Properties

Label 1008.2.r.m.673.2
Level 1008
Weight 2
Character 1008.673
Analytic conductor 8.049
Analytic rank 0
Dimension 8
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1008.r (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.04892052375\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.508277025.1
Defining polynomial: \(x^{8} - 3 x^{7} + 5 x^{6} - 15 x^{5} + 21 x^{4} + 3 x^{3} - 22 x^{2} + 3 x + 19\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 673.2
Root \(-0.734668 - 0.348716i\) of defining polynomial
Character \(\chi\) \(=\) 1008.673
Dual form 1008.2.r.m.337.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.434663 - 1.67662i) q^{3} +(-1.21814 - 2.10988i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-2.62214 - 1.45753i) q^{9} +O(q^{10})\) \(q+(0.434663 - 1.67662i) q^{3} +(-1.21814 - 2.10988i) q^{5} +(0.500000 - 0.866025i) q^{7} +(-2.62214 - 1.45753i) q^{9} +(0.379477 - 0.657274i) q^{11} +(-1.11414 - 1.92976i) q^{13} +(-4.06695 + 1.12527i) q^{15} -7.04904 q^{17} +1.37172 q^{19} +(-1.23467 - 1.21474i) q^{21} +(3.51814 + 6.09360i) q^{23} +(-0.467722 + 0.810117i) q^{25} +(-3.58348 + 3.76280i) q^{27} +(-0.418134 + 0.724229i) q^{29} +(-0.265332 - 0.459569i) q^{31} +(-0.937057 - 0.921933i) q^{33} -2.43628 q^{35} +4.53066 q^{37} +(-3.71975 + 1.02921i) q^{39} +(-4.42852 - 7.67042i) q^{41} +(3.70161 - 6.41137i) q^{43} +(0.118909 + 7.30786i) q^{45} +(-3.39762 + 5.88485i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-3.06396 + 11.8186i) q^{51} -0.607978 q^{53} -1.84902 q^{55} +(0.596236 - 2.29986i) q^{57} +(-0.581866 - 1.00782i) q^{59} +(-5.85680 + 10.1443i) q^{61} +(-2.57333 + 1.54207i) q^{63} +(-2.71436 + 4.70142i) q^{65} +(-0.152801 - 0.264659i) q^{67} +(11.7459 - 3.24994i) q^{69} -12.6192 q^{71} -10.1499 q^{73} +(1.15496 + 1.13632i) q^{75} +(-0.379477 - 0.657274i) q^{77} +(7.62453 - 13.2061i) q^{79} +(4.75120 + 7.64370i) q^{81} +(8.18909 - 14.1839i) q^{83} +(8.58671 + 14.8726i) q^{85} +(1.03251 + 1.01585i) q^{87} -9.63151 q^{89} -2.22829 q^{91} +(-0.885855 + 0.245105i) q^{93} +(-1.67094 - 2.89416i) q^{95} +(5.46718 - 9.46943i) q^{97} +(-1.95304 + 1.17036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 4q^{5} + 4q^{7} + 10q^{9} + O(q^{10}) \) \( 8q + 4q^{3} + 4q^{5} + 4q^{7} + 10q^{9} + 6q^{11} - 3q^{13} - 4q^{15} - 16q^{17} + 4q^{19} - q^{21} + 5q^{23} - 14q^{25} - 5q^{27} + q^{29} - 11q^{31} + 8q^{35} + 54q^{37} + 12q^{39} + 2q^{41} + 11q^{43} + 26q^{45} - 7q^{47} - 4q^{49} - 17q^{51} - 8q^{53} - 12q^{55} - 13q^{57} - 9q^{59} - 7q^{61} + 5q^{63} - 9q^{65} + 12q^{67} + 4q^{69} + 24q^{71} + 26q^{73} + 23q^{75} - 6q^{77} + 22q^{79} + 34q^{81} + 6q^{83} - 11q^{85} - 37q^{87} - 28q^{89} - 6q^{91} - 13q^{93} + 23q^{95} - q^{97} + 42q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(577\) \(757\) \(785\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) 0.434663 1.67662i 0.250953 0.967999i
\(4\) 0 0
\(5\) −1.21814 2.10988i −0.544768 0.943566i −0.998621 0.0524895i \(-0.983284\pi\)
0.453853 0.891076i \(-0.350049\pi\)
\(6\) 0 0
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 0 0
\(9\) −2.62214 1.45753i −0.874045 0.485844i
\(10\) 0 0
\(11\) 0.379477 0.657274i 0.114417 0.198176i −0.803130 0.595804i \(-0.796833\pi\)
0.917546 + 0.397629i \(0.130167\pi\)
\(12\) 0 0
\(13\) −1.11414 1.92976i −0.309008 0.535218i 0.669138 0.743139i \(-0.266664\pi\)
−0.978146 + 0.207921i \(0.933330\pi\)
\(14\) 0 0
\(15\) −4.06695 + 1.12527i −1.05008 + 0.290545i
\(16\) 0 0
\(17\) −7.04904 −1.70964 −0.854822 0.518922i \(-0.826334\pi\)
−0.854822 + 0.518922i \(0.826334\pi\)
\(18\) 0 0
\(19\) 1.37172 0.314694 0.157347 0.987543i \(-0.449706\pi\)
0.157347 + 0.987543i \(0.449706\pi\)
\(20\) 0 0
\(21\) −1.23467 1.21474i −0.269427 0.265078i
\(22\) 0 0
\(23\) 3.51814 + 6.09360i 0.733583 + 1.27060i 0.955342 + 0.295502i \(0.0954870\pi\)
−0.221759 + 0.975102i \(0.571180\pi\)
\(24\) 0 0
\(25\) −0.467722 + 0.810117i −0.0935443 + 0.162023i
\(26\) 0 0
\(27\) −3.58348 + 3.76280i −0.689641 + 0.724151i
\(28\) 0 0
\(29\) −0.418134 + 0.724229i −0.0776455 + 0.134486i −0.902234 0.431248i \(-0.858074\pi\)
0.824588 + 0.565733i \(0.191407\pi\)
\(30\) 0 0
\(31\) −0.265332 0.459569i −0.0476551 0.0825411i 0.841214 0.540702i \(-0.181842\pi\)
−0.888869 + 0.458161i \(0.848508\pi\)
\(32\) 0 0
\(33\) −0.937057 0.921933i −0.163121 0.160488i
\(34\) 0 0
\(35\) −2.43628 −0.411806
