Properties

Label 3150.2.bp.f.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.f.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 −0.0632797 0.997996i \(-0.520156\pi\)
0.832650 + 0.553800i \(0.186823\pi\)
\(12\) 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 −0.541379 0.840779i \(-0.682098\pi\)
0.457446 + 0.889237i \(0.348764\pi\)
\(18\) 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 −0.992328 0.123635i \(-0.960545\pi\)
0.603235 + 0.797564i \(0.293878\pi\)
\(24\) 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 \(-0.690470\pi\)
0.563304 0.826250i \(-0.309530\pi\)
\(30\) 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 \(-0.335977\pi\)
0.492790 + 0.870148i \(0.335977\pi\)
\(42\) 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 0.819519 0.573052i \(-0.194241\pi\)
−0.0865180 + 0.996250i \(0.527574\pi\)
\(48\) 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 0.679810 0.733388i \(-0.262062\pi\)
−0.975038 + 0.222039i \(0.928729\pi\)
\(54\) 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 0.625784 0.779997i \(-0.284779\pi\)
−0.988389 + 0.151946i \(0.951446\pi\)
\(60\) 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 \(0.0366153\pi\)
−0.993391 + 0.114777i \(0.963385\pi\)
\(72\) 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 \(0.192273\pi\)
−0.823046 + 0.567974i \(0.807727\pi\)
\(84\) 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 −0.654819 0.755786i \(-0.727255\pi\)
0.981939 + 0.189197i \(0.0605885\pi\)
\(90\) 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 \(-0.811702\pi\)
−0.0679057 0.997692i \(-0.521632\pi\)
\(102\) 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 \(0.475151\pi\)
−0.902381 + 0.430939i \(0.858182\pi\)
\(108\) 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 \(-0.720054\pi\)
−0.637554 + 0.770405i \(0.720054\pi\)
\(114\) 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 \(0.355227\pi\)
−0.997635 + 0.0687282i \(0.978106\pi\)
\(132\) 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 0.959513 0.281666i \(-0.0908870\pi\)
−0.723686 + 0.690129i \(0.757554\pi\)
\(138\) 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 \(0.00952537\pi\)
0.525688 + 0.850677i \(0.323808\pi\)
\(150\) 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 \(-0.888760\pi\)
0.939554 0.342402i \(-0.111240\pi\)
\(168\) 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 0.732593 0.680667i \(-0.238310\pi\)
−0.223178 + 0.974778i \(0.571643\pi\)
\(174\) 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 −0.484324 0.874889i \(-0.660934\pi\)
0.515514 + 0.856881i \(0.327601\pi\)
\(180\) 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 0.634168 0.773195i \(-0.281343\pi\)
−0.352523 + 0.935803i \(0.614676\pi\)
\(192\) 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 \(-0.658080\pi\)
−0.476458 + 0.879197i \(0.658080\pi\)
\(198\) 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 −0.449981 0.893038i \(-0.648569\pi\)
0.548403 + 0.836214i \(0.315236\pi\)
\(228\) 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 −0.725398 0.688330i \(-0.758344\pi\)
0.958810 + 0.284048i \(0.0916775\pi\)
\(234\) 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 \(-0.793002\pi\)
0.795900 0.605427i \(-0.206998\pi\)
\(240\) 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 \(-0.253273\pi\)
0.699798 + 0.714341i \(0.253273\pi\)
\(252\) 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 0.880222 0.474561i \(-0.157393\pi\)
0.0291289 + 0.999576i \(0.490727\pi\)
\(258\) 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 \(0.0722142\pi\)
−0.292396 + 0.956297i \(0.594452\pi\)
\(264\) 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 0.818413 0.574630i \(-0.194854\pi\)
−0.906851 + 0.421452i \(0.861521\pi\)
\(270\) 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 \(0.0920386\pi\)
−0.958487 + 0.285135i \(0.907961\pi\)
\(282\) 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 \(0.157200\pi\)
−0.880511 + 0.474026i \(0.842800\pi\)
\(294\) 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 \(0.0578136\pi\)
−0.335346 + 0.942095i \(0.608853\pi\)
\(312\) 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 −0.754849 0.655899i \(-0.772290\pi\)
0.945449 + 0.325769i \(0.105623\pi\)
\(318\) 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 0.580534 0.814236i \(-0.302844\pi\)
−0.995416 + 0.0956388i \(0.969511\pi\)
\(348\) 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 −0.412887 0.910782i \(-0.635480\pi\)
