Properties

Label 261.3.s.a.19.3
Level $261$
Weight $3$
Character 261.19
Analytic conductor $7.112$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 261 = 3^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 261.s (of order \(28\), degree \(12\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.11173489980\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(4\) over \(\Q(\zeta_{28})\)
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: $\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label 19.3
Character \(\chi\) \(=\) 261.19
Dual form 261.3.s.a.55.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.448531 + 0.713833i) q^{2} +(1.42716 - 2.96352i) q^{4} +(-4.21883 - 0.962920i) q^{5} +(-10.1429 + 4.88457i) q^{7} +(6.10659 - 0.688048i) q^{8} +O(q^{10})\) \(q+(0.448531 + 0.713833i) q^{2} +(1.42716 - 2.96352i) q^{4} +(-4.21883 - 0.962920i) q^{5} +(-10.1429 + 4.88457i) q^{7} +(6.10659 - 0.688048i) q^{8} +(-1.20491 - 3.44344i) q^{10} +(-1.54207 - 0.173749i) q^{11} +(-11.3208 + 9.02803i) q^{13} +(-8.03618 - 5.04946i) q^{14} +(-4.97314 - 6.23612i) q^{16} +(-16.8448 + 16.8448i) q^{17} +(0.448791 - 0.157039i) q^{19} +(-8.87457 + 11.1284i) q^{20} +(-0.567637 - 1.17871i) q^{22} +(-1.55197 - 6.79962i) q^{23} +(-5.65292 - 2.72230i) q^{25} +(-11.5222 - 4.03180i) q^{26} +37.0298i q^{28} +(20.2766 + 20.7330i) q^{29} +(-7.88671 - 12.5516i) q^{31} +(10.3395 - 29.5486i) q^{32} +(-19.5798 - 4.46896i) q^{34} +(47.4946 - 10.8403i) q^{35} +(26.2932 - 2.96253i) q^{37} +(0.313396 + 0.249925i) q^{38} +(-26.4252 - 2.97741i) q^{40} +(-46.1225 - 46.1225i) q^{41} +(-53.7324 - 33.7623i) q^{43} +(-2.71568 + 4.32198i) q^{44} +(4.15769 - 4.15769i) q^{46} +(-5.72285 + 50.7917i) q^{47} +(48.4686 - 60.7777i) q^{49} +(-0.592241 - 5.25628i) q^{50} +(10.5982 + 46.4338i) q^{52} +(9.09960 - 39.8680i) q^{53} +(6.33841 + 2.21790i) q^{55} +(-58.5778 + 36.8069i) q^{56} +(-5.70521 + 23.7735i) q^{58} -23.8690 q^{59} +(23.8851 - 68.2596i) q^{61} +(5.42233 - 11.2596i) q^{62} +(-5.37487 + 1.22678i) q^{64} +(56.4537 - 27.1867i) q^{65} +(89.8491 + 71.6523i) q^{67} +(25.8798 + 73.9602i) q^{68} +(29.0410 + 29.0410i) q^{70} +(54.7070 - 43.6274i) q^{71} +(-43.5770 + 69.3524i) q^{73} +(13.9081 + 17.4402i) q^{74} +(0.175107 - 1.55412i) q^{76} +(16.4897 - 5.77000i) q^{77} +(12.9255 + 114.717i) q^{79} +(14.9759 + 31.0978i) q^{80} +(12.2364 - 53.6111i) q^{82} +(1.11626 + 0.537563i) q^{83} +(87.2856 - 54.8452i) q^{85} -53.4995i q^{86} -9.53632 q^{88} +(35.1684 + 55.9701i) q^{89} +(70.7277 - 146.868i) q^{91} +(-22.3657 - 5.10483i) q^{92} +(-38.8237 + 18.6965i) q^{94} +(-2.04459 + 0.230370i) q^{95} +(-26.0062 - 74.3215i) q^{97} +(65.1248 + 7.33780i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} + O(q^{10}) \) \( 48q + 16q^{2} - 14q^{4} + 14q^{5} - 10q^{7} - 28q^{8} - 20q^{10} + 8q^{11} - 14q^{13} - 26q^{14} + 18q^{16} + 26q^{17} + 2q^{19} - 46q^{20} + 154q^{22} - 56q^{23} - 34q^{25} - 110q^{26} + 170q^{29} - 88q^{31} + 132q^{32} - 224q^{34} + 210q^{35} - 56q^{37} + 294q^{38} - 492q^{40} + 34q^{41} + 176q^{43} - 126q^{44} + 744q^{46} - 208q^{47} + 506q^{49} - 732q^{50} + 690q^{52} + 14q^{53} + 284q^{55} - 332q^{56} - 508q^{58} + 44q^{59} - 30q^{61} + 504q^{62} - 896q^{64} + 554q^{65} - 574q^{67} + 796q^{68} - 1066q^{70} - 224q^{71} - 22q^{73} - 820q^{74} + 514q^{76} - 436q^{77} + 564q^{79} - 1162q^{80} - 18q^{82} + 126q^{83} + 38q^{85} - 384q^{88} + 160q^{89} - 434q^{91} + 1022q^{92} - 2q^{94} + 642q^{95} + 604q^{97} + 102q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{9}{28}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.448531 + 0.713833i 0.224266 + 0.356917i 0.939837 0.341623i \(-0.110977\pi\)
−0.715572 + 0.698539i \(0.753834\pi\)
\(3\) 0 0
\(4\) 1.42716 2.96352i 0.356789 0.740881i
\(5\) −4.21883 0.962920i −0.843766 0.192584i −0.221275 0.975211i \(-0.571022\pi\)
−0.622490 + 0.782627i \(0.713879\pi\)
\(6\) 0 0
\(7\) −10.1429 + 4.88457i −1.44899 + 0.697795i −0.982419 0.186690i \(-0.940224\pi\)
−0.466568 + 0.884485i \(0.654510\pi\)
\(8\) 6.10659 0.688048i 0.763324 0.0860060i
\(9\) 0 0
\(10\) −1.20491 3.44344i −0.120491 0.344344i
\(11\) −1.54207 0.173749i −0.140188 0.0157954i 0.0415917 0.999135i \(-0.486757\pi\)
−0.181780 + 0.983339i \(0.558186\pi\)
\(12\) 0 0
\(13\) −11.3208 + 9.02803i −0.870830 + 0.694464i −0.953266 0.302133i \(-0.902301\pi\)
0.0824361 + 0.996596i \(0.473730\pi\)
\(14\) −8.03618 5.04946i −0.574013 0.360676i
\(15\) 0 0
\(16\) −4.97314 6.23612i −0.310821 0.389757i
\(17\) −16.8448 + 16.8448i −0.990872 + 0.990872i −0.999959 0.00908711i \(-0.997107\pi\)
0.00908711 + 0.999959i \(0.497107\pi\)
\(18\) 0 0
\(19\) 0.448791 0.157039i 0.0236206 0.00826520i −0.318443 0.947942i \(-0.603160\pi\)
0.342064 + 0.939677i \(0.388874\pi\)
\(20\) −8.87457 + 11.1284i −0.443728 + 0.556418i
\(21\) 0 0
\(22\) −0.567637 1.17871i −0.0258017 0.0535777i
\(23\) −1.55197 6.79962i −0.0674769 0.295636i 0.929918 0.367766i \(-0.119877\pi\)
−0.997395 + 0.0721306i \(0.977020\pi\)
\(24\) 0 0
\(25\) −5.65292 2.72230i −0.226117 0.108892i
\(26\) −11.5222 4.03180i −0.443163 0.155069i
\(27\) 0 0
\(28\) 37.0298i 1.32249i
\(29\) 20.2766 + 20.7330i 0.699195 + 0.714931i
