Properties

Label 576.2.bb.e.49.8
Level $576$
Weight $2$
Character 576.49
Analytic conductor $4.599$
Analytic rank $0$
Dimension $72$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 576 = 2^{6} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 576.bb (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.59938315643\)
Analytic rank: \(0\)
Dimension: \(72\)
Relative dimension: \(18\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 49.8
Character \(\chi\) \(=\) 576.49
Dual form 576.2.bb.e.529.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.162237 + 1.72444i) q^{3} +(-2.21121 + 0.592492i) q^{5} +(-2.67054 + 1.54184i) q^{7} +(-2.94736 + 0.559536i) q^{9} +O(q^{10})\) \(q+(0.162237 + 1.72444i) q^{3} +(-2.21121 + 0.592492i) q^{5} +(-2.67054 + 1.54184i) q^{7} +(-2.94736 + 0.559536i) q^{9} +(0.918760 - 3.42886i) q^{11} +(-0.375914 - 1.40293i) q^{13} +(-1.38046 - 3.71697i) q^{15} -1.69619 q^{17} +(5.41876 - 5.41876i) q^{19} +(-3.09206 - 4.35503i) q^{21} +(-3.69781 - 2.13493i) q^{23} +(0.208283 - 0.120252i) q^{25} +(-1.44306 - 4.99175i) q^{27} +(-0.550286 - 0.147449i) q^{29} +(-3.59297 + 6.22321i) q^{31} +(6.06191 + 1.02805i) q^{33} +(4.99161 - 4.99161i) q^{35} +(2.59734 + 2.59734i) q^{37} +(2.35827 - 0.875847i) q^{39} +(-8.14951 - 4.70512i) q^{41} +(-2.81997 + 10.5243i) q^{43} +(6.18571 - 2.98354i) q^{45} +(0.322401 + 0.558415i) q^{47} +(1.25453 - 2.17290i) q^{49} +(-0.275186 - 2.92497i) q^{51} +(-7.59951 - 7.59951i) q^{53} +8.12630i q^{55} +(10.2234 + 8.46517i) q^{57} +(-5.82026 + 1.55953i) q^{59} +(-3.88659 - 1.04141i) q^{61} +(7.00833 - 6.03861i) q^{63} +(1.66245 + 2.87945i) q^{65} +(1.07739 + 4.02086i) q^{67} +(3.08163 - 6.72300i) q^{69} +4.81741i q^{71} +0.0254428i q^{73} +(0.241158 + 0.339661i) q^{75} +(2.83316 + 10.5735i) q^{77} +(-7.90903 - 13.6988i) q^{79} +(8.37384 - 3.29831i) q^{81} +(-9.35105 - 2.50561i) q^{83} +(3.75064 - 1.00498i) q^{85} +(0.164989 - 0.972854i) q^{87} +1.29060i q^{89} +(3.16698 + 3.16698i) q^{91} +(-11.3144 - 5.18621i) q^{93} +(-8.77145 + 15.1926i) q^{95} +(4.31271 + 7.46984i) q^{97} +(-0.789344 + 10.6202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 72q - 2q^{3} + 4q^{5} + O(q^{10}) \) \( 72q - 2q^{3} + 4q^{5} + 2q^{11} - 16q^{13} + 20q^{15} - 16q^{17} - 28q^{19} - 16q^{21} - 8q^{27} + 4q^{29} - 28q^{31} - 32q^{33} + 16q^{35} + 16q^{37} + 10q^{43} + 40q^{45} + 56q^{47} + 4q^{49} + 54q^{51} - 8q^{53} + 14q^{59} - 32q^{61} + 108q^{63} - 64q^{65} + 18q^{67} + 32q^{69} - 86q^{75} - 36q^{77} - 44q^{79} - 44q^{81} - 20q^{83} - 8q^{85} + 80q^{91} - 4q^{93} - 48q^{95} + 40q^{97} - 28q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(325\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) 0.162237 + 1.72444i 0.0936678 + 0.995604i
\(4\) 0 0
\(5\) −2.21121 + 0.592492i −0.988884 + 0.264971i −0.716782 0.697298i \(-0.754386\pi\)
−0.272102 + 0.962268i \(0.587719\pi\)
\(6\) 0 0
\(7\) −2.67054 + 1.54184i −1.00937 + 0.582760i −0.911007 0.412391i \(-0.864694\pi\)
−0.0983627 + 0.995151i \(0.531361\pi\)
\(8\) 0 0
\(9\) −2.94736 + 0.559536i −0.982453 + 0.186512i
\(10\) 0 0
\(11\) 0.918760 3.42886i 0.277017 1.03384i −0.677461 0.735559i \(-0.736920\pi\)
0.954478 0.298282i \(-0.0964135\pi\)
\(12\) 0 0
\(13\) −0.375914 1.40293i −0.104260 0.389102i 0.894000 0.448066i \(-0.147887\pi\)
−0.998260 + 0.0589636i \(0.981220\pi\)
\(14\) 0 0
\(15\) −1.38046 3.71697i −0.356432 0.959717i
\(16\) 0 0
\(17\) −1.69619 −0.411387 −0.205693 0.978617i \(-0.565945\pi\)
−0.205693 + 0.978617i \(0.565945\pi\)
\(18\) 0 0
\(19\) 5.41876 5.41876i 1.24315 1.24315i 0.284460 0.958688i \(-0.408186\pi\)
0.958688 0.284460i \(-0.0918143\pi\)
\(20\) 0 0
\(21\) −3.09206 4.35503i −0.674743 0.950346i
\(22\) 0 0
\(23\) −3.69781 2.13493i −0.771047 0.445164i 0.0622012 0.998064i \(-0.480188\pi\)
−0.833248 + 0.552900i \(0.813521\pi\)
\(24\) 0 0
\(25\) 0.208283 0.120252i 0.0416566 0.0240504i
\(26\) 0 0
\(27\) −1.44306 4.99175i −0.277716 0.960663i
\(28\) 0 0
\(29\) −0.550286 0.147449i −0.102185 0.0273805i 0.207364 0.978264i \(-0.433512\pi\)
−0.309549 + 0.950883i \(0.600178\pi\)
\(30\) 0 0
\(31\) −3.59297 + 6.22321i −0.645317 + 1.11772i 0.338911 + 0.940818i \(0.389941\pi\)
−0.984228 + 0.176903i \(0.943392\pi\)
\(32\) 0 0
\(33\) 6.06191 + 1.02805i 1.05524 + 0.178961i
\(34\) 0 0
\(35\) 4.99161 4.99161i 0.843735 0.843735i
\(36\) 0 0
\(37\) 2.59734 + 2.59734i 0.427000 + 0.427000i 0.887605 0.460605i \(-0.152367\pi\)
−0.460605 + 0.887605i \(0.652367\pi\)
\(38\) 0 0
