Properties

Label 108.3.k.a.41.2
Level 108
Weight 3
Character 108.41
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 41.2
Character \(\chi\) \(=\) 108.41
Dual form 108.3.k.a.29.2

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{17}{18}\right)\) \(1\)

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 −0.795073 0.606514i \(-0.792567\pi\)
0.735363 + 0.677674i \(0.237012\pi\)
\(6\) 0 0
\(7\) −10.1488 3.69384i −1.44982 0.527692i −0.507281 0.861781i \(-0.669349\pi\)
−0.942542 + 0.334089i \(0.891571\pi\)
\(8\) 0 0
\(9\) 4.47934 7.80612i 0.497704 0.867347i
\(10\) 0 0
\(11\) −10.2314 12.1933i −0.930125 1.10848i −0.993875 0.110514i \(-0.964750\pi\)
0.0637495 0.997966i \(-0.479694\pi\)
\(12\) 0 0
\(13\) −3.11819 + 17.6841i −0.239861 + 1.36032i 0.592271 + 0.805739i \(0.298232\pi\)
−0.832131 + 0.554579i \(0.812879\pi\)
\(14\) 0 0
\(15\) 0.240142 1.37254i 0.0160095 0.0915028i
\(16\) 0 0
\(17\) −22.6442 13.0736i −1.33201 0.769038i −0.346405 0.938085i \(-0.612598\pi\)
−0.985608 + 0.169047i \(0.945931\pi\)
\(18\) 0 0
\(19\) 1.77864 + 3.08069i 0.0936126 + 0.162142i 0.909029 0.416733i \(-0.136825\pi\)
−0.815416 + 0.578875i \(0.803492\pi\)
\(20\) 0 0
\(21\) 31.9005 5.66850i 1.51907 0.269928i
\(22\) 0 0
\(23\) 1.41115 + 3.87710i 0.0613543 + 0.168570i 0.966582 0.256357i \(-0.0825222\pi\)
−0.905228 + 0.424926i \(0.860300\pi\)
\(24\) 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 0.586924 0.809642i \(-0.300339\pi\)
0.828442 + 0.560075i \(0.189228\pi\)
\(30\) 0 0
\(31\) −6.62361 + 2.41080i −0.213665 + 0.0777677i −0.446635 0.894716i \(-0.647378\pi\)
0.232970 + 0.972484i \(0.425156\pi\)
\(32\) 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 −0.791697 0.610914i \(-0.790802\pi\)
0.924916 + 0.380173i \(0.124135\pi\)
\(38\) 0 0
\(39\) −18.4919 50.5976i −0.474152 1.29737i
\(40\) 0 0
\(41\) −42.8820 7.56125i −1.04590 0.184421i −0.375808 0.926697i \(-0.622635\pi\)
−0.670094 + 0.742277i \(0.733746\pi\)
\(42\) 0 0
\(43\) −27.2523 + 22.8674i −0.633773 + 0.531799i −0.902099 0.431529i \(-0.857974\pi\)
0.268326 + 0.963328i \(0.413530\pi\)
\(44\) 0 0
\(45\) 1.44010 + 3.92428i 0.0320023 + 0.0872062i
\(46\) 0 0
\(47\) −5.51742 + 15.1590i −0.117392 + 0.322531i −0.984447 0.175680i \(-0.943788\pi\)
0.867055 + 0.498212i \(0.166010\pi\)
\(48\) 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 \(-0.746834\pi\)
0.700040 0.714104i \(-0.253166\pi\)
\(54\) 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 −0.899345 0.437240i \(-0.855956\pi\)
0.586767 + 0.809756i \(0.300400\pi\)
\(60\) 0 0
\(61\) −55.9422 20.3613i −0.917085 0.333792i −0.160007 0.987116i \(-0.551152\pi\)
−0.757078 + 0.653324i \(0.773374\pi\)
\(62\) 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 −1.00000 0.000251397i \(-0.999920\pi\)
0.939779 + 0.341784i \(0.111031\pi\)
\(68\) 0 0
\(69\) −9.49246 7.94372i −0.137572 0.115126i
\(70\) 0 0
\(71\) −32.2368 18.6119i −0.454039 0.262139i 0.255496 0.966810i \(-0.417761\pi\)
−0.709534 + 0.704671i \(0.751095\pi\)
\(72\) 0 0
\(73\) −26.0280 45.0817i −0.356547 0.617558i 0.630834 0.775918i \(-0.282713\pi\)
−0.987382 + 0.158360i \(0.949380\pi\)
\(74\) 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 −0.768063 0.640374i \(-0.778779\pi\)