\(30\) 0 0
\(31\) −7.88671 12.5516i −0.254410 0.404891i 0.694962 0.719047i \(-0.255421\pi\)
−0.949371 + 0.314156i \(0.898279\pi\)
\(32\) 10.3395 29.5486i 0.323110 0.923394i
\(33\) 0 0
\(34\) −19.5798 4.46896i −0.575877 0.131440i
\(35\) 47.4946 10.8403i 1.35699 0.309724i
\(36\) 0 0
\(37\) 26.2932 2.96253i 0.710627 0.0800685i 0.250751 0.968052i \(-0.419322\pi\)
0.459876 + 0.887983i \(0.347894\pi\)
\(38\) 0.313396 + 0.249925i 0.00824727 + 0.00657698i
\(39\) 0 0
\(40\) −26.4252 2.97741i −0.660630 0.0744351i
\(41\) −46.1225 46.1225i −1.12494 1.12494i −0.990988 0.133950i \(-0.957234\pi\)
−0.133950 0.990988i \(-0.542766\pi\)
\(42\) 0 0
\(43\) −53.7324 33.7623i −1.24959 0.785170i −0.265721 0.964050i \(-0.585610\pi\)
−0.983871 + 0.178880i \(0.942753\pi\)
\(44\) −2.71568 + 4.32198i −0.0617200 + 0.0982268i
\(45\) 0 0
\(46\) 4.15769 4.15769i 0.0903845 0.0903845i
\(47\) −5.72285 + 50.7917i −0.121763 + 1.08067i 0.773085 + 0.634302i \(0.218713\pi\)
−0.894848 + 0.446372i \(0.852716\pi\)
\(48\) 0 0
\(49\) 48.4686 60.7777i 0.989155 1.24036i
\(50\) −0.592241 5.25628i −0.0118448 0.105126i
\(51\) 0 0
\(52\) 10.5982 + 46.4338i 0.203812 + 0.892958i
\(53\) 9.09960 39.8680i 0.171691 0.752226i −0.813612 0.581408i \(-0.802502\pi\)
0.985303 0.170818i \(-0.0546409\pi\)
\(54\) 0 0
\(55\) 6.33841 + 2.21790i 0.115244 + 0.0403255i
\(56\) −58.5778 + 36.8069i −1.04603 + 0.657265i
\(57\) 0 0
\(58\) −5.70521 + 23.7735i −0.0983656 + 0.409889i
\(59\) −23.8690 −0.404559 −0.202280 0.979328i \(-0.564835\pi\)
−0.202280 + 0.979328i \(0.564835\pi\)
\(60\) 0 0
\(61\) 23.8851 68.2596i 0.391559 1.11901i −0.564398 0.825503i \(-0.690892\pi\)
0.955957 0.293507i \(-0.0948225\pi\)
\(62\) 5.42233 11.2596i 0.0874569 0.181606i
\(63\) 0 0
\(64\) −5.37487 + 1.22678i −0.0839824 + 0.0191684i
\(65\) 56.4537 27.1867i 0.868519 0.418257i
\(66\) 0 0
\(67\) 89.8491 + 71.6523i 1.34103 + 1.06944i 0.991165 + 0.132637i \(0.0423445\pi\)
0.349866 + 0.936800i \(0.386227\pi\)
\(68\) 25.8798 + 73.9602i 0.380585 + 1.08765i
\(69\) 0 0
\(70\) 29.0410 + 29.0410i 0.414872 + 0.414872i
\(71\) 54.7070 43.6274i 0.770521 0.614470i −0.157276 0.987555i \(-0.550271\pi\)
0.927797 + 0.373085i \(0.121700\pi\)
\(72\) 0 0
\(73\) −43.5770 + 69.3524i −0.596945 + 0.950032i 0.402457 + 0.915439i \(0.368156\pi\)
−0.999401 + 0.0345932i \(0.988986\pi\)
\(74\) 13.9081 + 17.4402i 0.187947 + 0.235678i
\(75\) 0 0
\(76\) 0.175107 1.55412i 0.00230405 0.0204490i
\(77\) 16.4897 5.77000i 0.214152 0.0749351i
\(78\) 0 0
\(79\) 12.9255 + 114.717i 0.163613 + 1.45211i 0.760267 + 0.649611i \(0.225068\pi\)
−0.596653 + 0.802499i \(0.703503\pi\)
\(80\) 14.9759 + 31.0978i 0.187199 + 0.388723i
\(81\) 0 0
\(82\) 12.2364 53.6111i 0.149224 0.653794i
\(83\) 1.11626 + 0.537563i 0.0134489 + 0.00647666i 0.440596 0.897705i \(-0.354767\pi\)
−0.427147 + 0.904182i \(0.640481\pi\)
\(84\) 0 0
\(85\) 87.2856 54.8452i 1.02689 0.645237i
\(86\) 53.4995i 0.622087i
\(87\) 0 0
\(88\) −9.53632 −0.108367
\(89\) 35.1684 + 55.9701i 0.395150 + 0.628878i 0.983749 0.179547i \(-0.0574632\pi\)
−0.588599 + 0.808425i \(0.700320\pi\)
\(90\) 0 0
\(91\) 70.7277 146.868i 0.777227 1.61393i
\(92\) −22.3657 5.10483i −0.243106 0.0554873i
\(93\) 0 0
\(94\) −38.8237 + 18.6965i −0.413018 + 0.198899i
\(95\) −2.04459 + 0.230370i −0.0215220 + 0.00242495i
\(96\) 0 0
\(97\) −26.0062 74.3215i −0.268105 0.766201i −0.996694 0.0812495i \(-0.974109\pi\)
0.728588 0.684952i \(-0.240177\pi\)
\(98\) 65.1248 + 7.33780i 0.664539 + 0.0748755i
\(99\) 0 0
\(100\) −16.1352 + 12.8674i −0.161352 + 0.128674i
\(101\) −71.2798 44.7881i −0.705741 0.443446i 0.130759 0.991414i \(-0.458259\pi\)
−0.836499 + 0.547968i \(0.815402\pi\)
\(102\) 0 0
\(103\) 30.3804 + 38.0958i 0.294955 + 0.369862i 0.907123 0.420866i \(-0.138274\pi\)
−0.612168 + 0.790728i \(0.709702\pi\)
\(104\) −62.9197 + 62.9197i −0.604997 + 0.604997i
\(105\) 0 0
\(106\) 32.5405 11.3864i 0.306986 0.107419i
\(107\) −83.6309 + 104.870i −0.781597 + 0.980092i 0.218394 + 0.975861i \(0.429918\pi\)
−0.999991 + 0.00423133i \(0.998653\pi\)
\(108\) 0 0
\(109\) 8.81881 + 18.3125i 0.0809066 + 0.168004i 0.937498 0.347992i \(-0.113136\pi\)
−0.856591 + 0.515996i \(0.827422\pi\)
\(110\) 1.25976 + 5.51936i 0.0114524 + 0.0501760i
\(111\) 0 0
\(112\) 80.9028 + 38.9607i 0.722347 + 0.347864i
\(113\) −22.6341 7.92002i −0.200302 0.0700886i 0.228264 0.973599i \(-0.426695\pi\)
−0.428566 + 0.903511i \(0.640981\pi\)
\(114\) 0 0
\(115\) 30.1808i 0.262442i
\(116\) 90.3807 30.5010i 0.779144 0.262940i
\(117\) 0 0
\(118\) −10.7060 17.0385i −0.0907287 0.144394i
\(119\) 88.5758 253.135i 0.744334 2.12719i
\(120\) 0 0
\(121\) −115.618 26.3892i −0.955525 0.218092i
\(122\) 59.4392 13.5666i 0.487206 0.111202i
\(123\) 0 0
\(124\) −48.4526 + 5.45930i −0.390747 + 0.0440266i
\(125\) 105.808 + 84.3793i 0.846466 + 0.675034i
\(126\) 0 0
\(127\) −8.21611 0.925733i −0.0646938 0.00728924i 0.0795583 0.996830i \(-0.474649\pi\)
−0.144252 + 0.989541i \(0.546078\pi\)
\(128\) −91.8315 91.8315i −0.717433 0.717433i
\(129\) 0 0
\(130\) 44.7280 + 28.1045i 0.344062 + 0.216188i
\(131\) −127.911 + 203.569i −0.976419 + 1.55396i −0.151694 + 0.988428i \(0.548473\pi\)
