Properties

Label 294.6.e.x.67.2
Level $294$
Weight $6$
Character 294.67
Analytic conductor $47.153$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [294,6,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 294.e (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: \(47.1528430250\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 294.67
Dual form 294.6.e.x.79.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-2.25126 - 3.89930i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\) \(q+(2.00000 + 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-2.25126 - 3.89930i) q^{5} -36.0000 q^{6} -64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(9.00505 - 15.5972i) q^{10} +(58.0955 - 100.624i) q^{11} +(-72.0000 - 124.708i) q^{12} -85.4773 q^{13} +40.5227 q^{15} +(-128.000 - 221.703i) q^{16} +(-16.6331 + 28.8093i) q^{17} +(162.000 - 280.592i) q^{18} +(-317.688 - 550.252i) q^{19} +72.0404 q^{20} +464.764 q^{22} +(-1363.71 - 2362.02i) q^{23} +(288.000 - 498.831i) q^{24} +(1552.36 - 2688.77i) q^{25} +(-170.955 - 296.102i) q^{26} +729.000 q^{27} +5860.48 q^{29} +(81.0455 + 140.375i) q^{30} +(-139.568 + 241.739i) q^{31} +(512.000 - 886.810i) q^{32} +(522.859 + 905.619i) q^{33} -133.065 q^{34} +1296.00 q^{36} +(-1519.25 - 2631.41i) q^{37} +(1270.75 - 2201.01i) q^{38} +(384.648 - 666.229i) q^{39} +(144.081 + 249.555i) q^{40} +819.415 q^{41} +11100.2 q^{43} +(929.527 + 1609.99i) q^{44} +(-182.352 + 315.843i) q^{45} +(5454.85 - 9448.09i) q^{46} +(3703.70 + 6415.00i) q^{47} +2304.00 q^{48} +12418.9 q^{50} +(-149.698 - 259.284i) q^{51} +(683.818 - 1184.41i) q^{52} +(6849.40 - 11863.5i) q^{53} +(1458.00 + 2525.33i) q^{54} -523.153 q^{55} +5718.39 q^{57} +(11721.0 + 20301.3i) q^{58} +(-11187.8 + 19377.9i) q^{59} +(-324.182 + 561.499i) q^{60} +(6346.04 + 10991.7i) q^{61} -1116.55 q^{62} +4096.00 q^{64} +(192.432 + 333.302i) q^{65} +(-2091.44 + 3622.47i) q^{66} +(26151.7 - 45296.0i) q^{67} +(-266.129 - 460.949i) q^{68} +24546.8 q^{69} +60230.2 q^{71} +(2592.00 + 4489.48i) q^{72} +(-38479.2 + 66647.9i) q^{73} +(6076.98 - 10525.6i) q^{74} +(13971.3 + 24199.0i) q^{75} +10166.0 q^{76} +3077.18 q^{78} +(16798.0 + 29095.0i) q^{79} +(-576.323 + 998.221i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(1638.83 + 2838.54i) q^{82} +60574.9 q^{83} +149.782 q^{85} +(22200.4 + 38452.3i) q^{86} +(-26372.2 + 45677.9i) q^{87} +(-3718.11 + 6439.95i) q^{88} +(-46095.1 - 79839.0i) q^{89} -1458.82 q^{90} +43638.8 q^{92} +(-1256.11 - 2175.65i) q^{93} +(-14814.8 + 25660.0i) q^{94} +(-1430.40 + 2477.53i) q^{95} +(4608.00 + 7981.29i) q^{96} +152287. q^{97} -9411.46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 8 q^{2} - 18 q^{3} - 32 q^{4} - 108 q^{5} - 144 q^{6} - 256 q^{8} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 8 q^{2} - 18 q^{3} - 32 q^{4} - 108 q^{5} - 144 q^{6} - 256 q^{8} - 162 q^{9} + 432 q^{10} - 124 q^{11} - 288 q^{12} + 1440 q^{13} + 1944 q^{15} - 512 q^{16} + 1260 q^{17} + 648 q^{18} - 360 q^{19} + 3456 q^{20} - 992 q^{22} - 6524 q^{23} + 1152 q^{24} - 4482 q^{25} + 2880 q^{26} + 2916 q^{27} + 14176 q^{29} + 3888 q^{30} - 5904 q^{31} + 2048 q^{32} - 1116 q^{33} + 10080 q^{34} + 5184 q^{36} + 6040 q^{37} + 1440 q^{38} - 6480 q^{39} + 6912 q^{40} - 34776 q^{41} - 1216 q^{43} - 1984 q^{44} - 8748 q^{45} + 26096 q^{46} + 30456 q^{47} + 9216 q^{48} - 35856 q^{50} + 11340 q^{51} - 11520 q^{52} - 3964 q^{53} + 5832 q^{54} + 48672 q^{55} + 6480 q^{57} + 28352 q^{58} - 40752 q^{59} - 15552 q^{60} + 1368 q^{61} - 47232 q^{62} + 16384 q^{64} - 82980 q^{65} + 4464 q^{66} + 16224 q^{67} + 20160 q^{68} + 117432 q^{69} - 6408 q^{71} + 10368 q^{72} - 23976 q^{73} - 24160 q^{74} - 40338 q^{75} + 11520 q^{76} - 51840 q^{78} + 82160 q^{79} - 27648 q^{80} - 13122 q^{81} - 69552 q^{82} + 347472 q^{83} - 267400 q^{85} - 2432 q^{86} - 63792 q^{87} + 7936 q^{88} - 200556 q^{89} - 69984 q^{90} + 208768 q^{92} - 53136 q^{93} - 121824 q^{94} + 25640 q^{95} + 18432 q^{96} + 503856 q^{97} + 20088 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 + 3.46410i 0.353553 + 0.612372i
\(3\) −4.50000 + 7.79423i −0.288675 + 0.500000i
\(4\) −8.00000 + 13.8564i −0.250000 + 0.433013i
\(5\) −2.25126 3.89930i −0.0402718 0.0697528i 0.845187 0.534471i \(-0.179489\pi\)
−0.885459 + 0.464718i \(0.846156\pi\)
\(6\) −36.0000 −0.408248
\(7\) 0 0
\(8\) −64.0000 −0.353553
\(9\) −40.5000 70.1481i −0.166667 0.288675i
\(10\) 9.00505 15.5972i 0.0284765 0.0493227i
\(11\) 58.0955 100.624i 0.144764 0.250739i −0.784521 0.620102i \(-0.787091\pi\)
0.929285 + 0.369364i \(0.120424\pi\)
\(12\) −72.0000 124.708i −0.144338 0.250000i
\(13\) −85.4773 −0.140279 −0.0701394 0.997537i \(-0.522344\pi\)
−0.0701394 + 0.997537i \(0.522344\pi\)
\(14\) 0 0
\(15\) 40.5227 0.0465019
\(16\) −128.000 221.703i −0.125000 0.216506i
\(17\) −16.6331 + 28.8093i −0.0139589 + 0.0241775i −0.872920 0.487863i \(-0.837777\pi\)
0.858962 + 0.512040i \(0.171110\pi\)
\(18\) 162.000 280.592i 0.117851 0.204124i
\(19\) −317.688 550.252i −0.201891 0.349686i 0.747247 0.664547i \(-0.231375\pi\)
−0.949138 + 0.314861i \(0.898042\pi\)
\(20\) 72.0404 0.0402718
\(21\) 0 0
\(22\) 464.764 0.204727
\(23\) −1363.71 2362.02i −0.537531 0.931031i −0.999036 0.0438936i \(-0.986024\pi\)
0.461505 0.887138i \(-0.347310\pi\)
\(24\) 288.000 498.831i 0.102062 0.176777i
\(25\) 1552.36 2688.77i 0.496756 0.860407i
