Properties

Label 144.3.o.a.31.2
Level $144$
Weight $3$
Character 144.31
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 31.2
Root \(0.385731i\) of defining polynomial
Character \(\chi\) \(=\) 144.31
Dual form 144.3.o.a.79.2

$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).

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

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 −0.907900 0.419188i \(-0.862315\pi\)
0.816977 + 0.576670i \(0.195648\pi\)
\(6\) 0 0
\(7\) −6.10709 + 3.52593i −0.872442 + 0.503704i −0.868159 0.496286i \(-0.834697\pi\)
−0.00428285 + 0.999991i \(0.501363\pi\)
\(8\) 0 0
\(9\) −5.68980 6.97325i −0.632200 0.774806i
\(10\) 0 0
\(11\) −6.96661 + 4.02218i −0.633329 + 0.365652i −0.782040 0.623228i \(-0.785821\pi\)
0.148711 + 0.988881i \(0.452487\pi\)
\(12\) 0 0
\(13\) 3.35952 5.81886i 0.258425 0.447605i −0.707395 0.706818i \(-0.750130\pi\)
0.965820 + 0.259213i \(0.0834632\pi\)
\(14\) 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 \(0.181977\pi\)
−0.840984 + 0.541059i \(0.818023\pi\)
\(20\) 0 0
\(21\) −1.69897 21.0873i −0.0809035 1.00416i
\(22\) 0 0
\(23\) −21.8305 12.6038i −0.949150 0.547992i −0.0563333 0.998412i \(-0.517941\pi\)
−0.892817 + 0.450420i \(0.851274\pi\)
\(24\) 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 0.999639 + 0.0268597i \(0.00855072\pi\)
−0.476558 + 0.879143i \(0.658116\pi\)
\(30\) 0 0
\(31\) −0.120040 0.0693050i −0.00387225 0.00223565i 0.498063 0.867141i \(-0.334045\pi\)
−0.501935 + 0.864905i \(0.667378\pi\)
\(32\) 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 0.245780 + 0.969326i \(0.420956\pi\)
−0.962351 + 0.271811i \(0.912377\pi\)
\(42\) 0 0
\(43\) 2.45853 1.41943i 0.0571751 0.0330100i −0.471140 0.882058i \(-0.656157\pi\)
0.528315 + 0.849048i \(0.322824\pi\)
\(44\) 0 0
\(45\) 8.07748 1.31009i 0.179500 0.0291131i
\(46\) 0 0
\(47\) 70.7583 40.8523i 1.50550 0.869198i 0.505516 0.862817i \(-0.331302\pi\)
0.999980 0.00638063i \(-0.00203103\pi\)
\(48\) 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 −0.325846 0.945423i \(-0.605649\pi\)
−0.981683 + 0.190520i \(0.938983\pi\)
\(60\) 0 0
\(61\) 24.0688 + 41.6885i 0.394571 + 0.683417i 0.993046 0.117724i \(-0.0375598\pi\)
−0.598475 + 0.801141i \(0.704226\pi\)
\(62\) 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 0.791497 0.611173i \(-0.209302\pi\)
−0.133543 + 0.991043i \(0.542636\pi\)
\(68\) 0 0
\(69\) 62.2432 42.9488i 0.902076 0.622447i
\(70\) 0 0
\(71\) 68.4355i 0.963881i 0.876204 + 0.481940i \(0.160068\pi\)
−0.876204 + 0.481940i \(0.839932\pi\)
\(72\) 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 −0.701847 0.712327i \(-0.747641\pi\)
0.265970 + 0.963981i \(0.414308\pi\)
\(80\) 0 0
\(81\) −16.2524 + 79.3527i −0.200647 + 0.979664i
\(82\) 0 0
\(83\) −23.0801 + 13.3253i −0.278073 + 0.160546i −0.632551 0.774519i \(-0.717992\pi\)
0.354478 + 0.935065i \(0.384659\pi\)
\(84\) 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 −0.998909 0.0466950i \(-0.985131\pi\)
0.459016 0.888428i \(-0.348202\pi\)
\(98\) 0 0
\(99\) 67.6863 + 25.6946i 0.683700 + 0.259541i
\(100\) 0 0
\(101\) 20.4790 + 35.4707i 0.202763 + 0.351195i 0.949418 0.314016i \(-0.101675\pi\)
−0.746655 + 0.665212i \(0.768341\pi\)
\(102\) 0 0
\(103\) −125.278 72.3293i −1.21629 0.702227i −0.252169 0.967683i \(-0.581144\pi\)
−0.964123 + 0.265456i \(0.914477\pi\)
\(104\) 0 0
