LMFDB - Embedded newform 69.7.h.a.2.6

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			2.6
Character	$\chi$	$=$	69.2
Dual form			69.7.h.a.35.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-6.88172 + 10.7082i) q^{2} +(18.5992 + 19.5722i) q^{3} +(-40.7202 - 89.1647i) q^{4} +(16.4113 - 55.8918i) q^{5} +(-337.576 + 64.4730i) q^{6} +(370.080 - 427.095i) q^{7} +(428.662 + 61.6324i) q^{8} +(-37.1400 + 728.053i) q^{9} +O(q^{10})$	\(q+(-6.88172 + 10.7082i) q^{2} +(18.5992 + 19.5722i) q^{3} +(-40.7202 - 89.1647i) q^{4} +(16.4113 - 55.8918i) q^{5} +(-337.576 + 64.4730i) q^{6} +(370.080 - 427.095i) q^{7} +(428.662 + 61.6324i) q^{8} +(-37.1400 + 728.053i) q^{9} +(485.560 + 560.366i) q^{10} +(398.099 + 619.454i) q^{11} +(987.785 - 2455.37i) q^{12} +(979.481 + 1130.38i) q^{13} +(2026.62 + 6902.03i) q^{14} +(1399.16 - 718.337i) q^{15} +(498.339 - 575.114i) q^{16} +(8682.88 + 3965.34i) q^{17} +(-7540.53 - 5407.96i) q^{18} +(-4662.87 - 10210.3i) q^{19} +(-5651.84 + 812.612i) q^{20} +(15242.4 - 700.354i) q^{21} -9372.82 q^{22} +(9.77808 + 12167.0i) q^{23} +(6766.50 + 9536.17i) q^{24} +(10290.0 + 6613.00i) q^{25} +(-18844.8 + 2709.48i) q^{26} +(-14940.4 + 12814.3i) q^{27} +(-53151.5 - 15606.7i) q^{28} +(-23340.5 - 10659.2i) q^{29} +(-1936.56 + 19925.8i) q^{30} +(-362.639 + 2522.21i) q^{31} +(10537.6 + 35887.9i) q^{32} +(-4719.74 + 19313.0i) q^{33} +(-102215. + 65689.4i) q^{34} +(-17797.6 - 27693.6i) q^{35} +(66429.0 - 26334.9i) q^{36} +(48446.9 - 14225.3i) q^{37} +(141422. + 20333.4i) q^{38} +(-3906.47 + 40194.8i) q^{39} +(10479.7 - 22947.2i) q^{40} +(8970.71 - 30551.4i) q^{41} +(-97394.2 + 168037. i) q^{42} +(4059.38 + 28233.6i) q^{43} +(39022.8 - 60720.6i) q^{44} +(40082.7 + 14024.1i) q^{45} +(-130353. - 83625.1i) q^{46} -9341.56i q^{47} +(20524.9 - 943.077i) q^{48} +(-28707.8 - 199667. i) q^{49} +(-141626. + 64678.5i) q^{50} +(83884.3 + 243695. i) q^{51} +(60905.5 - 133364. i) q^{52} +(20466.8 + 17734.6i) q^{53} +(-34402.2 - 248168. i) q^{54} +(41155.7 - 12084.4i) q^{55} +(184962. - 160271. i) q^{56} +(113112. - 281165. i) q^{57} +(274763. - 176580. i) q^{58} +(121222. - 105040. i) q^{59} +(-121024. - 95504.9i) q^{60} +(-34292.0 + 238506. i) q^{61} +(-24512.7 - 21240.4i) q^{62} +(297203. + 285300. i) q^{63} +(-410080. - 120410. i) q^{64} +(79253.6 - 36193.9i) q^{65} +(-174327. - 183446. i) q^{66} +(429453. + 275993. i) q^{67} -935676. i q^{68} +(-237953. + 226488. i) q^{69} +419026. q^{70} +(-64923.9 + 101024. i) q^{71} +(-60792.2 + 309800. i) q^{72} +(173515. + 379945. i) q^{73} +(-181071. + 616672. i) q^{74} +(61955.4 + 324395. i) q^{75} +(-720523. + 831528. i) q^{76} +(411894. + 59221.4i) q^{77} +(-403529. - 318440. i) q^{78} +(-592979. - 684335. i) q^{79} +(-23965.8 - 37291.4i) q^{80} +(-528682. - 54079.8i) q^{81} +(265416. + 306306. i) q^{82} +(59258.9 + 201817. i) q^{83} +(-683119. - 1.33056e6i) q^{84} +(364127. - 420225. i) q^{85} +(-330265. - 150827. i) q^{86} +(-225489. - 655077. i) q^{87} +(132472. + 290072. i) q^{88} +(13308.9 - 1913.54i) q^{89} +(-426010. + 332702. i) q^{90} +845267. q^{91} +(1.08447e6 - 496314. i) q^{92} +(-56110.0 + 39813.5i) q^{93} +(100031. + 64286.0i) q^{94} +(-647194. + 93052.4i) q^{95} +(-506412. + 873730. i) q^{96} +(185006. + 54322.8i) q^{97} +(2.33563e6 + 1.06665e6i) q^{98} +(-465781. + 266831. i) 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 $

$2$	−6.88172	+	10.7082i	−0.860215	+	1.33852i	0.0795966	+	0.996827i	$0.474637\pi$
$2$	−6.88172	+	10.7082i	−0.860215	+	1.33852i	−0.939812	+	0.341693i	$0.889000\pi$
$3$	18.5992	+	19.5722i	0.688859	+	0.724895i
$3$	18.5992	+	19.5722i	0.688859	+	0.724895i
$4$	−40.7202	−	89.1647i	−0.636252	−	1.39320i
$5$	16.4113	−	55.8918i	0.131290	−	0.447134i	−0.867438	−	0.497545i	$-0.834235\pi$
$5$	16.4113	−	55.8918i	0.131290	−	0.447134i	0.998729	+	0.0504109i	$0.0160531\pi$
$6$	−337.576	+	64.4730i	−1.56285	+	0.298486i
$7$	370.080	−	427.095i	1.07895	−	1.24518i	0.111058	−	0.993814i	$-0.464576\pi$
$7$	370.080	−	427.095i	1.07895	−	1.24518i	0.967893	−	0.251362i	$-0.0808783\pi$
$8$	428.662	+	61.6324i	0.837231	+	0.120376i
$9$	−37.1400	+	728.053i	−0.0509465	+	0.998701i
$10$	485.560	+	560.366i	0.485560	+	0.560366i
$11$	398.099	+	619.454i	0.299097	+	0.465405i	0.957978	−	0.286843i	$-0.0926059\pi$
$11$	398.099	+	619.454i	0.299097	+	0.465405i	−0.658880	+	0.752248i	$0.728970\pi$
$12$	987.785	−	2455.37i	0.571635	−	1.42093i
$13$	979.481	+	1130.38i	0.445827	+	0.514511i	0.933531	−	0.358498i	$-0.116711\pi$
$13$	979.481	+	1130.38i	0.445827	+	0.514511i	−0.487704	+	0.873009i	$0.662165\pi$
$14$	2026.62	+	6902.03i	0.738564	+	2.51532i
$15$	1399.16	−	718.337i	0.414566	−	0.212841i
$16$	498.339	−	575.114i	0.121665	−	0.140409i
$17$	8682.88	+	3965.34i	1.76733	+	0.807112i	0.982215	+	0.187760i	$0.0601226\pi$
$17$	8682.88	+	3965.34i	1.76733	+	0.807112i	0.785113	+	0.619352i	$0.212605\pi$
$18$	−7540.53	−	5407.96i	−1.29296	−	0.927291i
$19$	−4662.87	−	10210.3i	−0.679818	−	1.48859i	−0.862835	−	0.505485i	$-0.831314\pi$
$19$	−4662.87	−	10210.3i	−0.679818	−	1.48859i	0.183017	−	0.983110i	$-0.441414\pi$
$20$	−5651.84	+	812.612i	−0.706480	+	0.101577i
$21$	15242.4	−	700.354i	1.64587	−	0.0756240i
$22$	−9372.82			−0.880242
$23$	9.77808	+	12167.0i	0.000803656	+	1.00000i
$23$	9.77808	+	12167.0i	0.000803656	+	1.00000i
$24$	6766.50	+	9536.17i	0.489475	+	0.689827i
$25$	10290.0	+	6613.00i	0.658562	+	0.423232i
$26$	−18844.8	+	2709.48i	−1.07219	+	0.154158i
$27$	−14940.4	+	12814.3i	−0.759049	+	0.651034i
$28$	−53151.5	−	15606.7i	−2.42126	−	0.710947i
$29$	−23340.5	−	10659.2i	−0.957008	−	0.437051i	−0.125211	−	0.992130i	$-0.539961\pi$
$29$	−23340.5	−	10659.2i	−0.957008	−	0.437051i	−0.831797	+	0.555079i	$0.812688\pi$
$30$	−1936.56	+	19925.8i	−0.0717244	+	0.737994i
$31$	−362.639	+	2522.21i	−0.0121728	+	0.0846636i	−0.995002	−	0.0998528i	$-0.968163\pi$
$31$	−362.639	+	2522.21i	−0.0121728	+	0.0846636i	0.982829	+	0.184516i	$0.0590719\pi$
$32$	10537.6	+	35887.9i	0.321583	+	1.09521i
$33$	−4719.74	+	19313.0i	−0.131334	+	0.537413i
$34$	−102215.	+	65689.4i	−2.60062	+	1.67132i
$35$	−17797.6	−	27693.6i	−0.415105	−	0.645915i
$36$	66429.0	−	26334.9i	1.42380	−	0.564448i
$37$	48446.9	−	14225.3i	0.956448	−	0.280838i	0.233979	−	0.972242i	$-0.424825\pi$
$37$	48446.9	−	14225.3i	0.956448	−	0.280838i	0.722469	+	0.691403i	$0.243007\pi$
$38$	141422.	+	20333.4i	2.57730	+	0.370560i
$39$	−3906.47	+	40194.8i	−0.0658552	+	0.677604i
$40$	10479.7	−	22947.2i	0.163745	−	0.358551i
$41$	8970.71	−	30551.4i	0.130159	−	0.443282i	−0.868463	−	0.495754i	$-0.834892\pi$
$41$	8970.71	−	30551.4i	0.130159	−	0.443282i	0.998622	+	0.0524718i	$0.0167100\pi$
$42$	−97394.2	+	168037.i	−1.31457	+	2.26808i
$43$	4059.38	+	28233.6i	0.0510568	+	0.355108i	0.999295	+	0.0375475i	$0.0119546\pi$
$43$	4059.38	+	28233.6i	0.0510568	+	0.355108i	−0.948238	+	0.317560i	$0.897136\pi$
$44$	39022.8	−	60720.6i	0.458100	−	0.712817i
$45$	40082.7	+	14024.1i	0.439865	+	0.153900i
$46$	−130353.	−	83625.1i	−1.33921	−	0.859139i
$47$		−	9341.56i		−	0.0899759i	−0.998988	−	0.0449879i	$-0.985675\pi$
$47$		−	9341.56i		−	0.0899759i	0.998988	−	0.0449879i	$-0.0143249\pi$
$48$	20524.9	−	943.077i	0.185592	−	0.00852753i
$49$	−28707.8	−	199667.i	−0.244013	−	1.69714i
$50$	−141626.	+	64678.5i	−1.13301	+	0.517428i
$51$	83884.3	+	243695.i	0.632368	+	1.83711i
$52$	60905.5	−	133364.i	0.433158	−	0.948484i
$53$	20466.8	+	17734.6i	0.137474	+	0.119122i	0.720884	−	0.693056i	$-0.243736\pi$
$53$	20466.8	+	17734.6i	0.137474	+	0.119122i	−0.583409	+	0.812178i	$0.698282\pi$
$54$	−34402.2	−	248168.i	−0.218477	−	1.57603i
$55$	41155.7	−	12084.4i	0.247367	−	0.0726335i
$56$	184962.	−	160271.i	1.05322	−	0.912621i
$57$	113112.	−	281165.i	0.610776	−	1.51823i
$58$	274763.	−	176580.i	1.40823	−	0.905017i
$59$	121222.	−	105040.i	0.590237	−	0.511443i	−0.307749	−	0.951468i	$-0.599576\pi$
$59$	121222.	−	105040.i	0.590237	−	0.511443i	0.897986	+	0.440025i	$0.145030\pi$
$60$	−121024.	−	95504.9i	−0.560298	−	0.442152i
$61$	−34292.0	+	238506.i	−0.151079	+	1.05078i	0.763337	+	0.646000i	$0.223559\pi$
$61$	−34292.0	+	238506.i	−0.151079	+	1.05078i	−0.914416	+	0.404775i	$0.867350\pi$
$62$	−24512.7	−	21240.4i	−0.102853	−	0.0891224i
$63$	297203.	+	285300.i	1.18859	+	1.14099i
$64$	−410080.	−	120410.i	−1.56433	−	0.459329i
$65$	79253.6	−	36193.9i	0.288588	−	0.131794i
$66$	−174327.	−	183446.i	−0.606363	−	0.638083i
$67$	429453.	+	275993.i	1.42788	+	0.917642i	0.999904	+	0.0138515i	$0.00440922\pi$
$67$	429453.	+	275993.i	1.42788	+	0.917642i	0.427975	+	0.903791i	$0.359227\pi$
$68$		−	935676.i		−	2.97577i
$69$	−237953.	+	226488.i	−0.724342	+	0.689441i
$70$	419026.			1.22165
$71$	−64923.9	+	101024.i	−0.181397	+	0.282259i	−0.920029	−	0.391849i	$-0.871835\pi$
$71$	−64923.9	+	101024.i	−0.181397	+	0.282259i	0.738633	+	0.674108i	$0.235472\pi$
$72$	−60792.2	+	309800.i	−0.162873	+	0.830011i
$73$	173515.	+	379945.i	0.446035	+	0.976681i	0.990451	+	0.137865i	$0.0440241\pi$
$73$	173515.	+	379945.i	0.446035	+	0.976681i	−0.544416	+	0.838816i	$0.683249\pi$
$74$	−181071.	+	616672.i	−0.446843	+	1.52181i
$75$	61955.4	+	324395.i	0.146857	+	0.768936i
$76$	−720523.	+	831528.i	−1.64137	+	1.89424i
$77$	411894.	+	59221.4i	0.902222	+	0.129720i
$78$	−403529.	−	318440.i	−0.850337	−	0.671033i
$79$	−592979.	−	684335.i	−1.20270	−	1.38799i	−0.900561	−	0.434730i	$-0.856844\pi$
$79$	−592979.	−	684335.i	−1.20270	−	1.38799i	−0.302142	−	0.953263i	$-0.597702\pi$
$80$	−23965.8	−	37291.4i	−0.0468081	−	0.0728348i
$81$	−528682.	−	54079.8i	−0.994809	−	0.101761i
$82$	265416.	+	306306.i	0.481377	+	0.555539i
$83$	59258.9	+	201817.i	0.103638	+	0.352959i	0.994942	−	0.100447i	$-0.0320271\pi$
