LMFDB - Embedded newform 40.6.k.a.3.16

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			3.16
Character	$\chi$	$=$	40.3
Dual form			40.6.k.a.27.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.488434 + 5.63573i) q^{2} +(17.2238 + 17.2238i) q^{3} +(-31.5229 + 5.50537i) q^{4} +(-54.8737 + 10.6715i) q^{5} +(-88.6558 + 105.481i) q^{6} +(14.7411 + 14.7411i) q^{7} +(-46.4236 - 174.965i) q^{8} +350.316i q^{9} +O(q^{10})$	\(q+(0.488434 + 5.63573i) 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} +(-46.4236 - 174.965i) q^{8} +350.316i q^{9} +(-86.9437 - 304.041i) q^{10} +509.310 q^{11} +(-637.765 - 448.119i) 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} +(-1974.29 + 171.106i) q^{18} +688.865i q^{19} +(1671.02 - 638.495i) q^{20} +507.795i q^{21} +(248.765 + 2870.33i) 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} +(-545.838 - 383.527i) q^{28} +5972.48 q^{29} +(3739.23 - 6734.22i) q^{30} +9850.17i q^{31} +(2426.65 + 5259.83i) 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} +(-3882.26 + 336.465i) q^{38} -3774.25 q^{39} +(4414.57 + 9105.58i) q^{40} +10808.4 q^{41} +(-2861.80 + 248.025i) 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} +(22571.3 + 10614.9i) q^{48} -16372.4i q^{49} +(8015.48 + 15756.0i) q^{50} -45534.8 q^{51} +(2850.61 - 4057.01i) 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} +(2917.16 + 33659.3i) q^{58} -33254.7i q^{59} +(39778.6 + 17784.0i) q^{60} +36049.2i q^{61} +(-55512.9 + 4811.16i) 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} +(34391.5 - 48946.1i) q^{68} +23999.6 q^{69} +(3200.26 - 5763.55i) q^{70} -58102.6i q^{71} +(61293.1 - 16262.9i) 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} +(-1843.47 - 21270.7i) q^{78} -12102.9 q^{79} +(-49160.3 + 29326.8i) q^{80} +21454.5 q^{81} +(5279.22 + 60913.5i) 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} +(-23644.0 - 89111.6i) q^{88} -8030.44i q^{89} +(106510. - 30457.8i) q^{90} -3230.23 q^{91} +(-18126.4 + 25797.6i) 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} +(92270.4 - 7996.84i) 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 $

$2$	0.488434	+	5.63573i	0.0863438	+	0.996265i
$2$	0.488434	+	5.63573i	0.0863438	+	0.996265i
$3$	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	0.761671	−	0.647964i	$-0.224379\pi$
$7$	14.7411	+	14.7411i	0.113707	+	0.113707i	−0.647964	+	0.761671i	$0.724379\pi$
$8$	−46.4236	−	174.965i	−0.256457	−	0.966556i
$9$			350.316i			1.44163i
$10$	−86.9437	−	304.041i	−0.274940	−	0.961461i
$11$	509.310			1.26911			0.634557	−	0.772876i	$-0.281183\pi$
$11$	509.310			1.26911			0.634557	+	0.772876i	$0.281183\pi$
$12$	−637.765	−	448.119i	−1.27852	−	0.898339i
$13$	−109.565	+	109.565i	−0.179810	+	0.179810i	−0.791273	−	0.611463i	$-0.790581\pi$
$13$	−109.565	+	109.565i	−0.179810	+	0.179810i	0.611463	+	0.791273i	$0.290581\pi$
$14$	−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	$0.962962\pi$
$18$	−1974.29	+	171.106i	−1.43625	+	0.124476i
$19$			688.865i			0.437774i	0.975750	+	0.218887i	$0.0702427\pi$
$19$			688.865i			0.437774i	−0.975750	+	0.218887i	$0.929757\pi$
$20$	1671.02	−	638.495i	0.934131	−	0.356930i
$21$			507.795i			0.251270i
$22$	248.765	+	2870.33i	0.109580	+	1.26437i
$23$	696.700	−	696.700i	0.274616	−	0.274616i	−0.556339	−	0.830955i	$-0.687794\pi$
$23$	696.700	−	696.700i	0.274616	−	0.274616i	0.830955	+	0.556339i	$0.187794\pi$
$24$	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
$28$	−545.838	−	383.527i	−0.131574	−	0.0924488i
$29$	5972.48			1.31874			0.659371	−	0.751818i	$-0.270823\pi$
$29$	5972.48			1.31874			0.659371	+	0.751818i	$0.270823\pi$
$30$	3739.23	−	6734.22i	0.758541	−	1.36611i
$31$			9850.17i			1.84094i	0.390813	+	0.920470i	$0.372194\pi$
$31$			9850.17i			1.84094i	−0.390813	+	0.920470i	$0.627806\pi$
$32$	2426.65	+	5259.83i	0.418922	+	0.908022i
$33$	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	0.0950301	−	0.995474i	$-0.469705\pi$
$37$	−7498.27	−	7498.27i	−0.900444	−	0.900444i	−0.995474	+	0.0950301i	$0.969705\pi$
$38$	−3882.26	+	336.465i	−0.436139	+	0.0377991i
$39$	−3774.25			−0.397346
$40$	4414.57	+	9105.58i	0.436253	+	0.899824i
$41$	10808.4			1.00416			0.502081	−	0.864821i	$-0.332568\pi$
$41$	10808.4			1.00416			0.502081	+	0.864821i	$0.332568\pi$
$42$	−2861.80	+	248.025i	−0.250331	+	0.0216956i
$43$	−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	0.986559	−	0.163408i	$-0.0522488\pi$
$47$	12465.9	+	12465.9i	0.823150	+	0.823150i	−0.163408	+	0.986559i	$0.552249\pi$
$48$	22571.3	+	10614.9i	1.41401	+	0.664984i
$49$		−	16372.4i		−	0.974142i
$50$	8015.48	+	15756.0i	0.453424	+	0.891295i
$51$	−45534.8			−2.45142
$52$	2850.61	−	4057.01i	0.146194	−	0.208064i
$53$	14235.3	−	14235.3i	0.696109	−	0.696109i	−0.267460	−	0.963569i	$-0.586184\pi$
$53$	14235.3	−	14235.3i	0.696109	−	0.696109i	0.963569	+	0.267460i	$0.0861842\pi$
$54$	−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
$58$	2917.16	+	33659.3i	0.113865	+	1.31382i
$59$		−	33254.7i		−	1.24372i	−0.783127	−	0.621861i	$-0.786377\pi$
$59$		−	33254.7i		−	1.24372i	0.783127	−	0.621861i	$-0.213623\pi$
$60$	39778.6	+	17784.0i	1.42650	+	0.637753i
$61$			36049.2i			1.24043i	0.784433	+	0.620213i	$0.212954\pi$
$61$			36049.2i			1.24043i	−0.784433	+	0.620213i	$0.787046\pi$
$62$	−55512.9	+	4811.16i	−1.83406	+	0.158954i
$63$	−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	$0.122856\pi$
$68$	34391.5	−	48946.1i	0.901941	−	1.28365i
$69$	23999.6			0.606850
$70$	3200.26	−	5763.55i	0.0780620	−	0.140587i
$71$		−	58102.6i		−	1.36788i	−0.729536	−	0.683942i	$-0.760264\pi$
$71$		−	58102.6i		−	1.36788i	0.729536	−	0.683942i	$-0.239736\pi$
$72$	61293.1	−	16262.9i	1.39342	−	0.369715i
$73$	−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
