Properties

Label 768.3.h.g.641.12
Level $768$
Weight $3$
Character 768.641
Analytic conductor $20.926$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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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 641.12
Root \(-2.18318 - 0.904303i\) of defining polynomial
Character \(\chi\) \(=\) 768.641
Dual form 768.3.h.g.641.11

$q$-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 \(-0.520386\pi\)
−0.0640013 + 0.997950i \(0.520386\pi\)
\(6\) 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 \(-0.671426\pi\)
−0.512893 + 0.858452i \(0.671426\pi\)
\(12\) 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 \(-0.855897\pi\)
0.899264 0.437406i \(-0.144103\pi\)
\(18\) 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 \(-0.708937\pi\)
0.610266 0.792197i \(-0.291063\pi\)
\(24\) 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 \(-0.149362\pi\)
0.891914 + 0.452205i \(0.149362\pi\)
\(30\) 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 \(-0.952661\pi\)
0.988962 0.148171i \(-0.0473386\pi\)
\(42\) 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 \(0.225341\pi\)
−0.759709 + 0.650263i \(0.774659\pi\)
\(48\) 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 \(-0.688509\pi\)
−0.558203 + 0.829705i \(0.688509\pi\)
\(54\) 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 \(-0.397655\pi\)
0.316016 + 0.948754i \(0.397655\pi\)
\(60\) 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 \(-0.983637\pi\)
0.998679 0.0513842i \(-0.0163633\pi\)
\(72\) 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 \(-0.562517\pi\)
−0.195144 + 0.980775i \(0.562517\pi\)
\(84\) 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 \(-0.782777\pi\)
0.776046 0.630677i \(-0.217223\pi\)
\(90\) 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 \(-0.298751\pi\)
0.590954 + 0.806705i \(0.298751\pi\)
\(102\) 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 \(-0.255530\pi\)
0.694716 + 0.719284i \(0.255530\pi\)
\(108\) 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 \(0.196754\pi\)
−0.814969 + 0.579504i \(0.803246\pi\)
\(114\) 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 \(-0.732561\pi\)
−0.667326 + 0.744766i \(0.732561\pi\)
\(132\) 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 \(-0.797275\pi\)
0.803956 0.594689i \(-0.202725\pi\)
\(138\) 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 \(-0.590367\pi\)
−0.280099 + 0.959971i \(0.590367\pi\)
\(150\) 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 \(-0.882181\pi\)
0.932277 0.361745i \(-0.117819\pi\)
\(168\) 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 \(-0.527689\pi\)
−0.0868791 + 0.996219i \(0.527689\pi\)
\(174\) 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 \(-0.603893\pi\)
−0.320625 + 0.947206i \(0.603893\pi\)
\(180\) 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 \(-0.815498\pi\)
0.836666 0.547713i \(-0.184502\pi\)
\(192\) 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 \(-0.619923\pi\)
−0.367901 + 0.929865i \(0.619923\pi\)
\(198\) 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 \(-0.296607\pi\)
0.596376 + 0.802705i \(0.296607\pi\)
\(228\) 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 \(0.378394\pi\)
−0.372812 + 0.927907i \(0.621606\pi\)
\(234\) 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 \(0.195771\pi\)
−0.816754 + 0.576986i \(0.804229\pi\)
\(240\) 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 \(-0.607212\pi\)
−0.330483 + 0.943812i \(0.607212\pi\)
\(252\) 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 \(0.0370161\pi\)
−0.993246 + 0.116028i \(0.962984\pi\)
\(258\) 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 \(-0.959185\pi\)
0.991791 0.127872i \(-0.0408146\pi\)
\(264\) 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 \(-0.478596\pi\)
0.0671923 + 0.997740i \(0.478596\pi\)
\(270\) 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 \(0.226371\pi\)
−0.757602 + 0.652717i \(0.773629\pi\)
\(282\) 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 \(-0.747105\pi\)
−0.700647 + 0.713508i \(0.747105\pi\)
\(294\) 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 \(0.132530\pi\)
−0.914569 + 0.404429i \(0.867470\pi\)
\(312\) 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 \(-0.640440\pi\)
