Properties

Label 75.3.c.c.26.2
Level $75$
Weight $3$
Character 75.26
Analytic conductor $2.044$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 75.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.04360198270\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{-11}) \)
Defining polynomial: \(x^{2} - x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 26.2
Root \(0.500000 - 1.65831i\) of defining polynomial
Character \(\chi\) \(=\) 75.26
Dual form 75.3.c.c.26.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.31662i q^{2} +(-2.50000 + 1.65831i) q^{3} -7.00000 q^{4} +(-5.50000 - 8.29156i) q^{6} -9.94987i q^{8} +(3.50000 - 8.29156i) q^{9} +O(q^{10})\) \(q+3.31662i q^{2} +(-2.50000 + 1.65831i) q^{3} -7.00000 q^{4} +(-5.50000 - 8.29156i) q^{6} -9.94987i q^{8} +(3.50000 - 8.29156i) q^{9} +16.5831i q^{11} +(17.5000 - 11.6082i) q^{12} -10.0000 q^{13} +5.00000 q^{16} +3.31662i q^{17} +(27.5000 + 11.6082i) q^{18} +7.00000 q^{19} -55.0000 q^{22} +19.8997i q^{23} +(16.5000 + 24.8747i) q^{24} -33.1662i q^{26} +(5.00000 + 26.5330i) q^{27} +33.1662i q^{29} +42.0000 q^{31} -23.2164i q^{32} +(-27.5000 - 41.4578i) q^{33} -11.0000 q^{34} +(-24.5000 + 58.0409i) q^{36} +40.0000 q^{37} +23.2164i q^{38} +(25.0000 - 16.5831i) q^{39} -16.5831i q^{41} +50.0000 q^{43} -116.082i q^{44} -66.0000 q^{46} -46.4327i q^{47} +(-12.5000 + 8.29156i) q^{48} -49.0000 q^{49} +(-5.50000 - 8.29156i) q^{51} +70.0000 q^{52} -46.4327i q^{53} +(-88.0000 + 16.5831i) q^{54} +(-17.5000 + 11.6082i) q^{57} -110.000 q^{58} +66.3325i q^{59} -8.00000 q^{61} +139.298i q^{62} +97.0000 q^{64} +(137.500 - 91.2072i) q^{66} -45.0000 q^{67} -23.2164i q^{68} +(-33.0000 - 49.7494i) q^{69} +33.1662i q^{71} +(-82.5000 - 34.8246i) q^{72} +35.0000 q^{73} +132.665i q^{74} -49.0000 q^{76} +(55.0000 + 82.9156i) q^{78} +12.0000 q^{79} +(-56.5000 - 58.0409i) q^{81} +55.0000 q^{82} +69.6491i q^{83} +165.831i q^{86} +(-55.0000 - 82.9156i) q^{87} +165.000 q^{88} -149.248i q^{89} -139.298i q^{92} +(-105.000 + 69.6491i) q^{93} +154.000 q^{94} +(38.5000 + 58.0409i) q^{96} +70.0000 q^{97} -162.515i q^{98} +(137.500 + 58.0409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 5q^{3} - 14q^{4} - 11q^{6} + 7q^{9} + O(q^{10}) \) \( 2q - 5q^{3} - 14q^{4} - 11q^{6} + 7q^{9} + 35q^{12} - 20q^{13} + 10q^{16} + 55q^{18} + 14q^{19} - 110q^{22} + 33q^{24} + 10q^{27} + 84q^{31} - 55q^{33} - 22q^{34} - 49q^{36} + 80q^{37} + 50q^{39} + 100q^{43} - 132q^{46} - 25q^{48} - 98q^{49} - 11q^{51} + 140q^{52} - 176q^{54} - 35q^{57} - 220q^{58} - 16q^{61} + 194q^{64} + 275q^{66} - 90q^{67} - 66q^{69} - 165q^{72} + 70q^{73} - 98q^{76} + 110q^{78} + 24q^{79} - 113q^{81} + 110q^{82} - 110q^{87} + 330q^{88} - 210q^{93} + 308q^{94} + 77q^{96} + 140q^{97} + 275q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.31662i 1.65831i 0.559017 + 0.829156i \(0.311179\pi\)
−0.559017 + 0.829156i \(0.688821\pi\)
\(3\) −2.50000 + 1.65831i −0.833333 + 0.552771i
\(4\) −7.00000 −1.75000
\(5\) 0 0
\(6\) −5.50000 8.29156i −0.916667 1.38193i
\(7\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 9.94987i 1.24373i
\(9\) 3.50000 8.29156i 0.388889 0.921285i
\(10\) 0 0
\(11\) 16.5831i 1.50756i 0.657129 + 0.753778i \(0.271771\pi\)
−0.657129 + 0.753778i \(0.728229\pi\)
\(12\) 17.5000 11.6082i 1.45833 0.967349i
\(13\) −10.0000 −0.769231 −0.384615 0.923077i \(-0.625666\pi\)
−0.384615 + 0.923077i \(0.625666\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 5.00000 0.312500
\(17\) 3.31662i 0.195096i 0.995231 + 0.0975478i \(0.0310999\pi\)
−0.995231 + 0.0975478i \(0.968900\pi\)
\(18\) 27.5000 + 11.6082i 1.52778 + 0.644899i
\(19\) 7.00000 0.368421 0.184211 0.982887i \(-0.441027\pi\)
0.184211 + 0.982887i \(0.441027\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −55.0000 −2.50000
\(23\) 19.8997i 0.865206i 0.901584 + 0.432603i \(0.142405\pi\)
−0.901584 + 0.432603i \(0.857595\pi\)
\(24\) 16.5000 + 24.8747i 0.687500 + 1.03645i
\(25\) 0 0
\(26\) 33.1662i 1.27562i
\(27\) 5.00000 + 26.5330i 0.185185 + 0.982704i
\(28\) 0 0
\(29\) 33.1662i 1.14366i 0.820371 + 0.571832i \(0.193767\pi\)
−0.820371 + 0.571832i \(0.806233\pi\)
\(30\) 0 0
\(31\) 42.0000 1.35484 0.677419 0.735597i \(-0.263098\pi\)
0.677419 + 0.735597i \(0.263098\pi\)
\(32\) 23.2164i 0.725512i