$78$	−1843.47	−	21270.7i	−0.0343084	−	0.395862i
$79$	−12102.9			−0.218183			−0.109091	−	0.994032i	$-0.534794\pi$
$79$	−12102.9			−0.218183			−0.109091	+	0.994032i	$0.534794\pi$
$80$	−49160.3	+	29326.8i	−0.858796	+	0.512318i
$81$	21454.5			0.363334
$82$	5279.22	+	60913.5i	0.0867031	+	1.00041i
$83$	−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
$88$	−23644.0	−	89111.6i	−0.325473	−	1.22667i
$89$		−	8030.44i		−	0.107464i	−0.998555	−	0.0537322i	$-0.982888\pi$
$89$		−	8030.44i		−	0.107464i	0.998555	−	0.0537322i	$-0.0171117\pi$
$90$	106510.	−	30457.8i	1.38607	−	0.396362i
$91$	−3230.23			−0.0408912
$92$	−18126.4	+	25797.6i	−0.223276	+	0.317767i
$93$	−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	$0.438563\pi$
$98$	92270.4	−	7996.84i	0.970504	−	0.0841111i
$99$			178419.i			1.82959i
$100$	−84881.6	+	52868.9i	−0.848816	+	0.528689i
$101$		−	97263.1i		−	0.948735i	−0.880327	−	0.474367i	$-0.842677\pi$
$101$		−	97263.1i		−	0.948735i	0.880327	−	0.474367i	$-0.157323\pi$
$102$	−22240.7	−	256622.i	−0.211665	−	2.44226i
$103$	−75234.6	+	75234.6i	−0.698755	+	0.698755i	−0.964142	−	0.265387i	$-0.914500\pi$
$103$	−75234.6	+	75234.6i	−0.698755	+	0.698755i	0.265387	+	0.964142i	$0.414500\pi$
$104$	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	$0.244198\pi$
$108$	48090.3	−	68442.4i	0.396733	−	0.564632i
$109$	51487.6			0.415084			0.207542	−	0.978226i	$-0.433454\pi$
$109$	51487.6			0.415084			0.207542	+	0.978226i	$0.433454\pi$
$110$	−44281.3	−	154851.i	−0.348930	−	1.22020i
$111$		−	258297.i		−	1.98981i
$112$	19317.8	+	9084.84i	0.145517	+	0.0684340i
$113$	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
$118$	187415.	−	16242.8i	1.23908	−	0.107388i
$119$	−38971.4			−0.252277
$120$	−80796.8	+	232868.i	−0.512202	+	1.47624i
$121$	98345.8			0.610650
$122$	−203163.	+	17607.7i	−1.23579	+	0.107103i
$123$	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	0.876621	−	0.481181i	$-0.159792\pi$
$127$	71877.1	+	71877.1i	0.395440	+	0.395440i	−0.481181	+	0.876621i	$0.659792\pi$
$128$	−105452.	−	152445.i	−0.568894	−	0.822411i
$129$		−	161458.i		−	0.854251i
$130$	42838.3	+	23786.3i	0.222318	+	0.123444i
$131$	126943.			0.646296			0.323148	−	0.946348i	$-0.395259\pi$
$131$	126943.			0.646296			0.323148	+	0.946348i	$0.395259\pi$
$132$	−324820.	−	228232.i	−1.62259	−	1.14009i
$133$	−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	$0.367809\pi$
$138$	11722.2	+	135255.i	0.0523977	+	0.604584i
$139$		−	1803.19i		−	0.00791597i	−0.999992	−	0.00395798i	$-0.998740\pi$
$139$		−	1803.19i		−	0.00791597i	0.999992	−	0.00395798i	$-0.00125987\pi$
$140$	34044.9	+	15220.7i	0.146802	+	0.0656316i
$141$			429419.i			1.81901i
$142$	327450.	−	28379.3i	1.36278	−	0.118108i
$143$	−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
$148$	277648.	+	195086.i	1.04193	+	0.732103i
$149$	492553.			1.81755			0.908777	−	0.417282i	$-0.137017\pi$
$149$	492553.			1.81755			0.908777	+	0.417282i	$0.137017\pi$
$150$	−133321.	+	409435.i	−0.483805	+	1.48579i
$151$		−	142766.i		−	0.509547i	−0.967001	−	0.254773i	$-0.917999\pi$
$151$		−	142766.i		−	0.509547i	0.967001	−	0.254773i	$-0.0820008\pi$
$152$	120527.	−	31979.6i	0.423133	−	0.112270i
$153$	−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	0.857784	−	0.514011i	$-0.171841\pi$
$157$	106174.	+	106174.i	0.343772	+	0.343772i	−0.514011	+	0.857784i	$0.671841\pi$
$158$	−5911.46	−	68208.5i	−0.0188387	−	0.217368i
$159$	490372.			1.53827
$160$	−189289.	−	262730.i	−0.584556	−	0.811353i
$161$	20540.3			0.0624514
$162$	10479.1	+	120912.i	0.0313717	+	0.361977i
$163$	−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	0.191418	−	0.981509i	$-0.438691\pi$
$167$	−284753.	−	284753.i	−0.790090	−	0.790090i	−0.981509	+	0.191418i	$0.938691\pi$
$168$	88846.5	−	23573.7i	0.242866	−	0.0644398i
$169$			347284.i			0.935337i
$170$	516826.	+	286972.i	1.37158	+	0.761582i
$171$	−241320.			−0.631108
$172$	173554.	+	121946.i	0.447315	+	0.314301i
$173$	186125.	−	186125.i	0.472813	−	0.472813i	−0.430010	−	0.902824i	$-0.641490\pi$
$173$	186125.	−	186125.i	0.472813	−	0.472813i	0.902824	+	0.430010i	$0.141490\pi$
$174$	−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
$178$	45257.4	−	3922.34i	0.107063	−	0.00927888i
$179$			210311.i			0.490601i	0.969447	+	0.245300i	$0.0788866\pi$
$179$			210311.i			0.490601i	−0.969447	+	0.245300i	$0.921113\pi$
$180$	223675.	+	585387.i	0.514560	+	1.34667i
$181$		−	275853.i		−	0.625865i	−0.949775	−	0.312933i	$-0.898689\pi$
$181$		−	275853.i		−	0.625865i	0.949775	−	0.312933i	$-0.101311\pi$
$182$	−1577.76	−	18204.7i	−0.00353070	−	0.0407385i
$183$	−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
$188$	−461590.	−	324332.i	−0.952494	−	0.669260i
$189$	−54494.5			−0.110968
$190$	209443.	−	59892.5i	0.420903	−	0.120362i
$191$			338791.i			0.671968i	0.941868	+	0.335984i	$0.109069\pi$
$191$			338791.i			0.671968i	−0.941868	+	0.335984i	$0.890931\pi$
$192$	−769949.	−	210348.i	−1.50733	−	0.411799i
$193$	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	0.806934	−	0.590642i	$-0.201125\pi$
$197$	117816.	+	117816.i	0.216292	+	0.216292i	−0.590642	+	0.806934i	$0.701125\pi$
$198$	−1.00552e6	+	87146.2i	−1.82276	+	0.157974i
$199$	−240189.			−0.429952			−0.214976	−	0.976619i	$-0.568967\pi$
$199$	−240189.			−0.429952			−0.214976	+	0.976619i	$0.568967\pi$
$200$	−339414.	−	452547.i	−0.600004	−	0.799997i
$201$	696137.			1.21536
$202$	548148.	−	47506.6i	0.945191	−	0.0819173i
$203$	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
$208$	−67524.2	+	143582.i	−0.108218	+	0.230114i
$209$			350846.i			0.555585i
$210$	154390.	−	44149.6i	0.241586	−	0.0690842i
$211$	−896662.			−1.38651			−0.693254	−	0.720693i	$-0.743824\pi$
$211$	−896662.			−1.38651			−0.693254	+	0.720693i	$0.743824\pi$
