Properties

Label 912.2.bb.f.31.1
Level $912$
Weight $2$
Character 912.31
Analytic conductor $7.282$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 912.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.28235666434\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{6})\)
Coefficient field: 6.0.954288.1
Defining polynomial: \(x^{6} - x^{5} - 2 x^{4} + 3 x^{3} - 6 x^{2} - 9 x + 27\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 31.1
Root \(0.403374 - 1.68443i\) of defining polynomial
Character \(\chi\) \(=\) 912.31
Dual form 912.2.bb.f.559.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.66044 - 2.87597i) q^{5} +2.71781i q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{3} +(-1.66044 - 2.87597i) q^{5} +2.71781i q^{7} +(-0.500000 + 0.866025i) q^{9} +0.985762i q^{11} +(4.33502 + 2.50283i) q^{13} +(1.66044 - 2.87597i) q^{15} +(-2.51414 - 4.35461i) q^{17} +(0.193252 + 4.35461i) q^{19} +(-2.35369 + 1.35891i) q^{21} +(3.68872 + 2.12968i) q^{23} +(-3.01414 + 5.22064i) q^{25} -1.00000 q^{27} +(5.83502 + 3.36885i) q^{29} +2.32088 q^{31} +(-0.853695 + 0.492881i) q^{33} +(7.81635 - 4.51277i) q^{35} +8.27925i q^{37} +5.00565i q^{39} +(-9.96265 + 5.75194i) q^{41} +(9.48133 - 5.47405i) q^{43} +3.32088 q^{45} +(6.41478 + 3.70357i) q^{47} -0.386505 q^{49} +(2.51414 - 4.35461i) q^{51} +(5.14631 + 2.97122i) q^{53} +(2.83502 - 1.63680i) q^{55} +(-3.67458 + 2.34467i) q^{57} +(-1.66044 - 2.87597i) q^{59} +(3.62763 - 6.28324i) q^{61} +(-2.35369 - 1.35891i) q^{63} -16.6232i q^{65} +(-6.67458 + 11.5607i) q^{67} +4.25936i q^{69} +(2.19325 + 3.79882i) q^{71} +(-2.52827 - 4.37910i) q^{73} -6.02827 q^{75} -2.67912 q^{77} +(-5.48133 - 9.49394i) q^{79} +(-0.500000 - 0.866025i) q^{81} +8.70923i q^{83} +(-8.34916 + 14.4612i) q^{85} +6.73770i q^{87} +(-6.10896 - 3.52701i) q^{89} +(-6.80221 + 11.7818i) q^{91} +(1.16044 + 2.00994i) q^{93} +(12.2029 - 7.78637i) q^{95} +(-7.12763 + 4.11514i) q^{97} +(-0.853695 - 0.492881i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{3} - 2q^{5} - 3q^{9} + O(q^{10}) \) \( 6q + 3q^{3} - 2q^{5} - 3q^{9} - 3q^{13} + 2q^{15} - 2q^{17} + 4q^{19} - 9q^{21} - 12q^{23} - 5q^{25} - 6q^{27} + 6q^{29} - 2q^{31} - 6q^{35} - 12q^{41} + 33q^{43} + 4q^{45} + 18q^{47} - 8q^{49} + 2q^{51} + 36q^{53} - 12q^{55} - q^{57} - 2q^{59} + 3q^{61} - 9q^{63} - 19q^{67} + 16q^{71} + 11q^{73} - 10q^{75} - 32q^{77} - 9q^{79} - 3q^{81} - 8q^{85} + 6q^{89} - q^{91} - q^{93} + 26q^{95} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(229\) \(305\) \(799\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0 0
\(5\) −1.66044 2.87597i −0.742572 1.28617i −0.951320 0.308204i \(-0.900272\pi\)
0.208748 0.977969i \(-0.433061\pi\)
\(6\) 0 0
\(7\) 2.71781i 1.02724i 0.858019 + 0.513618i \(0.171695\pi\)
−0.858019 + 0.513618i \(0.828305\pi\)
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0.985762i 0.297218i 0.988896 + 0.148609i \(0.0474796\pi\)
−0.988896 + 0.148609i \(0.952520\pi\)
\(12\) 0 0
\(13\) 4.33502 + 2.50283i 1.20232 + 0.694159i 0.961070 0.276304i \(-0.0891098\pi\)
0.241248 + 0.970463i \(0.422443\pi\)
\(14\) 0 0
\(15\) 1.66044 2.87597i 0.428724 0.742572i
\(16\) 0 0
\(17\) −2.51414 4.35461i −0.609768 1.05615i −0.991278 0.131784i \(-0.957929\pi\)
0.381511 0.924364i \(-0.375404\pi\)
\(18\) 0 0
\(19\) 0.193252 + 4.35461i 0.0443351 + 0.999017i
\(20\) 0 0
\(21\) −2.35369 + 1.35891i −0.513618 + 0.296538i
\(22\) 0 0
\(23\) 3.68872 + 2.12968i 0.769150 + 0.444069i 0.832571 0.553918i \(-0.186868\pi\)
−0.0634210 + 0.997987i \(0.520201\pi\)
\(24\) 0 0
\(25\) −3.01414 + 5.22064i −0.602827 + 1.04413i
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 5.83502 + 3.36885i 1.08354 + 0.625580i 0.931848 0.362848i \(-0.118196\pi\)
0.151688 + 0.988428i \(0.451529\pi\)
\(30\) 0 0
\(31\) 2.32088 0.416843 0.208422 0.978039i \(-0.433167\pi\)
0.208422 + 0.978039i \(0.433167\pi\)
\(32\) 0 0
\(33\) −0.853695 + 0.492881i −0.148609 + 0.0857995i
\(34\) 0 0
\(35\) 7.81635 4.51277i 1.32120 0.762797i
\(36\) 0 0
\(37\) 8.27925i 1.36110i 0.732701 + 0.680550i \(0.238259\pi\)
−0.732701 + 0.680550i \(0.761741\pi\)
\(38\) 0 0
\(39\) 5.00565i 0.801546i
\(40\) 0 0
\(41\) −9.96265 + 5.75194i −1.55591 + 0.898302i −0.558263 + 0.829664i \(0.688532\pi\)
