Properties

Label 224.3.r.a.95.2
Level 224
Weight 3
Character 224.95
Analytic conductor 6.104
Analytic rank 0
Dimension 4
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 95.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 224.95
Dual form 224.3.r.a.191.2

$q$-expansion

\(f(q)\) \(=\) \(q+(4.33013 + 2.50000i) q^{3} +(-4.50000 - 7.79423i) q^{5} +(6.92820 + 1.00000i) q^{7} +(8.00000 + 13.8564i) q^{9} +O(q^{10})\) \(q+(4.33013 + 2.50000i) q^{3} +(-4.50000 - 7.79423i) q^{5} +(6.92820 + 1.00000i) q^{7} +(8.00000 + 13.8564i) q^{9} +(2.59808 + 1.50000i) q^{11} +16.0000 q^{13} -45.0000i q^{15} +(3.50000 - 6.06218i) q^{17} +(9.52628 - 5.50000i) q^{19} +(27.5000 + 21.6506i) q^{21} +(-16.4545 + 9.50000i) q^{23} +(-28.0000 + 48.4974i) q^{25} +35.0000i q^{27} -32.0000 q^{29} +(9.52628 + 5.50000i) q^{31} +(7.50000 + 12.9904i) q^{33} +(-23.3827 - 58.5000i) q^{35} +(0.500000 + 0.866025i) q^{37} +(69.2820 + 40.0000i) q^{39} -40.0000 q^{41} -40.0000i q^{43} +(72.0000 - 124.708i) q^{45} +(-73.6122 + 42.5000i) q^{47} +(47.0000 + 13.8564i) q^{49} +(30.3109 - 17.5000i) q^{51} +(-3.50000 + 6.06218i) q^{53} -27.0000i q^{55} +55.0000 q^{57} +(45.8993 + 26.5000i) q^{59} +(-39.5000 - 68.4160i) q^{61} +(41.5692 + 104.000i) q^{63} +(-72.0000 - 124.708i) q^{65} +(-9.52628 - 5.50000i) q^{67} -95.0000 q^{69} -48.0000i q^{71} +(-71.5000 + 123.842i) q^{73} +(-242.487 + 140.000i) q^{75} +(16.5000 + 12.9904i) q^{77} +(-30.3109 + 17.5000i) q^{79} +(-15.5000 + 26.8468i) q^{81} -8.00000i q^{83} -63.0000 q^{85} +(-138.564 - 80.0000i) q^{87} +(48.5000 + 84.0045i) q^{89} +(110.851 + 16.0000i) q^{91} +(27.5000 + 47.6314i) q^{93} +(-85.7365 - 49.5000i) q^{95} -88.0000 q^{97} +48.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 18q^{5} + 32q^{9} + O(q^{10}) \) \( 4q - 18q^{5} + 32q^{9} + 64q^{13} + 14q^{17} + 110q^{21} - 112q^{25} - 128q^{29} + 30q^{33} + 2q^{37} - 160q^{41} + 288q^{45} + 188q^{49} - 14q^{53} + 220q^{57} - 158q^{61} - 288q^{65} - 380q^{69} - 286q^{73} + 66q^{77} - 62q^{81} - 252q^{85} + 194q^{89} + 110q^{93} - 352q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) 4.33013 + 2.50000i 1.44338 + 0.833333i 0.998073 0.0620469i \(-0.0197628\pi\)
0.445302 + 0.895380i \(0.353096\pi\)
\(4\) 0 0
\(5\) −4.50000 7.79423i −0.900000 1.55885i −0.827492 0.561478i \(-0.810233\pi\)
−0.0725083 0.997368i \(-0.523100\pi\)
\(6\) 0 0
\(7\) 6.92820 + 1.00000i 0.989743 + 0.142857i
\(8\) 0 0
\(9\) 8.00000 + 13.8564i 0.888889 + 1.53960i
\(10\) 0 0
\(11\) 2.59808 + 1.50000i 0.236189 + 0.136364i 0.613424 0.789754i \(-0.289792\pi\)
−0.377235 + 0.926118i \(0.623125\pi\)
\(12\) 0 0
\(13\) 16.0000 1.23077 0.615385 0.788227i \(-0.289001\pi\)
0.615385 + 0.788227i \(0.289001\pi\)
\(14\) 0 0
\(15\) 45.0000i 3.00000i
\(16\) 0 0
\(17\) 3.50000 6.06218i 0.205882 0.356599i −0.744531 0.667588i \(-0.767327\pi\)
0.950414 + 0.310989i \(0.100660\pi\)
\(18\) 0 0
\(19\) 9.52628 5.50000i 0.501383 0.289474i −0.227901 0.973684i \(-0.573186\pi\)
0.729285 + 0.684211i \(0.239853\pi\)
\(20\) 0 0
\(21\) 27.5000 + 21.6506i 1.30952 + 1.03098i
\(22\) 0 0
\(23\) −16.4545 + 9.50000i −0.715412 + 0.413043i −0.813062 0.582177i \(-0.802201\pi\)
0.0976495 + 0.995221i \(0.468868\pi\)
\(24\) 0 0
\(25\) −28.0000 + 48.4974i −1.12000 + 1.93990i
\(26\) 0 0
\(27\) 35.0000i 1.29630i
\(28\) 0 0
\(29\) −32.0000 −1.10345 −0.551724 0.834027i \(-0.686030\pi\)
−0.551724 + 0.834027i \(0.686030\pi\)
\(30\) 0 0
\(31\) 9.52628 + 5.50000i 0.307299 + 0.177419i 0.645717 0.763577i \(-0.276558\pi\)
−0.338418 + 0.940996i \(0.609892\pi\)
\(32\) 0 0
\(33\) 7.50000 + 12.9904i 0.227273 + 0.393648i
\(34\) 0 0
\(35\) −23.3827 58.5000i −0.668077 1.67143i
\(36\) 0 0
\(37\) 0.500000 + 0.866025i 0.0135135 + 0.0234061i 0.872703 0.488251i \(-0.162365\pi\)
−0.859190 + 0.511657i \(0.829032\pi\)
\(38\) 0 0
\(39\) 69.2820 + 40.0000i 1.77646 + 1.02564i
\(40\) 0 0
\(41\) −40.0000 −0.975610 −0.487805 0.872953i \(-0.662202\pi\)
−0.487805 + 0.872953i \(0.662202\pi\)
\(42\) 0 0
\(43\) 40.0000i 0.930233i −0.885250 0.465116i \(-0.846013\pi\)
0.885250 0.465116i \(-0.153987\pi\)
\(44\) 0 0
\(45\) 72.0000 124.708i 1.60000 2.77128i
\(46\) 0 0
\(47\) −73.6122 + 42.5000i −1.56622 + 0.904255i −0.569612 + 0.821914i \(0.692907\pi\)