\(36\) 0 0
\(37\) 4.53066 0.744837 0.372418 0.928065i \(-0.378529\pi\)
0.372418 + 0.928065i \(0.378529\pi\)
\(38\) 0 0
\(39\) −3.71975 + 1.02921i −0.595637 + 0.164805i
\(40\) 0 0
\(41\) −4.42852 7.67042i −0.691618 1.19792i −0.971307 0.237828i \(-0.923565\pi\)
0.279689 0.960091i \(-0.409769\pi\)
\(42\) 0 0
\(43\) 3.70161 6.41137i 0.564490 0.977725i −0.432607 0.901583i \(-0.642406\pi\)
0.997097 0.0761428i \(-0.0242605\pi\)
\(44\) 0 0
\(45\) 0.118909 + 7.30786i 0.0177259 + 1.08939i
\(46\) 0 0
\(47\) −3.39762 + 5.88485i −0.495594 + 0.858394i −0.999987 0.00508036i \(-0.998383\pi\)
0.504393 + 0.863474i \(0.331716\pi\)
\(48\) 0 0
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 0 0
\(51\) −3.06396 + 11.8186i −0.429040 + 1.65493i
\(52\) 0 0
\(53\) −0.607978 −0.0835122 −0.0417561 0.999128i \(-0.513295\pi\)
−0.0417561 + 0.999128i \(0.513295\pi\)
\(54\) 0 0
\(55\) −1.84902 −0.249322
\(56\) 0 0
\(57\) 0.596236 2.29986i 0.0789733 0.304624i
\(58\) 0 0
\(59\) −0.581866 1.00782i −0.0757525 0.131207i 0.825661 0.564167i \(-0.190803\pi\)
−0.901413 + 0.432960i \(0.857469\pi\)
\(60\) 0 0
\(61\) −5.85680 + 10.1443i −0.749887 + 1.29884i 0.197990 + 0.980204i \(0.436559\pi\)
−0.947876 + 0.318638i \(0.896775\pi\)
\(62\) 0 0
\(63\) −2.57333 + 1.54207i −0.324209 + 0.194283i
\(64\) 0 0
\(65\) −2.71436 + 4.70142i −0.336676 + 0.583139i
\(66\) 0 0
\(67\) −0.152801 0.264659i −0.0186676 0.0323333i 0.856541 0.516080i \(-0.172609\pi\)
−0.875208 + 0.483746i \(0.839276\pi\)
\(68\) 0 0
\(69\) 11.7459 3.24994i 1.41404 0.391247i
\(70\) 0 0
\(71\) −12.6192 −1.49763 −0.748813 0.662781i \(-0.769376\pi\)
−0.748813 + 0.662781i \(0.769376\pi\)
\(72\) 0 0
\(73\) −10.1499 −1.18795 −0.593977 0.804482i \(-0.702443\pi\)
−0.593977 + 0.804482i \(0.702443\pi\)
\(74\) 0 0
\(75\) 1.15496 + 1.13632i 0.133363 + 0.131211i
\(76\) 0 0
\(77\) −0.379477 0.657274i −0.0432455 0.0749033i
\(78\) 0 0
\(79\) 7.62453 13.2061i 0.857827 1.48580i −0.0161711 0.999869i \(-0.505148\pi\)
0.873998 0.485930i \(-0.161519\pi\)
\(80\) 0 0
\(81\) 4.75120 + 7.64370i 0.527911 + 0.849300i
\(82\) 0 0
\(83\) 8.18909 14.1839i 0.898869 1.55689i 0.0699272 0.997552i \(-0.477723\pi\)
0.828942 0.559335i \(-0.188943\pi\)
\(84\) 0 0
\(85\) 8.58671 + 14.8726i 0.931359 + 1.61316i
\(86\) 0 0
\(87\) 1.03251 + 1.01585i 0.110697 + 0.108910i
\(88\) 0 0
\(89\) −9.63151 −1.02094 −0.510469 0.859896i \(-0.670528\pi\)
−0.510469 + 0.859896i \(0.670528\pi\)
\(90\) 0 0
\(91\) −2.22829 −0.233588
\(92\) 0 0
\(93\) −0.885855 + 0.245105i −0.0918589 + 0.0254162i
\(94\) 0 0
\(95\) −1.67094 2.89416i −0.171435 0.296935i
\(96\) 0 0
\(97\) 5.46718 9.46943i 0.555108 0.961474i −0.442788 0.896627i \(-0.646010\pi\)
0.997895 0.0648479i \(-0.0206562\pi\)
\(98\) 0 0
\(99\) −1.95304 + 1.17036i −0.196288 + 0.117626i
\(100\) 0 0
\(101\) −0.750417 + 1.29976i −0.0746693 + 0.129331i −0.900942 0.433939i \(-0.857123\pi\)
0.826273 + 0.563270i \(0.190457\pi\)
\(102\) 0 0
\(103\) 5.13229 + 8.88938i 0.505699 + 0.875897i 0.999978 + 0.00659356i \(0.00209881\pi\)
−0.494279 + 0.869303i \(0.664568\pi\)
\(104\) 0 0
\(105\) −1.05896 + 4.08472i −0.103344 + 0.398628i
\(106\) 0 0
\(107\) 7.84428 0.758335 0.379168 0.925328i \(-0.376210\pi\)
0.379168 + 0.925328i \(0.376210\pi\)
\(108\) 0 0
\(109\) 12.1754 1.16619 0.583096 0.812403i \(-0.301841\pi\)
0.583096 + 0.812403i \(0.301841\pi\)
\(110\) 0 0
\(111\) 1.96931 7.59622i 0.186919 0.721001i
\(112\) 0 0
\(113\) −1.98586 3.43962i −0.186814 0.323572i 0.757372 0.652984i \(-0.226483\pi\)
−0.944186 + 0.329412i \(0.893150\pi\)
\(114\) 0 0
\(115\) 8.57117 14.8457i 0.799266 1.38437i
\(116\) 0 0
\(117\) 0.108758 + 6.68398i 0.0100547 + 0.617935i
\(118\) 0 0
\(119\) −3.52452 + 6.10465i −0.323092 + 0.559612i
\(120\) 0 0
\(121\) 5.21199 + 9.02744i 0.473818 + 0.820676i
\(122\) 0 0
\(123\) −14.7853 + 4.09091i −1.33315 + 0.368865i
\(124\) 0 0
\(125\) −9.90238 −0.885696
\(126\) 0 0
\(127\) −15.7579 −1.39828 −0.699142 0.714983i \(-0.746435\pi\)
−0.699142 + 0.714983i \(0.746435\pi\)
\(128\) 0 0
\(129\) −9.14051 8.99299i −0.804777 0.791789i
\(130\) 0 0
\(131\) −5.93789 10.2847i −0.518796 0.898581i −0.999761 0.0218413i \(-0.993047\pi\)
0.480966 0.876739i \(-0.340286\pi\)
\(132\) 0 0
\(133\) 0.685860 1.18794i 0.0594716 0.103008i
\(134\) 0 0
\(135\) 12.3042 + 2.97709i 1.05898 + 0.256227i
\(136\) 0 0
\(137\) 10.1869 17.6443i 0.870328 1.50745i 0.00867008 0.999962i \(-0.497240\pi\)