\(33\) −27.5000 41.4578i −0.833333 1.25630i
\(34\) −11.0000 −0.323529
\(35\) 0 0
\(36\) −24.5000 + 58.0409i −0.680556 + 1.61225i
\(37\) 40.0000 1.08108 0.540541 0.841318i \(-0.318220\pi\)
0.540541 + 0.841318i \(0.318220\pi\)
\(38\) 23.2164i 0.610957i
\(39\) 25.0000 16.5831i 0.641026 0.425208i
\(40\) 0 0
\(41\) 16.5831i 0.404466i −0.979337 0.202233i \(-0.935180\pi\)
0.979337 0.202233i \(-0.0648199\pi\)
\(42\) 0 0
\(43\) 50.0000 1.16279 0.581395 0.813621i \(-0.302507\pi\)
0.581395 + 0.813621i \(0.302507\pi\)
\(44\) 116.082i 2.63822i
\(45\) 0 0
\(46\) −66.0000 −1.43478
\(47\) 46.4327i 0.987931i −0.869482 0.493965i \(-0.835547\pi\)
0.869482 0.493965i \(-0.164453\pi\)
\(48\) −12.5000 + 8.29156i −0.260417 + 0.172741i
\(49\) −49.0000 −1.00000
\(50\) 0 0
\(51\) −5.50000 8.29156i −0.107843 0.162580i
\(52\) 70.0000 1.34615
\(53\) 46.4327i 0.876090i −0.898953 0.438045i \(-0.855671\pi\)
0.898953 0.438045i \(-0.144329\pi\)
\(54\) −88.0000 + 16.5831i −1.62963 + 0.307095i
\(55\) 0 0
\(56\) 0 0
\(57\) −17.5000 + 11.6082i −0.307018 + 0.203652i
\(58\) −110.000 −1.89655
\(59\) 66.3325i 1.12428i 0.827042 + 0.562140i \(0.190022\pi\)
−0.827042 + 0.562140i \(0.809978\pi\)
\(60\) 0 0
\(61\) −8.00000 −0.131148 −0.0655738 0.997848i \(-0.520888\pi\)
−0.0655738 + 0.997848i \(0.520888\pi\)
\(62\) 139.298i 2.24675i
\(63\) 0 0
\(64\) 97.0000 1.51562
\(65\) 0 0
\(66\) 137.500 91.2072i 2.08333 1.38193i
\(67\) −45.0000 −0.671642 −0.335821 0.941926i \(-0.609014\pi\)
−0.335821 + 0.941926i \(0.609014\pi\)
\(68\) 23.2164i 0.341417i
\(69\) −33.0000 49.7494i −0.478261 0.721005i
\(70\) 0 0
\(71\) 33.1662i 0.467130i 0.972341 + 0.233565i \(0.0750392\pi\)
−0.972341 + 0.233565i \(0.924961\pi\)
\(72\) −82.5000 34.8246i −1.14583 0.483674i
\(73\) 35.0000 0.479452 0.239726 0.970841i \(-0.422942\pi\)
0.239726 + 0.970841i \(0.422942\pi\)
\(74\) 132.665i 1.79277i
\(75\) 0 0
\(76\) −49.0000 −0.644737
\(77\) 0 0
\(78\) 55.0000 + 82.9156i 0.705128 + 1.06302i
\(79\) 12.0000 0.151899 0.0759494 0.997112i \(-0.475801\pi\)
0.0759494 + 0.997112i \(0.475801\pi\)
\(80\) 0 0
\(81\) −56.5000 58.0409i −0.697531 0.716555i
\(82\) 55.0000 0.670732
\(83\) 69.6491i 0.839146i 0.907722 + 0.419573i \(0.137820\pi\)
−0.907722 + 0.419573i \(0.862180\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 165.831i 1.92827i
\(87\) −55.0000 82.9156i −0.632184 0.953053i
\(88\) 165.000 1.87500
\(89\) 149.248i 1.67695i −0.544944 0.838473i \(-0.683449\pi\)
0.544944 0.838473i \(-0.316551\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 139.298i 1.51411i
\(93\) −105.000 + 69.6491i −1.12903 + 0.748915i
\(94\) 154.000 1.63830
\(95\) 0 0
\(96\) 38.5000 + 58.0409i 0.401042 + 0.604593i
\(97\) 70.0000 0.721649 0.360825 0.932634i \(-0.382495\pi\)
0.360825 + 0.932634i \(0.382495\pi\)
\(98\) 162.515i 1.65831i
\(99\) 137.500 + 58.0409i 1.38889 + 0.586272i
\(100\) 0 0
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 27.5000 18.2414i 0.269608 0.178838i
\(103\) 70.0000 0.679612 0.339806 0.940496i \(-0.389639\pi\)
0.339806 + 0.940496i \(0.389639\pi\)
\(104\) 99.4987i 0.956719i
\(105\) 0 0
\(106\) 154.000 1.45283
\(107\) 69.6491i 0.650926i 0.945555 + 0.325463i \(0.105520\pi\)
−0.945555 + 0.325463i \(0.894480\pi\)
\(108\) −35.0000 185.731i −0.324074 1.71973i
\(109\) −88.0000 −0.807339 −0.403670 0.914905i \(-0.632266\pi\)
−0.403670 + 0.914905i \(0.632266\pi\)
\(110\) 0 0
\(111\) −100.000 + 66.3325i −0.900901 + 0.597590i
\(112\) 0 0
\(113\) 102.815i 0.909871i 0.890525 + 0.454935i \(0.150338\pi\)
−0.890525 + 0.454935i \(0.849662\pi\)
\(114\) −38.5000 58.0409i −0.337719 0.509131i
\(115\) 0 0
\(116\) 232.164i 2.00141i
\(117\) −35.0000 + 82.9156i −0.299145 + 0.708681i
\(118\) −220.000 −1.86441
\(119\) 0 0
\(120\) 0 0
\(121\) −154.000 −1.27273
\(122\) 26.5330i 0.217484i
\(123\) 27.5000 + 41.4578i 0.223577 + 0.337055i
\(124\) −294.000 −2.37097
\(125\) 0 0
\(126\) 0 0
\(127\) −190.000 −1.49606 −0.748031 0.663663i \(-0.769001\pi\)
−0.748031 + 0.663663i \(0.769001\pi\)
\(128\) 228.847i 1.78787i
\(129\) −125.000 + 82.9156i −0.968992 + 0.642757i
\(130\) 0 0
\(131\) 198.997i 1.51906i −0.650469 0.759532i \(-0.725428\pi\)
0.650469 0.759532i \(-0.274572\pi\)
\(132\) 192.500 + 290.205i 1.45833 + 2.19852i
\(133\) 0 0
\(134\) 149.248i 1.11379i
\(135\) 0 0
