Properties

Label 1900.2.i.g.201.3
Level $1900$
Weight $2$
Character 1900.201
Analytic conductor $15.172$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1900.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.1715763840\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
Defining polynomial: \(x^{20} + 20 x^{18} + 261 x^{16} + 1994 x^{14} + 11074 x^{12} + 39211 x^{10} + 99376 x^{8} + 134299 x^{6} + 124617 x^{4} + 24768 x^{2} + 4096\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: no (minimal twist has level 380)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.3
Root \(1.00667 + 1.74361i\) of defining polynomial
Character \(\chi\) \(=\) 1900.201
Dual form 1900.2.i.g.501.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00667 + 1.74361i) q^{3} -1.34403 q^{7} +(-0.526784 - 0.912416i) q^{9} +O(q^{10})\) \(q+(-1.00667 + 1.74361i) q^{3} -1.34403 q^{7} +(-0.526784 - 0.912416i) q^{9} +5.25594 q^{11} +(-1.21773 - 2.10918i) q^{13} +(0.679914 - 1.17765i) q^{17} +(-2.89815 - 3.25587i) q^{19} +(1.35300 - 2.34346i) q^{21} +(-4.07329 - 7.05514i) q^{23} -3.91884 q^{27} +(1.03597 + 1.79435i) q^{29} -0.513207 q^{31} +(-5.29102 + 9.16431i) q^{33} -5.57175 q^{37} +4.90344 q^{39} +(2.70353 - 4.68265i) q^{41} +(6.36221 - 11.0197i) q^{43} +(-1.63266 - 2.82785i) q^{47} -5.19359 q^{49} +(1.36890 + 2.37101i) q^{51} +(5.88276 + 10.1892i) q^{53} +(8.59447 - 1.77564i) q^{57} +(-0.0175979 + 0.0304805i) q^{59} +(0.518372 + 0.897846i) q^{61} +(0.708011 + 1.22631i) q^{63} +(-0.383377 - 0.664028i) q^{67} +16.4019 q^{69} +(5.68450 - 9.84583i) q^{71} +(1.07635 - 1.86429i) q^{73} -7.06413 q^{77} +(6.48576 - 11.2337i) q^{79} +(5.52535 - 9.57019i) q^{81} +4.20304 q^{83} -4.17153 q^{87} +(3.65426 + 6.32937i) q^{89} +(1.63667 + 2.83479i) q^{91} +(0.516632 - 0.894833i) q^{93} +(0.416683 - 0.721716i) q^{97} +(-2.76875 - 4.79561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q - 10 q^{9} + O(q^{10}) \) \( 20 q - 10 q^{9} - 14 q^{19} - 8 q^{21} + 16 q^{29} + 8 q^{31} + 8 q^{39} + 26 q^{41} + 44 q^{49} + 26 q^{51} - 4 q^{59} + 2 q^{61} - 48 q^{69} - 2 q^{71} + 16 q^{79} + 26 q^{81} + 40 q^{89} - 4 q^{91} + 20 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\) \(951\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00667 + 1.74361i −0.581203 + 1.00667i 0.414134 + 0.910216i \(0.364085\pi\)
−0.995337 + 0.0964577i \(0.969249\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.34403 −0.507994 −0.253997 0.967205i \(-0.581745\pi\)
−0.253997 + 0.967205i \(0.581745\pi\)
\(8\) 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
\(13\) −1.21773 2.10918i −0.337738 0.584980i 0.646269 0.763110i \(-0.276329\pi\)
−0.984007 + 0.178130i \(0.942995\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.679914 1.17765i 0.164903 0.285621i −0.771718 0.635965i \(-0.780602\pi\)
0.936621 + 0.350344i \(0.113935\pi\)
\(18\) 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
\(23\) −4.07329 7.05514i −0.849339 1.47110i −0.881799 0.471625i \(-0.843668\pi\)
0.0324603 0.999473i \(-0.489666\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −3.91884 −0.754182
\(28\) 0 0
\(29\) 1.03597 + 1.79435i 0.192375 + 0.333203i 0.946037 0.324059i \(-0.105048\pi\)
−0.753662 + 0.657262i \(0.771714\pi\)
\(30\) 0 0
\(31\) −0.513207 −0.0921747 −0.0460873 0.998937i \(-0.514675\pi\)
−0.0460873 + 0.998937i \(0.514675\pi\)
\(32\) 0 0