$212$	−370367.	+	527109.i	−0.565970	+	0.805491i
$213$	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
$218$	25148.3	+	290170.i	0.0358400	+	0.413534i
$219$		−	86846.9i		−	0.122361i
$220$	851070.	−	325192.i	1.18552	−	0.452984i
$221$		−	289660.i		−	0.398940i
$222$	1.45569e6	−	126161.i	1.98238	−	0.171808i
$223$	−39331.6	+	39331.6i	−0.0529639	+	0.0529639i	−0.733093	−	0.680129i	$-0.761924\pi$
$223$	−39331.6	+	39331.6i	−0.0529639	+	0.0529639i	0.680129	+	0.733093i	$0.261924\pi$
$224$	−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	$0.139716\pi$
$228$	308694.	−	439334.i	0.393270	−	0.559704i
$229$	−349083.			−0.439886			−0.219943	−	0.975513i	$-0.570587\pi$
$229$	−349083.			−0.439886			−0.219943	+	0.975513i	$0.570587\pi$
$230$	−272399.	−	151252.i	−0.339536	−	0.188530i
$231$			258625.i			0.318890i
$232$	−277264.	−	1.04498e6i	−0.338200	−	1.27464i
$233$	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
$238$	−19035.0	−	219632.i	−0.0217826	−	0.251335i
$239$	−987818.			−1.11862			−0.559310	−	0.828959i	$-0.688934\pi$
$239$	−987818.			−1.11862			−0.559310	+	0.828959i	$0.688934\pi$
$240$	−1.35184e6	−	341608.i	−1.51495	−	0.382825i
$241$	−482388.			−0.535000			−0.267500	−	0.963558i	$-0.586198\pi$
$241$	−482388.			−0.535000			−0.267500	+	0.963558i	$0.586198\pi$
$242$	48035.5	+	554250.i	0.0527259	+	0.608370i
$243$	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
$248$	1.72344e6	−	457280.i	1.77937	−	0.472121i
$249$		−	1.59688e6i		−	1.63220i
$250$	−607979.	−	779053.i	−0.615231	−	0.788347i
$251$	777624.			0.779086			0.389543	−	0.921008i	$-0.372633\pi$
$251$	777624.			0.779086			0.389543	+	0.921008i	$0.372633\pi$
$252$	134356.	−	191216.i	0.133277	−	0.189680i
$253$	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	$0.400995\pi$
$258$	909934.	−	78861.7i	0.851061	−	0.0737593i
$259$		−	221066.i		−	0.204773i
$260$	−113129.	+	253043.i	−0.103787	+	0.232146i
$261$			2.09225e6i			1.90114i
$262$	62003.5	+	715418.i	0.0558037	+	0.643883i
$263$	−491368.	+	491368.i	−0.438044	+	0.438044i	−0.891353	−	0.453309i	$-0.850243\pi$
$263$	−491368.	+	491368.i	−0.438044	+	0.438044i	0.453309	+	0.891353i	$0.350243\pi$
$264$	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
$268$	−525778.	+	748290.i	−0.447162	+	0.636404i
$269$	800055.			0.674123			0.337062	−	0.941483i	$-0.390567\pi$
$269$	800055.			0.674123			0.337062	+	0.941483i	$0.390567\pi$
$270$	722689.	+	401279.i	0.603312	+	0.334994i
$271$		−	2.24545e6i		−	1.85729i	−0.370966	−	0.928646i	$-0.620973\pi$
$271$		−	2.24545e6i		−	1.85729i	0.370966	−	0.928646i	$-0.379027\pi$
$272$	−814651.	+	1.73226e6i	−0.667651	+	1.41968i
$273$	−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	0.524644	−	0.851322i	$-0.324199\pi$
$277$	−417176.	−	417176.i	−0.326678	−	0.326678i	−0.851322	+	0.524644i	$0.824199\pi$
$278$	10162.3	−	880.739i	0.00788640	−	0.000683495i
$279$	−3.45067e6			−2.65395
$280$	−69150.7	+	199302.i	−0.0527111	+	0.151921i
$281$	1.07676e6			0.813492			0.406746	−	0.913541i	$-0.366663\pi$
$281$	1.07676e6			0.813492			0.406746	+	0.913541i	$0.366663\pi$
$282$	−2.42009e6	+	209743.i	−1.81221	+	0.157060i
$283$	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
$288$	−1.84260e6	+	850095.i	−1.30903	+	0.603929i
$289$		−	2.07477e6i		−	1.46125i
$290$	−519269.	−	1.81588e6i	−0.362575	−	1.26792i
$291$	−2.52060e6			−1.74490
$292$	93353.2	+	65593.7i	0.0640726	+	0.0450199i
$293$	−782068.	+	782068.i	−0.532201	+	0.532201i	−0.921227	−	0.389026i	$-0.872812\pi$
$293$	−782068.	+	782068.i	−0.532201	+	0.532201i	0.389026	+	0.921227i	$0.372812\pi$
$294$	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
$298$	240580.	+	2.77590e6i	0.156935	+	1.81077i
$299$			152668.i			0.0987577i
$300$	−2.37258e6	−	551380.i	−1.52201	−	0.353710i
$301$		−	138186.i		−	0.0879116i
$302$	804593.	−	69732.0i	0.507644	−	0.0439962i
$303$	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	$0.305310\pi$
$308$	−278001.	−	195334.i	−0.166982	−	0.117328i
$309$	−2.59165e6			−1.54411
$310$	2.99485e6	−	856410.i	1.76999	−	0.506148i
$311$		−	1.05819e6i		−	0.620387i	−0.950673	−	0.310194i	$-0.899606\pi$
$311$		−	1.05819e6i		−	0.620387i	0.950673	−	0.310194i	$-0.100394\pi$
$312$	175214.	+	660363.i	0.101902	+	0.384057i
$313$	−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	0.282982	−	0.959125i	$-0.408676\pi$
$317$	−1.20973e6	−	1.20973e6i	−0.676143	−	0.676143i	−0.959125	+	0.282982i	$0.908676\pi$
$318$	239514.	+	2.76360e6i	0.132820	+	1.53252i
$319$	3.04184e6			1.67363
$320$	1.38822e6	−	1.19511e6i	0.757850	−	0.652429i
$321$	105159.			0.0569619
$322$	10032.6	+	115760.i	0.00539229	+	0.0622181i
$323$	−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
$328$	−501767.	−	1.89110e6i	−0.257524	−	0.970578i
$329$			367523.i			0.187195i
$330$	1.90443e6	−	3.42981e6i	0.962674	−	1.73374i
$331$	487007.			0.244324			0.122162	−	0.992510i	$-0.461017\pi$
$331$	487007.			0.244324			0.122162	+	0.992510i	$0.461017\pi$
$332$	1.71652e6	+	1.20609e6i	0.854678	+	0.600531i
$333$	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	$0.209376\pi$
$338$	−1.95720e6	+	169625.i	−0.931843	+	0.0807605i
$339$			722511.i			0.341464i
$340$	−1.36486e6	+	3.05286e6i	−0.640310	+	1.43222i
$341$			5.01679e6i			2.33636i
$342$	−117869.	−	1.36002e6i	−0.0544923	−	0.628751i
$343$	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	$-0.0928436\pi$
$348$	−3.80904e6	−	2.67638e6i	−1.68604	−	1.18468i
$349$	1.69016e6			0.742788			0.371394	−	0.928475i	$-0.378880\pi$
$349$	1.69016e6			0.742788			0.371394	+	0.928475i	$0.378880\pi$
$350$	−114104.	+	350419.i	−0.0497888	+	0.152903i
$351$		−	405037.i		−	0.175480i
$352$	1.23592e6	+	2.67888e6i	0.531659	+	1.15238i
$353$	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
$358$	−1.18525e6	+	102723.i	−0.488769	+	0.0423604i
