.469614i
$751$			2.08720e7i			1.35041i	0.737631	+	0.675204i	$0.235944\pi$
$751$			2.08720e7i			1.35041i	−0.737631	+	0.675204i	$0.764056\pi$
$752$	2.27144e7	+	9.85869e6i	1.46473	+	0.635733i
$753$	7.35669e6	+	7.35669e6i	0.472819	+	0.472819i
$754$	719415.	+	7.63274e6i	0.0460841	+	0.488936i
$755$	−1.37151e7	−	2.19737e7i	−0.875650	−	1.40293i
$756$	609954.	−	896472.i	0.0388143	−	0.0570469i
$757$	−7.24355e6			−0.459422			−0.229711	−	0.973259i	$-0.573778\pi$
$757$	−7.24355e6			−0.459422			−0.229711	+	0.973259i	$0.573778\pi$
$758$	−490496.	−	5.20398e6i	−0.0310072	−	0.328975i
$759$			4.33124e6i			0.272903i
$760$	6.59650e6	−	7.35811e6i	0.414266	−	0.462096i
$761$			1.38296e7i			0.865660i	0.901476	+	0.432830i	$0.142485\pi$
$761$			1.38296e7i			0.865660i	−0.901476	+	0.432830i	$0.857515\pi$
$762$	1.48820e7	−	1.40269e6i	0.928484	−	0.0875132i
$763$	−70634.0			−0.00439241
$764$	−3.00779e6	+	572074.i	−0.186429	+	0.0354584i
$765$	1.52144e7	+	3.52074e6i	0.939945	+	0.217511i
$766$	−1.71909e7	+	1.62031e6i	−1.05859	+	0.0997758i
$767$	−5.58165e6	−	5.58165e6i	−0.342589	−	0.342589i
$768$	6.30173e6	+	6.73994e6i	0.385529	+	0.412338i
$769$			2.33481e7i			1.42376i	0.702303	+	0.711878i	$0.252155\pi$
$769$			2.33481e7i			1.42376i	−0.702303	+	0.711878i	$0.747845\pi$
$770$	−376374.	−	50519.4i	−0.0228767	−	0.00307066i
$771$	1.76696e6	+	1.76696e6i	0.107051	+	0.107051i
$772$	6.97637e6	−	1.02534e7i	0.421295	−	0.619193i
$773$			2.11121e7i			1.27082i	0.772176	+	0.635408i	$0.219168\pi$
$773$			2.11121e7i			1.27082i	−0.772176	+	0.635408i	$0.780832\pi$
$774$	5.70574e6	+	4.72281e6i	0.342342	+	0.283366i
$775$	−3.50037e6	−	1.71169e6i	−0.209343	−	0.102369i
$776$	3.77757e6	+	1.30421e7i	0.225194	+	0.777488i
$777$	576877.	+	576877.i	0.0342792	+	0.0342792i
$778$	2.34046e7	−	2.20597e6i	1.38628	−	0.130663i
$779$	−6.05808e6	−	6.05808e6i	−0.357677	−	0.357677i
$780$	−4.71986e6	−	5.10778e6i	−0.277774	−	0.300605i
$781$	1.02184e6	−	1.02184e6i	0.0599453	−	0.0599453i
$782$	2.84032e7	+	2.35102e7i	1.66093	+	1.37480i
$783$	−7.79836e6	+	7.79836e6i	−0.454568	+	0.454568i
$784$	−6.28478e6	−	1.59241e7i	−0.365174	−	0.925260i
$785$	−7.96749e6	+	4.97297e6i	−0.461474	+	0.288032i
$786$	−1.08898e7	+	1.02641e6i	−0.628729	+	0.0592601i
$787$	2.79553e6			0.160889			0.0804446	−	0.996759i	$-0.474366\pi$
$787$	2.79553e6			0.160889			0.0804446	+	0.996759i	$0.474366\pi$
$788$	−962467.	−	5.06036e6i	−0.0552167	−	0.290312i
$789$	−6.81854e6	+	6.81854e6i	−0.389941	+	0.389941i
$790$	−442645.	+	3.29775e6i	−0.0252341	+	0.187997i
$791$	−441148.			−0.0250694
$792$	−1.06241e6	−	3.66801e6i	−0.0601840	−	0.207786i
$793$	−1.44070e7	+	1.44070e7i	−0.813564	+	0.813564i
$794$	1.09335e7	−	1.32090e7i	0.615472	−	0.743566i
$795$	5.63198e6	+	9.02333e6i	0.316041	+	0.506348i