\(33\) −5.29102 + 9.16431i −0.921048 + 1.59530i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.57175 −0.915991 −0.457995 0.888955i \(-0.651432\pi\)
−0.457995 + 0.888955i \(0.651432\pi\)
\(38\) 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
\(43\) 6.36221 11.0197i 0.970228 1.68048i 0.275369 0.961339i \(-0.411200\pi\)
0.694859 0.719146i \(-0.255467\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.63266 2.82785i −0.238148 0.412485i 0.722035 0.691857i \(-0.243207\pi\)
−0.960183 + 0.279372i \(0.909874\pi\)
\(48\) 0 0
\(49\) −5.19359 −0.741942
\(50\) 0 0
\(51\) 1.36890 + 2.37101i 0.191685 + 0.332008i
\(52\) 0 0
\(53\) 5.88276 + 10.1892i 0.808060 + 1.39960i 0.914206 + 0.405250i \(0.132815\pi\)
−0.106146 + 0.994351i \(0.533851\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 8.59447 1.77564i 1.13837 0.235190i
\(58\) 0 0
\(59\) −0.0175979 + 0.0304805i −0.00229105 + 0.00396822i −0.867169 0.498015i \(-0.834063\pi\)
0.864878 + 0.501983i \(0.167396\pi\)
\(60\) 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
\(63\) 0.708011 + 1.22631i 0.0892010 + 0.154501i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −0.383377 0.664028i −0.0468369 0.0811239i 0.841657 0.540013i \(-0.181581\pi\)
−0.888493 + 0.458889i \(0.848247\pi\)
\(68\) 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
\(73\) 1.07635 1.86429i 0.125977 0.218199i −0.796137 0.605116i \(-0.793127\pi\)
0.922115 + 0.386917i \(0.126460\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −7.06413 −0.805032
\(78\) 0 0
\(79\) 6.48576 11.2337i 0.729705 1.26389i −0.227302 0.973824i \(-0.572991\pi\)
0.957008 0.290062i \(-0.0936761\pi\)
\(80\) 0 0
\(81\) 5.52535 9.57019i 0.613928 1.06335i
\(82\) 0 0
\(83\) 4.20304 0.461343 0.230672 0.973032i \(-0.425908\pi\)
0.230672 + 0.973032i \(0.425908\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −4.17153 −0.447235
\(88\) 0 0
\(89\) 3.65426 + 6.32937i 0.387351 + 0.670912i 0.992092 0.125510i \(-0.0400568\pi\)
−0.604741 + 0.796422i \(0.706723\pi\)
\(90\) 0 0
\(91\) 1.63667 + 2.83479i 0.171569 + 0.297166i
\(92\) 0 0
\(93\) 0.516632 0.894833i 0.0535722 0.0927898i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0.416683 0.721716i 0.0423077 0.0732791i −0.844096 0.536192i \(-0.819862\pi\)
0.886404 + 0.462913i \(0.153196\pi\)
\(98\) 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
\(103\) −9.40773 −0.926971 −0.463486 0.886104i \(-0.653401\pi\)
−0.463486 + 0.886104i \(0.653401\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.8130 1.23868 0.619338 0.785124i \(-0.287401\pi\)
0.619338 + 0.785124i \(0.287401\pi\)
\(108\) 0 0
\(109\) −0.996875 + 1.72664i −0.0954833 + 0.165382i −0.909810 0.415025i \(-0.863773\pi\)
0.814327 + 0.580406i \(0.197106\pi\)
\(110\) 0 0
\(111\) 5.60894 9.71497i 0.532377 0.922104i
\(112\) 0 0
\(113\) 8.34647 0.785170 0.392585 0.919716i \(-0.371581\pi\)
0.392585 + 0.919716i \(0.371581\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −1.28296 + 2.22216i −0.118610 + 0.205439i
\(118\) 0 0
\(119\) −0.913823 + 1.58279i −0.0837700 + 0.145094i
\(120\) 0 0
\(121\) 16.6249 1.51136
\(122\) 0 0
\(123\) 5.44314 + 9.42780i 0.490791 + 0.850076i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 10.2907 + 17.8240i 0.913153 + 1.58163i 0.809583 + 0.587005i \(0.199693\pi\)
0.103569 + 0.994622i \(0.466974\pi\)
\(128\) 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
\(133\) 3.89519 + 4.37598i 0.337756 + 0.379446i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.58931 + 14.8771i 0.733834 + 1.27104i 0.955233 + 0.295855i \(0.0956045\pi\)
