Properties

Label 108.3.k.a.29.2
Level 108
Weight 3
Character 108.29
Analytic conductor 2.943
Analytic rank 0
Dimension 36
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.k (of order \(18\), degree \(6\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 29.2
Character \(\chi\) \(=\) 108.29
Dual form 108.3.k.a.41.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.59609 - 1.50344i) q^{3} +(-0.298552 - 0.355800i) q^{5} +(-10.1488 + 3.69384i) q^{7} +(4.47934 + 7.80612i) q^{9} +O(q^{10})\) \(q+(-2.59609 - 1.50344i) q^{3} +(-0.298552 - 0.355800i) q^{5} +(-10.1488 + 3.69384i) q^{7} +(4.47934 + 7.80612i) q^{9} +(-10.2314 + 12.1933i) q^{11} +(-3.11819 - 17.6841i) q^{13} +(0.240142 + 1.37254i) q^{15} +(-22.6442 + 13.0736i) q^{17} +(1.77864 - 3.08069i) q^{19} +(31.9005 + 5.66850i) q^{21} +(1.41115 - 3.87710i) q^{23} +(4.30374 - 24.4077i) q^{25} +(0.107276 - 26.9998i) q^{27} +(41.0456 + 7.23745i) q^{29} +(-6.62361 - 2.41080i) q^{31} +(44.8934 - 16.2726i) q^{33} +(4.34420 + 2.50812i) q^{35} +(4.92909 + 8.53743i) q^{37} +(-18.4919 + 50.5976i) q^{39} +(-42.8820 + 7.56125i) q^{41} +(-27.2523 - 22.8674i) q^{43} +(1.44010 - 3.92428i) q^{45} +(-5.51742 - 15.1590i) q^{47} +(51.8166 - 43.4793i) q^{49} +(78.4418 + 0.103888i) q^{51} +75.6950i q^{53} +7.39296 q^{55} +(-9.24914 + 5.32367i) q^{57} +(-18.4421 - 21.9784i) q^{59} +(-55.9422 + 20.3613i) q^{61} +(-74.2943 - 62.6764i) q^{63} +(-5.36107 + 6.38908i) q^{65} +(-4.03483 - 22.8827i) q^{67} +(-9.49246 + 7.94372i) q^{69} +(-32.2368 + 18.6119i) q^{71} +(-26.0280 + 45.0817i) q^{73} +(-47.8685 + 56.8942i) q^{75} +(58.7957 - 161.540i) q^{77} +(-20.9619 + 118.881i) q^{79} +(-40.8710 + 69.9325i) q^{81} +(115.091 + 20.2937i) q^{83} +(11.4121 + 4.15365i) q^{85} +(-95.6769 - 80.4987i) q^{87} +(-117.767 - 67.9930i) q^{89} +(96.9682 + 167.954i) q^{91} +(13.5710 + 16.2168i) q^{93} +(-1.62713 + 0.286906i) q^{95} +(-72.3238 - 60.6869i) q^{97} +(-141.012 - 25.2495i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 9q^{5} + 6q^{9} + O(q^{10}) \) \( 36q - 9q^{5} + 6q^{9} + 36q^{11} + 45q^{15} + 42q^{21} - 18q^{23} - 9q^{25} - 18q^{29} + 45q^{31} - 153q^{33} - 243q^{35} - 123q^{39} - 198q^{41} + 90q^{43} - 333q^{45} - 243q^{47} + 72q^{49} - 99q^{51} + 243q^{57} + 252q^{59} - 144q^{61} + 381q^{63} + 747q^{65} + 108q^{67} + 585q^{69} + 324q^{71} - 63q^{73} + 597q^{75} + 495q^{77} + 36q^{79} - 54q^{81} - 27q^{83} - 180q^{85} - 441q^{87} - 567q^{89} + 99q^{91} - 699q^{93} - 1044q^{95} - 216q^{97} - 945q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{18}\right)\) \(1\)

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
\(3\) −2.59609 1.50344i −0.865362 0.501147i
\(4\) 0 0
\(5\) −0.298552 0.355800i −0.0597103 0.0711600i 0.735363 0.677674i \(-0.237012\pi\)
−0.795073 + 0.606514i \(0.792567\pi\)
\(6\) 0 0
\(7\) −10.1488 + 3.69384i −1.44982 + 0.527692i −0.942542 0.334089i \(-0.891571\pi\)
−0.507281 + 0.861781i \(0.669349\pi\)
\(8\) 0 0
\(9\) 4.47934 + 7.80612i 0.497704 + 0.867347i
\(10\) 0 0
\(11\) −10.2314 + 12.1933i −0.930125 + 1.10848i 0.0637495 + 0.997966i \(0.479694\pi\)
−0.993875 + 0.110514i \(0.964750\pi\)
\(12\) 0 0
\(13\) −3.11819 17.6841i −0.239861 1.36032i −0.832131 0.554579i \(-0.812879\pi\)
0.592271 0.805739i \(-0.298232\pi\)
\(14\) 0 0
\(15\) 0.240142 + 1.37254i 0.0160095 + 0.0915028i
\(16\) 0 0
\(17\) −22.6442 + 13.0736i −1.33201 + 0.769038i −0.985608 0.169047i \(-0.945931\pi\)
−0.346405 + 0.938085i \(0.612598\pi\)
\(18\) 0 0
\(19\) 1.77864 3.08069i 0.0936126 0.162142i −0.815416 0.578875i \(-0.803492\pi\)
0.909029 + 0.416733i \(0.136825\pi\)
\(20\) 0 0
\(21\) 31.9005 + 5.66850i 1.51907 + 0.269928i
\(22\) 0 0
\(23\) 1.41115 3.87710i 0.0613543 0.168570i −0.905228 0.424926i \(-0.860300\pi\)
0.966582 + 0.256357i \(0.0825222\pi\)
\(24\) 0 0
\(25\) 4.30374 24.4077i 0.172150 0.976310i
\(26\) 0 0
\(27\) 0.107276 26.9998i 0.00397319 0.999992i
\(28\) 0 0
\(29\) 41.0456 + 7.23745i 1.41537 + 0.249567i 0.828442 0.560075i \(-0.189228\pi\)
0.586924 + 0.809642i \(0.300339\pi\)
\(30\) 0 0
\(31\) −6.62361 2.41080i −0.213665 0.0777677i 0.232970 0.972484i \(-0.425156\pi\)
−0.446635 + 0.894716i \(0.647378\pi\)
\(32\) 0 0
\(33\) 44.8934 16.2726i 1.36041 0.493108i
\(34\) 0 0
\(35\) 4.34420 + 2.50812i 0.124120 + 0.0716606i
\(36\) 0 0
\(37\) 4.92909 + 8.53743i 0.133219 + 0.230741i 0.924916 0.380173i \(-0.124135\pi\)
−0.791697 + 0.610914i \(0.790802\pi\)
\(38\) 0 0
\(39\) −18.4919 + 50.5976i −0.474152 + 1.29737i
