Properties

Label 108.3.f.a.91.1
Level 108
Weight 3
Character 108.91
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 91.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 108.91
Dual form 108.3.f.a.19.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000 q^{2} +4.00000 q^{4} +(2.00000 - 3.46410i) q^{5} +(-3.00000 + 1.73205i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q-2.00000 q^{2} +4.00000 q^{4} +(2.00000 - 3.46410i) q^{5} +(-3.00000 + 1.73205i) q^{7} -8.00000 q^{8} +(-4.00000 + 6.92820i) q^{10} +(10.5000 - 6.06218i) q^{11} +(11.0000 - 19.0526i) q^{13} +(6.00000 - 3.46410i) q^{14} +16.0000 q^{16} +11.0000 q^{17} -15.5885i q^{19} +(8.00000 - 13.8564i) q^{20} +(-21.0000 + 12.1244i) q^{22} +(-21.0000 - 12.1244i) q^{23} +(4.50000 + 7.79423i) q^{25} +(-22.0000 + 38.1051i) q^{26} +(-12.0000 + 6.92820i) q^{28} +(17.0000 + 29.4449i) q^{29} +(6.00000 + 3.46410i) q^{31} -32.0000 q^{32} -22.0000 q^{34} +13.8564i q^{35} -16.0000 q^{37} +31.1769i q^{38} +(-16.0000 + 27.7128i) q^{40} +(6.50000 - 11.2583i) q^{41} +(-43.5000 + 25.1147i) q^{43} +(42.0000 - 24.2487i) q^{44} +(42.0000 + 24.2487i) q^{46} +(-3.00000 + 1.73205i) q^{47} +(-18.5000 + 32.0429i) q^{49} +(-9.00000 - 15.5885i) q^{50} +(44.0000 - 76.2102i) q^{52} -52.0000 q^{53} -48.4974i q^{55} +(24.0000 - 13.8564i) q^{56} +(-34.0000 - 58.8897i) q^{58} +(46.5000 + 26.8468i) q^{59} +(8.00000 + 13.8564i) q^{61} +(-12.0000 - 6.92820i) q^{62} +64.0000 q^{64} +(-44.0000 - 76.2102i) q^{65} +(100.500 + 58.0237i) q^{67} +44.0000 q^{68} -27.7128i q^{70} -25.0000 q^{73} +32.0000 q^{74} -62.3538i q^{76} +(-21.0000 + 36.3731i) q^{77} +(24.0000 - 13.8564i) q^{79} +(32.0000 - 55.4256i) q^{80} +(-13.0000 + 22.5167i) q^{82} +(-30.0000 + 17.3205i) q^{83} +(22.0000 - 38.1051i) q^{85} +(87.0000 - 50.2295i) q^{86} +(-84.0000 + 48.4974i) q^{88} +2.00000 q^{89} +76.2102i q^{91} +(-84.0000 - 48.4974i) q^{92} +(6.00000 - 3.46410i) q^{94} +(-54.0000 - 31.1769i) q^{95} +(21.5000 + 37.2391i) q^{97} +(37.0000 - 64.0859i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 4q^{2} + 8q^{4} + 4q^{5} - 6q^{7} - 16q^{8} + O(q^{10}) \) \( 2q - 4q^{2} + 8q^{4} + 4q^{5} - 6q^{7} - 16q^{8} - 8q^{10} + 21q^{11} + 22q^{13} + 12q^{14} + 32q^{16} + 22q^{17} + 16q^{20} - 42q^{22} - 42q^{23} + 9q^{25} - 44q^{26} - 24q^{28} + 34q^{29} + 12q^{31} - 64q^{32} - 44q^{34} - 32q^{37} - 32q^{40} + 13q^{41} - 87q^{43} + 84q^{44} + 84q^{46} - 6q^{47} - 37q^{49} - 18q^{50} + 88q^{52} - 104q^{53} + 48q^{56} - 68q^{58} + 93q^{59} + 16q^{61} - 24q^{62} + 128q^{64} - 88q^{65} + 201q^{67} + 88q^{68} - 50q^{73} + 64q^{74} - 42q^{77} + 48q^{79} + 64q^{80} - 26q^{82} - 60q^{83} + 44q^{85} + 174q^{86} - 168q^{88} + 4q^{89} - 168q^{92} + 12q^{94} - 108q^{95} + 43q^{97} + 74q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −1.00000
\(3\) 0 0
\(4\) 4.00000 1.00000
\(5\) 2.00000 3.46410i 0.400000 0.692820i −0.593725 0.804668i \(-0.702343\pi\)
0.993725 + 0.111847i \(0.0356768\pi\)
\(6\) 0 0
\(7\) −3.00000 + 1.73205i −0.428571 + 0.247436i −0.698738 0.715378i \(-0.746255\pi\)
0.270166 + 0.962814i \(0.412921\pi\)
\(8\) −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 \(-0.480872\pi\)
0.894490 + 0.447088i \(0.147539\pi\)
\(12\) 0 0
\(13\) 11.0000 19.0526i 0.846154 1.46558i −0.0384615 0.999260i \(-0.512246\pi\)
0.884615 0.466321i \(-0.154421\pi\)
\(14\) 6.00000 3.46410i 0.428571 0.247436i
\(15\) 0 0
