Properties

Label 483.2.h.b.160.9
Level $483$
Weight $2$
Character 483.160
Analytic conductor $3.857$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.h (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 14 x^{10} + 67 x^{8} + 141 x^{6} + 129 x^{4} + 39 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 160.9
Root \(2.61062i\) of defining polynomial
Character \(\chi\) \(=\) 483.160
Dual form 483.2.h.b.160.11

$q$-expansion

\(f(q)\) \(=\) \(q+1.86081 q^{2} -1.00000i q^{3} +1.46260 q^{4} -4.10256 q^{5} -1.86081i q^{6} +(-0.663393 - 2.56123i) q^{7} -1.00000 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.86081 q^{2} -1.00000i q^{3} +1.46260 q^{4} -4.10256 q^{5} -1.86081i q^{6} +(-0.663393 - 2.56123i) q^{7} -1.00000 q^{8} -1.00000 q^{9} -7.63407 q^{10} -1.89784i q^{11} -1.46260i q^{12} -2.18421i q^{13} +(-1.23445 - 4.76596i) q^{14} +4.10256i q^{15} -4.78600 q^{16} +1.18482 q^{17} -1.86081 q^{18} +4.98050 q^{19} -6.00040 q^{20} +(-2.56123 + 0.663393i) q^{21} -3.53151i q^{22} +(-4.25901 + 2.20472i) q^{23} +1.00000i q^{24} +11.8310 q^{25} -4.06439i q^{26} +1.00000i q^{27} +(-0.970278 - 3.74605i) q^{28} +2.39821 q^{29} +7.63407i q^{30} -9.32340i q^{31} -6.90582 q^{32} -1.89784 q^{33} +2.20472 q^{34} +(2.72161 + 10.5076i) q^{35} -1.46260 q^{36} +6.92106i q^{37} +9.26774 q^{38} -2.18421 q^{39} +4.10256 q^{40} +5.60179i q^{41} +(-4.76596 + 1.23445i) q^{42} -5.38663i q^{43} -2.77578i q^{44} +4.10256 q^{45} +(-7.92520 + 4.10256i) q^{46} -9.57201i q^{47} +4.78600i q^{48} +(-6.11982 + 3.39821i) q^{49} +22.0152 q^{50} -1.18482i q^{51} -3.19462i q^{52} -5.85844i q^{53} +1.86081i q^{54} +7.78600i q^{55} +(0.663393 + 2.56123i) q^{56} -4.98050i q^{57} +4.46260 q^{58} +3.50761i q^{59} +6.00040i q^{60} -1.49171 q^{61} -17.3490i q^{62} +(0.663393 + 2.56123i) q^{63} -3.27839 q^{64} +8.96086i q^{65} -3.53151 q^{66} -3.48879i q^{67} +1.73292 q^{68} +(2.20472 + 4.25901i) q^{69} +(5.06439 + 19.5526i) q^{70} +1.81579 q^{71} +1.00000 q^{72} +7.97021i q^{73} +12.8787i q^{74} -11.8310i q^{75} +7.28447 q^{76} +(-4.86081 + 1.25901i) q^{77} -4.06439 q^{78} -14.0833i q^{79} +19.6349 q^{80} +1.00000 q^{81} +10.4238i q^{82} -2.51161 q^{83} +(-3.74605 + 0.970278i) q^{84} -4.86081 q^{85} -10.0235i q^{86} -2.39821i q^{87} +1.89784i q^{88} +4.57437 q^{89} +7.63407 q^{90} +(-5.59427 + 1.44899i) q^{91} +(-6.22923 + 3.22463i) q^{92} -9.32340 q^{93} -17.8116i q^{94} -20.4328 q^{95} +6.90582i q^{96} -7.44939 q^{97} +(-11.3878 + 6.32340i) q^{98} +1.89784i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 8q^{4} - 12q^{8} - 12q^{9} + O(q^{10}) \) \( 12q + 8q^{4} - 12q^{8} - 12q^{9} - 16q^{16} - 16q^{23} + 24q^{25} + 16q^{29} + 16q^{32} - 12q^{35} - 8q^{36} + 28q^{39} - 76q^{46} - 16q^{49} + 92q^{50} + 44q^{58} - 84q^{64} + 64q^{70} + 76q^{71} + 12q^{72} - 36q^{77} - 52q^{78} + 12q^{81} - 36q^{85} + 56q^{92} - 80q^{93} - 140q^{95} - 108q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.86081 1.31579 0.657894 0.753110i \(-0.271447\pi\)
0.657894 + 0.753110i \(0.271447\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 1.46260 0.731299
\(5\) −4.10256 −1.83472 −0.917361 0.398057i \(-0.869685\pi\)
−0.917361 + 0.398057i \(0.869685\pi\)
\(6\) 1.86081i 0.759671i
\(7\) −0.663393 2.56123i −0.250739 0.968055i
\(8\) −1.00000 −0.353553
\(9\) −1.00000 −0.333333
\(10\) −7.63407 −2.41411
\(11\) 1.89784i 0.572220i −0.958197 0.286110i \(-0.907638\pi\)
0.958197 0.286110i \(-0.0923623\pi\)
\(12\) 1.46260i 0.422216i
\(13\) 2.18421i 0.605791i −0.953024 0.302895i \(-0.902047\pi\)
0.953024 0.302895i \(-0.0979533\pi\)
\(14\) −1.23445 4.76596i −0.329920 1.27376i
\(15\) 4.10256i 1.05928i
\(16\) −4.78600 −1.19650
\(17\) 1.18482 0.287362 0.143681 0.989624i \(-0.454106\pi\)
0.143681 + 0.989624i \(0.454106\pi\)
\(18\) −1.86081 −0.438596
\(19\) 4.98050 1.14261 0.571303 0.820740i \(-0.306438\pi\)
0.571303 + 0.820740i \(0.306438\pi\)
\(20\) −6.00040 −1.34173
\(21\) −2.56123 + 0.663393i −0.558907 + 0.144764i
\(22\) 3.53151i 0.752920i
\(23\) −4.25901 + 2.20472i −0.888066 + 0.459717i
\(24\) 1.00000i 0.204124i
\(25\) 11.8310 2.36620
\(26\) 4.06439i 0.797093i
\(27\) 1.00000i 0.192450i
\(28\) −0.970278 3.74605i −0.183365 0.707938i
\(29\) 2.39821 0.445336 0.222668 0.974894i \(-0.428523\pi\)
0.222668 + 0.974894i \(0.428523\pi\)
\(30\) 7.63407i 1.39378i
\(31\) 9.32340i 1.67453i −0.546795 0.837266i \(-0.684152\pi\)
0.546795 0.837266i \(-0.315848\pi\)
\(32\) −6.90582 −1.22079
\(33\) −1.89784 −0.330371
\(34\) 2.20472 0.378107
\(35\) 2.72161 + 10.5076i 0.460036 + 1.77611i
\(36\) −1.46260 −0.243766
\(37\) 6.92106i 1.13781i 0.822402 + 0.568907i \(0.192634\pi\)
