Properties

Label 276.2.i.a.13.2
Level $276$
Weight $2$
Character 276.13
Analytic conductor $2.204$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 276.i (of order \(11\), degree \(10\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.20387109579\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(2\) over \(\Q(\zeta_{11})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + 15500 x^{12} - 28190 x^{11} + 41920 x^{10} - 33520 x^{9} - 13837 x^{8} + 78980 x^{7} - 92652 x^{6} - 52852 x^{5} + 177374 x^{4} + 151360 x^{3} + 115323 x^{2} + 12834 x + 529\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 13.2
Root \(-0.962045 - 0.282482i\) of defining polynomial
Character \(\chi\) \(=\) 276.13
Dual form 276.2.i.a.85.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.841254 + 0.540641i) q^{3} +(1.11647 - 2.44474i) q^{5} +(0.161591 + 0.0474474i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\) \(q+(0.841254 + 0.540641i) q^{3} +(1.11647 - 2.44474i) q^{5} +(0.161591 + 0.0474474i) q^{7} +(0.415415 + 0.909632i) q^{9} +(3.48648 - 4.02361i) q^{11} +(-3.68628 + 1.08239i) q^{13} +(2.26096 - 1.45303i) q^{15} +(0.947403 + 6.58933i) q^{17} +(0.980961 - 6.82274i) q^{19} +(0.110287 + 0.127278i) q^{21} +(2.24153 + 4.23976i) q^{23} +(-1.45592 - 1.68022i) q^{25} +(-0.142315 + 0.989821i) q^{27} +(0.0811036 + 0.564088i) q^{29} +(-5.85469 + 3.76258i) q^{31} +(5.10834 - 1.49994i) q^{33} +(0.296409 - 0.342074i) q^{35} +(3.67937 + 8.05671i) q^{37} +(-3.68628 - 1.08239i) q^{39} +(2.02205 - 4.42768i) q^{41} +(-5.68465 - 3.65331i) q^{43} +2.68761 q^{45} -2.26730 q^{47} +(-5.86491 - 3.76915i) q^{49} +(-2.76546 + 6.05550i) q^{51} +(-4.67826 - 1.37366i) q^{53} +(-5.94411 - 13.0158i) q^{55} +(4.51389 - 5.20930i) q^{57} +(-2.18859 + 0.642628i) q^{59} +(-11.7447 + 7.54785i) q^{61} +(0.0239677 + 0.166699i) q^{63} +(-1.46948 + 10.2205i) q^{65} +(1.05513 + 1.21768i) q^{67} +(-0.406487 + 4.77857i) q^{69} +(6.21899 + 7.17709i) q^{71} +(-0.545240 + 3.79223i) q^{73} +(-0.316402 - 2.20063i) q^{75} +(0.754293 - 0.484755i) q^{77} +(-2.51952 + 0.739797i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(-3.72608 - 8.15898i) q^{83} +(17.1669 + 5.04067i) q^{85} +(-0.236740 + 0.518389i) q^{87} +(5.28849 + 3.39870i) q^{89} -0.647026 q^{91} -6.95948 q^{93} +(-15.5846 - 10.0156i) q^{95} +(-5.51602 + 12.0784i) q^{97} +(5.10834 + 1.49994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 2q^{3} - 4q^{5} - 2q^{9} + O(q^{10}) \) \( 20q - 2q^{3} - 4q^{5} - 2q^{9} - 22q^{13} + 7q^{15} + 7q^{17} + 19q^{19} + 20q^{23} + 20q^{25} - 2q^{27} + 32q^{29} - 3q^{31} + 11q^{33} - 26q^{35} - 10q^{37} - 22q^{39} - 40q^{41} + 8q^{43} - 4q^{45} - 18q^{47} - 34q^{49} - 26q^{51} - 34q^{53} - 17q^{55} - 3q^{57} - 32q^{59} + 32q^{61} + 49q^{65} + 35q^{67} - 2q^{69} + 33q^{71} - q^{73} - 2q^{75} - 50q^{77} + 22q^{79} - 2q^{81} - 14q^{83} - 9q^{85} - 12q^{87} + 10q^{89} - 72q^{91} + 30q^{93} - 51q^{95} - 4q^{97} + 11q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).

\(n\) \(97\) \(139\) \(185\)
\(\chi(n)\) \(e\left(\frac{7}{11}\right)\) \(1\) \(1\)

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
\(3\) 0.841254 + 0.540641i 0.485698 + 0.312139i
\(4\) 0 0
\(5\) 1.11647 2.44474i 0.499302 1.09332i −0.477393 0.878690i \(-0.658418\pi\)
0.976695 0.214630i \(-0.0688545\pi\)
\(6\) 0 0
\(7\) 0.161591 + 0.0474474i 0.0610756 + 0.0179334i 0.312128 0.950040i \(-0.398958\pi\)
−0.251052 + 0.967974i \(0.580777\pi\)
\(8\) 0 0
\(9\) 0.415415 + 0.909632i 0.138472 + 0.303211i
\(10\) 0 0
\(11\) 3.48648 4.02361i 1.05121 1.21316i 0.0748118 0.997198i \(-0.476164\pi\)
0.976401 0.215966i \(-0.0692901\pi\)
\(12\) 0 0
\(13\) −3.68628 + 1.08239i −1.02239 + 0.300201i −0.749613 0.661876i \(-0.769760\pi\)
−0.272777 + 0.962077i \(0.587942\pi\)
\(14\) 0 0
\(15\) 2.26096 1.45303i 0.583778 0.375171i
\(16\) 0 0
\(17\) 0.947403 + 6.58933i 0.229779 + 1.59815i 0.699036 + 0.715086i \(0.253613\pi\)
−0.469258 + 0.883061i \(0.655478\pi\)
\(18\) 0 0
\(19\) 0.980961 6.82274i 0.225048 1.56524i −0.493488 0.869753i \(-0.664278\pi\)
0.718536 0.695490i \(-0.244813\pi\)
\(20\) 0 0
\(21\) 0.110287 + 0.127278i 0.0240666 + 0.0277743i
\(22\) 0 0
\(23\) 2.24153 + 4.23976i 0.467392 + 0.884050i
\(24\) 0 0
\(25\) −1.45592 1.68022i −0.291185 0.336045i
\(26\) 0 0
\(27\) −0.142315 + 0.989821i −0.0273885 + 0.190491i
\(28\) 0 0
\(29\) 0.0811036 + 0.564088i 0.0150606 + 0.104748i 0.995965 0.0897412i \(-0.0286040\pi\)
−0.980905 + 0.194490i \(0.937695\pi\)
\(30\) 0 0
\(31\) −5.85469 + 3.76258i −1.05153 + 0.675779i −0.947813 0.318827i \(-0.896711\pi\)
