Properties

Label 49.6.c.c.18.1
Level $49$
Weight $6$
Character 49.18
Analytic conductor $7.859$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [49,6,Mod(18,49)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(49, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.18");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 49.c (of order \(3\), degree \(2\), not 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: \(7.85880717084\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 7)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 18.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 49.18
Dual form 49.6.c.c.30.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(5.00000 + 8.66025i) q^{2} +(7.00000 - 12.1244i) q^{3} +(-34.0000 + 58.8897i) q^{4} +(28.0000 + 48.4974i) q^{5} +140.000 q^{6} -360.000 q^{8} +(23.5000 + 40.7032i) q^{9} +O(q^{10})\) \(q+(5.00000 + 8.66025i) q^{2} +(7.00000 - 12.1244i) q^{3} +(-34.0000 + 58.8897i) q^{4} +(28.0000 + 48.4974i) q^{5} +140.000 q^{6} -360.000 q^{8} +(23.5000 + 40.7032i) q^{9} +(-280.000 + 484.974i) q^{10} +(-116.000 + 200.918i) q^{11} +(476.000 + 824.456i) q^{12} -140.000 q^{13} +784.000 q^{15} +(-712.000 - 1233.22i) q^{16} +(861.000 - 1491.30i) q^{17} +(-235.000 + 407.032i) q^{18} +(49.0000 + 84.8705i) q^{19} -3808.00 q^{20} -2320.00 q^{22} +(-912.000 - 1579.63i) q^{23} +(-2520.00 + 4364.77i) q^{24} +(-5.50000 + 9.52628i) q^{25} +(-700.000 - 1212.44i) q^{26} +4060.00 q^{27} +3418.00 q^{29} +(3920.00 + 6789.64i) q^{30} +(3822.00 - 6619.90i) q^{31} +(1360.00 - 2355.59i) q^{32} +(1624.00 + 2812.85i) q^{33} +17220.0 q^{34} -3196.00 q^{36} +(5199.00 + 9004.93i) q^{37} +(-490.000 + 848.705i) q^{38} +(-980.000 + 1697.41i) q^{39} +(-10080.0 - 17459.1i) q^{40} -17962.0 q^{41} +10880.0 q^{43} +(-7888.00 - 13662.4i) q^{44} +(-1316.00 + 2279.38i) q^{45} +(9120.00 - 15796.3i) q^{46} +(-4662.00 - 8074.82i) q^{47} -19936.0 q^{48} -110.000 q^{50} +(-12054.0 - 20878.1i) q^{51} +(4760.00 - 8244.56i) q^{52} +(-1131.00 + 1958.95i) q^{53} +(20300.0 + 35160.6i) q^{54} -12992.0 q^{55} +1372.00 q^{57} +(17090.0 + 29600.7i) q^{58} +(1365.00 - 2364.25i) q^{59} +(-26656.0 + 46169.5i) q^{60} +(-12824.0 - 22211.8i) q^{61} +76440.0 q^{62} -18368.0 q^{64} +(-3920.00 - 6789.64i) q^{65} +(-16240.0 + 28128.5i) q^{66} +(24202.0 - 41919.1i) q^{67} +(58548.0 + 101408. i) q^{68} -25536.0 q^{69} -58560.0 q^{71} +(-8460.00 - 14653.1i) q^{72} +(-34041.0 + 58960.7i) q^{73} +(-51990.0 + 90049.3i) q^{74} +(77.0000 + 133.368i) q^{75} -6664.00 q^{76} -19600.0 q^{78} +(-15892.0 - 27525.8i) q^{79} +(39872.0 - 69060.3i) q^{80} +(22709.5 - 39334.0i) q^{81} +(-89810.0 - 155555. i) q^{82} -20538.0 q^{83} +96432.0 q^{85} +(54400.0 + 94223.6i) q^{86} +(23926.0 - 41441.0i) q^{87} +(41760.0 - 72330.4i) q^{88} +(25291.0 + 43805.3i) q^{89} -26320.0 q^{90} +124032. q^{92} +(-53508.0 - 92678.6i) q^{93} +(46620.0 - 80748.2i) q^{94} +(-2744.00 + 4752.75i) q^{95} +(-19040.0 - 32978.2i) q^{96} -58506.0 q^{97} -10904.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 10 q^{2} + 14 q^{3} - 68 q^{4} + 56 q^{5} + 280 q^{6} - 720 q^{8} + 47 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 10 q^{2} + 14 q^{3} - 68 q^{4} + 56 q^{5} + 280 q^{6} - 720 q^{8} + 47 q^{9} - 560 q^{10} - 232 q^{11} + 952 q^{12} - 280 q^{13} + 1568 q^{15} - 1424 q^{16} + 1722 q^{17} - 470 q^{18} + 98 q^{19} - 7616 q^{20} - 4640 q^{22} - 1824 q^{23} - 5040 q^{24} - 11 q^{25} - 1400 q^{26} + 8120 q^{27} + 6836 q^{29} + 7840 q^{30} + 7644 q^{31} + 2720 q^{32} + 3248 q^{33} + 34440 q^{34} - 6392 q^{36} + 10398 q^{37} - 980 q^{38} - 1960 q^{39} - 20160 q^{40} - 35924 q^{41} + 21760 q^{43} - 15776 q^{44} - 2632 q^{45} + 18240 q^{46} - 9324 q^{47} - 39872 q^{48} - 220 q^{50} - 24108 q^{51} + 9520 q^{52} - 2262 q^{53} + 40600 q^{54} - 25984 q^{55} + 2744 q^{57} + 34180 q^{58} + 2730 q^{59} - 53312 q^{60} - 25648 q^{61} + 152880 q^{62} - 36736 q^{64} - 7840 q^{65} - 32480 q^{66} + 48404 q^{67} + 117096 q^{68} - 51072 q^{69} - 117120 q^{71} - 16920 q^{72} - 68082 q^{73} - 103980 q^{74} + 154 q^{75} - 13328 q^{76} - 39200 q^{78} - 31784 q^{79} + 79744 q^{80} + 45419 q^{81} - 179620 q^{82} - 41076 q^{83} + 192864 q^{85} + 108800 q^{86} + 47852 q^{87} + 83520 q^{88} + 50582 q^{89} - 52640 q^{90} + 248064 q^{92} - 107016 q^{93} + 93240 q^{94} - 5488 q^{95} - 38080 q^{96} - 117012 q^{97} - 21808 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 5.00000 + 8.66025i 0.883883 + 1.53093i 0.846988 + 0.531612i \(0.178414\pi\)
0.0368954 + 0.999319i \(0.488253\pi\)
\(3\) 7.00000 12.1244i 0.449050 0.777778i −0.549274 0.835642i \(-0.685096\pi\)
0.998324 + 0.0578644i \(0.0184291\pi\)
\(4\) −34.0000 + 58.8897i −1.06250 + 1.84030i
\(5\) 28.0000 + 48.4974i 0.500879 + 0.867548i 0.999999 + 0.00101554i \(0.000323257\pi\)
−0.499120 + 0.866533i \(0.666343\pi\)
\(6\) 140.000 1.58763
\(7\) 0 0
\(8\) −360.000 −1.98874
\(9\) 23.5000 + 40.7032i 0.0967078 + 0.167503i
\(10\) −280.000 + 484.974i −0.885438 + 1.53362i
\(11\) −116.000 + 200.918i −0.289052 + 0.500653i −0.973584 0.228330i \(-0.926673\pi\)
0.684532 + 0.728983i \(0.260007\pi\)
\(12\) 476.000 + 824.456i 0.954232 + 1.65278i
\(13\) −140.000 −0.229757 −0.114879 0.993380i \(-0.536648\pi\)
−0.114879 + 0.993380i \(0.536648\pi\)
\(14\) 0 0
\(15\) 784.000 0.899680
\(16\) −712.000 1233.22i −0.695312 1.20432i
\(17\) 861.000 1491.30i 0.722572 1.25153i −0.237394 0.971413i \(-0.576293\pi\)
