Properties

Label 483.2.h.c.160.12
Level $483$
Weight $2$
Character 483.160
Analytic conductor $3.857$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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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: \(x^{12} + 17 x^{10} + 92 x^{8} + 180 x^{6} + 92 x^{4} + 17 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 160.12
Root \(1.77931i\) of defining polynomial
Character \(\chi\) \(=\) 483.160
Dual form 483.2.h.c.160.10

$q$-expansion

\(f(q)\) \(=\) \(q+2.51820 q^{2} +1.00000i q^{3} +4.34132 q^{4} +1.21729 q^{5} +2.51820i q^{6} +(-2.34908 + 1.21729i) q^{7} +5.89592 q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+2.51820 q^{2} +1.00000i q^{3} +4.34132 q^{4} +1.21729 q^{5} +2.51820i q^{6} +(-2.34908 + 1.21729i) q^{7} +5.89592 q^{8} -1.00000 q^{9} +3.06538 q^{10} -1.13179i q^{11} +4.34132i q^{12} -0.518199i q^{13} +(-5.91546 + 3.06538i) q^{14} +1.21729i q^{15} +6.16445 q^{16} +3.06538 q^{17} -2.51820 q^{18} -1.13179 q^{19} +5.28466 q^{20} +(-1.21729 - 2.34908i) q^{21} -2.85008i q^{22} +(-0.341325 - 4.78367i) q^{23} +5.89592i q^{24} -3.51820 q^{25} -1.30493i q^{26} -1.00000i q^{27} +(-10.1981 + 5.28466i) q^{28} -2.17687 q^{29} +3.06538i q^{30} -6.85952i q^{31} +3.73147 q^{32} +1.13179 q^{33} +7.71925 q^{34} +(-2.85952 + 1.48180i) q^{35} -4.34132 q^{36} +10.1981i q^{37} -2.85008 q^{38} +0.518199 q^{39} +7.17706 q^{40} +5.00000i q^{41} +(-3.06538 - 5.91546i) q^{42} -6.71726i q^{43} -4.91348i q^{44} -1.21729 q^{45} +(-0.859523 - 12.0462i) q^{46} -4.21327i q^{47} +6.16445i q^{48} +(4.03640 - 5.71905i) q^{49} -8.85952 q^{50} +3.06538i q^{51} -2.24967i q^{52} +5.41447i q^{53} -2.51820i q^{54} -1.37772i q^{55} +(-13.8500 + 7.17706i) q^{56} -1.13179i q^{57} -5.48180 q^{58} +0.200848i q^{59} +5.28466i q^{60} +6.21627 q^{61} -17.2736i q^{62} +(2.34908 - 1.21729i) q^{63} -2.93232 q^{64} -0.630799i q^{65} +2.85008 q^{66} -3.65188i q^{67} +13.3078 q^{68} +(4.78367 - 0.341325i) q^{69} +(-7.20085 + 3.73147i) q^{70} +2.16445 q^{71} -5.89592 q^{72} +10.2248i q^{73} +25.6809i q^{74} -3.51820i q^{75} -4.91348 q^{76} +(1.37772 + 2.65868i) q^{77} +1.30493 q^{78} +8.59454i q^{79} +7.50394 q^{80} +1.00000 q^{81} +12.5910i q^{82} -11.6307 q^{83} +(-5.28466 - 10.1981i) q^{84} +3.73147 q^{85} -16.9154i q^{86} -2.17687i q^{87} -6.67296i q^{88} +5.11366 q^{89} -3.06538 q^{90} +(0.630799 + 1.21729i) q^{91} +(-1.48180 - 20.7675i) q^{92} +6.85952 q^{93} -10.6099i q^{94} -1.37772 q^{95} +3.73147i q^{96} -18.1619 q^{97} +(10.1645 - 