Properties

Label 1078.2.c.b.1077.1
Level $1078$
Weight $2$
Character 1078.1077
Analytic conductor $8.608$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} - 102 x^{7} + 144 x^{6} - 432 x^{5} + 502 x^{4} + 288 x^{3} + 72 x^{2} + 12 x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{12} \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1077.1
Root \(-0.186243 + 0.0499037i\) of defining polynomial
Character \(\chi\) \(=\) 1078.1077
Dual form 1078.2.c.b.1077.16

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -3.12703i q^{3} -1.00000 q^{4} +2.20288i q^{5} -3.12703 q^{6} +1.00000i q^{8} -6.77832 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -3.12703i q^{3} -1.00000 q^{4} +2.20288i q^{5} -3.12703 q^{6} +1.00000i q^{8} -6.77832 q^{9} +2.20288 q^{10} +(-1.49053 - 2.96282i) q^{11} +3.12703i q^{12} -1.45937 q^{13} +6.88847 q^{15} +1.00000 q^{16} -7.60732 q^{17} +6.77832i q^{18} -0.180645 q^{19} -2.20288i q^{20} +(-2.96282 + 1.49053i) q^{22} +2.28779 q^{23} +3.12703 q^{24} +0.147325 q^{25} +1.45937i q^{26} +11.8149i q^{27} +4.45335i q^{29} -6.88847i q^{30} +8.54897i q^{31} -1.00000i q^{32} +(-9.26484 + 4.66093i) q^{33} +7.60732i q^{34} +6.77832 q^{36} +1.50947 q^{37} +0.180645i q^{38} +4.56350i q^{39} -2.20288 q^{40} -7.10368 q^{41} +1.58174i q^{43} +(1.49053 + 2.96282i) q^{44} -14.9318i q^{45} -2.28779i q^{46} +0.545357i q^{47} -3.12703i q^{48} -0.147325i q^{50} +23.7883i q^{51} +1.45937 q^{52} +4.83444 q^{53} +11.8149 q^{54} +(6.52674 - 3.28346i) q^{55} +0.564883i q^{57} +4.45335 q^{58} -6.18967i q^{59} -6.88847 q^{60} -5.72621 q^{61} +8.54897 q^{62} -1.00000 q^{64} -3.21482i q^{65} +(4.66093 + 9.26484i) q^{66} -2.98176 q^{67} +7.60732 q^{68} -7.15399i q^{69} -7.57488 q^{71} -6.77832i q^{72} -9.67644 q^{73} -1.50947i q^{74} -0.460691i q^{75} +0.180645 q^{76} +4.56350 q^{78} -6.91879i q^{79} +2.20288i q^{80} +16.6107 q^{81} +7.10368i q^{82} -5.84246 q^{83} -16.7580i q^{85} +1.58174 q^{86} +13.9258 q^{87} +(2.96282 - 1.49053i) q^{88} -16.1111i q^{89} -14.9318 q^{90} -2.28779 q^{92} +26.7329 q^{93} +0.545357 q^{94} -0.397940i q^{95} -3.12703 q^{96} +11.3012i q^{97} +(10.1033 + 20.0830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{4} - 32 q^{9} - 16 q^{11} - 8 q^{15} + 16 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 32 q^{37} + 16 q^{44} + 56 q^{53} + 24 q^{58} + 8 q^{60} - 16 q^{64} - 24 q^{67} + 8 q^{71} - 16 q^{78} + 16 q^{81} - 40 q^{86} + 8 q^{88} + 32 q^{92} + 88 q^{93} + 56 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 3.12703i 1.80539i −0.430279 0.902696i \(-0.641585\pi\)
0.430279 0.902696i \(-0.358415\pi\)
\(4\) −1.00000 −0.500000
\(5\) 2.20288i 0.985157i 0.870268 + 0.492579i \(0.163946\pi\)
−0.870268 + 0.492579i \(0.836054\pi\)
\(6\) −3.12703 −1.27660
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −6.77832 −2.25944
\(10\) 2.20288 0.696611
\(11\) −1.49053 2.96282i −0.449412 0.893325i
\(12\) 3.12703i 0.902696i
\(13\) −1.45937 −0.404757 −0.202378 0.979307i \(-0.564867\pi\)
−0.202378 + 0.979307i \(0.564867\pi\)
\(14\) 0 0
\(15\) 6.88847 1.77860
\(16\) 1.00000 0.250000
\(17\) −7.60732 −1.84505 −0.922523 0.385943i \(-0.873876\pi\)
−0.922523 + 0.385943i \(0.873876\pi\)
\(18\) 6.77832i 1.59767i
\(19\) −0.180645 −0.0414429 −0.0207214 0.999785i \(-0.506596\pi\)
−0.0207214 + 0.999785i \(0.506596\pi\)
\(20\) 2.20288i 0.492579i
\(21\) 0 0
\(22\) −2.96282 + 1.49053i −0.631676 + 0.317782i
\(23\) 2.28779 0.477037 0.238519 0.971138i \(-0.423338\pi\)
0.238519 + 0.971138i \(0.423338\pi\)
\(24\) 3.12703 0.638302
\(25\) 0.147325 0.0294651
\(26\) 1.45937i 0.286206i
\(27\) 11.8149i 2.27378i
\(28\) 0 0
\(29\) 4.45335i 0.826967i 0.910512 + 0.413483i \(0.135688\pi\)
−0.910512 + 0.413483i \(0.864312\pi\)
\(30\) 6.88847i 1.25766i
\(31\) 8.54897i 1.53544i 0.640785 + 0.767720i \(0.278609\pi\)
−0.640785 + 0.767720i \(0.721391\pi\)
\(32\) 1.00000i 0.176777i
\(33\) −9.26484 + 4.66093i −1.61280 + 0.811364i
\(34\) 7.60732i 1.30464i
\(35\) 0 0
\(36\) 6.77832 1.12972
\(37\) 1.50947 0.248155 0.124078 0.992273i \(-0.460403\pi\)
0.124078 + 0.992273i \(0.460403\pi\)
\(38\) 0.180645i 0.0293045i
\(39\) 4.56350i 0.730745i
\(40\) −2.20288 −0.348306
