Properties

Label 144.3.o.a.79.2
Level $144$
Weight $3$
Character 144.79
Analytic conductor $3.924$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 144 = 2^{4} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 144.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.92371580679\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.856615824.2
Defining polynomial: \(x^{8} + 11 x^{6} + 36 x^{4} + 32 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 79.2
Root \(-0.385731i\) of defining polynomial
Character \(\chi\) \(=\) 144.79
Dual form 144.3.o.a.31.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.28651 - 2.71015i) q^{3} +(-0.454613 - 0.787412i) q^{5} +(-6.10709 - 3.52593i) q^{7} +(-5.68980 + 6.97325i) q^{9} +O(q^{10})\) \(q+(-1.28651 - 2.71015i) q^{3} +(-0.454613 - 0.787412i) q^{5} +(-6.10709 - 3.52593i) q^{7} +(-5.68980 + 6.97325i) q^{9} +(-6.96661 - 4.02218i) q^{11} +(3.35952 + 5.81886i) q^{13} +(-1.54914 + 2.24508i) q^{15} -26.3462 q^{17} -20.5603i q^{19} +(-1.69897 + 21.0873i) q^{21} +(-21.8305 + 12.6038i) q^{23} +(12.0867 - 20.9347i) q^{25} +(26.2185 + 6.44905i) q^{27} +(15.1693 - 26.2741i) q^{29} +(-0.120040 + 0.0693050i) q^{31} +(-1.93809 + 24.0551i) q^{33} +6.41173i q^{35} +69.7588 q^{37} +(11.4479 - 16.5908i) q^{39} +(-29.3794 - 50.8866i) q^{41} +(2.45853 + 1.41943i) q^{43} +(8.07748 + 1.31009i) q^{45} +(70.7583 + 40.8523i) q^{47} +(0.364383 + 0.631130i) q^{49} +(33.8946 + 71.4022i) q^{51} -30.0259 q^{53} +7.31413i q^{55} +(-55.7213 + 26.4509i) q^{57} +(-77.1442 + 44.5392i) q^{59} +(24.0688 - 41.6885i) q^{61} +(59.3353 - 22.5244i) q^{63} +(3.05456 - 5.29066i) q^{65} +(44.0829 - 25.4513i) q^{67} +(62.2432 + 42.9488i) q^{69} -68.4355i q^{71} -22.1474 q^{73} +(-72.2857 - 5.82397i) q^{75} +(28.3638 + 49.1276i) q^{77} +(-34.4343 - 19.8807i) q^{79} +(-16.2524 - 79.3527i) q^{81} +(-23.0801 - 13.3253i) q^{83} +(11.9773 + 20.7453i) q^{85} +(-90.7221 - 7.30936i) q^{87} -25.7926 q^{89} -47.3818i q^{91} +(0.342259 + 0.236164i) q^{93} +(-16.1894 + 9.34695i) q^{95} +(-52.3697 + 90.7070i) q^{97} +(67.6863 - 25.6946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 3q^{3} + 3q^{5} + 3q^{7} - 3q^{9} + O(q^{10}) \) \( 8q - 3q^{3} + 3q^{5} + 3q^{7} - 3q^{9} + 18q^{11} + 5q^{13} - 21q^{15} + 6q^{17} - 33q^{21} - 81q^{23} - 23q^{25} + 108q^{27} + 69q^{29} + 45q^{31} + 72q^{33} - 20q^{37} - 141q^{39} + 54q^{41} - 117q^{45} + 207q^{47} + 41q^{49} - 141q^{51} - 252q^{53} - 273q^{57} - 306q^{59} + 7q^{61} + 441q^{63} + 93q^{65} + 12q^{67} + 189q^{69} + 74q^{73} - 387q^{75} + 207q^{77} + 33q^{79} + 117q^{81} + 549q^{83} - 30q^{85} - 87q^{87} - 168q^{89} - 27q^{93} - 684q^{95} - 10q^{97} + 585q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

\(n\) \(37\) \(65\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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
\(3\) −1.28651 2.71015i −0.428836 0.903382i
\(4\) 0 0
\(5\) −0.454613 0.787412i −0.0909226 0.157482i 0.816977 0.576670i \(-0.195648\pi\)
−0.907900 + 0.419188i \(0.862315\pi\)
\(6\) 0 0
\(7\) −6.10709 3.52593i −0.872442 0.503704i −0.00428285 0.999991i \(-0.501363\pi\)
−0.868159 + 0.496286i \(0.834697\pi\)
\(8\) 0 0
\(9\) −5.68980 + 6.97325i −0.632200 + 0.774806i
\(10\) 0 0
\(11\) −6.96661 4.02218i −0.633329 0.365652i 0.148711 0.988881i \(-0.452487\pi\)
−0.782040 + 0.623228i \(0.785821\pi\)
\(12\) 0 0
\(13\) 3.35952 + 5.81886i 0.258425 + 0.447605i 0.965820 0.259213i \(-0.0834632\pi\)
−0.707395 + 0.706818i \(0.750130\pi\)
\(14\) 0 0
\(15\) −1.54914 + 2.24508i −0.103276 + 0.149672i
\(16\) 0 0
\(17\) −26.3462 −1.54978 −0.774889 0.632097i \(-0.782194\pi\)
−0.774889 + 0.632097i \(0.782194\pi\)
\(18\) 0 0
\(19\) 20.5603i 1.08212i −0.840984 0.541059i \(-0.818023\pi\)
0.840984 0.541059i \(-0.181977\pi\)
\(20\) 0 0
\(21\) −1.69897 + 21.0873i −0.0809035 + 1.00416i
\(22\) 0 0
\(23\) −21.8305 + 12.6038i −0.949150 + 0.547992i −0.892817 0.450420i \(-0.851274\pi\)
−0.0563333 + 0.998412i \(0.517941\pi\)
\(24\) 0 0
\(25\) 12.0867 20.9347i 0.483466 0.837388i
\(26\) 0 0
\(27\) 26.2185 + 6.44905i 0.971056 + 0.238854i
\(28\) 0 0
\(29\) 15.1693 26.2741i 0.523081 0.906002i −0.476558 0.879143i \(-0.658116\pi\)
0.999639 0.0268597i \(-0.00855072\pi\)
\(30\) 0 0
\(31\) −0.120040 + 0.0693050i −0.00387225 + 0.00223565i −0.501935 0.864905i \(-0.667378\pi\)
0.498063 + 0.867141i \(0.334045\pi\)
\(32\) 0 0