$359$	−1.39596e6			−0.571657			−0.285829	−	0.958281i	$-0.592269\pi$
$359$	−1.39596e6			−0.571657			−0.285829	+	0.958281i	$0.592269\pi$
$360$	−3.18983e6	+	1.54649e6i	−1.29721	+	0.628915i
$361$	2.00156e6			0.808354
$362$	1.55463e6	−	134736.i	0.623528	−	0.0540396i
$363$	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	0.690337	−	0.723488i	$-0.257462\pi$
$367$	−85536.5	−	85536.5i	−0.0331502	−	0.0331502i	−0.723488	+	0.690337i	$0.757462\pi$
$368$	429371.	−	913006.i	0.165277	−	0.351442i
$369$			3.78637e6i			1.44763i
$370$	−1.62785e6	+	2.93171e6i	−0.618174	+	1.11331i
$371$	419689.			0.158304
$372$	4.41405e6	−	6.28210e6i	1.65379	−	2.35368i
$373$	−2.12223e6	+	2.12223e6i	−0.789807	+	0.789807i	−0.981462	−	0.191656i	$-0.938614\pi$
$373$	−2.12223e6	+	2.12223e6i	−0.789807	+	0.789807i	0.191656	+	0.981462i	$0.438614\pi$
$374$	−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
$378$	−26617.0	−	307116.i	−0.00958141	−	0.110554i
$379$			3.51617e6i			1.25740i	0.777650	+	0.628698i	$0.216412\pi$
$379$			3.51617e6i			1.25740i	−0.777650	+	0.628698i	$0.783588\pi$
$380$	439837.	+	1.15111e6i	0.156255	+	0.408939i
$381$			2.47599e6i			0.873848i
$382$	−1.90933e6	+	165477.i	−0.669458	+	0.0580203i
$383$	3.23618e6	−	3.23618e6i	1.12729	−	1.12729i	0.136674	−	0.990616i	$-0.456359\pi$
$383$	3.23618e6	−	3.23618e6i	1.12729	−	1.12729i	0.990616	−	0.136674i	$-0.0436413\pi$
$384$	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
$388$	1.90375e6	−	2.70943e6i	0.641995	−	0.913690i
$389$	4.77783e6			1.60087			0.800436	−	0.599418i	$-0.204601\pi$
$389$	4.77783e6			1.60087			0.800436	+	0.599418i	$0.204601\pi$
$390$	328147.	+	1.14753e6i	0.109246	+	0.382033i
$391$			1.84188e6i			0.609283i
$392$	−2.86460e6	+	760066.i	−0.941562	+	0.249825i
$393$	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	0.0882604	−	0.996097i	$-0.471869\pi$
$397$	−2.85091e6	−	2.85091e6i	−0.907837	−	0.907837i	−0.996097	+	0.0882604i	$0.971869\pi$
$398$	−117316.	−	1.35364e6i	−0.0371237	−	0.428346i
$399$	−349802.			−0.109999
$400$	2.38465e6	−	2.13388e6i	0.745203	−	0.666838i
$401$	−2.86873e6			−0.890899			−0.445450	−	0.895307i	$-0.646956\pi$
$401$	−2.86873e6			−0.890899			−0.445450	+	0.895307i	$0.646956\pi$
$402$	340017.	+	3.92324e6i	0.104939	+	1.21082i
$403$	−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
$408$	2.11389e6	+	7.96700e6i	0.628683	+	2.36943i
$409$		−	4.38344e6i		−	1.29571i	−0.761765	−	0.647854i	$-0.775667\pi$
$409$		−	4.38344e6i		−	1.29571i	0.761765	−	0.647854i	$-0.224333\pi$
$410$	−939726.	−	3.28621e6i	−0.276084	−	0.965462i
$411$	−3.87118e6			−1.13042
$412$	1.95742e6	−	2.78581e6i	0.568120	−	0.808551i
$413$	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
$418$	−1.97727e6	+	171365.i	−0.553511	+	0.0479714i
$419$			1.83000e6i			0.509233i	0.967042	+	0.254617i	$0.0819493\pi$
$419$			1.83000e6i			0.509233i	−0.967042	+	0.254617i	$0.918051\pi$
$420$	324225.	+	848538.i	0.0896856	+	0.234719i
$421$		−	5.81932e6i		−	1.60017i	−0.599884	−	0.800087i	$-0.704787\pi$
$421$		−	5.81932e6i		−	1.60017i	0.599884	−	0.800087i	$-0.295213\pi$
$422$	−437960.	−	5.05334e6i	−0.119716	−	1.38133i
$423$	−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
$428$	−79424.5	+	113037.i	−0.0209578	+	0.0298272i
$429$	−1.92226e6			−0.504278
$430$	−1.01755e6	+	1.83257e6i	−0.265390	+	0.477959i
$431$		−	1.38778e6i		−	0.359855i	−0.983680	−	0.179927i	$-0.942414\pi$
$431$		−	1.38778e6i		−	0.359855i	0.983680	−	0.179927i	$-0.0575863\pi$
$432$	−1.13914e6	+	2.42225e6i	−0.293677	+	0.624468i
$433$	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
$438$	489446.	−	42419.0i	0.121904	−	0.0105651i
$439$	−3.04621e6			−0.754394			−0.377197	−	0.926133i	$-0.623112\pi$
$439$	−3.04621e6			−0.754394			−0.377197	+	0.926133i	$0.623112\pi$
$440$	2.24839e6	+	4.63756e6i	0.553655	+	1.14198i
$441$	5.73551e6			1.40435
$442$	1.63244e6	−	141480.i	0.397450	−	0.0344460i
$443$	−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
$448$	−658969.	−	180028.i	−0.155121	−	0.0423785i
$449$			6.04065e6i			1.41406i	0.707183	+	0.707030i	$0.249965\pi$
$449$			6.04065e6i			1.41406i	−0.707183	+	0.707030i	$0.750035\pi$
$450$	−5.51958e6	+	2.80795e6i	−1.28492	+	0.653670i
$451$	5.50485e6			1.27440
$452$	−776640.	−	545698.i	−0.178803	−	0.125634i
$453$	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	$0.0828529\pi$
$458$	−170504.	−	1.96734e6i	−0.0379814	−	0.438243i
$459$		−	4.88660e6i		−	1.08262i
$460$	719364.	−	1.60904e6i	0.158509	−	0.354546i
$461$		−	5.81450e6i		−	1.27427i	−0.770754	−	0.637133i	$-0.780120\pi$
$461$		−	5.81450e6i		−	1.27427i	0.770754	−	0.637133i	$-0.219880\pi$
$462$	−1.45754e6	+	126321.i	−0.317699	+	0.0275342i
$463$	−2.33240e6	+	2.33240e6i	−0.505651	+	0.505651i	−0.913188	−	0.407538i	$-0.866388\pi$
$463$	−2.33240e6	+	2.33240e6i	−0.505651	+	0.505651i	0.407538	+	0.913188i	$0.366388\pi$
$464$	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	$0.452462\pi$
$468$	1.42123e6	+	998615.i	0.299951	+	0.210758i
$469$	595796.			0.125074
$470$	2.70631e6	−	4.87397e6i	0.565110	−	1.01774i
$471$			3.65745e6i			0.759672i
$472$	−5.81842e6	+	1.54380e6i	−1.20213	+	0.318961i
$473$	−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
$478$	−482484.	−	5.56707e6i	−0.0965858	−	1.11444i
$479$	8.50896e6			1.69448			0.847242	−	0.531206i	$-0.178261\pi$
$479$	8.50896e6			1.69448			0.847242	+	0.531206i	$0.178261\pi$
$480$	1.26492e6	−	7.78548e6i	0.250589	−	1.54235i
$481$	1.64310e6			0.323818
$482$	−235615.	−	2.71861e6i	−0.0461940	−	0.533002i
$483$	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	0.681474	−	0.731843i	$-0.261339\pi$
$487$	−263623.	−	263623.i	−0.0503687	−	0.0503687i	−0.731843	+	0.681474i	$0.761339\pi$
$488$	6.30736e6	−	1.67353e6i	1.19894	−	0.318115i
$489$		−	4.33781e6i		−	0.820349i