−0.103720 + 0.994607i \(0.533075\pi\)
\(32\) 0 0
\(33\) 5.10834 1.49994i 0.889248 0.261107i
\(34\) 0 0
\(35\) 0.296409 0.342074i 0.0501022 0.0578210i
\(36\) 0 0
\(37\) 3.67937 + 8.05671i 0.604885 + 1.32451i 0.926018 + 0.377480i \(0.123209\pi\)
−0.321132 + 0.947034i \(0.604063\pi\)
\(38\) 0 0
\(39\) −3.68628 1.08239i −0.590277 0.173321i
\(40\) 0 0
\(41\) 2.02205 4.42768i 0.315792 0.691487i −0.683467 0.729981i \(-0.739529\pi\)
0.999259 + 0.0384940i \(0.0122561\pi\)
\(42\) 0 0
\(43\) −5.68465 3.65331i −0.866902 0.557124i 0.0299019 0.999553i \(-0.490480\pi\)
−0.896804 + 0.442429i \(0.854117\pi\)
\(44\) 0 0
\(45\) 2.68761 0.400645
\(46\) 0 0
\(47\) −2.26730 −0.330720 −0.165360 0.986233i \(-0.552879\pi\)
−0.165360 + 0.986233i \(0.552879\pi\)
\(48\) 0 0
\(49\) −5.86491 3.76915i −0.837845 0.538450i
\(50\) 0 0
\(51\) −2.76546 + 6.05550i −0.387241 + 0.847940i
\(52\) 0 0
\(53\) −4.67826 1.37366i −0.642608 0.188687i −0.0558372 0.998440i \(-0.517783\pi\)
−0.586771 + 0.809753i \(0.699601\pi\)
\(54\) 0 0
\(55\) −5.94411 13.0158i −0.801503 1.75505i
\(56\) 0 0
\(57\) 4.51389 5.20930i 0.597879 0.689989i
\(58\) 0 0
\(59\) −2.18859 + 0.642628i −0.284930 + 0.0836631i −0.421075 0.907026i \(-0.638347\pi\)
0.136145 + 0.990689i \(0.456529\pi\)
\(60\) 0 0
\(61\) −11.7447 + 7.54785i −1.50375 + 0.966404i −0.509372 + 0.860547i \(0.670122\pi\)
−0.994381 + 0.105857i \(0.966241\pi\)
\(62\) 0 0
\(63\) 0.0239677 + 0.166699i 0.00301964 + 0.0210021i
\(64\) 0 0
\(65\) −1.46948 + 10.2205i −0.182266 + 1.26769i
\(66\) 0 0
\(67\) 1.05513 + 1.21768i 0.128904 + 0.148763i 0.816532 0.577300i \(-0.195894\pi\)
−0.687628 + 0.726063i \(0.741348\pi\)
\(68\) 0 0
\(69\) −0.406487 + 4.77857i −0.0489353 + 0.575273i
\(70\) 0 0
\(71\) 6.21899 + 7.17709i 0.738058 + 0.851764i 0.993354 0.115099i \(-0.0367184\pi\)
−0.255296 + 0.966863i \(0.582173\pi\)
\(72\) 0 0
\(73\) −0.545240 + 3.79223i −0.0638156 + 0.443847i 0.932715 + 0.360615i \(0.117433\pi\)
−0.996530 + 0.0832317i \(0.973476\pi\)
\(74\) 0 0
\(75\) −0.316402 2.20063i −0.0365350 0.254106i
\(76\) 0 0
\(77\) 0.754293 0.484755i 0.0859597 0.0552429i
\(78\) 0 0
\(79\) −2.51952 + 0.739797i −0.283468 + 0.0832336i −0.420376 0.907350i \(-0.638102\pi\)
0.136908 + 0.990584i \(0.456284\pi\)
\(80\) 0 0
\(81\) −0.654861 + 0.755750i −0.0727623 + 0.0839722i
\(82\) 0 0
\(83\) −3.72608 8.15898i −0.408991 0.895565i −0.996279 0.0861869i \(-0.972532\pi\)
0.587288 0.809378i \(-0.300195\pi\)
\(84\) 0 0
\(85\) 17.1669 + 5.04067i 1.86202 + 0.546737i
\(86\) 0 0
\(87\) −0.236740 + 0.518389i −0.0253812 + 0.0555771i
\(88\) 0 0
\(89\) 5.28849 + 3.39870i 0.560578 + 0.360262i 0.790039 0.613056i \(-0.210060\pi\)
−0.229461 + 0.973318i \(0.573696\pi\)
\(90\) 0 0
\(91\) −0.647026 −0.0678268
\(92\) 0 0
\(93\) −6.95948 −0.721665
\(94\) 0 0
\(95\) −15.5846 10.0156i −1.59894 1.02758i
\(96\) 0 0
\(97\) −5.51602 + 12.0784i −0.560067 + 1.22638i 0.391853 + 0.920028i \(0.371834\pi\)
−0.951920 + 0.306348i \(0.900893\pi\)
\(98\) 0 0
\(99\) 5.10834 + 1.49994i 0.513407 + 0.150750i
\(100\) 0 0
\(101\) −3.01867 6.60995i −0.300368 0.657715i 0.697921 0.716174i \(-0.254108\pi\)
−0.998290 + 0.0584593i \(0.981381\pi\)
\(102\) 0 0
\(103\) 2.80445 3.23651i 0.276331 0.318903i −0.600572 0.799571i \(-0.705060\pi\)
0.876903 + 0.480668i \(0.159606\pi\)
\(104\) 0 0
\(105\) 0.434294 0.127520i 0.0423827 0.0124447i
\(106\) 0 0
\(107\) 8.16992 5.25049i 0.789816 0.507584i −0.0824617 0.996594i \(-0.526278\pi\)
0.872278 + 0.489010i \(0.162642\pi\)
\(108\) 0 0
\(109\) 1.25949 + 8.75997i 0.120638 + 0.839053i 0.956836 + 0.290627i \(0.0938638\pi\)
−0.836199 + 0.548426i \(0.815227\pi\)
\(110\) 0 0
\(111\) −1.26050 + 8.76695i −0.119641 + 0.832122i
\(112\) 0 0
\(113\) −5.59605 6.45819i −0.526432 0.607535i 0.428797 0.903401i \(-0.358937\pi\)
−0.955230 + 0.295865i \(0.904392\pi\)
\(114\) 0 0
\(115\) 12.8677 0.746382i 1.19992 0.0696005i
\(116\) 0 0
\(117\) −2.51591 2.90352i −0.232596 0.268430i
\(118\) 0 0
\(119\) −0.159555 + 1.10973i −0.0146264 + 0.101729i
\(120\) 0 0
\(121\) −2.46845 17.1684i −0.224404 1.56077i
\(122\) 0 0
\(123\) 4.09484 2.63160i 0.369220 0.237283i
\(124\) 0 0
\(125\) 7.16051 2.10252i 0.640456 0.188055i
\(126\) 0 0
\(127\) 9.93153 11.4616i 0.881281 1.01705i −0.118429 0.992963i \(-0.537786\pi\)
0.999710 0.0240899i \(-0.00766880\pi\)
\(128\) 0 0
\(129\) −2.80711 6.14671i −0.247152 0.541188i
\(130\) 0 0
\(131\) 1.68835 + 0.495744i 0.147512 + 0.0433133i 0.354655 0.934997i \(-0.384598\pi\)
−0.207143 + 0.978311i \(0.566417\pi\)
\(132\) 0 0
