Properties

Label 128.5.f.a.95.2
Level 128
Weight 5
Character 128.95
Analytic conductor 13.231
Analytic rank 0
Dimension 14
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 128.f (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2313552747\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} - 1048576 x + 2097152\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{42} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 95.2
Root \(0.336831 - 2.80830i\) of defining polynomial
Character \(\chi\) \(=\) 128.95
Dual form 128.5.f.a.31.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-7.86839 + 7.86839i) q^{3} +(-27.2309 + 27.2309i) q^{5} -50.3097 q^{7} -42.8233i q^{9} +O(q^{10})\) \(q+(-7.86839 + 7.86839i) q^{3} +(-27.2309 + 27.2309i) q^{5} -50.3097 q^{7} -42.8233i q^{9} +(-53.1047 - 53.1047i) q^{11} +(125.128 + 125.128i) q^{13} -428.528i q^{15} +286.271 q^{17} +(-99.5010 + 99.5010i) q^{19} +(395.857 - 395.857i) q^{21} +100.505 q^{23} -858.049i q^{25} +(-300.390 - 300.390i) q^{27} +(-343.872 - 343.872i) q^{29} +208.400i q^{31} +835.697 q^{33} +(1369.98 - 1369.98i) q^{35} +(1159.47 - 1159.47i) q^{37} -1969.12 q^{39} +2335.63i q^{41} +(-2079.41 - 2079.41i) q^{43} +(1166.12 + 1166.12i) q^{45} -1054.04i q^{47} +130.069 q^{49} +(-2252.49 + 2252.49i) q^{51} +(-2136.46 + 2136.46i) q^{53} +2892.18 q^{55} -1565.83i q^{57} +(3721.44 + 3721.44i) q^{59} +(-2496.46 - 2496.46i) q^{61} +2154.43i q^{63} -6814.72 q^{65} +(-329.116 + 329.116i) q^{67} +(-790.817 + 790.817i) q^{69} +1040.71 q^{71} -2673.24i q^{73} +(6751.46 + 6751.46i) q^{75} +(2671.68 + 2671.68i) q^{77} +4475.80i q^{79} +8195.85 q^{81} +(1457.69 - 1457.69i) q^{83} +(-7795.43 + 7795.43i) q^{85} +5411.44 q^{87} +1146.97i q^{89} +(-6295.17 - 6295.17i) q^{91} +(-1639.78 - 1639.78i) q^{93} -5419.01i q^{95} -13101.5 q^{97} +(-2274.11 + 2274.11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q - 2q^{3} + 2q^{5} + 4q^{7} + O(q^{10}) \) \( 14q - 2q^{3} + 2q^{5} + 4q^{7} + 94q^{11} + 2q^{13} - 4q^{17} - 706q^{19} + 164q^{21} - 1148q^{23} - 1664q^{27} - 862q^{29} - 4q^{33} + 1340q^{35} + 1826q^{37} - 2684q^{39} + 1694q^{43} - 1410q^{45} + 682q^{49} - 3012q^{51} + 482q^{53} + 11780q^{55} - 2786q^{59} + 3778q^{61} - 2020q^{65} + 7998q^{67} - 9628q^{69} - 19964q^{71} + 17570q^{75} + 9508q^{77} + 1454q^{81} - 17282q^{83} - 9948q^{85} + 49284q^{87} - 28036q^{91} - 8896q^{93} - 4q^{97} + 49214q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −7.86839 + 7.86839i −0.874266 + 0.874266i −0.992934 0.118668i \(-0.962138\pi\)
0.118668 + 0.992934i \(0.462138\pi\)
\(4\) 0 0
\(5\) −27.2309 + 27.2309i −1.08924 + 1.08924i −0.0936308 + 0.995607i \(0.529847\pi\)
−0.995607 + 0.0936308i \(0.970153\pi\)
\(6\) 0 0
\(7\) −50.3097 −1.02673 −0.513365 0.858171i \(-0.671601\pi\)
−0.513365 + 0.858171i \(0.671601\pi\)
\(8\) 0 0
\(9\) 42.8233i 0.528682i
\(10\) 0 0
\(11\) −53.1047 53.1047i −0.438881 0.438881i 0.452754 0.891635i \(-0.350442\pi\)
−0.891635 + 0.452754i \(0.850442\pi\)
\(12\) 0 0
\(13\) 125.128 + 125.128i 0.740404 + 0.740404i 0.972656 0.232252i \(-0.0746094\pi\)
−0.232252 + 0.972656i \(0.574609\pi\)
\(14\) 0 0
\(15\) 428.528i 1.90457i
\(16\) 0 0
\(17\) 286.271 0.990557 0.495279 0.868734i \(-0.335066\pi\)
0.495279 + 0.868734i \(0.335066\pi\)
\(18\) 0 0
\(19\) −99.5010 + 99.5010i −0.275626 + 0.275626i −0.831360 0.555734i \(-0.812437\pi\)
0.555734 + 0.831360i \(0.312437\pi\)
\(20\) 0 0
\(21\) 395.857 395.857i 0.897635 0.897635i
\(22\) 0 0
\(23\) 100.505 0.189991 0.0949957 0.995478i \(-0.469716\pi\)
0.0949957 + 0.995478i \(0.469716\pi\)
\(24\) 0 0
\(25\) 858.049i 1.37288i
\(26\) 0 0
\(27\) −300.390 300.390i −0.412057 0.412057i
\(28\) 0 0
\(29\) −343.872 343.872i −0.408885 0.408885i 0.472465 0.881350i \(-0.343364\pi\)
−0.881350 + 0.472465i \(0.843364\pi\)
\(30\) 0 0
\(31\) 208.400i 0.216858i 0.994104 + 0.108429i \(0.0345820\pi\)
−0.994104 + 0.108429i \(0.965418\pi\)
\(32\) 0 0
\(33\) 835.697 0.767398
\(34\) 0 0
\(35\) 1369.98 1369.98i 1.11835 1.11835i
\(36\) 0 0
