Properties

Label 108.3.d.a.55.2
Level 108
Weight 3
Character 108.55
Analytic conductor 2.943
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.2
Root \(0.500000 - 0.866025i\) of \(x^{2} - x + 1\)
Character \(\chi\) \(=\) 108.55
Dual form 108.3.d.a.55.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +7.00000 q^{5} -8.66025i q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 + 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +7.00000 q^{5} -8.66025i q^{7} +8.00000 q^{8} +(-7.00000 + 12.1244i) q^{10} +8.66025i q^{11} +20.0000 q^{13} +(15.0000 + 8.66025i) q^{14} +(-8.00000 + 13.8564i) q^{16} -8.00000 q^{17} +10.3923i q^{19} +(-14.0000 - 24.2487i) q^{20} +(-15.0000 - 8.66025i) q^{22} -3.46410i q^{23} +24.0000 q^{25} +(-20.0000 + 34.6410i) q^{26} +(-30.0000 + 17.3205i) q^{28} +10.0000 q^{29} -53.6936i q^{31} +(-16.0000 - 27.7128i) q^{32} +(8.00000 - 13.8564i) q^{34} -60.6218i q^{35} -10.0000 q^{37} +(-18.0000 - 10.3923i) q^{38} +56.0000 q^{40} -50.0000 q^{41} +17.3205i q^{43} +(30.0000 - 17.3205i) q^{44} +(6.00000 + 3.46410i) q^{46} +86.6025i q^{47} -26.0000 q^{49} +(-24.0000 + 41.5692i) q^{50} +(-40.0000 - 69.2820i) q^{52} -47.0000 q^{53} +60.6218i q^{55} -69.2820i q^{56} +(-10.0000 + 17.3205i) q^{58} -34.6410i q^{59} -64.0000 q^{61} +(93.0000 + 53.6936i) q^{62} +64.0000 q^{64} +140.000 q^{65} +86.6025i q^{67} +(16.0000 + 27.7128i) q^{68} +(105.000 + 60.6218i) q^{70} -55.0000 q^{73} +(10.0000 - 17.3205i) q^{74} +(36.0000 - 20.7846i) q^{76} +75.0000 q^{77} +6.92820i q^{79} +(-56.0000 + 96.9948i) q^{80} +(50.0000 - 86.6025i) q^{82} +29.4449i q^{83} -56.0000 q^{85} +(-30.0000 - 17.3205i) q^{86} +69.2820i q^{88} +10.0000 q^{89} -173.205i q^{91} +(-12.0000 + 6.92820i) q^{92} +(-150.000 - 86.6025i) q^{94} +72.7461i q^{95} -25.0000 q^{97} +(26.0000 - 45.0333i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 4q^{4} + 14q^{5} + 16q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 4q^{4} + 14q^{5} + 16q^{8} - 14q^{10} + 40q^{13} + 30q^{14} - 16q^{16} - 16q^{17} - 28q^{20} - 30q^{22} + 48q^{25} - 40q^{26} - 60q^{28} + 20q^{29} - 32q^{32} + 16q^{34} - 20q^{37} - 36q^{38} + 112q^{40} - 100q^{41} + 60q^{44} + 12q^{46} - 52q^{49} - 48q^{50} - 80q^{52} - 94q^{53} - 20q^{58} - 128q^{61} + 186q^{62} + 128q^{64} + 280q^{65} + 32q^{68} + 210q^{70} - 110q^{73} + 20q^{74} + 72q^{76} + 150q^{77} - 112q^{80} + 100q^{82} - 112q^{85} - 60q^{86} + 20q^{89} - 24q^{92} - 300q^{94} - 50q^{97} + 52q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 + 1.73205i −0.500000 + 0.866025i
\(3\) 0 0
\(4\) −2.00000 3.46410i −0.500000 0.866025i
\(5\) 7.00000 1.40000 0.700000 0.714143i \(-0.253183\pi\)
0.700000 + 0.714143i \(0.253183\pi\)
\(6\) 0 0
\(7\) 8.66025i 1.23718i −0.785714 0.618590i \(-0.787704\pi\)
0.785714 0.618590i \(-0.212296\pi\)
\(8\) 8.00000 1.00000
\(9\) 0 0
\(10\) −7.00000 + 12.1244i −0.700000 + 1.21244i
\(11\) 8.66025i 0.787296i 0.919261 + 0.393648i \(0.128787\pi\)
−0.919261 + 0.393648i \(0.871213\pi\)
\(12\) 0 0
\(13\) 20.0000 1.53846 0.769231 0.638971i \(-0.220640\pi\)
0.769231 + 0.638971i \(0.220640\pi\)
\(14\) 15.0000 + 8.66025i 1.07143 + 0.618590i
\(15\) 0 0
\(16\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(17\) −8.00000 −0.470588 −0.235294 0.971924i \(-0.575605\pi\)
−0.235294 + 0.971924i \(0.575605\pi\)
\(18\) 0 0
\(19\) 10.3923i 0.546963i 0.961877 + 0.273482i \(0.0881753\pi\)
−0.961877 + 0.273482i \(0.911825\pi\)
\(20\) −14.0000 24.2487i −0.700000 1.21244i
\(21\) 0 0
\(22\) −15.0000 8.66025i −0.681818 0.393648i
\(23\) 3.46410i 0.150613i −0.997160 0.0753066i \(-0.976006\pi\)
0.997160 0.0753066i \(-0.0239935\pi\)
\(24\) 0 0
\(25\) 24.0000 0.960000
\(26\) −20.0000 + 34.6410i −0.769231 + 1.33235i
\(27\) 0 0
\(28\) −30.0000 + 17.3205i −1.07143 + 0.618590i
\(29\) 10.0000 0.344828 0.172414 0.985025i \(-0.444843\pi\)
0.172414 + 0.985025i \(0.444843\pi\)
\(30\) 0 0
\(31\) 53.6936i 1.73205i −0.500000 0.866025i \(-0.666667\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(32\) −16.0000 27.7128i −0.500000 0.866025i
\(33\) 0 0
\(34\) 8.00000 13.8564i 0.235294 0.407541i
\(35\) 60.6218i 1.73205i
\(36\) 0 0
\(37\) −10.0000 −0.270270 −0.135135 0.990827i \(-0.543147\pi\)
−0.135135 + 0.990827i \(0.543147\pi\)
\(38\) −18.0000 10.3923i −0.473684 0.273482i
\(39\) 0 0
\(40\) 56.0000 1.40000