\(105\) 17.3767 + 8.24874i 0.165493 + 0.0785595i
\(106\) 0 0
\(107\) 177.858i 1.66222i 0.556105 + 0.831112i \(0.312295\pi\)
−0.556105 + 0.831112i \(0.687705\pi\)
\(108\) 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 0.0419835 0.999118i \(-0.486632\pi\)
0.844270 0.535918i \(-0.180034\pi\)
\(114\) 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 \(-0.746224\pi\)
0.698670 0.715445i \(-0.253776\pi\)
\(128\) 0 0
\(129\) 0.683954 + 8.48908i 0.00530197 + 0.0658068i
\(130\) 0 0
\(131\) −52.9361 30.5627i −0.404092 0.233303i 0.284156 0.958778i \(-0.408287\pi\)
−0.688248 + 0.725475i \(0.741620\pi\)
\(132\) 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 0.924529 0.381111i \(-0.124458\pi\)
−0.792317 + 0.610110i \(0.791125\pi\)
\(138\) 0 0
\(139\) 154.652 + 89.2885i 1.11261 + 0.642363i 0.939503 0.342541i \(-0.111287\pi\)
0.173103 + 0.984904i \(0.444621\pi\)
\(140\) 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 −0.110185 0.993911i \(-0.535144\pi\)
0.915845 0.401533i \(-0.131522\pi\)
\(150\) 0 0
\(151\) 98.1393 56.6607i 0.649929 0.375237i −0.138500 0.990362i \(-0.544228\pi\)
0.788429 + 0.615126i \(0.210895\pi\)
\(152\) 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 −0.991694 0.128617i \(-0.958946\pi\)
0.607233 + 0.794524i \(0.292280\pi\)
\(158\) 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 \(0.0198827\pi\)
−0.998050 + 0.0624226i \(0.980117\pi\)
\(164\) 0 0
\(165\) 19.8224 + 9.40969i 0.120136 + 0.0570284i
\(166\) 0 0
\(167\) 151.530 + 87.4858i 0.907365 + 0.523867i 0.879582 0.475747i \(-0.157822\pi\)
0.0277823 + 0.999614i \(0.491155\pi\)
\(168\) 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 0.981151 0.193243i \(-0.0619004\pi\)
−0.657928 + 0.753080i \(0.728567\pi\)
\(174\) 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 \(0.0166289\pi\)
−0.998636 + 0.0522176i \(0.983371\pi\)
\(180\) 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 0.287149 0.957886i \(-0.407293\pi\)
0.973128 + 0.230265i \(0.0739592\pi\)
\(192\) 0 0
\(193\) 81.1285 140.519i 0.420355 0.728076i −0.575619 0.817718i \(-0.695239\pi\)
0.995974 + 0.0896419i \(0.0285722\pi\)
\(194\) 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 \(-0.949087\pi\)
0.987236 0.159266i \(-0.0509128\pi\)
\(200\) 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 0.488152 0.872759i \(-0.337671\pi\)
−0.511755 + 0.859131i \(0.671004\pi\)
\(212\) 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 −0.845640 0.533754i \(-0.820781\pi\)
0.0394246 + 0.999223i \(0.487448\pi\)
\(224\) 0 0
\(225\) 77.2123 203.397i 0.343166 0.903989i
\(226\) 0 0
\(227\) −78.8889 + 45.5465i −0.347528 + 0.200646i −0.663596 0.748091i \(-0.730971\pi\)
0.316068 + 0.948737i \(0.397637\pi\)
\(228\) 0 0
\(229\) 2.04945 3.54974i 0.00894954 0.0155011i −0.861516 0.507731i \(-0.830485\pi\)
0.870465 + 0.492229i \(0.163818\pi\)
\(230\) 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 0.325755 0.945454i \(-0.394381\pi\)
−0.655909 + 0.754840i \(0.727715\pi\)
\(240\) 0 0
\(241\) 37.2352 + 64.4933i 0.154503 + 0.267607i 0.932878 0.360193i \(-0.117289\pi\)
−0.778375 + 0.627800i \(0.783956\pi\)
\(242\) 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 \(0.142194\pi\)
−0.901870 + 0.432007i \(0.857806\pi\)
\(252\) 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 0.438943 + 0.898515i \(0.355353\pi\)
−0.997608 + 0.0691212i \(0.977980\pi\)
