Properties

Label 49.6.c.b.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.b.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 −0.998324 0.0578644i \(-0.981571\pi\)
0.549274 + 0.835642i \(0.314904\pi\)
\(4\) −34.0000 + 58.8897i −1.06250 + 1.84030i
\(5\) −28.0000 48.4974i −0.500879 0.867548i −0.999999 0.00101554i \(-0.999677\pi\)
0.499120 0.866533i \(-0.333657\pi\)
\(6\) −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 \(-0.463352\pi\)
0.114879 + 0.993380i \(0.463352\pi\)
\(14\) 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 \(0.423707\pi\)
−0.959966 + 0.280117i \(0.909627\pi\)
\(18\) −235.000 + 407.032i −0.170957 + 0.296106i
\(19\) −49.0000 84.8705i −0.0311395 0.0539353i 0.850036 0.526725i \(-0.176580\pi\)
−0.881175 + 0.472790i \(0.843247\pi\)
\(20\) 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 \(0.419926\pi\)
−0.963225 + 0.268695i \(0.913408\pi\)
\(32\) 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 \(-0.185825\pi\)
0.834382 + 0.551186i \(0.185825\pi\)
\(42\) 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 0.977890 0.209120i \(-0.0670599\pi\)
−0.670048 + 0.742318i \(0.733727\pi\)
\(48\) 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 −0.890422 0.455137i \(-0.849590\pi\)
0.839371 + 0.543559i \(0.182924\pi\)
\(60\) −26656.0 + 46169.5i −0.955910 + 1.65568i
\(61\) 12824.0 + 22211.8i 0.441264 + 0.764292i 0.997784 0.0665424i \(-0.0211968\pi\)
−0.556519 + 0.830835i \(0.687863\pi\)
\(62\) −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 \(-0.564518\pi\)
0.948949 0.315430i \(-0.102149\pi\)
\(74\) −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 \(-0.447683\pi\)
0.163619 + 0.986524i \(0.447683\pi\)
\(84\) 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 0.645694 0.763597i \(-0.276568\pi\)
−0.984141 + 0.177389i \(0.943235\pi\)
\(90\) 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 \(-0.397769\pi\)
0.315676 + 0.948867i \(0.397769\pi\)
\(98\) 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 −0.756099 0.654457i \(-0.772897\pi\)
0.944826 + 0.327573i \(0.106231\pi\)
\(102\) 120540. 208781.i 1.14718 1.98697i
\(103\) 26530.0 + 45951.3i 0.246402 + 0.426781i 0.962525 0.271193i \(-0.0874183\pi\)
−0.716123 + 0.697974i \(0.754085\pi\)
\(104\) −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 0.776930 0.629587i \(-0.216776\pi\)
−0.933704 + 0.358047i \(0.883443\pi\)
\(132\) 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 \(-0.475237\pi\)
0.0777159 + 0.996976i \(0.475237\pi\)
\(140\) 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 −0.524409 0.851466i \(-0.675714\pi\)
0.999596 + 0.0284185i \(0.00904710\pi\)
\(158\) 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 \(-0.740111\pi\)
−0.684801 + 0.728730i \(0.740111\pi\)
\(168\) 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 0.977427 0.211274i \(-0.0677611\pi\)
−0.671682 + 0.740840i \(0.734428\pi\)
\(174\) −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 \(-0.375140\pi\)
0.382277 + 0.924048i \(0.375140\pi\)
\(182\) 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 \(0.437820\pi\)
−0.946607 + 0.322390i \(0.895514\pi\)
\(200\) 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 \(-0.312727\pi\)
0.554976 + 0.831866i \(0.312727\pi\)
\(224\) 0 0
\(225\) −517.000 −0.000680823
\(226\) −416770. 721867.i −0.542782 0.940126i
\(227\) 37191.0 64416.7i 0.0479042 0.0829724i −0.841079 0.540912i \(-0.818079\pi\)
0.888983 + 0.457940i \(0.151412\pi\)
\(228\) −46648.0 + 80796.7i −0.0594287 + 0.102933i
\(229\) 565978. + 980303.i 0.713199 + 1.23530i 0.963650 + 0.267168i \(0.0860878\pi\)
−0.250451 + 0.968129i \(0.580579\pi\)
\(230\) −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 −0.551279 0.834321i \(-0.685860\pi\)
0.998183 + 0.0602611i \(0.0191933\pi\)
\(242\) −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 \(-0.569227\pi\)
−0.215774 + 0.976443i \(0.569227\pi\)
\(252\) 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 \(-0.979097\pi\)
0.442093 0.896969i \(-0.354236\pi\)
\(258\) −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 \(0.347574\pi\)
−0.998999 + 0.0447238i \(0.985759\pi\)
\(270\) −1.13680e6 + 1.96900e6i −0.949018 + 1.64375i
\(271\) 825272. + 1.42941e6i 0.682612 + 1.18232i 0.974181 + 0.225769i \(0.0724894\pi\)
−0.291569 + 0.956550i \(0.594177\pi\)
\(272\) 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 \(0.543608\pi\)
−0.789626 + 0.613588i \(0.789726\pi\)
\(284\) 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 \(-0.271702\pi\)
0.657291 + 0.753637i \(0.271702\pi\)
\(294\) 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 \(-0.455612\pi\)
