Properties

Label 819.2.y.h.811.2
Level $819$
Weight $2$
Character 819.811
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.y (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \( x^{12} + 35x^{8} + 295x^{4} + 169 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 811.2
Root \(-1.33026 + 1.33026i\) of defining polynomial
Character \(\chi\) \(=\) 819.811
Dual form 819.2.y.h.307.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.854638 + 0.854638i) q^{2} +0.539189i q^{4} +(0.612999 + 0.612999i) q^{5} +(0.0148122 - 2.64571i) q^{7} +(-2.17009 - 2.17009i) q^{8} +O(q^{10})\) \(q+(-0.854638 + 0.854638i) q^{2} +0.539189i q^{4} +(0.612999 + 0.612999i) q^{5} +(0.0148122 - 2.64571i) q^{7} +(-2.17009 - 2.17009i) q^{8} -1.04778 q^{10} +(1.85464 + 1.85464i) q^{11} +(-0.104263 - 3.60404i) q^{13} +(2.24846 + 2.27378i) q^{14} +2.63090 q^{16} +3.04726 q^{17} +(0.104263 + 0.104263i) q^{19} +(-0.330522 + 0.330522i) q^{20} -3.17009 q^{22} -6.51026i q^{23} -4.24846i q^{25} +(3.16926 + 2.99104i) q^{26} +(1.42654 + 0.00798659i) q^{28} +3.78765 q^{29} +(6.77330 + 6.77330i) q^{31} +(2.09171 - 2.09171i) q^{32} +(-2.60430 + 2.60430i) q^{34} +(1.63090 - 1.61274i) q^{35} +(-2.02472 - 2.02472i) q^{37} -0.178214 q^{38} -2.66052i q^{40} +(2.27378 + 2.27378i) q^{41} -3.18342i q^{43} +(-1.00000 + 1.00000i) q^{44} +(5.56391 + 5.56391i) q^{46} +(-5.21678 + 5.21678i) q^{47} +(-6.99956 - 0.0783777i) q^{49} +(3.63090 + 3.63090i) q^{50} +(1.94326 - 0.0562174i) q^{52} -3.43188 q^{53} +2.27378i q^{55} +(-5.77356 + 5.70928i) q^{56} +(-3.23707 + 3.23707i) q^{58} +(9.15135 - 9.15135i) q^{59} +9.20756i q^{61} -11.5774 q^{62} +8.83710i q^{64} +(2.14536 - 2.27319i) q^{65} +(-1.04945 + 1.04945i) q^{67} +1.64305i q^{68} +(-0.0155200 + 2.77213i) q^{70} +(4.10310 - 4.10310i) q^{71} +(6.92561 - 6.92561i) q^{73} +3.46081 q^{74} +(-0.0562174 + 0.0562174i) q^{76} +(4.93430 - 4.87936i) q^{77} +17.5958 q^{79} +(1.61274 + 1.61274i) q^{80} -3.88652 q^{82} +(10.5474 + 10.5474i) q^{83} +(1.86797 + 1.86797i) q^{85} +(2.72067 + 2.72067i) q^{86} -8.04945i q^{88} +(-3.39552 + 3.39552i) q^{89} +(-9.53680 + 0.222465i) q^{91} +3.51026 q^{92} -8.91692i q^{94} +0.127826i q^{95} +(4.44330 + 4.44330i) q^{97} +(6.04907 - 5.91510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8} + 8 q^{11} - 8 q^{14} + 16 q^{16} - 16 q^{22} - 20 q^{28} + 4 q^{29} + 16 q^{32} + 4 q^{35} + 12 q^{37} - 12 q^{44} + 24 q^{46} + 28 q^{50} + 12 q^{53} - 44 q^{58} + 40 q^{65} + 60 q^{67} + 4 q^{70} + 48 q^{74} - 4 q^{79} + 12 q^{85} - 36 q^{86} - 32 q^{91} - 24 q^{92} + 28 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.854638 + 0.854638i −0.604320 + 0.604320i −0.941456 0.337136i \(-0.890542\pi\)
0.337136 + 0.941456i \(0.390542\pi\)
\(3\) 0 0
\(4\) 0.539189i 0.269594i
\(5\) 0.612999 + 0.612999i 0.274142 + 0.274142i 0.830765 0.556623i \(-0.187903\pi\)
−0.556623 + 0.830765i \(0.687903\pi\)
\(6\) 0 0
\(7\) 0.0148122 2.64571i 0.00559850 0.999984i
\(8\) −2.17009 2.17009i −0.767241 0.767241i
\(9\) 0 0
\(10\) −1.04778 −0.331338
\(11\) 1.85464 + 1.85464i 0.559194 + 0.559194i 0.929078 0.369884i \(-0.120602\pi\)
−0.369884 + 0.929078i \(0.620602\pi\)
\(12\) 0 0
\(13\) −0.104263 3.60404i −0.0289173 0.999582i
\(14\) 2.24846 + 2.27378i 0.600927 + 0.607694i
\(15\) 0 0
\(16\) 2.63090 0.657724
\(17\) 3.04726 0.739070 0.369535 0.929217i \(-0.379517\pi\)
0.369535 + 0.929217i \(0.379517\pi\)
\(18\) 0 0
\(19\) 0.104263 + 0.104263i 0.0239195 + 0.0239195i 0.718965 0.695046i \(-0.244616\pi\)
−0.695046 + 0.718965i \(0.744616\pi\)
\(20\) −0.330522 + 0.330522i −0.0739070 + 0.0739070i
\(21\) 0 0
\(22\) −3.17009 −0.675865
\(23\) 6.51026i 1.35748i −0.734377 0.678741i \(-0.762526\pi\)
0.734377 0.678741i \(-0.237474\pi\)
\(24\) 0 0
\(25\) 4.24846i 0.849693i
\(26\) 3.16926 + 2.99104i 0.621543 + 0.586592i
\(27\) 0 0
\(28\) 1.42654 + 0.00798659i 0.269590 + 0.00150932i
\(29\) 3.78765 0.703350 0.351675 0.936122i \(-0.385612\pi\)
0.351675 + 0.936122i \(0.385612\pi\)
\(30\) 0 0
\(31\) 6.77330 + 6.77330i 1.21652 + 1.21652i 0.968842 + 0.247679i \(0.0796677\pi\)
0.247679 + 0.968842i \(0.420332\pi\)
\(32\) 2.09171 2.09171i 0.369765 0.369765i
\(33\) 0 0
\(34\) −2.60430 + 2.60430i −0.446635 + 0.446635i
\(35\) 1.63090 1.61274i 0.275672 0.272602i
\(36\) 0 0
\(37\) −2.02472 2.02472i −0.332863 0.332863i 0.520810 0.853673i \(-0.325630\pi\)
−0.853673 + 0.520810i \(0.825630\pi\)
\(38\) −0.178214 −0.0289101
\(39\) 0 0
\(40\) 2.66052i 0.420665i
\(41\) 2.27378 + 2.27378i 0.355105 + 0.355105i 0.862005 0.506900i \(-0.169209\pi\)
−0.506900 + 0.862005i \(0.669209\pi\)
\(42\) 0 0
