LMFDB - Embedded newform 40.6.k.a.27.23

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			27.23
Character	$\chi$	$=$	40.27
Dual form			40.6.k.a.3.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.71279 + 3.12884i) q^{2} +(2.84747 - 2.84747i) q^{3} +(12.4207 + 29.4911i) q^{4} +(51.8149 - 20.9812i) q^{5} +(22.3288 - 4.51023i) q^{6} +(44.8183 - 44.8183i) q^{7} +(-33.7370 + 177.848i) q^{8} +226.784i q^{9} +O(q^{10})$	\(q+(4.71279 + 3.12884i) q^{2} +(2.84747 - 2.84747i) q^{3} +(12.4207 + 29.4911i) q^{4} +(51.8149 - 20.9812i) q^{5} +(22.3288 - 4.51023i) q^{6} +(44.8183 - 44.8183i) q^{7} +(-33.7370 + 177.848i) q^{8} +226.784i q^{9} +(309.840 + 63.2407i) q^{10} +162.348 q^{11} +(119.343 + 48.6075i) q^{12} +(-133.361 - 133.361i) q^{13} +(351.449 - 70.9897i) q^{14} +(87.7980 - 207.285i) q^{15} +(-715.452 + 732.601i) q^{16} +(-253.944 - 253.944i) q^{17} +(-709.571 + 1068.78i) q^{18} -450.049i q^{19} +(1262.34 + 1267.48i) q^{20} -255.238i q^{21} +(765.112 + 507.961i) q^{22} +(-2633.26 - 2633.26i) q^{23} +(410.351 + 602.481i) q^{24} +(2244.58 - 2174.28i) q^{25} +(-211.236 - 1045.77i) q^{26} +(1337.69 + 1337.69i) q^{27} +(1878.42 + 765.068i) q^{28} -3806.84 q^{29} +(1062.33 - 702.183i) q^{30} -8164.13i q^{31} +(-5663.97 + 1214.05i) q^{32} +(462.281 - 462.281i) q^{33} +(-402.233 - 1991.33i) q^{34} +(1381.92 - 3262.60i) q^{35} +(-6688.11 + 2816.81i) q^{36} +(-6714.43 + 6714.43i) q^{37} +(1408.13 - 2120.99i) q^{38} -759.483 q^{39} +(1983.39 + 9923.01i) q^{40} -10525.2 q^{41} +(798.598 - 1202.88i) q^{42} +(4224.63 - 4224.63i) q^{43} +(2016.48 + 4787.83i) q^{44} +(4758.20 + 11750.8i) q^{45} +(-4170.94 - 20649.1i) q^{46} +(13985.6 - 13985.6i) q^{47} +(48.8292 + 4123.29i) q^{48} +12789.6i q^{49} +(17381.2 - 3224.00i) q^{50} -1446.20 q^{51} +(2276.53 - 5589.40i) q^{52} +(21609.7 + 21609.7i) q^{53} +(2118.83 + 10489.7i) q^{54} +(8412.06 - 3406.26i) q^{55} +(6458.81 + 9482.87i) q^{56} +(-1281.50 - 1281.50i) q^{57} +(-17940.8 - 11911.0i) q^{58} +48931.8i q^{59} +(7203.58 + 14.6396i) q^{60} +31903.9i q^{61} +(25544.3 - 38475.8i) q^{62} +(10164.1 + 10164.1i) q^{63} +(-30491.6 - 12000.1i) q^{64} +(-9708.17 - 4112.01i) q^{65} +(3625.04 - 732.227i) q^{66} +(-24220.4 - 24220.4i) q^{67} +(4334.93 - 10643.3i) q^{68} -14996.3 q^{69} +(16720.8 - 11052.2i) q^{70} -14490.3i q^{71} +(-40333.0 - 7651.00i) q^{72} +(27506.2 - 27506.2i) q^{73} +(-52652.0 + 10635.3i) q^{74} +(200.159 - 12582.6i) q^{75} +(13272.5 - 5589.93i) q^{76} +(7276.17 - 7276.17i) q^{77} +(-3579.28 - 2376.30i) q^{78} -45231.1 q^{79} +(-21700.3 + 52970.7i) q^{80} -47490.4 q^{81} +(-49603.1 - 32931.7i) q^{82} +(52564.8 - 52564.8i) q^{83} +(7527.24 - 3170.23i) q^{84} +(-18486.2 - 7830.04i) q^{85} +(33128.0 - 6691.58i) q^{86} +(-10839.9 + 10839.9i) q^{87} +(-5477.13 + 28873.2i) q^{88} +30184.9i q^{89} +(-14342.0 + 70266.6i) q^{90} -11954.0 q^{91} +(44950.9 - 110365. i) q^{92} +(-23247.1 - 23247.1i) q^{93} +(109670. - 22152.4i) q^{94} +(-9442.59 - 23319.3i) q^{95} +(-12671.0 + 19584.9i) q^{96} +(57292.8 + 57292.8i) q^{97} +(-40016.7 + 60274.8i) q^{98} +36817.9i 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 $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

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

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 $

$2$	4.71279	+	3.12884i	0.833111	+	0.553106i
$2$	4.71279	+	3.12884i	0.833111	+	0.553106i
$3$	2.84747	−	2.84747i	0.182665	−	0.182665i	−0.609851	−	0.792516i	$-0.708771\pi$
$3$	2.84747	−	2.84747i	0.182665	−	0.182665i	0.792516	+	0.609851i	$0.208771\pi$
$4$	12.4207	+	29.4911i	0.388147	+	0.921598i
$5$	51.8149	−	20.9812i	0.926894	−	0.375324i
$5$	51.8149	−	20.9812i	0.926894	−	0.375324i
$6$	22.3288	−	4.51023i	0.253214	−	0.0511471i
$7$	44.8183	−	44.8183i	0.345709	−	0.345709i	−0.512799	−	0.858508i	$-0.671392\pi$
$7$	44.8183	−	44.8183i	0.345709	−	0.345709i	0.858508	+	0.512799i	$0.171392\pi$
$8$	−33.7370	+	177.848i	−0.186372	+	0.982479i
$9$			226.784i			0.933267i
$10$	309.840	+	63.2407i	0.979799	+	0.199985i
$11$	162.348			0.404544			0.202272	−	0.979329i	$-0.435168\pi$
$11$	162.348			0.404544			0.202272	+	0.979329i	$0.435168\pi$
$12$	119.343	+	48.6075i	0.239245	+	0.0974429i
$13$	−133.361	−	133.361i	−0.218862	−	0.218862i	0.589157	−	0.808019i	$-0.299460\pi$
$13$	−133.361	−	133.361i	−0.218862	−	0.218862i	−0.808019	+	0.589157i	$0.799460\pi$
$14$	351.449	−	70.9897i	0.479228	−	0.0968000i
$15$	87.7980	−	207.285i	0.100753	−	0.237870i
$16$	−715.452	+	732.601i	−0.698684	+	0.715430i
$17$	−253.944	−	253.944i	−0.213116	−	0.213116i	0.592474	−	0.805590i	$-0.298151\pi$
$17$	−253.944	−	253.944i	−0.213116	−	0.213116i	−0.805590	+	0.592474i	$0.798151\pi$
$18$	−709.571	+	1068.78i	−0.516196	+	0.777515i
$19$		−	450.049i		−	0.286007i	−0.989722	−	0.143003i	$-0.954324\pi$
$19$		−	450.049i		−	0.286007i	0.989722	−	0.143003i	$-0.0456760\pi$
$20$	1262.34	+	1267.48i	0.705668	+	0.708542i
$21$		−	255.238i		−	0.126298i
$22$	765.112	+	507.961i	0.337030	+	0.223756i
$23$	−2633.26	−	2633.26i	−1.03795	−	1.03795i	−0.999251	−	0.0386951i	$-0.987680\pi$
$23$	−2633.26	−	2633.26i	−1.03795	−	1.03795i	−0.0386951	−	0.999251i	$-0.512320\pi$
$24$	410.351	+	602.481i	0.145421	+	0.213508i
$25$	2244.58	−	2174.28i	0.718264	−	0.695770i
$26$	−211.236	−	1045.77i	−0.0612823	−	0.303390i
$27$	1337.69	+	1337.69i	0.353141	+	0.353141i
$28$	1878.42	+	765.068i	0.452790	+	0.184419i
$29$	−3806.84			−0.840563			−0.420281	−	0.907394i	$-0.638069\pi$
$29$	−3806.84			−0.840563			−0.420281	+	0.907394i	$0.638069\pi$
$30$	1062.33	−	702.183i	0.215505	−	0.142445i
$31$		−	8164.13i		−	1.52583i	−0.646500	−	0.762914i	$-0.723768\pi$
$31$		−	8164.13i		−	1.52583i	0.646500	−	0.762914i	$-0.276232\pi$
$32$	−5663.97	+	1214.05i	−0.977790	+	0.209586i
$33$	462.281	−	462.281i	0.0738961	−	0.0738961i
$34$	−402.233	−	1991.33i	−0.0596734	−	0.295425i
$35$	1381.92	−	3262.60i	0.190683	−	0.450188i
$36$	−6688.11	+	2816.81i	−0.860096	+	0.362245i
$37$	−6714.43	+	6714.43i	−0.806315	+	0.806315i	−0.984074	−	0.177759i	$-0.943115\pi$
$37$	−6714.43	+	6714.43i	−0.806315	+	0.806315i	0.177759	+	0.984074i	$0.443115\pi$
$38$	1408.13	−	2120.99i	0.158192	−	0.238275i
$39$	−759.483			−0.0799570
$40$	1983.39	+	9923.01i	0.196001	+	0.980604i
$41$	−10525.2			−0.977848			−0.488924	−	0.872327i	$-0.662610\pi$
$41$	−10525.2			−0.977848			−0.488924	+	0.872327i	$0.662610\pi$
$42$	798.598	−	1202.88i	0.0698562	−	0.105220i
$43$	4224.63	−	4224.63i	0.348432	−	0.348432i	−0.511094	−	0.859525i	$-0.670759\pi$
$43$	4224.63	−	4224.63i	0.348432	−	0.348432i	0.859525	+	0.511094i	$0.170759\pi$
$44$	2016.48	+	4787.83i	0.157022	+	0.372826i
$45$	4758.20	+	11750.8i	0.350277	+	0.865039i
$46$	−4170.94	−	20649.1i	−0.290629	−	1.43882i
$47$	13985.6	−	13985.6i	0.923500	−	0.923500i	−0.0737747	−	0.997275i	$-0.523505\pi$
$47$	13985.6	−	13985.6i	0.923500	−	0.923500i	0.997275	+	0.0737747i	$0.0235046\pi$
$48$	48.8292	+	4123.29i	0.00305898	+	0.258310i
$49$			12789.6i			0.760971i
$50$	17381.2	−	3224.00i	0.983229	−	0.182377i
$51$	−1446.20			−0.0778577
$52$	2276.53	−	5589.40i	0.116752	−	0.286653i
$53$	21609.7	+	21609.7i	1.05672	+	1.05672i	0.998292	+	0.0584283i	$0.0186089\pi$
$53$	21609.7	+	21609.7i	1.05672	+	1.05672i	0.0584283	+	0.998292i	$0.481391\pi$
$54$	2118.83	+	10489.7i	0.0988809	+	0.489530i
$55$	8412.06	−	3406.26i	0.374969	−	0.151835i
$56$	6458.81	+	9482.87i	0.275221	+	0.404082i
$57$	−1281.50	−	1281.50i	−0.0522435	−	0.0522435i
$58$	−17940.8	−	11911.0i	−0.700282	−	0.464920i
$59$			48931.8i			1.83004i	0.403407	+	0.915021i	$0.367826\pi$
$59$			48931.8i			1.83004i	−0.403407	+	0.915021i	$0.632174\pi$
$60$	7203.58	+	14.6396i	0.258327	+	0.000524990i
$61$			31903.9i			1.09779i	0.835892	+	0.548895i	$0.184951\pi$
$61$			31903.9i			1.09779i	−0.835892	+	0.548895i	$0.815049\pi$
$62$	25544.3	−	38475.8i	0.843945	−	1.27118i
$63$	10164.1	+	10164.1i	0.322639	+	0.322639i
$64$	−30491.6	−	12000.1i	−0.930531	−	0.366213i
$65$	−9708.17	−	4112.01i	−0.285006	−	0.120718i
$66$	3625.04	−	732.227i	0.102436	−	0.0206912i
$67$	−24220.4	−	24220.4i	−0.659164	−	0.659164i	0.296018	−	0.955182i	$-0.404341\pi$
$67$	−24220.4	−	24220.4i	−0.659164	−	0.659164i	−0.955182	+	0.296018i	$0.904341\pi$
$68$	4334.93	−	10643.3i	0.113687	−	0.279127i
$69$	−14996.3			−0.379193
$70$	16720.8	−	11052.2i	0.407862	−	0.269589i
$71$		−	14490.3i		−	0.341139i	−0.985346	−	0.170570i	$-0.945439\pi$
$71$		−	14490.3i		−	0.341139i	0.985346	−	0.170570i	$-0.0545608\pi$
$72$	−40333.0	−	7651.00i	−0.916915	−	0.173935i
$73$	27506.2	−	27506.2i	0.604120	−	0.604120i	−0.337283	−	0.941403i	$-0.609508\pi$
$73$	27506.2	−	27506.2i	0.604120	−	0.604120i	0.941403	+	0.337283i	$0.109508\pi$
$74$	−52652.0	+	10635.3i	−1.11773	+	0.225772i
$75$	200.159	−	12582.6i	0.00410886	−	0.258295i
$76$	13272.5	−	5589.93i	0.263583	−	0.111013i
$77$	7276.17	−	7276.17i	0.139854	−	0.139854i
$78$	−3579.28	−	2376.30i	−0.0666130	−	0.0442247i
$79$	−45231.1			−0.815398			−0.407699	−	0.913116i	$-0.633669\pi$
$79$	−45231.1			−0.815398			−0.407699	+	0.913116i	$0.633669\pi$
