Properties

Label 261.3.s.a.55.3
Level $261$
Weight $3$
Character 261.55
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 55.3
Character \(\chi\) \(=\) 261.55
Dual form 261.3.s.a.19.3

$q$-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 \(\left(\mathbb{Z}/261\mathbb{Z}\right)^\times\).

\(n\) \(118\) \(146\)
\(\chi(n)\) \(e\left(\frac{19}{28}\right)\) \(1\)

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 −0.715572 0.698539i \(-0.753834\pi\)
0.939837 + 0.341623i \(0.110977\pi\)
\(3\) 0 0
\(4\) 1.42716 + 2.96352i 0.356789 + 0.740881i
\(5\) −4.21883 + 0.962920i −0.843766 + 0.192584i −0.622490 0.782627i \(-0.713879\pi\)
−0.221275 + 0.975211i \(0.571022\pi\)
\(6\) 0 0
\(7\) −10.1429 4.88457i −1.44899 0.697795i −0.466568 0.884485i \(-0.654510\pi\)
−0.982419 + 0.186690i \(0.940224\pi\)
\(8\) 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 −0.181780 0.983339i \(-0.558186\pi\)
0.0415917 + 0.999135i \(0.486757\pi\)
\(12\) 0 0
\(13\) −11.3208 9.02803i −0.870830 0.694464i 0.0824361 0.996596i \(-0.473730\pi\)
−0.953266 + 0.302133i \(0.902301\pi\)
\(14\) −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 0.00908711 0.999959i \(-0.497107\pi\)
−0.999959 + 0.00908711i \(0.997107\pi\)
\(18\) 0 0
\(19\) 0.448791 + 0.157039i 0.0236206 + 0.00826520i 0.342064 0.939677i \(-0.388874\pi\)
−0.318443 + 0.947942i \(0.603160\pi\)
\(20\) −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 −0.997395 0.0721306i \(-0.977020\pi\)
0.929918 + 0.367766i \(0.119877\pi\)
\(24\) 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 −0.949371 0.314156i \(-0.898279\pi\)
0.694962 + 0.719047i \(0.255421\pi\)
\(32\) 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 0.459876 0.887983i \(-0.347894\pi\)
0.250751 + 0.968052i \(0.419322\pi\)
\(38\) 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 −0.133950 + 0.990988i \(0.542766\pi\)
−0.990988 + 0.133950i \(0.957234\pi\)
\(42\) 0 0
\(43\) −53.7324 + 33.7623i −1.24959 + 0.785170i −0.983871 0.178880i \(-0.942753\pi\)
−0.265721 + 0.964050i \(0.585610\pi\)
\(44\) −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 −0.894848 0.446372i \(-0.852716\pi\)
0.773085 0.634302i \(-0.218713\pi\)
\(48\) 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 0.985303 + 0.170818i \(0.0546409\pi\)
−0.813612 + 0.581408i \(0.802502\pi\)
\(54\) 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 0.955957 + 0.293507i \(0.0948225\pi\)
−0.564398 + 0.825503i \(0.690892\pi\)
\(62\) 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 0.349866 0.936800i \(-0.386227\pi\)
0.991165 0.132637i \(-0.0423445\pi\)
\(68\) 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 0.927797 0.373085i \(-0.121700\pi\)
−0.157276 + 0.987555i \(0.550271\pi\)
\(72\) 0 0
\(73\) −43.5770 69.3524i −0.596945 0.950032i −0.999401 0.0345932i \(-0.988986\pi\)
0.402457 0.915439i \(-0.368156\pi\)
\(74\) 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 −0.596653 0.802499i \(-0.703503\pi\)
0.760267 0.649611i \(-0.225068\pi\)
\(80\) 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 −0.427147 0.904182i \(-0.640481\pi\)
0.440596 + 0.897705i \(0.354767\pi\)
\(84\) 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 −0.588599 0.808425i \(-0.700320\pi\)
0.983749 + 0.179547i \(0.0574632\pi\)
\(90\) 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 0.728588 + 0.684952i \(0.240177\pi\)
−0.996694 + 0.0812495i \(0.974109\pi\)
\(98\) 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 −0.836499 0.547968i \(-0.815402\pi\)
0.130759 + 0.991414i \(0.458259\pi\)
\(102\) 0 0
\(103\) 30.3804 38.0958i 0.294955 0.369862i −0.612168 0.790728i \(-0.709702\pi\)
0.907123 + 0.420866i \(0.138274\pi\)
