Properties

Label 76.6.e.a.45.6
Level $76$
Weight $6$
Character 76.45
Analytic conductor $12.189$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} - 1275481376 x^{11} + 361098181456 x^{10} - 863969476320 x^{9} + 79755165392064 x^{8} - 375077568148992 x^{7} + 12736924096193536 x^{6} - 57314532742553600 x^{5} + 977121800205220864 x^{4} - 4977732006498379776 x^{3} + 53672321824823513088 x^{2} - 185653809995679793152 x + 804303742853852430336\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{3}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 45.6
Root \(-4.70426 + 8.14802i\) of defining polynomial
Character \(\chi\) \(=\) 76.45
Dual form 76.6.e.a.49.6

$q$-expansion

\(f(q)\) \(=\) \(q+(4.20426 + 7.28199i) q^{3} +(-18.6530 - 32.3080i) q^{5} +15.8772 q^{7} +(86.1484 - 149.213i) q^{9} +O(q^{10})\) \(q+(4.20426 + 7.28199i) q^{3} +(-18.6530 - 32.3080i) q^{5} +15.8772 q^{7} +(86.1484 - 149.213i) q^{9} -325.518 q^{11} +(519.710 - 900.165i) q^{13} +(156.844 - 271.662i) q^{15} +(778.938 + 1349.16i) q^{17} +(418.139 - 1516.99i) q^{19} +(66.7519 + 115.618i) q^{21} +(784.020 - 1357.96i) q^{23} +(866.629 - 1501.04i) q^{25} +3492.03 q^{27} +(4023.95 - 6969.69i) q^{29} -9529.39 q^{31} +(-1368.56 - 2370.42i) q^{33} +(-296.158 - 512.961i) q^{35} -451.140 q^{37} +8739.99 q^{39} +(2231.10 + 3864.38i) q^{41} +(5775.62 + 10003.7i) q^{43} -6427.72 q^{45} +(-3080.89 + 5336.26i) q^{47} -16554.9 q^{49} +(-6549.72 + 11344.4i) q^{51} +(-11186.9 + 19376.2i) q^{53} +(6071.91 + 10516.9i) q^{55} +(12804.7 - 3332.94i) q^{57} +(-3512.04 - 6083.03i) q^{59} +(4074.18 - 7056.68i) q^{61} +(1367.80 - 2369.09i) q^{63} -38776.7 q^{65} +(-27310.0 + 47302.3i) q^{67} +13184.9 q^{69} +(24835.7 + 43016.6i) q^{71} +(-29169.7 - 50523.3i) q^{73} +14574.1 q^{75} -5168.32 q^{77} +(-18324.7 - 31739.4i) q^{79} +(-6252.66 - 10829.9i) q^{81} +65668.7 q^{83} +(29059.1 - 50331.9i) q^{85} +67670.9 q^{87} +(-20103.8 + 34820.8i) q^{89} +(8251.55 - 14292.1i) q^{91} +(-40064.0 - 69393.0i) q^{93} +(-56810.5 + 14787.2i) q^{95} +(-5677.26 - 9833.30i) q^{97} +(-28042.9 + 48571.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10}) \) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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
\(3\) 4.20426 + 7.28199i 0.269703 + 0.467140i 0.968785 0.247902i \(-0.0797410\pi\)
−0.699082 + 0.715042i \(0.746408\pi\)
\(4\) 0 0
\(5\) −18.6530 32.3080i −0.333676 0.577943i 0.649554 0.760316i \(-0.274956\pi\)
−0.983230 + 0.182372i \(0.941622\pi\)
\(6\) 0 0
\(7\) 15.8772 0.122470 0.0612349 0.998123i \(-0.480496\pi\)
0.0612349 + 0.998123i \(0.480496\pi\)
\(8\) 0 0
\(9\) 86.1484 149.213i 0.354520 0.614047i
\(10\) 0 0
\(11\) −325.518 −0.811136 −0.405568 0.914065i \(-0.632926\pi\)
−0.405568 + 0.914065i \(0.632926\pi\)
\(12\) 0 0
\(13\) 519.710 900.165i 0.852909 1.47728i −0.0256616 0.999671i \(-0.508169\pi\)
0.878571 0.477612i \(-0.158497\pi\)
\(14\) 0 0
\(15\) 156.844 271.662i 0.179987 0.311746i
\(16\) 0 0
\(17\) 778.938 + 1349.16i 0.653703 + 1.13225i 0.982217 + 0.187748i \(0.0601190\pi\)
−0.328514 + 0.944499i \(0.606548\pi\)
\(18\) 0 0
\(19\) 418.139 1516.99i 0.265728 0.964048i
\(20\) 0 0
\(21\) 66.7519 + 115.618i 0.0330305 + 0.0572105i
\(22\) 0 0
\(23\) 784.020 1357.96i 0.309035 0.535264i −0.669116 0.743158i \(-0.733327\pi\)
0.978152 + 0.207893i \(0.0666606\pi\)
\(24\) 0 0
\(25\) 866.629 1501.04i 0.277321 0.480334i
\(26\) 0 0
\(27\) 3492.03 0.921868
\(28\) 0 0
\(29\) 4023.95 6969.69i 0.888501 1.53893i 0.0468525 0.998902i \(-0.485081\pi\)
0.841648 0.540026i \(-0.181586\pi\)
\(30\) 0 0
\(31\) −9529.39 −1.78099 −0.890494 0.454995i \(-0.849641\pi\)
−0.890494 + 0.454995i \(0.849641\pi\)
\(32\) 0 0
\(33\) −1368.56 2370.42i −0.218766 0.378914i
\(34\) 0 0
\(35\) −296.158 512.961i −0.0408652 0.0707806i
\(36\) 0 0
\(37\) −451.140 −0.0541760 −0.0270880 0.999633i \(-0.508623\pi\)
−0.0270880 + 0.999633i \(0.508623\pi\)
\(38\) 0 0
\(39\) 8739.99 0.920130
\(40\) 0 0
\(41\) 2231.10 + 3864.38i 0.207281 + 0.359021i 0.950857 0.309630i \(-0.100205\pi\)
−0.743576 + 0.668651i \(0.766872\pi\)
\(42\) 0 0
\(43\) 5775.62 + 10003.7i 0.476352 + 0.825066i 0.999633 0.0270946i \(-0.00862554\pi\)
−0.523281 + 0.852160i \(0.675292\pi\)
\(44\) 0 0
\(45\) −6427.72 −0.473179