$80$	−21700.3	+	52970.7i	−0.379088	+	0.925361i
$81$	−47490.4			−0.804254
$82$	−49603.1	−	32931.7i	−0.814655	−	0.540854i
$83$	52564.8	−	52564.8i	0.837529	−	0.837529i	−0.151004	−	0.988533i	$-0.548251\pi$
$83$	52564.8	−	52564.8i	0.837529	−	0.837529i	0.988533	+	0.151004i	$0.0482508\pi$
$84$	7527.24	−	3170.23i	0.116396	−	0.0490222i
$85$	−18486.2	−	7830.04i	−0.277523	−	0.117548i
$86$	33128.0	−	6691.58i	0.483002	−	0.0975624i
$87$	−10839.9	+	10839.9i	−0.153542	+	0.153542i
$88$	−5477.13	+	28873.2i	−0.0753956	+	0.397456i
$89$			30184.9i			0.403938i	0.979392	+	0.201969i	$0.0647340\pi$
$89$			30184.9i			0.403938i	−0.979392	+	0.201969i	$0.935266\pi$
$90$	−14342.0	+	70266.6i	−0.186639	+	0.914414i
$91$	−11954.0			−0.151325
$92$	44950.9	−	110365.i	0.553693	−	1.35944i
$93$	−23247.1	−	23247.1i	−0.278716	−	0.278716i
$94$	109670.	−	22152.4i	1.28017	−	0.258584i
$95$	−9442.59	−	23319.3i	−0.107345	−	0.265098i
$96$	−12671.0	+	19584.9i	−0.140324	+	0.216892i
$97$	57292.8	+	57292.8i	0.618259	+	0.618259i	0.945085	−	0.326825i	$-0.105979\pi$
$97$	57292.8	+	57292.8i	0.618259	+	0.618259i	−0.326825	+	0.945085i	$0.605979\pi$
$98$	−40016.7	+	60274.8i	−0.420898	+	0.633973i
$99$			36817.9i			0.377547i
$100$	92001.2	+	39189.0i	0.920012	+	0.391890i
$101$		−	174687.i		−	1.70395i	−0.523584	−	0.851974i	$-0.675406\pi$
$101$		−	174687.i		−	1.70395i	0.523584	−	0.851974i	$-0.324594\pi$
$102$	−6815.61	−	4524.92i	−0.0648641	−	0.0430636i
$103$	48055.5	+	48055.5i	0.446324	+	0.446324i	0.894130	−	0.447807i	$-0.147795\pi$
$103$	48055.5	+	48055.5i	0.446324	+	0.446324i	−0.447807	+	0.894130i	$0.647795\pi$
$104$	28217.1	−	19218.8i	0.255817	−	0.174238i
$105$	−5355.20	−	13225.1i	−0.0474026	−	0.117065i
$106$	34228.6	+	169456.i	0.295886	+	1.46484i
$107$	67326.0	+	67326.0i	0.568491	+	0.568491i	0.931706	−	0.363214i	$-0.118321\pi$
$107$	67326.0	+	67326.0i	0.568491	+	0.568491i	−0.363214	+	0.931706i	$0.618321\pi$
$108$	−22835.0	+	56065.2i	−0.188383	+	0.462524i
$109$	−14711.3			−0.118600			−0.0593001	−	0.998240i	$-0.518887\pi$
$109$	−14711.3			−0.118600			−0.0593001	+	0.998240i	$0.518887\pi$
$110$	50301.9	+	10267.0i	0.396372	+	0.0809025i
$111$			38238.3i			0.294571i
$112$	768.558	+	64899.3i	0.00578937	+	0.488872i
$113$	148203.	−	148203.i	1.09185	−	1.09185i	0.0965148	−	0.995332i	$-0.469230\pi$
$113$	148203.	−	148203.i	1.09185	−	1.09185i	0.995332	−	0.0965148i	$-0.0307695\pi$
$114$	−2029.83	−	10049.1i	−0.0146284	−	0.0724208i
$115$	−191692.	−	81193.3i	−1.35163	−	0.572500i
$116$	−47283.7	−	112268.i	−0.326262	−	0.774660i
$117$	30244.1	−	30244.1i	0.204257	−	0.204257i
$118$	−153100.	+	230605.i	−1.01221	+	1.52463i
$119$	−22762.7			−0.147352
$120$	33903.1	+	22607.8i	0.214925	+	0.143320i
$121$	−134694.			−0.836344
$122$	−99822.2	+	150356.i	−0.607194	+	0.914580i
$123$	−29970.2	+	29970.2i	−0.178619	+	0.178619i
$124$	240769.	−	101404.i	1.40620	−	0.592245i
$125$	70683.4	−	159754.i	0.404616	−	0.914487i
$126$	16099.3	+	79702.9i	0.0903403	+	0.447247i
$127$	−165147.	+	165147.i	−0.908575	+	0.908575i	−0.996157	−	0.0875826i	$-0.972086\pi$
$127$	−165147.	+	165147.i	−0.908575	+	0.908575i	0.0875826	+	0.996157i	$0.472086\pi$
$128$	−106154.	−	151957.i	−0.572680	−	0.819779i
$129$		−	24059.0i		−	0.127293i
$130$	−32886.7	−	49754.4i	−0.170672	−	0.258210i
$131$	140149.			0.713530			0.356765	−	0.934194i	$-0.383880\pi$
$131$	140149.			0.713530			0.356765	+	0.934194i	$0.383880\pi$
$132$	19375.0	+	7891.33i	0.0967850	+	0.0394199i
$133$	−20170.5	−	20170.5i	−0.0988751	−	0.0988751i
$134$	−38363.7	−	189927.i	−0.184569	−	0.913744i
$135$	97379.1	+	41246.1i	0.459866	+	0.194782i
$136$	53730.7	−	36596.1i	0.249101	−	0.169663i
$137$	201345.	+	201345.i	0.916513	+	0.916513i	0.996774	−	0.0802613i	$-0.0255755\pi$
$137$	201345.	+	201345.i	0.916513	+	0.916513i	−0.0802613	+	0.996774i	$0.525575\pi$
$138$	−70674.2	−	46921.0i	−0.315910	−	0.209734i
$139$			61124.4i			0.268335i	0.990959	+	0.134168i	$0.0428361\pi$
$139$			61124.4i			0.268335i	−0.990959	+	0.134168i	$0.957164\pi$
$140$	113382.	+	230.423i	0.488905	+	0.000993587i
$141$		−	79647.2i		−	0.337383i
$142$	45337.9	−	68289.7i	0.188686	−	0.284207i
$143$	−21650.9	−	21650.9i	−0.0885393	−	0.0885393i
$144$	−166142.	−	162253.i	−0.667687	−	0.652059i
$145$	−197251.	+	79872.3i	−0.779112	+	0.315483i
$146$	215693.	−	43568.3i	0.837442	−	0.169156i
$147$	36418.1	+	36418.1i	0.139003	+	0.139003i
$148$	−281414.	−	114618.i	−1.05607	−	0.430129i
$149$	118871.			0.438643			0.219321	−	0.975653i	$-0.429616\pi$
$149$	118871.			0.438643			0.219321	+	0.975653i	$0.429616\pi$
$150$	40312.1	−	58672.7i	0.146288	−	0.212916i
$151$			385588.i			1.37620i	0.725617	+	0.688099i	$0.241554\pi$
$151$			385588.i			1.37620i	−0.725617	+	0.688099i	$0.758446\pi$
$152$	80040.3	+	15183.3i	0.280996	+	0.0533037i
$153$	57590.4	−	57590.4i	0.198894	−	0.198894i
$154$	57057.0	−	11525.0i	0.193869	−	0.0391598i
$155$	−171293.	−	423024.i	−0.572679	−	1.41428i
$156$	−9433.31	−	22398.0i	−0.0310350	−	0.0736881i
$157$	−211783.	+	211783.i	−0.685712	+	0.685712i	−0.961281	−	0.275569i	$-0.911134\pi$
$157$	−211783.	+	211783.i	−0.685712	+	0.685712i	0.275569	+	0.961281i	$0.411134\pi$
$158$	−213165.	−	141521.i	−0.679317	−	0.451002i
$159$	123066.			0.386052
$160$	−268006.	+	181743.i	−0.827645	+	0.561252i
$161$	−236037.			−0.717655
$162$	−223812.	−	148590.i	−0.670032	−	0.444838i
$163$	−92326.0	+	92326.0i	−0.272179	+	0.272179i	−0.829977	−	0.557798i	$-0.811647\pi$
$163$	−92326.0	+	92326.0i	−0.272179	+	0.272179i	0.557798	+	0.829977i	$0.311647\pi$
$164$	−130730.	−	310400.i	−0.379548	−	0.901182i
$165$	14253.8	−	33652.3i	0.0407589	−	0.0962287i
$166$	412193.	−	83259.7i	1.16100	−	0.234512i
$167$	32283.3	−	32283.3i	0.0895749	−	0.0895749i	−0.660899	−	0.750474i	$-0.729825\pi$
$167$	32283.3	−	32283.3i	0.0895749	−	0.0895749i	0.750474	+	0.660899i	$0.229825\pi$
$168$	45393.4	+	8610.94i	0.124085	+	0.0235384i
$169$		−	335723.i		−	0.904199i
$170$	−62622.3	−	94741.5i	−0.166191	−	0.251431i
$171$	102064.			0.266921
$172$	177062.	+	72116.2i	0.456356	+	0.185871i
$173$	322605.	+	322605.i	0.819512	+	0.819512i	0.986037	−	0.166525i	$-0.0532546\pi$
$173$	322605.	+	322605.i	0.819512	+	0.819512i	−0.166525	+	0.986037i	$0.553255\pi$
$174$	−85002.2	+	17169.7i	−0.212842	+	0.0429923i
$175$	3150.44	−	198046.i	0.00777636	−	0.488844i
$176$	−116152.	+	118936.i	−0.282648	+	0.289423i
$177$	139332.	+	139332.i	0.334285	+	0.334285i
$178$	−94443.7	+	142255.i	−0.223421	+	0.336525i
$179$			539587.i			1.25872i	0.777114	+	0.629360i	$0.216683\pi$
$179$			539587.i			1.25872i	−0.777114	+	0.629360i	$0.783317\pi$
$180$	−287444.	+	286278.i	−0.661259	+	0.658577i
$181$			425582.i			0.965576i	0.875737	+	0.482788i	$0.160376\pi$
$181$			425582.i			0.965576i	−0.875737	+	0.482788i	$0.839624\pi$
$182$	−56336.8	−	37402.3i	−0.126071	−	0.0836989i
$183$	90845.3	+	90845.3i	0.200528	+	0.200528i
$184$	557158.	−	379482.i	1.21320	−	0.826316i
$185$	−207031.	+	488785.i	−0.444739	+	1.05000i
$186$	−36822.1	−	182295.i	−0.0780416	−	0.386360i
$187$	−41227.3	−	41227.3i	−0.0862147	−	0.0862147i
$188$	586163.	+	238740.i	1.20955	+	0.492642i
$189$	119907.			0.244168
$190$	28461.4	−	139443.i	0.0571969	−	0.280229i
$191$		−	694030.i		−	1.37656i	−0.725446	−	0.688279i	$-0.758366\pi$
$191$		−	694030.i		−	1.37656i	0.725446	−	0.688279i	$-0.241634\pi$
$192$	−120994.	+	52654.1i	−0.236870	+	0.103081i
$193$	304826.	−	304826.i	0.589059	−	0.589059i	−0.348317	−	0.937377i	$-0.613247\pi$
$193$	304826.	−	304826.i	0.589059	−	0.589059i	0.937377	+	0.348317i	$0.113247\pi$
$194$	90748.6	+	449269.i	0.173115	+	0.857042i
$195$	−39352.5	+	15934.9i	−0.0741116	+	0.0300097i
$196$	−377181.	+	158856.i	−0.701309	+	0.295368i
$197$	40777.7	−	40777.7i	0.0748612	−	0.0748612i	−0.668685	−	0.743546i	$-0.733142\pi$
$197$	40777.7	−	40777.7i	0.0748612	−	0.0748612i	0.743546	+	0.668685i	$0.233142\pi$
$198$	−115197.	+	173515.i	−0.208824	+	0.314539i
$199$	−16829.0			−0.0301248			−0.0150624	−	0.999887i	$-0.504795\pi$
$199$	−16829.0			−0.0301248			−0.0150624	+	0.999887i	$0.504795\pi$
$200$	310966.	+	472546.i	0.549716	+	0.835352i
$201$	−137933.			−0.240813
$202$	546567.	−	823261.i	0.942464	−	1.41958i
$203$	−170616.	+	170616.i	−0.290590	+	0.290590i
$204$	−17962.8	−	42649.9i	−0.0302202	−	0.0717535i
$205$	−545363.	+	220832.i	−0.906361	+	0.367009i
$206$	76117.2	+	376833.i	0.124973	+	0.618701i
$207$	597182.	−	597182.i	0.968681	−	0.968681i
$208$	193114.	−	2286.91i	0.309496	−	0.00366515i
$209$		−	73064.6i		−	0.115702i
$210$	16141.4	−	79082.7i	0.0252577	−	0.123747i
$211$	1.12463e6			1.73902			0.869509	−	0.493917i	$-0.164435\pi$
$211$	1.12463e6			1.73902			0.869509	+	0.493917i	$0.164435\pi$
$212$	−368887.	+	905704.i	−0.563708	+	1.38403i
$213$	−41260.7	−	41260.7i	−0.0623143	−	0.0623143i
$214$	106641.	+	527946.i	0.159180	+	0.788052i
$215$	130261.	−	307537.i	0.192184	−	0.453734i
$216$	−283036.	+	192776.i	−0.412769	+	0.281138i
$217$	−365903.	−	365903.i	−0.527492	−	0.527492i
$218$	−69331.2	−	46029.4i	−0.0988070	−	0.0655985i
$219$		−	156646.i		−	0.220703i