−0.221399 + 0.975183i \(0.571062\pi\)
\(138\) 0 0
\(139\) −3.66394 6.34613i −0.310771 0.538272i 0.667758 0.744378i \(-0.267254\pi\)
−0.978530 + 0.206106i \(0.933921\pi\)
\(140\) 0 0
\(141\) 6.57423 0.553650
\(142\) 0 0
\(143\) −6.40033 11.0857i −0.535223 0.927033i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 5.22825 9.05560i 0.431219 0.746893i
\(148\) 0 0
\(149\) 6.12292 10.6052i 0.501609 0.868812i −0.498389 0.866953i \(-0.666075\pi\)
0.999998 0.00185904i \(-0.000591751\pi\)
\(150\) 0 0
\(151\) −11.5577 −0.940549 −0.470274 0.882520i \(-0.655845\pi\)
−0.470274 + 0.882520i \(0.655845\pi\)
\(152\) 0 0
\(153\) −1.43267 −0.115825
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 2.06996 3.58528i 0.165201 0.286137i −0.771526 0.636198i \(-0.780506\pi\)
0.936727 + 0.350062i \(0.113839\pi\)
\(158\) 0 0
\(159\) −23.6881 −1.87859
\(160\) 0 0
\(161\) 5.47460 + 9.48229i 0.431459 + 0.747309i
\(162\) 0 0
\(163\) −9.41672 −0.737575 −0.368787 0.929514i \(-0.620227\pi\)
−0.368787 + 0.929514i \(0.620227\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.83551 11.8395i −0.528948 0.916164i −0.999430 0.0337550i \(-0.989253\pi\)
0.470482 0.882409i \(-0.344080\pi\)
\(168\) 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
\(173\) 5.88891 10.1999i 0.447726 0.775484i −0.550512 0.834827i \(-0.685567\pi\)
0.998238 + 0.0593437i \(0.0189008\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −0.0354307 0.0613678i −0.00266314 0.00461269i
\(178\) 0 0
\(179\) −16.5727 −1.23870 −0.619350 0.785115i \(-0.712604\pi\)
−0.619350 + 0.785115i \(0.712604\pi\)
\(180\) 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
\(183\) −2.08733 −0.154300
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 3.57359 6.18964i 0.261327 0.452631i
\(188\) 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
\(193\) −8.14331 + 14.1046i −0.586168 + 1.01527i 0.408560 + 0.912731i \(0.366031\pi\)
−0.994729 + 0.102542i \(0.967302\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 11.5233 0.820998 0.410499 0.911861i \(-0.365355\pi\)
0.410499 + 0.911861i \(0.365355\pi\)
\(198\) 0 0
\(199\) −4.79943 8.31285i −0.340222 0.589283i 0.644251 0.764814i \(-0.277169\pi\)
−0.984474 + 0.175531i \(0.943836\pi\)
\(200\) 0 0
\(201\) 1.54374 0.108887
\(202\) 0 0
\(203\) −1.39237 2.41166i −0.0977253 0.169265i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −4.29148 + 7.43307i −0.298279 + 0.516634i
\(208\) 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
\(213\) 11.4449 + 19.8231i 0.784189 + 1.35826i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0.689764 0.0468242
\(218\) 0 0
\(219\) 2.16707 + 3.75347i 0.146437 + 0.253636i
\(220\) 0 0
\(221\) −3.31182 −0.222777
\(222\) 0 0
\(223\) 3.78635 6.55816i 0.253553 0.439167i −0.710949 0.703244i \(-0.751734\pi\)
0.964501 + 0.264077i \(0.0850675\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.86640 0.455739 0.227869 0.973692i \(-0.426824\pi\)
0.227869 + 0.973692i \(0.426824\pi\)
\(228\) 0 0
\(229\) 22.1011 1.46048 0.730240 0.683191i \(-0.239408\pi\)
0.730240 + 0.683191i \(0.239408\pi\)
\(230\) 0 0
\(231\) 7.11127 12.3171i 0.467887 0.810404i
\(232\) 0 0
\(233\) −1.48844 + 2.57806i −0.0975111 + 0.168894i −0.910654 0.413170i \(-0.864421\pi\)
0.813143 + 0.582064i \(0.197755\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 13.0581 + 22.6173i 0.848214 + 1.46915i
\(238\) 0 0