\(40\) 0 0
\(41\) −42.8820 + 7.56125i −1.04590 + 0.184421i −0.670094 0.742277i \(-0.733746\pi\)
−0.375808 + 0.926697i \(0.622635\pi\)
\(42\) 0 0
\(43\) −27.2523 22.8674i −0.633773 0.531799i 0.268326 0.963328i \(-0.413530\pi\)
−0.902099 + 0.431529i \(0.857974\pi\)
\(44\) 0 0
\(45\) 1.44010 3.92428i 0.0320023 0.0872062i
\(46\) 0 0
\(47\) −5.51742 15.1590i −0.117392 0.322531i 0.867055 0.498212i \(-0.166010\pi\)
−0.984447 + 0.175680i \(0.943788\pi\)
\(48\) 0 0
\(49\) 51.8166 43.4793i 1.05748 0.887332i
\(50\) 0 0
\(51\) 78.4418 + 0.103888i 1.53807 + 0.00203703i
\(52\) 0 0
\(53\) 75.6950i 1.42821i 0.700040 + 0.714104i \(0.253166\pi\)
−0.700040 + 0.714104i \(0.746834\pi\)
\(54\) 0 0
\(55\) 7.39296 0.134417
\(56\) 0 0
\(57\) −9.24914 + 5.32367i −0.162266 + 0.0933977i
\(58\) 0 0
\(59\) −18.4421 21.9784i −0.312578 0.372516i 0.586767 0.809756i \(-0.300400\pi\)
−0.899345 + 0.437240i \(0.855956\pi\)
\(60\) 0 0
\(61\) −55.9422 + 20.3613i −0.917085 + 0.333792i −0.757078 0.653324i \(-0.773374\pi\)
−0.160007 + 0.987116i \(0.551152\pi\)
\(62\) 0 0
\(63\) −74.2943 62.6764i −1.17927 0.994864i
\(64\) 0 0
\(65\) −5.36107 + 6.38908i −0.0824780 + 0.0982935i
\(66\) 0 0
\(67\) −4.03483 22.8827i −0.0602214 0.341532i 0.939779 0.341784i \(-0.111031\pi\)
−1.00000 0.000251397i \(0.999920\pi\)
\(68\) 0 0
\(69\) −9.49246 + 7.94372i −0.137572 + 0.115126i
\(70\) 0 0
\(71\) −32.2368 + 18.6119i −0.454039 + 0.262139i −0.709534 0.704671i \(-0.751095\pi\)
0.255496 + 0.966810i \(0.417761\pi\)
\(72\) 0 0
\(73\) −26.0280 + 45.0817i −0.356547 + 0.617558i −0.987382 0.158360i \(-0.949380\pi\)
0.630834 + 0.775918i \(0.282713\pi\)
\(74\) 0 0
\(75\) −47.8685 + 56.8942i −0.638246 + 0.758590i
\(76\) 0 0
\(77\) 58.7957 161.540i 0.763580 2.09792i
\(78\) 0 0
\(79\) −20.9619 + 118.881i −0.265341 + 1.50482i 0.502722 + 0.864448i \(0.332332\pi\)
−0.768063 + 0.640374i \(0.778779\pi\)
\(80\) 0 0
\(81\) −40.8710 + 69.9325i −0.504581 + 0.863364i
\(82\) 0 0
\(83\) 115.091 + 20.2937i 1.38664 + 0.244502i 0.816642 0.577145i \(-0.195833\pi\)
0.569997 + 0.821647i \(0.306944\pi\)
\(84\) 0 0
\(85\) 11.4121 + 4.15365i 0.134260 + 0.0488665i
\(86\) 0 0
\(87\) −95.6769 80.4987i −1.09974 0.925272i
\(88\) 0 0
\(89\) −117.767 67.9930i −1.32323 0.763966i −0.338985 0.940792i \(-0.610084\pi\)
−0.984242 + 0.176826i \(0.943417\pi\)
\(90\) 0 0
\(91\) 96.9682 + 167.954i 1.06558 + 1.84565i
\(92\) 0 0
\(93\) 13.5710 + 16.2168i 0.145925 + 0.174375i
\(94\) 0 0
\(95\) −1.62713 + 0.286906i −0.0171276 + 0.00302006i
\(96\) 0 0
\(97\) −72.3238 60.6869i −0.745606 0.625638i 0.188731 0.982029i \(-0.439563\pi\)
−0.934337 + 0.356391i \(0.884007\pi\)
\(98\) 0 0
\(99\) −141.012 25.2495i −1.42436 0.255046i
\(100\) 0 0
\(101\) 52.1346 + 143.239i 0.516184 + 1.41820i 0.874693 + 0.484678i \(0.161063\pi\)
−0.358509 + 0.933526i \(0.616715\pi\)
\(102\) 0 0
\(103\) 16.6643 13.9830i 0.161790 0.135758i −0.558299 0.829640i \(-0.688546\pi\)
0.720088 + 0.693882i \(0.244101\pi\)
\(104\) 0 0
\(105\) −7.50710 13.0425i −0.0714962 0.124215i
\(106\) 0 0
\(107\) 49.8431i 0.465823i −0.972498 0.232912i \(-0.925175\pi\)
0.972498 0.232912i \(-0.0748253\pi\)
\(108\) 0 0
\(109\) 171.063 1.56939 0.784695 0.619882i \(-0.212820\pi\)
0.784695 + 0.619882i \(0.212820\pi\)
\(110\) 0 0
\(111\) 0.0391685 29.5745i 0.000352869 0.266437i
\(112\) 0 0
\(113\) 26.1647 + 31.1819i 0.231546 + 0.275946i 0.869290 0.494303i \(-0.164577\pi\)
−0.637744 + 0.770249i \(0.720132\pi\)
\(114\) 0 0
\(115\) −1.80077 + 0.655428i −0.0156589 + 0.00569937i
\(116\) 0 0
\(117\) 124.077 103.554i 1.06049 0.885078i
\(118\) 0 0
\(119\) 181.519 216.325i 1.52537 1.81786i
\(120\) 0 0
\(121\) −22.9836 130.346i −0.189947 1.07724i
\(122\) 0 0
\(123\) 122.693 + 44.8408i 0.997506 + 0.364559i
\(124\) 0 0
\(125\) −20.0251 + 11.5615i −0.160201 + 0.0924920i
\(126\) 0 0
\(127\) −30.8908 + 53.5044i −0.243235 + 0.421295i −0.961634 0.274336i \(-0.911542\pi\)
0.718399 + 0.695631i \(0.244875\pi\)
\(128\) 0 0
\(129\) 36.3695 + 100.338i 0.281934 + 0.777812i
\(130\) 0 0
\(131\) 77.3505 212.519i 0.590462 1.62228i −0.179189 0.983815i \(-0.557347\pi\)
0.769651 0.638465i \(-0.220430\pi\)
\(132\) 0 0
\(133\) −6.67137 + 37.8352i −0.0501607 + 0.284475i
\(134\) 0 0
\(135\) −9.63855 + 8.02266i −0.0713967 + 0.0594271i
\(136\) 0 0
\(137\) −149.613 26.3808i −1.09206 0.192560i −0.401519 0.915851i \(-0.631518\pi\)
−0.690544 + 0.723290i \(0.742629\pi\)
\(138\) 0 0
