LMFDB - Embedded newform 80.6.q.a.69.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("80.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			69.5
Character	$\chi$	$=$	80.69
Dual form			80.6.q.a.29.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.48884 + 1.36846i) q^{2} +(6.61300 + 6.61300i) q^{3} +(28.2546 - 15.0225i) q^{4} +(49.7455 - 25.5026i) q^{5} +(-45.3473 - 27.2480i) q^{6} +180.633 q^{7} +(-134.527 + 121.121i) q^{8} -155.536i q^{9} +O(q^{10})$	\(q+(-5.48884 + 1.36846i) q^{2} +(6.61300 + 6.61300i) q^{3} +(28.2546 - 15.0225i) q^{4} +(49.7455 - 25.5026i) q^{5} +(-45.3473 - 27.2480i) q^{6} +180.633 q^{7} +(-134.527 + 121.121i) q^{8} -155.536i q^{9} +(-238.146 + 208.054i) q^{10} +(-482.240 - 482.240i) q^{11} +(286.192 + 87.5040i) q^{12} +(85.7657 + 85.7657i) q^{13} +(-991.466 + 247.189i) q^{14} +(497.616 + 160.319i) q^{15} +(572.648 - 848.911i) q^{16} -1152.03i q^{17} +(212.846 + 853.714i) q^{18} +(-1207.86 + 1207.86i) q^{19} +(1022.43 - 1467.87i) q^{20} +(1194.53 + 1194.53i) q^{21} +(3306.86 + 1987.01i) q^{22} +950.477 q^{23} +(-1690.60 - 88.6528i) q^{24} +(1824.24 - 2537.28i) q^{25} +(-588.120 - 353.387i) q^{26} +(2635.52 - 2635.52i) q^{27} +(5103.72 - 2713.56i) q^{28} +(4751.04 - 4751.04i) q^{29} +(-2950.72 - 198.994i) q^{30} +3020.61 q^{31} +(-1981.47 + 5443.18i) q^{32} -6378.11i q^{33} +(1576.51 + 6323.29i) q^{34} +(8985.69 - 4606.61i) q^{35} +(-2336.55 - 4394.63i) q^{36} +(-6423.45 + 6423.45i) q^{37} +(4976.83 - 8282.65i) q^{38} +1134.34i q^{39} +(-3603.22 + 9456.05i) q^{40} +7582.56i q^{41} +(-8191.23 - 4921.90i) q^{42} +(701.501 - 701.501i) q^{43} +(-20870.0 - 6381.06i) q^{44} +(-3966.58 - 7737.25i) q^{45} +(-5217.01 + 1300.69i) q^{46} +18936.1i q^{47} +(9400.77 - 1826.93i) q^{48} +15821.3 q^{49} +(-6540.76 + 16423.1i) q^{50} +(7618.36 - 7618.36i) q^{51} +(3711.69 + 1134.86i) q^{52} +(16491.0 - 16491.0i) q^{53} +(-10859.3 + 18072.6i) q^{54} +(-36287.7 - 11690.9i) q^{55} +(-24300.1 + 21878.6i) q^{56} -15975.1 q^{57} +(-19576.0 + 32579.3i) q^{58} +(-3150.95 - 3150.95i) q^{59} +(16468.3 - 2945.70i) q^{60} +(-13648.7 + 13648.7i) q^{61} +(-16579.6 + 4133.59i) q^{62} -28095.1i q^{63} +(3427.18 - 32588.3i) q^{64} +(6453.70 + 2079.21i) q^{65} +(8728.19 + 35008.4i) q^{66} +(30053.5 + 30053.5i) q^{67} +(-17306.4 - 32550.1i) q^{68} +(6285.50 + 6285.50i) q^{69} +(-43017.0 + 37581.5i) q^{70} -6626.96i q^{71} +(18838.8 + 20923.9i) q^{72} -45377.9 q^{73} +(26467.0 - 44047.5i) q^{74} +(28842.7 - 4715.36i) q^{75} +(-15982.5 + 52272.7i) q^{76} +(-87108.6 - 87108.6i) q^{77} +(-1552.29 - 6226.19i) q^{78} +107510. q^{79} +(6837.26 - 56833.5i) q^{80} -2937.97 q^{81} +(-10376.4 - 41619.4i) q^{82} +(54532.6 + 54532.6i) q^{83} +(51695.7 + 15806.1i) q^{84} +(-29379.7 - 57308.3i) q^{85} +(-2890.45 + 4810.40i) q^{86} +62837.2 q^{87} +(123284. + 6464.83i) q^{88} -14396.1i q^{89} +(32360.0 + 37040.4i) q^{90} +(15492.1 + 15492.1i) q^{91} +(26855.4 - 14278.6i) q^{92} +(19975.3 + 19975.3i) q^{93} +(-25913.3 - 103937. i) q^{94} +(-29282.1 + 90889.1i) q^{95} +(-49099.2 + 22892.3i) q^{96} +53496.0i q^{97} +(-86840.8 + 21650.9i) q^{98} +(-75005.9 + 75005.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	$ 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) $ 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−5.48884	+	1.36846i	−0.970298	+	0.241912i
$2$	−5.48884	+	1.36846i	−0.970298	+	0.241912i
$3$	6.61300	+	6.61300i	0.424224	+	0.424224i	0.886655	−	0.462431i	$-0.153023\pi$
$3$	6.61300	+	6.61300i	0.424224	+	0.424224i	−0.462431	+	0.886655i	$0.653023\pi$
$4$	28.2546	−	15.0225i	0.882957	−	0.469454i
$5$	49.7455	−	25.5026i	0.889875	−	0.456204i
$5$	49.7455	−	25.5026i	0.889875	−	0.456204i
$6$	−45.3473	−	27.2480i	−0.514249	−	0.308999i
$7$	180.633			1.39333			0.696663	−	0.717399i	$-0.254668\pi$
$7$	180.633			1.39333			0.696663	+	0.717399i	$0.254668\pi$
$8$	−134.527	+	121.121i	−0.743165	+	0.669108i
$9$		−	155.536i		−	0.640068i
$10$	−238.146	+	208.054i	−0.753083	+	0.657926i
$11$	−482.240	−	482.240i	−1.20166	−	1.20166i	−0.973661	−	0.227999i	$-0.926782\pi$
$11$	−482.240	−	482.240i	−1.20166	−	1.20166i	−0.227999	−	0.973661i	$-0.573218\pi$
$12$	286.192	+	87.5040i	0.573725	+	0.175418i
$13$	85.7657	+	85.7657i	0.140752	+	0.140752i	0.773972	−	0.633220i	$-0.218267\pi$
$13$	85.7657	+	85.7657i	0.140752	+	0.140752i	−0.633220	+	0.773972i	$0.718267\pi$
$14$	−991.466	+	247.189i	−1.35194	+	0.337062i
$15$	497.616	+	160.319i	0.571039	+	0.183974i
$16$	572.648	−	848.911i	0.559227	−	0.829015i
$17$		−	1152.03i		−	0.966809i	−0.875397	−	0.483405i	$-0.839400\pi$
$17$		−	1152.03i		−	0.966809i	0.875397	−	0.483405i	$-0.160600\pi$
$18$	212.846	+	853.714i	0.154840	+	0.621057i
$19$	−1207.86	+	1207.86i	−0.767595	+	0.767595i	−0.977683	−	0.210087i	$-0.932625\pi$
$19$	−1207.86	+	1207.86i	−0.767595	+	0.767595i	0.210087	+	0.977683i	$0.432625\pi$
$20$	1022.43	−	1467.87i	0.571555	−	0.820564i
$21$	1194.53	+	1194.53i	0.591082	+	0.591082i
$22$	3306.86	+	1987.01i	1.45666	+	0.875273i
$23$	950.477			0.374647			0.187323	−	0.982298i	$-0.440019\pi$
$23$	950.477			0.374647			0.187323	+	0.982298i	$0.440019\pi$
$24$	−1690.60	−	88.6528i	−0.599120	−	0.0314170i
$25$	1824.24	−	2537.28i	0.583755	−	0.811930i
$26$	−588.120	−	353.387i	−0.170621	−	0.102522i
$27$	2635.52	−	2635.52i	0.695756	−	0.695756i
$28$	5103.72	−	2713.56i	1.23025	−	0.654101i
$29$	4751.04	−	4751.04i	1.04904	−	1.04904i	0.0503093	−	0.998734i	$-0.483979\pi$
$29$	4751.04	−	4751.04i	1.04904	−	1.04904i	0.998734	−	0.0503093i	$-0.0160207\pi$
$30$	−2950.72	−	198.994i	−0.598584	−	0.0403680i
$31$	3020.61			0.564534			0.282267	−	0.959336i	$-0.408914\pi$
$31$	3020.61			0.564534			0.282267	+	0.959336i	$0.408914\pi$
$32$	−1981.47	+	5443.18i	−0.342068	+	0.939675i
$33$		−	6378.11i		−	1.01955i
$34$	1576.51	+	6323.29i	0.233883	+	0.938093i
$35$	8985.69	−	4606.61i	1.23989	−	0.635641i
$36$	−2336.55	−	4394.63i	−0.300482	−	0.565153i
$37$	−6423.45	+	6423.45i	−0.771372	+	0.771372i	−0.978346	−	0.206975i	$-0.933638\pi$
$37$	−6423.45	+	6423.45i	−0.771372	+	0.771372i	0.206975	+	0.978346i	$0.433638\pi$
$38$	4976.83	−	8282.65i	0.559106	−	0.930487i
$39$			1134.34i			0.119421i
$40$	−3603.22	+	9456.05i	−0.356074	+	0.934458i
$41$			7582.56i			0.704460i	0.935913	+	0.352230i	$0.114576\pi$
$41$			7582.56i			0.704460i	−0.935913	+	0.352230i	$0.885424\pi$
$42$	−8191.23	−	4921.90i	−0.716516	−	0.430536i
$43$	701.501	−	701.501i	0.0578572	−	0.0578572i	−0.677586	−	0.735443i	$-0.736974\pi$
$43$	701.501	−	701.501i	0.0578572	−	0.0578572i	0.735443	+	0.677586i	$0.236974\pi$
$44$	−20870.0	−	6381.06i	−1.62514	−	0.496891i
$45$	−3966.58	−	7737.25i	−0.292002	−	0.569580i
$46$	−5217.01	+	1300.69i	−0.363519	+	0.0906316i
$47$			18936.1i			1.25039i	0.780469	+	0.625195i	$0.214981\pi$
$47$			18936.1i			1.25039i	−0.780469	+	0.625195i	$0.785019\pi$
$48$	9400.77	−	1826.93i	0.588925	−	0.114451i
$49$	15821.3			0.941355
$50$	−6540.76	+	16423.1i	−0.370001	+	0.929031i
$51$	7618.36	−	7618.36i	0.410144	−	0.410144i
$52$	3711.69	+	1134.86i	0.190355	+	0.0582015i
$53$	16491.0	−	16491.0i	0.806412	−	0.806412i	−0.177677	−	0.984089i	$-0.556858\pi$
$53$	16491.0	−	16491.0i	0.806412	−	0.806412i	0.984089	+	0.177677i	$0.0568582\pi$
$54$	−10859.3	+	18072.6i	−0.506779	+	0.843403i
$55$	−36287.7	−	11690.9i	−1.61753	−	0.521125i
$56$	−24300.1	+	21878.6i	−1.03547	+	0.932285i
$57$	−15975.1			−0.651265
$58$	−19576.0	+	32579.3i	−0.764108	+	1.27166i
$59$	−3150.95	−	3150.95i	−0.117845	−	0.117845i	0.645725	−	0.763570i	$-0.276555\pi$
$59$	−3150.95	−	3150.95i	−0.117845	−	0.117845i	−0.763570	+	0.645725i	$0.776555\pi$
$60$	16468.3	−	2945.70i	0.590570	−	0.105636i
$61$	−13648.7	+	13648.7i	−0.469642	+	0.469642i	−0.901799	−	0.432157i	$-0.857753\pi$
$61$	−13648.7	+	13648.7i	−0.469642	+	0.469642i	0.432157	+	0.901799i	$0.357753\pi$
$62$	−16579.6	+	4133.59i	−0.547767	+	0.136568i
$63$		−	28095.1i		−	0.891823i
$64$	3427.18	−	32588.3i	0.104589	−	0.994515i
$65$	6453.70	+	2079.21i	0.189464	+	0.0610401i
$66$	8728.19	+	35008.4i	0.246640	+	0.989264i
$67$	30053.5	+	30053.5i	0.817914	+	0.817914i	0.985806	−	0.167891i	$-0.0536957\pi$
$67$	30053.5	+	30053.5i	0.817914	+	0.817914i	−0.167891	+	0.985806i	$0.553696\pi$
$68$	−17306.4	−	32550.1i	−0.453872	−	0.853651i
$69$	6285.50	+	6285.50i	0.158934	+	0.158934i
$70$	−43017.0	+	37581.5i	−1.04929	+	0.916704i
$71$		−	6626.96i		−	0.156016i	−0.996953	−	0.0780079i	$-0.975144\pi$
$71$		−	6626.96i		−	0.156016i	0.996953	−	0.0780079i	$-0.0248559\pi$
$72$	18838.8	+	20923.9i	0.428274	+	0.475676i
$73$	−45377.9			−0.996637			−0.498319	−	0.866994i	$-0.666049\pi$
$73$	−45377.9			−0.996637			−0.498319	+	0.866994i	$0.666049\pi$
$74$	26467.0	−	44047.5i	0.561857	−	0.935065i
$75$	28842.7	−	4715.36i	0.592083	−	0.0967970i
$76$	−15982.5	+	52272.7i	−0.317403	+	1.03810i
$77$	−87108.6	−	87108.6i	−1.67430	−	1.67430i
$78$	−1552.29	−	6226.19i	−0.0288893	−	0.115874i
$79$	107510.			1.93813			0.969064	−	0.246811i	$-0.0793826\pi$
$79$	107510.			1.93813			0.969064	+	0.246811i	$0.0793826\pi$
$80$	6837.26	−	56833.5i	0.119442	−	0.992841i
$81$	−2937.97			−0.0497547
$82$	−10376.4	−	41619.4i	−0.170417	−	0.683536i
$83$	54532.6	+	54532.6i	0.868882	+	0.868882i	0.992349	−	0.123466i	$-0.0394011\pi$