\(37\) 1159.47 1159.47i 0.846946 0.846946i −0.142805 0.989751i \(-0.545612\pi\)
0.989751 + 0.142805i \(0.0456122\pi\)
\(38\) 0 0
\(39\) −1969.12 −1.29462
\(40\) 0 0
\(41\) 2335.63i 1.38943i 0.719286 + 0.694714i \(0.244469\pi\)
−0.719286 + 0.694714i \(0.755531\pi\)
\(42\) 0 0
\(43\) −2079.41 2079.41i −1.12461 1.12461i −0.991039 0.133575i \(-0.957354\pi\)
−0.133575 0.991039i \(-0.542646\pi\)
\(44\) 0 0
\(45\) 1166.12 + 1166.12i 0.575861 + 0.575861i
\(46\) 0 0
\(47\) 1054.04i 0.477159i −0.971123 0.238580i \(-0.923318\pi\)
0.971123 0.238580i \(-0.0766818\pi\)
\(48\) 0 0
\(49\) 130.069 0.0541728
\(50\) 0 0
\(51\) −2252.49 + 2252.49i −0.866011 + 0.866011i
\(52\) 0 0
\(53\) −2136.46 + 2136.46i −0.760576 + 0.760576i −0.976426 0.215850i \(-0.930748\pi\)
0.215850 + 0.976426i \(0.430748\pi\)
\(54\) 0 0
\(55\) 2892.18 0.956092
\(56\) 0 0
\(57\) 1565.83i 0.481941i
\(58\) 0 0
\(59\) 3721.44 + 3721.44i 1.06907 + 1.06907i 0.997431 + 0.0716407i \(0.0228235\pi\)
0.0716407 + 0.997431i \(0.477177\pi\)
\(60\) 0 0
\(61\) −2496.46 2496.46i −0.670912 0.670912i 0.287014 0.957926i \(-0.407337\pi\)
−0.957926 + 0.287014i \(0.907337\pi\)
\(62\) 0 0
\(63\) 2154.43i 0.542814i
\(64\) 0 0
\(65\) −6814.72 −1.61295
\(66\) 0 0
\(67\) −329.116 + 329.116i −0.0733162 + 0.0733162i −0.742814 0.669498i \(-0.766509\pi\)
0.669498 + 0.742814i \(0.266509\pi\)
\(68\) 0 0
\(69\) −790.817 + 790.817i −0.166103 + 0.166103i
\(70\) 0 0
\(71\) 1040.71 0.206449 0.103225 0.994658i \(-0.467084\pi\)
0.103225 + 0.994658i \(0.467084\pi\)
\(72\) 0 0
\(73\) 2673.24i 0.501639i −0.968034 0.250820i \(-0.919300\pi\)
0.968034 0.250820i \(-0.0807001\pi\)
\(74\) 0 0
\(75\) 6751.46 + 6751.46i 1.20026 + 1.20026i
\(76\) 0 0
\(77\) 2671.68 + 2671.68i 0.450612 + 0.450612i
\(78\) 0 0
\(79\) 4475.80i 0.717161i 0.933499 + 0.358580i \(0.116739\pi\)
−0.933499 + 0.358580i \(0.883261\pi\)
\(80\) 0 0
\(81\) 8195.85 1.24918
\(82\) 0 0
\(83\) 1457.69 1457.69i 0.211597 0.211597i −0.593349 0.804945i \(-0.702195\pi\)
0.804945 + 0.593349i \(0.202195\pi\)
\(84\) 0 0
\(85\) −7795.43 + 7795.43i −1.07895 + 1.07895i
\(86\) 0 0
\(87\) 5411.44 0.714948
\(88\) 0 0
\(89\) 1146.97i 0.144801i 0.997376 + 0.0724003i \(0.0230659\pi\)
−0.997376 + 0.0724003i \(0.976934\pi\)
\(90\) 0 0
\(91\) −6295.17 6295.17i −0.760194 0.760194i
\(92\) 0 0
\(93\) −1639.78 1639.78i −0.189592 0.189592i
\(94\) 0 0
\(95\) 5419.01i 0.600444i
\(96\) 0 0
\(97\) −13101.5 −1.39244 −0.696222 0.717826i \(-0.745137\pi\)
−0.696222 + 0.717826i \(0.745137\pi\)
\(98\) 0 0
\(99\) −2274.11 + 2274.11i −0.232029 + 0.232029i
\(100\) 0 0
\(101\) 7488.18 7488.18i 0.734063 0.734063i −0.237359 0.971422i \(-0.576282\pi\)
0.971422 + 0.237359i \(0.0762818\pi\)
\(102\) 0 0
\(103\) −7141.23 −0.673129 −0.336565 0.941660i \(-0.609265\pi\)
−0.336565 + 0.941660i \(0.609265\pi\)
\(104\) 0 0
\(105\) 21559.1i 1.95547i
\(106\) 0 0
\(107\) 1794.26 + 1794.26i 0.156718 + 0.156718i 0.781111 0.624393i \(-0.214654\pi\)
−0.624393 + 0.781111i \(0.714654\pi\)
\(108\) 0 0
\(109\) −5362.57 5362.57i −0.451357 0.451357i 0.444448 0.895805i \(-0.353400\pi\)
−0.895805 + 0.444448i \(0.853400\pi\)
\(110\) 0 0
\(111\) 18246.3i 1.48091i
\(112\) 0 0
\(113\) −5165.40 −0.404527 −0.202263 0.979331i \(-0.564830\pi\)
−0.202263 + 0.979331i \(0.564830\pi\)
\(114\) 0 0
\(115\) −2736.86 + 2736.86i −0.206946 + 0.206946i
\(116\) 0 0
\(117\) 5358.40 5358.40i 0.391438 0.391438i
\(118\) 0 0
\(119\) −14402.2 −1.01703
\(120\) 0 0
\(121\) 9000.79i 0.614766i
\(122\) 0 0
\(123\) −18377.6 18377.6i −1.21473 1.21473i
\(124\) 0 0
\(125\) 6346.13 + 6346.13i 0.406152 + 0.406152i
\(126\) 0 0
\(127\) 22886.9i 1.41899i −0.704711 0.709495i \(-0.748923\pi\)
0.704711 0.709495i \(-0.251077\pi\)
\(128\) 0 0
\(129\) 32723.3 1.96642
\(130\) 0 0
\(131\) 19202.2 19202.2i 1.11894 1.11894i 0.127048 0.991897i \(-0.459450\pi\)
0.991897 0.127048i \(-0.0405502\pi\)
\(132\) 0 0
\(133\) 5005.87 5005.87i 0.282993 0.282993i
\(134\) 0 0
\(135\) 16359.8 0.897656
\(136\) 0 0
\(137\) 33680.5i 1.79448i −0.441547 0.897238i \(-0.645570\pi\)
