Properties

Label 10.6.b.a.9.1
Level $10$
Weight $6$
Character 10.9
Analytic conductor $1.604$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 10.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.60383819813\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 9.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 10.9
Dual form 10.6.b.a.9.2

$q$-expansion

\(f(q)\) \(=\) \(q-4.00000i q^{2} -14.0000i q^{3} -16.0000 q^{4} +(55.0000 - 10.0000i) q^{5} -56.0000 q^{6} +158.000i q^{7} +64.0000i q^{8} +47.0000 q^{9} +O(q^{10})\) \(q-4.00000i q^{2} -14.0000i q^{3} -16.0000 q^{4} +(55.0000 - 10.0000i) q^{5} -56.0000 q^{6} +158.000i q^{7} +64.0000i q^{8} +47.0000 q^{9} +(-40.0000 - 220.000i) q^{10} -148.000 q^{11} +224.000i q^{12} -684.000i q^{13} +632.000 q^{14} +(-140.000 - 770.000i) q^{15} +256.000 q^{16} +2048.00i q^{17} -188.000i q^{18} -2220.00 q^{19} +(-880.000 + 160.000i) q^{20} +2212.00 q^{21} +592.000i q^{22} +1246.00i q^{23} +896.000 q^{24} +(2925.00 - 1100.00i) q^{25} -2736.00 q^{26} -4060.00i q^{27} -2528.00i q^{28} +270.000 q^{29} +(-3080.00 + 560.000i) q^{30} -2048.00 q^{31} -1024.00i q^{32} +2072.00i q^{33} +8192.00 q^{34} +(1580.00 + 8690.00i) q^{35} -752.000 q^{36} -4372.00i q^{37} +8880.00i q^{38} -9576.00 q^{39} +(640.000 + 3520.00i) q^{40} -2398.00 q^{41} -8848.00i q^{42} -2294.00i q^{43} +2368.00 q^{44} +(2585.00 - 470.000i) q^{45} +4984.00 q^{46} -10682.0i q^{47} -3584.00i q^{48} -8157.00 q^{49} +(-4400.00 - 11700.0i) q^{50} +28672.0 q^{51} +10944.0i q^{52} -2964.00i q^{53} -16240.0 q^{54} +(-8140.00 + 1480.00i) q^{55} -10112.0 q^{56} +31080.0i q^{57} -1080.00i q^{58} +39740.0 q^{59} +(2240.00 + 12320.0i) q^{60} -42298.0 q^{61} +8192.00i q^{62} +7426.00i q^{63} -4096.00 q^{64} +(-6840.00 - 37620.0i) q^{65} +8288.00 q^{66} +32098.0i q^{67} -32768.0i q^{68} +17444.0 q^{69} +(34760.0 - 6320.00i) q^{70} -4248.00 q^{71} +3008.00i q^{72} -30104.0i q^{73} -17488.0 q^{74} +(-15400.0 - 40950.0i) q^{75} +35520.0 q^{76} -23384.0i q^{77} +38304.0i q^{78} -35280.0 q^{79} +(14080.0 - 2560.00i) q^{80} -45419.0 q^{81} +9592.00i q^{82} +27826.0i q^{83} -35392.0 q^{84} +(20480.0 + 112640. i) q^{85} -9176.00 q^{86} -3780.00i q^{87} -9472.00i q^{88} +85210.0 q^{89} +(-1880.00 - 10340.0i) q^{90} +108072. q^{91} -19936.0i q^{92} +28672.0i q^{93} -42728.0 q^{94} +(-122100. + 22200.0i) q^{95} -14336.0 q^{96} -97232.0i q^{97} +32628.0i q^{98} -6956.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 32q^{4} + 110q^{5} - 112q^{6} + 94q^{9} + O(q^{10}) \) \( 2q - 32q^{4} + 110q^{5} - 112q^{6} + 94q^{9} - 80q^{10} - 296q^{11} + 1264q^{14} - 280q^{15} + 512q^{16} - 4440q^{19} - 1760q^{20} + 4424q^{21} + 1792q^{24} + 5850q^{25} - 5472q^{26} + 540q^{29} - 6160q^{30} - 4096q^{31} + 16384q^{34} + 3160q^{35} - 1504q^{36} - 19152q^{39} + 1280q^{40} - 4796q^{41} + 4736q^{44} + 5170q^{45} + 9968q^{46} - 16314q^{49} - 8800q^{50} + 57344q^{51} - 32480q^{54} - 16280q^{55} - 20224q^{56} + 79480q^{59} + 4480q^{60} - 84596q^{61} - 8192q^{64} - 13680q^{65} + 16576q^{66} + 34888q^{69} + 69520q^{70} - 8496q^{71} - 34976q^{74} - 30800q^{75} + 71040q^{76} - 70560q^{79} + 28160q^{80} - 90838q^{81} - 70784q^{84} + 40960q^{85} - 18352q^{86} + 170420q^{89} - 3760q^{90} + 216144q^{91} - 85456q^{94} - 244200q^{95} - 28672q^{96} - 13912q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000i 0.707107i
\(3\) 14.0000i 0.898100i −0.893507 0.449050i \(-0.851762\pi\)
0.893507 0.449050i \(-0.148238\pi\)
\(4\) −16.0000 −0.500000
\(5\) 55.0000 10.0000i 0.983870 0.178885i
\(6\) −56.0000 −0.635053
\(7\) 158.000i 1.21874i 0.792885 + 0.609371i \(0.208578\pi\)
−0.792885 + 0.609371i \(0.791422\pi\)
\(8\) 64.0000i 0.353553i
\(9\) 47.0000 0.193416
\(10\) −40.0000 220.000i −0.126491 0.695701i
\(11\) −148.000 −0.368791 −0.184395 0.982852i \(-0.559033\pi\)
−0.184395 + 0.982852i \(0.559033\pi\)
\(12\) 224.000i 0.449050i
\(13\) 684.000i 1.12253i −0.827636 0.561265i \(-0.810315\pi\)
0.827636 0.561265i \(-0.189685\pi\)
\(14\) 632.000 0.861781
\(15\) −140.000 770.000i −0.160657 0.883614i
\(16\) 256.000 0.250000
\(17\) 2048.00i 1.71873i 0.511363 + 0.859365i \(0.329141\pi\)
−0.511363 + 0.859365i \(0.670859\pi\)
\(18\) 188.000i 0.136766i
\(19\) −2220.00 −1.41081 −0.705406 0.708804i \(-0.749235\pi\)
−0.705406 + 0.708804i \(0.749235\pi\)
\(20\) −880.000 + 160.000i −0.491935 + 0.0894427i
\(21\) 2212.00 1.09455
\(22\) 592.000i 0.260774i
\(23\) 1246.00i 0.491132i 0.969380 + 0.245566i \(0.0789738\pi\)
−0.969380 + 0.245566i \(0.921026\pi\)
\(24\) 896.000 0.317526
\(25\) 2925.00 1100.00i 0.936000 0.352000i
\(26\) −2736.00 −0.793748
\(27\) 4060.00i 1.07181i
\(28\) 2528.00i 0.609371i
\(29\) 270.000 0.0596168 0.0298084 0.999556i \(-0.490510\pi\)
0.0298084 + 0.999556i \(0.490510\pi\)
\(30\) −3080.00 + 560.000i −0.624809 + 0.113602i
\(31\) −2048.00 −0.382759 −0.191380 0.981516i \(-0.561296\pi\)