\(39\) 2.35827 0.875847i 0.377626 0.140248i
\(40\) 0 0
\(41\) −8.14951 4.70512i −1.27274 0.734817i −0.297237 0.954804i \(-0.596065\pi\)
−0.975503 + 0.219987i \(0.929399\pi\)
\(42\) 0 0
\(43\) −2.81997 + 10.5243i −0.430042 + 1.60494i 0.322618 + 0.946529i \(0.395437\pi\)
−0.752660 + 0.658410i \(0.771230\pi\)
\(44\) 0 0
\(45\) 6.18571 2.98354i 0.922111 0.444760i
\(46\) 0 0
\(47\) 0.322401 + 0.558415i 0.0470270 + 0.0814532i 0.888581 0.458720i \(-0.151692\pi\)
−0.841554 + 0.540173i \(0.818359\pi\)
\(48\) 0 0
\(49\) 1.25453 2.17290i 0.179218 0.310415i
\(50\) 0 0
\(51\) −0.275186 2.92497i −0.0385337 0.409578i
\(52\) 0 0
\(53\) −7.59951 7.59951i −1.04387 1.04387i −0.998992 0.0448800i \(-0.985709\pi\)
−0.0448800 0.998992i \(-0.514291\pi\)
\(54\) 0 0
\(55\) 8.12630i 1.09575i
\(56\) 0 0
\(57\) 10.2234 + 8.46517i 1.35413 + 1.12124i
\(58\) 0 0
\(59\) −5.82026 + 1.55953i −0.757733 + 0.203034i −0.616946 0.787006i \(-0.711630\pi\)
−0.140788 + 0.990040i \(0.544963\pi\)
\(60\) 0 0
\(61\) −3.88659 1.04141i −0.497627 0.133339i 0.00127169 0.999999i \(-0.499595\pi\)
−0.498898 + 0.866661i \(0.666262\pi\)
\(62\) 0 0
\(63\) 7.00833 6.03861i 0.882966 0.760794i
\(64\) 0 0
\(65\) 1.66245 + 2.87945i 0.206201 + 0.357151i
\(66\) 0 0
\(67\) 1.07739 + 4.02086i 0.131624 + 0.491226i 0.999989 0.00469890i \(-0.00149571\pi\)
−0.868365 + 0.495925i \(0.834829\pi\)
\(68\) 0 0
\(69\) 3.08163 6.72300i 0.370985 0.809354i
\(70\) 0 0
\(71\) 4.81741i 0.571722i 0.958271 + 0.285861i \(0.0922795\pi\)
−0.958271 + 0.285861i \(0.907720\pi\)
\(72\) 0 0
\(73\) 0.0254428i 0.00297785i 0.999999 + 0.00148893i \(0.000473940\pi\)
−0.999999 + 0.00148893i \(0.999526\pi\)
\(74\) 0 0
\(75\) 0.241158 + 0.339661i 0.0278466 + 0.0392207i
\(76\) 0 0
\(77\) 2.83316 + 10.5735i 0.322868 + 1.20496i
\(78\) 0 0
\(79\) −7.90903 13.6988i −0.889835 1.54124i −0.840069 0.542479i \(-0.817486\pi\)
−0.0497661 0.998761i \(-0.515848\pi\)
\(80\) 0 0
\(81\) 8.37384 3.29831i 0.930427 0.366479i
\(82\) 0 0
\(83\) −9.35105 2.50561i −1.02641 0.275026i −0.293940 0.955824i \(-0.594967\pi\)
−0.732471 + 0.680798i \(0.761633\pi\)
\(84\) 0 0
\(85\) 3.75064 1.00498i 0.406814 0.109005i
\(86\) 0 0
\(87\) 0.164989 0.972854i 0.0176886 0.104301i
\(88\) 0 0
\(89\) 1.29060i 0.136803i 0.997658 + 0.0684014i \(0.0217899\pi\)
−0.997658 + 0.0684014i \(0.978210\pi\)
\(90\) 0 0
\(91\) 3.16698 + 3.16698i 0.331990 + 0.331990i
\(92\) 0 0
\(93\) −11.3144 5.18621i −1.17325 0.537785i
\(94\) 0 0
\(95\) −8.77145 + 15.1926i −0.899931 + 1.55873i
\(96\) 0 0
\(97\) 4.31271 + 7.46984i 0.437890 + 0.758447i 0.997527 0.0702907i \(-0.0223927\pi\)
−0.559637 + 0.828738i \(0.689059\pi\)
\(98\) 0 0
\(99\) −0.789344 + 10.6202i −0.0793321 + 1.06737i
\(100\) 0 0
\(101\) 3.30347 12.3287i 0.328708 1.22675i −0.581824 0.813315i \(-0.697661\pi\)
0.910532 0.413440i \(-0.135673\pi\)
\(102\) 0 0
\(103\) −0.777714 0.449013i −0.0766304 0.0442426i 0.461195 0.887299i \(-0.347421\pi\)
−0.537826 + 0.843056i \(0.680754\pi\)
\(104\) 0 0
\(105\) 9.41753 + 7.79788i 0.919057 + 0.760995i
\(106\) 0 0
\(107\) 3.43615 + 3.43615i 0.332185 + 0.332185i 0.853416 0.521230i \(-0.174527\pi\)
−0.521230 + 0.853416i \(0.674527\pi\)
\(108\) 0 0
\(109\) −10.7430 + 10.7430i −1.02900 + 1.02900i −0.0294299 + 0.999567i \(0.509369\pi\)
−0.999567 + 0.0294299i \(0.990631\pi\)
\(110\) 0 0
\(111\) −4.05756 + 4.90034i −0.385127 + 0.465119i
\(112\) 0 0
\(113\) −6.90863 + 11.9661i −0.649910 + 1.12568i 0.333234 + 0.942844i \(0.391860\pi\)
−0.983144 + 0.182833i \(0.941473\pi\)
\(114\) 0 0
\(115\) 9.44157 + 2.52986i 0.880431 + 0.235911i
\(116\) 0 0
\(117\) 1.89294 + 3.92460i 0.175002 + 0.362829i
\(118\) 0 0
\(119\) 4.52975 2.61525i 0.415241 0.239740i
\(120\) 0 0
\(121\) −1.38669 0.800604i −0.126062 0.0727821i
\(122\) 0 0
\(123\) 6.79153 14.8167i 0.612371 1.33597i
\(124\) 0 0
\(125\) 7.70429 7.70429i 0.689092 0.689092i
\(126\) 0 0
\(127\) 11.0753 0.982777 0.491389 0.870940i \(-0.336489\pi\)
0.491389 + 0.870940i \(0.336489\pi\)
\(128\) 0 0
\(129\) −18.6060 3.15543i −1.63816 0.277820i
\(130\) 0 0
\(131\) −0.410504 1.53202i −0.0358659 0.133854i 0.945671 0.325124i \(-0.105406\pi\)
−0.981537 + 0.191270i \(0.938739\pi\)
\(132\) 0 0
\(133\) −6.11617 + 22.8259i −0.530339 + 1.97925i
\(134\) 0 0
\(135\) 6.14848 + 10.1828i 0.529177 + 0.876398i
\(136\) 0 0
\(137\) −12.9206 + 7.45971i −1.10388 + 0.637326i −0.937238 0.348691i \(-0.886626\pi\)
−0.166643 + 0.986017i \(0.553293\pi\)
\(138\) 0 0
\(139\) 12.1316 3.25066i 1.02899 0.275717i 0.295447 0.955359i \(-0.404531\pi\)