14.4017i) q^{98} +1.13179i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 4q^{2} + 36q^{4} - 24q^{8} - 12q^{9} + O(q^{10}) \) \( 12q + 4q^{2} + 36q^{4} - 24q^{8} - 12q^{9} + 68q^{16} - 4q^{18} + 12q^{23} - 16q^{25} - 16q^{29} - 44q^{32} + 8q^{35} - 36q^{36} - 20q^{39} + 32q^{46} - 4q^{49} - 64q^{50} - 92q^{58} + 112q^{64} - 28q^{70} + 20q^{71} + 24q^{72} - 52q^{77} + 52q^{78} + 12q^{81} - 44q^{85} - 44q^{92} + 40q^{93} + 52q^{95} + 116q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.51820 1.78064 0.890318 0.455340i \(-0.150482\pi\)
0.890318 + 0.455340i \(0.150482\pi\)
\(3\) 1.00000i 0.577350i
\(4\) 4.34132 2.17066
\(5\) 1.21729 0.544390 0.272195 0.962242i \(-0.412250\pi\)
0.272195 + 0.962242i \(0.412250\pi\)
\(6\) 2.51820i 1.02805i
\(7\) −2.34908 + 1.21729i −0.887871 + 0.460093i
\(8\) 5.89592 2.08452
\(9\) −1.00000 −0.333333
\(10\) 3.06538 0.969360
\(11\) 1.13179i 0.341248i −0.985336 0.170624i \(-0.945422\pi\)
0.985336 0.170624i \(-0.0545784\pi\)
\(12\) 4.34132i 1.25323i
\(13\) 0.518199i 0.143722i −0.997415 0.0718612i \(-0.977106\pi\)
0.997415 0.0718612i \(-0.0228939\pi\)
\(14\) −5.91546 + 3.06538i −1.58097 + 0.819259i
\(15\) 1.21729i 0.314304i
\(16\) 6.16445 1.54111
\(17\) 3.06538 0.743465 0.371732 0.928340i \(-0.378764\pi\)
0.371732 + 0.928340i \(0.378764\pi\)
\(18\) −2.51820 −0.593545
\(19\) −1.13179 −0.259651 −0.129825 0.991537i \(-0.541442\pi\)
−0.129825 + 0.991537i \(0.541442\pi\)
\(20\) 5.28466 1.18169
\(21\) −1.21729 2.34908i −0.265635 0.512612i
\(22\) 2.85008i 0.607639i
\(23\) −0.341325 4.78367i −0.0711711 0.997464i
\(24\) 5.89592i 1.20350i
\(25\) −3.51820 −0.703640
\(26\) 1.30493i 0.255917i
\(27\) 1.00000i 0.192450i
\(28\) −10.1981 + 5.28466i −1.92727 + 0.998707i
\(29\) −2.17687 −0.404235 −0.202118 0.979361i \(-0.564782\pi\)
−0.202118 + 0.979361i \(0.564782\pi\)
\(30\) 3.06538i 0.559660i
\(31\) 6.85952i 1.23201i −0.787744 0.616003i \(-0.788751\pi\)
0.787744 0.616003i \(-0.211249\pi\)
\(32\) 3.73147 0.659637
\(33\) 1.13179 0.197020
\(34\) 7.71925 1.32384
\(35\) −2.85952 + 1.48180i −0.483348 + 0.250470i
\(36\) −4.34132 −0.723554
\(37\) 10.1981i 1.67656i 0.545237 + 0.838282i \(0.316440\pi\)
−0.545237 + 0.838282i \(0.683560\pi\)
\(38\) −2.85008 −0.462344
\(39\) 0.518199 0.0829782
\(40\) 7.17706 1.13479
\(41\) 5.00000i 0.780869i 0.920631 + 0.390434i \(0.127675\pi\)
−0.920631 + 0.390434i \(0.872325\pi\)
\(42\) −3.06538 5.91546i −0.472999 0.912776i
\(43\) 6.71726i 1.02437i −0.858874 0.512186i \(-0.828836\pi\)
0.858874 0.512186i \(-0.171164\pi\)
\(44\) 4.91348i 0.740734i
