Properties

Label 768.3.h.g.641.6
Level $768$
Weight $3$
Character 768.641
Analytic conductor $20.926$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 768 = 2^{8} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 768.h (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(20.9264843029\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 14 x^{14} - 28 x^{13} + 50 x^{12} - 104 x^{11} - 66 x^{10} + 640 x^{9} + 555 x^{8} - 7060 x^{7} + 17714 x^{6} - 25496 x^{5} + 24840 x^{4} - 17932 x^{3} + 11724 x^{2} - 7056 x + 2401\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{34}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 384)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 641.6
Root \(-0.280847 + 0.678024i\) of defining polynomial
Character \(\chi\) \(=\) 768.641
Dual form 768.3.h.g.641.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.32750 + 2.69031i) q^{3} +0.640013 q^{5} -2.72077 q^{7} +(-5.47550 - 7.14275i) q^{9} +O(q^{10})\) \(q+(-1.32750 + 2.69031i) q^{3} +0.640013 q^{5} -2.72077 q^{7} +(-5.47550 - 7.14275i) q^{9} +11.2836 q^{11} -5.25176i q^{13} +(-0.849616 + 1.72183i) q^{15} +14.8718i q^{17} +15.0798i q^{19} +(3.61181 - 7.31969i) q^{21} +36.4411i q^{23} -24.5904 q^{25} +(26.4849 - 5.24877i) q^{27} -51.7310 q^{29} -36.5009 q^{31} +(-14.9790 + 30.3565i) q^{33} -1.74133 q^{35} -63.6951i q^{37} +(14.1289 + 6.97170i) q^{39} +12.1500i q^{41} +11.8032i q^{43} +(-3.50439 - 4.57146i) q^{45} -61.1247i q^{47} -41.5974 q^{49} +(-40.0097 - 19.7423i) q^{51} +59.1695 q^{53} +7.22168 q^{55} +(-40.5694 - 20.0185i) q^{57} -37.2898 q^{59} -58.1987i q^{61} +(14.8975 + 19.4338i) q^{63} -3.36120i q^{65} +23.0991i q^{67} +(-98.0376 - 48.3754i) q^{69} +7.29656i q^{71} -73.4504 q^{73} +(32.6437 - 66.1557i) q^{75} -30.7002 q^{77} +58.5098 q^{79} +(-21.0379 + 78.2203i) q^{81} +32.3939 q^{83} +9.51815i q^{85} +(68.6728 - 139.172i) q^{87} +112.260i q^{89} +14.2888i q^{91} +(48.4549 - 98.1987i) q^{93} +9.65130i q^{95} -80.0338 q^{97} +(-61.7836 - 80.5963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 16q^{7} + O(q^{10}) \) \( 16q - 16q^{7} + 32q^{15} + 80q^{25} - 112q^{31} + 16q^{33} + 208q^{39} + 144q^{49} - 384q^{55} + 80q^{57} + 528q^{63} + 160q^{73} - 816q^{79} + 144q^{81} + 736q^{87} + 192q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).

\(n\) \(257\) \(511\) \(517\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

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
\(3\) −1.32750 + 2.69031i −0.442499 + 0.896769i
\(4\) 0 0
\(5\) 0.640013 0.128003 0.0640013 0.997950i \(-0.479614\pi\)
0.0640013 + 0.997950i \(0.479614\pi\)
\(6\) 0 0
\(7\) −2.72077 −0.388681 −0.194340 0.980934i \(-0.562257\pi\)
−0.194340 + 0.980934i \(0.562257\pi\)
\(8\) 0 0
\(9\) −5.47550 7.14275i −0.608389 0.793639i
\(10\) 0 0
\(11\) 11.2836 1.02579 0.512893 0.858452i \(-0.328574\pi\)
0.512893 + 0.858452i \(0.328574\pi\)
\(12\) 0 0
\(13\) 5.25176i 0.403982i −0.979387 0.201991i \(-0.935259\pi\)
0.979387 0.201991i \(-0.0647411\pi\)
\(14\) 0 0
\(15\) −0.849616 + 1.72183i −0.0566411 + 0.114789i
\(16\) 0 0
\(17\) 14.8718i 0.874812i 0.899264 + 0.437406i \(0.144103\pi\)
−0.899264 + 0.437406i \(0.855897\pi\)
\(18\) 0 0
\(19\) 15.0798i 0.793676i 0.917889 + 0.396838i \(0.129893\pi\)
−0.917889 + 0.396838i \(0.870107\pi\)
\(20\) 0 0
\(21\) 3.61181 7.31969i 0.171991 0.348557i
\(22\) 0 0
\(23\) 36.4411i 1.58439i 0.610266 + 0.792197i \(0.291063\pi\)
−0.610266 + 0.792197i \(0.708937\pi\)
\(24\) 0 0
\(25\) −24.5904 −0.983615
\(26\) 0 0
\(27\) 26.4849 5.24877i 0.980923 0.194399i
\(28\) 0 0
\(29\) −51.7310 −1.78383 −0.891914 0.452205i \(-0.850638\pi\)
−0.891914 + 0.452205i \(0.850638\pi\)
\(30\) 0 0
\(31\) −36.5009 −1.17745 −0.588724 0.808334i \(-0.700370\pi\)
−0.588724 + 0.808334i \(0.700370\pi\)
\(32\) 0 0
\(33\) −14.9790 + 30.3565i −0.453910 + 0.919893i
\(34\) 0 0
