Properties

Label 380.2.r.a.49.3
Level $380$
Weight $2$
Character 380.49
Analytic conductor $3.034$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.r (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \( x^{20} - 20 x^{18} + 261 x^{16} - 1994 x^{14} + 11074 x^{12} - 39211 x^{10} + 99376 x^{8} - 134299 x^{6} + 124617 x^{4} - 24768 x^{2} + 4096 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.3
Root \(-1.74361 + 1.00667i\) of defining polynomial
Character \(\chi\) \(=\) 380.49
Dual form 380.2.r.a.349.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.74361 - 1.00667i) q^{3} +(-1.95659 + 1.08248i) q^{5} +1.34403i q^{7} +(0.526784 + 0.912416i) q^{9} +O(q^{10})\) \(q+(-1.74361 - 1.00667i) q^{3} +(-1.95659 + 1.08248i) q^{5} +1.34403i q^{7} +(0.526784 + 0.912416i) q^{9} +5.25594 q^{11} +(2.10918 - 1.21773i) q^{13} +(4.50123 + 0.0822214i) q^{15} +(-1.17765 - 0.679914i) q^{17} +(2.89815 + 3.25587i) q^{19} +(1.35300 - 2.34346i) q^{21} +(7.05514 - 4.07329i) q^{23} +(2.65647 - 4.23594i) q^{25} +3.91884i q^{27} +(-1.03597 - 1.79435i) q^{29} -0.513207 q^{31} +(-9.16431 - 5.29102i) q^{33} +(-1.45488 - 2.62971i) q^{35} +5.57175i q^{37} -4.90344 q^{39} +(2.70353 - 4.68265i) q^{41} +(11.0197 + 6.36221i) q^{43} +(-2.01837 - 1.21499i) q^{45} +(-2.82785 + 1.63266i) q^{47} +5.19359 q^{49} +(1.36890 + 2.37101i) q^{51} +(-10.1892 + 5.88276i) q^{53} +(-10.2837 + 5.68946i) q^{55} +(-1.77564 - 8.59447i) q^{57} +(0.0175979 - 0.0304805i) q^{59} +(0.518372 + 0.897846i) q^{61} +(-1.22631 + 0.708011i) q^{63} +(-2.80861 + 4.66574i) q^{65} +(-0.664028 + 0.383377i) q^{67} -16.4019 q^{69} +(5.68450 - 9.84583i) q^{71} +(1.86429 + 1.07635i) q^{73} +(-8.89606 + 4.71162i) q^{75} +7.06413i q^{77} +(-6.48576 + 11.2337i) q^{79} +(5.52535 - 9.57019i) q^{81} +4.20304i q^{83} +(3.04016 + 0.0555329i) q^{85} +4.17153i q^{87} +(-3.65426 - 6.32937i) q^{89} +(1.63667 + 2.83479i) q^{91} +(0.894833 + 0.516632i) q^{93} +(-9.19491 - 3.23321i) q^{95} +(-0.721716 - 0.416683i) q^{97} +(2.76875 + 4.79561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + q^{5} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + q^{5} + 10 q^{9} - 5 q^{15} + 14 q^{19} - 8 q^{21} + 9 q^{25} - 16 q^{29} + 8 q^{31} - 2 q^{35} - 8 q^{39} + 26 q^{41} - 32 q^{45} - 44 q^{49} + 26 q^{51} - 12 q^{55} + 4 q^{59} + 2 q^{61} - 18 q^{65} + 48 q^{69} - 2 q^{71} + 46 q^{75} - 16 q^{79} + 26 q^{81} - 39 q^{85} - 40 q^{89} - 4 q^{91} - 43 q^{95} - 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.74361 1.00667i −1.00667 0.581203i −0.0964577 0.995337i \(-0.530751\pi\)
−0.910216 + 0.414134i \(0.864085\pi\)
\(4\) 0 0
\(5\) −1.95659 + 1.08248i −0.875013 + 0.484100i
\(6\) 0 0
\(7\) 1.34403i 0.507994i 0.967205 + 0.253997i \(0.0817454\pi\)
−0.967205 + 0.253997i \(0.918255\pi\)
\(8\) 0 0
\(9\) 0.526784 + 0.912416i 0.175595 + 0.304139i
\(10\) 0 0
\(11\) 5.25594 1.58473 0.792363 0.610050i \(-0.208851\pi\)
0.792363 + 0.610050i \(0.208851\pi\)
\(12\) 0 0
\(13\) 2.10918 1.21773i 0.584980 0.337738i −0.178130 0.984007i \(-0.557005\pi\)
0.763110 + 0.646269i \(0.223671\pi\)
\(14\) 0 0
\(15\) 4.50123 + 0.0822214i 1.16221 + 0.0212295i
\(16\) 0 0
\(17\) −1.17765 0.679914i −0.285621 0.164903i 0.350344 0.936621i \(-0.386065\pi\)
−0.635965 + 0.771718i \(0.719398\pi\)
\(18\) 0 0
\(19\) 2.89815 + 3.25587i 0.664882 + 0.746949i
\(20\) 0 0
\(21\) 1.35300 2.34346i 0.295248 0.511384i
\(22\) 0 0
\(23\) 7.05514 4.07329i 1.47110 0.849339i 0.471625 0.881799i \(-0.343668\pi\)
0.999473 + 0.0324603i \(0.0103342\pi\)
\(24\) 0 0
\(25\) 2.65647 4.23594i 0.531294 0.847187i
\(26\) 0 0
\(27\) 3.91884i 0.754182i
\(28\) 0 0
\(29\) −1.03597 1.79435i −0.192375 0.333203i 0.753662 0.657262i \(-0.228286\pi\)
−0.946037 + 0.324059i \(0.894952\pi\)
\(30\) 0 0
\(31\) −0.513207 −0.0921747 −0.0460873 0.998937i \(-0.514675\pi\)
−0.0460873 + 0.998937i \(0.514675\pi\)
\(32\) 0 0
\(33\) −9.16431 5.29102i −1.59530 0.921048i
\(34\) 0 0
\(35\) −1.45488 2.62971i −0.245920 0.444501i
\(36\) 0 0
\(37\) 5.57175i 0.915991i 0.888955 + 0.457995i \(0.151432\pi\)
−0.888955 + 0.457995i \(0.848568\pi\)
\(38\) 0 0
\(39\) −4.90344 −0.785179
\(40\) 0 0
\(41\) 2.70353 4.68265i 0.422220 0.731307i −0.573936 0.818900i \(-0.694584\pi\)
0.996156 + 0.0875933i \(0.0279176\pi\)
\(42\) 0 0