\(45\) −1.21729 −0.181463
\(46\) −0.859523 12.0462i −0.126730 1.77612i
\(47\) 4.21327i 0.614569i −0.951618 0.307284i \(-0.900580\pi\)
0.951618 0.307284i \(-0.0994203\pi\)
\(48\) 6.16445i 0.889762i
\(49\) 4.03640 5.71905i 0.576628 0.817007i
\(50\) −8.85952 −1.25293
\(51\) 3.06538i 0.429240i
\(52\) 2.24967i 0.311973i
\(53\) 5.41447i 0.743735i 0.928286 + 0.371867i \(0.121282\pi\)
−0.928286 + 0.371867i \(0.878718\pi\)
\(54\) 2.51820i 0.342683i
\(55\) 1.37772i 0.185772i
\(56\) −13.8500 + 7.17706i −1.85079 + 0.959075i
\(57\) 1.13179i 0.149910i
\(58\) −5.48180 −0.719796
\(59\) 0.200848i 0.0261482i 0.999915 + 0.0130741i \(0.00416173\pi\)
−0.999915 + 0.0130741i \(0.995838\pi\)
\(60\) 5.28466i 0.682247i
\(61\) 6.21627 0.795912 0.397956 0.917405i \(-0.369720\pi\)
0.397956 + 0.917405i \(0.369720\pi\)
\(62\) 17.2736i 2.19375i
\(63\) 2.34908 1.21729i 0.295957 0.153364i
\(64\) −2.93232 −0.366540
\(65\) 0.630799i 0.0782410i
\(66\) 2.85008 0.350820
\(67\) 3.65188i 0.446148i −0.974802 0.223074i \(-0.928391\pi\)
0.974802 0.223074i \(-0.0716091\pi\)
\(68\) 13.3078 1.61381
\(69\) 4.78367 0.341325i 0.575886 0.0410907i
\(70\) −7.20085 + 3.73147i −0.860666 + 0.445996i
\(71\) 2.16445 0.256873 0.128437 0.991718i \(-0.459004\pi\)
0.128437 + 0.991718i \(0.459004\pi\)
\(72\) −5.89592 −0.694841
\(73\) 10.2248i 1.19672i 0.801226 + 0.598362i \(0.204182\pi\)
−0.801226 + 0.598362i \(0.795818\pi\)
\(74\) 25.6809i 2.98535i
\(75\) 3.51820i 0.406247i
\(76\) −4.91348 −0.563614
\(77\) 1.37772 + 2.65868i 0.157006 + 0.302984i
\(78\) 1.30493 0.147754
\(79\) 8.59454i 0.966961i 0.875355 + 0.483481i \(0.160628\pi\)
−0.875355 + 0.483481i \(0.839372\pi\)
\(80\) 7.50394 0.838966
\(81\) 1.00000 0.111111
\(82\) 12.5910i 1.39044i
\(83\) −11.6307 −1.27664 −0.638320 0.769771i \(-0.720370\pi\)
−0.638320 + 0.769771i \(0.720370\pi\)
\(84\) −5.28466 10.1981i −0.576604 1.11271i
\(85\) 3.73147 0.404735
\(86\) 16.9154i 1.82403i
\(87\) 2.17687i 0.233385i
\(88\) 6.67296i 0.711340i
\(89\) 5.11366 0.542047 0.271024 0.962573i \(-0.412638\pi\)
0.271024 + 0.962573i \(0.412638\pi\)
\(90\) −3.06538 −0.323120
\(91\) 0.630799 + 1.21729i 0.0661257 + 0.127607i
\(92\) −1.48180 20.7675i −0.154488 2.16516i
\(93\) 6.85952 0.711299
\(94\) 10.6099i 1.09432i
\(95\) −1.37772 −0.141351
\(96\) 3.73147i 0.380842i
\(97\) −18.1619 −1.84406 −0.922030 0.387119i \(-0.873470\pi\)
−0.922030 + 0.387119i \(0.873470\pi\)
\(98\) 10.1645 14.4017i 1.02676 1.45479i
\(99\) 1.13179i 0.113749i
\(100\) −15.2736 −1.52736
\(101\) 8.88350i 0.883941i 0.897030 + 0.441971i \(0.145720\pi\)