\(35\) −1.74133 −0.0497522
\(36\) 0 0
\(37\) 63.6951i 1.72149i −0.509036 0.860745i \(-0.669998\pi\)
0.509036 0.860745i \(-0.330002\pi\)
\(38\) 0 0
\(39\) 14.1289 + 6.97170i 0.362278 + 0.178762i
\(40\) 0 0
\(41\) 12.1500i 0.296342i 0.988962 + 0.148171i \(0.0473386\pi\)
−0.988962 + 0.148171i \(0.952661\pi\)
\(42\) 0 0
\(43\) 11.8032i 0.274493i 0.990537 + 0.137247i \(0.0438253\pi\)
−0.990537 + 0.137247i \(0.956175\pi\)
\(44\) 0 0
\(45\) −3.50439 4.57146i −0.0778753 0.101588i
\(46\) 0 0
\(47\) 61.1247i 1.30053i −0.759709 0.650263i \(-0.774659\pi\)
0.759709 0.650263i \(-0.225341\pi\)
\(48\) 0 0
\(49\) −41.5974 −0.848927
\(50\) 0 0
\(51\) −40.0097 19.7423i −0.784504 0.387104i
\(52\) 0 0
\(53\) 59.1695 1.11641 0.558203 0.829705i \(-0.311491\pi\)
0.558203 + 0.829705i \(0.311491\pi\)
\(54\) 0 0
\(55\) 7.22168 0.131303
\(56\) 0 0
\(57\) −40.5694 20.0185i −0.711744 0.351201i
\(58\) 0 0
\(59\) −37.2898 −0.632031 −0.316016 0.948754i \(-0.602345\pi\)
−0.316016 + 0.948754i \(0.602345\pi\)
\(60\) 0 0
\(61\) 58.1987i 0.954076i −0.878883 0.477038i \(-0.841710\pi\)
0.878883 0.477038i \(-0.158290\pi\)
\(62\) 0 0
\(63\) 14.8975 + 19.4338i 0.236469 + 0.308472i
\(64\) 0 0
\(65\) 3.36120i 0.0517107i
\(66\) 0 0
\(67\) 23.0991i 0.344762i 0.985030 + 0.172381i \(0.0551461\pi\)
−0.985030 + 0.172381i \(0.944854\pi\)
\(68\) 0 0
\(69\) −98.0376 48.3754i −1.42084 0.701093i
\(70\) 0 0
\(71\) 7.29656i 0.102768i 0.998679 + 0.0513842i \(0.0163633\pi\)
−0.998679 + 0.0513842i \(0.983637\pi\)
\(72\) 0 0
\(73\) −73.4504 −1.00617 −0.503085 0.864237i \(-0.667802\pi\)
−0.503085 + 0.864237i \(0.667802\pi\)
\(74\) 0 0
\(75\) 32.6437 66.1557i 0.435249 0.882076i
\(76\) 0 0
\(77\) −30.7002 −0.398703
\(78\) 0 0
\(79\) 58.5098 0.740630 0.370315 0.928906i \(-0.379250\pi\)
0.370315 + 0.928906i \(0.379250\pi\)
\(80\) 0 0
\(81\) −21.0379 + 78.2203i −0.259727 + 0.965682i
\(82\) 0 0
\(83\) 32.3939 0.390287 0.195144 0.980775i \(-0.437483\pi\)
0.195144 + 0.980775i \(0.437483\pi\)
\(84\) 0 0
\(85\) 9.51815i 0.111978i
\(86\) 0 0
\(87\) 68.6728 139.172i 0.789343 1.59968i
\(88\) 0 0
\(89\) 112.260i 1.26135i 0.776046 + 0.630677i \(0.217223\pi\)
−0.776046 + 0.630677i \(0.782777\pi\)
\(90\) 0 0
\(91\) 14.2888i 0.157020i
\(92\) 0 0
\(93\) 48.4549 98.1987i 0.521020 1.05590i
\(94\) 0 0
\(95\) 9.65130i 0.101593i
\(96\) 0 0
\(97\) −80.0338 −0.825090 −0.412545 0.910937i \(-0.635360\pi\)
−0.412545 + 0.910937i \(0.635360\pi\)
\(98\) 0 0
\(99\) −61.7836 80.5963i −0.624077 0.814104i
\(100\) 0 0
\(101\) −119.373 −1.18191 −0.590954 0.806705i \(-0.701249\pi\)
−0.590954 + 0.806705i \(0.701249\pi\)
\(102\) 0 0
\(103\) −125.522 −1.21866 −0.609330 0.792917i \(-0.708562\pi\)
−0.609330 + 0.792917i \(0.708562\pi\)
\(104\) 0 0
\(105\) 2.31161 4.68470i 0.0220153 0.0446162i
\(106\) 0 0
\(107\) −148.669 −1.38943 −0.694716 0.719284i \(-0.744470\pi\)
−0.694716 + 0.719284i \(0.744470\pi\)
\(108\) 0 0
\(109\) 70.6664i 0.648316i −0.946003 0.324158i \(-0.894919\pi\)
0.946003 0.324158i \(-0.105081\pi\)
\(110\) 0 0
\(111\) 171.359 + 84.5552i 1.54378 + 0.761758i
\(112\) 0 0
\(113\) 130.968i 1.15901i −0.814969 0.579504i \(-0.803246\pi\)
0.814969 0.579504i \(-0.196754\pi\)
\(114\) 0 0
\(115\) 23.3228i 0.202807i
\(116\) 0 0
\(117\) −37.5120 + 28.7560i −0.320616 + 0.245778i
\(118\) 0 0
\(119\) 40.4627i 0.340023i
\(120\) 0 0
\(121\) 6.32073 0.0522374
\(122\) 0 0
\(123\) −32.6873 16.1291i −0.265750 0.131131i
\(124\) 0 0
\(125\) −31.7385 −0.253908
\(126\) 0 0
\(127\) −209.206 −1.64729 −0.823647 0.567103i \(-0.808064\pi\)
−0.823647 + 0.567103i \(0.808064\pi\)
\(128\) 0 0
\(129\) −31.7543 15.6687i −0.246157 0.121463i
\(130\) 0 0
\(131\) 174.839 1.33465 0.667326 0.744766i \(-0.267439\pi\)
0.667326 + 0.744766i \(0.267439\pi\)
\(132\) 0 0
\(133\) 41.0287i 0.308487i
\(134\) 0 0
\(135\) 16.9507 3.35929i 0.125561 0.0248836i
\(136\) 0 0
\(137\) 162.945i 1.18938i 0.803956 + 0.594689i \(0.202725\pi\)