−0.824725 + 0.565534i \(0.808670\pi\)
\(132\) 0 0
\(133\) −3.78498 + 3.78498i −0.0284585 + 0.0284585i
\(134\) −10.8476 + 96.2755i −0.0809526 + 0.718474i
\(135\) 0 0
\(136\) −91.2744 + 114.454i −0.671135 + 0.841577i
\(137\) −4.55051 40.3869i −0.0332154 0.294795i −0.999327 0.0366716i \(-0.988324\pi\)
0.966112 0.258123i \(-0.0831041\pi\)
\(138\) 0 0
\(139\) −12.4270 54.4464i −0.0894032 0.391701i 0.910352 0.413835i \(-0.135811\pi\)
−0.999755 + 0.0221342i \(0.992954\pi\)
\(140\) 35.6567 156.222i 0.254691 1.11587i
\(141\) 0 0
\(142\) 55.6805 + 19.4834i 0.392116 + 0.137207i
\(143\) 19.0260 11.9548i 0.133049 0.0836003i
\(144\) 0 0
\(145\) −65.5794 106.994i −0.452272 0.737888i
\(146\) −69.0516 −0.472956
\(147\) 0 0
\(148\) 28.7450 82.1485i 0.194223 0.555058i
\(149\) 45.3207 94.1095i 0.304166 0.631607i −0.691726 0.722161i \(-0.743149\pi\)
0.995892 + 0.0905531i \(0.0288635\pi\)
\(150\) 0 0
\(151\) 40.2640 9.18999i 0.266649 0.0608609i −0.0871059 0.996199i \(-0.527762\pi\)
0.353755 + 0.935338i \(0.384905\pi\)
\(152\) 2.63253 1.26776i 0.0173193 0.00834054i
\(153\) 0 0
\(154\) 11.5150 + 9.18289i 0.0747726 + 0.0596291i
\(155\) 21.1865 + 60.5474i 0.136687 + 0.390628i
\(156\) 0 0
\(157\) −57.9484 57.9484i −0.369098 0.369098i 0.498050 0.867148i \(-0.334050\pi\)
−0.867148 + 0.498050i \(0.834050\pi\)
\(158\) −76.0911 + 60.6806i −0.481589 + 0.384055i
\(159\) 0 0
\(160\) −72.0736 + 114.704i −0.450460 + 0.716903i
\(161\) 48.9547 + 61.3872i 0.304066 + 0.381287i
\(162\) 0 0
\(163\) 0.128402 1.13960i 0.000787743 0.00699141i −0.993312 0.115459i \(-0.963166\pi\)
0.994100 + 0.108468i \(0.0345945\pi\)
\(164\) −202.509 + 70.8610i −1.23481 + 0.432079i
\(165\) 0 0
\(166\) 0.116947 + 1.03794i 0.000704503 + 0.00625264i
\(167\) −84.8706 176.236i −0.508207 1.05530i −0.984397 0.175960i \(-0.943697\pi\)
0.476190 0.879342i \(-0.342017\pi\)
\(168\) 0 0
\(169\) 9.04891 39.6459i 0.0535439 0.234591i
\(170\) 78.3006 + 37.7076i 0.460592 + 0.221809i
\(171\) 0 0
\(172\) −176.740 + 111.053i −1.02756 + 0.645658i
\(173\) 93.9168i 0.542872i 0.962457 + 0.271436i \(0.0874985\pi\)
−0.962457 + 0.271436i \(0.912502\pi\)
\(174\) 0 0
\(175\) 70.6344 0.403625
\(176\) 6.58539 + 10.4806i 0.0374170 + 0.0595488i
\(177\) 0 0
\(178\) −24.1792 + 50.2087i −0.135838 + 0.282071i
\(179\) −168.864 38.5422i −0.943376 0.215319i −0.276945 0.960886i \(-0.589322\pi\)
−0.666431 + 0.745566i \(0.732179\pi\)
\(180\) 0 0
\(181\) −87.2784 + 42.0311i −0.482201 + 0.232216i −0.659160 0.752002i \(-0.729088\pi\)
0.176959 + 0.984218i \(0.443374\pi\)
\(182\) 136.563 15.3869i 0.750344 0.0845434i
\(183\) 0 0
\(184\) −14.1557 40.4547i −0.0769332 0.219862i
\(185\) −113.779 12.8198i −0.615023 0.0692964i
\(186\) 0 0
\(187\) 28.9026 23.0490i 0.154559 0.123257i
\(188\) 142.355 + 89.4475i 0.757207 + 0.475785i
\(189\) 0 0
\(190\) −1.08151 1.35617i −0.00569214 0.00713772i
\(191\) 253.146 253.146i 1.32537 1.32537i 0.416013 0.909359i \(-0.363427\pi\)
0.909359 0.416013i \(-0.136573\pi\)
\(192\) 0 0
\(193\) −281.027 + 98.3354i −1.45610 + 0.509510i −0.938248 0.345963i \(-0.887552\pi\)
−0.517848 + 0.855473i \(0.673267\pi\)
\(194\) 41.3886 51.8996i 0.213343 0.267524i
\(195\) 0 0
\(196\) −110.944 230.377i −0.566040 1.17539i
\(197\) 30.9336 + 135.529i 0.157024 + 0.687965i 0.990740 + 0.135773i \(0.0433516\pi\)
−0.833716 + 0.552193i \(0.813791\pi\)
\(198\) 0 0
\(199\) 10.4281 + 5.02191i 0.0524025 + 0.0252357i 0.459901 0.887970i \(-0.347885\pi\)
−0.407499 + 0.913206i \(0.633599\pi\)
\(200\) −36.3932 12.7345i −0.181966 0.0636726i
\(201\) 0 0
\(202\) 70.9707i 0.351340i
\(203\) −306.936 111.250i −1.51200 0.548032i
\(204\) 0 0
\(205\) 150.171 + 238.995i 0.732539 + 1.16583i
\(206\) −13.5675 + 38.7736i −0.0658616 + 0.188222i
\(207\) 0 0
\(208\) 112.600 + 25.7001i 0.541344 + 0.123558i
\(209\) −0.719351 + 0.164187i −0.00344187 + 0.000785585i
\(210\) 0 0
\(211\) −138.139 + 15.5646i −0.654688 + 0.0737657i −0.433059 0.901365i \(-0.642566\pi\)
−0.221629 + 0.975131i \(0.571137\pi\)
\(212\) −105.163 83.8647i −0.496052 0.395588i
\(213\) 0 0
\(214\) −112.371 12.6611i −0.525096 0.0591642i
\(215\) 194.178 + 194.178i 0.903151 + 0.903151i
\(216\) 0 0
\(217\) 141.303 + 88.7868i 0.651168 + 0.409156i
\(218\) −9.11653 + 14.5089i −0.0418189 + 0.0665544i
\(219\) 0 0
\(220\) 15.6187 15.6187i 0.0709941 0.0709941i
\(221\) 38.6211 342.772i 0.174756 1.55100i
\(222\) 0 0
\(223\) 71.7315 89.9485i 0.321666 0.403356i −0.594539 0.804067i \(-0.702665\pi\)
0.916205 + 0.400711i \(0.131237\pi\)
\(224\) 39.4595 + 350.213i 0.176159 + 1.56345i
\(225\) 0 0
\(226\) −4.49853 19.7094i −0.0199050 0.0872095i
\(227\) −50.8656 + 222.857i −0.224077 + 0.981747i 0.730296 + 0.683131i \(0.239382\pi\)
−0.954373 + 0.298616i \(0.903475\pi\)
\(228\) 0 0
\(229\) −195.058 68.2538i −0.851782 0.298051i −0.131144 0.991363i \(-0.541865\pi\)
−0.720638 + 0.693312i \(0.756151\pi\)
\(230\) −21.5441 + 13.5370i −0.0936700 + 0.0588567i
\(231\) 0 0
\(232\) 138.086 + 112.657i 0.595200 + 0.485589i
\(233\) −186.225 −0.799248 −0.399624 0.916679i \(-0.630859\pi\)
−0.399624 + 0.916679i \(0.630859\pi\)
\(234\) 0 0
\(235\) 73.0520 208.771i 0.310860 0.888386i
\(236\) −34.0648 + 70.7363i −0.144342 + 0.299730i
