Properties

Label 384.3.i.b.161.2
Level $384$
Weight $3$
Character 384.161
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 161.2
Root \(1.38255 + 0.297594i\) of defining polynomial
Character \(\chi\) \(=\) 384.161
Dual form 384.3.i.b.353.2

$q$-expansion

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

Character values

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

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.737922 + 2.90783i 0.245974 + 0.969276i
\(4\) 0 0
\(5\) 1.57472 + 1.57472i 0.314944 + 0.314944i 0.846821 0.531877i \(-0.178513\pi\)
−0.531877 + 0.846821i \(0.678513\pi\)
\(6\) 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 \(-0.274381\pi\)
−0.759142 + 0.650926i \(0.774381\pi\)
\(12\) 0 0
\(13\) 14.6458 + 14.6458i 1.12660 + 1.12660i 0.990727 + 0.135870i \(0.0433828\pi\)
0.135870 + 0.990727i \(0.456617\pi\)
\(14\) 0 0
\(15\) −3.41699 + 5.74103i −0.227800 + 0.382736i
\(16\) 0 0
\(17\) 28.0726i 1.65133i 0.564159 + 0.825666i \(0.309200\pi\)
−0.564159 + 0.825666i \(0.690800\pi\)
\(18\) 0 0
\(19\) 12.5830 + 12.5830i 0.662263 + 0.662263i 0.955913 0.293650i \(-0.0948699\pi\)
−0.293650 + 0.955913i \(0.594870\pi\)
\(20\) 0 0
\(21\) 10.6012 2.69028i 0.504820 0.128109i
\(22\) 0 0
\(23\) −29.2630 −1.27231 −0.636153 0.771563i \(-0.719475\pi\)
−0.636153 + 0.771563i \(0.719475\pi\)
\(24\) 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 −0.957122 0.289685i \(-0.906449\pi\)
0.289685 + 0.957122i \(0.406449\pi\)
\(30\) 0 0
\(31\) −11.6458 −0.375669 −0.187835 0.982201i \(-0.560147\pi\)
−0.187835 + 0.982201i \(0.560147\pi\)
\(32\) 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 −0.717452 0.696608i \(-0.754692\pi\)
0.696608 + 0.717452i \(0.254692\pi\)
\(38\) 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 \(-0.982576\pi\)
0.0547114 + 0.998502i \(0.482576\pi\)
\(44\) 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 0.992735 0.120321i \(-0.0383925\pi\)
−0.120321 + 0.992735i \(0.538392\pi\)
\(54\) 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 \(-0.337915\pi\)
−0.873132 + 0.487483i \(0.837915\pi\)
\(60\) 0 0
\(61\) −12.7712 12.7712i −0.209365 0.209365i 0.594633 0.803997i \(-0.297297\pi\)
−0.803997 + 0.594633i \(0.797297\pi\)
\(62\) 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 \(-0.214024\pi\)
−0.622847 + 0.782344i \(0.714024\pi\)
\(68\) 0 0
\(69\) −21.5938 85.0919i −0.312954 1.23322i
\(70\) 0 0
\(71\) 122.086 1.71952 0.859760 0.510699i \(-0.170613\pi\)
0.859760 + 0.510699i \(0.170613\pi\)
\(72\) 0 0
\(73\) 15.0405i 0.206034i 0.994680 + 0.103017i \(0.0328497\pi\)
−0.994680 + 0.103017i \(0.967150\pi\)
\(74\) 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 \(-0.394540\pi\)
0.325283 + 0.945617i \(0.394540\pi\)
\(80\) 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 \(-0.645440\pi\)
0.897419 + 0.441179i \(0.145440\pi\)
\(84\) 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 0.849260 0.527975i \(-0.177048\pi\)
−0.527975 + 0.849260i \(0.677048\pi\)
\(102\) 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 \(-0.0589438\pi\)
−0.184121 + 0.982904i \(0.558944\pi\)
\(108\) 0 0
\(109\) 52.8523 + 52.8523i 0.484883 + 0.484883i 0.906687 0.421804i \(-0.138603\pi\)
−0.421804 + 0.906687i \(0.638603\pi\)
\(110\) 0 0
\(111\) −2.81176 1.67353i −0.0253312 0.0150768i
\(112\) 0 0
\(113\) 73.5045i 0.650483i −0.945631 0.325241i \(-0.894554\pi\)
0.945631 0.325241i \(-0.105446\pi\)
\(114\) 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 \(-0.594013\pi\)
−0.291076 + 0.956700i \(0.594013\pi\)
\(128\) 0 0
