LMFDB - Embedded newform 49.7.h.a.3.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,7,Mod(3,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.3"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	49.h (of order $42$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.2726500974$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			3.19
Character	$\chi$	$=$	49.3
Dual form			49.7.h.a.33.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.29501 - 5.84759i) q^{2} +(-46.2118 - 3.46309i) q^{3} +(17.9881 + 16.6905i) q^{4} +(-95.8768 + 140.625i) q^{5} +(-126.307 + 262.280i) q^{6} +(-87.9175 - 331.541i) q^{7} +(501.105 - 241.319i) q^{8} +(1402.68 + 211.419i) q^{9} +(602.282 + 883.385i) q^{10} +(248.191 - 37.4088i) q^{11} +(-773.459 - 833.591i) q^{12} +(-626.337 + 499.487i) q^{13} +(-2140.49 - 246.785i) q^{14} +(4917.63 - 6166.52i) q^{15} +(-143.735 - 1918.01i) q^{16} +(1255.50 - 4070.23i) q^{17} +(4455.45 - 7717.07i) q^{18} +(3683.95 - 2126.93i) q^{19} +(-4071.74 + 929.349i) q^{20} +(2914.66 + 15625.6i) q^{21} +(350.850 - 1537.17i) q^{22} +(17744.9 - 5473.57i) q^{23} +(-23992.7 + 9416.42i) q^{24} +(-4874.70 - 12420.5i) q^{25} +(1483.35 + 4808.89i) q^{26} +(-31152.1 - 7110.27i) q^{27} +(3952.12 - 7431.17i) q^{28} +(5888.93 + 25801.1i) q^{29} +(-24773.3 - 42908.5i) q^{30} +(38772.7 + 22385.4i) q^{31} +(22468.8 + 6930.70i) q^{32} +(-11598.9 + 869.217i) q^{33} +(-20919.7 - 16682.9i) q^{34} +(55052.4 + 19423.7i) q^{35} +(21702.7 + 27214.4i) q^{36} +(15037.4 - 13952.7i) q^{37} +(-3982.72 - 26423.6i) q^{38} +(30673.9 - 20913.1i) q^{39} +(-14108.7 + 93605.0i) q^{40} +(-48526.5 - 100766. i) q^{41} +(98061.1 + 18817.1i) q^{42} +(-96246.3 - 46349.8i) q^{43} +(5088.84 + 3469.52i) q^{44} +(-164215. + 176982. i) q^{45} +(8717.48 - 116327. i) q^{46} +(161818. + 63508.7i) q^{47} +89132.4i q^{48} +(-102190. + 58296.5i) q^{49} -83817.7 q^{50} +(-72114.5 + 183745. i) q^{51} +(-19603.3 - 1469.06i) q^{52} +(-53706.7 - 49832.5i) q^{53} +(-113072. + 165847. i) q^{54} +(-18535.1 + 38488.6i) q^{55} +(-124063. - 144921. i) q^{56} +(-177608. + 85531.4i) q^{57} +(164389. + 24777.7i) q^{58} +(-82403.4 - 120864. i) q^{59} +(191381. - 28846.0i) q^{60} +(213108. + 229676. i) q^{61} +(219885. - 175352. i) q^{62} +(-53225.5 - 483632. i) q^{63} +(168844. - 211723. i) q^{64} +(-10189.4 - 135968. i) q^{65} +(-21536.8 + 69820.5i) q^{66} +(-34609.2 + 59944.9i) q^{67} +(90518.2 - 52260.7i) q^{68} +(-838977. + 191491. i) q^{69} +(239927. - 277346. i) q^{70} +(48818.8 - 213889. i) q^{71} +(753907. - 232550. i) q^{72} +(499663. - 196103. i) q^{73} +(-47078.6 - 119954. i) q^{74} +(182255. + 590856. i) q^{75} +(101767. + 23227.6i) q^{76} +(-34222.9 - 78996.6i) q^{77} +(-51894.4 - 227364. i) q^{78} +(196500. + 340348. i) q^{79} +(283502. + 163680. i) q^{80} +(426813. + 131654. i) q^{81} +(-700610. + 52503.4i) q^{82} +(-679250. - 541684. i) q^{83} +(-208369. + 329721. i) q^{84} +(452005. + 566796. i) q^{85} +(-491921. + 456436. i) q^{86} +(-182786. - 1.21271e6i) q^{87} +(115342. - 78639.0i) q^{88} +(61193.7 - 405994. i) q^{89} +(658042. + 1.36644e6i) q^{90} +(220667. + 163743. i) q^{91} +(410552. + 197711. i) q^{92} +(-1.71423e6 - 1.16874e6i) q^{93} +(742747. - 800490. i) q^{94} +(-54105.0 + 721981. i) q^{95} +(-1.01432e6 - 398091. i) q^{96} +449664. i q^{97} +(106367. + 731357. i) q^{98} +356040. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 13 q^{2} - 11 q^{3} + 819 q^{4} - 179 q^{5} + 770 q^{6} + 392 q^{7} + 828 q^{8} - 1160 q^{9} - 2594 q^{10} - 5305 q^{11} + 7497 q^{12} - 14 q^{13} - 11403 q^{14} - 6196 q^{15} + 27903 q^{16} - 5107 q^{17}+ \cdots - 4449616 q^{99}+O(q^{100}) $ 324 * q - 13 * q^2 - 11 * q^3 + 819 * q^4 - 179 * q^5 + 770 * q^6 + 392 * q^7 + 828 * q^8 - 1160 * q^9 - 2594 * q^10 - 5305 * q^11 + 7497 * q^12 - 14 * q^13 - 11403 * q^14 - 6196 * q^15 + 27903 * q^16 - 5107 * q^17 - 11538 * q^18 - 30006 * q^19 - 50190 * q^20 + 8953 * q^21 + 33042 * q^22 + 54531 * q^23 + 90184 * q^24 - 92804 * q^25 - 93366 * q^26 - 11774 * q^27 - 19180 * q^28 - 80398 * q^29 + 15851 * q^30 + 39378 * q^31 - 197841 * q^32 + 36697 * q^33 - 54698 * q^34 - 819 * q^35 + 706300 * q^36 + 15331 * q^37 - 304462 * q^38 - 179298 * q^39 - 515414 * q^40 - 116046 * q^41 + 1203482 * q^42 - 225018 * q^43 + 1373764 * q^44 + 465772 * q^45 + 1100364 * q^46 + 270021 * q^47 - 767900 * q^49 - 1164040 * q^50 - 1215743 * q^51 - 3954790 * q^52 + 141807 * q^53 - 1093487 * q^54 + 991354 * q^55 - 596680 * q^56 - 388207 * q^57 + 381012 * q^58 + 2015849 * q^59 + 5807298 * q^60 + 258821 * q^61 - 525742 * q^62 - 1265432 * q^63 + 872972 * q^64 - 70154 * q^65 + 497766 * q^66 - 324190 * q^67 - 799617 * q^68 - 2216774 * q^69 + 56140 * q^70 - 1031026 * q^71 + 4633092 * q^72 + 1268305 * q^73 - 1444192 * q^74 - 1699244 * q^75 - 5464011 * q^76 - 2274741 * q^77 - 1285956 * q^78 - 515710 * q^79 + 8314050 * q^80 - 1069027 * q^81 + 357910 * q^82 - 3183054 * q^83 - 10099096 * q^84 - 1596848 * q^85 - 5387681 * q^86 - 4197040 * q^87 - 1024645 * q^88 + 983769 * q^89 + 18547774 * q^90 + 13421086 * q^91 + 5294506 * q^92 + 15477850 * q^93 + 8903632 * q^94 + 5236430 * q^95 + 7804258 * q^96 - 10234553 * q^98 - 4449616 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{42}\right)$

Coefficient data

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

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

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

$2$	2.29501	−	5.84759i	0.286876	−	0.730949i	−0.712689	−	0.701480i	$-0.752523\pi$
$2$	2.29501	−	5.84759i	0.286876	−	0.730949i	0.999566	−	0.0294692i	$-0.00938171\pi$
$3$	−46.2118	−	3.46309i	−1.71155	−	0.128263i	−0.817410	−	0.576057i	$-0.804591\pi$
$3$	−46.2118	−	3.46309i	−1.71155	−	0.128263i	−0.894137	+	0.447794i	$0.852210\pi$
$4$	17.9881	+	16.6905i	0.281063	+	0.260789i
$5$	−95.8768	+	140.625i	−0.767014	+	1.12500i	0.221689	+	0.975117i	$0.428843\pi$
$5$	−95.8768	+	140.625i	−0.767014	+	1.12500i	−0.988703	+	0.149886i	$0.952109\pi$
$6$	−126.307	+	262.280i	−0.584756	+	1.21426i
$7$	−87.9175	−	331.541i	−0.256319	−	0.966592i
$7$	−87.9175	−	331.541i	−0.256319	−	0.966592i
$8$	501.105	−	241.319i	0.978721	−	0.471327i
$9$	1402.68	+	211.419i	1.92411	+	0.290013i
$10$	602.282	+	883.385i	0.602282	+	0.883385i
$11$	248.191	−	37.4088i	0.186470	−	0.0281058i	−0.0551435	−	0.998478i	$-0.517562\pi$
$11$	248.191	−	37.4088i	0.186470	−	0.0281058i	0.241613	+	0.970373i	$0.422324\pi$
$12$	−773.459	−	833.591i	−0.447604	−	0.482402i
$13$	−626.337	+	499.487i	−0.285088	+	0.227350i	−0.755583	−	0.655052i	$-0.772647\pi$
$13$	−626.337	+	499.487i	−0.285088	+	0.227350i	0.470496	+	0.882402i	$0.344075\pi$
$14$	−2140.49	−	246.785i	−0.780062	−	0.0899362i
$15$	4917.63	−	6166.52i	1.45708	−	1.82712i
$16$	−143.735	−	1918.01i	−0.0350915	−	0.468264i
$17$	1255.50	−	4070.23i	0.255547	−	0.828462i	−0.733349	−	0.679852i	$-0.762044\pi$
$17$	1255.50	−	4070.23i	0.255547	−	0.828462i	0.988896	−	0.148610i	$-0.0474799\pi$
$18$	4455.45	−	7717.07i	0.763966	−	1.32323i
$19$	3683.95	−	2126.93i	0.537098	−	0.310094i	−0.206804	−	0.978382i	$-0.566306\pi$
$19$	3683.95	−	2126.93i	0.537098	−	0.310094i	0.743902	+	0.668289i	$0.232973\pi$
$20$	−4071.74	+	929.349i	−0.508968	+	0.116169i
$21$	2914.66	+	15625.6i	0.314725	+	1.68724i
$22$	350.850	−	1537.17i	0.0329498	−	0.144363i
$23$	17744.9	−	5473.57i	1.45844	−	0.449870i	0.538735	−	0.842475i	$-0.318902\pi$
$23$	17744.9	−	5473.57i	1.45844	−	0.449870i	0.919707	+	0.392605i	$0.128426\pi$
$24$	−23992.7	+	9416.42i	−1.73558	+	0.681165i
$25$	−4874.70	−	12420.5i	−0.311981	−	0.794914i
$26$	1483.35	+	4808.89i	0.0843962	+	0.273606i
$27$	−31152.1	−	7110.27i	−1.58269	−	0.361239i
$28$	3952.12	−	7431.17i	0.180034	−	0.338519i
$29$	5888.93	+	25801.1i	0.241458	+	1.05790i	0.939690	+	0.342027i	$0.111113\pi$
$29$	5888.93	+	25801.1i	0.241458	+	1.05790i	−0.698232	+	0.715872i	$0.746029\pi$
$30$	−24773.3	−	42908.5i	−0.917528	−	1.58921i
$31$	38772.7	+	22385.4i	1.30149	+	0.751416i	0.980660	−	0.195720i	$-0.0627045\pi$
$31$	38772.7	+	22385.4i	1.30149	+	0.751416i	0.320831	+	0.947136i	$0.396038\pi$
$32$	22468.8	+	6930.70i	0.685693	+	0.211508i
$33$	−11598.9	+	869.217i	−0.322756	+	0.0241872i
$34$	−20919.7	−	16682.9i	−0.532253	−	0.424458i
$35$	55052.4	+	19423.7i	1.28402	+	0.453030i
$36$	21702.7	+	27214.4i	0.465165	+	0.583298i
$37$	15037.4	−	13952.7i	0.296872	−	0.275457i	−0.517647	−	0.855594i	$-0.673192\pi$
$37$	15037.4	−	13952.7i	0.296872	−	0.275457i	0.814518	+	0.580138i	$0.197001\pi$
$38$	−3982.72	−	26423.6i	−0.0725819	−	0.481550i
$39$	30673.9	−	20913.1i	0.517101	−	0.352554i
$40$	−14108.7	+	93605.0i	−0.220448	+	1.46258i
$41$	−48526.5	−	100766.i	−0.704089	−	1.46206i	−0.878678	−	0.477415i	$-0.841574\pi$
$41$	−48526.5	−	100766.i	−0.704089	−	1.46206i	0.174589	−	0.984641i	$-0.444140\pi$
$42$	98061.1	+	18817.1i	1.32358	+	0.253983i
$43$	−96246.3	−	46349.8i	−1.21054	−	0.582965i	−0.283877	−	0.958861i	$-0.591621\pi$
$43$	−96246.3	−	46349.8i	−1.21054	−	0.582965i	−0.926662	+	0.375896i	$0.877335\pi$
$44$	5088.84	+	3469.52i	0.0597394	+	0.0407297i
$45$	−164215.	+	176982.i	−1.80209	+	1.94219i
$46$	8717.48	−	116327.i	0.0895607	−	1.19510i
$47$	161818.	+	63508.7i	1.55859	+	0.611702i	0.979119	−	0.203289i	$-0.0651632\pi$
$47$	161818.	+	63508.7i	1.55859	+	0.611702i	0.579473	+	0.814992i	$0.303258\pi$
$48$			89132.4i			0.805957i
$49$	−102190.	+	58296.5i	−0.868601	+	0.495512i
$50$	−83817.7			−0.670542
$51$	−72114.5	+	183745.i	−0.543641	+	1.38517i
$52$	−19603.3	−	1469.06i	−0.139418	−	0.0104479i
$53$	−53706.7	−	49832.5i	−0.360745	−	0.334723i	0.478888	−	0.877876i	$-0.341040\pi$
$53$	−53706.7	−	49832.5i	−0.360745	−	0.334723i	−0.839634	+	0.543153i	$0.817230\pi$
$54$	−113072.	+	165847.i	−0.718084	+	1.05324i
$55$	−18535.1	+	38488.6i	−0.111406	+	0.231336i
$56$	−124063.	−	144921.i	−0.706446	−	0.825214i
$57$	−177608.	+	85531.4i	−0.959041	+	0.461850i
$58$	164389.	+	24777.7i	0.842539	+	0.126992i
$59$	−82403.4	−	120864.i	−0.401226	−	0.588491i	0.571456	−	0.820633i	$-0.306379\pi$
$59$	−82403.4	−	120864.i	−0.401226	−	0.588491i	−0.972682	+	0.232142i	$0.925426\pi$
$60$	191381.	−	28846.0i	0.886022	−	0.133546i
$61$	213108.	+	229676.i	0.938882	+	1.01187i	0.999906	+	0.0137383i	$0.00437317\pi$