$220$	204938.	+	205773.i	0.285474	+	0.286636i
$221$			67732.5i			0.0932859i
$222$	−119641.	+	180209.i	−0.162929	+	0.245411i
$223$	−798253.	−	798253.i	−1.07493	−	1.07493i	−0.996956	−	0.0779695i	$-0.975156\pi$
$223$	−798253.	−	798253.i	−1.07493	−	1.07493i	−0.0779695	−	0.996956i	$-0.524844\pi$
$224$	−199438.	+	308261.i	−0.265575	+	0.410487i
$225$	493092.	+	509034.i	0.649339	+	0.670332i
$226$	1.16215e6	−	234746.i	1.51354	−	0.305722i
$227$	−543674.	−	543674.i	−0.700284	−	0.700284i	0.264188	−	0.964471i	$-0.414896\pi$
$227$	−543674.	−	543674.i	−0.700284	−	0.700284i	−0.964471	+	0.264188i	$0.914896\pi$
$228$	21875.8	−	53710.1i	0.0278693	−	0.0684256i
$229$	−888768.			−1.11995			−0.559976	−	0.828508i	$-0.689190\pi$
$229$	−888768.			−1.11995			−0.559976	+	0.828508i	$0.689190\pi$
$230$	−649360.	−	982419.i	−0.809405	−	1.22455i
$231$		−	41437.3i		−	0.0510931i
$232$	128431.	−	677039.i	0.156657	−	0.825835i
$233$	464702.	−	464702.i	0.560770	−	0.560770i	−0.368756	−	0.929526i	$-0.620216\pi$
$233$	464702.	−	464702.i	0.560770	−	0.560770i	0.929526	+	0.368756i	$0.120216\pi$
$234$	237163.	−	47905.0i	0.283144	−	0.0571928i
$235$	431228.	−	1.01810e6i	0.509375	−	1.20260i
$236$	−1.44305e6	+	607767.i	−1.68656	+	0.710325i
$237$	−128794.	+	128794.i	−0.148945	+	0.148945i
$238$	−107276.	−	71220.9i	−0.122761	−	0.0815014i
$239$	−1.20042e6			−1.35937			−0.679685	−	0.733504i	$-0.737884\pi$
$239$	−1.20042e6			−1.35937			−0.679685	+	0.733504i	$0.737884\pi$
$240$	89041.7	+	212623.i	0.0997850	+	0.238277i
$241$	−1.26552e6			−1.40354			−0.701772	−	0.712402i	$-0.747607\pi$
$241$	−1.26552e6			−1.40354			−0.701772	+	0.712402i	$0.747607\pi$
$242$	−634784.	−	421437.i	−0.696767	−	0.462587i
$243$	−460287.	+	460287.i	−0.500050	+	0.500050i
$244$	−940881.	+	396269.i	−1.01172	+	0.426104i
$245$	268342.	+	662694.i	0.285610	+	0.705339i
$246$	−235015.	+	47471.1i	−0.247604	+	0.0500140i
$247$	−60019.0	+	60019.0i	−0.0625960	+	0.0625960i
$248$	1.45197e6	+	275433.i	1.49909	+	0.284372i
$249$		−	299353.i		−	0.305975i
$250$	832962.	−	531730.i	0.842898	−	0.538073i
$251$	410382.			0.411154			0.205577	−	0.978641i	$-0.434093\pi$
$251$	410382.			0.411154			0.205577	+	0.978641i	$0.434093\pi$
$252$	−173505.	+	425995.i	−0.172112	+	0.422574i
$253$	−427505.	−	427505.i	−0.419895	−	0.419895i
$254$	−1.29502e6	+	261583.i	−1.25948	+	0.254405i
$255$	−74934.5	+	30343.0i	−0.0721658	+	0.0292218i
$256$	−24831.6	−	1.04828e6i	−0.0236813	−	0.999720i
$257$	170786.	+	170786.i	0.161294	+	0.161294i	0.783140	−	0.621846i	$-0.213617\pi$
$257$	170786.	+	170786.i	0.161294	+	0.161294i	−0.621846	+	0.783140i	$0.713617\pi$
$258$	75276.8	−	113385.i	0.0704064	−	0.106049i
$259$			601859.i			0.557501i
$260$	685.645	−	337379.i	0.000629022	−	0.309517i
$261$		−	863331.i		−	0.784469i
$262$	660493.	+	438505.i	0.594450	+	0.394658i
$263$	636691.	+	636691.i	0.567596	+	0.567596i	0.931454	−	0.363859i	$-0.118541\pi$
$263$	636691.	+	636691.i	0.567596	+	0.567596i	−0.363859	+	0.931454i	$0.618541\pi$
$264$	66619.7	+	97811.6i	0.0588292	+	0.0863735i
$265$	1.57311e6	+	666308.i	1.37608	+	0.582855i
$266$	−31948.9	−	158169.i	−0.0276855	−	0.137062i
$267$	85950.5	+	85950.5i	0.0737854	+	0.0737854i
$268$	413452.	−	1.01512e6i	0.351631	−	0.863336i
$269$	1.53143e6			1.29037			0.645187	−	0.764025i	$-0.276780\pi$
$269$	1.53143e6			1.29037			0.645187	+	0.764025i	$0.276780\pi$
$270$	329874.	+	499068.i	0.275384	+	0.416630i
$271$			77421.1i			0.0640377i	0.999487	+	0.0320189i	$0.0101937\pi$
$271$			77421.1i			0.0640377i	−0.999487	+	0.0320189i	$0.989806\pi$
$272$	367724.	−	4354.71i	0.301370	−	0.00356892i
$273$	−34038.7	+	34038.7i	−0.0276418	+	0.0276418i
$274$	318918.	+	1.57887e6i	0.256628	+	1.27049i
$275$	364403.	−	352991.i	0.290569	−	0.281470i
$276$	−186264.	−	442257.i	−0.147183	−	0.349464i
$277$	271223.	−	271223.i	0.212387	−	0.212387i	−0.592894	−	0.805281i	$-0.702015\pi$
$277$	271223.	−	271223.i	0.212387	−	0.212387i	0.805281	+	0.592894i	$0.202015\pi$
$278$	−191249.	+	288066.i	−0.148418	+	0.223553i
$279$	1.85149e6			1.42400
$280$	533625.	+	355841.i	0.406763	+	0.271244i
$281$	−1.49262e6			−1.12767			−0.563837	−	0.825886i	$-0.690675\pi$
$281$	−1.49262e6			−1.12767			−0.563837	+	0.825886i	$0.690675\pi$
$282$	249204.	−	375360.i	0.186609	−	0.281077i
$283$	−1.71400e6	+	1.71400e6i	−1.27217	+	1.27217i	−0.327221	+	0.944948i	$0.606112\pi$
$283$	−1.71400e6	+	1.71400e6i	−1.27217	+	1.27217i	−0.944948	+	0.327221i	$0.893888\pi$
$284$	427336.	−	179980.i	0.314393	−	0.132412i
$285$	−93288.4	−	39513.4i	−0.0680324	−	0.0288159i
$286$	−34293.8	−	169778.i	−0.0247914	−	0.122735i
$287$	−471722.	+	471722.i	−0.338051	+	0.338051i
$288$	−275328.	−	1.28450e6i	−0.195600	−	0.912539i
$289$		−	1.29088e6i		−	0.909163i
$290$	−1.17951e6	−	240747.i	−0.823582	−	0.168100i
$291$	326279.			0.225869
$292$	1.15283e6	+	469542.i	0.791243	+	0.322268i
$293$	988662.	+	988662.i	0.672789	+	0.672789i	0.958358	−	0.285569i	$-0.0921826\pi$
$293$	988662.	+	988662.i	0.672789	+	0.672789i	−0.285569	+	0.958358i	$0.592183\pi$
$294$	57684.2	+	285577.i	0.0389214	+	0.192688i
$295$	1.02665e6	+	2.53540e6i	0.686858	+	1.69625i
$296$	−967622.	−	1.42067e6i	−0.641913	−	0.942462i
$297$	217172.	+	217172.i	0.142861	+	0.142861i
$298$	560214.	+	371929.i	0.365438	+	0.242616i
$299$			702349.i			0.454334i
$300$	373560.	−	150381.i	0.239639	−	0.0964697i
$301$		−	378682.i		−	0.240912i
$302$	−1.20644e6	+	1.81719e6i	−0.761184	+	1.14652i
$303$	−497415.	−	497415.i	−0.311252	−	0.311252i
$304$	329706.	+	321989.i	0.204618	+	0.199828i
$305$	669383.	+	1.65310e6i	0.412026	+	1.01753i
$306$	451603.	−	91220.0i	0.275710	−	0.0556912i
$307$	−1.93324e6	−	1.93324e6i	−1.17068	−	1.17068i	−0.982047	−	0.188636i	$-0.939593\pi$
$307$	−1.93324e6	−	1.93324e6i	−1.17068	−	1.17068i	−0.188636	−	0.982047i	$-0.560407\pi$
$308$	304958.	+	124207.i	0.183173	+	0.0746054i
$309$	273673.			0.163056
$310$	516305.	−	2.52957e6i	0.305142	−	1.49500i
$311$			2.94725e6i			1.72789i	0.503587	+	0.863944i	$0.332013\pi$
$311$			2.94725e6i			1.72789i	−0.503587	+	0.863944i	$0.667987\pi$
$312$	25622.6	−	135072.i	0.0149017	−	0.0785561i
$313$	−822248.	+	822248.i	−0.474397	+	0.474397i	−0.903334	−	0.428937i	$-0.858888\pi$
$313$	−822248.	+	822248.i	−0.474397	+	0.474397i	0.428937	+	0.903334i	$0.358888\pi$
$314$	−1.66072e6	+	335452.i	−0.950546	+	0.192002i
$315$	739906.	+	313396.i	0.420146	+	0.177958i
$316$	−561802.	−	1.33392e6i	−0.316494	−	0.751469i
$317$	876274.	−	876274.i	0.489770	−	0.489770i	−0.418464	−	0.908233i	$-0.637431\pi$
$317$	876274.	−	876274.i	0.489770	−	0.489770i	0.908233	+	0.418464i	$0.137431\pi$
$318$	579984.	+	385054.i	0.321624	+	0.213528i
$319$	−618034.			−0.340044
$320$	−1.83170e6	+	17968.6i	−0.999952	+	0.00980933i
$321$	383418.			0.207687
$322$	−1.11239e6	−	738522.i	−0.597886	−	0.396939i
$323$	−114287.	+	114287.i	−0.0609525	+	0.0609525i
$324$	−589864.	−	1.40054e6i	−0.312169	−	0.741198i
$325$	−589303.	−	9374.42i	−0.309479	−	0.00492307i
$326$	−723986.	+	146239.i	−0.377300	+	0.0762114i
$327$	−41890.0	+	41890.0i	−0.0216641	+	0.0216641i
$328$	355089.	−	1.87188e6i	0.182243	−	0.960715i
$329$		−	1.25362e6i		−	0.638525i
$330$	172468.	−	113998.i	0.0871814	−	0.0576252i
$331$	1.68402e6			0.844847			0.422423	−	0.906399i	$-0.361180\pi$
$331$	1.68402e6			0.844847			0.422423	+	0.906399i	$0.361180\pi$
$332$	2.20309e6	+	897303.i	1.09695	+	0.446780i
$333$	−1.52272e6	−	1.52272e6i	−0.752507	−	0.752507i
$334$	253153.	−	51134.9i	0.124170	−	0.0250814i
$335$	−1.76315e6	−	746803.i	−0.858375	−	0.363575i
$336$	186987.	+	182610.i	0.0903574	+	0.0882424i
$337$	−2236.15	−	2236.15i	−0.00107257	−	0.00107257i	0.706570	−	0.707643i	$-0.250241\pi$
$337$	−2236.15	−	2236.15i	−0.00107257	−	0.00107257i	−0.707643	+	0.706570i	$0.750241\pi$
$338$	1.05042e6	−	1.58219e6i	0.500118	−	0.753298i
$339$		−	844008.i		−	0.398885i
$340$	1305.59	−	642432.i	0.000612507	−	0.301391i
$341$		−	1.32543e6i		−	0.617264i
$342$	481005.	+	319342.i	0.222374	+	0.147635i
$343$	1.32647e6	+	1.32647e6i	0.608783	+	0.608783i
$344$	608815.	+	893867.i	0.277389	+	0.407265i
$345$	−777031.	+	314640.i	−0.351472	+	0.142320i
$346$	510988.	+	2.52975e6i	0.229467	+	1.13602i
$347$	−682344.	−	682344.i	−0.304215	−	0.304215i	0.538446	−	0.842660i	$-0.319012\pi$
$347$	−682344.	−	682344.i	−0.304215	−	0.304215i	−0.842660	+	0.538446i	$0.819012\pi$
$348$	−454319.	−	185041.i	−0.201100	−	0.0819068i
$349$	−1.30340e6			−0.572816			−0.286408	−	0.958108i	$-0.592461\pi$
$349$	−1.30340e6			−0.572816			−0.286408	+	0.958108i	$0.592461\pi$
$350$	634502.	−	923491.i	0.276861	−	0.402960i
$351$		−	356793.i		−	0.154578i
$352$	−919534.	+	197099.i	−0.395559	+	0.0847868i
$353$	44466.9	−	44466.9i	0.0189933	−	0.0189933i	−0.697546	−	0.716540i	$-0.745725\pi$
$353$	44466.9	−	44466.9i	0.0189933	−	0.0189933i	0.716540	+	0.697546i	$0.245725\pi$
$354$	220694.	+	1.09259e6i	0.0936012	+	0.463391i
$355$	−304025.	−	750815.i	−0.128038	−	0.316200i
$356$	−890186.	+	374917.i	−0.372268	+	0.156787i
$357$	−64816.1	+	64816.1i	−0.0269161	+	0.0269161i
$358$	−1.68828e6	+	2.54296e6i	−0.696206	+	1.04865i