$796$	−2.09221e7	+	3.97933e6i	−1.17037	+	0.222601i
$797$			2.75981e7i			1.53898i	0.638659	+	0.769490i	$0.279489\pi$
$797$			2.75981e7i			1.53898i	−0.638659	+	0.769490i	$0.720511\pi$
$798$	−352933.	−	292133.i	−0.0196194	−	0.0162395i
$799$	4.08004e7			2.26098
$800$	−1.26056e7	+	1.29914e7i	−0.696370	+	0.717683i
$801$	3.09504e6			0.170446
$802$	−2.47882e7	−	2.05180e7i	−1.36085	−	1.12641i
$803$			6.83108e6i			0.373853i
$804$	−768787.	+	146221.i	−0.0419436	+	0.00797757i
$805$	1.07764e6	+	1.72656e6i	0.0586119	+	0.0939056i
$806$	−1.98701e6	+	2.40056e6i	−0.107737	+	0.130159i
$807$	5.96200e6	−	5.96200e6i	0.322261	−	0.322261i
$808$	7.15188e6	−	2.07150e6i	0.385382	−	0.111624i
$809$	−278185.			−0.0149438			−0.00747192	−	0.999972i	$-0.502378\pi$
$809$	−278185.			−0.0149438			−0.00747192	+	0.999972i	$0.502378\pi$
$810$	−361629.	+	2.69417e6i	−0.0193665	+	0.144282i
$811$	−1.41698e7	+	1.41698e7i	−0.756506	+	0.756506i	−0.975685	−	0.219178i	$-0.929662\pi$
$811$	−1.41698e7	+	1.41698e7i	−0.756506	+	0.756506i	0.219178	+	0.975685i	$0.429662\pi$
$812$	−172863.	−	908862.i	−0.00920052	−	0.0483735i
$813$	1.29392e7			0.686565
$814$	7.05897e6	−	665336.i	0.373405	−	0.0351949i
$815$	−2.25672e7	+	1.40855e7i	−1.19010	+	0.742811i
$816$	1.39467e7	+	6.05326e6i	0.733239	+	0.318247i
$817$	5.46091e6	−	5.46091e6i	0.286226	−	0.286226i
$818$	8.10602e6	+	6.70959e6i	0.423569	+	0.350601i
$819$	487489.	−	487489.i	0.0253954	−	0.0253954i
$820$	1.06508e7	+	1.15262e7i	0.553156	+	0.598621i
$821$	−3.72415e6	−	3.72415e6i	−0.192828	−	0.192828i	0.604089	−	0.796917i	$-0.293537\pi$
$821$	−3.72415e6	−	3.72415e6i	−0.192828	−	0.192828i	−0.796917	+	0.604089i	$0.793537\pi$
$822$	9.72301e6	−	916432.i	0.501905	−	0.0473065i
$823$	3.65676e6	+	3.65676e6i	0.188190	+	0.188190i	0.794913	−	0.606723i	$-0.207516\pi$
$823$	3.65676e6	+	3.65676e6i	0.188190	+	0.188190i	−0.606723	+	0.794913i	$0.707516\pi$
$824$	−2.97551e7	+	8.61839e6i	−1.52667	+	0.442189i
$825$	−3.31407e6	+	1.13733e6i	−0.169522	+	0.0581770i
$826$	733793.	+	607382.i	0.0374217	+	0.0309750i
$827$			1.92734e7i			0.979930i	0.871742	+	0.489965i	$0.162990\pi$
$827$			1.92734e7i			0.979930i	−0.871742	+	0.489965i	$0.837010\pi$
$828$	−1.15132e7	+	1.69213e7i	−0.583605	+	0.857747i
$829$	−2.08910e7	−	2.08910e7i	−1.05578	−	1.05578i	−0.998349	−	0.0574308i	$-0.981709\pi$
$829$	−2.08910e7	−	2.08910e7i	−1.05578	−	1.05578i	−0.0574308	−	0.998349i	$-0.518291\pi$
$830$	2.34770e7	+	3.15124e6i	1.18290	+	0.158776i
$831$		−	1.13437e7i		−	0.569839i
$832$	7.73734e6	+	1.22361e7i	0.387510	+	0.612823i
$833$	−1.99462e7	−	1.99462e7i	−0.995971	−	0.995971i
$834$	−2.37648e6	+	223993.i	−0.118309	+	0.0111511i
$835$	−2.24556e7	−	5.19641e6i	−1.11457	−	0.257921i
$836$	−3.91162e6	+	743981.i	−0.193572	+	0.0368168i