\(33\) −1.93809 + 24.0551i −0.0587300 + 0.728943i
\(34\) 0 0
\(35\) 6.41173i 0.183192i
\(36\) 0 0
\(37\) 69.7588 1.88537 0.942687 0.333679i \(-0.108290\pi\)
0.942687 + 0.333679i \(0.108290\pi\)
\(38\) 0 0
\(39\) 11.4479 16.5908i 0.293537 0.425405i
\(40\) 0 0
\(41\) −29.3794 50.8866i −0.716571 1.24114i −0.962351 0.271811i \(-0.912377\pi\)
0.245780 0.969326i \(-0.420956\pi\)
\(42\) 0 0
\(43\) 2.45853 + 1.41943i 0.0571751 + 0.0330100i 0.528315 0.849048i \(-0.322824\pi\)
−0.471140 + 0.882058i \(0.656157\pi\)
\(44\) 0 0
\(45\) 8.07748 + 1.31009i 0.179500 + 0.0291131i
\(46\) 0 0
\(47\) 70.7583 + 40.8523i 1.50550 + 0.869198i 0.999980 + 0.00638063i \(0.00203103\pi\)
0.505516 + 0.862817i \(0.331302\pi\)
\(48\) 0 0
\(49\) 0.364383 + 0.631130i 0.00743639 + 0.0128802i
\(50\) 0 0
\(51\) 33.8946 + 71.4022i 0.664600 + 1.40004i
\(52\) 0 0
\(53\) −30.0259 −0.566526 −0.283263 0.959042i \(-0.591417\pi\)
−0.283263 + 0.959042i \(0.591417\pi\)
\(54\) 0 0
\(55\) 7.31413i 0.132984i
\(56\) 0 0
\(57\) −55.7213 + 26.4509i −0.977567 + 0.464051i
\(58\) 0 0
\(59\) −77.1442 + 44.5392i −1.30753 + 0.754902i −0.981683 0.190520i \(-0.938983\pi\)
−0.325846 + 0.945423i \(0.605649\pi\)
\(60\) 0 0
\(61\) 24.0688 41.6885i 0.394571 0.683417i −0.598475 0.801141i \(-0.704226\pi\)
0.993046 + 0.117724i \(0.0375598\pi\)
\(62\) 0 0
\(63\) 59.3353 22.5244i 0.941830 0.357531i
\(64\) 0 0
\(65\) 3.05456 5.29066i 0.0469933 0.0813948i
\(66\) 0 0
\(67\) 44.0829 25.4513i 0.657953 0.379870i −0.133543 0.991043i \(-0.542636\pi\)
0.791497 + 0.611173i \(0.209302\pi\)
\(68\) 0 0
\(69\) 62.2432 + 42.9488i 0.902076 + 0.622447i
\(70\) 0 0
\(71\) 68.4355i 0.963881i −0.876204 0.481940i \(-0.839932\pi\)
0.876204 0.481940i \(-0.160068\pi\)
\(72\) 0 0
\(73\) −22.1474 −0.303389 −0.151695 0.988427i \(-0.548473\pi\)
−0.151695 + 0.988427i \(0.548473\pi\)
\(74\) 0 0
\(75\) −72.2857 5.82397i −0.963809 0.0776529i
\(76\) 0 0
\(77\) 28.3638 + 49.1276i 0.368362 + 0.638021i
\(78\) 0 0
\(79\) −34.4343 19.8807i −0.435877 0.251654i 0.265970 0.963981i \(-0.414308\pi\)
−0.701847 + 0.712327i \(0.747641\pi\)
\(80\) 0 0
\(81\) −16.2524 79.3527i −0.200647 0.979664i
\(82\) 0 0
\(83\) −23.0801 13.3253i −0.278073 0.160546i 0.354478 0.935065i \(-0.384659\pi\)
−0.632551 + 0.774519i \(0.717992\pi\)
\(84\) 0 0
\(85\) 11.9773 + 20.7453i 0.140910 + 0.244063i
\(86\) 0 0
\(87\) −90.7221 7.30936i −1.04278 0.0840157i
\(88\) 0 0
\(89\) −25.7926 −0.289804 −0.144902 0.989446i \(-0.546287\pi\)
−0.144902 + 0.989446i \(0.546287\pi\)
\(90\) 0 0
\(91\) 47.3818i 0.520679i
\(92\) 0 0
\(93\) 0.342259 + 0.236164i 0.00368020 + 0.00253940i
\(94\) 0 0
\(95\) −16.1894 + 9.34695i −0.170415 + 0.0983890i
\(96\) 0 0
\(97\) −52.3697 + 90.7070i −0.539894 + 0.935123i 0.459016 + 0.888428i \(0.348202\pi\)
−0.998909 + 0.0466950i \(0.985131\pi\)
\(98\) 0 0
\(99\) 67.6863 25.6946i 0.683700 0.259541i
\(100\) 0 0
\(101\) 20.4790 35.4707i 0.202763 0.351195i −0.746655 0.665212i \(-0.768341\pi\)
0.949418 + 0.314016i \(0.101675\pi\)
\(102\) 0 0
\(103\) −125.278 + 72.3293i −1.21629 + 0.702227i −0.964123 0.265456i \(-0.914477\pi\)
−0.252169 + 0.967683i \(0.581144\pi\)
\(104\) 0 0
\(105\) 17.3767 8.24874i 0.165493 0.0785595i
\(106\) 0 0
\(107\) 177.858i 1.66222i −0.556105 0.831112i \(-0.687705\pi\)
0.556105 0.831112i \(-0.312295\pi\)
\(108\) 0 0
\(109\) −142.616 −1.30840 −0.654200 0.756322i \(-0.726994\pi\)
−0.654200 + 0.756322i \(0.726994\pi\)
\(110\) 0 0
\(111\) −89.7452 189.057i −0.808516 1.70321i
\(112\) 0 0
\(113\) 100.147 + 173.459i 0.886254 + 1.53504i 0.844270 + 0.535918i \(0.180034\pi\)
0.0419835 + 0.999118i \(0.486632\pi\)
\(114\) 0 0
\(115\) 19.8488 + 11.4597i 0.172598 + 0.0996497i
\(116\) 0 0
\(117\) −59.6914 9.68136i −0.510183 0.0827467i
\(118\) 0 0
\(119\) 160.899 + 92.8950i 1.35209 + 0.780630i
\(120\) 0 0
\(121\) −28.1442 48.7472i −0.232597 0.402869i
\(122\) 0 0
\(123\) −100.113 + 145.089i −0.813930 + 1.17958i
\(124\) 0 0
\(125\) −44.7096 −0.357677
\(126\) 0 0
\(127\) 181.723i 1.43089i 0.698670 + 0.715445i \(0.253776\pi\)
−0.698670 + 0.715445i \(0.746224\pi\)
\(128\) 0 0
\(129\) 0.683954 8.48908i 0.00530197 0.0658068i
\(130\) 0 0
\(131\) −52.9361 + 30.5627i −0.404092 + 0.233303i −0.688248 0.725475i \(-0.741620\pi\)
0.284156 + 0.958778i \(0.408287\pi\)
\(132\) 0 0
\(133\) −72.4940 + 125.563i −0.545068 + 0.944085i
\(134\) 0 0
\(135\) −6.84120 23.5766i −0.0506756 0.174641i
