Properties

Label 819.2.n.d.100.1
Level $819$
Weight $2$
Character 819.100
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 100.1
Root \(-0.181721 + 0.314749i\) of defining polynomial
Character \(\chi\) \(=\) 819.100
Dual form 819.2.n.d.172.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.19402 - 2.06810i) q^{2} +(-1.85136 + 3.20665i) q^{4} +(0.491140 - 0.850679i) q^{5} +(2.60682 + 0.452230i) q^{7} +4.06616 q^{8} +O(q^{10})\) \(q+(-1.19402 - 2.06810i) q^{2} +(-1.85136 + 3.20665i) q^{4} +(0.491140 - 0.850679i) q^{5} +(2.60682 + 0.452230i) q^{7} +4.06616 q^{8} -2.34572 q^{10} +0.587802 q^{11} +(2.39227 + 2.69760i) q^{13} +(-2.17733 - 5.93113i) q^{14} +(-1.15235 - 1.99593i) q^{16} +(-3.22710 + 5.58950i) q^{17} -3.82689 q^{19} +(1.81855 + 3.14983i) q^{20} +(-0.701847 - 1.21563i) q^{22} +(4.13001 + 7.15338i) q^{23} +(2.01756 + 3.49452i) q^{25} +(2.72249 - 8.16844i) q^{26} +(-6.27630 + 7.52191i) q^{28} +(-1.98009 + 3.42962i) q^{29} +(1.49436 + 2.58831i) q^{31} +(1.31430 - 2.27644i) q^{32} +15.4129 q^{34} +(1.66501 - 1.99546i) q^{35} +(-0.877941 - 1.52064i) q^{37} +(4.56938 + 7.91440i) q^{38} +(1.99705 - 3.45900i) q^{40} +(1.83584 - 3.17977i) q^{41} +(-3.19042 - 5.52598i) q^{43} +(-1.08823 + 1.88488i) q^{44} +(9.86261 - 17.0825i) q^{46} +(-2.17030 + 3.75906i) q^{47} +(6.59098 + 2.35776i) q^{49} +(4.81802 - 8.34505i) q^{50} +(-13.0792 + 2.67695i) q^{52} +(0.212770 + 0.368529i) q^{53} +(0.288693 - 0.500031i) q^{55} +(10.5997 + 1.83884i) q^{56} +9.45706 q^{58} +(3.00431 - 5.20362i) q^{59} +2.20674 q^{61} +(3.56859 - 6.18097i) q^{62} -10.8866 q^{64} +(3.46973 - 0.710156i) q^{65} +7.01303 q^{67} +(-11.9491 - 20.6964i) q^{68} +(-6.11486 - 1.06080i) q^{70} +(1.80127 + 3.11988i) q^{71} +(-2.46714 - 4.27321i) q^{73} +(-2.09656 + 3.63134i) q^{74} +(7.08496 - 12.2715i) q^{76} +(1.53229 + 0.265822i) q^{77} +(-1.39270 + 2.41223i) q^{79} -2.26386 q^{80} -8.76812 q^{82} +2.86819 q^{83} +(3.16992 + 5.49045i) q^{85} +(-7.61885 + 13.1962i) q^{86} +2.39010 q^{88} +(-1.04656 - 1.81269i) q^{89} +(5.01627 + 8.11400i) q^{91} -30.5845 q^{92} +10.3655 q^{94} +(-1.87954 + 3.25546i) q^{95} +(-3.84852 - 6.66584i) q^{97} +(-2.99367 - 16.4460i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} + O(q^{10}) \) \( 12q - 2q^{2} - 4q^{4} - q^{5} + 9q^{7} + 6q^{8} - 8q^{10} + 8q^{11} - 2q^{13} + 2q^{14} + 8q^{16} - 5q^{17} + 2q^{19} + q^{20} - 5q^{22} + q^{23} + 7q^{25} - 5q^{26} - 7q^{28} - 3q^{29} + 16q^{31} - 8q^{32} + 32q^{34} - 8q^{35} - 13q^{37} + 17q^{38} - 5q^{40} + 8q^{41} - 11q^{43} - 21q^{44} + 16q^{46} + q^{47} - 3q^{49} - 6q^{50} - 25q^{52} + 2q^{53} + 9q^{55} + 18q^{56} + 16q^{58} - 13q^{59} + 10q^{61} - 5q^{62} - 30q^{64} - 19q^{65} + 22q^{67} - 29q^{68} - 39q^{70} - 6q^{71} - 30q^{73} + 3q^{74} - 9q^{76} - 11q^{77} + 7q^{79} - 14q^{80} - 2q^{82} + 54q^{83} - q^{85} + 7q^{86} - 4q^{89} - 20q^{91} - 54q^{92} - 90q^{94} + 6q^{95} - 35q^{97} - 62q^{98} + O(q^{100}) \)

Character values

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

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.19402 2.06810i −0.844299 1.46237i −0.886229 0.463248i \(-0.846684\pi\)
0.0419302 0.999121i \(-0.486649\pi\)
\(3\) 0 0
\(4\) −1.85136 + 3.20665i −0.925680 + 1.60333i
\(5\) 0.491140 0.850679i 0.219644 0.380435i −0.735055 0.678008i \(-0.762844\pi\)
0.954699 + 0.297572i \(0.0961769\pi\)
\(6\) 0 0
\(7\) 2.60682 + 0.452230i 0.985284 + 0.170927i
\(8\) 4.06616 1.43761
\(9\) 0 0
\(10\) −2.34572 −0.741782
\(11\) 0.587802 0.177229 0.0886146 0.996066i \(-0.471756\pi\)
0.0886146 + 0.996066i \(0.471756\pi\)
\(12\) 0 0
\(13\) 2.39227 + 2.69760i 0.663496 + 0.748179i
\(14\) −2.17733 5.93113i −0.581916 1.58516i
\(15\) 0 0
\(16\) −1.15235 1.99593i −0.288088 0.498983i
\(17\) −3.22710 + 5.58950i −0.782687 + 1.35565i 0.147685 + 0.989035i \(0.452818\pi\)
−0.930371 + 0.366619i \(0.880515\pi\)
\(18\) 0 0
\(19\) −3.82689 −0.877950 −0.438975 0.898499i \(-0.644658\pi\)
−0.438975 + 0.898499i \(0.644658\pi\)
\(20\) 1.81855 + 3.14983i 0.406641 + 0.704323i
\(21\) 0 0
\(22\) −0.701847 1.21563i −0.149634 0.259174i
\(23\) 4.13001 + 7.15338i 0.861166 + 1.49158i 0.870805 + 0.491629i \(0.163598\pi\)
−0.00963902 + 0.999954i \(0.503068\pi\)
\(24\) 0 0
\(25\) 2.01756 + 3.49452i 0.403513 + 0.698904i
\(26\) 2.72249 8.16844i 0.533925 1.60196i
\(27\) 0 0
\(28\) −6.27630 + 7.52191i −1.18611 + 1.42151i
\(29\) −1.98009 + 3.42962i −0.367694 + 0.636864i −0.989205 0.146541i \(-0.953186\pi\)
0.621511 + 0.783406i \(0.286519\pi\)
\(30\) 0 0
\(31\) 1.49436 + 2.58831i 0.268395 + 0.464874i 0.968448 0.249218i \(-0.0801734\pi\)
−0.700053 + 0.714091i \(0.746840\pi\)
\(32\) 1.31430 2.27644i 0.232338 0.402421i
\(33\) 0 0
\(34\) 15.4129 2.64329
\(35\) 1.66501 1.99546i 0.281439 0.337294i
\(36\) 0 0
