Properties

Label 804.2.q.b.241.4
Level 804
Weight 2
Character 804.241
Analytic conductor 6.420
Analytic rank 0
Dimension 60
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 241.4
Character \(\chi\) = 804.241
Dual form 804.2.q.b.397.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.415415 + 0.909632i) q^{3} +(1.61021 + 0.472801i) q^{5} +(-1.73357 - 2.00064i) q^{7} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\) \(q+(-0.415415 + 0.909632i) q^{3} +(1.61021 + 0.472801i) q^{5} +(-1.73357 - 2.00064i) q^{7} +(-0.654861 - 0.755750i) q^{9} +(-4.86843 - 1.42950i) q^{11} +(-1.52774 - 0.981818i) q^{13} +(-1.09898 + 1.26829i) q^{15} +(-0.741435 - 5.15679i) q^{17} +(-5.41739 + 6.25200i) q^{19} +(2.54000 - 0.745811i) q^{21} +(-1.76573 + 3.86640i) q^{23} +(-1.83702 - 1.18058i) q^{25} +(0.959493 - 0.281733i) q^{27} -5.92850 q^{29} +(5.48491 - 3.52494i) q^{31} +(3.32273 - 3.83464i) q^{33} +(-1.84551 - 4.04109i) q^{35} +3.97126 q^{37} +(1.52774 - 0.981818i) q^{39} +(-0.509333 - 3.54249i) q^{41} +(0.150600 + 1.04744i) q^{43} +(-0.697146 - 1.52654i) q^{45} +(-2.23155 + 4.88641i) q^{47} +(-0.00111521 + 0.00775643i) q^{49} +(4.99879 + 1.46778i) q^{51} +(-0.275366 + 1.91521i) q^{53} +(-7.16333 - 4.60359i) q^{55} +(-3.43656 - 7.52501i) q^{57} +(-0.666382 + 0.428258i) q^{59} +(0.419761 - 0.123253i) q^{61} +(-0.376740 + 2.62029i) q^{63} +(-1.99578 - 2.30325i) q^{65} +(-1.49365 - 8.04792i) q^{67} +(-2.78350 - 3.21232i) q^{69} +(0.458922 - 3.19187i) q^{71} +(6.68618 - 1.96324i) q^{73} +(1.83702 - 1.18058i) q^{75} +(5.57983 + 12.2181i) q^{77} +(-9.05517 - 5.81941i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(-16.4522 - 4.83081i) q^{83} +(1.24427 - 8.65408i) q^{85} +(2.46279 - 5.39276i) q^{87} +(4.61371 + 10.1026i) q^{89} +(0.684170 + 4.75851i) q^{91} +(0.927882 + 6.45356i) q^{93} +(-11.6791 + 7.50571i) q^{95} +11.4218 q^{97} +(2.10780 + 4.61543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} + O(q^{10}) \) \( 60q + 6q^{3} + 2q^{5} + 2q^{7} - 6q^{9} - 11q^{11} - 2q^{13} + 9q^{15} + 21q^{17} + 10q^{19} - 2q^{21} - 10q^{23} - 36q^{25} + 6q^{27} + 4q^{29} - 24q^{31} - 32q^{35} + 2q^{37} + 2q^{39} + 10q^{41} + 23q^{43} + 2q^{45} + 66q^{47} + 34q^{49} + 23q^{51} - 13q^{53} + 27q^{55} + q^{57} + 35q^{59} + 56q^{61} - 9q^{63} + 48q^{65} + 13q^{67} + 10q^{69} + 76q^{71} - q^{73} + 36q^{75} - 38q^{77} - 46q^{79} - 6q^{81} - 26q^{83} + 42q^{85} + 7q^{87} + 58q^{89} - 40q^{91} - 9q^{93} - 29q^{95} - 46q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{11}\right)\) \(1\)

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
\(3\) −0.415415 + 0.909632i −0.239840 + 0.525176i
\(4\) 0 0
\(5\) 1.61021 + 0.472801i 0.720109 + 0.211443i 0.621198 0.783653i \(-0.286646\pi\)
0.0989104 + 0.995096i \(0.468464\pi\)
\(6\) 0 0
\(7\) −1.73357 2.00064i −0.655227 0.756172i 0.326763 0.945106i \(-0.394042\pi\)
−0.981990 + 0.188934i \(0.939497\pi\)
\(8\) 0 0
\(9\) −0.654861 0.755750i −0.218287 0.251917i
\(10\) 0 0
\(11\) −4.86843 1.42950i −1.46789 0.431010i −0.552474 0.833530i \(-0.686316\pi\)
−0.915411 + 0.402520i \(0.868134\pi\)
\(12\) 0 0
\(13\) −1.52774 0.981818i −0.423718 0.272307i 0.311357 0.950293i \(-0.399217\pi\)
−0.735075 + 0.677986i \(0.762853\pi\)
\(14\) 0 0
\(15\) −1.09898 + 1.26829i −0.283756 + 0.327472i
\(16\) 0 0
\(17\) −0.741435 5.15679i −0.179824 1.25071i −0.857167 0.515038i \(-0.827778\pi\)
0.677343 0.735668i \(-0.263131\pi\)
\(18\) 0 0
\(19\) −5.41739 + 6.25200i −1.24284 + 1.43431i −0.382991 + 0.923752i \(0.625106\pi\)
−0.859845 + 0.510556i \(0.829440\pi\)
\(20\) 0 0
\(21\) 2.54000 0.745811i 0.554274 0.162749i
\(22\) 0 0
\(23\) −1.76573 + 3.86640i −0.368180 + 0.806201i 0.631349 + 0.775499i \(0.282502\pi\)
−0.999529 + 0.0307021i \(0.990226\pi\)
\(24\) 0 0
\(25\) −1.83702 1.18058i −0.367405 0.236117i
\(26\) 0 0
\(27\) 0.959493 0.281733i 0.184655 0.0542195i
\(28\) 0 0
\(29\) −5.92850 −1.10090 −0.550448 0.834870i \(-0.685543\pi\)
−0.550448 + 0.834870i \(0.685543\pi\)
\(30\) 0 0
\(31\) 5.48491 3.52494i 0.985119 0.633098i 0.0542796 0.998526i \(-0.482714\pi\)
0.930840 + 0.365428i \(0.119077\pi\)
\(32\) 0 0
\(33\) 3.32273 3.83464i 0.578414 0.667525i
\(34\) 0 0
\(35\) −1.84551 4.04109i −0.311947 0.683070i
\(36\) 0 0
\(37\) 3.97126 0.652870 0.326435 0.945220i \(-0.394152\pi\)
0.326435 + 0.945220i \(0.394152\pi\)
\(38\) 0 0
\(39\) 1.52774 0.981818i 0.244634 0.157217i
\(40\) 0 0