\(129\) −147.956 88.0614i −1.14694 0.682646i
\(130\) 0 0
\(131\) 158.430 158.430i 1.20939 1.20939i 0.238161 0.971226i \(-0.423455\pi\)
0.971226 0.238161i \(-0.0765447\pi\)
\(132\) 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 \(-0.720368\pi\)
0.769776 + 0.638314i \(0.220368\pi\)
\(140\) 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 0.841730 0.539899i \(-0.181537\pi\)
−0.539899 + 0.841730i \(0.681537\pi\)
\(150\) 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 −0.993973 0.109628i \(-0.965034\pi\)
−0.109628 0.993973i \(-0.534966\pi\)
\(158\) 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 \(-0.177687\pi\)
−0.529678 + 0.848199i \(0.677687\pi\)
\(164\) 0 0
\(165\) 10.9015 2.76648i 0.0660697 0.0167666i
\(166\) 0 0
\(167\) 57.5333 0.344511 0.172255 0.985052i \(-0.444895\pi\)
0.172255 + 0.985052i \(0.444895\pi\)
\(168\) 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 −0.302334 0.953202i \(-0.597766\pi\)
0.953202 + 0.302334i \(0.0977657\pi\)
\(174\) 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 \(-0.778305\pi\)
0.641517 + 0.767109i \(0.278305\pi\)
\(180\) 0 0
\(181\) 18.6013 18.6013i 0.102770 0.102770i −0.653852 0.756622i \(-0.726848\pi\)
0.756622 + 0.653852i \(0.226848\pi\)
\(182\) 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 0.270932 0.962599i \(-0.412668\pi\)
−0.962599 + 0.270932i \(0.912668\pi\)
\(198\) 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 \(-0.478608\pi\)
−0.997743 + 0.0671538i \(0.978608\pi\)
\(212\) 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 \(-0.181736\pi\)
0.841393 + 0.540423i \(0.181736\pi\)
\(224\) 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 \(-0.940797\pi\)
0.184920 + 0.982754i \(0.440797\pi\)
\(228\) 0 0
\(229\) 153.937 153.937i 0.672215 0.672215i −0.286011 0.958226i \(-0.592329\pi\)
0.958226 + 0.286011i \(0.0923295\pi\)
\(230\) 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 \(-0.288947\pi\)
−0.788122 + 0.615519i \(0.788947\pi\)
\(252\) 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 \(0.113354\pi\)
−0.937259 + 0.348633i \(0.886646\pi\)
\(258\) 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 \(-0.793837\pi\)
−0.797486 + 0.603338i \(0.793837\pi\)
\(264\) 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 −0.641560 0.767073i \(-0.721712\pi\)
0.767073 + 0.641560i \(0.221712\pi\)
\(270\) 0 0
\(271\) −329.269 −1.21502 −0.607508 0.794314i \(-0.707831\pi\)
−0.607508 + 0.794314i \(0.707831\pi\)
\(272\) 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 −0.996037 0.0889417i \(-0.971652\pi\)
0.0889417 + 0.996037i \(0.471652\pi\)
\(278\) 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 \(-0.910606\pi\)
0.277163 + 0.960823i \(0.410606\pi\)
\(284\) 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 0.821312 0.570480i \(-0.193243\pi\)
−0.570480 + 0.821312i \(0.693243\pi\)
\(294\) 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 \(-0.0239493\pi\)
−0.0751680 + 0.997171i \(0.523949\pi\)
\(308\) 0 0
\(309\) 148.847 37.7729i 0.481704 0.122242i
\(310\) 0 0
\(311\) −54.0368 −0.173752 −0.0868759 0.996219i \(-0.527688\pi\)
−0.0868759 + 0.996219i \(0.527688\pi\)
\(312\) 0 0
\(313\) 490.280i 1.56639i −0.621777 0.783194i \(-0.713589\pi\)
0.621777 0.783194i \(-0.286411\pi\)
\(314\) 0 0
\(315\) −20.7793 + 70.0547i −0.0659661 + 0.222396i
\(316\) 0 0
\(317\) 319.550 319.550i 1.00804 1.00804i 0.00807607 0.999967i \(-0.497429\pi\)
0.999967 0.00807607i \(-0.00257072\pi\)
\(318\) 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 \(-0.945223\pi\)
0.171238 + 0.985230i \(0.445223\pi\)
