Properties

Label 128.5.f.a.31.2
Level 128
Weight 5
Character 128.31
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 31.2
Root \(0.336831 + 2.80830i\) of defining polynomial
Character \(\chi\) \(=\) 128.31
Dual form 128.5.f.a.95.2

$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

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

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 0.118668 0.992934i \(-0.462138\pi\)
−0.992934 + 0.118668i \(0.962138\pi\)
\(4\) 0 0
\(5\) −27.2309 27.2309i −1.08924 1.08924i −0.995607 0.0936308i \(-0.970153\pi\)
−0.0936308 0.995607i \(-0.529847\pi\)
\(6\) 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 −0.891635 0.452754i \(-0.850442\pi\)
0.452754 + 0.891635i \(0.350442\pi\)
\(12\) 0 0
\(13\) 125.128 125.128i 0.740404 0.740404i −0.232252 0.972656i \(-0.574609\pi\)
0.972656 + 0.232252i \(0.0746094\pi\)
\(14\) 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 0.555734 0.831360i \(-0.312437\pi\)
−0.831360 + 0.555734i \(0.812437\pi\)
\(20\) 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 −0.881350 0.472465i \(-0.843364\pi\)
0.472465 + 0.881350i \(0.343364\pi\)
\(30\) 0 0
\(31\) 208.400i 0.216858i −0.994104 0.108429i \(-0.965418\pi\)
0.994104 0.108429i \(-0.0345820\pi\)
\(32\) 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 0.989751 0.142805i \(-0.0456122\pi\)
−0.142805 + 0.989751i \(0.545612\pi\)
\(38\) 0 0
\(39\) −1969.12 −1.29462
\(40\) 0 0
\(41\) 2335.63i 1.38943i −0.719286 0.694714i \(-0.755531\pi\)
0.719286 0.694714i \(-0.244469\pi\)
\(42\) 0 0
\(43\) −2079.41 + 2079.41i −1.12461 + 1.12461i −0.133575 + 0.991039i \(0.542646\pi\)
−0.991039 + 0.133575i \(0.957354\pi\)
\(44\) 0 0
\(45\) 1166.12 1166.12i 0.575861 0.575861i
\(46\) 0 0
\(47\) 1054.04i 0.477159i 0.971123 + 0.238580i \(0.0766818\pi\)
−0.971123 + 0.238580i \(0.923318\pi\)
\(48\) 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 0.215850 0.976426i \(-0.430748\pi\)
−0.976426 + 0.215850i \(0.930748\pi\)
\(54\) 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 0.0716407 0.997431i \(-0.477177\pi\)
0.997431 0.0716407i \(-0.0228235\pi\)
\(60\) 0 0
\(61\) −2496.46 + 2496.46i −0.670912 + 0.670912i −0.957926 0.287014i \(-0.907337\pi\)
0.287014 + 0.957926i \(0.407337\pi\)
\(62\) 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 0.669498 0.742814i \(-0.266509\pi\)
−0.742814 + 0.669498i \(0.766509\pi\)
\(68\) 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 \(0.0807001\pi\)
−0.968034 + 0.250820i \(0.919300\pi\)
\(74\) 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 \(-0.883261\pi\)
0.933499 0.358580i \(-0.116739\pi\)
\(80\) 0 0
\(81\) 8195.85 1.24918
\(82\) 0 0
\(83\) 1457.69 + 1457.69i 0.211597 + 0.211597i 0.804945 0.593349i \(-0.202195\pi\)
−0.593349 + 0.804945i \(0.702195\pi\)
\(84\) 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 \(-0.976934\pi\)
0.997376 0.0724003i \(-0.0230659\pi\)
\(90\) 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 0.971422 0.237359i \(-0.0762818\pi\)
−0.237359 + 0.971422i \(0.576282\pi\)
\(102\) 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 −0.624393 0.781111i \(-0.714654\pi\)
0.781111 + 0.624393i \(0.214654\pi\)
\(108\) 0 0
\(109\) −5362.57 + 5362.57i −0.451357 + 0.451357i −0.895805 0.444448i \(-0.853400\pi\)
0.444448 + 0.895805i \(0.353400\pi\)
\(110\) 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 \(0.251077\pi\)
−0.704711 + 0.709495i \(0.748923\pi\)
\(128\) 0 0
\(129\) 32723.3 1.96642
\(130\) 0 0
\(131\) 19202.2 + 19202.2i 1.11894 + 1.11894i 0.991897 + 0.127048i \(0.0405502\pi\)
0.127048 + 0.991897i \(0.459450\pi\)