$359$	−1.02737e6			−0.420720			−0.210360	−	0.977624i	$-0.567464\pi$
$359$	−1.02737e6			−0.420720			−0.210360	+	0.977624i	$0.567464\pi$
$360$	−2.25038e6	+	449800.i	−0.915165	+	0.182921i
$361$	2.27355e6			0.918200
$362$	−1.33158e6	+	2.00568e6i	−0.534066	+	0.804432i
$363$	−383537.	+	383537.i	−0.152771	+	0.152771i
$364$	−148477.	−	352538.i	−0.0587364	−	0.139461i
$365$	848118.	−	2.00235e6i	0.333215	−	0.786696i
$366$	143894.	+	712375.i	0.0561487	+	0.277975i
$367$	1.10187e6	−	1.10187e6i	0.427038	−	0.427038i	−0.460580	−	0.887618i	$-0.652359\pi$
$367$	1.10187e6	−	1.10187e6i	0.427038	−	0.427038i	0.887618	+	0.460580i	$0.152359\pi$
$368$	3.81311e6	−	45156.0i	1.46777	−	0.0173818i
$369$		−	2.38695e6i		−	0.912593i
$370$	−2.50502e6	+	1.65577e6i	−0.951277	+	0.628776i
$371$	1.93703e6			0.730635
$372$	396838.	−	974328.i	0.148681	−	0.365046i
$373$	−1.38427e6	−	1.38427e6i	−0.515169	−	0.515169i	0.400937	−	0.916106i	$-0.368685\pi$
$373$	−1.38427e6	−	1.38427e6i	−0.515169	−	0.515169i	−0.916106	+	0.400937i	$0.868685\pi$
$374$	−65301.8	−	323289.i	−0.0241405	−	0.119512i
$375$	−253626.	−	656164.i	−0.0931357	−	0.240954i
$376$	2.01548e6	+	2.95914e6i	0.735205	+	1.07943i
$377$	507684.	+	507684.i	0.183967	+	0.183967i
$378$	565094.	+	375169.i	0.203419	+	0.135051i
$379$			452465.i			0.161803i	0.996722	+	0.0809017i	$0.0257800\pi$
$379$			452465.i			0.161803i	−0.996722	+	0.0809017i	$0.974220\pi$
$380$	570428.	−	568114.i	0.202648	−	0.201826i
$381$			940500.i			0.331930i
$382$	2.17151e6	−	3.27081e6i	0.761383	−	1.14683i
$383$	−3.93485e6	−	3.93485e6i	−1.37066	−	1.37066i	−0.859458	−	0.511206i	$-0.829199\pi$
$383$	−3.93485e6	−	3.93485e6i	−1.37066	−	1.37066i	−0.511206	−	0.859458i	$-0.670801\pi$
$384$	−734965.	−	130423.i	−0.254354	−	0.0451363i
$385$	224351.	−	529677.i	0.0771395	−	0.182121i
$386$	2.39033e6	−	482828.i	0.816564	−	0.164939i
$387$	958078.	+	958078.i	0.325180	+	0.325180i
$388$	−978012.	+	2.40125e6i	−0.329811	+	0.809762i
$389$	2.37516e6			0.795829			0.397914	−	0.917423i	$-0.369734\pi$
$389$	2.37516e6			0.795829			0.397914	+	0.917423i	$0.369734\pi$
$390$	−235318.	−	48030.2i	−0.0783418	−	0.0159902i
$391$			1.33740e6i			0.442406i
$392$	−2.27461e6	−	431483.i	−0.747638	−	0.141824i
$393$	399071.	−	399071.i	0.130337	−	0.130337i
$394$	319763.	−	64589.6i	0.103774	−	0.0209615i
$395$	−2.34365e6	+	949005.i	−0.755788	+	0.306038i
$396$	−1.08580e6	+	457304.i	−0.347947	+	0.146544i
$397$	−361147.	+	361147.i	−0.115003	+	0.115003i	−0.762266	−	0.647264i	$-0.775913\pi$
$397$	−361147.	+	361147.i	−0.115003	+	0.115003i	0.647264	+	0.762266i	$0.275913\pi$
$398$	−79311.3	−	52655.2i	−0.0250973	−	0.0166622i
$399$	−114870.			−0.0361221
$400$	−13006.5	+	3.19997e6i	−0.00406452	+	0.999992i
$401$	−835974.			−0.259616			−0.129808	−	0.991539i	$-0.541436\pi$
$401$	−835974.			−0.259616			−0.129808	+	0.991539i	$0.541436\pi$
$402$	−650051.	−	431572.i	−0.200624	−	0.133195i
$403$	−1.08878e6	+	1.08878e6i	−0.333946	+	0.333946i
$404$	5.15170e6	−	2.16973e6i	1.57035	−	0.661382i
$405$	−2.46071e6	+	996407.i	−0.745458	+	0.301855i
$406$	−1.33791e6	+	270247.i	−0.402821	+	0.0813665i
$407$	−1.09007e6	+	1.09007e6i	−0.326190	+	0.326190i
$408$	48790.2	−	257203.i	0.0145105	−	0.0764936i
$409$			1.88852e6i			0.558230i	0.960258	+	0.279115i	$0.0900410\pi$
$409$			1.88852e6i			0.558230i	−0.960258	+	0.279115i	$0.909959\pi$
$410$	−3.26113e6	−	665622.i	−0.958094	−	0.195554i
$411$	1.14664e6			0.334830
$412$	−820327.	+	2.01409e6i	−0.238092	+	0.584570i
$413$	2.19304e6	+	2.19304e6i	0.632662	+	0.632662i
$414$	4.68288e6	−	945902.i	1.34280	−	0.271235i
$415$	1.62077e6	−	3.82651e6i	0.461956	−	1.09064i
$416$	917259.	+	593445.i	0.259872	+	0.168131i
$417$	174050.	+	174050.i	0.0490155	+	0.0490155i
$418$	228608.	−	344338.i	0.0639956	−	0.0963927i
$419$		−	2.85044e6i		−	0.793190i	−0.917994	−	0.396595i	$-0.870192\pi$
$419$		−	2.85044e6i		−	0.793190i	0.917994	−	0.396595i	$-0.129808\pi$
$420$	323508.	−	322196.i	0.0894875	−	0.0891245i
$421$			2.95830e6i			0.813460i	0.913548	+	0.406730i	$0.133331\pi$
$421$			2.95830e6i			0.813460i	−0.913548	+	0.406730i	$0.866669\pi$
$422$	5.30015e6	+	3.51879e6i	1.44879	+	0.961862i
$423$	3.17171e6	+	3.17171e6i	0.861872	+	0.861872i
$424$	−4.57229e6	+	3.11420e6i	−1.23515	+	0.841262i
$425$	−1.12214e6	−	17850.6i	−0.301353	−	0.00479381i
$426$	−65354.7	−	323551.i	−0.0174483	−	0.0863811i
$427$	1.42988e6	+	1.42988e6i	0.379516	+	0.379516i
$428$	−1.14928e6	+	2.82176e6i	−0.303262	+	0.744578i
$429$	−123301.			−0.0323461
$430$	1.57613e6	−	1.04179e6i	0.411074	−	0.271712i
$431$		−	6.86223e6i		−	1.77939i	−0.456551	−	0.889697i	$-0.650916\pi$
$431$		−	6.86223e6i		−	1.77939i	0.456551	−	0.889697i	$-0.349084\pi$
$432$	−1.93705e6	+	22939.2i	−0.499381	+	0.00591383i
$433$	−561222.	+	561222.i	−0.143852	+	0.143852i	−0.775365	−	0.631513i	$-0.782434\pi$
$433$	−561222.	+	561222.i	−0.143852	+	0.143852i	0.631513	+	0.775365i	$0.282434\pi$
$434$	−579569.	−	2.86927e6i	−0.147700	−	0.731219i
$435$	−334233.	+	789101.i	−0.0846889	+	0.199944i
$436$	−182725.	−	433853.i	−0.0460343	−	0.109302i
$437$	−1.18510e6	+	1.18510e6i	−0.296859	+	0.296859i
$438$	490121.	−	738239.i	0.122072	−	0.183870i
$439$	6.03099e6			1.49358			0.746788	−	0.665062i	$-0.231595\pi$
$439$	6.03099e6			1.49358			0.746788	+	0.665062i	$0.231595\pi$
$440$	321999.	+	1.61098e6i	0.0792908	+	0.396697i
$441$	−2.90048e6			−0.710189
$442$	−211924.	+	319209.i	−0.0515970	+	0.0777175i
$443$	3.62984e6	−	3.62984e6i	0.878775	−	0.878775i	−0.114633	−	0.993408i	$-0.536569\pi$
$443$	3.62984e6	−	3.62984e6i	0.878775	−	0.878775i	0.993408	+	0.114633i	$0.0365691\pi$
$444$	−1.12769e6	+	474946.i	−0.271476	+	0.114337i
$445$	633316.	+	1.56403e6i	0.151607	+	0.374407i
$446$	−1.26439e6	−	6.25960e6i	−0.300984	−	1.49008i
$447$	338482.	−	338482.i	0.0801248	−	0.0801248i
$448$	−1.90441e6	+	828761.i	−0.448296	+	0.195090i
$449$			2.30175e6i			0.538817i	0.963026	+	0.269409i	$0.0868282\pi$
$449$			2.30175e6i			0.538817i	−0.963026	+	0.269409i	$0.913172\pi$
$450$	731152.	+	3.94177e6i	0.170207	+	0.917615i
$451$	−1.70875e6			−0.395582
$452$	6.21147e6	+	2.52989e6i	1.43004	+	0.582446i
$453$	1.09795e6	+	1.09795e6i	0.251383	+	0.251383i
$454$	−861149.	−	4.26329e6i	−0.196082	−	0.970745i
$455$	−619398.	+	250810.i	−0.140262	+	0.0567959i
$456$	271146.	−	184678.i	0.0610648	−	0.0415914i
$457$	5719.71	+	5719.71i	0.00128110	+	0.00128110i	0.707747	−	0.706466i	$-0.249712\pi$
$457$	5719.71	+	5719.71i	0.00128110	+	0.00128110i	−0.706466	+	0.707747i	$0.749712\pi$
$458$	−4.18857e6	−	2.78081e6i	−0.933045	−	0.619453i
$459$		−	679399.i		−	0.150520i
$460$	13538.3	−	6.66168e6i	0.00298312	−	1.46787i
$461$			3.18965e6i			0.699021i	0.936932	+	0.349511i	$0.113652\pi$
$461$			3.18965e6i			0.699021i	−0.936932	+	0.349511i	$0.886348\pi$
$462$	129651.	−	195285.i	0.0282599	−	0.0425662i
$463$	−1.48526e6	−	1.48526e6i	−0.321995	−	0.321995i	0.527537	−	0.849532i	$-0.323116\pi$
$463$	−1.48526e6	−	1.48526e6i	−0.321995	−	0.321995i	−0.849532	+	0.527537i	$0.823116\pi$
$464$	2.72362e6	−	2.78890e6i	0.587288	−	0.601364i
$465$	−1.69230e6	−	716794.i	−0.362948	−	0.153731i
$466$	3.64402e6	−	736062.i	0.777348	−	0.157018i
$467$	3.38074e6	+	3.38074e6i	0.717331	+	0.717331i	0.968058	−	0.250727i	$-0.0806695\pi$
$467$	3.38074e6	+	3.38074e6i	0.717331	+	0.717331i	−0.250727	+	0.968058i	$0.580670\pi$
$468$	1.26759e6	+	516280.i	0.267524	+	0.108961i
$469$	−2.17103e6			−0.455758
$470$	5.21776e6	−	3.44884e6i	1.08953	−	0.720159i
$471$			1.20609e6i			0.250512i
$472$	−8.70240e6	−	1.65081e6i	−1.79798	−	0.341069i
$473$	685860.	−	685860.i	0.140956	−	0.140956i
$474$	−1.00996e6	+	204003.i	−0.206470	+	0.0417052i
$475$	−978534.	−	1.01017e6i	−0.198995	−	0.205428i
$476$	−282729.	−	671298.i	−0.0571943	−	0.135799i
$477$	−4.90074e6	+	4.90074e6i	−0.986202	+	0.986202i
$478$	−5.65731e6	−	3.75592e6i	−1.13251	−	0.751876i
$479$	−6.30343e6			−1.25527			−0.627637	−	0.778506i	$-0.715978\pi$
$479$	−6.30343e6			−1.25527			−0.627637	+	0.778506i	$0.715978\pi$
$480$	−245630.	+	1.28065e6i	−0.0486608	+	0.253703i
$481$	1.79089e6			0.352943
$482$	−5.96412e6	−	3.95961e6i	−1.16931	−	0.776309i
$483$	−672108.	+	672108.i	−0.131091	+	0.131091i
$484$	−1.67300e6	−	3.97228e6i	−0.324624	−	0.770773i
$485$	4.17070e6	+	1.76655e6i	0.805108	+	0.341013i
$486$	−3.60940e6	+	729069.i	−0.693178	+	0.140016i
$487$	1.33324e6	−	1.33324e6i	0.254733	−	0.254733i	−0.568175	−	0.822908i	$-0.692350\pi$
$487$	1.33324e6	−	1.33324e6i	0.254733	−	0.254733i	0.822908	+	0.568175i	$0.192350\pi$
$488$	−5.67403e6	−	1.07634e6i	−1.07856	−	0.204597i
$489$			525791.i			0.0994354i
$490$	−808825.	+	3.96274e6i	−0.152182	+	0.745598i
$491$	−7.81891e6			−1.46367			−0.731834	−	0.681483i	$-0.761335\pi$
$491$	−7.81891e6			−1.46367			−0.731834	+	0.681483i	$0.761335\pi$
$492$	−1.25611e6	−	511604.i	−0.233945	−	0.0952843i
$493$	966725.	+	966725.i	0.179137	+	0.179137i
$494$	−470647.	+	95066.8i	−0.0867716	+	0.0175272i
$495$	772485.	+	1.90772e6i	0.141702	+	0.349946i
$496$	5.98105e6	+	5.84104e6i	1.09162	+	1.06607i
$497$	−649432.	−	649432.i	−0.117935	−	0.117935i