\(332\) 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 \(-0.166726\pi\)
−0.500162 + 0.865932i \(0.666726\pi\)
\(348\) 0 0
\(349\) −195.893 195.893i −0.561297 0.561297i 0.368378 0.929676i \(-0.379913\pi\)
−0.929676 + 0.368378i \(0.879913\pi\)
\(350\) 0 0
\(351\) 22.2653 558.787i 0.0634340 1.59198i
\(352\) 0 0
\(353\) 291.488i 0.825745i −0.910789 0.412873i \(-0.864525\pi\)
0.910789 0.412873i \(-0.135475\pi\)
\(354\) 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 \(-0.482102\pi\)
0.0561976 + 0.998420i \(0.482102\pi\)
\(360\) 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 \(-0.653636\pi\)
−0.464140 + 0.885762i \(0.653636\pi\)
\(368\) 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 −0.949866 0.312658i \(-0.898781\pi\)
0.312658 + 0.949866i \(0.398781\pi\)
\(374\) 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 \(-0.546102\pi\)
0.989530 + 0.144327i \(0.0461017\pi\)
\(380\) 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 −0.995435 0.0954418i \(-0.969574\pi\)
−0.0954418 0.995435i \(-0.530426\pi\)
\(390\) 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 0.991347 + 0.131269i \(0.0419051\pi\)
0.131269 + 0.991347i \(0.458095\pi\)
\(398\) 0 0
\(399\) 167.247 + 99.5434i 0.419166 + 0.249482i
\(400\) 0 0
\(401\) 555.896i 1.38627i −0.720806 0.693137i \(-0.756228\pi\)
0.720806 0.693137i \(-0.243772\pi\)
\(402\) 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 \(-0.982548\pi\)
0.998497 0.0547997i \(-0.0174520\pi\)
\(410\) 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 \(-0.758167\pi\)
0.688733 + 0.725016i \(0.258167\pi\)
\(420\) 0 0
\(421\) −262.889 + 262.889i −0.624439 + 0.624439i −0.946663 0.322224i \(-0.895569\pi\)
0.322224 + 0.946663i \(0.395569\pi\)
\(422\) 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 \(-0.113574\pi\)
−0.349282 + 0.937018i \(0.613574\pi\)
\(444\) 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 \(-0.964854\pi\)
0.993911 0.110190i \(-0.0351459\pi\)
\(450\) 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 \(-0.994978\pi\)
0.999876 0.0157778i \(-0.00502245\pi\)
\(458\) 0 0
\(459\) 556.873 514.196i 1.21323 1.12025i
\(460\) 0 0
\(461\) 328.278 328.278i 0.712099 0.712099i −0.254875 0.966974i \(-0.582034\pi\)
0.966974 + 0.254875i \(0.0820343\pi\)
\(462\) 0 0
\(463\) 848.427 1.83246 0.916228 0.400657i \(-0.131218\pi\)
0.916228 + 0.400657i \(0.131218\pi\)
\(464\) 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 \(-0.777057\pi\)
0.644521 + 0.764587i \(0.277057\pi\)
\(468\) 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 \(-0.0989044\pi\)
−0.305742 + 0.952114i \(0.598904\pi\)
\(492\) 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 \(-0.428007\pi\)
−0.974532 + 0.224250i \(0.928007\pi\)
\(500\) 0 0
\(501\) 42.4551 + 167.297i 0.0847407 + 0.333926i
\(502\) 0 0
\(503\) 386.094 0.767583 0.383791 0.923420i \(-0.374618\pi\)
0.383791 + 0.923420i \(0.374618\pi\)
\(504\) 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 −0.665034 0.746813i \(-0.731583\pi\)
0.746813 + 0.665034i \(0.231583\pi\)
\(510\) 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 \(-0.845912\pi\)
0.465397 + 0.885102i \(0.345912\pi\)
\(524\) 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 0.628762 0.777598i \(-0.283562\pi\)
−0.777598 + 0.628762i \(0.783562\pi\)
\(542\) 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 \(-0.249384\pi\)
−0.705736 + 0.708475i \(0.749384\pi\)
\(548\) 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 −0.934540 0.355858i \(-0.884189\pi\)
0.355858 + 0.934540i \(0.384189\pi\)
