LMFDB - Embedded newform 40.6.k.a.3.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(3,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("40.3");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.k (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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			3.2
Character	$\chi$	$=$	40.3
Dual form			40.6.k.a.27.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.63573 - 0.488434i) q^{2} +(17.2238 + 17.2238i) q^{3} +(31.5229 + 5.50537i) q^{4} +(54.8737 - 10.6715i) q^{5} +(-88.6558 - 105.481i) q^{6} +(-14.7411 - 14.7411i) q^{7} +(-174.965 - 46.4236i) q^{8} +350.316i q^{9} +O(q^{10})$	\(q+(-5.63573 - 0.488434i) q^{2} +(17.2238 + 17.2238i) q^{3} +(31.5229 + 5.50537i) q^{4} +(54.8737 - 10.6715i) q^{5} +(-88.6558 - 105.481i) q^{6} +(-14.7411 - 14.7411i) q^{7} +(-174.965 - 46.4236i) q^{8} +350.316i q^{9} +(-314.465 + 33.3393i) q^{10} +509.310 q^{11} +(448.119 + 637.765i) q^{12} +(109.565 - 109.565i) q^{13} +(75.8769 + 90.2770i) q^{14} +(1128.93 + 761.328i) q^{15} +(963.382 + 347.090i) q^{16} +(-1321.86 + 1321.86i) q^{17} +(171.106 - 1974.29i) q^{18} +688.865i q^{19} +(1788.53 - 34.2957i) q^{20} -507.795i q^{21} +(-2870.33 - 248.765i) q^{22} +(-696.700 + 696.700i) q^{23} +(-2213.97 - 3813.15i) q^{24} +(2897.24 - 1171.17i) q^{25} +(-670.995 + 563.965i) q^{26} +(-1848.38 + 1848.38i) q^{27} +(-383.527 - 545.838i) q^{28} -5972.48 q^{29} +(-5990.51 - 4842.05i) q^{30} -9850.17i q^{31} +(-5259.83 - 2426.65i) q^{32} +(8772.24 + 8772.24i) q^{33} +(8095.28 - 6804.00i) q^{34} +(-966.209 - 651.590i) q^{35} +(-1928.62 + 11043.0i) q^{36} +(7498.27 + 7498.27i) q^{37} +(336.465 - 3882.26i) q^{38} +3774.25 q^{39} +(-10096.4 - 680.296i) q^{40} +10808.4 q^{41} +(-248.025 + 2861.80i) q^{42} +(-4687.08 - 4687.08i) q^{43} +(16054.9 + 2803.94i) q^{44} +(3738.39 + 19223.1i) q^{45} +(4266.71 - 3586.12i) q^{46} +(-12465.9 - 12465.9i) q^{47} +(10614.9 + 22571.3i) q^{48} -16372.4i q^{49} +(-16900.1 + 5185.26i) q^{50} -45534.8 q^{51} +(4057.01 - 2850.61i) q^{52} +(-14235.3 + 14235.3i) q^{53} +(11319.8 - 9514.17i) q^{54} +(27947.7 - 5435.09i) q^{55} +(1894.85 + 3263.52i) q^{56} +(-11864.9 + 11864.9i) q^{57} +(33659.3 + 2917.16i) q^{58} -33254.7i q^{59} +(31395.8 + 30214.4i) q^{60} -36049.2i q^{61} +(-4811.16 + 55512.9i) q^{62} +(5164.05 - 5164.05i) q^{63} +(28457.7 + 16245.0i) q^{64} +(4843.02 - 7181.47i) q^{65} +(-45153.3 - 53722.6i) q^{66} +(20208.6 - 20208.6i) q^{67} +(-48946.1 + 34391.5i) q^{68} -23999.6 q^{69} +(5127.03 + 4144.11i) q^{70} +58102.6i q^{71} +(16262.9 - 61293.1i) q^{72} +(-2521.14 - 2521.14i) q^{73} +(-38595.8 - 45920.6i) q^{74} +(70073.2 + 29729.5i) q^{75} +(-3792.46 + 21715.0i) q^{76} +(-7507.80 - 7507.80i) q^{77} +(-21270.7 - 1843.47i) q^{78} +12102.9 q^{79} +(56568.3 + 8765.39i) q^{80} +21454.5 q^{81} +(-60913.5 - 5279.22i) q^{82} +(-46356.9 - 46356.9i) q^{83} +(2795.60 - 16007.2i) q^{84} +(-58429.1 + 86641.4i) q^{85} +(24125.8 + 28704.4i) q^{86} +(-102869. - 102869. i) q^{87} +(-89111.6 - 23644.0i) q^{88} -8030.44i q^{89} +(-11679.3 - 110162. i) q^{90} -3230.23 q^{91} +(-25797.6 + 18126.4i) q^{92} +(169657. - 169657. i) q^{93} +(64165.7 + 76343.2i) q^{94} +(7351.21 + 37800.6i) q^{95} +(-48797.9 - 132390. i) q^{96} +(-73172.1 + 73172.1i) q^{97} +(-7996.84 + 92270.4i) q^{98} +178419. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	$ 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) $ 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−5.63573	−	0.488434i	−0.996265	−	0.0863438i
$2$	−5.63573	−	0.488434i	−0.996265	−	0.0863438i
$3$	17.2238	+	17.2238i	1.10490	+	1.10490i	0.993810	+	0.111095i	$0.0354358\pi$
$3$	17.2238	+	17.2238i	1.10490	+	1.10490i	0.111095	+	0.993810i	$0.464564\pi$
$4$	31.5229	+	5.50537i	0.985089	+	0.172043i
$5$	54.8737	−	10.6715i	0.981610	−	0.190897i
$5$	54.8737	−	10.6715i	0.981610	−	0.190897i
$6$	−88.6558	−	105.481i	−1.00538	−	1.19618i
$7$	−14.7411	−	14.7411i	−0.113707	−	0.113707i	0.647964	−	0.761671i	$-0.275621\pi$
$7$	−14.7411	−	14.7411i	−0.113707	−	0.113707i	−0.761671	+	0.647964i	$0.775621\pi$
$8$	−174.965	−	46.4236i	−0.966556	−	0.256457i
$9$			350.316i			1.44163i
$10$	−314.465	+	33.3393i	−0.994427	+	0.105428i
$11$	509.310			1.26911			0.634557	−	0.772876i	$-0.281183\pi$
$11$	509.310			1.26911			0.634557	+	0.772876i	$0.281183\pi$
$12$	448.119	+	637.765i	0.898339	+	1.27852i
$13$	109.565	−	109.565i	0.179810	−	0.179810i	−0.611463	−	0.791273i	$-0.709419\pi$
$13$	109.565	−	109.565i	0.179810	−	0.179810i	0.791273	+	0.611463i	$0.209419\pi$
$14$	75.8769	+	90.2770i	0.103464	+	0.123100i
$15$	1128.93	+	761.328i	1.29551	+	0.873663i
$16$	963.382	+	347.090i	0.940803	+	0.338955i
$17$	−1321.86	+	1321.86i	−1.10934	+	1.10934i	−0.116097	+	0.993238i	$0.537038\pi$
$17$	−1321.86	+	1321.86i	−1.10934	+	1.10934i	−0.993238	+	0.116097i	$0.962962\pi$
$18$	171.106	−	1974.29i	0.124476	−	1.43625i
$19$			688.865i			0.437774i	0.975750	+	0.218887i	$0.0702427\pi$
$19$			688.865i			0.437774i	−0.975750	+	0.218887i	$0.929757\pi$
$20$	1788.53	−	34.2957i	0.999816	−	0.0191719i
$21$		−	507.795i		−	0.251270i
$22$	−2870.33	−	248.765i	−1.26437	−	0.109580i
$23$	−696.700	+	696.700i	−0.274616	+	0.274616i	−0.830955	−	0.556339i	$-0.812206\pi$
$23$	−696.700	+	696.700i	−0.274616	+	0.274616i	0.556339	+	0.830955i	$0.312206\pi$
$24$	−2213.97	−	3813.15i	−0.784592	−	1.35131i
$25$	2897.24	−	1171.17i	0.927117	−	0.374773i
$26$	−670.995	+	563.965i	−0.194664	+	0.163613i
$27$	−1848.38	+	1848.38i	−0.487958	+	0.487958i
$28$	−383.527	−	545.838i	−0.0924488	−	0.131574i
$29$	−5972.48			−1.31874			−0.659371	−	0.751818i	$-0.729177\pi$
$29$	−5972.48			−1.31874			−0.659371	+	0.751818i	$0.729177\pi$
$30$	−5990.51	−	4842.05i	−1.21524	−	0.982259i
$31$		−	9850.17i		−	1.84094i	−0.390813	−	0.920470i	$-0.627806\pi$
$31$		−	9850.17i		−	1.84094i	0.390813	−	0.920470i	$-0.372194\pi$
$32$	−5259.83	−	2426.65i	−0.908022	−	0.418922i
$33$	8772.24	+	8772.24i	1.40225	+	1.40225i
$34$	8095.28	−	6804.00i	1.20098	−	1.00941i
$35$	−966.209	−	651.590i	−0.133322	−	0.0899093i
$36$	−1928.62	+	11043.0i	−0.248022	+	1.42013i
$37$	7498.27	+	7498.27i	0.900444	+	0.900444i	0.995474	−	0.0950301i	$-0.0302947\pi$
$37$	7498.27	+	7498.27i	0.900444	+	0.900444i	−0.0950301	+	0.995474i	$0.530295\pi$
$38$	336.465	−	3882.26i	0.0377991	−	0.436139i
$39$	3774.25			0.397346
$40$	−10096.4	−	680.296i	−0.997738	−	0.0672276i
$41$	10808.4			1.00416			0.502081	−	0.864821i	$-0.332568\pi$
$41$	10808.4			1.00416			0.502081	+	0.864821i	$0.332568\pi$
$42$	−248.025	+	2861.80i	−0.0216956	+	0.250331i
$43$	−4687.08	−	4687.08i	−0.386572	−	0.386572i	0.486891	−	0.873463i	$-0.338131\pi$
$43$	−4687.08	−	4687.08i	−0.386572	−	0.386572i	−0.873463	+	0.486891i	$0.838131\pi$
$44$	16054.9	+	2803.94i	1.25019	+	0.218342i
$45$	3738.39	+	19223.1i	0.275203	+	1.41512i
$46$	4266.71	−	3586.12i	0.297302	−	0.249879i
$47$	−12465.9	−	12465.9i	−0.823150	−	0.823150i	0.163408	−	0.986559i	$-0.447751\pi$
$47$	−12465.9	−	12465.9i	−0.823150	−	0.823150i	−0.986559	+	0.163408i	$0.947751\pi$
$48$	10614.9	+	22571.3i	0.664984	+	1.41401i
$49$		−	16372.4i		−	0.974142i
$50$	−16900.1	+	5185.26i	−0.956014	+	0.293323i
$51$	−45534.8			−2.45142
$52$	4057.01	−	2850.61i	0.208064	−	0.146194i
$53$	−14235.3	+	14235.3i	−0.696109	+	0.696109i	−0.963569	−	0.267460i	$-0.913816\pi$
$53$	−14235.3	+	14235.3i	−0.696109	+	0.696109i	0.267460	+	0.963569i	$0.413816\pi$
$54$	11319.8	−	9514.17i	0.528268	−	0.444004i
$55$	27947.7	−	5435.09i	1.24578	−	0.242270i
$56$	1894.85	+	3263.52i	0.0807429	+	0.139065i
$57$	−11864.9	+	11864.9i	−0.483699	+	0.483699i
$58$	33659.3	+	2917.16i	1.31382	+	0.113865i
$59$		−	33254.7i		−	1.24372i	−0.783127	−	0.621861i	$-0.786377\pi$
$59$		−	33254.7i		−	1.24372i	0.783127	−	0.621861i	$-0.213623\pi$
$60$	31395.8	+	30214.4i	1.12588	+	1.08352i
$61$		−	36049.2i		−	1.24043i	−0.784433	−	0.620213i	$-0.787046\pi$
$61$		−	36049.2i		−	1.24043i	0.784433	−	0.620213i	$-0.212954\pi$
$62$	−4811.16	+	55512.9i	−0.158954	+	1.83406i
$63$	5164.05	−	5164.05i	0.163923	−	0.163923i
$64$	28457.7	+	16245.0i	0.868460	+	0.495759i
$65$	4843.02	−	7181.47i	0.142178	−	0.210829i
$66$	−45153.3	−	53722.6i	−1.27594	−	1.51809i
$67$	20208.6	−	20208.6i	0.549984	−	0.549984i	−0.376452	−	0.926436i	$-0.622856\pi$
$67$	20208.6	−	20208.6i	0.549984	−	0.549984i	0.926436	+	0.376452i	$0.122856\pi$
$68$	−48946.1	+	34391.5i	−1.28365	+	0.901941i
$69$	−23999.6			−0.606850
$70$	5127.03	+	4144.11i	0.125061	+	0.101085i
$71$			58102.6i			1.36788i	0.729536	+	0.683942i	$0.239736\pi$
$71$			58102.6i			1.36788i	−0.729536	+	0.683942i	$0.760264\pi$
$72$	16262.9	−	61293.1i	0.369715	−	1.39342i
$73$	−2521.14	−	2521.14i	−0.0553719	−	0.0553719i	0.678879	−	0.734251i	$-0.262466\pi$
$73$	−2521.14	−	2521.14i	−0.0553719	−	0.0553719i	−0.734251	+	0.678879i	$0.762466\pi$
$74$	−38595.8	−	45920.6i	−0.819334	−	0.974829i
$75$	70073.2	+	29729.5i	1.43846	+	0.610287i
$76$	−3792.46	+	21715.0i	−0.0753159	+	0.431247i
$77$	−7507.80	−	7507.80i	−0.144307	−	0.144307i
$78$	−21270.7	−	1843.47i	−0.395862	−	0.0343084i
$79$	12102.9			0.218183			0.109091	−	0.994032i	$-0.465206\pi$
$79$	12102.9			0.218183			0.109091	+	0.994032i	$0.465206\pi$
$80$	56568.3	+	8765.39i	0.988207	+	0.153125i
$81$	21454.5			0.363334