\(43\) 11.0197 + 6.36221i 1.68048 + 0.970228i 0.961339 + 0.275369i \(0.0888000\pi\)
0.719146 + 0.694859i \(0.244533\pi\)
\(44\) 0 0
\(45\) −2.01837 1.21499i −0.300881 0.181120i
\(46\) 0 0
\(47\) −2.82785 + 1.63266i −0.412485 + 0.238148i −0.691857 0.722035i \(-0.743207\pi\)
0.279372 + 0.960183i \(0.409874\pi\)
\(48\) 0 0
\(49\) 5.19359 0.741942
\(50\) 0 0
\(51\) 1.36890 + 2.37101i 0.191685 + 0.332008i
\(52\) 0 0
\(53\) −10.1892 + 5.88276i −1.39960 + 0.808060i −0.994351 0.106146i \(-0.966149\pi\)
−0.405250 + 0.914206i \(0.632815\pi\)
\(54\) 0 0
\(55\) −10.2837 + 5.68946i −1.38666 + 0.767166i
\(56\) 0 0
\(57\) −1.77564 8.59447i −0.235190 1.13837i
\(58\) 0 0
\(59\) 0.0175979 0.0304805i 0.00229105 0.00396822i −0.864878 0.501983i \(-0.832604\pi\)
0.867169 + 0.498015i \(0.165937\pi\)
\(60\) 0 0
\(61\) 0.518372 + 0.897846i 0.0663707 + 0.114957i 0.897301 0.441419i \(-0.145525\pi\)
−0.830930 + 0.556376i \(0.812191\pi\)
\(62\) 0 0
\(63\) −1.22631 + 0.708011i −0.154501 + 0.0892010i
\(64\) 0 0
\(65\) −2.80861 + 4.66574i −0.348366 + 0.578714i
\(66\) 0 0
\(67\) −0.664028 + 0.383377i −0.0811239 + 0.0468369i −0.540013 0.841657i \(-0.681581\pi\)
0.458889 + 0.888493i \(0.348247\pi\)
\(68\) 0 0
\(69\) −16.4019 −1.97455
\(70\) 0 0
\(71\) 5.68450 9.84583i 0.674625 1.16849i −0.301953 0.953323i \(-0.597638\pi\)
0.976578 0.215163i \(-0.0690282\pi\)
\(72\) 0 0
\(73\) 1.86429 + 1.07635i 0.218199 + 0.125977i 0.605116 0.796137i \(-0.293127\pi\)
−0.386917 + 0.922115i \(0.626460\pi\)
\(74\) 0 0
\(75\) −8.89606 + 4.71162i −1.02723 + 0.544051i
\(76\) 0 0
\(77\) 7.06413i 0.805032i
\(78\) 0 0
\(79\) −6.48576 + 11.2337i −0.729705 + 1.26389i 0.227302 + 0.973824i \(0.427009\pi\)
−0.957008 + 0.290062i \(0.906324\pi\)
\(80\) 0 0
\(81\) 5.52535 9.57019i 0.613928 1.06335i
\(82\) 0 0
\(83\) 4.20304i 0.461343i 0.973032 + 0.230672i \(0.0740923\pi\)
−0.973032 + 0.230672i \(0.925908\pi\)
\(84\) 0 0
\(85\) 3.04016 + 0.0555329i 0.329752 + 0.00602339i
\(86\) 0 0
\(87\) 4.17153i 0.447235i
\(88\) 0 0
\(89\) −3.65426 6.32937i −0.387351 0.670912i 0.604741 0.796422i \(-0.293277\pi\)
−0.992092 + 0.125510i \(0.959943\pi\)
\(90\) 0 0
\(91\) 1.63667 + 2.83479i 0.171569 + 0.297166i
\(92\) 0 0
\(93\) 0.894833 + 0.516632i 0.0927898 + 0.0535722i
\(94\) 0 0
\(95\) −9.19491 3.23321i −0.943378 0.331720i
\(96\) 0 0
\(97\) −0.721716 0.416683i −0.0732791 0.0423077i 0.462913 0.886404i \(-0.346804\pi\)
−0.536192 + 0.844096i \(0.680138\pi\)
\(98\) 0 0
\(99\) 2.76875 + 4.79561i 0.278269 + 0.481977i
\(100\) 0 0
\(101\) −7.40992 12.8344i −0.737315 1.27707i −0.953700 0.300759i \(-0.902760\pi\)
0.216385 0.976308i \(-0.430573\pi\)
\(102\) 0 0
\(103\) 9.40773i 0.926971i −0.886104 0.463486i \(-0.846599\pi\)
0.886104 0.463486i \(-0.153401\pi\)
\(104\) 0 0
\(105\) −0.110508 + 6.04977i −0.0107845 + 0.590397i
\(106\) 0 0
\(107\) 12.8130i 1.23868i −0.785124 0.619338i \(-0.787401\pi\)
0.785124 0.619338i \(-0.212599\pi\)
\(108\) 0 0
\(109\) 0.996875 1.72664i 0.0954833 0.165382i −0.814327 0.580406i \(-0.802894\pi\)
0.909810 + 0.415025i \(0.136227\pi\)
\(110\) 0 0
\(111\) 5.60894 9.71497i 0.532377 0.922104i
\(112\) 0 0
\(113\) 8.34647i 0.785170i 0.919716 + 0.392585i \(0.128419\pi\)
−0.919716 + 0.392585i \(0.871581\pi\)
\(114\) 0 0
\(115\) −9.39474 + 15.6068i −0.876064 + 1.45534i
\(116\) 0 0
\(117\) 2.22216 + 1.28296i 0.205439 + 0.118610i
\(118\) 0 0
\(119\) 0.913823 1.58279i 0.0837700 0.145094i
\(120\) 0 0
\(121\) 16.6249 1.51136
\(122\) 0 0
\(123\) −9.42780 + 5.44314i −0.850076 + 0.490791i
\(124\) 0 0
\(125\) −0.612300 + 11.1636i −0.0547658 + 0.998499i
\(126\) 0 0
\(127\) 17.8240 10.2907i 1.58163 0.913153i 0.587005 0.809583i \(-0.300307\pi\)
0.994622 0.103569i \(-0.0330264\pi\)
\(128\) 0 0
\(129\) −12.8093 22.1864i −1.12780 1.95341i
\(130\) 0 0
\(131\) −5.36554 + 9.29339i −0.468790 + 0.811967i −0.999364 0.0356712i \(-0.988643\pi\)
0.530574 + 0.847639i \(0.321976\pi\)
\(132\) 0 0
\(133\) −4.37598 + 3.89519i −0.379446 + 0.337756i
\(134\) 0 0
\(135\) −4.24207 7.66756i −0.365100 0.659919i
\(136\) 0 0
\(137\) 14.8771 8.58931i 1.27104 0.733834i 0.295855 0.955233i \(-0.404396\pi\)
0.975183 + 0.221399i \(0.0710622\pi\)
\(138\) 0 0
\(139\) 3.66394 + 6.34613i 0.310771 + 0.538272i 0.978530 0.206106i \(-0.0660793\pi\)
−0.667758 + 0.744378i \(0.732746\pi\)
\(140\) 0 0