0.582317 + 0.812962i \(0.302146\pi\)
\(354\) 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 0.883221 0.468958i \(-0.155370\pi\)
0.0354812 + 0.999370i \(0.488704\pi\)
\(360\) 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 −0.00623078 0.999981i \(-0.501983\pi\)
−0.869124 + 0.494594i \(0.835317\pi\)
\(384\) 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 −0.609531 0.792762i \(-0.708642\pi\)
0.381787 + 0.924250i \(0.375309\pi\)
\(390\) 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 0.0623335 0.998055i \(-0.480146\pi\)
−0.833175 + 0.553010i \(0.813479\pi\)
\(402\) 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 \(-0.378677\pi\)
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 \(0.364090\pi\)
\(422\) 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 −0.0784178 0.996921i \(-0.524987\pi\)
0.824150 + 0.566372i \(0.191653\pi\)
\(432\) 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 −0.994144 0.108067i \(-0.965534\pi\)
0.590661 + 0.806920i \(0.298867\pi\)
\(444\) 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 \(-0.903994\pi\)
0.954858 0.297061i \(-0.0960065\pi\)
\(450\) 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 \(-0.794547\pi\)
−0.798829 + 0.601558i \(0.794547\pi\)
\(462\) 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 0.413331 0.910581i \(-0.364365\pi\)
−0.581920 + 0.813246i \(0.697698\pi\)
\(468\) 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 0.983728 0.179662i \(-0.0575004\pi\)
−0.647456 + 0.762103i \(0.724167\pi\)
\(480\) 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 \(0.0756095\pi\)
−0.971921 + 0.235307i \(0.924391\pi\)
\(492\) 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 \(-0.704771\pi\)
0.599845 0.800116i \(-0.295229\pi\)
\(504\) 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 −0.991153 0.132726i \(-0.957627\pi\)
0.610520 + 0.792001i \(0.290960\pi\)
\(510\) 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 0.911374 0.411580i \(-0.135023\pi\)
−0.812125 + 0.583483i \(0.801689\pi\)
\(522\) 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 0.947168 0.320738i \(-0.103931\pi\)
−0.751351 + 0.659902i \(0.770598\pi\)
\(558\) 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 0.0757935 0.997124i \(-0.475851\pi\)
0.901431 + 0.432923i \(0.142518\pi\)
\(564\) 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 \(0.0762539\pi\)
0.691207 + 0.722657i \(0.257079\pi\)
\(570\) 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 \(0.310962\pi\)
−0.559582 + 0.828775i \(0.689038\pi\)
\(588\) 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 0.120683 0.992691i \(-0.461491\pi\)
−0.799354 + 0.600860i \(0.794825\pi\)
\(594\) 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 0.0965902 0.995324i \(-0.469206\pi\)
0.910271 + 0.414013i \(0.135873\pi\)
\(600\) 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 \(-0.278557\pi\)
0.640911 + 0.767615i \(0.278557\pi\)
\(618\) 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 −0.703233 0.710960i \(-0.748261\pi\)
0.264093 + 0.964497i \(0.414928\pi\)
\(642\) 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 \(-0.316077\pi\)
0.998531 0.0541854i \(-0.0172562\pi\)
\(648\) 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 \(0.388466\pi\)
−0.985038 + 0.172340i \(0.944867\pi\)
\(654\) 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 \(0.118734\pi\)
−0.931233 + 0.364425i \(0.881266\pi\)
\(660\) 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 0.991955 0.126591i \(-0.0404037\pi\)
0.386346 + 0.922354i \(0.373737\pi\)
\(678\) 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 \(-0.854763\pi\)
0.0672723 0.997735i \(-0.478570\pi\)
\(684\) 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 \(-0.652063\pi\)
0.459755 0.888046i \(-0.347937\pi\)
\(702\) 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 \(0.446713\pi\)
−0.937231 + 0.348709i \(0.886620\pi\)
\(720\) 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 \(-0.290381\pi\)
0.611960 + 0.790889i \(0.290381\pi\)
\(744\) 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 −0.997882 0.0650543i \(-0.979278\pi\)
0.555280 + 0.831664i \(0.312611\pi\)
\(762\) 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 0.417458 0.908696i \(-0.362921\pi\)
0.995683 + 0.0928193i \(0.0295879\pi\)
\(774\) 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 0.177188i
\(795\) 0 0
\(796\) −23.5169 13.5775i −0.833535