\(41\) −0.509333 3.54249i −0.0795444 0.553243i −0.990155 0.139977i \(-0.955297\pi\)
0.910610 0.413266i \(-0.135612\pi\)
\(42\) 0 0
\(43\) 0.150600 + 1.04744i 0.0229662 + 0.159734i 0.998077 0.0619840i \(-0.0197428\pi\)
−0.975111 + 0.221718i \(0.928834\pi\)
\(44\) 0 0
\(45\) −0.697146 1.52654i −0.103924 0.227563i
\(46\) 0 0
\(47\) −2.23155 + 4.88641i −0.325505 + 0.712756i −0.999666 0.0258281i \(-0.991778\pi\)
0.674162 + 0.738584i \(0.264505\pi\)
\(48\) 0 0
\(49\) −0.00111521 + 0.00775643i −0.000159315 + 0.00110806i
\(50\) 0 0
\(51\) 4.99879 + 1.46778i 0.699970 + 0.205530i
\(52\) 0 0
\(53\) −0.275366 + 1.91521i −0.0378244 + 0.263074i −0.999955 0.00951541i \(-0.996971\pi\)
0.962130 + 0.272590i \(0.0878802\pi\)
\(54\) 0 0
\(55\) −7.16333 4.60359i −0.965903 0.620748i
\(56\) 0 0
\(57\) −3.43656 7.52501i −0.455183 0.996712i
\(58\) 0 0
\(59\) −0.666382 + 0.428258i −0.0867556 + 0.0557544i −0.583299 0.812257i \(-0.698239\pi\)
0.496544 + 0.868012i \(0.334602\pi\)
\(60\) 0 0
\(61\) 0.419761 0.123253i 0.0537449 0.0157809i −0.254750 0.967007i \(-0.581993\pi\)
0.308494 + 0.951226i \(0.400175\pi\)
\(62\) 0 0
\(63\) −0.376740 + 2.62029i −0.0474648 + 0.330125i
\(64\) 0 0
\(65\) −1.99578 2.30325i −0.247546 0.285683i
\(66\) 0 0
\(67\) −1.49365 8.04792i −0.182479 0.983210i
\(68\) 0 0
\(69\) −2.78350 3.21232i −0.335093 0.386718i
\(70\) 0 0
\(71\) 0.458922 3.19187i 0.0544640 0.378805i −0.944299 0.329088i \(-0.893259\pi\)
0.998763 0.0497176i \(-0.0158321\pi\)
\(72\) 0 0
\(73\) 6.68618 1.96324i 0.782558 0.229780i 0.134037 0.990976i \(-0.457206\pi\)
0.648521 + 0.761196i \(0.275388\pi\)
\(74\) 0 0
\(75\) 1.83702 1.18058i 0.212121 0.136322i
\(76\) 0 0
\(77\) 5.57983 + 12.2181i 0.635881 + 1.39238i
\(78\) 0 0
\(79\) −9.05517 5.81941i −1.01879 0.654734i −0.0791338 0.996864i \(-0.525215\pi\)
−0.939653 + 0.342130i \(0.888852\pi\)
\(80\) 0 0
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) 0 0
\(83\) −16.4522 4.83081i −1.80587 0.530250i −0.807633 0.589686i \(-0.799252\pi\)
−0.998232 + 0.0594357i \(0.981070\pi\)
\(84\) 0 0
\(85\) 1.24427 8.65408i 0.134960 0.938667i
\(86\) 0 0
\(87\) 2.46279 5.39276i 0.264039 0.578164i
\(88\) 0 0
\(89\) 4.61371 + 10.1026i 0.489053 + 1.07088i 0.979874 + 0.199616i \(0.0639694\pi\)
−0.490822 + 0.871260i \(0.663303\pi\)
\(90\) 0 0
\(91\) 0.684170 + 4.75851i 0.0717205 + 0.498827i
\(92\) 0 0
\(93\) 0.927882 + 6.45356i 0.0962169 + 0.669203i
\(94\) 0 0
\(95\) −11.6791 + 7.50571i −1.19825 + 0.770069i
\(96\) 0 0
\(97\) 11.4218 1.15971 0.579853 0.814721i \(-0.303110\pi\)
0.579853 + 0.814721i \(0.303110\pi\)
\(98\) 0 0
\(99\) 2.10780 + 4.61543i 0.211842 + 0.463869i
\(100\) 0 0
\(101\) −3.93723 + 4.54381i −0.391769 + 0.452126i −0.917032 0.398815i \(-0.869422\pi\)
0.525262 + 0.850940i \(0.323967\pi\)
\(102\) 0 0
\(103\) 14.1228 9.07620i 1.39157 0.894305i 0.391896 0.920009i \(-0.371819\pi\)
0.999670 + 0.0257045i \(0.00818289\pi\)
\(104\) 0 0
\(105\) 4.44256 0.433549
\(106\) 0 0
\(107\) −10.2521 + 3.01029i −0.991108 + 0.291016i −0.736802 0.676108i \(-0.763665\pi\)
−0.254306 + 0.967124i \(0.581847\pi\)
\(108\) 0 0
\(109\) −6.17414 3.96788i −0.591375 0.380054i 0.210457 0.977603i \(-0.432505\pi\)
−0.801832 + 0.597549i \(0.796141\pi\)
\(110\) 0 0
\(111\) −1.64972 + 3.61238i −0.156584 + 0.342872i
\(112\) 0 0
\(113\) 4.11880 1.20939i 0.387464 0.113770i −0.0821981 0.996616i \(-0.526194\pi\)
0.469662 + 0.882846i \(0.344376\pi\)
\(114\) 0 0
\(115\) −4.67124 + 5.39089i −0.435595 + 0.502703i
\(116\) 0 0
\(117\) 0.258447 + 1.79754i 0.0238935 + 0.166183i
\(118\) 0 0
\(119\) −9.03158 + 10.4230i −0.827924 + 0.955475i
\(120\) 0 0
\(121\) 12.4043 + 7.97177i 1.12766 + 0.724706i
\(122\) 0 0
\(123\) 3.43394 + 1.00830i 0.309628 + 0.0909150i
\(124\) 0 0
\(125\) −7.89472 9.11100i −0.706126 0.814912i
\(126\) 0 0
\(127\) 8.62104 + 9.94922i 0.764994 + 0.882850i 0.995931 0.0901186i \(-0.0287246\pi\)
−0.230937 + 0.972969i \(0.574179\pi\)
\(128\) 0 0
\(129\) −1.01535 0.298134i −0.0893965 0.0262492i
\(130\) 0 0
\(131\) 2.47822 5.42653i 0.216523 0.474119i −0.769938 0.638119i \(-0.779713\pi\)
0.986460 + 0.164001i \(0.0524399\pi\)
\(132\) 0 0
\(133\) 21.8995 1.89892
\(134\) 0 0
\(135\) 1.67819 0.144436
\(136\) 0 0
\(137\) −6.13483 + 13.4334i −0.524134 + 1.14769i 0.443716 + 0.896167i \(0.353660\pi\)
−0.967850 + 0.251526i \(0.919068\pi\)
\(138\) 0 0
\(139\) 16.6169 + 4.87916i 1.40943 + 0.413845i 0.895910 0.444235i \(-0.146524\pi\)
0.513516 + 0.858080i \(0.328343\pi\)