−0.822402 + 0.568907i \(0.807366\pi\)
\(38\) 9.26774 1.50343
\(39\) −2.18421 −0.349754
\(40\) 4.10256 0.648672
\(41\) 5.60179i 0.874853i 0.899254 + 0.437427i \(0.144110\pi\)
−0.899254 + 0.437427i \(0.855890\pi\)
\(42\) −4.76596 + 1.23445i −0.735403 + 0.190479i
\(43\) 5.38663i 0.821454i −0.911758 0.410727i \(-0.865275\pi\)
0.911758 0.410727i \(-0.134725\pi\)
\(44\) 2.77578i 0.418464i
\(45\) 4.10256 0.611574
\(46\) −7.92520 + 4.10256i −1.16851 + 0.604890i
\(47\) 9.57201i 1.39622i −0.715990 0.698110i \(-0.754025\pi\)
0.715990 0.698110i \(-0.245975\pi\)
\(48\) 4.78600i 0.690800i
\(49\) −6.11982 + 3.39821i −0.874260 + 0.485458i
\(50\) 22.0152 3.11342
\(51\) 1.18482i 0.165908i
\(52\) 3.19462i 0.443014i
\(53\) 5.85844i 0.804718i −0.915482 0.402359i \(-0.868190\pi\)
0.915482 0.402359i \(-0.131810\pi\)
\(54\) 1.86081i 0.253224i
\(55\) 7.78600i 1.04986i
\(56\) 0.663393 + 2.56123i 0.0886496 + 0.342259i
\(57\) 4.98050i 0.659683i
\(58\) 4.46260 0.585968
\(59\) 3.50761i 0.456652i 0.973585 + 0.228326i \(0.0733253\pi\)
−0.973585 + 0.228326i \(0.926675\pi\)
\(60\) 6.00040i 0.774648i
\(61\) −1.49171 −0.190993 −0.0954967 0.995430i \(-0.530444\pi\)
−0.0954967 + 0.995430i \(0.530444\pi\)
\(62\) 17.3490i 2.20333i
\(63\) 0.663393 + 2.56123i 0.0835797 + 0.322685i
\(64\) −3.27839 −0.409799
\(65\) 8.96086i 1.11146i
\(66\) −3.53151 −0.434699
\(67\) 3.48879i 0.426224i −0.977028 0.213112i \(-0.931640\pi\)
0.977028 0.213112i \(-0.0683599\pi\)
\(68\) 1.73292 0.210147
\(69\) 2.20472 + 4.25901i 0.265418 + 0.512725i
\(70\) 5.06439 + 19.5526i 0.605311 + 2.33699i
\(71\) 1.81579 0.215495 0.107747 0.994178i \(-0.465636\pi\)
0.107747 + 0.994178i \(0.465636\pi\)
\(72\) 1.00000 0.117851
\(73\) 7.97021i 0.932843i 0.884563 + 0.466421i \(0.154457\pi\)
−0.884563 + 0.466421i \(0.845543\pi\)
\(74\) 12.8787i 1.49712i
\(75\) 11.8310i 1.36613i
\(76\) 7.28447 0.835586
\(77\) −4.86081 + 1.25901i −0.553940 + 0.143478i
\(78\) −4.06439 −0.460202
\(79\) 14.0833i 1.58450i −0.610198 0.792249i \(-0.708910\pi\)
0.610198 0.792249i \(-0.291090\pi\)
\(80\) 19.6349 2.19525
\(81\) 1.00000 0.111111
\(82\) 10.4238i 1.15112i
\(83\) −2.51161 −0.275685 −0.137842 0.990454i \(-0.544017\pi\)
−0.137842 + 0.990454i \(0.544017\pi\)
\(84\) −3.74605 + 0.970278i −0.408728 + 0.105866i
\(85\) −4.86081 −0.527228
\(86\) 10.0235i 1.08086i
\(87\) 2.39821i 0.257115i
\(88\) 1.89784i 0.202310i
\(89\) 4.57437 0.484882 0.242441 0.970166i \(-0.422052\pi\)
0.242441 + 0.970166i \(0.422052\pi\)
\(90\) 7.63407 0.804702
\(91\) −5.59427 + 1.44899i −0.586439 + 0.151895i
\(92\) −6.22923 + 3.22463i −0.649442 + 0.336190i
\(93\) −9.32340 −0.966792
\(94\) 17.8116i 1.83713i
\(95\) −20.4328 −2.09636
\(96\) 6.90582i 0.704822i
\(97\) −7.44939 −0.756371 −0.378186 0.925730i \(-0.623452\pi\)
−0.378186 + 0.925730i \(0.623452\pi\)
\(98\) −11.3878 + 6.32340i −1.15034 + 0.638760i
\(99\) 1.89784i 0.190740i
\(100\) 17.3040 1.73040
\(101\) 17.1004i 1.70156i −0.525524 0.850779i \(-0.676131\pi\)
0.525524 0.850779i \(-0.323869\pi\)
\(102\) 2.20472i 0.218300i
\(103\) 8.91814 0.878731 0.439365 0.898308i \(-0.355203\pi\)
0.439365 + 0.898308i \(0.355203\pi\)
\(104\) 2.18421i 0.214179i
\(105\) 10.5076 2.72161i 1.02544 0.265602i
\(106\) 10.9014i 1.05884i
\(107\) 6.51492i 0.629821i −0.949121 0.314911i \(-0.898025\pi\)
0.949121 0.314911i \(-0.101975\pi\)
\(108\) 1.46260i 0.140739i
\(109\) 16.2880i 1.56011i −0.625710 0.780056i \(-0.715191\pi\)
0.625710 0.780056i \(-0.284809\pi\)
\(110\) 14.4882i 1.38140i
\(111\) 6.92106 0.656917
\(112\) 3.17500 + 12.2581i 0.300009 + 1.15828i
\(113\) 15.5750i 1.46518i 0.680673 + 0.732588i \(0.261688\pi\)
−0.680673 + 0.732588i \(0.738312\pi\)
\(114\) 9.26774i 0.868004i
\(115\) 17.4729 9.04502i 1.62935 0.843452i
\(116\) 3.50761 0.325674
\(117\) 2.18421i 0.201930i
\(118\) 6.52699i 0.600858i
\(119\) −0.786003 3.03460i −0.0720527 0.278182i
\(120\) 4.10256i 0.374511i
\(121\) 7.39821 0.672564
\(122\) −2.77578 −0.251307
\(123\) 5.60179 0.505097
\(124\) 13.6364i 1.22458i
\(125\) −28.0247 −2.50660
\(126\) 1.23445 + 4.76596i 0.109973 + 0.424585i
\(127\) 1.10941 0.0984440 0.0492220 0.998788i \(-0.484326\pi\)
0.0492220 + 0.998788i \(0.484326\pi\)
\(128\) 7.71120 0.681580
\(129\) −5.38663 −0.474267
\(130\) 16.6744i 1.46244i
\(131\) 3.04502i 0.266044i 0.991113 + 0.133022i \(0.0424681\pi\)
−0.991113 + 0.133022i \(0.957532\pi\)
\(132\) −2.77578 −0.241600
\(133\) −3.30403 12.7562i −0.286496 1.10610i
\(134\) 6.49197i 0.560821i
\(135\) 4.10256i 0.353092i
\(136\) −1.18482 −0.101598
\(137\) 4.45216i 0.380374i −0.981748 0.190187i \(-0.939091\pi\)
0.981748 0.190187i \(-0.0609094\pi\)
