Properties

Label 819.2.et.c.145.1
Level $819$
Weight $2$
Character 819.145
Analytic conductor $6.540$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.et (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 273)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 145.1
Character \(\chi\) \(=\) 819.145
Dual form 819.2.et.c.514.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.92842 + 1.92842i) q^{2} -5.43762i q^{4} +(3.41458 - 0.914933i) q^{5} +(2.45097 - 0.996354i) q^{7} +(6.62917 + 6.62917i) q^{8} +O(q^{10})\) \(q+(-1.92842 + 1.92842i) q^{2} -5.43762i q^{4} +(3.41458 - 0.914933i) q^{5} +(2.45097 - 0.996354i) q^{7} +(6.62917 + 6.62917i) q^{8} +(-4.82036 + 8.34912i) q^{10} +(0.426935 - 0.114397i) q^{11} +(3.60449 - 0.0874303i) q^{13} +(-2.80512 + 6.64790i) q^{14} -14.6924 q^{16} -1.43104 q^{17} +(0.340943 - 1.27242i) q^{19} +(-4.97505 - 18.5671i) q^{20} +(-0.602706 + 1.04392i) q^{22} +7.18790i q^{23} +(6.49210 - 3.74822i) q^{25} +(-6.78237 + 7.11958i) q^{26} +(-5.41779 - 13.3275i) q^{28} +(-3.82097 - 6.61812i) q^{29} +(0.187215 - 0.698697i) q^{31} +(15.0748 - 15.0748i) q^{32} +(2.75965 - 2.75965i) q^{34} +(7.45744 - 5.64460i) q^{35} +(0.719109 + 0.719109i) q^{37} +(1.79627 + 3.11123i) q^{38} +(28.7010 + 16.5706i) q^{40} +(0.748673 - 2.79409i) q^{41} +(7.20261 + 4.15843i) q^{43} +(-0.622047 - 2.32151i) q^{44} +(-13.8613 - 13.8613i) q^{46} +(-0.242840 - 0.906290i) q^{47} +(5.01456 - 4.88408i) q^{49} +(-5.29136 + 19.7476i) q^{50} +(-0.475412 - 19.5998i) q^{52} +(-2.48381 - 4.30208i) q^{53} +(1.35314 - 0.781234i) q^{55} +(22.8529 + 9.64293i) q^{56} +(20.1310 + 5.39408i) q^{58} +(2.29996 - 2.29996i) q^{59} +(-11.2736 + 6.50883i) q^{61} +(0.986352 + 1.70841i) q^{62} +28.7565i q^{64} +(12.2278 - 3.59640i) q^{65} +(1.64481 + 6.13851i) q^{67} +7.78144i q^{68} +(-3.49591 + 25.2663i) q^{70} +(-0.487730 - 1.82023i) q^{71} +(-12.2890 - 3.29282i) q^{73} -2.77349 q^{74} +(-6.91890 - 1.85391i) q^{76} +(0.932428 - 0.705763i) q^{77} +(-1.77054 + 3.06666i) q^{79} +(-50.1684 + 13.4426i) q^{80} +(3.94442 + 6.83193i) q^{82} +(-2.33307 - 2.33307i) q^{83} +(-4.88639 + 1.30931i) q^{85} +(-21.9089 + 5.87046i) q^{86} +(3.58858 + 2.07187i) q^{88} +(-7.39789 + 7.39789i) q^{89} +(8.74741 - 3.80564i) q^{91} +39.0850 q^{92} +(2.21601 + 1.27941i) q^{94} -4.65670i q^{95} +(-2.51514 + 0.673929i) q^{97} +(-0.251615 + 19.0887i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 6q^{7} + O(q^{10}) \) \( 36q + 6q^{7} + 8q^{11} - 42q^{14} - 24q^{16} + 8q^{17} - 18q^{19} - 14q^{20} + 4q^{22} + 24q^{25} + 50q^{26} + 34q^{28} - 8q^{29} + 6q^{31} + 50q^{32} - 24q^{34} - 14q^{35} - 14q^{37} + 8q^{38} - 30q^{40} - 34q^{41} + 30q^{43} - 28q^{44} - 32q^{46} + 10q^{47} + 6q^{49} + 20q^{50} + 4q^{52} + 8q^{53} - 30q^{55} + 92q^{56} + 72q^{58} + 70q^{59} - 60q^{61} + 48q^{62} + 44q^{65} - 46q^{67} + 80q^{70} - 42q^{71} - 56q^{73} - 40q^{74} + 12q^{76} - 24q^{77} - 170q^{80} + 24q^{82} + 60q^{83} + 2q^{85} - 12q^{86} + 84q^{88} - 64q^{89} - 86q^{91} + 100q^{92} - 66q^{94} + 36q^{97} + 22q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{12}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.92842 + 1.92842i −1.36360 + 1.36360i −0.494319 + 0.869281i \(0.664583\pi\)
−0.869281 + 0.494319i \(0.835417\pi\)
\(3\) 0 0
\(4\) 5.43762i 2.71881i
\(5\) 3.41458 0.914933i 1.52704 0.409170i 0.604991 0.796232i \(-0.293177\pi\)
0.922054 + 0.387062i \(0.126510\pi\)
\(6\) 0 0
\(7\) 2.45097 0.996354i 0.926381 0.376587i
\(8\) 6.62917 + 6.62917i 2.34377 + 2.34377i
\(9\) 0 0
\(10\) −4.82036 + 8.34912i −1.52433 + 2.64022i
\(11\) 0.426935 0.114397i 0.128726 0.0344920i −0.193881 0.981025i \(-0.562108\pi\)
0.322607 + 0.946533i \(0.395441\pi\)
\(12\) 0 0
\(13\) 3.60449 0.0874303i 0.999706 0.0242488i
\(14\) −2.80512 + 6.64790i −0.749700 + 1.77673i
\(15\) 0 0
\(16\) −14.6924 −3.67311
\(17\) −1.43104 −0.347078 −0.173539 0.984827i \(-0.555520\pi\)
−0.173539 + 0.984827i \(0.555520\pi\)
\(18\) 0 0
\(19\) 0.340943 1.27242i 0.0782176 0.291912i −0.915726 0.401803i \(-0.868384\pi\)
0.993944 + 0.109891i \(0.0350502\pi\)
\(20\) −4.97505 18.5671i −1.11246 4.15174i
\(21\) 0 0
\(22\) −0.602706 + 1.04392i −0.128497 + 0.222564i
\(23\) 7.18790i 1.49878i 0.662129 + 0.749390i \(0.269653\pi\)
−0.662129 + 0.749390i \(0.730347\pi\)
\(24\) 0 0
\(25\) 6.49210 3.74822i 1.29842 0.749643i
\(26\) −6.78237 + 7.11958i −1.33013 + 1.39626i
\(27\) 0 0
\(28\) −5.41779 13.3275i −1.02387 2.51865i
\(29\) −3.82097 6.61812i −0.709537 1.22895i −0.965029 0.262143i \(-0.915571\pi\)
0.255492 0.966811i \(-0.417762\pi\)
\(30\) 0 0
\(31\) 0.187215 0.698697i 0.0336249 0.125490i −0.947073 0.321017i \(-0.895975\pi\)
0.980698 + 0.195528i \(0.0626419\pi\)
\(32\) 15.0748 15.0748i 2.66488 2.66488i
\(33\) 0 0
\(34\) 2.75965 2.75965i 0.473276 0.473276i
\(35\) 7.45744 5.64460i 1.26054 0.954112i
\(36\) 0 0
\(37\) 0.719109 + 0.719109i 0.118221 + 0.118221i 0.763742 0.645521i \(-0.223360\pi\)
−0.645521 + 0.763742i \(0.723360\pi\)