\(46\) 0 0
\(47\) −3080.89 + 5336.26i −0.203438 + 0.352365i −0.949634 0.313362i \(-0.898545\pi\)
0.746196 + 0.665726i \(0.231878\pi\)
\(48\) 0 0
\(49\) −16554.9 −0.985001
\(50\) 0 0
\(51\) −6549.72 + 11344.4i −0.352612 + 0.610742i
\(52\) 0 0
\(53\) −11186.9 + 19376.2i −0.547039 + 0.947500i 0.451436 + 0.892303i \(0.350912\pi\)
−0.998476 + 0.0551965i \(0.982421\pi\)
\(54\) 0 0
\(55\) 6071.91 + 10516.9i 0.270656 + 0.468791i
\(56\) 0 0
\(57\) 12804.7 3332.94i 0.522013 0.135875i
\(58\) 0 0
\(59\) −3512.04 6083.03i −0.131350 0.227504i 0.792847 0.609420i \(-0.208598\pi\)
−0.924197 + 0.381916i \(0.875264\pi\)
\(60\) 0 0
\(61\) 4074.18 7056.68i 0.140189 0.242815i −0.787378 0.616470i \(-0.788562\pi\)
0.927568 + 0.373655i \(0.121896\pi\)
\(62\) 0 0
\(63\) 1367.80 2369.09i 0.0434180 0.0752022i
\(64\) 0 0
\(65\) −38776.7 −1.13838
\(66\) 0 0
\(67\) −27310.0 + 47302.3i −0.743250 + 1.28735i 0.207758 + 0.978180i \(0.433383\pi\)
−0.951008 + 0.309167i \(0.899950\pi\)
\(68\) 0 0
\(69\) 13184.9 0.333391
\(70\) 0 0
\(71\) 24835.7 + 43016.6i 0.584696 + 1.01272i 0.994913 + 0.100735i \(0.0321194\pi\)
−0.410218 + 0.911988i \(0.634547\pi\)
\(72\) 0 0
\(73\) −29169.7 50523.3i −0.640655 1.10965i −0.985287 0.170909i \(-0.945330\pi\)
0.344632 0.938738i \(-0.388004\pi\)
\(74\) 0 0
\(75\) 14574.1 0.299178
\(76\) 0 0
\(77\) −5168.32 −0.0993397
\(78\) 0 0
\(79\) −18324.7 31739.4i −0.330347 0.572177i 0.652233 0.758018i \(-0.273832\pi\)
−0.982580 + 0.185841i \(0.940499\pi\)
\(80\) 0 0
\(81\) −6252.66 10829.9i −0.105889 0.183406i
\(82\) 0 0
\(83\) 65668.7 1.04632 0.523158 0.852236i \(-0.324754\pi\)
0.523158 + 0.852236i \(0.324754\pi\)
\(84\) 0 0
\(85\) 29059.1 50331.9i 0.436250 0.755607i
\(86\) 0 0
\(87\) 67670.9 0.958526
\(88\) 0 0
\(89\) −20103.8 + 34820.8i −0.269032 + 0.465976i −0.968612 0.248577i \(-0.920037\pi\)
0.699580 + 0.714554i \(0.253370\pi\)
\(90\) 0 0
\(91\) 8251.55 14292.1i 0.104456 0.180923i
\(92\) 0 0
\(93\) −40064.0 69393.0i −0.480338 0.831971i
\(94\) 0 0
\(95\) −56810.5 + 14787.2i −0.645832 + 0.168104i
\(96\) 0 0
\(97\) −5677.26 9833.30i −0.0612645 0.106113i 0.833766 0.552117i \(-0.186180\pi\)
−0.895031 + 0.446004i \(0.852847\pi\)
\(98\) 0 0
\(99\) −28042.9 + 48571.7i −0.287564 + 0.498076i
\(100\) 0 0
\(101\) 96363.2 166906.i 0.939957 1.62805i 0.174409 0.984673i \(-0.444199\pi\)
0.765548 0.643379i \(-0.222468\pi\)
\(102\) 0 0
\(103\) 174119. 1.61716 0.808579 0.588387i \(-0.200237\pi\)
0.808579 + 0.588387i \(0.200237\pi\)
\(104\) 0 0
\(105\) 2490.25 4313.24i 0.0220430 0.0381795i
\(106\) 0 0
\(107\) −24682.3 −0.208413 −0.104207 0.994556i \(-0.533230\pi\)
−0.104207 + 0.994556i \(0.533230\pi\)
\(108\) 0 0
\(109\) 16094.5 + 27876.5i 0.129751 + 0.224735i 0.923580 0.383406i \(-0.125249\pi\)
−0.793829 + 0.608141i \(0.791916\pi\)
\(110\) 0 0
\(111\) −1896.71 3285.20i −0.0146115 0.0253078i
\(112\) 0 0
\(113\) 115981. 0.854455 0.427228 0.904144i \(-0.359490\pi\)
0.427228 + 0.904144i \(0.359490\pi\)
\(114\) 0 0
\(115\) −58497.4 −0.412470
\(116\) 0 0
\(117\) −89544.4 155095.i −0.604747 1.04745i
\(118\) 0 0
\(119\) 12367.4 + 21420.9i 0.0800589 + 0.138666i
\(120\) 0 0
\(121\) −55088.7 −0.342058
\(122\) 0 0
\(123\) −18760.3 + 32493.7i −0.111809 + 0.193659i
\(124\) 0 0
\(125\) −181242. −1.03749
\(126\) 0 0
\(127\) 94476.0 163637.i 0.519771 0.900270i −0.479964 0.877288i \(-0.659350\pi\)
0.999736 0.0229825i \(-0.00731621\pi\)
\(128\) 0 0
\(129\) −48564.4 + 84116.1i −0.256947 + 0.445046i
\(130\) 0 0
\(131\) 156242. + 270619.i 0.795462 + 1.37778i 0.922545 + 0.385889i \(0.126105\pi\)
−0.127083 + 0.991892i \(0.540562\pi\)
\(132\) 0 0
\(133\) 6638.88 24085.6i 0.0325436 0.118067i
\(134\) 0 0
\(135\) −65137.0 112821.i −0.307605 0.532787i
\(136\) 0 0
\(137\) 8354.62 14470.6i 0.0380299 0.0658697i −0.846384 0.532573i \(-0.821225\pi\)
0.884414 + 0.466703i \(0.154558\pi\)
\(138\) 0 0
\(139\) −37890.7 + 65628.7i −0.166340 + 0.288109i −0.937130 0.348980i \(-0.886528\pi\)
0.770790 + 0.637089i \(0.219862\pi\)
\(140\) 0 0
\(141\) −51811.4 −0.219471
\(142\) 0 0
\(143\) −169175. + 293020.i −0.691826 + 1.19828i
\(144\) 0 0
\(145\) −300236. −1.18588
\(146\) 0 0
\(147\) −69601.2 120553.i −0.265658 0.460133i
\(148\) 0 0
\(149\) 213642. + 370039.i 0.788353 + 1.36547i 0.926975 + 0.375123i \(0.122399\pi\)