$82$	−60913.5	−	5279.22i	−1.00041	−	0.0867031i
$83$	−46356.9	−	46356.9i	−0.738617	−	0.738617i	0.233693	−	0.972310i	$-0.424919\pi$
$83$	−46356.9	−	46356.9i	−0.738617	−	0.738617i	−0.972310	+	0.233693i	$0.924919\pi$
$84$	2795.60	−	16007.2i	0.0432291	−	0.247523i
$85$	−58429.1	+	86641.4i	−0.877166	+	1.30070i
$86$	24125.8	+	28704.4i	0.351751	+	0.418507i
$87$	−102869.	−	102869.i	−1.45708	−	1.45708i
$88$	−89111.6	−	23644.0i	−1.22667	−	0.325473i
$89$		−	8030.44i		−	0.107464i	−0.998555	−	0.0537322i	$-0.982888\pi$
$89$		−	8030.44i		−	0.107464i	0.998555	−	0.0537322i	$-0.0171117\pi$
$90$	−11679.3	−	110162.i	−0.151988	−	1.43359i
$91$	−3230.23			−0.0408912
$92$	−25797.6	+	18126.4i	−0.317767	+	0.223276i
$93$	169657.	−	169657.i	2.03406	−	2.03406i
$94$	64165.7	+	76343.2i	0.749002	+	0.891150i
$95$	7351.21	+	37800.6i	0.0835698	+	0.429724i
$96$	−48797.9	−	132390.i	−0.540410	−	1.46615i
$97$	−73172.1	+	73172.1i	−0.789616	+	0.789616i	−0.981431	−	0.191815i	$-0.938563\pi$
$97$	−73172.1	+	73172.1i	−0.789616	+	0.789616i	0.191815	+	0.981431i	$0.438563\pi$
$98$	−7996.84	+	92270.4i	−0.0841111	+	0.970504i
$99$			178419.i			1.82959i
$100$	97777.0	−	20968.1i	0.977770	−	0.209681i
$101$			97263.1i			0.948735i	0.880327	+	0.474367i	$0.157323\pi$
$101$			97263.1i			0.948735i	−0.880327	+	0.474367i	$0.842677\pi$
$102$	256622.	+	22240.7i	2.44226	+	0.211665i
$103$	75234.6	−	75234.6i	0.698755	−	0.698755i	−0.265387	−	0.964142i	$-0.585500\pi$
$103$	75234.6	−	75234.6i	0.698755	−	0.698755i	0.964142	+	0.265387i	$0.0854998\pi$
$104$	−24256.5	+	14083.7i	−0.219910	+	0.127683i
$105$	−5418.92	−	27864.6i	−0.0479667	−	0.246649i
$106$	87179.4	−	73273.4i	0.753615	−	0.633405i
$107$	3052.73	−	3052.73i	0.0257768	−	0.0257768i	−0.694101	−	0.719878i	$-0.744198\pi$
$107$	3052.73	−	3052.73i	0.0257768	−	0.0257768i	0.719878	+	0.694101i	$0.244198\pi$
$108$	−68442.4	+	48090.3i	−0.564632	+	0.396733i
$109$	−51487.6			−0.415084			−0.207542	−	0.978226i	$-0.566546\pi$
$109$	−51487.6			−0.415084			−0.207542	+	0.978226i	$0.566546\pi$
$110$	−160160.	+	16980.1i	−1.26204	+	0.133800i
$111$			258297.i			1.98981i
$112$	−9084.84	−	19317.8i	−0.0684340	−	0.145517i
$113$	20974.3	+	20974.3i	0.154522	+	0.154522i	0.780134	−	0.625612i	$-0.215151\pi$
$113$	20974.3	+	20974.3i	0.154522	+	0.154522i	−0.625612	+	0.780134i	$0.715151\pi$
$114$	72662.3	−	61071.9i	0.523657	−	0.440128i
$115$	−30795.7	+	45665.3i	−0.217143	+	0.321990i
$116$	−188270.	−	32880.7i	−1.29908	−	0.226880i
$117$	38382.4	+	38382.4i	0.259220	+	0.259220i
$118$	−16242.8	+	187415.i	−0.107388	+	1.23908i
$119$	38971.4			0.252277
$120$	−162181.	−	185615.i	−1.02812	−	1.17669i
$121$	98345.8			0.610650
$122$	−17607.7	+	203163.i	−0.107103	+	1.23579i
$123$	186162.	+	186162.i	1.10950	+	1.10950i
$124$	54228.8	−	310506.i	0.316720	−	1.81349i
$125$	146484.	−	95184.0i	0.838524	−	0.544865i
$126$	−31625.5	+	26580.9i	−0.177464	+	0.149157i
$127$	−71877.1	−	71877.1i	−0.395440	−	0.395440i	0.481181	−	0.876621i	$-0.340208\pi$
$127$	−71877.1	−	71877.1i	−0.395440	−	0.395440i	−0.876621	+	0.481181i	$0.840208\pi$
$128$	−152445.	−	105452.i	−0.822411	−	0.568894i
$129$		−	161458.i		−	0.854251i
$130$	−30801.6	+	38107.3i	−0.159851	+	0.197765i
$131$	126943.			0.646296			0.323148	−	0.946348i	$-0.395259\pi$
$131$	126943.			0.646296			0.323148	+	0.946348i	$0.395259\pi$
$132$	228232.	+	324820.i	1.14009	+	1.62259i
$133$	10154.6	−	10154.6i	0.0497778	−	0.0497778i
$134$	−123761.	+	104020.i	−0.595417	+	0.500442i
$135$	−81702.6	+	121153.i	−0.385835	+	0.572135i
$136$	292645.	−	169914.i	1.35673	−	0.787738i
$137$	−112379.	+	112379.i	−0.511546	+	0.511546i	−0.915000	−	0.403454i	$-0.867809\pi$
$137$	−112379.	+	112379.i	−0.511546	+	0.511546i	0.403454	+	0.915000i	$0.367809\pi$
$138$	135255.	+	11722.2i	0.604584	+	0.0523977i
$139$		−	1803.19i		−	0.00791597i	−0.999992	−	0.00395798i	$-0.998740\pi$
$139$		−	1803.19i		−	0.00791597i	0.999992	−	0.00395798i	$-0.00125987\pi$
$140$	−26870.4	−	25859.3i	−0.115866	−	0.111506i
$141$		−	429419.i		−	1.81901i
$142$	28379.3	−	327450.i	0.118108	−	1.36278i
$143$	55802.7	−	55802.7i	0.228200	−	0.228200i
$144$	−121591.	+	337488.i	−0.488647	+	1.35629i
$145$	−327732.	+	63735.1i	−1.29449	+	0.251744i
$146$	12977.0	+	15439.9i	0.0503841	+	0.0599461i
$147$	281994.	−	281994.i	1.07633	−	1.07633i
$148$	195086.	+	277648.i	0.732103	+	1.04193i
$149$	−492553.			−1.81755			−0.908777	−	0.417282i	$-0.862983\pi$
$149$	−492553.			−1.81755			−0.908777	+	0.417282i	$0.862983\pi$
$150$	−380393.	−	201773.i	−1.38040	−	0.732210i
$151$			142766.i			0.509547i	0.967001	+	0.254773i	$0.0820008\pi$
$151$			142766.i			0.509547i	−0.967001	+	0.254773i	$0.917999\pi$
$152$	31979.6	−	120527.i	0.112270	−	0.423133i
$153$	−463068.	−	463068.i	−1.59925	−	1.59925i
$154$	38644.9	+	45979.0i	0.131308	+	0.156228i
$155$	−105116.	−	540515.i	−0.351430	−	1.80708i
$156$	118975.	+	20778.6i	0.391422	+	0.0683605i
$157$	−106174.	−	106174.i	−0.343772	−	0.343772i	0.514011	−	0.857784i	$-0.328159\pi$
$157$	−106174.	−	106174.i	−0.343772	−	0.343772i	−0.857784	+	0.514011i	$0.828159\pi$
$158$	−68208.5	−	5911.46i	−0.217368	−	0.0188387i
$159$	−490372.			−1.53827
$160$	−314522.	−	77029.2i	−0.971295	−	0.237879i
$161$	20540.3			0.0624514
$162$	−120912.	−	10479.1i	−0.361977	−	0.0313717i
$163$	−125925.	−	125925.i	−0.371231	−	0.371231i	0.496695	−	0.867925i	$-0.334547\pi$
$163$	−125925.	−	125925.i	−0.371231	−	0.371231i	−0.867925	+	0.496695i	$0.834547\pi$
$164$	340713.	+	59504.4i	0.989189	+	0.172759i
$165$	574978.	+	387752.i	1.64415	+	1.10878i
$166$	238613.	+	283897.i	0.672084	+	0.799634i
$167$	284753.	+	284753.i	0.790090	+	0.790090i	0.981509	−	0.191418i	$-0.0613087\pi$
$167$	284753.	+	284753.i	0.790090	+	0.790090i	−0.191418	+	0.981509i	$0.561309\pi$
$168$	−23573.7	+	88846.5i	−0.0644398	+	0.242866i
$169$			347284.i			0.935337i
$170$	371609.	−	459749.i	0.986198	−	1.22011i
$171$	−241320.			−0.631108
$172$	−121946.	−	173554.i	−0.314301	−	0.447315i
$173$	−186125.	+	186125.i	−0.472813	+	0.472813i	−0.902824	−	0.430010i	$-0.858510\pi$
$173$	−186125.	+	186125.i	−0.472813	+	0.472813i	0.430010	+	0.902824i	$0.358510\pi$
$174$	529495.	+	629984.i	1.32583	+	1.57745i
$175$	−59972.9	−	25444.3i	−0.148033	−	0.0628051i
$176$	490660.	+	176776.i	1.19399	+	0.430172i
$177$	572772.	−	572772.i	1.37419	−	1.37419i
$178$	−3922.34	+	45257.4i	−0.00927888	+	0.107063i
$179$			210311.i			0.490601i	0.969447	+	0.245300i	$0.0788866\pi$
$179$			210311.i			0.490601i	−0.969447	+	0.245300i	$0.921113\pi$
$180$	12014.3	+	626549.i	0.0276388	+	1.44136i
$181$			275853.i			0.625865i	0.949775	+	0.312933i	$0.101311\pi$
$181$			275853.i			0.625865i	−0.949775	+	0.312933i	$0.898689\pi$
$182$	18204.7	+	1577.76i	0.0407385	+	0.00353070i
$183$	620903.	−	620903.i	1.37055	−	1.37055i
$184$	154242.	−	89555.0i	0.335859	−	0.195005i
$185$	491475.	+	331440.i	1.05578	+	0.711993i
$186$	−1.03901e6	+	873274.i	−2.20210	+	1.85084i
$187$	−673236.	+	673236.i	−1.40787	+	1.40787i
$188$	−324332.	−	461590.i	−0.669260	−	0.952494i
$189$	54494.5			0.110968
$190$	−22966.3	−	216624.i	−0.0461538	−	0.435335i
$191$		−	338791.i		−	0.671968i	−0.941868	−	0.335984i	$-0.890931\pi$
$191$		−	338791.i		−	0.671968i	0.941868	−	0.335984i	$-0.109069\pi$
$192$	210348.	+	769949.i	0.411799	+	1.50733i
$193$	165073.	+	165073.i	0.318995	+	0.318995i	0.848381	−	0.529386i	$-0.177578\pi$
$193$	165073.	+	165073.i	0.318995	+	0.318995i	−0.529386	+	0.848381i	$0.677578\pi$
$194$	448118.	−	376638.i	0.854846	−	0.718489i
$195$	207107.	−	40276.8i	0.390039	−	0.0758523i
$196$	90136.0	−	516105.i	0.167594	−	0.959617i
$197$	−117816.	−	117816.i	−0.216292	−	0.216292i	0.590642	−	0.806934i	$-0.298875\pi$
$197$	−117816.	−	117816.i	−0.216292	−	0.216292i	−0.806934	+	0.590642i	$0.798875\pi$
$198$	87146.2	−	1.00552e6i	0.157974	−	1.82276i
$199$	240189.			0.429952			0.214976	−	0.976619i	$-0.431033\pi$
$199$	240189.			0.429952			0.214976	+	0.976619i	$0.431033\pi$
$200$	−561286.	+	70413.1i	−0.992223	+	0.124474i
$201$	696137.			1.21536
$202$	47506.6	−	548148.i	0.0819173	−	0.945191i
$203$	88041.0	+	88041.0i	0.149950	+	0.149950i
$204$	−1.43539e6	−	250686.i	−2.41487	−	0.421749i
$205$	593099.	−	115342.i	0.985695	−	0.191692i
$206$	−460749.	+	387255.i	−0.756478	+	0.635812i
$207$	−244065.	−	244065.i	−0.395895	−	0.395895i
$208$	143582.	−	67524.2i	0.230114	−	0.108218i
$209$			350846.i			0.555585i
$210$	16929.6	+	159684.i	0.0264909	+	0.249870i
$211$	−896662.			−1.38651			−0.693254	−	0.720693i	$-0.743824\pi$
$211$	−896662.			−1.38651			−0.693254	+	0.720693i	$0.743824\pi$
$212$	−527109.	+	370367.i	−0.805491	+	0.565970i
$213$	−1.00075e6	+	1.00075e6i	−1.51138	+	1.51138i
$214$	−18695.4	+	15713.3i	−0.0279062	+	0.0234549i
$215$	−307215.	−	207179.i	−0.453259	−	0.305668i
$216$	409212.	−	237594.i	0.596779	−	0.346499i
$217$	−145203.	+	145203.i	−0.209327	+	0.209327i
$218$	290170.	+	25148.3i	0.413534	+	0.0358400i
$219$		−	86846.9i		−	0.122361i
$220$	910914.	−	17467.2i	1.26888	−	0.0243313i
$221$			289660.i			0.398940i
$222$	126161.	−	1.45569e6i	0.171808	−	1.98238i
$223$	39331.6	−	39331.6i	0.0529639	−	0.0529639i	−0.680129	−	0.733093i	$-0.738076\pi$
$223$	39331.6	−	39331.6i	0.0529639	−	0.0529639i	0.733093	+	0.680129i	$0.238076\pi$
$224$	41764.2	+	113307.i	0.0556140	+	0.150882i