\(37\) −0.877941 1.52064i −0.144333 0.249991i 0.784791 0.619760i \(-0.212770\pi\)
−0.929124 + 0.369769i \(0.879437\pi\)
\(38\) 4.56938 + 7.91440i 0.741252 + 1.28389i
\(39\) 0 0
\(40\) 1.99705 3.45900i 0.315762 0.546916i
\(41\) 1.83584 3.17977i 0.286710 0.496597i −0.686312 0.727307i \(-0.740772\pi\)
0.973023 + 0.230710i \(0.0741049\pi\)
\(42\) 0 0
\(43\) −3.19042 5.52598i −0.486535 0.842703i 0.513345 0.858182i \(-0.328406\pi\)
−0.999880 + 0.0154788i \(0.995073\pi\)
\(44\) −1.08823 + 1.88488i −0.164058 + 0.284156i
\(45\) 0 0
\(46\) 9.86261 17.0825i 1.45416 2.51868i
\(47\) −2.17030 + 3.75906i −0.316570 + 0.548316i −0.979770 0.200127i \(-0.935865\pi\)
0.663200 + 0.748442i \(0.269198\pi\)
\(48\) 0 0
\(49\) 6.59098 + 2.35776i 0.941568 + 0.336823i
\(50\) 4.81802 8.34505i 0.681370 1.18017i
\(51\) 0 0
\(52\) −13.0792 + 2.67695i −1.81376 + 0.371226i
\(53\) 0.212770 + 0.368529i 0.0292263 + 0.0506214i 0.880269 0.474476i \(-0.157362\pi\)
−0.851042 + 0.525097i \(0.824029\pi\)
\(54\) 0 0
\(55\) 0.288693 0.500031i 0.0389274 0.0674242i
\(56\) 10.5997 + 1.83884i 1.41645 + 0.245725i
\(57\) 0 0
\(58\) 9.45706 1.24177
\(59\) 3.00431 5.20362i 0.391128 0.677454i −0.601470 0.798895i \(-0.705418\pi\)
0.992599 + 0.121441i \(0.0387516\pi\)
\(60\) 0 0
\(61\) 2.20674 0.282544 0.141272 0.989971i \(-0.454881\pi\)
0.141272 + 0.989971i \(0.454881\pi\)
\(62\) 3.56859 6.18097i 0.453211 0.784985i
\(63\) 0 0
\(64\) −10.8866 −1.36083
\(65\) 3.46973 0.710156i 0.430367 0.0880841i
\(66\) 0 0
\(67\) 7.01303 0.856778 0.428389 0.903594i \(-0.359081\pi\)
0.428389 + 0.903594i \(0.359081\pi\)
\(68\) −11.9491 20.6964i −1.44904 2.50980i
\(69\) 0 0
\(70\) −6.11486 1.06080i −0.730866 0.126790i
\(71\) 1.80127 + 3.11988i 0.213771 + 0.370262i 0.952892 0.303311i \(-0.0980920\pi\)
−0.739121 + 0.673573i \(0.764759\pi\)
\(72\) 0 0
\(73\) −2.46714 4.27321i −0.288756 0.500141i 0.684757 0.728772i \(-0.259908\pi\)
−0.973513 + 0.228631i \(0.926575\pi\)
\(74\) −2.09656 + 3.63134i −0.243720 + 0.422135i
\(75\) 0 0
\(76\) 7.08496 12.2715i 0.812701 1.40764i
\(77\) 1.53229 + 0.265822i 0.174621 + 0.0302932i
\(78\) 0 0
\(79\) −1.39270 + 2.41223i −0.156691 + 0.271397i −0.933674 0.358125i \(-0.883416\pi\)
0.776982 + 0.629522i \(0.216749\pi\)
\(80\) −2.26386 −0.253108
\(81\) 0 0
\(82\) −8.76812 −0.968277
\(83\) 2.86819 0.314825 0.157412 0.987533i \(-0.449685\pi\)
0.157412 + 0.987533i \(0.449685\pi\)
\(84\) 0 0
\(85\) 3.16992 + 5.49045i 0.343826 + 0.595523i
\(86\) −7.61885 + 13.1962i −0.821562 + 1.42299i
\(87\) 0 0
\(88\) 2.39010 0.254786
\(89\) −1.04656 1.81269i −0.110935 0.192145i 0.805213 0.592986i \(-0.202051\pi\)
−0.916147 + 0.400842i \(0.868718\pi\)
\(90\) 0 0
\(91\) 5.01627 + 8.11400i 0.525848 + 0.850578i
\(92\) −30.5845 −3.18866
\(93\) 0 0
\(94\) 10.3655 1.06912
\(95\) −1.87954 + 3.25546i −0.192837 + 0.334003i
\(96\) 0 0
\(97\) −3.84852 6.66584i −0.390758 0.676813i 0.601791 0.798653i \(-0.294454\pi\)
−0.992550 + 0.121840i \(0.961120\pi\)
\(98\) −2.99367 16.4460i −0.302406 1.66130i
\(99\) 0 0
\(100\) −14.9409 −1.49409
\(101\) 2.63732 0.262423 0.131212 0.991354i \(-0.458113\pi\)
0.131212 + 0.991354i \(0.458113\pi\)
\(102\) 0 0
\(103\) 5.43095 9.40669i 0.535128 0.926868i −0.464029 0.885820i \(-0.653597\pi\)
0.999157 0.0410486i \(-0.0130699\pi\)
\(104\) 9.72736 + 10.9689i 0.953846 + 1.07559i
\(105\) 0 0
\(106\) 0.508103 0.880061i 0.0493514 0.0854791i
\(107\) −7.99024 13.8395i −0.772446 1.33792i −0.936219 0.351418i \(-0.885700\pi\)
0.163773 0.986498i \(-0.447634\pi\)
\(108\) 0 0
\(109\) −4.61738 7.99754i −0.442265 0.766026i 0.555592 0.831455i \(-0.312492\pi\)
−0.997857 + 0.0654294i \(0.979158\pi\)
\(110\) −1.37882 −0.131465
\(111\) 0 0
\(112\) −2.10135 5.72416i −0.198559 0.540882i
\(113\) 5.09012 + 8.81635i 0.478838 + 0.829372i 0.999706 0.0242655i \(-0.00772470\pi\)
−0.520867 + 0.853638i \(0.674391\pi\)
\(114\) 0 0
\(115\) 8.11364 0.756601
\(116\) −7.33173 12.6989i −0.680734 1.17907i
\(117\) 0 0
\(118\) −14.3488 −1.32092
\(119\) −10.9402 + 13.1114i −1.00289 + 1.20192i
\(120\) 0 0
\(121\) −10.6545 −0.968590
\(122\) −2.63489 4.56376i −0.238552 0.413184i
\(123\) 0 0
\(124\) −11.0664 −0.993792
\(125\) 8.87502 0.793806
\(126\) 0 0
\(127\) −2.12513 + 3.68083i −0.188575 + 0.326621i −0.944775 0.327719i \(-0.893720\pi\)
0.756201 + 0.654340i \(0.227053\pi\)
\(128\) 10.3702 + 17.9617i 0.916606 + 1.58761i
\(129\) 0 0
\(130\) −5.61160 6.32781i −0.492170 0.554986i
\(131\) −1.08478 + 1.87890i −0.0947779 + 0.164160i −0.909516 0.415669i \(-0.863547\pi\)
0.814738 + 0.579829i \(0.196881\pi\)
\(132\) 0 0
\(133\) −9.97601 1.73063i −0.865030 0.150065i
\(134\) −8.37369 14.5037i −0.723376 1.25292i
\(135\) 0 0
\(136\) −13.1219 + 22.7278i −1.12519 + 1.94889i
\(137\) 4.18158 7.24271i 0.357257 0.618787i −0.630245 0.776396i \(-0.717045\pi\)
0.987501 + 0.157610i \(0.0503788\pi\)