−0.997642 + 0.0686385i \(0.978134\pi\)
\(42\) 0 0
\(43\) 9.48133 5.47405i 1.44589 0.834784i 0.447656 0.894206i \(-0.352259\pi\)
0.998233 + 0.0594217i \(0.0189257\pi\)
\(44\) 0 0
\(45\) 3.32088 0.495048
\(46\) 0 0
\(47\) 6.41478 + 3.70357i 0.935692 + 0.540222i 0.888607 0.458669i \(-0.151674\pi\)
0.0470845 + 0.998891i \(0.485007\pi\)
\(48\) 0 0
\(49\) −0.386505 −0.0552150
\(50\) 0 0
\(51\) 2.51414 4.35461i 0.352050 0.609768i
\(52\) 0 0
\(53\) 5.14631 + 2.97122i 0.706899 + 0.408129i 0.809912 0.586551i \(-0.199515\pi\)
−0.103013 + 0.994680i \(0.532848\pi\)
\(54\) 0 0
\(55\) 2.83502 1.63680i 0.382274 0.220706i
\(56\) 0 0
\(57\) −3.67458 + 2.34467i −0.486710 + 0.310559i
\(58\) 0 0
\(59\) −1.66044 2.87597i −0.216171 0.374419i 0.737463 0.675387i \(-0.236024\pi\)
−0.953634 + 0.300968i \(0.902690\pi\)
\(60\) 0 0
\(61\) 3.62763 6.28324i 0.464471 0.804487i −0.534707 0.845038i \(-0.679578\pi\)
0.999177 + 0.0405508i \(0.0129113\pi\)
\(62\) 0 0
\(63\) −2.35369 1.35891i −0.296538 0.171206i
\(64\) 0 0
\(65\) 16.6232i 2.06185i
\(66\) 0 0
\(67\) −6.67458 + 11.5607i −0.815430 + 1.41237i 0.0935894 + 0.995611i \(0.470166\pi\)
−0.909019 + 0.416755i \(0.863167\pi\)
\(68\) 0 0
\(69\) 4.25936i 0.512767i
\(70\) 0 0
\(71\) 2.19325 + 3.79882i 0.260291 + 0.450838i 0.966319 0.257346i \(-0.0828481\pi\)
−0.706028 + 0.708184i \(0.749515\pi\)
\(72\) 0 0
\(73\) −2.52827 4.37910i −0.295912 0.512535i 0.679285 0.733875i \(-0.262290\pi\)
−0.975197 + 0.221340i \(0.928957\pi\)
\(74\) 0 0
\(75\) −6.02827 −0.696085
\(76\) 0 0
\(77\) −2.67912 −0.305314
\(78\) 0 0
\(79\) −5.48133 9.49394i −0.616697 1.06815i −0.990084 0.140476i \(-0.955137\pi\)
0.373387 0.927676i \(-0.378196\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 8.70923i 0.955962i 0.878370 + 0.477981i \(0.158631\pi\)
−0.878370 + 0.477981i \(0.841369\pi\)
\(84\) 0 0
\(85\) −8.34916 + 14.4612i −0.905593 + 1.56853i
\(86\) 0 0
\(87\) 6.73770i 0.722358i
\(88\) 0 0
\(89\) −6.10896 3.52701i −0.647548 0.373862i 0.139968 0.990156i \(-0.455300\pi\)
−0.787516 + 0.616294i \(0.788633\pi\)
\(90\) 0 0
\(91\) −6.80221 + 11.7818i −0.713065 + 1.23507i
\(92\) 0 0
\(93\) 1.16044 + 2.00994i 0.120332 + 0.208422i
\(94\) 0 0
\(95\) 12.2029 7.78637i 1.25199 0.798865i
\(96\) 0 0
\(97\) −7.12763 + 4.11514i −0.723701 + 0.417829i −0.816113 0.577892i \(-0.803876\pi\)
0.0924121 + 0.995721i \(0.470542\pi\)
\(98\) 0 0
\(99\) −0.853695 0.492881i −0.0857995 0.0495364i
\(100\) 0 0
\(101\) 2.83502 4.91040i 0.282095 0.488603i −0.689805 0.723995i \(-0.742304\pi\)
0.971901 + 0.235392i \(0.0756373\pi\)
\(102\) 0 0
\(103\) −10.1222 −0.997367 −0.498683 0.866784i \(-0.666183\pi\)
−0.498683 + 0.866784i \(0.666183\pi\)
\(104\) 0 0
\(105\) 7.81635 + 4.51277i 0.762797 + 0.440401i
\(106\) 0 0
\(107\) 0.971726 0.0939403 0.0469702 0.998896i \(-0.485043\pi\)
0.0469702 + 0.998896i \(0.485043\pi\)
\(108\) 0 0
\(109\) −0.579757 + 0.334723i −0.0555307 + 0.0320607i −0.527508 0.849550i \(-0.676874\pi\)
0.471978 + 0.881611i \(0.343540\pi\)
\(110\) 0 0
\(111\) −7.17004 + 4.13963i −0.680550 + 0.392916i
\(112\) 0 0
\(113\) 8.39291i 0.789539i −0.918780 0.394769i \(-0.870825\pi\)
0.918780 0.394769i \(-0.129175\pi\)
\(114\) 0 0
\(115\) 14.1449i 1.31901i
\(116\) 0 0
\(117\) −4.33502 + 2.50283i −0.400773 + 0.231386i
\(118\) 0 0
\(119\) 11.8350 6.83295i 1.08491 0.626376i
\(120\) 0 0
\(121\) 10.0283 0.911661
\(122\) 0 0
\(123\) −9.96265 5.75194i −0.898302 0.518635i
\(124\) 0 0
\(125\) 3.41478 0.305427
\(126\) 0 0
\(127\) 3.70739 6.42139i 0.328978 0.569806i −0.653332 0.757072i \(-0.726629\pi\)
0.982309 + 0.187266i \(0.0599626\pi\)
\(128\) 0 0
\(129\) 9.48133 + 5.47405i 0.834784 + 0.481963i
\(130\) 0 0
\(131\) −16.5424 + 9.55077i −1.44532 + 0.834454i −0.998197 0.0600198i \(-0.980884\pi\)
−0.447120 + 0.894474i \(0.647550\pi\)
\(132\) 0 0
\(133\) −11.8350 + 0.525224i −1.02623 + 0.0455427i
\(134\) 0 0
\(135\) 1.66044 + 2.87597i 0.142908 + 0.247524i
\(136\) 0 0
\(137\) 10.5424 18.2600i 0.900699 1.56006i 0.0741101 0.997250i \(-0.476388\pi\)
0.826589 0.562806i \(-0.190278\pi\)
\(138\) 0 0
\(139\) 10.8588 + 6.26931i 0.921028 + 0.531756i 0.883963 0.467557i \(-0.154866\pi\)
0.0370651 + 0.999313i \(0.488199\pi\)
\(140\) 0 0
