Properties

Label 3150.2.bp.a.1349.1
Level 3150
Weight 2
Character 3150.1349
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.bp (of order \(6\), degree \(2\), not 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 1349.1
Root \(-0.965926 - 0.258819i\)
Character \(\chi\) = 3150.1349
Dual form 3150.2.bp.a.899.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.63896 - 0.189469i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-2.63896 - 0.189469i) q^{7} +1.00000 q^{8} +(-2.55171 + 1.47323i) q^{11} +3.93185 q^{13} +(1.48356 - 2.19067i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.346065 - 0.199801i) q^{17} +(-0.0305501 - 0.0176381i) q^{19} -2.94646i q^{22} +(1.86603 - 3.23205i) q^{23} +(-1.96593 + 3.40508i) q^{26} +(1.15539 + 2.38014i) q^{28} +8.89898i q^{29} +(0.717439 - 0.414214i) q^{31} +(-0.500000 - 0.866025i) q^{32} +0.399602i q^{34} +(-6.86919 - 3.96593i) q^{37} +(0.0305501 - 0.0176381i) q^{38} -6.31079 q^{41} -3.03528i q^{43} +(2.55171 + 1.47323i) q^{44} +(1.86603 + 3.23205i) q^{46} +(-5.02520 - 2.90130i) q^{47} +(6.92820 + 1.00000i) q^{49} +(-1.96593 - 3.40508i) q^{52} +(2.14929 + 3.72268i) q^{53} +(-2.63896 - 0.189469i) q^{56} +(-7.70674 - 4.44949i) q^{58} +(2.78522 + 4.82415i) q^{59} +(-9.97710 - 5.76028i) q^{61} +0.828427i q^{62} +1.00000 q^{64} +(10.8420 - 6.25966i) q^{67} +(-0.346065 - 0.199801i) q^{68} -1.93426i q^{71} +(-0.171573 - 0.297173i) q^{73} +(6.86919 - 3.96593i) q^{74} +0.0352762i q^{76} +(7.01299 - 3.40433i) q^{77} +(4.15331 - 7.19375i) q^{79} +(3.15539 - 5.46530i) q^{82} -10.3490i q^{83} +(2.62863 + 1.51764i) q^{86} +(-2.55171 + 1.47323i) q^{88} +(-3.08604 + 5.34519i) q^{89} +(-10.3760 - 0.744963i) q^{91} -3.73205 q^{92} +(5.02520 - 2.90130i) q^{94} -15.6344 q^{97} +(-4.33013 + 5.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 4q^{2} - 4q^{4} + 8q^{8} + O(q^{10}) \) \( 8q - 4q^{2} - 4q^{4} + 8q^{8} - 24q^{11} + 16q^{13} - 4q^{16} - 24q^{17} + 8q^{23} - 8q^{26} - 4q^{32} - 32q^{41} + 24q^{44} + 8q^{46} - 12q^{47} - 8q^{52} - 4q^{53} - 24q^{59} + 8q^{64} + 48q^{67} + 24q^{68} - 24q^{73} + 4q^{77} + 24q^{79} + 16q^{82} - 24q^{88} - 16q^{89} - 20q^{91} - 16q^{92} + 12q^{94} - 48q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(451\) \(2801\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) 0 0
\(7\) −2.63896 0.189469i −0.997433 0.0716124i
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −2.55171 + 1.47323i −0.769370 + 0.444196i −0.832650 0.553800i \(-0.813177\pi\)
0.0632797 + 0.997996i \(0.479844\pi\)
\(12\) 0 0
\(13\) 3.93185 1.09050 0.545250 0.838274i \(-0.316435\pi\)
0.545250 + 0.838274i \(0.316435\pi\)
\(14\) 1.48356 2.19067i 0.396499 0.585481i
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 0.346065 0.199801i 0.0839331 0.0484588i −0.457446 0.889237i \(-0.651236\pi\)
0.541379 + 0.840779i \(0.317902\pi\)
\(18\) 0 0
\(19\) −0.0305501 0.0176381i −0.00700867 0.00404646i 0.496492 0.868042i \(-0.334621\pi\)
−0.503500 + 0.863995i \(0.667955\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 2.94646i 0.628188i
\(23\) 1.86603 3.23205i 0.389093 0.673929i −0.603235 0.797564i \(-0.706122\pi\)
0.992328 + 0.123635i \(0.0394551\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −1.96593 + 3.40508i −0.385550 + 0.667792i
\(27\) 0 0
\(28\) 1.15539 + 2.38014i 0.218349 + 0.449804i
\(29\) 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 −0.434187 0.900823i \(-0.642964\pi\)
0.563042 + 0.826428i \(0.309631\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 0 0
\(34\) 0.399602i 0.0685311i
\(35\) 0 0
\(36\) 0 0
\(37\) −6.86919 3.96593i −1.12929 0.651994i −0.185532 0.982638i \(-0.559401\pi\)
−0.943756 + 0.330644i \(0.892734\pi\)
\(38\) 0.0305501 0.0176381i 0.00495588 0.00286128i
\(39\) 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
\(43\) 3.03528i 0.462875i −0.972850 0.231438i \(-0.925657\pi\)
0.972850 0.231438i \(-0.0743429\pi\)
\(44\) 2.55171 + 1.47323i 0.384685 + 0.222098i
\(45\) 0 0
\(46\) 1.86603 + 3.23205i 0.275130 + 0.476540i
\(47\) −5.02520 2.90130i −0.733001 0.423198i 0.0865180 0.996250i \(-0.472426\pi\)
−0.819519 + 0.573052i \(0.805759\pi\)
\(48\) 0 0
\(49\) 6.92820 + 1.00000i 0.989743 + 0.142857i
\(50\) 0 0
\(51\) 0 0
\(52\) −1.96593 3.40508i −0.272625 0.472200i
