Properties

Label 3150.2.bf.b.1151.3
Level 3150
Weight 2
Character 3150.1151
Analytic conductor 25.153
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 3150.bf (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(25.1528766367\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 630)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.3
Root \(-0.965926 + 0.258819i\)
Character \(\chi\) = 3150.1151
Dual form 3150.2.bf.b.1601.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.189469 - 2.63896i) q^{7} -1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.189469 - 2.63896i) q^{7} -1.00000i q^{8} +(-2.55171 - 1.47323i) q^{11} -3.93185i q^{13} +(-1.48356 - 2.19067i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.199801 + 0.346065i) q^{17} +(0.0305501 - 0.0176381i) q^{19} -2.94646 q^{22} +(3.23205 - 1.86603i) q^{23} +(-1.96593 - 3.40508i) q^{26} +(-2.38014 - 1.15539i) q^{28} +8.89898i q^{29} +(0.717439 + 0.414214i) q^{31} +(-0.866025 - 0.500000i) q^{32} +0.399602i q^{34} +(-3.96593 - 6.86919i) q^{37} +(0.0176381 - 0.0305501i) q^{38} -6.31079 q^{41} +3.03528 q^{43} +(-2.55171 + 1.47323i) q^{44} +(1.86603 - 3.23205i) q^{46} +(-2.90130 - 5.02520i) q^{47} +(-6.92820 + 1.00000i) q^{49} +(-3.40508 - 1.96593i) q^{52} +(-3.72268 - 2.14929i) q^{53} +(-2.63896 + 0.189469i) q^{56} +(4.44949 + 7.70674i) q^{58} +(-2.78522 + 4.82415i) q^{59} +(-9.97710 + 5.76028i) q^{61} +0.828427 q^{62} -1.00000 q^{64} +(-6.25966 + 10.8420i) q^{67} +(0.199801 + 0.346065i) q^{68} +1.93426i q^{71} +(0.297173 + 0.171573i) q^{73} +(-6.86919 - 3.96593i) q^{74} -0.0352762i q^{76} +(-3.40433 + 7.01299i) q^{77} +(-4.15331 - 7.19375i) q^{79} +(-5.46530 + 3.15539i) q^{82} +10.3490 q^{83} +(2.62863 - 1.51764i) q^{86} +(-1.47323 + 2.55171i) q^{88} +(3.08604 + 5.34519i) q^{89} +(-10.3760 + 0.744963i) q^{91} -3.73205i q^{92} +(-5.02520 - 2.90130i) q^{94} -15.6344i q^{97} +(-5.50000 + 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + O(q^{10}) \) \( 8q + 4q^{4} - 24q^{11} - 4q^{16} + 12q^{23} - 8q^{26} - 24q^{37} - 4q^{38} - 32q^{41} + 16q^{43} - 24q^{44} + 8q^{46} - 8q^{47} + 24q^{53} + 16q^{58} + 24q^{59} - 16q^{62} - 8q^{64} + 24q^{67} - 16q^{77} - 24q^{79} - 16q^{83} + 16q^{89} - 20q^{91} - 12q^{94} - 44q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0 0
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −0.189469 2.63896i −0.0716124 0.997433i
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0 0
\(11\) −2.55171 1.47323i −0.769370 0.444196i 0.0632797 0.997996i \(-0.479844\pi\)
−0.832650 + 0.553800i \(0.813177\pi\)
\(12\) 0 0
\(13\) 3.93185i 1.09050i −0.838274 0.545250i \(-0.816435\pi\)
0.838274 0.545250i \(-0.183565\pi\)
\(14\) −1.48356 2.19067i −0.396499 0.585481i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −0.199801 + 0.346065i −0.0484588 + 0.0839331i −0.889237 0.457446i \(-0.848764\pi\)
0.840779 + 0.541379i \(0.182098\pi\)
\(18\) 0 0
\(19\) 0.0305501 0.0176381i 0.00700867 0.00404646i −0.496492 0.868042i \(-0.665379\pi\)
0.503500 + 0.863995i \(0.332045\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.94646 −0.628188
\(23\) 3.23205 1.86603i 0.673929 0.389093i −0.123635 0.992328i \(-0.539455\pi\)
0.797564 + 0.603235i \(0.206122\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.96593 3.40508i −0.385550 0.667792i
\(27\) 0 0
\(28\) −2.38014 1.15539i −0.449804 0.218349i
\(29\) 8.89898i 1.65250i 0.563304 + 0.826250i \(0.309530\pi\)
−0.563304 + 0.826250i \(0.690470\pi\)
\(30\) 0 0
\(31\) 0.717439 + 0.414214i 0.128856 + 0.0743950i 0.563042 0.826428i \(-0.309631\pi\)
−0.434187 + 0.900823i \(0.642964\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) 0 0
\(34\) 0.399602i 0.0685311i
\(35\) 0 0
\(36\) 0 0
\(37\) −3.96593 6.86919i −0.651994 1.12929i −0.982638 0.185532i \(-0.940599\pi\)
0.330644 0.943756i \(-0.392734\pi\)
\(38\) 0.0176381 0.0305501i 0.00286128 0.00495588i
\(39\) 0 0
\(40\) 0 0
\(41\) −6.31079 −0.985580 −0.492790 0.870148i \(-0.664023\pi\)
−0.492790 + 0.870148i \(0.664023\pi\)
\(42\) 0 0
\(43\) 3.03528 0.462875 0.231438 0.972850i \(-0.425657\pi\)
0.231438 + 0.972850i \(0.425657\pi\)
\(44\) −2.55171 + 1.47323i −0.384685 + 0.222098i
\(45\) 0 0
\(46\) 1.86603 3.23205i 0.275130 0.476540i
\(47\) −2.90130 5.02520i −0.423198 0.733001i 0.573052 0.819519i \(-0.305759\pi\)
−0.996250 + 0.0865180i \(0.972426\pi\)
\(48\) 0 0