−0.803956 + 0.594689i \(0.797275\pi\)
\(138\) 0 0
\(139\) 194.227i 1.39732i 0.715454 + 0.698660i \(0.246220\pi\)
−0.715454 + 0.698660i \(0.753780\pi\)
\(140\) 0 0
\(141\) 164.444 + 81.1429i 1.16627 + 0.575482i
\(142\) 0 0
\(143\) 59.2590i 0.414399i
\(144\) 0 0
\(145\) −33.1085 −0.228335
\(146\) 0 0
\(147\) 55.2205 111.910i 0.375650 0.761291i
\(148\) 0 0
\(149\) 83.4695 0.560198 0.280099 0.959971i \(-0.409633\pi\)
0.280099 + 0.959971i \(0.409633\pi\)
\(150\) 0 0
\(151\) −60.3488 −0.399661 −0.199830 0.979830i \(-0.564039\pi\)
−0.199830 + 0.979830i \(0.564039\pi\)
\(152\) 0 0
\(153\) 106.226 81.4306i 0.694285 0.532226i
\(154\) 0 0
\(155\) −23.3611 −0.150717
\(156\) 0 0
\(157\) 100.762i 0.641798i 0.947113 + 0.320899i \(0.103985\pi\)
−0.947113 + 0.320899i \(0.896015\pi\)
\(158\) 0 0
\(159\) −78.5474 + 159.184i −0.494009 + 1.00116i
\(160\) 0 0
\(161\) 99.1476i 0.615824i
\(162\) 0 0
\(163\) 69.7149i 0.427699i 0.976867 + 0.213849i \(0.0686002\pi\)
−0.976867 + 0.213849i \(0.931400\pi\)
\(164\) 0 0
\(165\) −9.58677 + 19.4285i −0.0581016 + 0.117749i
\(166\) 0 0
\(167\) 120.823i 0.723491i 0.932277 + 0.361745i \(0.117819\pi\)
−0.932277 + 0.361745i \(0.882181\pi\)
\(168\) 0 0
\(169\) 141.419 0.836799
\(170\) 0 0
\(171\) 107.712 82.5697i 0.629893 0.482863i
\(172\) 0 0
\(173\) 30.0602 0.173758 0.0868791 0.996219i \(-0.472311\pi\)
0.0868791 + 0.996219i \(0.472311\pi\)
\(174\) 0 0
\(175\) 66.9047 0.382312
\(176\) 0 0
\(177\) 49.5022 100.321i 0.279673 0.566786i
\(178\) 0 0
\(179\) 114.784 0.641250 0.320625 0.947206i \(-0.396107\pi\)
0.320625 + 0.947206i \(0.396107\pi\)
\(180\) 0 0
\(181\) 181.627i 1.00347i 0.865022 + 0.501733i \(0.167304\pi\)
−0.865022 + 0.501733i \(0.832696\pi\)
\(182\) 0 0
\(183\) 156.572 + 77.2586i 0.855586 + 0.422178i
\(184\) 0 0
\(185\) 40.7657i 0.220355i
\(186\) 0 0
\(187\) 167.808i 0.897370i
\(188\) 0 0
\(189\) −72.0592 + 14.2807i −0.381266 + 0.0755592i
\(190\) 0 0
\(191\) 209.226i 1.09543i 0.836666 + 0.547713i \(0.184502\pi\)
−0.836666 + 0.547713i \(0.815498\pi\)
\(192\) 0 0
\(193\) 161.330 0.835907 0.417954 0.908468i \(-0.362747\pi\)
0.417954 + 0.908468i \(0.362747\pi\)
\(194\) 0 0
\(195\) 9.04265 + 4.46198i 0.0463726 + 0.0228820i
\(196\) 0 0
\(197\) 144.953 0.735801 0.367901 0.929865i \(-0.380077\pi\)
0.367901 + 0.929865i \(0.380077\pi\)
\(198\) 0 0
\(199\) −237.264 −1.19228 −0.596140 0.802880i \(-0.703300\pi\)
−0.596140 + 0.802880i \(0.703300\pi\)
\(200\) 0 0
\(201\) −62.1436 30.6640i −0.309172 0.152557i
\(202\) 0 0
\(203\) 140.748 0.693340
\(204\) 0 0
\(205\) 7.77617i 0.0379325i
\(206\) 0 0
\(207\) 260.289 199.533i 1.25744 0.963927i
\(208\) 0 0
\(209\) 170.156i 0.814142i
\(210\) 0 0
\(211\) 307.117i 1.45553i 0.685827 + 0.727765i \(0.259441\pi\)
−0.685827 + 0.727765i \(0.740559\pi\)
\(212\) 0 0
\(213\) −19.6300 9.68617i −0.0921595 0.0454750i
\(214\) 0 0
\(215\) 7.55422i 0.0351359i
\(216\) 0 0
\(217\) 99.3105 0.457652
\(218\) 0 0
\(219\) 97.5053 197.604i 0.445230 0.902302i
\(220\) 0 0
\(221\) 78.1032 0.353408
\(222\) 0 0
\(223\) −438.001 −1.96413 −0.982065 0.188544i \(-0.939623\pi\)
−0.982065 + 0.188544i \(0.939623\pi\)
\(224\) 0 0
\(225\) 134.645 + 175.643i 0.598420 + 0.780636i
\(226\) 0 0
\(227\) −270.755 −1.19275 −0.596376 0.802705i \(-0.703393\pi\)
−0.596376 + 0.802705i \(0.703393\pi\)
\(228\) 0 0
\(229\) 98.6778i 0.430907i 0.976514 + 0.215454i \(0.0691230\pi\)
−0.976514 + 0.215454i \(0.930877\pi\)
\(230\) 0 0
\(231\) 40.7544 82.5929i 0.176426 0.357545i
\(232\) 0 0
\(233\) 432.405i 1.85581i −0.372812 0.927907i \(-0.621606\pi\)
0.372812 0.927907i \(-0.378394\pi\)
\(234\) 0 0
\(235\) 39.1206i 0.166471i
\(236\) 0 0
\(237\) −77.6717 + 157.409i −0.327729 + 0.664174i
\(238\) 0 0
\(239\) 275.799i 1.15397i −0.816754 0.576986i \(-0.804229\pi\)
0.816754 0.576986i \(-0.195771\pi\)
\(240\) 0 0
\(241\) 416.770 1.72934 0.864669 0.502343i \(-0.167528\pi\)
