LMFDB - Embedded newform 43.6.g.a.24.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,6,Mod(9,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(42))

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

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

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

chi := DirichletCharacter("43.9");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	43.g (of order $21$, degree $12$, 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:	$6.89650425196$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			24.15
Character	$\chi$	$=$	43.24
Dual form			43.6.g.a.9.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(5.30682 - 6.65454i) q^{2} +(23.7101 - 3.57372i) q^{3} +(-8.99992 - 39.4312i) q^{4} +(-24.4442 + 16.6658i) q^{5} +(102.044 - 176.745i) q^{6} +(-48.7498 - 84.4371i) q^{7} +(-64.7633 - 31.1883i) q^{8} +(317.192 - 97.8407i) q^{9} +O(q^{10})$	\(q+(5.30682 - 6.65454i) q^{2} +(23.7101 - 3.57372i) q^{3} +(-8.99992 - 39.4312i) q^{4} +(-24.4442 + 16.6658i) q^{5} +(102.044 - 176.745i) q^{6} +(-48.7498 - 84.4371i) q^{7} +(-64.7633 - 31.1883i) q^{8} +(317.192 - 97.8407i) q^{9} +(-18.8179 + 251.108i) q^{10} +(0.448656 - 1.96569i) q^{11} +(-354.305 - 902.754i) q^{12} +(62.1741 + 829.656i) q^{13} +(-820.596 - 123.685i) q^{14} +(-520.016 + 482.504i) q^{15} +(614.847 - 296.095i) q^{16} +(763.227 + 520.359i) q^{17} +(1032.19 - 2629.99i) q^{18} +(-2527.76 - 779.712i) q^{19} +(877.149 + 813.875i) q^{20} +(-1457.61 - 1827.79i) q^{21} +(-10.6998 - 13.4172i) q^{22} +(144.703 + 134.265i) q^{23} +(-1647.00 - 508.032i) q^{24} +(-821.919 + 2094.22i) q^{25} +(5850.93 + 3989.10i) q^{26} +(1921.38 - 925.286i) q^{27} +(-2890.71 + 2682.19i) q^{28} +(2514.55 + 379.008i) q^{29} +(451.214 + 6021.03i) q^{30} +(2237.39 + 5700.79i) q^{31} +(1804.35 - 7905.39i) q^{32} +(3.61284 - 48.2100i) q^{33} +(7513.06 - 2317.47i) q^{34} +(2598.86 + 1251.55i) q^{35} +(-6712.68 - 11626.7i) q^{36} +(5029.16 - 8710.76i) q^{37} +(-18603.0 + 12683.3i) q^{38} +(4439.11 + 19449.0i) q^{39} +(2102.87 - 316.956i) q^{40} +(-2641.03 + 3311.75i) q^{41} -19898.4 q^{42} +(-11995.2 - 1767.18i) q^{43} -81.5474 q^{44} +(-6122.92 + 7677.89i) q^{45} +(1661.38 - 250.413i) q^{46} +(-3524.83 - 15443.3i) q^{47} +(13519.9 - 9217.71i) q^{48} +(3650.42 - 6322.72i) q^{49} +(9574.27 + 16583.1i) q^{50} +(19955.8 + 9610.20i) q^{51} +(32154.8 - 9918.44i) q^{52} +(1110.84 - 14823.2i) q^{53} +(4039.04 - 17696.2i) q^{54} +(21.7927 + 55.5269i) q^{55} +(523.741 + 6988.84i) q^{56} +(-62719.9 - 9453.51i) q^{57} +(15866.4 - 14721.9i) q^{58} +(-39852.3 + 19191.8i) q^{59} +(23705.8 + 16162.4i) q^{60} +(13022.8 - 33181.6i) q^{61} +(49809.6 + 15364.2i) q^{62} +(-23724.4 - 22013.0i) q^{63} +(-29415.8 - 36886.2i) q^{64} +(-15346.7 - 19244.1i) q^{65} +(-301.643 - 279.883i) q^{66} +(38424.5 + 11852.4i) q^{67} +(13649.4 - 34778.2i) q^{68} +(3910.74 + 2666.30i) q^{69} +(22120.1 - 10652.5i) q^{70} +(-31862.6 + 29564.2i) q^{71} +(-23593.9 - 3556.20i) q^{72} +(-2866.25 - 38247.4i) q^{73} +(-31277.3 - 79693.2i) q^{74} +(-12003.6 + 52591.3i) q^{75} +(-7995.32 + 106690. i) q^{76} +(-187.849 + 57.9437i) q^{77} +(152982. + 73672.2i) q^{78} +(14470.7 + 25064.0i) q^{79} +(-10094.8 + 17484.7i) q^{80} +(-24396.1 + 16633.0i) q^{81} +(8022.69 + 35149.7i) q^{82} +(-64384.3 + 9704.37i) q^{83} +(-58953.6 + 73925.5i) q^{84} -27328.7 q^{85} +(-75416.3 + 70444.7i) q^{86} +60974.7 q^{87} +(-90.3629 + 113.312i) q^{88} +(-138131. + 20819.9i) q^{89} +(18599.7 + 81490.4i) q^{90} +(67022.7 - 45695.3i) q^{91} +(3991.90 - 6914.18i) q^{92} +(73421.8 + 127170. i) q^{93} +(-121474. - 58498.6i) q^{94} +(74783.8 - 23067.7i) q^{95} +(14529.7 - 193886. i) q^{96} +(-11225.8 + 49183.5i) q^{97} +(-22702.7 - 57845.4i) q^{98} +(-50.0145 - 667.397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9}+O(q^{10}) $ 204 * q - 468 * q^4 - 85 * q^5 - 22 * q^6 + 454 * q^7 + 698 * q^8 - 333 * q^9	\( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9} + 303 q^{10} - 1340 q^{11} + 858 q^{12} + 814 q^{13} + 1202 q^{14} - 2083 q^{15} - 6248 q^{16} - 214 q^{17} - 174 q^{18} - 246 q^{19} - 17139 q^{20} + 3007 q^{21} + 2118 q^{22} + 3192 q^{23} + 15880 q^{24} + 3652 q^{25} - 1237 q^{26} + 108 q^{27} - 6780 q^{28} - 18827 q^{29} + 98080 q^{30} - 43196 q^{31} - 3930 q^{32} + 28181 q^{33} + 45155 q^{34} + 33275 q^{35} - 49399 q^{36} + 34607 q^{37} - 43374 q^{38} + 15155 q^{39} - 108727 q^{40} + 7156 q^{41} - 48066 q^{42} - 176452 q^{43} + 26068 q^{44} - 96386 q^{45} - 27185 q^{46} + 20402 q^{47} + 198899 q^{48} - 158742 q^{49} + 186243 q^{50} + 98589 q^{51} + 278918 q^{52} + 14102 q^{53} + 270894 q^{54} - 334770 q^{55} + 61999 q^{56} - 202490 q^{57} + 213658 q^{58} - 43753 q^{59} - 389005 q^{60} + 80516 q^{61} + 162349 q^{62} - 75177 q^{63} - 489850 q^{64} + 93726 q^{65} + 246095 q^{66} - 322922 q^{67} + 475089 q^{68} - 397079 q^{69} - 614985 q^{70} - 233345 q^{71} + 379655 q^{72} + 159391 q^{73} + 695938 q^{74} + 344081 q^{75} - 50808 q^{76} + 608177 q^{77} + 605548 q^{78} - 272109 q^{79} + 601054 q^{80} + 193536 q^{81} - 996896 q^{82} + 177813 q^{83} - 919009 q^{84} - 844524 q^{85} - 876752 q^{86} - 188214 q^{87} - 59998 q^{88} - 469041 q^{89} - 453431 q^{90} - 223189 q^{91} - 94922 q^{92} + 569174 q^{93} + 1175168 q^{94} + 435689 q^{95} + 1557688 q^{96} + 643751 q^{97} + 886196 q^{98} + 1422581 q^{99}+O(q^{100}) \) 204 * q - 468 * q^4 - 85 * q^5 - 22 * q^6 + 454 * q^7 + 698 * q^8 - 333 * q^9 + 303 * q^10 - 1340 * q^11 + 858 * q^12 + 814 * q^13 + 1202 * q^14 - 2083 * q^15 - 6248 * q^16 - 214 * q^17 - 174 * q^18 - 246 * q^19 - 17139 * q^20 + 3007 * q^21 + 2118 * q^22 + 3192 * q^23 + 15880 * q^24 + 3652 * q^25 - 1237 * q^26 + 108 * q^27 - 6780 * q^28 - 18827 * q^29 + 98080 * q^30 - 43196 * q^31 - 3930 * q^32 + 28181 * q^33 + 45155 * q^34 + 33275 * q^35 - 49399 * q^36 + 34607 * q^37 - 43374 * q^38 + 15155 * q^39 - 108727 * q^40 + 7156 * q^41 - 48066 * q^42 - 176452 * q^43 + 26068 * q^44 - 96386 * q^45 - 27185 * q^46 + 20402 * q^47 + 198899 * q^48 - 158742 * q^49 + 186243 * q^50 + 98589 * q^51 + 278918 * q^52 + 14102 * q^53 + 270894 * q^54 - 334770 * q^55 + 61999 * q^56 - 202490 * q^57 + 213658 * q^58 - 43753 * q^59 - 389005 * q^60 + 80516 * q^61 + 162349 * q^62 - 75177 * q^63 - 489850 * q^64 + 93726 * q^65 + 246095 * q^66 - 322922 * q^67 + 475089 * q^68 - 397079 * q^69 - 614985 * q^70 - 233345 * q^71 + 379655 * q^72 + 159391 * q^73 + 695938 * q^74 + 344081 * q^75 - 50808 * q^76 + 608177 * q^77 + 605548 * q^78 - 272109 * q^79 + 601054 * q^80 + 193536 * q^81 - 996896 * q^82 + 177813 * q^83 - 919009 * q^84 - 844524 * q^85 - 876752 * q^86 - 188214 * q^87 - 59998 * q^88 - 469041 * q^89 - 453431 * q^90 - 223189 * q^91 - 94922 * q^92 + 569174 * q^93 + 1175168 * q^94 + 435689 * q^95 + 1557688 * q^96 + 643751 * q^97 + 886196 * q^98 + 1422581 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{20}{21}\right)$

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 $

$2$	5.30682	−	6.65454i	0.938122	−	1.17637i	−0.0460118	−	0.998941i	$-0.514651\pi$
$2$	5.30682	−	6.65454i	0.938122	−	1.17637i	0.984134	−	0.177427i	$-0.0567774\pi$
$3$	23.7101	−	3.57372i	1.52100	−	0.229254i	0.665242	−	0.746628i	$-0.268328\pi$
$3$	23.7101	−	3.57372i	1.52100	−	0.229254i	0.855760	+	0.517374i	$0.173090\pi$
$4$	−8.99992	−	39.4312i	−0.281248	−	1.23223i
$5$	−24.4442	+	16.6658i	−0.437272	+	0.298127i	−0.761876	−	0.647723i	$-0.775721\pi$
$5$	−24.4442	+	16.6658i	−0.437272	+	0.298127i	0.324604	+	0.945850i	$0.394769\pi$
$6$	102.044	−	176.745i	1.15720	−	2.00433i
$7$	−48.7498	−	84.4371i	−0.376034	−	0.651310i	0.614447	−	0.788958i	$-0.289379\pi$
$7$	−48.7498	−	84.4371i	−0.376034	−	0.651310i	−0.990481	+	0.137648i	$0.956046\pi$
$8$	−64.7633	−	31.1883i	−0.357770	−	0.172293i
$9$	317.192	−	97.8407i	1.30532	−	0.402637i
$10$	−18.8179	+	251.108i	−0.0595075	+	0.794072i
$11$	0.448656	−	1.96569i	0.00111797	−	0.00489816i	−0.974366	−	0.224969i	$-0.927772\pi$
$11$	0.448656	−	1.96569i	0.00111797	−	0.00489816i	0.975484	+	0.220071i	$0.0706290\pi$
$12$	−354.305	−	902.754i	−0.710271	−	1.80974i
$13$	62.1741	+	829.656i	0.102036	+	1.36157i	0.779679	+	0.626179i	$0.215382\pi$
$13$	62.1741	+	829.656i	0.102036	+	1.36157i	−0.677644	+	0.735390i	$0.736999\pi$
$14$	−820.596	−	123.685i	−1.11895	−	0.168654i
$15$	−520.016	+	482.504i	−0.596744	+	0.553698i
$16$	614.847	−	296.095i	0.600436	−	0.289155i
$17$	763.227	+	520.359i	0.640518	+	0.436698i	0.839541	−	0.543297i	$-0.182824\pi$
$17$	763.227	+	520.359i	0.640518	+	0.436698i	−0.199022	+	0.979995i	$0.563777\pi$
$18$	1032.19	−	2629.99i	0.750897	−	1.91325i
$19$	−2527.76	−	779.712i	−1.60640	−	0.495507i	−0.643515	−	0.765434i	$-0.722524\pi$
$19$	−2527.76	−	779.712i	−1.60640	−	0.495507i	−0.962881	+	0.269926i	$0.913001\pi$
$20$	877.149	+	813.875i	0.490341	+	0.454970i
$21$	−1457.61	−	1827.79i	−0.721264	−	0.904437i
$22$	−10.6998	−	13.4172i	−0.00471324	−	0.00591022i
$23$	144.703	+	134.265i	0.0570371	+	0.0529227i	0.708176	−	0.706036i	$-0.249518\pi$
$23$	144.703	+	134.265i	0.0570371	+	0.0529227i	−0.651139	+	0.758958i	$0.725709\pi$
$24$	−1647.00	−	508.032i	−0.583667	−	0.180038i
$25$	−821.919	+	2094.22i	−0.263014	+	0.670149i
$26$	5850.93	+	3989.10i	1.69743	+	1.15729i
$27$	1921.38	−	925.286i	0.507228	−	0.244268i
$28$	−2890.71	+	2682.19i	−0.696803	+	0.646539i
$29$	2514.55	+	379.008i	0.555221	+	0.0836862i	0.420659	−	0.907219i	$-0.361799\pi$
$29$	2514.55	+	379.008i	0.555221	+	0.0836862i	0.134563	+	0.990905i	$0.457037\pi$
$30$	451.214	+	6021.03i	0.0915333	+	1.22143i
$31$	2237.39	+	5700.79i	0.418156	+	1.06544i	0.972448	+	0.233122i	$0.0748940\pi$
$31$	2237.39	+	5700.79i	0.418156	+	1.06544i	−0.554292	+	0.832323i	$0.687011\pi$
$32$	1804.35	−	7905.39i	0.311492	−	1.36474i
$33$	3.61284	−	48.2100i	0.000577516	−	0.00770641i
$34$	7513.06	−	2317.47i	1.11460	−	0.343809i
$35$	2598.86	+	1251.55i	0.358602	+	0.172694i
$36$	−6712.68	−	11626.7i	−0.863256	−	1.49520i
$37$	5029.16	−	8710.76i	0.603936	−	1.04605i	−0.388282	−	0.921541i	$-0.626931\pi$
$37$	5029.16	−	8710.76i	0.603936	−	1.04605i	0.992219	−	0.124508i	$-0.0397353\pi$
$38$	−18603.0	+	12683.3i	−2.08989	+	1.42487i
$39$	4439.11	+	19449.0i	0.467342	+	2.04756i
$40$	2102.87	−	316.956i	0.207808	−	0.0313220i
$41$	−2641.03	+	3311.75i	−0.245366	+	0.307679i	−0.889230	−	0.457461i	$-0.848759\pi$