$225$	410278.	+	1.01495e6i	0.540284	+	1.33656i
$226$	−107961.	−	128450.i	−0.140603	−	0.167287i
$227$	372837.	−	372837.i	0.480236	−	0.480236i	−0.424971	−	0.905207i	$-0.639716\pi$
$227$	372837.	−	372837.i	0.480236	−	0.480236i	0.905207	+	0.424971i	$0.139716\pi$
$228$	−439334.	+	308694.i	−0.559704	+	0.393270i
$229$	349083.			0.439886			0.219943	−	0.975513i	$-0.429413\pi$
$229$	349083.			0.439886			0.219943	+	0.975513i	$0.429413\pi$
$230$	195861.	−	242316.i	0.244134	−	0.302038i
$231$		−	258625.i		−	0.318890i
$232$	1.04498e6	+	277264.i	1.27464	+	0.338200i
$233$	63835.2	+	63835.2i	0.0770319	+	0.0770319i	0.744573	−	0.667541i	$-0.232653\pi$
$233$	63835.2	+	63835.2i	0.0770319	+	0.0770319i	−0.667541	+	0.744573i	$0.732653\pi$
$234$	−197566.	−	235060.i	−0.235870	−	0.280634i
$235$	−817079.	−	551020.i	−0.965149	−	0.650875i
$236$	183079.	−	1.04828e6i	0.213973	−	1.22518i
$237$	208457.	+	208457.i	0.241071	+	0.241071i
$238$	−219632.	−	19035.0i	−0.251335	−	0.0217826i
$239$	987818.			1.11862			0.559310	−	0.828959i	$-0.311066\pi$
$239$	987818.			1.11862			0.559310	+	0.828959i	$0.311066\pi$
$240$	823345.	+	1.12529e6i	0.922686	+	1.26106i
$241$	−482388.			−0.535000			−0.267500	−	0.963558i	$-0.586198\pi$
$241$	−482388.			−0.535000			−0.267500	+	0.963558i	$0.586198\pi$
$242$	−554250.	−	48035.5i	−0.608370	−	0.0527259i
$243$	818685.	+	818685.i	0.889408	+	0.889408i
$244$	198464.	−	1.13637e6i	0.213406	−	1.22193i
$245$	−174718.	−	898414.i	−0.185961	−	0.956227i
$246$	−958231.	−	1.14009e6i	−1.00956	−	1.20116i
$247$	75475.7	+	75475.7i	0.0787163	+	0.0787163i
$248$	−457280.	+	1.72344e6i	−0.472121	+	1.77937i
$249$		−	1.59688e6i		−	1.63220i
$250$	−872036.	+	464883.i	−0.882438	+	0.470429i
$251$	777624.			0.779086			0.389543	−	0.921008i	$-0.372633\pi$
$251$	777624.			0.779086			0.389543	+	0.921008i	$0.372633\pi$
$252$	191216.	−	134356.i	0.189680	−	0.133277i
$253$	−354837.	+	354837.i	−0.348519	+	0.348519i
$254$	369972.	+	440187.i	0.359820	+	0.428107i
$255$	−2.49866e6	+	485923.i	−2.40634	+	0.467969i
$256$	807633.	+	668760.i	0.770219	+	0.637779i
$257$	−683990.	+	683990.i	−0.645976	+	0.645976i	−0.952018	−	0.306042i	$-0.900995\pi$
$257$	−683990.	+	683990.i	−0.645976	+	0.645976i	0.306042	+	0.952018i	$0.400995\pi$
$258$	−78861.7	+	909934.i	−0.0737593	+	0.851061i
$259$		−	221066.i		−	0.204773i
$260$	192203.	−	199718.i	0.176330	−	0.183225i
$261$		−	2.09225e6i		−	1.90114i
$262$	−715418.	−	62003.5i	−0.643883	−	0.0558037i
$263$	491368.	−	491368.i	0.438044	−	0.438044i	−0.453309	−	0.891353i	$-0.649757\pi$
$263$	491368.	−	491368.i	0.438044	−	0.438044i	0.891353	+	0.453309i	$0.149757\pi$
$264$	−1.12760e6	−	1.94208e6i	−0.995737	−	1.71497i
$265$	−629232.	+	933056.i	−0.550423	+	0.816193i
$266$	−62188.7	+	52269.0i	−0.0538899	+	0.0452939i
$267$	138314.	−	138314.i	0.118738	−	0.118738i
$268$	748290.	−	525778.i	0.636404	−	0.447162i
$269$	−800055.			−0.674123			−0.337062	−	0.941483i	$-0.609433\pi$
$269$	−800055.			−0.674123			−0.337062	+	0.941483i	$0.609433\pi$
$270$	519629.	−	642877.i	0.433794	−	0.536683i
$271$			2.24545e6i			1.85729i	0.370966	+	0.928646i	$0.379027\pi$
$271$			2.24545e6i			1.85729i	−0.370966	+	0.928646i	$0.620973\pi$
$272$	−1.73226e6	+	814651.i	−1.41968	+	0.667651i
$273$	−55636.7	−	55636.7i	−0.0451809	−	0.0451809i
$274$	688228.	−	578448.i	0.553804	−	0.465466i
$275$	1.47559e6	−	596487.i	1.17662	−	0.475630i
$276$	−756536.	−	132127.i	−0.597801	−	0.104404i
$277$	417176.	+	417176.i	0.326678	+	0.326678i	0.851322	−	0.524644i	$-0.175801\pi$
$277$	417176.	+	417176.i	0.326678	+	0.326678i	−0.524644	+	0.851322i	$0.675801\pi$
$278$	−880.739	+	10162.3i	−0.000683495	+	0.00788640i
$279$	3.45067e6			2.65395
$280$	138804.	+	158861.i	0.105805	+	0.121094i
$281$	1.07676e6			0.813492			0.406746	−	0.913541i	$-0.366663\pi$
$281$	1.07676e6			0.813492			0.406746	+	0.913541i	$0.366663\pi$
$282$	−209743.	+	2.42009e6i	−0.157060	+	1.81221i
$283$	652652.	+	652652.i	0.484413	+	0.484413i	0.906538	−	0.422125i	$-0.138716\pi$
$283$	652652.	+	652652.i	0.484413	+	0.484413i	−0.422125	+	0.906538i	$0.638716\pi$
$284$	−319876.	+	1.83156e6i	−0.235335	+	1.34749i
$285$	−524452.	+	777683.i	−0.382467	+	0.567140i
$286$	−341745.	+	287233.i	−0.247051	+	0.207644i
$287$	−159329.	−	159329.i	−0.114180	−	0.114180i
$288$	850095.	−	1.84260e6i	0.603929	−	1.30903i
$289$		−	2.07477e6i		−	1.46125i
$290$	1.87814e6	−	199118.i	1.31139	−	0.139033i
$291$	−2.52060e6			−1.74490
$292$	−65593.7	−	93353.2i	−0.0450199	−	0.0640726i
$293$	782068.	−	782068.i	0.532201	−	0.532201i	−0.389026	−	0.921227i	$-0.627188\pi$
$293$	782068.	−	782068.i	0.532201	−	0.532201i	0.921227	+	0.389026i	$0.127188\pi$
$294$	−1.72698e6	+	1.45151e6i	−1.16525	+	0.979379i
$295$	−354877.	−	1.82481e6i	−0.237423	−	1.22085i
$296$	−963840.	−	1.66003e6i	−0.639405	−	1.10125i
$297$	−941401.	+	941401.i	−0.619275	+	0.619275i
$298$	2.77590e6	+	240580.i	1.81077	+	0.156935i
$299$			152668.i			0.0987577i
$300$	2.04524e6	+	1.32294e6i	1.31202	+	0.848665i
$301$			138186.i			0.0879116i
$302$	69732.0	−	804593.i	0.0439962	−	0.507644i
$303$	−1.67524e6	+	1.67524e6i	−1.04826	+	1.04826i
$304$	−239098.	+	663640.i	−0.148386	+	0.411859i
$305$	−384698.	−	1.97815e6i	−0.236794	−	1.21761i
$306$	2.38355e6	+	2.83590e6i	1.45519	+	1.73136i
$307$	−403766.	+	403766.i	−0.244503	+	0.244503i	−0.818710	−	0.574207i	$-0.805310\pi$
$307$	−403766.	+	403766.i	−0.244503	+	0.244503i	0.574207	+	0.818710i	$0.305310\pi$
$308$	−195334.	−	278001.i	−0.117328	−	0.166982i
$309$	2.59165e6			1.54411
$310$	328398.	+	3.09754e6i	0.194087	+	1.83068i
$311$			1.05819e6i			0.620387i	0.950673	+	0.310194i	$0.100394\pi$
$311$			1.05819e6i			0.620387i	−0.950673	+	0.310194i	$0.899606\pi$
$312$	−660363.	−	175214.i	−0.384057	−	0.101902i
$313$	−1.88504e6	−	1.88504e6i	−1.08758	−	1.08758i	−0.995777	−	0.0918012i	$-0.970738\pi$
$313$	−1.88504e6	−	1.88504e6i	−1.08758	−	1.08758i	−0.0918012	−	0.995777i	$-0.529262\pi$
$314$	546511.	+	650230.i	0.312806	+	0.372171i
$315$	228262.	−	338478.i	0.129616	−	0.192201i
$316$	381517.	+	66630.8i	0.214930	+	0.0375368i
$317$	1.20973e6	+	1.20973e6i	0.676143	+	0.676143i	0.959125	−	0.282982i	$-0.0913237\pi$
$317$	1.20973e6	+	1.20973e6i	0.676143	+	0.676143i	−0.282982	+	0.959125i	$0.591324\pi$
$318$	2.76360e6	+	239514.i	1.53252	+	0.132820i
$319$	−3.04184e6			−1.67363
$320$	1.73494e6	+	587739.i	0.947128	+	0.320856i
$321$	105159.			0.0569619
$322$	−115760.	−	10032.6i	−0.0622181	−	0.00539229i
$323$	−910583.	−	910583.i	−0.485638	−	0.485638i
$324$	676308.	+	118115.i	0.357917	+	0.0625090i
$325$	189118.	−	445756.i	0.0993170	−	0.234093i
$326$	648174.	+	771187.i	0.337791	+	0.401898i
$327$	−886810.	−	886810.i	−0.458629	−	0.458629i
$328$	−1.89110e6	−	501767.i	−0.970578	−	0.257524i
$329$			367523.i			0.187195i
$330$	−3.05103e6	−	2.46610e6i	−1.54227	−	1.24660i
$331$	487007.			0.244324			0.122162	−	0.992510i	$-0.461017\pi$
$331$	487007.			0.244324			0.122162	+	0.992510i	$0.461017\pi$
$332$	−1.20609e6	−	1.71652e6i	−0.600531	−	0.854678i
$333$	−2.62676e6	+	2.62676e6i	−1.29811	+	1.29811i
$334$	−1.46571e6	−	1.74387e6i	−0.718920	−	0.855359i
$335$	893266.	−	1.32458e6i	0.434879	−	0.644860i
$336$	176251.	−	489201.i	0.0851691	−	0.236395i
$337$	375270.	−	375270.i	0.179999	−	0.179999i	−0.611356	−	0.791355i	$-0.709376\pi$
$337$	375270.	−	375270.i	0.179999	−	0.179999i	0.791355	+	0.611356i	$0.209376\pi$
$338$	169625.	−	1.95720e6i	0.0807605	−	0.931843i
$339$			722511.i			0.341464i
$340$	−2.31884e6	+	2.40951e6i	−1.08786	+	1.13040i
$341$		−	5.01679e6i		−	2.33636i
$342$	1.36002e6	+	117869.i	0.628751	+	0.0544923i
$343$	−489102.	+	489102.i	−0.224473	+	0.224473i
$344$	602485.	+	1.03767e6i	0.274505	+	0.472783i
$345$	−1.31695e6	+	256111.i	−0.595690	+	0.115846i
$346$	1.13986e6	−	958041.i	0.511872	−	0.430223i
$347$	2.79322e6	−	2.79322e6i	1.24532	−	1.24532i	0.287559	−	0.957763i	$-0.407156\pi$
$347$	2.79322e6	−	2.79322e6i	1.24532	−	1.24532i	0.957763	−	0.287559i	$-0.0928436\pi$
$348$	−2.67638e6	−	3.80904e6i	−1.18468	−	1.68604i
$349$	−1.69016e6			−0.742788			−0.371394	−	0.928475i	$-0.621120\pi$
$349$	−1.69016e6			−0.742788			−0.371394	+	0.928475i	$0.621120\pi$
$350$	325563.	+	172690.i	0.142058	+	0.0753523i
$351$			405037.i			0.175480i
$352$	−2.67888e6	−	1.23592e6i	−1.15238	−	0.531659i
$353$	766651.	+	766651.i	0.327462	+	0.327462i	0.851621	−	0.524159i	$-0.175620\pi$
$353$	766651.	+	766651.i	0.327462	+	0.327462i	−0.524159	+	0.851621i	$0.675620\pi$
$354$	−3.50775e6	+	2.94822e6i	−1.48772	+	1.25041i
$355$	620040.	+	3.18830e6i	0.261125	+	1.34273i
$356$	44210.5	−	253142.i	0.0184885	−	0.105862i
$357$	671234.	+	671234.i	0.278743	+	0.278743i
$358$	102723.	−	1.18525e6i	0.0423604	−	0.488769i
$359$	1.39596e6			0.571657			0.285829	−	0.958281i	$-0.407731\pi$
$359$	1.39596e6			0.571657			0.285829	+	0.958281i	$0.407731\pi$
$360$	238318.	−	3.53693e6i	0.0969173	−	1.43837i
$361$	2.00156e6			0.808354
$362$	134736.	−	1.55463e6i	0.0540396	−	0.623528i
$363$	1.69389e6	+	1.69389e6i	0.674710	+	0.674710i
$364$	−101826.	−	17783.6i	−0.0402815	−	0.00703503i
$365$	−165248.	−	111440.i	−0.0649239	−	0.0437833i
$366$	−3.80251e6	+	3.19597e6i	−1.48377	+	1.24710i
$367$	85536.5	+	85536.5i	0.0331502	+	0.0331502i	0.723488	−	0.690337i	$-0.242538\pi$
$367$	85536.5	+	85536.5i	0.0331502	+	0.0331502i	−0.690337	+	0.723488i	$0.742538\pi$
