Properties

Label 1900.2.i.d.201.4
Level $1900$
Weight $2$
Character 1900.201
Analytic conductor $15.172$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} + 9 x^{6} + 2 x^{5} + 65 x^{4} - 20 x^{3} + 25 x^{2} + 6 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.4
Root \(1.58253 - 2.74101i\) of defining polynomial
Character \(\chi\) \(=\) 1900.201
Dual form 1900.2.i.d.501.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.58253 - 2.74101i) q^{3} +1.53315 q^{7} +(-3.50877 - 6.07738i) q^{9} +O(q^{10})\) \(q+(1.58253 - 2.74101i) q^{3} +1.53315 q^{7} +(-3.50877 - 6.07738i) q^{9} -3.79695 q^{11} +(-3.34910 - 5.80081i) q^{13} +(-3.00877 + 5.21135i) q^{17} +(-3.93502 - 1.87499i) q^{19} +(2.42625 - 4.20239i) q^{21} +(2.19282 + 3.79808i) q^{23} -12.7158 q^{27} +(0.549376 + 0.951547i) q^{29} -1.05555 q^{31} +(-6.00877 + 10.4075i) q^{33} +10.7970 q^{37} -21.2002 q^{39} +(-1.76658 + 3.05980i) q^{41} +(2.77535 - 4.80705i) q^{43} +(-5.61907 - 9.73252i) q^{47} -4.64945 q^{49} +(9.52293 + 16.4942i) q^{51} +(0.788178 + 1.36516i) q^{53} +(-11.3667 + 7.81874i) q^{57} +(-1.61568 + 2.79843i) q^{59} +(-0.0331500 - 0.0574175i) q^{61} +(-5.37948 - 9.31753i) q^{63} +(-2.85250 - 4.94067i) q^{67} +13.8808 q^{69} +(3.23880 - 5.60977i) q^{71} +(6.98978 - 12.1066i) q^{73} -5.82130 q^{77} +(0.996602 - 1.72617i) q^{79} +(-9.59668 + 16.6219i) q^{81} +10.3477 q^{83} +3.47760 q^{87} +(-1.53655 - 2.66138i) q^{89} +(-5.13467 - 8.89352i) q^{91} +(-1.67043 + 2.89327i) q^{93} +(4.43502 - 7.68169i) q^{97} +(13.3227 + 23.0755i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + q^{3} - 5q^{9} + O(q^{10}) \) \( 8q + q^{3} - 5q^{9} + 4q^{11} - 9q^{13} - q^{17} + 3q^{19} + 8q^{21} - 20q^{27} + 5q^{29} - 20q^{31} - 25q^{33} + 52q^{37} - 54q^{39} - 8q^{41} - 7q^{43} - 16q^{47} + 20q^{49} + 12q^{51} - 5q^{53} - 27q^{57} + 11q^{59} + 12q^{61} + 3q^{63} + 6q^{69} + 14q^{71} + 4q^{73} + 44q^{77} + 13q^{79} - 24q^{81} - 10q^{83} + 4q^{87} + 5q^{89} - 46q^{91} + 28q^{93} + q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0
\(3\) 1.58253 2.74101i 0.913672 1.58253i 0.104837 0.994489i \(-0.466568\pi\)
0.808835 0.588036i \(-0.200099\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.53315 0.579476 0.289738 0.957106i \(-0.406432\pi\)
0.289738 + 0.957106i \(0.406432\pi\)
\(8\) 0 0
\(9\) −3.50877 6.07738i −1.16959 2.02579i
\(10\) 0 0
\(11\) −3.79695 −1.14482 −0.572412 0.819966i \(-0.693992\pi\)
−0.572412 + 0.819966i \(0.693992\pi\)
\(12\) 0 0
\(13\) −3.34910 5.80081i −0.928873 1.60886i −0.785210 0.619229i \(-0.787445\pi\)
−0.143663 0.989627i \(-0.545888\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.00877 + 5.21135i −0.729735 + 1.26394i 0.227260 + 0.973834i \(0.427023\pi\)
−0.956995 + 0.290104i \(0.906310\pi\)
\(18\) 0 0
\(19\) −3.93502 1.87499i −0.902756 0.430152i
\(20\) 0 0
\(21\) 2.42625 4.20239i 0.529451 0.917036i
\(22\) 0 0
\(23\) 2.19282 + 3.79808i 0.457235 + 0.791955i 0.998814 0.0486953i \(-0.0155063\pi\)
−0.541578 + 0.840650i \(0.682173\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −12.7158 −2.44715
\(28\) 0 0
\(29\) 0.549376 + 0.951547i 0.102016 + 0.176698i 0.912515 0.409042i \(-0.134137\pi\)
−0.810499 + 0.585740i \(0.800804\pi\)
\(30\) 0 0
\(31\) −1.05555 −0.189582 −0.0947908 0.995497i \(-0.530218\pi\)
−0.0947908 + 0.995497i \(0.530218\pi\)
\(32\) 0 0
\(33\) −6.00877 + 10.4075i −1.04599 + 1.81171i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 10.7970 1.77501 0.887504 0.460800i \(-0.152437\pi\)
0.887504 + 0.460800i \(0.152437\pi\)
\(38\) 0 0
\(39\) −21.2002 −3.39474
\(40\) 0 0
\(41\) −1.76658 + 3.05980i −0.275893 + 0.477860i −0.970360 0.241664i \(-0.922307\pi\)
0.694467 + 0.719524i \(0.255640\pi\)
\(42\) 0 0
\(43\) 2.77535 4.80705i 0.423237 0.733068i −0.573017 0.819543i \(-0.694227\pi\)
0.996254 + 0.0864756i \(0.0275605\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.61907 9.73252i −0.819626 1.41963i −0.905958 0.423368i \(-0.860848\pi\)
