Properties

Label 108.3.f.b.19.1
Level 108
Weight 3
Character 108.19
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.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 108.19
Dual form 108.3.f.b.91.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.00000 + 3.46410i) q^{5} +(3.00000 + 1.73205i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(2.00000 + 3.46410i) q^{5} +(3.00000 + 1.73205i) q^{7} -8.00000 q^{8} +(-4.00000 + 6.92820i) q^{10} +(-10.5000 - 6.06218i) q^{11} +(11.0000 + 19.0526i) q^{13} +6.92820i q^{14} +(-8.00000 - 13.8564i) q^{16} +11.0000 q^{17} -15.5885i q^{19} -16.0000 q^{20} -24.2487i q^{22} +(21.0000 - 12.1244i) q^{23} +(4.50000 - 7.79423i) q^{25} +(-22.0000 + 38.1051i) q^{26} +(-12.0000 + 6.92820i) q^{28} +(17.0000 - 29.4449i) q^{29} +(-6.00000 + 3.46410i) q^{31} +(16.0000 - 27.7128i) q^{32} +(11.0000 + 19.0526i) q^{34} +13.8564i q^{35} -16.0000 q^{37} +(27.0000 - 15.5885i) q^{38} +(-16.0000 - 27.7128i) q^{40} +(6.50000 + 11.2583i) q^{41} +(43.5000 + 25.1147i) q^{43} +(42.0000 - 24.2487i) q^{44} +(42.0000 + 24.2487i) q^{46} +(3.00000 + 1.73205i) q^{47} +(-18.5000 - 32.0429i) q^{49} +18.0000 q^{50} -88.0000 q^{52} -52.0000 q^{53} -48.4974i q^{55} +(-24.0000 - 13.8564i) q^{56} +68.0000 q^{58} +(-46.5000 + 26.8468i) q^{59} +(8.00000 - 13.8564i) q^{61} +(-12.0000 - 6.92820i) q^{62} +64.0000 q^{64} +(-44.0000 + 76.2102i) q^{65} +(-100.500 + 58.0237i) q^{67} +(-22.0000 + 38.1051i) q^{68} +(-24.0000 + 13.8564i) q^{70} -25.0000 q^{73} +(-16.0000 - 27.7128i) q^{74} +(54.0000 + 31.1769i) q^{76} +(-21.0000 - 36.3731i) q^{77} +(-24.0000 - 13.8564i) q^{79} +(32.0000 - 55.4256i) q^{80} +(-13.0000 + 22.5167i) q^{82} +(30.0000 + 17.3205i) q^{83} +(22.0000 + 38.1051i) q^{85} +100.459i q^{86} +(84.0000 + 48.4974i) q^{88} +2.00000 q^{89} +76.2102i q^{91} +96.9948i q^{92} +6.92820i q^{94} +(54.0000 - 31.1769i) q^{95} +(21.5000 - 37.2391i) q^{97} +(37.0000 - 64.0859i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 2q^{2} - 4q^{4} + 4q^{5} + 6q^{7} - 16q^{8} + O(q^{10}) \) \( 2q + 2q^{2} - 4q^{4} + 4q^{5} + 6q^{7} - 16q^{8} - 8q^{10} - 21q^{11} + 22q^{13} - 16q^{16} + 22q^{17} - 32q^{20} + 42q^{23} + 9q^{25} - 44q^{26} - 24q^{28} + 34q^{29} - 12q^{31} + 32q^{32} + 22q^{34} - 32q^{37} + 54q^{38} - 32q^{40} + 13q^{41} + 87q^{43} + 84q^{44} + 84q^{46} + 6q^{47} - 37q^{49} + 36q^{50} - 176q^{52} - 104q^{53} - 48q^{56} + 136q^{58} - 93q^{59} + 16q^{61} - 24q^{62} + 128q^{64} - 88q^{65} - 201q^{67} - 44q^{68} - 48q^{70} - 50q^{73} - 32q^{74} + 108q^{76} - 42q^{77} - 48q^{79} + 64q^{80} - 26q^{82} + 60q^{83} + 44q^{85} + 168q^{88} + 4q^{89} + 108q^{95} + 43q^{97} + 74q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(5\) 2.00000 + 3.46410i 0.400000 + 0.692820i 0.993725 0.111847i \(-0.0356768\pi\)
−0.593725 + 0.804668i \(0.702343\pi\)
\(6\) 0 0
\(7\) 3.00000 + 1.73205i 0.428571 + 0.247436i 0.698738 0.715378i \(-0.253745\pi\)
−0.270166 + 0.962814i \(0.587079\pi\)
\(8\) −8.00000 −1.00000
\(9\) 0 0
\(10\) −4.00000 + 6.92820i −0.400000 + 0.692820i
\(11\) −10.5000 6.06218i −0.954545 0.551107i −0.0600555 0.998195i \(-0.519128\pi\)
−0.894490 + 0.447088i \(0.852461\pi\)
\(12\) 0 0
\(13\) 11.0000 + 19.0526i 0.846154 + 1.46558i 0.884615 + 0.466321i \(0.154421\pi\)
−0.0384615 + 0.999260i \(0.512246\pi\)
\(14\) 6.92820i 0.494872i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.500000 0.866025i
\(17\) 11.0000 0.647059 0.323529 0.946218i \(-0.395131\pi\)
0.323529 + 0.946218i \(0.395131\pi\)
\(18\) 0 0
\(19\) 15.5885i 0.820445i −0.911985 0.410223i \(-0.865451\pi\)
0.911985 0.410223i \(-0.134549\pi\)
\(20\) −16.0000 −0.800000
\(21\) 0 0
\(22\) 24.2487i 1.10221i
\(23\) 21.0000 12.1244i 0.913043 0.527146i 0.0316343 0.999500i \(-0.489929\pi\)
0.881409 + 0.472354i \(0.156595\pi\)
\(24\) 0 0
\(25\) 4.50000 7.79423i 0.180000 0.311769i
\(26\) −22.0000 + 38.1051i −0.846154 + 1.46558i
\(27\) 0 0
\(28\) −12.0000 + 6.92820i −0.428571 + 0.247436i
\(29\) 17.0000 29.4449i 0.586207 1.01534i −0.408517 0.912751i \(-0.633954\pi\)
0.994724 0.102589i \(-0.0327128\pi\)
\(30\) 0 0
\(31\) −6.00000 + 3.46410i −0.193548 + 0.111745i −0.593643 0.804729i \(-0.702311\pi\)
0.400094 + 0.916474i \(0.368977\pi\)
\(32\) 16.0000 27.7128i 0.500000 0.866025i
\(33\) 0 0
\(34\) 11.0000 + 19.0526i 0.323529 + 0.560369i
\(35\) 13.8564i 0.395897i
\(36\) 0 0
\(37\) −16.0000 −0.432432 −0.216216 0.976346i \(-0.569372\pi\)
−0.216216 + 0.976346i \(0.569372\pi\)
\(38\) 27.0000 15.5885i 0.710526 0.410223i
\(39\) 0 0
\(40\) −16.0000 27.7128i −0.400000 0.692820i
\(41\) 6.50000 + 11.2583i 0.158537 + 0.274593i 0.934341 0.356380i \(-0.115989\pi\)
−0.775805 + 0.630973i \(0.782656\pi\)
\(42\) 0 0