\(139\) 159.710 + 58.1298i 1.14899 + 0.418200i 0.845154 0.534523i \(-0.179509\pi\)
0.303841 + 0.952723i \(0.401731\pi\)
\(140\) 0 0
\(141\) −8.46691 + 47.6491i −0.0600490 + 0.337937i
\(142\) 0 0
\(143\) 247.531 + 142.912i 1.73099 + 0.999385i
\(144\) 0 0
\(145\) −9.67915 16.7648i −0.0667528 0.115619i
\(146\) 0 0
\(147\) −199.889 + 34.9729i −1.35979 + 0.237911i
\(148\) 0 0
\(149\) −176.331 + 31.0919i −1.18343 + 0.208671i −0.730524 0.682887i \(-0.760724\pi\)
−0.452907 + 0.891558i \(0.649613\pi\)
\(150\) 0 0
\(151\) 92.0549 + 77.2432i 0.609635 + 0.511544i 0.894526 0.447015i \(-0.147513\pi\)
−0.284891 + 0.958560i \(0.591958\pi\)
\(152\) 0 0
\(153\) −203.486 118.202i −1.32997 0.772563i
\(154\) 0 0
\(155\) 1.11973 + 3.07643i 0.00722405 + 0.0198479i
\(156\) 0 0
\(157\) 24.9795 20.9603i 0.159105 0.133505i −0.559760 0.828655i \(-0.689107\pi\)
0.718865 + 0.695150i \(0.244662\pi\)
\(158\) 0 0
\(159\) 113.803 196.511i 0.715741 1.23592i
\(160\) 0 0
\(161\) 44.5603i 0.276772i
\(162\) 0 0
\(163\) −219.827 −1.34863 −0.674316 0.738443i \(-0.735561\pi\)
−0.674316 + 0.738443i \(0.735561\pi\)
\(164\) 0 0
\(165\) −19.1928 11.1149i −0.116320 0.0673628i
\(166\) 0 0
\(167\) 78.0508 + 93.0173i 0.467370 + 0.556990i 0.947313 0.320310i \(-0.103787\pi\)
−0.479943 + 0.877300i \(0.659343\pi\)
\(168\) 0 0
\(169\) −144.197 + 52.4835i −0.853239 + 0.310553i
\(170\) 0 0
\(171\) 32.0154 + 0.0848025i 0.187224 + 0.000495921i
\(172\) 0 0
\(173\) −49.6240 + 59.1396i −0.286844 + 0.341847i −0.890154 0.455659i \(-0.849404\pi\)
0.603310 + 0.797506i \(0.293848\pi\)
\(174\) 0 0
\(175\) 46.4808 + 263.606i 0.265604 + 1.50632i
\(176\) 0 0
\(177\) 14.8340 + 84.7845i 0.0838082 + 0.479009i
\(178\) 0 0
\(179\) −128.588 + 74.2402i −0.718367 + 0.414750i −0.814151 0.580653i \(-0.802797\pi\)
0.0957841 + 0.995402i \(0.469464\pi\)
\(180\) 0 0
\(181\) 42.2135 73.1159i 0.233224 0.403955i −0.725531 0.688189i \(-0.758406\pi\)
0.958755 + 0.284234i \(0.0917393\pi\)
\(182\) 0 0
\(183\) 175.843 + 31.2460i 0.960890 + 0.170743i
\(184\) 0 0
\(185\) 1.56603 4.30263i 0.00846503 0.0232575i
\(186\) 0 0
\(187\) 72.2709 409.869i 0.386475 2.19181i
\(188\) 0 0
\(189\) 98.6443 + 274.410i 0.521928 + 1.45191i
\(190\) 0 0
\(191\) −1.92568 0.339550i −0.0100821 0.00177775i 0.168605 0.985684i \(-0.446074\pi\)
−0.178687 + 0.983906i \(0.557185\pi\)
\(192\) 0 0
\(193\) −311.970 113.548i −1.61643 0.588331i −0.633731 0.773554i \(-0.718477\pi\)
−0.982697 + 0.185223i \(0.940699\pi\)
\(194\) 0 0
\(195\) 23.5234 8.52655i 0.120633 0.0437259i
\(196\) 0 0
\(197\) −213.145 123.059i −1.08195 0.624666i −0.150531 0.988605i \(-0.548098\pi\)
−0.931423 + 0.363939i \(0.881432\pi\)
\(198\) 0 0
\(199\) −138.226 239.415i −0.694604 1.20309i −0.970314 0.241849i \(-0.922246\pi\)
0.275710 0.961241i \(-0.411087\pi\)
\(200\) 0 0
\(201\) −23.9279 + 65.4716i −0.119044 + 0.325729i
\(202\) 0 0
\(203\) −443.296 + 78.1650i −2.18372 + 0.385049i
\(204\) 0 0
\(205\) 15.4928 + 13.0000i 0.0755745 + 0.0634145i
\(206\) 0 0
\(207\) 36.5861 6.35125i 0.176745 0.0306824i
\(208\) 0 0
\(209\) 19.3658 + 53.2072i 0.0926594 + 0.254580i
\(210\) 0 0
\(211\) −40.7896 + 34.2265i −0.193316 + 0.162211i −0.734308 0.678816i \(-0.762493\pi\)
0.540992 + 0.841027i \(0.318049\pi\)
\(212\) 0 0
\(213\) 111.671 + 0.147898i 0.524279 + 0.000694355i
\(214\) 0 0
\(215\) 16.5234i 0.0768532i
\(216\) 0 0
\(217\) 76.1265 0.350813
\(218\) 0 0
\(219\) 135.349 77.9047i 0.618030 0.355729i
\(220\) 0 0
\(221\) 301.805 + 359.677i 1.36563 + 1.62750i
\(222\) 0 0
\(223\) 101.950 37.1068i 0.457175 0.166398i −0.103159 0.994665i \(-0.532895\pi\)
0.560334 + 0.828267i \(0.310673\pi\)
\(224\) 0 0
\(225\) 209.808 75.7350i 0.932479 0.336600i
\(226\) 0 0
\(227\) −232.991 + 277.668i −1.02639 + 1.22321i −0.0519295 + 0.998651i \(0.516537\pi\)
−0.974462 + 0.224554i \(0.927907\pi\)
\(228\) 0 0
\(229\) −50.2795 285.149i −0.219561 1.24519i −0.872814 0.488054i \(-0.837707\pi\)
0.653252 0.757140i \(-0.273404\pi\)
\(230\) 0 0
\(231\) −395.504 + 330.976i −1.71214 + 1.43279i
\(232\) 0 0
\(233\) 127.663 73.7062i 0.547910 0.316336i −0.200369 0.979721i \(-0.564214\pi\)
0.748279 + 0.663385i \(0.230881\pi\)
\(234\) 0 0
\(235\) −3.74633 + 6.48883i −0.0159418 + 0.0276120i
\(236\) 0 0
\(237\) 233.149 277.110i 0.983753 1.16924i
\(238\) 0 0
\(239\) −4.66249 + 12.8101i −0.0195083 + 0.0535987i −0.949065 0.315082i \(-0.897968\pi\)
0.929556 + 0.368680i \(0.120190\pi\)
\(240\) 0 0
\(241\) −51.5844 + 292.550i −0.214043 + 1.21390i 0.668516 + 0.743698i \(0.266930\pi\)
