LMFDB - Embedded newform 69.7.h.a.2.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,7,Mod(2,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 2]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("69.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	69.h (of order $22$, degree $10$, 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:	$15.8737317698$
Analytic rank:	$0$
Dimension:	$460$
Relative dimension:	$46$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			2.9
Character	$\chi$	$=$	69.2
Dual form			69.7.h.a.35.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.14428 + 9.56068i) q^{2} +(-26.2848 - 6.17310i) q^{3} +(-27.0679 - 59.2704i) q^{4} +(20.5398 - 69.9520i) q^{5} +(220.520 - 213.372i) q^{6} +(122.043 - 140.846i) q^{7} +(13.0344 + 1.87406i) q^{8} +(652.786 + 324.518i) q^{9} +O(q^{10})$	\(q+(-6.14428 + 9.56068i) q^{2} +(-26.2848 - 6.17310i) q^{3} +(-27.0679 - 59.2704i) q^{4} +(20.5398 - 69.9520i) q^{5} +(220.520 - 213.372i) q^{6} +(122.043 - 140.846i) q^{7} +(13.0344 + 1.87406i) q^{8} +(652.786 + 324.518i) q^{9} +(542.587 + 626.178i) q^{10} +(1196.67 + 1862.05i) q^{11} +(345.593 + 1725.01i) q^{12} +(-1939.75 - 2238.59i) q^{13} +(596.711 + 2032.21i) q^{14} +(-971.705 + 1711.88i) q^{15} +(2632.87 - 3038.49i) q^{16} +(239.365 + 109.314i) q^{17} +(-7113.51 + 4247.15i) q^{18} +(2850.19 + 6241.06i) q^{19} +(-4702.05 + 676.053i) q^{20} +(-4077.35 + 2948.72i) q^{21} -25155.1 q^{22} +(-6149.34 - 10498.6i) q^{23} +(-331.037 - 129.722i) q^{24} +(8673.19 + 5573.92i) q^{25} +(33320.8 - 4790.81i) q^{26} +(-15155.1 - 12559.6i) q^{27} +(-11651.4 - 3421.17i) q^{28} +(-37363.0 - 17063.1i) q^{29} +(-10396.3 - 19808.4i) q^{30} +(-2850.69 + 19827.0i) q^{31} +(13110.4 + 44650.0i) q^{32} +(-19959.6 - 56330.9i) q^{33} +(-2515.85 + 1616.84i) q^{34} +(-7345.69 - 11430.1i) q^{35} +(1564.78 - 47474.9i) q^{36} +(-43997.5 + 12918.8i) q^{37} +(-77181.1 - 11097.0i) q^{38} +(37167.0 + 70815.3i) q^{39} +(398.817 - 873.287i) q^{40} +(-14886.5 + 50698.9i) q^{41} +(-3139.42 - 57099.9i) q^{42} +(8890.53 + 61835.0i) q^{43} +(77973.3 - 121329. i) q^{44} +(36108.7 - 38998.1i) q^{45} +(138157. + 5714.69i) q^{46} +73650.4i q^{47} +(-87961.4 + 63613.3i) q^{48} +(11800.3 + 82072.9i) q^{49} +(-106581. + 48673.9i) q^{50} +(-5616.87 - 4350.94i) q^{51} +(-80177.3 + 175564. i) q^{52} +(61379.1 + 53185.3i) q^{53} +(213195. - 67723.2i) q^{54} +(154833. - 45463.2i) q^{55} +(1854.71 - 1607.12i) q^{56} +(-36390.3 - 181640. i) q^{57} +(392704. - 252375. i) q^{58} +(-223292. + 193484. i) q^{59} +(127766. + 11256.3i) q^{60} +(-33462.9 + 232740. i) q^{61} +(-172044. - 149077. i) q^{62} +(125375. - 52336.7i) q^{63} +(-260549. - 76504.1i) q^{64} +(-196436. + 89709.3i) q^{65} +(661198. + 155285. i) q^{66} +(-59466.4 - 38216.7i) q^{67} -17146.2i q^{68} +(96825.2 + 313916. i) q^{69} +154414. q^{70} +(205701. - 320077. i) q^{71} +(7900.48 + 5453.24i) q^{72} +(225844. + 494529. i) q^{73} +(146820. - 500023. i) q^{74} +(-193565. - 200050. i) q^{75} +(292761. - 337865. i) q^{76} +(408307. + 58705.7i) q^{77} +(-905407. - 79767.1i) q^{78} +(-258022. - 297773. i) q^{79} +(-158470. - 246584. i) q^{80} +(320817. + 423681. i) q^{81} +(-393249. - 453834. i) q^{82} +(-160082. - 545190. i) q^{83} +(285137. + 161850. i) q^{84} +(12563.3 - 14498.8i) q^{85} +(-645811. - 294932. i) q^{86} +(876749. + 679147. i) q^{87} +(12108.2 + 26513.3i) q^{88} +(-1.09760e6 + 157811. i) q^{89} +(150987. + 584839. i) q^{90} -552030. q^{91} +(-455809. + 648650. i) q^{92} +(197324. - 503551. i) q^{93} +(-704148. - 452528. i) q^{94} +(495117. - 71187.0i) q^{95} +(-68976.4 - 1.25455e6i) q^{96} +(330785. + 97127.1i) q^{97} +(-857177. - 391460. i) q^{98} +(176899. + 1.60386e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) $ 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9 - 1774 * q^10 - 630 * q^12 - 1842 * q^13 - 18179 * q^15 - 44990 * q^16 - 25536 * q^18 - 7794 * q^19 - 49959 * q^21 + 7720 * q^22 + 191290 * q^24 + 97900 * q^25 + 85007 * q^27 + 62574 * q^28 - 256521 * q^30 + 1662 * q^31 + 208277 * q^33 - 367948 * q^34 + 123802 * q^36 + 364110 * q^37 - 106127 * q^39 - 869392 * q^40 - 63343 * q^42 - 464490 * q^43 - 455494 * q^45 + 542498 * q^46 + 386726 * q^48 + 1394576 * q^49 + 218821 * q^51 + 592482 * q^52 + 604509 * q^54 - 1673998 * q^55 - 1160439 * q^57 - 1805128 * q^58 + 445865 * q^60 + 422670 * q^61 + 1245641 * q^63 + 2762020 * q^64 + 2925772 * q^66 + 255486 * q^67 - 770451 * q^69 - 1997900 * q^70 - 6119375 * q^72 - 2072562 * q^73 - 6740449 * q^75 + 1407414 * q^76 + 10410184 * q^78 + 1925886 * q^79 + 5228775 * q^81 + 3802304 * q^82 - 6586407 * q^84 + 229034 * q^85 - 6285451 * q^87 + 2567206 * q^88 - 6481942 * q^90 + 3137676 * q^91 + 10359558 * q^93 - 6984096 * q^94 + 18158553 * q^96 - 535890 * q^97 + 5359789 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{1}{11}\right)$	$-1$

Coefficient data

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

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

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

$2$	−6.14428	+	9.56068i	−0.768034	+	1.19508i	0.208140	+	0.978099i	$0.433259\pi$
$2$	−6.14428	+	9.56068i	−0.768034	+	1.19508i	−0.976175	+	0.216986i	$0.930377\pi$
$3$	−26.2848	−	6.17310i	−0.973513	−	0.228633i
$3$	−26.2848	−	6.17310i	−0.973513	−	0.228633i
$4$	−27.0679	−	59.2704i	−0.422936	−	0.926101i
$5$	20.5398	−	69.9520i	0.164318	−	0.559616i	−0.835629	−	0.549295i	$-0.814896\pi$
$5$	20.5398	−	69.9520i	0.164318	−	0.559616i	0.999947	−	0.0103212i	$-0.00328539\pi$
$6$	220.520	−	213.372i	1.02093	−	0.987832i
$7$	122.043	−	140.846i	0.355812	−	0.410629i	−0.549420	−	0.835546i	$-0.685151\pi$
$7$	122.043	−	140.846i	0.355812	−	0.410629i	0.905232	+	0.424917i	$0.139697\pi$
$8$	13.0344	+	1.87406i	0.0254577	+	0.00366027i
$9$	652.786	+	324.518i	0.895454	+	0.445155i
$10$	542.587	+	626.178i	0.542587	+	0.626178i
$11$	1196.67	+	1862.05i	0.899074	+	1.39899i	0.916888	+	0.399145i	$0.130693\pi$
$11$	1196.67	+	1862.05i	0.899074	+	1.39899i	−0.0178139	+	0.999841i	$0.505671\pi$
$12$	345.593	+	1725.01i	0.199996	+	0.998268i
$13$	−1939.75	−	2238.59i	−0.882909	−	1.01893i	−0.999668	−	0.0257711i	$-0.991796\pi$
$13$	−1939.75	−	2238.59i	−0.882909	−	1.01893i	0.116759	−	0.993160i	$-0.462750\pi$
$14$	596.711	+	2032.21i	0.217460	+	0.740602i
$15$	−971.705	+	1711.88i	−0.287913	+	0.507225i
$16$	2632.87	−	3038.49i	0.642790	−	0.741819i
$17$	239.365	+	109.314i	0.0487208	+	0.0222500i	0.439626	−	0.898181i	$-0.355111\pi$
$17$	239.365	+	109.314i	0.0487208	+	0.0222500i	−0.390906	+	0.920431i	$0.627838\pi$
$18$	−7113.51	+	4247.15i	−1.21974	+	0.728249i
$19$	2850.19	+	6241.06i	0.415541	+	0.909908i	0.995455	+	0.0952302i	$0.0303587\pi$
$19$	2850.19	+	6241.06i	0.415541	+	0.909908i	−0.579914	+	0.814677i	$0.696914\pi$
$20$	−4702.05	+	676.053i	−0.587757	+	0.0845066i
$21$	−4077.35	+	2948.72i	−0.440271	+	0.318402i
$22$	−25155.1			−2.36243
$23$	−6149.34	−	10498.6i	−0.505411	−	0.862879i
$23$	−6149.34	−	10498.6i	−0.505411	−	0.862879i
$24$	−331.037	−	129.722i	−0.0239466	−	0.00938381i
$25$	8673.19	+	5573.92i	0.555084	+	0.356731i
$26$	33320.8	−	4790.81i	1.89581	−	0.272577i
$27$	−15155.1	−	12559.6i	−0.769958	−	0.638094i
$28$	−11651.4	−	3421.17i	−0.530769	−	0.155848i
$29$	−37363.0	−	17063.1i	−1.53196	−	0.699624i	−0.541925	−	0.840427i	$-0.682304\pi$
$29$	−37363.0	−	17063.1i	−1.53196	−	0.699624i	−0.990038	+	0.140803i	$0.955032\pi$
$30$	−10396.3	−	19808.4i	−0.385050	−	0.733646i
$31$	−2850.69	+	19827.0i	−0.0956895	+	0.665535i	0.884363	+	0.466799i	$0.154593\pi$
$31$	−2850.69	+	19827.0i	−0.0956895	+	0.665535i	−0.980053	+	0.198736i	$0.936316\pi$
$32$	13110.4	+	44650.0i	0.400098	+	1.36261i
$33$	−19959.6	−	56330.9i	−0.555405	−	1.56749i
$34$	−2515.85	+	1616.84i	−0.0640099	+	0.0411367i
$35$	−7345.69	−	11430.1i	−0.171328	−	0.266592i
$36$	1564.78	−	47474.9i	0.0335386	−	1.01755i
$37$	−43997.5	+	12918.8i	−0.868606	+	0.255046i	−0.685522	−	0.728051i	$-0.740426\pi$
$37$	−43997.5	+	12918.8i	−0.868606	+	0.255046i	−0.183084	+	0.983097i	$0.558608\pi$
$38$	−77181.1	−	11097.0i	−1.40657	−	0.202234i
$39$	37167.0	+	70815.3i	0.626561	+	1.19380i
$40$	398.817	−	873.287i	0.00623151	−	0.0136451i
$41$	−14886.5	+	50698.9i	−0.215994	+	0.735609i	0.778201	+	0.628016i	$0.216133\pi$
$41$	−14886.5	+	50698.9i	−0.215994	+	0.735609i	−0.994195	+	0.107593i	$0.965686\pi$
$42$	−3139.42	−	57099.9i	−0.0423741	−	0.770704i
$43$	8890.53	+	61835.0i	0.111821	+	0.777731i	0.966147	+	0.257993i	$0.0830612\pi$
$43$	8890.53	+	61835.0i	0.111821	+	0.777731i	−0.854326	+	0.519738i	$0.826030\pi$
$44$	77973.3	−	121329.i	0.915351	−	1.42431i
$45$	36108.7	−	38998.1i	0.396255	−	0.427963i
$46$	138157.	+	5714.69i	1.41939	+	0.0587110i
$47$			73650.4i			0.709384i	0.934983	+	0.354692i	$0.115414\pi$
$47$			73650.4i			0.709384i	−0.934983	+	0.354692i	$0.884586\pi$
$48$	−87961.4	+	63613.3i	−0.795369	+	0.575207i
$49$	11800.3	+	82072.9i	0.100301	+	0.697608i
$50$	−106581.	+	48673.9i	−0.852647	+	0.389391i
$51$	−5616.87	−	4350.94i	−0.0423432	−	0.0327999i
$52$	−80177.3	+	175564.i	−0.570219	+	1.24861i
$53$	61379.1	+	53185.3i	0.412281	+	0.357243i	0.836170	−	0.548471i	$-0.184790\pi$
$53$	61379.1	+	53185.3i	0.412281	+	0.357243i	−0.423889	+	0.905714i	$0.639335\pi$
$54$	213195.	−	67723.2i	1.35393	−	0.430087i
$55$	154833.	−	45463.2i	0.930629	−	0.273257i
$56$	1854.71	−	1607.12i	0.0105612	−	0.00915131i
$57$	−36390.3	−	181640.i	−0.196499	−	0.980813i
$58$	392704.	−	252375.i	2.01271	−	1.29349i
$59$	−223292.	+	193484.i	−1.08722	+	0.942081i	−0.998542	−	0.0539792i	$-0.982810\pi$
$59$	−223292.	+	193484.i	−1.08722	+	0.942081i	−0.0886776	+	0.996060i	$0.528264\pi$
$60$	127766.	+	11256.3i	0.591510	+	0.0521125i
$61$	−33462.9	+	232740.i	−0.147426	+	1.02537i	0.772987	+	0.634422i	$0.218762\pi$
$61$	−33462.9	+	232740.i	−0.147426	+	1.02537i	−0.920413	+	0.390948i	$0.872147\pi$
$62$	−172044.	−	149077.i	−0.721878	−	0.625511i
$63$	125375.	−	52336.7i	0.501406	−	0.209308i
$64$	−260549.	−	76504.1i	−0.993915	−	0.291840i
$65$	−196436.	+	89709.3i	−0.715288	+	0.326661i
$66$	661198.	+	155285.i	2.29985	+	0.540130i
$67$	−59466.4	−	38216.7i	−0.197718	−	0.127066i	0.438036	−	0.898958i	$-0.355674\pi$