\(38\) 1.79627 + 3.11123i 0.291394 + 0.504709i
\(39\) 0 0
\(40\) 28.7010 + 16.5706i 4.53803 + 2.62003i
\(41\) 0.748673 2.79409i 0.116923 0.436363i −0.882500 0.470312i \(-0.844142\pi\)
0.999424 + 0.0339485i \(0.0108082\pi\)
\(42\) 0 0
\(43\) 7.20261 + 4.15843i 1.09839 + 0.634155i 0.935797 0.352539i \(-0.114682\pi\)
0.162591 + 0.986694i \(0.448015\pi\)
\(44\) −0.622047 2.32151i −0.0937771 0.349981i
\(45\) 0 0
\(46\) −13.8613 13.8613i −2.04374 2.04374i
\(47\) −0.242840 0.906290i −0.0354218 0.132196i 0.945951 0.324310i \(-0.105132\pi\)
−0.981373 + 0.192114i \(0.938466\pi\)
\(48\) 0 0
\(49\) 5.01456 4.88408i 0.716365 0.697726i
\(50\) −5.29136 + 19.7476i −0.748312 + 2.79274i
\(51\) 0 0
\(52\) −0.475412 19.5998i −0.0659278 2.71801i
\(53\) −2.48381 4.30208i −0.341177 0.590936i 0.643474 0.765468i \(-0.277492\pi\)
−0.984652 + 0.174531i \(0.944159\pi\)
\(54\) 0 0
\(55\) 1.35314 0.781234i 0.182457 0.105342i
\(56\) 22.8529 + 9.64293i 3.05385 + 1.28859i
\(57\) 0 0
\(58\) 20.1310 + 5.39408i 2.64332 + 0.708277i
\(59\) 2.29996 2.29996i 0.299429 0.299429i −0.541361 0.840790i \(-0.682091\pi\)
0.840790 + 0.541361i \(0.182091\pi\)
\(60\) 0 0
\(61\) −11.2736 + 6.50883i −1.44344 + 0.833370i −0.998077 0.0619805i \(-0.980258\pi\)
−0.445362 + 0.895351i \(0.646925\pi\)
\(62\) 0.986352 + 1.70841i 0.125267 + 0.216969i
\(63\) 0 0
\(64\) 28.7565i 3.59456i
\(65\) 12.2278 3.59640i 1.51667 0.446079i
\(66\) 0 0
\(67\) 1.64481 + 6.13851i 0.200945 + 0.749939i 0.990647 + 0.136448i \(0.0435686\pi\)
−0.789702 + 0.613491i \(0.789765\pi\)
\(68\) 7.78144i 0.943639i
\(69\) 0 0
\(70\) −3.49591 + 25.2663i −0.417842 + 3.01990i
\(71\) −0.487730 1.82023i −0.0578829 0.216022i 0.930926 0.365207i \(-0.119002\pi\)
−0.988809 + 0.149185i \(0.952335\pi\)
\(72\) 0 0
\(73\) −12.2890 3.29282i −1.43832 0.385396i −0.546373 0.837542i \(-0.683992\pi\)
−0.891944 + 0.452146i \(0.850659\pi\)
\(74\) −2.77349 −0.322412
\(75\) 0 0
\(76\) −6.91890 1.85391i −0.793653 0.212659i
\(77\) 0.932428 0.705763i 0.106260 0.0804292i
\(78\) 0 0
\(79\) −1.77054 + 3.06666i −0.199201 + 0.345026i −0.948270 0.317466i \(-0.897168\pi\)
0.749069 + 0.662493i \(0.230501\pi\)
\(80\) −50.1684 + 13.4426i −5.60900 + 1.50293i
\(81\) 0 0
\(82\) 3.94442 + 6.83193i 0.435588 + 0.754461i
\(83\) −2.33307 2.33307i −0.256087 0.256087i 0.567373 0.823461i \(-0.307960\pi\)
−0.823461 + 0.567373i \(0.807960\pi\)
\(84\) 0 0
\(85\) −4.88639 + 1.30931i −0.530004 + 0.142014i
\(86\) −21.9089 + 5.87046i −2.36249 + 0.633028i
\(87\) 0 0
\(88\) 3.58858 + 2.07187i 0.382544 + 0.220862i
\(89\) −7.39789 + 7.39789i −0.784175 + 0.784175i −0.980532 0.196357i \(-0.937089\pi\)
0.196357 + 0.980532i \(0.437089\pi\)
\(90\) 0 0
\(91\) 8.74741 3.80564i 0.916977 0.398939i
\(92\) 39.0850 4.07489
\(93\) 0 0
\(94\) 2.21601 + 1.27941i 0.228563 + 0.131961i
\(95\) 4.65670i 0.477767i
\(96\) 0 0
\(97\) −2.51514 + 0.673929i −0.255373 + 0.0684271i −0.384234 0.923236i \(-0.625535\pi\)
0.128861 + 0.991663i \(0.458868\pi\)
\(98\) −0.251615 + 19.0887i −0.0254170 + 1.92825i
\(99\) 0 0
\(100\) −20.3814 35.3015i −2.03814 3.53015i
\(101\) −0.722867 + 1.25204i −0.0719279 + 0.124583i −0.899746 0.436413i \(-0.856248\pi\)
0.827818 + 0.560996i \(0.189582\pi\)
\(102\) 0 0
\(103\) 6.70272 11.6095i 0.660439 1.14391i −0.320061 0.947397i \(-0.603704\pi\)
0.980500 0.196517i \(-0.0629631\pi\)
\(104\) 24.4744 + 23.3152i 2.39991 + 2.28624i
\(105\) 0 0
\(106\) 13.0860 + 3.50640i 1.27103 + 0.340571i
\(107\) −1.88975 −0.182689 −0.0913447 0.995819i \(-0.529117\pi\)
−0.0913447 + 0.995819i \(0.529117\pi\)
\(108\) 0 0
\(109\) 7.12442 + 1.90898i 0.682396 + 0.182847i 0.583332 0.812234i \(-0.301749\pi\)
0.0990637 + 0.995081i \(0.468415\pi\)
\(110\) −1.10287 + 4.11597i −0.105155 + 0.392442i
\(111\) 0 0
\(112\) −36.0108 + 14.6389i −3.40270 + 1.38324i
\(113\) 3.09382 5.35865i 0.291042 0.504100i −0.683014 0.730405i \(-0.739331\pi\)
0.974056 + 0.226305i \(0.0726647\pi\)
\(114\) 0 0
\(115\) 6.57644 + 24.5436i 0.613256 + 2.28870i
\(116\) −35.9868 + 20.7770i −3.34129 + 1.92909i
\(117\) 0 0
\(118\) 8.87058i 0.816603i
\(119\) −3.50744 + 1.42582i −0.321527 + 0.130705i
\(120\) 0 0
\(121\) −9.35709 + 5.40232i −0.850645 + 0.491120i
\(122\) 9.18853 34.2921i 0.831890 3.10466i
\(123\) 0 0
\(124\) −3.79925 1.01800i −0.341182 0.0914195i
\(125\) 6.24018 6.24018i 0.558139 0.558139i
\(126\) 0 0
\(127\) 5.90231 3.40770i 0.523745 0.302384i −0.214721 0.976676i \(-0.568884\pi\)
0.738466 + 0.674291i \(0.235551\pi\)
\(128\) −25.3048 25.3048i −2.23665 2.23665i
\(129\) 0 0
\(130\) −16.6450 + 30.5158i −1.45986 + 2.67641i
\(131\) 3.17967 + 1.83578i 0.277809 + 0.160393i 0.632431 0.774617i \(-0.282057\pi\)
−0.354622 + 0.935010i \(0.615390\pi\)
\(132\) 0 0
\(133\) −0.432135 3.45836i −0.0374708 0.299878i
\(134\) −15.0095 8.66575i −1.29662 0.748607i
\(135\) 0 0
\(136\) −9.48660 9.48660i −0.813470 0.813470i
\(137\) 5.57408 + 5.57408i 0.476225 + 0.476225i 0.903922 0.427697i \(-0.140675\pi\)
−0.427697 + 0.903922i \(0.640675\pi\)
\(138\) 0 0