$83$	54532.6	+	54532.6i	0.868882	+	0.868882i	−0.123466	+	0.992349i	$0.539401\pi$
$84$	51695.7	+	15806.1i	0.799386	+	0.244415i
$85$	−29379.7	−	57308.3i	−0.441063	−	0.860340i
$86$	−2890.45	+	4810.40i	−0.0421424	+	0.0701350i
$87$	62837.2			0.890059
$88$	123284.	+	6464.83i	1.69707	+	0.0889919i
$89$		−	14396.1i		−	0.192650i	−0.995350	−	0.0963251i	$-0.969291\pi$
$89$		−	14396.1i		−	0.192650i	0.995350	−	0.0963251i	$-0.0307089\pi$
$90$	32360.0	+	37040.4i	0.421117	+	0.482024i
$91$	15492.1	+	15492.1i	0.196113	+	0.196113i
$92$	26855.4	−	14278.6i	0.330797	−	0.175879i
$93$	19975.3	+	19975.3i	0.239489	+	0.239489i
$94$	−25913.3	−	103937.i	−0.302484	−	1.21325i
$95$	−29282.1	+	90889.1i	−0.332884	+	1.03324i
$96$	−49099.2	+	22892.3i	−0.543746	+	0.253519i
$97$			53496.0i			0.577288i	0.957437	+	0.288644i	$0.0932043\pi$
$97$			53496.0i			0.577288i	−0.957437	+	0.288644i	$0.906796\pi$
$98$	−86840.8	+	21650.9i	−0.913395	+	0.227725i
$99$	−75005.9	+	75005.9i	−0.769144	+	0.769144i
$100$	13426.8	−	99094.5i	0.134268	−	0.990945i
$101$	−100716.	−	100716.i	−0.982419	−	0.982419i	0.0174291	−	0.999848i	$-0.494452\pi$
$101$	−100716.	−	100716.i	−0.982419	−	0.982419i	−0.999848	+	0.0174291i	$0.994452\pi$
$102$	−31390.5	+	52241.4i	−0.298743	+	0.497181i
$103$	113664.			1.05567			0.527836	−	0.849346i	$-0.323003\pi$
$103$	113664.			1.05567			0.527836	+	0.849346i	$0.323003\pi$
$104$	−21925.9	−	1149.76i	−0.198780	−	0.0104237i
$105$	89885.9	+	28958.8i	0.795643	+	0.256335i
$106$	−67949.0	+	113084.i	−0.587379	+	0.977541i
$107$	−37760.8	+	37760.8i	−0.318847	+	0.318847i	−0.848324	−	0.529477i	$-0.822388\pi$
$107$	−37760.8	+	37760.8i	−0.318847	+	0.318847i	0.529477	+	0.848324i	$0.322388\pi$
$108$	34873.5	−	114058.i	0.287698	−	0.940948i
$109$	−145724.	+	145724.i	−1.17480	+	1.17480i	−0.193755	+	0.981050i	$0.562067\pi$
$109$	−145724.	+	145724.i	−1.17480	+	1.17480i	−0.981050	+	0.193755i	$0.937933\pi$
$110$	215176.	+	14511.3i	1.69555	+	0.114347i
$111$	−84956.5			−0.654469
$112$	103439.	−	153342.i	0.779185	−	1.15509i
$113$		−	191100.i		−	1.40787i	−0.710263	−	0.703937i	$-0.751424\pi$
$113$		−	191100.i		−	1.40787i	0.710263	−	0.703937i	$-0.248576\pi$
$114$	87684.9	−	21861.4i	0.631921	−	0.157549i
$115$	47282.0	−	24239.6i	0.333389	−	0.170915i
$116$	62866.3	−	205611.i	0.433783	−	1.41874i
$117$	13339.7	−	13339.7i	0.0900909	−	0.0900909i
$118$	21607.0	+	12983.1i	0.142853	+	0.0858367i
$119$		−	208095.i		−	1.34708i
$120$	−86360.9	+	38704.7i	−0.547475	+	0.245364i
$121$			304060.i			1.88797i
$122$	56237.8	−	93593.2i	0.342081	−	0.569305i
$123$	−50143.5	+	50143.5i	−0.298849	+	0.298849i
$124$	85346.2	−	45377.2i	0.498460	−	0.265023i
$125$	26040.4	−	172741.i	0.149064	−	0.988828i
$126$	38447.0	+	154209.i	0.215743	+	0.865334i
$127$			183279.i			1.00833i	0.863606	+	0.504167i	$0.168200\pi$
$127$			183279.i			1.00833i	−0.863606	+	0.504167i	$0.831800\pi$
$128$	25784.5	+	183562.i	0.139102	+	0.990278i
$129$	9278.05			0.0490888
$130$	−38268.6	−	2580.81i	−0.198602	−	0.0133936i
$131$	−232885.	+	232885.i	−1.18567	+	1.18567i	−0.207416	+	0.978253i	$0.566505\pi$
$131$	−232885.	+	232885.i	−1.18567	+	1.18567i	−0.978253	+	0.207416i	$0.933495\pi$
$132$	−95815.2	−	180211.i	−0.478630	−	0.900216i
$133$	−218179.	+	218179.i	−1.06951	+	1.06951i
$134$	−206086.	−	123832.i	−0.991484	−	0.595758i
$135$	63892.8	−	198318.i	0.301729	−	0.936543i
$136$	139535.	+	154979.i	0.646900	+	0.718499i
$137$	7580.74			0.0345072			0.0172536	−	0.999851i	$-0.494508\pi$
$137$	7580.74			0.0345072			0.0172536	+	0.999851i	$0.494508\pi$
$138$	−43101.6	−	25898.6i	−0.192662	−	0.115765i
$139$	−99564.5	−	99564.5i	−0.437087	−	0.437087i	0.453944	−	0.891030i	$-0.350017\pi$
$139$	−99564.5	−	99564.5i	−0.437087	−	0.437087i	−0.891030	+	0.453944i	$0.850017\pi$
$140$	184685.	−	265146.i	0.796362	−	1.14331i
$141$	−125224.	+	125224.i	−0.530446	+	0.530446i
$142$	9068.74	+	36374.3i	0.0377421	+	0.151382i
$143$		−	82719.3i		−	0.338272i
$144$	−132037.	−	89067.7i	−0.530626	−	0.357943i
$145$	115179.	−	357506.i	0.454939	−	1.41210i
$146$	249072.	−	62097.9i	0.967036	−	0.241099i
$147$	104627.	+	104627.i	0.399345	+	0.399345i
$148$	−84995.8	+	277988.i	−0.318965	+	1.04321i
$149$	99215.0	+	99215.0i	0.366110	+	0.366110i	0.866056	−	0.499946i	$-0.166647\pi$
$149$	99215.0	+	99215.0i	0.366110	+	0.366110i	−0.499946	+	0.866056i	$0.666647\pi$
$150$	−151860.	+	65351.9i	−0.551081	+	0.237154i
$151$			144858.i			0.517011i	0.966010	+	0.258505i	$0.0832299\pi$
$151$			144858.i			0.517011i	−0.966010	+	0.258505i	$0.916770\pi$
$152$	16192.4	−	308788.i	0.0568462	−	1.08405i
$153$	−179182.			−0.618824
$154$	597329.	+	358920.i	2.02961	+	1.21954i
$155$	150262.	−	77033.4i	0.502365	−	0.257543i
$156$	17040.6	+	32050.3i	0.0560626	+	0.105444i
$157$	280430.	+	280430.i	0.907977	+	0.907977i	0.996109	−	0.0881314i	$-0.0280895\pi$
$157$	280430.	+	280430.i	0.907977	+	0.907977i	−0.0881314	+	0.996109i	$0.528090\pi$
$158$	−590106.	+	147124.i	−1.88056	+	0.468856i
$159$	218110.			0.684199
$160$	40245.9	+	321306.i	0.124286	+	0.992246i
$161$	171688.			0.522005
$162$	16126.0	−	4020.49i	0.0482769	−	0.0120363i
$163$	87680.4	+	87680.4i	0.258484	+	0.258484i	0.824437	−	0.565953i	$-0.191492\pi$
$163$	87680.4	+	87680.4i	0.258484	+	0.258484i	−0.565953	+	0.824437i	$0.691492\pi$
$164$	113909.	+	214242.i	0.330711	+	0.622008i
$165$	−162658.	−	317282.i	−0.465121	−	0.907269i
$166$	−373946.	−	224695.i	−1.05327	−	0.632882i
$167$	−459052.			−1.27371			−0.636855	−	0.770983i	$-0.719765\pi$
$167$	−459052.			−1.27371			−0.636855	+	0.770983i	$0.719765\pi$
$168$	−305379.	−	16013.6i	−0.834769	−	0.0437740i
$169$		−	356582.i		−	0.960378i
$170$	239685.	+	274351.i	0.636089	+	0.728088i
$171$	187866.	+	187866.i	0.491313	+	0.491313i
$172$	9282.34	−	30359.0i	0.0239241	−	0.0782466i
$173$	−132433.	−	132433.i	−0.336418	−	0.336418i	0.518599	−	0.855017i	$-0.326454\pi$
$173$	−132433.	−	132433.i	−0.336418	−	0.336418i	−0.855017	+	0.518599i	$0.826454\pi$
$174$	−344903.	+	85990.2i	−0.863622	+	0.215316i
$175$	329518.	−	458317.i	0.813361	−	1.13128i
$176$	−685533.	+	133225.i	−1.66819	+	0.324193i
$177$		−	41674.4i		−	0.0999854i
$178$	19700.5	+	79017.8i	0.0466044	+	0.186928i
$179$	−524114.	+	524114.i	−1.22263	+	1.22263i	−0.255930	+	0.966695i	$0.582382\pi$
$179$	−524114.	+	524114.i	−1.22263	+	1.22263i	−0.966695	+	0.255930i	$0.917618\pi$
$180$	−228307.	−	159025.i	−0.525217	−	0.365834i
$181$	−428492.	−	428492.i	−0.972178	−	0.972178i	0.0274449	−	0.999623i	$-0.491263\pi$
$181$	−428492.	−	428492.i	−0.972178	−	0.972178i	−0.999623	+	0.0274449i	$0.991263\pi$
$182$	−106234.	−	63833.4i	−0.237731	−	0.142846i
$183$	−180518.			−0.398467
$184$	−127865.	+	115123.i	−0.278425	+	0.250679i
$185$	−155723.	+	483352.i	−0.334521	+	1.03833i
$186$	−136976.	−	82305.7i	−0.290311	−	0.174441i
$187$	−555554.	+	555554.i	−1.16178	+	1.16178i
$188$	284468.	+	535032.i	0.587000	+	1.10404i
$189$	476063.	−	476063.i	0.969415	−	0.969415i
$190$	36346.2	−	538947.i	0.0730423	−	1.08308i
$191$	301213.			0.597434			0.298717	−	0.954342i	$-0.403441\pi$
$191$	301213.			0.597434			0.298717	+	0.954342i	$0.403441\pi$
$192$	238170.	−	192842.i	0.466267	−	0.377528i
$193$			378699.i			0.731813i	0.930652	+	0.365907i	$0.119241\pi$
$193$			378699.i			0.731813i	−0.930652	+	0.365907i	$0.880759\pi$
$194$	−73207.2	−	293631.i	−0.139653	−	0.560141i
$195$	28928.5	+	56428.2i	0.0544803	+	0.106270i
$196$	447026.	−	237676.i	0.831176	−	0.441922i
$197$	−395086.	+	395086.i	−0.725313	+	0.725313i	−0.969682	−	0.244369i	$-0.921419\pi$
$197$	−395086.	+	395086.i	−0.725313	+	0.725313i	0.244369	+	0.969682i	$0.421419\pi$
$198$	309053.	−	514338.i	0.560234	−	0.932364i
$199$		−	498422.i		−	0.892205i	−0.894982	−	0.446103i	$-0.852812\pi$
$199$		−	498422.i		−	0.892205i	0.894982	−	0.446103i	$-0.147188\pi$
$200$	61909.6	+	562287.i	0.109442	+	0.993993i
$201$			397487.i			0.693958i
$202$	690642.	+	414989.i	1.19090	+	0.715580i
$203$	858195.	−	858195.i	1.46166	−	1.46166i
$204$	100807.	−	329701.i	0.169596	−	0.554683i
$205$	193375.	+	377199.i	0.321378	+	0.626881i
$206$	−623882.	+	155545.i	−1.02432	+	0.255380i
$207$		−	147834.i		−	0.239799i
$208$	121921.	−	23693.9i	0.195398	−	0.0379732i
$209$	1.16496e6			1.84478
$210$	−532998.	−	35945.0i	−0.834022	−	0.0562458i
$211$	400256.	−	400256.i	0.618916	−	0.618916i	−0.326338	−	0.945253i	$-0.605815\pi$
$211$	400256.	−	400256.i	0.618916	−	0.618916i	0.945253	+	0.326338i	$0.105815\pi$
$212$	218211.	−	713683.i	0.333454	−	1.09060i
$213$	43824.1	−	43824.1i	0.0661857	−	0.0661857i
$214$	155589.	−	258937.i	0.232243	−	0.386509i
$215$	17006.4	−	52786.6i	0.0250910	−	0.0778803i
$216$	−35331.4	+	673768.i	−0.0515259	+	0.982598i
$217$	545622.			0.786580
$218$	600439.	−	999275.i	0.855712	−	1.42411i
$219$	−300084.	−	300084.i	−0.422798	−	0.422798i
$220$	−1.20092e6	+	214809.i	−1.67285	+	0.299224i
$221$	98804.5	−	98804.5i	0.136080	−	0.136080i
$222$	466312.	−	116260.i	0.635030	−	0.158324i
$223$		−	548571.i		−	0.738705i	−0.929289	−	0.369352i	$-0.879580\pi$
$223$		−	548571.i		−	0.738705i	0.929289	−	0.369352i	$-0.120420\pi$
$224$	−357919.	+	983219.i	−0.476612	+	1.30927i
$225$	−394640.	−	283735.i	−0.519690	−	0.373643i
$226$	261512.	+	1.04891e6i	0.340582	+	1.36606i