\(237\) 0 0
\(238\) 220.425 50.3106i 0.926156 0.211389i
\(239\) −144.790 + 69.7270i −0.605814 + 0.291745i −0.711534 0.702651i \(-0.751999\pi\)
0.105720 + 0.994396i \(0.466285\pi\)
\(240\) 0 0
\(241\) −152.244 121.410i −0.631717 0.503777i 0.254485 0.967077i \(-0.418094\pi\)
−0.886202 + 0.463300i \(0.846665\pi\)
\(242\) −33.0210 94.3687i −0.136451 0.389953i
\(243\) 0 0
\(244\) −168.201 168.201i −0.689349 0.689349i
\(245\) −263.005 + 209.739i −1.07349 + 0.856079i
\(246\) 0 0
\(247\) −3.66292 + 5.82950i −0.0148296 + 0.0236012i
\(248\) −56.7970 71.2212i −0.229020 0.287182i
\(249\) 0 0
\(250\) −12.7744 + 113.376i −0.0510977 + 0.453505i
\(251\) 312.227 109.253i 1.24393 0.435270i 0.373532 0.927617i \(-0.378147\pi\)
0.870399 + 0.492347i \(0.163861\pi\)
\(252\) 0 0
\(253\) 1.21181 + 10.7551i 0.00478976 + 0.0425103i
\(254\) −3.02436 6.28015i −0.0119069 0.0247250i
\(255\) 0 0
\(256\) 19.4560 85.2421i 0.0759998 0.332977i
\(257\) −156.282 75.2612i −0.608099 0.292845i 0.104381 0.994537i \(-0.466714\pi\)
−0.712480 + 0.701692i \(0.752428\pi\)
\(258\) 0 0
\(259\) −252.219 + 158.480i −0.973818 + 0.611891i
\(260\) 206.102i 0.792698i
\(261\) 0 0
\(262\) −202.686 −0.773612
\(263\) 86.5688 + 137.774i 0.329159 + 0.523854i 0.969773 0.244010i \(-0.0784628\pi\)
−0.640614 + 0.767863i \(0.721320\pi\)
\(264\) 0 0
\(265\) −76.7793 + 159.434i −0.289733 + 0.601637i
\(266\) −4.39953 1.00416i −0.0165396 0.00377505i
\(267\) 0 0
\(268\) 340.572 164.011i 1.27079 0.611980i
\(269\) −29.2546 + 3.29620i −0.108753 + 0.0122535i −0.166173 0.986097i \(-0.553141\pi\)
0.0574202 + 0.998350i \(0.481713\pi\)
\(270\) 0 0
\(271\) 168.083 + 480.355i 0.620234 + 1.77253i 0.634852 + 0.772634i \(0.281061\pi\)
−0.0146174 + 0.999893i \(0.504653\pi\)
\(272\) 188.818 + 21.2747i 0.694183 + 0.0782157i
\(273\) 0 0
\(274\) 26.7885 21.3631i 0.0977682 0.0779675i
\(275\) 8.24418 + 5.18016i 0.0299789 + 0.0188370i
\(276\) 0 0
\(277\) −130.918 164.166i −0.472629 0.592657i 0.487184 0.873299i \(-0.338024\pi\)
−0.959813 + 0.280642i \(0.909453\pi\)
\(278\) 33.2918 33.2918i 0.119755 0.119755i
\(279\) 0 0
\(280\) 282.572 98.8761i 1.00918 0.353129i
\(281\) 287.055 359.956i 1.02155 1.28098i 0.0624084 0.998051i \(-0.480122\pi\)
0.959140 0.282931i \(-0.0913067\pi\)
\(282\) 0 0
\(283\) 194.833 + 404.574i 0.688455 + 1.42959i 0.892691 + 0.450669i \(0.148815\pi\)
−0.204237 + 0.978922i \(0.565471\pi\)
\(284\) −51.2152 224.389i −0.180335 0.790101i
\(285\) 0 0
\(286\) 17.0675 + 8.21928i 0.0596766 + 0.0287388i
\(287\) 693.104 + 242.528i 2.41500 + 0.845044i
\(288\) 0 0
\(289\) 278.496i 0.963653i
\(290\) 46.9613 94.8028i 0.161936 0.326906i
\(291\) 0 0
\(292\) 143.336 + 228.118i 0.490877 + 0.781226i
\(293\) −37.1090 + 106.051i −0.126652 + 0.361950i −0.989697 0.143176i \(-0.954268\pi\)
0.863045 + 0.505126i \(0.168554\pi\)
\(294\) 0 0
\(295\) 100.699 + 22.9839i 0.341353 + 0.0779117i
\(296\) 158.524 36.1820i 0.535553 0.122236i
\(297\) 0 0
\(298\) 87.5063 9.85959i 0.293645 0.0330859i
\(299\) 78.9566 + 62.9658i 0.264069 + 0.210588i
\(300\) 0 0
\(301\) 709.918 + 79.9885i 2.35853 + 0.265743i
\(302\) 24.6198 + 24.6198i 0.0815224 + 0.0815224i
\(303\) 0 0
\(304\) −3.21121 2.01774i −0.0105632 0.00663730i
\(305\) −166.496 + 264.976i −0.545887 + 0.868774i
\(306\) 0 0
\(307\) 131.221 131.221i 0.427429 0.427429i −0.460323 0.887752i \(-0.652266\pi\)
0.887752 + 0.460323i \(0.152266\pi\)
\(308\) 6.43389 57.1024i 0.0208893 0.185397i
\(309\) 0 0
\(310\) −33.7180 + 42.2810i −0.108768 + 0.136390i
\(311\) 56.3391 + 500.023i 0.181155 + 1.60779i 0.674714 + 0.738079i \(0.264267\pi\)
−0.493560 + 0.869712i \(0.664305\pi\)
\(312\) 0 0
\(313\) −36.9386 161.838i −0.118015 0.517056i −0.999033 0.0439731i \(-0.985998\pi\)
0.881018 0.473082i \(-0.156859\pi\)
\(314\) 15.3738 67.3572i 0.0489613 0.214513i
\(315\) 0 0
\(316\) 358.412 + 125.414i 1.13422 + 0.396879i
\(317\) −16.0893 + 10.1096i −0.0507550 + 0.0318915i −0.557171 0.830398i \(-0.688113\pi\)
0.506416 + 0.862290i \(0.330970\pi\)
\(318\) 0 0
\(319\) −27.6656 35.4947i −0.0867260 0.111269i
\(320\) 23.8570 0.0745530
\(321\) 0 0
\(322\) −21.8625 + 62.4795i −0.0678961 + 0.194036i
\(323\) −4.91451 + 10.2051i −0.0152152 + 0.0315947i
\(324\) 0 0
\(325\) 88.5726 20.2161i 0.272531 0.0622034i
\(326\) 0.871077 0.419489i 0.00267202 0.00128677i
\(327\) 0 0
\(328\) −313.386 249.917i −0.955444 0.761941i
\(329\) −190.049 543.129i −0.577657 1.65085i
\(330\) 0 0
\(331\) −34.0680 34.0680i −0.102924 0.102924i 0.653769 0.756694i \(-0.273187\pi\)
−0.756694 + 0.653769i \(0.773187\pi\)
\(332\) 3.18616 2.54088i 0.00959686 0.00765324i
\(333\) 0 0
\(334\) 87.7357 139.631i 0.262682 0.418056i
\(335\) −310.062 388.806i −0.925560 1.16062i
\(336\) 0 0
\(337\) 24.9408 221.356i 0.0740083 0.656841i −0.900868 0.434093i \(-0.857069\pi\)
0.974876 0.222748i \(-0.0715027\pi\)
\(338\) 32.3593 11.3230i 0.0957375 0.0335000i
\(339\) 0 0
\(340\) −37.9646 336.946i −0.111661 0.991016i
\(341\) 9.98099 + 20.7257i 0.0292698 + 0.0607793i
\(342\) 0 0
\(343\) −71.9903 + 315.410i −0.209884 + 0.919563i
\(344\) −351.352 169.202i −1.02137 0.491867i
\(345\) 0 0
\(346\) −67.0409 + 42.1246i −0.193760 + 0.121747i