\(138\) 4.10256 + 7.92520i 0.349233 + 0.674638i
\(139\) 7.35801i 0.624098i 0.950066 + 0.312049i \(0.101015\pi\)
−0.950066 + 0.312049i \(0.898985\pi\)
\(140\) 3.98062 + 15.3684i 0.336424 + 1.29887i
\(141\) −9.57201 −0.806108
\(142\) 3.37883 0.283545
\(143\) −4.14528 −0.346646
\(144\) 4.78600 0.398834
\(145\) −9.83880 −0.817068
\(146\) 14.8310i 1.22742i
\(147\) 3.39821 + 6.11982i 0.280279 + 0.504754i
\(148\) 10.1227i 0.832083i
\(149\) 20.7204i 1.69749i 0.528806 + 0.848743i \(0.322640\pi\)
−0.528806 + 0.848743i \(0.677360\pi\)
\(150\) 22.0152i 1.79754i
\(151\) 21.6620 1.76283 0.881416 0.472341i \(-0.156591\pi\)
0.881416 + 0.472341i \(0.156591\pi\)
\(152\) −4.98050 −0.403972
\(153\) −1.18482 −0.0957872
\(154\) −9.04502 + 2.34278i −0.728868 + 0.188787i
\(155\) 38.2498i 3.07230i
\(156\) −3.19462 −0.255774
\(157\) −12.2847 −0.980428 −0.490214 0.871602i \(-0.663081\pi\)
−0.490214 + 0.871602i \(0.663081\pi\)
\(158\) 26.2063i 2.08486i
\(159\) −5.85844 −0.464604
\(160\) 28.3316 2.23981
\(161\) 8.47221 + 9.44572i 0.667704 + 0.744427i
\(162\) 1.86081 0.146199
\(163\) −10.4328 −0.817161 −0.408580 0.912722i \(-0.633976\pi\)
−0.408580 + 0.912722i \(0.633976\pi\)
\(164\) 8.19317i 0.639779i
\(165\) 7.78600 0.606139
\(166\) −4.67362 −0.362743
\(167\) 11.9702i 0.926283i 0.886284 + 0.463141i \(0.153278\pi\)
−0.886284 + 0.463141i \(0.846722\pi\)
\(168\) 2.56123 0.663393i 0.197603 0.0511819i
\(169\) 8.22923 0.633017
\(170\) −9.04502 −0.693721
\(171\) −4.98050 −0.380868
\(172\) 7.87848i 0.600728i
\(173\) 5.17380i 0.393357i −0.980468 0.196678i \(-0.936985\pi\)
0.980468 0.196678i \(-0.0630155\pi\)
\(174\) 4.46260i 0.338309i
\(175\) −7.84862 30.3020i −0.593300 2.29061i
\(176\) 9.08306i 0.684662i
\(177\) 3.50761 0.263648
\(178\) 8.51201 0.638002
\(179\) −14.5616 −1.08838 −0.544192 0.838961i \(-0.683164\pi\)
−0.544192 + 0.838961i \(0.683164\pi\)
\(180\) 6.00040 0.447244
\(181\) −17.4499 −1.29704 −0.648521 0.761197i \(-0.724612\pi\)
−0.648521 + 0.761197i \(0.724612\pi\)
\(182\) −10.4098 + 2.69629i −0.771629 + 0.199862i
\(183\) 1.49171i 0.110270i
\(184\) 4.25901 2.20472i 0.313979 0.162534i
\(185\) 28.3941i 2.08757i
\(186\) −17.3490 −1.27209
\(187\) 2.24860i 0.164434i
\(188\) 14.0000i 1.02105i
\(189\) 2.56123 0.663393i 0.186302 0.0482547i
\(190\) −38.0215 −2.75837
\(191\) 4.07961i 0.295190i 0.989048 + 0.147595i \(0.0471532\pi\)
−0.989048 + 0.147595i \(0.952847\pi\)
\(192\) 3.27839i 0.236597i
\(193\) 22.8864 1.64740 0.823701 0.567024i \(-0.191905\pi\)
0.823701 + 0.567024i \(0.191905\pi\)
\(194\) −13.8619 −0.995224
\(195\) 8.96086 0.641700
\(196\) −8.95084 + 4.97021i −0.639346 + 0.355015i
\(197\) −0.702237 −0.0500323 −0.0250161 0.999687i \(-0.507964\pi\)
−0.0250161 + 0.999687i \(0.507964\pi\)
\(198\) 3.53151i 0.250973i
\(199\) 23.6947 1.67967 0.839837 0.542838i \(-0.182650\pi\)
0.839837 + 0.542838i \(0.182650\pi\)
\(200\) −11.8310 −0.836579
\(201\) −3.48879 −0.246081
\(202\) 31.8206i 2.23889i
\(203\) −1.59095 6.14237i −0.111663 0.431110i
\(204\) 1.73292i 0.121329i
\(205\) 22.9817i 1.60511i
\(206\) 16.5949 1.15622
\(207\) 4.25901 2.20472i 0.296022 0.153239i
\(208\) 10.4536i 0.724829i
\(209\) 9.45219i 0.653821i
\(210\) 19.5526 5.06439i 1.34926 0.349476i
\(211\) −20.7666 −1.42963 −0.714817 0.699312i \(-0.753490\pi\)
−0.714817 + 0.699312i \(0.753490\pi\)
\(212\) 8.56854i 0.588490i
\(213\) 1.81579i 0.124416i
\(214\) 12.1230i 0.828712i
\(215\) 22.0990i 1.50714i
\(216\) 1.00000i 0.0680414i
\(217\) −23.8794 + 6.18508i −1.62104 + 0.419871i
\(218\) 30.3089i 2.05278i
\(219\) 7.97021 0.538577
\(220\) 11.3878i 0.767765i
\(221\) 2.58790i 0.174081i
\(222\) 12.8787 0.864364
\(223\) 24.5228i 1.64217i 0.570805 + 0.821086i \(0.306631\pi\)
−0.570805 + 0.821086i \(0.693369\pi\)
\(224\) 4.58127 + 17.6874i 0.306099 + 1.18179i
\(225\) −11.8310 −0.788735
\(226\) 28.9821i 1.92786i
\(227\) −21.5098 −1.42765 −0.713826 0.700323i \(-0.753039\pi\)
−0.713826 + 0.700323i \(0.753039\pi\)
\(228\) 7.28447i 0.482426i
\(229\) 10.4526 0.690725 0.345362 0.938469i \(-0.387756\pi\)
0.345362 + 0.938469i \(0.387756\pi\)
\(230\) 32.5136 16.8310i 2.14388 1.10980i
\(231\) 1.25901 + 4.86081i 0.0828370 + 0.319818i
\(232\) −2.39821 −0.157450
\(233\) 4.19317 0.274704 0.137352 0.990522i \(-0.456141\pi\)
0.137352 + 0.990522i \(0.456141\pi\)
\(234\) 4.06439i 0.265698i
\(235\) 39.2697i 2.56168i
\(236\) 5.13023i 0.333950i
\(237\) −14.0833 −0.914810
\(238\) −1.46260 5.64681i −0.0948062 0.366028i
\(239\) 21.8552 1.41370 0.706848 0.707365i \(-0.250116\pi\)
0.706848 + 0.707365i \(0.250116\pi\)
\(240\) 19.6349i 1.26743i
\(241\) 19.8196 1.27669 0.638345 0.769750i \(-0.279619\pi\)
