LMFDB - Embedded newform 43.5.d.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,5,Mod(7,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("43.7");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	43.d (of order $6$, 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:	$4.44490841261$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	43.7
Dual form			43.5.d.a.37.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.38404i q^{2} +(15.2777 - 8.82059i) q^{3} -38.5241 q^{4} +(-17.1186 + 9.88344i) q^{5} +(-65.1316 - 112.811i) q^{6} +(36.3076 + 20.9622i) q^{7} +166.319i q^{8} +(115.106 - 199.369i) q^{9} +O(q^{10})$	\(q-7.38404i q^{2} +(15.2777 - 8.82059i) q^{3} -38.5241 q^{4} +(-17.1186 + 9.88344i) q^{5} +(-65.1316 - 112.811i) q^{6} +(36.3076 + 20.9622i) q^{7} +166.319i q^{8} +(115.106 - 199.369i) q^{9} +(72.9798 + 126.405i) q^{10} +56.0930 q^{11} +(-588.560 + 339.805i) q^{12} +(-36.9428 + 63.9869i) q^{13} +(154.786 - 268.097i) q^{14} +(-174.356 + 301.993i) q^{15} +611.722 q^{16} +(84.5100 - 146.376i) q^{17} +(-1472.15 - 849.944i) q^{18} +(-147.491 + 85.1540i) q^{19} +(659.480 - 380.751i) q^{20} +739.596 q^{21} -414.193i q^{22} +(240.154 + 415.960i) q^{23} +(1467.03 + 2540.97i) q^{24} +(-117.135 + 202.884i) q^{25} +(472.482 + 272.788i) q^{26} -2632.26i q^{27} +(-1398.72 - 807.551i) q^{28} +(499.097 + 288.154i) q^{29} +(2229.93 + 1287.45i) q^{30} +(-649.211 - 1124.47i) q^{31} -1855.88i q^{32} +(856.973 - 494.773i) q^{33} +(-1080.84 - 624.026i) q^{34} -828.715 q^{35} +(-4434.34 + 7680.50i) q^{36} +(-673.776 + 389.005i) q^{37} +(628.781 + 1089.08i) q^{38} +1303.43i q^{39} +(-1643.81 - 2847.15i) q^{40} +1607.43 q^{41} -5461.21i q^{42} +(105.398 + 1845.99i) q^{43} -2160.93 q^{44} +4550.55i q^{45} +(3071.46 - 1773.31i) q^{46} -876.593 q^{47} +(9345.71 - 5395.75i) q^{48} +(-321.672 - 557.152i) q^{49} +(1498.10 + 864.931i) q^{50} -2981.71i q^{51} +(1423.19 - 2465.04i) q^{52} +(2175.56 + 3768.18i) q^{53} -19436.7 q^{54} +(-960.236 + 554.392i) q^{55} +(-3486.42 + 6038.65i) q^{56} +(-1502.22 + 2601.92i) q^{57} +(2127.74 - 3685.35i) q^{58} -944.218 q^{59} +(6716.89 - 11634.0i) q^{60} +(3648.62 + 2106.53i) q^{61} +(-8303.11 + 4793.80i) q^{62} +(8358.41 - 4825.73i) q^{63} -3916.32 q^{64} -1460.49i q^{65} +(-3653.43 - 6327.92i) q^{66} +(-841.544 - 1457.60i) q^{67} +(-3255.67 + 5638.99i) q^{68} +(7338.02 + 4236.61i) q^{69} +6119.27i q^{70} +(-1825.13 - 1053.74i) q^{71} +(33158.8 + 19144.2i) q^{72} +(-7296.97 - 4212.91i) q^{73} +(2872.43 + 4975.20i) q^{74} +4132.80i q^{75} +(5681.97 - 3280.48i) q^{76} +(2036.60 + 1175.83i) q^{77} +9624.59 q^{78} +(-5320.11 + 9214.69i) q^{79} +(-10471.8 + 6045.92i) q^{80} +(-13894.5 - 24066.0i) q^{81} -11869.3i q^{82} +(1324.56 + 2294.21i) q^{83} -28492.3 q^{84} +3341.00i q^{85} +(13630.9 - 778.265i) q^{86} +10166.7 q^{87} +9329.34i q^{88} +(-3600.92 + 2078.99i) q^{89} +33601.5 q^{90} +(-2682.61 + 1548.81i) q^{91} +(-9251.74 - 16024.5i) q^{92} +(-19836.9 - 11452.8i) q^{93} +6472.80i q^{94} +(1683.23 - 2915.44i) q^{95} +(-16369.9 - 28353.5i) q^{96} +5999.67 q^{97} +(-4114.04 + 2375.24i) q^{98} +(6456.62 - 11183.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9}+O(q^{10}) $ 28 * q + 6 * q^3 - 234 * q^4 - 3 * q^5 + 15 * q^6 + 129 * q^7 + 534 * q^9	\( 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9} + 91 q^{10} - 376 q^{11} - 1026 q^{12} - 198 q^{13} + 78 q^{14} - 289 q^{15} + 806 q^{16} + 23 q^{17} - 435 q^{18} - 438 q^{19} + 177 q^{20} + 1684 q^{21} - 214 q^{23} + 1450 q^{24} + 463 q^{25} + 45 q^{26} - 3828 q^{28} + 1725 q^{29} + 8127 q^{30} + 2135 q^{31} - 474 q^{33} + 201 q^{34} - 6882 q^{35} - 12052 q^{36} + 1638 q^{37} - 2124 q^{38} - 6721 q^{40} + 3014 q^{41} + 157 q^{43} + 17162 q^{44} - 6240 q^{46} - 3670 q^{47} + 11547 q^{48} + 3085 q^{49} + 9738 q^{50} + 13746 q^{52} + 1208 q^{53} - 32416 q^{54} - 11202 q^{55} - 16245 q^{56} + 6207 q^{57} - 5756 q^{58} - 8716 q^{59} - 281 q^{60} + 8382 q^{61} - 25191 q^{62} + 23625 q^{63} + 17564 q^{64} - 21909 q^{66} - 9295 q^{67} + 6758 q^{68} + 30663 q^{69} + 24828 q^{71} + 46194 q^{72} + 5307 q^{73} + 13866 q^{74} + 5178 q^{76} - 27645 q^{77} - 10592 q^{78} - 24914 q^{79} - 13683 q^{80} - 43222 q^{81} + 7010 q^{83} - 21568 q^{84} + 15366 q^{86} + 57084 q^{87} - 80787 q^{89} + 114772 q^{90} - 24438 q^{91} + 22049 q^{92} - 39723 q^{93} + 29955 q^{95} + 1378 q^{96} - 12210 q^{97} + 28845 q^{98} - 49211 q^{99}+O(q^{100}) \) 28 * q + 6 * q^3 - 234 * q^4 - 3 * q^5 + 15 * q^6 + 129 * q^7 + 534 * q^9 + 91 * q^10 - 376 * q^11 - 1026 * q^12 - 198 * q^13 + 78 * q^14 - 289 * q^15 + 806 * q^16 + 23 * q^17 - 435 * q^18 - 438 * q^19 + 177 * q^20 + 1684 * q^21 - 214 * q^23 + 1450 * q^24 + 463 * q^25 + 45 * q^26 - 3828 * q^28 + 1725 * q^29 + 8127 * q^30 + 2135 * q^31 - 474 * q^33 + 201 * q^34 - 6882 * q^35 - 12052 * q^36 + 1638 * q^37 - 2124 * q^38 - 6721 * q^40 + 3014 * q^41 + 157 * q^43 + 17162 * q^44 - 6240 * q^46 - 3670 * q^47 + 11547 * q^48 + 3085 * q^49 + 9738 * q^50 + 13746 * q^52 + 1208 * q^53 - 32416 * q^54 - 11202 * q^55 - 16245 * q^56 + 6207 * q^57 - 5756 * q^58 - 8716 * q^59 - 281 * q^60 + 8382 * q^61 - 25191 * q^62 + 23625 * q^63 + 17564 * q^64 - 21909 * q^66 - 9295 * q^67 + 6758 * q^68 + 30663 * q^69 + 24828 * q^71 + 46194 * q^72 + 5307 * q^73 + 13866 * q^74 + 5178 * q^76 - 27645 * q^77 - 10592 * q^78 - 24914 * q^79 - 13683 * q^80 - 43222 * q^81 + 7010 * q^83 - 21568 * q^84 + 15366 * q^86 + 57084 * q^87 - 80787 * q^89 + 114772 * q^90 - 24438 * q^91 + 22049 * q^92 - 39723 * q^93 + 29955 * q^95 + 1378 * q^96 - 12210 * q^97 + 28845 * q^98 - 49211 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	7.38404i		−	1.84601i	−0.384786	−	0.923006i	$-0.625725\pi$
$2$		−	7.38404i		−	1.84601i	0.384786	−	0.923006i	$-0.374275\pi$
$3$	15.2777	−	8.82059i	1.69752	−	0.980065i	0.749423	−	0.662091i	$-0.230331\pi$
$3$	15.2777	−	8.82059i	1.69752	−	0.980065i	0.948099	−	0.317974i	$-0.103002\pi$
$4$	−38.5241			−2.40776
$5$	−17.1186	+	9.88344i	−0.684745	+	0.395338i	−0.801640	−	0.597806i	$-0.796039\pi$
$5$	−17.1186	+	9.88344i	−0.684745	+	0.395338i	0.116895	+	0.993144i	$0.462706\pi$
$6$	−65.1316	−	112.811i	−1.80921	−	3.13365i
$7$	36.3076	+	20.9622i	0.740972	+	0.427800i	0.822422	−	0.568877i	$-0.192622\pi$
$7$	36.3076	+	20.9622i	0.740972	+	0.427800i	−0.0814509	+	0.996677i	$0.525955\pi$
$8$			166.319i			2.59874i
$9$	115.106	−	199.369i	1.42106	−	2.46134i
$10$	72.9798	+	126.405i	0.729798	+	1.26405i
$11$	56.0930			0.463579			0.231789	−	0.972766i	$-0.425542\pi$
$11$	56.0930			0.463579			0.231789	+	0.972766i	$0.425542\pi$
$12$	−588.560	+	339.805i	−4.08722	+	2.35976i
$13$	−36.9428	+	63.9869i	−0.218597	+	0.378621i	−0.954379	−	0.298597i	$-0.903481\pi$
$13$	−36.9428	+	63.9869i	−0.218597	+	0.378621i	0.735782	+	0.677218i	$0.236815\pi$
$14$	154.786	−	268.097i	0.789724	−	1.36784i
$15$	−174.356	+	301.993i	−0.774914	+	1.34219i
$16$	611.722			2.38954
$17$	84.5100	−	146.376i	0.292422	−	0.506490i	−0.681960	−	0.731390i	$-0.738872\pi$
$17$	84.5100	−	146.376i	0.292422	−	0.506490i	0.974382	+	0.224900i	$0.0722054\pi$
$18$	−1472.15	−	849.944i	−4.54366	−	2.62328i
$19$	−147.491	+	85.1540i	−0.408563	+	0.235884i	−0.690172	−	0.723645i	$-0.742465\pi$
$19$	−147.491	+	85.1540i	−0.408563	+	0.235884i	0.281609	+	0.959529i	$0.409132\pi$
$20$	659.480	−	380.751i	1.64870	−	0.951877i
$21$	739.596			1.67709
$22$		−	414.193i		−	0.855772i
$23$	240.154	+	415.960i	0.453978	+	0.786313i	0.998629	−	0.0523499i	$-0.0166711\pi$
$23$	240.154	+	415.960i	0.453978	+	0.786313i	−0.544651	+	0.838663i	$0.683338\pi$
$24$	1467.03	+	2540.97i	2.54693	+	4.41141i
$25$	−117.135	+	202.884i	−0.187416	+	0.324614i
$26$	472.482	+	272.788i	0.698938	+	0.403532i
$27$		−	2632.26i		−	3.61078i
$28$	−1398.72	−	807.551i	−1.78408	−	1.03004i
$29$	499.097	+	288.154i	0.593456	+	0.342632i	0.766463	−	0.642289i	$-0.222015\pi$
$29$	499.097	+	288.154i	0.593456	+	0.342632i	−0.173007	+	0.984921i	$0.555348\pi$
$30$	2229.93	+	1287.45i	2.47770	+	1.43050i
$31$	−649.211	−	1124.47i	−0.675558	−	1.17010i	−0.976306	−	0.216396i	$-0.930570\pi$
$31$	−649.211	−	1124.47i	−0.675558	−	1.17010i	0.300748	−	0.953704i	$-0.402764\pi$
$32$		−	1855.88i		−	1.81238i
$33$	856.973	−	494.773i	0.786935	−	0.454337i
$34$	−1080.84	−	624.026i	−0.934986	−	0.539815i
$35$	−828.715			−0.676502
$36$	−4434.34	+	7680.50i	−3.42156	+	5.92631i
$37$	−673.776	+	389.005i	−0.492167	+	0.284153i	−0.725473	−	0.688251i	$-0.758379\pi$
$37$	−673.776	+	389.005i	−0.492167	+	0.284153i	0.233306	+	0.972403i	$0.425046\pi$
$38$	628.781	+	1089.08i	0.435444	+	0.754211i
$39$			1303.43i			0.856956i
$40$	−1643.81	−	2847.15i	−1.02738	−	1.77947i
$41$	1607.43			0.956235			0.478118	−	0.878296i	$-0.341319\pi$
$41$	1607.43			0.956235			0.478118	+	0.878296i	$0.341319\pi$
$42$		−	5461.21i		−	3.09592i
$43$	105.398	+	1845.99i	0.0570028	+	0.998374i
$43$	105.398	+	1845.99i	0.0570028	+	0.998374i
$44$	−2160.93			−1.11619
$45$			4550.55i			2.24719i
