Properties

Label 384.3.i.a.353.3
Level $384$
Weight $3$
Character 384.353
Analytic conductor $10.463$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.i (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: 8.0.629407744.1
Defining polynomial: \(x^{8} - 2 x^{6} + 2 x^{4} - 8 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 353.3
Root \(1.38255 - 0.297594i\) of defining polynomial
Character \(\chi\) \(=\) 384.353
Dual form 384.3.i.a.161.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.737922 + 2.90783i) q^{3} +(1.57472 - 1.57472i) q^{5} -3.64575i q^{7} +(-7.91094 - 4.29150i) q^{9} +O(q^{10})\) \(q+(-0.737922 + 2.90783i) q^{3} +(1.57472 - 1.57472i) q^{5} -3.64575i q^{7} +(-7.91094 - 4.29150i) q^{9} +(1.19038 - 1.19038i) q^{11} +(14.6458 - 14.6458i) q^{13} +(3.41699 + 5.74103i) q^{15} -28.0726i q^{17} +(-12.5830 + 12.5830i) q^{19} +(10.6012 + 2.69028i) q^{21} +29.2630 q^{23} +20.0405i q^{25} +(18.3166 - 19.8369i) q^{27} +(-19.3557 - 19.3557i) q^{29} +11.6458 q^{31} +(2.58301 + 4.33981i) q^{33} +(-5.74103 - 5.74103i) q^{35} +(-0.771243 - 0.771243i) q^{37} +(31.7799 + 53.3948i) q^{39} +25.6919 q^{41} +(40.5830 + 40.5830i) q^{43} +(-19.2154 + 5.69960i) q^{45} -50.2681i q^{47} +35.7085 q^{49} +(81.6304 + 20.7154i) q^{51} +(46.2379 - 46.2379i) q^{53} -3.74902i q^{55} +(-27.3040 - 45.8745i) q^{57} +(22.7533 - 22.7533i) q^{59} +(-12.7712 + 12.7712i) q^{61} +(-15.6458 + 28.8413i) q^{63} -46.1259i q^{65} +(-10.6863 + 10.6863i) q^{67} +(-21.5938 + 85.0919i) q^{69} -122.086 q^{71} -15.0405i q^{73} +(-58.2744 - 14.7883i) q^{75} +(-4.33981 - 4.33981i) q^{77} -51.3948 q^{79} +(44.1660 + 67.8997i) q^{81} +(-37.8680 - 37.8680i) q^{83} +(-44.2065 - 44.2065i) q^{85} +(70.5659 - 42.0000i) q^{87} -5.45550 q^{89} +(-53.3948 - 53.3948i) q^{91} +(-8.59366 + 33.8639i) q^{93} +39.6294i q^{95} -81.1660 q^{97} +(-14.5255 + 4.30849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{3} + O(q^{10}) \) \( 8q - 4q^{3} + 96q^{13} + 112q^{15} - 16q^{19} + 32q^{21} + 68q^{27} + 72q^{31} - 64q^{33} - 112q^{37} + 240q^{43} + 112q^{45} + 328q^{49} + 32q^{51} - 208q^{61} - 104q^{63} + 232q^{67} - 324q^{75} - 136q^{79} + 184q^{81} + 112q^{85} - 152q^{91} - 64q^{93} - 480q^{97} - 160q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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
\(3\) −0.737922 + 2.90783i −0.245974 + 0.969276i
\(4\) 0 0
\(5\) 1.57472 1.57472i 0.314944 0.314944i −0.531877 0.846821i \(-0.678513\pi\)
0.846821 + 0.531877i \(0.178513\pi\)
\(6\) 0 0
\(7\) 3.64575i 0.520822i −0.965498 0.260411i \(-0.916142\pi\)
0.965498 0.260411i \(-0.0838580\pi\)
\(8\) 0 0
\(9\) −7.91094 4.29150i −0.878994 0.476834i
\(10\) 0 0
\(11\) 1.19038 1.19038i 0.108216 0.108216i −0.650926 0.759142i \(-0.725619\pi\)
0.759142 + 0.650926i \(0.225619\pi\)
\(12\) 0 0
\(13\) 14.6458 14.6458i 1.12660 1.12660i 0.135870 0.990727i \(-0.456617\pi\)
0.990727 0.135870i \(-0.0433828\pi\)
\(14\) 0 0
\(15\) 3.41699 + 5.74103i 0.227800 + 0.382736i
\(16\) 0 0
\(17\) 28.0726i 1.65133i −0.564159 0.825666i \(-0.690800\pi\)
0.564159 0.825666i \(-0.309200\pi\)
\(18\) 0 0
\(19\) −12.5830 + 12.5830i −0.662263 + 0.662263i −0.955913 0.293650i \(-0.905130\pi\)
0.293650 + 0.955913i \(0.405130\pi\)
\(20\) 0 0
\(21\) 10.6012 + 2.69028i 0.504820 + 0.128109i
\(22\) 0 0
\(23\) 29.2630 1.27231 0.636153 0.771563i \(-0.280525\pi\)
0.636153 + 0.771563i \(0.280525\pi\)
\(24\) 0 0
\(25\) 20.0405i 0.801621i
\(26\) 0 0
\(27\) 18.3166 19.8369i 0.678393 0.734699i
\(28\) 0 0
\(29\) −19.3557 19.3557i −0.667437 0.667437i 0.289685 0.957122i \(-0.406449\pi\)
−0.957122 + 0.289685i \(0.906449\pi\)
\(30\) 0 0
\(31\) 11.6458 0.375669 0.187835 0.982201i \(-0.439853\pi\)
0.187835 + 0.982201i \(0.439853\pi\)
\(32\) 0 0
\(33\) 2.58301 + 4.33981i 0.0782729 + 0.131510i
\(34\) 0 0
\(35\) −5.74103 5.74103i −0.164030 0.164030i
\(36\) 0 0
\(37\) −0.771243 0.771243i −0.0208444 0.0208444i 0.696608 0.717452i \(-0.254692\pi\)
−0.717452 + 0.696608i \(0.754692\pi\)
\(38\) 0 0
\(39\) 31.7799 + 53.3948i 0.814870 + 1.36910i
\(40\) 0 0
\(41\) 25.6919 0.626631 0.313316 0.949649i \(-0.398560\pi\)
0.313316 + 0.949649i \(0.398560\pi\)
\(42\) 0 0