\(140\) 0 0
\(141\) −3.51781 4.05977i −0.296253 0.341895i
\(142\) 0 0
\(143\) 6.03417 + 6.96381i 0.504603 + 0.582343i
\(144\) 0 0
\(145\) −9.54615 2.80300i −0.792764 0.232777i
\(146\) 0 0
\(147\) −0.00659222 0.00423657i −0.000543717 0.000349426i
\(148\) 0 0
\(149\) 7.35489 8.48800i 0.602536 0.695364i −0.369757 0.929128i \(-0.620559\pi\)
0.972293 + 0.233765i \(0.0751045\pi\)
\(150\) 0 0
\(151\) 1.29080 + 8.97771i 0.105044 + 0.730595i 0.972470 + 0.233029i \(0.0748638\pi\)
−0.867426 + 0.497566i \(0.834227\pi\)
\(152\) 0 0
\(153\) −3.41171 + 3.93732i −0.275820 + 0.318313i
\(154\) 0 0
\(155\) 10.4985 3.08263i 0.843257 0.247603i
\(156\) 0 0
\(157\) −6.63386 + 14.5261i −0.529439 + 1.15931i 0.436301 + 0.899801i \(0.356288\pi\)
−0.965740 + 0.259510i \(0.916439\pi\)
\(158\) 0 0
\(159\) −1.62775 1.04609i −0.129089 0.0829602i
\(160\) 0 0
\(161\) 10.7963 3.17008i 0.850868 0.249837i
\(162\) 0 0
\(163\) −1.49646 −0.117211 −0.0586057 0.998281i \(-0.518665\pi\)
−0.0586057 + 0.998281i \(0.518665\pi\)
\(164\) 0 0
\(165\) 7.16333 4.60359i 0.557665 0.358389i
\(166\) 0 0
\(167\) 7.41150 8.55333i 0.573519 0.661876i −0.392679 0.919675i \(-0.628452\pi\)
0.966199 + 0.257799i \(0.0829972\pi\)
\(168\) 0 0
\(169\) −4.03038 8.82529i −0.310029 0.678869i
\(170\) 0 0
\(171\) 8.27259 0.632621
\(172\) 0 0
\(173\) −16.9901 + 10.9188i −1.29173 + 0.830144i −0.992286 0.123970i \(-0.960437\pi\)
−0.299444 + 0.954114i \(0.596801\pi\)
\(174\) 0 0
\(175\) 0.822679 + 5.72186i 0.0621887 + 0.432532i
\(176\) 0 0
\(177\) −0.112732 0.784067i −0.00847345 0.0589341i
\(178\) 0 0
\(179\) 7.16229 + 15.6832i 0.535335 + 1.17222i 0.963301 + 0.268425i \(0.0865031\pi\)
−0.427966 + 0.903795i \(0.640770\pi\)
\(180\) 0 0
\(181\) 5.95049 13.0298i 0.442297 0.968495i −0.548874 0.835905i \(-0.684943\pi\)
0.991171 0.132590i \(-0.0423293\pi\)
\(182\) 0 0
\(183\) −0.0622602 + 0.433029i −0.00460241 + 0.0320104i
\(184\) 0 0
\(185\) 6.39457 + 1.87761i 0.470138 + 0.138045i
\(186\) 0 0
\(187\) −3.76201 + 26.1653i −0.275105 + 1.91340i
\(188\) 0 0
\(189\) −2.22699 1.43120i −0.161990 0.104105i
\(190\) 0 0
\(191\) −4.01728 8.79662i −0.290680 0.636501i 0.706802 0.707411i \(-0.250137\pi\)
−0.997483 + 0.0709098i \(0.977410\pi\)
\(192\) 0 0
\(193\) 2.63028 1.69038i 0.189332 0.121676i −0.442541 0.896748i \(-0.645923\pi\)
0.631873 + 0.775072i \(0.282286\pi\)
\(194\) 0 0
\(195\) 2.92419 0.858619i 0.209405 0.0614870i
\(196\) 0 0
\(197\) −2.71248 + 18.8657i −0.193256 + 1.34413i 0.630061 + 0.776546i \(0.283030\pi\)
−0.823317 + 0.567582i \(0.807879\pi\)
\(198\) 0 0
\(199\) −14.2587 16.4554i −1.01077 1.16650i −0.985990 0.166802i \(-0.946656\pi\)
−0.0247834 0.999693i \(-0.507890\pi\)
\(200\) 0 0
\(201\) 7.94113 + 1.98455i 0.560124 + 0.139980i
\(202\) 0 0
\(203\) 10.2775 + 11.8608i 0.721336 + 0.832467i
\(204\) 0 0
\(205\) 0.854757 5.94497i 0.0596988 0.415215i
\(206\) 0 0
\(207\) 4.07834 1.19751i 0.283464 0.0832326i
\(208\) 0 0
\(209\) 35.3114 22.6933i 2.44254 1.56973i
\(210\) 0 0
\(211\) 4.55090 + 9.96509i 0.313297 + 0.686025i 0.999129 0.0417353i \(-0.0132886\pi\)
−0.685832 + 0.727760i \(0.740561\pi\)
\(212\) 0 0
\(213\) 2.71279 + 1.74340i 0.185877 + 0.119456i
\(214\) 0 0
\(215\) −0.252735 + 1.75781i −0.0172364 + 0.119882i
\(216\) 0 0
\(217\) −16.5606 4.86264i −1.12421 0.330097i
\(218\) 0 0
\(219\) −0.991714 + 6.89752i −0.0670138 + 0.466091i
\(220\) 0 0
\(221\) −3.93031 + 8.60618i −0.264381 + 0.578915i
\(222\) 0 0
\(223\) 7.95184 + 17.4121i 0.532495 + 1.16600i 0.964489 + 0.264124i \(0.0850828\pi\)
−0.431994 + 0.901876i \(0.642190\pi\)
\(224\) 0 0
\(225\) 0.310769 + 2.16145i 0.0207180 + 0.144097i
\(226\) 0 0
\(227\) −2.92142 20.3189i −0.193901 1.34861i −0.821559 0.570123i \(-0.806895\pi\)
0.627658 0.778489i \(-0.284014\pi\)
\(228\) 0 0
\(229\) −1.32079 + 0.848820i −0.0872802 + 0.0560916i −0.583553 0.812075i \(-0.698338\pi\)
0.496273 + 0.868167i \(0.334702\pi\)
\(230\) 0 0
\(231\) −13.4319 −0.883757
\(232\) 0 0
\(233\) 2.19195 + 4.79970i 0.143599 + 0.314439i 0.967742 0.251944i \(-0.0810698\pi\)
−0.824143 + 0.566382i \(0.808343\pi\)
\(234\) 0 0
\(235\) −5.90356 + 6.81307i −0.385106 + 0.444436i
\(236\) 0 0
\(237\) 9.05517 5.81941i 0.588197 0.378011i
\(238\) 0 0
\(239\) −19.0673 −1.23336 −0.616680 0.787214i \(-0.711523\pi\)
−0.616680 + 0.787214i \(0.711523\pi\)
\(240\) 0 0
\(241\) −10.6389 + 3.12385i −0.685309 + 0.201225i −0.605809 0.795610i \(-0.707151\pi\)