0.733544 + 0.679642i \(0.237865\pi\)
\(140\) 0 0
\(141\) −0.910645 + 0.646556i −0.0766902 + 0.0544498i
\(142\) 0 0
\(143\) −5.15582 −0.431151
\(144\) 0 0
\(145\) 1.30416 0.108305
\(146\) 0 0
\(147\) 3.95057 + 1.81083i 0.325837 + 0.149354i
\(148\) 0 0
\(149\) 14.9396 4.00304i 1.22390 0.327942i 0.411696 0.911321i \(-0.364936\pi\)
0.812200 + 0.583379i \(0.198270\pi\)
\(150\) 0 0
\(151\) 1.44969 0.836978i 0.117974 0.0681123i −0.439852 0.898070i \(-0.644969\pi\)
0.557826 + 0.829958i \(0.311636\pi\)
\(152\) 0 0
\(153\) 4.99928 0.949080i 0.404168 0.0767286i
\(154\) 0 0
\(155\) 4.25762 15.8896i 0.341980 1.27629i
\(156\) 0 0
\(157\) −1.28384 4.79137i −0.102462 0.382393i 0.895583 0.444894i \(-0.146759\pi\)
−0.998045 + 0.0625016i \(0.980092\pi\)
\(158\) 0 0
\(159\) 11.8719 14.3378i 0.941506 1.13706i
\(160\) 0 0
\(161\) 13.1669 1.03769
\(162\) 0 0
\(163\) −3.42775 + 3.42775i −0.268482 + 0.268482i −0.828488 0.560006i \(-0.810799\pi\)
0.560006 + 0.828488i \(0.310799\pi\)
\(164\) 0 0
\(165\) −14.0133 + 1.31839i −1.09093 + 0.102636i
\(166\) 0 0
\(167\) 7.20275 + 4.15851i 0.557366 + 0.321795i 0.752088 0.659063i \(-0.229047\pi\)
−0.194722 + 0.980859i \(0.562380\pi\)
\(168\) 0 0
\(169\) 9.43143 5.44524i 0.725495 0.418865i
\(170\) 0 0
\(171\) −12.9390 + 19.0030i −0.989472 + 1.45320i
\(172\) 0 0
\(173\) −0.548704 0.147025i −0.0417172 0.0111781i 0.237900 0.971290i \(-0.423541\pi\)
−0.279617 + 0.960112i \(0.590208\pi\)
\(174\) 0 0
\(175\) −0.370819 + 0.642277i −0.0280312 + 0.0485515i
\(176\) 0 0
\(177\) −3.63358 9.78365i −0.273117 0.735384i
\(178\) 0 0
\(179\) −0.445920 + 0.445920i −0.0333297 + 0.0333297i −0.723575 0.690246i \(-0.757503\pi\)
0.690246 + 0.723575i \(0.257503\pi\)
\(180\) 0 0
\(181\) 9.08467 + 9.08467i 0.675258 + 0.675258i 0.958923 0.283665i \(-0.0915505\pi\)
−0.283665 + 0.958923i \(0.591551\pi\)
\(182\) 0 0
\(183\) 1.16529 6.87113i 0.0861408 0.507928i
\(184\) 0 0
\(185\) −7.28218 4.20437i −0.535396 0.309111i
\(186\) 0 0
\(187\) −1.55839 + 5.81600i −0.113961 + 0.425308i
\(188\) 0 0
\(189\) 11.5502 + 11.1057i 0.840154 + 0.807822i
\(190\) 0 0
\(191\) 6.96468 + 12.0632i 0.503946 + 0.872861i 0.999990 + 0.00456281i \(0.00145239\pi\)
−0.496043 + 0.868298i \(0.665214\pi\)
\(192\) 0 0
\(193\) −0.664728 + 1.15134i −0.0478482 + 0.0828754i −0.888958 0.457990i \(-0.848570\pi\)
0.841109 + 0.540865i \(0.181903\pi\)
\(194\) 0 0
\(195\) −4.69571 + 3.33394i −0.336267 + 0.238748i
\(196\) 0 0
\(197\) 16.7957 + 16.7957i 1.19665 + 1.19665i 0.975164 + 0.221482i \(0.0710894\pi\)
0.221482 + 0.975164i \(0.428911\pi\)
\(198\) 0 0
\(199\) 2.87623i 0.203891i −0.994790 0.101945i \(-0.967493\pi\)
0.994790 0.101945i \(-0.0325067\pi\)
\(200\) 0 0
\(201\) −6.75892 + 2.51022i −0.476738 + 0.177057i
\(202\) 0 0
\(203\) 1.69690 0.454684i 0.119099 0.0319125i
\(204\) 0 0
\(205\) 20.8080 + 5.57550i 1.45330 + 0.389410i
\(206\) 0 0
\(207\) 12.0933 + 4.22335i 0.840545 + 0.293543i
\(208\) 0 0
\(209\) −13.6016 23.5587i −0.940844 1.62959i
\(210\) 0 0
\(211\) −0.797494 2.97629i −0.0549017 0.204896i 0.933027 0.359807i \(-0.117158\pi\)
−0.987928 + 0.154911i \(0.950491\pi\)
\(212\) 0 0
\(213\) −8.30732 + 0.781565i −0.569208 + 0.0535520i
\(214\) 0 0
\(215\) 24.9422i 1.70105i
\(216\) 0 0
\(217\) 22.1591i 1.50426i
\(218\) 0 0
\(219\) −0.0438745 + 0.00412777i −0.00296476 + 0.000278929i
\(220\) 0 0
\(221\) 0.637621 + 2.37963i 0.0428910 + 0.160072i
\(222\) 0 0
\(223\) −5.89459 10.2097i −0.394731 0.683694i 0.598336 0.801245i \(-0.295829\pi\)
−0.993067 + 0.117552i \(0.962495\pi\)
\(224\) 0 0
\(225\) −0.546599 + 0.470968i −0.0364399 + 0.0313979i
\(226\) 0 0
\(227\) −25.6612 6.87589i −1.70319 0.456369i −0.729451 0.684033i \(-0.760225\pi\)
−0.973740 + 0.227664i \(0.926891\pi\)
\(228\) 0 0
\(229\) −16.4490 + 4.40749i −1.08698 + 0.291255i −0.757451 0.652891i \(-0.773556\pi\)
−0.329526 + 0.944146i \(0.606889\pi\)
\(230\) 0 0
\(231\) −17.7737 + 6.60102i −1.16942 + 0.434315i
\(232\) 0 0
\(233\) 2.20632i 0.144541i −0.997385 0.0722703i \(-0.976976\pi\)
0.997385 0.0722703i \(-0.0230244\pi\)
\(234\) 0 0
\(235\) −1.04375 1.04375i −0.0680870 0.0680870i
\(236\) 0 0
\(237\) 22.3396 15.8611i 1.45112 1.03029i
\(238\) 0 0
\(239\) −4.25004 + 7.36128i −0.274912 + 0.476161i −0.970113 0.242654i \(-0.921982\pi\)
0.695201 + 0.718815i \(0.255315\pi\)
\(240\) 0 0
\(241\) −9.09368 15.7507i −0.585775 1.01459i −0.994778 0.102060i \(-0.967457\pi\)
0.409003 0.912533i \(-0.365877\pi\)
\(242\) 0 0