\(141\) 6.57423 0.553650
\(142\) 0 0
\(143\) 11.0857 6.40033i 0.927033 0.535223i
\(144\) 0 0
\(145\) 3.96932 + 2.38939i 0.329634 + 0.198428i
\(146\) 0 0
\(147\) −9.05560 5.22825i −0.746893 0.431219i
\(148\) 0 0
\(149\) −6.12292 + 10.6052i −0.501609 + 0.868812i 0.498389 + 0.866953i \(0.333925\pi\)
−0.999998 + 0.00185904i \(0.999408\pi\)
\(150\) 0 0
\(151\) −11.5577 −0.940549 −0.470274 0.882520i \(-0.655845\pi\)
−0.470274 + 0.882520i \(0.655845\pi\)
\(152\) 0 0
\(153\) 1.43267i 0.115825i
\(154\) 0 0
\(155\) 1.00413 0.555537i 0.0806540 0.0446218i
\(156\) 0 0
\(157\) −3.58528 2.06996i −0.286137 0.165201i 0.350062 0.936727i \(-0.386161\pi\)
−0.636198 + 0.771526i \(0.719494\pi\)
\(158\) 0 0
\(159\) 23.6881 1.87859
\(160\) 0 0
\(161\) 5.47460 + 9.48229i 0.431459 + 0.747309i
\(162\) 0 0
\(163\) 9.41672i 0.737575i −0.929514 0.368787i \(-0.879773\pi\)
0.929514 0.368787i \(-0.120227\pi\)
\(164\) 0 0
\(165\) 23.6582 + 0.432151i 1.84179 + 0.0336429i
\(166\) 0 0
\(167\) −11.8395 + 6.83551i −0.916164 + 0.528948i −0.882409 0.470482i \(-0.844080\pi\)
−0.0337550 + 0.999430i \(0.510747\pi\)
\(168\) 0 0
\(169\) −3.53425 + 6.12151i −0.271866 + 0.470885i
\(170\) 0 0
\(171\) −1.44401 + 4.35946i −0.110426 + 0.333376i
\(172\) 0 0
\(173\) 10.1999 + 5.88891i 0.775484 + 0.447726i 0.834827 0.550512i \(-0.185567\pi\)
−0.0593437 + 0.998238i \(0.518901\pi\)
\(174\) 0 0
\(175\) 5.69321 + 3.57037i 0.430366 + 0.269894i
\(176\) 0 0
\(177\) −0.0613678 + 0.0354307i −0.00461269 + 0.00266314i
\(178\) 0 0
\(179\) 16.5727 1.23870 0.619350 0.785115i \(-0.287396\pi\)
0.619350 + 0.785115i \(0.287396\pi\)
\(180\) 0 0
\(181\) 7.19552 + 12.4630i 0.534839 + 0.926368i 0.999171 + 0.0407069i \(0.0129610\pi\)
−0.464332 + 0.885661i \(0.653706\pi\)
\(182\) 0 0
\(183\) 2.08733i 0.154300i
\(184\) 0 0
\(185\) −6.03132 10.9016i −0.443431 0.801504i
\(186\) 0 0
\(187\) −6.18964 3.57359i −0.452631 0.261327i
\(188\) 0 0
\(189\) −5.26703 −0.383120
\(190\) 0 0
\(191\) −5.97170 −0.432097 −0.216049 0.976383i \(-0.569317\pi\)
−0.216049 + 0.976383i \(0.569317\pi\)
\(192\) 0 0
\(193\) −14.1046 8.14331i −1.01527 0.586168i −0.102542 0.994729i \(-0.532698\pi\)
−0.912731 + 0.408560i \(0.866031\pi\)
\(194\) 0 0
\(195\) 9.59401 5.30788i 0.687041 0.380105i
\(196\) 0 0
\(197\) 11.5233i 0.820998i −0.911861 0.410499i \(-0.865355\pi\)
0.911861 0.410499i \(-0.134645\pi\)
\(198\) 0 0
\(199\) 4.79943 + 8.31285i 0.340222 + 0.589283i 0.984474 0.175531i \(-0.0561643\pi\)
−0.644251 + 0.764814i \(0.722831\pi\)
\(200\) 0 0
\(201\) 1.54374 0.108887
\(202\) 0 0
\(203\) 2.41166 1.39237i 0.169265 0.0977253i
\(204\) 0 0
\(205\) −0.220814 + 12.0885i −0.0154223 + 0.844299i
\(206\) 0 0
\(207\) 7.43307 + 4.29148i 0.516634 + 0.298279i
\(208\) 0 0
\(209\) 15.2325 + 17.1127i 1.05366 + 1.18371i
\(210\) 0 0
\(211\) 7.28207 12.6129i 0.501318 0.868308i −0.498681 0.866786i \(-0.666182\pi\)
0.999999 0.00152265i \(-0.000484675\pi\)
\(212\) 0 0
\(213\) −19.8231 + 11.4449i −1.35826 + 0.784189i
\(214\) 0 0
\(215\) −28.4479 0.519642i −1.94013 0.0354393i
\(216\) 0 0
\(217\) 0.689764i 0.0468242i
\(218\) 0 0
\(219\) −2.16707 3.75347i −0.146437 0.253636i
\(220\) 0 0
\(221\) −3.31182 −0.222777
\(222\) 0 0
\(223\) 6.55816 + 3.78635i 0.439167 + 0.253553i 0.703244 0.710949i \(-0.251734\pi\)
−0.264077 + 0.964501i \(0.585067\pi\)
\(224\) 0 0
\(225\) 5.26432 + 0.192385i 0.350955 + 0.0128257i
\(226\) 0 0
\(227\) 6.86640i 0.455739i −0.973692 0.227869i \(-0.926824\pi\)
0.973692 0.227869i \(-0.0731759\pi\)
\(228\) 0 0
\(229\) −22.1011 −1.46048 −0.730240 0.683191i \(-0.760592\pi\)
−0.730240 + 0.683191i \(0.760592\pi\)
\(230\) 0 0
\(231\) 7.11127 12.3171i 0.467887 0.810404i
\(232\) 0 0
\(233\) −2.57806 1.48844i −0.168894 0.0975111i 0.413170 0.910654i \(-0.364421\pi\)
−0.582064 + 0.813143i \(0.697755\pi\)
\(234\) 0 0
\(235\) 3.76562 6.25555i 0.245642 0.408067i
\(236\) 0 0
\(237\) 22.6173 13.0581i 1.46915 0.848214i
\(238\) 0 0
\(239\) 9.71289 0.628275 0.314137 0.949378i \(-0.398285\pi\)
0.314137 + 0.949378i \(0.398285\pi\)
\(240\) 0 0
\(241\) 9.34287 + 16.1823i 0.601827 + 1.04239i 0.992544 + 0.121884i \(0.0388937\pi\)
−0.390717 + 0.920511i \(0.627773\pi\)
\(242\) 0 0
\(243\) −9.08665 + 5.24618i −0.582909 + 0.336543i
\(244\) 0 0
\(245\) −10.1617 + 5.62196i −0.649209 + 0.359174i
\(246\) 0 0