\(49\) −6.92820 + 1.00000i −0.989743 + 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −3.40508 1.96593i −0.472200 0.272625i
\(53\) −3.72268 2.14929i −0.511349 0.295228i 0.222039 0.975038i \(-0.428729\pi\)
−0.733388 + 0.679810i \(0.762062\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.63896 + 0.189469i −0.352646 + 0.0253188i
\(57\) 0 0
\(58\) 4.44949 + 7.70674i 0.584247 + 1.01194i
\(59\) −2.78522 + 4.82415i −0.362605 + 0.628050i −0.988389 0.151946i \(-0.951446\pi\)
0.625784 + 0.779997i \(0.284779\pi\)
\(60\) 0 0
\(61\) −9.97710 + 5.76028i −1.27744 + 0.737528i −0.976376 0.216077i \(-0.930674\pi\)
−0.301060 + 0.953605i \(0.597340\pi\)
\(62\) 0.828427 0.105210
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −6.25966 + 10.8420i −0.764739 + 1.32457i 0.175646 + 0.984453i \(0.443799\pi\)
−0.940385 + 0.340113i \(0.889535\pi\)
\(68\) 0.199801 + 0.346065i 0.0242294 + 0.0419666i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.93426i 0.229554i 0.993391 + 0.114777i \(0.0366153\pi\)
−0.993391 + 0.114777i \(0.963385\pi\)
\(72\) 0 0
\(73\) 0.297173 + 0.171573i 0.0347815 + 0.0200811i 0.517290 0.855810i \(-0.326941\pi\)
−0.482508 + 0.875891i \(0.660274\pi\)
\(74\) −6.86919 3.96593i −0.798527 0.461030i
\(75\) 0 0
\(76\) 0.0352762i 0.00404646i
\(77\) −3.40433 + 7.01299i −0.387959 + 0.799205i
\(78\) 0 0
\(79\) −4.15331 7.19375i −0.467284 0.809360i 0.532017 0.846734i \(-0.321434\pi\)
−0.999301 + 0.0373736i \(0.988101\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −5.46530 + 3.15539i −0.603542 + 0.348455i
\(83\) 10.3490 1.13595 0.567974 0.823046i \(-0.307727\pi\)
0.567974 + 0.823046i \(0.307727\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2.62863 1.51764i 0.283452 0.163651i
\(87\) 0 0
\(88\) −1.47323 + 2.55171i −0.157047 + 0.272013i
\(89\) 3.08604 + 5.34519i 0.327120 + 0.566589i 0.981939 0.189197i \(-0.0605885\pi\)
−0.654819 + 0.755786i \(0.727255\pi\)
\(90\) 0 0
\(91\) −10.3760 + 0.744963i −1.08770 + 0.0780933i
\(92\) 3.73205i 0.389093i
\(93\) 0 0
\(94\) −5.02520 2.90130i −0.518310 0.299246i
\(95\) 0 0
\(96\) 0 0
\(97\) 15.6344i 1.58744i −0.608286 0.793718i \(-0.708143\pi\)
0.608286 0.793718i \(-0.291857\pi\)
\(98\) −5.50000 + 4.33013i −0.555584 + 0.437409i
\(99\) 0 0
\(100\) 0 0
\(101\) 9.02458 15.6310i 0.897979 1.55535i 0.0679057 0.997692i \(-0.478368\pi\)
0.830074 0.557654i \(-0.188298\pi\)
\(102\) 0 0
\(103\) 7.37857 4.26002i 0.727032 0.419752i −0.0903031 0.995914i \(-0.528784\pi\)
0.817336 + 0.576162i \(0.195450\pi\)
\(104\) −3.93185 −0.385550
\(105\) 0 0
\(106\) −4.29858 −0.417515
\(107\) −14.7702 + 8.52761i −1.42789 + 0.824395i −0.996954 0.0779862i \(-0.975151\pi\)
−0.430939 + 0.902381i \(0.641818\pi\)
\(108\) 0 0
\(109\) 5.84909 10.1309i 0.560241 0.970366i −0.437234 0.899348i \(-0.644042\pi\)
0.997475 0.0710185i \(-0.0226249\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −2.19067 + 1.48356i −0.206999 + 0.140184i
\(113\) 13.5546i 1.27511i −0.770405 0.637554i \(-0.779946\pi\)
0.770405 0.637554i \(-0.220054\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 7.70674 + 4.44949i 0.715553 + 0.413125i
\(117\) 0 0
\(118\) 5.57045i 0.512801i
\(119\) 0.951108 + 0.461698i 0.0871879 + 0.0423237i
\(120\) 0 0
\(121\) −1.15918 2.00775i −0.105380 0.182523i
\(122\) −5.76028 + 9.97710i −0.521511 + 0.903284i
\(123\) 0 0
\(124\) 0.717439 0.414214i 0.0644279 0.0371975i
\(125\) 0 0
\(126\) 0 0
\(127\) −8.95983 −0.795056 −0.397528 0.917590i \(-0.630132\pi\)
−0.397528 + 0.917590i \(0.630132\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 0 0
\(130\) 0 0
\(131\) 6.39047 + 11.0686i 0.558338 + 0.967070i 0.997635 + 0.0687282i \(0.0218941\pi\)
−0.439297 + 0.898342i \(0.644773\pi\)
\(132\) 0 0
\(133\) −0.0523345 0.0772785i −0.00453797 0.00670090i
\(134\) 12.5193i 1.08150i
\(135\) 0 0
\(136\) 0.346065 + 0.199801i 0.0296748 + 0.0171328i
\(137\) −4.78094 2.76028i −0.408464 0.235827i 0.281666 0.959513i \(-0.409113\pi\)
−0.690129 + 0.723686i \(0.742446\pi\)
\(138\) 0 0
\(139\) 21.8471i 1.85305i −0.376235 0.926524i \(-0.622782\pi\)
0.376235 0.926524i \(-0.377218\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.967128 + 1.67511i 0.0811596 + 0.140572i
\(143\) −5.79253 + 10.0330i −0.484396 + 0.838998i
\(144\) 0 0
\(145\) 0 0
\(146\) 0.343146 0.0283989
\(147\) 0 0
\(148\) −7.93185 −0.651994
\(149\) 18.6179 10.7491i 1.52524 0.880598i 0.525688 0.850677i \(-0.323808\pi\)
0.999552 0.0299204i \(-0.00952537\pi\)
\(150\) 0 0