$46$	3071.46	−	1773.31i	1.45154	−	0.838049i
$47$	−876.593			−0.396828			−0.198414	−	0.980118i	$-0.563579\pi$
$47$	−876.593			−0.396828			−0.198414	+	0.980118i	$0.563579\pi$
$48$	9345.71	−	5395.75i	4.05630	−	2.34190i
$49$	−321.672	−	557.152i	−0.133974	−	0.232050i
$50$	1498.10	+	864.931i	0.599242	+	0.345972i
$51$		−	2981.71i		−	1.14637i
$52$	1423.19	−	2465.04i	0.526328	−	0.911627i
$53$	2175.56	+	3768.18i	0.774496	+	1.34147i	0.935077	+	0.354444i	$0.115330\pi$
$53$	2175.56	+	3768.18i	0.774496	+	1.34147i	−0.160582	+	0.987023i	$0.551337\pi$
$54$	−19436.7			−6.66554
$55$	−960.236	+	554.392i	−0.317433	+	0.183270i
$56$	−3486.42	+	6038.65i	−1.11174	+	1.92559i
$57$	−1502.22	+	2601.92i	−0.462363	+	0.800836i
$58$	2127.74	−	3685.35i	0.632503	−	1.09553i
$59$	−944.218			−0.271249			−0.135624	−	0.990760i	$-0.543304\pi$
$59$	−944.218			−0.271249			−0.135624	+	0.990760i	$0.543304\pi$
$60$	6716.89	−	11634.0i	1.86580	−	3.23167i
$61$	3648.62	+	2106.53i	0.980548	+	0.566120i	0.902436	−	0.430825i	$-0.141777\pi$
$61$	3648.62	+	2106.53i	0.980548	+	0.566120i	0.0781127	+	0.996945i	$0.475111\pi$
$62$	−8303.11	+	4793.80i	−2.16002	+	1.24709i
$63$	8358.41	−	4825.73i	2.10592	−	1.21586i
$64$	−3916.32			−0.956133
$65$		−	1460.49i		−	0.345678i
$66$	−3653.43	−	6327.92i	−0.838712	−	1.45269i
$67$	−841.544	−	1457.60i	−0.187468	−	0.324704i	0.756937	−	0.653487i	$-0.226695\pi$
$67$	−841.544	−	1457.60i	−0.187468	−	0.324704i	−0.944405	+	0.328783i	$0.893361\pi$
$68$	−3255.67	+	5638.99i	−0.704082	+	1.21951i
$69$	7338.02	+	4236.61i	1.54128	+	0.889856i
$70$			6119.27i			1.24883i
$71$	−1825.13	−	1053.74i	−0.362057	−	0.209034i	0.307925	−	0.951410i	$-0.400365\pi$
$71$	−1825.13	−	1053.74i	−0.362057	−	0.209034i	−0.669983	+	0.742377i	$0.733699\pi$
$72$	33158.8	+	19144.2i	6.39637	+	3.69295i
$73$	−7296.97	−	4212.91i	−1.36929	−	0.790563i	−0.378457	−	0.925619i	$-0.623545\pi$
$73$	−7296.97	−	4212.91i	−1.36929	−	0.790563i	−0.990838	+	0.135056i	$0.956878\pi$
$74$	2872.43	+	4975.20i	0.524549	+	0.908546i
$75$			4132.80i			0.734720i
$76$	5681.97	−	3280.48i	0.983720	−	0.567951i
$77$	2036.60	+	1175.83i	0.343499	+	0.198319i
$78$	9624.59			1.58195
$79$	−5320.11	+	9214.69i	−0.852444	+	1.47648i	0.0265514	+	0.999647i	$0.491547\pi$
$79$	−5320.11	+	9214.69i	−0.852444	+	1.47648i	−0.878996	+	0.476830i	$0.841786\pi$
$80$	−10471.8	+	6045.92i	−1.63622	+	0.944675i
$81$	−13894.5	−	24066.0i	−2.11774	−	3.66804i
$82$		−	11869.3i		−	1.76522i
$83$	1324.56	+	2294.21i	0.192272	+	0.333026i	0.946003	−	0.324158i	$-0.105081\pi$
$83$	1324.56	+	2294.21i	0.192272	+	0.333026i	−0.753731	+	0.657184i	$0.771748\pi$
$84$	−28492.3			−4.03802
$85$			3341.00i			0.462422i
$86$	13630.9	−	778.265i	1.84301	−	0.105228i
$87$	10166.7			1.34321
$88$			9329.34i			1.20472i
$89$	−3600.92	+	2078.99i	−0.454604	+	0.262466i	−0.709773	−	0.704431i	$-0.751202\pi$
$89$	−3600.92	+	2078.99i	−0.454604	+	0.262466i	0.255169	+	0.966897i	$0.417869\pi$
$90$	33601.5			4.14833
$91$	−2682.61	+	1548.81i	−0.323948	+	0.187031i
$92$	−9251.74	−	16024.5i	−1.09307	−	1.89325i
$93$	−19836.9	−	11452.8i	−2.29355	−	1.32418i
$94$			6472.80i			0.732549i
$95$	1683.23	−	2915.44i	0.186508	−	0.323041i
$96$	−16369.9	−	28353.5i	−1.77625	−	3.07655i
$97$	5999.67			0.637653			0.318826	−	0.947813i	$-0.396711\pi$
$97$	5999.67			0.637653			0.318826	+	0.947813i	$0.396711\pi$
$98$	−4114.04	+	2375.24i	−0.428367	+	0.247318i
$99$	6456.62	−	11183.2i	0.658771	−	1.14103i
$100$	4512.53	−	7815.92i	0.451253	−	0.781592i
$101$	1195.97	−	2071.47i	0.117240	−	0.203066i	−0.801433	−	0.598085i	$-0.795929\pi$
$101$	1195.97	−	2071.47i	0.117240	−	0.203066i	0.918673	+	0.395019i	$0.129262\pi$
$102$	−22017.1			−2.11621
$103$	−1640.65	+	2841.68i	−0.154647	+	0.267856i	−0.932930	−	0.360057i	$-0.882757\pi$
$103$	−1640.65	+	2841.68i	−0.154647	+	0.267856i	0.778284	+	0.627913i	$0.216091\pi$
$104$	−10642.2	−	6144.30i	−0.983935	−	0.568075i
$105$	−12660.9	+	7309.75i	−1.14838	+	0.663016i
$106$	27824.4	−	16064.4i	2.47636	−	1.42973i
$107$	1324.39			0.115677			0.0578385	−	0.998326i	$-0.481579\pi$
$107$	1324.39			0.115677			0.0578385	+	0.998326i	$0.481579\pi$
$108$			101405.i			8.69388i
$109$	−5770.61	−	9994.99i	−0.485701	−	0.841258i	0.514164	−	0.857692i	$-0.328102\pi$
$109$	−5770.61	−	9994.99i	−0.485701	−	0.841258i	−0.999865	+	0.0164336i	$0.994769\pi$
$110$	4093.66	+	7090.42i	0.338319	+	0.585985i
$111$	−6862.51	+	11886.2i	−0.556976	+	0.964711i
$112$	22210.2	+	12823.0i	1.77058	+	1.02224i
$113$		−	12656.8i		−	0.991210i	−0.868548	−	0.495605i	$-0.834946\pi$
$113$		−	12656.8i		−	0.991210i	0.868548	−	0.495605i	$-0.165054\pi$
$114$	19212.7	+	11092.4i	1.47835	+	0.853527i
$115$	−8222.23	−	4747.11i	−0.621718	−	0.358949i
$116$	−19227.3	−	11100.9i	−1.42890	−	0.824975i
$117$	8504.65	+	14730.5i	0.621276	+	1.07608i
$118$			6972.15i			0.500729i
$119$	6136.71	−	3543.03i	0.433353	−	0.250196i
$120$	−50227.2	−	28998.7i	−3.48800	−	2.01380i
$121$	−11494.6			−0.785095
$122$	15554.7	−	26941.6i	1.04506	−	1.81010i
$123$	24557.9	−	14178.5i	1.62323	−	0.937173i
$124$	25010.3	+	43319.1i	1.62658	+	2.81732i
$125$		−	16985.1i		−	1.08705i
$126$	−35633.4	−	61718.9i	−2.24448	−	3.88756i
$127$	2417.23			0.149869			0.0749343	−	0.997188i	$-0.476125\pi$
$127$	2417.23			0.149869			0.0749343	+	0.997188i	$0.476125\pi$
$128$		−	775.717i		−	0.0473460i
$129$	17893.0	+	27272.9i	1.07524	+	1.63890i
$130$	−10784.3			−0.638126
$131$			10529.3i			0.613560i	0.951780	+	0.306780i	$0.0992516\pi$
$131$			10529.3i			0.613560i	−0.951780	+	0.306780i	$0.900748\pi$
$132$	−33014.1	+	19060.7i	−1.89475	+	1.09393i
$133$	−7140.07			−0.403644
$134$	−10763.0	+	6214.00i	−0.599408	+	0.346068i
$135$	26015.8	+	45060.6i	1.42748	+	2.47246i
$136$	24345.1	+	14055.6i	1.31623	+	0.759928i
$137$			12517.3i			0.666913i	0.942766	+	0.333456i	$0.108215\pi$
$137$			12517.3i			0.666913i	−0.942766	+	0.333456i	$0.891785\pi$
$138$	31283.3	−	54184.2i	1.64268	−	2.84521i
$139$	−6205.72	−	10748.6i	−0.321191	−	0.556318i	0.659543	−	0.751666i	$-0.270750\pi$
$139$	−6205.72	−	10748.6i	−0.321191	−	0.556318i	−0.980734	+	0.195348i	$0.937416\pi$
$140$	31925.5			1.62885
$141$	−13392.3	+	7732.07i	−0.673625	+	0.388917i
$142$	−7780.86	+	13476.9i	−0.385879	+	0.668362i
$143$	−2072.24	+	3589.22i	−0.101337	+	0.175520i
$144$	70412.6	−	121958.i	3.39567	−	5.88147i
$145$	−11391.8			−0.541822
$146$	−31108.3	+	53881.2i	−1.45939	+	2.52773i
$147$	−9828.82	−	5674.67i	−0.454848	−	0.262607i
$148$	25956.6	−	14986.1i	1.18502	−	0.684171i
$149$	−25560.4	+	14757.3i	−1.15132	+	0.664713i	−0.949208	−	0.314650i	$-0.898113\pi$
$149$	−25560.4	+	14757.3i	−1.15132	+	0.664713i	−0.202109	+	0.979363i	$0.564780\pi$
$150$	30516.8			1.35630
$151$		−	34505.8i		−	1.51334i	−0.653794	−	0.756672i	$-0.726824\pi$
$151$		−	34505.8i		−	1.51334i	0.653794	−	0.756672i	$-0.273176\pi$
$152$	−14162.7	−	24530.6i	−0.613000	−	1.06175i
$153$	−19455.1	−	33697.3i	−0.831096	−	1.43950i
$154$	8682.41	−	15038.4i	0.366099	−	0.634102i
$155$	22227.2	+	12832.9i	0.925169	+	0.534147i
$156$		−	50213.5i		−	2.06334i
$157$	−1596.40	−	921.681i	−0.0647653	−	0.0373922i	0.467268	−	0.884116i	$-0.345238\pi$
$157$	−1596.40	−	921.681i	−0.0647653	−	0.0373922i	−0.532033	+	0.846724i	$0.678572\pi$
$158$	68041.7	+	39283.9i	2.72559	+	1.57362i
$159$	66475.1	+	38379.4i	2.62945	+	1.51811i
$160$	18342.4	+	31770.0i	0.716502	+	1.24102i
$161$			20136.7i			0.776847i
$162$	−177704.	+	102598.i	−6.77124	+	3.90938i
$163$	−24978.7	−	14421.4i	−0.940144	−	0.542792i	−0.0501382	−	0.998742i	$-0.515966\pi$
$163$	−24978.7	−	14421.4i	−0.940144	−	0.542792i	−0.890005	+	0.455950i	$0.849300\pi$
$164$	−61924.9			−2.30238
$165$	−9780.13	+	16939.7i	−0.359233	+	0.622211i
$166$	16940.6	−	9780.65i	0.614769	−	0.354937i
$167$	−7976.02	−	13814.9i	−0.285992	−	0.495352i	0.686858	−	0.726792i	$-0.258990\pi$
$167$	−7976.02	−	13814.9i	−0.285992	−	0.495352i	−0.972849	+	0.231440i	$0.925656\pi$
$168$			123009.i			4.35831i
$169$	11551.0	+	20006.8i	0.404431	+	0.700495i
$170$	24670.1			0.853636
$171$			39206.8i			1.34082i
$172$	−4060.37	−	71115.3i	−0.137249	−	2.40384i
$173$	−21186.0			−0.707875			−0.353937	−	0.935269i	$-0.615157\pi$
$173$	−21186.0			−0.707875			−0.353937	+	0.935269i	$0.615157\pi$
$174$		−	75071.6i		−	2.47958i
$175$	−8505.79	+	4910.82i	−0.277740	+	0.160353i
$176$	34313.3			1.10774
$177$	−14425.5	+	8328.55i	−0.460451	+	0.265842i
$178$	15351.4	+	26589.3i	0.484514	+	0.839204i
$179$	17692.1	+	10214.5i	0.552171	+	0.318796i	0.749997	−	0.661441i	$-0.230055\pi$
$179$	17692.1	+	10214.5i	0.552171	+	0.318796i	−0.197826	+	0.980237i	$0.563388\pi$
$180$		−	175306.i		−	5.41068i
$181$	22542.8	−	39045.3i	0.688100	−	1.19182i	−0.284352	−	0.958720i	$-0.591779\pi$
$181$	22542.8	−	39045.3i	0.688100	−	1.19182i	0.972452	−	0.233104i	$-0.0748881\pi$
$182$	11436.5	+	19808.5i	0.345262	+	0.598011i
$183$	74323.4			2.21934
$184$	−69182.0	+	39942.3i	−2.04342	+	1.17977i
$185$	7689.42	−	13318.5i	0.224673	−	0.389144i
$186$	−84568.3	+	146477.i	−2.44445	+	4.23392i
$187$	4740.42	−	8210.65i	0.135561	−	0.234798i