$837$	−4.48278e6			−0.221174
$838$	6.94181e6	−	654293.i	0.341478	−	0.0321856i
$839$		−	3.15396e7i		−	1.54686i	−0.633882	−	0.773430i	$-0.718540\pi$
$839$		−	3.15396e7i		−	1.54686i	0.633882	−	0.773430i	$-0.281460\pi$
$840$	624890.	+	560210.i	0.0305566	+	0.0273938i
$841$		−	1.11013e7i		−	0.541231i
$842$	−2.42895e6	−	2.57703e7i	−0.118070	−	1.25268i
$843$	9.53494e6			0.462114
$844$	1.52071e7	−	2.23505e7i	0.734836	−	1.08002i
$845$	5.21235e6	+	8.35102e6i	0.251126	+	0.402344i
$846$	2.12523e6	+	2.25479e7i	0.102089	+	1.08313i
$847$	−965105.	−	965105.i	−0.0462238	−	0.0462238i
$848$	−8.12869e6	−	2.05960e7i	−0.388178	−	0.983545i
$849$			1.15099e7i			0.548026i
$850$	−1.05306e7	+	2.79063e7i	−0.499925	+	1.32481i
$851$	−2.68702e7	−	2.68702e7i	−1.27188	−	1.27188i
$852$	−3.13740e6	+	596725.i	−0.148071	+	0.0281628i
$853$			1.22259e7i			0.575317i	0.957733	+	0.287659i	$0.0928768\pi$
$853$			1.22259e7i			0.575317i	−0.957733	+	0.287659i	$0.907123\pi$
$854$	1.56774e6	−	1.89403e6i	0.0735580	−	0.0888672i
$855$	8.80582e6	+	2.03774e6i	0.411959	+	0.0953306i
$856$	4.79733e6	+	2.64244e6i	0.223777	+	0.123260i
$857$	2.55907e7	+	2.55907e7i	1.19023	+	1.19023i	0.977004	+	0.213223i	$0.0683960\pi$
$857$	2.55907e7	+	2.55907e7i	1.19023	+	1.19023i	0.213223	+	0.977004i	$0.431604\pi$
$858$	262952.	+	2.78982e6i	0.0121943	+	0.129377i
$859$	−7.03689e6	−	7.03689e6i	−0.325385	−	0.325385i	0.525443	−	0.850829i	$-0.323900\pi$
$859$	−7.03689e6	−	7.03689e6i	−0.325385	−	0.325385i	−0.850829	+	0.525443i	$0.823900\pi$
$860$	−1.03900e7	+	9.60091e6i	−0.479038	+	0.442656i
$861$	514485.	−	514485.i	0.0236518	−	0.0236518i
$862$	−2.36580e7	+	2.85818e7i	−1.08445	+	1.31015i
$863$	−2.46447e6	+	2.46447e6i	−0.112641	+	0.112641i	−0.761181	−	0.648540i	$-0.775380\pi$
$863$	−2.46447e6	+	2.46447e6i	−0.112641	+	0.112641i	0.648540	+	0.761181i	$0.275380\pi$
$864$	−6.46241e6	+	1.97978e7i	−0.294517	+	0.902260i
$865$	−1.53252e6	−	2.45534e6i	−0.0696411	−	0.111576i
$866$	616537.	+	6.54124e6i	0.0279360	+	0.296391i
$867$	1.25573e7			0.567349
$868$	211539.	−	310907.i	0.00952997	−	0.0140066i
$869$	947994.	−	947994.i	0.0425849	−	0.0425849i
$870$	−5.17926e6	−	6.78520e6i	−0.231990	−	0.303924i
$871$	−1.22784e6			−0.0548400
$872$	1.30309e6	−	377431.i	0.0580339	−	0.0168092i
$873$	−8.78162e6	+	8.78162e6i	−0.389977	+	0.389977i
$874$	1.64392e7	+	1.36072e7i	0.727951	+	0.602546i
$875$	−1.03811e6	+	1.27794e6i	−0.0458377	+	0.0564272i
$876$	8.49230e6	−	1.24815e7i	0.373908	−	0.549547i
$877$		−	3.28729e7i		−	1.44324i	−0.692288	−	0.721621i	$-0.743397\pi$
$877$		−	3.28729e7i		−	1.44324i	0.692288	−	0.721621i	$-0.256603\pi$
$878$	5.14114e6	−	6.21114e6i	0.225073	−	0.271916i
$879$	9.89822e6			0.432101
$880$	7.21346e6	−	1.07914e6i	0.314005	−	0.0469756i