−0.191380 + 0.981516i \(0.561296\pi\)
\(32\) 1024.00i 0.176777i
\(33\) 2072.00i 0.331211i
\(34\) 8192.00 1.21533
\(35\) 1580.00 + 8690.00i 0.218015 + 1.19908i
\(36\) −752.000 −0.0967078
\(37\) 4372.00i 0.525020i −0.964929 0.262510i \(-0.915450\pi\)
0.964929 0.262510i \(-0.0845503\pi\)
\(38\) 8880.00i 0.997594i
\(39\) −9576.00 −1.00814
\(40\) 640.000 + 3520.00i 0.0632456 + 0.347851i
\(41\) −2398.00 −0.222787 −0.111393 0.993776i \(-0.535531\pi\)
−0.111393 + 0.993776i \(0.535531\pi\)
\(42\) 8848.00i 0.773966i
\(43\) 2294.00i 0.189200i −0.995515 0.0946002i \(-0.969843\pi\)
0.995515 0.0946002i \(-0.0301573\pi\)
\(44\) 2368.00 0.184395
\(45\) 2585.00 470.000i 0.190296 0.0345992i
\(46\) 4984.00 0.347283
\(47\) 10682.0i 0.705355i −0.935745 0.352678i \(-0.885271\pi\)
0.935745 0.352678i \(-0.114729\pi\)
\(48\) 3584.00i 0.224525i
\(49\) −8157.00 −0.485333
\(50\) −4400.00 11700.0i −0.248902 0.661852i
\(51\) 28672.0 1.54359
\(52\) 10944.0i 0.561265i
\(53\) 2964.00i 0.144940i −0.997371 0.0724700i \(-0.976912\pi\)
0.997371 0.0724700i \(-0.0230882\pi\)
\(54\) −16240.0 −0.757882
\(55\) −8140.00 + 1480.00i −0.362842 + 0.0659713i
\(56\) −10112.0 −0.430891
\(57\) 31080.0i 1.26705i
\(58\) 1080.00i 0.0421555i
\(59\) 39740.0 1.48627 0.743135 0.669141i \(-0.233338\pi\)
0.743135 + 0.669141i \(0.233338\pi\)
\(60\) 2240.00 + 12320.0i 0.0803285 + 0.441807i
\(61\) −42298.0 −1.45544 −0.727722 0.685873i \(-0.759421\pi\)
−0.727722 + 0.685873i \(0.759421\pi\)
\(62\) 8192.00i 0.270652i
\(63\) 7426.00i 0.235724i
\(64\) −4096.00 −0.125000
\(65\) −6840.00 37620.0i −0.200804 1.10442i
\(66\) 8288.00 0.234202
\(67\) 32098.0i 0.873556i 0.899569 + 0.436778i \(0.143881\pi\)
−0.899569 + 0.436778i \(0.856119\pi\)
\(68\) 32768.0i 0.859365i
\(69\) 17444.0 0.441086
\(70\) 34760.0 6320.00i 0.847881 0.154160i
\(71\) −4248.00 −0.100009 −0.0500044 0.998749i \(-0.515924\pi\)
−0.0500044 + 0.998749i \(0.515924\pi\)
\(72\) 3008.00i 0.0683828i
\(73\) 30104.0i 0.661176i −0.943775 0.330588i \(-0.892753\pi\)
0.943775 0.330588i \(-0.107247\pi\)
\(74\) −17488.0 −0.371245
\(75\) −15400.0 40950.0i −0.316131 0.840622i
\(76\) 35520.0 0.705406
\(77\) 23384.0i 0.449461i
\(78\) 38304.0i 0.712866i
\(79\) −35280.0 −0.636005 −0.318003 0.948090i \(-0.603012\pi\)
−0.318003 + 0.948090i \(0.603012\pi\)
\(80\) 14080.0 2560.00i 0.245967 0.0447214i
\(81\) −45419.0 −0.769175
\(82\) 9592.00i 0.157534i
\(83\) 27826.0i 0.443359i 0.975120 + 0.221680i \(0.0711539\pi\)
−0.975120 + 0.221680i \(0.928846\pi\)
\(84\) −35392.0 −0.547277
\(85\) 20480.0 + 112640.i 0.307456 + 1.69101i
\(86\) −9176.00 −0.133785
\(87\) 3780.00i 0.0535419i
\(88\) 9472.00i 0.130387i
\(89\) 85210.0 1.14029 0.570145 0.821544i \(-0.306887\pi\)
0.570145 + 0.821544i \(0.306887\pi\)
\(90\) −1880.00 10340.0i −0.0244654 0.134559i
\(91\) 108072. 1.36807
\(92\) 19936.0i 0.245566i
\(93\) 28672.0i 0.343756i
\(94\) −42728.0 −0.498762
\(95\) −122100. + 22200.0i −1.38805 + 0.252374i
\(96\) −14336.0 −0.158763
\(97\) 97232.0i 1.04925i −0.851333 0.524626i \(-0.824205\pi\)
0.851333 0.524626i \(-0.175795\pi\)
\(98\) 32628.0i 0.343183i
\(99\) −6956.00 −0.0713299
\(100\) −46800.0 + 17600.0i −0.468000 + 0.176000i
\(101\) −4298.00 −0.0419240 −0.0209620 0.999780i \(-0.506673\pi\)
−0.0209620 + 0.999780i \(0.506673\pi\)
\(102\) 114688.i 1.09148i
\(103\) 124114.i 1.15273i −0.817192 0.576365i \(-0.804471\pi\)
0.817192 0.576365i \(-0.195529\pi\)
\(104\) 43776.0 0.396874
\(105\) 121660. 22120.0i 1.07690 0.195800i
\(106\) −11856.0 −0.102488
\(107\) 42342.0i 0.357530i −0.983892 0.178765i \(-0.942790\pi\)
0.983892 0.178765i \(-0.0572101\pi\)
\(108\) 64960.0i 0.535904i
\(109\) 35990.0 0.290145 0.145073 0.989421i \(-0.453658\pi\)
0.145073 + 0.989421i \(0.453658\pi\)
\(110\) 5920.00 + 32560.0i 0.0466487 + 0.256568i
\(111\) −61208.0 −0.471521
\(112\) 40448.0i 0.304686i
\(113\) 228816.i 1.68574i 0.538118 + 0.842869i \(0.319135\pi\)
−0.538118 + 0.842869i \(0.680865\pi\)
\(114\) 124320. 0.895940
\(115\) 12460.0 + 68530.0i 0.0878564 + 0.483210i
\(116\) −4320.00 −0.0298084
\(117\) 32148.0i 0.217115i
\(118\) 158960.i 1.05095i
\(119\) −323584. −2.09469
\(120\) 49280.0 8960.00i 0.312405 0.0568009i
\(121\) −139147. −0.863993
\(122\) 169192.i 1.02915i
\(123\) 33572.0i 0.200085i
\(124\) 32768.0 0.191380
\(125\) 149875. 89750.0i 0.857935 0.513759i
\(126\) 29704.0 0.166682
\(127\) 175238.i 0.964093i 0.876146 + 0.482047i \(0.160106\pi\)
−0.876146 + 0.482047i \(0.839894\pi\)
\(128\) 16384.0i 0.0883883i
\(129\) −32116.0 −0.169921
\(130\) −150480. + 27360.0i −0.780945 + 0.141990i
\(131\) 299652. 1.52559 0.762797 0.646638i \(-0.223826\pi\)
0.762797 + 0.646638i \(0.223826\pi\)
\(132\) 33152.0i 0.165606i
\(133\) 350760.i 1.71942i
\(134\) 128392. 0.617698
\(135\) −40600.0 223300.i −0.191731 1.05452i
\(136\) −131072. −0.607663
\(137\) 107928.i 0.491284i 0.969361 + 0.245642i \(0.0789988\pi\)