\(53\) 2.14929 + 3.72268i 0.295228 + 0.511349i 0.975038 0.222039i \(-0.0712711\pi\)
−0.679810 + 0.733388i \(0.737938\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.63896 0.189469i −0.352646 0.0253188i
\(57\) 0 0
\(58\) −7.70674 4.44949i −1.01194 0.584247i
\(59\) 2.78522 + 4.82415i 0.362605 + 0.628050i 0.988389 0.151946i \(-0.0485540\pi\)
−0.625784 + 0.779997i \(0.715221\pi\)
\(60\) 0 0
\(61\) −9.97710 5.76028i −1.27744 0.737528i −0.301060 0.953605i \(-0.597340\pi\)
−0.976376 + 0.216077i \(0.930674\pi\)
\(62\) 0.828427i 0.105210i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 10.8420 6.25966i 1.32457 0.764739i 0.340113 0.940385i \(-0.389535\pi\)
0.984453 + 0.175646i \(0.0562013\pi\)
\(68\) −0.346065 0.199801i −0.0419666 0.0242294i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.93426i 0.229554i −0.993391 0.114777i \(-0.963385\pi\)
0.993391 0.114777i \(-0.0366153\pi\)
\(72\) 0 0
\(73\) −0.171573 0.297173i −0.0200811 0.0347815i 0.855810 0.517290i \(-0.173059\pi\)
−0.875891 + 0.482508i \(0.839726\pi\)
\(74\) 6.86919 3.96593i 0.798527 0.461030i
\(75\) 0 0
\(76\) 0.0352762i 0.00404646i
\(77\) 7.01299 3.40433i 0.799205 0.387959i
\(78\) 0 0
\(79\) 4.15331 7.19375i 0.467284 0.809360i −0.532017 0.846734i \(-0.678566\pi\)
0.999301 + 0.0373736i \(0.0118992\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 3.15539 5.46530i 0.348455 0.603542i
\(83\) 10.3490i 1.13595i −0.823046 0.567974i \(-0.807727\pi\)
0.823046 0.567974i \(-0.192273\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 2.62863 + 1.51764i 0.283452 + 0.163651i
\(87\) 0 0
\(88\) −2.55171 + 1.47323i −0.272013 + 0.157047i
\(89\) −3.08604 + 5.34519i −0.327120 + 0.566589i −0.981939 0.189197i \(-0.939411\pi\)
0.654819 + 0.755786i \(0.272745\pi\)
\(90\) 0 0
\(91\) −10.3760 0.744963i −1.08770 0.0780933i
\(92\) −3.73205 −0.389093
\(93\) 0 0
\(94\) 5.02520 2.90130i 0.518310 0.299246i
\(95\) 0 0
\(96\) 0 0
\(97\) −15.6344 −1.58744 −0.793718 0.608286i \(-0.791857\pi\)
−0.793718 + 0.608286i \(0.791857\pi\)
\(98\) −4.33013 + 5.50000i −0.437409 + 0.555584i
\(99\) 0 0
\(100\) 0 0
\(101\) 9.02458 + 15.6310i 0.897979 + 1.55535i 0.830074 + 0.557654i \(0.188298\pi\)
0.0679057 + 0.997692i \(0.478368\pi\)
\(102\) 0 0
\(103\) 4.26002 7.37857i 0.419752 0.727032i −0.576162 0.817336i \(-0.695450\pi\)
0.995914 + 0.0903031i \(0.0287836\pi\)
\(104\) 3.93185 0.385550
\(105\) 0 0
\(106\) −4.29858 −0.417515
\(107\) 8.52761 14.7702i 0.824395 1.42789i −0.0779862 0.996954i \(-0.524849\pi\)
0.902381 0.430939i \(-0.141818\pi\)
\(108\) 0 0
\(109\) −5.84909 10.1309i −0.560241 0.970366i −0.997475 0.0710185i \(-0.977375\pi\)
0.437234 0.899348i \(-0.355958\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.48356 2.19067i 0.140184 0.206999i
\(113\) 13.5546 1.27511 0.637554 0.770405i \(-0.279946\pi\)
0.637554 + 0.770405i \(0.279946\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 7.70674 4.44949i 0.715553 0.413125i
\(117\) 0 0
\(118\) −5.57045 −0.512801
\(119\) −0.951108 + 0.461698i −0.0871879 + 0.0423237i
\(120\) 0 0
\(121\) −1.15918 + 2.00775i −0.105380 + 0.182523i
\(122\) 9.97710 5.76028i 0.903284 0.521511i
\(123\) 0 0
\(124\) −0.717439 0.414214i −0.0644279 0.0371975i
\(125\) 0 0
\(126\) 0 0
\(127\) 8.95983i 0.795056i −0.917590 0.397528i \(-0.869868\pi\)
0.917590 0.397528i \(-0.130132\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) 0 0
\(131\) 6.39047 11.0686i 0.558338 0.967070i −0.439297 0.898342i \(-0.644773\pi\)
0.997635 0.0687282i \(-0.0218941\pi\)
\(132\) 0 0
\(133\) 0.0772785 + 0.0523345i 0.00670090 + 0.00453797i
\(134\) 12.5193i 1.08150i
\(135\) 0 0
\(136\) 0.346065 0.199801i 0.0296748 0.0171328i
\(137\) −2.76028 4.78094i −0.235827 0.408464i 0.723686 0.690129i \(-0.242446\pi\)
−0.959513 + 0.281666i \(0.909113\pi\)
\(138\) 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
\(142\) 1.67511 + 0.967128i 0.140572 + 0.0811596i
\(143\) −10.0330 + 5.79253i −0.838998 + 0.484396i
\(144\) 0 0
\(145\) 0 0
\(146\) 0.343146 0.0283989
\(147\) 0 0
\(148\) 7.93185i 0.651994i
\(149\) −18.6179 10.7491i −1.52524 0.880598i −0.999552 0.0299204i \(-0.990475\pi\)
−0.525688 0.850677i \(-0.676192\pi\)
\(150\) 0 0
\(151\) −1.47531 2.55532i −0.120059 0.207949i 0.799732 0.600358i \(-0.204975\pi\)
−0.919791 + 0.392409i \(0.871642\pi\)