0.138997 + 0.990293i \(0.455612\pi\)
\(308\) 0 0
\(309\) −742840. −0.442587
\(310\) 2.14032e6 + 3.70714e6i 1.26495 + 2.19096i
\(311\) 333564. 577750.i 0.195559 0.338718i −0.751525 0.659705i \(-0.770681\pi\)
0.947084 + 0.320987i \(0.104014\pi\)
\(312\) 352800. 611068.i 0.205183 0.355388i
\(313\) −55517.0 96158.3i −0.0320306 0.0554786i 0.849566 0.527483i \(-0.176864\pi\)
−0.881596 + 0.472004i \(0.843531\pi\)
\(314\) 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 \(-0.333610\pi\)
0.499247 + 0.866460i \(0.333610\pi\)
\(350\) 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 \(-0.506495\pi\)
0.876047 0.482227i \(-0.160172\pi\)
\(354\) 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 −0.697281 0.716798i \(-0.745607\pi\)
0.969406 + 0.245464i \(0.0789402\pi\)
\(368\) −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 0.603717 0.797199i \(-0.293686\pi\)
−0.992253 + 0.124235i \(0.960352\pi\)
\(384\) 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 0.934347 0.356364i \(-0.115984\pi\)
−0.775794 + 0.630986i \(0.782650\pi\)
\(398\) −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 −0.544501 0.838760i \(-0.683281\pi\)
0.998638 + 0.0521720i \(0.0166144\pi\)
\(410\) 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 \(-0.628070\pi\)
−0.391577 + 0.920145i \(0.628070\pi\)
\(420\) 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 \(-0.668862\pi\)
−0.505961 + 0.862557i \(0.668862\pi\)
\(434\) 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 \(-0.796070\pi\)
−0.116800 0.993155i \(-0.537264\pi\)
\(440\) −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 \(-0.467762\pi\)
0.101105 + 0.994876i \(0.467762\pi\)
\(462\) 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 0.831701 0.555224i \(-0.187368\pi\)
−0.896689 + 0.442662i \(0.854034\pi\)
\(468\) −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 −0.706819 0.707395i \(-0.749870\pi\)
0.966031 + 0.258426i \(0.0832038\pi\)
\(480\) 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 \(-0.292185\pi\)
0.607469 + 0.794343i \(0.292185\pi\)
\(504\) 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 0.947604 0.319447i \(-0.103497\pi\)
−0.750452 + 0.660925i \(0.770164\pi\)
\(510\) −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 \(0.597016\pi\)
−0.676068 + 0.736839i \(0.736318\pi\)
\(522\) −803230. + 1.39124e6i −0.129022 + 0.223473i
\(523\) 2.74221e6 + 4.74966e6i 0.438377 + 0.759290i 0.997564 0.0697505i \(-0.0222203\pi\)
−0.559188 + 0.829041i \(0.688887\pi\)
\(524\) 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 \(-0.524674\pi\)
0.902143 0.431437i \(-0.141993\pi\)
\(564\) 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 −0.771079 0.636740i \(-0.780283\pi\)
0.936972 + 0.349404i \(0.113616\pi\)
\(578\) 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 \(-0.172493\pi\)
0.856729 + 0.515766i \(0.172493\pi\)
\(588\) 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 \(-0.967588\pi\)
0.409378 0.912365i \(-0.365746\pi\)
\(594\) 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 \(-0.561240\pi\)
−0.191207 + 0.981550i \(0.561240\pi\)
\(602\) 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 0.610608 0.791933i \(-0.290925\pi\)
−0.991138 + 0.132836i \(0.957592\pi\)
\(608\) −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 \(0.346295\pi\)
−0.999171 + 0.0407086i \(0.987038\pi\)
\(620\) −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 \(-0.804484\pi\)
−0.817217 + 0.576330i \(0.804484\pi\)
\(644\) 0 0
\(645\) 8.52992e6 0.807320
\(646\) 843780. + 1.46147e6i 0.0795514 + 0.137787i
\(647\) −27482.0 + 47600.2i −0.00258100 + 0.00447042i −0.867313 0.497763i \(-0.834155\pi\)
0.864732 + 0.502234i \(0.167488\pi\)
\(648\) −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 −0.909812 0.415021i \(-0.863774\pi\)
0.814325 + 0.580409i \(0.197107\pi\)
\(662\) −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 \(-0.975162\pi\)
0.430969 0.902367i \(-0.358172\pi\)
\(678\) 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 \(0.144823\pi\)
−0.0685703 + 0.997646i \(0.521844\pi\)
\(692\) −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 \(-0.775631\pi\)
−0.180287 0.983614i \(-0.557702\pi\)
\(720\) −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 \(-0.681866\pi\)
−0.540768 + 0.841172i \(0.681866\pi\)
\(728\) 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 \(-0.968201\pi\)
0.411136 0.911574i \(-0.365132\pi\)
\(734\) 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 \(0.0390795\pi\)
−0.390180 + 0.920739i \(0.627587\pi\)
\(762\) −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