$498$	936629.	−	1.41079e6i	0.169237	−	0.254911i
$499$			3.92749e6i			0.706096i	0.935605	+	0.353048i	$0.114855\pi$
$499$			3.92749e6i			0.706096i	−0.935605	+	0.353048i	$0.885145\pi$
$500$	5.58927e6	+	100274.i	0.999839	+	0.0179376i
$501$		−	183851.i		−	0.0327244i
$502$	1.93404e6	+	1.28402e6i	0.342537	+	0.227412i
$503$	1.92930e6	+	1.92930e6i	0.340000	+	0.340000i	0.856367	−	0.516367i	$-0.172716\pi$
$503$	1.92930e6	+	1.92930e6i	0.340000	+	0.340000i	−0.516367	+	0.856367i	$0.672716\pi$
$504$	−2.15056e6	+	1.46475e6i	−0.377117	+	0.256855i
$505$	−3.66514e6	−	9.05138e6i	−0.639532	−	1.57938i
$506$	−677145.	−	3.35234e6i	−0.117572	−	0.582065i
$507$	−955960.	−	955960.i	−0.165166	−	0.165166i
$508$	−6.92160e6	−	2.81912e6i	−1.19000	−	0.484680i
$509$	1.31746e6			0.225394			0.112697	−	0.993629i	$-0.464051\pi$
$509$	1.31746e6			0.225394			0.112697	+	0.993629i	$0.464051\pi$
$510$	−448089.	−	91458.4i	−0.0762849	−	0.0155703i
$511$		−	2.46556e6i		−	0.417699i
$512$	3.16288e6	−	5.01802e6i	0.533222	−	0.845975i
$513$	602029.	−	602029.i	0.101001	−	0.101001i
$514$	270515.	+	1.33924e6i	0.0451631	+	0.223589i
$515$	3.49825e6	+	1.48173e6i	0.581210	+	0.246179i
$516$	709527.	−	298830.i	0.117313	−	0.0494082i
$517$	2.27054e6	−	2.27054e6i	0.373596	−	0.373596i
$518$	−1.88312e6	+	2.83643e6i	−0.308357	+	0.464460i
$519$	1.83721e6			0.299393
$520$	1.05884e6	−	1.58785e6i	0.171720	−	0.257514i
$521$	5.66671e6			0.914611			0.457306	−	0.889310i	$-0.348815\pi$
$521$	5.66671e6			0.914611			0.457306	+	0.889310i	$0.348815\pi$
$522$	2.70122e6	−	4.06869e6i	0.433895	−	0.653550i
$523$	5.93111e6	−	5.93111e6i	0.948161	−	0.948161i	−0.0505605	−	0.998721i	$-0.516101\pi$
$523$	5.93111e6	−	5.93111e6i	0.948161	−	0.948161i	0.998721	+	0.0505605i	$0.0161008\pi$
$524$	1.74075e6	+	4.13316e6i	0.276955	+	0.657588i
$525$	−554959.	−	572900.i	−0.0878744	−	0.0907153i
$526$	1.00848e6	+	4.99269e6i	0.158929	+	0.786811i
$527$	−2.07323e6	+	2.07323e6i	−0.325178	+	0.325178i
$528$	7927.33	+	669408.i	0.00123749	+	0.104497i
$529$			7.43182e6i			1.15466i
$530$	5.32894e6	+	8.06217e6i	0.824045	+	1.24670i
$531$	−1.10969e7			−1.70792
$532$	344318.	−	845381.i	0.0527450	−	0.129501i
$533$	1.40365e6	+	1.40365e6i	0.214014	+	0.214014i
$534$	136141.	+	673992.i	0.0206602	+	0.102283i
$535$	4.90108e6	+	2.07591e6i	0.740299	+	0.313563i
$536$	5.12466e6	−	3.49041e6i	0.770465	−	0.524765i
$537$	1.53646e6	+	1.53646e6i	0.229924	+	0.229924i
$538$	7.21728e6	+	4.79159e6i	1.07502	+	0.713714i
$539$			2.07637e6i			0.307846i
$540$	−6877.45	+	3.38412e6i	−0.00101495	+	0.499415i
$541$		−	6.18168e6i		−	0.908058i	−0.890987	−	0.454029i	$-0.849986\pi$
$541$		−	6.18168e6i		−	0.908058i	0.890987	−	0.454029i	$-0.150014\pi$
$542$	−242238.	+	364869.i	−0.0354197	+	0.0533505i
$543$	1.21183e6	+	1.21183e6i	0.176377	+	0.176377i
$544$	1.74663e6	+	1.13003e6i	0.253049	+	0.163716i
$545$	−762266.	+	308661.i	−0.109930	+	0.0445134i
$546$	−266919.	+	53915.5i	−0.0383176	+	0.00773984i
$547$	5.84113e6	+	5.84113e6i	0.834697	+	0.834697i	0.988155	−	0.153458i	$-0.0490410\pi$
$547$	5.84113e6	+	5.84113e6i	0.834697	+	0.834697i	−0.153458	+	0.988155i	$0.549041\pi$
$548$	−3.43704e6	+	8.43872e6i	−0.488914	+	1.20040i
$549$	−7.23529e6			−1.02453
$550$	2.82180e6	−	523411.i	0.397759	−	0.0737796i
$551$			1.71327e6i			0.240406i
$552$	505929.	−	2.66705e6i	0.0706710	−	0.372550i
$553$	−2.02718e6	+	2.02718e6i	−0.281890	+	0.281890i
$554$	2.12683e6	−	429603.i	0.294414	−	0.0594693i
$555$	802286.	+	1.98131e6i	0.110560	+	0.273036i
$556$	−1.80263e6	+	759208.i	−0.247297	+	0.104154i
$557$	7.29900e6	−	7.29900e6i	0.996840	−	0.996840i	−0.00315472	−	0.999995i	$-0.501004\pi$
$557$	7.29900e6	−	7.29900e6i	0.996840	−	0.996840i	0.999995	+	0.00315472i	$0.00100418\pi$
$558$	8.72569e6	+	5.79303e6i	1.18635	+	0.787626i
$559$	−1.12680e6			−0.152517
$560$	1.40149e6	+	3.34663e6i	0.188851	+	0.450960i
$561$	−234787.			−0.0314968
$562$	−7.03440e6	−	4.67017e6i	−0.939477	−	0.623724i
$563$	7.41145e6	−	7.41145e6i	0.985445	−	0.985445i	−0.0144511	−	0.999896i	$-0.504600\pi$
$563$	7.41145e6	−	7.41145e6i	0.985445	−	0.985445i	0.999896	+	0.0144511i	$0.00460007\pi$
$564$	2.34889e6	−	989274.i	0.310931	−	0.130954i
$565$	4.56965e6	−	1.07886e7i	0.602230	−	1.42182i
$566$	−1.34406e7	+	2.71488e6i	−1.76350	+	0.356213i
$567$	−2.12844e6	+	2.12844e6i	−0.278038	+	0.278038i
$568$	2.57707e6	+	488859.i	0.335162	+	0.0635789i
$569$			1.01281e7i			1.31144i	0.755005	+	0.655719i	$0.227634\pi$
$569$			1.01281e7i			1.31144i	−0.755005	+	0.655719i	$0.772366\pi$
$570$	−316017.	−	478103.i	−0.0407402	−	0.0616360i
$571$	−2.39436e6			−0.307326			−0.153663	−	0.988123i	$-0.549107\pi$
$571$	−2.39436e6			−0.307326			−0.153663	+	0.988123i	$0.549107\pi$
$572$	369590.	−	907429.i	0.0472313	−	0.115964i
$573$	−1.97623e6	−	1.97623e6i	−0.251449	−	0.251449i
$574$	−3.69907e6	+	747182.i	−0.468612	+	0.0946557i
$575$	−1.16360e7	−	185101.i	−1.46769	−	0.0233475i
$576$	2.72142e6	−	6.91501e6i	0.341775	−	0.868434i
$577$	−2.71492e6	−	2.71492e6i	−0.339483	−	0.339483i	0.516690	−	0.856173i	$-0.327164\pi$
$577$	−2.71492e6	−	2.71492e6i	−0.339483	−	0.339483i	−0.856173	+	0.516690i	$0.827164\pi$
$578$	4.03896e6	−	6.08365e6i	0.502864	−	0.757434i
$579$		−	1.73597e6i		−	0.215201i
$580$	−4.80552e6	−	4.82509e6i	−0.593158	−	0.595574i
$581$		−	4.71173e6i		−	0.579082i
$582$	1.53768e6	+	1.02088e6i	0.188174	+	0.124930i
$583$	3.50830e6	+	3.50830e6i	0.427489	+	0.427489i
$584$	3.96394e6	+	5.81989e6i	0.480944	+	0.706127i
$585$	932538.	−	2.20166e6i	0.112662	−	0.265987i
$586$	1.56599e6	+	7.75272e6i	0.188384	+	0.932632i
$587$	−4.93004e6	−	4.93004e6i	−0.590548	−	0.590548i	0.347231	−	0.937780i	$-0.387122\pi$
$587$	−4.93004e6	−	4.93004e6i	−0.590548	−	0.590548i	−0.937780	+	0.347231i	$0.887122\pi$
$588$	−621672.	+	1.52635e6i	−0.0741512	+	0.182058i
$589$	−3.67426e6			−0.436397
$590$	−3.09448e6	+	1.51610e7i	−0.365980	+	1.79307i
$591$		−	232226.i		−	0.0273491i
$592$	−115141.	−	9.72285e6i	−0.0135029	−	1.14022i
$593$	4.85092e6	−	4.85092e6i	0.566483	−	0.566483i	−0.364658	−	0.931141i	$-0.618814\pi$
$593$	4.85092e6	−	4.85092e6i	0.566483	−	0.566483i	0.931141	+	0.364658i	$0.118814\pi$
$594$	343989.	+	1.70298e6i	0.0400017	+	0.198036i
$595$	−1.17945e6	+	477589.i	−0.136580	+	0.0553047i
$596$	1.47646e6	+	3.50564e6i	0.170258	+	0.404252i
$597$	−47919.9	+	47919.9i	−0.00550276	+	0.00550276i
$598$	−2.19754e6	+	3.31002e6i	−0.251295	+	0.378511i
$599$	−8.77341e6			−0.999083			−0.499541	−	0.866290i	$-0.666498\pi$
$599$	−8.77341e6			−0.999083			−0.499541	+	0.866290i	$0.666498\pi$
$600$	2.23103e6	+	460095.i	0.253004	+	0.0521758i
$601$	1.04528e7			1.18044			0.590221	−	0.807241i	$-0.299040\pi$
$601$	1.04528e7			1.18044			0.590221	+	0.807241i	$0.299040\pi$
$602$	1.18484e6	−	1.78465e6i	0.133250	−	0.200706i
$603$	5.49278e6	−	5.49278e6i	0.615176	−	0.615176i
$604$	−1.13714e7	+	4.78927e6i	−1.26830	+	0.534167i
$605$	−6.97917e6	+	2.82605e6i	−0.775202	+	0.313900i
$606$	−787877.	−	3.90054e6i	−0.0871519	−	0.431463i
$607$	1.37249e6	−	1.37249e6i	0.151195	−	0.151195i	−0.627457	−	0.778651i	$-0.715904\pi$
$607$	1.37249e6	−	1.37249e6i	0.151195	−	0.151195i	0.778651	+	0.627457i	$0.215904\pi$
$608$	546384.	+	2.54906e6i	0.0599430	+	0.279654i
$609$			971650.i			0.106161i
$610$	−2.01762e6	+	9.88509e6i	−0.219541	+	1.07561i
$611$	−3.73027e6			−0.404238
$612$	2.41372e6	+	983092.i	0.260500	+	0.106100i
$613$	−6.45877e6	−	6.45877e6i	−0.694222	−	0.694222i	0.268936	−	0.963158i	$-0.413328\pi$
$613$	−6.45877e6	−	6.45877e6i	−0.694222	−	0.694222i	−0.963158	+	0.268936i	$0.913328\pi$
$614$	−3.06214e6	−	1.51597e7i	−0.327796	−	1.62282i
$615$	−924093.	+	2.18172e6i	−0.0985208	+	0.232600i
$616$	1.04857e6	+	1.53953e6i	0.111339	+	0.163469i
$617$	−1.02295e7	−	1.02295e7i	−1.08179	−	1.08179i	−0.996343	−	0.0854452i	$-0.972769\pi$
$617$	−1.02295e7	−	1.02295e7i	−1.08179	−	1.08179i	−0.0854452	−	0.996343i	$-0.527231\pi$
$618$	1.28976e6	+	856279.i	0.135843	+	0.0901871i
$619$			339048.i			0.0355659i	0.999842	+	0.0177830i	$0.00566079\pi$
$619$			339048.i			0.0355659i	−0.999842	+	0.0177830i	$0.994339\pi$
$620$	1.03479e7	−	1.03059e7i	1.08111	−	1.07673i
$621$		−	7.04501e6i		−	0.733082i
$622$	−9.22147e6	+	1.38897e7i	−0.955706	+	1.43952i
$623$	1.35284e6	+	1.35284e6i	0.139645	+	0.139645i
$624$	543374.	−	556397.i	0.0558647	−	0.0572036i
$625$	310617.	−	9.76068e6i	0.0318072	−	0.999494i
$626$	−6.44776e6	+	1.30239e6i	−0.657617	+	0.132833i
$627$	−208049.	−	208049.i	−0.0211348	−	0.0211348i
$628$	−8.87621e6	−	3.61522e6i	−0.898108	−	0.365794i
$629$	3.41018e6			0.343677
$630$	2.50645e6	+	3.79202e6i	0.251598	+	0.380644i
$631$			3.94331e6i			0.394265i	0.980377	+	0.197132i	$0.0631629\pi$
$631$			3.94331e6i			0.394265i	−0.980377	+	0.197132i	$0.936837\pi$
$632$	1.52596e6	−	8.04425e6i	0.151967	−	0.801112i
$633$	3.20235e6	−	3.20235e6i	0.317658	−	0.317658i
$634$	6.87142e6	−	1.38797e6i	0.678927	−	0.137138i
$635$	−5.09209e6	+	1.20220e7i	−0.501143	+	1.18316i
$636$	1.52857e6	+	3.62936e6i	0.149845	+	0.355785i
$637$	1.70564e6	−	1.70564e6i	0.166548	−	0.166548i