\(132\) 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 \(0.354430\pi\)
−0.441547 + 0.897238i \(0.645570\pi\)
\(138\) 0 0
\(139\) 11747.9 11747.9i 0.608036 0.608036i −0.334397 0.942432i \(-0.608532\pi\)
0.942432 + 0.334397i \(0.108532\pi\)
\(140\) 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 0.957747 0.287611i \(-0.0928611\pi\)
−0.287611 + 0.957747i \(0.592861\pi\)
\(150\) 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 −0.909237 0.416279i \(-0.863334\pi\)
0.416279 + 0.909237i \(0.363334\pi\)
\(158\) 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 0.104520 0.994523i \(-0.466669\pi\)
−0.994523 + 0.104520i \(0.966669\pi\)
\(164\) 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 −0.383990 0.923337i \(-0.625450\pi\)
0.923337 + 0.383990i \(0.125450\pi\)
\(174\) 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 0.264084 0.964500i \(-0.414930\pi\)
−0.964500 + 0.264084i \(0.914930\pi\)
\(180\) 0 0
\(181\) 9891.06 + 9891.06i 0.301916 + 0.301916i 0.841763 0.539847i \(-0.181518\pi\)
−0.539847 + 0.841763i \(0.681518\pi\)
\(182\) 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 \(-0.991127\pi\)
0.999611 0.0278721i \(-0.00887311\pi\)
\(192\) 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 0.243417 0.969922i \(-0.421732\pi\)
−0.969922 + 0.243417i \(0.921732\pi\)
\(198\) 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 0.249694 0.968325i \(-0.419670\pi\)
−0.968325 + 0.249694i \(0.919670\pi\)
\(212\) 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 \(-0.604107\pi\)
0.321261 0.946991i \(-0.395893\pi\)
\(224\) 0 0
\(225\) −36744.4 −0.725816
\(226\) 0 0
\(227\) 62683.9 + 62683.9i 1.21648 + 1.21648i 0.968857 + 0.247622i \(0.0796490\pi\)
0.247622 + 0.968857i \(0.420351\pi\)
\(228\) 0 0
\(229\) 19781.9 + 19781.9i 0.377221 + 0.377221i 0.870099 0.492877i \(-0.164055\pi\)
−0.492877 + 0.870099i \(0.664055\pi\)
\(230\) 0 0
\(231\) −42043.7 −0.787910
\(232\) 0 0
\(233\) 25062.1i 0.461642i −0.972996 0.230821i \(-0.925859\pi\)
0.972996 0.230821i \(-0.0741412\pi\)
\(234\) 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 \(-0.697051\pi\)
0.580265 0.814427i \(-0.302949\pi\)
\(240\) 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 −0.470915 0.882179i \(-0.656076\pi\)
0.882179 + 0.470915i \(0.156076\pi\)
\(252\) 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 −0.461314 0.887237i \(-0.652622\pi\)
0.887237 + 0.461314i \(0.152622\pi\)
\(270\) 0 0
\(271\) 110808.i 1.50880i 0.656412 + 0.754402i \(0.272073\pi\)
−0.656412 + 0.754402i \(0.727927\pi\)
\(272\) 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 0.520051 0.854135i \(-0.325913\pi\)
−0.854135 + 0.520051i \(0.825913\pi\)
\(278\) 0 0
\(279\) 8924.39 0.114649
\(280\) 0 0
\(281\) 48800.5i 0.618033i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.0999999\pi\)
\(282\) 0 0
\(283\) −111466. + 111466.i −1.39178 + 1.39178i −0.570439 + 0.821340i \(0.693227\pi\)
−0.821340 + 0.570439i \(0.806773\pi\)
\(284\) 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 0.626726 0.779240i \(-0.284395\pi\)
−0.779240 + 0.626726i \(0.784395\pi\)
\(294\) 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 0.828363 0.560192i \(-0.189273\pi\)
−0.560192 + 0.828363i \(0.689273\pi\)
\(308\) 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 \(0.247245\pi\)
−0.713199 + 0.700961i \(0.752755\pi\)
\(314\) 0 0
\(315\) −58667.1 + 58667.1i −0.591253 + 0.591253i
\(316\) 0 0
\(317\) −115546. + 115546.i −1.14984 + 1.14984i −0.163252 + 0.986584i \(0.552198\pi\)
−0.986584 + 0.163252i \(0.947802\pi\)