−0.969361 + 0.245642i \(0.921001\pi\)
\(138\) 69776.0i 0.311895i
\(139\) 196460. 0.862456 0.431228 0.902243i \(-0.358080\pi\)
0.431228 + 0.902243i \(0.358080\pi\)
\(140\) −25280.0 139040.i −0.109008 0.599542i
\(141\) −149548. −0.633480
\(142\) 16992.0i 0.0707170i
\(143\) 101232.i 0.413978i
\(144\) 12032.0 0.0483539
\(145\) 14850.0 2700.00i 0.0586552 0.0106646i
\(146\) −120416. −0.467522
\(147\) 114198.i 0.435878i
\(148\) 69952.0i 0.262510i
\(149\) −138850. −0.512366 −0.256183 0.966628i \(-0.582465\pi\)
−0.256183 + 0.966628i \(0.582465\pi\)
\(150\) −163800. + 61600.0i −0.594410 + 0.223539i
\(151\) 416152. 1.48528 0.742642 0.669688i \(-0.233572\pi\)
0.742642 + 0.669688i \(0.233572\pi\)
\(152\) 142080.i 0.498797i
\(153\) 96256.0i 0.332429i
\(154\) −93536.0 −0.317817
\(155\) −112640. + 20480.0i −0.376585 + 0.0684701i
\(156\) 153216. 0.504072
\(157\) 433108.i 1.40232i 0.713004 + 0.701160i \(0.247334\pi\)
−0.713004 + 0.701160i \(0.752666\pi\)
\(158\) 141120.i 0.449724i
\(159\) −41496.0 −0.130171
\(160\) −10240.0 56320.0i −0.0316228 0.173925i
\(161\) −196868. −0.598564
\(162\) 181676.i 0.543889i
\(163\) 149134.i 0.439651i −0.975539 0.219825i \(-0.929451\pi\)
0.975539 0.219825i \(-0.0705487\pi\)
\(164\) 38368.0 0.111393
\(165\) 20720.0 + 113960.i 0.0592488 + 0.325869i
\(166\) 111304. 0.313502
\(167\) 559602.i 1.55270i −0.630301 0.776351i \(-0.717068\pi\)
0.630301 0.776351i \(-0.282932\pi\)
\(168\) 141568.i 0.386983i
\(169\) −96563.0 −0.260072
\(170\) 450560. 81920.0i 1.19572 0.217404i
\(171\) −104340. −0.272873
\(172\) 36704.0i 0.0946002i
\(173\) 343804.i 0.873365i −0.899616 0.436682i \(-0.856153\pi\)
0.899616 0.436682i \(-0.143847\pi\)
\(174\) −15120.0 −0.0378598
\(175\) 173800. + 462150.i 0.428997 + 1.14074i
\(176\) −37888.0 −0.0921977
\(177\) 556360.i 1.33482i
\(178\) 340840.i 0.806307i
\(179\) −23980.0 −0.0559392 −0.0279696 0.999609i \(-0.508904\pi\)
−0.0279696 + 0.999609i \(0.508904\pi\)
\(180\) −41360.0 + 7520.00i −0.0951479 + 0.0172996i
\(181\) −651898. −1.47905 −0.739526 0.673128i \(-0.764950\pi\)
−0.739526 + 0.673128i \(0.764950\pi\)
\(182\) 432288.i 0.967375i
\(183\) 592172.i 1.30713i
\(184\) −79744.0 −0.173641
\(185\) −43720.0 240460.i −0.0939184 0.516551i
\(186\) 114688. 0.243072
\(187\) 303104.i 0.633852i
\(188\) 170912.i 0.352678i
\(189\) 641480. 1.30626
\(190\) 88800.0 + 488400.i 0.178455 + 0.981503i
\(191\) 202752. 0.402144 0.201072 0.979576i \(-0.435557\pi\)
0.201072 + 0.979576i \(0.435557\pi\)
\(192\) 57344.0i 0.112263i
\(193\) 452656.i 0.874732i 0.899284 + 0.437366i \(0.144089\pi\)
−0.899284 + 0.437366i \(0.855911\pi\)
\(194\) −388928. −0.741933
\(195\) −526680. + 95760.0i −0.991883 + 0.180342i
\(196\) 130512. 0.242667
\(197\) 337468.i 0.619537i 0.950812 + 0.309768i \(0.100252\pi\)
−0.950812 + 0.309768i \(0.899748\pi\)
\(198\) 27824.0i 0.0504379i
\(199\) 561000. 1.00422 0.502112 0.864803i \(-0.332557\pi\)
0.502112 + 0.864803i \(0.332557\pi\)
\(200\) 70400.0 + 187200.i 0.124451 + 0.330926i
\(201\) 449372. 0.784541
\(202\) 17192.0i 0.0296448i
\(203\) 42660.0i 0.0726576i
\(204\) −458752. −0.771796
\(205\) −131890. + 23980.0i −0.219193 + 0.0398533i
\(206\) −496456. −0.815103
\(207\) 58562.0i 0.0949927i
\(208\) 175104.i 0.280632i
\(209\) 328560. 0.520294
\(210\) −88480.0 486640.i −0.138451 0.761482i
\(211\) −805548. −1.24562 −0.622810 0.782373i \(-0.714009\pi\)
−0.622810 + 0.782373i \(0.714009\pi\)
\(212\) 47424.0i 0.0724700i
\(213\) 59472.0i 0.0898180i
\(214\) −169368. −0.252812
\(215\) −22940.0 126170.i −0.0338452 0.186149i
\(216\) 259840. 0.378941
\(217\) 323584.i 0.466485i
\(218\) 143960.i 0.205164i
\(219\) −421456. −0.593802
\(220\) 130240. 23680.0i 0.181421 0.0329856i
\(221\) 1.40083e6 1.92932
\(222\) 244832.i 0.333415i
\(223\) 1.21855e6i 1.64090i −0.571717 0.820451i \(-0.693722\pi\)
0.571717 0.820451i \(-0.306278\pi\)
\(224\) 161792. 0.215445
\(225\) 137475. 51700.0i 0.181037 0.0680823i
\(226\) 915264. 1.19200
\(227\) 564338.i 0.726900i 0.931614 + 0.363450i \(0.118401\pi\)
−0.931614 + 0.363450i \(0.881599\pi\)
\(228\) 497280.i 0.633525i
\(229\) −560330. −0.706082 −0.353041 0.935608i \(-0.614852\pi\)
−0.353041 + 0.935608i \(0.614852\pi\)
\(230\) 274120. 49840.0i 0.341681 0.0621239i
\(231\) −327376. −0.403661
\(232\) 17280.0i 0.0210777i
\(233\) 293576.i 0.354267i 0.984187 + 0.177134i \(0.0566824\pi\)
−0.984187 + 0.177134i \(0.943318\pi\)
\(234\) −128592. −0.153523
\(235\) −106820. 587510.i −0.126178 0.693978i
\(236\) −635840. −0.743135
\(237\) 493920.i 0.571197i
\(238\) 1.29434e6i 1.48117i
\(239\) −584240. −0.661602 −0.330801 0.943701i \(-0.607319\pi\)
−0.330801 + 0.943701i \(0.607319\pi\)
\(240\) −35840.0 197120.i −0.0401643 0.220903i
\(241\) −563798. −0.625289 −0.312645 0.949870i \(-0.601215\pi\)
−0.312645 + 0.949870i \(0.601215\pi\)
\(242\) 556588.i 0.610936i
\(243\) 350714.i 0.381011i
\(244\) 676768. 0.727722