\(243\) 7.04627 + 13.9050i 0.452018 + 0.892009i
\(244\) 0 0
\(245\) −1.48660 + 5.54805i −0.0949751 + 0.354452i
\(246\) 0 0
\(247\) −9.63911 5.56514i −0.613322 0.354102i
\(248\) 0 0
\(249\) 2.80367 16.5318i 0.177675 1.04766i
\(250\) 0 0
\(251\) −4.42291 4.42291i −0.279171 0.279171i 0.553607 0.832778i \(-0.313251\pi\)
−0.832778 + 0.553607i \(0.813251\pi\)
\(252\) 0 0
\(253\) −10.7178 + 10.7178i −0.673821 + 0.673821i
\(254\) 0 0
\(255\) 2.34152 + 6.30469i 0.146631 + 0.394815i
\(256\) 0 0
\(257\) 0.433089 0.750132i 0.0270153 0.0467920i −0.852202 0.523213i \(-0.824733\pi\)
0.879217 + 0.476422i \(0.158066\pi\)
\(258\) 0 0
\(259\) −10.9410 2.93163i −0.679840 0.182163i
\(260\) 0 0
\(261\) 1.70439 + 0.126679i 0.105499 + 0.00784124i
\(262\) 0 0
\(263\) −7.59086 + 4.38259i −0.468073 + 0.270242i −0.715433 0.698682i \(-0.753770\pi\)
0.247360 + 0.968924i \(0.420437\pi\)
\(264\) 0 0
\(265\) 21.3068 + 12.3015i 1.30886 + 0.755673i
\(266\) 0 0
\(267\) −2.22555 + 0.209383i −0.136201 + 0.0128140i
\(268\) 0 0
\(269\) −6.48858 + 6.48858i −0.395616 + 0.395616i −0.876683 0.481068i \(-0.840249\pi\)
0.481068 + 0.876683i \(0.340249\pi\)
\(270\) 0 0
\(271\) −27.4975 −1.67035 −0.835177 0.549981i \(-0.814635\pi\)
−0.835177 + 0.549981i \(0.814635\pi\)
\(272\) 0 0
\(273\) −4.94745 + 5.97506i −0.299433 + 0.361627i
\(274\) 0 0
\(275\) −0.220966 0.824656i −0.0133247 0.0497286i
\(276\) 0 0
\(277\) 5.27098 19.6716i 0.316703 1.18195i −0.605691 0.795700i \(-0.707103\pi\)
0.922394 0.386251i \(-0.126230\pi\)
\(278\) 0 0
\(279\) 7.10766 20.3524i 0.425525 1.21847i
\(280\) 0 0
\(281\) 12.6319 7.29301i 0.753554 0.435065i −0.0734227 0.997301i \(-0.523392\pi\)
0.826977 + 0.562236i \(0.190059\pi\)
\(282\) 0 0
\(283\) −4.95213 + 1.32692i −0.294374 + 0.0788772i −0.402983 0.915207i \(-0.632027\pi\)
0.108610 + 0.994084i \(0.465360\pi\)
\(284\) 0 0
\(285\) −27.6217 12.6610i −1.63617 0.749972i
\(286\) 0 0
\(287\) 29.0182 1.71289
\(288\) 0 0
\(289\) −14.1229 −0.830761
\(290\) 0 0
\(291\) −12.1816 + 8.64889i −0.714097 + 0.507007i
\(292\) 0 0
\(293\) −9.85233 + 2.63992i −0.575579 + 0.154226i −0.534854 0.844944i \(-0.679633\pi\)
−0.0407250 + 0.999170i \(0.512967\pi\)
\(294\) 0 0
\(295\) 11.9458 6.89692i 0.695512 0.401554i
\(296\) 0 0
\(297\) −18.4418 + 0.361814i −1.07010 + 0.0209946i
\(298\) 0 0
\(299\) −1.60510 + 5.99031i −0.0928253 + 0.346429i
\(300\) 0 0
\(301\) −8.69589 32.4535i −0.501223 1.87059i
\(302\) 0 0
\(303\) 21.7961 + 3.69645i 1.25215 + 0.212355i
\(304\) 0 0
\(305\) 9.21109 0.527426
\(306\) 0 0
\(307\) 13.8230 13.8230i 0.788919 0.788919i −0.192398 0.981317i \(-0.561626\pi\)
0.981317 + 0.192398i \(0.0616263\pi\)
\(308\) 0 0
\(309\) 0.648120 1.41396i 0.0368703 0.0804376i
\(310\) 0 0
\(311\) 2.07629 + 1.19875i 0.117736 + 0.0679747i 0.557711 0.830035i \(-0.311680\pi\)
−0.439976 + 0.898010i \(0.645013\pi\)
\(312\) 0 0
\(313\) −11.1437 + 6.43381i −0.629878 + 0.363660i −0.780705 0.624900i \(-0.785140\pi\)
0.150827 + 0.988560i \(0.451806\pi\)
\(314\) 0 0
\(315\) −11.9191 + 17.5050i −0.671563 + 0.986297i
\(316\) 0 0
\(317\) 6.11177 + 1.63764i 0.343271 + 0.0919792i 0.426336 0.904565i \(-0.359804\pi\)
−0.0830647 + 0.996544i \(0.526471\pi\)
\(318\) 0 0
\(319\) −1.01116 + 1.75138i −0.0566142 + 0.0980586i
\(320\) 0 0
\(321\) −5.36795 + 6.48290i −0.299610 + 0.361840i
\(322\) 0 0
\(323\) −9.19124 + 9.19124i −0.511414 + 0.511414i
\(324\) 0 0
\(325\) −0.247002 0.247002i −0.0137012 0.0137012i
\(326\) 0 0
\(327\) −20.2686 16.7828i −1.12086 0.928089i
\(328\) 0 0
\(329\) −1.72197 0.994180i −0.0949353 0.0548109i
\(330\) 0 0
\(331\) 0.286391 1.06882i 0.0157415 0.0587479i −0.957608 0.288073i \(-0.906985\pi\)
0.973350 + 0.229325i \(0.0736520\pi\)
\(332\) 0 0
\(333\) −9.10860 6.20199i −0.499148 0.339867i
\(334\) 0 0
\(335\) −4.76466 8.25263i −0.260321 0.450889i
\(336\) 0 0
\(337\) −12.1196 + 20.9918i −0.660199 + 1.14350i 0.320364 + 0.947294i \(0.396195\pi\)
−0.980563 + 0.196204i \(0.937139\pi\)
\(338\) 0 0
\(339\) −21.7556 9.97215i −1.18160 0.541613i
\(340\) 0 0
\(341\) 18.0374 + 18.0374i 0.976782 + 0.976782i
\(342\) 0 0
\(343\) 13.8486i 0.747755i
\(344\) 0 0
\(345\) −2.83081 + 16.6918i −0.152406 + 0.898657i
\(346\) 0 0
\(347\) 4.93905 1.32342i 0.265142 0.0710447i −0.123799 0.992307i \(-0.539508\pi\)
0.388941 + 0.921263i \(0.372841\pi\)
\(348\) 0 0
\(349\) 6.12667 + 1.64164i 0.327953 + 0.0878748i 0.419039 0.907968i \(-0.362367\pi\)
−0.0910858 + 0.995843i \(0.529034\pi\)
\(350\) 0 0
\(351\) −6.46061 + 3.90097i −0.344842 + 0.208219i