\(141\) 7.40715i 0.623794i
\(142\) 0 0
\(143\) −2.46719 + 4.27330i −0.206317 + 0.357351i
\(144\) 0 0
\(145\) 22.3751i 1.85815i
\(146\) 0 0
\(147\) −0.193252 0.334723i −0.0159392 0.0276075i
\(148\) 0 0
\(149\) 3.04695 + 5.27747i 0.249616 + 0.432347i 0.963419 0.267999i \(-0.0863624\pi\)
−0.713804 + 0.700346i \(0.753029\pi\)
\(150\) 0 0
\(151\) −12.6983 −1.03337 −0.516687 0.856174i \(-0.672835\pi\)
−0.516687 + 0.856174i \(0.672835\pi\)
\(152\) 0 0
\(153\) 5.02827 0.406512
\(154\) 0 0
\(155\) −3.85369 6.67479i −0.309536 0.536132i
\(156\) 0 0
\(157\) −8.43438 14.6088i −0.673137 1.16591i −0.977010 0.213195i \(-0.931613\pi\)
0.303873 0.952713i \(-0.401720\pi\)
\(158\) 0 0
\(159\) 5.94244i 0.471266i
\(160\) 0 0
\(161\) −5.78807 + 10.0252i −0.456164 + 0.790100i
\(162\) 0 0
\(163\) 16.1932i 1.26835i −0.773189 0.634175i \(-0.781340\pi\)
0.773189 0.634175i \(-0.218660\pi\)
\(164\) 0 0
\(165\) 2.83502 + 1.63680i 0.220706 + 0.127425i
\(166\) 0 0
\(167\) 6.68872 11.5852i 0.517588 0.896489i −0.482203 0.876060i \(-0.660163\pi\)
0.999791 0.0204298i \(-0.00650347\pi\)
\(168\) 0 0
\(169\) 6.02827 + 10.4413i 0.463713 + 0.803175i
\(170\) 0 0
\(171\) −3.86783 2.00994i −0.295780 0.153704i
\(172\) 0 0
\(173\) 10.9572 6.32614i 0.833060 0.480967i −0.0218394 0.999761i \(-0.506952\pi\)
0.854899 + 0.518794i \(0.173619\pi\)
\(174\) 0 0
\(175\) −14.1887 8.19186i −1.07257 0.619246i
\(176\) 0 0
\(177\) 1.66044 2.87597i 0.124806 0.216171i
\(178\) 0 0
\(179\) 0.735663 0.0549861 0.0274930 0.999622i \(-0.491248\pi\)
0.0274930 + 0.999622i \(0.491248\pi\)
\(180\) 0 0
\(181\) 5.42024 + 3.12938i 0.402883 + 0.232605i 0.687727 0.725969i \(-0.258608\pi\)
−0.284844 + 0.958574i \(0.591942\pi\)
\(182\) 0 0
\(183\) 7.25526 0.536325
\(184\) 0 0
\(185\) 23.8109 13.7472i 1.75061 1.01072i
\(186\) 0 0
\(187\) 4.29261 2.47834i 0.313907 0.181234i
\(188\) 0 0
\(189\) 2.71781i 0.197692i
\(190\) 0 0
\(191\) 1.84571i 0.133551i −0.997768 0.0667754i \(-0.978729\pi\)
0.997768 0.0667754i \(-0.0212711\pi\)
\(192\) 0 0
\(193\) −3.92024 + 2.26335i −0.282185 + 0.162920i −0.634412 0.772995i \(-0.718758\pi\)
0.352227 + 0.935915i \(0.385424\pi\)
\(194\) 0 0
\(195\) 14.3961 8.31160i 1.03093 0.595206i
\(196\) 0 0
\(197\) −13.6892 −0.975318 −0.487659 0.873034i \(-0.662149\pi\)
−0.487659 + 0.873034i \(0.662149\pi\)
\(198\) 0 0
\(199\) 2.10389 + 1.21468i 0.149141 + 0.0861067i 0.572714 0.819756i \(-0.305891\pi\)
−0.423572 + 0.905862i \(0.639224\pi\)
\(200\) 0 0
\(201\) −13.3492 −0.941577
\(202\) 0 0
\(203\) −9.15591 + 15.8585i −0.642619 + 1.11305i
\(204\) 0 0
\(205\) 33.0848 + 19.1015i 2.31074 + 1.33411i
\(206\) 0 0
\(207\) −3.68872 + 2.12968i −0.256383 + 0.148023i
\(208\) 0 0
\(209\) −4.29261 + 0.190501i −0.296926 + 0.0131772i
\(210\) 0 0
\(211\) 6.77394 + 11.7328i 0.466337 + 0.807720i 0.999261 0.0384438i \(-0.0122401\pi\)
−0.532924 + 0.846163i \(0.678907\pi\)
\(212\) 0 0
\(213\) −2.19325 + 3.79882i −0.150279 + 0.260291i
\(214\) 0 0
\(215\) −31.4864 18.1787i −2.14735 1.23978i
\(216\) 0 0
\(217\) 6.30773i 0.428197i
\(218\) 0 0
\(219\) 2.52827 4.37910i 0.170845 0.295912i
\(220\) 0 0
\(221\) 25.1698i 1.69310i
\(222\) 0 0
\(223\) 7.80221 + 13.5138i 0.522475 + 0.904953i 0.999658 + 0.0261490i \(0.00832443\pi\)
−0.477183 + 0.878804i \(0.658342\pi\)
\(224\) 0 0
\(225\) −3.01414 5.22064i −0.200942 0.348043i
\(226\) 0 0
\(227\) 16.2926 1.08138 0.540689 0.841222i \(-0.318163\pi\)
0.540689 + 0.841222i \(0.318163\pi\)
\(228\) 0 0
\(229\) 11.3118 0.747506 0.373753 0.927528i \(-0.378071\pi\)
0.373753 + 0.927528i \(0.378071\pi\)
\(230\) 0 0
\(231\) −1.33956 2.32018i −0.0881364 0.152657i
\(232\) 0 0
\(233\) −12.7977 22.1662i −0.838404 1.45216i −0.891229 0.453554i \(-0.850156\pi\)
0.0528253 0.998604i \(-0.483177\pi\)
\(234\) 0 0
\(235\) 24.5983i 1.60462i
\(236\) 0 0
\(237\) 5.48133 9.49394i 0.356050 0.616697i
\(238\) 0 0
\(239\) 2.47834i 0.160310i −0.996782 0.0801552i \(-0.974458\pi\)
0.996782 0.0801552i \(-0.0255416\pi\)
\(240\) 0 0
\(241\) −13.9148 8.03370i −0.896330 0.517496i −0.0203221 0.999793i \(-0.506469\pi\)
−0.876008 + 0.482297i \(0.839803\pi\)
\(242\) 0 0
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0 0
\(245\) 0.641769 + 1.11158i 0.0410011 + 0.0710160i
\(246\) 0 0