$227$	−327258.	−	327258.i	−0.421528	−	0.421528i	0.464202	−	0.885730i	$-0.346341\pi$
$227$	−327258.	−	327258.i	−0.421528	−	0.421528i	−0.885730	+	0.464202i	$0.846341\pi$
$228$	−451372.	+	239987.i	−0.575039	+	0.305739i
$229$	−529209.	−	529209.i	−0.666865	−	0.666865i	0.290124	−	0.956989i	$-0.406304\pi$
$229$	−529209.	−	529209.i	−0.666865	−	0.666865i	−0.956989	+	0.290124i	$0.906304\pi$
$230$	−226352.	+	197751.i	−0.282140	+	0.246490i
$231$		−	1.15210e6i		−	1.42056i
$232$	−63691.6	+	1.21460e6i	−0.0776895	+	1.48154i
$233$	1.41790e6			1.71103			0.855514	−	0.517779i	$-0.173241\pi$
$233$	1.41790e6			1.71103			0.855514	+	0.517779i	$0.173241\pi$
$234$	−54964.5	+	91474.2i	−0.0656210	+	0.109209i
$235$	482919.	+	941985.i	0.570433	+	1.11269i
$236$	−136364.	−	41693.7i	−0.159375	−	0.0487293i
$237$	710965.	+	710965.i	0.822200	+	0.822200i
$238$	284769.	+	1.14220e6i	0.325875	+	1.30707i
$239$	431827.			0.489007			0.244503	−	0.969648i	$-0.421375\pi$
$239$	431827.			0.489007			0.244503	+	0.969648i	$0.421375\pi$
$240$	421055.	−	330625.i	0.471857	−	0.370517i
$241$	1.48829e6			1.65061			0.825307	−	0.564685i	$-0.191002\pi$
$241$	1.48829e6			1.65061			0.825307	+	0.564685i	$0.191002\pi$
$242$	−416094.	−	1.66894e6i	−0.456723	−	1.83190i
$243$	−659860.	−	659860.i	−0.716863	−	0.716863i
$244$	−180601.	+	590677.i	−0.194199	+	0.635149i
$245$	787041.	−	403485.i	0.837688	−	0.429450i
$246$	206610.	−	343849.i	0.217677	−	0.362268i
$247$	−207186.			−0.216081
$248$	−406354.	+	365861.i	−0.419542	+	0.377734i
$249$			721248.i			0.737202i
$250$	93458.1	+	983783.i	0.0945730	+	0.995518i
$251$	−37098.0	−	37098.0i	−0.0371677	−	0.0371677i	0.688279	−	0.725446i	$-0.258367\pi$
$251$	−37098.0	−	37098.0i	−0.0371677	−	0.0371677i	−0.725446	+	0.688279i	$0.758367\pi$
$252$	−422058.	−	793815.i	−0.418669	−	0.787441i
$253$	−458358.	−	458358.i	−0.450198	−	0.450198i
$254$	−250811.	−	1.00599e6i	−0.243928	−	0.978384i
$255$	184692.	−	573267.i	0.177867	−	0.552086i
$256$	−392724.	−	972255.i	−0.374531	−	0.927214i
$257$			1.07734e6i			1.01747i	0.860924	+	0.508734i	$0.169886\pi$
$257$			1.07734e6i			1.01747i	−0.860924	+	0.508734i	$0.830114\pi$
$258$	−50925.7	+	12696.6i	−0.0476308	+	0.0118752i
$259$	−1.16029e6	+	1.16029e6i	−1.07477	+	1.07477i
$260$	213582.	−	38203.5i	0.195944	−	0.0350485i
$261$	−738959.	−	738959.i	−0.671459	−	0.671459i
$262$	959573.	−	1.59696e6i	0.863625	−	1.43728i
$263$	−448419.			−0.399755			−0.199878	−	0.979821i	$-0.564054\pi$
$263$	−448419.			−0.399755			−0.199878	+	0.979821i	$0.564054\pi$
$264$	772526.	+	858029.i	0.682186	+	0.757691i
$265$	399790.	−	1.24092e6i	0.349717	−	1.08549i
$266$	898981.	−	1.49612e6i	0.779016	−	1.29647i
$267$	95201.4	−	95201.4i	0.0817269	−	0.0817269i
$268$	1.30063e6	+	397671.i	1.10616	+	0.338211i
$269$	−585909.	+	585909.i	−0.493684	+	0.493684i	−0.909465	−	0.415781i	$-0.863508\pi$
$269$	−585909.	+	585909.i	−0.493684	+	0.493684i	0.415781	+	0.909465i	$0.363508\pi$
$270$	−79306.5	+	1.17597e6i	−0.0662063	+	0.981718i
$271$	285873.			0.236456			0.118228	−	0.992986i	$-0.462279\pi$
$271$	285873.			0.236456			0.118228	+	0.992986i	$0.462279\pi$
$272$	−977970.	−	659707.i	−0.801499	−	0.540666i
$273$			204899.i			0.166392i
$274$	−41609.4	+	10373.9i	−0.0334823	+	0.00834771i
$275$	−2.10330e6	+	343859.i	−1.67714	+	0.274188i
$276$	272019.	+	83170.5i	0.214944	+	0.0657199i
$277$	−1.24059e6	+	1.24059e6i	−0.971470	+	0.971470i	−0.999604	−	0.0281345i	$-0.991043\pi$
$277$	−1.24059e6	+	1.24059e6i	−0.971470	+	0.971470i	0.0281345	+	0.999604i	$0.491043\pi$
$278$	682743.	+	410243.i	0.529841	+	0.318368i
$279$		−	469815.i		−	0.361340i
$280$	−650861.	+	1.70808e6i	−0.496128	+	1.30200i
$281$		−	436208.i		−	0.329555i	−0.986331	−	0.164777i	$-0.947309\pi$
$281$		−	436208.i		−	0.329555i	0.986331	−	0.164777i	$-0.0526906\pi$
$282$	515971.	−	858700.i	0.386369	−	0.643011i
$283$	−314715.	+	314715.i	−0.233589	+	0.233589i	−0.814189	−	0.580600i	$-0.802818\pi$
$283$	−314715.	+	314715.i	−0.233589	+	0.233589i	0.580600	+	0.814189i	$0.302818\pi$
$284$	−99553.7	−	187242.i	−0.0732422	−	0.137755i
$285$	−794692.	+	407408.i	−0.579544	+	0.297110i
$286$	113198.	+	454032.i	0.0818322	+	0.328225i
$287$			1.36966e6i			0.981542i
$288$	846613.	+	308191.i	0.601456	+	0.218947i
$289$	92687.6			0.0652795
$290$	−142965.	+	2.11991e6i	−0.0998241	+	1.48021i
$291$	−353769.	+	353769.i	−0.244899	+	0.244899i
$292$	−1.28214e6	+	681690.i	−0.879988	+	0.467875i
$293$	293479.	−	293479.i	0.199714	−	0.199714i	−0.600163	−	0.799877i	$-0.704898\pi$
$293$	293479.	−	293479.i	0.199714	−	0.199714i	0.799877	+	0.600163i	$0.204898\pi$
$294$	−717455.	−	431101.i	−0.484091	−	0.290878i
$295$	−237103.	−	76388.2i	−0.158629	−	0.0511059i
$296$	86111.6	−	1.64215e6i	0.0571258	−	1.08939i
$297$	−2.54191e6			−1.67212
$298$	−680347.	−	408803.i	−0.443803	−	0.266670i
$299$	81518.3	+	81518.3i	0.0527323	+	0.0527323i
$300$	744103.	−	566521.i	0.477342	−	0.363423i
$301$	126714.	−	126714.i	0.0806138	−	0.0806138i
$302$	−198232.	−	795100.i	−0.125071	−	0.501654i
$303$		−	1.33207e6i		−	0.833532i
$304$	333687.	+	1.71704e6i	0.207088	+	1.06561i
$305$	−330885.	+	1.02704e6i	−0.203670	+	0.632175i
$306$	983503.	−	245204.i	0.600443	−	0.149701i
$307$	1.71858e6	+	1.71858e6i	1.04070	+	1.04070i	0.999136	+	0.0415615i	$0.0132332\pi$
$307$	1.71858e6	+	1.71858e6i	1.04070	+	1.04070i	0.0415615	+	0.999136i	$0.486767\pi$
$308$	−3.76981e6	−	1.15263e6i	−2.26435	−	0.692330i
$309$	751659.	+	751659.i	0.447842	+	0.447842i
$310$	−719345.	+	628451.i	−0.425141	+	0.371422i
$311$			2.37015e6i			1.38956i	0.719225	+	0.694778i	$0.244497\pi$
$311$			2.37015e6i			1.38956i	−0.719225	+	0.694778i	$0.755503\pi$
$312$	−137392.	−	152599.i	−0.0799055	−	0.0887495i
$313$	1.04515e6			0.602998			0.301499	−	0.953466i	$-0.402513\pi$
$313$	1.04515e6			0.602998			0.301499	+	0.953466i	$0.402513\pi$
$314$	−1.92299e6	−	1.15548e6i	−1.10066	−	0.661358i
$315$	−716497.	−	1.39760e6i	−0.406853	−	0.793611i
$316$	3.03766e6	−	1.61507e6i	1.71128	−	0.909861i
$317$	−457830.	−	457830.i	−0.255891	−	0.255891i	0.567489	−	0.823381i	$-0.307915\pi$
$317$	−457830.	−	457830.i	−0.255891	−	0.255891i	−0.823381	+	0.567489i	$0.807915\pi$
$318$	−1.19717e6	+	298475.i	−0.663877	+	0.165516i
$319$	−4.58228e6			−2.52119
$320$	−660599.	−	1.70852e6i	−0.360631	−	0.932709i
$321$	−499424.			−0.270525
$322$	−942366.	+	234948.i	−0.506500	+	0.126279i
$323$	1.39149e6	+	1.39149e6i	0.742118	+	0.742118i
$324$	−83011.2	+	44135.6i	−0.0439313	+	0.0233575i
$325$	374068.	−	61154.7i	0.196446	−	0.0321160i
$326$	−601250.	−	361276.i	−0.313337	−	0.188276i
$327$	−1.92735e6			−0.996761
$328$	−918411.	−	1.02006e6i	−0.471360	−	0.523530i
$329$			3.42048e6i			1.74220i
$330$	1.32699e6	+	1.51892e6i	0.670786	+	0.767803i
$331$	−507646.	−	507646.i	−0.254678	−	0.254678i	0.568208	−	0.822885i	$-0.307637\pi$
$331$	−507646.	−	507646.i	−0.254678	−	0.254678i	−0.822885	+	0.568208i	$0.807637\pi$
$332$	2.36002e6	+	721582.i	1.17509	+	0.359286i
$333$	999080.	+	999080.i	0.493730	+	0.493730i
$334$	2.51966e6	−	628195.i	1.23588	−	0.308126i
$335$	2.26147e6	+	728585.i	1.10098	+	0.354706i
$336$	1.69809e6	−	330004.i	0.820565	−	0.159467i
$337$			1.00658e6i			0.482805i	0.970425	+	0.241403i	$0.0776075\pi$
$337$			1.00658e6i			0.482805i	−0.970425	+	0.241403i	$0.922393\pi$
$338$	487968.	+	1.95722e6i	0.232327	+	0.931853i
$339$	1.26374e6	−	1.26374e6i	0.597254	−	0.597254i
$340$	−1.69103e6	−	1.17787e6i	−0.793329	−	0.552585i
$341$	−1.45666e6	−	1.45666e6i	−0.678378	−	0.678378i
$342$	−1.28825e6	−	774079.i	−0.595575	−	0.357866i
$343$	−178041.			−0.0817118
$344$	−9404.20	+	179338.i	−0.00428475	+	0.0817101i
$345$	472972.	+	152379.i	0.213938	+	0.0689251i
$346$	908129.	+	545672.i	0.407810	+	0.245042i
$347$	1.11860e6	−	1.11860e6i	0.498713	−	0.498713i	−0.412324	−	0.911037i	$-0.635283\pi$
$347$	1.11860e6	−	1.11860e6i	0.498713	−	0.498713i	0.911037	+	0.412324i	$0.135283\pi$
$348$	1.77544e6	−	943972.i	0.785884	−	0.417841i
$349$	2.57009e6	−	2.57009e6i	1.12950	−	1.12950i	0.139237	−	0.990259i	$-0.455535\pi$
$349$	2.57009e6	−	2.57009e6i	1.12950	−	1.12950i	0.990259	−	0.139237i	$-0.0444650\pi$
$350$	−1.18148e6	+	2.96656e6i	−0.515532	+	1.29444i
$351$	452074.			0.195858
$352$	3.58046e6	−	1.66938e6i	1.54022	−	0.718120i
$353$		−	2.67361e6i		−	1.14199i	−0.820955	−	0.570993i	$-0.806558\pi$
$353$		−	2.67361e6i		−	1.14199i	0.820955	−	0.570993i	$-0.193442\pi$
$354$	57029.8	+	228744.i	0.0241877	+	0.0970156i
$355$	−169005.	−	329662.i	−0.0711751	−	0.138835i
$356$	−216266.	−	406756.i	−0.0904404	−	0.170102i
$357$	1.37613e6	−	1.37613e6i	0.571464	−	0.571464i
$358$	2.15955e6	−	3.59401e6i	0.890543	−	1.48208i
$359$			1.93780e6i			0.793547i	0.917917	+	0.396773i	$0.129870\pi$
$359$			1.93780e6i			0.793547i	−0.917917	+	0.396773i	$0.870130\pi$
$360$	1.47076e6	+	560432.i	0.598116	+	0.227912i
$361$		−	441749.i		−	0.178405i
$362$	2.93829e6	+	1.76555e6i	1.17848	+	0.708121i
$363$	−2.01075e6	+	2.01075e6i	−0.800924	+	0.800924i
$364$	670455.	+	204994.i	0.265226	+	0.0810936i
$365$	−2.25735e6	+	1.15725e6i	−0.886883	+	0.454670i
$366$	990832.	−	247032.i	0.386632	−	0.0963939i
$367$			1.20372e6i			0.466510i	0.972416	+	0.233255i	$0.0749377\pi$
$367$			1.20372e6i			0.466510i	−0.972416	+	0.233255i	$0.925062\pi$