0.502722 0.864448i \(-0.332332\pi\)
\(80\) 0 0
\(81\) −40.8710 69.9325i −0.504581 0.863364i
\(82\) 0 0
\(83\) 115.091 20.2937i 1.38664 0.244502i 0.569997 0.821647i \(-0.306944\pi\)
0.816642 + 0.577145i \(0.195833\pi\)
\(84\) 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 −0.984242 0.176826i \(-0.943417\pi\)
−0.338985 + 0.940792i \(0.610084\pi\)
\(90\) 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 −0.934337 0.356391i \(-0.884007\pi\)
0.188731 + 0.982029i \(0.439563\pi\)
\(98\) 0 0
\(99\) −141.012 + 25.2495i −1.42436 + 0.255046i
\(100\) 0 0
\(101\) 52.1346 143.239i 0.516184 1.41820i −0.358509 0.933526i \(-0.616715\pi\)
0.874693 0.484678i \(-0.161063\pi\)
\(102\) 0 0
\(103\) 16.6643 + 13.9830i 0.161790 + 0.135758i 0.720088 0.693882i \(-0.244101\pi\)
−0.558299 + 0.829640i \(0.688546\pi\)
\(104\) 0 0
\(105\) −7.50710 + 13.0425i −0.0714962 + 0.124215i
\(106\) 0 0
\(107\) 49.8431i 0.465823i 0.972498 + 0.232912i \(0.0748253\pi\)
−0.972498 + 0.232912i \(0.925175\pi\)
\(108\) 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 −0.637744 0.770249i \(-0.720132\pi\)
0.869290 + 0.494303i \(0.164577\pi\)
\(114\) 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 0.718399 0.695631i \(-0.244875\pi\)
−0.961634 + 0.274336i \(0.911542\pi\)
\(128\) 0 0
\(129\) 36.3695 100.338i 0.281934 0.777812i
\(130\) 0 0
\(131\) 77.3505 + 212.519i 0.590462 + 1.62228i 0.769651 + 0.638465i \(0.220430\pi\)
−0.179189 + 0.983815i \(0.557347\pi\)
\(132\) 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 −0.690544 0.723290i \(-0.742629\pi\)
−0.401519 + 0.915851i \(0.631518\pi\)
\(138\) 0 0
\(139\) 159.710 58.1298i 1.14899 0.418200i 0.303841 0.952723i \(-0.401731\pi\)
0.845154 + 0.534523i \(0.179509\pi\)
\(140\) 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 −0.452907 0.891558i \(-0.649613\pi\)
−0.730524 + 0.682887i \(0.760724\pi\)
\(150\) 0 0
\(151\) 92.0549 77.2432i 0.609635 0.511544i −0.284891 0.958560i \(-0.591958\pi\)
0.894526 + 0.447015i \(0.147513\pi\)
\(152\) 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 0.718865 0.695150i \(-0.244662\pi\)
−0.559760 + 0.828655i \(0.689107\pi\)
\(158\) 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 −0.479943 0.877300i \(-0.659343\pi\)
0.947313 + 0.320310i \(0.103787\pi\)
\(168\) 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 0.603310 0.797506i \(-0.293848\pi\)
−0.890154 + 0.455659i \(0.849404\pi\)
\(174\) 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 0.0957841 0.995402i \(-0.469464\pi\)
−0.814151 + 0.580653i \(0.802797\pi\)
\(180\) 0 0
\(181\) 42.2135 + 73.1159i 0.233224 + 0.403955i 0.958755 0.284234i \(-0.0917393\pi\)
−0.725531 + 0.688189i \(0.758406\pi\)
\(182\) 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 −0.178687 0.983906i \(-0.557185\pi\)
0.168605 + 0.985684i \(0.446074\pi\)
\(192\) 0 0
\(193\) −311.970 + 113.548i −1.61643 + 0.588331i −0.982697 0.185223i \(-0.940699\pi\)
−0.633731 + 0.773554i \(0.718477\pi\)
\(194\) 0 0
\(195\) 23.5234 + 8.52655i 0.120633 + 0.0437259i
\(196\) 0 0
\(197\) −213.145 + 123.059i −1.08195 + 0.624666i −0.931423 0.363939i \(-0.881432\pi\)