\(247\) 10.0775 + 3.33803i 0.641216 + 0.212394i
\(248\) 0 0
\(249\) 4.23109 7.32846i 0.268134 0.464422i
\(250\) 0 0
\(251\) 2.10091 + 3.63888i 0.132608 + 0.229684i 0.924681 0.380742i \(-0.124332\pi\)
−0.792073 + 0.610426i \(0.790998\pi\)
\(252\) 0 0
\(253\) 37.0814 21.4090i 2.33129 1.34597i
\(254\) 0 0
\(255\) −5.24495 3.15728i −0.328452 0.197716i
\(256\) 0 0
\(257\) −24.3946 + 14.0842i −1.52169 + 0.878548i −0.522018 + 0.852934i \(0.674821\pi\)
−0.999672 + 0.0256140i \(0.991846\pi\)
\(258\) 0 0
\(259\) −7.48859 −0.465318
\(260\) 0 0
\(261\) 1.09146 1.89047i 0.0675599 0.117017i
\(262\) 0 0
\(263\) −2.34563 1.35425i −0.144637 0.0835065i 0.425935 0.904754i \(-0.359945\pi\)
−0.570572 + 0.821247i \(0.693279\pi\)
\(264\) 0 0
\(265\) 13.5682 22.5398i 0.833486 1.38461i
\(266\) 0 0
\(267\) 14.7146i 0.900519i
\(268\) 0 0
\(269\) 5.64101 9.77052i 0.343938 0.595719i −0.641222 0.767356i \(-0.721572\pi\)
0.985160 + 0.171637i \(0.0549055\pi\)
\(270\) 0 0
\(271\) −3.16690 + 5.48523i −0.192375 + 0.333204i −0.946037 0.324059i \(-0.894952\pi\)
0.753662 + 0.657263i \(0.228286\pi\)
\(272\) 0 0
\(273\) 6.59035i 0.398866i
\(274\) 0 0
\(275\) 13.9623 22.2638i 0.841956 1.34256i
\(276\) 0 0
\(277\) 11.1435i 0.669549i 0.942298 + 0.334774i \(0.108660\pi\)
−0.942298 + 0.334774i \(0.891340\pi\)
\(278\) 0 0
\(279\) −0.270349 0.468258i −0.0161854 0.0280339i
\(280\) 0 0
\(281\) −12.9061 22.3541i −0.769916 1.33353i −0.937608 0.347694i \(-0.886965\pi\)
0.167693 0.985839i \(-0.446368\pi\)
\(282\) 0 0
\(283\) 24.9942 + 14.4304i 1.48575 + 0.857799i 0.999868 0.0162249i \(-0.00516476\pi\)
0.485883 + 0.874024i \(0.338498\pi\)
\(284\) 0 0
\(285\) 12.7775 + 14.8937i 0.756877 + 0.882228i
\(286\) 0 0
\(287\) 6.29360 + 3.63361i 0.371500 + 0.214485i
\(288\) 0 0
\(289\) −7.57543 13.1210i −0.445614 0.771826i
\(290\) 0 0
\(291\) 0.838927 + 1.45306i 0.0491788 + 0.0851801i
\(292\) 0 0
\(293\) 22.7742i 1.33048i −0.746628 0.665242i \(-0.768328\pi\)
0.746628 0.665242i \(-0.231672\pi\)
\(294\) 0 0
\(295\) −0.00143733 + 0.0786871i −8.36848e−5 + 0.00458134i
\(296\) 0 0
\(297\) 20.5972i 1.19517i
\(298\) 0 0
\(299\) 9.92035 17.1825i 0.573709 0.993692i
\(300\) 0 0
\(301\) −8.55098 + 14.8107i −0.492870 + 0.853676i
\(302\) 0 0
\(303\) 29.8375i 1.71412i
\(304\) 0 0
\(305\) −1.98614 1.19559i −0.113726 0.0684592i
\(306\) 0 0
\(307\) −14.0275 8.09880i −0.800593 0.462223i 0.0430854 0.999071i \(-0.486281\pi\)
−0.843679 + 0.536849i \(0.819615\pi\)
\(308\) 0 0
\(309\) −9.47052 + 16.4034i −0.538759 + 0.933158i
\(310\) 0 0
\(311\) −28.3483 −1.60749 −0.803743 0.594977i \(-0.797161\pi\)
−0.803743 + 0.594977i \(0.797161\pi\)
\(312\) 0 0
\(313\) −2.67539 + 1.54464i −0.151222 + 0.0873081i −0.573702 0.819064i \(-0.694493\pi\)
0.422480 + 0.906372i \(0.361160\pi\)
\(314\) 0 0
\(315\) 1.63298 2.71275i 0.0920079 0.152846i
\(316\) 0 0
\(317\) −20.8236 + 12.0225i −1.16957 + 0.675251i −0.953579 0.301144i \(-0.902632\pi\)
−0.215991 + 0.976395i \(0.569298\pi\)
\(318\) 0 0
\(319\) −5.44500 9.43101i −0.304861 0.528035i
\(320\) 0 0
\(321\) −12.8985 + 22.3408i −0.719923 + 1.24694i
\(322\) 0 0
\(323\) −1.19928 5.80476i −0.0667298 0.322986i
\(324\) 0 0
\(325\) 0.444724 12.1692i 0.0246689 0.675026i
\(326\) 0 0
\(327\) −3.47632 + 2.00706i −0.192241 + 0.110990i
\(328\) 0 0
\(329\) −2.19434 3.80071i −0.120978 0.209540i
\(330\) 0 0
\(331\) −20.7717 −1.14171 −0.570857 0.821049i \(-0.693389\pi\)
−0.570857 + 0.821049i \(0.693389\pi\)
\(332\) 0 0
\(333\) −5.08376 + 2.93511i −0.278588 + 0.160843i
\(334\) 0 0
\(335\) 0.884231 1.46891i 0.0483107 0.0802550i
\(336\) 0 0
\(337\) 2.10139 + 1.21324i 0.114470 + 0.0660892i 0.556142 0.831087i \(-0.312281\pi\)
−0.441672 + 0.897177i \(0.645614\pi\)
\(338\) 0 0
\(339\) 8.40217 14.5530i 0.456343 0.790410i
\(340\) 0 0
\(341\) −2.69739 −0.146072
\(342\) 0 0
\(343\) 16.3885i 0.884896i
\(344\) 0 0
\(345\) 32.0917 17.7547i 1.72776 0.955882i
\(346\) 0 0
\(347\) −2.48834 1.43664i −0.133581 0.0771230i 0.431720 0.902008i \(-0.357907\pi\)
−0.565301 + 0.824885i \(0.691240\pi\)
\(348\) 0 0
\(349\) 5.89385 0.315490 0.157745 0.987480i \(-0.449578\pi\)
0.157745 + 0.987480i \(0.449578\pi\)
\(350\) 0 0
\(351\) 4.77211 + 8.26553i 0.254716 + 0.441181i
\(352\) 0 0
\(353\) 12.0238i 0.639962i −0.947424 0.319981i \(-0.896324\pi\)
0.947424 0.319981i \(-0.103676\pi\)