\(136\) 0 0
\(137\) 18.1131 31.3729i 0.132213 0.228999i −0.792317 0.610110i \(-0.791125\pi\)
0.924529 + 0.381111i \(0.124458\pi\)
\(138\) 0 0
\(139\) 154.652 89.2885i 1.11261 0.642363i 0.173103 0.984904i \(-0.444621\pi\)
0.939503 + 0.342541i \(0.111287\pi\)
\(140\) 0 0
\(141\) 19.6847 244.322i 0.139608 1.73278i
\(142\) 0 0
\(143\) 54.0504i 0.377975i
\(144\) 0 0
\(145\) −27.5847 −0.190239
\(146\) 0 0
\(147\) 1.24167 1.79949i 0.00844676 0.0122414i
\(148\) 0 0
\(149\) 120.043 + 207.921i 0.805660 + 1.39544i 0.915845 + 0.401533i \(0.131522\pi\)
−0.110185 + 0.993911i \(0.535144\pi\)
\(150\) 0 0
\(151\) 98.1393 + 56.6607i 0.649929 + 0.375237i 0.788429 0.615126i \(-0.210895\pi\)
−0.138500 + 0.990362i \(0.544228\pi\)
\(152\) 0 0
\(153\) 149.905 183.719i 0.979769 1.20078i
\(154\) 0 0
\(155\) 0.109143 + 0.0630139i 0.000704150 + 0.000406541i
\(156\) 0 0
\(157\) −60.3604 104.547i −0.384461 0.665907i 0.607233 0.794524i \(-0.292280\pi\)
−0.991694 + 0.128617i \(0.958946\pi\)
\(158\) 0 0
\(159\) 38.6285 + 81.3746i 0.242947 + 0.511790i
\(160\) 0 0
\(161\) 177.761 1.10410
\(162\) 0 0
\(163\) 20.3498i 0.124845i −0.998050 0.0624226i \(-0.980117\pi\)
0.998050 0.0624226i \(-0.0198827\pi\)
\(164\) 0 0
\(165\) 19.8224 9.40969i 0.120136 0.0570284i
\(166\) 0 0
\(167\) 151.530 87.4858i 0.907365 0.523867i 0.0277823 0.999614i \(-0.491155\pi\)
0.879582 + 0.475747i \(0.157822\pi\)
\(168\) 0 0
\(169\) 61.9272 107.261i 0.366433 0.634681i
\(170\) 0 0
\(171\) 143.372 + 116.984i 0.838431 + 0.684115i
\(172\) 0 0
\(173\) 55.9175 96.8520i 0.323223 0.559838i −0.657928 0.753080i \(-0.728567\pi\)
0.981151 + 0.193243i \(0.0619004\pi\)
\(174\) 0 0
\(175\) −147.629 + 85.2334i −0.843592 + 0.487048i
\(176\) 0 0
\(177\) 219.955 + 151.772i 1.24268 + 0.857470i
\(178\) 0 0
\(179\) 18.6939i 0.104435i −0.998636 0.0522176i \(-0.983371\pi\)
0.998636 0.0522176i \(-0.0166289\pi\)
\(180\) 0 0
\(181\) −98.0536 −0.541733 −0.270866 0.962617i \(-0.587310\pi\)
−0.270866 + 0.962617i \(0.587310\pi\)
\(182\) 0 0
\(183\) −143.947 11.5976i −0.786594 0.0633748i
\(184\) 0 0
\(185\) −31.7132 54.9290i −0.171423 0.296913i
\(186\) 0 0
\(187\) 183.544 + 105.969i 0.981519 + 0.566680i
\(188\) 0 0
\(189\) −137.380 131.830i −0.726878 0.697511i
\(190\) 0 0
\(191\) 240.713 + 138.976i 1.26028 + 0.727621i 0.973128 0.230265i \(-0.0739592\pi\)
0.287149 + 0.957886i \(0.407293\pi\)
\(192\) 0 0
\(193\) 81.1285 + 140.519i 0.420355 + 0.728076i 0.995974 0.0896419i \(-0.0285722\pi\)
−0.575619 + 0.817718i \(0.695239\pi\)
\(194\) 0 0
\(195\) −18.2682 1.47184i −0.0936830 0.00754792i
\(196\) 0 0
\(197\) −106.182 −0.538993 −0.269496 0.963001i \(-0.586857\pi\)
−0.269496 + 0.963001i \(0.586857\pi\)
\(198\) 0 0
\(199\) 63.3880i 0.318532i 0.987236 + 0.159266i \(0.0509128\pi\)
−0.987236 + 0.159266i \(0.949087\pi\)
\(200\) 0 0
\(201\) −125.690 86.7278i −0.625321 0.431482i
\(202\) 0 0
\(203\) −185.281 + 106.972i −0.912715 + 0.526956i
\(204\) 0 0
\(205\) −26.7125 + 46.2674i −0.130305 + 0.225695i
\(206\) 0 0
\(207\) 36.3213 223.942i 0.175465 1.08185i
\(208\) 0 0
\(209\) −82.6970 + 143.235i −0.395679 + 0.685337i
\(210\) 0 0
\(211\) −4.98019 + 2.87531i −0.0236028 + 0.0136271i −0.511755 0.859131i \(-0.671004\pi\)
0.488152 + 0.872759i \(0.337671\pi\)
\(212\) 0 0
\(213\) −185.470 + 88.0428i −0.870753 + 0.413347i
\(214\) 0 0
\(215\) 2.58117i 0.0120054i
\(216\) 0 0
\(217\) 0.977459 0.00450442
\(218\) 0 0
\(219\) 28.4928 + 60.0228i 0.130104 + 0.274076i
\(220\) 0 0
\(221\) −88.5107 153.305i −0.400501 0.693688i
\(222\) 0 0
\(223\) −179.786 103.799i −0.806215 0.465469i 0.0394246 0.999223i \(-0.487448\pi\)
−0.845640 + 0.533754i \(0.820781\pi\)
\(224\) 0 0
\(225\) 77.2123 + 203.397i 0.343166 + 0.903989i
\(226\) 0 0
\(227\) −78.8889 45.5465i −0.347528 0.200646i 0.316068 0.948737i \(-0.397637\pi\)
−0.663596 + 0.748091i \(0.730971\pi\)
\(228\) 0 0
\(229\) 2.04945 + 3.54974i 0.00894954 + 0.0155011i 0.870465 0.492229i \(-0.163818\pi\)
−0.861516 + 0.507731i \(0.830485\pi\)
\(230\) 0 0
\(231\) 96.6528 140.073i 0.418410 0.606378i
\(232\) 0 0
\(233\) 171.761 0.737170 0.368585 0.929594i \(-0.379842\pi\)
0.368585 + 0.929594i \(0.379842\pi\)
\(234\) 0 0
\(235\) 74.2879i 0.316119i
\(236\) 0 0
\(237\) −9.57951 + 118.899i −0.0404199 + 0.501682i
\(238\) 0 0
\(239\) −78.9068 + 45.5569i −0.330154 + 0.190614i −0.655909 0.754840i \(-0.727715\pi\)