\(347\) 400.531i 1.15427i 0.816649 + 0.577134i \(0.195829\pi\)
−0.816649 + 0.577134i \(0.804171\pi\)
\(348\) 0 0
\(349\) 191.095 0.547550 0.273775 0.961794i \(-0.411728\pi\)
0.273775 + 0.961794i \(0.411728\pi\)
\(350\) 31.6817 + 50.4212i 0.0905192 + 0.144060i
\(351\) 0 0
\(352\) −21.0782 + 43.7694i −0.0598814 + 0.124345i
\(353\) −170.891 39.0048i −0.484111 0.110495i −0.0265018 0.999649i \(-0.508437\pi\)
−0.457609 + 0.889154i \(0.651294\pi\)
\(354\) 0 0
\(355\) −272.809 + 131.378i −0.768476 + 0.370079i
\(356\) 216.060 24.3441i 0.606909 0.0683822i
\(357\) 0 0
\(358\) −48.2282 137.828i −0.134716 0.384995i
\(359\) 302.179 + 34.0473i 0.841723 + 0.0948394i 0.522288 0.852769i \(-0.325078\pi\)
0.319435 + 0.947608i \(0.396507\pi\)
\(360\) 0 0
\(361\) −282.064 + 224.939i −0.781342 + 0.623099i
\(362\) −69.1502 43.4500i −0.191023 0.120028i
\(363\) 0 0
\(364\) −334.306 419.206i −0.918423 1.15167i
\(365\) 250.625 250.625i 0.686643 0.686643i
\(366\) 0 0
\(367\) 102.535 35.8787i 0.279388 0.0977622i −0.186948 0.982370i \(-0.559860\pi\)
0.466336 + 0.884608i \(0.345574\pi\)
\(368\) −34.6851 + 43.4937i −0.0942529 + 0.118189i
\(369\) 0 0
\(370\) −41.8823 86.9695i −0.113195 0.235053i
\(371\) 102.441 + 448.825i 0.276122 + 1.20977i
\(372\) 0 0
\(373\) −391.003 188.297i −1.04826 0.504818i −0.171223 0.985232i \(-0.554772\pi\)
−0.877042 + 0.480414i \(0.840486\pi\)
\(374\) 29.4169 + 10.2934i 0.0786548 + 0.0275225i
\(375\) 0 0
\(376\) 314.102i 0.835377i
\(377\) −416.726 51.6559i −1.10537 0.137018i
\(378\) 0 0
\(379\) 146.333 + 232.888i 0.386104 + 0.614481i 0.982067 0.188530i \(-0.0603724\pi\)
−0.595963 + 0.803012i \(0.703230\pi\)
\(380\) −2.23524 + 6.38796i −0.00588222 + 0.0168104i
\(381\) 0 0
\(382\) 294.248 + 67.1601i 0.770282 + 0.175812i
\(383\) 213.072 48.6323i 0.556323 0.126977i 0.0648901 0.997892i \(-0.479330\pi\)
0.491433 + 0.870915i \(0.336473\pi\)
\(384\) 0 0
\(385\) −75.1234 + 8.46437i −0.195126 + 0.0219854i
\(386\) −196.244 156.500i −0.508405 0.405439i
\(387\) 0 0
\(388\) −257.368 28.9985i −0.663321 0.0747383i
\(389\) −25.9695 25.9695i −0.0667597 0.0667597i 0.672939 0.739698i \(-0.265032\pi\)
−0.739698 + 0.672939i \(0.765032\pi\)
\(390\) 0 0
\(391\) 140.681 + 88.3957i 0.359798 + 0.226076i
\(392\) 254.160 404.493i 0.648367 1.03187i
\(393\) 0 0
\(394\) −82.8705 + 82.8705i −0.210331 + 0.210331i
\(395\) 55.9327 496.416i 0.141602 1.25675i
\(396\) 0 0
\(397\) 83.6502 104.894i 0.210706 0.264217i −0.665236 0.746633i \(-0.731669\pi\)
0.875942 + 0.482416i \(0.160241\pi\)
\(398\) 1.09252 + 9.69641i 0.00274503 + 0.0243628i
\(399\) 0 0
\(400\) 11.1362 + 48.7907i 0.0278404 + 0.121977i
\(401\) −105.732 + 463.241i −0.263670 + 1.15521i 0.653566 + 0.756870i \(0.273272\pi\)
−0.917236 + 0.398345i \(0.869585\pi\)
\(402\) 0 0
\(403\) 202.600 + 70.8928i 0.502730 + 0.175913i
\(404\) −234.458 + 147.320i −0.580342 + 0.364653i
\(405\) 0 0
\(406\) −58.2561 269.000i −0.143488 0.662562i
\(407\) −41.0606 −0.100886
\(408\) 0 0
\(409\) 9.65215 27.5843i 0.0235994 0.0674432i −0.931481 0.363790i \(-0.881483\pi\)
0.955080 + 0.296347i \(0.0957684\pi\)
\(410\) −103.246 + 214.393i −0.251821 + 0.522911i
\(411\) 0 0
\(412\) 156.255 35.6642i 0.379260 0.0865637i
\(413\) 242.101 116.590i 0.586201 0.282300i
\(414\) 0 0
\(415\) −4.19168 3.34275i −0.0101004 0.00805483i
\(416\) 149.714 + 427.859i 0.359890 + 1.02851i
\(417\) 0 0
\(418\) −0.439854 0.439854i −0.00105228 0.00105228i
\(419\) −173.110 + 138.050i −0.413149 + 0.329476i −0.807907 0.589309i \(-0.799400\pi\)
0.394758 + 0.918785i \(0.370828\pi\)
\(420\) 0 0
\(421\) 65.2084 103.779i 0.154889 0.246505i −0.760261 0.649618i \(-0.774929\pi\)
0.915150 + 0.403113i \(0.132072\pi\)
\(422\) −73.0702 91.6272i −0.173152 0.217126i
\(423\) 0 0
\(424\) 28.1365 249.718i 0.0663597 0.588958i
\(425\) 141.079 49.3657i 0.331951 0.116155i
\(426\) 0 0
\(427\) 91.1546 + 809.019i 0.213477 + 1.89466i
\(428\) 191.430 + 397.508i 0.447266 + 0.928757i
\(429\) 0 0
\(430\) −51.5157 + 225.705i −0.119804 + 0.524895i
\(431\) −178.177 85.8056i −0.413404 0.199085i 0.215609 0.976480i \(-0.430826\pi\)
−0.629013 + 0.777395i \(0.716541\pi\)
\(432\) 0 0
\(433\) −148.885 + 93.5509i −0.343846 + 0.216053i −0.692873 0.721060i \(-0.743655\pi\)
0.349026 + 0.937113i \(0.386512\pi\)
\(434\) 140.691i 0.324172i
\(435\) 0 0
\(436\) 66.8552 0.153338
\(437\) −1.76431 2.80789i −0.00403733 0.00642538i
\(438\) 0 0
\(439\) −97.1608 + 201.756i −0.221323 + 0.459582i −0.981834 0.189743i \(-0.939234\pi\)
0.760511 + 0.649325i \(0.224949\pi\)
\(440\) 40.2321 + 9.18271i 0.0914366 + 0.0208698i
\(441\) 0 0
\(442\) 262.005 126.175i 0.592771 0.285463i
\(443\) −172.978 + 19.4899i −0.390470 + 0.0439954i −0.305017 0.952347i \(-0.598662\pi\)
−0.0854526 + 0.996342i \(0.527234\pi\)
\(444\) 0 0
\(445\) −94.4746 269.993i −0.212302 0.606725i
\(446\) 96.3820 + 10.8596i 0.216103 + 0.0243490i
\(447\) 0 0
\(448\) 48.5246 38.6970i 0.108314 0.0863773i
\(449\) 378.601 + 237.891i 0.843209 + 0.529823i 0.882994 0.469385i \(-0.155524\pi\)
−0.0397845 + 0.999208i \(0.512667\pi\)
\(450\) 0 0
\(451\) 63.1102 + 79.1376i 0.139934 + 0.175471i
\(452\) −55.7736 + 55.7736i −0.123393 + 0.123393i
\(453\) 0 0