$368$	−913006.	+	429371.i	−0.351442	+	0.165277i
$369$			3.78637e6i			1.44763i
$370$	−2.60793e6	−	2.10796e6i	−0.990358	−	0.800494i
$371$	419689.			0.158304
$372$	6.28210e6	−	4.41405e6i	2.35368	−	1.65379i
$373$	2.12223e6	−	2.12223e6i	0.789807	−	0.789807i	−0.191656	−	0.981462i	$-0.561386\pi$
$373$	2.12223e6	−	2.12223e6i	0.789807	−	0.789807i	0.981462	+	0.191656i	$0.0613857\pi$
$374$	4.12301e6	−	3.46534e6i	1.52418	−	1.28105i
$375$	4.16243e6	+	883581.i	1.52851	+	0.324465i
$376$	1.60239e6	+	2.75981e6i	0.584518	+	1.00672i
$377$	−654376.	+	654376.i	−0.237123	+	0.237123i
$378$	−307116.	−	26617.0i	−0.110554	−	0.00958141i
$379$			3.51617e6i			1.25740i	0.777650	+	0.628698i	$0.216412\pi$
$379$			3.51617e6i			1.25740i	−0.777650	+	0.628698i	$0.783588\pi$
$380$	23625.1	+	1.23205e6i	0.00839297	+	0.437694i
$381$		−	2.47599e6i		−	0.873848i
$382$	−165477.	+	1.90933e6i	−0.0580203	+	0.669458i
$383$	−3.23618e6	+	3.23618e6i	−1.12729	+	1.12729i	−0.136674	+	0.990616i	$0.543641\pi$
$383$	−3.23618e6	+	3.23618e6i	−1.12729	+	1.12729i	−0.990616	+	0.136674i	$0.956359\pi$
$384$	−809395.	−	4.44197e6i	−0.280112	−	1.53726i
$385$	−492100.	−	331861.i	−0.169201	−	0.114105i
$386$	−849681.	−	1.01094e6i	−0.290260	−	0.345347i
$387$	1.64196e6	−	1.64196e6i	0.557294	−	0.557294i
$388$	−2.70943e6	+	1.90375e6i	−0.913690	+	0.641995i
$389$	−4.77783e6			−1.60087			−0.800436	−	0.599418i	$-0.795399\pi$
$389$	−4.77783e6			−1.60087			−0.800436	+	0.599418i	$0.795399\pi$
$390$	−1.18687e6	+	125831.i	−0.395132	+	0.0418915i
$391$		−	1.84188e6i		−	0.609283i
$392$	−760066.	+	2.86460e6i	−0.249825	+	0.941562i
$393$	2.18644e6	+	2.18644e6i	0.714096	+	0.714096i
$394$	606435.	+	721526.i	0.196809	+	0.234159i
$395$	664129.	−	129156.i	0.214171	−	0.0416505i
$396$	−982264.	+	5.62429e6i	−0.314768	+	1.80231i
$397$	2.85091e6	+	2.85091e6i	0.907837	+	0.907837i	0.996097	−	0.0882604i	$-0.0281308\pi$
$397$	2.85091e6	+	2.85091e6i	0.907837	+	0.907837i	−0.0882604	+	0.996097i	$0.528131\pi$
$398$	−1.35364e6	−	117316.i	−0.428346	−	0.0371237i
$399$	349802.			0.109999
$400$	3.19765e6	−	122678.i	0.999265	−	0.0383368i
$401$	−2.86873e6			−0.890899			−0.445450	−	0.895307i	$-0.646956\pi$
$401$	−2.86873e6			−0.890899			−0.445450	+	0.895307i	$0.646956\pi$
$402$	−3.92324e6	−	340017.i	−1.21082	−	0.104939i
$403$	−1.07924e6	−	1.07924e6i	−0.331020	−	0.331020i
$404$	−535469.	+	3.06601e6i	−0.163223	+	0.934588i
$405$	1.17729e6	−	228951.i	0.356653	−	0.0693595i
$406$	−453173.	−	539178.i	−0.136442	−	0.162337i
$407$	3.81895e6	+	3.81895e6i	1.14277	+	1.14277i
$408$	7.96700e6	+	2.11389e6i	2.36943	+	0.628683i
$409$		−	4.38344e6i		−	1.29571i	−0.761765	−	0.647854i	$-0.775667\pi$
$409$		−	4.38344e6i		−	1.29571i	0.761765	−	0.647854i	$-0.224333\pi$
$410$	−3.39888e6	+	360346.i	−0.998565	+	0.105867i
$411$	−3.87118e6			−1.13042
$412$	2.78581e6	−	1.95742e6i	0.808551	−	0.568120i
$413$	−490212.	+	490212.i	−0.141419	+	0.141419i
$414$	1.25628e6	+	1.49469e6i	0.360233	+	0.428600i
$415$	−3.03847e6	−	2.04908e6i	−0.866034	−	0.584034i
$416$	−842171.	+	310418.i	−0.238598	+	0.0879454i
$417$	31057.7	−	31057.7i	0.00874639	−	0.00874639i
$418$	171365.	−	1.97727e6i	0.0479714	−	0.553511i
$419$			1.83000e6i			0.509233i	0.967042	+	0.254617i	$0.0819493\pi$
$419$			1.83000e6i			0.509233i	−0.967042	+	0.254617i	$0.918051\pi$
$420$	−17415.2	−	908205.i	−0.00481732	−	0.251224i
$421$			5.81932e6i			1.60017i	0.599884	+	0.800087i	$0.295213\pi$
$421$			5.81932e6i			1.60017i	−0.599884	+	0.800087i	$0.704787\pi$
$422$	5.05334e6	+	437960.i	1.38133	+	0.119716i
$423$	4.36700e6	−	4.36700e6i	1.18668	−	1.18668i
$424$	3.15154e6	−	1.82983e6i	0.851350	−	0.494307i
$425$	−2.28163e6	+	5.37786e6i	−0.612734	+	1.44423i
$426$	6.12873e6	−	5.15113e6i	1.63624	−	1.37524i
$427$	−531406.	+	531406.i	−0.141045	+	0.141045i
$428$	113037.	−	79424.5i	0.0298272	−	0.0209578i
$429$	1.92226e6			0.504278
$430$	1.63019e6	+	1.31766e6i	0.425174	+	0.343662i
$431$			1.38778e6i			0.359855i	0.983680	+	0.179927i	$0.0575863\pi$
$431$			1.38778e6i			0.359855i	−0.983680	+	0.179927i	$0.942414\pi$
$432$	−2.42225e6	+	1.13914e6i	−0.624468	+	0.293677i
$433$	1.01509e6	+	1.01509e6i	0.260186	+	0.260186i	0.825130	−	0.564943i	$-0.191102\pi$
$433$	1.01509e6	+	1.01509e6i	0.260186	+	0.260186i	−0.564943	+	0.825130i	$0.691102\pi$
$434$	889244.	−	747401.i	0.226619	−	0.190471i
$435$	−6.74253e6	−	4.54701e6i	−1.70844	−	1.15213i
$436$	−1.62304e6	−	283458.i	−0.408895	−	0.0714122i
$437$	−479933.	−	479933.i	−0.120220	−	0.120220i
$438$	−42419.0	+	489446.i	−0.0105651	+	0.121904i
$439$	3.04621e6			0.754394			0.377197	−	0.926133i	$-0.376888\pi$
$439$	3.04621e6			0.754394			0.377197	+	0.926133i	$0.376888\pi$
$440$	−5.14220e6	−	346482.i	−1.26624	−	0.0853195i
$441$	5.73551e6			1.40435
$442$	141480.	−	1.63244e6i	0.0344460	−	0.397450i
$443$	−4.41095e6	−	4.41095e6i	−1.06788	−	1.06788i	−0.997522	−	0.0703580i	$-0.977586\pi$
$443$	−4.41095e6	−	4.41095e6i	−1.06788	−	1.06788i	−0.0703580	−	0.997522i	$-0.522414\pi$
$444$	−1.42202e6	+	8.14226e6i	−0.342332	+	1.96014i
$445$	−85696.6	−	440660.i	−0.0205146	−	0.105488i
$446$	−240873.	+	202451.i	−0.0573392	+	0.0481930i
$447$	−8.48362e6	−	8.48362e6i	−2.00822	−	2.00822i
$448$	−180028.	−	658969.i	−0.0423785	−	0.155121i
$449$			6.04065e6i			1.41406i	0.707183	+	0.707030i	$0.249965\pi$
$449$			6.04065e6i			1.41406i	−0.707183	+	0.707030i	$0.750035\pi$
$450$	−1.81648e6	−	5.92037e6i	−0.422862	−	1.37822i
$451$	5.50485e6			1.27440
$452$	545698.	+	776640.i	0.125634	+	0.178803i
$453$	−2.45898e6	+	2.45898e6i	−0.563000	+	0.563000i
$454$	−2.28331e6	+	1.91910e6i	−0.519907	+	0.436977i
$455$	−177255.	+	34471.3i	−0.0401392	+	0.00780601i
$456$	2.62675e6	−	1.52513e6i	0.591570	−	0.343474i
$457$	3.16526e6	−	3.16526e6i	0.708954	−	0.708954i	−0.257361	−	0.966315i	$-0.582853\pi$
$457$	3.16526e6	−	3.16526e6i	0.708954	−	0.708954i	0.966315	+	0.257361i	$0.0828529\pi$
$458$	−1.96734e6	−	170504.i	−0.438243	−	0.0379814i
$459$		−	4.88660e6i		−	1.08262i
$460$	−1.22217e6	+	1.26996e6i	−0.269301	+	0.279831i
$461$			5.81450e6i			1.27427i	0.770754	+	0.637133i	$0.219880\pi$
$461$			5.81450e6i			1.27427i	−0.770754	+	0.637133i	$0.780120\pi$
$462$	−126321.	+	1.45754e6i	−0.0275342	+	0.317699i
$463$	2.33240e6	−	2.33240e6i	0.505651	−	0.505651i	−0.407538	−	0.913188i	$-0.633612\pi$
$463$	2.33240e6	−	2.33240e6i	0.505651	−	0.505651i	0.913188	+	0.407538i	$0.133612\pi$
$464$	−5.75378e6	−	2.07299e6i	−1.24068	−	0.446994i
$465$	7.49921e6	−	1.11202e7i	1.60836	−	2.38495i
$466$	−328579.	−	390937.i	−0.0700930	−	0.0833954i
$467$	−3.95924e6	+	3.95924e6i	−0.840077	+	0.840077i	−0.988869	−	0.148791i	$-0.952462\pi$
$467$	−3.95924e6	+	3.95924e6i	−0.840077	+	0.840077i	0.148791	+	0.988869i	$0.452462\pi$
$468$	998615.	+	1.42123e6i	0.210758	+	0.299951i
$469$	−595796.			−0.125074
$470$	4.33570e6	+	3.50449e6i	0.905346	+	0.731779i
$471$		−	3.65745e6i		−	0.759672i
$472$	−1.54380e6	+	5.81842e6i	−0.318961	+	1.20213i
$473$	−2.38718e6	−	2.38718e6i	−0.490604	−	0.490604i
$474$	−1.07299e6	−	1.27662e6i	−0.219356	−	0.260986i
$475$	806775.	+	1.99581e6i	0.164066	+	0.405868i
$476$	1.22849e6	+	214552.i	0.248516	+	0.0434025i
$477$	−4.98686e6	−	4.98686e6i	−1.00353	−	1.00353i
$478$	−5.56707e6	−	482484.i	−1.11444	−	0.0965858i
$479$	−8.50896e6			−1.69448			−0.847242	−	0.531206i	$-0.821739\pi$
$479$	−8.50896e6			−1.69448			−0.847242	+	0.531206i	$0.821739\pi$
$480$	−4.09052e6	−	6.74399e6i	−0.810355	−	1.33602i
$481$	1.64310e6			0.323818
$482$	2.71861e6	+	235615.i	0.533002	+	0.0461940i
$483$	353781.	+	353781.i	0.0690028	+	0.0690028i
$484$	3.10014e6	+	541430.i	0.601545	+	0.105058i
$485$	−3.23437e6	+	4.79607e6i	−0.624360	+	0.925831i
$486$	−4.21401e6	−	5.01376e6i	−0.809292	−	0.962881i
$487$	263623.	+	263623.i	0.0503687	+	0.0503687i	0.731843	−	0.681474i	$-0.238661\pi$
$487$	263623.	+	263623.i	0.0503687	+	0.0503687i	−0.681474	+	0.731843i	$0.738661\pi$
$488$	−1.67353e6	+	6.30736e6i	−0.318115	+	1.19894i
$489$		−	4.33781e6i		−	0.820349i
$490$	545845.	+	5.14855e6i	0.102702	+	0.968713i
$491$	−3.54302e6			−0.663238			−0.331619	−	0.943413i	$-0.607595\pi$
$491$	−3.54302e6			−0.663238			−0.331619	+	0.943413i	$0.607595\pi$
$492$	4.84347e6	+	6.89325e6i	0.902078	+	1.28384i
$493$	7.89477e6	−	7.89477e6i	1.46293	−	1.46293i
$494$	−388496.	−	462225.i	−0.0716257	−	0.0852190i
$495$	1.90400e6	+	9.79053e6i	0.349264	+	1.79595i
$496$	3.41889e6	−	9.48948e6i	0.623996	−	1.73196i
$497$	856497.	−	856497.i	0.155537	−	0.155537i
$498$	−779972.	+	8.99959e6i	−0.140931	+	1.62611i
$499$		−	5.63099e6i		−	1.01236i	−0.862429	−	0.506178i	$-0.831058\pi$
$499$		−	5.63099e6i		−	1.01236i	0.862429	−	0.506178i	$-0.168942\pi$
$500$	5.14162e6	−	2.19402e6i	0.919761	−	0.392479i
$501$			9.80903e6i			1.74595i
$502$	−4.38248e6	−	379818.i	−0.776177	−	0.0672693i
$503$	7.50633e6	−	7.50633e6i	1.32284	−	1.32284i	0.411376	−	0.911466i	$-0.365048\pi$
$503$	7.50633e6	−	7.50633e6i	1.32284	−	1.32284i	0.911466	−	0.411376i	$-0.134952\pi$
$504$	−1.14326e6	+	663796.i	−0.200479	+	0.116401i
$505$	1.03794e6	+	5.33718e6i	0.181111	+	0.931287i
$506$	2.17308e6	−	1.82645e6i	0.377310	−	0.317125i
$507$	−5.98154e6	+	5.98154e6i	−1.03346	+	1.03346i
$508$	−1.87006e6	−	2.66148e6i	−0.321512	−	0.457577i
$509$	720493.			0.123264			0.0616318	−	0.998099i	$-0.480370\pi$