$67$	−59466.4	−	38216.7i	−0.197718	−	0.127066i	−0.635754	+	0.771892i	$0.719311\pi$
$68$		−	17146.2i		−	0.0545307i
$69$	96825.2	+	313916.i	0.294742	+	0.955577i
$70$	154414.			0.450185
$71$	205701.	−	320077.i	0.574727	−	0.894293i	−0.425214	−	0.905093i	$-0.639801\pi$
$71$	205701.	−	320077.i	0.574727	−	0.894293i	0.999942	+	0.0107995i	$0.00343765\pi$
$72$	7900.48	+	5453.24i	0.0211668	+	0.0146102i
$73$	225844.	+	494529.i	0.580550	+	1.27123i	0.940987	+	0.338443i	$0.109900\pi$
$73$	225844.	+	494529.i	0.580550	+	1.27123i	−0.360437	+	0.932783i	$0.617373\pi$
$74$	146820.	−	500023.i	0.362318	−	1.23394i
$75$	−193565.	−	200050.i	−0.458821	−	0.474193i
$76$	292761.	−	337865.i	0.666919	−	0.769665i
$77$	408307.	+	58705.7i	0.894365	+	0.128590i
$78$	−905407.	−	79767.1i	−1.90792	−	0.168089i
$79$	−258022.	−	297773.i	−0.523330	−	0.603954i	0.431132	−	0.902289i	$-0.358114\pi$
$79$	−258022.	−	297773.i	−0.523330	−	0.603954i	−0.954461	+	0.298334i	$0.903569\pi$
$80$	−158470.	−	246584.i	−0.309512	−	0.481610i
$81$	320817.	+	423681.i	0.603674	+	0.797231i
$82$	−393249.	−	453834.i	−0.713224	−	0.823105i
$83$	−160082.	−	545190.i	−0.279968	−	0.953484i	−0.972657	−	0.232247i	$-0.925392\pi$
$83$	−160082.	−	545190.i	−0.279968	−	0.953484i	0.692689	−	0.721237i	$-0.256426\pi$
$84$	285137.	+	161850.i	0.481078	+	0.273071i
$85$	12563.3	−	14498.8i	0.0204572	−	0.0236088i
$86$	−645811.	−	294932.i	−1.01534	−	0.463689i
$87$	876749.	+	679147.i	1.33143	+	1.03135i
$88$	12108.2	+	26513.3i	0.0177677	+	0.0389059i
$89$	−1.09760e6	+	157811.i	−1.55694	+	0.223855i	−0.866368	−	0.499406i	$-0.833551\pi$
$89$	−1.09760e6	+	157811.i	−1.55694	+	0.223855i	−0.690575	+	0.723261i	$0.742642\pi$
$90$	150987.	+	584839.i	0.207115	+	0.802249i
$91$	−552030.			−0.732552
$92$	−455809.	+	648650.i	−0.585356	+	0.833004i
$93$	197324.	−	503551.i	0.245319	−	0.626029i
$94$	−704148.	−	452528.i	−0.847775	−	0.544832i
$95$	495117.	−	71187.0i	0.577480	−	0.0830290i
$96$	−68976.4	−	1.25455e6i	−0.0779627	−	1.41799i
$97$	330785.	+	97127.1i	0.362435	+	0.106420i	0.457880	−	0.889014i	$-0.348609\pi$
$97$	330785.	+	97127.1i	0.362435	+	0.106420i	−0.0954446	+	0.995435i	$0.530427\pi$
$98$	−857177.	−	391460.i	−0.910736	−	0.415919i
$99$	176899.	+	1.60386e6i	0.182313	+	1.65295i
$100$	95603.6	−	664938.i	0.0956036	−	0.664938i
$101$	93217.8	+	317471.i	0.0904763	+	0.308134i	0.992281	−	0.124010i	$-0.0395754\pi$
$101$	93217.8	+	317471.i	0.0904763	+	0.308134i	−0.901805	+	0.432144i	$0.857757\pi$
$102$	76109.5	−	26967.7i	0.0717197	−	0.0254123i
$103$	−583267.	+	374843.i	−0.533772	+	0.343034i	−0.779599	−	0.626279i	$-0.784577\pi$
$103$	−583267.	+	374843.i	−0.533772	+	0.343034i	0.245827	+	0.969314i	$0.420941\pi$
$104$	−21088.2	−	32813.8i	−0.0187473	−	0.0291714i
$105$	122521.	+	345784.i	0.105838	+	0.298702i
$106$	−885618.	+	260041.i	−0.743582	+	0.218335i
$107$	1.28886e6	+	185310.i	1.05209	+	0.151268i	0.646599	−	0.762830i	$-0.276191\pi$
$107$	1.28886e6	+	185310.i	1.05209	+	0.151268i	0.405494	+	0.914098i	$0.367100\pi$
$108$	−334197.	+	1.23821e6i	−0.265297	+	0.982932i
$109$	−64192.7	+	140562.i	−0.0495685	+	0.108540i	−0.932796	−	0.360405i	$-0.882638\pi$
$109$	−64192.7	+	140562.i	−0.0495685	+	0.108540i	0.883227	+	0.468945i	$0.155366\pi$
$110$	−516680.	+	1.75965e6i	−0.388189	+	1.32205i
$111$	1.23622e6	−	67968.5i	0.903911	−	0.0496980i
$112$	−106634.	−	741656.i	−0.0759000	−	0.527896i
$113$	−1.14505e6	+	1.78173e6i	−0.793575	+	1.23483i	0.174621	+	0.984636i	$0.444130\pi$
$113$	−1.14505e6	+	1.78173e6i	−0.793575	+	1.23483i	−0.968196	+	0.250191i	$0.919506\pi$
$114$	1.96019e6	+	768129.i	1.32307	+	0.518465i
$115$	−860707.	+	214519.i	−0.565929	+	0.141050i
$116$			2.67639e6i			1.71465i
$117$	−539779.	−	2.09080e6i	−0.337022	−	1.30544i
$118$	−477867.	−	3.32364e6i	−0.290845	−	2.02287i
$119$	44609.4	−	20372.4i	0.0264719	−	0.0120893i
$120$	−15873.7	+	20492.3i	−0.00918618	+	0.0118590i
$121$	−1.29929e6	+	2.84504e6i	−0.733414	+	1.60595i
$122$	−2.01954e6	−	1.74995e6i	−1.11218	−	0.963707i
$123$	704260.	−	1.24072e6i	0.378458	−	0.666741i
$124$	1.25232e6	−	367713.i	0.656823	−	0.192861i
$125$	1.42896e6	−	1.23820e6i	0.731627	−	0.633958i
$126$	−269965.	+	1.52024e6i	−0.134957	+	0.759979i
$127$	2.61623e6	−	1.68135e6i	1.27722	−	0.820817i	0.286675	−	0.958028i	$-0.407450\pi$
$127$	2.61623e6	−	1.68135e6i	1.27722	−	0.820817i	0.990542	+	0.137211i	$0.0438138\pi$
$128$	81513.5	−	70631.9i	0.0388687	−	0.0336799i
$129$	148027.	−	1.68021e6i	0.0689562	−	0.782696i
$130$	349275.	−	2.42926e6i	0.158978	−	1.10572i
$131$	1.68283e6	+	1.45818e6i	0.748561	+	0.648632i	0.943193	−	0.332245i	$-0.107806\pi$
$131$	1.68283e6	+	1.45818e6i	0.748561	+	0.648632i	−0.194632	+	0.980876i	$0.562351\pi$
$132$	−2.79849e6	+	2.70777e6i	−1.21675	+	1.17731i
$133$	1.22687e6	+	360242.i	0.521489	+	0.153123i
$134$	730755.	−	333725.i	0.303709	−	0.138699i
$135$	−1.18985e6	+	802157.i	−0.483606	+	0.326030i
$136$	2915.11	+	1873.43i	0.00115888	+	0.000744767i
$137$		−	2.46046e6i		−	0.956873i	−0.878122	−	0.478437i	$-0.841204\pi$
$137$		−	2.46046e6i		−	0.956873i	0.878122	−	0.478437i	$-0.158796\pi$
$138$	−3.59617e6	−	1.00307e6i	−1.36837	−	0.381675i
$139$	−2.42610e6			−0.903369			−0.451684	−	0.892178i	$-0.649177\pi$
$139$	−2.42610e6			−0.903369			−0.451684	+	0.892178i	$0.649177\pi$
$140$	−478636.	+	744772.i	−0.174430	+	0.271418i
$141$	454651.	−	1.93589e6i	0.162189	−	0.690595i
$142$	1.79627e6	+	3.93329e6i	0.627346	+	1.37370i
$143$	1.84714e6	−	6.29077e6i	0.631671	−	2.15127i
$144$	2.70474e6	−	1.12907e6i	0.905813	−	0.378124i
$145$	−1.96103e6	+	2.26315e6i	−0.643250	+	0.742350i
$146$	−6.11567e6	−	879301.i	−1.96511	−	0.282539i
$147$	196475.	−	2.23012e6i	0.0618523	−	0.702063i
$148$	1.95663e6	+	2.25807e6i	0.603563	+	0.696549i
$149$	−999533.	−	1.55530e6i	−0.302161	−	0.470172i	0.656658	−	0.754188i	$-0.271969\pi$
$149$	−999533.	−	1.55530e6i	−0.302161	−	0.470172i	−0.958819	+	0.284016i	$0.908333\pi$
$150$	3.10193e6	−	621450.i	0.919091	−	0.184133i
$151$	725663.	+	837460.i	0.210768	+	0.243239i	0.851283	−	0.524706i	$-0.175825\pi$
$151$	725663.	+	837460.i	0.210768	+	0.243239i	−0.640516	+	0.767945i	$0.721279\pi$
$152$	25454.4	+	86689.6i	0.00724823	+	0.0246852i
$153$	120780.	+	149037.i	0.0337225	+	0.0416122i
$154$	−3.07002e6	+	3.54299e6i	−0.840579	+	0.970080i
$155$	1.32838e6	+	606652.i	0.356721	+	0.162909i
$156$	3.19122e6	−	4.11973e6i	0.840588	−	1.08516i
$157$	1.63939e6	+	3.58976e6i	0.423626	+	0.927612i	0.994318	+	0.106448i	$0.0339477\pi$
$157$	1.63939e6	+	3.58976e6i	0.423626	+	0.927612i	−0.570692	+	0.821164i	$0.693325\pi$
$158$	4.43227e6	−	637264.i	1.12371	−	0.161565i
$159$	−1.28502e6	−	1.77687e6i	−0.319683	−	0.442042i
$160$	3.39264e6			0.828281
$161$	−2.22917e6	−	415183.i	−0.534154	−	0.0994860i
$162$	−6.02187e6	+	464017.i	−1.41640	+	0.109141i
$163$	−777643.	−	499761.i	−0.179563	−	0.115398i	0.447771	−	0.894148i	$-0.352218\pi$
$163$	−777643.	−	499761.i	−0.179563	−	0.115398i	−0.627335	+	0.778750i	$0.715854\pi$
$164$	3.40789e6	−	489981.i	0.772600	−	0.111083i
$165$	−4.35042e6	+	239191.i	−0.968455	+	0.0532467i
$166$	6.19597e6	+	1.81930e6i	1.35452	+	0.397723i
$167$	393364.	+	179643.i	0.0844588	+	0.0385711i	0.457197	−	0.889366i	$-0.348854\pi$
$167$	393364.	+	179643.i	0.0844588	+	0.0385711i	−0.372738	+	0.927937i	$0.621581\pi$
$168$	−58671.7	+	30793.5i	−0.0123737	+	0.00649428i
$169$	−561734.	+	3.90695e6i	−0.116378	+	0.809426i
$170$	61426.0	+	209198.i	0.0125027	+	0.0425805i
$171$	−164768.	+	4.99901e6i	−0.0329522	+	0.999760i
$172$	3.42434e6	−	2.20069e6i	0.672964	−	0.432488i
$173$	3.71295e6	+	5.77746e6i	0.717101	+	1.11583i	0.988184	+	0.153275i	$0.0489821\pi$
$173$	3.71295e6	+	5.77746e6i	0.717101	+	1.11583i	−0.271082	+	0.962556i	$0.587381\pi$
$174$	−1.18801e7	+	4.20945e6i	−2.25513	+	0.799056i
$175$	1.84357e6	−	541320.i	0.343989	−	0.101004i
$176$	8.80849e6	+	1.26647e6i	1.61571	+	0.232304i
$177$	7.06359e6	−	3.70728e6i	1.27381	−	0.668553i
$178$	5.23516e6	−	1.14634e7i	0.928260	−	2.03261i
$179$	−1.40044e6	+	4.76947e6i	−0.244178	+	0.831593i	0.742631	+	0.669701i	$0.233578\pi$
$179$	−1.40044e6	+	4.76947e6i	−0.244178	+	0.831593i	−0.986809	+	0.161892i	$0.948240\pi$
$180$	−3.28882e6	−	1.08458e6i	−0.563927	−	0.185971i
$181$	236744.	+	1.64659e6i	0.0399248	+	0.277683i	0.999998	−	0.00206627i	$-0.000657715\pi$
$181$	236744.	+	1.64659e6i	0.0399248	+	0.277683i	−0.960073	+	0.279749i	$0.909749\pi$
$182$	3.39182e6	−	5.27778e6i	0.562625	−	0.875462i
$183$	2.31629e6	−	5.91096e6i	0.377955	−	0.964505i
$184$	−60477.7	−	148367.i	−0.00970826	−	0.0238169i
$185$			3.34306e6i			0.527995i
$186$	3.60188e6	+	4.98050e6i	0.559745	+	0.773989i
$187$	82891.5	+	576523.i	0.0126761	+	0.0881641i
$188$	4.36529e6	−	1.99356e6i	0.656961	−	0.300024i
$189$	−3.61855e6	+	601710.i	−0.535980	+	0.0891254i
$190$	−2.36154e6	+	5.17104e6i	−0.344297	+	0.753906i
$191$	5.60176e6	+	4.85395e6i	0.803941	+	0.696619i	0.956518	−	0.291672i	$-0.0942117\pi$
$191$	5.60176e6	+	4.85395e6i	0.803941	+	0.696619i	−0.152577	+	0.988292i	$0.548757\pi$
$192$	6.37622e6	+	3.61929e6i	0.900865	+	0.511352i
$193$	−5.94841e6	+	1.74661e6i	−0.827426	+	0.242954i	−0.667911	−	0.744241i	$-0.732811\pi$
$193$	−5.94841e6	+	1.74661e6i	−0.827426	+	0.242954i	−0.159515	+	0.987195i	$0.550993\pi$
$194$	−2.96103e6	+	2.56575e6i	−0.405544	+	0.351406i
$195$	5.71707e6	−	1.14538e6i	0.771028	−	0.154470i
$196$	4.54509e6	−	2.92095e6i	0.603635	−	0.387932i
$197$	1.00237e6	−	868555.i	0.131107	−	0.113605i	−0.586839	−	0.809704i	$-0.699628\pi$
$197$	1.00237e6	−	868555.i	0.131107	−	0.113605i	0.717946	+	0.696099i	$0.245082\pi$
$198$	−1.64209e7	−	8.16329e6i	−2.11544	−	1.05165i
$199$	222844.	−	1.54991e6i	0.0282775	−	0.196674i	−0.970786	−	0.239948i	$-0.922870\pi$
$199$	222844.	−	1.54991e6i	0.0282775	−	0.196674i	0.999063	+	0.0432736i	$0.0137787\pi$
$200$	102604.	+	88906.6i	0.0128255	+	0.0111133i
$201$	1.32715e6	+	1.37161e6i	0.163430	+	0.168905i
$202$	−3.60799e6	−	1.05940e6i	−0.437735	−	0.128531i
$203$	−6.96318e6	+	3.17998e6i	−0.832376	+	0.380133i
$204$	−105845.	+	450685.i	−0.0124675	+	0.0530863i
$205$	3.24072e6	+	2.08269e6i	0.376167	+	0.241748i
$206$		−	7.87957e6i		−	0.901365i
$207$	−607204.	−	8.84893e6i	−0.0684579	−	0.997654i
$208$	−1.19091e7			−1.32339
$209$	−8.21043e6	+	1.27757e7i	−0.899346	+	1.39941i