\(138\) 0 0
\(139\) 0.288457 + 0.499622i 0.0244666 + 0.0423774i 0.877999 0.478662i \(-0.158878\pi\)
−0.853533 + 0.521039i \(0.825545\pi\)
\(140\) 3.31619 + 9.03343i 0.280269 + 0.763464i
\(141\) 0 0
\(142\) 4.30149 7.45040i 0.360973 0.625224i
\(143\) 1.40618 + 1.58566i 0.117591 + 0.132599i
\(144\) 0 0
\(145\) 1.94500 + 3.36885i 0.161524 + 0.279767i
\(146\) −5.89161 + 10.2046i −0.487593 + 0.844537i
\(147\) 0 0
\(148\) 6.50154 0.534423
\(149\) −2.80662 −0.229928 −0.114964 0.993370i \(-0.536675\pi\)
−0.114964 + 0.993370i \(0.536675\pi\)
\(150\) 0 0
\(151\) 11.5054 + 19.9280i 0.936300 + 1.62172i 0.772300 + 0.635258i \(0.219106\pi\)
0.164000 + 0.986460i \(0.447560\pi\)
\(152\) −15.5608 −1.26215
\(153\) 0 0
\(154\) −1.27984 3.48633i −0.103132 0.280937i
\(155\) 2.93576 0.235806
\(156\) 0 0
\(157\) −11.2880 19.5513i −0.900879 1.56037i −0.826356 0.563148i \(-0.809590\pi\)
−0.0745227 0.997219i \(-0.523743\pi\)
\(158\) 6.65165 0.529177
\(159\) 0 0
\(160\) −1.29101 2.23610i −0.102064 0.176779i
\(161\) 7.53119 + 20.5153i 0.593541 + 1.61683i
\(162\) 0 0
\(163\) 8.17714 0.640483 0.320242 0.947336i \(-0.396236\pi\)
0.320242 + 0.947336i \(0.396236\pi\)
\(164\) 6.79761 + 11.7738i 0.530804 + 0.919380i
\(165\) 0 0
\(166\) −3.42467 5.93170i −0.265806 0.460389i
\(167\) −1.16386 + 2.01586i −0.0900619 + 0.155992i −0.907537 0.419972i \(-0.862040\pi\)
0.817475 + 0.575964i \(0.195373\pi\)
\(168\) 0 0
\(169\) −1.55408 + 12.9068i −0.119545 + 0.992829i
\(170\) 7.56988 13.1114i 0.580583 1.00560i
\(171\) 0 0
\(172\) 23.6265 1.80150
\(173\) 8.13372 0.618396 0.309198 0.950998i \(-0.399939\pi\)
0.309198 + 0.950998i \(0.399939\pi\)
\(174\) 0 0
\(175\) 3.67909 + 10.0220i 0.278113 + 0.757590i
\(176\) −0.677355 1.17321i −0.0510576 0.0884343i
\(177\) 0 0
\(178\) −2.49922 + 4.32877i −0.187324 + 0.324455i
\(179\) 20.9925 1.56906 0.784528 0.620093i \(-0.212905\pi\)
0.784528 + 0.620093i \(0.212905\pi\)
\(180\) 0 0
\(181\) −1.60807 −0.119527 −0.0597635 0.998213i \(-0.519035\pi\)
−0.0597635 + 0.998213i \(0.519035\pi\)
\(182\) 10.7910 20.0624i 0.799885 1.48713i
\(183\) 0 0
\(184\) 16.7933 + 29.0868i 1.23802 + 2.14431i
\(185\) −1.72477 −0.126807
\(186\) 0 0
\(187\) −1.89690 + 3.28552i −0.138715 + 0.240261i
\(188\) −8.03601 13.9188i −0.586086 1.01513i
\(189\) 0 0
\(190\) 8.97683 0.651247
\(191\) 11.5622 0.836614 0.418307 0.908306i \(-0.362624\pi\)
0.418307 + 0.908306i \(0.362624\pi\)
\(192\) 0 0
\(193\) 23.5788 1.69724 0.848621 0.529001i \(-0.177433\pi\)
0.848621 + 0.529001i \(0.177433\pi\)
\(194\) −9.19041 + 15.9183i −0.659833 + 1.14286i
\(195\) 0 0
\(196\) −19.7628 + 16.7699i −1.41163 + 1.19785i
\(197\) −0.735472 + 1.27387i −0.0524002 + 0.0907598i −0.891036 0.453933i \(-0.850020\pi\)
0.838636 + 0.544693i \(0.183354\pi\)
\(198\) 0 0
\(199\) −4.69700 + 8.13543i −0.332961 + 0.576706i −0.983091 0.183117i \(-0.941381\pi\)
0.650130 + 0.759823i \(0.274714\pi\)
\(200\) 8.20374 + 14.2093i 0.580092 + 1.00475i
\(201\) 0 0
\(202\) −3.14901 5.45425i −0.221564 0.383760i
\(203\) −6.71271 + 8.04493i −0.471140 + 0.564643i
\(204\) 0 0
\(205\) −1.80331 3.12343i −0.125949 0.218150i
\(206\) −25.9386 −1.80723
\(207\) 0 0
\(208\) 2.62749 7.88340i 0.182183 0.546615i
\(209\) −2.24946 −0.155598
\(210\) 0 0
\(211\) 4.47109 7.74416i 0.307803 0.533130i −0.670079 0.742290i \(-0.733740\pi\)
0.977881 + 0.209160i \(0.0670730\pi\)
\(212\) −1.57566 −0.108217
\(213\) 0 0
\(214\) −19.0810 + 33.0493i −1.30435 + 2.25920i
\(215\) −6.26778 −0.427459
\(216\) 0 0
\(217\) 2.72501 + 7.42303i 0.184986 + 0.503908i
\(218\) −11.0265 + 19.0984i −0.746808 + 1.29351i
\(219\) 0 0
\(220\) 1.06895 + 1.85148i 0.0720686 + 0.124827i
\(221\) −22.7983 + 4.66618i −1.53358 + 0.313881i
\(222\) 0 0
\(223\) −10.9098 + 18.8963i −0.730574 + 1.26539i 0.226064 + 0.974112i \(0.427414\pi\)
−0.956638 + 0.291279i \(0.905919\pi\)
\(224\) 4.45562 5.33989i 0.297704 0.356786i
\(225\) 0 0
\(226\) 12.1554 21.0538i 0.808565 1.40048i
\(227\) −9.27627 + 16.0670i −0.615687 + 1.06640i 0.374576 + 0.927196i \(0.377788\pi\)
−0.990263 + 0.139206i \(0.955545\pi\)
\(228\) 0 0
\(229\) −9.67525 + 16.7580i −0.639359 + 1.10740i 0.346215 + 0.938155i \(0.387467\pi\)
−0.985574 + 0.169247i \(0.945867\pi\)
\(230\) −9.68784 16.7798i −0.638797 1.10643i
\(231\) 0 0
\(232\) −8.05137 + 13.9454i −0.528599 + 0.915560i
\(233\) 8.08170 13.9979i 0.529450 0.917034i −0.469960 0.882688i \(-0.655732\pi\)
0.999410 0.0343462i \(-0.0109349\pi\)
\(234\) 0 0
\(235\) 2.13184 + 3.69245i 0.139066 + 0.240869i
\(236\) 11.1241 + 19.2676i 0.724119 + 1.25421i
\(237\) 0 0
\(238\) 40.1785 + 6.97016i 2.60439 + 0.451808i
\(239\) −16.1037 −1.04166 −0.520831 0.853660i \(-0.674378\pi\)
−0.520831 + 0.853660i \(0.674378\pi\)
\(240\) 0 0
\(241\) 2.00300 3.46930i 0.129025 0.223477i −0.794274 0.607559i \(-0.792149\pi\)