\(43\) 43.5000 + 25.1147i 1.01163 + 0.584064i 0.911668 0.410928i \(-0.134795\pi\)
0.0999600 + 0.994991i \(0.468129\pi\)
\(44\) 42.0000 24.2487i 0.954545 0.551107i
\(45\) 0 0
\(46\) 42.0000 + 24.2487i 0.913043 + 0.527146i
\(47\) 3.00000 + 1.73205i 0.0638298 + 0.0368521i 0.531575 0.847011i \(-0.321600\pi\)
−0.467745 + 0.883863i \(0.654934\pi\)
\(48\) 0 0
\(49\) −18.5000 32.0429i −0.377551 0.653938i
\(50\) 18.0000 0.360000
\(51\) 0 0
\(52\) −88.0000 −1.69231
\(53\) −52.0000 −0.981132 −0.490566 0.871404i \(-0.663210\pi\)
−0.490566 + 0.871404i \(0.663210\pi\)
\(54\) 0 0
\(55\) 48.4974i 0.881771i
\(56\) −24.0000 13.8564i −0.428571 0.247436i
\(57\) 0 0
\(58\) 68.0000 1.17241
\(59\) −46.5000 + 26.8468i −0.788136 + 0.455030i −0.839306 0.543660i \(-0.817038\pi\)
0.0511702 + 0.998690i \(0.483705\pi\)
\(60\) 0 0
\(61\) 8.00000 13.8564i 0.131148 0.227154i −0.792972 0.609259i \(-0.791467\pi\)
0.924119 + 0.382104i \(0.124801\pi\)
\(62\) −12.0000 6.92820i −0.193548 0.111745i
\(63\) 0 0
\(64\) 64.0000 1.00000
\(65\) −44.0000 + 76.2102i −0.676923 + 1.17247i
\(66\) 0 0
\(67\) −100.500 + 58.0237i −1.50000 + 0.866025i −0.500000 + 0.866025i \(0.666667\pi\)
−1.00000 \(-1.00000\pi\)
\(68\) −22.0000 + 38.1051i −0.323529 + 0.560369i
\(69\) 0 0
\(70\) −24.0000 + 13.8564i −0.342857 + 0.197949i
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 0 0
\(73\) −25.0000 −0.342466 −0.171233 0.985231i \(-0.554775\pi\)
−0.171233 + 0.985231i \(0.554775\pi\)
\(74\) −16.0000 27.7128i −0.216216 0.374497i
\(75\) 0 0
\(76\) 54.0000 + 31.1769i 0.710526 + 0.410223i
\(77\) −21.0000 36.3731i −0.272727 0.472377i
\(78\) 0 0
\(79\) −24.0000 13.8564i −0.303797 0.175398i 0.340350 0.940299i \(-0.389454\pi\)
−0.644148 + 0.764901i \(0.722788\pi\)
\(80\) 32.0000 55.4256i 0.400000 0.692820i
\(81\) 0 0
\(82\) −13.0000 + 22.5167i −0.158537 + 0.274593i
\(83\) 30.0000 + 17.3205i 0.361446 + 0.208681i 0.669715 0.742618i \(-0.266416\pi\)
−0.308269 + 0.951299i \(0.599750\pi\)
\(84\) 0 0
\(85\) 22.0000 + 38.1051i 0.258824 + 0.448296i
\(86\) 100.459i 1.16813i
\(87\) 0 0
\(88\) 84.0000 + 48.4974i 0.954545 + 0.551107i
\(89\) 2.00000 0.0224719 0.0112360 0.999937i \(-0.496423\pi\)
0.0112360 + 0.999937i \(0.496423\pi\)
\(90\) 0 0
\(91\) 76.2102i 0.837475i
\(92\) 96.9948i 1.05429i
\(93\) 0 0
\(94\) 6.92820i 0.0737043i
\(95\) 54.0000 31.1769i 0.568421 0.328178i
\(96\) 0 0
\(97\) 21.5000 37.2391i 0.221649 0.383908i −0.733659 0.679517i \(-0.762189\pi\)
0.955309 + 0.295609i \(0.0955226\pi\)
\(98\) 37.0000 64.0859i 0.377551 0.653938i
\(99\) 0 0
\(100\) 18.0000 + 31.1769i 0.180000 + 0.311769i
\(101\) −10.0000 + 17.3205i −0.0990099 + 0.171490i −0.911275 0.411798i \(-0.864901\pi\)
0.812265 + 0.583288i \(0.198234\pi\)
\(102\) 0 0
\(103\) 21.0000 12.1244i 0.203883 0.117712i −0.394582 0.918861i \(-0.629111\pi\)
0.598466 + 0.801148i \(0.295777\pi\)
\(104\) −88.0000 152.420i −0.846154 1.46558i
\(105\) 0 0
\(106\) −52.0000 90.0666i −0.490566 0.849685i
\(107\) 15.5885i 0.145687i 0.997343 + 0.0728433i \(0.0232073\pi\)
−0.997343 + 0.0728433i \(0.976793\pi\)
\(108\) 0 0
\(109\) −88.0000 −0.807339 −0.403670 0.914905i \(-0.632266\pi\)
−0.403670 + 0.914905i \(0.632266\pi\)
\(110\) 84.0000 48.4974i 0.763636 0.440886i
\(111\) 0 0
\(112\) 55.4256i 0.494872i
\(113\) −25.0000 43.3013i −0.221239 0.383197i 0.733946 0.679208i \(-0.237677\pi\)
−0.955184 + 0.296011i \(0.904343\pi\)
\(114\) 0 0
\(115\) 84.0000 + 48.4974i 0.730435 + 0.421717i
\(116\) 68.0000 + 117.779i 0.586207 + 1.01534i
\(117\) 0 0
\(118\) −93.0000 53.6936i −0.788136 0.455030i
\(119\) 33.0000 + 19.0526i 0.277311 + 0.160106i
\(120\) 0 0
\(121\) 13.0000 + 22.5167i 0.107438 + 0.186088i
\(122\) 32.0000 0.262295
\(123\) 0 0
\(124\) 27.7128i 0.223490i
\(125\) 136.000 1.08800
\(126\) 0 0
\(127\) 218.238i 1.71841i −0.511629 0.859206i \(-0.670958\pi\)
0.511629 0.859206i \(-0.329042\pi\)
\(128\) 64.0000 + 110.851i 0.500000 + 0.866025i
\(129\) 0 0
\(130\) −176.000 −1.35385
\(131\) −168.000 + 96.9948i −1.28244 + 0.740419i −0.977294 0.211886i \(-0.932039\pi\)
−0.305148 + 0.952305i \(0.598706\pi\)
\(132\) 0 0
\(133\) 27.0000 46.7654i 0.203008 0.351619i
\(134\) −201.000 116.047i −1.50000 0.866025i
\(135\) 0 0
\(136\) −88.0000 −0.647059
\(137\) 84.5000 146.358i 0.616788 1.06831i −0.373280 0.927719i \(-0.621767\pi\)
0.990068 0.140590i \(-0.0448999\pi\)
\(138\) 0 0
\(139\) 169.500 97.8609i 1.21942 0.704035i 0.254630 0.967039i \(-0.418046\pi\)
0.964795 + 0.263004i \(0.0847131\pi\)
\(140\) −48.0000 27.7128i −0.342857 0.197949i
\(141\) 0 0
\(142\) 0 0
\(143\) 266.736i 1.86529i
\(144\) 0 0
\(145\) 136.000 0.937931
\(146\) −25.0000 43.3013i −0.171233 0.296584i
\(147\) 0 0
\(148\) 32.0000 55.4256i 0.216216 0.374497i