\(239\) −9.71289 −0.628275 −0.314137 0.949378i \(-0.601715\pi\)
−0.314137 + 0.949378i \(0.601715\pi\)
\(240\) 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
\(243\) 5.24618 + 9.08665i 0.336543 + 0.582909i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −3.33803 + 10.0775i −0.212394 + 0.641216i
\(248\) 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
\(253\) −21.4090 37.0814i −1.34597 2.33129i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −14.0842 24.3946i −0.878548 1.52169i −0.852934 0.522018i \(-0.825179\pi\)
−0.0256140 0.999672i \(-0.508154\pi\)
\(258\) 0 0
\(259\) 7.48859 0.465318
\(260\) 0 0
\(261\) 1.09146 1.89047i 0.0675599 0.117017i
\(262\) 0 0
\(263\) −1.35425 + 2.34563i −0.0835065 + 0.144637i −0.904754 0.425935i \(-0.859945\pi\)
0.821247 + 0.570572i \(0.193279\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −14.7146 −0.900519
\(268\) 0 0
\(269\) −5.64101 + 9.77052i −0.343938 + 0.595719i −0.985160 0.171637i \(-0.945094\pi\)
0.641222 + 0.767356i \(0.278428\pi\)
\(270\) 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
\(273\) −6.59035 −0.398866
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −11.1435 −0.669549 −0.334774 0.942298i \(-0.608660\pi\)
−0.334774 + 0.942298i \(0.608660\pi\)
\(278\) 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
\(283\) 14.4304 24.9942i 0.857799 1.48575i −0.0162249 0.999868i \(-0.505165\pi\)
0.874024 0.485883i \(-0.161502\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.63361 + 6.29360i −0.214485 + 0.371500i
\(288\) 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
\(293\) −22.7742 −1.33048 −0.665242 0.746628i \(-0.731672\pi\)
−0.665242 + 0.746628i \(0.731672\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −20.5972 −1.19517
\(298\) 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
\(303\) 29.8375 1.71412
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 8.09880 14.0275i 0.462223 0.800593i −0.536849 0.843679i \(-0.680385\pi\)
0.999071 + 0.0430854i \(0.0137187\pi\)
\(308\) 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
\(313\) 1.54464 + 2.67539i 0.0873081 + 0.151222i 0.906372 0.422480i \(-0.138840\pi\)
−0.819064 + 0.573702i \(0.805507\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.0225 20.8236i −0.675251 1.16957i −0.976395 0.215991i \(-0.930702\pi\)
0.301144 0.953579i \(-0.402632\pi\)
\(318\) 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
\(323\) −5.80476 + 1.19928i −0.322986 + 0.0667298i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −2.00706 3.47632i −0.110990 0.192241i
\(328\) 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
\(333\) 2.93511 + 5.08376i 0.160843 + 0.278588i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.21324 + 2.10139i −0.0660892 + 0.114470i −0.897177 0.441672i \(-0.854386\pi\)
0.831087 + 0.556142i \(0.187719\pi\)
\(338\) 0 0
\(339\) −8.40217 + 14.5530i −0.456343 + 0.790410i
\(340\) 0 0
\(341\) −2.69739 −0.146072
\(342\) 0 0
\(343\) 16.3885 0.884896
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.43664 2.48834i 0.0771230 0.133581i −0.824885 0.565301i \(-0.808760\pi\)
0.902008 + 0.431720i \(0.142093\pi\)
\(348\) 0 0
\(349\) −5.89385 −0.315490 −0.157745 0.987480i \(-0.550422\pi\)
−0.157745 + 0.987480i \(0.550422\pi\)
\(350\) 0 0
\(351\) 4.77211 + 8.26553i 0.254716 + 0.441181i
\(352\) 0 0
\(353\) −12.0238 −0.639962 −0.319981 0.947424i \(-0.603676\pi\)