\(41\) −7.10368 −1.10941 −0.554705 0.832047i \(-0.687169\pi\)
−0.554705 + 0.832047i \(0.687169\pi\)
\(42\) 0 0
\(43\) 1.58174i 0.241213i 0.992700 + 0.120606i \(0.0384839\pi\)
−0.992700 + 0.120606i \(0.961516\pi\)
\(44\) 1.49053 + 2.96282i 0.224706 + 0.446662i
\(45\) 14.9318i 2.22590i
\(46\) 2.28779i 0.337316i
\(47\) 0.545357i 0.0795486i 0.999209 + 0.0397743i \(0.0126639\pi\)
−0.999209 + 0.0397743i \(0.987336\pi\)
\(48\) 3.12703i 0.451348i
\(49\) 0 0
\(50\) 0.147325i 0.0208349i
\(51\) 23.7883i 3.33103i
\(52\) 1.45937 0.202378
\(53\) 4.83444 0.664061 0.332031 0.943269i \(-0.392266\pi\)
0.332031 + 0.943269i \(0.392266\pi\)
\(54\) 11.8149 1.60781
\(55\) 6.52674 3.28346i 0.880065 0.442741i
\(56\) 0 0
\(57\) 0.564883i 0.0748206i
\(58\) 4.45335 0.584754
\(59\) 6.18967i 0.805826i −0.915238 0.402913i \(-0.867998\pi\)
0.915238 0.402913i \(-0.132002\pi\)
\(60\) −6.88847 −0.889298
\(61\) −5.72621 −0.733166 −0.366583 0.930385i \(-0.619472\pi\)
−0.366583 + 0.930385i \(0.619472\pi\)
\(62\) 8.54897 1.08572
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 3.21482i 0.398749i
\(66\) 4.66093 + 9.26484i 0.573721 + 1.14042i
\(67\) −2.98176 −0.364280 −0.182140 0.983273i \(-0.558302\pi\)
−0.182140 + 0.983273i \(0.558302\pi\)
\(68\) 7.60732 0.922523
\(69\) 7.15399i 0.861240i
\(70\) 0 0
\(71\) −7.57488 −0.898973 −0.449486 0.893287i \(-0.648393\pi\)
−0.449486 + 0.893287i \(0.648393\pi\)
\(72\) 6.77832i 0.798833i
\(73\) −9.67644 −1.13254 −0.566271 0.824219i \(-0.691614\pi\)
−0.566271 + 0.824219i \(0.691614\pi\)
\(74\) 1.50947i 0.175472i
\(75\) 0.460691i 0.0531960i
\(76\) 0.180645 0.0207214
\(77\) 0 0
\(78\) 4.56350 0.516715
\(79\) 6.91879i 0.778424i −0.921148 0.389212i \(-0.872747\pi\)
0.921148 0.389212i \(-0.127253\pi\)
\(80\) 2.20288i 0.246289i
\(81\) 16.6107 1.84563
\(82\) 7.10368i 0.784471i
\(83\) −5.84246 −0.641293 −0.320647 0.947199i \(-0.603900\pi\)
−0.320647 + 0.947199i \(0.603900\pi\)
\(84\) 0 0
\(85\) 16.7580i 1.81766i
\(86\) 1.58174 0.170563
\(87\) 13.9258 1.49300
\(88\) 2.96282 1.49053i 0.315838 0.158891i
\(89\) 16.1111i 1.70778i −0.520455 0.853889i \(-0.674238\pi\)
0.520455 0.853889i \(-0.325762\pi\)
\(90\) −14.9318 −1.57395
\(91\) 0 0
\(92\) −2.28779 −0.238519
\(93\) 26.7329 2.77207
\(94\) 0.545357 0.0562493
\(95\) 0.397940i 0.0408278i
\(96\) −3.12703 −0.319151
\(97\) 11.3012i 1.14746i 0.819045 + 0.573729i \(0.194504\pi\)
−0.819045 + 0.573729i \(0.805496\pi\)
\(98\) 0 0
\(99\) 10.1033 + 20.0830i 1.01542 + 2.01841i
\(100\) −0.147325 −0.0147325
\(101\) −0.517716 −0.0515147 −0.0257573 0.999668i \(-0.508200\pi\)
−0.0257573 + 0.999668i \(0.508200\pi\)
\(102\) 23.7883 2.35539
\(103\) 2.88716i 0.284480i 0.989832 + 0.142240i \(0.0454305\pi\)
−0.989832 + 0.142240i \(0.954570\pi\)
\(104\) 1.45937i 0.143103i
\(105\) 0 0
\(106\) 4.83444i 0.469562i
\(107\) 5.21959i 0.504597i −0.967649 0.252299i \(-0.918814\pi\)
0.967649 0.252299i \(-0.0811865\pi\)
\(108\) 11.8149i 1.13689i
\(109\) 10.0540i 0.963002i −0.876446 0.481501i \(-0.840092\pi\)
0.876446 0.481501i \(-0.159908\pi\)
\(110\) −3.28346 6.52674i −0.313065 0.622300i
\(111\) 4.72016i 0.448018i
\(112\) 0 0
\(113\) 7.83235 0.736806 0.368403 0.929666i \(-0.379905\pi\)
0.368403 + 0.929666i \(0.379905\pi\)
\(114\) 0.564883 0.0529062
\(115\) 5.03973i 0.469957i
\(116\) 4.45335i 0.413483i
\(117\) 9.89209 0.914524
\(118\) −6.18967 −0.569805
\(119\) 0 0
\(120\) 6.88847i 0.628828i
\(121\) −6.55664 + 8.83235i −0.596058 + 0.802941i
\(122\) 5.72621i 0.518427i
\(123\) 22.2134i 2.00292i
\(124\) 8.54897i 0.767720i
\(125\) 11.3389i 1.01419i
\(126\) 0 0
\(127\) 13.4702i 1.19529i −0.801762 0.597644i \(-0.796104\pi\)
0.801762 0.597644i \(-0.203896\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 4.94614 0.435484
\(130\) −3.21482 −0.281958
\(131\) −2.62462 −0.229314 −0.114657 0.993405i \(-0.536577\pi\)
−0.114657 + 0.993405i \(0.536577\pi\)
\(132\) 9.26484 4.66093i 0.806401 0.405682i
\(133\) 0 0
\(134\) 2.98176i 0.257585i
\(135\) −26.0268 −2.24003
\(136\) 7.60732i 0.652322i
\(137\) −8.72291 −0.745248 −0.372624 0.927982i \(-0.621542\pi\)
−0.372624 + 0.927982i \(0.621542\pi\)
\(138\) −7.15399 −0.608988
\(139\) 4.09291 0.347156 0.173578 0.984820i \(-0.444467\pi\)