0.959966 0.280117i \(-0.0903733\pi\)
\(18\) −235.000 + 407.032i −0.170957 + 0.296106i
\(19\) 49.0000 + 84.8705i 0.0311395 + 0.0539353i 0.881175 0.472790i \(-0.156753\pi\)
−0.850036 + 0.526725i \(0.823420\pi\)
\(20\) −3808.00 −2.12874
\(21\) 0 0
\(22\) −2320.00 −1.02195
\(23\) −912.000 1579.63i −0.359480 0.622638i 0.628394 0.777895i \(-0.283713\pi\)
−0.987874 + 0.155257i \(0.950379\pi\)
\(24\) −2520.00 + 4364.77i −0.893043 + 1.54680i
\(25\) −5.50000 + 9.52628i −0.00176000 + 0.00304841i
\(26\) −700.000 1212.44i −0.203079 0.351743i
\(27\) 4060.00 1.07181
\(28\) 0 0
\(29\) 3418.00 0.754705 0.377352 0.926070i \(-0.376835\pi\)
0.377352 + 0.926070i \(0.376835\pi\)
\(30\) 3920.00 + 6789.64i 0.795212 + 1.37735i
\(31\) 3822.00 6619.90i 0.714310 1.23722i −0.248916 0.968525i \(-0.580074\pi\)
0.963225 0.268695i \(-0.0865925\pi\)
\(32\) 1360.00 2355.59i 0.234782 0.406654i
\(33\) 1624.00 + 2812.85i 0.259598 + 0.449637i
\(34\) 17220.0 2.55468
\(35\) 0 0
\(36\) −3196.00 −0.411008
\(37\) 5199.00 + 9004.93i 0.624332 + 1.08137i 0.988670 + 0.150108i \(0.0479620\pi\)
−0.364338 + 0.931267i \(0.618705\pi\)
\(38\) −490.000 + 848.705i −0.0550474 + 0.0953450i
\(39\) −980.000 + 1697.41i −0.103173 + 0.178700i
\(40\) −10080.0 17459.1i −0.996117 1.72533i
\(41\) −17962.0 −1.66876 −0.834382 0.551186i \(-0.814175\pi\)
−0.834382 + 0.551186i \(0.814175\pi\)
\(42\) 0 0
\(43\) 10880.0 0.897342 0.448671 0.893697i \(-0.351898\pi\)
0.448671 + 0.893697i \(0.351898\pi\)
\(44\) −7888.00 13662.4i −0.614236 1.06389i
\(45\) −1316.00 + 2279.38i −0.0968779 + 0.167797i
\(46\) 9120.00 15796.3i 0.635478 1.10068i
\(47\) −4662.00 8074.82i −0.307842 0.533198i 0.670048 0.742318i \(-0.266273\pi\)
−0.977890 + 0.209120i \(0.932940\pi\)
\(48\) −19936.0 −1.24892
\(49\) 0 0
\(50\) −110.000 −0.00622254
\(51\) −12054.0 20878.1i −0.648942 1.12400i
\(52\) 4760.00 8244.56i 0.244117 0.422824i
\(53\) −1131.00 + 1958.95i −0.0553061 + 0.0957930i −0.892353 0.451338i \(-0.850947\pi\)
0.837047 + 0.547131i \(0.184280\pi\)
\(54\) 20300.0 + 35160.6i 0.947353 + 1.64086i
\(55\) −12992.0 −0.579121
\(56\) 0 0
\(57\) 1372.00 0.0559329
\(58\) 17090.0 + 29600.7i 0.667071 + 1.15540i
\(59\) 1365.00 2364.25i 0.0510508 0.0884226i −0.839371 0.543559i \(-0.817076\pi\)
0.890422 + 0.455137i \(0.150410\pi\)
\(60\) −26656.0 + 46169.5i −0.955910 + 1.65568i
\(61\) −12824.0 22211.8i −0.441264 0.764292i 0.556519 0.830835i \(-0.312137\pi\)
−0.997784 + 0.0665424i \(0.978803\pi\)
\(62\) 76440.0 2.52547
\(63\) 0 0
\(64\) −18368.0 −0.560547
\(65\) −3920.00 6789.64i −0.115081 0.199326i
\(66\) −16240.0 + 28128.5i −0.458909 + 0.794853i
\(67\) 24202.0 41919.1i 0.658664 1.14084i −0.322297 0.946639i \(-0.604455\pi\)
0.980962 0.194202i \(-0.0622117\pi\)
\(68\) 58548.0 + 101408.i 1.53546 + 2.65950i
\(69\) −25536.0 −0.645699
\(70\) 0 0
\(71\) −58560.0 −1.37865 −0.689327 0.724450i \(-0.742094\pi\)
−0.689327 + 0.724450i \(0.742094\pi\)
\(72\) −8460.00 14653.1i −0.192326 0.333119i
\(73\) −34041.0 + 58960.7i −0.747645 + 1.29496i 0.201304 + 0.979529i \(0.435482\pi\)
−0.948949 + 0.315430i \(0.897851\pi\)
\(74\) −51990.0 + 90049.3i −1.10367 + 1.91162i
\(75\) 77.0000 + 133.368i 0.00158066 + 0.00273778i
\(76\) −6664.00 −0.132343
\(77\) 0 0
\(78\) −19600.0 −0.364770
\(79\) −15892.0 27525.8i −0.286491 0.496217i 0.686479 0.727150i \(-0.259155\pi\)
−0.972970 + 0.230933i \(0.925822\pi\)
\(80\) 39872.0 69060.3i 0.696535 1.20643i
\(81\) 22709.5 39334.0i 0.384587 0.666125i
\(82\) −89810.0 155555.i −1.47499 2.55476i
\(83\) −20538.0 −0.327237 −0.163619 0.986524i \(-0.552317\pi\)
−0.163619 + 0.986524i \(0.552317\pi\)
\(84\) 0 0
\(85\) 96432.0 1.44768
\(86\) 54400.0 + 94223.6i 0.793145 + 1.37377i
\(87\) 23926.0 41441.0i 0.338900 0.586993i
\(88\) 41760.0 72330.4i 0.574849 0.995668i
\(89\) 25291.0 + 43805.3i 0.338447 + 0.586208i 0.984141 0.177389i \(-0.0567650\pi\)
−0.645694 + 0.763597i \(0.723432\pi\)
\(90\) −26320.0 −0.342515
\(91\) 0 0
\(92\) 124032. 1.52779
\(93\) −53508.0 92678.6i −0.641522 1.11115i
\(94\) 46620.0 80748.2i 0.544193 0.942569i
\(95\) −2744.00 + 4752.75i −0.0311943 + 0.0540301i
\(96\) −19040.0 32978.2i −0.210857 0.365216i
\(97\) −58506.0 −0.631351 −0.315676 0.948867i \(-0.602231\pi\)
−0.315676 + 0.948867i \(0.602231\pi\)
\(98\) 0 0
\(99\) −10904.0 −0.111814
\(100\) −374.000 647.787i −0.00374000 0.00647787i
\(101\) −19348.0 + 33511.7i −0.188726 + 0.326884i −0.944826 0.327573i \(-0.893769\pi\)
0.756099 + 0.654457i \(0.227103\pi\)
\(102\) 120540. 208781.i 1.14718 1.98697i
\(103\) −26530.0 45951.3i −0.246402 0.426781i 0.716123 0.697974i \(-0.245915\pi\)
−0.962525 + 0.271193i \(0.912582\pi\)
\(104\) 50400.0 0.456927
\(105\) 0 0
\(106\) −22620.0 −0.195537
\(107\) 73162.0 + 126720.i 0.617769 + 1.07001i 0.989892 + 0.141824i \(0.0452967\pi\)
−0.372123 + 0.928183i \(0.621370\pi\)
\(108\) −138040. + 239092.i −1.13880 + 1.97245i
\(109\) −46449.0 + 80452.0i −0.374464 + 0.648591i −0.990247 0.139325i \(-0.955507\pi\)
0.615783 + 0.787916i \(0.288840\pi\)
\(110\) −64960.0 112514.i −0.511875 0.886594i
\(111\) 145572. 1.12143
\(112\) 0 0
\(113\) −83354.0 −0.614088 −0.307044 0.951695i \(-0.599340\pi\)
−0.307044 + 0.951695i \(0.599340\pi\)
\(114\) 6860.00 + 11881.9i 0.0494381 + 0.0856293i
\(115\) 51072.0 88459.3i 0.360113 0.623733i
\(116\) −116212. + 201285.i −0.801874 + 1.38889i
\(117\) −3290.00 5698.45i −0.0222193 0.0384850i
\(118\) 27300.0 0.180492
\(119\) 0 0
\(120\) −282240. −1.78923