0.861658 0.507490i \(-0.169426\pi\)
\(138\) 0 0
\(139\) −3.13489 5.42979i −0.265898 0.460549i 0.701900 0.712275i \(-0.252335\pi\)
−0.967799 + 0.251726i \(0.919002\pi\)
\(140\) 0 0
\(141\) 8.38986 + 8.25446i 0.706554 + 0.695151i
\(142\) 0 0
\(143\) −1.69117 −0.141423
\(144\) 0 0
\(145\) 2.03738 0.169195
\(146\) 0 0
\(147\) −1.66933 + 0.461883i −0.137684 + 0.0380955i
\(148\) 0 0
\(149\) 2.45679 + 4.25529i 0.201268 + 0.348607i 0.948937 0.315465i \(-0.102160\pi\)
−0.747669 + 0.664071i \(0.768827\pi\)
\(150\) 0 0
\(151\) −2.80878 + 4.86494i −0.228575 + 0.395903i −0.957386 0.288811i \(-0.906740\pi\)
0.728811 + 0.684715i \(0.240073\pi\)
\(152\) 0 0
\(153\) 18.4835 + 10.2742i 1.49431 + 0.830621i
\(154\) 0 0
\(155\) −0.646423 + 1.11964i −0.0519220 + 0.0899315i
\(156\) 0 0
\(157\) −10.3174 17.8702i −0.823416 1.42620i −0.903124 0.429379i \(-0.858732\pi\)
0.0797087 0.996818i \(-0.474601\pi\)
\(158\) 0 0
\(159\) −0.264265 + 1.01935i −0.0209576 + 0.0808397i
\(160\) 0 0
\(161\) 7.03629 0.554537
\(162\) 0 0
\(163\) −4.95096 −0.387789 −0.193895 0.981022i \(-0.562112\pi\)
−0.193895 + 0.981022i \(0.562112\pi\)
\(164\) 0 0
\(165\) −0.803702 + 3.10012i −0.0625681 + 0.241344i
\(166\) 0 0
\(167\) −0.485864 0.841542i −0.0375973 0.0651205i 0.846614 0.532207i \(-0.178637\pi\)
−0.884212 + 0.467086i \(0.845304\pi\)
\(168\) 0 0
\(169\) 4.01736 6.95828i 0.309028 0.535252i
\(170\) 0 0
\(171\) −3.59684 1.99933i −0.275057 0.152892i
\(172\) 0 0
\(173\) 8.90960 15.4319i 0.677384 1.17326i −0.298382 0.954447i \(-0.596447\pi\)
0.975766 0.218817i \(-0.0702198\pi\)
\(174\) 0 0
\(175\) 0.467722 + 0.810117i 0.0353564 + 0.0612391i
\(176\) 0 0
\(177\) −1.94265 + 0.537508i −0.146019 + 0.0404016i
\(178\) 0 0
\(179\) 10.6065 0.792764 0.396382 0.918086i \(-0.370266\pi\)
0.396382 + 0.918086i \(0.370266\pi\)
\(180\) 0 0
\(181\) 24.7360 1.83862 0.919308 0.393539i \(-0.128749\pi\)
0.919308 + 0.393539i \(0.128749\pi\)
\(182\) 0 0
\(183\) 14.4624 + 14.2290i 1.06909 + 1.05184i
\(184\) 0 0
\(185\) −5.51898 9.55915i −0.405763 0.702802i
\(186\) 0 0
\(187\) −2.67495 + 4.63315i −0.195612 + 0.338810i
\(188\) 0 0
\(189\) 1.46694 + 4.98479i 0.106704 + 0.362590i
\(190\) 0 0
\(191\) 9.25120 16.0235i 0.669393 1.15942i −0.308681 0.951166i \(-0.599888\pi\)
0.978074 0.208257i \(-0.0667791\pi\)
\(192\) 0 0
\(193\) −8.24505 14.2808i −0.593492 1.02796i −0.993758 0.111559i \(-0.964416\pi\)
0.400266 0.916399i \(-0.368918\pi\)
\(194\) 0 0
\(195\) 6.70268 + 6.59450i 0.479989 + 0.472242i
\(196\) 0 0
\(197\) −8.68164 −0.618541 −0.309271 0.950974i \(-0.600085\pi\)
−0.309271 + 0.950974i \(0.600085\pi\)
\(198\) 0 0
\(199\) 19.2352 1.36355 0.681774 0.731563i \(-0.261209\pi\)
0.681774 + 0.731563i \(0.261209\pi\)
\(200\) 0 0
\(201\) −0.510151 + 0.141152i −0.0359833 + 0.00995613i
\(202\) 0 0
\(203\) 0.418134 + 0.724229i 0.0293472 + 0.0508309i
\(204\) 0 0
\(205\) −10.7891 + 18.6873i −0.753543 + 1.30518i
\(206\) 0 0
\(207\) −0.343425 21.1061i −0.0238697 1.46697i
\(208\) 0 0
\(209\) 0.520536 0.901595i 0.0360063 0.0623647i
\(210\) 0 0
\(211\) 11.3584 + 19.6734i 0.781946 + 1.35437i 0.930807 + 0.365512i \(0.119106\pi\)
−0.148861 + 0.988858i \(0.547561\pi\)
\(212\) 0 0
\(213\) −5.48511 + 21.1577i −0.375833 + 1.44970i
\(214\) 0 0
\(215\) −18.0363 −1.23006
\(216\) 0 0
\(217\) −0.530665 −0.0360239
\(218\) 0 0
\(219\) −4.41178 + 17.0175i −0.298120 + 1.14994i
\(220\) 0 0
\(221\) 7.85365 + 13.6029i 0.528294 + 0.915032i
\(222\) 0 0
\(223\) 7.76320 13.4462i 0.519862 0.900427i −0.479871 0.877339i \(-0.659317\pi\)
0.999733 0.0230886i \(-0.00734998\pi\)
\(224\) 0 0
\(225\) 2.40720 1.44252i 0.160480 0.0961679i
\(226\) 0 0
\(227\) 1.13468 1.96533i 0.0753114 0.130443i −0.825910 0.563802i \(-0.809338\pi\)
0.901222 + 0.433358i \(0.142672\pi\)
\(228\) 0 0
\(229\) −4.61037 7.98540i −0.304662 0.527690i 0.672524 0.740075i \(-0.265210\pi\)
−0.977186 + 0.212385i \(0.931877\pi\)
\(230\) 0 0
\(231\) −1.26695 + 0.350548i −0.0833589 + 0.0230644i
\(232\) 0 0
\(233\) −24.0842 −1.57781 −0.788905 0.614515i \(-0.789352\pi\)
−0.788905 + 0.614515i \(0.789352\pi\)
\(234\) 0 0
\(235\) 16.5551 1.07993
\(236\) 0 0
\(237\) −18.8275 18.5237i −1.22298 1.20324i
\(238\) 0 0
\(239\) 2.50000 + 4.33013i 0.161712 + 0.280093i 0.935483 0.353373i \(-0.114965\pi\)
−0.773771 + 0.633465i \(0.781632\pi\)
\(240\) 0 0
\(241\) 8.61761 14.9261i 0.555109 0.961477i −0.442786 0.896627i \(-0.646010\pi\)