\(133\) 0.482235 1.05595i 0.0418151 0.0915623i
\(134\) 0 0
\(135\) 2.26096 + 1.45303i 0.194593 + 0.125057i
\(136\) 0 0
\(137\) 14.6865 1.25475 0.627375 0.778717i \(-0.284129\pi\)
0.627375 + 0.778717i \(0.284129\pi\)
\(138\) 0 0
\(139\) 22.3528 1.89594 0.947972 0.318355i \(-0.103130\pi\)
0.947972 + 0.318355i \(0.103130\pi\)
\(140\) 0 0
\(141\) −1.90737 1.22580i −0.160630 0.103231i
\(142\) 0 0
\(143\) −8.49702 + 18.6059i −0.710557 + 1.55590i
\(144\) 0 0
\(145\) 1.46960 + 0.431512i 0.122043 + 0.0358352i
\(146\) 0 0
\(147\) −2.89612 6.34162i −0.238868 0.523048i
\(148\) 0 0
\(149\) 4.49440 5.18681i 0.368195 0.424920i −0.541173 0.840911i \(-0.682020\pi\)
0.909369 + 0.415991i \(0.136565\pi\)
\(150\) 0 0
\(151\) 1.45687 0.427777i 0.118559 0.0348120i −0.221915 0.975066i \(-0.571231\pi\)
0.340474 + 0.940254i \(0.389413\pi\)
\(152\) 0 0
\(153\) −5.60030 + 3.59909i −0.452757 + 0.290970i
\(154\) 0 0
\(155\) 2.66191 + 18.5140i 0.213810 + 1.48708i
\(156\) 0 0
\(157\) 0.937916 6.52335i 0.0748538 0.520620i −0.917552 0.397615i \(-0.869838\pi\)
0.992406 0.123005i \(-0.0392530\pi\)
\(158\) 0 0
\(159\) −3.19294 3.68485i −0.253217 0.292228i
\(160\) 0 0
\(161\) 0.161046 + 0.791461i 0.0126922 + 0.0623759i
\(162\) 0 0
\(163\) −1.60484 1.85208i −0.125701 0.145066i 0.689411 0.724371i \(-0.257870\pi\)
−0.815111 + 0.579305i \(0.803324\pi\)
\(164\) 0 0
\(165\) 2.03636 14.1632i 0.158530 1.10260i
\(166\) 0 0
\(167\) −1.46665 10.2008i −0.113493 0.789362i −0.964476 0.264169i \(-0.914902\pi\)
0.850983 0.525193i \(-0.176007\pi\)
\(168\) 0 0
\(169\) 1.48081 0.951657i 0.113908 0.0732044i
\(170\) 0 0
\(171\) 6.61368 1.94195i 0.505761 0.148505i
\(172\) 0 0
\(173\) 1.97409 2.27822i 0.150088 0.173210i −0.675727 0.737152i \(-0.736170\pi\)
0.825815 + 0.563942i \(0.190716\pi\)
\(174\) 0 0
\(175\) −0.155542 0.340589i −0.0117578 0.0257461i
\(176\) 0 0
\(177\) −2.18859 0.642628i −0.164505 0.0483029i
\(178\) 0 0
\(179\) −5.61315 + 12.2911i −0.419547 + 0.918679i 0.575362 + 0.817899i \(0.304861\pi\)
−0.994909 + 0.100780i \(0.967866\pi\)
\(180\) 0 0
\(181\) 11.6931 + 7.51470i 0.869141 + 0.558563i 0.897490 0.441035i \(-0.145389\pi\)
−0.0283489 + 0.999598i \(0.509025\pi\)
\(182\) 0 0
\(183\) −13.9609 −1.03202
\(184\) 0 0
\(185\) 23.8045 1.75014
\(186\) 0 0
\(187\) 29.8160 + 19.1616i 2.18036 + 1.40123i
\(188\) 0 0
\(189\) −0.0699612 + 0.153194i −0.00508893 + 0.0111432i
\(190\) 0 0
\(191\) −12.2796 3.60563i −0.888524 0.260894i −0.194549 0.980893i \(-0.562324\pi\)
−0.693975 + 0.719999i \(0.744142\pi\)
\(192\) 0 0
\(193\) 6.70400 + 14.6797i 0.482564 + 1.05667i 0.981750 + 0.190174i \(0.0609052\pi\)
−0.499186 + 0.866495i \(0.666368\pi\)
\(194\) 0 0
\(195\) −6.76180 + 7.80353i −0.484222 + 0.558822i
\(196\) 0 0
\(197\) −12.6411 + 3.71175i −0.900639 + 0.264451i −0.699095 0.715028i \(-0.746414\pi\)
−0.201543 + 0.979480i \(0.564596\pi\)
\(198\) 0 0
\(199\) −7.78674 + 5.00423i −0.551987 + 0.354741i −0.786711 0.617321i \(-0.788218\pi\)
0.234724 + 0.972062i \(0.424581\pi\)
\(200\) 0 0
\(201\) 0.229301 + 1.59482i 0.0161736 + 0.112490i
\(202\) 0 0
\(203\) −0.0136589 + 0.0949996i −0.000958666 + 0.00666767i
\(204\) 0 0
\(205\) −8.56694 9.88678i −0.598341 0.690522i
\(206\) 0 0
\(207\) −2.92545 + 3.80023i −0.203333 + 0.264134i
\(208\) 0 0
\(209\) −24.0319 27.7343i −1.66232 1.91842i
\(210\) 0 0
\(211\) 2.10427 14.6355i 0.144864 1.00755i −0.779599 0.626279i \(-0.784577\pi\)
0.924463 0.381271i \(-0.124514\pi\)
\(212\) 0 0
\(213\) 1.35152 + 9.39999i 0.0926043 + 0.644077i
\(214\) 0 0
\(215\) −15.2781 + 9.81866i −1.04196 + 0.669627i
\(216\) 0 0
\(217\) −1.12459 + 0.330209i −0.0763421 + 0.0224161i
\(218\) 0 0
\(219\) −2.50892 + 2.89545i −0.169537 + 0.195656i
\(220\) 0 0
\(221\) −10.6246 23.2647i −0.714689 1.56495i
\(222\) 0 0
\(223\) −14.3582 4.21594i −0.961495 0.282320i −0.236930 0.971527i \(-0.576141\pi\)
−0.724565 + 0.689206i \(0.757959\pi\)
\(224\) 0 0
\(225\) 0.923574 2.02234i 0.0615716 0.134823i
\(226\) 0 0
\(227\) 16.2385 + 10.4358i 1.07779 + 0.692651i 0.954045 0.299664i \(-0.0968744\pi\)
0.123741 + 0.992315i \(0.460511\pi\)
\(228\) 0 0
\(229\) −26.6442 −1.76070 −0.880349 0.474326i \(-0.842692\pi\)
−0.880349 + 0.474326i \(0.842692\pi\)
\(230\) 0 0
\(231\) 0.896630 0.0589939
\(232\) 0 0
\(233\) −12.1545 7.81123i −0.796269 0.511731i 0.0781274 0.996943i \(-0.475106\pi\)
−0.874396 + 0.485212i \(0.838742\pi\)
\(234\) 0 0
\(235\) −2.53138 + 5.54295i −0.165129 + 0.361582i
\(236\) 0 0
\(237\) −2.51952 0.739797i −0.163660 0.0480550i
\(238\) 0 0
\(239\) −10.0163 21.9326i −0.647901 1.41870i −0.893380 0.449303i \(-0.851672\pi\)