\(151\) −1.47531 + 2.55532i −0.120059 + 0.207949i −0.919791 0.392409i \(-0.871642\pi\)
0.799732 + 0.600358i \(0.204975\pi\)
\(152\) −0.0176381 0.0305501i −0.00143064 0.00247794i
\(153\) 0 0
\(154\) 0.558263 + 7.77559i 0.0449861 + 0.626575i
\(155\) 0 0
\(156\) 0 0
\(157\) −19.4823 11.2481i −1.55486 0.897698i −0.997735 0.0672682i \(-0.978572\pi\)
−0.557123 0.830430i \(-0.688095\pi\)
\(158\) −7.19375 4.15331i −0.572304 0.330420i
\(159\) 0 0
\(160\) 0 0
\(161\) −5.53674 8.17569i −0.436356 0.644335i
\(162\) 0 0
\(163\) 11.4035 + 19.7515i 0.893192 + 1.54705i 0.836026 + 0.548690i \(0.184873\pi\)
0.0571664 + 0.998365i \(0.481793\pi\)
\(164\) −3.15539 + 5.46530i −0.246395 + 0.426769i
\(165\) 0 0
\(166\) 8.96248 5.17449i 0.695624 0.401618i
\(167\) 8.84961 0.684803 0.342402 0.939554i \(-0.388760\pi\)
0.342402 + 0.939554i \(0.388760\pi\)
\(168\) 0 0
\(169\) −2.45946 −0.189189
\(170\) 0 0
\(171\) 0 0
\(172\) 1.51764 2.62863i 0.115719 0.200431i
\(173\) 3.86843 + 6.70032i 0.294111 + 0.509416i 0.974778 0.223178i \(-0.0716430\pi\)
−0.680667 + 0.732593i \(0.738310\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.94646i 0.222098i
\(177\) 0 0
\(178\) 5.34519 + 3.08604i 0.400639 + 0.231309i
\(179\) 0.417291 + 0.240923i 0.0311898 + 0.0180074i 0.515514 0.856881i \(-0.327601\pi\)
−0.484324 + 0.874889i \(0.660934\pi\)
\(180\) 0 0
\(181\) 2.44876i 0.182015i −0.995850 0.0910075i \(-0.970991\pi\)
0.995850 0.0910075i \(-0.0290087\pi\)
\(182\) −8.61339 + 5.83315i −0.638467 + 0.432382i
\(183\) 0 0
\(184\) −1.86603 3.23205i −0.137565 0.238270i
\(185\) 0 0
\(186\) 0 0
\(187\) 1.01967 0.588706i 0.0745655 0.0430504i
\(188\) −5.80260 −0.423198
\(189\) 0 0
\(190\) 0 0
\(191\) −3.89241 + 2.24728i −0.281645 + 0.162608i −0.634168 0.773195i \(-0.718657\pi\)
0.352523 + 0.935803i \(0.385324\pi\)
\(192\) 0 0
\(193\) −6.28497 + 10.8859i −0.452402 + 0.783583i −0.998535 0.0541158i \(-0.982766\pi\)
0.546133 + 0.837698i \(0.316099\pi\)
\(194\) −7.81722 13.5398i −0.561243 0.972102i
\(195\) 0 0
\(196\) −2.59808 + 6.50000i −0.185577 + 0.464286i
\(197\) 13.3748i 0.952916i 0.879197 + 0.476458i \(0.158080\pi\)
−0.879197 + 0.476458i \(0.841920\pi\)
\(198\) 0 0
\(199\) −23.5169 13.5775i −1.66707 0.962483i −0.969206 0.246253i \(-0.920801\pi\)
−0.697864 0.716231i \(-0.745866\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 18.0492i 1.26993i
\(203\) 23.4840 1.68608i 1.64826 0.118339i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.26002 7.37857i 0.296810 0.514090i
\(207\) 0 0
\(208\) −3.40508 + 1.96593i −0.236100 + 0.136312i
\(209\) −0.103940 −0.00718968
\(210\) 0 0
\(211\) 18.4183 1.26797 0.633984 0.773346i \(-0.281419\pi\)
0.633984 + 0.773346i \(0.281419\pi\)
\(212\) −3.72268 + 2.14929i −0.255675 + 0.147614i
\(213\) 0 0
\(214\) −8.52761 + 14.7702i −0.582935 + 1.00967i
\(215\) 0 0
\(216\) 0 0
\(217\) 0.957160 1.97177i 0.0649763 0.133853i
\(218\) 11.6982i 0.792301i
\(219\) 0 0
\(220\) 0 0
\(221\) 1.36068 + 0.785587i 0.0915290 + 0.0528443i
\(222\) 0 0
\(223\) 17.8045i 1.19228i −0.802881 0.596140i \(-0.796700\pi\)
0.802881 0.596140i \(-0.203300\pi\)
\(224\) −1.15539 + 2.38014i −0.0771980 + 0.159030i
\(225\) 0 0
\(226\) −6.77729 11.7386i −0.450819 0.780841i
\(227\) 0.856140 1.48288i 0.0568240 0.0984220i −0.836214 0.548403i \(-0.815236\pi\)
0.893038 + 0.449981i \(0.148569\pi\)
\(228\) 0 0
\(229\) 5.26142 3.03768i 0.347684 0.200736i −0.315981 0.948766i \(-0.602333\pi\)
0.663665 + 0.748030i \(0.269000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.89898 0.584247
\(233\) −6.17109 + 3.56288i −0.404282 + 0.233412i −0.688330 0.725398i \(-0.741656\pi\)
0.284048 + 0.958810i \(0.408322\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 2.78522 + 4.82415i 0.181303 + 0.314025i
\(237\) 0 0
\(238\) 1.05453 0.0757120i 0.0683552 0.00490768i
\(239\) 18.7194i 1.21085i 0.795900 + 0.605427i \(0.206998\pi\)
−0.795900 + 0.605427i \(0.793002\pi\)
\(240\) 0 0
\(241\) 7.68036 + 4.43426i 0.494735 + 0.285636i 0.726537 0.687128i \(-0.241129\pi\)
−0.231802 + 0.972763i \(0.574462\pi\)
\(242\) −2.00775 1.15918i −0.129063 0.0745147i
\(243\) 0 0
\(244\) 11.5206i 0.737528i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.0693504 0.120118i −0.00441266 0.00764295i
\(248\) 0.414214 0.717439i 0.0263026 0.0455574i
\(249\) 0 0
\(250\) 0 0
\(251\) −22.1738 −1.39960 −0.699798 0.714341i \(-0.746727\pi\)
−0.699798 + 0.714341i \(0.746727\pi\)