0.0863319 0.996266i \(-0.472485\pi\)
\(48\) 0 0
\(49\) −4.64945 −0.664207
\(50\) 0 0
\(51\) 9.52293 + 16.4942i 1.33348 + 2.30965i
\(52\) 0 0
\(53\) 0.788178 + 1.36516i 0.108265 + 0.187520i 0.915067 0.403301i \(-0.132137\pi\)
−0.806803 + 0.590821i \(0.798804\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −11.3667 + 7.81874i −1.50555 + 1.03562i
\(58\) 0 0
\(59\) −1.61568 + 2.79843i −0.210343 + 0.364325i −0.951822 0.306651i \(-0.900791\pi\)
0.741479 + 0.670976i \(0.234125\pi\)
\(60\) 0 0
\(61\) −0.0331500 0.0574175i −0.00424442 0.00735156i 0.863895 0.503671i \(-0.168018\pi\)
−0.868140 + 0.496320i \(0.834684\pi\)
\(62\) 0 0
\(63\) −5.37948 9.31753i −0.677751 1.17390i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.85250 4.94067i −0.348488 0.603599i 0.637493 0.770456i \(-0.279972\pi\)
−0.985981 + 0.166857i \(0.946638\pi\)
\(68\) 0 0
\(69\) 13.8808 1.67105
\(70\) 0 0
\(71\) 3.23880 5.60977i 0.384375 0.665757i −0.607307 0.794467i \(-0.707750\pi\)
0.991682 + 0.128710i \(0.0410836\pi\)
\(72\) 0 0
\(73\) 6.98978 12.1066i 0.818091 1.41698i −0.0889951 0.996032i \(-0.528366\pi\)
0.907087 0.420944i \(-0.138301\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −5.82130 −0.663398
\(78\) 0 0
\(79\) 0.996602 1.72617i 0.112127 0.194209i −0.804501 0.593951i \(-0.797567\pi\)
0.916627 + 0.399743i \(0.130900\pi\)
\(80\) 0 0
\(81\) −9.59668 + 16.6219i −1.06630 + 1.84688i
\(82\) 0 0
\(83\) 10.3477 1.13580 0.567901 0.823097i \(-0.307756\pi\)
0.567901 + 0.823097i \(0.307756\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 3.47760 0.372838
\(88\) 0 0
\(89\) −1.53655 2.66138i −0.162874 0.282106i 0.773024 0.634376i \(-0.218743\pi\)
−0.935898 + 0.352271i \(0.885410\pi\)
\(90\) 0 0
\(91\) −5.13467 8.89352i −0.538260 0.932294i
\(92\) 0 0
\(93\) −1.67043 + 2.89327i −0.173215 + 0.300018i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 4.43502 7.68169i 0.450308 0.779957i −0.548097 0.836415i \(-0.684647\pi\)
0.998405 + 0.0564579i \(0.0179807\pi\)
\(98\) 0 0
\(99\) 13.3227 + 23.0755i 1.33898 + 2.31918i
\(100\) 0 0
\(101\) −3.10413 5.37651i −0.308872 0.534983i 0.669244 0.743043i \(-0.266618\pi\)
−0.978116 + 0.208060i \(0.933285\pi\)
\(102\) 0 0
\(103\) 0.253048 0.0249336 0.0124668 0.999922i \(-0.496032\pi\)
0.0124668 + 0.999922i \(0.496032\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.05555 0.585412 0.292706 0.956203i \(-0.405444\pi\)
0.292706 + 0.956203i \(0.405444\pi\)
\(108\) 0 0
\(109\) −2.62445 + 4.54568i −0.251377 + 0.435397i −0.963905 0.266246i \(-0.914217\pi\)
0.712528 + 0.701643i \(0.247550\pi\)
\(110\) 0 0
\(111\) 17.0865 29.5946i 1.62177 2.80900i
\(112\) 0 0
\(113\) −2.42885 −0.228487 −0.114244 0.993453i \(-0.536444\pi\)
−0.114244 + 0.993453i \(0.536444\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −23.5025 + 40.7075i −2.17281 + 3.76341i
\(118\) 0 0
\(119\) −4.61290 + 7.98978i −0.422864 + 0.732422i
\(120\) 0 0
\(121\) 3.41685 0.310623
\(122\) 0 0
\(123\) 5.59130 + 9.68442i 0.504151 + 0.873214i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −9.64945 16.7133i −0.856250 1.48307i −0.875480 0.483254i \(-0.839455\pi\)
0.0192299 0.999815i \(-0.493879\pi\)
\(128\) 0 0
\(129\) −8.78412 15.2146i −0.773399 1.33957i
\(130\) 0 0
\(131\) 6.62983 11.4832i 0.579251 1.00329i −0.416315 0.909221i \(-0.636679\pi\)
0.995565 0.0940711i \(-0.0299881\pi\)
\(132\) 0 0
\(133\) −6.03298 2.87464i −0.523126 0.249263i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −7.77535 13.4673i −0.664293 1.15059i −0.979476 0.201558i \(-0.935399\pi\)
0.315184 0.949031i \(-0.397934\pi\)
\(138\) 0 0
\(139\) 9.31110 + 16.1273i 0.789758 + 1.36790i 0.926115 + 0.377241i \(0.123127\pi\)
−0.136358 + 0.990660i \(0.543540\pi\)
\(140\) 0 0
\(141\) −35.5693 −2.99548
\(142\) 0 0
\(143\) 12.7164 + 22.0254i 1.06340 + 1.84186i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −7.35788 + 12.7442i −0.606867 + 1.05113i
\(148\) 0 0