$490$	−4.97788e6	+	1.42348e6i	−0.936600	+	0.267831i
$491$	−3.54302e6			−0.663238			−0.331619	−	0.943413i	$-0.607595\pi$
$491$	−3.54302e6			−0.663238			−0.331619	+	0.943413i	$0.607595\pi$
$492$	−6.89325e6	−	4.84347e6i	−1.28384	−	0.902078i
$493$	−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
$498$	8.99959e6	−	779972.i	1.62611	−	0.140931i
$499$		−	5.63099e6i		−	1.01236i	−0.862429	−	0.506178i	$-0.831058\pi$
$499$		−	5.63099e6i		−	1.01236i	0.862429	−	0.506178i	$-0.168942\pi$
$500$	4.09358e6	−	3.80692e6i	0.732281	−	0.681003i
$501$		−	9.80903e6i		−	1.74595i
$502$	379818.	+	4.38248e6i	0.0672693	+	0.776177i
$503$	−7.50633e6	+	7.50633e6i	−1.32284	+	1.32284i	−0.411376	+	0.911466i	$0.634952\pi$
$503$	−7.50633e6	+	7.50633e6i	−1.32284	+	1.32284i	−0.911466	+	0.411376i	$0.865048\pi$
$504$	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
$508$	−2.66148e6	−	1.87006e6i	−0.457577	−	0.321512i
$509$	−720493.			−0.123264			−0.0616318	−	0.998099i	$-0.519630\pi$
$509$	−720493.			−0.123264			−0.0616318	+	0.998099i	$0.519630\pi$
$510$	3.95896e6	+	1.38444e7i	0.673994	+	2.35695i
$511$		−	74328.8i		−	0.0125923i
$512$	4.16343e6	+	4.22496e6i	0.701901	+	0.712274i
$513$	−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
$518$	1.24587e6	−	107976.i	0.204008	−	0.0176809i
$519$	6.41155e6			1.04483
$520$	−1.48134e6	−	513972.i	−0.240240	−	0.0833548i
$521$	−8.81132e6			−1.42215			−0.711077	−	0.703114i	$-0.751792\pi$
$521$	−8.81132e6			−1.42215			−0.711077	+	0.703114i	$0.751792\pi$
$522$	−1.17914e7	+	1.02193e6i	−1.89404	+	0.164151i
$523$	−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
$528$	1.14958e7	+	5.40626e6i	1.79454	+	0.843941i
$529$			5.46556e6i			0.849172i
$530$	−5.56579e6	−	3.09045e6i	−0.860671	−	0.477894i
$531$	1.16497e7			1.79299
$532$	264199.	−	376009.i	0.0404717	−	0.0575995i
$533$	−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
$538$	390775.	+	4.50889e6i	0.0582064	+	0.671606i
$539$		−	8.33863e6i		−	1.23630i
$540$	−1.90851e6	+	4.26888e6i	−0.281650	+	0.629984i
$541$			272627.i			0.0400475i	0.999800	+	0.0200238i	$0.00637419\pi$
$541$			272627.i			0.0400475i	−0.999800	+	0.0200238i	$0.993626\pi$
$542$	1.26548e7	−	1.09676e6i	1.85036	−	0.160366i
$543$	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	$0.332174\pi$
$548$	2.92382e6	−	4.16120e6i	0.415910	−	0.591926i
$549$	−1.26286e7			−1.78823
$550$	4.08237e6	+	8.02470e6i	0.575447	+	1.13115i
$551$			4.11423e6i			0.577311i
$552$	−1.11415e6	−	4.19910e6i	−0.155631	−	0.586554i
$553$	−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	$0.155327\pi$
$557$	9.90042e6	+	9.90042e6i	1.35212	+	1.35212i	0.468836	+	0.883285i	$0.344673\pi$
$558$	−1.68543e6	−	1.94470e7i	−0.229152	−	2.64404i
$559$	1.02708e6			0.139019
$560$	−1.15699e6	−	292369.i	−0.155905	−	0.0393968i
$561$	−2.31913e7			−3.11113
$562$	525927.	+	6.06833e6i	0.0702400	+	0.810454i
$563$	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
$568$	−1.01659e7	+	2.69733e6i	−1.32214	+	0.350803i
$569$			4.28630e6i			0.555011i	0.960724	+	0.277505i	$0.0895077\pi$
$569$			4.28630e6i			0.555011i	−0.960724	+	0.277505i	$0.910492\pi$
$570$	4.63897e6	+	2.57582e6i	0.598046	+	0.332070i
$571$	7.75507e6			0.995396			0.497698	−	0.867351i	$-0.334179\pi$
$571$	7.75507e6			0.995396			0.497698	+	0.867351i	$0.334179\pi$
$572$	1.45185e6	−	2.06627e6i	0.185537	−	0.264057i
$573$	−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	$0.0243737\pi$
$578$	1.16928e7	−	1.01339e6i	1.45579	−	0.126170i
$579$			5.68637e6i			0.704918i
$580$	9.98016e6	−	3.81340e6i	1.23188	−	0.470698i
$581$		−	1.36671e6i		−	0.167971i
$582$	−1.23115e6	−	1.42054e7i	−0.150661	−	1.73838i
$583$	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	$0.0779085\pi$
$588$	−7.33679e6	+	1.04417e7i	−0.875110	+	1.24546i
$589$	−6.78544e6			−0.805916
$590$	−1.01108e7	+	2.89129e6i	−1.19579	+	0.341949i
$591$			4.05848e6i			0.477964i
$592$	−9.82627e6	−	4.62113e6i	−1.15235	−	0.541930i
$593$	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
$598$	−860397.	+	74568.4i	−0.0983888	+	0.00852711i
$599$	−5.28835e6			−0.602217			−0.301108	−	0.953590i	$-0.597357\pi$
$599$	−5.28835e6			−0.602217			−0.301108	+	0.953590i	$0.597357\pi$
$600$	1.94858e6	−	1.36405e7i	0.220973	−	1.54687i
$601$	1.35758e7			1.53313			0.766565	−	0.642167i	$-0.221964\pi$
$601$	1.35758e7			1.53313			0.766565	+	0.642167i	$0.221964\pi$
$602$	778776.	−	67494.6i	0.0875833	−	0.00759063i
$603$	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	0.986491	−	0.163817i	$-0.0523807\pi$
$607$	7.46791e6	+	7.46791e6i	0.822674	+	0.822674i	−0.163817	+	0.986491i	$0.552381\pi$
$608$	−3.62331e6	+	1.67164e6i	−0.397509	+	0.183393i
$609$			3.03280e6i			0.331360i
$610$	1.09604e7	−	3.13425e6i	1.19262	−	0.341043i
$611$	−2.73166e6			−0.296022
$612$	1.71466e7	+	1.20479e7i	1.85054	+	1.30027i
$613$	5.63189e6	−	5.63189e6i	0.605345	−	0.605345i	−0.336381	−	0.941726i	$-0.609203\pi$
$613$	5.63189e6	−	5.63189e6i	0.605345	−	0.605345i	0.941726	+	0.336381i	$0.109203\pi$
$614$	−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	$0.259570\pi$
$618$	−1.26585e6	−	1.46058e7i	−0.133325	−	1.53835i
$619$			5.67335e6i			0.595131i	0.954701	+	0.297566i	$0.0961747\pi$
$619$			5.67335e6i			0.595131i	−0.954701	+	0.297566i	$0.903825\pi$
$620$	6.28929e6	+	1.64599e7i	0.657086	+	1.71968i
$621$			2.57554e6i			0.268003i
$622$	5.96368e6	−	516857.i	0.618071	−	0.0535666i
$623$	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
$628$	−3.93145e6	−	2.76239e6i	−0.397790	−	0.279503i
$629$	1.98233e7			1.99779
$630$	2.01906e6	+	1.12110e6i	0.202674	+	0.112536i
$631$			782842.i			0.0782710i	0.999234	+	0.0391355i	$0.0124604\pi$
$631$			782842.i			0.0782710i	−0.999234	+	0.0391355i	$0.987540\pi$
$632$	561859.	+	2.11758e6i	0.0559544	+	0.210886i