−0.897030 + 0.441971i \(0.854280\pi\)
\(102\) 7.71925i 0.764319i
\(103\) 11.5009 1.13322 0.566610 0.823986i \(-0.308255\pi\)
0.566610 + 0.823986i \(0.308255\pi\)
\(104\) 3.05526i 0.299593i
\(105\) −1.48180 2.85952i −0.144609 0.279061i
\(106\) 13.6347i 1.32432i
\(107\) 2.67908i 0.258996i −0.991580 0.129498i \(-0.958663\pi\)
0.991580 0.129498i \(-0.0413366\pi\)
\(108\) 4.34132i 0.417744i
\(109\) 17.7464i 1.69980i −0.526948 0.849898i \(-0.676664\pi\)
0.526948 0.849898i \(-0.323336\pi\)
\(110\) 3.46938i 0.330792i
\(111\) −10.1981 −0.967965
\(112\) −14.4808 + 7.50394i −1.36831 + 0.709056i
\(113\) 2.21928i 0.208772i 0.994537 + 0.104386i \(0.0332878\pi\)
−0.994537 + 0.104386i \(0.966712\pi\)
\(114\) 2.85008i 0.266934i
\(115\) −0.415492 5.82313i −0.0387448 0.543009i
\(116\) −9.45052 −0.877458
\(117\) 0.518199i 0.0479075i
\(118\) 0.505775i 0.0465604i
\(119\) −7.20085 + 3.73147i −0.660101 + 0.342063i
\(120\) 7.17706i 0.655173i
\(121\) 9.71905 0.883550
\(122\) 15.6538 1.41723
\(123\) −5.00000 −0.450835
\(124\) 29.7794i 2.67427i
\(125\) −10.3691 −0.927444
\(126\) 5.91546 3.06538i 0.526991 0.273086i
\(127\) −2.73147 −0.242379 −0.121189 0.992629i \(-0.538671\pi\)
−0.121189 + 0.992629i \(0.538671\pi\)
\(128\) −14.8471 −1.31231
\(129\) 6.71726 0.591422
\(130\) 1.58848i 0.139319i
\(131\) 18.7190i 1.63549i 0.575580 + 0.817745i \(0.304776\pi\)
−0.575580 + 0.817745i \(0.695224\pi\)
\(132\) 4.91348 0.427663
\(133\) 2.65868 1.37772i 0.230536 0.119464i
\(134\) 9.19615i 0.794427i
\(135\) 1.21729i 0.104768i
\(136\) 18.0733 1.54977
\(137\) 12.3027i 1.05109i 0.850765 + 0.525547i \(0.176139\pi\)
−0.850765 + 0.525547i \(0.823861\pi\)
\(138\) 12.0462 0.859523i 1.02544 0.0731675i
\(139\) 13.7794i 1.16876i −0.811482 0.584378i \(-0.801339\pi\)
0.811482 0.584378i \(-0.198661\pi\)
\(140\) −12.4141 + 6.43298i −1.04918 + 0.543686i
\(141\) 4.21327 0.354821
\(142\) 5.45052 0.457397
\(143\) −0.586493 −0.0490450
\(144\) −6.16445 −0.513704
\(145\) −2.64989 −0.220062
\(146\) 25.7481i 2.13093i
\(147\) 5.71905 + 4.03640i 0.471699 + 0.332916i
\(148\) 44.2734i 3.63925i
\(149\) 8.46473i 0.693458i −0.937965 0.346729i \(-0.887292\pi\)
0.937965 0.346729i \(-0.112708\pi\)
\(150\) 8.85952i 0.723377i
\(151\) 17.5786 1.43052 0.715262 0.698857i \(-0.246307\pi\)
0.715262 + 0.698857i \(0.246307\pi\)
\(152\) −6.67296 −0.541248
\(153\) −3.06538 −0.247822
\(154\) 3.46938 + 6.69507i 0.279570 + 0.539504i
\(155\) 8.35005i 0.670692i
\(156\) 2.24967 0.180118
\(157\) 18.6337 1.48713 0.743565 0.668664i \(-0.233133\pi\)