\(43\) 40.5830 + 40.5830i 0.943791 + 0.943791i 0.998502 0.0547114i \(-0.0174239\pi\)
−0.0547114 + 0.998502i \(0.517424\pi\)
\(44\) 0 0
\(45\) −19.2154 + 5.69960i −0.427009 + 0.126658i
\(46\) 0 0
\(47\) 50.2681i 1.06953i −0.845000 0.534767i \(-0.820399\pi\)
0.845000 0.534767i \(-0.179601\pi\)
\(48\) 0 0
\(49\) 35.7085 0.728745
\(50\) 0 0
\(51\) 81.6304 + 20.7154i 1.60060 + 0.406185i
\(52\) 0 0
\(53\) 46.2379 46.2379i 0.872414 0.872414i −0.120321 0.992735i \(-0.538392\pi\)
0.992735 + 0.120321i \(0.0383925\pi\)
\(54\) 0 0
\(55\) 3.74902i 0.0681639i
\(56\) 0 0
\(57\) −27.3040 45.8745i −0.479017 0.804816i
\(58\) 0 0
\(59\) 22.7533 22.7533i 0.385649 0.385649i −0.487483 0.873132i \(-0.662085\pi\)
0.873132 + 0.487483i \(0.162085\pi\)
\(60\) 0 0
\(61\) −12.7712 + 12.7712i −0.209365 + 0.209365i −0.803997 0.594633i \(-0.797297\pi\)
0.594633 + 0.803997i \(0.297297\pi\)
\(62\) 0 0
\(63\) −15.6458 + 28.8413i −0.248345 + 0.457799i
\(64\) 0 0
\(65\) 46.1259i 0.709629i
\(66\) 0 0
\(67\) −10.6863 + 10.6863i −0.159497 + 0.159497i −0.782344 0.622847i \(-0.785976\pi\)
0.622847 + 0.782344i \(0.285976\pi\)
\(68\) 0 0
\(69\) −21.5938 + 85.0919i −0.312954 + 1.23322i
\(70\) 0 0
\(71\) −122.086 −1.71952 −0.859760 0.510699i \(-0.829387\pi\)
−0.859760 + 0.510699i \(0.829387\pi\)
\(72\) 0 0
\(73\) 15.0405i 0.206034i −0.994680 0.103017i \(-0.967150\pi\)
0.994680 0.103017i \(-0.0328497\pi\)
\(74\) 0 0
\(75\) −58.2744 14.7883i −0.776992 0.197178i
\(76\) 0 0
\(77\) −4.33981 4.33981i −0.0563612 0.0563612i
\(78\) 0 0
\(79\) −51.3948 −0.650567 −0.325283 0.945617i \(-0.605460\pi\)
−0.325283 + 0.945617i \(0.605460\pi\)
\(80\) 0 0
\(81\) 44.1660 + 67.8997i 0.545259 + 0.838267i
\(82\) 0 0
\(83\) −37.8680 37.8680i −0.456240 0.456240i 0.441179 0.897419i \(-0.354560\pi\)
−0.897419 + 0.441179i \(0.854560\pi\)
\(84\) 0 0
\(85\) −44.2065 44.2065i −0.520077 0.520077i
\(86\) 0 0
\(87\) 70.5659 42.0000i 0.811103 0.482759i
\(88\) 0 0
\(89\) −5.45550 −0.0612977 −0.0306489 0.999530i \(-0.509757\pi\)
−0.0306489 + 0.999530i \(0.509757\pi\)
\(90\) 0 0
\(91\) −53.3948 53.3948i −0.586756 0.586756i
\(92\) 0 0
\(93\) −8.59366 + 33.8639i −0.0924049 + 0.364127i
\(94\) 0 0
\(95\) 39.6294i 0.417152i
\(96\) 0 0
\(97\) −81.1660 −0.836763 −0.418381 0.908271i \(-0.637402\pi\)
−0.418381 + 0.908271i \(0.637402\pi\)
\(98\) 0 0
\(99\) −14.5255 + 4.30849i −0.146722 + 0.0435201i
\(100\) 0 0
\(101\) 32.4498 32.4498i 0.321285 0.321285i −0.527975 0.849260i \(-0.677048\pi\)
0.849260 + 0.527975i \(0.177048\pi\)
\(102\) 0 0
\(103\) 51.1882i 0.496973i −0.968635 0.248487i \(-0.920067\pi\)
0.968635 0.248487i \(-0.0799332\pi\)
\(104\) 0 0
\(105\) 20.9304 12.4575i 0.199337 0.118643i
\(106\) 0 0
\(107\) −85.4698 + 85.4698i −0.798783 + 0.798783i −0.982904 0.184121i \(-0.941056\pi\)
0.184121 + 0.982904i \(0.441056\pi\)
\(108\) 0 0
\(109\) 52.8523 52.8523i 0.484883 0.484883i −0.421804 0.906687i \(-0.638603\pi\)
0.906687 + 0.421804i \(0.138603\pi\)
\(110\) 0 0
\(111\) 2.81176 1.67353i 0.0253312 0.0150768i
\(112\) 0 0
\(113\) 73.5045i 0.650483i 0.945631 + 0.325241i \(0.105446\pi\)
−0.945631 + 0.325241i \(0.894554\pi\)
\(114\) 0 0
\(115\) 46.0810 46.0810i 0.400705 0.400705i
\(116\) 0 0
\(117\) −178.714 + 53.0094i −1.52747 + 0.453072i
\(118\) 0 0
\(119\) −102.346 −0.860049
\(120\) 0 0
\(121\) 118.166i 0.976579i
\(122\) 0 0
\(123\) −18.9586 + 74.7076i −0.154135 + 0.607379i
\(124\) 0 0
\(125\) 70.9262 + 70.9262i 0.567409 + 0.567409i
\(126\) 0 0
\(127\) 73.9333 0.582152 0.291076 0.956700i \(-0.405987\pi\)
0.291076 + 0.956700i \(0.405987\pi\)
\(128\) 0 0
\(129\) −147.956 + 88.0614i −1.14694 + 0.682646i
\(130\) 0 0
\(131\) −158.430 158.430i −1.20939 1.20939i −0.971226 0.238161i \(-0.923455\pi\)
−0.238161 0.971226i \(-0.576545\pi\)
\(132\) 0 0
\(133\) 45.8745 + 45.8745i 0.344921 + 0.344921i
\(134\) 0 0
\(135\) −2.39398 60.0810i −0.0177332 0.445045i
\(136\) 0 0
\(137\) 100.734 0.735283 0.367642 0.929968i \(-0.380165\pi\)
0.367642 + 0.929968i \(0.380165\pi\)
\(138\) 0 0
\(139\) −18.2732 18.2732i −0.131462 0.131462i 0.638314 0.769776i \(-0.279632\pi\)
−0.769776 + 0.638314i \(0.779632\pi\)
\(140\) 0 0
\(141\) 146.171 + 37.0939i 1.03667 + 0.263078i
\(142\) 0 0