\(258\) 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 −0.991606 0.129295i \(-0.958728\pi\)
−0.383830 + 0.923404i \(0.625395\pi\)
\(264\) 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 \(0.204784\pi\)
−0.800093 + 0.599876i \(0.795216\pi\)
\(272\) 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 0.978533 0.206089i \(-0.0660738\pi\)
−0.667745 + 0.744390i \(0.732740\pi\)
\(278\) 0 0
\(279\) 0.199721 + 1.23140i 0.000715846 + 0.00441362i
\(280\) 0 0
\(281\) −60.1019 104.100i −0.213886 0.370461i 0.739042 0.673660i \(-0.235279\pi\)
−0.952927 + 0.303199i \(0.901945\pi\)
\(282\) 0 0
\(283\) 95.8910 + 55.3627i 0.338837 + 0.195628i 0.659758 0.751478i \(-0.270659\pi\)
−0.320920 + 0.947106i \(0.603992\pi\)
\(284\) 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 −0.784691 0.619888i \(-0.787178\pi\)
0.929184 + 0.369618i \(0.120512\pi\)
\(294\) 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 \(0.116911\pi\)
−0.933306 + 0.359083i \(0.883089\pi\)
\(308\) 0 0
\(309\) 357.194 246.470i 1.15597 0.797637i
\(310\) 0 0
\(311\) 268.968 + 155.289i 0.864849 + 0.499321i 0.865633 0.500679i \(-0.166916\pi\)
−0.000784168 1.00000i \(0.500250\pi\)
\(312\) 0 0
\(313\) −65.5787 113.586i −0.209516 0.362893i 0.742046 0.670349i \(-0.233856\pi\)
−0.951562 + 0.307456i \(0.900522\pi\)
\(314\) 0 0
\(315\) −44.7106 + 36.4815i −0.141938 + 0.115814i
\(316\) 0 0
\(317\) 169.980 + 294.414i 0.536214 + 0.928750i 0.999104 + 0.0423342i \(0.0134794\pi\)
−0.462889 + 0.886416i \(0.653187\pi\)
\(318\) 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 0.232994 0.972478i \(-0.425148\pi\)
0.958688 + 0.284460i \(0.0918143\pi\)
\(332\) 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 −0.896759 0.442520i \(-0.854085\pi\)
0.831613 + 0.555356i \(0.187418\pi\)
\(338\) 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 0.902464 0.430766i \(-0.141756\pi\)
0.0781781 + 0.996939i \(0.475090\pi\)
\(348\) 0 0
\(349\) 271.979 + 471.082i 0.779310 + 1.34981i 0.932340 + 0.361584i \(0.117764\pi\)
−0.153029 + 0.988222i \(0.548903\pi\)
\(350\) 0 0
\(351\) 50.5555 174.228i 0.144033 0.496375i
\(352\) 0 0
\(353\) −63.7961 110.498i −0.180725 0.313026i 0.761402 0.648280i \(-0.224511\pi\)
−0.942128 + 0.335254i \(0.891178\pi\)
\(354\) 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 \(-0.870037\pi\)
0.917800 0.397043i \(-0.129963\pi\)
\(360\) 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 −0.830433 0.557119i \(-0.811907\pi\)
0.0672623 + 0.997735i \(0.478574\pi\)
\(368\) 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 −0.280520 0.959848i \(-0.590507\pi\)
0.971513 0.236987i \(-0.0761597\pi\)
\(374\) 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 \(-0.991074\pi\)
0.999607 0.0280389i \(-0.00892624\pi\)
\(380\) 0 0
\(381\) 492.496 + 233.788i 1.29264 + 0.613617i
\(382\) 0 0
\(383\) −93.4125 53.9317i −0.243897 0.140814i 0.373070 0.927803i \(-0.378305\pi\)
−0.616966 + 0.786989i \(0.711639\pi\)
\(384\) 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 0.946303 0.323282i \(-0.104786\pi\)
−0.753122 + 0.657881i \(0.771453\pi\)
\(390\) 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 −0.983017 0.183512i \(-0.941253\pi\)
0.650435 + 0.759562i \(0.274587\pi\)
\(402\) 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 0.0595226 + 0.998227i \(0.481042\pi\)
−0.894251 + 0.447565i \(0.852291\pi\)