$368$	544289.	−	806871.i	0.209513	−	0.310588i
$369$	1.17936e6			0.450902
$370$	193290.	−	2.86614e6i	0.0734017	−	1.08841i
$371$	2.97882e6	−	2.97882e6i	1.12359	−	1.12359i
$372$	864473.	+	264315.i	0.323888	+	0.0990296i
$373$	−54942.3	+	54942.3i	−0.0204473	+	0.0204473i	−0.717256	−	0.696809i	$-0.754602\pi$
$373$	−54942.3	+	54942.3i	−0.0204473	+	0.0204473i	0.696809	+	0.717256i	$0.254602\pi$
$374$	2.28909e6	−	3.80960e6i	0.846222	−	1.40832i
$375$	1.31454e6	−	970132.i	0.482721	−	0.356248i
$376$	−2.29357e6	−	2.54742e6i	−0.836646	−	0.929246i
$377$	814951.			0.295310
$378$	−1.96156e6	+	3.26450e6i	−0.706108	+	1.17513i
$379$	171099.	+	171099.i	0.0611856	+	0.0611856i	0.737037	−	0.675852i	$-0.236224\pi$
$379$	171099.	+	171099.i	0.0611856	+	0.0611856i	−0.675852	+	0.737037i	$0.736224\pi$
$380$	538030.	+	3.00793e6i	0.191138	+	1.06858i
$381$	−1.21203e6	+	1.21203e6i	−0.427759	+	0.427759i
$382$	−1.65331e6	+	412198.i	−0.579689	+	0.144526i
$383$			174611.i			0.0608240i	0.999537	+	0.0304120i	$0.00968194\pi$
$383$			174611.i			0.0608240i	−0.999537	+	0.0304120i	$0.990318\pi$
$384$	−1.04338e6	+	1.38441e6i	−0.361089	+	0.479110i
$385$	−6.55476e6	−	2.11177e6i	−2.25374	−	0.726096i
$386$	−518234.	−	2.07861e6i	−0.177034	−	0.710077i
$387$	−109109.	−	109109.i	−0.0370325	−	0.0370325i
$388$	803645.	+	1.51151e6i	0.271010	+	0.509720i
$389$	2.32384e6	+	2.32384e6i	0.778631	+	0.778631i	0.979598	−	0.200967i	$-0.0644084\pi$
$389$	2.32384e6	+	2.32384e6i	0.778631	+	0.778631i	−0.200967	+	0.979598i	$0.564408\pi$
$390$	−236004.	−	270137.i	−0.0785701	−	0.0899338i
$391$		−	1.09498e6i		−	0.362212i
$392$	−2.12840e6	+	1.91630e6i	−0.699582	+	0.629868i
$393$	−3.08014e6			−1.00598
$394$	1.62790e6	−	2.70922e6i	0.528308	−	0.879232i
$395$	5.34816e6	−	2.74179e6i	1.72469	−	0.884182i
$396$	−992487.	+	3.24604e6i	−0.318044	+	1.04020i
$397$	−319592.	−	319592.i	−0.101770	−	0.101770i	0.654389	−	0.756158i	$-0.272926\pi$
$397$	−319592.	−	319592.i	−0.101770	−	0.101770i	−0.756158	+	0.654389i	$0.772926\pi$
$398$	682071.	+	2.73576e6i	0.215835	+	0.865705i
$399$	−2.88564e6			−0.907424
$400$	−1.10928e6	−	3.00158e6i	−0.346650	−	0.937995i
$401$	−3.10654e6			−0.964751			−0.482376	−	0.875964i	$-0.660226\pi$
$401$	−3.10654e6			−0.964751			−0.482376	+	0.875964i	$0.660226\pi$
$402$	−543946.	−	2.18174e6i	−0.167877	−	0.673346i
$403$	259065.	+	259065.i	0.0794594	+	0.0794594i
$404$	−4.35872e6	−	1.33269e6i	−1.32863	−	0.406234i
$405$	−146151.	+	74925.8i	−0.0442755	+	0.0226983i
$406$	−3.53608e6	+	5.88490e6i	−1.06465	+	1.77184i
$407$	6.19529e6			1.85385
$408$	−102130.	+	1.94762e6i	−0.0303742	+	0.579235i
$409$		−	4.80829e6i		−	1.42129i	−0.703552	−	0.710644i	$-0.748404\pi$
$409$		−	4.80829e6i		−	1.42129i	0.703552	−	0.710644i	$-0.251596\pi$
$410$	−1.57758e6	−	1.80575e6i	−0.463482	−	0.530517i
$411$	50131.4	+	50131.4i	0.0146388	+	0.0146388i
$412$	3.21153e6	−	1.70752e6i	0.932114	−	0.495589i
$413$	−569166.	−	569166.i	−0.164196	−	0.164196i
$414$	202305.	+	811436.i	0.0580103	+	0.232677i
$415$	4.10348e6	+	1.32203e6i	1.16958	+	0.376809i
$416$	−636780.	+	296896.i	−0.180408	+	0.0841145i
$417$		−	1.31684e6i		−	0.370845i
$418$	−6.39425e6	+	1.59420e6i	−1.78998	+	0.446274i
$419$	−738866.	+	738866.i	−0.205603	+	0.205603i	−0.802396	−	0.596792i	$-0.796442\pi$
$419$	−738866.	+	738866.i	−0.205603	+	0.205603i	0.596792	+	0.802396i	$0.296442\pi$
$420$	2.97473e6	−	532091.i	0.822856	−	0.147185i
$421$	2.83404e6	+	2.83404e6i	0.779292	+	0.779292i	0.979710	−	0.200419i	$-0.0642303\pi$
$421$	2.83404e6	+	2.83404e6i	0.779292	+	0.779292i	−0.200419	+	0.979710i	$0.564230\pi$
$422$	−1.64920e6	+	2.74467e6i	−0.450810	+	0.750256i
$423$	2.94525e6			0.800334
$424$	−221075.	+	4.21590e6i	−0.0597208	+	1.13887i
$425$	−2.92302e6	−	2.10157e6i	−0.784981	−	0.564380i
$426$	−180572.	+	300515.i	−0.0482087	+	0.0802310i
$427$	−2.46541e6	+	2.46541e6i	−0.654364	+	0.654364i
$428$	−499655.	+	1.63418e6i	−0.131844	+	0.431212i
$429$	547022.	−	547022.i	0.143503	−	0.143503i
$430$	−21109.1	+	313010.i	−0.00550553	+	0.0816369i
$431$	2.67868e6			0.694588			0.347294	−	0.937756i	$-0.387101\pi$
$431$	2.67868e6			0.694588			0.347294	+	0.937756i	$0.387101\pi$
$432$	−728097.	−	3.74655e6i	−0.187707	−	0.965878i
$433$		−	3.12848e6i		−	0.801888i	−0.916103	−	0.400944i	$-0.868682\pi$
$433$		−	3.12848e6i		−	0.801888i	0.916103	−	0.400944i	$-0.131318\pi$
$434$	−2.99483e6	+	746663.i	−0.763217	+	0.190283i
$435$	3.12587e6	−	1.60251e6i	0.792041	−	0.406048i
$436$	−1.92824e6	+	6.30653e6i	−0.485786	+	1.58882i
$437$	−1.14804e6	+	1.14804e6i	−0.287577	+	0.287577i
$438$	2.05776e6	+	1.23646e6i	0.512520	+	0.307960i
$439$		−	79281.8i		−	0.0196342i	−0.999952	−	0.00981708i	$-0.996875\pi$
$439$		−	79281.8i		−	0.0196342i	0.999952	−	0.00981708i	$-0.00312492\pi$
$440$	6.29770e6	−	2.82247e6i	1.55078	−	0.695020i
$441$		−	2.46080e6i		−	0.602531i
$442$	−407111.	+	677531.i	−0.0991192	+	0.164958i
$443$	−4.52736e6	+	4.52736e6i	−1.09606	+	1.09606i	−0.101198	+	0.994866i	$0.532267\pi$
$443$	−4.52736e6	+	4.52736e6i	−1.09606	+	1.09606i	−0.994866	+	0.101198i	$0.967733\pi$
$444$	−2.40041e6	+	1.27626e6i	−0.577868	+	0.307243i
$445$	−367138.	−	716141.i	−0.0878879	−	0.171435i
$446$	750698.	+	3.01102e6i	0.178702	+	0.716764i
$447$			1.31222e6i			0.310626i
$448$	619063.	−	5.88653e6i	0.145727	−	1.38568i
$449$	4.22239e6			0.988421			0.494211	−	0.869342i	$-0.335457\pi$
$449$	4.22239e6			0.988421			0.494211	+	0.869342i	$0.335457\pi$
$450$	2.55439e6	+	1.01733e6i	0.594643	+	0.236826i
$451$	3.65661e6	−	3.65661e6i	0.846521	−	0.846521i
$452$	−2.87080e6	−	5.39945e6i	−0.660931	−	1.24309i
$453$	−957944.	+	957944.i	−0.219328	+	0.219328i
$454$	2.24411e6	+	1.34843e6i	0.510980	+	0.307035i
$455$	1.16575e6	+	375575.i	0.263984	+	0.0850487i
$456$	2.14909e6	−	1.93493e6i	0.483997	−	0.435766i
$457$	1.75807e6			0.393773			0.196886	−	0.980426i	$-0.436917\pi$
$457$	1.75807e6			0.393773			0.196886	+	0.980426i	$0.436917\pi$
$458$	3.62894e6	+	2.18054e6i	0.808381	+	0.485736i
$459$	−3.03620e6	−	3.03620e6i	−0.672664	−	0.672664i
$460$	971795.	−	1.39518e6i	0.214131	−	0.307422i
$461$	826496.	−	826496.i	0.181129	−	0.181129i	−0.610719	−	0.791848i	$-0.709119\pi$
$461$	826496.	−	826496.i	0.181129	−	0.181129i	0.791848	+	0.610719i	$0.209119\pi$
$462$	1.57660e6	+	6.32367e6i	0.343650	+	1.37837i
$463$			1.50365e6i			0.325982i	0.986628	+	0.162991i	$0.0521141\pi$
$463$			1.50365e6i			0.325982i	−0.986628	+	0.162991i	$0.947886\pi$
$464$	−1.31253e6	−	6.75388e6i	−0.283019	−	1.45632i
$465$	1.50310e6	+	484260.i	0.322371	+	0.103859i
$466$	−7.78264e6	+	1.94035e6i	−1.66021	+	0.413918i
$467$	−6.43293e6	−	6.43293e6i	−1.36495	−	1.36495i	−0.867483	−	0.497467i	$-0.834264\pi$
$467$	−6.43293e6	−	6.43293e6i	−1.36495	−	1.36495i	−0.497467	−	0.867483i	$-0.665736\pi$
$468$	176512.	−	577304.i	0.0372529	−	0.121840i
$469$	5.42866e6	+	5.42866e6i	1.13962	+	1.13962i
$470$	−3.93973e6	−	4.50955e6i	−0.822664	−	0.941647i
$471$			3.70896e6i			0.770372i
$472$	805536.	+	42241.1i	0.166429	+	0.00872730i
$473$	−676584.			−0.139049
$474$	−4.87530e6	−	2.92944e6i	−0.996680	−	0.598879i
$475$	861257.	+	5.26810e6i	0.175145	+	1.07132i
$476$	−3.12610e6	−	5.87963e6i	−0.632391	−	1.18941i
$477$	−2.56495e6	−	2.56495e6i	−0.516158	−	0.516158i
$478$	−2.37023e6	+	590938.i	−0.474483	+	0.118297i
$479$	−3.90308e6			−0.777265			−0.388632	−	0.921393i	$-0.627052\pi$
$479$	−3.90308e6			−0.777265			−0.388632	+	0.921393i	$0.627052\pi$
$480$	−1.85865e6	+	2.39095e6i	−0.368210	+	0.473660i
$481$	−1.10182e6			−0.217144
$482$	−8.16899e6	+	2.03667e6i	−1.60159	+	0.399303i
$483$	1.13537e6	+	1.13537e6i	0.221447	+	0.221447i
$484$	4.56775e6	+	8.59110e6i	0.886316	+	1.66700i
$485$	1.36429e6	+	2.66119e6i	0.263361	+	0.513714i
$486$	4.52486e6	+	2.71887e6i	0.868989	+	0.522153i
$487$	−245075.			−0.0468248			−0.0234124	−	0.999726i	$-0.507453\pi$
$487$	−245075.			−0.0468248			−0.0234124	+	0.999726i	$0.507453\pi$
$488$	182972.	−	3.48928e6i	0.0347805	−	0.663263i
$489$			1.15966e6i			0.219310i
$490$	−3.76779e6	+	3.29170e6i	−0.708918	+	0.619341i
$491$	3.93841e6	+	3.93841e6i	0.737254	+	0.737254i	0.972046	−	0.234792i	$-0.0754409\pi$
$491$	3.93841e6	+	3.93841e6i	0.737254	+	0.737254i	−0.234792	+	0.972046i	$0.575441\pi$
$492$	−663504.	+	2.17007e6i	−0.123575	+	0.404166i
$493$	−5.47333e6	−	5.47333e6i	−1.01422	−	1.01422i
$494$	1.13721e6	−	283525.i	0.209663	−	0.0522727i
$495$	−1.81836e6	+	5.64406e6i	−0.333555	+	1.03533i
$496$	1.72975e6	−	2.56423e6i	0.315703	−	0.468007i
$497$		−	1.19705e6i		−	0.217381i
$498$	−987000.	−	3.95881e6i	−0.178338	−	0.715305i
$499$	1.06957e6	−	1.06957e6i	0.192291	−	0.192291i	−0.604395	−	0.796685i	$-0.706585\pi$
$499$	1.06957e6	−	1.06957e6i	0.192291	−	0.192291i	0.796685	+	0.604395i	$0.206585\pi$
$500$	−1.85924e6	−	5.27193e6i	−0.332592	−	0.943071i
$501$	−3.03571e6	−	3.03571e6i	−0.540339	−	0.540339i
$502$	254392.	+	152857.i	0.0450551	+	0.0270724i
$503$	1.40071e6			0.246848			0.123424	−	0.992354i	$-0.460612\pi$
$503$	1.40071e6			0.246848			0.123424	+	0.992354i	$0.460612\pi$
$504$	3.40291e6	+	3.77955e6i	0.596726	+	0.662772i
$505$	−7.57872e6	−	2.44166e6i	−1.32241	−	0.426047i
$506$	3.14310e6	+	1.88861e6i	0.545735	+	0.327918i