\(149\) 2.34372 4.05945i 0.192005 0.332563i −0.753909 0.656978i \(-0.771834\pi\)
0.945915 + 0.324415i \(0.105168\pi\)
\(150\) 0 0
\(151\) −5.93370 −0.482878 −0.241439 0.970416i \(-0.577619\pi\)
−0.241439 + 0.970416i \(0.577619\pi\)
\(152\) 0 0
\(153\) 42.2285 3.41397
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −4.64685 + 8.04857i −0.370859 + 0.642346i −0.989698 0.143172i \(-0.954270\pi\)
0.618839 + 0.785518i \(0.287603\pi\)
\(158\) 0 0
\(159\) 4.98925 0.395673
\(160\) 0 0
\(161\) 3.36193 + 5.82303i 0.264957 + 0.458919i
\(162\) 0 0
\(163\) −5.88495 −0.460945 −0.230472 0.973079i \(-0.574027\pi\)
−0.230472 + 0.973079i \(0.574027\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.39848 + 11.0825i 0.495129 + 0.857589i 0.999984 0.00561549i \(-0.00178747\pi\)
−0.504855 + 0.863204i \(0.668454\pi\)
\(168\) 0 0
\(169\) −15.9330 + 27.5967i −1.22561 + 2.12282i
\(170\) 0 0
\(171\) 2.41210 + 30.4935i 0.184458 + 2.33190i
\(172\) 0 0
\(173\) −7.52032 + 13.0256i −0.571760 + 0.990317i 0.424626 + 0.905369i \(0.360406\pi\)
−0.996385 + 0.0849476i \(0.972928\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.11370 + 8.85718i 0.384369 + 0.665747i
\(178\) 0 0
\(179\) 21.5452 1.61036 0.805180 0.593030i \(-0.202069\pi\)
0.805180 + 0.593030i \(0.202069\pi\)
\(180\) 0 0
\(181\) −2.13530 3.69845i −0.158716 0.274903i 0.775690 0.631114i \(-0.217402\pi\)
−0.934406 + 0.356210i \(0.884069\pi\)
\(182\) 0 0
\(183\) −0.209843 −0.0155120
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 11.4242 19.7873i 0.835418 1.44699i
\(188\) 0 0
\(189\) −19.4952 −1.41806
\(190\) 0 0
\(191\) −6.30180 −0.455982 −0.227991 0.973663i \(-0.573216\pi\)
−0.227991 + 0.973663i \(0.573216\pi\)
\(192\) 0 0
\(193\) −7.68943 + 13.3185i −0.553497 + 0.958685i 0.444522 + 0.895768i \(0.353374\pi\)
−0.998019 + 0.0629169i \(0.979960\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.7210 0.906331 0.453165 0.891426i \(-0.350295\pi\)
0.453165 + 0.891426i \(0.350295\pi\)
\(198\) 0 0
\(199\) −5.10885 8.84879i −0.362157 0.627274i 0.626159 0.779696i \(-0.284626\pi\)
−0.988316 + 0.152422i \(0.951293\pi\)
\(200\) 0 0
\(201\) −18.0566 −1.27361
\(202\) 0 0
\(203\) 0.842275 + 1.45886i 0.0591161 + 0.102392i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 15.3883 26.6532i 1.06956 1.85253i
\(208\) 0 0
\(209\) 14.9411 + 7.11925i 1.03350 + 0.492449i
\(210\) 0 0
\(211\) −2.53655 + 4.39343i −0.174623 + 0.302456i −0.940031 0.341090i \(-0.889204\pi\)
0.765408 + 0.643546i \(0.222537\pi\)
\(212\) 0 0
\(213\) −10.2510 17.7552i −0.702385 1.21657i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −1.61831 −0.109858
\(218\) 0 0
\(219\) −22.1230 38.3182i −1.49493 2.58930i
\(220\) 0 0
\(221\) 40.3068 2.71133
\(222\) 0 0
\(223\) −4.26318 + 7.38404i −0.285483 + 0.494472i −0.972726 0.231956i \(-0.925487\pi\)
0.687243 + 0.726428i \(0.258821\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 20.0566 1.33120 0.665602 0.746307i \(-0.268175\pi\)
0.665602 + 0.746307i \(0.268175\pi\)
\(228\) 0 0
\(229\) 7.92955 0.524000 0.262000 0.965068i \(-0.415618\pi\)
0.262000 + 0.965068i \(0.415618\pi\)
\(230\) 0 0
\(231\) −9.21235 + 15.9563i −0.606128 + 1.04985i
\(232\) 0 0
\(233\) 5.28950 9.16169i 0.346527 0.600202i −0.639103 0.769121i \(-0.720694\pi\)
0.985630 + 0.168919i \(0.0540276\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −3.15430 5.46340i −0.204894 0.354886i
\(238\) 0 0
\(239\) −5.68065 −0.367451 −0.183725 0.982978i \(-0.558816\pi\)
−0.183725 + 0.982978i \(0.558816\pi\)
\(240\) 0 0
\(241\) −4.75714 8.23962i −0.306435 0.530760i 0.671145 0.741326i \(-0.265803\pi\)
−0.977580 + 0.210566i \(0.932469\pi\)
\(242\) 0 0
\(243\) 11.3004 + 19.5728i 0.724918 + 1.25559i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 2.30233 + 29.1059i 0.146494 + 1.85196i
\(248\) 0 0
\(249\) 16.3754 28.3631i 1.03775 1.79744i
\(250\) 0 0
\(251\) −6.26658 10.8540i −0.395543 0.685100i 0.597628 0.801774i \(-0.296110\pi\)