\(139\) 10.3222 + 5.95952i 0.875517 + 0.505480i 0.869178 0.494500i \(-0.164649\pi\)
0.00633943 + 0.999980i \(0.497982\pi\)
\(140\) −30.6932 40.5507i −2.59405 3.42716i
\(141\) 0 0
\(142\) 4.45073 + 2.56963i 0.373497 + 0.215638i
\(143\) 1.52888 0.449670i 0.127852 0.0376033i
\(144\) 0 0
\(145\) −19.1021 19.1021i −1.58635 1.58635i
\(146\) 30.0483 17.3484i 2.48681 1.43576i
\(147\) 0 0
\(148\) 3.91024 3.91024i 0.321420 0.321420i
\(149\) 21.0304 + 5.63507i 1.72287 + 0.461643i 0.978522 0.206144i \(-0.0660914\pi\)
0.744353 + 0.667787i \(0.232758\pi\)
\(150\) 0 0
\(151\) −3.61340 + 13.4854i −0.294054 + 1.09742i 0.647912 + 0.761715i \(0.275643\pi\)
−0.941966 + 0.335709i \(0.891024\pi\)
\(152\) 10.6952 6.17489i 0.867497 0.500850i
\(153\) 0 0
\(154\) −0.437105 + 3.15912i −0.0352230 + 0.254569i
\(155\) 2.55704i 0.205387i
\(156\) 0 0
\(157\) 12.9689 7.48759i 1.03503 0.597574i 0.116608 0.993178i \(-0.462798\pi\)
0.918421 + 0.395604i \(0.129465\pi\)
\(158\) −2.49947 9.32816i −0.198847 0.742108i
\(159\) 0 0
\(160\) 37.6817 65.2667i 2.97900 5.15978i
\(161\) 7.16169 + 17.6174i 0.564420 + 1.38844i
\(162\) 0 0
\(163\) −2.28941 + 8.54420i −0.179320 + 0.669233i 0.816455 + 0.577409i \(0.195936\pi\)
−0.995775 + 0.0918237i \(0.970730\pi\)
\(164\) −15.1932 4.07100i −1.18639 0.317891i
\(165\) 0 0
\(166\) 8.99827 0.698401
\(167\) 0.331336 + 0.0887813i 0.0256396 + 0.00687010i 0.271616 0.962406i \(-0.412442\pi\)
−0.245976 + 0.969276i \(0.579109\pi\)
\(168\) 0 0
\(169\) 12.9847 0.630284i 0.998824 0.0484833i
\(170\) 6.89813 11.9479i 0.529063 0.916363i
\(171\) 0 0
\(172\) 22.6119 39.1650i 1.72414 2.98631i
\(173\) −4.62536 8.01137i −0.351660 0.609093i 0.634880 0.772610i \(-0.281049\pi\)
−0.986540 + 0.163517i \(0.947716\pi\)
\(174\) 0 0
\(175\) 12.1774 15.6552i 0.920527 1.18342i
\(176\) −6.27272 + 1.68077i −0.472824 + 0.126693i
\(177\) 0 0
\(178\) 28.5325i 2.13860i
\(179\) 12.6486 + 7.30269i 0.945403 + 0.545829i 0.891650 0.452725i \(-0.149548\pi\)
0.0537533 + 0.998554i \(0.482882\pi\)
\(180\) 0 0
\(181\) −8.63806 −0.642062 −0.321031 0.947069i \(-0.604029\pi\)
−0.321031 + 0.947069i \(0.604029\pi\)
\(182\) −9.52981 + 24.2076i −0.706396 + 1.79438i
\(183\) 0 0
\(184\) −47.6498 + 47.6498i −3.51279 + 3.51279i
\(185\) 3.11339 + 1.79752i 0.228901 + 0.132156i
\(186\) 0 0
\(187\) −0.610962 + 0.163707i −0.0446779 + 0.0119714i
\(188\) −4.92806 + 1.32047i −0.359415 + 0.0963051i
\(189\) 0 0
\(190\) 8.98007 + 8.98007i 0.651483 + 0.651483i
\(191\) −3.52411 6.10394i −0.254996 0.441666i 0.709899 0.704304i \(-0.248741\pi\)
−0.964894 + 0.262638i \(0.915407\pi\)
\(192\) 0 0
\(193\) −22.3236 + 5.98160i −1.60689 + 0.430565i −0.947114 0.320897i \(-0.896016\pi\)
−0.659776 + 0.751462i \(0.729349\pi\)
\(194\) 3.55062 6.14986i 0.254920 0.441534i
\(195\) 0 0
\(196\) −26.5577 27.2672i −1.89698 1.94766i
\(197\) 18.7705 + 5.02954i 1.33734 + 0.358340i 0.855448 0.517889i \(-0.173282\pi\)
0.481895 + 0.876229i \(0.339949\pi\)
\(198\) 0 0
\(199\) 17.8108 1.26257 0.631285 0.775551i \(-0.282528\pi\)
0.631285 + 0.775551i \(0.282528\pi\)
\(200\) 67.8848 + 18.1897i 4.80018 + 1.28620i
\(201\) 0 0
\(202\) −1.02047 3.80846i −0.0718002 0.267962i
\(203\) −15.9591 12.4138i −1.12011 0.871278i
\(204\) 0 0
\(205\) 10.2256i 0.714187i
\(206\) 9.46225 + 35.3136i 0.659266 + 2.46041i
\(207\) 0 0
\(208\) −52.9587 + 1.28456i −3.67203 + 0.0890685i
\(209\) 0.582242i 0.0402745i
\(210\) 0 0
\(211\) −5.03848 8.72690i −0.346863 0.600785i 0.638827 0.769350i \(-0.279420\pi\)
−0.985690 + 0.168565i \(0.946087\pi\)
\(212\) −23.3931 + 13.5060i −1.60664 + 0.927595i
\(213\) 0 0
\(214\) 3.64424 3.64424i 0.249115 0.249115i
\(215\) 28.3985 + 7.60937i 1.93676 + 0.518955i
\(216\) 0 0
\(217\) −0.237290 1.89902i −0.0161083 0.128914i
\(218\) −17.4202 + 10.0576i −1.17985 + 0.681184i
\(219\) 0 0
\(220\) −4.24805 7.35784i −0.286404 0.496066i
\(221\) −5.15817 + 0.125116i −0.346976 + 0.00841623i
\(222\) 0 0
\(223\) 0.246185 0.918774i 0.0164857 0.0615256i −0.957193 0.289451i \(-0.906527\pi\)
0.973679 + 0.227925i \(0.0731941\pi\)
\(224\) 21.9282 51.9680i 1.46514 3.47226i
\(225\) 0 0
\(226\) 4.36755 + 16.2999i 0.290525 + 1.08425i
\(227\) −17.3431 17.3431i −1.15110 1.15110i −0.986333 0.164766i \(-0.947313\pi\)
−0.164766 0.986333i \(-0.552687\pi\)
\(228\) 0 0
\(229\) −5.33978 19.9283i −0.352863 1.31690i −0.883153 0.469085i \(-0.844584\pi\)
0.530290 0.847816i \(-0.322083\pi\)
\(230\) −60.0126 34.6483i −3.95711 2.28464i
\(231\) 0 0
\(232\) 18.5428 69.2025i 1.21739 4.54337i
\(233\) −19.6906 11.3684i −1.28998 0.744768i −0.311326 0.950303i \(-0.600773\pi\)
−0.978650 + 0.205536i \(0.934106\pi\)
\(234\) 0 0
\(235\) −1.65839 2.87241i −0.108181 0.187376i
\(236\) −12.5063 12.5063i −0.814091 0.814091i
\(237\) 0 0
\(238\) 4.01424 9.51341i 0.260205 0.616663i
\(239\) −20.7640 + 20.7640i −1.34311 + 1.34311i −0.450171 + 0.892943i \(0.648637\pi\)
−0.892943 + 0.450171i \(0.851363\pi\)
\(240\) 0 0
\(241\) −4.79541 + 4.79541i −0.308900 + 0.308900i −0.844483 0.535583i \(-0.820092\pi\)