\(149\) 65.0000 + 112.583i 0.436242 + 0.755593i 0.997396 0.0721185i \(-0.0229760\pi\)
−0.561154 + 0.827711i \(0.689643\pi\)
\(150\) 0 0
\(151\) −105.000 60.6218i −0.695364 0.401469i 0.110254 0.993903i \(-0.464833\pi\)
−0.805618 + 0.592435i \(0.798167\pi\)
\(152\) 124.708i 0.820445i
\(153\) 0 0
\(154\) 42.0000 72.7461i 0.272727 0.472377i
\(155\) −24.0000 13.8564i −0.154839 0.0893962i
\(156\) 0 0
\(157\) 2.00000 + 3.46410i 0.0127389 + 0.0220643i 0.872325 0.488927i \(-0.162612\pi\)
−0.859586 + 0.510992i \(0.829278\pi\)
\(158\) 55.4256i 0.350795i
\(159\) 0 0
\(160\) 128.000 0.800000
\(161\) 84.0000 0.521739
\(162\) 0 0
\(163\) 311.769i 1.91269i 0.292233 + 0.956347i \(0.405602\pi\)
−0.292233 + 0.956347i \(0.594398\pi\)
\(164\) −52.0000 −0.317073
\(165\) 0 0
\(166\) 69.2820i 0.417362i
\(167\) 156.000 90.0666i 0.934132 0.539321i 0.0460158 0.998941i \(-0.485348\pi\)
0.888116 + 0.459620i \(0.152014\pi\)
\(168\) 0 0
\(169\) −157.500 + 272.798i −0.931953 + 1.61419i
\(170\) −44.0000 + 76.2102i −0.258824 + 0.448296i
\(171\) 0 0
\(172\) −174.000 + 100.459i −1.01163 + 0.584064i
\(173\) −1.00000 + 1.73205i −0.00578035 + 0.0100119i −0.868901 0.494986i \(-0.835173\pi\)
0.863121 + 0.504998i \(0.168507\pi\)
\(174\) 0 0
\(175\) 27.0000 15.5885i 0.154286 0.0890769i
\(176\) 193.990i 1.10221i
\(177\) 0 0
\(178\) 2.00000 + 3.46410i 0.0112360 + 0.0194612i
\(179\) 187.061i 1.04504i 0.852628 + 0.522518i \(0.175007\pi\)
−0.852628 + 0.522518i \(0.824993\pi\)
\(180\) 0 0
\(181\) 254.000 1.40331 0.701657 0.712514i \(-0.252444\pi\)
0.701657 + 0.712514i \(0.252444\pi\)
\(182\) −132.000 + 76.2102i −0.725275 + 0.418738i
\(183\) 0 0
\(184\) −168.000 + 96.9948i −0.913043 + 0.527146i
\(185\) −32.0000 55.4256i −0.172973 0.299598i
\(186\) 0 0
\(187\) −115.500 66.6840i −0.617647 0.356599i
\(188\) −12.0000 + 6.92820i −0.0638298 + 0.0368521i
\(189\) 0 0
\(190\) 108.000 + 62.3538i 0.568421 + 0.328178i
\(191\) 3.00000 + 1.73205i 0.0157068 + 0.00906833i 0.507833 0.861456i \(-0.330447\pi\)
−0.492126 + 0.870524i \(0.663780\pi\)
\(192\) 0 0
\(193\) 33.5000 + 58.0237i 0.173575 + 0.300641i 0.939667 0.342090i \(-0.111135\pi\)
−0.766092 + 0.642731i \(0.777801\pi\)
\(194\) 86.0000 0.443299
\(195\) 0 0
\(196\) 148.000 0.755102
\(197\) −268.000 −1.36041 −0.680203 0.733024i \(-0.738108\pi\)
−0.680203 + 0.733024i \(0.738108\pi\)
\(198\) 0 0
\(199\) 31.1769i 0.156668i 0.996927 + 0.0783340i \(0.0249600\pi\)
−0.996927 + 0.0783340i \(0.975040\pi\)
\(200\) −36.0000 + 62.3538i −0.180000 + 0.311769i
\(201\) 0 0
\(202\) −40.0000 −0.198020
\(203\) 102.000 58.8897i 0.502463 0.290097i
\(204\) 0 0
\(205\) −26.0000 + 45.0333i −0.126829 + 0.219675i
\(206\) 42.0000 + 24.2487i 0.203883 + 0.117712i
\(207\) 0 0
\(208\) 176.000 304.841i 0.846154 1.46558i
\(209\) −94.5000 + 163.679i −0.452153 + 0.783152i
\(210\) 0 0
\(211\) −114.000 + 65.8179i −0.540284 + 0.311933i −0.745194 0.666848i \(-0.767643\pi\)
0.204910 + 0.978781i \(0.434310\pi\)
\(212\) 104.000 180.133i 0.490566 0.849685i
\(213\) 0 0
\(214\) −27.0000 + 15.5885i −0.126168 + 0.0728433i
\(215\) 200.918i 0.934502i
\(216\) 0 0
\(217\) −24.0000 −0.110599
\(218\) −88.0000 152.420i −0.403670 0.699176i
\(219\) 0 0
\(220\) 168.000 + 96.9948i 0.763636 + 0.440886i
\(221\) 121.000 + 209.578i 0.547511 + 0.948317i
\(222\) 0 0
\(223\) −51.0000 29.4449i −0.228700 0.132040i 0.381272 0.924463i \(-0.375486\pi\)
−0.609972 + 0.792423i \(0.708819\pi\)
\(224\) 96.0000 55.4256i 0.428571 0.247436i
\(225\) 0 0
\(226\) 50.0000 86.6025i 0.221239 0.383197i
\(227\) −388.500 224.301i −1.71145 0.988108i −0.932607 0.360894i \(-0.882471\pi\)
−0.778847 0.627214i \(1.21580\pi\)
\(228\) 0 0
\(229\) −205.000 355.070i −0.895197 1.55053i −0.833561 0.552427i \(-0.813702\pi\)
−0.0616353 0.998099i \(-0.519632\pi\)
\(230\) 193.990i 0.843433i
\(231\) 0 0
\(232\) −136.000 + 235.559i −0.586207 + 1.01534i
\(233\) 65.0000 0.278970 0.139485 0.990224i \(-0.455455\pi\)
0.139485 + 0.990224i \(0.455455\pi\)
\(234\) 0 0
\(235\) 13.8564i 0.0589634i
\(236\) 214.774i 0.910061i
\(237\) 0 0
\(238\) 76.2102i 0.320211i
\(239\) −33.0000 + 19.0526i −0.138075 + 0.0797178i −0.567446 0.823410i \(-0.692069\pi\)
0.429371 + 0.903128i \(0.358735\pi\)
\(240\) 0 0
\(241\) 111.500 193.124i 0.462656 0.801343i −0.536437 0.843941i \(-0.680230\pi\)
0.999092 + 0.0425975i \(0.0135633\pi\)
\(242\) −26.0000 + 45.0333i −0.107438 + 0.186088i
\(243\) 0 0
\(244\) 32.0000 + 55.4256i 0.131148 + 0.227154i
\(245\) 74.0000 128.172i 0.302041 0.523150i
\(246\) 0 0
\(247\) 297.000 171.473i 1.20243 0.694223i
\(248\) 48.0000 27.7128i 0.193548 0.111745i
\(249\) 0 0
\(250\) 136.000 + 235.559i 0.544000 + 0.942236i
\(251\) 109.119i 0.434738i 0.976090 + 0.217369i \(0.0697475\pi\)