−0.993170 + 0.116674i \(0.962777\pi\)
\(252\) 0 0
\(253\) −8.32605 14.4211i −0.523454 0.906649i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.54453 14.7996i −0.532993 0.923171i −0.999258 0.0385258i \(-0.987734\pi\)
0.466264 0.884645i \(-0.345600\pi\)
\(258\) 0 0
\(259\) 16.5533 1.02857
\(260\) 0 0
\(261\) 3.85527 6.67753i 0.238635 0.413328i
\(262\) 0 0
\(263\) 0.460054 0.796838i 0.0283682 0.0491351i −0.851493 0.524366i \(-0.824302\pi\)
0.879861 + 0.475231i \(0.157636\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −9.72651 −0.595252
\(268\) 0 0
\(269\) −12.6826 + 21.9669i −0.773272 + 1.33935i 0.162489 + 0.986710i \(0.448048\pi\)
−0.935761 + 0.352636i \(0.885285\pi\)
\(270\) 0 0
\(271\) 5.61828 9.73115i 0.341286 0.591125i −0.643386 0.765542i \(-0.722471\pi\)
0.984672 + 0.174417i \(0.0558041\pi\)
\(272\) 0 0
\(273\) −32.5030 −1.96717
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −16.5491 −0.994340 −0.497170 0.867653i \(-0.665627\pi\)
−0.497170 + 0.867653i \(0.665627\pi\)
\(278\) 0 0
\(279\) 3.70367 + 6.41495i 0.221733 + 0.384053i
\(280\) 0 0
\(281\) 5.28950 + 9.16169i 0.315545 + 0.546540i 0.979553 0.201185i \(-0.0644793\pi\)
−0.664008 + 0.747725i \(0.731146\pi\)
\(282\) 0 0
\(283\) 10.3707 17.9626i 0.616474 1.06776i −0.373650 0.927570i \(-0.621894\pi\)
0.990124 0.140195i \(-0.0447729\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.70842 + 4.69113i −0.159873 + 0.276909i
\(288\) 0 0
\(289\) −9.60545 16.6371i −0.565027 0.978655i
\(290\) 0 0
\(291\) −14.0371 24.3129i −0.822868 1.42525i
\(292\) 0 0
\(293\) −13.6846 −0.799460 −0.399730 0.916633i \(-0.630896\pi\)
−0.399730 + 0.916633i \(0.630896\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 48.2811 2.80155
\(298\) 0 0
\(299\) 14.6880 25.4403i 0.849428 1.47125i
\(300\) 0 0
\(301\) 4.25503 7.36992i 0.245256 0.424795i
\(302\) 0 0
\(303\) −19.6495 −1.12883
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −4.31872 + 7.48025i −0.246483 + 0.426920i −0.962547 0.271113i \(-0.912608\pi\)
0.716065 + 0.698034i \(0.245941\pi\)
\(308\) 0 0
\(309\) 0.400456 0.693609i 0.0227811 0.0394581i
\(310\) 0 0
\(311\) 29.7658 1.68786 0.843930 0.536453i \(-0.180236\pi\)
0.843930 + 0.536453i \(0.180236\pi\)
\(312\) 0 0
\(313\) 5.60413 + 9.70664i 0.316764 + 0.548651i 0.979811 0.199926i \(-0.0640703\pi\)
−0.663047 + 0.748578i \(0.730737\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.34650 4.06425i −0.131792 0.228271i 0.792575 0.609774i \(-0.208740\pi\)
−0.924368 + 0.381503i \(0.875407\pi\)
\(318\) 0 0
\(319\) −2.08595 3.61298i −0.116791 0.202288i
\(320\) 0 0
\(321\) 9.58306 16.5983i 0.534874 0.926429i
\(322\) 0 0
\(323\) 21.6108 14.8654i 1.20246 0.827131i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 8.30652 + 14.3873i 0.459352 + 0.795620i
\(328\) 0 0
\(329\) −8.61488 14.9214i −0.474954 0.822644i
\(330\) 0 0
\(331\) 29.1137 1.60024 0.800118 0.599843i \(-0.204770\pi\)
0.800118 + 0.599843i \(0.204770\pi\)
\(332\) 0 0
\(333\) −37.8841 65.6171i −2.07603 3.59580i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 11.5790 20.0554i 0.630749 1.09249i −0.356650 0.934238i \(-0.616081\pi\)
0.987399 0.158251i \(-0.0505854\pi\)
\(338\) 0 0
\(339\) −3.84372 + 6.65752i −0.208762 + 0.361587i
\(340\) 0 0
\(341\) 4.00786 0.217038
\(342\) 0 0
\(343\) −17.8604 −0.964369
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.83090 13.5635i 0.420385 0.728127i −0.575592 0.817737i \(-0.695229\pi\)
0.995977 + 0.0896094i \(0.0285619\pi\)
\(348\) 0 0
\(349\) −9.72130 −0.520369 −0.260185 0.965559i \(-0.583783\pi\)
−0.260185 + 0.965559i \(0.583783\pi\)
\(350\) 0 0
\(351\) 42.5863 + 73.7617i 2.27309 + 3.93711i
\(352\) 0 0
\(353\) −11.3789 −0.605635 −0.302818 0.953049i \(-0.597927\pi\)
−0.302818 + 0.953049i \(0.597927\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 14.6001 + 25.2881i 0.772718 + 1.33839i
\(358\) 0 0
\(359\) −14.3876 + 24.9201i −0.759350 + 1.31523i 0.183833 + 0.982958i \(0.441150\pi\)