$61$	213108.	+	229676.i	0.938882	+	1.01187i	−0.0610232	+	0.998136i	$0.519436\pi$
$62$	219885.	−	175352.i	0.922614	−	0.735760i
$63$	−53225.5	−	483632.i	−0.212862	−	1.93417i
$64$	168844.	−	211723.i	0.644087	−	0.807660i
$65$	−10189.4	−	135968.i	−0.0371030	−	0.495105i
$66$	−21536.8	+	69820.5i	−0.0749115	+	0.242857i
$67$	−34609.2	+	59944.9i	−0.115071	+	0.199309i	−0.917808	−	0.397024i	$-0.870043\pi$
$67$	−34609.2	+	59944.9i	−0.115071	+	0.199309i	0.802737	+	0.596333i	$0.203376\pi$
$68$	90518.2	−	52260.7i	0.287878	−	0.166207i
$69$	−838977.	+	191491.i	−2.55389	+	0.582909i
$70$	239927.	−	277346.i	0.699497	−	0.808590i
$71$	48818.8	−	213889.i	0.136399	−	0.597605i	−0.859810	−	0.510614i	$-0.829418\pi$
$71$	48818.8	−	213889.i	0.136399	−	0.597605i	0.996209	−	0.0869902i	$-0.0277249\pi$
$72$	753907.	−	232550.i	2.01986	−	0.623043i
$73$	499663.	−	196103.i	1.28442	−	0.504099i	0.377740	−	0.925912i	$-0.376701\pi$
$73$	499663.	−	196103.i	1.28442	−	0.504099i	0.906683	+	0.421813i	$0.138606\pi$
$74$	−47078.6	−	119954.i	−0.116179	−	0.296020i
$75$	182255.	+	590856.i	0.432012	+	1.40055i
$76$	101767.	+	23227.6i	0.231827	+	0.0529131i
$77$	−34222.9	−	78996.6i	−0.0749625	−	0.173036i
$78$	−51894.4	−	227364.i	−0.109355	−	0.479114i
$79$	196500.	+	340348.i	0.398548	+	0.690306i	0.993547	−	0.113421i	$-0.0361808\pi$
$79$	196500.	+	340348.i	0.398548	+	0.690306i	−0.594999	+	0.803727i	$0.702848\pi$
$80$	283502.	+	163680.i	0.553714	+	0.319687i
$81$	426813.	+	131654.i	0.803123	+	0.247731i
$82$	−700610.	+	52503.4i	−1.27067	+	0.0952239i
$83$	−679250.	−	541684.i	−1.18794	−	0.947353i	−0.188546	−	0.982064i	$-0.560377\pi$
$83$	−679250.	−	541684.i	−1.18794	−	0.947353i	−0.999397	+	0.0347114i	$0.988949\pi$
$84$	−208369.	+	329721.i	−0.351557	+	0.556299i
$85$	452005.	+	566796.i	0.736015	+	0.922933i
$86$	−491921.	+	456436.i	−0.773392	+	0.717603i
$87$	−182786.	−	1.21271e6i	−0.277579	−	1.84161i
$88$	115342.	−	78639.0i	0.169255	−	0.115396i
$89$	61193.7	−	405994.i	0.0868034	−	0.575903i	−0.902574	−	0.430534i	$-0.858325\pi$
$89$	61193.7	−	405994.i	0.0868034	−	0.575903i	0.989378	−	0.145369i	$-0.0464368\pi$
$90$	658042.	+	1.36644e6i	0.902663	+	1.87440i
$91$	220667.	+	163743.i	0.292828	+	0.217289i
$92$	410552.	+	197711.i	0.527236	+	0.253903i
$93$	−1.71423e6	−	1.16874e6i	−2.13118	−	1.45302i
$94$	742747.	−	800490.i	0.894246	−	0.963768i
$95$	−54105.0	+	721981.i	−0.0631054	+	0.842083i
$96$	−1.01432e6	−	398091.i	−1.14647	−	0.449955i
$97$			449664.i			0.492689i	0.969182	+	0.246345i	$0.0792295\pi$
$97$			449664.i			0.492689i	−0.969182	+	0.246345i	$0.920771\pi$
$98$	106367.	+	731357.i	0.113013	+	0.777054i
$99$	356040.			0.366939
$100$	119618.	−	304782.i	0.119618	−	0.304782i
$101$	−243248.	−	18228.9i	−0.236094	−	0.0176928i	−0.0438424	−	0.999038i	$-0.513960\pi$
$101$	−243248.	−	18228.9i	−0.236094	−	0.0176928i	−0.192252	+	0.981346i	$0.561579\pi$
$102$	908961.	+	843392.i	0.856534	+	0.794747i
$103$	706042.	−	1.03557e6i	0.646128	−	0.947696i	−0.353795	−	0.935323i	$-0.615109\pi$
$103$	706042.	−	1.03557e6i	0.646128	−	0.947696i	0.999923	−	0.0123732i	$-0.00393861\pi$
$104$	−193325.	+	401443.i	−0.171865	+	0.356881i
$105$	−2.47680e6	−	1.08825e6i	−2.13955	−	0.940074i
$106$	−414657.	+	199689.i	−0.348154	+	0.167662i
$107$	815161.	+	122866.i	0.665414	+	0.100295i	0.473060	−	0.881030i	$-0.343150\pi$
$107$	815161.	+	122866.i	0.665414	+	0.100295i	0.192355	+	0.981325i	$0.438388\pi$
$108$	−441693.	−	647844.i	−0.350630	−	0.514279i
$109$	364246.	−	54901.2i	0.281264	−	0.0423938i	−0.00689505	−	0.999976i	$-0.502195\pi$
$109$	364246.	−	54901.2i	0.281264	−	0.0423938i	0.288159	+	0.957582i	$0.406957\pi$
$110$	182527.	+	196718.i	0.137135	+	0.147797i
$111$	−743226.	+	592703.i	−0.543440	+	0.433379i
$112$	−623262.	+	216281.i	−0.443626	+	0.153944i
$113$	1.63403e6	−	2.04901e6i	1.13247	−	1.42007i	0.238951	−	0.971032i	$-0.423197\pi$
$113$	1.63403e6	−	2.04901e6i	1.13247	−	1.42007i	0.893514	−	0.449035i	$-0.148232\pi$
$114$	92541.0	+	1.23487e6i	0.0624625	+	0.833504i
$115$	−931598.	+	3.02017e6i	−0.612541	+	1.98581i
$116$	−324702.	+	562401.i	−0.208023	+	0.360306i
$117$	−984150.	+	568199.i	−0.614474	+	0.354767i
$118$	−895878.	+	204478.i	−0.545259	+	0.124452i
$119$	−1.45983e6	−	58405.4i	−0.866286	−	0.0346587i
$120$	976150.	−	4.27679e6i	0.564902	−	2.47500i
$121$	−1.63266e6	+	503608.i	−0.921592	+	0.284273i
$122$	1.83214e6	−	719062.i	1.00897	−	0.395992i
$123$	1.89353e6	+	4.82464e6i	1.01755	+	2.59269i
$124$	323822.	+	1.04981e6i	0.169841	+	0.550610i
$125$	−378678.	−	86430.8i	−0.193883	−	0.0442526i
$126$	−2.95024e6	−	798700.i	−1.47484	−	0.399275i
$127$	362113.	+	1.58652e6i	0.176780	+	0.774524i	0.983104	+	0.183049i	$0.0585968\pi$
$127$	362113.	+	1.58652e6i	0.176780	+	0.774524i	−0.806324	+	0.591474i	$0.798546\pi$
$128$	−98143.8	−	169990.i	−0.0467986	−	0.0810576i
$129$	4.28720e6	+	2.47521e6i	1.99712	+	1.15304i
$130$	−818472.	−	252465.i	−0.372541	−	0.114914i
$131$	2.83384e6	−	212367.i	1.26055	−	0.0944654i	0.572366	−	0.819998i	$-0.306026\pi$
$131$	2.83384e6	−	212367.i	1.26055	−	0.0944654i	0.688188	+	0.725533i	$0.258407\pi$
$132$	−223149.	−	177956.i	−0.0970227	−	0.0773731i
$133$	−1.02905e6	−	1.03439e6i	−0.437403	−	0.439672i
$134$	271105.	+	339954.i	0.112674	+	0.141288i
$135$	3.98665e6	−	3.69907e6i	1.62034	−	1.50346i
$136$	−353089.	−	2.34259e6i	−0.140368	−	0.931279i
$137$	−1.39824e6	+	953303.i	−0.543775	+	0.370740i	−0.803835	−	0.594853i	$-0.797210\pi$
$137$	−1.39824e6	+	953303.i	−0.543775	+	0.370740i	0.260059	+	0.965593i	$0.416258\pi$
$138$	−805700.	+	5.34547e6i	−0.306574	+	2.03399i
$139$	2.05087e6	+	4.25867e6i	0.763648	+	1.58573i	0.809736	+	0.586794i	$0.199610\pi$
$139$	2.05087e6	+	4.25867e6i	0.763648	+	1.58573i	−0.0460881	+	0.998937i	$0.514676\pi$
$140$	666095.	+	1.26824e6i	0.242746	+	0.462188i
$141$	−7.25794e6	−	3.49524e6i	−2.58914	−	1.24687i
$142$	−1.13870e6	−	776351.i	−0.397689	−	0.271140i
$143$	−136766.	+	147399.i	−0.0467703	+	0.0504064i
$144$	203891.	−	2.72073e6i	0.0682826	−	0.911169i
$145$	−4.19290e6	−	1.64559e6i	−1.37534	−	0.539782i
$146$		−	3.37188e6i		−	1.08346i
$147$	4.92427e6	−	2.34009e6i	1.55021	−	0.736683i
$148$	503371.			0.155276
$149$	2.06810e6	−	5.26943e6i	0.625191	−	1.59296i	−0.169220	−	0.985578i	$-0.554125\pi$
$149$	2.06810e6	−	5.26943e6i	0.625191	−	1.59296i	0.794410	−	0.607381i	$-0.207780\pi$
$150$	3.87336e6	+	290268.i	1.14766	+	0.0860055i
$151$	216087.	+	200499.i	0.0627621	+	0.0582347i	0.710930	−	0.703263i	$-0.248274\pi$
$151$	216087.	+	200499.i	0.0627621	+	0.0582347i	−0.648168	+	0.761497i	$0.724465\pi$
$152$	1.33278e6	−	1.95483e6i	0.379513	−	0.556644i
$153$	2.62159e6	−	5.44378e6i	0.731964	−	1.51994i
$154$	−540482.	+	18823.3i	−0.147985	+	0.00515387i
$155$	−6.86537e6	+	3.30619e6i	−1.84361	+	0.887835i
$156$	900814.	+	135776.i	0.237280	+	0.0357642i
$157$	1.65201e6	+	2.42306e6i	0.426889	+	0.626131i	0.978075	−	0.208251i	$-0.0667771\pi$
$157$	1.65201e6	+	2.42306e6i	0.426889	+	0.626131i	−0.551186	+	0.834382i	$0.685825\pi$
$158$	2.44118e6	−	367949.i	0.618912	−	0.0932860i
$159$	2.30930e6	+	2.48884e6i	0.574500	+	0.619163i
$160$	−3.12887e6	+	2.49519e6i	−0.763884	+	0.609177i
$161$	−3.37480e6	−	5.40193e6i	−0.808667	−	1.29441i
$162$	1.74940e6	−	2.19368e6i	0.411476	−	0.515974i
$163$	−184976.	−	2.46833e6i	−0.0427123	−	0.569956i	−0.976973	−	0.213364i	$-0.931558\pi$
$163$	−184976.	−	2.46833e6i	−0.0427123	−	0.569956i	0.934260	−	0.356591i	$-0.116061\pi$
$164$	808941.	−	2.62252e6i	0.183394	−	0.594549i
$165$	989831.	−	1.71444e6i	0.220348	−	0.381654i
$166$	−4.72644e6	+	2.72881e6i	−1.03326	+	0.596553i
$167$	1.73820e6	−	396733.i	0.373208	−	0.0851822i	−0.0318030	−	0.999494i	$-0.510125\pi$
$167$	1.73820e6	−	396733.i	0.373208	−	0.0851822i	0.405011	+	0.914312i	$0.367268\pi$
$168$	5.23130e6	+	7.12668e6i	1.10327	+	1.50300i
$169$	−931255.	+	4.08010e6i	−0.192934	+	0.845299i
$170$	4.35175e6	−	1.34234e6i	0.885762	−	0.273221i
$171$	5.61707e6	−	2.20454e6i	1.12337	−	0.440889i
$172$	−957684.	−	2.44014e6i	−0.188207	−	0.479545i
$173$	1.96403e6	+	6.36723e6i	0.379324	+	1.22974i	0.921137	+	0.389239i	$0.127262\pi$
$173$	1.96403e6	+	6.36723e6i	0.379324	+	1.22974i	−0.541813	+	0.840499i	$0.682262\pi$
$174$	−7.51092e6	−	1.71432e6i	−1.42576	−	0.325420i
$175$	−3.68935e6	+	2.70815e6i	−0.688391	+	0.505310i
$176$	−107424.	−	470656.i	−0.0197044	−	0.0863307i
$177$	3.38944e6	+	5.87069e6i	0.611236	+	1.05869i
$178$	−2.23365e6	−	1.28960e6i	−0.396054	−	0.228662i
$179$	1.37284e6	+	423465.i	0.239365	+	0.0738343i	0.412117	−	0.911131i	$-0.364790\pi$
$179$	1.37284e6	+	423465.i	0.239365	+	0.0738343i	−0.172752	+	0.984965i	$0.555266\pi$
$180$	−5.90782e6	+	442730.i	−1.01300	+	0.0759139i
$181$	−3.51780e6	−	2.80536e6i	−0.593248	−	0.473099i	0.280250	−	0.959927i	$-0.409583\pi$
$181$	−3.51780e6	−	2.80536e6i	−0.593248	−	0.473099i	−0.873498	+	0.486828i	$0.838154\pi$
$182$	1.46393e6	−	914577.i	0.242833	−	0.151707i
$183$	−9.05273e6	−	1.13518e7i	−1.47716	−	1.85229i
$184$	7.57116e6	−	7.02501e6i	1.21537	−	1.12770i
$185$	520363.	+	3.45239e6i	0.0821848	+	0.545261i
$186$	−1.07685e7	+	7.34185e6i	−1.67347	+	1.14095i
$187$	159342.	−	1.05716e6i	0.0243671	−	0.161665i
$188$	1.85079e6	+	3.84321e6i	0.278538	+	0.578390i
$189$	381470.	+	1.09533e7i	0.0565035	+	1.62241i
$190$	4.09768e6	+	1.97334e6i	0.597416	+	0.287701i
$191$	−2.80709e6	−	1.91384e6i	−0.402862	−	0.274667i	0.344892	−	0.938642i	$-0.387916\pi$
$191$	−2.80709e6	−	1.91384e6i	−0.402862	−	0.274667i	−0.747754	+	0.663976i	$0.768868\pi$
$192$	−8.53578e6	+	9.19938e6i	−1.20598	+	1.29974i
$193$	9843.93	−	131358.i	0.00136929	−	0.0182719i	−0.996477	−	0.0838629i	$-0.973274\pi$
$193$	9843.93	−	131358.i	0.00136929	−	0.0182719i	0.997847	+	0.0655910i	$0.0208933\pi$
$194$	2.62945e6	+	1.03198e6i	0.360131	+	0.141341i
$195$			6.31862e6i			0.852154i
$196$	−2.81120e6	−	656959.i	−0.373356	−	0.0872510i
$197$	7.52065e6			0.983686			0.491843	−	0.870684i	$-0.336323\pi$
$197$	7.52065e6			0.983686			0.491843	+	0.870684i	$0.336323\pi$
$198$	817117.	−	2.08198e6i	0.105266	−	0.268214i
$199$	1.44018e6	+	107926.i	0.182750	+	0.0136952i	0.165791	−	0.986161i	$-0.446982\pi$
$199$	1.44018e6	+	107926.i	0.182750	+	0.0136952i	0.0169592	+	0.999856i	$0.494601\pi$
$200$	−5.44005e6	−	5.04763e6i	−0.680006	−	0.630954i