−0.976090 + 0.217369i \(0.930253\pi\)
\(252\) 0 0
\(253\) −294.000 −1.16206
\(254\) 378.000 218.238i 1.48819 0.859206i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.500000 + 0.866025i
\(257\) −218.500 378.453i −0.850195 1.47258i −0.881032 0.473056i \(-0.843151\pi\)
0.0308379 0.999524i \(-0.490182\pi\)
\(258\) 0 0
\(259\) −48.0000 27.7128i −0.185328 0.106999i
\(260\) −176.000 304.841i −0.676923 1.17247i
\(261\) 0 0
\(262\) −336.000 193.990i −1.28244 0.740419i
\(263\) 273.000 + 157.617i 1.03802 + 0.599303i 0.919273 0.393621i \(-0.128778\pi\)
0.118750 + 0.992924i \(0.462111\pi\)
\(264\) 0 0
\(265\) −104.000 180.133i −0.392453 0.679748i
\(266\) 108.000 0.406015
\(267\) 0 0
\(268\) 464.190i 1.73205i
\(269\) −304.000 −1.13011 −0.565056 0.825053i \(-0.691145\pi\)
−0.565056 + 0.825053i \(0.691145\pi\)
\(270\) 0 0
\(271\) 311.769i 1.15044i 0.817999 + 0.575220i \(0.195083\pi\)
−0.817999 + 0.575220i \(0.804917\pi\)
\(272\) −88.0000 152.420i −0.323529 0.560369i
\(273\) 0 0
\(274\) 338.000 1.23358
\(275\) −94.5000 + 54.5596i −0.343636 + 0.198399i
\(276\) 0 0
\(277\) 17.0000 29.4449i 0.0613718 0.106299i −0.833707 0.552207i \(-0.813786\pi\)
0.895079 + 0.445908i \(0.147119\pi\)
\(278\) 339.000 + 195.722i 1.21942 + 0.704035i
\(279\) 0 0
\(280\) 110.851i 0.395897i
\(281\) −109.000 + 188.794i −0.387900 + 0.671863i −0.992167 0.124919i \(-0.960133\pi\)
0.604267 + 0.796782i \(0.293466\pi\)
\(282\) 0 0
\(283\) −6.00000 + 3.46410i −0.0212014 + 0.0122406i −0.510563 0.859840i \(-0.670563\pi\)
0.489362 + 0.872081i \(0.337230\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 462.000 266.736i 1.61538 0.932643i
\(287\) 45.0333i 0.156911i
\(288\) 0 0
\(289\) −168.000 −0.581315
\(290\) 136.000 + 235.559i 0.468966 + 0.812272i
\(291\) 0 0
\(292\) 50.0000 86.6025i 0.171233 0.296584i
\(293\) 101.000 + 174.937i 0.344710 + 0.597055i 0.985301 0.170827i \(-0.0546440\pi\)
−0.640591 + 0.767882i \(0.721311\pi\)
\(294\) 0 0
\(295\) −186.000 107.387i −0.630508 0.364024i
\(296\) 128.000 0.432432
\(297\) 0 0
\(298\) −130.000 + 225.167i −0.436242 + 0.755593i
\(299\) 462.000 + 266.736i 1.54515 + 0.892093i
\(300\) 0 0
\(301\) 87.0000 + 150.688i 0.289037 + 0.500626i
\(302\) 242.487i 0.802937i
\(303\) 0 0
\(304\) −216.000 + 124.708i −0.710526 + 0.410223i
\(305\) 64.0000 0.209836
\(306\) 0 0
\(307\) 109.119i 0.355437i −0.984081 0.177719i \(-0.943128\pi\)
0.984081 0.177719i \(-0.0568717\pi\)
\(308\) 168.000 0.545455
\(309\) 0 0
\(310\) 55.4256i 0.178792i
\(311\) 237.000 136.832i 0.762058 0.439974i −0.0679762 0.997687i \(-0.521654\pi\)
0.830034 + 0.557713i \(0.188321\pi\)
\(312\) 0 0
\(313\) 39.5000 68.4160i 0.126198 0.218581i −0.796003 0.605293i \(-0.793056\pi\)
0.922201 + 0.386712i \(0.126389\pi\)
\(314\) −4.00000 + 6.92820i −0.0127389 + 0.0220643i
\(315\) 0 0
\(316\) 96.0000 55.4256i 0.303797 0.175398i
\(317\) 251.000 434.745i 0.791798 1.37143i −0.133054 0.991109i \(-0.542479\pi\)
0.924853 0.380326i \(-0.124188\pi\)
\(318\) 0 0
\(319\) −357.000 + 206.114i −1.11912 + 0.646126i
\(320\) 128.000 + 221.703i 0.400000 + 0.692820i
\(321\) 0 0
\(322\) 84.0000 + 145.492i 0.260870 + 0.451839i
\(323\) 171.473i 0.530876i
\(324\) 0 0
\(325\) 198.000 0.609231
\(326\) −540.000 + 311.769i −1.65644 + 0.956347i
\(327\) 0 0
\(328\) −52.0000 90.0666i −0.158537 0.274593i
\(329\) 6.00000 + 10.3923i 0.0182371 + 0.0315876i
\(330\) 0 0
\(331\) 354.000 + 204.382i 1.06949 + 0.617468i 0.928041 0.372478i \(-0.121492\pi\)
0.141445 + 0.989946i \(0.454825\pi\)
\(332\) −120.000 + 69.2820i −0.361446 + 0.208681i
\(333\) 0 0
\(334\) 312.000 + 180.133i 0.934132 + 0.539321i
\(335\) −402.000 232.095i −1.20000 0.692820i
\(336\) 0 0
\(337\) 168.500 + 291.851i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(338\) −630.000 −1.86391
\(339\) 0 0
\(340\) −176.000 −0.517647
\(341\) 84.0000 0.246334
\(342\) 0 0
\(343\) 297.913i 0.868550i
\(344\) −348.000 200.918i −1.01163 0.584064i
\(345\) 0 0
\(346\) −4.00000 −0.0115607
\(347\) −235.500 + 135.966i −0.678674 + 0.391833i −0.799355 0.600859i \(-0.794826\pi\)
0.120681 + 0.992691i \(0.461492\pi\)
\(348\) 0 0
\(349\) −136.000 + 235.559i −0.389685 + 0.674954i −0.992407 0.122997i \(-0.960749\pi\)
0.602722 + 0.797951i \(0.294083\pi\)
\(350\) 54.0000 + 31.1769i 0.154286 + 0.0890769i
\(351\) 0 0
\(352\) −336.000 + 193.990i −0.954545 + 0.551107i
\(353\) −230.500 + 399.238i −0.652975 + 1.13099i 0.329423 + 0.944182i \(0.393146\pi\)
−0.982397 + 0.186803i \(0.940188\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −4.00000 + 6.92820i −0.0112360 + 0.0194612i
\(357\) 0 0
\(358\) −324.000 + 187.061i −0.905028 + 0.522518i
\(359\) 530.008i 1.47634i −0.674612 0.738172i \(-0.735689\pi\)