−0.996604 + 0.0823416i \(0.973760\pi\)
\(48\) 0 0
\(49\) 47.0000 + 13.8564i 0.959184 + 0.282784i
\(50\) 0 0
\(51\) 30.3109 17.5000i 0.594331 0.343137i
\(52\) 0 0
\(53\) −3.50000 + 6.06218i −0.0660377 + 0.114381i −0.897154 0.441718i \(-0.854369\pi\)
0.831116 + 0.556099i \(0.187702\pi\)
\(54\) 0 0
\(55\) 27.0000i 0.490909i
\(56\) 0 0
\(57\) 55.0000 0.964912
\(58\) 0 0
\(59\) 45.8993 + 26.5000i 0.777955 + 0.449153i 0.835705 0.549179i \(-0.185059\pi\)
−0.0577500 + 0.998331i \(0.518393\pi\)
\(60\) 0 0
\(61\) −39.5000 68.4160i −0.647541 1.12157i −0.983708 0.179772i \(-0.942464\pi\)
0.336167 0.941802i \(-0.390869\pi\)
\(62\) 0 0
\(63\) 41.5692 + 104.000i 0.659829 + 1.65079i
\(64\) 0 0
\(65\) −72.0000 124.708i −1.10769 1.91858i
\(66\) 0 0
\(67\) −9.52628 5.50000i −0.142183 0.0820896i 0.427221 0.904147i \(-0.359493\pi\)
−0.569404 + 0.822058i \(0.692826\pi\)
\(68\) 0 0
\(69\) −95.0000 −1.37681
\(70\) 0 0
\(71\) 48.0000i 0.676056i −0.941136 0.338028i \(-0.890240\pi\)
0.941136 0.338028i \(-0.109760\pi\)
\(72\) 0 0
\(73\) −71.5000 + 123.842i −0.979452 + 1.69646i −0.315068 + 0.949069i \(0.602027\pi\)
−0.664384 + 0.747392i \(0.731306\pi\)
\(74\) 0 0
\(75\) −242.487 + 140.000i −3.23316 + 1.86667i
\(76\) 0 0
\(77\) 16.5000 + 12.9904i 0.214286 + 0.168706i
\(78\) 0 0
\(79\) −30.3109 + 17.5000i −0.383682 + 0.221519i −0.679419 0.733750i \(-0.737768\pi\)
0.295737 + 0.955269i \(0.404435\pi\)
\(80\) 0 0
\(81\) −15.5000 + 26.8468i −0.191358 + 0.331442i
\(82\) 0 0
\(83\) 8.00000i 0.0963855i −0.998838 0.0481928i \(-0.984654\pi\)
0.998838 0.0481928i \(-0.0153462\pi\)
\(84\) 0 0
\(85\) −63.0000 −0.741176
\(86\) 0 0
\(87\) −138.564 80.0000i −1.59269 0.919540i
\(88\) 0 0
\(89\) 48.5000 + 84.0045i 0.544944 + 0.943870i 0.998610 + 0.0526989i \(0.0167824\pi\)
−0.453667 + 0.891171i \(0.649884\pi\)
\(90\) 0 0
\(91\) 110.851 + 16.0000i 1.21815 + 0.175824i
\(92\) 0 0
\(93\) 27.5000 + 47.6314i 0.295699 + 0.512166i
\(94\) 0 0
\(95\) −85.7365 49.5000i −0.902490 0.521053i
\(96\) 0 0
\(97\) −88.0000 −0.907216 −0.453608 0.891201i \(-0.649863\pi\)
−0.453608 + 0.891201i \(0.649863\pi\)
\(98\) 0 0
\(99\) 48.0000i 0.484848i
\(100\) 0 0
\(101\) 7.50000 12.9904i 0.0742574 0.128618i −0.826506 0.562928i \(-0.809675\pi\)
0.900763 + 0.434311i \(0.143008\pi\)
\(102\) 0 0
\(103\) 80.5404 46.5000i 0.781945 0.451456i −0.0551740 0.998477i \(-0.517571\pi\)
0.837119 + 0.547020i \(0.184238\pi\)
\(104\) 0 0
\(105\) 45.0000 311.769i 0.428571 2.96923i
\(106\) 0 0
\(107\) 9.52628 5.50000i 0.0890306 0.0514019i −0.454824 0.890581i \(-0.650298\pi\)
0.543854 + 0.839180i \(0.316964\pi\)
\(108\) 0 0
\(109\) −56.5000 + 97.8609i −0.518349 + 0.897806i 0.481424 + 0.876488i \(0.340120\pi\)
−0.999773 + 0.0213184i \(0.993214\pi\)
\(110\) 0 0
\(111\) 5.00000i 0.0450450i
\(112\) 0 0
\(113\) 56.0000 0.495575 0.247788 0.968814i \(-0.420296\pi\)
0.247788 + 0.968814i \(0.420296\pi\)
\(114\) 0 0
\(115\) 148.090 + 85.5000i 1.28774 + 0.743478i
\(116\) 0 0
\(117\) 128.000 + 221.703i 1.09402 + 1.89489i
\(118\) 0 0
\(119\) 30.3109 38.5000i 0.254713 0.323529i
\(120\) 0 0
\(121\) −56.0000 96.9948i −0.462810 0.801610i
\(122\) 0 0
\(123\) −173.205 100.000i −1.40817 0.813008i
\(124\) 0 0
\(125\) 279.000 2.23200
\(126\) 0 0
\(127\) 96.0000i 0.755906i 0.925825 + 0.377953i \(0.123372\pi\)
−0.925825 + 0.377953i \(0.876628\pi\)
\(128\) 0 0
\(129\) 100.000 173.205i 0.775194 1.34268i
\(130\) 0 0
\(131\) 122.110 70.5000i 0.932134 0.538168i 0.0446483 0.999003i \(-0.485783\pi\)
0.887486 + 0.460835i \(0.152450\pi\)
\(132\) 0 0
\(133\) 71.5000 28.5788i 0.537594 0.214878i
\(134\) 0 0
\(135\) 272.798 157.500i 2.02073 1.16667i
\(136\) 0 0
\(137\) −4.50000 + 7.79423i −0.0328467 + 0.0568922i −0.881981 0.471284i \(-0.843791\pi\)
0.849135 + 0.528176i \(0.177124\pi\)
\(138\) 0 0
\(139\) 136.000i 0.978417i −0.872167 0.489209i \(-0.837286\pi\)
0.872167 0.489209i \(-0.162714\pi\)
\(140\) 0 0
\(141\) −425.000 −3.01418
\(142\) 0 0
\(143\) 41.5692 + 24.0000i 0.290694 + 0.167832i
\(144\) 0 0
\(145\) 144.000 + 249.415i 0.993103 + 1.72011i
\(146\) 0 0
\(147\) 168.875 + 177.500i 1.14881 + 1.20748i
\(148\) 0 0
\(149\) −28.5000 49.3634i −0.191275 0.331298i 0.754398 0.656417i \(-0.227929\pi\)