0.441547 0.897238i \(-0.354430\pi\)
\(138\) 0 0
\(139\) 11747.9 + 11747.9i 0.608036 + 0.608036i 0.942432 0.334397i \(-0.108532\pi\)
−0.334397 + 0.942432i \(0.608532\pi\)
\(140\) 0 0
\(141\) 8293.64 + 8293.64i 0.417164 + 0.417164i
\(142\) 0 0
\(143\) 13289.8i 0.649899i
\(144\) 0 0
\(145\) 18727.9 0.890746
\(146\) 0 0
\(147\) −1023.43 + 1023.43i −0.0473615 + 0.0473615i
\(148\) 0 0
\(149\) 14877.7 14877.7i 0.670136 0.670136i −0.287611 0.957747i \(-0.592861\pi\)
0.957747 + 0.287611i \(0.0928611\pi\)
\(150\) 0 0
\(151\) 8005.74 0.351114 0.175557 0.984469i \(-0.443827\pi\)
0.175557 + 0.984469i \(0.443827\pi\)
\(152\) 0 0
\(153\) 12259.1i 0.523690i
\(154\) 0 0
\(155\) −5674.94 5674.94i −0.236210 0.236210i
\(156\) 0 0
\(157\) −12150.9 12150.9i −0.492958 0.492958i 0.416279 0.909237i \(-0.363334\pi\)
−0.909237 + 0.416279i \(0.863334\pi\)
\(158\) 0 0
\(159\) 33621.0i 1.32989i
\(160\) 0 0
\(161\) −5056.40 −0.195070
\(162\) 0 0
\(163\) −23646.5 + 23646.5i −0.890002 + 0.890002i −0.994523 0.104520i \(-0.966669\pi\)
0.104520 + 0.994523i \(0.466669\pi\)
\(164\) 0 0
\(165\) −22756.8 + 22756.8i −0.835879 + 0.835879i
\(166\) 0 0
\(167\) −42493.7 −1.52367 −0.761836 0.647770i \(-0.775702\pi\)
−0.761836 + 0.647770i \(0.775702\pi\)
\(168\) 0 0
\(169\) 2753.14i 0.0963950i
\(170\) 0 0
\(171\) 4260.96 + 4260.96i 0.145719 + 0.145719i
\(172\) 0 0
\(173\) 16142.1 + 16142.1i 0.539347 + 0.539347i 0.923337 0.383990i \(-0.125450\pi\)
−0.383990 + 0.923337i \(0.625450\pi\)
\(174\) 0 0
\(175\) 43168.2i 1.40957i
\(176\) 0 0
\(177\) −58563.5 −1.86931
\(178\) 0 0
\(179\) −22442.0 + 22442.0i −0.700415 + 0.700415i −0.964500 0.264084i \(-0.914930\pi\)
0.264084 + 0.964500i \(0.414930\pi\)
\(180\) 0 0
\(181\) 9891.06 9891.06i 0.301916 0.301916i −0.539847 0.841763i \(-0.681518\pi\)
0.841763 + 0.539847i \(0.181518\pi\)
\(182\) 0 0
\(183\) 39286.3 1.17311
\(184\) 0 0
\(185\) 63146.9i 1.84505i
\(186\) 0 0
\(187\) −15202.3 15202.3i −0.434737 0.434737i
\(188\) 0 0
\(189\) 15112.5 + 15112.5i 0.423071 + 0.423071i
\(190\) 0 0
\(191\) 2033.60i 0.0557442i 0.999611 + 0.0278721i \(0.00887311\pi\)
−0.999611 + 0.0278721i \(0.991127\pi\)
\(192\) 0 0
\(193\) 29257.4 0.785453 0.392727 0.919655i \(-0.371532\pi\)
0.392727 + 0.919655i \(0.371532\pi\)
\(194\) 0 0
\(195\) 53620.9 53620.9i 1.41015 1.41015i
\(196\) 0 0
\(197\) −28194.9 + 28194.9i −0.726504 + 0.726504i −0.969922 0.243417i \(-0.921732\pi\)
0.243417 + 0.969922i \(0.421732\pi\)
\(198\) 0 0
\(199\) −54100.9 −1.36615 −0.683075 0.730348i \(-0.739358\pi\)
−0.683075 + 0.730348i \(0.739358\pi\)
\(200\) 0 0
\(201\) 5179.24i 0.128196i
\(202\) 0 0
\(203\) 17300.1 + 17300.1i 0.419814 + 0.419814i
\(204\) 0 0
\(205\) −63601.4 63601.4i −1.51342 1.51342i
\(206\) 0 0
\(207\) 4303.97i 0.100445i
\(208\) 0 0
\(209\) 10567.9 0.241934
\(210\) 0 0
\(211\) −31994.1 + 31994.1i −0.718630 + 0.718630i −0.968325 0.249694i \(-0.919670\pi\)
0.249694 + 0.968325i \(0.419670\pi\)
\(212\) 0 0
\(213\) −8188.73 + 8188.73i −0.180492 + 0.180492i
\(214\) 0 0
\(215\) 113249. 2.44994
\(216\) 0 0
\(217\) 10484.6i 0.222654i
\(218\) 0 0
\(219\) 21034.1 + 21034.1i 0.438566 + 0.438566i
\(220\) 0 0
\(221\) 35820.6 + 35820.6i 0.733412 + 0.733412i
\(222\) 0 0
\(223\) 94185.8i 1.89398i 0.321261 + 0.946991i \(0.395893\pi\)
−0.321261 + 0.946991i \(0.604107\pi\)
\(224\) 0 0
\(225\) −36744.4 −0.725816
\(226\) 0 0
\(227\) 62683.9 62683.9i 1.21648 1.21648i 0.247622 0.968857i \(-0.420351\pi\)
0.968857 0.247622i \(-0.0796490\pi\)
\(228\) 0 0
\(229\) 19781.9 19781.9i 0.377221 0.377221i −0.492877 0.870099i \(-0.664055\pi\)
0.870099 + 0.492877i \(0.164055\pi\)
\(230\) 0 0
\(231\) −42043.7 −0.787910
\(232\) 0 0
\(233\) 25062.1i 0.461642i 0.972996 + 0.230821i \(0.0741412\pi\)
−0.972996 + 0.230821i \(0.925859\pi\)
\(234\) 0 0
\(235\) 28702.6 + 28702.6i 0.519740 + 0.519740i
\(236\) 0 0
\(237\) −35217.4 35217.4i −0.626989 0.626989i
\(238\) 0 0
\(239\) 93041.8i 1.62885i 0.580265 + 0.814427i \(0.302949\pi\)
−0.580265 + 0.814427i \(0.697051\pi\)
\(240\) 0 0