\(16\) 16.0000 1.00000
\(17\) 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 \(-0.134549\pi\)
\(20\) 8.00000 13.8564i 0.400000 0.692820i
\(21\) 0 0
\(22\) −21.0000 + 12.1244i −0.954545 + 0.551107i
\(23\) −21.0000 12.1244i −0.913043 0.527146i −0.0316343 0.999500i \(-0.510071\pi\)
−0.881409 + 0.472354i \(0.843405\pi\)
\(24\) 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 0.994724 + 0.102589i \(0.0327128\pi\)
−0.408517 + 0.912751i \(0.633954\pi\)
\(30\) 0 0
\(31\) 6.00000 + 3.46410i 0.193548 + 0.111745i 0.593643 0.804729i \(-0.297689\pi\)
−0.400094 + 0.916474i \(0.631023\pi\)
\(32\) −32.0000 −1.00000
\(33\) 0 0
\(34\) −22.0000 −0.647059
\(35\) 13.8564i 0.395897i
\(36\) 0 0
\(37\) −16.0000 −0.432432 −0.216216 0.976346i \(-0.569372\pi\)
−0.216216 + 0.976346i \(0.569372\pi\)
\(38\) 31.1769i 0.820445i
\(39\) 0 0
\(40\) −16.0000 + 27.7128i −0.400000 + 0.692820i
\(41\) 6.50000 11.2583i 0.158537 0.274593i −0.775805 0.630973i \(-0.782656\pi\)
0.934341 + 0.356380i \(0.115989\pi\)
\(42\) 0 0
\(43\) −43.5000 + 25.1147i −1.01163 + 0.584064i −0.911668 0.410928i \(-0.865205\pi\)
−0.0999600 + 0.994991i \(0.531871\pi\)
\(44\) 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 \(-0.678400\pi\)
0.467745 + 0.883863i \(0.345066\pi\)
\(48\) 0 0
\(49\) −18.5000 + 32.0429i −0.377551 + 0.653938i
\(50\) −9.00000 15.5885i −0.180000 0.311769i
\(51\) 0 0
\(52\) 44.0000 76.2102i 0.846154 1.46558i
\(53\) −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
\(58\) −34.0000 58.8897i −0.586207 1.01534i
\(59\) 46.5000 + 26.8468i 0.788136 + 0.455030i 0.839306 0.543660i \(-0.182962\pi\)
−0.0511702 + 0.998690i \(0.516295\pi\)
\(60\) 0 0
\(61\) 8.00000 + 13.8564i 0.131148 + 0.227154i 0.924119 0.382104i \(-0.124801\pi\)
−0.792972 + 0.609259i \(0.791467\pi\)
\(62\) −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 1.00000 \(0\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) 44.0000 0.647059
\(69\) 0 0
\(70\) 27.7128i 0.395897i
\(71\) 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 \(0.554775\pi\)
\(74\) 32.0000 0.432432
\(75\) 0 0
\(76\) 62.3538i 0.820445i
\(77\) −21.0000 + 36.3731i −0.272727 + 0.472377i
\(78\) 0 0
\(79\) 24.0000 13.8564i 0.303797 0.175398i −0.340350 0.940299i \(-0.610546\pi\)
0.644148 + 0.764901i \(0.277212\pi\)
\(80\) 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 \(-0.733584\pi\)
0.308269 + 0.951299i \(0.400250\pi\)
\(84\) 0 0
\(85\) 22.0000 38.1051i 0.258824 0.448296i
\(86\) 87.0000 50.2295i 1.01163 0.584064i
\(87\) 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
\(92\) −84.0000 48.4974i −0.913043 0.527146i
\(93\) 0 0
\(94\) 6.00000 3.46410i 0.0638298 0.0368521i
\(95\) −54.0000 31.1769i −0.568421 0.328178i
\(96\) 0 0
\(97\) 21.5000 + 37.2391i 0.221649 + 0.383908i 0.955309 0.295609i \(-0.0955226\pi\)
−0.733659 + 0.679517i \(0.762189\pi\)
\(98\) 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 0.812265 0.583288i \(-0.198234\pi\)
−0.911275 + 0.411798i \(0.864901\pi\)
\(102\) 0 0
\(103\) −21.0000 12.1244i −0.203883 0.117712i 0.394582 0.918861i \(-0.370889\pi\)
−0.598466 + 0.801148i \(0.704223\pi\)
\(104\) −88.0000 + 152.420i −0.846154 + 1.46558i
\(105\) 0 0
\(106\) 104.000 0.981132
\(107\) 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 \(0.632266\pi\)
\(110\) 96.9948i 0.881771i
\(111\) 0 0
\(112\) −48.0000 + 27.7128i −0.428571 + 0.247436i