$881$	8.16736e6			0.354521			0.177260	−	0.984164i	$-0.443276\pi$
$881$	8.16736e6			0.354521			0.177260	+	0.984164i	$0.443276\pi$
$882$	9.98408e6	−	1.20620e7i	0.432152	−	0.522093i
$883$		−	4.57221e7i		−	1.97344i	−0.162420	−	0.986722i	$-0.551930\pi$
$883$		−	4.57221e7i		−	1.97344i	0.162420	−	0.986722i	$-0.448070\pi$
$884$	1.97223e7	+	1.34189e7i	0.848840	+	0.577546i
$885$	8.56258e6	+	1.98145e6i	0.367491	+	0.0850402i
$886$	−2.78476e7	−	2.30503e7i	−1.19180	−	0.986488i
$887$	6.35873e6	−	6.35873e6i	0.271370	−	0.271370i	−0.558282	−	0.829651i	$-0.688539\pi$
$887$	6.35873e6	−	6.35873e6i	0.271370	−	0.271370i	0.829651	+	0.558282i	$0.188539\pi$
$888$	−1.37250e7	−	7.55994e6i	−0.584090	−	0.321726i
$889$	−2.83020e6			−0.120105
$890$	−786419.	+	5.85890e6i	−0.0332797	+	0.247937i
$891$	774484.	−	774484.i	0.0326827	−	0.0326827i
$892$	−3.18741e7	−	2.16869e7i	−1.34130	−	0.912611i
$893$	2.36144e7			0.990943
$894$	455349.	+	4.83109e6i	0.0190546	+	0.202163i
$895$	4.55236e7	+	1.05345e7i	1.89968	+	0.439600i
$896$	−1.06813e6	−	1.38245e6i	−0.0444484	−	0.0575279i
$897$	1.06196e7	−	1.06196e7i	0.440682	−	0.440682i
$898$	6.64128e6	−	8.02349e6i	0.274828	−	0.332026i
$899$	−2.70457e6	+	2.70457e6i	−0.111609	+	0.111609i
$900$	−1.59706e7	−	4.36603e6i	−0.657228	−	0.179672i
$901$	−2.57982e7	−	2.57982e7i	−1.05871	−	1.05871i
$902$	−593376.	−	6.29551e6i	−0.0242836	−	0.257641i
$903$	463770.	+	463770.i	0.0189270	+	0.0189270i
$904$	8.13848e6	−	2.35726e6i	0.331225	−	0.0959371i
$905$	−9.84910e6	+	4.25617e7i	−0.399738	+	1.72742i
$906$	1.47072e7	−	1.77681e7i	0.595262	−	0.719150i
$907$			3.12900e6i			0.126295i	0.998004	+	0.0631476i	$0.0201139\pi$
$907$			3.12900e6i			0.126295i	−0.998004	+	0.0631476i	$0.979886\pi$
$908$	653208.	+	3.43437e6i	0.0262928	+	0.138240i
$909$	4.81556e6	+	4.81556e6i	0.193302	+	0.193302i
$910$	798948.	+	1.04668e6i	0.0319827	+	0.0418997i
$911$		−	1.24615e7i		−	0.497478i	−0.968571	−	0.248739i	$-0.919984\pi$
$911$		−	1.24615e7i		−	0.497478i	0.968571	−	0.248739i	$-0.0800162\pi$
$912$	8.07206e6	+	3.50351e6i	0.321364	+	0.139481i
$913$	−6.74887e6	−	6.74887e6i	−0.267950	−	0.267950i
$914$	4.62220e6	+	4.90399e7i	0.183014	+	1.94171i
$915$	5.11440e6	−	2.21012e7i	0.201949	−	0.872698i
$916$	3.07748e6	+	2.09390e6i	0.121187	+	0.0824550i
$917$	2.07097e6			0.0813300
$918$	3.22007e6	+	3.41638e7i	0.126113	+	1.33801i
$919$		−	4.39035e6i		−	0.171479i	−0.996318	−	0.0857394i	$-0.972675\pi$
$919$		−	4.39035e6i		−	0.171479i	0.996318	−	0.0857394i	$-0.0273253\pi$
$920$	−2.91066e7	−	2.60939e7i	−1.13376	−	1.01641i
$921$			2.14418e7i			0.832936i
$922$	3.79770e7	−	3.57948e6i	1.47127	−	0.138673i
$923$	−5.01080e6			−0.193599
$924$	−63182.9	−	332196.i	−0.00243455	−	0.0128001i
$925$	1.35041e7	−	2.76156e7i	0.518933	−	1.06121i