$188$	33770.0			0.955466
$189$	55177.9	−	95571.0i	1.54469	−	2.67548i
$190$	−21527.7	−	12429.0i	−0.596336	−	0.344295i
$191$	−21529.8	+	12430.2i	−0.590164	+	0.340731i	−0.765162	−	0.643837i	$-0.777341\pi$
$191$	−21529.8	+	12430.2i	−0.590164	+	0.340731i	0.174998	+	0.984569i	$0.444008\pi$
$192$	−59832.4	+	34544.3i	−1.62306	+	0.937073i
$193$	−59214.1			−1.58968			−0.794842	−	0.606816i	$-0.792446\pi$
$193$	−59214.1			−1.58968			−0.794842	+	0.606816i	$0.792446\pi$
$194$		−	44301.9i		−	1.17711i
$195$	−12882.4	−	22312.9i	−0.338787	−	0.586796i
$196$	12392.1	+	21463.8i	0.322577	+	0.558720i
$197$	35881.2	−	62148.0i	0.924558	−	1.60138i	0.132287	−	0.991211i	$-0.457768\pi$
$197$	35881.2	−	62148.0i	0.924558	−	1.60138i	0.792271	−	0.610170i	$-0.208899\pi$
$198$	−82577.2	−	47675.9i	−2.10635	−	1.21610i
$199$			6453.62i			0.162966i	0.996675	+	0.0814830i	$0.0259656\pi$
$199$			6453.62i			0.162966i	−0.996675	+	0.0814830i	$0.974034\pi$
$200$	−33743.5	−	19481.8i	−0.843587	−	0.487045i
$201$	−25713.7	−	14845.8i	−0.636463	−	0.367462i
$202$	−15295.9	−	8831.07i	−0.374862	−	0.216426i
$203$	12080.7	+	20924.3i	0.293156	+	0.507761i
$204$			114868.i			2.76018i
$205$	−27517.0	+	15887.0i	−0.654777	+	0.378036i
$206$	20983.1	+	12114.6i	0.494465	+	0.285479i
$207$	110572.			2.58051
$208$	−22598.7	+	39142.2i	−0.522345	+	0.904729i
$209$	−8273.22	+	4776.55i	−0.189401	+	0.109351i
$210$	53975.5	+	93488.4i	1.22394	+	2.11992i
$211$		−	65380.8i		−	1.46854i	−0.678858	−	0.734269i	$-0.737525\pi$
$211$		−	65380.8i		−	1.46854i	0.678858	−	0.734269i	$-0.262475\pi$
$212$	−83811.5	−	145166.i	−1.86480	−	3.22992i
$213$	−37178.4			−0.819468
$214$		−	9779.33i		−	0.213541i
$215$	−20049.0	−	30559.2i	−0.433727	−	0.661096i
$216$	437795.			9.38346
$217$		−	54435.6i		−	1.15601i
$218$	−73803.4	+	42610.4i	−1.55297	+	0.896609i
$219$	−148641.			−3.09921
$220$	36992.2	−	21357.5i	0.764302	−	0.441270i
$221$	6244.08	+	10815.1i	0.127845	+	0.221434i
$222$	87768.3	+	50673.0i	1.78087	+	1.02818i
$223$			82296.0i			1.65489i	0.561548	+	0.827444i	$0.310206\pi$
$223$			82296.0i			1.65489i	−0.561548	+	0.827444i	$0.689794\pi$
$224$	38903.3	−	67382.4i	0.775336	−	1.34292i
$225$	26965.8	+	46706.1i	0.532658	+	0.922590i
$226$	−93458.1			−1.82979
$227$	48622.9	−	28072.5i	0.943603	−	0.544790i	0.0525154	−	0.998620i	$-0.483276\pi$
$227$	48622.9	−	28072.5i	0.943603	−	0.544790i	0.891088	+	0.453830i	$0.149943\pi$
$228$	57871.6	−	100237.i	1.11326	−	1.92822i
$229$	−13173.2	+	22816.7i	−0.251201	+	0.435093i	−0.963857	−	0.266421i	$-0.914159\pi$
$229$	−13173.2	+	22816.7i	−0.251201	+	0.435093i	0.712656	+	0.701514i	$0.247492\pi$
$230$	−35052.8	+	60713.3i	−0.662625	+	1.14770i
$231$	41486.2			0.777462
$232$	−47925.4	+	83009.3i	−0.890410	+	1.54224i
$233$	18956.4	+	10944.5i	0.349175	+	0.201596i	0.664322	−	0.747447i	$-0.268720\pi$
$233$	18956.4	+	10944.5i	0.349175	+	0.201596i	−0.315147	+	0.949043i	$0.602054\pi$
$234$	108771.	−	62798.7i	1.98646	−	1.14688i
$235$	15006.1	−	8663.76i	0.271726	−	0.156881i
$236$	36375.2			0.653102
$237$			187706.i			3.34180i
$238$	−26161.9	−	45313.8i	−0.461865	−	0.799975i
$239$	16730.7	+	28978.5i	0.292900	+	0.507317i	0.974494	−	0.224413i	$-0.0720465\pi$
$239$	16730.7	+	28978.5i	0.292900	+	0.507317i	−0.681595	+	0.731730i	$0.738713\pi$
$240$	−106657.	+	184736.i	−1.85169	+	3.20721i
$241$	92293.5	+	53285.7i	1.58905	+	0.917437i	0.993464	+	0.114143i	$0.0364123\pi$
$241$	92293.5	+	53285.7i	1.58905	+	0.917437i	0.595583	+	0.803294i	$0.296921\pi$
$242$			84876.4i			1.44929i
$243$	−239905.	−	138509.i	−4.06281	−	2.34566i
$244$	−140560.	−	81152.3i	−2.36092	−	1.36308i
$245$	11013.2	+	6358.45i	0.183476	+	0.105930i
$246$	−104695.	−	181336.i	−1.73003	−	2.99650i
$247$		−	12583.3i		−	0.206254i
$248$	187020.	−	107976.i	3.04078	−	1.75560i
$249$	40472.6	+	23366.9i	0.652774	+	0.376879i
$250$	−125419.			−2.00670
$251$	59691.4	−	103389.i	0.947468	−	1.64106i	0.196736	−	0.980456i	$-0.436966\pi$
$251$	59691.4	−	103389.i	0.947468	−	1.64106i	0.750732	−	0.660607i	$-0.229701\pi$
$252$	−322000.	+	185907.i	−5.07055	+	2.92749i
$253$	13471.0	+	23332.4i	0.210455	+	0.364518i
$254$		−	17849.0i		−	0.276659i
$255$	29469.6	+	51042.8i	0.453204	+	0.784972i
$256$	−68389.1			−1.04353
$257$			62695.3i			0.949225i	0.880195	+	0.474612i	$0.157412\pi$
$257$			62695.3i			0.949225i	−0.880195	+	0.474612i	$0.842588\pi$
$258$	201384.	−	132123.i	3.02542	−	1.98490i
$259$	−32617.6			−0.486242
$260$			56264.1i			0.832309i
$261$	114898.	−	66336.1i	1.68667	−	0.973798i
$262$	77748.8			1.13264
$263$	85354.8	−	49279.6i	1.23400	−	0.712452i	0.266141	−	0.963934i	$-0.414251\pi$
$263$	85354.8	−	49279.6i	1.23400	−	0.712452i	0.967862	+	0.251482i	$0.0809179\pi$
$264$	82290.3	+	142531.i	1.18070	+	2.04504i
$265$	−74485.2	−	43004.0i	−1.06066	−	0.612375i
$266$			52722.6i			0.745132i
$267$	−36675.8	+	63524.4i	−0.514467	+	0.891083i
$268$	32419.7	+	56152.7i	0.451378	+	0.781809i
$269$	58863.9			0.813476			0.406738	−	0.913545i	$-0.366666\pi$
$269$	58863.9			0.813476			0.406738	+	0.913545i	$0.366666\pi$
$270$	332730.	−	192102.i	4.56419	−	2.63514i
$271$	−4126.43	+	7147.18i	−0.0561870	+	0.0973187i	−0.892751	−	0.450551i	$-0.851228\pi$
$271$	−4126.43	+	7147.18i	−0.0561870	+	0.0973187i	0.836564	+	0.547869i	$0.184561\pi$
$272$	51696.6	−	89541.2i	0.698754	−	1.21028i
$273$	−27322.8	+	47324.4i	−0.366606	+	0.634980i
$274$	92428.2			1.23113
$275$	−6570.46	+	11380.4i	−0.0868821	+	0.150484i
$276$	−282691.	−	163212.i	−3.71102	−	2.14256i
$277$	11407.7	−	6586.25i	0.148675	−	0.0858378i	−0.423817	−	0.905748i	$-0.639310\pi$
$277$	11407.7	−	6586.25i	0.148675	−	0.0858378i	0.572492	+	0.819910i	$0.305977\pi$
$278$	−79368.3	+	45823.3i	−1.02697	+	0.592921i
$279$	−298911.			−3.84002
$280$		−	137831.i		−	1.75805i
$281$	−26594.9	−	46063.7i	−0.336811	−	0.583373i	0.647020	−	0.762473i	$-0.276015\pi$
$281$	−26594.9	−	46063.7i	−0.336811	−	0.583373i	−0.983831	+	0.179100i	$0.942682\pi$
$282$	57093.9	+	98889.6i	0.717946	+	1.24352i
$283$	−38739.4	+	67098.5i	−0.483704	+	0.837800i	−0.999825	−	0.0187161i	$-0.994042\pi$
$283$	−38739.4	+	67098.5i	−0.483704	+	0.837800i	0.516121	+	0.856516i	$0.327375\pi$
$284$	70311.6	+	40594.4i	0.871746	+	0.503303i
$285$		−	59388.3i		−	0.731158i
$286$	26502.9	+	15301.5i	0.324013	+	0.187069i
$287$	58362.0	+	33695.3i	0.708543	+	0.409078i
$288$	−370003.	−	213622.i	−4.46088	−	2.57549i
$289$	27476.6	+	47590.9i	0.328979	+	0.569808i
$290$			84117.5i			1.00021i
$291$	91661.3	−	52920.7i	1.08243	−	0.624941i
$292$	281109.	+	162299.i	3.29693	+	1.90348i
$293$	−2932.30			−0.0341565			−0.0170782	−	0.999854i	$-0.505436\pi$
$293$	−2932.30			−0.0341565			−0.0170782	+	0.999854i	$0.505436\pi$
$294$	−41902.0	+	72576.4i	−0.484775	+	0.839655i
$295$	16163.7	−	9332.12i	0.185736	−	0.107235i
$296$	−64699.0	−	112062.i	−0.738438	−	1.27901i
$297$		−	147651.i		−	1.67388i
$298$	108969.	+	188739.i	1.22707	+	2.12534i
$299$	−35487.9			−0.396952
$300$		−	159213.i		−	1.76903i
$301$	−34869.3	+	69233.0i	−0.384867	+	0.764153i
$302$	−254792.			−2.79365
$303$		−	42196.5i		−	0.459612i
$304$	−90223.6	+	52090.6i	−0.976276	+	0.563653i
$305$	−83279.2			−0.895234
$306$	−248822.	+	143658.i	−2.65734	+	1.53421i
$307$	28377.1	+	49150.6i	0.301087	+	0.521497i	0.976382	−	0.216050i	$-0.0693174\pi$
$307$	28377.1	+	49150.6i	0.301087	+	0.521497i	−0.675296	+	0.737547i	$0.735984\pi$
$308$	−78458.4	−	45298.0i	−0.827061	−	0.477504i
$309$			57885.8i			0.606255i
$310$	94758.5	−	164127.i	0.986041	−	1.70787i
$311$	30917.6	+	53550.9i	0.319658	+	0.553663i	0.980417	−	0.196935i	$-0.0630988\pi$
$311$	30917.6	+	53550.9i	0.319658	+	0.553663i	−0.660759	+	0.750598i	$0.729765\pi$
$312$	−216785.			−2.22700
$313$	−49025.7	+	28305.0i	−0.500420	+	0.288918i	−0.728887	−	0.684634i	$-0.759962\pi$
$313$	−49025.7	+	28305.0i	−0.500420	+	0.288918i	0.228467	+	0.973552i	$0.426629\pi$
$314$	−6805.74	+	11787.9i	−0.0690265	+	0.119557i
$315$	−95389.7	+	165220.i	−0.961347	+	1.66510i
$316$	204952.	−	354988.i	2.05248	−	3.55500i
$317$	−159200.			−1.58426			−0.792128	−	0.610354i	$-0.791027\pi$
$317$	−159200.			−1.58426			−0.792128	+	0.610354i	$0.791027\pi$
$318$	283395.	−	490855.i	2.80245	−	4.85399i
$319$	27995.8	+	16163.4i	0.275114	+	0.158837i
$320$	67042.1	−	38706.8i	0.654708	−	0.377996i
$321$	20233.6	−	11681.9i	0.196364	−	0.113371i
$322$	148690.			1.43407
$323$			28785.5i			0.275911i
$324$	535274.	+	927121.i	5.09901	+	8.83174i
$325$	−8654.61	−	14990.2i	−0.0819371	−	0.141919i
$326$	−106489.	+	184444.i	−1.00200	+	1.73552i
$327$	−176323.	−	101800.i	−1.64898	−	0.952037i
$328$			267347.i			2.48500i
$329$	−31827.0	−	18375.3i	−0.294038	−	0.169763i
$330$	125083.	+	72216.9i	1.14861	+	0.663149i
$331$	92985.1	+	53685.0i	0.848706	+	0.490001i	0.860214	−	0.509933i	$-0.170330\pi$
$331$	92985.1	+	53685.0i	0.848706	+	0.490001i	−0.0115080	+	0.999934i	$0.503663\pi$
$332$	−51027.7	−	88382.6i	−0.462945	−	0.801845i
$333$			179106.i			1.61519i
$334$	−102010.	+	58895.3i	−0.914425	+	0.527944i
$335$	28812.2	+	16634.7i	0.256736	+	0.148226i