\(558\) 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 \(-0.978625\pi\)
0.0671003 + 0.997746i \(0.478625\pi\)
\(564\) 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 \(-0.751356\pi\)
0.704089 + 0.710112i \(0.251356\pi\)
\(572\) 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 \(-0.430855\pi\)
−0.976499 + 0.215522i \(0.930855\pi\)
\(588\) 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 \(0.249804\pi\)
−0.707542 + 0.706671i \(0.750196\pi\)
\(594\) 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 \(-0.612385\pi\)
−0.345777 + 0.938317i \(0.612385\pi\)
\(600\) 0 0
\(601\) 305.786i 0.508795i 0.967100 + 0.254397i \(0.0818771\pi\)
−0.967100 + 0.254397i \(0.918123\pi\)
\(602\) 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 \(-0.472904\pi\)
0.0850222 + 0.996379i \(0.472904\pi\)
\(608\) 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 −0.311842 0.950134i \(-0.600946\pi\)
0.950134 + 0.311842i \(0.100946\pi\)
\(614\) 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 \(-0.900956\pi\)
0.306159 + 0.951980i \(0.400956\pi\)
\(620\) 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 \(0.00650162\pi\)
−0.999791 + 0.0204240i \(0.993498\pi\)
\(642\) 0 0
\(643\) 625.336 + 625.336i 0.972529 + 0.972529i 0.999633 0.0271039i \(-0.00862850\pi\)
−0.0271039 + 0.999633i \(0.508629\pi\)
\(644\) 0 0
\(645\) −94.3165 371.660i −0.146227 0.576218i
\(646\) 0 0
\(647\) −97.2591 −0.150323 −0.0751616 0.997171i \(-0.523947\pi\)
−0.0751616 + 0.997171i \(0.523947\pi\)
\(648\) 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 −0.799089 0.601213i \(-0.794684\pi\)
0.601213 + 0.799089i \(0.294684\pi\)
\(654\) 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 \(-0.748938\pi\)
0.709462 + 0.704743i \(0.248938\pi\)
\(660\) 0 0
\(661\) 22.3424 22.3424i 0.0338010 0.0338010i −0.690004 0.723805i \(-0.742391\pi\)
0.723805 + 0.690004i \(0.242391\pi\)
\(662\) 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 0.973663 + 0.227991i \(0.0732157\pi\)
0.227991 + 0.973663i \(0.426784\pi\)
\(678\) 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 \(-0.104111\pi\)
−0.321273 + 0.946986i \(0.604111\pi\)
\(684\) 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 \(-0.391474\pi\)
−0.942439 + 0.334378i \(0.891474\pi\)
\(692\) 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 −0.110260 + 0.993903i \(0.535168\pi\)
−0.993903 + 0.110260i \(0.964832\pi\)
\(702\) 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 −0.832963 0.553328i \(-0.813358\pi\)
0.553328 + 0.832963i \(0.313358\pi\)
\(710\) 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 0.740302 0.672275i \(-0.234683\pi\)
−0.672275 + 0.740302i \(0.734683\pi\)
\(734\) 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 \(-0.201818\pi\)
−0.592395 + 0.805647i \(0.701818\pi\)
\(740\) 0 0
\(741\) −1071.75 + 271.980i −1.44636 + 0.367044i
\(742\) 0 0
\(743\) 1305.03 1.75643 0.878216 0.478265i \(-0.158734\pi\)
0.878216 + 0.478265i \(0.158734\pi\)
\(744\) 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 \(-0.677244\pi\)
−0.528495 + 0.848936i \(0.677244\pi\)
\(752\) 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 −0.00855438 0.999963i \(-0.502723\pi\)
0.999963 + 0.00855438i \(0.00272298\pi\)
\(758\) 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 0.985074 + 0.172129i \(0.0550647\pi\)
0.172129 + 0.985074i \(0.444935\pi\)
\(774\) 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 \(-0.496841\pi\)
−0.999951 + 0.00992500i \(0.996841\pi\)
\(788\) 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
\(795\) −423.448 + 107.459i