0.535583 + 0.844483i \(0.320092\pi\)
\(242\) 7.62647 28.4624i 0.490248 1.82963i
\(243\) 0 0
\(244\) 35.3925 + 61.3016i 2.26577 + 3.92443i
\(245\) 12.6540 21.2650i 0.808433 1.35857i
\(246\) 0 0
\(247\) 1.11768 4.61622i 0.0711161 0.293723i
\(248\) 5.87286 3.39070i 0.372927 0.215310i
\(249\) 0 0
\(250\) 24.0674i 1.52216i
\(251\) −2.83547 + 4.91118i −0.178973 + 0.309991i −0.941529 0.336932i \(-0.890611\pi\)
0.762556 + 0.646922i \(0.223944\pi\)
\(252\) 0 0
\(253\) 0.822274 + 3.06877i 0.0516959 + 0.192932i
\(254\) −4.81065 + 17.9536i −0.301847 + 1.12651i
\(255\) 0 0
\(256\) 40.0839 2.50524
\(257\) −1.19397 −0.0744781 −0.0372390 0.999306i \(-0.511856\pi\)
−0.0372390 + 0.999306i \(0.511856\pi\)
\(258\) 0 0
\(259\) 2.47901 + 1.04603i 0.154038 + 0.0649972i
\(260\) −19.5559 66.4902i −1.21280 4.12354i
\(261\) 0 0
\(262\) −9.67191 + 2.59158i −0.597533 + 0.160108i
\(263\) −12.0587 + 20.8862i −0.743569 + 1.28790i 0.207292 + 0.978279i \(0.433535\pi\)
−0.950861 + 0.309619i \(0.899798\pi\)
\(264\) 0 0
\(265\) −12.4173 12.4173i −0.762786 0.762786i
\(266\) 7.50251 + 5.83583i 0.460008 + 0.357818i
\(267\) 0 0
\(268\) 33.3789 8.94384i 2.03894 0.546332i
\(269\) 18.4510i 1.12498i 0.826804 + 0.562490i \(0.190156\pi\)
−0.826804 + 0.562490i \(0.809844\pi\)
\(270\) 0 0
\(271\) 0.695084 0.695084i 0.0422234 0.0422234i −0.685680 0.727903i \(-0.740495\pi\)
0.727903 + 0.685680i \(0.240495\pi\)
\(272\) 21.0254 1.27486
\(273\) 0 0
\(274\) −21.4983 −1.29876
\(275\) 2.34292 2.34292i 0.141284 0.141284i
\(276\) 0 0
\(277\) 18.0478i 1.08439i −0.840254 0.542194i \(-0.817594\pi\)
0.840254 0.542194i \(-0.182406\pi\)
\(278\) −31.3980 + 8.41307i −1.88313 + 0.504582i
\(279\) 0 0
\(280\) 86.8557 + 12.0176i 5.19062 + 0.718189i
\(281\) −15.4188 15.4188i −0.919807 0.919807i 0.0772077 0.997015i \(-0.475400\pi\)
−0.997015 + 0.0772077i \(0.975400\pi\)
\(282\) 0 0
\(283\) −13.7360 + 23.7915i −0.816521 + 1.41426i 0.0917093 + 0.995786i \(0.470767\pi\)
−0.908230 + 0.418470i \(0.862566\pi\)
\(284\) −9.89773 + 2.65209i −0.587323 + 0.157373i
\(285\) 0 0
\(286\) −2.08118 + 3.81548i −0.123063 + 0.225614i
\(287\) −0.948921 7.59418i −0.0560130 0.448270i
\(288\) 0 0
\(289\) −14.9521 −0.879537
\(290\) 73.6739 4.32628
\(291\) 0 0
\(292\) −17.9051 + 66.8228i −1.04782 + 3.91051i
\(293\) −2.03171 7.58244i −0.118694 0.442971i 0.880843 0.473409i \(-0.156977\pi\)
−0.999537 + 0.0304377i \(0.990310\pi\)
\(294\) 0 0
\(295\) 5.74908 9.95770i 0.334724 0.579760i
\(296\) 9.53419i 0.554163i
\(297\) 0 0
\(298\) −51.4222 + 29.6886i −2.97881 + 1.71982i
\(299\) 0.628440 + 25.9087i 0.0363436 + 1.49834i
\(300\) 0 0
\(301\) 21.7967 + 3.01585i 1.25634 + 0.173831i
\(302\) −19.0373 32.9736i −1.09548 1.89742i
\(303\) 0 0
\(304\) −5.00927 + 18.6949i −0.287302 + 1.07222i
\(305\) −32.5395 + 32.5395i −1.86321 + 1.86321i
\(306\) 0 0
\(307\) −16.1223 + 16.1223i −0.920147 + 0.920147i −0.997039 0.0768923i \(-0.975500\pi\)
0.0768923 + 0.997039i \(0.475500\pi\)
\(308\) −3.83767 5.07019i −0.218671 0.288901i
\(309\) 0 0
\(310\) 4.93106 + 4.93106i 0.280065 + 0.280065i
\(311\) 2.75580 + 4.77319i 0.156267 + 0.270663i 0.933520 0.358526i \(-0.116721\pi\)
−0.777253 + 0.629189i \(0.783387\pi\)
\(312\) 0 0
\(313\) 16.8101 + 9.70534i 0.950165 + 0.548578i 0.893132 0.449794i \(-0.148503\pi\)
0.0570329 + 0.998372i \(0.481836\pi\)
\(314\) −10.5702 + 39.4487i −0.596513 + 2.22622i
\(315\) 0 0
\(316\) 16.6753 + 9.62750i 0.938060 + 0.541589i
\(317\) −7.26716 27.1214i −0.408164 1.52329i −0.798144 0.602467i \(-0.794185\pi\)
0.389980 0.920823i \(-0.372482\pi\)
\(318\) 0 0
\(319\) −2.38840 2.38840i −0.133725 0.133725i
\(320\) 26.3102 + 98.1911i 1.47079 + 5.48905i
\(321\) 0 0
\(322\) −47.7844 20.1629i −2.66292 1.12364i
\(323\) −0.487902 + 1.82088i −0.0271476 + 0.101316i
\(324\) 0 0
\(325\) 23.0730 14.0780i 1.27986 0.780908i
\(326\) −12.0619 20.8918i −0.668045 1.15709i
\(327\) 0 0
\(328\) 23.4856 13.5594i 1.29677 0.748692i
\(329\) −1.49818 1.97934i −0.0825973 0.109125i
\(330\) 0 0
\(331\) −7.33428 1.96521i −0.403129 0.108018i 0.0515569 0.998670i \(-0.483582\pi\)
−0.454685 + 0.890652i \(0.650248\pi\)
\(332\) −12.6863 + 12.6863i −0.696252 + 0.696252i
\(333\) 0 0
\(334\) −0.810163 + 0.467748i −0.0443302 + 0.0255940i
\(335\) 11.2327 + 19.4555i 0.613705 + 1.06297i
\(336\) 0 0
\(337\) 3.26189i 0.177686i 0.996046 + 0.0888431i \(0.0283170\pi\)
−0.996046 + 0.0888431i \(0.971683\pi\)
\(338\) −23.8245 + 26.2554i −1.29588 + 1.42811i
\(339\) 0 0
\(340\) 7.11950 + 26.5703i 0.386109 + 1.44098i
\(341\) 0.319715i 0.0173136i
\(342\) 0 0
\(343\) 7.42428 16.9670i 0.400873 0.916133i
\(344\) 20.1804 + 75.3143i 1.08805 + 4.06067i
\(345\) 0 0
\(346\) 24.3689 + 6.52964i 1.31008 + 0.351035i
\(347\) 30.9665 1.66237 0.831185 0.555996i \(-0.187663\pi\)
0.831185 + 0.555996i \(0.187663\pi\)
\(348\) 0 0
\(349\) −11.7105 3.13781i −0.626847 0.167963i −0.0686086 0.997644i \(-0.521856\pi\)
−0.558239 + 0.829680i \(0.688523\pi\)
\(350\) 6.70664 + 53.6730i 0.358485 + 2.86894i
\(351\) 0 0
\(352\) 4.71147 8.16050i 0.251122 0.434956i