0.245479 0.969402i \(-0.421055\pi\)
\(240\) 0 0
\(241\) 7.34261 8.47382i 0.472979 0.545847i −0.468259 0.883591i \(-0.655119\pi\)
0.941238 + 0.337745i \(0.109664\pi\)
\(242\) 0 0
\(243\) −0.959493 + 0.281733i −0.0615515 + 0.0180732i
\(244\) 0 0
\(245\) −15.7626 + 10.1300i −1.00704 + 0.647183i
\(246\) 0 0
\(247\) 3.76876 + 26.2123i 0.239801 + 1.66785i
\(248\) 0 0
\(249\) 1.27650 8.87825i 0.0808948 0.562636i
\(250\) 0 0
\(251\) 18.7772 + 21.6700i 1.18520 + 1.36780i 0.914221 + 0.405215i \(0.132803\pi\)
0.270983 + 0.962584i \(0.412651\pi\)
\(252\) 0 0
\(253\) 24.8742 + 5.76276i 1.56383 + 0.362302i
\(254\) 0 0
\(255\) 11.7166 + 13.5216i 0.733719 + 0.846757i
\(256\) 0 0
\(257\) −2.64973 + 18.4293i −0.165286 + 1.14959i 0.723185 + 0.690655i \(0.242678\pi\)
−0.888471 + 0.458934i \(0.848232\pi\)
\(258\) 0 0
\(259\) 0.212284 + 1.47647i 0.0131907 + 0.0917432i
\(260\) 0 0
\(261\) −0.479421 + 0.308105i −0.0296754 + 0.0190712i
\(262\) 0 0
\(263\) 13.7309 4.03175i 0.846683 0.248608i 0.170514 0.985355i \(-0.445457\pi\)
0.676169 + 0.736747i \(0.263639\pi\)
\(264\) 0 0
\(265\) −8.58139 + 9.90345i −0.527151 + 0.608364i
\(266\) 0 0
\(267\) 2.61148 + 5.71834i 0.159820 + 0.349957i
\(268\) 0 0
\(269\) 6.73185 + 1.97665i 0.410448 + 0.120518i 0.480437 0.877029i \(-0.340478\pi\)
−0.0699888 + 0.997548i \(0.522296\pi\)
\(270\) 0 0
\(271\) 4.44140 9.72532i 0.269796 0.590771i −0.725438 0.688288i \(-0.758363\pi\)
0.995234 + 0.0975167i \(0.0310899\pi\)
\(272\) 0 0
\(273\) −0.544313 0.349809i −0.0329433 0.0211714i
\(274\) 0 0
\(275\) −11.8366 −0.713774
\(276\) 0 0
\(277\) 22.1540 1.33111 0.665553 0.746351i \(-0.268196\pi\)
0.665553 + 0.746351i \(0.268196\pi\)
\(278\) 0 0
\(279\) −5.85469 3.76258i −0.350511 0.225260i
\(280\) 0 0
\(281\) 2.93397 6.42449i 0.175026 0.383253i −0.801706 0.597719i \(-0.796074\pi\)
0.976731 + 0.214466i \(0.0688012\pi\)
\(282\) 0 0
\(283\) −25.8425 7.58804i −1.53618 0.451062i −0.599243 0.800567i \(-0.704532\pi\)
−0.936934 + 0.349505i \(0.886350\pi\)
\(284\) 0 0
\(285\) −7.69574 16.8513i −0.455856 0.998186i
\(286\) 0 0
\(287\) 0.536827 0.619532i 0.0316879 0.0365698i
\(288\) 0 0
\(289\) −26.2103 + 7.69605i −1.54178 + 0.452709i
\(290\) 0 0
\(291\) −11.1704 + 7.17881i −0.654823 + 0.420829i
\(292\) 0 0
\(293\) −4.06035 28.2404i −0.237208 1.64982i −0.665659 0.746256i \(-0.731850\pi\)
0.428451 0.903565i \(-0.359059\pi\)
\(294\) 0 0
\(295\) −0.872448 + 6.06801i −0.0507959 + 0.353293i
\(296\) 0 0
\(297\) 3.48648 + 4.02361i 0.202306 + 0.233474i
\(298\) 0 0
\(299\) −12.8520 13.2027i −0.743250 0.763533i
\(300\) 0 0
\(301\) −0.745249 0.860063i −0.0429554 0.0495732i
\(302\) 0 0
\(303\) 1.03415 7.19266i 0.0594103 0.413208i
\(304\) 0 0
\(305\) 5.33988 + 37.1397i 0.305760 + 2.12661i
\(306\) 0 0
\(307\) −9.78399 + 6.28779i −0.558402 + 0.358863i −0.789198 0.614139i \(-0.789503\pi\)
0.230796 + 0.973002i \(0.425867\pi\)
\(308\) 0 0
\(309\) 4.10904 1.20652i 0.233755 0.0686367i
\(310\) 0 0
\(311\) −17.1917 + 19.8402i −0.974850 + 1.12504i 0.0172830 + 0.999851i \(0.494498\pi\)
−0.992133 + 0.125186i \(0.960047\pi\)
\(312\) 0 0
\(313\) −10.6415 23.3016i −0.601491 1.31708i −0.928244 0.371972i \(-0.878682\pi\)
0.326753 0.945110i \(-0.394046\pi\)
\(314\) 0 0
\(315\) 0.434294 + 0.127520i 0.0244697 + 0.00718495i
\(316\) 0 0
\(317\) 8.38985 18.3712i 0.471221 1.03183i −0.513564 0.858051i \(-0.671675\pi\)
0.984785 0.173778i \(-0.0555976\pi\)
\(318\) 0 0
\(319\) 2.55243 + 1.64035i 0.142909 + 0.0918420i
\(320\) 0 0
\(321\) 9.71161 0.542049
\(322\) 0 0
\(323\) 45.8866 2.55320
\(324\) 0 0
\(325\) 7.18560 + 4.61790i 0.398585 + 0.256155i
\(326\) 0 0
\(327\) −3.67644 + 8.05029i −0.203308 + 0.445182i
\(328\) 0 0
\(329\) −0.366375 0.107577i −0.0201989 0.00593094i
\(330\) 0 0
\(331\) −8.94888 19.5953i −0.491875 1.07706i −0.979025 0.203738i \(-0.934691\pi\)
0.487150 0.873318i \(-0.338036\pi\)
\(332\) 0 0
\(333\) −5.80017 + 6.69375i −0.317847 + 0.366815i
\(334\) 0 0
\(335\) 4.15493 1.22000i 0.227008 0.0666556i
\(336\) 0 0
\(337\) 1.64816 1.05921i 0.0897811 0.0576988i −0.494980 0.868904i \(-0.664825\pi\)
0.584761 + 0.811206i \(0.301188\pi\)
\(338\) 0 0
\(339\) −1.21614 8.45843i −0.0660516 0.459399i
\(340\) 0 0
\(341\) −5.27309 + 36.6751i −0.285554 + 1.98607i
\(342\) 0 0
\(343\) −1.54089 1.77828i −0.0832002 0.0960182i
\(344\) 0 0
\(345\) 11.2285 + 6.32891i 0.604523 + 0.340737i
\(346\) 0 0
\(347\) −6.39079 7.37537i −0.343076 0.395931i 0.557823 0.829960i \(-0.311637\pi\)
−0.900899 + 0.434029i \(0.857091\pi\)
\(348\) 0 0