−0.319981 + 0.947424i \(0.603676\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −1.83984 3.18670i −0.0973748 0.168658i
\(358\) 0 0
\(359\) 2.26590 3.92466i 0.119590 0.207136i −0.800015 0.599979i \(-0.795175\pi\)
0.919605 + 0.392844i \(0.128509\pi\)
\(360\) 0 0
\(361\) −2.20143 + 18.8720i −0.115865 + 0.993265i
\(362\) 0 0
\(363\) −16.7359 + 28.9874i −0.878406 + 1.52144i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −17.2710 29.9143i −0.901539 1.56151i −0.825496 0.564407i \(-0.809105\pi\)
−0.0760429 0.997105i \(-0.524229\pi\)
\(368\) 0 0
\(369\) −5.69670 −0.296558
\(370\) 0 0
\(371\) −7.90659 13.6946i −0.410490 0.710989i
\(372\) 0 0
\(373\) 24.0801 1.24682 0.623411 0.781894i \(-0.285746\pi\)
0.623411 + 0.781894i \(0.285746\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 2.52307 4.37008i 0.129945 0.225071i
\(378\) 0 0
\(379\) 30.1565 1.54904 0.774518 0.632552i \(-0.217992\pi\)
0.774518 + 0.632552i \(0.217992\pi\)
\(380\) 0 0
\(381\) −41.4375 −2.12291
\(382\) 0 0
\(383\) −19.4101 + 33.6192i −0.991809 + 1.71786i −0.385286 + 0.922797i \(0.625897\pi\)
−0.606522 + 0.795066i \(0.707436\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −13.4060 −0.681467
\(388\) 0 0
\(389\) −18.6935 32.3781i −0.947799 1.64164i −0.750048 0.661383i \(-0.769970\pi\)
−0.197750 0.980252i \(-0.563364\pi\)
\(390\) 0 0
\(391\) −11.0779 −0.560236
\(392\) 0 0
\(393\) −10.8027 18.7108i −0.544924 0.943836i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −7.78211 + 13.4790i −0.390573 + 0.676492i −0.992525 0.122040i \(-0.961056\pi\)
0.601952 + 0.798532i \(0.294390\pi\)
\(398\) 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
\(403\) 0.624949 + 1.08244i 0.0311309 + 0.0539203i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −29.2848 −1.45159
\(408\) 0 0
\(409\) 18.1239 + 31.3915i 0.896169 + 1.55221i 0.832351 + 0.554249i \(0.186995\pi\)
0.0638187 + 0.997962i \(0.479672\pi\)
\(410\) 0 0
\(411\) −34.5865 −1.70603
\(412\) 0 0
\(413\) 0.0236521 0.0409666i 0.00116384 0.00201583i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 14.7536 0.722486
\(418\) 0 0
\(419\) −14.5598 −0.711293 −0.355647 0.934621i \(-0.615739\pi\)
−0.355647 + 0.934621i \(0.615739\pi\)
\(420\) 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
\(423\) −1.72012 + 2.97934i −0.0836351 + 0.144860i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −0.696705 1.20673i −0.0337159 0.0583977i
\(428\) 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
\(433\) 8.44155 + 14.6212i 0.405675 + 0.702650i 0.994400 0.105684i \(-0.0337031\pi\)
−0.588725 + 0.808334i \(0.700370\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −11.1656 + 33.7090i −0.534125 + 1.61252i
\(438\) 0 0
\(439\) −9.93240 + 17.2034i −0.474048 + 0.821075i −0.999558 0.0297121i \(-0.990541\pi\)
0.525511 + 0.850787i \(0.323874\pi\)
\(440\) 0 0
\(441\) 2.73590 + 4.73872i 0.130281 + 0.225653i
\(442\) 0 0
\(443\) 2.57742 + 4.46422i 0.122457 + 0.212101i 0.920736 0.390186i \(-0.127589\pi\)
−0.798279 + 0.602288i \(0.794256\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 12.3276 + 21.3520i 0.583074 + 1.00991i
\(448\) 0 0
\(449\) −33.2207 −1.56778 −0.783892 0.620897i \(-0.786768\pi\)
−0.783892 + 0.620897i \(0.786768\pi\)
\(450\) 0 0
\(451\) 14.2096 24.6117i 0.669103 1.15892i
\(452\) 0 0
\(453\) 11.6348 20.1520i 0.546650 0.946826i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 11.7126 0.547894 0.273947 0.961745i \(-0.411671\pi\)
0.273947 + 0.961745i \(0.411671\pi\)