−0.150531 + 0.988605i \(0.548098\pi\)
\(198\) 0 0
\(199\) −138.226 + 239.415i −0.694604 + 1.20309i 0.275710 + 0.961241i \(0.411087\pi\)
−0.970314 + 0.241849i \(0.922246\pi\)
\(200\) 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 0.540992 0.841027i \(-0.318049\pi\)
−0.734308 + 0.678816i \(0.762493\pi\)
\(212\) 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 0.560334 0.828267i \(-0.310673\pi\)
−0.103159 + 0.994665i \(0.532895\pi\)
\(224\) 0 0
\(225\) 209.808 + 75.7350i 0.932479 + 0.336600i
\(226\) 0 0
\(227\) −232.991 277.668i −1.02639 1.22321i −0.974462 0.224554i \(-0.927907\pi\)
−0.0519295 0.998651i \(-0.516537\pi\)
\(228\) 0 0
\(229\) −50.2795 + 285.149i −0.219561 + 1.24519i 0.653252 + 0.757140i \(0.273404\pi\)
−0.872814 + 0.488054i \(0.837707\pi\)
\(230\) 0 0
\(231\) −395.504 330.976i −1.71214 1.43279i
\(232\) 0 0
\(233\) 127.663 + 73.7062i 0.547910 + 0.316336i 0.748279 0.663385i \(-0.230881\pi\)
−0.200369 + 0.979721i \(0.564214\pi\)
\(234\) 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 0.929556 0.368680i \(-0.120190\pi\)
−0.949065 + 0.315082i \(0.897968\pi\)
\(240\) 0 0
\(241\) −51.5844 292.550i −0.214043 1.21390i −0.882559 0.470201i \(-0.844181\pi\)
0.668516 0.743698i \(-0.266930\pi\)
\(242\) 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 −0.500364 0.865815i \(-0.666801\pi\)
0.499636 + 0.866236i \(0.333467\pi\)
\(252\) 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 0.532353 0.846523i \(-0.321308\pi\)
0.210720 + 0.977546i \(0.432419\pi\)
\(258\) 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 0.325363 + 0.945589i \(0.394513\pi\)
−0.857056 + 0.515224i \(0.827709\pi\)
\(264\) 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 \(0.0716557\pi\)
−0.974769 + 0.223216i \(0.928344\pi\)
\(270\) 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 0.819919 0.572479i \(-0.194018\pi\)
0.260112 + 0.965578i \(0.416240\pi\)
\(278\) 0 0
\(279\) −10.8504 + 62.5035i −0.0388904 + 0.224027i
\(280\) 0 0
\(281\) −154.692 184.354i −0.550504 0.656065i 0.417004 0.908905i \(-0.363080\pi\)
−0.967508 + 0.252839i \(0.918636\pi\)
\(282\) 0 0
\(283\) 15.5135 87.9813i 0.0548179 0.310888i −0.945054 0.326915i \(-0.893991\pi\)
0.999872 + 0.0160274i \(0.00510189\pi\)
\(284\) 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 0.977741 + 0.209814i \(0.0672860\pi\)
−0.614127 + 0.789207i \(0.710492\pi\)
\(294\) 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 −0.261885 + 0.965099i \(0.584344\pi\)
−0.704858 + 0.709348i \(0.748989\pi\)
\(308\) 0 0
\(309\) −64.2847 11.2474i −0.208041 0.0363992i
\(310\) 0 0
\(311\) −538.372 94.9296i −1.73110 0.305240i −0.782720 0.622374i \(-0.786168\pi\)
−0.948381 + 0.317134i \(0.897280\pi\)
\(312\) 0 0
\(313\) 119.991 100.684i 0.383357 0.321675i −0.430662 0.902513i \(-0.641720\pi\)
0.814019 + 0.580839i \(0.197275\pi\)
\(314\) 0 0
\(315\) −0.119583 45.1461i −0.000379629 0.143321i
\(316\) 0 0
\(317\) −14.4734 + 39.7653i −0.0456574 + 0.125443i −0.960426 0.278536i \(-0.910151\pi\)
0.914768 + 0.403979i \(0.132373\pi\)
\(318\) 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 0.927277 0.374376i \(-0.122143\pi\)
0.469691 + 0.882831i \(0.344365\pi\)