\(247\) −10.0611 + 19.3610i −0.640171 + 1.23191i
\(248\) 0 0
\(249\) −7.54241 + 4.35461i −0.477981 + 0.275962i
\(250\) 0 0
\(251\) −2.45213 1.41574i −0.154777 0.0893604i 0.420611 0.907241i \(-0.361816\pi\)
−0.575388 + 0.817881i \(0.695149\pi\)
\(252\) 0 0
\(253\) −2.09936 + 3.63620i −0.131986 + 0.228606i
\(254\) 0 0
\(255\) −16.6983 −1.04569
\(256\) 0 0
\(257\) −2.23113 1.28814i −0.139174 0.0803521i 0.428796 0.903401i \(-0.358938\pi\)
−0.567970 + 0.823049i \(0.692271\pi\)
\(258\) 0 0
\(259\) −22.5015 −1.39817
\(260\) 0 0
\(261\) −5.83502 + 3.36885i −0.361179 + 0.208527i
\(262\) 0 0
\(263\) −24.7977 + 14.3169i −1.52909 + 0.882821i −0.529690 + 0.848191i \(0.677692\pi\)
−0.999400 + 0.0346292i \(0.988975\pi\)
\(264\) 0 0
\(265\) 19.7342i 1.21226i
\(266\) 0 0
\(267\) 7.05402i 0.431699i
\(268\) 0 0
\(269\) −19.2685 + 11.1247i −1.17482 + 0.678282i −0.954810 0.297215i \(-0.903942\pi\)
−0.220009 + 0.975498i \(0.570609\pi\)
\(270\) 0 0
\(271\) −2.67004 + 1.54155i −0.162194 + 0.0936425i −0.578900 0.815399i \(-0.696518\pi\)
0.416706 + 0.909041i \(0.363184\pi\)
\(272\) 0 0
\(273\) −13.6044 −0.823377
\(274\) 0 0
\(275\) −5.14631 2.97122i −0.310334 0.179171i
\(276\) 0 0
\(277\) 4.25526 0.255674 0.127837 0.991795i \(-0.459197\pi\)
0.127837 + 0.991795i \(0.459197\pi\)
\(278\) 0 0
\(279\) −1.16044 + 2.00994i −0.0694739 + 0.120332i
\(280\) 0 0
\(281\) 13.2366 + 7.64215i 0.789629 + 0.455892i 0.839832 0.542847i \(-0.182654\pi\)
−0.0502030 + 0.998739i \(0.515987\pi\)
\(282\) 0 0
\(283\) −24.3027 + 14.0312i −1.44465 + 0.834068i −0.998155 0.0607193i \(-0.980661\pi\)
−0.446493 + 0.894787i \(0.647327\pi\)
\(284\) 0 0
\(285\) 12.8446 + 6.67479i 0.760850 + 0.395381i
\(286\) 0 0
\(287\) −15.6327 27.0766i −0.922769 1.59828i
\(288\) 0 0
\(289\) −4.14177 + 7.17375i −0.243633 + 0.421986i
\(290\) 0 0
\(291\) −7.12763 4.11514i −0.417829 0.241234i
\(292\) 0 0
\(293\) 1.11158i 0.0649390i 0.999473 + 0.0324695i \(0.0103372\pi\)
−0.999473 + 0.0324695i \(0.989663\pi\)
\(294\) 0 0
\(295\) −5.51414 + 9.55077i −0.321045 + 0.556067i
\(296\) 0 0
\(297\) 0.985762i 0.0571997i
\(298\) 0 0
\(299\) 10.6604 + 18.4644i 0.616509 + 1.06783i
\(300\) 0 0
\(301\) 14.8774 + 25.7685i 0.857521 + 1.48527i
\(302\) 0 0
\(303\) 5.67004 0.325735
\(304\) 0 0
\(305\) −24.0939 −1.37961
\(306\) 0 0
\(307\) −12.4485 21.5615i −0.710474 1.23058i −0.964679 0.263427i \(-0.915147\pi\)
0.254205 0.967150i \(-0.418186\pi\)
\(308\) 0 0
\(309\) −5.06108 8.76605i −0.287915 0.498683i
\(310\) 0 0
\(311\) 9.06236i 0.513879i −0.966427 0.256940i \(-0.917286\pi\)
0.966427 0.256940i \(-0.0827141\pi\)
\(312\) 0 0
\(313\) 3.19325 5.53088i 0.180493 0.312624i −0.761555 0.648100i \(-0.775564\pi\)
0.942049 + 0.335476i \(0.108897\pi\)
\(314\) 0 0
\(315\) 9.02554i 0.508532i
\(316\) 0 0
\(317\) 2.39611 + 1.38339i 0.134579 + 0.0776990i 0.565778 0.824558i \(-0.308576\pi\)
−0.431199 + 0.902257i \(0.641909\pi\)
\(318\) 0 0
\(319\) −3.32088 + 5.75194i −0.185934 + 0.322047i
\(320\) 0 0
\(321\) 0.485863 + 0.841540i 0.0271182 + 0.0469702i
\(322\) 0 0
\(323\) 18.4768 11.7896i 1.02808 0.655993i
\(324\) 0 0
\(325\) −26.1327 + 15.0877i −1.44958 + 0.836916i
\(326\) 0 0
\(327\) −0.579757 0.334723i −0.0320607 0.0185102i
\(328\) 0 0
\(329\) −10.0656 + 17.4342i −0.554936 + 0.961177i
\(330\) 0 0
\(331\) 27.6610 1.52038 0.760192 0.649698i \(-0.225105\pi\)
0.760192 + 0.649698i \(0.225105\pi\)
\(332\) 0 0
\(333\) −7.17004 4.13963i −0.392916 0.226850i
\(334\) 0 0
\(335\) 44.3310 2.42206
\(336\) 0 0
\(337\) 15.9202 9.19156i 0.867231 0.500696i 0.000803838 1.00000i \(-0.499744\pi\)
0.866427 + 0.499304i \(0.166411\pi\)
\(338\) 0 0
\(339\) 7.26847 4.19646i 0.394769 0.227920i
\(340\) 0 0
\(341\) 2.28784i 0.123893i
\(342\) 0 0
\(343\) 17.9742i 0.970518i
\(344\) 0 0
\(345\) 12.2498 7.07243i 0.659507 0.380767i
\(346\) 0 0
\(347\) 4.73153 2.73175i 0.254002 0.146648i −0.367594 0.929987i \(-0.619818\pi\)
0.621595 + 0.783339i \(0.286485\pi\)
\(348\) 0 0
\(349\) 22.6700 1.21350 0.606750 0.794893i \(-0.292473\pi\)
0.606750 + 0.794893i \(0.292473\pi\)
\(350\) 0 0
\(351\) −4.33502 2.50283i −0.231386 0.133591i
\(352\) 0 0
\(353\) 2.03735 0.108437 0.0542185 0.998529i \(-0.482733\pi\)
0.0542185 + 0.998529i \(0.482733\pi\)
\(354\) 0 0