0.325755 + 0.945454i \(0.394381\pi\)
\(240\) 0 0
\(241\) 37.2352 64.4933i 0.154503 0.267607i −0.778375 0.627800i \(-0.783956\pi\)
0.932878 + 0.360193i \(0.117289\pi\)
\(242\) 0 0
\(243\) −194.149 + 146.134i −0.798966 + 0.601376i
\(244\) 0 0
\(245\) 0.331306 0.573840i 0.00135227 0.00234220i
\(246\) 0 0
\(247\) 119.637 69.0726i 0.484362 0.279646i
\(248\) 0 0
\(249\) −6.42081 + 79.6935i −0.0257864 + 0.320054i
\(250\) 0 0
\(251\) 216.868i 0.864014i −0.901870 0.432007i \(-0.857806\pi\)
0.901870 0.432007i \(-0.142194\pi\)
\(252\) 0 0
\(253\) 202.779 0.801499
\(254\) 0 0
\(255\) 40.8140 59.1494i 0.160055 0.231958i
\(256\) 0 0
\(257\) −143.577 248.682i −0.558665 0.967636i −0.997608 0.0691212i \(-0.977980\pi\)
0.438943 0.898515i \(-0.355353\pi\)
\(258\) 0 0
\(259\) −426.023 245.965i −1.64488 0.949671i
\(260\) 0 0
\(261\) 96.9052 + 255.274i 0.371284 + 0.978060i
\(262\) 0 0
\(263\) −361.740 208.851i −1.37544 0.794108i −0.383830 0.923404i \(-0.625395\pi\)
−0.991606 + 0.129295i \(0.958728\pi\)
\(264\) 0 0
\(265\) 13.6502 + 23.6428i 0.0515100 + 0.0892180i
\(266\) 0 0
\(267\) 33.1823 + 69.9016i 0.124278 + 0.261804i
\(268\) 0 0
\(269\) −489.868 −1.82107 −0.910535 0.413433i \(-0.864330\pi\)
−0.910535 + 0.413433i \(0.864330\pi\)
\(270\) 0 0
\(271\) 325.133i 1.19975i −0.800093 0.599876i \(-0.795216\pi\)
0.800093 0.599876i \(-0.204784\pi\)
\(272\) 0 0
\(273\) −128.412 + 60.9570i −0.470372 + 0.223286i
\(274\) 0 0
\(275\) −168.406 + 97.2293i −0.612386 + 0.353561i
\(276\) 0 0
\(277\) 86.0882 149.109i 0.310788 0.538300i −0.667745 0.744390i \(-0.732740\pi\)
0.978533 + 0.206089i \(0.0660738\pi\)
\(278\) 0 0
\(279\) 0.199721 1.23140i 0.000715846 0.00441362i
\(280\) 0 0
\(281\) −60.1019 + 104.100i −0.213886 + 0.370461i −0.952927 0.303199i \(-0.901945\pi\)
0.739042 + 0.673660i \(0.235279\pi\)
\(282\) 0 0
\(283\) 95.8910 55.3627i 0.338837 0.195628i −0.320920 0.947106i \(-0.603992\pi\)
0.659758 + 0.751478i \(0.270659\pi\)
\(284\) 0 0
\(285\) 46.1594 + 31.8507i 0.161963 + 0.111757i
\(286\) 0 0
\(287\) 414.359i 1.44376i
\(288\) 0 0
\(289\) 405.124 1.40181
\(290\) 0 0
\(291\) 313.203 + 25.2344i 1.07630 + 0.0867161i
\(292\) 0 0
\(293\) 42.3365 + 73.3289i 0.144493 + 0.250269i 0.929184 0.369618i \(-0.120512\pi\)
−0.784691 + 0.619888i \(0.787178\pi\)
\(294\) 0 0
\(295\) 70.1415 + 40.4962i 0.237768 + 0.137275i
\(296\) 0 0
\(297\) −156.715 150.383i −0.527660 0.506342i
\(298\) 0 0
\(299\) −146.680 84.6856i −0.490568 0.283229i
\(300\) 0 0
\(301\) −10.0096 17.3372i −0.0332546 0.0575987i
\(302\) 0 0
\(303\) −122.477 9.86784i −0.404215 0.0325671i
\(304\) 0 0
\(305\) −43.7680 −0.143502
\(306\) 0 0
\(307\) 220.477i 0.718167i −0.933306 0.359083i \(-0.883089\pi\)
0.933306 0.359083i \(-0.116911\pi\)
\(308\) 0 0
\(309\) 357.194 + 246.470i 1.15597 + 0.797637i
\(310\) 0 0
\(311\) 268.968 155.289i 0.864849 0.499321i −0.000784168 1.00000i \(-0.500250\pi\)
0.865633 + 0.500679i \(0.166916\pi\)
\(312\) 0 0
\(313\) −65.5787 + 113.586i −0.209516 + 0.362893i −0.951562 0.307456i \(-0.900522\pi\)
0.742046 + 0.670349i \(0.233856\pi\)
\(314\) 0 0
\(315\) −44.7106 36.4815i −0.141938 0.115814i
\(316\) 0 0
\(317\) 169.980 294.414i 0.536214 0.928750i −0.462889 0.886416i \(-0.653187\pi\)
0.999104 0.0423342i \(-0.0134794\pi\)
\(318\) 0 0
\(319\) −211.358 + 122.028i −0.662564 + 0.382532i
\(320\) 0 0
\(321\) −482.022 + 228.816i −1.50162 + 0.712822i
\(322\) 0 0
\(323\) 541.685i 1.67704i
\(324\) 0 0
\(325\) 162.422 0.499759
\(326\) 0 0
\(327\) 183.476 + 386.509i 0.561089 + 1.18199i
\(328\) 0 0
\(329\) −288.085 498.978i −0.875638 1.51665i
\(330\) 0 0
\(331\) 394.447 + 227.734i 1.19168 + 0.688018i 0.958688 0.284460i \(-0.0918143\pi\)
0.232994 + 0.972478i \(0.425148\pi\)
\(332\) 0 0
\(333\) −396.913 + 486.446i −1.19193 + 1.46080i
\(334\) 0 0
\(335\) −40.0813 23.1409i −0.119646 0.0690774i
\(336\) 0 0
\(337\) −21.9543 38.0259i −0.0651462 0.112837i 0.831613 0.555356i \(-0.187418\pi\)
−0.896759 + 0.442520i \(0.854085\pi\)
\(338\) 0 0
\(339\) 341.260 494.569i 1.00667 1.45890i
\(340\) 0 0
\(341\) 1.11503 0.00326988
\(342\) 0 0
\(343\) 340.402i 0.992426i
\(344\) 0 0
\(345\) 5.52187 68.5362i 0.0160054 0.198656i
\(346\) 0 0
\(347\) 340.283 196.462i 0.980642 0.566174i 0.0781781 0.996939i \(-0.475090\pi\)
0.902464 + 0.430766i \(0.141756\pi\)
\(348\) 0 0
\(349\) 271.979 471.082i 0.779310 1.34981i −0.153029 0.988222i \(-0.548903\pi\)