−0.138622 + 0.990345i \(0.544267\pi\)
\(150\) 0 0
\(151\) −123090. −0.439319 −0.219659 0.975577i \(-0.570495\pi\)
−0.219659 + 0.975577i \(0.570495\pi\)
\(152\) 0 0
\(153\) 268417. 0.927004
\(154\) 0 0
\(155\) 177752. + 307876.i 0.594272 + 1.02931i
\(156\) 0 0
\(157\) 262647. + 454918.i 0.850401 + 1.47294i 0.880847 + 0.473401i \(0.156974\pi\)
−0.0304458 + 0.999536i \(0.509693\pi\)
\(158\) 0 0
\(159\) −188130. −0.590153
\(160\) 0 0
\(161\) 12448.1 21560.7i 0.0378475 0.0655537i
\(162\) 0 0
\(163\) −201402. −0.593737 −0.296868 0.954918i \(-0.595942\pi\)
−0.296868 + 0.954918i \(0.595942\pi\)
\(164\) 0 0
\(165\) −51055.7 + 88431.1i −0.145994 + 0.252869i
\(166\) 0 0
\(167\) −84718.2 + 146736.i −0.235064 + 0.407142i −0.959291 0.282419i \(-0.908863\pi\)
0.724227 + 0.689561i \(0.242197\pi\)
\(168\) 0 0
\(169\) −354551. 614100.i −0.954909 1.65395i
\(170\) 0 0
\(171\) −190333. 193078.i −0.497765 0.504944i
\(172\) 0 0
\(173\) 31933.9 + 55311.1i 0.0811216 + 0.140507i 0.903732 0.428099i \(-0.140816\pi\)
−0.822610 + 0.568605i \(0.807483\pi\)
\(174\) 0 0
\(175\) 13759.6 23832.4i 0.0339635 0.0588265i
\(176\) 0 0
\(177\) 29531.0 51149.3i 0.0708509 0.122717i
\(178\) 0 0
\(179\) 116034. 0.270677 0.135339 0.990799i \(-0.456788\pi\)
0.135339 + 0.990799i \(0.456788\pi\)
\(180\) 0 0
\(181\) 26722.9 46285.5i 0.0606301 0.105014i −0.834117 0.551587i \(-0.814022\pi\)
0.894747 + 0.446573i \(0.147356\pi\)
\(182\) 0 0
\(183\) 68515.6 0.151238
\(184\) 0 0
\(185\) 8415.13 + 14575.4i 0.0180772 + 0.0313107i
\(186\) 0 0
\(187\) −253559. 439177.i −0.530243 0.918407i
\(188\) 0 0
\(189\) 55443.7 0.112901
\(190\) 0 0
\(191\) 564257. 1.11916 0.559582 0.828775i \(-0.310962\pi\)
0.559582 + 0.828775i \(0.310962\pi\)
\(192\) 0 0
\(193\) 146535. + 253806.i 0.283170 + 0.490466i 0.972164 0.234302i \(-0.0752804\pi\)
−0.688993 + 0.724768i \(0.741947\pi\)
\(194\) 0 0
\(195\) −163027. 282372.i −0.307025 0.531783i
\(196\) 0 0
\(197\) 377908. 0.693778 0.346889 0.937906i \(-0.387238\pi\)
0.346889 + 0.937906i \(0.387238\pi\)
\(198\) 0 0
\(199\) 443715. 768537.i 0.794276 1.37573i −0.129021 0.991642i \(-0.541184\pi\)
0.923298 0.384085i \(-0.125483\pi\)
\(200\) 0 0
\(201\) −459274. −0.801828
\(202\) 0 0
\(203\) 63889.1 110659.i 0.108815 0.188472i
\(204\) 0 0
\(205\) 83233.6 144165.i 0.138329 0.239593i
\(206\) 0 0
\(207\) −135084. 233973.i −0.219118 0.379524i
\(208\) 0 0
\(209\) −136112. + 493808.i −0.215541 + 0.781975i
\(210\) 0 0
\(211\) 62683.9 + 108572.i 0.0969282 + 0.167885i 0.910412 0.413703i \(-0.135765\pi\)
−0.813484 + 0.581588i \(0.802432\pi\)
\(212\) 0 0
\(213\) −208831. + 361706.i −0.315389 + 0.546269i
\(214\) 0 0
\(215\) 215466. 373198.i 0.317894 0.550608i
\(216\) 0 0
\(217\) −151300. −0.218117
\(218\) 0 0
\(219\) 245274. 424826.i 0.345574 0.598551i
\(220\) 0 0
\(221\) 1.61929e6 2.23020
\(222\) 0 0
\(223\) 214409. + 371367.i 0.288723 + 0.500082i 0.973505 0.228665i \(-0.0734361\pi\)
−0.684782 + 0.728748i \(0.740103\pi\)
\(224\) 0 0
\(225\) −149317. 258625.i −0.196632 0.340576i
\(226\) 0 0
\(227\) 169489. 0.218312 0.109156 0.994025i \(-0.465185\pi\)
0.109156 + 0.994025i \(0.465185\pi\)
\(228\) 0 0
\(229\) −380975. −0.480073 −0.240037 0.970764i \(-0.577159\pi\)
−0.240037 + 0.970764i \(0.577159\pi\)
\(230\) 0 0
\(231\) −21729.0 37635.7i −0.0267923 0.0464056i
\(232\) 0 0
\(233\) −137211. 237656.i −0.165576 0.286787i 0.771283 0.636492i \(-0.219615\pi\)
−0.936860 + 0.349705i \(0.886282\pi\)
\(234\) 0 0
\(235\) 229872. 0.271529
\(236\) 0 0
\(237\) 154084. 266881.i 0.178191 0.308636i
\(238\) 0 0
\(239\) −1.30763e6 −1.48078 −0.740390 0.672178i \(-0.765359\pi\)
−0.740390 + 0.672178i \(0.765359\pi\)
\(240\) 0 0
\(241\) 284474. 492723.i 0.315500 0.546463i −0.664043 0.747694i \(-0.731161\pi\)
0.979544 + 0.201231i \(0.0644943\pi\)
\(242\) 0 0
\(243\) 476857. 825941.i 0.518051 0.897291i
\(244\) 0 0
\(245\) 308799. + 534856.i 0.328671 + 0.569275i
\(246\) 0 0
\(247\) −1.14823e6 1.16479e6i −1.19753 1.21480i
\(248\) 0 0
\(249\) 276088. + 478199.i 0.282195 + 0.488776i
\(250\) 0 0
\(251\) −687152. + 1.19018e6i −0.688443 + 1.19242i 0.283898 + 0.958855i \(0.408372\pi\)
−0.972341 + 0.233565i \(0.924961\pi\)
\(252\) 0 0
\(253\) −255213. + 442042.i −0.250670 + 0.434172i