\(352\) 0 0
\(353\) 6.16156 + 10.6721i 0.327947 + 0.568021i 0.982104 0.188338i \(-0.0603100\pi\)
−0.654157 + 0.756358i \(0.726977\pi\)
\(354\) 0 0
\(355\) −2.85428 10.6523i −0.151490 0.565367i
\(356\) 0 0
\(357\) 5.24473 + 7.38697i 0.277580 + 0.390960i
\(358\) 0 0
\(359\) 25.7836i 1.36081i 0.732838 + 0.680403i \(0.238195\pi\)
−0.732838 + 0.680403i \(0.761805\pi\)
\(360\) 0 0
\(361\) 39.7258i 2.09083i
\(362\) 0 0
\(363\) 1.15562 2.52114i 0.0606542 0.132325i
\(364\) 0 0
\(365\) −0.0150747 0.0562594i −0.000789044 0.00294475i
\(366\) 0 0
\(367\) 1.72726 + 2.99170i 0.0901622 + 0.156166i 0.907579 0.419881i \(-0.137928\pi\)
−0.817417 + 0.576046i \(0.804595\pi\)
\(368\) 0 0
\(369\) 26.6522 + 9.30774i 1.38746 + 0.484541i
\(370\) 0 0
\(371\) 32.0120 + 8.57759i 1.66198 + 0.445326i
\(372\) 0 0
\(373\) 17.3353 4.64499i 0.897590 0.240508i 0.219609 0.975588i \(-0.429522\pi\)
0.677981 + 0.735080i \(0.262855\pi\)
\(374\) 0 0
\(375\) 14.5355 + 12.0356i 0.750609 + 0.621517i
\(376\) 0 0
\(377\) 0.827440i 0.0426153i
\(378\) 0 0
\(379\) −19.9585 19.9585i −1.02520 1.02520i −0.999674 0.0255265i \(-0.991874\pi\)
−0.0255265 0.999674i \(-0.508126\pi\)
\(380\) 0 0
\(381\) 1.79683 + 19.0987i 0.0920546 + 0.978457i
\(382\) 0 0
\(383\) 5.88309 10.1898i 0.300612 0.520675i −0.675663 0.737211i \(-0.736142\pi\)
0.976275 + 0.216536i \(0.0694758\pi\)
\(384\) 0 0
\(385\) −12.5294 21.7016i −0.638559 1.10602i
\(386\) 0 0
\(387\) 2.42275 32.5967i 0.123156 1.65698i
\(388\) 0 0
\(389\) 7.61717 28.4276i 0.386206 1.44134i −0.450052 0.893002i \(-0.648595\pi\)
0.836258 0.548337i \(-0.184739\pi\)
\(390\) 0 0
\(391\) 6.27219 + 3.62125i 0.317198 + 0.183135i
\(392\) 0 0
\(393\) 2.57528 0.956440i 0.129906 0.0482460i
\(394\) 0 0
\(395\) 25.6050 + 25.6050i 1.28833 + 1.28833i
\(396\) 0 0
\(397\) −7.53419 + 7.53419i −0.378130 + 0.378130i −0.870427 0.492297i \(-0.836157\pi\)
0.492297 + 0.870427i \(0.336157\pi\)
\(398\) 0 0
\(399\) −40.3540 6.84373i −2.02023 0.342615i
\(400\) 0 0
\(401\) −4.77831 + 8.27628i −0.238617 + 0.413297i −0.960318 0.278908i \(-0.910028\pi\)
0.721700 + 0.692206i \(0.243361\pi\)
\(402\) 0 0
\(403\) 10.0814 + 2.70129i 0.502189 + 0.134561i
\(404\) 0 0
\(405\) −16.5621 + 12.2547i −0.822978 + 0.608940i
\(406\) 0 0
\(407\) 11.2923 6.51959i 0.559737 0.323164i
\(408\) 0 0
\(409\) −17.7240 10.2330i −0.876395 0.505987i −0.00692724 0.999976i \(-0.502205\pi\)
−0.869468 + 0.493989i \(0.835538\pi\)
\(410\) 0 0
\(411\) −14.9600 21.0705i −0.737922 1.03933i
\(412\) 0 0
\(413\) 13.1387 13.1387i 0.646513 0.646513i
\(414\) 0 0
\(415\) 22.1617 1.08788
\(416\) 0 0
\(417\) 7.57376 + 20.3928i 0.370889 + 0.998642i
\(418\) 0 0
\(419\) 0.851695 + 3.17857i 0.0416080 + 0.155283i 0.983604 0.180340i \(-0.0577198\pi\)
−0.941996 + 0.335623i \(0.891053\pi\)
\(420\) 0 0
\(421\) 2.22646 8.30926i 0.108511 0.404969i −0.890209 0.455553i \(-0.849442\pi\)
0.998720 + 0.0505841i \(0.0161083\pi\)
\(422\) 0 0
\(423\) −1.26268 1.46545i −0.0613938 0.0712528i
\(424\) 0 0
\(425\) −0.353287 + 0.203971i −0.0171370 + 0.00989402i
\(426\) 0 0
\(427\) 11.9850 3.21136i 0.579994 0.155409i
\(428\) 0 0
\(429\) −0.836467 8.89088i −0.0403850 0.429256i
\(430\) 0 0
\(431\) 7.01916 0.338101 0.169051 0.985607i \(-0.445930\pi\)
0.169051 + 0.985607i \(0.445930\pi\)
\(432\) 0 0
\(433\) 25.2759 1.21468 0.607342 0.794440i \(-0.292236\pi\)
0.607342 + 0.794440i \(0.292236\pi\)
\(434\) 0 0
\(435\) 0.211584 + 2.24894i 0.0101447 + 0.107828i
\(436\) 0 0
\(437\) −31.6062 + 8.46886i −1.51193 + 0.405120i
\(438\) 0 0
\(439\) 22.3355 12.8954i 1.06602 0.615464i 0.138925 0.990303i \(-0.455635\pi\)
0.927090 + 0.374839i \(0.122302\pi\)
\(440\) 0 0
\(441\) −2.48172 + 7.10628i −0.118177 + 0.338394i
\(442\) 0 0
\(443\) −1.27907 + 4.77356i −0.0607705 + 0.226799i −0.989631 0.143630i \(-0.954122\pi\)
0.928861 + 0.370429i \(0.120789\pi\)
\(444\) 0 0
\(445\) −0.764668 2.85378i −0.0362487 0.135282i
\(446\) 0 0
\(447\) 9.32675 + 25.1129i 0.441140 + 1.18780i
\(448\) 0 0
\(449\) −6.88400 −0.324876 −0.162438 0.986719i \(-0.551936\pi\)
−0.162438 + 0.986719i \(0.551936\pi\)
\(450\) 0 0
\(451\) −23.6207 + 23.6207i −1.11225 + 1.11225i
\(452\) 0 0
\(453\) 1.67851 + 2.36411i 0.0788632 + 0.111075i
\(454\) 0 0
\(455\) −8.87928 5.12645i −0.416267 0.240332i
\(456\) 0 0
\(457\) −5.49636 + 3.17333i −0.257109 + 0.148442i −0.623015 0.782210i \(-0.714092\pi\)
0.365906 + 0.930652i \(0.380759\pi\)
\(458\) 0 0
\(459\) 2.44770 + 8.46696i 0.114249 + 0.395204i
\(460\) 0 0