−0.0795001 + 0.996835i \(0.525332\pi\)
\(242\) 0 0
\(243\) −0.841254 0.540641i −0.0539664 0.0346821i
\(244\) 0 0
\(245\) −0.00546297 + 0.0119622i −0.000349016 + 0.000764239i
\(246\) 0 0
\(247\) 14.4147 4.23253i 0.917185 0.269310i
\(248\) 0 0
\(249\) 11.2288 12.9587i 0.711593 0.821222i
\(250\) 0 0
\(251\) −3.15856 21.9683i −0.199366 1.38662i −0.806128 0.591741i \(-0.798441\pi\)
0.606762 0.794884i \(-0.292468\pi\)
\(252\) 0 0
\(253\) 14.1233 16.2992i 0.887926 1.02472i
\(254\) 0 0
\(255\) 7.35514 + 4.72686i 0.460597 + 0.296008i
\(256\) 0 0
\(257\) −19.1886 5.63428i −1.19695 0.351457i −0.378265 0.925697i \(-0.623479\pi\)
−0.818687 + 0.574240i \(0.805298\pi\)
\(258\) 0 0
\(259\) −6.88444 7.94507i −0.427778 0.493683i
\(260\) 0 0
\(261\) 3.88234 + 4.48046i 0.240311 + 0.277334i
\(262\) 0 0
\(263\) −13.8674 4.07184i −0.855101 0.251080i −0.175335 0.984509i \(-0.556101\pi\)
−0.679767 + 0.733428i \(0.737919\pi\)
\(264\) 0 0
\(265\) −1.34891 + 2.95370i −0.0828629 + 0.181445i
\(266\) 0 0
\(267\) −11.1063 −0.679693
\(268\) 0 0
\(269\) 6.97062 0.425006 0.212503 0.977160i \(-0.431838\pi\)
0.212503 + 0.977160i \(0.431838\pi\)
\(270\) 0 0
\(271\) 0.0831706 0.182118i 0.00505226 0.0110629i −0.907089 0.420939i \(-0.861701\pi\)
0.912141 + 0.409876i \(0.134428\pi\)
\(272\) 0 0
\(273\) −4.61271 1.35441i −0.279174 0.0819728i
\(274\) 0 0
\(275\) 7.25578 + 8.37361i 0.437540 + 0.504948i
\(276\) 0 0
\(277\) −10.2155 11.7893i −0.613789 0.708350i 0.360726 0.932672i \(-0.382529\pi\)
−0.974515 + 0.224322i \(0.927983\pi\)
\(278\) 0 0
\(279\) −6.25582 1.83688i −0.374526 0.109971i
\(280\) 0 0
\(281\) 8.36473 + 5.37569i 0.498998 + 0.320687i 0.765815 0.643060i \(-0.222336\pi\)
−0.266817 + 0.963747i \(0.585972\pi\)
\(282\) 0 0
\(283\) −16.5128 + 19.0567i −0.981582 + 1.13281i 0.00955400 + 0.999954i \(0.496959\pi\)
−0.991136 + 0.132852i \(0.957587\pi\)
\(284\) 0 0
\(285\) −1.97575 13.7417i −0.117034 0.813986i
\(286\) 0 0
\(287\) −6.20429 + 7.16013i −0.366228 + 0.422649i
\(288\) 0 0
\(289\) −9.73140 + 2.85740i −0.572435 + 0.168082i
\(290\) 0 0
\(291\) −4.74478 + 10.3896i −0.278144 + 0.609050i
\(292\) 0 0
\(293\) −17.8261 11.4561i −1.04141 0.669274i −0.0960754 0.995374i \(-0.530629\pi\)
−0.945335 + 0.326100i \(0.894265\pi\)
\(294\) 0 0
\(295\) −1.27550 + 0.374520i −0.0742624 + 0.0218054i
\(296\) 0 0
\(297\) −5.07396 −0.294421
\(298\) 0 0
\(299\) 6.49367 4.17323i 0.375539 0.241344i
\(300\) 0 0
\(301\) 1.83449 2.11711i 0.105738 0.122028i
\(302\) 0 0
\(303\) −2.49761 5.46900i −0.143484 0.314186i
\(304\) 0 0
\(305\) 0.734178 0.0420389
\(306\) 0 0
\(307\) 7.21936 4.63960i 0.412030 0.264796i −0.318163 0.948036i \(-0.603066\pi\)
0.730194 + 0.683240i \(0.239430\pi\)
\(308\) 0 0
\(309\) 2.38916 + 16.6170i 0.135915 + 0.945307i
\(310\) 0 0
\(311\) −3.63552 25.2856i −0.206151 1.43381i −0.785565 0.618779i \(-0.787627\pi\)
0.579414 0.815034i \(-0.303282\pi\)
\(312\) 0 0
\(313\) 6.72899 + 14.7344i 0.380345 + 0.832839i 0.998891 + 0.0470902i \(0.0149948\pi\)
−0.618546 + 0.785749i \(0.712278\pi\)
\(314\) 0 0
\(315\) −1.84551 + 4.04109i −0.103982 + 0.227690i
\(316\) 0 0
\(317\) −1.02496 + 7.12874i −0.0575674 + 0.400390i 0.940581 + 0.339569i \(0.110281\pi\)
−0.998149 + 0.0608214i \(0.980628\pi\)
\(318\) 0 0
\(319\) 28.8625 + 8.47479i 1.61599 + 0.474497i
\(320\) 0 0
\(321\) 1.52062 10.5762i 0.0848728 0.590303i
\(322\) 0 0
\(323\) 36.2569 + 23.3009i 2.01739 + 1.29650i
\(324\) 0 0
\(325\) 1.64737 + 3.60725i 0.0913799 + 0.200094i
\(326\) 0 0
\(327\) 6.17414 3.96788i 0.341431 0.219424i
\(328\) 0 0
\(329\) 13.6445 4.00639i 0.752246 0.220879i
\(330\) 0 0
\(331\) 4.99668 34.7527i 0.274642 1.91018i −0.122585 0.992458i \(-0.539118\pi\)
0.397227 0.917720i \(-0.369973\pi\)
\(332\) 0 0
\(333\) −2.60062 3.00128i −0.142513 0.164469i
\(334\) 0 0
\(335\) 1.39997 13.6651i 0.0764883 0.746602i
\(336\) 0 0
\(337\) 1.36067 + 1.57030i 0.0741207 + 0.0855398i 0.791599 0.611041i \(-0.209249\pi\)
−0.717478 + 0.696581i \(0.754704\pi\)
\(338\) 0 0
\(339\) −0.610912 + 4.24899i −0.0331802 + 0.230773i
\(340\) 0 0
\(341\) −31.7418 + 9.32023i −1.71891 + 0.504719i
\(342\) 0 0
\(343\) −15.5715 + 10.0072i −0.840782 + 0.540338i
\(344\) 0 0
\(345\) −2.96323 6.48856i −0.159535 0.349333i
\(346\) 0 0
\(347\) 18.1731 + 11.6792i 0.975585 + 0.626971i 0.928269 0.371909i \(-0.121297\pi\)
0.0473163 + 0.998880i \(0.484933\pi\)
\(348\) 0 0
\(349\) −1.61808 + 11.2540i −0.0866140 + 0.602414i 0.899572 + 0.436773i \(0.143879\pi\)