\(332\) 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 −0.0638222 0.997961i \(-0.520329\pi\)
0.401296 0.915948i \(-0.368560\pi\)
\(338\) 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 0.858948 0.512062i \(-0.171118\pi\)
−0.987140 + 0.159859i \(0.948896\pi\)
\(348\) 0 0
\(349\) 14.3449 + 81.3537i 0.0411027 + 0.233105i 0.998438 0.0558751i \(-0.0177949\pi\)
−0.957335 + 0.288980i \(0.906684\pi\)
\(350\) 0 0
\(351\) −477.802 82.2934i −1.36126 0.234454i
\(352\) 0 0
\(353\) −65.5878 + 11.5649i −0.185801 + 0.0327618i −0.265774 0.964035i \(-0.585628\pi\)
0.0799732 + 0.996797i \(0.474517\pi\)
\(354\) 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 −0.0390844 0.999236i \(-0.512444\pi\)
0.845821 + 0.533466i \(0.179111\pi\)
\(360\) 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 −0.107742 0.994179i \(-0.534362\pi\)
0.960366 + 0.278742i \(0.0899175\pi\)
\(368\) 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 0.271244 0.962511i \(-0.412565\pi\)
−0.900787 + 0.434262i \(0.857009\pi\)
\(374\) 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 −0.166268 0.986081i \(-0.553172\pi\)
0.999972 0.00748907i \(-0.00238387\pi\)
\(384\) 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 0.999171 0.0407223i \(-0.0129659\pi\)
−0.213608 + 0.976920i \(0.568521\pi\)
\(390\) 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 −0.998498 0.0547849i \(-0.982553\pi\)
0.451804 0.892117i \(-0.350781\pi\)
\(398\) 0 0
\(399\) 74.2024 + 88.1935i 0.185971 + 0.221036i
\(400\) 0 0
\(401\) 84.0625 + 230.960i 0.209632 + 0.575960i 0.999294 0.0375831i \(-0.0119659\pi\)
−0.789661 + 0.613543i \(0.789744\pi\)
\(402\) 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 −0.710865 0.703329i \(-0.751696\pi\)
−0.0924633 + 0.995716i \(0.529474\pi\)
\(410\) 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 −0.160015 0.987115i \(-0.551154\pi\)
−0.487978 + 0.872856i \(0.662265\pi\)
\(420\) 0 0
\(421\) 50.0550 42.0012i 0.118896 0.0997652i −0.581401 0.813617i \(-0.697495\pi\)
0.700297 + 0.713852i \(0.253051\pi\)
\(422\) 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 \(0.0390589\pi\)
−0.992481 + 0.122399i \(0.960941\pi\)
\(432\) 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 0.409338 0.912383i \(-0.365760\pi\)
−0.272897 + 0.962043i \(0.587982\pi\)
\(440\) 0 0
\(441\) 571.508 209.728i 1.29594 0.475574i
\(442\) 0 0
\(443\) −85.6046 102.020i −0.193238 0.230292i 0.660722 0.750631i \(-0.270250\pi\)
−0.853960 + 0.520338i \(0.825806\pi\)
\(444\) 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 0.359794 0.933032i \(-0.382847\pi\)
−0.628132 + 0.778106i \(0.716180\pi\)
\(450\) 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 0.953149 0.302500i \(-0.0978212\pi\)
−0.999129 + 0.0417393i \(0.986710\pi\)
\(458\) 0 0
\(459\) 350.556 612.791i 0.763739 1.33506i
\(460\) 0 0
\(461\) −266.202 + 46.9386i −0.577445 + 0.101819i −0.454740 0.890624i \(-0.650268\pi\)
−0.122705 + 0.992443i \(0.539157\pi\)
\(462\) 0 0
\(463\) 16.9878 6.18304i 0.0366906 0.0133543i −0.323610 0.946191i \(-0.604896\pi\)
0.360300 + 0.932836i \(0.382674\pi\)
\(464\) 0 0
\(465\) 1.71831 + 9.67012i 0.00369529 + 0.0207960i
\(466\) 0 0