\(241\) −80981.9 −1.39429 −0.697146 0.716929i \(-0.745547\pi\)
−0.697146 + 0.716929i \(0.745547\pi\)
\(242\) 0 0
\(243\) −40156.6 + 40156.6i −0.680056 + 0.680056i
\(244\) 0 0
\(245\) −3541.90 + 3541.90i −0.0590071 + 0.0590071i
\(246\) 0 0
\(247\) −24900.8 −0.408149
\(248\) 0 0
\(249\) 22939.3i 0.369984i
\(250\) 0 0
\(251\) 25910.0 + 25910.0i 0.411264 + 0.411264i 0.882179 0.470915i \(-0.156076\pi\)
−0.470915 + 0.882179i \(0.656076\pi\)
\(252\) 0 0
\(253\) −5337.31 5337.31i −0.0833837 0.0833837i
\(254\) 0 0
\(255\) 122675.i 1.88658i
\(256\) 0 0
\(257\) 15800.6 0.239225 0.119613 0.992821i \(-0.461835\pi\)
0.119613 + 0.992821i \(0.461835\pi\)
\(258\) 0 0
\(259\) −58332.6 + 58332.6i −0.869584 + 0.869584i
\(260\) 0 0
\(261\) −14725.7 + 14725.7i −0.216170 + 0.216170i
\(262\) 0 0
\(263\) 82043.7 1.18613 0.593067 0.805153i \(-0.297917\pi\)
0.593067 + 0.805153i \(0.297917\pi\)
\(264\) 0 0
\(265\) 116356.i 1.65690i
\(266\) 0 0
\(267\) −9024.78 9024.78i −0.126594 0.126594i
\(268\) 0 0
\(269\) 30820.2 + 30820.2i 0.425923 + 0.425923i 0.887237 0.461314i \(-0.152622\pi\)
−0.461314 + 0.887237i \(0.652622\pi\)
\(270\) 0 0
\(271\) 110808.i 1.50880i −0.656412 0.754402i \(-0.727927\pi\)
0.656412 0.754402i \(-0.272073\pi\)
\(272\) 0 0
\(273\) 99065.7 1.32922
\(274\) 0 0
\(275\) −45566.4 + 45566.4i −0.602531 + 0.602531i
\(276\) 0 0
\(277\) −25634.0 + 25634.0i −0.334084 + 0.334084i −0.854135 0.520051i \(-0.825913\pi\)
0.520051 + 0.854135i \(0.325913\pi\)
\(278\) 0 0
\(279\) 8924.39 0.114649
\(280\) 0 0
\(281\) 48800.5i 0.618033i 0.951057 + 0.309017i \(0.0999999\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(282\) 0 0
\(283\) −111466. 111466.i −1.39178 1.39178i −0.821340 0.570439i \(-0.806773\pi\)
−0.570439 0.821340i \(-0.693227\pi\)
\(284\) 0 0
\(285\) 42638.9 + 42638.9i 0.524948 + 0.524948i
\(286\) 0 0
\(287\) 117505.i 1.42657i
\(288\) 0 0
\(289\) −1569.88 −0.0187963
\(290\) 0 0
\(291\) 103088. 103088.i 1.21737 1.21737i
\(292\) 0 0
\(293\) −13093.1 + 13093.1i −0.152514 + 0.152514i −0.779240 0.626726i \(-0.784395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(294\) 0 0
\(295\) −202676. −2.32895
\(296\) 0 0
\(297\) 31904.2i 0.361688i
\(298\) 0 0
\(299\) 12576.1 + 12576.1i 0.140670 + 0.140670i
\(300\) 0 0
\(301\) 104615. + 104615.i 1.15467 + 1.15467i
\(302\) 0 0
\(303\) 117840.i 1.28353i
\(304\) 0 0
\(305\) 135962. 1.46156
\(306\) 0 0
\(307\) 25274.9 25274.9i 0.268171 0.268171i −0.560192 0.828363i \(-0.689273\pi\)
0.828363 + 0.560192i \(0.189273\pi\)
\(308\) 0 0
\(309\) 56190.0 56190.0i 0.588494 0.588494i
\(310\) 0 0
\(311\) −53808.0 −0.556322 −0.278161 0.960534i \(-0.589725\pi\)
−0.278161 + 0.960534i \(0.589725\pi\)
\(312\) 0 0
\(313\) 137345.i 1.40192i −0.713199 0.700961i \(-0.752755\pi\)
0.713199 0.700961i \(-0.247245\pi\)
\(314\) 0 0
\(315\) −58667.1 58667.1i −0.591253 0.591253i
\(316\) 0 0
\(317\) −115546. 115546.i −1.14984 1.14984i −0.986584 0.163252i \(-0.947802\pi\)
−0.163252 0.986584i \(-0.552198\pi\)
\(318\) 0 0
\(319\) 36522.4i 0.358904i
\(320\) 0 0
\(321\) −28235.9 −0.274026
\(322\) 0 0
\(323\) −28484.2 + 28484.2i −0.273023 + 0.273023i
\(324\) 0 0
\(325\) 107366. 107366.i 1.01648 1.01648i
\(326\) 0 0
\(327\) 84389.7 0.789213
\(328\) 0 0
\(329\) 53028.7i 0.489913i
\(330\) 0 0
\(331\) 68009.3 + 68009.3i 0.620744 + 0.620744i 0.945722 0.324978i \(-0.105357\pi\)
−0.324978 + 0.945722i \(0.605357\pi\)
\(332\) 0 0
\(333\) −49652.2 49652.2i −0.447765 0.447765i
\(334\) 0 0
\(335\) 17924.3i 0.159718i
\(336\) 0 0
\(337\) −146703. −1.29176 −0.645878 0.763440i \(-0.723509\pi\)
−0.645878 + 0.763440i \(0.723509\pi\)
\(338\) 0 0
\(339\) 40643.4 40643.4i 0.353664 0.353664i
\(340\) 0 0
\(341\) 11067.0 11067.0i 0.0951749 0.0951749i
\(342\) 0 0
\(343\) 114250. 0.971108
\(344\) 0 0
\(345\) 43069.4i 0.361851i
\(346\) 0 0
\(347\) −80120.9 80120.9i −0.665406 0.665406i 0.291243 0.956649i \(-0.405931\pi\)
−0.956649 + 0.291243i \(0.905931\pi\)
\(348\) 0 0
\(349\) −100990. 100990.i −0.829143 0.829143i 0.158255 0.987398i \(-0.449413\pi\)
−0.987398 + 0.158255i \(0.949413\pi\)