0.923299 + 0.384082i \(0.125482\pi\)
\(242\) 12.7217 + 22.0346i 0.817779 + 1.41643i
\(243\) 0 0
\(244\) −4.08548 + 7.07625i −0.261546 + 0.453011i
\(245\) 5.24279 4.44882i 0.334949 0.284225i
\(246\) 0 0
\(247\) −9.15497 10.3234i −0.582517 0.656864i
\(248\) 6.07631 + 10.5245i 0.385846 + 0.668305i
\(249\) 0 0
\(250\) −10.5969 18.3544i −0.670209 1.16084i
\(251\) 1.62344 + 2.81188i 0.102471 + 0.177484i 0.912702 0.408626i \(-0.133992\pi\)
−0.810231 + 0.586110i \(0.800659\pi\)
\(252\) 0 0
\(253\) 2.42763 + 4.20477i 0.152624 + 0.264352i
\(254\) 10.1498 0.636853
\(255\) 0 0
\(256\) 13.8778 24.0371i 0.867365 1.50232i
\(257\) −13.4462 23.2895i −0.838751 1.45276i −0.890940 0.454122i \(-0.849953\pi\)
0.0521891 0.998637i \(-0.483380\pi\)
\(258\) 0 0
\(259\) −1.60095 4.36106i −0.0994784 0.270983i
\(260\) −4.14650 + 12.4410i −0.257155 + 0.771556i
\(261\) 0 0
\(262\) 5.18100 0.320084
\(263\) 3.80706 0.234753 0.117377 0.993087i \(-0.462552\pi\)
0.117377 + 0.993087i \(0.462552\pi\)
\(264\) 0 0
\(265\) 0.418000 0.0256775
\(266\) 8.33241 + 22.6978i 0.510893 + 1.39169i
\(267\) 0 0
\(268\) −12.9836 + 22.4883i −0.793102 + 1.37369i
\(269\) −11.9190 + 20.6444i −0.726716 + 1.25871i 0.231548 + 0.972824i \(0.425621\pi\)
−0.958264 + 0.285886i \(0.907712\pi\)
\(270\) 0 0
\(271\) −4.95068 8.57482i −0.300732 0.520883i 0.675570 0.737296i \(-0.263898\pi\)
−0.976302 + 0.216413i \(0.930564\pi\)
\(272\) 14.8750 0.901931
\(273\) 0 0
\(274\) −19.9715 −1.20653
\(275\) 1.18593 + 2.05409i 0.0715142 + 0.123866i
\(276\) 0 0
\(277\) −5.89289 + 10.2068i −0.354069 + 0.613266i −0.986958 0.160977i \(-0.948536\pi\)
0.632889 + 0.774243i \(0.281869\pi\)
\(278\) 0.688846 1.19312i 0.0413142 0.0715584i
\(279\) 0 0
\(280\) 6.77022 8.11385i 0.404598 0.484895i
\(281\) −12.9976 −0.775372 −0.387686 0.921791i \(-0.626726\pi\)
−0.387686 + 0.921791i \(0.626726\pi\)
\(282\) 0 0
\(283\) −16.8050 −0.998952 −0.499476 0.866328i \(-0.666474\pi\)
−0.499476 + 0.866328i \(0.666474\pi\)
\(284\) −13.3392 −0.791534
\(285\) 0 0
\(286\) 1.60029 4.80143i 0.0946270 0.283914i
\(287\) 6.22369 7.45886i 0.367373 0.440283i
\(288\) 0 0
\(289\) −12.3283 21.3533i −0.725197 1.25608i
\(290\) 4.64474 8.04493i 0.272749 0.472414i
\(291\) 0 0
\(292\) 18.2702 1.06918
\(293\) −7.04782 12.2072i −0.411738 0.713151i 0.583342 0.812227i \(-0.301745\pi\)
−0.995080 + 0.0990757i \(0.968411\pi\)
\(294\) 0 0
\(295\) −2.95108 5.11141i −0.171818 0.297598i
\(296\) −3.56985 6.18316i −0.207493 0.359389i
\(297\) 0 0
\(298\) 3.35116 + 5.80438i 0.194128 + 0.336239i
\(299\) −9.41686 + 28.2539i −0.544591 + 1.63397i
\(300\) 0 0
\(301\) −5.81784 15.8480i −0.335335 0.913464i
\(302\) 27.4754 47.5888i 1.58103 2.73843i
\(303\) 0 0
\(304\) 4.40993 + 7.63822i 0.252927 + 0.438082i
\(305\) 1.08382 1.87723i 0.0620593 0.107490i
\(306\) 0 0
\(307\) 15.8786 0.906240 0.453120 0.891450i \(-0.350311\pi\)
0.453120 + 0.891450i \(0.350311\pi\)
\(308\) −3.68922 + 4.42140i −0.210213 + 0.251932i
\(309\) 0 0
\(310\) −3.50535 6.07145i −0.199091 0.344835i
\(311\) −14.3017 24.7713i −0.810975 1.40465i −0.912183 0.409784i \(-0.865604\pi\)
0.101208 0.994865i \(-0.467729\pi\)
\(312\) 0 0
\(313\) 9.28962 16.0901i 0.525080 0.909465i −0.474493 0.880259i \(-0.657369\pi\)
0.999573 0.0292063i \(-0.00929798\pi\)
\(314\) −26.9561 + 46.6893i −1.52122 + 2.63483i
\(315\) 0 0
\(316\) −5.15679 8.93182i −0.290092 0.502454i
\(317\) 15.3223 26.5389i 0.860584 1.49057i −0.0107826 0.999942i \(-0.503432\pi\)
0.871366 0.490633i \(-0.163234\pi\)
\(318\) 0 0
\(319\) −1.16390 + 2.01594i −0.0651660 + 0.112871i
\(320\) −5.34685 + 9.26102i −0.298898 + 0.517707i
\(321\) 0 0
\(322\) 33.4352 40.0709i 1.86327 2.23306i
\(323\) 12.3498 21.3904i 0.687160 1.19020i
\(324\) 0 0
\(325\) −4.60026 + 13.8024i −0.255177 + 0.765620i
\(326\) −9.76366 16.9112i −0.540759 0.936622i
\(327\) 0 0
\(328\) 7.46483 12.9295i 0.412177 0.713911i
\(329\) −7.35752 + 8.81772i −0.405633 + 0.486136i
\(330\) 0 0
\(331\) 27.2277 1.49657 0.748284 0.663378i \(-0.230878\pi\)
0.748284 + 0.663378i \(0.230878\pi\)
\(332\) −5.31005 + 9.19728i −0.291427 + 0.504766i
\(333\) 0 0
\(334\) 5.55867 0.304157
\(335\) 3.44438 5.96584i 0.188187 0.325949i
\(336\) 0 0
\(337\) −12.3160 −0.670898 −0.335449 0.942058i \(-0.608888\pi\)
−0.335449 + 0.942058i \(0.608888\pi\)
\(338\) 28.5481 12.1969i 1.55281 0.663426i
\(339\) 0 0
\(340\) −23.4746 −1.27309
\(341\) 0.878389 + 1.52141i 0.0475674 + 0.0823892i
\(342\) 0 0
\(343\) 16.1152 + 9.12688i 0.870140 + 0.492805i
\(344\) −12.9728 22.4695i −0.699445 1.21148i
\(345\) 0 0
\(346\) −9.71182 16.8214i −0.522111 0.904322i
\(347\) 3.07253 5.32177i 0.164942 0.285688i −0.771693 0.635996i \(-0.780590\pi\)
0.936635 + 0.350308i \(0.113923\pi\)
\(348\) 0 0
\(349\) −6.51563 + 11.2854i −0.348774 + 0.604094i −0.986032 0.166557i \(-0.946735\pi\)