$210$	−4.05874e6	−	953211.i	−0.438261	−	0.102927i
$211$	−6.02923e6	−	1.32022e7i	−0.641822	−	1.40539i	−0.898533	−	0.438906i	$-0.855366\pi$
$211$	−6.02923e6	−	1.32022e7i	−0.641822	−	1.40539i	0.256711	−	0.966488i	$-0.417361\pi$
$212$	1.49091e6	−	5.07758e6i	0.156475	−	0.532905i
$213$	−7.38269e6	+	7.14337e6i	−0.763970	+	0.739204i
$214$	−9.69080e6	+	1.11838e7i	−0.988822	+	1.14116i
$215$	4.50809e6	+	648166.i	0.453605	+	0.0652185i
$216$	−174000.	−	192108.i	−0.0172658	−	0.0190627i
$217$	2.44463e6	+	2.82126e6i	0.239240	+	0.276098i
$218$	−949454.	−	1.47738e6i	−0.0916441	−	0.142601i
$219$	−2.88349e6	−	1.43928e7i	−0.274528	−	1.37029i
$220$	−6.88564e6	−	7.94645e6i	−0.646660	−	0.746286i
$221$	−219598.	−	747884.i	−0.0203448	−	0.0692879i
$222$	−6.94583e6	+	1.22367e7i	−0.634842	+	1.11842i
$223$	−8.41832e6	+	9.71526e6i	−0.759121	+	0.876072i	−0.995419	−	0.0956082i	$-0.969520\pi$
$223$	−8.41832e6	+	9.71526e6i	−0.759121	+	0.876072i	0.236298	+	0.971681i	$0.424066\pi$
$224$	7.88879e6	+	3.60269e6i	0.701886	+	0.320541i
$225$	3.85290e6	+	6.45318e6i	0.338252	+	0.566534i
$226$	−9.99905e6	−	2.18949e7i	−0.866230	−	1.89678i
$227$	−1.98449e7	+	2.85327e6i	−1.69657	+	0.243930i	−0.921620	−	0.388094i	$-0.873134\pi$
$227$	−1.98449e7	+	2.85327e6i	−1.69657	+	0.243930i	−0.774949	+	0.632023i	$0.782225\pi$
$228$	−9.78086e6	+	7.07347e6i	−0.825225	+	0.596799i
$229$	−1.88189e7			−1.56707			−0.783534	−	0.621348i	$-0.786585\pi$
$229$	−1.88189e7			−1.56707			−0.783534	+	0.621348i	$0.786585\pi$
$230$	3.23747e6	−	9.54701e6i	0.266086	−	0.784664i
$231$	−1.03699e7	−	4.06359e6i	−0.841276	−	0.329666i
$232$	−455026.	−	292428.i	−0.0364395	−	0.0234182i
$233$	2.62030e6	−	376742.i	0.207149	−	0.0297835i	−0.0379591	−	0.999279i	$-0.512086\pi$
$233$	2.62030e6	−	376742.i	0.207149	−	0.0297835i	0.245108	+	0.969496i	$0.421177\pi$
$234$	2.33061e7	+	7.68583e6i	1.81895	+	0.599851i
$235$	5.15199e6	+	1.51276e6i	0.396983	+	0.116565i
$236$	1.75119e7	+	7.99742e6i	1.33229	+	0.608435i
$237$	4.94388e6	+	9.41971e6i	0.371384	+	0.707608i
$238$	−79318.2	+	551670.i	−0.00588358	+	0.0409212i
$239$	−117282.	−	399426.i	−0.00859089	−	0.0292579i	0.955086	−	0.296329i	$-0.0957624\pi$
$239$	−117282.	−	399426.i	−0.00859089	−	0.0292579i	−0.963677	+	0.267071i	$0.913944\pi$
$240$	2.64317e6	+	7.45968e6i	0.191202	+	0.539618i
$241$	1.67955e7	−	1.07938e7i	1.19989	−	0.771122i	0.220952	−	0.975285i	$-0.429084\pi$
$241$	1.67955e7	−	1.07938e7i	1.19989	−	0.771122i	0.978937	+	0.204163i	$0.0654472\pi$
$242$	−1.92174e7	−	2.99028e7i	−1.35596	−	2.10992i
$243$	−5.81721e6	−	1.31168e7i	−0.405411	−	0.914134i
$244$	1.47004e7	−	4.31641e6i	1.01195	−	0.297135i
$245$	5.98354e6	+	860303.i	0.406874	+	0.0584996i
$246$	7.53493e6	+	1.43565e7i	0.506144	+	0.964370i
$247$	8.44251e6	−	1.84865e7i	0.560249	−	1.22677i
$248$	−74313.8	+	253090.i	−0.00487208	+	0.0165928i
$249$	842224.	+	1.53184e7i	0.0545543	+	0.992239i
$250$	3.05811e6	+	2.12697e7i	0.195719	+	1.36126i
$251$	1.10967e7	−	1.72668e7i	0.701734	−	1.09192i	−0.289160	−	0.957281i	$-0.593376\pi$
$251$	1.10967e7	−	1.72668e7i	0.701734	−	1.09192i	0.990895	−	0.134639i	$-0.0429876\pi$
$252$	−6.49566e6	−	6.01439e6i	−0.405903	−	0.375829i
$253$	1.21903e7	−	2.40138e7i	0.752753	−	1.48286i
$254$			3.53436e7i			2.15680i
$255$	−419726.	+	303544.i	−0.0253131	+	0.0183063i
$256$	−2.29886e6	−	1.59889e7i	−0.137023	−	0.953013i
$257$	−9.77796e6	+	4.46544e6i	−0.576035	+	0.263066i	−0.682059	−	0.731297i	$-0.738915\pi$
$257$	−9.77796e6	+	4.46544e6i	−0.576035	+	0.263066i	0.106024	+	0.994364i	$0.466188\pi$
$258$	1.51544e7	+	1.17389e7i	0.882428	+	0.683546i
$259$	−3.55005e6	+	7.77352e6i	−0.204331	+	0.447423i
$260$	1.06342e7	+	9.21460e6i	0.605042	+	0.524272i
$261$	−1.88528e7	−	2.32635e7i	−1.06036	−	1.30844i
$262$	−2.42810e7	+	7.12955e6i	−1.35009	+	0.396422i
$263$	8.97205e6	−	7.77433e6i	0.493202	−	0.427362i	−0.372417	−	0.928066i	$-0.621471\pi$
$263$	8.97205e6	−	7.77433e6i	0.493202	−	0.427362i	0.865619	+	0.500704i	$0.166925\pi$
$264$	−154593.	−	771642.i	−0.00840192	−	0.0419377i
$265$	4.98113e6	−	3.20118e6i	0.267664	−	0.172017i
$266$	−1.09824e7	+	9.51631e6i	−0.583516	+	0.505619i
$267$	2.98243e7	+	2.62755e6i	1.56688	+	0.138044i
$268$	−655492.	+	4.55904e6i	−0.0340536	+	0.236848i
$269$	7.33550e6	+	6.35625e6i	0.376854	+	0.326546i	0.822607	−	0.568610i	$-0.192519\pi$
$269$	7.33550e6	+	6.35625e6i	0.376854	+	0.326546i	−0.445753	+	0.895156i	$0.647064\pi$
$270$	−358391.	−	1.63045e7i	−0.0182081	−	0.828353i
$271$	9.15903e6	+	2.68933e6i	0.460195	+	0.135125i	0.503609	−	0.863932i	$-0.332005\pi$
$271$	9.15903e6	+	2.68933e6i	0.460195	+	0.135125i	−0.0434141	+	0.999057i	$0.513823\pi$
$272$	962368.	−	439499.i	0.0478227	−	0.0218399i
$273$	1.45100e7	+	3.40774e6i	0.713149	+	0.167486i
$274$	2.35237e7	+	1.51177e7i	1.14354	+	0.734912i
$275$			2.28200e7i			1.09728i
$276$	1.59851e7	−	1.42359e7i	0.760304	−	0.677108i
$277$	−2.50929e7			−1.18062			−0.590312	−	0.807175i	$-0.700995\pi$
$277$	−2.50929e7			−1.18062			−0.590312	+	0.807175i	$0.700995\pi$
$278$	1.49067e7	−	2.31952e7i	0.693818	−	1.07960i
$279$	−8.29509e6	+	1.20177e7i	−0.381952	+	0.553359i
$280$	−74325.7	−	162751.i	−0.00338583	−	0.00741393i
$281$	4.03318e6	−	1.37357e7i	0.181773	−	0.619060i	−0.817309	−	0.576200i	$-0.804535\pi$
$281$	4.03318e6	−	1.37357e7i	0.181773	−	0.619060i	0.999081	−	0.0428602i	$-0.0136470\pi$
$282$	1.57149e7	+	1.62414e7i	0.700753	+	0.724230i
$283$	−1.75384e7	+	2.02403e7i	−0.773802	+	0.893015i	−0.996646	−	0.0818393i	$-0.973921\pi$
$283$	−1.75384e7	+	2.02403e7i	−0.773802	+	0.893015i	0.222844	+	0.974854i	$0.428466\pi$
$284$	−2.45390e7	−	3.52818e6i	−1.07128	−	0.154027i
$285$	−1.34535e7	−	1.18526e6i	−0.581167	−	0.0512013i
$286$	4.87947e7	+	5.63121e7i	2.08581	+	2.40715i
$287$	5.32392e6	+	8.28418e6i	0.225209	+	0.350432i
$288$	−5.93142e6	+	3.34014e7i	−0.248303	+	1.39826i
$289$	−1.57614e7	−	1.81896e7i	−0.652982	−	0.753581i
$290$	−9.58812e6	−	3.26541e7i	−0.393133	−	1.33889i
$291$	−8.09504e6	−	4.59494e6i	−0.328504	−	0.186466i
$292$	2.31978e7	−	2.67717e7i	0.931748	−	1.07529i
$293$	−1.16740e7	−	5.33134e6i	−0.464106	−	0.211950i	0.169617	−	0.985510i	$-0.445747\pi$
$293$	−1.16740e7	−	5.33134e6i	−0.464106	−	0.211950i	−0.633723	+	0.773560i	$0.718474\pi$
$294$	2.01142e7	+	1.55809e7i	0.791520	+	0.613127i
$295$	8.94820e6	+	1.95938e7i	0.348554	+	0.763226i
$296$	−597690.	+	85934.9i	−0.0230463	+	0.00331356i
$297$	5.25104e6	−	4.32492e7i	0.200436	−	1.65085i
$298$	2.10112e7			0.793965
$299$	−1.15740e7	+	3.41306e7i	−0.432982	+	1.27682i
$300$	−6.61765e6	+	1.68876e7i	−0.245098	+	0.625467i
$301$	9.79423e6	+	6.29437e6i	0.359146	+	0.230809i
$302$	−1.24654e7	+	1.79225e6i	−0.452568	+	0.0650695i
$303$	−490437.	−	8.92011e6i	−0.0176301	−	0.320658i
$304$	2.64676e7	+	7.77158e6i	0.942092	+	0.276623i
$305$	1.55933e7	+	7.12121e6i	0.549589	+	0.250989i
$306$	−2.16700e6	+	239010.i	−0.0756301	+	0.00834166i
$307$	−3.56977e6	+	2.48283e7i	−0.123375	+	0.858089i	0.830315	+	0.557295i	$0.188161\pi$
$307$	−3.56977e6	+	2.48283e7i	−0.123375	+	0.858089i	−0.953689	+	0.300794i	$0.902748\pi$
$308$	−7.57251e6	−	2.57896e7i	−0.259172	−	0.882657i
$309$	1.76450e7	−	6.25212e6i	0.598063	−	0.211910i
$310$	−1.39620e7	+	8.97281e6i	−0.468664	+	0.301192i
$311$	−1.90151e7	−	2.95881e7i	−0.632146	−	0.983639i	−0.998584	−	0.0531964i	$-0.983059\pi$
$311$	−1.90151e7	−	2.95881e7i	−0.632146	−	0.983639i	0.366438	−	0.930443i	$-0.380577\pi$
$312$	351736.	+	992686.i	0.0115812	+	0.0326850i
$313$	−3.65477e7	+	1.07314e7i	−1.19187	+	0.349963i	−0.816737	−	0.577010i	$-0.804219\pi$
$313$	−3.65477e7	+	1.07314e7i	−1.19187	+	0.349963i	−0.375128	+	0.926973i	$0.622401\pi$
$314$	−4.43934e7	−	6.38280e6i	−1.43393	−	0.206169i
$315$	−1.08588e6	−	9.84522e6i	−0.0347418	−	0.314988i
$316$	−1.06650e7	+	2.33532e7i	−0.337988	+	0.740090i
$317$	1.49039e7	−	5.07579e7i	0.467865	−	1.59340i	−0.300757	−	0.953701i	$-0.597239\pi$
$317$	1.49039e7	−	5.07579e7i	0.467865	−	1.59340i	0.768623	−	0.639703i	$-0.220942\pi$
$318$	2.48836e7	−	1.36813e6i	0.773805	−	0.0425446i
$319$	−1.29387e7	−	8.99908e7i	−0.398583	−	2.77221i
$320$	−1.07032e7	+	1.66545e7i	−0.326636	+	0.508256i
$321$	−3.27335e7	−	1.28271e7i	−0.989641	−	0.387805i
$322$	1.76661e7	−	1.87614e7i	0.529143	−	0.561951i
$323$			1.80546e6i			0.0535772i
$324$	1.64279e7	−	3.04831e7i	0.483000	−	0.896241i
$325$	−4.34609e6	−	3.02277e7i	−0.126604	−	0.880553i
$326$	9.55610e6	−	4.36413e6i	0.275821	−	0.125963i
$327$	2.55500e6	−	3.29839e6i	0.0730714	−	0.0943319i
$328$	−289049.	+	632930.i	−0.00819126	+	0.0179364i
$329$	1.03733e7	+	8.98855e6i	0.291294	+	0.252407i
$330$	2.44434e7	−	4.30626e7i	0.680172	−	1.19828i
$331$	4.85680e7	−	1.42609e7i	1.33926	−	0.393244i	0.467858	−	0.883804i	$-0.345026\pi$
$331$	4.85680e7	−	1.42609e7i	1.33926	−	0.393244i	0.871407	+	0.490560i	$0.163208\pi$
$332$	−2.79806e7	+	2.42453e7i	−0.764614	+	0.662541i
$333$	−3.29133e7	−	5.84475e6i	−0.891332	−	0.158283i
$334$	−4.13445e6	+	2.65705e6i	−0.110963	+	0.0713116i
$335$	−3.89476e6	+	3.37483e6i	−0.103597	+	0.0897671i
$336$	−1.77546e6	+	2.01526e7i	−0.0468050	+	0.531267i
$337$	−5.94396e6	+	4.13412e7i	−0.155305	+	1.08017i	0.751837	+	0.659349i	$0.229168\pi$
$337$	−5.94396e6	+	4.13412e7i	−0.155305	+	1.08017i	−0.907143	+	0.420823i	$0.861741\pi$
$338$	−3.39016e7	−	2.93759e7i	−0.877951	−	0.760749i
$339$	4.10962e7	−	3.97640e7i	1.05488	−	1.02068i
$340$	−1.19941e6	−	352179.i	−0.0305162	−	0.00896037i
$341$	−4.03301e7	+	1.84182e7i	−1.01711	+	0.464497i
$342$	−4.67816e7	−	3.22906e7i	−1.16949	−	0.807231i
$343$	3.14448e7	+	2.02084e7i	0.779233	+	0.500782i
$344$			822642.i			0.0202086i
$345$	2.39478e7	−	325367.i	0.583187	−	0.00792349i
$346$	−7.80498e7			−1.88427
$347$	−1.96116e6	+	3.05162e6i	−0.0469379	+	0.0730368i	−0.863929	−	0.503613i	$-0.832004\pi$
$347$	−1.96116e6	+	3.05162e6i	−0.0469379	+	0.0730368i	0.816992	+	0.576650i	$0.195640\pi$
$348$	1.65216e7	−	7.03484e7i	0.392026	−	1.66923i
$349$	2.68542e7	+	5.88025e7i	0.631736	+	1.38331i	0.906668	+	0.421846i	$0.138618\pi$
$349$	2.68542e7	+	5.88025e7i	0.631736	+	1.38331i	−0.274931	+	0.961464i	$0.588655\pi$
$350$	−6.15200e6	+	2.09518e7i	−0.143487	+	0.488671i
$351$	1.28125e6	+	5.82886e7i	0.0296287	+	1.34791i
$352$	−6.74517e7	+	7.78434e7i	−1.54655	+	1.78482i