\(353\) 28.4026 7.61046i 1.51172 0.405064i 0.594713 0.803938i \(-0.297266\pi\)
0.917006 + 0.398874i \(0.130599\pi\)
\(354\) 0 0
\(355\) −3.33078 5.76909i −0.176780 0.306191i
\(356\) 40.2269 + 40.2269i 2.13202 + 2.13202i
\(357\) 0 0
\(358\) −38.4746 + 10.3092i −2.03344 + 0.544860i
\(359\) −8.99331 + 2.40975i −0.474649 + 0.127182i −0.488210 0.872726i \(-0.662350\pi\)
0.0135610 + 0.999908i \(0.495683\pi\)
\(360\) 0 0
\(361\) 14.9517 + 8.63236i 0.786931 + 0.454335i
\(362\) 16.6578 16.6578i 0.875516 0.875516i
\(363\) 0 0
\(364\) −20.6936 47.5650i −1.08464 2.49308i
\(365\) −44.9744 −2.35407
\(366\) 0 0
\(367\) 21.8442 + 12.6118i 1.14026 + 0.658329i 0.946495 0.322720i \(-0.104597\pi\)
0.193764 + 0.981048i \(0.437930\pi\)
\(368\) 105.608i 5.50518i
\(369\) 0 0
\(370\) −9.47029 + 2.53756i −0.492337 + 0.131921i
\(371\) −10.3741 8.06954i −0.538599 0.418950i
\(372\) 0 0
\(373\) 0.524168 + 0.907886i 0.0271404 + 0.0470086i 0.879277 0.476312i \(-0.158027\pi\)
−0.852136 + 0.523320i \(0.824693\pi\)
\(374\) 0.862496 1.49389i 0.0445986 0.0772470i
\(375\) 0 0
\(376\) 4.39812 7.61777i 0.226816 0.392857i
\(377\) −14.3513 23.5209i −0.739129 1.21139i
\(378\) 0 0
\(379\) −15.3006 4.09979i −0.785941 0.210592i −0.156539 0.987672i \(-0.550034\pi\)
−0.629402 + 0.777080i \(0.716700\pi\)
\(380\) −25.3213 −1.29896
\(381\) 0 0
\(382\) 18.5669 + 4.97500i 0.949968 + 0.254543i
\(383\) 6.72323 25.0914i 0.343541 1.28211i −0.550767 0.834659i \(-0.685665\pi\)
0.894308 0.447453i \(-0.147669\pi\)
\(384\) 0 0
\(385\) 2.53812 3.26299i 0.129355 0.166297i
\(386\) 31.5143 54.5844i 1.60404 2.77827i
\(387\) 0 0
\(388\) 3.66457 + 13.6763i 0.186040 + 0.694311i
\(389\) −20.0494 + 11.5755i −1.01655 + 0.586903i −0.913102 0.407732i \(-0.866320\pi\)
−0.103444 + 0.994635i \(0.532986\pi\)
\(390\) 0 0
\(391\) 10.2862i 0.520194i
\(392\) 65.6197 + 0.864956i 3.31430 + 0.0436869i
\(393\) 0 0
\(394\) −45.8965 + 26.4984i −2.31223 + 1.33497i
\(395\) −3.23985 + 12.0913i −0.163014 + 0.608378i
\(396\) 0 0
\(397\) −11.4194 3.05983i −0.573125 0.153569i −0.0393958 0.999224i \(-0.512543\pi\)
−0.533730 + 0.845655i \(0.679210\pi\)
\(398\) −34.3466 + 34.3466i −1.72164 + 1.72164i
\(399\) 0 0
\(400\) −95.3847 + 55.0704i −4.76923 + 2.75352i
\(401\) −14.7302 14.7302i −0.735592 0.735592i 0.236129 0.971722i \(-0.424121\pi\)
−0.971722 + 0.236129i \(0.924121\pi\)
\(402\) 0 0
\(403\) 0.613729 2.53482i 0.0305720 0.126268i
\(404\) 6.80812 + 3.93067i 0.338717 + 0.195558i
\(405\) 0 0
\(406\) 54.7149 6.83683i 2.71545 0.339306i
\(407\) 0.389277 + 0.224749i 0.0192957 + 0.0111404i
\(408\) 0 0
\(409\) −11.2439 11.2439i −0.555974 0.555974i 0.372185 0.928159i \(-0.378609\pi\)
−0.928159 + 0.372185i \(0.878609\pi\)
\(410\) 19.7193 + 19.7193i 0.973865 + 0.973865i
\(411\) 0 0
\(412\) −63.1278 36.4468i −3.11008 1.79561i
\(413\) 3.34557 7.92872i 0.164625 0.390147i
\(414\) 0 0
\(415\) −10.1010 5.83183i −0.495840 0.286274i
\(416\) 53.0192 55.6552i 2.59948 2.72872i
\(417\) 0 0
\(418\) 1.12281 + 1.12281i 0.0549183 + 0.0549183i
\(419\) 4.29128 2.47757i 0.209643 0.121037i −0.391503 0.920177i \(-0.628045\pi\)
0.601145 + 0.799140i \(0.294711\pi\)
\(420\) 0 0
\(421\) 0.811225 0.811225i 0.0395367 0.0395367i −0.687062 0.726599i \(-0.741100\pi\)
0.726599 + 0.687062i \(0.241100\pi\)
\(422\) 26.5455 + 7.11283i 1.29221 + 0.346247i
\(423\) 0 0
\(424\) 12.0536 44.9848i 0.585376 2.18465i
\(425\) −9.29045 + 5.36385i −0.450653 + 0.260185i
\(426\) 0 0
\(427\) −21.1463 + 27.1855i −1.02334 + 1.31560i
\(428\) 10.2758i 0.496697i
\(429\) 0 0
\(430\) −69.4384 + 40.0903i −3.34862 + 1.93333i
\(431\) 5.30567 + 19.8010i 0.255565 + 0.953783i 0.967775 + 0.251816i \(0.0810278\pi\)
−0.712210 + 0.701967i \(0.752306\pi\)
\(432\) 0 0
\(433\) −0.246122 + 0.426295i −0.0118279 + 0.0204864i −0.871879 0.489722i \(-0.837098\pi\)
0.860051 + 0.510208i \(0.170432\pi\)
\(434\) 4.11971 + 3.20452i 0.197752 + 0.153822i
\(435\) 0 0
\(436\) 10.3803 38.7399i 0.497127 1.85530i
\(437\) 9.14599 + 2.45066i 0.437512 + 0.117231i
\(438\) 0 0
\(439\) 22.3782 1.06806 0.534028 0.845467i \(-0.320678\pi\)
0.534028 + 0.845467i \(0.320678\pi\)
\(440\) 14.1491 + 3.79124i 0.674533 + 0.180740i
\(441\) 0 0
\(442\) 9.70585 10.1884i 0.461660 0.484613i
\(443\) −4.77420 + 8.26916i −0.226829 + 0.392880i −0.956867 0.290527i \(-0.906169\pi\)
0.730038 + 0.683407i \(0.239503\pi\)
\(444\) 0 0
\(445\) −18.4921 + 32.0292i −0.876609 + 1.51833i
\(446\) 1.29703 + 2.24653i 0.0614164 + 0.106376i
\(447\) 0 0
\(448\) 28.6516 + 70.4813i 1.35366 + 3.32993i
\(449\) 17.1874 4.60535i 0.811124 0.217340i 0.170662 0.985330i \(-0.445409\pi\)
0.640462 + 0.767990i \(0.278743\pi\)
\(450\) 0 0
\(451\) 1.27854i 0.0602041i
\(452\) −29.1383 16.8230i −1.37055 0.791287i
\(453\) 0 0
\(454\) 66.8894 3.13928
\(455\) 26.3868 20.9979i 1.23703 0.984398i
\(456\) 0 0
\(457\) −19.4797 + 19.4797i −0.911220 + 0.911220i −0.996368 0.0851486i \(-0.972864\pi\)
0.0851486 + 0.996368i \(0.472864\pi\)
\(458\) 48.7276 + 28.1329i 2.27689 + 1.31456i