0.997895 0.0648494i \(-0.0206567\pi\)
\(242\) 0 0
\(243\) 14.8808 4.64354i 0.954602 0.297883i
\(244\) 0 0
\(245\) −1.21814 + 2.10988i −0.0778240 + 0.134795i
\(246\) 0 0
\(247\) −1.52829 2.64708i −0.0972430 0.168430i
\(248\) 0 0
\(249\) −20.2216 19.8952i −1.28149 1.26081i
\(250\) 0 0
\(251\) −15.2725 −0.963994 −0.481997 0.876173i \(-0.660088\pi\)
−0.481997 + 0.876173i \(0.660088\pi\)
\(252\) 0 0
\(253\) 5.34022 0.335737
\(254\) 0 0
\(255\) 28.6681 7.93211i 1.79527 0.496728i
\(256\) 0 0
\(257\) 5.79524 + 10.0377i 0.361497 + 0.626131i 0.988207 0.153121i \(-0.0489324\pi\)
−0.626710 + 0.779252i \(0.715599\pi\)
\(258\) 0 0
\(259\) 2.26533 3.92367i 0.140761 0.243805i
\(260\) 0 0
\(261\) 2.15199 1.28958i 0.133205 0.0798232i
\(262\) 0 0
\(263\) −4.05602 + 7.02523i −0.250105 + 0.433194i −0.963554 0.267512i \(-0.913798\pi\)
0.713450 + 0.700707i \(0.247132\pi\)
\(264\) 0 0
\(265\) 0.740601 + 1.28276i 0.0454948 + 0.0787992i
\(266\) 0 0
\(267\) −4.18646 + 16.1484i −0.256207 + 0.988267i
\(268\) 0 0
\(269\) 11.4598 0.698717 0.349358 0.936989i \(-0.386400\pi\)
0.349358 + 0.936989i \(0.386400\pi\)
\(270\) 0 0
\(271\) 3.30404 0.200706 0.100353 0.994952i \(-0.468003\pi\)
0.100353 + 0.994952i \(0.468003\pi\)
\(272\) 0 0
\(273\) −0.968555 + 3.73600i −0.0586196 + 0.226113i
\(274\) 0 0
\(275\) 0.354979 + 0.614842i 0.0214061 + 0.0370764i
\(276\) 0 0
\(277\) 5.12453 8.87595i 0.307903 0.533304i −0.670000 0.742361i \(-0.733706\pi\)
0.977903 + 0.209057i \(0.0670394\pi\)
\(278\) 0 0
\(279\) 0.0259006 + 1.59178i 0.00155063 + 0.0952976i
\(280\) 0 0
\(281\) 0.861334 1.49188i 0.0513829 0.0889978i −0.839190 0.543838i \(-0.816970\pi\)
0.890573 + 0.454841i \(0.150304\pi\)
\(282\) 0 0
\(283\) 12.0752 + 20.9148i 0.717795 + 1.24326i 0.961872 + 0.273501i \(0.0881817\pi\)
−0.244077 + 0.969756i \(0.578485\pi\)
\(284\) 0 0
\(285\) −5.57872 + 1.54356i −0.330455 + 0.0914326i
\(286\) 0 0
\(287\) −8.85704 −0.522814
\(288\) 0 0
\(289\) 32.6890 1.92288
\(290\) 0 0
\(291\) −13.5003 13.2824i −0.791401 0.778628i
\(292\) 0 0
\(293\) 7.46533 + 12.9303i 0.436129 + 0.755398i 0.997387 0.0722432i \(-0.0230158\pi\)
−0.561258 + 0.827641i \(0.689682\pi\)
\(294\) 0 0
\(295\) −1.41759 + 2.45533i −0.0825351 + 0.142955i
\(296\) 0 0
\(297\) 1.11334 + 3.78323i 0.0646026 + 0.219525i
\(298\) 0 0
\(299\) 7.83944 13.5783i 0.453367 0.785254i
\(300\) 0 0
\(301\) −3.70161 6.41137i −0.213357 0.369545i
\(302\) 0 0
\(303\) 1.85303 + 1.82312i 0.106454 + 0.104736i
\(304\) 0 0
\(305\) 28.5376 1.63406
\(306\) 0 0
\(307\) 17.9563 1.02482 0.512411 0.858741i \(-0.328753\pi\)
0.512411 + 0.858741i \(0.328753\pi\)
\(308\) 0 0
\(309\) 17.1350 4.74103i 0.974774 0.269708i
\(310\) 0 0
\(311\) 10.8931 + 18.8673i 0.617689 + 1.06987i 0.989906 + 0.141723i \(0.0452643\pi\)
−0.372217 + 0.928146i \(0.621402\pi\)
\(312\) 0 0
\(313\) −11.0624 + 19.1606i −0.625284 + 1.08302i 0.363202 + 0.931710i \(0.381683\pi\)
−0.988486 + 0.151313i \(0.951650\pi\)
\(314\) 0 0
\(315\) 6.38825 + 3.55095i 0.359937 + 0.200074i
\(316\) 0 0
\(317\) −2.86480 + 4.96197i −0.160903 + 0.278692i −0.935193 0.354139i \(-0.884774\pi\)
0.774290 + 0.632831i \(0.218107\pi\)
\(318\) 0 0
\(319\) 0.317344 + 0.549657i 0.0177679 + 0.0307749i
\(320\) 0 0
\(321\) 3.40962 13.1519i 0.190306 0.734068i
\(322\) 0 0
\(323\) −9.66931 −0.538015
\(324\) 0 0
\(325\) 2.08444 0.115624
\(326\) 0 0
\(327\) 5.29219 20.4136i 0.292659 1.12887i
\(328\) 0 0
\(329\) 3.39762 + 5.88485i 0.187317 + 0.324442i
\(330\) 0 0
\(331\) −15.8178 + 27.3973i −0.869427 + 1.50589i −0.00684339 + 0.999977i \(0.502178\pi\)
−0.862583 + 0.505915i \(0.831155\pi\)
\(332\) 0 0
\(333\) −11.8800 6.60359i −0.651021 0.361875i
\(334\) 0 0
\(335\) −0.372266 + 0.644784i −0.0203391 + 0.0352283i
\(336\) 0 0
\(337\) −11.7771 20.3985i −0.641539 1.11118i −0.985089 0.172044i \(-0.944963\pi\)
0.343550 0.939134i \(-0.388371\pi\)
\(338\) 0 0
\(339\) −6.63013 + 1.83447i −0.360099 + 0.0996349i
\(340\) 0 0
\(341\) −0.402751 −0.0218102
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −21.1651 20.8235i −1.13949 1.12110i
\(346\) 0 0
\(347\) −9.81359 16.9976i −0.526821 0.912481i −0.999512 0.0312526i \(-0.990050\pi\)
0.472690 0.881229i \(-0.343283\pi\)
\(348\) 0 0
\(349\) 13.0363 22.5795i 0.697816 1.20865i −0.271406 0.962465i \(-0.587488\pi\)
0.969222 0.246188i \(-0.0791782\pi\)
\(350\) 0 0
\(351\) 11.2538 + 2.72293i 0.600683 + 0.145339i
\(352\) 0 0