−0.943183 + 0.332275i \(0.892184\pi\)
\(360\) 0 0
\(361\) 11.9688 + 14.7563i 0.629938 + 0.776645i
\(362\) 0 0
\(363\) 5.40725 9.36563i 0.283807 0.491568i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −12.0649 20.8969i −0.629780 1.09081i −0.987596 0.157019i \(-0.949812\pi\)
0.357815 0.933792i \(-0.383522\pi\)
\(368\) 0 0
\(369\) 24.7941 1.29073
\(370\) 0 0
\(371\) 1.20839 + 2.09300i 0.0627367 + 0.108663i
\(372\) 0 0
\(373\) 26.7281 1.38393 0.691964 0.721932i \(-0.256746\pi\)
0.691964 + 0.721932i \(0.256746\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.67983 6.37365i 0.189521 0.328260i
\(378\) 0 0
\(379\) 4.29369 0.220552 0.110276 0.993901i \(-0.464826\pi\)
0.110276 + 0.993901i \(0.464826\pi\)
\(380\) 0 0
\(381\) −61.0820 −3.12933
\(382\) 0 0
\(383\) 2.78610 4.82567i 0.142363 0.246580i −0.786023 0.618197i \(-0.787863\pi\)
0.928386 + 0.371617i \(0.121197\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −38.9523 −1.98006
\(388\) 0 0
\(389\) −14.0743 24.3774i −0.713594 1.23598i −0.963499 0.267711i \(-0.913733\pi\)
0.249905 0.968270i \(-0.419601\pi\)
\(390\) 0 0
\(391\) −26.3909 −1.33464
\(392\) 0 0
\(393\) −20.9837 36.3449i −1.05849 1.83336i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 17.3712 30.0879i 0.871837 1.51007i 0.0117431 0.999931i \(-0.496262\pi\)
0.860094 0.510135i \(-0.170405\pi\)
\(398\) 0 0
\(399\) −17.4268 + 11.9873i −0.872430 + 0.600116i
\(400\) 0 0
\(401\) 11.9370 20.6755i 0.596106 1.03249i −0.397284 0.917696i \(-0.630047\pi\)
0.993390 0.114789i \(-0.0366193\pi\)
\(402\) 0 0
\(403\) 3.53513 + 6.12302i 0.176097 + 0.305010i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −40.9955 −2.03207
\(408\) 0 0
\(409\) 18.7346 + 32.4492i 0.926365 + 1.60451i 0.789350 + 0.613943i \(0.210418\pi\)
0.137015 + 0.990569i \(0.456249\pi\)
\(410\) 0 0
\(411\) −49.2188 −2.42778
\(412\) 0 0
\(413\) −2.47707 + 4.29042i −0.121889 + 0.211118i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 58.9402 2.88632
\(418\) 0 0
\(419\) −0.360241 −0.0175989 −0.00879947 0.999961i \(-0.502801\pi\)
−0.00879947 + 0.999961i \(0.502801\pi\)
\(420\) 0 0
\(421\) −12.1243 + 20.9999i −0.590901 + 1.02347i 0.403210 + 0.915108i \(0.367894\pi\)
−0.994111 + 0.108364i \(0.965439\pi\)
\(422\) 0 0
\(423\) −39.4321 + 68.2984i −1.91726 + 3.32078i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.0508239 0.0880297i −0.00245954 0.00426005i
\(428\) 0 0
\(429\) 80.4960 3.88638
\(430\) 0 0
\(431\) 6.32067 + 10.9477i 0.304456 + 0.527333i 0.977140 0.212596i \(-0.0681920\pi\)
−0.672684 + 0.739930i \(0.734859\pi\)
\(432\) 0 0
\(433\) −12.2320 21.1864i −0.587831 1.01815i −0.994516 0.104585i \(-0.966649\pi\)
0.406685 0.913569i \(-0.366685\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.50745 19.0571i −0.0721111 0.911623i
\(438\) 0 0
\(439\) 12.4004 21.4782i 0.591840 1.02510i −0.402144 0.915576i \(-0.631735\pi\)
0.993985 0.109521i \(-0.0349316\pi\)
\(440\) 0 0
\(441\) 16.3139 + 28.2565i 0.776851 + 1.34555i
\(442\) 0 0
\(443\) 15.1318 + 26.2090i 0.718932 + 1.24523i 0.961423 + 0.275074i \(0.0887023\pi\)
−0.242491 + 0.970154i \(0.577964\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −7.41801 12.8484i −0.350860 0.607707i
\(448\) 0 0
\(449\) −29.0742 −1.37209 −0.686047 0.727557i \(-0.740656\pi\)
−0.686047 + 0.727557i \(0.740656\pi\)
\(450\) 0 0
\(451\) 6.70760 11.6179i 0.315849 0.547066i
\(452\) 0 0
\(453\) −9.39023 + 16.2644i −0.441192 + 0.764166i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 3.06234 0.143250 0.0716251 0.997432i \(-0.477181\pi\)
0.0716251 + 0.997432i \(0.477181\pi\)
\(458\) 0 0
\(459\) 38.2588 66.2662i 1.78577 3.09304i
\(460\) 0 0
\(461\) 13.2934 23.0249i 0.619137 1.07238i −0.370507 0.928830i \(-0.620816\pi\)
0.989644 0.143547i \(-0.0458507\pi\)
\(462\) 0 0
\(463\) −4.82684 −0.224322 −0.112161 0.993690i \(-0.535777\pi\)
−0.112161 + 0.993690i \(0.535777\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.31539 0.0608690 0.0304345 0.999537i \(-0.490311\pi\)