\(41\) −50.0000 −1.21951 −0.609756 0.792589i \(-0.708733\pi\)
−0.609756 + 0.792589i \(0.708733\pi\)
\(42\) 0 0
\(43\) 17.3205i 0.402803i 0.979509 + 0.201401i \(0.0645495\pi\)
−0.979509 + 0.201401i \(0.935450\pi\)
\(44\) 30.0000 17.3205i 0.681818 0.393648i
\(45\) 0 0
\(46\) 6.00000 + 3.46410i 0.130435 + 0.0753066i
\(47\) 86.6025i 1.84261i 0.388844 + 0.921304i \(0.372875\pi\)
−0.388844 + 0.921304i \(0.627125\pi\)
\(48\) 0 0
\(49\) −26.0000 −0.530612
\(50\) −24.0000 + 41.5692i −0.480000 + 0.831384i
\(51\) 0 0
\(52\) −40.0000 69.2820i −0.769231 1.33235i
\(53\) −47.0000 −0.886792 −0.443396 0.896326i \(-0.646227\pi\)
−0.443396 + 0.896326i \(0.646227\pi\)
\(54\) 0 0
\(55\) 60.6218i 1.10221i
\(56\) 69.2820i 1.23718i
\(57\) 0 0
\(58\) −10.0000 + 17.3205i −0.172414 + 0.298629i
\(59\) 34.6410i 0.587136i −0.955938 0.293568i \(-0.905157\pi\)
0.955938 0.293568i \(-0.0948427\pi\)
\(60\) 0 0
\(61\) −64.0000 −1.04918 −0.524590 0.851355i \(-0.675781\pi\)
−0.524590 + 0.851355i \(0.675781\pi\)
\(62\) 93.0000 + 53.6936i 1.50000 + 0.866025i
\(63\) 0 0
\(64\) 64.0000 1.00000
\(65\) 140.000 2.15385
\(66\) 0 0
\(67\) 86.6025i 1.29258i 0.763094 + 0.646288i \(0.223679\pi\)
−0.763094 + 0.646288i \(0.776321\pi\)
\(68\) 16.0000 + 27.7128i 0.235294 + 0.407541i
\(69\) 0 0
\(70\) 105.000 + 60.6218i 1.50000 + 0.866025i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −55.0000 −0.753425 −0.376712 0.926330i \(-0.622945\pi\)
−0.376712 + 0.926330i \(0.622945\pi\)
\(74\) 10.0000 17.3205i 0.135135 0.234061i
\(75\) 0 0
\(76\) 36.0000 20.7846i 0.473684 0.273482i
\(77\) 75.0000 0.974026
\(78\) 0 0
\(79\) 6.92820i 0.0876988i 0.999038 + 0.0438494i \(0.0139622\pi\)
−0.999038 + 0.0438494i \(0.986038\pi\)
\(80\) −56.0000 + 96.9948i −0.700000 + 1.21244i
\(81\) 0 0
\(82\) 50.0000 86.6025i 0.609756 1.05613i
\(83\) 29.4449i 0.354757i 0.984143 + 0.177379i \(0.0567617\pi\)
−0.984143 + 0.177379i \(0.943238\pi\)
\(84\) 0 0
\(85\) −56.0000 −0.658824
\(86\) −30.0000 17.3205i −0.348837 0.201401i
\(87\) 0 0
\(88\) 69.2820i 0.787296i
\(89\) 10.0000 0.112360 0.0561798 0.998421i \(-0.482108\pi\)
0.0561798 + 0.998421i \(0.482108\pi\)
\(90\) 0 0
\(91\) 173.205i 1.90335i
\(92\) −12.0000 + 6.92820i −0.130435 + 0.0753066i
\(93\) 0 0
\(94\) −150.000 86.6025i −1.59574 0.921304i
\(95\) 72.7461i 0.765749i
\(96\) 0 0
\(97\) −25.0000 −0.257732 −0.128866 0.991662i \(-0.541134\pi\)
−0.128866 + 0.991662i \(0.541134\pi\)
\(98\) 26.0000 45.0333i 0.265306 0.459524i
\(99\) 0 0
\(100\) −48.0000 83.1384i −0.480000 0.831384i
\(101\) −155.000 −1.53465 −0.767327 0.641256i \(-0.778414\pi\)
−0.767327 + 0.641256i \(0.778414\pi\)
\(102\) 0 0
\(103\) 138.564i 1.34528i 0.739969 + 0.672641i \(0.234840\pi\)
−0.739969 + 0.672641i \(0.765160\pi\)
\(104\) 160.000 1.53846
\(105\) 0 0
\(106\) 47.0000 81.4064i 0.443396 0.767985i
\(107\) 129.904i 1.21405i −0.794681 0.607027i \(-0.792362\pi\)
0.794681 0.607027i \(-0.207638\pi\)
\(108\) 0 0
\(109\) 134.000 1.22936 0.614679 0.788777i \(-0.289286\pi\)
0.614679 + 0.788777i \(0.289286\pi\)
\(110\) −105.000 60.6218i −0.954545 0.551107i
\(111\) 0 0
\(112\) 120.000 + 69.2820i 1.07143 + 0.618590i
\(113\) −74.0000 −0.654867 −0.327434 0.944874i \(-0.606184\pi\)
−0.327434 + 0.944874i \(0.606184\pi\)
\(114\) 0 0
\(115\) 24.2487i 0.210858i
\(116\) −20.0000 34.6410i −0.172414 0.298629i
\(117\) 0 0
\(118\) 60.0000 + 34.6410i 0.508475 + 0.293568i
\(119\) 69.2820i 0.582202i
\(120\) 0 0
\(121\) 46.0000 0.380165
\(122\) 64.0000 110.851i 0.524590 0.908617i
\(123\) 0 0
\(124\) −186.000 + 107.387i −1.50000 + 0.866025i
\(125\) −7.00000 −0.0560000
\(126\) 0 0
\(127\) 25.9808i 0.204573i −0.994755 0.102286i \(-0.967384\pi\)
0.994755 0.102286i \(-0.0326158\pi\)
\(128\) −64.0000 + 110.851i −0.500000 + 0.866025i
\(129\) 0 0
\(130\) −140.000 + 242.487i −1.07692 + 1.86529i
\(131\) 164.545i 1.25607i −0.778186 0.628034i \(-0.783860\pi\)
0.778186 0.628034i \(-0.216140\pi\)
\(132\) 0 0
\(133\) 90.0000 0.676692
\(134\) −150.000 86.6025i −1.11940 0.646288i
\(135\) 0 0
\(136\) −64.0000 −0.470588
\(137\) −62.0000 −0.452555 −0.226277 0.974063i \(-0.572656\pi\)
−0.226277 + 0.974063i \(0.572656\pi\)
\(138\) 0 0
\(139\) 173.205i 1.24608i −0.782190 0.623040i \(-0.785897\pi\)
0.782190 0.623040i \(-0.214103\pi\)
\(140\) −210.000 + 121.244i −1.50000 + 0.866025i
\(141\) 0 0
\(142\) 0 0
\(143\) 173.205i 1.21122i
\(144\) 0 0