\(143\) 34.8679i 0.243831i
\(144\) 0 0
\(145\) −60.9595 −0.420410
\(146\) 0 0
\(147\) −26.3501 + 103.834i −0.179252 + 0.706355i
\(148\) 0 0
\(149\) 44.9729 44.9729i 0.301831 0.301831i −0.539899 0.841730i \(-0.681537\pi\)
0.841730 + 0.539899i \(0.181537\pi\)
\(150\) 0 0
\(151\) 28.1033i 0.186114i −0.995661 0.0930572i \(-0.970336\pi\)
0.995661 0.0930572i \(-0.0296639\pi\)
\(152\) 0 0
\(153\) −120.474 + 222.081i −0.787411 + 1.45151i
\(154\) 0 0
\(155\) 18.3388 18.3388i 0.118315 0.118315i
\(156\) 0 0
\(157\) −173.265 + 173.265i −1.10360 + 1.10360i −0.109628 + 0.993973i \(0.534966\pi\)
−0.993973 + 0.109628i \(0.965034\pi\)
\(158\) 0 0
\(159\) 100.332 + 168.572i 0.631019 + 1.06020i
\(160\) 0 0
\(161\) 106.686i 0.662644i
\(162\) 0 0
\(163\) −51.9190 + 51.9190i −0.318521 + 0.318521i −0.848199 0.529678i \(-0.822313\pi\)
0.529678 + 0.848199i \(0.322313\pi\)
\(164\) 0 0
\(165\) 10.9015 + 2.76648i 0.0660697 + 0.0167666i
\(166\) 0 0
\(167\) −57.5333 −0.344511 −0.172255 0.985052i \(-0.555105\pi\)
−0.172255 + 0.985052i \(0.555105\pi\)
\(168\) 0 0
\(169\) 259.996i 1.53844i
\(170\) 0 0
\(171\) 153.543 45.5434i 0.897915 0.266336i
\(172\) 0 0
\(173\) 112.600 + 112.600i 0.650868 + 0.650868i 0.953202 0.302334i \(-0.0977657\pi\)
−0.302334 + 0.953202i \(0.597766\pi\)
\(174\) 0 0
\(175\) 73.0627 0.417501
\(176\) 0 0
\(177\) 49.3725 + 82.9529i 0.278941 + 0.468660i
\(178\) 0 0
\(179\) 22.4810 + 22.4810i 0.125592 + 0.125592i 0.767109 0.641517i \(-0.221695\pi\)
−0.641517 + 0.767109i \(0.721695\pi\)
\(180\) 0 0
\(181\) 18.6013 + 18.6013i 0.102770 + 0.102770i 0.756622 0.653852i \(-0.226848\pi\)
−0.653852 + 0.756622i \(0.726848\pi\)
\(182\) 0 0
\(183\) −27.7124 46.5608i −0.151434 0.254430i
\(184\) 0 0
\(185\) −2.42898 −0.0131296
\(186\) 0 0
\(187\) −33.4170 33.4170i −0.178701 0.178701i
\(188\) 0 0
\(189\) −72.3203 66.7778i −0.382647 0.353322i
\(190\) 0 0
\(191\) 191.672i 1.00352i −0.865007 0.501760i \(-0.832686\pi\)
0.865007 0.501760i \(-0.167314\pi\)
\(192\) 0 0
\(193\) 48.6275 0.251956 0.125978 0.992033i \(-0.459793\pi\)
0.125978 + 0.992033i \(0.459793\pi\)
\(194\) 0 0
\(195\) 134.126 + 34.0373i 0.687827 + 0.174550i
\(196\) 0 0
\(197\) −136.258 + 136.258i −0.691667 + 0.691667i −0.962599 0.270932i \(-0.912668\pi\)
0.270932 + 0.962599i \(0.412668\pi\)
\(198\) 0 0
\(199\) 144.767i 0.727474i 0.931502 + 0.363737i \(0.118499\pi\)
−0.931502 + 0.363737i \(0.881501\pi\)
\(200\) 0 0
\(201\) −23.1882 38.9595i −0.115364 0.193828i
\(202\) 0 0
\(203\) −70.5659 + 70.5659i −0.347615 + 0.347615i
\(204\) 0 0
\(205\) 40.4575 40.4575i 0.197354 0.197354i
\(206\) 0 0
\(207\) −231.498 125.582i −1.11835 0.606678i
\(208\) 0 0
\(209\) 29.9570i 0.143335i
\(210\) 0 0
\(211\) 196.354 196.354i 0.930589 0.930589i −0.0671538 0.997743i \(-0.521392\pi\)
0.997743 + 0.0671538i \(0.0213918\pi\)
\(212\) 0 0
\(213\) 90.0899 355.005i 0.422957 1.66669i
\(214\) 0 0
\(215\) 127.814 0.594482
\(216\) 0 0
\(217\) 42.4575i 0.195657i
\(218\) 0 0
\(219\) 43.7353 + 11.0987i 0.199704 + 0.0506791i
\(220\) 0 0
\(221\) −411.145 411.145i −1.86038 1.86038i
\(222\) 0 0
\(223\) −375.261 −1.68279 −0.841393 0.540423i \(-0.818264\pi\)
−0.841393 + 0.540423i \(0.818264\pi\)
\(224\) 0 0
\(225\) 86.0039 158.539i 0.382240 0.704619i
\(226\) 0 0
\(227\) 181.108 + 181.108i 0.797834 + 0.797834i 0.982754 0.184920i \(-0.0592025\pi\)
−0.184920 + 0.982754i \(0.559203\pi\)
\(228\) 0 0
\(229\) 153.937 + 153.937i 0.672215 + 0.672215i 0.958226 0.286011i \(-0.0923295\pi\)
−0.286011 + 0.958226i \(0.592329\pi\)
\(230\) 0 0
\(231\) 15.8219 9.41699i 0.0684930 0.0407662i
\(232\) 0 0
\(233\) 51.7790 0.222228 0.111114 0.993808i \(-0.464558\pi\)
0.111114 + 0.993808i \(0.464558\pi\)
\(234\) 0 0
\(235\) −79.1581 79.1581i −0.336843 0.336843i
\(236\) 0 0
\(237\) 37.9253 149.447i 0.160022 0.630579i
\(238\) 0 0
\(239\) 249.900i 1.04560i 0.852454 + 0.522802i \(0.175113\pi\)
−0.852454 + 0.522802i \(0.824887\pi\)
\(240\) 0 0
\(241\) 442.531 1.83623 0.918113 0.396318i \(-0.129712\pi\)
0.918113 + 0.396318i \(0.129712\pi\)
\(242\) 0 0
\(243\) −230.032 + 78.3226i −0.946632 + 0.322315i
\(244\) 0 0
\(245\) 56.2309 56.2309i 0.229514 0.229514i
\(246\) 0 0
\(247\) 368.575i 1.49221i
\(248\) 0 0