$83$	59258.9	+	201817.i	0.103638	+	0.352959i	−0.891304	+	0.453405i	$0.850209\pi$
$84$	−683119.	−	1.33056e6i	−1.15255	−	2.24490i
$85$	364127.	−	420225.i	0.592921	−	0.684267i
$86$	−330265.	−	150827.i	−0.519239	−	0.237129i
$87$	−225489.	−	655077.i	−0.342427	−	0.994797i
$88$	132472.	+	290072.i	0.194390	+	0.425656i
$89$	13308.9	−	1913.54i	0.0188788	−	0.00271436i	−0.132869	−	0.991134i	$-0.542419\pi$
$89$	13308.9	−	1913.54i	0.0188788	−	0.00271436i	0.151748	+	0.988419i	$0.451510\pi$
$90$	−426010.	+	332702.i	−0.584376	+	0.456381i
$91$	845267.			1.12168
$92$	1.08447e6	−	496314.i	1.39269	−	0.637372i
$93$	−56110.0	+	39813.5i	−0.0697576	+	0.0494973i
$94$	100031.	+	64286.0i	0.120435	+	0.0773986i
$95$	−647194.	+	93052.4i	−0.754855	+	0.108532i
$96$	−506412.	+	873730.i	−0.572388	+	0.987560i
$97$	185006.	+	54322.8i	0.202708	+	0.0595205i	0.381510	−	0.924365i	$-0.375404\pi$
$97$	185006.	+	54322.8i	0.202708	+	0.0595205i	−0.178802	+	0.983885i	$0.557222\pi$
$98$	2.33563e6	+	1.06665e6i	2.48157	+	1.13329i
$99$	−465781.	+	266831.i	−0.480038	+	0.274998i
$100$	170635.	−	1.18679e6i	0.170635	−	1.18679i
$101$	53014.9	+	180552.i	0.0514557	+	0.175242i	0.981212	−	0.192934i	$-0.0618004\pi$
$101$	53014.9	+	180552.i	0.0514557	+	0.175242i	−0.929756	+	0.368176i	$0.879982\pi$
$102$	−3.18679e6	−	778794.i	−3.00299	−	0.733875i
$103$	−305657.	+	196434.i	−0.279719	+	0.179765i	−0.672977	−	0.739664i	$-0.734985\pi$
$103$	−305657.	+	196434.i	−0.279719	+	0.179765i	0.393257	+	0.919428i	$0.371348\pi$
$104$	350199.	+	544920.i	0.311325	+	0.484432i
$105$	211003.	−	863417.i	0.182273	−	0.745852i
$106$	−330751.	+	97117.3i	−0.277705	+	0.0815415i
$107$	−1.05160e6	−	151197.i	−0.858415	−	0.123421i	−0.300968	−	0.953634i	$-0.597310\pi$
$107$	−1.05160e6	−	151197.i	−0.858415	−	0.123421i	−0.557447	+	0.830213i	$0.688219\pi$
$108$	1.75096e6	+	810353.i	1.38997	+	0.643284i
$109$	−633720.	+	1.38765e6i	−0.489348	+	1.07152i	0.490438	+	0.871476i	$0.336837\pi$
$109$	−633720.	+	1.38765e6i	−0.489348	+	1.07152i	−0.979786	+	0.200047i	$0.935890\pi$
$110$	−153820.	+	523863.i	−0.115567	+	0.393586i
$111$	1.17949e6	+	683633.i	0.862436	+	0.499866i
$112$	−61203.1	−	425677.i	−0.0435631	−	0.302988i
$113$	87729.4	−	136510.i	0.0608009	−	0.0946080i	−0.809522	−	0.587089i	$-0.800274\pi$
$113$	87729.4	−	136510.i	0.0608009	−	0.0946080i	0.870323	+	0.492481i	$0.163910\pi$
$114$	2.23236e6	+	3.14612e6i	1.50678	+	2.12354i
$115$	680195.	+	199130.i	0.447240	+	0.130931i
$116$			2.51519e6i			1.61138i
$117$	−859356.	+	671132.i	−0.536557	+	0.419035i
$118$	290565.	+	2.02092e6i	0.176847	+	1.22999i
$119$	4.90694e6	−	2.24092e6i	2.91186	−	1.32980i
$120$	644040.	−	221691.i	0.372709	−	0.128293i
$121$	510693.	−	1.11826e6i	0.288273	−	0.631229i
$122$	−2.31797e6	−	2.00854e6i	−1.27652	−	1.10611i
$123$	764806.	−	392656.i	0.410995	−	0.211007i
$124$	239659.	−	70370.2i	0.125698	−	0.0369083i
$125$	1.22635e6	−	1.06264e6i	0.627892	−	0.544071i
$126$	−5.10031e6	+	1.21914e6i	−2.54968	+	0.609458i
$127$	946313.	−	608159.i	0.461981	−	0.296897i	−0.288871	−	0.957368i	$-0.593280\pi$
$127$	946313.	−	608159.i	0.461981	−	0.296897i	0.750851	+	0.660471i	$0.229643\pi$
$128$	2.30232e6	−	1.99498e6i	1.09783	−	0.951278i
$129$	−477091.	+	604573.i	−0.222245	+	0.281630i
$130$	−157831.	+	1.09774e6i	−0.0718392	+	0.499653i
$131$	−2.04302e6	−	1.77029e6i	−0.908780	−	0.787462i	0.0688864	−	0.997625i	$-0.478055\pi$
$131$	−2.04302e6	−	1.77029e6i	−0.908780	−	0.787462i	−0.977667	+	0.210162i	$0.932601\pi$
$132$	1.91423e6	−	365594.i	0.832284	−	0.158956i
$133$	−6.08640e6	−	1.78713e6i	−2.58705	−	0.759627i
$134$	−5.91075e6	+	2.69935e6i	−2.45657	+	1.12188i
$135$	471023.	+	1.04534e6i	0.191443	+	0.424871i
$136$	3.47763e6	+	2.23494e6i	1.38251	+	0.888483i
$137$		−	1.62420e6i		−	0.631651i	−0.948817	−	0.315826i	$-0.897719\pi$
$137$		−	1.62420e6i		−	0.631651i	0.948817	−	0.315826i	$-0.102281\pi$
$138$	−787744.	−	4.10666e6i	−0.299742	−	1.56261i
$139$	3.44026e6			1.28099			0.640497	−	0.767961i	$-0.278728\pi$
$139$	3.44026e6			1.28099			0.640497	+	0.767961i	$0.278728\pi$
$140$	−1.74457e6	+	2.71461e6i	−0.635777	+	0.989288i
$141$	182835.	−	173746.i	0.0652231	−	0.0619807i
$142$	−634989.	−	1.39043e6i	−0.221769	−	0.485607i
$143$	−310289.	+	1.05675e6i	−0.106110	+	0.361379i
$144$	400205.	+	384177.i	0.134028	+	0.128660i
$145$	−978811.	+	1.12961e6i	−0.321066	+	0.370530i
$146$	−5.26260e6	−	756648.i	−1.69099	−	0.243128i
$147$	3.37398e6	−	4.27553e6i	1.06216	−	1.34598i
$148$	−3.24116e6	−	3.74050e6i	−0.999806	−	1.15384i
$149$	1.04338e6	+	1.62353e6i	0.315417	+	0.490798i	0.962374	−	0.271728i	$-0.0875952\pi$
$149$	1.04338e6	+	1.62353e6i	0.315417	+	0.490798i	−0.646957	+	0.762526i	$0.723959\pi$
$150$	−3.90003e6	−	1.56896e6i	−1.15556	−	0.464878i
$151$	−1.63409e6	−	1.88584e6i	−0.474620	−	0.547740i	0.467071	−	0.884220i	$-0.345309\pi$
$151$	−1.63409e6	−	1.88584e6i	−0.474620	−	0.547740i	−0.941691	+	0.336479i	$0.890764\pi$
$152$	−1.36952e6	−	4.66414e6i	−0.389975	−	1.32813i
$153$	−3.20946e6	+	6.17433e6i	−0.896103	+	1.72391i
$154$	−3.46869e6	+	4.00308e6i	−0.949738	+	1.09606i
$155$	135020.	+	61661.3i	0.0362578	+	0.0165584i
$156$	3.74303e6	−	1.28842e6i	0.985937	−	0.339378i
$157$	−942211.	−	2.06315e6i	−0.243472	−	0.533129i	0.747961	−	0.663742i	$-0.231033\pi$
$157$	−942211.	−	2.06315e6i	−0.243472	−	0.533129i	−0.991433	+	0.130613i	$0.958306\pi$
$158$	1.14087e7	−	1.64032e6i	2.89244	−	0.415870i
$159$	33561.6	+	730427.i	0.00834931	+	0.181713i
$160$	2.17877e6			0.531927
$161$	5.20008e6	+	4.49859e6i	1.24604	+	1.07795i
$162$	4.21734e6	−	5.28905e6i	0.991958	−	1.24404i
$163$	−535235.	−	343974.i	−0.123589	−	0.0794261i	0.477386	−	0.878694i	$-0.341585\pi$
$163$	−535235.	−	343974.i	−0.123589	−	0.0794261i	−0.600975	+	0.799268i	$0.705221\pi$
$164$	−3.08940e6	+	444189.i	−0.700394	+	0.100701i
$165$	1.00198e6	+	580746.i	0.223053	+	0.129281i
$166$	−2.56890e6	−	754296.i	−0.561594	−	0.164899i
$167$	−6.21422e6	−	2.83794e6i	−1.33425	−	0.609331i	−0.384727	−	0.923030i	$-0.625705\pi$
$167$	−6.21422e6	−	2.83794e6i	−1.33425	−	0.609331i	−0.949523	+	0.313699i	$0.898432\pi$
$168$	6.57700e6	+	639208.i	1.38707	+	0.134808i
$169$	368547.	−	2.56330e6i	0.0763543	−	0.531056i
$170$	1.99402e6	+	6.79101e6i	0.405866	+	1.38225i
$171$	7.60680e6	−	3.01561e6i	1.52130	−	0.603097i
$172$	2.35214e6	−	1.51163e6i	0.462251	−	0.297071i
$173$	−3.86799e6	−	6.01871e6i	−0.747045	−	1.16242i	−0.981716	−	0.190350i	$-0.939038\pi$
$173$	−3.86799e6	−	6.01871e6i	−0.747045	−	1.16242i	0.234671	−	0.972075i	$-0.424599\pi$
$174$	8.56643e6	+	2.09348e6i	1.62612	+	0.397393i
$175$	6.63252e6	−	1.94748e6i	1.23755	−	0.363379i
$176$	554645.	+	79745.9i	0.101737	+	0.0146275i
$177$	4.31049e6	+	418930.i	0.777333	+	0.0755477i
$178$	−71098.0	+	155683.i	−0.0126066	+	0.0276046i
$179$	−533331.	+	1.81636e6i	−0.0929904	+	0.316696i	−0.992832	−	0.119521i	$-0.961864\pi$
$179$	−533331.	+	1.81636e6i	−0.0929904	+	0.316696i	0.899841	+	0.436218i	$0.143682\pi$
$180$	−381716.	−	4.14502e6i	−0.0654519	−	0.710738i
$181$	−1.47025e6	−	1.02258e7i	−0.247944	−	1.72449i	−0.610057	−	0.792357i	$-0.708853\pi$
$181$	−1.47025e6	−	1.02258e7i	−0.247944	−	1.72449i	0.362113	−	0.932134i	$-0.382056\pi$
$182$	−5.81689e6	+	9.05126e6i	−0.964888	+	1.50139i
$183$	−5.30589e6	+	3.76485e6i	−0.865774	+	0.614320i
$184$	−745689.	+	5.21614e6i	−0.119703	+	0.837328i
$185$		−	2.94124e6i		−	0.464532i
$186$	−40196.1	−	874820.i	−0.00624662	−	0.135950i
$187$	1.00030e6	+	6.95724e6i	0.152970	+	1.06393i
$188$	−832938.	+	380390.i	−0.125354	+	0.0572474i
$189$	−56207.0	+	1.11233e7i	−0.00832540	+	1.64758i
$190$	3.45739e6	−	7.57062e6i	0.504066	−	1.10375i
$191$	−2.72811e6	−	2.36392e6i	−0.391527	−	0.339260i	0.436746	−	0.899585i	$-0.356131\pi$
$191$	−2.72811e6	−	2.36392e6i	−0.391527	−	0.339260i	−0.828273	+	0.560325i	$0.810676\pi$
$192$	−5.27046e6	−	1.02657e7i	−0.744638	−	1.45039i
$193$	8.51945e6	−	2.50154e6i	1.18506	−	0.347964i	0.370936	−	0.928658i	$-0.379037\pi$
$193$	8.51945e6	−	2.50154e6i	1.18506	−	0.347964i	0.814122	+	0.580694i	$0.197219\pi$
$194$	−1.85486e6	+	1.60724e6i	−0.254042	+	0.220129i
$195$	2.18245e6	+	877988.i	0.294334	+	0.118409i
$196$	−1.66343e7	+	1.06902e7i	−2.20921	+	1.41977i
$197$	−5.21248e6	+	4.51664e6i	−0.681783	+	0.590768i	−0.925349	−	0.379116i	$-0.876228\pi$
$197$	−5.21248e6	+	4.51664e6i	−0.681783	+	0.590768i	0.243566	+	0.969884i	$0.421683\pi$
$198$	348107.	−	6.82391e6i	0.0448453	−	0.879099i
$199$	−624959.	+	4.34668e6i	−0.0793034	+	0.551567i	0.910974	+	0.412463i	$0.135331\pi$
$199$	−624959.	+	4.34668e6i	−0.0793034	+	0.551567i	−0.990278	+	0.139104i	$0.955578\pi$
$200$	4.00337e6	+	3.46894e6i	0.500422	+	0.433618i
$201$	2.58570e6	+	1.35386e7i	0.318413	+	1.66719i
$202$	−2.29821e6	−	674816.i	−0.278828	−	0.0818713i
$203$	−1.31904e7	+	6.02383e6i	−1.57677	+	0.720087i
$204$	1.83132e7	−	1.74028e7i	2.15712	−	2.04988i
$205$	−1.56035e6	−	1.00278e6i	−0.181118	−	0.116397i
$206$		−	4.62482e6i		−	0.529046i
$207$	−8.85858e6	−	444764.i	−0.998742	−	0.0501439i
$208$	1.13821e6			0.126483
$209$	4.46851e6	−	6.95313e6i	0.489467	−	0.761626i
$210$	7.79355e6	+	8.20125e6i	0.841545	+	0.885568i
$211$	2.19596e6	+	4.80848e6i	0.233763	+	0.511871i	0.989766	−	0.142698i	$-0.0455777\pi$
$211$	2.19596e6	+	4.80848e6i	0.233763	+	0.511871i	−0.756003	+	0.654568i	$0.772850\pi$
$212$	747886.	−	2.54707e6i	0.0784925	−	0.267321i
$213$	−3.18478e6	+	608255.i	−0.329565	+	0.0629429i
$214$	8.85583e6	−	1.02202e7i	0.903624	−	1.04284i
$215$	1.64464e6	+	236464.i	0.165484	+	0.0237930i
$216$	−7.19415e6	+	4.57220e6i	−0.713868	+	0.453695i
$217$	943019.	+	1.08830e6i	0.0922872	+	0.106505i
$218$	−1.04981e7	−	1.63354e7i	−1.01331	−	1.57674i
$219$	−4.20911e6	+	1.04627e7i	−0.400736	+	0.996124i
$220$	−2.75337e6	−	3.17756e6i	−0.258581	−	0.298418i