$507$	2.35807e6	−	2.35807e6i	0.407415	−	0.407415i
$508$	2.75332e6	+	5.17849e6i	0.473366	+	0.890315i
$509$	5.07930e6	−	5.07930e6i	0.868980	−	0.868980i	−0.123380	−	0.992360i	$-0.539373\pi$
$509$	5.07930e6	−	5.07930e6i	0.868980	−	0.868980i	0.992360	+	0.123380i	$0.0393733\pi$
$510$	−229247.	+	3.39931e6i	−0.0390282	+	0.578716i
$511$	−8.19675e6			−1.38864
$512$	3.48609e6	+	4.79912e6i	0.587711	+	0.809071i
$513$			6.36668e6i			1.06812i
$514$	−1.47430e6	−	5.91335e6i	−0.246138	−	0.987247i
$515$	5.65427e6	−	2.89872e6i	0.939417	−	0.481602i
$516$	262148.	−	139380.i	0.0433433	−	0.0230449i
$517$	9.13174e6	−	9.13174e6i	1.50254	−	1.50254i
$518$	4.78082e6	−	7.95643e6i	0.782849	−	1.30285i
$519$		−	1.75155e6i		−	0.285433i
$520$	−1.12004e6	+	501971.i	−0.181645	+	0.0814087i
$521$			8.31440e6i			1.34195i	0.741480	+	0.670975i	$0.234124\pi$
$521$			8.31440e6i			1.34195i	−0.741480	+	0.670975i	$0.765876\pi$
$522$	5.06726e6	+	3.04479e6i	0.813949	+	0.489081i
$523$	3.45269e6	−	3.45269e6i	0.551954	−	0.551954i	−0.375050	−	0.927004i	$-0.622375\pi$
$523$	3.45269e6	−	3.45269e6i	0.551954	−	0.551954i	0.927004	+	0.375050i	$0.122375\pi$
$524$	−3.08156e6	+	1.00786e7i	−0.490278	+	1.60351i
$525$	5.20995e6	−	851751.i	0.824964	−	0.134870i
$526$	2.46130e6	−	613643.i	0.387882	−	0.0967056i
$527$		−	3.47983e6i		−	0.545797i
$528$	−5.41445e6	−	3.65241e6i	−0.845219	−	0.570158i
$529$	−5.53294e6			−0.859640
$530$	−496237.	+	7.35828e6i	−0.0767360	+	1.13785i
$531$	−490087.	+	490087.i	−0.0754288	+	0.0754288i
$532$	−2.88698e6	+	9.44218e6i	−0.442246	+	1.44642i
$533$	−650323.	+	650323.i	−0.0991542	+	0.0991542i
$534$	−392265.	+	652824.i	−0.0595287	+	0.0990702i
$535$	−915433.	+	2.84143e6i	−0.138275	+	0.429193i
$536$	−7.68314e6	−	402892.i	−1.15512	−	0.0605727i
$537$	−6.93193e6			−1.03733
$538$	2.41416e6	−	4.01775e6i	0.359593	−	0.598449i
$539$	−7.62969e6	−	7.62969e6i	−1.13119	−	1.13119i
$540$	−1.17397e6	−	6.56323e6i	−0.173249	−	0.968575i
$541$	−7.49612e6	+	7.49612e6i	−1.10114	+	1.10114i	−0.106869	+	0.994273i	$0.534083\pi$
$541$	−7.49612e6	+	7.49612e6i	−1.10114	+	1.10114i	−0.994273	+	0.106869i	$0.965917\pi$
$542$	−1.56911e6	+	391206.i	−0.229433	+	0.0572015i
$543$		−	5.66723e6i		−	0.824843i
$544$	6.27070e6	+	2.28271e6i	0.908487	+	0.330715i
$545$	−3.53279e6	+	1.09655e7i	−0.509479	+	1.58138i
$546$	−280396.	−	1.12466e6i	−0.0402523	−	0.161450i
$547$	−1.45538e6	−	1.45538e6i	−0.207973	−	0.207973i	0.595432	−	0.803406i	$-0.296981\pi$
$547$	−1.45538e6	−	1.45538e6i	−0.207973	−	0.207973i	−0.803406	+	0.595432i	$0.796981\pi$
$548$	214191.	−	113882.i	0.0304684	−	0.0161995i
$549$	2.12287e6	+	2.12287e6i	0.300603	+	0.300603i
$550$	1.10741e7	−	4.76566e6i	1.56100	−	0.671764i
$551$			1.14772e7i			1.61048i
$552$	−1.60688e6	−	84262.4i	−0.224459	−	0.0117703i
$553$	1.94199e7			2.70044
$554$	5.11170e6	−	8.50710e6i	0.707605	−	1.17763i
$555$	−4.22620e6	+	2.16661e6i	−0.582396	+	0.298571i
$556$	−4.30887e6	−	1.31745e6i	−0.591120	−	0.180737i
$557$	3.94460e6	+	3.94460e6i	0.538723	+	0.538723i	0.923154	−	0.384431i	$-0.125602\pi$
$557$	3.94460e6	+	3.94460e6i	0.538723	+	0.538723i	−0.384431	+	0.923154i	$0.625602\pi$
$558$	642924.	+	2.57874e6i	0.0874126	+	0.350608i
$559$	120329.			0.0162870
$560$	1.23504e6	−	1.02660e7i	0.166421	−	1.38335i
$561$	−7.34776e6			−0.985707
$562$	596933.	+	2.39427e6i	0.0797233	+	0.319766i
$563$	8.11291e6	+	8.11291e6i	1.07871	+	1.07871i	0.996625	+	0.0820870i	$0.0261586\pi$
$563$	8.11291e6	+	8.11291e6i	1.07871	+	1.07871i	0.0820870	+	0.996625i	$0.473841\pi$
$564$	−1.65698e6	+	5.41935e6i	−0.219341	+	0.717380i
$565$	−4.87354e6	−	9.50635e6i	−0.642278	−	1.25283i
$566$	1.29674e6	−	2.15810e6i	0.170143	−	0.283158i
$567$	−530694.			−0.0693245
$568$	802668.	+	891508.i	0.104391	+	0.115946i
$569$		−	1.10526e7i		−	1.43115i	−0.698535	−	0.715576i	$-0.746164\pi$
$569$		−	1.10526e7i		−	1.43115i	0.698535	−	0.715576i	$-0.253836\pi$
$570$	3.80441e6	−	3.32370e6i	0.490456	−	0.428484i
$571$	−1.87413e6	−	1.87413e6i	−0.240552	−	0.240552i	0.576526	−	0.817079i	$-0.304408\pi$
$571$	−1.87413e6	−	1.87413e6i	−0.240552	−	0.240552i	−0.817079	+	0.576526i	$0.804408\pi$
$572$	−1.24265e6	−	2.33720e6i	−0.158803	−	0.298680i
$573$	1.99192e6	+	1.99192e6i	0.253446	+	0.253446i
$574$	−1.87433e6	−	7.51785e6i	−0.237447	−	0.952388i
$575$	1.73389e6	−	2.41163e6i	0.218702	−	0.304187i
$576$	−5.06867e6	−	533052.i	−0.636557	−	0.0669443i
$577$		−	1.55810e6i		−	0.194829i	−0.995244	−	0.0974147i	$-0.968943\pi$
$577$		−	1.55810e6i		−	0.194829i	0.995244	−	0.0974147i	$-0.0310573\pi$
$578$	−508747.	+	126839.i	−0.0633406	+	0.0157919i
$579$	−2.50433e6	+	2.50433e6i	−0.310453	+	0.310453i
$580$	−2.11630e6	−	1.18315e7i	−0.261221	−	1.46039i
$581$	9.85040e6	+	9.85040e6i	1.21064	+	1.21064i
$582$	1.45766e6	−	2.42590e6i	0.178381	−	0.296869i
$583$	−1.59052e7			−1.93807
$584$	6.10457e6	−	5.49624e6i	0.740666	−	0.666858i
$585$	323393.	−	1.00379e6i	0.0390698	−	0.121270i
$586$	−1.20924e6	+	2.01247e6i	−0.145469	+	0.242095i
$587$	5.77821e6	−	5.77821e6i	0.692147	−	0.692147i	−0.270557	−	0.962704i	$-0.587208\pi$
$587$	5.77821e6	−	5.77821e6i	0.692147	−	0.692147i	0.962704	+	0.270557i	$0.0872080\pi$
$588$	4.52794e6	+	1.38443e6i	0.540079	+	0.165131i
$589$	−3.64847e6	+	3.64847e6i	−0.433334	+	0.433334i
$590$	1.40595e6	+	94816.4i	0.166280	+	0.0112138i
$591$	−5.22540e6			−0.615391
$592$	1.77456e6	+	9.13131e6i	0.208107	+	1.07085i
$593$			4.47682e6i			0.522797i	0.965231	+	0.261398i	$0.0841837\pi$
$593$			4.47682e6i			0.522797i	−0.965231	+	0.261398i	$0.915816\pi$
$594$	1.39521e7	−	3.47850e6i	1.62246	−	0.404507i
$595$	−5.30695e6	−	1.03518e7i	−0.614544	−	1.19873i
$596$	4.29374e6	+	1.31282e6i	0.495131	+	0.151388i
$597$	3.29607e6	−	3.29607e6i	0.378495	−	0.378495i
$598$	−558995.	−	335886.i	−0.0639227	−	0.0384095i
$599$		−	285208.i		−	0.0324784i	−0.999868	−	0.0162392i	$-0.994831\pi$
$599$		−	285208.i		−	0.0324784i	0.999868	−	0.0162392i	$-0.00516932\pi$
$600$	−3.30900e6	+	4.12781e6i	−0.375248	+	0.468104i
$601$		−	6.18050e6i		−	0.697971i	−0.937128	−	0.348986i	$-0.886526\pi$
$601$		−	6.18050e6i		−	0.697971i	0.937128	−	0.348986i	$-0.113474\pi$
$602$	−522111.	+	868918.i	−0.0587180	+	0.0977209i
$603$	4.67441e6	−	4.67441e6i	0.523521	−	0.523521i
$604$	2.17613e6	+	4.09290e6i	0.242712	+	0.456498i
$605$	7.75432e6	+	1.51256e7i	0.861301	+	1.68006i
$606$	1.82289e6	+	7.31154e6i	0.201641	+	0.808774i
$607$		−	2.38265e6i		−	0.262476i	−0.991351	−	0.131238i	$-0.958105\pi$
$607$		−	2.38265e6i		−	0.262476i	0.991351	−	0.131238i	$-0.0418952\pi$
$608$	−4.18126e6	−	8.96793e6i	−0.458720	−	0.983860i
$609$	1.13505e7			1.24014
$610$	410709.	−	6.09005e6i	0.0446899	−	0.662669i
$611$	−1.62407e6	+	1.62407e6i	−0.175995	+	0.175995i
$612$	−5.06273e6	+	2.69177e6i	−0.546395	+	0.290509i
$613$	−7.87449e6	+	7.87449e6i	−0.846392	+	0.846392i	−0.989681	−	0.143289i	$-0.954232\pi$
$613$	−7.87449e6	+	7.87449e6i	−0.846392	+	0.846392i	0.143289	+	0.989681i	$0.454232\pi$
$614$	−1.17848e7	−	7.08120e6i	−1.26154	−	0.758030i
$615$	−1.21563e6	+	3.77320e6i	−0.129602	+	0.402274i
$616$	2.22692e7	+	1.16776e6i	2.36457	+	0.123995i
$617$	−1.66343e6			−0.175910			−0.0879550	−	0.996124i	$-0.528033\pi$
$617$	−1.66343e6			−0.175910			−0.0879550	+	0.996124i	$0.528033\pi$
$618$	−5.15435e6	−	3.09712e6i	−0.542878	−	0.326202i
$619$	−6.46110e6	−	6.46110e6i	−0.677766	−	0.677766i	0.281728	−	0.959494i	$-0.409092\pi$
$619$	−6.46110e6	−	6.46110e6i	−0.677766	−	0.677766i	−0.959494	+	0.281728i	$0.909092\pi$
$620$	3.08836e6	−	4.43386e6i	0.322662	−	0.463236i
$621$	2.50500e6	−	2.50500e6i	0.260663	−	0.260663i
$622$	−3.24346e6	−	1.30094e7i	−0.336150	−	1.34828i
$623$		−	2.60041e6i		−	0.268424i
$624$	962951.	+	649576.i	0.0990017	+	0.0667834i
$625$	−3.10995e6	−	9.25719e6i	−0.318459	−	0.947937i
$626$	−5.73664e6	+	1.43024e6i	−0.585088	+	0.145873i
$627$	7.70385e6	+	7.70385e6i	0.782599	+	0.782599i
$628$	1.21362e7	+	3.71068e6i	1.22796	+	0.375452i
$629$	7.39999e6	+	7.39999e6i	0.745769	+	0.745769i
$630$	5.84530e6	+	6.69072e6i	0.586753	+	0.671616i
$631$		−	2.16886e6i		−	0.216850i	−0.994105	−	0.108425i	$-0.965419\pi$
$631$		−	2.16886e6i		−	0.216850i	0.994105	−	0.108425i	$-0.0345807\pi$
$632$	−1.44631e7	+	1.30218e7i	−1.44035	+	1.29682i
$633$	5.29378e6			0.525118
$634$	3.13947e6	+	1.88643e6i	0.310194	+	0.186388i
$635$	4.67410e6	+	9.11733e6i	0.460006	+	0.897291i
$636$	6.16261e6	−	3.27656e6i	0.604118	−	0.321199i
$637$	1.35693e6	+	1.35693e6i	0.132498	+	0.132498i
$638$	2.51514e7	−	6.27067e6i	2.44630	−	0.609905i
$639$	−1.03073e6			−0.0998607
$640$	5.96396e6	+	8.47380e6i	0.575553	+	0.817765i
$641$	−9.92178e6			−0.953772			−0.476886	−	0.878965i	$-0.658234\pi$
$641$	−9.92178e6			−0.953772			−0.476886	+	0.878965i	$0.658234\pi$
$642$	2.74126e6	−	683443.i	0.262490	−	0.0654432i
$643$	−9.95703e6	−	9.95703e6i	−0.949735	−	0.949735i	0.0490609	−	0.998796i	$-0.484377\pi$
$643$	−9.95703e6	−	9.95703e6i	−0.949735	−	0.949735i	−0.998796	+	0.0490609i	$0.984377\pi$
$644$	4.85097e6	−	2.57918e6i	0.460908	−	0.245057i
$645$	461541.	−	236614.i	0.0436829	−	0.0223945i
$646$	−9.54185e6	−	5.73345e6i	−0.899603	−	0.540549i
$647$	3.57802e6			0.336033			0.168016	−	0.985784i	$-0.446264\pi$
$647$	3.57802e6			0.336033			0.168016	+	0.985784i	$0.446264\pi$
$648$	395237.	−	355851.i	0.0369760	−	0.0332913i