\(43\) 3.18342i 0.485467i −0.970093 0.242733i \(-0.921956\pi\)
0.970093 0.242733i \(-0.0780440\pi\)
\(44\) −1.00000 + 1.00000i −0.150756 + 0.150756i
\(45\) 0 0
\(46\) 5.56391 + 5.56391i 0.820354 + 0.820354i
\(47\) −5.21678 + 5.21678i −0.760946 + 0.760946i −0.976493 0.215548i \(-0.930846\pi\)
0.215548 + 0.976493i \(0.430846\pi\)
\(48\) 0 0
\(49\) −6.99956 0.0783777i −0.999937 0.0111968i
\(50\) 3.63090 + 3.63090i 0.513486 + 0.513486i
\(51\) 0 0
\(52\) 1.94326 0.0562174i 0.269482 0.00779595i
\(53\) −3.43188 −0.471405 −0.235703 0.971825i \(-0.575739\pi\)
−0.235703 + 0.971825i \(0.575739\pi\)
\(54\) 0 0
\(55\) 2.27378i 0.306597i
\(56\) −5.77356 + 5.70928i −0.771525 + 0.762934i
\(57\) 0 0
\(58\) −3.23707 + 3.23707i −0.425048 + 0.425048i
\(59\) 9.15135 9.15135i 1.19140 1.19140i 0.214731 0.976673i \(-0.431113\pi\)
0.976673 0.214731i \(-0.0688873\pi\)
\(60\) 0 0
\(61\) 9.20756i 1.17891i 0.807802 + 0.589454i \(0.200657\pi\)
−0.807802 + 0.589454i \(0.799343\pi\)
\(62\) −11.5774 −1.47034
\(63\) 0 0
\(64\) 8.83710i 1.10464i
\(65\) 2.14536 2.27319i 0.266099 0.281954i
\(66\) 0 0
\(67\) −1.04945 + 1.04945i −0.128211 + 0.128211i −0.768300 0.640090i \(-0.778897\pi\)
0.640090 + 0.768300i \(0.278897\pi\)
\(68\) 1.64305i 0.199249i
\(69\) 0 0
\(70\) −0.0155200 + 2.77213i −0.00185500 + 0.331333i
\(71\) 4.10310 4.10310i 0.486949 0.486949i −0.420393 0.907342i \(-0.638108\pi\)
0.907342 + 0.420393i \(0.138108\pi\)
\(72\) 0 0
\(73\) 6.92561 6.92561i 0.810581 0.810581i −0.174140 0.984721i \(-0.555714\pi\)
0.984721 + 0.174140i \(0.0557144\pi\)
\(74\) 3.46081 0.402311
\(75\) 0 0
\(76\) −0.0562174 + 0.0562174i −0.00644858 + 0.00644858i
\(77\) 4.93430 4.87936i 0.562316 0.556055i
\(78\) 0 0
\(79\) 17.5958 1.97968 0.989842 0.142168i \(-0.0454074\pi\)
0.989842 + 0.142168i \(0.0454074\pi\)
\(80\) 1.61274 + 1.61274i 0.180310 + 0.180310i
\(81\) 0 0
\(82\) −3.88652 −0.429194
\(83\) 10.5474 + 10.5474i 1.15773 + 1.15773i 0.984963 + 0.172763i \(0.0552694\pi\)
0.172763 + 0.984963i \(0.444731\pi\)
\(84\) 0 0
\(85\) 1.86797 + 1.86797i 0.202610 + 0.202610i
\(86\) 2.72067 + 2.72067i 0.293377 + 0.293377i
\(87\) 0 0
\(88\) 8.04945i 0.858074i
\(89\) −3.39552 + 3.39552i −0.359924 + 0.359924i −0.863785 0.503861i \(-0.831912\pi\)
0.503861 + 0.863785i \(0.331912\pi\)
\(90\) 0 0
\(91\) −9.53680 + 0.222465i −0.999728 + 0.0233207i
\(92\) 3.51026 0.365970
\(93\) 0 0
\(94\) 8.91692i 0.919710i
\(95\) 0.127826i 0.0131147i
\(96\) 0 0
\(97\) 4.44330 + 4.44330i 0.451149 + 0.451149i 0.895736 0.444587i \(-0.146649\pi\)
−0.444587 + 0.895736i \(0.646649\pi\)
\(98\) 6.04907 5.91510i 0.611049 0.597516i
\(99\) 0 0
\(100\) 2.29072 0.229072
\(101\) −1.16022 −0.115446 −0.0577231 0.998333i \(-0.518384\pi\)
−0.0577231 + 0.998333i \(0.518384\pi\)
\(102\) 0 0
\(103\) −5.32104 −0.524298 −0.262149 0.965027i \(-0.584431\pi\)
−0.262149 + 0.965027i \(0.584431\pi\)
\(104\) −7.59483 + 8.04735i −0.744734 + 0.789107i
\(105\) 0 0
\(106\) 2.93302 2.93302i 0.284880 0.284880i
\(107\) −10.2485 −0.990756 −0.495378 0.868677i \(-0.664971\pi\)
−0.495378 + 0.868677i \(0.664971\pi\)
\(108\) 0 0
\(109\) −5.85464 + 5.85464i −0.560773 + 0.560773i −0.929527 0.368754i \(-0.879784\pi\)
0.368754 + 0.929527i \(0.379784\pi\)
\(110\) −1.94326 1.94326i −0.185283 0.185283i
\(111\) 0 0
\(112\) 0.0389695 6.96059i 0.00368227 0.657714i
\(113\) −5.74539 −0.540481 −0.270241 0.962793i \(-0.587103\pi\)
−0.270241 + 0.962793i \(0.587103\pi\)
\(114\) 0 0
\(115\) 3.99078 3.99078i 0.372142 0.372142i
\(116\) 2.04226i 0.189619i
\(117\) 0 0
\(118\) 15.6422i 1.43998i
\(119\) 0.0451368 8.06217i 0.00413768 0.739058i
\(120\) 0 0
\(121\) 4.12064i 0.374603i
\(122\) −7.86913 7.86913i −0.712438 0.712438i
\(123\) 0 0
\(124\) −3.65209 + 3.65209i −0.327967 + 0.327967i
\(125\) 5.66930 5.66930i 0.507078 0.507078i
\(126\) 0 0
\(127\) 7.37629i 0.654540i −0.944931 0.327270i \(-0.893871\pi\)
0.944931 0.327270i \(-0.106129\pi\)
\(128\) −3.36910 3.36910i −0.297789 0.297789i
\(129\) 0 0
\(130\) 0.109245 + 3.77626i 0.00958142 + 0.331200i
\(131\) 11.9642i 1.04532i −0.852543 0.522658i \(-0.824941\pi\)
0.852543 0.522658i \(-0.175059\pi\)
\(132\) 0 0
\(133\) 0.277394 0.274305i 0.0240531 0.0237853i
\(134\) 1.79380i 0.154960i
\(135\) 0 0
\(136\) −6.61282 6.61282i −0.567045 0.567045i
\(137\) −1.88357 1.88357i −0.160924 0.160924i 0.622052 0.782976i \(-0.286299\pi\)
−0.782976 + 0.622052i \(0.786299\pi\)
\(138\) 0 0
\(139\) 6.36883i 0.540197i −0.962833 0.270098i \(-0.912944\pi\)
0.962833 0.270098i \(-0.0870563\pi\)
\(140\) 0.869570 + 0.879362i 0.0734921 + 0.0743196i
\(141\) 0 0
\(142\) 7.01333i 0.588546i
\(143\) 6.49082 6.87756i 0.542790 0.575131i