\(113\) −25.0000 + 43.3013i −0.221239 + 0.383197i −0.955184 0.296011i \(-0.904343\pi\)
0.733946 + 0.679208i \(0.237677\pi\)
\(114\) 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
\(122\) −16.0000 27.7128i −0.131148 0.227154i
\(123\) 0 0
\(124\) 24.0000 + 13.8564i 0.193548 + 0.111745i
\(125\) 136.000 1.08800
\(126\) 0 0
\(127\) 218.238i 1.71841i −0.511629 0.859206i \(-0.670958\pi\)
0.511629 0.859206i \(-0.329042\pi\)
\(128\) −128.000 −1.00000
\(129\) 0 0
\(130\) 88.0000 + 152.420i 0.676923 + 1.17247i
\(131\) 168.000 + 96.9948i 1.28244 + 0.740419i 0.977294 0.211886i \(-0.0679606\pi\)
0.305148 + 0.952305i \(0.401294\pi\)
\(132\) 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 0.990068 + 0.140590i \(0.0448999\pi\)
−0.373280 + 0.927719i \(0.621767\pi\)
\(138\) 0 0
\(139\) −169.500 97.8609i −1.21942 0.704035i −0.254630 0.967039i \(-0.581954\pi\)
−0.964795 + 0.263004i \(0.915287\pi\)
\(140\) 55.4256i 0.395897i
\(141\) 0 0
\(142\) 0 0
\(143\) 266.736i 1.86529i
\(144\) 0 0
\(145\) 136.000 0.937931
\(146\) 50.0000 0.342466
\(147\) 0 0
\(148\) −64.0000 −0.432432
\(149\) 65.0000 112.583i 0.436242 0.755593i −0.561154 0.827711i \(-0.689643\pi\)
0.997396 + 0.0721185i \(0.0229760\pi\)
\(150\) 0 0
\(151\) 105.000 60.6218i 0.695364 0.401469i −0.110254 0.993903i \(-0.535167\pi\)
0.805618 + 0.592435i \(0.201833\pi\)
\(152\) 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 −0.859586 0.510992i \(-0.829278\pi\)
0.872325 + 0.488927i \(0.162612\pi\)
\(158\) −48.0000 + 27.7128i −0.303797 + 0.175398i
\(159\) 0 0
\(160\) −64.0000 + 110.851i −0.400000 + 0.692820i
\(161\) 84.0000 0.521739
\(162\) 0 0
\(163\) 311.769i 1.91269i 0.292233 + 0.956347i \(0.405602\pi\)
−0.292233 + 0.956347i \(0.594398\pi\)
\(164\) 26.0000 45.0333i 0.158537 0.274593i
\(165\) 0 0
\(166\) 60.0000 34.6410i 0.361446 0.208681i
\(167\) −156.000 90.0666i −0.934132 0.539321i −0.0460158 0.998941i \(-0.514652\pi\)
−0.888116 + 0.459620i \(0.847986\pi\)
\(168\) 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 0.863121 0.504998i \(-0.168507\pi\)
−0.868901 + 0.494986i \(0.835173\pi\)
\(174\) 0 0
\(175\) −27.0000 15.5885i −0.154286 0.0890769i
\(176\) 168.000 96.9948i 0.954545 0.551107i
\(177\) 0 0
\(178\) −4.00000 −0.0224719
\(179\) 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 \(0.252444\pi\)
\(182\) 152.420i 0.837475i
\(183\) 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 \(-0.669553\pi\)
0.492126 + 0.870524i \(0.336220\pi\)
\(192\) 0 0
\(193\) 33.5000 58.0237i 0.173575 0.300641i −0.766092 0.642731i \(-0.777801\pi\)
0.939667 + 0.342090i \(0.111135\pi\)
\(194\) −43.0000 74.4782i −0.221649 0.383908i
\(195\) 0 0
\(196\) −74.0000 + 128.172i −0.377551 + 0.653938i
\(197\) −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
\(202\) 20.0000 + 34.6410i 0.0990099 + 0.171490i
\(203\) −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 \(-0.232357\pi\)
−0.204910 + 0.978781i \(0.565690\pi\)
\(212\) −208.000 −0.981132
\(213\) 0 0
\(214\) 31.1769i 0.145687i
\(215\) 200.918i 0.934502i
\(216\) 0 0
\(217\) −24.0000 −0.110599
\(218\) 176.000 0.807339
\(219\) 0 0
\(220\) 193.990i 0.881771i
\(221\) 121.000 209.578i 0.547511 0.948317i
\(222\) 0 0
\(223\) 51.0000 29.4449i 0.228700 0.132040i −0.381272 0.924463i \(-0.624514\pi\)
0.609972 + 0.792423i \(0.291181\pi\)
\(224\) 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 0.778847 0.627214i \(-0.215805\pi\)
0.932607 0.360894i \(-0.117529\pi\)