$649$			3.03903e6i			0.283219i
$650$	−1.96951e6	+	847566.i	−0.182842	+	0.0786847i
$651$	3.60820e6	+	3.60820e6i	0.333686	+	0.333686i
$652$	3.79456e6	+	1.16020e6i	0.349576	+	0.106884i
$653$	−5.27870e6	−	5.27870e6i	−0.484445	−	0.484445i	0.422103	−	0.906548i	$-0.361292\pi$
$653$	−5.27870e6	−	5.27870e6i	−0.484445	−	0.484445i	−0.906548	+	0.422103i	$0.861292\pi$
$654$	1.05789e7	−	2.63750e6i	0.967155	−	0.241128i
$655$	−5.64582e6	+	1.75242e7i	−0.514190	+	1.59600i
$656$	6.43692e6	+	4.34214e6i	0.584008	+	0.393953i
$657$			7.05792e6i			0.637916i
$658$	−4.68080e6	−	1.87745e7i	−0.421459	−	1.69045i
$659$	−1.21548e7	+	1.21548e7i	−1.09027	+	1.09027i	−0.0947722	+	0.995499i	$0.530212\pi$
$659$	−1.21548e7	+	1.21548e7i	−1.09027	+	1.09027i	−0.995499	+	0.0947722i	$0.969788\pi$
$660$	−9.36223e6	−	6.52116e6i	−0.836603	−	0.582727i
$661$	−1.52299e7	−	1.52299e7i	−1.35579	−	1.35579i	−0.879033	−	0.476761i	$-0.841811\pi$
$661$	−1.52299e7	−	1.52299e7i	−1.35579	−	1.35579i	−0.476761	−	0.879033i	$-0.658189\pi$
$662$	3.48108e6	+	2.09169e6i	0.308723	+	0.185504i
$663$	1.30679e6			0.115457
$664$	−1.39412e7	−	731055.i	−1.22710	−	0.0643472i
$665$	−5.28931e6	+	1.64176e7i	−0.463815	+	1.43965i
$666$	−6.85099e6	−	4.11658e6i	−0.598505	−	0.359626i
$667$	4.51575e6	−	4.51575e6i	0.393021	−	0.393021i
$668$	−1.29703e7	+	6.89611e6i	−1.12463	+	0.597948i
$669$	3.62770e6	−	3.62770e6i	0.313376	−	0.313376i
$670$	−1.34099e7	−	904351.i	−1.15408	−	0.0778306i
$671$	1.31639e7			1.12870
$672$	−8.86895e6	+	4.13511e6i	−0.757615	+	0.353235i
$673$			6.95910e6i			0.592264i	0.955147	+	0.296132i	$0.0956968\pi$
$673$			6.95910e6i			0.592264i	−0.955147	+	0.296132i	$0.904303\pi$
$674$	−1.37746e6	−	5.52493e6i	−0.116796	−	0.468465i
$675$	−1.87924e6	−	1.14949e7i	−0.158754	−	0.971057i
$676$	−5.35675e6	−	1.00751e7i	−0.450853	−	0.847972i
$677$	−7.40998e6	+	7.40998e6i	−0.621363	+	0.621363i	−0.945880	−	0.324517i	$-0.894798\pi$
$677$	−7.40998e6	+	7.40998e6i	−0.621363	+	0.621363i	0.324517	+	0.945880i	$0.394798\pi$
$678$	−5.20709e6	+	8.66585e6i	−0.435032	+	0.723997i
$679$			9.66316e6i			0.804349i
$680$	1.08936e7	+	4.15101e6i	0.903442	+	0.344256i
$681$		−	4.32832e6i		−	0.357644i
$682$	9.98874e6	+	6.00198e6i	0.822337	+	0.494121i
$683$	−8.05004e6	+	8.05004e6i	−0.660307	+	0.660307i	−0.955452	−	0.295145i	$-0.904632\pi$
$683$	−8.05004e6	+	8.05004e6i	−0.660307	+	0.660307i	0.295145	+	0.955452i	$0.404632\pi$
$684$	8.13031e6	+	2.48587e6i	0.664457	+	0.203160i
$685$	377108.	−	193328.i	0.0307071	−	0.0157423i
$686$	977238.	−	243642.i	0.0792849	−	0.0197671i
$687$		−	6.99931e6i		−	0.565801i
$688$	−193799.	−	997225.i	−0.0156092	−	0.0803197i
$689$	2.82872e6			0.227008
$690$	−2.80459e6	−	189140.i	−0.224258	−	0.0151238i
$691$	−481321.	+	481321.i	−0.0383477	+	0.0383477i	−0.726021	−	0.687673i	$-0.758632\pi$
$691$	−481321.	+	481321.i	−0.0383477	+	0.0383477i	0.687673	+	0.726021i	$0.258632\pi$
$692$	−5.73130e6	−	1.75236e6i	−0.454976	−	0.139110i
$693$	−1.35486e7	+	1.35486e7i	−1.07167	+	1.07167i
$694$	−4.60904e6	+	7.67056e6i	−0.363255	+	0.604545i
$695$	−7.49204e6	−	2.41374e6i	−0.588353	−	0.189552i
$696$	−8.45332e6	+	7.61093e6i	−0.661461	+	0.595545i
$697$	8.73533e6			0.681078
$698$	−1.05897e7	+	1.76239e7i	−0.822709	+	1.36919i
$699$	9.37660e6	+	9.37660e6i	0.725859	+	0.725859i
$700$	2.42532e6	−	1.78998e7i	0.187079	−	1.38071i
$701$	1.33011e7	−	1.33011e7i	1.02233	−	1.02233i	0.0225894	−	0.999745i	$-0.492809\pi$
$701$	1.33011e7	−	1.33011e7i	1.02233	−	1.02233i	0.999745	−	0.0225894i	$-0.00719103\pi$
$702$	−2.48136e6	+	618646.i	−0.190041	+	0.0473805i
$703$		−	1.55172e7i		−	1.18420i
$704$	−1.73681e7	+	1.40627e7i	−1.32075	+	1.06939i
$705$	−3.03580e6	+	9.42289e6i	−0.230039	+	0.714022i
$706$	3.65873e6	+	1.46750e7i	0.276260	+	1.10807i
$707$	−1.81927e7	−	1.81927e7i	−1.36883	−	1.36883i
$708$	−626055.	−	1.17750e6i	−0.0469385	−	0.0882828i
$709$	1.94471e6	+	1.94471e6i	0.145291	+	0.145291i	0.776011	−	0.630720i	$-0.217240\pi$
$709$	1.94471e6	+	1.94471e6i	0.145291	+	0.145291i	−0.630720	+	0.776011i	$0.717240\pi$
$710$	1.37877e6	+	1.57818e6i	0.102647	+	0.117493i
$711$		−	1.67218e7i		−	1.24053i
$712$	1.74368e6	+	1.93667e6i	0.128904	+	0.143171i
$713$	2.87102e6			0.211501
$714$	−5.67017e6	+	9.43653e6i	−0.416246	+	0.692734i
$715$	−2.10956e6	−	4.11491e6i	−0.154321	−	0.301020i
$716$	−6.93514e6	+	2.26822e7i	−0.505560	+	1.65349i
$717$	2.85567e6	+	2.85567e6i	0.207449	+	0.207449i
$718$	−2.65180e6	−	1.06363e7i	−0.191969	−	0.769977i
$719$	−1.86113e7			−1.34263			−0.671313	−	0.741174i	$-0.734269\pi$
$719$	−1.86113e7			−1.34263			−0.671313	+	0.741174i	$0.734269\pi$
$720$	−8.83969e6	−	1.06344e6i	−0.635486	−	0.0764509i
$721$	2.05315e7			1.47090
$722$	604516.	+	2.42469e6i	0.0431583	+	0.173106i
$723$	9.84207e6	+	9.84207e6i	0.700230	+	0.700230i
$724$	−1.85439e7	−	5.66985e6i	−1.31478	−	0.401999i
$725$	−3.38770e6	−	2.07217e7i	−0.239364	−	1.46413i
$726$	8.28504e6	−	1.37883e7i	0.583382	−	0.970888i
$727$	−8.03905e6			−0.564117			−0.282058	−	0.959397i	$-0.591017\pi$
$727$	−8.03905e6			−0.564117			−0.282058	+	0.959397i	$0.591017\pi$
$728$	−3.96054e6	−	207685.i	−0.276966	−	0.0145237i
$729$		−	8.01339e6i		−	0.558467i
$730$	1.08066e7	−	9.44107e6i	0.750551	−	0.655713i
$731$	−808149.	−	808149.i	−0.0559368	−	0.0559368i
$732$	−5.10046e6	+	2.71183e6i	−0.351829	+	0.187062i
$733$	−428767.	−	428767.i	−0.0294755	−	0.0294755i	0.692215	−	0.721691i	$-0.256635\pi$
$733$	−428767.	−	428767.i	−0.0294755	−	0.0294755i	−0.721691	+	0.692215i	$0.756635\pi$
$734$	−1.64725e6	−	6.60703e6i	−0.112854	−	0.452654i
$735$	7.87295e6	+	2.53646e6i	0.537551	+	0.173184i
$736$	−1.88334e6	+	5.17362e6i	−0.128155	+	0.352046i
$737$		−	2.89860e7i		−	1.96571i
$738$	−6.47334e6	+	1.61391e6i	−0.437510	+	0.109079i
$739$	−1.37567e6	+	1.37567e6i	−0.0926624	+	0.0926624i	−0.751918	−	0.659256i	$-0.770871\pi$
$739$	−1.37567e6	+	1.37567e6i	−0.0926624	+	0.0926624i	0.659256	+	0.751918i	$0.270871\pi$
$740$	2.86126e6	+	1.59963e7i	0.192078	+	1.07384i
$741$	−1.37012e6	−	1.37012e6i	−0.0916669	−	0.0916669i
$742$	−1.22739e7	+	2.04266e7i	−0.818410	+	1.36203i
$743$	1.46961e7			0.976629			0.488315	−	0.872668i	$-0.337612\pi$
$743$	1.46961e7			0.976629			0.488315	+	0.872668i	$0.337612\pi$
$744$	−5.10666e6	−	267785.i	−0.338224	−	0.0177360i
$745$	7.46575e6	+	2.40526e6i	0.492813	+	0.158771i
$746$	226383.	−	376756.i	0.0148935	−	0.0247864i
$747$	8.48181e6	−	8.48181e6i	0.556144	−	0.556144i
$748$	−7.35116e6	+	2.40428e7i	−0.480399	+	1.57120i
$749$	−6.82086e6	+	6.82086e6i	−0.444257	+	0.444257i
$750$	−5.88771e6	+	7.12379e6i	−0.382203	+	0.462443i
$751$	2.84779e7			1.84250			0.921251	−	0.388970i	$-0.127169\pi$
$751$	2.84779e7			1.84250			0.921251	+	0.388970i	$0.127169\pi$
$752$	1.60750e7	+	1.08437e7i	1.03659	+	0.699251i
$753$		−	490658.i		−	0.0315349i
$754$	−4.47313e6	+	1.11523e6i	−0.286539	+	0.0714391i
$755$	3.69425e6	+	7.20603e6i	0.235862	+	0.460075i
$756$	6.29932e6	−	2.06026e7i	0.400856	−	1.31105i
$757$	1.48920e7	−	1.48920e7i	0.944522	−	0.944522i	−0.0540181	−	0.998540i	$-0.517203\pi$
$757$	1.48920e7	−	1.48920e7i	0.944522	−	0.944522i	0.998540	+	0.0540181i	$0.0172029\pi$
$758$	−1.17328e6	−	704992.i	−0.0741699	−	0.0445668i
$759$		−	6.06224e6i		−	0.381970i
$760$	−7.06939e6	−	1.57738e7i	−0.443964	−	0.990606i
$761$			7.62607e6i			0.477352i	0.971099	+	0.238676i	$0.0767134\pi$
$761$			7.62607e6i			0.477352i	−0.971099	+	0.238676i	$0.923287\pi$
$762$	4.99400e6	−	8.31122e6i	0.311574	−	0.518534i
$763$	−2.63226e7	+	2.63226e7i	−1.63688	+	1.63688i
$764$	8.51065e6	−	4.52497e6i	0.527509	−	0.280468i
$765$	−8.91353e6	+	4.56962e6i	−0.550676	+	0.282310i
$766$	−238949.	−	958412.i	−0.0147141	−	0.0590174i
$767$		−	540486.i		−	0.0331739i
$768$	3.83244e6	−	9.02660e6i	0.234462	−	0.552232i
$769$	2.86135e7			1.74484			0.872420	−	0.488757i	$-0.162550\pi$
$769$	2.86135e7			1.74484			0.872420	+	0.488757i	$0.162550\pi$
$770$	3.88678e7	+	2.62122e6i	2.36246	+	0.159322i
$771$	−7.12446e6	+	7.12446e6i	−0.431634	+	0.431634i
$772$	5.68900e6	+	1.07000e7i	0.343552	+	0.646160i
$773$	−5.02050e6	+	5.02050e6i	−0.302203	+	0.302203i	−0.841875	−	0.539672i	$-0.818548\pi$
$773$	−5.02050e6	+	5.02050e6i	−0.302203	+	0.302203i	0.539672	+	0.841875i	$0.318548\pi$
$774$	748193.	+	449570.i	0.0448912	+	0.0269740i
$775$	5.51030e6	−	7.66413e6i	0.329550	−	0.458362i
$776$	−6.47952e6	−	7.19668e6i	−0.386268	−	0.429020i
$777$	−1.53460e7			−0.911888
$778$	−1.59352e7	−	9.57508e6i	−0.943865	−	0.567144i
$779$	−9.15867e6	−	9.15867e6i	−0.540740	−	0.540740i
$780$	1.66506e6	+	1.15978e6i	0.0979925	+	0.0682556i
$781$	−3.19579e6	+	3.19579e6i	−0.187478	+	0.187478i
$782$	1.49843e6	+	6.01015e6i	0.0876234	+	0.351454i
$783$		−	2.50429e7i		−	1.45976i
$784$	9.06007e6	−	1.34309e7i	0.526431	−	0.780397i
$785$	2.11018e7	+	6.79844e6i	1.22221	+	0.393763i
$786$	1.69064e7	−	4.21505e6i	0.976099	−	0.243358i
$787$	4.07071e6	+	4.07071e6i	0.234279	+	0.234279i	0.814476	−	0.580197i	$-0.197024\pi$
$787$	4.07071e6	+	4.07071e6i	0.234279	+	0.234279i	−0.580197	+	0.814476i	$0.697024\pi$
$788$	−5.22782e6	+	1.70982e7i	−0.299920	+	0.980921i
$789$	−2.96539e6	−	2.96539e6i	−0.169586	−	0.169586i
$790$	−2.56031e7	+	2.23680e7i	−1.45957	+	1.27514i
$791$		−	3.45189e7i		−	1.96163i