−0.986186 + 0.165641i \(0.947031\pi\)
\(350\) 0 0
\(351\) −1.74246 0.511634i −0.0930059 0.0273090i
\(352\) 0 0
\(353\) −3.46565 + 24.1041i −0.184458 + 1.28293i 0.661605 + 0.749852i \(0.269875\pi\)
−0.846064 + 0.533082i \(0.821034\pi\)
\(354\) 0 0
\(355\) 2.24808 4.92261i 0.119316 0.261265i
\(356\) 0 0
\(357\) −5.72924 12.5453i −0.303223 0.663967i
\(358\) 0 0
\(359\) −3.01852 20.9942i −0.159311 1.10803i −0.899907 0.436082i \(-0.856366\pi\)
0.740596 0.671951i \(-0.234543\pi\)
\(360\) 0 0
\(361\) −7.03543 48.9325i −0.370286 2.57540i
\(362\) 0 0
\(363\) −12.4043 + 7.97177i −0.651058 + 0.418409i
\(364\) 0 0
\(365\) 11.6944 0.612113
\(366\) 0 0
\(367\) −10.0305 21.9636i −0.523586 1.14649i −0.968064 0.250703i \(-0.919338\pi\)
0.444478 0.895790i \(-0.353389\pi\)
\(368\) 0 0
\(369\) −2.34369 + 2.70476i −0.122008 + 0.140804i
\(370\) 0 0
\(371\) 4.30902 2.76924i 0.223713 0.143772i
\(372\) 0 0
\(373\) 21.0568 1.09028 0.545140 0.838345i \(-0.316476\pi\)
0.545140 + 0.838345i \(0.316476\pi\)
\(374\) 0 0
\(375\) 11.5672 3.39645i 0.597330 0.175392i
\(376\) 0 0
\(377\) 9.05720 + 5.82071i 0.466469 + 0.299782i
\(378\) 0 0
\(379\) −11.1517 + 24.4189i −0.572826 + 1.25431i 0.372452 + 0.928051i \(0.378517\pi\)
−0.945279 + 0.326264i \(0.894210\pi\)
\(380\) 0 0
\(381\) −12.6314 + 3.70892i −0.647128 + 0.190014i
\(382\) 0 0
\(383\) −0.620007 + 0.715526i −0.0316809 + 0.0365617i −0.771369 0.636388i \(-0.780428\pi\)
0.739688 + 0.672950i \(0.234973\pi\)
\(384\) 0 0
\(385\) 3.20797 + 22.3119i 0.163493 + 1.13712i
\(386\) 0 0
\(387\) 0.692983 0.799745i 0.0352263 0.0406533i
\(388\) 0 0
\(389\) 13.8761 + 8.91765i 0.703548 + 0.452143i 0.842879 0.538103i \(-0.180859\pi\)
−0.139331 + 0.990246i \(0.544495\pi\)
\(390\) 0 0
\(391\) 21.2474 + 6.23880i 1.07453 + 0.315510i
\(392\) 0 0
\(393\) 3.90666 + 4.50853i 0.197065 + 0.227425i
\(394\) 0 0
\(395\) −11.8293 13.6518i −0.595198 0.686895i
\(396\) 0 0
\(397\) −20.8431 6.12008i −1.04608 0.307158i −0.286850 0.957976i \(-0.592608\pi\)
−0.759234 + 0.650818i \(0.774426\pi\)
\(398\) 0 0
\(399\) −9.09736 + 19.9204i −0.455438 + 0.997270i
\(400\) 0 0
\(401\) −7.88131 −0.393574 −0.196787 0.980446i \(-0.563051\pi\)
−0.196787 + 0.980446i \(0.563051\pi\)
\(402\) 0 0
\(403\) −11.8404 −0.589810
\(404\) 0 0
\(405\) −0.697146 + 1.52654i −0.0346414 + 0.0758542i
\(406\) 0 0
\(407\) −19.3338 5.67691i −0.958339 0.281394i
\(408\) 0 0
\(409\) −25.0522 28.9118i −1.23875 1.42960i −0.864774 0.502160i \(-0.832539\pi\)
−0.373979 0.927437i \(-0.622007\pi\)
\(410\) 0 0
\(411\) −9.67096 11.1609i −0.477033 0.550526i
\(412\) 0 0
\(413\) 2.01201 + 0.590780i 0.0990046 + 0.0290704i
\(414\) 0 0
\(415\) −24.2075 15.5572i −1.18830 0.763675i
\(416\) 0 0
\(417\) −11.3411 + 13.0884i −0.555378 + 0.640941i
\(418\) 0 0
\(419\) 3.86162 + 26.8582i 0.188652 + 1.31211i 0.835501 + 0.549489i \(0.185177\pi\)
−0.646849 + 0.762618i \(0.723913\pi\)
\(420\) 0 0
\(421\) 15.0416 17.3590i 0.733084 0.846024i −0.259731 0.965681i \(-0.583634\pi\)
0.992815 + 0.119657i \(0.0381794\pi\)
\(422\) 0 0
\(423\) 5.15425 1.51342i 0.250608 0.0735852i
\(424\) 0 0
\(425\) −4.72599 + 10.3485i −0.229244 + 0.501975i
\(426\) 0 0
\(427\) −0.974269 0.626125i −0.0471482 0.0303003i
\(428\) 0 0
\(429\) −8.84119 + 2.59601i −0.426857 + 0.125336i
\(430\) 0 0
\(431\) −3.96385 −0.190932 −0.0954659 0.995433i \(-0.530434\pi\)
−0.0954659 + 0.995433i \(0.530434\pi\)
\(432\) 0 0
\(433\) −13.0531 + 8.38873i −0.627293 + 0.403137i −0.815306 0.579030i \(-0.803432\pi\)
0.188013 + 0.982166i \(0.439795\pi\)
\(434\) 0 0
\(435\) 6.51531 7.51907i 0.312385 0.360512i
\(436\) 0 0
\(437\) −14.6071 31.9852i −0.698754 1.53006i
\(438\) 0 0
\(439\) −36.9397 −1.76303 −0.881517 0.472153i \(-0.843477\pi\)
−0.881517 + 0.472153i \(0.843477\pi\)
\(440\) 0 0
\(441\) 0.00659222 0.00423657i 0.000313915 0.000201741i
\(442\) 0 0
\(443\) 1.29625 + 9.01564i 0.0615869 + 0.428346i 0.997166 + 0.0752296i \(0.0239690\pi\)
−0.935579 + 0.353116i \(0.885122\pi\)
\(444\) 0 0
\(445\) 2.65253 + 18.4487i 0.125742 + 0.874554i
\(446\) 0 0
\(447\) 4.66562 + 10.2163i 0.220676 + 0.483214i
\(448\) 0 0
\(449\) 17.3679 38.0304i 0.819642 1.79477i 0.261046 0.965326i \(-0.415932\pi\)
0.558596 0.829440i \(-0.311340\pi\)
\(450\) 0 0
\(451\) −2.58433 + 17.9744i −0.121691 + 0.846382i
\(452\) 0 0
\(453\) −8.70263 2.55532i −0.408885 0.120059i
\(454\) 0 0
\(455\) −1.14817 + 7.98569i −0.0538270 + 0.374375i
\(456\) 0 0