0.932340 0.361584i \(-0.117764\pi\)
\(350\) 0 0
\(351\) 50.5555 + 174.228i 0.144033 + 0.496375i
\(352\) 0 0
\(353\) −63.7961 + 110.498i −0.180725 + 0.313026i −0.942128 0.335254i \(-0.891178\pi\)
0.761402 + 0.648280i \(0.224511\pi\)
\(354\) 0 0
\(355\) −53.8870 + 31.1117i −0.151794 + 0.0876385i
\(356\) 0 0
\(357\) 44.7615 555.570i 0.125382 1.55622i
\(358\) 0 0
\(359\) 285.077i 0.794085i 0.917800 + 0.397043i \(0.129963\pi\)
−0.917800 + 0.397043i \(0.870037\pi\)
\(360\) 0 0
\(361\) −61.7239 −0.170980
\(362\) 0 0
\(363\) −95.9043 + 138.988i −0.264199 + 0.382888i
\(364\) 0 0
\(365\) 10.0685 + 17.4391i 0.0275849 + 0.0477785i
\(366\) 0 0
\(367\) −280.084 161.706i −0.763171 0.440617i 0.0672623 0.997735i \(-0.478574\pi\)
−0.830433 + 0.557119i \(0.811907\pi\)
\(368\) 0 0
\(369\) 522.008 + 84.6646i 1.41466 + 0.229443i
\(370\) 0 0
\(371\) 183.371 + 105.869i 0.494261 + 0.285362i
\(372\) 0 0
\(373\) 257.740 + 446.419i 0.690993 + 1.19683i 0.971513 + 0.236987i \(0.0761597\pi\)
−0.280520 + 0.959848i \(0.590507\pi\)
\(374\) 0 0
\(375\) 57.5193 + 121.170i 0.153385 + 0.323119i
\(376\) 0 0
\(377\) 203.847 0.540708
\(378\) 0 0
\(379\) 21.2535i 0.0560779i 0.999607 + 0.0280389i \(0.00892624\pi\)
−0.999607 + 0.0280389i \(0.991074\pi\)
\(380\) 0 0
\(381\) 492.496 233.788i 1.29264 0.613617i
\(382\) 0 0
\(383\) −93.4125 + 53.9317i −0.243897 + 0.140814i −0.616966 0.786989i \(-0.711639\pi\)
0.373070 + 0.927803i \(0.378305\pi\)
\(384\) 0 0
\(385\) 25.7891 44.6681i 0.0669847 0.116021i
\(386\) 0 0
\(387\) −23.8866 + 9.06765i −0.0617224 + 0.0234306i
\(388\) 0 0
\(389\) 75.1474 130.159i 0.193181 0.334599i −0.753122 0.657881i \(-0.771453\pi\)
0.946303 + 0.323282i \(0.104786\pi\)
\(390\) 0 0
\(391\) 575.150 332.063i 1.47097 0.849266i
\(392\) 0 0
\(393\) 150.932 + 104.145i 0.384051 + 0.265001i
\(394\) 0 0
\(395\) 36.1520i 0.0915241i
\(396\) 0 0
\(397\) 137.203 0.345600 0.172800 0.984957i \(-0.444719\pi\)
0.172800 + 0.984957i \(0.444719\pi\)
\(398\) 0 0
\(399\) 433.559 + 34.9313i 1.08661 + 0.0875472i
\(400\) 0 0
\(401\) −133.366 230.996i −0.332583 0.576050i 0.650435 0.759562i \(-0.274587\pi\)
−0.983017 + 0.183512i \(0.941253\pi\)
\(402\) 0 0
\(403\) −0.806553 0.465664i −0.00200137 0.00115549i
\(404\) 0 0
\(405\) −55.0948 + 48.8721i −0.136037 + 0.120672i
\(406\) 0 0
\(407\) −485.983 280.582i −1.19406 0.689391i
\(408\) 0 0
\(409\) −341.404 591.329i −0.834729 1.44579i −0.894251 0.447565i \(-0.852291\pi\)
0.0595226 0.998227i \(-0.481042\pi\)
\(410\) 0 0
\(411\) −108.328 8.72784i −0.263571 0.0212356i
\(412\) 0 0
\(413\) 628.169 1.52099
\(414\) 0 0
\(415\) 24.2314i 0.0583889i
\(416\) 0 0
\(417\) −440.946 304.260i −1.05742 0.729640i
\(418\) 0 0
\(419\) 449.030 259.248i 1.07167 0.618730i 0.143034 0.989718i \(-0.454314\pi\)
0.928638 + 0.370988i \(0.120981\pi\)
\(420\) 0 0
\(421\) −170.758 + 295.761i −0.405601 + 0.702521i −0.994391 0.105765i \(-0.966271\pi\)
0.588790 + 0.808286i \(0.299604\pi\)
\(422\) 0 0
\(423\) −687.474 + 260.974i −1.62523 + 0.616959i
\(424\) 0 0
\(425\) −318.438 + 551.550i −0.749265 + 1.29777i
\(426\) 0 0
\(427\) −293.981 + 169.730i −0.688481 + 0.397495i
\(428\) 0 0
\(429\) −146.484 + 69.5362i −0.341456 + 0.162089i
\(430\) 0 0
\(431\) 166.603i 0.386550i −0.981145 0.193275i \(-0.938089\pi\)
0.981145 0.193275i \(-0.0619110\pi\)
\(432\) 0 0
\(433\) −677.766 −1.56528 −0.782640 0.622475i \(-0.786127\pi\)
−0.782640 + 0.622475i \(0.786127\pi\)
\(434\) 0 0
\(435\) 35.4879 + 74.7586i 0.0815815 + 0.171859i
\(436\) 0 0
\(437\) 259.138 + 448.840i 0.592992 + 1.02709i
\(438\) 0 0
\(439\) 427.032 + 246.547i 0.972738 + 0.561610i 0.900070 0.435746i \(-0.143515\pi\)
0.0726678 + 0.997356i \(0.476849\pi\)
\(440\) 0 0
\(441\) −6.47429 1.05007i −0.0146809 0.00238111i
\(442\) 0 0
\(443\) −284.084 164.016i −0.641273 0.370239i 0.143832 0.989602i \(-0.454058\pi\)
−0.785105 + 0.619363i \(0.787391\pi\)
\(444\) 0 0
\(445\) 11.7256 + 20.3094i 0.0263497 + 0.0456391i
\(446\) 0 0
\(447\) 409.060 592.827i 0.915124 1.32624i
\(448\) 0 0
\(449\) 19.0862 0.0425082 0.0212541 0.999774i \(-0.493234\pi\)
0.0212541 + 0.999774i \(0.493234\pi\)
\(450\) 0 0
\(451\) 472.677i 1.04806i
\(452\) 0 0
\(453\) 27.3020 338.866i 0.0602694 0.748049i
\(454\) 0 0
\(455\) −37.3090 + 21.5404i −0.0819978 + 0.0473415i
\(456\) 0 0
\(457\) −137.806 + 238.686i −0.301544 + 0.522289i −0.976486 0.215581i \(-0.930835\pi\)