\(26\) −170.955 296.102i −0.0495961 0.0859029i
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) 5860.48 1.29401 0.647006 0.762485i \(-0.276021\pi\)
0.647006 + 0.762485i \(0.276021\pi\)
\(30\) 81.0455 + 140.375i 0.0164409 + 0.0284765i
\(31\) −139.568 + 241.739i −0.0260845 + 0.0451796i −0.878773 0.477240i \(-0.841637\pi\)
0.852688 + 0.522420i \(0.174971\pi\)
\(32\) 512.000 886.810i 0.0883883 0.153093i
\(33\) 522.859 + 905.619i 0.0835795 + 0.144764i
\(34\) −133.065 −0.0197408
\(35\) 0 0
\(36\) 1296.00 0.166667
\(37\) −1519.25 2631.41i −0.182442 0.315998i 0.760270 0.649607i \(-0.225067\pi\)
−0.942711 + 0.333609i \(0.891733\pi\)
\(38\) 1270.75 2201.01i 0.142759 0.247265i
\(39\) 384.648 666.229i 0.0404950 0.0701394i
\(40\) 144.081 + 249.555i 0.0142382 + 0.0246613i
\(41\) 819.415 0.0761279 0.0380640 0.999275i \(-0.487881\pi\)
0.0380640 + 0.999275i \(0.487881\pi\)
\(42\) 0 0
\(43\) 11100.2 0.915504 0.457752 0.889080i \(-0.348655\pi\)
0.457752 + 0.889080i \(0.348655\pi\)
\(44\) 929.527 + 1609.99i 0.0723820 + 0.125369i
\(45\) −182.352 + 315.843i −0.0134239 + 0.0232509i
\(46\) 5454.85 9448.09i 0.380092 0.658338i
\(47\) 3703.70 + 6415.00i 0.244563 + 0.423596i 0.962009 0.273019i \(-0.0880221\pi\)
−0.717446 + 0.696615i \(0.754689\pi\)
\(48\) 2304.00 0.144338
\(49\) 0 0
\(50\) 12418.9 0.702520
\(51\) −149.698 259.284i −0.00805916 0.0139589i
\(52\) 683.818 1184.41i 0.0350697 0.0607425i
\(53\) 6849.40 11863.5i 0.334937 0.580128i −0.648536 0.761184i \(-0.724618\pi\)
0.983473 + 0.181057i \(0.0579517\pi\)
\(54\) 1458.00 + 2525.33i 0.0680414 + 0.117851i
\(55\) −523.153 −0.0233196
\(56\) 0 0
\(57\) 5718.39 0.233124
\(58\) 11721.0 + 20301.3i 0.457502 + 0.792417i
\(59\) −11187.8 + 19377.9i −0.418424 + 0.724732i −0.995781 0.0917601i \(-0.970751\pi\)
0.577357 + 0.816492i \(0.304084\pi\)
\(60\) −324.182 + 561.499i −0.0116255 + 0.0201359i
\(61\) 6346.04 + 10991.7i 0.218363 + 0.378215i 0.954308 0.298826i \(-0.0965951\pi\)
−0.735945 + 0.677041i \(0.763262\pi\)
\(62\) −1116.55 −0.0368890
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) 192.432 + 333.302i 0.00564928 + 0.00978485i
\(66\) −2091.44 + 3622.47i −0.0590996 + 0.102364i
\(67\) 26151.7 45296.0i 0.711725 1.23274i −0.252484 0.967601i \(-0.581247\pi\)
0.964209 0.265143i \(-0.0854193\pi\)
\(68\) −266.129 460.949i −0.00697944 0.0120887i
\(69\) 24546.8 0.620687
\(70\) 0 0
\(71\) 60230.2 1.41798 0.708988 0.705221i \(-0.249152\pi\)
0.708988 + 0.705221i \(0.249152\pi\)
\(72\) 2592.00 + 4489.48i 0.0589256 + 0.102062i
\(73\) −38479.2 + 66647.9i −0.845121 + 1.46379i 0.0403954 + 0.999184i \(0.487138\pi\)
−0.885516 + 0.464608i \(0.846195\pi\)
\(74\) 6076.98 10525.6i 0.129006 0.223444i
\(75\) 13971.3 + 24199.0i 0.286802 + 0.496756i
\(76\) 10166.0 0.201891
\(77\) 0 0
\(78\) 3077.18 0.0572686
\(79\) 16798.0 + 29095.0i 0.302824 + 0.524506i 0.976774 0.214270i \(-0.0687374\pi\)
−0.673951 + 0.738776i \(0.735404\pi\)
\(80\) −576.323 + 998.221i −0.0100680 + 0.0174382i
\(81\) −3280.50 + 5681.99i −0.0555556 + 0.0962250i
\(82\) 1638.83 + 2838.54i 0.0269153 + 0.0466187i
\(83\) 60574.9 0.965157 0.482578 0.875853i \(-0.339700\pi\)
0.482578 + 0.875853i \(0.339700\pi\)
\(84\) 0 0
\(85\) 149.782 0.00224860
\(86\) 22200.4 + 38452.3i 0.323680 + 0.560630i
\(87\) −26372.2 + 45677.9i −0.373549 + 0.647006i
\(88\) −3718.11 + 6439.95i −0.0511818 + 0.0886495i
\(89\) −46095.1 79839.0i −0.616850 1.06841i −0.990057 0.140667i \(-0.955075\pi\)
0.373207 0.927748i \(-0.378258\pi\)
\(90\) −1458.82 −0.0189843
\(91\) 0 0
\(92\) 43638.8 0.537531
\(93\) −1256.11 2175.65i −0.0150599 0.0260845i
\(94\) −14814.8 + 25660.0i −0.172932 + 0.299528i
\(95\) −1430.40 + 2477.53i −0.0162610 + 0.0281650i
\(96\) 4608.00 + 7981.29i 0.0510310 + 0.0883883i
\(97\) 152287. 1.64336 0.821680 0.569949i \(-0.193037\pi\)
0.821680 + 0.569949i \(0.193037\pi\)
\(98\) 0 0
\(99\) −9411.46 −0.0965093
\(100\) 24837.8 + 43020.4i 0.248378 + 0.430204i
\(101\) −53822.1 + 93222.6i −0.524997 + 0.909322i 0.474579 + 0.880213i \(0.342600\pi\)
−0.999576 + 0.0291091i \(0.990733\pi\)
\(102\) 598.791 1037.14i 0.00569869 0.00987041i
\(103\) −60319.6 104477.i −0.560229 0.970345i −0.997476 0.0710033i \(-0.977380\pi\)
0.437247 0.899341i \(-0.355953\pi\)
\(104\) 5470.55 0.0495961
\(105\) 0 0
\(106\) 54795.2 0.473672
\(107\) −43057.2 74577.2i −0.363568 0.629719i 0.624977 0.780643i \(-0.285108\pi\)
−0.988545 + 0.150924i \(0.951775\pi\)
\(108\) −5832.00 + 10101.3i −0.0481125 + 0.0833333i
\(109\) 33069.6 57278.2i 0.266602 0.461767i −0.701380 0.712787i \(-0.747433\pi\)
0.967982 + 0.251020i \(0.0807659\pi\)
\(110\) −1046.31 1812.25i −0.00824473 0.0142803i
\(111\) 27346.4 0.210665
\(112\) 0 0
\(113\) 131608. 0.969588 0.484794 0.874628i \(-0.338895\pi\)
0.484794 + 0.874628i \(0.338895\pi\)
\(114\) 11436.8 + 19809.1i 0.0824217 + 0.142759i
\(115\) −6140.16 + 10635.1i −0.0432947 + 0.0749886i
\(116\) −46883.9 + 81205.2i −0.323503 + 0.560324i
\(117\) 3461.83 + 5996.06i 0.0233798 + 0.0404950i
\(118\) −89502.8 −0.591741
\(119\) 0 0
\(120\) −2593.45 −0.0164409
\(121\) 73775.3 + 127783.i 0.458087 + 0.793430i
\(122\) −25384.2 + 43966.7i −0.154406 + 0.267439i
\(123\) −3687.37 + 6386.71i −0.0219762 + 0.0380640i
\(124\) −2233.09 3867.83i −0.0130422 0.0225898i
\(125\) −28049.5 −0.160565
\(126\) 0 0
\(127\) 14437.3 0.0794284 0.0397142 0.999211i \(-0.487355\pi\)
0.0397142 + 0.999211i \(0.487355\pi\)