$926$	1.20879e7	−	1.13933e6i	0.463259	−	0.0436640i
$927$	−2.00350e7	−	2.00350e7i	−0.765754	−	0.765754i
$928$	8.04553e6	+	1.58434e7i	0.306679	+	0.603918i
$929$			3.30311e7i			1.25569i	0.778337	+	0.627847i	$0.216064\pi$
$929$			3.30311e7i			1.25569i	−0.778337	+	0.627847i	$0.783936\pi$
$930$	461578.	−	3.43880e6i	0.0175000	−	0.130377i
$931$	−1.15444e7	−	1.15444e7i	−0.436514	−	0.436514i
$932$	−2.65109e7	−	1.80378e7i	−0.999734	−	0.680212i
$933$			9.78726e6i			0.368092i
$934$	−2.89637e7	−	2.39741e7i	−1.08639	−	0.899239i
$935$	1.01952e7	−	6.36339e6i	0.381387	−	0.238045i
$936$	−6.38852e6	+	1.15983e7i	−0.238347	+	0.432717i
$937$	−1.32246e7	−	1.32246e7i	−0.492078	−	0.492078i	0.416883	−	0.908960i	$-0.363123\pi$
$937$	−1.32246e7	−	1.32246e7i	−0.492078	−	0.492078i	−0.908960	+	0.416883i	$0.863123\pi$
$938$	147515.	−	13903.9i	0.00547430	−	0.000515974i
$939$	−1.48172e7	−	1.48172e7i	−0.548407	−	0.548407i
$940$	−4.32231e7	−	1.70615e6i	−1.59550	−	0.0629792i
$941$	2.40987e7	−	2.40987e7i	0.887197	−	0.887197i	−0.107056	−	0.994253i	$-0.534142\pi$
$941$	2.40987e7	−	2.40987e7i	0.887197	−	0.887197i	0.994253	+	0.107056i	$0.0341424\pi$
$942$	−6.44256e6	−	5.33269e6i	−0.236554	−	0.195803i
$943$	−2.39641e7	+	2.39641e7i	−0.877569	+	0.877569i
$944$	−1.67828e7	−	7.28424e6i	−0.612965	−	0.266044i
$945$	−427046.	+	1.84543e6i	−0.0155559	+	0.0672229i
$946$	5.67493e6	−	534884.i	0.206173	−	0.0194326i
$947$	1.07849e7			0.390788			0.195394	−	0.980725i	$-0.437401\pi$
$947$	1.07849e7			0.390788			0.195394	+	0.980725i	$0.437401\pi$
$948$	−2.91067e6	+	553601.i	−0.105189	+	0.0200067i
$949$	1.67488e7	−	1.67488e7i	0.603695	−	0.603695i
$950$	−6.09489e6	+	1.61516e7i	−0.219107	+	0.580639i
$951$	1.98695e7			0.712420
$952$	−2.52142e6	−	1.38884e6i	−0.0901679	−	0.0496659i
$953$	1.03134e7	−	1.03134e7i	0.367849	−	0.367849i	−0.498843	−	0.866692i	$-0.666242\pi$
$953$	1.03134e7	−	1.03134e7i	0.367849	−	0.367849i	0.866692	+	0.498843i	$0.166242\pi$
$954$	1.29133e7	−	1.56009e7i	0.459375	−	0.554982i
$955$	4.53731e6	−	2.83200e6i	0.160987	−	0.100481i
$956$	−1.79777e6	−	9.45211e6i	−0.0636192	−	0.334491i
$957$			3.43938e6i			0.121395i
$958$	−2.14385e7	−	1.77453e7i	−0.754712	−	0.624697i
$959$	−1.84908e6			−0.0649246
$960$	−1.45217e7	−	6.99591e6i	−0.508557	−	0.245000i
$961$	2.70745e7			0.945696
$962$	−1.89389e7	−	1.56762e7i	−0.659806	−	0.546140i
$963$			5.00941e6i			0.174069i
$964$	−7.84066e6	−	4.12238e7i	−0.271744	−	1.42875i
$965$	−4.88436e6	+	2.11072e7i	−0.168846	+	0.729645i
$966$	−1.15560e6	+	1.39610e6i	−0.0398440	+	0.0481366i
$967$	−3.68713e6	+	3.68713e6i	−0.126801	+	0.126801i	−0.767659	−	0.640858i	$-0.778579\pi$
$967$	−3.68713e6	+	3.68713e6i	−0.126801	+	0.126801i	0.640858	+	0.767659i	$0.278579\pi$