$201$	1.80695e6	−	2.65030e6i	0.222514	−	0.326368i
$202$	−664852.	+	1.38058e6i	−0.0806623	+	0.167497i
$203$	8.03638e6	−	4.22079e6i	0.960666	−	0.504552i
$204$	−4.36399e6	+	2.10159e6i	−0.514035	+	0.247546i
$205$	1.88229e7	+	2.83709e6i	2.18486	+	0.329315i
$206$	−4.43524e6	−	6.50530e6i	−0.507359	−	0.744158i
$207$	2.60475e7	−	3.92603e6i	2.93667	−	0.442632i
$208$	1.04805e6	+	1.12953e6i	0.116464	+	0.125518i
$209$	834758.	−	665697.i	0.0914370	−	0.0729186i
$210$	−1.20479e7	+	1.19858e7i	−1.30093	+	1.29422i
$211$	−5.13735e6	+	6.44203e6i	−0.546879	+	0.685765i	−0.976072	−	0.217448i	$-0.930227\pi$
$211$	−5.13735e6	+	6.44203e6i	−0.546879	+	0.685765i	0.429193	+	0.903213i	$0.358798\pi$
$212$	−134350.	−	1.79278e6i	−0.0141004	−	0.188157i
$213$	−2.99672e6	+	9.71514e6i	−0.310104	+	1.00533i
$214$	2.58927e6	−	4.48475e6i	0.264202	−	0.457612i
$215$	1.57457e7	−	9.09081e6i	1.58434	−	0.914718i
$216$	−1.73263e7	+	3.95462e6i	−1.71928	+	0.392413i
$217$	4.01289e6	−	1.48228e7i	0.392716	−	1.45061i
$218$	514908.	−	2.25596e6i	0.0497004	−	0.217752i
$219$	−2.37694e7	+	7.33189e6i	−2.26301	+	0.698045i
$220$	−975804.	+	382975.i	−0.0916420	+	0.0359668i
$221$	1.24666e6	+	3.17645e6i	0.115497	+	0.294283i
$222$	1.76017e6	+	5.70634e6i	0.160878	+	0.521553i
$223$	−7.95022e6	−	1.81459e6i	−0.716910	−	0.163630i	−0.151521	−	0.988454i	$-0.548417\pi$
$223$	−7.95022e6	−	1.81459e6i	−0.716910	−	0.163630i	−0.565389	+	0.824824i	$0.691274\pi$
$224$	322413.	−	8.05865e6i	0.0286859	−	0.716999i
$225$	−4.21168e6	−	1.84526e7i	−0.369750	−	1.61998i
$226$	−8.23165e6	−	1.42576e7i	−0.713119	−	1.23516i
$227$	80747.5	+	46619.6i	0.00690322	+	0.00398558i	0.503448	−	0.864026i	$-0.332065\pi$
$227$	80747.5	+	46619.6i	0.00690322	+	0.00398558i	−0.496544	+	0.868011i	$0.665398\pi$
$228$	−4.62238e6	−	1.42581e6i	−0.389997	−	0.120298i
$229$	−1.43703e7	+	1.07691e6i	−1.19663	+	0.0896750i	−0.658099	−	0.752931i	$-0.728639\pi$
$229$	−1.43703e7	+	1.07691e6i	−1.19663	+	0.0896750i	−0.538530	+	0.842606i	$0.681020\pi$
$230$	1.55227e7	+	1.23789e7i	1.27580	+	1.01742i
$231$	1.30793e6	+	3.76909e6i	0.106108	+	0.305774i
$232$	9.17728e6	+	1.15079e7i	0.734937	+	0.921581i
$233$	−1.38352e7	+	1.28371e7i	−1.09375	+	1.01485i	−0.0939312	+	0.995579i	$0.529943\pi$
$233$	−1.38352e7	+	1.28371e7i	−1.09375	+	1.01485i	−0.999814	+	0.0192689i	$0.993866\pi$
$234$	1.06396e6	+	7.05893e6i	0.0830383	+	0.550923i
$235$	−2.44455e7	+	1.66667e7i	−1.88363	+	1.28424i
$236$	534994.	−	3.54945e6i	0.0407017	−	0.270038i
$237$	−7.90195e6	−	1.64086e7i	−0.593593	−	1.23261i
$238$	−3.69186e6	+	8.40245e6i	−0.273851	+	0.623268i
$239$	−2.78394e6	−	1.34068e6i	−0.203923	−	0.0982043i	0.329135	−	0.944283i	$-0.393243\pi$
$239$	−2.78394e6	−	1.34068e6i	−0.203923	−	0.0982043i	−0.533058	+	0.846079i	$0.678957\pi$
$240$	−1.25343e7	−	8.54573e6i	−0.906704	−	0.618180i
$241$	2.59289e6	−	2.79447e6i	0.185239	−	0.199641i	−0.633604	−	0.773657i	$-0.718425\pi$
$241$	2.59289e6	−	2.79447e6i	0.185239	−	0.199641i	0.818843	+	0.574017i	$0.194616\pi$
$242$	−802071.	+	1.07029e7i	−0.0565935	+	0.755188i
$243$	2.41588e6	+	948163.i	0.168367	+	0.0660791i
$244$			7.68831e6i			0.529251i
$245$	1.59968e6	−	1.99598e7i	0.108776	−	1.35724i
$246$	3.25582e7			2.18703
$247$	−1.24502e6	+	3.17227e6i	−0.0826202	+	0.210513i
$248$	2.48312e7	+	1.86084e6i	1.62796	+	0.121999i
$249$	2.95135e7	+	2.73845e7i	1.91171	+	1.77381i
$250$	−1.37448e6	+	2.01600e6i	−0.0879669	+	0.129024i
$251$	8.78134e6	−	1.82346e7i	0.555315	−	1.15312i	−0.414673	−	0.909971i	$-0.636104\pi$
$251$	8.78134e6	−	1.82346e7i	0.555315	−	1.15312i	0.969988	−	0.243153i	$-0.0781819\pi$
$252$	7.11463e6	−	9.58796e6i	0.444581	−	0.599135i
$253$	4.19936e6	−	2.02230e6i	0.259311	−	0.124878i
$254$	1.01084e7	+	1.52359e6i	0.616851	+	0.0929754i
$255$	−1.89251e7	−	2.77580e7i	−1.14135	−	1.67405i
$256$	1.59186e7	−	2.39934e6i	0.948823	−	0.143012i
$257$	−1.40162e7	−	1.51058e7i	−0.825715	−	0.889909i	0.169707	−	0.985495i	$-0.445718\pi$
$257$	−1.40162e7	−	1.51058e7i	−0.825715	−	0.889909i	−0.995421	+	0.0955860i	$0.969528\pi$
$258$	2.43132e7	−	1.93891e7i	1.41574	−	1.12901i
$259$	−5.94795e6	−	3.75884e6i	−0.342348	−	0.216349i
$260$	2.08609e6	−	2.61587e6i	0.118690	−	0.148832i
$261$	2.80541e6	+	3.74356e7i	0.157788	+	2.10554i
$262$	5.26186e6	−	1.70585e7i	0.292574	−	0.948500i
$263$	7.96763e6	−	1.38003e7i	0.437988	−	0.758617i	−0.559546	−	0.828799i	$-0.689025\pi$
$263$	7.96763e6	−	1.38003e7i	0.437988	−	0.758617i	0.997534	+	0.0701818i	$0.0223579\pi$
$264$	−5.60250e6	+	3.23461e6i	−0.304488	+	0.175796i
$265$	1.21569e7	−	2.77474e6i	0.653261	−	0.149103i
$266$	−8.41036e6	+	3.64353e6i	−0.446858	+	0.193588i
$267$	−4.23386e6	+	1.85498e7i	−0.222435	+	0.974551i
$268$	−1.62306e6	+	500648.i	−0.0843199	+	0.0260093i
$269$	626099.	−	245726.i	0.0321652	−	0.0126239i	−0.349204	−	0.937047i	$-0.613548\pi$
$269$	626099.	−	245726.i	0.0321652	−	0.0126239i	0.381369	+	0.924423i	$0.375453\pi$
$270$	−1.24813e7	−	3.18017e7i	−0.634114	−	1.61569i
$271$	−1.16770e6	−	3.78558e6i	−0.0586708	−	0.190206i	0.921493	−	0.388395i	$-0.126970\pi$
$271$	−1.16770e6	−	3.78558e6i	−0.0586708	−	0.190206i	−0.980164	+	0.198189i	$0.936494\pi$
$272$	−7.98721e6	−	1.82303e6i	−0.396907	−	0.0905913i
$273$	−9.63034e6	−	8.33104e6i	−0.473318	−	0.409460i
$274$	2.36555e6	+	1.03642e7i	0.114996	+	0.503828i
$275$	−1.67449e6	−	2.90031e6i	−0.0805166	−	0.139459i
$276$	−1.82876e7	−	1.05584e7i	−0.869822	−	0.502192i
$277$	−3.13742e7	−	9.67767e6i	−1.47616	−	0.455336i	−0.550870	−	0.834591i	$-0.685704\pi$
$277$	−3.13742e7	−	9.67767e6i	−1.47616	−	0.455336i	−0.925292	+	0.379256i	$0.876180\pi$
$278$	2.96097e7	−	2.21894e6i	1.37816	−	0.103279i
$279$	4.96528e7	+	3.95968e7i	2.28629	+	1.82326i
$280$	3.22743e7	−	3.55191e6i	1.47022	−	0.161803i
$281$	3.42497e6	+	4.29477e6i	0.154361	+	0.193563i	0.852999	−	0.521913i	$-0.174781\pi$
$281$	3.42497e6	+	4.29477e6i	0.154361	+	0.193563i	−0.698638	+	0.715476i	$0.746210\pi$
$282$	−3.70958e7	+	3.44199e7i	−1.65416	+	1.53484i
$283$	−5.95287e6	−	3.94947e7i	−0.262644	−	1.74253i	−0.598961	−	0.800778i	$-0.704420\pi$
$283$	−5.95287e6	−	3.94947e7i	−0.262644	−	1.74253i	0.336317	−	0.941749i	$-0.390819\pi$
$284$	4.44807e6	−	3.03264e6i	0.194185	−	0.132393i
$285$	5.00057e6	−	3.31766e7i	0.216016	−	1.43317i
$286$	548048.	+	1.13803e6i	0.0234272	+	0.0486471i
$287$	−2.91419e7	+	2.49477e7i	−1.23274	+	1.05532i
$288$	3.00511e7	+	1.44719e7i	1.25801	+	0.605825i
$289$	4.95288e6	+	3.37681e6i	0.205194	+	0.139899i
$290$	−1.92455e7	+	2.07417e7i	−0.789106	+	0.850454i
$291$	1.55723e6	−	2.07798e7i	0.0631936	−	0.843261i
$292$	1.22610e7	+	4.81209e6i	0.492468	+	0.193279i
$293$			1.87579e7i			0.745730i	0.927886	+	0.372865i	$0.121625\pi$
$293$			1.87579e7i			0.745730i	−0.927886	+	0.372865i	$0.878375\pi$
$294$	−2.38265e6	−	3.41656e7i	−0.0937603	−	1.34446i
$295$	2.48971e7			0.969800
$296$	4.16828e6	−	1.06206e7i	0.160724	−	0.409519i
$297$	−7.99766e6	−	599342.i	−0.305277	−	0.0228773i
$298$	−2.60672e7	−	2.41868e7i	−0.985020	−	0.913965i
$299$	−8.38029e6	+	1.22916e7i	−0.313506	+	0.459829i
$300$	−6.58326e6	+	1.36703e7i	−0.243824	+	0.506307i
$301$	−6.90512e6	+	3.59846e7i	−0.253205	+	1.31952i
$302$	1.66836e6	−	803440.i	0.0605716	−	0.0291697i
$303$	1.11778e7	+	1.68478e6i	0.401817	+	0.0605641i
$304$	−4.60899e6	−	6.76015e6i	−0.164053	−	0.240622i
$305$	−5.27305e7	+	7.94784e6i	−1.85850	+	0.280124i
$306$	−2.58164e7	−	2.78235e7i	−0.901015	−	0.971064i
$307$	−1.18061e7	+	9.41503e6i	−0.408029	+	0.325392i	−0.805903	−	0.592048i	$-0.798320\pi$
$307$	−1.18061e7	+	9.41503e6i	−0.408029	+	0.325392i	0.397874	+	0.917440i	$0.369748\pi$
$308$	702889.	−	1.99219e6i	0.0240566	−	0.0681835i
$309$	−3.62137e7	+	4.54106e7i	−1.22743	+	1.53915i
$310$	3.57714e6	+	4.77336e7i	0.120074	+	1.60228i
$311$	−1.11595e7	+	3.61782e7i	−0.370991	+	1.20272i	0.557125	+	0.830429i	$0.311905\pi$
$311$	−1.11595e7	+	3.61782e7i	−0.370991	+	1.20272i	−0.928115	+	0.372293i	$0.878572\pi$
$312$	1.03241e7	−	1.78819e7i	0.339929	−	0.588775i
$313$	−9.45829e6	+	5.46074e6i	−0.308446	+	0.178082i	−0.646231	−	0.763142i	$-0.723656\pi$
$313$	−9.45829e6	+	5.46074e6i	−0.308446	+	0.178082i	0.337785	+	0.941223i	$0.390322\pi$
$314$	1.79605e7	−	4.09936e6i	0.580134	−	0.132412i
$315$	7.31141e7	+	3.88842e7i	2.33921	+	1.24406i
$316$	−2.14592e6	+	9.40187e6i	−0.0680066	+	0.297957i
$317$	−3.10169e7	+	9.56744e6i	−0.973689	+	0.300343i	−0.740476	−	0.672082i	$-0.765400\pi$
$317$	−3.10169e7	+	9.56744e6i	−0.973689	+	0.300343i	−0.233213	+	0.972426i	$0.574924\pi$
$318$	1.98536e7	−	7.79196e6i	0.617387	−	0.242307i
$319$	2.42677e6	+	6.18330e6i	0.0747577	+	0.190480i
$320$	1.35855e7	+	4.40430e7i	0.414596	+	1.34409i
$321$	−3.72445e7	−	8.50082e6i	−1.12602	−	0.257007i
$322$	−3.93335e7	+	7.33694e6i	−1.17813	+	0.219759i
$323$	−4.03190e6	−	1.76649e7i	−0.119647	−	0.524208i
$324$	5.48016e6	+	9.49191e6i	0.161123	+	0.279074i
$325$	9.25711e6	+	5.34459e6i	0.269665	+	0.155691i
$326$	−1.48583e7	−	4.58319e6i	−0.428862	−	0.132286i
$327$	−1.70226e7	+	1.27566e6i	−0.486835	+	0.0364832i
$328$	−4.86338e7	−	3.87841e7i	−1.37821	−	1.09909i
$329$	6.82916e6	−	5.92327e7i	0.191770	−	1.66331i
$330$	−7.75366e6	−	9.72278e6i	−0.215757	−	0.270551i
$331$	1.26694e7	−	1.17555e7i	0.349360	−	0.324159i	−0.485900	−	0.874015i	$-0.661508\pi$
$331$	1.26694e7	−	1.17555e7i	0.349360	−	0.324159i	0.835259	+	0.549856i	$0.185317\pi$
$332$	−3.17743e6	−	2.10809e7i	−0.0868284	−	0.576068i
$333$	2.40425e7	−	1.63919e7i	0.651099	−	0.443912i
$334$	1.66926e6	−	1.10748e7i	0.0448006	−	0.297233i
$335$	−5.11155e6	−	1.06143e7i	−0.135962	−	0.282329i
$336$	2.95510e7	−	7.83629e6i	0.779032	−	0.206582i
$337$	−289973.	−	139644.i	−0.00757649	−	0.00364864i	0.430092	−	0.902785i	$-0.358481\pi$
$337$	−289973.	−	139644.i	−0.00757649	−	0.00364864i	−0.437668	+	0.899137i	$0.644196\pi$
$338$	2.17215e7	+	1.48095e7i	0.562522	+	0.383521i
$339$	−8.26073e7	+	8.90295e7i	−2.12041	+	2.28526i
$340$	−1.32941e6	+	1.77397e7i	−0.0338238	+	0.451347i
$341$	1.04604e7	+	4.10542e6i	0.263808	+	0.103537i
$342$		−	3.79058e7i		−	0.947604i
$343$	2.83120e7	+	2.87549e7i	0.701597	+	0.712574i
$344$	−5.94146e7			−1.45955
$345$	5.35099e7	−	1.36341e8i	1.30310	−	3.32024i
$346$	4.17405e7	+	3.12802e6i	1.00769	+	0.0755163i
$347$	2.23667e7	+	2.07533e7i	0.535320	+	0.496704i	0.900871	−	0.434087i	$-0.142929\pi$