\(461\) −14.3089 3.83405i −0.666430 0.178569i −0.0902836 0.995916i \(-0.528777\pi\)
−0.576146 + 0.817347i \(0.695444\pi\)
\(462\) 0 0
\(463\) −6.15194 + 10.6555i −0.285905 + 0.495202i −0.972828 0.231528i \(-0.925628\pi\)
0.686923 + 0.726730i \(0.258961\pi\)
\(464\) 0 0
\(465\) 28.0914 + 4.76409i 1.30271 + 0.220929i
\(466\) 0 0
\(467\) 12.7214 12.7214i 0.588676 0.588676i −0.348596 0.937273i \(-0.613342\pi\)
0.937273 + 0.348596i \(0.113342\pi\)
\(468\) 0 0
\(469\) −9.07672 9.07672i −0.419124 0.419124i
\(470\) 0 0
\(471\) 8.05412 2.99124i 0.371114 0.137829i
\(472\) 0 0
\(473\) 33.4954 + 19.3386i 1.54012 + 0.889190i
\(474\) 0 0
\(475\) 0.477017 1.78025i 0.0218870 0.0816835i
\(476\) 0 0
\(477\) 26.6507 + 18.1463i 1.22025 + 0.830860i
\(478\) 0 0
\(479\) −20.3626 35.2690i −0.930389 1.61148i −0.782657 0.622454i \(-0.786136\pi\)
−0.147732 0.989027i \(-0.547197\pi\)
\(480\) 0 0
\(481\) 2.66751 4.62026i 0.121628 0.210666i
\(482\) 0 0
\(483\) 2.13616 + 22.7054i 0.0971986 + 1.03313i
\(484\) 0 0
\(485\) −13.9621 13.9621i −0.633988 0.633988i
\(486\) 0 0
\(487\) 33.9729i 1.53946i 0.638370 + 0.769730i \(0.279609\pi\)
−0.638370 + 0.769730i \(0.720391\pi\)
\(488\) 0 0
\(489\) −6.46704 5.35482i −0.292449 0.242153i
\(490\) 0 0
\(491\) 31.3167 8.39129i 1.41330 0.378694i 0.530200 0.847872i \(-0.322117\pi\)
0.883103 + 0.469179i \(0.155450\pi\)
\(492\) 0 0
\(493\) 0.933389 + 0.250101i 0.0420377 + 0.0112640i
\(494\) 0 0
\(495\) −4.54696 23.9511i −0.204370 1.07652i
\(496\) 0 0
\(497\) −7.42767 12.8651i −0.333177 0.577079i
\(498\) 0 0
\(499\) 3.79403 + 14.1595i 0.169844 + 0.633867i 0.997373 + 0.0724432i \(0.0230796\pi\)
−0.827528 + 0.561424i \(0.810254\pi\)
\(500\) 0 0
\(501\) −6.00253 + 13.0954i −0.268173 + 0.585057i
\(502\) 0 0
\(503\) 29.4642i 1.31374i 0.754002 + 0.656872i \(0.228121\pi\)
−0.754002 + 0.656872i \(0.771879\pi\)
\(504\) 0 0
\(505\) 29.2187i 1.30022i
\(506\) 0 0
\(507\) 10.9201 + 15.3805i 0.484979 + 0.683071i
\(508\) 0 0
\(509\) 1.54692 + 5.77318i 0.0685659 + 0.255892i 0.991697 0.128593i \(-0.0410460\pi\)
−0.923132 + 0.384484i \(0.874379\pi\)
\(510\) 0 0
\(511\) −0.0392286 0.0679460i −0.00173537 0.00300575i
\(512\) 0 0
\(513\) −34.8687 19.2295i −1.53949 0.849004i
\(514\) 0 0
\(515\) 1.98573 + 0.532074i 0.0875016 + 0.0234460i
\(516\) 0 0
\(517\) 2.21094 0.592419i 0.0972369 0.0260545i
\(518\) 0 0
\(519\) 0.164514 0.970057i 0.00722138 0.0425808i
\(520\) 0 0
\(521\) 26.7544i 1.17213i 0.810264 + 0.586065i \(0.199324\pi\)
−0.810264 + 0.586065i \(0.800676\pi\)
\(522\) 0 0
\(523\) −22.3142 22.3142i −0.975731 0.975731i 0.0239815 0.999712i \(-0.492366\pi\)
−0.999712 + 0.0239815i \(0.992366\pi\)
\(524\) 0 0
\(525\) −1.16773 0.535251i −0.0509637 0.0233603i
\(526\) 0 0
\(527\) 6.09436 10.5557i 0.265475 0.459816i
\(528\) 0 0
\(529\) −2.38414 4.12944i −0.103658 0.179541i
\(530\) 0 0
\(531\) 16.2818 7.85315i 0.706569 0.340798i
\(532\) 0 0
\(533\) −3.53744 + 13.2019i −0.153224 + 0.571838i
\(534\) 0 0
\(535\) −9.63396 5.56217i −0.416512 0.240473i
\(536\) 0 0
\(537\) −0.841306 0.696616i −0.0363050 0.0300612i
\(538\) 0 0
\(539\) −6.29798 6.29798i −0.271273 0.271273i
\(540\) 0 0
\(541\) 8.87843 8.87843i 0.381713 0.381713i −0.490006 0.871719i \(-0.663005\pi\)
0.871719 + 0.490006i \(0.163005\pi\)
\(542\) 0 0
\(543\) −14.1921 + 17.1398i −0.609039 + 0.735539i
\(544\) 0 0
\(545\) 17.3900 30.1203i 0.744904 1.29021i
\(546\) 0 0
\(547\) 29.2821 + 7.84612i 1.25201 + 0.335476i 0.823114 0.567876i \(-0.192235\pi\)
0.428899 + 0.903352i \(0.358901\pi\)
\(548\) 0 0
\(549\) 12.0379 + 0.894716i 0.513764 + 0.0381855i
\(550\) 0 0
\(551\) −3.78085 + 2.18288i −0.161070 + 0.0929936i
\(552\) 0 0
\(553\) 42.2428 + 24.3889i 1.79635 + 1.03712i
\(554\) 0 0
\(555\) 6.06872 13.2398i 0.257603 0.561996i
\(556\) 0 0
\(557\) −21.6018 + 21.6018i −0.915297 + 0.915297i −0.996683 0.0813861i \(-0.974065\pi\)
0.0813861 + 0.996683i \(0.474065\pi\)
\(558\) 0 0
\(559\) 15.8249 0.669322
\(560\) 0 0
\(561\) −10.2822 1.74378i −0.434113 0.0736222i
\(562\) 0 0
\(563\) −1.89104 7.05746i −0.0796979 0.297437i 0.914560 0.404451i \(-0.132537\pi\)
−0.994257 + 0.107015i \(0.965871\pi\)
\(564\) 0 0
\(565\) 8.18663 30.5529i 0.344414 1.28537i
\(566\) 0 0
\(567\) −17.2772 + 21.7194i −0.725575 + 0.912128i
\(568\) 0 0
\(569\) −23.2350 + 13.4148i −0.974063 + 0.562376i −0.900473 0.434913i \(-0.856779\pi\)
−0.0735908 + 0.997289i \(0.523446\pi\)
\(570\) 0 0
\(571\) 18.7332 5.01955i 0.783960 0.210062i 0.155430 0.987847i \(-0.450324\pi\)