\(354\) 0 0
\(355\) −0.464289 + 25.4176i −0.0246419 + 1.34903i
\(356\) 0 0
\(357\) −3.18670 + 1.83984i −0.168658 + 0.0973748i
\(358\) 0 0
\(359\) −2.26590 + 3.92466i −0.119590 + 0.207136i −0.919605 0.392844i \(-0.871491\pi\)
0.800015 + 0.599979i \(0.204825\pi\)
\(360\) 0 0
\(361\) −2.20143 + 18.8720i −0.115865 + 0.993265i
\(362\) 0 0
\(363\) −28.9874 16.7359i −1.52144 0.878406i
\(364\) 0 0
\(365\) −4.81278 0.0879123i −0.251912 0.00460154i
\(366\) 0 0
\(367\) −29.9143 + 17.2710i −1.56151 + 0.901539i −0.564407 + 0.825496i \(0.690895\pi\)
−0.997105 + 0.0760429i \(0.975771\pi\)
\(368\) 0 0
\(369\) 5.69670 0.296558
\(370\) 0 0
\(371\) −7.90659 13.6946i −0.410490 0.710989i
\(372\) 0 0
\(373\) 24.0801i 1.24682i 0.781894 + 0.623411i \(0.214254\pi\)
−0.781894 + 0.623411i \(0.785746\pi\)
\(374\) 0 0
\(375\) 12.3057 18.8485i 0.635462 0.973333i
\(376\) 0 0
\(377\) −4.37008 2.52307i −0.225071 0.129945i
\(378\) 0 0
\(379\) −30.1565 −1.54904 −0.774518 0.632552i \(-0.782008\pi\)
−0.774518 + 0.632552i \(0.782008\pi\)
\(380\) 0 0
\(381\) −41.4375 −2.12291
\(382\) 0 0
\(383\) −33.6192 19.4101i −1.71786 0.991809i −0.922797 0.385286i \(-0.874103\pi\)
−0.795066 0.606522i \(-0.792564\pi\)
\(384\) 0 0
\(385\) −7.64678 13.8216i −0.389716 0.704413i
\(386\) 0 0
\(387\) 13.4060i 0.681467i
\(388\) 0 0
\(389\) 18.6935 + 32.3781i 0.947799 + 1.64164i 0.750048 + 0.661383i \(0.230030\pi\)
0.197750 + 0.980252i \(0.436636\pi\)
\(390\) 0 0
\(391\) −11.0779 −0.560236
\(392\) 0 0
\(393\) 18.7108 10.8027i 0.943836 0.544924i
\(394\) 0 0
\(395\) 0.529733 29.0004i 0.0266538 1.45917i
\(396\) 0 0
\(397\) 13.4790 + 7.78211i 0.676492 + 0.390573i 0.798532 0.601952i \(-0.205610\pi\)
−0.122040 + 0.992525i \(0.538944\pi\)
\(398\) 0 0
\(399\) 11.5512 2.38651i 0.578283 0.119475i
\(400\) 0 0
\(401\) −11.3113 + 19.5918i −0.564860 + 0.978366i 0.432203 + 0.901777i \(0.357737\pi\)
−0.997063 + 0.0765898i \(0.975597\pi\)
\(402\) 0 0
\(403\) −1.08244 + 0.624949i −0.0539203 + 0.0311309i
\(404\) 0 0
\(405\) −0.451290 + 24.7060i −0.0224248 + 1.22765i
\(406\) 0 0
\(407\) 29.2848i 1.45159i
\(408\) 0 0
\(409\) −18.1239 31.3915i −0.896169 1.55221i −0.832351 0.554249i \(-0.813005\pi\)
−0.0638187 0.997962i \(-0.520328\pi\)
\(410\) 0 0
\(411\) −34.5865 −1.70603
\(412\) 0 0
\(413\) 0.0409666 + 0.0236521i 0.00201583 + 0.00116384i
\(414\) 0 0
\(415\) −4.54970 8.22361i −0.223336 0.403681i
\(416\) 0 0
\(417\) 14.7536i 0.722486i
\(418\) 0 0
\(419\) 14.5598 0.711293 0.355647 0.934621i \(-0.384261\pi\)
0.355647 + 0.934621i \(0.384261\pi\)
\(420\) 0 0
\(421\) −0.784161 + 1.35821i −0.0382177 + 0.0661950i −0.884502 0.466537i \(-0.845501\pi\)
0.846284 + 0.532732i \(0.178835\pi\)
\(422\) 0 0
\(423\) −2.97934 1.72012i −0.144860 0.0836351i
\(424\) 0 0
\(425\) −6.00846 + 3.18226i −0.291453 + 0.154362i
\(426\) 0 0
\(427\) −1.20673 + 0.696705i −0.0583977 + 0.0337159i
\(428\) 0 0
\(429\) −25.7722 −1.24429
\(430\) 0 0
\(431\) 12.7303 + 22.0495i 0.613197 + 1.06209i 0.990698 + 0.136080i \(0.0434503\pi\)
−0.377500 + 0.926009i \(0.623216\pi\)
\(432\) 0 0
\(433\) −14.6212 + 8.44155i −0.702650 + 0.405675i −0.808334 0.588725i \(-0.799630\pi\)
0.105684 + 0.994400i \(0.466297\pi\)
\(434\) 0 0
\(435\) −4.51560 8.16197i −0.216507 0.391337i
\(436\) 0 0
\(437\) 33.7090 + 11.1656i 1.61252 + 0.534125i
\(438\) 0 0
\(439\) 9.93240 17.2034i 0.474048 0.821075i −0.525511 0.850787i \(-0.676126\pi\)
0.999558 + 0.0297121i \(0.00945905\pi\)
\(440\) 0 0
\(441\) 2.73590 + 4.73872i 0.130281 + 0.225653i
\(442\) 0 0
\(443\) −4.46422 + 2.57742i −0.212101 + 0.122457i −0.602288 0.798279i \(-0.705744\pi\)
0.390186 + 0.920736i \(0.372411\pi\)
\(444\) 0 0
\(445\) 14.0013 + 8.42830i 0.663726 + 0.399540i
\(446\) 0 0
\(447\) 21.3520 12.3276i 1.00991 0.583074i
\(448\) 0 0
\(449\) 33.2207 1.56778 0.783892 0.620897i \(-0.213232\pi\)
0.783892 + 0.620897i \(0.213232\pi\)
\(450\) 0 0
\(451\) 14.2096 24.6117i 0.669103 1.15892i
\(452\) 0 0
\(453\) 20.1520 + 11.6348i 0.946826 + 0.546650i
\(454\) 0 0
\(455\) −6.27088 3.77485i −0.293983 0.176968i
\(456\) 0 0
\(457\) 11.7126i 0.547894i −0.961745 0.273947i \(-0.911671\pi\)
0.961745 0.273947i \(-0.0883293\pi\)
\(458\) 0 0
\(459\) 2.66448 4.61501i 0.124367 0.215410i
\(460\) 0 0
\(461\) 3.68501 6.38263i 0.171628 0.297269i −0.767361 0.641215i \(-0.778431\pi\)