\(252\) 0 0
\(253\) −10.9964 −0.691335
\(254\) −7.75944 + 4.47992i −0.486871 + 0.281095i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −8.41662 14.5780i −0.525014 0.909351i −0.999576 0.0291289i \(-0.990727\pi\)
0.474561 0.880222i \(-0.342607\pi\)
\(258\) 0 0
\(259\) −17.3761 + 11.7674i −1.07970 + 0.731191i
\(260\) 0 0
\(261\) 0 0
\(262\) 11.0686 + 6.39047i 0.683822 + 0.394805i
\(263\) 19.1562 + 11.0599i 1.18122 + 0.681980i 0.956297 0.292396i \(-0.0944525\pi\)
0.224926 + 0.974376i \(0.427786\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.0839622 0.0407579i −0.00514805 0.00249903i
\(267\) 0 0
\(268\) 6.25966 + 10.8420i 0.382369 + 0.662283i
\(269\) −1.45049 + 2.51231i −0.0884377 + 0.153179i −0.906851 0.421452i \(-0.861521\pi\)
0.818413 + 0.574630i \(0.194854\pi\)
\(270\) 0 0
\(271\) 15.1244 8.73205i 0.918739 0.530434i 0.0355066 0.999369i \(-0.488696\pi\)
0.883233 + 0.468935i \(0.155362\pi\)
\(272\) 0.399602 0.0242294
\(273\) 0 0
\(274\) −5.52056 −0.333509
\(275\) 0 0
\(276\) 0 0
\(277\) 2.28825 3.96336i 0.137488 0.238135i −0.789057 0.614319i \(-0.789431\pi\)
0.926545 + 0.376184i \(0.122764\pi\)
\(278\) −10.9236 18.9202i −0.655152 1.13476i
\(279\) 0 0
\(280\) 0 0
\(281\) 9.55948i 0.570271i 0.958487 + 0.285135i \(0.0920386\pi\)
−0.958487 + 0.285135i \(0.907961\pi\)
\(282\) 0 0
\(283\) −9.46238 5.46311i −0.562480 0.324748i 0.191660 0.981461i \(-0.438613\pi\)
−0.754140 + 0.656713i \(0.771946\pi\)
\(284\) 1.67511 + 0.967128i 0.0993998 + 0.0573885i
\(285\) 0 0
\(286\) 11.5851i 0.685039i
\(287\) 1.19570 + 16.6539i 0.0705798 + 0.983049i
\(288\) 0 0
\(289\) 8.42016 + 14.5841i 0.495303 + 0.857891i
\(290\) 0 0
\(291\) 0 0
\(292\) 0.297173 0.171573i 0.0173907 0.0100405i
\(293\) 16.2280 0.948052 0.474026 0.880511i \(-0.342800\pi\)
0.474026 + 0.880511i \(0.342800\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −6.86919 + 3.96593i −0.399263 + 0.230515i
\(297\) 0 0
\(298\) 10.7491 18.6179i 0.622677 1.07851i
\(299\) −7.33694 12.7079i −0.424306 0.734919i
\(300\) 0 0
\(301\) −0.575090 8.00997i −0.0331476 0.461687i
\(302\) 2.95063i 0.169790i
\(303\) 0 0
\(304\) −0.0305501 0.0176381i −0.00175217 0.00101161i
\(305\) 0 0
\(306\) 0 0
\(307\) 12.3782i 0.706462i −0.935536 0.353231i \(-0.885083\pi\)
0.935536 0.353231i \(-0.114917\pi\)
\(308\) 4.37127 + 6.45473i 0.249076 + 0.367792i
\(309\) 0 0
\(310\) 0 0
\(311\) −11.4312 + 19.7995i −0.648206 + 1.12272i 0.335346 + 0.942095i \(0.391147\pi\)
−0.983551 + 0.180630i \(0.942186\pi\)
\(312\) 0 0
\(313\) 30.1399 17.4013i 1.70361 0.983578i 0.761563 0.648091i \(-0.224432\pi\)
0.942045 0.335487i \(-0.108901\pi\)
\(314\) −22.4962 −1.26954
\(315\) 0 0
\(316\) −8.30663 −0.467284
\(317\) 5.87780 3.39355i 0.330130 0.190601i −0.325769 0.945449i \(-0.605623\pi\)
0.655899 + 0.754849i \(0.272290\pi\)
\(318\) 0 0
\(319\) 13.1103 22.7076i 0.734034 1.27138i
\(320\) 0 0
\(321\) 0 0
\(322\) −8.88280 4.31199i −0.495019 0.240298i
\(323\) 0.0140964i 0.000784346i
\(324\) 0 0
\(325\) 0 0
\(326\) 19.7515 + 11.4035i 1.09393 + 0.631582i
\(327\) 0 0
\(328\) 6.31079i 0.348455i
\(329\) −12.7116 + 8.60853i −0.700813 + 0.474604i
\(330\) 0 0
\(331\) −5.56985 9.64726i −0.306147 0.530261i 0.671369 0.741123i \(-0.265706\pi\)
−0.977516 + 0.210862i \(0.932373\pi\)
\(332\) 5.17449 8.96248i 0.283987 0.491880i
\(333\) 0 0
\(334\) 7.66398 4.42480i 0.419355 0.242114i
\(335\) 0 0
\(336\) 0 0
\(337\) −1.59111 −0.0866733 −0.0433366 0.999061i \(-0.513799\pi\)
−0.0433366 + 0.999061i \(0.513799\pi\)
\(338\) −2.12995 + 1.22973i −0.115854 + 0.0668884i
\(339\) 0 0
\(340\) 0 0
\(341\) −1.22047 2.11391i −0.0660919 0.114475i
\(342\) 0 0
\(343\) 3.95164 + 18.0938i 0.213368 + 0.976972i
\(344\) 3.03528i 0.163651i
\(345\) 0 0
\(346\) 6.70032 + 3.86843i 0.360211 + 0.207968i
\(347\) 13.3860 + 7.72840i 0.718597 + 0.414882i 0.814236 0.580534i \(-0.197156\pi\)
−0.0956388 + 0.995416i \(0.530489\pi\)
\(348\) 0 0
\(349\) 0.585057i 0.0313174i −0.999877 0.0156587i \(-0.995015\pi\)
0.999877 0.0156587i \(-0.00498452\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.47323 + 2.55171i 0.0785235 + 0.136007i
\(353\) −1.83788 + 3.18330i −0.0978204 + 0.169430i −0.910782 0.412887i \(-0.864520\pi\)
0.812962 + 0.582317i \(0.197854\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.17209 0.327120
\(357\) 0 0
\(358\) 0.481846 0.0254664
\(359\) 17.4069 10.0499i 0.918702 0.530413i 0.0354812 0.999370i \(-0.488704\pi\)