\(350\) 0 0
\(351\) 75174.4i 0.610177i
\(352\) 0 0
\(353\) 129855. 1.04210 0.521052 0.853525i \(-0.325540\pi\)
0.521052 + 0.853525i \(0.325540\pi\)
\(354\) 0 0
\(355\) −28339.6 + 28339.6i −0.224873 + 0.224873i
\(356\) 0 0
\(357\) 113322. 113322.i 0.889158 0.889158i
\(358\) 0 0
\(359\) 55943.2 0.434068 0.217034 0.976164i \(-0.430362\pi\)
0.217034 + 0.976164i \(0.430362\pi\)
\(360\) 0 0
\(361\) 110520.i 0.848061i
\(362\) 0 0
\(363\) 70821.8 + 70821.8i 0.537469 + 0.537469i
\(364\) 0 0
\(365\) 72794.8 + 72794.8i 0.546405 + 0.546405i
\(366\) 0 0
\(367\) 144947.i 1.07616i 0.842892 + 0.538082i \(0.180851\pi\)
−0.842892 + 0.538082i \(0.819149\pi\)
\(368\) 0 0
\(369\) 100019. 0.734566
\(370\) 0 0
\(371\) 107485. 107485.i 0.780906 0.780906i
\(372\) 0 0
\(373\) −24034.7 + 24034.7i −0.172751 + 0.172751i −0.788187 0.615436i \(-0.788980\pi\)
0.615436 + 0.788187i \(0.288980\pi\)
\(374\) 0 0
\(375\) −99867.8 −0.710171
\(376\) 0 0
\(377\) 86056.2i 0.605480i
\(378\) 0 0
\(379\) −27907.2 27907.2i −0.194284 0.194284i 0.603260 0.797544i \(-0.293868\pi\)
−0.797544 + 0.603260i \(0.793868\pi\)
\(380\) 0 0
\(381\) 180083. + 180083.i 1.24057 + 1.24057i
\(382\) 0 0
\(383\) 96652.7i 0.658895i −0.944174 0.329448i \(-0.893137\pi\)
0.944174 0.329448i \(-0.106863\pi\)
\(384\) 0 0
\(385\) −145505. −0.981648
\(386\) 0 0
\(387\) −89047.2 + 89047.2i −0.594564 + 0.594564i
\(388\) 0 0
\(389\) −133129. + 133129.i −0.879777 + 0.879777i −0.993511 0.113734i \(-0.963719\pi\)
0.113734 + 0.993511i \(0.463719\pi\)
\(390\) 0 0
\(391\) 28771.8 0.188197
\(392\) 0 0
\(393\) 302181.i 1.95651i
\(394\) 0 0
\(395\) −121880. 121880.i −0.781159 0.781159i
\(396\) 0 0
\(397\) −33406.1 33406.1i −0.211956 0.211956i 0.593142 0.805098i \(-0.297887\pi\)
−0.805098 + 0.593142i \(0.797887\pi\)
\(398\) 0 0
\(399\) 78776.3i 0.494823i
\(400\) 0 0
\(401\) −87329.7 −0.543092 −0.271546 0.962425i \(-0.587535\pi\)
−0.271546 + 0.962425i \(0.587535\pi\)
\(402\) 0 0
\(403\) −26076.8 + 26076.8i −0.160562 + 0.160562i
\(404\) 0 0
\(405\) −223181. + 223181.i −1.36065 + 1.36065i
\(406\) 0 0
\(407\) −123146. −0.743418
\(408\) 0 0
\(409\) 47133.9i 0.281765i −0.990026 0.140883i \(-0.955006\pi\)
0.990026 0.140883i \(-0.0449940\pi\)
\(410\) 0 0
\(411\) 265012. + 265012.i 1.56885 + 1.56885i
\(412\) 0 0
\(413\) −187224. 187224.i −1.09765 1.09765i
\(414\) 0 0
\(415\) 79388.5i 0.460958i
\(416\) 0 0
\(417\) −184874. −1.06317
\(418\) 0 0
\(419\) −70487.1 + 70487.1i −0.401497 + 0.401497i −0.878760 0.477264i \(-0.841629\pi\)
0.477264 + 0.878760i \(0.341629\pi\)
\(420\) 0 0
\(421\) −109929. + 109929.i −0.620225 + 0.620225i −0.945589 0.325364i \(-0.894513\pi\)
0.325364 + 0.945589i \(0.394513\pi\)
\(422\) 0 0
\(423\) −45137.6 −0.252266
\(424\) 0 0
\(425\) 245634.i 1.35991i
\(426\) 0 0
\(427\) 125596. + 125596.i 0.688845 + 0.688845i
\(428\) 0 0
\(429\) 104569. + 104569.i 0.568184 + 0.568184i
\(430\) 0 0
\(431\) 8391.44i 0.0451733i −0.999745 0.0225867i \(-0.992810\pi\)
0.999745 0.0225867i \(-0.00719017\pi\)
\(432\) 0 0
\(433\) 112221. 0.598545 0.299272 0.954168i \(-0.403256\pi\)
0.299272 + 0.954168i \(0.403256\pi\)
\(434\) 0 0
\(435\) −147359. + 147359.i −0.778749 + 0.778749i
\(436\) 0 0
\(437\) −10000.4 + 10000.4i −0.0523666 + 0.0523666i
\(438\) 0 0
\(439\) 95834.1 0.497269 0.248634 0.968597i \(-0.420018\pi\)
0.248634 + 0.968597i \(0.420018\pi\)
\(440\) 0 0
\(441\) 5569.98i 0.0286402i
\(442\) 0 0
\(443\) 48800.8 + 48800.8i 0.248668 + 0.248668i 0.820424 0.571756i \(-0.193738\pi\)
−0.571756 + 0.820424i \(0.693738\pi\)
\(444\) 0 0
\(445\) −31233.0 31233.0i −0.157722 0.157722i
\(446\) 0 0
\(447\) 234127.i 1.17175i
\(448\) 0 0
\(449\) −246669. −1.22355 −0.611776 0.791031i \(-0.709545\pi\)
−0.611776 + 0.791031i \(0.709545\pi\)
\(450\) 0 0
\(451\) 124033. 124033.i 0.609794 0.609794i
\(452\) 0 0
\(453\) −62992.3 + 62992.3i −0.306967 + 0.306967i
\(454\) 0 0
\(455\) 342847. 1.65606
\(456\) 0 0
\(457\) 6030.04i 0.0288727i 0.999896 + 0.0144364i \(0.00459540\pi\)
−0.999896 + 0.0144364i \(0.995405\pi\)