−0.945673 + 0.325119i \(0.894596\pi\)
\(150\) 0 0
\(151\) 23.3827 + 13.5000i 0.154852 + 0.0894040i 0.575424 0.817855i \(-0.304837\pi\)
−0.420572 + 0.907259i \(0.638170\pi\)
\(152\) 0 0
\(153\) 112.000 0.732026
\(154\) 0 0
\(155\) 99.0000i 0.638710i
\(156\) 0 0
\(157\) −83.5000 + 144.626i −0.531847 + 0.921186i 0.467462 + 0.884013i \(0.345169\pi\)
−0.999309 + 0.0371729i \(0.988165\pi\)
\(158\) 0 0
\(159\) −30.3109 + 17.5000i −0.190635 + 0.110063i
\(160\) 0 0
\(161\) −123.500 + 49.3634i −0.767081 + 0.306605i
\(162\) 0 0
\(163\) −16.4545 + 9.50000i −0.100948 + 0.0582822i −0.549624 0.835412i \(-0.685229\pi\)
0.448676 + 0.893694i \(0.351896\pi\)
\(164\) 0 0
\(165\) 67.5000 116.913i 0.409091 0.708566i
\(166\) 0 0
\(167\) 190.000i 1.13772i 0.822433 + 0.568862i \(0.192616\pi\)
−0.822433 + 0.568862i \(0.807384\pi\)
\(168\) 0 0
\(169\) 87.0000 0.514793
\(170\) 0 0
\(171\) 152.420 + 88.0000i 0.891348 + 0.514620i
\(172\) 0 0
\(173\) 72.5000 + 125.574i 0.419075 + 0.725859i 0.995847 0.0910461i \(-0.0290210\pi\)
−0.576772 + 0.816905i \(0.695688\pi\)
\(174\) 0 0
\(175\) −242.487 + 308.000i −1.38564 + 1.76000i
\(176\) 0 0
\(177\) 132.500 + 229.497i 0.748588 + 1.29659i
\(178\) 0 0
\(179\) −274.530 158.500i −1.53369 0.885475i −0.999187 0.0403064i \(-0.987167\pi\)
−0.534500 0.845168i \(1.32050\pi\)
\(180\) 0 0
\(181\) −186.000 −1.02762 −0.513812 0.857903i \(-0.671767\pi\)
−0.513812 + 0.857903i \(0.671767\pi\)
\(182\) 0 0
\(183\) 395.000i 2.15847i
\(184\) 0 0
\(185\) 4.50000 7.79423i 0.0243243 0.0421310i
\(186\) 0 0
\(187\) 18.1865 10.5000i 0.0972542 0.0561497i
\(188\) 0 0
\(189\) −35.0000 + 242.487i −0.185185 + 1.28300i
\(190\) 0 0
\(191\) 245.085 141.500i 1.28317 0.740838i 0.305742 0.952114i \(-0.401095\pi\)
0.977426 + 0.211277i \(0.0677621\pi\)
\(192\) 0 0
\(193\) 147.500 255.477i 0.764249 1.32372i −0.176394 0.984320i \(-0.556443\pi\)
0.940643 0.339398i \(-0.110223\pi\)
\(194\) 0 0
\(195\) 720.000i 3.69231i
\(196\) 0 0
\(197\) 128.000 0.649746 0.324873 0.945758i \(-0.394678\pi\)
0.324873 + 0.945758i \(0.394678\pi\)
\(198\) 0 0
\(199\) 245.085 + 141.500i 1.23158 + 0.711055i 0.967360 0.253406i \(-0.0815509\pi\)
0.264224 + 0.964461i \(0.414884\pi\)
\(200\) 0 0
\(201\) −27.5000 47.6314i −0.136816 0.236972i
\(202\) 0 0
\(203\) −221.703 32.0000i −1.09213 0.157635i
\(204\) 0 0
\(205\) 180.000 + 311.769i 0.878049 + 1.52083i
\(206\) 0 0
\(207\) −263.272 152.000i −1.27184 0.734300i
\(208\) 0 0
\(209\) 33.0000 0.157895
\(210\) 0 0
\(211\) 40.0000i 0.189573i −0.995498 0.0947867i \(-0.969783\pi\)
0.995498 0.0947867i \(-0.0302169\pi\)
\(212\) 0 0
\(213\) 120.000 207.846i 0.563380 0.975803i
\(214\) 0 0
\(215\) −311.769 + 180.000i −1.45009 + 0.837209i
\(216\) 0 0
\(217\) 60.5000 + 47.6314i 0.278802 + 0.219500i
\(218\) 0 0
\(219\) −619.208 + 357.500i −2.82743 + 1.63242i
\(220\) 0 0
\(221\) 56.0000 96.9948i 0.253394 0.438891i
\(222\) 0 0
\(223\) 176.000i 0.789238i 0.918845 + 0.394619i \(0.129123\pi\)
−0.918845 + 0.394619i \(0.870877\pi\)
\(224\) 0 0
\(225\) −896.000 −3.98222
\(226\) 0 0
\(227\) 335.152 + 193.500i 1.47644 + 0.852423i 0.999646 0.0265925i \(-0.00846564\pi\)
0.476793 + 0.879015i \(0.341799\pi\)
\(228\) 0 0
\(229\) 91.5000 + 158.483i 0.399563 + 0.692064i 0.993672 0.112321i \(-0.0358284\pi\)
−0.594109 + 0.804385i \(0.702495\pi\)
\(230\) 0 0
\(231\) 38.9711 + 97.5000i 0.168706 + 0.422078i
\(232\) 0 0
\(233\) −180.500 312.635i −0.774678 1.34178i −0.934975 0.354713i \(-0.884579\pi\)
0.160297 0.987069i \(-0.448755\pi\)
\(234\) 0 0
\(235\) 662.509 + 382.500i 2.81919 + 1.62766i
\(236\) 0 0
\(237\) −175.000 −0.738397
\(238\) 0 0
\(239\) 50.0000i 0.209205i 0.994514 + 0.104603i \(0.0333570\pi\)
−0.994514 + 0.104603i \(0.966643\pi\)
\(240\) 0 0
\(241\) 64.5000 111.717i 0.267635 0.463557i −0.700616 0.713539i \(-0.747091\pi\)
0.968251 + 0.249982i \(0.0804246\pi\)
\(242\) 0 0
\(243\) 138.564 80.0000i 0.570222 0.329218i
\(244\) 0 0
\(245\) −103.500 428.683i −0.422449 1.74972i
\(246\) 0 0
\(247\) 152.420 88.0000i 0.617087 0.356275i
\(248\) 0 0
\(249\) 20.0000 34.6410i 0.0803213 0.139121i
\(250\) 0 0
\(251\) 394.000i 1.56972i 0.619672 + 0.784861i \(0.287265\pi\)
−0.619672 + 0.784861i \(0.712735\pi\)
\(252\) 0 0
\(253\) −57.0000 −0.225296