$792$	1.00552e6	−	1.91752e7i	0.0569609	−	1.08624i
$793$	−2.34118e6			−0.132206
$794$	2.19154e6	+	1.31684e6i	0.123367	+	0.0741278i
$795$	1.08500e7	−	5.56236e6i	0.608851	−	0.312134i
$796$	−7.48755e6	−	1.40827e7i	−0.418849	−	0.787779i
$797$	−7.10983e6	−	7.10983e6i	−0.396473	−	0.396473i	0.480514	−	0.876987i	$-0.340450\pi$
$797$	−7.10983e6	−	7.10983e6i	−0.396473	−	0.396473i	−0.876987	+	0.480514i	$0.840450\pi$
$798$	1.58388e7	−	3.94889e6i	0.880471	−	0.219517i
$799$	2.18149e7			1.20889
$800$	1.01962e7	+	1.49572e7i	0.563266	+	0.826276i
$801$	−2.23912e6			−0.123309
$802$	1.70513e7	−	4.25117e6i	0.936096	−	0.233385i
$803$	2.18830e7	+	2.18830e7i	1.19762	+	1.19762i
$804$	5.97126e6	+	1.12309e7i	0.325781	+	0.612735i
$805$	8.54070e6	−	4.37848e6i	0.464519	−	0.238141i
$806$	−1.77648e6	−	1.06744e6i	−0.0963215	−	0.0578771i
$807$	−7.74923e6			−0.418865
$808$	2.57480e7	+	1.35019e6i	1.38744	+	0.0727555i
$809$			3.61724e7i			1.94315i	0.236740	+	0.971573i	$0.423921\pi$
$809$			3.61724e7i			1.94315i	−0.236740	+	0.971573i	$0.576079\pi$
$810$	699664.	−	611257.i	0.0374694	−	0.0327349i
$811$	1.47344e6	+	1.47344e6i	0.0786649	+	0.0786649i	0.745344	−	0.666680i	$-0.232285\pi$
$811$	1.47344e6	+	1.47344e6i	0.0786649	+	0.0786649i	−0.666680	+	0.745344i	$0.732285\pi$
$812$	1.13557e7	−	3.71402e7i	0.604401	−	1.97676i
$813$	1.89048e6	+	1.89048e6i	0.100310	+	0.100310i
$814$	−3.40049e7	+	8.47801e6i	−1.79879	+	0.448469i
$815$	6.59779e6	+	2.12563e6i	0.347940	+	0.112097i
$816$	−2.10467e6	−	1.08300e7i	−0.110652	−	0.569379i
$817$			1.69463e6i			0.0888218i
$818$	6.57995e6	+	2.63919e7i	0.343827	+	1.37907i
$819$	2.40959e6	−	2.40959e6i	0.125526	−	0.125526i
$820$	1.11302e7	+	7.75263e6i	0.578054	+	0.402638i
$821$	1.72016e7	+	1.72016e7i	0.890656	+	0.890656i	0.994585	−	0.103929i	$-0.0331415\pi$
$821$	1.72016e7	+	1.72016e7i	0.890656	+	0.890656i	−0.103929	+	0.994585i	$0.533141\pi$
$822$	−343766.	−	206560.i	−0.0177453	−	0.0106627i
$823$	1.17157e6			0.0602934			0.0301467	−	0.999545i	$-0.490403\pi$
$823$	1.17157e6			0.0602934			0.0301467	+	0.999545i	$0.490403\pi$
$824$	−1.52909e7	+	1.37671e7i	−0.784539	+	0.706359i
$825$	−1.61830e7	−	1.16352e7i	−0.827800	−	0.595166i
$826$	3.90294e6	+	2.34518e6i	0.199041	+	0.119598i
$827$	−5.84277e6	+	5.84277e6i	−0.297067	+	0.297067i	−0.839864	−	0.542797i	$-0.817365\pi$
$827$	−5.84277e6	+	5.84277e6i	−0.297067	+	0.297067i	0.542797	+	0.839864i	$0.317365\pi$
$828$	−2.22084e6	−	4.17699e6i	−0.112575	−	0.211733i
$829$	1.29359e7	−	1.29359e7i	0.653746	−	0.653746i	−0.300147	−	0.953893i	$-0.597036\pi$
$829$	1.29359e7	−	1.29359e7i	0.653746	−	0.653746i	0.953893	+	0.300147i	$0.0970358\pi$
$830$	−2.43325e7	−	1.64096e6i	−1.22600	−	0.0826805i
$831$	−1.64081e7			−0.824242
$832$	3.08889e6	−	2.50102e6i	0.154701	−	0.125259i
$833$		−	1.82266e7i		−	0.910111i
$834$	1.80204e6	+	7.22792e6i	0.0897119	+	0.359830i
$835$	−2.28358e7	+	1.17070e7i	−1.13344	+	0.581072i
$836$	3.29154e7	−	1.75006e7i	1.62886	−	0.866037i
$837$	7.96088e6	−	7.96088e6i	0.392778	−	0.392778i
$838$	3.04440e6	−	5.06662e6i	0.149759	−	0.249235i
$839$		−	1.67838e7i		−	0.823160i	−0.911374	−	0.411580i	$-0.864977\pi$
$839$		−	1.67838e7i		−	0.823160i	0.911374	−	0.411580i	$-0.135023\pi$
$840$	−1.55996e7	+	6.99136e6i	−0.762810	+	0.341872i
$841$		−	2.46335e7i		−	1.20098i
$842$	−1.94338e7	−	1.16773e7i	−0.944665	−	0.567625i
$843$	2.88464e6	−	2.88464e6i	0.139805	−	0.139805i
$844$	5.29623e6	−	1.73219e7i	0.255924	−	0.837028i
$845$	−9.09375e6	−	1.77383e7i	−0.438128	−	0.854616i
$846$	−1.61660e7	+	4.03046e6i	−0.776563	+	0.193610i
$847$			5.49233e7i			2.63056i
$848$	−4.55585e6	−	2.34429e7i	−0.217560	−	1.11949i
$849$	−4.16242e6			−0.198188
$850$	1.89199e7	+	7.53514e6i	0.898196	+	0.357721i
$851$	−6.10534e6	+	6.10534e6i	−0.288992	+	0.288992i
$852$	579886.	−	1.89658e6i	0.0273680	−	0.0895102i
$853$	−1.32955e7	+	1.32955e7i	−0.625649	+	0.625649i	−0.946970	−	0.321321i	$-0.895873\pi$
$853$	−1.32955e7	+	1.32955e7i	−0.625649	+	0.625649i	0.321321	+	0.946970i	$0.395873\pi$
$854$	1.01584e7	−	1.69060e7i	0.476630	−	0.793227i
$855$	1.41366e7	+	4.55443e6i	0.661346	+	0.213068i
$856$	506215.	−	9.65350e6i	0.0236130	−	0.450299i
$857$	2.29434e7			1.06710			0.533550	−	0.845769i	$-0.320858\pi$
$857$	2.29434e7			1.06710			0.533550	+	0.845769i	$0.320858\pi$
$858$	−2.25394e6	+	3.75110e6i	−0.104526	+	0.173956i
$859$	2.66573e7	+	2.66573e7i	1.23263	+	1.23263i	0.962949	+	0.269684i	$0.0869194\pi$
$859$	2.66573e7	+	2.66573e7i	1.23263	+	1.23263i	0.269684	+	0.962949i	$0.413081\pi$
$860$	−312477.	−	1.74695e6i	−0.0144069	−	0.0805440i
$861$	−9.05757e6	+	9.05757e6i	−0.416394	+	0.416394i
$862$	−1.47028e7	+	3.66566e6i	−0.673957	+	0.168029i
$863$		−	3.41204e7i		−	1.55951i	−0.626087	−	0.779753i	$-0.715345\pi$
$863$		−	3.41204e7i		−	1.55951i	0.626087	−	0.779753i	$-0.284655\pi$
$864$	9.12341e6	+	1.95678e7i	0.415789	+	0.891781i
$865$	−9.96530e6	−	3.21055e6i	−0.452846	−	0.145895i
$866$	4.28120e6	+	1.71717e7i	0.193986	+	0.778070i
$867$	612943.	+	612943.i	0.0276932	+	0.0276932i
$868$	1.54164e7	−	8.19662e6i	0.694516	−	0.369263i
$869$	−5.18458e7	−	5.18458e7i	−2.32897	−	2.32897i
$870$	−1.49644e7	+	1.30735e7i	−0.670288	+	0.585592i
$871$			5.15511e6i			0.230246i
$872$	1.95356e6	−	3.72542e7i	0.0870031	−	1.65915i
$873$	8.32059e6			0.369503
$874$	4.73036e6	−	7.87247e6i	0.209467	−	0.348604i
$875$	4.70375e6	−	3.12028e7i	0.207694	−	1.37776i
$876$	−1.29868e7	−	3.97075e6i	−0.571796	−	0.174828i
$877$	2.63864e7	+	2.63864e7i	1.15846	+	1.15846i	0.984807	+	0.173651i	$0.0555565\pi$
$877$	2.63864e7	+	2.63864e7i	1.15846	+	1.15846i	0.173651	+	0.984807i	$0.444443\pi$
$878$	108494.	+	435165.i	0.00474974	+	0.0190510i
$879$	3.88156e6			0.169447
$880$	−3.07046e7	+	2.41102e7i	−1.33659	+	1.04953i
$881$	8.03101e6			0.348602			0.174301	−	0.984692i	$-0.444233\pi$
$881$	8.03101e6			0.348602			0.174301	+	0.984692i	$0.444233\pi$
$882$	3.36750e6	+	1.35069e7i	0.145759	+	0.584635i
$883$	2.61818e7	+	2.61818e7i	1.13005	+	1.13005i	0.990168	+	0.139883i	$0.0446727\pi$
$883$	2.61818e7	+	2.61818e7i	1.13005	+	1.13005i	0.139883	+	0.990168i	$0.455327\pi$
$884$	1.30739e6	−	4.27597e6i	0.0562698	−	0.184037i
$885$	−1.06281e6	−	2.07312e6i	−0.0456137	−	0.0889745i
$886$	1.86544e7	−	3.10455e7i	0.798358	−	1.32866i
$887$	2.02575e7			0.864523			0.432262	−	0.901748i	$-0.357716\pi$
$887$	2.02575e7			0.864523			0.432262	+	0.901748i	$0.357716\pi$
$888$	1.14290e7	−	1.02901e7i	0.486379	−	0.437910i
$889$			3.31063e7i			1.40494i
$890$	2.99517e6	+	3.42837e6i	0.126750	+	0.145082i
$891$	1.41681e6	+	1.41681e6i	0.0597883	+	0.0597883i
$892$	−8.24092e6	−	1.54997e7i	−0.346788	−	0.652245i
$893$	−2.28721e7	−	2.28721e7i	−0.959793	−	0.959793i
$894$	−1.79572e6	−	7.20255e6i	−0.0751440	−	0.301399i
$895$	−1.27061e7	+	3.94386e7i	−0.530217	+	1.64575i
$896$	4.65754e6	+	3.31573e7i	0.193815	+	1.37978i
$897$			1.07816e6i			0.0447407i
$898$	−2.31760e7	+	5.77817e6i	−0.959063	+	0.239111i
$899$	1.43510e7	−	1.43510e7i	0.592221	−	0.592221i
$900$	−1.54128e7	−	2.08835e6i	−0.634272	−	0.0859405i
$901$	−1.89981e7	−	1.89981e7i	−0.779647	−	0.779647i
$902$	−1.50666e7	+	2.50745e7i	−0.616594	+	1.02616i
$903$	1.67592e6			0.0683967
$904$	2.31463e7	+	2.57081e7i	0.942019	+	1.04628i
$905$	−3.22432e7	−	1.03879e7i	−1.30863	−	0.421605i
$906$	3.94709e6	−	6.56891e6i	0.159756	−	0.265872i
$907$	−4.36829e6	+	4.36829e6i	−0.176316	+	0.176316i	−0.789748	−	0.613432i	$-0.789789\pi$
$907$	−4.36829e6	+	4.36829e6i	−0.176316	+	0.176316i	0.613432	+	0.789748i	$0.289789\pi$
$908$	−1.41628e7	−	4.33032e6i	−0.570079	−	0.174303i
$909$	−1.56651e7	+	1.56651e7i	−0.628815	+	0.628815i
$910$	−6.91259e6	−	466180.i	−0.276718	−	0.0186616i
$911$	2.19241e7			0.875237			0.437618	−	0.899161i	$-0.355822\pi$
$911$	2.19241e7			0.875237			0.437618	+	0.899161i	$0.355822\pi$
$912$	−9.14814e6	+	1.35615e7i	−0.364205	+	0.539908i
$913$		−	5.25956e7i		−	2.08820i
$914$	−9.64976e6	+	2.40585e6i	−0.382077	+	0.0952584i
$915$	−8.97995e6	+	4.60367e6i	−0.354586	+	0.181782i
$916$	−2.29026e7	−	7.00255e6i	−0.901876	−	0.275751i
$917$	−4.20668e7	+	4.20668e7i	−1.65202	+	1.65202i
$918$	2.08201e7	+	1.25103e7i	0.815410	+	0.489959i
$919$		−	1.23136e7i		−	0.480946i	−0.970656	−	0.240473i	$-0.922697\pi$
$919$		−	1.23136e7i		−	0.480946i	0.970656	−	0.240473i	$-0.0773026\pi$
$920$	−3.42478e6	+	8.98775e6i	−0.133402	+	0.350092i
$921$			2.27300e7i			0.882978i
$922$	−3.40547e6	+	5.66753e6i	−0.131932	+	0.219567i
$923$	568366.	−	568366.i	0.0219596	−	0.0219596i
$924$	−1.73074e7	−	3.25521e7i	−0.666887	−	1.25429i
$925$	4.58020e6	+	2.80160e7i	0.176007	+	1.07659i
$926$	−2.05768e6	−	8.25326e6i	−0.0788589	−	0.316299i
$927$		−	1.76789e7i		−	0.675702i
$928$	1.64467e7	+	3.52748e7i	0.626915	+	1.34460i
$929$	−4.04066e7			−1.53608			−0.768039	−	0.640403i	$-0.778767\pi$
$929$	−4.04066e7			−1.53608			−0.768039	+	0.640403i	$0.778767\pi$
$930$	−8.91298e6	−	601084.i	−0.337921	−	0.0227891i
$931$	−1.91100e7	+	1.91100e7i	−0.722580	+	0.722580i
$932$	4.00624e7	−	2.13005e7i	1.51076	−	0.803248i
$933$	−1.56738e7	+	1.56738e7i	−0.589483	+	0.589483i
$934$	4.41125e7	+	2.65061e7i	1.65461	+	0.994211i
$935$	−1.34683e7	+	4.18044e7i	−0.503829	+	1.56384i
$936$	−178830.	+	3.41027e6i	−0.00667191	+	0.127233i