\(145\) 70.0000 0.482759
\(146\) 55.0000 95.2628i 0.376712 0.652485i
\(147\) 0 0
\(148\) 20.0000 + 34.6410i 0.135135 + 0.234061i
\(149\) 115.000 0.771812 0.385906 0.922538i \(-0.373889\pi\)
0.385906 + 0.922538i \(0.373889\pi\)
\(150\) 0 0
\(151\) 43.3013i 0.286763i 0.989667 + 0.143382i \(0.0457977\pi\)
−0.989667 + 0.143382i \(0.954202\pi\)
\(152\) 83.1384i 0.546963i
\(153\) 0 0
\(154\) −75.0000 + 129.904i −0.487013 + 0.843531i
\(155\) 375.855i 2.42487i
\(156\) 0 0
\(157\) 20.0000 0.127389 0.0636943 0.997969i \(-0.479712\pi\)
0.0636943 + 0.997969i \(0.479712\pi\)
\(158\) −12.0000 6.92820i −0.0759494 0.0438494i
\(159\) 0 0
\(160\) −112.000 193.990i −0.700000 1.21244i
\(161\) −30.0000 −0.186335
\(162\) 0 0
\(163\) 103.923i 0.637565i 0.947828 + 0.318782i \(0.103274\pi\)
−0.947828 + 0.318782i \(0.896726\pi\)
\(164\) 100.000 + 173.205i 0.609756 + 1.05613i
\(165\) 0 0
\(166\) −51.0000 29.4449i −0.307229 0.177379i
\(167\) 245.951i 1.47276i 0.676567 + 0.736381i \(0.263467\pi\)
−0.676567 + 0.736381i \(0.736533\pi\)
\(168\) 0 0
\(169\) 231.000 1.36686
\(170\) 56.0000 96.9948i 0.329412 0.570558i
\(171\) 0 0
\(172\) 60.0000 34.6410i 0.348837 0.201401i
\(173\) 127.000 0.734104 0.367052 0.930200i \(-0.380367\pi\)
0.367052 + 0.930200i \(0.380367\pi\)
\(174\) 0 0
\(175\) 207.846i 1.18769i
\(176\) −120.000 69.2820i −0.681818 0.393648i
\(177\) 0 0
\(178\) −10.0000 + 17.3205i −0.0561798 + 0.0973062i
\(179\) 233.827i 1.30630i 0.757231 + 0.653148i \(0.226552\pi\)
−0.757231 + 0.653148i \(0.773448\pi\)
\(180\) 0 0
\(181\) 56.0000 0.309392 0.154696 0.987962i \(-0.450560\pi\)
0.154696 + 0.987962i \(0.450560\pi\)
\(182\) 300.000 + 173.205i 1.64835 + 0.951676i
\(183\) 0 0
\(184\) 27.7128i 0.150613i
\(185\) −70.0000 −0.378378
\(186\) 0 0
\(187\) 69.2820i 0.370492i
\(188\) 300.000 173.205i 1.59574 0.921304i
\(189\) 0 0
\(190\) −126.000 72.7461i −0.663158 0.382874i
\(191\) 34.6410i 0.181367i 0.995880 + 0.0906833i \(0.0289051\pi\)
−0.995880 + 0.0906833i \(0.971095\pi\)
\(192\) 0 0
\(193\) 65.0000 0.336788 0.168394 0.985720i \(-0.446142\pi\)
0.168394 + 0.985720i \(0.446142\pi\)
\(194\) 25.0000 43.3013i 0.128866 0.223202i
\(195\) 0 0
\(196\) 52.0000 + 90.0666i 0.265306 + 0.459524i
\(197\) 253.000 1.28426 0.642132 0.766594i \(-0.278050\pi\)
0.642132 + 0.766594i \(0.278050\pi\)
\(198\) 0 0
\(199\) 129.904i 0.652783i −0.945235 0.326391i \(-0.894167\pi\)
0.945235 0.326391i \(-0.105833\pi\)
\(200\) 192.000 0.960000
\(201\) 0 0
\(202\) 155.000 268.468i 0.767327 1.32905i
\(203\) 86.6025i 0.426613i
\(204\) 0 0
\(205\) −350.000 −1.70732
\(206\) −240.000 138.564i −1.16505 0.672641i
\(207\) 0 0
\(208\) −160.000 + 277.128i −0.769231 + 1.33235i
\(209\) −90.0000 −0.430622
\(210\) 0 0
\(211\) 148.956i 0.705954i 0.935632 + 0.352977i \(0.114831\pi\)
−0.935632 + 0.352977i \(0.885169\pi\)
\(212\) 94.0000 + 162.813i 0.443396 + 0.767985i
\(213\) 0 0
\(214\) 225.000 + 129.904i 1.05140 + 0.607027i
\(215\) 121.244i 0.563924i
\(216\) 0 0
\(217\) −465.000 −2.14286
\(218\) −134.000 + 232.095i −0.614679 + 1.06466i
\(219\) 0 0
\(220\) 210.000 121.244i 0.954545 0.551107i
\(221\) −160.000 −0.723982
\(222\) 0 0
\(223\) 34.6410i 0.155341i −0.996979 0.0776704i \(-0.975252\pi\)
0.996979 0.0776704i \(-0.0247482\pi\)
\(224\) −240.000 + 138.564i −1.07143 + 0.618590i
\(225\) 0 0
\(226\) 74.0000 128.172i 0.327434 0.567132i
\(227\) 90.0666i 0.396769i −0.980124 0.198385i \(-0.936430\pi\)
0.980124 0.198385i \(-0.0635695\pi\)
\(228\) 0 0
\(229\) 146.000 0.637555 0.318777 0.947830i \(-0.396728\pi\)
0.318777 + 0.947830i \(0.396728\pi\)
\(230\) 42.0000 + 24.2487i 0.182609 + 0.105429i
\(231\) 0 0
\(232\) 80.0000 0.344828
\(233\) 334.000 1.43348 0.716738 0.697342i \(-0.245634\pi\)
0.716738 + 0.697342i \(0.245634\pi\)
\(234\) 0 0
\(235\) 606.218i 2.57965i
\(236\) −120.000 + 69.2820i −0.508475 + 0.293568i
\(237\) 0 0
\(238\) −120.000 69.2820i −0.504202 0.291101i
\(239\) 17.3205i 0.0724707i 0.999343 + 0.0362354i \(0.0115366\pi\)
−0.999343 + 0.0362354i \(0.988463\pi\)
\(240\) 0 0
\(241\) 134.000 0.556017 0.278008 0.960579i \(-0.410326\pi\)
0.278008 + 0.960579i \(0.410326\pi\)
\(242\) −46.0000 + 79.6743i −0.190083 + 0.329233i
\(243\) 0 0
\(244\) 128.000 + 221.703i 0.524590 + 0.908617i
\(245\) −182.000 −0.742857
\(246\) 0 0
\(247\) 207.846i 0.841482i
\(248\) 429.549i 1.73205i
\(249\) 0 0