0.173578 + 0.984820i \(0.444467\pi\)
\(140\) 0 0
\(141\) 1.70535 0.143616
\(142\) 7.57488i 0.635670i
\(143\) 2.17524 + 4.32386i 0.181902 + 0.361579i
\(144\) −6.77832 −0.564860
\(145\) −9.81020 −0.814692
\(146\) 9.67644i 0.800828i
\(147\) 0 0
\(148\) −1.50947 −0.124078
\(149\) 18.5917i 1.52309i −0.648110 0.761547i \(-0.724440\pi\)
0.648110 0.761547i \(-0.275560\pi\)
\(150\) −0.460691 −0.0376152
\(151\) 13.2045i 1.07457i 0.843402 + 0.537283i \(0.180549\pi\)
−0.843402 + 0.537283i \(0.819451\pi\)
\(152\) 0.180645i 0.0146523i
\(153\) 51.5648 4.16877
\(154\) 0 0
\(155\) −18.8324 −1.51265
\(156\) 4.56350i 0.365373i
\(157\) 5.75901i 0.459619i 0.973236 + 0.229810i \(0.0738104\pi\)
−0.973236 + 0.229810i \(0.926190\pi\)
\(158\) −6.91879 −0.550429
\(159\) 15.1174i 1.19889i
\(160\) 2.20288 0.174153
\(161\) 0 0
\(162\) 16.6107i 1.30506i
\(163\) −5.31289 −0.416137 −0.208069 0.978114i \(-0.566718\pi\)
−0.208069 + 0.978114i \(0.566718\pi\)
\(164\) 7.10368 0.554705
\(165\) −10.2675 20.4093i −0.799321 1.58886i
\(166\) 5.84246i 0.453463i
\(167\) −16.0519 −1.24213 −0.621067 0.783757i \(-0.713301\pi\)
−0.621067 + 0.783757i \(0.713301\pi\)
\(168\) 0 0
\(169\) −10.8702 −0.836172
\(170\) −16.7580 −1.28528
\(171\) 1.22447 0.0936377
\(172\) 1.58174i 0.120606i
\(173\) −7.09477 −0.539405 −0.269703 0.962944i \(-0.586925\pi\)
−0.269703 + 0.962944i \(0.586925\pi\)
\(174\) 13.9258i 1.05571i
\(175\) 0 0
\(176\) −1.49053 2.96282i −0.112353 0.223331i
\(177\) −19.3553 −1.45483
\(178\) −16.1111 −1.20758
\(179\) −24.9728 −1.86656 −0.933278 0.359155i \(-0.883065\pi\)
−0.933278 + 0.359155i \(0.883065\pi\)
\(180\) 14.9318i 1.11295i
\(181\) 19.3579i 1.43886i −0.694566 0.719429i \(-0.744404\pi\)
0.694566 0.719429i \(-0.255596\pi\)
\(182\) 0 0
\(183\) 17.9060i 1.32365i
\(184\) 2.28779i 0.168658i
\(185\) 3.32518i 0.244472i
\(186\) 26.7329i 1.96015i
\(187\) 11.3389 + 22.5391i 0.829185 + 1.64822i
\(188\) 0.545357i 0.0397743i
\(189\) 0 0
\(190\) −0.397940 −0.0288696
\(191\) 6.00000 0.434145 0.217072 0.976156i \(-0.430349\pi\)
0.217072 + 0.976156i \(0.430349\pi\)
\(192\) 3.12703i 0.225674i
\(193\) 16.6114i 1.19571i −0.801603 0.597857i \(-0.796019\pi\)
0.801603 0.597857i \(-0.203981\pi\)
\(194\) 11.3012 0.811376
\(195\) −10.0528 −0.719899
\(196\) 0 0
\(197\) 20.6396i 1.47051i 0.677790 + 0.735256i \(0.262938\pi\)
−0.677790 + 0.735256i \(0.737062\pi\)
\(198\) 20.0830 10.1033i 1.42723 0.718009i
\(199\) 0.726003i 0.0514650i 0.999669 + 0.0257325i \(0.00819181\pi\)
−0.999669 + 0.0257325i \(0.991808\pi\)
\(200\) 0.147325i 0.0104175i
\(201\) 9.32407i 0.657669i
\(202\) 0.517716i 0.0364264i
\(203\) 0 0
\(204\) 23.7883i 1.66552i
\(205\) 15.6486i 1.09294i
\(206\) 2.88716 0.201158
\(207\) −15.5074 −1.07784
\(208\) −1.45937 −0.101189
\(209\) 0.269257 + 0.535220i 0.0186249 + 0.0370219i
\(210\) 0 0
\(211\) 10.2878i 0.708241i 0.935200 + 0.354120i \(0.115220\pi\)
−0.935200 + 0.354120i \(0.884780\pi\)
\(212\) −4.83444 −0.332031
\(213\) 23.6869i 1.62300i
\(214\) −5.21959 −0.356804
\(215\) −3.48438 −0.237632
\(216\) −11.8149 −0.803904
\(217\) 0 0
\(218\) −10.0540 −0.680945
\(219\) 30.2585i 2.04468i
\(220\) −6.52674 + 3.28346i −0.440033 + 0.221371i
\(221\) 11.1019 0.746795
\(222\) −4.72016 −0.316796
\(223\) 0.894768i 0.0599181i 0.999551 + 0.0299590i \(0.00953768\pi\)
−0.999551 + 0.0299590i \(0.990462\pi\)
\(224\) 0 0
\(225\) −0.998618 −0.0665745
\(226\) 7.83235i 0.521000i
\(227\) 13.4848 0.895017 0.447508 0.894280i \(-0.352311\pi\)
0.447508 + 0.894280i \(0.352311\pi\)
\(228\) 0.564883i 0.0374103i
\(229\) 4.88550i 0.322843i 0.986886 + 0.161422i \(0.0516079\pi\)
−0.986886 + 0.161422i \(0.948392\pi\)
\(230\) 5.03973 0.332310
\(231\) 0 0
\(232\) −4.45335 −0.292377
\(233\) 22.6606i 1.48455i 0.670097 + 0.742274i \(0.266253\pi\)
−0.670097 + 0.742274i \(0.733747\pi\)
\(234\) 9.89209i 0.646666i
\(235\) −1.20136 −0.0783678
\(236\) 6.18967i 0.402913i
\(237\) −21.6353 −1.40536
\(238\) 0 0
\(239\) 25.2410i 1.63270i −0.577556 0.816351i \(-0.695993\pi\)
0.577556 0.816351i \(-0.304007\pi\)
\(240\) 6.88847 0.444649
\(241\) −14.0669 −0.906128 −0.453064 0.891478i \(-0.649669\pi\)
−0.453064 + 0.891478i \(0.649669\pi\)