\(228\) 0 0
\(229\) −205.000 + 355.070i −0.895197 + 1.55053i −0.0616353 + 0.998099i \(0.519632\pi\)
−0.833561 + 0.552427i \(0.813702\pi\)
\(230\) 168.000 96.9948i 0.730435 0.421717i
\(231\) 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
\(236\) 186.000 + 107.387i 0.788136 + 0.455030i
\(237\) 0 0
\(238\) 66.0000 38.1051i 0.277311 0.160106i
\(239\) 33.0000 + 19.0526i 0.138075 + 0.0797178i 0.567446 0.823410i \(-0.307931\pi\)
−0.429371 + 0.903128i \(0.641265\pi\)
\(240\) 0 0
\(241\) 111.500 + 193.124i 0.462656 + 0.801343i 0.999092 0.0425975i \(-0.0135633\pi\)
−0.536437 + 0.843941i \(0.680230\pi\)
\(242\) −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
\(250\) −272.000 −1.08800
\(251\) 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
\(254\) 436.477i 1.71841i
\(255\) 0 0
\(256\) 256.000 1.00000
\(257\) −218.500 + 378.453i −0.850195 + 1.47258i 0.0308379 + 0.999524i \(0.490182\pi\)
−0.881032 + 0.473056i \(0.843151\pi\)
\(258\) 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 \(-0.871222\pi\)
−0.118750 + 0.992924i \(0.537889\pi\)
\(264\) 0 0
\(265\) −104.000 + 180.133i −0.392453 + 0.679748i
\(266\) −54.0000 93.5307i −0.203008 0.351619i
\(267\) 0 0
\(268\) 402.000 + 232.095i 1.50000 + 0.866025i
\(269\) −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 \(0.804917\pi\)
\(272\) 176.000 0.647059
\(273\) 0 0
\(274\) −169.000 292.717i −0.616788 1.06831i
\(275\) 94.5000 + 54.5596i 0.343636 + 0.198399i
\(276\) 0 0
\(277\) 17.0000 + 29.4449i 0.0613718 + 0.106299i 0.895079 0.445908i \(-0.147119\pi\)
−0.833707 + 0.552207i \(0.813786\pi\)
\(278\) 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 0.604267 0.796782i \(-0.293466\pi\)
−0.992167 + 0.124919i \(0.960133\pi\)
\(282\) 0 0
\(283\) 6.00000 + 3.46410i 0.0212014 + 0.0122406i 0.510563 0.859840i \(-0.329437\pi\)
−0.489362 + 0.872081i \(0.662770\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 533.472i 1.86529i
\(287\) 45.0333i 0.156911i
\(288\) 0 0
\(289\) −168.000 −0.581315
\(290\) −272.000 −0.937931
\(291\) 0 0
\(292\) −100.000 −0.342466
\(293\) 101.000 174.937i 0.344710 0.597055i −0.640591 0.767882i \(-0.721311\pi\)
0.985301 + 0.170827i \(0.0546440\pi\)
\(294\) 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
\(302\) −210.000 + 121.244i −0.695364 + 0.401469i
\(303\) 0 0
\(304\) 249.415i 0.820445i
\(305\) 64.0000 0.209836
\(306\) 0 0
\(307\) 109.119i 0.355437i −0.984081 0.177719i \(-0.943128\pi\)
0.984081 0.177719i \(-0.0568717\pi\)
\(308\) −84.0000 + 145.492i −0.272727 + 0.472377i
\(309\) 0 0
\(310\) −48.0000 + 27.7128i −0.154839 + 0.0893962i
\(311\) −237.000 136.832i −0.762058 0.439974i 0.0679762 0.997687i \(-0.478346\pi\)
−0.830034 + 0.557713i \(0.811679\pi\)
\(312\) 0 0
\(313\) 39.5000 + 68.4160i 0.126198 + 0.218581i 0.922201 0.386712i \(-0.126389\pi\)
−0.796003 + 0.605293i \(0.793056\pi\)
\(314\) −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 0.924853 + 0.380326i \(0.124188\pi\)
−0.133054 + 0.991109i \(0.542479\pi\)
\(318\) 0 0
\(319\) 357.000 + 206.114i 1.11912 + 0.646126i
\(320\) 128.000 221.703i 0.400000 0.692820i
\(321\) 0 0
\(322\) −168.000 −0.521739
\(323\) 171.473i 0.530876i
\(324\) 0 0
\(325\) 198.000 0.609231
\(326\) 623.538i 1.91269i
\(327\) 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 \(-0.878508\pi\)
−0.141445 + 0.989946i \(0.545175\pi\)