0.637258 + 0.770650i \(0.280068\pi\)
\(350\) 16.3336 19.5752i 0.873065 1.04634i
\(351\) 0 0
\(352\) 0.772550 1.33810i 0.0411771 0.0713208i
\(353\) −31.6665 −1.68544 −0.842718 0.538356i \(-0.819046\pi\)
−0.842718 + 0.538356i \(0.819046\pi\)
\(354\) 0 0
\(355\) 3.53870 0.187814
\(356\) 7.75021 0.410761
\(357\) 0 0
\(358\) −25.0655 43.4147i −1.32475 2.29454i
\(359\) 9.96610 17.2618i 0.525991 0.911043i −0.473551 0.880767i \(-0.657028\pi\)
0.999542 0.0302764i \(-0.00963874\pi\)
\(360\) 0 0
\(361\) −4.35488 −0.229204
\(362\) 1.92007 + 3.32566i 0.100917 + 0.174793i
\(363\) 0 0
\(364\) −35.3057 + 1.06350i −1.85052 + 0.0557426i
\(365\) −4.84684 −0.253695
\(366\) 0 0
\(367\) 19.7190 1.02932 0.514662 0.857393i \(-0.327918\pi\)
0.514662 + 0.857393i \(0.327918\pi\)
\(368\) 9.51844 16.4864i 0.496183 0.859414i
\(369\) 0 0
\(370\) 2.05940 + 3.56699i 0.107063 + 0.185439i
\(371\) 0.387993 + 1.05691i 0.0201436 + 0.0548719i
\(372\) 0 0
\(373\) 17.5469 0.908544 0.454272 0.890863i \(-0.349899\pi\)
0.454272 + 0.890863i \(0.349899\pi\)
\(374\) 9.05972 0.468467
\(375\) 0 0
\(376\) −8.82478 + 15.2850i −0.455103 + 0.788262i
\(377\) −13.9887 + 2.86308i −0.720452 + 0.147456i
\(378\) 0 0
\(379\) 5.85068 10.1337i 0.300529 0.520532i −0.675727 0.737152i \(-0.736170\pi\)
0.976256 + 0.216620i \(0.0695034\pi\)
\(380\) −6.95942 12.0541i −0.357010 0.618360i
\(381\) 0 0
\(382\) −13.8055 23.9119i −0.706352 1.22344i
\(383\) 21.5288 1.10007 0.550036 0.835141i \(-0.314614\pi\)
0.550036 + 0.835141i \(0.314614\pi\)
\(384\) 0 0
\(385\) 0.978699 1.17293i 0.0498791 0.0597783i
\(386\) −28.1536 48.7634i −1.43298 2.48199i
\(387\) 0 0
\(388\) 28.5000 1.44687
\(389\) 13.2455 + 22.9419i 0.671574 + 1.16320i 0.977458 + 0.211131i \(0.0677147\pi\)
−0.305884 + 0.952069i \(0.598952\pi\)
\(390\) 0 0
\(391\) −53.3118 −2.69609
\(392\) 26.8000 + 9.58703i 1.35360 + 0.484218i
\(393\) 0 0
\(394\) 3.51267 0.176966
\(395\) 1.36802 + 2.36949i 0.0688327 + 0.119222i
\(396\) 0 0
\(397\) −33.7989 −1.69632 −0.848160 0.529740i \(-0.822289\pi\)
−0.848160 + 0.529740i \(0.822289\pi\)
\(398\) 22.4332 1.12447
\(399\) 0 0
\(400\) 4.64989 8.05384i 0.232494 0.402692i
\(401\) 10.8059 + 18.7164i 0.539623 + 0.934655i 0.998924 + 0.0463741i \(0.0147666\pi\)
−0.459301 + 0.888281i \(0.651900\pi\)
\(402\) 0 0
\(403\) −3.40730 + 10.2231i −0.169730 + 0.509250i
\(404\) −4.88264 + 8.45697i −0.242920 + 0.420750i
\(405\) 0 0
\(406\) 24.6528 + 4.27676i 1.22350 + 0.212252i
\(407\) −0.516056 0.893835i −0.0255799 0.0443058i
\(408\) 0 0
\(409\) −3.87109 + 6.70492i −0.191413 + 0.331537i −0.945719 0.324986i \(-0.894640\pi\)
0.754306 + 0.656523i \(0.227974\pi\)
\(410\) −4.30637 + 7.45886i −0.212677 + 0.368367i
\(411\) 0 0
\(412\) 20.1093 + 34.8303i 0.990714 + 1.71597i
\(413\) 10.1849 12.2062i 0.501167 0.600630i
\(414\) 0 0
\(415\) 1.40868 2.43991i 0.0691495 0.119770i
\(416\) 9.28509 1.90040i 0.455239 0.0931746i
\(417\) 0 0
\(418\) 2.68589 + 4.65211i 0.131371 + 0.227542i
\(419\) −4.05097 + 7.01649i −0.197903 + 0.342778i −0.947848 0.318722i \(-0.896746\pi\)
0.749945 + 0.661500i \(0.230080\pi\)
\(420\) 0 0
\(421\) −32.1124 −1.56506 −0.782530 0.622612i \(-0.786071\pi\)
−0.782530 + 0.622612i \(0.786071\pi\)
\(422\) −21.3543 −1.03951
\(423\) 0 0
\(424\) 0.865159 + 1.49850i 0.0420158 + 0.0727735i
\(425\) −26.0435 −1.26330
\(426\) 0 0
\(427\) 5.75257 + 0.997954i 0.278386 + 0.0482944i
\(428\) 59.1713 2.86015
\(429\) 0 0
\(430\) 7.48384 + 12.9624i 0.360903 + 0.625102i
\(431\) 29.5281 1.42232 0.711159 0.703031i \(-0.248171\pi\)
0.711159 + 0.703031i \(0.248171\pi\)
\(432\) 0 0
\(433\) −11.0455 19.1314i −0.530813 0.919395i −0.999353 0.0359531i \(-0.988553\pi\)
0.468540 0.883442i \(-0.344780\pi\)
\(434\) 12.0979 14.4988i 0.580716 0.695967i
\(435\) 0 0
\(436\) 34.1938 1.63758
\(437\) −15.8051 27.3752i −0.756060 1.30953i
\(438\) 0 0
\(439\) 3.17790 + 5.50428i 0.151673 + 0.262705i 0.931843 0.362863i \(-0.118201\pi\)
−0.780170 + 0.625568i \(0.784867\pi\)
\(440\) 1.17387 2.03321i 0.0559622 0.0969294i
\(441\) 0 0
\(442\) 36.8718 + 41.5777i 1.75381 + 1.97765i
\(443\) −6.78135 + 11.7456i −0.322192 + 0.558052i −0.980940 0.194311i \(-0.937753\pi\)
0.658748 + 0.752363i \(0.271086\pi\)
\(444\) 0 0
\(445\) −2.05602 −0.0974648
\(446\) 52.1060 2.46729
\(447\) 0 0
\(448\) −28.3794 4.92325i −1.34080 0.232602i
\(449\) 10.9559 + 18.9762i 0.517041 + 0.895541i 0.999804 + 0.0197900i \(0.00629977\pi\)
−0.482763 + 0.875751i \(0.660367\pi\)
\(450\) 0 0
\(451\) 1.07911 1.86908i 0.0508134 0.0880115i
\(452\) −37.6946 −1.77300
\(453\) 0 0
\(454\) 44.3041 2.07930
\(455\) 9.36610 0.282132i 0.439090 0.0132265i
\(456\) 0 0
\(457\) −7.60732 13.1763i −0.355855 0.616359i 0.631409 0.775450i \(-0.282477\pi\)
−0.987264 + 0.159091i \(0.949144\pi\)
\(458\) 46.2097 2.15924
\(459\) 0 0
\(460\) −15.0213 + 26.0176i −0.700371 + 1.21308i