\(459\) 0 0
\(460\) 133.459 35.7602i 6.22255 1.66733i
\(461\) 10.0918 2.70408i 0.470021 0.125942i −0.0160314 0.999871i \(-0.505103\pi\)
0.486052 + 0.873930i \(0.338437\pi\)
\(462\) 0 0
\(463\) −10.7292 10.7292i −0.498628 0.498628i 0.412382 0.911011i \(-0.364697\pi\)
−0.911011 + 0.412382i \(0.864697\pi\)
\(464\) 56.1394 + 97.2362i 2.60620 + 4.51408i
\(465\) 0 0
\(466\) 59.8948 16.0488i 2.77457 0.743445i
\(467\) 7.08987 12.2800i 0.328080 0.568251i −0.654051 0.756451i \(-0.726932\pi\)
0.982131 + 0.188199i \(0.0602651\pi\)
\(468\) 0 0
\(469\) 10.1475 + 13.4065i 0.468569 + 0.619056i
\(470\) 8.73729 + 2.34115i 0.403021 + 0.107989i
\(471\) 0 0
\(472\) 30.4937 1.40358
\(473\) 3.55076 + 0.951424i 0.163264 + 0.0437465i
\(474\) 0 0
\(475\) −2.55585 9.53857i −0.117271 0.437660i
\(476\) 7.75308 + 19.0721i 0.355362 + 0.874169i
\(477\) 0 0
\(478\) 80.0836i 3.66294i
\(479\) 6.49544 + 24.2413i 0.296784 + 1.10761i 0.939790 + 0.341752i \(0.111020\pi\)
−0.643006 + 0.765861i \(0.722313\pi\)
\(480\) 0 0
\(481\) 2.65489 + 2.52915i 0.121053 + 0.115319i
\(482\) 18.4951i 0.842431i
\(483\) 0 0
\(484\) 29.3757 + 50.8803i 1.33526 + 2.31274i
\(485\) −7.97153 + 4.60236i −0.361968 + 0.208983i
\(486\) 0 0
\(487\) −17.1606 + 17.1606i −0.777620 + 0.777620i −0.979426 0.201805i \(-0.935319\pi\)
0.201805 + 0.979426i \(0.435319\pi\)
\(488\) −117.883 31.5866i −5.33631 1.42986i
\(489\) 0 0
\(490\) 16.6058 + 65.4101i 0.750171 + 2.95493i
\(491\) 9.68019 5.58886i 0.436861 0.252222i −0.265404 0.964137i \(-0.585505\pi\)
0.702265 + 0.711915i \(0.252172\pi\)
\(492\) 0 0
\(493\) 5.46796 + 9.47079i 0.246265 + 0.426543i
\(494\) 6.74666 + 11.0574i 0.303547 + 0.497494i
\(495\) 0 0
\(496\) −2.75065 + 10.2656i −0.123508 + 0.460937i
\(497\) −3.00901 3.97540i −0.134973 0.178321i
\(498\) 0 0
\(499\) −10.2127 38.1144i −0.457184 1.70623i −0.681587 0.731737i \(-0.738710\pi\)
0.224403 0.974496i \(-0.427957\pi\)
\(500\) −33.9317 33.9317i −1.51747 1.51747i
\(501\) 0 0
\(502\) −4.00284 14.9388i −0.178655 0.666751i
\(503\) 7.48538 + 4.32169i 0.333757 + 0.192694i 0.657508 0.753448i \(-0.271611\pi\)
−0.323751 + 0.946142i \(0.604944\pi\)
\(504\) 0 0
\(505\) −1.32275 + 4.93657i −0.0588616 + 0.219674i
\(506\) −7.50357 4.33219i −0.333574 0.192589i
\(507\) 0 0
\(508\) −18.5297 32.0945i −0.822125 1.42396i
\(509\) −3.95593 3.95593i −0.175343 0.175343i 0.613979 0.789322i \(-0.289568\pi\)
−0.789322 + 0.613979i \(0.789568\pi\)
\(510\) 0 0
\(511\) −33.4008 + 4.17355i −1.47756 + 0.184627i
\(512\) −26.6889 + 26.6889i −1.17950 + 1.17950i
\(513\) 0 0
\(514\) 2.30249 2.30249i 0.101558 0.101558i
\(515\) 12.2651 45.7739i 0.540464 2.01704i
\(516\) 0 0
\(517\) −0.207354 0.359147i −0.00911940 0.0157953i
\(518\) −6.79775 + 2.76338i −0.298676 + 0.121416i
\(519\) 0 0
\(520\) 104.901 + 57.2191i 4.60023 + 2.50922i
\(521\) −5.55782 + 3.20881i −0.243493 + 0.140581i −0.616781 0.787135i \(-0.711564\pi\)
0.373288 + 0.927715i \(0.378230\pi\)
\(522\) 0 0
\(523\) 31.6355i 1.38333i 0.722221 + 0.691663i \(0.243121\pi\)
−0.722221 + 0.691663i \(0.756879\pi\)
\(524\) 9.98229 17.2898i 0.436078 0.755310i
\(525\) 0 0
\(526\) −17.0232 63.5316i −0.742248 2.77011i
\(527\) −0.267913 + 0.999863i −0.0116705 + 0.0435547i
\(528\) 0 0
\(529\) −28.6659 −1.24634
\(530\) 47.8914 2.08027
\(531\) 0 0
\(532\) −18.8052 + 2.34978i −0.815310 + 0.101876i
\(533\) 2.45430 10.1367i 0.106307 0.439070i
\(534\) 0 0
\(535\) −6.45271 + 1.72900i −0.278975 + 0.0747511i
\(536\) −29.7895 + 51.5969i −1.28671 + 2.22865i
\(537\) 0 0
\(538\) −35.5814 35.5814i −1.53402 1.53402i
\(539\) 1.58217 2.65884i 0.0681488 0.114524i
\(540\) 0 0
\(541\) −18.2900 + 4.90078i −0.786347 + 0.210701i −0.629581 0.776935i \(-0.716773\pi\)
−0.156766 + 0.987636i \(0.550107\pi\)
\(542\) 2.68083i 0.115152i
\(543\) 0 0
\(544\) −21.5727 + 21.5727i −0.924922 + 0.924922i
\(545\) 26.0735 1.11686
\(546\) 0 0
\(547\) −13.7543 −0.588091 −0.294046 0.955791i \(-0.595002\pi\)
−0.294046 + 0.955791i \(0.595002\pi\)
\(548\) 30.3097 30.3097i 1.29477 1.29477i
\(549\) 0 0
\(550\) 9.03628i 0.385308i
\(551\) −9.72373 + 2.60546i −0.414245 + 0.110997i
\(552\) 0 0
\(553\) −1.28406 + 9.28039i −0.0546039 + 0.394643i
\(554\) 34.8038 + 34.8038i 1.47867 + 1.47867i
\(555\) 0 0
\(556\) 32.4056 56.1281i 1.37430 2.38036i
\(557\) −16.6591 + 4.46378i −0.705867 + 0.189137i −0.593857 0.804571i \(-0.702396\pi\)
−0.112010 + 0.993707i \(0.535729\pi\)
\(558\) 0 0
\(559\) 26.3253 + 14.3593i 1.11344 + 0.607334i
\(560\) −109.568 + 82.9329i −4.63009 + 3.50456i
\(561\) 0 0
\(562\) 59.4678 2.50850
\(563\) −33.0554 −1.39312 −0.696559 0.717499i \(-0.745287\pi\)
−0.696559 + 0.717499i \(0.745287\pi\)
\(564\) 0 0
\(565\) 5.66127 21.1282i 0.238172 0.888868i
\(566\) −19.3912 72.3688i −0.815071 3.04189i
\(567\) 0 0
\(568\) 8.83340 15.2999i 0.370641 0.641969i
\(569\) 32.9428i 1.38104i −0.723316 0.690518i \(-0.757383\pi\)
0.723316 0.690518i \(-0.242617\pi\)
\(570\) 0 0
\(571\) 6.40074 3.69547i 0.267862 0.154650i −0.360053 0.932932i \(-0.617242\pi\)