$41$	−2641.03	+	3311.75i	−0.245366	+	0.307679i	0.643864	+	0.765140i	$0.277330\pi$
$42$	−19898.4			−1.74058
$43$	−11995.2	−	1767.18i	−0.989321	−	0.145750i
$43$	−11995.2	−	1767.18i	−0.989321	−	0.145750i
$44$	−81.5474			−0.00635007
$45$	−6122.92	+	7677.89i	−0.450741	+	0.565211i
$46$	1661.38	−	250.413i	0.115764	−	0.0174487i
$47$	−3524.83	−	15443.3i	−0.232752	−	1.01975i	−0.947346	−	0.320213i	$-0.896246\pi$
$47$	−3524.83	−	15443.3i	−0.232752	−	1.01975i	0.714594	−	0.699540i	$-0.246612\pi$
$48$	13519.9	−	9217.71i	0.846975	−	0.577458i
$49$	3650.42	−	6322.72i	0.217197	−	0.376195i
$50$	9574.27	+	16583.1i	0.541602	+	0.938083i
$51$	19955.8	+	9610.20i	1.07434	+	0.517377i
$52$	32154.8	−	9918.44i	1.64906	−	0.508669i
$53$	1110.84	−	14823.2i	0.0543204	−	0.724855i	−0.901851	−	0.432047i	$-0.857791\pi$
$53$	1110.84	−	14823.2i	0.0543204	−	0.724855i	0.956171	−	0.292808i	$-0.0945896\pi$
$54$	4039.04	−	17696.2i	0.188493	−	0.825840i
$55$	21.7927	+	55.5269i	0.000971415	+	0.00247512i
$56$	523.741	+	6988.84i	0.0223176	+	0.297807i
$57$	−62719.9	−	9453.51i	−2.55693	−	0.385395i
$58$	15866.4	−	14721.9i	0.619311	−	0.574637i
$59$	−39852.3	+	19191.8i	−1.49047	+	0.717772i	−0.989070	−	0.147444i	$-0.952895\pi$
$59$	−39852.3	+	19191.8i	−1.49047	+	0.717772i	−0.501399	+	0.865216i	$0.667181\pi$
$60$	23705.8	+	16162.4i	0.850113	+	0.579598i
$61$	13022.8	−	33181.6i	0.448105	−	1.14175i	−0.511220	−	0.859450i	$-0.670806\pi$
$61$	13022.8	−	33181.6i	0.448105	−	1.14175i	0.959325	−	0.282304i	$-0.0910986\pi$
$62$	49809.6	+	15364.2i	1.64564	+	0.507611i
$63$	−23724.4	−	22013.0i	−0.753085	−	0.698761i
$64$	−29415.8	−	36886.2i	−0.897699	−	1.12568i
$65$	−15346.7	−	19244.1i	−0.450538	−	0.564956i
$66$	−301.643	−	279.883i	−0.00852379	−	0.00790892i
$67$	38424.5	+	11852.4i	1.04573	+	0.322566i	0.769582	−	0.638548i	$-0.220465\pi$
$67$	38424.5	+	11852.4i	1.04573	+	0.322566i	0.276151	+	0.961114i	$0.410941\pi$
$68$	13649.4	−	34778.2i	0.357966	−	0.912083i
$69$	3910.74	+	2666.30i	0.0988863	+	0.0674195i
$70$	22120.1	−	10652.5i	0.539564	−	0.259840i
$71$	−31862.6	+	29564.2i	−0.750129	+	0.696018i	−0.959466	−	0.281826i	$-0.909060\pi$
$71$	−31862.6	+	29564.2i	−0.750129	+	0.696018i	0.209337	+	0.977844i	$0.432870\pi$
$72$	−23593.9	−	3556.20i	−0.536374	−	0.0808454i
$73$	−2866.25	−	38247.4i	−0.0629516	−	0.840031i	−0.935911	−	0.352237i	$-0.885421\pi$
$73$	−2866.25	−	38247.4i	−0.0629516	−	0.840031i	0.872959	−	0.487793i	$-0.162198\pi$
$74$	−31277.3	−	79693.2i	−0.663972	−	1.69177i
$75$	−12003.6	+	52591.3i	−0.246410	+	1.07959i
$76$	−7995.32	+	106690.i	−0.158782	+	2.11880i
$77$	−187.849	+	57.9437i	−0.00361062	+	0.00111373i
$78$	152982.	+	73672.2i	2.84710	+	1.37109i
$79$	14470.7	+	25064.0i	0.260869	+	0.451838i	0.966473	−	0.256768i	$-0.0826576\pi$
$79$	14470.7	+	25064.0i	0.260869	+	0.451838i	−0.705604	+	0.708606i	$0.749324\pi$
$80$	−10094.8	+	17484.7i	−0.176349	+	0.305445i
$81$	−24396.1	+	16633.0i	−0.413150	+	0.281681i
$82$	8022.69	+	35149.7i	0.131761	+	0.577280i
$83$	−64384.3	+	9704.37i	−1.02585	+	0.154622i	−0.640349	−	0.768084i	$-0.721210\pi$
$83$	−64384.3	+	9704.37i	−1.02585	+	0.154622i	−0.385503	+	0.922706i	$0.625972\pi$
$84$	−58953.6	+	73925.5i	−0.911617	+	1.14313i
$85$	−27328.7			−0.410272
$86$	−75416.3	+	70444.7i	−1.09956	+	1.02707i
$87$	60974.7			0.863678
$88$	−90.3629	+	113.312i	−0.00124389	+	0.00155979i
$89$	−138131.	+	20819.9i	−1.84849	+	0.278615i	−0.977225	−	0.212204i	$-0.931936\pi$
$89$	−138131.	+	20819.9i	−1.84849	+	0.278615i	−0.871262	+	0.490819i	$0.836698\pi$
$90$	18599.7	+	81490.4i	0.242046	+	1.06047i
$91$	67022.7	−	45695.3i	0.848435	−	0.578453i
$92$	3991.90	−	6914.18i	0.0491712	−	0.0851670i
$93$	73421.8	+	127170.i	0.880274	+	1.52468i
$94$	−121474.	−	58498.6i	−1.41795	−	0.682850i
$95$	74783.8	−	23067.7i	0.850155	−	0.262238i
$96$	14529.7	−	193886.i	0.160909	−	2.14718i
$97$	−11225.8	+	49183.5i	−0.121140	+	0.530751i	0.877545	+	0.479494i	$0.159180\pi$
$97$	−11225.8	+	49183.5i	−0.121140	+	0.530751i	−0.998686	+	0.0512566i	$0.983677\pi$
$98$	−22702.7	−	57845.4i	−0.238787	−	0.608420i
$99$	−50.0145	−	667.397i	−0.000512871	−	0.00684378i
$100$	89974.7	+	13561.5i	0.899747	+	0.135615i
$101$	146642.	−	136064.i	1.43039	−	1.32721i	0.565978	−	0.824421i	$-0.308499\pi$
$101$	146642.	−	136064.i	1.43039	−	1.32721i	0.864411	−	0.502786i	$-0.167692\pi$
$102$	169853.	−	81797.0i	1.61649	−	0.778461i
$103$	−41079.4	−	28007.4i	−0.381532	−	0.260124i	0.357334	−	0.933977i	$-0.383686\pi$
$103$	−41079.4	−	28007.4i	−0.381532	−	0.260124i	−0.738866	+	0.673853i	$0.764638\pi$
$104$	21849.0	−	55670.3i	0.198083	−	0.504708i
$105$	66091.8	+	20386.6i	0.585025	+	0.180456i
$106$	−92746.3	−	86056.0i	−0.801737	−	0.743903i
$107$	−32642.7	−	40932.7i	−0.275630	−	0.345629i	0.624678	−	0.780882i	$-0.285230\pi$
$107$	−32642.7	−	40932.7i	−0.275630	−	0.345629i	−0.900308	+	0.435253i	$0.856659\pi$
$108$	−53777.4	−	67434.7i	−0.443650	−	0.556319i
$109$	43168.3	+	40054.3i	0.348015	+	0.322911i	0.834740	−	0.550645i	$-0.185618\pi$
$109$	43168.3	+	40054.3i	0.348015	+	0.322911i	−0.486725	+	0.873555i	$0.661808\pi$
$110$	485.156	+	149.651i	0.00382296	+	0.00117923i
$111$	88112.0	−	224506.i	0.678777	−	1.72950i
$112$	−54975.0	−	37481.3i	−0.414114	−	0.282338i
$113$	151691.	−	73050.5i	1.11754	−	0.538180i	0.218409	−	0.975857i	$-0.429913\pi$
$113$	151691.	−	73050.5i	1.11754	−	0.538180i	0.899132	+	0.437678i	$0.144199\pi$
$114$	−395752.	+	367204.i	−2.85208	+	2.64634i
$115$	−5774.78	−	870.407i	−0.0407184	−	0.00613731i
$116$	−7686.04	−	102563.i	−0.0530344	−	0.707695i
$117$	100895.	+	257077.i	0.681406	+	1.73619i
$118$	−83775.9	+	367046.i	−0.553878	+	2.42670i
$119$	6730.48	−	89812.0i	0.0435691	−	0.581390i
$120$	48726.4	−	15030.1i	0.308895	−	0.0952816i
$121$	145098.	+	69875.6i	0.900946	+	0.433873i
$122$	−151699.	−	262750.i	−0.922745	−	1.59824i
$123$	−50783.8	+	87960.0i	−0.302665	+	0.524231i
$124$	204653.	−	139530.i	1.19526	−	0.814916i
$125$	−35383.3	−	155024.i	−0.202546	−	0.887411i
$126$	−272388.	+	41055.9i	−1.52849	+	0.230382i
$127$	95398.4	−	119626.i	0.524846	−	0.658136i	−0.446784	−	0.894642i	$-0.647431\pi$
$127$	95398.4	−	119626.i	0.524846	−	0.658136i	0.971630	+	0.236506i	$0.0760022\pi$
$128$	−142087.			−0.766531
$129$	−290723.	+	967.655i	−1.53817	+	0.00511972i
$130$	−209503.			−1.08726
$131$	−25292.6	+	31716.0i	−0.128770	+	0.161473i	−0.842037	−	0.539420i	$-0.818644\pi$
$131$	−25292.6	+	31716.0i	−0.128770	+	0.161473i	0.713266	+	0.700893i	$0.247215\pi$
$132$	−1933.49	+	291.427i	−0.00965846	+	0.00145578i
$133$	57391.3	+	251448.i	0.281331	+	1.23259i
$134$	282784.	−	192799.i	1.36048	−	0.927561i
$135$	−31545.9	+	54639.2i	−0.148974	+	0.258030i
$136$	−33199.9	−	57504.0i	−0.153918	−	0.266594i
$137$	357102.	+	171971.i	1.62551	+	0.782806i	0.999997	+	0.00259474i	$0.000825932\pi$
$137$	357102.	+	171971.i	1.62551	+	0.782806i	0.625516	+	0.780211i	$0.284888\pi$
$138$	38496.6	−	11874.6i	0.172078	−	0.0530789i
$139$	−25667.3	+	342506.i	−0.112679	+	1.50360i	0.598805	+	0.800895i	$0.295642\pi$
$139$	−25667.3	+	342506.i	−0.112679	+	1.50360i	−0.711484	+	0.702702i	$0.751977\pi$
$140$	25960.4	−	113740.i	0.111942	−	0.490449i
$141$	−138764.	−	353564.i	−0.587798	−	1.49769i
$142$	27647.0	+	368923.i	0.115061	+	1.53538i
$143$	1658.74	+	250.015i	0.00678326	+	0.00102241i
$144$	166054.	−	154076.i	0.667335	−	0.619196i
$145$	−67782.8	+	32642.5i	−0.267732	+	0.128933i
$146$	−269730.	−	183899.i	−1.04724	−	0.713997i
$147$	63956.2	−	162958.i	0.244112	−	0.621987i
$148$	−388738.	−	119910.i	−1.45882	−	0.449988i
$149$	132947.	+	123357.i	0.490585	+	0.455196i	0.886256	−	0.463196i	$-0.153298\pi$
$149$	132947.	+	123357.i	0.490585	+	0.455196i	−0.395671	+	0.918392i	$0.629488\pi$
$150$	286270.	+	358971.i	1.03884	+	1.30266i
$151$	−234566.	−	294137.i	−0.837188	−	1.04980i	−0.998025	−	0.0628191i	$-0.979991\pi$
$151$	−234566.	−	294137.i	−0.837188	−	1.04980i	0.160837	−	0.986981i	$-0.448581\pi$
$152$	139388.	+	129333.i	0.489347	+	0.454048i
$153$	293002.	+	90379.1i	1.01191	+	0.312133i
$154$	−611.291	+	1557.54i	−0.00207705	+	0.00529223i
$155$	−149700.	−	102063.i	−0.500485	−	0.341225i
$156$	726947.	−	350079.i	2.39161	−	1.15174i
$157$	94616.1	−	87790.9i	0.306349	−	0.284250i	−0.511984	−	0.858995i	$-0.671089\pi$
$157$	94616.1	−	87790.9i	0.306349	−	0.284250i	0.818332	+	0.574745i	$0.194899\pi$
$158$	243583.	+	36714.3i	0.776255	+	0.117002i
$159$	−26635.6	−	355428.i	−0.0835546	−	1.11496i
$160$	87643.6	+	223312.i	0.270658	+	0.689624i
$161$	4282.68	−	18763.7i	0.0130212	−	0.0570496i
$162$	−18780.9	+	250613.i	−0.0562248	+	0.750268i
$163$	454097.	−	140070.i	1.33869	−	0.412931i	0.458982	−	0.888446i	$-0.348214\pi$
$163$	454097.	−	140070.i	1.33869	−	0.412931i	0.879708	+	0.475515i	$0.157738\pi$
$164$	154355.	+	74333.6i	0.448138	+	0.215812i
$165$	715.145	+	1238.67i	0.00204496	+	0.00354197i
$166$	−277098.	+	479947.i	−0.780482	+	1.35183i
$167$	−502167.	+	342371.i	−1.39334	+	0.949962i	−0.393812	+	0.919191i	$0.628844\pi$
$167$	−502167.	+	342371.i	−1.39334	+	0.949962i	−0.999526	+	0.0307709i	$0.990204\pi$
$168$	37394.1	+	163834.i	0.102219	+	0.447849i
$169$	−317318.	+	47828.0i	−0.854629	+	0.128815i
$170$	−145029.	+	181860.i	−0.384885	+	0.482631i
$171$	−878074.			−2.29636
$172$	38274.1	+	488891.i	0.0986470	+	1.26006i
$173$	10619.0			0.0269755			0.0134877	−	0.999909i	$-0.495707\pi$
$173$	10619.0			0.0269755			0.0134877	+	0.999909i	$0.495707\pi$
$174$	323582.	−	405759.i	0.810235	−	1.01600i
$175$	216898.	−	32692.1i	0.535377	−	0.0806951i
$176$	−306.175	−	1341.44i	−0.000745055	−	0.00326430i
$177$	−876314.	+	597461.i	−2.10245	+	1.43343i
$178$	−594490.	+	1.02969e6i	−1.40635	+	2.43588i
$179$	−151721.	−	262789.i	−0.353928	−	0.613020i	0.633006	−	0.774147i	$-0.281821\pi$
$179$	−151721.	−	262789.i	−0.353928	−	0.613020i	−0.986934	+	0.161126i	$0.948487\pi$
$180$	357855.	+	172334.i	0.823238	+	0.396450i
$181$	447788.	−	138124.i	1.01596	−	0.313382i	0.258323	−	0.966059i	$-0.416830\pi$
$181$	447788.	−	138124.i	1.01596	−	0.313382i	0.757637	+	0.652677i	$0.226354\pi$
$182$	51596.1	−	688503.i	0.115462	−	1.54073i
$183$	190190.	−	833277.i	0.419817	−	1.83934i
$184$	−5183.94	−	13208.5i	−0.0112880	−	0.0287612i
$185$	22237.8	+	296743.i	0.0477708	+	0.637457i
$186$	1.23590e6	+	186281.i	2.61939	+	0.394809i
$187$	1365.29	−	1266.80i	0.00285510	−	0.00264914i
$188$	−577224.	+	277976.i	−1.19110	+	0.573606i
$189$	−171795.	−	117128.i	−0.349829	−	0.238510i
$190$	243359.	−	620068.i	0.489061	−	1.24611i