\(121\) 53613.5 + 92861.3i 0.332898 + 0.576596i
\(122\) 128240. 222118.i 0.780053 1.35109i
\(123\) −125734. + 217778.i −0.749359 + 1.29793i
\(124\) 259896. + 450153.i 1.51791 + 2.62909i
\(125\) 174384. 0.998232
\(126\) 0 0
\(127\) 60384.0 0.332210 0.166105 0.986108i \(-0.446881\pi\)
0.166105 + 0.986108i \(0.446881\pi\)
\(128\) −135360. 234450.i −0.730240 1.26481i
\(129\) 76160.0 131913.i 0.402951 0.697932i
\(130\) 39200.0 67896.4i 0.203436 0.352361i
\(131\) 30793.0 + 53335.0i 0.156774 + 0.271540i 0.933704 0.358047i \(-0.116557\pi\)
−0.776930 + 0.629587i \(0.783224\pi\)
\(132\) −220864. −1.10329
\(133\) 0 0
\(134\) 484040. 2.32873
\(135\) 113680. + 196900.i 0.536846 + 0.929844i
\(136\) −309960. + 536866.i −1.43701 + 2.48897i
\(137\) 102231. 177069.i 0.465352 0.806013i −0.533866 0.845569i \(-0.679261\pi\)
0.999217 + 0.0395567i \(0.0125946\pi\)
\(138\) −127680. 221148.i −0.570723 0.988521i
\(139\) −35406.0 −0.155432 −0.0777159 0.996976i \(-0.524763\pi\)
−0.0777159 + 0.996976i \(0.524763\pi\)
\(140\) 0 0
\(141\) −130536. −0.552946
\(142\) −292800. 507144.i −1.21857 2.11062i
\(143\) 16240.0 28128.5i 0.0664119 0.115029i
\(144\) 33464.0 57961.3i 0.134484 0.232934i
\(145\) 95704.0 + 165764.i 0.378016 + 0.654743i
\(146\) −680820. −2.64332
\(147\) 0 0
\(148\) −707064. −2.65341
\(149\) 10113.0 + 17516.2i 0.0373177 + 0.0646361i 0.884081 0.467334i \(-0.154785\pi\)
−0.846763 + 0.531970i \(0.821452\pi\)
\(150\) −770.000 + 1333.68i −0.00279423 + 0.00483975i
\(151\) −35452.0 + 61404.7i −0.126531 + 0.219159i −0.922331 0.386402i \(-0.873718\pi\)
0.795799 + 0.605561i \(0.207051\pi\)
\(152\) −17640.0 30553.4i −0.0619284 0.107263i
\(153\) 80934.0 0.279513
\(154\) 0 0
\(155\) 428064. 1.43113
\(156\) −66640.0 115424.i −0.219242 0.379738i
\(157\) −146762. + 254199.i −0.475187 + 0.823048i −0.999596 0.0284185i \(-0.990953\pi\)
0.524409 + 0.851466i \(0.324286\pi\)
\(158\) 158920. 275258.i 0.506449 0.877196i
\(159\) 15834.0 + 27425.3i 0.0496704 + 0.0860317i
\(160\) 152320. 0.470389
\(161\) 0 0
\(162\) 454190. 1.35972
\(163\) −6596.00 11424.6i −0.0194452 0.0336800i 0.856139 0.516745i \(-0.172857\pi\)
−0.875584 + 0.483065i \(0.839523\pi\)
\(164\) 610708. 1.05778e6i 1.77306 3.07103i
\(165\) −90944.0 + 157520.i −0.260054 + 0.450427i
\(166\) −102690. 177864.i −0.289240 0.500978i
\(167\) 493612. 1.36960 0.684801 0.728730i \(-0.259889\pi\)
0.684801 + 0.728730i \(0.259889\pi\)
\(168\) 0 0
\(169\) −351693. −0.947212
\(170\) 482160. + 835126.i 1.27958 + 2.21630i
\(171\) −2303.00 + 3988.91i −0.00602287 + 0.0104319i
\(172\) −369920. + 640720.i −0.953425 + 1.65138i
\(173\) −120358. 208466.i −0.305745 0.529566i 0.671682 0.740840i \(-0.265572\pi\)
−0.977427 + 0.211274i \(0.932239\pi\)
\(174\) 478520. 1.19819
\(175\) 0 0
\(176\) 330368. 0.803926
\(177\) −19110.0 33099.5i −0.0458488 0.0794124i
\(178\) −252910. + 438053.i −0.598296 + 1.03628i
\(179\) −147466. + 255419.i −0.344001 + 0.595827i −0.985172 0.171571i \(-0.945116\pi\)
0.641171 + 0.767398i \(0.278449\pi\)
\(180\) −89488.0 154998.i −0.205865 0.356569i
\(181\) −336980. −0.764553 −0.382277 0.924048i \(-0.624860\pi\)
−0.382277 + 0.924048i \(0.624860\pi\)
\(182\) 0 0
\(183\) −359072. −0.792600
\(184\) 328320. + 568667.i 0.714912 + 1.23826i
\(185\) −291144. + 504276.i −0.625430 + 1.08328i
\(186\) 535080. 926786.i 1.13406 1.96425i
\(187\) 199752. + 345981.i 0.417722 + 0.723515i
\(188\) 634032. 1.30833
\(189\) 0 0
\(190\) −54880.0 −0.110288
\(191\) −179132. 310266.i −0.355296 0.615390i 0.631873 0.775072i \(-0.282286\pi\)
−0.987168 + 0.159682i \(0.948953\pi\)
\(192\) −128576. + 222700.i −0.251714 + 0.435981i
\(193\) 494777. 856979.i 0.956128 1.65606i 0.224364 0.974505i \(-0.427970\pi\)
0.731764 0.681558i \(-0.238697\pi\)
\(194\) −292530. 506677.i −0.558041 0.966555i
\(195\) −109760. −0.206708
\(196\) 0 0
\(197\) −990050. −1.81757 −0.908786 0.417263i \(-0.862989\pi\)
−0.908786 + 0.417263i \(0.862989\pi\)
\(198\) −54520.0 94431.4i −0.0988309 0.171180i
\(199\) 420378. 728116.i 0.752501 1.30337i −0.194106 0.980981i \(-0.562180\pi\)
0.946607 0.322390i \(-0.104486\pi\)
\(200\) 1980.00 3429.46i 0.00350018 0.00606249i
\(201\) −338828. 586867.i −0.591547 1.02459i
\(202\) −386960. −0.667249
\(203\) 0 0
\(204\) 1.63934e6 2.75800
\(205\) −502936. 871111.i −0.835849 1.44773i
\(206\) 265300. 459513.i 0.435581 0.754449i
\(207\) 42864.0 74242.6i 0.0695291 0.120428i
\(208\) 99680.0 + 172651.i 0.159753 + 0.276701i
\(209\) −22736.0 −0.0360038
\(210\) 0 0
\(211\) 1.15073e6 1.77938 0.889689 0.456568i \(-0.150921\pi\)
0.889689 + 0.456568i \(0.150921\pi\)
\(212\) −76908.0 133209.i −0.117525 0.203560i
\(213\) −409920. + 710002.i −0.619085 + 1.07229i
\(214\) −731620. + 1.26720e6i −1.09207 + 1.89152i
\(215\) 304640. + 527652.i 0.449460 + 0.778487i
\(216\) −1.46160e6 −2.13154
\(217\) 0 0
\(218\) −928980. −1.32393
\(219\) 476574. + 825450.i 0.671460 + 1.16300i
\(220\) 441728. 765095.i 0.615316 1.06576i
\(221\) −120540. + 208781.i −0.166016 + 0.287549i
\(222\) 727860. + 1.26069e6i 0.991209 + 1.71683i
\(223\) −824264. −1.10995 −0.554976 0.831866i \(-0.687273\pi\)
−0.554976 + 0.831866i \(0.687273\pi\)
\(224\) 0 0
\(225\) −517.000 −0.000680823
\(226\) −416770. 721867.i −0.542782 0.940126i
\(227\) −37191.0 + 64416.7i −0.0479042 + 0.0829724i −0.888983 0.457940i \(-0.848588\pi\)
0.841079 + 0.540912i \(0.181921\pi\)
\(228\) −46648.0 + 80796.7i −0.0594287 + 0.102933i