\(349\) 2.32886 16.1975i 0.124661 0.867035i −0.827506 0.561457i \(-0.810241\pi\)
0.952167 0.305578i \(-0.0988497\pi\)
\(350\) 0 0
\(351\) −0.546760 3.80280i −0.0291839 0.202978i
\(352\) 0 0
\(353\) −15.8365 + 10.1775i −0.842894 + 0.541695i −0.889351 0.457225i \(-0.848843\pi\)
0.0464568 + 0.998920i \(0.485207\pi\)
\(354\) 0 0
\(355\) 24.4894 7.19075i 1.29976 0.381645i
\(356\) 0 0
\(357\) −0.734190 + 0.847301i −0.0388575 + 0.0448439i
\(358\) 0 0
\(359\) −5.47158 11.9811i −0.288779 0.632338i 0.708527 0.705683i \(-0.249360\pi\)
−0.997307 + 0.0733451i \(0.976633\pi\)
\(360\) 0 0
\(361\) −27.3571 8.03276i −1.43985 0.422777i
\(362\) 0 0
\(363\) 7.20536 15.7775i 0.378183 0.828106i
\(364\) 0 0
\(365\) 8.66226 + 5.56690i 0.453403 + 0.291385i
\(366\) 0 0
\(367\) 12.2223 0.638000 0.319000 0.947755i \(-0.396653\pi\)
0.319000 + 0.947755i \(0.396653\pi\)
\(368\) 0 0
\(369\) 4.86755 0.253394
\(370\) 0 0
\(371\) −0.690787 0.443942i −0.0358639 0.0230483i
\(372\) 0 0
\(373\) −10.6821 + 23.3904i −0.553096 + 1.21111i 0.402225 + 0.915541i \(0.368237\pi\)
−0.955321 + 0.295571i \(0.904490\pi\)
\(374\) 0 0
\(375\) 7.16051 + 2.10252i 0.369767 + 0.108573i
\(376\) 0 0
\(377\) −0.909533 1.99160i −0.0468434 0.102573i
\(378\) 0 0
\(379\) −12.6498 + 14.5987i −0.649779 + 0.749884i −0.981072 0.193643i \(-0.937970\pi\)
0.331293 + 0.943528i \(0.392515\pi\)
\(380\) 0 0
\(381\) 14.5515 4.27272i 0.745498 0.218898i
\(382\) 0 0
\(383\) 22.4745 14.4435i 1.14839 0.738027i 0.179074 0.983836i \(-0.442690\pi\)
0.969318 + 0.245808i \(0.0790534\pi\)
\(384\) 0 0
\(385\) −0.342949 2.38526i −0.0174783 0.121564i
\(386\) 0 0
\(387\) 0.961673 6.68858i 0.0488846 0.340000i
\(388\) 0 0
\(389\) 3.70667 + 4.27773i 0.187936 + 0.216889i 0.841896 0.539639i \(-0.181439\pi\)
−0.653961 + 0.756528i \(0.726894\pi\)
\(390\) 0 0
\(391\) −25.8135 + 18.7870i −1.30545 + 0.950097i
\(392\) 0 0
\(393\) 1.15231 + 1.32984i 0.0581263 + 0.0670813i
\(394\) 0 0
\(395\) −1.00437 + 6.98552i −0.0505351 + 0.351480i
\(396\) 0 0
\(397\) −1.11388 7.74722i −0.0559041 0.388822i −0.998494 0.0548680i \(-0.982526\pi\)
0.942590 0.333954i \(-0.108383\pi\)
\(398\) 0 0
\(399\) 0.976571 0.627604i 0.0488897 0.0314195i
\(400\) 0 0
\(401\) 8.50273 2.49663i 0.424606 0.124676i −0.0624463 0.998048i \(-0.519890\pi\)
0.487053 + 0.873373i \(0.338072\pi\)
\(402\) 0 0
\(403\) 17.5094 20.2070i 0.872208 1.00658i
\(404\) 0 0
\(405\) 1.11647 + 2.44474i 0.0554780 + 0.121480i
\(406\) 0 0
\(407\) 45.2451 + 13.2852i 2.24272 + 0.658521i
\(408\) 0 0
\(409\) 5.62678 12.3209i 0.278226 0.609231i −0.717998 0.696045i \(-0.754941\pi\)
0.996225 + 0.0868141i \(0.0276686\pi\)
\(410\) 0 0
\(411\) 12.3550 + 7.94011i 0.609429 + 0.391657i
\(412\) 0 0
\(413\) −0.384147 −0.0189027
\(414\) 0 0
\(415\) −24.1066 −1.18335
\(416\) 0 0
\(417\) 18.8044 + 12.0849i 0.920856 + 0.591798i
\(418\) 0 0
\(419\) 3.92505 8.59466i 0.191751 0.419877i −0.789199 0.614138i \(-0.789504\pi\)
0.980950 + 0.194261i \(0.0622310\pi\)
\(420\) 0 0
\(421\) 29.8747 + 8.77200i 1.45600 + 0.427521i 0.911522 0.411252i \(-0.134908\pi\)
0.544481 + 0.838773i \(0.316727\pi\)
\(422\) 0 0
\(423\) −0.941871 2.06241i −0.0457953 0.100278i
\(424\) 0 0
\(425\) 9.69221 11.1854i 0.470141 0.542572i
\(426\) 0 0
\(427\) −2.25596 + 0.662410i −0.109174 + 0.0320563i
\(428\) 0 0
\(429\) −17.2073 + 11.0584i −0.830774 + 0.533906i
\(430\) 0 0
\(431\) 3.07047 + 21.3556i 0.147900 + 1.02866i 0.919650 + 0.392739i \(0.128472\pi\)
−0.771751 + 0.635925i \(0.780619\pi\)
\(432\) 0 0
\(433\) 0.0751560 0.522721i 0.00361176 0.0251204i −0.987936 0.154864i \(-0.950506\pi\)
0.991548 + 0.129743i \(0.0414153\pi\)
\(434\) 0 0
\(435\) 1.00301 + 1.15754i 0.0480906 + 0.0554996i
\(436\) 0 0
\(437\) 31.1256 11.1344i 1.48894 0.532628i
\(438\) 0 0
\(439\) −14.1594 16.3408i −0.675790 0.779903i 0.309481 0.950906i \(-0.399845\pi\)
−0.985271 + 0.171003i \(0.945299\pi\)
\(440\) 0 0
\(441\) 0.992167 6.90068i 0.0472461 0.328604i
\(442\) 0 0
\(443\) −3.16475 22.0113i −0.150362 1.04579i −0.915614 0.402059i \(-0.868295\pi\)
0.765252 0.643731i \(-0.222615\pi\)
\(444\) 0 0
\(445\) 14.2134 9.13439i 0.673779 0.433012i
\(446\) 0 0
\(447\) 6.58513 1.93357i 0.311466 0.0914547i
\(448\) 0 0
\(449\) 27.3177 31.5263i 1.28920 1.48782i 0.511343 0.859377i \(-0.329148\pi\)
0.777858 0.628440i \(-0.216306\pi\)
\(450\) 0 0
\(451\) −10.7654 23.5730i −0.506923 1.11001i
\(452\) 0 0
\(453\) 1.45687 + 0.427777i 0.0684500 + 0.0200987i
\(454\) 0 0
\(455\) −0.722388 + 1.58181i −0.0338661 + 0.0741564i
\(456\) 0 0
\(457\) 16.5228 + 10.6185i 0.772903 + 0.496714i 0.866671 0.498880i \(-0.166255\pi\)