0.674612 0.738172i \(-0.264311\pi\)
\(360\) 0 0
\(361\) 118.000 0.326870
\(362\) 254.000 + 439.941i 0.701657 + 1.21531i
\(363\) 0 0
\(364\) −264.000 152.420i −0.725275 0.418738i
\(365\) −50.0000 86.6025i −0.136986 0.237267i
\(366\) 0 0
\(367\) 84.0000 + 48.4974i 0.228883 + 0.132146i 0.610057 0.792358i \(-0.291147\pi\)
−0.381174 + 0.924503i \(0.624480\pi\)
\(368\) −336.000 193.990i −0.913043 0.527146i
\(369\) 0 0
\(370\) 64.0000 110.851i 0.172973 0.299598i
\(371\) −156.000 90.0666i −0.420485 0.242767i
\(372\) 0 0
\(373\) 173.000 + 299.645i 0.463807 + 0.803337i 0.999147 0.0412995i \(-0.0131498\pi\)
−0.535340 + 0.844637i \(0.679816\pi\)
\(374\) 266.736i 0.713197i
\(375\) 0 0
\(376\) −24.0000 13.8564i −0.0638298 0.0368521i
\(377\) 748.000 1.98408
\(378\) 0 0
\(379\) 327.358i 0.863740i −0.901936 0.431870i \(-0.857854\pi\)
0.901936 0.431870i \(-0.142146\pi\)
\(380\) 249.415i 0.656356i
\(381\) 0 0
\(382\) 6.92820i 0.0181367i
\(383\) −546.000 + 315.233i −1.42559 + 0.823063i −0.996769 0.0803272i \(-0.974403\pi\)
−0.428819 + 0.903390i \(0.641070\pi\)
\(384\) 0 0
\(385\) 84.0000 145.492i 0.218182 0.377902i
\(386\) −67.0000 + 116.047i −0.173575 + 0.300641i
\(387\) 0 0
\(388\) 86.0000 + 148.956i 0.221649 + 0.383908i
\(389\) −73.0000 + 126.440i −0.187661 + 0.325038i −0.944470 0.328598i \(-0.893424\pi\)
0.756809 + 0.653636i \(0.226757\pi\)
\(390\) 0 0
\(391\) 231.000 133.368i 0.590793 0.341094i
\(392\) 148.000 + 256.344i 0.377551 + 0.653938i
\(393\) 0 0
\(394\) −268.000 464.190i −0.680203 1.17815i
\(395\) 110.851i 0.280636i
\(396\) 0 0
\(397\) 488.000 1.22922 0.614610 0.788831i \(-0.289314\pi\)
0.614610 + 0.788831i \(0.289314\pi\)
\(398\) −54.0000 + 31.1769i −0.135678 + 0.0783340i
\(399\) 0 0
\(400\) −144.000 −0.360000
\(401\) 222.500 + 385.381i 0.554863 + 0.961051i 0.997914 + 0.0645544i \(0.0205626\pi\)
−0.443051 + 0.896496i \(0.646104\pi\)
\(402\) 0 0
\(403\) −132.000 76.2102i −0.327543 0.189107i
\(404\) −40.0000 69.2820i −0.0990099 0.171490i
\(405\) 0 0
\(406\) 204.000 + 117.779i 0.502463 + 0.290097i
\(407\) 168.000 + 96.9948i 0.412776 + 0.238317i
\(408\) 0 0
\(409\) 33.5000 + 58.0237i 0.0819071 + 0.141867i 0.904069 0.427386i \(-0.140566\pi\)
−0.822162 + 0.569254i \(0.807232\pi\)
\(410\) −104.000 −0.253659
\(411\) 0 0
\(412\) 96.9948i 0.235424i
\(413\) −186.000 −0.450363
\(414\) 0 0
\(415\) 138.564i 0.333889i
\(416\) 704.000 1.69231
\(417\) 0 0
\(418\) −378.000 −0.904306
\(419\) 534.000 308.305i 1.27446 0.735812i 0.298638 0.954366i \(-0.403468\pi\)
0.975825 + 0.218555i \(0.0701342\pi\)
\(420\) 0 0
\(421\) −136.000 + 235.559i −0.323040 + 0.559522i −0.981114 0.193431i \(-0.938038\pi\)
0.658073 + 0.752954i \(0.271372\pi\)
\(422\) −228.000 131.636i −0.540284 0.311933i
\(423\) 0 0
\(424\) 416.000 0.981132
\(425\) 49.5000 85.7365i 0.116471 0.201733i
\(426\) 0 0
\(427\) 48.0000 27.7128i 0.112412 0.0649012i
\(428\) −54.0000 31.1769i −0.126168 0.0728433i
\(429\) 0 0
\(430\) −348.000 + 200.918i −0.809302 + 0.467251i
\(431\) 405.300i 0.940371i 0.882568 + 0.470185i \(0.155813\pi\)
−0.882568 + 0.470185i \(0.844187\pi\)
\(432\) 0 0
\(433\) −439.000 −1.01386 −0.506928 0.861988i \(-0.669219\pi\)
−0.506928 + 0.861988i \(0.669219\pi\)
\(434\) −24.0000 41.5692i −0.0552995 0.0957816i
\(435\) 0 0
\(436\) 176.000 304.841i 0.403670 0.699176i
\(437\) −189.000 327.358i −0.432494 0.749102i
\(438\) 0 0
\(439\) 732.000 + 422.620i 1.66743 + 0.962689i 0.969018 + 0.246989i \(0.0794410\pi\)
0.698408 + 0.715700i \(0.253892\pi\)
\(440\) 387.979i 0.881771i
\(441\) 0 0
\(442\) −242.000 + 419.156i −0.547511 + 0.948317i
\(443\) 286.500 + 165.411i 0.646727 + 0.373388i 0.787201 0.616696i \(-0.211529\pi\)
−0.140474 + 0.990084i \(0.544863\pi\)
\(444\) 0 0
\(445\) 4.00000 + 6.92820i 0.00898876 + 0.0155690i
\(446\) 117.779i 0.264079i
\(447\) 0 0
\(448\) 192.000 + 110.851i 0.428571 + 0.247436i
\(449\) 47.0000 0.104677 0.0523385 0.998629i \(-0.483333\pi\)
0.0523385 + 0.998629i \(0.483333\pi\)
\(450\) 0 0
\(451\) 157.617i 0.349483i
\(452\) 200.000 0.442478
\(453\) 0 0
\(454\) 897.202i 1.97622i
\(455\) −264.000 + 152.420i −0.580220 + 0.334990i
\(456\) 0 0
\(457\) 165.500 286.654i 0.362144 0.627253i −0.626169 0.779687i \(-0.715378\pi\)
0.988314 + 0.152435i \(0.0487114\pi\)
\(458\) 410.000 710.141i 0.895197 1.55053i
\(459\) 0 0
\(460\) −336.000 + 193.990i −0.730435 + 0.421717i
\(461\) 269.000 465.922i 0.583514 1.01068i −0.411545 0.911390i \(-0.635011\pi\)
0.995059 0.0992865i \(-0.0316560\pi\)
\(462\) 0 0
\(463\) −492.000 + 284.056i −1.06263 + 0.613513i −0.926160 0.377131i \(-0.876911\pi\)
−0.136475 + 0.990644i \(0.543577\pi\)
\(464\) −544.000 −1.17241
\(465\) 0 0
\(466\) 65.0000 + 112.583i 0.139485 + 0.241595i