\(457\) −13.6356 8.76304i −0.637845 0.409918i 0.181362 0.983416i \(-0.441949\pi\)
−0.819207 + 0.573499i \(0.805586\pi\)
\(458\) 0 0
\(459\) −2.16424 4.73902i −0.101018 0.221199i
\(460\) 0 0
\(461\) 13.6537 8.77472i 0.635918 0.408680i −0.182579 0.983191i \(-0.558444\pi\)
0.818496 + 0.574512i \(0.194808\pi\)
\(462\) 0 0
\(463\) −12.9356 + 3.79825i −0.601170 + 0.176519i −0.568136 0.822935i \(-0.692335\pi\)
−0.0330342 + 0.999454i \(0.510517\pi\)
\(464\) 0 0
\(465\) −1.55716 + 10.8303i −0.0722117 + 0.502244i
\(466\) 0 0
\(467\) −15.3044 17.6622i −0.708202 0.817309i 0.281634 0.959522i \(-0.409124\pi\)
−0.989836 + 0.142213i \(0.954578\pi\)
\(468\) 0 0
\(469\) −13.5117 + 16.9399i −0.623911 + 0.782211i
\(470\) 0 0
\(471\) −10.4576 12.0687i −0.481862 0.556098i
\(472\) 0 0
\(473\) 0.764136 5.31468i 0.0351350 0.244369i
\(474\) 0 0
\(475\) 17.3329 5.08940i 0.795288 0.233518i
\(476\) 0 0
\(477\) 1.62775 1.04609i 0.0745294 0.0478971i
\(478\) 0 0
\(479\) −4.75082 10.4028i −0.217070 0.475318i 0.769502 0.638645i \(-0.220505\pi\)
−0.986572 + 0.163327i \(0.947777\pi\)
\(480\) 0 0
\(481\) −6.06704 3.89905i −0.276633 0.177781i
\(482\) 0 0
\(483\) −1.60134 + 11.1376i −0.0728635 + 0.506777i
\(484\) 0 0
\(485\) 18.3915 + 5.40023i 0.835114 + 0.245212i
\(486\) 0 0
\(487\) 3.59573 25.0088i 0.162938 1.13326i −0.730121 0.683318i \(-0.760536\pi\)
0.893059 0.449940i \(-0.148555\pi\)
\(488\) 0 0
\(489\) 0.621650 1.36122i 0.0281120 0.0615567i
\(490\) 0 0
\(491\) −15.1560 33.1870i −0.683980 1.49771i −0.858370 0.513030i \(-0.828523\pi\)
0.174391 0.984677i \(-0.444204\pi\)
\(492\) 0 0
\(493\) 4.39560 + 30.5721i 0.197968 + 1.37690i
\(494\) 0 0
\(495\) 1.21182 + 8.42840i 0.0544673 + 0.378828i
\(496\) 0 0
\(497\) −7.18137 + 4.61519i −0.322129 + 0.207019i
\(498\) 0 0
\(499\) −19.2669 −0.862505 −0.431252 0.902231i \(-0.641928\pi\)
−0.431252 + 0.902231i \(0.641928\pi\)
\(500\) 0 0
\(501\) 4.70153 + 10.2949i 0.210049 + 0.459943i
\(502\) 0 0
\(503\) 16.0562 18.5298i 0.715910 0.826204i −0.274899 0.961473i \(-0.588644\pi\)
0.990809 + 0.135269i \(0.0431898\pi\)
\(504\) 0 0
\(505\) −8.48809 + 5.45497i −0.377715 + 0.242743i
\(506\) 0 0
\(507\) 9.70205 0.430883
\(508\) 0 0
\(509\) 2.78890 0.818895i 0.123616 0.0362969i −0.219340 0.975649i \(-0.570390\pi\)
0.342955 + 0.939352i \(0.388572\pi\)
\(510\) 0 0
\(511\) −15.5187 9.97326i −0.686507 0.441191i
\(512\) 0 0
\(513\) −3.43656 + 7.52501i −0.151728 + 0.332237i
\(514\) 0 0
\(515\) 27.0320 7.93732i 1.19117 0.349760i
\(516\) 0 0
\(517\) 17.8492 20.5991i 0.785008 0.905948i
\(518\) 0 0
\(519\) −2.87421 19.9905i −0.126164 0.877488i
\(520\) 0 0
\(521\) 4.68821 5.41048i 0.205394 0.237037i −0.643702 0.765277i \(-0.722602\pi\)
0.849096 + 0.528239i \(0.177148\pi\)
\(522\) 0 0
\(523\) 31.9973 + 20.5634i 1.39914 + 0.899175i 0.999844 0.0176464i \(-0.00561730\pi\)
0.399299 + 0.916821i \(0.369254\pi\)
\(524\) 0 0
\(525\) −5.54654 1.62861i −0.242071 0.0710784i
\(526\) 0 0
\(527\) −22.2441 25.6710i −0.968967 1.11825i
\(528\) 0 0
\(529\) 3.23051 + 3.72821i 0.140457 + 0.162096i
\(530\) 0 0
\(531\) 0.760043 + 0.223169i 0.0329831 + 0.00968470i
\(532\) 0 0
\(533\) −2.69995 + 5.91206i −0.116948 + 0.256080i
\(534\) 0 0
\(535\) −17.9313 −0.775239
\(536\) 0 0
\(537\) −17.2413 −0.744017
\(538\) 0 0
\(539\) 0.0165171 0.0361674i 0.000711442 0.00155784i
\(540\) 0 0
\(541\) 0.843627 + 0.247711i 0.0362703 + 0.0106499i 0.299817 0.953997i \(-0.403074\pi\)
−0.263547 + 0.964647i \(0.584892\pi\)
\(542\) 0 0
\(543\) 9.38037 + 10.8255i 0.402550 + 0.464568i
\(544\) 0 0
\(545\) −8.06566 9.30826i −0.345495 0.398722i
\(546\) 0 0
\(547\) 33.2485 + 9.76265i 1.42160 + 0.417421i 0.900046 0.435794i \(-0.143533\pi\)
0.521559 + 0.853215i \(0.325351\pi\)
\(548\) 0 0
\(549\) −0.368033 0.236521i −0.0157073 0.0100945i
\(550\) 0 0
\(551\) 32.1170 37.0650i 1.36823 1.57902i
\(552\) 0 0
\(553\) 4.05520 + 28.2045i 0.172445 + 1.19938i
\(554\) 0 0
\(555\) −4.36434 + 5.03671i −0.185256 + 0.213797i
\(556\) 0 0
\(557\) 10.7331 3.15152i 0.454776 0.133534i −0.0463187 0.998927i \(-0.514749\pi\)
0.501095 + 0.865392i \(0.332931\pi\)
\(558\) 0 0
\(559\) 0.798322 1.74808i 0.0337654 0.0739360i
\(560\) 0 0
\(561\) −22.2380 14.2915i −0.938891 0.603388i
\(562\) 0 0
\(563\) 1.22039 0.358338i 0.0514332 0.0151021i −0.255915 0.966699i \(-0.582377\pi\)
0.307348 + 0.951597i \(0.400558\pi\)
\(564\) 0 0
\(565\) 7.20393 0.303072
\(566\) 0 0
\(567\) 2.22699 1.43120i 0.0935249 0.0601048i