0.627916 + 0.778281i \(0.283908\pi\)
\(572\) −2.44513 8.31348i −0.102236 0.347604i
\(573\) 0 0
\(574\) 16.4747 + 12.8149i 0.687640 + 0.534882i
\(575\) 26.9418 + 46.6645i 1.12355 + 1.94605i
\(576\) 0 0
\(577\) −10.1455 + 37.8634i −0.422362 + 1.57627i 0.347257 + 0.937770i \(0.387113\pi\)
−0.769618 + 0.638505i \(0.779553\pi\)
\(578\) 28.8340 28.8340i 1.19934 1.19934i
\(579\) 0 0
\(580\) −103.870 + 103.870i −4.31297 + 4.31297i
\(581\) −8.04285 3.39373i −0.333674 0.140796i
\(582\) 0 0
\(583\) −1.55257 1.55257i −0.0643009 0.0643009i
\(584\) −59.6371 103.294i −2.46780 4.27435i
\(585\) 0 0
\(586\) 18.5401 + 10.7041i 0.765886 + 0.442184i
\(587\) −5.58839 + 20.8562i −0.230658 + 0.860826i 0.749401 + 0.662117i \(0.230342\pi\)
−0.980058 + 0.198709i \(0.936325\pi\)
\(588\) 0 0
\(589\) −0.825203 0.476431i −0.0340019 0.0196310i
\(590\) 8.11599 + 30.2893i 0.334130 + 1.24699i
\(591\) 0 0
\(592\) −10.5655 10.5655i −0.434238 0.434238i
\(593\) 7.82600 + 29.2070i 0.321375 + 1.19939i 0.917906 + 0.396799i \(0.129879\pi\)
−0.596530 + 0.802591i \(0.703454\pi\)
\(594\) 0 0
\(595\) −10.6719 + 8.07765i −0.437505 + 0.331152i
\(596\) 30.6413 114.355i 1.25512 4.68416i
\(597\) 0 0
\(598\) −51.1748 48.7510i −2.09269 1.99358i
\(599\) −9.06280 15.6972i −0.370296 0.641371i 0.619315 0.785143i \(-0.287410\pi\)
−0.989611 + 0.143771i \(0.954077\pi\)
\(600\) 0 0
\(601\) −30.9648 + 17.8775i −1.26308 + 0.729240i −0.973669 0.227965i \(-0.926793\pi\)
−0.289411 + 0.957205i \(0.593459\pi\)
\(602\) −47.8490 + 36.2174i −1.95018 + 1.47611i
\(603\) 0 0
\(604\) 73.3283 + 19.6483i 2.98369 + 0.799476i
\(605\) −27.0077 + 27.0077i −1.09802 + 1.09802i
\(606\) 0 0
\(607\) 3.30264 1.90678i 0.134050 0.0773937i −0.431475 0.902125i \(-0.642007\pi\)
0.565525 + 0.824731i \(0.308673\pi\)
\(608\) −14.0418 24.3211i −0.569470 0.986352i
\(609\) 0 0
\(610\) 125.500i 5.08133i
\(611\) −0.954550 3.24548i −0.0386170 0.131298i
\(612\) 0 0
\(613\) 1.06673 + 3.98111i 0.0430850 + 0.160795i 0.984117 0.177523i \(-0.0568085\pi\)
−0.941032 + 0.338319i \(0.890142\pi\)
\(614\) 62.1811i 2.50942i
\(615\) 0 0
\(616\) 10.8598 + 1.50260i 0.437556 + 0.0605415i
\(617\) −4.26184 15.9054i −0.171575 0.640327i −0.997110 0.0759754i \(-0.975793\pi\)
0.825535 0.564351i \(-0.190874\pi\)
\(618\) 0 0
\(619\) 9.82581 + 2.63282i 0.394933 + 0.105822i 0.450819 0.892615i \(-0.351132\pi\)
−0.0558866 + 0.998437i \(0.517799\pi\)
\(620\) −13.9042 −0.558407
\(621\) 0 0
\(622\) −14.5191 3.89037i −0.582161 0.155990i
\(623\) −10.7611 + 25.5030i −0.431135 + 1.02176i
\(624\) 0 0
\(625\) −3.14284 + 5.44356i −0.125714 + 0.217743i
\(626\) −51.1330 + 13.7010i −2.04369 + 0.547604i
\(627\) 0 0
\(628\) −40.7146 70.5198i −1.62469 2.81405i
\(629\) −1.02907 1.02907i −0.0410318 0.0410318i
\(630\) 0 0
\(631\) −35.7618 + 9.58236i −1.42366 + 0.381468i −0.886779 0.462193i \(-0.847063\pi\)
−0.536877 + 0.843661i \(0.680396\pi\)
\(632\) −32.0666 + 8.59222i −1.27554 + 0.341780i
\(633\) 0 0
\(634\) 66.3156 + 38.2873i 2.63373 + 1.52058i
\(635\) 17.0361 17.0361i 0.676055 0.676055i
\(636\) 0 0
\(637\) 17.6479 18.0430i 0.699236 0.714891i
\(638\) 9.21169 0.364694
\(639\) 0 0
\(640\) −109.558 63.2531i −4.33064 2.50030i
\(641\) 30.1425i 1.19056i 0.803520 + 0.595278i \(0.202958\pi\)
−0.803520 + 0.595278i \(0.797042\pi\)
\(642\) 0 0
\(643\) 36.7921 9.85840i 1.45094 0.388778i 0.554588 0.832125i \(-0.312876\pi\)
0.896350 + 0.443348i \(0.146209\pi\)
\(644\) 95.7964 38.9425i 3.77491 1.53455i
\(645\) 0 0
\(646\) −2.57054 4.45230i −0.101136 0.175173i
\(647\) 19.3901 33.5847i 0.762305 1.32035i −0.179354 0.983785i \(-0.557401\pi\)
0.941660 0.336567i \(-0.109266\pi\)
\(648\) 0 0
\(649\) 0.718826 1.24504i 0.0282164 0.0488722i
\(650\) −17.3461 + 71.6428i −0.680371 + 2.81006i
\(651\) 0 0
\(652\) 46.4600 + 12.4489i 1.81952 + 0.487538i
\(653\) 13.0170 0.509396 0.254698 0.967021i \(-0.418024\pi\)
0.254698 + 0.967021i \(0.418024\pi\)
\(654\) 0 0
\(655\) 12.5368 + 3.35924i 0.489855 + 0.131256i
\(656\) −10.9998 + 41.0519i −0.429471 + 1.60281i
\(657\) 0 0
\(658\) 6.70612 + 0.927878i 0.261432 + 0.0361725i
\(659\) −25.0015 + 43.3039i −0.973921 + 1.68688i −0.290470 + 0.956884i \(0.593812\pi\)
−0.683451 + 0.729996i \(0.739522\pi\)
\(660\) 0 0
\(661\) 3.33584 + 12.4495i 0.129749 + 0.484231i 0.999964 0.00844118i \(-0.00268694\pi\)
−0.870215 + 0.492672i \(0.836020\pi\)
\(662\) 17.9333 10.3538i 0.696999 0.402413i
\(663\) 0 0
\(664\) 30.9326i 1.20042i
\(665\) −4.63972 11.4134i −0.179921 0.442595i
\(666\) 0 0
\(667\) 47.5704 27.4648i 1.84193 1.06344i
\(668\) 0.482758 1.80168i 0.0186785 0.0697090i
\(669\) 0 0
\(670\) −59.1797 15.8572i −2.28631 0.612615i
\(671\) −4.06852 + 4.06852i −0.157063 + 0.157063i
\(672\) 0 0
\(673\) 34.5128 19.9259i 1.33037 0.768089i 0.345013 0.938598i \(-0.387875\pi\)
0.985356 + 0.170509i \(0.0545413\pi\)
\(674\) −6.29029 6.29029i −0.242293 0.242293i
\(675\) 0 0
\(676\) −3.42724 70.6059i −0.131817 2.71561i
\(677\) 3.61272 + 2.08580i 0.138848 + 0.0801640i 0.567815 0.823156i \(-0.307789\pi\)