−0.0937686 + 0.995594i \(0.529891\pi\)
\(458\) 0 0
\(459\) −6.65709 −0.310726
\(460\) 0 0
\(461\) −14.8017 −0.689383 −0.344692 0.938716i \(-0.612017\pi\)
−0.344692 + 0.938716i \(0.612017\pi\)
\(462\) 0 0
\(463\) 12.8377 + 8.25026i 0.596617 + 0.383422i 0.803817 0.594876i \(-0.202799\pi\)
−0.207201 + 0.978298i \(0.566435\pi\)
\(464\) 0 0
\(465\) −7.77008 + 17.0141i −0.360329 + 0.789010i
\(466\) 0 0
\(467\) −14.8229 4.35240i −0.685923 0.201405i −0.0798415 0.996808i \(-0.525441\pi\)
−0.606082 + 0.795402i \(0.707260\pi\)
\(468\) 0 0
\(469\) 0.112723 + 0.246829i 0.00520507 + 0.0113975i
\(470\) 0 0
\(471\) 4.31581 4.98071i 0.198862 0.229499i
\(472\) 0 0
\(473\) −34.5189 + 10.1357i −1.58718 + 0.466038i
\(474\) 0 0
\(475\) −12.8919 + 8.28514i −0.591522 + 0.380148i
\(476\) 0 0
\(477\) −0.693893 4.82613i −0.0317712 0.220973i
\(478\) 0 0
\(479\) −2.68993 + 18.7089i −0.122906 + 0.854832i 0.831330 + 0.555779i \(0.187580\pi\)
−0.954237 + 0.299053i \(0.903329\pi\)
\(480\) 0 0
\(481\) −22.2837 25.7168i −1.01605 1.17258i
\(482\) 0 0
\(483\) −0.292416 + 0.752888i −0.0133054 + 0.0342576i
\(484\) 0 0
\(485\) 23.3700 + 26.9704i 1.06118 + 1.22466i
\(486\) 0 0
\(487\) −1.46822 + 10.2117i −0.0665313 + 0.462735i 0.929135 + 0.369740i \(0.120553\pi\)
−0.995667 + 0.0929953i \(0.970356\pi\)
\(488\) 0 0
\(489\) −0.348765 2.42571i −0.0157717 0.109694i
\(490\) 0 0
\(491\) 5.85642 3.76369i 0.264296 0.169853i −0.401781 0.915736i \(-0.631609\pi\)
0.666077 + 0.745883i \(0.267972\pi\)
\(492\) 0 0
\(493\) −3.64012 + 1.06884i −0.163943 + 0.0481380i
\(494\) 0 0
\(495\) 9.37030 10.8139i 0.421164 0.486049i
\(496\) 0 0
\(497\) 0.664398 + 1.45483i 0.0298023 + 0.0652580i
\(498\) 0 0
\(499\) 0.979391 + 0.287575i 0.0438435 + 0.0128736i 0.303581 0.952806i \(-0.401818\pi\)
−0.259737 + 0.965679i \(0.583636\pi\)
\(500\) 0 0
\(501\) 4.28114 9.37440i 0.191267 0.418817i
\(502\) 0 0
\(503\) −12.1305 7.79581i −0.540873 0.347598i 0.241507 0.970399i \(-0.422358\pi\)
−0.782380 + 0.622801i \(0.785995\pi\)
\(504\) 0 0
\(505\) −19.5299 −0.869068
\(506\) 0 0
\(507\) 1.76024 0.0781750
\(508\) 0 0
\(509\) −21.0513 13.5289i −0.933084 0.599657i −0.0166583 0.999861i \(-0.505303\pi\)
−0.916426 + 0.400204i \(0.868939\pi\)
\(510\) 0 0
\(511\) −0.268037 + 0.586920i −0.0118573 + 0.0259638i
\(512\) 0 0
\(513\) 6.61368 + 1.94195i 0.292001 + 0.0857393i
\(514\) 0 0
\(515\) −4.78132 10.4696i −0.210690 0.461347i
\(516\) 0 0
\(517\) −7.90489 + 9.12273i −0.347657 + 0.401217i
\(518\) 0 0
\(519\) 2.89241 0.849289i 0.126963 0.0372797i
\(520\) 0 0
\(521\) 29.0057 18.6408i 1.27076 0.816670i 0.281045 0.959695i \(-0.409319\pi\)
0.989719 + 0.143024i \(0.0456827\pi\)
\(522\) 0 0
\(523\) 1.78837 + 12.4384i 0.0781998 + 0.543892i 0.990831 + 0.135108i \(0.0431380\pi\)
−0.912631 + 0.408784i \(0.865953\pi\)
\(524\) 0 0
\(525\) 0.0532862 0.370614i 0.00232560 0.0161749i
\(526\) 0 0
\(527\) −30.3396 35.0138i −1.32161 1.52522i
\(528\) 0 0
\(529\) −12.9511 + 19.0071i −0.563090 + 0.826396i
\(530\) 0 0
\(531\) −1.49373 1.72385i −0.0648223 0.0748089i
\(532\) 0 0
\(533\) −2.66138 + 18.5103i −0.115277 + 0.801771i
\(534\) 0 0
\(535\) −3.71456 25.8354i −0.160595 1.11696i
\(536\) 0 0
\(537\) −11.3672 + 7.30523i −0.490529 + 0.315244i
\(538\) 0 0
\(539\) −35.6135 + 10.4571i −1.53398 + 0.450418i
\(540\) 0 0
\(541\) 8.60529 9.93103i 0.369970 0.426969i −0.539985 0.841675i \(-0.681570\pi\)
0.909955 + 0.414706i \(0.136116\pi\)
\(542\) 0 0
\(543\) 5.77411 + 12.6435i 0.247791 + 0.542586i
\(544\) 0 0
\(545\) 22.8220 + 6.70115i 0.977588 + 0.287046i
\(546\) 0 0
\(547\) −14.5743 + 31.9134i −0.623154 + 1.36452i 0.290049 + 0.957012i \(0.406328\pi\)
−0.913203 + 0.407505i \(0.866399\pi\)
\(548\) 0 0
\(549\) −11.7447 7.54785i −0.501251 0.322135i
\(550\) 0 0
\(551\) 3.92818 0.167346
\(552\) 0 0
\(553\) −0.442233 −0.0188056
\(554\) 0 0
\(555\) 20.0256 + 12.8697i 0.850039 + 0.546287i
\(556\) 0 0
\(557\) −0.267339 + 0.585391i −0.0113275 + 0.0248038i −0.915211 0.402974i \(-0.867976\pi\)
0.903884 + 0.427778i \(0.140704\pi\)
\(558\) 0 0
\(559\) 24.9095 + 7.31410i 1.05356 + 0.309353i
\(560\) 0 0
\(561\) 14.7233 + 32.2395i 0.621617 + 1.36115i
\(562\) 0 0
\(563\) 7.62376 8.79829i 0.321303 0.370804i −0.572004 0.820251i \(-0.693834\pi\)
0.893307 + 0.449447i \(0.148379\pi\)
\(564\) 0 0
\(565\) −22.0364 + 6.47048i −0.927079 + 0.272215i
\(566\) 0 0
\(567\) −0.141678 + 0.0910509i −0.00594991 + 0.00382378i
\(568\) 0 0
\(569\) 5.06376 + 35.2193i 0.212284 + 1.47647i 0.765503 + 0.643432i \(0.222490\pi\)
−0.553219 + 0.833036i \(0.686601\pi\)