\(245\) −448635. + 81570.0i −0.477505 + 0.0868191i
\(246\) 134288. 0.141481
\(247\) 1.51848e6i 1.58368i
\(248\) 131072.i 0.135326i
\(249\) 389564. 0.398181
\(250\) −359000. 599500.i −0.363282 0.606651i
\(251\) −1.01975e6 −1.02167 −0.510833 0.859680i \(-0.670663\pi\)
−0.510833 + 0.859680i \(0.670663\pi\)
\(252\) 118816.i 0.117862i
\(253\) 184408.i 0.181125i
\(254\) 700952. 0.681717
\(255\) 1.57696e6 286720.i 1.51869 0.276126i
\(256\) 65536.0 0.0625000
\(257\) 657408.i 0.620872i 0.950594 + 0.310436i \(0.100475\pi\)
−0.950594 + 0.310436i \(0.899525\pi\)
\(258\) 128464.i 0.120152i
\(259\) 690776. 0.639864
\(260\) 109440. + 601920.i 0.100402 + 0.552211i
\(261\) 12690.0 0.0115308
\(262\) 1.19861e6i 1.07876i
\(263\) 562366.i 0.501337i 0.968073 + 0.250668i \(0.0806504\pi\)
−0.968073 + 0.250668i \(0.919350\pi\)
\(264\) −132608. −0.117101
\(265\) −29640.0 163020.i −0.0259277 0.142602i
\(266\) −1.40304e6 −1.21581
\(267\) 1.19294e6i 1.02410i
\(268\) 513568.i 0.436778i
\(269\) −366570. −0.308870 −0.154435 0.988003i \(-0.549356\pi\)
−0.154435 + 0.988003i \(0.549356\pi\)
\(270\) −893200. + 162400.i −0.745657 + 0.135574i
\(271\) 1.16075e6 0.960099 0.480050 0.877241i \(-0.340619\pi\)
0.480050 + 0.877241i \(0.340619\pi\)
\(272\) 524288.i 0.429682i
\(273\) 1.51301e6i 1.22867i
\(274\) 431712. 0.347390
\(275\) −432900. + 162800.i −0.345188 + 0.129814i
\(276\) −279104. −0.220543
\(277\) 2.51501e6i 1.96943i −0.174172 0.984715i \(-0.555725\pi\)
0.174172 0.984715i \(-0.444275\pi\)
\(278\) 785840.i 0.609849i
\(279\) −96256.0 −0.0740316
\(280\) −556160. + 101120.i −0.423940 + 0.0770800i
\(281\) 2.08600e6 1.57597 0.787987 0.615692i \(-0.211124\pi\)
0.787987 + 0.615692i \(0.211124\pi\)
\(282\) 598192.i 0.447938i
\(283\) 2.23803e6i 1.66111i 0.556935 + 0.830556i \(0.311977\pi\)
−0.556935 + 0.830556i \(0.688023\pi\)
\(284\) 67968.0 0.0500044
\(285\) 310800. + 1.70940e6i 0.226657 + 1.24661i
\(286\) 404928. 0.292727
\(287\) 378884.i 0.271520i
\(288\) 48128.0i 0.0341914i
\(289\) −2.77445e6 −1.95403
\(290\) −10800.0 59400.0i −0.00754100 0.0414755i
\(291\) −1.36125e6 −0.942334
\(292\) 481664.i 0.330588i
\(293\) 975756.i 0.664006i 0.943278 + 0.332003i \(0.107724\pi\)
−0.943278 + 0.332003i \(0.892276\pi\)
\(294\) 456792. 0.308212
\(295\) 2.18570e6 397400.i 1.46230 0.265872i
\(296\) 279808. 0.185623
\(297\) 600880.i 0.395273i
\(298\) 555400.i 0.362297i
\(299\) 852264. 0.551310
\(300\) 246400. + 655200.i 0.158066 + 0.420311i
\(301\) 362452. 0.230587
\(302\) 1.66461e6i 1.05025i
\(303\) 60172.0i 0.0376520i
\(304\) −568320. −0.352703
\(305\) −2.32639e6 + 422980.i −1.43197 + 0.260358i
\(306\) 385024. 0.235063
\(307\) 87858.0i 0.0532029i 0.999646 + 0.0266015i \(0.00846850\pi\)
−0.999646 + 0.0266015i \(0.991531\pi\)
\(308\) 374144.i 0.224730i
\(309\) −1.73760e6 −1.03527
\(310\) 81920.0 + 450560.i 0.0484156 + 0.266286i
\(311\) 599352. 0.351383 0.175692 0.984445i \(-0.443784\pi\)
0.175692 + 0.984445i \(0.443784\pi\)
\(312\) 612864.i 0.356433i
\(313\) 2.09342e6i 1.20780i 0.797060 + 0.603900i \(0.206387\pi\)
−0.797060 + 0.603900i \(0.793613\pi\)
\(314\) 1.73243e6 0.991590
\(315\) 74260.0 + 408430.i 0.0421676 + 0.231922i
\(316\) 564480. 0.318003
\(317\) 2.41625e6i 1.35050i −0.737590 0.675249i \(-0.764036\pi\)
0.737590 0.675249i \(-0.235964\pi\)
\(318\) 165984.i 0.0920446i
\(319\) −39960.0 −0.0219861
\(320\) −225280. + 40960.0i −0.122984 + 0.0223607i
\(321\) −592788. −0.321097
\(322\) 787472.i 0.423249i
\(323\) 4.54656e6i 2.42480i
\(324\) 726704. 0.384587
\(325\) −752400. 2.00070e6i −0.395130 1.05069i
\(326\) −596536. −0.310880
\(327\) 503860.i 0.260580i
\(328\) 153472.i 0.0787670i
\(329\) 1.68776e6 0.859647
\(330\) 455840. 82880.0i 0.230424 0.0418953i
\(331\) −1.64095e6 −0.823237 −0.411618 0.911356i \(-0.635036\pi\)
−0.411618 + 0.911356i \(0.635036\pi\)
\(332\) 445216.i 0.221680i
\(333\) 205484.i 0.101547i
\(334\) −2.23841e6 −1.09793
\(335\) 320980. + 1.76539e6i 0.156267 + 0.859466i
\(336\) 566272. 0.273638
\(337\) 2.18773e6i 1.04935i 0.851304 + 0.524673i \(0.175812\pi\)
−0.851304 + 0.524673i \(0.824188\pi\)
\(338\) 386252.i 0.183899i
\(339\) 3.20342e6 1.51396
\(340\) −327680. 1.80224e6i −0.153728 0.845503i
\(341\) 303104. 0.141158
\(342\) 417360.i 0.192950i
\(343\) 1.36670e6i 0.627246i
\(344\) 146816. 0.0668925
\(345\) 959420. 174440.i 0.433971 0.0789039i
\(346\) −1.37522e6 −0.617562
\(347\) 2.74502e6i 1.22383i 0.790923 + 0.611916i \(0.209601\pi\)
−0.790923 + 0.611916i \(0.790399\pi\)
\(348\) 60480.0i 0.0267709i
\(349\) 2.65115e6 1.16512 0.582560 0.812788i \(-0.302051\pi\)
0.582560 + 0.812788i \(0.302051\pi\)
\(350\) 1.84860e6 695200.i 0.806627 0.303347i
\(351\) −2.77704e6 −1.20313
\(352\) 151552.i 0.0651936i
\(353\) 3.05766e6i 1.30603i −0.757345 0.653015i \(-0.773504\pi\)
0.757345 0.653015i \(-0.226496\pi\)
\(354\) −2.22544e6 −0.943860
\(355\) −233640. + 42480.0i −0.0983957 + 0.0178901i
\(356\) −1.36336e6 −0.570145