0.743565 + 0.668664i \(0.233133\pi\)
\(158\) 21.6428i 1.72181i
\(159\) −5.41447 −0.429395
\(160\) 4.54229 0.359100
\(161\) 6.62493 + 10.8218i 0.522117 + 0.852874i
\(162\) 2.51820 0.197848
\(163\) 7.23725 0.566865 0.283432 0.958992i \(-0.408527\pi\)
0.283432 + 0.958992i \(0.408527\pi\)
\(164\) 21.7066i 1.69500i
\(165\) 1.37772 0.107256
\(166\) −29.2885 −2.27323
\(167\) 17.8282i 1.37959i 0.724004 + 0.689795i \(0.242299\pi\)
−0.724004 + 0.689795i \(0.757701\pi\)
\(168\) −7.17706 13.8500i −0.553722 1.06855i
\(169\) 12.7315 0.979344
\(170\) 9.39658 0.720685
\(171\) 1.13179 0.0865503
\(172\) 29.1618i 2.22357i
\(173\) 20.2248i 1.53766i 0.639450 + 0.768832i \(0.279162\pi\)
−0.639450 + 0.768832i \(0.720838\pi\)
\(174\) 5.48180i 0.415574i
\(175\) 8.26455 4.28268i 0.624741 0.323740i
\(176\) 6.97688i 0.525902i
\(177\) −0.200848 −0.0150967
\(178\) 12.8772 0.965188
\(179\) −10.4141 −0.778388 −0.389194 0.921156i \(-0.627246\pi\)
−0.389194 + 0.921156i \(0.627246\pi\)
\(180\) −5.28466 −0.393895
\(181\) −14.0653 −1.04547 −0.522734 0.852496i \(-0.675088\pi\)
−0.522734 + 0.852496i \(0.675088\pi\)
\(182\) 1.58848 + 3.06538i 0.117746 + 0.227221i
\(183\) 6.21627i 0.459520i
\(184\) −2.01242 28.2041i −0.148358 2.07924i
\(185\) 12.4141i 0.912704i
\(186\) 17.2736 1.26656
\(187\) 3.46938i 0.253706i
\(188\) 18.2912i 1.33402i
\(189\) 1.21729 + 2.34908i 0.0885450 + 0.170871i
\(190\) −3.46938 −0.251695
\(191\) 12.3319i 0.892306i 0.894957 + 0.446153i \(0.147206\pi\)
−0.894957 + 0.446153i \(0.852794\pi\)
\(192\) 2.93232i 0.211622i
\(193\) −3.17687 −0.228676 −0.114338 0.993442i \(-0.536475\pi\)
−0.114338 + 0.993442i \(0.536475\pi\)
\(194\) −45.7352 −3.28360
\(195\) 0.630799 0.0451725
\(196\) 17.5233 24.8282i 1.25167 1.77345i
\(197\) 16.5661 1.18029 0.590145 0.807298i \(-0.299071\pi\)
0.590145 + 0.807298i \(0.299071\pi\)
\(198\) 2.85008i 0.202546i
\(199\) 9.28165 0.657959 0.328980 0.944337i \(-0.393295\pi\)
0.328980 + 0.944337i \(0.393295\pi\)
\(200\) −20.7430 −1.46675
\(201\) 3.65188 0.257584
\(202\) 22.3704i 1.57398i
\(203\) 5.11366 2.64989i 0.358909 0.185986i
\(204\) 13.3078i 0.931734i
\(205\) 6.08646i 0.425097i
\(206\) 28.9616 2.01785
\(207\) 0.341325 + 4.78367i 0.0237237 + 0.332488i
\(208\) 3.19441i 0.221493i
\(209\) 1.28095i 0.0886054i
\(210\) −3.73147 7.20085i −0.257496 0.496906i
\(211\) 7.96360 0.548237 0.274119 0.961696i \(-0.411614\pi\)
0.274119 + 0.961696i \(0.411614\pi\)
\(212\) 23.5060i 1.61440i
\(213\) 2.16445i 0.148306i
\(214\) 6.74645i 0.461178i
\(215\) 8.17687i 0.557658i