$353$	4.05190e7	+	5.82576e6i	0.921160	+	0.132443i	0.586549	−	0.809914i	$-0.300486\pi$
$353$	4.05190e7	+	5.82576e6i	0.921160	+	0.132443i	0.334611	+	0.942356i	$0.391395\pi$
$354$	−7.95650e6	+	9.03113e7i	−0.179354	+	2.03579i
$355$	−1.81650e7	−	2.09635e7i	−0.406023	−	0.468575i
$356$	3.90631e7	+	6.07834e7i	0.865799	+	1.34721i
$357$	−1.29831e6	+	260108.i	−0.0285348	+	0.00571674i
$358$	−3.69946e7	−	4.26941e7i	−0.806287	−	0.930505i
$359$	3.40967e6	+	1.16123e7i	0.0736934	+	0.250977i	0.988098	−	0.153824i	$-0.0491590\pi$
$359$	3.40967e6	+	1.16123e7i	0.0736934	+	0.250977i	−0.914405	+	0.404801i	$0.867341\pi$
$360$	543739.	−	440646.i	0.0116542	−	0.00944458i
$361$	−18668.0	+	21544.0i	−0.000396805	+	0.000457937i
$362$	−1.71971e7	−	7.85366e6i	−0.362519	−	0.165557i
$363$	5.17143e7	−	6.67609e7i	1.08116	−	1.39573i
$364$	1.49423e7	+	3.27191e7i	0.309823	+	0.678417i
$365$	3.92320e7	−	5.64071e6i	0.806793	−	0.115999i
$366$	4.22808e7	+	5.84639e7i	0.862383	+	1.19246i
$367$	6.68967e7			1.35334			0.676670	−	0.736287i	$-0.263422\pi$
$367$	6.68967e7			1.35334			0.676670	+	0.736287i	$0.263422\pi$
$368$	−4.80904e7	−	8.95682e6i	−0.964973	−	0.179726i
$369$	−2.61704e7	+	2.82646e7i	−0.520873	+	0.562553i
$370$	−3.19620e7	−	2.05407e7i	−0.630998	−	0.405518i
$371$	1.49818e7	−	2.15406e6i	0.293389	−	0.0421829i
$372$	−3.51868e7	+	1.93461e6i	−0.683520	+	0.0375807i
$373$	−5.41422e7	−	1.58976e7i	−1.04330	−	0.306340i	−0.285192	−	0.958470i	$-0.592058\pi$
$373$	−5.41422e7	−	1.58976e7i	−1.04330	−	0.306340i	−0.758107	+	0.652130i	$0.773876\pi$
$374$	−6.02126e6	−	2.74982e6i	−0.115099	−	0.0525641i
$375$	−4.52035e7	+	2.37248e7i	−0.857192	+	0.449892i
$376$	−138025.	+	959987.i	−0.00259654	+	0.0180593i
$377$	3.42776e7	+	1.16739e8i	0.639715	+	2.17867i
$378$	1.64806e7	−	3.82928e7i	0.305139	−	0.708993i
$379$	7.35964e7	−	4.72975e7i	1.35188	−	0.868802i	0.354090	−	0.935211i	$-0.384791\pi$
$379$	7.35964e7	−	4.72975e7i	1.35188	−	0.868802i	0.997792	+	0.0664094i	$0.0211543\pi$
$380$	−1.76211e7	−	2.74189e7i	−0.321130	−	0.499688i
$381$	−7.91463e7	+	2.80437e7i	−1.43105	+	0.507062i
$382$	−8.08258e7	+	2.37326e7i	−1.44997	+	0.425751i
$383$	−2.81189e7	−	4.04289e6i	−0.500498	−	0.0719608i	−0.112558	−	0.993645i	$-0.535904\pi$
$383$	−2.81189e7	−	4.04289e6i	−0.500498	−	0.0719608i	−0.387941	+	0.921684i	$0.626813\pi$
$384$	−2.57859e6	+	1.35336e6i	−0.0455395	+	0.0239011i
$385$	1.24931e7	−	2.73561e7i	0.218921	−	0.479371i
$386$	1.98499e7	−	6.76025e7i	0.345141	−	1.17544i
$387$	−1.42630e7	+	4.32502e7i	−0.246080	+	0.746199i
$388$	−3.19688e6	−	2.22348e7i	−0.0547307	−	0.380660i
$389$	−5.42915e7	+	8.44793e7i	−0.922324	+	1.43516i	−0.0220904	+	0.999756i	$0.507032\pi$
$389$	−5.42915e7	+	8.44793e7i	−0.922324	+	1.43516i	−0.900233	+	0.435408i	$0.856604\pi$
$390$	−2.41767e7	+	6.16966e7i	−0.407571	+	1.04008i
$391$	−324285.	−	3.18522e6i	−0.00542496	−	0.0532855i
$392$			1.09188e6i			0.0181267i
$393$	−3.52315e7	−	4.87164e7i	−0.580435	−	0.802597i
$394$	2.14516e6	+	1.49199e7i	0.0350729	+	0.243937i
$395$	−2.61295e7	+	1.19330e7i	−0.423975	+	0.193623i
$396$	9.02732e7	−	5.38980e7i	1.45370	−	0.867935i
$397$	−6.48538e6	+	1.42010e7i	−0.103649	+	0.226959i	−0.954350	−	0.298690i	$-0.903450\pi$
$397$	−6.48538e6	+	1.42010e7i	−0.103649	+	0.226959i	0.850701	+	0.525649i	$0.176178\pi$
$398$	1.34490e7	+	1.16536e7i	0.213324	+	0.184847i
$399$	−3.00244e7	−	1.70425e7i	−0.472667	−	0.268297i
$400$	3.97717e7	−	1.16780e7i	0.621432	−	0.182469i
$401$	6.72601e7	−	5.82812e7i	1.04310	−	0.903848i	0.0476203	−	0.998866i	$-0.484836\pi$
$401$	6.72601e7	−	5.82812e7i	1.04310	−	0.903848i	0.995476	+	0.0950178i	$0.0302908\pi$
$402$	−2.12679e7	+	4.26088e6i	−0.327376	+	0.0655875i
$403$	4.99141e7	−	3.20779e7i	0.762620	−	0.490106i
$404$	1.62934e7	−	1.41183e7i	0.247097	−	0.214111i
$405$	3.62269e7	−	1.37395e7i	0.545338	−	0.206826i
$406$	1.23809e7	−	8.61114e7i	0.185002	−	1.28672i
$407$	−7.67059e7	−	6.64661e7i	−1.13775	−	0.985863i
$408$	−65058.4	−	67238.0i	−0.000957906	−	0.000989998i
$409$	2.26601e7	+	6.65362e6i	0.331202	+	0.0972496i	0.443106	−	0.896469i	$-0.353877\pi$
$409$	2.26601e7	+	6.65362e6i	0.331202	+	0.0972496i	−0.111904	+	0.993719i	$0.535695\pi$
$410$	−3.98238e7	+	1.81869e7i	−0.577818	+	0.263881i
$411$	−1.51887e7	+	6.46728e7i	−0.218773	+	0.931528i
$412$	3.80049e7	+	2.44243e7i	0.543436	+	0.349245i
$413$			5.50631e7i			0.781647i
$414$	8.83326e7	+	4.85650e7i	1.24486	+	0.684420i
$415$	−4.14252e7			−0.579589
$416$	7.45221e7	−	1.15959e8i	1.03515	−	1.61073i
$417$	6.37698e7	+	1.49766e7i	0.879441	+	0.206540i
$418$	−7.16970e7	−	1.56995e8i	−0.981685	−	2.14959i
$419$	−3.30580e6	+	1.12585e7i	−0.0449402	+	0.153052i	−0.978906	−	0.204309i	$-0.934505\pi$
$419$	−3.30580e6	+	1.12585e7i	−0.0449402	+	0.153052i	0.933966	+	0.357361i	$0.116323\pi$
$420$	1.71784e7	−	1.66215e7i	0.231865	−	0.224349i
$421$	−5.06981e7	+	5.85087e7i	−0.679431	+	0.784105i	−0.985821	−	0.167801i	$-0.946333\pi$
$421$	−5.06981e7	+	5.85087e7i	−0.679431	+	0.784105i	0.306390	+	0.951906i	$0.400879\pi$
$422$	1.63267e8	+	2.34743e7i	2.17251	+	0.312359i
$423$	−2.39009e7	+	4.80779e7i	−0.315786	+	0.635221i
$424$	700366.	+	808265.i	0.00918813	+	0.0106037i
$425$	1.46675e6	+	2.28231e6i	0.0191068	+	0.0297308i
$426$	−2.29342e7	−	1.14474e8i	−0.296657	−	1.48074i
$427$	2.86964e7	+	3.31175e7i	0.368591	+	0.425376i
$428$	−2.39033e7	−	8.14072e7i	−0.304878	−	1.03832i
$429$	−8.73852e7	+	1.53949e8i	−1.10679	+	1.94987i
$430$	−3.38959e7	+	3.91179e7i	−0.426326	+	0.492006i
$431$	7.98389e7	+	3.64612e7i	0.997201	+	0.455406i	0.846050	−	0.533104i	$-0.178975\pi$
$431$	7.98389e7	+	3.64612e7i	0.997201	+	0.455406i	0.151151	+	0.988511i	$0.451702\pi$
$432$	−7.80636e7	+	1.29808e7i	−0.968272	+	0.161009i
$433$	5.73657e6	+	1.25613e7i	0.0706624	+	0.154729i	0.941667	−	0.336545i	$-0.109259\pi$
$433$	5.73657e6	+	1.25613e7i	0.0706624	+	0.154729i	−0.871005	+	0.491274i	$0.836531\pi$
$434$	−4.19936e7	+	6.03778e6i	−0.513706	+	0.0738597i
$435$	6.55159e7	−	4.73808e7i	0.795938	−	0.575619i
$436$	1.00688e7			0.121483
$437$	4.79958e7	−	6.83015e7i	0.575121	−	0.818439i
$438$	1.55322e8	+	6.08650e7i	1.84846	+	0.724344i
$439$	1.13484e8	+	7.29316e7i	1.34134	+	0.862029i	0.997044	−	0.0768307i	$-0.0244801\pi$
$439$	1.13484e8	+	7.29316e7i	1.34134	+	0.862029i	0.344299	+	0.938860i	$0.388116\pi$
$440$	2.10336e6	−	302417.i	0.0246919	−	0.00355016i
$441$	−1.89311e7	+	5.74054e7i	−0.220729	+	0.669325i
$442$	8.49955e6	+	2.49569e6i	0.0984304	+	0.0289018i
$443$	−1.81116e7	−	8.27128e6i	−0.208327	−	0.0951397i	0.308519	−	0.951218i	$-0.400167\pi$
$443$	−1.81116e7	−	8.27128e6i	−0.208327	−	0.0951397i	−0.516846	+	0.856079i	$0.672894\pi$
$444$	−3.74903e7	−	7.14314e7i	−0.428322	−	0.816094i
$445$	−1.15052e7	+	8.00204e7i	−0.130561	+	0.908073i
$446$	−4.11600e7	−	1.40178e8i	−0.463950	−	1.58007i
$447$	1.66715e7	+	4.70511e7i	0.186661	+	0.526802i
$448$	−4.25736e7	+	2.73604e7i	−0.473485	+	0.304290i
$449$	1.87960e7	+	2.92471e7i	0.207647	+	0.323105i	0.929419	−	0.369025i	$-0.120308\pi$
$449$	1.87960e7	+	2.92471e7i	0.207647	+	0.323105i	−0.721772	+	0.692131i	$0.756672\pi$
$450$	−8.53700e7	−	2.81380e6i	−0.936845	−	0.0308785i
$451$	−1.12218e8	+	3.29502e7i	−1.22330	+	0.359194i
$452$	1.36598e8	+	1.96398e7i	1.47921	+	0.212678i
$453$	−1.39042e7	−	2.64921e7i	−0.149573	−	0.284985i
$454$	9.46534e7	−	2.07262e8i	1.01151	−	2.21489i
$455$	−1.13386e7	+	3.86156e7i	−0.120372	+	0.409948i
$456$	−133920.	−	2.43576e6i	−0.00141238	−	0.0256885i
$457$	−2.24212e7	−	1.55943e8i	−0.234915	−	1.63387i	−0.676352	−	0.736579i	$-0.736440\pi$
$457$	−2.24212e7	−	1.55943e8i	−0.234915	−	1.63387i	0.441437	−	0.897292i	$-0.354469\pi$
$458$	1.15629e8	−	1.79922e8i	1.20356	−	1.87278i
$459$	−2.25465e6	−	4.66300e6i	−0.0233153	−	0.0482200i
$460$	3.60122e7	+	4.52079e7i	0.369978	+	0.464452i
$461$			2.99222e7i			0.305415i	0.988271	+	0.152708i	$0.0487993\pi$
$461$			2.99222e7i			0.305415i	−0.988271	+	0.152708i	$0.951201\pi$
$462$	1.02566e8	−	7.41754e7i	1.04011	−	0.752201i
$463$	−1.84386e7	−	1.28243e8i	−0.185774	−	1.29209i	−0.842803	−	0.538222i	$-0.819096\pi$
$463$	−1.84386e7	−	1.28243e8i	−0.185774	−	1.29209i	0.657029	−	0.753865i	$-0.271813\pi$
$464$	−1.50218e8	+	6.86023e7i	−1.50372	+	0.686728i
$465$	−3.11714e7	−	2.41460e7i	−0.310026	−	0.240152i
$466$	−1.24979e7	+	2.73666e7i	−0.123504	+	0.270435i
$467$	−5.65804e7	−	4.90272e7i	−0.555540	−	0.481378i	0.331255	−	0.943541i	$-0.392528\pi$
$467$	−5.65804e7	−	4.90272e7i	−0.555540	−	0.481378i	−0.886795	+	0.462163i	$0.847073\pi$
$468$	−1.09312e8	+	8.85866e7i	−1.06643	+	0.864232i
$469$	−1.26401e7	+	3.71148e6i	−0.122527	+	0.0359773i
$470$	−4.61183e7	+	3.99617e7i	−0.444201	+	0.384902i
$471$	−2.09311e7	−	1.04476e8i	−0.200322	−	0.999897i
$472$	−3.27307e6	+	2.10347e6i	−0.0311264	+	0.0200037i
$473$	−1.04501e8	+	9.05506e7i	−0.987499	+	0.855673i
$474$	−1.20435e8	−	1.06105e7i	−1.13089	−	0.0996320i
$475$	−1.00669e7	+	7.00166e7i	−0.0939320	+	0.653311i
$476$	−2.41497e6	−	2.09258e6i	−0.0223919	−	0.0194027i
$477$	2.28078e7	+	5.46372e7i	0.210150	+	0.503424i
$478$	4.53940e6	+	1.33289e6i	0.0415638	+	0.0122042i
$479$	1.01081e8	−	4.61619e7i	0.919731	−	0.420027i	0.101447	−	0.994841i	$-0.467653\pi$
$479$	1.01081e8	−	4.61619e7i	0.919731	−	0.420027i	0.818284	+	0.574814i	$0.194925\pi$
$480$	−8.91750e7	−	2.09431e7i	−0.806342	−	0.189373i
$481$	1.14264e8	+	7.34332e7i	1.02677	+	0.659868i
$482$			2.26896e8i			2.02622i
$483$	5.60305e7	+	2.46739e7i	0.497260	+	0.218976i
$484$	2.03796e8			1.79746
$485$	1.35885e7	−	2.11441e7i	0.119109	−	0.185338i
$486$	1.61148e8	+	2.49770e7i	1.40384	+	0.217586i
$487$	−4.67056e7	−	1.02271e8i	−0.404373	−	0.885454i	−0.996808	−	0.0798355i	$-0.974560\pi$
$487$	−4.67056e7	−	1.02271e8i	−0.404373	−	0.885454i	0.592435	−	0.805618i	$-0.298167\pi$
$488$	−872336.	+	2.97090e6i	−0.00750627	+	0.0255640i
$489$	1.73551e7	+	1.79366e7i	0.148423	+	0.153396i
$490$	−4.49896e7	+	5.19208e7i	−0.382405	+	0.441319i
$491$	1.14419e8	+	1.64510e7i	0.966618	+	0.138979i	0.607506	−	0.794315i	$-0.292170\pi$
$491$	1.14419e8	+	1.64510e7i	0.966618	+	0.138979i	0.359113	+	0.933294i	$0.383079\pi$
$492$	−9.26007e7	−	8.15819e6i	−0.777533	−	0.0685013i
$493$	−7.07816e6	−	8.16863e6i	−0.0590717	−	0.0681724i
$494$	1.24871e8	+	1.94302e8i	1.03581	+	1.61175i
$495$	1.15827e8	+	2.05685e7i	0.954977	+	0.169585i