\(568\) 0 0
\(569\) −11.5191 + 13.2938i −0.482907 + 0.557305i −0.943957 0.330070i \(-0.892928\pi\)
0.461049 + 0.887375i \(0.347473\pi\)
\(570\) 0 0
\(571\) −4.36488 9.55776i −0.182665 0.399980i 0.796043 0.605241i \(-0.206923\pi\)
−0.978707 + 0.205261i \(0.934196\pi\)
\(572\) 0 0
\(573\) 9.67053 0.403992
\(574\) 0 0
\(575\) 7.80830 5.01809i 0.325629 0.209269i
\(576\) 0 0
\(577\) 1.26105 + 8.77078i 0.0524981 + 0.365132i 0.999088 + 0.0426931i \(0.0135938\pi\)
−0.946590 + 0.322439i \(0.895497\pi\)
\(578\) 0 0
\(579\) 0.444965 + 3.09480i 0.0184921 + 0.128615i
\(580\) 0 0
\(581\) 18.8563 + 41.2896i 0.782292 + 1.71298i
\(582\) 0 0
\(583\) 4.07839 8.93043i 0.168910 0.369860i
\(584\) 0 0
\(585\) −0.433724 + 3.01662i −0.0179323 + 0.124722i
\(586\) 0 0
\(587\) 29.9078 + 8.78172i 1.23443 + 0.362460i 0.832919 0.553395i \(-0.186668\pi\)
0.401508 + 0.915856i \(0.368486\pi\)
\(588\) 0 0
\(589\) −7.67599 + 53.3877i −0.316284 + 2.19980i
\(590\) 0 0
\(591\) −16.0341 10.3045i −0.659553 0.423869i
\(592\) 0 0
\(593\) 6.36103 + 13.9287i 0.261216 + 0.571984i 0.994112 0.108357i \(-0.0345590\pi\)
−0.732896 + 0.680341i \(0.761832\pi\)
\(594\) 0 0
\(595\) −19.4708 + 12.5131i −0.798224 + 0.512987i
\(596\) 0 0
\(597\) 20.8917 6.13435i 0.855039 0.251062i
\(598\) 0 0
\(599\) 1.74042 12.1049i 0.0711115 0.494592i −0.922876 0.385097i \(-0.874168\pi\)
0.993987 0.109494i \(-0.0349231\pi\)
\(600\) 0 0
\(601\) −10.0951 11.6504i −0.411789 0.475230i 0.511529 0.859266i \(-0.329079\pi\)
−0.923318 + 0.384036i \(0.874534\pi\)
\(602\) 0 0
\(603\) −5.10408 + 6.39909i −0.207854 + 0.260591i
\(604\) 0 0
\(605\) 16.2045 + 18.7010i 0.658807 + 0.760304i
\(606\) 0 0
\(607\) 1.53254 10.6591i 0.0622039 0.432638i −0.934793 0.355194i \(-0.884415\pi\)
0.996997 0.0774441i \(-0.0246759\pi\)
\(608\) 0 0
\(609\) −15.0584 + 4.42154i −0.610197 + 0.179170i
\(610\) 0 0
\(611\) 8.20678 5.27418i 0.332011 0.213370i
\(612\) 0 0
\(613\) −12.8600 28.1595i −0.519411 1.13735i −0.969662 0.244449i \(-0.921393\pi\)
0.450252 0.892902i \(-0.351334\pi\)
\(614\) 0 0
\(615\) 5.05265 + 3.24714i 0.203743 + 0.130937i
\(616\) 0 0
\(617\) −1.94881 + 13.5543i −0.0784562 + 0.545675i 0.912248 + 0.409639i \(0.134345\pi\)
−0.990704 + 0.136036i \(0.956564\pi\)
\(618\) 0 0
\(619\) 26.2432 + 7.70571i 1.05480 + 0.309719i 0.762757 0.646685i \(-0.223845\pi\)
0.292048 + 0.956404i \(0.405663\pi\)
\(620\) 0 0
\(621\) −0.604911 + 4.20725i −0.0242743 + 0.168831i
\(622\) 0 0
\(623\) 12.2136 26.7440i 0.489326 1.07147i
\(624\) 0 0
\(625\) −3.86884 8.47157i −0.154753 0.338863i
\(626\) 0 0
\(627\) 5.97363 + 41.5475i 0.238564 + 1.65925i
\(628\) 0 0
\(629\) −2.94443 20.4789i −0.117402 0.816549i
\(630\) 0 0
\(631\) 16.9163 10.8714i 0.673426 0.432785i −0.158733 0.987322i \(-0.550741\pi\)
0.832159 + 0.554537i \(0.187104\pi\)
\(632\) 0 0
\(633\) −10.9551 −0.435425
\(634\) 0 0
\(635\) 9.17771 + 20.0964i 0.364206 + 0.797501i
\(636\) 0 0
\(637\) 0.00931915 0.0107549i 0.000369238 0.000426123i
\(638\) 0 0
\(639\) −2.71279 + 1.74340i −0.107316 + 0.0689679i
\(640\) 0 0
\(641\) 17.7914 0.702717 0.351358 0.936241i \(-0.385720\pi\)
0.351358 + 0.936241i \(0.385720\pi\)
\(642\) 0 0
\(643\) 44.5785 13.0894i 1.75800 0.516196i 0.766048 0.642784i \(-0.222221\pi\)
0.991955 + 0.126587i \(0.0404024\pi\)
\(644\) 0 0
\(645\) −1.49397 0.960117i −0.0588250 0.0378046i
\(646\) 0 0
\(647\) −8.03423 + 17.5925i −0.315858 + 0.691633i −0.999262 0.0384076i \(-0.987771\pi\)
0.683404 + 0.730040i \(0.260499\pi\)
\(648\) 0 0
\(649\) 3.85643 1.13235i 0.151378 0.0444486i
\(650\) 0 0
\(651\) 11.3027 13.0441i 0.442989 0.511237i
\(652\) 0 0
\(653\) 0.492449 + 3.42506i 0.0192710 + 0.134033i 0.997186 0.0749718i \(-0.0238867\pi\)
−0.977915 + 0.209005i \(0.932978\pi\)
\(654\) 0 0
\(655\) 6.55612 7.56617i 0.256169 0.295635i
\(656\) 0 0
\(657\) −5.86224 3.76743i −0.228708 0.146981i
\(658\) 0 0
\(659\) 5.53366 + 1.62483i 0.215561 + 0.0632943i 0.387730 0.921773i \(-0.373259\pi\)
−0.172169 + 0.985067i \(0.555078\pi\)
\(660\) 0 0
\(661\) −22.8765 26.4009i −0.889793 1.02688i −0.999458 0.0329074i \(-0.989523\pi\)
0.109665 0.993969i \(-0.465022\pi\)
\(662\) 0 0
\(663\) −6.19575 7.15028i −0.240623 0.277694i
\(664\) 0 0
\(665\) 35.2628 + 10.3541i 1.36743 + 0.401514i
\(666\) 0 0
\(667\) 10.4681 22.9220i 0.405327 0.887543i
\(668\) 0 0
\(669\) −19.1419 −0.740069
\(670\) 0 0
\(671\) −2.21976 −0.0856931
\(672\) 0 0