\(353\) −3.30878 + 5.73097i −0.176108 + 0.305029i −0.940544 0.339671i \(-0.889684\pi\)
0.764436 + 0.644700i \(0.223018\pi\)
\(354\) 0 0
\(355\) 15.3720 + 26.6250i 0.815859 + 1.41311i
\(356\) 0 0
\(357\) 8.70322 + 8.56276i 0.460623 + 0.453189i
\(358\) 0 0
\(359\) 23.0527 1.21668 0.608338 0.793678i \(-0.291836\pi\)
0.608338 + 0.793678i \(0.291836\pi\)
\(360\) 0 0
\(361\) −17.1184 −0.900968
\(362\) 0 0
\(363\) 17.4011 4.81466i 0.913320 0.252704i
\(364\) 0 0
\(365\) 12.3640 + 21.4150i 0.647159 + 1.12091i
\(366\) 0 0
\(367\) 4.08931 7.08289i 0.213460 0.369724i −0.739335 0.673338i \(-0.764860\pi\)
0.952795 + 0.303614i \(0.0981933\pi\)
\(368\) 0 0
\(369\) 0.432292 + 26.5676i 0.0225042 + 1.38305i
\(370\) 0 0
\(371\) −0.303989 + 0.526524i −0.0157823 + 0.0273358i
\(372\) 0 0
\(373\) −7.75341 13.4293i −0.401456 0.695343i 0.592446 0.805610i \(-0.298163\pi\)
−0.993902 + 0.110268i \(0.964829\pi\)
\(374\) 0 0
\(375\) −4.30420 + 16.6026i −0.222268 + 0.857353i
\(376\) 0 0
\(377\) 1.86345 0.0959723
\(378\) 0 0
\(379\) −18.5814 −0.954461 −0.477231 0.878778i \(-0.658359\pi\)
−0.477231 + 0.878778i \(0.658359\pi\)
\(380\) 0 0
\(381\) −6.84936 + 26.4200i −0.350903 + 1.35354i
\(382\) 0 0
\(383\) 8.30959 + 14.3926i 0.424600 + 0.735429i 0.996383 0.0849761i \(-0.0270814\pi\)
−0.571783 + 0.820405i \(0.693748\pi\)
\(384\) 0 0
\(385\) −0.924512 + 1.60130i −0.0471175 + 0.0816099i
\(386\) 0 0
\(387\) −19.0509 + 11.4163i −0.968412 + 0.580322i
\(388\) 0 0
\(389\) 12.9112 22.3629i 0.654624 1.13384i −0.327364 0.944898i \(-0.606160\pi\)
0.981988 0.188944i \(-0.0605065\pi\)
\(390\) 0 0
\(391\) −24.7995 42.9541i −1.25417 2.17228i
\(392\) 0 0
\(393\) −19.8246 + 5.48522i −1.00002 + 0.276693i
\(394\) 0 0
\(395\) −37.1509 −1.86927
\(396\) 0 0
\(397\) −0.729016 −0.0365883 −0.0182941 0.999833i \(-0.505824\pi\)
−0.0182941 + 0.999833i \(0.505824\pi\)
\(398\) 0 0
\(399\) −1.69362 1.66628i −0.0847869 0.0834185i
\(400\) 0 0
\(401\) 8.67094 + 15.0185i 0.433006 + 0.749989i 0.997131 0.0757010i \(-0.0241195\pi\)
−0.564124 + 0.825690i \(0.690786\pi\)
\(402\) 0 0
\(403\) −0.591238 + 1.02405i −0.0294516 + 0.0510117i
\(404\) 0 0
\(405\) 10.3397 19.3355i 0.513781 0.960790i
\(406\) 0 0
\(407\) 1.71928 2.97789i 0.0852218 0.147608i
\(408\) 0 0
\(409\) 1.82351 + 3.15841i 0.0901668 + 0.156174i 0.907581 0.419877i \(-0.137927\pi\)
−0.817414 + 0.576050i \(0.804593\pi\)
\(410\) 0 0
\(411\) −25.1549 24.7490i −1.24080 1.22078i
\(412\) 0 0
\(413\) −1.16373 −0.0572635
\(414\) 0 0
\(415\) −39.9018 −1.95870
\(416\) 0 0
\(417\) −10.4663 + 2.89591i −0.512539 + 0.141813i
\(418\) 0 0
\(419\) 0.117685 + 0.203836i 0.00574927 + 0.00995803i 0.868886 0.495013i \(-0.164837\pi\)
−0.863136 + 0.504971i \(0.831503\pi\)
\(420\) 0 0
\(421\) −10.8985 + 18.8767i −0.531158 + 0.919993i 0.468181 + 0.883633i \(0.344910\pi\)
−0.999339 + 0.0363601i \(0.988424\pi\)
\(422\) 0 0
\(423\) 17.4864 10.4787i 0.850217 0.509494i
\(424\) 0 0
\(425\) 3.29699 5.71055i 0.159927 0.277002i
\(426\) 0 0
\(427\) 5.85680 + 10.1443i 0.283431 + 0.490916i
\(428\) 0 0
\(429\) −0.735089 + 2.83546i −0.0354904 + 0.136897i
\(430\) 0 0
\(431\) 4.28806 0.206549 0.103274 0.994653i \(-0.467068\pi\)
0.103274 + 0.994653i \(0.467068\pi\)
\(432\) 0 0
\(433\) −13.9263 −0.669257 −0.334628 0.942350i \(-0.608611\pi\)
−0.334628 + 0.942350i \(0.608611\pi\)
\(434\) 0 0
\(435\) 0.885573 3.41592i 0.0424600 0.163781i
\(436\) 0 0
\(437\) 4.82591 + 8.35871i 0.230854 + 0.399851i
\(438\) 0 0
\(439\) −15.9397 + 27.6084i −0.760762 + 1.31768i 0.181696 + 0.983355i \(0.441841\pi\)
−0.942458 + 0.334324i \(0.891492\pi\)
\(440\) 0 0
\(441\) 0.0488078 + 2.99960i 0.00232418 + 0.142838i
\(442\) 0 0
\(443\) 2.56216 4.43780i 0.121732 0.210846i −0.798719 0.601705i \(-0.794488\pi\)
0.920451 + 0.390858i \(0.127822\pi\)
\(444\) 0 0
\(445\) 11.7325 + 20.3213i 0.556174 + 0.963322i
\(446\) 0 0
\(447\) 8.20239 2.26950i 0.387960 0.107344i
\(448\) 0 0
\(449\) −33.9914 −1.60415 −0.802077 0.597221i \(-0.796272\pi\)
−0.802077 + 0.597221i \(0.796272\pi\)
\(450\) 0 0
\(451\) −6.72209 −0.316531
\(452\) 0 0
\(453\) 6.93581 + 6.82387i 0.325873 + 0.320613i
\(454\) 0 0
\(455\) 2.71436 + 4.70142i 0.127251 + 0.220406i
\(456\) 0 0
\(457\) −2.78826 + 4.82941i −0.130429 + 0.225910i −0.923842 0.382774i \(-0.874969\pi\)
0.793413 + 0.608684i \(0.208302\pi\)
\(458\) 0 0
\(459\) 25.2601 26.5241i 1.17904 1.23804i
\(460\) 0 0