$633$	−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
$638$	1.48574e6	+	1.71430e7i	0.144508	+	1.66738i
$639$	2.03543e7			1.97198
$640$	7.41337e6	+	7.23990e6i	0.715428	+	0.698687i
$641$	−1.77905e7			−1.71018			−0.855090	−	0.518479i	$-0.826498\pi$
$641$	−1.77905e7			−1.71018			−0.855090	+	0.518479i	$0.826498\pi$
$642$	51363.3	+	592648.i	0.00491830	+	0.0567491i
$643$	−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	0.765101	−	0.643911i	$-0.222689\pi$
$647$	1.29041e6	+	1.29041e6i	0.121190	+	0.121190i	−0.643911	+	0.765101i	$0.722689\pi$
$648$	−995996.	−	3.75380e6i	−0.0931795	−	0.351183i
$649$		−	1.69370e7i		−	1.57843i
$650$	−2.60453e6	−	848093.i	−0.241794	−	0.0787336i
$651$	−5.00187e6			−0.462573
$652$	4.66279e6	+	3.27626e6i	0.429563	+	0.301828i
$653$	−4.78461e6	+	4.78461e6i	−0.439100	+	0.439100i	−0.891709	−	0.452609i	$-0.850493\pi$
$653$	−4.78461e6	+	4.78461e6i	−0.439100	+	0.439100i	0.452609	+	0.891709i	$0.350493\pi$
$654$	−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
$658$	−2.07126e6	+	179511.i	−0.186496	+	0.0161631i
$659$		−	4.07985e6i		−	0.365957i	−0.983117	−	0.182979i	$-0.941426\pi$
$659$		−	4.07985e6i		−	0.365957i	0.983117	−	0.182979i	$-0.0585739\pi$
$660$	2.02597e7	+	9.05760e6i	1.81039	+	0.809381i
$661$		−	4.24912e6i		−	0.378265i	−0.981952	−	0.189132i	$-0.939432\pi$
$661$		−	4.24912e6i		−	0.378265i	0.981952	−	0.189132i	$-0.0605675\pi$
$662$	237871.	+	2.74464e6i	0.0210958	+	0.243411i
$663$	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
$668$	1.05439e7	+	7.40855e6i	0.914239	+	0.642380i
$669$	−1.35488e6			−0.117040
$670$	−7.90126e6	−	4.38723e6i	−0.680001	−	0.377575i
$671$			1.83602e7i			1.57424i
$672$	−2.67092e6	+	1.23224e6i	−0.228159	+	0.105262i
$673$	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	0.0151933	−	0.999885i	$-0.495164\pi$
$677$	−1.17428e7	−	1.17428e7i	−0.984691	−	0.984691i	−0.999885	+	0.0151933i	$0.995164\pi$
$678$	−4.07188e6	+	352899.i	−0.340189	+	0.0294833i
$679$	−2.15728e6			−0.179569
$680$	−1.78717e7	−	6.20085e6i	−1.48216	−	0.514256i
$681$	1.28433e7			1.06123
$682$	−2.82733e7	+	2.45037e6i	−2.32764	+	0.201730i
$683$	−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
$688$	−6.14228e6	−	2.88861e6i	−0.494719	−	0.232658i
$689$			3.11939e6i			0.250335i
$690$	−2.08661e6	−	7.29686e6i	−0.166847	−	0.583463i
$691$	9.51389e6			0.757989			0.378995	−	0.925399i	$-0.376270\pi$
$691$	9.51389e6			0.757989			0.378995	+	0.925399i	$0.376270\pi$
$692$	−4.84251e6	+	6.89189e6i	−0.384419	+	0.547108i
$693$	−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
$698$	825533.	+	9.52529e6i	0.0641351	+	0.740014i
$699$			2.19896e6i			0.170226i
$700$	−2.03060e6	−	471904.i	−0.156631	−	0.0364006i
$701$			1.03313e7i			0.794069i	0.917804	+	0.397034i	$0.129961\pi$
$701$			1.03313e7i			0.794069i	−0.917804	+	0.397034i	$0.870039\pi$
$702$	2.28268e6	−	197834.i	0.174824	−	0.0151516i
$703$	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
$708$	−1.49021e7	+	2.12087e7i	−1.11728	+	1.59013i
$709$	−6.08555e6			−0.454657			−0.227329	−	0.973818i	$-0.572999\pi$
$709$	−6.08555e6			−0.454657			−0.227329	+	0.973818i	$0.572999\pi$
$710$	−1.76656e7	+	5.05165e6i	−1.31517	+	0.376086i
$711$		−	4.23983e6i		−	0.314539i
$712$	−1.40505e6	+	372802.i	−0.103870	+	0.0275599i
$713$	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
$718$	−681833.	−	7.86723e6i	−0.0493590	−	0.569522i
$719$	−1.95226e7			−1.40836			−0.704182	−	0.710019i	$-0.748686\pi$
$719$	−1.95226e7			−1.40836			−0.704182	+	0.710019i	$0.748686\pi$
$720$	−1.02736e7	−	1.72216e7i	−0.738573	−	1.23807i
$721$	−2.21809e6			−0.158906
$722$	977632.	+	1.12803e7i	0.0697963	+	0.805335i
$723$	−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	0.418527	−	0.908204i	$-0.362547\pi$
$727$	−6.97825e6	−	6.97825e6i	−0.489678	−	0.489678i	−0.908204	+	0.418527i	$0.862547\pi$
$728$	149959.	+	565178.i	0.0104868	+	0.0395236i
$729$			2.29882e7i			1.60209i
$730$	−547332.	+	985726.i	−0.0380140	+	0.0684619i
$731$	1.23913e7			0.857677
$732$	1.61543e7	−	2.29909e7i	1.11432	−	1.58591i
$733$	5.90984e6	−	5.90984e6i	0.406271	−	0.406271i	−0.474165	−	0.880436i	$-0.657250\pi$
$733$	5.90984e6	−	5.90984e6i	0.406271	−	0.406271i	0.880436	+	0.474165i	$0.157250\pi$
$734$	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
$738$	−2.13390e7	+	1.84939e6i	−1.44222	+	0.124994i
$739$		−	1.16561e7i		−	0.785128i	−0.919725	−	0.392564i	$-0.871588\pi$
$739$		−	1.16561e7i		−	0.785128i	0.919725	−	0.392564i	$-0.128412\pi$
$740$	−1.73174e7	−	7.74219e6i	−1.16253	−	0.519738i
$741$		−	2.59995e6i		−	0.173948i
$742$	204991.	+	2.36525e6i	0.0136686	+	0.157713i
$743$	1.06995e7	−	1.06995e7i	0.711038	−	0.711038i	−0.255714	−	0.966752i	$-0.582311\pi$
$743$	1.06995e7	−	1.06995e7i	0.711038	−	0.711038i	0.966752	+	0.255714i	$0.0823106\pi$
$744$	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
$748$	1.75159e7	−	2.49287e7i	1.14467	−	1.62909i
$749$	90001.4			0.00586199
$750$	2.94655e6	−	2.38899e7i	0.191276	−	1.55082i
$751$		−	1.31404e7i		−	0.850176i	−0.905152	−	0.425088i	$-0.860243\pi$
$751$		−	1.31404e7i		−	0.850176i	0.905152	−	0.425088i	$-0.139757\pi$
$752$	1.63362e7	+	7.68264e6i	1.05343	+	0.495411i
$753$	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	$0.140120\pi$
$757$	2.09821e7	+	2.09821e7i	1.33079	+	1.33079i	0.426121	+	0.904666i	$0.359880\pi$
$758$	−1.98162e7	+	1.71742e6i	−1.25270	+	0.108568i
$759$	1.22232e7			0.770162
$760$	−6.27252e6	+	3.04104e6i	−0.393920	+	0.190980i
$761$	2.53115e7			1.58437			0.792184	−	0.610282i	$-0.208944\pi$
$761$	2.53115e7			1.58437			0.792184	+	0.610282i	$0.208944\pi$
$762$	−1.39540e7	+	1.20936e6i	−0.870585	+	0.0754514i
$763$	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
$768$	2.54290e7	+	2.39192e6i	1.55570	+	0.146333i