\(254\) 0 0
\(255\) 488688. 0.470632
\(256\) 0 0
\(257\) −628934. + 1.08935e6i −0.593981 + 1.02880i 0.399709 + 0.916642i \(0.369111\pi\)
−0.993690 + 0.112162i \(0.964222\pi\)
\(258\) 0 0
\(259\) −7162.85 −0.00663493
\(260\) 0 0
\(261\) −693314. 1.20086e6i −0.629983 1.09116i
\(262\) 0 0
\(263\) 130295. + 225678.i 0.116155 + 0.201187i 0.918241 0.396022i \(-0.129610\pi\)
−0.802086 + 0.597209i \(0.796276\pi\)
\(264\) 0 0
\(265\) 834675. 0.730135
\(266\) 0 0
\(267\) −338086. −0.290235
\(268\) 0 0
\(269\) 649714. + 1.12534e6i 0.547447 + 0.948205i 0.998449 + 0.0556823i \(0.0177334\pi\)
−0.451002 + 0.892523i \(0.648933\pi\)
\(270\) 0 0
\(271\) 249281. + 431768.i 0.206189 + 0.357130i 0.950511 0.310691i \(-0.100560\pi\)
−0.744322 + 0.667821i \(0.767227\pi\)
\(272\) 0 0
\(273\) 138767. 0.112688
\(274\) 0 0
\(275\) −282104. + 488618.i −0.224945 + 0.389617i
\(276\) 0 0
\(277\) 420798. 0.329514 0.164757 0.986334i \(-0.447316\pi\)
0.164757 + 0.986334i \(0.447316\pi\)
\(278\) 0 0
\(279\) −820942. + 1.42191e6i −0.631396 + 1.09361i
\(280\) 0 0
\(281\) −1.22359e6 + 2.11933e6i −0.924425 + 1.60115i −0.131942 + 0.991257i \(0.542121\pi\)
−0.792483 + 0.609894i \(0.791212\pi\)
\(282\) 0 0
\(283\) −995765. 1.72472e6i −0.739079 1.28012i −0.952910 0.303252i \(-0.901928\pi\)
0.213831 0.976871i \(-0.431406\pi\)
\(284\) 0 0
\(285\) −346526. 351524.i −0.252711 0.256356i
\(286\) 0 0
\(287\) 35423.7 + 61355.6i 0.0253857 + 0.0439693i
\(288\) 0 0
\(289\) −503561. + 872194.i −0.354656 + 0.614283i
\(290\) 0 0
\(291\) 47737.3 82683.5i 0.0330465 0.0572382i
\(292\) 0 0
\(293\) 1.82155e6 1.23957 0.619786 0.784771i \(-0.287220\pi\)
0.619786 + 0.784771i \(0.287220\pi\)
\(294\) 0 0
\(295\) −131020. + 226934.i −0.0876564 + 0.151825i
\(296\) 0 0
\(297\) −1.13672e6 −0.747761
\(298\) 0 0
\(299\) −814927. 1.41149e6i −0.527158 0.913064i
\(300\) 0 0
\(301\) 91700.8 + 158830.i 0.0583387 + 0.101046i
\(302\) 0 0
\(303\) 1.62054e6 1.01404
\(304\) 0 0
\(305\) −303983. −0.187111
\(306\) 0 0
\(307\) 1.04066e6 + 1.80247e6i 0.630177 + 1.09150i 0.987515 + 0.157523i \(0.0503508\pi\)
−0.357339 + 0.933975i \(0.616316\pi\)
\(308\) 0 0
\(309\) 732041. + 1.26793e6i 0.436153 + 0.755439i
\(310\) 0 0
\(311\) −2.82534e6 −1.65642 −0.828208 0.560421i \(-0.810639\pi\)
−0.828208 + 0.560421i \(0.810639\pi\)
\(312\) 0 0
\(313\) −231895. + 401655.i −0.133792 + 0.231735i −0.925135 0.379637i \(-0.876049\pi\)
0.791343 + 0.611372i \(0.209382\pi\)
\(314\) 0 0
\(315\) −102054. −0.0579501
\(316\) 0 0
\(317\) 1.37200e6 2.37637e6i 0.766840 1.32821i −0.172428 0.985022i \(-0.555161\pi\)
0.939268 0.343184i \(-0.111505\pi\)
\(318\) 0 0
\(319\) −1.30987e6 + 2.26876e6i −0.720695 + 1.24828i
\(320\) 0 0
\(321\) −103771. 179736.i −0.0562098 0.0973582i
\(322\) 0 0
\(323\) 2.37237e6 617505.i 1.26525 0.329332i
\(324\) 0 0
\(325\) −900792. 1.56022e6i −0.473060 0.819363i
\(326\) 0 0
\(327\) −135331. + 234400.i −0.0699886 + 0.121224i
\(328\) 0 0
\(329\) −48915.9 + 84724.9i −0.0249150 + 0.0431540i
\(330\) 0 0
\(331\) −402928. −0.202142 −0.101071 0.994879i \(-0.532227\pi\)
−0.101071 + 0.994879i \(0.532227\pi\)
\(332\) 0 0
\(333\) −38865.0 + 67316.2i −0.0192065 + 0.0332666i
\(334\) 0 0
\(335\) 2.03766e6 0.992018
\(336\) 0 0
\(337\) −1.94189e6 3.36345e6i −0.931429 1.61328i −0.780880 0.624681i \(-0.785229\pi\)
−0.150549 0.988603i \(-0.548104\pi\)
\(338\) 0 0
\(339\) 487613. + 844570.i 0.230449 + 0.399150i
\(340\) 0 0
\(341\) 3.10199e6 1.44462
\(342\) 0 0
\(343\) −529694. −0.243103
\(344\) 0 0
\(345\) −245938. 425978.i −0.111244 0.192681i
\(346\) 0 0
\(347\) −308844. 534934.i −0.137694 0.238493i 0.788929 0.614484i \(-0.210636\pi\)
−0.926623 + 0.375991i \(0.877302\pi\)
\(348\) 0 0
\(349\) 3.25327e6 1.42974 0.714869 0.699258i \(-0.246486\pi\)
0.714869 + 0.699258i \(0.246486\pi\)
\(350\) 0 0
\(351\) 1.81484e6 3.14340e6i 0.786270 1.36186i
\(352\) 0 0
\(353\) −3.59695e6 −1.53637 −0.768187 0.640225i \(-0.778841\pi\)
−0.768187 + 0.640225i \(0.778841\pi\)
\(354\) 0 0
\(355\) 926521. 1.60478e6i 0.390197 0.675842i
\(356\) 0 0
\(357\) −103991. + 180118.i −0.0431843 + 0.0747975i
\(358\) 0 0
\(359\) 637110. + 1.10351e6i 0.260903 + 0.451897i 0.966482 0.256734i \(-0.0826465\pi\)
−0.705579 + 0.708631i \(0.749313\pi\)