\(332\) −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 −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(338\) 315.000 + 545.596i 0.931953 + 1.61419i
\(339\) 0 0
\(340\) 88.0000 152.420i 0.258824 0.448296i
\(341\) 84.0000 0.246334
\(342\) 0 0
\(343\) 297.913i 0.868550i
\(344\) 348.000 200.918i 1.01163 0.584064i
\(345\) 0 0
\(346\) 2.00000 + 3.46410i 0.00578035 + 0.0100119i
\(347\) 235.500 + 135.966i 0.678674 + 0.391833i 0.799355 0.600859i \(-0.205174\pi\)
−0.120681 + 0.992691i \(0.538508\pi\)
\(348\) 0 0
\(349\) −136.000 235.559i −0.389685 0.674954i 0.602722 0.797951i \(-0.294083\pi\)
−0.992407 + 0.122997i \(0.960749\pi\)
\(350\) 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 −0.982397 0.186803i \(-0.940188\pi\)
0.329423 0.944182i \(-0.393146\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 8.00000 0.0224719
\(357\) 0 0
\(358\) 374.123i 1.04504i
\(359\) 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
\(362\) −508.000 −1.40331
\(363\) 0 0
\(364\) 304.841i 0.837475i
\(365\) −50.0000 + 86.6025i −0.136986 + 0.237267i
\(366\) 0 0
\(367\) −84.0000 + 48.4974i −0.228883 + 0.132146i −0.610057 0.792358i \(-0.708853\pi\)
0.381174 + 0.924503i \(0.375520\pi\)
\(368\) −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 −0.535340 0.844637i \(-0.679816\pi\)
0.999147 + 0.0412995i \(0.0131498\pi\)
\(374\) −231.000 + 133.368i −0.617647 + 0.356599i
\(375\) 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 \(-0.142146\pi\)
\(380\) −216.000 124.708i −0.568421 0.328178i
\(381\) 0 0
\(382\) 6.00000 3.46410i 0.0157068 0.00906833i
\(383\) 546.000 + 315.233i 1.42559 + 0.823063i 0.996769 0.0803272i \(-0.0255965\pi\)
0.428819 + 0.903390i \(0.358930\pi\)
\(384\) 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 0.756809 0.653636i \(-0.226757\pi\)
−0.944470 + 0.328598i \(0.893424\pi\)
\(390\) 0 0
\(391\) −231.000 133.368i −0.590793 0.341094i
\(392\) 148.000 256.344i 0.377551 0.653938i
\(393\) 0 0
\(394\) 536.000 1.36041
\(395\) 110.851i 0.280636i
\(396\) 0 0
\(397\) 488.000 1.22922 0.614610 0.788831i \(-0.289314\pi\)
0.614610 + 0.788831i \(0.289314\pi\)
\(398\) 62.3538i 0.156668i
\(399\) 0 0
\(400\) 72.0000 + 124.708i 0.180000 + 0.311769i
\(401\) 222.500 385.381i 0.554863 0.961051i −0.443051 0.896496i \(-0.646104\pi\)
0.997914 0.0645544i \(-0.0205626\pi\)
\(402\) 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 −0.822162 0.569254i \(-0.807232\pi\)
0.904069 + 0.427386i \(0.140566\pi\)
\(410\) 52.0000 + 90.0666i 0.126829 + 0.219675i
\(411\) 0 0
\(412\) −84.0000 48.4974i −0.203883 0.117712i
\(413\) −186.000 −0.450363
\(414\) 0 0
\(415\) 138.564i 0.333889i
\(416\) −352.000 + 609.682i −0.846154 + 1.46558i
\(417\) 0 0
\(418\) 189.000 + 327.358i 0.452153 + 0.783152i
\(419\) −534.000 308.305i −1.27446 0.735812i −0.298638 0.954366i \(-0.596532\pi\)
−0.975825 + 0.218555i \(0.929866\pi\)
\(420\) 0 0
\(421\) −136.000 235.559i −0.323040 0.559522i 0.658073 0.752954i \(-0.271372\pi\)
−0.981114 + 0.193431i \(0.938038\pi\)
\(422\) −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
\(428\) 62.3538i 0.145687i
\(429\) 0 0
\(430\) 401.836i 0.934502i
\(431\) 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 \(0.669219\pi\)
\(434\) 48.0000 0.110599
\(435\) 0 0
\(436\) −352.000 −0.807339
\(437\) −189.000 + 327.358i −0.432494 + 0.749102i
\(438\) 0 0
\(439\) −732.000 + 422.620i −1.66743 + 0.962689i −0.698408 + 0.715700i \(0.746108\pi\)
−0.969018 + 0.246989i \(0.920559\pi\)