$496$	5.27386e7	+	6.08636e7i	0.432199	+	0.498784i
$497$	−1.99770e7	−	6.80355e7i	−0.162728	−	0.554200i
$498$	−1.51629e8	−	8.60684e7i	−1.22771	−	0.696877i
$499$	−1.61363e7	+	1.86223e7i	−0.129868	+	0.149876i	−0.816959	−	0.576695i	$-0.804342\pi$
$499$	−1.61363e7	+	1.86223e7i	−0.129868	+	0.149876i	0.687091	+	0.726571i	$0.258887\pi$
$500$	−1.12068e8	−	5.11795e7i	−0.896541	−	0.409436i
$501$	−9.23055e6	−	7.15017e6i	−0.0734031	−	0.0568595i
$502$	9.69012e7	+	2.12184e8i	0.765981	+	1.67726i
$503$	−1.37509e8	+	1.97708e7i	−1.08050	+	0.155353i	−0.659499	−	0.751705i	$-0.729232\pi$
$503$	−1.37509e8	+	1.97708e7i	−1.08050	+	0.155353i	−0.421005	+	0.907058i	$0.638323\pi$
$504$	1.73227e6	−	447216.i	0.0135308	−	0.00349322i
$505$	2.41224e7			0.187304
$506$	1.54687e8	+	2.64095e8i	1.19400	+	2.03849i
$507$	3.88830e7	−	9.92258e7i	0.298357	−	0.761379i
$508$	−1.70470e8	−	1.09554e8i	−1.30034	−	0.835678i
$509$	3.76176e6	−	540860.i	0.0285258	−	0.00410140i	−0.128037	−	0.991769i	$-0.540868\pi$
$509$	3.76176e6	−	540860.i	0.0285258	−	0.00410140i	0.156563	+	0.987668i	$0.449959\pi$
$510$	−323174.	−	5.87792e6i	−0.00243627	−	0.0443112i
$511$	9.72149e7	+	2.85449e7i	0.728568	+	0.213927i
$512$	1.73269e8	+	7.91292e7i	1.29095	+	0.589558i
$513$	3.51903e7	−	1.30381e8i	0.260658	−	0.965745i
$514$	1.73858e7	−	1.20921e8i	0.128028	−	0.890455i
$515$	1.42409e7	+	4.84999e7i	0.104259	+	0.355074i
$516$	−1.03593e8	+	3.67060e7i	−0.754020	+	0.267170i
$517$	−1.37141e8	+	8.81351e7i	−0.992419	+	0.637789i
$518$	−5.25076e7	−	8.17035e7i	−0.377775	−	0.587829i
$519$	−6.19294e7	−	1.74780e8i	−0.442991	−	1.25023i
$520$	−2.72854e6	+	801171.i	−0.0194053	+	0.00569791i
$521$	6.00054e7	+	8.62748e6i	0.424304	+	0.0610057i	0.351160	−	0.936316i	$-0.385787\pi$
$521$	6.00054e7	+	8.62748e6i	0.424304	+	0.0610057i	0.0731445	+	0.997321i	$0.476697\pi$
$522$	3.38252e8	−	3.73077e7i	2.37809	−	0.262293i
$523$	2.42324e7	−	5.30616e7i	0.169392	−	0.370916i	−0.805830	−	0.592147i	$-0.798280\pi$
$523$	2.42324e7	−	5.30616e7i	0.169392	−	0.370916i	0.975221	+	0.221232i	$0.0710077\pi$
$524$	4.08764e7	−	1.39212e8i	0.284105	−	0.967572i
$525$	−5.17995e7	+	2.84799e6i	−0.357971	+	0.0196816i
$526$	1.92011e7	+	1.33547e8i	0.131938	+	0.917646i
$527$	−2.84973e6	+	4.43426e6i	−0.0194703	+	0.0302963i
$528$	−2.23712e8	−	8.76647e7i	−1.51980	−	0.595556i
$529$	−7.24071e7	+	1.29119e8i	−0.489119	+	0.872217i
$530$			6.72919e7i			0.451997i
$531$	−2.08551e8	+	5.38411e7i	−1.39293	+	0.359609i
$532$	−1.18572e7	−	8.24683e7i	−0.0787491	−	0.547712i
$533$	1.42370e8	−	6.50184e7i	0.940239	−	0.429393i
$534$	−2.08370e8	+	2.68996e8i	−1.36839	+	1.76654i
$535$	3.94357e7	−	8.63520e7i	0.257530	−	0.563912i
$536$	−703486.	−	609574.i	−0.00456837	−	0.00395851i
$537$	6.62528e7	−	1.16720e8i	0.427840	−	0.753739i
$538$	−1.05841e8	+	3.10778e7i	−0.679687	+	0.199574i
$539$	−1.38703e8	+	1.20187e8i	−0.885767	+	0.767521i
$540$	7.97510e7	+	4.88103e7i	0.506471	+	0.309978i
$541$	−2.40682e8	+	1.54677e8i	−1.52003	+	0.976864i	−0.528225	+	0.849104i	$0.677142\pi$
$541$	−2.40682e8	+	1.54677e8i	−1.52003	+	0.976864i	−0.991805	+	0.127760i	$0.959221\pi$
$542$	−8.19874e7	+	7.10425e7i	−0.514932	+	0.446191i
$543$	3.94179e6	−	4.47418e7i	0.0246203	−	0.279456i
$544$	−1.74271e6	+	1.21208e7i	−0.0108250	+	0.0752896i
$545$	8.51411e6	+	7.37752e6i	0.0525956	+	0.0455744i
$546$	−1.21734e8	+	1.17788e8i	−0.747882	+	0.723638i
$547$	5.72196e6	+	1.68012e6i	0.0349609	+	0.0102654i	0.299166	−	0.954201i	$-0.403291\pi$
$547$	5.72196e6	+	1.68012e6i	0.0349609	+	0.0102654i	−0.264205	+	0.964466i	$0.585110\pi$
$548$	−1.45832e8	+	6.65995e7i	−0.886161	+	0.404696i
$549$	−9.73723e7	+	1.41070e8i	−0.588462	+	0.852545i
$550$	−2.18175e8	−	1.40213e8i	−1.31135	−	0.842751i
$551$		−	2.81818e8i		−	1.68467i
$552$	673759.	+	4.27315e6i	0.00400578	+	0.0254057i
$553$	−7.34299e7			−0.434208
$554$	1.54178e8	−	2.39905e8i	0.906760	−	1.41095i
$555$	2.06371e7	−	8.78719e7i	0.120717	−	0.514009i
$556$	6.56695e7	+	1.43796e8i	0.382067	+	0.836610i
$557$	7.66250e7	−	2.60961e8i	0.443409	−	1.51011i	−0.370339	−	0.928896i	$-0.620759\pi$
$557$	7.66250e7	−	2.60961e8i	0.443409	−	1.51011i	0.813749	−	0.581217i	$-0.197423\pi$
$558$	−6.39297e7	−	1.53147e8i	−0.367959	−	0.881464i
$559$	1.21178e8	−	1.39847e8i	0.693727	−	0.800603i
$560$	−5.40705e7	−	7.77417e6i	−0.307891	−	0.0442680i
$561$	1.38014e6	−	1.56655e7i	0.00781692	−	0.0887270i
$562$	1.06542e8	+	1.22956e8i	0.600222	+	0.692693i
$563$	1.78215e8	+	2.77309e8i	0.998666	+	1.55395i	0.821845	+	0.569712i	$0.192945\pi$
$563$	1.78215e8	+	2.77309e8i	0.998666	+	1.55395i	0.176821	+	0.984243i	$0.443419\pi$
$564$	−1.27047e8	+	2.54531e7i	−0.708156	+	0.141874i
$565$	1.01116e8	+	1.16695e8i	0.560630	+	0.647002i
$566$	−8.57510e7	−	2.92041e8i	−0.472922	−	1.61062i
$567$	9.88273e7	+	6.52180e6i	0.542160	+	0.0357782i
$568$	3.28103e6	−	3.78651e6i	0.0179046	−	0.0206630i
$569$	1.94064e8	+	8.86262e7i	1.05344	+	0.481089i	0.865405	−	0.501074i	$-0.167061\pi$
$569$	1.94064e8	+	8.86262e7i	1.05344	+	0.481089i	0.188033	+	0.982163i	$0.439789\pi$
$570$	9.39940e7	−	1.21342e8i	0.507546	−	0.655219i
$571$	−8.84102e7	−	1.93591e8i	−0.474891	−	1.03987i	−0.983837	−	0.179068i	$-0.942692\pi$
$571$	−8.84102e7	−	1.93591e8i	−0.474891	−	1.03987i	0.508946	−	0.860799i	$-0.330035\pi$
$572$	−4.22855e8	+	6.07973e7i	−2.25945	+	0.324860i
$573$	−1.17277e8	−	1.62166e8i	−0.623377	−	0.861975i
$574$	−1.11914e8			−0.591764
$575$	5.18421e6	−	1.25333e8i	0.0272696	−	0.659266i
$576$	−1.45256e8	−	1.34494e8i	−0.760091	−	0.703775i
$577$	1.50551e8	+	9.67533e7i	0.783712	+	0.503661i	0.870264	−	0.492586i	$-0.163948\pi$
$577$	1.50551e8	+	9.67533e7i	0.783712	+	0.503661i	−0.0865515	+	0.996247i	$0.527585\pi$
$578$	2.70748e8	−	3.89276e7i	1.40211	−	0.201592i
$579$	1.67135e8	−	9.18927e6i	0.861057	−	0.0473418i
$580$	1.87219e8	+	5.49723e7i	0.959544	+	0.281748i
$581$	−9.63246e7	−	4.39900e7i	−0.491144	−	0.224298i
$582$	9.36689e7	−	4.91616e7i	0.475145	−	0.249377i
$583$	−2.55834e7	+	1.77936e8i	−0.129108	+	0.897963i
$584$	2.01695e6	+	6.86911e6i	0.0101265	+	0.0344875i
$585$	−1.57343e8	−	5.18603e6i	−0.785922	−	0.0259041i
$586$	1.22700e8	−	7.88542e7i	0.609748	−	0.391861i
$587$	−1.61391e8	−	2.51130e8i	−0.797931	−	1.24161i	−0.966691	−	0.255948i	$-0.917612\pi$
$587$	−1.61391e8	−	2.51130e8i	−0.797931	−	1.24161i	0.168759	−	0.985657i	$-0.446024\pi$
$588$	−1.37498e8	+	4.87195e7i	−0.676340	+	0.239646i
$589$	−1.31866e8	+	3.87194e7i	−0.645339	+	0.189489i
$590$	−2.42311e8	−	3.48390e7i	−1.17982	−	0.169633i
$591$	−3.17087e7	+	1.66421e7i	−0.153609	+	0.0806206i
$592$	−7.65859e7	+	1.67700e8i	−0.369134	+	0.808290i
$593$	−4.66878e7	+	1.59004e8i	−0.223892	+	0.762507i	0.768549	+	0.639790i	$0.220979\pi$
$593$	−4.66878e7	+	1.59004e8i	−0.223892	+	0.762507i	−0.992442	+	0.122717i	$0.960839\pi$
$594$	3.81228e8	+	3.15939e8i	1.81897	+	1.50745i
$595$	−508826.	−	3.53896e6i	−0.00241556	−	0.0168006i
$596$	−6.51283e7	+	1.01342e8i	−0.307632	+	0.478684i
$597$	−1.54252e7	+	3.93635e7i	−0.0724948	+	0.185000i
$598$	−2.55198e8	−	3.20363e8i	−1.19337	−	1.49809i
$599$			8.09208e7i			0.376513i	0.982120	+	0.188256i	$0.0602836\pi$
$599$			8.09208e7i			0.376513i	−0.982120	+	0.188256i	$0.939716\pi$
$600$	−2.14809e6	−	2.97028e6i	−0.00994487	−	0.0137513i
$601$	4.36579e6	+	3.03647e7i	0.0201112	+	0.139877i	0.997403	−	0.0720207i	$-0.0229448\pi$
$601$	4.36579e6	+	3.03647e7i	0.0201112	+	0.139877i	−0.977292	+	0.211898i	$0.932036\pi$
$602$	−1.20357e8	+	5.49651e7i	−0.551672	+	0.251940i
$603$	−2.64168e7	−	4.42452e7i	−0.120484	−	0.201797i
$604$	2.99944e7	−	6.56787e7i	0.136123	−	0.298067i
$605$	1.72329e8	+	1.49324e8i	0.778203	+	0.674317i
$606$	8.82957e7	+	5.01187e7i	0.396754	+	0.225207i
$607$	2.70874e8	−	7.95359e7i	1.21116	−	0.355629i	0.387051	−	0.922058i	$-0.373494\pi$
$607$	2.70874e8	−	7.95359e7i	1.21116	−	0.355629i	0.824110	+	0.566429i	$0.191676\pi$
$608$	−2.41296e8	+	2.09084e8i	−1.07359	+	0.930272i
$609$	2.02656e8	−	4.06008e7i	0.897240	−	0.179756i
$610$	−1.63893e8	+	1.05328e8i	−0.722056	+	0.464037i
$611$	1.64873e8	−	1.42863e8i	0.722814	−	0.626322i
$612$	5.56424e6	−	1.11928e7i	0.0242746	−	0.0488297i
$613$	1.65941e7	−	1.15415e8i	0.0720399	−	0.501048i	−0.921573	−	0.388205i	$-0.873095\pi$
$613$	1.65941e7	−	1.15415e8i	0.0720399	−	0.501048i	0.993613	−	0.112843i	$-0.0359958\pi$
$614$	−2.15442e8	−	1.86681e8i	−0.930733	−	0.806485i
$615$	−7.23253e7	−	7.47484e7i	−0.310932	−	0.321349i
$616$	5.21201e6	+	1.53038e6i	0.0222978	+	0.00654724i
$617$	−3.58369e8	+	1.63662e8i	−1.52572	+	0.696773i	−0.989126	−	0.147068i	$-0.953016\pi$
$617$	−3.58369e8	+	1.63662e8i	−1.52572	+	0.696773i	−0.536593	+	0.843841i	$0.680289\pi$
$618$	−4.86414e7	+	2.07113e8i	−0.206082	+	0.877490i
$619$	−3.67776e8	−	2.36355e8i	−1.55064	−	0.996536i	−0.985133	−	0.171792i	$-0.945044\pi$
$619$	−3.67776e8	−	2.36355e8i	−1.55064	−	0.996536i	−0.565507	−	0.824744i	$-0.691319\pi$
$620$		−	9.51547e7i		−	0.399259i
$621$	−3.86651e7	+	2.36341e8i	−0.161452	+	0.986881i
$622$	3.99716e8			1.66104
$623$	−1.11728e8	+	1.73851e8i	−0.462057	+	0.718976i
$624$	3.13028e8	+	7.35158e7i	1.28833	+	0.302571i
$625$	9.65564e6	+	2.11429e7i	0.0395495	+	0.0866013i
$626$	1.21960e8	−	4.15358e8i	0.497158	−	1.69316i
$627$	2.94675e8	−	2.85123e8i	1.19548	−	1.15672i
$628$	1.68392e8	−	1.94334e8i	0.679895	−	0.784641i
$629$	−1.19437e7	−	1.71724e6i	−0.0479939	−	0.00690049i
$630$	1.00799e8	+	5.01100e7i	0.403120	+	0.200402i
$631$	1.35616e8	+	1.56510e8i	0.539789	+	0.622950i	0.958473	−	0.285182i	$-0.0920541\pi$
$631$	1.35616e8	+	1.56510e8i	0.539789	+	0.622950i	−0.418684	+	0.908132i	$0.637509\pi$
$632$	−2.80511e6	−	4.36483e6i	−0.0111122	−	0.0172908i
$633$	7.69790e7	+	3.84236e8i	0.303502	+	1.51491i
$634$	3.93706e8	+	4.54361e8i	1.54492	+	1.78293i
$635$	−6.38769e7	−	2.17545e8i	−0.249473	−	0.849626i
$636$	−7.05328e7	+	1.24260e8i	−0.274170	+	0.483014i
$637$	1.60838e8	−	1.85617e8i	0.622258	−	0.718125i
$638$	9.39872e8	+	4.29225e8i	3.61915	+	1.65281i
$639$	2.38150e8	−	1.42188e8i	0.912741	−	0.544955i
$640$	−3.26657e6	−	7.15280e6i	−0.0124610	−	0.0272857i
$641$	−2.67179e8	+	3.84146e7i	−1.01445	+	0.145855i	−0.629432	−	0.777056i	$-0.716712\pi$
$641$	−2.67179e8	+	3.84146e7i	−1.01445	+	0.145855i	−0.385014	+	0.922911i	$0.625803\pi$