\(360\) 0 0
\(361\) −2.12642e6 1.26863e6i −0.858778 0.512348i
\(362\) 0 0
\(363\) −231607. 401156.i −0.0922541 0.159789i
\(364\) 0 0
\(365\) −1.08821e6 + 1.88483e6i −0.427542 + 0.740524i
\(366\) 0 0
\(367\) 466637. 808238.i 0.180848 0.313238i −0.761322 0.648374i \(-0.775449\pi\)
0.942170 + 0.335137i \(0.108782\pi\)
\(368\) 0 0
\(369\) 768823. 0.293941
\(370\) 0 0
\(371\) −177616. + 307640.i −0.0669958 + 0.116040i
\(372\) 0 0
\(373\) −218803. −0.0814295 −0.0407147 0.999171i \(-0.512963\pi\)
−0.0407147 + 0.999171i \(0.512963\pi\)
\(374\) 0 0
\(375\) −761990. 1.31981e6i −0.279815 0.484654i
\(376\) 0 0
\(377\) −4.18258e6 7.24444e6i −1.51562 2.62513i
\(378\) 0 0
\(379\) 5.19678e6 1.85839 0.929193 0.369594i \(-0.120503\pi\)
0.929193 + 0.369594i \(0.120503\pi\)
\(380\) 0 0
\(381\) 1.58881e6 0.560736
\(382\) 0 0
\(383\) 1.96378e6 + 3.40136e6i 0.684062 + 1.18483i 0.973731 + 0.227703i \(0.0731214\pi\)
−0.289669 + 0.957127i \(0.593545\pi\)
\(384\) 0 0
\(385\) 96404.9 + 166978.i 0.0331472 + 0.0574127i
\(386\) 0 0
\(387\) 1.99024e6 0.675505
\(388\) 0 0
\(389\) 1.80860e6 3.13258e6i 0.605993 1.04961i −0.385901 0.922540i \(-0.626109\pi\)
0.991894 0.127070i \(-0.0405574\pi\)
\(390\) 0 0
\(391\) 2.44281e6 0.808069
\(392\) 0 0
\(393\) −1.31376e6 + 2.27551e6i −0.429078 + 0.743184i
\(394\) 0 0
\(395\) −683624. + 1.18407e6i −0.220457 + 0.381843i
\(396\) 0 0
\(397\) −456990. 791530.i −0.145523 0.252053i 0.784045 0.620704i \(-0.213153\pi\)
−0.929568 + 0.368651i \(0.879820\pi\)
\(398\) 0 0
\(399\) 203302. 52917.7i 0.0639308 0.0166406i
\(400\) 0 0
\(401\) 255520. + 442574.i 0.0793533 + 0.137444i 0.902971 0.429701i \(-0.141381\pi\)
−0.823618 + 0.567145i \(0.808048\pi\)
\(402\) 0 0
\(403\) −4.95252e6 + 8.57802e6i −1.51902 + 2.63102i
\(404\) 0 0
\(405\) −233262. + 404022.i −0.0706654 + 0.122396i
\(406\) 0 0
\(407\) 146854. 0.0439442
\(408\) 0 0
\(409\) 423156. 732928.i 0.125081 0.216647i −0.796683 0.604397i \(-0.793414\pi\)
0.921765 + 0.387750i \(0.126747\pi\)
\(410\) 0 0
\(411\) 140500. 0.0410272
\(412\) 0 0
\(413\) −55761.4 96581.5i −0.0160864 0.0278624i
\(414\) 0 0
\(415\) −1.22492e6 2.12162e6i −0.349130 0.604711i
\(416\) 0 0
\(417\) −637210. −0.179450
\(418\) 0 0
\(419\) −2.38214e6 −0.662877 −0.331438 0.943477i \(-0.607534\pi\)
−0.331438 + 0.943477i \(0.607534\pi\)
\(420\) 0 0
\(421\) 1.20667e6 + 2.09001e6i 0.331805 + 0.574704i 0.982866 0.184322i \(-0.0590090\pi\)
−0.651061 + 0.759026i \(0.725676\pi\)
\(422\) 0 0
\(423\) 530828. + 919420.i 0.144246 + 0.249841i
\(424\) 0 0
\(425\) 2.70020e6 0.725143
\(426\) 0 0
\(427\) 64686.6 112040.i 0.0171690 0.0297375i
\(428\) 0 0
\(429\) −2.84503e6 −0.746351
\(430\) 0 0
\(431\) −811120. + 1.40490e6i −0.210326 + 0.364295i −0.951816 0.306668i \(-0.900786\pi\)
0.741491 + 0.670963i \(0.234119\pi\)
\(432\) 0 0
\(433\) −1.54921e6 + 2.68330e6i −0.397090 + 0.687781i −0.993366 0.114999i \(-0.963313\pi\)
0.596275 + 0.802780i \(0.296647\pi\)
\(434\) 0 0
\(435\) −1.26227e6 2.18631e6i −0.319837 0.553974i
\(436\) 0 0
\(437\) −1.73219e6 1.75717e6i −0.433902 0.440159i
\(438\) 0 0
\(439\) 1.27415e6 + 2.20689e6i 0.315544 + 0.546538i 0.979553 0.201187i \(-0.0644798\pi\)
−0.664009 + 0.747724i \(0.731146\pi\)
\(440\) 0 0
\(441\) −1.42618e6 + 2.47022e6i −0.349203 + 0.604837i
\(442\) 0 0
\(443\) 2.21590e6 3.83805e6i 0.536463 0.929182i −0.462627 0.886553i \(-0.653093\pi\)
0.999091 0.0426292i \(-0.0135734\pi\)
\(444\) 0 0
\(445\) 1.49999e6 0.359077
\(446\) 0 0
\(447\) −1.79641e6 + 3.11148e6i −0.425243 + 0.736543i
\(448\) 0 0
\(449\) 3.77649e6 0.884041 0.442020 0.897005i \(-0.354262\pi\)
0.442020 + 0.897005i \(0.354262\pi\)
\(450\) 0 0
\(451\) −726265. 1.25793e6i −0.168133 0.291215i
\(452\) 0 0
\(453\) −517501. 896339.i −0.118486 0.205223i
\(454\) 0 0
\(455\) −615666. −0.139417
\(456\) 0 0
\(457\) −2.33032e6 −0.521946 −0.260973 0.965346i \(-0.584043\pi\)
−0.260973 + 0.965346i \(0.584043\pi\)
\(458\) 0 0
\(459\) 2.72008e6 + 4.71131e6i 0.602628 + 1.04378i
\(460\) 0 0
\(461\) −1.33563e6 2.31338e6i −0.292707 0.506984i 0.681742 0.731593i \(-0.261223\pi\)
−0.974449 + 0.224609i \(0.927889\pi\)
\(462\) 0 0
\(463\) −4.04208e6 −0.876299 −0.438150 0.898902i \(-0.644366\pi\)
−0.438150 + 0.898902i \(0.644366\pi\)
\(464\) 0 0