\(357\) 4.53018e6i 1.88124i
\(358\) 95920.0i 0.0395550i
\(359\) −3.79356e6 −1.55350 −0.776749 0.629810i \(-0.783133\pi\)
−0.776749 + 0.629810i \(0.783133\pi\)
\(360\) 30080.0 + 165440.i 0.0122327 + 0.0672797i
\(361\) 2.45230e6 0.990389
\(362\) 2.60759e6i 1.04585i
\(363\) 1.94806e6i 0.775953i
\(364\) −1.72915e6 −0.684037
\(365\) −301040. 1.65572e6i −0.118275 0.650511i
\(366\) 2.36869e6 0.924283
\(367\) 3.11060e6i 1.20553i −0.797917 0.602767i \(-0.794065\pi\)
0.797917 0.602767i \(-0.205935\pi\)
\(368\) 318976.i 0.122783i
\(369\) −112706. −0.0430905
\(370\) −961840. + 174880.i −0.365257 + 0.0664104i
\(371\) 468312. 0.176645
\(372\) 458752.i 0.171878i
\(373\) 1.41520e6i 0.526677i 0.964703 + 0.263339i \(0.0848236\pi\)
−0.964703 + 0.263339i \(0.915176\pi\)
\(374\) −1.21242e6 −0.448201
\(375\) −1.25650e6 2.09825e6i −0.461407 0.770511i
\(376\) 683648. 0.249381
\(377\) 184680.i 0.0669216i
\(378\) 2.56592e6i 0.923663i
\(379\) 3.90262e6 1.39559 0.697796 0.716297i \(-0.254164\pi\)
0.697796 + 0.716297i \(0.254164\pi\)
\(380\) 1.95360e6 355200.i 0.694027 0.126187i
\(381\) 2.45333e6 0.865852
\(382\) 811008.i 0.284359i
\(383\) 695674.i 0.242331i −0.992632 0.121165i \(-0.961337\pi\)
0.992632 0.121165i \(-0.0386632\pi\)
\(384\) 229376. 0.0793816
\(385\) −233840. 1.28612e6i −0.0804020 0.442211i
\(386\) 1.81062e6 0.618529
\(387\) 107818.i 0.0365943i
\(388\) 1.55571e6i 0.524626i
\(389\) −498290. −0.166958 −0.0834792 0.996510i \(-0.526603\pi\)
−0.0834792 + 0.996510i \(0.526603\pi\)
\(390\) 383040. + 2.10672e6i 0.127521 + 0.701367i
\(391\) −2.55181e6 −0.844124
\(392\) 522048.i 0.171591i
\(393\) 4.19513e6i 1.37014i
\(394\) 1.34987e6 0.438079
\(395\) −1.94040e6 + 352800.i −0.625747 + 0.113772i
\(396\) 111296. 0.0356649
\(397\) 1.09567e6i 0.348901i 0.984666 + 0.174451i \(0.0558150\pi\)
−0.984666 + 0.174451i \(0.944185\pi\)
\(398\) 2.24400e6i 0.710093i
\(399\) −4.91064e6 −1.54421
\(400\) 748800. 281600.i 0.234000 0.0880000i
\(401\) −2.49160e6 −0.773779 −0.386890 0.922126i \(-0.626451\pi\)
−0.386890 + 0.922126i \(0.626451\pi\)
\(402\) 1.79749e6i 0.554755i
\(403\) 1.40083e6i 0.429659i
\(404\) 68768.0 0.0209620
\(405\) −2.49805e6 + 454190.i −0.756768 + 0.137594i
\(406\) 170640. 0.0513766
\(407\) 647056.i 0.193623i
\(408\) 1.83501e6i 0.545742i
\(409\) 3.63349e6 1.07403 0.537014 0.843573i \(-0.319552\pi\)
0.537014 + 0.843573i \(0.319552\pi\)
\(410\) 95920.0 + 527560.i 0.0281806 + 0.154993i
\(411\) 1.51099e6 0.441222
\(412\) 1.98582e6i 0.576365i
\(413\) 6.27892e6i 1.81138i
\(414\) 234248. 0.0671700
\(415\) 278260. + 1.53043e6i 0.0793105 + 0.436208i
\(416\) −700416. −0.198437
\(417\) 2.75044e6i 0.774572i
\(418\) 1.31424e6i 0.367904i
\(419\) 3.64378e6 1.01395 0.506976 0.861960i \(-0.330763\pi\)
0.506976 + 0.861960i \(0.330763\pi\)
\(420\) −1.94656e6 + 353920.i −0.538449 + 0.0978998i
\(421\) −1.82530e6 −0.501913 −0.250957 0.967998i \(-0.580745\pi\)
−0.250957 + 0.967998i \(0.580745\pi\)
\(422\) 3.22219e6i 0.880786i
\(423\) 502054.i 0.136427i
\(424\) 189696. 0.0512441
\(425\) 2.25280e6 + 5.99040e6i 0.604993 + 1.60873i
\(426\) 237888. 0.0635109
\(427\) 6.68308e6i 1.77381i
\(428\) 677472.i 0.178765i
\(429\) 1.41725e6 0.371794
\(430\) −504680. + 91760.0i −0.131627 + 0.0239322i
\(431\) 2.85435e6 0.740141 0.370070 0.929004i \(-0.379334\pi\)
0.370070 + 0.929004i \(0.379334\pi\)
\(432\) 1.03936e6i 0.267952i
\(433\) 587776.i 0.150658i 0.997159 + 0.0753290i \(0.0240007\pi\)
−0.997159 + 0.0753290i \(0.975999\pi\)
\(434\) −1.29434e6 −0.329855
\(435\) −37800.0 207900.i −0.00957786 0.0526783i
\(436\) −575840. −0.145073
\(437\) 2.76612e6i 0.692895i
\(438\) 1.68582e6i 0.419882i
\(439\) −6.11604e6 −1.51464 −0.757319 0.653045i \(-0.773491\pi\)
−0.757319 + 0.653045i \(0.773491\pi\)
\(440\) −94720.0 520960.i −0.0233244 0.128284i
\(441\) −383379. −0.0938711
\(442\) 5.60333e6i 1.36424i
\(443\) 2.35771e6i 0.570795i 0.958409 + 0.285398i \(0.0921257\pi\)
−0.958409 + 0.285398i \(0.907874\pi\)
\(444\) 979328. 0.235760
\(445\) 4.68655e6 852100.i 1.12190 0.203981i
\(446\) −4.87422e6 −1.16029
\(447\) 1.94390e6i 0.460156i
\(448\) 647168.i 0.152343i
\(449\) −5.49735e6 −1.28688 −0.643439 0.765497i \(-0.722493\pi\)
−0.643439 + 0.765497i \(0.722493\pi\)
\(450\) −206800. 549900.i −0.0481415 0.128013i
\(451\) 354904. 0.0821617
\(452\) 3.66106e6i 0.842869i
\(453\) 5.82613e6i 1.33393i
\(454\) 2.25735e6 0.513996
\(455\) 5.94396e6 1.08072e6i 1.34601 0.244729i
\(456\) −1.98912e6 −0.447970
\(457\) 1.16039e6i 0.259905i −0.991520 0.129952i \(-0.958518\pi\)
0.991520 0.129952i \(-0.0414824\pi\)
\(458\) 2.24132e6i 0.499275i
\(459\) 8.31488e6 1.84215
\(460\) −199360. 1.09648e6i −0.0439282 0.241605i
\(461\) −2.30330e6 −0.504775 −0.252387 0.967626i \(-0.581216\pi\)
−0.252387 + 0.967626i \(0.581216\pi\)
\(462\) 1.30950e6i 0.285431i
\(463\) 2.71343e6i 0.588257i −0.955766 0.294128i \(-0.904971\pi\)