\(152\) −0.0305501 0.0176381i −0.00247794 0.00143064i
\(153\) 0 0
\(154\) −0.558263 + 7.77559i −0.0449861 + 0.626575i
\(155\) 0 0
\(156\) 0 0
\(157\) −11.2481 19.4823i −0.897698 1.55486i −0.830430 0.557123i \(-0.811905\pi\)
−0.0672682 0.997735i \(-0.521428\pi\)
\(158\) 4.15331 + 7.19375i 0.330420 + 0.572304i
\(159\) 0 0
\(160\) 0 0
\(161\) −5.53674 + 8.17569i −0.436356 + 0.644335i
\(162\) 0 0
\(163\) −19.7515 11.4035i −1.54705 0.893192i −0.998365 0.0571664i \(-0.981793\pi\)
−0.548690 0.836026i \(-0.684873\pi\)
\(164\) 3.15539 + 5.46530i 0.246395 + 0.426769i
\(165\) 0 0
\(166\) 8.96248 + 5.17449i 0.695624 + 0.401618i
\(167\) 8.84961i 0.684803i 0.939554 + 0.342402i \(0.111240\pi\)
−0.939554 + 0.342402i \(0.888760\pi\)
\(168\) 0 0
\(169\) 2.45946 0.189189
\(170\) 0 0
\(171\) 0 0
\(172\) −2.62863 + 1.51764i −0.200431 + 0.115719i
\(173\) −6.70032 3.86843i −0.509416 0.294111i 0.223178 0.974778i \(-0.428357\pi\)
−0.732593 + 0.680667i \(0.761690\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 2.94646i 0.222098i
\(177\) 0 0
\(178\) −3.08604 5.34519i −0.231309 0.400639i
\(179\) −0.417291 + 0.240923i −0.0311898 + 0.0180074i −0.515514 0.856881i \(-0.672399\pi\)
0.484324 + 0.874889i \(0.339066\pi\)
\(180\) 0 0
\(181\) 2.44876i 0.182015i 0.995850 + 0.0910075i \(0.0290087\pi\)
−0.995850 + 0.0910075i \(0.970991\pi\)
\(182\) 5.83315 8.61339i 0.432382 0.638467i
\(183\) 0 0
\(184\) 1.86603 3.23205i 0.137565 0.238270i
\(185\) 0 0
\(186\) 0 0
\(187\) −0.588706 + 1.01967i −0.0430504 + 0.0745655i
\(188\) 5.80260i 0.423198i
\(189\) 0 0
\(190\) 0 0
\(191\) −3.89241 2.24728i −0.281645 0.162608i 0.352523 0.935803i \(-0.385324\pi\)
−0.634168 + 0.773195i \(0.718657\pi\)
\(192\) 0 0
\(193\) −10.8859 + 6.28497i −0.783583 + 0.452402i −0.837698 0.546133i \(-0.816099\pi\)
0.0541158 + 0.998535i \(0.482766\pi\)
\(194\) 7.81722 13.5398i 0.561243 0.972102i
\(195\) 0 0
\(196\) −2.59808 6.50000i −0.185577 0.464286i
\(197\) 13.3748 0.952916 0.476458 0.879197i \(-0.341920\pi\)
0.476458 + 0.879197i \(0.341920\pi\)
\(198\) 0 0
\(199\) 23.5169 13.5775i 1.66707 0.962483i 0.697864 0.716231i \(-0.254134\pi\)
0.969206 0.246253i \(-0.0791993\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −18.0492 −1.26993
\(203\) 1.68608 23.4840i 0.118339 1.64826i
\(204\) 0 0
\(205\) 0 0
\(206\) 4.26002 + 7.37857i 0.296810 + 0.514090i
\(207\) 0 0
\(208\) −1.96593 + 3.40508i −0.136312 + 0.236100i
\(209\) 0.103940 0.00718968
\(210\) 0 0
\(211\) 18.4183 1.26797 0.633984 0.773346i \(-0.281419\pi\)
0.633984 + 0.773346i \(0.281419\pi\)
\(212\) 2.14929 3.72268i 0.147614 0.255675i
\(213\) 0 0
\(214\) 8.52761 + 14.7702i 0.582935 + 1.00967i
\(215\) 0 0
\(216\) 0 0
\(217\) −1.97177 + 0.957160i −0.133853 + 0.0649763i
\(218\) 11.6982 0.792301
\(219\) 0 0
\(220\) 0 0
\(221\) 1.36068 0.785587i 0.0915290 0.0528443i
\(222\) 0 0
\(223\) 17.8045 1.19228 0.596140 0.802881i \(-0.296700\pi\)
0.596140 + 0.802881i \(0.296700\pi\)
\(224\) 1.15539 + 2.38014i 0.0771980 + 0.159030i
\(225\) 0 0
\(226\) −6.77729 + 11.7386i −0.450819 + 0.780841i
\(227\) −1.48288 + 0.856140i −0.0984220 + 0.0568240i −0.548403 0.836214i \(-0.684764\pi\)
0.449981 + 0.893038i \(0.351431\pi\)
\(228\) 0 0
\(229\) −5.26142 3.03768i −0.347684 0.200736i 0.315981 0.948766i \(-0.397667\pi\)
−0.663665 + 0.748030i \(0.731000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 8.89898i 0.584247i
\(233\) −3.56288 + 6.17109i −0.233412 + 0.404282i −0.958810 0.284048i \(-0.908322\pi\)
0.725398 + 0.688330i \(0.241656\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 2.78522 4.82415i 0.181303 0.314025i
\(237\) 0 0
\(238\) 0.0757120 1.05453i 0.00490768 0.0683552i
\(239\) 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 −0.231802 0.972763i \(-0.574462\pi\)
0.726537 + 0.687128i \(0.241129\pi\)
\(242\) −1.15918 2.00775i −0.0745147 0.129063i
\(243\) 0 0
\(244\) 11.5206i 0.737528i
\(245\) 0 0
\(246\) 0 0
\(247\) −0.120118 0.0693504i −0.00764295 0.00441266i
\(248\) 0.717439 0.414214i 0.0455574 0.0263026i
\(249\) 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
\(253\) 10.9964i 0.691335i
\(254\) 7.75944 + 4.47992i 0.486871 + 0.281095i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −14.5780 8.41662i −0.909351 0.525014i −0.0291289 0.999576i \(-0.509273\pi\)