$937$	−3.49906e7			−1.30197			−0.650987	−	0.759088i	$-0.725645\pi$
$937$	−3.49906e7			−1.30197			−0.650987	+	0.759088i	$0.725645\pi$
$938$	−3.72259e7	−	2.23681e7i	−1.38146	−	0.830084i
$939$	6.91155e6	+	6.91155e6i	0.255806	+	0.255806i
$940$	2.77957e7	+	1.93608e7i	1.02602	+	0.714667i
$941$	−84726.5	+	84726.5i	−0.00311921	+	0.00311921i	−0.708665	−	0.705545i	$-0.750702\pi$
$941$	−84726.5	+	84726.5i	−0.00311921	+	0.00311921i	0.705545	+	0.708665i	$0.250702\pi$
$942$	−5.07557e6	−	2.03579e7i	−0.186362	−	0.747490i
$943$			7.20705e6i			0.263924i
$944$	−4.47926e6	+	870490.i	−0.163597	+	0.0317932i
$945$	1.15412e7	−	3.58228e7i	0.420407	−	1.30491i
$946$	3.71366e6	−	925878.i	0.134919	−	0.0336377i
$947$	4.56028e6	+	4.56028e6i	0.165240	+	0.165240i	0.784884	−	0.619643i	$-0.212723\pi$
$947$	4.56028e6	+	4.56028e6i	0.165240	+	0.165240i	−0.619643	+	0.784884i	$0.712723\pi$
$948$	3.07686e7	+	9.40758e6i	1.11195	+	0.339983i
$949$	−3.89186e6	−	3.89186e6i	−0.140279	−	0.140279i
$950$	−1.19365e7	−	2.77371e7i	−0.429109	−	0.997131i
$951$		−	6.05525e6i		−	0.217111i
$952$	2.52047e7	+	2.79944e7i	0.901342	+	1.00110i
$953$	5.36678e7			1.91417			0.957087	−	0.289799i	$-0.0935886\pi$
$953$	5.36678e7			1.91417			0.957087	+	0.289799i	$0.0935886\pi$
$954$	1.75886e7	+	1.05686e7i	0.625692	+	0.375963i
$955$	1.49840e7	−	7.68171e6i	0.531642	−	0.272552i
$956$	1.22011e7	−	6.48713e6i	0.431772	−	0.229566i
$957$	−3.03026e7	−	3.03026e7i	−1.06955	−	1.06955i
$958$	2.14234e7	−	5.34122e6i	0.754179	−	0.188030i
$959$	1.36933e6			0.0480798
$960$	6.92993e6	−	1.56670e7i	0.242689	−	0.548666i
$961$	−1.95051e7			−0.681301
$962$	6.04772e6	−	1.50780e6i	0.210695	−	0.0525298i
$963$	5.87318e6	+	5.87318e6i	0.204083	+	0.204083i
$964$	4.20511e7	−	2.23579e7i	1.45742	−	0.774886i
$965$	9.65779e6	+	1.88386e7i	0.333856	+	0.651223i
$966$	−7.78557e6	−	4.67815e6i	−0.268440	−	0.161299i
$967$	−3.13955e7			−1.07970			−0.539848	−	0.841763i	$-0.681518\pi$
$967$	−3.13955e7			−1.07970			−0.539848	+	0.841763i	$0.681518\pi$
$968$	−3.68282e7	−	4.09044e7i	−1.26326	−	1.40308i
$969$			1.84038e7i			0.629649i
$970$	−1.11301e7	−	1.27399e7i	−0.379812	−	0.434745i
$971$	−1.88069e7	−	1.88069e7i	−0.640131	−	0.640131i	0.310456	−	0.950588i	$-0.399518\pi$
$971$	−1.88069e7	−	1.88069e7i	−0.640131	−	0.640131i	−0.950588	+	0.310456i	$0.899518\pi$
$972$	−2.85569e7	−	8.73135e6i	−0.969494	−	0.296426i
$973$	−1.79846e7	−	1.79846e7i	−0.609004	−	0.609004i
$974$	1.34517e6	−	335375.i	0.0454340	−	0.0113275i
$975$	2.87813e6	+	2.06930e6i	0.0969614	+	0.0697126i
$976$	3.77063e6	+	1.94024e7i	0.126704	+	0.651977i
$977$			5.66132e7i			1.89750i	0.316033	+	0.948748i	$0.397649\pi$
$977$			5.66132e7i			1.89750i	−0.316033	+	0.948748i	$0.602351\pi$
$978$	−1.58695e6	−	6.36519e6i	−0.0530538	−	0.212796i
$979$	−6.94237e6	+	6.94237e6i	−0.231500	+	0.231500i
$980$	1.61762e7	−	2.32237e7i	0.538036	−	0.772442i
$981$	2.26654e7	+	2.26654e7i	0.751955	+	0.751955i
$982$	−2.70068e7	−	1.62277e7i	−0.893707	−	0.537005i
$983$	−1.85849e7			−0.613448			−0.306724	−	0.951799i	$-0.599233\pi$
$983$	−1.85849e7			−0.613448			−0.306724	+	0.951799i	$0.599233\pi$
$984$	672215.	−	1.28191e7i	0.0221320	−	0.422056i
$985$	−9.57804e6	+	2.97294e7i	−0.314547	+	0.976329i
$986$	3.75322e7	+	2.25522e7i	1.22945	+	0.738747i
$987$	−2.26197e7	+	2.26197e7i	−0.739083	+	0.739083i
$988$	−5.85395e6	+	3.11245e6i	−0.190791	+	0.101440i
$989$	666760.	−	666760.i	0.0216760	−	0.0216760i
$990$	2.25703e6	−	3.34677e7i	0.0731897	−	1.08527i
$991$	1.61242e7			0.521549			0.260774	−	0.965400i	$-0.416022\pi$
$991$	1.61242e7			0.521549			0.260774	+	0.965400i	$0.416022\pi$
$992$	−5.98525e6	+	1.64417e7i	−0.193109	+	0.530479i
$993$		−	6.71412e6i		−	0.216081i
$994$	1.63812e6	+	6.57041e6i	0.0525870	+	0.210924i
$995$	−1.27111e7	−	2.47943e7i	−0.407028	−	0.793951i
$996$	1.08350e7	+	2.03786e7i	0.346082	+	0.650917i
$997$	3.82944e7	−	3.82944e7i	1.22011	−	1.22011i	0.252513	−	0.967593i	$-0.418743\pi$
$997$	3.82944e7	−	3.82944e7i	1.22011	−	1.22011i	0.967593	−	0.252513i	$-0.0812571\pi$
$998$	−4.40703e6	+	7.33436e6i	−0.140062	+	0.233097i
$999$			3.38583e7i			1.07337i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.q.a.69.5	yes	116
5.4	even	2	inner	80.6.q.a.69.54	yes	116
16.13	even	4	inner	80.6.q.a.29.54	yes	116
80.29	even	4	inner	80.6.q.a.29.5	✓	116

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.q.a.29.5	✓	116	80.29	even	4	inner
80.6.q.a.29.54	yes	116	16.13	even	4	inner
80.6.q.a.69.5	yes	116	1.1	even	1	trivial
80.6.q.a.69.54	yes	116	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-5.48884 + 1.36846i) q^{2} +(6.61300 + 6.61300i) q^{3} +(28.2546 - 15.0225i) q^{4} +(49.7455 - 25.5026i) q^{5} +(-45.3473 - 27.2480i) q^{6} +180.633 q^{7} +(-134.527 + 121.121i) q^{8} -155.536i q^{9} +O(q^{10})\)	\(q+(-5.48884 + 1.36846i) q^{2} +(6.61300 + 6.61300i) q^{3} +(28.2546 - 15.0225i) q^{4} +(49.7455 - 25.5026i) q^{5} +(-45.3473 - 27.2480i) q^{6} +180.633 q^{7} +(-134.527 + 121.121i) q^{8} -155.536i q^{9} +(-238.146 + 208.054i) q^{10} +(-482.240 - 482.240i) q^{11} +(286.192 + 87.5040i) q^{12} +(85.7657 + 85.7657i) q^{13} +(-991.466 + 247.189i) q^{14} +(497.616 + 160.319i) q^{15} +(572.648 - 848.911i) q^{16} -1152.03i q^{17} +(212.846 + 853.714i) q^{18} +(-1207.86 + 1207.86i) q^{19} +(1022.43 - 1467.87i) q^{20} +(1194.53 + 1194.53i) q^{21} +(3306.86 + 1987.01i) q^{22} +950.477 q^{23} +(-1690.60 - 88.6528i) q^{24} +(1824.24 - 2537.28i) q^{25} +(-588.120 - 353.387i) q^{26} +(2635.52 - 2635.52i) q^{27} +(5103.72 - 2713.56i) q^{28} +(4751.04 - 4751.04i) q^{29} +(-2950.72 - 198.994i) q^{30} +3020.61 q^{31} +(-1981.47 + 5443.18i) q^{32} -6378.11i q^{33} +(1576.51 + 6323.29i) q^{34} +(8985.69 - 4606.61i) q^{35} +(-2336.55 - 4394.63i) q^{36} +(-6423.45 + 6423.45i) q^{37} +(4976.83 - 8282.65i) q^{38} +1134.34i q^{39} +(-3603.22 + 9456.05i) q^{40} +7582.56i q^{41} +(-8191.23 - 4921.90i) q^{42} +(701.501 - 701.501i) q^{43} +(-20870.0 - 6381.06i) q^{44} +(-3966.58 - 7737.25i) q^{45} +(-5217.01 + 1300.69i) q^{46} +18936.1i q^{47} +(9400.77 - 1826.93i) q^{48} +15821.3 q^{49} +(-6540.76 + 16423.1i) q^{50} +(7618.36 - 7618.36i) q^{51} +(3711.69 + 1134.86i) q^{52} +(16491.0 - 16491.0i) q^{53} +(-10859.3 + 18072.6i) q^{54} +(-36287.7 - 11690.9i) q^{55} +(-24300.1 + 21878.6i) q^{56} -15975.1 q^{57} +(-19576.0 + 32579.3i) q^{58} +(-3150.95 - 3150.95i) q^{59} +(16468.3 - 2945.70i) q^{60} +(-13648.7 + 13648.7i) q^{61} +(-16579.6 + 4133.59i) q^{62} -28095.1i q^{63} +(3427.18 - 32588.3i) q^{64} +(6453.70 + 2079.21i) q^{65} +(8728.19 + 35008.4i) q^{66} +(30053.5 + 30053.5i) q^{67} +(-17306.4 - 32550.1i) q^{68} +(6285.50 + 6285.50i) q^{69} +(-43017.0 + 37581.5i) q^{70} -6626.96i q^{71} +(18838.8 + 20923.9i) q^{72} -45377.9 q^{73} +(26467.0 - 44047.5i) q^{74} +(28842.7 - 4715.36i) q^{75} +(-15982.5 + 52272.7i) q^{76} +(-87108.6 - 87108.6i) q^{77} +(-1552.29 - 6226.19i) q^{78} +107510. q^{79} +(6837.26 - 56833.5i) q^{80} -2937.97 q^{81} +(-10376.4 - 41619.4i) q^{82} +(54532.6 + 54532.6i) q^{83} +(51695.7 + 15806.1i) q^{84} +(-29379.7 - 57308.3i) q^{85} +(-2890.45 + 4810.40i) q^{86} +62837.2 q^{87} +(123284. + 6464.83i) q^{88} -14396.1i q^{89} +(32360.0 + 37040.4i) q^{90} +(15492.1 + 15492.1i) q^{91} +(26855.4 - 14278.6i) q^{92} +(19975.3 + 19975.3i) q^{93} +(-25913.3 - 103937. i) q^{94} +(-29282.1 + 90889.1i) q^{95} +(-49099.2 + 22892.3i) q^{96} +53496.0i q^{97} +(-86840.8 + 21650.9i) q^{98} +(-75005.9 + 75005.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6}+O(q^{10}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6	\( 116 q - 4 q^{4} - 2 q^{5} - 4 q^{6} + 532 q^{10} - 4 q^{11} + 1108 q^{14} - 4 q^{15} + 1216 q^{16} + 2356 q^{19} + 824 q^{20} - 976 q^{21} - 2864 q^{24} - 12104 q^{26} - 4 q^{29} + 736 q^{30} + 23056 q^{31} - 38304 q^{34} - 3864 q^{35} - 20588 q^{36} + 15144 q^{40} - 25536 q^{44} + 6734 q^{45} - 36052 q^{46} + 220884 q^{49} + 56116 q^{50} - 9472 q^{51} - 104360 q^{54} - 2552 q^{56} + 14476 q^{59} + 1008 q^{60} - 48084 q^{61} + 72944 q^{64} - 27692 q^{65} - 56736 q^{66} - 23296 q^{69} + 135260 q^{70} - 186128 q^{74} - 33244 q^{75} - 35824 q^{76} + 427312 q^{79} - 129128 q^{80} - 551132 q^{81} - 418448 q^{84} + 6248 q^{85} + 177516 q^{86} + 449576 q^{90} - 231952 q^{91} + 607356 q^{94} + 38420 q^{95} - 440264 q^{96} + 406924 q^{99}+O(q^{100}) \) 116 * q - 4 * q^4 - 2 * q^5 - 4 * q^6 + 532 * q^10 - 4 * q^11 + 1108 * q^14 - 4 * q^15 + 1216 * q^16 + 2356 * q^19 + 824 * q^20 - 976 * q^21 - 2864 * q^24 - 12104 * q^26 - 4 * q^29 + 736 * q^30 + 23056 * q^31 - 38304 * q^34 - 3864 * q^35 - 20588 * q^36 + 15144 * q^40 - 25536 * q^44 + 6734 * q^45 - 36052 * q^46 + 220884 * q^49 + 56116 * q^50 - 9472 * q^51 - 104360 * q^54 - 2552 * q^56 + 14476 * q^59 + 1008 * q^60 - 48084 * q^61 + 72944 * q^64 - 27692 * q^65 - 56736 * q^66 - 23296 * q^69 + 135260 * q^70 - 186128 * q^74 - 33244 * q^75 - 35824 * q^76 + 427312 * q^79 - 129128 * q^80 - 551132 * q^81 - 418448 * q^84 + 6248 * q^85 + 177516 * q^86 + 449576 * q^90 - 231952 * q^91 + 607356 * q^94 + 38420 * q^95 - 440264 * q^96 + 406924 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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