0.938989 + 0.343947i \(0.111764\pi\)
\(462\) 0 0
\(463\) 28.8020i 1.33854i −0.743019 0.669271i \(-0.766607\pi\)
0.743019 0.669271i \(-0.233393\pi\)
\(464\) 0 0
\(465\) −2.31006 0.0421966i −0.107127 0.00195682i
\(466\) 0 0
\(467\) 34.1251i 1.57912i −0.613673 0.789561i \(-0.710309\pi\)
0.613673 0.789561i \(-0.289691\pi\)
\(468\) 0 0
\(469\) −0.515268 0.892471i −0.0237929 0.0412105i
\(470\) 0 0
\(471\) 4.16756 + 7.21842i 0.192031 + 0.332607i
\(472\) 0 0
\(473\) 57.9188 + 33.4394i 2.66311 + 1.53755i
\(474\) 0 0
\(475\) 21.4905 3.62725i 0.986053 0.166430i
\(476\) 0 0
\(477\) −10.7351 6.19789i −0.491525 0.283782i
\(478\) 0 0
\(479\) 14.4130 + 24.9640i 0.658546 + 1.14064i 0.980992 + 0.194048i \(0.0621617\pi\)
−0.322446 + 0.946588i \(0.604505\pi\)
\(480\) 0 0
\(481\) 6.78491 + 11.7518i 0.309365 + 0.535836i
\(482\) 0 0
\(483\) 22.0446i 1.00306i
\(484\) 0 0
\(485\) 1.86315 + 0.0340331i 0.0846013 + 0.00154536i
\(486\) 0 0
\(487\) 16.5796i 0.751294i −0.926763 0.375647i \(-0.877421\pi\)
0.926763 0.375647i \(-0.122579\pi\)
\(488\) 0 0
\(489\) −9.47957 + 16.4191i −0.428681 + 0.742497i
\(490\) 0 0
\(491\) −4.94615 + 8.56698i −0.223217 + 0.386623i −0.955783 0.294073i \(-0.904989\pi\)
0.732566 + 0.680696i \(0.238322\pi\)
\(492\) 0 0
\(493\) 2.81748i 0.126893i
\(494\) 0 0
\(495\) −10.6084 6.38591i −0.476814 0.287026i
\(496\) 0 0
\(497\) 13.2331 + 7.64011i 0.593584 + 0.342706i
\(498\) 0 0
\(499\) −15.4949 + 26.8380i −0.693649 + 1.20144i 0.276985 + 0.960874i \(0.410665\pi\)
−0.970634 + 0.240561i \(0.922669\pi\)
\(500\) 0 0
\(501\) 27.5245 1.22970
\(502\) 0 0
\(503\) −11.1406 + 6.43203i −0.496735 + 0.286790i −0.727364 0.686252i \(-0.759255\pi\)
0.230629 + 0.973042i \(0.425922\pi\)
\(504\) 0 0
\(505\) 28.3911 + 17.0905i 1.26339 + 0.760516i
\(506\) 0 0
\(507\) 12.3247 7.11568i 0.547360 0.316018i
\(508\) 0 0
\(509\) −7.35312 12.7360i −0.325921 0.564512i 0.655777 0.754955i \(-0.272341\pi\)
−0.981698 + 0.190442i \(0.939008\pi\)
\(510\) 0 0
\(511\) −1.44664 + 2.50566i −0.0639957 + 0.110844i
\(512\) 0 0
\(513\) −12.7593 + 11.3574i −0.563335 + 0.501442i
\(514\) 0 0
\(515\) 10.1837 + 18.4071i 0.448747 + 0.811112i
\(516\) 0 0
\(517\) −14.8630 + 8.58118i −0.653676 + 0.377400i
\(518\) 0 0
\(519\) −11.8564 20.5359i −0.520439 0.901427i
\(520\) 0 0
\(521\) 5.35528 0.234619 0.117310 0.993095i \(-0.462573\pi\)
0.117310 + 0.993095i \(0.462573\pi\)
\(522\) 0 0
\(523\) 13.8388 7.98981i 0.605127 0.349370i −0.165929 0.986138i \(-0.553062\pi\)
0.771056 + 0.636768i \(0.219729\pi\)
\(524\) 0 0
\(525\) −6.33254 11.9565i −0.276375 0.521826i
\(526\) 0 0
\(527\) 0.604376 + 0.348937i 0.0263270 + 0.0151999i
\(528\) 0 0
\(529\) 21.6833 37.5566i 0.942753 1.63290i
\(530\) 0 0
\(531\) 0.0370812 0.00160919
\(532\) 0 0
\(533\) 13.1687i 0.570400i
\(534\) 0 0
\(535\) 13.8698 + 25.0697i 0.599643 + 1.08386i
\(536\) 0 0
\(537\) −28.8963 16.6833i −1.24697 0.719937i
\(538\) 0 0
\(539\) 27.2972 1.17577
\(540\) 0 0
\(541\) −17.9500 31.0904i −0.771732 1.33668i −0.936613 0.350366i \(-0.886057\pi\)
0.164881 0.986313i \(-0.447276\pi\)
\(542\) 0 0
\(543\) 28.9742i 1.24340i
\(544\) 0 0
\(545\) −0.0814211 + 4.45742i −0.00348770 + 0.190935i
\(546\) 0 0
\(547\) 22.6473 13.0754i 0.968327 0.559064i 0.0696011 0.997575i \(-0.477827\pi\)
0.898726 + 0.438511i \(0.144494\pi\)
\(548\) 0 0
\(549\) −0.546140 + 0.945942i −0.0233087 + 0.0403718i
\(550\) 0 0
\(551\) 2.83979 8.57329i 0.120979 0.365235i
\(552\) 0 0
\(553\) −15.0983 8.71704i −0.642047 0.370686i
\(554\) 0 0
\(555\) −0.458118 + 25.0798i −0.0194460 + 1.06458i
\(556\) 0 0
\(557\) 3.64444 2.10412i 0.154420 0.0891543i −0.420799 0.907154i \(-0.638250\pi\)
0.575219 + 0.818000i \(0.304917\pi\)
\(558\) 0 0
\(559\) 30.9899 1.31073
\(560\) 0 0
\(561\) 7.19488 + 12.4619i 0.303768 + 0.526142i
\(562\) 0 0
\(563\) 40.5225i 1.70782i 0.520422 + 0.853909i \(0.325775\pi\)
−0.520422 + 0.853909i \(0.674225\pi\)
\(564\) 0 0
\(565\) −9.03489 16.3306i −0.380101 0.687034i
\(566\) 0 0
\(567\) 12.8626 + 7.42622i 0.540178 + 0.311872i
\(568\) 0 0
\(569\) −23.9522 −1.00413 −0.502064 0.864831i \(-0.667426\pi\)
−0.502064 + 0.864831i \(0.667426\pi\)
\(570\) 0 0
\(571\) −7.78949 −0.325980 −0.162990 0.986628i \(-0.552114\pi\)
−0.162990 + 0.986628i \(0.552114\pi\)
\(572\) 0 0