$191$	−132617.	−	40907.0i	−0.263037	−	0.0811361i	0.160432	−	0.987047i	$-0.448711\pi$
$191$	−132617.	−	40907.0i	−0.263037	−	0.0811361i	−0.423468	+	0.905911i	$0.639188\pi$
$192$	−829271.	−	769451.i	−1.62347	−	1.50636i
$193$	447060.	+	560595.i	0.863918	+	1.08332i	0.995755	+	0.0920470i	$0.0293410\pi$
$193$	447060.	+	560595.i	0.863918	+	1.08332i	−0.131837	+	0.991271i	$0.542088\pi$
$194$	267721.	+	335711.i	0.510714	+	0.640415i
$195$	−432644.	−	401435.i	−0.814787	−	0.756012i
$196$	−282166.	−	87036.7i	−0.524644	−	0.161831i
$197$	−101605.	+	258886.i	−0.186531	+	0.475272i	−0.993296	−	0.115600i	$-0.963121\pi$
$197$	−101605.	+	258886.i	−0.186531	+	0.475272i	0.806765	+	0.590872i	$0.201216\pi$
$198$	−4706.64	−	3208.93i	−0.00853194	−	0.00581698i
$199$	33919.7	−	16334.9i	0.0607183	−	0.0292404i	−0.403278	−	0.915077i	$-0.632129\pi$
$199$	33919.7	−	16334.9i	0.0607183	−	0.0292404i	0.463996	+	0.885837i	$0.346415\pi$
$200$	118545.	−	109994.i	0.209560	−	0.194444i
$201$	953404.	+	143703.i	1.66451	+	0.250885i
$202$	−127240.	−	1.69790e6i	−0.219404	−	2.92775i
$203$	−90581.6	−	230798.i	−0.154277	−	0.393090i
$204$	199342.	−	873372.i	0.335369	−	1.46935i
$205$	9365.05	−	124968.i	0.0155642	−	0.207689i
$206$	−404377.	+	124734.i	−0.663925	+	0.204794i
$207$	59035.1	+	28429.8i	0.0957601	+	0.0461156i
$208$	283884.	+	491702.i	0.454970	+	0.788032i
$209$	−2666.77	+	4618.97i	−0.00422298	+	0.00731442i
$210$	486401.	−	331623.i	0.761108	−	0.518915i
$211$	115216.	+	504794.i	0.178159	+	0.780564i	0.982480	+	0.186369i	$0.0596720\pi$
$211$	115216.	+	504794.i	0.178159	+	0.780564i	−0.804321	+	0.594195i	$0.797471\pi$
$212$	−594493.	+	89605.4i	−0.908462	+	0.136929i
$213$	−649811.	+	814838.i	−0.981382	+	1.23061i
$214$	−445617.			−0.665162
$215$	322666.	−	156713.i	0.476054	−	0.231211i
$216$	−153293.			−0.223556
$217$	372285.	−	466831.i	0.536694	−	0.672993i
$218$	495629.	−	74704.1i	0.706343	−	0.106464i
$219$	−204644.	−	896606.i	−0.288330	−	1.26326i
$220$	1993.36	−	1359.05i	0.00277670	−	0.00189313i
$221$	−384266.	+	665569.i	−0.529239	+	0.916669i
$222$	−1.02639e6	−	1.77776e6i	−1.39775	−	2.42097i
$223$	923100.	+	444541.i	1.24304	+	0.598619i	0.935638	−	0.352960i	$-0.114825\pi$
$223$	923100.	+	444541.i	1.24304	+	0.598619i	0.307406	+	0.951579i	$0.400539\pi$
$224$	−755470.	+	233032.i	−1.00600	+	0.310309i
$225$	−55806.4	+	744685.i	−0.0734900	+	0.980655i
$226$	318879.	−	1.39710e6i	0.415293	−	1.81952i
$227$	−275744.	−	702585.i	−0.355175	−	0.904971i	−0.991088	−	0.133210i	$-0.957472\pi$
$227$	−275744.	−	702585.i	−0.355175	−	0.904971i	0.635913	−	0.771761i	$-0.280624\pi$
$228$	191711.	+	2.55820e6i	0.244236	+	3.25910i
$229$	447658.	+	67473.6i	0.564102	+	0.0850247i	0.424901	−	0.905240i	$-0.360309\pi$
$229$	447658.	+	67473.6i	0.564102	+	0.0850247i	0.139200	+	0.990264i	$0.455547\pi$
$230$	−36437.9	+	33809.4i	−0.0454186	+	0.0421423i
$231$	−4246.83	+	2045.17i	−0.00523643	+	0.00252173i
$232$	−151030.	−	102971.i	−0.184223	−	0.125601i
$233$	337274.	−	859360.i	0.406999	−	1.03702i	−0.569595	−	0.821925i	$-0.692900\pi$
$233$	337274.	−	859360.i	0.406999	−	1.03702i	0.976594	−	0.215091i	$-0.0690047\pi$
$234$	2.24616e6	+	692849.i	2.68165	+	0.827178i
$235$	343536.	+	318755.i	0.405791	+	0.376519i
$236$	1.11543e6	+	1.39870e6i	1.30365	+	1.63472i
$237$	432674.	+	542556.i	0.500368	+	0.627442i
$238$	−561941.	−	521405.i	−0.643055	−	0.596668i
$239$	192149.	+	59270.0i	0.217592	+	0.0671182i	0.401634	−	0.915800i	$-0.368442\pi$
$239$	192149.	+	59270.0i	0.217592	+	0.0671182i	−0.184043	+	0.982918i	$0.558918\pi$
$240$	−176863.	+	450640.i	−0.198203	+	0.505012i
$241$	122966.	+	83836.5i	0.136377	+	0.0929802i	0.629587	−	0.776930i	$-0.283224\pi$
$241$	122966.	+	83836.5i	0.136377	+	0.0929802i	−0.493210	+	0.869910i	$0.664177\pi$
$242$	1.23500e6	−	594745.i	1.35559	−	0.652819i
$243$	−898870.	+	834029.i	−0.976520	+	0.906078i
$244$	−1.42559e6	−	214874.i	−1.53293	−	0.231052i
$245$	16141.3	+	215391.i	0.0171800	+	0.229252i
$246$	315834.	+	804731.i	0.332752	+	0.847838i
$247$	489731.	−	2.14565e6i	0.510758	−	2.23778i
$248$	32897.2	−	438982.i	0.0339648	−	0.453229i
$249$	−1.49188e6	+	460183.i	−1.52488	+	0.470362i
$250$	−1.21939e6	−	587227.i	−1.23394	−	0.594232i
$251$	374485.	+	648627.i	0.375189	+	0.649846i	0.990355	−	0.138551i	$-0.0442445\pi$
$251$	374485.	+	648627.i	0.375189	+	0.649846i	−0.615166	+	0.788397i	$0.710911\pi$
$252$	−654483.	+	1.13360e6i	−0.649228	+	1.12450i
$253$	328.844	−	224.202i	0.000322990	−	0.000220211i
$254$	−289793.	−	1.26967e6i	−0.281841	−	1.23482i
$255$	−647965.	+	97665.1i	−0.624024	+	0.0940565i
$256$	187274.	−	234835.i	0.178599	−	0.223956i
$257$	−317895.			−0.300228			−0.150114	−	0.988669i	$-0.547964\pi$
$257$	−317895.			−0.300228			−0.150114	+	0.988669i	$0.547964\pi$
$258$	−1.53638e6	+	1.93976e6i	−1.43697	+	1.81426i
$259$	−980682.			−0.908403
$260$	−620701.	+	778334.i	−0.569441	+	0.714057i
$261$	834679.	−	125808.i	0.758434	−	0.114316i
$262$	76831.8	+	336622.i	0.0691493	+	0.302963i
$263$	−680241.	+	463780.i	−0.606420	+	0.413450i	−0.827227	−	0.561867i	$-0.810083\pi$
$263$	−680241.	+	463780.i	−0.606420	+	0.413450i	0.220807	+	0.975317i	$0.429131\pi$
$264$	−1737.57	+	3009.56i	−0.00153438	+	0.00265762i
$265$	219886.	+	380854.i	0.192346	+	0.333153i
$266$	1.97783e6	+	952475.i	1.71390	+	0.825372i
$267$	−3.20069e6	+	987283.i	−2.74768	+	0.847547i
$268$	121537.	−	1.62179e6i	0.103364	−	1.37930i
$269$	−141800.	+	621264.i	−0.119480	+	0.523475i	0.879397	+	0.476089i	$0.157946\pi$
$269$	−141800.	+	621264.i	−0.119480	+	0.523475i	−0.998877	+	0.0473855i	$0.984911\pi$
$270$	196190.	+	499884.i	0.163783	+	0.417311i
$271$	−33631.9	−	448786.i	−0.0278181	−	0.371207i	−0.993688	−	0.112179i	$-0.964217\pi$
$271$	−33631.9	−	448786.i	−0.0278181	−	0.371207i	0.965870	−	0.259028i	$-0.0834022\pi$
$272$	623343.	+	93953.9i	0.510864	+	0.0770003i
$273$	1.42581e6	−	1.32296e6i	1.15786	−	1.07434i
$274$	3.03946e6	−	1.46373e6i	2.44580	−	1.17783i
$275$	3747.82	+	2555.22i	0.00298845	+	0.00203749i
$276$	69939.0	−	178202.i	0.0552646	−	0.140812i
$277$	−83482.0	−	25750.8i	−0.0653722	−	0.0201647i	0.261897	−	0.965096i	$-0.415652\pi$
$277$	−83482.0	−	25750.8i	−0.0653722	−	0.0201647i	−0.327269	+	0.944931i	$0.606128\pi$
$278$	2.14301e6	+	1.98842e6i	1.66308	+	1.54311i
$279$	1.26745e6	+	1.58934e6i	0.974813	+	1.22238i
$280$	−129277.	−	162108.i	−0.0985431	−	0.123569i
$281$	−1.15843e6	−	1.07487e6i	−0.875194	−	0.812061i	0.108090	−	0.994141i	$-0.465527\pi$
$281$	−1.15843e6	−	1.07487e6i	−0.875194	−	0.812061i	−0.983284	+	0.182080i	$0.941717\pi$
$282$	−3.08920e6	−	952893.i	−2.31326	−	0.713545i
$283$	−571026.	+	1.45495e6i	−0.423828	+	1.07990i	0.546361	+	0.837550i	$0.316013\pi$
$283$	−571026.	+	1.45495e6i	−0.423828	+	1.07990i	−0.970190	+	0.242347i	$0.922083\pi$
$284$	1.45251e6	+	990307.i	1.06862	+	0.728575i
$285$	1.69069e6	−	814194.i	1.23297	−	0.593766i
$286$	10466.4	−	9711.37i	0.00756626	−	0.00702046i
$287$	408384.	+	61553.9i	0.292660	+	0.0441114i
$288$	−201143.	−	2.68406e6i	−0.142897	−	1.90683i
$289$	−206990.	−	527403.i	−0.145783	−	0.371448i
$290$	−142490.	+	624292.i	−0.0994926	+	0.435906i
$291$	−90396.9	+	1.20626e6i	−0.0625779	+	0.835045i
$292$	−1.48235e6	+	457244.i	−1.01740	+	0.313827i
$293$	136988.	+	65969.9i	0.0932209	+	0.0448928i	0.479913	−	0.877316i	$-0.340668\pi$
$293$	136988.	+	65969.9i	0.0932209	+	0.0448928i	−0.386692	+	0.922209i	$0.626382\pi$
$294$	−745005.	−	1.29039e6i	−0.502679	−	0.870665i
$295$	654311.	−	1.13330e6i	0.437753	−	0.758210i
$296$	−597379.	+	407286.i	−0.396297	+	0.270191i
$297$	−956.788	−	4191.96i	−0.000629397	−	0.00275757i
$298$	1.52641e6	−	230070.i	0.995706	−	0.150079i
$299$	−102397.	+	128401.i	−0.0662381	+	0.0830600i
$300$	2.18177e6			1.39961
$301$	435549.	+	1.09899e6i	0.277090	+	0.699162i
$302$	−3.20214e6			−2.02034
$303$	2.99063e6	−	3.75013e6i	1.87136	−	2.34661i
$304$	−1.78506e6	+	269054.i	−1.10782	+	0.166977i
$305$	234665.	+	1.02813e6i	0.144444	+	0.632849i
$306$	2.15634e6	−	1.47017e6i	1.31648	−	0.897559i
$307$	816165.	−	1.41364e6i	0.494233	−	0.856037i	−0.505745	−	0.862683i	$-0.668782\pi$
$307$	816165.	−	1.41364e6i	0.494233	−	0.856037i	0.999978	+	0.00664628i	$0.00211559\pi$
$308$	3975.41	+	6885.62i	0.00238784	+	0.00413586i
$309$	−1.07408e6	−	517252.i	−0.639945	−	0.308181i
$310$	−1.47361e6	+	454550.i	−0.870923	+	0.268644i
$311$	−141327.	+	1.88588e6i	−0.0828561	+	1.10564i	0.788516	+	0.615015i	$0.210850\pi$
$311$	−141327.	+	1.88588e6i	−0.0828561	+	1.10564i	−0.871372	+	0.490623i	$0.836769\pi$
$312$	319091.	−	1.39803e6i	0.185579	−	0.813074i
$313$	−863011.	−	2.19892e6i	−0.497915	−	1.26867i	−0.930241	−	0.366950i	$-0.880402\pi$
$313$	−863011.	−	2.19892e6i	−0.497915	−	1.26867i	0.432325	−	0.901718i	$-0.357693\pi$
$314$	−82097.7	−	1.09552e6i	−0.0469901	−	0.627040i
$315$	946789.	+	142706.i	0.537622	+	0.0810335i
$316$	858070.	−	796173.i	0.483398	−	0.448528i
$317$	−1.11284e6	+	535918.i	−0.621994	+	0.299537i	−0.718213	−	0.695824i	$-0.755040\pi$
$317$	−1.11284e6	+	535918.i	−0.621994	+	0.299537i	0.0962186	+	0.995360i	$0.469325\pi$
$318$	−2.50656e6	−	1.70894e6i	−1.38999	−	0.947676i
$319$	1873.18	−	4772.79i	0.00103063	−	0.00262600i
$320$	1.33378e6	+	411418.i	0.728133	+	0.224599i
$321$	−920243.	−	853860.i	−0.498471	−	0.462513i
$322$	−102136.	−	128075.i	−0.0548959	−	0.0688372i
$323$	−1.52353e6	−	1.91044e6i	−0.812539	−	1.01889i
$324$	875422.	+	812273.i	0.463292	+	0.429872i
$325$	−1.78858e6	−	551704.i	−0.939291	−	0.289733i
$326$	1.47771e6	−	3.76514e6i	0.770095	−	1.96217i
$327$	1.16667e6	+	795419.i	0.603360	+	0.411364i
$328$	274330.	−	132110.i	0.140795	−	0.0678034i
$329$	−1.13215e6	+	1.05048e6i	−0.576653	+	0.535055i
$330$	12037.9	+	1814.42i	0.00608508	+	0.000917178i
$331$	120749.	+	1.61129e6i	0.0605780	+	0.808357i	0.941911	+	0.335862i	$0.109028\pi$
$331$	120749.	+	1.61129e6i	0.0605780	+	0.808357i	−0.881333	+	0.472495i	$0.843353\pi$
$332$	962109.	+	2.45141e6i	0.479048	+	1.22059i
$333$	742941.	−	3.25504e6i	0.367150	−	1.60859i
$334$	−386583.	+	5.15859e6i	−0.189617	+	2.53026i
$335$	−1.13679e6	+	350652.i	−0.553435	+	0.170712i
$336$	−1.43741e6	−	692220.i	−0.694596	−	0.334500i
$337$	562058.	+	973513.i	0.269592	+	0.466946i	0.968756	−	0.248014i	$-0.0797780\pi$
$337$	562058.	+	973513.i	0.269592	+	0.466946i	−0.699165	+	0.714961i	$0.746445\pi$
$338$	−1.36568e6	+	2.36542e6i	−0.650213	+	1.12620i
$339$	3.33554e6	−	2.27413e6i	1.57640	−	1.07477i
$340$	245956.	+	1.07760e6i	0.115388	+	0.505548i
$341$	12209.8	−	1840.33i	0.00568620	−	0.000857057i