\(254\) 0 0
\(255\) −272.798 157.500i −1.06980 0.617647i
\(256\) 0 0
\(257\) −44.5000 77.0763i −0.173152 0.299908i 0.766368 0.642401i \(-0.222062\pi\)
−0.939520 + 0.342494i \(0.888728\pi\)
\(258\) 0 0
\(259\) 2.59808 + 6.50000i 0.0100312 + 0.0250965i
\(260\) 0 0
\(261\) −256.000 443.405i −0.980843 1.69887i
\(262\) 0 0
\(263\) 38.9711 + 22.5000i 0.148179 + 0.0855513i 0.572257 0.820075i \(-0.306068\pi\)
−0.424077 + 0.905626i \(0.639402\pi\)
\(264\) 0 0
\(265\) 63.0000 0.237736
\(266\) 0 0
\(267\) 485.000i 1.81648i
\(268\) 0 0
\(269\) 228.500 395.774i 0.849442 1.47128i −0.0322643 0.999479i \(-0.510272\pi\)
0.881707 0.471798i \(-0.156395\pi\)
\(270\) 0 0
\(271\) 343.812 198.500i 1.26868 0.732472i 0.293941 0.955823i \(-0.405033\pi\)
0.974738 + 0.223351i \(0.0716997\pi\)
\(272\) 0 0
\(273\) 440.000 + 346.410i 1.61172 + 1.26890i
\(274\) 0 0
\(275\) −145.492 + 84.0000i −0.529063 + 0.305455i
\(276\) 0 0
\(277\) −115.500 + 200.052i −0.416968 + 0.722209i −0.995633 0.0933562i \(-0.970240\pi\)
0.578665 + 0.815565i \(0.303574\pi\)
\(278\) 0 0
\(279\) 176.000i 0.630824i
\(280\) 0 0
\(281\) 104.000 0.370107 0.185053 0.982728i \(-0.440754\pi\)
0.185053 + 0.982728i \(0.440754\pi\)
\(282\) 0 0
\(283\) −343.812 198.500i −1.21488 0.701413i −0.251065 0.967970i \(-0.580781\pi\)
−0.963819 + 0.266557i \(0.914114\pi\)
\(284\) 0 0
\(285\) −247.500 428.683i −0.868421 1.50415i
\(286\) 0 0
\(287\) −277.128 40.0000i −0.965603 0.139373i
\(288\) 0 0
\(289\) 120.000 + 207.846i 0.415225 + 0.719191i
\(290\) 0 0
\(291\) −381.051 220.000i −1.30945 0.756014i
\(292\) 0 0
\(293\) 154.000 0.525597 0.262799 0.964851i \(-0.415355\pi\)
0.262799 + 0.964851i \(0.415355\pi\)
\(294\) 0 0
\(295\) 477.000i 1.61695i
\(296\) 0 0
\(297\) −52.5000 + 90.9327i −0.176768 + 0.306171i
\(298\) 0 0
\(299\) −263.272 + 152.000i −0.880507 + 0.508361i
\(300\) 0 0
\(301\) 40.0000 277.128i 0.132890 0.920691i
\(302\) 0 0
\(303\) 64.9519 37.5000i 0.214363 0.123762i
\(304\) 0 0
\(305\) −355.500 + 615.744i −1.16557 + 2.01883i
\(306\) 0 0
\(307\) 376.000i 1.22476i 0.790565 + 0.612378i \(0.209787\pi\)
−0.790565 + 0.612378i \(0.790213\pi\)
\(308\) 0 0
\(309\) 465.000 1.50485
\(310\) 0 0
\(311\) −279.726 161.500i −0.899441 0.519293i −0.0224223 0.999749i \(-0.507138\pi\)
−0.877019 + 0.480456i \(0.840471\pi\)
\(312\) 0 0
\(313\) −95.5000 165.411i −0.305112 0.528469i 0.672174 0.740393i \(-0.265361\pi\)
−0.977286 + 0.211924i \(0.932027\pi\)
\(314\) 0 0
\(315\) 623.538 792.000i 1.97949 2.51429i
\(316\) 0 0
\(317\) −167.500 290.119i −0.528391 0.915200i −0.999452 0.0330997i \(-0.989462\pi\)
0.471061 0.882101i \(-0.343871\pi\)
\(318\) 0 0
\(319\) −83.1384 48.0000i −0.260622 0.150470i
\(320\) 0 0
\(321\) 55.0000 0.171340
\(322\) 0 0
\(323\) 77.0000i 0.238390i
\(324\) 0 0
\(325\) −448.000 + 775.959i −1.37846 + 2.38757i
\(326\) 0 0
\(327\) −489.304 + 282.500i −1.49634 + 0.863914i
\(328\) 0 0
\(329\) −552.500 + 220.836i −1.67933 + 0.671235i
\(330\) 0 0
\(331\) −30.3109 + 17.5000i −0.0915737 + 0.0528701i −0.545088 0.838379i \(-0.683504\pi\)
0.453514 + 0.891249i \(0.350170\pi\)
\(332\) 0 0
\(333\) −8.00000 + 13.8564i −0.0240240 + 0.0416108i
\(334\) 0 0
\(335\) 99.0000i 0.295522i
\(336\) 0 0
\(337\) 184.000 0.545994 0.272997 0.962015i \(-0.411985\pi\)
0.272997 + 0.962015i \(0.411985\pi\)
\(338\) 0 0
\(339\) 242.487 + 140.000i 0.715301 + 0.412979i
\(340\) 0 0
\(341\) 16.5000 + 28.5788i 0.0483871 + 0.0838089i
\(342\) 0 0
\(343\) 311.769 + 143.000i 0.908948 + 0.416910i
\(344\) 0 0
\(345\) 427.500 + 740.452i 1.23913 + 2.14624i
\(346\) 0 0
\(347\) −161.947 93.5000i −0.466705 0.269452i 0.248154 0.968721i \(-0.420176\pi\)
−0.714860 + 0.699268i \(0.753509\pi\)
\(348\) 0 0
\(349\) −208.000 −0.595989 −0.297994 0.954568i \(-0.596318\pi\)
−0.297994 + 0.954568i \(0.596318\pi\)
\(350\) 0 0
\(351\) 560.000i 1.59544i
\(352\) 0 0
\(353\) 115.500 200.052i 0.327195 0.566719i −0.654759 0.755838i \(-0.727230\pi\)
0.981954 + 0.189119i \(0.0605631\pi\)
\(354\) 0 0
\(355\) −374.123 + 216.000i −1.05387 + 0.608451i
\(356\) 0 0
\(357\) 227.500 90.9327i 0.637255 0.254713i
\(358\) 0 0
\(359\) −32.0429 + 18.5000i −0.0892561 + 0.0515320i −0.543964 0.839109i \(-0.683077\pi\)
0.454708 + 0.890641i \(0.349744\pi\)