\(250\) 7.00000 12.1244i 0.0280000 0.0484974i
\(251\) 207.846i 0.828072i −0.910260 0.414036i \(-0.864119\pi\)
0.910260 0.414036i \(-0.135881\pi\)
\(252\) 0 0
\(253\) 30.0000 0.118577
\(254\) 45.0000 + 25.9808i 0.177165 + 0.102286i
\(255\) 0 0
\(256\) −128.000 221.703i −0.500000 0.866025i
\(257\) 268.000 1.04280 0.521401 0.853312i \(-0.325410\pi\)
0.521401 + 0.853312i \(0.325410\pi\)
\(258\) 0 0
\(259\) 86.6025i 0.334373i
\(260\) −280.000 484.974i −1.07692 1.86529i
\(261\) 0 0
\(262\) 285.000 + 164.545i 1.08779 + 0.628034i
\(263\) 433.013i 1.64644i −0.567725 0.823218i \(-0.692176\pi\)
0.567725 0.823218i \(-0.307824\pi\)
\(264\) 0 0
\(265\) −329.000 −1.24151
\(266\) −90.0000 + 155.885i −0.338346 + 0.586032i
\(267\) 0 0
\(268\) 300.000 173.205i 1.11940 0.646288i
\(269\) −350.000 −1.30112 −0.650558 0.759457i \(-0.725465\pi\)
−0.650558 + 0.759457i \(0.725465\pi\)
\(270\) 0 0
\(271\) 36.3731i 0.134218i −0.997746 0.0671090i \(-0.978622\pi\)
0.997746 0.0671090i \(-0.0213775\pi\)
\(272\) 64.0000 110.851i 0.235294 0.407541i
\(273\) 0 0
\(274\) 62.0000 107.387i 0.226277 0.391924i
\(275\) 207.846i 0.755804i
\(276\) 0 0
\(277\) −520.000 −1.87726 −0.938628 0.344931i \(-0.887902\pi\)
−0.938628 + 0.344931i \(0.887902\pi\)
\(278\) 300.000 + 173.205i 1.07914 + 0.623040i
\(279\) 0 0
\(280\) 484.974i 1.73205i
\(281\) −440.000 −1.56584 −0.782918 0.622125i \(-0.786270\pi\)
−0.782918 + 0.622125i \(0.786270\pi\)
\(282\) 0 0
\(283\) 329.090i 1.16286i −0.813596 0.581430i \(-0.802493\pi\)
0.813596 0.581430i \(-0.197507\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −300.000 173.205i −1.04895 0.605612i
\(287\) 433.013i 1.50876i
\(288\) 0 0
\(289\) −225.000 −0.778547
\(290\) −70.0000 + 121.244i −0.241379 + 0.418081i
\(291\) 0 0
\(292\) 110.000 + 190.526i 0.376712 + 0.652485i
\(293\) −218.000 −0.744027 −0.372014 0.928227i \(-0.621333\pi\)
−0.372014 + 0.928227i \(0.621333\pi\)
\(294\) 0 0
\(295\) 242.487i 0.821990i
\(296\) −80.0000 −0.270270
\(297\) 0 0
\(298\) −115.000 + 199.186i −0.385906 + 0.668409i
\(299\) 69.2820i 0.231712i
\(300\) 0 0
\(301\) 150.000 0.498339
\(302\) −75.0000 43.3013i −0.248344 0.143382i
\(303\) 0 0
\(304\) −144.000 83.1384i −0.473684 0.273482i
\(305\) −448.000 −1.46885
\(306\) 0 0
\(307\) 207.846i 0.677023i −0.940962 0.338512i \(-0.890077\pi\)
0.940962 0.338512i \(-0.109923\pi\)
\(308\) −150.000 259.808i −0.487013 0.843531i
\(309\) 0 0
\(310\) 651.000 + 375.855i 2.10000 + 1.21244i
\(311\) 294.449i 0.946780i −0.880853 0.473390i \(-0.843030\pi\)
0.880853 0.473390i \(-0.156970\pi\)
\(312\) 0 0
\(313\) 485.000 1.54952 0.774760 0.632255i \(-0.217870\pi\)
0.774760 + 0.632255i \(0.217870\pi\)
\(314\) −20.0000 + 34.6410i −0.0636943 + 0.110322i
\(315\) 0 0
\(316\) 24.0000 13.8564i 0.0759494 0.0438494i
\(317\) 217.000 0.684543 0.342271 0.939601i \(-0.388804\pi\)
0.342271 + 0.939601i \(0.388804\pi\)
\(318\) 0 0
\(319\) 86.6025i 0.271481i
\(320\) 448.000 1.40000
\(321\) 0 0
\(322\) 30.0000 51.9615i 0.0931677 0.161371i
\(323\) 83.1384i 0.257395i
\(324\) 0 0
\(325\) 480.000 1.47692
\(326\) −180.000 103.923i −0.552147 0.318782i
\(327\) 0 0
\(328\) −400.000 −1.21951
\(329\) 750.000 2.27964
\(330\) 0 0
\(331\) 433.013i 1.30820i 0.756410 + 0.654098i \(0.226952\pi\)
−0.756410 + 0.654098i \(0.773048\pi\)
\(332\) 102.000 58.8897i 0.307229 0.177379i
\(333\) 0 0
\(334\) −426.000 245.951i −1.27545 0.736381i
\(335\) 606.218i 1.80961i
\(336\) 0 0
\(337\) −310.000 −0.919881 −0.459941 0.887950i \(-0.652129\pi\)
−0.459941 + 0.887950i \(0.652129\pi\)
\(338\) −231.000 + 400.104i −0.683432 + 1.18374i
\(339\) 0 0
\(340\) 112.000 + 193.990i 0.329412 + 0.570558i
\(341\) 465.000 1.36364
\(342\) 0 0
\(343\) 199.186i 0.580717i
\(344\) 138.564i 0.402803i
\(345\) 0 0
\(346\) −127.000 + 219.970i −0.367052 + 0.635753i
\(347\) 216.506i 0.623938i −0.950092 0.311969i \(-0.899012\pi\)
0.950092 0.311969i \(-0.100988\pi\)
\(348\) 0 0
\(349\) 74.0000 0.212034 0.106017 0.994364i \(-0.466190\pi\)
0.106017 + 0.994364i \(0.466190\pi\)
\(350\) 360.000 + 207.846i 1.02857 + 0.593846i
\(351\) 0 0
\(352\) 240.000 138.564i 0.681818 0.393648i
\(353\) 394.000 1.11615 0.558074 0.829791i \(-0.311541\pi\)
0.558074 + 0.829791i \(0.311541\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −20.0000 34.6410i −0.0561798 0.0973062i
\(357\) 0 0
\(358\) −405.000 233.827i −1.13128 0.653148i