0.883221 + 0.468958i \(0.155370\pi\)
\(360\) 0 0
\(361\) −9.49938 + 16.4534i −0.499967 + 0.865969i
\(362\) −1.22438 2.12069i −0.0643520 0.111461i
\(363\) 0 0
\(364\) −4.54284 + 9.35835i −0.238110 + 0.490511i
\(365\) 0 0
\(366\) 0 0
\(367\) 17.2665 + 9.96885i 0.901306 + 0.520369i 0.877624 0.479350i \(-0.159128\pi\)
0.0236826 + 0.999720i \(0.492461\pi\)
\(368\) −3.23205 1.86603i −0.168482 0.0972733i
\(369\) 0 0
\(370\) 0 0
\(371\) −4.96656 + 10.2312i −0.257851 + 0.531179i
\(372\) 0 0
\(373\) −16.9081 29.2856i −0.875467 1.51635i −0.856265 0.516537i \(-0.827221\pi\)
−0.0192016 0.999816i \(-0.506112\pi\)
\(374\) 0.588706 1.01967i 0.0304413 0.0527258i
\(375\) 0 0
\(376\) −5.02520 + 2.90130i −0.259155 + 0.149623i
\(377\) 34.9895 1.80205
\(378\) 0 0
\(379\) 26.7614 1.37464 0.687321 0.726353i \(-0.258786\pi\)
0.687321 + 0.726353i \(0.258786\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −2.24728 + 3.89241i −0.114981 + 0.199153i
\(383\) −9.89060 17.1310i −0.505386 0.875355i −0.999981 0.00623078i \(-0.998017\pi\)
0.494594 0.869124i \(-0.335317\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 12.5699i 0.639793i
\(387\) 0 0
\(388\) −13.5398 7.81722i −0.687380 0.396859i
\(389\) −4.49181 2.59335i −0.227744 0.131488i 0.381787 0.924250i \(-0.375309\pi\)
−0.609531 + 0.792762i \(0.708642\pi\)
\(390\) 0 0
\(391\) 1.49133i 0.0754200i
\(392\) 1.00000 + 6.92820i 0.0505076 + 0.349927i
\(393\) 0 0
\(394\) 6.68740 + 11.5829i 0.336907 + 0.583539i
\(395\) 0 0
\(396\) 0 0
\(397\) −4.99280 + 2.88259i −0.250581 + 0.144673i −0.620030 0.784578i \(-0.712880\pi\)
0.369449 + 0.929251i \(0.379546\pi\)
\(398\) −27.1550 −1.36116
\(399\) 0 0
\(400\) 0 0
\(401\) 15.4361 8.91202i 0.770841 0.445045i −0.0623335 0.998055i \(-0.519854\pi\)
0.833175 + 0.553010i \(0.186521\pi\)
\(402\) 0 0
\(403\) 1.62863 2.82086i 0.0811277 0.140517i
\(404\) −9.02458 15.6310i −0.448990 0.777673i
\(405\) 0 0
\(406\) 19.4947 13.2022i 0.967507 0.655214i
\(407\) 23.3709i 1.15845i
\(408\) 0 0
\(409\) −28.5617 16.4901i −1.41228 0.815382i −0.416681 0.909053i \(-0.636807\pi\)
−0.995603 + 0.0936705i \(0.970140\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 8.52004i 0.419752i
\(413\) 13.2584 + 6.43606i 0.652405 + 0.316698i
\(414\) 0 0
\(415\) 0 0
\(416\) −1.96593 + 3.40508i −0.0963874 + 0.166948i
\(417\) 0 0
\(418\) −0.0900147 + 0.0519700i −0.00440276 + 0.00254194i
\(419\) 15.2287 0.743969 0.371985 0.928239i \(-0.378677\pi\)
0.371985 + 0.928239i \(0.378677\pi\)
\(420\) 0 0
\(421\) 16.9939 0.828234 0.414117 0.910224i \(-0.364090\pi\)
0.414117 + 0.910224i \(0.364090\pi\)
\(422\) 15.9507 9.20915i 0.776468 0.448294i
\(423\) 0 0
\(424\) −2.14929 + 3.72268i −0.104379 + 0.180789i
\(425\) 0 0
\(426\) 0 0
\(427\) 17.0915 + 25.2377i 0.827115 + 1.22134i
\(428\) 17.0552i 0.824395i
\(429\) 0 0
\(430\) 0 0
\(431\) −15.4818 8.93842i −0.745732 0.430549i 0.0784178 0.996921i \(-0.475013\pi\)
−0.824150 + 0.566372i \(0.808347\pi\)
\(432\) 0 0
\(433\) 5.56388i 0.267383i −0.991023 0.133691i \(-0.957317\pi\)
0.991023 0.133691i \(-0.0426831\pi\)
\(434\) −0.156961 2.18618i −0.00753437 0.104940i
\(435\) 0 0
\(436\) −5.84909 10.1309i −0.280121 0.485183i
\(437\) 0.0658262 0.114014i 0.00314890 0.00545405i
\(438\) 0 0
\(439\) 9.53568 5.50543i 0.455113 0.262760i −0.254874 0.966974i \(-0.582034\pi\)
0.709987 + 0.704214i \(0.248701\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 1.57117 0.0747332
\(443\) 14.7091 8.49233i 0.698853 0.403483i −0.108067 0.994144i \(-0.534466\pi\)
0.806920 + 0.590661i \(0.201133\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −8.90226 15.4192i −0.421534 0.730119i
\(447\) 0 0
\(448\) 0.189469 + 2.63896i 0.00895155 + 0.124679i
\(449\) 12.5892i 0.594122i 0.954858 + 0.297061i \(0.0960065\pi\)
−0.954858 + 0.297061i \(0.903994\pi\)
\(450\) 0 0
\(451\) 16.1033 + 9.29725i 0.758276 + 0.437791i
\(452\) −11.7386 6.77729i −0.552138 0.318777i
\(453\) 0 0
\(454\) 1.71228i 0.0803612i
\(455\) 0 0
\(456\) 0 0
\(457\) −1.08417 1.87783i −0.0507153 0.0878414i 0.839553 0.543277i \(-0.182817\pi\)
−0.890269 + 0.455436i \(0.849483\pi\)
\(458\) 3.03768 5.26142i 0.141941 0.245850i
\(459\) 0 0
\(460\) 0 0
\(461\) 34.3032 1.59766 0.798829 0.601558i \(-0.205453\pi\)
0.798829 + 0.601558i \(0.205453\pi\)
\(462\) 0 0
\(463\) −28.2133 −1.31118 −0.655592 0.755115i \(-0.727581\pi\)
−0.655592 + 0.755115i \(0.727581\pi\)
\(464\) 7.70674 4.44949i 0.357777 0.206562i