$968$	2.29617e7	+	1.26476e7i	0.787617	+	0.433832i
$969$	1.44993e7			0.496065
$970$	−1.43922e7	−	1.88549e7i	−0.491133	−	0.643419i
$971$	−2.93117e7	+	2.93117e7i	−0.997684	+	0.997684i	−0.999997	−	0.00231379i	$-0.999263\pi$
$971$	−2.93117e7	+	2.93117e7i	−0.997684	+	0.997684i	0.00231379	+	0.999997i	$0.499263\pi$
$972$	−2.98421e7	+	5.67589e6i	−1.01313	+	0.192694i
$973$	451949.			0.0153041
$974$	4.08528e7	−	3.85053e6i	1.37983	−	0.130054i
$975$	1.09142e7	+	5.33704e6i	0.367687	+	0.179800i
$976$	−1.88017e7	+	4.33189e7i	−0.631789	+	1.45564i
$977$	2.03390e7	−	2.03390e7i	0.681699	−	0.681699i	−0.278684	−	0.960383i	$-0.589898\pi$
$977$	2.03390e7	−	2.03390e7i	0.681699	−	0.681699i	0.960383	+	0.278684i	$0.0898982\pi$
$978$	−1.82480e7	−	1.51044e7i	−0.610054	−	0.504959i
$979$	1.68424e6	−	1.68424e6i	0.0561626	−	0.0561626i
$980$	2.02965e7	+	2.19646e7i	0.675080	+	0.730565i
$981$	877404.	+	877404.i	0.0291090	+	0.0291090i
$982$	−4.47756e7	+	4.22028e6i	−1.48171	+	0.139657i
$983$	−3.42448e6	−	3.42448e6i	−0.113035	−	0.113035i	0.648327	−	0.761362i	$-0.275469\pi$
$983$	−3.42448e6	−	3.42448e6i	−0.113035	−	0.113035i	−0.761362	+	0.648327i	$0.775469\pi$
$984$	−6.74229e6	+	1.22406e7i	−0.221983	+	0.403008i
$985$	4.76460e6	+	7.63365e6i	0.156472	+	0.250693i
$986$	2.25546e7	+	1.86691e7i	0.738827	+	0.611549i
$987$			2.00546e6i			0.0655272i
$988$	1.14148e7	+	7.76659e6i	0.372030	+	0.253127i
$989$	−2.16018e7	−	2.16018e7i	−0.702263	−	0.702263i
$990$	4.04772e6	+	5.30280e6i	0.131257	+	0.171956i
$991$		−	4.58796e7i		−	1.48400i	−0.670397	−	0.742002i	$-0.733876\pi$
$991$		−	4.58796e7i		−	1.48400i	0.670397	−	0.742002i	$-0.266124\pi$
$992$	−2.24124e6	+	6.86610e6i	−0.0723118	+	0.221529i
$993$	−4.91981e6	−	4.91981e6i	−0.158334	−	0.158334i
$994$	602005.	−	56741.3i	0.0193256	−	0.00182152i
$995$	3.15614e7	−	1.96993e7i	1.01064	−	0.630801i
$996$	3.94115e6	+	2.07213e7i	0.125885	+	0.661865i
$997$	3.77300e7			1.20212			0.601061	−	0.799203i	$-0.294745\pi$
$997$	3.77300e7			1.20212			0.601061	+	0.799203i	$0.294745\pi$
$998$	3.80931e7	−	3.59042e6i	1.21065	−	0.114109i
$999$		−	3.53662e7i		−	1.12118i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.j.a.43.13	✓	116
5.2	odd	4		80.6.s.a.27.43	yes	116
16.3	odd	4		80.6.s.a.3.43	yes	116
80.67	even	4	inner	80.6.j.a.67.13	yes	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.j.a.43.13	✓	116	1.1	even	1	trivial
80.6.j.a.67.13	yes	116	80.67	even	4	inner
80.6.s.a.3.43	yes	116	16.3	odd	4