$638$	−2.91266e6	−	1.93373e6i	−0.283295	−	0.188081i
$639$	3.28617e6			0.318374
$640$	−8.68862e6	−	5.64641e6i	−0.838496	−	0.544907i
$641$	5.60671e6			0.538968			0.269484	−	0.963005i	$-0.413147\pi$
$641$	5.60671e6			0.538968			0.269484	+	0.963005i	$0.413147\pi$
$642$	1.80697e6	+	1.19965e6i	0.173026	+	0.114873i
$643$	−6.01251e6	+	6.01251e6i	−0.573493	+	0.573493i	−0.933103	−	0.359610i	$-0.882910\pi$
$643$	−6.01251e6	+	6.01251e6i	−0.573493	+	0.573493i	0.359610	+	0.933103i	$0.382910\pi$
$644$	−2.93175e6	−	6.96100e6i	−0.278555	−	0.661389i
$645$	−504787.	−	1.24662e6i	−0.0477759	−	0.117987i
$646$	−896199.	+	181025.i	−0.0844935	+	0.0170670i
$647$	−4.32220e6	+	4.32220e6i	−0.405923	+	0.405923i	−0.880314	−	0.474391i	$-0.842668\pi$
$647$	−4.32220e6	+	4.32220e6i	−0.405923	+	0.405923i	0.474391	+	0.880314i	$0.342668\pi$
$648$	1.60218e6	−	8.44606e6i	0.149890	−	0.790163i
$649$			7.94398e6i			0.740332i
$650$	−2.74793e6	−	1.88802e6i	−0.255107	−	0.175276i
$651$	−2.08379e6			−0.192709
$652$	−3.86955e6	−	1.57604e6i	−0.356485	−	0.145194i
$653$	3.27502e6	+	3.27502e6i	0.300559	+	0.300559i	0.841233	−	0.540673i	$-0.181830\pi$
$653$	3.27502e6	+	3.27502e6i	0.300559	+	0.300559i	−0.540673	+	0.841233i	$0.681830\pi$
$654$	−328486.	+	66351.4i	−0.0300312	+	0.00606605i
$655$	7.26182e6	−	2.94050e6i	0.661367	−	0.267805i
$656$	7.53029e6	−	7.71078e6i	0.683206	−	0.699582i
$657$	6.23796e6	+	6.23796e6i	0.563805	+	0.563805i
$658$	3.92239e6	−	5.90806e6i	0.353172	−	0.531962i
$659$		−	1.30557e7i		−	1.17108i	−0.810644	−	0.585540i	$-0.800883\pi$
$659$		−	1.30557e7i		−	1.17108i	0.810644	−	0.585540i	$-0.199117\pi$
$660$	1.16949e6	+	2376.71i	0.104505	+	0.000212382i
$661$			1.02730e7i			0.914523i	0.889332	+	0.457262i	$0.151170\pi$
$661$			1.02730e7i			0.914523i	−0.889332	+	0.457262i	$0.848830\pi$
$662$	7.93644e6	+	5.26904e6i	0.703851	+	0.467290i
$663$	192866.	+	192866.i	0.0170401	+	0.0170401i
$664$	7.57515e6	+	1.11219e7i	0.666763	+	0.978946i
$665$	−1.46833e6	−	621930.i	−0.128757	−	0.0545365i
$666$	−2.41191e6	−	1.19406e7i	−0.210705	−	1.04314i
$667$	1.00244e7	+	1.00244e7i	0.872459	+	0.872459i
$668$	1.35305e6	+	551089.i	0.117320	+	0.0477838i
$669$	−4.54600e6			−0.392703
$670$	−5.97271e6	−	9.03614e6i	−0.514026	−	0.777671i
$671$			5.17953e6i			0.444104i
$672$	309872.	+	1.44566e6i	0.0264703	+	0.123493i
$673$	−1.28945e7	+	1.28945e7i	−1.09740	+	1.09740i	−0.102690	+	0.994713i	$0.532745\pi$
$673$	−1.28945e7	+	1.28945e7i	−1.09740	+	1.09740i	−0.994713	+	0.102690i	$0.967255\pi$
$674$	−3541.94	−	17535.1i	−0.000300325	−	0.00148682i
$675$	5.91108e6	+	94031.3i	0.499353	+	0.00794352i
$676$	9.90084e6	−	4.16991e6i	0.833307	−	0.350962i
$677$	1.84920e6	−	1.84920e6i	0.155065	−	0.155065i	−0.625311	−	0.780376i	$-0.715028\pi$
$677$	1.84920e6	−	1.84920e6i	0.155065	−	0.155065i	0.780376	+	0.625311i	$0.215028\pi$
$678$	2.64077e6	−	3.97763e6i	0.220626	−	0.332315i
$679$	5.13554e6			0.427476
$680$	2.01622e6	−	3.02356e6i	0.167211	−	0.250753i
$681$	−3.09619e6			−0.255835
$682$	4.14706e6	−	6.24647e6i	0.341413	−	0.514249i
$683$	−1.91440e6	+	1.91440e6i	−0.157029	+	0.157029i	−0.781249	−	0.624220i	$-0.785417\pi$
$683$	−1.91440e6	+	1.91440e6i	−0.157029	+	0.157029i	0.624220	+	0.781249i	$0.285417\pi$
$684$	1.26771e6	+	3.00998e6i	0.103604	+	0.245993i
$685$	1.46571e7	+	6.20820e6i	1.19350	+	0.505521i
$686$	2.10106e6	+	1.04017e7i	0.170462	+	0.843906i
$687$	−2.53074e6	+	2.53074e6i	−0.204576	+	0.204576i
$688$	72445.2	+	6.11749e6i	0.00583497	+	0.492722i
$689$		−	5.76379e6i		−	0.462552i
$690$	−4.64644e6	−	948375.i	−0.371533	−	0.0758328i
$691$	840497.			0.0669639			0.0334820	−	0.999439i	$-0.489340\pi$
$691$	840497.			0.0669639			0.0334820	+	0.999439i	$0.489340\pi$
$692$	−5.50700e6	+	1.35210e7i	−0.437169	+	1.07335i
$693$	1.65012e6	+	1.65012e6i	0.130521	+	0.130521i
$694$	−1.08080e6	−	5.35069e6i	−0.0851814	−	0.421707i
$695$	1.28247e6	+	3.16716e6i	0.100713	+	0.248718i
$696$	−1.56214e6	−	2.29355e6i	−0.122236	−	0.179467i
$697$	2.67281e6	+	2.67281e6i	0.208395	+	0.208395i
$698$	−6.14266e6	−	4.07814e6i	−0.477219	−	0.316828i
$699$		−	2.64645e6i		−	0.204866i
$700$	5.87973e6	−	2.36696e6i	0.453536	−	0.182577i
$701$			1.89270e7i			1.45474i	0.686243	+	0.727372i	$0.259259\pi$
$701$			1.89270e7i			1.45474i	−0.686243	+	0.727372i	$0.740741\pi$
$702$	1.11635e6	−	1.68149e6i	0.0854981	−	0.128781i
$703$	3.02182e6	+	3.02182e6i	0.230611	+	0.230611i
$704$	−4.95026e6	−	1.94819e6i	−0.376440	−	0.148149i
$705$	−1.67110e6	−	4.12692e6i	−0.126628	−	0.312718i
$706$	348693.	−	70433.1i	0.0263288	−	0.00531820i
$707$	−7.82916e6	−	7.82916e6i	−0.589070	−	0.589070i
$708$	−2.37845e6	+	5.83964e6i	−0.178324	+	0.437828i
$709$	1.68667e7			1.26013			0.630065	−	0.776543i	$-0.283028\pi$
$709$	1.68667e7			1.26013			0.630065	+	0.776543i	$0.283028\pi$
$710$	916377.	−	4.48967e6i	0.0682226	−	0.334248i
$711$		−	1.02577e7i		−	0.760984i
$712$	−5.36831e6	−	1.01835e6i	−0.396861	−	0.0752827i
$713$	−2.14983e7	+	2.14983e7i	−1.58373	+	1.58373i
$714$	−508264.	+	102665.i	−0.0373116	+	0.00753663i
$715$	−1.57610e6	−	667578.i	−0.115297	−	0.0488356i
$716$	−1.59130e7	+	6.70205e6i	−1.16003	+	0.488568i
$717$	−3.41815e6	+	3.41815e6i	−0.248310	+	0.248310i
$718$	−4.84180e6	−	3.21449e6i	−0.350506	−	0.232703i
$719$	1.64633e7			1.18767			0.593834	−	0.804588i	$-0.297614\pi$
$719$	1.64633e7			1.18767			0.593834	+	0.804588i	$0.297614\pi$
$720$	−1.20129e7	−	4.92127e6i	−0.863608	−	0.353790i
$721$	4.30753e6			0.308596
$722$	1.07148e7	+	7.11359e6i	0.764962	+	0.507862i
$723$	−3.60353e6	+	3.60353e6i	−0.256379	+	0.256379i
$724$	−1.25509e7	+	5.28602e6i	−0.889872	+	0.374785i
$725$	−8.54475e6	+	8.27715e6i	−0.603746	+	0.584839i
$726$	−3.00756e6	+	607502.i	−0.211774	+	0.0427766i
$727$	5.31302e6	−	5.31302e6i	0.372825	−	0.372825i	−0.495680	−	0.868505i	$-0.665081\pi$
$727$	5.31302e6	−	5.31302e6i	0.372825	−	0.372825i	0.868505	+	0.495680i	$0.165081\pi$
$728$	403293.	−	2.12600e6i	0.0282028	−	0.148674i
$729$		−	8.91886e6i		−	0.621570i
$730$	1.02620e7	−	6.78300e6i	0.712731	−	0.471102i
$731$	−2.14564e6			−0.148513
$732$	−1.55077e6	+	3.80749e6i	−0.106972	+	0.262640i
$733$	−3.81861e6	−	3.81861e6i	−0.262509	−	0.262509i	0.563563	−	0.826073i	$-0.309430\pi$
$733$	−3.81861e6	−	3.81861e6i	−0.262509	−	0.262509i	−0.826073	+	0.563563i	$0.809430\pi$
$734$	8.64049e6	−	1.74531e6i	0.591968	−	0.119573i
$735$	2.65110e6	+	1.12290e6i	0.181012	+	0.0766698i
$736$	1.81116e7	+	1.17178e7i	1.23243	+	0.797354i
$737$	−3.93213e6	−	3.93213e6i	−0.266661	−	0.266661i
$738$	7.46838e6	−	1.12492e7i	0.504761	−	0.760291i
$739$		−	1.66587e7i		−	1.12210i	−0.827783	−	0.561049i	$-0.810398\pi$
$739$		−	1.66587e7i		−	1.12210i	0.827783	−	0.561049i	$-0.189602\pi$
$740$	−1.69863e7	−	34520.7i	−1.14030	−	0.00231740i
$741$			341805.i			0.0228682i
$742$	9.12878e6	+	6.06065e6i	0.608700	+	0.404119i
$743$	−1.01081e7	−	1.01081e7i	−0.671734	−	0.671734i	0.286381	−	0.958116i	$-0.407548\pi$
$743$	−1.01081e7	−	1.01081e7i	−0.671734	−	0.671734i	−0.958116	+	0.286381i	$0.907548\pi$
$744$	4.91873e6	−	3.35016e6i	0.325777	−	0.221888i
$745$	6.15930e6	−	2.49406e6i	0.406575	−	0.164633i
$746$	−2.19261e6	−	1.08550e7i	−0.144250	−	0.714136i
$747$	1.19208e7	+	1.19208e7i	0.781638	+	0.781638i
$748$	703768.	−	1.72791e6i	0.0459913	−	0.112919i
$749$	6.03488e6			0.393065
$750$	857747.	−	3.88592e6i	0.0556809	−	0.252255i
$751$		−	2.48823e6i		−	0.160987i	−0.996755	−	0.0804936i	$-0.974350\pi$
$751$		−	2.48823e6i		−	0.160987i	0.996755	−	0.0804936i	$-0.0256496\pi$
$752$	239829.	+	2.02519e7i	0.0154653	+	1.30593i
$753$	1.16855e6	−	1.16855e6i	0.0751035	−	0.0751035i
$754$	804144.	+	3.98107e6i	0.0515116	+	0.255019i
$755$	8.09010e6	+	1.99792e7i	0.516520	+	1.27559i
$756$	1.48932e6	+	3.53618e6i	0.0947729	+	0.225024i
$757$	−1.64168e7	+	1.64168e7i	−1.04123	+	1.04123i	−0.0421208	+	0.999113i	$0.513411\pi$
$757$	−1.64168e7	+	1.64168e7i	−1.04123	+	1.04123i	−0.999113	+	0.0421208i	$0.986589\pi$
$758$	−1.41569e6	+	2.13237e6i	−0.0894944	+	0.134800i
$759$	−2.43462e6			−0.153400
$760$	4.46585e6	−	892622.i	0.280459	−	0.0560575i
$761$	1.79829e7			1.12564			0.562820	−	0.826580i	$-0.309717\pi$
$761$	1.79829e7			1.12564			0.562820	+	0.826580i	$0.309717\pi$
$762$	−2.94268e6	+	4.43238e6i	−0.183593	+	0.276534i
$763$	−659336.	+	659336.i	−0.0410011	+	0.0410011i
$764$	2.04677e7	−	8.62033e6i	1.26863	−	0.534307i
$765$	1.77573e6	−	4.19236e6i	0.109704	−	0.259003i
$766$	−6.23258e6	−	3.08556e7i	−0.383792	−	1.90004i
$767$	6.52559e6	−	6.52559e6i	0.400527	−	0.400527i
$768$	−3.05566e6	−	2.91424e6i	−0.186940	−	0.178288i
$769$		−	1.25030e7i		−	0.762430i	−0.924486	−	0.381215i	$-0.875506\pi$
$769$		−	1.25030e7i		−	0.762430i	0.924486	−	0.381215i	$-0.124494\pi$
$770$	2.71460e6	−	1.79430e6i	0.164998	−	0.109060i
$771$	972614.			0.0589257
$772$	1.27758e7	+	5.20351e6i	0.771517	+	0.314234i
$773$	−1.81917e6	−	1.81917e6i	−0.109503	−	0.109503i	0.650233	−	0.759735i	$-0.274671\pi$
$773$	−1.81917e6	−	1.81917e6i	−0.109503	−	0.109503i	−0.759735	+	0.650233i	$0.774671\pi$
$774$	1.51754e6	+	7.51289e6i	0.0910517	+	0.450770i
$775$	−1.77511e7	−	1.83250e7i	−1.06163	−	1.09595i