\(128\) 8192.00 + 14189.0i 0.0441942 + 0.0765466i
\(129\) −49951.0 + 86517.6i −0.264283 + 0.457752i
\(130\) −769.727 + 1333.21i −0.00399465 + 0.00691893i
\(131\) −159608. 276450.i −0.812600 1.40747i −0.911038 0.412322i \(-0.864718\pi\)
0.0984380 0.995143i \(-0.468615\pi\)
\(132\) −16731.5 −0.0835795
\(133\) 0 0
\(134\) 209213. 1.00653
\(135\) −1641.17 2842.59i −0.00775031 0.0134239i
\(136\) 1064.52 1843.80i 0.00493521 0.00854803i
\(137\) 25267.0 43763.7i 0.115014 0.199211i −0.802771 0.596287i \(-0.796642\pi\)
0.917785 + 0.397077i \(0.129975\pi\)
\(138\) 49093.7 + 85032.8i 0.219446 + 0.380092i
\(139\) 223787. 0.982422 0.491211 0.871041i \(-0.336554\pi\)
0.491211 + 0.871041i \(0.336554\pi\)
\(140\) 0 0
\(141\) −66666.6 −0.282397
\(142\) 120460. + 208644.i 0.501330 + 0.868329i
\(143\) −4965.84 + 8601.09i −0.0203073 + 0.0351733i
\(144\) −10368.0 + 17957.9i −0.0416667 + 0.0721688i
\(145\) −13193.5 22851.8i −0.0521122 0.0902610i
\(146\) −307834. −1.19518
\(147\) 0 0
\(148\) 48615.9 0.182442
\(149\) −129761. 224752.i −0.478825 0.829350i 0.520880 0.853630i \(-0.325604\pi\)
−0.999705 + 0.0242802i \(0.992271\pi\)
\(150\) −55885.1 + 96795.8i −0.202800 + 0.351260i
\(151\) 55446.4 96036.0i 0.197893 0.342761i −0.749952 0.661492i \(-0.769923\pi\)
0.947845 + 0.318731i \(0.103257\pi\)
\(152\) 20332.1 + 35216.2i 0.0713793 + 0.123633i
\(153\) 2694.56 0.00930592
\(154\) 0 0
\(155\) 1256.82 0.00420188
\(156\) 6154.36 + 10659.7i 0.0202475 + 0.0350697i
\(157\) 202693. 351074.i 0.656280 1.13671i −0.325291 0.945614i \(-0.605462\pi\)
0.981571 0.191096i \(-0.0612042\pi\)
\(158\) −67192.0 + 116380.i −0.214129 + 0.370882i
\(159\) 61644.6 + 106772.i 0.193376 + 0.334937i
\(160\) −4610.59 −0.0142382
\(161\) 0 0
\(162\) −26244.0 −0.0785674
\(163\) −19309.3 33444.8i −0.0569244 0.0985959i 0.836159 0.548487i \(-0.184796\pi\)
−0.893083 + 0.449891i \(0.851463\pi\)
\(164\) −6555.32 + 11354.1i −0.0190320 + 0.0329644i
\(165\) 2354.19 4077.57i 0.00673180 0.0116598i
\(166\) 121150. + 209838.i 0.341234 + 0.591035i
\(167\) −207255. −0.575060 −0.287530 0.957772i \(-0.592834\pi\)
−0.287530 + 0.957772i \(0.592834\pi\)
\(168\) 0 0
\(169\) −363987. −0.980322
\(170\) 299.563 + 518.859i 0.000794999 + 0.00137698i
\(171\) −25732.8 + 44570.4i −0.0672971 + 0.116562i
\(172\) −88801.7 + 153809.i −0.228876 + 0.396425i
\(173\) 64128.7 + 111074.i 0.162906 + 0.282161i 0.935910 0.352240i \(-0.114580\pi\)
−0.773004 + 0.634401i \(0.781247\pi\)
\(174\) −210977. −0.528278
\(175\) 0 0
\(176\) −29744.9 −0.0723820
\(177\) −100691. 174401.i −0.241577 0.418424i
\(178\) 184380. 319356.i 0.436179 0.755483i
\(179\) 49299.7 85389.6i 0.115004 0.199192i −0.802778 0.596279i \(-0.796645\pi\)
0.917781 + 0.397086i \(0.129979\pi\)
\(180\) −2917.64 5053.49i −0.00671197 0.0116255i
\(181\) 599225. 1.35954 0.679772 0.733423i \(-0.262079\pi\)
0.679772 + 0.733423i \(0.262079\pi\)
\(182\) 0 0
\(183\) −114229. −0.252144
\(184\) 87277.7 + 151169.i 0.190046 + 0.329169i
\(185\) −6840.44 + 11848.0i −0.0146945 + 0.0254516i
\(186\) 5024.45 8702.61i 0.0106489 0.0184445i
\(187\) 1932.61 + 3347.38i 0.00404148 + 0.00700005i
\(188\) −118518. −0.244563
\(189\) 0 0
\(190\) −11443.2 −0.0229966
\(191\) −414608. 718122.i −0.822346 1.42434i −0.903931 0.427678i \(-0.859332\pi\)
0.0815852 0.996666i \(-0.474002\pi\)
\(192\) −18432.0 + 31925.2i −0.0360844 + 0.0625000i
\(193\) 208193. 360600.i 0.402320 0.696839i −0.591685 0.806169i \(-0.701537\pi\)
0.994006 + 0.109330i \(0.0348705\pi\)
\(194\) 304574. + 527537.i 0.581016 + 1.00635i
\(195\) −3463.77 −0.00652323
\(196\) 0 0
\(197\) −592061. −1.08693 −0.543464 0.839433i \(-0.682887\pi\)
−0.543464 + 0.839433i \(0.682887\pi\)
\(198\) −18822.9 32602.3i −0.0341212 0.0590996i
\(199\) 533040. 923253.i 0.954173 1.65268i 0.217925 0.975966i \(-0.430071\pi\)
0.736249 0.676711i \(-0.236595\pi\)
\(200\) −99351.3 + 172081.i −0.175630 + 0.304200i
\(201\) 235365. + 407664.i 0.410915 + 0.711725i
\(202\) −430577. −0.742458
\(203\) 0 0
\(204\) 4790.33 0.00805916
\(205\) −1844.72 3195.14i −0.00306581 0.00531014i
\(206\) 241278. 417906.i 0.396142 0.686137i
\(207\) −110461. + 191324.i −0.179177 + 0.310344i
\(208\) 10941.1 + 18950.5i 0.0175349 + 0.0303713i
\(209\) −73825.0 −0.116906
\(210\) 0 0
\(211\) −846029. −1.30822 −0.654108 0.756401i \(-0.726956\pi\)
−0.654108 + 0.756401i \(0.726956\pi\)
\(212\) 109590. + 189816.i 0.167468 + 0.290064i
\(213\) −271036. + 469448.i −0.409334 + 0.708988i
\(214\) 172229. 298309.i 0.257082 0.445278i
\(215\) −24989.5 43283.1i −0.0368690 0.0638590i
\(216\) −46656.0 −0.0680414
\(217\) 0 0
\(218\) 264557. 0.377032
\(219\) −346313. 599831.i −0.487931 0.845121i
\(220\) 4185.22 7249.01i 0.00582991 0.0100977i
\(221\) 1421.75 2462.54i 0.00195814 0.00339159i
\(222\) 54692.8 + 94730.8i 0.0744814 + 0.129006i
\(223\) 112299. 0.151222 0.0756109 0.997137i \(-0.475909\pi\)
0.0756109 + 0.997137i \(0.475909\pi\)
\(224\) 0 0
\(225\) −251483. −0.331171
\(226\) 263217. + 455904.i 0.342801 + 0.593749i
\(227\) 89238.4 154565.i 0.114944 0.199089i −0.802813 0.596231i \(-0.796664\pi\)
0.917757 + 0.397141i \(0.129998\pi\)
\(228\) −45747.1 + 79236.3i −0.0582810 + 0.100946i
\(229\) −229877. 398158.i −0.289672 0.501726i 0.684060 0.729426i \(-0.260213\pi\)
−0.973731 + 0.227700i \(0.926880\pi\)
\(230\) −49121.2 −0.0612280
\(231\) 0 0
\(232\) −375071. −0.457502
\(233\) −374334. 648365.i −0.451720 0.782402i 0.546773 0.837281i \(-0.315856\pi\)