\(242\) 8.83235 + 6.55664i 0.567765 + 0.421477i
\(243\) 16.4973i 1.05830i
\(244\) 5.72621 0.366583
\(245\) 0 0
\(246\) 22.2134 1.41628
\(247\) 0.263629 0.0167743
\(248\) −8.54897 −0.542860
\(249\) 18.2696i 1.15779i
\(250\) 11.3389 0.717137
\(251\) 3.03720i 0.191706i −0.995395 0.0958532i \(-0.969442\pi\)
0.995395 0.0958532i \(-0.0305579\pi\)
\(252\) 0 0
\(253\) −3.41002 6.77832i −0.214386 0.426149i
\(254\) −13.4702 −0.845196
\(255\) −52.4028 −3.28159
\(256\) 1.00000 0.0625000
\(257\) 25.7683i 1.60738i −0.595045 0.803692i \(-0.702866\pi\)
0.595045 0.803692i \(-0.297134\pi\)
\(258\) 4.94614i 0.307933i
\(259\) 0 0
\(260\) 3.21482i 0.199375i
\(261\) 30.1863i 1.86848i
\(262\) 2.62462i 0.162149i
\(263\) 6.41002i 0.395259i 0.980277 + 0.197629i \(0.0633243\pi\)
−0.980277 + 0.197629i \(0.936676\pi\)
\(264\) −4.66093 9.26484i −0.286861 0.570211i
\(265\) 10.6497i 0.654205i
\(266\) 0 0
\(267\) −50.3800 −3.08321
\(268\) 2.98176 0.182140
\(269\) 2.74152i 0.167153i 0.996501 + 0.0835767i \(0.0266344\pi\)
−0.996501 + 0.0835767i \(0.973366\pi\)
\(270\) 26.0268i 1.58394i
\(271\) 28.6002 1.73734 0.868670 0.495392i \(-0.164976\pi\)
0.868670 + 0.495392i \(0.164976\pi\)
\(272\) −7.60732 −0.461261
\(273\) 0 0
\(274\) 8.72291i 0.526970i
\(275\) −0.219593 0.436499i −0.0132419 0.0263219i
\(276\) 7.15399i 0.430620i
\(277\) 10.7683i 0.647006i 0.946227 + 0.323503i \(0.104861\pi\)
−0.946227 + 0.323503i \(0.895139\pi\)
\(278\) 4.09291i 0.245476i
\(279\) 57.9477i 3.46924i
\(280\) 0 0
\(281\) 19.6289i 1.17096i −0.810686 0.585481i \(-0.800906\pi\)
0.810686 0.585481i \(-0.199094\pi\)
\(282\) 1.70535i 0.101552i
\(283\) 10.6233 0.631487 0.315744 0.948845i \(-0.397746\pi\)
0.315744 + 0.948845i \(0.397746\pi\)
\(284\) 7.57488 0.449486
\(285\) −1.24437 −0.0737101
\(286\) 4.32386 2.17524i 0.255675 0.128624i
\(287\) 0 0
\(288\) 6.77832i 0.399416i
\(289\) 40.8713 2.40419
\(290\) 9.81020i 0.576075i
\(291\) 35.3391 2.07161
\(292\) 9.67644 0.566271
\(293\) 0.277651 0.0162206 0.00811028 0.999967i \(-0.497418\pi\)
0.00811028 + 0.999967i \(0.497418\pi\)
\(294\) 0 0
\(295\) 13.6351 0.793866
\(296\) 1.50947i 0.0877362i
\(297\) 35.0055 17.6105i 2.03123 1.02186i
\(298\) −18.5917 −1.07699
\(299\) −3.33874 −0.193084
\(300\) 0.460691i 0.0265980i
\(301\) 0 0
\(302\) 13.2045 0.759833
\(303\) 1.61891i 0.0930042i
\(304\) −0.180645 −0.0103607
\(305\) 12.6141i 0.722284i
\(306\) 51.5648i 2.94777i
\(307\) 6.41443 0.366091 0.183045 0.983104i \(-0.441404\pi\)
0.183045 + 0.983104i \(0.441404\pi\)
\(308\) 0 0
\(309\) 9.02823 0.513598
\(310\) 18.8324i 1.06961i
\(311\) 11.3024i 0.640899i −0.947266 0.320449i \(-0.896166\pi\)
0.947266 0.320449i \(-0.103834\pi\)
\(312\) −4.56350 −0.258357
\(313\) 16.4467i 0.929621i 0.885410 + 0.464810i \(0.153877\pi\)
−0.885410 + 0.464810i \(0.846123\pi\)
\(314\) 5.75901 0.325000
\(315\) 0 0
\(316\) 6.91879i 0.389212i
\(317\) −28.1910 −1.58337 −0.791683 0.610932i \(-0.790795\pi\)
−0.791683 + 0.610932i \(0.790795\pi\)
\(318\) −15.1174 −0.847744
\(319\) 13.1945 6.63786i 0.738750 0.371649i
\(320\) 2.20288i 0.123145i
\(321\) −16.3218 −0.910996
\(322\) 0 0
\(323\) 1.37423 0.0764640
\(324\) −16.6107 −0.922815
\(325\) −0.215002 −0.0119262
\(326\) 5.31289i 0.294254i
\(327\) −31.4393 −1.73860
\(328\) 7.10368i 0.392235i
\(329\) 0 0
\(330\) −20.4093 + 10.2675i −1.12350 + 0.565206i
\(331\) 19.1126 1.05052 0.525261 0.850941i \(-0.323968\pi\)
0.525261 + 0.850941i \(0.323968\pi\)
\(332\) 5.84246 0.320647
\(333\) −10.2317 −0.560692
\(334\) 16.0519i 0.878322i
\(335\) 6.56846i 0.358874i
\(336\) 0 0
\(337\) 16.0358i 0.873525i −0.899577 0.436763i \(-0.856125\pi\)
0.899577 0.436763i \(-0.143875\pi\)
\(338\) 10.8702i 0.591263i
\(339\) 24.4920i 1.33022i
\(340\) 16.7580i 0.908830i
\(341\) 25.3291 12.7425i 1.37165 0.690045i
\(342\) 1.22447i 0.0662119i
\(343\) 0 0
\(344\) −1.58174 −0.0852816
\(345\) 15.7594 0.848457
\(346\) 7.09477i 0.381417i
\(347\) 9.87094i 0.529900i 0.964262 + 0.264950i \(0.0853554\pi\)
−0.964262 + 0.264950i \(0.914645\pi\)
\(348\) −13.9258 −0.746500
\(349\) 31.1871 1.66940 0.834702 0.550701i \(-0.185640\pi\)
0.834702 + 0.550701i \(0.185640\pi\)
\(350\) 0 0
\(351\) 17.2424i 0.920330i