\(458\) 0 0
\(459\) −85992.8 85992.8i −0.408166 0.408166i
\(460\) 0 0
\(461\) −13122.6 13122.6i −0.0617473 0.0617473i 0.675559 0.737306i \(-0.263902\pi\)
−0.737306 + 0.675559i \(0.763902\pi\)
\(462\) 0 0
\(463\) 408077.i 1.90362i −0.306689 0.951810i \(-0.599221\pi\)
0.306689 0.951810i \(-0.400779\pi\)
\(464\) 0 0
\(465\) 89305.3 0.413020
\(466\) 0 0
\(467\) −108240. + 108240.i −0.496311 + 0.496311i −0.910288 0.413977i \(-0.864140\pi\)
0.413977 + 0.910288i \(0.364140\pi\)
\(468\) 0 0
\(469\) 16557.8 16557.8i 0.0752759 0.0752759i
\(470\) 0 0
\(471\) 191216. 0.861953
\(472\) 0 0
\(473\) 220853.i 0.987144i
\(474\) 0 0
\(475\) 85376.7 + 85376.7i 0.378401 + 0.378401i
\(476\) 0 0
\(477\) 91490.1 + 91490.1i 0.402103 + 0.402103i
\(478\) 0 0
\(479\) 223150.i 0.972583i 0.873797 + 0.486291i \(0.161651\pi\)
−0.873797 + 0.486291i \(0.838349\pi\)
\(480\) 0 0
\(481\) 290165. 1.25416
\(482\) 0 0
\(483\) 39785.8 39785.8i 0.170543 0.170543i
\(484\) 0 0
\(485\) 356767. 356767.i 1.51670 1.51670i
\(486\) 0 0
\(487\) −225880. −0.952399 −0.476200 0.879337i \(-0.657986\pi\)
−0.476200 + 0.879337i \(0.657986\pi\)
\(488\) 0 0
\(489\) 372120.i 1.55620i
\(490\) 0 0
\(491\) −101698. 101698.i −0.421842 0.421842i 0.463996 0.885837i \(-0.346415\pi\)
−0.885837 + 0.463996i \(0.846415\pi\)
\(492\) 0 0
\(493\) −98440.7 98440.7i −0.405024 0.405024i
\(494\) 0 0
\(495\) 123853.i 0.505469i
\(496\) 0 0
\(497\) −52357.9 −0.211968
\(498\) 0 0
\(499\) 226481. 226481.i 0.909559 0.909559i −0.0866770 0.996236i \(-0.527625\pi\)
0.996236 + 0.0866770i \(0.0276248\pi\)
\(500\) 0 0
\(501\) 334357. 334357.i 1.33209 1.33209i
\(502\) 0 0
\(503\) −125734. −0.496956 −0.248478 0.968637i \(-0.579930\pi\)
−0.248478 + 0.968637i \(0.579930\pi\)
\(504\) 0 0
\(505\) 407820.i 1.59914i
\(506\) 0 0
\(507\) −21662.8 21662.8i −0.0842749 0.0842749i
\(508\) 0 0
\(509\) 82499.2 + 82499.2i 0.318430 + 0.318430i 0.848164 0.529734i \(-0.177708\pi\)
−0.529734 + 0.848164i \(0.677708\pi\)
\(510\) 0 0
\(511\) 134490.i 0.515048i
\(512\) 0 0
\(513\) 59778.1 0.227147
\(514\) 0 0
\(515\) 194462. 194462.i 0.733198 0.733198i
\(516\) 0 0
\(517\) −55974.7 + 55974.7i −0.209416 + 0.209416i
\(518\) 0 0
\(519\) −254025. −0.943066
\(520\) 0 0
\(521\) 225057.i 0.829120i 0.910022 + 0.414560i \(0.136064\pi\)
−0.910022 + 0.414560i \(0.863936\pi\)
\(522\) 0 0
\(523\) −230384. 230384.i −0.842264 0.842264i 0.146889 0.989153i \(-0.453074\pi\)
−0.989153 + 0.146889i \(0.953074\pi\)
\(524\) 0 0
\(525\) −339664. 339664.i −1.23234 1.23234i
\(526\) 0 0
\(527\) 59659.0i 0.214810i
\(528\) 0 0
\(529\) −269740. −0.963903
\(530\) 0 0
\(531\) 159364. 159364.i 0.565199 0.565199i
\(532\) 0 0
\(533\) −292253. + 292253.i −1.02874 + 1.02874i
\(534\) 0 0
\(535\) −97718.9 −0.341406
\(536\) 0 0
\(537\) 353165.i 1.22470i
\(538\) 0 0
\(539\) −6907.27 6907.27i −0.0237755 0.0237755i
\(540\) 0 0
\(541\) 183995. + 183995.i 0.628655 + 0.628655i 0.947730 0.319074i \(-0.103372\pi\)
−0.319074 + 0.947730i \(0.603372\pi\)
\(542\) 0 0
\(543\) 155654.i 0.527909i
\(544\) 0 0
\(545\) 292056. 0.983271
\(546\) 0 0
\(547\) −416851. + 416851.i −1.39318 + 1.39318i −0.575075 + 0.818100i \(0.695027\pi\)
−0.818100 + 0.575075i \(0.804973\pi\)
\(548\) 0 0
\(549\) −106907. + 106907.i −0.354699 + 0.354699i
\(550\) 0 0
\(551\) 68431.2 0.225399
\(552\) 0 0
\(553\) 225176.i 0.736330i
\(554\) 0 0
\(555\) −496864. 496864.i −1.61307 1.61307i
\(556\) 0 0
\(557\) 233211. + 233211.i 0.751691 + 0.751691i 0.974795 0.223104i \(-0.0716189\pi\)
−0.223104 + 0.974795i \(0.571619\pi\)
\(558\) 0 0
\(559\) 520386.i 1.66534i
\(560\) 0 0
\(561\) 239236. 0.760152
\(562\) 0 0
\(563\) −82256.5 + 82256.5i −0.259510 + 0.259510i −0.824855 0.565345i \(-0.808743\pi\)
0.565345 + 0.824855i \(0.308743\pi\)
\(564\) 0 0
\(565\) 140659. 140659.i 0.440626 0.440626i
\(566\) 0 0
\(567\) −412331. −1.28257
\(568\) 0 0
\(569\) 130218.i 0.402203i −0.979570 0.201102i \(-0.935548\pi\)
0.979570 0.201102i \(-0.0644522\pi\)
\(570\) 0 0
\(571\) 62508.2 + 62508.2i 0.191719 + 0.191719i 0.796438 0.604720i \(-0.206715\pi\)