0.674942 + 0.737871i \(0.264169\pi\)
\(458\) 0 0
\(459\) −690.759 169.908i −1.50492 0.370170i
\(460\) 0 0
\(461\) −199.467 + 345.486i −0.432683 + 0.749428i −0.997103 0.0760589i \(-0.975766\pi\)
0.564421 + 0.825487i \(0.309100\pi\)
\(462\) 0 0
\(463\) 15.7881 9.11524i 0.0340995 0.0196873i −0.482853 0.875701i \(-0.660400\pi\)
0.516953 + 0.856014i \(0.327066\pi\)
\(464\) 0 0
\(465\) 0.0303633 0.376862i 6.52974e−5 0.000810456i
\(466\) 0 0
\(467\) 499.275i 1.06911i 0.845133 + 0.534555i \(0.179521\pi\)
−0.845133 + 0.534555i \(0.820479\pi\)
\(468\) 0 0
\(469\) −358.958 −0.765368
\(470\) 0 0
\(471\) −205.685 + 298.087i −0.436698 + 0.632880i
\(472\) 0 0
\(473\) −11.4184 19.7773i −0.0241404 0.0418124i
\(474\) 0 0
\(475\) −430.423 248.505i −0.906153 0.523168i
\(476\) 0 0
\(477\) 170.841 209.378i 0.358158 0.438948i
\(478\) 0 0
\(479\) 52.4473 + 30.2805i 0.109493 + 0.0632160i 0.553747 0.832685i \(-0.313198\pi\)
−0.444253 + 0.895901i \(0.646531\pi\)
\(480\) 0 0
\(481\) 234.356 + 405.917i 0.487227 + 0.843902i
\(482\) 0 0
\(483\) −228.691 481.758i −0.473479 0.997428i
\(484\) 0 0
\(485\) 95.2317 0.196354
\(486\) 0 0
\(487\) 852.354i 1.75021i −0.483931 0.875106i \(-0.660791\pi\)
0.483931 0.875106i \(-0.339209\pi\)
\(488\) 0 0
\(489\) −55.1509 + 26.1801i −0.112783 + 0.0535381i
\(490\) 0 0
\(491\) 585.457 338.014i 1.19238 0.688419i 0.233532 0.972349i \(-0.424972\pi\)
0.958845 + 0.283930i \(0.0916382\pi\)
\(492\) 0 0
\(493\) −399.655 + 692.223i −0.810659 + 1.40410i
\(494\) 0 0
\(495\) −51.0033 41.6159i −0.103037 0.0840726i
\(496\) 0 0
\(497\) −241.299 + 417.942i −0.485511 + 0.840930i
\(498\) 0 0
\(499\) −736.084 + 424.978i −1.47512 + 0.851660i −0.999607 0.0280487i \(-0.991071\pi\)
−0.475512 + 0.879709i \(0.657737\pi\)
\(500\) 0 0
\(501\) −432.044 298.117i −0.862363 0.595044i
\(502\) 0 0
\(503\) 945.179i 1.87908i −0.342433 0.939542i \(-0.611251\pi\)
0.342433 0.939542i \(-0.388749\pi\)
\(504\) 0 0
\(505\) −37.2401 −0.0737428
\(506\) 0 0
\(507\) −370.363 29.8397i −0.730499 0.0588554i
\(508\) 0 0
\(509\) 125.931 + 218.119i 0.247409 + 0.428524i 0.962806 0.270194i \(-0.0870877\pi\)
−0.715397 + 0.698718i \(0.753754\pi\)
\(510\) 0 0
\(511\) 135.256 + 78.0903i 0.264689 + 0.152819i
\(512\) 0 0
\(513\) 132.594 539.059i 0.258468 1.05080i
\(514\) 0 0
\(515\) 113.906 + 65.7637i 0.221177 + 0.127696i
\(516\) 0 0
\(517\) −328.630 569.205i −0.635649 1.10098i
\(518\) 0 0
\(519\) −334.421 26.9439i −0.644357 0.0519150i
\(520\) 0 0
\(521\) 856.423 1.64381 0.821903 0.569628i \(-0.192913\pi\)
0.821903 + 0.569628i \(0.192913\pi\)
\(522\) 0 0
\(523\) 741.634i 1.41804i 0.705189 + 0.709019i \(0.250862\pi\)
−0.705189 + 0.709019i \(0.749138\pi\)
\(524\) 0 0
\(525\) 420.920 + 290.442i 0.801753 + 0.553223i
\(526\) 0 0
\(527\) 3.16260 1.82593i 0.00600113 0.00346475i
\(528\) 0 0
\(529\) 53.2125 92.1667i 0.100591 0.174228i
\(530\) 0 0
\(531\) 128.352 791.365i 0.241717 1.49033i
\(532\) 0 0
\(533\) 197.402 341.910i 0.370359 0.641481i
\(534\) 0 0
\(535\) −140.048 + 80.8565i −0.261771 + 0.151134i
\(536\) 0 0
\(537\) −50.6632 + 24.0498i −0.0943449 + 0.0447856i
\(538\) 0 0
\(539\) 5.86245i 0.0108765i
\(540\) 0 0
\(541\) −434.157 −0.802509 −0.401254 0.915967i \(-0.631426\pi\)
−0.401254 + 0.915967i \(0.631426\pi\)
\(542\) 0 0
\(543\) 126.147 + 265.740i 0.232314 + 0.489392i
\(544\) 0 0
\(545\) 64.8349 + 112.297i 0.118963 + 0.206050i
\(546\) 0 0
\(547\) 235.269 + 135.832i 0.430107 + 0.248323i 0.699392 0.714738i \(-0.253454\pi\)
−0.269285 + 0.963061i \(0.586787\pi\)
\(548\) 0 0
\(549\) 153.757 + 405.037i 0.280068 + 0.737772i
\(550\) 0 0
\(551\) −540.201 311.885i −0.980402 0.566035i
\(552\) 0 0
\(553\) 140.196 + 242.826i 0.253518 + 0.439107i
\(554\) 0 0
\(555\) −108.066 + 156.614i −0.194714 + 0.282188i
\(556\) 0 0
\(557\) 41.7759 0.0750016 0.0375008 0.999297i \(-0.488060\pi\)
0.0375008 + 0.999297i \(0.488060\pi\)
\(558\) 0 0
\(559\) 19.0744i 0.0341224i
\(560\) 0 0
\(561\) 51.0614 633.761i 0.0910185 1.12970i
\(562\) 0 0
\(563\) 388.403 224.245i 0.689882 0.398303i −0.113686 0.993517i \(-0.536266\pi\)
0.803568 + 0.595213i \(0.202932\pi\)
\(564\) 0 0
\(565\) 91.0559 157.713i 0.161161 0.279139i
\(566\) 0 0
\(567\) −180.537 + 541.919i −0.318408 + 0.955766i
\(568\) 0 0
\(569\) −180.208 + 312.130i −0.316710 + 0.548559i −0.979800 0.199982i \(-0.935912\pi\)
0.663089 + 0.748540i \(0.269245\pi\)
\(570\) 0 0