$221$	4.02237e6	+	1.36989e7i	0.372654	+	1.26914i
$222$	−1.54374e7	+	7.92565e6i	−1.41096	+	0.724396i
$223$	−5.08484e6	+	5.86822e6i	−0.458525	+	0.529166i	−0.937184	−	0.348835i	$-0.886577\pi$
$223$	−5.08484e6	+	5.86822e6i	−0.458525	+	0.529166i	0.478659	+	0.878001i	$0.341123\pi$
$224$	1.92273e7	+	8.78082e6i	1.71070	+	0.781252i
$225$	−5.19679e6	+	7.24608e6i	−0.456234	+	0.636144i
$226$	858038.	+	1.87884e6i	0.0743329	+	0.162766i
$227$	1.09007e7	−	1.56728e6i	0.931915	−	0.133989i	0.340398	−	0.940282i	$-0.389438\pi$
$227$	1.09007e7	−	1.56728e6i	0.931915	−	0.133989i	0.591517	+	0.806292i	$0.298529\pi$
$228$	−2.96760e7	+	1.36355e6i	−2.50380	+	0.115044i
$229$	−3.49299e6			−0.290865			−0.145432	−	0.989368i	$-0.546457\pi$
$229$	−3.49299e6			−0.290865			−0.145432	+	0.989368i	$0.546457\pi$
$230$	−6.81323e6	+	5.91329e6i	−0.559976	+	0.486010i
$231$	6.50181e6	+	9.16313e6i	0.527470	+	0.743375i
$232$	−9.34823e6	−	6.00774e6i	−0.748627	−	0.481113i
$233$	971879.	−	139735.i	0.0768324	−	0.0110468i	−0.103791	−	0.994599i	$-0.533097\pi$
$233$	971879.	−	139735.i	0.0768324	−	0.0110468i	0.180624	+	0.983552i	$0.442188\pi$
$234$	−1.27275e6	−	1.38207e7i	−0.0993332	−	1.07865i
$235$	−522117.	−	153307.i	−0.0402313	−	0.0118130i
$236$	−1.43020e7	−	6.53151e6i	−1.08808	−	0.496910i
$237$	2.36498e6	−	2.43340e7i	0.177657	−	1.82797i
$238$	−9.77200e6	+	6.79657e7i	−0.724857	+	5.04149i
$239$	−4.89606e6	−	1.66744e7i	−0.358635	−	1.22140i	−0.919367	−	0.393402i	$-0.871298\pi$
$239$	−4.89606e6	−	1.66744e7i	−0.358635	−	1.22140i	0.560732	−	0.827998i	$-0.310520\pi$
$240$	284131.	−	1.16265e6i	0.0205534	−	0.0841039i
$241$	1.16011e6	−	745559.i	0.0828798	−	0.0532636i	−0.498545	−	0.866864i	$-0.666132\pi$
$241$	1.16011e6	−	745559.i	0.0828798	−	0.0532636i	0.581424	+	0.813600i	$0.302496\pi$
$242$	8.46008e6	+	1.31641e7i	0.596937	+	0.928852i
$243$	−8.77460e6	−	1.13533e7i	−0.611517	−	0.791231i
$244$	2.26627e7	−	6.65437e6i	1.56006	−	0.458076i
$245$	−1.16309e7	−	1.67227e6i	−0.790888	−	0.113713i
$246$	−1.05856e6	+	1.08918e7i	−0.0711065	+	0.731636i
$247$	6.97431e6	−	1.52716e7i	0.462818	−	1.01343i
$248$	−310900.	+	1.05883e6i	−0.0203829	+	0.0694177i
$249$	−2.84784e6	+	4.91347e6i	−0.184466	+	0.318266i
$250$	2.93951e6	+	2.04448e7i	0.188129	+	1.30846i
$251$	−1.50980e7	+	2.34930e7i	−0.954772	+	1.48565i	−0.0825242	+	0.996589i	$0.526298\pi$
$251$	−1.50980e7	+	2.34930e7i	−0.954772	+	1.48565i	−0.872248	+	0.489065i	$0.837338\pi$
$252$	1.33366e7	−	3.81175e7i	0.833378	−	2.38190i
$253$	−7.53300e6	+	4.84972e6i	−0.465164	+	0.299471i
$254$			1.43185e7i			0.873766i
$255$	1.49972e7	−	689089.i	0.904460	−	0.0415580i
$256$	1.62582e6	+	1.13078e7i	0.0969064	+	0.673999i
$257$	1.79823e7	−	8.21225e6i	1.05937	−	0.483796i	0.191963	−	0.981402i	$-0.438515\pi$
$257$	1.79823e7	−	8.21225e6i	1.05937	−	0.483796i	0.867403	+	0.497606i	$0.165787\pi$
$258$	−3.19065e6	−	9.26927e6i	−0.185789	−	0.539742i
$259$	1.18537e7	−	2.59560e7i	0.682267	−	1.49396i
$260$	−6.45444e6	−	5.59280e6i	−0.367230	−	0.318207i
$261$	8.62736e6	−	1.65972e7i	0.485240	−	0.933499i
$262$	3.30160e7	−	9.69438e6i	1.83578	−	0.539034i
$263$	−2.72610e7	+	2.36218e7i	−1.49856	+	1.29851i	−0.663778	+	0.747930i	$0.731048\pi$
$263$	−2.72610e7	+	2.36218e7i	−1.49856	+	1.29851i	−0.834783	+	0.550580i	$0.814407\pi$
$264$	−3.21348e6	+	7.98787e6i	−0.174648	+	0.434129i
$265$	1.32710e6	−	852876.i	0.0713127	−	0.0458299i
$266$	6.10217e7	−	5.28756e7i	3.24220	−	2.80938i
$267$	284988.	+	224895.i	0.0149724	+	0.0118153i
$268$	7.12142e6	−	4.95305e7i	0.369966	−	2.57317i
$269$	5.10934e6	+	4.42727e6i	0.262487	+	0.227446i	0.776154	−	0.630543i	$-0.217168\pi$
$269$	5.10934e6	+	4.42727e6i	0.262487	+	0.227446i	−0.513667	+	0.857990i	$0.671713\pi$
$270$	−1.44351e7	−	2.14996e6i	−0.733381	−	0.109230i
$271$	−2.23876e7	−	6.57360e6i	−1.12486	−	0.330290i	−0.334177	−	0.942510i	$-0.608458\pi$
$271$	−2.23876e7	−	6.57360e6i	−1.12486	−	0.330290i	−0.790687	+	0.612221i	$0.790276\pi$
$272$	6.60755e6	−	3.01757e6i	0.328347	−	0.149951i
$273$	1.57213e7	+	1.65437e7i	0.772681	+	0.813102i
$274$	1.73922e7	+	1.11773e7i	0.845478	+	0.543356i
$275$			9.00682e6i			0.433085i
$276$	2.98842e7	+	1.19944e7i	1.42139	+	0.570493i
$277$	−3.13257e7			−1.47388			−0.736938	−	0.675961i	$-0.763729\pi$
$277$	−3.13257e7			−1.47388			−0.736938	+	0.675961i	$0.763729\pi$
$278$	−2.36749e7	+	3.68389e7i	−1.10193	+	1.71464i
$279$	−1.82284e6	−	357696.i	−0.0839335	−	0.0164703i
$280$	−5.92234e6	−	1.29681e7i	−0.269786	−	0.590749i
$281$	4.99970e6	−	1.70274e7i	0.225333	−	0.767414i	−0.766763	−	0.641931i	$-0.778134\pi$
$281$	4.99970e6	−	1.70274e7i	0.225333	−	0.767414i	0.992096	−	0.125483i	$-0.0400482\pi$
$282$	602279.	+	3.15349e6i	0.0268565	+	0.140619i
$283$	1.84714e7	−	2.13172e7i	0.814969	−	0.940524i	−0.184133	−	0.982901i	$-0.558948\pi$
$283$	1.84714e7	−	2.13172e7i	0.814969	−	0.940524i	0.999102	+	0.0423770i	$0.0134931\pi$
$284$	1.16515e7	+	1.67523e6i	0.508657	+	0.0731338i
$285$	−1.38585e7	−	1.09363e7i	−0.598663	−	0.472428i
$286$	−9.18050e6	−	1.05949e7i	−0.392435	−	0.452895i
$287$	−9.72849e6	−	1.51378e7i	−0.411529	−	0.640351i
$288$	−2.65197e7	+	6.33908e6i	−1.11017	+	0.265368i
$289$	4.38618e7	+	5.06192e7i	1.81716	+	2.09711i
$290$	−5.36013e6	−	1.82549e7i	−0.219776	−	0.748490i
$291$	2.37775e6	+	4.63134e6i	0.0964913	+	0.187944i
$292$	2.68122e7	−	3.09429e7i	1.07692	−	1.24283i
$293$	−1.71140e7	−	7.81568e6i	−0.680374	−	0.310716i	0.0450836	−	0.998983i	$-0.485645\pi$
$293$	−1.71140e7	−	7.81568e6i	−0.680374	−	0.310716i	−0.725458	+	0.688267i	$0.758372\pi$
$294$	2.25642e7	+	6.55521e7i	0.887930	+	2.57956i
$295$	−3.88144e6	−	8.49916e6i	−0.151191	−	0.331063i
$296$	2.16441e7	−	3.11196e6i	0.834574	−	0.119994i
$297$	−1.38856e7	−	4.15351e6i	−0.530024	−	0.158542i
$298$	−2.45653e7			−0.928269
$299$	−1.37438e7	+	1.19284e7i	−0.514153	+	0.446240i
$300$	2.64017e7	−	1.87336e7i	0.977841	−	0.693839i
$301$	1.35607e7	+	8.71495e6i	0.497260	+	0.319569i
$302$	3.14393e7	−	4.52029e6i	1.14144	−	0.164114i
$303$	−2.54776e6	+	4.39574e6i	−0.0915864	+	0.158017i
$304$	−8.19577e6	−	2.40649e6i	−0.291722	−	0.0856572i
$305$	1.27677e7	+	5.83084e6i	0.450002	+	0.205509i
$306$	−4.40291e7	−	7.68574e7i	−1.53665	−	2.68239i
$307$	2.57601e6	−	1.79166e7i	0.0890293	−	0.619212i	−0.895640	−	0.444780i	$-0.853282\pi$
$307$	2.57601e6	−	1.79166e7i	0.0890293	−	0.619212i	0.984669	−	0.174432i	$-0.0558090\pi$
$308$	−1.14919e7	−	3.91379e7i	−0.393315	−	1.33951i
$309$	−9.52960e6	−	2.32886e6i	−0.322998	−	0.0789347i
$310$	−1.58945e6	+	1.02148e6i	−0.0533532	+	0.0342880i
$311$	−6.55634e6	−	1.02019e7i	−0.217962	−	0.339155i	0.715004	−	0.699121i	$-0.246425\pi$
$311$	−6.55634e6	−	1.02019e7i	−0.217962	−	0.339155i	−0.932966	+	0.359965i	$0.882789\pi$
$312$	−4.15185e6	+	1.69892e7i	−0.136703	+	0.559384i
$313$	−3.26358e7	+	9.58274e6i	−1.06429	+	0.312505i	−0.766579	−	0.642150i	$-0.778042\pi$
$313$	−3.26358e7	+	9.58274e6i	−1.06429	+	0.312505i	−0.297714	+	0.954655i	$0.596224\pi$
$314$	2.85766e7	+	4.10870e6i	0.923043	+	0.132714i
$315$	2.08234e7	−	1.19291e7i	0.666225	−	0.381658i
$316$	−3.68723e7	+	8.07391e7i	−1.16853	+	2.55872i
$317$	−5.15760e6	+	1.75652e7i	−0.161909	+	0.551410i	0.838074	+	0.545556i	$0.183682\pi$
$317$	−5.15760e6	+	1.75652e7i	−0.161909	+	0.551410i	−0.999983	+	0.00585388i	$0.998137\pi$
$318$	−8.05250e6	−	4.66721e6i	−0.250409	−	0.145136i
$319$	−2.68891e6	−	1.87018e7i	−0.0828331	−	0.576117i
$320$	−1.34599e7	+	2.09440e7i	−0.410763	+	0.639160i
$321$	−1.65996e7	−	2.33942e7i	−0.501859	−	0.707281i
$322$	−8.39571e7	+	2.47253e7i	−2.51472	+	0.740585i
$323$		−	1.07144e8i		−	3.17953i
$324$	1.67060e7	+	4.93419e7i	0.491177	+	1.45071i
$325$	2.60368e6	+	1.81090e7i	0.0758467	+	0.527526i
$326$	7.36667e6	−	3.36425e6i	0.212627	−	0.0971035i
$327$	−3.89461e7	+	1.34060e7i	−1.11383	+	0.383402i
$328$	5.72837e6	−	1.25434e7i	0.162334	−	0.355462i
$329$	−3.98974e6	−	3.45713e6i	−0.112036	−	0.0970795i
$330$	−1.31141e7	+	6.73284e6i	−0.364918	+	0.187351i
$331$	−5.70374e7	+	1.67477e7i	−1.57281	+	0.461818i	−0.947818	−	0.318813i	$-0.896716\pi$
$331$	−5.70374e7	+	1.67477e7i	−1.57281	+	0.461818i	−0.624992	+	0.780631i	$0.714898\pi$
$332$	1.55820e7	−	1.35018e7i	0.425802	−	0.368959i
$333$	8.55746e6	+	3.58003e7i	0.231746	+	0.969513i
$334$	7.31536e7	−	4.70130e7i	1.96334	−	1.26176i
$335$	2.24736e7	−	1.94735e7i	0.597776	−	0.517976i
$336$	7.19309e6	−	9.11512e6i	0.189626	−	0.240295i
$337$	3.03968e6	−	2.11414e7i	0.0794215	−	0.552389i	−0.910796	−	0.412857i	$-0.864531\pi$
$337$	3.03968e6	−	2.11414e7i	0.0794215	−	0.552389i	0.990218	−	0.139532i	$-0.0445598\pi$
$338$	2.49120e7	+	2.15864e7i	0.645148	+	0.559024i
$339$	4.30348e6	−	821913.i	0.110464	−	0.0210973i
$340$	−5.22966e7	−	1.53557e7i	−1.33057	−	0.390690i
$341$	−1.70676e6	+	779451.i	−0.0430437	+	0.0196574i
$342$	−2.00562e7	+	1.02207e8i	−0.501384	+	2.55508i
$343$	−3.99690e7	−	2.56865e7i	−0.990469	−	0.636536i
$344$			1.23529e7i			0.303454i
$345$	8.75368e6	+	1.70166e7i	0.213174	+	0.414395i
$346$	9.10677e7			2.19855
$347$	−2.99105e7	+	4.65416e7i	−0.715871	+	1.11392i	0.272545	+	0.962143i	$0.412135\pi$
$347$	−2.99105e7	+	4.65416e7i	−0.715871	+	1.11392i	−0.988415	+	0.151773i	$0.951502\pi$
$348$	−4.92278e7	+	4.67805e7i	−1.16808	+	1.11001i
$349$	2.82286e6	+	6.18121e6i	0.0664070	+	0.145411i	0.939925	−	0.341380i	$-0.110894\pi$
$349$	2.82286e6	+	6.18121e6i	0.0664070	+	0.145411i	−0.873518	+	0.486791i	$0.838167\pi$
$350$	−2.47891e7	+	8.44241e7i	−0.578173	+	1.96907i
$351$	−2.91188e7	−	4.33695e6i	−0.673369	−	0.100291i
$352$	−1.80359e7	+	2.08145e7i	−0.413532	+	0.477241i
$353$	3.61764e7	+	5.20138e6i	0.822435	+	0.118248i	0.540670	−	0.841235i	$-0.318171\pi$
$353$	3.61764e7	+	5.20138e6i	0.822435	+	0.118248i	0.281765	+	0.959483i	$0.409080\pi$