−0.604720 + 0.796438i \(0.706715\pi\)
\(572\) 0 0
\(573\) −16001.2 16001.2i −0.0487353 0.0487353i
\(574\) 0 0
\(575\) 86238.6i 0.260835i
\(576\) 0 0
\(577\) 522256. 1.56867 0.784336 0.620336i \(-0.213004\pi\)
0.784336 + 0.620336i \(0.213004\pi\)
\(578\) 0 0
\(579\) −230208. + 230208.i −0.686695 + 0.686695i
\(580\) 0 0
\(581\) −73336.0 + 73336.0i −0.217252 + 0.217252i
\(582\) 0 0
\(583\) 226912. 0.667606
\(584\) 0 0
\(585\) 291829.i 0.852739i
\(586\) 0 0
\(587\) 309702. + 309702.i 0.898811 + 0.898811i 0.995331 0.0965202i \(-0.0307712\pi\)
−0.0965202 + 0.995331i \(0.530771\pi\)
\(588\) 0 0
\(589\) −20736.0 20736.0i −0.0597717 0.0597717i
\(590\) 0 0
\(591\) 443697.i 1.27032i
\(592\) 0 0
\(593\) −447350. −1.27215 −0.636075 0.771628i \(-0.719443\pi\)
−0.636075 + 0.771628i \(0.719443\pi\)
\(594\) 0 0
\(595\) 392186. 392186.i 1.10779 1.10779i
\(596\) 0 0
\(597\) 425687. 425687.i 1.19438 1.19438i
\(598\) 0 0
\(599\) −462149. −1.28804 −0.644019 0.765009i \(-0.722734\pi\)
−0.644019 + 0.765009i \(0.722734\pi\)
\(600\) 0 0
\(601\) 374481.i 1.03677i 0.855149 + 0.518383i \(0.173466\pi\)
−0.855149 + 0.518383i \(0.826534\pi\)
\(602\) 0 0
\(603\) 14093.8 + 14093.8i 0.0387610 + 0.0387610i
\(604\) 0 0
\(605\) 245100. + 245100.i 0.669627 + 0.669627i
\(606\) 0 0
\(607\) 86755.6i 0.235462i −0.993046 0.117731i \(-0.962438\pi\)
0.993046 0.117731i \(-0.0375620\pi\)
\(608\) 0 0
\(609\) −272248. −0.734058
\(610\) 0 0
\(611\) 131891. 131891.i 0.353290 0.353290i
\(612\) 0 0
\(613\) 112325. 112325.i 0.298920 0.298920i −0.541671 0.840591i \(-0.682208\pi\)
0.840591 + 0.541671i \(0.182208\pi\)
\(614\) 0 0
\(615\) 1.00088e6 2.64626
\(616\) 0 0
\(617\) 602706.i 1.58320i −0.611041 0.791599i \(-0.709249\pi\)
0.611041 0.791599i \(-0.290751\pi\)
\(618\) 0 0
\(619\) −150969. 150969.i −0.394010 0.394010i 0.482104 0.876114i \(-0.339873\pi\)
−0.876114 + 0.482104i \(0.839873\pi\)
\(620\) 0 0
\(621\) −30190.8 30190.8i −0.0782873 0.0782873i
\(622\) 0 0
\(623\) 57703.6i 0.148671i
\(624\) 0 0
\(625\) 190658. 0.488084
\(626\) 0 0
\(627\) −83152.6 + 83152.6i −0.211515 + 0.211515i
\(628\) 0 0
\(629\) 331922. 331922.i 0.838948 0.838948i
\(630\) 0 0
\(631\) 693714. 1.74230 0.871148 0.491020i \(-0.163376\pi\)
0.871148 + 0.491020i \(0.163376\pi\)
\(632\) 0 0
\(633\) 503485.i 1.25655i
\(634\) 0 0
\(635\) 623231. + 623231.i 1.54562 + 1.54562i
\(636\) 0 0
\(637\) 16275.3 + 16275.3i 0.0401098 + 0.0401098i
\(638\) 0 0
\(639\) 44566.7i 0.109146i
\(640\) 0 0
\(641\) −17843.0 −0.0434261 −0.0217131 0.999764i \(-0.506912\pi\)
−0.0217131 + 0.999764i \(0.506912\pi\)
\(642\) 0 0
\(643\) −230136. + 230136.i −0.556626 + 0.556626i −0.928345 0.371719i \(-0.878768\pi\)
0.371719 + 0.928345i \(0.378768\pi\)
\(644\) 0 0
\(645\) −891085. + 891085.i −2.14190 + 2.14190i
\(646\) 0 0
\(647\) −568528. −1.35814 −0.679068 0.734075i \(-0.737616\pi\)
−0.679068 + 0.734075i \(0.737616\pi\)
\(648\) 0 0
\(649\) 395251.i 0.938391i
\(650\) 0 0
\(651\) 82496.7 + 82496.7i 0.194659 + 0.194659i
\(652\) 0 0
\(653\) −371799. 371799.i −0.871932 0.871932i 0.120751 0.992683i \(-0.461470\pi\)
−0.992683 + 0.120751i \(0.961470\pi\)
\(654\) 0 0
\(655\) 1.04579e6i 2.43759i
\(656\) 0 0
\(657\) −114477. −0.265208
\(658\) 0 0
\(659\) −71107.3 + 71107.3i −0.163736 + 0.163736i −0.784219 0.620484i \(-0.786936\pi\)
0.620484 + 0.784219i \(0.286936\pi\)
\(660\) 0 0
\(661\) −570193. + 570193.i −1.30502 + 1.30502i −0.380065 + 0.924960i \(0.624098\pi\)
−0.924960 + 0.380065i \(0.875902\pi\)
\(662\) 0 0
\(663\) −563701. −1.28239
\(664\) 0 0
\(665\) 272629.i 0.616494i
\(666\) 0 0
\(667\) −34561.0 34561.0i −0.0776846 0.0776846i
\(668\) 0 0
\(669\) −741091. 741091.i −1.65584 1.65584i
\(670\) 0 0
\(671\) 265148.i 0.588901i
\(672\) 0 0
\(673\) −57084.2 −0.126033 −0.0630167 0.998012i \(-0.520072\pi\)
−0.0630167 + 0.998012i \(0.520072\pi\)
\(674\) 0 0
\(675\) −257749. + 257749.i −0.565704 + 0.565704i
\(676\) 0 0
\(677\) 107264. 107264.i 0.234032 0.234032i −0.580341 0.814373i \(-0.697081\pi\)
0.814373 + 0.580341i \(0.197081\pi\)