0.864669 + 0.502343i \(0.167528\pi\)
\(242\) 0 0
\(243\) −182.509 160.436i −0.751065 0.660228i
\(244\) 0 0
\(245\) −26.6229 −0.108665
\(246\) 0 0
\(247\) 79.1958 0.320631
\(248\) 0 0
\(249\) −43.0028 + 87.1494i −0.172702 + 0.349998i
\(250\) 0 0
\(251\) 165.903 0.660966 0.330483 0.943812i \(-0.392788\pi\)
0.330483 + 0.943812i \(0.392788\pi\)
\(252\) 0 0
\(253\) 411.188i 1.62525i
\(254\) 0 0
\(255\) −25.6068 12.6353i −0.100419 0.0495503i
\(256\) 0 0
\(257\) 59.6381i 0.232055i −0.993246 0.116028i \(-0.962984\pi\)
0.993246 0.116028i \(-0.0370161\pi\)
\(258\) 0 0
\(259\) 173.300i 0.669110i
\(260\) 0 0
\(261\) 283.253 + 369.502i 1.08526 + 1.41572i
\(262\) 0 0
\(263\) 67.2606i 0.255744i 0.991791 + 0.127872i \(0.0408146\pi\)
−0.991791 + 0.127872i \(0.959185\pi\)
\(264\) 0 0
\(265\) 37.8693 0.142903
\(266\) 0 0
\(267\) −302.015 149.026i −1.13114 0.558148i
\(268\) 0 0
\(269\) −36.1495 −0.134385 −0.0671923 0.997740i \(-0.521404\pi\)
−0.0671923 + 0.997740i \(0.521404\pi\)
\(270\) 0 0
\(271\) 328.311 1.21148 0.605741 0.795662i \(-0.292877\pi\)
0.605741 + 0.795662i \(0.292877\pi\)
\(272\) 0 0
\(273\) −38.4413 18.9684i −0.140811 0.0694812i
\(274\) 0 0
\(275\) −277.469 −1.00898
\(276\) 0 0
\(277\) 60.7455i 0.219298i −0.993970 0.109649i \(-0.965027\pi\)
0.993970 0.109649i \(-0.0349727\pi\)
\(278\) 0 0
\(279\) 199.861 + 260.717i 0.716347 + 0.934470i
\(280\) 0 0
\(281\) 366.827i 1.30543i −0.757602 0.652717i \(-0.773629\pi\)
0.757602 0.652717i \(-0.226371\pi\)
\(282\) 0 0
\(283\) 104.032i 0.367603i −0.982963 0.183801i \(-0.941160\pi\)
0.982963 0.183801i \(-0.0588404\pi\)
\(284\) 0 0
\(285\) −25.9650 12.8121i −0.0911051 0.0449547i
\(286\) 0 0
\(287\) 33.0574i 0.115182i
\(288\) 0 0
\(289\) 67.8293 0.234703
\(290\) 0 0
\(291\) 106.245 215.315i 0.365102 0.739915i
\(292\) 0 0
\(293\) 410.579 1.40129 0.700647 0.713508i \(-0.252895\pi\)
0.700647 + 0.713508i \(0.252895\pi\)
\(294\) 0 0
\(295\) −23.8660 −0.0809017
\(296\) 0 0
\(297\) 298.846 59.2253i 1.00622 0.199412i
\(298\) 0 0
\(299\) 191.380 0.640066
\(300\) 0 0
\(301\) 32.1138i 0.106690i
\(302\) 0 0
\(303\) 158.467 321.149i 0.522994 1.05990i
\(304\) 0 0
\(305\) 37.2479i 0.122124i
\(306\) 0 0
\(307\) 270.025i 0.879561i −0.898105 0.439781i \(-0.855056\pi\)
0.898105 0.439781i \(-0.144944\pi\)
\(308\) 0 0
\(309\) 166.630 337.693i 0.539256 1.09286i
\(310\) 0 0
\(311\) 251.555i 0.808858i −0.914569 0.404429i \(-0.867470\pi\)
0.914569 0.404429i \(-0.132530\pi\)
\(312\) 0 0
\(313\) 83.9560 0.268230 0.134115 0.990966i \(-0.457181\pi\)
0.134115 + 0.990966i \(0.457181\pi\)
\(314\) 0 0
\(315\) 9.53463 + 12.4379i 0.0302687 + 0.0394853i
\(316\) 0 0
\(317\) 270.737 0.854060 0.427030 0.904238i \(-0.359560\pi\)
0.427030 + 0.904238i \(0.359560\pi\)
\(318\) 0 0
\(319\) −583.715 −1.82983
\(320\) 0 0
\(321\) 197.358 399.966i 0.614823 1.24600i
\(322\) 0 0
\(323\) −224.265 −0.694318
\(324\) 0 0
\(325\) 129.143i 0.397363i
\(326\) 0 0
\(327\) 190.114 + 93.8095i 0.581389 + 0.286879i
\(328\) 0 0
\(329\) 166.306i 0.505489i
\(330\) 0 0
\(331\) 9.91562i 0.0299566i −0.999888 0.0149783i \(-0.995232\pi\)
0.999888 0.0149783i \(-0.00476791\pi\)
\(332\) 0 0
\(333\) −454.959 + 348.763i −1.36624 + 1.04733i
\(334\) 0 0
\(335\) 14.7837i 0.0441305i
\(336\) 0 0
\(337\) −289.542 −0.859174 −0.429587 0.903025i \(-0.641341\pi\)
−0.429587 + 0.903025i \(0.641341\pi\)
\(338\) 0 0
\(339\) 352.344 + 173.860i 1.03936 + 0.512860i
\(340\) 0 0
\(341\) −411.864 −1.20781
\(342\) 0 0
\(343\) 246.494 0.718643
\(344\) 0 0
\(345\) −62.7454 30.9609i −0.181871 0.0897418i
\(346\) 0 0
\(347\) −331.079 −0.954119 −0.477060 0.878871i \(-0.658297\pi\)
−0.477060 + 0.878871i \(0.658297\pi\)
\(348\) 0 0
\(349\) 302.280i 0.866133i 0.901362 + 0.433067i \(0.142569\pi\)
−0.901362 + 0.433067i \(0.857431\pi\)
\(350\) 0 0
\(351\) −27.5653 139.092i −0.0785337 0.396275i
\(352\) 0 0