$342$	−4.65978e6	+	5.84318e6i	−2.15427	+	2.70137i
$343$	−2.35050e6			−1.07876
$344$	721735.	+	488559.i	0.328838	+	0.222598i
$345$	−140031.			−0.0633397
$346$	56353.2	−	70664.7i	0.0253063	−	0.0317331i
$347$	−2.97679e6	+	448679.i	−1.32716	+	0.200038i	−0.774080	−	0.633087i	$-0.781787\pi$
$347$	−2.97679e6	+	448679.i	−1.32716	+	0.200038i	−0.553084	+	0.833125i	$0.686549\pi$
$348$	−548768.	−	2.40431e6i	−0.242907	−	1.06425i
$349$	−779005.	+	531117.i	−0.342355	+	0.233414i	−0.722276	−	0.691605i	$-0.756904\pi$
$349$	−779005.	+	531117.i	−0.342355	+	0.233414i	0.379920	+	0.925019i	$0.375951\pi$
$350$	933487.	−	1.61685e6i	0.407322	−	0.705503i
$351$	887129.	+	1.53655e6i	0.384343	+	0.665702i
$352$	−14730.0	−	7093.60i	−0.00633645	−	0.00305147i
$353$	2.09986e6	−	647722.i	0.896921	−	0.276663i	0.188182	−	0.982134i	$-0.439741\pi$
$353$	2.09986e6	−	647722.i	0.896921	−	0.276663i	0.708739	+	0.705471i	$0.249264\pi$
$354$	−674613.	+	9.00208e6i	−0.286119	+	3.81799i
$355$	286147.	−	1.25369e6i	0.120509	−	0.527982i
$356$	2.06412e6	+	5.25930e6i	0.863199	+	2.19939i
$357$	−161383.	−	2.15350e6i	−0.0670172	−	0.894283i
$358$	−2.55390e6	−	384939.i	−1.05316	−	0.158739i
$359$	1.43987e6	−	1.33601e6i	0.589641	−	0.547107i	−0.327918	−	0.944706i	$-0.606347\pi$
$359$	1.43987e6	−	1.33601e6i	0.589641	−	0.547107i	0.917559	+	0.397599i	$0.130157\pi$
$360$	636001.	−	306282.i	0.258643	−	0.124556i
$361$	3.73579e6	+	2.54702e6i	1.50874	+	1.02864i
$362$	1.45718e6	−	3.71283e6i	0.584442	−	1.48913i
$363$	3.69001e6	+	1.13822e6i	1.46981	+	0.453376i
$364$	−2.40502e6	−	2.23153e6i	−0.951406	−	0.882775i
$365$	707487.	+	887161.i	0.277963	+	0.348554i
$366$	−4.53578e6	−	5.68768e6i	−1.76990	−	2.21938i
$367$	3.31354e6	+	3.07451e6i	1.28418	+	1.19155i	0.970251	+	0.242102i	$0.0778369\pi$
$367$	3.31354e6	+	3.07451e6i	1.28418	+	1.19155i	0.313932	+	0.949445i	$0.398354\pi$
$368$	128725.	+	39706.4i	0.0495500	+	0.0152842i
$369$	−513689.	+	1.30886e6i	−0.196397	+	0.500411i
$370$	2.09270e6	+	1.42678e6i	0.794699	+	0.541817i
$371$	−1.30578e6	+	628829.i	−0.492532	+	0.237191i
$372$	4.35369e6	−	4.03963e6i	1.63117	−	1.51351i
$373$	2.57348e6	+	387890.i	0.957742	+	0.144356i	0.609270	−	0.792963i	$-0.291462\pi$
$373$	2.57348e6	+	387890.i	0.957742	+	0.144356i	0.348472	+	0.937319i	$0.386701\pi$
$374$	−1184.65	−	15808.1i	−0.000437937	−	0.00584387i
$375$	−1.39295e6	−	3.54919e6i	−0.511515	−	1.30332i
$376$	−253371.	+	1.11009e6i	−0.0924245	+	0.404938i
$377$	−158106.	+	2.10978e6i	−0.0572922	+	0.764511i
$378$	−1.69112e6	+	521641.i	−0.608758	+	0.187777i
$379$	1.07266e6	+	516568.i	0.383589	+	0.184727i	0.615733	−	0.787955i	$-0.288860\pi$
$379$	1.07266e6	+	516568.i	0.383589	+	0.184727i	−0.232144	+	0.972681i	$0.574574\pi$
$380$	−1.58264e6	−	2.74121e6i	−0.562241	−	0.973830i
$381$	1.83439e6	−	3.17726e6i	0.647411	−	1.12135i
$382$	−975993.	+	665421.i	−0.342207	+	0.233312i
$383$	−567764.	−	2.48754e6i	−0.197775	−	0.866509i	−0.972257	−	0.233913i	$-0.924847\pi$
$383$	−567764.	−	2.48754e6i	−0.197775	−	0.866509i	0.774483	−	0.632595i	$-0.218010\pi$
$384$	−3.36890e6	+	507779.i	−1.16589	+	0.175730i
$385$	3626.14	−	4547.04i	0.00124679	−	0.00156342i
$386$	6.10297e6			2.08484
$387$	−3.97769e6	+	613087.i	−1.35006	+	0.208087i
$388$	2.04040e6			0.688075
$389$	472652.	−	592686.i	0.158368	−	0.198587i	−0.696317	−	0.717735i	$-0.745179\pi$
$389$	472652.	−	592686.i	0.158368	−	0.198587i	0.854685	+	0.519148i	$0.173751\pi$
$390$	−4.96733e6	+	748704.i	−1.65372	+	0.249258i
$391$	40575.3	+	177772.i	0.0134221	+	0.0588059i
$392$	−433608.	+	295629.i	−0.142522	+	0.0971700i
$393$	−486346.	+	842377.i	−0.158842	+	0.275122i
$394$	1.18357e6	+	2.04999e6i	0.384106	+	0.665292i
$395$	−771438.	−	371505.i	−0.248776	−	0.119804i
$396$	−25866.2	+	7978.65i	−0.00828884	+	0.00255677i
$397$	80205.4	−	1.07027e6i	0.0255404	−	0.340813i	−0.969766	−	0.244037i	$-0.921528\pi$
$397$	80205.4	−	1.07027e6i	0.0255404	−	0.340813i	0.995306	−	0.0967754i	$-0.0308529\pi$
$398$	71304.7	−	312406.i	0.0225637	−	0.0988581i
$399$	2.25935e6	+	5.75674e6i	0.710481	+	1.81028i
$400$	114732.	+	1.53099e6i	0.0358536	+	0.478434i
$401$	−2.51134e6	−	378523.i	−0.779909	−	0.117552i	−0.252991	−	0.967469i	$-0.581414\pi$
$401$	−2.51134e6	−	378523.i	−0.779909	−	0.117552i	−0.526918	+	0.849916i	$0.676652\pi$
$402$	6.01582e6	−	5.58186e6i	1.85665	−	1.72272i
$403$	−4.59059e6	+	2.21071e6i	−1.40801	+	0.678062i
$404$	−6.68492e6	−	4.55770e6i	−2.03771	−	1.38929i
$405$	319142.	−	813161.i	0.0966823	−	0.246342i
$406$	−2.01656e6	−	622025.i	−0.607149	−	0.187281i
$407$	−14866.3	−	13793.9i	−0.00444853	−	0.00412763i
$408$	−992675.	−	1.24478e6i	−0.295228	−	0.370204i
$409$	−3.33961e6	−	4.18773e6i	−0.987159	−	1.23786i	−0.971269	−	0.237984i	$-0.923513\pi$
$409$	−3.33961e6	−	4.18773e6i	−0.987159	−	1.23786i	−0.0158900	−	0.999874i	$-0.505058\pi$
$410$	−781906.	−	725503.i	−0.229718	−	0.213147i
$411$	9.08148e6	+	2.80127e6i	2.65187	+	0.817993i
$412$	−734656.	+	1.87187e6i	−0.213227	+	0.543292i
$413$	3.56329e6	+	2.42941e6i	1.02796	+	0.700851i
$414$	502476.	−	241980.i	0.144084	−	0.0693870i
$415$	1.41209e6	−	1.31023e6i	0.402479	−	0.373446i
$416$	6.67094e6	+	1.00548e6i	1.88996	+	0.284866i
$417$	615447.	+	8.21258e6i	0.173321	+	2.31281i
$418$	16585.1	+	42258.2i	0.00464278	+	0.0118296i
$419$	−21486.6	+	94139.1i	−0.00597907	+	0.0261960i	−0.977829	−	0.209403i	$-0.932848\pi$
$419$	−21486.6	+	94139.1i	−0.00597907	+	0.0261960i	0.971850	+	0.235599i	$0.0757051\pi$
$420$	209049.	−	2.78956e6i	0.0578261	−	0.771636i
$421$	−761748.	+	234968.i	−0.209462	+	0.0646106i	−0.397711	−	0.917511i	$-0.630195\pi$
$421$	−761748.	+	234968.i	−0.209462	+	0.0646106i	0.188248	+	0.982121i	$0.439719\pi$
$422$	3.97061e6	+	1.91214e6i	1.08536	+	0.522684i
$423$	−2.62903e6	−	4.55361e6i	−0.714404	−	1.23738i
$424$	−534251.	+	925351.i	−0.144321	+	0.249972i
$425$	−1.71706e6	+	1.17067e6i	−0.461118	+	0.314385i
$426$	1.97394e6	+	8.64839e6i	0.526999	+	2.30893i
$427$	−3.43661e6	+	517986.i	−0.912139	+	0.137483i
$428$	−1.32024e6	+	1.65553e6i	−0.348373	+	0.436846i
$429$	40222.3			0.0105517
$430$	669477.	−	2.97884e6i	0.174608	−	0.776919i
$431$	−6.93152e6			−1.79736			−0.898680	−	0.438604i	$-0.855473\pi$
$431$	−6.93152e6			−1.79736			−0.898680	+	0.438604i	$0.855473\pi$
$432$	907380.	−	1.13782e6i	0.233927	−	0.293335i
$433$	−1.85718e6	+	279925.i	−0.476031	+	0.0717501i	−0.382676	−	0.923883i	$-0.624997\pi$
$433$	−1.85718e6	+	279925.i	−0.476031	+	0.0717501i	−0.0933552	+	0.995633i	$0.529759\pi$
$434$	−1.13090e6	−	4.95478e6i	−0.288203	−	1.26270i
$435$	−1.49048e6	+	1.01619e6i	−0.377662	+	0.257486i
$436$	1.19088e6	−	2.06266e6i	0.300021	−	0.519651i
$437$	−261087.	−	452216.i	−0.0654006	−	0.113277i
$438$	−7.05251e6	−	3.39631e6i	−1.75654	−	0.845906i
$439$	714307.	−	220335.i	0.176898	−	0.0545659i	−0.205041	−	0.978753i	$-0.565733\pi$
$439$	714307.	−	220335.i	0.176898	−	0.0545659i	0.381939	+	0.924188i	$0.375256\pi$
$440$	320.426	−	4275.78i	7.89034e−5	−	0.00105289i
$441$	539265.	−	2.36267e6i	0.132040	−	0.578505i
$442$	2.38982e6	+	6.08917e6i	0.581849	+	1.48253i
$443$	−197880.	−	2.64053e6i	−0.0479063	−	0.639266i	−0.968543	−	0.248846i	$-0.919949\pi$
$443$	−197880.	−	2.64053e6i	−0.0479063	−	0.639266i	0.920637	−	0.390420i	$-0.127670\pi$
$444$	−9.64553e6	−	1.45383e6i	−2.32203	−	0.349990i
$445$	3.02953e6	−	2.81099e6i	0.725229	−	0.672914i
$446$	7.85695e6	−	3.78371e6i	1.87032	−	0.900700i
$447$	3.59303e6	+	2.44969e6i	0.850536	+	0.579885i
$448$	−1.68055e6	+	4.28198e6i	−0.395601	+	1.00797i
$449$	−2.16890e6	−	669017.i	−0.507719	−	0.156611i	0.0303040	−	0.999541i	$-0.490352\pi$
$449$	−2.16890e6	−	669017.i	−0.507719	−	0.156611i	−0.538023	+	0.842930i	$0.680829\pi$
$450$	4.65938e6	+	4.32328e6i	1.08467	+	1.00643i
$451$	5324.95	+	6677.28i	0.00123275	+	0.00154582i
$452$	−4.24568e6	−	5.32391e6i	−0.977464	−	1.22570i
$453$	−6.61274e6	−	6.13572e6i	−1.51403	−	1.40482i
$454$	−6.13871e6	−	1.89354e6i	−1.39778	−	0.431157i
$455$	−876770.	+	2.23397e6i	−0.198544	+	0.505883i
$456$	3.76711e6	+	2.56837e6i	0.848391	+	0.578423i
$457$	−5.46059e6	+	2.62968e6i	−1.22306	+	0.588997i	−0.930163	−	0.367146i	$-0.880335\pi$
$457$	−5.46059e6	+	2.62968e6i	−1.22306	+	0.588997i	−0.292901	+	0.956143i	$0.594621\pi$
$458$	2.82464e6	−	2.62089e6i	0.629217	−	0.583828i
$459$	1.94793e6	+	293603.i	0.431560	+	0.0650472i
$460$	17651.3	+	235540.i	0.00388939	+	0.0519004i
$461$	1.90737e6	+	4.85990e6i	0.418006	+	1.06506i	0.972506	+	0.232879i	$0.0748146\pi$
$461$	1.90737e6	+	4.85990e6i	0.418006	+	1.06506i	−0.554499	+	0.832184i	$0.687090\pi$
$462$	−8927.53	+	39114.1i	−0.00194593	+	0.00852566i
$463$	−283012.	+	3.77653e6i	−0.0613554	+	0.818730i	0.878627	+	0.477508i	$0.158460\pi$
$463$	−283012.	+	3.77653e6i	−0.0613554	+	0.818730i	−0.939983	+	0.341222i	$0.889159\pi$
$464$	1.65829e6	−	511514.i	0.357573	−	0.110297i
$465$	−3.91413e6	−	1.88495e6i	−0.839466	−	0.404266i
$466$	−3.92880e6	−	6.80487e6i	−0.838098	−	1.45163i
$467$	1.44622e6	−	2.50493e6i	0.306861	−	0.531499i	−0.670813	−	0.741627i	$-0.734055\pi$
$467$	1.44622e6	−	2.50493e6i	0.306861	−	0.531499i	0.977674	+	0.210127i	$0.0673879\pi$
$468$	9.22881e6	−	6.29210e6i	1.94774	−	1.32795i
$469$	−872404.	−	3.82225e6i	−0.183141	−	0.802393i
$470$	3.94425e6	−	594500.i	0.823607	−	0.124139i
$471$	1.92961e6	−	2.41966e6i	0.400791	−	0.502576i
$472$	3.17952e6			0.656912
$473$	−8855.45	+	22786.0i	−0.00181994	+	0.00468291i
$474$	5.90658e6			1.20751
$475$	3.71050e6	−	4.65282e6i	0.754568	−	0.946199i
$476$	−3.60197e6	+	542910.i	−0.728657	+	0.109827i
$477$	−1.09796e6	−	4.81047e6i	−0.220948	−	0.968036i
$478$	1.41411e6	−	964125.i	0.283083	−	0.193003i
$479$	1.39625e6	−	2.41838e6i	0.278051	−	0.481599i	−0.692849	−	0.721083i	$-0.743645\pi$
$479$	1.39625e6	−	2.41838e6i	0.278051	−	0.481599i	0.970900	+	0.239484i	$0.0769782\pi$
$480$	2.87609e6	+	4.98153e6i	0.569770	+	0.986870i
$481$	7.53962e6	+	3.63089e6i	1.48589	+	0.715567i
$482$	1.21045e6	−	373374.i	0.237317	−	0.0732027i
$483$	34486.7	−	460193.i	0.00672641	−	0.0897577i
$484$	1.44941e6	−	6.35028e6i	0.281240	−	1.23219i
$485$	−545276.	−	1.38934e6i	−0.105260	−	0.268197i
$486$	779942.	+	1.04076e7i	0.149786	+	1.99876i
$487$	−1.94688e6	−	293445.i	−0.371977	−	0.0560665i	−0.0396064	−	0.999215i	$-0.512610\pi$
$487$	−1.94688e6	−	293445.i	−0.371977	−	0.0560665i	−0.332371	+	0.943149i	$0.607849\pi$
$488$	−1.87828e6	+	1.74279e6i	−0.357035	+	0.331280i
$489$	1.02661e7	−	4.94390e6i	1.94148	−	0.934969i