80.6.s.a.27.43	yes	116	5.2	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.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.35770 - 3.60700i) q^{2} +8.79961i q^{3} +(5.97913 + 31.4364i) q^{4} +(-29.5991 - 47.4225i) q^{5} +(31.7402 - 38.3461i) q^{6} +(-6.66435 + 6.66435i) q^{7} +(87.3359 - 158.557i) q^{8} +165.567 q^{9} +O(q^{10})\)	\(q+(-4.35770 - 3.60700i) q^{2} +8.79961i q^{3} +(5.97913 + 31.4364i) q^{4} +(-29.5991 - 47.4225i) q^{5} +(31.7402 - 38.3461i) q^{6} +(-6.66435 + 6.66435i) q^{7} +(87.3359 - 158.557i) q^{8} +165.567 q^{9} +(-42.0688 + 313.417i) q^{10} +(90.0969 - 90.0969i) q^{11} +(-276.628 + 52.6140i) q^{12} -441.808 q^{13} +(53.0795 - 5.00295i) q^{14} +(417.300 - 260.461i) q^{15} +(-952.500 + 375.925i) q^{16} +(-1193.08 + 1193.08i) q^{17} +(-721.491 - 597.199i) q^{18} +(-690.532 + 690.532i) q^{19} +(1313.82 - 1214.04i) q^{20} +(-58.6437 - 58.6437i) q^{21} +(-717.595 + 67.6361i) q^{22} +(2731.55 + 2731.55i) q^{23} +(1395.24 + 768.522i) q^{24} +(-1372.79 + 2807.33i) q^{25} +(1925.27 + 1593.60i) q^{26} +3595.23i q^{27} +(-249.350 - 169.656i) q^{28} +(2169.09 + 2169.09i) q^{29} +(-2757.95 - 370.189i) q^{30} +1246.87i q^{31} +(5506.67 + 1797.50i) q^{32} +(792.818 + 792.818i) q^{33} +(9502.54 - 895.652i) q^{34} +(513.299 + 118.781i) q^{35} +(989.946 + 5204.83i) q^{36} -9836.99 q^{37} +(5499.88 - 518.385i) q^{38} -3887.74i q^{39} +(-10104.3 + 551.467i) q^{40} +8773.06i q^{41} +(44.0240 + 467.079i) q^{42} -7908.26 q^{43} +(3371.03 + 2293.63i) q^{44} +(-4900.63 - 7851.59i) q^{45} +(-2050.59 - 21756.0i) q^{46} +(-17098.7 - 17098.7i) q^{47} +(-3308.00 - 8381.63i) q^{48} +16718.2i q^{49} +(16108.2 - 7281.85i) q^{50} +(-10498.7 - 10498.7i) q^{51} +(-2641.63 - 13888.9i) q^{52} +21623.1i q^{53} +(12968.0 - 15666.9i) q^{54} +(-6939.41 - 1605.83i) q^{55} +(474.644 + 1638.72i) q^{56} +(-6076.41 - 6076.41i) q^{57} +(-1628.34 - 17276.1i) q^{58} +(12633.6 + 12633.6i) q^{59} +(10683.0 + 11561.1i) q^{60} +(32609.2 - 32609.2i) q^{61} +(4497.45 - 5433.48i) q^{62} +(-1103.39 + 1103.39i) q^{63} +(-17512.9 - 27695.5i) q^{64} +(13077.1 + 20951.7i) q^{65} +(-595.172 - 6314.56i) q^{66} +2779.13 q^{67} +(-44639.9 - 30372.7i) q^{68} +(-24036.6 + 24036.6i) q^{69} +(-1808.36 - 2369.08i) q^{70} +11341.6 q^{71} +(14459.9 - 26251.8i) q^{72} +(-37909.6 + 37909.6i) q^{73} +(42866.7 + 35482.0i) q^{74} +(-24703.4 - 12080.0i) q^{75} +(-25836.6 - 17579.1i) q^{76} +1200.87i q^{77} +(-14023.1 + 16941.6i) q^{78} +10521.9 q^{79} +(46020.5 + 34042.9i) q^{80} +8596.12 q^{81} +(31644.4 - 38230.4i) q^{82} -74906.8i q^{83} +(1492.91 - 2194.19i) q^{84} +(91893.1 + 21264.8i) q^{85} +(34461.9 + 28525.1i) q^{86} +(-19087.1 + 19087.1i) q^{87} +(-6416.83 - 22154.2i) q^{88} +18693.6 q^{89} +(-6965.20 + 51891.5i) q^{90} +(2944.36 - 2944.36i) q^{91} +(-69537.9 + 102203. i) q^{92} -10972.0 q^{93} +(12836.1 + 136186. i) q^{94} +(53185.9 + 12307.6i) q^{95} +(-15817.3 + 48456.6i) q^{96} +(-53039.7 + 53039.7i) q^{97} +(60302.4 - 72852.8i) q^{98} +(14917.1 - 14917.1i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 