\(458\) 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
\(463\) −28.8020 −1.33854 −0.669271 0.743019i \(-0.733393\pi\)
−0.669271 + 0.743019i \(0.733393\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 34.1251 1.57912 0.789561 0.613673i \(-0.210309\pi\)
0.789561 + 0.613673i \(0.210309\pi\)
\(468\) 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
\(473\) 33.4394 57.9188i 1.53755 2.66311i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 6.19789 10.7351i 0.283782 0.491525i
\(478\) 0 0
\(479\) −14.4130 24.9640i −0.658546 1.14064i −0.980992 0.194048i \(-0.937838\pi\)
0.322446 0.946588i \(-0.395495\pi\)
\(480\) 0 0
\(481\) 6.78491 + 11.7518i 0.309365 + 0.535836i
\(482\) 0 0
\(483\) −22.0446 −1.00306
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 16.5796 0.751294 0.375647 0.926763i \(-0.377421\pi\)
0.375647 + 0.926763i \(0.377421\pi\)
\(488\) 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
\(493\) 2.81748 0.126893
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7.64011 + 13.2331i −0.342706 + 0.593584i
\(498\) 0 0
\(499\) 15.4949 26.8380i 0.693649 1.20144i −0.276985 0.960874i \(-0.589335\pi\)
0.970634 0.240561i \(-0.0773315\pi\)
\(500\) 0 0
\(501\) 27.5245 1.22970
\(502\) 0 0
\(503\) 6.43203 + 11.1406i 0.286790 + 0.496735i 0.973042 0.230629i \(-0.0740784\pi\)
−0.686252 + 0.727364i \(0.740745\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 7.11568 + 12.3247i 0.316018 + 0.547360i
\(508\) 0 0
\(509\) 7.35312 + 12.7360i 0.325921 + 0.564512i 0.981698 0.190442i \(-0.0609922\pi\)
−0.655777 + 0.754955i \(0.727659\pi\)
\(510\) 0 0
\(511\) −1.44664 + 2.50566i −0.0639957 + 0.110844i
\(512\) 0 0
\(513\) 11.3574 + 12.7593i 0.501442 + 0.563335i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −8.58118 14.8630i −0.377400 0.653676i
\(518\) 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
\(523\) −7.98981 13.8388i −0.349370 0.605127i 0.636768 0.771056i \(-0.280271\pi\)
−0.986138 + 0.165929i \(0.946938\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −0.348937 + 0.604376i −0.0151999 + 0.0263270i
\(528\) 0 0
\(529\) −21.6833 + 37.5566i −0.942753 + 1.63290i
\(530\) 0 0
\(531\) 0.0370812 0.00160919
\(532\) 0 0
\(533\) −13.1687 −0.570400
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 16.6833 28.8963i 0.719937 1.24697i
\(538\) 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
\(543\) −28.9742 −1.24340
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 13.0754 + 22.6473i 0.559064 + 0.968327i 0.997575 + 0.0696011i \(0.0221727\pi\)
−0.438511 + 0.898726i \(0.644494\pi\)
\(548\) 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
\(553\) −8.71704 + 15.0983i −0.370686 + 0.642047i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 2.10412 + 3.64444i 0.0891543 + 0.154420i 0.907154 0.420799i \(-0.138250\pi\)
−0.818000 + 0.575219i \(0.804917\pi\)
\(558\) 0 0
\(559\) −30.9899 −1.31073
\(560\) 0 0
\(561\) 7.19488 + 12.4619i 0.303768 + 0.526142i
\(562\) 0 0
\(563\) 40.5225 1.70782 0.853909 0.520422i \(-0.174225\pi\)
0.853909 + 0.520422i \(0.174225\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −7.42622 + 12.8626i −0.311872 + 0.540178i
\(568\) 0 0
\(569\) 23.9522 1.00413 0.502064 0.864831i \(-0.332574\pi\)
0.502064 + 0.864831i \(0.332574\pi\)
\(570\) 0 0
\(571\) −7.78949 −0.325980 −0.162990 0.986628i \(-0.552114\pi\)
−0.162990 + 0.986628i \(0.552114\pi\)
\(572\) 0 0