$354$	−3.41495e7	+	4.32745e7i	−0.769795	+	0.975488i
$355$	4.58090e6	+	5.28664e6i	0.102392	+	0.118167i
$356$	−712563.	−	1.10877e6i	−0.0157933	−	0.0245749i
$357$	1.35125e8	+	5.43601e7i	2.96982	+	1.19475i
$358$	−1.57796e7	−	1.82107e7i	−0.343913	−	0.396896i
$359$	−2.35893e7	−	8.03377e7i	−0.509837	−	1.73634i	−0.663457	−	0.748215i	$-0.730911\pi$
$359$	−2.35893e7	−	8.03377e7i	−0.509837	−	1.73634i	0.153620	−	0.988130i	$-0.450907\pi$
$360$	1.63176e7	+	8.48201e6i	0.349743	+	0.181799i
$361$	−5.16987e7	+	5.96635e7i	−1.09890	+	1.26820i
$362$	1.19617e8	+	5.46274e7i	2.52155	+	1.15155i
$363$	3.13853e7	−	1.08034e7i	0.656154	−	0.225860i
$364$	−3.44194e7	−	7.53680e7i	−0.713673	−	1.56273i
$365$	2.40834e7	−	3.46268e6i	0.495267	−	0.0712087i
$366$	−3.80103e6	−	8.27249e7i	−0.0775279	−	1.68730i
$367$	4.41491e7			0.893148			0.446574	−	0.894747i	$-0.352644\pi$
$367$	4.41491e7			0.893148			0.446574	+	0.894747i	$0.352644\pi$
$368$	7.00229e6	+	6.05767e6i	0.140506	+	0.121552i
$369$	2.19099e7	+	7.66584e6i	0.436075	+	0.152574i
$370$	3.14953e7	+	2.02408e7i	0.621785	+	0.399597i
$371$	1.51487e7	−	2.17805e6i	0.296656	−	0.0426527i
$372$	5.83476e6	+	3.38182e6i	0.113343	+	0.0656934i
$373$	−9.98793e6	−	2.93272e6i	−0.192464	−	0.0565125i	0.184080	−	0.982911i	$-0.441069\pi$
$373$	−9.98793e6	−	2.93272e6i	−0.192464	−	0.0565125i	−0.376544	+	0.926399i	$0.622888\pi$
$374$	−8.13831e7	−	3.71664e7i	−1.55568	−	0.710454i
$375$	4.36073e7	+	4.23812e6i	0.826924	+	0.0803674i
$376$	575743.	−	4.00438e6i	0.0108309	−	0.0753306i
$377$	−1.08125e7	−	3.68242e7i	−0.201792	−	0.687241i
$378$	−1.18723e8	−	7.71491e7i	−2.19816	−	1.42842i
$379$	4.20917e7	−	2.70507e7i	0.773176	−	0.496890i	−0.0935863	−	0.995611i	$-0.529833\pi$
$379$	4.20917e7	−	2.70507e7i	0.773176	−	0.496890i	0.866763	+	0.498721i	$0.166197\pi$
$380$	3.46508e7	+	5.39178e7i	0.631485	+	0.982610i
$381$	2.95037e7	+	7.21015e6i	0.533459	+	0.130367i
$382$	4.40873e7	−	1.29452e7i	0.790903	−	0.232230i
$383$	7.16713e7	+	1.03048e7i	1.27570	+	0.183418i	0.746676	−	0.665188i	$-0.231649\pi$
$383$	7.16713e7	+	1.03048e7i	1.27570	+	0.183418i	0.529025	+	0.848606i	$0.322558\pi$
$384$	8.18674e7	+	7.95656e6i	1.44583	+	0.140518i
$385$	1.00697e7	−	2.20496e7i	0.176455	−	0.386383i
$386$	−3.18416e7	+	1.08443e8i	−0.553647	+	1.88555i
$387$	−2.07063e7	+	1.90685e6i	−0.357248	+	0.0328990i
$388$	−2.68981e6	−	1.87081e7i	−0.0460497	−	0.320283i
$389$	−3.20025e7	+	4.97968e7i	−0.543670	+	0.845966i	−0.999016	−	0.0443479i	$-0.985879\pi$
$389$	−3.20025e7	+	4.97968e7i	−0.543670	+	0.845966i	0.455347	+	0.890314i	$0.349515\pi$
$390$	−2.44206e7	+	1.73279e7i	−0.411683	+	0.292114i
$391$	−4.81614e7	+	1.05683e8i	−0.805691	+	1.76798i
$392$		−	8.73593e7i		−	1.45028i
$393$	−3.35016e6	−	7.29123e7i	−0.0551935	−	1.20122i
$394$	−1.24941e7	−	8.68984e7i	−0.204276	−	1.42077i
$395$	−4.79802e7	+	2.19118e7i	−0.778522	+	0.355539i
$396$	4.27585e7	+	3.06658e7i	0.688553	+	0.493820i
$397$	−2.49961e7	+	5.47339e7i	−0.399486	+	0.874752i	0.597836	+	0.801618i	$0.296027\pi$
$397$	−2.49961e7	+	5.47339e7i	−0.399486	+	0.874752i	−0.997322	+	0.0731340i	$0.976700\pi$
$398$	−4.22442e7	−	3.66048e7i	−0.670066	−	0.580616i
$399$	−7.82241e7	−	1.52363e8i	−1.23146	−	2.39862i
$400$	8.93116e6	−	2.62242e6i	0.139549	−	0.0409754i
$401$	−7.56704e7	+	6.55687e7i	−1.17353	+	1.01687i	−0.174042	+	0.984738i	$0.555683\pi$
$401$	−7.56704e7	+	6.55687e7i	−1.17353	+	1.01687i	−0.999484	+	0.0321279i	$0.989772\pi$
$402$	−1.62767e8	−	6.54805e7i	−2.50547	−	1.00794i
$403$	−3.20626e6	+	2.06054e6i	−0.0489873	+	0.0314822i
$404$	1.39401e7	−	1.20792e7i	0.211408	−	0.183186i
$405$	−1.16990e7	+	2.86615e7i	−0.176110	+	0.431453i
$406$	2.62681e7	−	1.82699e8i	0.392510	−	2.72997i
$407$	2.80986e7	+	2.43476e7i	0.416775	+	0.361137i
$408$	2.09386e7	+	1.09633e8i	0.308295	+	1.61421i
$409$	4.92079e7	+	1.44488e7i	0.719226	+	0.211184i	0.620809	−	0.783962i	$-0.286804\pi$
$409$	4.92079e7	+	1.44488e7i	0.719226	+	0.211184i	0.0984164	+	0.995145i	$0.468622\pi$
$410$	2.14758e7	−	9.80768e6i	0.311601	−	0.142303i
$411$	3.17891e7	−	3.02088e7i	0.457881	−	0.435119i
$412$	2.99613e7	+	1.92550e7i	0.428420	+	0.275329i
$413$		−	9.06465e7i		−	1.28677i
$414$	6.57249e7	−	9.17984e7i	0.926251	−	1.29370i
$415$	1.22524e7			0.171427
$416$	−3.02456e7	+	4.70630e7i	−0.420128	+	0.653732i
$417$	6.39861e7	+	6.73334e7i	0.882424	+	0.928587i
$418$	4.37043e7	+	9.56990e7i	0.598405	+	1.31032i
$419$	8.98861e6	−	3.06124e7i	0.122194	−	0.416155i	−0.875562	−	0.483106i	$-0.839509\pi$
$419$	8.98861e6	−	3.06124e7i	0.122194	−	0.416155i	0.997756	+	0.0669503i	$0.0213269\pi$
$420$	−8.55784e7	+	1.63444e7i	−1.15509	+	0.220608i
$421$	−5.52499e7	+	6.37618e7i	−0.740432	+	0.854504i	−0.993604	−	0.112917i	$-0.963981\pi$
$421$	−5.52499e7	+	6.37618e7i	−0.740432	+	0.854504i	0.253172	+	0.967421i	$0.418526\pi$
$422$	−6.66019e7	−	9.57591e6i	−0.886236	−	0.127422i
$423$	6.80116e6	+	346946.i	0.0898590	+	0.00458396i
$424$	7.68031e6	+	8.86355e6i	0.100758	+	0.116281i
$425$	6.31243e7	+	9.82234e7i	0.822299	+	1.27952i
$426$	1.54035e7	−	3.82890e7i	0.199246	−	0.495274i
$427$	8.91740e7	+	1.02912e8i	1.14539	+	1.32185i
$428$	2.93397e7	+	9.99220e7i	0.374218	+	1.27447i
$429$	−2.64540e7	+	1.35816e7i	−0.335057	+	0.172020i
$430$	−1.38501e7	+	1.59838e7i	−0.174199	+	0.201037i
$431$	−8.00573e7	−	3.65609e7i	−0.999929	−	0.456652i	−0.152924	−	0.988238i	$-0.548869\pi$
$431$	−8.00573e7	−	3.65609e7i	−0.999929	−	0.456652i	−0.847005	+	0.531586i	$0.821596\pi$
$432$	−75686.7	+	1.49783e7i	−0.000938790	+	0.185785i
$433$	1.42024e7	+	3.10989e7i	0.174944	+	0.383073i	0.976710	−	0.214565i	$-0.0688333\pi$
$433$	1.42024e7	+	3.10989e7i	0.174944	+	0.383073i	−0.801766	+	0.597638i	$0.796106\pi$
$434$	−1.81433e7	+	2.60861e6i	−0.221946	+	0.0319110i
$435$	−4.03140e7	+	1.85234e6i	−0.489765	+	0.0225036i
$436$	1.49535e8			1.80419
$437$	1.24183e8	−	5.68330e7i	1.48805	−	0.681015i
$438$	−8.30709e7	−	1.17074e8i	−0.988614	−	1.39327i
$439$	1.08379e8	+	6.96508e7i	1.28100	+	0.823252i	0.991011	−	0.133777i	$-0.0427106\pi$
$439$	1.08379e8	+	6.96508e7i	1.28100	+	0.823252i	0.289993	+	0.957029i	$0.406347\pi$
$440$	1.83867e7	−	2.64361e6i	0.215847	−	0.0310341i
$441$	1.46435e8	−	1.34852e7i	1.70737	−	0.157232i
$442$	−1.74371e8	−	5.12001e7i	−2.01934	−	0.592931i
$443$	−1.09987e8	−	5.02294e7i	−1.26512	−	0.577759i	−0.334031	−	0.942562i	$-0.608409\pi$
$443$	−1.09987e8	−	5.02294e7i	−1.26512	−	0.577759i	−0.931085	+	0.364804i	$0.881136\pi$
$444$	1.29267e7	−	1.33007e8i	0.147686	−	1.51959i
$445$	111466.	−	775264.i	0.00126492	−	0.00879771i
$446$	−2.78454e7	−	9.48328e7i	−0.313870	−	1.06894i
$447$	−1.23700e7	+	5.06177e7i	−0.138499	+	0.566735i
$448$	−2.03189e8	+	1.30582e8i	−2.25978	+	1.45227i
$449$	8.78146e6	+	1.36642e7i	0.0970125	+	0.150954i	0.886367	−	0.462983i	$-0.153221\pi$
$449$	8.78146e6	+	1.36642e7i	0.0970125	+	0.150954i	−0.789355	+	0.613938i	$0.789585\pi$
$450$	−4.18294e7	−	1.05514e8i	−0.459033	−	1.15790i
$451$	2.24964e7	−	6.60555e6i	0.245236	−	0.0720078i
$452$	−1.57442e7	−	2.26367e6i	−0.170492	−	0.0245131i
$453$	6.51725e6	−	6.70579e7i	0.0701084	−	0.721366i
$454$	−5.82327e7	+	1.27512e8i	−0.622300	+	1.36265i
$455$	1.38719e7	−	4.72435e7i	0.147266	−	0.501542i
$456$	6.58155e7	−	1.13554e8i	0.694119	−	1.19759i
$457$	1.21015e7	+	8.41677e7i	0.126792	+	0.881855i	0.949584	+	0.313513i	$0.101506\pi$
$457$	1.21015e7	+	8.41677e7i	0.126792	+	0.881855i	−0.822792	+	0.568342i	$0.807585\pi$
$458$	2.40378e7	−	3.74035e7i	0.250206	−	0.389329i
$459$	−1.80538e8	+	5.20214e7i	−1.86695	+	0.537953i
$460$	−9.94232e6	−	6.87580e7i	−0.102144	−	0.706399i
$461$			3.47339e7i			0.354528i	0.984163	+	0.177264i	$0.0567247\pi$
$461$			3.47339e7i			0.354528i	−0.984163	+	0.177264i	$0.943275\pi$
$462$	−1.42864e8	+	6.56429e6i	−1.44876	+	0.0665674i
$463$	−1.78975e6	−	1.24480e7i	−0.0180323	−	0.125417i	0.978817	−	0.204738i	$-0.0656341\pi$
$463$	−1.78975e6	−	1.24480e7i	−0.0180323	−	0.125417i	−0.996849	+	0.0793204i	$0.974725\pi$
$464$	−1.77617e7	+	8.11152e6i	−0.177800	+	0.0811985i
$465$	1.30441e6	+	3.78948e6i	0.0129734	+	0.0376895i
$466$	−5.19189e6	+	1.13687e7i	−0.0513060	+	0.112344i
$467$	−3.09512e7	−	2.68193e7i	−0.303897	−	0.263328i	0.489540	−	0.871981i	$-0.337165\pi$
$467$	−3.09512e7	−	2.68193e7i	−0.303897	−	0.263328i	−0.793437	+	0.608653i	$0.791710\pi$
$468$	9.48344e7	+	4.92956e7i	0.925185	+	0.480918i
$469$	2.76807e8	−	8.12780e7i	2.68324	−	0.787869i
$470$	5.23470e6	−	4.53589e6i	0.0504194	−	0.0436887i
$471$	2.28560e7	−	5.68141e7i	0.218745	−	0.543743i
$472$	5.84373e7	−	3.75553e7i	0.555730	−	0.357146i
$473$	−1.58734e7	+	1.37543e7i	−0.149998	+	0.129974i
$474$	2.44297e8	+	1.92784e8i	2.29395	+	1.81024i
$475$	1.95394e7	−	1.35900e8i	0.182318	−	1.26805i
$476$	−3.99623e8	−	3.46275e8i	−3.70535	−	3.21071i
$477$	−1.36718e7	+	1.42422e7i	−0.125971	+	0.131227i
$478$	2.12246e8	+	6.23210e7i	1.94337	+	0.570625i
$479$	5.56422e7	−	2.54109e7i	0.506288	−	0.231214i	−0.145861	−	0.989305i	$-0.546595\pi$
$479$	5.56422e7	−	2.54109e7i	0.506288	−	0.231214i	0.652148	+	0.758091i	$0.273868\pi$
$480$	4.05234e7	+	4.26433e7i	0.366423	+	0.385591i
$481$	6.35329e7	+	4.08301e7i	0.570904	+	0.366898i
$482$			1.75534e7i			0.156754i
$483$	8.67025e6	+	1.85447e8i	0.0769467	+	1.64581i
$484$	−1.20505e8			−1.06284
$485$	6.07239e6	−	9.44883e6i	0.0532273	−	0.0828233i
$486$	1.81957e8	−	1.58297e7i	1.58512	−	0.137899i
$487$	−7.42521e7	−	1.62589e8i	−0.642868	−	1.40769i	−0.897660	−	0.440689i	$-0.854734\pi$
$487$	−7.42521e7	−	1.62589e8i	−0.642868	−	1.40769i	0.254792	−	0.966996i	$-0.417993\pi$
$488$	−2.93994e7	+	1.00125e8i	−0.252976	+	0.861556i
$489$	−3.22261e6	−	1.68734e7i	−0.0275601	−	0.144303i
$490$	9.79475e7	−	1.13037e8i	0.832540	−	0.960803i
$491$	2.83973e7	+	4.08291e6i	0.239901	+	0.0344926i	0.261217	−	0.965280i	$-0.415876\pi$