\(318\) 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 −0.324978 0.945722i \(-0.605357\pi\)
0.945722 + 0.324978i \(0.105357\pi\)
\(332\) 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 −0.956649 0.291243i \(-0.905931\pi\)
0.291243 + 0.956649i \(0.405931\pi\)
\(348\) 0 0
\(349\) −100990. + 100990.i −0.829143 + 0.829143i −0.987398 0.158255i \(-0.949413\pi\)
0.158255 + 0.987398i \(0.449413\pi\)
\(350\) 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 \(-0.819149\pi\)
0.842892 0.538082i \(-0.180851\pi\)
\(368\) 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 0.615436 0.788187i \(-0.288980\pi\)
−0.788187 + 0.615436i \(0.788980\pi\)
\(374\) 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 −0.797544 0.603260i \(-0.793868\pi\)
0.603260 + 0.797544i \(0.293868\pi\)
\(380\) 0 0
\(381\) 180083. 180083.i 1.24057 1.24057i
\(382\) 0 0
\(383\) 96652.7i 0.658895i 0.944174 + 0.329448i \(0.106863\pi\)
−0.944174 + 0.329448i \(0.893137\pi\)
\(384\) 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 0.113734 0.993511i \(-0.463719\pi\)
−0.993511 + 0.113734i \(0.963719\pi\)
\(390\) 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 −0.805098 0.593142i \(-0.797887\pi\)
0.593142 + 0.805098i \(0.297887\pi\)
\(398\) 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 \(0.0449940\pi\)
−0.990026 + 0.140883i \(0.955006\pi\)
\(410\) 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 0.477264 0.878760i \(-0.341629\pi\)
−0.878760 + 0.477264i \(0.841629\pi\)
\(420\) 0 0
\(421\) −109929. 109929.i −0.620225 0.620225i 0.325364 0.945589i \(-0.394513\pi\)
−0.945589 + 0.325364i \(0.894513\pi\)
\(422\) 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 \(0.00719017\pi\)
−0.999745 + 0.0225867i \(0.992810\pi\)
\(432\) 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 −0.571756 0.820424i \(-0.693738\pi\)
0.820424 + 0.571756i \(0.193738\pi\)
\(444\) 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 \(-0.995405\pi\)
0.999896 0.0144364i \(-0.00459540\pi\)
\(458\) 0 0
\(459\) −85992.8 + 85992.8i −0.408166 + 0.408166i
\(460\) 0 0
\(461\) −13122.6 + 13122.6i −0.0617473 + 0.0617473i −0.737306 0.675559i \(-0.763902\pi\)
0.675559 + 0.737306i \(0.263902\pi\)
\(462\) 0 0
\(463\) 408077.i 1.90362i 0.306689 + 0.951810i \(0.400779\pi\)
−0.306689 + 0.951810i \(0.599221\pi\)
\(464\) 0 0
\(465\) 89305.3 0.413020
\(466\) 0 0
\(467\) −108240. 108240.i −0.496311 0.496311i 0.413977 0.910288i \(-0.364140\pi\)
−0.910288 + 0.413977i \(0.864140\pi\)
\(468\) 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 \(-0.838349\pi\)
0.873797 0.486291i \(-0.161651\pi\)
\(480\) 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 −0.885837 0.463996i \(-0.846415\pi\)
0.463996 + 0.885837i \(0.346415\pi\)
\(492\) 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 0.996236 0.0866770i \(-0.0276248\pi\)
−0.0866770 + 0.996236i \(0.527625\pi\)
\(500\) 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 −0.529734 0.848164i \(-0.677708\pi\)
0.848164 + 0.529734i \(0.177708\pi\)
\(510\) 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 \(-0.863936\pi\)
0.910022 0.414560i \(-0.136064\pi\)
\(522\) 0 0
\(523\) −230384. + 230384.i −0.842264 + 0.842264i −0.989153 0.146889i \(-0.953074\pi\)
0.146889 + 0.989153i \(0.453074\pi\)
\(524\) 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 −0.319074 0.947730i \(-0.603372\pi\)
0.947730 + 0.319074i \(0.103372\pi\)
\(542\) 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 −0.818100 0.575075i \(-0.804973\pi\)
−0.575075 0.818100i \(-0.695027\pi\)
\(548\) 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 −0.223104 0.974795i \(-0.571619\pi\)