\(359\) 571.577i 1.59214i −0.605207 0.796068i \(-0.706910\pi\)
0.605207 0.796068i \(-0.293090\pi\)
\(360\) 0 0
\(361\) 253.000 0.700831
\(362\) −56.0000 + 96.9948i −0.154696 + 0.267942i
\(363\) 0 0
\(364\) −600.000 + 346.410i −1.64835 + 0.951676i
\(365\) −385.000 −1.05479
\(366\) 0 0
\(367\) 562.917i 1.53383i 0.641747 + 0.766916i \(0.278210\pi\)
−0.641747 + 0.766916i \(0.721790\pi\)
\(368\) 48.0000 + 27.7128i 0.130435 + 0.0753066i
\(369\) 0 0
\(370\) 70.0000 121.244i 0.189189 0.327685i
\(371\) 407.032i 1.09712i
\(372\) 0 0
\(373\) −40.0000 −0.107239 −0.0536193 0.998561i \(-0.517076\pi\)
−0.0536193 + 0.998561i \(0.517076\pi\)
\(374\) 120.000 + 69.2820i 0.320856 + 0.185246i
\(375\) 0 0
\(376\) 692.820i 1.84261i
\(377\) 200.000 0.530504
\(378\) 0 0
\(379\) 685.892i 1.80974i −0.425686 0.904871i \(-0.639967\pi\)
0.425686 0.904871i \(-0.360033\pi\)
\(380\) 252.000 145.492i 0.663158 0.382874i
\(381\) 0 0
\(382\) −60.0000 34.6410i −0.157068 0.0906833i
\(383\) 360.267i 0.940644i 0.882495 + 0.470322i \(0.155862\pi\)
−0.882495 + 0.470322i \(0.844138\pi\)
\(384\) 0 0
\(385\) 525.000 1.36364
\(386\) −65.0000 + 112.583i −0.168394 + 0.291667i
\(387\) 0 0
\(388\) 50.0000 + 86.6025i 0.128866 + 0.223202i
\(389\) 475.000 1.22108 0.610540 0.791986i \(-0.290953\pi\)
0.610540 + 0.791986i \(0.290953\pi\)
\(390\) 0 0
\(391\) 27.7128i 0.0708768i
\(392\) −208.000 −0.530612
\(393\) 0 0
\(394\) −253.000 + 438.209i −0.642132 + 1.11221i
\(395\) 48.4974i 0.122778i
\(396\) 0 0
\(397\) 260.000 0.654912 0.327456 0.944866i \(-0.393809\pi\)
0.327456 + 0.944866i \(0.393809\pi\)
\(398\) 225.000 + 129.904i 0.565327 + 0.326391i
\(399\) 0 0
\(400\) −192.000 + 332.554i −0.480000 + 0.831384i
\(401\) −740.000 −1.84539 −0.922693 0.385535i \(-0.874017\pi\)
−0.922693 + 0.385535i \(0.874017\pi\)
\(402\) 0 0
\(403\) 1073.87i 2.66469i
\(404\) 310.000 + 536.936i 0.767327 + 1.32905i
\(405\) 0 0
\(406\) 150.000 + 86.6025i 0.369458 + 0.213307i
\(407\) 86.6025i 0.212783i
\(408\) 0 0
\(409\) 659.000 1.61125 0.805623 0.592428i \(-0.201830\pi\)
0.805623 + 0.592428i \(0.201830\pi\)
\(410\) 350.000 606.218i 0.853659 1.47858i
\(411\) 0 0
\(412\) 480.000 277.128i 1.16505 0.672641i
\(413\) −300.000 −0.726392
\(414\) 0 0
\(415\) 206.114i 0.496660i
\(416\) −320.000 554.256i −0.769231 1.33235i
\(417\) 0 0
\(418\) 90.0000 155.885i 0.215311 0.372930i
\(419\) 588.897i 1.40548i 0.711445 + 0.702741i \(0.248041\pi\)
−0.711445 + 0.702741i \(0.751959\pi\)
\(420\) 0 0
\(421\) −496.000 −1.17815 −0.589074 0.808079i \(-0.700507\pi\)
−0.589074 + 0.808079i \(0.700507\pi\)
\(422\) −258.000 148.956i −0.611374 0.352977i
\(423\) 0 0
\(424\) −376.000 −0.886792
\(425\) −192.000 −0.451765
\(426\) 0 0
\(427\) 554.256i 1.29802i
\(428\) −450.000 + 259.808i −1.05140 + 0.607027i
\(429\) 0 0
\(430\) −210.000 121.244i −0.488372 0.281962i
\(431\) 571.577i 1.32616i −0.748547 0.663082i \(-0.769248\pi\)
0.748547 0.663082i \(-0.230752\pi\)
\(432\) 0 0
\(433\) −235.000 −0.542725 −0.271363 0.962477i \(-0.587474\pi\)
−0.271363 + 0.962477i \(0.587474\pi\)
\(434\) 465.000 805.404i 1.07143 1.85577i
\(435\) 0 0
\(436\) −268.000 464.190i −0.614679 1.06466i
\(437\) 36.0000 0.0823799
\(438\) 0 0
\(439\) 413.960i 0.942962i −0.881876 0.471481i \(-0.843720\pi\)
0.881876 0.471481i \(-0.156280\pi\)
\(440\) 484.974i 1.10221i
\(441\) 0 0
\(442\) 160.000 277.128i 0.361991 0.626987i
\(443\) 575.041i 1.29806i 0.760763 + 0.649030i \(0.224825\pi\)
−0.760763 + 0.649030i \(0.775175\pi\)
\(444\) 0 0
\(445\) 70.0000 0.157303
\(446\) 60.0000 + 34.6410i 0.134529 + 0.0776704i
\(447\) 0 0
\(448\) 554.256i 1.23718i
\(449\) −470.000 −1.04677 −0.523385 0.852096i \(-0.675331\pi\)
−0.523385 + 0.852096i \(0.675331\pi\)
\(450\) 0 0
\(451\) 433.013i 0.960117i
\(452\) 148.000 + 256.344i 0.327434 + 0.567132i
\(453\) 0 0
\(454\) 156.000 + 90.0666i 0.343612 + 0.198385i
\(455\) 1212.44i 2.66469i
\(456\) 0 0
\(457\) −325.000 −0.711160 −0.355580 0.934646i \(-0.615717\pi\)
−0.355580 + 0.934646i \(0.615717\pi\)
\(458\) −146.000 + 252.879i −0.318777 + 0.552138i
\(459\) 0 0
\(460\) −84.0000 + 48.4974i −0.182609 + 0.105429i
\(461\) 655.000 1.42082 0.710412 0.703786i \(-0.248509\pi\)
0.710412 + 0.703786i \(0.248509\pi\)
\(462\) 0 0
\(463\) 164.545i 0.355388i 0.984086 + 0.177694i \(0.0568638\pi\)
−0.984086 + 0.177694i \(0.943136\pi\)