0.638345 + 0.769750i \(0.279619\pi\)
\(242\) 13.7666 0.884952
\(243\) 1.00000i 0.0641500i
\(244\) −2.18177 −0.139673
\(245\) 25.1069 13.9414i 1.60402 0.890681i
\(246\) 10.4238 0.664600
\(247\) 10.8785i 0.692180i
\(248\) 9.32340i 0.592037i
\(249\) 2.51161i 0.159167i
\(250\) −52.1485 −3.29816
\(251\) −7.92120 −0.499981 −0.249991 0.968248i \(-0.580428\pi\)
−0.249991 + 0.968248i \(0.580428\pi\)
\(252\) 0.970278 + 3.74605i 0.0611218 + 0.235979i
\(253\) 4.18421 + 8.08292i 0.263059 + 0.508169i
\(254\) 2.06439 0.129531
\(255\) 4.86081i 0.304395i
\(256\) 20.9058 1.30661
\(257\) 12.0900i 0.754155i −0.926182 0.377078i \(-0.876929\pi\)
0.926182 0.377078i \(-0.123071\pi\)
\(258\) −10.0235 −0.624034
\(259\) 17.7264 4.59138i 1.10147 0.285294i
\(260\) 13.1061i 0.812808i
\(261\) −2.39821 −0.148445
\(262\) 5.66618i 0.350058i
\(263\) 13.3703i 0.824448i 0.911082 + 0.412224i \(0.135248\pi\)
−0.911082 + 0.412224i \(0.864752\pi\)
\(264\) 1.89784 0.116804
\(265\) 24.0346i 1.47643i
\(266\) −6.14816 23.7368i −0.376968 1.45540i
\(267\) 4.57437i 0.279947i
\(268\) 5.10270i 0.311697i
\(269\) 15.6066i 0.951552i −0.879567 0.475776i \(-0.842167\pi\)
0.879567 0.475776i \(-0.157833\pi\)
\(270\) 7.63407i 0.464595i
\(271\) 2.78745i 0.169326i −0.996410 0.0846628i \(-0.973019\pi\)
0.996410 0.0846628i \(-0.0269813\pi\)
\(272\) −5.67056 −0.343828
\(273\) 1.44899 + 5.59427i 0.0876969 + 0.338581i
\(274\) 8.28461i 0.500492i
\(275\) 22.4534i 1.35399i
\(276\) 3.22463 + 6.22923i 0.194100 + 0.374955i
\(277\) −26.1246 −1.56968 −0.784839 0.619700i \(-0.787254\pi\)
−0.784839 + 0.619700i \(0.787254\pi\)
\(278\) 13.6918i 0.821181i
\(279\) 9.32340i 0.558178i
\(280\) −2.72161 10.5076i −0.162647 0.627950i
\(281\) 25.4138i 1.51606i −0.652219 0.758031i \(-0.726162\pi\)
0.652219 0.758031i \(-0.273838\pi\)
\(282\) −17.8116 −1.06067
\(283\) 5.24467 0.311763 0.155882 0.987776i \(-0.450178\pi\)
0.155882 + 0.987776i \(0.450178\pi\)
\(284\) 2.65577 0.157591
\(285\) 20.4328i 1.21034i
\(286\) −7.71356 −0.456112
\(287\) 14.3475 3.71619i 0.846906 0.219360i
\(288\) 6.90582 0.406929
\(289\) −15.5962 −0.917423
\(290\) −18.3081 −1.07509
\(291\) 7.44939i 0.436691i
\(292\) 11.6572i 0.682187i
\(293\) 24.5161 1.43225 0.716124 0.697973i \(-0.245915\pi\)
0.716124 + 0.697973i \(0.245915\pi\)
\(294\) 6.32340 + 11.3878i 0.368788 + 0.664150i
\(295\) 14.3902i 0.837830i
\(296\) 6.92106i 0.402278i
\(297\) 1.89784 0.110124
\(298\) 38.5567i 2.23353i
\(299\) 4.81558 + 9.30258i 0.278492 + 0.537982i
\(300\) 17.3040i 0.999049i
\(301\) −13.7964 + 3.57345i −0.795212 + 0.205971i
\(302\) 40.3088 2.31951
\(303\) −17.1004 −0.982395
\(304\) −23.8367 −1.36713
\(305\) 6.11982 0.350420
\(306\) −2.20472 −0.126036
\(307\) 33.2043i 1.89507i −0.319657 0.947533i \(-0.603568\pi\)
0.319657 0.947533i \(-0.396432\pi\)
\(308\) −7.10941 + 1.84143i −0.405096 + 0.104925i
\(309\) 8.91814i 0.507335i
\(310\) 71.1755i 4.04250i
\(311\) 22.5526i 1.27884i −0.768857 0.639421i \(-0.779174\pi\)
0.768857 0.639421i \(-0.220826\pi\)
\(312\) 2.18421 0.123657
\(313\) −4.07961 −0.230593 −0.115296 0.993331i \(-0.536782\pi\)
−0.115296 + 0.993331i \(0.536782\pi\)
\(314\) −22.8595 −1.29004
\(315\) −2.72161 10.5076i −0.153345 0.592037i
\(316\) 20.5982i 1.15874i
\(317\) −12.8608 −0.722335 −0.361167 0.932501i \(-0.617622\pi\)
−0.361167 + 0.932501i \(0.617622\pi\)
\(318\) −10.9014 −0.611321
\(319\) 4.55141i 0.254830i
\(320\) 13.4498 0.751866
\(321\) −6.51492 −0.363628
\(322\) 15.7651 + 17.5767i 0.878557 + 0.979509i
\(323\) 5.90101 0.328341
\(324\) 1.46260 0.0812555
\(325\) 25.8414i 1.43342i
\(326\) −19.4134 −1.07521
\(327\) −16.2880 −0.900731
\(328\) 5.60179i 0.309307i
\(329\) −24.5161 + 6.35000i −1.35162 + 0.350087i
\(330\) 14.4882 0.797551
\(331\) 24.6081 1.35258 0.676291 0.736635i \(-0.263586\pi\)
0.676291 + 0.736635i \(0.263586\pi\)
\(332\) −3.67347 −0.201608
\(333\) 6.92106i 0.379271i
\(334\) 22.2742i 1.21879i
\(335\) 14.3130i 0.782002i
\(336\) 12.2581 3.17500i 0.668732 0.173211i
\(337\) 1.77564i 0.0967250i −0.998830 0.0483625i \(-0.984600\pi\)
0.998830 0.0483625i \(-0.0154003\pi\)
\(338\) 15.3130 0.832917
\(339\) 15.5750 0.845919
\(340\) −7.10941 −0.385562
\(341\) −17.6943 −0.958201
\(342\) −9.26774 −0.501142
\(343\) 12.7634 + 13.4199i 0.689161 + 0.724608i
\(344\) 5.38663i 0.290428i
\(345\) −9.04502 17.4729i −0.486967 0.940708i
\(346\) 9.62743i 0.517574i
\(347\) 0.766628 0.0411547 0.0205774 0.999788i \(-0.493450\pi\)
0.0205774 + 0.999788i \(0.493450\pi\)
\(348\) 3.50761i 0.188028i
\(349\) 12.9896i 0.695317i −0.937621 0.347658i \(-0.886977\pi\)
0.937621 0.347658i \(-0.113023\pi\)
\(350\) −14.6048 56.3861i −0.780657 3.01396i