\(229\) −565978. 980303.i −0.713199 1.23530i −0.963650 0.267168i \(-0.913912\pi\)
0.250451 0.968129i \(-0.419421\pi\)
\(230\) 1.02144e6 1.27319
\(231\) 0 0
\(232\) −1.23048e6 −1.50091
\(233\) 99363.0 + 172102.i 0.119904 + 0.207680i 0.919730 0.392553i \(-0.128408\pi\)
−0.799825 + 0.600233i \(0.795075\pi\)
\(234\) 32900.0 56984.5i 0.0392786 0.0680326i
\(235\) 261072. 452190.i 0.308383 0.534135i
\(236\) 92820.0 + 160769.i 0.108483 + 0.187898i
\(237\) −444976. −0.514595
\(238\) 0 0
\(239\) 482904. 0.546847 0.273424 0.961894i \(-0.411844\pi\)
0.273424 + 0.961894i \(0.411844\pi\)
\(240\) −558208. 966845.i −0.625559 1.08350i
\(241\) −402955. + 697939.i −0.446904 + 0.774060i −0.998183 0.0602611i \(-0.980807\pi\)
0.551279 + 0.834321i \(0.314140\pi\)
\(242\) −536135. + 928613.i −0.588485 + 1.01929i
\(243\) 175357. + 303727.i 0.190505 + 0.329965i
\(244\) 1.74406e6 1.87537
\(245\) 0 0
\(246\) −2.51468e6 −2.64938
\(247\) −6860.00 11881.9i −0.00715454 0.0123920i
\(248\) −1.37592e6 + 2.38316e6i −1.42057 + 2.46051i
\(249\) −143766. + 249010.i −0.146946 + 0.254518i
\(250\) 871920. + 1.51021e6i 0.882321 + 1.52822i
\(251\) 430738. 0.431548 0.215774 0.976443i \(-0.430773\pi\)
0.215774 + 0.976443i \(0.430773\pi\)
\(252\) 0 0
\(253\) 423168. 0.415634
\(254\) 301920. + 522941.i 0.293635 + 0.508590i
\(255\) 675024. 1.16918e6i 0.650083 1.12598i
\(256\) 1.05971e6 1.83548e6i 1.01062 1.75045i
\(257\) 588455. + 1.01923e6i 0.555751 + 0.962589i 0.997845 + 0.0656204i \(0.0209026\pi\)
−0.442093 + 0.896969i \(0.645764\pi\)
\(258\) 1.52320e6 1.42465
\(259\) 0 0
\(260\) 533120. 0.489093
\(261\) 80323.0 + 139124.i 0.0729858 + 0.126415i
\(262\) −307930. + 533350.i −0.277140 + 0.480020i
\(263\) −645488. + 1.11802e6i −0.575438 + 0.996688i 0.420556 + 0.907267i \(0.361835\pi\)
−0.995994 + 0.0894216i \(0.971498\pi\)
\(264\) −584640. 1.01263e6i −0.516272 0.894210i
\(265\) −126672. −0.110807
\(266\) 0 0
\(267\) 708148. 0.607919
\(268\) 1.64574e6 + 2.85050e6i 1.39966 + 2.42429i
\(269\) 638778. 1.10640e6i 0.538232 0.932245i −0.460768 0.887521i \(-0.652426\pi\)
0.998999 0.0447238i \(-0.0142408\pi\)
\(270\) −1.13680e6 + 1.96900e6i −0.949018 + 1.64375i
\(271\) −825272. 1.42941e6i −0.682612 1.18232i −0.974181 0.225769i \(-0.927511\pi\)
0.291569 0.956550i \(-0.405823\pi\)
\(272\) −2.45213e6 −2.00965
\(273\) 0 0
\(274\) 2.04462e6 1.64527
\(275\) −1276.00 2210.10i −0.00101746 0.00176230i
\(276\) 868224. 1.50381e6i 0.686055 1.18828i
\(277\) 532045. 921529.i 0.416628 0.721622i −0.578969 0.815349i \(-0.696545\pi\)
0.995598 + 0.0937276i \(0.0298783\pi\)
\(278\) −177030. 306625.i −0.137384 0.237955i
\(279\) 359268. 0.276317
\(280\) 0 0
\(281\) −22342.0 −0.0168794 −0.00843969 0.999964i \(-0.502686\pi\)
−0.00843969 + 0.999964i \(0.502686\pi\)
\(282\) −652680. 1.13047e6i −0.488740 0.846522i
\(283\) 1.24787e6 2.16137e6i 0.926196 1.60422i 0.136570 0.990630i \(-0.456392\pi\)
0.789626 0.613588i \(-0.210274\pi\)
\(284\) 1.99104e6 3.44858e6i 1.46482 2.53714i
\(285\) 38416.0 + 66538.5i 0.0280156 + 0.0485244i
\(286\) 324800. 0.234802
\(287\) 0 0
\(288\) 127840. 0.0908208
\(289\) −772714. 1.33838e6i −0.544219 0.942615i
\(290\) −957040. + 1.65764e6i −0.668244 + 1.15743i
\(291\) −409542. + 709348.i −0.283508 + 0.491051i
\(292\) −2.31479e6 4.00933e6i −1.58874 2.75179i
\(293\) −1.93178e6 −1.31458 −0.657291 0.753637i \(-0.728298\pi\)
−0.657291 + 0.753637i \(0.728298\pi\)
\(294\) 0 0
\(295\) 152880. 0.102281
\(296\) −1.87164e6 3.24178e6i −1.24163 2.15057i
\(297\) −470960. + 815727.i −0.309808 + 0.536604i
\(298\) −101130. + 175162.i −0.0659689 + 0.114262i
\(299\) 127680. + 221148.i 0.0825933 + 0.143056i
\(300\) −10472.0 −0.00671779
\(301\) 0 0
\(302\) −709040. −0.447356
\(303\) 270872. + 469164.i 0.169495 + 0.293574i
\(304\) 69776.0 120856.i 0.0433034 0.0750037i
\(305\) 718144. 1.24386e6i 0.442040 0.765636i
\(306\) 404670. + 700909.i 0.247057 + 0.427916i
\(307\) −459074. −0.277995 −0.138997 0.990293i \(-0.544388\pi\)
−0.138997 + 0.990293i \(0.544388\pi\)
\(308\) 0 0
\(309\) −742840. −0.442587
\(310\) 2.14032e6 + 3.70714e6i 1.26495 + 2.19096i
\(311\) −333564. + 577750.i −0.195559 + 0.338718i −0.947084 0.320987i \(-0.895986\pi\)
0.751525 + 0.659705i \(0.229319\pi\)
\(312\) 352800. 611068.i 0.205183 0.355388i
\(313\) 55517.0 + 96158.3i 0.0320306 + 0.0554786i 0.881596 0.472004i \(-0.156469\pi\)
−0.849566 + 0.527483i \(0.823136\pi\)
\(314\) −2.93524e6 −1.68004
\(315\) 0 0
\(316\) 2.16131e6 1.21759
\(317\) 34389.0 + 59563.5i 0.0192208 + 0.0332914i 0.875476 0.483262i \(-0.160548\pi\)
−0.856255 + 0.516553i \(0.827215\pi\)
\(318\) −158340. + 274253.i −0.0878057 + 0.152084i
\(319\) −396488. + 686737.i −0.218149 + 0.377845i
\(320\) −514304. 890801.i −0.280766 0.486301i
\(321\) 2.04854e6 1.10964
\(322\) 0 0
\(323\) 168756. 0.0900022
\(324\) 1.54425e6 + 2.67471e6i 0.817248 + 1.41552i
\(325\) 770.000 1333.68i 0.000404373 0.000700395i
\(326\) 65960.0 114246.i 0.0343745 0.0595384i
\(327\) 650286. + 1.12633e6i 0.336306 + 0.582500i
\(328\) 6.46632e6 3.31874
\(329\) 0 0
\(330\) −1.81888e6 −0.919431
\(331\) 282224. + 488826.i 0.141587 + 0.245236i 0.928094 0.372345i \(-0.121446\pi\)
−0.786507 + 0.617581i \(0.788113\pi\)
\(332\) 698292. 1.20948e6i 0.347690 0.602216i
\(333\) −244353. + 423232.i −0.120756 + 0.209155i
\(334\) 2.46806e6 + 4.27481e6i 1.21057 + 2.09677i
\(335\) 2.71062e6 1.31965
\(336\) 0 0
\(337\) 2.07729e6 0.996376 0.498188 0.867069i \(-0.333999\pi\)
0.498188 + 0.867069i \(0.333999\pi\)