0.974795 + 0.223104i \(0.0716189\pi\)
\(558\) 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 0.565345 0.824855i \(-0.308743\pi\)
−0.824855 + 0.565345i \(0.808743\pi\)
\(564\) 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 \(0.0644522\pi\)
−0.979570 + 0.201102i \(0.935548\pi\)
\(570\) 0 0
\(571\) 62508.2 62508.2i 0.191719 0.191719i −0.604720 0.796438i \(-0.706715\pi\)
0.796438 + 0.604720i \(0.206715\pi\)
\(572\) 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 −0.0965202 0.995331i \(-0.530771\pi\)
0.995331 + 0.0965202i \(0.0307712\pi\)
\(588\) 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 \(-0.826534\pi\)
0.855149 0.518383i \(-0.173466\pi\)
\(602\) 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 \(0.0375620\pi\)
−0.993046 + 0.117731i \(0.962438\pi\)
\(608\) 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 0.840591 0.541671i \(-0.182208\pi\)
−0.541671 + 0.840591i \(0.682208\pi\)
\(614\) 0 0
\(615\) 1.00088e6 2.64626
\(616\) 0 0
\(617\) 602706.i 1.58320i 0.611041 + 0.791599i \(0.290751\pi\)
−0.611041 + 0.791599i \(0.709249\pi\)
\(618\) 0 0
\(619\) −150969. + 150969.i −0.394010 + 0.394010i −0.876114 0.482104i \(-0.839873\pi\)
0.482104 + 0.876114i \(0.339873\pi\)
\(620\) 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 0.371719 0.928345i \(-0.378768\pi\)
−0.928345 + 0.371719i \(0.878768\pi\)
\(644\) 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 −0.992683 0.120751i \(-0.961470\pi\)
0.120751 + 0.992683i \(0.461470\pi\)
\(654\) 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 0.620484 0.784219i \(-0.286936\pi\)
−0.784219 + 0.620484i \(0.786936\pi\)
\(660\) 0 0
\(661\) −570193. 570193.i −1.30502 1.30502i −0.924960 0.380065i \(-0.875902\pi\)
−0.380065 0.924960i \(-0.624098\pi\)
\(662\) 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 0.814373 0.580341i \(-0.197081\pi\)
−0.580341 + 0.814373i \(0.697081\pi\)
\(678\) 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 −0.660924 0.750452i \(-0.729836\pi\)
0.750452 + 0.660924i \(0.229836\pi\)
\(684\) 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 0.999967 0.00808568i \(-0.00257378\pi\)
−0.00808568 + 0.999967i \(0.502574\pi\)
\(692\) 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 −0.550599 0.834770i \(-0.685601\pi\)
0.834770 + 0.550599i \(0.185601\pi\)
\(702\) 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 0.848912 0.528535i \(-0.177258\pi\)
−0.528535 + 0.848912i \(0.677258\pi\)
\(710\) 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 \(0.0408154\pi\)
−0.991790 + 0.127874i \(0.959185\pi\)
\(720\) 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 −0.273584 0.961848i \(-0.588209\pi\)
0.961848 + 0.273584i \(0.0882090\pi\)
\(734\) 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 0.806438 0.591318i \(-0.201392\pi\)
−0.591318 + 0.806438i \(0.701392\pi\)
\(740\) 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 \(0.282993\pi\)
−0.630150 + 0.776473i \(0.717007\pi\)
\(752\) 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 0.647104 0.762402i \(-0.275980\pi\)
−0.762402 + 0.647104i \(0.775980\pi\)
\(758\) 0 0
\(759\) 83992.1 0.145799
\(760\) 0 0
\(761\) 333176.i 0.575314i 0.957734 + 0.287657i \(0.0928763\pi\)
−0.957734 + 0.287657i \(0.907124\pi\)
\(762\) 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 0.895544 + 0.444972i \(0.146787\pi\)
0.444972 + 0.895544i \(0.353213\pi\)
\(774\) 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 0.136879 0.990588i \(-0.456293\pi\)
−0.990588 + 0.136879i \(0.956293\pi\)
\(788\) 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