\(144\) 0 0
\(145\) 2.32183 + 2.32183i 0.192817 + 0.192817i
\(146\) 11.8378i 0.979701i
\(147\) 0 0
\(148\) 1.09171 1.09171i 0.0897379 0.0897379i
\(149\) −13.3360 + 13.3360i −1.09253 + 1.09253i −0.0972667 + 0.995258i \(0.531010\pi\)
−0.995258 + 0.0972667i \(0.968990\pi\)
\(150\) 0 0
\(151\) 7.64229 + 7.64229i 0.621921 + 0.621921i 0.946022 0.324102i \(-0.105062\pi\)
−0.324102 + 0.946022i \(0.605062\pi\)
\(152\) 0.452519i 0.0367041i
\(153\) 0 0
\(154\) −0.0469561 + 8.38713i −0.00378383 + 0.675854i
\(155\) 8.30406i 0.666998i
\(156\) 0 0
\(157\) 21.0290i 1.67830i −0.543903 0.839148i \(-0.683054\pi\)
0.543903 0.839148i \(-0.316946\pi\)
\(158\) −15.0381 + 15.0381i −1.19636 + 1.19636i
\(159\) 0 0
\(160\) 2.56443 0.202736
\(161\) −17.2243 0.0964315i −1.35746 0.00759987i
\(162\) 0 0
\(163\) −7.03612 7.03612i −0.551111 0.551111i 0.375650 0.926762i \(-0.377419\pi\)
−0.926762 + 0.375650i \(0.877419\pi\)
\(164\) −1.22600 + 1.22600i −0.0957344 + 0.0957344i
\(165\) 0 0
\(166\) −18.0284 −1.39927
\(167\) −12.0684 + 12.0684i −0.933884 + 0.933884i −0.997946 0.0640620i \(-0.979594\pi\)
0.0640620 + 0.997946i \(0.479594\pi\)
\(168\) 0 0
\(169\) −12.9783 + 0.751536i −0.998328 + 0.0578104i
\(170\) −3.19287 −0.244882
\(171\) 0 0
\(172\) 1.71646 0.130879
\(173\) 7.48239 0.568876 0.284438 0.958694i \(-0.408193\pi\)
0.284438 + 0.958694i \(0.408193\pi\)
\(174\) 0 0
\(175\) −11.2402 0.0629292i −0.849680 0.00475700i
\(176\) 4.87936 + 4.87936i 0.367796 + 0.367796i
\(177\) 0 0
\(178\) 5.80387i 0.435019i
\(179\) 22.7009i 1.69674i −0.529402 0.848371i \(-0.677584\pi\)
0.529402 0.848371i \(-0.322416\pi\)
\(180\) 0 0
\(181\) −1.91735 −0.142516 −0.0712579 0.997458i \(-0.522701\pi\)
−0.0712579 + 0.997458i \(0.522701\pi\)
\(182\) 7.96038 8.34063i 0.590063 0.618249i
\(183\) 0 0
\(184\) −14.1278 + 14.1278i −1.04152 + 1.04152i
\(185\) 2.48231i 0.182503i
\(186\) 0 0
\(187\) 5.65157 + 5.65157i 0.413283 + 0.413283i
\(188\) −2.81283 2.81283i −0.205147 0.205147i
\(189\) 0 0
\(190\) −0.109245 0.109245i −0.00792546 0.00792546i
\(191\) 10.0072 0.724095 0.362047 0.932160i \(-0.382078\pi\)
0.362047 + 0.932160i \(0.382078\pi\)
\(192\) 0 0
\(193\) −10.2351 10.2351i −0.736741 0.736741i 0.235205 0.971946i \(-0.424424\pi\)
−0.971946 + 0.235205i \(0.924424\pi\)
\(194\) −7.59483 −0.545277
\(195\) 0 0
\(196\) 0.0422604 3.77409i 0.00301860 0.269578i
\(197\) −15.2690 + 15.2690i −1.08787 + 1.08787i −0.0921223 + 0.995748i \(0.529365\pi\)
−0.995748 + 0.0921223i \(0.970635\pi\)
\(198\) 0 0
\(199\) 22.4635 1.59240 0.796198 0.605036i \(-0.206841\pi\)
0.796198 + 0.605036i \(0.206841\pi\)
\(200\) −9.21953 + 9.21953i −0.651920 + 0.651920i
\(201\) 0 0
\(202\) 0.991567 0.991567i 0.0697664 0.0697664i
\(203\) 0.0561036 10.0210i 0.00393770 0.703339i
\(204\) 0 0
\(205\) 2.78765i 0.194698i
\(206\) 4.54756 4.54756i 0.316844 0.316844i
\(207\) 0 0
\(208\) −0.274305 9.48187i −0.0190196 0.657449i
\(209\) 0.386740i 0.0267513i
\(210\) 0 0
\(211\) −18.8504 −1.29772 −0.648859 0.760909i \(-0.724753\pi\)
−0.648859 + 0.760909i \(0.724753\pi\)
\(212\) 1.85043i 0.127088i
\(213\) 0 0
\(214\) 8.75872 8.75872i 0.598734 0.598734i
\(215\) 1.95143 1.95143i 0.133087 0.133087i
\(216\) 0 0
\(217\) 18.0205 17.8199i 1.22331 1.20969i
\(218\) 10.0072i 0.677772i
\(219\) 0 0
\(220\) −1.22600 −0.0826568
\(221\) −0.317716 10.9825i −0.0213719 0.738760i
\(222\) 0 0
\(223\) 4.32131 + 4.32131i 0.289376 + 0.289376i 0.836833 0.547457i \(-0.184404\pi\)
−0.547457 + 0.836833i \(0.684404\pi\)
\(224\) −5.50307 5.56504i −0.367689 0.371830i
\(225\) 0 0
\(226\) 4.91023 4.91023i 0.326624 0.326624i
\(227\) 4.69031 + 4.69031i 0.311307 + 0.311307i 0.845416 0.534109i \(-0.179353\pi\)
−0.534109 + 0.845416i \(0.679353\pi\)
\(228\) 0 0
\(229\) −0.264743 + 0.264743i −0.0174947 + 0.0174947i −0.715800 0.698305i \(-0.753938\pi\)
0.698305 + 0.715800i \(0.253938\pi\)
\(230\) 6.82135i 0.449786i
\(231\) 0 0
\(232\) −8.21953 8.21953i −0.539639 0.539639i
\(233\) 6.16290i 0.403745i −0.979412 0.201872i \(-0.935297\pi\)
0.979412 0.201872i \(-0.0647026\pi\)
\(234\) 0 0
\(235\) −6.39576 −0.417214
\(236\) 4.93430 + 4.93430i 0.321196 + 0.321196i
\(237\) 0 0
\(238\) 6.85166 + 6.92881i 0.444127 + 0.449128i
\(239\) 5.63090 5.63090i 0.364232 0.364232i −0.501136 0.865369i \(-0.667084\pi\)
0.865369 + 0.501136i \(0.167084\pi\)
\(240\) 0 0
\(241\) 1.11217 1.11217i 0.0716414 0.0716414i −0.670378 0.742020i \(-0.733868\pi\)
0.742020 + 0.670378i \(0.233868\pi\)
\(242\) 3.52165 + 3.52165i 0.226380 + 0.226380i
\(243\) 0 0
\(244\) −4.96462 −0.317827
\(245\) −4.24268 4.33877i −0.271055 0.277194i
\(246\) 0 0