\(467\) 639.127i 1.36858i −0.729210 0.684290i \(-0.760112\pi\)
0.729210 0.684290i \(-0.239888\pi\)
\(468\) 0 0
\(469\) −402.000 −0.857143
\(470\) −24.0000 + 13.8564i −0.0510638 + 0.0294817i
\(471\) 0 0
\(472\) 372.000 214.774i 0.788136 0.455030i
\(473\) −304.500 527.409i −0.643763 1.11503i
\(474\) 0 0
\(475\) −121.500 70.1481i −0.255789 0.147680i
\(476\) −132.000 + 76.2102i −0.277311 + 0.160106i
\(477\) 0 0
\(478\) −66.0000 38.1051i −0.138075 0.0797178i
\(479\) −105.000 60.6218i −0.219207 0.126559i 0.386376 0.922341i \(-0.373727\pi\)
−0.605583 + 0.795782i \(0.707060\pi\)
\(480\) 0 0
\(481\) −176.000 304.841i −0.365904 0.633765i
\(482\) 446.000 0.925311
\(483\) 0 0
\(484\) −104.000 −0.214876
\(485\) 172.000 0.354639
\(486\) 0 0
\(487\) 405.300i 0.832238i −0.909310 0.416119i \(-0.863390\pi\)
0.909310 0.416119i \(-0.136610\pi\)
\(488\) −64.0000 + 110.851i −0.131148 + 0.227154i
\(489\) 0 0
\(490\) 296.000 0.604082
\(491\) 628.500 362.865i 1.28004 0.739032i 0.303185 0.952932i \(-0.401950\pi\)
0.976856 + 0.213900i \(0.0686166\pi\)
\(492\) 0 0
\(493\) 187.000 323.894i 0.379310 0.656985i
\(494\) 594.000 + 342.946i 1.20243 + 0.694223i
\(495\) 0 0
\(496\) 96.0000 + 55.4256i 0.193548 + 0.111745i
\(497\) 0 0
\(498\) 0 0
\(499\) −451.500 + 260.674i −0.904810 + 0.522392i −0.878758 0.477269i \(-0.841627\pi\)
−0.0260521 + 0.999661i \(0.508294\pi\)
\(500\) −272.000 + 471.118i −0.544000 + 0.942236i
\(501\) 0 0
\(502\) −189.000 + 109.119i −0.376494 + 0.217369i
\(503\) 872.954i 1.73549i 0.497006 + 0.867747i \(0.334433\pi\)
−0.497006 + 0.867747i \(0.665567\pi\)
\(504\) 0 0
\(505\) −80.0000 −0.158416
\(506\) −294.000 509.223i −0.581028 1.00637i
\(507\) 0 0
\(508\) 756.000 + 436.477i 1.48819 + 0.859206i
\(509\) 380.000 + 658.179i 0.746562 + 1.29308i 0.949461 + 0.313884i \(0.101630\pi\)
−0.202900 + 0.979200i \(0.565037\pi\)
\(510\) 0 0
\(511\) −75.0000 43.3013i −0.146771 0.0847383i
\(512\) −512.000 −1.00000
\(513\) 0 0
\(514\) 437.000 756.906i 0.850195 1.47258i
\(515\) 84.0000 + 48.4974i 0.163107 + 0.0941698i
\(516\) 0 0
\(517\) −21.0000 36.3731i −0.0406190 0.0703541i
\(518\) 110.851i 0.213999i
\(519\) 0 0
\(520\) 352.000 609.682i 0.676923 1.17247i
\(521\) −745.000 −1.42994 −0.714971 0.699154i \(-0.753560\pi\)
−0.714971 + 0.699154i \(0.753560\pi\)
\(522\) 0 0
\(523\) 561.184i 1.07301i −0.843897 0.536505i \(-0.819744\pi\)
0.843897 0.536505i \(-0.180256\pi\)
\(524\) 775.959i 1.48084i
\(525\) 0 0
\(526\) 630.466i 1.19861i
\(527\) −66.0000 + 38.1051i −0.125237 + 0.0723057i
\(528\) 0 0
\(529\) 29.5000 51.0955i 0.0557656 0.0965888i
\(530\) 208.000 360.267i 0.392453 0.679748i
\(531\) 0 0
\(532\) 108.000 + 187.061i 0.203008 + 0.351619i
\(533\) −143.000 + 247.683i −0.268293 + 0.464697i
\(534\) 0 0
\(535\) −54.0000 + 31.1769i −0.100935 + 0.0582746i
\(536\) 804.000 464.190i 1.50000 0.866025i
\(537\) 0 0
\(538\) −304.000 526.543i −0.565056 0.978705i
\(539\) 448.601i 0.832284i
\(540\) 0 0
\(541\) −520.000 −0.961183 −0.480591 0.876945i \(-0.659578\pi\)
−0.480591 + 0.876945i \(0.659578\pi\)
\(542\) −540.000 + 311.769i −0.996310 + 0.575220i
\(543\) 0 0
\(544\) 176.000 304.841i 0.323529 0.560369i
\(545\) −176.000 304.841i −0.322936 0.559341i
\(546\) 0 0
\(547\) −334.500 193.124i −0.611517 0.353060i 0.162042 0.986784i \(-0.448192\pi\)
−0.773559 + 0.633724i \(0.781525\pi\)
\(548\) 338.000 + 585.433i 0.616788 + 1.06831i
\(549\) 0 0
\(550\) −189.000 109.119i −0.343636 0.198399i
\(551\) −459.000 265.004i −0.833031 0.480951i
\(552\) 0 0
\(553\) −48.0000 83.1384i −0.0867993 0.150341i
\(554\) 68.0000 0.122744
\(555\) 0 0
\(556\) 782.887i 1.40807i
\(557\) −934.000 −1.67684 −0.838420 0.545025i \(-0.816520\pi\)
−0.838420 + 0.545025i \(0.816520\pi\)
\(558\) 0 0
\(559\) 1105.05i 1.97683i
\(560\) 192.000 110.851i 0.342857 0.197949i
\(561\) 0 0
\(562\) −436.000 −0.775801
\(563\) −613.500 + 354.204i −1.08970 + 0.629137i −0.933496 0.358588i \(-0.883258\pi\)
−0.156202 + 0.987725i \(0.549925\pi\)
\(564\) 0 0
\(565\) 100.000 173.205i 0.176991 0.306558i
\(566\) −12.0000 6.92820i −0.0212014 0.0122406i
\(567\) 0 0
\(568\) 0 0
\(569\) −347.500 + 601.888i −0.610721 + 1.05780i 0.380399 + 0.924823i \(0.375787\pi\)
−0.991119 + 0.132976i \(0.957547\pi\)
\(570\) 0 0
\(571\) 466.500 269.334i 0.816988 0.471688i −0.0323889 0.999475i \(-0.510311\pi\)
0.849377 + 0.527787i \(0.176978\pi\)
\(572\) 924.000 + 533.472i 1.61538 + 0.932643i
\(573\) 0 0
\(574\) −78.0000 + 45.0333i −0.135889 + 0.0784553i
\(575\) 218.238i 0.379545i
\(576\) 0 0
\(577\) 227.000 0.393414 0.196707 0.980462i \(-0.436975\pi\)
0.196707 + 0.980462i \(0.436975\pi\)
\(578\) −168.000 290.985i −0.290657 0.503433i
\(579\) 0 0
\(580\) −272.000 + 471.118i −0.468966 + 0.812272i