\(461\) −1.24904 + 2.16340i −0.0581734 + 0.100759i −0.893646 0.448774i \(-0.851861\pi\)
0.835472 + 0.549533i \(0.185194\pi\)
\(462\) 0 0
\(463\) −4.77517 8.27084i −0.221921 0.384378i 0.733470 0.679722i \(-0.237899\pi\)
−0.955391 + 0.295343i \(0.904566\pi\)
\(464\) 0 0
\(465\) 1.59624 + 1.57047i 0.0740237 + 0.0728290i
\(466\) 0 0
\(467\) −18.2128 −0.842787 −0.421393 0.906878i \(-0.638459\pi\)
−0.421393 + 0.906878i \(0.638459\pi\)
\(468\) 0 0
\(469\) −0.305602 −0.0141114
\(470\) 0 0
\(471\) −34.4462 + 9.53083i −1.58720 + 0.439157i
\(472\) 0 0
\(473\) −2.80935 4.86594i −0.129174 0.223736i
\(474\) 0 0
\(475\) −0.641583 + 1.11125i −0.0294378 + 0.0509878i
\(476\) 0 0
\(477\) 1.59420 + 0.886147i 0.0729934 + 0.0405739i
\(478\) 0 0
\(479\) −2.87648 + 4.98222i −0.131430 + 0.227643i −0.924228 0.381841i \(-0.875290\pi\)
0.792798 + 0.609484i \(0.208623\pi\)
\(480\) 0 0
\(481\) −5.04782 8.74308i −0.230161 0.398650i
\(482\) 0 0
\(483\) 3.05841 11.7972i 0.139163 0.536791i
\(484\) 0 0
\(485\) −26.6391 −1.20962
\(486\) 0 0
\(487\) −23.8918 −1.08264 −0.541321 0.840816i \(-0.682075\pi\)
−0.541321 + 0.840816i \(0.682075\pi\)
\(488\) 0 0
\(489\) −2.15200 + 8.30090i −0.0973167 + 0.375379i
\(490\) 0 0
\(491\) 7.31437 + 12.6689i 0.330093 + 0.571738i 0.982530 0.186105i \(-0.0595865\pi\)
−0.652437 + 0.757843i \(0.726253\pi\)
\(492\) 0 0
\(493\) 2.94744 5.10512i 0.132746 0.229923i
\(494\) 0 0
\(495\) 4.84839 + 2.69501i 0.217919 + 0.121132i
\(496\) 0 0
\(497\) −6.30961 + 10.9286i −0.283025 + 0.490213i
\(498\) 0 0
\(499\) −11.9579 20.7117i −0.535308 0.927181i −0.999148 0.0412621i \(-0.986862\pi\)
0.463840 0.885919i \(-0.346471\pi\)
\(500\) 0 0
\(501\) −1.62214 + 0.448825i −0.0724717 + 0.0200520i
\(502\) 0 0
\(503\) −7.57496 −0.337751 −0.168875 0.985637i \(-0.554014\pi\)
−0.168875 + 0.985637i \(0.554014\pi\)
\(504\) 0 0
\(505\) 3.65645 0.162710
\(506\) 0 0
\(507\) −9.92021 9.76011i −0.440572 0.433462i
\(508\) 0 0
\(509\) 3.50078 + 6.06353i 0.155169 + 0.268761i 0.933121 0.359563i \(-0.117074\pi\)
−0.777951 + 0.628325i \(0.783741\pi\)
\(510\) 0 0
\(511\) −5.07494 + 8.79006i −0.224502 + 0.388849i
\(512\) 0 0
\(513\) −4.91553 + 5.16151i −0.217026 + 0.227886i
\(514\) 0 0
\(515\) 12.5037 21.6570i 0.550978 0.954321i
\(516\) 0 0
\(517\) 2.57864 + 4.46633i 0.113408 + 0.196429i
\(518\) 0 0
\(519\) −22.0008 21.6457i −0.965727 0.950141i
\(520\) 0 0
\(521\) 42.4564 1.86005 0.930025 0.367497i \(-0.119785\pi\)
0.930025 + 0.367497i \(0.119785\pi\)
\(522\) 0 0
\(523\) 18.6096 0.813743 0.406871 0.913485i \(-0.366620\pi\)
0.406871 + 0.913485i \(0.366620\pi\)
\(524\) 0 0
\(525\) 1.56156 0.432065i 0.0681522 0.0188569i
\(526\) 0 0
\(527\) 1.87034 + 3.23952i 0.0814733 + 0.141116i
\(528\) 0 0
\(529\) −13.2547 + 22.9577i −0.576289 + 0.998163i
\(530\) 0 0
\(531\) 0.0567992 + 3.49074i 0.00246487 + 0.151485i
\(532\) 0 0
\(533\) −9.86802 + 17.0919i −0.427431 + 0.740333i
\(534\) 0 0
\(535\) −9.55542 16.5505i −0.413117 0.715539i
\(536\) 0 0
\(537\) 4.61024 17.7831i 0.198946 0.767395i
\(538\) 0 0
\(539\) −0.758955 −0.0326905
\(540\) 0 0
\(541\) −0.694443 −0.0298564 −0.0149282 0.999889i \(-0.504752\pi\)
−0.0149282 + 0.999889i \(0.504752\pi\)
\(542\) 0 0
\(543\) 10.7518 41.4730i 0.461406 1.77978i
\(544\) 0 0
\(545\) −14.8313 25.6886i −0.635304 1.10038i
\(546\) 0 0
\(547\) 8.77655 15.2014i 0.375258 0.649966i −0.615107 0.788443i \(-0.710887\pi\)
0.990366 + 0.138477i \(0.0442207\pi\)
\(548\) 0 0
\(549\) 30.1430 18.0632i 1.28647 0.770919i
\(550\) 0 0
\(551\) −0.573562 + 0.993439i −0.0244346 + 0.0423219i
\(552\) 0 0
\(553\) −7.62453 13.2061i −0.324228 0.561579i
\(554\) 0 0
\(555\) −18.4260 + 5.09824i −0.782140 + 0.216408i
\(556\) 0 0
\(557\) 14.2666 0.604495 0.302248 0.953229i \(-0.402263\pi\)
0.302248 + 0.953229i \(0.402263\pi\)
\(558\) 0 0
\(559\) −16.4965 −0.697728
\(560\) 0 0
\(561\) 6.60535 + 6.49875i 0.278878 + 0.274377i
\(562\) 0 0
\(563\) −16.8742 29.2270i −0.711162 1.23177i −0.964421 0.264371i \(-0.914836\pi\)
0.253259 0.967399i \(-0.418498\pi\)
\(564\) 0 0
\(565\) −4.83811 + 8.37986i −0.203541 + 0.352543i
\(566\) 0 0
\(567\) 8.99524 0.292808i 0.377764 0.0122968i
\(568\) 0 0
\(569\) −19.9867 + 34.6180i −0.837886 + 1.45126i 0.0537729 + 0.998553i \(0.482875\pi\)
−0.891659 + 0.452708i \(0.850458\pi\)
\(570\) 0 0
\(571\) 20.2266 + 35.0335i 0.846457 + 1.46611i 0.884350 + 0.466824i \(0.154602\pi\)
−0.0378934 + 0.999282i \(0.512065\pi\)
\(572\) 0 0