$336$	452427.			4.00747
$337$	41142.8	−	71261.5i	0.362272	−	0.627473i	−0.626063	−	0.779773i	$-0.715335\pi$
$337$	41142.8	−	71261.5i	0.362272	−	0.627473i	0.988334	+	0.152300i	$0.0486680\pi$
$338$	147731.	−	85292.8i	1.29312	−	0.746584i
$339$	−111640.	−	193366.i	−0.971451	−	1.68260i
$340$		−	128709.i		−	1.11340i
$341$	−36416.2	−	63074.7i	−0.313174	−	0.542434i
$342$	289505.			2.47516
$343$		−	127632.i		−	1.08486i
$344$	−307024.	+	17529.7i	−2.59451	+	0.148135i
$345$	−167489.			−1.40718
$346$			156438.i			1.30674i
$347$	152752.	−	88191.5i	1.26861	−	0.732433i	0.293885	−	0.955841i	$-0.405052\pi$
$347$	152752.	−	88191.5i	1.26861	−	0.732433i	0.974725	+	0.223408i	$0.0717183\pi$
$348$	−391664.			−3.23412
$349$	168769.	−	97438.6i	1.38561	−	0.799982i	0.392793	−	0.919627i	$-0.371509\pi$
$349$	168769.	−	97438.6i	1.38561	−	0.799982i	0.992817	+	0.119645i	$0.0381755\pi$
$350$	36261.7	+	62807.1i	0.296014	+	0.512711i
$351$	168430.	+	97243.1i	1.36712	+	0.789304i
$352$		−	104102.i		−	0.840180i
$353$	66621.7	−	115392.i	0.534646	−	0.926034i	−0.464534	−	0.885555i	$-0.653778\pi$
$353$	66621.7	−	115392.i	0.534646	−	0.926034i	0.999180	−	0.0404790i	$-0.0128884\pi$
$354$	61498.4	+	106518.i	0.490747	+	0.849998i
$355$	41658.3			0.330556
$356$	138722.	−	80091.3i	1.09458	−	0.631953i
$357$	62503.2	−	108259.i	0.490418	−	0.849428i
$358$	75424.7	−	130639.i	0.588501	−	1.01931i
$359$	16863.9	−	29209.2i	0.130849	−	0.226637i	−0.793155	−	0.609020i	$-0.791563\pi$
$359$	16863.9	−	29209.2i	0.130849	−	0.226637i	0.924004	+	0.382383i	$0.124896\pi$
$360$	−756844.			−5.83985
$361$	−50658.1	+	87742.4i	−0.388718	+	0.673279i
$362$	−288312.	−	166457.i	−2.20012	−	1.27024i
$363$	−175611.	+	101389.i	−1.33272	+	0.769444i
$364$	103345.	−	59666.4i	0.779988	−	0.450326i
$365$	166552.			1.25016
$366$		−	548807.i		−	4.09692i
$367$	30709.5	+	53190.3i	0.228003	+	0.394912i	0.957216	−	0.289374i	$-0.0934472\pi$
$367$	30709.5	+	53190.3i	0.228003	+	0.394912i	−0.729213	+	0.684286i	$0.760114\pi$
$368$	146908.	+	254452.i	1.08480	+	1.87893i
$369$	185024.	−	320471.i	1.35886	−	2.35362i
$370$	−98344.1	−	56779.0i	−0.718365	−	0.414748i
$371$			182418.i			1.32532i
$372$	764199.	+	441211.i	5.52231	+	3.18831i
$373$	−30294.0	−	17490.3i	−0.217741	−	0.125713i	0.387163	−	0.922011i	$-0.373455\pi$
$373$	−30294.0	−	17490.3i	−0.217741	−	0.125713i	−0.604904	+	0.796299i	$0.706788\pi$
$374$	−60627.8	−	35003.5i	−0.433440	−	0.250247i
$375$	−149819.	−	259493.i	−1.06538	−	1.84529i
$376$		−	145794.i		−	1.03125i
$377$	−36876.1	+	21290.4i	−0.259455	+	0.149796i
$378$	−705700.	−	407436.i	−4.93897	−	2.85152i
$379$	−158781.			−1.10540			−0.552700	−	0.833380i	$-0.686402\pi$
$379$	−158781.			−1.10540			−0.552700	+	0.833380i	$0.686402\pi$
$380$	−64845.0	+	112315.i	−0.449065	+	0.777803i
$381$	36929.8	−	21321.4i	0.254406	−	0.146881i
$382$	91785.3	+	158977.i	0.628994	+	1.08945i
$383$		−	36067.2i		−	0.245875i	−0.992414	−	0.122938i	$-0.960769\pi$
$383$		−	36067.2i		−	0.245875i	0.992414	−	0.122938i	$-0.0392315\pi$
$384$	−6842.28	−	11851.2i	−0.0464022	−	0.0803710i
$385$	−46485.1			−0.313612
$386$			437240.i			2.93457i
$387$	380165.	+	191471.i	2.53834	+	1.27844i
$388$	−231132.			−1.53531
$389$			123339.i			0.815080i	0.913187	+	0.407540i	$0.133613\pi$
$389$			123339.i			0.815080i	−0.913187	+	0.407540i	$0.866387\pi$
$390$	−164760.	+	95124.1i	−1.08323	+	0.625405i
$391$	81181.8			0.531013
$392$	92665.0	−	53500.2i	0.603037	−	0.348163i
$393$	92874.6	+	160864.i	0.601329	+	1.04153i
$394$	−458904.	−	264948.i	−2.95617	−	1.70674i
$395$		−	210324.i		−	1.34801i
$396$	−248735.	+	430822.i	−1.58616	+	2.74731i
$397$	79934.2	+	138450.i	0.507168	+	0.878440i	0.999966	+	0.00829637i	$0.00264085\pi$
$397$	79934.2	+	138450.i	0.507168	+	0.878440i	−0.492798	+	0.870144i	$0.664026\pi$
$398$	47653.8			0.300837
$399$	−109084.	+	62979.6i	−0.685196	+	0.395598i
$400$	−71654.1	+	124109.i	−0.447838	+	0.775678i
$401$	56325.9	−	97559.2i	0.350283	−	0.606708i	−0.636016	−	0.771676i	$-0.719419\pi$
$401$	56325.9	−	97559.2i	0.350283	−	0.606708i	0.986299	+	0.164968i	$0.0527521\pi$
$402$	−109622.	+	189871.i	−0.678339	+	1.17492i
$403$	95934.8			0.590699
$404$	−46073.5	+	79801.7i	−0.282286	+	0.488933i
$405$	475710.	+	274651.i	2.90023	+	1.67445i
$406$	154506.	−	89204.2i	0.937333	−	0.541169i
$407$	−37794.2	+	21820.5i	−0.228158	+	0.131727i
$408$	495916.			2.97912
$409$			15847.2i			0.0947342i	0.998878	+	0.0473671i	$0.0150831\pi$
$409$			15847.2i			0.0947342i	−0.998878	+	0.0473671i	$0.984917\pi$
$410$	117310.	+	203187.i	0.697859	+	1.20873i
$411$	110410.	+	191235.i	0.653618	+	1.13210i
$412$	63204.4	−	109473.i	0.372352	−	0.644932i
$413$	−34282.3	−	19792.9i	−0.200988	−	0.116040i
$414$		−	816471.i		−	4.76365i
$415$	−45349.5	−	26182.5i	−0.263315	−	0.152025i
$416$	118752.	+	68561.3i	0.686204	+	0.396180i
$417$	−189618.	−	109476.i	−1.09046	−	0.629575i
$418$	35270.2	+	61089.9i	0.201863	+	0.349636i
$419$		−	295587.i		−	1.68367i	−0.539736	−	0.841835i	$-0.681476\pi$
$419$		−	295587.i		−	1.68367i	0.539736	−	0.841835i	$-0.318524\pi$
$420$	487749.	−	281602.i	2.76501	−	1.59638i
$421$	−98173.0	−	56680.2i	−0.553896	−	0.319792i	0.196796	−	0.980444i	$-0.436946\pi$
$421$	−98173.0	−	56680.2i	−0.553896	−	0.319792i	−0.750692	+	0.660653i	$0.770280\pi$
$422$	−482775.			−2.71094
$423$	−100901.	+	174765.i	−0.563915	+	0.976729i
$424$	−626720.	+	361837.i	−3.48612	+	2.01271i
$425$	19798.2	+	34291.4i	0.109609	+	0.189849i
$426$			274527.i			1.51275i
$427$	88315.1	+	152966.i	0.484372	+	0.838957i
$428$	−51020.8			−0.278522
$429$			73113.3i			0.397267i
$430$	−225650.	+	148043.i	−1.22039	+	0.800666i
$431$	−51158.7			−0.275401			−0.137700	−	0.990474i	$-0.543971\pi$
$431$	−51158.7			−0.275401			−0.137700	+	0.990474i	$0.543971\pi$
$432$		−	1.61021e6i		−	8.62809i
$433$	−150987.	+	87172.6i	−0.805313	+	0.464948i	−0.845326	−	0.534252i	$-0.820594\pi$
$433$	−150987.	+	87172.6i	−0.805313	+	0.464948i	0.0400126	+	0.999199i	$0.487260\pi$
$434$	−401955.			−2.13402
$435$	−174041.	+	100482.i	−0.919754	+	0.531020i
$436$	222308.	+	385048.i	1.16945	+	2.02555i
$437$	−70841.3	−	40900.2i	−0.370957	−	0.214172i
$438$			1.09757e6i			5.72118i
$439$	16853.6	−	29191.3i	0.0874507	−	0.151469i	−0.818982	−	0.573819i	$-0.805461\pi$
$439$	16853.6	−	29191.3i	0.0874507	−	0.151469i	0.906433	+	0.422350i	$0.138795\pi$
$440$	−92206.0	−	159706.i	−0.476271	−	0.824925i
$441$	−148105.			−0.761539
$442$	79858.9	−	46106.6i	0.408770	−	0.236003i
$443$	154722.	−	267987.i	0.788398	−	1.36555i	−0.138549	−	0.990356i	$-0.544244\pi$
$443$	154722.	−	267987.i	0.788398	−	1.36555i	0.926948	−	0.375191i	$-0.122423\pi$
$444$	264372.	−	457906.i	1.34106	−	2.32279i
$445$	41095.2	−	71178.9i	0.207525	−	0.359444i
$446$	607677.			3.05494
$447$	−260336.	+	450915.i	−1.30292	+	2.25673i
$448$	−142192.	−	82094.8i	−0.708468	−	0.409034i
$449$	−148238.	+	85585.2i	−0.735304	+	0.424528i	−0.820359	−	0.571848i	$-0.806227\pi$
$449$	−148238.	+	85585.2i	−0.735304	+	0.424528i	0.0850556	+	0.996376i	$0.472893\pi$
$450$	344880.	−	199117.i	1.70311	−	0.983292i
$451$	90165.7			0.443290
$452$			487591.i			2.38659i
$453$	−304361.	−	527169.i	−1.48318	−	2.56894i
$454$	−207288.	−	359034.i	−1.00569	−	1.74190i
$455$	30615.1	−	53026.9i	0.147881	−	0.256138i
$456$	−432748.	−	249847.i	−2.08116	−	1.20156i
$457$			155503.i			0.744571i	0.928118	+	0.372285i	$0.121426\pi$
$457$			155503.i			0.744571i	−0.928118	+	0.372285i	$0.878574\pi$
$458$	168480.	+	97271.7i	0.803186	+	0.463720i
$459$	−385298.	−	222452.i	−1.82882	−	1.05587i
$460$	316754.	+	182878.i	1.49695	+	0.864263i
$461$	32292.8	+	55932.8i	0.151951	+	0.263187i	0.931945	−	0.362600i	$-0.118111\pi$
$461$	32292.8	+	55932.8i	0.151951	+	0.263187i	−0.779994	+	0.625788i	$0.784778\pi$
$462$		−	306336.i		−	1.43520i
$463$	−75983.4	+	43869.0i	−0.354451	+	0.204643i	−0.666644	−	0.745376i	$-0.732270\pi$
$463$	−75983.4	+	43869.0i	−0.354451	+	0.204643i	0.312193	+	0.950019i	$0.398937\pi$
$464$	305308.	+	176270.i	1.41809	+	0.818733i
$465$	452774.			2.09399
$466$	80814.4	−	139975.i	0.372149	−	0.644581i
$467$	187987.	−	108535.i	0.861976	−	0.497662i	−0.00269750	−	0.999996i	$-0.500859\pi$
$467$	187987.	−	108535.i	0.861976	−	0.497662i	0.864674	+	0.502334i	$0.167525\pi$
$468$	−327634.	−	567479.i	−1.49588	−	2.59094i
$469$		−	70562.5i		−	0.320795i
$470$	−63973.6	−	110805.i	−0.289604	−	0.501609i
$471$	−32519.1			−0.146587
$472$		−	157041.i		−	0.704905i
$473$	5912.11	+	103547.i	0.0264253	+	0.462825i
$474$	1.38603e6			6.16901
$475$		−	39898.1i		−	0.176834i
$476$	−236411.	+	136492.i	−1.04341	+	0.602412i
$477$	1.00168e6			4.40241
$478$	213978.	−	123540.i	0.936513	−	0.540696i
$479$	−32081.2	−	55566.3i	−0.139823	−	0.242181i	0.787606	−	0.616179i	$-0.211320\pi$
$479$	−32081.2	−	55566.3i	−0.139823	−	0.242181i	−0.927430	+	0.373998i	$0.877987\pi$
$480$	560461.	+	323582.i	2.43256	+	1.40444i
$481$		−	57483.8i		−	0.248459i
$482$	393464.	−	681499.i	1.69360	−	2.93340i
$483$	177617.	+	307642.i	0.761361	+	1.31872i
$484$	442818.			1.89032