−0.880222 + 0.474561i \(0.842607\pi\)
\(258\) 0 0
\(259\) 17.3761 + 11.7674i 1.07970 + 0.731191i
\(260\) 0 0
\(261\) 0 0
\(262\) 6.39047 + 11.0686i 0.394805 + 0.683822i
\(263\) −11.0599 19.1562i −0.681980 1.18122i −0.974376 0.224926i \(-0.927786\pi\)
0.292396 0.956297i \(-0.405548\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.0839622 + 0.0407579i −0.00514805 + 0.00249903i
\(267\) 0 0
\(268\) −10.8420 6.25966i −0.662283 0.382369i
\(269\) 1.45049 + 2.51231i 0.0884377 + 0.153179i 0.906851 0.421452i \(-0.138479\pi\)
−0.818413 + 0.574630i \(0.805146\pi\)
\(270\) 0 0
\(271\) 15.1244 + 8.73205i 0.918739 + 0.530434i 0.883233 0.468935i \(-0.155362\pi\)
0.0355066 + 0.999369i \(0.488696\pi\)
\(272\) 0.399602i 0.0242294i
\(273\) 0 0
\(274\) 5.52056 0.333509
\(275\) 0 0
\(276\) 0 0
\(277\) −3.96336 + 2.28825i −0.238135 + 0.137488i −0.614319 0.789057i \(-0.710569\pi\)
0.376184 + 0.926545i \(0.377236\pi\)
\(278\) 18.9202 + 10.9236i 1.13476 + 0.655152i
\(279\) 0 0
\(280\) 0 0
\(281\) 9.55948i 0.570271i −0.958487 0.285135i \(-0.907961\pi\)
0.958487 0.285135i \(-0.0920386\pi\)
\(282\) 0 0
\(283\) 5.46311 + 9.46238i 0.324748 + 0.562480i 0.981461 0.191660i \(-0.0613872\pi\)
−0.656713 + 0.754140i \(0.728054\pi\)
\(284\) −1.67511 + 0.967128i −0.0993998 + 0.0573885i
\(285\) 0 0
\(286\) 11.5851i 0.685039i
\(287\) 16.6539 + 1.19570i 0.983049 + 0.0705798i
\(288\) 0 0
\(289\) −8.42016 + 14.5841i −0.495303 + 0.857891i
\(290\) 0 0
\(291\) 0 0
\(292\) −0.171573 + 0.297173i −0.0100405 + 0.0173907i
\(293\) 16.2280i 0.948052i −0.880511 0.474026i \(-0.842800\pi\)
0.880511 0.474026i \(-0.157200\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −6.86919 3.96593i −0.399263 0.230515i
\(297\) 0 0
\(298\) 18.6179 10.7491i 1.07851 0.622677i
\(299\) 7.33694 12.7079i 0.424306 0.734919i
\(300\) 0 0
\(301\) −0.575090 + 8.00997i −0.0331476 + 0.461687i
\(302\) 2.95063 0.169790
\(303\) 0 0
\(304\) 0.0305501 0.0176381i 0.00175217 0.00101161i
\(305\) 0 0
\(306\) 0 0
\(307\) −12.3782 −0.706462 −0.353231 0.935536i \(-0.614917\pi\)
−0.353231 + 0.935536i \(0.614917\pi\)
\(308\) −6.45473 4.37127i −0.367792 0.249076i
\(309\) 0 0
\(310\) 0 0
\(311\) −11.4312 19.7995i −0.648206 1.12272i −0.983551 0.180630i \(-0.942186\pi\)
0.335346 0.942095i \(-0.391147\pi\)
\(312\) 0 0
\(313\) 17.4013 30.1399i 0.983578 1.70361i 0.335487 0.942045i \(-0.391099\pi\)
0.648091 0.761563i \(-0.275568\pi\)
\(314\) 22.4962 1.26954
\(315\) 0 0
\(316\) −8.30663 −0.467284
\(317\) −3.39355 + 5.87780i −0.190601 + 0.330130i −0.945449 0.325769i \(-0.894377\pi\)
0.754849 + 0.655899i \(0.227710\pi\)
\(318\) 0 0
\(319\) −13.1103 22.7076i −0.734034 1.27138i
\(320\) 0 0
\(321\) 0 0
\(322\) −4.31199 8.88280i −0.240298 0.495019i
\(323\) −0.0140964 −0.000784346
\(324\) 0 0
\(325\) 0 0
\(326\) 19.7515 11.4035i 1.09393 0.631582i
\(327\) 0 0
\(328\) −6.31079 −0.348455
\(329\) 12.7116 + 8.60853i 0.700813 + 0.474604i
\(330\) 0 0
\(331\) −5.56985 + 9.64726i −0.306147 + 0.530261i −0.977516 0.210862i \(-0.932373\pi\)
0.671369 + 0.741123i \(0.265706\pi\)
\(332\) −8.96248 + 5.17449i −0.491880 + 0.283987i
\(333\) 0 0
\(334\) −7.66398 4.42480i −0.419355 0.242114i
\(335\) 0 0
\(336\) 0 0
\(337\) 1.59111i 0.0866733i −0.999061 0.0433366i \(-0.986201\pi\)
0.999061 0.0433366i \(-0.0137988\pi\)
\(338\) −1.22973 + 2.12995i −0.0668884 + 0.115854i
\(339\) 0 0
\(340\) 0 0
\(341\) −1.22047 + 2.11391i −0.0660919 + 0.114475i
\(342\) 0 0
\(343\) −18.0938 3.95164i −0.976972 0.213368i
\(344\) 3.03528i 0.163651i
\(345\) 0 0
\(346\) 6.70032 3.86843i 0.360211 0.207968i
\(347\) 7.72840 + 13.3860i 0.414882 + 0.718597i 0.995416 0.0956388i \(-0.0304894\pi\)
−0.580534 + 0.814236i \(0.697156\pi\)
\(348\) 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
\(352\) 2.55171 + 1.47323i 0.136007 + 0.0785235i
\(353\) −3.18330 + 1.83788i −0.169430 + 0.0978204i −0.582317 0.812962i \(-0.697854\pi\)
0.412887 + 0.910782i \(0.364520\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.17209 0.327120
\(357\) 0 0
\(358\) 0.481846i 0.0254664i
\(359\) −17.4069 10.0499i −0.918702 0.530413i −0.0354812 0.999370i \(-0.511296\pi\)
−0.883221 + 0.468958i \(0.844630\pi\)
\(360\) 0 0
\(361\) −9.49938 16.4534i −0.499967 0.865969i
\(362\) −2.12069 1.22438i −0.111461 0.0643520i
\(363\) 0 0