$490$	1.51899e6	+	1.03563e6i	0.285801	+	0.194856i
$491$	−1.24473e6	+	3.17151e6i	−0.233008	+	0.593694i	−0.998778	−	0.0494202i	$-0.984263\pi$
$491$	−1.24473e6	+	3.17151e6i	−0.233008	+	0.593694i	0.765770	+	0.643114i	$0.222358\pi$
$492$	3.92542e6	+	1.21083e6i	0.731095	+	0.225513i
$493$	1.72196e6	+	1.59774e6i	0.319084	+	0.296067i
$494$	−1.16794e7	−	1.46455e7i	−2.15330	−	2.70015i
$495$	12345.3	+	15480.5i	0.00226458	+	0.00283969i
$496$	3.06363e6	+	2.84263e6i	0.559155	+	0.518820i
$497$	4.04961e6	+	1.24914e6i	0.735398	+	0.226840i
$498$	−4.85481e6	+	1.23699e7i	−0.877201	+	2.23507i
$499$	2.54518e6	+	1.73527e6i	0.457580	+	0.311973i	0.770083	−	0.637944i	$-0.220215\pi$
$499$	2.54518e6	+	1.73527e6i	0.457580	+	0.311973i	−0.312503	+	0.949917i	$0.601167\pi$
$500$	−5.79436e6	+	2.79041e6i	−1.03653	+	0.499164i
$501$	−1.06829e7	+	9.91225e6i	−1.90149	+	1.76432i
$502$	6.30364e6	+	950120.i	1.11643	+	0.168275i
$503$	−256305.	−	3.42015e6i	−0.0451686	−	0.602734i	−0.973160	−	0.230131i	$-0.926085\pi$
$503$	−256305.	−	3.42015e6i	−0.0451686	−	0.602734i	0.927991	−	0.372603i	$-0.121535\pi$
$504$	849920.	+	2.16556e6i	0.149040	+	0.379747i
$505$	−1.31694e6	+	5.76987e6i	−0.229793	+	1.00679i
$506$	253.154	−	3378.11i	4.39551e−5	−	0.000586539i
$507$	−7.35270e6	+	2.26801e6i	−1.27036	+	0.391854i
$508$	−5.57557e6	−	2.68505e6i	−0.958584	−	0.461630i
$509$	4.90295e6	+	8.49216e6i	0.838809	+	1.45286i	0.890891	+	0.454217i	$0.150081\pi$
$509$	4.90295e6	+	8.49216e6i	0.838809	+	1.45286i	−0.0520824	+	0.998643i	$0.516586\pi$
$510$	−2.78872e6	+	4.83020e6i	−0.474766	+	0.822319i
$511$	−3.08977e6	+	2.10657e6i	−0.523449	+	0.356881i
$512$	−1.58064e6	−	6.92524e6i	−0.266476	−	1.16751i
$513$	−5.57824e6	+	840785.i	−0.935845	+	0.141056i
$514$	−1.68701e6	+	2.11544e6i	−0.281650	+	0.353178i
$515$	1.47092e6			0.244383
$516$	2.65464e6	+	1.14549e7i	0.438916	+	1.89394i
$517$	−31938.1			−0.00525512
$518$	−5.20430e6	+	6.52599e6i	−0.852193	+	1.06862i
$519$	251777.	−	37949.4i	0.0410297	−	0.00618423i
$520$	393708.	+	1.72495e6i	0.0638508	+	0.279749i
$521$	−6.31450e6	+	4.30515e6i	−1.01917	+	0.694855i	−0.953005	−	0.302954i	$-0.902027\pi$
$521$	−6.31450e6	+	4.30515e6i	−1.01917	+	0.694855i	−0.0661603	+	0.997809i	$0.521075\pi$
$522$	3.59230e6	−	6.22204e6i	0.577027	−	0.999440i
$523$	−3.98053e6	−	6.89447e6i	−0.636336	−	1.10217i	−0.986230	−	0.165377i	$-0.947116\pi$
$523$	−3.98053e6	−	6.89447e6i	−0.636336	−	1.10217i	0.349895	−	0.936789i	$-0.386217\pi$
$524$	1.47823e6	+	711879.i	0.235187	+	0.113260i
$525$	5.02583e6	−	1.55026e6i	0.795810	−	0.245475i
$526$	−523670.	+	6.98789e6i	−0.0825265	+	1.10124i
$527$	−1.25882e6	+	5.51525e6i	−0.197441	+	0.865044i
$528$	−12053.4	−	30711.5i	−0.00188158	−	0.00479420i
$529$	−478077.	−	6.37949e6i	−0.0742777	−	0.991167i
$530$	3.70130e6	+	557882.i	0.572354	+	0.0862685i
$531$	−1.07631e7	+	9.98667e6i	−1.65653	+	1.53704i
$532$	9.39837e6	−	4.52602e6i	1.43971	−	0.693326i
$533$	−2.91181e6	−	1.98524e6i	−0.443962	−	0.302688i
$534$	−1.04156e7	+	2.65385e7i	−1.58063	+	4.02738i
$535$	1.48010e6	+	456551.i	0.223567	+	0.0689612i
$536$	−2.11884e6	−	1.96599e6i	−0.318556	−	0.295577i
$537$	−4.53646e6	−	5.68854e6i	−0.678862	−	0.851266i
$538$	3.38172e6	+	4.24055e6i	0.503712	+	0.631635i
$539$	−10790.7	−	10012.3i	−0.00159985	−	0.00148444i
$540$	2.43840e6	+	752147.i	0.359849	+	0.110999i
$541$	3.36507e6	−	8.57407e6i	0.494312	−	1.25949i	−0.438372	−	0.898793i	$-0.644445\pi$
$541$	3.36507e6	−	8.57407e6i	0.494312	−	1.25949i	0.932684	−	0.360693i	$-0.117460\pi$
$542$	−3.16495e6	−	2.15782e6i	−0.462773	−	0.315513i
$543$	1.01235e7	−	4.87521e6i	1.47343	−	0.709568i
$544$	5.49078e6	−	5.09470e6i	0.795493	−	0.738110i
$545$	−1.72275e6	−	259663.i	−0.248446	−	0.0374471i
$546$	−1.23717e6	−	1.65088e7i	−0.177601	−	2.36993i
$547$	−700833.	−	1.78569e6i	−0.100149	−	0.255175i	0.872014	−	0.489481i	$-0.162814\pi$
$547$	−700833.	−	1.78569e6i	−0.100149	−	0.255175i	−0.972163	+	0.234305i	$0.924718\pi$
$548$	3.56714e6	−	1.56287e7i	0.507422	−	2.22316i
$549$	884219.	−	1.17991e7i	0.125207	−	1.67077i
$550$	36892.8	−	11379.9i	0.00520038	−	0.00160410i
$551$	−6.06068e6	−	2.91867e6i	−0.850438	−	0.409549i
$552$	−170115.	−	294647.i	−0.0237626	−	0.0411581i
$553$	1.41089e6	−	2.44373e6i	0.196191	−	0.339813i
$554$	−614384.	+	418880.i	−0.0850482	+	0.0579849i
$555$	1.58774e6	+	6.95632e6i	0.218799	+	0.958622i
$556$	1.37364e7	−	2.07044e6i	1.88446	−	0.284037i
$557$	−487722.	+	611584.i	−0.0666092	+	0.0835253i	−0.814020	−	0.580837i	$-0.802725\pi$
$557$	−487722.	+	611584.i	−0.0666092	+	0.0835253i	0.747411	+	0.664362i	$0.231297\pi$
$558$	1.73024e7			2.35246
$559$	720357.	−	1.00618e7i	0.0975031	−	1.36190i
$560$	1.96848e6			0.265253
$561$	27843.9	−	34915.2i	0.00373528	−	0.00468390i
$562$	−1.33003e7	+	2.00470e6i	−1.77632	+	0.267737i
$563$	1.72378e6	+	7.55236e6i	0.229198	+	1.00418i	0.950296	+	0.311348i	$0.100780\pi$
$563$	1.72378e6	+	7.55236e6i	0.229198	+	1.00418i	−0.721098	+	0.692833i	$0.756362\pi$
$564$	−1.26926e7	+	8.65368e6i	−1.68017	+	1.14552i
$565$	−2.49052e6	+	4.31371e6i	−0.328223	+	0.568500i
$566$	6.65170e6	+	1.15211e7i	0.872754	+	1.51165i
$567$	2.59375e6	+	1.24908e6i	0.338821	+	0.163167i
$568$	2.98559e6	−	920931.i	0.388292	−	0.119772i
$569$	829477.	−	1.10686e7i	0.107405	−	1.43322i	−0.639758	−	0.768576i	$-0.720966\pi$
$569$	829477.	−	1.10686e7i	0.107405	−	1.43322i	0.747163	−	0.664641i	$-0.231415\pi$
$570$	3.55411e6	−	1.55716e7i	0.458187	−	2.00745i
$571$	−1.77155e6	−	4.51384e6i	−0.227386	−	0.579370i	0.770959	−	0.636885i	$-0.219778\pi$
$571$	−1.77155e6	−	4.51384e6i	−0.227386	−	0.579370i	−0.998345	+	0.0575150i	$0.981682\pi$
$572$	−5070.14	−	67656.3i	−0.000647932	−	0.00864606i
$573$	−3.29055e6	−	495971.i	−0.418680	−	0.0631059i
$574$	2.57683e6	−	2.39095e6i	0.326442	−	0.302894i
$575$	−400113.	+	192684.i	−0.0504677	+	0.0243039i
$576$	−1.29394e7	−	8.82195e6i	−1.62502	−	1.10792i
$577$	−5.08103e6	+	1.29463e7i	−0.635349	+	1.61884i	0.142067	+	0.989857i	$0.454625\pi$
$577$	−5.08103e6	+	1.29463e7i	−0.635349	+	1.61884i	−0.777416	+	0.628986i	$0.783470\pi$
$578$	−4.60808e6	−	1.42141e6i	−0.573721	−	0.176970i
$579$	1.26032e7	+	1.16941e7i	1.56238	+	1.44967i
$580$	1.89717e6	+	2.37898e6i	0.234173	+	0.293644i
$581$	3.95813e6	+	4.96334e6i	0.486463	+	0.610005i
$582$	7.54741e6	+	7.00297e6i	0.923614	+	0.856988i
$583$	−28639.3	−	8834.06i	−0.00348973	−	0.00107644i
$584$	−1.00725e6	+	2.56642e6i	−0.122209	+	0.311384i
$585$	−6.75070e6	−	4.60255e6i	−0.815566	−	0.556043i
$586$	1.16597e6	−	561502.i	0.140263	−	0.0675471i
$587$	5.99905e6	−	5.56631e6i	0.718600	−	0.666764i	−0.233567	−	0.972341i	$-0.575040\pi$
$587$	5.99905e6	−	5.56631e6i	0.718600	−	0.666764i	0.952167	+	0.305577i	$0.0988494\pi$
$588$	−7.00122e6	−	1.05526e6i	−0.835085	−	0.125869i
$589$	−1.21063e6	−	1.61548e7i	−0.143789	−	1.91872i
$590$	−4.06928e6	−	1.03684e7i	−0.481269	−	1.22625i
$591$	−1.48388e6	+	6.50130e6i	−0.174755	+	0.765653i
$592$	512954.	−	6.84489e6i	0.0601553	−	0.802717i
$593$	−8.43401e6	+	2.60155e6i	−0.984912	+	0.303805i	−0.745055	−	0.667003i	$-0.767577\pi$
$593$	−8.43401e6	+	2.60155e6i	−0.984912	+	0.303805i	−0.239857	+	0.970808i	$0.577101\pi$
$594$	−32973.1	−	15879.0i	−0.00383437	−	0.00184653i
$595$	1.33227e6	+	2.30756e6i	0.154276	+	0.267214i
$596$	3.66761e6	−	6.35248e6i	0.422929	−	0.732534i
$597$	745863.	−	508520.i	0.0856491	−	0.0583946i
$598$	311052.	+	1.36281e6i	0.0355696	+	0.155841i
$599$	3.27362e6	−	493419.i	0.372787	−	0.0561886i	0.0400232	−	0.999199i	$-0.487257\pi$
$599$	3.27362e6	−	493419.i	0.372787	−	0.0561886i	0.332764	+	0.943010i	$0.392019\pi$
$600$	2.41763e6	−	3.03161e6i	0.274165	−	0.343792i
$601$	8.55842e6			0.966513			0.483256	−	0.875479i	$-0.339454\pi$
$601$	8.55842e6			0.966513			0.483256	+	0.875479i	$0.339454\pi$
$602$	9.62467e6	+	2.93377e6i	1.08242	+	0.329940i
$603$	1.33476e7			1.49489
$604$	−9.48709e6	+	1.18964e7i	−1.05813	+	1.32686i
$605$	−4.71135e6	+	710122.i	−0.523307	+	0.0788759i
$606$	−9.08468e6	−	3.98026e7i	−1.00491	−	4.40281i
$607$	−1.17548e7	+	8.01426e6i	−1.29492	+	0.882859i	−0.997415	−	0.0718616i	$-0.977106\pi$
$607$	−1.17548e7	+	8.01426e6i	−1.29492	+	0.882859i	−0.297502	+	0.954721i	$0.596154\pi$
$608$	−1.07249e7	+	1.85761e7i	−1.17662	+	2.03796i
$609$	−2.97250e6	−	5.14853e6i	−0.324772	−	0.562522i
$610$	8.08708e6	+	3.89453e6i	0.879969	+	0.423771i
$611$	1.25935e7	−	3.88457e6i	1.36471	−	0.420959i
$612$	926765.	−	1.23668e7i	0.100021	−	1.33469i
$613$	−515600.	+	2.25899e6i	−0.0554193	+	0.242808i	−0.995049	−	0.0993849i	$-0.968312\pi$
$613$	−515600.	+	2.25899e6i	−0.0554193	+	0.242808i	0.939630	+	0.342193i	$0.111170\pi$
$614$	−5.07588e6	−	1.29331e7i	−0.543363	−	1.38447i
$615$	−224554.	−	2.99647e6i	−0.0239405	−	0.319464i
$616$	13972.9	+	2106.07i	0.00148366	+	0.000223625i
$617$	−2.07957e6	+	1.92956e6i	−0.219918	+	0.204054i	−0.782436	−	0.622731i	$-0.786023\pi$
$617$	−2.07957e6	+	1.92956e6i	−0.219918	+	0.204054i	0.562518	+	0.826785i	$0.309833\pi$
$618$	−9.14205e6	+	4.40258e6i	−0.962881	+	0.463699i
$619$	5.54588e6	+	3.78111e6i	0.581760	+	0.396637i	0.818136	−	0.575025i	$-0.195007\pi$
$619$	5.54588e6	+	3.78111e6i	0.581760	+	0.396637i	−0.236377	+	0.971662i	$0.575960\pi$
$620$	−2.67720e6	+	6.82140e6i	−0.279706	+	0.712680i
$621$	402262.	+	124081.i	0.0418581	+	0.0129115i
$622$	1.17997e7	+	1.09485e7i	1.22291	+	1.13469i
$623$	8.49183e6	+	1.06484e7i	0.876559	+	1.09917i
$624$	8.48812e6	+	1.06438e7i	0.872670	+	1.09429i
$625$	−1.70513e6	−	1.58213e6i	−0.174606	−	0.162010i
$626$	−1.92126e7	−	5.92631e6i	−1.95953	−	0.604434i
$627$	−46722.3	+	119046.i	−0.00474630	+	0.0120934i
$628$	−4.31324e6	−	2.94072e6i	−0.436420	−	0.297546i
$629$	8.37112e6	−	4.03132e6i	0.843640	−	0.406275i
$630$	5.97408e6	−	5.54314e6i	0.599680	−	0.556422i
$631$	2.62251e6	+	395280.i	0.262207	+	0.0395213i	0.278830	−	0.960341i	$-0.410053\pi$
$631$	2.62251e6	+	395280.i	0.262207	+	0.0395213i	−0.0166231	+	0.999862i	$0.505292\pi$
$632$	−155466.	−	2.07455e6i	−0.0154825	−	0.206600i
$633$	4.53577e6	+	1.15570e7i	0.449927	+	1.14640i
$634$	−2.33938e6	+	1.02495e7i	−0.231141	+	1.01270i
$635$	−338281.	+	4.51405e6i	−0.0332923	+	0.444255i
$636$	−1.37752e7	+	4.24910e6i	−1.35038	+	0.416537i
$637$	5.47264e6	+	2.63549e6i	0.534378	+	0.257343i
$638$	−21820.1	−	37793.5i	−0.00212229	−	0.00367591i
$639$	−7.21398e6	+	1.24950e7i	−0.698913	+	1.21055i
$640$	3.47321e6	−	2.36799e6i	0.335182	−	0.228523i
$641$	−1.18961e6	−	5.21203e6i	−0.114356	−	0.501028i	−0.999371	−	0.0354645i	$-0.988709\pi$