\(467\) −439.219 + 253.583i −0.940511 + 0.543004i −0.890120 0.455725i \(-0.849380\pi\)
−0.0503903 + 0.998730i \(0.516047\pi\)
\(468\) 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 −0.501629 0.865083i \(-0.667266\pi\)
0.940335 0.340251i \(-0.110512\pi\)
\(480\) 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 −0.880924 0.473258i \(-0.843078\pi\)
0.619039 + 0.785360i \(0.287522\pi\)
\(492\) 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 −0.999182 0.0404381i \(-0.987125\pi\)
0.952755 + 0.303741i \(0.0982358\pi\)
\(500\) 0 0
\(501\) −62.7808 + 358.826i −0.125311 + 0.716219i
\(502\) 0 0
\(503\) 156.930 + 90.6037i 0.311989 + 0.180127i 0.647816 0.761797i \(-0.275683\pi\)
−0.335827 + 0.941924i \(0.609016\pi\)
\(504\) 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 0.860961 + 0.508671i \(0.169863\pi\)
−0.332567 + 0.943080i \(0.607915\pi\)
\(510\) 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 −0.653790 0.756676i \(-0.726822\pi\)
0.328406 + 0.944537i \(0.393489\pi\)
\(522\) 0 0
\(523\) −79.9831 + 138.535i −0.152931 + 0.264885i −0.932304 0.361676i \(-0.882205\pi\)
0.779373 + 0.626561i \(0.215538\pi\)
\(524\) 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 0.586155 0.810199i \(-0.300641\pi\)
−0.0717647 + 0.997422i \(0.522863\pi\)
\(548\) 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 −0.264348 0.964427i \(-0.585157\pi\)
−0.967393 + 0.253282i \(0.918490\pi\)
\(558\) 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 −0.761450 0.648224i \(-0.775512\pi\)
0.166634 0.986019i \(-0.446710\pi\)
\(564\) 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 −0.636219 0.771508i \(-0.719503\pi\)
−0.333979 + 0.942580i \(0.608392\pi\)
\(570\) 0 0
\(571\) −29.2223 + 10.6361i −0.0511775 + 0.0186271i −0.367482 0.930031i \(-0.619780\pi\)
0.316305 + 0.948658i \(0.397558\pi\)
\(572\) 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 −0.936637 0.350302i \(-0.886079\pi\)
0.771689 + 0.636000i \(0.219412\pi\)
\(578\) 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 0.742141 + 0.670244i \(0.233810\pi\)
−0.999337 + 0.0363972i \(0.988412\pi\)
\(588\) 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 \(-0.880275\pi\)
0.930095 0.367320i \(-0.119725\pi\)
\(594\) 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 −0.0531765 + 0.998585i \(0.516935\pi\)
−0.974180 + 0.225771i \(0.927510\pi\)
\(600\) 0 0
\(601\) −214.739 78.1585i −0.357302 0.130047i 0.157131 0.987578i \(-0.449775\pi\)
−0.514433 + 0.857530i \(0.671998\pi\)
\(602\) 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 −0.959069 0.283173i \(-0.908613\pi\)
0.998081 + 0.0619256i \(0.0197241\pi\)
\(608\) 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 0.835554 0.549409i \(-0.185147\pi\)
−0.893579 + 0.448906i \(0.851814\pi\)
\(614\) 0 0
\(615\) −20.6759 + 57.0415i −0.0336194 + 0.0927505i
\(616\) 0 0
\(617\) −348.112 956.431i −0.564201 1.55013i −0.813416 0.581682i \(-0.802395\pi\)
0.249215 0.968448i \(-0.419828\pi\)
\(618\) 0 0
\(619\) 63.4363 + 359.765i 0.102482 + 0.581204i 0.992196 + 0.124686i \(0.0397924\pi\)
−0.889714 + 0.456518i \(0.849097\pi\)
\(620\) 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 −0.371371 0.928485i \(-0.621112\pi\)