\(351\) 2.18421 0.116585
\(352\) 13.1061i 0.698559i
\(353\) 0.736170i 0.0391824i −0.999808 0.0195912i \(-0.993764\pi\)
0.999808 0.0195912i \(-0.00623647\pi\)
\(354\) 6.52699 0.346906
\(355\) −7.44939 −0.395373
\(356\) 6.69046 0.354594
\(357\) −3.03460 + 0.786003i −0.160608 + 0.0415997i
\(358\) −27.0963 −1.43208
\(359\) 24.8230i 1.31011i 0.755582 + 0.655054i \(0.227354\pi\)
−0.755582 + 0.655054i \(0.772646\pi\)
\(360\) −4.10256 −0.216224
\(361\) 5.80538 0.305546
\(362\) −32.4709 −1.70663
\(363\) 7.39821i 0.388305i
\(364\) −8.18217 + 2.11929i −0.428862 + 0.111081i
\(365\) 32.6983i 1.71151i
\(366\) 2.77578i 0.145092i
\(367\) −22.7405 −1.18704 −0.593522 0.804818i \(-0.702263\pi\)
−0.593522 + 0.804818i \(0.702263\pi\)
\(368\) 20.3836 10.5518i 1.06257 0.550051i
\(369\) 5.60179i 0.291618i
\(370\) 52.8358i 2.74680i
\(371\) −15.0048 + 3.88645i −0.779011 + 0.201774i
\(372\) −13.6364 −0.707014
\(373\) 28.9224i 1.49754i 0.662828 + 0.748772i \(0.269356\pi\)
−0.662828 + 0.748772i \(0.730644\pi\)
\(374\) 4.18421i 0.216360i
\(375\) 28.0247i 1.44719i
\(376\) 9.57201i 0.493638i
\(377\) 5.23819i 0.269780i
\(378\) 4.76596 1.23445i 0.245134 0.0634930i
\(379\) 5.53774i 0.284454i −0.989834 0.142227i \(-0.954574\pi\)
0.989834 0.142227i \(-0.0454264\pi\)
\(380\) −29.8850 −1.53307
\(381\) 1.10941i 0.0568366i
\(382\) 7.59136i 0.388408i
\(383\) 25.6550 1.31091 0.655456 0.755234i \(-0.272477\pi\)
0.655456 + 0.755234i \(0.272477\pi\)
\(384\) 7.71120i 0.393511i
\(385\) 19.9418 5.16518i 1.01633 0.263242i
\(386\) 42.5872 2.16763
\(387\) 5.38663i 0.273818i
\(388\) −10.8955 −0.553134
\(389\) 9.10602i 0.461693i −0.972990 0.230847i \(-0.925850\pi\)
0.972990 0.230847i \(-0.0741496\pi\)
\(390\) 16.6744 0.844342
\(391\) −5.04617 + 2.61220i −0.255196 + 0.132105i
\(392\) 6.11982 3.39821i 0.309098 0.171635i
\(393\) 3.04502 0.153601
\(394\) −1.30673 −0.0658319
\(395\) 57.7777i 2.90711i
\(396\) 2.77578i 0.139488i
\(397\) 18.6468i 0.935856i 0.883766 + 0.467928i \(0.154999\pi\)
−0.883766 + 0.467928i \(0.845001\pi\)
\(398\) 44.0913 2.21010
\(399\) −12.7562 + 3.30403i −0.638610 + 0.165408i
\(400\) −56.6233 −2.83116
\(401\) 28.7377i 1.43509i −0.696511 0.717546i \(-0.745265\pi\)
0.696511 0.717546i \(-0.254735\pi\)
\(402\) −6.49197 −0.323790
\(403\) −20.3643 −1.01442
\(404\) 25.0111i 1.24435i
\(405\) −4.10256 −0.203858
\(406\) −2.96046 11.4298i −0.146925 0.567249i
\(407\) 13.1350 0.651080
\(408\) 1.18482i 0.0586574i
\(409\) 20.6170i 1.01945i 0.860339 + 0.509723i \(0.170252\pi\)
−0.860339 + 0.509723i \(0.829748\pi\)
\(410\) 42.7645i 2.11199i
\(411\) −4.45216 −0.219609
\(412\) 13.0437 0.642615
\(413\) 8.98381 2.32693i 0.442065 0.114501i
\(414\) 7.92520 4.10256i 0.389502 0.201630i
\(415\) 10.3040 0.505805
\(416\) 15.0838i 0.739542i
\(417\) 7.35801 0.360323
\(418\) 17.5887i 0.860291i
\(419\) 36.4940 1.78285 0.891424 0.453171i \(-0.149707\pi\)
0.891424 + 0.453171i \(0.149707\pi\)
\(420\) 15.3684 3.98062i 0.749902 0.194235i
\(421\) 16.7599i 0.816825i −0.912797 0.408413i \(-0.866082\pi\)
0.912797 0.408413i \(-0.133918\pi\)
\(422\) −38.6427 −1.88110
\(423\) 9.57201i 0.465407i
\(424\) 5.85844i 0.284511i
\(425\) 14.0177 0.679956
\(426\) 3.37883i 0.163705i
\(427\) 0.989588 + 3.82061i 0.0478895 + 0.184892i
\(428\) 9.52872i 0.460588i
\(429\) 4.14528i 0.200136i
\(430\) 41.1219i 1.98308i
\(431\) 13.6910i 0.659472i 0.944073 + 0.329736i \(0.106960\pi\)
−0.944073 + 0.329736i \(0.893040\pi\)
\(432\) 4.78600i 0.230267i
\(433\) −8.81889 −0.423809 −0.211905 0.977290i \(-0.567967\pi\)
−0.211905 + 0.977290i \(0.567967\pi\)
\(434\) −44.4349 + 11.5092i −2.13294 + 0.552461i
\(435\) 9.83880i 0.471734i
\(436\) 23.8229i 1.14091i
\(437\) −21.2120 + 10.9806i −1.01471 + 0.525275i
\(438\) 14.8310 0.708653
\(439\) 19.0034i 0.906981i 0.891261 + 0.453491i \(0.149821\pi\)
−0.891261 + 0.453491i \(0.850179\pi\)
\(440\) 7.78600i 0.371183i
\(441\) 6.11982 3.39821i 0.291420 0.161819i
\(442\) 4.81558i 0.229054i
\(443\) 20.3476 0.966743 0.483372 0.875415i \(-0.339412\pi\)
0.483372 + 0.875415i \(0.339412\pi\)
\(444\) 10.1227 0.480403
\(445\) −18.7666 −0.889623
\(446\) 45.6323i 2.16075i
\(447\) 20.7204 0.980044
\(448\) 2.17486 + 8.39671i 0.102752 + 0.396707i
\(449\) −20.6724 −0.975593 −0.487797 0.872957i \(-0.662199\pi\)
−0.487797 + 0.872957i \(0.662199\pi\)
\(450\) −22.0152 −1.03781
\(451\) 10.6313 0.500608
\(452\) 22.7800i 1.07148i
\(453\) 21.6620i 1.01777i
\(454\) −40.0255 −1.87849
\(455\) 22.9508 5.94457i 1.07595 0.278686i
\(456\) 4.98050i 0.233233i
\(457\) 33.5565i 1.56971i 0.619682 + 0.784853i \(0.287261\pi\)
−0.619682 + 0.784853i \(0.712739\pi\)