\(360\) 0 0
\(361\) −120.000 + 207.846i −0.332410 + 0.575751i
\(362\) 0 0
\(363\) 560.000i 1.54270i
\(364\) 0 0
\(365\) 1287.00 3.52603
\(366\) 0 0
\(367\) −418.290 241.500i −1.13976 0.658038i −0.193385 0.981123i \(-0.561947\pi\)
−0.946370 + 0.323085i \(0.895280\pi\)
\(368\) 0 0
\(369\) −320.000 554.256i −0.867209 1.50205i
\(370\) 0 0
\(371\) −30.3109 + 38.5000i −0.0817005 + 0.103774i
\(372\) 0 0
\(373\) −215.500 373.257i −0.577748 1.00069i −0.995737 0.0922368i \(-0.970598\pi\)
0.417989 0.908452i \(-0.362735\pi\)
\(374\) 0 0
\(375\) 1208.11 + 697.500i 3.22161 + 1.86000i
\(376\) 0 0
\(377\) −512.000 −1.35809
\(378\) 0 0
\(379\) 714.000i 1.88391i −0.335746 0.941953i \(-0.608988\pi\)
0.335746 0.941953i \(-0.391012\pi\)
\(380\) 0 0
\(381\) −240.000 + 415.692i −0.629921 + 1.09106i
\(382\) 0 0
\(383\) 563.783 325.500i 1.47202 0.849869i 0.472512 0.881324i \(-0.343347\pi\)
0.999505 + 0.0314548i \(0.0100140\pi\)
\(384\) 0 0
\(385\) 27.0000 187.061i 0.0701299 0.485874i
\(386\) 0 0
\(387\) 554.256 320.000i 1.43219 0.826873i
\(388\) 0 0
\(389\) −232.500 + 402.702i −0.597686 + 1.03522i 0.395475 + 0.918477i \(0.370580\pi\)
−0.993162 + 0.116747i \(0.962753\pi\)
\(390\) 0 0
\(391\) 133.000i 0.340153i
\(392\) 0 0
\(393\) 705.000 1.79389
\(394\) 0 0
\(395\) 272.798 + 157.500i 0.690628 + 0.398734i
\(396\) 0 0
\(397\) −92.5000 160.215i −0.232997 0.403563i 0.725691 0.688020i \(-0.241520\pi\)
−0.958689 + 0.284457i \(0.908187\pi\)
\(398\) 0 0
\(399\) 381.051 + 55.0000i 0.955015 + 0.137845i
\(400\) 0 0
\(401\) −52.5000 90.9327i −0.130923 0.226765i 0.793110 0.609079i \(-0.208461\pi\)
−0.924033 + 0.382314i \(0.875127\pi\)
\(402\) 0 0
\(403\) 152.420 + 88.0000i 0.378215 + 0.218362i
\(404\) 0 0
\(405\) 279.000 0.688889
\(406\) 0 0
\(407\) 3.00000i 0.00737101i
\(408\) 0 0
\(409\) 3.50000 6.06218i 0.00855746 0.0148220i −0.861715 0.507393i \(-0.830609\pi\)
0.870272 + 0.492571i \(0.163943\pi\)
\(410\) 0 0
\(411\) −38.9711 + 22.5000i −0.0948203 + 0.0547445i
\(412\) 0 0
\(413\) 291.500 + 229.497i 0.705811 + 0.555682i
\(414\) 0 0
\(415\) −62.3538 + 36.0000i −0.150250 + 0.0867470i
\(416\) 0 0
\(417\) 340.000 588.897i 0.815348 1.41222i
\(418\) 0 0
\(419\) 392.000i 0.935561i −0.883845 0.467780i \(-0.845054\pi\)
0.883845 0.467780i \(-0.154946\pi\)
\(420\) 0 0
\(421\) 64.0000 0.152019 0.0760095 0.997107i \(-0.475782\pi\)
0.0760095 + 0.997107i \(0.475782\pi\)
\(422\) 0 0
\(423\) −1177.79 680.000i −2.78438 1.60757i
\(424\) 0 0
\(425\) 196.000 + 339.482i 0.461176 + 0.798781i
\(426\) 0 0
\(427\) −205.248 513.500i −0.480675 1.20258i
\(428\) 0 0
\(429\) 120.000 + 207.846i 0.279720 + 0.484490i
\(430\) 0 0
\(431\) 633.065 + 365.500i 1.46883 + 0.848028i 0.999389 0.0349377i \(-0.0111233\pi\)
0.469438 + 0.882966i \(0.344457\pi\)
\(432\) 0 0
\(433\) 376.000 0.868360 0.434180 0.900826i \(-0.357038\pi\)
0.434180 + 0.900826i \(0.357038\pi\)
\(434\) 0 0
\(435\) 1440.00i 3.31034i
\(436\) 0 0
\(437\) −104.500 + 180.999i −0.239130 + 0.414186i
\(438\) 0 0
\(439\) 549.926 317.500i 1.25268 0.723235i 0.281038 0.959697i \(-0.409321\pi\)
0.971641 + 0.236462i \(0.0759879\pi\)
\(440\) 0 0
\(441\) 184.000 + 762.102i 0.417234 + 1.72812i
\(442\) 0 0
\(443\) 425.218 245.500i 0.959861 0.554176i 0.0637308 0.997967i \(-0.479700\pi\)
0.896130 + 0.443791i \(0.146367\pi\)
\(444\) 0 0
\(445\) 436.500 756.040i 0.980899 1.69897i
\(446\) 0 0
\(447\) 285.000i 0.637584i
\(448\) 0 0
\(449\) −344.000 −0.766147 −0.383073 0.923718i \(-0.625134\pi\)
−0.383073 + 0.923718i \(0.625134\pi\)
\(450\) 0 0
\(451\) −103.923 60.0000i −0.230428 0.133038i
\(452\) 0 0
\(453\) 67.5000 + 116.913i 0.149007 + 0.258087i
\(454\) 0 0
\(455\) −374.123 936.000i −0.822248 2.05714i
\(456\) 0 0
\(457\) −263.500 456.395i −0.576586 0.998677i −0.995867 0.0908204i \(-0.971051\pi\)
0.419281 0.907857i \(-0.362282\pi\)
\(458\) 0 0
\(459\) 212.176 + 122.500i 0.462258 + 0.266885i
\(460\) 0 0
\(461\) −704.000 −1.52711 −0.763557 0.645740i \(-0.776549\pi\)
−0.763557 + 0.645740i \(0.776549\pi\)
\(462\) 0 0
\(463\) 160.000i 0.345572i −0.984959 0.172786i \(-0.944723\pi\)
0.984959 0.172786i \(-0.0552770\pi\)
\(464\) 0 0
\(465\) 247.500 428.683i 0.532258 0.921898i
\(466\) 0 0
\(467\) 468.520 270.500i 1.00325 0.579229i 0.0940447 0.995568i \(-0.470020\pi\)