\(338\) −1.75847e6 3.04575e6i −0.837225 1.45012i
\(339\) −583478. + 1.01061e6i −0.275756 + 0.477624i
\(340\) −3.27869e6 + 5.67885e6i −1.53816 + 2.66418i
\(341\) 886704. + 1.53582e6i 0.412945 + 0.715243i
\(342\) −46060.0 −0.0212941
\(343\) 0 0
\(344\) −3.91680e6 −1.78458
\(345\) −715008. 1.23843e6i −0.323417 0.560175i
\(346\) 1.20358e6 2.08466e6i 0.540486 0.936150i
\(347\) 26624.0 46114.1i 0.0118700 0.0205594i −0.860029 0.510244i \(-0.829555\pi\)
0.871899 + 0.489685i \(0.162888\pi\)
\(348\) 1.62697e6 + 2.81799e6i 0.720163 + 1.24736i
\(349\) −2.27200e6 −0.998494 −0.499247 0.866460i \(-0.666390\pi\)
−0.499247 + 0.866460i \(0.666390\pi\)
\(350\) 0 0
\(351\) −568400. −0.246256
\(352\) 315520. + 546497.i 0.135728 + 0.235088i
\(353\) −2.00322e6 + 3.46969e6i −0.855644 + 1.48202i 0.0204028 + 0.999792i \(0.493505\pi\)
−0.876047 + 0.482227i \(0.839828\pi\)
\(354\) 191100. 330995.i 0.0810499 0.140383i
\(355\) −1.63968e6 2.84001e6i −0.690539 1.19605i
\(356\) −3.43958e6 −1.43840
\(357\) 0 0
\(358\) −2.94932e6 −1.21623
\(359\) −36892.0 63898.8i −0.0151076 0.0261672i 0.858373 0.513027i \(-0.171476\pi\)
−0.873480 + 0.486859i \(0.838142\pi\)
\(360\) 473760. 820576.i 0.192665 0.333705i
\(361\) 1.23325e6 2.13605e6i 0.498061 0.862666i
\(362\) −1.68490e6 2.91833e6i −0.675776 1.17048i
\(363\) 1.50118e6 0.597951
\(364\) 0 0
\(365\) −3.81259e6 −1.49792
\(366\) −1.79536e6 3.10965e6i −0.700566 1.21342i
\(367\) −702156. + 1.21617e6i −0.272125 + 0.471334i −0.969406 0.245464i \(-0.921060\pi\)
0.697281 + 0.716798i \(0.254393\pi\)
\(368\) −1.29869e6 + 2.24939e6i −0.499902 + 0.865856i
\(369\) −422107. 731111.i −0.161383 0.279523i
\(370\) −5.82288e6 −2.21123
\(371\) 0 0
\(372\) 7.27709e6 2.72647
\(373\) 801617. + 1.38844e6i 0.298329 + 0.516720i 0.975754 0.218872i \(-0.0702376\pi\)
−0.677425 + 0.735592i \(0.736904\pi\)
\(374\) −1.99752e6 + 3.45981e6i −0.738435 + 1.27901i
\(375\) 1.22069e6 2.11429e6i 0.448256 0.776403i
\(376\) 1.67832e6 + 2.90694e6i 0.612217 + 1.06039i
\(377\) −478520. −0.173399
\(378\) 0 0
\(379\) −4.77012e6 −1.70581 −0.852906 0.522064i \(-0.825162\pi\)
−0.852906 + 0.522064i \(0.825162\pi\)
\(380\) −186592. 323187.i −0.0662879 0.114814i
\(381\) 422688. 732117.i 0.149179 0.258385i
\(382\) 1.79132e6 3.10266e6i 0.628080 1.08787i
\(383\) 1.11539e6 + 1.93192e6i 0.388536 + 0.672964i 0.992253 0.124235i \(-0.0396475\pi\)
−0.603717 + 0.797199i \(0.706314\pi\)
\(384\) −3.79008e6 −1.31166
\(385\) 0 0
\(386\) 9.89554e6 3.38042
\(387\) 255680. + 442851.i 0.0867799 + 0.150307i
\(388\) 1.98920e6 3.44540e6i 0.670811 1.16188i
\(389\) −2.42012e6 + 4.19177e6i −0.810892 + 1.40451i 0.101348 + 0.994851i \(0.467684\pi\)
−0.912240 + 0.409655i \(0.865649\pi\)
\(390\) −548800. 950549.i −0.182706 0.316456i
\(391\) −3.14093e6 −1.03900
\(392\) 0 0
\(393\) 862204. 0.281597
\(394\) −4.95025e6 8.57408e6i −1.60652 2.78258i
\(395\) 889952. 1.54144e6i 0.286995 0.497089i
\(396\) 370736. 642134.i 0.118803 0.205773i
\(397\) −497910. 862405.i −0.158553 0.274622i 0.775794 0.630986i \(-0.217350\pi\)
−0.934347 + 0.356364i \(0.884016\pi\)
\(398\) 8.40756e6 2.66049
\(399\) 0 0
\(400\) 15664.0 0.00489500
\(401\) 1.65802e6 + 2.87178e6i 0.514909 + 0.891848i 0.999850 + 0.0173014i \(0.00550748\pi\)
−0.484942 + 0.874546i \(0.661159\pi\)
\(402\) 3.38828e6 5.86867e6i 1.04572 1.81123i
\(403\) −535080. + 926786.i −0.164118 + 0.284261i
\(404\) −1.31566e6 2.27880e6i −0.401044 0.694628i
\(405\) 2.54346e6 0.770527
\(406\) 0 0
\(407\) −2.41234e6 −0.721858
\(408\) 4.33944e6 + 7.51613e6i 1.29058 + 2.23534i
\(409\) −1.53637e6 + 2.66107e6i −0.454137 + 0.786588i −0.998638 0.0521720i \(-0.983386\pi\)
0.544501 + 0.838760i \(0.316719\pi\)
\(410\) 5.02936e6 8.71111e6i 1.47759 2.55926i
\(411\) −1.43123e6 2.47897e6i −0.417932 0.723880i
\(412\) 3.60808e6 1.04721
\(413\) 0 0
\(414\) 857280. 0.245823
\(415\) −575064. 996040.i −0.163906 0.283894i
\(416\) −190400. + 329782.i −0.0539428 + 0.0934317i
\(417\) −247842. + 429275.i −0.0697967 + 0.120891i
\(418\) −113680. 196900.i −0.0318232 0.0551193i
\(419\) 2.81438e6 0.783154 0.391577 0.920145i \(-0.371930\pi\)
0.391577 + 0.920145i \(0.371930\pi\)
\(420\) 0 0
\(421\) 3.05802e6 0.840883 0.420441 0.907320i \(-0.361875\pi\)
0.420441 + 0.907320i \(0.361875\pi\)
\(422\) 5.75366e6 + 9.96563e6i 1.57276 + 2.72410i
\(423\) 219114. 379517.i 0.0595414 0.103129i
\(424\) 407160. 705222.i 0.109989 0.190507i
\(425\) 9471.00 + 16404.3i 0.00254345 + 0.00440539i
\(426\) −8.19840e6 −2.18880
\(427\) 0 0
\(428\) −9.95003e6 −2.62552
\(429\) −227360. 393799.i −0.0596446 0.103307i
\(430\) −3.04640e6 + 5.27652e6i −0.794540 + 1.37618i
\(431\) −968748. + 1.67792e6i −0.251199 + 0.435089i −0.963856 0.266423i \(-0.914158\pi\)
0.712657 + 0.701512i \(0.247491\pi\)
\(432\) −2.89072e6 5.00687e6i −0.745241 1.29080i
\(433\) 3.94790e6 1.01192 0.505961 0.862557i \(-0.331138\pi\)
0.505961 + 0.862557i \(0.331138\pi\)
\(434\) 0 0
\(435\) 2.67971e6 0.678993
\(436\) −3.15853e6 5.47074e6i −0.795736 1.37826i
\(437\) 89376.0 154804.i 0.0223881 0.0387773i
\(438\) −4.76574e6 + 8.25450e6i −1.18698 + 2.05592i
\(439\) 3.70885e6 + 6.42392e6i 0.918498 + 1.59089i 0.801698 + 0.597730i \(0.203930\pi\)
0.116800 + 0.993155i \(0.462736\pi\)
\(440\) 4.67712e6 1.15172
\(441\) 0 0
\(442\) −2.41080e6 −0.586956
\(443\) −701346. 1.21477e6i −0.169794 0.294092i 0.768553 0.639786i \(-0.220977\pi\)
−0.938347 + 0.345694i \(0.887644\pi\)
\(444\) −4.94945e6 + 8.57270e6i −1.19151 + 2.06376i