−0.998493 + 0.0548792i \(0.982523\pi\)
\(234\) −13847.3 + 23984.3i −0.0165320 + 0.0286343i
\(235\) 16676.0 28883.7i 0.0196980 0.0341179i
\(236\) −179006. 310047.i −0.209212 0.362366i
\(237\) −302364. −0.349670
\(238\) 0 0
\(239\) −814752. −0.922637 −0.461319 0.887235i \(-0.652623\pi\)
−0.461319 + 0.887235i \(0.652623\pi\)
\(240\) −5186.91 8983.99i −0.00581274 0.0100680i
\(241\) 523816. 907276.i 0.580947 1.00623i −0.414421 0.910085i \(-0.636016\pi\)
0.995367 0.0961439i \(-0.0306509\pi\)
\(242\) −295101. + 511131.i −0.323916 + 0.561039i
\(243\) −29524.5 51137.9i −0.0320750 0.0555556i
\(244\) −203073. −0.218363
\(245\) 0 0
\(246\) −29498.9 −0.0310791
\(247\) 27155.1 + 47034.1i 0.0283211 + 0.0490535i
\(248\) 8932.36 15471.3i 0.00922226 0.0159734i
\(249\) −272587. + 472135.i −0.278617 + 0.482578i
\(250\) −56099.0 97166.3i −0.0567682 0.0983254i
\(251\) −1.09401e6 −1.09607 −0.548034 0.836456i \(-0.684623\pi\)
−0.548034 + 0.836456i \(0.684623\pi\)
\(252\) 0 0
\(253\) −316902. −0.311261
\(254\) 28874.5 + 50012.2i 0.0280822 + 0.0486398i
\(255\) −674.018 + 1167.43i −0.000649114 + 0.00112430i
\(256\) −32768.0 + 56755.8i −0.0312500 + 0.0541266i
\(257\) 389195. + 674106.i 0.367566 + 0.636642i 0.989184 0.146678i \(-0.0468580\pi\)
−0.621619 + 0.783320i \(0.713525\pi\)
\(258\) −399608. −0.373753
\(259\) 0 0
\(260\) −6157.82 −0.00564928
\(261\) −237350. 411101.i −0.215669 0.373549i
\(262\) 638433. 1.10580e6i 0.574595 0.995228i
\(263\) −554881. + 961083.i −0.494664 + 0.856784i −0.999981 0.00615004i \(-0.998042\pi\)
0.505317 + 0.862934i \(0.331376\pi\)
\(264\) −33463.0 57959.6i −0.0295498 0.0511818i
\(265\) −61679.2 −0.0539540
\(266\) 0 0
\(267\) 829711. 0.712277
\(268\) 418427. + 724736.i 0.355863 + 0.616372i
\(269\) −668202. + 1.15736e6i −0.563024 + 0.975187i 0.434206 + 0.900813i \(0.357029\pi\)
−0.997230 + 0.0743731i \(0.976304\pi\)
\(270\) 6564.68 11370.4i 0.00548030 0.00949216i
\(271\) −896005. 1.55193e6i −0.741118 1.28365i −0.951987 0.306140i \(-0.900963\pi\)
0.210869 0.977514i \(-0.432371\pi\)
\(272\) 8516.14 0.00697944
\(273\) 0 0
\(274\) 202136. 0.162655
\(275\) −180371. 312411.i −0.143825 0.249112i
\(276\) −196375. + 340131.i −0.155172 + 0.268766i
\(277\) −28788.8 + 49863.6i −0.0225436 + 0.0390467i −0.877077 0.480350i \(-0.840510\pi\)
0.854533 + 0.519396i \(0.173843\pi\)
\(278\) 447574. + 775221.i 0.347339 + 0.601608i
\(279\) 22610.0 0.0173897
\(280\) 0 0
\(281\) −550257. −0.415719 −0.207860 0.978159i \(-0.566650\pi\)
−0.207860 + 0.978159i \(0.566650\pi\)
\(282\) −133333. 230940.i −0.0998425 0.172932i
\(283\) 588940. 1.02007e6i 0.437125 0.757122i −0.560342 0.828261i \(-0.689330\pi\)
0.997466 + 0.0711395i \(0.0226635\pi\)
\(284\) −481842. + 834575.i −0.354494 + 0.614001i
\(285\) −12873.6 22297.7i −0.00938832 0.0162610i
\(286\) −39726.7 −0.0287189
\(287\) 0 0
\(288\) −82944.0 −0.0589256
\(289\) 709375. + 1.22867e6i 0.499610 + 0.865350i
\(290\) 52773.9 91407.1i 0.0368489 0.0638242i
\(291\) −685290. + 1.18696e6i −0.474397 + 0.821680i
\(292\) −615667. 1.06637e6i −0.422560 0.731896i
\(293\) 300762. 0.204670 0.102335 0.994750i \(-0.467369\pi\)
0.102335 + 0.994750i \(0.467369\pi\)
\(294\) 0 0
\(295\) 100747. 0.0674028
\(296\) 97231.7 + 168410.i 0.0645028 + 0.111722i
\(297\) 42351.6 73355.1i 0.0278598 0.0482547i
\(298\) 519042. 899008.i 0.338581 0.586439i
\(299\) 116567. + 201899.i 0.0754043 + 0.130604i
\(300\) −447081. −0.286802
\(301\) 0 0
\(302\) 443571. 0.279863
\(303\) −484399. 839003.i −0.303107 0.524997i
\(304\) −81328.2 + 140865.i −0.0504728 + 0.0874214i
\(305\) 28573.2 49490.3i 0.0175877 0.0304628i
\(306\) 5389.12 + 9334.23i 0.00329014 + 0.00569869i
\(307\) 146787. 0.0888874 0.0444437 0.999012i \(-0.485848\pi\)
0.0444437 + 0.999012i \(0.485848\pi\)
\(308\) 0 0
\(309\) 1.08575e6 0.646896
\(310\) 2513.64 + 4353.75i 0.00148559 + 0.00257311i
\(311\) −851554. + 1.47494e6i −0.499242 + 0.864713i −1.00000 0.000874814i \(-0.999722\pi\)
0.500757 + 0.865588i \(0.333055\pi\)
\(312\) −24617.5 + 42638.7i −0.0143172 + 0.0247980i
\(313\) −558474. 967305.i −0.322212 0.558088i 0.658732 0.752378i \(-0.271093\pi\)
−0.980944 + 0.194290i \(0.937760\pi\)
\(314\) 1.62154e6 0.928120
\(315\) 0 0
\(316\) −537536. −0.302824
\(317\) 481447. + 833891.i 0.269092 + 0.466081i 0.968628 0.248517i \(-0.0799432\pi\)
−0.699536 + 0.714598i \(0.746610\pi\)
\(318\) −246578. + 427086.i −0.136737 + 0.236836i
\(319\) 340467. 589707.i 0.187326 0.324459i
\(320\) −9221.17 15971.5i −0.00503398 0.00871910i
\(321\) 775029. 0.419812
\(322\) 0 0
\(323\) 21136.5 0.0112727
\(324\) −52488.0 90911.9i −0.0277778 0.0481125i
\(325\) −132692. + 229829.i −0.0696844 + 0.120697i
\(326\) 77237.3 133779.i 0.0402516 0.0697178i
\(327\) 297626. + 515504.i 0.153922 + 0.266602i
\(328\) −52442.5 −0.0269153
\(329\) 0 0
\(330\) 18833.5 0.00952020
\(331\) 1.12998e6 + 1.95718e6i 0.566891 + 0.981883i 0.996871 + 0.0790451i \(0.0251871\pi\)
−0.429980 + 0.902838i \(0.641480\pi\)
\(332\) −484600. + 839351.i −0.241289 + 0.417925i
\(333\) −123059. + 213144.i −0.0608138 + 0.105333i
\(334\) −414509. 717951.i −0.203314 0.352151i
\(335\) −235497. −0.114650
\(336\) 0 0
\(337\) 1.33338e6 0.639557 0.319778 0.947492i \(-0.396392\pi\)
0.319778 + 0.947492i \(0.396392\pi\)
\(338\) −727973. 1.26089e6i −0.346596 0.600322i
\(339\) −592237. + 1.02578e6i −0.279896 + 0.484794i
\(340\) −1198.25 + 2075.44i −0.000562149 + 0.000973671i