\(573\) 6.01155 10.4123i 0.251136 0.434981i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 34.1385 1.42121 0.710603 0.703593i \(-0.248422\pi\)
0.710603 + 0.703593i \(0.248422\pi\)
\(578\) 0 0
\(579\) −16.3953 28.3975i −0.681366 1.18016i
\(580\) 0 0
\(581\) −5.64899 −0.234360
\(582\) 0 0
\(583\) 30.9195 + 53.5541i 1.28055 + 2.21798i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 11.0700 19.1737i 0.456906 0.791384i −0.541890 0.840450i \(-0.682291\pi\)
0.998796 + 0.0490654i \(0.0156243\pi\)
\(588\) 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
\(593\) −20.6767 35.8131i −0.849089 1.47067i −0.882022 0.471208i \(-0.843818\pi\)
0.0329325 0.999458i \(-0.489515\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 19.3258 0.790954
\(598\) 0 0
\(599\) −16.8243 29.1406i −0.687423 1.19065i −0.972669 0.232197i \(-0.925409\pi\)
0.285246 0.958454i \(-0.407925\pi\)
\(600\) 0 0
\(601\) 38.4939 1.57020 0.785100 0.619369i \(-0.212611\pi\)
0.785100 + 0.619369i \(0.212611\pi\)
\(602\) 0 0
\(603\) −0.403913 + 0.699598i −0.0164486 + 0.0284899i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −22.1827 −0.900367 −0.450183 0.892936i \(-0.648641\pi\)
−0.450183 + 0.892936i \(0.648641\pi\)
\(608\) 0 0
\(609\) 5.60665 0.227193
\(610\) 0 0
\(611\) −3.97629 + 6.88714i −0.160864 + 0.278624i
\(612\) 0 0
\(613\) −2.38703 + 4.13445i −0.0964111 + 0.166989i −0.910197 0.414176i \(-0.864070\pi\)
0.813786 + 0.581165i \(0.197403\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 8.09317 + 14.0178i 0.325819 + 0.564335i 0.981678 0.190549i \(-0.0610267\pi\)
−0.655859 + 0.754883i \(0.727693\pi\)
\(618\) 0 0
\(619\) 13.4892 0.542176 0.271088 0.962555i \(-0.412617\pi\)
0.271088 + 0.962555i \(0.412617\pi\)
\(620\) 0 0
\(621\) 15.9626 + 27.6480i 0.640556 + 1.10948i
\(622\) 0 0
\(623\) −4.91143 8.50684i −0.196772 0.340819i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 45.1720 9.33268i 1.80400 0.372711i
\(628\) 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
\(633\) 14.6613 + 25.3942i 0.582735 + 1.00933i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 6.32441 + 10.9542i 0.250582 + 0.434021i
\(638\) 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
\(643\) 14.0112 24.2681i 0.552548 0.957042i −0.445541 0.895261i \(-0.646989\pi\)
0.998090 0.0617804i \(-0.0196779\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −9.57376 −0.376383 −0.188192 0.982132i \(-0.560263\pi\)
−0.188192 + 0.982132i \(0.560263\pi\)
\(648\) 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
\(653\) 16.4168 0.642439 0.321219 0.947005i \(-0.395907\pi\)
0.321219 + 0.947005i \(0.395907\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −2.26801 −0.0884837
\(658\) 0 0
\(659\) −7.08162 12.2657i −0.275861 0.477805i 0.694491 0.719501i \(-0.255629\pi\)
−0.970352 + 0.241697i \(0.922296\pi\)
\(660\) 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
\(663\) 3.33392 5.77452i 0.129479 0.224264i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 8.43960 14.6178i 0.326783 0.566004i
\(668\) 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
\(673\) −42.3293 −1.63167 −0.815837 0.578282i \(-0.803723\pi\)
−0.815837 + 0.578282i \(0.803723\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −13.9856 −0.537510 −0.268755 0.963209i \(-0.586612\pi\)
−0.268755 + 0.963209i \(0.586612\pi\)
\(678\) 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
\(683\) 11.6668 0.446416 0.223208 0.974771i \(-0.428347\pi\)