\(353\) 528.345i 1.49673i 0.663289 + 0.748364i \(0.269160\pi\)
−0.663289 + 0.748364i \(0.730840\pi\)
\(354\) 0 0
\(355\) 4.66989i 0.0131546i
\(356\) 0 0
\(357\) 108.857 + 53.7142i 0.304922 + 0.150460i
\(358\) 0 0
\(359\) 59.5167i 0.165785i 0.996559 + 0.0828923i \(0.0264158\pi\)
−0.996559 + 0.0828923i \(0.973584\pi\)
\(360\) 0 0
\(361\) 133.598 0.370078
\(362\) 0 0
\(363\) −8.39076 + 17.0047i −0.0231150 + 0.0468449i
\(364\) 0 0
\(365\) −47.0092 −0.128792
\(366\) 0 0
\(367\) 423.762 1.15466 0.577332 0.816509i \(-0.304094\pi\)
0.577332 + 0.816509i \(0.304094\pi\)
\(368\) 0 0
\(369\) 86.7846 66.5274i 0.235189 0.180291i
\(370\) 0 0
\(371\) −160.986 −0.433925
\(372\) 0 0
\(373\) 26.5076i 0.0710660i −0.999369 0.0355330i \(-0.988687\pi\)
0.999369 0.0355330i \(-0.0113129\pi\)
\(374\) 0 0
\(375\) 42.1328 85.3863i 0.112354 0.227697i
\(376\) 0 0
\(377\) 271.679i 0.720634i
\(378\) 0 0
\(379\) 383.169i 1.01100i 0.862827 + 0.505500i \(0.168692\pi\)
−0.862827 + 0.505500i \(0.831308\pi\)
\(380\) 0 0
\(381\) 277.721 562.829i 0.728927 1.47724i
\(382\) 0 0
\(383\) 299.496i 0.781973i 0.920396 + 0.390987i \(0.127866\pi\)
−0.920396 + 0.390987i \(0.872134\pi\)
\(384\) 0 0
\(385\) −19.6485 −0.0510351
\(386\) 0 0
\(387\) 84.3075 64.6285i 0.217849 0.166999i
\(388\) 0 0
\(389\) −437.687 −1.12516 −0.562580 0.826743i \(-0.690191\pi\)
−0.562580 + 0.826743i \(0.690191\pi\)
\(390\) 0 0
\(391\) −541.944 −1.38605
\(392\) 0 0
\(393\) −232.099 + 470.372i −0.590583 + 1.19687i
\(394\) 0 0
\(395\) 37.4470 0.0948027
\(396\) 0 0
\(397\) 669.283i 1.68585i −0.538029 0.842926i \(-0.680831\pi\)
0.538029 0.842926i \(-0.319169\pi\)
\(398\) 0 0
\(399\) 110.380 + 54.4656i 0.276641 + 0.136505i
\(400\) 0 0
\(401\) 56.1062i 0.139916i 0.997550 + 0.0699578i \(0.0222865\pi\)
−0.997550 + 0.0699578i \(0.977714\pi\)
\(402\) 0 0
\(403\) 191.694i 0.475668i
\(404\) 0 0
\(405\) −13.4645 + 50.0620i −0.0332457 + 0.123610i
\(406\) 0 0
\(407\) 718.713i 1.76588i
\(408\) 0 0
\(409\) −248.582 −0.607779 −0.303889 0.952707i \(-0.598285\pi\)
−0.303889 + 0.952707i \(0.598285\pi\)
\(410\) 0 0
\(411\) −438.371 216.309i −1.06660 0.526299i
\(412\) 0 0
\(413\) 101.457 0.245658
\(414\) 0 0
\(415\) 20.7325 0.0499578
\(416\) 0 0
\(417\) −522.531 257.836i −1.25307 0.618313i
\(418\) 0 0
\(419\) 459.935 1.09770 0.548849 0.835922i \(-0.315066\pi\)
0.548849 + 0.835922i \(0.315066\pi\)
\(420\) 0 0
\(421\) 97.4789i 0.231541i 0.993276 + 0.115771i \(0.0369338\pi\)
−0.993276 + 0.115771i \(0.963066\pi\)
\(422\) 0 0
\(423\) −436.599 + 334.688i −1.03215 + 0.791225i
\(424\) 0 0
\(425\) 365.703i 0.860479i
\(426\) 0 0
\(427\) 158.345i 0.370831i
\(428\) 0 0
\(429\) 159.425 + 78.6663i 0.371620 + 0.183371i
\(430\) 0 0
\(431\) 545.207i 1.26498i 0.774568 + 0.632490i \(0.217967\pi\)
−0.774568 + 0.632490i \(0.782033\pi\)
\(432\) 0 0
\(433\) −24.5297 −0.0566506 −0.0283253 0.999599i \(-0.509017\pi\)
−0.0283253 + 0.999599i \(0.509017\pi\)
\(434\) 0 0
\(435\) 43.9515 89.0721i 0.101038 0.204763i
\(436\) 0 0
\(437\) −549.526 −1.25750
\(438\) 0 0
\(439\) −81.8743 −0.186502 −0.0932509 0.995643i \(-0.529726\pi\)
−0.0932509 + 0.995643i \(0.529726\pi\)
\(440\) 0 0
\(441\) 227.767 + 297.120i 0.516478 + 0.673742i
\(442\) 0 0
\(443\) 831.356 1.87665 0.938325 0.345753i \(-0.112377\pi\)
0.938325 + 0.345753i \(0.112377\pi\)
\(444\) 0 0
\(445\) 71.8482i 0.161457i
\(446\) 0 0
\(447\) −110.806 + 224.559i −0.247887 + 0.502368i
\(448\) 0 0
\(449\) 259.553i 0.578070i −0.957319 0.289035i \(-0.906666\pi\)
0.957319 0.289035i \(-0.0933344\pi\)
\(450\) 0 0
\(451\) 137.097i 0.303983i
\(452\) 0 0
\(453\) 80.1129 162.357i 0.176850 0.358403i
\(454\) 0 0
\(455\) 9.14503i 0.0200990i
\(456\) 0 0
\(457\) −373.184 −0.816596 −0.408298 0.912849i \(-0.633878\pi\)
−0.408298 + 0.912849i \(0.633878\pi\)
\(458\) 0 0
\(459\) 78.0588 + 393.879i 0.170063 + 0.858123i
\(460\) 0 0
\(461\) 672.996 1.45986 0.729930 0.683522i \(-0.239553\pi\)