\(364\) 4.54284 + 9.35835i 0.238110 + 0.490511i
\(365\) 0 0
\(366\) 0 0
\(367\) 9.96885 + 17.2665i 0.520369 + 0.901306i 0.999720 + 0.0236826i \(0.00753911\pi\)
−0.479350 + 0.877624i \(0.659128\pi\)
\(368\) 1.86603 + 3.23205i 0.0972733 + 0.168482i
\(369\) 0 0
\(370\) 0 0
\(371\) −4.96656 10.2312i −0.257851 0.531179i
\(372\) 0 0
\(373\) 29.2856 + 16.9081i 1.51635 + 0.875467i 0.999816 + 0.0192016i \(0.00611243\pi\)
0.516537 + 0.856265i \(0.327221\pi\)
\(374\) −0.588706 1.01967i −0.0304413 0.0527258i
\(375\) 0 0
\(376\) −5.02520 2.90130i −0.259155 0.149623i
\(377\) 34.9895i 1.80205i
\(378\) 0 0
\(379\) −26.7614 −1.37464 −0.687321 0.726353i \(-0.741214\pi\)
−0.687321 + 0.726353i \(0.741214\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 3.89241 2.24728i 0.199153 0.114981i
\(383\) 17.1310 + 9.89060i 0.875355 + 0.505386i 0.869124 0.494594i \(-0.164683\pi\)
0.00623078 + 0.999981i \(0.498017\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 12.5699i 0.639793i
\(387\) 0 0
\(388\) 7.81722 + 13.5398i 0.396859 + 0.687380i
\(389\) 4.49181 2.59335i 0.227744 0.131488i −0.381787 0.924250i \(-0.624691\pi\)
0.609531 + 0.792762i \(0.291358\pi\)
\(390\) 0 0
\(391\) 1.49133i 0.0754200i
\(392\) 6.92820 + 1.00000i 0.349927 + 0.0505076i
\(393\) 0 0
\(394\) −6.68740 + 11.5829i −0.336907 + 0.583539i
\(395\) 0 0
\(396\) 0 0
\(397\) 2.88259 4.99280i 0.144673 0.250581i −0.784578 0.620030i \(-0.787120\pi\)
0.929251 + 0.369449i \(0.120454\pi\)
\(398\) 27.1550i 1.36116i
\(399\) 0 0
\(400\) 0 0
\(401\) 15.4361 + 8.91202i 0.770841 + 0.445045i 0.833175 0.553010i \(-0.186521\pi\)
−0.0623335 + 0.998055i \(0.519854\pi\)
\(402\) 0 0
\(403\) 2.82086 1.62863i 0.140517 0.0811277i
\(404\) 9.02458 15.6310i 0.448990 0.777673i
\(405\) 0 0
\(406\) 19.4947 + 13.2022i 0.967507 + 0.655214i
\(407\) 23.3709 1.15845
\(408\) 0 0
\(409\) 28.5617 16.4901i 1.41228 0.815382i 0.416681 0.909053i \(-0.363193\pi\)
0.995603 + 0.0936705i \(0.0298600\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −8.52004 −0.419752
\(413\) −6.43606 13.2584i −0.316698 0.652405i
\(414\) 0 0
\(415\) 0 0
\(416\) −1.96593 3.40508i −0.0963874 0.166948i
\(417\) 0 0
\(418\) −0.0519700 + 0.0900147i −0.00254194 + 0.00440276i
\(419\) −15.2287 −0.743969 −0.371985 0.928239i \(-0.621323\pi\)
−0.371985 + 0.928239i \(0.621323\pi\)
\(420\) 0 0
\(421\) 16.9939 0.828234 0.414117 0.910224i \(-0.364090\pi\)
0.414117 + 0.910224i \(0.364090\pi\)
\(422\) −9.20915 + 15.9507i −0.448294 + 0.776468i
\(423\) 0 0
\(424\) 2.14929 + 3.72268i 0.104379 + 0.180789i
\(425\) 0 0
\(426\) 0 0
\(427\) 25.2377 + 17.0915i 1.22134 + 0.827115i
\(428\) −17.0552 −0.824395
\(429\) 0 0
\(430\) 0 0
\(431\) −15.4818 + 8.93842i −0.745732 + 0.430549i −0.824150 0.566372i \(-0.808347\pi\)
0.0784178 + 0.996921i \(0.475013\pi\)
\(432\) 0 0
\(433\) 5.56388 0.267383 0.133691 0.991023i \(-0.457317\pi\)
0.133691 + 0.991023i \(0.457317\pi\)
\(434\) 0.156961 2.18618i 0.00753437 0.104940i
\(435\) 0 0
\(436\) −5.84909 + 10.1309i −0.280121 + 0.485183i
\(437\) −0.114014 + 0.0658262i −0.00545405 + 0.00314890i
\(438\) 0 0
\(439\) −9.53568 5.50543i −0.455113 0.262760i 0.254874 0.966974i \(-0.417966\pi\)
−0.709987 + 0.704214i \(0.751299\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 1.57117i 0.0747332i
\(443\) 8.49233 14.7091i 0.403483 0.698853i −0.590661 0.806920i \(-0.701133\pi\)
0.994144 + 0.108067i \(0.0344662\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −8.90226 + 15.4192i −0.421534 + 0.730119i
\(447\) 0 0
\(448\) −2.63896 0.189469i −0.124679 0.00895155i
\(449\) 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
\(452\) −6.77729 11.7386i −0.318777 0.552138i
\(453\) 0 0
\(454\) 1.71228i 0.0803612i
\(455\) 0 0
\(456\) 0 0
\(457\) −1.87783 1.08417i −0.0878414 0.0507153i 0.455436 0.890269i \(-0.349483\pi\)
−0.543277 + 0.839553i \(0.682817\pi\)
\(458\) 5.26142 3.03768i 0.245850 0.141941i
\(459\) 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
\(463\) 28.2133i 1.31118i 0.755115 + 0.655592i \(0.227581\pi\)
−0.755115 + 0.655592i \(0.772419\pi\)
\(464\) −7.70674 4.44949i −0.357777 0.206562i
\(465\) 0 0
\(466\) −3.56288 6.17109i −0.165047 0.285870i
\(467\) 3.64324 + 2.10342i 0.168589 + 0.0973349i 0.581920 0.813246i \(-0.302302\pi\)
−0.413331 + 0.910581i \(0.635635\pi\)