\(247\) 0.364897 0.386639i 0.0232178 0.0246012i
\(248\) 29.3973i 1.86673i
\(249\) 0 0
\(250\) 9.69040i 0.612874i
\(251\) −12.1069 −0.764182 −0.382091 0.924125i \(-0.624796\pi\)
−0.382091 + 0.924125i \(0.624796\pi\)
\(252\) 0 0
\(253\) 12.0742 12.0742i 0.759097 0.759097i
\(254\) 6.30406 + 6.30406i 0.395552 + 0.395552i
\(255\) 0 0
\(256\) −11.9155 −0.744717
\(257\) −17.5759 −1.09635 −0.548176 0.836363i \(-0.684678\pi\)
−0.548176 + 0.836363i \(0.684678\pi\)
\(258\) 0 0
\(259\) −5.38682 + 5.32684i −0.334721 + 0.330994i
\(260\) 1.22568 + 1.15676i 0.0760133 + 0.0717389i
\(261\) 0 0
\(262\) 10.2250 + 10.2250i 0.631705 + 0.631705i
\(263\) 14.5259 0.895703 0.447851 0.894108i \(-0.352189\pi\)
0.447851 + 0.894108i \(0.352189\pi\)
\(264\) 0 0
\(265\) −2.10374 2.10374i −0.129232 0.129232i
\(266\) −0.00263975 + 0.471502i −0.000161853 + 0.0289097i
\(267\) 0 0
\(268\) −0.565851 0.565851i −0.0345648 0.0345648i
\(269\) 23.4152i 1.42765i −0.700324 0.713825i \(-0.746961\pi\)
0.700324 0.713825i \(-0.253039\pi\)
\(270\) 0 0
\(271\) 2.41653 2.41653i 0.146794 0.146794i −0.629890 0.776684i \(-0.716900\pi\)
0.776684 + 0.629890i \(0.216900\pi\)
\(272\) 8.01703 0.486104
\(273\) 0 0
\(274\) 3.21953 0.194499
\(275\) 7.87936 7.87936i 0.475143 0.475143i
\(276\) 0 0
\(277\) 29.0722i 1.74678i 0.487020 + 0.873391i \(0.338084\pi\)
−0.487020 + 0.873391i \(0.661916\pi\)
\(278\) 5.44304 + 5.44304i 0.326452 + 0.326452i
\(279\) 0 0
\(280\) −7.03897 0.0394083i −0.420659 0.00235509i
\(281\) −9.68455 9.68455i −0.577732 0.577732i 0.356546 0.934278i \(-0.383954\pi\)
−0.934278 + 0.356546i \(0.883954\pi\)
\(282\) 0 0
\(283\) −4.30357 −0.255821 −0.127910 0.991786i \(-0.540827\pi\)
−0.127910 + 0.991786i \(0.540827\pi\)
\(284\) 2.21235 + 2.21235i 0.131279 + 0.131279i
\(285\) 0 0
\(286\) 0.330522 + 11.4251i 0.0195442 + 0.675582i
\(287\) 6.04945 5.98209i 0.357088 0.353112i
\(288\) 0 0
\(289\) −7.71420 −0.453776
\(290\) −3.96864 −0.233047
\(291\) 0 0
\(292\) 3.73421 + 3.73421i 0.218528 + 0.218528i
\(293\) −3.57373 + 3.57373i −0.208780 + 0.208780i −0.803749 0.594969i \(-0.797164\pi\)
0.594969 + 0.803749i \(0.297164\pi\)
\(294\) 0 0
\(295\) 11.2195 0.653227
\(296\) 8.78765i 0.510772i
\(297\) 0 0
\(298\) 22.7948i 1.32047i
\(299\) −23.4633 + 0.678778i −1.35692 + 0.0392548i
\(300\) 0 0
\(301\) −8.42240 0.0471535i −0.485459 0.00271788i
\(302\) −13.0628 −0.751678
\(303\) 0 0
\(304\) 0.274305 + 0.274305i 0.0157325 + 0.0157325i
\(305\) −5.64423 + 5.64423i −0.323188 + 0.323188i
\(306\) 0 0
\(307\) −8.59457 + 8.59457i −0.490518 + 0.490518i −0.908469 0.417952i \(-0.862748\pi\)
0.417952 + 0.908469i \(0.362748\pi\)
\(308\) 2.63090 + 2.66052i 0.149909 + 0.151597i
\(309\) 0 0
\(310\) −7.09696 7.09696i −0.403080 0.403080i
\(311\) 22.5405 1.27815 0.639077 0.769143i \(-0.279317\pi\)
0.639077 + 0.769143i \(0.279317\pi\)
\(312\) 0 0
\(313\) 4.30873i 0.243544i 0.992558 + 0.121772i \(0.0388576\pi\)
−0.992558 + 0.121772i \(0.961142\pi\)
\(314\) 17.9722 + 17.9722i 1.01423 + 1.01423i
\(315\) 0 0
\(316\) 9.48747i 0.533712i
\(317\) −3.97107 + 3.97107i −0.223038 + 0.223038i −0.809776 0.586739i \(-0.800412\pi\)
0.586739 + 0.809776i \(0.300412\pi\)
\(318\) 0 0
\(319\) 7.02472 + 7.02472i 0.393309 + 0.393309i
\(320\) −5.41714 + 5.41714i −0.302827 + 0.302827i
\(321\) 0 0
\(322\) 14.8029 14.6381i 0.824934 0.815749i
\(323\) 0.317716 + 0.317716i 0.0176782 + 0.0176782i
\(324\) 0 0
\(325\) −15.3116 + 0.442957i −0.849338 + 0.0245708i
\(326\) 12.0267 0.666095
\(327\) 0 0
\(328\) 9.86861i 0.544903i
\(329\) 13.7248 + 13.8794i 0.756674 + 0.765194i
\(330\) 0 0
\(331\) 1.70928 1.70928i 0.0939503 0.0939503i −0.658570 0.752520i \(-0.728838\pi\)
0.752520 + 0.658570i \(0.228838\pi\)
\(332\) −5.68703 + 5.68703i −0.312117 + 0.312117i
\(333\) 0 0
\(334\) 20.6283i 1.12873i
\(335\) −1.28662 −0.0702957
\(336\) 0 0
\(337\) 23.1327i 1.26012i 0.776546 + 0.630061i \(0.216970\pi\)
−0.776546 + 0.630061i \(0.783030\pi\)
\(338\) 10.4494 11.7340i 0.568373 0.638245i
\(339\) 0 0
\(340\) −1.00719 + 1.00719i −0.0546224 + 0.0546224i
\(341\) 25.1240i 1.36054i
\(342\) 0 0
\(343\) −0.311044 + 18.5176i −0.0167948 + 0.999859i
\(344\) −6.90829 + 6.90829i −0.372470 + 0.372470i
\(345\) 0 0
\(346\) −6.39473 + 6.39473i −0.343783 + 0.343783i
\(347\) 8.60424 0.461900 0.230950 0.972966i \(-0.425817\pi\)
0.230950 + 0.972966i \(0.425817\pi\)
\(348\) 0 0
\(349\) −19.0680 + 19.0680i −1.02069 + 1.02069i −0.0209053 + 0.999781i \(0.506655\pi\)
−0.999781 + 0.0209053i \(0.993345\pi\)
\(350\) 9.66008 9.55252i 0.516353 0.510604i
\(351\) 0 0
\(352\) 7.75872 0.413541