$769$			6.63393e6i			0.404534i	0.979330	+	0.202267i	$0.0648308\pi$
$769$			6.63393e6i			0.404534i	−0.979330	+	0.202267i	$0.935169\pi$
$770$	1.62992e6	−	2.93544e6i	0.0990695	−	0.178421i
$771$	−2.35617e7			−1.42748
$772$	−6.11237e6	−	4.29480e6i	−0.369119	−	0.259358i
$773$	−1.93715e7	+	1.93715e7i	−1.16604	+	1.16604i	−0.182915	+	0.983129i	$0.558553\pi$
$773$	−1.93715e7	+	1.93715e7i	−1.16604	+	1.16604i	−0.983129	+	0.182915i	$0.941447\pi$
$774$	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
$778$	2.33366e6	+	2.69265e7i	0.138225	+	1.59489i
$779$			7.44556e6i			0.439596i
$780$	−6.30687e6	+	2.40984e6i	−0.371174	+	0.141825i
$781$		−	2.95922e7i		−	1.73600i
$782$	−1.03803e7	+	899637.i	−0.607008	+	0.0526078i
$783$	−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	$0.985679\pi$
$788$	−4.36253e6	−	3.06529e6i	−0.250278	−	0.175855i
$789$	−1.69264e7			−0.967994
$790$	1.05227e6	+	3.67977e6i	0.0599873	+	0.209774i
$791$			618369.i			0.0351404i
$792$	3.12172e7	−	8.28287e6i	1.76840	−	0.469211i
$793$	−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	0.342789	−	0.939413i	$-0.388628\pi$
$797$	−1.06991e7	−	1.06991e7i	−0.596624	−	0.596624i	−0.939413	+	0.342789i	$0.888628\pi$
$798$	−170856.	−	1.97139e6i	−0.00949777	−	0.109589i
$799$	−3.29563e7			−1.82630
$800$	1.31907e7	+	1.23970e7i	0.728691	+	0.684842i
$801$	2.81319e6			0.154924
$802$	−1.40119e6	−	1.61674e7i	−0.0769236	−	0.887572i
$803$	−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
$808$	−1.70177e7	+	4.51530e6i	−0.917005	+	0.243309i
$809$		−	2.83714e7i		−	1.52409i	−0.647526	−	0.762043i	$-0.724196\pi$
$809$		−	2.83714e7i		−	1.52409i	0.647526	−	0.762043i	$-0.275804\pi$
$810$	−1.86534e6	−	6.52305e6i	−0.0998952	−	0.349332i
$811$	−1.34252e7			−0.716752			−0.358376	−	0.933577i	$-0.616669\pi$
$811$	−1.34252e7			−0.716752			−0.358376	+	0.933577i	$0.616669\pi$
$812$	−3.26000e6	−	2.29061e6i	−0.173511	−	0.121916i
$813$	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
$818$	2.47039e7	−	2.14102e6i	1.29087	−	0.111876i
$819$		−	1.13160e6i		−	0.0589500i
$820$	1.80612e7	−	6.90114e6i	0.938019	−	0.358415i
$821$			1.77101e7i			0.916987i	0.888698	+	0.458494i	$0.151611\pi$
$821$			1.77101e7i			0.916987i	−0.888698	+	0.458494i	$0.848389\pi$
$822$	−1.89082e6	−	2.18169e7i	−0.0976046	−	1.12620i
$823$	−564216.	+	564216.i	−0.0290366	+	0.0290366i	−0.721476	−	0.692439i	$-0.756536\pi$
$823$	−564216.	+	564216.i	−0.0290366	+	0.0290366i	0.692439	+	0.721476i	$0.256536\pi$
$824$	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	$0.255083\pi$
$828$	−9.03730e6	−	6.34997e6i	−0.458103	−	0.321881i
$829$	−4.84536e6			−0.244872			−0.122436	−	0.992476i	$-0.539071\pi$
$829$	−4.84536e6			−0.244872			−0.122436	+	0.992476i	$0.539071\pi$
$830$	−1.00640e7	+	1.81248e7i	−0.507077	+	0.913228i
$831$		−	1.43707e7i		−	0.721897i
$832$	1.33808e6	−	4.89787e6i	0.0670155	−	0.245301i
$833$	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
$838$	−1.03134e7	+	893836.i	−0.507331	+	0.0439691i
$839$	7.31295e6			0.358664			0.179332	−	0.983789i	$-0.442606\pi$
$839$	7.31295e6			0.358664			0.179332	+	0.983789i	$0.442606\pi$
$840$	−4.62377e6	+	2.24170e6i	−0.226099	+	0.109617i
$841$	1.51593e7			0.739078
$842$	3.27961e7	−	2.84236e6i	1.59420	−	0.138165i
$843$	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
$848$	8.77312e6	−	1.86550e7i	0.418952	−	0.890851i
$849$			2.24822e7i			1.07046i
$850$	−3.14226e7	−	1.02319e7i	−1.49174	−	0.485745i
$851$	−1.04481e7			−0.494553
$852$	−2.60369e7	+	3.70558e7i	−1.22882	+	1.74887i
$853$	−3.80964e6	+	3.80964e6i	−0.179272	+	0.179272i	−0.791038	−	0.611767i	$-0.790459\pi$
$853$	−3.80964e6	+	3.80964e6i	−0.179272	+	0.179272i	0.611767	+	0.791038i	$0.290459\pi$
$854$	−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	$0.348198\pi$
$858$	−938900.	−	1.08334e7i	−0.0435413	−	0.502395i
$859$			272935.i			0.0126205i	0.999980	+	0.00631024i	$0.00200863\pi$
$859$			272935.i			0.0126205i	−0.999980	+	0.00631024i	$0.997991\pi$
$860$	−1.08249e7	−	4.83955e6i	−0.499089	−	0.223130i
$861$			5.48848e6i			0.252316i
$862$	7.82115e6	−	677839.i	0.358511	−	0.0310712i
$863$	3.16913e6	−	3.16913e6i	0.144848	−	0.144848i	−0.630964	−	0.775812i	$-0.717340\pi$
$863$	3.16913e6	−	3.16913e6i	0.144848	−	0.144848i	0.775812	+	0.630964i	$0.217340\pi$
$864$	−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
$868$	3.77781e6	−	5.37660e6i	0.170193	−	0.242219i
$869$	−6.16412e6			−0.276899
$870$	2.23325e7	−	4.02200e7i	1.00032	−	1.80154i
$871$			4.42833e6i			0.197785i
$872$	−2.39024e6	−	9.00854e6i	−0.106451	−	0.401202i
$873$	−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	0.505512	−	0.862820i	$-0.331304\pi$
$877$	−8.13844e6	−	8.13844e6i	−0.357308	−	0.357308i	−0.862820	+	0.505512i	$0.831304\pi$
$878$	−1.48787e6	−	1.71676e7i	−0.0651373	−	0.751577i
$879$	−2.69403e7			−1.17606
$880$	−2.50379e7	+	1.49364e7i	−1.08991	+	0.650190i
$881$	−1.39725e7			−0.606504			−0.303252	−	0.952910i	$-0.598072\pi$
$881$	−1.39725e7			−0.606504			−0.303252	+	0.952910i	$0.598072\pi$
$882$	2.80142e6	+	3.23238e7i	0.121257	+	1.39911i
$883$	−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	0.686270	−	0.727347i	$-0.259247\pi$
$887$	−962500.	−	962500.i	−0.0410763	−	0.0410763i	−0.727347	+	0.686270i	$0.759247\pi$
$888$	−4.51930e7	+	1.19911e7i	−1.92326	+	0.510300i
$889$			2.11910e6i			0.0899283i
$890$	−2.44158e6	+	698196.i	−0.103323	+	0.0295463i
$891$	1.09270e7			0.461113
$892$	1.02331e6	−	1.45638e6i	0.0430621	−	0.0612862i
$893$	−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
$898$	−3.40435e7	+	2.95046e6i	−1.40878	+	0.122095i
$899$			5.88299e7i			2.42772i
$900$	−1.85208e7	−	2.97354e7i	−0.762173	−	1.22368i
$901$			3.76342e7i			1.54444i
$902$	2.68876e6	+	3.10238e7i	0.110036	+	1.26964i