\(136\) 33.0000 0.242647
\(137\) 69.6491i 0.508388i 0.967153 + 0.254194i \(0.0818101\pi\)
−0.967153 + 0.254194i \(0.918190\pi\)
\(138\) 165.000 109.449i 1.19565 0.793106i
\(139\) 77.0000 0.553957 0.276978 0.960876i \(-0.410667\pi\)
0.276978 + 0.960876i \(0.410667\pi\)
\(140\) 0 0
\(141\) 77.0000 + 116.082i 0.546099 + 0.823276i
\(142\) −110.000 −0.774648
\(143\) 165.831i 1.15966i
\(144\) 17.5000 41.4578i 0.121528 0.287901i
\(145\) 0 0
\(146\) 116.082i 0.795081i
\(147\) 122.500 81.2573i 0.833333 0.552771i
\(148\) −280.000 −1.89189
\(149\) 165.831i 1.11296i −0.830861 0.556481i \(-0.812151\pi\)
0.830861 0.556481i \(-0.187849\pi\)
\(150\) 0 0
\(151\) 172.000 1.13907 0.569536 0.821966i \(-0.307123\pi\)
0.569536 + 0.821966i \(0.307123\pi\)
\(152\) 69.6491i 0.458218i
\(153\) 27.5000 + 11.6082i 0.179739 + 0.0758705i
\(154\) 0 0
\(155\) 0 0
\(156\) −175.000 + 116.082i −1.12179 + 0.744115i
\(157\) 250.000 1.59236 0.796178 0.605062i \(-0.206852\pi\)
0.796178 + 0.605062i \(0.206852\pi\)
\(158\) 39.7995i 0.251896i
\(159\) 77.0000 + 116.082i 0.484277 + 0.730075i
\(160\) 0 0
\(161\) 0 0
\(162\) 192.500 187.389i 1.18827 1.15672i
\(163\) −35.0000 −0.214724 −0.107362 0.994220i \(-0.534240\pi\)
−0.107362 + 0.994220i \(0.534240\pi\)
\(164\) 116.082i 0.707816i
\(165\) 0 0
\(166\) −231.000 −1.39157
\(167\) 179.098i 1.07244i −0.844078 0.536221i \(-0.819851\pi\)
0.844078 0.536221i \(-0.180149\pi\)
\(168\) 0 0
\(169\) −69.0000 −0.408284
\(170\) 0 0
\(171\) 24.5000 58.0409i 0.143275 0.339421i
\(172\) −350.000 −2.03488
\(173\) 278.596i 1.61038i −0.593014 0.805192i \(-0.702062\pi\)
0.593014 0.805192i \(-0.297938\pi\)
\(174\) 275.000 182.414i 1.58046 1.04836i
\(175\) 0 0
\(176\) 82.9156i 0.471111i
\(177\) −110.000 165.831i −0.621469 0.936900i
\(178\) 495.000 2.78090
\(179\) 116.082i 0.648502i 0.945971 + 0.324251i \(0.105112\pi\)
−0.945971 + 0.324251i \(0.894888\pi\)
\(180\) 0 0
\(181\) 182.000 1.00552 0.502762 0.864425i \(-0.332317\pi\)
0.502762 + 0.864425i \(0.332317\pi\)
\(182\) 0 0
\(183\) 20.0000 13.2665i 0.109290 0.0724945i
\(184\) 198.000 1.07609
\(185\) 0 0
\(186\) −231.000 348.246i −1.24194 1.87229i
\(187\) −55.0000 −0.294118
\(188\) 325.029i 1.72888i
\(189\) 0 0
\(190\) 0 0
\(191\) 232.164i 1.21552i 0.794122 + 0.607758i \(0.207931\pi\)
−0.794122 + 0.607758i \(0.792069\pi\)
\(192\) −242.500 + 160.856i −1.26302 + 0.837793i
\(193\) 25.0000 0.129534 0.0647668 0.997900i \(-0.479370\pi\)
0.0647668 + 0.997900i \(0.479370\pi\)
\(194\) 232.164i 1.19672i
\(195\) 0 0
\(196\) 343.000 1.75000
\(197\) 218.897i 1.11115i 0.831465 + 0.555577i \(0.187502\pi\)
−0.831465 + 0.555577i \(0.812498\pi\)
\(198\) −192.500 + 456.036i −0.972222 + 2.30321i
\(199\) −68.0000 −0.341709 −0.170854 0.985296i \(-0.554653\pi\)
−0.170854 + 0.985296i \(0.554653\pi\)
\(200\) 0 0
\(201\) 112.500 74.6241i 0.559701 0.371264i
\(202\) 0 0
\(203\) 0 0
\(204\) 38.5000 + 58.0409i 0.188725 + 0.284514i
\(205\) 0 0
\(206\) 232.164i 1.12701i
\(207\) 165.000 + 69.6491i 0.797101 + 0.336469i
\(208\) −50.0000 −0.240385
\(209\) 116.082i 0.555416i
\(210\) 0 0
\(211\) 77.0000 0.364929 0.182464 0.983212i \(-0.441593\pi\)
0.182464 + 0.983212i \(0.441593\pi\)
\(212\) 325.029i 1.53316i
\(213\) −55.0000 82.9156i −0.258216 0.389275i
\(214\) −231.000 −1.07944
\(215\) 0 0
\(216\) 264.000 49.7494i 1.22222 0.230321i
\(217\) 0 0
\(218\) 291.863i 1.33882i
\(219\) −87.5000 + 58.0409i −0.399543 + 0.265027i
\(220\) 0 0
\(221\) 33.1662i 0.150074i
\(222\) −220.000 331.662i −0.990991 1.49398i
\(223\) −140.000 −0.627803 −0.313901 0.949456i \(-0.601636\pi\)
−0.313901 + 0.949456i \(0.601636\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −341.000 −1.50885
\(227\) 185.731i 0.818198i 0.912490 + 0.409099i \(0.134157\pi\)
−0.912490 + 0.409099i \(0.865843\pi\)
\(228\) 122.500 81.2573i 0.537281 0.356392i
\(229\) 372.000 1.62445 0.812227 0.583341i \(-0.198255\pi\)
0.812227 + 0.583341i \(0.198255\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 330.000 1.42241
\(233\) 119.398i 0.512440i 0.966619 + 0.256220i \(0.0824771\pi\)
−0.966619 + 0.256220i \(0.917523\pi\)
\(234\) −275.000 116.082i −1.17521 0.496076i
\(235\) 0 0
\(236\) 464.327i 1.96749i
\(237\) −30.0000 + 19.8997i −0.126582 + 0.0839652i
\(238\) 0 0
\(239\) 232.164i 0.971396i −0.874127 0.485698i \(-0.838565\pi\)