\(465\) −1.49463e6 + 2.58878e6i −0.320554 + 0.555217i
\(466\) 0 0
\(467\) −8.27237e6 −1.75525 −0.877623 0.479352i \(-0.840872\pi\)
−0.877623 + 0.479352i \(0.840872\pi\)
\(468\) 0 0
\(469\) −433607. + 751029.i −0.0910257 + 0.157661i
\(470\) 0 0
\(471\) −2.20847e6 + 3.82519e6i −0.458712 + 0.794513i
\(472\) 0 0
\(473\) −1.88007e6 3.25638e6i −0.386386 0.669241i
\(474\) 0 0
\(475\) −1.91470e6 1.94231e6i −0.389374 0.394989i
\(476\) 0 0
\(477\) 1.92746e6 + 3.33846e6i 0.387873 + 0.671816i
\(478\) 0 0
\(479\) −316364. + 547958.i −0.0630011 + 0.109121i −0.895806 0.444446i \(-0.853400\pi\)
0.832804 + 0.553567i \(0.186734\pi\)
\(480\) 0 0
\(481\) −234462. + 406100.i −0.0462073 + 0.0800333i
\(482\) 0 0
\(483\) 209339. 0.0408304
\(484\) 0 0
\(485\) −211796. + 366842.i −0.0408850 + 0.0708148i
\(486\) 0 0
\(487\) 6.59560e6 1.26018 0.630089 0.776523i \(-0.283019\pi\)
0.630089 + 0.776523i \(0.283019\pi\)
\(488\) 0 0
\(489\) −846745. 1.46660e6i −0.160133 0.277358i
\(490\) 0 0
\(491\) 1.84714e6 + 3.19933e6i 0.345776 + 0.598902i 0.985494 0.169707i \(-0.0542823\pi\)
−0.639718 + 0.768610i \(0.720949\pi\)
\(492\) 0 0
\(493\) 1.25376e7 2.32326
\(494\) 0 0
\(495\) 2.09234e6 0.383813
\(496\) 0 0
\(497\) 394321. + 682984.i 0.0716076 + 0.124028i
\(498\) 0 0
\(499\) 5.21061e6 + 9.02504e6i 0.936779 + 1.62255i 0.771431 + 0.636313i \(0.219541\pi\)
0.165347 + 0.986235i \(0.447125\pi\)
\(500\) 0 0
\(501\) −1.42471e6 −0.253590
\(502\) 0 0
\(503\) 2.40212e6 4.16060e6i 0.423326 0.733222i −0.572937 0.819600i \(-0.694196\pi\)
0.996262 + 0.0863777i \(0.0275292\pi\)
\(504\) 0 0
\(505\) −7.18986e6 −1.25456
\(506\) 0 0
\(507\) 2.98125e6 5.16367e6i 0.515084 0.892152i
\(508\) 0 0
\(509\) −3.40004e6 + 5.88905e6i −0.581688 + 1.00751i 0.413592 + 0.910462i \(0.364274\pi\)
−0.995279 + 0.0970502i \(0.969059\pi\)
\(510\) 0 0
\(511\) −463133. 802169.i −0.0784609 0.135898i
\(512\) 0 0
\(513\) 1.46015e6 5.29738e6i 0.244966 0.888725i
\(514\) 0 0
\(515\) −3.24784e6 5.62543e6i −0.539606 0.934626i
\(516\) 0 0
\(517\) 1.00289e6 1.73705e6i 0.165016 0.285816i
\(518\) 0 0
\(519\) −268517. + 465084.i −0.0437575 + 0.0757903i
\(520\) 0 0
\(521\) 1.12409e6 0.181429 0.0907145 0.995877i \(-0.471085\pi\)
0.0907145 + 0.995877i \(0.471085\pi\)
\(522\) 0 0
\(523\) −3.80982e6 + 6.59880e6i −0.609046 + 1.05490i 0.382352 + 0.924017i \(0.375114\pi\)
−0.991398 + 0.130882i \(0.958219\pi\)
\(524\) 0 0
\(525\) 231396. 0.0366403
\(526\) 0 0
\(527\) −7.42281e6 1.28567e7i −1.16424 2.01652i
\(528\) 0 0
\(529\) 1.98880e6 + 3.44470e6i 0.308995 + 0.535194i
\(530\) 0 0
\(531\) −1.21023e6 −0.186265
\(532\) 0 0
\(533\) 4.63811e6 0.707168
\(534\) 0 0
\(535\) 460399. + 797435.i 0.0695425 + 0.120451i
\(536\) 0 0
\(537\) 487836. + 844956.i 0.0730025 + 0.126444i
\(538\) 0 0
\(539\) 5.38893e6 0.798970
\(540\) 0 0
\(541\) 1.96214e6 3.39853e6i 0.288228 0.499226i −0.685159 0.728394i \(-0.740267\pi\)
0.973387 + 0.229168i \(0.0736004\pi\)
\(542\) 0 0
\(543\) 449401. 0.0654085
\(544\) 0 0
\(545\) 600422. 1.03996e6i 0.0865895 0.149977i
\(546\) 0 0
\(547\) 6.72115e6 1.16414e7i 0.960451 1.66355i 0.239080 0.971000i \(-0.423154\pi\)
0.721370 0.692549i \(-0.243513\pi\)
\(548\) 0 0
\(549\) −701968. 1.21584e6i −0.0994000 0.172166i
\(550\) 0 0
\(551\) −8.89038e6 9.01859e6i −1.24750 1.26549i
\(552\) 0 0
\(553\) −290946. 503933.i −0.0404575 0.0700745i
\(554\) 0 0
\(555\) −70758.8 + 122558.i −0.00975098 + 0.0168892i
\(556\) 0 0
\(557\) 969505. 1.67923e6i 0.132407 0.229336i −0.792197 0.610266i \(-0.791063\pi\)
0.924604 + 0.380930i \(0.124396\pi\)
\(558\) 0 0
\(559\) 1.20066e7 1.62514
\(560\) 0 0
\(561\) 2.13205e6 3.69283e6i 0.286016 0.495395i
\(562\) 0 0
\(563\) −7.32095e6 −0.973412 −0.486706 0.873566i \(-0.661802\pi\)
−0.486706 + 0.873566i \(0.661802\pi\)
\(564\) 0 0
\(565\) −2.16339e6 3.74710e6i −0.285111 0.493826i
\(566\) 0 0
\(567\) −99274.8 171949.i −0.0129682 0.0224617i
\(568\) 0 0
\(569\) 6.26910e6 0.811754 0.405877 0.913928i \(-0.366966\pi\)
0.405877 + 0.913928i \(0.366966\pi\)
\(570\) 0 0
\(571\) 7.57087e6 0.971753 0.485876 0.874028i \(-0.338501\pi\)
0.485876 + 0.874028i \(0.338501\pi\)
\(572\) 0 0
\(573\) 2.37228e6 + 4.10892e6i 0.301842 + 0.522806i
\(574\) 0 0
\(575\) −1.35891e6 2.35370e6i −0.171404 0.296880i
\(576\) 0 0