\(465\) 0 0
\(466\) −3.56288 + 6.17109i −0.165047 + 0.285870i
\(467\) 2.10342 + 3.64324i 0.0973349 + 0.168589i 0.910581 0.413331i \(-0.135635\pi\)
−0.813246 + 0.581920i \(0.802302\pi\)
\(468\) 0 0
\(469\) 29.7977 + 14.4647i 1.37593 + 0.667920i
\(470\) 0 0
\(471\) 0 0
\(472\) 4.82415 + 2.78522i 0.222049 + 0.128200i
\(473\) −7.74515 4.47167i −0.356122 0.205607i
\(474\) 0 0
\(475\) 0 0
\(476\) 0.875396 0.592835i 0.0401237 0.0271725i
\(477\) 0 0
\(478\) 9.35968 + 16.2114i 0.428102 + 0.741494i
\(479\) 7.35968 12.7473i 0.336272 0.582441i −0.647456 0.762103i \(-0.724167\pi\)
0.983728 + 0.179662i \(0.0575004\pi\)
\(480\) 0 0
\(481\) −27.0086 + 15.5934i −1.23149 + 0.710999i
\(482\) 8.86851 0.403950
\(483\) 0 0
\(484\) −2.31835 −0.105380
\(485\) 0 0
\(486\) 0 0
\(487\) −0.938784 + 1.62602i −0.0425404 + 0.0736821i −0.886512 0.462706i \(-0.846878\pi\)
0.843971 + 0.536388i \(0.180212\pi\)
\(488\) 5.76028 + 9.97710i 0.260756 + 0.451642i
\(489\) 0 0
\(490\) 0 0
\(491\) 10.4281i 0.470613i 0.971921 + 0.235307i \(0.0756095\pi\)
−0.971921 + 0.235307i \(0.924391\pi\)
\(492\) 0 0
\(493\) −3.07963 1.77802i −0.138699 0.0800782i
\(494\) −0.120118 0.0693504i −0.00540438 0.00312022i
\(495\) 0 0
\(496\) 0.828427i 0.0371975i
\(497\) 5.10442 0.366481i 0.228965 0.0164389i
\(498\) 0 0
\(499\) 18.8822 + 32.7050i 0.845285 + 1.46408i 0.885374 + 0.464880i \(0.153903\pi\)
−0.0400890 + 0.999196i \(0.512764\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −19.2030 + 11.0869i −0.857074 + 0.494832i
\(503\) −35.8895 −1.60023 −0.800116 0.599845i \(-0.795229\pi\)
−0.800116 + 0.599845i \(0.795229\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −9.52312 + 5.49818i −0.423354 + 0.244424i
\(507\) 0 0
\(508\) −4.47992 + 7.75944i −0.198764 + 0.344270i
\(509\) −8.58746 14.8739i −0.380633 0.659275i 0.610520 0.792001i \(-0.290960\pi\)
−0.991153 + 0.132726i \(0.957627\pi\)
\(510\) 0 0
\(511\) 0.396469 0.816735i 0.0175387 0.0361302i
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −14.5780 8.41662i −0.643008 0.371241i
\(515\) 0 0
\(516\) 0 0
\(517\) 17.0972i 0.751932i
\(518\) −9.16442 + 18.8789i −0.402661 + 0.829492i
\(519\) 0 0
\(520\) 0 0
\(521\) −2.26539 + 3.92377i −0.0992484 + 0.171903i −0.911374 0.411580i \(-0.864977\pi\)
0.812125 + 0.583483i \(0.198311\pi\)
\(522\) 0 0
\(523\) 22.9267 13.2368i 1.00252 0.578803i 0.0935241 0.995617i \(-0.470187\pi\)
0.908992 + 0.416814i \(0.136853\pi\)
\(524\) 12.7809 0.558338
\(525\) 0 0
\(526\) 22.1197 0.964465
\(527\) −0.286690 + 0.165520i −0.0124884 + 0.00721018i
\(528\) 0 0
\(529\) −4.53590 + 7.85641i −0.197213 + 0.341583i
\(530\) 0 0
\(531\) 0 0
\(532\) −0.0930924 + 0.00668373i −0.00403607 + 0.000289777i
\(533\) 24.8131i 1.07477i
\(534\) 0 0
\(535\) 0 0
\(536\) 10.8420 + 6.25966i 0.468305 + 0.270376i
\(537\) 0 0
\(538\) 2.90097i 0.125070i
\(539\) 19.1520 + 7.65514i 0.824936 + 0.329730i
\(540\) 0 0
\(541\) −3.16504 5.48201i −0.136076 0.235690i 0.789932 0.613194i \(-0.210116\pi\)
−0.926008 + 0.377504i \(0.876782\pi\)
\(542\) 8.73205 15.1244i 0.375074 0.649647i
\(543\) 0 0
\(544\) 0.346065 0.199801i 0.0148374 0.00856639i
\(545\) 0 0
\(546\) 0 0
\(547\) 38.5271 1.64730 0.823651 0.567097i \(-0.191934\pi\)
0.823651 + 0.567097i \(0.191934\pi\)
\(548\) −4.78094 + 2.76028i −0.204232 + 0.117913i
\(549\) 0 0
\(550\) 0 0
\(551\) 0.156961 + 0.271864i 0.00668676 + 0.0115818i
\(552\) 0 0
\(553\) −18.1971 + 12.3234i −0.773819 + 0.524045i
\(554\) 4.57650i 0.194437i
\(555\) 0 0
\(556\) −18.9202 10.9236i −0.802393 0.463262i
\(557\) −8.00456 4.62144i −0.339164 0.195817i 0.320738 0.947168i \(-0.396069\pi\)
−0.659902 + 0.751351i \(0.729402\pi\)
\(558\) 0 0
\(559\) 11.9343i 0.504765i
\(560\) 0 0
\(561\) 0 0
\(562\) 4.77974 + 8.27875i 0.201621 + 0.349218i
\(563\) −13.3871 + 23.1872i −0.564201 + 0.977225i 0.432923 + 0.901431i \(0.357482\pi\)
−0.997124 + 0.0757935i \(0.975851\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −10.9262 −0.459263
\(567\) 0 0
\(568\) 1.93426 0.0811596
\(569\) 39.6604 22.8979i 1.66265 0.959931i 0.691207 0.722657i \(-0.257079\pi\)
0.971443 0.237274i \(-0.0762539\pi\)
\(570\) 0 0
\(571\) −0.390149 + 0.675759i −0.0163272 + 0.0282796i −0.874074 0.485794i \(-0.838531\pi\)
0.857746 + 0.514073i \(0.171864\pi\)
\(572\) 5.79253 + 10.0330i 0.242198 + 0.419499i
\(573\) 0 0
\(574\) 9.36246 + 13.8249i 0.390781 + 0.577039i
\(575\) 0 0
\(576\) 0 0