$641$	−1.18961e6	−	5.21203e6i	−0.114356	−	0.501028i	0.885015	−	0.465563i	$-0.154148\pi$
$642$	−1.05656e7	+	1.59251e6i	−1.01171	+	0.152491i
$643$	5.34623e6	−	6.70396e6i	0.509941	−	0.639446i	−0.458498	−	0.888695i	$-0.651612\pi$
$643$	5.34623e6	−	6.70396e6i	0.509941	−	0.639446i	0.968439	+	0.249249i	$0.0801839\pi$
$644$	−778418.			−0.0739602
$645$	7.09038e6	−	4.86879e6i	0.671073	−	0.460809i
$646$	−2.07982e7			−1.96085
$647$	−1.22154e7	+	1.53176e7i	−1.14722	+	1.43857i	−0.267195	+	0.963643i	$0.586097\pi$
$647$	−1.22154e7	+	1.53176e7i	−1.14722	+	1.43857i	−0.880026	+	0.474926i	$0.842475\pi$
$648$	2.09873e6	−	316332.i	0.196344	−	0.0295942i
$649$	19845.2	+	86947.7i	0.00184946	+	0.00810301i
$650$	−1.31630e7	+	8.97439e6i	−1.22200	+	0.833147i
$651$	7.15859e6	−	1.23990e7i	0.662026	−	1.14666i
$652$	−9.60999e6	−	1.66450e7i	−0.885327	−	1.53343i
$653$	6.26741e6	+	3.01823e6i	0.575182	+	0.276993i	0.698777	−	0.715340i	$-0.253728\pi$
$653$	6.26741e6	+	3.01823e6i	0.575182	+	0.276993i	−0.123595	+	0.992333i	$0.539442\pi$
$654$	1.14844e7	−	3.54248e6i	1.04994	−	0.323864i
$655$	89687.3	−	1.19679e6i	0.00816823	−	0.108997i
$656$	−643238.	+	2.81821e6i	−0.0583596	+	0.255690i
$657$	−4.65131e6	−	1.18513e7i	−0.420399	−	1.07116i
$658$	982358.	+	1.31087e7i	0.0884515	+	1.18030i
$659$	7.34368e6	+	1.10688e6i	0.658719	+	0.0992859i	0.469891	−	0.882724i	$-0.344293\pi$
$659$	7.34368e6	+	1.10688e6i	0.658719	+	0.0992859i	0.188828	+	0.982010i	$0.439531\pi$
$660$	42405.9	−	39346.9i	0.00378937	−	0.00351602i
$661$	−3.98516e6	+	1.91915e6i	−0.354766	+	0.170847i	−0.602775	−	0.797911i	$-0.705938\pi$
$661$	−3.98516e6	+	1.91915e6i	−0.354766	+	0.170847i	0.248008	+	0.968758i	$0.420224\pi$
$662$	1.13632e7	+	7.74729e6i	1.00776	+	0.687076i
$663$	−6.73243e6	+	1.71539e7i	−0.594823	+	1.51558i
$664$	4.47240e6	+	1.37955e6i	0.393659	+	0.121428i
$665$	−5.59346e6	−	5.18997e6i	−0.490486	−	0.455104i
$666$	−1.77181e7	−	2.22178e7i	−1.54786	−	1.94096i
$667$	312976.	+	392459.i	0.0272393	+	0.0341570i
$668$	1.80196e7	+	1.67197e7i	1.56244	+	1.44973i
$669$	2.34754e7	+	7.24121e6i	2.02791	+	0.625527i
$670$	−3.69929e6	+	9.42564e6i	−0.318369	+	0.811192i
$671$	−59381.9	−	40485.9i	−0.00509152	−	0.00347134i
$672$	−1.70795e7	+	8.22503e6i	−1.45898	+	0.702610i
$673$	2.21474e6	−	2.05498e6i	0.188489	−	0.174892i	−0.580284	−	0.814414i	$-0.697058\pi$
$673$	2.21474e6	−	2.05498e6i	0.188489	−	0.174892i	0.768772	+	0.639522i	$0.220868\pi$
$674$	9.46102e6	+	1.42602e6i	0.802211	+	0.120914i
$675$	358533.	+	4.78429e6i	0.0302879	+	0.404164i
$676$	4.74175e6	+	1.20818e7i	0.399091	+	1.01687i
$677$	4.07774e6	−	1.78657e7i	0.341938	−	1.49813i	−0.453040	−	0.891490i	$-0.649660\pi$
$677$	4.07774e6	−	1.78657e7i	0.341938	−	1.49813i	0.794978	−	0.606639i	$-0.207482\pi$
$678$	2.56780e6	−	3.42649e7i	0.214530	−	2.86270i
$679$	4.70017e6	−	1.44981e6i	0.391236	−	0.120680i
$680$	1.76990e6	+	852337.i	0.146783	+	0.0706869i
$681$	−9.04876e6	−	1.56729e7i	−0.747690	−	1.29504i
$682$	52548.6	−	91016.9i	0.00432614	−	0.00749309i
$683$	4.08718e6	−	2.78659e6i	0.335253	−	0.228571i	−0.383979	−	0.923342i	$-0.625446\pi$
$683$	4.08718e6	−	2.78659e6i	0.335253	−	0.228571i	0.719232	+	0.694770i	$0.244494\pi$
$684$	7.90259e6	+	3.46235e7i	0.645846	+	2.82964i
$685$	−1.15951e7	+	1.74768e6i	−0.944166	+	0.142310i
$686$	−1.24737e7	+	1.56415e7i	−1.01201	+	1.26902i
$687$	1.08551e7			0.877492
$688$	−7.89848e6	+	2.46518e6i	−0.636169	+	0.198553i
$689$	1.23672e7			0.992483
$690$	−743119.	+	931842.i	−0.0594204	+	0.0745108i
$691$	1.71727e7	−	2.58836e6i	1.36818	−	0.206220i	0.576469	−	0.817119i	$-0.304430\pi$
$691$	1.71727e7	−	2.58836e6i	1.36818	−	0.206220i	0.791708	+	0.610899i	$0.209192\pi$
$692$	−95570.3	−	418721.i	−0.00758678	−	0.0332399i
$693$	−53914.8	+	36758.5i	−0.00426457	+	0.00290753i
$694$	−1.28115e7	+	2.21902e7i	−1.00972	+	1.74889i
$695$	−5.08072e6	−	8.80007e6i	−0.398991	−	0.691073i
$696$	−3.94892e6	−	1.90170e6i	−0.308998	−	0.148806i
$697$	−3.73900e6	+	1.15333e6i	−0.291524	+	0.0899232i
$698$	−599702.	+	8.00246e6i	−0.0465904	+	0.621706i
$699$	4.92568e6	−	2.15808e7i	0.381306	−	1.67061i
$700$	−3.24115e6	−	8.25832e6i	−0.250008	−	0.637010i
$701$	−495719.	−	6.61492e6i	−0.0381014	−	0.508428i	−0.983307	−	0.181953i	$-0.941758\pi$
$701$	−495719.	−	6.61492e6i	−0.0381014	−	0.508428i	0.945206	−	0.326475i	$-0.105861\pi$
$702$	1.49329e7	+	2.25077e6i	1.14367	+	0.172381i
$703$	−1.95044e7	+	1.80975e7i	−1.48849	+	1.38111i
$704$	−85704.4	+	41273.1i	−0.00651736	+	0.00313859i
$705$	9.28440e6	+	6.33000e6i	0.703528	+	0.479657i
$706$	6.83330e6	−	1.74110e7i	0.515963	−	1.31465i
$707$	−1.86376e7	−	5.74893e6i	−1.40230	−	0.432552i
$708$	3.14454e7	+	2.91770e7i	2.35762	+	2.18755i
$709$	−1.43905e7	−	1.80452e7i	−1.07513	−	1.34817i	−0.933632	−	0.358234i	$-0.883379\pi$
$709$	−1.43905e7	−	1.80452e7i	−1.07513	−	1.34817i	−0.141499	−	0.989938i	$-0.545192\pi$
$710$	−6.82421e6	−	8.55728e6i	−0.508050	−	0.637074i
$711$	7.04228e6	+	6.53428e6i	0.522443	+	0.484756i
$712$	9.59516e6	+	2.95971e6i	0.709336	+	0.218801i
$713$	−441657.	+	1.12532e6i	−0.0325358	+	0.0828998i
$714$	−1.51870e7	−	1.03543e7i	−1.11488	−	0.760110i
$715$	−44713.3	+	21532.8i	−0.00327093	+	0.00157520i
$716$	−8.99662e6	+	8.34764e6i	−0.655838	+	0.608529i
$717$	4.76767e6	+	718611.i	0.346344	+	0.0522030i
$718$	−1.24937e6	−	1.66716e7i	−0.0904438	−	1.20689i
$719$	5.78041e6	+	1.47282e7i	0.417000	+	1.06250i	0.972895	+	0.231247i	$0.0742805\pi$
$719$	5.78041e6	+	1.47282e7i	0.417000	+	1.06250i	−0.555895	+	0.831253i	$0.687624\pi$
$720$	−1.49127e6	+	6.53369e6i	−0.107208	+	0.469707i
$721$	−362256.	+	4.83397e6i	−0.0259524	+	0.346311i
$722$	3.67744e7	−	1.13434e7i	2.62544	−	0.809842i
$723$	3.21513e6	+	1.54833e6i	0.228746	+	0.110158i
$724$	−9.47648e6	−	1.64137e7i	−0.671894	−	1.16375i
$725$	−2.86049e6	+	4.95451e6i	−0.202113	+	0.350070i
$726$	2.71565e7	−	1.85150e7i	1.91220	−	1.30371i
$727$	3.34159e6	+	1.46405e7i	0.234486	+	1.02735i	0.945869	+	0.324547i	$0.105212\pi$
$727$	3.34159e6	+	1.46405e7i	0.234486	+	1.02735i	−0.711383	+	0.702804i	$0.751931\pi$
$728$	−5.76577e6	+	869050.i	−0.403208	+	0.0607738i
$729$	−1.38581e7	+	1.73776e7i	−0.965798	+	1.21107i
$730$	9.65815e6			0.670791
$731$	−8.23552e6	−	7.59059e6i	−0.570030	−	0.525390i
$732$	−3.45688e7			−2.38455
$733$	859196.	−	1.07740e6i	0.0590653	−	0.0740655i	−0.751421	−	0.659823i	$-0.770631\pi$
$733$	859196.	−	1.07740e6i	0.0590653	−	0.0740655i	0.810487	+	0.585757i	$0.199203\pi$
$734$	3.80438e7	−	5.73419e6i	2.60642	−	0.392854i
$735$	1.15246e6	+	5.04925e6i	0.0786878	+	0.344754i
$736$	1.32251e6	−	901672.i	0.0899921	−	0.0613556i
$737$	40537.4	−	70212.9i	0.00274908	−	0.00476155i
$738$	5.98380e6	+	1.03642e7i	0.404423	+	0.700482i
$739$	−2.16926e7	−	1.04466e7i	−1.46117	−	0.703663i	−0.476677	−	0.879079i	$-0.658159\pi$
$739$	−2.16926e7	−	1.04466e7i	−1.46117	−	0.703663i	−0.984494	+	0.175415i	$0.943873\pi$
$740$	1.15008e7	−	3.54753e6i	0.772056	−	0.238148i
$741$	3.94360e6	−	5.26237e7i	0.263844	−	3.52076i
$742$	−2.74495e6	+	1.20264e7i	−0.183031	+	0.801913i
$743$	−6.80189e6	−	1.73309e7i	−0.452020	−	1.15173i	−0.957383	−	0.288822i	$-0.906737\pi$
$743$	−6.80189e6	−	1.73309e7i	−0.452020	−	1.15173i	0.505363	−	0.862907i	$-0.331359\pi$
$744$	−788805.	−	1.05259e7i	−0.0522441	−	0.697149i
$745$	−5.30564e6	−	799696.i	−0.350225	−	0.0527879i
$746$	1.62382e7	−	1.50669e7i	1.06830	−	0.991233i
$747$	−1.94727e7	+	9.37755e6i	−1.27680	+	0.614877i
$748$	−62239.2	−	42433.9i	−0.00406733	−	0.00277306i
$749$	−1.86491e6	+	4.75171e6i	−0.121466	+	0.309489i
$750$	−3.10104e7	−	9.56544e6i	−2.01305	−	0.620943i
$751$	−1.94046e7	−	1.80049e7i	−1.25547	−	1.16490i	−0.978996	−	0.203881i	$-0.934644\pi$
$751$	−1.94046e7	−	1.80049e7i	−1.25547	−	1.16490i	−0.276471	−	0.961022i	$-0.589165\pi$
$752$	−6.73990e6	−	8.45156e6i	−0.434619	−	0.544995i
$753$	1.11971e7	+	1.40407e7i	0.719643	+	0.902403i
$754$	1.32006e7	+	1.22484e7i	0.845600	+	0.784602i
$755$	1.06358e7	+	3.28071e6i	0.679052	+	0.209460i
$756$	−3.07235e6	+	7.82823e6i	−0.195509	+	0.498149i
$757$	2.29392e7	+	1.56397e7i	1.45492	+	0.991948i	0.994554	+	0.104219i	$0.0332342\pi$
$757$	2.29392e7	+	1.56397e7i	1.45492	+	0.991948i	0.460366	+	0.887729i	$0.347718\pi$
$758$	9.12996e6	−	4.39676e6i	0.577160	−	0.277945i
$759$	6995.68	−	6491.05i	0.000440784	−	0.000408988i
$760$	−5.56268e6	−	838440.i	−0.349342	−	0.0526548i
$761$	2.25366e6	+	3.00729e7i	0.141067	+	1.88241i	0.400000	+	0.916515i	$0.369010\pi$
$761$	2.25366e6	+	3.00729e7i	0.141067	+	1.88241i	−0.258933	+	0.965895i	$0.583371\pi$
$762$	−1.14084e7	−	2.90682e7i	−0.711769	−	1.81356i
$763$	1.27762e6	−	5.59764e6i	0.0794496	−	0.348091i
$764$	−419469.	+	5.59742e6i	−0.0259996	+	0.346940i
$765$	−8.66844e6	+	2.67386e6i	−0.535534	+	0.165190i
$766$	−1.95665e7	−	9.42271e6i	−1.20487	−	0.580235i
$767$	−1.84004e7	−	3.18704e7i	−1.12938	−	1.95614i
$768$	3.60106e6	−	6.23722e6i	0.220306	−	0.381582i
$769$	−2.15636e7	+	1.47018e7i	−1.31494	+	0.896509i	−0.998639	−	0.0521510i	$-0.983392\pi$
$769$	−2.15636e7	+	1.47018e7i	−1.31494	+	0.896509i	−0.316298	+	0.948660i	$0.602440\pi$
$770$	−11015.2	−	48260.6i	−0.000669521	−	0.00293337i
$771$	−7.53731e6	+	1.13607e6i	−0.456647	+	0.0688284i
$772$	1.80815e7	−	2.26734e7i	1.09192	−	1.36922i
$773$	2.61399e7			1.57346			0.786730	−	0.617297i	$-0.211772\pi$
$773$	2.61399e7			1.57346			0.786730	+	0.617297i	$0.211772\pi$
$774$	−1.70291e7	+	2.97233e7i	−1.02174	+	1.78338i
$775$	−1.37776e7			−0.823987
$776$	2.26097e6	−	2.83517e6i	0.134785	−	0.169015i
$777$	−2.32520e7	+	3.50468e6i	−1.38168	+	0.208255i
$778$	−1.43578e6	−	6.29056e6i	−0.0850430	−	0.372598i
$779$	9.25811e6	−	6.31207e6i	0.546611	−	0.372673i
$780$	−1.19353e7	+	2.06726e7i	−0.702420	+	1.21663i
$781$	43818.7	+	75896.2i	0.00257058	+	0.00445238i
$782$	1.39832e6	+	673394.i	0.0817690	+	0.0393779i
$783$	5.18210e6	−	1.59847e6i	0.302066	−	0.0931749i
$784$	372328.	−	4.96837e6i	0.0216339	−	0.288685i
$785$	−849712.	+	3.72283e6i	−0.0492150	+	0.215625i
$786$	3.02468e6	+	7.70675e6i	0.174632	+	0.444954i
$787$	−139271.	−	1.85845e6i	−0.00801540	−	0.106958i	0.991761	−	0.128102i	$-0.0408884\pi$
$787$	−139271.	−	1.85845e6i	−0.00801540	−	0.106958i	−0.999776	+	0.0211435i	$0.993269\pi$
$788$	1.11226e7	+	1.67646e6i	0.638104	+	0.0961787i
$789$	−1.44711e7	+	1.34273e7i	−0.827581	+	0.767882i
$790$	−6.56608e6	+	3.16206e6i	−0.374316	+	0.180261i
$791$	−1.35631e7	−	9.24714e6i	−0.770756	−	0.525492i
$792$	−17575.9	+	44782.7i	−0.000995645	+	0.00253686i