\(352\) −2.96282 + 1.49053i −0.157919 + 0.0794455i
\(353\) 25.9682i 1.38215i −0.722783 0.691075i \(-0.757138\pi\)
0.722783 0.691075i \(-0.242862\pi\)
\(354\) 19.3553i 1.02872i
\(355\) 16.6865i 0.885630i
\(356\) 16.1111i 0.853889i
\(357\) 0 0
\(358\) 24.9728i 1.31985i
\(359\) 4.01067i 0.211675i −0.994383 0.105838i \(-0.966248\pi\)
0.994383 0.105838i \(-0.0337524\pi\)
\(360\) 14.9318 0.786976
\(361\) −18.9674 −0.998282
\(362\) −19.3579 −1.01743
\(363\) 27.6190 + 20.5028i 1.44962 + 1.07612i
\(364\) 0 0
\(365\) 21.3160i 1.11573i
\(366\) 17.9060 0.935963
\(367\) 19.1851i 1.00145i 0.865605 + 0.500727i \(0.166934\pi\)
−0.865605 + 0.500727i \(0.833066\pi\)
\(368\) 2.28779 0.119259
\(369\) 48.1510 2.50664
\(370\) 3.32518 0.172868
\(371\) 0 0
\(372\) −26.7329 −1.38604
\(373\) 21.0289i 1.08884i 0.838814 + 0.544419i \(0.183250\pi\)
−0.838814 + 0.544419i \(0.816750\pi\)
\(374\) 22.5391 11.3389i 1.16547 0.586322i
\(375\) 35.4572 1.83100
\(376\) −0.545357 −0.0281247
\(377\) 6.49910i 0.334721i
\(378\) 0 0
\(379\) 20.7525 1.06599 0.532993 0.846120i \(-0.321067\pi\)
0.532993 + 0.846120i \(0.321067\pi\)
\(380\) 0.397940i 0.0204139i
\(381\) −42.1218 −2.15796
\(382\) 6.00000i 0.306987i
\(383\) 1.25606i 0.0641816i 0.999485 + 0.0320908i \(0.0102166\pi\)
−0.999485 + 0.0320908i \(0.989783\pi\)
\(384\) 3.12703 0.159576
\(385\) 0 0
\(386\) −16.6114 −0.845497
\(387\) 10.7215i 0.545006i
\(388\) 11.3012i 0.573729i
\(389\) −16.6479 −0.844080 −0.422040 0.906577i \(-0.638686\pi\)
−0.422040 + 0.906577i \(0.638686\pi\)
\(390\) 10.0528i 0.509045i
\(391\) −17.4040 −0.880156
\(392\) 0 0
\(393\) 8.20726i 0.414001i
\(394\) 20.6396 1.03981
\(395\) 15.2412 0.766870
\(396\) −10.1033 20.0830i −0.507709 1.00921i
\(397\) 14.1742i 0.711384i −0.934603 0.355692i \(-0.884245\pi\)
0.934603 0.355692i \(-0.115755\pi\)
\(398\) 0.726003 0.0363912
\(399\) 0 0
\(400\) 0.147325 0.00736626
\(401\) −4.85270 −0.242332 −0.121166 0.992632i \(-0.538663\pi\)
−0.121166 + 0.992632i \(0.538663\pi\)
\(402\) 9.32407 0.465042
\(403\) 12.4761i 0.621480i
\(404\) 0.517716 0.0257573
\(405\) 36.5913i 1.81824i
\(406\) 0 0
\(407\) −2.24991 4.47229i −0.111524 0.221683i
\(408\) −23.7883 −1.17770
\(409\) 10.6280 0.525523 0.262761 0.964861i \(-0.415367\pi\)
0.262761 + 0.964861i \(0.415367\pi\)
\(410\) −15.6486 −0.772827
\(411\) 27.2768i 1.34547i
\(412\) 2.88716i 0.142240i
\(413\) 0 0
\(414\) 15.5074i 0.762146i
\(415\) 12.8702i 0.631775i
\(416\) 1.45937i 0.0715516i
\(417\) 12.7986i 0.626752i
\(418\) 0.535220 0.269257i 0.0261785 0.0131698i
\(419\) 11.3690i 0.555410i −0.960666 0.277705i \(-0.910426\pi\)
0.960666 0.277705i \(-0.0895739\pi\)
\(420\) 0 0
\(421\) 27.2464 1.32791 0.663955 0.747772i \(-0.268877\pi\)
0.663955 + 0.747772i \(0.268877\pi\)
\(422\) 10.2878 0.500802
\(423\) 3.69661i 0.179735i
\(424\) 4.83444i 0.234781i
\(425\) −1.12075 −0.0543644
\(426\) 23.6869 1.14763
\(427\) 0 0
\(428\) 5.21959i 0.252299i
\(429\) 13.5208 6.80203i 0.652793 0.328405i
\(430\) 3.48438i 0.168032i
\(431\) 15.2210i 0.733169i 0.930385 + 0.366584i \(0.119473\pi\)
−0.930385 + 0.366584i \(0.880527\pi\)
\(432\) 11.8149i 0.568446i
\(433\) 1.85534i 0.0891619i −0.999006 0.0445810i \(-0.985805\pi\)
0.999006 0.0445810i \(-0.0141953\pi\)
\(434\) 0 0
\(435\) 30.6768i 1.47084i
\(436\) 10.0540i 0.481501i
\(437\) −0.413279 −0.0197698
\(438\) 30.2585 1.44581
\(439\) −32.9404 −1.57216 −0.786079 0.618126i \(-0.787892\pi\)
−0.786079 + 0.618126i \(0.787892\pi\)
\(440\) 3.28346 + 6.52674i 0.156533 + 0.311150i
\(441\) 0 0
\(442\) 11.1019i 0.528064i
\(443\) −32.8613 −1.56129 −0.780643 0.624977i \(-0.785108\pi\)
−0.780643 + 0.624977i \(0.785108\pi\)
\(444\) 4.72016i 0.224009i
\(445\) 35.4909 1.68243
\(446\) 0.894768 0.0423685
\(447\) −58.1369 −2.74978
\(448\) 0 0
\(449\) 3.62716 0.171176 0.0855880 0.996331i \(-0.472723\pi\)
0.0855880 + 0.996331i \(0.472723\pi\)
\(450\) 0.998618i 0.0470753i
\(451\) 10.5883 + 21.0470i 0.498581 + 0.991063i
\(452\) −7.83235 −0.368403
\(453\) 41.2909 1.94001
\(454\) 13.4848i 0.632872i
\(455\) 0 0
\(456\) −0.564883 −0.0264531
\(457\) 2.73567i 0.127969i 0.997951 + 0.0639846i \(0.0203808\pi\)
−0.997951 + 0.0639846i \(0.979619\pi\)
\(458\) 4.88550 0.228285
\(459\) 89.8799i 4.19523i