\(577\) 9.74401 + 5.62571i 0.405648 + 0.234201i 0.688918 0.724839i \(-0.258086\pi\)
−0.283270 + 0.959040i \(0.591419\pi\)
\(578\) 14.5841 + 8.42016i 0.606620 + 0.350232i
\(579\) 0 0
\(580\) 0 0
\(581\) −1.96081 27.3105i −0.0813480 1.13303i
\(582\) 0 0
\(583\) 6.33281 + 10.9687i 0.262278 + 0.454279i
\(584\) 0.171573 0.297173i 0.00709974 0.0122971i
\(585\) 0 0
\(586\) 14.0539 8.11401i 0.580561 0.335187i
\(587\) −40.1593 −1.65755 −0.828775 0.559582i \(-0.810962\pi\)
−0.828775 + 0.559582i \(0.810962\pi\)
\(588\) 0 0
\(589\) 0.0292237 0.00120414
\(590\) 0 0
\(591\) 0 0
\(592\) −3.96593 + 6.86919i −0.162999 + 0.282322i
\(593\) −9.54170 16.5267i −0.391831 0.678671i 0.600860 0.799354i \(-0.294825\pi\)
−0.992691 + 0.120683i \(0.961491\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 21.4981i 0.880598i
\(597\) 0 0
\(598\) −12.7079 7.33694i −0.519666 0.300030i
\(599\) 24.6424 + 14.2273i 1.00686 + 0.581312i 0.910271 0.414013i \(-0.135873\pi\)
0.0965902 + 0.995324i \(0.469206\pi\)
\(600\) 0 0
\(601\) 29.2553i 1.19335i −0.802484 0.596673i \(-0.796489\pi\)
0.802484 0.596673i \(-0.203511\pi\)
\(602\) −4.50303 6.64929i −0.183530 0.271005i
\(603\) 0 0
\(604\) 1.47531 + 2.55532i 0.0600297 + 0.103974i
\(605\) 0 0
\(606\) 0 0
\(607\) 22.3712 12.9160i 0.908020 0.524246i 0.0282267 0.999602i \(-0.491014\pi\)
0.879794 + 0.475356i \(0.157681\pi\)
\(608\) −0.0352762 −0.00143064
\(609\) 0 0
\(610\) 0 0
\(611\) −19.7583 + 11.4075i −0.799337 + 0.461498i
\(612\) 0 0
\(613\) 8.12216 14.0680i 0.328051 0.568201i −0.654074 0.756430i \(-0.726942\pi\)
0.982125 + 0.188230i \(0.0602749\pi\)
\(614\) −6.18910 10.7198i −0.249772 0.432618i
\(615\) 0 0
\(616\) 7.01299 + 3.40433i 0.282562 + 0.137164i
\(617\) 31.8398i 1.28182i −0.767615 0.640911i \(-0.778557\pi\)
0.767615 0.640911i \(-0.221443\pi\)
\(618\) 0 0
\(619\) 8.01055 + 4.62490i 0.321971 + 0.185890i 0.652271 0.757986i \(-0.273816\pi\)
−0.330300 + 0.943876i \(0.607150\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 22.8625i 0.916701i
\(623\) 13.5210 9.15669i 0.541708 0.366855i
\(624\) 0 0
\(625\) 0 0
\(626\) 17.4013 30.1399i 0.695495 1.20463i
\(627\) 0 0
\(628\) −19.4823 + 11.2481i −0.777429 + 0.448849i
\(629\) 3.16958 0.126379
\(630\) 0 0
\(631\) −10.3096 −0.410421 −0.205210 0.978718i \(-0.565788\pi\)
−0.205210 + 0.978718i \(0.565788\pi\)
\(632\) −7.19375 + 4.15331i −0.286152 + 0.165210i
\(633\) 0 0
\(634\) 3.39355 5.87780i 0.134775 0.233437i
\(635\) 0 0
\(636\) 0 0
\(637\) 3.93185 + 27.2407i 0.155786 + 1.07931i
\(638\) 26.2205i 1.03808i
\(639\) 0 0
\(640\) 0 0
\(641\) 11.1181 + 6.41906i 0.439140 + 0.253538i 0.703233 0.710960i \(-0.251739\pi\)
−0.264093 + 0.964497i \(0.585072\pi\)
\(642\) 0 0
\(643\) 8.96224i 0.353436i −0.984262 0.176718i \(-0.943452\pi\)
0.984262 0.176718i \(-0.0565481\pi\)
\(644\) −9.84873 + 0.707107i −0.388094 + 0.0278639i
\(645\) 0 0
\(646\) 0.00704821 + 0.0122079i 0.000277308 + 0.000480312i
\(647\) 22.6852 39.2919i 0.891846 1.54472i 0.0541854 0.998531i \(-0.482744\pi\)
0.837660 0.546191i \(-0.183923\pi\)
\(648\) 0 0
\(649\) 14.2142 8.20656i 0.557955 0.322136i
\(650\) 0 0
\(651\) 0 0
\(652\) 22.8070 0.893192
\(653\) 28.4051 16.3997i 1.11158 0.641769i 0.172340 0.985038i \(-0.444867\pi\)
0.939237 + 0.343268i \(0.111534\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.15539 + 5.46530i 0.123197 + 0.213384i
\(657\) 0 0
\(658\) −6.70430 + 13.8110i −0.261361 + 0.538409i
\(659\) 18.7103i 0.728850i −0.931233 0.364425i \(-0.881266\pi\)
0.931233 0.364425i \(-0.118734\pi\)
\(660\) 0 0
\(661\) 7.41761 + 4.28256i 0.288512 + 0.166572i 0.637270 0.770640i \(-0.280063\pi\)
−0.348759 + 0.937213i \(0.613397\pi\)
\(662\) −9.64726 5.56985i −0.374951 0.216478i
\(663\) 0 0
\(664\) 10.3490i 0.401618i
\(665\) 0 0
\(666\) 0 0
\(667\) 16.6057 + 28.7620i 0.642976 + 1.11367i
\(668\) 4.42480 7.66398i 0.171201 0.296528i
\(669\) 0 0
\(670\) 0 0
\(671\) 33.9449 1.31043
\(672\) 0 0
\(673\) 0.179617 0.00692372 0.00346186 0.999994i \(-0.498898\pi\)
0.00346186 + 0.999994i \(0.498898\pi\)
\(674\) −1.37794 + 0.795555i −0.0530763 + 0.0306436i
\(675\) 0 0
\(676\) −1.22973 + 2.12995i −0.0472973 + 0.0819213i
\(677\) −20.7051 35.8623i −0.795763 1.37830i −0.922354 0.386346i \(-0.873737\pi\)
0.126591 0.991955i \(-0.459596\pi\)
\(678\) 0 0
\(679\) −41.2586 + 2.96224i −1.58336 + 0.113680i
\(680\) 0 0
\(681\) 0 0
\(682\) −2.11391 1.22047i −0.0809457 0.0467340i