\(445\) −1.41630e6 + 2.45310e6i −0.339042 + 0.587239i
\(446\) −4.12132e6 7.13834e6i −0.981068 1.69926i
\(447\) 283164. 0.0670300
\(448\) 0 0
\(449\) −590574. −0.138248 −0.0691239 0.997608i \(-0.522020\pi\)
−0.0691239 + 0.997608i \(0.522020\pi\)
\(450\) −2585.00 4477.35i −0.000601768 0.00104229i
\(451\) 2.08359e6 3.60889e6i 0.482360 0.835472i
\(452\) 2.83404e6 4.90869e6i 0.652468 1.13011i
\(453\) 496328. + 859665.i 0.113638 + 0.196827i
\(454\) −743820. −0.169367
\(455\) 0 0
\(456\) −493920. −0.111236
\(457\) 1.45242e6 + 2.51567e6i 0.325313 + 0.563459i 0.981576 0.191073i \(-0.0611969\pi\)
−0.656262 + 0.754533i \(0.727864\pi\)
\(458\) 5.65978e6 9.80303e6i 1.26077 2.18372i
\(459\) 3.49566e6 6.05466e6i 0.774457 1.34140i
\(460\) 3.47290e6 + 6.01523e6i 0.765239 + 1.32543i
\(461\) −922684. −0.202209 −0.101105 0.994876i \(-0.532238\pi\)
−0.101105 + 0.994876i \(0.532238\pi\)
\(462\) 0 0
\(463\) 7.18235e6 1.55709 0.778546 0.627588i \(-0.215958\pi\)
0.778546 + 0.627588i \(0.215958\pi\)
\(464\) −2.43362e6 4.21515e6i −0.524756 0.908903i
\(465\) 2.99645e6 5.19000e6i 0.642650 1.11310i
\(466\) −993630. + 1.72102e6i −0.211963 + 0.367131i
\(467\) 306285. + 530501.i 0.0649881 + 0.112563i 0.896689 0.442662i \(-0.145966\pi\)
−0.831701 + 0.555224i \(0.812632\pi\)
\(468\) 447440. 0.0944322
\(469\) 0 0
\(470\) 5.22144e6 1.09030
\(471\) 2.05467e6 + 3.55879e6i 0.426766 + 0.739180i
\(472\) −491400. + 851130.i −0.101527 + 0.175849i
\(473\) −1.26208e6 + 2.18599e6i −0.259379 + 0.449257i
\(474\) −2.22488e6 3.85361e6i −0.454842 0.787810i
\(475\) −1078.00 −0.000219222
\(476\) 0 0
\(477\) −106314. −0.0213941
\(478\) 2.41452e6 + 4.18207e6i 0.483349 + 0.837185i
\(479\) −1.30165e6 + 2.25452e6i −0.259212 + 0.448969i −0.966031 0.258426i \(-0.916796\pi\)
0.706819 + 0.707395i \(0.250130\pi\)
\(480\) 1.06624e6 1.84678e6i 0.211228 0.365858i
\(481\) −727860. 1.26069e6i −0.143445 0.248454i
\(482\) −8.05910e6 −1.58004
\(483\) 0 0
\(484\) −7.29144e6 −1.41482
\(485\) −1.63817e6 2.83739e6i −0.316231 0.547728i
\(486\) −1.75357e6 + 3.03727e6i −0.336769 + 0.583301i
\(487\) −2.73154e6 + 4.73117e6i −0.521898 + 0.903954i 0.477777 + 0.878481i \(0.341443\pi\)
−0.999676 + 0.0254732i \(0.991891\pi\)
\(488\) 4.61664e6 + 7.99626e6i 0.877559 + 1.51998i
\(489\) −184688. −0.0349274
\(490\) 0 0
\(491\) 1.64090e6 0.307170 0.153585 0.988135i \(-0.450918\pi\)
0.153585 + 0.988135i \(0.450918\pi\)
\(492\) −8.54991e6 1.48089e7i −1.59239 2.75810i
\(493\) 2.94290e6 5.09725e6i 0.545328 0.944536i
\(494\) 68600.0 118819.i 0.0126476 0.0219062i
\(495\) −305312. 528816.i −0.0560055 0.0970044i
\(496\) −1.08851e7 −1.98667
\(497\) 0 0
\(498\) −2.87532e6 −0.519533
\(499\) −1.49898e6 2.59631e6i −0.269491 0.466773i 0.699239 0.714888i \(-0.253522\pi\)
−0.968731 + 0.248115i \(0.920189\pi\)
\(500\) −5.92906e6 + 1.02694e7i −1.06062 + 1.83705i
\(501\) 3.45528e6 5.98473e6i 0.615020 1.06525i
\(502\) 2.15369e6 + 3.73030e6i 0.381438 + 0.660670i
\(503\) −6.89405e6 −1.21494 −0.607469 0.794343i \(-0.707815\pi\)
−0.607469 + 0.794343i \(0.707815\pi\)
\(504\) 0 0
\(505\) −2.16698e6 −0.378117
\(506\) 2.11584e6 + 3.66474e6i 0.367372 + 0.636308i
\(507\) −2.46185e6 + 4.26405e6i −0.425346 + 0.736720i
\(508\) −2.05306e6 + 3.55600e6i −0.352973 + 0.611367i
\(509\) −1.15238e6 1.99598e6i −0.197152 0.341478i 0.750452 0.660925i \(-0.229836\pi\)
−0.947604 + 0.319447i \(0.896503\pi\)
\(510\) 1.35005e7 2.29839
\(511\) 0 0
\(512\) 1.25312e7 2.11260
\(513\) 198940. + 344574.i 0.0333756 + 0.0578082i
\(514\) −5.88455e6 + 1.01923e7i −0.982439 + 1.70163i
\(515\) 1.48568e6 2.57327e6i 0.246835 0.427531i
\(516\) 5.17888e6 + 8.97008e6i 0.856272 + 1.48311i
\(517\) 2.16317e6 0.355929
\(518\) 0 0
\(519\) −3.37002e6 −0.549180
\(520\) 1.41120e6 + 2.44427e6i 0.228865 + 0.396407i
\(521\) 6.04802e6 1.04755e7i 0.976155 1.69075i 0.300087 0.953912i \(-0.402984\pi\)
0.676068 0.736839i \(-0.263682\pi\)
\(522\) −803230. + 1.39124e6i −0.129022 + 0.223473i
\(523\) −2.74221e6 4.74966e6i −0.438377 0.759290i 0.559188 0.829041i \(-0.311113\pi\)
−0.997564 + 0.0697505i \(0.977780\pi\)
\(524\) −4.18785e6 −0.666289
\(525\) 0 0
\(526\) −1.29098e7 −2.03448
\(527\) −6.58148e6 1.13995e7i −1.03228 1.78796i
\(528\) 2.31258e6 4.00550e6i 0.361003 0.625276i
\(529\) 1.55468e6 2.69279e6i 0.241548 0.418373i
\(530\) −633360. 1.09701e6i −0.0979402 0.169637i
\(531\) 128310. 0.0197480
\(532\) 0 0
\(533\) 2.51468e6 0.383411
\(534\) 3.54074e6 + 6.13274e6i 0.537330 + 0.930682i
\(535\) −4.09707e6 + 7.09634e6i −0.618855 + 1.07189i
\(536\) −8.71272e6 + 1.50909e7i −1.30991 + 2.26883i
\(537\) 2.06452e6 + 3.57586e6i 0.308947 + 0.535112i
\(538\) 1.27756e7 1.90294
\(539\) 0 0
\(540\) −1.54605e7 −2.28160
\(541\) 3.35900e6 + 5.81795e6i 0.493420 + 0.854628i 0.999971 0.00758172i \(-0.00241336\pi\)
−0.506552 + 0.862210i \(0.669080\pi\)
\(542\) 8.25272e6 1.42941e7i 1.20670 2.09006i
\(543\) −2.35886e6 + 4.08567e6i −0.343323 + 0.594652i
\(544\) −2.34192e6 4.05632e6i −0.339293 0.587673i
\(545\) −5.20229e6 −0.750245
\(546\) 0 0
\(547\) −5.00235e6 −0.714835 −0.357418 0.933945i \(-0.616343\pi\)
−0.357418 + 0.933945i \(0.616343\pi\)
\(548\) 6.95171e6 + 1.20407e7i 0.988872 + 1.71278i
\(549\) 602728. 1.04396e6i 0.0853474 0.147826i
\(550\) 12760.0 22101.0i 0.00179864 0.00311533i
\(551\) 167482. + 290087.i 0.0235012 + 0.0407052i
\(552\) 9.19296e6 1.28413
\(553\) 0 0
\(554\) 1.06409e7 1.47300
\(555\) 4.07602e6 + 7.05987e6i 0.561699 + 0.972891i