−0.882559 + 0.470201i \(0.844181\pi\)
\(242\) 0 0
\(243\) 211.244 120.104i 0.869317 0.494254i
\(244\) 0 0
\(245\) −30.9398 5.45553i −0.126285 0.0222675i
\(246\) 0 0
\(247\) −60.0255 21.8475i −0.243018 0.0884514i
\(248\) 0 0
\(249\) −268.276 225.717i −1.07741 0.906492i
\(250\) 0 0
\(251\) −0.182848 0.105567i −0.000728476 0.000420586i 0.499636 0.866236i \(-0.333467\pi\)
−0.500364 + 0.865815i \(0.666801\pi\)
\(252\) 0 0
\(253\) 32.8366 + 56.8746i 0.129789 + 0.224801i
\(254\) 0 0
\(255\) −23.3820 27.9406i −0.0916939 0.109571i
\(256\) 0 0
\(257\) 190.970 33.6731i 0.743073 0.131024i 0.210720 0.977546i \(-0.432419\pi\)
0.532353 + 0.846523i \(0.321308\pi\)
\(258\) 0 0
\(259\) −81.5601 68.4370i −0.314904 0.264236i
\(260\) 0 0
\(261\) 127.361 + 352.826i 0.487973 + 1.35182i
\(262\) 0 0
\(263\) −139.835 384.194i −0.531692 1.46081i −0.857056 0.515224i \(-0.827709\pi\)
0.325363 0.945589i \(-0.394513\pi\)
\(264\) 0 0
\(265\) 26.9323 22.5989i 0.101631 0.0852787i
\(266\) 0 0
\(267\) 203.511 + 353.572i 0.762213 + 1.32424i
\(268\) 0 0
\(269\) 120.090i 0.446433i −0.974769 0.223216i \(-0.928344\pi\)
0.974769 0.223216i \(-0.0716557\pi\)
\(270\) 0 0
\(271\) 19.0289 0.0702175 0.0351088 0.999383i \(-0.488822\pi\)
0.0351088 + 0.999383i \(0.488822\pi\)
\(272\) 0 0
\(273\) 0.770547 581.809i 0.00282252 2.13117i
\(274\) 0 0
\(275\) 253.577 + 302.202i 0.922099 + 1.09891i
\(276\) 0 0
\(277\) 299.169 108.889i 1.08003 0.393099i 0.260112 0.965578i \(-0.416240\pi\)
0.819919 + 0.572479i \(0.194018\pi\)
\(278\) 0 0
\(279\) −10.8504 62.5035i −0.0388904 0.224027i
\(280\) 0 0
\(281\) −154.692 + 184.354i −0.550504 + 0.656065i −0.967508 0.252839i \(-0.918636\pi\)
0.417004 + 0.908905i \(0.363080\pi\)
\(282\) 0 0
\(283\) 15.5135 + 87.9813i 0.0548179 + 0.310888i 0.999872 0.0160274i \(-0.00510189\pi\)
−0.945054 + 0.326915i \(0.893991\pi\)
\(284\) 0 0
\(285\) 4.65551 + 1.70145i 0.0163351 + 0.00597000i
\(286\) 0 0
\(287\) 407.269 235.137i 1.41905 0.819292i
\(288\) 0 0
\(289\) 197.340 341.803i 0.682838 1.18271i
\(290\) 0 0
\(291\) 96.5199 + 266.283i 0.331683 + 0.915062i
\(292\) 0 0
\(293\) 106.539 292.713i 0.363614 0.999022i −0.614127 0.789207i \(-0.710492\pi\)
0.977741 0.209814i \(-0.0672860\pi\)
\(294\) 0 0
\(295\) −2.31401 + 13.1234i −0.00784410 + 0.0444861i
\(296\) 0 0
\(297\) 328.118 + 277.553i 1.10478 + 0.934522i
\(298\) 0 0
\(299\) −72.9634 12.8654i −0.244025 0.0430282i
\(300\) 0 0
\(301\) 361.045 + 131.410i 1.19948 + 0.436577i
\(302\) 0 0
\(303\) 80.0047 450.241i 0.264042 1.48594i
\(304\) 0 0
\(305\) 23.9462 + 13.8253i 0.0785120 + 0.0453289i
\(306\) 0 0
\(307\) −296.790 514.055i −0.966743 1.67445i −0.704858 0.709348i \(-0.748989\pi\)
−0.261885 0.965099i \(-0.584344\pi\)
\(308\) 0 0
\(309\) −64.2847 + 11.2474i −0.208041 + 0.0363992i
\(310\) 0 0
\(311\) −538.372 + 94.9296i −1.73110 + 0.305240i −0.948381 0.317134i \(-0.897280\pi\)
−0.782720 + 0.622374i \(0.786168\pi\)
\(312\) 0 0
\(313\) 119.991 + 100.684i 0.383357 + 0.321675i 0.814019 0.580839i \(-0.197275\pi\)
−0.430662 + 0.902513i \(0.641720\pi\)
\(314\) 0 0
\(315\) −0.119583 + 45.1461i −0.000379629 + 0.143321i
\(316\) 0 0
\(317\) −14.4734 39.7653i −0.0456574 0.125443i 0.914768 0.403979i \(-0.132373\pi\)
−0.960426 + 0.278536i \(0.910151\pi\)
\(318\) 0 0
\(319\) −508.201 + 426.432i −1.59311 + 1.33678i
\(320\) 0 0
\(321\) −74.9361 + 129.397i −0.233446 + 0.403106i
\(322\) 0 0
\(323\) 93.0132i 0.287966i
\(324\) 0 0
\(325\) −445.050 −1.36938
\(326\) 0 0
\(327\) −444.096 257.184i −1.35809 0.786494i
\(328\) 0 0
\(329\) 111.990 + 133.464i 0.340395 + 0.405666i
\(330\) 0 0
\(331\) 462.396 168.298i 1.39697 0.508455i 0.469691 0.882831i \(-0.344365\pi\)
0.927277 + 0.374376i \(0.122143\pi\)
\(332\) 0 0
\(333\) −44.5652 + 76.7191i −0.133829 + 0.230388i
\(334\) 0 0
\(335\) −6.93705 + 8.26725i −0.0207076 + 0.0246784i
\(336\) 0 0
\(337\) 113.729 + 644.988i 0.337474 + 1.91391i 0.401296 + 0.915948i \(0.368560\pi\)
−0.0638222 + 0.997961i \(0.520329\pi\)
\(338\) 0 0
\(339\) −21.0458 120.288i −0.0620820 0.354832i
\(340\) 0 0
\(341\) 97.1642 56.0978i 0.284939 0.164510i
\(342\) 0 0
\(343\) −100.666 + 174.359i −0.293487 + 0.508335i
\(344\) 0 0
\(345\) 5.66036 + 1.00581i 0.0164068 + 0.00291538i
\(346\) 0 0
\(347\) −44.4825 + 122.215i −0.128192 + 0.352204i −0.987140 0.159859i \(-0.948896\pi\)
0.858948 + 0.512062i \(0.171118\pi\)
\(348\) 0 0
\(349\) 14.3449 81.3537i 0.0411027 0.233105i −0.957335 0.288980i \(-0.906684\pi\)