\(577\) −8.39531e6 −1.04978 −0.524889 0.851171i \(-0.675893\pi\)
−0.524889 + 0.851171i \(0.675893\pi\)
\(578\) 0 0
\(579\) −1.23214e6 + 2.13413e6i −0.152744 + 0.264560i
\(580\) 0 0
\(581\) 1.04264e6 0.128142
\(582\) 0 0
\(583\) 3.64153e6 6.30731e6i 0.443723 0.768552i
\(584\) 0 0
\(585\) −3.34055e6 + 5.78600e6i −0.403579 + 0.699019i
\(586\) 0 0
\(587\) −5.58455e6 9.67272e6i −0.668949 1.15865i −0.978199 0.207672i \(-0.933411\pi\)
0.309250 0.950981i \(-0.399922\pi\)
\(588\) 0 0
\(589\) −3.98461e6 + 1.44560e7i −0.473258 + 1.71696i
\(590\) 0 0
\(591\) 1.58882e6 + 2.75192e6i 0.187114 + 0.324091i
\(592\) 0 0
\(593\) −3.63578e6 + 6.29735e6i −0.424581 + 0.735396i −0.996381 0.0849969i \(-0.972912\pi\)
0.571800 + 0.820393i \(0.306245\pi\)
\(594\) 0 0
\(595\) 461378. 799130.i 0.0534274 0.0925390i
\(596\) 0 0
\(597\) 7.46198e6 0.856876
\(598\) 0 0
\(599\) 1.55634e6 2.69567e6i 0.177231 0.306972i −0.763700 0.645571i \(-0.776620\pi\)
0.940931 + 0.338599i \(0.109953\pi\)
\(600\) 0 0
\(601\) 1.24917e6 0.141070 0.0705350 0.997509i \(-0.477529\pi\)
0.0705350 + 0.997509i \(0.477529\pi\)
\(602\) 0 0
\(603\) 4.70543e6 + 8.15004e6i 0.526994 + 0.912781i
\(604\) 0 0
\(605\) 1.02757e6 + 1.77981e6i 0.114136 + 0.197690i
\(606\) 0 0
\(607\) −7.52150e6 −0.828577 −0.414288 0.910146i \(-0.635969\pi\)
−0.414288 + 0.910146i \(0.635969\pi\)
\(608\) 0 0
\(609\) 1.07443e6 0.117391
\(610\) 0 0
\(611\) 3.20234e6 + 5.54662e6i 0.347028 + 0.601070i
\(612\) 0 0
\(613\) −1.18369e6 2.05021e6i −0.127229 0.220367i 0.795373 0.606120i \(-0.207275\pi\)
−0.922602 + 0.385753i \(0.873942\pi\)
\(614\) 0 0
\(615\) 1.39974e6 0.149231
\(616\) 0 0
\(617\) 8.23863e6 1.42697e7i 0.871249 1.50905i 0.0105434 0.999944i \(-0.496644\pi\)
0.860706 0.509103i \(-0.170023\pi\)
\(618\) 0 0
\(619\) −1.22489e7 −1.28491 −0.642453 0.766325i \(-0.722083\pi\)
−0.642453 + 0.766325i \(0.722083\pi\)
\(620\) 0 0
\(621\) 2.73782e6 4.74205e6i 0.284889 0.493443i
\(622\) 0 0
\(623\) −319192. + 552857.i −0.0329483 + 0.0570680i
\(624\) 0 0
\(625\) 672507. + 1.16482e6i 0.0688647 + 0.119277i
\(626\) 0 0
\(627\) −4.16816e6 + 1.08493e6i −0.423424 + 0.110213i
\(628\) 0 0
\(629\) −351410. 608661.i −0.0354151 0.0613407i
\(630\) 0 0
\(631\) −8.33519e6 + 1.44370e7i −0.833378 + 1.44345i 0.0619660 + 0.998078i \(0.480263\pi\)
−0.895344 + 0.445375i \(0.853070\pi\)
\(632\) 0 0
\(633\) −527079. + 912928.i −0.0522837 + 0.0905580i
\(634\) 0 0
\(635\) −7.04906e6 −0.693740
\(636\) 0 0
\(637\) −8.60376e6 + 1.49021e7i −0.840117 + 1.45512i
\(638\) 0 0
\(639\) 8.55821e6 0.829146
\(640\) 0 0
\(641\) 7.23074e6 + 1.25240e7i 0.695084 + 1.20392i 0.970152 + 0.242496i \(0.0779663\pi\)
−0.275068 + 0.961425i \(0.588700\pi\)
\(642\) 0 0
\(643\) −2.79841e6 4.84699e6i −0.266922 0.462322i 0.701144 0.713020i \(-0.252673\pi\)
−0.968065 + 0.250698i \(0.919340\pi\)
\(644\) 0 0
\(645\) 3.62350e6 0.342948
\(646\) 0 0
\(647\) −8.75822e6 −0.822536 −0.411268 0.911514i \(-0.634914\pi\)
−0.411268 + 0.911514i \(0.634914\pi\)
\(648\) 0 0
\(649\) 1.14323e6 + 1.98014e6i 0.106543 + 0.184537i
\(650\) 0 0
\(651\) −636105. 1.10177e6i −0.0588270 0.101891i
\(652\) 0 0
\(653\) 4.42311e6 0.405924 0.202962 0.979187i \(-0.434943\pi\)
0.202962 + 0.979187i \(0.434943\pi\)
\(654\) 0 0
\(655\) 5.82877e6 1.00957e7i 0.530853 0.919464i
\(656\) 0 0
\(657\) −1.00517e7 −0.908500
\(658\) 0 0
\(659\) −3.31380e6 + 5.73967e6i −0.297244 + 0.514842i −0.975504 0.219980i \(-0.929401\pi\)
0.678260 + 0.734822i \(0.262734\pi\)
\(660\) 0 0
\(661\) −4.70847e6 + 8.15532e6i −0.419157 + 0.726001i −0.995855 0.0909565i \(-0.971008\pi\)
0.576698 + 0.816957i \(0.304341\pi\)
\(662\) 0 0
\(663\) 6.80791e6 + 1.17916e7i 0.601492 + 1.04182i
\(664\) 0 0
\(665\) −901992. + 234780.i −0.0790949 + 0.0205877i
\(666\) 0 0
\(667\) −6.30972e6 1.09288e7i −0.549156 0.951166i
\(668\) 0 0
\(669\) −1.80286e6 + 3.12265e6i −0.155739 + 0.269748i
\(670\) 0 0
\(671\) −1.32622e6 + 2.29708e6i −0.113713 + 0.196956i
\(672\) 0 0
\(673\) −6.15773e6 −0.524062 −0.262031 0.965059i \(-0.584392\pi\)
−0.262031 + 0.965059i \(0.584392\pi\)
\(674\) 0 0
\(675\) 3.02629e6 5.24170e6i 0.255653 0.442805i
\(676\) 0 0
\(677\) −4.98624e6 −0.418120 −0.209060 0.977903i \(-0.567040\pi\)
−0.209060 + 0.977903i \(0.567040\pi\)
\(678\) 0 0