\(571\) 665.784 384.391i 1.16600 0.673189i 0.213263 0.976995i \(-0.431591\pi\)
0.952734 + 0.303806i \(0.0982574\pi\)
\(572\) 0 0
\(573\) 66.9656 831.161i 0.116868 1.45054i
\(574\) 0 0
\(575\) 609.352i 1.05974i
\(576\) 0 0
\(577\) −413.359 −0.716394 −0.358197 0.933646i \(-0.616608\pi\)
−0.358197 + 0.933646i \(0.616608\pi\)
\(578\) 0 0
\(579\) 276.454 400.649i 0.477468 0.691966i
\(580\) 0 0
\(581\) 93.9682 + 162.758i 0.161735 + 0.280134i
\(582\) 0 0
\(583\) 209.179 + 120.769i 0.358797 + 0.207152i
\(584\) 0 0
\(585\) 19.5132 + 51.4030i 0.0333560 + 0.0878684i
\(586\) 0 0
\(587\) 1.41240 + 0.815451i 0.00240614 + 0.00138918i 0.501203 0.865330i \(-0.332891\pi\)
−0.498796 + 0.866719i \(0.666224\pi\)
\(588\) 0 0
\(589\) 1.42493 + 2.46805i 0.00241923 + 0.00419024i
\(590\) 0 0
\(591\) 136.603 + 287.768i 0.231139 + 0.486916i
\(592\) 0 0
\(593\) 652.407 1.10018 0.550091 0.835105i \(-0.314593\pi\)
0.550091 + 0.835105i \(0.314593\pi\)
\(594\) 0 0
\(595\) 168.925i 0.283908i
\(596\) 0 0
\(597\) 171.791 81.5491i 0.287757 0.136598i
\(598\) 0 0
\(599\) −148.315 + 85.6298i −0.247605 + 0.142955i −0.618667 0.785653i \(-0.712327\pi\)
0.371062 + 0.928608i \(0.378994\pi\)
\(600\) 0 0
\(601\) −65.9875 + 114.294i −0.109796 + 0.190173i −0.915688 0.401891i \(-0.868353\pi\)
0.805891 + 0.592063i \(0.201686\pi\)
\(602\) 0 0
\(603\) −73.3446 + 452.213i −0.121633 + 0.749939i
\(604\) 0 0
\(605\) −25.5894 + 44.3222i −0.0422966 + 0.0732598i
\(606\) 0 0
\(607\) 514.763 297.199i 0.848045 0.489619i −0.0119458 0.999929i \(-0.503803\pi\)
0.859991 + 0.510310i \(0.170469\pi\)
\(608\) 0 0
\(609\) 528.276 + 364.519i 0.867448 + 0.598553i
\(610\) 0 0
\(611\) 548.977i 0.898489i
\(612\) 0 0
\(613\) 367.632 0.599727 0.299863 0.953982i \(-0.403059\pi\)
0.299863 + 0.953982i \(0.403059\pi\)
\(614\) 0 0
\(615\) 159.757 + 12.8714i 0.259768 + 0.0209292i
\(616\) 0 0
\(617\) 21.0806 + 36.5126i 0.0341662 + 0.0591776i 0.882603 0.470119i \(-0.155789\pi\)
−0.848437 + 0.529297i \(0.822456\pi\)
\(618\) 0 0
\(619\) 214.298 + 123.725i 0.346200 + 0.199879i 0.663010 0.748610i \(-0.269279\pi\)
−0.316810 + 0.948489i \(0.602612\pi\)
\(620\) 0 0
\(621\) −653.644 + 189.668i −1.05257 + 0.305423i
\(622\) 0 0
\(623\) 157.518 + 90.9428i 0.252837 + 0.145976i
\(624\) 0 0
\(625\) −281.841 488.163i −0.450945 0.781060i
\(626\) 0 0
\(627\) 494.579 + 39.8476i 0.788802 + 0.0635528i
\(628\) 0 0
\(629\) −1837.88 −2.92191
\(630\) 0 0
\(631\) 725.556i 1.14985i 0.818206 + 0.574926i \(0.194969\pi\)
−0.818206 + 0.574926i \(0.805031\pi\)
\(632\) 0 0
\(633\) 14.1996 + 9.79793i 0.0224322 + 0.0154786i
\(634\) 0 0
\(635\) 143.091 82.6136i 0.225340 0.130100i
\(636\) 0 0
\(637\) −2.44831 + 4.24059i −0.00384349 + 0.00665713i
\(638\) 0 0
\(639\) 477.218 + 389.384i 0.746820 + 0.609365i
\(640\) 0 0
\(641\) 458.006 793.290i 0.714518 1.23758i −0.248626 0.968599i \(-0.579979\pi\)
0.963145 0.268983i \(-0.0866875\pi\)
\(642\) 0 0
\(643\) −686.803 + 396.526i −1.06812 + 0.616681i −0.927668 0.373406i \(-0.878190\pi\)
−0.140455 + 0.990087i \(0.544857\pi\)
\(644\) 0 0
\(645\) −6.99534 + 3.32069i −0.0108455 + 0.00514836i
\(646\) 0 0
\(647\) 78.3837i 0.121150i −0.998164 0.0605748i \(-0.980707\pi\)
0.998164 0.0605748i \(-0.0192934\pi\)
\(648\) 0 0
\(649\) 716.579 1.10413
\(650\) 0 0
\(651\) −1.25751 2.64906i −0.00193166 0.00406921i
\(652\) 0 0
\(653\) 131.250 + 227.332i 0.200996 + 0.348135i 0.948850 0.315728i \(-0.102249\pi\)
−0.747854 + 0.663864i \(0.768915\pi\)
\(654\) 0 0
\(655\) 48.1308 + 27.7883i 0.0734822 + 0.0424250i
\(656\) 0 0
\(657\) 126.014 154.439i 0.191803 0.235068i
\(658\) 0 0
\(659\) 1116.03 + 644.339i 1.69352 + 0.977753i 0.951638 + 0.307221i \(0.0993990\pi\)
0.741880 + 0.670533i \(0.233934\pi\)
\(660\) 0 0
\(661\) −184.429 319.441i −0.279016 0.483270i 0.692125 0.721778i \(-0.256675\pi\)
−0.971140 + 0.238508i \(0.923342\pi\)
\(662\) 0 0
\(663\) −301.610 + 437.105i −0.454917 + 0.659284i
\(664\) 0 0
\(665\) 131.827 0.198236
\(666\) 0 0
\(667\) 764.766i 1.14658i
\(668\) 0 0
\(669\) −50.0159 + 620.785i −0.0747622 + 0.927930i
\(670\) 0 0
\(671\) −335.357 + 193.618i −0.499787 + 0.288552i
\(672\) 0 0
\(673\) 127.862 221.463i 0.189988 0.329069i −0.755258 0.655428i \(-0.772488\pi\)
0.945246 + 0.326359i \(0.105822\pi\)
\(674\) 0 0
\(675\) 451.903 470.929i 0.669486 0.697673i
\(676\) 0 0
\(677\) 566.571 981.330i 0.836885 1.44953i −0.0556014 0.998453i \(-0.517708\pi\)