0.998438 + 0.0558751i \(0.0177949\pi\)
\(350\) 0 0
\(351\) −477.802 + 82.2934i −1.36126 + 0.234454i
\(352\) 0 0
\(353\) −65.5878 11.5649i −0.185801 0.0327618i 0.0799732 0.996797i \(-0.474517\pi\)
−0.265774 + 0.964035i \(0.585628\pi\)
\(354\) 0 0
\(355\) 16.2464 + 5.91322i 0.0457646 + 0.0166570i
\(356\) 0 0
\(357\) −796.470 + 288.697i −2.23101 + 0.808676i
\(358\) 0 0
\(359\) 289.619 + 167.211i 0.806737 + 0.465770i 0.845821 0.533466i \(-0.179111\pi\)
−0.0390844 + 0.999236i \(0.512444\pi\)
\(360\) 0 0
\(361\) 174.173 + 301.676i 0.482473 + 0.835668i
\(362\) 0 0
\(363\) −136.300 + 372.945i −0.375483 + 1.02740i
\(364\) 0 0
\(365\) 23.8108 4.19848i 0.0652350 0.0115027i
\(366\) 0 0
\(367\) 312.913 + 262.565i 0.852624 + 0.715437i 0.960366 0.278742i \(-0.0899175\pi\)
−0.107742 + 0.994179i \(0.534362\pi\)
\(368\) 0 0
\(369\) −251.107 300.873i −0.680507 0.815373i
\(370\) 0 0
\(371\) −279.606 768.210i −0.753654 2.07065i
\(372\) 0 0
\(373\) −234.819 + 197.037i −0.629543 + 0.528249i −0.900787 0.434262i \(-0.857009\pi\)
0.271244 + 0.962511i \(0.412565\pi\)
\(374\) 0 0
\(375\) 69.3689 + 0.0918722i 0.184984 + 0.000244993i
\(376\) 0 0
\(377\) 748.424i 1.98521i
\(378\) 0 0
\(379\) −98.9004 −0.260951 −0.130475 0.991452i \(-0.541650\pi\)
−0.130475 + 0.991452i \(0.541650\pi\)
\(380\) 0 0
\(381\) 160.636 92.4597i 0.421616 0.242676i
\(382\) 0 0
\(383\) 319.309 + 380.537i 0.833704 + 0.993570i 0.999972 + 0.00748907i \(0.00238387\pi\)
−0.166268 + 0.986081i \(0.553172\pi\)
\(384\) 0 0
\(385\) −75.0293 + 27.3084i −0.194881 + 0.0709310i
\(386\) 0 0
\(387\) 56.4333 315.165i 0.145822 0.814380i
\(388\) 0 0
\(389\) 305.584 364.181i 0.785563 0.936197i −0.213608 0.976920i \(-0.568521\pi\)
0.999171 + 0.0407223i \(0.0129659\pi\)
\(390\) 0 0
\(391\) 18.7335 + 106.243i 0.0479117 + 0.271721i
\(392\) 0 0
\(393\) −520.317 + 435.425i −1.32396 + 1.10795i
\(394\) 0 0
\(395\) 48.5561 28.0339i 0.122927 0.0709718i
\(396\) 0 0
\(397\) −217.038 + 375.920i −0.546694 + 0.946902i 0.451804 + 0.892117i \(0.350781\pi\)
−0.998498 + 0.0547849i \(0.982553\pi\)
\(398\) 0 0
\(399\) 74.2024 88.1935i 0.185971 0.221036i
\(400\) 0 0
\(401\) 84.0625 230.960i 0.209632 0.575960i −0.789661 0.613543i \(-0.789744\pi\)
0.999294 + 0.0375831i \(0.0119659\pi\)
\(402\) 0 0
\(403\) −21.9792 + 124.650i −0.0545389 + 0.309306i
\(404\) 0 0
\(405\) 37.0841 6.33655i 0.0915657 0.0156458i
\(406\) 0 0
\(407\) −154.531 27.2479i −0.379682 0.0669482i
\(408\) 0 0
\(409\) −328.561 119.587i −0.803328 0.292388i −0.0924633 0.995716i \(-0.529474\pi\)
−0.710865 + 0.703329i \(0.751696\pi\)
\(410\) 0 0
\(411\) 348.746 + 293.420i 0.848530 + 0.713918i
\(412\) 0 0
\(413\) 268.349 + 154.932i 0.649756 + 0.375137i
\(414\) 0 0
\(415\) −27.1401 47.0081i −0.0653979 0.113272i
\(416\) 0 0
\(417\) −327.227 391.025i −0.784718 0.937709i
\(418\) 0 0
\(419\) −271.509 + 47.8743i −0.647993 + 0.114259i −0.487978 0.872856i \(-0.662265\pi\)
−0.160015 + 0.987115i \(0.551154\pi\)
\(420\) 0 0
\(421\) 50.0550 + 42.0012i 0.118896 + 0.0997652i 0.700297 0.713852i \(-0.253051\pi\)
−0.581401 + 0.813617i \(0.697495\pi\)
\(422\) 0 0
\(423\) 93.6184 110.972i 0.221320 0.262345i
\(424\) 0 0
\(425\) 221.643 + 608.960i 0.521514 + 1.43285i
\(426\) 0 0
\(427\) 492.532 413.284i 1.15347 0.967877i
\(428\) 0 0
\(429\) −427.752 743.160i −0.997091 1.73231i
\(430\) 0 0
\(431\) 105.508i 0.244799i −0.992481 0.122399i \(-0.960941\pi\)
0.992481 0.122399i \(-0.0390589\pi\)
\(432\) 0 0
\(433\) 599.181 1.38379 0.691895 0.721998i \(-0.256776\pi\)
0.691895 + 0.721998i \(0.256776\pi\)
\(434\) 0 0
\(435\) −0.0769143 + 58.0748i −0.000176815 + 0.133505i
\(436\) 0 0
\(437\) −9.43423 11.2433i −0.0215886 0.0257283i
\(438\) 0 0
\(439\) 59.8973 21.8008i 0.136440 0.0496602i −0.272897 0.962043i \(-0.587982\pi\)
0.409338 + 0.912383i \(0.365760\pi\)
\(440\) 0 0
\(441\) 571.508 + 209.728i 1.29594 + 0.475574i
\(442\) 0 0
\(443\) −85.6046 + 102.020i −0.193238 + 0.230292i −0.853960 0.520338i \(-0.825806\pi\)
0.660722 + 0.750631i \(0.270250\pi\)
\(444\) 0 0
\(445\) 10.9677 + 62.2010i 0.0246465 + 0.139777i
\(446\) 0 0
\(447\) 504.516 + 184.386i 1.12867 + 0.412496i
\(448\) 0 0
\(449\) −120.484 + 69.5615i −0.268339 + 0.154925i −0.628132 0.778106i \(-0.716180\pi\)
0.359794 + 0.933032i \(0.382847\pi\)
\(450\) 0 0
\(451\) 346.545 600.234i 0.768393 1.33090i
\(452\) 0 0
\(453\) −122.852 338.929i −0.271196 0.748188i
\(454\) 0 0
\(455\) 30.8079 84.6441i 0.0677098 0.186031i
\(456\) 0 0