0.874127 0.485698i \(-0.161435\pi\)
\(240\) 0 0
\(241\) −413.000 −1.71369 −0.856846 0.515572i \(-0.827580\pi\)
−0.856846 + 0.515572i \(0.827580\pi\)
\(242\) 510.760i 2.11058i
\(243\) 237.500 + 51.4077i 0.977366 + 0.211554i
\(244\) 56.0000 0.229508
\(245\) 0 0
\(246\) −137.500 + 91.2072i −0.558943 + 0.370761i
\(247\) −70.0000 −0.283401
\(248\) 417.895i 1.68506i
\(249\) −115.500 174.123i −0.463855 0.699288i
\(250\) 0 0
\(251\) 248.747i 0.991023i 0.868601 + 0.495512i \(0.165019\pi\)
−0.868601 + 0.495512i \(0.834981\pi\)
\(252\) 0 0
\(253\) −330.000 −1.30435
\(254\) 630.159i 2.48094i
\(255\) 0 0
\(256\) −371.000 −1.44922
\(257\) 278.596i 1.08403i −0.840368 0.542017i \(-0.817661\pi\)
0.840368 0.542017i \(-0.182339\pi\)
\(258\) −275.000 414.578i −1.06589 1.60689i
\(259\) 0 0
\(260\) 0 0
\(261\) 275.000 + 116.082i 1.05364 + 0.444758i
\(262\) 660.000 2.51908
\(263\) 285.230i 1.08452i 0.840210 + 0.542262i \(0.182432\pi\)
−0.840210 + 0.542262i \(0.817568\pi\)
\(264\) −412.500 + 273.622i −1.56250 + 1.03645i
\(265\) 0 0
\(266\) 0 0
\(267\) 247.500 + 373.120i 0.926966 + 1.39745i
\(268\) 315.000 1.17537
\(269\) 464.327i 1.72612i 0.505098 + 0.863062i \(0.331456\pi\)
−0.505098 + 0.863062i \(0.668544\pi\)
\(270\) 0 0
\(271\) 22.0000 0.0811808 0.0405904 0.999176i \(-0.487076\pi\)
0.0405904 + 0.999176i \(0.487076\pi\)
\(272\) 16.5831i 0.0609674i
\(273\) 0 0
\(274\) −231.000 −0.843066
\(275\) 0 0
\(276\) 231.000 + 348.246i 0.836957 + 1.26176i
\(277\) 210.000 0.758123 0.379061 0.925372i \(-0.376247\pi\)
0.379061 + 0.925372i \(0.376247\pi\)
\(278\) 255.380i 0.918633i
\(279\) 147.000 348.246i 0.526882 1.24819i
\(280\) 0 0
\(281\) 198.997i 0.708176i −0.935212 0.354088i \(-0.884791\pi\)
0.935212 0.354088i \(-0.115209\pi\)
\(282\) −385.000 + 255.380i −1.36525 + 0.905603i
\(283\) −345.000 −1.21908 −0.609541 0.792755i \(-0.708646\pi\)
−0.609541 + 0.792755i \(0.708646\pi\)
\(284\) 232.164i 0.817478i
\(285\) 0 0
\(286\) 550.000 1.92308
\(287\) 0 0
\(288\) −192.500 81.2573i −0.668403 0.282143i
\(289\) 278.000 0.961938
\(290\) 0 0
\(291\) −175.000 + 116.082i −0.601375 + 0.398907i
\(292\) −245.000 −0.839041
\(293\) 318.396i 1.08668i 0.839514 + 0.543338i \(0.182840\pi\)
−0.839514 + 0.543338i \(0.817160\pi\)
\(294\) 269.500 + 406.287i 0.916667 + 1.38193i
\(295\) 0 0
\(296\) 397.995i 1.34458i
\(297\) −440.000 + 82.9156i −1.48148 + 0.279177i
\(298\) 550.000 1.84564
\(299\) 198.997i 0.665543i
\(300\) 0 0
\(301\) 0 0
\(302\) 570.459i 1.88894i
\(303\) 0 0
\(304\) 35.0000 0.115132
\(305\) 0 0
\(306\) −38.5000 + 91.2072i −0.125817 + 0.298063i
\(307\) −325.000 −1.05863 −0.529316 0.848425i \(-0.677551\pi\)
−0.529316 + 0.848425i \(0.677551\pi\)
\(308\) 0 0
\(309\) −175.000 + 116.082i −0.566343 + 0.375669i
\(310\) 0 0
\(311\) 397.995i 1.27973i −0.768489 0.639863i \(-0.778991\pi\)
0.768489 0.639863i \(-0.221009\pi\)
\(312\) −165.000 248.747i −0.528846 0.797266i
\(313\) 490.000 1.56550 0.782748 0.622339i \(-0.213818\pi\)
0.782748 + 0.622339i \(0.213818\pi\)
\(314\) 829.156i 2.64062i
\(315\) 0 0
\(316\) −84.0000 −0.265823
\(317\) 212.264i 0.669602i −0.942289 0.334801i \(-0.891331\pi\)
0.942289 0.334801i \(-0.108669\pi\)
\(318\) −385.000 + 255.380i −1.21069 + 0.803082i
\(319\) −550.000 −1.72414
\(320\) 0 0
\(321\) −115.500 174.123i −0.359813 0.542439i
\(322\) 0 0
\(323\) 23.2164i 0.0718773i
\(324\) 395.500 + 406.287i 1.22068 + 1.25397i
\(325\) 0 0
\(326\) 116.082i 0.356079i
\(327\) 220.000 145.931i 0.672783 0.446274i
\(328\) −165.000 −0.503049
\(329\) 0 0
\(330\) 0 0
\(331\) −243.000 −0.734139 −0.367069 0.930194i \(-0.619639\pi\)
−0.367069 + 0.930194i \(0.619639\pi\)
\(332\) 487.544i 1.46851i
\(333\) 140.000 331.662i 0.420420 0.995983i
\(334\) 594.000 1.77844
\(335\) 0 0
\(336\) 0 0
\(337\) −385.000 −1.14243 −0.571217 0.820799i \(-0.693528\pi\)
−0.571217 + 0.820799i \(0.693528\pi\)
\(338\) 228.847i 0.677062i
\(339\) −170.500 257.038i −0.502950 0.758225i
\(340\) 0 0
\(341\) 696.491i 2.04250i
\(342\) 192.500 + 81.2573i 0.562865 + 0.237594i
\(343\) 0 0
\(344\) 497.494i 1.44620i
\(345\) 0 0
\(346\) 924.000 2.67052
\(347\) 295.180i 0.850662i −0.905038 0.425331i \(-0.860158\pi\)
0.905038 0.425331i \(-0.139842\pi\)
\(348\) 385.000 + 580.409i 1.10632 + 1.66784i
\(349\) 532.000 1.52436 0.762178 0.647368i \(-0.224130\pi\)