\(683\) −37.5900 21.7026i −1.43834 0.830427i −0.440608 0.897700i \(-0.645237\pi\)
−0.997735 + 0.0672723i \(0.978570\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 12.4691 + 13.6938i 0.476073 + 0.522834i
\(687\) 0 0
\(688\) −1.51764 2.62863i −0.0578594 0.100215i
\(689\) −8.45069 + 14.6370i −0.321946 + 0.557626i
\(690\) 0 0
\(691\) −16.8728 + 9.74150i −0.641871 + 0.370584i −0.785335 0.619071i \(-0.787509\pi\)
0.143464 + 0.989656i \(0.454176\pi\)
\(692\) 7.73686 0.294111
\(693\) 0 0
\(694\) 15.4568 0.586732
\(695\) 0 0
\(696\) 0 0
\(697\) 1.26090 2.18394i 0.0477600 0.0827228i
\(698\) −0.292529 0.506675i −0.0110724 0.0191779i
\(699\) 0 0
\(700\) 0 0
\(701\) 47.0245i 1.77609i −0.459755 0.888046i \(-0.652063\pi\)
0.459755 0.888046i \(-0.347937\pi\)
\(702\) 0 0
\(703\) −0.242319 0.139903i −0.00913922 0.00527653i
\(704\) 2.55171 + 1.47323i 0.0961713 + 0.0555245i
\(705\) 0 0
\(706\) 3.67576i 0.138339i
\(707\) −42.9595 20.8539i −1.61566 0.784292i
\(708\) 0 0
\(709\) 24.2227 + 41.9549i 0.909701 + 1.57565i 0.814480 + 0.580192i \(0.197023\pi\)
0.0952213 + 0.995456i \(0.469644\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 5.34519 3.08604i 0.200319 0.115654i
\(713\) 3.09173 0.115786
\(714\) 0 0
\(715\) 0 0
\(716\) 0.417291 0.240923i 0.0155949 0.00900372i
\(717\) 0 0
\(718\) 10.0499 17.4069i 0.375058 0.649620i
\(719\) −20.6632 35.7897i −0.770606 1.33473i −0.937231 0.348709i \(-0.886620\pi\)
0.166625 0.986020i \(-0.446713\pi\)
\(720\) 0 0
\(721\) −12.6400 18.6646i −0.470739 0.695106i
\(722\) 18.9988i 0.707060i
\(723\) 0 0
\(724\) −2.12069 1.22438i −0.0788148 0.0455037i
\(725\) 0 0
\(726\) 0 0
\(727\) 16.7905i 0.622726i −0.950291 0.311363i \(-0.899214\pi\)
0.950291 0.311363i \(-0.100786\pi\)
\(728\) 0.744963 + 10.3760i 0.0276102 + 0.384560i
\(729\) 0 0
\(730\) 0 0
\(731\) −0.606451 + 1.05040i −0.0224304 + 0.0388506i
\(732\) 0 0
\(733\) 26.6043 15.3600i 0.982652 0.567335i 0.0795826 0.996828i \(-0.474641\pi\)
0.903070 + 0.429494i \(0.141308\pi\)
\(734\) 19.9377 0.735914
\(735\) 0 0
\(736\) −3.73205 −0.137565
\(737\) 31.9457 18.4438i 1.17673 0.679388i
\(738\) 0 0
\(739\) −15.3876 + 26.6521i −0.566041 + 0.980412i 0.430911 + 0.902395i \(0.358192\pi\)
−0.996952 + 0.0780176i \(0.975141\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.814447 + 11.3438i 0.0298993 + 0.416443i
\(743\) 33.3616i 1.22392i 0.790889 + 0.611960i \(0.209619\pi\)
−0.790889 + 0.611960i \(0.790381\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −29.2856 16.9081i −1.07222 0.619048i
\(747\) 0 0
\(748\) 1.17741i 0.0430504i
\(749\) 25.3025 + 37.3624i 0.924533 + 1.36519i
\(750\) 0 0
\(751\) 15.9452 + 27.6179i 0.581849 + 1.00779i 0.995260 + 0.0972480i \(0.0310040\pi\)
−0.413411 + 0.910545i \(0.635663\pi\)
\(752\) −2.90130 + 5.02520i −0.105800 + 0.183250i
\(753\) 0 0
\(754\) 30.3018 17.4947i 1.10353 0.637121i
\(755\) 0 0
\(756\) 0 0
\(757\) 10.9065 0.396404 0.198202 0.980161i \(-0.436490\pi\)
0.198202 + 0.980161i \(0.436490\pi\)
\(758\) 23.1761 13.3807i 0.841793 0.486010i
\(759\) 0 0
\(760\) 0 0
\(761\) 12.2097 + 21.1479i 0.442602 + 0.766610i 0.997882 0.0650543i \(-0.0207220\pi\)
−0.555280 + 0.831664i \(0.687389\pi\)
\(762\) 0 0
\(763\) −27.8433 13.5160i −1.00800 0.489313i
\(764\) 4.49457i 0.162608i
\(765\) 0 0
\(766\) −17.1310 9.89060i −0.618969 0.357362i
\(767\) 18.9678 + 10.9511i 0.684889 + 0.395421i
\(768\) 0 0
\(769\) 22.9416i 0.827294i −0.910437 0.413647i \(-0.864255\pi\)
0.910437 0.413647i \(-0.135745\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6.28497 + 10.8859i 0.226201 + 0.391791i
\(773\) −22.6837 + 39.2894i −0.815877 + 1.41314i 0.0928193 + 0.995683i \(0.470412\pi\)
−0.908696 + 0.417458i \(0.862921\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −15.6344 −0.561243
\(777\) 0 0
\(778\) −5.18670 −0.185952
\(779\) −0.192795 + 0.111310i −0.00690760 + 0.00398810i
\(780\) 0 0
\(781\) 2.84961 4.93566i 0.101967 0.176612i
\(782\) 0.745667 + 1.29153i 0.0266650 + 0.0461851i
\(783\) 0 0
\(784\) 4.33013 + 5.50000i 0.154647 + 0.196429i
\(785\) 0 0
\(786\) 0 0
\(787\) −2.89834 1.67335i −0.103314 0.0596487i 0.447452 0.894308i \(-0.352331\pi\)
−0.550767 + 0.834659i \(0.685665\pi\)
\(788\) 11.5829 + 6.68740i 0.412625 + 0.238229i
\(789\) 0 0
\(790\) 0 0
\(791\) −35.7700 + 2.56817i −1.27183 + 0.0913136i
\(792\) 0 0
\(793\) 22.6486 + 39.2285i 0.804274 + 1.39304i
\(794\) −2.88259 + 4.99280i −0.102299 + 0.177188i
\(795\) 0 0
\(796\) −23.