\(353\) 4.81231 + 4.81231i 0.256133 + 0.256133i 0.823479 0.567346i \(-0.192030\pi\)
−0.567346 + 0.823479i \(0.692030\pi\)
\(354\) 0 0
\(355\) 5.03040 0.266986
\(356\) −1.83083 1.83083i −0.0970336 0.0970336i
\(357\) 0 0
\(358\) 19.4010 + 19.4010i 1.02538 + 1.02538i
\(359\) 12.5506 + 12.5506i 0.662394 + 0.662394i 0.955944 0.293549i \(-0.0948365\pi\)
−0.293549 + 0.955944i \(0.594837\pi\)
\(360\) 0 0
\(361\) 18.9783i 0.998856i
\(362\) 1.63864 1.63864i 0.0861252 0.0861252i
\(363\) 0 0
\(364\) −0.119951 5.14214i −0.00628713 0.269521i
\(365\) 8.49079 0.444428
\(366\) 0 0
\(367\) 22.8806i 1.19436i 0.802109 + 0.597178i \(0.203711\pi\)
−0.802109 + 0.597178i \(0.796289\pi\)
\(368\) 17.1278i 0.892850i
\(369\) 0 0
\(370\) 2.12147 + 2.12147i 0.110290 + 0.110290i
\(371\) −0.0508338 + 9.07976i −0.00263916 + 0.471398i
\(372\) 0 0
\(373\) 10.5041 0.543883 0.271941 0.962314i \(-0.412334\pi\)
0.271941 + 0.962314i \(0.412334\pi\)
\(374\) −9.66008 −0.499511
\(375\) 0 0
\(376\) 22.6417 1.16766
\(377\) −0.394912 13.6509i −0.0203390 0.703055i
\(378\) 0 0
\(379\) 3.64229 3.64229i 0.187092 0.187092i −0.607346 0.794438i \(-0.707766\pi\)
0.794438 + 0.607346i \(0.207766\pi\)
\(380\) −0.0689224 −0.00353564
\(381\) 0 0
\(382\) −8.55252 + 8.55252i −0.437585 + 0.437585i
\(383\) 24.5591 + 24.5591i 1.25491 + 1.25491i 0.953492 + 0.301419i \(0.0974603\pi\)
0.301419 + 0.953492i \(0.402540\pi\)
\(384\) 0 0
\(385\) 6.01577 + 0.0336798i 0.306592 + 0.00171648i
\(386\) 17.4947 0.890455
\(387\) 0 0
\(388\) −2.39578 + 2.39578i −0.121627 + 0.121627i
\(389\) 6.48974i 0.329043i 0.986374 + 0.164521i \(0.0526080\pi\)
−0.986374 + 0.164521i \(0.947392\pi\)
\(390\) 0 0
\(391\) 19.8385i 1.00327i
\(392\) 15.0196 + 15.3597i 0.758603 + 0.775784i
\(393\) 0 0
\(394\) 26.0989i 1.31484i
\(395\) 10.7862 + 10.7862i 0.542714 + 0.542714i
\(396\) 0 0
\(397\) −6.89530 + 6.89530i −0.346065 + 0.346065i −0.858642 0.512576i \(-0.828691\pi\)
0.512576 + 0.858642i \(0.328691\pi\)
\(398\) −19.1982 + 19.1982i −0.962317 + 0.962317i
\(399\) 0 0
\(400\) 11.1773i 0.558864i
\(401\) −9.02279 9.02279i −0.450576 0.450576i 0.444969 0.895546i \(-0.353215\pi\)
−0.895546 + 0.444969i \(0.853215\pi\)
\(402\) 0 0
\(403\) 23.7051 25.1175i 1.18083 1.25119i
\(404\) 0.625577i 0.0311236i
\(405\) 0 0
\(406\) 8.51640 + 8.61230i 0.422662 + 0.427421i
\(407\) 7.51026i 0.372270i
\(408\) 0 0
\(409\) 2.86088 + 2.86088i 0.141461 + 0.141461i 0.774291 0.632830i \(-0.218107\pi\)
−0.632830 + 0.774291i \(0.718107\pi\)
\(410\) −2.38243 2.38243i −0.117660 0.117660i
\(411\) 0 0
\(412\) 2.86905i 0.141348i
\(413\) −24.0763 24.3474i −1.18472 1.19806i
\(414\) 0 0
\(415\) 12.9311i 0.634762i
\(416\) −7.75670 7.32052i −0.380303 0.358918i
\(417\) 0 0
\(418\) −0.330522 0.330522i −0.0161664 0.0161664i
\(419\) 35.4097i 1.72988i 0.501878 + 0.864939i \(0.332643\pi\)
−0.501878 + 0.864939i \(0.667357\pi\)
\(420\) 0 0
\(421\) 18.9307 18.9307i 0.922628 0.922628i −0.0745864 0.997215i \(-0.523764\pi\)
0.997215 + 0.0745864i \(0.0237636\pi\)
\(422\) 16.1103 16.1103i 0.784237 0.784237i
\(423\) 0 0
\(424\) 7.44748 + 7.44748i 0.361682 + 0.361682i
\(425\) 12.9462i 0.627982i
\(426\) 0 0
\(427\) 24.3605 + 0.136385i 1.17889 + 0.00660011i
\(428\) 5.52586i 0.267102i
\(429\) 0 0
\(430\) 3.33553i 0.160854i
\(431\) −12.6042 + 12.6042i −0.607125 + 0.607125i −0.942194 0.335069i \(-0.891240\pi\)
0.335069 + 0.942194i \(0.391240\pi\)
\(432\) 0 0
\(433\) 14.3392 0.689098 0.344549 0.938768i \(-0.388032\pi\)
0.344549 + 0.938768i \(0.388032\pi\)
\(434\) −0.171488 + 30.6305i −0.00823167 + 1.47031i
\(435\) 0 0
\(436\) −3.15676 3.15676i −0.151181 0.151181i
\(437\) 0.678778 0.678778i 0.0324704 0.0324704i
\(438\) 0 0
\(439\) −19.9812 −0.953651 −0.476826 0.878998i \(-0.658213\pi\)
−0.476826 + 0.878998i \(0.658213\pi\)
\(440\) 4.93430 4.93430i 0.235234 0.235234i
\(441\) 0 0
\(442\) 9.65756 + 9.11450i 0.459363 + 0.433532i
\(443\) 5.63809 0.267874 0.133937 0.990990i \(-0.457238\pi\)
0.133937 + 0.990990i \(0.457238\pi\)
\(444\) 0 0
\(445\) −4.16290 −0.197340
\(446\) −7.38630 −0.349751
\(447\) 0 0
\(448\) 23.3804 + 0.130897i 1.10462 + 0.00618431i
\(449\) 12.9060 + 12.9060i 0.609073 + 0.609073i 0.942704 0.333631i \(-0.108274\pi\)
−0.333631 + 0.942704i \(0.608274\pi\)
\(450\) 0 0
\(451\) 8.43409i 0.397146i
\(452\) 3.09785i 0.145711i
\(453\) 0 0
\(454\) −8.01703 −0.376258
\(455\) −5.98242 5.70968i −0.280460 0.267674i
\(456\) 0 0
\(457\) 6.96687 6.96687i 0.325896 0.325896i −0.525127 0.851024i \(-0.675982\pi\)
0.851024 + 0.525127i \(0.175982\pi\)
\(458\) 0.452519i 0.0211448i
\(459\) 0 0
\(460\) 2.15179 + 2.15179i 0.100328 + 0.100328i