0.628530 + 0.777785i \(0.283657\pi\)
\(572\) 0 0
\(573\) −19.6722 + 13.9672i −0.821820 + 0.583490i
\(574\) 0 0
\(575\) −1.02692 −0.0428255
\(576\) 0 0
\(577\) 35.0568 1.45943 0.729717 0.683750i \(-0.239652\pi\)
0.729717 + 0.683750i \(0.239652\pi\)
\(578\) 0 0
\(579\) −2.09326 0.959490i −0.0869929 0.0398750i
\(580\) 0 0
\(581\) 28.8356 7.72648i 1.19630 0.320548i
\(582\) 0 0
\(583\) −33.0398 + 19.0755i −1.36837 + 0.790027i
\(584\) 0 0
\(585\) −6.51099 7.55656i −0.269196 0.312425i
\(586\) 0 0
\(587\) −4.80045 + 17.9155i −0.198136 + 0.739453i 0.793297 + 0.608835i \(0.208363\pi\)
−0.991433 + 0.130618i \(0.958304\pi\)
\(588\) 0 0
\(589\) 14.2526 + 53.1915i 0.587269 + 2.19172i
\(590\) 0 0
\(591\) −26.2383 + 31.6881i −1.07930 + 1.30347i
\(592\) 0 0
\(593\) −5.47582 −0.224865 −0.112432 0.993659i \(-0.535864\pi\)
−0.112432 + 0.993659i \(0.535864\pi\)
\(594\) 0 0
\(595\) −8.46671 + 8.46671i −0.347101 + 0.347101i
\(596\) 0 0
\(597\) 4.95988 0.466633i 0.202994 0.0190980i
\(598\) 0 0
\(599\) 17.2378 + 9.95227i 0.704319 + 0.406639i 0.808954 0.587872i \(-0.200034\pi\)
−0.104635 + 0.994511i \(0.533367\pi\)
\(600\) 0 0
\(601\) −30.3863 + 17.5435i −1.23948 + 0.715616i −0.968989 0.247105i \(-0.920521\pi\)
−0.270495 + 0.962721i \(0.587187\pi\)
\(602\) 0 0
\(603\) −5.42526 11.2481i −0.220934 0.458057i
\(604\) 0 0
\(605\) 3.54061 + 0.948703i 0.143946 + 0.0385703i
\(606\) 0 0
\(607\) −7.86595 + 13.6242i −0.319269 + 0.552991i −0.980336 0.197337i \(-0.936771\pi\)
0.661067 + 0.750327i \(0.270104\pi\)
\(608\) 0 0
\(609\) 1.05937 + 2.85243i 0.0429280 + 0.115586i
\(610\) 0 0
\(611\) 0.662222 0.662222i 0.0267906 0.0267906i
\(612\) 0 0
\(613\) −19.8523 19.8523i −0.801828 0.801828i 0.181553 0.983381i \(-0.441888\pi\)
−0.983381 + 0.181553i \(0.941888\pi\)
\(614\) 0 0
\(615\) −6.23875 + 36.7867i −0.251571 + 1.48338i
\(616\) 0 0
\(617\) 14.2878 + 8.24909i 0.575207 + 0.332096i 0.759226 0.650827i \(-0.225578\pi\)
−0.184019 + 0.982923i \(0.558911\pi\)
\(618\) 0 0
\(619\) −10.8215 + 40.3865i −0.434954 + 1.62327i 0.306221 + 0.951960i \(0.400935\pi\)
−0.741176 + 0.671311i \(0.765731\pi\)
\(620\) 0 0
\(621\) −5.32090 + 21.5394i −0.213520 + 0.864345i
\(622\) 0 0
\(623\) −1.98989 3.44659i −0.0797232 0.138085i
\(624\) 0 0
\(625\) −13.0723 + 22.6420i −0.522894 + 0.905678i
\(626\) 0 0
\(627\) 38.4188 27.2772i 1.53430 1.08935i
\(628\) 0 0
\(629\) −4.40559 4.40559i −0.175662 0.175662i
\(630\) 0 0
\(631\) 1.27009i 0.0505615i 0.999680 + 0.0252808i \(0.00804797\pi\)
−0.999680 + 0.0252808i \(0.991952\pi\)
\(632\) 0 0
\(633\) 5.00303 1.85809i 0.198853 0.0738525i
\(634\) 0 0
\(635\) −24.4899 + 6.56205i −0.971853 + 0.260407i
\(636\) 0 0
\(637\) −3.52002 0.943188i −0.139468 0.0373705i
\(638\) 0 0
\(639\) −2.69552 14.1986i −0.106633 0.561690i
\(640\) 0 0
\(641\) 22.6338 + 39.2028i 0.893979 + 1.54842i 0.835063 + 0.550155i \(0.185431\pi\)
0.0589168 + 0.998263i \(0.481235\pi\)
\(642\) 0 0
\(643\) −5.89901 22.0154i −0.232634 0.868203i −0.979201 0.202892i \(-0.934966\pi\)
0.746567 0.665311i \(-0.231701\pi\)
\(644\) 0 0
\(645\) 43.0113 4.04657i 1.69357 0.159333i
\(646\) 0 0
\(647\) 14.3883i 0.565662i −0.959170 0.282831i \(-0.908726\pi\)
0.959170 0.282831i \(-0.0912735\pi\)
\(648\) 0 0
\(649\) 21.3897i 0.839619i
\(650\) 0 0
\(651\) 38.2120 3.59504i 1.49765 0.140901i
\(652\) 0 0
\(653\) −5.91845 22.0879i −0.231607 0.864368i −0.979649 0.200717i \(-0.935673\pi\)
0.748043 0.663651i \(-0.230994\pi\)
\(654\) 0 0
\(655\) 1.81542 + 3.14441i 0.0709345 + 0.122862i
\(656\) 0 0
\(657\) −0.0142362 0.0749890i −0.000555406 0.00292560i
\(658\) 0 0
\(659\) 21.4351 + 5.74352i 0.834993 + 0.223736i 0.650891 0.759172i \(-0.274396\pi\)
0.184102 + 0.982907i \(0.441062\pi\)
\(660\) 0 0
\(661\) −16.0487 + 4.30024i −0.624223 + 0.167260i −0.557047 0.830481i \(-0.688066\pi\)
−0.0671760 + 0.997741i \(0.521399\pi\)
\(662\) 0 0
\(663\) −4.00008 + 1.48560i −0.155350 + 0.0576960i
\(664\) 0 0
\(665\) 54.0966i 2.09778i
\(666\) 0 0
\(667\) 1.72006 + 1.72006i 0.0666010 + 0.0666010i
\(668\) 0 0
\(669\) 16.6497 11.8212i 0.643714 0.457035i
\(670\) 0 0
\(671\) −7.14169 + 12.3698i −0.275702 + 0.477529i
\(672\) 0 0
\(673\) −8.32057 14.4116i −0.320734 0.555528i 0.659905 0.751349i \(-0.270596\pi\)
−0.980640 + 0.195821i \(0.937263\pi\)
\(674\) 0 0
\(675\) −0.900833 0.866166i −0.0346731 0.0333387i
\(676\) 0 0
\(677\) −3.57166 + 13.3296i −0.137270 + 0.512298i 0.862708 + 0.505702i \(0.168766\pi\)
−0.999978 + 0.00659653i \(0.997900\pi\)
\(678\) 0 0