\(457\) −21.0125 + 119.168i −0.0459792 + 0.260761i −0.999129 0.0417393i \(-0.986710\pi\)
0.953149 + 0.302500i \(0.0978212\pi\)
\(458\) 0 0
\(459\) 350.556 + 612.791i 0.763739 + 1.33506i
\(460\) 0 0
\(461\) −266.202 46.9386i −0.577445 0.101819i −0.122705 0.992443i \(-0.539157\pi\)
−0.454740 + 0.890624i \(0.650268\pi\)
\(462\) 0 0
\(463\) 16.9878 + 6.18304i 0.0366906 + 0.0133543i 0.360300 0.932836i \(-0.382674\pi\)
−0.323610 + 0.946191i \(0.604896\pi\)
\(464\) 0 0
\(465\) 1.71831 9.67012i 0.00369529 0.0207960i
\(466\) 0 0
\(467\) −439.219 253.583i −0.940511 0.543004i −0.0503903 0.998730i \(-0.516047\pi\)
−0.890120 + 0.455725i \(0.849380\pi\)
\(468\) 0 0
\(469\) 125.474 + 217.327i 0.267534 + 0.463383i
\(470\) 0 0
\(471\) −96.3614 + 16.8596i −0.204589 + 0.0357952i
\(472\) 0 0
\(473\) 557.656 98.3298i 1.17898 0.207885i
\(474\) 0 0
\(475\) −67.5380 56.6711i −0.142185 0.119308i
\(476\) 0 0
\(477\) −590.884 + 339.064i −1.23875 + 0.710825i
\(478\) 0 0
\(479\) 210.140 + 577.355i 0.438705 + 1.20533i 0.940335 + 0.340251i \(0.110512\pi\)
−0.501629 + 0.865083i \(0.667266\pi\)
\(480\) 0 0
\(481\) 135.607 113.788i 0.281928 0.236565i
\(482\) 0 0
\(483\) 66.9938 115.683i 0.138703 0.239508i
\(484\) 0 0
\(485\) 43.8510i 0.0904144i
\(486\) 0 0
\(487\) −218.562 −0.448793 −0.224396 0.974498i \(-0.572041\pi\)
−0.224396 + 0.974498i \(0.572041\pi\)
\(488\) 0 0
\(489\) 570.690 + 330.496i 1.16705 + 0.675862i
\(490\) 0 0
\(491\) −128.585 153.242i −0.261885 0.312102i 0.619039 0.785360i \(-0.287522\pi\)
−0.880924 + 0.473258i \(0.843078\pi\)
\(492\) 0 0
\(493\) −1024.07 + 372.729i −2.07721 + 0.756043i
\(494\) 0 0
\(495\) 33.1156 + 57.7103i 0.0669001 + 0.116587i
\(496\) 0 0
\(497\) 258.414 307.965i 0.519947 0.619648i
\(498\) 0 0
\(499\) −23.1673 131.388i −0.0464274 0.263303i 0.952755 0.303741i \(-0.0982358\pi\)
−0.999182 + 0.0404381i \(0.987125\pi\)
\(500\) 0 0
\(501\) −62.7808 358.826i −0.125311 0.716219i
\(502\) 0 0
\(503\) 156.930 90.6037i 0.311989 0.180127i −0.335827 0.941924i \(-0.609016\pi\)
0.647816 + 0.761797i \(0.275683\pi\)
\(504\) 0 0
\(505\) 35.3994 61.3136i 0.0700979 0.121413i
\(506\) 0 0
\(507\) 453.255 + 80.5401i 0.893993 + 0.158856i
\(508\) 0 0
\(509\) 268.953 738.941i 0.528394 1.45175i −0.332567 0.943080i \(-0.607915\pi\)
0.860961 0.508671i \(-0.169863\pi\)
\(510\) 0 0
\(511\) 97.6264 553.667i 0.191050 1.08350i
\(512\) 0 0
\(513\) −82.9872 48.3534i −0.161769 0.0942560i
\(514\) 0 0
\(515\) −9.95032 1.75451i −0.0193210 0.00340682i
\(516\) 0 0
\(517\) 241.288 + 87.8218i 0.466709 + 0.169868i
\(518\) 0 0
\(519\) 217.741 78.9248i 0.419539 0.152071i
\(520\) 0 0
\(521\) −169.525 97.8752i −0.325384 0.187860i 0.328406 0.944537i \(-0.393489\pi\)
−0.653790 + 0.756676i \(0.726822\pi\)
\(522\) 0 0
\(523\) −79.9831 138.535i −0.152931 0.264885i 0.779373 0.626561i \(-0.215538\pi\)
−0.932304 + 0.361676i \(0.882205\pi\)
\(524\) 0 0
\(525\) 275.647 754.224i 0.525042 1.43662i
\(526\) 0 0
\(527\) 181.504 32.0041i 0.344411 0.0607289i
\(528\) 0 0
\(529\) 392.197 + 329.092i 0.741393 + 0.622103i
\(530\) 0 0
\(531\) 88.9579 242.410i 0.167529 0.456516i
\(532\) 0 0
\(533\) 267.428 + 734.753i 0.501742 + 1.37852i
\(534\) 0 0
\(535\) −17.7342 + 14.8807i −0.0331480 + 0.0278145i
\(536\) 0 0
\(537\) 445.441 + 0.589942i 0.829499 + 0.00109859i
\(538\) 0 0
\(539\) 1076.67i 1.99753i
\(540\) 0 0
\(541\) −34.2145 −0.0632430 −0.0316215 0.999500i \(-0.510067\pi\)
−0.0316215 + 0.999500i \(0.510067\pi\)
\(542\) 0 0
\(543\) −219.515 + 126.350i −0.404264 + 0.232688i
\(544\) 0 0
\(545\) −51.0713 60.8644i −0.0937087 0.111678i
\(546\) 0 0
\(547\) 281.372 102.411i 0.514391 0.187223i −0.0717647 0.997422i \(-0.522863\pi\)
0.586155 + 0.810199i \(0.300641\pi\)
\(548\) 0 0
\(549\) −409.527 345.486i −0.745950 0.629301i
\(550\) 0 0
\(551\) 95.3017 113.576i 0.172961 0.206127i
\(552\) 0 0
\(553\) −226.390 1283.92i −0.409386 2.32174i
\(554\) 0 0
\(555\) −10.5343 + 8.81558i −0.0189807 + 0.0158839i
\(556\) 0 0
\(557\) −686.079 + 396.108i −1.23174 + 0.711146i −0.967393 0.253282i \(-0.918490\pi\)
−0.264348 + 0.964427i \(0.585157\pi\)
\(558\) 0 0
\(559\) −319.412 + 553.237i −0.571398 + 0.989691i
\(560\) 0 0
\(561\) −803.834 + 955.400i −1.43286 + 1.70303i
\(562\) 0 0
\(563\) −334.881 + 920.079i −0.594816 + 1.63424i 0.166634 + 0.986019i \(0.446710\pi\)
−0.761450 + 0.648224i \(0.775512\pi\)
\(564\) 0 0
\(565\) 3.28300 18.6188i 0.00581061 0.0329536i
\(566\) 0 0
\(567\) 156.470 860.699i 0.275962 1.51799i