\(460\) 5.03973i 0.234978i
\(461\) −20.4439 −0.952169 −0.476084 0.879400i \(-0.657944\pi\)
−0.476084 + 0.879400i \(0.657944\pi\)
\(462\) 0 0
\(463\) 30.1701 1.40212 0.701062 0.713100i \(-0.252710\pi\)
0.701062 + 0.713100i \(0.252710\pi\)
\(464\) 4.45335i 0.206742i
\(465\) 58.8893i 2.73093i
\(466\) 22.6606 1.04973
\(467\) 27.1722i 1.25738i −0.777656 0.628691i \(-0.783591\pi\)
0.777656 0.628691i \(-0.216409\pi\)
\(468\) −9.89209 −0.457262
\(469\) 0 0
\(470\) 1.20136i 0.0554144i
\(471\) 18.0086 0.829793
\(472\) 6.18967 0.284903
\(473\) 4.68641 2.35763i 0.215481 0.108404i
\(474\) 21.6353i 0.993740i
\(475\) −0.0266136 −0.00122112
\(476\) 0 0
\(477\) −32.7694 −1.50041
\(478\) −25.2410 −1.15449
\(479\) −21.6184 −0.987770 −0.493885 0.869527i \(-0.664424\pi\)
−0.493885 + 0.869527i \(0.664424\pi\)
\(480\) 6.88847i 0.314414i
\(481\) −2.20288 −0.100443
\(482\) 14.0669i 0.640730i
\(483\) 0 0
\(484\) 6.55664 8.83235i 0.298029 0.401471i
\(485\) −24.8951 −1.13043
\(486\) −16.4973 −0.748333
\(487\) 2.08573 0.0945135 0.0472567 0.998883i \(-0.484952\pi\)
0.0472567 + 0.998883i \(0.484952\pi\)
\(488\) 5.72621i 0.259213i
\(489\) 16.6136i 0.751291i
\(490\) 0 0
\(491\) 2.47983i 0.111913i 0.998433 + 0.0559566i \(0.0178208\pi\)
−0.998433 + 0.0559566i \(0.982179\pi\)
\(492\) 22.2134i 1.00146i
\(493\) 33.8781i 1.52579i
\(494\) 0.263629i 0.0118612i
\(495\) −44.2403 + 22.2563i −1.98846 + 1.00035i
\(496\) 8.54897i 0.383860i
\(497\) 0 0
\(498\) 18.2696 0.818678
\(499\) 15.3838 0.688672 0.344336 0.938846i \(-0.388104\pi\)
0.344336 + 0.938846i \(0.388104\pi\)
\(500\) 11.3389i 0.507093i
\(501\) 50.1948i 2.24254i
\(502\) −3.03720 −0.135557
\(503\) −15.5714 −0.694295 −0.347147 0.937811i \(-0.612850\pi\)
−0.347147 + 0.937811i \(0.612850\pi\)
\(504\) 0 0
\(505\) 1.14047i 0.0507501i
\(506\) −6.77832 + 3.41002i −0.301333 + 0.151594i
\(507\) 33.9916i 1.50962i
\(508\) 13.4702i 0.597644i
\(509\) 30.7550i 1.36319i 0.731729 + 0.681595i \(0.238714\pi\)
−0.731729 + 0.681595i \(0.761286\pi\)
\(510\) 52.4028i 2.32043i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 2.13431i 0.0942321i
\(514\) −25.7683 −1.13659
\(515\) −6.36006 −0.280258
\(516\) −4.94614 −0.217742
\(517\) 1.61580 0.812872i 0.0710627 0.0357500i
\(518\) 0 0
\(519\) 22.1856i 0.973838i
\(520\) 3.21482 0.140979
\(521\) 3.69331i 0.161807i −0.996722 0.0809035i \(-0.974219\pi\)
0.996722 0.0809035i \(-0.0257806\pi\)
\(522\) −30.1863 −1.32122
\(523\) −29.2014 −1.27689 −0.638444 0.769669i \(-0.720421\pi\)
−0.638444 + 0.769669i \(0.720421\pi\)
\(524\) 2.62462 0.114657
\(525\) 0 0
\(526\) 6.41002 0.279490
\(527\) 65.0348i 2.83296i
\(528\) −9.26484 + 4.66093i −0.403200 + 0.202841i
\(529\) −17.7660 −0.772435
\(530\) 10.6497 0.462593
\(531\) 41.9556i 1.82072i
\(532\) 0 0
\(533\) 10.3669 0.449041
\(534\) 50.3800i 2.18016i
\(535\) 11.4981 0.497107
\(536\) 2.98176i 0.128793i
\(537\) 78.0908i 3.36987i
\(538\) 2.74152 0.118195
\(539\) 0 0
\(540\) 26.0268 1.12002
\(541\) 16.1749i 0.695411i 0.937604 + 0.347706i \(0.113039\pi\)
−0.937604 + 0.347706i \(0.886961\pi\)
\(542\) 28.6002i 1.22848i
\(543\) −60.5326 −2.59770
\(544\) 7.60732i 0.326161i
\(545\) 22.1478 0.948708
\(546\) 0 0
\(547\) 34.0719i 1.45681i 0.685146 + 0.728405i \(0.259738\pi\)
−0.685146 + 0.728405i \(0.740262\pi\)
\(548\) 8.72291 0.372624
\(549\) 38.8141 1.65654
\(550\) −0.436499 + 0.219593i −0.0186124 + 0.00936346i
\(551\) 0.804477i 0.0342719i
\(552\) 7.15399 0.304494
\(553\) 0 0
\(554\) 10.7683 0.457502
\(555\) 10.3979 0.441368
\(556\) −4.09291 −0.173578
\(557\) 25.6864i 1.08837i 0.838966 + 0.544185i \(0.183161\pi\)
−0.838966 + 0.544185i \(0.816839\pi\)
\(558\) −57.9477 −2.45312
\(559\) 2.30834i 0.0976325i
\(560\) 0 0
\(561\) 70.4806 35.4572i 2.97569 1.49700i
\(562\) −19.6289 −0.827996
\(563\) 21.9366 0.924516 0.462258 0.886746i \(-0.347039\pi\)
0.462258 + 0.886746i \(0.347039\pi\)
\(564\) −1.70535 −0.0718082
\(565\) 17.2537i 0.725870i
\(566\) 10.6233i 0.446529i
\(567\) 0 0
\(568\) 7.57488i 0.317835i
\(569\) 2.56697i 0.107613i −0.998551 0.0538065i \(-0.982865\pi\)
0.998551 0.0538065i \(-0.0171354\pi\)
\(570\) 1.24437i 0.0521209i
\(571\) 34.3092i 1.43579i −0.696149 0.717897i \(-0.745105\pi\)