$642$	3.23760e8	−	2.34141e8i	1.22354	−	0.884857i
$643$	7.62629e7			0.286867			0.143433	−	0.989660i	$-0.454186\pi$
$643$	7.62629e7			0.286867			0.143433	+	0.989660i	$0.454186\pi$
$644$	3.57310e7	+	1.43362e8i	0.133779	+	0.536757i
$645$	−1.14493e8	−	4.48658e7i	−0.426679	−	0.167200i
$646$	−1.72614e7	−	1.10932e7i	−0.0640293	−	0.0411491i
$647$	1.37530e8	−	1.97738e7i	0.507790	−	0.0730091i	0.116341	−	0.993209i	$-0.462883\pi$
$647$	1.37530e8	−	1.97738e7i	0.507790	−	0.0730091i	0.391448	+	0.920200i	$0.371974\pi$
$648$	3.38765e6	+	6.12365e6i	0.0124501	+	0.0225053i
$649$	−6.27483e8	−	1.84246e8i	−2.29545	−	0.674005i
$650$	3.15701e8	+	1.44176e8i	1.14957	+	0.524992i
$651$	−4.68409e7	−	8.92473e7i	−0.169778	−	0.323483i
$652$	−8.57188e6	+	5.96187e7i	−0.0309267	+	0.215100i
$653$	−8.97116e7	−	3.05530e8i	−0.322188	−	1.09727i	−0.948257	−	0.317504i	$-0.897155\pi$
$653$	−8.97116e7	−	3.05530e8i	−0.322188	−	1.09727i	0.626069	−	0.779768i	$-0.284663\pi$
$654$	1.58362e7	+	4.46937e7i	0.0566133	+	0.159777i
$655$	1.36568e8	−	8.77668e7i	0.485987	−	0.312325i
$656$	1.14854e8	+	1.78716e8i	0.406850	+	0.633071i
$657$	−1.30559e7	+	3.96111e8i	−0.0460373	+	1.39676i
$658$	−1.49673e8	+	4.39481e7i	−0.525372	+	0.154263i
$659$	2.91640e8	+	4.19315e7i	1.01904	+	0.146516i	0.631531	−	0.775350i	$-0.282427\pi$
$659$	2.91640e8	+	4.19315e7i	1.01904	+	0.146516i	0.387509	+	0.921866i	$0.373336\pi$
$660$	1.31934e8	+	2.51377e8i	0.458906	+	0.874367i
$661$	3.54112e7	−	7.75396e7i	0.122613	−	0.268485i	−0.838365	−	0.545109i	$-0.816488\pi$
$661$	3.54112e7	−	7.75396e7i	0.122613	−	0.268485i	0.960978	+	0.276624i	$0.0892157\pi$
$662$	−1.62072e8	+	5.51966e8i	−0.558642	+	1.90256i
$663$	1.15535e6	+	2.10136e7i	0.00396436	+	0.0721041i
$664$	−1.06485e6	−	7.40621e6i	−0.00363735	−	0.0252983i
$665$	5.03994e7	−	7.84229e7i	0.171380	−	0.266672i
$666$	2.58108e8	−	2.78762e8i	0.873734	−	0.943650i
$667$	5.06183e7	+	4.97188e8i	0.170581	+	1.67550i
$668$		−	2.81774e7i		−	0.0945305i
$669$	2.81248e8	−	2.03397e8i	0.939313	−	0.679307i
$670$	−8.33518e6	−	5.79724e7i	−0.0277134	−	0.192751i
$671$	−4.73417e8	+	2.16202e8i	−1.56703	+	0.715637i
$672$	−1.85116e8	−	1.43394e8i	−0.610009	−	0.472525i
$673$	1.19692e8	−	2.62089e8i	0.392663	−	0.859812i	−0.605299	−	0.795998i	$-0.706946\pi$
$673$	1.19692e8	−	2.62089e8i	0.392663	−	0.859812i	0.997962	−	0.0638139i	$-0.0203264\pi$
$674$	−3.58728e8	−	3.10840e8i	−1.17162	−	1.01521i
$675$	−6.14367e7	−	1.93405e8i	−0.199764	−	0.628864i
$676$	2.46771e8	−	7.24586e7i	0.798830	−	0.234558i
$677$	−3.47601e8	+	3.01198e8i	−1.12025	+	0.970703i	−0.999758	−	0.0220112i	$-0.992993\pi$
$677$	−3.47601e8	+	3.01198e8i	−1.12025	+	0.970703i	−0.120493	+	0.992714i	$0.538448\pi$
$678$	1.27664e8	+	6.37228e8i	0.409619	+	2.04459i
$679$	5.40500e7	−	3.47358e7i	0.172658	−	0.110961i
$680$	190926.	−	165438.i	0.000607208	−	0.000526149i
$681$	5.39234e8	+	4.75069e7i	1.70740	+	0.150423i
$682$	7.17094e7	−	4.98750e8i	0.226060	−	1.57228i
$683$	−2.57534e8	−	2.23154e8i	−0.808300	−	0.700396i	0.149207	−	0.988806i	$-0.452328\pi$
$683$	−2.57534e8	−	2.23154e8i	−0.808300	−	0.700396i	−0.957507	+	0.288410i	$0.906873\pi$
$684$	3.00753e8	−	1.25547e8i	0.939815	−	0.392317i
$685$	−1.72114e8	−	5.05372e7i	−0.535482	−	0.157232i
$686$	−3.86412e8	+	1.76468e8i	−1.19696	+	0.546631i
$687$	4.94652e8	+	1.16171e8i	1.52556	+	0.358284i
$688$	2.11293e8	+	1.35790e8i	0.648813	+	0.416967i
$689$		−	2.40569e8i		−	0.735499i
$690$	−1.44031e8	+	2.30956e8i	−0.438439	+	0.703044i
$691$	3.74839e8			1.13608			0.568042	−	0.823000i	$-0.307701\pi$
$691$	3.74839e8			1.13608			0.568042	+	0.823000i	$0.307701\pi$
$692$	2.41931e8	−	3.76452e8i	0.730084	−	1.13603i
$693$	2.47486e8	+	1.70825e8i	0.743620	+	0.513278i
$694$	−1.71257e7	−	3.75000e7i	−0.0512353	−	0.112190i
$695$	−4.98316e7	+	1.69711e8i	−0.148440	+	0.505539i
$696$	1.01551e7	+	1.04953e7i	0.0301201	+	0.0311292i
$697$	−9.10544e6	+	1.05082e7i	−0.0268907	+	0.0310336i
$698$	−7.27191e8	−	1.04554e8i	−2.13837	−	0.307451i
$699$	−7.11997e7	−	6.27275e6i	−0.208472	−	0.0183665i
$700$	−8.19858e7	−	9.46167e7i	−0.239026	−	0.275850i
$701$	−3.20900e6	−	4.99330e6i	−0.00931570	−	0.0144955i	0.836564	−	0.547869i	$-0.184561\pi$
$701$	−3.20900e6	−	4.99330e6i	−0.00931570	−	0.0144955i	−0.845880	+	0.533373i	$0.820924\pi$
$702$	−5.65151e8	−	3.45891e8i	−1.63363	−	0.999835i
$703$	−2.06029e8	−	2.37770e8i	−0.593010	−	0.684370i
$704$	−1.69336e8	−	5.76705e8i	−0.485323	−	1.65286i
$705$	−1.26081e8	−	7.15665e7i	−0.359817	−	0.204241i
$706$	−3.04658e8	+	3.51594e8i	−0.865763	+	0.999144i
$707$	5.60910e7	+	2.56159e7i	0.158721	+	0.0724855i
$708$	−4.10929e8	−	3.18314e8i	−1.15789	−	0.896924i
$709$	−2.45034e8	−	5.36550e8i	−0.687525	−	1.50547i	−0.854469	−	0.519503i	$-0.826117\pi$
$709$	−2.45034e8	−	5.36550e8i	−0.687525	−	1.50547i	0.166944	−	0.985966i	$-0.446610\pi$
$710$	3.12036e8	−	4.48640e7i	0.871826	−	0.125350i
$711$	−7.18003e7	−	2.78115e8i	−0.199764	−	0.773776i
$712$	−1.46022e7			−0.0404556
$713$	2.25686e8	−	9.19944e7i	0.622639	−	0.253801i
$714$	5.49038e6	−	1.40109e7i	0.0150837	−	0.0384921i
$715$	−4.02112e8	−	2.58422e8i	−1.10009	−	0.706986i
$716$	3.20595e8	−	4.60947e7i	0.873410	−	0.125577i
$717$	617044.	+	1.12229e7i	0.00167401	+	0.0304471i
$718$	−1.31971e8	−	3.87502e7i	−0.356537	−	0.104689i
$719$	−2.16964e8	−	9.90843e7i	−0.583716	−	0.266574i	0.101594	−	0.994826i	$-0.467606\pi$
$719$	−2.16964e8	−	9.90843e7i	−0.583716	−	0.266574i	−0.685310	+	0.728252i	$0.740333\pi$
$720$	−2.34260e7	−	2.12393e8i	−0.0627626	−	0.569040i
$721$	−1.83889e7	+	1.27898e8i	−0.0490626	+	0.341238i
$722$	−91274.3	−	310852.i	−0.000242514	−	0.000825927i
$723$	−5.08097e8	+	1.80033e8i	−1.34441	+	0.476362i
$724$	9.11859e7	−	5.86016e7i	0.240277	−	0.154417i
$725$	−2.28948e8	−	3.56250e8i	−0.600791	−	0.934848i
$726$	3.20532e8	+	9.04621e8i	0.837649	+	2.36405i
$727$	−3.12113e8	+	9.16447e7i	−0.812286	+	0.238509i	−0.661391	−	0.750041i	$-0.730034\pi$
$727$	−3.12113e8	+	9.16447e7i	−0.812286	+	0.238509i	−0.150895	+	0.988550i	$0.548215\pi$
$728$	−7.19536e6	−	1.03454e6i	−0.0186491	−	0.00268134i
$729$	7.19328e7	+	3.80684e8i	0.185671	+	0.982612i
$730$	−1.87123e8	+	4.09743e8i	−0.481016	+	1.05328i
$731$	−4.63137e6	+	1.57730e7i	−0.0118565	+	0.0403796i
$732$	−4.13042e8	+	2.27095e7i	−1.05308	+	0.0578994i
$733$	9.85440e7	+	6.85389e8i	0.250218	+	1.74030i	0.596895	+	0.802319i	$0.296401\pi$
$733$	9.85440e7	+	6.85389e8i	0.250218	+	1.74030i	−0.346677	+	0.937984i	$0.612690\pi$
$734$	−4.11032e8	+	6.39578e8i	−1.03941	+	1.61736i
$735$	−1.51966e8	−	5.95499e7i	−0.382722	−	0.149975i
$736$	3.88144e8	−	4.12209e8i	0.973552	−	1.03391i
$737$		−	1.56462e8i		−	0.390847i
$738$	−1.09430e8	−	4.23872e8i	−0.272250	−	1.05455i
$739$	6.20996e7	+	4.31912e8i	0.153870	+	1.07019i	0.909653	+	0.415369i	$0.136348\pi$
$739$	6.20996e7	+	4.31912e8i	0.153870	+	1.07019i	−0.755782	+	0.654823i	$0.772743\pi$
$740$	1.98145e8	−	9.04897e7i	0.488976	−	0.223308i
$741$	−3.36029e8	+	4.33799e8i	−0.825890	+	1.06619i
$742$	−7.14583e7	+	1.56472e8i	−0.174920	+	0.383022i
$743$	−4.35451e7	−	3.77320e7i	−0.106163	−	0.0919907i	0.600162	−	0.799878i	$-0.295103\pi$
$743$	−4.35451e7	−	3.77320e7i	−0.106163	−	0.0919907i	−0.706325	+	0.707888i	$0.749648\pi$
$744$	3.51567e6	−	6.19367e6i	0.00853669	−	0.0150394i
$745$	−1.29327e8	+	3.79738e7i	−0.312766	+	0.0918364i
$746$	4.84656e8	−	4.19957e8i	1.16739	−	1.01155i
$747$	7.24245e7	−	4.07842e8i	0.173750	−	0.978430i
$748$	3.19271e7	−	2.05183e7i	0.0762877	−	0.0490271i
$749$	1.83397e8	−	1.58914e8i	0.436462	−	0.378197i
$750$	5.09176e7	−	5.77948e8i	0.120694	−	1.36995i
$751$	−8.52744e7	+	5.93096e8i	−0.201326	+	1.40025i	0.599031	+	0.800726i	$0.295553\pi$
$751$	−8.52744e7	+	5.93096e8i	−0.201326	+	1.40025i	−0.800357	+	0.599524i	$0.795357\pi$
$752$	2.23786e8	+	1.93912e8i	0.526235	+	0.455985i
$753$	−3.98265e8	+	3.85354e8i	−0.932797	+	0.902558i
$754$	−1.32671e9	−	3.89558e8i	−3.09502	−	0.908779i
$755$	7.34870e7	−	3.35604e7i	0.170753	−	0.0779805i
$756$	1.33610e8	+	1.98186e8i	0.309224	+	0.458677i
$757$	−1.28880e8	−	8.28260e7i	−0.297096	−	0.190932i	0.383597	−	0.923500i	$-0.374685\pi$
$757$	−1.28880e8	−	8.28260e7i	−0.297096	−	0.190932i	−0.680693	+	0.732568i	$0.738321\pi$
$758$			9.94241e8i			2.28288i
$759$	−4.68659e8	+	5.55946e8i	−1.07184	+	1.27147i
$760$	6.58694e6			0.0150052
$761$	5.43721e7	−	8.46046e7i	0.123374	−	0.191973i	−0.774073	−	0.633097i	$-0.781784\pi$
$761$	5.43721e7	−	8.46046e7i	0.123374	−	0.191973i	0.897446	+	0.441124i	$0.145420\pi$
$762$	2.18179e8	−	9.29000e8i	0.493116	−	2.09967i
$763$	1.19633e7	+	2.61960e7i	0.0269325	+	0.0589740i
$764$	1.36068e8	−	4.63405e8i	0.305124	−	1.03916i
$765$	1.29062e7	−	5.38759e6i	0.0288280	−	0.0120340i
$766$	2.11423e8	−	2.43996e8i	0.470399	−	0.542870i
$767$	8.66262e8	+	1.24550e8i	1.91983	+	0.276030i
$768$	−3.82760e7	+	4.34457e8i	−0.0844973	+	0.959098i
$769$	−2.89274e8	−	3.33840e8i	−0.636108	−	0.734108i	0.342574	−	0.939491i	$-0.388701\pi$
$769$	−2.89274e8	−	3.33840e8i	−0.636108	−	0.734108i	−0.978682	+	0.205383i	$0.934156\pi$
$770$	1.84782e8	+	2.87526e8i	0.404750	+	0.629803i
$771$	2.84578e8	−	5.70132e7i	0.620923	−	0.124398i
$772$	2.64534e8	+	3.05288e8i	0.574948	+	0.663526i
$773$	−9.17698e7	−	3.12539e8i	−0.198683	−	0.676653i	−0.997207	−	0.0746897i	$-0.976203\pi$
$773$	−9.17698e7	−	3.12539e8i	−0.198683	−	0.676653i	0.798523	−	0.601964i	$-0.205615\pi$
$774$	−3.25865e8	−	4.02104e8i	−0.702773	−	0.867193i
$775$	−1.35238e8	+	1.56073e8i	−0.290533	+	0.335293i
$776$	4.12954e6	+	1.88590e6i	0.00883725	+	0.00403584i
$777$	1.41299e8	−	1.82411e8i	0.301215	−	0.388855i
$778$	−4.74097e8	−	1.03813e9i	−1.00677	−	2.20451i
$779$	−3.58844e8	+	5.15940e7i	−0.759091	+	0.109141i
$780$	−2.22636e8	−	3.07851e8i	−0.469150	−	0.648718i
$781$	8.42156e8			1.76783
$782$	3.24454e7	+	1.64705e7i	0.0678473	+	0.0344418i
$783$	3.51934e8	+	7.27858e8i	0.733121	+	1.51622i
$784$	2.80447e8	+	1.80232e8i	0.581972	+	0.374011i
$785$	2.84783e8	−	4.09457e7i	0.588716	−	0.0846445i
$786$	6.82234e8	−	3.75099e7i	1.40497	−	0.0772465i
$787$	1.79220e8	+	5.26238e7i	0.367674	+	0.107959i	0.460350	−	0.887737i	$-0.347724\pi$
$787$	1.79220e8	+	5.26238e7i	0.367674	+	0.107959i	−0.0926760	+	0.995696i	$0.529542\pi$
$788$	−7.86115e7	−	3.59007e7i	−0.160660	−	0.0733709i
$789$	−2.83821e8	+	1.48962e8i	−0.577847	+	0.303280i