\(104\) −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 −0.999991 0.00423133i \(-0.998653\pi\)
0.218394 0.975861i \(-0.429918\pi\)
\(108\) 0 0
\(109\) 8.81881 18.3125i 0.0809066 0.168004i −0.856591 0.515996i \(-0.827422\pi\)
0.937498 + 0.347992i \(0.113136\pi\)
\(110\) 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 −0.428566 0.903511i \(-0.640981\pi\)
0.228264 + 0.973599i \(0.426695\pi\)
\(114\) 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 −0.144252 0.989541i \(-0.546078\pi\)
0.0795583 + 0.996830i \(0.474649\pi\)
\(128\) −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 −0.824725 0.565534i \(-0.808670\pi\)
−0.151694 0.988428i \(-0.548473\pi\)
\(132\) 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 0.966112 + 0.258123i \(0.0831041\pi\)
−0.999327 + 0.0366716i \(0.988324\pi\)
\(138\) 0 0
\(139\) −12.4270 + 54.4464i −0.0894032 + 0.391701i −0.999755 0.0221342i \(-0.992954\pi\)
0.910352 + 0.413835i \(0.135811\pi\)
\(140\) 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 0.995892 0.0905531i \(-0.0288635\pi\)
−0.691726 + 0.722161i \(0.743149\pi\)
\(150\) 0 0
\(151\) 40.2640 + 9.18999i 0.266649 + 0.0608609i 0.353755 0.935338i \(-0.384905\pi\)
−0.0871059 + 0.996199i \(0.527762\pi\)
\(152\) 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 −0.867148 0.498050i \(-0.834050\pi\)
0.498050 + 0.867148i \(0.334050\pi\)
\(158\) −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 0.994100 0.108468i \(-0.0345945\pi\)
−0.993312 + 0.115459i \(0.963166\pi\)
\(164\) −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 0.476190 + 0.879342i \(0.342017\pi\)
−0.984397 + 0.175960i \(0.943697\pi\)
\(168\) 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 \(-0.912502\pi\)
0.962457 0.271436i \(-0.0874985\pi\)
\(174\) 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 −0.666431 0.745566i \(-0.732179\pi\)
−0.276945 + 0.960886i \(0.589322\pi\)
\(180\) 0 0
\(181\) −87.2784 42.0311i −0.482201 0.232216i 0.176959 0.984218i \(-0.443374\pi\)
−0.659160 + 0.752002i \(0.729088\pi\)
\(182\) 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 0.909359 + 0.416013i \(0.136573\pi\)
0.416013 + 0.909359i \(0.363427\pi\)
\(192\) 0 0
\(193\) −281.027 98.3354i −1.45610 0.509510i −0.517848 0.855473i \(-0.673267\pi\)
−0.938248 + 0.345963i \(0.887552\pi\)
\(194\) 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 −0.833716 0.552193i \(-0.813791\pi\)
0.990740 0.135773i \(-0.0433516\pi\)
\(198\) 0 0
\(199\) 10.4281 5.02191i 0.0524025 0.0252357i −0.407499 0.913206i \(-0.633599\pi\)
0.459901 + 0.887970i \(0.347885\pi\)
\(200\) −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 −0.221629 0.975131i \(-0.571137\pi\)
−0.433059 + 0.901365i \(0.642566\pi\)
\(212\) −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 0.916205 0.400711i \(-0.131237\pi\)
−0.594539 + 0.804067i \(0.702665\pi\)
\(224\) 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 −0.954373 0.298616i \(-0.903475\pi\)
0.730296 0.683131i \(-0.239382\pi\)
\(228\) 0 0
\(229\) −195.058 + 68.2538i −0.851782 + 0.298051i −0.720638 0.693312i \(-0.756151\pi\)
−0.131144 + 0.991363i \(0.541865\pi\)
\(230\) −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 0.105720 0.994396i \(-0.466285\pi\)
−0.711534 + 0.702651i \(0.751999\pi\)
\(240\) 0 0
\(241\) −152.244 + 121.410i −0.631717 + 0.503777i −0.886202 0.463300i \(-0.846665\pi\)
0.254485 + 0.967077i \(0.418094\pi\)
\(242\) −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 0.870399 0.492347i \(-0.163861\pi\)
0.373532 + 0.927617i \(0.378147\pi\)
\(252\) 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 −0.712480 0.701692i \(-0.752428\pi\)
0.104381 + 0.994537i \(0.466714\pi\)