\(679\) −90139.0 156125.i −0.00750306 0.0129957i
\(680\) 0 0
\(681\) 712577. + 1.23422e6i 0.0588795 + 0.101982i
\(682\) 0 0
\(683\) −4.31513e6 −0.353951 −0.176975 0.984215i \(-0.556631\pi\)
−0.176975 + 0.984215i \(0.556631\pi\)
\(684\) 0 0
\(685\) −623356. −0.0507586
\(686\) 0 0
\(687\) −1.60172e6 2.77426e6i −0.129477 0.224261i
\(688\) 0 0
\(689\) 1.16279e7 + 2.01400e7i 0.933150 + 1.61626i
\(690\) 0 0
\(691\) 4.03514e6 0.321487 0.160744 0.986996i \(-0.448611\pi\)
0.160744 + 0.986996i \(0.448611\pi\)
\(692\) 0 0
\(693\) −445243. + 771183.i −0.0352179 + 0.0609993i
\(694\) 0 0
\(695\) 2.82711e6 0.222014
\(696\) 0 0
\(697\) −3.47578e6 + 6.02023e6i −0.271001 + 0.469387i
\(698\) 0 0
\(699\) 1.15374e6 1.99834e6i 0.0893130 0.154695i
\(700\) 0 0
\(701\) −8.80091e6 1.52436e7i −0.676445 1.17164i −0.976044 0.217572i \(-0.930186\pi\)
0.299599 0.954065i \(-0.403147\pi\)
\(702\) 0 0
\(703\) −188639. + 684375.i −0.0143961 + 0.0522283i
\(704\) 0 0
\(705\) 966441. + 1.67392e6i 0.0732322 + 0.126842i
\(706\) 0 0
\(707\) 1.52998e6 2.65000e6i 0.115116 0.199387i
\(708\) 0 0
\(709\) 1.41587e6 2.45236e6i 0.105781 0.183218i −0.808276 0.588804i \(-0.799599\pi\)
0.914057 + 0.405586i \(0.132932\pi\)
\(710\) 0 0
\(711\) −6.31459e6 −0.468458
\(712\) 0 0
\(713\) −7.47124e6 + 1.29406e7i −0.550388 + 0.953300i
\(714\) 0 0
\(715\) 1.26225e7 0.923382
\(716\) 0 0
\(717\) −5.49762e6 9.52215e6i −0.399371 0.691731i
\(718\) 0 0
\(719\) −2.92205e6 5.06114e6i −0.210797 0.365112i 0.741167 0.671321i \(-0.234273\pi\)
−0.951964 + 0.306209i \(0.900939\pi\)
\(720\) 0 0
\(721\) 2.76452e6 0.198053
\(722\) 0 0
\(723\) 4.78401e6 0.340366
\(724\) 0 0
\(725\) −6.97454e6 1.20803e7i −0.492800 0.853555i
\(726\) 0 0
\(727\) −3.41280e6 5.91114e6i −0.239483 0.414797i 0.721083 0.692849i \(-0.243645\pi\)
−0.960566 + 0.278052i \(0.910311\pi\)
\(728\) 0 0
\(729\) 4.98054e6 0.347102
\(730\) 0 0
\(731\) −8.99771e6 + 1.55845e7i −0.622786 + 1.07870i
\(732\) 0 0
\(733\) 1.74557e7 1.19999 0.599994 0.800005i \(-0.295170\pi\)
0.599994 + 0.800005i \(0.295170\pi\)
\(734\) 0 0
\(735\) −2.59655e6 + 4.49735e6i −0.177287 + 0.307071i
\(736\) 0 0
\(737\) 8.88991e6 1.53978e7i 0.602877 1.04421i
\(738\) 0 0
\(739\) 887503. + 1.53720e6i 0.0597804 + 0.103543i 0.894367 0.447334i \(-0.147627\pi\)
−0.834586 + 0.550877i \(0.814293\pi\)
\(740\) 0 0
\(741\) 3.65453e6 1.32585e7i 0.244504 0.887050i
\(742\) 0 0
\(743\) 1.00081e7 + 1.73345e7i 0.665089 + 1.15197i 0.979261 + 0.202602i \(0.0649398\pi\)
−0.314172 + 0.949366i \(0.601727\pi\)
\(744\) 0 0
\(745\) 7.97014e6 1.38047e7i 0.526109 0.911247i
\(746\) 0 0
\(747\) 5.65725e6 9.79865e6i 0.370940 0.642488i
\(748\) 0 0
\(749\) −391886. −0.0255244
\(750\) 0 0
\(751\) 4.81707e6 8.34342e6i 0.311662 0.539814i −0.667061 0.745004i \(-0.732448\pi\)
0.978722 + 0.205190i \(0.0657811\pi\)
\(752\) 0 0
\(753\) −1.15559e7 −0.742702
\(754\) 0 0
\(755\) 2.29600e6 + 3.97679e6i 0.146590 + 0.253901i
\(756\) 0 0
\(757\) −1.23551e6 2.13997e6i −0.0783623 0.135728i 0.824181 0.566326i \(-0.191636\pi\)
−0.902543 + 0.430599i \(0.858302\pi\)
\(758\) 0 0
\(759\) −4.29193e6 −0.270426
\(760\) 0 0
\(761\) 2.42819e7 1.51992 0.759960 0.649970i \(-0.225218\pi\)
0.759960 + 0.649970i \(0.225218\pi\)
\(762\) 0 0
\(763\) 255536. + 442601.i 0.0158906 + 0.0275233i
\(764\) 0 0
\(765\) −5.00679e6 8.67202e6i −0.309319 0.535756i
\(766\) 0 0
\(767\) −7.30097e6 −0.448118
\(768\) 0 0
\(769\) −2.98240e6 + 5.16567e6i −0.181866 + 0.315000i −0.942516 0.334161i \(-0.891547\pi\)
0.760650 + 0.649162i \(0.224880\pi\)
\(770\) 0 0
\(771\) −1.05768e7 −0.640794
\(772\) 0 0
\(773\) −4.87274e6 + 8.43984e6i −0.293308 + 0.508025i −0.974590 0.223996i \(-0.928090\pi\)
0.681282 + 0.732022i \(0.261423\pi\)
\(774\) 0 0
\(775\) −8.25845e6 + 1.43040e7i −0.493906 + 0.855470i
\(776\) 0 0
\(777\) −30114.5 52159.8i −0.00178946 0.00309944i
\(778\) 0 0
\(779\) 6.79514e6 1.76871e6i 0.401194 0.104427i
\(780\) 0 0
\(781\) −8.08447e6 1.40027e7i −0.474268 0.821456i
\(782\) 0 0
\(783\) 1.40518e7 2.43384e7i 0.819080 1.41869i
\(784\) 0 0
\(785\) 9.79834e6 1.69712e7i 0.567516 0.982967i
\(786\) 0 0
\(787\) 1.96481e7 1.13080 0.565398 0.824818i \(-0.308723\pi\)
0.565398 + 0.824818i \(0.308723\pi\)
\(788\) 0 0
\(789\) −1.09559e6 + 1.89762e6i −0.0626550