$347$	2.23667e7	+	2.07533e7i	0.535320	+	0.496704i	−0.365551	+	0.930791i	$0.619119\pi$
$348$	1.69527e7	−	2.48651e7i	0.402255	−	0.589999i
$349$	1.13573e7	−	2.35836e7i	0.267176	−	0.554797i	−0.723614	−	0.690205i	$-0.757520\pi$
$349$	1.13573e7	−	2.35836e7i	0.267176	−	0.554797i	0.990790	+	0.135408i	$0.0432346\pi$
$350$	7.36904e6	+	2.77890e7i	0.171873	+	0.648140i
$351$	2.30632e7	−	1.11067e7i	0.533333	−	0.256840i
$352$	5.83582e6	+	879608.i	0.133805	+	0.0201679i
$353$	−2.55753e7	−	3.75121e7i	−0.581429	−	0.852800i	0.416996	−	0.908909i	$-0.363083\pi$
$353$	−2.55753e7	−	3.75121e7i	−0.581429	−	0.852800i	−0.998425	+	0.0561086i	$0.982131\pi$
$354$	4.21082e7	−	6.34679e6i	0.949199	−	0.143069i
$355$	2.53977e7	+	2.73722e7i	0.567687	+	0.611821i
$356$	7.87699e6	−	6.28169e6i	0.174586	−	0.139228i
$357$	6.72591e7	+	7.75454e6i	1.47824	+	0.170432i
$358$	5.62693e6	−	7.05595e6i	0.122637	−	0.153782i
$359$	−874637.	−	1.16712e7i	−0.0189036	−	0.252251i	−0.998647	−	0.0519956i	$-0.983442\pi$
$359$	−874637.	−	1.16712e7i	−0.0189036	−	0.252251i	0.979744	−	0.200255i	$-0.0641772\pi$
$360$	−3.95798e7	+	1.28315e8i	−0.848333	+	2.75023i
$361$	−1.44753e7	+	2.50719e7i	−0.307684	+	0.532924i
$362$	−2.44780e7	+	1.41324e7i	−0.516000	+	0.297913i
$363$	7.71920e7	−	1.76186e7i	1.61381	−	0.368341i
$364$	1.23642e6	+	6.62845e6i	0.0256366	+	0.137438i
$365$	−2.03290e7	+	8.90670e7i	−0.418058	+	1.83163i
$366$	−8.71566e7	+	2.68842e7i	−1.77769	+	0.548346i
$367$	4.19466e7	−	1.64628e7i	0.848591	−	0.333048i	0.0991128	−	0.995076i	$-0.468400\pi$
$367$	4.19466e7	−	1.64628e7i	0.848591	−	0.333048i	0.749479	+	0.662029i	$0.230304\pi$
$368$	−1.30489e7	−	3.32481e7i	−0.261837	−	0.667149i
$369$	−4.67630e7	−	1.51602e8i	−0.930730	−	3.01735i
$370$	2.13824e7	+	4.88039e6i	0.422135	+	0.0963495i
$371$	−1.17998e7	+	2.21871e7i	−0.231074	+	0.434489i
$372$	−1.13288e7	−	4.96348e7i	−0.220067	−	0.964178i
$373$	2.70220e7	+	4.68035e7i	0.520704	+	0.901886i	0.999710	+	0.0240747i	$0.00766396\pi$
$373$	2.70220e7	+	4.68035e7i	0.520704	+	0.901886i	−0.479006	+	0.877812i	$0.659003\pi$
$374$	−5.81616e6	−	3.35796e6i	−0.111179	−	0.0641891i
$375$	1.72001e7	+	5.30552e6i	0.326164	+	0.100608i
$376$	9.64135e7	−	7.22519e6i	1.81374	−	0.135921i
$377$	−1.65758e7	−	1.32187e7i	−0.309350	−	0.246698i
$378$	6.49261e7	+	2.29073e7i	1.20211	+	0.424130i
$379$	2.88601e7	+	3.61894e7i	0.530127	+	0.664758i	0.972725	−	0.231962i	$-0.0745145\pi$
$379$	2.88601e7	+	3.61894e7i	0.530127	+	0.664758i	−0.442598	+	0.896720i	$0.645943\pi$
$380$	−1.30235e7	+	1.20840e7i	−0.237342	+	0.220222i
$381$	−1.12396e7	−	7.45699e7i	−0.203225	−	1.34831i
$382$	−1.76337e7	+	1.20224e7i	−0.316339	+	0.215676i
$383$	721866.	−	4.78926e6i	0.0128487	−	0.0852457i	−0.981487	−	0.191527i	$-0.938656\pi$
$383$	721866.	−	4.78926e6i	0.0128487	−	0.0852457i	0.994336	+	0.106281i	$0.0338943\pi$
$384$	3.94671e6	+	8.19542e6i	0.0697014	+	0.144736i
$385$	1.43901e7	+	2.76134e6i	0.252163	+	0.0483880i
$386$	−745536.	−	359031.i	−0.0129630	−	0.00624267i
$387$	−1.25203e8	−	8.53620e7i	−2.16014	−	1.47276i
$388$	−7.50511e6	+	8.08858e6i	−0.128488	+	0.138477i
$389$	−1.37754e6	+	1.83821e7i	−0.0234022	+	0.312281i	0.973203	+	0.229949i	$0.0738559\pi$
$389$	−1.37754e6	+	1.83821e7i	−0.0234022	+	0.312281i	−0.996605	+	0.0823321i	$0.973763\pi$
$390$	3.69487e7	+	1.45013e7i	0.622881	+	0.244463i
$391$		−	7.90978e7i		−	1.32323i
$392$	−3.71398e7	+	5.38731e7i	−0.616569	+	0.894363i
$393$	−1.31692e8			−2.16961
$394$	1.72600e7	−	4.39777e7i	0.282196	−	0.719024i
$395$	−6.67013e7	−	4.99857e6i	−1.08229	−	0.0811063i
$396$	6.40448e6	+	5.94249e6i	0.103133	+	0.0956935i
$397$	−3.30405e7	+	4.84615e7i	−0.528050	+	0.774508i	−0.993892	−	0.110361i	$-0.964799\pi$
$397$	−3.30405e7	+	4.84615e7i	−0.528050	+	0.774508i	0.465841	+	0.884868i	$0.345752\pi$
$398$	3.93633e6	−	8.17388e6i	0.0624371	−	0.129652i
$399$	4.39720e7	+	5.13646e7i	0.692241	+	0.808621i
$400$	−2.31220e7	+	1.11350e7i	−0.361282	+	0.173984i
$401$	6.77085e7	+	1.02054e7i	1.05005	+	0.158270i	0.651324	−	0.758800i	$-0.274214\pi$
$401$	6.77085e7	+	1.02054e7i	1.05005	+	0.158270i	0.398727	+	0.917070i	$0.369452\pi$
$402$	−1.13509e7	−	1.66488e7i	−0.174724	−	0.256273i
$403$	−3.54660e7	+	5.34565e6i	−0.541873	+	0.0816742i
$404$	−4.07131e6	−	4.38783e6i	−0.0617433	−	0.0665435i
$405$	−5.94354e7	+	4.73981e7i	−0.894705	+	0.713503i
$406$	−6.23787e6	−	5.66803e7i	−0.0932091	−	0.846942i
$407$	3.21020e6	−	4.02547e6i	0.0476156	−	0.0597081i
$408$	8.20424e6	+	1.09478e8i	0.120798	+	1.61193i
$409$	−2.27785e7	+	7.38460e7i	−0.332932	+	1.07934i	0.622126	+	0.782917i	$0.286269\pi$
$409$	−2.27785e7	+	7.38460e7i	−0.332932	+	1.07934i	−0.955058	+	0.296420i	$0.904207\pi$
$410$	5.97889e7	−	1.03557e8i	0.867499	−	1.50255i
$411$	6.79164e7	−	3.92116e7i	0.978249	−	0.564792i
$412$	2.99845e7	−	6.84377e6i	0.428752	−	0.0978597i
$413$	−3.28266e7	+	3.79461e7i	−0.465988	+	0.538663i
$414$	3.68215e7	−	1.61326e8i	0.518920	−	2.27354i
$415$	1.41299e8	−	4.35849e7i	1.97695	−	0.609807i
$416$	−1.75348e7	+	6.88191e6i	−0.243569	+	0.0955937i
$417$	−8.00260e7	−	2.03903e8i	−1.10363	−	2.81200i
$418$	−1.97695e6	−	6.40911e6i	−0.0270686	−	0.0877544i
$419$	9.04617e7	+	2.06473e7i	1.22977	+	0.280686i	0.787566	−	0.616230i	$-0.211341\pi$
$419$	9.04617e7	+	2.06473e7i	1.22977	+	0.280686i	0.442200	+	0.896916i	$0.354198\pi$
$420$	−2.63894e7	−	6.09146e7i	−0.356189	−	0.822192i
$421$	−1.17611e7	−	5.15288e7i	−0.157617	−	0.690563i	−0.990546	−	0.137184i	$-0.956195\pi$
$421$	−1.17611e7	−	5.15288e7i	−0.157617	−	0.690563i	0.832929	−	0.553380i	$-0.186662\pi$
$422$	2.58801e7	+	4.48256e7i	0.344372	+	0.596471i
$423$	2.13551e8	+	1.23294e8i	2.82150	+	1.62899i
$424$	−3.89382e7	−	1.20108e7i	−0.510832	−	0.157571i
$425$	−5.66747e7	+	4.24718e6i	−0.738282	+	0.0553266i
$426$	4.99326e7	+	3.98200e7i	0.645886	+	0.515077i
$427$	5.74112e7	−	9.08468e7i	0.737416	−	1.16688i
$428$	1.26125e7	+	1.58155e7i	0.160868	+	0.201722i
$429$	6.83066e6	−	6.33792e6i	0.0865148	−	0.0802740i
$430$	−1.70227e7	−	1.12938e8i	−0.214103	−	1.42048i
$431$	−1.24791e8	+	8.50810e7i	−1.55866	+	1.06268i	−0.592220	+	0.805776i	$0.701749\pi$
$431$	−1.24791e8	+	8.50810e7i	−1.55866	+	1.06268i	−0.966438	+	0.256899i	$0.917299\pi$
$432$	−9.15992e6	+	6.07721e7i	−0.113616	+	0.753794i
$433$	−1.79660e7	−	3.73068e7i	−0.221303	−	0.459541i	0.760526	−	0.649308i	$-0.224941\pi$
$433$	−1.79660e7	−	3.73068e7i	−0.221303	−	0.459541i	−0.981829	+	0.189766i	$0.939227\pi$
$434$	−7.74682e7	−	5.74843e7i	−0.947663	−	0.703202i
$435$	1.88063e8	+	9.05661e7i	2.28473	+	1.10027i
$436$	7.46840e6	+	5.09187e6i	0.0901090	+	0.0614352i
$437$	5.37294e7	−	5.79065e7i	0.643824	−	0.693878i
$438$	−1.16771e7	+	1.55821e8i	−0.138968	+	1.85440i
$439$	−8.43399e7	−	3.31010e7i	−0.996872	−	0.391243i	−0.189881	−	0.981807i	$-0.560810\pi$
$439$	−8.43399e7	−	3.31010e7i	−0.996872	−	0.391243i	−0.806991	+	0.590564i	$0.798905\pi$
$440$			2.37597e7i			0.278922i
$441$	−1.55665e8	+	6.01662e7i	−1.81499	+	0.701515i
$442$	2.14357e7			0.248239
$443$	2.31356e7	−	5.89486e7i	0.266116	−	0.678051i	−0.733884	−	0.679275i	$-0.762294\pi$
$443$	2.31356e7	−	5.89486e7i	0.266116	−	0.678051i	0.999999	+	0.00122372i	$0.000389521\pi$
$444$	−2.32617e7	−	1.74322e6i	−0.265762	−	0.0199161i
$445$	5.12260e7	+	4.75308e7i	0.581313	+	0.539380i
$446$	−2.88568e7	+	4.23252e7i	−0.325270	+	0.477083i
$447$	−1.13819e8	+	2.36348e8i	−1.27436	+	2.64624i
$448$	−8.50392e7	−	3.73644e7i	−0.945770	−	0.415551i
$449$	−9.49969e7	+	4.57481e7i	−1.04947	+	0.505398i	−0.877437	−	0.479693i	$-0.840748\pi$
$449$	−9.49969e7	+	4.57481e7i	−1.04947	+	0.505398i	−0.172034	+	0.985091i	$0.555034\pi$
$450$	−1.17569e8	−	1.77207e7i	−1.29020	−	0.194466i
$451$	−1.58134e7	−	2.31940e7i	−0.172383	−	0.252840i
$452$	6.35920e7	−	9.58495e6i	0.688632	−	0.103795i
$453$	−9.29140e6	−	1.00138e7i	−0.0999509	−	0.107721i
$454$	457929.	−	365186.i	0.00489362	−	0.00390253i
$455$	−4.41832e7	+	1.53322e7i	−0.469054	+	0.162768i
$456$	−6.83597e7	+	8.57204e7i	−0.720951	+	0.904044i
$457$	8.62957e6	+	1.15154e8i	0.0904150	+	1.20650i	0.839249	+	0.543747i	$0.182995\pi$
$457$	8.62957e6	+	1.15154e8i	0.0904150	+	1.20650i	−0.748834	+	0.662757i	$0.769386\pi$
$458$	−2.66827e7	+	8.65032e7i	−0.277737	+	0.900401i
$459$	−6.80520e7	+	1.17869e8i	−0.703725	+	1.21889i
$460$	−6.71657e7	+	3.87781e7i	−0.690040	+	0.398395i
$461$	1.06332e8	−	2.42696e7i	1.08533	−	0.247719i	0.357801	−	0.933798i	$-0.383526\pi$
$461$	1.06332e8	−	2.42696e7i	1.08533	−	0.247719i	0.727528	+	0.686078i	$0.240669\pi$
$462$	2.50418e7	+	1.00188e6i	0.253945	+	0.0101599i
$463$	1.92017e7	−	8.41281e7i	0.193462	−	0.847614i	−0.781262	−	0.624203i	$-0.785424\pi$
$463$	1.92017e7	−	8.41281e7i	0.193462	−	0.847614i	0.974724	−	0.223411i	$-0.0717191\pi$
$464$	4.86403e7	−	1.50035e7i	0.486903	−	0.150190i
$465$	3.28710e8	−	1.29009e8i	3.26930	−	1.28310i
$466$	4.33146e7	+	1.10364e8i	0.428032	+	1.09061i
$467$	2.57460e6	+	8.34664e6i	0.0252789	+	0.0819523i	0.967333	−	0.253508i	$-0.0815844\pi$
$467$	2.57460e6	+	8.34664e6i	0.0252789	+	0.0819523i	−0.942054	+	0.335460i	$0.891108\pi$
$468$	−2.71865e7	−	6.20513e6i	−0.265225	−	0.0605360i
$469$	2.29169e7	+	6.20416e6i	0.222146	+	0.0601402i
$470$	4.13572e7	+	1.81198e8i	0.398343	+	1.74525i
$471$	−6.79512e7	−	1.17695e8i	−0.650331	−	1.12641i
$472$	−7.04595e7	−	4.06798e7i	−0.670060	−	0.386859i
$473$	−2.56213e7	−	7.90314e6i	−0.242113	−	0.0746820i
$474$	−1.14086e8	+	8.54954e6i	−1.07126	+	0.0802800i
$475$	−4.43758e7	−	3.53885e7i	−0.414062	−	0.330203i
$476$	−2.52847e7	−	2.54159e7i	−0.234443	−	0.235659i
$477$	−6.47975e7	−	8.12535e7i	−0.597039	−	0.748664i
$478$	−1.42289e7	+	1.32025e7i	−0.130283	+	0.120885i
$479$	−1.89221e7	−	1.25540e8i	−0.172172	−	1.14229i	−0.893292	−	0.449477i	$-0.851610\pi$
$479$	−1.89221e7	−	1.25540e8i	−0.172172	−	1.14229i	0.721120	−	0.692810i	$-0.243628\pi$
$480$	1.53232e8	−	1.04471e8i	1.38556	−	0.944657i
$481$	−2.44931e6	+	1.62501e7i	−0.0220094	+	0.146023i
$482$	−1.03902e7	−	2.15755e7i	−0.0927863	−	0.192673i
$483$	1.37248e8	+	2.61320e8i	1.21805	+	2.31916i
$484$	−3.77738e7	−	1.81909e7i	−0.333161	−	0.160442i
$485$	−6.32342e7	−	4.31124e7i	−0.554277	−	0.377900i
$486$	1.10889e7	−	1.19510e7i	0.0966009	−	0.104111i
$487$	−4.15539e6	+	5.54499e7i	−0.0359770	+	0.480080i	0.949894	+	0.312573i	$0.101191\pi$