\(464\) −80.0000 + 138.564i −0.172414 + 0.298629i
\(465\) 0 0
\(466\) −334.000 + 578.505i −0.716738 + 1.24143i
\(467\) 57.1577i 0.122393i 0.998126 + 0.0611967i \(0.0194917\pi\)
−0.998126 + 0.0611967i \(0.980508\pi\)
\(468\) 0 0
\(469\) 750.000 1.59915
\(470\) −1050.00 606.218i −2.23404 1.28983i
\(471\) 0 0
\(472\) 277.128i 0.587136i
\(473\) −150.000 −0.317125
\(474\) 0 0
\(475\) 249.415i 0.525085i
\(476\) 240.000 138.564i 0.504202 0.291101i
\(477\) 0 0
\(478\) −30.0000 17.3205i −0.0627615 0.0362354i
\(479\) 329.090i 0.687035i −0.939146 0.343517i \(-0.888382\pi\)
0.939146 0.343517i \(-0.111618\pi\)
\(480\) 0 0
\(481\) −200.000 −0.415800
\(482\) −134.000 + 232.095i −0.278008 + 0.481524i
\(483\) 0 0
\(484\) −92.0000 159.349i −0.190083 0.329233i
\(485\) −175.000 −0.360825
\(486\) 0 0
\(487\) 519.615i 1.06697i 0.845809 + 0.533486i \(0.179118\pi\)
−0.845809 + 0.533486i \(0.820882\pi\)
\(488\) −512.000 −1.04918
\(489\) 0 0
\(490\) 182.000 315.233i 0.371429 0.643333i
\(491\) 216.506i 0.440950i −0.975393 0.220475i \(-0.929239\pi\)
0.975393 0.220475i \(-0.0707607\pi\)
\(492\) 0 0
\(493\) −80.0000 −0.162272
\(494\) −360.000 207.846i −0.728745 0.420741i
\(495\) 0 0
\(496\) 744.000 + 429.549i 1.50000 + 0.866025i
\(497\) 0 0
\(498\) 0 0
\(499\) 45.0333i 0.0902471i 0.998981 + 0.0451236i \(0.0143682\pi\)
−0.998981 + 0.0451236i \(0.985632\pi\)
\(500\) 14.0000 + 24.2487i 0.0280000 + 0.0484974i
\(501\) 0 0
\(502\) 360.000 + 207.846i 0.717131 + 0.414036i
\(503\) 384.515i 0.764444i −0.924071 0.382222i \(-0.875159\pi\)
0.924071 0.382222i \(-0.124841\pi\)
\(504\) 0 0
\(505\) −1085.00 −2.14851
\(506\) −30.0000 + 51.9615i −0.0592885 + 0.102691i
\(507\) 0 0
\(508\) −90.0000 + 51.9615i −0.177165 + 0.102286i
\(509\) 265.000 0.520629 0.260314 0.965524i \(-0.416174\pi\)
0.260314 + 0.965524i \(0.416174\pi\)
\(510\) 0 0
\(511\) 476.314i 0.932121i
\(512\) 512.000 1.00000
\(513\) 0 0
\(514\) −268.000 + 464.190i −0.521401 + 0.903093i
\(515\) 969.948i 1.88340i
\(516\) 0 0
\(517\) −750.000 −1.45068
\(518\) −150.000 86.6025i −0.289575 0.167186i
\(519\) 0 0
\(520\) 1120.00 2.15385
\(521\) −380.000 −0.729367 −0.364683 0.931132i \(-0.618823\pi\)
−0.364683 + 0.931132i \(0.618823\pi\)
\(522\) 0 0
\(523\) 623.538i 1.19223i 0.802898 + 0.596117i \(0.203291\pi\)
−0.802898 + 0.596117i \(0.796709\pi\)
\(524\) −570.000 + 329.090i −1.08779 + 0.628034i
\(525\) 0 0
\(526\) 750.000 + 433.013i 1.42586 + 0.823218i
\(527\) 429.549i 0.815083i
\(528\) 0 0
\(529\) 517.000 0.977316
\(530\) 329.000 569.845i 0.620755 1.07518i
\(531\) 0 0
\(532\) −180.000 311.769i −0.338346 0.586032i
\(533\) −1000.00 −1.87617
\(534\) 0 0
\(535\) 909.327i 1.69968i
\(536\) 692.820i 1.29258i
\(537\) 0 0
\(538\) 350.000 606.218i 0.650558 1.12680i
\(539\) 225.167i 0.417749i
\(540\) 0 0
\(541\) −532.000 −0.983364 −0.491682 0.870775i \(-0.663618\pi\)
−0.491682 + 0.870775i \(0.663618\pi\)
\(542\) 63.0000 + 36.3731i 0.116236 + 0.0671090i
\(543\) 0 0
\(544\) 128.000 + 221.703i 0.235294 + 0.407541i
\(545\) 938.000 1.72110
\(546\) 0 0
\(547\) 900.666i 1.64656i 0.567638 + 0.823278i \(0.307857\pi\)
−0.567638 + 0.823278i \(0.692143\pi\)
\(548\) 124.000 + 214.774i 0.226277 + 0.391924i
\(549\) 0 0
\(550\) −360.000 207.846i −0.654545 0.377902i
\(551\) 103.923i 0.188608i
\(552\) 0 0
\(553\) 60.0000 0.108499
\(554\) 520.000 900.666i 0.938628 1.62575i
\(555\) 0 0
\(556\) −600.000 + 346.410i −1.07914 + 0.623040i
\(557\) −89.0000 −0.159785 −0.0798923 0.996804i \(-0.525458\pi\)
−0.0798923 + 0.996804i \(0.525458\pi\)
\(558\) 0 0
\(559\) 346.410i 0.619696i
\(560\) 840.000 + 484.974i 1.50000 + 0.866025i
\(561\) 0 0
\(562\) 440.000 762.102i 0.782918 1.35605i
\(563\) 303.109i 0.538382i 0.963087 + 0.269191i \(0.0867562\pi\)
−0.963087 + 0.269191i \(0.913244\pi\)
\(564\) 0 0
\(565\) −518.000 −0.916814
\(566\) 570.000 + 329.090i 1.00707 + 0.581430i
\(567\) 0 0
\(568\) 0 0
\(569\) 100.000 0.175747 0.0878735 0.996132i \(-0.471993\pi\)
0.0878735 + 0.996132i \(0.471993\pi\)
\(570\) 0 0
\(571\) 339.482i 0.594539i −0.954794 0.297270i \(-0.903924\pi\)
0.954794 0.297270i \(-0.0960760\pi\)
\(572\) 600.000 346.410i 1.04895 0.605612i
\(573\) 0 0
\(574\) −750.000 433.013i −1.30662 0.754378i
\(575\) 83.1384i 0.144589i
\(576\) 0 0
\(577\) −730.000 −1.26516 −0.632582 0.774493i \(-0.718005\pi\)
−0.632582 + 0.774493i \(0.718005\pi\)
\(578\) 225.000 389.711i 0.389273 0.674241i