\(249\) 138.057 82.1699i 0.554446 0.330000i
\(250\) 0 0
\(251\) 43.3235 43.3235i 0.172603 0.172603i −0.615519 0.788122i \(-0.711053\pi\)
0.788122 + 0.615519i \(0.211053\pi\)
\(252\) 0 0
\(253\) 34.8340 34.8340i 0.137684 0.137684i
\(254\) 0 0
\(255\) 161.166 95.9241i 0.632024 0.376173i
\(256\) 0 0
\(257\) 179.197i 0.697266i −0.937259 0.348633i \(-0.886646\pi\)
0.937259 0.348633i \(-0.113354\pi\)
\(258\) 0 0
\(259\) −2.81176 + 2.81176i −0.0108562 + 0.0108562i
\(260\) 0 0
\(261\) 70.0567 + 236.186i 0.268416 + 0.904929i
\(262\) 0 0
\(263\) 419.478 1.59497 0.797486 0.603338i \(-0.206163\pi\)
0.797486 + 0.603338i \(0.206163\pi\)
\(264\) 0 0
\(265\) 145.624i 0.549523i
\(266\) 0 0
\(267\) 4.02573 15.8637i 0.0150777 0.0594145i
\(268\) 0 0
\(269\) 33.7631 + 33.7631i 0.125513 + 0.125513i 0.767073 0.641560i \(-0.221712\pi\)
−0.641560 + 0.767073i \(0.721712\pi\)
\(270\) 0 0
\(271\) 329.269 1.21502 0.607508 0.794314i \(-0.292169\pi\)
0.607508 + 0.794314i \(0.292169\pi\)
\(272\) 0 0
\(273\) 194.664 115.862i 0.713055 0.424402i
\(274\) 0 0
\(275\) 23.8557 + 23.8557i 0.0867482 + 0.0867482i
\(276\) 0 0
\(277\) −251.265 251.265i −0.907095 0.907095i 0.0889417 0.996037i \(-0.471652\pi\)
−0.996037 + 0.0889417i \(0.971652\pi\)
\(278\) 0 0
\(279\) −92.1289 49.9778i −0.330211 0.179132i
\(280\) 0 0
\(281\) −171.809 −0.611421 −0.305711 0.952124i \(-0.598894\pi\)
−0.305711 + 0.952124i \(0.598894\pi\)
\(282\) 0 0
\(283\) 193.476 + 193.476i 0.683660 + 0.683660i 0.960823 0.277163i \(-0.0893942\pi\)
−0.277163 + 0.960823i \(0.589394\pi\)
\(284\) 0 0
\(285\) −115.236 29.2434i −0.404335 0.102608i
\(286\) 0 0
\(287\) 93.6662i 0.326363i
\(288\) 0 0
\(289\) −499.073 −1.72690
\(290\) 0 0
\(291\) 59.8942 236.017i 0.205822 0.811055i
\(292\) 0 0
\(293\) 73.4937 73.4937i 0.250832 0.250832i −0.570480 0.821312i \(-0.693243\pi\)
0.821312 + 0.570480i \(0.193243\pi\)
\(294\) 0 0
\(295\) 71.6601i 0.242916i
\(296\) 0 0
\(297\) −1.80968 45.4170i −0.00609320 0.152919i
\(298\) 0 0
\(299\) 428.579 428.579i 1.43337 1.43337i
\(300\) 0 0
\(301\) 147.956 147.956i 0.491547 0.491547i
\(302\) 0 0
\(303\) 70.4131 + 118.304i 0.232386 + 0.390442i
\(304\) 0 0
\(305\) 40.2222i 0.131876i
\(306\) 0 0
\(307\) −283.055 + 283.055i −0.922003 + 0.922003i −0.997171 0.0751680i \(-0.976051\pi\)
0.0751680 + 0.997171i \(0.476051\pi\)
\(308\) 0 0
\(309\) 148.847 + 37.7729i 0.481704 + 0.122242i
\(310\) 0 0
\(311\) 54.0368 0.173752 0.0868759 0.996219i \(-0.472312\pi\)
0.0868759 + 0.996219i \(0.472312\pi\)
\(312\) 0 0
\(313\) 490.280i 1.56639i 0.621777 + 0.783194i \(0.286411\pi\)
−0.621777 + 0.783194i \(0.713589\pi\)
\(314\) 0 0
\(315\) 20.7793 + 70.0547i 0.0659661 + 0.222396i
\(316\) 0 0
\(317\) 319.550 + 319.550i 1.00804 + 1.00804i 0.999967 + 0.00807607i \(0.00257072\pi\)
0.00807607 + 0.999967i \(0.497429\pi\)
\(318\) 0 0
\(319\) −46.0810 −0.144455
\(320\) 0 0
\(321\) −185.461 311.601i −0.577762 0.970721i
\(322\) 0 0
\(323\) 353.238 + 353.238i 1.09362 + 1.09362i
\(324\) 0 0
\(325\) 293.508 + 293.508i 0.903103 + 0.903103i
\(326\) 0 0
\(327\) 114.685 + 192.686i 0.350717 + 0.589255i
\(328\) 0 0
\(329\) −183.265 −0.557036
\(330\) 0 0
\(331\) 269.431 + 269.431i 0.813992 + 0.813992i 0.985230 0.171238i \(-0.0547766\pi\)
−0.171238 + 0.985230i \(0.554777\pi\)
\(332\) 0 0
\(333\) 2.79147 + 9.41106i 0.00838279 + 0.0282614i
\(334\) 0 0
\(335\) 33.6557i 0.100465i
\(336\) 0 0
\(337\) 143.041 0.424453 0.212226 0.977221i \(-0.431929\pi\)
0.212226 + 0.977221i \(0.431929\pi\)
\(338\) 0 0
\(339\) −213.739 54.2406i −0.630497 0.160002i
\(340\) 0 0
\(341\) 13.8628 13.8628i 0.0406534 0.0406534i
\(342\) 0 0
\(343\) 308.826i 0.900368i
\(344\) 0 0
\(345\) 99.9916 + 168.000i 0.289831 + 0.486957i
\(346\) 0 0
\(347\) −126.922 + 126.922i −0.365770 + 0.365770i −0.865932 0.500162i \(-0.833274\pi\)
0.500162 + 0.865932i \(0.333274\pi\)
\(348\) 0 0
\(349\) −195.893 + 195.893i −0.561297 + 0.561297i −0.929676 0.368378i \(-0.879913\pi\)
0.368378 + 0.929676i \(0.379913\pi\)
\(350\) 0 0
\(351\) −22.2653 558.787i −0.0634340 1.59198i
\(352\) 0 0
\(353\) 291.488i 0.825745i 0.910789 + 0.412873i \(0.135475\pi\)
−0.910789 + 0.412873i \(0.864525\pi\)
\(354\) 0 0