$487$	−4.15539e6	+	5.54499e7i	−0.0359770	+	0.480080i	−0.985871	+	0.167507i	$0.946428\pi$
$488$	1.62215e8	+	6.36647e7i	1.39583	+	0.547822i
$489$			1.14707e8i			0.980984i
$490$	−1.13046e8	−	5.51622e7i	−0.960871	−	0.468871i
$491$	9.91670e7			0.837766			0.418883	−	0.908040i	$-0.362422\pi$
$491$	9.91670e7			0.837766			0.418883	+	0.908040i	$0.362422\pi$
$492$	−4.64646e7	+	1.18390e8i	−0.390146	+	0.994076i
$493$	1.12410e8	+	8.42397e6i	0.938133	+	0.0703033i
$494$	1.56928e7	+	1.45608e7i	0.130172	+	0.120782i
$495$	−3.41360e7	+	5.00683e7i	−0.281447	+	0.412808i
$496$	3.73625e7	−	7.75840e7i	0.306190	−	0.635810i
$497$	−7.52051e7	+	2.61916e6i	−0.612602	+	0.0213350i
$498$	2.27867e8	−	1.09735e8i	1.84499	−	0.888499i
$499$	3.55151e7	+	5.35304e6i	0.285832	+	0.0430823i	0.290394	−	0.956907i	$-0.406214\pi$
$499$	3.55151e7	+	5.35304e6i	0.285832	+	0.0430823i	−0.00456124	+	0.999990i	$0.501452\pi$
$500$	−5.36911e6	−	7.87504e6i	−0.0429529	−	0.0630003i
$501$	−8.16992e7	+	1.23142e7i	−0.649688	+	0.0979247i
$502$	−8.64755e7	−	9.31984e7i	−0.683568	−	0.736711i
$503$	1.69838e7	−	1.35441e7i	0.133454	−	0.106426i	−0.554488	−	0.832192i	$-0.687086\pi$
$503$	1.69838e7	−	1.35441e7i	0.133454	−	0.106426i	0.687942	+	0.725766i	$0.258514\pi$
$504$	−1.43381e8	−	2.29506e8i	−1.11996	−	1.79268i
$505$	2.58853e7	−	3.24591e7i	0.200992	−	0.252036i
$506$	−2.18804e6	−	2.91973e7i	−0.0168890	−	0.225368i
$507$	5.71647e7	−	1.85323e8i	0.438636	−	1.42202i
$508$	−1.99661e7	+	3.45823e7i	−0.152301	+	0.263792i
$509$	−1.04625e7	+	6.04055e6i	−0.0793385	+	0.0458061i	−0.539144	−	0.842213i	$-0.681252\pi$
$509$	−1.04625e7	+	6.04055e6i	−0.0793385	+	0.0458061i	0.459806	+	0.888019i	$0.347919\pi$
$510$	−2.05751e8	+	4.69612e7i	−1.55107	+	0.354021i
$511$	−1.08945e8	−	1.48418e8i	−0.816481	−	1.11230i
$512$	2.52984e7	−	1.10840e8i	0.188488	−	0.825819i
$513$	−1.29886e8	+	4.00645e7i	−0.962078	+	0.296762i
$514$	−1.20500e8	+	4.72928e7i	−0.887356	+	0.348261i
$515$	7.79349e7	+	1.98575e8i	0.570572	+	1.45379i
$516$	3.58058e7	+	1.16080e8i	0.260618	+	0.844903i
$517$	4.25375e7	+	9.70890e6i	0.307822	+	0.0702584i
$518$	−3.56308e7	+	2.61546e7i	−0.256352	+	0.188174i
$519$	−6.87110e7	−	3.01043e8i	−0.491501	−	2.15341i
$520$	−3.79177e7	−	6.56754e7i	−0.269670	−	0.467082i
$521$	−7.18630e7	−	4.14901e7i	−0.508150	−	0.293381i	0.223923	−	0.974607i	$-0.428114\pi$
$521$	−7.18630e7	−	4.14901e7i	−0.508150	−	0.293381i	−0.732073	+	0.681226i	$0.761447\pi$
$522$	2.25347e8	+	6.95102e7i	1.58431	+	0.488694i
$523$	3.97553e7	−	2.97924e6i	0.277901	−	0.0208258i	0.0649492	−	0.997889i	$-0.479311\pi$
$523$	3.97553e7	−	2.97924e6i	0.277901	−	0.0208258i	0.212951	+	0.977063i	$0.431692\pi$
$524$	5.45198e7	+	4.34781e7i	0.378931	+	0.302187i
$525$	1.79870e8	−	1.12372e8i	1.24303	−	0.776567i
$526$	−6.24130e7	−	7.82634e7i	−0.428862	−	0.537776i
$527$	1.39793e8	−	1.29709e8i	0.955111	−	0.886214i
$528$	3.33433e6	+	2.21219e7i	0.0226520	+	0.150286i
$529$	1.62607e8	−	1.10864e8i	1.09843	−	0.748898i
$530$	1.16747e7	−	7.74569e7i	0.0784187	−	0.520274i
$531$	−9.00324e7	−	1.86954e8i	−0.601333	−	1.24868i
$532$	−1.24617e6	−	3.57820e7i	−0.00827644	−	0.237645i
$533$	8.07255e7	+	3.88754e7i	0.533125	+	0.256740i
$534$	9.87547e7	+	6.73298e7i	0.648536	+	0.442164i
$535$	−9.54331e7	+	1.02852e8i	−0.623214	+	0.671665i
$536$	−2.87697e6	+	3.83905e7i	−0.0186828	+	0.249304i
$537$	−6.19748e7	−	2.43233e7i	−0.400214	−	0.157072i
$538$		−	4.22511e6i		−	0.0271326i
$539$	−2.31818e7	+	1.82915e7i	−0.148041	+	0.116811i
$540$	1.33451e8			0.847504
$541$	−4.65794e7	+	1.18682e8i	−0.294172	+	0.749539i	0.705013	+	0.709194i	$0.250941\pi$
$541$	−4.65794e7	+	1.18682e8i	−0.294172	+	0.749539i	−0.999186	+	0.0403451i	$0.987154\pi$
$542$	−2.48164e7	−	1.85973e6i	−0.155862	−	0.0116803i
$543$	1.52849e8	+	1.41823e8i	0.954690	+	0.885823i
$544$	5.64191e7	−	8.27517e7i	0.350453	−	0.514020i
$545$	−2.72022e7	+	5.64859e7i	−0.168041	+	0.348940i
$546$	−7.08182e7	+	3.71945e7i	−0.435078	+	0.228507i
$547$	−1.35375e8	+	6.51931e7i	−0.827135	+	0.398327i	−0.799040	−	0.601278i	$-0.794658\pi$
$547$	−1.35375e8	+	6.51931e7i	−0.827135	+	0.398327i	−0.0280949	+	0.999605i	$0.508944\pi$
$548$	−4.10627e7	−	6.18920e6i	−0.249520	−	0.0376091i
$549$	2.50364e8	+	3.67217e8i	1.51306	+	2.21925i
$550$	−2.08028e7	+	3.13552e6i	−0.125036	+	0.0188461i
$551$	7.65717e7	+	8.25247e7i	0.457734	+	0.493320i
$552$	−3.74205e8	+	2.98419e8i	−2.22481	+	1.77422i
$553$	9.55635e7	−	9.50703e7i	0.565089	−	0.562172i
$554$	−1.28595e8	+	1.61253e8i	−0.756303	+	0.948374i
$555$	−1.20910e7	−	1.61343e8i	−0.0707266	−	0.943780i
$556$	−3.41881e7	+	1.10835e8i	−0.198907	+	0.644842i
$557$	1.23137e8	−	2.13280e8i	0.712564	−	1.23420i	−0.251328	−	0.967902i	$-0.580867\pi$
$557$	1.23137e8	−	2.13280e8i	0.712564	−	1.23420i	0.963892	−	0.266295i	$-0.0857995\pi$
$558$	3.45500e8	−	1.99474e8i	1.98859	−	1.14811i
$559$	8.34338e7	−	1.90432e7i	0.477646	−	0.109020i
$560$	2.93418e7	−	1.08383e8i	0.167079	−	0.617158i
$561$	−1.10245e7	+	4.83015e7i	−0.0624411	+	0.273572i
$562$	3.29744e7	−	1.01713e7i	0.185767	−	0.0573015i
$563$	−1.66964e8	+	6.55285e7i	−0.935616	+	0.367202i	−0.783663	−	0.621186i	$-0.786651\pi$
$563$	−1.66964e8	+	6.55285e7i	−0.935616	+	0.367202i	−0.151953	+	0.988388i	$0.548556\pi$
$564$	−7.22190e7	−	1.84011e8i	−0.402545	−	1.02567i
$565$	1.31477e8	+	4.26239e8i	0.728963	+	2.36324i
$566$	−2.44611e8	−	5.58308e7i	−1.34904	−	0.307911i
$567$	6.12450e6	−	1.53081e8i	0.0335986	−	0.839791i
$568$	−2.71523e7	−	1.18962e8i	−0.148170	−	0.649177i
$569$	5.82317e7	+	1.00860e8i	0.316099	+	0.547499i	0.979670	−	0.200614i	$-0.0642937\pi$
$569$	5.82317e7	+	1.00860e8i	0.316099	+	0.547499i	−0.663572	+	0.748113i	$0.730960\pi$
$570$	−1.82527e8	−	1.05382e8i	−0.985605	−	0.569039i
$571$	−1.33622e8	−	4.12168e7i	−0.717742	−	0.221394i	−0.0856918	−	0.996322i	$-0.527310\pi$
$571$	−1.33622e8	−	4.12168e7i	−0.717742	−	0.221394i	−0.632050	+	0.774928i	$0.717786\pi$
$572$	−4.92031e6	+	368726.i	−0.0262908	+	0.00197023i
$573$	1.23093e8	+	9.81633e7i	0.654288	+	0.521777i
$574$	7.90029e7	+	2.27665e8i	0.417741	+	1.20382i
$575$	−1.54486e8	−	1.93719e8i	−0.812614	−	1.01899i
$576$	2.81595e8	−	2.61282e8i	1.47353	−	1.36723i
$577$	2.20147e7	+	1.46058e8i	0.114600	+	0.760324i	0.970133	+	0.242574i	$0.0779919\pi$
$577$	2.20147e7	+	1.46058e8i	0.114600	+	0.760324i	−0.855532	+	0.517749i	$0.826770\pi$
$578$	3.11131e7	−	2.12126e7i	0.161124	−	0.109852i
$579$	−909810.	+	6.03620e6i	−0.00468722	+	0.0310977i
$580$	−4.79564e7	−	9.95826e7i	−0.245789	−	0.510387i
$581$	−1.19873e8	+	2.72823e8i	−0.611211	+	1.39108i
$582$	−1.17938e8	−	5.67958e7i	−0.598252	−	0.288103i
$583$	−1.51937e7	−	1.03589e7i	−0.0766756	−	0.0522766i
$584$	2.03060e8	−	2.18847e8i	1.01950	−	1.09876i
$585$	1.44539e7	−	1.92874e8i	0.0721966	−	0.963397i
$586$	1.09689e8	+	4.30496e7i	0.545091	+	0.213932i
$587$		−	5.07818e7i		−	0.251069i	−0.992089	−	0.125535i	$-0.959935\pi$
$587$		−	5.07818e7i		−	0.251069i	0.992089	−	0.125535i	$-0.0400646\pi$
$588$	1.27635e8	+	4.00947e7i	0.627825	+	0.197222i
$589$	1.90449e8			0.932037
$590$	5.71391e7	−	1.45588e8i	0.278213	−	0.708874i
$591$	−3.47542e8	−	2.60447e7i	−1.68362	−	0.126170i
$592$	−2.89228e7	−	2.68365e7i	−0.139404	−	0.129348i
$593$	−8.02944e7	+	1.17770e8i	−0.385053	+	0.564770i	−0.969012	−	0.247014i	$-0.920551\pi$
$593$	−8.02944e7	+	1.17770e8i	−0.385053	+	0.564770i	0.583959	+	0.811784i	$0.301503\pi$
$594$	−2.18594e7	+	4.53916e7i	−0.104299	+	0.216579i
$595$	1.48177e8	−	1.99690e8i	0.703445	−	0.947991i
$596$	1.25150e8	−	6.02692e7i	0.591144	−	0.284680i
$597$	−6.61794e7	−	9.97494e6i	−0.311028	−	0.0468800i
$598$	5.26436e7	+	7.72140e7i	0.246174	+	0.361071i
$599$	3.73644e6	−	563177.i	0.0173851	−	0.00262038i	−0.140344	−	0.990103i	$-0.544821\pi$
$599$	3.73644e6	−	563177.i	0.0173851	−	0.00262038i	0.157729	+	0.987482i	$0.449583\pi$
$600$	2.33914e8	+	2.52099e8i	1.08293	+	1.16713i
$601$	1.00969e8	−	8.05198e7i	0.465118	−	0.370919i	−0.362709	−	0.931902i	$-0.618148\pi$
$601$	1.00969e8	−	8.05198e7i	0.465118	−	0.370919i	0.827827	+	0.560983i	$0.189577\pi$
$602$	1.94576e8	+	1.22963e8i	0.891865	+	0.563619i
$603$	−6.12190e7	+	7.67662e7i	−0.279212	+	0.350121i
$604$	540554.	+	7.21319e6i	0.00245317	+	0.0327353i
$605$	8.57138e7	−	2.77877e8i	0.387066	−	1.25484i
$606$	3.55050e7	−	6.14965e7i	0.159541	−	0.276333i
$607$	−2.62237e8	+	1.51403e8i	−1.17254	+	0.676967i	−0.954277	−	0.298922i	$-0.903373\pi$
$607$	−2.62237e8	+	1.51403e8i	−1.17254	+	0.676967i	−0.218264	+	0.975890i	$0.570039\pi$
$608$	9.75151e7	−	2.22572e7i	0.433871	−	0.0990283i
$609$	−3.85992e8	+	1.67219e8i	−1.70894	+	0.740346i
$610$	−7.45413e7	+	3.26587e8i	−0.328403	+	1.43883i
$611$	−1.33074e8	+	4.10480e7i	−0.583405	+	0.179957i
$612$	1.38017e8	−	5.41675e7i	0.602112	−	0.236311i
$613$	8.03915e7	+	2.04834e8i	0.349002	+	0.889244i	0.992326	+	0.123649i	$0.0394598\pi$
$613$	8.03915e7	+	2.04834e8i	0.349002	+	0.889244i	−0.643324	+	0.765594i	$0.722445\pi$
$614$	2.79602e7	+	9.06447e7i	0.120791	+	0.391595i
$615$	−8.60013e8	−	1.96292e8i	−3.69726	−	0.843875i
$616$	−3.62127e7	−	3.13270e7i	−0.154924	−	0.134022i
$617$	3.84389e7	+	1.68412e8i	0.163650	+	0.716996i	0.988447	+	0.151568i	$0.0484321\pi$
$617$	3.84389e7	+	1.68412e8i	0.163650	+	0.716996i	−0.824797	+	0.565429i	$0.808711\pi$
$618$	1.82432e8	+	3.15981e8i	0.772920	+	1.33874i
$619$	6.97316e7	+	4.02595e7i	0.294007	+	0.169745i	0.639747	−	0.768585i	$-0.279039\pi$
$619$	6.97316e7	+	4.02595e7i	0.294007	+	0.169745i	−0.345741	+	0.938330i	$0.612372\pi$
$620$	−1.78676e8	−	5.51144e7i	−0.749708	−	0.231254i
$621$	−5.91709e8	+	4.43425e7i	−2.47078	+	0.185159i
$622$	1.85944e8	+	1.48285e8i	0.772700	+	0.616208i
$623$	−1.39984e8	+	1.54057e7i	−0.578913	+	0.0637115i
$624$	−4.45205e7	−	5.58269e7i	−0.183234	−	0.229768i
$625$	2.01289e8	−	1.86769e8i	0.824481	−	0.765006i
$626$	1.02253e7	+	6.78407e7i	0.0416826	+	0.276546i
$627$	−4.08810e7	+	2.78722e7i	−0.165851	+	0.113076i
$628$	−1.07255e7	+	7.11591e7i	−0.0433051	+	0.287310i
$629$	−3.79112e7	−	7.87235e7i	−0.152341	−	0.316339i
$630$	3.95177e8	−	3.38302e8i	1.58041	−	1.35295i
$631$	−1.62299e8	−	7.81590e7i	−0.645992	−	0.311094i	0.0820473	−	0.996628i	$-0.473854\pi$
$631$	−1.62299e8	−	7.81590e7i	−0.645992	−	0.311094i	−0.728040	+	0.685535i	$0.759568\pi$