0.762178 + 0.647368i \(0.224130\pi\)
\(350\) 0 0
\(351\) −50.0000 265.330i −0.142450 0.755926i
\(352\) 385.000 1.09375
\(353\) 278.596i 0.789225i −0.918848 0.394613i \(-0.870879\pi\)
0.918848 0.394613i \(-0.129121\pi\)
\(354\) 550.000 364.829i 1.55367 1.03059i
\(355\) 0 0
\(356\) 1044.74i 2.93465i
\(357\) 0 0
\(358\) −385.000 −1.07542
\(359\) 397.995i 1.10862i 0.832310 + 0.554311i \(0.187018\pi\)
−0.832310 + 0.554311i \(0.812982\pi\)
\(360\) 0 0
\(361\) −312.000 −0.864266
\(362\) 603.626i 1.66747i
\(363\) 385.000 255.380i 1.06061 0.703526i
\(364\) 0 0
\(365\) 0 0
\(366\) 44.0000 + 66.3325i 0.120219 + 0.181236i
\(367\) 180.000 0.490463 0.245232 0.969465i \(-0.421136\pi\)
0.245232 + 0.969465i \(0.421136\pi\)
\(368\) 99.4987i 0.270377i
\(369\) −137.500 58.0409i −0.372629 0.157293i
\(370\) 0 0
\(371\) 0 0
\(372\) 735.000 487.544i 1.97581 1.31060i
\(373\) 110.000 0.294906 0.147453 0.989069i \(-0.452892\pi\)
0.147453 + 0.989069i \(0.452892\pi\)
\(374\) 182.414i 0.487739i
\(375\) 0 0
\(376\) −462.000 −1.22872
\(377\) 331.662i 0.879741i
\(378\) 0 0
\(379\) −533.000 −1.40633 −0.703166 0.711025i \(-0.748231\pi\)
−0.703166 + 0.711025i \(0.748231\pi\)
\(380\) 0 0
\(381\) 475.000 315.079i 1.24672 0.826980i
\(382\) −770.000 −2.01571
\(383\) 79.5990i 0.207830i −0.994586 0.103915i \(-0.966863\pi\)
0.994586 0.103915i \(-0.0331370\pi\)
\(384\) −379.500 572.118i −0.988281 1.48989i
\(385\) 0 0
\(386\) 82.9156i 0.214807i
\(387\) 175.000 414.578i 0.452196 1.07126i
\(388\) −490.000 −1.26289
\(389\) 99.4987i 0.255781i 0.991788 + 0.127890i \(0.0408206\pi\)
−0.991788 + 0.127890i \(0.959179\pi\)
\(390\) 0 0
\(391\) −66.0000 −0.168798
\(392\) 487.544i 1.24373i
\(393\) 330.000 + 497.494i 0.839695 + 1.26589i
\(394\) −726.000 −1.84264
\(395\) 0 0
\(396\) −962.500 406.287i −2.43056 1.02598i
\(397\) 20.0000 0.0503778 0.0251889 0.999683i \(-0.491981\pi\)
0.0251889 + 0.999683i \(0.491981\pi\)
\(398\) 225.530i 0.566660i
\(399\) 0 0
\(400\) 0 0
\(401\) 746.241i 1.86095i −0.366357 0.930475i \(-0.619395\pi\)
0.366357 0.930475i \(-0.380605\pi\)
\(402\) 247.500 + 373.120i 0.615672 + 0.928160i
\(403\) −420.000 −1.04218
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 663.325i 1.62979i
\(408\) −82.5000 + 54.7243i −0.202206 + 0.134128i
\(409\) 77.0000 0.188264 0.0941320 0.995560i \(-0.469992\pi\)
0.0941320 + 0.995560i \(0.469992\pi\)
\(410\) 0 0
\(411\) −115.500 174.123i −0.281022 0.423656i
\(412\) −490.000 −1.18932
\(413\) 0 0
\(414\) −231.000 + 547.243i −0.557971 + 1.32184i
\(415\) 0 0
\(416\) 232.164i 0.558086i
\(417\) −192.500 + 127.690i −0.461631 + 0.306211i
\(418\) −385.000 −0.921053
\(419\) 116.082i 0.277045i −0.990359 0.138523i \(-0.955765\pi\)
0.990359 0.138523i \(-0.0442353\pi\)
\(420\) 0 0
\(421\) 412.000 0.978622 0.489311 0.872109i \(-0.337248\pi\)
0.489311 + 0.872109i \(0.337248\pi\)
\(422\) 255.380i 0.605166i
\(423\) −385.000 162.515i −0.910165 0.384195i
\(424\) −462.000 −1.08962
\(425\) 0 0
\(426\) 275.000 182.414i 0.645540 0.428203i
\(427\) 0 0
\(428\) 487.544i 1.13912i
\(429\) 275.000 + 414.578i 0.641026 + 0.966383i
\(430\) 0 0
\(431\) 198.997i 0.461711i −0.972988 0.230856i \(-0.925848\pi\)
0.972988 0.230856i \(-0.0741525\pi\)
\(432\) 25.0000 + 132.665i 0.0578704 + 0.307095i
\(433\) 455.000 1.05081 0.525404 0.850853i \(-0.323914\pi\)
0.525404 + 0.850853i \(0.323914\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 616.000 1.41284
\(437\) 139.298i 0.318760i
\(438\) −192.500 290.205i −0.439498 0.662568i
\(439\) 22.0000 0.0501139 0.0250569 0.999686i \(-0.492023\pi\)
0.0250569 + 0.999686i \(0.492023\pi\)
\(440\) 0 0
\(441\) −171.500 + 406.287i −0.388889 + 0.921285i
\(442\) 110.000 0.248869
\(443\) 527.343i 1.19039i −0.803581 0.595196i \(-0.797075\pi\)
0.803581 0.595196i \(-0.202925\pi\)
\(444\) 700.000 464.327i 1.57658 1.04578i
\(445\) 0 0
\(446\) 464.327i 1.04109i
\(447\) 275.000 + 414.578i 0.615213 + 0.927468i
\(448\) 0 0
\(449\) 82.9156i 0.184667i −0.995728 0.0923337i \(-0.970567\pi\)
0.995728 0.0923337i \(-0.0294326\pi\)
\(450\) 0 0
\(451\) 275.000 0.609756
\(452\) 719.708i 1.59227i
\(453\) −430.000 + 285.230i −0.949227 + 0.629646i
\(454\) −616.000 −1.35683
\(455\) 0 0
\(456\) 115.500 + 174.123i 0.253289 + 0.381848i