0.955766 0.294128i \(-0.0950293\pi\)
\(464\) 69120.0 0.0149042
\(465\) 286720. + 1.57696e6i 0.0614930 + 0.338211i
\(466\) 1.17430e6 0.250505
\(467\) 4.05050e6i 0.859441i 0.902962 + 0.429721i \(0.141388\pi\)
−0.902962 + 0.429721i \(0.858612\pi\)
\(468\) 514368.i 0.108557i
\(469\) −5.07148e6 −1.06464
\(470\) −2.35004e6 + 427280.i −0.490716 + 0.0892212i
\(471\) 6.06351e6 1.25942
\(472\) 2.54336e6i 0.525476i
\(473\) 339512.i 0.0697754i
\(474\) 1.97568e6 0.403897
\(475\) −6.49350e6 + 2.44200e6i −1.32052 + 0.496606i
\(476\) 5.17734e6 1.04734
\(477\) 139308.i 0.0280337i
\(478\) 2.33696e6i 0.467823i
\(479\) −5.60528e6 −1.11624 −0.558121 0.829759i \(-0.688478\pi\)
−0.558121 + 0.829759i \(0.688478\pi\)
\(480\) −788480. + 143360.i −0.156202 + 0.0284004i
\(481\) −2.99045e6 −0.589350
\(482\) 2.25519e6i 0.442146i
\(483\) 2.75615e6i 0.537570i
\(484\) 2.22635e6 0.431997
\(485\) −972320. 5.34776e6i −0.187696 1.03233i
\(486\) −1.40286e6 −0.269415
\(487\) 7.13168e6i 1.36260i 0.732003 + 0.681301i \(0.238586\pi\)
−0.732003 + 0.681301i \(0.761414\pi\)
\(488\) 2.70707e6i 0.514577i
\(489\) −2.08788e6 −0.394850
\(490\) 326280. + 1.79454e6i 0.0613904 + 0.337647i
\(491\) 5.88145e6 1.10098 0.550492 0.834841i \(-0.314440\pi\)
0.550492 + 0.834841i \(0.314440\pi\)
\(492\) 537152.i 0.100042i
\(493\) 552960.i 0.102465i
\(494\) 6.07392e6 1.11983
\(495\) −382580. + 69560.0i −0.0701793 + 0.0127599i
\(496\) −524288. −0.0956898
\(497\) 671184.i 0.121885i
\(498\) 1.55826e6i 0.281556i
\(499\) −1.75710e6 −0.315897 −0.157948 0.987447i \(-0.550488\pi\)
−0.157948 + 0.987447i \(0.550488\pi\)
\(500\) −2.39800e6 + 1.43600e6i −0.428967 + 0.256879i
\(501\) −7.83443e6 −1.39448
\(502\) 4.07899e6i 0.722426i
\(503\) 4.91411e6i 0.866015i −0.901390 0.433007i \(-0.857452\pi\)
0.901390 0.433007i \(-0.142548\pi\)
\(504\) −475264. −0.0833410
\(505\) −236390. + 42980.0i −0.0412478 + 0.00749960i
\(506\) −737632. −0.128075
\(507\) 1.35188e6i 0.233571i
\(508\) 2.80381e6i 0.482047i
\(509\) 5.75499e6 0.984578 0.492289 0.870432i \(-0.336160\pi\)
0.492289 + 0.870432i \(0.336160\pi\)
\(510\) −1.14688e6 6.30784e6i −0.195251 1.07388i
\(511\) 4.75643e6 0.805803
\(512\) 262144.i 0.0441942i
\(513\) 9.01320e6i 1.51212i
\(514\) 2.62963e6 0.439023
\(515\) −1.24114e6 6.82627e6i −0.206207 1.13414i
\(516\) 513856. 0.0849605
\(517\) 1.58094e6i 0.260128i
\(518\) 2.76310e6i 0.452452i
\(519\) −4.81326e6 −0.784369
\(520\) 2.40768e6 437760.i 0.390472 0.0709950i
\(521\) −1.61980e6 −0.261437 −0.130718 0.991420i \(-0.541728\pi\)
−0.130718 + 0.991420i \(0.541728\pi\)
\(522\) 50760.0i 0.00815352i
\(523\) 1.19117e7i 1.90422i −0.305751 0.952112i \(-0.598907\pi\)
0.305751 0.952112i \(-0.401093\pi\)
\(524\) −4.79443e6 −0.762797
\(525\) 6.47010e6 2.43320e6i 1.02450 0.385283i
\(526\) 2.24946e6 0.354499
\(527\) 4.19430e6i 0.657860i
\(528\) 530432.i 0.0828028i
\(529\) 4.88383e6 0.758789
\(530\) −652080. + 118560.i −0.100835 + 0.0183336i
\(531\) 1.86778e6 0.287468
\(532\) 5.61216e6i 0.859708i
\(533\) 1.64023e6i 0.250085i
\(534\) −4.77176e6 −0.724145
\(535\) −423420. 2.32881e6i −0.0639568 0.351763i
\(536\) −2.05427e6 −0.308849
\(537\) 335720.i 0.0502391i
\(538\) 1.46628e6i 0.218404i
\(539\) 1.20724e6 0.178986
\(540\) 649600. + 3.57280e6i 0.0958653 + 0.527259i
\(541\) 4.07630e6 0.598788 0.299394 0.954130i \(-0.403215\pi\)
0.299394 + 0.954130i \(0.403215\pi\)
\(542\) 4.64301e6i 0.678893i
\(543\) 9.12657e6i 1.32834i
\(544\) 2.09715e6 0.303831
\(545\) 1.97945e6 359900.i 0.285465 0.0519028i
\(546\) −6.05203e6 −0.868800
\(547\) 1.23680e7i 1.76739i 0.468065 + 0.883694i \(0.344951\pi\)
−0.468065 + 0.883694i \(0.655049\pi\)
\(548\) 1.72685e6i 0.245642i
\(549\) −1.98801e6 −0.281505
\(550\) 651200. + 1.73160e6i 0.0917926 + 0.244085i
\(551\) −599400. −0.0841081
\(552\) 1.11642e6i 0.155947i
\(553\) 5.57424e6i 0.775127i
\(554\) −1.00600e7 −1.39260
\(555\) −3.36644e6 + 612080.i −0.463915 + 0.0843482i
\(556\) −3.14336e6 −0.431228
\(557\) 130308.i 0.0177964i 0.999960 + 0.00889822i \(0.00283243\pi\)
−0.999960 + 0.00889822i \(0.997168\pi\)
\(558\) 385024.i 0.0523483i
\(559\) −1.56910e6 −0.212383
\(560\) 404480. + 2.22464e6i 0.0545038 + 0.299771i
\(561\) −4.24346e6 −0.569262
\(562\) 8.34401e6i 1.11438i
\(563\) 5.91687e6i 0.786721i 0.919384 + 0.393361i \(0.128688\pi\)
−0.919384 + 0.393361i \(0.871312\pi\)
\(564\) 2.39277e6 0.316740
\(565\) 2.28816e6 + 1.25849e7i 0.301554 + 1.65855i
\(566\) 8.95210e6 1.17458
\(567\) 7.17620e6i 0.937426i
\(568\) 271872.i 0.0353585i
\(569\) 9.03013e6 1.16927 0.584633 0.811298i \(-0.301239\pi\)
0.584633 + 0.811298i \(0.301239\pi\)
\(570\) 6.83760e6 1.24320e6i 0.881488 0.160271i
\(571\) −1.07093e7 −1.37459 −0.687294 0.726379i \(-0.741202\pi\)
−0.687294 + 0.726379i \(0.741202\pi\)
\(572\) 1.61971e6i 0.206989i
\(573\) 2.83853e6i 0.361166i
\(574\) −1.51554e6 −0.191994
\(575\) 1.37060e6 + 3.64455e6i 0.172879 + 0.459700i
\(576\) −192512. −0.0241770