$776$	−1.21223e7	+	8.25651e6i	−0.722653	+	0.492201i
$777$	1.71377e6	+	1.71377e6i	0.101836	+	0.101836i
$778$	1.11936e7	+	7.43151e6i	0.663014	+	0.440178i
$779$			4.73686e6i			0.279671i
$780$	−958724.	−	962628.i	−0.0564231	−	0.0566529i
$781$		−	2.35247e6i		−	0.138006i
$782$	−4.18452e6	+	6.30290e6i	−0.244697	+	0.368573i
$783$	−5.09240e6	−	5.09240e6i	−0.296837	−	0.296837i
$784$	−9.36969e6	−	9.15037e6i	−0.544422	−	0.531678i
$785$	−6.53005e6	+	1.54170e7i	−0.378218	+	0.892947i
$786$	3.12936e6	−	632106.i	0.180676	−	0.0364950i
$787$	−1.16865e7	−	1.16865e7i	−0.672584	−	0.672584i	0.285727	−	0.958311i	$-0.407765\pi$
$787$	−1.16865e7	−	1.16865e7i	−0.672584	−	0.672584i	−0.958311	+	0.285727i	$0.907765\pi$
$788$	1.70907e6	+	696092.i	0.0980491	+	0.0399348i
$789$	3.62591e6			0.207360
$790$	−1.40144e7	−	2.86045e6i	−0.798926	−	0.163067i
$791$		−	1.32844e7i		−	0.754922i
$792$	−6.54798e6	−	1.24212e6i	−0.370932	−	0.0703643i
$793$	4.25473e6	−	4.25473e6i	0.240264	−	0.240264i
$794$	−2.83198e6	+	572036.i	−0.159418	+	0.0322012i
$795$	6.37666e6	−	2.58208e6i	0.357829	−	0.144894i
$796$	−209027.	−	496305.i	−0.0116929	−	0.0277630i
$797$	−6.26999e6	+	6.26999e6i	−0.349640	+	0.349640i	−0.859975	−	0.510336i	$-0.829521\pi$
$797$	−6.26999e6	+	6.26999e6i	−0.349640	+	0.349640i	0.510336	+	0.859975i	$0.329521\pi$
$798$	−541355.	−	359409.i	−0.0300937	−	0.0199793i
$799$	−7.10313e6			−0.393625
$800$	−1.00735e7	+	1.50401e7i	−0.556488	+	0.830856i
$801$	−6.84544e6			−0.376982
$802$	−3.93976e6	−	2.61563e6i	−0.216289	−	0.143595i
$803$	4.46558e6	−	4.46558e6i	0.244393	−	0.244393i
$804$	−1.71323e6	−	4.06781e6i	−0.0934707	−	0.221932i
$805$	−1.22302e7	+	4.95235e6i	−0.665190	+	0.269353i
$806$	−8.53778e6	+	1.72456e6i	−0.462921	+	0.0935063i
$807$	4.36069e6	−	4.36069e6i	0.235706	−	0.235706i
$808$	3.10676e7	+	5.89339e6i	1.67409	+	0.317568i
$809$		−	2.59747e7i		−	1.39534i	−0.716419	−	0.697670i	$-0.754220\pi$
$809$		−	2.59747e7i		−	1.39534i	0.716419	−	0.697670i	$-0.245780\pi$
$810$	−1.47144e7	−	3.00332e6i	−0.788007	−	0.160838i
$811$	5.30606e6			0.283283			0.141641	−	0.989918i	$-0.454762\pi$
$811$	5.30606e6			0.283283			0.141641	+	0.989918i	$0.454762\pi$
$812$	−7.15084e6	−	2.91249e6i	−0.380599	−	0.155015i
$813$	220454.	+	220454.i	0.0116975	+	0.0116975i
$814$	−8.54796e6	+	1.72662e6i	−0.452170	+	0.0913345i
$815$	−2.84675e6	+	6.72098e6i	−0.150126	+	0.354437i
$816$	1.03468e6	−	1.05948e6i	0.0543979	−	0.0557018i
$817$	−1.90129e6	−	1.90129e6i	−0.0996537	−	0.0996537i
$818$	−5.90887e6	+	8.90018e6i	−0.308760	+	0.465067i
$819$		−	2.71098e6i		−	0.141227i
$820$	−1.32864e7	−	1.33405e7i	−0.690036	−	0.692846i
$821$			4.92332e6i			0.254918i	0.991844	+	0.127459i	$0.0406821\pi$
$821$			4.92332e6i			0.254918i	−0.991844	+	0.127459i	$0.959318\pi$
$822$	5.40389e6	+	3.58767e6i	0.278950	+	0.185197i
$823$	−2.16510e7	−	2.16510e7i	−1.11424	−	1.11424i	−0.992571	−	0.121669i	$-0.961175\pi$
$823$	−2.16510e7	−	2.16510e7i	−1.11424	−	1.11424i	−0.121669	−	0.992571i	$-0.538825\pi$
$824$	−1.01678e7	+	6.92531e6i	−0.521686	+	0.355321i
$825$	32495.4	−	2.04275e6i	0.00166221	−	0.104492i
$826$	3.47365e6	+	1.71970e7i	0.177148	+	0.877006i
$827$	−8.96397e6	−	8.96397e6i	−0.455761	−	0.455761i	0.441500	−	0.897261i	$-0.354446\pi$
$827$	−8.96397e6	−	8.96397e6i	−0.455761	−	0.455761i	−0.897261	+	0.441500i	$0.854446\pi$
$828$	2.50290e7	+	1.01941e7i	1.26872	+	0.516743i
$829$	−2.70989e7			−1.36951			−0.684756	−	0.728773i	$-0.740091\pi$
$829$	−2.70989e7			−1.36951			−0.684756	+	0.728773i	$0.740091\pi$
$830$	1.96109e7	−	1.29624e7i	0.988103	−	0.653117i
$831$		−	1.54460e6i		−	0.0775914i
$832$	2.46605e6	+	5.66674e6i	0.123508	+	0.283808i
$833$	3.24785e6	−	3.24785e6i	0.162175	−	0.162175i
$834$	275685.	+	1.36483e6i	0.0137246	+	0.0679462i
$835$	995413.	−	2.35010e6i	0.0494069	−	0.116646i
$836$	2.15476e6	−	907514.i	0.106631	−	0.0449094i
$837$	1.09211e7	−	1.09211e7i	0.538832	−	0.538832i
$838$	8.91859e6	−	1.34335e7i	0.438719	−	0.660815i
$839$	1.16465e7			0.571205			0.285603	−	0.958348i	$-0.407806\pi$
$839$	1.16465e7			0.571205			0.285603	+	0.958348i	$0.407806\pi$
$840$	2.53273e6	−	506235.i	0.123848	−	0.0247545i
$841$	−6.01909e6			−0.293455
$842$	−9.25604e6	+	1.39418e7i	−0.449930	+	0.677702i
$843$	−4.25019e6	+	4.25019e6i	−0.205987	+	0.205987i
$844$	1.39687e7	+	3.31666e7i	0.674994	+	1.60267i
$845$	−7.04388e6	−	1.73955e7i	−0.339367	−	0.838096i
$846$	5.02381e6	+	2.48714e7i	0.241328	+	1.19474i
$847$	−6.03677e6	+	6.03677e6i	−0.289132	+	0.289132i
$848$	−3.12921e7	+	370570.i	−1.49432	+	0.0176962i
$849$			9.76112e6i			0.464762i
$850$	−5.23257e6	−	3.59513e6i	−0.248409	−	0.170674i
$851$	3.53617e7			1.67382
$852$	704338.	−	1.72931e6i	0.0332416	−	0.0816158i
$853$	2.65427e6	+	2.65427e6i	0.124903	+	0.124903i	0.766795	−	0.641892i	$-0.221850\pi$
$853$	2.65427e6	+	2.65427e6i	0.124903	+	0.124903i	−0.641892	+	0.766795i	$0.721850\pi$
$854$	2.26485e6	+	1.12126e7i	0.106266	+	0.526091i
$855$	5.28844e6	−	2.14143e6i	0.247407	−	0.100182i
$856$	−1.42452e7	+	9.70241e6i	−0.664482	+	0.452580i
$857$	−5.26645e6	−	5.26645e6i	−0.244944	−	0.244944i	0.573948	−	0.818892i	$-0.305411\pi$
$857$	−5.26645e6	−	5.26645e6i	−0.244944	−	0.244944i	−0.818892	+	0.573948i	$0.805411\pi$
$858$	−581089.	−	385788.i	−0.0269479	−	0.0178908i
$859$		−	1.21919e7i		−	0.563754i	−0.959451	−	0.281877i	$-0.909043\pi$
$859$		−	1.21919e7i		−	0.563754i	0.959451	−	0.281877i	$-0.0909570\pi$
$860$	1.06875e7	+	21720.0i	0.492756	+	0.00100141i
$861$			2.68643e6i			0.123500i
$862$	2.14708e7	−	3.23402e7i	0.984194	−	1.48243i
$863$	1.50377e7	+	1.50377e7i	0.687313	+	0.687313i	0.961637	−	0.274324i	$-0.0884542\pi$
$863$	1.50377e7	+	1.50377e7i	0.687313	+	0.687313i	−0.274324	+	0.961637i	$0.588454\pi$
$864$	−9.20069e6	−	5.95263e6i	−0.419311	−	0.271284i
$865$	2.34844e7	+	9.94710e6i	1.06718	+	0.452019i
$866$	−4.40089e6	+	888944.i	−0.199409	+	0.0402791i
$867$	−3.67575e6	−	3.67575e6i	−0.166073	−	0.166073i
$868$	6.24611e6	−	1.53356e7i	0.281391	−	0.690880i
$869$	−7.34319e6			−0.329864
$870$	−4.04414e6	+	2.67310e6i	−0.181146	+	0.119734i
$871$			6.46010e6i			0.288532i
$872$	496315.	−	2.61637e6i	0.0221037	−	0.116522i
$873$	−1.29931e7	+	1.29931e7i	−0.577001	+	0.577001i
$874$	−9.29310e6	+	1.87713e6i	−0.411512	+	0.0831220i
$875$	−3.99201e6	−	1.03278e7i	−0.176267	−	0.456026i
$876$	4.61967e6	−	1.94565e6i	0.203400	−	0.0856654i
$877$	2.05535e7	−	2.05535e7i	0.902374	−	0.902374i	−0.0932667	−	0.995641i	$-0.529731\pi$
$877$	2.05535e7	−	2.05535e7i	0.902374	−	0.902374i	0.995641	+	0.0932667i	$0.0297309\pi$
$878$	2.84228e7	+	1.88700e7i	1.24431	+	0.826107i
$879$	5.63037e6			0.245790
$880$	−3.52300e6	+	8.59970e6i	−0.153358	+	0.374349i
$881$	−2.26167e6			−0.0981722			−0.0490861	−	0.998795i	$-0.515631\pi$
$881$	−2.26167e6			−0.0981722			−0.0490861	+	0.998795i	$0.515631\pi$
$882$	−1.36694e7	−	9.07515e6i	−0.591666	−	0.392810i
$883$	−2.22755e7	+	2.22755e7i	−0.961447	+	0.961447i	−0.999284	−	0.0378369i	$-0.987953\pi$
$883$	−2.22755e7	+	2.22755e7i	−0.961447	+	0.961447i	0.0378369	+	0.999284i	$0.487953\pi$
$884$	−1.99751e6	+	841285.i	−0.0859721	+	0.0362086i
$885$	1.01428e7	+	4.29611e6i	0.435312	+	0.184382i
$886$	2.84638e7	−	5.74946e6i	1.21817	−	0.246061i
$887$	2.17811e7	−	2.17811e7i	0.929546	−	0.929546i	−0.0681306	−	0.997676i	$-0.521703\pi$
$887$	2.17811e7	−	2.17811e7i	0.929546	−	0.929546i	0.997676	+	0.0681306i	$0.0217035\pi$
$888$	−6.80059e6	−	1.29004e6i	−0.289410	−	0.0548999i
$889$			1.48032e7i			0.628205i
$890$	−1.90891e6	+	9.35247e6i	−0.0807814	+	0.395778i
$891$	−7.70997e6			−0.325356
$892$	1.36265e7	−	3.34562e7i	0.573420	−	1.40788i
$893$	−6.29422e6	−	6.29422e6i	−0.264127	−	0.264127i
$894$	2.65425e6	−	536136.i	0.111070	−	0.0224353i
$895$	1.13212e7	+	2.79587e7i	0.472427	+	1.16670i
$896$	−1.15681e7	−	2.05282e6i	−0.481386	−	0.0854242i
$897$	1.99992e6	+	1.99992e6i	0.0829910	+	0.0829910i
$898$	−7.20180e6	+	1.08476e7i	−0.298023	+	0.448894i
$899$			3.10796e7i			1.28255i
$900$	−8.88742e6	+	2.08644e7i	−0.365737	+	0.858617i
$901$		−	1.09753e7i		−	0.450407i
$902$	−8.05296e6	−	5.34640e6i	−0.329564	−	0.218799i
$903$	−1.07828e6	−	1.07828e6i	−0.0440062	−	0.0440062i
$904$	2.13577e7	+	3.13575e7i	0.869227	+	1.27621i
$905$	8.92923e6	+	2.20515e7i	0.362404	+	0.894986i
$906$	1.73909e6	+	8.60971e6i	0.0703885	+	0.348472i
$907$	2.03843e6	+	2.03843e6i	0.0822769	+	0.0822769i	0.747048	−	0.664771i	$-0.231471\pi$
$907$	2.03843e6	+	2.03843e6i	0.0822769	+	0.0822769i	−0.664771	+	0.747048i	$0.731471\pi$
$908$	9.28074e6	−	2.27864e7i	0.373567	−	0.917192i
$909$	3.96161e7			1.59024
$910$	−3.70383e6	−	755982.i	−0.148268	−	0.0302627i
$911$			4.66042e7i			1.86050i	0.366927	+	0.930250i	$0.380410\pi$
$911$			4.66042e7i			1.86050i	−0.366927	+	0.930250i	$0.619590\pi$
$912$	1.85568e6	−	21975.6i	0.0738782	−	0.000874889i
$913$	8.53379e6	−	8.53379e6i	0.338817	−	0.338817i
$914$	9059.70	+	44851.8i	0.000358714	+	0.00177588i
$915$	6.61319e6	+	2.80110e6i	0.261131	+	0.110605i
$916$	−1.10391e7	−	2.62108e7i	−0.434706	−	1.03215i
$917$	6.28126e6	−	6.28126e6i	0.246674	−	0.246674i