\(355\) 7.28354 12.6155i 0.386570 0.669559i
\(356\) 0 0
\(357\) 11.8350 + 6.83295i 0.626376 + 0.361638i
\(358\) 0 0
\(359\) 30.7175 17.7348i 1.62121 0.936005i 0.634611 0.772832i \(-0.281160\pi\)
0.986597 0.163174i \(-0.0521731\pi\)
\(360\) 0 0
\(361\) −18.9253 + 1.68308i −0.996069 + 0.0885831i
\(362\) 0 0
\(363\) 5.01414 + 8.68474i 0.263174 + 0.455831i
\(364\) 0 0
\(365\) −8.39611 + 14.5425i −0.439472 + 0.761188i
\(366\) 0 0
\(367\) 1.44398 + 0.833682i 0.0753752 + 0.0435179i 0.537214 0.843446i \(-0.319477\pi\)
−0.461839 + 0.886964i \(0.652810\pi\)
\(368\) 0 0
\(369\) 11.5039i 0.598868i
\(370\) 0 0
\(371\) −8.07522 + 13.9867i −0.419245 + 0.726153i
\(372\) 0 0
\(373\) 17.5110i 0.906686i −0.891336 0.453343i \(-0.850231\pi\)
0.891336 0.453343i \(-0.149769\pi\)
\(374\) 0 0
\(375\) 1.70739 + 2.95729i 0.0881692 + 0.152714i
\(376\) 0 0
\(377\) 16.8633 + 29.2081i 0.868504 + 1.50429i
\(378\) 0 0
\(379\) 22.4905 1.15526 0.577630 0.816298i \(-0.303978\pi\)
0.577630 + 0.816298i \(0.303978\pi\)
\(380\) 0 0
\(381\) 7.41478 0.379871
\(382\) 0 0
\(383\) 10.1746 + 17.6229i 0.519897 + 0.900488i 0.999732 + 0.0231292i \(0.00736291\pi\)
−0.479836 + 0.877358i \(0.659304\pi\)
\(384\) 0 0
\(385\) 4.44852 + 7.70506i 0.226717 + 0.392686i
\(386\) 0 0
\(387\) 10.9481i 0.556523i
\(388\) 0 0
\(389\) 11.7881 20.4175i 0.597679 1.03521i −0.395484 0.918473i \(-0.629423\pi\)
0.993163 0.116738i \(-0.0372436\pi\)
\(390\) 0 0
\(391\) 21.4172i 1.08312i
\(392\) 0 0
\(393\) −16.5424 9.55077i −0.834454 0.481772i
\(394\) 0 0
\(395\) −18.2029 + 31.5283i −0.915885 + 1.58636i
\(396\) 0 0
\(397\) −16.3633 28.3421i −0.821250 1.42245i −0.904752 0.425939i \(-0.859944\pi\)
0.0835014 0.996508i \(-0.473390\pi\)
\(398\) 0 0
\(399\) −6.37237 9.98682i −0.319017 0.499966i
\(400\) 0 0
\(401\) −16.3533 + 9.44158i −0.816645 + 0.471490i −0.849258 0.527978i \(-0.822950\pi\)
0.0326134 + 0.999468i \(0.489617\pi\)
\(402\) 0 0
\(403\) 10.0611 + 5.80877i 0.501178 + 0.289355i
\(404\) 0 0
\(405\) −1.66044 + 2.87597i −0.0825080 + 0.142908i
\(406\) 0 0
\(407\) −8.16137 −0.404544
\(408\) 0 0
\(409\) 15.6646 + 9.04395i 0.774564 + 0.447194i 0.834500 0.551008i \(-0.185757\pi\)
−0.0599366 + 0.998202i \(0.519090\pi\)
\(410\) 0 0
\(411\) 21.0848 1.04004
\(412\) 0 0
\(413\) 7.81635 4.51277i 0.384617 0.222059i
\(414\) 0 0
\(415\) 25.0475 14.4612i 1.22953 0.709871i
\(416\) 0 0
\(417\) 12.5386i 0.614019i
\(418\) 0 0
\(419\) 0.353130i 0.0172515i 0.999963 + 0.00862577i \(0.00274570\pi\)
−0.999963 + 0.00862577i \(0.997254\pi\)
\(420\) 0 0
\(421\) 24.7977 14.3169i 1.20856 0.697765i 0.246119 0.969240i \(-0.420845\pi\)
0.962446 + 0.271474i \(0.0875112\pi\)
\(422\) 0 0
\(423\) −6.41478 + 3.70357i −0.311897 + 0.180074i
\(424\) 0 0
\(425\) 30.3118 1.47034
\(426\) 0 0
\(427\) 17.0767 + 9.85922i 0.826398 + 0.477121i
\(428\) 0 0
\(429\) −4.93438 −0.238234
\(430\) 0 0
\(431\) −6.41478 + 11.1107i −0.308989 + 0.535185i −0.978141 0.207940i \(-0.933324\pi\)
0.669152 + 0.743125i \(0.266657\pi\)
\(432\) 0 0
\(433\) −20.0525 11.5773i −0.963664 0.556371i −0.0663649 0.997795i \(-0.521140\pi\)
−0.897299 + 0.441424i \(0.854473\pi\)
\(434\) 0 0
\(435\) 19.3774 11.1876i 0.929077 0.536403i
\(436\) 0 0
\(437\) −8.56108 + 16.4745i −0.409532 + 0.788082i
\(438\) 0 0
\(439\) 13.0894 + 22.6714i 0.624721 + 1.08205i 0.988595 + 0.150600i \(0.0481206\pi\)
−0.363874 + 0.931448i \(0.618546\pi\)
\(440\) 0 0
\(441\) 0.193252 0.334723i 0.00920250 0.0159392i
\(442\) 0 0
\(443\) −17.2871 9.98074i −0.821337 0.474199i 0.0295402 0.999564i \(-0.490596\pi\)
−0.850877 + 0.525364i \(0.823929\pi\)
\(444\) 0 0
\(445\) 23.4256i 1.11048i
\(446\) 0 0
\(447\) −3.04695 + 5.27747i −0.144116 + 0.249616i
\(448\) 0 0
\(449\) 30.3224i 1.43100i 0.698613 + 0.715500i \(0.253801\pi\)
−0.698613 + 0.715500i \(0.746199\pi\)
\(450\) 0 0
\(451\) −5.67004 9.82080i −0.266992 0.462444i
\(452\) 0 0
\(453\) −6.34916 10.9971i −0.298309 0.516687i
\(454\) 0 0
\(455\) 45.1787 2.11801
\(456\) 0 0
\(457\) −14.5569 −0.680945 −0.340473 0.940254i \(-0.610587\pi\)
−0.340473 + 0.940254i \(0.610587\pi\)
\(458\) 0 0
\(459\) 2.51414 + 4.35461i 0.117350 + 0.203256i
\(460\) 0 0
\(461\) 18.5147 + 32.0683i 0.862314 + 1.49357i 0.869690 + 0.493599i \(0.164319\pi\)