$903$	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	$0.908658\pi$
$908$	−9.70029e6	+	1.38055e7i	−0.390454	+	0.555696i
$909$	3.40728e7			1.36772
$910$	280848.	+	982122.i	0.0112426	+	0.0393153i
$911$			3.26334e7i			1.30277i	0.758749	+	0.651383i	$0.225811\pi$
$911$			3.26334e7i			1.30277i	−0.758749	+	0.651383i	$0.774189\pi$
$912$	−7.31221e6	+	1.55486e7i	−0.291113	+	0.619017i
$913$	−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
$918$	2.75396e7	−	2.38679e6i	1.07858	−	0.0934774i
$919$	1.37192e7			0.535845			0.267923	−	0.963440i	$-0.413663\pi$
$919$	1.37192e7			0.535845			0.267923	+	0.963440i	$0.413663\pi$
$920$	9.41949e6	+	3.26823e6i	0.366909	+	0.127304i
$921$	−1.39087e7			−0.540305
$922$	3.27690e7	−	2.84000e6i	1.26951	−	0.110025i
$923$	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
$928$	1.44931e7	+	3.14142e7i	0.552449	+	1.19745i
$929$		−	5.06594e7i		−	1.92584i	−0.269782	−	0.962922i	$-0.586952\pi$
$929$		−	5.06594e7i		−	1.92584i	0.269782	−	0.962922i	$-0.413048\pi$
$930$	6.63333e7	+	3.68320e7i	2.51492	+	1.39643i
$931$	1.12784e7			0.426454
$932$	−2.36370e6	−	1.66083e6i	−0.0891361	−	0.0626305i
$933$	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	$0.311257\pi$
$938$	291007.	+	3.35774e6i	0.0107993	+	0.124606i
$939$		−	6.49351e7i		−	2.40334i
$940$	2.87902e7	+	1.28714e7i	1.06274	+	0.475124i
$941$			795711.i			0.0292942i	0.999893	+	0.0146471i	$0.00466248\pi$
$941$			795711.i			0.0292942i	−0.999893	+	0.0146471i	$0.995338\pi$
$942$	−2.06124e7	+	1.78642e6i	−0.756834	+	0.0655929i
$943$	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	$0.217092\pi$
$948$	7.71879e6	+	5.42353e6i	0.278951	+	0.196002i
$949$	552458.			0.0199129
$950$	−1.08538e7	+	5.52159e6i	−0.390186	+	0.198497i
$951$		−	4.16720e7i		−	1.49415i
$952$	1.80919e6	+	6.81864e6i	0.0646982	+	0.243840i
$953$	−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
$958$	4.15607e6	+	4.79542e7i	0.146308	+	1.68816i
$959$	−3.31319e6			−0.116332
$960$	4.44947e7	+	3.32608e6i	1.55822	+	0.116481i
$961$	−6.83967e7			−2.38906
$962$	802546.	+	9.26006e6i	0.0279597	+	0.322609i
$963$	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	0.587181	−	0.809456i	$-0.300238\pi$
$967$	−6.46334e6	−	6.46334e6i	−0.222275	−	0.222275i	−0.809456	+	0.587181i	$0.800238\pi$
$968$	−4.56557e6	−	1.72071e7i	−0.156605	−	0.590228i
$969$		−	3.13673e7i		−	1.07317i
$970$	2.86091e7	+	1.58854e7i	0.976283	+	0.542088i
$971$	8.63113e6			0.293778			0.146889	−	0.989153i	$-0.453074\pi$
$971$	8.63113e6			0.293778			0.146889	+	0.989153i	$0.453074\pi$
$972$	−3.03145e7	−	2.13001e7i	−1.02916	−	0.723130i
$973$	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	$0.195603\pi$
$978$	2.44467e7	−	2.11874e6i	0.817285	−	0.0708320i
$979$		−	4.08998e6i		−	0.136384i
$980$	−1.04537e7	−	2.73587e7i	−0.347700	−	0.909976i
$981$			1.80369e7i			0.598398i
$982$	−1.73053e6	−	1.99675e7i	−0.0572665	−	0.660762i
$983$	3.06048e7	−	3.06048e7i	1.01020	−	1.01020i	0.0102486	−	0.999947i	$-0.496738\pi$
$983$	3.06048e7	−	3.06048e7i	1.01020	−	1.01020i	0.999947	−	0.0102486i	$-0.00326229\pi$
$984$	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
$988$	2.79473e6	+	1.96369e6i	0.0910852	+	0.0640000i
$989$	−6.53097e6			−0.212318
$990$	5.42468e7	−	1.55124e7i	1.75908	−	0.503028i
$991$		−	873414.i		−	0.0282511i	−0.999900	−	0.0141256i	$-0.995504\pi$
$991$		−	873414.i		−	0.0282511i	0.999900	−	0.0141256i	$-0.00449646\pi$
$992$	−5.18102e7	+	2.39029e7i	−1.67161	+	0.771209i
$993$	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	0.979069	−	0.203530i	$-0.0652413\pi$
$997$	2.43412e7	+	2.43412e7i	0.775539	+	0.775539i	−0.203530	+	0.979069i	$0.565241\pi$
$998$	3.17347e7	−	2.75037e6i	1.00858	−	0.0874107i
$999$	2.77194e7			0.878758

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.488434 + 5.63573i) q^{2} +(17.2238 + 17.2238i) q^{3} +(-31.5229 + 5.50537i) q^{4} +(-54.8737 + 10.6715i) q^{5} +(-88.6558 + 105.481i) q^{6} +(14.7411 + 14.7411i) q^{7} +(-46.4236 - 174.965i) q^{8} +350.316i q^{9} +O(q^{10})\)	\(q+(0.488434 + 5.63573i) 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} +(-46.4236 - 174.965i) q^{8} +350.316i q^{9} +(-86.9437 - 304.041i) q^{10} +509.310 q^{11} +(-637.765 - 448.119i) 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} +(-1974.29 + 171.106i) q^{18} +688.865i q^{19} +(1671.02 - 638.495i) q^{20} +507.795i q^{21} +(248.765 + 2870.33i) 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} +(-545.838 - 383.527i) q^{28} +5972.48 q^{29} +(3739.23 - 6734.22i) q^{30} +9850.17i q^{31} +(2426.65 + 5259.83i) 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} +(-3882.26 + 336.465i) q^{38} -3774.25 q^{39} +(4414.57 + 9105.58i) q^{40} +10808.4 q^{41} +(-2861.80 + 248.025i) 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} +(22571.3 + 10614.9i) q^{48} -16372.4i q^{49} +(8015.48 + 15756.0i) q^{50} -45534.8 q^{51} +(2850.61 - 4057.01i) 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} +(2917.16 + 33659.3i) q^{58} -33254.7i q^{59} +(39778.6 + 17784.0i) q^{60} +36049.2i q^{61} +(-55512.9 + 4811.16i) 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} +(34391.5 - 48946.1i) q^{68} +23999.6 q^{69} +(3200.26 - 5763.55i) q^{70} -58102.6i q^{71} +(61293.1 - 16262.9i) 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} +(-1843.47 - 21270.7i) q^{78} -12102.9 q^{79} +(-49160.3 + 29326.8i) q^{80} +21454.5 q^{81} +(5279.22 + 60913.5i) 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} +(-23644.0 - 89111.6i) q^{88} -8030.44i q^{89} +(106510. - 30457.8i) q^{90} -3230.23 q^{91} +(-18126.4 + 25797.6i) 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} +(92270.4 - 7996.84i) 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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