\(568\) 0 0
\(569\) −552.043 97.3401i −0.970199 0.171072i −0.333979 0.942580i \(-0.608392\pi\)
−0.636219 + 0.771508i \(0.719503\pi\)
\(570\) 0 0
\(571\) −29.2223 10.6361i −0.0511775 0.0186271i 0.316305 0.948658i \(-0.397558\pi\)
−0.367482 + 0.930031i \(0.619780\pi\)
\(572\) 0 0
\(573\) 4.48875 + 3.77665i 0.00783377 + 0.00659102i
\(574\) 0 0
\(575\) −88.5581 51.1290i −0.154014 0.0889201i
\(576\) 0 0
\(577\) −95.1751 164.848i −0.164948 0.285699i 0.771689 0.636000i \(-0.219412\pi\)
−0.936637 + 0.350302i \(0.886079\pi\)
\(578\) 0 0
\(579\) 639.190 + 763.809i 1.10396 + 1.31919i
\(580\) 0 0
\(581\) −1242.99 + 219.173i −2.13940 + 0.377234i
\(582\) 0 0
\(583\) −922.970 774.464i −1.58314 1.32841i
\(584\) 0 0
\(585\) −73.8879 13.2303i −0.126304 0.0226160i
\(586\) 0 0
\(587\) −150.974 414.798i −0.257196 0.706641i −0.999337 0.0363972i \(-0.988412\pi\)
0.742141 0.670244i \(-0.233810\pi\)
\(588\) 0 0
\(589\) −19.2079 + 16.1174i −0.0326111 + 0.0273640i
\(590\) 0 0
\(591\) 368.331 + 639.923i 0.623233 + 1.08278i
\(592\) 0 0
\(593\) 435.642i 0.734640i 0.930095 + 0.367320i \(0.119725\pi\)
−0.930095 + 0.367320i \(0.880275\pi\)
\(594\) 0 0
\(595\) −131.161 −0.220439
\(596\) 0 0
\(597\) −1.09840 + 829.357i −0.00183987 + 1.38921i
\(598\) 0 0
\(599\) −615.387 733.389i −1.02736 1.22436i −0.974180 0.225771i \(-0.927510\pi\)
−0.0531765 0.998585i \(-0.516935\pi\)
\(600\) 0 0
\(601\) −214.739 + 78.1585i −0.357302 + 0.130047i −0.514433 0.857530i \(-0.671998\pi\)
0.157131 + 0.987578i \(0.449775\pi\)
\(602\) 0 0
\(603\) 160.552 133.996i 0.266255 0.222215i
\(604\) 0 0
\(605\) −39.5154 + 47.0926i −0.0653147 + 0.0778391i
\(606\) 0 0
\(607\) 23.6802 + 134.297i 0.0390118 + 0.221247i 0.998081 0.0619256i \(-0.0197241\pi\)
−0.959069 + 0.283173i \(0.908613\pi\)
\(608\) 0 0
\(609\) 1268.35 + 463.545i 2.08268 + 0.761158i
\(610\) 0 0
\(611\) −250.869 + 144.839i −0.410587 + 0.237053i
\(612\) 0 0
\(613\) −35.5694 + 61.6081i −0.0580252 + 0.100503i −0.893579 0.448906i \(-0.851814\pi\)
0.835554 + 0.549409i \(0.185147\pi\)
\(614\) 0 0
\(615\) −20.6759 57.0415i −0.0336194 0.0927505i
\(616\) 0 0
\(617\) −348.112 + 956.431i −0.564201 + 1.55013i 0.249215 + 0.968448i \(0.419828\pi\)
−0.813416 + 0.581682i \(0.802395\pi\)
\(618\) 0 0
\(619\) 63.4363 359.765i 0.102482 0.581204i −0.889714 0.456518i \(-0.849097\pi\)
0.992196 0.124686i \(-0.0397924\pi\)
\(620\) 0 0
\(621\) −104.530 38.5167i −0.168325 0.0620236i
\(622\) 0 0
\(623\) 1446.35 + 255.030i 2.32158 + 0.409358i
\(624\) 0 0
\(625\) −572.148 208.245i −0.915437 0.333192i
\(626\) 0 0
\(627\) 29.7184 167.246i 0.0473977 0.266740i
\(628\) 0 0
\(629\) −223.231 128.882i −0.354898 0.204900i
\(630\) 0 0
\(631\) 390.214 + 675.871i 0.618406 + 1.07111i 0.989777 + 0.142626i \(0.0455546\pi\)
−0.371371 + 0.928485i \(0.621112\pi\)
\(632\) 0 0
\(633\) 157.351 27.5304i 0.248580 0.0434919i
\(634\) 0 0
\(635\) 28.2594 4.98289i 0.0445029 0.00784707i
\(636\) 0 0
\(637\) −930.467 780.754i −1.46070 1.22567i
\(638\) 0 0
\(639\) −289.686 168.275i −0.453343 0.263341i
\(640\) 0 0
\(641\) −96.5071 265.151i −0.150557 0.413652i 0.841370 0.540459i \(-0.181749\pi\)
−0.991927 + 0.126807i \(0.959527\pi\)
\(642\) 0 0
\(643\) −32.0195 + 26.8675i −0.0497970 + 0.0417846i −0.667346 0.744747i \(-0.732570\pi\)
0.617549 + 0.786532i \(0.288126\pi\)
\(644\) 0 0
\(645\) 24.8420 42.8963i 0.0385147 0.0665059i
\(646\) 0 0
\(647\) 383.618i 0.592918i 0.955046 + 0.296459i \(0.0958058\pi\)
−0.955046 + 0.296459i \(0.904194\pi\)
\(648\) 0 0
\(649\) 456.677 0.703663
\(650\) 0 0
\(651\) −197.631 114.452i −0.303581 0.175809i
\(652\) 0 0
\(653\) 39.3773 + 46.9281i 0.0603022 + 0.0718653i 0.795352 0.606147i \(-0.207286\pi\)
−0.735050 + 0.678013i \(0.762841\pi\)
\(654\) 0 0
\(655\) −98.7072 + 35.9265i −0.150698 + 0.0548496i
\(656\) 0 0
\(657\) −468.502 1.24097i −0.713092 0.00188884i
\(658\) 0 0
\(659\) −329.590 + 392.790i −0.500137 + 0.596040i −0.955765 0.294130i \(-0.904970\pi\)
0.455629 + 0.890170i \(0.349415\pi\)
\(660\) 0 0
\(661\) −33.1600 188.060i −0.0501664 0.284508i 0.949396 0.314081i \(-0.101696\pi\)
−0.999563 + 0.0295731i \(0.990585\pi\)
\(662\) 0 0
\(663\) −242.759 1387.50i −0.366153 2.09276i
\(664\) 0 0
\(665\) 15.4535 8.92209i 0.0232384 0.0134167i
\(666\) 0 0
\(667\) 85.9819 148.925i 0.128908 0.223276i
\(668\) 0 0
\(669\) −320.459 56.9432i −0.479012 0.0851170i
\(670\) 0 0
\(671\) 324.095 890.443i 0.483003 1.32704i
\(672\) 0 0