$491$	2.83973e7	+	4.08291e6i	0.239901	+	0.0344926i	−0.0213155	+	0.999773i	$0.506785\pi$
$492$	−6.61541e7	−	5.22047e7i	−0.555471	−	0.438343i
$493$	−1.60395e8	−	1.85106e8i	−1.33860	−	1.54482i
$494$	1.15536e8	+	1.79777e8i	0.958374	+	1.49126i
$495$	7.26956e6	+	3.04123e7i	0.0599367	+	0.250746i
$496$	1.26984e6	+	1.46548e6i	0.0104065	+	0.0120097i
$497$	1.91196e7	+	6.51155e7i	0.155744	+	0.530414i
$498$	−3.30162e7	−	6.43082e7i	−0.267325	−	0.520689i
$499$	−6.63037e7	+	7.65186e7i	−0.533625	+	0.615836i	−0.956989	−	0.290123i	$-0.906304\pi$
$499$	−6.63037e7	+	7.65186e7i	−0.533625	+	0.615836i	0.423364	+	0.905960i	$0.360849\pi$
$500$	−1.44687e8	−	6.60764e7i	−1.15750	−	0.528611i
$501$	−6.00348e7	−	1.74409e8i	−0.477408	−	1.38693i
$502$	−1.47667e8	−	3.23345e8i	−1.16727	−	2.55596i
$503$	1.92442e7	−	2.76690e6i	0.151215	−	0.0217415i	−0.0662914	−	0.997800i	$-0.521117\pi$
$503$	1.92442e7	−	2.76690e6i	0.151215	−	0.0217415i	0.217507	+	0.976059i	$0.430208\pi$
$504$	1.09816e8	+	1.40615e8i	0.857778	+	1.09835i
$505$	1.09614e7			0.0851123
$506$	−91648.1	−	1.14039e8i	−0.000707411	−	0.880242i
$507$	5.70241e7	−	4.04621e7i	0.437557	−	0.310474i
$508$	−9.27603e7	−	5.96134e7i	−0.707573	−	0.454729i
$509$	−1.67393e8	+	2.40675e7i	−1.26936	+	0.182506i	−0.743887	−	0.668306i	$-0.767020\pi$
$509$	−1.67393e8	+	2.40675e7i	−1.26936	+	0.182506i	−0.525471	+	0.850812i	$0.676111\pi$
$510$	−9.58276e7	+	1.65335e8i	−0.722404	+	1.24639i
$511$	2.26487e8	+	6.65027e7i	1.69739	+	0.498398i
$512$	4.50768e7	+	2.05859e7i	0.335848	+	0.153377i
$513$	2.00502e8	+	9.27937e7i	1.48514	+	0.687332i
$514$	−3.58111e7	+	2.49072e8i	−0.263711	+	1.83415i
$515$	5.96280e6	+	2.03074e7i	0.0436544	+	0.148673i
$516$	7.33338e7	+	1.79214e7i	0.533771	+	0.130444i
$517$	5.78667e6	−	3.71886e6i	0.0418752	−	0.0269116i
$518$	1.96367e8	+	3.05553e8i	1.41279	+	2.19835i
$519$	4.58577e7	−	1.87648e8i	0.328028	−	1.34228i
$520$	3.62038e7	−	1.06304e7i	0.257480	−	0.0756030i
$521$	−4.53693e7	−	6.52312e6i	−0.320811	−	0.0461256i	−0.0199717	−	0.999801i	$-0.506358\pi$
$521$	−4.53693e7	−	6.52312e6i	−0.320811	−	0.0461256i	−0.300839	+	0.953675i	$0.597267\pi$
$522$	1.18355e8	+	2.06601e8i	0.832097	+	1.45251i
$523$	1.53974e7	−	3.37155e7i	0.107632	−	0.235681i	−0.848151	−	0.529755i	$-0.822284\pi$
$523$	1.53974e7	−	3.37155e7i	0.107632	−	0.235681i	0.955783	+	0.294074i	$0.0950112\pi$
$524$	−7.46550e7	+	2.54252e8i	−0.518878	+	1.76714i
$525$	1.61476e8	+	9.35911e7i	1.11591	+	0.646780i
$526$	−6.53434e7	−	4.54473e8i	−0.448998	−	3.12285i
$527$	−1.31502e7	+	2.04621e7i	−0.0898463	+	0.139804i
$528$	8.75515e6	+	1.23388e7i	0.0594787	+	0.0838246i
$529$	−1.48036e8	+	237940.i	−0.999999	+	0.00160731i
$530$			2.00801e7i			0.134877i
$531$	7.19723e7	+	9.21574e7i	0.480708	+	0.615526i
$532$	8.84903e7	+	6.15464e8i	0.587707	+	4.08759i
$533$	4.33214e7	−	1.97842e7i	0.286102	−	0.130659i
$534$	−4.36942e6	+	1.50403e6i	−0.0286946	+	0.00987720i
$535$	−2.57087e7	+	5.62942e7i	−0.167888	+	0.367623i
$536$	1.67080e8	+	1.44776e8i	1.08500	+	0.940161i
$537$	−4.54697e7	+	2.33444e7i	−0.293629	+	0.150751i
$538$	−8.25689e7	+	2.42444e7i	−0.530237	+	0.155692i
$539$	1.12256e8	−	9.72705e7i	0.716876	−	0.621176i
$540$	7.40275e7	−	8.45651e7i	0.470124	−	0.537044i
$541$	−2.75854e7	+	1.77281e7i	−0.174216	+	0.111962i	−0.624843	−	0.780751i	$-0.714837\pi$
$541$	−2.75854e7	+	1.77281e7i	−0.174216	+	0.111962i	0.450627	+	0.892712i	$0.351201\pi$
$542$	2.24456e8	−	1.94493e8i	1.40972	−	1.22153i
$543$	1.72796e8	−	2.18967e8i	1.07928	−	1.36767i
$544$	−5.08106e7	+	3.53396e8i	−0.315615	+	2.19515i
$545$	6.71583e7	+	5.81930e7i	0.414868	+	0.359485i
$546$	−2.85342e8	+	5.44969e7i	−1.75303	+	0.334807i
$547$	−2.59029e8	−	7.60577e7i	−1.58265	−	0.464709i	−0.632002	−	0.774967i	$-0.717767\pi$
$547$	−2.59029e8	−	7.60577e7i	−1.58265	−	0.464709i	−0.950653	+	0.310258i	$0.899585\pi$
$548$	−1.44821e8	+	6.61376e7i	−0.880016	+	0.401890i
$549$	−1.72372e8	−	3.38245e7i	−1.04171	−	0.204416i
$550$	−9.64465e7	−	6.19824e7i	−0.579694	−	0.372546i
$551$			2.88015e8i			1.72171i
$552$	−1.15960e8	+	8.24212e7i	−0.689433	+	0.490029i
$553$	−5.11726e8			−3.02595
$554$	2.15574e8	−	3.35440e8i	1.26785	−	1.97281i
$555$	5.75665e7	−	5.47047e7i	0.336737	−	0.319997i
$556$	−1.40088e8	−	3.06750e8i	−0.815036	−	1.78468i
$557$	2.11852e7	−	7.21502e7i	0.122593	−	0.417515i	−0.875211	−	0.483741i	$-0.839278\pi$
$557$	2.11852e7	−	7.21502e7i	0.122593	−	0.417515i	0.997805	+	0.0662260i	$0.0210958\pi$
$558$	1.63745e7	−	1.70577e7i	0.0942466	−	0.0981787i
$559$	−2.79386e7	+	3.22429e7i	−0.159945	+	0.184586i
$560$	−2.47962e7	−	3.56516e6i	−0.141196	−	0.0203009i
$561$	−1.17564e8	+	1.48977e8i	−0.665862	+	0.843783i
$562$	1.47926e8	+	1.70716e8i	0.833365	+	0.961754i
$563$	−7.35927e7	−	1.14512e8i	−0.412391	−	0.641694i	0.571471	−	0.820623i	$-0.306373\pi$
$563$	−7.35927e7	−	1.14512e8i	−0.412391	−	0.641694i	−0.983862	+	0.178929i	$0.942737\pi$
$564$	−2.29370e7	−	9.22746e6i	−0.127850	−	0.0514333i
$565$	−6.19001e6	−	7.14365e6i	−0.0343199	−	0.0396073i
$566$	1.01152e8	+	3.44494e8i	0.557863	+	1.89991i
$567$	−2.18752e8	+	2.05784e8i	−1.20006	+	1.12892i
$568$	−3.40568e7	+	3.93036e7i	−0.185848	+	0.214480i
$569$	−9.96413e7	−	4.55047e7i	−0.540882	−	0.247013i	0.126190	−	0.992006i	$-0.459725\pi$
$569$	−9.96413e7	−	4.55047e7i	−0.540882	−	0.247013i	−0.667072	+	0.744994i	$0.732453\pi$
$570$	2.12478e8	−	7.31389e7i	1.14733	−	0.394933i
$571$	−5.65002e7	−	1.23718e8i	−0.303488	−	0.664546i	0.695029	−	0.718981i	$-0.255391\pi$
$571$	−5.65002e7	−	1.23718e8i	−0.303488	−	0.664546i	−0.998517	+	0.0544355i	$0.982664\pi$
$572$	1.06860e8	−	1.53641e7i	0.570986	−	0.0820953i
$573$	−4.47357e6	−	9.73619e7i	−0.0237788	−	0.517518i
$574$	2.29047e8			1.21113
$575$	−8.03597e7	+	1.25263e8i	−0.422703	+	0.658902i
$576$	1.02896e8	−	2.94088e8i	0.538430	−	1.53890i
$577$	2.26962e7	+	1.45859e7i	0.118148	+	0.0759289i	0.598380	−	0.801212i	$-0.295811\pi$
$577$	2.26962e7	+	1.45859e7i	0.118148	+	0.0759289i	−0.480232	+	0.877141i	$0.659448\pi$
$578$	−8.43883e8	+	1.21332e8i	−4.37018	+	0.628337i
$579$	2.07415e8	+	1.20218e8i	1.06858	+	0.619345i
$580$	1.40579e8	+	4.12776e7i	0.720502	+	0.211558i
$581$	1.08126e8	+	4.93794e7i	0.551316	+	0.251778i
$582$	−6.59562e7	−	6.41017e6i	−0.334570	−	0.0325163i
$583$	−2.83794e6	+	1.97383e7i	−0.0143218	+	0.0996103i
$584$	5.09626e7	+	1.73563e8i	0.255866	+	0.871400i
$585$	2.34076e7	+	5.90451e7i	0.116920	+	0.294928i
$586$	2.01465e8	−	1.29474e8i	1.00117	−	0.643412i
$587$	−2.04916e8	−	3.18856e8i	−1.01312	−	1.57645i	−0.800517	−	0.599310i	$-0.795442\pi$
$587$	−2.04916e8	−	3.18856e8i	−1.01312	−	1.57645i	−0.212605	−	0.977138i	$-0.568195\pi$
$588$	−5.18615e8	−	1.26740e8i	−2.55102	−	0.623422i
$589$	2.74434e7	−	8.05811e6i	0.134305	−	0.0394355i
$590$	1.17721e8	+	1.69258e7i	0.573191	+	0.0824124i
$591$	−1.85349e8	−	1.80137e7i	−0.897897	−	0.0872652i
$592$	1.59618e7	−	3.49516e7i	0.0769339	−	0.168462i
$593$	−6.74179e7	+	2.29604e8i	−0.323304	+	1.10107i	0.624183	+	0.781278i	$0.285432\pi$
$593$	−6.74179e7	+	2.29604e8i	−0.323304	+	1.10107i	−0.947487	+	0.319794i	$0.896386\pi$
$594$	1.40033e8	−	1.20106e8i	0.668147	−	0.573067i
$595$	−4.47199e7	−	3.11034e8i	−0.212300	−	1.47658i
$596$	1.02275e8	−	1.59143e8i	0.483094	−	0.751709i
$597$	−9.66977e7	+	6.86130e7i	−0.454458	+	0.322466i
$598$	−3.31505e7	−	2.29258e8i	−0.155019	−	1.07207i
$599$		−	1.69723e8i		−	0.789696i	−0.918747	−	0.394848i	$-0.870797\pi$
$599$		−	1.69723e8i		−	0.789696i	0.918747	−	0.394848i	$-0.129203\pi$
$600$	6.56476e6	+	1.42874e8i	0.0303924	+	0.661455i
$601$	−1.72122e7	−	1.19713e8i	−0.0792889	−	0.551466i	−0.990285	−	0.139052i	$-0.955595\pi$
$601$	−1.72122e7	−	1.19713e8i	−0.0792889	−	0.551466i	0.910996	−	0.412415i	$-0.135314\pi$
$602$	−1.86642e8	+	8.52366e7i	−0.855500	+	0.390694i
$603$	−2.16887e8	+	3.02414e8i	−0.989196	+	1.37927i
$604$	−1.01610e8	+	2.22495e8i	−0.461133	+	1.00974i
$605$	−5.41205e7	−	4.68956e7i	−0.244397	−	0.211771i
$606$	−2.95373e7	−	5.75321e7i	−0.132725	−	0.258519i
$607$	9.73813e7	−	2.85937e7i	0.435421	−	0.127851i	−0.0566737	−	0.998393i	$-0.518049\pi$
$607$	9.73813e7	−	2.85937e7i	0.435421	−	0.127851i	0.492095	+	0.870542i	$0.336231\pi$
$608$	3.17289e8	−	2.74933e8i	1.41171	−	1.22325i
$609$	−3.63229e8	−	1.46125e8i	−1.60816	−	0.646955i
$610$	−1.50302e8	+	9.65930e7i	−0.662177	+	0.425555i
$611$	1.05595e7	−	9.14989e6i	0.0462936	−	0.0401136i
$612$	6.81222e8	+	3.47510e7i	2.97190	+	0.151605i
$613$	−1.23326e7	+	8.57749e7i	−0.0535392	+	0.372373i	0.945383	+	0.325961i	$0.105688\pi$
$613$	−1.23326e7	+	8.57749e7i	−0.0535392	+	0.372373i	−0.998922	+	0.0464123i	$0.985221\pi$
$614$	1.74126e8	+	1.50881e8i	0.752244	+	0.651823i
$615$	−9.39476e6	−	4.91904e7i	−0.0403888	−	0.211473i
$616$	1.72914e8	+	5.07720e7i	0.739754	+	0.217211i
$617$	2.24779e8	−	1.02653e8i	0.956976	−	0.437036i	0.125190	−	0.992133i	$-0.460046\pi$
$617$	2.24779e8	−	1.02653e8i	0.956976	−	0.437036i	0.831786	+	0.555097i	$0.187319\pi$
$618$	9.05178e7	−	8.60180e7i	0.383503	−	0.364438i
$619$	−3.62231e7	−	2.32792e7i	−0.152726	−	0.0981512i	0.462046	−	0.886856i	$-0.347116\pi$
$619$	−3.62231e7	−	2.32792e7i	−0.152726	−	0.0981512i	−0.614772	+	0.788705i	$0.710752\pi$
$620$		−	1.45498e7i		−	0.0610496i
$621$	−1.56058e8	−	1.81654e8i	−0.651643	−	0.758526i
$622$	1.54362e8			0.641460
$623$	4.10811e6	−	6.39235e6i	0.0169894	−	0.0264360i
$624$	2.11698e7	+	2.22773e7i	0.0871292	+	0.0916872i
$625$	4.01280e7	+	8.78680e7i	0.164364	+	0.359908i
$626$	1.21977e8	−	4.15415e8i	0.497227	−	1.69340i
$627$	2.19199e8	−	4.18643e7i	0.889273	−	0.169840i
$628$	−1.45594e8	+	1.68024e8i	−0.587845	+	0.678410i
$629$	4.77067e8	+	6.85919e7i	1.91702	+	0.275627i
$630$	−1.55626e7	+	3.05073e8i	−0.0622388	+	1.22006i