\(216\) 5.89592i 0.401167i
\(217\) 8.35005 + 16.1136i 0.566838 + 1.09386i
\(218\) 44.6889i 3.02672i
\(219\) −10.2248 −0.690929
\(220\) 5.98114i 0.403248i
\(221\) 1.58848i 0.106853i
\(222\) −25.6809 −1.72359
\(223\) 21.0968i 1.41274i −0.707841 0.706372i \(-0.750331\pi\)
0.707841 0.706372i \(-0.249669\pi\)
\(224\) −8.76554 + 4.54229i −0.585672 + 0.303495i
\(225\) 3.51820 0.234547
\(226\) 5.58858i 0.371747i
\(227\) 24.8791 1.65129 0.825643 0.564193i \(-0.190812\pi\)
0.825643 + 0.564193i \(0.190812\pi\)
\(228\) 4.91348i 0.325403i
\(229\) −19.5090 −1.28919 −0.644595 0.764524i \(-0.722974\pi\)
−0.644595 + 0.764524i \(0.722974\pi\)
\(230\) −1.04629 14.6638i −0.0689904 0.966902i
\(231\) −2.65868 + 1.37772i −0.174928 + 0.0906475i
\(232\) −12.8347 −0.842638
\(233\) −8.34132 −0.546458 −0.273229 0.961949i \(-0.588092\pi\)
−0.273229 + 0.961949i \(0.588092\pi\)
\(234\) 1.30493i 0.0853058i
\(235\) 5.12878i 0.334565i
\(236\) 0.871947i 0.0567589i
\(237\) −8.59454 −0.558275
\(238\) −18.1332 + 9.39658i −1.17540 + 0.609090i
\(239\) −21.3777 −1.38281 −0.691405 0.722467i \(-0.743008\pi\)
−0.691405 + 0.722467i \(0.743008\pi\)
\(240\) 7.50394i 0.484377i
\(241\) 8.86616 0.571120 0.285560 0.958361i \(-0.407820\pi\)
0.285560 + 0.958361i \(0.407820\pi\)
\(242\) 24.4745 1.57328
\(243\) 1.00000i 0.0641500i
\(244\) 26.9868 1.72766
\(245\) 4.91348 6.96175i 0.313911 0.444770i
\(246\) −12.5910 −0.802772
\(247\) 0.586493i 0.0373177i
\(248\) 40.4432i 2.56815i
\(249\) 11.6307i 0.737068i
\(250\) −26.1116 −1.65144
\(251\) −13.0925 −0.826393 −0.413196 0.910642i \(-0.635588\pi\)
−0.413196 + 0.910642i \(0.635588\pi\)
\(252\) 10.1981 5.28466i 0.642422 0.332902i
\(253\) −5.41412 + 0.386309i −0.340383 + 0.0242870i
\(254\) −6.87838 −0.431588
\(255\) 3.73147i 0.233674i
\(256\) −31.5233 −1.97021
\(257\) 13.9075i 0.867524i −0.901027 0.433762i \(-0.857186\pi\)
0.901027 0.433762i \(-0.142814\pi\)
\(258\) 16.9154 1.05311
\(259\) −12.4141 23.9563i −0.771376 1.48857i
\(260\) 2.73851i 0.169835i
\(261\) 2.17687 0.134745
\(262\) 47.1383i 2.91221i
\(263\) 23.7917i 1.46706i 0.679659 + 0.733528i \(0.262128\pi\)
−0.679659 + 0.733528i \(0.737872\pi\)
\(264\) 6.67296 0.410692
\(265\) 6.59099i 0.404882i
\(266\) 6.69507 3.46938i 0.410501 0.212721i
\(267\) 5.11366i 0.312951i
\(268\) 15.8540i 0.968436i
\(269\) 5.76275i 0.351361i −0.984447 0.175681i \(-0.943787\pi\)
0.984447 0.175681i \(-0.0562126\pi\)
\(270\) 3.06538i 0.186553i
\(271\) 11.5422i 0.701137i −0.936537 0.350569i \(-0.885988\pi\)
0.936537 0.350569i \(-0.114012\pi\)
\(272\) 18.8964 1.14576