\(440\) 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 \(-0.788471\pi\)
0.140474 + 0.990084i \(0.455137\pi\)
\(444\) 0 0
\(445\) 4.00000 6.92820i 0.00898876 0.0155690i
\(446\) −102.000 + 58.8897i −0.228700 + 0.132040i
\(447\) 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
\(452\) −100.000 + 173.205i −0.221239 + 0.383197i
\(453\) 0 0
\(454\) −777.000 + 448.601i −1.71145 + 0.988108i
\(455\) 264.000 + 152.420i 0.580220 + 0.334990i
\(456\) 0 0
\(457\) 165.500 + 286.654i 0.362144 + 0.627253i 0.988314 0.152435i \(-0.0487114\pi\)
−0.626169 + 0.779687i \(0.715378\pi\)
\(458\) 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 0.995059 + 0.0992865i \(0.0316560\pi\)
−0.411545 + 0.911390i \(0.635011\pi\)
\(462\) 0 0
\(463\) 492.000 + 284.056i 1.06263 + 0.613513i 0.926160 0.377131i \(-0.123089\pi\)
0.136475 + 0.990644i \(0.456423\pi\)
\(464\) 272.000 + 471.118i 0.586207 + 1.01534i
\(465\) 0 0
\(466\) −130.000 −0.278970
\(467\) 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
\(470\) 27.7128i 0.0589634i
\(471\) 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 \(-0.626273\pi\)
0.605583 + 0.795782i \(0.292940\pi\)
\(480\) 0 0
\(481\) −176.000 + 304.841i −0.365904 + 0.633765i
\(482\) −223.000 386.247i −0.462656 0.801343i
\(483\) 0 0
\(484\) 52.0000 90.0666i 0.107438 0.186088i
\(485\) 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
\(490\) −148.000 256.344i −0.302041 0.523150i
\(491\) −628.500 362.865i −1.28004 0.739032i −0.303185 0.952932i \(-0.598050\pi\)
−0.976856 + 0.213900i \(0.931383\pi\)
\(492\) 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 \(-0.158373\pi\)
0.0260521 + 0.999661i \(0.491706\pi\)
\(500\) 544.000 1.08800
\(501\) 0 0
\(502\) 218.238i 0.434738i
\(503\) 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
\(506\) 588.000 1.16206
\(507\) 0 0
\(508\) 872.954i 1.71841i
\(509\) 380.000 658.179i 0.746562 1.29308i −0.202900 0.979200i \(-0.565037\pi\)
0.949461 0.313884i \(-0.101630\pi\)
\(510\) 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
\(518\) −96.0000 + 55.4256i −0.185328 + 0.106999i
\(519\) 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 \(-0.180256\pi\)
\(524\) 672.000 + 387.979i 1.28244 + 0.740419i
\(525\) 0 0
\(526\) 546.000 315.233i 1.03802 0.599303i
\(527\) 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
\(538\) 608.000 1.13011
\(539\) 448.601i 0.832284i
\(540\) 0 0
\(541\) −520.000 −0.961183 −0.480591 0.876945i \(-0.659578\pi\)
−0.480591 + 0.876945i \(0.659578\pi\)
\(542\) 623.538i 1.15044i
\(543\) 0 0
\(544\) −352.000 −0.647059
\(545\) −176.000 + 304.841i −0.322936 + 0.559341i
\(546\) 0 0
\(547\) 334.500 193.124i 0.611517 0.353060i −0.162042 0.986784i \(-0.551808\pi\)
0.773559 + 0.633724i \(0.218475\pi\)
\(548\) 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
\(554\) −34.0000 58.8897i −0.0613718 0.106299i
\(555\) 0 0
\(556\) −678.000 391.443i −1.21942 0.704035i
\(557\) −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
\(560\) 221.703i 0.395897i
\(561\) 0 0
\(562\) 218.000 + 377.587i 0.387900 + 0.671863i
\(563\) 613.500 + 354.204i 1.08970 + 0.629137i 0.933496 0.358588i \(-0.116742\pi\)
0.156202 + 0.987725i \(0.450075\pi\)
\(564\) 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 −0.991119 0.132976i \(-0.957547\pi\)
0.380399 0.924823i \(-0.375787\pi\)
\(570\) 0 0
\(571\) −466.500 269.334i −0.816988 0.471688i 0.0323889 0.999475i \(-0.489689\pi\)