\(355\) −192.251 + 192.251i −0.541552 + 0.541552i
\(356\) 0 0
\(357\) 75.5233 297.604i 0.211550 0.833626i
\(358\) 0 0
\(359\) −40.3499 −0.112395 −0.0561976 0.998420i \(-0.517898\pi\)
−0.0561976 + 0.998420i \(0.517898\pi\)
\(360\) 0 0
\(361\) 44.3360i 0.122814i
\(362\) 0 0
\(363\) −343.607 87.1973i −0.946575 0.240213i
\(364\) 0 0
\(365\) −23.6846 23.6846i −0.0648893 0.0648893i
\(366\) 0 0
\(367\) 340.678 0.928279 0.464140 0.885762i \(-0.346364\pi\)
0.464140 + 0.885762i \(0.346364\pi\)
\(368\) 0 0
\(369\) −203.247 110.257i −0.550805 0.298799i
\(370\) 0 0
\(371\) −168.572 168.572i −0.454372 0.454372i
\(372\) 0 0
\(373\) −237.678 237.678i −0.637207 0.637207i 0.312658 0.949866i \(-0.398781\pi\)
−0.949866 + 0.312658i \(0.898781\pi\)
\(374\) 0 0
\(375\) −258.579 + 153.903i −0.689544 + 0.410409i
\(376\) 0 0
\(377\) −566.957 −1.50386
\(378\) 0 0
\(379\) −320.332 320.332i −0.845203 0.845203i 0.144327 0.989530i \(-0.453898\pi\)
−0.989530 + 0.144327i \(0.953898\pi\)
\(380\) 0 0
\(381\) −54.5570 + 214.985i −0.143194 + 0.564266i
\(382\) 0 0
\(383\) 632.700i 1.65196i 0.563702 + 0.825978i \(0.309377\pi\)
−0.563702 + 0.825978i \(0.690623\pi\)
\(384\) 0 0
\(385\) −13.6680 −0.0355012
\(386\) 0 0
\(387\) −146.888 495.212i −0.379555 1.27962i
\(388\) 0 0
\(389\) −424.351 + 424.351i −1.09088 + 1.09088i −0.0954418 + 0.995435i \(0.530426\pi\)
−0.995435 + 0.0954418i \(0.969574\pi\)
\(390\) 0 0
\(391\) 821.490i 2.10100i
\(392\) 0 0
\(393\) 577.595 343.778i 1.46971 0.874752i
\(394\) 0 0
\(395\) −80.9323 + 80.9323i −0.204892 + 0.204892i
\(396\) 0 0
\(397\) 445.678 445.678i 1.12262 1.12262i 0.131269 0.991347i \(-0.458095\pi\)
0.991347 0.131269i \(-0.0419051\pi\)
\(398\) 0 0
\(399\) −167.247 + 99.5434i −0.419166 + 0.249482i
\(400\) 0 0
\(401\) 555.896i 1.38627i 0.720806 + 0.693137i \(0.243772\pi\)
−0.720806 + 0.693137i \(0.756228\pi\)
\(402\) 0 0
\(403\) 170.561 170.561i 0.423228 0.423228i
\(404\) 0 0
\(405\) 176.472 + 37.3738i 0.435733 + 0.0922811i
\(406\) 0 0
\(407\) −1.83614 −0.00451140
\(408\) 0 0
\(409\) 44.8261i 0.109599i 0.998497 + 0.0547997i \(0.0174520\pi\)
−0.998497 + 0.0547997i \(0.982548\pi\)
\(410\) 0 0
\(411\) −74.3337 + 292.917i −0.180861 + 0.712693i
\(412\) 0 0
\(413\) −82.9529 82.9529i −0.200854 0.200854i
\(414\) 0 0
\(415\) −119.263 −0.287380
\(416\) 0 0
\(417\) 66.6196 39.6512i 0.159759 0.0950868i
\(418\) 0 0
\(419\) 15.2026 + 15.2026i 0.0362830 + 0.0362830i 0.725016 0.688733i \(-0.241833\pi\)
−0.688733 + 0.725016i \(0.741833\pi\)
\(420\) 0 0
\(421\) −262.889 262.889i −0.624439 0.624439i 0.322224 0.946663i \(-0.395569\pi\)
−0.946663 + 0.322224i \(0.895569\pi\)
\(422\) 0 0
\(423\) −215.726 + 397.668i −0.509990 + 0.940113i
\(424\) 0 0
\(425\) 562.590 1.32374
\(426\) 0 0
\(427\) 46.5608 + 46.5608i 0.109042 + 0.109042i
\(428\) 0 0
\(429\) 101.390 + 25.7298i 0.236340 + 0.0599762i
\(430\) 0 0
\(431\) 163.103i 0.378430i 0.981936 + 0.189215i \(0.0605943\pi\)
−0.981936 + 0.189215i \(0.939406\pi\)
\(432\) 0 0
\(433\) −140.737 −0.325028 −0.162514 0.986706i \(-0.551960\pi\)
−0.162514 + 0.986706i \(0.551960\pi\)
\(434\) 0 0
\(435\) 44.9833 177.260i 0.103410 0.407494i
\(436\) 0 0
\(437\) −368.217 + 368.217i −0.842601 + 0.842601i
\(438\) 0 0
\(439\) 434.893i 0.990644i 0.868709 + 0.495322i \(0.164950\pi\)
−0.868709 + 0.495322i \(0.835050\pi\)
\(440\) 0 0
\(441\) −282.488 153.243i −0.640562 0.347490i
\(442\) 0 0
\(443\) −260.367 + 260.367i −0.587736 + 0.587736i −0.937018 0.349282i \(-0.886426\pi\)
0.349282 + 0.937018i \(0.386426\pi\)
\(444\) 0 0
\(445\) −8.59088 + 8.59088i −0.0193053 + 0.0193053i
\(446\) 0 0
\(447\) 97.5869 + 163.960i 0.218315 + 0.366801i
\(448\) 0 0
\(449\) 98.9506i 0.220380i 0.993911 + 0.110190i \(0.0351459\pi\)
−0.993911 + 0.110190i \(0.964854\pi\)
\(450\) 0 0
\(451\) 30.5830 30.5830i 0.0678115 0.0678115i
\(452\) 0 0
\(453\) 81.7195 + 20.7380i 0.180396 + 0.0457793i
\(454\) 0 0
\(455\) −168.164 −0.369590
\(456\) 0 0
\(457\) 14.4209i 0.0315556i 0.999876 + 0.0157778i \(0.00502245\pi\)
−0.999876 + 0.0157778i \(0.994978\pi\)
\(458\) 0 0
\(459\) −556.873 514.196i −1.21323 1.12025i
\(460\) 0 0
\(461\) 328.278 + 328.278i 0.712099 + 0.712099i 0.966974 0.254875i \(-0.0820343\pi\)