\(570\) 0 0
\(571\) −0.588588 + 4.09372i −0.0246316 + 0.171317i −0.998424 0.0561226i \(-0.982126\pi\)
0.973792 + 0.227439i \(0.0730353\pi\)
\(572\) 0 0
\(573\) −8.38095 9.67213i −0.350119 0.404059i
\(574\) 0 0
\(575\) 3.86024 9.93904i 0.160983 0.414486i
\(576\) 0 0
\(577\) 2.18302 + 2.51934i 0.0908803 + 0.104881i 0.799368 0.600842i \(-0.205168\pi\)
−0.708488 + 0.705723i \(0.750622\pi\)
\(578\) 0 0
\(579\) −2.29669 + 15.9738i −0.0954471 + 0.663849i
\(580\) 0 0
\(581\) −0.214979 1.49521i −0.00891883 0.0620318i
\(582\) 0 0
\(583\) −21.8377 + 14.0342i −0.904425 + 0.581239i
\(584\) 0 0
\(585\) −9.90729 + 2.90904i −0.409616 + 0.120274i
\(586\) 0 0
\(587\) −9.03818 + 10.4306i −0.373045 + 0.430517i −0.910968 0.412477i \(-0.864664\pi\)
0.537923 + 0.842994i \(0.319209\pi\)
\(588\) 0 0
\(589\) 19.9279 + 43.6359i 0.821113 + 1.79799i
\(590\) 0 0
\(591\) −12.6411 3.71175i −0.519984 0.152681i
\(592\) 0 0
\(593\) −15.0251 + 32.9004i −0.617006 + 1.35106i 0.300670 + 0.953728i \(0.402790\pi\)
−0.917677 + 0.397328i \(0.869938\pi\)
\(594\) 0 0
\(595\) 2.53485 + 1.62905i 0.103919 + 0.0667846i
\(596\) 0 0
\(597\) −9.25611 −0.378828
\(598\) 0 0
\(599\) 18.8219 0.769041 0.384520 0.923117i \(-0.374367\pi\)
0.384520 + 0.923117i \(0.374367\pi\)
\(600\) 0 0
\(601\) −37.3898 24.0289i −1.52516 0.980161i −0.990864 0.134864i \(-0.956940\pi\)
−0.534296 0.845297i \(-0.679423\pi\)
\(602\) 0 0
\(603\) −0.669326 + 1.46562i −0.0272571 + 0.0596846i
\(604\) 0 0
\(605\) −44.7282 13.1334i −1.81846 0.533948i
\(606\) 0 0
\(607\) −10.1913 22.3159i −0.413654 0.905775i −0.995701 0.0926204i \(-0.970476\pi\)
0.582048 0.813154i \(-0.302252\pi\)
\(608\) 0 0
\(609\) −0.0628513 + 0.0725342i −0.00254686 + 0.00293924i
\(610\) 0 0
\(611\) 8.35791 2.45410i 0.338125 0.0992824i
\(612\) 0 0
\(613\) −1.91550 + 1.23102i −0.0773665 + 0.0497204i −0.578752 0.815503i \(-0.696460\pi\)
0.501386 + 0.865224i \(0.332824\pi\)
\(614\) 0 0
\(615\) −1.86177 12.9489i −0.0750740 0.522151i
\(616\) 0 0
\(617\) 1.75141 12.1813i 0.0705091 0.490402i −0.923715 0.383080i \(-0.874863\pi\)
0.994224 0.107322i \(-0.0342275\pi\)
\(618\) 0 0
\(619\) −5.84291 6.74307i −0.234846 0.271027i 0.626078 0.779761i \(-0.284659\pi\)
−0.860924 + 0.508734i \(0.830114\pi\)
\(620\) 0 0
\(621\) −4.51560 + 1.61534i −0.181205 + 0.0648213i
\(622\) 0 0
\(623\) 0.693312 + 0.800125i 0.0277770 + 0.0320563i
\(624\) 0 0
\(625\) 4.43644 30.8561i 0.177458 1.23424i
\(626\) 0 0
\(627\) −5.22264 36.3242i −0.208572 1.45065i
\(628\) 0 0
\(629\) −49.6025 + 31.8776i −1.97778 + 1.27104i
\(630\) 0 0
\(631\) 31.7431 9.32063i 1.26367 0.371048i 0.419814 0.907610i \(-0.362095\pi\)
0.843861 + 0.536562i \(0.180277\pi\)
\(632\) 0 0
\(633\) 9.68278 11.1745i 0.384856 0.444147i
\(634\) 0 0
\(635\) −16.9323 37.0766i −0.671938 1.47134i
\(636\) 0 0
\(637\) 25.6994 + 7.54603i 1.01825 + 0.298985i
\(638\) 0 0
\(639\) −3.94505 + 8.63846i −0.156064 + 0.341732i
\(640\) 0 0
\(641\) 38.3241 + 24.6294i 1.51371 + 0.972802i 0.992877 + 0.119143i \(0.0380147\pi\)
0.520832 + 0.853659i \(0.325622\pi\)
\(642\) 0 0
\(643\) −6.72806 −0.265329 −0.132664 0.991161i \(-0.542353\pi\)
−0.132664 + 0.991161i \(0.542353\pi\)
\(644\) 0 0
\(645\) −18.1612 −0.715095
\(646\) 0 0
\(647\) −4.02439 2.58632i −0.158215 0.101679i 0.459138 0.888365i \(-0.348158\pi\)
−0.617353 + 0.786687i \(0.711795\pi\)
\(648\) 0 0
\(649\) −5.04479 + 11.0465i −0.198025 + 0.433615i
\(650\) 0 0
\(651\) −1.12459 0.330209i −0.0440761 0.0129419i
\(652\) 0 0
\(653\) 13.0075 + 28.4825i 0.509023 + 1.11460i 0.973430 + 0.228983i \(0.0735401\pi\)
−0.464407 + 0.885622i \(0.653733\pi\)
\(654\) 0 0
\(655\) 3.09696 3.57408i 0.121008 0.139651i
\(656\) 0 0
\(657\) −3.67603 + 1.07938i −0.143416 + 0.0421107i
\(658\) 0 0
\(659\) −6.56570 + 4.21952i −0.255763 + 0.164369i −0.662239 0.749292i \(-0.730394\pi\)
0.406476 + 0.913661i \(0.366757\pi\)
\(660\) 0 0
\(661\) −6.64686 46.2299i −0.258533 1.79814i −0.543300 0.839539i \(-0.682825\pi\)
0.284767 0.958597i \(-0.408084\pi\)
\(662\) 0 0
\(663\) 3.63983 25.3156i 0.141359 0.983176i
\(664\) 0 0
\(665\) −2.04311 2.35788i −0.0792285 0.0914346i
\(666\) 0 0
\(667\) −2.20980 + 1.60828i −0.0855637 + 0.0622729i
\(668\) 0 0
\(669\) −9.79956 11.3093i −0.378873 0.437243i
\(670\) 0 0
\(671\) −10.5780 + 73.5715i −0.408358 + 2.84019i
\(672\) 0 0
\(673\) 6.23439 + 43.3611i 0.240318 + 1.67145i 0.650547 + 0.759466i \(0.274540\pi\)
−0.410229 + 0.911982i \(0.634551\pi\)
\(674\) 0 0
\(675\) 1.87032 1.20198i 0.0719887 0.0462643i
\(676\) 0 0
\(677\) −24.9943 + 7.33900i −0.960610 + 0.282061i −0.724198 0.689592i \(-0.757790\pi\)