\(556\) 1.20380e6 2.08505e6i 0.165146 0.286042i
\(557\) −4.50980e6 + 7.81121e6i −0.615913 + 1.06679i 0.374310 + 0.927304i \(0.377880\pi\)
−0.990224 + 0.139490i \(0.955454\pi\)
\(558\) 1.79634e6 + 3.11135e6i 0.244232 + 0.423023i
\(559\) −1.52320e6 −0.206171
\(560\) 0 0
\(561\) 5.59306e6 0.750312
\(562\) −111710. 193487.i −0.0149194 0.0258412i
\(563\) −6.20255e6 + 1.07431e7i −0.824707 + 1.42843i 0.0774366 + 0.996997i \(0.475326\pi\)
−0.902143 + 0.431437i \(0.858007\pi\)
\(564\) 4.43822e6 7.68723e6i 0.587505 1.01759i
\(565\) −2.33391e6 4.04245e6i −0.307584 0.532751i
\(566\) 2.49574e7 3.27460
\(567\) 0 0
\(568\) 2.10816e7 2.74178
\(569\) −3.24402e6 5.61881e6i −0.420052 0.727551i 0.575892 0.817526i \(-0.304655\pi\)
−0.995944 + 0.0899747i \(0.971321\pi\)
\(570\) −384160. + 665385.i −0.0495251 + 0.0857799i
\(571\) 5.11425e6 8.85814e6i 0.656435 1.13698i −0.325097 0.945681i \(-0.605397\pi\)
0.981532 0.191298i \(-0.0612698\pi\)
\(572\) 1.10432e6 + 1.91274e6i 0.141125 + 0.244436i
\(573\) −5.01570e6 −0.638182
\(574\) 0 0
\(575\) 20064.0 0.00253074
\(576\) −431648. 747636.i −0.0542093 0.0938932i
\(577\) −1.32669e6 + 2.29789e6i −0.165894 + 0.287336i −0.936972 0.349404i \(-0.886384\pi\)
0.771079 + 0.636740i \(0.219717\pi\)
\(578\) 7.72714e6 1.33838e7i 0.962053 1.66632i
\(579\) −6.92688e6 1.19977e7i −0.858699 1.48731i
\(580\) −1.30157e7 −1.60657
\(581\) 0 0
\(582\) −8.19084e6 −1.00235
\(583\) −262392. 454476.i −0.0319727 0.0553783i
\(584\) 1.22548e7 2.12259e7i 1.48687 2.57533i
\(585\) 184240. 319113.i 0.0222584 0.0385527i
\(586\) −9.65888e6 1.67297e7i −1.16194 2.01253i
\(587\) −1.43044e7 −1.71346 −0.856729 0.515766i \(-0.827507\pi\)
−0.856729 + 0.515766i \(0.827507\pi\)
\(588\) 0 0
\(589\) 749112. 0.0889731
\(590\) 764400. + 1.32398e6i 0.0904046 + 0.156585i
\(591\) −6.93035e6 + 1.20037e7i −0.816181 + 1.41367i
\(592\) 7.40338e6 1.28230e7i 0.868212 1.50379i
\(593\) 5.01327e6 + 8.68323e6i 0.585442 + 1.01402i 0.994820 + 0.101651i \(0.0324125\pi\)
−0.409378 + 0.912365i \(0.634254\pi\)
\(594\) −9.41920e6 −1.09534
\(595\) 0 0
\(596\) −1.37537e6 −0.158600
\(597\) −5.88529e6 1.01936e7i −0.675822 1.17056i
\(598\) −1.27680e6 + 2.21148e6i −0.146006 + 0.252889i
\(599\) 3.76146e6 6.51504e6i 0.428341 0.741908i −0.568385 0.822763i \(-0.692432\pi\)
0.996726 + 0.0808547i \(0.0257650\pi\)
\(600\) −27720.0 48012.4i −0.00314351 0.00544472i
\(601\) 3.38625e6 0.382413 0.191207 0.981550i \(-0.438760\pi\)
0.191207 + 0.981550i \(0.438760\pi\)
\(602\) 0 0
\(603\) 2.27499e6 0.254792
\(604\) −2.41074e6 4.17552e6i −0.268879 0.465713i
\(605\) −3.00236e6 + 5.20023e6i −0.333483 + 0.577610i
\(606\) −2.70872e6 + 4.69164e6i −0.299628 + 0.518971i
\(607\) 3.45430e6 + 5.98303e6i 0.380530 + 0.659097i 0.991138 0.132836i \(-0.0424083\pi\)
−0.610608 + 0.791933i \(0.709075\pi\)
\(608\) 266560. 0.0292439
\(609\) 0 0
\(610\) 1.43629e7 1.56285
\(611\) 652680. + 1.13047e6i 0.0707290 + 0.122506i
\(612\) −2.75176e6 + 4.76618e6i −0.296983 + 0.514389i
\(613\) 4.84448e6 8.39088e6i 0.520710 0.901896i −0.479000 0.877815i \(-0.659001\pi\)
0.999710 0.0240812i \(-0.00766604\pi\)
\(614\) −2.29537e6 3.97570e6i −0.245715 0.425591i
\(615\) −1.40822e7 −1.50135
\(616\) 0 0
\(617\) −7.84742e6 −0.829877 −0.414939 0.909849i \(-0.636197\pi\)
−0.414939 + 0.909849i \(0.636197\pi\)
\(618\) −3.71420e6 6.43318e6i −0.391196 0.677571i
\(619\) 5.09860e6 8.83103e6i 0.534840 0.926370i −0.464331 0.885662i \(-0.653705\pi\)
0.999171 0.0407086i \(-0.0129615\pi\)
\(620\) −1.45542e7 + 2.52086e7i −1.52058 + 2.63372i
\(621\) −3.70272e6 6.41330e6i −0.385294 0.667348i
\(622\) −6.67128e6 −0.691406
\(623\) 0 0
\(624\) 2.79104e6 0.286949
\(625\) 4.89994e6 + 8.48694e6i 0.501754 + 0.869063i
\(626\) −555170. + 961583.i −0.0566226 + 0.0980733i
\(627\) −159152. + 275659.i −0.0161675 + 0.0280030i
\(628\) −9.97982e6 1.72855e7i −1.00977 1.74898i
\(629\) 1.79054e7 1.80450
\(630\) 0 0
\(631\) −8.36258e6 −0.836116 −0.418058 0.908420i \(-0.637289\pi\)
−0.418058 + 0.908420i \(0.637289\pi\)
\(632\) 5.72112e6 + 9.90927e6i 0.569755 + 0.986845i
\(633\) 8.05512e6 1.39519e7i 0.799030 1.38396i
\(634\) −343890. + 595635.i −0.0339779 + 0.0588514i
\(635\) 1.69075e6 + 2.92847e6i 0.166397 + 0.288208i
\(636\) −2.15342e6 −0.211099
\(637\) 0 0
\(638\) −7.92976e6 −0.771273
\(639\) −1.37616e6 2.38358e6i −0.133327 0.230928i
\(640\) 7.58016e6 1.31292e7i 0.731524 1.26704i
\(641\) −551415. + 955079.i −0.0530070 + 0.0918109i −0.891311 0.453392i \(-0.850214\pi\)
0.838304 + 0.545203i \(0.183547\pi\)
\(642\) 1.02427e7 + 1.77408e7i 0.980790 + 1.69878i
\(643\) 1.71354e7 1.63443 0.817217 0.576330i \(-0.195516\pi\)
0.817217 + 0.576330i \(0.195516\pi\)
\(644\) 0 0
\(645\) 8.52992e6 0.807320
\(646\) 843780. + 1.46147e6i 0.0795514 + 0.137787i
\(647\) 27482.0 47600.2i 0.00258100 0.00447042i −0.864732 0.502234i \(-0.832512\pi\)
0.867313 + 0.497763i \(0.165845\pi\)
\(648\) −8.17542e6 + 1.41602e7i −0.764843 + 1.32475i
\(649\) 316680. + 548506.i 0.0295127 + 0.0511175i
\(650\) 15400.0 0.00142968
\(651\) 0 0
\(652\) 897056. 0.0826420
\(653\) 242583. + 420166.i 0.0222627 + 0.0385601i 0.876942 0.480596i \(-0.159580\pi\)
−0.854679 + 0.519156i \(0.826246\pi\)
\(654\) −6.50286e6 + 1.12633e7i −0.594511 + 1.02972i
\(655\) −1.72441e6 + 2.98676e6i −0.157050 + 0.272018i
\(656\) 1.27889e7 + 2.21511e7i 1.16031 + 2.00972i
\(657\) −3.19985e6 −0.289212
\(658\) 0 0
\(659\) −2.72136e6 −0.244103 −0.122051 0.992524i \(-0.538947\pi\)