\(273\) −1.21729 + 0.630799i −0.0736739 + 0.0381777i
\(274\) 30.9807i 1.87161i
\(275\) 3.98187i 0.240116i
\(276\) 20.7675 1.48180i 1.25005 0.0891940i
\(277\) 24.5713 1.47634 0.738172 0.674613i \(-0.235689\pi\)
0.738172 + 0.674613i \(0.235689\pi\)
\(278\) 34.6993i 2.08113i
\(279\) 6.85952i 0.410669i
\(280\) −16.8595 + 8.73658i −1.00755 + 0.522111i
\(281\) 16.7001i 0.996244i −0.867107 0.498122i \(-0.834023\pi\)
0.867107 0.498122i \(-0.165977\pi\)
\(282\) 10.6099 0.631808
\(283\) −12.2172 −0.726239 −0.363120 0.931743i \(-0.618288\pi\)
−0.363120 + 0.931743i \(0.618288\pi\)
\(284\) 9.39658 0.557585
\(285\) 1.37772i 0.0816092i
\(286\) −1.47691 −0.0873313
\(287\) −6.08646 11.7454i −0.359273 0.693310i
\(288\) −3.73147 −0.219879
\(289\) −7.60342 −0.447260
\(290\) −6.67296 −0.391849
\(291\) 18.1619i 1.06467i
\(292\) 44.3893i 2.59769i
\(293\) −22.0582 −1.28866 −0.644328 0.764749i \(-0.722863\pi\)
−0.644328 + 0.764749i \(0.722863\pi\)
\(294\) 14.4017 + 10.1645i 0.839924 + 0.592803i
\(295\) 0.244491i 0.0142348i
\(296\) 60.1274i 3.49484i
\(297\) −1.13179 −0.0656732
\(298\) 21.3159i 1.23480i
\(299\) −2.47889 + 0.176874i −0.143358 + 0.0102289i
\(300\) 15.2736i 0.881824i
\(301\) 8.17687 + 15.7794i 0.471307 + 0.909511i
\(302\) 44.2663 2.54724
\(303\) −8.88350 −0.510344
\(304\) −6.97688 −0.400151
\(305\) 7.56702 0.433286
\(306\) −7.71925 −0.441280
\(307\) 20.0167i 1.14241i 0.820807 + 0.571206i \(0.193524\pi\)
−0.820807 + 0.571206i \(0.806476\pi\)
\(308\) 5.98114 + 11.5422i 0.340807 + 0.657676i
\(309\) 11.5009i 0.654265i
\(310\) 21.0271i 1.19426i
\(311\) 15.7430i 0.892705i −0.894857 0.446352i \(-0.852723\pi\)
0.894857 0.446352i \(-0.147277\pi\)
\(312\) 3.05526 0.172970
\(313\) 8.46473 0.478455 0.239227 0.970964i \(-0.423106\pi\)
0.239227 + 0.970964i \(0.423106\pi\)
\(314\) 46.9233 2.64804
\(315\) 2.85952 1.48180i 0.161116 0.0834900i
\(316\) 37.3117i 2.09895i
\(317\) 28.1083 1.57872 0.789360 0.613930i \(-0.210412\pi\)
0.789360 + 0.613930i \(0.210412\pi\)
\(318\) −13.6347 −0.764597
\(319\) 2.46377i 0.137945i
\(320\) −3.56949 −0.199541
\(321\) 2.67908 0.149531
\(322\) 16.6829 + 27.2513i 0.929701 + 1.51866i
\(323\) −3.46938 −0.193041
\(324\) 4.34132 0.241185
\(325\) 1.82313i 0.101129i
\(326\) 18.2248 1.00938
\(327\) 17.7464 0.981377
\(328\) 29.4796i 1.62774i
\(329\) 5.12878 + 9.89733i 0.282759 + 0.545658i
\(330\) 3.46938 0.190983
\(331\) −9.22482 −0.507042 −0.253521 0.967330i \(-0.581589\pi\)
−0.253521 + 0.967330i \(0.581589\pi\)
\(332\) −50.4928 −2.77115
\(333\) 10.1981i 0.558855i