$631$	1.05246e8	+	1.21460e8i	0.418906	+	0.483443i	0.925503	−	0.378740i	$-0.123642\pi$
$631$	1.05246e8	+	1.21460e8i	0.418906	+	0.483443i	−0.506598	+	0.862183i	$0.669097\pi$
$632$	−2.12011e8	−	3.29895e8i	−0.839860	−	1.30685i
$633$	−5.32693e7	+	1.32413e8i	−0.210023	+	0.522061i
$634$	−1.52598e8	−	1.76107e8i	−0.598797	−	0.691049i
$635$	−1.84608e7	−	6.28718e7i	−0.0720991	−	0.245547i
$636$	6.37617e7	−	3.27356e7i	0.247850	−	0.127248i
$637$	1.97582e8	−	2.28021e8i	0.764413	−	0.882180i
$638$	2.18766e8	+	9.99070e7i	0.842398	+	0.384710i
$639$	−7.11393e7	−	5.10201e7i	−0.272651	−	0.195541i
$640$	−7.37186e7	−	1.61421e8i	−0.281214	−	0.615773i
$641$	−2.41321e7	+	3.46968e6i	−0.0916266	+	0.0131739i	−0.187976	−	0.982174i	$-0.560193\pi$
$641$	−2.41321e7	+	3.46968e6i	−0.0916266	+	0.0131739i	0.0963490	+	0.995348i	$0.469284\pi$
$642$	3.64742e8	−	1.67591e7i	1.37842	−	0.0633353i
$643$	2.29620e8			0.863728			0.431864	−	0.901939i	$-0.357856\pi$
$643$	2.29620e8			0.863728			0.431864	+	0.901939i	$0.357856\pi$
$644$	1.89367e8	−	6.46847e8i	0.709001	−	2.42183i
$645$	2.59609e7	+	3.65873e7i	0.0967478	+	0.136349i
$646$	1.14732e9	+	7.37338e8i	4.25586	+	2.73507i
$647$	−2.39270e8	+	3.44018e7i	−0.883436	+	0.127019i	−0.569076	−	0.822285i	$-0.692699\pi$
$647$	−2.39270e8	+	3.44018e7i	−0.883436	+	0.127019i	−0.314360	+	0.949304i	$0.601790\pi$
$648$	−2.23293e8	−	5.57659e7i	−0.820636	−	0.204948i
$649$	1.13326e8	+	3.32754e7i	0.414566	+	0.121728i
$650$	−2.11832e8	−	9.67402e7i	−0.771348	−	0.352263i
$651$	−3.76104e6	+	3.86985e7i	−0.0136322	+	0.140266i
$652$	−8.87554e6	+	6.17307e7i	−0.0320223	+	0.222720i
$653$	1.15525e8	+	3.93440e8i	0.414892	+	1.41299i	0.856669	+	0.515867i	$0.172530\pi$
$653$	1.15525e8	+	3.93440e8i	0.414892	+	1.41299i	−0.441777	+	0.897125i	$0.645652\pi$
$654$	1.24463e8	−	5.09297e8i	0.444945	−	1.82070i
$655$	−1.32473e8	+	8.51353e7i	−0.471416	+	0.302960i
$656$	−1.31001e7	−	2.03842e7i	−0.0464049	−	0.0722074i
$657$	−2.83065e8	+	1.12217e8i	−0.998136	+	0.395697i
$658$	6.44757e7	−	1.89318e7i	0.226318	−	0.0664529i
$659$	2.64996e8	+	3.81006e7i	0.925939	+	0.133130i	0.588757	−	0.808310i	$-0.299617\pi$
$659$	2.64996e8	+	3.81006e7i	0.925939	+	0.133130i	0.337181	+	0.941440i	$0.390526\pi$
$660$	1.09813e7	−	1.12989e8i	0.0381962	−	0.393012i
$661$	1.50947e8	−	3.30527e8i	0.522660	−	1.14446i	−0.445763	−	0.895151i	$-0.647068\pi$
$661$	1.50947e8	−	3.30527e8i	0.522660	−	1.14446i	0.968423	−	0.249314i	$-0.0802051\pi$
$662$	2.13178e8	−	7.26019e8i	0.734800	−	2.50250i
$663$	−1.93305e8	+	3.33516e8i	−0.663290	+	1.14440i
$664$	1.29636e7	+	9.01638e7i	0.0442814	+	0.307984i
$665$	−1.99771e8	+	3.10850e8i	−0.679310	+	1.05703i
$666$	−4.42245e8	−	1.54733e8i	−1.49706	−	0.523793i
$667$	1.29463e8	−	2.84088e8i	0.436282	−	0.957359i
$668$			6.69650e8i			2.24656i
$669$	−2.09428e8	+	9.62276e6i	−0.699449	+	0.0321382i
$670$	5.38683e7	+	3.74662e8i	0.179105	+	1.24571i
$671$	−1.61395e8	+	7.37067e7i	−0.534223	+	0.243972i
$672$	1.85753e8	+	5.39636e8i	0.612107	+	1.77825i
$673$	−1.52997e8	+	3.35016e8i	−0.501922	+	1.09906i	0.473918	+	0.880569i	$0.342839\pi$
$673$	−1.52997e8	+	3.35016e8i	−0.501922	+	1.09906i	−0.975840	+	0.218487i	$0.929888\pi$
$674$	2.05468e8	+	1.78039e8i	0.671064	+	0.581480i
$675$	−2.38478e8	+	3.30588e7i	−0.775419	+	0.107492i
$676$	−2.43564e8	+	7.15167e7i	−0.788446	+	0.231509i
$677$	1.48736e8	−	1.28880e8i	0.479346	−	0.415356i	−0.381384	−	0.924417i	$-0.624553\pi$
$677$	1.48736e8	−	1.28880e8i	0.479346	−	0.415356i	0.860731	+	0.509061i	$0.170007\pi$
$678$	−2.08142e7	+	5.17386e7i	−0.0667837	+	0.166007i
$679$	9.16682e7	−	5.89116e7i	0.292826	−	0.188188i
$680$	1.81987e8	−	1.57693e8i	0.578781	−	0.501516i
$681$	2.33419e8	+	1.84200e8i	0.739086	+	0.583241i
$682$	3.39895e6	−	2.36402e7i	0.0107150	−	0.0745244i
$683$	−3.40933e8	−	2.95420e8i	−1.07006	−	0.927210i	−0.0725212	−	0.997367i	$-0.523105\pi$
$683$	−3.40933e8	−	2.95420e8i	−1.07006	−	0.927210i	−0.997536	+	0.0701570i	$0.977650\pi$
$684$	−5.78636e8	−	5.55462e8i	−1.80816	−	1.73575i
$685$	−9.07793e7	−	2.66552e7i	−0.282433	−	0.0829298i
$686$	5.50111e8	−	2.51227e8i	1.70403	−	0.778205i
$687$	−6.49669e7	−	6.83655e7i	−0.200365	−	0.210847i
$688$	1.82605e7	+	1.17353e7i	0.0560721	+	0.0360353i
$689$			4.05059e7i			0.123840i
$690$	−2.42456e8	−	2.33673e7i	−0.738051	−	0.0711313i
$691$	3.04914e8			0.924152			0.462076	−	0.886840i	$-0.347105\pi$
$691$	3.04914e8			0.924152			0.462076	+	0.886840i	$0.347105\pi$
$692$	−3.79151e8	+	5.89971e8i	−1.14418	+	1.78038i
$693$	−5.84141e7	+	2.97681e8i	−0.175517	+	0.894442i
$694$	−2.92539e8	−	6.40572e8i	−0.875198	−	1.91642i
$695$	5.64592e7	−	1.92282e8i	0.168182	−	0.572776i
$696$	−5.62849e7	−	2.94704e8i	−0.166942	−	0.874095i
$697$	1.99039e8	−	2.29703e8i	0.587813	−	0.678372i
$698$	−8.56156e7	−	1.23097e7i	−0.251760	−	0.0361976i
$699$	2.08111e7	+	1.64228e7i	0.0609345	+	0.0480857i
$700$	−4.43724e8	−	5.12084e8i	−1.29366	−	1.49296i
$701$	−1.24137e8	−	1.93162e8i	−0.360370	−	0.560747i	0.612972	−	0.790105i	$-0.289974\pi$
$701$	−1.24137e8	−	1.93162e8i	−0.360370	−	0.560747i	−0.973342	+	0.229358i	$0.926337\pi$
$702$	2.46828e8	−	2.81964e8i	0.713484	−	0.815046i
$703$	−3.71146e8	−	4.28326e8i	−1.06827	−	1.23284i
$704$	−8.86637e7	−	3.01961e8i	−0.254114	−	0.865431i
$705$	−6.71039e6	−	1.30703e7i	−0.0191505	−	0.0373009i
$706$	−3.04653e8	+	3.51589e8i	−0.865748	+	0.999127i
$707$	9.67326e7	+	4.41763e7i	0.273725	+	0.125006i
$708$	−1.38170e8	−	4.01402e8i	−0.389327	−	1.13105i
$709$	1.76458e8	+	3.86389e8i	0.495111	+	1.08414i	0.978027	+	0.208476i	$0.0668503\pi$
$709$	1.76458e8	+	3.86389e8i	0.495111	+	1.08414i	−0.482916	+	0.875667i	$0.660422\pi$
$710$	−8.81347e7	+	1.26719e7i	−0.246248	+	0.0354051i
$711$	5.20255e8	−	4.06304e8i	1.44746	−	1.13043i
$712$	5.82298e6			0.0161326
$713$	−3.06913e7	−	4.38757e6i	−0.0846733	−	0.0121047i
$714$	−1.51199e9	+	1.07285e9i	−4.15388	+	2.94743i
$715$	5.39712e7	+	3.46852e7i	0.147654	+	0.0948912i
$716$	1.83673e8	−	2.64081e7i	0.500386	−	0.0719447i
$717$	2.35292e8	−	4.05958e8i	0.638337	−	1.10134i
$718$	1.02260e9	+	3.00264e8i	2.76270	+	0.811203i
$719$	4.28342e8	+	1.95617e8i	1.15240	+	0.526284i	0.897644	−	0.440721i	$-0.145277\pi$
$719$	4.28342e8	+	1.95617e8i	1.15240	+	0.526284i	0.254757	+	0.967005i	$0.418004\pi$
$720$	2.80402e7	−	1.60633e7i	0.0751250	−	0.0430366i
$721$	−2.92216e7	+	2.03241e8i	−0.0779647	+	0.542257i
$722$	−2.83111e8	−	9.64186e8i	−0.752220	−	2.56182i
$723$	3.61693e7	+	8.83912e6i	0.0957030	+	0.0233881i
$724$	−8.51911e8	+	5.47490e8i	−2.24480	+	1.44265i
$725$	−1.69685e8	−	2.64034e8i	−0.445275	−	0.692861i
$726$	−1.00300e8	+	4.10425e8i	−0.262115	+	1.07256i
$727$	−2.85195e8	+	8.37407e7i	−0.742229	+	0.217938i	−0.630920	−	0.775848i	$-0.717323\pi$
$727$	−2.85195e8	+	8.37407e7i	−0.742229	+	0.217938i	−0.111309	+	0.993786i	$0.535504\pi$
$728$	3.62334e8	+	5.20958e7i	0.939108	+	0.135023i
$729$	5.90083e7	−	3.82900e8i	0.152311	−	0.988333i
$730$	−1.28657e8	+	2.81719e8i	−0.330722	+	0.724180i
$731$	−7.67086e7	+	2.61246e8i	−0.196378	+	0.668801i
$732$	5.51748e8	+	3.19792e8i	1.40672	+	0.815333i
$733$	−1.03121e7	−	7.17220e7i	−0.0261839	−	0.182113i	0.972532	−	0.232768i	$-0.0747782\pi$
$733$	−1.03121e7	−	7.17220e7i	−0.0261839	−	0.182113i	−0.998716	+	0.0506550i	$0.983869\pi$
$734$	−3.03822e8	+	4.72756e8i	−0.768299	+	1.19550i
$735$	−1.83595e8	−	2.58745e8i	−0.462381	−	0.651643i
$736$	−4.36545e8	+	1.28562e8i	−1.09495	+	0.322463i
$737$			3.75899e8i			0.939006i
$738$	−2.32865e8	+	1.81861e8i	−0.579342	+	0.452449i
$739$	1.86784e7	+	1.29911e8i	0.0462814	+	0.321894i	0.999789	+	0.0205262i	$0.00653415\pi$
$739$	1.86784e7	+	1.29911e8i	0.0462814	+	0.321894i	−0.953508	+	0.301368i	$0.902557\pi$
$740$	−2.62255e8	+	1.19768e8i	−0.647185	+	0.295559i
$741$	4.28615e8	−	1.47537e8i	1.05345	−	0.362616i
$742$	−8.09261e7	+	1.77203e8i	−0.198096	+	0.433771i
$743$	5.29229e8	+	4.58580e8i	1.29026	+	1.11802i	0.986234	+	0.165354i	$0.0528765\pi$
$743$	5.29229e8	+	4.58580e8i	1.29026	+	1.11802i	0.304026	+	0.952664i	$0.401669\pi$
$744$	−2.65060e7	+	1.36084e7i	−0.0643615	+	0.0330436i
$745$	1.07865e8	−	3.16722e7i	0.260864	−	0.0765965i
$746$	1.00138e8	−	8.67703e7i	0.241203	−	0.209004i
$747$	−1.49135e8	+	3.56481e7i	−0.357781	+	0.0855215i
$748$	5.79608e8	−	3.72491e8i	1.38494	−	0.890044i
$749$	−4.53750e8	+	3.93177e8i	−1.07987	+	0.935712i
$750$	−3.45476e8	+	4.37789e8i	−0.818906	+	1.03772i
$751$	6.79459e7	−	4.72574e8i	0.160414	−	1.11571i	−0.737440	−	0.675413i	$-0.763965\pi$
$751$	6.79459e7	−	4.72574e8i	0.160414	−	1.11571i	0.897854	−	0.440293i	$-0.145126\pi$
$752$	−5.37247e6	−	4.65527e6i	−0.0126334	−	0.0109469i
$753$	−7.40621e8	+	1.41450e8i	−1.73465	+	0.331296i
$754$	4.68728e8	+	1.37631e8i	1.09347	+	0.321072i
$755$	−1.32221e8	+	6.03832e7i	−0.307227	+	0.140306i
$756$	9.94092e8	−	4.47930e8i	2.30071	−	1.03668i
$757$	7.72747e7	+	4.96614e7i	0.178135	+	0.114480i	0.626670	−	0.779285i	$-0.284418\pi$
$757$	7.72747e7	+	4.96614e7i	0.178135	+	0.114480i	−0.448535	+	0.893765i	$0.648054\pi$
$758$			6.36880e8i			1.46234i
$759$	−2.35027e8	−	5.72362e7i	−0.537518	−	0.130902i
$760$	−2.83163e8			−0.645053
$761$	−1.79766e8	+	2.79722e8i	−0.407900	+	0.634705i	−0.983049	−	0.183344i	$-0.941308\pi$
$761$	−1.79766e8	+	2.79722e8i	−0.407900	+	0.634705i	0.575149	+	0.818049i	$0.304944\pi$
$762$	−2.80243e8	+	2.66312e8i	−0.633389	+	0.601901i
$763$	3.58133e8	+	7.84202e8i	0.806252	+	1.76545i
$764$	−9.96891e7	+	3.39510e8i	−0.223546	+	0.761329i
$765$	2.92423e8	+	2.80711e8i	0.653171	+	0.627012i
$766$	−6.03567e8	+	6.96553e8i	−1.34289	+	1.54977i
$767$	2.37470e8	+	3.41430e7i	0.526287	+	0.0756686i
$768$	−1.91080e8	+	2.42137e8i	−0.421824	+	0.534537i
$769$	6.23344e7	+	7.19377e7i	0.137072	+	0.158189i	0.820135	−	0.572170i	$-0.193898\pi$