0.696149 0.717897i \(-0.254895\pi\)
\(572\) −2.17524 4.32386i −0.0909512 0.180790i
\(573\) 18.7622i 0.783801i
\(574\) 0 0
\(575\) 0.337049 0.0140559
\(576\) 6.77832 0.282430
\(577\) 20.6988i 0.861701i −0.902423 0.430851i \(-0.858214\pi\)
0.902423 0.430851i \(-0.141786\pi\)
\(578\) 40.8713i 1.70002i
\(579\) −51.9443 −2.15873
\(580\) 9.81020 0.407346
\(581\) 0 0
\(582\) 35.3391i 1.46485i
\(583\) −7.20587 14.3236i −0.298437 0.593222i
\(584\) 9.67644i 0.400414i
\(585\) 21.7911i 0.900950i
\(586\) 0.277651i 0.0114697i
\(587\) 16.0435i 0.662184i 0.943598 + 0.331092i \(0.107417\pi\)
−0.943598 + 0.331092i \(0.892583\pi\)
\(588\) 0 0
\(589\) 1.54433i 0.0636331i
\(590\) 13.6351i 0.561348i
\(591\) 64.5407 2.65485
\(592\) 1.50947 0.0620388
\(593\) 35.4872 1.45728 0.728641 0.684895i \(-0.240152\pi\)
0.728641 + 0.684895i \(0.240152\pi\)
\(594\) −17.6105 35.0055i −0.722568 1.43629i
\(595\) 0 0
\(596\) 18.5917i 0.761547i
\(597\) 2.27023 0.0929144
\(598\) 3.33874i 0.136531i
\(599\) 0.749386 0.0306191 0.0153095 0.999883i \(-0.495127\pi\)
0.0153095 + 0.999883i \(0.495127\pi\)
\(600\) 0.460691 0.0188076
\(601\) 18.5168 0.755317 0.377658 0.925945i \(-0.376729\pi\)
0.377658 + 0.925945i \(0.376729\pi\)
\(602\) 0 0
\(603\) 20.2114 0.823070
\(604\) 13.2045i 0.537283i
\(605\) −19.4566 14.4435i −0.791023 0.587211i
\(606\) 1.61891 0.0657639
\(607\) 36.9910 1.50142 0.750710 0.660632i \(-0.229712\pi\)
0.750710 + 0.660632i \(0.229712\pi\)
\(608\) 0.180645i 0.00732613i
\(609\) 0 0
\(610\) −12.6141 −0.510732
\(611\) 0.795879i 0.0321978i
\(612\) −51.5648 −2.08439
\(613\) 3.22552i 0.130277i 0.997876 + 0.0651387i \(0.0207490\pi\)
−0.997876 + 0.0651387i \(0.979251\pi\)
\(614\) 6.41443i 0.258865i
\(615\) −48.9335 −1.97319
\(616\) 0 0
\(617\) −10.8351 −0.436206 −0.218103 0.975926i \(-0.569987\pi\)
−0.218103 + 0.975926i \(0.569987\pi\)
\(618\) 9.02823i 0.363169i
\(619\) 5.12834i 0.206125i 0.994675 + 0.103063i \(0.0328642\pi\)
−0.994675 + 0.103063i \(0.967136\pi\)
\(620\) 18.8324 0.756325
\(621\) 27.0301i 1.08468i
\(622\) −11.3024 −0.453184
\(623\) 0 0
\(624\) 4.56350i 0.182686i
\(625\) −24.2417 −0.969667
\(626\) 16.4467 0.657341
\(627\) 1.67365 0.841976i 0.0668391 0.0336253i
\(628\) 5.75901i 0.229810i
\(629\) −11.4830 −0.457858
\(630\) 0 0
\(631\) −29.9567 −1.19256 −0.596278 0.802778i \(-0.703354\pi\)
−0.596278 + 0.802778i \(0.703354\pi\)
\(632\) 6.91879 0.275215
\(633\) 32.1702 1.27865
\(634\) 28.1910i 1.11961i
\(635\) 29.6732 1.17755
\(636\) 15.1174i 0.599445i
\(637\) 0 0
\(638\) −6.63786 13.1945i −0.262795 0.522375i
\(639\) 51.3450 2.03118
\(640\) −2.20288 −0.0870764
\(641\) 9.22690 0.364441 0.182220 0.983258i \(-0.441672\pi\)
0.182220 + 0.983258i \(0.441672\pi\)
\(642\) 16.3218i 0.644171i
\(643\) 1.79941i 0.0709616i 0.999370 + 0.0354808i \(0.0112963\pi\)
−0.999370 + 0.0354808i \(0.988704\pi\)
\(644\) 0 0
\(645\) 10.8958i 0.429020i
\(646\) 1.37423i 0.0540682i
\(647\) 40.7244i 1.60104i −0.599306 0.800520i \(-0.704557\pi\)
0.599306 0.800520i \(-0.295443\pi\)
\(648\) 16.6107i 0.652529i
\(649\) −18.3389 + 9.22589i −0.719865 + 0.362148i
\(650\) 0.215002i 0.00843309i
\(651\) 0 0
\(652\) 5.31289 0.208069
\(653\) −37.7384 −1.47682 −0.738408 0.674354i \(-0.764422\pi\)
−0.738408 + 0.674354i \(0.764422\pi\)
\(654\) 31.4393i 1.22937i
\(655\) 5.78171i 0.225910i
\(656\) −7.10368 −0.277352
\(657\) 65.5900 2.55891
\(658\) 0 0
\(659\) 32.5997i 1.26991i 0.772551 + 0.634953i \(0.218981\pi\)
−0.772551 + 0.634953i \(0.781019\pi\)
\(660\) 10.2675 + 20.4093i 0.399661 + 0.794432i
\(661\) 12.6725i 0.492902i 0.969155 + 0.246451i \(0.0792645\pi\)
−0.969155 + 0.246451i \(0.920735\pi\)
\(662\) 19.1126i 0.742832i
\(663\) 34.7160i 1.34826i
\(664\) 5.84246i 0.226731i
\(665\) 0 0
\(666\) 10.2317i 0.396469i
\(667\) 10.1883i 0.394494i
\(668\) 16.0519 0.621067
\(669\) 2.79797 0.108176
\(670\) −6.56846 −0.253762
\(671\) 8.53508 + 16.9657i 0.329493 + 0.654955i
\(672\) 0 0
\(673\) 1.20344i 0.0463893i 0.999731 + 0.0231947i \(0.00738375\pi\)
−0.999731 + 0.0231947i \(0.992616\pi\)
\(674\) −16.0358 −0.617676
\(675\) 1.74064i 0.0669971i
\(676\) 10.8702 0.418086
\(677\) −26.3159 −1.01140 −0.505701 0.862709i \(-0.668766\pi\)