\(468\) 0 0
\(469\) −29.7977 + 14.4647i −1.37593 + 0.667920i
\(470\) 0 0
\(471\) 0 0
\(472\) 2.78522 + 4.82415i 0.128200 + 0.222049i
\(473\) 4.47167 + 7.74515i 0.205607 + 0.356122i
\(474\) 0 0
\(475\) 0 0
\(476\) 0.875396 + 0.592835i 0.0401237 + 0.0271725i
\(477\) 0 0
\(478\) −16.2114 9.35968i −0.741494 0.428102i
\(479\) −7.35968 12.7473i −0.336272 0.582441i 0.647456 0.762103i \(-0.275833\pi\)
−0.983728 + 0.179662i \(0.942500\pi\)
\(480\) 0 0
\(481\) −27.0086 15.5934i −1.23149 0.710999i
\(482\) 8.86851i 0.403950i
\(483\) 0 0
\(484\) 2.31835 0.105380
\(485\) 0 0
\(486\) 0 0
\(487\) 1.62602 0.938784i 0.0736821 0.0425404i −0.462706 0.886512i \(-0.653122\pi\)
0.536388 + 0.843971i \(0.319788\pi\)
\(488\) −9.97710 5.76028i −0.451642 0.260756i
\(489\) 0 0
\(490\) 0 0
\(491\) 10.4281i 0.470613i −0.971921 0.235307i \(-0.924391\pi\)
0.971921 0.235307i \(-0.0756095\pi\)
\(492\) 0 0
\(493\) 1.77802 + 3.07963i 0.0800782 + 0.138699i
\(494\) 0.120118 0.0693504i 0.00540438 0.00312022i
\(495\) 0 0
\(496\) 0.828427i 0.0371975i
\(497\) −0.366481 + 5.10442i −0.0164389 + 0.228965i
\(498\) 0 0
\(499\) −18.8822 + 32.7050i −0.845285 + 1.46408i 0.0400890 + 0.999196i \(0.487236\pi\)
−0.885374 + 0.464880i \(0.846097\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 11.0869 19.2030i 0.494832 0.857074i
\(503\) 35.8895i 1.60023i 0.599845 + 0.800116i \(0.295229\pi\)
−0.599845 + 0.800116i \(0.704771\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −9.52312 5.49818i −0.423354 0.244424i
\(507\) 0 0
\(508\) −7.75944 + 4.47992i −0.344270 + 0.198764i
\(509\) 8.58746 14.8739i 0.380633 0.659275i −0.610520 0.792001i \(-0.709040\pi\)
0.991153 + 0.132726i \(0.0423729\pi\)
\(510\) 0 0
\(511\) 0.396469 + 0.816735i 0.0175387 + 0.0361302i
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 14.5780 8.41662i 0.643008 0.371241i
\(515\) 0 0
\(516\) 0 0
\(517\) 17.0972 0.751932
\(518\) −18.8789 + 9.16442i −0.829492 + 0.402661i
\(519\) 0 0
\(520\) 0 0
\(521\) −2.26539 3.92377i −0.0992484 0.171903i 0.812125 0.583483i \(-0.198311\pi\)
−0.911374 + 0.411580i \(0.864977\pi\)
\(522\) 0 0
\(523\) 13.2368 22.9267i 0.578803 1.00252i −0.416814 0.908992i \(-0.636853\pi\)
0.995617 0.0935241i \(-0.0298132\pi\)
\(524\) −12.7809 −0.558338
\(525\) 0 0
\(526\) 22.1197 0.964465
\(527\) 0.165520 0.286690i 0.00721018 0.0124884i
\(528\) 0 0
\(529\) 4.53590 + 7.85641i 0.197213 + 0.341583i
\(530\) 0 0
\(531\) 0 0
\(532\) 0.00668373 0.0930924i 0.000289777 0.00403607i
\(533\) −24.8131 −1.07477
\(534\) 0 0
\(535\) 0 0
\(536\) 10.8420 6.25966i 0.468305 0.270376i
\(537\) 0 0
\(538\) −2.90097 −0.125070
\(539\) −19.1520 + 7.65514i −0.824936 + 0.329730i
\(540\) 0 0
\(541\) −3.16504 + 5.48201i −0.136076 + 0.235690i −0.926008 0.377504i \(-0.876782\pi\)
0.789932 + 0.613194i \(0.210116\pi\)
\(542\) −15.1244 + 8.73205i −0.649647 + 0.375074i
\(543\) 0 0
\(544\) −0.346065 0.199801i −0.0148374 0.00856639i
\(545\) 0 0
\(546\) 0 0
\(547\) 38.5271i 1.64730i 0.567097 + 0.823651i \(0.308066\pi\)
−0.567097 + 0.823651i \(0.691934\pi\)
\(548\) −2.76028 + 4.78094i −0.117913 + 0.204232i
\(549\) 0 0
\(550\) 0 0
\(551\) 0.156961 0.271864i 0.00668676 0.0115818i
\(552\) 0 0
\(553\) −12.3234 + 18.1971i −0.524045 + 0.773819i
\(554\) 4.57650i 0.194437i
\(555\) 0 0
\(556\) −18.9202 + 10.9236i −0.802393 + 0.463262i
\(557\) −4.62144 8.00456i −0.195817 0.339164i 0.751351 0.659902i \(-0.229402\pi\)
−0.947168 + 0.320738i \(0.896069\pi\)
\(558\) 0 0
\(559\) 11.9343i 0.504765i
\(560\) 0 0
\(561\) 0 0
\(562\) 8.27875 + 4.77974i 0.349218 + 0.201621i
\(563\) −23.1872 + 13.3871i −0.977225 + 0.564201i −0.901431 0.432923i \(-0.857482\pi\)
−0.0757935 + 0.997124i \(0.524149\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −10.9262 −0.459263
\(567\) 0 0
\(568\) 1.93426i 0.0811596i
\(569\) −39.6604 22.8979i −1.66265 0.959931i −0.971443 0.237274i \(-0.923746\pi\)
−0.691207 0.722657i \(-0.742921\pi\)
\(570\) 0 0
\(571\) −0.390149 0.675759i −0.0163272 0.0282796i 0.857746 0.514073i \(-0.171864\pi\)
−0.874074 + 0.485794i \(0.838531\pi\)
\(572\) 10.0330 + 5.79253i 0.419499 + 0.242198i
\(573\) 0 0
\(574\) −9.36246 + 13.8249i −0.390781 + 0.577039i
\(575\) 0 0
\(576\) 0 0
\(577\) 5.62571 + 9.74401i 0.234201 + 0.405648i 0.959040 0.283270i \(-0.0914192\pi\)