$769$	6.23344e7	+	7.19377e7i	0.137072	+	0.158189i	−0.683063	+	0.730359i	$0.739353\pi$
$770$	1.66814e8	+	2.59567e8i	0.365392	+	0.568562i
$771$	4.95188e8	+	1.99212e8i	1.08046	+	0.434662i
$772$	−5.69962e8	−	6.57771e8i	−1.23878	−	1.42963i
$773$	1.50471e8	+	5.12456e8i	0.325771	+	1.10948i	0.945760	+	0.324865i	$0.105319\pi$
$773$	1.50471e8	+	5.12456e8i	0.325771	+	1.10948i	−0.619989	+	0.784611i	$0.712863\pi$
$774$	1.22076e8	−	2.34849e8i	0.263274	−	0.506484i
$775$	−2.04110e7	+	2.35555e7i	−0.0438489	+	0.0506043i
$776$	7.59573e7	+	3.46885e7i	0.162549	+	0.0742336i
$777$	7.28484e8	−	2.50757e8i	1.55295	−	0.534553i
$778$	−3.13001e8	−	6.85376e8i	−0.664671	−	1.45543i
$779$	−3.53768e8	+	5.08641e7i	−0.748352	+	0.107597i
$780$	−1.05840e7	−	2.30349e8i	−0.0223032	−	0.485403i
$781$	−8.84256e7			−0.185620
$782$	−8.00242e8	−	1.24300e9i	−1.67341	−	2.59927i
$783$	4.85306e8	−	1.39839e8i	1.01095	−	0.291301i
$784$	−1.29138e8	−	8.29918e7i	−0.267982	−	0.172221i
$785$	−1.30776e8	+	1.88028e7i	−0.270346	+	0.0388699i
$786$	8.03811e8	+	4.65888e8i	1.65534	+	0.959431i
$787$	−6.17863e8	−	1.81421e8i	−1.26756	−	0.372189i	−0.422256	−	0.906477i	$-0.638762\pi$
$787$	−6.17863e8	−	1.81421e8i	−1.26756	−	0.372189i	−0.845302	+	0.534288i	$0.820580\pi$
$788$	6.14978e8	+	2.80851e8i	1.25684	+	0.573981i
$789$	−9.69362e8	−	9.42107e7i	−1.97358	−	0.191809i
$790$	9.55510e7	−	6.64571e8i	0.193800	−	1.34791i
$791$	−2.58357e7	−	8.79883e7i	−0.0522024	−	0.177785i
$792$	−2.16108e8	+	8.56731e7i	−0.435006	+	0.172452i
$793$	−3.03191e8	+	1.94849e8i	−0.607991	+	0.390732i
$794$	−4.14083e8	−	6.44326e8i	−0.827230	−	1.28720i
$795$	4.13757e7	+	1.01115e7i	0.0823462	+	0.0201239i
$796$	4.13019e8	−	1.21273e8i	0.818900	−	0.240451i
$797$	3.47451e8	+	4.99560e7i	0.686308	+	0.0986762i	0.476643	−	0.879097i	$-0.341853\pi$
$797$	3.47451e8	+	4.99560e7i	0.686308	+	0.0986762i	0.209665	+	0.977773i	$0.432763\pi$
$798$	2.16985e9	+	2.10884e8i	4.26992	+	0.414987i
$799$	3.70425e7	−	8.11117e7i	0.0726206	−	0.159017i
$800$	−1.28894e8	+	4.38973e8i	−0.251746	+	0.857368i
$801$	898863.	+	9.76069e6i	0.00174902	+	0.0189925i
$802$	−1.81379e8	−	1.26152e9i	−0.351612	−	2.44551i
$803$	−1.66282e8	+	2.58740e8i	−0.321144	+	0.499710i
$804$	1.10187e9	−	7.81846e8i	2.12013	−	1.50437i
$805$	3.36774e8	−	2.16814e8i	0.645582	−	0.415624i
$806$		−	4.85132e7i		−	0.0926520i
$807$	8.37833e6	+	1.82344e8i	0.0159418	+	0.346954i
$808$	1.15976e7	+	8.06633e7i	0.0219854	+	0.152912i
$809$	7.97746e8	−	3.64318e8i	1.50667	−	0.688075i	0.520511	−	0.853855i	$-0.325742\pi$
$809$	7.97746e8	−	3.64318e8i	1.50667	−	0.688075i	0.986163	+	0.165781i	$0.0530143\pi$
$810$	−2.26403e8	−	3.22515e8i	−0.426016	−	0.606868i
$811$	−6.02837e7	+	1.32003e8i	−0.113015	+	0.247469i	−0.957685	−	0.287819i	$-0.907070\pi$
$811$	−6.02837e7	+	1.32003e8i	−0.113015	+	0.247469i	0.844669	+	0.535288i	$0.179797\pi$
$812$	1.07423e9	+	9.30822e8i	2.00645	+	1.73860i
$813$	−2.87732e8	−	5.60438e8i	−0.535447	−	1.04293i
$814$	−4.54084e8	+	1.33331e8i	−0.841905	+	0.247206i
$815$	−2.80092e7	+	2.42701e7i	−0.0517403	+	0.0448332i
$816$	1.81955e8	+	7.31998e7i	0.334884	+	0.134722i
$817$	2.69344e8	−	1.73097e8i	0.493903	−	0.317412i
$818$	−4.93355e8	+	4.27494e8i	−0.901363	+	0.781035i
$819$	−3.13932e7	+	6.15400e8i	−0.0571458	+	1.12023i
$820$	−2.58746e7	+	1.79962e8i	−0.0469280	+	0.326391i
$821$	−2.82237e8	−	2.44560e8i	−0.510017	−	0.441932i	0.361447	−	0.932393i	$-0.382283\pi$
$821$	−2.82237e8	−	2.44560e8i	−0.510017	−	0.441932i	−0.871463	+	0.490461i	$0.836828\pi$
$822$	1.04717e8	+	5.48291e8i	0.188539	+	0.987179i
$823$	4.95482e8	+	1.45487e8i	0.888850	+	0.260990i	0.694114	−	0.719866i	$-0.255797\pi$
$823$	4.95482e8	+	1.45487e8i	0.888850	+	0.260990i	0.194737	+	0.980856i	$0.437615\pi$
$824$	−1.43130e8	+	6.53654e7i	−0.255829	+	0.116833i
$825$	−1.76283e8	+	1.67520e8i	−0.313942	+	0.298335i
$826$	9.70658e8	+	6.23804e8i	1.72237	+	1.10690i
$827$			2.73934e8i			0.484317i	0.970237	+	0.242158i	$0.0778553\pi$
$827$			2.73934e8i			0.484317i	−0.970237	+	0.242158i	$0.922145\pi$
$828$	3.21066e8	+	8.07984e8i	0.565592	+	1.42335i
$829$	1.60922e8			0.282457			0.141228	−	0.989977i	$-0.454895\pi$
$829$	1.60922e8			0.282457			0.141228	+	0.989977i	$0.454895\pi$
$830$	−8.43179e7	+	1.31201e8i	−0.147464	+	0.229458i
$831$	−5.82632e8	−	6.13111e8i	−1.01529	−	1.06841i
$832$	−2.65556e8	−	5.81487e8i	−0.461091	−	1.00965i
$833$	5.42482e8	−	1.84753e9i	0.938535	−	3.19636i
$834$	−1.16135e9	+	2.21804e8i	−2.00201	+	0.382359i
$835$	−2.60601e8	+	3.00749e8i	−0.447627	+	0.516589i
$836$	−8.01932e8	−	1.15300e8i	−1.37252	−	0.197339i
$837$	−2.69024e7	−	4.23297e7i	−0.0458791	−	0.0721887i
$838$	2.65946e8	+	3.06918e8i	0.451919	+	0.521542i
$839$	−8.31848e7	−	1.29438e8i	−0.140850	−	0.219168i	0.763660	−	0.645618i	$-0.223400\pi$
$839$	−8.31848e7	−	1.29438e8i	−0.140850	−	0.219168i	−0.904511	+	0.426451i	$0.859764\pi$
$840$	1.43664e8	−	3.57110e8i	0.242387	−	0.602510i
$841$	4.16317e7	+	4.80455e7i	0.0699900	+	0.0807728i
$842$	−3.02557e8	−	1.03042e9i	−0.506841	−	1.72614i
$843$	4.26254e8	−	2.18841e8i	0.711518	−	0.365297i
$844$	3.39327e8	−	3.91604e8i	0.564405	−	0.651358i
$845$	−1.37219e8	−	6.26659e7i	−0.227428	−	0.103863i
$846$	−5.05188e7	+	7.04403e7i	−0.0834338	+	0.116335i
$847$	−2.88607e8	−	6.31961e8i	−0.474959	−	1.04002i
$848$	2.03988e7	−	2.93290e6i	0.0334516	−	0.00480961i
$849$	7.60777e8	−	3.49560e7i	1.24318	−	0.0571214i
$850$	−1.48620e9			−2.42002
$851$	1.73553e8	+	5.89315e8i	0.281607	+	0.956222i
$852$	1.83920e8	+	2.59202e8i	0.297379	+	0.419102i
$853$	−2.68816e8	−	1.72758e8i	−0.433120	−	0.278350i	0.305860	−	0.952077i	$-0.401056\pi$
$853$	−2.68816e8	−	1.72758e8i	−0.433120	−	0.278350i	−0.738980	+	0.673727i	$0.764692\pi$
$854$	−1.71567e9	+	2.46676e8i	−2.75461	+	0.396054i
$855$	−4.37103e7	−	4.74648e8i	−0.0699336	−	0.759404i
$856$	−4.41461e8	−	1.29625e8i	−0.703835	−	0.206665i
$857$	2.31711e8	+	1.05819e8i	0.368132	+	0.168120i	0.590887	−	0.806754i	$-0.298778\pi$
$857$	2.31711e8	+	1.05819e8i	0.368132	+	0.168120i	−0.222755	+	0.974874i	$0.571505\pi$
$858$	3.66146e7	−	3.76738e8i	0.0579685	−	0.596455i
$859$	−5.14991e6	+	3.58184e7i	−0.00812493	+	0.0565101i	−0.993481	−	0.114002i	$-0.963633\pi$
$859$	−5.14991e6	+	3.58184e7i	−0.00812493	+	0.0565101i	0.985356	+	0.170512i	$0.0545421\pi$
$860$	−4.58859e7	−	1.56273e8i	−0.0721413	−	0.245691i
$861$	1.15338e8	−	4.71959e8i	0.180702	−	0.739427i
$862$	9.42432e8	−	6.05665e8i	1.47139	−	0.945606i
$863$	4.63658e8	+	7.21466e8i	0.721382	+	1.12249i	0.987357	+	0.158512i	$0.0506697\pi$
$863$	4.63658e8	+	7.21466e8i	0.721382	+	1.12249i	−0.265975	+	0.963980i	$0.585694\pi$
$864$	−6.17314e8	−	4.01145e8i	−0.957116	−	0.621957i
$865$	−3.99875e8	+	1.17414e8i	−0.617840	+	0.181414i
$866$	−4.30749e8	−	6.19324e7i	−0.663241	−	0.0953596i
$867$	−1.74934e8	+	1.79995e9i	−0.268421	+	2.76187i
$868$	5.86383e7	−	1.28400e8i	0.0896648	−	0.196338i
$869$	1.87849e8	−	6.39756e8i	0.286253	−	0.974889i
$870$	2.57594e8	−	4.44436e8i	0.391182	−	0.674919i
$871$	1.08664e8	+	7.55776e8i	0.164449	+	1.14377i
$872$	−3.57177e8	+	5.55778e8i	−0.538683	+	0.838208i
$873$	−4.64210e7	+	1.32677e8i	−0.0697705	+	0.199413i
$874$	−2.46013e8	+	1.72088e9i	−0.368489	+	2.57760i
$875$		−	9.17030e8i		−	1.36886i
$876$	1.10430e9	−	5.07404e7i	1.64277	−	0.0754816i
$877$	−8.86434e7	−	6.16529e8i	−0.131416	−	0.914017i	−0.943711	−	0.330771i	$-0.892691\pi$
$877$	−8.86434e7	−	6.16529e8i	−0.131416	−	0.914017i	0.812295	−	0.583246i	$-0.198218\pi$
$878$	−1.49166e9	+	6.81220e8i	−2.20388	+	1.00648i
$879$	−1.65336e8	−	4.80323e8i	−0.243445	−	0.707240i
$880$	1.35596e7	−	2.96913e7i	0.0198975	−	0.0435694i
$881$	8.76084e8	+	7.59131e8i	1.28120	+	1.11017i	0.988055	+	0.154102i	$0.0492485\pi$
$881$	8.76084e8	+	7.59131e8i	1.28120	+	1.11017i	0.293148	+	0.956067i	$0.405297\pi$
$882$	−8.63321e8	+	1.66085e9i	−1.25825	+	2.42061i
$883$	−1.14323e9	+	3.35683e8i	−1.66055	+	0.487582i	−0.971482	−	0.237112i	$-0.923799\pi$
$883$	−1.14323e9	+	3.35683e8i	−1.66055	+	0.487582i	−0.689070	+	0.724695i	$0.741981\pi$
$884$	1.05767e9	−	9.16477e8i	1.53107	−	1.32668i
$885$	9.41555e7	−	2.34046e8i	0.135836	−	0.337653i
$886$	1.29476e9	−	8.32094e8i	1.86161	−	1.19639i
$887$	1.05214e9	−	9.11682e8i	1.50765	−	1.30639i	0.707146	−	0.707068i	$-0.249982\pi$
$887$	1.05214e9	−	9.11682e8i	1.50765	−	1.30639i	0.800508	−	0.599322i	$-0.204563\pi$
$888$	4.63471e8	+	3.65743e8i	0.661887	+	0.522320i
$889$	9.04701e7	−	6.29233e8i	0.128766	−	0.895584i
$890$	7.53458e6	+	6.52875e6i	0.0106878	+	0.00926105i
$891$	−1.76968e8	−	3.49023e8i	−0.250185	−	0.493425i
$892$	7.30294e8	+	2.14434e8i	1.02897	+	0.302133i
$893$	−9.53799e7	+	4.35585e7i	−0.133938	+	0.0611673i
$894$	−4.56895e8	−	4.80797e8i	−0.639446	−	0.672898i
$895$	9.27669e7	+	5.96177e7i	0.129397	+	0.0831584i
$896$		−	1.72161e9i		−	2.39338i
$897$	−4.89088e8	−	4.71369e7i	−0.677656	−	0.0653106i
$898$	−2.06750e8			−0.285507
$899$	3.53490e7	−	5.50042e7i	0.0486517	−	0.0757036i
$900$	8.57709e8	+	1.68308e8i	1.17656	+	0.230876i
$901$	1.07387e8	+	2.35145e8i	0.146817	+	0.321485i
$902$	−8.40808e7	+	2.86353e8i	−0.114572	+	0.390195i
$903$	8.16480e7	+	4.27504e8i	0.110887	+	0.580599i
$904$	4.60197e7	−	5.31096e7i	0.0622929	−	0.0718898i
$905$	−5.95666e8	−	8.56439e7i	−0.803632	−	0.115545i
$906$	6.73217e8	+	5.31262e8i	0.905254	+	0.714371i
$907$	4.15408e8	+	4.79406e8i	0.556741	+	0.642513i	0.962440	−	0.271494i	$-0.0875176\pi$
$907$	4.15408e8	+	4.79406e8i	0.556741	+	0.642513i	−0.405700	+	0.914006i	$0.632972\pi$
$908$	−5.83624e8	−	9.08136e8i	−0.779606	−	1.21309i
$909$	−1.33420e8	+	3.18919e7i	−0.177636	+	0.0424609i
$910$	4.10428e8	+	4.73659e8i	0.544644	+	0.628553i
$911$	−2.10344e8	−	7.16365e8i	−0.278211	−	0.947500i	−0.973484	−	0.228754i	$-0.926535\pi$
$911$	−2.10344e8	−	7.16365e8i	−0.278211	−	0.947500i	0.695273	−	0.718745i	$-0.255283\pi$