\(461\) −7.20809 7.20809i −0.335714 0.335714i 0.519037 0.854752i \(-0.326291\pi\)
−0.854752 + 0.519037i \(0.826291\pi\)
\(462\) 0 0
\(463\) −4.06084 4.06084i −0.188723 0.188723i 0.606421 0.795144i \(-0.292605\pi\)
−0.795144 + 0.606421i \(0.792605\pi\)
\(464\) 9.96493 0.462610
\(465\) 0 0
\(466\) 5.26705 + 5.26705i 0.243991 + 0.243991i
\(467\) 17.3673 0.803665 0.401832 0.915713i \(-0.368373\pi\)
0.401832 + 0.915713i \(0.368373\pi\)
\(468\) 0 0
\(469\) 2.76099 + 2.79208i 0.127491 + 0.128926i
\(470\) 5.46606 5.46606i 0.252131 0.252131i
\(471\) 0 0
\(472\) −39.7184 −1.82819
\(473\) 5.90409 5.90409i 0.271470 0.271470i
\(474\) 0 0
\(475\) 0.442957 0.442957i 0.0203243 0.0203243i
\(476\) 4.34703 + 0.0243372i 0.199246 + 0.00111550i
\(477\) 0 0
\(478\) 9.62475i 0.440226i
\(479\) −9.88634 + 9.88634i −0.451719 + 0.451719i −0.895925 0.444206i \(-0.853486\pi\)
0.444206 + 0.895925i \(0.353486\pi\)
\(480\) 0 0
\(481\) −7.08609 + 7.50830i −0.323098 + 0.342349i
\(482\) 1.90101i 0.0865887i
\(483\) 0 0
\(484\) 2.22180 0.100991
\(485\) 5.44748i 0.247357i
\(486\) 0 0
\(487\) −12.6092 + 12.6092i −0.571375 + 0.571375i −0.932513 0.361137i \(-0.882389\pi\)
0.361137 + 0.932513i \(0.382389\pi\)
\(488\) 19.9812 19.9812i 0.904507 0.904507i
\(489\) 0 0
\(490\) 7.33403 + 0.0821230i 0.331318 + 0.00370994i
\(491\) 1.72487i 0.0778425i 0.999242 + 0.0389212i \(0.0123921\pi\)
−0.999242 + 0.0389212i \(0.987608\pi\)
\(492\) 0 0
\(493\) 11.5420 0.519824
\(494\) 0.0185811 + 0.642291i 0.000836003 + 0.0288980i
\(495\) 0 0
\(496\) 17.8199 + 17.8199i 0.800135 + 0.800135i
\(497\) −10.7948 10.9164i −0.484215 0.489667i
\(498\) 0 0
\(499\) −27.5555 + 27.5555i −1.23355 + 1.23355i −0.270964 + 0.962589i \(0.587343\pi\)
−0.962589 + 0.270964i \(0.912657\pi\)
\(500\) 3.05682 + 3.05682i 0.136705 + 0.136705i
\(501\) 0 0
\(502\) 10.3470 10.3470i 0.461811 0.461811i
\(503\) 20.8862i 0.931272i 0.884976 + 0.465636i \(0.154174\pi\)
−0.884976 + 0.465636i \(0.845826\pi\)
\(504\) 0 0
\(505\) −0.711213 0.711213i −0.0316486 0.0316486i
\(506\) 20.6381i 0.917475i
\(507\) 0 0
\(508\) 3.97721 0.176460
\(509\) −15.2473 15.2473i −0.675823 0.675823i 0.283229 0.959052i \(-0.408594\pi\)
−0.959052 + 0.283229i \(0.908594\pi\)
\(510\) 0 0
\(511\) −18.2206 18.4257i −0.806031 0.815107i
\(512\) 16.9216 16.9216i 0.747837 0.747837i
\(513\) 0 0
\(514\) 15.0210 15.0210i 0.662548 0.662548i
\(515\) −3.26180 3.26180i −0.143732 0.143732i
\(516\) 0 0
\(517\) −19.3505 −0.851033
\(518\) 0.0512623 9.15630i 0.00225234 0.402305i
\(519\) 0 0
\(520\) −9.58864 + 0.277394i −0.420490 + 0.0121645i
\(521\) 20.1543i 0.882975i 0.897268 + 0.441487i \(0.145549\pi\)
−0.897268 + 0.441487i \(0.854451\pi\)
\(522\) 0 0
\(523\) 11.3031i 0.494251i −0.968983 0.247126i \(-0.920514\pi\)
0.968983 0.247126i \(-0.0794861\pi\)
\(524\) 6.45095 0.281811
\(525\) 0 0
\(526\) −12.4143 + 12.4143i −0.541291 + 0.541291i
\(527\) 20.6400 + 20.6400i 0.899094 + 0.899094i
\(528\) 0 0
\(529\) −19.3835 −0.842760
\(530\) 3.59587 0.156195
\(531\) 0 0
\(532\) 0.147902 + 0.149568i 0.00641237 + 0.00648458i
\(533\) 7.95774 8.43188i 0.344688 0.365225i
\(534\) 0 0
\(535\) −6.28230 6.28230i −0.271607 0.271607i
\(536\) 4.55479 0.196737
\(537\) 0 0
\(538\) 20.0115 + 20.0115i 0.862758 + 0.862758i
\(539\) −12.8363 13.1270i −0.552898 0.565420i
\(540\) 0 0
\(541\) −9.28879 9.28879i −0.399356 0.399356i 0.478650 0.878006i \(-0.341126\pi\)
−0.878006 + 0.478650i \(0.841126\pi\)
\(542\) 4.13051i 0.177421i
\(543\) 0 0
\(544\) 6.37398 6.37398i 0.273282 0.273282i
\(545\) −7.17778 −0.307462
\(546\) 0 0
\(547\) 12.8999 0.551559 0.275780 0.961221i \(-0.411064\pi\)
0.275780 + 0.961221i \(0.411064\pi\)
\(548\) 1.01560 1.01560i 0.0433842 0.0433842i
\(549\) 0 0
\(550\) 13.4680i 0.574277i
\(551\) 0.394912 + 0.394912i 0.0168238 + 0.0168238i
\(552\) 0 0
\(553\) 0.260633 46.5534i 0.0110833 1.97965i
\(554\) −24.8462 24.8462i −1.05562 1.05562i
\(555\) 0 0
\(556\) 3.43400 0.145634
\(557\) 16.6153 + 16.6153i 0.704013 + 0.704013i 0.965269 0.261257i \(-0.0841369\pi\)
−0.261257 + 0.965269i \(0.584137\pi\)
\(558\) 0 0
\(559\) −11.4732 + 0.331912i −0.485264 + 0.0140384i
\(560\) 4.29072 4.24295i 0.181316 0.179297i
\(561\) 0 0
\(562\) 16.5536 0.698270
\(563\) 21.6761 0.913538 0.456769 0.889585i \(-0.349007\pi\)
0.456769 + 0.889585i \(0.349007\pi\)
\(564\) 0 0
\(565\) −3.52192 3.52192i −0.148168 0.148168i
\(566\) 3.67799 3.67799i 0.154598 0.154598i
\(567\) 0 0
\(568\) −17.8082 −0.747214
\(569\) 18.0738i 0.757695i −0.925459 0.378847i \(-0.876321\pi\)
0.925459 0.378847i \(-0.123679\pi\)
\(570\) 0 0
\(571\) 8.53692i 0.357259i −0.983916 0.178630i \(-0.942834\pi\)