−0.00737587 + 0.999973i \(0.502348\pi\)
\(462\) 0 0
\(463\) 39.4283i 1.83239i 0.400735 + 0.916194i \(0.368755\pi\)
−0.400735 + 0.916194i \(0.631245\pi\)
\(464\) 0 0
\(465\) 3.85369 6.67479i 0.178711 0.309536i
\(466\) 0 0
\(467\) 6.16620i 0.285338i 0.989770 + 0.142669i \(0.0455684\pi\)
−0.989770 + 0.142669i \(0.954432\pi\)
\(468\) 0 0
\(469\) −31.4198 18.1403i −1.45083 0.837639i
\(470\) 0 0
\(471\) 8.43438 14.6088i 0.388636 0.673137i
\(472\) 0 0
\(473\) 5.39611 + 9.34633i 0.248113 + 0.429745i
\(474\) 0 0
\(475\) −23.3163 12.1165i −1.06983 0.555943i
\(476\) 0 0
\(477\) −5.14631 + 2.97122i −0.235633 + 0.136043i
\(478\) 0 0
\(479\) −29.6382 17.1116i −1.35420 0.781849i −0.365367 0.930864i \(-0.619057\pi\)
−0.988835 + 0.149015i \(0.952390\pi\)
\(480\) 0 0
\(481\) −20.7215 + 35.8907i −0.944820 + 1.63648i
\(482\) 0 0
\(483\) −11.5761 −0.526733
\(484\) 0 0
\(485\) 23.6700 + 13.6659i 1.07480 + 0.620537i
\(486\) 0 0
\(487\) 18.0565 0.818220 0.409110 0.912485i \(-0.365839\pi\)
0.409110 + 0.912485i \(0.365839\pi\)
\(488\) 0 0
\(489\) 14.0237 8.09661i 0.634175 0.366141i
\(490\) 0 0
\(491\) −14.2871 + 8.24869i −0.644770 + 0.372258i −0.786450 0.617654i \(-0.788083\pi\)
0.141680 + 0.989913i \(0.454750\pi\)
\(492\) 0 0
\(493\) 33.8790i 1.52583i
\(494\) 0 0
\(495\) 3.27360i 0.147137i
\(496\) 0 0
\(497\) −10.3245 + 5.96085i −0.463117 + 0.267381i
\(498\) 0 0
\(499\) 29.0237 16.7569i 1.29928 0.750140i 0.319001 0.947754i \(-0.396653\pi\)
0.980280 + 0.197614i \(0.0633193\pi\)
\(500\) 0 0
\(501\) 13.3774 0.597660
\(502\) 0 0
\(503\) −4.62723 2.67153i −0.206318 0.119118i 0.393281 0.919418i \(-0.371340\pi\)
−0.599599 + 0.800301i \(0.704673\pi\)
\(504\) 0 0
\(505\) −18.8296 −0.837904
\(506\) 0 0
\(507\) −6.02827 + 10.4413i −0.267725 + 0.463713i
\(508\) 0 0
\(509\) 22.7074 + 13.1101i 1.00649 + 0.581096i 0.910161 0.414254i \(-0.135958\pi\)
0.0963261 + 0.995350i \(0.469291\pi\)
\(510\) 0 0
\(511\) 11.9016 6.87137i 0.526494 0.303972i
\(512\) 0 0
\(513\) −0.193252 4.35461i −0.00853230 0.192261i
\(514\) 0 0
\(515\) 16.8073 + 29.1111i 0.740617 + 1.28279i
\(516\) 0 0
\(517\) −3.65084 + 6.32344i −0.160564 + 0.278105i
\(518\) 0 0
\(519\) 10.9572 + 6.32614i 0.480967 + 0.277687i
\(520\) 0 0
\(521\) 29.6197i 1.29766i −0.760933 0.648830i \(-0.775259\pi\)
0.760933 0.648830i \(-0.224741\pi\)
\(522\) 0 0
\(523\) 3.70285 6.41353i 0.161914 0.280444i −0.773641 0.633624i \(-0.781566\pi\)
0.935555 + 0.353180i \(0.114900\pi\)
\(524\) 0 0
\(525\) 16.3837i 0.715044i
\(526\) 0 0
\(527\) −5.83502 10.1066i −0.254178 0.440248i
\(528\) 0 0
\(529\) −2.42892 4.20701i −0.105605 0.182913i
\(530\) 0 0
\(531\) 3.32088 0.144114
\(532\) 0 0
\(533\) −57.5844 −2.49426
\(534\) 0 0
\(535\) −1.61350 2.79466i −0.0697575 0.120823i
\(536\) 0 0
\(537\) 0.367832 + 0.637103i 0.0158731 + 0.0274930i
\(538\) 0 0
\(539\) 0.381002i 0.0164109i
\(540\) 0 0
\(541\) 7.30128 12.6462i 0.313907 0.543702i −0.665298 0.746578i \(-0.731695\pi\)
0.979204 + 0.202876i \(0.0650288\pi\)
\(542\) 0 0
\(543\) 6.25876i 0.268589i
\(544\) 0 0
\(545\) 1.92531 + 1.11158i 0.0824711 + 0.0476147i
\(546\) 0 0
\(547\) −20.8022 + 36.0305i −0.889438 + 1.54055i −0.0488977 + 0.998804i \(0.515571\pi\)
−0.840541 + 0.541749i \(0.817762\pi\)
\(548\) 0 0
\(549\) 3.62763 + 6.28324i 0.154824 + 0.268162i
\(550\) 0 0
\(551\) −13.5424 + 26.0603i −0.576926 + 1.11021i
\(552\) 0 0
\(553\) 25.8027 14.8972i 1.09724 0.633494i
\(554\) 0 0
\(555\) 23.8109 + 13.7472i 1.01072 + 0.583537i
\(556\) 0 0
\(557\) −22.2125 + 38.4731i −0.941172 + 1.63016i −0.177931 + 0.984043i \(0.556941\pi\)
−0.763240 + 0.646115i \(0.776393\pi\)
\(558\) 0 0
\(559\) 54.8023 2.31789
\(560\) 0 0
\(561\) 4.29261 + 2.47834i 0.181234 + 0.104636i
\(562\) 0 0
\(563\) −39.2545 −1.65438 −0.827189 0.561923i \(-0.810062\pi\)
−0.827189 + 0.561923i \(0.810062\pi\)
\(564\) 0 0
\(565\) −24.1378 + 13.9359i −1.01548 + 0.586290i
\(566\) 0 0
\(567\) 2.35369 1.35891i 0.0988459 0.0570687i
\(568\) 0 0
\(569\) 27.2761i 1.14347i 0.820438 + 0.571736i \(0.193730\pi\)
−0.820438 + 0.571736i \(0.806270\pi\)
\(570\) 0 0
\(571\) 1.07155i 0.0448429i 0.999749 + 0.0224214i \(0.00713757\pi\)
−0.999749 + 0.0224214i \(0.992862\pi\)
\(572\) 0 0
\(573\) 1.59843 0.922854i 0.0667754 0.0385528i
\(574\) 0 0