−0.122051 + 0.992524i \(0.538947\pi\)
\(660\) −6.18419e6 1.07113e7i −0.552616 0.957158i
\(661\) 1.07262e6 1.85784e6i 0.0954869 0.165388i −0.814325 0.580409i \(-0.802893\pi\)
0.909812 + 0.415021i \(0.136226\pi\)
\(662\) −2.82224e6 + 4.88826e6i −0.250293 + 0.433520i
\(663\) 1.68756e6 + 2.92294e6i 0.149099 + 0.258247i
\(664\) 7.39368e6 0.650789
\(665\) 0 0
\(666\) −4.88706e6 −0.426935
\(667\) −3.11722e6 5.39918e6i −0.271302 0.469908i
\(668\) −1.67828e7 + 2.90687e7i −1.45520 + 2.52048i
\(669\) −5.76985e6 + 9.99367e6i −0.498424 + 0.863296i
\(670\) 1.35531e7 + 2.34747e7i 1.16641 + 2.02029i
\(671\) 5.95034e6 0.510194
\(672\) 0 0
\(673\) 2.92796e6 0.249188 0.124594 0.992208i \(-0.460237\pi\)
0.124594 + 0.992208i \(0.460237\pi\)
\(674\) 1.03865e7 + 1.79899e7i 0.880680 + 1.52538i
\(675\) −22330.0 + 38676.7i −0.00188638 + 0.00326731i
\(676\) 1.19576e7 2.07111e7i 1.00641 1.74316i
\(677\) 6.74961e6 + 1.16907e7i 0.565988 + 0.980319i 0.996957 + 0.0779529i \(0.0248384\pi\)
−0.430969 + 0.902367i \(0.641828\pi\)
\(678\) −1.16696e7 −0.974945
\(679\) 0 0
\(680\) −3.47155e7 −2.87906
\(681\) 520674. + 901834.i 0.0430227 + 0.0745176i
\(682\) −8.86704e6 + 1.53582e7i −0.729991 + 1.26438i
\(683\) 2.71486e6 4.70228e6i 0.222688 0.385706i −0.732936 0.680298i \(-0.761850\pi\)
0.955623 + 0.294592i \(0.0951837\pi\)
\(684\) −156604. 271246.i −0.0127986 0.0221678i
\(685\) 1.14499e7 0.932340
\(686\) 0 0
\(687\) −1.58474e7 −1.28105
\(688\) −7.74656e6 1.34174e7i −0.623933 1.08068i
\(689\) 158340. 274253.i 0.0127070 0.0220091i
\(690\) 7.15008e6 1.23843e7i 0.571726 0.990259i
\(691\) −1.04140e7 1.80376e7i −0.829702 1.43709i −0.898272 0.439440i \(-0.855177\pi\)
0.0685703 0.997646i \(-0.478156\pi\)
\(692\) 1.63687e7 1.29942
\(693\) 0 0
\(694\) 532480. 0.0419667
\(695\) −991368. 1.71710e6i −0.0778526 0.134845i
\(696\) −8.61336e6 + 1.49188e7i −0.673984 + 1.16737i
\(697\) −1.54653e7 + 2.67867e7i −1.20580 + 2.08851i
\(698\) −1.13600e7 1.96761e7i −0.882552 1.52863i
\(699\) 2.78216e6 0.215372
\(700\) 0 0
\(701\) 2.35141e7 1.80731 0.903655 0.428261i \(-0.140874\pi\)
0.903655 + 0.428261i \(0.140874\pi\)
\(702\) −2.84200e6 4.92249e6i −0.217661 0.377000i
\(703\) −509502. + 882483.i −0.0388828 + 0.0673470i
\(704\) 2.13069e6 3.69046e6i 0.162027 0.280640i
\(705\) −3.65501e6 6.33066e6i −0.276959 0.479707i
\(706\) −4.00645e7 −3.02516
\(707\) 0 0
\(708\) 2.59896e6 0.194857
\(709\) 9.78734e6 + 1.69522e7i 0.731221 + 1.26651i 0.956361 + 0.292186i \(0.0943827\pi\)
−0.225140 + 0.974326i \(0.572284\pi\)
\(710\) 1.63968e7 2.84001e7i 1.22071 2.11434i
\(711\) 746924. 1.29371e6i 0.0554118 0.0959761i
\(712\) −9.10476e6 1.57699e7i −0.673083 1.16581i
\(713\) −1.39427e7 −1.02712
\(714\) 0 0
\(715\) 1.81888e6 0.133057
\(716\) −1.00277e7 1.73685e7i −0.731001 1.26613i
\(717\) 3.38033e6 5.85490e6i 0.245562 0.425326i
\(718\) 368920. 638988.i 0.0267068 0.0462575i
\(719\) 1.30576e7 + 2.26164e7i 0.941978 + 1.63155i 0.761692 + 0.647940i \(0.224369\pi\)
0.180287 + 0.983614i \(0.442298\pi\)
\(720\) 3.74797e6 0.269442
\(721\) 0 0
\(722\) 2.46650e7 1.76091
\(723\) 5.64137e6 + 9.77114e6i 0.401364 + 0.695184i
\(724\) 1.14573e7 1.98447e7i 0.812338 1.40701i
\(725\) −18799.0 + 32560.8i −0.00132828 + 0.00230065i
\(726\) 7.50589e6 + 1.30006e7i 0.528519 + 0.915422i
\(727\) 1.54126e7 1.08154 0.540768 0.841172i \(-0.318134\pi\)
0.540768 + 0.841172i \(0.318134\pi\)
\(728\) 0 0
\(729\) 1.59468e7 1.11136
\(730\) −1.90630e7 3.30180e7i −1.32399 2.29321i
\(731\) 9.36768e6 1.62253e7i 0.648393 1.12305i
\(732\) 1.22084e7 2.11457e7i 0.842137 1.45862i
\(733\) 8.49341e6 + 1.47110e7i 0.583878 + 1.01131i 0.995014 + 0.0997324i \(0.0317987\pi\)
−0.411136 + 0.911574i \(0.634868\pi\)
\(734\) −1.40431e7 −0.962107
\(735\) 0 0
\(736\) −4.96128e6 −0.337597
\(737\) 5.61486e6 + 9.72523e6i 0.380777 + 0.659525i
\(738\) 4.22107e6 7.31111e6i 0.285287 0.494131i
\(739\) −1.00756e6 + 1.74514e6i −0.0678669 + 0.117549i −0.897962 0.440073i \(-0.854953\pi\)
0.830095 + 0.557622i \(0.188286\pi\)
\(740\) −1.97978e7 3.42908e7i −1.32904 2.30196i
\(741\) −192080. −0.0128510
\(742\) 0 0
\(743\) −1.51381e7 −1.00600 −0.503001 0.864286i \(-0.667771\pi\)
−0.503001 + 0.864286i \(0.667771\pi\)
\(744\) 1.92629e7 + 3.33643e7i 1.27582 + 2.20978i
\(745\) −566328. + 980909.i −0.0373833 + 0.0647497i
\(746\) −8.01617e6 + 1.38844e7i −0.527375 + 0.913441i
\(747\) −482643. 835962.i −0.0316464 0.0548132i
\(748\) −2.71663e7 −1.77532
\(749\) 0 0
\(750\) 2.44138e7 1.58483
\(751\) −3.60700e6 6.24751e6i −0.233371 0.404210i 0.725427 0.688299i \(-0.241642\pi\)
−0.958798 + 0.284089i \(0.908309\pi\)
\(752\) −6.63869e6 + 1.14985e7i −0.428093 + 0.741478i
\(753\) 3.01517e6 5.22242e6i 0.193787 0.335648i
\(754\) −2.39260e6 4.14410e6i −0.153265 0.265462i
\(755\) −3.97062e6 −0.253508
\(756\) 0 0
\(757\) −1.09697e7 −0.695755 −0.347877 0.937540i \(-0.613097\pi\)
−0.347877 + 0.937540i \(0.613097\pi\)
\(758\) −2.38506e7 4.13105e7i −1.50774 2.61148i
\(759\) 2.96218e6 5.13064e6i 0.186641 0.323271i
\(760\) 987840. 1.71099e6i 0.0620373 0.107452i
\(761\) −9.62210e6 1.66660e7i −0.602293 1.04320i −0.992473 0.122464i \(-0.960920\pi\)
0.390180 0.920739i \(-0.372413\pi\)
\(762\) 8.45376e6 0.527427
\(763\) 0 0
\(764\) 2.43620e7 1.51001
\(765\) 2.26615e6 + 3.92509e6i 0.140002 + 0.242491i
\(766\) −1.11539e7 + 1.93192e7i −0.686841 + 1.18964i
\(767\) −191100. + 330995.i −0.0117293 + 0.0203158i
\(768\) −1.48360e7 2.56967e7i −0.907638 1.57208i