0.729930 + 0.683522i \(0.239553\pi\)
\(462\) 0 0
\(463\) −28.0435 −0.0605690 −0.0302845 0.999541i \(-0.509641\pi\)
−0.0302845 + 0.999541i \(0.509641\pi\)
\(464\) 0 0
\(465\) 31.0118 62.8484i 0.0666920 0.135158i
\(466\) 0 0
\(467\) 373.758 0.800339 0.400169 0.916441i \(-0.368951\pi\)
0.400169 + 0.916441i \(0.368951\pi\)
\(468\) 0 0
\(469\) 62.8472i 0.134003i
\(470\) 0 0
\(471\) −271.082 133.762i −0.575545 0.283995i
\(472\) 0 0
\(473\) 133.183i 0.281572i
\(474\) 0 0
\(475\) 370.819i 0.780672i
\(476\) 0 0
\(477\) −323.982 422.633i −0.679208 0.886023i
\(478\) 0 0
\(479\) 915.154i 1.91055i 0.295718 + 0.955275i \(0.404441\pi\)
−0.295718 + 0.955275i \(0.595559\pi\)
\(480\) 0 0
\(481\) −334.512 −0.695451
\(482\) 0 0
\(483\) 266.737 + 131.618i 0.552251 + 0.272502i
\(484\) 0 0
\(485\) −51.2227 −0.105614
\(486\) 0 0
\(487\) 238.560 0.489856 0.244928 0.969541i \(-0.421236\pi\)
0.244928 + 0.969541i \(0.421236\pi\)
\(488\) 0 0
\(489\) −187.555 92.5464i −0.383547 0.189257i
\(490\) 0 0
\(491\) −435.657 −0.887286 −0.443643 0.896204i \(-0.646314\pi\)
−0.443643 + 0.896204i \(0.646314\pi\)
\(492\) 0 0
\(493\) 769.334i 1.56052i
\(494\) 0 0
\(495\) −39.5423 51.5827i −0.0798835 0.104207i
\(496\) 0 0
\(497\) 19.8522i 0.0399441i
\(498\) 0 0
\(499\) 209.499i 0.419838i −0.977719 0.209919i \(-0.932680\pi\)
0.977719 0.209919i \(-0.0673200\pi\)
\(500\) 0 0
\(501\) −325.051 160.392i −0.648804 0.320144i
\(502\) 0 0
\(503\) 558.314i 1.10997i 0.831861 + 0.554984i \(0.187276\pi\)
−0.831861 + 0.554984i \(0.812724\pi\)
\(504\) 0 0
\(505\) −76.4002 −0.151287
\(506\) 0 0
\(507\) −187.733 + 380.460i −0.370283 + 0.750415i
\(508\) 0 0
\(509\) −319.621 −0.627939 −0.313969 0.949433i \(-0.601659\pi\)
−0.313969 + 0.949433i \(0.601659\pi\)
\(510\) 0 0
\(511\) 199.841 0.391079
\(512\) 0 0
\(513\) 79.1507 + 399.388i 0.154290 + 0.778535i
\(514\) 0 0
\(515\) −80.3357 −0.155992
\(516\) 0 0
\(517\) 689.710i 1.33406i
\(518\) 0 0
\(519\) −39.9048 + 80.8710i −0.0768879 + 0.155821i
\(520\) 0 0
\(521\) 771.602i 1.48100i 0.672055 + 0.740501i \(0.265412\pi\)
−0.672055 + 0.740501i \(0.734588\pi\)
\(522\) 0 0
\(523\) 288.856i 0.552306i −0.961114 0.276153i \(-0.910940\pi\)
0.961114 0.276153i \(-0.0890597\pi\)
\(524\) 0 0
\(525\) −88.8158 + 179.994i −0.169173 + 0.342846i
\(526\) 0 0
\(527\) 542.835i 1.03005i
\(528\) 0 0
\(529\) −798.951 −1.51030
\(530\) 0 0
\(531\) 204.180 + 266.352i 0.384521 + 0.501605i
\(532\) 0 0
\(533\) 63.8090 0.119717
\(534\) 0 0
\(535\) −95.1503 −0.177851
\(536\) 0 0
\(537\) −152.375 + 308.803i −0.283753 + 0.575053i
\(538\) 0 0
\(539\) −469.371 −0.870818
\(540\) 0 0
\(541\) 232.871i 0.430446i 0.976565 + 0.215223i \(0.0690478\pi\)
−0.976565 + 0.215223i \(0.930952\pi\)
\(542\) 0 0
\(543\) −488.633 241.110i −0.899877 0.444033i
\(544\) 0 0
\(545\) 45.2274i 0.0829861i
\(546\) 0 0
\(547\) 910.003i 1.66363i −0.555056 0.831813i \(-0.687303\pi\)
0.555056 0.831813i \(-0.312697\pi\)
\(548\) 0 0
\(549\) −415.699 + 318.667i −0.757192 + 0.580449i
\(550\) 0 0
\(551\) 780.096i 1.41578i
\(552\) 0 0
\(553\) −159.191 −0.287869
\(554\) 0 0
\(555\) 109.672 + 54.1164i 0.197608 + 0.0975071i
\(556\) 0 0
\(557\) −297.809 −0.534666 −0.267333 0.963604i \(-0.586142\pi\)
−0.267333 + 0.963604i \(0.586142\pi\)
\(558\) 0 0
\(559\) 61.9877 0.110890
\(560\) 0 0
\(561\) −451.456 222.765i −0.804734 0.397086i
\(562\) 0 0
\(563\) −184.465 −0.327647 −0.163824 0.986490i \(-0.552383\pi\)
−0.163824 + 0.986490i \(0.552383\pi\)
\(564\) 0 0
\(565\) 83.8212i 0.148356i
\(566\) 0 0
\(567\) 57.2391 212.819i 0.100951 0.375342i
\(568\) 0 0
\(569\) 404.137i 0.710258i −0.934817 0.355129i \(-0.884437\pi\)
0.934817 0.355129i \(-0.115563\pi\)
\(570\) 0 0
\(571\) 762.365i 1.33514i 0.744547 + 0.667570i \(0.232666\pi\)
−0.744547 + 0.667570i \(0.767334\pi\)
\(572\) 0 0
\(573\) −562.883 277.748i −0.982344 0.484726i
\(574\) 0 0