\(573\) 10.4123 + 6.01155i 0.434981 + 0.251136i
\(574\) 0 0
\(575\) 1.48759 40.7057i 0.0620369 1.69754i
\(576\) 0 0
\(577\) 34.1385i 1.42121i −0.703593 0.710603i \(-0.748422\pi\)
0.703593 0.710603i \(-0.251578\pi\)
\(578\) 0 0
\(579\) 16.3953 + 28.3975i 0.681366 + 1.18016i
\(580\) 0 0
\(581\) −5.64899 −0.234360
\(582\) 0 0
\(583\) −53.5541 + 30.9195i −2.21798 + 1.28055i
\(584\) 0 0
\(585\) −5.73663 0.104788i −0.237181 0.00433244i
\(586\) 0 0
\(587\) −19.1737 11.0700i −0.791384 0.456906i 0.0490654 0.998796i \(-0.484376\pi\)
−0.840450 + 0.541890i \(0.817709\pi\)
\(588\) 0 0
\(589\) −1.48735 1.67094i −0.0612853 0.0688498i
\(590\) 0 0
\(591\) −11.6002 + 20.0921i −0.477167 + 0.826477i
\(592\) 0 0
\(593\) 35.8131 20.6767i 1.47067 0.849089i 0.471208 0.882022i \(-0.343818\pi\)
0.999458 + 0.0329325i \(0.0104846\pi\)
\(594\) 0 0
\(595\) −0.0746377 + 4.08606i −0.00305985 + 0.167512i
\(596\) 0 0
\(597\) 19.3258i 0.790954i
\(598\) 0 0
\(599\) 16.8243 + 29.1406i 0.687423 + 1.19065i 0.972669 + 0.232197i \(0.0745912\pi\)
−0.285246 + 0.958454i \(0.592075\pi\)
\(600\) 0 0
\(601\) 38.4939 1.57020 0.785100 0.619369i \(-0.212611\pi\)
0.785100 + 0.619369i \(0.212611\pi\)
\(602\) 0 0
\(603\) −0.699598 0.403913i −0.0284899 0.0164486i
\(604\) 0 0
\(605\) −32.5281 + 17.9962i −1.32246 + 0.731648i
\(606\) 0 0
\(607\) 22.1827i 0.900367i 0.892936 + 0.450183i \(0.148641\pi\)
−0.892936 + 0.450183i \(0.851359\pi\)
\(608\) 0 0
\(609\) −5.60665 −0.227193
\(610\) 0 0
\(611\) −3.97629 + 6.88714i −0.160864 + 0.278624i
\(612\) 0 0
\(613\) −4.13445 2.38703i −0.166989 0.0964111i 0.414176 0.910197i \(-0.364070\pi\)
−0.581165 + 0.813786i \(0.697403\pi\)
\(614\) 0 0
\(615\) 12.5542 20.8554i 0.506235 0.840970i
\(616\) 0 0
\(617\) 14.0178 8.09317i 0.564335 0.325819i −0.190549 0.981678i \(-0.561027\pi\)
0.754883 + 0.655859i \(0.227693\pi\)
\(618\) 0 0
\(619\) −13.4892 −0.542176 −0.271088 0.962555i \(-0.587383\pi\)
−0.271088 + 0.962555i \(0.587383\pi\)
\(620\) 0 0
\(621\) 15.9626 + 27.6480i 0.640556 + 1.10948i
\(622\) 0 0
\(623\) 8.50684 4.91143i 0.340819 0.196772i
\(624\) 0 0
\(625\) −10.8863 22.5053i −0.435453 0.900212i
\(626\) 0 0
\(627\) −9.33268 45.1720i −0.372711 1.80400i
\(628\) 0 0
\(629\) 3.78832 6.56156i 0.151050 0.261626i
\(630\) 0 0
\(631\) 13.2207 + 22.8989i 0.526308 + 0.911592i 0.999530 + 0.0306488i \(0.00975735\pi\)
−0.473222 + 0.880943i \(0.656909\pi\)
\(632\) 0 0
\(633\) −25.3942 + 14.6613i −1.00933 + 0.582735i
\(634\) 0 0
\(635\) −23.7348 + 39.4288i −0.941886 + 1.56469i
\(636\) 0 0
\(637\) 10.9542 6.32441i 0.434021 0.250582i
\(638\) 0 0
\(639\) 11.9780 0.473842
\(640\) 0 0
\(641\) −4.27817 + 7.41000i −0.168977 + 0.292677i −0.938061 0.346471i \(-0.887380\pi\)
0.769083 + 0.639149i \(0.220713\pi\)
\(642\) 0 0
\(643\) 24.2681 + 14.0112i 0.957042 + 0.552548i 0.895261 0.445541i \(-0.146989\pi\)
0.0617804 + 0.998090i \(0.480322\pi\)
\(644\) 0 0
\(645\) 49.0790 + 29.5438i 1.93248 + 1.16329i
\(646\) 0 0
\(647\) 9.57376i 0.376383i 0.982132 + 0.188192i \(0.0602626\pi\)
−0.982132 + 0.188192i \(0.939737\pi\)
\(648\) 0 0
\(649\) 0.0924936 0.160204i 0.00363069 0.00628854i
\(650\) 0 0
\(651\) −0.694367 + 1.20268i −0.0272144 + 0.0471367i
\(652\) 0 0
\(653\) 16.4168i 0.642439i 0.947005 + 0.321219i \(0.104093\pi\)
−0.947005 + 0.321219i \(0.895907\pi\)
\(654\) 0 0
\(655\) 0.438238 23.9914i 0.0171234 0.937423i
\(656\) 0 0
\(657\) 2.26801i 0.0884837i
\(658\) 0 0
\(659\) 7.08162 + 12.2657i 0.275861 + 0.477805i 0.970352 0.241697i \(-0.0777039\pi\)
−0.694491 + 0.719501i \(0.744371\pi\)
\(660\) 0 0
\(661\) −18.5170 32.0724i −0.720229 1.24747i −0.960908 0.276868i \(-0.910704\pi\)
0.240679 0.970605i \(-0.422630\pi\)
\(662\) 0 0
\(663\) 5.77452 + 3.33392i 0.224264 + 0.129479i
\(664\) 0 0
\(665\) 4.34552 12.3582i 0.168512 0.479230i
\(666\) 0 0
\(667\) −14.6178 8.43960i −0.566004 0.326783i
\(668\) 0 0
\(669\) −7.62324 13.2038i −0.294732 0.510490i
\(670\) 0 0
\(671\) 2.72453 + 4.71903i 0.105179 + 0.182176i
\(672\) 0 0
\(673\) 42.3293i 1.63167i −0.578282 0.815837i \(-0.696277\pi\)
0.578282 0.815837i \(-0.303723\pi\)
\(674\) 0 0
\(675\) 16.6000 + 10.4103i 0.638933 + 0.400693i
\(676\) 0 0
\(677\) 13.9856i 0.537510i 0.963209 + 0.268755i \(0.0866121\pi\)
−0.963209 + 0.268755i \(0.913388\pi\)
\(678\) 0 0
\(679\) 0.560033 0.970005i 0.0214921 0.0372254i