\(458\) 19.4502 0.908848
\(459\) 1.18482i 0.0553028i
\(460\) 25.5558 13.2292i 1.19154 0.616816i
\(461\) 3.26798i 0.152205i 0.997100 + 0.0761024i \(0.0242476\pi\)
−0.997100 + 0.0761024i \(0.975752\pi\)
\(462\) 2.34278 + 9.04502i 0.108996 + 0.420812i
\(463\) −4.65577 −0.216372 −0.108186 0.994131i \(-0.534504\pi\)
−0.108186 + 0.994131i \(0.534504\pi\)
\(464\) −11.4778 −0.532845
\(465\) 38.2498 1.77379
\(466\) 7.80268 0.361452
\(467\) 17.2514 0.798300 0.399150 0.916886i \(-0.369305\pi\)
0.399150 + 0.916886i \(0.369305\pi\)
\(468\) 3.19462i 0.147671i
\(469\) −8.93561 + 2.31444i −0.412608 + 0.106871i
\(470\) 73.0734i 3.37062i
\(471\) 12.2847i 0.566051i
\(472\) 3.50761i 0.161451i
\(473\) −10.2230 −0.470052
\(474\) −26.2063 −1.20370
\(475\) 58.9244 2.70364
\(476\) −1.14961 4.43841i −0.0526921 0.203434i
\(477\) 5.85844i 0.268239i
\(478\) 40.6683 1.86012
\(479\) 20.4333 0.933622 0.466811 0.884357i \(-0.345403\pi\)
0.466811 + 0.884357i \(0.345403\pi\)
\(480\) 28.3316i 1.29315i
\(481\) 15.1170 0.689278
\(482\) 36.8803 1.67985
\(483\) 9.44572 8.47221i 0.429795 0.385499i
\(484\) 10.8206 0.491846
\(485\) 30.5616 1.38773
\(486\) 1.86081i 0.0844079i
\(487\) 3.36215 0.152354 0.0761769 0.997094i \(-0.475729\pi\)
0.0761769 + 0.997094i \(0.475729\pi\)
\(488\) 1.49171 0.0675264
\(489\) 10.4328i 0.471788i
\(490\) 46.7191 25.9422i 2.11056 1.17195i
\(491\) 2.76181 0.124639 0.0623194 0.998056i \(-0.480150\pi\)
0.0623194 + 0.998056i \(0.480150\pi\)
\(492\) 8.19317 0.369377
\(493\) 2.84145 0.127972
\(494\) 20.2427i 0.910762i
\(495\) 7.78600i 0.349955i
\(496\) 44.6218i 2.00358i
\(497\) −1.20458 4.65066i −0.0540329 0.208611i
\(498\) 4.67362i 0.209430i
\(499\) 38.4328 1.72049 0.860244 0.509882i \(-0.170311\pi\)
0.860244 + 0.509882i \(0.170311\pi\)
\(500\) −40.9889 −1.83308
\(501\) 11.9702 0.534790
\(502\) −14.7398 −0.657870
\(503\) −11.5092 −0.513172 −0.256586 0.966521i \(-0.582598\pi\)
−0.256586 + 0.966521i \(0.582598\pi\)
\(504\) −0.663393 2.56123i −0.0295499 0.114086i
\(505\) 70.1556i 3.12189i
\(506\) 7.78600 + 15.0407i 0.346130 + 0.668643i
\(507\) 8.22923i 0.365473i
\(508\) 1.62262 0.0719920
\(509\) 2.12878i 0.0943566i 0.998886 + 0.0471783i \(0.0150229\pi\)
−0.998886 + 0.0471783i \(0.984977\pi\)
\(510\) 9.04502i 0.400520i
\(511\) 20.4136 5.28738i 0.903043 0.233900i
\(512\) 23.4793 1.03765
\(513\) 4.98050i 0.219894i
\(514\) 22.4972i 0.992309i
\(515\) −36.5872 −1.61223
\(516\) −7.87848 −0.346831
\(517\) −18.1661 −0.798945
\(518\) 32.9854 8.54367i 1.44930 0.375387i
\(519\) −5.17380 −0.227105
\(520\) 8.96086i 0.392960i
\(521\) 24.4702 1.07206 0.536030 0.844199i \(-0.319923\pi\)
0.536030 + 0.844199i \(0.319923\pi\)
\(522\) −4.46260 −0.195323
\(523\) 27.4141 1.19874 0.599368 0.800474i \(-0.295419\pi\)
0.599368 + 0.800474i \(0.295419\pi\)
\(524\) 4.45364i 0.194558i
\(525\) −30.3020 + 7.84862i −1.32249 + 0.342542i
\(526\) 24.8795i 1.08480i
\(527\) 11.0466i 0.481196i
\(528\) 9.08306 0.395290
\(529\) 13.2784 18.7799i 0.577321 0.816517i
\(530\) 44.7237i 1.94267i
\(531\) 3.50761i 0.152217i
\(532\) −4.83247 18.6572i −0.209514 0.808893i
\(533\) 12.2355 0.529978
\(534\) 8.51201i 0.368351i
\(535\) 26.7279i 1.15555i
\(536\) 3.48879i 0.150693i
\(537\) 14.5616i 0.628379i
\(538\) 29.0409i 1.25204i
\(539\) 6.44925 + 11.6144i 0.277789 + 0.500269i
\(540\) 6.00040i 0.258216i
\(541\) −22.6468 −0.973662 −0.486831 0.873496i \(-0.661847\pi\)
−0.486831 + 0.873496i \(0.661847\pi\)
\(542\) 5.18691i 0.222797i
\(543\) 17.4499i 0.748847i
\(544\) −8.18217 −0.350808
\(545\) 66.8227i 2.86237i
\(546\) 2.69629 + 10.4098i 0.115391 + 0.445500i
\(547\) 24.1544 1.03277 0.516384 0.856357i \(-0.327278\pi\)
0.516384 + 0.856357i \(0.327278\pi\)
\(548\) 6.51173i 0.278167i
\(549\) 1.49171 0.0636645
\(550\) 41.7814i 1.78156i
\(551\) 11.9443 0.508843
\(552\) −2.20472 4.25901i −0.0938393 0.181276i
\(553\) −36.0707 + 9.34278i −1.53388 + 0.397295i
\(554\) −48.6129 −2.06536
\(555\) −28.3941 −1.20526
\(556\) 10.7618i 0.456402i
\(557\) 12.6008i 0.533911i 0.963709 + 0.266956i \(0.0860177\pi\)
−0.963709 + 0.266956i \(0.913982\pi\)
\(558\) 17.3490i 0.734444i
\(559\) −11.7655 −0.497629
\(560\) −13.0256 50.2895i −0.550434 2.12512i
\(561\) −2.24860 −0.0949360
\(562\) 47.2902i 1.99482i
\(563\) −2.96365 −0.124903 −0.0624515 0.998048i \(-0.519892\pi\)
−0.0624515 + 0.998048i \(0.519892\pi\)
\(564\) −14.0000 −0.589506
\(565\) 63.8975i 2.68819i
\(566\) 9.75931 0.410214
\(567\) −0.663393 2.56123i −0.0278599 0.107562i
\(568\) −1.81579 −0.0761889
\(569\) 14.1399i 0.592774i 0.955068 + 0.296387i \(0.0957817\pi\)
−0.955068 + 0.296387i \(0.904218\pi\)
\(570\) 38.0215i 1.59255i