0.0304345 + 0.999537i \(0.490311\pi\)
\(468\) 0 0
\(469\) −4.37331 7.57479i −0.201941 0.349771i
\(470\) 0 0
\(471\) 14.7075 + 25.4741i 0.677686 + 1.17379i
\(472\) 0 0
\(473\) −10.5379 + 18.2521i −0.484532 + 0.839234i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 5.53108 9.58011i 0.253251 0.438643i
\(478\) 0 0
\(479\) −9.53915 16.5223i −0.435855 0.754923i 0.561510 0.827470i \(-0.310221\pi\)
−0.997365 + 0.0725469i \(0.976887\pi\)
\(480\) 0 0
\(481\) −36.1601 62.6311i −1.64876 2.85573i
\(482\) 0 0
\(483\) 21.2814 0.968335
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 8.23656 0.373234 0.186617 0.982433i \(-0.440248\pi\)
0.186617 + 0.982433i \(0.440248\pi\)
\(488\) 0 0
\(489\) −9.31308 + 16.1307i −0.421152 + 0.729457i
\(490\) 0 0
\(491\) −15.4776 + 26.8079i −0.698493 + 1.20983i 0.270496 + 0.962721i \(0.412812\pi\)
−0.968989 + 0.247104i \(0.920521\pi\)
\(492\) 0 0
\(493\) −6.61179 −0.297780
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.96557 8.60062i 0.222736 0.385790i
\(498\) 0 0
\(499\) −0.554753 + 0.960860i −0.0248341 + 0.0430140i −0.878175 0.478339i \(-0.841239\pi\)
0.853341 + 0.521353i \(0.174572\pi\)
\(500\) 0 0
\(501\) 40.5030 1.80954
\(502\) 0 0
\(503\) 4.32552 + 7.49202i 0.192865 + 0.334053i 0.946199 0.323586i \(-0.104889\pi\)
−0.753333 + 0.657639i \(0.771555\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 50.4286 + 87.3449i 2.23961 + 3.87912i
\(508\) 0 0
\(509\) 10.3944 + 18.0037i 0.460725 + 0.797999i 0.998997 0.0447722i \(-0.0142562\pi\)
−0.538273 + 0.842771i \(0.680923\pi\)
\(510\) 0 0
\(511\) 10.7164 18.5613i 0.474065 0.821104i
\(512\) 0 0
\(513\) 50.0368 + 23.8419i 2.20918 + 1.05265i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 21.3354 + 36.9539i 0.938328 + 1.62523i
\(518\) 0 0
\(519\) 23.8022 + 41.2266i 1.04480 + 1.80965i
\(520\) 0 0
\(521\) −24.5098 −1.07379 −0.536897 0.843648i \(-0.680404\pi\)
−0.536897 + 0.843648i \(0.680404\pi\)
\(522\) 0 0
\(523\) 9.03447 + 15.6482i 0.395050 + 0.684247i 0.993108 0.117207i \(-0.0373939\pi\)
−0.598058 + 0.801453i \(0.704061\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.17590 5.50082i 0.138344 0.239619i
\(528\) 0 0
\(529\) 1.88304 3.26153i 0.0818715 0.141806i
\(530\) 0 0
\(531\) 22.6762 0.984062
\(532\) 0 0
\(533\) 23.6658 1.02508
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 34.0958 59.0556i 1.47134 2.54844i
\(538\) 0 0
\(539\) 17.6537 0.760401
\(540\) 0 0
\(541\) 8.75440 + 15.1631i 0.376381 + 0.651911i 0.990533 0.137277i \(-0.0438350\pi\)
−0.614152 + 0.789188i \(0.710502\pi\)
\(542\) 0 0
\(543\) −13.5167 −0.580055
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 13.4864 + 23.3591i 0.576636 + 0.998763i 0.995862 + 0.0908807i \(0.0289682\pi\)
−0.419226 + 0.907882i \(0.637698\pi\)
\(548\) 0 0
\(549\) −0.232632 + 0.402930i −0.00992849 + 0.0171966i
\(550\) 0 0
\(551\) −0.377667 4.77443i −0.0160891 0.203398i
\(552\) 0 0
\(553\) 1.52794 2.64647i 0.0649746 0.112539i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −7.98361 13.8280i −0.338276 0.585912i 0.645832 0.763479i \(-0.276510\pi\)
−0.984109 + 0.177568i \(0.943177\pi\)
\(558\) 0 0
\(559\) −37.1797 −1.57253
\(560\) 0 0
\(561\) −36.1581 62.6277i −1.52660 2.64414i
\(562\) 0 0
\(563\) 8.58711 0.361904 0.180952 0.983492i \(-0.442082\pi\)
0.180952 + 0.983492i \(0.442082\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −14.7131 + 25.4839i −0.617894 + 1.07022i
\(568\) 0 0
\(569\) 22.5910 0.947064 0.473532 0.880777i \(-0.342979\pi\)
0.473532 + 0.880777i \(0.342979\pi\)
\(570\) 0 0
\(571\) 17.1000 0.715613 0.357806 0.933796i \(-0.383525\pi\)
0.357806 + 0.933796i \(0.383525\pi\)
\(572\) 0 0
\(573\) −9.97276 + 17.2733i −0.416618 + 0.721603i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0.677755 0.0282153 0.0141077 0.999900i \(-0.495509\pi\)
0.0141077 + 0.999900i \(0.495509\pi\)
\(578\) 0 0
\(579\) 24.3374 + 42.1537i 1.01143 + 1.75185i