0.909210 + 0.416339i \(0.136687\pi\)
\(468\) 0 0
\(469\) −60.5000 47.6314i −0.128998 0.101559i
\(470\) 0 0
\(471\) −723.131 + 417.500i −1.53531 + 0.886412i
\(472\) 0 0
\(473\) 60.0000 103.923i 0.126850 0.219710i
\(474\) 0 0
\(475\) 616.000i 1.29684i
\(476\) 0 0
\(477\) −112.000 −0.234801
\(478\) 0 0
\(479\) 413.094 + 238.500i 0.862409 + 0.497912i 0.864818 0.502085i \(-0.167433\pi\)
−0.00240897 + 0.999997i \(0.500767\pi\)
\(480\) 0 0
\(481\) 8.00000 + 13.8564i 0.0166320 + 0.0288075i
\(482\) 0 0
\(483\) −658.179 95.0000i −1.36269 0.196687i
\(484\) 0 0
\(485\) 396.000 + 685.892i 0.816495 + 1.41421i
\(486\) 0 0
\(487\) −265.870 153.500i −0.545934 0.315195i 0.201547 0.979479i \(-0.435403\pi\)
−0.747480 + 0.664284i \(0.768737\pi\)
\(488\) 0 0
\(489\) −95.0000 −0.194274
\(490\) 0 0
\(491\) 22.0000i 0.0448065i 0.999749 + 0.0224033i \(0.00713178\pi\)
−0.999749 + 0.0224033i \(0.992868\pi\)
\(492\) 0 0
\(493\) −112.000 + 193.990i −0.227181 + 0.393488i
\(494\) 0 0
\(495\) 374.123 216.000i 0.755804 0.436364i
\(496\) 0 0
\(497\) 48.0000 332.554i 0.0965795 0.669122i
\(498\) 0 0
\(499\) −792.413 + 457.500i −1.58800 + 0.916834i −0.594367 + 0.804194i \(0.702597\pi\)
−0.993636 + 0.112639i \(0.964070\pi\)
\(500\) 0 0
\(501\) −475.000 + 822.724i −0.948104 + 1.64216i
\(502\) 0 0
\(503\) 192.000i 0.381710i −0.981618 0.190855i \(-0.938874\pi\)
0.981618 0.190855i \(-0.0611260\pi\)
\(504\) 0 0
\(505\) −135.000 −0.267327
\(506\) 0 0
\(507\) 376.721 + 217.500i 0.743040 + 0.428994i
\(508\) 0 0
\(509\) 35.5000 + 61.4878i 0.0697446 + 0.120801i 0.898789 0.438382i \(-0.144448\pi\)
−0.829044 + 0.559183i \(0.811115\pi\)
\(510\) 0 0
\(511\) −619.208 + 786.500i −1.21176 + 1.53914i
\(512\) 0 0
\(513\) 192.500 + 333.420i 0.375244 + 0.649941i
\(514\) 0 0
\(515\) −724.863 418.500i −1.40750 0.812621i
\(516\) 0 0
\(517\) −255.000 −0.493230
\(518\) 0 0
\(519\) 725.000i 1.39692i
\(520\) 0 0
\(521\) −351.500 + 608.816i −0.674664 + 1.16855i 0.301903 + 0.953339i \(0.402378\pi\)
−0.976567 + 0.215214i \(0.930955\pi\)
\(522\) 0 0
\(523\) −281.458 + 162.500i −0.538161 + 0.310707i −0.744333 0.667808i \(-0.767233\pi\)
0.206172 + 0.978516i \(0.433899\pi\)
\(524\) 0 0
\(525\) −1820.00 + 727.461i −3.46667 + 1.38564i
\(526\) 0 0
\(527\) 66.6840 38.5000i 0.126535 0.0730550i
\(528\) 0 0
\(529\) −84.0000 + 145.492i −0.158790 + 0.275033i
\(530\) 0 0
\(531\) 848.000i 1.59699i
\(532\) 0 0
\(533\) −640.000 −1.20075
\(534\) 0 0
\(535\) −85.7365 49.5000i −0.160255 0.0925234i
\(536\) 0 0
\(537\) −792.500 1372.65i −1.47579 2.55615i
\(538\) 0 0
\(539\) 101.325 + 106.500i 0.187987 + 0.197588i
\(540\) 0 0
\(541\) −132.500 229.497i −0.244917 0.424208i 0.717191 0.696876i \(-0.245427\pi\)
−0.962108 + 0.272668i \(0.912094\pi\)
\(542\) 0 0
\(543\) −805.404 465.000i −1.48325 0.856354i
\(544\) 0 0
\(545\) 1017.00 1.86606
\(546\) 0 0
\(547\) 134.000i 0.244973i −0.992470 0.122486i \(-0.960913\pi\)
0.992470 0.122486i \(-0.0390868\pi\)
\(548\) 0 0
\(549\) 632.000 1094.66i 1.15118 1.99391i
\(550\) 0 0
\(551\) −304.841 + 176.000i −0.553250 + 0.319419i
\(552\) 0 0
\(553\) −227.500 + 90.9327i −0.411392 + 0.164435i
\(554\) 0 0
\(555\) 38.9711 22.5000i 0.0702183 0.0405405i
\(556\) 0 0
\(557\) 287.500 497.965i 0.516158 0.894012i −0.483666 0.875253i \(-0.660695\pi\)
0.999824 0.0187592i \(-0.00597160\pi\)
\(558\) 0 0
\(559\) 640.000i 1.14490i
\(560\) 0 0
\(561\) 105.000 0.187166
\(562\) 0 0
\(563\) 156.751 + 90.5000i 0.278420 + 0.160746i 0.632708 0.774390i \(-0.281943\pi\)
−0.354288 + 0.935136i \(0.615277\pi\)
\(564\) 0 0
\(565\) −252.000 436.477i −0.446018 0.772525i
\(566\) 0 0
\(567\) −134.234 + 170.500i −0.236744 + 0.300705i
\(568\) 0 0
\(569\) −159.500 276.262i −0.280316 0.485522i 0.691146 0.722715i \(-0.257106\pi\)
−0.971463 + 0.237193i \(0.923773\pi\)
\(570\) 0 0
\(571\) 141.162 + 81.5000i 0.247219 + 0.142732i 0.618490 0.785792i \(-0.287745\pi\)
−0.371271 + 0.928525i \(0.621078\pi\)
\(572\) 0 0
\(573\) 1415.00 2.46946
\(574\) 0 0
\(575\) 1064.00i 1.85043i
\(576\) 0 0
\(577\) −359.500 + 622.672i −0.623050 + 1.07915i 0.365864 + 0.930668i \(0.380773\pi\)
−0.988914 + 0.148486i \(0.952560\pi\)
\(578\) 0 0
\(579\) 1277.39 737.500i 2.20620 1.27375i