$632$	1.80600e8	+	1.23131e8i	0.715427	+	0.487770i
$633$	2.59715e8	−	2.79906e8i	1.02397	−	1.10357i
$634$	−1.52376e7	+	2.03331e8i	−0.0597927	+	0.797879i
$635$	−2.57823e8	−	1.01188e8i	−1.00693	−	0.395193i
$636$			8.33128e7i			0.323847i
$637$	3.48871e7	−	8.75559e7i	0.134973	−	0.338741i
$638$	4.17269e7			0.160677
$639$	1.13697e8	−	2.89696e8i	0.435760	−	1.11030i
$640$	3.33146e7	+	2.49659e6i	0.127085	+	0.00952373i
$641$	−1.72611e8	−	1.60160e8i	−0.655382	−	0.608106i	0.280739	−	0.959784i	$-0.409421\pi$
$641$	−1.72611e8	−	1.60160e8i	−0.655382	−	0.608106i	−0.936121	+	0.351679i	$0.885611\pi$
$642$	−1.35186e8	+	1.98281e8i	−0.510889	+	0.749336i
$643$	4.87854e7	−	1.01304e8i	0.183509	−	0.381060i	−0.788838	−	0.614601i	$-0.789317\pi$
$643$	4.87854e7	−	1.01304e8i	0.183509	−	0.381060i	0.972347	+	0.233541i	$0.0750313\pi$
$644$	2.94548e7	−	1.53497e8i	0.110280	−	0.574702i
$645$	−7.59121e8	+	3.65573e8i	−2.82899	+	1.36237i
$646$	−1.12550e8	−	1.69643e7i	−0.417494	−	0.0629270i
$647$	1.65457e8	+	2.42681e8i	0.610902	+	0.896029i	0.999680	−	0.0253024i	$-0.00805488\pi$
$647$	1.65457e8	+	2.42681e8i	0.610902	+	0.896029i	−0.388777	+	0.921332i	$0.627102\pi$
$648$	2.45649e8	−	3.70256e7i	0.902795	−	0.136074i
$649$	−2.49731e7	−	2.69146e7i	−0.0913564	−	0.0984588i
$650$	5.24982e7	−	4.18659e7i	0.191163	−	0.152447i
$651$	−2.36776e8	+	6.71092e8i	−0.858211	+	2.43242i
$652$	3.78703e7	−	4.74879e7i	0.136633	−	0.171333i
$653$	−1.40503e7	−	1.87488e8i	−0.0504597	−	0.673338i	−0.963883	−	0.266327i	$-0.914190\pi$
$653$	−1.40503e7	−	1.87488e8i	−0.0504597	−	0.673338i	0.913423	−	0.407011i	$-0.133429\pi$
$654$	−3.16074e7	+	1.02469e8i	−0.112994	+	0.366318i
$655$	−2.41835e8	+	4.18871e8i	−0.860589	+	1.49058i
$656$	−1.86296e8	+	1.07558e8i	−0.659921	+	0.381005i
$657$	7.42325e8	−	1.69431e8i	2.61757	−	0.597443i
$658$	−3.30696e8	−	1.75874e8i	−1.16078	−	0.617339i
$659$	5.32659e7	−	2.33373e8i	0.186120	−	0.815445i	−0.792517	−	0.609850i	$-0.791230\pi$
$659$	5.32659e7	−	2.33373e8i	0.186120	−	0.815445i	0.978637	−	0.205595i	$-0.0659131\pi$
$660$	4.64199e7	−	1.43186e7i	0.161463	−	0.0498047i
$661$	−1.99295e8	+	7.82177e7i	−0.690070	+	0.270832i	−0.684353	−	0.729151i	$-0.739915\pi$
$661$	−1.99295e8	+	7.82177e7i	−0.690070	+	0.270832i	−0.00571709	+	0.999984i	$0.501820\pi$
$662$	−3.96650e7	−	1.01065e8i	−0.136720	−	0.348358i
$663$	−4.66102e7	−	1.51106e8i	−0.159934	−	0.518492i
$664$	−4.71095e8	−	1.07524e8i	−1.60918	−	0.367284i
$665$	2.44123e8	−	4.55367e7i	0.830126	−	0.154845i
$666$	−4.06754e7	−	1.78210e8i	−0.137692	−	0.603268i
$667$	2.45722e8	+	4.25603e8i	0.828070	+	1.43426i
$668$	3.78885e7	+	2.18749e7i	0.127110	+	0.0733868i
$669$	3.61110e8	+	1.11388e8i	1.20604	+	0.372013i
$670$	−7.37989e7	+	5.53046e6i	−0.245372	+	0.0183881i
$671$	6.14835e7	+	4.90315e7i	0.203512	+	0.162296i
$672$	−4.28072e7	+	3.71288e8i	−0.141062	+	1.22350i
$673$	−1.48510e8	−	1.86225e8i	−0.487202	−	0.610932i	0.476087	−	0.879398i	$-0.342055\pi$
$673$	−1.48510e8	−	1.86225e8i	−0.487202	−	0.610932i	−0.963289	+	0.268466i	$0.913483\pi$
$674$	−1.48207e6	+	1.37516e6i	−0.00484049	+	0.00449132i
$675$	6.35439e7	+	4.21586e8i	0.206615	+	1.37080i
$676$	−8.48502e7	+	5.78499e7i	−0.274671	+	0.187268i
$677$	−5.61299e6	+	3.72398e7i	−0.0180896	+	0.120017i	−0.996053	−	0.0887593i	$-0.971710\pi$
$677$	−5.61299e6	+	3.72398e7i	−0.0180896	+	0.120017i	0.977964	+	0.208776i	$0.0669479\pi$
$678$	3.31024e8	+	6.87378e8i	1.06211	+	2.20550i
$679$	1.49082e8	−	3.95333e7i	0.476230	−	0.126286i
$680$	3.63281e8	+	1.74947e8i	1.15536	+	0.556390i
$681$	−3.57004e6	−	2.43401e6i	−0.0113040	−	0.00770693i
$682$	4.80137e7	−	5.17465e7i	0.151360	−	0.163128i
$683$	3.36094e7	−	4.48486e8i	0.105487	−	1.40762i	−0.653701	−	0.756753i	$-0.726785\pi$
$683$	3.36094e7	−	4.48486e8i	0.105487	−	1.40762i	0.759188	−	0.650872i	$-0.225596\pi$
$684$	1.37835e8	+	5.40962e7i	0.430716	+	0.169044i
$685$		−	2.88027e8i		−	0.896112i
$686$	2.33123e8	−	9.95641e7i	0.722127	−	0.308411i
$687$	6.67807e8			2.05959
$688$	−7.50653e7	+	1.91263e8i	−0.230502	+	0.587309i
$689$	5.85292e7	+	4.38616e6i	0.178943	+	0.0134099i
$690$	−6.74461e8	−	6.25808e8i	−2.05310	−	1.90500i
$691$	3.16600e8	−	4.64366e8i	0.959569	−	1.40743i	0.0468226	−	0.998903i	$-0.485090\pi$
$691$	3.16600e8	−	4.64366e8i	0.959569	−	1.40743i	0.912747	−	0.408526i	$-0.133957\pi$
$692$	−7.09431e7	+	1.47315e8i	−0.214088	+	0.444558i
$693$	−3.13022e7	−	1.18042e8i	−0.0940535	−	0.354680i
$694$	1.72688e8	−	8.31624e7i	0.516636	−	0.248799i
$695$	−7.95508e8	−	1.19904e8i	−2.36968	−	0.357172i
$696$	−3.84245e8	−	5.63584e8i	−1.13967	−	1.67159i
$697$	−4.71068e8	+	7.10020e7i	−1.39119	+	0.209687i
$698$	−1.11842e8	−	1.20537e8i	−0.328882	−	0.354450i
$699$	6.83803e8	−	5.45315e8i	2.00216	−	1.59667i
$700$	−1.11564e8	−	1.28627e7i	−0.325261	−	0.0375005i
$701$	−1.43290e8	+	1.79680e8i	−0.415970	+	0.521610i	−0.945034	−	0.326972i	$-0.893972\pi$
$701$	−1.43290e8	+	1.79680e8i	−0.415970	+	0.521610i	0.529064	+	0.848582i	$0.322543\pi$
$702$	−1.20169e7	−	1.60354e8i	−0.0347361	−	0.463521i
$703$	2.57208e7	−	8.33847e7i	0.0740318	−	0.240005i
$704$	3.39852e7	−	5.88640e7i	0.0974028	−	0.168707i
$705$	1.18739e9	−	6.85539e8i	3.38864	−	1.95643i
$706$	−2.78051e8	+	6.34633e7i	−0.790152	+	0.180347i
$707$	1.53421e7	+	8.22493e7i	0.0434137	+	0.232742i
$708$	−3.70151e7	+	1.62174e8i	−0.104299	+	0.456963i
$709$	−3.55323e8	+	1.09603e8i	−0.996976	+	0.307526i	−0.749959	−	0.661484i	$-0.769927\pi$
$709$	−3.55323e8	+	1.09603e8i	−0.996976	+	0.307526i	−0.247018	+	0.969011i	$0.579451\pi$
$710$	2.18349e8	−	8.56958e7i	0.610066	−	0.239433i
$711$	2.03669e8	+	5.18941e8i	0.566653	+	1.44381i
$712$	−6.73097e7	−	2.18213e8i	−0.186482	−	0.604561i
$713$	8.10545e8	+	1.85002e8i	2.23619	+	0.510395i
$714$	1.99706e8	−	3.75507e8i	0.548651	−	1.03163i
$715$	−7.61532e6	−	3.33649e7i	−0.0208339	−	0.0912792i
$716$	1.76269e7	+	3.05307e7i	0.0480216	+	0.0831758i
$717$	1.24008e8	+	7.15961e7i	0.336428	+	0.194237i
$718$	−7.02559e7	−	2.16711e7i	−0.189806	−	0.0585473i
$719$	5.86748e8	−	4.39707e7i	1.57857	−	0.118298i	0.743614	−	0.668609i	$-0.233110\pi$
$719$	5.86748e8	−	4.39707e7i	1.57857	−	0.118298i	0.834959	+	0.550312i	$0.185491\pi$
$720$	3.63056e8	+	2.89528e8i	0.972694	+	0.775698i
$721$	−4.05409e8	−	1.43037e8i	−1.08165	−	0.381630i
$722$	1.13389e8	+	1.42186e8i	0.301273	+	0.377785i
$723$	−1.29500e8	+	1.20158e8i	−0.342652	+	0.317935i
$724$	−1.64557e7	−	1.09177e8i	−0.0433613	−	0.287683i
$725$	2.91757e8	−	1.98916e8i	0.765608	−	0.521983i
$726$	7.41302e7	−	4.91822e8i	0.193725	−	1.28528i
$727$	−2.61025e7	−	5.42024e7i	−0.0679328	−	0.141064i	0.864237	−	0.503084i	$-0.167801\pi$
$727$	−2.61025e7	−	5.42024e7i	−0.0679328	−	0.141064i	−0.932170	+	0.362020i	$0.882087\pi$
$728$	1.50091e8	+	2.88012e7i	0.389011	+	0.0746478i
$729$	−4.01725e8	−	1.93461e8i	−1.03692	−	0.499356i
$730$	4.74172e8	+	3.23285e8i	1.21890	+	0.831031i
$731$	−3.09492e8	+	3.33553e8i	−0.792313	+	0.853910i
$732$	2.66253e7	−	3.55290e8i	0.0678831	−	0.905838i
$733$	1.52381e8	+	5.98051e7i	0.386918	+	0.151854i	0.550823	−	0.834622i	$-0.314314\pi$
$733$	1.52381e8	+	5.98051e7i	0.386918	+	0.151854i	−0.163905	+	0.986476i	$0.552409\pi$
$734$		−	2.83069e8i		−	0.715820i
$735$	−1.43047e8	+	9.16838e8i	−0.360260	+	2.30903i
$736$	4.36641e8			1.09519
$737$	−6.34722e6	+	1.61725e7i	−0.0158555	+	0.0403993i
$738$	−9.93828e8	−	7.44771e7i	−2.47253	−	0.185291i
$739$	2.44529e8	+	2.26889e8i	0.605893	+	0.562187i	0.922319	−	0.386431i	$-0.126292\pi$
$739$	2.44529e8	+	2.26889e8i	0.605893	+	0.562187i	−0.316425	+	0.948618i	$0.602483\pi$
$740$	−4.82616e7	+	7.07868e7i	−0.119099	+	0.174686i
$741$	6.85205e7	−	1.42284e8i	0.168409	−	0.349706i
$742$	1.02661e8	+	1.19920e8i	0.251300	+	0.293548i
$743$	−1.45393e8	+	7.00173e7i	−0.354467	+	0.170702i	−0.602639	−	0.798014i	$-0.705884\pi$
$743$	−1.45393e8	+	7.00173e7i	−0.354467	+	0.170702i	0.248173	+	0.968716i	$0.420170\pi$
$744$	−1.14105e9	−	1.71986e8i	−2.77068	−	0.417613i
$745$	5.42733e8	+	7.96043e8i	1.31256	+	1.92516i
$746$	3.35704e8	−	5.05992e7i	0.808611	−	0.121878i
$747$	−8.38246e8	−	9.03414e8i	−2.01099	−	2.16733i
$748$	2.05108e7	−	1.63568e7i	0.0490092	−	0.0390835i
$749$	−3.09319e7	−	2.81061e8i	−0.0736140	−	0.668892i
$750$	7.04988e7	−	8.84027e7i	0.167108	−	0.209547i
$751$	−5.35441e7	−	7.14497e8i	−0.126413	−	1.68686i	−0.595219	−	0.803564i	$-0.702935\pi$
$751$	−5.35441e7	−	7.14497e8i	−0.126413	−	1.68686i	0.468806	−	0.883301i	$-0.344684\pi$
$752$	9.85515e7	−	3.19496e8i	0.231745	−	0.751298i
$753$	−4.68949e8	+	8.12244e8i	−1.09835	+	1.90240i
$754$	−1.15339e8	+	6.65912e7i	−0.269069	+	0.155347i
$755$	−4.89130e7	+	1.11641e7i	−0.113654	+	0.0259407i
$756$	−1.75954e8	+	2.03396e8i	−0.407225	+	0.470736i
$757$	4.18177e7	−	1.83215e8i	0.0963990	−	0.422352i	−0.903583	−	0.428414i	$-0.859073\pi$
$757$	4.18177e7	−	1.83215e8i	0.0963990	−	0.422352i	0.999982	+	0.00606219i	$0.00192967\pi$
$758$	2.77855e8	−	8.57069e7i	0.637985	−	0.196792i
$759$	−2.01063e8	+	7.89114e7i	−0.459840	+	0.180474i
$760$	1.47116e8	+	3.74845e8i	0.335134	+	0.853907i
$761$	−3.36508e7	−	1.09093e8i	−0.0763557	−	0.247539i	0.909346	−	0.416042i	$-0.136583\pi$
$761$	−3.36508e7	−	1.09093e8i	−0.0763557	−	0.247539i	−0.985701	+	0.168503i	$0.946107\pi$
$762$	−4.61850e8	−	1.05414e8i	−1.04384	−	0.238251i
$763$	−5.02256e7	−	1.15936e8i	−0.113071	−	0.261002i
$764$	−1.85512e7	−	8.12780e7i	−0.0415998	−	0.182261i
$765$	5.14185e8	+	8.90594e8i	1.14851	+	1.98928i
$766$	−2.63490e7	−	1.52126e7i	−0.0586243	−	0.0338467i
$767$	1.11982e8	+	3.45419e7i	0.248178	+	0.0765527i
$768$	−7.43936e8	+	5.57503e7i	−1.64230	+	0.123073i
$769$	4.04016e8	+	3.22192e8i	0.888423	+	0.708493i	0.957289	−	0.289133i	$-0.0933668\pi$
$769$	4.04016e8	+	3.22192e8i	0.888423	+	0.708493i	−0.0688665	+	0.997626i	$0.521938\pi$
$770$	4.91726e7	−	7.78102e7i	0.107709	−	0.170437i
$771$	5.95399e8	+	7.46607e8i	1.29911	+	1.62903i
$772$	2.36950e6	−	2.19858e6i	0.00514998	−	0.00477848i
$773$	−6.90088e7	−	4.57844e8i	−0.149405	−	0.991240i	−0.930359	−	0.366650i	$-0.880505\pi$
$773$	−6.90088e7	−	4.57844e8i	−0.149405	−	0.991240i	0.780953	−	0.624589i	$-0.214734\pi$
$774$	−7.86505e8	+	5.36230e8i	−1.69621	+	1.15645i
$775$	8.90337e7	−	5.90700e8i	0.191271	−	1.26900i
$776$	1.08513e8	+	2.25329e8i	0.232218	+	0.482205i