0.892486 0.451074i \(-0.148959\pi\)
\(678\) 0 0
\(679\) 639.653 369.304i 0.942052 0.543894i
\(680\) 0 0
\(681\) −21.9466 + 272.397i −0.0322271 + 0.399995i
\(682\) 0 0
\(683\) 941.046i 1.37781i −0.724850 0.688907i \(-0.758091\pi\)
0.724850 0.688907i \(-0.241909\pi\)
\(684\) 0 0
\(685\) −32.9379 −0.0480845
\(686\) 0 0
\(687\) 6.98370 10.1211i 0.0101655 0.0147323i
\(688\) 0 0
\(689\) −100.873 174.717i −0.146404 0.253580i
\(690\) 0 0
\(691\) −1163.81 671.923i −1.68423 0.972393i −0.958792 0.284109i \(-0.908302\pi\)
−0.725441 0.688284i \(-0.758364\pi\)
\(692\) 0 0
\(693\) −503.964 81.7380i −0.727220 0.117948i
\(694\) 0 0
\(695\) −140.614 81.1834i −0.202322 0.116811i
\(696\) 0 0
\(697\) 774.036 + 1340.67i 1.11053 + 1.92349i
\(698\) 0 0
\(699\) −220.971 465.497i −0.316125 0.665946i
\(700\) 0 0
\(701\) −28.1783 −0.0401973 −0.0200986 0.999798i \(-0.506398\pi\)
−0.0200986 + 0.999798i \(0.506398\pi\)
\(702\) 0 0
\(703\) 1434.26i 2.04020i
\(704\) 0 0
\(705\) −201.331 + 95.5720i −0.285576 + 0.135563i
\(706\) 0 0
\(707\) −250.135 + 144.415i −0.353797 + 0.204265i
\(708\) 0 0
\(709\) 624.660 1081.94i 0.881043 1.52601i 0.0308605 0.999524i \(-0.490175\pi\)
0.850183 0.526488i \(-0.176491\pi\)
\(710\) 0 0
\(711\) 334.557 127.002i 0.470544 0.178625i
\(712\) 0 0
\(713\) 1.74702 3.02592i 0.00245023 0.00424393i
\(714\) 0 0
\(715\) −42.5599 + 24.5720i −0.0595244 + 0.0343664i
\(716\) 0 0
\(717\) 224.980 + 155.240i 0.313780 + 0.216513i
\(718\) 0 0
\(719\) 738.132i 1.02661i 0.858206 + 0.513305i \(0.171579\pi\)
−0.858206 + 0.513305i \(0.828421\pi\)
\(720\) 0 0
\(721\) 1020.11 1.41486
\(722\) 0 0
\(723\) −222.690 17.9418i −0.308008 0.0248158i
\(724\) 0 0
\(725\) −366.693 635.131i −0.505784 0.876043i
\(726\) 0 0
\(727\) 326.676 + 188.606i 0.449348 + 0.259431i 0.707555 0.706659i \(-0.249798\pi\)
−0.258207 + 0.966090i \(0.583132\pi\)
\(728\) 0 0
\(729\) 645.820 + 338.169i 0.885898 + 0.463880i
\(730\) 0 0
\(731\) −64.7729 37.3967i −0.0886087 0.0511582i
\(732\) 0 0
\(733\) 280.849 + 486.445i 0.383150 + 0.663635i 0.991511 0.130025i \(-0.0415059\pi\)
−0.608361 + 0.793661i \(0.708173\pi\)
\(734\) 0 0
\(735\) −1.98142 0.159640i −0.00269581 0.000217198i
\(736\) 0 0
\(737\) −409.478 −0.555601
\(738\) 0 0
\(739\) 912.732i 1.23509i −0.786535 0.617545i \(-0.788127\pi\)
0.786535 0.617545i \(-0.211873\pi\)
\(740\) 0 0
\(741\) −341.111 235.372i −0.460339 0.317641i
\(742\) 0 0
\(743\) −913.005 + 527.123i −1.22881 + 0.709453i −0.966781 0.255608i \(-0.917725\pi\)
−0.262028 + 0.965060i \(0.584391\pi\)
\(744\) 0 0
\(745\) 109.146 189.047i 0.146505 0.253755i
\(746\) 0 0
\(747\) 224.242 85.1250i 0.300190 0.113956i
\(748\) 0 0
\(749\) −627.115 + 1086.20i −0.837270 + 1.45019i
\(750\) 0 0
\(751\) −916.482 + 529.131i −1.22035 + 0.704569i −0.964992 0.262278i \(-0.915526\pi\)
−0.255357 + 0.966847i \(0.582193\pi\)
\(752\) 0 0
\(753\) −587.743 + 279.002i −0.780535 + 0.370520i
\(754\) 0 0
\(755\) 103.035i 0.136470i
\(756\) 0 0
\(757\) −359.804 −0.475302 −0.237651 0.971351i \(-0.576377\pi\)
−0.237651 + 0.971351i \(0.576377\pi\)
\(758\) 0 0
\(759\) −260.877 549.561i −0.343711 0.724060i
\(760\) 0 0
\(761\) −311.474 539.489i −0.409296 0.708921i 0.585515 0.810661i \(-0.300892\pi\)
−0.994811 + 0.101740i \(0.967559\pi\)
\(762\) 0 0
\(763\) 870.966 + 502.853i 1.14150 + 0.659047i
\(764\) 0 0
\(765\) −212.811 34.5159i −0.278184 0.0451188i
\(766\) 0 0
\(767\) −518.336 299.261i −0.675796 0.390171i
\(768\) 0 0
\(769\) −534.453 925.699i −0.694997 1.20377i −0.970182 0.242379i \(-0.922072\pi\)
0.275185 0.961391i \(-0.411261\pi\)
\(770\) 0 0
\(771\) −489.253 + 709.046i −0.634570 + 0.919645i
\(772\) 0 0
\(773\) −512.261 −0.662692 −0.331346 0.943509i \(-0.607503\pi\)
−0.331346 + 0.943509i \(0.607503\pi\)
\(774\) 0 0
\(775\) 3.35066i 0.00432344i
\(776\) 0 0
\(777\) −118.518 + 1471.02i −0.152533 + 1.89321i
\(778\) 0 0
\(779\) −1046.24 + 604.048i −1.34306 + 0.775415i
\(780\) 0 0
\(781\) −275.260 + 476.764i −0.352445 + 0.610453i
\(782\) 0 0
\(783\) 567.160 591.039i 0.724343 0.754839i
\(784\) 0 0
\(785\) −54.8813 + 95.0571i −0.0699124 + 0.121092i
\(786\) 0 0
\(787\) 153.809 88.8019i 0.195438 0.112836i −0.399088 0.916913i \(-0.630673\pi\)
0.594526 + 0.804077i \(0.297340\pi\)
\(788\) 0 0
\(789\) −100.635 + 1249.06i −0.127547 + 1.58309i
\(790\) 0 0
\(791\) 1412.44i 1.78564i
\(792\) 0 0
\(793\) 323.439 0.407868
\(794\) 0 0