\(461\) −8.10813 14.0437i −0.377633 0.654080i 0.613084 0.790018i \(-0.289929\pi\)
−0.990717 + 0.135937i \(0.956595\pi\)
\(462\) 0 0
\(463\) −1.44769 −0.0672799 −0.0336400 0.999434i \(-0.510710\pi\)
−0.0336400 + 0.999434i \(0.510710\pi\)
\(464\) 9.12705 0.423713
\(465\) 0 0
\(466\) −38.5988 −1.78805
\(467\) 7.00337 12.1302i 0.324078 0.561319i −0.657248 0.753675i \(-0.728279\pi\)
0.981325 + 0.192356i \(0.0616128\pi\)
\(468\) 0 0
\(469\) 18.2817 + 3.17150i 0.844169 + 0.146446i
\(470\) 5.09091 8.81772i 0.234826 0.406731i
\(471\) 0 0
\(472\) 12.2160 21.1588i 0.562288 0.973912i
\(473\) −1.87534 3.24818i −0.0862282 0.149352i
\(474\) 0 0
\(475\) −7.72100 13.3732i −0.354264 0.613603i
\(476\) −21.7895 59.3553i −0.998719 2.72055i
\(477\) 0 0
\(478\) 19.2281 + 33.3041i 0.879474 + 1.52329i
\(479\) 30.0243 1.37185 0.685923 0.727674i \(-0.259399\pi\)
0.685923 + 0.727674i \(0.259399\pi\)
\(480\) 0 0
\(481\) 2.00180 6.00611i 0.0912742 0.273855i
\(482\) −9.56649 −0.435742
\(483\) 0 0
\(484\) 19.7253 34.1652i 0.896605 1.55296i
\(485\) −7.56065 −0.343312
\(486\) 0 0
\(487\) 14.2452 24.6733i 0.645510 1.11806i −0.338674 0.940904i \(-0.609978\pi\)
0.984184 0.177152i \(-0.0566884\pi\)
\(488\) 8.97297 0.406187
\(489\) 0 0
\(490\) −15.4606 5.53064i −0.698438 0.249849i
\(491\) −14.2339 + 24.6538i −0.642365 + 1.11261i 0.342539 + 0.939504i \(0.388713\pi\)
−0.984903 + 0.173105i \(0.944620\pi\)
\(492\) 0 0
\(493\) −12.7799 22.1354i −0.575578 0.996930i
\(494\) −10.4187 + 31.2598i −0.468759 + 1.40644i
\(495\) 0 0
\(496\) 3.44406 5.96528i 0.154643 0.267849i
\(497\) 3.28467 + 8.94755i 0.147337 + 0.401353i
\(498\) 0 0
\(499\) 13.1164 22.7183i 0.587172 1.01701i −0.407429 0.913237i \(-0.633575\pi\)
0.994601 0.103775i \(-0.0330921\pi\)
\(500\) −16.4309 + 28.4591i −0.734811 + 1.27273i
\(501\) 0 0
\(502\) 3.87684 6.71488i 0.173032 0.299700i
\(503\) 4.26588 + 7.38872i 0.190206 + 0.329447i 0.945318 0.326149i \(-0.105751\pi\)
−0.755112 + 0.655595i \(0.772418\pi\)
\(504\) 0 0
\(505\) 1.29529 2.24352i 0.0576398 0.0998351i
\(506\) 5.79726 10.0412i 0.257720 0.446384i
\(507\) 0 0
\(508\) −7.86876 13.6291i −0.349120 0.604693i
\(509\) −6.51298 11.2808i −0.288683 0.500014i 0.684813 0.728719i \(-0.259884\pi\)
−0.973496 + 0.228706i \(0.926551\pi\)
\(510\) 0 0
\(511\) −4.49890 12.2552i −0.199020 0.542137i
\(512\) −24.8008 −1.09605
\(513\) 0 0
\(514\) −32.1100 + 55.6162i −1.41631 + 2.45312i
\(515\) −5.33472 9.24000i −0.235076 0.407163i
\(516\) 0 0
\(517\) −1.27571 + 2.20959i −0.0561055 + 0.0971775i
\(518\) −7.10753 + 8.51811i −0.312287 + 0.374264i
\(519\) 0 0
\(520\) 14.1085 2.88761i 0.618698 0.126630i
\(521\) 2.23285 + 3.86741i 0.0978230 + 0.169434i 0.910783 0.412885i \(-0.135479\pi\)
−0.812960 + 0.582319i \(0.802145\pi\)
\(522\) 0 0
\(523\) 1.45406 + 2.51850i 0.0635815 + 0.110126i 0.896064 0.443925i \(-0.146414\pi\)
−0.832482 + 0.554051i \(0.813081\pi\)
\(524\) −4.01665 6.95704i −0.175468 0.303920i
\(525\) 0 0
\(526\) −4.54570 7.87339i −0.198202 0.343296i
\(527\) −19.2898 −0.840277
\(528\) 0 0
\(529\) −22.6139 + 39.1684i −0.983213 + 1.70297i
\(530\) −0.499100 0.864466i −0.0216795 0.0375500i
\(531\) 0 0
\(532\) 24.0187 28.7855i 1.04134 1.24801i
\(533\) 12.9696 2.65451i 0.561775 0.114980i
\(534\) 0 0
\(535\) −15.6973 −0.678654
\(536\) 28.5161 1.23171
\(537\) 0 0
\(538\) 56.9262 2.45426
\(539\) 3.87419 + 1.38590i 0.166873 + 0.0596948i
\(540\) 0 0
\(541\) 9.23193 15.9902i 0.396912 0.687471i −0.596431 0.802664i \(-0.703415\pi\)
0.993343 + 0.115193i \(0.0367486\pi\)
\(542\) −11.8224 + 20.4770i −0.507815 + 0.879562i
\(543\) 0 0
\(544\) 8.48277 + 14.6926i 0.363696 + 0.629940i
\(545\) −9.07112 −0.388564
\(546\) 0 0
\(547\) 34.9817 1.49571 0.747856 0.663861i \(-0.231083\pi\)
0.747856 + 0.663861i \(0.231083\pi\)
\(548\) 15.4832 + 26.8177i 0.661411 + 1.14560i
\(549\) 0 0
\(550\) 2.83204 4.90524i 0.120759 0.209160i
\(551\) 7.57760 13.1248i 0.322817 0.559135i
\(552\) 0 0
\(553\) −4.72140 + 5.65842i −0.200774 + 0.240621i
\(554\) 28.1449 1.19576
\(555\) 0 0
\(556\) −2.13615 −0.0905930
\(557\) −0.0531413 −0.00225167 −0.00112583 0.999999i \(-0.500358\pi\)
−0.00112583 + 0.999999i \(0.500358\pi\)
\(558\) 0 0
\(559\) 7.27451 21.8261i 0.307679 0.923146i
\(560\) −5.90148 1.02379i −0.249383 0.0432629i
\(561\) 0 0
\(562\) 15.5194 + 26.8804i 0.654646 + 1.13388i
\(563\) 3.99253 6.91527i 0.168265 0.291444i −0.769545 0.638593i \(-0.779517\pi\)
0.937810 + 0.347149i \(0.112850\pi\)
\(564\) 0 0
\(565\) 9.99985 0.420697
\(566\) 20.0655 + 34.7544i 0.843414 + 1.46084i
\(567\) 0 0
\(568\) 7.32424 + 12.6860i 0.307318 + 0.532291i
\(569\) −13.3621 23.1438i −0.560167 0.970237i −0.997481 0.0709285i \(-0.977404\pi\)
0.437315 0.899308i \(-0.355930\pi\)
\(570\) 0 0
\(571\) −6.74647 11.6852i −0.282331 0.489012i 0.689627 0.724164i \(-0.257774\pi\)