\(680\) 0 0
\(681\) −6.91222 + 11.9723i −0.264877 + 0.458780i
\(682\) 0 0
\(683\) 11.6668i 0.446416i 0.974771 + 0.223208i \(0.0716529\pi\)
−0.974771 + 0.223208i \(0.928347\pi\)
\(684\) 0 0
\(685\) −19.8106 + 32.9099i −0.756925 + 1.25742i
\(686\) 0 0
\(687\) 38.5356 + 22.2486i 1.47023 + 0.848835i
\(688\) 0 0
\(689\) −14.3273 + 24.8156i −0.545825 + 0.945397i
\(690\) 0 0
\(691\) −15.7886 −0.600627 −0.300313 0.953841i \(-0.597091\pi\)
−0.300313 + 0.953841i \(0.597091\pi\)
\(692\) 0 0
\(693\) −6.44542 + 3.72127i −0.244841 + 0.141359i
\(694\) 0 0
\(695\) −14.0384 8.45062i −0.532506 0.320550i
\(696\) 0 0
\(697\) −6.36760 + 3.67633i −0.241190 + 0.139251i
\(698\) 0 0
\(699\) 2.99675 + 5.19053i 0.113348 + 0.196324i
\(700\) 0 0
\(701\) 2.64450 4.58042i 0.0998816 0.173000i −0.811754 0.584000i \(-0.801487\pi\)
0.911635 + 0.411000i \(0.134820\pi\)
\(702\) 0 0
\(703\) −18.1409 + 16.1478i −0.684198 + 0.609025i
\(704\) 0 0
\(705\) −12.8631 + 7.11648i −0.484451 + 0.268022i
\(706\) 0 0
\(707\) 17.2497 9.95913i 0.648743 0.374552i
\(708\) 0 0
\(709\) −12.2529 21.2226i −0.460166 0.797031i 0.538803 0.842432i \(-0.318877\pi\)
−0.998969 + 0.0454011i \(0.985543\pi\)
\(710\) 0 0
\(711\) −13.6664 −0.512529
\(712\) 0 0
\(713\) −3.62075 + 2.09044i −0.135598 + 0.0782875i
\(714\) 0 0
\(715\) −14.7619 + 24.5229i −0.552064 + 0.917104i
\(716\) 0 0
\(717\) −16.9355 9.77771i −0.632467 0.365155i
\(718\) 0 0
\(719\) 22.4239 38.8393i 0.836269 1.44846i −0.0567236 0.998390i \(-0.518065\pi\)
0.892993 0.450071i \(-0.148601\pi\)
\(720\) 0 0
\(721\) 12.6442 0.470896
\(722\) 0 0
\(723\) 37.6209i 1.39914i
\(724\) 0 0
\(725\) −10.3528 0.378343i −0.384493 0.0140513i
\(726\) 0 0
\(727\) 28.1376 + 16.2453i 1.04357 + 0.602504i 0.920842 0.389937i \(-0.127503\pi\)
0.122726 + 0.992441i \(0.460836\pi\)
\(728\) 0 0
\(729\) −12.0273 −0.445457
\(730\) 0 0
\(731\) −8.65152 14.9849i −0.319988 0.554235i
\(732\) 0 0
\(733\) 11.1969i 0.413568i −0.978387 0.206784i \(-0.933700\pi\)
0.978387 0.206784i \(-0.0662998\pi\)
\(734\) 0 0
\(735\) 23.3776 + 0.427025i 0.862294 + 0.0157510i
\(736\) 0 0
\(737\) −3.49009 + 2.01501i −0.128559 + 0.0742237i
\(738\) 0 0
\(739\) 0.466361 0.807761i 0.0171554 0.0297140i −0.857320 0.514783i \(-0.827872\pi\)
0.874476 + 0.485069i \(0.161206\pi\)
\(740\) 0 0
\(741\) −14.2109 15.9650i −0.522051 0.586488i
\(742\) 0 0
\(743\) 23.3370 + 13.4736i 0.856153 + 0.494300i 0.862722 0.505678i \(-0.168758\pi\)
−0.00656939 + 0.999978i \(0.502091\pi\)
\(744\) 0 0
\(745\) 0.500098 27.3780i 0.0183222 1.00305i
\(746\) 0 0
\(747\) −3.83492 + 2.21409i −0.140312 + 0.0810094i
\(748\) 0 0
\(749\) 17.2210 0.629240
\(750\) 0 0
\(751\) 2.33645 + 4.04686i 0.0852584 + 0.147672i 0.905501 0.424343i \(-0.139495\pi\)
−0.820243 + 0.572015i \(0.806162\pi\)
\(752\) 0 0
\(753\) 8.45971i 0.308289i
\(754\) 0 0
\(755\) 22.6136 12.5109i 0.822992 0.455320i
\(756\) 0 0
\(757\) −37.0902 21.4140i −1.34807 0.778306i −0.360090 0.932918i \(-0.617254\pi\)
−0.987975 + 0.154612i \(0.950587\pi\)
\(758\) 0 0
\(759\) −86.2073 −3.12913
\(760\) 0 0
\(761\) −16.7169 −0.605987 −0.302994 0.952993i \(-0.597986\pi\)
−0.302994 + 0.952993i \(0.597986\pi\)
\(762\) 0 0
\(763\) 2.32065 + 1.33983i 0.0840131 + 0.0485050i
\(764\) 0 0
\(765\) 1.55084 + 2.80315i 0.0560707 + 0.101348i
\(766\) 0 0
\(767\) 0.0857182i 0.00309511i
\(768\) 0 0
\(769\) −7.70852 13.3516i −0.277976 0.481469i 0.692905 0.721029i \(-0.256330\pi\)
−0.970882 + 0.239559i \(0.922997\pi\)
\(770\) 0 0
\(771\) 56.7128 2.04246
\(772\) 0 0
\(773\) −28.7343 + 16.5897i −1.03350 + 0.596691i −0.917985 0.396615i \(-0.870185\pi\)
−0.115514 + 0.993306i \(0.536852\pi\)
\(774\) 0 0
\(775\) −1.36332 + 2.17391i −0.0489719 + 0.0780892i
\(776\) 0 0
\(777\) 13.0572 + 7.53856i 0.468423 + 0.270444i
\(778\) 0 0
\(779\) 23.0813 4.76868i 0.826975 0.170856i
\(780\) 0 0
\(781\) 29.8774 51.7491i 1.06910 1.85173i
\(782\) 0 0
\(783\) 7.03179 4.05980i 0.251296 0.145086i
\(784\) 0 0
\(785\) 9.25562 + 0.169067i 0.330347 + 0.00603427i
\(786\) 0 0
\(787\) 12.8318i 0.457405i 0.973496 + 0.228702i \(0.0734483\pi\)
−0.973496 + 0.228702i \(0.926552\pi\)
\(788\) 0 0
\(789\) 2.72657 + 4.72256i 0.0970685 + 0.168128i
\(790\) 0 0
\(791\) −11.2179 −0.398862
\(792\) 0 0
\(793\) 2.18667 + 1.26248i 0.0776511 + 0.0448319i
\(794\) 0 0