\(577\) 1.22051e6i 0.152617i −0.997084 0.0763084i \(-0.975687\pi\)
0.997084 0.0763084i \(-0.0243134\pi\)
\(578\) 1.10978e7i 1.38171i
\(579\) 6.33718e6 0.785597
\(580\) −237600. + 43200.0i −0.0293276 + 0.00533229i
\(581\) −4.39651e6 −0.540341
\(582\) 5.44499e6i 0.666331i
\(583\) 438672.i 0.0534526i
\(584\) 1.92666e6 0.233761
\(585\) −321480. 1.76814e6i −0.0388387 0.213613i
\(586\) 3.90302e6 0.469523
\(587\) 1.47104e7i 1.76210i −0.473026 0.881049i \(-0.656838\pi\)
0.473026 0.881049i \(-0.343162\pi\)
\(588\) 1.82717e6i 0.217939i
\(589\) 4.54656e6 0.540001
\(590\) −1.58960e6 8.74280e6i −0.188000 1.03400i
\(591\) 4.72455e6 0.556406
\(592\) 1.11923e6i 0.131255i
\(593\) 8.52014e6i 0.994970i −0.867472 0.497485i \(-0.834257\pi\)
0.867472 0.497485i \(-0.165743\pi\)
\(594\) 2.40352e6 0.279500
\(595\) −1.77971e7 + 3.23584e6i −2.06090 + 0.374709i
\(596\) 2.22160e6 0.256183
\(597\) 7.85400e6i 0.901893i
\(598\) 3.40906e6i 0.389835i
\(599\) −2.90100e6 −0.330355 −0.165177 0.986264i \(-0.552820\pi\)
−0.165177 + 0.986264i \(0.552820\pi\)
\(600\) 2.62080e6 985600.i 0.297205 0.111769i
\(601\) 5.72760e6 0.646825 0.323412 0.946258i \(-0.395170\pi\)
0.323412 + 0.946258i \(0.395170\pi\)
\(602\) 1.44981e6i 0.163049i
\(603\) 1.50861e6i 0.168959i
\(604\) −6.65843e6 −0.742642
\(605\) −7.65308e6 + 1.39147e6i −0.850057 + 0.154556i
\(606\) 240688. 0.0266240
\(607\) 8.79924e6i 0.969334i −0.874699 0.484667i \(-0.838941\pi\)
0.874699 0.484667i \(-0.161059\pi\)
\(608\) 2.27328e6i 0.249399i
\(609\) 597240. 0.0652538
\(610\) 1.69192e6 + 9.30556e6i 0.184101 + 1.01255i
\(611\) −7.30649e6 −0.791782
\(612\) 1.54010e6i 0.166215i
\(613\) 1.03408e6i 0.111149i −0.998455 0.0555744i \(-0.982301\pi\)
0.998455 0.0555744i \(-0.0176990\pi\)
\(614\) 351432. 0.0376201
\(615\) 335720. + 1.84646e6i 0.0357923 + 0.196858i
\(616\) 1.49658e6 0.158908
\(617\) 1.29854e7i 1.37323i 0.727020 + 0.686616i \(0.240905\pi\)
−0.727020 + 0.686616i \(0.759095\pi\)
\(618\) 6.95038e6i 0.732045i
\(619\) −7.92002e6 −0.830806 −0.415403 0.909637i \(-0.636359\pi\)
−0.415403 + 0.909637i \(0.636359\pi\)
\(620\) 1.80224e6 327680.i 0.188293 0.0342350i
\(621\) 5.05876e6 0.526399
\(622\) 2.39741e6i 0.248465i
\(623\) 1.34632e7i 1.38972i
\(624\) −2.45146e6 −0.252036
\(625\) 7.34562e6 6.43500e6i 0.752192 0.658944i
\(626\) 8.37366e6 0.854043
\(627\) 4.59984e6i 0.467276i
\(628\) 6.92973e6i 0.701160i
\(629\) 8.95386e6 0.902368
\(630\) 1.63372e6 297040.i 0.163993 0.0298170i
\(631\) 1.68218e7 1.68189 0.840945 0.541120i \(-0.181999\pi\)
0.840945 + 0.541120i \(0.181999\pi\)
\(632\) 2.25792e6i 0.224862i
\(633\) 1.12777e7i 1.11869i
\(634\) −9.66501e6 −0.954947
\(635\) 1.75238e6 + 9.63809e6i 0.172462 + 0.948542i
\(636\) 663936. 0.0650854
\(637\) 5.57939e6i 0.544801i
\(638\) 159840.i 0.0155465i
\(639\) −199656. −0.0193433
\(640\) 163840. + 901120.i 0.0158114 + 0.0869626i
\(641\) −1.55154e7 −1.49148 −0.745741 0.666236i \(-0.767904\pi\)
−0.745741 + 0.666236i \(0.767904\pi\)
\(642\) 2.37115e6i 0.227050i
\(643\) 1.05801e7i 1.00916i −0.863364 0.504582i \(-0.831646\pi\)
0.863364 0.504582i \(-0.168354\pi\)
\(644\) 3.14989e6 0.299282
\(645\) −1.76638e6 + 321160.i −0.167180 + 0.0303964i
\(646\) −1.81862e7 −1.71460
\(647\) 1.37883e7i 1.29494i 0.762090 + 0.647471i \(0.224173\pi\)
−0.762090 + 0.647471i \(0.775827\pi\)
\(648\) 2.90682e6i 0.271944i
\(649\) −5.88152e6 −0.548123
\(650\) −8.00280e6 + 3.00960e6i −0.742948 + 0.279399i
\(651\) −4.53018e6 −0.418950
\(652\) 2.38614e6i 0.219825i
\(653\) 1.58924e6i 0.145850i 0.997337 + 0.0729248i \(0.0232333\pi\)
−0.997337 + 0.0729248i \(0.976767\pi\)
\(654\) −2.01544e6 −0.184258
\(655\) 1.64809e7 2.99652e6i 1.50099 0.272907i
\(656\) −613888. −0.0556967
\(657\) 1.41489e6i 0.127882i
\(658\) 6.75102e6i 0.607862i
\(659\) 9.12434e6 0.818442 0.409221 0.912435i \(-0.365801\pi\)
0.409221 + 0.912435i \(0.365801\pi\)
\(660\) −331520. 1.82336e6i −0.0296244 0.162934i
\(661\) 6.50310e6 0.578918 0.289459 0.957190i \(-0.406525\pi\)
0.289459 + 0.957190i \(0.406525\pi\)
\(662\) 6.56379e6i 0.582116i
\(663\) 1.96116e7i 1.73273i
\(664\) −1.78086e6 −0.156751
\(665\) −3.50760e6 1.92918e7i −0.307578 1.69168i
\(666\) −821936. −0.0718046
\(667\) 336420.i 0.0292797i
\(668\) 8.95363e6i 0.776351i
\(669\) −1.70598e7 −1.47369
\(670\) 7.06156e6 1.28392e6i 0.607734 0.110497i
\(671\) 6.26010e6 0.536754
\(672\) 2.26509e6i 0.193492i
\(673\) 2.17810e6i 0.185370i 0.995695 + 0.0926850i \(0.0295449\pi\)
−0.995695 + 0.0926850i \(0.970455\pi\)
\(674\) 8.75091e6 0.741999
\(675\) −4.46600e6 1.18755e7i −0.377276 1.00321i
\(676\) 1.54501e6 0.130036
\(677\) 3.98419e6i 0.334094i 0.985949 + 0.167047i \(0.0534231\pi\)
−0.985949 + 0.167047i \(0.946577\pi\)
\(678\) 1.28137e7i 1.07053i
\(679\) 1.53627e7 1.27877
\(680\) −7.20896e6 + 1.31072e6i −0.597861 + 0.108702i
\(681\) 7.90073e6 0.652829
\(682\) 1.21242e6i 0.0998138i