\(454\) −181.897 + 63.6486i −0.400655 + 0.140195i
\(455\) −439.810 + 551.504i −0.966615 + 1.21210i
\(456\) 0 0
\(457\) 21.1875 + 43.9964i 0.0463622 + 0.0962722i 0.922863 0.385128i \(-0.125843\pi\)
−0.876501 + 0.481400i \(0.840128\pi\)
\(458\) −38.7678 169.853i −0.0846459 0.370858i
\(459\) 0 0
\(460\) 89.4416 + 43.0728i 0.194438 + 0.0936366i
\(461\) −536.238 187.638i −1.16321 0.407023i −0.321474 0.946918i \(-0.604178\pi\)
−0.841732 + 0.539895i \(0.818464\pi\)
\(462\) 0 0
\(463\) 50.1618i 0.108341i −0.998532 0.0541704i \(-0.982749\pi\)
0.998532 0.0541704i \(-0.0172514\pi\)
\(464\) 28.4549 229.556i 0.0613253 0.494732i
\(465\) 0 0
\(466\) −83.5276 132.933i −0.179244 0.285265i
\(467\) 61.9948 177.171i 0.132751 0.379381i −0.858250 0.513231i \(-0.828448\pi\)
0.991002 + 0.133850i \(0.0427340\pi\)
\(468\) 0 0
\(469\) −1261.32 287.888i −2.68938 0.613834i
\(470\) 181.794 41.4932i 0.386795 0.0882834i
\(471\) 0 0
\(472\) −145.758 + 16.4230i −0.308810 + 0.0347945i
\(473\) 76.9928 + 61.3997i 0.162775 + 0.129809i
\(474\) 0 0
\(475\) −2.96449 0.334018i −0.00624103 0.000703195i
\(476\) −623.760 623.760i −1.31042 1.31042i
\(477\) 0 0
\(478\) −114.716 72.0809i −0.239992 0.150797i
\(479\) −15.6633 + 24.9280i −0.0327000 + 0.0520418i −0.862674 0.505760i \(-0.831212\pi\)
0.829974 + 0.557802i \(0.188355\pi\)
\(480\) 0 0
\(481\) −270.914 + 270.914i −0.563231 + 0.563231i
\(482\) 18.3807 163.133i 0.0381342 0.338450i
\(483\) 0 0
\(484\) −243.211 + 304.977i −0.502501 + 0.630117i
\(485\) 38.1501 + 338.592i 0.0786600 + 0.698127i
\(486\) 0 0
\(487\) 39.7649 + 174.221i 0.0816527 + 0.357744i 0.999205 0.0398716i \(-0.0126949\pi\)
−0.917552 + 0.397616i \(0.869838\pi\)
\(488\) 98.8905 433.268i 0.202645 0.887844i
\(489\) 0 0
\(490\) −267.685 93.6669i −0.546295 0.191157i
\(491\) −319.674 + 200.864i −0.651066 + 0.409092i −0.816674 0.577100i \(-0.804184\pi\)
0.165607 + 0.986192i \(0.447042\pi\)
\(492\) 0 0
\(493\) −690.800 7.68743i −1.40122 0.0155932i
\(494\) −5.80422 −0.0117494
\(495\) 0 0
\(496\) −39.0517 + 111.603i −0.0787333 + 0.225007i
\(497\) −341.787 + 709.728i −0.687701 + 1.42803i
\(498\) 0 0
\(499\) −575.053 + 131.252i −1.15241 + 0.263030i −0.755703 0.654915i \(-0.772704\pi\)
−0.396707 + 0.917945i \(0.629847\pi\)
\(500\) 401.065 193.143i 0.802130 0.386286i
\(501\) 0 0
\(502\) 218.032 + 173.875i 0.434326 + 0.346364i
\(503\) −122.173 349.151i −0.242889 0.694137i −0.999203 0.0399278i \(-0.987287\pi\)
0.756313 0.654209i \(-0.226999\pi\)
\(504\) 0 0
\(505\) 257.590 + 257.590i 0.510079 + 0.510079i
\(506\) −7.13382 + 5.68903i −0.0140985 + 0.0112432i
\(507\) 0 0
\(508\) −14.4691 + 23.0275i −0.0284825 + 0.0453296i
\(509\) −595.965 747.316i −1.17085 1.46820i −0.854414 0.519592i \(-0.826084\pi\)
−0.316440 0.948613i \(-0.602487\pi\)
\(510\) 0 0
\(511\) 103.241 916.289i 0.202037 1.79313i
\(512\) −420.751 + 147.227i −0.821779 + 0.287553i
\(513\) 0 0
\(514\) −16.3732 145.316i −0.0318544 0.282716i
\(515\) −91.4863 189.973i −0.177643 0.368880i
\(516\) 0 0
\(517\) 17.6500 77.3298i 0.0341393 0.149574i
\(518\) −226.256 108.959i −0.436788 0.210346i
\(519\) 0 0
\(520\) 326.034 204.861i 0.626989 0.393963i
\(521\) 165.340i 0.317352i −0.987331 0.158676i \(-0.949278\pi\)
0.987331 0.158676i \(-0.0507225\pi\)
\(522\) 0 0
\(523\) −680.975 −1.30205 −0.651027 0.759054i \(-0.725662\pi\)
−0.651027 + 0.759054i \(0.725662\pi\)
\(524\) 420.732 + 669.592i 0.802924 + 1.27785i
\(525\) 0 0
\(526\) −59.5185 + 123.591i −0.113153 + 0.234965i
\(527\) 344.280 + 78.5796i 0.653283 + 0.149107i
\(528\) 0 0
\(529\) 432.786 208.419i 0.818122 0.393987i
\(530\) −148.247 + 16.7034i −0.279712 + 0.0315159i
\(531\) 0 0
\(532\) 5.81511 + 16.6186i 0.0109307 + 0.0312380i
\(533\) 938.537 + 105.748i 1.76086 + 0.198401i
\(534\) 0 0
\(535\) 453.806 361.898i 0.848235 0.676445i
\(536\) 597.972 + 375.731i 1.11562 + 0.700990i
\(537\) 0 0
\(538\) −15.4745 19.4044i −0.0287630 0.0360677i
\(539\) −85.3018 + 85.3018i −0.158259 + 0.158259i
\(540\) 0 0
\(541\) 259.030 90.6386i 0.478799 0.167539i −0.0800798 0.996788i \(-0.525518\pi\)
0.558879 + 0.829250i \(0.311232\pi\)
\(542\) −267.503 + 335.438i −0.493547 + 0.618889i
\(543\) 0 0
\(544\) 323.574 + 671.908i 0.594805 + 1.23513i
\(545\) −19.5716 85.7489i −0.0359113 0.157337i
\(546\) 0 0
\(547\) 506.415 + 243.877i 0.925805 + 0.445844i 0.835140 0.550037i \(-0.185387\pi\)
0.0906647 + 0.995881i \(0.471101\pi\)
\(548\) −126.182 44.1529i −0.230259 0.0805711i
\(549\) 0 0
\(550\) 8.20844i 0.0149244i
\(551\) 12.3559 + 6.12057i 0.0224244 + 0.0111081i
\(552\) 0 0
\(553\) −691.443 1100.43i −1.25035 1.98992i
\(554\) 58.4664 167.087i 0.105535 0.301602i
\(555\) 0 0
\(556\) −179.089 40.8758i −0.322102 0.0735176i
\(557\) 328.386 74.9521i 0.589563 0.134564i 0.0826759 0.996576i \(-0.473653\pi\)
0.506887 + 0.862013i \(0.330796\pi\)
\(558\) 0 0
\(559\) 913.101 102.882i 1.63345 0.184046i
\(560\) −303.799 242.272i −0.542498 0.432628i
\(561\) 0 0
\(562\) 385.702 + 43.4581i 0.686302 + 0.0773276i
\(563\) −156.332 156.332i −0.277677 0.277677i 0.554504 0.832181i \(-0.312908\pi\)
−0.832181 + 0.554504i \(0.812908\pi\)
\(564\) 0 0
\(565\) 87.8631 + 55.2080i 0.155510 + 0.0977133i