\(258\) 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 −0.640614 0.767863i \(-0.721320\pi\)
0.969773 + 0.244010i \(0.0784628\pi\)
\(264\) 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 0.0574202 0.998350i \(-0.481713\pi\)
−0.166173 + 0.986097i \(0.553141\pi\)
\(270\) 0 0
\(271\) 168.083 480.355i 0.620234 1.77253i −0.0146174 0.999893i \(-0.504653\pi\)
0.634852 0.772634i \(-0.281061\pi\)
\(272\) 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 −0.959813 0.280642i \(-0.909453\pi\)
0.487184 + 0.873299i \(0.338024\pi\)
\(278\) 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 0.959140 + 0.282931i \(0.0913067\pi\)
0.0624084 + 0.998051i \(0.480122\pi\)
\(282\) 0 0
\(283\) 194.833 404.574i 0.688455 1.42959i −0.204237 0.978922i \(-0.565471\pi\)
0.892691 0.450669i \(-0.148815\pi\)
\(284\) −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 0.863045 0.505126i \(-0.168554\pi\)
−0.989697 + 0.143176i \(0.954268\pi\)
\(294\) 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 0.887752 0.460323i \(-0.152266\pi\)
−0.460323 + 0.887752i \(0.652266\pi\)
\(308\) 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 −0.493560 0.869712i \(-0.664305\pi\)
0.674714 0.738079i \(-0.264267\pi\)
\(312\) 0 0
\(313\) −36.9386 + 161.838i −0.118015 + 0.517056i 0.881018 + 0.473082i \(0.156859\pi\)
−0.999033 + 0.0439731i \(0.985998\pi\)
\(314\) 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 0.506416 0.862290i \(-0.330970\pi\)
−0.557171 + 0.830398i \(0.688113\pi\)
\(318\) 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 −0.756694 0.653769i \(-0.773187\pi\)
0.653769 + 0.756694i \(0.273187\pi\)
\(332\) 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 0.974876 + 0.222748i \(0.0715027\pi\)
−0.900868 + 0.434093i \(0.857069\pi\)
\(338\) 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 \(-0.804171\pi\)
0.816649 0.577134i \(-0.195829\pi\)
\(348\) 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 −0.457609 0.889154i \(-0.651294\pi\)
−0.0265018 + 0.999649i \(0.508437\pi\)
\(354\) 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 0.319435 0.947608i \(-0.396507\pi\)
0.522288 + 0.852769i \(0.325078\pi\)
\(360\) 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 0.466336 0.884608i \(-0.345574\pi\)
−0.186948 + 0.982370i \(0.559860\pi\)
\(368\) −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 −0.877042 0.480414i \(-0.840486\pi\)
−0.171223 + 0.985232i \(0.554772\pi\)
\(374\) 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 −0.595963 0.803012i \(-0.703230\pi\)
0.982067 + 0.188530i \(0.0603724\pi\)
\(380\) −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 0.491433 0.870915i \(-0.336473\pi\)
0.0648901 + 0.997892i \(0.479330\pi\)
\(384\) 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 −0.739698 0.672939i \(-0.765032\pi\)
0.672939 + 0.739698i \(0.265032\pi\)
\(390\) 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 0.875942 0.482416i \(-0.160241\pi\)
−0.665236 + 0.746633i \(0.731669\pi\)
\(398\) 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 −0.917236 0.398345i \(-0.869585\pi\)
0.653566 0.756870i \(-0.273272\pi\)
\(402\) 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 0.955080 0.296347i \(-0.0957684\pi\)
−0.931481 + 0.363790i \(0.881483\pi\)
\(410\) −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 0.394758 0.918785i \(-0.370828\pi\)
−0.807907 + 0.589309i \(0.799400\pi\)
\(420\) 0 0
\(421\) 65.2084 + 103.779i 0.154889 + 0.246505i 0.915150 0.403113i \(-0.132072\pi\)
−0.760261 + 0.649618i \(0.774929\pi\)
\(422\) −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 −0.629013 0.777395i \(-0.716541\pi\)