\(683\) 5.91563e6i 0.485231i 0.970122 + 0.242616i \(0.0780054\pi\)
−0.970122 + 0.242616i \(0.921995\pi\)
\(684\) 1.66944e6 0.136436
\(685\) 1.07928e6 + 5.93604e6i 0.0878836 + 0.483360i
\(686\) 5.46680e6 0.443530
\(687\) 7.84462e6i 0.634133i
\(688\) 587264.i 0.0473001i
\(689\) −2.02738e6 −0.162700
\(690\) −697760. 3.83768e6i −0.0557935 0.306864i
\(691\) −1.55471e7 −1.23867 −0.619335 0.785127i \(-0.712598\pi\)
−0.619335 + 0.785127i \(0.712598\pi\)
\(692\) 5.50086e6i 0.436682i
\(693\) 1.09905e6i 0.0869328i
\(694\) 1.09801e7 0.865379
\(695\) 1.08053e7 1.96460e6i 0.848545 0.154281i
\(696\) 241920. 0.0189299
\(697\) 4.91110e6i 0.382910i
\(698\) 1.06046e7i 0.823864i
\(699\) 4.11006e6 0.318167
\(700\) −2.78080e6 7.39440e6i −0.214499 0.570372i
\(701\) −2.27103e7 −1.74553 −0.872766 0.488139i \(-0.837676\pi\)
−0.872766 + 0.488139i \(0.837676\pi\)
\(702\) 1.11082e7i 0.850745i
\(703\) 9.70584e6i 0.740704i
\(704\) 606208. 0.0460988
\(705\) −8.22514e6 + 1.49548e6i −0.623262 + 0.113320i
\(706\) −1.22307e7 −0.923502
\(707\) 679084.i 0.0510946i
\(708\) 8.90176e6i 0.667410i
\(709\) −6.29841e6 −0.470560 −0.235280 0.971928i \(-0.575601\pi\)
−0.235280 + 0.971928i \(0.575601\pi\)
\(710\) 169920. + 934560.i 0.0126502 + 0.0695763i
\(711\) −1.65816e6 −0.123013
\(712\) 5.45344e6i 0.403154i
\(713\) 2.55181e6i 0.187985i
\(714\) 1.81207e7 1.33024
\(715\) 1.01232e6 + 5.56776e6i 0.0740547 + 0.407301i
\(716\) 383680. 0.0279696
\(717\) 8.17936e6i 0.594185i
\(718\) 1.51742e7i 1.09849i
\(719\) −2.11911e7 −1.52873 −0.764367 0.644782i \(-0.776948\pi\)
−0.764367 + 0.644782i \(0.776948\pi\)
\(720\) 661760. 120320.i 0.0475740 0.00864981i
\(721\) 1.96100e7 1.40488
\(722\) 9.80920e6i 0.700311i
\(723\) 7.89317e6i 0.561572i
\(724\) 1.04304e7 0.739526
\(725\) 789750. 297000.i 0.0558013 0.0209851i
\(726\) 7.79223e6 0.548682
\(727\) 1.35610e7i 0.951605i 0.879552 + 0.475803i \(0.157842\pi\)
−0.879552 + 0.475803i \(0.842158\pi\)
\(728\) 6.91661e6i 0.483687i
\(729\) −1.59468e7 −1.11136
\(730\) −6.62288e6 + 1.20416e6i −0.459981 + 0.0836329i
\(731\) 4.69811e6 0.325185
\(732\) 9.47475e6i 0.653567i
\(733\) 2.69413e7i 1.85208i −0.377429 0.926038i \(-0.623192\pi\)
0.377429 0.926038i \(-0.376808\pi\)
\(734\) −1.24424e7 −0.852441
\(735\) 1.14198e6 + 6.28089e6i 0.0779723 + 0.428847i
\(736\) 1.27590e6 0.0868207
\(737\) 4.75050e6i 0.322160i
\(738\) 450824.i 0.0304696i
\(739\) −2.77414e6 −0.186860 −0.0934302 0.995626i \(-0.529783\pi\)
−0.0934302 + 0.995626i \(0.529783\pi\)
\(740\) 699520. + 3.84736e6i 0.0469592 + 0.258276i
\(741\) 2.12587e7 1.42230
\(742\) 1.87325e6i 0.124907i
\(743\) 1.85538e7i 1.23299i −0.787358 0.616497i \(-0.788551\pi\)
0.787358 0.616497i \(-0.211449\pi\)
\(744\) −1.83501e6 −0.121536
\(745\) −7.63675e6 + 1.38850e6i −0.504101 + 0.0916548i
\(746\) 5.66078e6 0.372417
\(747\) 1.30782e6i 0.0857526i
\(748\) 4.84966e6i 0.316926i
\(749\) 6.69004e6 0.435736
\(750\) −8.39300e6 + 5.02600e6i −0.544834 + 0.326264i
\(751\) −2.19285e6 −0.141876 −0.0709380 0.997481i \(-0.522599\pi\)
−0.0709380 + 0.997481i \(0.522599\pi\)
\(752\) 2.73459e6i 0.176339i
\(753\) 1.42765e7i 0.917558i
\(754\) −738720. −0.0473207
\(755\) 2.28884e7 4.16152e6i 1.46133 0.265696i
\(756\) −1.02637e7 −0.653128
\(757\) 9.48749e6i 0.601744i −0.953665 0.300872i \(-0.902722\pi\)
0.953665 0.300872i \(-0.0972777\pi\)
\(758\) 1.56105e7i 0.986832i
\(759\) −2.58171e6 −0.162668
\(760\) −1.42080e6 7.81440e6i −0.0892275 0.490752i
\(761\) 9.69580e6 0.606907 0.303453 0.952846i \(-0.401860\pi\)
0.303453 + 0.952846i \(0.401860\pi\)
\(762\) 9.81333e6i 0.612250i
\(763\) 5.68642e6i 0.353612i
\(764\) −3.24403e6 −0.201072
\(765\) 962560. + 5.29408e6i 0.0594668 + 0.327067i
\(766\) −2.78270e6 −0.171354
\(767\) 2.71822e7i 1.66838i
\(768\) 917504.i 0.0561313i
\(769\) −9.32787e6 −0.568809 −0.284405 0.958704i \(-0.591796\pi\)
−0.284405 + 0.958704i \(0.591796\pi\)
\(770\) −5.14448e6 + 935360.i −0.312690 + 0.0568528i
\(771\) 9.20371e6 0.557606
\(772\) 7.24250e6i 0.437366i
\(773\) 9.68080e6i 0.582723i 0.956613 + 0.291362i \(0.0941083\pi\)
−0.956613 + 0.291362i \(0.905892\pi\)
\(774\) −431272. −0.0258761
\(775\) −5.99040e6 + 2.25280e6i −0.358263 + 0.134731i
\(776\) 6.22285e6 0.370967
\(777\) 9.67086e6i 0.574662i
\(778\) 1.99316e6i 0.118057i
\(779\) 5.32356e6 0.314310
\(780\) 8.42688e6 1.53216e6i 0.495941 0.0901712i
\(781\) 628704. 0.0368824
\(782\) 1.02072e7i 0.596886i
\(783\) 1.09620e6i 0.0638977i
\(784\) −2.08819e6 −0.121333
\(785\) 4.33108e6 + 2.38209e7i 0.250855 + 1.37970i
\(786\) −1.67805e7 −0.968833
\(787\) 5.52302e6i 0.317863i −0.987290 0.158931i \(-0.949195\pi\)
0.987290 0.158931i \(-0.0508049\pi\)
\(788\) 5.39949e6i 0.309768i
\(789\) 7.87312e6 0.450251
\(790\) 1.41120e6 + 7.76160e6i 0.0804490 + 0.442470i
\(791\) −3.61529e7 −2.05448
\(792\) 445184.i 0.0252189i
\(793\) 2.89318e7i 1.63378i
\(794\) 4.38267e6 0.246711
\(795\) −2.28228e6 + 414960.i −0.128071 + 0.0232857i