0.983916 0.178630i \(-0.0571664\pi\)
\(572\) 3.70831 + 3.49978i 0.155052 + 0.146333i
\(573\) 0 0
\(574\) −0.0575680 + 10.2826i −0.00240284 + 0.429188i
\(575\) −27.6586 −1.15344
\(576\) 0 0
\(577\) −8.56564 8.56564i −0.356592 0.356592i 0.505963 0.862555i \(-0.331137\pi\)
−0.862555 + 0.505963i \(0.831137\pi\)
\(578\) 6.59284 6.59284i 0.274226 0.274226i
\(579\) 0 0
\(580\) −1.25190 + 1.25190i −0.0519825 + 0.0519825i
\(581\) 28.0616 27.7491i 1.16419 1.15123i
\(582\) 0 0
\(583\) −6.36490 6.36490i −0.263607 0.263607i
\(584\) −30.0583 −1.24382
\(585\) 0 0
\(586\) 6.10849i 0.252339i
\(587\) 0.308382 + 0.308382i 0.0127283 + 0.0127283i 0.713442 0.700714i \(-0.247135\pi\)
−0.700714 + 0.713442i \(0.747135\pi\)
\(588\) 0 0
\(589\) 1.41241i 0.0581972i
\(590\) −9.58864 + 9.58864i −0.394758 + 0.394758i
\(591\) 0 0
\(592\) −5.32684 5.32684i −0.218932 0.218932i
\(593\) 4.95204 4.95204i 0.203356 0.203356i −0.598080 0.801436i \(-0.704070\pi\)
0.801436 + 0.598080i \(0.204070\pi\)
\(594\) 0 0
\(595\) 4.96977 4.91443i 0.203741 0.201472i
\(596\) −7.19061 7.19061i −0.294539 0.294539i
\(597\) 0 0
\(598\) 19.4725 20.6327i 0.796289 0.843734i
\(599\) 17.6309 0.720379 0.360189 0.932879i \(-0.382712\pi\)
0.360189 + 0.932879i \(0.382712\pi\)
\(600\) 0 0
\(601\) 7.14746i 0.291551i −0.989318 0.145776i \(-0.953432\pi\)
0.989318 0.145776i \(-0.0465677\pi\)
\(602\) 7.23840 7.15780i 0.295015 0.291730i
\(603\) 0 0
\(604\) −4.12064 + 4.12064i −0.167666 + 0.167666i
\(605\) 2.52595 2.52595i 0.102694 0.102694i
\(606\) 0 0
\(607\) 29.8550i 1.21178i 0.795550 + 0.605888i \(0.207182\pi\)
−0.795550 + 0.605888i \(0.792818\pi\)
\(608\) 0.436175 0.0176892
\(609\) 0 0
\(610\) 9.64754i 0.390618i
\(611\) 19.3454 + 18.2576i 0.782632 + 0.738623i
\(612\) 0 0
\(613\) −6.43907 + 6.43907i −0.260072 + 0.260072i −0.825083 0.565011i \(-0.808872\pi\)
0.565011 + 0.825083i \(0.308872\pi\)
\(614\) 14.6905i 0.592859i
\(615\) 0 0
\(616\) −21.2965 0.119230i −0.858061 0.00480393i
\(617\) −16.4908 + 16.4908i −0.663894 + 0.663894i −0.956296 0.292402i \(-0.905546\pi\)
0.292402 + 0.956296i \(0.405546\pi\)
\(618\) 0 0
\(619\) −22.3208 + 22.3208i −0.897148 + 0.897148i −0.995183 0.0980353i \(-0.968744\pi\)
0.0980353 + 0.995183i \(0.468744\pi\)
\(620\) −4.47745 −0.179819
\(621\) 0 0
\(622\) −19.2639 + 19.2639i −0.772414 + 0.772414i
\(623\) 8.93326 + 9.03385i 0.357903 + 0.361934i
\(624\) 0 0
\(625\) −14.2918 −0.571671
\(626\) −3.68240 3.68240i −0.147178 0.147178i
\(627\) 0 0
\(628\) 11.3386 0.452459
\(629\) −6.16986 6.16986i −0.246009 0.246009i
\(630\) 0 0
\(631\) 3.75154 + 3.75154i 0.149346 + 0.149346i 0.777826 0.628480i \(-0.216322\pi\)
−0.628480 + 0.777826i \(0.716322\pi\)
\(632\) −38.1845 38.1845i −1.51890 1.51890i
\(633\) 0 0
\(634\) 6.78765i 0.269572i
\(635\) 4.52166 4.52166i 0.179437 0.179437i
\(636\) 0 0
\(637\) 0.447317 + 25.2349i 0.0177234 + 0.999843i
\(638\) −12.0072 −0.475369
\(639\) 0 0
\(640\) 4.13051i 0.163273i
\(641\) 25.6947i 1.01488i 0.861687 + 0.507440i \(0.169408\pi\)
−0.861687 + 0.507440i \(0.830592\pi\)
\(642\) 0 0
\(643\) 22.1537 + 22.1537i 0.873658 + 0.873658i 0.992869 0.119211i \(-0.0380363\pi\)
−0.119211 + 0.992869i \(0.538036\pi\)
\(644\) 0.0519948 9.28713i 0.00204888 0.365964i
\(645\) 0 0
\(646\) −0.543065 −0.0213666
\(647\) −32.4446 −1.27553 −0.637764 0.770232i \(-0.720140\pi\)
−0.637764 + 0.770232i \(0.720140\pi\)
\(648\) 0 0
\(649\) 33.9449 1.33245
\(650\) 12.7073 13.4645i 0.498423 0.528120i
\(651\) 0 0
\(652\) 3.79380 3.79380i 0.148577 0.148577i
\(653\) −31.6514 −1.23862 −0.619308 0.785148i \(-0.712587\pi\)
−0.619308 + 0.785148i \(0.712587\pi\)
\(654\) 0 0
\(655\) 7.33403 7.33403i 0.286564 0.286564i
\(656\) 5.98209 + 5.98209i 0.233561 + 0.233561i
\(657\) 0 0
\(658\) −23.5916 0.132079i −0.919695 0.00514899i
\(659\) −30.5330 −1.18940 −0.594699 0.803948i \(-0.702729\pi\)
−0.594699 + 0.803948i \(0.702729\pi\)
\(660\) 0 0
\(661\) 9.20895 9.20895i 0.358187 0.358187i −0.504957 0.863144i \(-0.668492\pi\)
0.863144 + 0.504957i \(0.168492\pi\)
\(662\) 2.92162i 0.113552i
\(663\) 0 0
\(664\) 45.7775i 1.77651i
\(665\) 0.338191 + 0.00189339i 0.0131145 + 7.34225e-5i
\(666\) 0 0
\(667\) 24.6586i 0.954785i
\(668\) −6.50717 6.50717i −0.251770 0.251770i
\(669\) 0 0
\(670\) 1.09960 1.09960i 0.0424811 0.0424811i
\(671\) −17.0767 + 17.0767i −0.659239 + 0.659239i
\(672\) 0 0
\(673\) 22.6319i 0.872397i 0.899850 + 0.436199i \(0.143675\pi\)
−0.899850 + 0.436199i \(0.856325\pi\)
\(674\) −19.7701 19.7701i −0.761516 0.761516i
\(675\) 0 0
\(676\) −0.405220 6.99773i −0.0155854 0.269144i
\(677\) 10.7242i 0.412165i 0.978535 + 0.206082i \(0.0660715\pi\)