\(581\) 60.0000 + 103.923i 0.103270 + 0.178869i
\(582\) 0 0
\(583\) 546.000 + 315.233i 0.936535 + 0.540709i
\(584\) 200.000 0.342466
\(585\) 0 0
\(586\) −202.000 + 349.874i −0.344710 + 0.597055i
\(587\) 124.500 + 71.8801i 0.212095 + 0.122453i 0.602285 0.798281i \(-0.294257\pi\)
−0.390189 + 0.920735i \(0.627590\pi\)
\(588\) 0 0
\(589\) 54.0000 + 93.5307i 0.0916808 + 0.158796i
\(590\) 429.549i 0.728048i
\(591\) 0 0
\(592\) 128.000 + 221.703i 0.216216 + 0.374497i
\(593\) 506.000 0.853288 0.426644 0.904420i \(-0.359696\pi\)
0.426644 + 0.904420i \(0.359696\pi\)
\(594\) 0 0
\(595\) 152.420i 0.256169i
\(596\) −520.000 −0.872483
\(597\) 0 0
\(598\) 1066.94i 1.78419i
\(599\) 48.0000 27.7128i 0.0801336 0.0462651i −0.459398 0.888231i \(-0.651935\pi\)
0.539531 + 0.841965i \(0.318601\pi\)
\(600\) 0 0
\(601\) −167.500 + 290.119i −0.278702 + 0.482726i −0.971062 0.238826i \(-0.923238\pi\)
0.692360 + 0.721552i \(0.256571\pi\)
\(602\) −174.000 + 301.377i −0.289037 + 0.500626i
\(603\) 0 0
\(604\) 420.000 242.487i 0.695364 0.401469i
\(605\) −52.0000 + 90.0666i −0.0859504 + 0.148870i
\(606\) 0 0
\(607\) −546.000 + 315.233i −0.899506 + 0.519330i −0.877040 0.480418i \(-0.840485\pi\)
−0.0224660 + 0.999748i \(0.507152\pi\)
\(608\) −432.000 249.415i −0.710526 0.410223i
\(609\) 0 0
\(610\) 64.0000 + 110.851i 0.104918 + 0.181723i
\(611\) 76.2102i 0.124730i
\(612\) 0 0
\(613\) −340.000 −0.554649 −0.277325 0.960776i \(-0.589448\pi\)
−0.277325 + 0.960776i \(0.589448\pi\)
\(614\) 189.000 109.119i 0.307818 0.177719i
\(615\) 0 0
\(616\) 168.000 + 290.985i 0.272727 + 0.472377i
\(617\) 195.500 + 338.616i 0.316856 + 0.548810i 0.979830 0.199832i \(-0.0640396\pi\)
−0.662974 + 0.748642i \(0.730706\pi\)
\(618\) 0 0
\(619\) −10.5000 6.06218i −0.0169628 0.00979350i 0.491495 0.870881i \(-0.336451\pi\)
−0.508457 + 0.861087i \(0.669784\pi\)
\(620\) 96.0000 55.4256i 0.154839 0.0893962i
\(621\) 0 0
\(622\) 474.000 + 273.664i 0.762058 + 0.439974i
\(623\) 6.00000 + 3.46410i 0.00963082 + 0.00556036i
\(624\) 0 0
\(625\) 159.500 + 276.262i 0.255200 + 0.442019i
\(626\) 158.000 0.252396
\(627\) 0 0
\(628\) −16.0000 −0.0254777
\(629\) −176.000 −0.279809
\(630\) 0 0
\(631\) 436.477i 0.691722i 0.938286 + 0.345861i \(0.112413\pi\)
−0.938286 + 0.345861i \(0.887587\pi\)
\(632\) 192.000 + 110.851i 0.303797 + 0.175398i
\(633\) 0 0
\(634\) 1004.00 1.58360
\(635\) 756.000 436.477i 1.19055 0.687365i
\(636\) 0 0
\(637\) 407.000 704.945i 0.638932 1.10666i
\(638\) −714.000 412.228i −1.11912 0.646126i
\(639\) 0 0
\(640\) −256.000 + 443.405i −0.400000 + 0.692820i
\(641\) 210.500 364.597i 0.328393 0.568794i −0.653800 0.756667i \(-0.726826\pi\)
0.982193 + 0.187874i \(0.0601596\pi\)
\(642\) 0 0
\(643\) 358.500 206.980i 0.557543 0.321897i −0.194616 0.980880i \(-0.562346\pi\)
0.752159 + 0.658982i \(0.229013\pi\)
\(644\) −168.000 + 290.985i −0.260870 + 0.451839i
\(645\) 0 0
\(646\) 297.000 171.473i 0.459752 0.265438i
\(647\) 405.300i 0.626430i 0.949682 + 0.313215i \(0.101406\pi\)
−0.949682 + 0.313215i \(0.898594\pi\)
\(648\) 0 0
\(649\) 651.000 1.00308
\(650\) 198.000 + 342.946i 0.304615 + 0.527609i
\(651\) 0 0
\(652\) −1080.00 623.538i −1.65644 0.956347i
\(653\) 443.000 + 767.299i 0.678407 + 1.17504i 0.975460 + 0.220175i \(0.0706628\pi\)
−0.297053 + 0.954861i \(0.596004\pi\)
\(654\) 0 0
\(655\) −672.000 387.979i −1.02595 0.592335i
\(656\) 104.000 180.133i 0.158537 0.274593i
\(657\) 0 0
\(658\) −12.0000 + 20.7846i −0.0182371 + 0.0315876i
\(659\) −726.000 419.156i −1.10167 0.636049i −0.165010 0.986292i \(-0.552766\pi\)
−0.936659 + 0.350243i \(0.886099\pi\)
\(660\) 0 0
\(661\) −124.000 214.774i −0.187595 0.324923i 0.756853 0.653585i \(-0.226736\pi\)
−0.944448 + 0.328662i \(0.893402\pi\)
\(662\) 817.528i 1.23494i
\(663\) 0 0
\(664\) −240.000 138.564i −0.361446 0.208681i
\(665\) 216.000 0.324812
\(666\) 0 0
\(667\) 824.456i 1.23607i
\(668\) 720.533i 1.07864i
\(669\) 0 0
\(670\) 928.379i 1.38564i
\(671\) −168.000 + 96.9948i −0.250373 + 0.144553i
\(672\) 0 0
\(673\) −577.000 + 999.393i −0.857355 + 1.48498i 0.0170877 + 0.999854i \(0.494561\pi\)
−0.874443 + 0.485129i \(0.838773\pi\)
\(674\) −337.000 + 583.701i −0.500000 + 0.866025i
\(675\) 0 0
\(676\) −630.000 1091.19i −0.931953 1.61419i
\(677\) 566.000 980.341i 0.836041 1.44807i −0.0571384 0.998366i \(-0.518198\pi\)
0.893180 0.449700i \(-0.148469\pi\)
\(678\) 0 0
\(679\) 129.000 74.4782i 0.189985 0.109688i
\(680\) −176.000 304.841i −0.258824 0.448296i
\(681\) 0 0
\(682\) 84.0000 + 145.492i 0.123167 + 0.213332i
\(683\) 795.011i 1.16400i −0.813189 0.582000i \(-0.802271\pi\)
0.813189 0.582000i \(-0.197729\pi\)
\(684\) 0 0
\(685\) 676.000 0.986861
\(686\) 516.000 297.913i 0.752187 0.434275i