−0.971958 + 0.235153i \(0.924441\pi\)
\(572\) −7.68799 + 1.57352i −0.321451 + 0.0657920i
\(573\) 0 0
\(574\) −22.8569 3.96520i −0.954028 0.165504i
\(575\) −16.6651 + 28.8648i −0.694982 + 1.20374i
\(576\) 0 0
\(577\) −6.00662 10.4038i −0.250059 0.433115i 0.713483 0.700673i \(-0.247117\pi\)
−0.963542 + 0.267558i \(0.913783\pi\)
\(578\) −29.4406 + 50.9925i −1.22457 + 2.12101i
\(579\) 0 0
\(580\) −14.4036 −0.598078
\(581\) 7.47684 + 1.29708i 0.310192 + 0.0538119i
\(582\) 0 0
\(583\) 0.125067 + 0.216622i 0.00517974 + 0.00897158i
\(584\) −10.0318 17.3756i −0.415118 0.719005i
\(585\) 0 0
\(586\) −16.8305 + 29.1512i −0.695260 + 1.20422i
\(587\) 5.21177 9.02705i 0.215113 0.372586i −0.738195 0.674588i \(-0.764321\pi\)
0.953307 + 0.302002i \(0.0976548\pi\)
\(588\) 0 0
\(589\) −5.71876 9.90518i −0.235637 0.408136i
\(590\) −7.04728 + 12.2062i −0.290132 + 0.502523i
\(591\) 0 0
\(592\) −2.02339 + 3.50462i −0.0831610 + 0.144039i
\(593\) −11.1751 + 19.3558i −0.458905 + 0.794847i −0.998903 0.0468194i \(-0.985091\pi\)
0.539998 + 0.841666i \(0.318425\pi\)
\(594\) 0 0
\(595\) 5.78044 + 15.7461i 0.236975 + 0.645528i
\(596\) 5.19607 8.99986i 0.212839 0.368649i
\(597\) 0 0
\(598\) 69.6759 14.2607i 2.84926 0.583163i
\(599\) 0.579463 + 1.00366i 0.0236762 + 0.0410084i 0.877621 0.479356i \(-0.159130\pi\)
−0.853945 + 0.520364i \(0.825796\pi\)
\(600\) 0 0
\(601\) −21.0907 + 36.5301i −0.860306 + 1.49009i 0.0113271 + 0.999936i \(0.496394\pi\)
−0.871633 + 0.490158i \(0.836939\pi\)
\(602\) −25.8287 + 30.9547i −1.05270 + 1.26162i
\(603\) 0 0
\(604\) −85.2029 −3.46686
\(605\) −5.23284 + 9.06355i −0.212745 + 0.368486i
\(606\) 0 0
\(607\) −18.1569 −0.736965 −0.368482 0.929635i \(-0.620123\pi\)
−0.368482 + 0.929635i \(0.620123\pi\)
\(608\) −5.02970 + 8.71169i −0.203981 + 0.353306i
\(609\) 0 0
\(610\) −5.17640 −0.209586
\(611\) −15.3324 + 3.13811i −0.620282 + 0.126954i
\(612\) 0 0
\(613\) −0.902645 −0.0364575 −0.0182288 0.999834i \(-0.505803\pi\)
−0.0182288 + 0.999834i \(0.505803\pi\)
\(614\) −18.9594 32.8386i −0.765137 1.32526i
\(615\) 0 0
\(616\) 6.23055 + 1.08087i 0.251036 + 0.0435497i
\(617\) −13.0218 22.5544i −0.524238 0.908008i −0.999602 0.0282180i \(-0.991017\pi\)
0.475363 0.879790i \(-0.342317\pi\)
\(618\) 0 0
\(619\) −13.4171 23.2390i −0.539277 0.934056i −0.998943 0.0459638i \(-0.985364\pi\)
0.459666 0.888092i \(-0.347969\pi\)
\(620\) −5.43515 + 9.41396i −0.218281 + 0.378074i
\(621\) 0 0
\(622\) −34.1530 + 59.1547i −1.36941 + 2.37189i
\(623\) −1.90843 5.19863i −0.0764596 0.208279i
\(624\) 0 0
\(625\) −5.72894 + 9.92281i −0.229158 + 0.396912i
\(626\) −44.3679 −1.77330
\(627\) 0 0
\(628\) 83.5925 3.33570
\(629\) 11.3328 0.451869
\(630\) 0 0
\(631\) 16.8061 + 29.1089i 0.669039 + 1.15881i 0.978173 + 0.207791i \(0.0666273\pi\)
−0.309135 + 0.951018i \(0.600039\pi\)
\(632\) −5.66296 + 9.80853i −0.225260 + 0.390162i
\(633\) 0 0
\(634\) −73.1802 −2.90636
\(635\) 2.08747 + 3.61561i 0.0828388 + 0.143481i
\(636\) 0 0
\(637\) 9.40711 + 23.4202i 0.372723 + 0.927942i
\(638\) 5.55889 0.220078
\(639\) 0 0
\(640\) 20.3729 0.805310
\(641\) 10.5921 18.3460i 0.418361 0.724622i −0.577414 0.816452i \(-0.695938\pi\)
0.995775 + 0.0918294i \(0.0292714\pi\)
\(642\) 0 0
\(643\) −0.330770 0.572910i −0.0130443 0.0225933i 0.859430 0.511254i \(-0.170819\pi\)
−0.872474 + 0.488661i \(0.837486\pi\)
\(644\) −79.7282 13.8312i −3.14173 0.545027i
\(645\) 0 0
\(646\) −58.9834 −2.32067
\(647\) 40.0323 1.57383 0.786916 0.617060i \(-0.211676\pi\)
0.786916 + 0.617060i \(0.211676\pi\)
\(648\) 0 0
\(649\) 1.76594 3.05870i 0.0693193 0.120065i
\(650\) 34.0376 6.96654i 1.33506 0.273250i
\(651\) 0 0
\(652\) −15.1388 + 26.2212i −0.592883 + 1.02690i
\(653\) 6.35602 + 11.0089i 0.248730 + 0.430813i 0.963174 0.268880i \(-0.0866534\pi\)
−0.714444 + 0.699693i \(0.753320\pi\)
\(654\) 0 0
\(655\) 1.06556 + 1.84560i 0.0416349 + 0.0721138i
\(656\) −8.46215 −0.330391
\(657\) 0 0
\(658\) 27.0209 + 4.68759i 1.05339 + 0.182741i
\(659\) −7.09522 12.2893i −0.276391 0.478723i 0.694094 0.719884i \(-0.255805\pi\)
−0.970485 + 0.241161i \(0.922472\pi\)
\(660\) 0 0
\(661\) 50.1780 1.95170 0.975848 0.218449i \(-0.0700996\pi\)
0.975848 + 0.218449i \(0.0700996\pi\)
\(662\) −32.5104 56.3096i −1.26355 2.18853i
\(663\) 0 0
\(664\) 11.6625 0.452594
\(665\) −6.37183 + 7.63640i −0.247089 + 0.296127i
\(666\) 0 0
\(667\) −32.7112 −1.26658
\(668\) −4.30944 7.46417i −0.166737 0.288797i
\(669\) 0 0
\(670\) −16.4506 −0.635542
\(671\) 1.29713 0.0500751
\(672\) 0 0
\(673\) 0.937137 1.62317i 0.0361240 0.0625685i −0.847398 0.530958i \(-0.821832\pi\)
0.883522 + 0.468389i \(0.155166\pi\)
\(674\) 14.7056 + 25.4708i 0.566438 + 0.981100i
\(675\) 0 0
\(676\) −38.5104 28.8785i −1.48117 1.11071i
\(677\) −1.00439 + 1.73966i −0.0386020 + 0.0668607i −0.884681 0.466197i \(-0.845624\pi\)