$485$	−102706.	+	59297.4i	−0.436630	+	0.252088i
$486$	−1.02276e6	+	1.77147e6i	−4.33012	+	7.49999i
$487$	−5255.42	+	9102.66i	−0.0221590	+	0.0383805i	−0.876892	−	0.480687i	$-0.840387\pi$
$487$	−5255.42	+	9102.66i	−0.0221590	+	0.0383805i	0.854733	+	0.519067i	$0.173721\pi$
$488$	−350357.	+	606835.i	−1.47120	+	2.54819i
$489$	−508822.			−2.12789
$490$	46951.1	−	81321.7i	0.195548	−	0.338699i
$491$	−109762.	−	63370.8i	−0.455289	−	0.262861i	0.254772	−	0.967001i	$-0.417999\pi$
$491$	−109762.	−	63370.8i	−0.455289	−	0.262861i	−0.710061	+	0.704140i	$0.751333\pi$
$492$	−946070.	+	546214.i	−3.90835	+	2.25649i
$493$	84357.3	−	48703.7i	0.347079	−	0.200386i
$494$	−92915.9			−0.380747
$495$			255254.i			1.04175i
$496$	−397137.	−	687861.i	−1.61427	−	2.79600i
$497$	−44177.4	−	76517.6i	−0.178849	−	0.309776i
$498$	172542.	−	298852.i	0.695723	−	1.20503i
$499$	−25154.8	−	14523.1i	−0.101023	−	0.0583256i	0.448637	−	0.893714i	$-0.351909\pi$
$499$	−25154.8	−	14523.1i	−0.101023	−	0.0583256i	−0.549660	+	0.835388i	$0.685243\pi$
$500$			654336.i			2.61734i
$501$	−243711.	−	140706.i	−0.970955	−	0.560581i
$502$	−763426.	−	440764.i	−3.02942	−	1.74904i
$503$	−55152.5	−	31842.3i	−0.217986	−	0.125854i	0.387031	−	0.922067i	$-0.373501\pi$
$503$	−55152.5	−	31842.3i	−0.217986	−	0.125854i	−0.605017	+	0.796212i	$0.706834\pi$
$504$	802611.	+	1.39016e6i	3.15969	+	5.47274i
$505$			47281.1i			0.185398i
$506$	172288.	−	99470.4i	0.672904	−	0.388502i
$507$	352944.	+	203772.i	1.37306	+	0.792737i
$508$	−93121.7			−0.360847
$509$	88976.1	−	154111.i	0.343430	−	0.594838i	−0.641638	−	0.767008i	$-0.721745\pi$
$509$	88976.1	−	154111.i	0.343430	−	0.594838i	0.985067	+	0.172170i	$0.0550780\pi$
$510$	376902.	−	217605.i	1.44907	−	0.836619i
$511$	−176624.	−	305921.i	−0.676406	−	1.17157i
$512$			492577.i			1.87903i
$513$	224147.	+	388235.i	0.851724	+	1.47523i
$514$	462945.			1.75228
$515$		−	64860.9i		−	0.244551i
$516$	−689312.	−	1.05066e6i	−2.58891	−	3.94606i
$517$	−49170.8			−0.183961
$518$			240850.i			0.897609i
$519$	−323673.	+	186873.i	−1.20163	+	0.693764i
$520$	242907.			0.898326
$521$	−331271.	+	191259.i	−1.22042	+	0.704608i	−0.965007	−	0.262225i	$-0.915544\pi$
$521$	−331271.	+	191259.i	−1.22042	+	0.704608i	−0.255410	+	0.966833i	$0.582210\pi$
$522$	−489829.	−	848409.i	−1.79764	−	3.11361i
$523$	306642.	+	177040.i	1.12106	+	0.647244i	0.941671	−	0.336534i	$-0.109255\pi$
$523$	306642.	+	177040.i	1.12106	+	0.647244i	0.179388	+	0.983778i	$0.442588\pi$
$524$		−	405632.i		−	1.47730i
$525$	−86632.6	+	150052.i	−0.314313	+	0.544407i
$526$	−363883.	−	630263.i	−1.31519	−	2.27798i
$527$	−219459.			−0.790192
$528$	524229.	−	302664.i	1.88041	−	1.08566i
$529$	24572.2	−	42560.3i	0.0878078	−	0.152088i
$530$	−317544.	+	550002.i	−1.13045	+	1.95800i
$531$	−108685.	+	188247.i	−0.385460	+	0.667636i
$532$	275065.			0.971878
$533$	−59383.1	+	102855.i	−0.209030	+	0.362050i
$534$	469067.	+	270816.i	1.64495	+	0.949711i
$535$	−22671.7	+	13089.5i	−0.0792093	+	0.0457315i
$536$	242426.	−	139965.i	0.843821	−	0.487180i
$537$	360393.			1.24976
$538$		−	434654.i		−	1.50169i
$539$	−18043.6	−	31252.3i	−0.0621076	−	0.107573i
$540$	−1.00223e6	−	1.73592e6i	−3.43702	−	5.95309i
$541$	−100711.	+	174437.i	−0.344099	+	0.595998i	−0.985190	−	0.171468i	$-0.945149\pi$
$541$	−100711.	+	174437.i	−0.344099	+	0.595998i	0.641090	+	0.767465i	$0.278482\pi$
$542$	52775.1	+	30469.7i	0.179651	+	0.103722i
$543$		−	795364.i		−	2.69753i
$544$	−271655.	−	156840.i	−0.917952	−	0.529980i
$545$	197570.	+	114067.i	0.665162	+	0.384032i
$546$	349446.	+	201753.i	1.17218	+	0.676759i
$547$	168763.	+	292307.i	0.564032	+	0.976932i	0.997139	+	0.0755894i	$0.0240838\pi$
$547$	168763.	+	292307.i	0.564032	+	0.976932i	−0.433107	+	0.901342i	$0.642583\pi$
$548$		−	482218.i		−	1.60576i
$549$	839953.	−	484947.i	2.78683	−	1.60898i
$550$	84033.2	+	48516.6i	0.277796	+	0.160385i
$551$	−98149.8			−0.323285
$552$	−704628.	+	1.22045e6i	−2.31250	+	4.00537i
$553$	−386321.	+	223042.i	−1.26327	+	0.729352i
$554$	−48633.1	−	84235.1i	−0.158457	−	0.274456i
$555$		−	271301.i		−	0.880775i
$556$	239070.	+	414081.i	0.773349	+	1.33948i
$557$	−503456.			−1.62275			−0.811374	−	0.584527i	$-0.801280\pi$
$557$	−503456.			−1.62275			−0.811374	+	0.584527i	$0.801280\pi$
$558$			2.20717e6i			7.08872i
$559$	−122013.	−	61452.1i	−0.390466	−	0.196659i
$560$	−506943.			−1.61653
$561$		−	167253.i		−	0.531433i
$562$	−340137.	+	196378.i	−1.07691	+	0.621756i
$563$	178279.			0.562450			0.281225	−	0.959642i	$-0.409259\pi$
$563$	178279.			0.562450			0.281225	+	0.959642i	$0.409259\pi$
$564$	515928.	−	297871.i	1.62192	−	0.936419i
$565$	125092.	+	216666.i	0.391863	+	0.678726i
$566$	495459.	+	286053.i	1.54659	+	0.892923i
$567$		−	1.16504e6i		−	3.62388i
$568$	175257.	−	303554.i	0.543224	−	0.940892i
$569$	−172783.	−	299269.i	−0.533675	−	0.924353i	−0.999226	−	0.0393318i	$-0.987477\pi$
$569$	−172783.	−	299269.i	−0.533675	−	0.924353i	0.465551	−	0.885021i	$-0.345856\pi$
$570$	−438526.			−1.34973
$571$	−66343.3	+	38303.3i	−0.203481	+	0.117480i	−0.598278	−	0.801288i	$-0.704148\pi$
$571$	−66343.3	+	38303.3i	−0.203481	+	0.117480i	0.394797	+	0.918768i	$0.370815\pi$
$572$	79831.1	−	138271.i	0.243994	−	0.422611i
$573$	−219284.	+	379810.i	−0.667878	+	1.15680i
$574$	248808.	−	430948.i	0.755162	−	1.30798i
$575$	−112522.			−0.340331
$576$	−450790.	+	780792.i	−1.35872	+	2.35337i
$577$	302647.	+	174733.i	0.909044	+	0.524837i	0.880123	−	0.474745i	$-0.157460\pi$
$577$	302647.	+	174733.i	0.909044	+	0.524837i	0.0289204	+	0.999582i	$0.490793\pi$
$578$	351413.	−	202889.i	1.05187	−	0.607298i
$579$	−904656.	+	522303.i	−2.69852	+	1.55799i
$580$	438859.			1.30457
$581$			111063.i			0.329017i
$582$	−390768.	−	676831.i	−1.15365	−	1.99818i
$583$	122034.	+	211369.i	0.359040	+	0.621875i
$584$	700687.	−	1.21363e6i	2.05446	−	3.55844i
$585$	−291176.	−	168110.i	−0.850832	−	0.491228i
$586$			21652.2i			0.0630532i
$587$	322302.	+	186081.i	0.935377	+	0.540040i	0.888508	−	0.458861i	$-0.151742\pi$
$587$	322302.	+	186081.i	0.935377	+	0.540040i	0.0468686	+	0.998901i	$0.485076\pi$
$588$	378647.	+	218612.i	1.09516	+	0.632293i
$589$	191506.	+	110566.i	0.552015	+	0.318706i
$590$	−68908.8	−	119354.i	−0.197957	−	0.342871i
$591$		−	1.26597e6i		−	3.62451i
$592$	−412164.	+	237963.i	−1.17605	+	0.678994i
$593$	83193.5	+	48031.8i	0.236581	+	0.136590i	0.613604	−	0.789614i	$-0.289719\pi$
$593$	83193.5	+	48031.8i	0.236581	+	0.136590i	−0.377023	+	0.926204i	$0.623052\pi$
$594$	−1.09026e6			−3.09000
$595$	−70034.7	+	121304.i	−0.197824	+	0.342642i
$596$	984691.	−	568512.i	2.77209	−	1.60047i
$597$	56924.7	+	98596.4i	0.159717	+	0.276638i
$598$			262045.i			0.732779i
$599$	−24493.2	−	42423.5i	−0.0682641	−	0.118237i	0.829873	−	0.557952i	$-0.188413\pi$
$599$	−24493.2	−	42423.5i	−0.0682641	−	0.118237i	−0.898137	+	0.439715i	$0.855079\pi$
$600$	−687364.			−1.90934
$601$		−	487871.i		−	1.35069i	−0.737501	−	0.675346i	$-0.763994\pi$
$601$		−	487871.i		−	1.35069i	0.737501	−	0.675346i	$-0.236006\pi$
$602$	511219.	+	257477.i	1.41063	+	0.710469i
$603$	−387465.			−1.06561
$604$			1.32930e6i			3.64377i
$605$	196771.	−	113606.i	0.537590	−	0.310378i
$606$	−311581.			−0.848448
$607$	230828.	−	133269.i	0.626486	−	0.361702i	−0.152904	−	0.988241i	$-0.548863\pi$
$607$	230828.	−	133269.i	0.626486	−	0.361702i	0.779390	+	0.626539i	$0.215529\pi$
$608$	158035.	+	273725.i	0.427511	+	0.740470i
$609$	369130.	+	213117.i	0.995278	+	0.574624i
$610$			614937.i			1.65261i
$611$	32383.8	−	56090.5i	0.0867453	−	0.150247i
$612$	749492.	+	1.29816e6i	2.00108	+	3.46597i
$613$	169836.			0.451970			0.225985	−	0.974131i	$-0.427440\pi$
$613$	169836.			0.451970			0.225985	+	0.974131i	$0.427440\pi$
$614$	362930.	−	209538.i	0.962690	−	0.555809i
$615$	−280265.	+	485433.i	−0.741000	+	1.28345i
$616$	−195564.	+	338726.i	−0.515379	+	0.892662i
$617$	−101106.	+	175121.i	−0.265587	+	0.460010i	−0.967717	−	0.252038i	$-0.918899\pi$
$617$	−101106.	+	175121.i	−0.265587	+	0.460010i	0.702130	+	0.712049i	$0.252232\pi$
$618$	427432.			1.11915
$619$	−5883.25	+	10190.1i	−0.0153545	+	0.0265948i	−0.873601	−	0.486644i	$-0.838221\pi$
$619$	−5883.25	+	10190.1i	−0.0153545	+	0.0265948i	0.858246	+	0.513238i	$0.171554\pi$
$620$	−856283.	−	494375.i	−2.22758	−	1.28610i
$621$	1.09491e6	−	632148.i	2.83920	−	1.63921i
$622$	395422.	−	228297.i	1.02207	−	0.590092i
$623$	−174321.			−0.449131
$624$			797337.i			2.04773i
$625$	94661.8	+	163959.i	0.242334	+	0.419735i
$626$	209005.	+	362008.i	0.533345	+	0.923781i
$627$	−84263.9	+	145949.i	−0.214342	+	0.371251i
$628$	61499.9	+	35507.0i	0.155939	+	0.0900314i
$629$			131499.i			0.332370i
$630$	1.21999e6	+	704362.i	3.07380	+	1.77466i
$631$	−47101.3	−	27194.0i	−0.118297	−	0.0682989i	0.439684	−	0.898153i	$-0.355090\pi$
$631$	−47101.3	−	27194.0i	−0.118297	−	0.0682989i	−0.557981	+	0.829854i	$0.688424\pi$
$632$	−1.53258e6	−	884835.i	−3.83697	−	2.21528i
$633$	−576697.	−	998868.i	−1.43926	−	2.49288i
$634$			1.17554e6i			2.92456i