\(579\) 0 0
\(580\) −140.000 242.487i −0.241379 0.418081i
\(581\) 255.000 0.438898
\(582\) 0 0
\(583\) 407.032i 0.698168i
\(584\) −440.000 −0.753425
\(585\) 0 0
\(586\) 218.000 377.587i 0.372014 0.644347i
\(587\) 801.940i 1.36617i −0.730341 0.683083i \(-0.760639\pi\)
0.730341 0.683083i \(-0.239361\pi\)
\(588\) 0 0
\(589\) 558.000 0.947368
\(590\) 420.000 + 242.487i 0.711864 + 0.410995i
\(591\) 0 0
\(592\) 80.0000 138.564i 0.135135 0.234061i
\(593\) 982.000 1.65599 0.827993 0.560738i \(-0.189483\pi\)
0.827993 + 0.560738i \(0.189483\pi\)
\(594\) 0 0
\(595\) 484.974i 0.815083i
\(596\) −230.000 398.372i −0.385906 0.668409i
\(597\) 0 0
\(598\) 120.000 + 69.2820i 0.200669 + 0.115856i
\(599\) 225.167i 0.375904i 0.982178 + 0.187952i \(0.0601850\pi\)
−0.982178 + 0.187952i \(0.939815\pi\)
\(600\) 0 0
\(601\) 251.000 0.417637 0.208819 0.977954i \(-0.433038\pi\)
0.208819 + 0.977954i \(0.433038\pi\)
\(602\) −150.000 + 259.808i −0.249169 + 0.431574i
\(603\) 0 0
\(604\) 150.000 86.6025i 0.248344 0.143382i
\(605\) 322.000 0.532231
\(606\) 0 0
\(607\) 381.051i 0.627761i −0.949462 0.313881i \(-0.898371\pi\)
0.949462 0.313881i \(-0.101629\pi\)
\(608\) 288.000 166.277i 0.473684 0.273482i
\(609\) 0 0
\(610\) 448.000 775.959i 0.734426 1.27206i
\(611\) 1732.05i 2.83478i
\(612\) 0 0
\(613\) 650.000 1.06036 0.530179 0.847885i \(-0.322125\pi\)
0.530179 + 0.847885i \(0.322125\pi\)
\(614\) 360.000 + 207.846i 0.586319 + 0.338512i
\(615\) 0 0
\(616\) 600.000 0.974026
\(617\) −758.000 −1.22853 −0.614263 0.789102i \(-0.710546\pi\)
−0.614263 + 0.789102i \(0.710546\pi\)
\(618\) 0 0
\(619\) 173.205i 0.279814i 0.990165 + 0.139907i \(0.0446804\pi\)
−0.990165 + 0.139907i \(0.955320\pi\)
\(620\) −1302.00 + 751.710i −2.10000 + 1.21244i
\(621\) 0 0
\(622\) 510.000 + 294.449i 0.819936 + 0.473390i
\(623\) 86.6025i 0.139009i
\(624\) 0 0
\(625\) −649.000 −1.03840
\(626\) −485.000 + 840.045i −0.774760 + 1.34192i
\(627\) 0 0
\(628\) −40.0000 69.2820i −0.0636943 0.110322i
\(629\) 80.0000 0.127186
\(630\) 0 0
\(631\) 119.512i 0.189400i −0.995506 0.0947001i \(-0.969811\pi\)
0.995506 0.0947001i \(-0.0301892\pi\)
\(632\) 55.4256i 0.0876988i
\(633\) 0 0
\(634\) −217.000 + 375.855i −0.342271 + 0.592831i
\(635\) 181.865i 0.286402i
\(636\) 0 0
\(637\) −520.000 −0.816327
\(638\) −150.000 86.6025i −0.235110 0.135741i
\(639\) 0 0
\(640\) −448.000 + 775.959i −0.700000 + 1.21244i
\(641\) 910.000 1.41966 0.709828 0.704375i \(-0.248772\pi\)
0.709828 + 0.704375i \(0.248772\pi\)
\(642\) 0 0
\(643\) 34.6410i 0.0538741i 0.999637 + 0.0269370i \(0.00857536\pi\)
−0.999637 + 0.0269370i \(0.991425\pi\)
\(644\) 60.0000 + 103.923i 0.0931677 + 0.161371i
\(645\) 0 0
\(646\) 144.000 + 83.1384i 0.222910 + 0.128697i
\(647\) 914.523i 1.41348i −0.707472 0.706741i \(-0.750165\pi\)
0.707472 0.706741i \(-0.249835\pi\)
\(648\) 0 0
\(649\) 300.000 0.462250
\(650\) −480.000 + 831.384i −0.738462 + 1.27905i
\(651\) 0 0
\(652\) 360.000 207.846i 0.552147 0.318782i
\(653\) 103.000 0.157734 0.0788668 0.996885i \(-0.474870\pi\)
0.0788668 + 0.996885i \(0.474870\pi\)
\(654\) 0 0
\(655\) 1151.81i 1.75849i
\(656\) 400.000 692.820i 0.609756 1.05613i
\(657\) 0 0
\(658\) −750.000 + 1299.04i −1.13982 + 1.97422i
\(659\) 60.6218i 0.0919906i 0.998942 + 0.0459953i \(0.0146459\pi\)
−0.998942 + 0.0459953i \(0.985354\pi\)
\(660\) 0 0
\(661\) 578.000 0.874433 0.437216 0.899356i \(-0.355964\pi\)
0.437216 + 0.899356i \(0.355964\pi\)
\(662\) −750.000 433.013i −1.13293 0.654098i
\(663\) 0 0
\(664\) 235.559i 0.354757i
\(665\) 630.000 0.947368
\(666\) 0 0
\(667\) 34.6410i 0.0519356i
\(668\) 852.000 491.902i 1.27545 0.736381i
\(669\) 0 0
\(670\) −1050.00 606.218i −1.56716 0.904803i
\(671\) 554.256i 0.826015i
\(672\) 0 0
\(673\) 845.000 1.25557 0.627786 0.778386i \(-0.283961\pi\)
0.627786 + 0.778386i \(0.283961\pi\)
\(674\) 310.000 536.936i 0.459941 0.796641i
\(675\) 0 0
\(676\) −462.000 800.207i −0.683432 1.18374i
\(677\) −1154.00 −1.70458 −0.852290 0.523070i \(-0.824786\pi\)
−0.852290 + 0.523070i \(0.824786\pi\)
\(678\) 0 0
\(679\) 216.506i 0.318861i
\(680\) −448.000 −0.658824
\(681\) 0 0
\(682\) −465.000 + 805.404i −0.681818 + 1.18094i
\(683\) 187.061i 0.273882i −0.990579 0.136941i \(-0.956273\pi\)
0.990579 0.136941i \(-0.0437271\pi\)
\(684\) 0 0
\(685\) −434.000 −0.633577
\(686\) 345.000 + 199.186i 0.502915 + 0.290358i