$509$	720493.			0.123264			0.0616318	+	0.998099i	$0.480370\pi$
$510$	1.43191e7	−	1.51810e6i	2.43776	−	0.258449i
$511$			74328.8i			0.0125923i
$512$	−4.22496e6	−	4.16343e6i	−0.712274	−	0.701901i
$513$	−1.27329e6	−	1.27329e6i	−0.213616	−	0.213616i
$514$	4.18886e6	−	3.52070e6i	0.699340	−	0.587788i
$515$	3.32554e6	−	4.93126e6i	0.552514	−	0.819295i
$516$	888886.	−	5.08962e6i	0.146968	−	0.841514i
$517$	−6.34901e6	−	6.34901e6i	−1.04467	−	1.04467i
$518$	−107976.	+	1.24587e6i	−0.0176809	+	0.204008i
$519$	−6.41155e6			−1.04483
$520$	−1.18075e6	+	1.03168e6i	−0.191492	+	0.167315i
$521$	−8.81132e6			−1.42215			−0.711077	−	0.703114i	$-0.751792\pi$
$521$	−8.81132e6			−1.42215			−0.711077	+	0.703114i	$0.751792\pi$
$522$	−1.02193e6	+	1.17914e7i	−0.164151	+	1.89404i
$523$	−1.65743e6	−	1.65743e6i	−0.264961	−	0.264961i	0.562105	−	0.827066i	$-0.309992\pi$
$523$	−1.65743e6	−	1.65743e6i	−0.264961	−	0.264961i	−0.827066	+	0.562105i	$0.809992\pi$
$524$	4.00162e6	+	698870.i	0.636660	+	0.111191i
$525$	−594712.	−	1.47120e6i	−0.0941692	−	0.232956i
$526$	−3.00922e6	+	2.52922e6i	−0.474231	+	0.398586i
$527$	1.30205e7	+	1.30205e7i	2.04222	+	2.04222i
$528$	5.40626e6	+	1.14958e7i	0.843941	+	1.79454i
$529$			5.46556e6i			0.849172i
$530$	4.00192e6	−	4.95111e6i	0.618840	−	0.765620i
$531$	1.16497e7			1.79299
$532$	376009.	−	264199.i	0.0575995	−	0.0404717i
$533$	1.18423e6	−	1.18423e6i	0.180559	−	0.180559i
$534$	−847060.	+	711945.i	−0.128547	+	0.108042i
$535$	134938.	−	200092.i	0.0203821	−	0.0302235i
$536$	−4.47397e6	+	2.59765e6i	−0.672637	+	0.390543i
$537$	−3.62234e6	+	3.62234e6i	−0.542067	+	0.542067i
$538$	4.50889e6	+	390775.i	0.671606	+	0.0582064i
$539$		−	8.33863e6i		−	1.23630i
$540$	−3.24249e6	+	3.36927e6i	−0.478513	+	0.497224i
$541$		−	272627.i		−	0.0400475i	−0.999800	−	0.0200238i	$-0.993626\pi$
$541$		−	272627.i		−	0.0400475i	0.999800	−	0.0200238i	$-0.00637419\pi$
$542$	1.09676e6	−	1.26548e7i	0.160366	−	1.85036i
$543$	−4.75122e6	+	4.75122e6i	−0.691522	+	0.691522i
$544$	1.01604e7	−	3.74506e6i	1.47203	−	0.542577i
$545$	−2.82531e6	+	549448.i	−0.407451	+	0.0792384i
$546$	286379.	+	340728.i	0.0411111	+	0.0489133i
$547$	−2.52658e6	+	2.52658e6i	−0.361047	+	0.361047i	−0.864198	−	0.503151i	$-0.832174\pi$
$547$	−2.52658e6	+	2.52658e6i	−0.361047	+	0.361047i	0.503151	+	0.864198i	$0.332174\pi$
$548$	−4.16120e6	+	2.92382e6i	−0.591926	+	0.415910i
$549$	1.26286e7			1.78823
$550$	−8.60739e6	+	2.64091e6i	−1.21329	+	0.372260i
$551$		−	4.11423e6i		−	0.577311i
$552$	4.19910e6	+	1.11415e6i	0.586554	+	0.155631i
$553$	−178410.	−	178410.i	−0.0248088	−	0.0248088i
$554$	−2.14733e6	−	2.55486e6i	−0.297252	−	0.353665i
$555$	2.75641e6	+	1.41737e7i	0.379849	+	1.95322i
$556$	9927.21	−	56841.6i	0.00136188	−	0.00779793i
$557$	−9.90042e6	−	9.90042e6i	−1.35212	−	1.35212i	−0.883285	−	0.468836i	$-0.844673\pi$
$557$	−9.90042e6	−	9.90042e6i	−1.35212	−	1.35212i	−0.468836	−	0.883285i	$-0.655327\pi$
$558$	−1.94470e7	−	1.68543e6i	−2.64404	−	0.229152i
$559$	−1.02708e6			−0.139019
$560$	−704668.	−	963091.i	−0.0949543	−	0.129777i
$561$	−2.31913e7			−3.11113
$562$	−6.06833e6	−	525927.i	−0.810454	−	0.0702400i
$563$	7.61172e6	+	7.61172e6i	1.01207	+	1.01207i	0.999926	+	0.0121466i	$0.00386649\pi$
$563$	7.61172e6	+	7.61172e6i	1.01207	+	1.01207i	0.0121466	+	0.999926i	$0.496134\pi$
$564$	2.36411e6	−	1.35365e7i	0.312947	−	1.79188i
$565$	1.37476e6	+	927109.i	0.181178	+	0.122183i
$566$	−3.35939e6	−	3.99695e6i	−0.440778	−	0.524430i
$567$	−316264.	−	316264.i	−0.0413135	−	0.0413135i
$568$	2.69733e6	−	1.01659e7i	0.350803	−	1.32214i
$569$			4.28630e6i			0.555011i	0.960724	+	0.277505i	$0.0895077\pi$
$569$			4.28630e6i			0.555011i	−0.960724	+	0.277505i	$0.910492\pi$
$570$	3.33552e6	−	4.12665e6i	0.430008	−	0.531999i
$571$	7.75507e6			0.995396			0.497698	−	0.867351i	$-0.334179\pi$
$571$	7.75507e6			0.995396			0.497698	+	0.867351i	$0.334179\pi$
$572$	2.06627e6	−	1.45185e6i	0.264057	−	0.185537i
$573$	5.83526e6	−	5.83526e6i	0.742461	−	0.742461i
$574$	820111.	+	975754.i	0.103895	+	0.123612i
$575$	−1.20256e6	+	2.83446e6i	−0.151683	+	0.357520i
$576$	−5.69089e6	+	9.96918e6i	−0.714701	+	1.25200i
$577$	7.36203e6	−	7.36203e6i	0.920572	−	0.920572i	−0.0764975	−	0.997070i	$-0.524374\pi$
$577$	7.36203e6	−	7.36203e6i	0.920572	−	0.920572i	0.997070	+	0.0764975i	$0.0243737\pi$
$578$	−1.01339e6	+	1.16928e7i	−0.126170	+	1.45579i
$579$			5.68637e6i			0.704918i
$580$	−1.06819e7	+	204831.i	−1.31850	+	0.0252828i
$581$			1.36671e6i			0.167971i
$582$	1.42054e7	+	1.23115e6i	1.73838	+	0.150661i
$583$	−7.25019e6	+	7.25019e6i	−0.883442	+	0.883442i
$584$	324071.	+	558152.i	0.0393195	+	0.0677205i
$585$	2.51578e6	+	1.69659e6i	0.303937	+	0.204968i
$586$	−4.78951e6	+	4.02554e6i	−0.576166	+	0.484261i
$587$	6.07649e6	−	6.07649e6i	0.727876	−	0.727876i	−0.242321	−	0.970196i	$-0.577909\pi$
$587$	6.07649e6	−	6.07649e6i	0.727876	−	0.727876i	0.970196	+	0.242321i	$0.0779085\pi$
$588$	1.04417e7	−	7.33679e6i	1.24546	−	0.875110i
$589$	6.78544e6			0.805916
$590$	1.10869e6	+	1.04575e7i	0.131123	+	1.23679i
$591$		−	4.05848e6i		−	0.477964i
$592$	4.62113e6	+	9.82627e6i	0.541930	+	1.15235i
$593$	1.10736e7	+	1.10736e7i	1.29316	+	1.29316i	0.932821	+	0.360341i	$0.117340\pi$
$593$	1.10736e7	+	1.10736e7i	1.29316	+	1.29316i	0.360341	+	0.932821i	$0.382660\pi$
$594$	5.76529e6	−	4.84567e6i	0.670432	−	0.563491i
$595$	2.13850e6	−	415882.i	0.247638	−	0.0481590i
$596$	−1.55267e7	−	2.71168e6i	−1.79045	−	0.312697i
$597$	4.13695e6	+	4.13695e6i	0.475056	+	0.475056i
$598$	74568.4	−	860397.i	0.00852711	−	0.0983888i
$599$	5.28835e6			0.602217			0.301108	−	0.953590i	$-0.402643\pi$
$599$	5.28835e6			0.602217			0.301108	+	0.953590i	$0.402643\pi$
$600$	−1.08802e7	−	8.45468e6i	−1.23384	−	0.958780i
$601$	1.35758e7			1.53313			0.766565	−	0.642167i	$-0.221964\pi$
$601$	1.35758e7			1.53313			0.766565	+	0.642167i	$0.221964\pi$
$602$	67494.6	−	778776.i	0.00759063	−	0.0875833i
$603$	7.07940e6	+	7.07940e6i	0.792873	+	0.792873i
$604$	−785982.	+	4.50041e6i	−0.0876638	+	0.501949i
$605$	5.39660e6	−	1.04949e6i	0.599420	−	0.116571i
$606$	1.02594e7	−	8.62293e6i	1.13486	−	0.953836i
$607$	−7.46791e6	−	7.46791e6i	−0.822674	−	0.822674i	0.163817	−	0.986491i	$-0.447619\pi$
$607$	−7.46791e6	−	7.46791e6i	−0.822674	−	0.822674i	−0.986491	+	0.163817i	$0.947619\pi$
$608$	1.67164e6	−	3.62331e6i	0.183393	−	0.397509i
$609$			3.03280e6i			0.331360i
$610$	1.20186e6	+	1.13362e7i	0.130776	+	1.23351i
$611$	−2.73166e6			−0.296022
$612$	−1.20479e7	−	1.71466e7i	−1.30027	−	1.85054i
$613$	−5.63189e6	+	5.63189e6i	−0.605345	+	0.605345i	−0.941726	−	0.336381i	$-0.890797\pi$
$613$	−5.63189e6	+	5.63189e6i	−0.605345	+	0.605345i	0.336381	+	0.941726i	$0.390797\pi$
$614$	2.47273e6	−	2.07830e6i	0.264701	−	0.222478i
$615$	1.22020e7	+	8.22877e6i	1.30090	+	0.877298i
$616$	965066.	+	1.66214e6i	0.102472	+	0.176489i
$617$	−402006.	+	402006.i	−0.0425128	+	0.0425128i	−0.728044	−	0.685531i	$-0.759570\pi$
$617$	−402006.	+	402006.i	−0.0425128	+	0.0425128i	0.685531	+	0.728044i	$0.259570\pi$
$618$	−1.46058e7	−	1.26585e6i	−1.53835	−	0.133325i
$619$			5.67335e6i			0.595131i	0.954701	+	0.297566i	$0.0961747\pi$
$619$			5.67335e6i			0.595131i	−0.954701	+	0.297566i	$0.903825\pi$
$620$	−337819.	−	1.76173e7i	−0.0352943	−	1.84060i
$621$		−	2.57554e6i		−	0.268003i
$622$	516857.	−	5.96368e6i	0.0535666	−	0.618071i
$623$	−118378.	+	118378.i	−0.0122194	+	0.0122194i
$624$	3.63605e6	+	1.31000e6i	0.373825	+	0.134683i
$625$	7.02237e6	−	6.78629e6i	0.719090	−	0.694917i
$626$	9.70287e6	+	1.15443e7i	0.989611	+	1.17742i
$627$	−6.04289e6	+	6.04289e6i	−0.613869	+	0.613869i
$628$	−2.76239e6	−	3.93145e6i	−0.279503	−	0.397790i
$629$	−1.98233e7			−1.99779
$630$	−1.45175e6	+	1.79608e6i	−0.145727	+	0.180291i
$631$		−	782842.i		−	0.0782710i	−0.999234	−	0.0391355i	$-0.987540\pi$
$631$		−	782842.i		−	0.0782710i	0.999234	−	0.0391355i	$-0.0124604\pi$
$632$	−2.11758e6	−	561859.i	−0.210886	−	0.0559544i
$633$	−1.54439e7	−	1.54439e7i	−1.53196	−	1.53196i
$634$	−6.22681e6	−	7.40856e6i	−0.615237	−	0.731999i
$635$	−4.71119e6	−	3.17712e6i	−0.463657	−	0.312680i
$636$	−1.54579e7	−	2.69967e6i	−1.51533	−	0.264648i
$637$	−1.79385e6	−	1.79385e6i	−0.175161	−	0.175161i
$638$	1.71430e7	+	1.48574e6i	1.66738	+	0.144508i
$639$	−2.03543e7			−1.97198
$640$	−9.49056e6	−	4.15974e6i	−0.915887	−	0.401436i
$641$	−1.77905e7			−1.71018			−0.855090	−	0.518479i	$-0.826498\pi$
$641$	−1.77905e7			−1.71018			−0.855090	+	0.518479i	$0.826498\pi$
$642$	−592648.	−	51363.3i	−0.0567491	−	0.00491830i
$643$	−1.25143e7	−	1.25143e7i	−1.19366	−	1.19366i	−0.976032	−	0.217625i	$-0.930169\pi$
$643$	−1.25143e7	−	1.25143e7i	−1.19366	−	1.19366i	−0.217625	−	0.976032i	$-0.569831\pi$
$644$	647489.	+	113082.i	0.0615202	+	0.0107443i
$645$	−1.72300e6	−	8.85980e6i	−0.163074	−	0.838542i
$646$	4.68704e6	+	5.57656e6i	0.441893	+	0.525757i
$647$	−1.29041e6	−	1.29041e6i	−0.121190	−	0.121190i	0.643911	−	0.765101i	$-0.277311\pi$
$647$	−1.29041e6	−	1.29041e6i	−0.121190	−	0.121190i	−0.765101	+	0.643911i	$0.777311\pi$
$648$	−3.75380e6	−	995996.i	−0.351183	−	0.0931795i
$649$		−	1.69370e7i		−	1.57843i
$650$	−1.28354e6	+	2.41979e6i	−0.119159	+	0.224643i
$651$	−5.00187e6			−0.462573
$652$	−3.27626e6	−	4.66279e6i	−0.301828	−	0.429563i