\(410\) 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 0.928638 0.370988i \(-0.120981\pi\)
0.143034 + 0.989718i \(0.454314\pi\)
\(420\) 0 0
\(421\) −170.758 295.761i −0.405601 0.702521i 0.588790 0.808286i \(-0.299604\pi\)
−0.994391 + 0.105765i \(0.966271\pi\)
\(422\) 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 \(0.0619110\pi\)
−0.981145 + 0.193275i \(0.938089\pi\)
\(432\) 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 0.0726678 0.997356i \(-0.476849\pi\)
0.900070 + 0.435746i \(0.143515\pi\)
\(440\) 0 0
\(441\) −6.47429 + 1.05007i −0.0146809 + 0.00238111i
\(442\) 0 0
\(443\) −284.084 + 164.016i −0.641273 + 0.370239i −0.785105 0.619363i \(-0.787391\pi\)
0.143832 + 0.989602i \(0.454058\pi\)
\(444\) 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 0.674942 0.737871i \(-0.264169\pi\)
−0.976486 + 0.215581i \(0.930835\pi\)
\(458\) 0 0
\(459\) −690.759 + 169.908i −1.50492 + 0.370170i
\(460\) 0 0
\(461\) −199.467 345.486i −0.432683 0.749428i 0.564421 0.825487i \(-0.309100\pi\)
−0.997103 + 0.0760589i \(0.975766\pi\)
\(462\) 0 0
\(463\) 15.7881 + 9.11524i 0.0340995 + 0.0196873i 0.516953 0.856014i \(-0.327066\pi\)
−0.482853 + 0.875701i \(0.660400\pi\)
\(464\) 0 0
\(465\) 0.0303633 + 0.376862i 6.52974e−5 + 0.000810456i
\(466\) 0 0
\(467\) 499.275i 1.06911i −0.845133 0.534555i \(-0.820479\pi\)
0.845133 0.534555i \(-0.179521\pi\)
\(468\) 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 −0.444253 0.895901i \(-0.646531\pi\)
0.553747 + 0.832685i \(0.313198\pi\)
\(480\) 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 \(0.339209\pi\)
−0.483931 + 0.875106i \(0.660791\pi\)
\(488\) 0 0
\(489\) −55.1509 26.1801i −0.112783 0.0535381i
\(490\) 0 0
\(491\) 585.457 + 338.014i 1.19238 + 0.688419i 0.958845 0.283930i \(-0.0916382\pi\)
0.233532 + 0.972349i \(0.424972\pi\)
\(492\) 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 −0.475512 0.879709i \(-0.657737\pi\)
−0.999607 + 0.0280487i \(0.991071\pi\)
\(500\) 0 0
\(501\) −432.044 + 298.117i −0.862363 + 0.595044i
\(502\) 0 0
\(503\) 945.179i 1.87908i 0.342433 + 0.939542i \(0.388749\pi\)
−0.342433 + 0.939542i \(0.611251\pi\)
\(504\) 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 −0.715397 0.698718i \(-0.753754\pi\)
0.962806 + 0.270194i \(0.0870877\pi\)
\(510\) 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 \(-0.749138\pi\)
0.705189 0.709019i \(-0.250862\pi\)
\(524\) 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 −0.269285 0.963061i \(-0.586787\pi\)
0.699392 + 0.714738i \(0.253454\pi\)
\(548\) 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 0.803568 0.595213i \(-0.202932\pi\)
−0.113686 + 0.993517i \(0.536266\pi\)
\(564\) 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 0.663089 0.748540i \(-0.269245\pi\)
−0.979800 + 0.199982i \(0.935912\pi\)
\(570\) 0 0
\(571\) 665.784 + 384.391i 1.16600 + 0.673189i 0.952734 0.303806i \(-0.0982574\pi\)
0.213263 + 0.976995i \(0.431591\pi\)
\(572\) 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 −0.498796 0.866719i \(-0.666224\pi\)
0.501203 + 0.865330i \(0.332891\pi\)
\(588\) 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 0.371062 0.928608i \(-0.378994\pi\)
−0.618667 + 0.785653i \(0.712327\pi\)
\(600\) 0 0
\(601\) −65.9875 114.294i −0.109796 0.190173i 0.805891 0.592063i \(-0.201686\pi\)
−0.915688 + 0.401891i \(0.868353\pi\)
\(602\) 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 0.859991 0.510310i \(-0.170469\pi\)