−0.254875 + 0.966974i \(0.582034\pi\)
\(462\) 0 0
\(463\) −848.427 −1.83246 −0.916228 0.400657i \(-0.868782\pi\)
−0.916228 + 0.400657i \(0.868782\pi\)
\(464\) 0 0
\(465\) 39.7935 + 66.8587i 0.0855774 + 0.143782i
\(466\) 0 0
\(467\) 56.0706 + 56.0706i 0.120066 + 0.120066i 0.764587 0.644521i \(-0.222943\pi\)
−0.644521 + 0.764587i \(0.722943\pi\)
\(468\) 0 0
\(469\) 38.9595 + 38.9595i 0.0830693 + 0.0830693i
\(470\) 0 0
\(471\) −375.970 631.682i −0.798237 1.34115i
\(472\) 0 0
\(473\) 96.6181 0.204267
\(474\) 0 0
\(475\) −252.170 252.170i −0.530884 0.530884i
\(476\) 0 0
\(477\) −564.216 + 167.355i −1.18284 + 0.350850i
\(478\) 0 0
\(479\) 648.794i 1.35448i −0.735764 0.677238i \(-0.763177\pi\)
0.735764 0.677238i \(-0.236823\pi\)
\(480\) 0 0
\(481\) −22.5909 −0.0469665
\(482\) 0 0
\(483\) 310.224 + 78.7257i 0.642285 + 0.162993i
\(484\) 0 0
\(485\) −127.814 + 127.814i −0.263533 + 0.263533i
\(486\) 0 0
\(487\) 176.783i 0.363004i −0.983391 0.181502i \(-0.941904\pi\)
0.983391 0.181502i \(-0.0580959\pi\)
\(488\) 0 0
\(489\) −112.659 189.284i −0.230387 0.387083i
\(490\) 0 0
\(491\) −317.369 + 317.369i −0.646373 + 0.646373i −0.952114 0.305742i \(-0.901096\pi\)
0.305742 + 0.952114i \(0.401096\pi\)
\(492\) 0 0
\(493\) −543.365 + 543.365i −1.10216 + 1.10216i
\(494\) 0 0
\(495\) −16.0889 + 29.6582i −0.0325029 + 0.0599156i
\(496\) 0 0
\(497\) 445.095i 0.895563i
\(498\) 0 0
\(499\) 374.391 374.391i 0.750282 0.750282i −0.224250 0.974532i \(-0.571993\pi\)
0.974532 + 0.224250i \(0.0719931\pi\)
\(500\) 0 0
\(501\) 42.4551 167.297i 0.0847407 0.333926i
\(502\) 0 0
\(503\) −386.094 −0.767583 −0.383791 0.923420i \(-0.625382\pi\)
−0.383791 + 0.923420i \(0.625382\pi\)
\(504\) 0 0
\(505\) 102.199i 0.202374i
\(506\) 0 0
\(507\) 756.024 + 191.857i 1.49117 + 0.378416i
\(508\) 0 0
\(509\) 41.6258 + 41.6258i 0.0817796 + 0.0817796i 0.746813 0.665034i \(-0.231583\pi\)
−0.665034 + 0.746813i \(0.731583\pi\)
\(510\) 0 0
\(511\) −54.8340 −0.107307
\(512\) 0 0
\(513\) 19.1294 + 480.086i 0.0372893 + 0.935839i
\(514\) 0 0
\(515\) −80.6071 80.6071i −0.156519 0.156519i
\(516\) 0 0
\(517\) −59.8379 59.8379i −0.115741 0.115741i
\(518\) 0 0
\(519\) −410.512 + 244.332i −0.790968 + 0.470775i
\(520\) 0 0
\(521\) −233.704 −0.448569 −0.224284 0.974524i \(-0.572004\pi\)
−0.224284 + 0.974524i \(0.572004\pi\)
\(522\) 0 0
\(523\) 219.506 + 219.506i 0.419705 + 0.419705i 0.885102 0.465397i \(-0.154088\pi\)
−0.465397 + 0.885102i \(0.654088\pi\)
\(524\) 0 0
\(525\) −53.9146 + 212.454i −0.102694 + 0.404674i
\(526\) 0 0
\(527\) 326.927i 0.620355i
\(528\) 0 0
\(529\) 327.324 0.618760
\(530\) 0 0
\(531\) −277.646 + 82.3542i −0.522873 + 0.155093i
\(532\) 0 0
\(533\) 376.277 376.277i 0.705961 0.705961i
\(534\) 0 0
\(535\) 269.182i 0.503143i
\(536\) 0 0
\(537\) −81.9601 + 48.7817i −0.152626 + 0.0908411i
\(538\) 0 0
\(539\) 42.5065 42.5065i 0.0788618 0.0788618i
\(540\) 0 0
\(541\) −80.5203 + 80.5203i −0.148836 + 0.148836i −0.777598 0.628762i \(-0.783562\pi\)
0.628762 + 0.777598i \(0.283562\pi\)
\(542\) 0 0
\(543\) −67.8157 + 40.3631i −0.124891 + 0.0743335i
\(544\) 0 0
\(545\) 166.455i 0.305422i
\(546\) 0 0
\(547\) −1.49803 + 1.49803i −0.00273863 + 0.00273863i −0.708475 0.705736i \(-0.750616\pi\)
0.705736 + 0.708475i \(0.250616\pi\)
\(548\) 0 0
\(549\) 155.840 46.2247i 0.283862 0.0841981i
\(550\) 0 0
\(551\) 487.105 0.884038
\(552\) 0 0
\(553\) 187.373i 0.338829i
\(554\) 0 0
\(555\) 1.79240 7.06307i 0.00322955 0.0127263i
\(556\) 0 0
\(557\) −322.326 322.326i −0.578682 0.578682i 0.355858 0.934540i \(-0.384189\pi\)
−0.934540 + 0.355858i \(0.884189\pi\)
\(558\) 0 0
\(559\) 1188.74 2.12654
\(560\) 0 0
\(561\) 121.830 72.5118i 0.217166 0.129255i
\(562\) 0 0
\(563\) 523.954 + 523.954i 0.930646 + 0.930646i 0.997746 0.0671003i \(-0.0213748\pi\)
−0.0671003 + 0.997746i \(0.521375\pi\)
\(564\) 0 0
\(565\) 115.749 + 115.749i 0.204866 + 0.204866i
\(566\) 0 0
\(567\) 247.545 161.018i 0.436588 0.283983i
\(568\) 0 0
\(569\) 767.880 1.34952 0.674762 0.738035i \(-0.264246\pi\)
0.674762 + 0.738035i \(0.264246\pi\)
\(570\) 0 0
\(571\) 3.43922 + 3.43922i 0.00602316 + 0.00602316i 0.710112 0.704089i \(-0.248644\pi\)
−0.704089 + 0.710112i \(0.748644\pi\)