\(580\) 0 0
\(581\) 15.8645 0.658171
\(582\) 0 0
\(583\) −2.99267 5.18346i −0.123944 0.214677i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 13.6859 23.7047i 0.564878 0.978397i −0.432183 0.901786i \(-0.642257\pi\)
0.997061 0.0766112i \(-0.0244100\pi\)
\(588\) 0 0
\(589\) 4.15360 + 1.97914i 0.171146 + 0.0815489i
\(590\) 0 0
\(591\) 20.1312 34.8683i 0.828089 1.43429i
\(592\) 0 0
\(593\) 4.18940 + 7.25625i 0.172038 + 0.297978i 0.939132 0.343556i \(-0.111632\pi\)
−0.767094 + 0.641534i \(0.778298\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −32.3395 −1.32357
\(598\) 0 0
\(599\) 16.9553 + 29.3675i 0.692777 + 1.19992i 0.970924 + 0.239386i \(0.0769462\pi\)
−0.278148 + 0.960538i \(0.589720\pi\)
\(600\) 0 0
\(601\) −5.74951 −0.234528 −0.117264 0.993101i \(-0.537412\pi\)
−0.117264 + 0.993101i \(0.537412\pi\)
\(602\) 0 0
\(603\) −20.0175 + 34.6714i −0.815178 + 1.41193i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 8.87815 0.360353 0.180177 0.983634i \(-0.442333\pi\)
0.180177 + 0.983634i \(0.442333\pi\)
\(608\) 0 0
\(609\) 5.33169 0.216051
\(610\) 0 0
\(611\) −37.6377 + 65.1904i −1.52266 + 2.63732i
\(612\) 0 0
\(613\) −6.02098 + 10.4286i −0.243185 + 0.421209i −0.961620 0.274386i \(-0.911526\pi\)
0.718435 + 0.695594i \(0.244859\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 23.4362 + 40.5927i 0.943505 + 1.63420i 0.758717 + 0.651420i \(0.225827\pi\)
0.184788 + 0.982778i \(0.440840\pi\)
\(618\) 0 0
\(619\) 14.8700 0.597678 0.298839 0.954304i \(-0.403401\pi\)
0.298839 + 0.954304i \(0.403401\pi\)
\(620\) 0 0
\(621\) −27.8834 48.2955i −1.11892 1.93803i
\(622\) 0 0
\(623\) −2.35576 4.08029i −0.0943815 0.163473i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 43.1586 29.6874i 1.72359 1.18560i
\(628\) 0 0
\(629\) −32.4856 + 56.2667i −1.29529 + 2.24350i
\(630\) 0 0
\(631\) −8.71235 15.0902i −0.346833 0.600733i 0.638852 0.769330i \(-0.279410\pi\)
−0.985685 + 0.168597i \(0.946076\pi\)
\(632\) 0 0
\(633\) 8.02830 + 13.9054i 0.319096 + 0.552691i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 15.5715 + 26.9706i 0.616964 + 1.06861i
\(638\) 0 0
\(639\) −45.4569 −1.79825
\(640\) 0 0
\(641\) −15.9973 + 27.7081i −0.631854 + 1.09440i 0.355318 + 0.934745i \(0.384373\pi\)
−0.987172 + 0.159658i \(0.948961\pi\)
\(642\) 0 0
\(643\) 17.5203 30.3461i 0.690934 1.19673i −0.280598 0.959825i \(-0.590533\pi\)
0.971532 0.236908i \(-0.0761339\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −17.4260 −0.685087 −0.342544 0.939502i \(-0.611288\pi\)
−0.342544 + 0.939502i \(0.611288\pi\)
\(648\) 0 0
\(649\) 6.13464 10.6255i 0.240806 0.417088i
\(650\) 0 0
\(651\) −2.56102 + 4.43581i −0.100374 + 0.173853i
\(652\) 0 0
\(653\) 49.1457 1.92322 0.961609 0.274422i \(-0.0884866\pi\)
0.961609 + 0.274422i \(0.0884866\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −98.1022 −3.82733
\(658\) 0 0
\(659\) −0.862722 1.49428i −0.0336069 0.0582088i 0.848733 0.528822i \(-0.177366\pi\)
−0.882340 + 0.470613i \(0.844033\pi\)
\(660\) 0 0
\(661\) −10.9594 18.9822i −0.426270 0.738321i 0.570268 0.821459i \(-0.306839\pi\)
−0.996538 + 0.0831373i \(0.973506\pi\)
\(662\) 0 0
\(663\) 63.7865 110.481i 2.47726 4.29074i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −2.40937 + 4.17315i −0.0932911 + 0.161585i
\(668\) 0 0
\(669\) 13.4932 + 23.3709i 0.521676 + 0.903570i
\(670\) 0 0
\(671\) 0.125869 + 0.218012i 0.00485912 + 0.00841624i
\(672\) 0 0
\(673\) −6.63165 −0.255631 −0.127816 0.991798i \(-0.540797\pi\)
−0.127816 + 0.991798i \(0.540797\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −32.7008 −1.25679 −0.628397 0.777893i \(-0.716289\pi\)
−0.628397 + 0.777893i \(0.716289\pi\)
\(678\) 0 0
\(679\) 6.79956 11.7772i 0.260943 0.451967i
\(680\) 0 0
\(681\) 31.7401 54.9755i 1.21628 2.10666i
\(682\) 0 0
\(683\) 51.9872 1.98923 0.994617 0.103622i \(-0.0330432\pi\)
0.994617 + 0.103622i \(0.0330432\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 12.5487 21.7350i 0.478764 0.829243i