\(457\) 275.000 0.601751 0.300875 0.953663i \(-0.402721\pi\)
0.300875 + 0.953663i \(0.402721\pi\)
\(458\) 1233.78i 2.69385i
\(459\) −88.0000 + 16.5831i −0.191721 + 0.0361288i
\(460\) 0 0
\(461\) 596.992i 1.29499i 0.762068 + 0.647497i \(0.224184\pi\)
−0.762068 + 0.647497i \(0.775816\pi\)
\(462\) 0 0
\(463\) 240.000 0.518359 0.259179 0.965829i \(-0.416548\pi\)
0.259179 + 0.965829i \(0.416548\pi\)
\(464\) 165.831i 0.357395i
\(465\) 0 0
\(466\) −396.000 −0.849785
\(467\) 13.2665i 0.0284079i −0.999899 0.0142040i \(-0.995479\pi\)
0.999899 0.0142040i \(-0.00452141\pi\)
\(468\) 245.000 580.409i 0.523504 1.24019i
\(469\) 0 0
\(470\) 0 0
\(471\) −625.000 + 414.578i −1.32696 + 0.880208i
\(472\) 660.000 1.39831
\(473\) 829.156i 1.75297i
\(474\) −66.0000 99.4987i −0.139241 0.209913i
\(475\) 0 0
\(476\) 0 0
\(477\) −385.000 162.515i −0.807128 0.340701i
\(478\) 770.000 1.61088
\(479\) 298.496i 0.623165i −0.950219 0.311583i \(-0.899141\pi\)
0.950219 0.311583i \(-0.100859\pi\)
\(480\) 0 0
\(481\) −400.000 −0.831601
\(482\) 1369.77i 2.84184i
\(483\) 0 0
\(484\) 1078.00 2.22727
\(485\) 0 0
\(486\) −170.500 + 787.698i −0.350823 + 1.62078i
\(487\) −410.000 −0.841889 −0.420945 0.907086i \(-0.638301\pi\)
−0.420945 + 0.907086i \(0.638301\pi\)
\(488\) 79.5990i 0.163113i
\(489\) 87.5000 58.0409i 0.178937 0.118693i
\(490\) 0 0
\(491\) 265.330i 0.540387i −0.962806 0.270193i \(-0.912912\pi\)
0.962806 0.270193i \(-0.0870877\pi\)
\(492\) −192.500 290.205i −0.391260 0.589847i
\(493\) −110.000 −0.223124
\(494\) 232.164i 0.469967i
\(495\) 0 0
\(496\) 210.000 0.423387
\(497\) 0 0
\(498\) 577.500 383.070i 1.15964 0.769217i
\(499\) 322.000 0.645291 0.322645 0.946520i \(-0.395428\pi\)
0.322645 + 0.946520i \(0.395428\pi\)
\(500\) 0 0
\(501\) 297.000 + 447.744i 0.592814 + 0.893701i
\(502\) −825.000 −1.64343
\(503\) 411.261i 0.817617i −0.912620 0.408809i \(-0.865944\pi\)
0.912620 0.408809i \(-0.134056\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 1094.49i 2.16302i
\(507\) 172.500 114.424i 0.340237 0.225687i
\(508\) 1330.00 2.61811
\(509\) 431.161i 0.847075i −0.905879 0.423538i \(-0.860788\pi\)
0.905879 0.423538i \(-0.139212\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 315.079i 0.615389i
\(513\) 35.0000 + 185.731i 0.0682261 + 0.362049i
\(514\) 924.000 1.79767
\(515\) 0 0
\(516\) 875.000 580.409i 1.69574 1.12482i
\(517\) 770.000 1.48936
\(518\) 0 0
\(519\) 462.000 + 696.491i 0.890173 + 1.34199i
\(520\) 0 0
\(521\) 281.913i 0.541100i 0.962706 + 0.270550i \(0.0872055\pi\)
−0.962706 + 0.270550i \(0.912794\pi\)
\(522\) −385.000 + 912.072i −0.737548 + 1.74726i
\(523\) −1015.00 −1.94073 −0.970363 0.241651i \(-0.922311\pi\)
−0.970363 + 0.241651i \(0.922311\pi\)
\(524\) 1392.98i 2.65836i
\(525\) 0 0
\(526\) −946.000 −1.79848
\(527\) 139.298i 0.264323i
\(528\) −137.500 207.289i −0.260417 0.392593i
\(529\) 133.000 0.251418
\(530\) 0 0
\(531\) 550.000 + 232.164i 1.03578 + 0.437220i
\(532\) 0 0
\(533\) 165.831i 0.311128i
\(534\) −1237.50 + 820.865i −2.31742 + 1.53720i
\(535\) 0 0
\(536\) 447.744i 0.835344i
\(537\) −192.500 290.205i −0.358473 0.540418i
\(538\) −1540.00 −2.86245
\(539\) 812.573i 1.50756i
\(540\) 0 0
\(541\) 912.000 1.68577 0.842884 0.538096i \(-0.180856\pi\)
0.842884 + 0.538096i \(0.180856\pi\)
\(542\) 72.9657i 0.134623i
\(543\) −455.000 + 301.813i −0.837937 + 0.555825i
\(544\) 77.0000 0.141544
\(545\) 0 0
\(546\) 0 0
\(547\) −55.0000 −0.100548 −0.0502742 0.998735i \(-0.516010\pi\)
−0.0502742 + 0.998735i \(0.516010\pi\)
\(548\) 487.544i 0.889679i
\(549\) −28.0000 + 66.3325i −0.0510018 + 0.120824i
\(550\) 0 0
\(551\) 232.164i 0.421350i
\(552\) −495.000 + 328.346i −0.896739 + 0.594829i
\(553\) 0 0
\(554\) 696.491i 1.25720i
\(555\) 0 0
\(556\) −539.000 −0.969424
\(557\) 1014.89i 1.82206i 0.412341 + 0.911030i \(0.364711\pi\)
−0.412341 + 0.911030i \(0.635289\pi\)
\(558\) 1155.00 + 487.544i 2.06989 + 0.873734i
\(559\) −500.000 −0.894454
\(560\) 0 0
\(561\) 137.500 91.2072i 0.245098 0.162580i
\(562\) 660.000 1.17438
\(563\) 119.398i 0.212075i 0.994362 + 0.106038i \(0.0338164\pi\)
−0.994362 + 0.106038i \(0.966184\pi\)
\(564\) −539.000 812.573i −0.955674 1.44073i
\(565\) 0 0
\(566\) 1144.24i 2.02162i
\(567\) 0 0
\(568\) 330.000 0.580986
\(569\) 49.7494i 0.0874330i 0.999044 + 0.0437165i \(0.0139198\pi\)