$653$	4.78461e6	−	4.78461e6i	0.439100	−	0.439100i	−0.452609	−	0.891709i	$-0.649507\pi$
$653$	4.78461e6	−	4.78461e6i	0.439100	−	0.439100i	0.891709	+	0.452609i	$0.149507\pi$
$654$	4.56467e6	+	5.43097e6i	0.417316	+	0.496516i
$655$	6.96585e6	−	1.35467e6i	0.634411	−	0.123376i
$656$	1.04127e7	+	3.75150e6i	0.944718	+	0.340365i
$657$	883194.	−	883194.i	0.0798257	−	0.0798257i
$658$	179511.	−	2.07126e6i	0.0161631	−	0.186496i
$659$		−	4.07985e6i		−	0.365957i	−0.983117	−	0.182979i	$-0.941426\pi$
$659$		−	4.07985e6i		−	0.365957i	0.983117	−	0.182979i	$-0.0585739\pi$
$660$	1.59902e7	+	1.53885e7i	1.42888	+	1.37511i
$661$			4.24912e6i			0.378265i	0.981952	+	0.189132i	$0.0605675\pi$
$661$			4.24912e6i			0.378265i	−0.981952	+	0.189132i	$0.939432\pi$
$662$	−2.74464e6	−	237871.i	−0.243411	−	0.0210958i
$663$	−4.98903e6	+	4.98903e6i	−0.440790	+	0.440790i
$664$	5.95880e6	+	1.02629e7i	0.524492	+	0.903338i
$665$	448858.	−	665588.i	0.0393600	−	0.0583648i
$666$	1.60867e7	−	1.35207e7i	1.40534	−	1.18118i
$667$	4.16103e6	−	4.16103e6i	0.362148	−	0.362148i
$668$	7.40855e6	+	1.05439e7i	0.642380	+	0.914239i
$669$	1.35488e6			0.117040
$670$	−5.68117e6	+	7.02866e6i	−0.488935	+	0.604902i
$671$		−	1.83602e7i		−	1.57424i
$672$	−1.23224e6	+	2.67092e6i	−0.105262	+	0.228159i
$673$	7.08151e6	+	7.08151e6i	0.602682	+	0.602682i	0.941023	−	0.338341i	$-0.109866\pi$
$673$	7.08151e6	+	7.08151e6i	0.602682	+	0.602682i	−0.338341	+	0.941023i	$0.609866\pi$
$674$	−2.29822e6	+	1.93163e6i	−0.194868	+	0.163785i
$675$	−3.19045e6	+	7.51997e6i	−0.269521	+	0.635268i
$676$	−1.91193e6	+	1.09474e7i	−0.160918	+	0.921390i
$677$	1.17428e7	+	1.17428e7i	0.984691	+	0.984691i	0.999885	−	0.0151933i	$-0.00483636\pi$
$677$	1.17428e7	+	1.17428e7i	0.984691	+	0.984691i	−0.0151933	+	0.999885i	$0.504836\pi$
$678$	352899.	−	4.07188e6i	0.0294833	−	0.340189i
$679$	2.15728e6			0.179569
$680$	1.42453e7	−	1.24468e7i	1.18140	−	1.03225i
$681$	1.28433e7			1.06123
$682$	−2.45037e6	+	2.82733e7i	−0.201730	+	2.32764i
$683$	−9.30853e6	−	9.30853e6i	−0.763536	−	0.763536i	0.213424	−	0.976960i	$-0.431538\pi$
$683$	−9.30853e6	−	9.30853e6i	−0.763536	−	0.763536i	−0.976960	+	0.213424i	$0.931538\pi$
$684$	−7.60711e6	−	1.32856e6i	−0.621698	−	0.108578i
$685$	−4.96741e6	+	7.36591e6i	−0.404486	+	0.599791i
$686$	2.99534e6	−	2.51755e6i	0.243016	−	0.204253i
$687$	6.01252e6	+	6.01252e6i	0.486032	+	0.486032i
$688$	−2.88861e6	−	6.14228e6i	−0.232658	−	0.494719i
$689$			3.11939e6i			0.250335i
$690$	7.54704e6	−	800131.i	0.603468	−	0.0639791i
$691$	9.51389e6			0.757989			0.378995	−	0.925399i	$-0.376270\pi$
$691$	9.51389e6			0.757989			0.378995	+	0.925399i	$0.376270\pi$
$692$	−6.89189e6	+	4.84251e6i	−0.547108	+	0.384419i
$693$	2.63010e6	−	2.63010e6i	0.208037	−	0.208037i
$694$	−1.71061e7	+	1.43775e7i	−1.34820	+	1.13315i
$695$	−19242.7	−	98947.5i	−0.00151113	−	0.00777039i
$696$	1.32229e7	+	2.27739e7i	1.03467	+	1.78203i
$697$	−1.42872e7	+	1.42872e7i	−1.11395	+	1.11395i
$698$	9.52529e6	+	825533.i	0.740014	+	0.0641351i
$699$			2.19896e6i			0.170226i
$700$	−1.75044e6	−	1.13225e6i	−0.135021	−	0.0873367i
$701$		−	1.03313e7i		−	0.794069i	−0.917804	−	0.397034i	$-0.870039\pi$
$701$		−	1.03313e7i		−	0.794069i	0.917804	−	0.397034i	$-0.129961\pi$
$702$	197834.	−	2.28268e6i	0.0151516	−	0.174824i
$703$	−5.16530e6	+	5.16530e6i	−0.394191	+	0.394191i
$704$	1.44938e7	+	8.27376e6i	1.10217	+	0.629175i
$705$	−4.58254e6	−	2.35638e7i	−0.347243	−	1.78555i
$706$	−3.94618e6	−	4.69510e6i	−0.297965	−	0.354514i
$707$	1.43377e6	−	1.43377e6i	0.107877	−	0.107877i
$708$	2.12087e7	−	1.49021e7i	1.59013	−	1.11728i
$709$	6.08555e6			0.454657			0.227329	−	0.973818i	$-0.427001\pi$
$709$	6.08555e6			0.454657			0.227329	+	0.973818i	$0.427001\pi$
$710$	−1.93710e6	−	1.82713e7i	−0.144214	−	1.36026i
$711$			4.23983e6i			0.314539i
$712$	−372802.	+	1.40505e6i	−0.0275599	+	0.103870i
$713$	6.86262e6	+	6.86262e6i	0.505552	+	0.505552i
$714$	−3.45504e6	−	4.11074e6i	−0.253634	−	0.301769i
$715$	2.46660e6	−	3.65760e6i	0.180440	−	0.267566i
$716$	−1.15784e6	+	6.62959e6i	−0.0844043	+	0.483286i
$717$	1.70139e7	+	1.70139e7i	1.23597	+	1.23597i
$718$	−7.86723e6	−	681833.i	−0.569522	−	0.0493590i
$719$	1.95226e7			1.40836			0.704182	−	0.710019i	$-0.251314\pi$
$719$	1.95226e7			1.40836			0.704182	+	0.710019i	$0.251314\pi$
$720$	−3.07065e6	+	1.98168e7i	−0.220750	+	1.42463i
$721$	−2.21809e6			−0.158906
$722$	−1.12803e7	−	977632.i	−0.805335	−	0.0697963i
$723$	−8.30854e6	−	8.30854e6i	−0.591125	−	0.591125i
$724$	−1.51867e6	+	8.69567e6i	−0.107676	+	0.616533i
$725$	−1.73037e7	+	6.99476e6i	−1.22263	+	0.494229i
$726$	−8.71893e6	−	1.03736e7i	−0.613934	−	0.730448i
$727$	6.97825e6	+	6.97825e6i	0.489678	+	0.489678i	0.908204	−	0.418527i	$-0.137453\pi$
$727$	6.97825e6	+	6.97825e6i	0.489678	+	0.489678i	−0.418527	+	0.908204i	$0.637453\pi$
$728$	565178.	+	149959.i	0.0395236	+	0.0104868i
$729$			2.29882e7i			1.60209i
$730$	876863.	+	708757.i	0.0609011	+	0.0492255i
$731$	1.23913e7			0.857677
$732$	2.29909e7	−	1.61543e7i	1.58591	−	1.11432i
$733$	−5.90984e6	+	5.90984e6i	−0.406271	+	0.406271i	−0.880436	−	0.474165i	$-0.842750\pi$
$733$	−5.90984e6	+	5.90984e6i	−0.406271	+	0.406271i	0.474165	+	0.880436i	$0.342750\pi$
$734$	−440282.	−	523839.i	−0.0301641	−	0.0358887i
$735$	1.24648e7	−	1.84834e7i	0.851071	−	1.26201i
$736$	5.35517e6	−	1.97387e6i	0.364401	−	0.134315i
$737$	1.02925e7	−	1.02925e7i	0.697992	−	0.697992i
$738$	1.84939e6	−	2.13390e7i	0.124994	−	1.44222i
$739$		−	1.16561e7i		−	0.785128i	−0.919725	−	0.392564i	$-0.871588\pi$
$739$		−	1.16561e7i		−	0.785128i	0.919725	−	0.392564i	$-0.128412\pi$
$740$	1.36680e7	+	1.31537e7i	0.917542	+	0.883016i
$741$			2.59995e6i			0.173948i
$742$	−2.36525e6	−	204991.i	−0.157713	−	0.0136686i
$743$	−1.06995e7	+	1.06995e7i	−0.711038	+	0.711038i	−0.966752	−	0.255714i	$-0.917689\pi$
$743$	−1.06995e7	+	1.06995e7i	−0.711038	+	0.711038i	0.255714	+	0.966752i	$0.417689\pi$
$744$	−3.75602e7	+	2.18080e7i	−2.48768	+	1.44439i
$745$	−2.70282e7	+	5.25627e6i	−1.78413	+	0.346966i
$746$	−1.29969e7	+	1.09238e7i	−0.855052	+	0.718662i
$747$	1.62396e7	−	1.62396e7i	1.06481	−	1.06481i
$748$	−2.49287e7	+	1.75159e7i	−1.62909	+	1.14467i
$749$	−90001.4			−0.00586199
$750$	−2.30268e7	−	7.01270e6i	−1.49479	−	0.455231i
$751$			1.31404e7i			0.850176i	0.905152	+	0.425088i	$0.139757\pi$
$751$			1.31404e7i			0.850176i	−0.905152	+	0.425088i	$0.860243\pi$
$752$	−7.68264e6	−	1.63362e7i	−0.495411	−	1.05343i
$753$	1.33936e7	+	1.33936e7i	0.860816	+	0.860816i
$754$	4.00750e6	−	3.36827e6i	0.256712	−	0.215763i
$755$	1.52353e6	+	7.83412e6i	0.0972710	+	0.500176i
$756$	1.71782e6	+	300012.i	0.109314	+	0.0190913i
$757$	−2.09821e7	−	2.09821e7i	−1.33079	−	1.33079i	−0.904666	−	0.426121i	$-0.859880\pi$
$757$	−2.09821e7	−	2.09821e7i	−1.33079	−	1.33079i	−0.426121	−	0.904666i	$-0.640120\pi$
$758$	1.71742e6	−	1.98162e7i	0.108568	−	1.25270i
$759$	−1.22232e7			−0.770162
$760$	468632.	−	6.95506e6i	0.0294305	−	0.436784i
$761$	2.53115e7			1.58437			0.792184	−	0.610282i	$-0.208944\pi$
$761$	2.53115e7			1.58437			0.792184	+	0.610282i	$0.208944\pi$
$762$	−1.20936e6	+	1.39540e7i	−0.0754514	+	0.870585i
$763$	758985.	+	758985.i	0.0471978	+	0.0471978i
$764$	1.86517e6	−	1.06797e7i	0.115607	−	0.661949i
$765$	−3.03519e7	−	2.04686e7i	−1.87513	−	1.26455i
$766$	1.98189e7	−	1.66576e7i	1.22041	−	1.02575i
$767$	−3.64356e6	−	3.64356e6i	−0.223634	−	0.223634i
$768$	2.39192e6	+	2.54290e7i	0.146333	+	1.55570i
$769$			6.63393e6i			0.404534i	0.979330	+	0.202267i	$0.0648308\pi$
$769$			6.63393e6i			0.404534i	−0.979330	+	0.202267i	$0.935169\pi$
$770$	2.61125e6	+	2.11064e6i	0.158716	+	0.128288i
$771$	−2.35617e7			−1.42748
$772$	4.29480e6	+	6.11237e6i	0.259358	+	0.369119i
$773$	1.93715e7	−	1.93715e7i	1.16604	−	1.16604i	0.182915	−	0.983129i	$-0.441447\pi$
$773$	1.93715e7	−	1.93715e7i	1.16604	−	1.16604i	0.983129	−	0.182915i	$-0.0585532\pi$
$774$	−1.00556e7	+	8.45164e6i	−0.603332	+	0.507094i
$775$	−1.15362e7	−	2.85383e7i	−0.689935	−	1.70677i
$776$	1.61995e7	−	9.40566e6i	0.965710	−	0.560706i
$777$	3.80759e6	−	3.80759e6i	0.226255	−	0.226255i
$778$	2.69265e7	+	2.33366e6i	1.59489	+	0.138225i
$779$			7.44556e6i			0.439596i
$780$	6.75034e6	−	129441.i	0.397273	−	0.00761789i
$781$			2.95922e7i			1.73600i
$782$	−899637.	+	1.03803e7i	−0.0526078	+	0.607008i
$783$	1.10394e7	−	1.10394e7i	0.643491	−	0.643491i
$784$	5.68269e6	−	1.57729e7i	0.330190	−	0.916475i
$785$	−6.95922e6	−	4.69315e6i	−0.403076	−	0.271825i
$786$	−1.12543e7	−	1.33901e7i	−0.649771	−	0.773087i
$787$	−1.81394e7	+	1.81394e7i	−1.04396	+	1.04396i	−0.0449752	+	0.998988i	$0.514321\pi$
$787$	−1.81394e7	+	1.81394e7i	−1.04396	+	1.04396i	−0.998988	+	0.0449752i	$0.985679\pi$
$788$	−3.06529e6	−	4.36253e6i	−0.175855	−	0.250278i
$789$	1.69264e7			0.967994
$790$	−3.80594e6	+	403502.i	−0.216967	+	0.0230026i
$791$		−	618369.i		−	0.0351404i
$792$	8.28287e6	−	3.12172e7i	0.469211	−	1.76840i
$793$	−3.94974e6	−	3.94974e6i	−0.223041	−	0.223041i
$794$	−1.46745e7	−	1.74595e7i	−0.826060	−	0.982833i
$795$	−2.69085e7	+	5.23299e6i	−1.50998	+	0.293651i
$796$	7.57144e6	+	1.32233e6i	0.423541	+	0.0739701i
$797$	1.06991e7	+	1.06991e7i	0.596624	+	0.596624i	0.939413	−	0.342789i	$-0.111372\pi$
$797$	1.06991e7	+	1.06991e7i	0.596624	+	0.596624i	−0.342789	+	0.939413i	$0.611372\pi$