\(341\) 16216.6 + 28087.9i 0.00755219 + 0.0130808i
\(342\) −205862. −0.0951724
\(343\) 0 0
\(344\) −710414. −0.323680
\(345\) −55261.4 95715.5i −0.0249962 0.0432947i
\(346\) −256515. + 444296.i −0.115192 + 0.199518i
\(347\) 717431. 1.24263e6i 0.319857 0.554009i −0.660601 0.750737i \(-0.729698\pi\)
0.980458 + 0.196728i \(0.0630317\pi\)
\(348\) −421955. 730847.i −0.186775 0.323503i
\(349\) 3.34711e6 1.47098 0.735489 0.677536i \(-0.236952\pi\)
0.735489 + 0.677536i \(0.236952\pi\)
\(350\) 0 0
\(351\) −62312.9 −0.0269967
\(352\) −59489.7 103039.i −0.0255909 0.0443247i
\(353\) −2.00209e6 + 3.46772e6i −0.855160 + 1.48118i 0.0213370 + 0.999772i \(0.493208\pi\)
−0.876497 + 0.481408i \(0.840126\pi\)
\(354\) 402763. 697605.i 0.170821 0.295870i
\(355\) −135594. 234856.i −0.0571044 0.0989078i
\(356\) 1.47504e6 0.616850
\(357\) 0 0
\(358\) 394398. 0.162640
\(359\) 297993. + 516139.i 0.122031 + 0.211364i 0.920568 0.390581i \(-0.127726\pi\)
−0.798538 + 0.601945i \(0.794393\pi\)
\(360\) 11670.5 20214.0i 0.00474608 0.00822045i
\(361\) 1.03620e6 1.79475e6i 0.418480 0.724828i
\(362\) 1.19845e6 + 2.07578e6i 0.480672 + 0.832548i
\(363\) −1.32796e6 −0.528953
\(364\) 0 0
\(365\) 346507. 0.136138
\(366\) −228458. 395700.i −0.0891462 0.154406i
\(367\) 1.65195e6 2.86126e6i 0.640224 1.10890i −0.345159 0.938544i \(-0.612175\pi\)
0.985383 0.170356i \(-0.0544918\pi\)
\(368\) −349111. + 604677.i −0.134383 + 0.232758i
\(369\) −33186.3 57480.3i −0.0126880 0.0219762i
\(370\) −54723.5 −0.0207812
\(371\) 0 0
\(372\) 40195.6 0.0150599
\(373\) 1.41532e6 + 2.45140e6i 0.526722 + 0.912309i 0.999515 + 0.0311353i \(0.00991229\pi\)
−0.472794 + 0.881173i \(0.656754\pi\)
\(374\) −7730.45 + 13389.5i −0.00285776 + 0.00494979i
\(375\) 126223. 218624.i 0.0463510 0.0802824i
\(376\) −237037. 410560.i −0.0864661 0.149764i
\(377\) −500938. −0.181523
\(378\) 0 0
\(379\) 2.45025e6 0.876218 0.438109 0.898922i \(-0.355648\pi\)
0.438109 + 0.898922i \(0.355648\pi\)
\(380\) −22886.4 39640.4i −0.00813052 0.0140825i
\(381\) −64967.7 + 112527.i −0.0229290 + 0.0397142i
\(382\) 1.65843e6 2.87249e6i 0.581486 1.00716i
\(383\) 1.69202e6 + 2.93067e6i 0.589399 + 1.02087i 0.994311 + 0.106514i \(0.0339689\pi\)
−0.404912 + 0.914356i \(0.632698\pi\)
\(384\) −147456. −0.0510310
\(385\) 0 0
\(386\) 1.66554e6 0.568967
\(387\) −449559. 778659.i −0.152584 0.264283i
\(388\) −1.21829e6 + 2.11015e6i −0.410840 + 0.711596i
\(389\) 2.07480e6 3.59366e6i 0.695189 1.20410i −0.274928 0.961465i \(-0.588654\pi\)
0.970117 0.242638i \(-0.0780127\pi\)
\(390\) −6927.54 11998.9i −0.00230631 0.00399465i
\(391\) 90731.0 0.0300133
\(392\) 0 0
\(393\) 2.87295e6 0.938310
\(394\) −1.18412e6 2.05096e6i −0.384287 0.665605i
\(395\) 75633.4 131001.i 0.0243905 0.0422456i
\(396\) 75291.7 130409.i 0.0241273 0.0417898i
\(397\) 823330. + 1.42605e6i 0.262179 + 0.454107i 0.966821 0.255456i \(-0.0822256\pi\)
−0.704642 + 0.709563i \(0.748892\pi\)
\(398\) 4.26432e6 1.34940
\(399\) 0 0
\(400\) −794810. −0.248378
\(401\) 2.19332e6 + 3.79894e6i 0.681147 + 1.17978i 0.974631 + 0.223817i \(0.0718520\pi\)
−0.293484 + 0.955964i \(0.594815\pi\)
\(402\) −941460. + 1.63066e6i −0.290561 + 0.503266i
\(403\) 11929.9 20663.2i 0.00365910 0.00633775i
\(404\) −861153. 1.49156e6i −0.262499 0.454661i
\(405\) 29541.1 0.00894929
\(406\) 0 0
\(407\) −353045. −0.105644
\(408\) 9580.65 + 16594.2i 0.00284934 + 0.00493521i
\(409\) −177296. + 307086.i −0.0524072 + 0.0907719i −0.891039 0.453927i \(-0.850023\pi\)
0.838632 + 0.544699i \(0.183356\pi\)
\(410\) 7378.87 12780.6i 0.00216786 0.00375484i
\(411\) 227403. + 393873.i 0.0664035 + 0.115014i
\(412\) 1.93023e6 0.560229
\(413\) 0 0
\(414\) −883686. −0.253395
\(415\) −136370. 236200.i −0.0388686 0.0673224i
\(416\) −43764.4 + 75802.1i −0.0123990 + 0.0214757i
\(417\) −1.00704e6 + 1.74425e6i −0.283601 + 0.491211i
\(418\) −147650. 255737.i −0.0413326 0.0715902i
\(419\) −1.79802e6 −0.500335 −0.250167 0.968203i \(-0.580486\pi\)
−0.250167 + 0.968203i \(0.580486\pi\)
\(420\) 0 0
\(421\) 6.10881e6 1.67978 0.839888 0.542760i \(-0.182621\pi\)
0.839888 + 0.542760i \(0.182621\pi\)
\(422\) −1.69206e6 2.93073e6i −0.462524 0.801115i
\(423\) 300000. 519615.i 0.0815211 0.141199i
\(424\) −438362. + 759265.i −0.118418 + 0.205106i
\(425\) 51641.2 + 89445.1i 0.0138683 + 0.0240206i
\(426\) −2.16829e6 −0.578886
\(427\) 0 0
\(428\) 1.37783e6 0.363568
\(429\) −44692.6 77409.8i −0.0117244 0.0203073i
\(430\) 99958.0 173132.i 0.0260703 0.0451551i
\(431\) 955880. 1.65563e6i 0.247862 0.429310i −0.715070 0.699053i \(-0.753605\pi\)
0.962932 + 0.269743i \(0.0869387\pi\)
\(432\) −93312.0 161621.i −0.0240563 0.0416667i
\(433\) 385530. 0.0988186 0.0494093 0.998779i \(-0.484266\pi\)
0.0494093 + 0.998779i \(0.484266\pi\)
\(434\) 0 0
\(435\) 237483. 0.0601740
\(436\) 529114. + 916452.i 0.133301 + 0.230884i
\(437\) −866472. + 1.50077e6i −0.217046 + 0.375934i
\(438\) 1.38525e6 2.39933e6i 0.345019 0.597591i
\(439\) 916909. + 1.58813e6i 0.227073 + 0.393302i 0.956939 0.290288i \(-0.0937511\pi\)
−0.729866 + 0.683590i \(0.760418\pi\)
\(440\) 33481.8 0.00824473
\(441\) 0 0
\(442\) 11374.0 0.00276922
\(443\) 966960. + 1.67482e6i 0.234099 + 0.405471i 0.959010 0.283371i \(-0.0914527\pi\)
−0.724912 + 0.688842i \(0.758119\pi\)
\(444\) −218771. + 378923.i −0.0526663 + 0.0912208i
\(445\) −207544. + 359477.i −0.0496833 + 0.0860540i