0.846079 + 0.533058i \(0.178957\pi\)
\(678\) 0 0
\(679\) −7.01790 19.1170i −0.269322 0.733644i
\(680\) 12.8894 + 22.3251i 0.494286 + 0.856128i
\(681\) 0 0
\(682\) 2.09762 3.63319i 0.0803222 0.139122i
\(683\) −7.05061 + 12.2120i −0.269784 + 0.467280i −0.968806 0.247820i \(-0.920286\pi\)
0.699022 + 0.715100i \(0.253619\pi\)
\(684\) 0 0
\(685\) −4.10748 7.11437i −0.156939 0.271826i
\(686\) −0.366563 44.2255i −0.0139955 1.68854i
\(687\) 0 0
\(688\) −7.35298 + 12.7357i −0.280330 + 0.485546i
\(689\) −0.485139 + 1.45559i −0.0184823 + 0.0554536i
\(690\) 0 0
\(691\) 17.8460 + 30.9102i 0.678895 + 1.17588i 0.975314 + 0.220822i \(0.0708741\pi\)
−0.296419 + 0.955058i \(0.595793\pi\)
\(692\) −15.0585 + 26.0820i −0.572437 + 0.991489i
\(693\) 0 0
\(694\) −14.6746 −0.557041
\(695\) 0.566691 0.0214958
\(696\) 0 0
\(697\) 11.8489 + 20.5229i 0.448809 + 0.777360i
\(698\) 31.1191 1.17788
\(699\) 0 0
\(700\) −38.9483 6.75674i −1.47211 0.255381i
\(701\) 6.15865 0.232609 0.116305 0.993214i \(-0.462895\pi\)
0.116305 + 0.993214i \(0.462895\pi\)
\(702\) 0 0
\(703\) 3.35979 + 5.81932i 0.126717 + 0.219480i
\(704\) −6.39918 −0.241178
\(705\) 0 0
\(706\) 37.8103 + 65.4894i 1.42301 + 2.46473i
\(707\) 6.87501 + 1.19268i 0.258561 + 0.0448552i
\(708\) 0 0
\(709\) 34.0371 1.27829 0.639144 0.769087i \(-0.279289\pi\)
0.639144 + 0.769087i \(0.279289\pi\)
\(710\) −4.22527 7.31838i −0.158571 0.274654i
\(711\) 0 0
\(712\) −4.25547 7.37069i −0.159480 0.276228i
\(713\) −12.3434 + 21.3794i −0.462265 + 0.800667i
\(714\) 0 0
\(715\) 2.03952 0.417432i 0.0762736 0.0156111i
\(716\) −38.8648 + 67.3158i −1.45244 + 2.51571i
\(717\) 0 0
\(718\) −47.5989 −1.77637
\(719\) 22.9648 0.856444 0.428222 0.903674i \(-0.359140\pi\)
0.428222 + 0.903674i \(0.359140\pi\)
\(720\) 0 0
\(721\) 18.4115 22.0655i 0.685679 0.821761i
\(722\) 5.19981 + 9.00633i 0.193517 + 0.335181i
\(723\) 0 0
\(724\) 2.97712 5.15653i 0.110644 0.191641i
\(725\) −15.9798 −0.593476
\(726\) 0 0
\(727\) 1.06558 0.0395203 0.0197601 0.999805i \(-0.493710\pi\)
0.0197601 + 0.999805i \(0.493710\pi\)
\(728\) 20.3970 + 32.9928i 0.755963 + 1.22280i
\(729\) 0 0
\(730\) 5.78721 + 10.0237i 0.214194 + 0.370996i
\(731\) 41.1833 1.52322
\(732\) 0 0
\(733\) 13.1689 22.8092i 0.486404 0.842476i −0.513474 0.858105i \(-0.671642\pi\)
0.999878 + 0.0156289i \(0.00497504\pi\)
\(734\) −23.5448 40.7809i −0.869056 1.50525i
\(735\) 0 0
\(736\) 21.7123 0.800326
\(737\) 4.12228 0.151846
\(738\) 0 0
\(739\) 34.2149 1.25862 0.629308 0.777156i \(-0.283338\pi\)
0.629308 + 0.777156i \(0.283338\pi\)
\(740\) 3.19317 5.53073i 0.117383 0.203314i
\(741\) 0 0
\(742\) 1.72252 2.06438i 0.0632358 0.0757857i
\(743\) 11.2391 19.4667i 0.412322 0.714163i −0.582821 0.812600i \(-0.698051\pi\)
0.995143 + 0.0984379i \(0.0313846\pi\)
\(744\) 0 0
\(745\) −1.37845 + 2.38754i −0.0505023 + 0.0874726i
\(746\) −20.9513 36.2888i −0.767083 1.32863i
\(747\) 0 0
\(748\) −7.02368 12.1654i −0.256811 0.444810i
\(749\) −14.5705 39.6905i −0.532393 1.45026i
\(750\) 0 0
\(751\) 21.2712 + 36.8428i 0.776197 + 1.34441i 0.934119 + 0.356961i \(0.116187\pi\)
−0.157923 + 0.987451i \(0.550480\pi\)
\(752\) 10.0038 0.364801
\(753\) 0 0
\(754\) 22.6239 + 25.5114i 0.823912 + 0.929069i
\(755\) 22.6031 0.822612
\(756\) 0 0
\(757\) 5.61902 9.73243i 0.204227 0.353731i −0.745659 0.666327i \(-0.767865\pi\)
0.949886 + 0.312596i \(0.101199\pi\)
\(758\) −27.9433 −1.01495
\(759\) 0 0
\(760\) −7.64252 + 13.2372i −0.277223 + 0.480165i
\(761\) −12.8084 −0.464306 −0.232153 0.972679i \(-0.574577\pi\)
−0.232153 + 0.972679i \(0.574577\pi\)
\(762\) 0 0
\(763\) −8.41994 22.9362i −0.304822 0.830347i
\(764\) −21.4059 + 37.0760i −0.774437 + 1.34136i
\(765\) 0 0
\(766\) −25.7058 44.5238i −0.928789 1.60871i
\(767\) 21.2244 4.34404i 0.766369 0.156854i
\(768\) 0 0
\(769\) 25.6759 44.4719i 0.925895 1.60370i 0.135780 0.990739i \(-0.456646\pi\)
0.790115 0.612958i \(-0.210021\pi\)
\(770\) −3.59433 0.623543i −0.129531 0.0224709i
\(771\) 0 0
\(772\) −43.6529 + 75.6091i −1.57110 + 2.72123i
\(773\) 10.0023 17.3245i 0.359759 0.623120i −0.628162 0.778083i \(-0.716192\pi\)
0.987920 + 0.154963i \(0.0495257\pi\)
\(774\) 0 0
\(775\) −6.02993 + 10.4441i −0.216602 + 0.375165i
\(776\) −15.6487 27.1044i −0.561756 0.972990i
\(777\) 0 0
\(778\) 31.6308 54.7861i 1.13402 1.96418i
\(779\) −7.02558 + 12.1687i −0.251717 + 0.435987i
\(780\) 0 0
\(781\) 1.05879 + 1.83388i 0.0378864 + 0.0656212i
\(782\) 63.6552 + 110.254i 2.27631 + 3.94268i
\(783\) 0 0
\(784\) −2.88920 15.8721i −0.103186 0.566861i
\(785\) −22.1759 −0.791492
\(786\) 0 0
\(787\) −14.6596 + 25.3911i −0.522558 + 0.905096i 0.477098 + 0.878850i \(0.341689\pi\)
−0.999656 + 0.0262462i \(0.991645\pi\)
\(788\) −2.72325 4.71680i −0.0970117 0.168029i
\(789\) 0 0
\(790\) 3.26689 5.65842i 0.116231