$798$	−1.97139e6	−	170856.i	−0.109589	−	0.00949777i
$799$	3.29563e7			1.82630
$800$	−1.80810e7	−	870463.i	−0.998843	−	0.0480867i
$801$	2.81319e6			0.154924
$802$	1.61674e7	+	1.40119e6i	0.887572	+	0.0769236i
$803$	−1.28404e6	−	1.28404e6i	−0.0702732	−	0.0702732i
$804$	2.19442e7	+	3.83249e6i	1.19724	+	0.209094i
$805$	1.12712e6	−	219195.i	0.0613029	−	0.0119218i
$806$	5.55515e6	+	6.60942e6i	0.301202	+	0.358365i
$807$	−1.37800e7	−	1.37800e7i	−0.744842	−	0.744842i
$808$	4.51530e6	−	1.70177e7i	0.243309	−	0.917005i
$809$		−	2.83714e7i		−	1.52409i	−0.647526	−	0.762043i	$-0.724196\pi$
$809$		−	2.83714e7i		−	1.52409i	0.647526	−	0.762043i	$-0.275804\pi$
$810$	−6.74671e6	+	715280.i	−0.361309	+	0.0383057i
$811$	−1.34252e7			−0.716752			−0.358376	−	0.933577i	$-0.616669\pi$
$811$	−1.34252e7			−0.716752			−0.358376	+	0.933577i	$0.616669\pi$
$812$	2.29061e6	+	3.26000e6i	0.121916	+	0.173511i
$813$	−3.86751e7	+	3.86751e7i	−2.05213	+	2.05213i
$814$	−1.96572e7	−	2.33878e7i	−1.03983	−	1.23717i
$815$	−8.25379e6	−	5.56617e6i	−0.435271	−	0.293537i
$816$	−4.38674e7	−	1.58047e7i	−2.30630	−	0.830921i
$817$	3.22876e6	−	3.22876e6i	0.169231	−	0.169231i
$818$	−2.14102e6	+	2.47039e7i	−0.111876	+	1.29087i
$819$		−	1.13160e6i		−	0.0589500i
$820$	1.93312e7	−	370684.i	1.00398	−	0.0192517i
$821$		−	1.77101e7i		−	0.916987i	−0.888698	−	0.458494i	$-0.848389\pi$
$821$		−	1.77101e7i		−	0.916987i	0.888698	−	0.458494i	$-0.151611\pi$
$822$	2.18169e7	+	1.89082e6i	1.12620	+	0.0976046i
$823$	564216.	−	564216.i	0.0290366	−	0.0290366i	−0.692439	−	0.721476i	$-0.743464\pi$
$823$	564216.	−	564216.i	0.0290366	−	0.0290366i	0.721476	+	0.692439i	$0.243464\pi$
$824$	−1.66561e7	+	9.67079e6i	−0.854586	+	0.496185i
$825$	3.56890e7	+	1.51415e7i	1.82557	+	0.774524i
$826$	3.00214e6	−	2.52327e6i	0.153102	−	0.128681i
$827$	−444181.	+	444181.i	−0.0225838	+	0.0225838i	−0.718309	−	0.695725i	$-0.755083\pi$
$827$	−444181.	+	444181.i	−0.0225838	+	0.0225838i	0.695725	+	0.718309i	$0.255083\pi$
$828$	−6.34997e6	−	9.03730e6i	−0.321881	−	0.458103i
$829$	4.84536e6			0.244872			0.122436	−	0.992476i	$-0.460929\pi$
$829$	4.84536e6			0.244872			0.122436	+	0.992476i	$0.460929\pi$
$830$	1.61232e7	+	1.30321e7i	0.812372	+	0.656630i
$831$			1.43707e7i			0.721897i
$832$	4.89787e6	−	1.33808e6i	0.245301	−	0.0670155i
$833$	2.16420e7	+	2.16420e7i	1.08065	+	1.08065i
$834$	−190202.	+	159863.i	−0.00946892	+	0.00795853i
$835$	1.86642e7	+	1.25867e7i	0.926386	+	0.624735i
$836$	−1.93154e6	+	1.10597e7i	−0.0955844	+	0.547301i
$837$	1.82069e7	+	1.82069e7i	0.898302	+	0.898302i
$838$	893836.	−	1.03134e7i	0.0439691	−	0.507331i
$839$	−7.31295e6			−0.358664			−0.179332	−	0.983789i	$-0.557394\pi$
$839$	−7.31295e6			−0.358664			−0.179332	+	0.983789i	$0.557394\pi$
$840$	−345451.	+	5.12690e6i	−0.0168923	+	0.250701i
$841$	1.51593e7			0.739078
$842$	2.84236e6	−	3.27961e7i	0.138165	−	1.59420i
$843$	1.85459e7	+	1.85459e7i	0.898831	+	0.898831i
$844$	−2.82653e7	−	4.93645e6i	−1.36583	−	0.238539i
$845$	3.70603e6	+	1.90567e7i	0.178553	+	0.918136i
$846$	−2.67442e7	+	2.24783e7i	−1.28471	+	1.07978i
$847$	−1.44973e6	−	1.44973e6i	−0.0694349	−	0.0694349i
$848$	−1.86550e7	+	8.77312e6i	−0.890851	+	0.418952i
$849$			2.24822e7i			1.07046i
$850$	1.54854e7	−	2.91937e7i	0.735146	−	1.38593i
$851$	−1.04481e7			−0.494553
$852$	−3.70558e7	+	2.60369e7i	−1.74887	+	1.22882i
$853$	3.80964e6	−	3.80964e6i	0.179272	−	0.179272i	−0.611767	−	0.791038i	$-0.709541\pi$
$853$	3.80964e6	−	3.80964e6i	0.179272	−	0.179272i	0.791038	+	0.611767i	$0.209541\pi$
$854$	3.25441e6	−	2.73530e6i	0.152696	−	0.128340i
$855$	−1.32421e7	+	2.57524e6i	−0.619502	+	0.120477i
$856$	−675841.	+	392403.i	−0.0315254	+	0.0183041i
$857$	−9.23229e6	+	9.23229e6i	−0.429395	+	0.429395i	−0.888422	−	0.459027i	$-0.848198\pi$
$857$	−9.23229e6	+	9.23229e6i	−0.429395	+	0.429395i	0.459027	+	0.888422i	$0.348198\pi$
$858$	−1.08334e7	−	938900.i	−0.502395	−	0.0435413i
$859$			272935.i			0.0126205i	0.999980	+	0.00631024i	$0.00200863\pi$
$859$			272935.i			0.0126205i	−0.999980	+	0.00631024i	$0.997991\pi$
$860$	−8.54370e6	−	8.22221e6i	−0.393913	−	0.379090i
$861$		−	5.48848e6i		−	0.252316i
$862$	677839.	−	7.82115e6i	0.0310712	−	0.358511i
$863$	−3.16913e6	+	3.16913e6i	−0.144848	+	0.144848i	−0.775812	−	0.630964i	$-0.782660\pi$
$863$	−3.16913e6	+	3.16913e6i	−0.144848	+	0.144848i	0.630964	+	0.775812i	$0.282660\pi$
$864$	1.42076e7	−	5.23679e6i	0.647493	−	0.238661i
$865$	−8.22714e6	+	1.21996e7i	−0.373860	+	0.554377i
$866$	−5.22496e6	−	6.21657e6i	−0.236749	−	0.281680i
$867$	3.57353e7	−	3.57353e7i	1.61454	−	1.61454i
$868$	−5.37660e6	+	3.77781e6i	−0.242219	+	0.170193i
$869$	6.16412e6			0.276899
$870$	3.57782e7	+	2.89190e7i	1.60258	+	1.29535i
$871$		−	4.42833e6i		−	0.197785i
$872$	9.00854e6	+	2.39024e6i	0.401202	+	0.106451i
$873$	−2.56333e7	−	2.56333e7i	−1.13833	−	1.13833i
$874$	2.47035e6	+	2.93919e6i	0.109391	+	0.130151i
$875$	−3.56246e6	−	756222.i	−0.157300	−	0.0333910i
$876$	478124.	−	2.73766e6i	0.0210514	−	0.120537i
$877$	8.13844e6	+	8.13844e6i	0.357308	+	0.357308i	0.862820	−	0.505512i	$-0.168696\pi$
$877$	8.13844e6	+	8.13844e6i	0.357308	+	0.357308i	−0.505512	+	0.862820i	$0.668696\pi$
$878$	−1.71676e7	−	1.48787e6i	−0.751577	−	0.0651373i
$879$	2.69403e7			1.17606
$880$	2.88108e7	+	4.46430e6i	1.25415	+	0.194333i
$881$	−1.39725e7			−0.606504			−0.303252	−	0.952910i	$-0.598072\pi$
$881$	−1.39725e7			−0.606504			−0.303252	+	0.952910i	$0.598072\pi$
$882$	−3.23238e7	−	2.80142e6i	−1.39911	−	0.121257i
$883$	−4.80471e6	−	4.80471e6i	−0.207379	−	0.207379i	0.595773	−	0.803153i	$-0.296846\pi$
$883$	−4.80471e6	−	4.80471e6i	−0.207379	−	0.207379i	−0.803153	+	0.595773i	$0.796846\pi$
$884$	−1.59468e6	+	9.13090e6i	−0.0686347	+	0.392991i
$885$	2.53178e7	−	3.75424e7i	1.08659	−	1.61125i
$886$	2.27044e7	+	2.70133e7i	0.971687	+	1.15610i
$887$	962500.	+	962500.i	0.0410763	+	0.0410763i	0.727347	−	0.686270i	$-0.240753\pi$
$887$	962500.	+	962500.i	0.0410763	+	0.0410763i	−0.686270	+	0.727347i	$0.740753\pi$
$888$	1.19911e7	−	4.51930e7i	0.510300	−	1.92326i
$889$			2.11910e6i			0.0899283i
$890$	267730.	+	2.52530e6i	0.0113298	+	0.106865i
$891$	1.09270e7			0.461113
$892$	1.45638e6	−	1.02331e6i	0.0612862	−	0.0430621i
$893$	8.58733e6	−	8.58733e6i	0.360354	−	0.360354i
$894$	4.36677e7	+	5.19550e7i	1.82733	+	2.17412i
$895$	2.24432e6	+	1.15405e7i	0.0936543	+	0.481579i
$896$	692728.	+	3.80170e6i	0.0288266	+	0.158200i
$897$	−2.62952e6	+	2.62952e6i	−0.109118	+	0.109118i
$898$	2.95046e6	−	3.40435e7i	0.122095	−	1.40878i
$899$			5.88299e7i			2.42772i
$900$	7.34547e6	+	3.42528e7i	0.302283	+	1.40958i
$901$		−	3.76342e7i		−	1.54444i
$902$	−3.10238e7	−	2.68876e6i	−1.26964	−	0.110036i
$903$	−2.38007e6	+	2.38007e6i	−0.0971340	+	0.0971340i
$904$	−2.69607e6	−	4.64347e6i	−0.109726	−	0.188982i
$905$	2.94375e6	+	1.51371e7i	0.119476	+	0.614356i
$906$	1.50592e7	−	1.26571e7i	0.609509	−	0.512286i
$907$	−3.07745e7	+	3.07745e7i	−1.24215	+	1.24215i	−0.283038	+	0.959109i	$0.591342\pi$
$907$	−3.07745e7	+	3.07745e7i	−1.24215	+	1.24215i	−0.959109	+	0.283038i	$0.908658\pi$
$908$	1.38055e7	−	9.70029e6i	0.555696	−	0.390454i
$909$	−3.40728e7			−1.36772
$910$	1.01580e6	−	107694.i	0.0406633	−	0.00431109i
$911$		−	3.26334e7i		−	1.30277i	−0.758749	−	0.651383i	$-0.774189\pi$
$911$		−	3.26334e7i		−	1.30277i	0.758749	−	0.651383i	$-0.225811\pi$
$912$	−1.55486e7	+	7.31221e6i	−0.619017	+	0.291113i
$913$	−2.36101e7	−	2.36101e7i	−0.937390	−	0.937390i
$914$	−1.93845e7	+	1.62925e7i	−0.767521	+	0.645093i
$915$	2.74453e7	−	4.06972e7i	1.08371	−	1.60698i
$916$	1.10041e7	+	1.92183e6i	0.433327	+	0.0756791i
$917$	−1.87129e6	−	1.87129e6i	−0.0734881	−	0.0734881i
$918$	−2.38679e6	+	2.75396e7i	−0.0934774	+	1.07858i
$919$	−1.37192e7			−0.535845			−0.267923	−	0.963440i	$-0.586337\pi$
$919$	−1.37192e7			−0.535845			−0.267923	+	0.963440i	$0.586337\pi$
$920$	7.50812e6	−	6.56020e6i	0.292457	−	0.255533i
$921$	−1.39087e7			−0.540305
$922$	2.84000e6	−	3.27690e7i	0.110025	−	1.26951i
$923$	6.36602e6	+	6.36602e6i	0.245960	+	0.245960i
$924$	1.42383e6	−	8.15261e6i	0.0548627	−	0.314135i
$925$	3.05060e7	+	1.29426e7i	1.17228	+	0.497355i
$926$	−1.42840e7	+	1.20056e7i	−0.547422	+	0.460103i
$927$	2.63559e7	+	2.63559e7i	1.00735	+	1.00735i
$928$	3.14142e7	+	1.44931e7i	1.19745	+	0.552449i
$929$		−	5.06594e7i		−	1.92584i	−0.269782	−	0.962922i	$-0.586952\pi$
$929$		−	5.06594e7i		−	1.92584i	0.269782	−	0.962922i	$-0.413048\pi$
$930$	−4.76950e7	+	5.90075e7i	−1.80828	+	2.23717i
$931$	1.12784e7			0.426454
$932$	1.66083e6	+	2.36370e6i	0.0626305	+	0.0891361i
$933$	−1.82260e7	+	1.82260e7i	−0.685469	+	0.685469i
$934$	2.42470e7	−	2.03794e7i	0.909476	−	0.764405i
$935$	−2.97585e7	+	4.41274e7i	−1.11322	+	1.65074i
$936$	−4.93374e6	−	8.49745e6i	−0.184072	−	0.317029i
$937$	−7.26923e6	+	7.26923e6i	−0.270483	+	0.270483i	−0.829294	−	0.558812i	$-0.811257\pi$
$937$	−7.26923e6	+	7.26923e6i	−0.270483	+	0.270483i	0.558812	+	0.829294i	$0.311257\pi$
$938$	3.35774e6	+	291007.i	0.124606	+	0.0107993i
$939$		−	6.49351e7i		−	2.40334i
$940$	−2.27231e7	−	2.18681e7i	−0.838780	−	0.807217i
$941$		−	795711.i		−	0.0292942i	−0.999893	−	0.0146471i	$-0.995338\pi$
$941$		−	795711.i		−	0.0292942i	0.999893	−	0.0146471i	$-0.00466248\pi$