−0.428967 + 0.903320i \(0.641122\pi\)
\(678\) 0 0
\(679\) −5.49307 + 4.15775i −0.210805 + 0.159560i
\(680\) −41.0723 23.7131i −1.57505 0.909357i
\(681\) 0 0
\(682\) 0.616546 + 0.616546i 0.0236088 + 0.0236088i
\(683\) −4.99136 4.99136i −0.190989 0.190989i 0.605134 0.796123i \(-0.293119\pi\)
−0.796123 + 0.605134i \(0.793119\pi\)
\(684\) 0 0
\(685\) 24.1330 + 13.9332i 0.922075 + 0.532360i
\(686\) 18.4024 + 47.0367i 0.702609 + 1.79587i
\(687\) 0 0
\(688\) −105.824 61.0974i −4.03450 2.32932i
\(689\) −9.32899 15.2896i −0.355406 0.582489i
\(690\) 0 0
\(691\) −15.9631 15.9631i −0.607264 0.607264i 0.334966 0.942230i \(-0.391275\pi\)
−0.942230 + 0.334966i \(0.891275\pi\)
\(692\) −43.5627 + 25.1510i −1.65601 + 0.956096i
\(693\) 0 0
\(694\) −59.7165 + 59.7165i −2.26681 + 2.26681i
\(695\) 40.6985 + 10.9051i 1.54378 + 0.413655i
\(696\) 0 0
\(697\) −1.07138 + 3.99845i −0.0405815 + 0.151452i
\(698\) 28.6337 16.5317i 1.08380 0.625734i
\(699\) 0 0
\(700\) −85.1270 66.2161i −3.21750 2.50273i
\(701\) 38.0674i 1.43779i 0.695120 + 0.718894i \(0.255351\pi\)
−0.695120 + 0.718894i \(0.744649\pi\)
\(702\) 0 0
\(703\) 1.16018 0.669830i 0.0437570 0.0252631i
\(704\) 3.28965 + 12.2771i 0.123983 + 0.462712i
\(705\) 0 0
\(706\) −40.0960 + 69.4484i −1.50903 + 2.61372i
\(707\) −0.524251 + 3.78896i −0.0197165 + 0.142498i
\(708\) 0 0
\(709\) −0.469956 + 1.75390i −0.0176496 + 0.0658691i −0.974189 0.225734i \(-0.927522\pi\)
0.956539 + 0.291603i \(0.0941886\pi\)
\(710\) 17.5484 + 4.70208i 0.658579 + 0.176466i
\(711\) 0 0
\(712\) −98.0838 −3.67584
\(713\) 5.02216 + 1.34568i 0.188081 + 0.0503963i
\(714\) 0 0
\(715\) 4.80907 2.93426i 0.179849 0.109735i
\(716\) 39.7092 68.7784i 1.48400 2.57037i
\(717\) 0 0
\(718\) 12.6959 21.9899i 0.473806 0.820656i
\(719\) −13.7958 23.8950i −0.514496 0.891133i −0.999859 0.0168198i \(-0.994646\pi\)
0.485363 0.874313i \(-0.338688\pi\)
\(720\) 0 0
\(721\) 4.86107 35.1328i 0.181036 1.30841i
\(722\) −45.4800 + 12.1863i −1.69259 + 0.453528i
\(723\) 0 0
\(724\) 46.9705i 1.74564i
\(725\) −49.6123 28.6437i −1.84255 1.06380i
\(726\) 0 0
\(727\) 1.57479 0.0584058 0.0292029 0.999574i \(-0.490703\pi\)
0.0292029 + 0.999574i \(0.490703\pi\)
\(728\) 83.2163 + 32.7598i 3.08420 + 1.21416i
\(729\) 0 0
\(730\) 86.7295 86.7295i 3.21000 3.21000i
\(731\) −10.3072 5.95088i −0.381226 0.220101i
\(732\) 0 0
\(733\) −37.5443 + 10.0600i −1.38673 + 0.371574i −0.873562 0.486713i \(-0.838196\pi\)
−0.513170 + 0.858287i \(0.671529\pi\)
\(734\) −66.4456 + 17.8040i −2.45255 + 0.657159i
\(735\) 0 0
\(736\) 108.356 + 108.356i 3.99407 + 3.99407i
\(737\) 1.40445 + 2.43259i 0.0517337 + 0.0896055i
\(738\) 0 0
\(739\) −42.2979 + 11.3337i −1.55595 + 0.416917i −0.931380 0.364049i \(-0.881394\pi\)
−0.624574 + 0.780966i \(0.714727\pi\)
\(740\) 9.77420 16.9294i 0.359307 0.622337i
\(741\) 0 0
\(742\) 35.5672 4.44425i 1.30571 0.163154i
\(743\) −18.3147 4.90740i −0.671900 0.180035i −0.0932893 0.995639i \(-0.529738\pi\)
−0.578610 + 0.815604i \(0.696405\pi\)
\(744\) 0 0
\(745\) 76.9655 2.81980
\(746\) −2.76160 0.739970i −0.101110 0.0270922i
\(747\) 0 0
\(748\) 0.890174 + 3.32217i 0.0325480 + 0.121471i
\(749\) −4.63174 + 1.88286i −0.169240 + 0.0687984i
\(750\) 0 0
\(751\) 11.4855i 0.419110i −0.977797 0.209555i \(-0.932798\pi\)
0.977797 0.209555i \(-0.0672016\pi\)
\(752\) 3.56790 + 13.3156i 0.130108 + 0.485570i
\(753\) 0 0
\(754\) 73.0335 + 17.6828i 2.65972 + 0.643971i
\(755\) 49.3529i 1.79613i
\(756\) 0 0
\(757\) 0.505532 + 0.875607i 0.0183739 + 0.0318245i 0.875066 0.484003i \(-0.160818\pi\)
−0.856692 + 0.515828i \(0.827484\pi\)
\(758\) 37.4122 21.5999i 1.35887 0.784545i
\(759\) 0 0
\(760\) 30.8700 30.8700i 1.11977 1.11977i
\(761\) −44.9154 12.0351i −1.62818 0.436270i −0.674792 0.738008i \(-0.735767\pi\)
−0.953391 + 0.301737i \(0.902433\pi\)
\(762\) 0 0
\(763\) 19.3638 2.41958i 0.701017 0.0875946i
\(764\) −33.1909 + 19.1628i −1.20080 + 0.693285i
\(765\) 0 0
\(766\) 35.4216 + 61.3520i 1.27983 + 2.21674i
\(767\) 8.08910 8.49127i 0.292080 0.306602i
\(768\) 0 0
\(769\) 10.0112 37.3624i 0.361014 1.34732i −0.511730 0.859146i \(-0.670995\pi\)
0.872745 0.488177i \(-0.162338\pi\)
\(770\) 1.39786 + 11.1870i 0.0503752 + 0.403151i
\(771\) 0 0
\(772\) 32.5256 + 121.387i 1.17062 + 4.36882i
\(773\) 21.0972 + 21.0972i 0.758814 + 0.758814i 0.976107 0.217293i \(-0.0697226\pi\)
−0.217293 + 0.976107i \(0.569723\pi\)
\(774\) 0 0
\(775\) −1.40345 5.23773i −0.0504133 0.188145i
\(776\) −21.1409 12.2057i −0.758913 0.438158i
\(777\) 0 0
\(778\) 16.3412 60.9862i 0.585861 2.18646i
\(779\) −3.29998 1.90525i −0.118234 0.0682625i
\(780\) 0 0
\(781\) −0.416459 0.721328i −0.0149021 0.0258111i
\(782\) 19.8361 + 19.8361i 0.709336 + 0.709336i
\(783\) 0 0
\(784\) −73.6760 + 71.7590i −2.63129 + 2.56282i
\(785\) 37.4326 37.4326i 1.33603 1.33603i
\(786\) 0 0
\(787\) 3.12615 3.12615i 0.111435 0.111435i −0.649191 0.760626i \(-0.724892\pi\)
0.760626 + 0.649191i \(0.224892\pi\)
\(788\) 27.3487 102.067i 0.974258 3.63598i