\(687\) 0 0
\(688\) −240.000 138.564i −0.348837 0.201401i
\(689\) −940.000 −1.36430
\(690\) 0 0
\(691\) 491.902i 0.711870i −0.934511 0.355935i \(-0.884162\pi\)
0.934511 0.355935i \(-0.115838\pi\)
\(692\) −254.000 439.941i −0.367052 0.635753i
\(693\) 0 0
\(694\) 375.000 + 216.506i 0.540346 + 0.311969i
\(695\) 1212.44i 1.74451i
\(696\) 0 0
\(697\) 400.000 0.573888
\(698\) −74.0000 + 128.172i −0.106017 + 0.183627i
\(699\) 0 0
\(700\) −720.000 + 415.692i −1.02857 + 0.593846i
\(701\) −215.000 −0.306705 −0.153352 0.988172i \(-0.549007\pi\)
−0.153352 + 0.988172i \(0.549007\pi\)
\(702\) 0 0
\(703\) 103.923i 0.147828i
\(704\) 554.256i 0.787296i
\(705\) 0 0
\(706\) −394.000 + 682.428i −0.558074 + 0.966612i
\(707\) 1342.34i 1.89864i
\(708\) 0 0
\(709\) −532.000 −0.750353 −0.375176 0.926953i \(-0.622418\pi\)
−0.375176 + 0.926953i \(0.622418\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 80.0000 0.112360
\(713\) −186.000 −0.260870
\(714\) 0 0
\(715\) 1212.44i 1.69571i
\(716\) 810.000 467.654i 1.13128 0.653148i
\(717\) 0 0
\(718\) 990.000 + 571.577i 1.37883 + 0.796068i
\(719\) 1143.15i 1.58992i 0.606661 + 0.794961i \(0.292509\pi\)
−0.606661 + 0.794961i \(0.707491\pi\)
\(720\) 0 0
\(721\) 1200.00 1.66436
\(722\) −253.000 + 438.209i −0.350416 + 0.606937i
\(723\) 0 0
\(724\) −112.000 193.990i −0.154696 0.267942i
\(725\) 240.000 0.331034
\(726\) 0 0
\(727\) 1238.42i 1.70346i 0.523980 + 0.851731i \(0.324447\pi\)
−0.523980 + 0.851731i \(0.675553\pi\)
\(728\) 1385.64i 1.90335i
\(729\) 0 0
\(730\) 385.000 666.840i 0.527397 0.913479i
\(731\) 138.564i 0.189554i
\(732\) 0 0
\(733\) 950.000 1.29604 0.648022 0.761622i \(-0.275597\pi\)
0.648022 + 0.761622i \(0.275597\pi\)
\(734\) −975.000 562.917i −1.32834 0.766916i
\(735\) 0 0
\(736\) −96.0000 + 55.4256i −0.130435 + 0.0753066i
\(737\) −750.000 −1.01764
\(738\) 0 0
\(739\) 581.969i 0.787509i −0.919216 0.393754i \(-0.871176\pi\)
0.919216 0.393754i \(-0.128824\pi\)
\(740\) 140.000 + 242.487i 0.189189 + 0.327685i
\(741\) 0 0
\(742\) −705.000 407.032i −0.950135 0.548561i
\(743\) 866.025i 1.16558i −0.812623 0.582790i \(-0.801961\pi\)
0.812623 0.582790i \(-0.198039\pi\)
\(744\) 0 0
\(745\) 805.000 1.08054
\(746\) 40.0000 69.2820i 0.0536193 0.0928714i
\(747\) 0 0
\(748\) −240.000 + 138.564i −0.320856 + 0.185246i
\(749\) −1125.00 −1.50200
\(750\) 0 0
\(751\) 174.937i 0.232939i 0.993194 + 0.116469i \(0.0371577\pi\)
−0.993194 + 0.116469i \(0.962842\pi\)
\(752\) −1200.00 692.820i −1.59574 0.921304i
\(753\) 0 0
\(754\) −200.000 + 346.410i −0.265252 + 0.459430i
\(755\) 303.109i 0.401469i
\(756\) 0 0
\(757\) 830.000 1.09643 0.548217 0.836336i \(-0.315307\pi\)
0.548217 + 0.836336i \(0.315307\pi\)
\(758\) 1188.00 + 685.892i 1.56728 + 0.904871i
\(759\) 0 0
\(760\) 581.969i 0.765749i
\(761\) −560.000 −0.735874 −0.367937 0.929851i \(-0.619936\pi\)
−0.367937 + 0.929851i \(0.619936\pi\)
\(762\) 0 0
\(763\) 1160.47i 1.52094i
\(764\) 120.000 69.2820i 0.157068 0.0906833i
\(765\) 0 0
\(766\) −624.000 360.267i −0.814621 0.470322i
\(767\) 692.820i 0.903286i
\(768\) 0 0
\(769\) −331.000 −0.430429 −0.215215 0.976567i \(-0.569045\pi\)
−0.215215 + 0.976567i \(0.569045\pi\)
\(770\) −525.000 + 909.327i −0.681818 + 1.18094i
\(771\) 0 0
\(772\) −130.000 225.167i −0.168394 0.291667i
\(773\) 298.000 0.385511 0.192755 0.981247i \(-0.438258\pi\)
0.192755 + 0.981247i \(0.438258\pi\)
\(774\) 0 0
\(775\) 1288.65i 1.66277i
\(776\) −200.000 −0.257732
\(777\) 0 0
\(778\) −475.000 + 822.724i −0.610540 + 1.05749i
\(779\) 519.615i 0.667029i
\(780\) 0 0
\(781\) 0 0
\(782\) −48.0000 27.7128i −0.0613811 0.0354384i
\(783\) 0 0
\(784\) 208.000 360.267i 0.265306 0.459524i
\(785\) 140.000 0.178344
\(786\) 0 0
\(787\) 1108.51i 1.40853i −0.709938 0.704265i \(-0.751277\pi\)
0.709938 0.704265i \(-0.248723\pi\)
\(788\) −506.000 876.418i −0.642132 1.11221i
\(789\) 0 0
\(790\) −84.0000 48.4974i −0.106329 0.0613891i
\(791\) 640.859i 0.810188i
\(792\) 0 0
\(793\) −1280.00 −1.61412
\(794\) −260.000 + 450.333i −0.327456 + 0.567170i
\(795\) 0 0
\(796\) −450.000 + 259.808i −0.565327 + 0.326391i
\(797\) 1303.00 1.63488 0.817440 0.576013i \(-0.195392\pi\)
0.817440 + 0.576013i \(0.195392\pi\)
\(798\) 0 0
\(799\) 692.820i 0.867109i
\(800\) −384.000 665.108i −0.480000 0.831384i
\(801\) 0 0
\(802\) 740.000 1281.72i 0.922693 1.59815i
\(803\)