\(573\) −22.8443 22.4756i −0.954335 0.938932i
\(574\) 0 0
\(575\) −6.58204 −0.274490
\(576\) 0 0
\(577\) −31.6758 −1.31868 −0.659340 0.751845i \(-0.729164\pi\)
−0.659340 + 0.751845i \(0.729164\pi\)
\(578\) 0 0
\(579\) −27.5274 + 7.61650i −1.14400 + 0.316531i
\(580\) 0 0
\(581\) −8.18909 14.1839i −0.339741 0.588448i
\(582\) 0 0
\(583\) −0.230714 + 0.399608i −0.00955519 + 0.0165501i
\(584\) 0 0
\(585\) 13.9699 8.37148i 0.577584 0.346118i
\(586\) 0 0
\(587\) 7.65220 13.2540i 0.315840 0.547051i −0.663776 0.747932i \(-0.731047\pi\)
0.979616 + 0.200881i \(0.0643803\pi\)
\(588\) 0 0
\(589\) −0.363962 0.630400i −0.0149968 0.0259752i
\(590\) 0 0
\(591\) −3.77359 + 14.5558i −0.155225 + 0.598748i
\(592\) 0 0
\(593\) 39.2583 1.61214 0.806072 0.591817i \(-0.201589\pi\)
0.806072 + 0.591817i \(0.201589\pi\)
\(594\) 0 0
\(595\) 17.1734 0.704041
\(596\) 0 0
\(597\) 8.36083 32.2502i 0.342186 1.31991i
\(598\) 0 0
\(599\) 8.77972 + 15.2069i 0.358730 + 0.621338i 0.987749 0.156052i \(-0.0498766\pi\)
−0.629019 + 0.777390i \(0.716543\pi\)
\(600\) 0 0
\(601\) −9.12937 + 15.8125i −0.372395 + 0.645007i −0.989933 0.141534i \(-0.954797\pi\)
0.617539 + 0.786541i \(0.288130\pi\)
\(602\) 0 0
\(603\) 0.0149158 + 0.916686i 0.000607417 + 0.0373303i
\(604\) 0 0
\(605\) 12.6979 21.9933i 0.516241 0.894156i
\(606\) 0 0
\(607\) −3.71415 6.43310i −0.150753 0.261112i 0.780752 0.624842i \(-0.214836\pi\)
−0.931504 + 0.363730i \(0.881503\pi\)
\(608\) 0 0
\(609\) 1.39601 0.386258i 0.0565690 0.0156519i
\(610\) 0 0
\(611\) 15.1418 0.612570
\(612\) 0 0
\(613\) −39.8772 −1.61062 −0.805312 0.592851i \(-0.798002\pi\)
−0.805312 + 0.592851i \(0.798002\pi\)
\(614\) 0 0
\(615\) 26.6419 + 26.2119i 1.07430 + 1.05697i
\(616\) 0 0
\(617\) −0.187473 0.324713i −0.00754739 0.0130725i 0.862227 0.506522i \(-0.169069\pi\)
−0.869774 + 0.493450i \(0.835736\pi\)
\(618\) 0 0
\(619\) −6.95166 + 12.0406i −0.279411 + 0.483954i −0.971238 0.238109i \(-0.923472\pi\)
0.691828 + 0.722063i \(0.256806\pi\)
\(620\) 0 0
\(621\) −35.5362 8.59823i −1.42602 0.345035i
\(622\) 0 0
\(623\) −4.81575 + 8.34113i −0.192939 + 0.334180i
\(624\) 0 0
\(625\) 14.4011 + 24.9434i 0.576043 + 0.997736i
\(626\) 0 0
\(627\) −1.28538 1.26463i −0.0513331 0.0505046i
\(628\) 0 0
\(629\) −31.9368 −1.27341
\(630\) 0 0
\(631\) −28.6049 −1.13874 −0.569372 0.822080i \(-0.692813\pi\)
−0.569372 + 0.822080i \(0.692813\pi\)
\(632\) 0 0
\(633\) 37.9219 10.4925i 1.50726 0.417040i
\(634\) 0 0
\(635\) 19.1953 + 33.2472i 0.761740 + 1.31937i
\(636\) 0 0
\(637\) −1.11414 + 1.92976i −0.0441440 + 0.0764597i
\(638\) 0 0
\(639\) 33.0893 + 18.3929i 1.30899 + 0.727613i
\(640\) 0 0
\(641\) 10.9011 18.8812i 0.430566 0.745762i −0.566356 0.824161i \(-0.691647\pi\)
0.996922 + 0.0783986i \(0.0249807\pi\)
\(642\) 0 0
\(643\) −20.9205 36.2354i −0.825025 1.42899i −0.901900 0.431945i \(-0.857828\pi\)
0.0768751 0.997041i \(-0.475506\pi\)
\(644\) 0 0
\(645\) −7.83971 + 30.2401i −0.308688 + 1.19070i
\(646\) 0 0
\(647\) −17.2614 −0.678615 −0.339308 0.940675i \(-0.610193\pi\)
−0.339308 + 0.940675i \(0.610193\pi\)
\(648\) 0 0
\(649\) −0.883220 −0.0346694
\(650\) 0 0
\(651\) −0.230660 + 0.889726i −0.00904029 + 0.0348711i
\(652\) 0 0
\(653\) −0.237661 0.411641i −0.00930039 0.0161087i 0.861338 0.508033i \(-0.169627\pi\)
−0.870638 + 0.491924i \(0.836294\pi\)
\(654\) 0 0
\(655\) −14.4663 + 25.0564i −0.565247 + 0.979036i
\(656\) 0 0
\(657\) 26.6144 + 14.7938i 1.03833 + 0.577161i
\(658\) 0 0
\(659\) 18.2344 31.5828i 0.710310 1.23029i −0.254431 0.967091i \(-0.581888\pi\)
0.964741 0.263201i \(-0.0847784\pi\)
\(660\) 0 0
\(661\) −5.04982 8.74655i −0.196415 0.340201i 0.750948 0.660361i \(-0.229597\pi\)
−0.947364 + 0.320160i \(0.896263\pi\)
\(662\) 0 0
\(663\) 26.2207 7.25494i 1.01833 0.281758i
\(664\) 0 0
\(665\) −3.34189 −0.129593
\(666\) 0 0
\(667\) −5.88422 −0.227838
\(668\) 0 0
\(669\) −19.1699 18.8605i −0.741152 0.729191i
\(670\) 0 0
\(671\) 4.44505 + 7.69905i 0.171599 + 0.297218i
\(672\) 0 0
\(673\) 9.51044 16.4726i 0.366600 0.634971i −0.622431 0.782675i \(-0.713855\pi\)
0.989032 + 0.147704i \(0.0471883\pi\)
\(674\) 0 0
\(675\) −1.37224 4.66298i −0.0528175 0.179478i
\(676\) 0 0
\(677\) 22.6374 39.2091i 0.870024 1.50693i 0.00805435 0.999968i \(-0.497436\pi\)
0.861970 0.506959i \(-0.169230\pi\)
\(678\) 0 0
\(679\) −5.46718 9.46943i −0.209811 0.363403i
\(680\) 0 0
\(681\) −2.80191 2.75669i −0.107369 0.105637i
\(682\) 0 0