\(580\) 0 0
\(581\) 8.00000 55.4256i 0.0137694 0.0953969i
\(582\) 0 0
\(583\) −18.1865 + 10.5000i −0.0311947 + 0.0180103i
\(584\) 0 0
\(585\) 1152.00 1995.32i 1.96923 3.41081i
\(586\) 0 0
\(587\) 296.000i 0.504259i 0.967694 + 0.252129i \(0.0811309\pi\)
−0.967694 + 0.252129i \(0.918869\pi\)
\(588\) 0 0
\(589\) 121.000 0.205433
\(590\) 0 0
\(591\) 554.256 + 320.000i 0.937828 + 0.541455i
\(592\) 0 0
\(593\) −180.500 312.635i −0.304384 0.527209i 0.672740 0.739879i \(-0.265117\pi\)
−0.977124 + 0.212670i \(0.931784\pi\)
\(594\) 0 0
\(595\) −436.477 63.0000i −0.733574 0.105882i
\(596\) 0 0
\(597\) 707.500 + 1225.43i 1.18509 + 2.05264i
\(598\) 0 0
\(599\) 108.253 + 62.5000i 0.180723 + 0.104341i 0.587632 0.809128i \(-0.300060\pi\)
−0.406909 + 0.913469i \(0.633393\pi\)
\(600\) 0 0
\(601\) 1000.00 1.66389 0.831947 0.554855i \(-0.187226\pi\)
0.831947 + 0.554855i \(0.187226\pi\)
\(602\) 0 0
\(603\) 176.000i 0.291874i
\(604\) 0 0
\(605\) −504.000 + 872.954i −0.833058 + 1.44290i
\(606\) 0 0
\(607\) 355.936 205.500i 0.586386 0.338550i −0.177281 0.984160i \(-0.556730\pi\)
0.763667 + 0.645610i \(0.223397\pi\)
\(608\) 0 0
\(609\) −880.000 692.820i −1.44499 1.13764i
\(610\) 0 0
\(611\) −1177.79 + 680.000i −1.92765 + 1.11293i
\(612\) 0 0
\(613\) 519.500 899.800i 0.847471 1.46786i −0.0359860 0.999352i \(-0.511457\pi\)
0.883457 0.468511i \(-0.155209\pi\)
\(614\) 0 0
\(615\) 1800.00i 2.92683i
\(616\) 0 0
\(617\) −248.000 −0.401945 −0.200972 0.979597i \(-0.564410\pi\)
−0.200972 + 0.979597i \(0.564410\pi\)
\(618\) 0 0
\(619\) −522.213 301.500i −0.843640 0.487076i 0.0148597 0.999890i \(-0.495270\pi\)
−0.858500 + 0.512814i \(0.828603\pi\)
\(620\) 0 0
\(621\) −332.500 575.907i −0.535427 0.927386i
\(622\) 0 0
\(623\) 252.013 + 630.500i 0.404516 + 1.01204i
\(624\) 0 0
\(625\) −555.500 962.154i −0.888800 1.53945i
\(626\) 0 0
\(627\) 142.894 + 82.5000i 0.227901 + 0.131579i
\(628\) 0 0
\(629\) 7.00000 0.0111288
\(630\) 0 0
\(631\) 816.000i 1.29319i 0.762835 + 0.646593i \(0.223807\pi\)
−0.762835 + 0.646593i \(0.776193\pi\)
\(632\) 0 0
\(633\) 100.000 173.205i 0.157978 0.273626i
\(634\) 0 0
\(635\) 748.246 432.000i 1.17834 0.680315i
\(636\) 0 0
\(637\) 752.000 + 221.703i 1.18053 + 0.348042i
\(638\) 0 0
\(639\) 665.108 384.000i 1.04086 0.600939i
\(640\) 0 0
\(641\) −319.500 + 553.390i −0.498440 + 0.863323i −0.999998 0.00180047i \(-0.999427\pi\)
0.501558 + 0.865124i \(0.332760\pi\)
\(642\) 0 0
\(643\) 664.000i 1.03266i −0.856390 0.516330i \(-0.827298\pi\)
0.856390 0.516330i \(-0.172702\pi\)
\(644\) 0 0
\(645\) −1800.00 −2.79070
\(646\) 0 0
\(647\) 1092.06 + 630.500i 1.68788 + 0.974498i 0.956139 + 0.292915i \(0.0946252\pi\)
0.731741 + 0.681583i \(0.238708\pi\)
\(648\) 0 0
\(649\) 79.5000 + 137.698i 0.122496 + 0.212170i
\(650\) 0 0
\(651\) 142.894 + 357.500i 0.219500 + 0.549155i
\(652\) 0 0
\(653\) 296.500 + 513.553i 0.454058 + 0.786452i 0.998634 0.0522601i \(-0.0166425\pi\)
−0.544575 + 0.838712i \(0.683309\pi\)
\(654\) 0 0
\(655\) −1098.99 634.500i −1.67784 0.968702i
\(656\) 0 0
\(657\) −2288.00 −3.48250
\(658\) 0 0
\(659\) 1192.00i 1.80880i 0.426684 + 0.904401i \(0.359682\pi\)
−0.426684 + 0.904401i \(0.640318\pi\)
\(660\) 0 0
\(661\) 236.500 409.630i 0.357791 0.619713i −0.629800 0.776757i \(-0.716863\pi\)
0.987592 + 0.157045i \(0.0501966\pi\)
\(662\) 0 0
\(663\) 484.974 280.000i 0.731485 0.422323i
\(664\) 0 0
\(665\) −544.500 428.683i −0.818797 0.644635i
\(666\) 0 0
\(667\) 526.543 304.000i 0.789420 0.455772i
\(668\) 0 0
\(669\) −440.000 + 762.102i −0.657698 + 1.13917i
\(670\) 0 0
\(671\) 237.000i 0.353204i
\(672\) 0 0
\(673\) 824.000 1.22437 0.612184 0.790715i \(-0.290291\pi\)
0.612184 + 0.790715i \(0.290291\pi\)
\(674\) 0 0
\(675\) −1697.41 980.000i −2.51468 1.45185i
\(676\) 0 0
\(677\) 131.500 + 227.765i 0.194239 + 0.336432i 0.946651 0.322261i \(-0.104443\pi\)
−0.752412 + 0.658693i \(0.771110\pi\)
\(678\) 0 0
\(679\) −609.682 88.0000i −0.897911 0.129602i
\(680\) 0 0
\(681\) 967.500 + 1675.76i 1.42070 + 2.46073i
\(682\) 0 0
\(683\) 556.854 + 321.500i 0.815306 + 0.470717i 0.848795 0.528722i \(-0.177328\pi\)
−0.0334888 + 0.999439i \(0.510662\pi\)
\(684\) 0 0
\(685\) 81.0000 0.118248
\(686\) 0 0
\(687\) 915.000i 1.33188i