−0.427030 + 0.904238i \(0.640440\pi\)
\(318\) 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 \(-0.341703\pi\)
0.477060 + 0.878871i \(0.341703\pi\)
\(348\) 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 \(-0.730840\pi\)
0.663289 0.748364i \(-0.269160\pi\)
\(354\) 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 \(-0.973584\pi\)
0.996559 0.0828923i \(-0.0264158\pi\)
\(360\) 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 \(-0.872134\pi\)
0.920396 0.390987i \(-0.127866\pi\)
\(384\) 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 \(-0.309809\pi\)
0.562580 + 0.826743i \(0.309809\pi\)
\(390\) 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 \(-0.977714\pi\)
0.997550 0.0699578i \(-0.0222865\pi\)
\(402\) 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 \(-0.684934\pi\)
−0.548849 + 0.835922i \(0.684934\pi\)
\(420\) 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 \(-0.782033\pi\)
0.774568 0.632490i \(-0.217967\pi\)
\(432\) 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 \(-0.887623\pi\)
−0.938325 + 0.345753i \(0.887623\pi\)
\(444\) 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 \(0.0933344\pi\)
−0.957319 + 0.289035i \(0.906666\pi\)
\(450\) 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 \(-0.760447\pi\)
−0.729930 + 0.683522i \(0.760447\pi\)
\(462\) 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 \(-0.631049\pi\)
−0.400169 + 0.916441i \(0.631049\pi\)
\(468\) 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 \(-0.595559\pi\)
0.295718 0.955275i \(-0.404441\pi\)
\(480\) 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 \(-0.353686\pi\)
0.443643 + 0.896204i \(0.353686\pi\)
\(492\) 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 \(-0.812724\pi\)
0.831861 0.554984i \(-0.187276\pi\)
\(504\) 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 \(-0.398341\pi\)
0.313969 + 0.949433i \(0.398341\pi\)
\(510\) 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 \(-0.734588\pi\)
0.672055 0.740501i \(-0.265412\pi\)
\(522\) 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 \(-0.413858\pi\)
0.267333 + 0.963604i \(0.413858\pi\)
\(558\) 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 \(-0.447617\pi\)
0.163824 + 0.986490i \(0.447617\pi\)
\(564\) 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 \(0.115563\pi\)
−0.934817 + 0.355129i \(0.884437\pi\)
\(570\) 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 \(-0.561248\pi\)
−0.191232 + 0.981545i \(0.561248\pi\)
\(588\) 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 \(-0.866599\pi\)
0.913459 0.406931i \(-0.133401\pi\)
\(594\) 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 \(-0.766073\pi\)
0.741896 0.670515i \(-0.233927\pi\)
\(600\) 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 \(-0.891840\pi\)
0.942823 0.333293i \(-0.108160\pi\)
\(618\) 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 \(-0.966627\pi\)
0.994509 0.104653i \(-0.0333731\pi\)
\(642\) 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 \(0.0563193\pi\)
−0.984388 + 0.176011i \(0.943681\pi\)
\(648\) 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 \(-0.134788\pi\)
0.911678 + 0.410906i \(0.134788\pi\)
\(654\) 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 \(-0.435099\pi\)
0.202484 + 0.979286i \(0.435099\pi\)
\(660\) 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 \(-0.313259\pi\)
0.553587 + 0.832791i \(0.313259\pi\)
\(678\) 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 \(-0.560541\pi\)
−0.189050 + 0.981968i \(0.560541\pi\)
\(684\) 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 \(-0.423028\pi\)
0.239466 + 0.970905i \(0.423028\pi\)
\(702\) 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 \(0.00702274\pi\)
−0.999757 + 0.0220608i \(0.992977\pi\)
\(720\) 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 \(-0.755236\pi\)
0.718642 0.695380i \(-0.244764\pi\)
\(744\) 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 \(-0.806898\pi\)
0.821564 0.570116i \(-0.193102\pi\)
\(762\) 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 \(-0.587606\pi\)
−0.271760 + 0.962365i \(0.587606\pi\)
\(774\) 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 \(-0.337426\pi\)
0.488824 + 0.872382i \(0.337426\pi\)
\(798\) 0 0
\(799\) 909.035 1.13772
\(800\) 0 0
\(801\)