$635$	−41379.7	+	23890.6i	−0.102622	+	0.0592487i
$636$	−2.56089e6	−	1.47853e6i	−6.33107	−	3.65525i
$637$	47533.9			0.117145
$638$	119351.	−	206723.i	0.293215	−	0.507863i
$639$	−420165.	+	242583.i	−1.02901	+	0.594098i
$640$	7666.76	+	13279.2i	0.0187177	+	0.0324200i
$641$			805577.i			1.96061i	0.197491	+	0.980305i	$0.436721\pi$
$641$			805577.i			1.96061i	−0.197491	+	0.980305i	$0.563279\pi$
$642$	−86259.4	−	149406.i	−0.209284	−	0.362491i
$643$	737784.			1.78446			0.892230	−	0.451580i	$-0.149140\pi$
$643$	737784.			1.78446			0.892230	+	0.451580i	$0.149140\pi$
$644$		−	775747.i		−	1.87046i
$645$	−575853.	−	290030.i	−1.38418	−	0.697145i
$646$	212553.			0.509334
$647$		−	326333.i		−	0.779566i	−0.920907	−	0.389783i	$-0.872550\pi$
$647$		−	326333.i		−	0.779566i	0.920907	−	0.389783i	$-0.127450\pi$
$648$	4.00263e6	−	2.31092e6i	9.53226	−	5.50345i
$649$	−52964.0			−0.125745
$650$	−110688.	+	63906.0i	−0.261984	+	0.151257i
$651$	−480154.	−	831650.i	−1.13297	−	1.96236i
$652$	962281.	+	555573.i	2.26364	+	1.30691i
$653$			649839.i			1.52398i	0.647589	+	0.761990i	$0.275777\pi$
$653$			649839.i			1.52398i	−0.647589	+	0.761990i	$0.724223\pi$
$654$	−751698.	+	1.30198e6i	−1.75747	+	3.04403i
$655$	−104066.	−	180247.i	−0.242563	−	0.420132i
$656$	983301.			2.28496
$657$	−1.67984e6	+	969858.i	−3.89169	+	2.24687i
$658$	−135684.	+	235012.i	−0.313385	+	0.542798i
$659$	159716.	−	276635.i	0.367770	−	0.636996i	−0.621447	−	0.783457i	$-0.713455\pi$
$659$	159716.	−	276635.i	0.367770	−	0.636996i	0.989217	+	0.146460i	$0.0467880\pi$
$660$	376771.	−	652586.i	0.864947	−	1.49813i
$661$	−610091.			−1.39634			−0.698171	−	0.715931i	$-0.746002\pi$
$661$	−610091.			−1.39634			−0.698171	+	0.715931i	$0.746002\pi$
$662$	396412.	−	686606.i	0.904547	−	1.56672i
$663$	190790.	+	110153.i	0.434040	+	0.250593i
$664$	−381572.	+	220300.i	−0.865446	+	0.499665i
$665$	122228.	−	70568.4i	0.276394	−	0.159576i
$666$	1.32253e6			2.98165
$667$			276805.i			0.622190i
$668$	307269.	+	532206.i	0.688599	+	1.19269i
$669$	725899.	+	1.25729e6i	1.62190	+	2.80921i
$670$	122831.	−	212750.i	0.273628	−	0.473937i
$671$	204662.	+	118162.i	0.454561	+	0.262441i
$672$		−	1.37260e6i		−	3.03952i
$673$	−436637.	−	252092.i	−0.964029	−	0.556583i	−0.0666185	−	0.997779i	$-0.521221\pi$
$673$	−436637.	−	252092.i	−0.964029	−	0.556583i	−0.897411	+	0.441196i	$0.854554\pi$
$674$	−526198.	−	303800.i	−1.15832	−	0.668757i
$675$	534043.	+	308330.i	1.17211	+	0.676718i
$676$	−444990.	−	770746.i	−0.973772	−	1.68662i
$677$		−	114609.i		−	0.250059i	−0.992153	−	0.125030i	$-0.960097\pi$
$677$		−	114609.i		−	0.250059i	0.992153	−	0.125030i	$-0.0399026\pi$
$678$	−1.42783e6	+	824355.i	−3.10610	+	1.79331i
$679$	217834.	+	125766.i	0.472483	+	0.272788i
$680$	−555672.			−1.20171
$681$	495231.	−	857766.i	1.06786	−	1.84959i
$682$	−465747.	+	268899.i	−1.00134	+	0.578123i
$683$	9601.79	+	16630.8i	0.0205831	+	0.0356510i	0.876133	−	0.482069i	$-0.160114\pi$
$683$	9601.79	+	16630.8i	0.0205831	+	0.0356510i	−0.855550	+	0.517720i	$0.826781\pi$
$684$		−	1.51041e6i		−	3.22836i
$685$	−123714.	−	214279.i	−0.263656	−	0.456665i
$686$	−942443.			−2.00266
$687$			464782.i			0.984773i
$688$	64474.4	+	1.12923e6i	0.136210	+	2.38565i
$689$	−321485.			−0.677209
$690$			1.23675e6i			2.59766i
$691$	−771760.	+	445576.i	−1.61632	+	0.933181i	−0.628455	+	0.777846i	$0.716312\pi$
$691$	−771760.	+	445576.i	−1.61632	+	0.933181i	−0.987862	+	0.155335i	$0.950354\pi$
$692$	816171.			1.70439
$693$	468849.	−	270690.i	0.976261	−	0.563645i
$694$	−651210.	−	1.12793e6i	−1.35208	−	2.34187i
$695$	212467.	+	122668.i	0.439867	+	0.253957i
$696$			1.69092e6i			3.49064i
$697$	135844.	−	235289.i	0.279624	−	0.484324i
$698$	−719491.	−	1.24620e6i	−1.47678	−	2.55785i
$699$	386146.			0.790310
$700$	327678.	−	189185.i	0.668731	−	0.386092i
$701$	−196591.	+	340506.i	−0.400063	+	0.692929i	−0.993733	−	0.111779i	$-0.964345\pi$
$701$	−196591.	+	340506.i	−0.400063	+	0.692929i	0.593670	+	0.804708i	$0.297678\pi$
$702$	718047.	−	1.24369e6i	1.45706	−	2.52371i
$703$	66250.7	−	114750.i	0.134054	−	0.232188i
$704$	−219678.			−0.443243
$705$	152839.	−	264725.i	0.307507	−	0.532618i
$706$	−852061.	−	491938.i	−1.70947	−	0.986963i
$707$	86845.3	−	50140.2i	0.173743	−	0.100311i
$708$	555729.	−	320850.i	1.10866	−	0.640082i
$709$	−195388.			−0.388692			−0.194346	−	0.980933i	$-0.562258\pi$
$709$	−195388.			−0.388692			−0.194346	+	0.980933i	$0.562258\pi$
$710$		−	307607.i		−	0.610210i
$711$	1.22475e6	+	2.12132e6i	2.42274	+	4.19631i
$712$	−345776.	−	598901.i	−0.682079	−	1.18140i
$713$	311822.	−	540091.i	0.613377	−	1.06240i
$714$	−799388.	−	461527.i	−1.56805	−	0.905317i
$715$		−	81923.3i		−	0.160249i
$716$	−681573.	−	393506.i	−1.32949	−	0.767584i
$717$	511214.	+	295150.i	0.994407	+	0.574121i
$718$	−215682.	−	124524.i	−0.418374	−	0.241548i
$719$	399071.	+	691211.i	0.771955	+	1.33707i	0.936490	+	0.350695i	$0.114054\pi$
$719$	399071.	+	691211.i	0.771955	+	1.33707i	−0.164534	+	0.986371i	$0.552612\pi$
$720$			2.78367e6i			5.36974i
$721$	−119136.	+	68783.1i	−0.229177	+	0.132316i
$722$	647894.	+	374062.i	1.24288	+	0.717577i
$723$	1.88004e6			3.59659
$724$	−868443.	+	1.50419e6i	−1.65678	+	2.86962i
$725$	−116923.	+	67505.8i	−0.222447	+	0.128430i
$726$	748660.	+	1.29672e6i	1.42040	+	2.46021i
$727$		−	164509.i		−	0.311259i	−0.987816	−	0.155629i	$-0.950259\pi$
$727$		−	164509.i		−	0.311259i	0.987816	−	0.155629i	$-0.0497406\pi$
$728$	−257596.	−	446170.i	−0.486045	−	0.841855i
$729$	−2.63601e6			−4.96012
$730$		−	1.22983e6i		−	2.30780i
$731$	279116.	+	140577.i	0.522335	+	0.263075i
$732$	−2.86324e6			−5.34363
$733$		−	309963.i		−	0.576902i	−0.957495	−	0.288451i	$-0.906860\pi$
$733$		−	309963.i		−	0.576902i	0.957495	−	0.288451i	$-0.0931402\pi$
$734$	392760.	−	226760.i	0.729013	−	0.420896i
$735$	224341.			0.415273
$736$	771970.	−	445697.i	1.42510	−	0.822780i
$737$	−47204.8	−	81761.0i	−0.0869062	−	0.150526i
$738$	−2.36638e6	−	1.36623e6i	−4.34481	−	2.50848i
$739$		−	169596.i		−	0.310546i	−0.987872	−	0.155273i	$-0.950374\pi$
$739$		−	169596.i		−	0.310546i	0.987872	−	0.155273i	$-0.0496257\pi$
$740$	−296228.	+	513082.i	−0.540957	+	0.936965i
$741$	−110992.	−	192244.i	−0.202142	−	0.350120i
$742$	1.34698e6			2.44655
$743$	−152141.	+	87838.4i	−0.275593	+	0.159113i	−0.631426	−	0.775436i	$-0.717530\pi$
$743$	−152141.	+	87838.4i	−0.275593	+	0.159113i	0.355834	+	0.934549i	$0.384197\pi$
$744$	1.90483e6	−	3.29926e6i	3.44120	−	5.96033i
$745$	291706.	−	505249.i	0.525572	−	0.910318i
$746$	−129149.	+	223692.i	−0.232067	+	0.401951i
$747$	609859.			1.09292
$748$	−182621.	+	316308.i	−0.326397	+	0.565337i
$749$	48085.3	+	27762.1i	0.0857134	+	0.0494866i
$750$	−1.91611e6	+	1.10627e6i	−3.40642	+	1.96670i
$751$	−439714.	+	253869.i	−0.779633	+	0.450121i	−0.836300	−	0.548272i	$-0.815286\pi$
$751$	−439714.	+	253869.i	−0.779633	+	0.450121i	0.0566673	+	0.998393i	$0.481953\pi$
$752$	−536231.			−0.948236
$753$		−	2.10605e6i		−	3.71432i
$754$	157209.	+	272295.i	0.276526	+	0.478957i
$755$	341036.	+	590691.i	0.598282	+	1.03626i
$756$	−2.12568e6	+	3.68179e6i	−3.71924	+	6.44192i
$757$	−183093.	−	105709.i	−0.319507	−	0.184467i	0.331666	−	0.943397i	$-0.392389\pi$
$757$	−183093.	−	105709.i	−0.319507	−	0.184467i	−0.651173	+	0.758929i	$0.725723\pi$
$758$			1.17244e6i			2.04058i
$759$	411612.	+	237644.i	0.714503	+	0.412518i
$760$	484893.	+	279953.i	0.839497	+	0.484684i
$761$	−773975.	−	446855.i	−1.33646	−	0.771608i	−0.350183	−	0.936681i	$-0.613881\pi$
$761$	−773975.	−	446855.i	−1.33646	−	0.771608i	−0.986281	+	0.165073i	$0.947214\pi$
$762$	−157438.	−	272691.i	−0.271144	−	0.469635i
$763$		−	483859.i		−	0.831131i
$764$	829415.	−	478863.i	1.42097	−	0.820398i
$765$	666090.	+	384567.i	1.13818	+	0.657127i
$766$	−266322.			−0.453888
$767$	34882.1	−	60417.5i	0.0592941	−	0.102700i
$768$	−1.04483e6	+	603232.i	−1.77142	+	1.02273i
$769$	193627.	+	335372.i	0.327426	+	0.567118i	0.982000	−	0.188879i	$-0.0604855\pi$
$769$	193627.	+	335372.i	0.327426	+	0.567118i	−0.654574	+	0.755998i	$0.727152\pi$
$770$			343248.i			0.578931i
$771$	553010.	+	957841.i	0.930302	+	1.61133i
$772$	2.28117e6			3.82757
$773$			307190.i			0.514101i	0.966398	+	0.257051i	$0.0827507\pi$
$773$			307190.i			0.514101i	−0.966398	+	0.257051i	$0.917249\pi$
$774$	1.41383e6	−	2.80716e6i	2.36002	−	4.68581i
$775$	304181.			0.506442
$776$			997861.i			1.65709i
$777$	−498322.	+	287706.i	−0.825407	+	0.476549i
$778$	910739.			1.50465
$779$	−237082.	+	136879.i	−0.390682	+	0.225560i
$780$	496282.	+	859586.i	0.815717	+	1.41286i
$781$	−102377.	−	59107.5i	−0.167842	−	0.0969037i
$782$		−	599450.i		−	0.980256i
$783$	758494.	−	1.31375e6i	1.23717	−	2.14284i
$784$	−196774.	−	340822.i	−0.320136	−	0.554492i
$785$	36437.5			0.0591303
$786$	1.18782e6	−	685790.i	1.92268	−	1.11006i
$787$	38851.5	−	67292.8i	0.0627276	−	0.108647i	−0.832956	−	0.553339i	$-0.813353\pi$
$787$	38851.5	−	67292.8i	0.0627276	−	0.108647i	0.895684	+	0.444692i	$0.146687\pi$
$788$	−1.38229e6	+	2.39420e6i	−2.22611	+	3.85574i