\(688\) 0 0
\(689\) −56.0000 + 96.9948i −0.0812772 + 0.140776i
\(690\) 0 0
\(691\) 108.253 62.5000i 0.156662 0.0904486i −0.419620 0.907700i \(-0.637837\pi\)
0.576281 + 0.817251i \(0.304503\pi\)
\(692\) 0 0
\(693\) −48.0000 + 332.554i −0.0692641 + 0.479876i
\(694\) 0 0
\(695\) −1060.02 + 612.000i −1.52520 + 0.880576i
\(696\) 0 0
\(697\) −140.000 + 242.487i −0.200861 + 0.347901i
\(698\) 0 0
\(699\) 1805.00i 2.58226i
\(700\) 0 0
\(701\) −54.0000 −0.0770328 −0.0385164 0.999258i \(-0.512263\pi\)
−0.0385164 + 0.999258i \(0.512263\pi\)
\(702\) 0 0
\(703\) 9.52628 + 5.50000i 0.0135509 + 0.00782361i
\(704\) 0 0
\(705\) 1912.50 + 3312.55i 2.71277 + 4.69865i
\(706\) 0 0
\(707\) 64.9519 82.5000i 0.0918697 0.116690i
\(708\) 0 0
\(709\) −575.500 996.795i −0.811707 1.40592i −0.911669 0.410926i \(-0.865205\pi\)
0.0999621 0.994991i \(-0.468128\pi\)
\(710\) 0 0
\(711\) −484.974 280.000i −0.682102 0.393812i
\(712\) 0 0
\(713\) −209.000 −0.293128
\(714\) 0 0
\(715\) 432.000i 0.604196i
\(716\) 0 0
\(717\) −125.000 + 216.506i −0.174338 + 0.301961i
\(718\) 0 0
\(719\) −349.008 + 201.500i −0.485408 + 0.280250i −0.722667 0.691196i \(-0.757084\pi\)
0.237260 + 0.971446i \(0.423751\pi\)
\(720\) 0 0
\(721\) 604.500 241.621i 0.838419 0.335119i
\(722\) 0 0
\(723\) 558.586 322.500i 0.772595 0.446058i
\(724\) 0 0
\(725\) 896.000 1551.92i 1.23586 2.14058i
\(726\) 0 0
\(727\) 496.000i 0.682256i −0.940017 0.341128i \(-0.889191\pi\)
0.940017 0.341128i \(-0.110809\pi\)
\(728\) 0 0
\(729\) 1079.00 1.48011
\(730\) 0 0
\(731\) −242.487 140.000i −0.331720 0.191518i
\(732\) 0 0
\(733\) 80.5000 + 139.430i 0.109823 + 0.190218i 0.915698 0.401866i \(-0.131638\pi\)
−0.805876 + 0.592085i \(0.798305\pi\)
\(734\) 0 0
\(735\) 623.538 2115.00i 0.848351 2.87755i
\(736\) 0 0
\(737\) −16.5000 28.5788i −0.0223881 0.0387773i
\(738\) 0 0
\(739\) 473.716 + 273.500i 0.641023 + 0.370095i 0.785008 0.619485i \(-0.212659\pi\)
−0.143986 + 0.989580i \(0.545992\pi\)
\(740\) 0 0
\(741\) 880.000 1.18758
\(742\) 0 0
\(743\) 256.000i 0.344549i 0.985049 + 0.172275i \(0.0551116\pi\)
−0.985049 + 0.172275i \(0.944888\pi\)
\(744\) 0 0
\(745\) −256.500 + 444.271i −0.344295 + 0.596337i
\(746\) 0 0
\(747\) 110.851 64.0000i 0.148395 0.0856760i
\(748\) 0 0
\(749\) 71.5000 28.5788i 0.0954606 0.0381560i
\(750\) 0 0
\(751\) 979.475 565.500i 1.30423 0.752996i 0.323101 0.946364i \(-0.395275\pi\)
0.981126 + 0.193368i \(0.0619413\pi\)
\(752\) 0 0
\(753\) −985.000 + 1706.07i −1.30810 + 2.26570i
\(754\) 0 0
\(755\) 243.000i 0.321854i
\(756\) 0 0
\(757\) −336.000 −0.443857 −0.221929 0.975063i \(-0.571235\pi\)
−0.221929 + 0.975063i \(0.571235\pi\)
\(758\) 0 0
\(759\) −246.817 142.500i −0.325187 0.187747i
\(760\) 0 0
\(761\) −172.500 298.779i −0.226675 0.392613i 0.730145 0.683292i \(-0.239452\pi\)
−0.956821 + 0.290678i \(0.906119\pi\)
\(762\) 0 0
\(763\) −489.304 + 621.500i −0.641290 + 0.814548i
\(764\) 0 0
\(765\) −504.000 872.954i −0.658824 1.14112i
\(766\) 0 0
\(767\) 734.390 + 424.000i 0.957483 + 0.552803i
\(768\) 0 0
\(769\) 568.000 0.738622 0.369311 0.929306i \(-0.379594\pi\)
0.369311 + 0.929306i \(0.379594\pi\)
\(770\) 0 0
\(771\) 445.000i 0.577173i
\(772\) 0 0
\(773\) 279.500 484.108i 0.361578 0.626272i −0.626643 0.779307i \(-0.715571\pi\)
0.988221 + 0.153035i \(0.0489047\pi\)
\(774\) 0 0
\(775\) −533.472 + 308.000i −0.688351 + 0.397419i
\(776\) 0 0
\(777\) −5.00000 + 34.6410i −0.00643501 + 0.0445830i
\(778\) 0 0
\(779\) −381.051 + 220.000i −0.489154 + 0.282413i
\(780\) 0 0
\(781\) 72.0000 124.708i 0.0921895 0.159677i
\(782\) 0 0
\(783\) 1120.00i 1.43040i
\(784\) 0 0
\(785\) 1503.00 1.91465
\(786\) 0 0
\(787\) 572.443 + 330.500i 0.727373 + 0.419949i 0.817460 0.575985i \(-0.195381\pi\)
−0.0900872 + 0.995934i \(0.528715\pi\)
\(788\) 0 0
\(789\) 112.500 + 194.856i 0.142586 + 0.246965i
\(790\) 0 0
\(791\) 387.979 + 56.0000i 0.490492 + 0.0707965i
\(792\) 0 0
\(793\) −632.000 1094.66i −0.796974 1.38040i
\(794\) 0 0
\(795\) 272.798 + 157.500i 0.343142 + 0.198113i
\(796\) 0 0
\(797\) −736.000 −0.923463 −0.461731 0.887020i \(-0.652772\pi\)
−0.461731 + 0.887020i \(0.652772\pi\)
\(798\) 0 0
\(799\) 595.000i 0.744681i
\(800\) 0 0
\(801\) −776.000 + 1344.07i −0.968789 + 1.67799i
\(802\) 0 0