\(571\) 19.0211i 0.796009i −0.917384 0.398004i \(-0.869703\pi\)
0.917384 0.398004i \(-0.130297\pi\)
\(572\) −6.06288 −0.253502
\(573\) 4.07961 0.170428
\(574\) 26.6979 6.91511i 1.11435 0.288631i
\(575\) −50.3885 + 26.0841i −2.10134 + 1.08778i
\(576\) 3.27839 0.136600
\(577\) 7.11355i 0.296141i 0.988977 + 0.148071i \(0.0473063\pi\)
−0.988977 + 0.148071i \(0.952694\pi\)
\(578\) −29.0215 −1.20714
\(579\) 22.8864i 0.951128i
\(580\) −14.3902 −0.597521
\(581\) 1.66618 + 6.43281i 0.0691249 + 0.266878i
\(582\) 13.8619i 0.574593i
\(583\) −11.1184 −0.460476
\(584\) 7.97021i 0.329810i
\(585\) 8.96086i 0.370486i
\(586\) 45.6198 1.88453
\(587\) 30.9419i 1.27711i −0.769577 0.638554i \(-0.779533\pi\)
0.769577 0.638554i \(-0.220467\pi\)
\(588\) 4.97021 + 8.95084i 0.204968 + 0.369126i
\(589\) 46.4352i 1.91333i
\(590\) 26.7774i 1.10241i
\(591\) 0.702237i 0.0288862i
\(592\) 33.1242i 1.36140i
\(593\) 25.4253i 1.04409i −0.852917 0.522046i \(-0.825169\pi\)
0.852917 0.522046i \(-0.174831\pi\)
\(594\) 3.53151 0.144900
\(595\) 3.22463 + 12.4497i 0.132197 + 0.510386i
\(596\) 30.3057i 1.24137i
\(597\) 23.6947i 0.969760i
\(598\) 8.96086 + 17.3103i 0.366437 + 0.707871i
\(599\) 5.08858 0.207914 0.103957 0.994582i \(-0.466850\pi\)
0.103957 + 0.994582i \(0.466850\pi\)
\(600\) 11.8310i 0.482999i
\(601\) 29.1004i 1.18703i 0.804822 + 0.593516i \(0.202261\pi\)
−0.804822 + 0.593516i \(0.797739\pi\)
\(602\) −25.6724 + 6.64951i −1.04633 + 0.271014i
\(603\) 3.48879i 0.142075i
\(604\) 31.6829 1.28916
\(605\) −30.3516 −1.23397
\(606\) −31.8206 −1.29262
\(607\) 19.5679i 0.794235i 0.917768 + 0.397117i \(0.129989\pi\)
−0.917768 + 0.397117i \(0.870011\pi\)
\(608\) −34.3944 −1.39488
\(609\) −6.14237 + 1.59095i −0.248901 + 0.0644687i
\(610\) 11.3878 0.461078
\(611\) −20.9073 −0.845818
\(612\) −1.73292 −0.0700491
\(613\) 1.89784i 0.0766530i 0.999265 + 0.0383265i \(0.0122027\pi\)
−0.999265 + 0.0383265i \(0.987797\pi\)
\(614\) 61.7867i 2.49351i
\(615\) −22.9817 −0.926712
\(616\) 4.86081 1.25901i 0.195847 0.0507271i
\(617\) 26.4903i 1.06646i −0.845971 0.533229i \(-0.820978\pi\)
0.845971 0.533229i \(-0.179022\pi\)
\(618\) 16.5949i 0.667546i
\(619\) −28.9058 −1.16182 −0.580911 0.813967i \(-0.697304\pi\)
−0.580911 + 0.813967i \(0.697304\pi\)
\(620\) 55.9442i 2.24677i
\(621\) −2.20472 4.25901i −0.0884725 0.170908i
\(622\) 41.9661i 1.68269i
\(623\) −3.03460 11.7160i −0.121579 0.469392i
\(624\) 10.4536 0.418480
\(625\) 55.8179 2.23272
\(626\) −7.59136 −0.303412
\(627\) −9.45219 −0.377484
\(628\) −17.9676 −0.716986
\(629\) 8.20022i 0.326964i
\(630\) −5.06439 19.5526i −0.201770 0.778995i
\(631\) 11.9976i 0.477617i −0.971067 0.238809i \(-0.923243\pi\)
0.971067 0.238809i \(-0.0767569\pi\)
\(632\) 14.0833i 0.560204i
\(633\) 20.7666i 0.825399i
\(634\) −23.9315 −0.950440
\(635\) −4.55141 −0.180617
\(636\) −8.56854 −0.339765
\(637\) 7.42240 + 13.3670i 0.294086 + 0.529619i
\(638\) 8.46929i 0.335303i
\(639\) −1.81579 −0.0718315
\(640\) −31.6357 −1.25051
\(641\) 24.2520i 0.957895i −0.877844 0.478947i \(-0.841018\pi\)
0.877844 0.478947i \(-0.158982\pi\)
\(642\) −12.1230 −0.478457
\(643\) −22.8931 −0.902815 −0.451407 0.892318i \(-0.649078\pi\)
−0.451407 + 0.892318i \(0.649078\pi\)
\(644\) 12.3914 + 13.8153i 0.488291 + 0.544399i
\(645\) 22.0990 0.870147
\(646\) 10.9806 0.432027
\(647\) 22.0948i 0.868638i −0.900759 0.434319i \(-0.856989\pi\)
0.900759 0.434319i \(-0.143011\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 6.65689 0.261306
\(650\) 48.0859i 1.88608i
\(651\) 6.18508 + 23.8794i 0.242412 + 0.935908i
\(652\) −15.2590 −0.597589
\(653\) 0.680742 0.0266395 0.0133197 0.999911i \(-0.495760\pi\)
0.0133197 + 0.999911i \(0.495760\pi\)
\(654\) −30.3089 −1.18517
\(655\) 12.4924i 0.488117i
\(656\) 26.8102i 1.04676i
\(657\) 7.97021i 0.310948i
\(658\) −45.6198 + 11.8161i −1.77844 + 0.460640i
\(659\) 10.1425i 0.395095i 0.980293 + 0.197548i \(0.0632977\pi\)
−0.980293 + 0.197548i \(0.936702\pi\)
\(660\) 11.3878 0.443269
\(661\) −3.93764 −0.153157 −0.0765783 0.997064i \(-0.524400\pi\)
−0.0765783 + 0.997064i \(0.524400\pi\)
\(662\) 45.7908 1.77971
\(663\) −2.58790 −0.100506
\(664\) 2.51161 0.0974693
\(665\) 13.5550 + 52.3332i 0.525640 + 2.02939i
\(666\) 12.8787i 0.499041i
\(667\) −10.2140 + 5.28738i −0.395488 + 0.204728i
\(668\) 17.5076i 0.677390i
\(669\) 24.5228 0.948108
\(670\) 26.6337i 1.02895i
\(671\) 2.83102i 0.109290i
\(672\) 17.6874 4.58127i 0.682307 0.176727i
\(673\) 14.5062 0.559172 0.279586 0.960121i \(-0.409803\pi\)
0.279586 + 0.960121i \(0.409803\pi\)
\(674\) 3.30411i 0.127270i
\(675\) 11.8310i 0.455376i
\(676\) 12.0361 0.462925