\(566\) −201.410 + 320.542i −0.355848 + 0.566329i
\(567\) 0 0
\(568\) 304.056 304.056i 0.535309 0.535309i
\(569\) 36.9493 327.934i 0.0649373 0.576334i −0.918543 0.395321i \(-0.870634\pi\)
0.983481 0.181014i \(-0.0579379\pi\)
\(570\) 0 0
\(571\) 126.849 159.064i 0.222153 0.278570i −0.658248 0.752801i \(-0.728702\pi\)
0.880401 + 0.474231i \(0.157274\pi\)
\(572\) −8.27532 73.4455i −0.0144673 0.128401i
\(573\) 0 0
\(574\) 137.755 + 603.542i 0.239990 + 1.05147i
\(575\) −9.73747 + 42.6627i −0.0169347 + 0.0741959i
\(576\) 0 0
\(577\) 612.104 + 214.185i 1.06084 + 0.371204i 0.803616 0.595148i \(-0.202907\pi\)
0.257223 + 0.966352i \(0.417192\pi\)
\(578\) 198.799 124.914i 0.343944 0.216114i
\(579\) 0 0
\(580\) −410.671 + 41.6492i −0.708053 + 0.0718090i
\(581\) −13.9479 −0.0240067
\(582\) 0 0
\(583\) −20.9592 + 59.8980i −0.0359506 + 0.102741i
\(584\) −218.389 + 453.490i −0.373954 + 0.776523i
\(585\) 0 0
\(586\) −92.3475 + 21.0777i −0.157590 + 0.0359688i
\(587\) 702.630 338.369i 1.19698 0.576437i 0.274170 0.961681i \(-0.411597\pi\)
0.922815 + 0.385244i \(0.125883\pi\)
\(588\) 0 0
\(589\) −5.51058 4.39454i −0.00935582 0.00746101i
\(590\) 28.7600 + 82.1915i 0.0487458 + 0.139308i
\(591\) 0 0
\(592\) −149.234 149.234i −0.252085 0.252085i
\(593\) 694.472 553.823i 1.17112 0.933934i 0.172422 0.985023i \(-0.444841\pi\)
0.998694 + 0.0510897i \(0.0162694\pi\)
\(594\) 0 0
\(595\) −617.435 + 982.642i −1.03771 + 1.65150i
\(596\) −214.216 268.618i −0.359423 0.450702i
\(597\) 0 0
\(598\) −9.53258 + 84.6040i −0.0159408 + 0.141478i
\(599\) −153.834 + 53.8288i −0.256818 + 0.0898645i −0.455617 0.890176i \(-0.650581\pi\)
0.198799 + 0.980040i \(0.436296\pi\)
\(600\) 0 0
\(601\) 56.1166 + 498.048i 0.0933720 + 0.828699i 0.949890 + 0.312583i \(0.101194\pi\)
−0.856518 + 0.516116i \(0.827377\pi\)
\(602\) 261.322 + 542.640i 0.434089 + 0.901395i
\(603\) 0 0
\(604\) 30.2283 132.439i 0.0500468 0.219270i
\(605\) 462.364 + 222.663i 0.764238 + 0.368038i
\(606\) 0 0
\(607\) 791.990 497.641i 1.30476 0.819836i 0.313227 0.949678i \(-0.398590\pi\)
0.991535 + 0.129842i \(0.0414471\pi\)
\(608\) 14.8849i 0.0244817i
\(609\) 0 0
\(610\) −263.827 −0.432504
\(611\) −393.761 626.668i −0.644454 1.02564i
\(612\) 0 0
\(613\) 152.936 317.575i 0.249488 0.518067i −0.738185 0.674598i \(-0.764317\pi\)
0.987673 + 0.156531i \(0.0500312\pi\)
\(614\) 152.526 + 34.8131i 0.248414 + 0.0566989i
\(615\) 0 0
\(616\) 96.7260 46.5808i 0.157023 0.0756182i
\(617\) 839.013 94.5340i 1.35983 0.153216i 0.598260 0.801302i \(-0.295859\pi\)
0.761566 + 0.648087i \(0.224431\pi\)
\(618\) 0 0
\(619\) −171.638 490.514i −0.277283 0.792430i −0.995338 0.0964436i \(-0.969253\pi\)
0.718055 0.695986i \(-0.245032\pi\)
\(620\) 209.670 + 23.6241i 0.338177 + 0.0381034i
\(621\) 0 0
\(622\) −331.663 + 264.493i −0.533221 + 0.425229i
\(623\) −630.100 395.918i −1.01140 0.635502i
\(624\) 0 0
\(625\) −267.338 335.231i −0.427741 0.536370i
\(626\) 98.9575 98.9575i 0.158079 0.158079i
\(627\) 0 0
\(628\) −254.433 + 89.0300i −0.405148 + 0.141767i
\(629\) −393.001 + 492.808i −0.624803 + 0.783478i
\(630\) 0 0
\(631\) −226.898 471.158i −0.359584 0.746685i 0.640184 0.768222i \(-0.278858\pi\)
−0.999768 + 0.0215372i \(0.993144\pi\)
\(632\) 157.861 + 691.635i 0.249780 + 1.09436i
\(633\) 0 0
\(634\) −14.4331 6.95062i −0.0227652 0.0109631i
\(635\) 33.7709 + 11.8170i 0.0531826 + 0.0186094i
\(636\) 0 0
\(637\) 1125.63i 1.76708i
\(638\) 12.9284 35.6691i 0.0202640 0.0559077i
\(639\) 0 0
\(640\) 298.995 + 475.848i 0.467179 + 0.743512i
\(641\) 284.960 814.368i 0.444555 1.27046i −0.475860 0.879521i \(-0.657863\pi\)
0.920415 0.390944i \(-0.127851\pi\)
\(642\) 0 0
\(643\) 221.189 + 50.4849i 0.343995 + 0.0785147i 0.391028 0.920379i \(-0.372119\pi\)
−0.0470331 + 0.998893i \(0.514977\pi\)
\(644\) 251.788 57.4691i 0.390976 0.0892377i
\(645\) 0 0
\(646\) −9.48905 + 1.06916i −0.0146889 + 0.00165504i
\(647\) −639.749 510.183i −0.988794 0.788537i −0.0113937 0.999935i \(-0.503627\pi\)
−0.977400 + 0.211398i \(0.932198\pi\)
\(648\) 0 0
\(649\) 36.8076 + 4.14722i 0.0567143 + 0.00639017i
\(650\) 54.1585 + 54.1585i 0.0833208 + 0.0833208i
\(651\) 0 0
\(652\) −3.19398 2.00691i −0.00489875 0.00307809i
\(653\) −430.330 + 684.867i −0.659005 + 1.04880i 0.335288 + 0.942116i \(0.391166\pi\)
−0.994293 + 0.106685i \(0.965976\pi\)
\(654\) 0 0
\(655\) 735.655 735.655i 1.12314 1.12314i
\(656\) −58.2517 + 516.998i −0.0887984 + 0.788107i
\(657\) 0 0
\(658\) 302.461 379.274i 0.459667 0.576404i
\(659\) 11.9427 + 105.994i 0.0181225 + 0.160841i 0.999514 0.0311765i \(-0.00992540\pi\)
−0.981391 + 0.192018i \(0.938497\pi\)
\(660\) 0 0
\(661\) 58.7442 + 257.375i 0.0888717 + 0.389372i 0.999727 0.0233529i \(-0.00743414\pi\)
−0.910856 + 0.412725i \(0.864577\pi\)
\(662\) 9.03830 39.5994i 0.0136530 0.0598178i
\(663\) 0 0
\(664\) 7.18642 + 2.51464i 0.0108229 + 0.00378710i
\(665\) 19.6128 12.3236i 0.0294930 0.0185317i
\(666\) 0 0
\(667\) 109.508 170.050i 0.164180 0.254948i
\(668\) −643.402 −0.963176
\(669\) 0 0
\(670\) 138.470 395.724i 0.206672 0.590634i
\(671\) −48.6924 + 101.111i −0.0725669 + 0.150687i
\(672\) 0 0
\(673\) 396.421 90.4804i 0.589035 0.134443i 0.0823931 0.996600i \(-0.473744\pi\)