\(673\) −180.046 + 1021.09i −0.267527 + 1.51722i 0.494214 + 0.869340i \(0.335456\pi\)
−0.761741 + 0.647882i \(0.775655\pi\)
\(674\) 0 0
\(675\) −658.542 118.819i −0.975618 0.176027i
\(676\) 0 0
\(677\) 482.182 + 85.0218i 0.712234 + 0.125586i 0.518014 0.855372i \(-0.326671\pi\)
0.194220 + 0.980958i \(0.437782\pi\)
\(678\) 0 0
\(679\) 958.165 + 348.743i 1.41114 + 0.513613i
\(680\) 0 0
\(681\) 1022.32 370.562i 1.50121 0.544144i
\(682\) 0 0
\(683\) 251.274 + 145.073i 0.367897 + 0.212406i 0.672540 0.740061i \(-0.265204\pi\)
−0.304642 + 0.952467i \(0.598537\pi\)
\(684\) 0 0
\(685\) 35.2808 + 61.1082i 0.0515049 + 0.0892090i
\(686\) 0 0
\(687\) −298.175 + 815.865i −0.434024 + 1.18758i
\(688\) 0 0
\(689\) 1338.60 236.031i 1.94282 0.342571i
\(690\) 0 0
\(691\) 148.698 + 124.773i 0.215193 + 0.180568i 0.744012 0.668166i \(-0.232921\pi\)
−0.528819 + 0.848735i \(0.677365\pi\)
\(692\) 0 0
\(693\) 1524.36 264.625i 2.19966 0.381855i
\(694\) 0 0
\(695\) −26.9992 74.1796i −0.0388477 0.106733i
\(696\) 0 0
\(697\) 872.176 731.842i 1.25133 1.04999i
\(698\) 0 0
\(699\) −442.237 0.585699i −0.632671 0.000837910i
\(700\) 0 0
\(701\) 294.780i 0.420513i −0.977646 0.210257i \(-0.932570\pi\)
0.977646 0.210257i \(-0.0674299\pi\)
\(702\) 0 0
\(703\) 35.0683 0.0498837
\(704\) 0 0
\(705\) 19.4814 11.2132i 0.0276331 0.0159052i
\(706\) 0 0
\(707\) −1058.20 1261.12i −1.49675 1.78376i
\(708\) 0 0
\(709\) 916.038 333.410i 1.29201 0.470255i 0.397626 0.917548i \(-0.369834\pi\)
0.894387 + 0.447293i \(0.147612\pi\)
\(710\) 0 0
\(711\) −1021.89 + 368.877i −1.43726 + 0.518814i
\(712\) 0 0
\(713\) −18.6938 + 22.2784i −0.0262185 + 0.0312460i
\(714\) 0 0
\(715\) −23.0526 130.738i −0.0322415 0.182850i
\(716\) 0 0
\(717\) 31.3634 26.2463i 0.0437426 0.0366058i
\(718\) 0 0
\(719\) −574.371 + 331.613i −0.798848 + 0.461215i −0.843068 0.537807i \(-0.819253\pi\)
0.0442205 + 0.999022i \(0.485920\pi\)
\(720\) 0 0
\(721\) −117.471 + 203.466i −0.162928 + 0.282200i
\(722\) 0 0
\(723\) 573.748 681.930i 0.793566 0.943196i
\(724\) 0 0
\(725\) 353.300 970.683i 0.487310 1.33887i
\(726\) 0 0
\(727\) −178.695 + 1013.43i −0.245797 + 1.39399i 0.572836 + 0.819670i \(0.305843\pi\)
−0.818633 + 0.574316i \(0.805268\pi\)
\(728\) 0 0
\(729\) −728.977 5.79286i −0.999968 0.00794631i
\(730\) 0 0
\(731\) 916.066 + 161.527i 1.25317 + 0.220967i
\(732\) 0 0
\(733\) −93.4865 34.0263i −0.127540 0.0464206i 0.277462 0.960737i \(-0.410507\pi\)
−0.405001 + 0.914316i \(0.632729\pi\)
\(734\) 0 0
\(735\) 72.1205 + 60.6792i 0.0981231 + 0.0825567i
\(736\) 0 0
\(737\) 320.297 + 184.923i 0.434595 + 0.250914i
\(738\) 0 0
\(739\) 28.7996 + 49.8824i 0.0389710 + 0.0674998i 0.884853 0.465870i \(-0.154259\pi\)
−0.845882 + 0.533370i \(0.820925\pi\)
\(740\) 0 0
\(741\) 122.985 + 146.963i 0.165972 + 0.198330i
\(742\) 0 0
\(743\) 1203.21 212.158i 1.61939 0.285543i 0.710853 0.703340i \(-0.248309\pi\)
0.908540 + 0.417798i \(0.137198\pi\)
\(744\) 0 0
\(745\) 63.7064 + 53.4560i 0.0855120 + 0.0717531i
\(746\) 0 0
\(747\) 357.117 + 989.317i 0.478068 + 1.32439i
\(748\) 0 0
\(749\) 184.113 + 505.845i 0.245811 + 0.675361i
\(750\) 0 0
\(751\) 623.699 523.346i 0.830492 0.696865i −0.124912 0.992168i \(-0.539865\pi\)
0.955404 + 0.295302i \(0.0954204\pi\)
\(752\) 0 0
\(753\) 0.315974 + 0.548962i 0.000419621 + 0.000729033i
\(754\) 0 0
\(755\) 55.8142i 0.0739261i
\(756\) 0 0
\(757\) 646.428 0.853933 0.426967 0.904267i \(-0.359582\pi\)
0.426967 + 0.904267i \(0.359582\pi\)
\(758\) 0 0
\(759\) 0.260932 197.019i 0.000343785 0.259578i
\(760\) 0 0
\(761\) −132.824 158.293i −0.174539 0.208007i 0.671682 0.740840i \(-0.265572\pi\)
−0.846221 + 0.532832i \(0.821128\pi\)
\(762\) 0 0
\(763\) −1736.08 + 631.882i −2.27534 + 0.828154i
\(764\) 0 0
\(765\) 18.6946 + 107.690i 0.0244374 + 0.140771i
\(766\) 0 0
\(767\) −331.164 + 394.665i −0.431765 + 0.514557i
\(768\) 0 0
\(769\) 27.9808 + 158.687i 0.0363860 + 0.206355i 0.997581 0.0695149i \(-0.0221451\pi\)
−0.961195 + 0.275870i \(0.911034\pi\)
\(770\) 0 0
\(771\) −546.400 199.693i −0.708689 0.259005i
\(772\) 0 0
\(773\) −769.088 + 444.033i −0.994940 + 0.574429i −0.906747 0.421675i \(-0.861442\pi\)
−0.0881925 + 0.996103i \(0.528109\pi\)
\(774\) 0 0
\(775\) −87.3485 + 151.292i −0.112708 + 0.195215i
\(776\) 0 0
\(777\) 108.846 + 300.289i 0.140085 + 0.386472i
\(778\) 0 0
\(779\) −52.9777 + 145.555i −0.0680073 + 0.186848i
\(780\) 0 0
\(781\) 102.886 583.497i 0.131737 0.747116i
\(782\) 0 0
\(783\) 199.813 1107.45i 0.255189 1.41436i
\(784\)