\(677\) −7.46596 −0.286940 −0.143470 0.989655i \(-0.545826\pi\)
−0.143470 + 0.989655i \(0.545826\pi\)
\(678\) 28.9821 1.11305
\(679\) 4.94187 + 19.0796i 0.189652 + 0.732209i
\(680\) 4.86081 0.186403
\(681\) 21.5098i 0.824256i
\(682\) −32.9257 −1.26079
\(683\) 17.5243 0.670548 0.335274 0.942121i \(-0.391171\pi\)
0.335274 + 0.942121i \(0.391171\pi\)
\(684\) −7.28447 −0.278529
\(685\) 18.2653i 0.697880i
\(686\) 23.7503 + 24.9719i 0.906790 + 0.953431i
\(687\) 10.4526i 0.398790i
\(688\) 25.7804i 0.982870i
\(689\) −12.7961 −0.487491
\(690\) −16.8310 32.5136i −0.640746 1.23777i
\(691\) 23.4391i 0.891665i 0.895117 + 0.445832i \(0.147092\pi\)
−0.895117 + 0.445832i \(0.852908\pi\)
\(692\) 7.56719i 0.287661i
\(693\) 4.86081 1.25901i 0.184647 0.0478260i
\(694\) 1.42655 0.0541509
\(695\) 30.1867i 1.14505i
\(696\) 2.39821i 0.0909038i
\(697\) 6.63713i 0.251399i
\(698\) 24.1711i 0.914890i
\(699\) 4.19317i 0.158600i
\(700\) −11.4794 44.3196i −0.433880 1.67512i
\(701\) 5.57451i 0.210546i 0.994443 + 0.105273i \(0.0335717\pi\)
−0.994443 + 0.105273i \(0.966428\pi\)
\(702\) 4.06439 0.153401
\(703\) 34.4703i 1.30007i
\(704\) 6.22185i 0.234495i
\(705\) 39.2697 1.47898
\(706\) 1.36987i 0.0515557i
\(707\) −43.7982 + 11.3443i −1.64720 + 0.426647i
\(708\) 5.13023 0.192806
\(709\) 10.9244i 0.410273i 0.978733 + 0.205137i \(0.0657639\pi\)
−0.978733 + 0.205137i \(0.934236\pi\)
\(710\) −13.8619 −0.520227
\(711\) 14.0833i 0.528166i
\(712\) −4.57437 −0.171432
\(713\) 20.5555 + 39.7085i 0.769811 + 1.48710i
\(714\) −5.64681 + 1.46260i −0.211326 + 0.0547364i
\(715\) 17.0063 0.635998
\(716\) −21.2978 −0.795935
\(717\) 21.8552i 0.816198i
\(718\) 46.1908i 1.72383i
\(719\) 40.9162i 1.52592i −0.646447 0.762959i \(-0.723746\pi\)
0.646447 0.762959i \(-0.276254\pi\)
\(720\) −19.6349 −0.731749
\(721\) −5.91623 22.8414i −0.220332 0.850659i
\(722\) 10.8027 0.402034
\(723\) 19.8196i 0.737097i
\(724\) −25.5222 −0.948526
\(725\) 28.3732 1.05376
\(726\) 13.7666i 0.510927i
\(727\) −20.8165 −0.772041 −0.386021 0.922490i \(-0.626151\pi\)
−0.386021 + 0.922490i \(0.626151\pi\)
\(728\) 5.59427 1.44899i 0.207337 0.0537031i
\(729\) −1.00000 −0.0370370
\(730\) 60.8452i 2.25198i
\(731\) 6.38220i 0.236054i
\(732\) 2.18177i 0.0806405i
\(733\) −43.2639 −1.59799 −0.798995 0.601338i \(-0.794635\pi\)
−0.798995 + 0.601338i \(0.794635\pi\)
\(734\) −42.3156 −1.56190
\(735\) −13.9414 25.1069i −0.514235 0.926083i
\(736\) 29.4120 15.2254i 1.08414 0.561217i
\(737\) −6.62117 −0.243894
\(738\) 10.4238i 0.383707i
\(739\) −17.4343 −0.641330 −0.320665 0.947193i \(-0.603906\pi\)
−0.320665 + 0.947193i \(0.603906\pi\)
\(740\) 41.5291i 1.52664i
\(741\) −10.8785 −0.399630
\(742\) −27.9211 + 7.23192i −1.02501 + 0.265492i
\(743\) 45.3129i 1.66237i −0.555998 0.831184i \(-0.687664\pi\)
0.555998 0.831184i \(-0.312336\pi\)
\(744\) 9.32340 0.341813
\(745\) 85.0069i 3.11441i
\(746\) 53.8189i 1.97045i
\(747\) 2.51161 0.0918949
\(748\) 3.28880i 0.120250i
\(749\) −16.6862 + 4.32195i −0.609702 + 0.157921i
\(750\) 52.1485i 1.90419i
\(751\) 7.41582i 0.270607i 0.990804 + 0.135303i \(0.0432009\pi\)
−0.990804 + 0.135303i \(0.956799\pi\)
\(752\) 45.8116i 1.67058i
\(753\) 7.92120i 0.288664i
\(754\) 9.74725i 0.354974i
\(755\) −88.8699 −3.23431
\(756\) 3.74605 0.970278i 0.136243 0.0352887i
\(757\) 37.6558i 1.36862i −0.729189 0.684312i \(-0.760102\pi\)
0.729189 0.684312i \(-0.239898\pi\)
\(758\) 10.3047i 0.374282i
\(759\) 8.08292 4.18421i 0.293391 0.151877i
\(760\) 20.4328 0.741176
\(761\) 31.7312i 1.15026i 0.818063 + 0.575128i \(0.195048\pi\)
−0.818063 + 0.575128i \(0.804952\pi\)
\(762\) 2.06439i 0.0747850i
\(763\) −41.7175 + 10.8054i −1.51027 + 0.391181i
\(764\) 5.96683i 0.215872i
\(765\) 4.86081 0.175743
\(766\) 47.7390 1.72488
\(767\) 7.66137 0.276636
\(768\) 20.9058i 0.754374i
\(769\) 19.4332 0.700779 0.350389 0.936604i \(-0.386049\pi\)
0.350389 + 0.936604i \(0.386049\pi\)
\(770\) 37.1077 9.61140i 1.33727 0.346371i
\(771\) −12.0900 −0.435412
\(772\) 33.4737 1.20474
\(773\) −25.3849 −0.913032 −0.456516 0.889715i \(-0.650903\pi\)
−0.456516 + 0.889715i \(0.650903\pi\)
\(774\) 10.0235i 0.360286i
\(775\) 110.305i 3.96229i
\(776\) 7.44939 0.267418
\(777\) −4.59138 17.7264i −0.164715 0.635932i
\(778\) 16.9445i 0.607491i
\(779\) 27.8997i 0.999611i
\(780\) 13.1061 0.469275
\(781\) 3.44608i 0.123310i
\(782\) −9.38995 + 4.86081i −0.335784 + 0.173822i
\(783\) 2.39821i 0.0857049i
\(784\) 29.2895 16.2638i 1.04605 0.580851i
\(785\) 50.3989 1.79881
\(786\) 5.66618 0.202106
\(787\) 25.9054 0.923427 0.461714 0.887029i \(-0.347235\pi\)
0.461714 + 0.887029i \(0.347235\pi\)
\(788\) −1.02709 −0.0365886
\(789\) 13.3703 0.475995