$777$	2.61848e8	+	1.94301e8i	0.558195	+	0.414202i
$778$	1.04329e8	+	5.02423e7i	0.221548	+	0.106692i
$779$	−3.93093e8	−	2.68006e8i	−0.831539	−	0.566934i
$780$	−1.05461e8	+	1.13660e8i	−0.222232	+	0.239509i
$781$	4.11506e6	−	5.49116e7i	0.00863819	−	0.115269i
$782$	−4.62532e8	−	1.81530e8i	−0.967211	−	0.379602i
$783$		−	8.45631e8i		−	1.76155i
$784$	1.26502e8	+	1.87622e8i	0.262511	+	0.389346i
$785$	−4.99134e8			−1.03183
$786$	−3.02235e8	+	7.70082e8i	−0.622411	+	1.58588i
$787$	−1.85197e8	−	1.38786e7i	−0.379934	−	0.0284721i	−0.116606	−	0.993178i	$-0.537201\pi$
$787$	−1.85197e8	−	1.38786e7i	−0.379934	−	0.0284721i	−0.263329	+	0.964706i	$0.584820\pi$
$788$	1.35282e8	+	1.25523e8i	0.276478	+	0.256534i
$789$	−4.15990e8	+	6.10146e8i	−0.846939	+	1.24223i
$790$	−1.82310e8	+	3.78570e8i	−0.369768	+	0.767830i
$791$	−8.22991e8	−	3.61605e8i	−1.66290	−	0.730642i
$792$	1.78414e8	−	8.59195e7i	0.359131	−	0.172948i
$793$	−2.48198e8	−	3.74099e7i	−0.497713	−	0.0750182i
$794$	2.07555e8	+	3.04427e8i	0.414640	+	0.608166i
$795$	−5.71403e8	+	8.61251e7i	−1.13721	+	0.171407i
$796$	2.41047e7	+	2.59786e7i	0.0477927	+	0.0515083i
$797$	−1.15878e8	+	9.24095e7i	−0.228889	+	0.182533i	−0.731219	−	0.682143i	$-0.761048\pi$
$797$	−1.15878e8	+	9.24095e7i	−0.228889	+	0.182533i	0.502329	+	0.864676i	$0.332477\pi$
$798$	4.01275e8	−	1.39248e8i	0.789648	−	0.274019i
$799$	4.61658e8	−	5.78900e8i	0.905065	−	1.13492i
$800$	−2.34456e7	−	3.12859e8i	−0.0457921	−	0.611053i
$801$	1.71670e8	−	5.56540e8i	0.334039	−	1.08293i
$802$	2.15069e8	−	3.72510e8i	0.416922	−	0.722130i
$803$	1.16676e8	−	6.73628e7i	0.225338	−	0.130099i
$804$	7.67383e7	−	1.75150e7i	0.147654	−	0.0337010i
$805$	1.08321e9	+	4.33376e7i	2.07647	+	0.0830763i
$806$	−5.01358e7	+	2.19659e8i	−0.0957509	+	0.419512i
$807$	−2.97841e7	+	9.18718e6i	−0.0566714	+	0.0174808i
$808$	−1.26292e8	+	4.95658e7i	−0.239409	+	0.0939612i
$809$	2.24640e8	+	5.72373e8i	0.424269	+	1.08102i	0.970010	+	0.243066i	$0.0781531\pi$
$809$	2.24640e8	+	5.72373e8i	0.424269	+	1.08102i	−0.545741	+	0.837954i	$0.683752\pi$
$810$	1.40760e8	+	4.56333e8i	0.264865	+	0.858671i
$811$	−7.14327e8	−	1.63040e8i	−1.33917	−	0.305656i	−0.507845	−	0.861448i	$-0.669558\pi$
$811$	−7.14327e8	−	1.63040e8i	−1.33917	−	0.305656i	−0.831321	+	0.555792i	$0.812415\pi$
$812$	2.15006e8	+	5.82073e7i	0.401590	+	0.108720i
$813$	4.08515e7	+	1.78982e8i	0.0760214	+	0.333072i
$814$	−1.61718e7	−	2.80104e7i	−0.0299838	−	0.0519334i
$815$	3.64845e8	+	2.10644e8i	0.673963	+	0.389113i
$816$	3.62790e8	+	1.11906e8i	0.667705	+	0.205960i
$817$	−4.53150e8	+	3.39589e7i	−0.830951	+	0.0622712i
$818$	3.79545e8	+	3.02677e8i	0.693431	+	0.552992i
$819$	2.74905e8	+	2.76331e8i	0.500416	+	0.503012i
$820$	2.91235e8	+	3.65197e8i	0.528204	+	0.662347i
$821$	8.37719e7	−	7.77289e7i	0.151380	−	0.140460i	−0.600847	−	0.799364i	$-0.705170\pi$
$821$	8.37719e7	−	7.77289e7i	0.151380	−	0.140460i	0.752227	+	0.658904i	$0.228980\pi$
$822$	−7.34243e7	−	4.87139e8i	−0.132198	−	0.877076i
$823$	4.16609e8	−	2.84039e8i	0.747359	−	0.509541i	−0.128736	−	0.991679i	$-0.541092\pi$
$823$	4.16609e8	−	2.84039e8i	0.747359	−	0.509541i	0.876095	+	0.482138i	$0.160140\pi$
$824$	1.03897e8	−	6.89312e8i	0.185704	−	1.23207i
$825$	6.73372e7	+	1.39827e8i	0.119921	+	0.249018i
$826$	1.46556e8	+	2.79043e8i	0.260054	+	0.495144i
$827$	5.78547e8	+	2.78613e8i	1.02287	+	0.492590i	0.868640	−	0.495444i	$-0.164995\pi$
$827$	5.78547e8	+	2.78613e8i	1.02287	+	0.492590i	0.154234	+	0.988034i	$0.450709\pi$
$828$	5.34072e8	+	3.64124e8i	0.940824	+	0.641443i
$829$	5.55722e8	−	5.98926e8i	0.975426	−	1.05126i	−0.0232459	−	0.999730i	$-0.507400\pi$
$829$	5.55722e8	−	5.98926e8i	0.975426	−	1.05126i	0.998671	−	0.0515290i	$-0.0164095\pi$
$830$	6.94156e7	−	9.26286e8i	0.121401	−	1.61999i
$831$	1.41634e9	+	5.55874e8i	2.46812	+	0.968664i
$832$			2.16945e8i			0.376687i
$833$	1.08981e8	+	4.89129e8i	0.188545	+	0.846229i
$834$	−1.37600e9			−2.37203
$835$	−1.10862e8	+	2.82473e8i	−0.190425	+	0.485196i
$836$	2.61265e7	+	1.95791e6i	0.0447159	+	0.00335100i
$837$	−1.04869e9	−	9.73039e8i	−1.78842	−	1.65941i
$838$	3.28347e8	−	4.81597e8i	0.557958	−	0.818374i
$839$	−9.30344e7	+	1.93188e8i	−0.157528	+	0.327110i	−0.964763	−	0.263120i	$-0.915249\pi$
$839$	−9.30344e7	+	1.93188e8i	−0.157528	+	0.327110i	0.807235	+	0.590230i	$0.200963\pi$
$840$	−1.50375e9	+	5.23710e7i	−2.53711	+	0.0883595i
$841$	−9.50996e7	+	4.57976e7i	−0.159879	+	0.0769935i
$842$	−3.28311e8	−	4.94849e7i	−0.549983	−	0.0828966i
$843$	−1.43401e8	−	2.10330e8i	−0.239369	−	0.351090i
$844$	−1.99931e8	+	3.01348e7i	−0.332548	+	0.0501235i
$845$	−4.84479e8	−	5.22145e8i	−0.802981	−	0.865408i
$846$	1.21107e9	−	9.65798e8i	2.00013	−	1.59505i
$847$	3.10506e8	+	4.97017e8i	0.510998	+	0.817939i
$848$	−8.78597e7	+	1.10173e8i	−0.144079	+	0.180670i
$849$	1.38319e8	+	1.84573e9i	0.226026	+	3.01610i
$850$	−1.05233e8	+	3.41158e8i	−0.171355	+	0.555518i
$851$	1.90466e8	−	3.29897e8i	0.309050	−	0.535291i
$852$	−2.16055e8	+	1.24740e8i	−0.349339	+	0.201691i
$853$	−7.47016e8	+	1.70501e8i	−1.20360	+	0.274714i	−0.776868	−	0.629663i	$-0.783193\pi$
$853$	−7.47016e8	+	1.70501e8i	−1.20360	+	0.274714i	−0.426733	+	0.904378i	$0.640336\pi$
$854$	−3.99476e8	−	5.44212e8i	−0.641382	−	0.873764i
$855$	−2.28533e8	+	1.00127e9i	−0.365637	+	1.60196i
$856$	4.38131e8	−	1.35146e8i	0.698526	−	0.215467i
$857$	−7.89264e8	+	3.09763e8i	−1.25395	+	0.492139i	−0.897019	−	0.441992i	$-0.854272\pi$
$857$	−7.89264e8	+	3.09763e8i	−1.25395	+	0.492139i	−0.356930	+	0.934131i	$0.616177\pi$
$858$	−2.13852e7	−	5.44885e7i	−0.0338572	−	0.0862667i
$859$	2.21045e8	+	7.16611e8i	0.348740	+	1.13059i	0.944800	+	0.327648i	$0.106256\pi$
$859$	2.21045e8	+	7.16611e8i	0.348740	+	1.13059i	−0.596060	+	0.802940i	$0.703268\pi$
$860$	4.34965e8	+	9.92780e7i	0.683847	+	0.156084i
$861$	1.43309e9	−	1.05195e9i	2.24525	−	1.64811i
$862$	2.11122e8	+	9.24988e8i	0.329619	+	1.44416i
$863$	−3.96196e8	−	6.86232e8i	−0.616422	−	1.06767i	−0.990133	−	0.140129i	$-0.955248\pi$
$863$	−3.96196e8	−	6.86232e8i	−0.616422	−	1.06767i	0.373712	−	0.927545i	$-0.378085\pi$
$864$	−6.50671e8	−	3.75665e8i	−1.00884	−	0.582451i
$865$	−1.08370e9	−	3.34277e8i	−1.67441	−	0.516486i
$866$	−2.59387e8	+	1.94384e7i	−0.399388	+	0.0299300i
$867$	−2.17187e8	−	1.73201e8i	−0.333255	−	0.265762i
$868$	3.19584e8	−	1.99657e8i	0.488682	−	0.305298i
$869$	6.15015e7	+	7.71204e7i	0.0937187	+	0.117519i
$870$	9.61199e8	−	8.91863e8i	1.45967	−	1.35438i
$871$	−8.26468e6	−	5.48325e7i	−0.0125075	−	0.0829820i
$872$	1.69277e8	−	1.15411e8i	0.255298	−	0.174059i
$873$	−9.50677e7	+	6.30733e8i	−0.142886	+	0.947988i
$874$	−2.15304e8	−	4.47083e8i	−0.322491	−	0.669660i
$875$	4.63706e6	+	1.33146e8i	0.00692179	+	0.198749i
$876$	−5.49938e8	−	2.64836e8i	−0.818091	−	0.393972i
$877$	1.79403e8	+	1.22315e8i	0.265969	+	0.181334i	0.688960	−	0.724799i	$-0.258068\pi$
$877$	1.79403e8	+	1.22315e8i	0.265969	+	0.181334i	−0.422991	+	0.906134i	$0.639020\pi$
$878$	−3.87122e8	+	4.17218e8i	−0.571958	+	0.616424i
$879$	6.49604e7	−	8.66836e8i	0.0956493	−	1.27635i
$880$	7.64857e7	+	3.00184e7i	0.112236	+	0.0440494i
$881$			5.82019e7i			0.0851157i	0.999094	+	0.0425579i	$0.0135507\pi$
$881$			5.82019e7i			0.0851157i	−0.999094	+	0.0425579i	$0.986449\pi$
$882$	−5.42444e6	+	1.04834e9i	−0.00790586	+	1.52791i
$883$	−8.79341e8			−1.27725			−0.638624	−	0.769519i	$-0.720496\pi$
$883$	−8.79341e8			−1.27725			−0.638624	+	0.769519i	$0.720496\pi$
$884$	−3.05914e7	+	7.79455e7i	−0.0442835	+	0.112833i
$885$	−1.15054e9	−	8.62209e7i	−1.65986	−	0.124389i
$886$	−2.91611e8	−	2.70576e8i	−0.419279	−	0.389034i
$887$	−5.58249e8	+	8.18801e8i	−0.799940	+	1.17330i	0.181850	+	0.983326i	$0.441791\pi$
$887$	−5.58249e8	+	8.18801e8i	−0.799940	+	1.17330i	−0.981790	+	0.189970i	$0.939161\pi$
$888$	−2.29403e8	+	4.76361e8i	−0.327613	+	0.680295i
$889$	4.94161e8	−	2.59538e8i	0.703336	−	0.369399i
$890$	3.95505e8	−	1.90465e8i	0.561024	−	0.270175i
$891$	1.10856e8	+	1.67089e7i	0.156721	+	0.0236218i
$892$	−1.12723e8	−	1.65334e8i	−0.158824	−	0.232952i
$893$	7.31208e8	−	1.10212e8i	1.02680	−	0.154765i
$894$	1.12085e9	+	1.20799e9i	1.56868	+	1.69063i
$895$	−1.91173e8	+	1.52456e8i	−0.266660	+	0.212654i
$896$	−4.77301e7	+	4.74838e7i	−0.0663542	+	0.0660118i
$897$	4.29835e8	−	5.38996e8i	0.595559	−	0.746807i
$898$	4.94973e7	+	6.60495e8i	0.0683522	+	0.912096i
$899$	−3.49239e8	+	1.13220e9i	−0.480666	+	1.55828i
$900$	2.32223e8	−	4.02221e8i	0.318549	−	0.551744i
$901$	−2.70259e8	+	1.56034e8i	−0.369492	+	0.213326i
$902$	−1.71921e8	+	3.92398e7i	−0.234266	+	0.0534697i
$903$	4.43716e8	−	1.63900e9i	0.602617	−	2.22595i
$904$	3.24355e8	−	1.42109e9i	0.439051	−	1.92361i
$905$	7.31780e8	−	2.25724e8i	0.987268	−	0.304532i
$906$	−7.98802e7	+	3.13507e7i	−0.107412	+	0.0421563i
$907$	−5.04815e8	−	1.28625e9i	−0.676566	−	1.72386i	−0.689851	−	0.723951i	$-0.742324\pi$
$907$	−5.04815e8	−	1.28625e9i	−0.676566	−	1.72386i	0.0132844	−	0.999912i	$-0.495771\pi$
$908$	674388.	+	2.18631e6i	0.000900849	+	0.00292048i
$909$	−3.37344e8	−	7.69966e7i	−0.449140	−	0.102513i
$910$	−1.17446e7	+	2.93553e8i	−0.0155852	+	0.389549i
$911$	1.19587e8	+	5.23943e8i	0.158171	+	0.692994i	0.990362	+	0.138504i	$0.0442294\pi$
$911$	1.19587e8	+	5.23943e8i	0.158171	+	0.692994i	−0.832191	+	0.554490i	$0.812913\pi$
$912$	1.89578e8	+	3.28360e8i	0.249922	+	0.432878i
$913$	−1.88848e8	−	1.09031e8i	−0.248141	−	0.143264i
$914$	6.93176e8	+	2.13816e8i	0.907831	+	0.280029i
$915$	2.46429e9	−	1.84673e8i	3.21684	−	0.241069i
$916$	−2.76468e8	−	2.20476e8i	−0.359715	−	0.286863i
$917$	−3.19552e8	−	9.20863e8i	−0.414414	−	1.19423i
$918$	5.33073e8	+	6.68452e8i	0.689062	+	0.864057i
$919$	−2.35576e8	+	2.18583e8i	−0.303519	+	0.281624i	−0.817197	−	0.576359i	$-0.804473\pi$
$919$	−2.35576e8	+	2.18583e8i	−0.303519	+	0.281624i	0.513678	+	0.857983i	$0.328283\pi$
$920$	2.61997e8	+	1.73823e9i	0.336459	+	2.23226i
$921$	5.78185e8	−	3.94200e8i	0.740095	−	0.504589i
$922$	1.02115e8	−	6.77485e8i	0.130285	−	0.864385i
$923$	7.62579e7	+	1.58351e8i	0.0969795	+	0.201380i
$924$	−3.93809e7	+	8.96285e7i	−0.0499194	+	0.113614i
$925$	−2.46603e8	−	1.18758e8i	−0.311582	−	0.150050i
$926$	−4.47879e8	−	3.05358e8i	−0.564063	−	0.384571i
$927$	1.20929e9	−	1.30330e9i	1.51807	−	1.63609i
$928$	−4.65025e7	+	6.20533e8i	−0.0581879	+	0.776464i