0.215609 + 0.976480i \(0.430826\pi\)
\(432\) 0 0
\(433\) −148.885 93.5509i −0.343846 0.216053i 0.349026 0.937113i \(-0.386512\pi\)
−0.692873 + 0.721060i \(0.743655\pi\)
\(434\) 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 0.760511 0.649325i \(-0.224949\pi\)
−0.981834 + 0.189743i \(0.939234\pi\)
\(440\) 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 −0.0854526 0.996342i \(-0.527234\pi\)
−0.305017 + 0.952347i \(0.598662\pi\)
\(444\) 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 −0.0397845 0.999208i \(-0.512667\pi\)
0.882994 + 0.469385i \(0.155524\pi\)
\(450\) 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 −0.876501 0.481400i \(-0.840128\pi\)
0.922863 + 0.385128i \(0.125843\pi\)
\(458\) −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 −0.841732 0.539895i \(-0.818464\pi\)
−0.321474 + 0.946918i \(0.604178\pi\)
\(462\) 0 0
\(463\) 50.1618i 0.108341i 0.998532 + 0.0541704i \(0.0172514\pi\)
−0.998532 + 0.0541704i \(0.982749\pi\)
\(464\) 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 0.991002 0.133850i \(-0.0427340\pi\)
−0.858250 + 0.513231i \(0.828448\pi\)
\(468\) 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 0.829974 0.557802i \(-0.188355\pi\)
−0.862674 + 0.505760i \(0.831212\pi\)
\(480\) 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 −0.917552 0.397616i \(-0.869838\pi\)
0.999205 + 0.0398716i \(0.0126949\pi\)
\(488\) 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 0.165607 0.986192i \(-0.447042\pi\)
−0.816674 + 0.577100i \(0.804184\pi\)
\(492\) 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 −0.396707 0.917945i \(-0.629847\pi\)
−0.755703 + 0.654915i \(0.772704\pi\)
\(500\) 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 0.756313 + 0.654209i \(0.226999\pi\)
−0.999203 + 0.0399278i \(0.987287\pi\)
\(504\) 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 −0.316440 + 0.948613i \(0.602487\pi\)
−0.854414 + 0.519592i \(0.826084\pi\)
\(510\) 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 \(0.0507225\pi\)
−0.987331 + 0.158676i \(0.949278\pi\)
\(522\) 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 0.558879 0.829250i \(-0.311232\pi\)
−0.0800798 + 0.996788i \(0.525518\pi\)
\(542\) −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 0.0906647 0.995881i \(-0.471101\pi\)
0.835140 + 0.550037i \(0.185387\pi\)
\(548\) −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 0.506887 0.862013i \(-0.330796\pi\)
0.0826759 + 0.996576i \(0.473653\pi\)
\(558\) 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 −0.832181 0.554504i \(-0.812908\pi\)
0.554504 + 0.832181i \(0.312908\pi\)
\(564\) 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 0.983481 + 0.181014i \(0.0579379\pi\)
−0.918543 + 0.395321i \(0.870634\pi\)
\(570\) 0 0
\(571\) 126.849 + 159.064i 0.222153 + 0.278570i 0.880401 0.474231i \(-0.157274\pi\)
−0.658248 + 0.752801i \(0.728702\pi\)
\(572\) −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 0.257223 0.966352i \(-0.417192\pi\)
0.803616 + 0.595148i \(0.202907\pi\)
\(578\) 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 0.922815 0.385244i \(-0.125883\pi\)
0.274170 + 0.961681i \(0.411597\pi\)
\(588\) 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 0.998694 0.0510897i \(-0.0162694\pi\)
0.172422 + 0.985023i \(0.444841\pi\)
\(594\) 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 0.198799 0.980040i \(-0.436296\pi\)
−0.455617 + 0.890176i \(0.650581\pi\)
\(600\) 0 0
\(601\) 56.1166 498.048i 0.0933720 0.828699i −0.856518 0.516116i \(-0.827377\pi\)
0.949890 0.312583i \(-0.101194\pi\)
\(602\) 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 0.991535 0.129842i \(-0.0414471\pi\)