\(688\) 0 0
\(689\) 5.27937 9.14414i 0.201128 0.348364i
\(690\) 0 0
\(691\) −8.93635 −0.339955 −0.169977 0.985448i \(-0.554369\pi\)
−0.169977 + 0.985448i \(0.554369\pi\)
\(692\) 0 0
\(693\) 20.4256 + 35.3782i 0.775905 + 1.34391i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −10.6305 18.4125i −0.402657 0.697423i
\(698\) 0 0
\(699\) −16.7415 28.9972i −0.633223 1.09678i
\(700\) 0 0
\(701\) −1.12927 + 1.95595i −0.0426518 + 0.0738751i −0.886563 0.462607i \(-0.846914\pi\)
0.843911 + 0.536483i \(0.180247\pi\)
\(702\) 0 0
\(703\) −42.4863 20.2442i −1.60240 0.763523i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −4.75909 8.24299i −0.178984 0.310010i
\(708\) 0 0
\(709\) −23.4045 40.5378i −0.878975 1.52243i −0.852467 0.522781i \(-0.824894\pi\)
−0.0265084 0.999649i \(-0.508439\pi\)
\(710\) 0 0
\(711\) −13.9874 −0.524569
\(712\) 0 0
\(713\) −2.31463 4.00905i −0.0866834 0.150140i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −8.98978 + 15.5708i −0.335729 + 0.581500i
\(718\) 0 0
\(719\) 11.7570 20.3637i 0.438462 0.759439i −0.559109 0.829094i \(-0.688857\pi\)
0.997571 + 0.0696552i \(0.0221899\pi\)
\(720\) 0 0
\(721\) 0.387961 0.0144484
\(722\) 0 0
\(723\) −30.1132 −1.11992
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −12.7374 + 22.0617i −0.472402 + 0.818225i −0.999501 0.0315791i \(-0.989946\pi\)
0.527099 + 0.849804i \(0.323280\pi\)
\(728\) 0 0
\(729\) 13.9523 0.516752
\(730\) 0 0
\(731\) 16.7008 + 28.9266i 0.617702 + 1.06989i
\(732\) 0 0
\(733\) 1.41916 0.0524179 0.0262090 0.999656i \(-0.491656\pi\)
0.0262090 + 0.999656i \(0.491656\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 10.8308 + 18.7595i 0.398958 + 0.691015i
\(738\) 0 0
\(739\) 10.7699 18.6540i 0.396176 0.686198i −0.597074 0.802186i \(-0.703670\pi\)
0.993251 + 0.115988i \(0.0370035\pi\)
\(740\) 0 0
\(741\) 83.4231 + 39.7501i 3.06462 + 1.46025i
\(742\) 0 0
\(743\) −21.2813 + 36.8602i −0.780734 + 1.35227i 0.150781 + 0.988567i \(0.451821\pi\)
−0.931515 + 0.363703i \(0.881512\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −36.3076 62.8866i −1.32842 2.30090i
\(748\) 0 0
\(749\) 9.28406 0.339232
\(750\) 0 0
\(751\) −9.30708 16.1203i −0.339620 0.588239i 0.644741 0.764401i \(-0.276965\pi\)
−0.984361 + 0.176162i \(0.943632\pi\)
\(752\) 0 0
\(753\) −39.6681 −1.44558
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −15.3842 + 26.6462i −0.559148 + 0.968473i 0.438420 + 0.898770i \(0.355538\pi\)
−0.997568 + 0.0697028i \(0.977795\pi\)
\(758\) 0 0
\(759\) −52.7047 −1.91306
\(760\) 0 0
\(761\) 13.9270 0.504853 0.252427 0.967616i \(-0.418771\pi\)
0.252427 + 0.967616i \(0.418771\pi\)
\(762\) 0 0
\(763\) −4.02368 + 6.96921i −0.145667 + 0.252302i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 21.6442 0.781528
\(768\) 0 0
\(769\) 24.3166 + 42.1176i 0.876880 + 1.51880i 0.854747 + 0.519045i \(0.173712\pi\)
0.0221329 + 0.999755i \(0.492954\pi\)
\(770\) 0 0
\(771\) −54.0877 −1.94792
\(772\) 0 0
\(773\) −9.79276 16.9616i −0.352221 0.610065i 0.634417 0.772991i \(-0.281240\pi\)
−0.986638 + 0.162926i \(0.947907\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 26.1961 45.3730i 0.939780 1.62775i
\(778\) 0 0
\(779\) 12.6886 8.72807i 0.454616 0.312715i
\(780\) 0 0
\(781\) −12.2976 + 21.3000i −0.440042 + 0.762175i
\(782\) 0 0
\(783\) −6.98572 12.0996i −0.249649 0.432405i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −13.4029 −0.477760 −0.238880 0.971049i \(-0.576780\pi\)
−0.238880 + 0.971049i \(0.576780\pi\)
\(788\) 0 0
\(789\) −1.45610 2.52203i −0.0518384 0.0897867i
\(790\) 0 0
\(791\) −3.72380 −0.132403
\(792\) 0 0
\(793\) −0.222045 + 0.384594i −0.00788507 + 0.0136573i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −30.0201 −1.06337 −0.531684 0.846943i \(-0.678441\pi\)
−0.531684 + 0.846943i \(0.678441\pi\)
\(798\) 0 0
\(799\) 67.6261 2.39244
\(800\) 0 0
\(801\) −10.7828 + 18.6764i −0.380992 + 0.659897i