$793$	2.83390e7	+	8.74142e6i	1.60030	+	0.493627i
$794$	−6.69650e6	−	6.21344e6i	−0.376961	−	0.349769i
$795$	6.57458e6	+	8.24426e6i	0.368935	+	0.462630i
$796$	−949379.	−	1.19048e6i	−0.0531076	−	0.0665948i
$797$	1.21203e7	+	1.12460e7i	0.675878	+	0.627123i	0.941523	−	0.336947i	$-0.109394\pi$
$797$	1.21203e7	+	1.12460e7i	0.675878	+	0.627123i	−0.265645	+	0.964071i	$0.585585\pi$
$798$	5.02985e7	+	1.55150e7i	2.79607	+	0.862473i
$799$	5.34581e6	−	1.36209e7i	0.296242	−	0.754812i
$800$	1.50726e7	+	1.02763e7i	0.832649	+	0.567691i
$801$	−4.17770e7	+	2.01188e7i	−2.30068	+	1.10795i
$802$	−1.58461e7	+	1.47030e7i	−0.869935	+	0.807181i
$803$	−76468.5	−	11525.8i	−0.00418498	−	0.000630785i
$804$	−2.91419e6	−	3.88872e7i	−0.158993	−	2.12161i
$805$	208024.	+	530037.i	0.0113142	+	0.0288281i
$806$	−9.65015e6	+	4.22801e7i	−0.523235	+	2.29244i
$807$	−1.14185e6	+	1.52370e7i	−0.0617201	+	0.823597i
$808$	−1.37406e7	+	4.23841e6i	−0.740418	+	0.228389i
$809$	−1.37563e7	−	6.62469e6i	−0.738977	−	0.355873i	0.0262308	−	0.999656i	$-0.491650\pi$
$809$	−1.37563e7	−	6.62469e6i	−0.738977	−	0.355873i	−0.765208	+	0.643783i	$0.777364\pi$
$810$	−3.71759e6	−	6.43905e6i	−0.199090	−	0.344833i
$811$	5.37485e6	−	9.30952e6i	0.286956	−	0.497022i	−0.686126	−	0.727483i	$-0.740690\pi$
$811$	5.37485e6	−	9.30952e6i	0.286956	−	0.497022i	0.973082	+	0.230461i	$0.0740235\pi$
$812$	−8.28543e6	+	5.64891e6i	−0.440986	+	0.300659i
$813$	−2.40125e6	−	1.05206e7i	−0.127412	−	0.558230i
$814$	−170685.	+	25726.6i	−0.00902888	+	0.00136088i
$815$	−8.76567e6	+	1.09918e7i	−0.462265	+	0.579662i
$816$	1.51153e7			0.794677
$817$	2.89432e7	+	1.38198e7i	1.51702	+	0.724349i
$818$	−4.55902e7			−2.38225
$819$	1.67882e7	−	2.10517e7i	0.874570	−	1.09668i
$820$	−5.01192e6	+	755426.i	−0.260297	+	0.0392335i
$821$	4.73414e6	+	2.07416e7i	0.245123	+	1.07395i	0.936282	+	0.351250i	$0.114243\pi$
$821$	4.73414e6	+	2.07416e7i	0.245123	+	1.07395i	−0.691159	+	0.722702i	$0.742900\pi$
$822$	6.68349e7	−	4.55673e7i	3.45004	−	2.35220i
$823$	1.34867e7	−	2.33597e7i	0.694075	−	1.20217i	−0.276417	−	0.961038i	$-0.589147\pi$
$823$	1.34867e7	−	2.33597e7i	0.694075	−	1.20217i	0.970492	−	0.241135i	$-0.0775197\pi$
$824$	1.78693e6	+	3.09505e6i	0.0916830	+	0.158800i
$825$	97992.6	+	47190.8i	0.00501255	+	0.00241392i
$826$	3.50764e7	−	1.08196e7i	1.78881	−	0.551775i
$827$	202270.	−	2.69910e6i	0.0102841	−	0.137232i	−0.989698	−	0.143169i	$-0.954271\pi$
$827$	202270.	−	2.69910e6i	0.0102841	−	0.137232i	0.999982	+	0.00593698i	$0.00188981\pi$
$828$	589711.	−	2.58369e6i	0.0298926	−	0.130968i
$829$	7.68568e6	+	1.95828e7i	0.388415	+	0.989666i	0.982666	+	0.185386i	$0.0593535\pi$
$829$	7.68568e6	+	1.95828e7i	0.388415	+	0.989666i	−0.594251	+	0.804280i	$0.702551\pi$
$830$	−1.22526e6	−	1.63500e7i	−0.0617354	−	0.823801i
$831$	−2.07139e6	−	312212.i	−0.104054	−	0.0156836i
$832$	2.87740e7	−	2.66984e7i	1.44109	−	1.33714i
$833$	6.07619e6	−	2.92614e6i	0.303402	−	0.146111i
$834$	5.79170e7	+	3.94871e7i	2.88331	+	1.96581i
$835$	6.56918e6	−	1.67380e7i	0.326058	−	0.830783i
$836$	206133.	+	63583.5i	0.0102007	+	0.00314651i
$837$	9.57374e6	+	8.88313e6i	0.472354	+	0.438281i
$838$	512427.	+	642563.i	0.0252071	+	0.0316086i
$839$	−8.68389e6	−	1.08893e7i	−0.425902	−	0.534064i	0.521865	−	0.853028i	$-0.325236\pi$
$839$	−8.68389e6	−	1.08893e7i	−0.425902	−	0.534064i	−0.947767	+	0.318964i	$0.896665\pi$
$840$	−3.64450e6	−	3.38160e6i	−0.178213	−	0.165358i
$841$	−1.34206e7	−	4.13969e6i	−0.654305	−	0.201827i
$842$	−2.47885e6	+	6.31602e6i	−0.120495	+	0.307017i
$843$	−3.13077e7	−	2.13453e7i	−1.51734	−	1.03450i
$844$	1.88677e7	−	9.08622e6i	0.911724	−	0.439063i
$845$	6.95950e6	−	6.45747e6i	0.335302	−	0.311115i
$846$	−4.42539e7	−	6.67021e6i	−2.12582	−	0.320415i
$847$	−1.17341e6	−	1.56581e7i	−0.0562007	−	0.749947i
$848$	−3.70606e6	−	9.44289e6i	−0.176979	−	0.450936i
$849$	−8.33949e6	+	3.65377e7i	−0.397073	+	1.73969i
$850$	−1.32184e6	+	1.76387e7i	−0.0627526	+	0.837376i
$851$	1.89728e6	−	585234.i	0.0898065	−	0.0277016i
$852$	3.79783e7	+	1.82894e7i	1.79241	+	0.863177i
$853$	−1.54108e7	−	2.66923e7i	−0.725193	−	1.25607i	−0.958895	−	0.283763i	$-0.908417\pi$
$853$	−1.54108e7	−	2.66923e7i	−0.725193	−	1.25607i	0.233702	−	0.972308i	$-0.424916\pi$
$854$	−1.47905e7	+	2.56180e7i	−0.693967	+	1.20199i
$855$	2.14638e7	−	1.46338e7i	1.00413	−	0.684607i
$856$	837426.	+	3.66900e6i	0.0390627	+	0.171145i
$857$	−3.24578e7	+	4.89222e6i	−1.50962	+	0.227538i	−0.851090	−	0.525020i	$-0.824058\pi$
$857$	−3.24578e7	+	4.89222e6i	−1.50962	+	0.227538i	−0.658526	+	0.752558i	$0.728820\pi$
$858$	213453.	−	267661.i	0.00989882	−	0.0124127i
$859$	−7.22209e6			−0.333949			−0.166974	−	0.985961i	$-0.553400\pi$
$859$	−7.22209e6			−0.333949			−0.166974	+	0.985961i	$0.553400\pi$
$860$	−9.08334e6	−	1.13127e7i	−0.418793	−	0.521579i
$861$	9.90278e6			0.455249
$862$	−3.67843e7	+	4.61261e7i	−1.68614	+	2.11436i
$863$	−3.39432e7	+	5.11611e6i	−1.55141	+	0.233837i	−0.868135	−	0.496328i	$-0.834681\pi$
$863$	−3.39432e7	+	5.11611e6i	−1.55141	+	0.233837i	−0.683271	+	0.730165i	$0.739443\pi$
$864$	−3.84791e6	−	1.68588e7i	−0.175364	−	0.768319i
$865$	−259574.	+	176974.i	−0.0117956	+	0.00804211i
$866$	−7.99296e6	+	1.38442e7i	−0.362171	+	0.627298i
$867$	−6.79254e6	−	1.17650e7i	−0.306891	−	0.531551i
$868$	−2.17583e7	−	1.04782e7i	−0.980223	−	0.472051i
$869$	55760.4	−	17199.8i	0.00250482	−	0.000772635i
$870$	−1.14742e6	+	1.53112e7i	−0.0513953	+	0.685822i
$871$	−7.44439e6	+	3.26160e7i	−0.332494	+	1.45675i
$872$	−1.54649e6	−	3.94039e6i	−0.0688741	−	0.175488i
$873$	1.25141e6	+	1.66990e7i	0.0555732	+	0.741573i
$874$	−4.39483e6	−	662414.i	−0.194609	−	0.0293326i
$875$	−1.13649e7	+	1.05451e7i	−0.501816	+	0.465617i
$876$	−3.35125e7	+	1.61388e7i	−1.47552	+	0.710575i
$877$	1.23621e7	+	8.42836e6i	0.542743	+	0.370036i	0.803441	−	0.595384i	$-0.203000\pi$
$877$	1.23621e7	+	8.42836e6i	0.542743	+	0.370036i	−0.260698	+	0.965420i	$0.583953\pi$
$878$	2.32447e6	−	5.92266e6i	0.101763	−	0.259287i
$879$	3.48375e6	+	1.07460e6i	0.152081	+	0.0469108i
$880$	29840.4	+	27687.9i	0.00129897	+	0.00120527i
$881$	2.04853e7	+	2.56878e7i	0.889208	+	1.11503i	0.992725	+	0.120404i	$0.0384190\pi$
$881$	2.04853e7	+	2.56878e7i	0.889208	+	1.11503i	−0.103517	+	0.994628i	$0.533010\pi$
$882$	−1.28607e7	−	1.61268e7i	−0.556665	−	0.698036i
$883$	2.63128e7	+	2.44147e7i	1.13570	+	1.05378i	0.997994	+	0.0633062i	$0.0201645\pi$
$883$	2.63128e7	+	2.44147e7i	1.13570	+	1.05378i	0.137709	+	0.990473i	$0.456026\pi$
$884$	2.97026e7	+	9.16203e6i	1.27839	+	0.394331i
$885$	1.14637e7	−	2.92089e7i	0.492000	−	1.25360i
$886$	−1.86216e7	−	1.26960e7i	−0.796954	−	0.543354i
$887$	2.41764e7	−	1.16427e7i	1.03177	−	0.496874i	0.160168	−	0.987090i	$-0.448796\pi$
$887$	2.41764e7	−	1.16427e7i	1.03177	−	0.496874i	0.871601	+	0.490216i	$0.163082\pi$
$888$	−1.27084e7	+	1.17916e7i	−0.540826	+	0.501813i
$889$	−1.47515e7	−	2.22343e6i	−0.626011	−	0.0943560i
$890$	−2.62870e6	−	3.50775e7i	−0.111241	−	1.48441i
$891$	21749.8	+	55417.7i	0.000917828	+	0.00233859i
$892$	9.22099e6	−	4.03998e7i	0.388030	−	1.70007i
$893$	−3.13137e6	+	4.17853e7i	−0.131403	+	1.75346i
$894$	3.53691e7	−	1.09099e7i	1.48006	−	0.456540i
$895$	8.08830e6	+	3.89512e6i	0.337520	+	0.162541i
$896$	6.92671e6	+	1.19974e7i	0.288242	+	0.499250i
$897$	−1.96896e6	+	3.41034e6i	−0.0817064	+	0.141520i
$898$	−1.59620e7	+	1.08827e7i	−0.660534	+	0.450344i
$899$	3.46541e6	+	1.51829e7i	0.143006	+	0.626551i
$900$	2.98661e7	−	4.50159e6i	1.22906	−	0.185251i
$901$	8.56119e6	−	1.07354e7i	0.351336	−	0.440561i
$902$	72692.8			0.00297492
$903$	1.42544e7	+	2.45006e7i	0.581740	+	0.999903i
$904$	−1.21023e7			−0.492547
$905$	−8.64389e6	+	1.08391e7i	−0.350823	+	0.439918i
$906$	−7.59231e7	+	1.14436e7i	−3.07293	+	0.463170i
$907$	−1.24868e6	−	5.47082e6i	−0.0504002	−	0.220818i	0.943456	−	0.331498i	$-0.107554\pi$
$907$	−1.24868e6	−	5.47082e6i	−0.0504002	−	0.220818i	−0.993856	+	0.110680i	$0.964697\pi$
$908$	−2.52221e7	+	1.71962e7i	−1.01524	+	0.692176i
$909$	3.32010e7	−	5.75058e7i	1.33273	−	2.30835i
$910$	1.02132e7	+	1.76898e7i	0.408845	+	0.708141i
$911$	2.71347e7	+	1.30674e7i	1.08325	+	0.521667i	0.888355	−	0.459157i	$-0.151848\pi$
$911$	2.71347e7	+	1.30674e7i	1.08325	+	0.521667i	0.194897	+	0.980824i	$0.437563\pi$
$912$	−4.13623e7	+	1.27586e7i	−1.64671	+	0.507943i
$913$	−9810.60	+	130913.i	−0.000389510	+	0.00519765i
$914$	−1.14791e7	+	5.02930e7i	−0.454507	+	1.99132i
$915$	9.23818e6	+	2.35385e7i	0.364782	+	0.929450i
$916$	−1.36832e6	−	1.82590e7i	−0.0538826	−	0.719014i
$917$	3.91101e6	+	589490.i	0.153591	+	0.0231501i
$918$	1.22911e7	−	1.14045e7i	0.481375	−	0.446651i
$919$	1.61365e7	−	7.77095e6i	0.630263	−	0.303519i	−0.0913463	−	0.995819i	$-0.529117\pi$
$919$	1.61365e7	−	7.77095e6i	0.630263	−	0.303519i	0.721609	+	0.692301i	$0.243403\pi$
$920$	346847.	+	236476.i	0.0135104	+	0.00921123i
$921$	1.42994e7	−	3.64342e7i	0.555479	−	1.41534i
$922$	4.24625e7	+	1.30979e7i	1.64505	+	0.507430i
$923$	−2.65092e7	−	2.45969e7i	−1.02422	−	0.950334i
$924$	118865.	+	149052.i	0.00458008	+	0.00574323i
$925$	1.41087e7	+	1.76917e7i	0.542165	+	0.679853i
$926$	2.36292e7	+	2.19247e7i	0.905569	+	0.840246i
$927$	−1.57703e7	−	4.86449e6i	−0.602755	−	0.185925i
$928$	7.53336e6	−	1.91947e7i	0.287156	−	0.731663i
$929$	1.85939e7	+	1.26771e7i	0.706856	+	0.481926i	0.862610	−	0.505870i	$-0.168828\pi$
$929$	1.85939e7	+	1.26771e7i	0.706856	+	0.481926i	−0.155754	+	0.987796i	$0.549781\pi$
$930$	−3.33151e7	+	1.60437e7i	−1.26309	+	0.608271i
$931$	−1.41573e7	+	1.31361e7i	−0.535311	+	0.496696i
$932$	−3.69211e7	−	5.56496e6i	−1.39231	−	0.209856i
$933$	3.38873e6	+	4.52194e7i	0.127448	+	1.70067i
$934$	−8.99431e6	−	2.29171e7i	−0.337365	−	0.859593i
$935$	−12261.2	+	53719.7i	−0.000458673	+	0.00200958i
$936$	1.48350e6	−	1.97959e7i	0.0553474	−	0.738560i
$937$	−3.93208e6	+	1.21289e6i	−0.146310	+	0.0451306i	−0.367045	−	0.930203i	$-0.619631\pi$
$937$	−3.93208e6	+	1.21289e6i	−0.146310	+	0.0451306i	0.220735	+	0.975334i	$0.429154\pi$
$938$	−3.00650e7	−	1.44785e7i	−1.11572	−	0.537301i
$939$	−2.83204e7	−	4.90523e7i	−1.04818	−	1.81550i
$940$	9.47710e6	−	1.64148e7i	0.349829	−	0.605921i
$941$	2.61245e7	−	1.78114e7i	0.961776	−	0.655728i	0.0228107	−	0.999740i	$-0.492739\pi$
$941$	2.61245e7	−	1.78114e7i	0.961776	−	0.655728i	0.938965	+	0.344012i	$0.111786\pi$
$942$	−5.86161e6	−	2.56814e7i	−0.215224	−	0.942956i
$943$	−826815.	+	124622.i	−0.0302781	+	0.00456369i
$944$	−1.88204e7	+	2.36001e7i	−0.687385	+	0.861953i