0.223208 + 0.974771i \(0.428347\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −22.2486 + 38.5356i −0.848835 + 1.47023i
\(688\) 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
\(693\) 3.72127 + 6.44542i 0.141359 + 0.244841i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −3.67633 6.36760i −0.139251 0.241190i
\(698\) 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
\(703\) 16.1478 + 18.1409i 0.609025 + 0.684198i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 9.95913 + 17.2497i 0.374552 + 0.648743i
\(708\) 0 0
\(709\) 12.2529 + 21.2226i 0.460166 + 0.797031i 0.998969 0.0454011i \(-0.0144566\pi\)
−0.538803 + 0.842432i \(0.681123\pi\)
\(710\) 0 0
\(711\) −13.6664 −0.512529
\(712\) 0 0
\(713\) 2.09044 + 3.62075i 0.0782875 + 0.135598i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 9.77771 16.9355i 0.365155 0.632467i
\(718\) 0 0
\(719\) −22.4239 + 38.8393i −0.836269 + 1.44846i 0.0567236 + 0.998390i \(0.481935\pi\)
−0.892993 + 0.450071i \(0.851399\pi\)
\(720\) 0 0
\(721\) 12.6442 0.470896
\(722\) 0 0
\(723\) −37.6209 −1.39914
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −16.2453 + 28.1376i −0.602504 + 1.04357i 0.389937 + 0.920842i \(0.372497\pi\)
−0.992441 + 0.122726i \(0.960836\pi\)
\(728\) 0 0
\(729\) 12.0273 0.445457
\(730\) 0 0
\(731\) −8.65152 14.9849i −0.319988 0.554235i
\(732\) 0 0
\(733\) −11.1969 −0.413568 −0.206784 0.978387i \(-0.566300\pi\)
−0.206784 + 0.978387i \(0.566300\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −2.01501 3.49009i −0.0742237 0.128559i
\(738\) 0 0
\(739\) −0.466361 + 0.807761i −0.0171554 + 0.0297140i −0.874476 0.485069i \(-0.838794\pi\)
0.857320 + 0.514783i \(0.172128\pi\)
\(740\) 0 0
\(741\) −14.2109 15.9650i −0.522051 0.586488i
\(742\) 0 0
\(743\) 13.4736 23.3370i 0.494300 0.856153i −0.505678 0.862722i \(-0.668758\pi\)
0.999978 + 0.00656939i \(0.00209112\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −2.21409 3.83492i −0.0810094 0.140312i
\(748\) 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
\(753\) −8.45971 −0.308289
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 21.4140 37.0902i 0.778306 1.34807i −0.154612 0.987975i \(-0.549413\pi\)
0.932918 0.360090i \(-0.117254\pi\)
\(758\) 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
\(763\) 1.33983 2.32065i 0.0485050 0.0840131i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.0857182 0.00309511
\(768\) 0 0
\(769\) 7.70852 + 13.3516i 0.277976 + 0.481469i 0.970882 0.239559i \(-0.0770029\pi\)
−0.692905 + 0.721029i \(0.743670\pi\)
\(770\) 0 0
\(771\) 56.7128 2.04246
\(772\) 0 0
\(773\) 16.5897 + 28.7343i 0.596691 + 1.03350i 0.993306 + 0.115514i \(0.0368516\pi\)
−0.396615 + 0.917985i \(0.629815\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −7.53856 + 13.0572i −0.270444 + 0.468423i
\(778\) 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
\(783\) −4.05980 7.03179i −0.145086 0.251296i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −12.8318 −0.457405 −0.228702 0.973496i \(-0.573448\pi\)
−0.228702 + 0.973496i \(0.573448\pi\)
\(788\) 0 0
\(789\) −2.72657 4.72256i −0.0970685 0.168128i
\(790\) 0 0
\(791\) −11.2179 −0.398862
\(792\) 0 0
\(793\) 1.26248 2.18667i 0.0448319 0.0776511i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −2.28485 −0.0809336 −0.0404668 0.999181i \(-0.512885\pi\)
−0.0404668 + 0.999181i \(0.512885\pi\)
\(798\) 0 0
\(799\) −4.44028 −0.157086
\(800\) 0 0
\(801\) 3.85001 6.66842i 0.136034 0.235617i
\(802\) 0