\(678\) 0 0
\(679\) 659134. 1.42966
\(680\) 0 0
\(681\) 986444.i 2.12705i
\(682\) 0 0
\(683\) 41763.8 + 41763.8i 0.0895280 + 0.0895280i 0.750452 0.660924i \(-0.229836\pi\)
−0.660924 + 0.750452i \(0.729836\pi\)
\(684\) 0 0
\(685\) 917153. + 917153.i 1.95461 + 1.95461i
\(686\) 0 0
\(687\) 311303.i 0.659583i
\(688\) 0 0
\(689\) −534662. −1.12627
\(690\) 0 0
\(691\) 473605. 473605.i 0.991882 0.991882i −0.00808568 0.999967i \(-0.502574\pi\)
0.999967 + 0.00808568i \(0.00257378\pi\)
\(692\) 0 0
\(693\) 114410. 114410.i 0.238231 0.238231i
\(694\) 0 0
\(695\) −639811. −1.32459
\(696\) 0 0
\(697\) 668623.i 1.37631i
\(698\) 0 0
\(699\) −197198. 197198.i −0.403598 0.403598i
\(700\) 0 0
\(701\) 139642. + 139642.i 0.284170 + 0.284170i 0.834770 0.550599i \(-0.185601\pi\)
−0.550599 + 0.834770i \(0.685601\pi\)
\(702\) 0 0
\(703\) 230737.i 0.466880i
\(704\) 0 0
\(705\) −451687. −0.908782
\(706\) 0 0
\(707\) −376728. + 376728.i −0.753684 + 0.753684i
\(708\) 0 0
\(709\) 161047. 161047.i 0.320377 0.320377i −0.528535 0.848912i \(-0.677258\pi\)
0.848912 + 0.528535i \(0.177258\pi\)
\(710\) 0 0
\(711\) 191668. 0.379150
\(712\) 0 0
\(713\) 20945.4i 0.0412011i
\(714\) 0 0
\(715\) 361893. + 361893.i 0.707894 + 0.707894i
\(716\) 0 0
\(717\) −732090. 732090.i −1.42405 1.42405i
\(718\) 0 0
\(719\) 132212.i 0.255749i −0.991790 0.127874i \(-0.959185\pi\)
0.991790 0.127874i \(-0.0408154\pi\)
\(720\) 0 0
\(721\) 359273. 0.691122
\(722\) 0 0
\(723\) 637198. 637198.i 1.21898 1.21898i
\(724\) 0 0
\(725\) −295059. + 295059.i −0.561349 + 0.561349i
\(726\) 0 0
\(727\) −98417.4 −0.186210 −0.0931050 0.995656i \(-0.529679\pi\)
−0.0931050 + 0.995656i \(0.529679\pi\)
\(728\) 0 0
\(729\) 31927.4i 0.0600770i
\(730\) 0 0
\(731\) −595275. 595275.i −1.11399 1.11399i
\(732\) 0 0
\(733\) 369797. + 369797.i 0.688265 + 0.688265i 0.961848 0.273584i \(-0.0882090\pi\)
−0.273584 + 0.961848i \(0.588209\pi\)
\(734\) 0 0
\(735\) 55738.2i 0.103176i
\(736\) 0 0
\(737\) 34955.2 0.0643542
\(738\) 0 0
\(739\) 117481. 117481.i 0.215120 0.215120i −0.591318 0.806438i \(-0.701392\pi\)
0.806438 + 0.591318i \(0.201392\pi\)
\(740\) 0 0
\(741\) 195929. 195929.i 0.356831 0.356831i
\(742\) 0 0
\(743\) 273733. 0.495849 0.247925 0.968779i \(-0.420251\pi\)
0.247925 + 0.968779i \(0.420251\pi\)
\(744\) 0 0
\(745\) 810267.i 1.45988i
\(746\) 0 0
\(747\) −62423.0 62423.0i −0.111867 0.111867i
\(748\) 0 0
\(749\) −90268.8 90268.8i −0.160907 0.160907i
\(750\) 0 0
\(751\) 875863.i 1.55295i −0.630150 0.776473i \(-0.717007\pi\)
0.630150 0.776473i \(-0.282993\pi\)
\(752\) 0 0
\(753\) −407741. −0.719108
\(754\) 0 0
\(755\) −218004. + 218004.i −0.382446 + 0.382446i
\(756\) 0 0
\(757\) −66071.4 + 66071.4i −0.115298 + 0.115298i −0.762402 0.647104i \(-0.775980\pi\)
0.647104 + 0.762402i \(0.275980\pi\)
\(758\) 0 0
\(759\) 83992.1 0.145799
\(760\) 0 0
\(761\) 333176.i 0.575314i −0.957734 0.287657i \(-0.907124\pi\)
0.957734 0.287657i \(-0.0928763\pi\)
\(762\) 0 0
\(763\) 269790. + 269790.i 0.463422 + 0.463422i
\(764\) 0 0
\(765\) 333826. + 333826.i 0.570423 + 0.570423i
\(766\) 0 0
\(767\) 931313.i 1.58309i
\(768\) 0 0
\(769\) −110911. −0.187552 −0.0937762 0.995593i \(-0.529894\pi\)
−0.0937762 + 0.995593i \(0.529894\pi\)
\(770\) 0 0
\(771\) −124325. + 124325.i −0.209146 + 0.209146i
\(772\) 0 0
\(773\) 800998. 800998.i 1.34052 1.34052i 0.444972 0.895544i \(-0.353213\pi\)
0.895544 0.444972i \(-0.146787\pi\)
\(774\) 0 0
\(775\) 178818. 0.297719
\(776\) 0 0
\(777\) 917967.i 1.52050i
\(778\) 0 0
\(779\) −232397. 232397.i −0.382962 0.382962i
\(780\) 0 0
\(781\) −55266.6 55266.6i −0.0906068 0.0906068i
\(782\) 0 0
\(783\) 206591.i 0.336968i
\(784\) 0 0
\(785\) 661762. 1.07390
\(786\) 0 0
\(787\) −528761. + 528761.i −0.853709 + 0.853709i −0.990588 0.136879i \(-0.956293\pi\)
0.136879 + 0.990588i \(0.456293\pi\)
\(788\) 0 0
\(789\) −645552. + 645552.i −1.03700 + 1.03700i
\(790\) 0 0
\(791\) 259870. 0.415340
\(792\) 0 0
\(793\) 624756.i 0.993491i
\(794\) 0 0
\(795\) 915532. + 915532.i 1.44857 + 1.44857i