−0.236412 + 0.971653i \(0.575972\pi\)
\(678\) 0 0
\(679\) −1.46443 + 1.69004i −0.0561996 + 0.0648578i
\(680\) 0 0
\(681\) 8.01864 + 17.5584i 0.307275 + 0.672838i
\(682\) 0 0
\(683\) −11.5806 3.40037i −0.443119 0.130111i 0.0525591 0.998618i \(-0.483262\pi\)
−0.495678 + 0.868506i \(0.665080\pi\)
\(684\) 0 0
\(685\) 16.3971 35.9046i 0.626500 1.37184i
\(686\) 0 0
\(687\) −22.4145 14.4049i −0.855168 0.549583i
\(688\) 0 0
\(689\) 18.7322 0.713640
\(690\) 0 0
\(691\) −41.2368 −1.56872 −0.784360 0.620305i \(-0.787009\pi\)
−0.784360 + 0.620305i \(0.787009\pi\)
\(692\) 0 0
\(693\) 0.754293 + 0.484755i 0.0286532 + 0.0184143i
\(694\) 0 0
\(695\) 24.9564 54.6468i 0.946649 2.07287i
\(696\) 0 0
\(697\) 31.0911 + 9.12918i 1.17766 + 0.345792i
\(698\) 0 0
\(699\) −6.00196 13.1425i −0.227015 0.497093i
\(700\) 0 0
\(701\) 10.4429 12.0517i 0.394422 0.455187i −0.523454 0.852054i \(-0.675357\pi\)
0.917876 + 0.396867i \(0.129902\pi\)
\(702\) 0 0
\(703\) 58.5781 17.2001i 2.20932 0.648713i
\(704\) 0 0
\(705\) −5.12628 + 3.29446i −0.193067 + 0.124077i
\(706\) 0 0
\(707\) −0.174164 1.21134i −0.00655011 0.0455570i
\(708\) 0 0
\(709\) 0.774067 5.38375i 0.0290707 0.202191i −0.970110 0.242666i \(-0.921978\pi\)
0.999181 + 0.0404751i \(0.0128871\pi\)
\(710\) 0 0
\(711\) −1.71959 1.98451i −0.0644896 0.0744249i
\(712\) 0 0
\(713\) −29.0759 16.3885i −1.08890 0.613754i
\(714\) 0 0
\(715\) 35.9998 + 41.5460i 1.34632 + 1.55373i
\(716\) 0 0
\(717\) 3.43143 23.8661i 0.128149 0.891297i
\(718\) 0 0
\(719\) 0.797299 + 5.54533i 0.0297342 + 0.206806i 0.999273 0.0381331i \(-0.0121411\pi\)
−0.969538 + 0.244939i \(0.921232\pi\)
\(720\) 0 0
\(721\) 0.606738 0.389927i 0.0225961 0.0145216i
\(722\) 0 0
\(723\) 10.7583 3.15892i 0.400105 0.117481i
\(724\) 0 0
\(725\) 0.829713 0.957540i 0.0308148 0.0355622i
\(726\) 0 0
\(727\) 16.3042 + 35.7013i 0.604691 + 1.32409i 0.926147 + 0.377164i \(0.123101\pi\)
−0.321456 + 0.946925i \(0.604172\pi\)
\(728\) 0 0
\(729\) −0.959493 0.281733i −0.0355368 0.0104345i
\(730\) 0 0
\(731\) 18.6872 40.9192i 0.691170 1.51345i
\(732\) 0 0
\(733\) −25.4156 16.3336i −0.938748 0.603297i −0.0207088 0.999786i \(-0.506592\pi\)
−0.918040 + 0.396489i \(0.870229\pi\)
\(734\) 0 0
\(735\) −18.7371 −0.691127
\(736\) 0 0
\(737\) 8.57814 0.315980
\(738\) 0 0
\(739\) −11.4468 7.35638i −0.421076 0.270609i 0.312898 0.949787i \(-0.398700\pi\)
−0.733974 + 0.679178i \(0.762337\pi\)
\(740\) 0 0
\(741\) −11.0010 + 24.0887i −0.404130 + 0.884922i
\(742\) 0 0
\(743\) 3.15632 + 0.926778i 0.115794 + 0.0340002i 0.339116 0.940744i \(-0.389872\pi\)
−0.223322 + 0.974745i \(0.571690\pi\)
\(744\) 0 0
\(745\) −7.66251 16.7786i −0.280733 0.614719i
\(746\) 0 0
\(747\) 5.87380 6.77873i 0.214911 0.248021i
\(748\) 0 0
\(749\) 1.56931 0.460790i 0.0573413 0.0168369i
\(750\) 0 0
\(751\) −17.2369 + 11.0775i −0.628984 + 0.404223i −0.815933 0.578146i \(-0.803776\pi\)
0.186949 + 0.982370i \(0.440140\pi\)
\(752\) 0 0
\(753\) 4.08067 + 28.3817i 0.148708 + 1.03429i
\(754\) 0 0
\(755\) 0.580761 4.03928i 0.0211360 0.147004i
\(756\) 0 0
\(757\) 31.2769 + 36.0955i 1.13678 + 1.31191i 0.943727 + 0.330724i \(0.107293\pi\)
0.193052 + 0.981189i \(0.438162\pi\)
\(758\) 0 0
\(759\) 17.8099 + 18.2959i 0.646459 + 0.664100i
\(760\) 0 0
\(761\) −9.27655 10.7057i −0.336275 0.388081i 0.562277 0.826949i \(-0.309925\pi\)
−0.898552 + 0.438867i \(0.855380\pi\)
\(762\) 0 0
\(763\) −0.212115 + 1.47529i −0.00767908 + 0.0534092i
\(764\) 0 0
\(765\) 2.54625 + 17.7096i 0.0920599 + 0.640291i
\(766\) 0 0
\(767\) 7.37219 4.73782i 0.266194 0.171073i
\(768\) 0 0
\(769\) 43.1487 12.6696i 1.55598 0.456878i 0.613101 0.790004i \(-0.289922\pi\)
0.942882 + 0.333126i \(0.108104\pi\)
\(770\) 0 0
\(771\) −12.1927 + 14.0712i −0.439110 + 0.506761i
\(772\) 0 0
\(773\) 12.9716 + 28.4038i 0.466555 + 1.02161i 0.985944 + 0.167075i \(0.0534322\pi\)
−0.519389 + 0.854538i \(0.673841\pi\)
\(774\) 0 0
\(775\) 14.8460 + 4.35916i 0.533282 + 0.156586i
\(776\) 0 0
\(777\) −0.619654 + 1.35685i −0.0222300 + 0.0486768i
\(778\) 0 0
\(779\) −28.2253 18.1393i −1.01128 0.649908i
\(780\) 0 0
\(781\) 50.5602 1.80919
\(782\) 0 0
\(783\) −0.569888 −0.0203661
\(784\) 0 0
\(785\) −14.9007 9.57611i −0.531829 0.341786i
\(786\) 0 0
\(787\) −2.90152 + 6.35343i −0.103428 + 0.226475i −0.954270 0.298946i \(-0.903365\pi\)
0.850842 + 0.525421i \(0.176092\pi\)
\(788\) 0 0
\(789\) 13.7309 + 4.03175i 0.488832 + 0.143534i
\(790\) 0 0
\(791\) −0.597847 1.30910i −0.0212570 0.0465463i
\(792\) 0 0
\(793\) 35.1245 40.5358i 1.24731 1.43947i
\(794\) 0