0.989777 0.142626i \(-0.0455546\pi\)
\(632\) 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 −0.991927 0.126807i \(-0.959527\pi\)
0.841370 + 0.540459i \(0.181749\pi\)
\(642\) 0 0
\(643\) −32.0195 26.8675i −0.0497970 0.0417846i 0.617549 0.786532i \(-0.288126\pi\)
−0.667346 + 0.744747i \(0.732570\pi\)
\(644\) 0 0
\(645\) 24.8420 + 42.8963i 0.0385147 + 0.0665059i
\(646\) 0 0
\(647\) 383.618i 0.592918i −0.955046 0.296459i \(-0.904194\pi\)
0.955046 0.296459i \(-0.0958058\pi\)
\(648\) 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 −0.735050 0.678013i \(-0.762841\pi\)
0.795352 + 0.606147i \(0.207286\pi\)
\(654\) 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 0.455629 0.890170i \(-0.349415\pi\)
−0.955765 + 0.294130i \(0.904970\pi\)
\(660\) 0 0
\(661\) −33.1600 + 188.060i −0.0501664 + 0.284508i −0.999563 0.0295731i \(-0.990585\pi\)
0.949396 + 0.314081i \(0.101696\pi\)
\(662\) 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 −0.761741 0.647882i \(-0.775655\pi\)
0.494214 0.869340i \(-0.335456\pi\)
\(674\) 0 0
\(675\) −658.542 + 118.819i −0.975618 + 0.176027i
\(676\) 0 0
\(677\) 482.182 85.0218i 0.712234 0.125586i 0.194220 0.980958i \(-0.437782\pi\)
0.518014 + 0.855372i \(0.326671\pi\)
\(678\) 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 −0.304642 0.952467i \(-0.598537\pi\)
0.672540 + 0.740061i \(0.265204\pi\)
\(684\) 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 −0.528819 0.848735i \(-0.677365\pi\)
0.744012 + 0.668166i \(0.232921\pi\)
\(692\) 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 \(0.0674299\pi\)
−0.977646 + 0.210257i \(0.932570\pi\)
\(702\) 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 0.894387 0.447293i \(-0.147612\pi\)
0.397626 + 0.917548i \(0.369834\pi\)
\(710\) 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 0.0442205 0.999022i \(-0.485920\pi\)
−0.843068 + 0.537807i \(0.819253\pi\)
\(720\) 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 −0.818633 0.574316i \(-0.805268\pi\)
0.572836 0.819670i \(-0.305843\pi\)
\(728\) 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 −0.405001 0.914316i \(-0.632729\pi\)
0.277462 + 0.960737i \(0.410507\pi\)
\(734\) 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 −0.845882 0.533370i \(-0.820925\pi\)
0.884853 + 0.465870i \(0.154259\pi\)
\(740\) 0 0
\(741\) 122.985 146.963i 0.165972 0.198330i
\(742\) 0 0
\(743\) 1203.21 + 212.158i 1.61939 + 0.285543i 0.908540 0.417798i \(-0.137198\pi\)
0.710853 + 0.703340i \(0.248309\pi\)
\(744\) 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 0.955404 0.295302i \(-0.0954204\pi\)
−0.124912 + 0.992168i \(0.539865\pi\)
\(752\) 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 −0.846221 0.532832i \(-0.821128\pi\)
0.671682 + 0.740840i \(0.265572\pi\)
\(762\) 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 −0.961195 0.275870i \(-0.911034\pi\)
0.997581 + 0.0695149i \(0.0221451\pi\)
\(770\) 0 0
\(771\) −546.400 + 199.693i −0.708689 + 0.259005i
\(772\) 0 0
\(773\) −769.088 444.033i −0.994940 0.574429i −0.0881925 0.996103i \(-0.528109\pi\)
−0.906747 + 0.421675i \(0.861442\pi\)
\(774\) 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