\(683\) 45.5318 1.74222 0.871112 0.491084i \(-0.163399\pi\)
0.871112 + 0.491084i \(0.163399\pi\)
\(684\) 0 0
\(685\) −49.6363 −1.89651
\(686\) 0 0
\(687\) −15.3925 + 4.25890i −0.587259 + 0.162487i
\(688\) 0 0
\(689\) 0.677375 + 1.17325i 0.0258059 + 0.0446972i
\(690\) 0 0
\(691\) −8.09446 + 14.0200i −0.307928 + 0.533347i −0.977909 0.209031i \(-0.932969\pi\)
0.669981 + 0.742378i \(0.266302\pi\)
\(692\) 0 0
\(693\) 0.0370429 + 2.27656i 0.00140714 + 0.0864795i
\(694\) 0 0
\(695\) −7.63746 + 13.2285i −0.289706 + 0.501785i
\(696\) 0 0
\(697\) 31.2168 + 54.0691i 1.18242 + 2.04801i
\(698\) 0 0
\(699\) −10.4685 + 40.3802i −0.395956 + 1.52732i
\(700\) 0 0
\(701\) −2.61120 −0.0986238 −0.0493119 0.998783i \(-0.515703\pi\)
−0.0493119 + 0.998783i \(0.515703\pi\)
\(702\) 0 0
\(703\) 6.21480 0.234396
\(704\) 0 0
\(705\) 7.19588 27.7567i 0.271013 1.04538i
\(706\) 0 0
\(707\) 0.750417 + 1.29976i 0.0282223 + 0.0488825i
\(708\) 0 0
\(709\) −23.1702 + 40.1319i −0.870175 + 1.50719i −0.00835896 + 0.999965i \(0.502661\pi\)
−0.861816 + 0.507222i \(0.830673\pi\)
\(710\) 0 0
\(711\) −39.2408 + 23.5151i −1.47165 + 0.881886i
\(712\) 0 0
\(713\) 1.86696 3.23366i 0.0699180 0.121102i
\(714\) 0 0
\(715\) 2.06008 + 3.56816i 0.0770426 + 0.133442i
\(716\) 0 0
\(717\) 8.34665 2.30941i 0.311711 0.0862467i
\(718\) 0 0
\(719\) 46.2069 1.72323 0.861614 0.507564i \(-0.169454\pi\)
0.861614 + 0.507564i \(0.169454\pi\)
\(720\) 0 0
\(721\) 10.2646 0.382273
\(722\) 0 0
\(723\) −21.2798 20.9363i −0.791403 0.778630i
\(724\) 0 0
\(725\) −0.391140 0.677475i −0.0145266 0.0251608i
\(726\) 0 0
\(727\) −9.72988 + 16.8526i −0.360861 + 0.625030i −0.988103 0.153795i \(-0.950851\pi\)
0.627242 + 0.778825i \(0.284184\pi\)
\(728\) 0 0
\(729\) −1.31734 26.9678i −0.0487905 0.998809i
\(730\) 0 0
\(731\) −26.0928 + 45.1940i −0.965077 + 1.67156i
\(732\) 0 0
\(733\) −7.68617 13.3128i −0.283895 0.491721i 0.688445 0.725288i \(-0.258293\pi\)
−0.972341 + 0.233567i \(0.924960\pi\)
\(734\) 0 0
\(735\) 3.00799 + 2.95945i 0.110951 + 0.109161i
\(736\) 0 0
\(737\) −0.231938 −0.00854356
\(738\) 0 0
\(739\) 32.4962 1.19539 0.597696 0.801723i \(-0.296083\pi\)
0.597696 + 0.801723i \(0.296083\pi\)
\(740\) 0 0
\(741\) −5.10246 + 1.41179i −0.187443 + 0.0518632i
\(742\) 0 0
\(743\) 20.8664 + 36.1417i 0.765514 + 1.32591i 0.939974 + 0.341245i \(0.110849\pi\)
−0.174460 + 0.984664i \(0.555818\pi\)
\(744\) 0 0
\(745\) 5.98542 10.3671i 0.219289 0.379819i
\(746\) 0 0
\(747\) −42.1464 + 25.2563i −1.54206 + 0.924079i
\(748\) 0 0
\(749\) 3.92214 6.79335i 0.143312 0.248224i
\(750\) 0 0
\(751\) 5.02452 + 8.70273i 0.183347 + 0.317567i 0.943018 0.332741i \(-0.107973\pi\)
−0.759671 + 0.650308i \(0.774640\pi\)
\(752\) 0 0
\(753\) −6.63841 + 25.6063i −0.241917 + 0.933146i
\(754\) 0 0
\(755\) 13.6859 0.498081
\(756\) 0 0
\(757\) −31.7989 −1.15575 −0.577876 0.816125i \(-0.696118\pi\)
−0.577876 + 0.816125i \(0.696118\pi\)
\(758\) 0 0
\(759\) 2.32120 8.95354i 0.0842541 0.324993i
\(760\) 0 0
\(761\) 27.4352 + 47.5192i 0.994526 + 1.72257i 0.587751 + 0.809042i \(0.300013\pi\)
0.406775 + 0.913528i \(0.366653\pi\)
\(762\) 0 0
\(763\) 6.08770 10.5442i 0.220389 0.381726i
\(764\) 0 0
\(765\) −0.838196 51.5134i −0.0303050 1.86247i
\(766\) 0 0
\(767\) −1.29657 + 2.24572i −0.0468163 + 0.0810882i
\(768\) 0 0
\(769\) 5.39041 + 9.33646i 0.194383 + 0.336681i 0.946698 0.322122i \(-0.104396\pi\)
−0.752315 + 0.658804i \(0.771063\pi\)
\(770\) 0 0
\(771\) 19.3483 5.35344i 0.696814 0.192800i
\(772\) 0 0
\(773\) −47.4885 −1.70804 −0.854022 0.520237i \(-0.825844\pi\)
−0.854022 + 0.520237i \(0.825844\pi\)
\(774\) 0 0
\(775\) 0.496407 0.0178315
\(776\) 0 0
\(777\) −5.59386 5.50359i −0.200679 0.197440i
\(778\) 0 0
\(779\) −6.07469 10.5217i −0.217648 0.376978i
\(780\) 0 0
\(781\) −4.78871 + 8.29428i −0.171353 + 0.296793i
\(782\) 0 0
\(783\) −1.22676 4.16861i −0.0438407 0.148974i
\(784\) 0 0
\(785\) −25.1360 + 43.5368i −0.897141 + 1.55389i
\(786\) 0 0
\(787\) −12.0563 20.8820i −0.429759 0.744364i 0.567093 0.823654i \(-0.308068\pi\)
−0.996852 + 0.0792896i \(0.974735\pi\)
\(788\) 0 0
\(789\) 10.0157 + 9.85403i 0.356567 + 0.350813i
\(790\) 0 0
\(791\) −3.97173 −0.141218
\(792\) 0 0
\(793\) 26.1013 0.926885
\(794\) 0 0
\(795\) 2.47262 0.684142i 0.0876946 0.0242640i
\(796\) 0 0
\(797\) 7.54620 + 13.0704i 0.267300 + 0.462978i 0.968164 0.250318i \(-0.0805351\pi\)
−0.700863 + 0.713295i \(0.747202\pi\)
\(798