\(446\) 224598. + 389016.i 0.0534650 + 0.0926041i
\(447\) 2.33569e6 0.552900
\(448\) 0 0
\(449\) 6.76354e6 1.58328 0.791641 0.610987i \(-0.209227\pi\)
0.791641 + 0.610987i \(0.209227\pi\)
\(450\) −502966. 871162.i −0.117087 0.202800i
\(451\) 47604.3 82453.0i 0.0110206 0.0190882i
\(452\) −1.05287e6 + 1.82362e6i −0.242397 + 0.419844i
\(453\) 499018. + 864324.i 0.114254 + 0.197893i
\(454\) 713907. 0.162556
\(455\) 0 0
\(456\) −365977. −0.0824217
\(457\) 1.19746e6 + 2.07406e6i 0.268207 + 0.464548i 0.968399 0.249407i \(-0.0802356\pi\)
−0.700192 + 0.713955i \(0.746902\pi\)
\(458\) 919507. 1.59263e6i 0.204829 0.354774i
\(459\) −12125.5 + 21002.0i −0.00268639 + 0.00465296i
\(460\) −98242.5 170161.i −0.0216474 0.0374943i
\(461\) −6.42949e6 −1.40904 −0.704522 0.709682i \(-0.748838\pi\)
−0.704522 + 0.709682i \(0.748838\pi\)
\(462\) 0 0
\(463\) 1.36524e6 0.295976 0.147988 0.988989i \(-0.452720\pi\)
0.147988 + 0.988989i \(0.452720\pi\)
\(464\) −750142. 1.29928e6i −0.161752 0.280162i
\(465\) −5655.68 + 9795.93i −0.00121298 + 0.00210094i
\(466\) 1.49733e6 2.59346e6i 0.319414 0.553241i
\(467\) −2.18181e6 3.77900e6i −0.462940 0.801835i 0.536166 0.844113i \(-0.319872\pi\)
−0.999106 + 0.0422772i \(0.986539\pi\)
\(468\) −110779. −0.0233798
\(469\) 0 0
\(470\) 133408. 0.0278572
\(471\) 1.82423e6 + 3.15967e6i 0.378903 + 0.656280i
\(472\) 716022. 1.24019e6i 0.147935 0.256231i
\(473\) 644872. 1.11695e6i 0.132532 0.229552i
\(474\) −604728. 1.04742e6i −0.123627 0.214129i
\(475\) −1.97267e6 −0.401163
\(476\) 0 0
\(477\) −1.10960e6 −0.223291
\(478\) −1.62950e6 2.82239e6i −0.326201 0.564998i
\(479\) 696248. 1.20594e6i 0.138652 0.240152i −0.788335 0.615247i \(-0.789056\pi\)
0.926986 + 0.375095i \(0.122390\pi\)
\(480\) 20747.6 35936.0i 0.00411022 0.00711912i
\(481\) 129861. + 224926.i 0.0255927 + 0.0443278i
\(482\) 4.19053e6 0.821583
\(483\) 0 0
\(484\) −2.36081e6 −0.458087
\(485\) −342837. 593812.i −0.0661811 0.114629i
\(486\) 118098. 204552.i 0.0226805 0.0392837i
\(487\) −4.91460e6 + 8.51233e6i −0.939000 + 1.62640i −0.171659 + 0.985156i \(0.554913\pi\)
−0.767341 + 0.641239i \(0.778421\pi\)
\(488\) −406147. 703467.i −0.0772029 0.133719i
\(489\) 347568. 0.0657306
\(490\) 0 0
\(491\) −7.67255e6 −1.43627 −0.718135 0.695904i \(-0.755004\pi\)
−0.718135 + 0.695904i \(0.755004\pi\)
\(492\) −58997.9 102187.i −0.0109881 0.0190320i
\(493\) −97477.9 + 168837.i −0.0180630 + 0.0312859i
\(494\) −108621. + 188136.i −0.0200260 + 0.0346861i
\(495\) 21187.7 + 36698.1i 0.00388660 + 0.00673180i
\(496\) 71458.9 0.0130422
\(497\) 0 0
\(498\) −2.18070e6 −0.394024
\(499\) −1.69691e6 2.93914e6i −0.305076 0.528408i 0.672202 0.740368i \(-0.265349\pi\)
−0.977278 + 0.211960i \(0.932015\pi\)
\(500\) 224396. 388665.i 0.0401412 0.0695266i
\(501\) 932646. 1.61539e6i 0.166006 0.287530i
\(502\) −2.18802e6 3.78976e6i −0.387518 0.671201i
\(503\) −8.36268e6 −1.47376 −0.736878 0.676026i \(-0.763701\pi\)
−0.736878 + 0.676026i \(0.763701\pi\)
\(504\) 0 0
\(505\) 484671. 0.0845704
\(506\) −633805. 1.09778e6i −0.110047 0.190607i
\(507\) 1.63794e6 2.83700e6i 0.282995 0.490161i
\(508\) −115498. + 200049.i −0.0198571 + 0.0343935i
\(509\) −1.93662e6 3.35432e6i −0.331322 0.573866i 0.651450 0.758692i \(-0.274161\pi\)
−0.982771 + 0.184826i \(0.940828\pi\)
\(510\) −5392.14 −0.000917986
\(511\) 0 0
\(512\) −262144. −0.0441942
\(513\) −231595. 401134.i −0.0388540 0.0672971i
\(514\) −1.55678e6 + 2.69642e6i −0.259908 + 0.450174i
\(515\) −271590. + 470409.i −0.0451228 + 0.0781551i
\(516\) −799216. 1.38428e6i −0.132142 0.228876i
\(517\) 860672. 0.141616
\(518\) 0 0
\(519\) −1.15432e6 −0.188108
\(520\) −12315.6 21331.3i −0.00199732 0.00345947i
\(521\) −365532. + 633120.i −0.0589971 + 0.102186i −0.894015 0.448036i \(-0.852124\pi\)
0.835018 + 0.550222i \(0.185457\pi\)
\(522\) 949398. 1.64441e6i 0.152501 0.264139i
\(523\) 3.55427e6 + 6.15618e6i 0.568193 + 0.984140i 0.996745 + 0.0806223i \(0.0256908\pi\)
−0.428551 + 0.903517i \(0.640976\pi\)
\(524\) 5.10746e6 0.812600
\(525\) 0 0
\(526\) −4.43905e6 −0.699561
\(527\) −4642.90 8041.73i −0.000728220 0.00126131i
\(528\) 133852. 231838.i 0.0208949 0.0361910i
\(529\) −501258. + 868205.i −0.0778794 + 0.134891i
\(530\) −123358. 213663.i −0.0190756 0.0330400i
\(531\) 1.81243e6 0.278949
\(532\) 0 0
\(533\) −70041.3 −0.0106791
\(534\) 1.65942e6 + 2.87420e6i 0.251828 + 0.436179i
\(535\) −193866. + 335786.i −0.0292831 + 0.0507198i
\(536\) −1.67371e6 + 2.89895e6i −0.251633 + 0.435841i
\(537\) 443698. + 768507.i 0.0663974 + 0.115004i
\(538\) −5.34562e6 −0.796237
\(539\) 0 0
\(540\) 52517.5 0.00775031
\(541\) −1.89757e6 3.28669e6i −0.278743 0.482798i 0.692329 0.721582i \(-0.256585\pi\)
−0.971073 + 0.238784i \(0.923251\pi\)
\(542\) 3.58402e6 6.20771e6i 0.524050 0.907680i
\(543\) −2.69651e6 + 4.67050e6i −0.392467 + 0.679772i
\(544\) 17032.3 + 29500.8i 0.00246760 + 0.00427401i
\(545\) −297793. −0.0429461
\(546\) 0 0
\(547\) −1.34686e7 −1.92466 −0.962332 0.271879i \(-0.912355\pi\)
−0.962332 + 0.271879i \(0.912355\pi\)
\(548\) 404272. + 700219.i 0.0575072 + 0.0996053i
\(549\) 514030. 890325.i 0.0727876 0.126072i
\(550\) 721482. 1.24964e6i 0.101700 0.176149i
\(551\) −1.86181e6 3.22474e6i −0.261250 0.452498i
\(552\) −1.57100e6 −0.219446
\(553\) 0 0
\(554\) −230310. −0.0318815
\(555\) −61564.0 106632.i −0.00848387 0.0146945i
\(556\) −1.79030e6 + 3.10089e6i −0.245606 + 0.425401i