0.313227 + 0.949678i \(0.398590\pi\)
\(608\) 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 0.987673 0.156531i \(-0.0500312\pi\)
−0.738185 + 0.674598i \(0.764317\pi\)
\(614\) 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 0.761566 0.648087i \(-0.224431\pi\)
0.598260 + 0.801302i \(0.295859\pi\)
\(618\) 0 0
\(619\) −171.638 + 490.514i −0.277283 + 0.792430i 0.718055 + 0.695986i \(0.245032\pi\)
−0.995338 + 0.0964436i \(0.969253\pi\)
\(620\) 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 −0.999768 0.0215372i \(-0.993144\pi\)
0.640184 + 0.768222i \(0.278858\pi\)
\(632\) 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 0.920415 + 0.390944i \(0.127851\pi\)
−0.475860 + 0.879521i \(0.657863\pi\)
\(642\) 0 0
\(643\) 221.189 50.4849i 0.343995 0.0785147i −0.0470331 0.998893i \(-0.514977\pi\)
0.391028 + 0.920379i \(0.372119\pi\)
\(644\) 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 −0.977400 0.211398i \(-0.932198\pi\)
−0.0113937 + 0.999935i \(0.503627\pi\)
\(648\) 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 −0.994293 0.106685i \(-0.965976\pi\)
0.335288 0.942116i \(-0.391166\pi\)
\(654\) 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 −0.981391 0.192018i \(-0.938497\pi\)
0.999514 + 0.0311765i \(0.00992540\pi\)
\(660\) 0 0
\(661\) 58.7442 257.375i 0.0888717 0.389372i −0.910856 0.412725i \(-0.864577\pi\)
0.999727 + 0.0233529i \(0.00743414\pi\)
\(662\) 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 0.506642 0.862156i \(-0.330887\pi\)
0.0823931 + 0.996600i \(0.473744\pi\)
\(674\) 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 −0.746256 0.665659i \(-0.768150\pi\)
0.998478 0.0551504i \(-0.0175638\pi\)
\(678\) 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 −0.910359 0.413820i \(-0.864194\pi\)
0.606018 + 0.795451i \(0.292766\pi\)
\(684\) 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 0.994122 0.108266i \(-0.0345298\pi\)
−0.942648 + 0.333789i \(0.891673\pi\)
\(692\) 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 −0.903240 0.429135i \(-0.858818\pi\)
−0.627597 + 0.778539i \(0.715961\pi\)
\(702\) 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 0.758859 0.651255i \(-0.225757\pi\)
−0.466065 + 0.884751i \(0.654329\pi\)
\(710\) −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 −0.426279 0.904592i \(-0.640176\pi\)
0.776552 0.630054i \(-0.216967\pi\)
\(720\) 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 −0.829007 0.559238i \(-0.811094\pi\)
0.863549 + 0.504265i \(0.168237\pi\)
\(728\) 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 0.191488 0.981495i \(-0.438669\pi\)
−0.0317165 + 0.999497i \(0.510097\pi\)
\(734\) 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 −0.989913 0.141674i \(-0.954752\pi\)
−0.301864 + 0.953351i \(0.597609\pi\)
\(740\) −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 −0.914098 0.405492i \(-0.867100\pi\)
0.800950 0.598732i \(-0.204328\pi\)
\(744\) 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 −0.961303 0.275495i \(-0.911158\pi\)
−0.579808 + 0.814753i \(0.696873\pi\)
\(752\) 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 0.908741 + 0.417360i \(0.137045\pi\)
−0.450263 + 0.892896i \(0.648670\pi\)
\(758\) −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 0.334491 0.942399i \(-0.391435\pi\)
−0.528245 + 0.849092i \(0.677150\pi\)
\(762\) 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 0.999711 + 0.0240371i \(0.00765197\pi\)
−0.412102 + 0.911138i \(0.635205\pi\)
\(770\) −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 −0.521897 0.853008i \(-0.674776\pi\)
−0.939878 + 0.341511i \(0.889061\pi\)
\(774\) 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 1.70227i