\(575\) −22.2366 + 12.8383i −0.927330 + 0.535394i
\(576\) 0 0
\(577\) 17.6135 0.733259 0.366630 0.930367i \(-0.380512\pi\)
0.366630 + 0.930367i \(0.380512\pi\)
\(578\) 0 0
\(579\) −3.92024 2.26335i −0.162920 0.0940617i
\(580\) 0 0
\(581\) −23.6700 −0.981999
\(582\) 0 0
\(583\) −2.92892 + 5.07303i −0.121303 + 0.210103i
\(584\) 0 0
\(585\) 14.3961 + 8.31160i 0.595206 + 0.343642i
\(586\) 0 0
\(587\) −19.2366 + 11.1063i −0.793979 + 0.458404i −0.841361 0.540473i \(-0.818245\pi\)
0.0473824 + 0.998877i \(0.484912\pi\)
\(588\) 0 0
\(589\) 0.448517 + 10.1066i 0.0184808 + 0.416433i
\(590\) 0 0
\(591\) −6.84462 11.8552i −0.281550 0.487659i
\(592\) 0 0
\(593\) −6.10896 + 10.5810i −0.250865 + 0.434511i −0.963764 0.266756i \(-0.914048\pi\)
0.712899 + 0.701266i \(0.247382\pi\)
\(594\) 0 0
\(595\) −39.3027 22.6914i −1.61126 0.930259i
\(596\) 0 0
\(597\) 2.42937i 0.0994274i
\(598\) 0 0
\(599\) 13.4955 23.3748i 0.551410 0.955070i −0.446763 0.894652i \(-0.647423\pi\)
0.998173 0.0604175i \(-0.0192432\pi\)
\(600\) 0 0
\(601\) 24.4514i 0.997392i −0.866777 0.498696i \(-0.833812\pi\)
0.866777 0.498696i \(-0.166188\pi\)
\(602\) 0 0
\(603\) −6.67458 11.5607i −0.271810 0.470789i
\(604\) 0 0
\(605\) −16.6514 28.8410i −0.676974 1.17255i
\(606\) 0 0
\(607\) −13.7175 −0.556777 −0.278388 0.960469i \(-0.589800\pi\)
−0.278388 + 0.960469i \(0.589800\pi\)
\(608\) 0 0
\(609\) −18.3118 −0.742032
\(610\) 0 0
\(611\) 18.5388 + 32.1101i 0.750000 + 1.29904i
\(612\) 0 0
\(613\) −20.6646 35.7921i −0.834634 1.44563i −0.894328 0.447413i \(-0.852346\pi\)
0.0596932 0.998217i \(-0.480988\pi\)
\(614\) 0 0
\(615\) 38.2031i 1.54050i
\(616\) 0 0
\(617\) 12.9157 22.3707i 0.519967 0.900609i −0.479764 0.877398i \(-0.659278\pi\)
0.999731 0.0232112i \(-0.00738901\pi\)
\(618\) 0 0
\(619\) 38.1873i 1.53488i −0.641121 0.767440i \(-0.721530\pi\)
0.641121 0.767440i \(-0.278470\pi\)
\(620\) 0 0
\(621\) −3.68872 2.12968i −0.148023 0.0854612i
\(622\) 0 0
\(623\) 9.58575 16.6030i 0.384045 0.665185i
\(624\) 0 0
\(625\) 9.40064 + 16.2824i 0.376026 + 0.651296i
\(626\) 0 0
\(627\) −2.31128 3.62226i −0.0923038 0.144659i
\(628\) 0 0
\(629\) 36.0529 20.8152i 1.43752 0.829955i
\(630\) 0 0
\(631\) −22.6090 13.0533i −0.900048 0.519643i −0.0228325 0.999739i \(-0.507268\pi\)
−0.877216 + 0.480096i \(0.840602\pi\)
\(632\) 0 0
\(633\) −6.77394 + 11.7328i −0.269240 + 0.466337i
\(634\) 0 0
\(635\) −24.6236 −0.977159
\(636\) 0 0
\(637\) −1.67551 0.967354i −0.0663860 0.0383280i
\(638\) 0 0
\(639\) −4.38650 −0.173527
\(640\) 0 0
\(641\) −11.4249 + 6.59617i −0.451257 + 0.260533i −0.708361 0.705851i \(-0.750565\pi\)
0.257104 + 0.966384i \(0.417232\pi\)
\(642\) 0 0
\(643\) 28.2790 16.3269i 1.11521 0.643870i 0.175040 0.984561i \(-0.443995\pi\)
0.940175 + 0.340692i \(0.110661\pi\)
\(644\) 0 0
\(645\) 36.3574i 1.43157i
\(646\) 0 0
\(647\) 23.5235i 0.924805i −0.886670 0.462403i \(-0.846988\pi\)
0.886670 0.462403i \(-0.153012\pi\)
\(648\) 0 0
\(649\) 2.83502 1.63680i 0.111284 0.0642500i
\(650\) 0 0
\(651\) −5.46265 + 3.15386i −0.214098 + 0.123610i
\(652\) 0 0
\(653\) 49.5953 1.94082 0.970408 0.241471i \(-0.0776299\pi\)
0.970408 + 0.241471i \(0.0776299\pi\)
\(654\) 0 0
\(655\) 54.9354 + 31.7170i 2.14651 + 1.23929i
\(656\) 0 0
\(657\) 5.05655 0.197275
\(658\) 0 0
\(659\) 7.49546 12.9825i 0.291982 0.505727i −0.682296 0.731076i \(-0.739019\pi\)
0.974278 + 0.225348i \(0.0723520\pi\)
\(660\) 0 0
\(661\) −19.5953 11.3134i −0.762171 0.440040i 0.0679038 0.997692i \(-0.478369\pi\)
−0.830075 + 0.557652i \(0.811702\pi\)
\(662\) 0 0
\(663\) 21.7977 12.5849i 0.846552 0.488757i
\(664\) 0 0
\(665\) 21.1619 + 33.1651i 0.820623 + 1.28609i
\(666\) 0 0
\(667\) 14.3492 + 24.8535i 0.555602 + 0.962330i
\(668\) 0 0
\(669\) −7.80221 + 13.5138i −0.301651 + 0.522475i
\(670\) 0 0
\(671\) 6.19378 + 3.57598i 0.239108 + 0.138049i
\(672\) 0 0
\(673\) 26.1398i 1.00762i 0.863815 + 0.503808i \(0.168068\pi\)
−0.863815 + 0.503808i \(0.831932\pi\)
\(674\) 0 0
\(675\) 3.01414 5.22064i 0.116014 0.200942i
\(676\) 0 0
\(677\) 4.42199i 0.169951i −0.996383 0.0849755i \(-0.972919\pi\)
0.996383 0.0849755i \(-0.0270812\pi\)
\(678\) 0 0
\(679\) −11.1842 19.3716i −0.429209 0.743413i
\(680\) 0 0
\(681\) 8.14631 + 14.1098i 0.312167 + 0.540689i