$912$	−1.05334e8	−	2.05168e8i	−0.138863	−	0.270474i
$913$	−1.01426e8	+	1.17051e8i	−0.133271	+	0.153803i
$914$	−9.84561e8	−	4.49634e8i	−1.28945	−	0.588871i
$915$	1.23348e8	+	3.58341e8i	0.161016	+	0.467772i
$916$	1.42235e8	+	3.11452e8i	0.185064	+	0.405233i
$917$	−1.51216e9	+	2.17416e8i	−1.96106	+	0.281958i
$918$	6.85361e8	−	2.29123e9i	0.885914	−	2.96170i
$919$	1.68225e8			0.216743			0.108371	−	0.994110i	$-0.465436\pi$
$919$	1.68225e8			0.216743			0.108371	+	0.994110i	$0.465436\pi$
$920$	2.79301e8	+	1.27282e8i	0.358682	+	0.163456i
$921$	3.98578e8	−	2.82815e8i	0.510193	−	0.362013i
$922$	−3.71936e8	−	2.39029e8i	−0.474543	−	0.304970i
$923$	−1.77787e8	+	2.55619e7i	−0.226097	+	0.0325078i
$924$	5.52274e8	−	9.52856e8i	0.700065	−	1.20785i
$925$	5.92592e8	+	1.74001e8i	0.748740	+	0.219850i
$926$	1.45612e8	+	6.64987e7i	0.183385	+	0.0837492i
$927$	−1.31662e8	−	2.29830e8i	−0.165280	−	0.288514i
$928$	1.36584e8	−	9.49963e8i	0.170905	−	1.18867i
$929$	6.67498e7	+	2.27329e8i	0.0832535	+	0.283535i	0.990589	−	0.136873i	$-0.0437051\pi$
$929$	6.67498e7	+	2.27329e8i	0.0832535	+	0.283535i	−0.907335	+	0.420408i	$0.861887\pi$
$930$	−4.95549e7	−	1.21103e7i	−0.0616081	−	0.0150559i
$931$	−1.90480e9	+	1.22414e9i	−2.36048	+	1.51699i
$932$	−5.20345e7	−	8.09673e7i	−0.0642752	−	0.100014i
$933$	7.77301e7	−	3.18068e8i	0.0957071	−	0.391630i
$934$	5.00183e8	−	1.46867e8i	0.613887	−	0.180254i
$935$	4.05269e8	+	5.82688e7i	0.495802	+	0.0712856i
$936$	−4.09737e8	+	2.34725e8i	−0.499664	+	0.286241i
$937$	−2.10568e8	+	4.61079e8i	−0.255961	+	0.560476i	−0.993369	−	0.114972i	$-0.963322\pi$
$937$	−2.10568e8	+	4.61079e8i	−0.255961	+	0.560476i	0.737408	+	0.675448i	$0.236050\pi$
$938$	−1.03457e9	+	3.52343e9i	−1.25358	+	4.26930i
$939$	−7.94554e8	−	4.60522e8i	−0.959681	−	0.556229i
$940$	7.59107e6	+	5.27971e7i	0.00913944	+	0.0635662i
$941$	−6.01539e8	+	9.36013e8i	−0.721930	+	1.12335i	0.265319	+	0.964161i	$0.414523\pi$
$941$	−6.01539e8	+	9.36013e8i	−0.721930	+	1.12335i	−0.987249	+	0.159184i	$0.949114\pi$
$942$	4.51086e8	+	6.35725e8i	0.539643	+	0.760530i
$943$	3.71807e8	+	1.08848e8i	0.443387	+	0.129803i
$944$		−	1.22062e8i		−	0.145099i
$945$	6.20777e8	+	1.85689e8i	0.735597	+	0.220034i
$946$	−3.80478e7	−	2.64628e8i	−0.0449424	−	0.312581i
$947$	7.86473e8	−	3.59170e8i	0.926049	−	0.422912i	0.105455	−	0.994424i	$-0.466370\pi$
$947$	7.86473e8	−	3.59170e8i	0.926049	−	0.422912i	0.820594	+	0.571512i	$0.193643\pi$
$948$	−2.26603e9	+	7.80010e8i	−2.65975	+	0.915536i
$949$	−2.59528e8	+	5.68288e8i	−0.303659	+	0.664921i
$950$	1.32077e9	+	1.14445e9i	1.54048	+	1.33483i
$951$	−4.39716e8	+	2.25753e8i	−0.511247	+	0.262477i
$952$	2.24153e9	−	6.58174e8i	2.59797	−	0.762834i
$953$	6.60836e7	−	5.72617e7i	0.0763510	−	0.0661585i	−0.615849	−	0.787864i	$-0.711187\pi$
$953$	6.60836e7	−	5.72617e7i	0.0763510	−	0.0661585i	0.692200	+	0.721706i	$0.256642\pi$
$954$	−5.84224e7	−	2.44411e8i	−0.0672875	−	0.281499i
$955$	−1.76895e8	+	1.13684e8i	−0.203098	+	0.130523i
$956$	−1.28740e9	+	1.11554e9i	−1.47347	+	1.27677i
$957$	3.16023e8	−	4.00466e8i	0.360564	−	0.456909i
$958$	−1.10809e8	+	7.70696e8i	−0.126032	+	0.876570i
$959$	−6.93688e8	−	6.01084e8i	−0.786517	−	0.681521i
$960$	−6.60263e8	+	1.26102e8i	−0.746282	+	0.142531i
$961$	8.45323e8	+	2.48209e8i	0.952473	+	0.279671i
$962$	−8.74431e8	+	3.99339e8i	−0.982201	+	0.448556i
$963$	1.49136e8	−	7.60002e8i	0.166995	−	0.851013i
$964$	−1.13717e8	−	7.30818e7i	−0.126939	−	0.0815789i
$965$		−	5.17220e8i		−	0.575564i
$966$	−2.04546e9	−	1.18335e9i	−2.26914	−	1.31275i
$967$	−1.02406e8			−0.113252			−0.0566260	−	0.998395i	$-0.518034\pi$
$967$	−1.02406e8			−0.113252			−0.0566260	+	0.998395i	$0.518034\pi$
$968$	2.87836e8	−	4.47881e8i	0.317336	−	0.493784i
$969$	2.09705e9	−	1.99280e9i	2.30482	−	2.19024i
$970$	5.93911e7	+	1.30048e8i	0.0650738	+	0.142492i
$971$	2.41407e8	−	8.22158e8i	0.263689	−	0.898044i	−0.716098	−	0.698000i	$-0.754073\pi$
$971$	2.41407e8	−	8.22158e8i	0.263689	−	0.898044i	0.979787	−	0.200043i	$-0.0641083\pi$
$972$	−6.55011e8	+	1.24469e9i	−0.713263	+	1.35539i
$973$	1.27317e9	−	1.46932e9i	1.38213	−	1.59506i
$974$	2.25202e9	+	3.23791e8i	2.43722	+	0.350419i
$975$	−3.06006e8	+	3.87772e8i	−0.330153	+	0.418372i
$976$	1.20079e8	+	1.38579e8i	0.129157	+	0.149055i
$977$	4.97328e8	+	7.73858e8i	0.533285	+	0.829808i	0.998464	−	0.0554088i	$-0.0176462\pi$
$977$	4.97328e8	+	7.73858e8i	0.533285	+	0.829808i	−0.465178	+	0.885217i	$0.654010\pi$
$978$	2.02860e8	+	8.16095e7i	0.216860	+	0.0872417i
$979$	6.48362e6	+	7.48250e6i	0.00690987	+	0.00797441i
$980$	3.24504e8	+	1.10516e9i	0.344780	+	1.17421i
$981$	−9.86750e8	−	5.12920e8i	−1.04520	−	0.543303i
$982$	−2.39143e8	+	2.75985e8i	−0.252535	+	0.291441i
$983$	7.58638e8	+	3.46459e8i	0.798683	+	0.364746i	0.772583	−	0.634913i	$-0.218964\pi$
$983$	7.58638e8	+	3.46459e8i	0.798683	+	0.364746i	0.0260992	+	0.999659i	$0.491691\pi$
$984$	3.52044e8	−	1.21180e8i	0.369498	−	0.127188i
$985$	1.66900e8	+	3.65459e8i	0.174641	+	0.382411i
$986$	3.08594e9	−	4.43691e8i	3.21926	−	0.462860i
$987$	−6.54240e6	−	1.42388e8i	−0.00680434	−	0.148088i
$988$	−1.64568e9			−1.70638
$989$	−3.43478e8	+	4.96665e7i	−0.355067	+	0.0513422i
$990$	−3.75687e8	−	1.31446e8i	−0.387187	−	0.135469i
$991$	−2.59390e8	−	1.66700e8i	−0.266522	−	0.171283i	0.400554	−	0.916273i	$-0.368818\pi$
$991$	−2.59390e8	−	1.66700e8i	−0.266522	−	0.171283i	−0.667075	+	0.744990i	$0.732454\pi$
$992$	−9.43382e7	+	1.35638e7i	−0.0966390	+	0.0138946i
$993$	−1.38864e9	−	8.04853e8i	−1.41821	−	0.821994i
$994$	−8.28844e8	−	2.43370e8i	−0.843944	−	0.247804i
$995$	2.32687e8	+	1.06265e8i	0.236213	+	0.107875i
$996$	5.54072e8	+	5.38494e7i	0.560774	+	0.0545008i
$997$	−1.71555e8	+	1.19319e9i	−0.173108	+	1.20399i	0.699160	+	0.714965i	$0.253557\pi$
$997$	−1.71555e8	+	1.19319e9i	−0.173108	+	1.20399i	−0.872268	+	0.489027i	$0.837352\pi$
$998$	−3.63090e8	−	1.23657e9i	−0.365277	−	1.24402i
$999$	−5.41527e8	+	8.33344e8i	−0.543155	+	0.835849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.7.h.a.2.6	✓	460
3.2	odd	2	inner	69.7.h.a.2.41	yes	460
23.12	even	11	inner	69.7.h.a.35.41	yes	460
69.35	odd	22	inner	69.7.h.a.35.6	yes	460

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.7.h.a.2.6	✓	460	1.1	even	1	trivial
69.7.h.a.2.41	yes	460	3.2	odd	2	inner
69.7.h.a.35.6	yes	460	69.35	odd	22	inner
69.7.h.a.35.41	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)

\(f(q)\)	\(=\)	\(q+(-6.88172 + 10.7082i) q^{2} +(18.5992 + 19.5722i) q^{3} +(-40.7202 - 89.1647i) q^{4} +(16.4113 - 55.8918i) q^{5} +(-337.576 + 64.4730i) q^{6} +(370.080 - 427.095i) q^{7} +(428.662 + 61.6324i) q^{8} +(-37.1400 + 728.053i) q^{9} +O(q^{10})\)	\(q+(-6.88172 + 10.7082i) q^{2} +(18.5992 + 19.5722i) q^{3} +(-40.7202 - 89.1647i) q^{4} +(16.4113 - 55.8918i) q^{5} +(-337.576 + 64.4730i) q^{6} +(370.080 - 427.095i) q^{7} +(428.662 + 61.6324i) q^{8} +(-37.1400 + 728.053i) q^{9} +(485.560 + 560.366i) q^{10} +(398.099 + 619.454i) q^{11} +(987.785 - 2455.37i) q^{12} +(979.481 + 1130.38i) q^{13} +(2026.62 + 6902.03i) q^{14} +(1399.16 - 718.337i) q^{15} +(498.339 - 575.114i) q^{16} +(8682.88 + 3965.34i) q^{17} +(-7540.53 - 5407.96i) q^{18} +(-4662.87 - 10210.3i) q^{19} +(-5651.84 + 812.612i) q^{20} +(15242.4 - 700.354i) q^{21} -9372.82 q^{22} +(9.77808 + 12167.0i) q^{23} +(6766.50 + 9536.17i) q^{24} +(10290.0 + 6613.00i) q^{25} +(-18844.8 + 2709.48i) q^{26} +(-14940.4 + 12814.3i) q^{27} +(-53151.5 - 15606.7i) q^{28} +(-23340.5 - 10659.2i) q^{29} +(-1936.56 + 19925.8i) q^{30} +(-362.639 + 2522.21i) q^{31} +(10537.6 + 35887.9i) q^{32} +(-4719.74 + 19313.0i) q^{33} +(-102215. + 65689.4i) q^{34} +(-17797.6 - 27693.6i) q^{35} +(66429.0 - 26334.9i) q^{36} +(48446.9 - 14225.3i) q^{37} +(141422. + 20333.4i) q^{38} +(-3906.47 + 40194.8i) q^{39} +(10479.7 - 22947.2i) q^{40} +(8970.71 - 30551.4i) q^{41} +(-97394.2 + 168037. i) q^{42} +(4059.38 + 28233.6i) q^{43} +(39022.8 - 60720.6i) q^{44} +(40082.7 + 14024.1i) q^{45} +(-130353. - 83625.1i) q^{46} -9341.56i q^{47} +(20524.9 - 943.077i) q^{48} +(-28707.8 - 199667. i) q^{49} +(-141626. + 64678.5i) q^{50} +(83884.3 + 243695. i) q^{51} +(60905.5 - 133364. i) q^{52} +(20466.8 + 17734.6i) q^{53} +(-34402.2 - 248168. i) q^{54} +(41155.7 - 12084.4i) q^{55} +(184962. - 160271. i) q^{56} +(113112. - 281165. i) q^{57} +(274763. - 176580. i) q^{58} +(121222. - 105040. i) q^{59} +(-121024. - 95504.9i) q^{60} +(-34292.0 + 238506. i) q^{61} +(-24512.7 - 21240.4i) q^{62} +(297203. + 285300. i) q^{63} +(-410080. - 120410. i) q^{64} +(79253.6 - 36193.9i) q^{65} +(-174327. - 183446. i) q^{66} +(429453. + 275993. i) q^{67} -935676. i q^{68} +(-237953. + 226488. i) q^{69} +419026. q^{70} +(-64923.9 + 101024. i) q^{71} +(-60792.2 + 309800. i) q^{72} +(173515. + 379945. i) q^{73} +(-181071. + 616672. i) q^{74} +(61955.4 + 324395. i) q^{75} +(-720523. + 831528. i) q^{76} +(411894. + 59221.4i) q^{77} +(-403529. - 318440. i) q^{78} +(-592979. - 684335. i) q^{79} +(-23965.8 - 37291.4i) q^{80} +(-528682. - 54079.8i) q^{81} +(265416. + 306306. i) q^{82} +(59258.9 + 201817. i) q^{83} +(-683119. - 1.33056e6i) q^{84} +(364127. - 420225. i) q^{85} +(-330265. - 150827. i) q^{86} +(-225489. - 655077. i) q^{87} +(132472. + 290072. i) q^{88} +(13308.9 - 1913.54i) q^{89} +(-426010. + 332702. i) q^{90} +845267. q^{91} +(1.08447e6 - 496314. i) q^{92} +(-56110.0 + 39813.5i) q^{93} +(100031. + 64286.0i) q^{94} +(-647194. + 93052.4i) q^{95} +(-506412. + 873730. i) q^{96} +(185006. + 54322.8i) q^{97} +(2.33563e6 + 1.06665e6i) q^{98} +(-465781. + 266831. i) 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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