\(557\) −2.44744e6 + 4.23908e6i −0.334251 + 0.578941i −0.983341 0.181772i \(-0.941817\pi\)
0.649089 + 0.760712i \(0.275150\pi\)
\(558\) 45220.1 + 78323.5i 0.00614817 + 0.0106489i
\(559\) −948816. −0.128426
\(560\) 0 0
\(561\) −34787.0 −0.00466670
\(562\) −1.10051e6 1.90615e6i −0.146979 0.254575i
\(563\) 3.12803e6 5.41790e6i 0.415910 0.720378i −0.579613 0.814892i \(-0.696796\pi\)
0.995524 + 0.0945139i \(0.0301297\pi\)
\(564\) 533333. 923759.i 0.0705993 0.122282i
\(565\) −296285. 513180.i −0.0390470 0.0676315i
\(566\) 4.71152e6 0.618188
\(567\) 0 0
\(568\) −3.85474e6 −0.501330
\(569\) −714125. 1.23690e6i −0.0924685 0.160160i 0.816081 0.577938i \(-0.196142\pi\)
−0.908549 + 0.417778i \(0.862809\pi\)
\(570\) 51494.4 89190.9i 0.00663854 0.0114983i
\(571\) −4.52573e6 + 7.83880e6i −0.580897 + 1.00614i 0.414477 + 0.910060i \(0.363965\pi\)
−0.995373 + 0.0960825i \(0.969369\pi\)
\(572\) −79453.5 137617.i −0.0101537 0.0175867i
\(573\) 7.46295e6 0.949563
\(574\) 0 0
\(575\) −8.46792e6 −1.06809
\(576\) −165888. 287326.i −0.0208333 0.0360844i
\(577\) −4.00960e6 + 6.94482e6i −0.501373 + 0.868404i 0.498626 + 0.866817i \(0.333838\pi\)
−0.999999 + 0.00158626i \(0.999495\pi\)
\(578\) −2.83750e6 + 4.91470e6i −0.353278 + 0.611895i
\(579\) 1.87373e6 + 3.24540e6i 0.232280 + 0.402320i
\(580\) 422191. 0.0521122
\(581\) 0 0
\(582\) −5.48232e6 −0.670899
\(583\) −795838. 1.37843e6i −0.0969735 0.167963i
\(584\) 2.46267e6 4.26547e6i 0.298795 0.517529i
\(585\) 15587.0 26997.4i 0.00188309 0.00326162i
\(586\) 601524. + 1.04187e6i 0.0723617 + 0.125334i
\(587\) −8.28470e6 −0.992388 −0.496194 0.868212i \(-0.665270\pi\)
−0.496194 + 0.868212i \(0.665270\pi\)
\(588\) 0 0
\(589\) 177357. 0.0210649
\(590\) 201494. + 348998.i 0.0238305 + 0.0412756i
\(591\) 2.66427e6 4.61466e6i 0.313769 0.543464i
\(592\) −388927. + 673641.i −0.0456104 + 0.0789995i
\(593\) −2.95722e6 5.12205e6i −0.345340 0.598146i 0.640076 0.768312i \(-0.278903\pi\)
−0.985415 + 0.170166i \(0.945570\pi\)
\(594\) 338813. 0.0393998
\(595\) 0 0
\(596\) 4.15234e6 0.478825
\(597\) 4.79736e6 + 8.30927e6i 0.550892 + 0.954173i
\(598\) −466266. + 807597.i −0.0533189 + 0.0923510i
\(599\) −1.66449e6 + 2.88298e6i −0.189545 + 0.328302i −0.945099 0.326785i \(-0.894035\pi\)
0.755553 + 0.655087i \(0.227368\pi\)
\(600\) −894161. 1.54873e6i −0.101400 0.175630i
\(601\) −4.87081e6 −0.550066 −0.275033 0.961435i \(-0.588689\pi\)
−0.275033 + 0.961435i \(0.588689\pi\)
\(602\) 0 0
\(603\) −4.23657e6 −0.474484
\(604\) 887142. + 1.53658e6i 0.0989466 + 0.171381i
\(605\) 332175. 575345.i 0.0368960 0.0639057i
\(606\) 1.93760e6 3.35601e6i 0.214329 0.371229i
\(607\) 7.58504e6 + 1.31377e7i 0.835577 + 1.44726i 0.893560 + 0.448944i \(0.148200\pi\)
−0.0579835 + 0.998318i \(0.518467\pi\)
\(608\) −650626. −0.0713793
\(609\) 0 0
\(610\) 228586. 0.0248728
\(611\) −316582. 548336.i −0.0343070 0.0594216i
\(612\) −21556.5 + 37336.9i −0.00232648 + 0.00402958i
\(613\) −2.59078e6 + 4.48736e6i −0.278471 + 0.482325i −0.971005 0.239060i \(-0.923161\pi\)
0.692534 + 0.721385i \(0.256494\pi\)
\(614\) 293573. + 508483.i 0.0314264 + 0.0544322i
\(615\) 33204.9 0.00354009
\(616\) 0 0
\(617\) 1.55854e6 0.164818 0.0824092 0.996599i \(-0.473739\pi\)
0.0824092 + 0.996599i \(0.473739\pi\)
\(618\) 2.17151e6 + 3.76116e6i 0.228712 + 0.396142i
\(619\) 703756. 1.21894e6i 0.0738236 0.127866i −0.826750 0.562569i \(-0.809813\pi\)
0.900574 + 0.434703i \(0.143146\pi\)
\(620\) −10054.5 + 17415.0i −0.00105047 + 0.00181947i
\(621\) −994147. 1.72191e6i −0.103448 0.179177i
\(622\) −6.81243e6 −0.706035
\(623\) 0 0
\(624\) −196940. −0.0202475
\(625\) −4.78799e6 8.29304e6i −0.490290 0.849207i
\(626\) 2.23389e6 3.86922e6i 0.227838 0.394628i
\(627\) 332213. 575409.i 0.0337479 0.0584531i
\(628\) 3.24308e6 + 5.61719e6i 0.328140 + 0.568355i
\(629\) 101079. 0.0101867
\(630\) 0 0
\(631\) −1.09643e7 −1.09624 −0.548120 0.836399i \(-0.684656\pi\)
−0.548120 + 0.836399i \(0.684656\pi\)
\(632\) −1.07507e6 1.86208e6i −0.107064 0.185441i
\(633\) 3.80713e6 6.59415e6i 0.377649 0.654108i
\(634\) −1.92579e6 + 3.33556e6i −0.190277 + 0.329569i
\(635\) −32502.1 56295.3i −0.00319873 0.00554036i
\(636\) −1.97263e6 −0.193376
\(637\) 0 0
\(638\) 2.72374e6 0.264919
\(639\) −2.43932e6 4.22503e6i −0.236329 0.409334i
\(640\) 36884.7 63886.2i 0.00355956 0.00616534i
\(641\) 7.10609e6 1.23081e7i 0.683103 1.18317i −0.290926 0.956745i \(-0.593964\pi\)
0.974029 0.226423i \(-0.0727032\pi\)
\(642\) 1.55006e6 + 2.68478e6i 0.148426 + 0.257082i
\(643\) −9.13928e6 −0.871735 −0.435868 0.900011i \(-0.643558\pi\)
−0.435868 + 0.900011i \(0.643558\pi\)
\(644\) 0 0
\(645\) 449811. 0.0425727
\(646\) 42273.1 + 73219.1i 0.00398550 + 0.00690309i
\(647\) 9.46362e6 1.63915e7i 0.888785 1.53942i 0.0474724 0.998873i \(-0.484883\pi\)
0.841313 0.540549i \(-0.181783\pi\)
\(648\) 209952. 363648.i 0.0196419 0.0340207i
\(649\) 1.29993e6 + 2.25154e6i 0.121145 + 0.209830i
\(650\) −1.06153e6 −0.0985487
\(651\) 0 0
\(652\) 617899. 0.0569244
\(653\) 2.14991e6 + 3.72376e6i 0.197305 + 0.341742i 0.947654 0.319300i \(-0.103448\pi\)
−0.750349 + 0.661042i \(0.770114\pi\)
\(654\) −1.19051e6 + 2.06202e6i −0.108840 + 0.188516i
\(655\) −718640. + 1.24472e6i −0.0654498 + 0.113362i
\(656\) −104885. 181666.i −0.00951599 0.0164822i
\(657\) 6.23363e6 0.563414
\(658\) 0 0
\(659\) −1.15303e7 −1.03425 −0.517126 0.855909i \(-0.672998\pi\)
−0.517126 + 0.855909i \(0.672998\pi\)