\(575\) 896.100i 1.55843i
\(576\) 0 0
\(577\) −290.766 −0.503927 −0.251964 0.967737i \(-0.581076\pi\)
−0.251964 + 0.967737i \(0.581076\pi\)
\(578\) 0 0
\(579\) −214.165 + 434.027i −0.369888 + 0.749616i
\(580\) 0 0
\(581\) −88.1361 −0.151697
\(582\) 0 0
\(583\) 667.648 1.14519
\(584\) 0 0
\(585\) −24.0082 + 18.4042i −0.0410397 + 0.0314602i
\(586\) 0 0
\(587\) 224.506 0.382464 0.191232 0.981545i \(-0.438752\pi\)
0.191232 + 0.981545i \(0.438752\pi\)
\(588\) 0 0
\(589\) 550.428i 0.934513i
\(590\) 0 0
\(591\) −192.425 + 389.968i −0.325592 + 0.659844i
\(592\) 0 0
\(593\) 482.620i 0.813862i 0.913459 + 0.406931i \(0.133401\pi\)
−0.913459 + 0.406931i \(0.866599\pi\)
\(594\) 0 0
\(595\) 25.8967i 0.0435238i
\(596\) 0 0
\(597\) 314.967 638.312i 0.527583 1.06920i
\(598\) 0 0
\(599\) 803.277i 1.34103i 0.741896 + 0.670515i \(0.233927\pi\)
−0.741896 + 0.670515i \(0.766073\pi\)
\(600\) 0 0
\(601\) 126.365 0.210258 0.105129 0.994459i \(-0.466474\pi\)
0.105129 + 0.994459i \(0.466474\pi\)
\(602\) 0 0
\(603\) 164.991 126.479i 0.273617 0.209750i
\(604\) 0 0
\(605\) 4.04535 0.00668653
\(606\) 0 0
\(607\) 397.356 0.654623 0.327312 0.944916i \(-0.393857\pi\)
0.327312 + 0.944916i \(0.393857\pi\)
\(608\) 0 0
\(609\) −186.843 + 378.655i −0.306802 + 0.621766i
\(610\) 0 0
\(611\) −321.012 −0.525388
\(612\) 0 0
\(613\) 1056.55i 1.72357i −0.507275 0.861785i \(-0.669347\pi\)
0.507275 0.861785i \(-0.330653\pi\)
\(614\) 0 0
\(615\) −20.9203 10.3229i −0.0340167 0.0167851i
\(616\) 0 0
\(617\) 411.284i 0.666586i 0.942823 + 0.333293i \(0.108160\pi\)
−0.942823 + 0.333293i \(0.891840\pi\)
\(618\) 0 0
\(619\) 691.383i 1.11693i −0.829526 0.558467i \(-0.811390\pi\)
0.829526 0.558467i \(-0.188610\pi\)
\(620\) 0 0
\(621\) 191.271 + 965.138i 0.308005 + 1.55417i
\(622\) 0 0
\(623\) 305.435i 0.490264i
\(624\) 0 0
\(625\) 594.447 0.951114
\(626\) 0 0
\(627\) −457.771 225.881i −0.730097 0.360257i
\(628\) 0 0
\(629\) 947.262 1.50598
\(630\) 0 0
\(631\) 528.057 0.836858 0.418429 0.908250i \(-0.362581\pi\)
0.418429 + 0.908250i \(0.362581\pi\)
\(632\) 0 0
\(633\) −826.238 407.697i −1.30527 0.644071i
\(634\) 0 0
\(635\) −133.895 −0.210858
\(636\) 0 0
\(637\) 218.460i 0.342951i
\(638\) 0 0
\(639\) 52.1175 39.9523i 0.0815611 0.0625232i
\(640\) 0 0
\(641\) 134.165i 0.209306i 0.994509 + 0.104653i \(0.0333731\pi\)
−0.994509 + 0.104653i \(0.966627\pi\)
\(642\) 0 0
\(643\) 633.985i 0.985979i 0.870035 + 0.492990i \(0.164096\pi\)
−0.870035 + 0.492990i \(0.835904\pi\)
\(644\) 0 0
\(645\) −20.3232 10.0282i −0.0315088 0.0155476i
\(646\) 0 0
\(647\) 227.758i 0.352021i −0.984388 0.176011i \(-0.943681\pi\)
0.984388 0.176011i \(-0.0563193\pi\)
\(648\) 0 0
\(649\) −420.766 −0.648329
\(650\) 0 0
\(651\) −131.834 + 267.176i −0.202511 + 0.410408i
\(652\) 0 0
\(653\) −1190.65 −1.82336 −0.911678 0.410906i \(-0.865212\pi\)
−0.911678 + 0.410906i \(0.865212\pi\)
\(654\) 0 0
\(655\) 111.900 0.170839
\(656\) 0 0
\(657\) 402.178 + 524.638i 0.612142 + 0.798536i
\(658\) 0 0
\(659\) −266.873 −0.404967 −0.202484 0.979286i \(-0.564901\pi\)
−0.202484 + 0.979286i \(0.564901\pi\)
\(660\) 0 0
\(661\) 1045.10i 1.58109i 0.612405 + 0.790544i \(0.290202\pi\)
−0.612405 + 0.790544i \(0.709798\pi\)
\(662\) 0 0
\(663\) −103.682 + 210.122i −0.156383 + 0.316925i
\(664\) 0 0
\(665\) 26.2589i 0.0394871i
\(666\) 0 0
\(667\) 1885.13i 2.82629i
\(668\) 0 0
\(669\) 581.445 1178.36i 0.869126 1.76137i
\(670\) 0 0
\(671\) 656.693i 0.978678i
\(672\) 0 0
\(673\) 408.300 0.606687 0.303343 0.952881i \(-0.401897\pi\)
0.303343 + 0.952881i \(0.401897\pi\)
\(674\) 0 0
\(675\) −651.274 + 129.069i −0.964850 + 0.191214i
\(676\) 0 0
\(677\) −749.557 −1.10717 −0.553587 0.832791i \(-0.686741\pi\)
−0.553587 + 0.832791i \(0.686741\pi\)
\(678\) 0 0
\(679\) 217.753 0.320697
\(680\) 0 0
\(681\) 359.426 728.413i 0.527792 1.06962i
\(682\) 0 0
\(683\) 258.242 0.378099 0.189050 0.981968i \(-0.439459\pi\)