0.506642 + 0.862156i \(0.330887\pi\)
\(674\) 169.198 81.4813i 0.251035 0.120892i
\(675\) 0 0
\(676\) −104.577 83.3976i −0.154700 0.123369i
\(677\) 170.754 + 487.988i 0.252222 + 0.720810i 0.998478 + 0.0551504i \(0.0175638\pi\)
−0.746256 + 0.665659i \(0.768150\pi\)
\(678\) 0 0
\(679\) 626.807 + 626.807i 0.923133 + 0.923133i
\(680\) 495.282 394.974i 0.728355 0.580844i
\(681\) 0 0
\(682\) −10.3179 + 16.4209i −0.0151289 + 0.0240776i
\(683\) −207.865 260.654i −0.304341 0.381631i 0.606018 0.795451i \(-0.292766\pi\)
−0.910359 + 0.413820i \(0.864194\pi\)
\(684\) 0 0
\(685\) −19.6915 + 174.767i −0.0287468 + 0.255135i
\(686\) −257.440 + 90.0822i −0.375277 + 0.131315i
\(687\) 0 0
\(688\) 56.6730 + 502.986i 0.0823735 + 0.731085i
\(689\) 256.914 + 533.488i 0.372880 + 0.774293i
\(690\) 0 0
\(691\) 35.5687 155.837i 0.0514743 0.225523i −0.942648 0.333789i \(-0.891673\pi\)
0.994122 + 0.108266i \(0.0345298\pi\)
\(692\) 278.325 + 134.034i 0.402203 + 0.193691i
\(693\) 0 0
\(694\) −285.912 + 179.651i −0.411978 + 0.258863i
\(695\) 241.666i 0.347722i
\(696\) 0 0
\(697\) 1553.85 2.22934
\(698\) 85.7120 + 136.410i 0.122797 + 0.195430i
\(699\) 0 0
\(700\) 100.806 209.327i 0.144009 0.299038i
\(701\) −1073.12 244.932i −1.53084 0.349404i −0.627597 0.778539i \(-0.715961\pi\)
−0.903240 + 0.429135i \(0.858818\pi\)
\(702\) 0 0
\(703\) 11.3349 5.45861i 0.0161237 0.00776474i
\(704\) 8.50156 0.957896i 0.0120761 0.00136065i
\(705\) 0 0
\(706\) −48.8070 139.483i −0.0691318 0.197567i
\(707\) 941.755 + 106.110i 1.33204 + 0.150085i
\(708\) 0 0
\(709\) 207.591 165.548i 0.292794 0.233496i −0.466065 0.884751i \(-0.654329\pi\)
0.758859 + 0.651255i \(0.225757\pi\)
\(710\) −216.145 135.813i −0.304430 0.191286i
\(711\) 0 0
\(712\) 253.269 + 317.589i 0.355715 + 0.446052i
\(713\) −73.1063 + 73.1063i −0.102533 + 0.102533i
\(714\) 0 0
\(715\) −91.7790 + 32.1149i −0.128362 + 0.0449159i
\(716\) −355.217 + 445.428i −0.496113 + 0.622106i
\(717\) 0 0
\(718\) 111.232 + 230.976i 0.154920 + 0.321694i
\(719\) 251.846 + 1103.41i 0.350273 + 1.53465i 0.776552 + 0.630054i \(0.216967\pi\)
−0.426279 + 0.904592i \(0.640176\pi\)
\(720\) 0 0
\(721\) −494.226 238.007i −0.685474 0.330107i
\(722\) −287.083 100.455i −0.397623 0.139134i
\(723\) 0 0
\(724\) 318.636i 0.440106i
\(725\) −58.1808 172.401i −0.0802493 0.237795i
\(726\) 0 0
\(727\) 25.1121 + 39.9657i 0.0345421 + 0.0549734i 0.863549 0.504265i \(-0.168237\pi\)
−0.829007 + 0.559238i \(0.811094\pi\)
\(728\) 330.853 945.524i 0.454469 1.29880i
\(729\) 0 0
\(730\) 291.317 + 66.4912i 0.399064 + 0.0910838i
\(731\) 1473.83 336.393i 2.01619 0.460182i
\(732\) 0 0
\(733\) 117.112 13.1954i 0.159771 0.0180019i −0.0317165 0.999497i \(-0.510097\pi\)
0.191488 + 0.981495i \(0.438669\pi\)
\(734\) 71.6018 + 57.1005i 0.0975501 + 0.0777936i
\(735\) 0 0
\(736\) −216.966 24.4462i −0.294791 0.0332149i
\(737\) −126.104 126.104i −0.171104 0.171104i
\(738\) 0 0
\(739\) −954.623 599.830i −1.29178 0.811677i −0.301864 0.953351i \(-0.597609\pi\)
−0.989913 + 0.141674i \(0.954752\pi\)
\(740\) −200.373 + 318.891i −0.270774 + 0.430934i
\(741\) 0 0
\(742\) −274.438 + 274.438i −0.369862 + 0.369862i
\(743\) −84.0696 + 746.139i −0.113149 + 1.00422i 0.800950 + 0.598732i \(0.204328\pi\)
−0.914098 + 0.405492i \(0.867100\pi\)
\(744\) 0 0
\(745\) −281.820 + 353.392i −0.378282 + 0.474351i
\(746\) −40.9643 363.568i −0.0549119 0.487356i
\(747\) 0 0
\(748\) −27.0578 118.548i −0.0361736 0.158487i
\(749\) 336.017 1472.19i 0.448621 1.96554i
\(750\) 0 0
\(751\) −1157.37 404.983i −1.54111 0.539258i −0.579808 0.814753i \(-0.696873\pi\)
−0.961303 + 0.275495i \(0.911158\pi\)
\(752\) 345.203 216.906i 0.459047 0.288438i
\(753\) 0 0
\(754\) −150.041 320.642i −0.198993 0.425255i
\(755\) −178.716 −0.236710
\(756\) 0 0
\(757\) 347.068 991.864i 0.458478 1.31026i −0.450263 0.892896i \(-0.648670\pi\)
0.908741 0.417360i \(-0.137045\pi\)
\(758\) −100.608 + 208.915i −0.132729 + 0.275614i
\(759\) 0 0
\(760\) −12.3270 + 2.81355i −0.0162197 + 0.00370204i
\(761\) −147.446 + 71.0065i −0.193754 + 0.0933068i −0.528245 0.849092i \(-0.677150\pi\)
0.334491 + 0.942399i \(0.391435\pi\)
\(762\) 0 0
\(763\) −178.897 142.665i −0.234465 0.186980i
\(764\) −388.925 1111.48i −0.509064 1.45482i
\(765\) 0 0
\(766\) 130.285 + 130.285i 0.170084 + 0.170084i
\(767\) 270.216 215.490i 0.352302 0.280952i
\(768\) 0 0
\(769\) 451.872 719.149i 0.587609 0.935175i −0.412102 0.911138i \(-0.635205\pi\)
0.999711 0.0240371i \(-0.00765197\pi\)
\(770\) −39.7373 49.8290i −0.0516069 0.0647130i
\(771\) 0 0
\(772\) −109.650 + 973.169i −0.142033 + 1.26058i
\(773\) −1129.95 + 395.387i −1.46177 + 0.511497i −0.939878 0.341511i \(-0.889061\pi\)
−0.521897 + 0.853008i \(0.674776\pi\)
\(774\) 0 0
\(775\) 10.4136 + 92.4234i 0.0134369 + 0.119256i
\(776\) −209.946 435.958i −0.270549 0.561801i
\(777\) 0 0
\(778\) 6.88977 30.1860i 0.00885574 0.0387995i
\(779\) −27.9424 13.4563i −0.0358695 0.0172739i
\(780\) 0 0
\(781\) −91.9420 + 57.7710i −0.117723 + 0.0739706i
\(782\) 140.071i 0.179119i
\(783\) 0 0
\(784\) −620.058 −0.790890
\(785\) 188.675 + 300.274i 0.240350 + 0.382515i
\(786\) 0 0
\(787\) −645.160 + 1339.69i −0.819772 + </