\(660\) 37667.0 + 65241.1i 0.00336590 + 0.00582991i
\(661\) −7.35237e6 + 1.27347e7i −0.654521 + 1.13366i 0.327492 + 0.944854i \(0.393796\pi\)
−0.982014 + 0.188810i \(0.939537\pi\)
\(662\) −4.51990e6 + 7.82870e6i −0.400852 + 0.694296i
\(663\) 12795.8 + 22162.9i 0.00113053 + 0.00195814i
\(664\) −3.87680e6 −0.341234
\(665\) 0 0
\(666\) −984471. −0.0860037
\(667\) −7.99202e6 1.38426e7i −0.695572 1.20477i
\(668\) 1.65804e6 2.87181e6i 0.143765 0.249008i
\(669\) −505346. + 875286.i −0.0436540 + 0.0756109i
\(670\) −470994. 815786.i −0.0405349 0.0702084i
\(671\) 1.47471e6 0.126444
\(672\) 0 0
\(673\) 1.42971e7 1.21678 0.608389 0.793639i \(-0.291816\pi\)
0.608389 + 0.793639i \(0.291816\pi\)
\(674\) 2.66676e6 + 4.61896e6i 0.226117 + 0.391647i
\(675\) 1.13167e6 1.96012e6i 0.0956008 0.165585i
\(676\) 2.91189e6 5.04355e6i 0.245080 0.424492i
\(677\) −4.56012e6 7.89836e6i −0.382389 0.662316i 0.609015 0.793159i \(-0.291565\pi\)
−0.991403 + 0.130843i \(0.958232\pi\)
\(678\) −4.73790e6 −0.395832
\(679\) 0 0
\(680\) −9586.03 −0.000794999
\(681\) 803146. + 1.39109e6i 0.0663631 + 0.114944i
\(682\) −64866.2 + 112352.i −0.00534020 + 0.00924950i
\(683\) 7.25762e6 1.25706e7i 0.595309 1.03111i −0.398194 0.917301i \(-0.630363\pi\)
0.993503 0.113804i \(-0.0363037\pi\)
\(684\) −411724. 713127.i −0.0336485 0.0582810i
\(685\) −227530. −0.0185273
\(686\) 0 0
\(687\) 4.13778e6 0.334484
\(688\) −1.42083e6 2.46095e6i −0.114438 0.198212i
\(689\) −585468. + 1.01406e6i −0.0469846 + 0.0813796i
\(690\) 221046. 382862.i 0.0176750 0.0306140i
\(691\) −1.04254e6 1.80573e6i −0.0830608 0.143866i 0.821502 0.570205i \(-0.193136\pi\)
−0.904563 + 0.426339i \(0.859803\pi\)
\(692\) −2.05212e6 −0.162906
\(693\) 0 0
\(694\) 5.73945e6 0.452347
\(695\) −503804. 872613.i −0.0395639 0.0685267i
\(696\) 1.68782e6 2.92339e6i 0.132070 0.228751i
\(697\) −13629.4 + 23606.8i −0.00106266 + 0.00184058i
\(698\) 6.69422e6 + 1.15947e7i 0.520069 + 0.900787i
\(699\) 6.73801e6 0.521601
\(700\) 0 0
\(701\) 9.96513e6 0.765928 0.382964 0.923763i \(-0.374903\pi\)
0.382964 + 0.923763i \(0.374903\pi\)
\(702\) −124626. 215858.i −0.00954477 0.0165320i
\(703\) −965293. + 1.67194e6i −0.0736667 + 0.127594i
\(704\) 237959. 412157.i 0.0180955 0.0313423i
\(705\) 150084. + 259953.i 0.0113726 + 0.0196980i
\(706\) −1.60167e7 −1.20938
\(707\) 0 0
\(708\) 3.22210e6 0.241577
\(709\) −3.54518e6 6.14043e6i −0.264864 0.458757i 0.702664 0.711522i \(-0.251994\pi\)
−0.967528 + 0.252764i \(0.918660\pi\)
\(710\) 542376. 939423.i 0.0403789 0.0699384i
\(711\) 1.36064e6 2.35669e6i 0.100941 0.174835i
\(712\) 2.95008e6 + 5.10969e6i 0.218089 + 0.377742i
\(713\) 761324. 0.0560849
\(714\) 0 0
\(715\) 44717.6 0.00327125
\(716\) 788796. + 1.36623e6i 0.0575019 + 0.0995962i
\(717\) 3.66639e6 6.35037e6i 0.266342 0.461319i
\(718\) −1.19197e6 + 2.06456e6i −0.0862889 + 0.149457i
\(719\) −6.00833e6 1.04067e7i −0.433443 0.750745i 0.563724 0.825963i \(-0.309368\pi\)
−0.997167 + 0.0752181i \(0.976035\pi\)
\(720\) 93364.4 0.00671197
\(721\) 0 0
\(722\) 8.28958e6 0.591820
\(723\) 4.71435e6 + 8.16549e6i 0.335410 + 0.580947i
\(724\) −4.79380e6 + 8.30310e6i −0.339886 + 0.588700i
\(725\) 9.09760e6 1.57575e7i 0.642809 1.11338i
\(726\) −2.65591e6 4.60017e6i −0.187013 0.323916i
\(727\) 1.32577e7 0.930318 0.465159 0.885227i \(-0.345997\pi\)
0.465159 + 0.885227i \(0.345997\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 693014. + 1.20034e6i 0.0481321 + 0.0833673i
\(731\) −184631. + 319790.i −0.0127794 + 0.0221346i
\(732\) 913830. 1.58280e6i 0.0630359 0.109181i
\(733\) 454651. + 787479.i 0.0312549 + 0.0541351i 0.881230 0.472688i \(-0.156716\pi\)
−0.849975 + 0.526823i \(0.823383\pi\)
\(734\) 1.32156e7 0.905413
\(735\) 0 0
\(736\) −2.79289e6 −0.190046
\(737\) −3.03859e6 5.26299e6i −0.206064 0.356914i
\(738\) 132745. 229921.i 0.00897176 0.0155396i
\(739\) 143426. 248421.i 0.00966086 0.0167331i −0.861155 0.508343i \(-0.830258\pi\)
0.870815 + 0.491610i \(0.163591\pi\)
\(740\) −109447. 189568.i −0.00734725 0.0127258i
\(741\) −488792. −0.0327024
\(742\) 0 0
\(743\) −1.35906e6 −0.0903163 −0.0451582 0.998980i \(-0.514379\pi\)
−0.0451582 + 0.998980i \(0.514379\pi\)
\(744\) 80391.3 + 139242.i 0.00532447 + 0.00922226i
\(745\) −584250. + 1.01195e6i −0.0385663 + 0.0667988i
\(746\) −5.66126e6 + 9.80559e6i −0.372448 + 0.645100i
\(747\) −2.45329e6 4.24921e6i −0.160859 0.278617i
\(748\) −61843.6 −0.00404148
\(749\) 0 0
\(750\) 1.00978e6 0.0655503
\(751\) −7.72018e6 1.33718e7i −0.499491 0.865144i 0.500509 0.865732i \(-0.333146\pi\)
−1.00000 0.000587430i \(0.999813\pi\)
\(752\) 948147. 1.64224e6i 0.0611408 0.105899i
\(753\) 4.92305e6 8.52697e6i 0.316407 0.548034i
\(754\) −1.00188e6 1.73530e6i −0.0641779 0.111159i
\(755\) −499298. −0.0318781
\(756\) 0 0
\(757\) 1.70683e7 1.08256 0.541279 0.840843i \(-0.317940\pi\)
0.541279 + 0.840843i \(0.317940\pi\)
\(758\) 4.90050e6 + 8.48792e6i 0.309790 + 0.536572i
\(759\) 1.42606e6 2.47001e6i 0.0898532 0.155630i
\(760\) 91545.6 158562.i 0.00574915 0.00995782i
\(761\) −1.54173e6 2.67035e6i −0.0965041 0.167150i 0.813731 0.581241i \(-0.197433\pi\)
−0.910235 + 0.414091i \(0.864099\pi\)
\(762\) −519742. −0.0324265
\(763\) 0 0
\(764\) 1.32675e7 0.822346
\(765\) −6066.16 10506.9i −0.000374766 0.000649114i
\(766\) −6.76810e6 + 1.17227e7i −0.416768 + 0.721864i
\(767\) 956307. 1.65637e6i 0.0586960 0.101665i
\(768\) −294912. 510803.i −0.0180422 0.0312500i