2 q^{2} - 20 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 248 q^{8} - 8748 q^{9}+O(q^{10}) \) 116 * q - 2 * q^2 - 20 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 248 * q^8 - 8748 * q^9	\( 116 q - 2 q^{2} - 20 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} - 248 q^{8} - 8748 q^{9} - 66 q^{10} - 4 q^{11} - 308 q^{12} - 4 q^{13} + 972 q^{15} - 1224 q^{16} - 4 q^{17} + 4214 q^{18} - 2360 q^{19} - 836 q^{20} - 4 q^{21} - 2440 q^{22} - 4 q^{23} + 972 q^{24} - 884 q^{26} - 12416 q^{28} + 15336 q^{30} - 17612 q^{32} - 4 q^{33} - 12520 q^{34} - 8640 q^{35} + 2380 q^{36} - 4 q^{37} + 15108 q^{38} + 11864 q^{40} - 41092 q^{42} - 1316 q^{43} + 8200 q^{44} - 5766 q^{45} - 35924 q^{46} + 65256 q^{47} + 5180 q^{48} - 44378 q^{50} + 10436 q^{51} + 63080 q^{52} + 33820 q^{54} - 4 q^{55} - 64684 q^{56} + 972 q^{57} - 66940 q^{58} - 14480 q^{59} + 136260 q^{60} + 48076 q^{61} + 109524 q^{62} + 972 q^{63} + 71920 q^{64} - 4 q^{65} + 72436 q^{66} - 89260 q^{67} + 36360 q^{68} - 21348 q^{69} + 59552 q^{70} - 143848 q^{71} + 179728 q^{72} - 10072 q^{73} - 82508 q^{74} - 32272 q^{75} - 128004 q^{76} + 111388 q^{78} + 313732 q^{80} + 551116 q^{81} - 282876 q^{82} - 80928 q^{84} - 6252 q^{85} - 85324 q^{86} - 282188 q^{87} + 80224 q^{88} + 115550 q^{90} - 164724 q^{91} + 474536 q^{92} + 968 q^{93} - 106060 q^{94} + 204760 q^{95} - 62264 q^{96} - 4 q^{97} + 50214 q^{98} - 168788 q^{99}+O(q^{100}) \) 116 * q - 2 * q^2 - 20 * q^4 - 2 * q^5 - 4 * q^6 - 4 * q^7 - 248 * q^8 - 8748 * q^9 - 66 * q^10 - 4 * q^11 - 308 * q^12 - 4 * q^13 + 972 * q^15 - 1224 * q^16 - 4 * q^17 + 4214 * q^18 - 2360 * q^19 - 836 * q^20 - 4 * q^21 - 2440 * q^22 - 4 * q^23 + 972 * q^24 - 884 * q^26 - 12416 * q^28 + 15336 * q^30 - 17612 * q^32 - 4 * q^33 - 12520 * q^34 - 8640 * q^35 + 2380 * q^36 - 4 * q^37 + 15108 * q^38 + 11864 * q^40 - 41092 * q^42 - 1316 * q^43 + 8200 * q^44 - 5766 * q^45 - 35924 * q^46 + 65256 * q^47 + 5180 * q^48 - 44378 * q^50 + 10436 * q^51 + 63080 * q^52 + 33820 * q^54 - 4 * q^55 - 64684 * q^56 + 972 * q^57 - 66940 * q^58 - 14480 * q^59 + 136260 * q^60 + 48076 * q^61 + 109524 * q^62 + 972 * q^63 + 71920 * q^64 - 4 * q^65 + 72436 * q^66 - 89260 * q^67 + 36360 * q^68 - 21348 * q^69 + 59552 * q^70 - 143848 * q^71 + 179728 * q^72 - 10072 * q^73 - 82508 * q^74 - 32272 * q^75 - 128004 * q^76 + 111388 * q^78 + 313732 * q^80 + 551116 * q^81 - 282876 * q^82 - 80928 * q^84 - 6252 * q^85 - 85324 * q^86 - 282188 * q^87 + 80224 * q^88 + 115550 * q^90 - 164724 * q^91 + 474536 * q^92 + 968 * q^93 - 106060 * q^94 + 204760 * q^95 - 62264 * q^96 - 4 * q^97 + 50214 * q^98 - 168788 * q^99

Introduction

L-functions

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