\(682\) 0 0
\(683\) 18.2361 0.697784 0.348892 0.937163i \(-0.386558\pi\)
0.348892 + 0.937163i \(0.386558\pi\)
\(684\) 0 0
\(685\) −70.0203 −2.67534
\(686\) 0 0
\(687\) 5.65591 + 9.79632i 0.215786 + 0.373753i
\(688\) 0 0
\(689\) 14.8729 + 25.7606i 0.566612 + 0.981401i
\(690\) 0 0
\(691\) 9.05341i 0.344408i 0.985061 + 0.172204i \(0.0550888\pi\)
−0.985061 + 0.172204i \(0.944911\pi\)
\(692\) 0 0
\(693\) 1.33956 2.32018i 0.0508856 0.0881364i
\(694\) 0 0
\(695\) 41.6393i 1.57947i
\(696\) 0 0
\(697\) 50.0950 + 28.9223i 1.89748 + 1.09551i
\(698\) 0 0
\(699\) 12.7977 22.1662i 0.484053 0.838404i
\(700\) 0 0
\(701\) −10.6514 18.4487i −0.402297 0.696798i 0.591706 0.806154i \(-0.298455\pi\)
−0.994003 + 0.109356i \(0.965121\pi\)
\(702\) 0 0
\(703\) −36.0529 + 1.59999i −1.35976 + 0.0603446i
\(704\) 0 0
\(705\) 21.3027 12.2991i 0.802308 0.463212i
\(706\) 0 0
\(707\) 13.3455 + 7.70506i 0.501911 + 0.289778i
\(708\) 0 0
\(709\) −2.50546 + 4.33959i −0.0940947 + 0.162977i −0.909230 0.416293i \(-0.863329\pi\)
0.815136 + 0.579270i \(0.196662\pi\)
\(710\) 0 0
\(711\) 10.9627 0.411132
\(712\) 0 0
\(713\) 8.56108 + 4.94274i 0.320615 + 0.185107i
\(714\) 0 0
\(715\) 16.3865 0.612821
\(716\) 0 0
\(717\) 2.14631 1.23917i 0.0801552 0.0462776i
\(718\) 0 0
\(719\) −28.2366 + 16.3024i −1.05305 + 0.607977i −0.923501 0.383596i \(-0.874685\pi\)
−0.129546 + 0.991573i \(0.541352\pi\)
\(720\) 0 0
\(721\) 27.5102i 1.02453i
\(722\) 0 0
\(723\) 16.0674i 0.597553i
\(724\) 0 0
\(725\) −35.1751 + 20.3084i −1.30637 + 0.754233i
\(726\) 0 0
\(727\) −15.8113 + 9.12865i −0.586408 + 0.338563i −0.763676 0.645600i \(-0.776607\pi\)
0.177268 + 0.984163i \(0.443274\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −47.6747 27.5250i −1.76331 1.01805i
\(732\) 0 0
\(733\) 46.0275 1.70006 0.850032 0.526731i \(-0.176583\pi\)
0.850032 + 0.526731i \(0.176583\pi\)
\(734\) 0 0
\(735\) −0.641769 + 1.11158i −0.0236720 + 0.0410011i
\(736\) 0 0
\(737\) −11.3961 6.57954i −0.419781 0.242361i
\(738\) 0 0
\(739\) 25.5607 14.7575i 0.940265 0.542862i 0.0502216 0.998738i \(-0.484007\pi\)
0.890043 + 0.455876i \(0.150674\pi\)
\(740\) 0 0
\(741\) −21.7977 + 0.967354i −0.800758 + 0.0355366i
\(742\) 0 0
\(743\) −7.18365 12.4424i −0.263543 0.456469i 0.703638 0.710558i \(-0.251558\pi\)
−0.967181 + 0.254089i \(0.918224\pi\)
\(744\) 0 0
\(745\) 10.1186 17.5259i 0.370715 0.642098i
\(746\) 0 0
\(747\) −7.54241 4.35461i −0.275962 0.159327i
\(748\) 0 0
\(749\) 2.64097i 0.0964989i
\(750\) 0 0
\(751\) −4.90157 + 8.48977i −0.178861 + 0.309796i −0.941491 0.337039i \(-0.890575\pi\)
0.762630 + 0.646835i \(0.223908\pi\)
\(752\) 0 0
\(753\) 2.83147i 0.103185i
\(754\) 0 0
\(755\) 21.0848 + 36.5200i 0.767355 + 1.32910i
\(756\) 0 0
\(757\) 12.5620 + 21.7580i 0.456574 + 0.790810i 0.998777 0.0494379i \(-0.0157430\pi\)
−0.542203 + 0.840247i \(0.682410\pi\)
\(758\) 0 0
\(759\) −4.19872 −0.152404
\(760\) 0 0
\(761\) −24.8778 −0.901821 −0.450910 0.892569i \(-0.648901\pi\)
−0.450910 + 0.892569i \(0.648901\pi\)
\(762\) 0 0
\(763\) −0.909714 1.57567i −0.0329339 0.0570431i
\(764\) 0 0
\(765\) −8.34916 14.4612i −0.301864 0.522845i
\(766\) 0 0
\(767\) 16.6232i 0.600229i
\(768\) 0 0
\(769\) 9.36876 16.2272i 0.337846 0.585167i −0.646181 0.763184i \(-0.723635\pi\)
0.984027 + 0.178017i \(0.0569683\pi\)
\(770\) 0 0
\(771\) 2.57628i 0.0927826i
\(772\) 0 0
\(773\) −18.9627 10.9481i −0.682039 0.393776i 0.118584 0.992944i \(-0.462165\pi\)
−0.800623 + 0.599169i \(0.795498\pi\)
\(774\) 0 0
\(775\) −6.99546 + 12.1165i −0.251284 + 0.435237i
\(776\) 0 0
\(777\) −11.2507 19.4868i −0.403618 0.699086i
\(778\) 0 0
\(779\) −26.9728 42.2719i −0.966400 1.51455i
\(780\) 0 0
\(781\) −3.74474 + 2.16202i −0.133997 + 0.0773633i
\(782\) 0 0
\(783\) −5.83502 3.36885i −0.208527 0.120393i
\(784\) 0 0
\(785\) −28.0096 + 48.5141i −0.999706 + 1.73154i
\(786\) 0 0
\(787\) −42.9336 −1.53042 −0.765208 0.643783i \(-0.777364\pi\)
−0.765208 + 0.643783i \(0.777364\pi\)
\(788\) 0 0
\(789\) −24.7977 14.3169i −0.882821 0.509697i
\(790\) 0 0
\(791\) 22.8104 0.811043
\(792\) 0 0
\(793\) 31.4517 18.1587i 1.11688 0.644833i
\(794\) 0 0
\(795\) 17.0903 9.86708i 0.606130 0.349949i
\(796\) 0 0
\(797\) 1.30208i 0.0461219i 0.999734 + 0.0230610i