−0.724839 + 0.688918i \(0.758086\pi\)
\(578\) −8.42016 14.5841i −0.350232 0.606620i
\(579\) 0 0
\(580\) 0 0
\(581\) −1.96081 + 27.3105i −0.0813480 + 1.13303i
\(582\) 0 0
\(583\) −10.9687 6.33281i −0.454279 0.262278i
\(584\) −0.171573 0.297173i −0.00709974 0.0122971i
\(585\) 0 0
\(586\) 14.0539 + 8.11401i 0.580561 + 0.335187i
\(587\) 40.1593i 1.65755i −0.559582 0.828775i \(-0.689038\pi\)
0.559582 0.828775i \(-0.310962\pi\)
\(588\) 0 0
\(589\) −0.0292237 −0.00120414
\(590\) 0 0
\(591\) 0 0
\(592\) 6.86919 3.96593i 0.282322 0.162999i
\(593\) 16.5267 + 9.54170i 0.678671 + 0.391831i 0.799354 0.600860i \(-0.205175\pi\)
−0.120683 + 0.992691i \(0.538509\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 21.4981i 0.880598i
\(597\) 0 0
\(598\) 7.33694 + 12.7079i 0.300030 + 0.519666i
\(599\) −24.6424 + 14.2273i −1.00686 + 0.581312i −0.910271 0.414013i \(-0.864127\pi\)
−0.0965902 + 0.995324i \(0.530794\pi\)
\(600\) 0 0
\(601\) 29.2553i 1.19335i 0.802484 + 0.596673i \(0.203511\pi\)
−0.802484 + 0.596673i \(0.796489\pi\)
\(602\) −6.64929 4.50303i −0.271005 0.183530i
\(603\) 0 0
\(604\) −1.47531 + 2.55532i −0.0600297 + 0.103974i
\(605\) 0 0
\(606\) 0 0
\(607\) −12.9160 + 22.3712i −0.524246 + 0.908020i 0.475356 + 0.879794i \(0.342319\pi\)
−0.999602 + 0.0282267i \(0.991014\pi\)
\(608\) 0.0352762i 0.00143064i
\(609\) 0 0
\(610\) 0 0
\(611\) −19.7583 11.4075i −0.799337 0.461498i
\(612\) 0 0
\(613\) 14.0680 8.12216i 0.568201 0.328051i −0.188230 0.982125i \(-0.560275\pi\)
0.756430 + 0.654074i \(0.226942\pi\)
\(614\) 6.18910 10.7198i 0.249772 0.432618i
\(615\) 0 0
\(616\) 7.01299 3.40433i 0.282562 0.137164i
\(617\) −31.8398 −1.28182 −0.640911 0.767615i \(-0.721443\pi\)
−0.640911 + 0.767615i \(0.721443\pi\)
\(618\) 0 0
\(619\) −8.01055 + 4.62490i −0.321971 + 0.185890i −0.652271 0.757986i \(-0.726184\pi\)
0.330300 + 0.943876i \(0.392850\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 22.8625 0.916701
\(623\) 9.15669 13.5210i 0.366855 0.541708i
\(624\) 0 0
\(625\) 0 0
\(626\) 17.4013 + 30.1399i 0.695495 + 1.20463i
\(627\) 0 0
\(628\) −11.2481 + 19.4823i −0.448849 + 0.777429i
\(629\) −3.16958 −0.126379
\(630\) 0 0
\(631\) −10.3096 −0.410421 −0.205210 0.978718i \(-0.565788\pi\)
−0.205210 + 0.978718i \(0.565788\pi\)
\(632\) 4.15331 7.19375i 0.165210 0.286152i
\(633\) 0 0
\(634\) −3.39355 5.87780i −0.134775 0.233437i
\(635\) 0 0
\(636\) 0 0
\(637\) 27.2407 + 3.93185i 1.07931 + 0.155786i
\(638\) 26.2205 1.03808
\(639\) 0 0
\(640\) 0 0
\(641\) 11.1181 6.41906i 0.439140 0.253538i −0.264093 0.964497i \(-0.585072\pi\)
0.703233 + 0.710960i \(0.251739\pi\)
\(642\) 0 0
\(643\) 8.96224 0.353436 0.176718 0.984262i \(-0.443452\pi\)
0.176718 + 0.984262i \(0.443452\pi\)
\(644\) 9.84873 + 0.707107i 0.388094 + 0.0278639i
\(645\) 0 0
\(646\) 0.00704821 0.0122079i 0.000277308 0.000480312i
\(647\) −39.2919 + 22.6852i −1.54472 + 0.891846i −0.546191 + 0.837660i \(0.683923\pi\)
−0.998531 + 0.0541854i \(0.982744\pi\)
\(648\) 0 0
\(649\) −14.2142 8.20656i −0.557955 0.322136i
\(650\) 0 0
\(651\) 0 0
\(652\) 22.8070i 0.893192i
\(653\) 16.3997 28.4051i 0.641769 1.11158i −0.343268 0.939237i \(-0.611534\pi\)
0.985038 0.172340i \(-0.0551326\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 3.15539 5.46530i 0.123197 0.213384i
\(657\) 0 0
\(658\) −13.8110 + 6.70430i −0.538409 + 0.261361i
\(659\) 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 −0.348759 0.937213i \(-0.613397\pi\)
0.637270 + 0.770640i \(0.280063\pi\)
\(662\) −5.56985 9.64726i −0.216478 0.374951i
\(663\) 0 0
\(664\) 10.3490i 0.401618i
\(665\) 0 0
\(666\) 0 0
\(667\) 28.7620 + 16.6057i 1.11367 + 0.642976i
\(668\) 7.66398 4.42480i 0.296528 0.171201i
\(669\) 0 0
\(670\) 0 0
\(671\) 33.9449 1.31043
\(672\) 0 0
\(673\) 0.179617i 0.00692372i −0.999994 0.00346186i \(-0.998898\pi\)
0.999994 0.00346186i \(-0.00110195\pi\)
\(674\) 1.37794 + 0.795555i 0.0530763 + 0.0306436i
\(675\) 0 0
\(676\) −1.22973 2.12995i −0.0472973 0.0819213i
\(677\) −35.8623 20.7051i −1.37830 0.795763i −0.386346 0.922354i \(-0.626263\pi\)
−0.991955 + 0.126591i \(0.959596\pi\)
\(678\) 0 0
\(679\) 41.2586 + 2.96224i 1.58336 + 0.113680i
\(680\) 0 0
\(681\) 0 0
\(682\) −1.22047 2.11391i −0.0467340 0.0809457i
\(683\) 21.7026 + 37.5900i 0.830427 + 1.43834i 0.897700 + 0.440608i \(0.145237\pi\)