$929$	5.76627e8	+	2.26309e8i	0.719196	+	0.282264i	0.696579	−	0.717480i	$-0.254705\pi$
$929$	5.76627e8	+	2.26309e8i	0.719196	+	0.282264i	0.0226177	+	0.999744i	$0.492800\pi$
$930$		−	2.21824e9i		−	2.75778i
$931$	−2.52471e8	+	4.32113e8i	−0.312868	+	0.535486i
$932$	−4.63126e8			−0.572073
$933$	6.40988e8	−	1.63321e9i	0.789232	−	2.01093i
$934$	5.47165e7	+	4.10044e6i	0.0671549	+	0.00503256i
$935$	1.33387e8	+	1.23765e8i	0.163184	+	0.151413i
$936$	−3.56045e8	+	5.22222e8i	−0.434187	+	0.636836i
$937$	−3.48070e8	+	7.22775e8i	−0.423105	+	0.878586i	0.575065	+	0.818108i	$0.304977\pi$
$937$	−3.48070e8	+	7.22775e8i	−0.423105	+	0.878586i	−0.998170	+	0.0604781i	$0.980737\pi$
$938$	8.88740e7	−	1.19770e8i	0.107688	−	0.145124i
$939$	4.55995e8	−	2.19596e8i	0.550761	−	0.265233i
$940$	−7.17902e8	−	1.08206e8i	−0.864334	−	0.130277i
$941$	1.33127e8	+	1.95261e8i	0.159770	+	0.234340i	0.897774	−	0.440457i	$-0.145184\pi$
$941$	1.33127e8	+	1.95261e8i	0.159770	+	0.234340i	−0.738003	+	0.674797i	$0.764231\pi$
$942$	−8.44181e8	+	1.27240e8i	−1.00991	+	0.152220i
$943$	−1.41265e9	−	1.52247e9i	−1.68461	−	1.81558i
$944$	−2.19973e8	+	1.75423e8i	−0.261489	+	0.208531i
$945$	−1.57689e9	−	9.96526e8i	−1.86856	−	1.18085i
$946$	−1.05016e8	+	1.31685e8i	−0.124045	+	0.155548i
$947$	−2.72216e7	−	3.63246e8i	−0.0320526	−	0.427712i	−0.990029	−	0.140865i	$-0.955012\pi$
$947$	−2.72216e7	−	3.63246e8i	−0.0320526	−	0.427712i	0.957976	−	0.286847i	$-0.0926073\pi$
$948$	1.31726e8	−	4.27045e8i	0.154613	−	0.501244i
$949$	−2.15006e8	+	3.72402e8i	−0.251566	+	0.435726i
$950$	−3.08781e8	+	1.78275e8i	−0.360146	+	0.207931i
$951$	1.46648e9	−	3.34714e8i	1.70504	−	0.389164i
$952$	−7.45623e8	+	3.23018e8i	−0.864188	+	0.374383i
$953$	−1.81219e8	+	7.93972e8i	−0.209375	+	0.917332i	0.755609	+	0.655023i	$0.227341\pi$
$953$	−1.81219e8	+	7.93972e8i	−0.209375	+	0.917332i	−0.964984	+	0.262309i	$0.915516\pi$
$954$	−6.23848e8	+	1.92432e8i	−0.718512	+	0.221631i
$955$	5.38270e8	−	2.11255e8i	0.618002	−	0.242548i
$956$	−2.77012e7	−	7.05816e7i	−0.0317048	−	0.0807825i
$957$	−9.07318e7	−	2.94145e8i	−0.103520	−	0.335603i
$958$	−7.77533e8	−	1.77467e8i	−0.884346	−	0.201846i
$959$	4.38989e8	+	3.79761e8i	0.497734	+	0.430581i
$960$	−4.75284e8	−	2.08235e9i	−0.537204	−	2.35365i
$961$	5.58464e8	+	9.67288e8i	0.629252	+	1.08990i
$962$	8.94028e7	+	5.16167e7i	0.100421	+	0.0579783i
$963$	1.11743e9	+	3.44682e8i	1.25124	+	0.385957i
$964$	9.32822e7	−	6.99053e6i	0.104128	−	0.00780332i
$965$	1.75285e7	+	1.39785e7i	0.0195057	+	0.0155553i
$966$	1.84308e9	−	2.02838e8i	2.04462	−	0.225018i
$967$	−6.85126e8	−	8.59121e8i	−0.757689	−	0.950113i	0.242108	−	0.970249i	$-0.422161\pi$
$967$	−6.85126e8	−	8.59121e8i	−0.757689	−	0.950113i	−0.999797	+	0.0201368i	$0.993590\pi$
$968$	−6.96602e8	+	6.46352e8i	−0.767995	+	0.712595i
$969$	1.25146e8	+	8.30290e8i	0.137545	+	0.912554i
$970$	−3.97227e8	+	2.70825e8i	−0.435234	+	0.296738i
$971$	−1.40526e8	+	9.32327e8i	−0.153496	+	1.01838i	0.770902	+	0.636954i	$0.219806\pi$
$971$	−1.40526e8	+	9.32327e8i	−0.153496	+	1.01838i	−0.924399	+	0.381428i	$0.875432\pi$
$972$	2.76317e7	+	5.73778e7i	0.0300891	+	0.0624806i
$973$	1.23162e9	−	1.05436e9i	1.33702	−	1.14459i
$974$	3.14712e8	+	1.51557e8i	0.340593	+	0.164021i
$975$	−4.09278e8	−	2.79041e8i	−0.441575	−	0.301061i
$976$	4.09890e8	−	4.41757e8i	0.440878	−	0.475153i
$977$	−5.30341e7	+	7.07691e8i	−0.0568685	+	0.758857i	0.893764	+	0.448538i	$0.148055\pi$
$977$	−5.30341e7	+	7.07691e8i	−0.0568685	+	0.758857i	−0.950632	+	0.310319i	$0.899564\pi$
$978$	6.70758e8	+	2.63253e8i	0.717049	+	0.281421i
$979$		−	1.03053e8i		−	0.109828i
$980$	3.61914e8	−	3.32339e8i	0.384527	−	0.353104i
$981$	5.22526e8			0.553478
$982$	2.27589e8	−	5.79888e8i	0.240335	−	0.612364i
$983$	−1.32472e9	−	9.92741e7i	−1.39465	−	0.104514i	−0.643902	−	0.765108i	$-0.722686\pi$
$983$	−1.32472e9	−	9.92741e7i	−1.39465	−	0.104514i	−0.750744	+	0.660594i	$0.770305\pi$
$984$	2.11314e9	+	1.96071e9i	2.21790	+	2.05791i
$985$	−7.21055e8	+	1.05759e9i	−0.754501	+	1.10665i
$986$	3.07242e8	−	6.37995e8i	0.320516	−	0.665559i
$987$	−5.20716e8	+	2.71360e9i	−0.541564	+	2.82224i
$988$	−7.53422e7	+	3.62829e7i	−0.0781209	+	0.0376210i
$989$	−1.96158e9	−	2.95660e8i	−2.02776	−	0.305635i
$990$	2.14437e8	+	3.14521e8i	0.221001	+	0.324148i
$991$	1.49885e9	−	2.25916e8i	1.54006	−	0.232127i	0.676527	−	0.736418i	$-0.263484\pi$
$991$	1.49885e9	−	2.25916e8i	1.54006	−	0.232127i	0.863534	+	0.504291i	$0.168246\pi$
$992$	7.16029e8	+	7.71695e8i	0.733492	+	0.790516i
$993$	−6.26187e8	+	4.99367e8i	−0.639523	+	0.510003i
$994$	−1.57281e8	+	4.45780e8i	−0.160146	+	0.453901i
$995$	−1.53257e8	+	1.92178e8i	−0.155579	+	0.195090i
$996$	7.38296e7	+	9.85187e8i	0.0747227	+	0.997105i
$997$	2.32050e8	−	7.52289e8i	0.234151	−	0.759100i	−0.759886	−	0.650057i	$-0.774745\pi$
$997$	2.32050e8	−	7.52289e8i	0.234151	−	0.759100i	0.994037	−	0.109043i	$-0.0347788\pi$
$998$	1.12810e8	−	1.95392e8i	0.113489	−	0.196570i
$999$	−5.67656e8	+	3.27736e8i	−0.569362	+	0.328721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.7.h.a.3.19	✓	324
49.33	odd	42	inner	49.7.h.a.33.19	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.7.h.a.3.19	✓	324	1.1	even	1	trivial
49.7.h.a.33.19	yes	324	49.33	odd	42	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	49.h (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(2.29501 - 5.84759i) q^{2} +(-46.2118 - 3.46309i) q^{3} +(17.9881 + 16.6905i) q^{4} +(-95.8768 + 140.625i) q^{5} +(-126.307 + 262.280i) q^{6} +(-87.9175 - 331.541i) q^{7} +(501.105 - 241.319i) q^{8} +(1402.68 + 211.419i) q^{9} +(602.282 + 883.385i) q^{10} +(248.191 - 37.4088i) q^{11} +(-773.459 - 833.591i) q^{12} +(-626.337 + 499.487i) q^{13} +(-2140.49 - 246.785i) q^{14} +(4917.63 - 6166.52i) q^{15} +(-143.735 - 1918.01i) q^{16} +(1255.50 - 4070.23i) q^{17} +(4455.45 - 7717.07i) q^{18} +(3683.95 - 2126.93i) q^{19} +(-4071.74 + 929.349i) q^{20} +(2914.66 + 15625.6i) q^{21} +(350.850 - 1537.17i) q^{22} +(17744.9 - 5473.57i) q^{23} +(-23992.7 + 9416.42i) q^{24} +(-4874.70 - 12420.5i) q^{25} +(1483.35 + 4808.89i) q^{26} +(-31152.1 - 7110.27i) q^{27} +(3952.12 - 7431.17i) q^{28} +(5888.93 + 25801.1i) q^{29} +(-24773.3 - 42908.5i) q^{30} +(38772.7 + 22385.4i) q^{31} +(22468.8 + 6930.70i) q^{32} +(-11598.9 + 869.217i) q^{33} +(-20919.7 - 16682.9i) q^{34} +(55052.4 + 19423.7i) q^{35} +(21702.7 + 27214.4i) q^{36} +(15037.4 - 13952.7i) q^{37} +(-3982.72 - 26423.6i) q^{38} +(30673.9 - 20913.1i) q^{39} +(-14108.7 + 93605.0i) q^{40} +(-48526.5 - 100766. i) q^{41} +(98061.1 + 18817.1i) q^{42} +(-96246.3 - 46349.8i) q^{43} +(5088.84 + 3469.52i) q^{44} +(-164215. + 176982. i) q^{45} +(8717.48 - 116327. i) q^{46} +(161818. + 63508.7i) q^{47} +89132.4i q^{48} +(-102190. + 58296.5i) q^{49} -83817.7 q^{50} +(-72114.5 + 183745. i) q^{51} +(-19603.3 - 1469.06i) q^{52} +(-53706.7 - 49832.5i) q^{53} +(-113072. + 165847. i) q^{54} +(-18535.1 + 38488.6i) q^{55} +(-124063. - 144921. i) q^{56} +(-177608. + 85531.4i) q^{57} +(164389. + 24777.7i) q^{58} +(-82403.4 - 120864. i) q^{59} +(191381. - 28846.0i) q^{60} +(213108. + 229676. i) q^{61} +(219885. - 175352. i) q^{62} +(-53225.5 - 483632. i) q^{63} +(168844. - 211723. i) q^{64} +(-10189.4 - 135968. i) q^{65} +(-21536.8 + 69820.5i) q^{66} +(-34609.2 + 59944.9i) q^{67} +(90518.2 - 52260.7i) q^{68} +(-838977. + 191491. i) q^{69} +(239927. - 277346. i) q^{70} +(48818.8 - 213889. i) q^{71} +(753907. - 232550. i) q^{72} +(499663. - 196103. i) q^{73} +(-47078.6 - 119954. i) q^{74} +(182255. + 590856. i) q^{75} +(101767. + 23227.6i) q^{76} +(-34222.9 - 78996.6i) q^{77} +(-51894.4 - 227364. i) q^{78} +(196500. + 340348. i) q^{79} +(283502. + 163680. i) q^{80} +(426813. + 131654. i) q^{81} +(-700610. + 52503.4i) q^{82} +(-679250. - 541684. i) q^{83} +(-208369. + 329721. i) q^{84} +(452005. + 566796. i) q^{85} +(-491921. + 456436. i) q^{86} +(-182786. - 1.21271e6i) q^{87} +(115342. - 78639.0i) q^{88} +(61193.7 - 405994. i) q^{89} +(658042. + 1.36644e6i) q^{90} +(220667. + 163743. i) q^{91} +(410552. + 197711. i) q^{92} +(-1.71423e6 - 1.16874e6i) q^{93} +(742747. - 800490. i) q^{94} +(-54105.0 + 721981. i) q^{95} +(-1.01432e6 - 398091. i) q^{96} +449664. i q^{97} +(106367. + 731357. i) q^{98} +356040. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 13 q^{2} - 11 q^{3} + 819 q^{4} - 179 q^{5} + 770 q^{6} + 392 q^{7} + 828 q^{8} - 1160 q^{9} - 2594 q^{10} - 5305 q^{11} + 7497 q^{12} - 14 q^{13} - 11403 q^{14} - 6196 q^{15} + 27903 q^{16} - 5107 q^{17}+ \cdots - 4449616 q^{99}+O(q^{100}) \) 324 * q - 13 * q^2 - 11 * q^3 + 819 * q^4 - 179 * q^5 + 770 * q^6 + 392 * q^7 + 828 * q^8 - 1160 * q^9 - 2594 * q^10 - 5305 * q^11 + 7497 * q^12 - 14 * q^13 - 11403 * q^14 - 6196 * q^15 + 27903 * q^16 - 5107 * q^17 - 11538 * q^18 - 30006 * q^19 - 50190 * q^20 + 8953 * q^21 + 33042 * q^22 + 54531 * q^23 + 90184 * q^24 - 92804 * q^25 - 93366 * q^26 - 11774 * q^27 - 19180 * q^28 - 80398 * q^29 + 15851 * q^30 + 39378 * q^31 - 197841 * q^32 + 36697 * q^33 - 54698 * q^34 - 819 * q^35 + 706300 * q^36 + 15331 * q^37 - 304462 * q^38 - 179298 * q^39 - 515414 * q^40 - 116046 * q^41 + 1203482 * q^42 - 225018 * q^43 + 1373764 * q^44 + 465772 * q^45 + 1100364 * q^46 + 270021 * q^47 - 767900 * q^49 - 1164040 * q^50 - 1215743 * q^51 - 3954790 * q^52 + 141807 * q^53 - 1093487 * q^54 + 991354 * q^55 - 596680 * q^56 - 388207 * q^57 + 381012 * q^58 + 2015849 * q^59 + 5807298 * q^60 + 258821 * q^61 - 525742 * q^62 - 1265432 * q^63 + 872972 * q^64 - 70154 * q^65 + 497766 * q^66 - 324190 * q^67 - 799617 * q^68 - 2216774 * q^69 + 56140 * q^70 - 1031026 * q^71 + 4633092 * q^72 + 1268305 * q^73 - 1444192 * q^74 - 1699244 * q^75 - 5464011 * q^76 - 2274741 * q^77 - 1285956 * q^78 - 515710 * q^79 + 8314050 * q^80 - 1069027 * q^81 + 357910 * q^82 - 3183054 * q^83 - 10099096 * q^84 - 1596848 * q^85 - 5387681 * q^86 - 4197040 * q^87 - 1024645 * q^88 + 983769 * q^89 + 18547774 * q^90 + 13421086 * q^91 + 5294506 * q^92 + 15477850 * q^93 + 8903632 * q^94 + 5236430 * q^95 + 7804258 * q^96 - 10234553 * q^98 - 4449616 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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