−0.999044 + 0.0437165i \(0.986080\pi\)
\(570\) 0 0
\(571\) 242.000 0.423818 0.211909 0.977289i \(-0.432032\pi\)
0.211909 + 0.977289i \(0.432032\pi\)
\(572\) 1160.82i 2.02940i
\(573\) −385.000 580.409i −0.671902 1.01293i
\(574\) 0 0
\(575\) 0 0
\(576\) 339.500 804.282i 0.589410 1.39632i
\(577\) −665.000 −1.15251 −0.576256 0.817269i \(-0.695487\pi\)
−0.576256 + 0.817269i \(0.695487\pi\)
\(578\) 922.022i 1.59519i
\(579\) −62.5000 + 41.4578i −0.107945 + 0.0716024i
\(580\) 0 0
\(581\) 0 0
\(582\) −385.000 580.409i −0.661512 0.997267i
\(583\) 770.000 1.32075
\(584\) 348.246i 0.596311i
\(585\) 0 0
\(586\) −1056.00 −1.80205
\(587\) 626.842i 1.06787i −0.845524 0.533937i \(-0.820712\pi\)
0.845524 0.533937i \(-0.179288\pi\)
\(588\) −857.500 + 568.801i −1.45833 + 0.967349i
\(589\) 294.000 0.499151
\(590\) 0 0
\(591\) −363.000 547.243i −0.614213 0.925961i
\(592\) 200.000 0.337838
\(593\) 859.006i 1.44858i −0.689497 0.724288i \(-0.742169\pi\)
0.689497 0.724288i \(-0.257831\pi\)
\(594\) −275.000 1459.31i −0.462963 2.45676i
\(595\) 0 0
\(596\) 1160.82i 1.94768i
\(597\) 170.000 112.765i 0.284757 0.188887i
\(598\) 660.000 1.10368
\(599\) 331.662i 0.553694i 0.960914 + 0.276847i \(0.0892895\pi\)
−0.960914 + 0.276847i \(0.910711\pi\)
\(600\) 0 0
\(601\) −343.000 −0.570715 −0.285358 0.958421i \(-0.592112\pi\)
−0.285358 + 0.958421i \(0.592112\pi\)
\(602\) 0 0
\(603\) −157.500 + 373.120i −0.261194 + 0.618773i
\(604\) −1204.00 −1.99338
\(605\) 0 0
\(606\) 0 0
\(607\) 1100.00 1.81219 0.906096 0.423073i \(-0.139049\pi\)
0.906096 + 0.423073i \(0.139049\pi\)
\(608\) 162.515i 0.267294i
\(609\) 0 0
\(610\) 0 0
\(611\) 464.327i 0.759947i
\(612\) −192.500 81.2573i −0.314542 0.132773i
\(613\) 290.000 0.473083 0.236542 0.971621i \(-0.423986\pi\)
0.236542 + 0.971621i \(0.423986\pi\)
\(614\) 1077.90i 1.75554i
\(615\) 0 0
\(616\) 0 0
\(617\) 79.5990i 0.129010i −0.997917 0.0645049i \(-0.979453\pi\)
0.997917 0.0645049i \(-0.0205468\pi\)
\(618\) −385.000 580.409i −0.622977 0.939174i
\(619\) −58.0000 −0.0936995 −0.0468498 0.998902i \(-0.514918\pi\)
−0.0468498 + 0.998902i \(0.514918\pi\)
\(620\) 0 0
\(621\) −528.000 + 99.4987i −0.850242 + 0.160223i
\(622\) 1320.00 2.12219
\(623\) 0 0
\(624\) 125.000 82.9156i 0.200321 0.132878i
\(625\) 0 0
\(626\) 1625.15i 2.59608i
\(627\) −192.500 290.205i −0.307018 0.462846i
\(628\) −1750.00 −2.78662
\(629\) 132.665i 0.210914i
\(630\) 0 0
\(631\) 862.000 1.36609 0.683043 0.730378i \(-0.260656\pi\)
0.683043 + 0.730378i \(0.260656\pi\)
\(632\) 119.398i 0.188922i
\(633\) −192.500 + 127.690i −0.304107 + 0.201722i
\(634\) 704.000 1.11041
\(635\) 0 0
\(636\) −539.000 812.573i −0.847484 1.27763i
\(637\) 490.000 0.769231
\(638\) 1824.14i 2.85916i
\(639\) 275.000 + 116.082i 0.430360 + 0.181662i
\(640\) 0 0
\(641\) 596.992i 0.931345i −0.884957 0.465673i \(-0.845812\pi\)
0.884957 0.465673i \(-0.154188\pi\)
\(642\) 577.500 383.070i 0.899533 0.596682i
\(643\) 1050.00 1.63297 0.816485 0.577366i \(-0.195920\pi\)
0.816485 + 0.577366i \(0.195920\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −77.0000 −0.119195
\(647\) 252.063i 0.389588i 0.980844 + 0.194794i \(0.0624038\pi\)
−0.980844 + 0.194794i \(0.937596\pi\)
\(648\) −577.500 + 562.168i −0.891204 + 0.867543i
\(649\) −1100.00 −1.69492
\(650\) 0 0
\(651\) 0 0
\(652\) 245.000 0.375767
\(653\) 1207.25i 1.84878i −0.381452 0.924389i \(-0.624576\pi\)
0.381452 0.924389i \(-0.375424\pi\)
\(654\) 484.000 + 729.657i 0.740061 + 1.11568i
\(655\) 0 0
\(656\) 82.9156i 0.126396i
\(657\) 122.500 290.205i 0.186454 0.441712i
\(658\) 0 0
\(659\) 812.573i 1.23304i 0.787339 + 0.616520i \(0.211458\pi\)
−0.787339 + 0.616520i \(0.788542\pi\)
\(660\) 0 0
\(661\) −98.0000 −0.148260 −0.0741301 0.997249i \(-0.523618\pi\)
−0.0741301 + 0.997249i \(0.523618\pi\)
\(662\) 805.940i 1.21743i
\(663\) 55.0000 + 82.9156i 0.0829563 + 0.125061i
\(664\) 693.000 1.04367
\(665\) 0 0
\(666\) 1100.00 + 464.327i 1.65165 + 0.697188i
\(667\) −660.000 −0.989505
\(668\) 1253.68i 1.87677i
\(669\) 350.000 232.164i 0.523169 0.347031i
\(670\) 0 0
\(671\) 132.665i 0.197712i
\(672\) 0 0
\(673\) 210.000 0.312036 0.156018 0.987754i \(-0.450134\pi\)
0.156018 + 0.987754i \(0.450134\pi\)
\(674\) 1276.90i 1.89451i
\(675\) 0 0
\(676\) 483.000 0.714497