$942$	−1.78642e6	+	2.06124e7i	−0.0655929	+	0.756834i
$943$	−7.53025e6	+	7.53025e6i	−0.275759	+	0.275759i
$944$	1.15424e7	−	3.20370e7i	0.421566	−	1.17010i
$945$	2.99031e6	−	581537.i	0.108927	−	0.0211835i
$946$	1.22875e7	+	1.46195e7i	0.446412	+	0.531133i
$947$	4.02780e6	−	4.02780e6i	0.145946	−	0.145946i	−0.630358	−	0.776304i	$-0.717092\pi$
$947$	4.02780e6	−	4.02780e6i	0.145946	−	0.145946i	0.776304	+	0.630358i	$0.217092\pi$
$948$	5.42353e6	+	7.71879e6i	0.196002	+	0.278951i
$949$	−552458.			−0.0199129
$950$	−3.57195e6	−	1.16419e7i	−0.128409	−	0.418518i
$951$			4.16720e7i			1.49415i
$952$	−6.81864e6	−	1.80919e6i	−0.243840	−	0.0646982i
$953$	−2.67453e7	−	2.67453e7i	−0.953929	−	0.953929i	0.0450557	−	0.998984i	$-0.485653\pi$
$953$	−2.67453e7	−	2.67453e7i	−0.953929	−	0.953929i	−0.998984	+	0.0450557i	$0.985653\pi$
$954$	2.56688e7	+	3.05403e7i	0.913135	+	1.08643i
$955$	−3.61540e6	−	1.85907e7i	−0.128277	−	0.659610i
$956$	3.11389e7	+	5.43830e6i	1.10194	+	0.192450i
$957$	−5.23920e7	−	5.23920e7i	−1.84920	−	1.84920i
$958$	4.79542e7	+	4.15607e6i	1.68816	+	0.146308i
$959$	3.31319e6			0.116332
$960$	1.97591e7	+	4.00052e7i	0.691971	+	1.40100i
$961$	−6.83967e7			−2.38906
$962$	−9.26006e6	−	802546.i	−0.322609	−	0.0279597i
$963$	1.06942e6	+	1.06942e6i	0.0371606	+	0.0371606i
$964$	−1.52063e7	−	2.65572e6i	−0.527023	−	0.0920429i
$965$	1.08198e7	+	7.29660e6i	0.374024	+	0.252233i
$966$	−1.82102e6	−	2.16661e6i	−0.0627872	−	0.0747031i
$967$	6.46334e6	+	6.46334e6i	0.222275	+	0.222275i	0.809456	−	0.587181i	$-0.199762\pi$
$967$	6.46334e6	+	6.46334e6i	0.222275	+	0.222275i	−0.587181	+	0.809456i	$0.699762\pi$
$968$	−1.72071e7	−	4.56557e6i	−0.590228	−	0.156605i
$969$		−	3.13673e7i		−	1.07317i
$970$	2.05706e7	−	2.54496e7i	0.701968	−	0.868463i
$971$	8.63113e6			0.293778			0.146889	−	0.989153i	$-0.453074\pi$
$971$	8.63113e6			0.293778			0.146889	+	0.989153i	$0.453074\pi$
$972$	2.13001e7	+	3.03145e7i	0.723130	+	1.02916i
$973$	−26581.0	+	26581.0i	−0.000900097	+	0.000900097i
$974$	−1.35694e6	−	1.61447e6i	−0.0458316	−	0.0545296i
$975$	1.09349e7	−	4.42027e6i	0.368386	−	0.148915i
$976$	1.25123e7	−	3.47291e7i	0.420449	−	1.16700i
$977$	7.17562e6	−	7.17562e6i	0.240504	−	0.240504i	−0.576554	−	0.817059i	$-0.695603\pi$
$977$	7.17562e6	−	7.17562e6i	0.240504	−	0.240504i	0.817059	+	0.576554i	$0.195603\pi$
$978$	−2.11874e6	+	2.44467e7i	−0.0708320	+	0.817285i
$979$		−	4.08998e6i		−	0.136384i
$980$	−561503.	−	2.92825e7i	−0.0186761	−	0.973963i
$981$		−	1.80369e7i		−	0.598398i
$982$	1.99675e7	+	1.73053e6i	0.660762	+	0.0572665i
$983$	−3.06048e7	+	3.06048e7i	−1.01020	+	1.01020i	−0.0102486	+	0.999947i	$0.503262\pi$
$983$	−3.06048e7	+	3.06048e7i	−1.01020	+	1.01020i	−0.999947	+	0.0102486i	$0.996738\pi$
$984$	−2.39296e7	−	4.12142e7i	−0.787857	−	1.35694i
$985$	−7.72229e6	−	5.20774e6i	−0.253604	−	0.171025i
$986$	−4.83489e7	+	4.06367e7i	−1.58378	+	1.33115i
$987$	−6.33013e6	+	6.33013e6i	−0.206833	+	0.206833i
$988$	1.96369e6	+	2.79473e6i	0.0640000	+	0.0910852i
$989$	6.53097e6			0.212318
$990$	−5.94839e6	−	5.61067e7i	−0.192891	−	1.81940i
$991$			873414.i			0.0282511i	0.999900	+	0.0141256i	$0.00449646\pi$
$991$			873414.i			0.0282511i	−0.999900	+	0.0141256i	$0.995504\pi$
$992$	−2.39029e7	+	5.18102e7i	−0.771209	+	1.67161i
$993$	8.38810e6	+	8.38810e6i	0.269954	+	0.269954i
$994$	−5.24533e6	+	4.40864e6i	−0.168386	+	0.141527i
$995$	1.31800e7	−	2.56317e6i	0.422045	−	0.0820766i
$996$	8.79142e6	−	5.03383e7i	0.280809	−	1.60787i
$997$	−2.43412e7	−	2.43412e7i	−0.775539	−	0.775539i	0.203530	−	0.979069i	$-0.434759\pi$
$997$	−2.43412e7	−	2.43412e7i	−0.775539	−	0.775539i	−0.979069	+	0.203530i	$0.934759\pi$
$998$	−2.75037e6	+	3.17347e7i	−0.0874107	+	1.00858i
$999$	−2.77194e7			−0.878758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.k.a.3.2	✓	56
4.3	odd	2		160.6.o.a.143.4		56
5.2	odd	4	inner	40.6.k.a.27.16	yes	56
8.3	odd	2	inner	40.6.k.a.3.16	yes	56
8.5	even	2		160.6.o.a.143.3		56
20.7	even	4		160.6.o.a.47.3		56
40.27	even	4	inner	40.6.k.a.27.2	yes	56
40.37	odd	4		160.6.o.a.47.4		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.2	✓	56	1.1	even	1	trivial
40.6.k.a.3.16	yes	56	8.3	odd	2	inner
40.6.k.a.27.2	yes	56	40.27	even	4	inner
40.6.k.a.27.16	yes	56	5.2	odd	4	inner
160.6.o.a.47.3		56	20.7	even	4
160.6.o.a.47.4		56	40.37	odd	4
160.6.o.a.143.3		56	8.5	even	2
160.6.o.a.143.4		56	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.63573 - 0.488434i) q^{2} +(17.2238 + 17.2238i) q^{3} +(31.5229 + 5.50537i) q^{4} +(54.8737 - 10.6715i) q^{5} +(-88.6558 - 105.481i) q^{6} +(-14.7411 - 14.7411i) q^{7} +(-174.965 - 46.4236i) q^{8} +350.316i q^{9} +O(q^{10})\)	\(q+(-5.63573 - 0.488434i) q^{2} +(17.2238 + 17.2238i) q^{3} +(31.5229 + 5.50537i) q^{4} +(54.8737 - 10.6715i) q^{5} +(-88.6558 - 105.481i) q^{6} +(-14.7411 - 14.7411i) q^{7} +(-174.965 - 46.4236i) q^{8} +350.316i q^{9} +(-314.465 + 33.3393i) q^{10} +509.310 q^{11} +(448.119 + 637.765i) q^{12} +(109.565 - 109.565i) q^{13} +(75.8769 + 90.2770i) q^{14} +(1128.93 + 761.328i) q^{15} +(963.382 + 347.090i) q^{16} +(-1321.86 + 1321.86i) q^{17} +(171.106 - 1974.29i) q^{18} +688.865i q^{19} +(1788.53 - 34.2957i) q^{20} -507.795i q^{21} +(-2870.33 - 248.765i) q^{22} +(-696.700 + 696.700i) q^{23} +(-2213.97 - 3813.15i) q^{24} +(2897.24 - 1171.17i) q^{25} +(-670.995 + 563.965i) q^{26} +(-1848.38 + 1848.38i) q^{27} +(-383.527 - 545.838i) q^{28} -5972.48 q^{29} +(-5990.51 - 4842.05i) q^{30} -9850.17i q^{31} +(-5259.83 - 2426.65i) q^{32} +(8772.24 + 8772.24i) q^{33} +(8095.28 - 6804.00i) q^{34} +(-966.209 - 651.590i) q^{35} +(-1928.62 + 11043.0i) q^{36} +(7498.27 + 7498.27i) q^{37} +(336.465 - 3882.26i) q^{38} +3774.25 q^{39} +(-10096.4 - 680.296i) q^{40} +10808.4 q^{41} +(-248.025 + 2861.80i) q^{42} +(-4687.08 - 4687.08i) q^{43} +(16054.9 + 2803.94i) q^{44} +(3738.39 + 19223.1i) q^{45} +(4266.71 - 3586.12i) q^{46} +(-12465.9 - 12465.9i) q^{47} +(10614.9 + 22571.3i) q^{48} -16372.4i q^{49} +(-16900.1 + 5185.26i) q^{50} -45534.8 q^{51} +(4057.01 - 2850.61i) q^{52} +(-14235.3 + 14235.3i) q^{53} +(11319.8 - 9514.17i) q^{54} +(27947.7 - 5435.09i) q^{55} +(1894.85 + 3263.52i) q^{56} +(-11864.9 + 11864.9i) q^{57} +(33659.3 + 2917.16i) q^{58} -33254.7i q^{59} +(31395.8 + 30214.4i) q^{60} -36049.2i q^{61} +(-4811.16 + 55512.9i) q^{62} +(5164.05 - 5164.05i) q^{63} +(28457.7 + 16245.0i) q^{64} +(4843.02 - 7181.47i) q^{65} +(-45153.3 - 53722.6i) q^{66} +(20208.6 - 20208.6i) q^{67} +(-48946.1 + 34391.5i) q^{68} -23999.6 q^{69} +(5127.03 + 4144.11i) q^{70} +58102.6i q^{71} +(16262.9 - 61293.1i) q^{72} +(-2521.14 - 2521.14i) q^{73} +(-38595.8 - 45920.6i) q^{74} +(70073.2 + 29729.5i) q^{75} +(-3792.46 + 21715.0i) q^{76} +(-7507.80 - 7507.80i) q^{77} +(-21270.7 - 1843.47i) q^{78} +12102.9 q^{79} +(56568.3 + 8765.39i) q^{80} +21454.5 q^{81} +(-60913.5 - 5279.22i) q^{82} +(-46356.9 - 46356.9i) q^{83} +(2795.60 - 16007.2i) q^{84} +(-58429.1 + 86641.4i) q^{85} +(24125.8 + 28704.4i) q^{86} +(-102869. - 102869. i) q^{87} +(-89111.6 - 23644.0i) q^{88} -8030.44i q^{89} +(-11679.3 - 110162. i) q^{90} -3230.23 q^{91} +(-25797.6 + 18126.4i) q^{92} +(169657. - 169657. i) q^{93} +(64165.7 + 76343.2i) q^{94} +(7351.21 + 37800.6i) q^{95} +(-48797.9 - 132390. i) q^{96} +(-73172.1 + 73172.1i) q^{97} +(-7996.84 + 92270.4i) q^{98} +178419. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8}+O(q^{10}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8	\( 56 q - 2 q^{2} - 4 q^{3} + 176 q^{6} + 244 q^{8} - 570 q^{10} - 8 q^{11} - 308 q^{12} + 456 q^{16} - 408 q^{17} + 3370 q^{18} + 1360 q^{20} - 3148 q^{22} - 3120 q^{25} - 5084 q^{26} + 968 q^{27} - 10020 q^{28} + 21100 q^{30} + 7968 q^{32} - 976 q^{33} - 4780 q^{35} + 23132 q^{36} - 49524 q^{38} - 58980 q^{40} - 8 q^{41} + 42060 q^{42} + 1308 q^{43} + 42416 q^{46} + 93776 q^{48} - 94010 q^{50} + 20872 q^{51} - 67180 q^{52} - 43384 q^{56} + 968 q^{57} + 86100 q^{58} + 118180 q^{60} + 6240 q^{62} + 17680 q^{65} - 41128 q^{66} + 89252 q^{67} - 158164 q^{68} + 116980 q^{70} + 1180 q^{72} - 25184 q^{73} - 127740 q^{75} + 41592 q^{76} - 161440 q^{78} - 167360 q^{80} - 67792 q^{81} + 23412 q^{82} - 126444 q^{83} - 192704 q^{86} + 100176 q^{88} - 82330 q^{90} + 329432 q^{91} + 226020 q^{92} + 358176 q^{96} + 212576 q^{97} + 65834 q^{98}+O(q^{100}) \) 56 * q - 2 * q^2 - 4 * q^3 + 176 * q^6 + 244 * q^8 - 570 * q^10 - 8 * q^11 - 308 * q^12 + 456 * q^16 - 408 * q^17 + 3370 * q^18 + 1360 * q^20 - 3148 * q^22 - 3120 * q^25 - 5084 * q^26 + 968 * q^27 - 10020 * q^28 + 21100 * q^30 + 7968 * q^32 - 976 * q^33 - 4780 * q^35 + 23132 * q^36 - 49524 * q^38 - 58980 * q^40 - 8 * q^41 + 42060 * q^42 + 1308 * q^43 + 42416 * q^46 + 93776 * q^48 - 94010 * q^50 + 20872 * q^51 - 67180 * q^52 - 43384 * q^56 + 968 * q^57 + 86100 * q^58 + 118180 * q^60 + 6240 * q^62 + 17680 * q^65 - 41128 * q^66 + 89252 * q^67 - 158164 * q^68 + 116980 * q^70 + 1180 * q^72 - 25184 * q^73 - 127740 * q^75 + 41592 * q^76 - 161440 * q^78 - 167360 * q^80 - 67792 * q^81 + 23412 * q^82 - 126444 * q^83 - 192704 * q^86 + 100176 * q^88 - 82330 * q^90 + 329432 * q^91 + 226020 * q^92 + 358176 * q^96 + 212576 * q^97 + 65834 * q^98

Introduction

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