$789$	869350.	−	1.50576e6i	1.39650	−	2.41881i
$790$	−1.55304e6			−2.48845
$791$	265314.	−	459537.i	0.424040	−	0.734459i
$792$	1.85998e6	+	1.07386e6i	2.96522	+	1.71197i
$793$	−269581.	+	155643.i	−0.428689	+	0.247504i
$794$	1.02232e6	−	590238.i	1.62161	−	0.936237i
$795$	−1.51728e6			−2.40067
$796$		−	248620.i		−	0.392383i
$797$	160244.	+	277550.i	0.252269	+	0.436943i	0.964150	−	0.265357i	$-0.0854898\pi$
$797$	160244.	+	277550.i	0.252269	+	0.436943i	−0.711881	+	0.702300i	$0.752156\pi$
$798$	465044.	+	805480.i	0.730278	+	1.26488i
$799$	−74080.9	+	128312.i	−0.116041	+	0.200989i
$800$	376527.	+	217388.i	0.588324	+	0.339669i
$801$			957213.i			1.49191i
$802$	−720382.	−	415913.i	−1.11999	−	0.646626i
$803$	−409309.	−	236315.i	−0.634776	−	0.366488i
$804$	990599.	+	571922.i	1.53245	+	0.884759i
$805$	−199020.	−	344712.i	−0.307117	−	0.531942i
$806$		−	708387.i		−	1.09044i
$807$	899306.	−	519215.i	1.38089	−	0.797260i
$808$	344526.	+	198912.i	0.527714	+	0.304676i
$809$	119356.			0.182368			0.0911840	−	0.995834i	$-0.470935\pi$
$809$	119356.			0.182368			0.0911840	+	0.995834i	$0.470935\pi$
$810$	2.02804e6	−	3.51266e6i	3.09105	−	5.35385i
$811$	348631.	−	201282.i	0.530059	−	0.306030i	−0.210982	−	0.977490i	$-0.567666\pi$
$811$	348631.	−	201282.i	0.530059	−	0.306030i	0.741040	+	0.671460i	$0.234333\pi$
$812$	−465397.	−	806091.i	−0.705849	−	1.22257i
$813$			145590.i			0.220268i
$814$	161123.	+	279074.i	0.243170	+	0.421182i
$815$	570134.			0.858345
$816$		−	1.82398e6i		−	2.73930i
$817$	−172739.	−	263293.i	−0.258789	−	0.394452i
$818$	117017.			0.174880
$819$			713105.i			1.06313i
$820$	1.06007e6	−	612031.i	1.57655	−	0.910219i
$821$	82531.4			0.122443			0.0612213	−	0.998124i	$-0.480500\pi$
$821$	82531.4			0.122443			0.0612213	+	0.998124i	$0.480500\pi$
$822$	1.41209e6	−	815271.i	2.08987	−	1.20659i
$823$	−302613.	−	524141.i	−0.446774	−	0.773835i	0.551400	−	0.834241i	$-0.314094\pi$
$823$	−302613.	−	524141.i	−0.446774	−	0.773835i	−0.998174	+	0.0604061i	$0.980760\pi$
$824$	−472626.	−	272871.i	−0.696087	−	0.401886i
$825$			231821.i			0.340601i
$826$	−146152.	+	253142.i	−0.214212	+	0.371026i
$827$	−395177.	−	684466.i	−0.577804	−	1.00079i	−0.995731	−	0.0923047i	$-0.970577\pi$
$827$	−395177.	−	684466.i	−0.577804	−	1.00079i	0.417927	−	0.908481i	$-0.362757\pi$
$828$	−4.25970e6			−6.21325
$829$	−434937.	+	251111.i	−0.632874	+	0.365390i	−0.781864	−	0.623449i	$-0.785731\pi$
$829$	−434937.	+	251111.i	−0.632874	+	0.365390i	0.148991	+	0.988839i	$0.452398\pi$
$830$	−193333.	+	334862.i	−0.280640	+	0.486083i
$831$	116189.	−	201245.i	0.168253	−	0.291423i
$832$	144680.	−	250593.i	0.209008	−	0.362012i
$833$	−108738.			−0.156708
$834$	−808377.	+	1.40015e6i	−1.16220	+	2.01299i
$835$	273077.	+	157661.i	0.391663	+	0.226127i
$836$	318719.	−	184012.i	0.456032	−	0.263290i
$837$	−2.95988e6	+	1.70889e6i	−4.22497	+	2.43929i
$838$	−2.18262e6			−3.10807
$839$			1.35141e6i			1.91984i	0.280279	+	0.959919i	$0.409573\pi$
$839$			1.35141e6i			1.91984i	−0.280279	+	0.959919i	$0.590427\pi$
$840$	−1.21575e6	−	2.10574e6i	−1.72300	−	2.98433i
$841$	−187576.	−	324890.i	−0.265207	−	0.459351i
$842$	−418529.	+	724914.i	−0.590339	+	1.02250i
$843$	−812618.	−	469165.i	−1.14349	−	0.660193i
$844$			2.51874e6i			3.53588i
$845$	−395473.	−	228326.i	−0.553864	−	0.319774i
$846$	1.29047e6	+	745055.i	1.80305	+	1.04099i
$847$	−417340.	−	240952.i	−0.581733	−	0.335864i
$848$	1.33084e6	+	2.30508e6i	1.85069	+	3.20548i
$849$			1.36682e6i			1.89625i
$850$	253210.	−	146191.i	0.350463	−	0.202340i
$851$	−323621.	−	186843.i	−0.446866	−	0.257998i
$852$	1.43227e6			1.97308
$853$	−149585.	+	259089.i	−0.205585	+	0.356083i	−0.950319	−	0.311278i	$-0.899243\pi$
$853$	−149585.	+	259089.i	−0.205585	+	0.356083i	0.744734	+	0.667361i	$0.232576\pi$
$854$	1.12951e6	−	652123.i	1.54872	−	0.894157i
$855$	−387498.	−	671167.i	−0.530075	−	0.918117i
$856$			220271.i			0.300614i
$857$	−349299.	−	605003.i	−0.475593	−	0.823751i	0.524016	−	0.851708i	$-0.324433\pi$
$857$	−349299.	−	605003.i	−0.475593	−	0.823751i	−0.999609	+	0.0279573i	$0.991100\pi$
$858$	539872.			0.733359
$859$		−	741281.i		−	1.00461i	−0.864691	−	0.502304i	$-0.832486\pi$
$859$		−	741281.i		−	1.00461i	0.864691	−	0.502304i	$-0.167514\pi$
$860$	772372.	+	1.17727e6i	1.04431	+	1.59176i
$861$	1.18885e6			1.60369
$862$			377758.i			0.508393i
$863$	−338907.	+	195668.i	−0.455050	+	0.262723i	−0.709961	−	0.704241i	$-0.751287\pi$
$863$	−338907.	+	195668.i	−0.455050	+	0.262723i	0.254911	+	0.966965i	$0.417954\pi$
$864$	−4.88514e6			−6.54410
$865$	362675.	−	209391.i	0.484714	−	0.279850i
$866$	643686.	+	1.11490e6i	0.858299	+	1.48662i
$867$	839559.	+	484720.i	1.11690	+	0.644841i
$868$			2.09708e6i			2.78340i
$869$	−298421.	+	516880.i	−0.395175	+	0.684463i
$870$	741966.	+	1.28512e6i	0.980270	+	1.69788i
$871$	124356.			0.163920
$872$	1.66236e6	−	959763.i	2.18621	−	1.26221i
$873$	690596.	−	1.19615e6i	0.906140	−	1.56948i
$874$	−302009.	+	523095.i	−0.395364	+	0.684791i
$875$	356045.	−	616688.i	0.465038	−	0.805470i
$876$	5.72628e6			7.46215
$877$	611378.	−	1.05894e6i	0.794897	−	1.37680i	−0.128007	−	0.991773i	$-0.540858\pi$
$877$	611378.	−	1.05894e6i	0.794897	−	1.37680i	0.922904	−	0.385029i	$-0.125809\pi$
$878$	−215550.	−	124448.i	−0.279614	−	0.161435i
$879$	−44798.8	+	25864.6i	−0.0579814	+	0.0334756i
$880$	−587397.	+	339134.i	−0.758519	+	0.437931i
$881$	1.33045e6			1.71414			0.857068	−	0.515203i	$-0.172283\pi$
$881$	1.33045e6			1.71414			0.857068	+	0.515203i	$0.172283\pi$
$882$			1.09361e6i			1.40581i
$883$	−479101.	−	829828.i	−0.614477	−	1.06431i	−0.990476	−	0.137686i	$-0.956034\pi$
$883$	−479101.	−	829828.i	−0.614477	−	1.06431i	0.375999	−	0.926620i	$-0.377300\pi$
$884$	−240548.	−	416641.i	−0.307820	−	0.533160i
$885$	164630.	−	285147.i	0.210195	−	0.364068i
$886$	−1.97883e6	−	1.14248e6i	−2.52081	−	1.45539i
$887$		−	23906.3i		−	0.0303854i	−0.999885	−	0.0151927i	$-0.995164\pi$
$887$		−	23906.3i		−	0.0303854i	0.999885	−	0.0151927i	$-0.00483617\pi$
$888$	−1.97690e6	−	1.14137e6i	−2.50703	−	1.44743i
$889$	87763.9	+	50670.5i	0.111048	+	0.0641138i
$890$	−525588.	−	303449.i	−0.663538	−	0.383094i
$891$	−779385.	−	1.34993e6i	−0.981740	−	1.70042i
$892$		−	3.17038e6i		−	3.98457i
$893$	129290.	−	74645.5i	0.162129	−	0.0936053i
$894$	3.32958e6	+	1.92233e6i	4.16595	+	2.40521i
$895$	−403820.			−0.504129
$896$	16260.7	−	28164.4i	0.0202546	−	0.0350821i
$897$	−542174.	+	313025.i	−0.673836	+	0.389039i
$898$	631965.	+	1.09460e6i	0.783683	+	1.35738i
$899$		−	748290.i		−	0.925871i
$900$	−1.03883e6	−	1.79931e6i	−1.28251	−	2.22137i
$901$	735426.			0.905919
$902$		−	665788.i		−	0.818319i
$903$	77952.1	+	1.36529e6i	0.0955988	+	1.67436i
$904$	2.10506e6			2.57589
$905$			891203.i			1.08813i
$906$	−3.89264e6	+	2.24742e6i	−4.74229	+	2.73796i
$907$	−435235.			−0.529066			−0.264533	−	0.964377i	$-0.585218\pi$
$907$	−435235.			−0.529066			−0.264533	+	0.964377i	$0.585218\pi$
$908$	−1.87316e6	+	1.08147e6i	−2.27197	+	1.31172i
$909$	−275325.	−	476876.i	−0.333209	−	0.577135i
$910$	−391553.	−	226063.i	−0.472833	−	0.272990i
$911$		−	1.48226e6i		−	1.78603i	−0.450027	−	0.893015i	$-0.648586\pi$
$911$		−	1.48226e6i		−	1.78603i	0.450027	−	0.893015i	$-0.351414\pi$
$912$	−918939.	+	1.59165e6i	−1.10483	+	1.91363i
$913$	74298.9	+	128689.i	0.0891334	+	0.154384i
$914$	1.14824e6			1.37449
$915$	−1.27231e6	+	734571.i	−1.51968	+	0.877388i
$916$	507487.	−	878993.i	0.604831	−	1.04760i
$917$	−220717.	+	382294.i	−0.262481	+	0.454630i
$918$	−1.64260e6	+	2.84506e6i	−1.94915	+	3.37603i
$919$	−56853.8			−0.0673175			−0.0336588	−	0.999433i	$-0.510716\pi$
$919$	−56853.8			−0.0673175			−0.0336588	+	0.999433i	$0.510716\pi$
$920$	789534.	−	1.36751e6i	0.932815	−	1.61568i
$921$	867074.	+	500605.i	1.02220	+	0.590169i
$922$	413010.	−	238452.i	0.485846	−	0.280504i
$923$	134851.	−	77856.3i	0.158289	−	0.0913883i
$924$	−1.59822e6			−1.87194
$925$		−	182265.i		−	0.213019i
$926$	323931.	+	561065.i	0.377772	+	0.654321i
$927$	377695.	+	654187.i	0.439523	+	0.761276i
$928$	534777.	−	926261.i	0.620979	−	1.07557i
$929$	256820.	+	148275.i	0.297576	+	0.171806i	0.641354	−	0.767245i	$-0.278373\pi$
$929$	256820.	+	148275.i	0.297576	+	0.171806i	−0.343777	+	0.939051i	$0.611707\pi$
$930$		−	3.34330e6i		−	3.86554i
$931$	94887.5	+	54783.3i	0.109474	+	0.0632047i
$932$	−730277.	−	421626.i	−0.840729	−	0.485395i
$933$	944700.	+	545423.i	1.08525	+	0.626571i
$934$	−801425.	−	1.38811e6i	−0.918690	−	1.59122i
$935$			187407.i			0.214369i
$936$	−2.44996e6	+	1.41449e6i	−2.79645	+	1.61453i
$937$	−761892.	−	439878.i	−0.867789	−	0.501018i	−0.00117594	−	0.999999i	$-0.500374\pi$
$937$	−761892.	−	439878.i	−0.867789	−	0.501018i	−0.866613	+	0.498981i	$0.833708\pi$
$938$	−521037.			−0.592192
$939$	−499333.	+	864870.i	−0.566316	+	0.980889i
$940$	−578096.	+	333764.i	−0.654250	+	0.377732i
$941$	−779649.	−	1.35039e6i	−0.880480	−	1.52504i	−0.850808	−	0.525477i	$-0.823887\pi$
$941$	−779649.	−	1.35039e6i	−0.880480	−	1.52504i	−0.0296725	−	0.999560i	$-0.509446\pi$