\(572\) 0 0
\(573\) 557.350 + 141.439i 0.972688 + 0.246840i
\(574\) 0 0
\(575\) 586.446i 1.01991i
\(576\) 0 0
\(577\) −572.442 −0.992100 −0.496050 0.868294i \(-0.665217\pi\)
−0.496050 + 0.868294i \(0.665217\pi\)
\(578\) 0 0
\(579\) −35.8833 + 141.400i −0.0619746 + 0.244215i
\(580\) 0 0
\(581\) −138.057 + 138.057i −0.237620 + 0.237620i
\(582\) 0 0
\(583\) 110.081i 0.188818i
\(584\) 0 0
\(585\) −197.949 + 364.899i −0.338375 + 0.623759i
\(586\) 0 0
\(587\) 446.694 446.694i 0.760977 0.760977i −0.215522 0.976499i \(-0.569145\pi\)
0.976499 + 0.215522i \(0.0691453\pi\)
\(588\) 0 0
\(589\) −146.539 + 146.539i −0.248792 + 0.248792i
\(590\) 0 0
\(591\) −295.668 496.764i −0.500284 0.840548i
\(592\) 0 0
\(593\) 838.112i 1.41334i −0.707542 0.706671i \(-0.750196\pi\)
0.707542 0.706671i \(-0.249804\pi\)
\(594\) 0 0
\(595\) −161.166 + 161.166i −0.270867 + 0.270867i
\(596\) 0 0
\(597\) −420.959 106.827i −0.705123 0.178940i
\(598\) 0 0
\(599\) 414.241 0.691555 0.345777 0.938317i \(-0.387615\pi\)
0.345777 + 0.938317i \(0.387615\pi\)
\(600\) 0 0
\(601\) 305.786i 0.508795i −0.967100 0.254397i \(-0.918123\pi\)
0.967100 0.254397i \(-0.0818771\pi\)
\(602\) 0 0
\(603\) 130.399 38.6783i 0.216250 0.0641431i
\(604\) 0 0
\(605\) 186.078 + 186.078i 0.307567 + 0.307567i
\(606\) 0 0
\(607\) −103.217 −0.170044 −0.0850222 0.996379i \(-0.527096\pi\)
−0.0850222 + 0.996379i \(0.527096\pi\)
\(608\) 0 0
\(609\) −153.122 257.266i −0.251431 0.422440i
\(610\) 0 0
\(611\) −736.214 736.214i −1.20493 1.20493i
\(612\) 0 0
\(613\) 391.273 + 391.273i 0.638292 + 0.638292i 0.950134 0.311842i \(-0.100946\pi\)
−0.311842 + 0.950134i \(0.600946\pi\)
\(614\) 0 0
\(615\) 87.7891 + 147.498i 0.142746 + 0.239834i
\(616\) 0 0
\(617\) −713.373 −1.15620 −0.578098 0.815967i \(-0.696205\pi\)
−0.578098 + 0.815967i \(0.696205\pi\)
\(618\) 0 0
\(619\) 399.763 + 399.763i 0.645821 + 0.645821i 0.951980 0.306159i \(-0.0990440\pi\)
−0.306159 + 0.951980i \(0.599044\pi\)
\(620\) 0 0
\(621\) 535.999 580.487i 0.863123 0.934761i
\(622\) 0 0
\(623\) 19.8894i 0.0319252i
\(624\) 0 0
\(625\) −277.635 −0.444217
\(626\) 0 0
\(627\) −87.1099 22.1059i −0.138931 0.0352567i
\(628\) 0 0
\(629\) −21.6508 + 21.6508i −0.0344210 + 0.0344210i
\(630\) 0 0
\(631\) 934.242i 1.48057i 0.672291 + 0.740287i \(0.265310\pi\)
−0.672291 + 0.740287i \(0.734690\pi\)
\(632\) 0 0
\(633\) 426.071 + 715.859i 0.673097 + 1.13090i
\(634\) 0 0
\(635\) 116.424 116.424i 0.183345 0.183345i
\(636\) 0 0
\(637\) 522.978 522.978i 0.821001 0.821001i
\(638\) 0 0
\(639\) 965.814 + 523.932i 1.51145 + 0.819925i
\(640\) 0 0
\(641\) 26.1836i 0.0408480i −0.999791 0.0204240i \(-0.993498\pi\)
0.999791 0.0204240i \(-0.00650162\pi\)
\(642\) 0 0
\(643\) −625.336 + 625.336i −0.972529 + 0.972529i −0.999633 0.0271039i \(-0.991371\pi\)
0.0271039 + 0.999633i \(0.491371\pi\)
\(644\) 0 0
\(645\) −94.3165 + 371.660i −0.146227 + 0.576218i
\(646\) 0 0
\(647\) 97.2591 0.150323 0.0751616 0.997171i \(-0.476053\pi\)
0.0751616 + 0.997171i \(0.476053\pi\)
\(648\) 0 0
\(649\) 54.1699i 0.0834668i
\(650\) 0 0
\(651\) 123.459 + 31.3303i 0.189645 + 0.0481265i
\(652\) 0 0
\(653\) −129.213 129.213i −0.197875 0.197875i 0.601213 0.799089i \(-0.294684\pi\)
−0.799089 + 0.601213i \(0.794684\pi\)
\(654\) 0 0
\(655\) −498.965 −0.761778
\(656\) 0 0
\(657\) −64.5464 + 118.985i −0.0982442 + 0.181103i
\(658\) 0 0
\(659\) −3.10975 3.10975i −0.00471889 0.00471889i 0.704743 0.709462i \(-0.251062\pi\)
−0.709462 + 0.704743i \(0.751062\pi\)
\(660\) 0 0
\(661\) 22.3424 + 22.3424i 0.0338010 + 0.0338010i 0.723805 0.690004i \(-0.242391\pi\)
−0.690004 + 0.723805i \(0.742391\pi\)
\(662\) 0 0
\(663\) 1498.93 892.146i 2.26083 1.34562i
\(664\) 0 0
\(665\) 144.479 0.217262
\(666\) 0 0
\(667\) −566.405 566.405i −0.849183 0.849183i
\(668\) 0 0
\(669\) 276.914 1091.20i 0.413922 1.63109i
\(670\) 0 0
\(671\) 30.4052i 0.0453132i
\(672\) 0 0
\(673\) 1085.74 1.61329 0.806643 0.591039i \(-0.201282\pi\)
0.806643 + 0.591039i \(0.201282\pi\)
\(674\) 0 0
\(675\) 397.541 + 367.074i 0.588950 + 0.543814i
\(676\) 0 0
\(677\) 813.520 813.520i 1.20165 1.20165i 0.227991 0.973663i \(-0.426784\pi\)
0.973663 0.227991i \(-0.0732157\pi\)
\(678\) 0 0
\(679\) 295.911i 0.435804i