\(677\) 79.5990i 0.117576i −0.998270 0.0587880i \(-0.981276\pi\)
0.998270 0.0587880i \(-0.0187236\pi\)
\(678\) 852.500 565.485i 1.25737 0.834048i
\(679\) 0 0
\(680\) 0 0
\(681\) −308.000 464.327i −0.452276 0.681832i
\(682\) −2310.00 −3.38710
\(683\) 169.148i 0.247654i 0.992304 + 0.123827i \(0.0395168\pi\)
−0.992304 + 0.123827i \(0.960483\pi\)
\(684\) −171.500 + 406.287i −0.250731 + 0.593986i
\(685\) 0 0
\(686\) 0 0
\(687\) −930.000 + 616.892i −1.35371 + 0.897951i
\(688\) 250.000 0.363372
\(689\) 464.327i 0.673915i
\(690\) 0 0
\(691\) −713.000 −1.03184 −0.515919 0.856637i \(-0.672549\pi\)
−0.515919 + 0.856637i \(0.672549\pi\)
\(692\) 1950.18i 2.81817i
\(693\) 0 0
\(694\) 979.000 1.41066
\(695\) 0 0
\(696\) −825.000 + 547.243i −1.18534 + 0.786269i
\(697\) 55.0000 0.0789096
\(698\) 1764.44i 2.52786i
\(699\) −198.000 298.496i −0.283262 0.427033i
\(700\) 0 0
\(701\) 1160.82i 1.65595i −0.560767 0.827973i \(-0.689494\pi\)
0.560767 0.827973i \(-0.310506\pi\)
\(702\) 880.000 165.831i 1.25356 0.236227i
\(703\) 280.000 0.398293
\(704\) 1608.56i 2.28489i
\(705\) 0 0
\(706\) 924.000 1.30878
\(707\) 0 0
\(708\) 770.000 + 1160.82i 1.08757 + 1.63957i
\(709\) −248.000 −0.349788 −0.174894 0.984587i \(-0.555958\pi\)
−0.174894 + 0.984587i \(0.555958\pi\)
\(710\) 0 0
\(711\) 42.0000 99.4987i 0.0590717 0.139942i
\(712\) −1485.00 −2.08567
\(713\) 835.789i 1.17222i
\(714\) 0 0
\(715\) 0 0
\(716\) 812.573i 1.13488i
\(717\) 385.000 + 580.409i 0.536960 + 0.809497i
\(718\) −1320.00 −1.83844
\(719\) 198.997i 0.276770i −0.990379 0.138385i \(-0.955809\pi\)
0.990379 0.138385i \(-0.0441911\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1034.79i 1.43322i
\(723\) 1032.50 684.883i 1.42808 0.947279i
\(724\) −1274.00 −1.75967
\(725\) 0 0
\(726\) 847.000 + 1276.90i 1.16667 + 1.75882i
\(727\) 10.0000 0.0137552 0.00687758 0.999976i \(-0.497811\pi\)
0.00687758 + 0.999976i \(0.497811\pi\)
\(728\) 0 0
\(729\) −679.000 + 265.330i −0.931413 + 0.363964i
\(730\) 0 0
\(731\) 165.831i 0.226855i
\(732\) −140.000 + 92.8655i −0.191257 + 0.126865i
\(733\) −770.000 −1.05048 −0.525239 0.850955i \(-0.676024\pi\)
−0.525239 + 0.850955i \(0.676024\pi\)
\(734\) 596.992i 0.813341i
\(735\) 0 0
\(736\) 462.000 0.627717
\(737\) 746.241i 1.01254i
\(738\) 192.500 456.036i 0.260840 0.617935i
\(739\) 802.000 1.08525 0.542625 0.839975i \(-0.317430\pi\)
0.542625 + 0.839975i \(0.317430\pi\)
\(740\) 0 0
\(741\) 175.000 116.082i 0.236167 0.156656i
\(742\) 0 0
\(743\) 1346.55i 1.81231i 0.422941 + 0.906157i \(0.360998\pi\)
−0.422941 + 0.906157i \(0.639002\pi\)
\(744\) 693.000 + 1044.74i 0.931452 + 1.40422i
\(745\) 0 0
\(746\) 364.829i 0.489047i
\(747\) 577.500 + 243.772i 0.773092 + 0.326335i
\(748\) 385.000 0.514706
\(749\) 0 0
\(750\) 0 0
\(751\) 322.000 0.428762 0.214381 0.976750i \(-0.431227\pi\)
0.214381 + 0.976750i \(0.431227\pi\)
\(752\) 232.164i 0.308728i
\(753\) −412.500 621.867i −0.547809 0.825853i
\(754\) 1100.00 1.45889
\(755\) 0 0
\(756\) 0 0
\(757\) −400.000 −0.528402 −0.264201 0.964468i \(-0.585108\pi\)
−0.264201 + 0.964468i \(0.585108\pi\)
\(758\) 1767.76i 2.33214i
\(759\) 825.000 547.243i 1.08696 0.721005i
\(760\) 0 0
\(761\) 348.246i 0.457616i 0.973472 + 0.228808i \(0.0734828\pi\)
−0.973472 + 0.228808i \(0.926517\pi\)
\(762\) 1045.00 + 1575.40i 1.37139 + 2.06745i
\(763\) 0 0
\(764\) 1625.15i 2.12715i
\(765\) 0 0
\(766\) 264.000 0.344648
\(767\) 663.325i 0.864830i
\(768\) 927.500 615.234i 1.20768 0.801086i
\(769\) −193.000 −0.250975 −0.125488 0.992095i \(-0.540050\pi\)
−0.125488 + 0.992095i \(0.540050\pi\)
\(770\) 0 0
\(771\) 462.000 + 696.491i 0.599222 + 0.903361i
\(772\) −175.000 −0.226684
\(773\) 417.895i 0.540614i 0.962774 + 0.270307i \(0.0871252\pi\)
−0.962774 + 0.270307i \(0.912875\pi\)
\(774\) 1375.00 + 580.409i 1.77649 + 0.749883i
\(775\) 0 0
\(776\) 696.491i 0.897540i
\(777\) 0 0
\(778\) −330.000 −0.424165
\(779\) 116.082i 0.149014i
\(780\) 0 0
\(781\) −550.000 −0.704225
\(782\) 218.897i 0.279920i
\(783\) −880.000 + 165.831i −1.12388 + 0.211790i
\(784\) −245.000 −0.312500
\(785\) 0 0
\(786\) −1650.00 + 1094.49i −2.09924 + 1.39248i
\(787\) −910.000 −1.15629 −0.578145 0.815934i \(-0.696223\pi\)
−0.578145 + 0.815934i \(0.696223\pi\)
\(788\) 1532.28i 1.94452i
\(789\) −473.000 713.074i −0.599493 0.903770i
\(790\) 0 0