$942$			240122.i			0.270602i
$943$	386032.	+	668627.i	0.434110	+	0.751900i
$944$	−577599.			−0.648160
$945$			2.18139e6i			2.44270i
$946$	764598.	−	43655.3i	0.854380	−	0.0487814i
$947$	873932.			0.974491			0.487245	−	0.873265i	$-0.338002\pi$
$947$	873932.			0.974491			0.487245	+	0.873265i	$0.338002\pi$
$948$		−	7.23120e6i		−	8.04625i
$949$	539142.	−	311274.i	0.598647	−	0.345629i
$950$	−294609.			−0.326437
$951$	−2.43222e6	+	1.40424e6i	−2.68931	+	1.55268i
$952$	589274.	+	1.02065e6i	0.650195	+	1.12617i
$953$	409747.	+	236568.i	0.451160	+	0.260477i	0.708320	−	0.705892i	$-0.249453\pi$
$953$	409747.	+	236568.i	0.451160	+	0.260477i	−0.257160	+	0.966369i	$0.582787\pi$
$954$		−	7.39641e6i		−	8.12689i
$955$	245707.	−	425576.i	0.269408	−	0.466628i
$956$	−644536.	−	1.11637e6i	−0.705231	−	1.22150i
$957$	570283.			0.622682
$958$	−410304.	+	236889.i	−0.447070	+	0.258116i
$959$	−262390.	+	454473.i	−0.285305	+	0.494163i
$960$	682833.	−	1.18270e6i	0.740921	−	1.28331i
$961$	−381189.	+	660239.i	−0.412756	+	0.714915i
$962$	−424463.			−0.458659
$963$	152444.	−	264041.i	0.164383	−	0.284721i
$964$	−3.55552e6	−	2.05278e6i	−3.82604	−	2.20897i
$965$	1.01366e6	−	585240.i	1.08853	−	0.628462i
$966$	2.27164e6	−	1.31153e6i	2.43437	−	1.40548i
$967$	465575.			0.497893			0.248947	−	0.968517i	$-0.419916\pi$
$967$	465575.			0.497893			0.248947	+	0.968517i	$0.419916\pi$
$968$		−	1.91177e6i		−	2.04025i
$969$	253905.	+	439776.i	0.270410	+	0.468365i
$970$	437855.	+	758387.i	0.465358	+	0.806023i
$971$	−464980.	+	805368.i	−0.493169	+	0.854193i	−0.999969	−	0.00787028i	$-0.997495\pi$
$971$	−464980.	+	805368.i	−0.493169	+	0.854193i	0.506800	+	0.862063i	$0.330828\pi$
$972$	9.24212e6	+	5.33594e6i	9.78225	+	5.64779i
$973$		−	520343.i		−	0.549621i
$974$	67214.4	+	38806.3i	0.0708508	+	0.0409057i
$975$	−264445.	−	152677.i	−0.278180	−	0.160607i
$976$	2.23194e6	+	1.28861e6i	2.34306	+	1.35277i
$977$	688493.	+	1.19251e6i	0.721291	+	1.24931i	0.960482	+	0.278340i	$0.0897843\pi$
$977$	688493.	+	1.19251e6i	0.721291	+	1.24931i	−0.239191	+	0.970972i	$0.576882\pi$
$978$			3.75717e6i			3.92810i
$979$	−201986.	+	116617.i	−0.210745	+	0.121673i
$980$	−424272.	−	244954.i	−0.441766	−	0.255054i
$981$	−2.65692e6			−2.76083
$982$	−467933.	+	810484.i	−0.485245	+	0.840469i
$983$	357341.	−	206311.i	0.369807	−	0.213508i	−0.303567	−	0.952810i	$-0.598178\pi$
$983$	357341.	−	206311.i	0.369807	−	0.213508i	0.673374	+	0.739302i	$0.264844\pi$
$984$	2.35815e6	+	4.08444e6i	2.43547	+	4.21835i
$985$			1.41852e6i			1.46205i
$986$	−359630.	−	622898.i	−0.369916	−	0.640713i
$987$	−648325.			−0.665516
$988$			484762.i			0.496609i
$989$	−742547.	+	487165.i	−0.759157	+	0.498062i
$990$	1.88481e6			1.92308
$991$			1.11021e6i			1.13047i	0.824930	+	0.565235i	$0.191214\pi$
$991$			1.11021e6i			1.13047i	−0.824930	+	0.565235i	$0.808786\pi$
$992$	−2.08687e6	+	1.20485e6i	−2.12066	+	1.22437i
$993$	1.89413e6			1.92093
$994$	−565009.	+	326208.i	−0.571851	+	0.330158i
$995$	−63783.9	−	110477.i	−0.0644266	−	0.111590i
$996$	−1.55917e6	−	900188.i	−1.57172	−	0.907433i
$997$			543810.i			0.547087i	0.961860	+	0.273544i	$0.0881958\pi$
$997$			543810.i			0.547087i	−0.961860	+	0.273544i	$0.911804\pi$
$998$	−107239.	+	185744.i	−0.107670	+	0.186489i
$999$	1.02396e6	+	1.77355e6i	1.02601	+	1.77711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.5.d.a.7.1	✓	28
43.37	odd	6	inner	43.5.d.a.37.14	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.5.d.a.7.1	✓	28	1.1	even	1	trivial
43.5.d.a.37.14	yes	28	43.37	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	43.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-7.38404i q^{2} +(15.2777 - 8.82059i) q^{3} -38.5241 q^{4} +(-17.1186 + 9.88344i) q^{5} +(-65.1316 - 112.811i) q^{6} +(36.3076 + 20.9622i) q^{7} +166.319i q^{8} +(115.106 - 199.369i) q^{9} +O(q^{10})\)	\(q-7.38404i q^{2} +(15.2777 - 8.82059i) q^{3} -38.5241 q^{4} +(-17.1186 + 9.88344i) q^{5} +(-65.1316 - 112.811i) q^{6} +(36.3076 + 20.9622i) q^{7} +166.319i q^{8} +(115.106 - 199.369i) q^{9} +(72.9798 + 126.405i) q^{10} +56.0930 q^{11} +(-588.560 + 339.805i) q^{12} +(-36.9428 + 63.9869i) q^{13} +(154.786 - 268.097i) q^{14} +(-174.356 + 301.993i) q^{15} +611.722 q^{16} +(84.5100 - 146.376i) q^{17} +(-1472.15 - 849.944i) q^{18} +(-147.491 + 85.1540i) q^{19} +(659.480 - 380.751i) q^{20} +739.596 q^{21} -414.193i q^{22} +(240.154 + 415.960i) q^{23} +(1467.03 + 2540.97i) q^{24} +(-117.135 + 202.884i) q^{25} +(472.482 + 272.788i) q^{26} -2632.26i q^{27} +(-1398.72 - 807.551i) q^{28} +(499.097 + 288.154i) q^{29} +(2229.93 + 1287.45i) q^{30} +(-649.211 - 1124.47i) q^{31} -1855.88i q^{32} +(856.973 - 494.773i) q^{33} +(-1080.84 - 624.026i) q^{34} -828.715 q^{35} +(-4434.34 + 7680.50i) q^{36} +(-673.776 + 389.005i) q^{37} +(628.781 + 1089.08i) q^{38} +1303.43i q^{39} +(-1643.81 - 2847.15i) q^{40} +1607.43 q^{41} -5461.21i q^{42} +(105.398 + 1845.99i) q^{43} -2160.93 q^{44} +4550.55i q^{45} +(3071.46 - 1773.31i) q^{46} -876.593 q^{47} +(9345.71 - 5395.75i) q^{48} +(-321.672 - 557.152i) q^{49} +(1498.10 + 864.931i) q^{50} -2981.71i q^{51} +(1423.19 - 2465.04i) q^{52} +(2175.56 + 3768.18i) q^{53} -19436.7 q^{54} +(-960.236 + 554.392i) q^{55} +(-3486.42 + 6038.65i) q^{56} +(-1502.22 + 2601.92i) q^{57} +(2127.74 - 3685.35i) q^{58} -944.218 q^{59} +(6716.89 - 11634.0i) q^{60} +(3648.62 + 2106.53i) q^{61} +(-8303.11 + 4793.80i) q^{62} +(8358.41 - 4825.73i) q^{63} -3916.32 q^{64} -1460.49i q^{65} +(-3653.43 - 6327.92i) q^{66} +(-841.544 - 1457.60i) q^{67} +(-3255.67 + 5638.99i) q^{68} +(7338.02 + 4236.61i) q^{69} +6119.27i q^{70} +(-1825.13 - 1053.74i) q^{71} +(33158.8 + 19144.2i) q^{72} +(-7296.97 - 4212.91i) q^{73} +(2872.43 + 4975.20i) q^{74} +4132.80i q^{75} +(5681.97 - 3280.48i) q^{76} +(2036.60 + 1175.83i) q^{77} +9624.59 q^{78} +(-5320.11 + 9214.69i) q^{79} +(-10471.8 + 6045.92i) q^{80} +(-13894.5 - 24066.0i) q^{81} -11869.3i q^{82} +(1324.56 + 2294.21i) q^{83} -28492.3 q^{84} +3341.00i q^{85} +(13630.9 - 778.265i) q^{86} +10166.7 q^{87} +9329.34i q^{88} +(-3600.92 + 2078.99i) q^{89} +33601.5 q^{90} +(-2682.61 + 1548.81i) q^{91} +(-9251.74 - 16024.5i) q^{92} +(-19836.9 - 11452.8i) q^{93} +6472.80i q^{94} +(1683.23 - 2915.44i) q^{95} +(-16369.9 - 28353.5i) q^{96} +5999.67 q^{97} +(-4114.04 + 2375.24i) q^{98} +(6456.62 - 11183.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9}+O(q^{10}) \) 28 * q + 6 * q^3 - 234 * q^4 - 3 * q^5 + 15 * q^6 + 129 * q^7 + 534 * q^9	\( 28 q + 6 q^{3} - 234 q^{4} - 3 q^{5} + 15 q^{6} + 129 q^{7} + 534 q^{9} + 91 q^{10} - 376 q^{11} - 1026 q^{12} - 198 q^{13} + 78 q^{14} - 289 q^{15} + 806 q^{16} + 23 q^{17} - 435 q^{18} - 438 q^{19} + 177 q^{20} + 1684 q^{21} - 214 q^{23} + 1450 q^{24} + 463 q^{25} + 45 q^{26} - 3828 q^{28} + 1725 q^{29} + 8127 q^{30} + 2135 q^{31} - 474 q^{33} + 201 q^{34} - 6882 q^{35} - 12052 q^{36} + 1638 q^{37} - 2124 q^{38} - 6721 q^{40} + 3014 q^{41} + 157 q^{43} + 17162 q^{44} - 6240 q^{46} - 3670 q^{47} + 11547 q^{48} + 3085 q^{49} + 9738 q^{50} + 13746 q^{52} + 1208 q^{53} - 32416 q^{54} - 11202 q^{55} - 16245 q^{56} + 6207 q^{57} - 5756 q^{58} - 8716 q^{59} - 281 q^{60} + 8382 q^{61} - 25191 q^{62} + 23625 q^{63} + 17564 q^{64} - 21909 q^{66} - 9295 q^{67} + 6758 q^{68} + 30663 q^{69} + 24828 q^{71} + 46194 q^{72} + 5307 q^{73} + 13866 q^{74} + 5178 q^{76} - 27645 q^{77} - 10592 q^{78} - 24914 q^{79} - 13683 q^{80} - 43222 q^{81} + 7010 q^{83} - 21568 q^{84} + 15366 q^{86} + 57084 q^{87} - 80787 q^{89} + 114772 q^{90} - 24438 q^{91} + 22049 q^{92} - 39723 q^{93} + 29955 q^{95} + 1378 q^{96} - 12210 q^{97} + 28845 q^{98} - 49211 q^{99}+O(q^{100}) \) 28 * q + 6 * q^3 - 234 * q^4 - 3 * q^5 + 15 * q^6 + 129 * q^7 + 534 * q^9 + 91 * q^10 - 376 * q^11 - 1026 * q^12 - 198 * q^13 + 78 * q^14 - 289 * q^15 + 806 * q^16 + 23 * q^17 - 435 * q^18 - 438 * q^19 + 177 * q^20 + 1684 * q^21 - 214 * q^23 + 1450 * q^24 + 463 * q^25 + 45 * q^26 - 3828 * q^28 + 1725 * q^29 + 8127 * q^30 + 2135 * q^31 - 474 * q^33 + 201 * q^34 - 6882 * q^35 - 12052 * q^36 + 1638 * q^37 - 2124 * q^38 - 6721 * q^40 + 3014 * q^41 + 157 * q^43 + 17162 * q^44 - 6240 * q^46 - 3670 * q^47 + 11547 * q^48 + 3085 * q^49 + 9738 * q^50 + 13746 * q^52 + 1208 * q^53 - 32416 * q^54 - 11202 * q^55 - 16245 * q^56 + 6207 * q^57 - 5756 * q^58 - 8716 * q^59 - 281 * q^60 + 8382 * q^61 - 25191 * q^62 + 23625 * q^63 + 17564 * q^64 - 21909 * q^66 - 9295 * q^67 + 6758 * q^68 + 30663 * q^69 + 24828 * q^71 + 46194 * q^72 + 5307 * q^73 + 13866 * q^74 + 5178 * q^76 - 27645 * q^77 - 10592 * q^78 - 24914 * q^79 - 13683 * q^80 - 43222 * q^81 + 7010 * q^83 - 21568 * q^84 + 15366 * q^86 + 57084 * q^87 - 80787 * q^89 + 114772 * q^90 - 24438 * q^91 + 22049 * q^92 - 39723 * q^93 + 29955 * q^95 + 1378 * q^96 - 12210 * q^97 + 28845 * q^98 - 49211 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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