−0.0672723 + 0.997735i \(0.521430\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 12.4691 13.6938i 0.476073 0.522834i
\(687\) 0 0
\(688\) 2.62863 + 1.51764i 0.100215 + 0.0578594i
\(689\) 8.45069 + 14.6370i 0.321946 + 0.557626i
\(690\) 0 0
\(691\) −16.8728 9.74150i −0.641871 0.370584i 0.143464 0.989656i \(-0.454176\pi\)
−0.785335 + 0.619071i \(0.787509\pi\)
\(692\) 7.73686i 0.294111i
\(693\) 0 0
\(694\) −15.4568 −0.586732
\(695\) 0 0
\(696\) 0 0
\(697\) −2.18394 + 1.26090i −0.0827228 + 0.0477600i
\(698\) 0.506675 + 0.292529i 0.0191779 + 0.0110724i
\(699\) 0 0
\(700\) 0 0
\(701\) 47.0245i 1.77609i 0.459755 + 0.888046i \(0.347937\pi\)
−0.459755 + 0.888046i \(0.652063\pi\)
\(702\) 0 0
\(703\) 0.139903 + 0.242319i 0.00527653 + 0.00913922i
\(704\) −2.55171 + 1.47323i −0.0961713 + 0.0555245i
\(705\) 0 0
\(706\) 3.67576i 0.138339i
\(707\) −20.8539 42.9595i −0.784292 1.61566i
\(708\) 0 0
\(709\) −24.2227 + 41.9549i −0.909701 + 1.57565i −0.0952213 + 0.995456i \(0.530356\pi\)
−0.814480 + 0.580192i \(0.802977\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −3.08604 + 5.34519i −0.115654 + 0.200319i
\(713\) 3.09173i 0.115786i
\(714\) 0 0
\(715\) 0 0
\(716\) 0.417291 + 0.240923i 0.0155949 + 0.00900372i
\(717\) 0 0
\(718\) 17.4069 10.0499i 0.649620 0.375058i
\(719\) 20.6632 35.7897i 0.770606 1.33473i −0.166625 0.986020i \(-0.553287\pi\)
0.937231 0.348709i \(-0.113380\pi\)
\(720\) 0 0
\(721\) −12.6400 + 18.6646i −0.470739 + 0.695106i
\(722\) 18.9988 0.707060
\(723\) 0 0
\(724\) 2.12069 1.22438i 0.0788148 0.0455037i
\(725\) 0 0
\(726\) 0 0
\(727\) −16.7905 −0.622726 −0.311363 0.950291i \(-0.600786\pi\)
−0.311363 + 0.950291i \(0.600786\pi\)
\(728\) −10.3760 0.744963i −0.384560 0.0276102i
\(729\) 0 0
\(730\) 0 0
\(731\) −0.606451 1.05040i −0.0224304 0.0388506i
\(732\) 0 0
\(733\) 15.3600 26.6043i 0.567335 0.982652i −0.429494 0.903070i \(-0.641308\pi\)
0.996828 0.0795826i \(-0.0253587\pi\)
\(734\) −19.9377 −0.735914
\(735\) 0 0
\(736\) −3.73205 −0.137565
\(737\) −18.4438 + 31.9457i −0.679388 + 1.17673i
\(738\) 0 0
\(739\) 15.3876 + 26.6521i 0.566041 + 0.980412i 0.996952 + 0.0780176i \(0.0248590\pi\)
−0.430911 + 0.902395i \(0.641808\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 11.3438 + 0.814447i 0.416443 + 0.0298993i
\(743\) −33.3616 −1.22392 −0.611960 0.790889i \(-0.709619\pi\)
−0.611960 + 0.790889i \(0.709619\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −29.2856 + 16.9081i −1.07222 + 0.619048i
\(747\) 0 0
\(748\) 1.17741 0.0430504
\(749\) −25.3025 + 37.3624i −0.924533 + 1.36519i
\(750\) 0 0
\(751\) 15.9452 27.6179i 0.581849 1.00779i −0.413411 0.910545i \(-0.635663\pi\)
0.995260 0.0972480i \(-0.0310040\pi\)
\(752\) 5.02520 2.90130i 0.183250 0.105800i
\(753\) 0 0
\(754\) −30.3018 17.4947i −1.10353 0.637121i
\(755\) 0 0
\(756\) 0 0
\(757\) 10.9065i 0.396404i 0.980161 + 0.198202i \(0.0635102\pi\)
−0.980161 + 0.198202i \(0.936490\pi\)
\(758\) 13.3807 23.1761i 0.486010 0.841793i
\(759\) 0 0
\(760\) 0 0
\(761\) 12.2097 21.1479i 0.442602 0.766610i −0.555280 0.831664i \(-0.687389\pi\)
0.997882 + 0.0650543i \(0.0207220\pi\)
\(762\) 0 0
\(763\) 13.5160 + 27.8433i 0.489313 + 1.00800i
\(764\) 4.49457i 0.162608i
\(765\) 0 0
\(766\) −17.1310 + 9.89060i −0.618969 + 0.357362i
\(767\) 10.9511 + 18.9678i 0.395421 + 0.684889i
\(768\) 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
\(772\) 10.8859 + 6.28497i 0.391791 + 0.226201i
\(773\) −39.2894 + 22.6837i −1.41314 + 0.815877i −0.995683 0.0928193i \(-0.970412\pi\)
−0.417458 + 0.908696i \(0.637079\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −15.6344 −0.561243
\(777\) 0 0
\(778\) 5.18670i 0.185952i
\(779\) 0.192795 + 0.111310i 0.00690760 + 0.00398810i
\(780\) 0 0
\(781\) 2.84961 + 4.93566i 0.101967 + 0.176612i
\(782\) 1.29153 + 0.745667i 0.0461851 + 0.0266650i
\(783\) 0 0
\(784\) −4.33013 + 5.50000i −0.154647 + 0.196429i
\(785\) 0 0
\(786\) 0 0
\(787\) −1.67335 2.89834i −0.0596487 0.103314i 0.834659 0.550767i \(-0.185665\pi\)
−0.894308 + 0.447452i \(0.852331\pi\)
\(788\) −6.68740 11.5829i −0.238229 0.412625i
\(789\) 0 0
\(790\) 0 0
\(791\) −35.7700 2.56817i −1.27183 0.0913136i
\(792\) 0 0
\(793\) −39.2285 22.6486i −1.39304 0.804274i
\(794\) 2.88259 + 4.99280i 0.102299 +