−0.849377 + 0.527787i \(0.823022\pi\)
\(572\) 1066.94i 1.86529i
\(573\) 0 0
\(574\) 90.0666i 0.156911i
\(575\) 218.238i 0.379545i
\(576\) 0 0
\(577\) 227.000 0.393414 0.196707 0.980462i \(-0.436975\pi\)
0.196707 + 0.980462i \(0.436975\pi\)
\(578\) 336.000 0.581315
\(579\) 0 0
\(580\) 544.000 0.937931
\(581\) 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 \(-0.705743\pi\)
0.390189 + 0.920735i \(0.372410\pi\)
\(588\) 0 0
\(589\) 54.0000 93.5307i 0.0916808 0.158796i
\(590\) −372.000 + 214.774i −0.630508 + 0.364024i
\(591\) 0 0
\(592\) −256.000 −0.432432
\(593\) 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
\(596\) 260.000 450.333i 0.436242 0.755593i
\(597\) 0 0
\(598\) 924.000 533.472i 1.54515 0.892093i
\(599\) −48.0000 27.7128i −0.0801336 0.0462651i 0.459398 0.888231i \(-0.348065\pi\)
−0.539531 + 0.841965i \(0.681399\pi\)
\(600\) 0 0
\(601\) −167.500 290.119i −0.278702 0.482726i 0.692360 0.721552i \(-0.256571\pi\)
−0.971062 + 0.238826i \(0.923238\pi\)
\(602\) −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 \(-0.159515\pi\)
0.0224660 + 0.999748i \(0.492848\pi\)
\(608\) 498.831i 0.820445i
\(609\) 0 0
\(610\) −128.000 −0.209836
\(611\) 76.2102i 0.124730i
\(612\) 0 0
\(613\) −340.000 −0.554649 −0.277325 0.960776i \(-0.589448\pi\)
−0.277325 + 0.960776i \(0.589448\pi\)
\(614\) 218.238i 0.355437i
\(615\) 0 0
\(616\) 168.000 290.985i 0.272727 0.472377i
\(617\) 195.500 338.616i 0.316856 0.548810i −0.662974 0.748642i \(-0.730706\pi\)
0.979830 + 0.199832i \(0.0640396\pi\)
\(618\) 0 0
\(619\) 10.5000 6.06218i 0.0169628 0.00979350i −0.491495 0.870881i \(-0.663549\pi\)
0.508457 + 0.861087i \(0.330216\pi\)
\(620\) 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
\(626\) −79.0000 136.832i −0.126198 0.218581i
\(627\) 0 0
\(628\) 8.00000 13.8564i 0.0127389 0.0220643i
\(629\) −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
\(634\) −502.000 869.490i −0.791798 1.37143i
\(635\) −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 0.982193 0.187874i \(-0.0601596\pi\)
−0.653800 + 0.756667i \(0.726826\pi\)
\(642\) 0 0
\(643\) −358.500 206.980i −0.557543 0.321897i 0.194616 0.980880i \(-0.437654\pi\)
−0.752159 + 0.658982i \(0.770987\pi\)
\(644\) 336.000 0.521739
\(645\) 0 0
\(646\) 342.946i 0.530876i
\(647\) 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
\(650\) −396.000 −0.609231
\(651\) 0 0
\(652\) 1247.08i 1.91269i
\(653\) 443.000 767.299i 0.678407 1.17504i −0.297053 0.954861i \(-0.596004\pi\)
0.975460 0.220175i \(-0.0706628\pi\)
\(654\) 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 \(-0.447234\pi\)
0.936659 + 0.350243i \(0.113901\pi\)
\(660\) 0 0
\(661\) −124.000 + 214.774i −0.187595 + 0.324923i −0.944448 0.328662i \(-0.893402\pi\)
0.756853 + 0.653585i \(0.226736\pi\)
\(662\) 708.000 408.764i 1.06949 0.617468i
\(663\) 0 0
\(664\) 240.000 138.564i 0.361446 0.208681i
\(665\) 216.000 0.324812
\(666\) 0 0
\(667\) 824.456i 1.23607i
\(668\) −624.000 360.267i −0.934132 0.539321i
\(669\) 0 0
\(670\) −804.000 + 464.190i −1.20000 + 0.692820i
\(671\) 168.000 + 96.9948i 0.250373 + 0.144553i
\(672\) 0 0
\(673\) −577.000 999.393i −0.857355 1.48498i −0.874443 0.485129i \(-0.838773\pi\)
0.0170877 0.999854i \(-0.494561\pi\)
\(674\) −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 0.893180 + 0.449700i \(0.148469\pi\)
−0.0571384 + 0.998366i \(0.518198\pi\)
\(678\) 0 0