\(679\) −23.0346 13.2990i −0.883985 0.510369i
\(680\) 0 0
\(681\) 7.69383 45.3666i 0.294828 1.73845i
\(682\) 0 0
\(683\) −32.4757 32.4757i −1.24265 1.24265i −0.958898 0.283751i \(-0.908421\pi\)
−0.283751 0.958898i \(-0.591579\pi\)
\(684\) 0 0
\(685\) 24.1504 24.1504i 0.922737 0.922737i
\(686\) 0 0
\(687\) −10.2691 27.6501i −0.391789 1.05492i
\(688\) 0 0
\(689\) −7.80481 + 13.5183i −0.297339 + 0.515007i
\(690\) 0 0
\(691\) −39.0522 10.4640i −1.48562 0.398070i −0.577362 0.816489i \(-0.695918\pi\)
−0.908254 + 0.418419i \(0.862584\pi\)
\(692\) 0 0
\(693\) −14.2666 29.5786i −0.541943 1.12360i
\(694\) 0 0
\(695\) −24.8996 + 14.3758i −0.944496 + 0.545305i
\(696\) 0 0
\(697\) 13.8231 + 7.98079i 0.523588 + 0.302294i
\(698\) 0 0
\(699\) 3.80465 0.357947i 0.143905 0.0135388i
\(700\) 0 0
\(701\) 8.81145 8.81145i 0.332804 0.332804i −0.520847 0.853650i \(-0.674384\pi\)
0.853650 + 0.520847i \(0.174384\pi\)
\(702\) 0 0
\(703\) 28.1487 1.06165
\(704\) 0 0
\(705\) 1.63055 1.96922i 0.0614101 0.0741652i
\(706\) 0 0
\(707\) 10.1868 + 38.0178i 0.383116 + 1.42981i
\(708\) 0 0
\(709\) 2.50097 9.33375i 0.0939260 0.350537i −0.902928 0.429791i \(-0.858587\pi\)
0.996854 + 0.0792544i \(0.0252539\pi\)
\(710\) 0 0
\(711\) 30.9757 + 35.9500i 1.16168 + 1.34823i
\(712\) 0 0
\(713\) 26.5723 15.3415i 0.995139 0.574544i
\(714\) 0 0
\(715\) 11.4006 3.05479i 0.426359 0.114242i
\(716\) 0 0
\(717\) −13.3836 6.13464i −0.499818 0.229102i
\(718\) 0 0
\(719\) −17.6869 −0.659611 −0.329805 0.944049i \(-0.606983\pi\)
−0.329805 + 0.944049i \(0.606983\pi\)
\(720\) 0 0
\(721\) 2.76922 0.103131
\(722\) 0 0
\(723\) 25.6858 18.2368i 0.955264 0.678235i
\(724\) 0 0
\(725\) −0.132346 + 0.0354620i −0.00491521 + 0.00131703i
\(726\) 0 0
\(727\) 32.8260 18.9521i 1.21745 0.702894i 0.253077 0.967446i \(-0.418557\pi\)
0.964371 + 0.264552i \(0.0852241\pi\)
\(728\) 0 0
\(729\) −22.8352 + 14.4068i −0.845747 + 0.533584i
\(730\) 0 0
\(731\) 4.78321 17.8512i 0.176914 0.660250i
\(732\) 0 0
\(733\) −10.2081 38.0971i −0.377044 1.40715i −0.850335 0.526242i \(-0.823601\pi\)
0.473291 0.880906i \(-0.343066\pi\)
\(734\) 0 0
\(735\) −9.80844 1.66344i −0.361790 0.0613568i
\(736\) 0 0
\(737\) 14.7768 0.544311
\(738\) 0 0
\(739\) 4.56683 4.56683i 0.167993 0.167993i −0.618103 0.786097i \(-0.712099\pi\)
0.786097 + 0.618103i \(0.212099\pi\)
\(740\) 0 0
\(741\) 8.03291 17.5249i 0.295096 0.643794i
\(742\) 0 0
\(743\) −10.7721 6.21930i −0.395192 0.228164i 0.289216 0.957264i \(-0.406606\pi\)
−0.684407 + 0.729100i \(0.739939\pi\)
\(744\) 0 0
\(745\) −30.6628 + 17.7032i −1.12340 + 0.648593i
\(746\) 0 0
\(747\) 28.9629 + 2.15267i 1.05970 + 0.0787620i
\(748\) 0 0
\(749\) −14.4744 3.87840i −0.528882 0.141714i
\(750\) 0 0
\(751\) 6.54573 11.3375i 0.238857 0.413713i −0.721530 0.692384i \(-0.756561\pi\)
0.960387 + 0.278671i \(0.0898939\pi\)
\(752\) 0 0
\(753\) 6.90946 8.34458i 0.251795 0.304093i
\(754\) 0 0
\(755\) −2.70966 + 2.70966i −0.0986148 + 0.0986148i
\(756\) 0 0
\(757\) −6.71290 6.71290i −0.243985 0.243985i 0.574512 0.818496i \(-0.305192\pi\)
−0.818496 + 0.574512i \(0.805192\pi\)
\(758\) 0 0
\(759\) −20.2210 16.7433i −0.733974 0.607743i
\(760\) 0 0
\(761\) 2.25713 + 1.30315i 0.0818208 + 0.0472393i 0.540352 0.841439i \(-0.318291\pi\)
−0.458531 + 0.888678i \(0.651624\pi\)
\(762\) 0 0
\(763\) 12.1257 45.2538i 0.438980 1.63830i
\(764\) 0 0
\(765\) −10.4921 + 5.06065i −0.379344 + 0.182968i
\(766\) 0 0
\(767\) 4.37583 + 7.57916i 0.158002 + 0.273668i
\(768\) 0 0
\(769\) 16.7811 29.0657i 0.605142 1.04814i −0.386887 0.922127i \(-0.626450\pi\)
0.992029 0.126010i \(-0.0402170\pi\)
\(770\) 0 0
\(771\) 1.36382 + 0.625135i 0.0491167 + 0.0225137i
\(772\) 0 0
\(773\) −22.0710 22.0710i −0.793837 0.793837i 0.188279 0.982116i \(-0.439709\pi\)
−0.982116 + 0.188279i \(0.939709\pi\)
\(774\) 0 0
\(775\) 1.72825i 0.0620806i
\(776\) 0 0
\(777\) 3.28037 19.3427i 0.117683 0.693914i
\(778\) 0 0
\(779\) −69.6561 + 18.6643i −2.49569 + 0.668718i
\(780\) 0 0
\(781\) 16.5182 + 4.42605i 0.591069 + 0.158377i
\(782\) 0 0
\(783\) 0.0580663 + 2.95967i 0.00207512 + 0.105770i
\(784\) 0 0
\(785\) 5.67770 + 9.83406i 0.202646 + 0.350993i
\(786\) 0 0
\(787\) 0.297829 + 1.11151i 0.0106165 + 0.0396212i 0.971031 0.238954i \(-0.0768045\pi\)
−0.960414 + 0.278575i \(0.910138\pi\)
\(788\) 0 0
\(789\) −8.78901 12.3789i −0.312897 0.440702i
\(790\) 0 0
\(791\) 42.6080i 1.51497i
\(792\) 0 0
\(793\) 5.84409i 0.207530i
\(794\) 0 0
\(795\) −17.7563 + 38.7379i −0.629752 + 1.37389i
\(796\) 0 0