\(687\) 0 0
\(688\) 803.672i 1.16813i
\(689\) −572.000 990.733i −0.830189 1.43793i
\(690\) 0 0
\(691\) −780.000 450.333i −1.12880 0.651712i −0.185166 0.982707i \(-0.559282\pi\)
−0.943633 + 0.330995i \(0.892616\pi\)
\(692\) −4.00000 6.92820i −0.00578035 0.0100119i
\(693\) 0 0
\(694\) −471.000 271.932i −0.678674 0.391833i
\(695\) 678.000 + 391.443i 0.975540 + 0.563228i
\(696\) 0 0
\(697\) 71.5000 + 123.842i 0.102582 + 0.177678i
\(698\) −544.000 −0.779370
\(699\) 0 0
\(700\) 124.708i 0.178154i
\(701\) −142.000 −0.202568 −0.101284 0.994858i \(-0.532295\pi\)
−0.101284 + 0.994858i \(0.532295\pi\)
\(702\) 0 0
\(703\) 249.415i 0.354787i
\(704\) −672.000 387.979i −0.954545 0.551107i
\(705\) 0 0
\(706\) −922.000 −1.30595
\(707\) −60.0000 + 34.6410i −0.0848656 + 0.0489972i
\(708\) 0 0
\(709\) −370.000 + 640.859i −0.521862 + 0.903891i 0.477815 + 0.878461i \(0.341429\pi\)
−0.999677 + 0.0254305i \(0.991904\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −16.0000 −0.0224719
\(713\) −84.0000 + 145.492i −0.117812 + 0.204056i
\(714\) 0 0
\(715\) 924.000 533.472i 1.29231 0.746114i
\(716\) −648.000 374.123i −0.905028 0.522518i
\(717\) 0 0
\(718\) 918.000 530.008i 1.27855 0.738172i
\(719\) 124.708i 0.173446i 0.996232 + 0.0867230i \(0.0276395\pi\)
−0.996232 + 0.0867230i \(0.972360\pi\)
\(720\) 0 0
\(721\) 84.0000 0.116505
\(722\) 118.000 + 204.382i 0.163435 + 0.283078i
\(723\) 0 0
\(724\) −508.000 + 879.882i −0.701657 + 1.21531i
\(725\) −153.000 265.004i −0.211034 0.365522i
\(726\) 0 0
\(727\) 705.000 + 407.032i 0.969739 + 0.559879i 0.899157 0.437627i \(-0.144181\pi\)
0.0705821 + 0.997506i \(0.477514\pi\)
\(728\) 609.682i 0.837475i
\(729\) 0 0
\(730\) 100.000 173.205i 0.136986 0.237267i
\(731\) 478.500 + 276.262i 0.654583 + 0.377924i
\(732\) 0 0
\(733\) −457.000 791.547i −0.623465 1.07987i −0.988836 0.149011i \(-0.952391\pi\)
0.365370 0.930862i \(-0.380942\pi\)
\(734\) 193.990i 0.264291i
\(735\) 0 0
\(736\) 775.959i 1.05429i
\(737\) 1407.00 1.90909
\(738\) 0 0
\(739\) 358.535i 0.485162i 0.970131 + 0.242581i \(0.0779940\pi\)
−0.970131 + 0.242581i \(0.922006\pi\)
\(740\) 256.000 0.345946
\(741\) 0 0
\(742\) 360.267i 0.485534i
\(743\) 345.000 199.186i 0.464334 0.268083i −0.249531 0.968367i \(-0.580276\pi\)
0.713865 + 0.700284i \(0.246943\pi\)
\(744\) 0 0
\(745\) −260.000 + 450.333i −0.348993 + 0.604474i
\(746\) −346.000 + 599.290i −0.463807 + 0.803337i
\(747\) 0 0
\(748\) 462.000 266.736i 0.617647 0.356599i
\(749\) −27.0000 + 46.7654i −0.0360481 + 0.0624371i
\(750\) 0 0
\(751\) 966.000 557.720i 1.28628 0.742637i 0.308295 0.951291i \(-0.400241\pi\)
0.977990 + 0.208654i \(0.0669082\pi\)
\(752\) 55.4256i 0.0737043i
\(753\) 0 0
\(754\) 748.000 + 1295.57i 0.992042 + 1.71827i
\(755\) 484.974i 0.642350i
\(756\) 0 0
\(757\) 758.000 1.00132 0.500661 0.865644i \(-0.333091\pi\)
0.500661 + 0.865644i \(0.333091\pi\)
\(758\) 567.000 327.358i 0.748021 0.431870i
\(759\) 0 0
\(760\) −432.000 + 249.415i −0.568421 + 0.328178i
\(761\) −187.000 323.894i −0.245729 0.425616i 0.716607 0.697477i \(-0.245694\pi\)
−0.962336 + 0.271861i \(0.912361\pi\)
\(762\) 0 0
\(763\) −264.000 152.420i −0.346003 0.199765i
\(764\) −12.0000 + 6.92820i −0.0157068 + 0.00906833i
\(765\) 0 0
\(766\) −1092.00 630.466i −1.42559 0.823063i
\(767\) −1023.00 590.629i −1.33377 0.770051i
\(768\) 0 0
\(769\) 11.0000 + 19.0526i 0.0143043 + 0.0247758i 0.873089 0.487561i \(-0.162113\pi\)
−0.858785 + 0.512337i \(0.828780\pi\)
\(770\) 336.000 0.436364
\(771\) 0 0
\(772\) −268.000 −0.347150
\(773\) 1334.00 1.72574 0.862872 0.505423i \(-0.168663\pi\)
0.862872 + 0.505423i \(0.168663\pi\)
\(774\) 0 0
\(775\) 62.3538i 0.0804566i
\(776\) −172.000 + 297.913i −0.221649 + 0.383908i
\(777\) 0 0
\(778\) −292.000 −0.375321
\(779\) 175.500 101.325i 0.225289 0.130071i
\(780\) 0 0
\(781\) 0 0
\(782\) 462.000 + 266.736i 0.590793 + 0.341094i
\(783\) 0 0
\(784\) −296.000 + 512.687i −0.377551 + 0.653938i
\(785\) −8.00000 + 13.8564i −0.0101911 + 0.0176515i
\(786\) 0 0
\(787\) −762.000 + 439.941i −0.968234 + 0.559010i −0.898697 0.438569i \(-0.855485\pi\)
−0.0695365 + 0.997579i \(0.522152\pi\)
\(788\) 536.000 928.379i 0.680203 1.17815i
\(789\) 0 0
\(790\) 192.000 110.851i 0.243038 0.140318i
\(791\) 173.205i 0.218970i
\(792\) 0 0
\(793\) 352.000 0.443884
\(794\) 488.000 + 845.241i 0.614610 + 1.06454i
\(795\) 0 0
\(796\) −108.000 62.3538i −0.135678 0.0783340i
\(797\) 416.000 + 720.533i 0.521957 + 0.904057i 0.999674 + 0.0255425i \(0.00813132\pi\)
−0.477716 + 0.878514i \(0.658535\pi\)
\(798\) 0 0
\(799\) 33.0000 + 19.0526i 0.0413016 + 0.0238455i
\(800\) −144.000 249.415i −0.180000 0.311769i
\(801\) 0 0
\(802\) −445.000 + 770.763i −0.554863 + 0.961051i