\(679\) −129.000 74.4782i −0.189985 0.109688i
\(680\) −176.000 + 304.841i −0.258824 + 0.448296i
\(681\) 0 0
\(682\) −168.000 −0.246334
\(683\) 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
\(686\) 595.825i 0.868550i
\(687\) 0 0
\(688\) −696.000 + 401.836i −1.01163 + 0.584064i
\(689\) −572.000 + 990.733i −0.830189 + 1.43793i
\(690\) 0 0
\(691\) 780.000 450.333i 1.12880 0.651712i 0.185166 0.982707i \(-0.440718\pi\)
0.943633 + 0.330995i \(0.107384\pi\)
\(692\) −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
\(698\) 272.000 + 471.118i 0.389685 + 0.674954i
\(699\) 0 0
\(700\) −108.000 62.3538i −0.154286 0.0890769i
\(701\) −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
\(706\) 461.000 + 798.475i 0.652975 + 1.13099i
\(707\) 60.0000 + 34.6410i 0.0848656 + 0.0489972i
\(708\) 0 0
\(709\) −370.000 640.859i −0.521862 0.903891i −0.999677 0.0254305i \(-0.991904\pi\)
0.477815 0.878461i \(-0.341429\pi\)
\(710\) 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
\(716\) 748.246i 1.04504i
\(717\) 0 0
\(718\) 1060.02i 1.47634i
\(719\) 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
\(722\) −236.000 −0.326870
\(723\) 0 0
\(724\) 1016.00 1.40331
\(725\) −153.000 + 265.004i −0.211034 + 0.365522i
\(726\) 0 0
\(727\) −705.000 + 407.032i −0.969739 + 0.559879i −0.899157 0.437627i \(-0.855819\pi\)
−0.0705821 + 0.997506i \(0.522486\pi\)
\(728\) 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 0.365370 + 0.930862i \(0.380942\pi\)
−0.988836 + 0.149011i \(0.952391\pi\)
\(734\) 168.000 96.9948i 0.228883 0.132146i
\(735\) 0 0
\(736\) 672.000 + 387.979i 0.913043 + 0.527146i
\(737\) 1407.00 1.90909
\(738\) 0 0
\(739\) 358.535i 0.485162i 0.970131 + 0.242581i \(0.0779940\pi\)
−0.970131 + 0.242581i \(0.922006\pi\)
\(740\) −128.000 + 221.703i −0.172973 + 0.299598i
\(741\) 0 0
\(742\) −312.000 + 180.133i −0.420485 + 0.242767i
\(743\) −345.000 199.186i −0.464334 0.268083i 0.249531 0.968367i \(-0.419724\pi\)
−0.713865 + 0.700284i \(0.753057\pi\)
\(744\) 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 \(-0.599759\pi\)
−0.977990 + 0.208654i \(0.933092\pi\)
\(752\) −48.0000 + 27.7128i −0.0638298 + 0.0368521i
\(753\) 0 0
\(754\) −1496.00 −1.98408
\(755\) 484.974i 0.642350i
\(756\) 0 0
\(757\) 758.000 1.00132 0.500661 0.865644i \(-0.333091\pi\)
0.500661 + 0.865644i \(0.333091\pi\)
\(758\) 654.715i 0.863740i
\(759\) 0 0
\(760\) 432.000 + 249.415i 0.568421 + 0.328178i
\(761\) −187.000 + 323.894i −0.245729 + 0.425616i −0.962336 0.271861i \(-0.912361\pi\)
0.716607 + 0.697477i \(0.245694\pi\)
\(762\) 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 −0.858785 0.512337i \(-0.828780\pi\)
0.873089 + 0.487561i \(0.162113\pi\)
\(770\) −168.000 290.985i −0.218182 0.377902i
\(771\) 0 0
\(772\) 134.000 232.095i 0.173575 0.300641i
\(773\) 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
\(778\) 146.000 + 252.879i 0.187661 + 0.325038i
\(779\) −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 \(-0.144515\pi\)
0.0695365 + 0.997579i \(0.477848\pi\)
\(788\) −1072.00 −1.36041
\(789\) 0 0
\(790\) 221.703i 0.280636i
\(791\) 173.205i 0.218970i
\(792\) 0 0
\(793\) 352.000 0.443884
\(794\) −976.000 −1.22922
\(795\) 0 0
\(796\) 124.708i 0.156668i
\(797\) 416.000 720.533i 0.521957 0.904057i −0.477716 0.878514i \(-0.658535\pi\)
0.999674 0.0255425i \(-0.00813132\pi\)
\(798\) 0 0
\(799\) −33.0000 + 19.0526i −0.0413016 + 0.0238455i