−0.505701 + 0.862709i \(0.668766\pi\)
\(678\) −24.4920 −0.940610
\(679\) 0 0
\(680\) 16.7580 0.642640
\(681\) 42.1673i 1.61586i
\(682\) −12.7425 25.3291i −0.487936 0.969901i
\(683\) 32.9274 1.25993 0.629966 0.776623i \(-0.283069\pi\)
0.629966 + 0.776623i \(0.283069\pi\)
\(684\) −1.22447 −0.0468189
\(685\) 19.2155i 0.734187i
\(686\) 0 0
\(687\) 15.2771 0.582858
\(688\) 1.58174i 0.0603032i
\(689\) −7.05524 −0.268783
\(690\) 15.7594i 0.599949i
\(691\) 28.2336i 1.07406i −0.843565 0.537028i \(-0.819547\pi\)
0.843565 0.537028i \(-0.180453\pi\)
\(692\) 7.09477 0.269703
\(693\) 0 0
\(694\) 9.87094 0.374696
\(695\) 9.01618i 0.342003i
\(696\) 13.9258i 0.527855i
\(697\) 54.0400 2.04691
\(698\) 31.1871i 1.18045i
\(699\) 70.8605 2.68019
\(700\) 0 0
\(701\) 24.2464i 0.915775i 0.889010 + 0.457888i \(0.151394\pi\)
−0.889010 + 0.457888i \(0.848606\pi\)
\(702\) −17.2424 −0.650771
\(703\) −0.272679 −0.0102843
\(704\) 1.49053 + 2.96282i 0.0561765 + 0.111666i
\(705\) 3.75668i 0.141485i
\(706\) −25.9682 −0.977327
\(707\) 0 0
\(708\) 19.3553 0.727416
\(709\) 43.2699 1.62504 0.812518 0.582936i \(-0.198096\pi\)
0.812518 + 0.582936i \(0.198096\pi\)
\(710\) −16.6865 −0.626235
\(711\) 46.8978i 1.75880i
\(712\) 16.1111 0.603791
\(713\) 19.5583i 0.732463i
\(714\) 0 0
\(715\) −9.52494 + 4.79178i −0.356213 + 0.179203i
\(716\) 24.9728 0.933278
\(717\) −78.9293 −2.94767
\(718\) −4.01067 −0.149677
\(719\) 23.0095i 0.858110i −0.903278 0.429055i \(-0.858847\pi\)
0.903278 0.429055i \(-0.141153\pi\)
\(720\) 14.9318i 0.556476i
\(721\) 0 0
\(722\) 18.9674i 0.705892i
\(723\) 43.9876i 1.63592i
\(724\) 19.3579i 0.719429i
\(725\) 0.656091i 0.0243666i
\(726\) 20.5028 27.6190i 0.760931 1.02504i
\(727\) 39.3745i 1.46032i 0.683276 + 0.730160i \(0.260555\pi\)
−0.683276 + 0.730160i \(0.739445\pi\)
\(728\) 0 0
\(729\) −1.75557 −0.0650210
\(730\) −21.3160 −0.788941
\(731\) 12.0328i 0.445048i
\(732\) 17.9060i 0.661826i
\(733\) −8.18529 −0.302331 −0.151165 0.988509i \(-0.548303\pi\)
−0.151165 + 0.988509i \(0.548303\pi\)
\(734\) 19.1851 0.708135
\(735\) 0 0
\(736\) 2.28779i 0.0843291i
\(737\) 4.44441 + 8.83444i 0.163712 + 0.325421i
\(738\) 48.1510i 1.77246i
\(739\) 38.1924i 1.40493i 0.711718 + 0.702466i \(0.247918\pi\)
−0.711718 + 0.702466i \(0.752082\pi\)
\(740\) 3.32518i 0.122236i
\(741\) 0.824375i 0.0302842i
\(742\) 0 0
\(743\) 27.3005i 1.00156i 0.865575 + 0.500779i \(0.166953\pi\)
−0.865575 + 0.500779i \(0.833047\pi\)
\(744\) 26.7329i 0.980076i
\(745\) 40.9553 1.50049
\(746\) 21.0289 0.769924
\(747\) 39.6021 1.44896
\(748\) −11.3389 22.5391i −0.414592 0.824112i
\(749\) 0 0
\(750\) 35.4572i 1.29471i
\(751\) −2.23167 −0.0814349 −0.0407175 0.999171i \(-0.512964\pi\)
−0.0407175 + 0.999171i \(0.512964\pi\)
\(752\) 0.545357i 0.0198871i
\(753\) −9.49742 −0.346105
\(754\) −6.49910 −0.236683
\(755\) −29.0879 −1.05862
\(756\) 0 0
\(757\) −16.6709 −0.605913 −0.302956 0.953004i \(-0.597974\pi\)
−0.302956 + 0.953004i \(0.597974\pi\)
\(758\) 20.7525i 0.753766i
\(759\) −21.1960 + 10.6632i −0.769367 + 0.387051i
\(760\) 0.397940 0.0144348
\(761\) 45.6321 1.65416 0.827081 0.562083i \(-0.190000\pi\)
0.827081 + 0.562083i \(0.190000\pi\)
\(762\) 42.1218i 1.52591i
\(763\) 0 0
\(764\) −6.00000 −0.217072
\(765\) 113.591i 4.10689i
\(766\) 1.25606 0.0453832
\(767\) 9.03303i 0.326164i
\(768\) 3.12703i 0.112837i
\(769\) −51.3570 −1.85198 −0.925991 0.377546i \(-0.876768\pi\)
−0.925991 + 0.377546i \(0.876768\pi\)
\(770\) 0 0
\(771\) −80.5784 −2.90196
\(772\) 16.6114i 0.597857i
\(773\) 21.8478i 0.785812i −0.919579 0.392906i \(-0.871470\pi\)
0.919579 0.392906i \(-0.128530\pi\)
\(774\) −10.7215 −0.385377
\(775\) 1.25948i 0.0452418i
\(776\) −11.3012 −0.405688
\(777\) 0 0
\(778\) 16.6479i 0.596854i
\(779\) 1.28325 0.0459771
\(780\) 10.0528 0.359949
\(781\) 11.2906 + 22.4430i 0.404009 + 0.803075i
\(782\) 17.4040i 0.622364i
\(783\) −52.6160 −1.88034
\(784\) 0 0
\(785\) −12.6864 −0.452797
\(786\) 8.20726 0.292743
\(787\) 20.4402 0.728613 0.364307 0.931279i \(-0.381306\pi\)
0.364307 + 0.931279i \(0.381306\pi\)
\(788\) 20.6396i 0.735256i
\(789\) 20.0443 0.713597
\(790\) 15.2412i 0.542259i
\(791\) 0 0
\(792\) −20.0830 + 10.1033i −0.713617 + 0.359005i