−0.0119458 + 0.999929i \(0.503803\pi\)
\(608\) 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 −0.848437 0.529297i \(-0.822456\pi\)
0.882603 + 0.470119i \(0.155789\pi\)
\(618\) 0 0
\(619\) 214.298 123.725i 0.346200 0.199879i −0.316810 0.948489i \(-0.602612\pi\)
0.663010 + 0.748610i \(0.269279\pi\)
\(620\) 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 \(-0.805031\pi\)
0.818206 0.574926i \(-0.194969\pi\)
\(632\) 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 0.963145 + 0.268983i \(0.0866875\pi\)
−0.248626 + 0.968599i \(0.579979\pi\)
\(642\) 0 0
\(643\) −686.803 396.526i −1.06812 0.616681i −0.140455 0.990087i \(-0.544857\pi\)
−0.927668 + 0.373406i \(0.878190\pi\)
\(644\) 0 0
\(645\) −6.99534 3.32069i −0.0108455 0.00514836i
\(646\) 0 0
\(647\) 78.3837i 0.121150i 0.998164 + 0.0605748i \(0.0192934\pi\)
−0.998164 + 0.0605748i \(0.980707\pi\)
\(648\) 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 −0.747854 0.663864i \(-0.768915\pi\)
0.948850 + 0.315728i \(0.102249\pi\)
\(654\) 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 0.741880 0.670533i \(-0.233934\pi\)
0.951638 0.307221i \(-0.0993990\pi\)
\(660\) 0 0
\(661\) −184.429 + 319.441i −0.279016 + 0.483270i −0.971140 0.238508i \(-0.923342\pi\)
0.692125 + 0.721778i \(0.256675\pi\)
\(662\) 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 0.945246 0.326359i \(-0.105822\pi\)
−0.755258 + 0.655428i \(0.772488\pi\)
\(674\) 0 0
\(675\) 451.903 + 470.929i 0.669486 + 0.697673i
\(676\) 0 0
\(677\) 566.571 + 981.330i 0.836885 + 1.44953i 0.892486 + 0.451074i \(0.148959\pi\)
−0.0556014 + 0.998453i \(0.517708\pi\)
\(678\) 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 \(0.241909\pi\)
−0.724850 + 0.688907i \(0.758091\pi\)
\(684\) 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 −0.725441 + 0.688284i \(0.758364\pi\)
−0.958792 + 0.284109i \(0.908302\pi\)
\(692\) 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 0.850183 + 0.526488i \(0.176491\pi\)
0.0308605 + 0.999524i \(0.490175\pi\)
\(710\) 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 \(-0.828421\pi\)
0.858206 0.513305i \(-0.171579\pi\)
\(720\) 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 −0.258207 0.966090i \(-0.583132\pi\)
0.707555 + 0.706659i \(0.249798\pi\)
\(728\) 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 −0.608361 0.793661i \(-0.708173\pi\)
0.991511 + 0.130025i \(0.0415059\pi\)
\(734\) 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 \(0.211873\pi\)
−0.786535 + 0.617545i \(0.788127\pi\)
\(740\) 0 0
\(741\) −341.111 + 235.372i −0.460339 + 0.317641i
\(742\) 0 0
\(743\) −913.005 527.123i −1.22881 0.709453i −0.262028 0.965060i \(-0.584391\pi\)
−0.966781 + 0.255608i \(0.917725\pi\)
\(744\) 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 −0.255357 0.966847i \(-0.582193\pi\)
−0.964992 + 0.262278i \(0.915526\pi\)
\(752\) 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 −0.994811 0.101740i \(-0.967559\pi\)
0.585515 + 0.810661i \(0.300892\pi\)
\(762\) 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 0.275185 + 0.961391i \(0.411261\pi\)
−0.970182 + 0.242379i \(0.922072\pi\)
\(770\) 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 0.594526 0.804077i \(-0.297340\pi\)
−0.399088 + 0.916913i \(0.630673\pi\)
\(788\) 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