\(673\) −5.22524 + 11.4417i −0.201418 + 0.441044i −0.983206 0.182501i \(-0.941581\pi\)
0.781788 + 0.623545i \(0.214308\pi\)
\(674\) 0 0
\(675\) −2.09522 0.615213i −0.0806451 0.0236795i
\(676\) 0 0
\(677\) −5.33057 6.15181i −0.204871 0.236433i 0.644011 0.765016i \(-0.277269\pi\)
−0.848882 + 0.528583i \(0.822724\pi\)
\(678\) 0 0
\(679\) −19.8004 22.8509i −0.759870 0.876937i
\(680\) 0 0
\(681\) 19.6963 + 5.78336i 0.754764 + 0.221619i
\(682\) 0 0
\(683\) −29.3219 18.8441i −1.12197 0.721048i −0.158103 0.987423i \(-0.550538\pi\)
−0.963870 + 0.266374i \(0.914174\pi\)
\(684\) 0 0
\(685\) −16.2297 + 18.7301i −0.620105 + 0.715640i
\(686\) 0 0
\(687\) −0.223438 1.55405i −0.00852469 0.0592905i
\(688\) 0 0
\(689\) 2.30107 2.65558i 0.0876640 0.101170i
\(690\) 0 0
\(691\) −5.91932 + 1.73807i −0.225182 + 0.0661193i −0.392377 0.919804i \(-0.628347\pi\)
0.167195 + 0.985924i \(0.446529\pi\)
\(692\) 0 0
\(693\) 5.57983 12.2181i 0.211960 0.464128i
\(694\) 0 0
\(695\) 24.4499 + 15.7130i 0.927436 + 0.596027i
\(696\) 0 0
\(697\) −17.8902 + 5.25305i −0.677641 + 0.198973i
\(698\) 0 0
\(699\) −5.27653 −0.199577
\(700\) 0 0
\(701\) −34.0420 + 21.8775i −1.28575 + 0.826300i −0.991585 0.129455i \(-0.958677\pi\)
−0.294163 + 0.955755i \(0.595041\pi\)
\(702\) 0 0
\(703\) −21.5139 + 24.8283i −0.811410 + 0.936418i
\(704\) 0 0
\(705\) −3.74496 8.20032i −0.141043 0.308842i
\(706\) 0 0
\(707\) 15.9160 0.598583
\(708\) 0 0
\(709\) 37.5760 24.1486i 1.41120 0.906921i 0.411207 0.911542i \(-0.365107\pi\)
0.999989 + 0.00462069i \(0.00147082\pi\)
\(710\) 0 0
\(711\) 1.53186 + 10.6543i 0.0574494 + 0.399569i
\(712\) 0 0
\(713\) 3.94398 + 27.4310i 0.147703 + 1.02730i
\(714\) 0 0
\(715\) 6.42380 + 14.0662i 0.240237 + 0.526045i
\(716\) 0 0
\(717\) 7.92083 17.3442i 0.295809 0.647731i
\(718\) 0 0
\(719\) 2.73405 19.0158i 0.101963 0.709169i −0.873149 0.487454i \(-0.837926\pi\)
0.975112 0.221714i \(-0.0711653\pi\)
\(720\) 0 0
\(721\) −42.6412 12.5206i −1.58804 0.466291i
\(722\) 0 0
\(723\) 1.57799 10.9751i 0.0586860 0.408170i
\(724\) 0 0
\(725\) 10.8908 + 6.99910i 0.404474 + 0.259940i
\(726\) 0 0
\(727\) 16.5275 + 36.1903i 0.612972 + 1.34222i 0.920522 + 0.390690i \(0.127764\pi\)
−0.307550 + 0.951532i \(0.599509\pi\)
\(728\) 0 0
\(729\) 0.841254 0.540641i 0.0311575 0.0200237i
\(730\) 0 0
\(731\) 5.28979 1.55322i 0.195650 0.0574480i
\(732\) 0 0
\(733\) −0.552337 + 3.84159i −0.0204010 + 0.141892i −0.997476 0.0710026i \(-0.977380\pi\)
0.977075 + 0.212895i \(0.0682892\pi\)
\(734\) 0 0
\(735\) −0.00861183 0.00993858i −0.000317652 0.000366590i
\(736\) 0 0
\(737\) −4.23275 + 41.3159i −0.155915 + 1.52189i
\(738\) 0 0
\(739\) 22.7304 + 26.2323i 0.836151 + 0.964970i 0.999768 0.0215544i \(-0.00686150\pi\)
−0.163617 + 0.986524i \(0.552316\pi\)
\(740\) 0 0
\(741\) −2.13803 + 14.8703i −0.0785425 + 0.546275i
\(742\) 0 0
\(743\) −23.5115 + 6.90359i −0.862552 + 0.253268i −0.682945 0.730470i \(-0.739301\pi\)
−0.179608 + 0.983738i \(0.557483\pi\)
\(744\) 0 0
\(745\) 15.8561 10.1901i 0.580921 0.373336i
\(746\) 0 0
\(747\) 7.12303 + 15.5973i 0.260618 + 0.570674i
\(748\) 0 0
\(749\) 23.7952 + 15.2923i 0.869459 + 0.558767i
\(750\) 0 0
\(751\) −3.68204 + 25.6091i −0.134360 + 0.934491i 0.805419 + 0.592706i \(0.201940\pi\)
−0.939778 + 0.341785i \(0.888969\pi\)
\(752\) 0 0
\(753\) 21.2951 + 6.25282i 0.776038 + 0.227865i
\(754\) 0 0
\(755\) −2.16621 + 15.0663i −0.0788364 + 0.548319i
\(756\) 0 0
\(757\) −2.17451 + 4.76152i −0.0790341 + 0.173060i −0.945024 0.327001i \(-0.893962\pi\)
0.865990 + 0.500061i \(0.166689\pi\)
\(758\) 0 0
\(759\) 8.95923 + 19.6180i 0.325199 + 0.712087i
\(760\) 0 0
\(761\) 1.02457 + 7.12605i 0.0371407 + 0.258319i 0.999929 0.0119385i \(-0.00380023\pi\)
−0.962788 + 0.270258i \(0.912891\pi\)
\(762\) 0 0
\(763\) 2.76498 + 19.2308i 0.100099 + 0.696203i
\(764\) 0 0
\(765\) −7.35514 + 4.72686i −0.265926 + 0.170900i
\(766\) 0 0
\(767\) 1.43853 0.0519423
\(768\) 0 0
\(769\) 14.6808 + 32.1465i 0.529404 + 1.15923i 0.965755 + 0.259456i \(0.0835433\pi\)
−0.436351 + 0.899777i \(0.643729\pi\)
\(770\) 0 0
\(771\) 13.0964 15.1140i 0.471654 0.544317i
\(772\) 0 0
\(773\) −15.4667 + 9.93985i −0.556299 + 0.357512i −0.788384 0.615184i \(-0.789082\pi\)
0.232085 + 0.972696i \(0.425445\pi\)
\(774\) 0 0
\(775\) −14.2374 −0.511423
\(776\) 0 0
\(777\) 10.0870 2.96181i 0.361869 0.106254i
\(778\) 0 0
\(779\) 24.9069 + 16.0067i 0.892382 + 0.573499i
\(780\) 0 0
\(781\) −6.79700 + 14.8834i −0.243216 + 0.532569i