$945$	6.15143e6			0.224077
$946$	104636.	+	179850.i	0.00380150	+	0.00653406i
$947$	2.11845e7			0.767614			0.383807	−	0.923413i	$-0.374613\pi$
$947$	2.11845e7			0.767614			0.383807	+	0.923413i	$0.374613\pi$
$948$	1.74996e7	−	2.19438e7i	0.632423	−	0.793033i
$949$	3.15540e7	−	4.75600e6i	1.13734	−	0.171426i
$950$	−1.12714e7	−	4.93834e7i	−0.405201	−	1.77530i
$951$	−2.44704e7	+	1.66836e7i	−0.877384	+	0.598190i
$952$	−3.23698e6	+	5.60661e6i	−0.115757	+	0.200497i
$953$	1.86506e7	+	3.23038e7i	0.665212	+	1.15218i	0.979228	+	0.202763i	$0.0649922\pi$
$953$	1.86506e7	+	3.23038e7i	0.665212	+	1.15218i	−0.314016	+	0.949418i	$0.601674\pi$
$954$	−3.78381e7	−	1.82219e7i	−1.34604	−	0.648220i
$955$	3.92347e6	−	1.21023e6i	0.139207	−	0.0429398i
$956$	607766.	−	8.11008e6i	0.0215076	−	0.286999i
$957$	27356.7	−	119857.i	0.000965569	−	0.00423043i
$958$	−8.68354e6	−	2.21253e7i	−0.305691	−	0.778889i
$959$	−2.88789e6	−	3.85362e7i	−0.101399	−	1.35308i
$960$	3.30944e7	+	4.98818e6i	1.15898	+	0.174688i
$961$	−6.50640e6	+	6.03706e6i	−0.227265	+	0.210871i
$962$	6.41733e7	−	3.09042e7i	2.23572	−	1.07666i
$963$	−1.43589e7	−	9.78972e6i	−0.498947	−	0.340177i
$964$	2.19910e6	−	5.60321e6i	0.0762170	−	0.194198i
$965$	−2.02708e7	−	6.25271e6i	−0.700733	−	0.216147i
$966$	−2.87936e6	−	2.67165e6i	−0.0992779	−	0.0921164i
$967$	1.32594e7	+	1.66268e7i	0.455993	+	0.571798i	0.955680	−	0.294409i	$-0.0951228\pi$
$967$	1.32594e7	+	1.66268e7i	0.455993	+	0.571798i	−0.499686	+	0.866207i	$0.666551\pi$
$968$	−7.21773e6	−	9.05075e6i	−0.247578	−	0.310453i
$969$	−4.29503e7	−	3.98521e7i	−1.46946	−	1.36346i
$970$	−1.21391e7	−	3.74442e6i	−0.414245	−	0.127778i
$971$	9.12244e6	−	2.32436e7i	0.310501	−	0.791144i	−0.687394	−	0.726285i	$-0.741245\pi$
$971$	9.12244e6	−	2.32436e7i	0.310501	−	0.791144i	0.997894	−	0.0648584i	$-0.0206596\pi$
$972$	4.09765e7	+	2.79373e7i	1.39114	+	0.948461i
$973$	3.01715e7	−	1.45298e7i	1.02168	−	0.492015i
$974$	−1.22845e7	+	1.13983e7i	−0.414915	+	0.384985i
$975$	−4.43790e7	−	6.68906e6i	−1.49509	−	0.225348i
$976$	−1.81785e6	−	2.42576e7i	−0.0610850	−	0.815122i
$977$	−6.83062e6	−	1.74041e7i	−0.228941	−	0.583332i	0.769530	−	0.638611i	$-0.220491\pi$
$977$	−6.83062e6	−	1.74041e7i	−0.228941	−	0.583332i	−0.998471	+	0.0552787i	$0.982395\pi$
$978$	2.15810e7	−	9.45526e7i	0.721481	−	3.16101i
$979$	−21047.8	+	280864.i	−0.000701860	+	0.00936567i
$980$	8.34787e6	−	2.57498e6i	0.277658	−	0.0856462i
$981$	1.76116e7	+	8.48128e6i	0.584286	+	0.281377i
$982$	1.44994e7	+	2.51137e7i	0.479813	+	0.831060i
$983$	2.63472e7	−	4.56346e7i	0.869661	−	1.50630i	0.00731760	−	0.999973i	$-0.497671\pi$
$983$	2.63472e7	−	4.56346e7i	0.869661	−	1.50630i	0.862343	−	0.506324i	$-0.168996\pi$
$984$	6.03225e6	−	4.11272e6i	0.198606	−	0.135407i
$985$	−1.83088e6	−	8.02159e6i	−0.0601268	−	0.263433i
$986$	1.97704e7	−	2.97990e6i	0.647623	−	0.0976134i
$987$	−2.30892e7	+	2.89530e7i	−0.754426	+	0.946020i
$988$	−8.90133e7			−2.90110
$989$	−1.49847e6	−	1.86625e6i	−0.0487145	−	0.0606707i
$990$	168530.			0.00546498
$991$	2.08523e7	−	2.61479e7i	0.674481	−	0.845772i	−0.320352	−	0.947299i	$-0.603801\pi$
$991$	2.08523e7	−	2.61479e7i	0.674481	−	0.845772i	0.994833	+	0.101526i	$0.0323727\pi$
$992$	4.91040e7	−	7.40124e6i	1.58430	−	0.238795i
$993$	8.62127e6	+	3.77723e7i	0.277459	+	1.21563i
$994$	2.98030e7	−	2.03193e7i	0.956740	−	0.652295i
$995$	−556908.	+	964592.i	−0.0178330	+	0.0308877i
$996$	3.15723e7	+	5.46849e7i	1.00846	+	1.74670i
$997$	7.82788e6	+	3.76971e6i	0.249406	+	0.120107i	0.554410	−	0.832243i	$-0.312944\pi$
$997$	7.82788e6	+	3.76971e6i	0.249406	+	0.120107i	−0.305005	+	0.952351i	$0.598658\pi$
$998$	2.50542e7	−	7.72821e6i	0.796260	−	0.245614i
$999$	1.60296e6	−	2.13901e7i	0.0508171	−	0.678107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.6.g.a.24.15	yes	204
43.9	even	21	inner	43.6.g.a.9.15	✓	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.6.g.a.9.15	✓	204	43.9	even	21	inner
43.6.g.a.24.15	yes	204	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	43.g (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(5.30682 - 6.65454i) q^{2} +(23.7101 - 3.57372i) q^{3} +(-8.99992 - 39.4312i) q^{4} +(-24.4442 + 16.6658i) q^{5} +(102.044 - 176.745i) q^{6} +(-48.7498 - 84.4371i) q^{7} +(-64.7633 - 31.1883i) q^{8} +(317.192 - 97.8407i) q^{9} +O(q^{10})\)	\(q+(5.30682 - 6.65454i) q^{2} +(23.7101 - 3.57372i) q^{3} +(-8.99992 - 39.4312i) q^{4} +(-24.4442 + 16.6658i) q^{5} +(102.044 - 176.745i) q^{6} +(-48.7498 - 84.4371i) q^{7} +(-64.7633 - 31.1883i) q^{8} +(317.192 - 97.8407i) q^{9} +(-18.8179 + 251.108i) q^{10} +(0.448656 - 1.96569i) q^{11} +(-354.305 - 902.754i) q^{12} +(62.1741 + 829.656i) q^{13} +(-820.596 - 123.685i) q^{14} +(-520.016 + 482.504i) q^{15} +(614.847 - 296.095i) q^{16} +(763.227 + 520.359i) q^{17} +(1032.19 - 2629.99i) q^{18} +(-2527.76 - 779.712i) q^{19} +(877.149 + 813.875i) q^{20} +(-1457.61 - 1827.79i) q^{21} +(-10.6998 - 13.4172i) q^{22} +(144.703 + 134.265i) q^{23} +(-1647.00 - 508.032i) q^{24} +(-821.919 + 2094.22i) q^{25} +(5850.93 + 3989.10i) q^{26} +(1921.38 - 925.286i) q^{27} +(-2890.71 + 2682.19i) q^{28} +(2514.55 + 379.008i) q^{29} +(451.214 + 6021.03i) q^{30} +(2237.39 + 5700.79i) q^{31} +(1804.35 - 7905.39i) q^{32} +(3.61284 - 48.2100i) q^{33} +(7513.06 - 2317.47i) q^{34} +(2598.86 + 1251.55i) q^{35} +(-6712.68 - 11626.7i) q^{36} +(5029.16 - 8710.76i) q^{37} +(-18603.0 + 12683.3i) q^{38} +(4439.11 + 19449.0i) q^{39} +(2102.87 - 316.956i) q^{40} +(-2641.03 + 3311.75i) q^{41} -19898.4 q^{42} +(-11995.2 - 1767.18i) q^{43} -81.5474 q^{44} +(-6122.92 + 7677.89i) q^{45} +(1661.38 - 250.413i) q^{46} +(-3524.83 - 15443.3i) q^{47} +(13519.9 - 9217.71i) q^{48} +(3650.42 - 6322.72i) q^{49} +(9574.27 + 16583.1i) q^{50} +(19955.8 + 9610.20i) q^{51} +(32154.8 - 9918.44i) q^{52} +(1110.84 - 14823.2i) q^{53} +(4039.04 - 17696.2i) q^{54} +(21.7927 + 55.5269i) q^{55} +(523.741 + 6988.84i) q^{56} +(-62719.9 - 9453.51i) q^{57} +(15866.4 - 14721.9i) q^{58} +(-39852.3 + 19191.8i) q^{59} +(23705.8 + 16162.4i) q^{60} +(13022.8 - 33181.6i) q^{61} +(49809.6 + 15364.2i) q^{62} +(-23724.4 - 22013.0i) q^{63} +(-29415.8 - 36886.2i) q^{64} +(-15346.7 - 19244.1i) q^{65} +(-301.643 - 279.883i) q^{66} +(38424.5 + 11852.4i) q^{67} +(13649.4 - 34778.2i) q^{68} +(3910.74 + 2666.30i) q^{69} +(22120.1 - 10652.5i) q^{70} +(-31862.6 + 29564.2i) q^{71} +(-23593.9 - 3556.20i) q^{72} +(-2866.25 - 38247.4i) q^{73} +(-31277.3 - 79693.2i) q^{74} +(-12003.6 + 52591.3i) q^{75} +(-7995.32 + 106690. i) q^{76} +(-187.849 + 57.9437i) q^{77} +(152982. + 73672.2i) q^{78} +(14470.7 + 25064.0i) q^{79} +(-10094.8 + 17484.7i) q^{80} +(-24396.1 + 16633.0i) q^{81} +(8022.69 + 35149.7i) q^{82} +(-64384.3 + 9704.37i) q^{83} +(-58953.6 + 73925.5i) q^{84} -27328.7 q^{85} +(-75416.3 + 70444.7i) q^{86} +60974.7 q^{87} +(-90.3629 + 113.312i) q^{88} +(-138131. + 20819.9i) q^{89} +(18599.7 + 81490.4i) q^{90} +(67022.7 - 45695.3i) q^{91} +(3991.90 - 6914.18i) q^{92} +(73421.8 + 127170. i) q^{93} +(-121474. - 58498.6i) q^{94} +(74783.8 - 23067.7i) q^{95} +(14529.7 - 193886. i) q^{96} +(-11225.8 + 49183.5i) q^{97} +(-22702.7 - 57845.4i) q^{98} +(-50.0145 - 667.397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9}+O(q^{10}) \) 204 * q - 468 * q^4 - 85 * q^5 - 22 * q^6 + 454 * q^7 + 698 * q^8 - 333 * q^9	\( 204 q - 468 q^{4} - 85 q^{5} - 22 q^{6} + 454 q^{7} + 698 q^{8} - 333 q^{9} + 303 q^{10} - 1340 q^{11} + 858 q^{12} + 814 q^{13} + 1202 q^{14} - 2083 q^{15} - 6248 q^{16} - 214 q^{17} - 174 q^{18} - 246 q^{19} - 17139 q^{20} + 3007 q^{21} + 2118 q^{22} + 3192 q^{23} + 15880 q^{24} + 3652 q^{25} - 1237 q^{26} + 108 q^{27} - 6780 q^{28} - 18827 q^{29} + 98080 q^{30} - 43196 q^{31} - 3930 q^{32} + 28181 q^{33} + 45155 q^{34} + 33275 q^{35} - 49399 q^{36} + 34607 q^{37} - 43374 q^{38} + 15155 q^{39} - 108727 q^{40} + 7156 q^{41} - 48066 q^{42} - 176452 q^{43} + 26068 q^{44} - 96386 q^{45} - 27185 q^{46} + 20402 q^{47} + 198899 q^{48} - 158742 q^{49} + 186243 q^{50} + 98589 q^{51} + 278918 q^{52} + 14102 q^{53} + 270894 q^{54} - 334770 q^{55} + 61999 q^{56} - 202490 q^{57} + 213658 q^{58} - 43753 q^{59} - 389005 q^{60} + 80516 q^{61} + 162349 q^{62} - 75177 q^{63} - 489850 q^{64} + 93726 q^{65} + 246095 q^{66} - 322922 q^{67} + 475089 q^{68} - 397079 q^{69} - 614985 q^{70} - 233345 q^{71} + 379655 q^{72} + 159391 q^{73} + 695938 q^{74} + 344081 q^{75} - 50808 q^{76} + 608177 q^{77} + 605548 q^{78} - 272109 q^{79} + 601054 q^{80} + 193536 q^{81} - 996896 q^{82} + 177813 q^{83} - 919009 q^{84} - 844524 q^{85} - 876752 q^{86} - 188214 q^{87} - 59998 q^{88} - 469041 q^{89} - 453431 q^{90} - 223189 q^{91} - 94922 q^{92} + 569174 q^{93} + 1175168 q^{94} + 435689 q^{95} + 1557688 q^{96} + 643751 q^{97} + 886196 q^{98} + 1422581 q^{99}+O(q^{100}) \) 204 * q - 468 * q^4 - 85 * q^5 - 22 * q^6 + 454 * q^7 + 698 * q^8 - 333 * q^9 + 303 * q^10 - 1340 * q^11 + 858 * q^12 + 814 * q^13 + 1202 * q^14 - 2083 * q^15 - 6248 * q^16 - 214 * q^17 - 174 * q^18 - 246 * q^19 - 17139 * q^20 + 3007 * q^21 + 2118 * q^22 + 3192 * q^23 + 15880 * q^24 + 3652 * q^25 - 1237 * q^26 + 108 * q^27 - 6780 * q^28 - 18827 * q^29 + 98080 * q^30 - 43196 * q^31 - 3930 * q^32 + 28181 * q^33 + 45155 * q^34 + 33275 * q^35 - 49399 * q^36 + 34607 * q^37 - 43374 * q^38 + 15155 * q^39 - 108727 * q^40 + 7156 * q^41 - 48066 * q^42 - 176452 * q^43 + 26068 * q^44 - 96386 * q^45 - 27185 * q^46 + 20402 * q^47 + 198899 * q^48 - 158742 * q^49 + 186243 * q^50 + 98589 * q^51 + 278918 * q^52 + 14102 * q^53 + 270894 * q^54 - 334770 * q^55 + 61999 * q^56 - 202490 * q^57 + 213658 * q^58 - 43753 * q^59 - 389005 * q^60 + 80516 * q^61 + 162349 * q^62 - 75177 * q^63 - 489850 * q^64 + 93726 * q^65 + 246095 * q^66 - 322922 * q^67 + 475089 * q^68 - 397079 * q^69 - 614985 * q^70 - 233345 * q^71 + 379655 * q^72 + 159391 * q^73 + 695938 * q^74 + 344081 * q^75 - 50808 * q^76 + 608177 * q^77 + 605548 * q^78 - 272109 * q^79 + 601054 * q^80 + 193536 * q^81 - 996896 * q^82 + 177813 * q^83 - 919009 * q^84 - 844524 * q^85 - 876752 * q^86 - 188214 * q^87 - 59998 * q^88 - 469041 * q^89 - 453431 * q^90 - 223189 * q^91 - 94922 * q^92 + 569174 * q^93 + 1175168 * q^94 + 435689 * q^95 + 1557688 * q^96 + 643751 * q^97 + 886196 * q^98 + 1422581 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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