\(680\) 0 0
\(681\) −660.276 + 392.988i −0.969568 + 0.577075i
\(682\) 0 0
\(683\) −427.362 + 427.362i −0.625713 + 0.625713i −0.946986 0.321273i \(-0.895889\pi\)
0.321273 + 0.946986i \(0.395889\pi\)
\(684\) 0 0
\(685\) 158.627 158.627i 0.231573 0.231573i
\(686\) 0 0
\(687\) −561.217 + 334.030i −0.816910 + 0.486215i
\(688\) 0 0
\(689\) 1354.38i 1.96572i
\(690\) 0 0
\(691\) 420.170 420.170i 0.608061 0.608061i −0.334378 0.942439i \(-0.608526\pi\)
0.942439 + 0.334378i \(0.108526\pi\)
\(692\) 0 0
\(693\) 15.7077 + 52.9563i 0.0226662 + 0.0764161i
\(694\) 0 0
\(695\) −57.5504 −0.0828063
\(696\) 0 0
\(697\) 721.239i 1.03478i
\(698\) 0 0
\(699\) −38.2089 + 150.565i −0.0546622 + 0.215400i
\(700\) 0 0
\(701\) −774.018 774.018i −1.10416 1.10416i −0.993903 0.110260i \(-0.964832\pi\)
−0.110260 0.993903i \(-0.535168\pi\)
\(702\) 0 0
\(703\) 19.4091 0.0276090
\(704\) 0 0
\(705\) 288.591 171.766i 0.409349 0.243639i
\(706\) 0 0
\(707\) −118.304 118.304i −0.167332 0.167332i
\(708\) 0 0
\(709\) −198.261 198.261i −0.279635 0.279635i 0.553328 0.832963i \(-0.313358\pi\)
−0.832963 + 0.553328i \(0.813358\pi\)
\(710\) 0 0
\(711\) 406.581 + 220.561i 0.571844 + 0.310212i
\(712\) 0 0
\(713\) 340.790 0.477966
\(714\) 0 0
\(715\) −54.9072 54.9072i −0.0767932 0.0767932i
\(716\) 0 0
\(717\) −726.665 184.406i −1.01348 0.257192i
\(718\) 0 0
\(719\) 639.218i 0.889037i −0.895770 0.444519i \(-0.853375\pi\)
0.895770 0.444519i \(-0.146625\pi\)
\(720\) 0 0
\(721\) −186.620 −0.258834
\(722\) 0 0
\(723\) −326.553 + 1286.80i −0.451664 + 1.77981i
\(724\) 0 0
\(725\) 387.898 387.898i 0.535031 0.535031i
\(726\) 0 0
\(727\) 789.136i 1.08547i −0.839904 0.542734i \(-0.817389\pi\)
0.839904 0.542734i \(-0.182611\pi\)
\(728\) 0 0
\(729\) −58.0032 726.689i −0.0795654 0.996830i
\(730\) 0 0
\(731\) 1139.27 1139.27i 1.55851 1.55851i
\(732\) 0 0
\(733\) 49.8641 49.8641i 0.0680274 0.0680274i −0.672275 0.740302i \(-0.734683\pi\)
0.740302 + 0.672275i \(0.234683\pi\)
\(734\) 0 0
\(735\) 122.016 + 205.004i 0.166008 + 0.278917i
\(736\) 0 0
\(737\) 25.4414i 0.0345202i
\(738\) 0 0
\(739\) −157.593 + 157.593i −0.213252 + 0.213252i −0.805647 0.592395i \(-0.798182\pi\)
0.592395 + 0.805647i \(0.298182\pi\)
\(740\) 0 0
\(741\) −1071.75 271.980i −1.44636 0.367044i
\(742\) 0 0
\(743\) −1305.03 −1.75643 −0.878216 0.478265i \(-0.841266\pi\)
−0.878216 + 0.478265i \(0.841266\pi\)
\(744\) 0 0
\(745\) 141.639i 0.190120i
\(746\) 0 0
\(747\) 137.061 + 462.082i 0.183482 + 0.618583i
\(748\) 0 0
\(749\) 311.601 + 311.601i 0.416023 + 0.416023i
\(750\) 0 0
\(751\) 793.800 1.05699 0.528495 0.848936i \(-0.322756\pi\)
0.528495 + 0.848936i \(0.322756\pi\)
\(752\) 0 0
\(753\) 94.0079 + 157.947i 0.124844 + 0.209756i
\(754\) 0 0
\(755\) −44.2548 44.2548i −0.0586156 0.0586156i
\(756\) 0 0
\(757\) 750.497 + 750.497i 0.991409 + 0.991409i 0.999963 0.00855438i \(-0.00272298\pi\)
−0.00855438 + 0.999963i \(0.502723\pi\)
\(758\) 0 0
\(759\) 75.5865 + 126.996i 0.0995870 + 0.167320i
\(760\) 0 0
\(761\) −1055.45 −1.38692 −0.693462 0.720493i \(-0.743916\pi\)
−0.693462 + 0.720493i \(0.743916\pi\)
\(762\) 0 0
\(763\) −192.686 192.686i −0.252538 0.252538i
\(764\) 0 0
\(765\) 160.003 + 539.428i 0.209154 + 0.705134i
\(766\) 0 0
\(767\) 666.478i 0.868942i
\(768\) 0 0
\(769\) 883.681 1.14913 0.574565 0.818459i \(-0.305171\pi\)
0.574565 + 0.818459i \(0.305171\pi\)
\(770\) 0 0
\(771\) 521.076 + 132.234i 0.675844 + 0.171509i
\(772\) 0 0
\(773\) 894.518 894.518i 1.15720 1.15720i 0.172129 0.985074i \(-0.444935\pi\)
0.985074 0.172129i \(-0.0550647\pi\)
\(774\) 0 0
\(775\) 233.387i 0.301144i
\(776\) 0 0
\(777\) −6.10126 10.2510i −0.00785233 0.0131930i
\(778\) 0 0
\(779\) −323.281 + 323.281i −0.414995 + 0.414995i
\(780\) 0 0
\(781\) −145.328 + 145.328i −0.186079 + 0.186079i
\(782\) 0 0
\(783\) −738.486 + 29.4256i −0.943150 + 0.0375806i
\(784\) 0 0
\(785\) 545.689i 0.695145i
\(786\) 0 0
\(787\) 779.150 779.150i 0.990026 0.990026i −0.00992500 0.999951i \(-0.503159\pi\)
0.999951 + 0.00992500i \(0.00315928\pi\)
\(788\) 0 0
\(789\) −309.542 + 1219.77i −0.392322 + 1.54597i
\(790\) 0 0
\(791\) 267.979 0.338785
\(792\) 0 0
\(793\) 374.089i 0.471739i
\(794\) 0 0
\(795\)