$790$	4.64599e7	−	3.23135e8i	0.0942316	−	0.655395i
$791$	1.11203e8	+	3.78723e8i	0.224692	+	0.765231i
$792$	−699967.	+	2.12368e7i	−0.00140897	+	0.0427478i
$793$	5.85919e8	−	3.76547e8i	1.17495	−	0.755092i
$794$	−9.59233e7	−	1.49259e8i	−0.191630	−	0.298181i
$795$	−1.50689e8	+	5.33935e7i	−0.299903	+	0.106264i
$796$	−9.78959e7	+	2.87448e7i	−0.194100	+	0.0569928i
$797$	−3.65975e8	−	5.26192e7i	−0.722897	−	0.103937i	−0.228961	−	0.973435i	$-0.573533\pi$
$797$	−3.65975e8	−	5.26192e7i	−0.722897	−	0.103937i	−0.493935	+	0.869499i	$0.664442\pi$
$798$	3.47416e8	−	1.82339e8i	0.683662	−	0.358816i
$799$	−8.05105e6	+	1.76293e7i	−0.0157838	+	0.0345618i
$800$	−1.35166e8	+	4.60334e8i	−0.263997	+	0.899090i
$801$	−7.67708e8	−	2.53173e8i	−1.49382	−	0.492629i
$802$	1.43943e8	+	1.00115e9i	0.279041	+	1.94077i
$803$	−6.50578e8	+	1.01232e9i	−1.25647	+	1.95511i
$804$	4.53729e7	−	1.15787e8i	0.0873029	−	0.222789i
$805$	−7.48296e7	+	1.47407e8i	−0.143445	+	0.282574i
$806$			6.74308e8i			1.28781i
$807$	−1.53575e8	−	2.12356e8i	−0.292213	−	0.404058i
$808$	620076.	+	4.31273e6i	0.00117547	+	0.00817557i
$809$	7.10600e8	−	3.24520e8i	1.34208	−	0.612909i	0.390586	−	0.920566i	$-0.372272\pi$
$809$	7.10600e8	−	3.24520e8i	1.34208	−	0.612909i	0.951497	+	0.307657i	$0.0995451\pi$
$810$	−9.12288e7	+	4.30773e8i	−0.171663	+	0.810575i
$811$	3.14601e7	−	6.88880e7i	0.0589790	−	0.129146i	−0.877848	−	0.478940i	$-0.841021\pi$
$811$	3.14601e7	−	6.88880e7i	0.0589790	−	0.129146i	0.936827	+	0.349794i	$0.113748\pi$
$812$	3.76957e8	+	3.26635e8i	0.704084	+	0.610092i
$813$	−2.24142e8	−	1.27228e8i	−0.417111	−	0.236762i
$814$	1.10676e9	−	3.24975e8i	2.05202	−	0.602527i
$815$	−5.09318e7	+	4.41327e7i	−0.0940842	+	0.0815244i
$816$	−2.80087e7	+	5.61136e6i	−0.0515494	+	0.0103276i
$817$	−3.60576e8	+	2.31728e8i	−0.661197	+	0.424925i
$818$	−2.02843e8	+	1.75765e8i	−0.370596	+	0.321123i
$819$	−3.60357e8	−	1.79144e8i	−0.655966	−	0.326099i
$820$	3.57222e7	−	2.48453e8i	0.0647882	−	0.450612i
$821$	9.32154e6	+	8.07716e6i	0.0168445	+	0.0145959i	0.663242	−	0.748405i	$-0.269180\pi$
$821$	9.32154e6	+	8.07716e6i	0.0168445	+	0.0145959i	−0.646398	+	0.763001i	$0.723725\pi$
$822$	−5.24992e8	−	5.42581e8i	−0.945230	−	0.976898i
$823$	3.80833e8	+	1.11823e8i	0.683180	+	0.200600i	0.604864	−	0.796329i	$-0.293228\pi$
$823$	3.80833e8	+	1.11823e8i	0.683180	+	0.200600i	0.0783159	+	0.996929i	$0.475046\pi$
$824$	−8.30500e6	+	3.79276e6i	−0.0148442	+	0.00677913i
$825$	1.40870e8	−	5.99821e8i	0.250875	−	1.06822i
$826$	−5.26441e8	−	3.38323e8i	−0.934135	−	0.600332i
$827$		−	8.15354e7i		−	0.144155i	−0.997399	−	0.0720775i	$-0.977037\pi$
$827$		−	8.15354e7i		−	0.144155i	0.997399	−	0.0720775i	$-0.0229629\pi$
$828$	−5.08045e8	+	2.75511e8i	−0.894975	+	0.485343i
$829$	4.62822e8			0.812364			0.406182	−	0.913792i	$-0.366860\pi$
$829$	4.62822e8			0.812364			0.406182	+	0.913792i	$0.366860\pi$
$830$	2.54528e8	−	3.96053e8i	0.445144	−	0.692658i
$831$	6.59563e8	+	1.54901e8i	1.14935	+	0.269930i
$832$	3.34139e8	+	7.31662e8i	0.580172	+	1.27040i
$833$	−6.14717e6	+	2.09353e7i	−0.0106351	+	0.0362197i
$834$	−5.35005e8	+	5.17662e8i	−0.922274	+	0.892376i
$835$	2.06460e7	−	2.38268e7i	0.0354631	−	0.0409266i
$836$	9.79459e8	+	1.40825e8i	1.67636	+	0.241024i
$837$	2.92221e8	−	2.64676e8i	0.498351	−	0.451375i
$838$	−8.73274e7	−	1.00781e8i	−0.148395	−	0.171257i
$839$	−5.01423e8	−	7.80230e8i	−0.849022	−	1.32110i	−0.945451	−	0.325764i	$-0.894379\pi$
$839$	−5.01423e8	−	7.80230e8i	−0.849022	−	1.32110i	0.0964295	−	0.995340i	$-0.469258\pi$
$840$	948964.	+	4.73669e6i	0.00160108	+	0.00799167i
$841$	7.15320e8	+	8.25523e8i	1.20258	+	1.38785i
$842$	−2.47880e8	−	8.44202e8i	−0.415246	−	1.41420i
$843$	−1.90803e8	+	3.36144e8i	−0.318496	+	0.561104i
$844$	−6.19300e8	+	7.14710e8i	−1.03009	+	1.18878i
$845$	2.61761e8	+	1.19542e8i	0.433845	+	0.198130i
$846$	−3.12804e8	−	5.23913e8i	−0.516608	−	0.865262i
$847$	2.42142e8	+	5.30218e8i	0.398493	+	0.872578i
$848$	3.23206e8	−	4.64701e7i	0.530020	−	0.0762054i
$849$	5.85939e8	−	4.23748e8i	0.957479	−	0.692444i
$850$	−3.08325e7			−0.0502056
$851$	4.06186e8	+	3.82472e8i	0.659077	+	0.620599i
$852$	6.23225e8	+	2.44219e8i	1.00769	+	0.394877i
$853$	−8.12767e8	−	5.22334e8i	−1.30954	−	0.841591i	−0.315325	−	0.948984i	$-0.602113\pi$
$853$	−8.12767e8	−	5.22334e8i	−1.30954	−	0.841591i	−0.994217	+	0.107393i	$0.965750\pi$
$854$	−4.92944e8	+	7.08747e7i	−0.791451	+	0.113794i
$855$	3.46306e8	+	1.14204e8i	0.554067	+	0.182719i
$856$	1.64522e7	+	4.83080e6i	0.0262302	+	0.00770189i
$857$	6.02506e8	+	2.75155e8i	0.957236	+	0.437155i	0.831879	−	0.554957i	$-0.187265\pi$
$857$	6.02506e8	+	2.75155e8i	0.957236	+	0.437155i	0.125357	+	0.992112i	$0.459992\pi$
$858$	−9.34940e8	−	1.78137e9i	−1.48021	−	2.82028i
$859$	1.05065e7	−	7.30742e7i	0.0165759	−	0.115288i	−0.979854	−	0.199717i	$-0.935998\pi$
$859$	1.05065e7	−	7.30742e7i	0.0165759	−	0.115288i	0.996429	+	0.0844292i	$0.0269067\pi$
$860$	−8.36075e7	−	2.84741e8i	−0.131447	−	0.447667i
$861$	−8.87992e7	−	2.50613e8i	−0.139123	−	0.392640i
$862$	−8.39146e8	+	5.39286e8i	−1.31013	+	0.841972i
$863$	−1.15538e8	−	1.79781e8i	−0.179760	−	0.279712i	0.739667	−	0.672973i	$-0.234983\pi$
$863$	−1.15538e8	−	1.79781e8i	−0.179760	−	0.279712i	−0.919427	+	0.393261i	$0.871347\pi$
$864$	3.62097e8	−	8.41336e8i	0.561414	−	1.30445i
$865$	4.80408e8	−	1.41060e8i	0.742270	−	0.217950i
$866$	−1.55342e8	−	2.23348e7i	−0.239186	−	0.0343897i
$867$	3.02000e8	+	5.75408e8i	0.463392	+	0.882915i
$868$	1.01046e8	−	2.21260e8i	0.154511	−	0.338333i
$869$	2.45702e8	−	8.36785e8i	0.374412	−	1.27513i
$870$	5.04450e7	+	9.17497e8i	0.0766055	+	1.39331i
$871$	2.97983e7	+	2.07252e8i	0.0450959	+	0.313649i
$872$	−1.10013e6	+	1.71184e6i	−0.00165919	+	0.00258175i
$873$	1.84412e8	+	1.70749e8i	0.277170	+	0.256634i
$874$	3.58110e8	+	8.78536e8i	0.536391	+	1.31591i
$875$		−	3.52377e8i		−	0.525997i
$876$	−7.75015e8	+	5.60488e8i	−1.15292	+	0.833784i
$877$	1.42795e8	+	9.93162e8i	0.211697	+	1.47239i	0.767488	+	0.641063i	$0.221506\pi$
$877$	1.42795e8	+	9.93162e8i	0.211697	+	1.47239i	−0.555791	+	0.831322i	$0.687585\pi$
$878$	−1.39455e9	+	6.36870e8i	−2.06040	+	0.940951i
$879$	2.73938e8	+	2.12198e8i	0.403354	+	0.312446i
$880$	2.69516e8	−	5.90159e8i	0.395492	−	0.866006i
$881$	5.99726e8	+	5.19665e8i	0.877052	+	0.759969i	0.971868	−	0.235525i	$-0.0756810\pi$
$881$	5.99726e8	+	5.19665e8i	0.877052	+	0.759969i	−0.0948167	+	0.995495i	$0.530226\pi$
$882$	−4.32517e8	−	5.33709e8i	−0.630373	−	0.777855i
$883$	−6.00052e8	+	1.76191e8i	−0.871579	+	0.255919i	−0.686787	−	0.726859i	$-0.740979\pi$
$883$	−6.00052e8	+	1.76191e8i	−0.871579	+	0.255919i	−0.184792	+	0.982778i	$0.559161\pi$
$884$	−3.83833e7	+	3.32593e7i	−0.0555630	+	0.0481456i
$885$	−1.14247e8	−	5.70259e8i	−0.164823	−	0.822701i
$886$	1.90362e8	−	1.22338e8i	0.273702	−	0.175898i
$887$	2.00160e8	−	1.73440e8i	0.286818	−	0.248529i	−0.499554	−	0.866283i	$-0.666503\pi$
$887$	2.00160e8	−	1.73440e8i	0.286818	−	0.248529i	0.786372	+	0.617754i	$0.211957\pi$
$888$	1.62407e7	+	1.43082e6i	0.0231935	+	0.00204336i
$889$	8.24830e7	−	5.73682e8i	0.117398	−	0.816518i
$890$	−6.94359e8	−	6.01665e8i	−0.984949	−	0.853463i
$891$	−4.05004e8	+	1.10438e9i	−0.572567	+	1.56130i
$892$	8.03694e8	+	2.35986e8i	1.13239	+	0.332500i
$893$	−4.59656e8	+	2.09918e8i	−0.645474	+	0.294778i
$894$	−5.52275e8	−	1.29704e8i	−0.772935	−	0.181527i
$895$	3.04869e8	+	1.95927e8i	0.425250	+	0.273291i
$896$		−	2.01010e7i		−	0.0279443i
$897$	5.14912e8	−	8.25671e8i	0.713437	−	1.14401i
$898$	−3.95110e8			−0.545618
$899$	4.44820e8	−	6.92154e8i	0.612217	−	0.952629i
$900$	2.78193e8	−	4.03037e8i	0.381609	−	0.552863i
$901$	8.87810e6	+	1.94403e7i	0.0121380	+	0.0265784i
$902$	3.74473e8	−	1.27534e9i	0.510271	−	1.73782i
$903$	−2.18584e8	−	2.25907e8i	−0.296862	−	0.306808i
$904$	−1.82640e7	+	2.10778e7i	−0.0247224	+	0.0285312i
$905$	1.20045e8	+	1.72598e7i	0.161956	+	0.0232858i
$906$	3.38714e8	+	2.98410e7i	0.455458	+	0.0401262i
$907$	−7.27184e8	−	8.39216e8i	−0.974592	−	1.12474i	−0.992170	−	0.124893i	$-0.960141\pi$
$907$	−7.27184e8	−	8.39216e8i	−0.974592	−	1.12474i	0.0175785	−	0.999845i	$-0.494404\pi$
$908$	7.06275e8	+	1.09898e9i	0.943444	+	1.46803i
$909$	−4.21737e7	+	2.37491e8i	−0.0561500	+	0.316196i
$910$	−2.99524e8	−	3.45669e8i	−0.397473	−	0.458708i
$911$	−2.12284e8	−	7.22974e8i	−0.280778	−	0.956241i	−0.972271	−	0.233858i	$-0.924865\pi$
$911$	−2.12284e8	−	7.22974e8i	−0.280778	−	0.956241i	0.691493	−	0.722383i	$-0.256953\pi$
$912$	−6.47721e8	−	3.67662e8i	−0.853894	−	0.484690i
$913$	8.23606e8	−	9.50492e8i	1.08220	−	1.24892i
$914$	1.62868e9	+	7.43795e8i	2.13304	+	0.974126i
$915$	−3.65907e8	−	2.83439e8i	−0.477647	−	0.369995i
$916$	5.09388e8	+	1.11541e9i	0.662770	+	1.45126i
$917$	4.10757e8	−	5.90580e7i	0.532694	−	0.0765898i
$918$	5.84347e7	+	7.09475e6i	0.0755340	+	0.00917084i
$919$	−1.08763e7			−0.0140131			−0.00700656	−	0.999975i	$-0.502230\pi$
$919$	−1.08763e7			−0.0140131			−0.00700656	+	0.999975i	$0.502230\pi$
$920$	−1.16208e7	+	1.18310e6i	−0.0149236	+	0.00151935i
$921$	2.47099e8	−	6.30572e8i	0.316294	−	0.807152i
$922$	−2.86076e8	−	1.83850e8i	−0.364997	−	0.234569i
$923$	−1.11553e9	+	1.60389e8i	−1.41866	+	0.203972i
$924$	3.98404e7	+	7.24621e8i	0.0505019	+	0.918533i
$925$	−4.53607e8	−	1.33191e8i	−0.573132	−	0.168287i
$926$	1.33938e9	+	6.11677e8i	1.68683	+	0.770351i
$927$	−5.02392e8	+	5.54116e7i	−0.630672	+	0.0695603i
$928$	2.72023e8	−	1.89196e9i	0.340378	−	2.36738i
$929$	−2.11076e8	−	7.18859e8i	−0.263264	−	0.896596i	−0.979957	−	0.199207i	$-0.936163\pi$
$929$	−2.11076e8	−	7.18859e8i	−0.263264	−	0.896596i	0.716693	−	0.697389i	$-0.245655\pi$
$930$	4.22378e8	−	1.49660e8i	0.525113	−	0.186062i
$931$	−4.78589e8	+	3.07570e8i	−0.593080	+	0.381149i
$932$	−9.32556e7	−	1.45109e8i	−0.115193	−	0.179244i
$933$	3.17159e8	+	8.95100e8i	0.390510	+	1.10211i
$934$	8.16379e8	−	2.39710e8i	1.00196	−	0.294202i
$935$	4.20315e7	+	6.04322e6i	0.0514209	+	0.00739322i
$936$	−3.11738e6	−	2.82639e7i	−0.00380156	−	0.0344671i
$937$	−4.27989e8	+	9.37165e8i	−0.520252	+	1.13919i	0.449092	+	0.893485i	$0.351747\pi$
$937$	−4.27989e8	+	9.37165e8i	−0.520252	+	1.13919i	−0.969344	+	0.245707i	$0.920980\pi$
$938$	4.21802e7	−	1.43653e8i	0.0511094	−	0.174062i