0.189050 + 0.981968i \(0.439459\pi\)
\(684\) 0 0
\(685\) 104.287i 0.152244i
\(686\) 0 0
\(687\) −265.474 130.995i −0.386424 0.190676i
\(688\) 0 0
\(689\) 310.744i 0.451007i
\(690\) 0 0
\(691\) 929.714i 1.34546i −0.739887 0.672731i \(-0.765121\pi\)
0.739887 0.672731i \(-0.234879\pi\)
\(692\) 0 0
\(693\) 168.099 + 219.284i 0.242567 + 0.316427i
\(694\) 0 0
\(695\) 124.308i 0.178861i
\(696\) 0 0
\(697\) −180.693 −0.259244
\(698\) 0 0
\(699\) 1163.30 + 574.016i 1.66424 + 0.821197i
\(700\) 0 0
\(701\) −335.731 −0.478932 −0.239466 0.970905i \(-0.576972\pi\)
−0.239466 + 0.970905i \(0.576972\pi\)
\(702\) 0 0
\(703\) 960.513 1.36631
\(704\) 0 0
\(705\) 105.246 + 51.9325i 0.149286 + 0.0736632i
\(706\) 0 0
\(707\) 324.785 0.459385
\(708\) 0 0
\(709\) 356.121i 0.502287i −0.967950 0.251143i \(-0.919193\pi\)
0.967950 0.251143i \(-0.0808065\pi\)
\(710\) 0 0
\(711\) −320.370 417.921i −0.450591 0.587793i
\(712\) 0 0
\(713\) 1330.13i 1.86554i
\(714\) 0 0
\(715\) 37.9266i 0.0530442i
\(716\) 0 0
\(717\) 741.985 + 366.123i 1.03485 + 0.510632i
\(718\) 0 0
\(719\) 31.7234i 0.0441216i −0.999757 0.0220608i \(-0.992977\pi\)
0.999757 0.0220608i \(-0.00702274\pi\)
\(720\) 0 0
\(721\) 341.516 0.473670
\(722\) 0 0
\(723\) −553.262 + 1121.24i −0.765231 + 1.55082i
\(724\) 0 0
\(725\) 1272.09 1.75460
\(726\) 0 0
\(727\) 234.202 0.322148 0.161074 0.986942i \(-0.448504\pi\)
0.161074 + 0.986942i \(0.448504\pi\)
\(728\) 0 0
\(729\) 673.901 278.027i 0.924418 0.381381i
\(730\) 0 0
\(731\) −175.535 −0.240130
\(732\) 0 0
\(733\) 616.813i 0.841491i 0.907179 + 0.420745i \(0.138231\pi\)
−0.907179 + 0.420745i \(0.861769\pi\)
\(734\) 0 0
\(735\) 35.3419 71.6238i 0.0480842 0.0974473i
\(736\) 0 0
\(737\) 260.642i 0.353653i
\(738\) 0 0
\(739\) 605.806i 0.819764i −0.912138 0.409882i \(-0.865570\pi\)
0.912138 0.409882i \(-0.134430\pi\)
\(740\) 0 0
\(741\) −105.132 + 213.061i −0.141879 + 0.287532i
\(742\) 0 0
\(743\) 1033.33i 1.39076i 0.718642 + 0.695380i \(0.244764\pi\)
−0.718642 + 0.695380i \(0.755236\pi\)
\(744\) 0 0
\(745\) 53.4216 0.0717068
\(746\) 0 0
\(747\) −177.372 231.381i −0.237446 0.309747i
\(748\) 0 0
\(749\) 404.494 0.540046
\(750\) 0 0
\(751\) −969.301 −1.29068 −0.645340 0.763896i \(-0.723284\pi\)
−0.645340 + 0.763896i \(0.723284\pi\)
\(752\) 0 0
\(753\) −220.235 + 446.329i −0.292477 + 0.592734i
\(754\) 0 0
\(755\) −38.6240 −0.0511577
\(756\) 0 0
\(757\) 533.594i 0.704880i 0.935835 + 0.352440i \(0.114648\pi\)
−0.935835 + 0.352440i \(0.885352\pi\)
\(758\) 0 0
\(759\) −1106.22 545.851i −1.45747 0.719172i
\(760\) 0 0
\(761\) 867.717i 1.14023i 0.821564 + 0.570116i \(0.193102\pi\)
−0.821564 + 0.570116i \(0.806898\pi\)
\(762\) 0 0
\(763\) 192.267i 0.251988i
\(764\) 0 0
\(765\) 67.9858 52.1166i 0.0888704 0.0681263i
\(766\) 0 0
\(767\) 195.837i 0.255329i
\(768\) 0 0
\(769\) 194.555 0.252997 0.126498 0.991967i \(-0.459626\pi\)
0.126498 + 0.991967i \(0.459626\pi\)
\(770\) 0 0
\(771\) 160.445 + 79.1695i 0.208100 + 0.102684i
\(772\) 0 0
\(773\) 420.140 0.543519 0.271760 0.962365i \(-0.412394\pi\)
0.271760 + 0.962365i \(0.412394\pi\)
\(774\) 0 0
\(775\) 897.572 1.15816
\(776\) 0 0
\(777\) −466.229 230.055i −0.600037 0.296081i
\(778\) 0 0
\(779\) −183.220 −0.235199
\(780\) 0 0
\(781\) 82.3318i 0.105418i
\(782\) 0 0
\(783\) −1370.09 + 271.524i −1.74980 + 0.346775i
\(784\) 0 0
\(785\) 64.4892i 0.0821519i
\(786\) 0 0
\(787\) 849.081i 1.07888i 0.842023 + 0.539441i \(0.181365\pi\)
−0.842023 + 0.539441i \(0.818635\pi\)
\(788\) 0 0
\(789\) −180.952 89.2883i −0.229343 0.113166i
\(790\) 0 0
\(791\) 356.333i 0.450484i
\(792\) 0 0
\(793\) −305.646 −0.385429
\(794\) 0 0
\(795\) −50.2714 + 101.880i −0.0632344 + 0.128151i
\(796\) 0 0
\(797\) −779.186 −0.977648 −0.488824 0.872382i \(-0.662574\pi\)
−0.488824 + 0.872382i \(0.662574\pi\)
\(798\) 0 0
\(799\) 909.035 1.13772
\(800\) 0 0
\(801\) 801.849