−0.978535 + 0.206082i \(0.933928\pi\)
\(678\) 0 0
\(679\) 11.8215 11.6899i 0.453668 0.448616i
\(680\) 8.10731i 0.310901i
\(681\) 0 0
\(682\) −21.4720 21.4720i −0.822204 0.822204i
\(683\) 3.70701 + 3.70701i 0.141845 + 0.141845i 0.774463 0.632619i \(-0.218020\pi\)
−0.632619 + 0.774463i \(0.718020\pi\)
\(684\) 0 0
\(685\) 2.30925i 0.0882319i
\(686\) −15.5600 16.0917i −0.594085 0.614384i
\(687\) 0 0
\(688\) 8.37525i 0.319303i
\(689\) 0.357818 + 12.3687i 0.0136318 + 0.471208i
\(690\) 0 0
\(691\) −0.266133 0.266133i −0.0101242 0.0101242i 0.702027 0.712151i \(-0.252279\pi\)
−0.712151 + 0.702027i \(0.752279\pi\)
\(692\) 4.03442i 0.153366i
\(693\) 0 0
\(694\) −7.35350 + 7.35350i −0.279135 + 0.279135i
\(695\) 3.90409 3.90409i 0.148090 0.148090i
\(696\) 0 0
\(697\) 6.92881 + 6.92881i 0.262447 + 0.262447i
\(698\) 32.5925i 1.23364i
\(699\) 0 0
\(700\) 0.0339307 6.06059i 0.00128246 0.229069i
\(701\) 34.0349i 1.28548i 0.766084 + 0.642740i \(0.222202\pi\)
−0.766084 + 0.642740i \(0.777798\pi\)
\(702\) 0 0
\(703\) 0.422207i 0.0159238i
\(704\) −16.3896 + 16.3896i −0.617707 + 0.617707i
\(705\) 0 0
\(706\) −8.22556 −0.309573
\(707\) −0.0171854 + 3.06960i −0.000646325 + 0.115444i
\(708\) 0 0
\(709\) 11.4989 + 11.4989i 0.431849 + 0.431849i 0.889257 0.457408i \(-0.151222\pi\)
−0.457408 + 0.889257i \(0.651222\pi\)
\(710\) −4.29917 + 4.29917i −0.161345 + 0.161345i
\(711\) 0 0
\(712\) 14.7371 0.552297
\(713\) 44.0960 44.0960i 1.65141 1.65141i
\(714\) 0 0
\(715\) 8.19481 0.237071i 0.306469 0.00886596i
\(716\) 12.2401 0.457432
\(717\) 0 0
\(718\) −21.4524 −0.800596
\(719\) −35.0445 −1.30694 −0.653469 0.756953i \(-0.726687\pi\)
−0.653469 + 0.756953i \(0.726687\pi\)
\(720\) 0 0
\(721\) −0.0788166 + 14.0779i −0.00293528 + 0.524290i
\(722\) 16.2195 + 16.2195i 0.603629 + 0.603629i
\(723\) 0 0
\(724\) 1.03382i 0.0384215i
\(725\) 16.0917i 0.597631i
\(726\) 0 0
\(727\) 15.0936 0.559789 0.279895 0.960031i \(-0.409700\pi\)
0.279895 + 0.960031i \(0.409700\pi\)
\(728\) 21.1784 + 20.2129i 0.784925 + 0.749140i
\(729\) 0 0
\(730\) −7.25655 + 7.25655i −0.268577 + 0.268577i
\(731\) 9.70071i 0.358794i
\(732\) 0 0
\(733\) −14.8155 14.8155i −0.547223 0.547223i 0.378414 0.925637i \(-0.376470\pi\)
−0.925637 + 0.378414i \(0.876470\pi\)
\(734\) −19.5546 19.5546i −0.721773 0.721773i
\(735\) 0 0
\(736\) −13.6176 13.6176i −0.501950 0.501950i
\(737\) −3.89269 −0.143389
\(738\) 0 0
\(739\) 16.1370 + 16.1370i 0.593607 + 0.593607i 0.938604 0.344997i \(-0.112120\pi\)
−0.344997 + 0.938604i \(0.612120\pi\)
\(740\) 1.33843 0.0492018
\(741\) 0 0
\(742\) −7.71646 7.80335i −0.283280 0.286470i
\(743\) 24.1350 24.1350i 0.885428 0.885428i −0.108652 0.994080i \(-0.534653\pi\)
0.994080 + 0.108652i \(0.0346534\pi\)
\(744\) 0 0
\(745\) −16.3499 −0.599013
\(746\) −8.97721 + 8.97721i −0.328679 + 0.328679i
\(747\) 0 0
\(748\) −3.04726 + 3.04726i −0.111419 + 0.111419i
\(749\) −0.151803 + 27.1145i −0.00554675 + 0.990741i
\(750\) 0 0
\(751\) 16.7770i 0.612201i −0.951999 0.306100i \(-0.900976\pi\)
0.951999 0.306100i \(-0.0990243\pi\)
\(752\) −13.7248 + 13.7248i −0.500493 + 0.500493i
\(753\) 0 0
\(754\) 12.0041 + 11.3290i 0.437162 + 0.412579i
\(755\) 9.36943i 0.340989i
\(756\) 0 0
\(757\) −20.7321 −0.753520 −0.376760 0.926311i \(-0.622962\pi\)
−0.376760 + 0.926311i \(0.622962\pi\)
\(758\) 6.22568i 0.226127i
\(759\) 0 0
\(760\) 0.277394 0.277394i 0.0100621 0.0100621i
\(761\) 2.11330 2.11330i 0.0766071 0.0766071i −0.667765 0.744372i \(-0.732749\pi\)
0.744372 + 0.667765i \(0.232749\pi\)
\(762\) 0 0
\(763\) 15.4030 + 15.5764i 0.557624 + 0.563903i
\(764\) 5.39576i 0.195212i
\(765\) 0 0
\(766\) −41.9782 −1.51674
\(767\) −33.9360 32.0277i −1.22536 1.15645i
\(768\) 0 0
\(769\) −25.9456 25.9456i −0.935621 0.935621i 0.0624284 0.998049i \(-0.480115\pi\)
−0.998049 + 0.0624284i \(0.980115\pi\)
\(770\) −5.17009 + 5.11252i −0.186317 + 0.184242i
\(771\) 0 0
\(772\) 5.51867 5.51867i 0.198621 0.198621i
\(773\) 0.951693 + 0.951693i 0.0342300 + 0.0342300i 0.724015 0.689785i \(-0.242295\pi\)
−0.689785 + 0.724015i \(0.742295\pi\)
\(774\) 0 0
\(775\) 28.7761 28.7761i 1.03367 1.03367i
\(776\) 19.2847i 0.692280i
\(777\) 0 0
\(778\) −5.54638 5.54638i −0.198847 0.198847i
\(779\) 0.474142i 0.0169879i
\(780\) 0 0
\(781\) 15.2195 0.544598
\(782\) 16.9547 + 16.9547i 0.606299 + 0.606299i
\(783\) 0 0
\(784\) −18.4151 0.206204i −0.657683 0.00736442i
\(785\) 12.8908 12.8908i 0.460091 0.460091i
\(786\) 0 0
\(787\) −24.8017 + 24.8017i −0.884085 + 0.884085i −0.993947 0.109862i \(-0.964959\pi\)
0.109862 + 0.993947i \(0.464959\pi\)
\(788\) −8.23287 8.23287i −0.293284 0.293284i
\(789\) 0