$939$	1.02690e9	−	5.64599e7i	1.24031	−	0.0681935i
$940$	−4.97916e7	−	3.46308e8i	−0.0599477	−	0.416945i
$941$	−4.77502e8	+	7.43008e8i	−0.573069	+	0.891712i	−0.999920	−	0.0126095i	$-0.995986\pi$
$941$	−4.77502e8	+	7.43008e8i	−0.573069	+	0.891712i	0.426852	+	0.904322i	$0.359623\pi$
$942$	1.12747e9	+	4.41816e8i	1.34882	+	0.528553i
$943$	6.23812e8	−	1.55476e8i	0.743907	−	0.185408i
$944$			1.18789e9i			1.41208i
$945$	−3.22333e7	+	2.65483e8i	−0.0381952	+	0.314588i
$946$	−2.23642e8	−	1.55547e9i	−0.264168	−	1.83733i
$947$	1.68115e8	−	7.67753e7i	0.197950	−	0.0904007i	−0.313974	−	0.949432i	$-0.601660\pi$
$947$	1.68115e8	−	7.67753e7i	0.197950	−	0.0904007i	0.511924	+	0.859031i	$0.328933\pi$
$948$	4.24490e8	−	5.47998e8i	0.498245	−	0.643212i
$949$	6.68967e8	−	1.46483e9i	0.782720	−	1.71392i
$950$	−6.07553e8	−	5.26447e8i	−0.708620	−	0.614022i
$951$	−7.05079e8	+	1.24216e9i	−0.819778	+	1.44423i
$952$	619634.	−	181941.i	0.000718166	−	0.000210872i
$953$	9.62860e8	−	8.34323e8i	1.11246	−	0.963952i	0.112900	−	0.993606i	$-0.463986\pi$
$953$	9.62860e8	−	8.34323e8i	1.11246	−	0.963952i	0.999560	+	0.0296543i	$0.00944066\pi$
$954$	−6.62507e8	−	1.17648e8i	−0.763036	−	0.135500i
$955$	4.54602e8	−	2.92155e8i	0.521941	−	0.335431i
$956$	−2.04996e7	+	1.77630e7i	−0.0234624	+	0.0203302i
$957$	−2.15430e8	+	2.44526e9i	−0.245793	+	2.78991i
$958$	−1.79727e8	+	1.25003e9i	−0.204417	+	1.42175i
$959$	−3.46545e8	−	3.00283e8i	−0.392920	−	0.340467i
$960$	3.84143e8	−	3.71690e8i	0.434189	−	0.420114i
$961$	4.66571e8	+	1.36998e8i	0.525712	+	0.154363i
$962$	−1.40414e9	+	6.41250e8i	−1.57720	+	0.720282i
$963$	7.81213e8	+	5.39226e8i	0.874763	+	0.603798i
$964$	−1.09437e9	−	7.03310e8i	−1.22161	−	0.785083i
$965$			4.51978e8i			0.502963i
$966$	−5.80167e8	+	3.84087e8i	−0.643608	+	0.426086i
$967$	−1.25493e9			−1.38784			−0.693920	−	0.720052i	$-0.744118\pi$
$967$	−1.25493e9			−1.38784			−0.693920	+	0.720052i	$0.744118\pi$
$968$	−2.22672e7	+	3.46484e7i	−0.0245493	+	0.0381994i
$969$	1.11453e7	−	4.74562e7i	0.0122495	−	0.0521581i
$970$	1.18660e8	+	2.59830e8i	0.130014	+	0.284691i
$971$	−3.03558e8	+	1.03382e9i	−0.331577	+	1.12925i	0.609987	+	0.792412i	$0.291175\pi$
$971$	−3.03558e8	+	1.03382e9i	−0.331577	+	1.12925i	−0.941563	+	0.336836i	$0.890643\pi$
$972$	−6.19981e8	+	6.99833e8i	−0.675118	+	0.762072i
$973$	−2.96090e8	+	3.41706e8i	−0.321429	+	0.370949i
$974$	1.26475e9	+	1.81844e8i	1.36877	+	0.196799i
$975$	−7.23625e7	+	8.21360e8i	−0.0780728	+	0.886176i
$976$	6.19074e8	+	7.14450e8i	0.665876	+	0.768462i
$977$	2.58178e8	+	4.01732e8i	0.276844	+	0.430778i	0.951635	−	0.307231i	$-0.0994025\pi$
$977$	2.58178e8	+	4.01732e8i	0.276844	+	0.430778i	−0.674791	+	0.738009i	$0.735766\pi$
$978$	−2.78121e8	+	5.57196e7i	−0.297315	+	0.0595650i
$979$	−1.60731e9	−	1.85493e9i	−1.71298	−	1.97688i
$980$	−1.10971e8	−	3.77934e8i	−0.117905	−	0.401548i
$981$	−8.75190e7	+	7.09254e7i	−0.0927034	+	0.0751268i
$982$	−8.60307e8	+	9.92847e8i	−0.908487	+	1.04845i
$983$	9.68069e8	+	4.42102e8i	1.01917	+	0.465438i	0.853693	−	0.520776i	$-0.174357\pi$
$983$	9.68069e8	+	4.42102e8i	1.01917	+	0.465438i	0.165474	+	0.986214i	$0.447085\pi$
$984$	1.15048e7	−	1.48521e7i	0.0120751	−	0.0155885i
$985$	−4.01688e7	−	8.79573e7i	−0.0420320	−	0.0920372i
$986$	1.21588e8	−	1.74817e7i	0.126841	−	0.0182370i
$987$	−2.17174e8	−	3.00298e8i	−0.225869	−	0.312321i
$988$	−1.32423e9			−1.37306
$989$	5.94513e8	−	4.73583e8i	0.614572	−	0.489562i
$990$	−9.08320e8	+	9.81003e8i	−0.936123	+	1.01103i
$991$	2.09981e8	+	1.34947e8i	0.215754	+	0.138657i	0.644054	−	0.764980i	$-0.277251\pi$
$991$	2.09981e8	+	1.34947e8i	0.215754	+	0.138657i	−0.428300	+	0.903636i	$0.640887\pi$
$992$	−9.22647e8	+	1.32657e8i	−0.945150	+	0.135892i
$993$	−1.36464e9	+	7.50292e7i	−1.39370	+	0.0766271i
$994$	7.73210e8	+	2.27035e8i	0.787296	+	0.231171i
$995$	−1.03842e8	−	4.74232e7i	−0.105416	−	0.0481417i
$996$	8.85133e8	−	4.64557e8i	0.895840	−	0.470176i
$997$	9.88794e7	−	6.87721e8i	0.0997747	−	0.693948i	−0.877127	−	0.480259i	$-0.840543\pi$
$997$	9.88794e7	−	6.87721e8i	0.0997747	−	0.693948i	0.976902	−	0.213690i	$-0.0685481\pi$
$998$	−7.88960e7	−	2.68695e8i	−0.0793713	−	0.270314i
$999$	8.29042e8	+	3.56806e8i	0.831534	+	0.357878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.h.a.2.9	✓	460
3.2	odd	2	inner	69.7.h.a.2.38	yes	460
23.12	even	11	inner	69.7.h.a.35.38	yes	460
69.35	odd	22	inner	69.7.h.a.35.9	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.h.a.2.9	✓	460	1.1	even	1	trivial
69.7.h.a.2.38	yes	460	3.2	odd	2	inner
69.7.h.a.35.9	yes	460	69.35	odd	22	inner
69.7.h.a.35.38	yes	460	23.12	even	11	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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	69.h (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.14428 + 9.56068i) q^{2} +(-26.2848 - 6.17310i) q^{3} +(-27.0679 - 59.2704i) q^{4} +(20.5398 - 69.9520i) q^{5} +(220.520 - 213.372i) q^{6} +(122.043 - 140.846i) q^{7} +(13.0344 + 1.87406i) q^{8} +(652.786 + 324.518i) q^{9} +O(q^{10})\)	\(q+(-6.14428 + 9.56068i) q^{2} +(-26.2848 - 6.17310i) q^{3} +(-27.0679 - 59.2704i) q^{4} +(20.5398 - 69.9520i) q^{5} +(220.520 - 213.372i) q^{6} +(122.043 - 140.846i) q^{7} +(13.0344 + 1.87406i) q^{8} +(652.786 + 324.518i) q^{9} +(542.587 + 626.178i) q^{10} +(1196.67 + 1862.05i) q^{11} +(345.593 + 1725.01i) q^{12} +(-1939.75 - 2238.59i) q^{13} +(596.711 + 2032.21i) q^{14} +(-971.705 + 1711.88i) q^{15} +(2632.87 - 3038.49i) q^{16} +(239.365 + 109.314i) q^{17} +(-7113.51 + 4247.15i) q^{18} +(2850.19 + 6241.06i) q^{19} +(-4702.05 + 676.053i) q^{20} +(-4077.35 + 2948.72i) q^{21} -25155.1 q^{22} +(-6149.34 - 10498.6i) q^{23} +(-331.037 - 129.722i) q^{24} +(8673.19 + 5573.92i) q^{25} +(33320.8 - 4790.81i) q^{26} +(-15155.1 - 12559.6i) q^{27} +(-11651.4 - 3421.17i) q^{28} +(-37363.0 - 17063.1i) q^{29} +(-10396.3 - 19808.4i) q^{30} +(-2850.69 + 19827.0i) q^{31} +(13110.4 + 44650.0i) q^{32} +(-19959.6 - 56330.9i) q^{33} +(-2515.85 + 1616.84i) q^{34} +(-7345.69 - 11430.1i) q^{35} +(1564.78 - 47474.9i) q^{36} +(-43997.5 + 12918.8i) q^{37} +(-77181.1 - 11097.0i) q^{38} +(37167.0 + 70815.3i) q^{39} +(398.817 - 873.287i) q^{40} +(-14886.5 + 50698.9i) q^{41} +(-3139.42 - 57099.9i) q^{42} +(8890.53 + 61835.0i) q^{43} +(77973.3 - 121329. i) q^{44} +(36108.7 - 38998.1i) q^{45} +(138157. + 5714.69i) q^{46} +73650.4i q^{47} +(-87961.4 + 63613.3i) q^{48} +(11800.3 + 82072.9i) q^{49} +(-106581. + 48673.9i) q^{50} +(-5616.87 - 4350.94i) q^{51} +(-80177.3 + 175564. i) q^{52} +(61379.1 + 53185.3i) q^{53} +(213195. - 67723.2i) q^{54} +(154833. - 45463.2i) q^{55} +(1854.71 - 1607.12i) q^{56} +(-36390.3 - 181640. i) q^{57} +(392704. - 252375. i) q^{58} +(-223292. + 193484. i) q^{59} +(127766. + 11256.3i) q^{60} +(-33462.9 + 232740. i) q^{61} +(-172044. - 149077. i) q^{62} +(125375. - 52336.7i) q^{63} +(-260549. - 76504.1i) q^{64} +(-196436. + 89709.3i) q^{65} +(661198. + 155285. i) q^{66} +(-59466.4 - 38216.7i) q^{67} -17146.2i q^{68} +(96825.2 + 313916. i) q^{69} +154414. q^{70} +(205701. - 320077. i) q^{71} +(7900.48 + 5453.24i) q^{72} +(225844. + 494529. i) q^{73} +(146820. - 500023. i) q^{74} +(-193565. - 200050. i) q^{75} +(292761. - 337865. i) q^{76} +(408307. + 58705.7i) q^{77} +(-905407. - 79767.1i) q^{78} +(-258022. - 297773. i) q^{79} +(-158470. - 246584. i) q^{80} +(320817. + 423681. i) q^{81} +(-393249. - 453834. i) q^{82} +(-160082. - 545190. i) q^{83} +(285137. + 161850. i) q^{84} +(12563.3 - 14498.8i) q^{85} +(-645811. - 294932. i) q^{86} +(876749. + 679147. i) q^{87} +(12108.2 + 26513.3i) q^{88} +(-1.09760e6 + 157811. i) q^{89} +(150987. + 584839. i) q^{90} -552030. q^{91} +(-455809. + 648650. i) q^{92} +(197324. - 503551. i) q^{93} +(-704148. - 452528. i) q^{94} +(495117. - 71187.0i) q^{95} +(-68976.4 - 1.25455e6i) q^{96} +(330785. + 97127.1i) q^{97} +(-857177. - 391460. i) q^{98} +(176899. + 1.60386e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9}+O(q^{10}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9	\( 460 q + 23 q^{3} + 1258 q^{4} - 106 q^{6} - 18 q^{7} - 921 q^{9} - 1774 q^{10} - 630 q^{12} - 1842 q^{13} - 18179 q^{15} - 44990 q^{16} - 25536 q^{18} - 7794 q^{19} - 49959 q^{21} + 7720 q^{22} + 191290 q^{24} + 97900 q^{25} + 85007 q^{27} + 62574 q^{28} - 256521 q^{30} + 1662 q^{31} + 208277 q^{33} - 367948 q^{34} + 123802 q^{36} + 364110 q^{37} - 106127 q^{39} - 869392 q^{40} - 63343 q^{42} - 464490 q^{43} - 455494 q^{45} + 542498 q^{46} + 386726 q^{48} + 1394576 q^{49} + 218821 q^{51} + 592482 q^{52} + 604509 q^{54} - 1673998 q^{55} - 1160439 q^{57} - 1805128 q^{58} + 445865 q^{60} + 422670 q^{61} + 1245641 q^{63} + 2762020 q^{64} + 2925772 q^{66} + 255486 q^{67} - 770451 q^{69} - 1997900 q^{70} - 6119375 q^{72} - 2072562 q^{73} - 6740449 q^{75} + 1407414 q^{76} + 10410184 q^{78} + 1925886 q^{79} + 5228775 q^{81} + 3802304 q^{82} - 6586407 q^{84} + 229034 q^{85} - 6285451 q^{87} + 2567206 q^{88} - 6481942 q^{90} + 3137676 q^{91} + 10359558 q^{93} - 6984096 q^{94} + 18158553 q^{96} - 535890 q^{97} + 5359789 q^{99}+O(q^{100}) \) 460 * q + 23 * q^3 + 1258 * q^4 - 106 * q^6 - 18 * q^7 - 921 * q^9 - 1774 * q^10 - 630 * q^12 - 1842 * q^13 - 18179 * q^15 - 44990 * q^16 - 25536 * q^18 - 7794 * q^19 - 49959 * q^21 + 7720 * q^22 + 191290 * q^24 + 97900 * q^25 + 85007 * q^27 + 62574 * q^28 - 256521 * q^30 + 1662 * q^31 + 208277 * q^33 - 367948 * q^34 + 123802 * q^36 + 364110 * q^37 - 106127 * q^39 - 869392 * q^40 - 63343 * q^42 - 464490 * q^43 - 455494 * q^45 + 542498 * q^46 + 386726 * q^48 + 1394576 * q^49 + 218821 * q^51 + 592482 * q^52 + 604509 * q^54 - 1673998 * q^55 - 1160439 * q^57 - 1805128 * q^58 + 445865 * q^60 + 422670 * q^61 + 1245641 * q^63 + 2762020 * q^64 + 2925772 * q^66 + 255486 * q^67 - 770451 * q^69 - 1997900 * q^70 - 6119375 * q^72 - 2072562 * q^73 - 6740449 * q^75 + 1407414 * q^76 + 10410184 * q^78 + 1925886 * q^79 + 5228775 * q^81 + 3802304 * q^82 - 6586407 * q^84 + 229034 * q^85 - 6285451 * q^87 + 2567206 * q^88 - 6481942 * q^90 + 3137676 * q^91 + 10359558 * q^93 - 6984096 * q^94 + 18158553 * q^96 - 535890 * q^97 + 5359789 * q^99

Introduction

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