$918$	2.12573e6	−	3.20186e6i	0.0832534	−	0.125400i
$919$	−4.04857e7			−1.58129			−0.790647	−	0.612273i	$-0.790255\pi$
$919$	−4.04857e7			−1.58129			−0.790647	+	0.612273i	$0.790255\pi$
$920$	2.09071e7	−	3.13527e7i	0.814376	−	1.22125i
$921$	−1.10097e7			−0.427686
$922$	−9.97990e6	+	1.50321e7i	−0.386633	+	0.582362i
$923$	−1.93244e6	+	1.93244e6i	−0.0746625	+	0.0746625i
$924$	1.22203e6	−	514681.i	0.0470872	−	0.0198316i
$925$	−471981.	+	2.96701e7i	−0.0181372	+	1.14016i
$926$	−2.35257e6	−	1.16468e7i	−0.0901601	−	0.446355i
$927$	−1.08982e7	+	1.08982e7i	−0.416539	+	0.416539i
$928$	2.15618e7	−	4.62171e6i	0.821894	−	0.176170i
$929$			4.30491e6i			0.163653i	0.996647	+	0.0818266i	$0.0260754\pi$
$929$			4.30491e6i			0.163653i	−0.996647	+	0.0818266i	$0.973925\pi$
$930$	−5.73271e6	−	8.67304e6i	−0.217346	−	0.328824i
$931$	5.75597e6			0.217643
$932$	1.94765e7	+	7.93266e6i	0.734465	+	0.299143i
$933$	8.39220e6	+	8.39220e6i	0.315625	+	0.315625i
$934$	5.35491e6	+	2.65105e7i	0.200856	+	0.994377i
$935$	−3.00119e6	−	1.27119e6i	−0.112270	−	0.0475534i
$936$	4.35850e6	+	6.39919e6i	0.162610	+	0.238746i
$937$	−1.44578e7	−	1.44578e7i	−0.537963	−	0.537963i	0.384968	−	0.922930i	$-0.374213\pi$
$937$	−1.44578e7	−	1.44578e7i	−0.537963	−	0.537963i	−0.922930	+	0.384968i	$0.874213\pi$
$938$	−1.02316e7	−	6.79281e6i	−0.379697	−	0.252082i
$939$			4.68265e6i			0.173312i
$940$	3.53811e7	+	71903.8i	1.30602	+	0.00265419i
$941$		−	3.49788e7i		−	1.28775i	−0.765132	−	0.643873i	$-0.777326\pi$
$941$		−	3.49788e7i		−	1.28775i	0.765132	−	0.643873i	$-0.222674\pi$
$942$	−3.77367e6	+	5.68405e6i	−0.138560	+	0.208704i
$943$	2.77157e7	+	2.77157e7i	1.01495	+	1.01495i
$944$	−3.58474e7	−	3.50084e7i	−1.30927	−	1.27862i
$945$	6.21295e6	−	2.51579e6i	0.226318	−	0.0916419i
$946$	5.37826e6	−	1.08636e6i	0.195395	−	0.0394682i
$947$	−1.50689e7	−	1.50689e7i	−0.546019	−	0.546019i	0.379268	−	0.925287i	$-0.376176\pi$
$947$	−1.50689e7	−	1.50689e7i	−0.546019	−	0.546019i	−0.925287	+	0.379268i	$0.876176\pi$
$948$	−5.39800e6	−	2.19857e6i	−0.195080	−	0.0794548i
$949$	−7.33651e6			−0.264438
$950$	−1.45096e6	−	7.82239e6i	−0.0521611	−	0.281210i
$951$		−	4.99033e6i		−	0.178928i
$952$	767944.	−	4.04829e6i	0.0274623	−	0.144770i
$953$	3.59441e7	−	3.59441e7i	1.28202	−	1.28202i	0.342508	−	0.939515i	$-0.388724\pi$
$953$	3.59441e7	−	3.59441e7i	1.28202	−	1.28202i	0.939515	−	0.342508i	$-0.111276\pi$
$954$	−3.84298e7	+	7.76250e6i	−1.36709	+	0.276141i
$955$	−1.45616e7	−	3.59611e7i	−0.516655	−	1.27592i
$956$	−1.49100e7	−	3.54017e7i	−0.527635	−	1.25279i
$957$	−1.75983e6	+	1.75983e6i	−0.0621143	+	0.0621143i
$958$	−2.97067e7	−	1.97224e7i	−1.04578	−	0.694300i
$959$	1.80479e7			0.633693
$960$	−5.16454e6	+	5.26687e6i	−0.180865	+	0.184448i
$961$	−3.80238e7			−1.32815
$962$	8.44006e6	+	5.60340e6i	0.294041	+	0.195215i
$963$	−1.52685e7	+	1.52685e7i	−0.530554	+	0.530554i
$964$	−1.57186e7	−	3.73216e7i	−0.544781	−	1.29350i
$965$	9.39892e6	−	2.21902e7i	0.324907	−	0.767083i
$966$	−5.27042e6	+	1.06458e6i	−0.181720	+	0.0367059i
$967$	−3.62125e7	+	3.62125e7i	−1.24535	+	1.24535i	−0.287603	+	0.957750i	$0.592858\pi$
$967$	−3.62125e7	+	3.62125e7i	−1.24535	+	1.24535i	−0.957750	+	0.287603i	$0.907142\pi$
$968$	4.54417e6	−	2.39550e7i	0.155871	−	0.821691i
$969$			650859.i			0.0222678i
$970$	1.41283e7	+	2.13748e7i	0.482127	+	0.729412i
$971$	−5.26128e6			−0.179079			−0.0895393	−	0.995983i	$-0.528539\pi$
$971$	−5.26128e6			−0.179079			−0.0895393	+	0.995983i	$0.528539\pi$
$972$	−1.92915e7	−	7.85730e6i	−0.654937	−	0.266752i
$973$	2.73950e6	+	2.73950e6i	0.0927659	+	0.0927659i
$974$	1.04548e7	−	2.11178e6i	0.353115	−	0.0713264i
$975$	−1.70472e6	+	1.65133e6i	−0.0574302	+	0.0556317i
$976$	−2.33728e7	−	2.28257e7i	−0.785392	−	0.767008i
$977$	82708.3	+	82708.3i	0.00277212	+	0.00277212i	0.708491	−	0.705719i	$-0.249376\pi$
$977$	82708.3	+	82708.3i	0.00277212	+	0.00277212i	−0.705719	+	0.708491i	$0.749376\pi$
$978$	−1.64512e6	+	2.47794e6i	−0.0549983	+	0.0828407i
$979$			4.90046e6i			0.163410i
$980$	−1.62106e7	+	1.61448e7i	−0.539180	+	0.536993i
$981$		−	3.33629e6i		−	0.110686i
$982$	−3.68489e7	−	2.44641e7i	−1.21940	−	0.809564i
$983$	1.09551e7	+	1.09551e7i	0.361604	+	0.361604i	0.864403	−	0.502799i	$-0.167697\pi$
$983$	1.09551e7	+	1.09551e7i	0.361604	+	0.361604i	−0.502799	+	0.864403i	$0.667697\pi$
$984$	−4.31903e6	−	6.34124e6i	−0.142200	−	0.208779i
$985$	1.25733e6	−	2.96846e6i	0.0412912	−	0.0974856i
$986$	1.53124e6	+	7.58070e6i	0.0501592	+	0.248323i
$987$	−3.56966e6	−	3.56966e6i	−0.116636	−	0.116636i
$988$	−2.51551e6	−	1.02455e6i	−0.0819848	−	0.0333919i
$989$	−2.22491e7			−0.723306
$990$	−2.32839e6	+	1.14077e7i	−0.0755036	+	0.369920i
$991$			2.92399e7i			0.945785i	0.881120	+	0.472892i	$0.156790\pi$
$991$			2.92399e7i			0.945785i	−0.881120	+	0.472892i	$0.843210\pi$
$992$	9.91168e6	+	4.62413e7i	0.319792	+	1.49194i
$993$	4.79520e6	−	4.79520e6i	0.154324	−	0.154324i
$994$	−1.02866e6	−	5.09260e6i	−0.0330223	−	0.163483i
$995$	−871992.	+	353092.i	−0.0279225	+	0.0113066i
$996$	8.82826e6	−	3.71818e6i	0.281986	−	0.118763i
$997$	−5.95122e6	+	5.95122e6i	−0.189613	+	0.189613i	−0.795529	−	0.605916i	$-0.792807\pi$
$997$	−5.95122e6	+	5.95122e6i	−0.189613	+	0.189613i	0.605916	+	0.795529i	$0.292807\pi$
$998$	−1.22885e7	+	1.85094e7i	−0.390546	+	0.588256i
$999$	−1.79637e7			−0.569485

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.k.a.27.23	yes	56
4.3	odd	2		160.6.o.a.47.13		56
5.3	odd	4	inner	40.6.k.a.3.19	✓	56
8.3	odd	2	inner	40.6.k.a.27.19	yes	56
8.5	even	2		160.6.o.a.47.14		56
20.3	even	4		160.6.o.a.143.14		56
40.3	even	4	inner	40.6.k.a.3.23	yes	56
40.13	odd	4		160.6.o.a.143.13		56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.k.a.3.19	✓	56	5.3	odd	4	inner
40.6.k.a.3.23	yes	56	40.3	even	4	inner
40.6.k.a.27.19	yes	56	8.3	odd	2	inner
40.6.k.a.27.23	yes	56	1.1	even	1	trivial
160.6.o.a.47.13		56	4.3	odd	2
160.6.o.a.47.14		56	8.5	even	2
160.6.o.a.143.13		56	40.13	odd	4
160.6.o.a.143.14		56	20.3	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(4.71279 + 3.12884i) q^{2} +(2.84747 - 2.84747i) q^{3} +(12.4207 + 29.4911i) q^{4} +(51.8149 - 20.9812i) q^{5} +(22.3288 - 4.51023i) q^{6} +(44.8183 - 44.8183i) q^{7} +(-33.7370 + 177.848i) q^{8} +226.784i q^{9} +O(q^{10})\)	\(q+(4.71279 + 3.12884i) q^{2} +(2.84747 - 2.84747i) q^{3} +(12.4207 + 29.4911i) q^{4} +(51.8149 - 20.9812i) q^{5} +(22.3288 - 4.51023i) q^{6} +(44.8183 - 44.8183i) q^{7} +(-33.7370 + 177.848i) q^{8} +226.784i q^{9} +(309.840 + 63.2407i) q^{10} +162.348 q^{11} +(119.343 + 48.6075i) q^{12} +(-133.361 - 133.361i) q^{13} +(351.449 - 70.9897i) q^{14} +(87.7980 - 207.285i) q^{15} +(-715.452 + 732.601i) q^{16} +(-253.944 - 253.944i) q^{17} +(-709.571 + 1068.78i) q^{18} -450.049i q^{19} +(1262.34 + 1267.48i) q^{20} -255.238i q^{21} +(765.112 + 507.961i) q^{22} +(-2633.26 - 2633.26i) q^{23} +(410.351 + 602.481i) q^{24} +(2244.58 - 2174.28i) q^{25} +(-211.236 - 1045.77i) q^{26} +(1337.69 + 1337.69i) q^{27} +(1878.42 + 765.068i) q^{28} -3806.84 q^{29} +(1062.33 - 702.183i) q^{30} -8164.13i q^{31} +(-5663.97 + 1214.05i) q^{32} +(462.281 - 462.281i) q^{33} +(-402.233 - 1991.33i) q^{34} +(1381.92 - 3262.60i) q^{35} +(-6688.11 + 2816.81i) q^{36} +(-6714.43 + 6714.43i) q^{37} +(1408.13 - 2120.99i) q^{38} -759.483 q^{39} +(1983.39 + 9923.01i) q^{40} -10525.2 q^{41} +(798.598 - 1202.88i) q^{42} +(4224.63 - 4224.63i) q^{43} +(2016.48 + 4787.83i) q^{44} +(4758.20 + 11750.8i) q^{45} +(-4170.94 - 20649.1i) q^{46} +(13985.6 - 13985.6i) q^{47} +(48.8292 + 4123.29i) q^{48} +12789.6i q^{49} +(17381.2 - 3224.00i) q^{50} -1446.20 q^{51} +(2276.53 - 5589.40i) q^{52} +(21609.7 + 21609.7i) q^{53} +(2118.83 + 10489.7i) q^{54} +(8412.06 - 3406.26i) q^{55} +(6458.81 + 9482.87i) q^{56} +(-1281.50 - 1281.50i) q^{57} +(-17940.8 - 11911.0i) q^{58} +48931.8i q^{59} +(7203.58 + 14.6396i) q^{60} +31903.9i q^{61} +(25544.3 - 38475.8i) q^{62} +(10164.1 + 10164.1i) q^{63} +(-30491.6 - 12000.1i) q^{64} +(-9708.17 - 4112.01i) q^{65} +(3625.04 - 732.227i) q^{66} +(-24220.4 - 24220.4i) q^{67} +(4334.93 - 10643.3i) q^{68} -14996.3 q^{69} +(16720.8 - 11052.2i) q^{70} -14490.3i q^{71} +(-40333.0 - 7651.00i) q^{72} +(27506.2 - 27506.2i) q^{73} +(-52652.0 + 10635.3i) q^{74} +(200.159 - 12582.6i) q^{75} +(13272.5 - 5589.93i) q^{76} +(7276.17 - 7276.17i) q^{77} +(-3579.28 - 2376.30i) q^{78} -45231.1 q^{79} +(-21700.3 + 52970.7i) q^{80} -47490.4 q^{81} +(-49603.1 - 32931.7i) q^{82} +(52564.8 - 52564.8i) q^{83} +(7527.24 - 3170.23i) q^{84} +(-18486.2 - 7830.04i) q^{85} +(33128.0 - 6691.58i) q^{86} +(-10839.9 + 10839.9i) q^{87} +(-5477.13 + 28873.2i) q^{88} +30184.9i q^{89} +(-14342.0 + 70266.6i) q^{90} -11954.0 q^{91} +(44950.9 - 110365. i) q^{92} +(-23247.1 - 23247.1i) q^{93} +(109670. - 22152.4i) q^{94} +(-9442.59 - 23319.3i) q^{95} +(-12671.0 + 19584.9i) q^{96} +(57292.8 + 57292.8i) q^{97} +(-40016.7 + 60274.8i) q^{98} +36817.9i 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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