\(334\) 44.8950i 2.45655i
\(335\) 4.44540i 0.242878i
\(336\) −7.50394 14.4808i −0.409374 0.789993i
\(337\) 14.0794i 0.766953i −0.923551 0.383476i \(-0.874727\pi\)
0.923551 0.383476i \(-0.125273\pi\)
\(338\) 32.0604 1.74385
\(339\) −2.21928 −0.120535
\(340\) 16.1995 0.878543
\(341\) −7.76355 −0.420420
\(342\) 2.85008 0.154115
\(343\) −2.52009 + 18.3480i −0.136072 + 0.990699i
\(344\) 39.6044i 2.13533i
\(345\) 5.82313 0.415492i 0.313507 0.0223693i
\(346\) 50.9301i 2.73802i
\(347\) −4.50578 −0.241883 −0.120941 0.992660i \(-0.538591\pi\)
−0.120941 + 0.992660i \(0.538591\pi\)
\(348\) 9.45052i 0.506601i
\(349\) 11.8522i 0.634434i −0.948353 0.317217i \(-0.897252\pi\)
0.948353 0.317217i \(-0.102748\pi\)
\(350\) 20.8118 10.7846i 1.11244 0.576463i
\(351\) −0.518199 −0.0276594
\(352\) 4.22325i 0.225100i
\(353\) 24.0167i 1.27828i −0.769091 0.639139i \(-0.779291\pi\)
0.769091 0.639139i \(-0.220709\pi\)
\(354\) −0.505775 −0.0268817
\(355\) 2.63477 0.139839
\(356\) 22.2001 1.17660
\(357\) −3.73147 7.20085i −0.197490 0.381109i
\(358\) −26.2248 −1.38602
\(359\) 1.21729i 0.0642462i 0.999484 + 0.0321231i \(0.0102269\pi\)
−0.999484 + 0.0321231i \(0.989773\pi\)
\(360\) −7.17706 −0.378264
\(361\) −17.7190 −0.932581
\(362\) −35.4193 −1.86160
\(363\) 9.71905i 0.510118i
\(364\) 2.73851 + 5.28466i 0.143537 + 0.276992i
\(365\) 12.4466i 0.651485i
\(366\) 15.6538i 0.818237i
\(367\) −10.7434 −0.560803 −0.280401 0.959883i \(-0.590468\pi\)
−0.280401 + 0.959883i \(0.590468\pi\)
\(368\) −2.10408 29.4887i −0.109683 1.53720i
\(369\) 5.00000i 0.260290i
\(370\) 31.2612i 1.62519i
\(371\) −6.59099 12.7190i −0.342187 0.660340i
\(372\) 29.7794 1.54399
\(373\) 28.3308i 1.46691i −0.679735 0.733457i \(-0.737905\pi\)
0.679735 0.733457i \(-0.262095\pi\)
\(374\) 8.73658i 0.451758i
\(375\) 10.3691i 0.535460i
\(376\) 24.8411i 1.28108i
\(377\) 1.12805i 0.0580977i
\(378\) 3.06538 + 5.91546i 0.157666 + 0.304259i
\(379\) 4.86917i 0.250112i −0.992150 0.125056i \(-0.960089\pi\)
0.992150 0.125056i \(-0.0399111\pi\)
\(380\) −5.98114 −0.306826
\(381\) 2.73147i 0.139937i
\(382\) 31.0542i 1.58887i
\(383\) 34.6326 1.76964 0.884822 0.465930i \(-0.154280\pi\)
0.884822 + 0.465930i \(0.154280\pi\)
\(384\) 14.8471i 0.757663i
\(385\) 1.67709 + 3.23639i 0.0854725 + 0.164941i
\(386\) −8.00000 −0.407189
\(387\) 6.71726i 0.341458i
\(388\) −78.8466 −4.00283
\(389\) 11.6307i 0.589702i 0.955543 + 0.294851i \(0.0952700\pi\)
−0.955543 + 0.294851i \(0.904730\pi\)
\(390\) 1.58848 0.0804357
\(391\) −1.04629 14.6638i −0.0529132 0.741580i
\(392\) 23.7983 33.7190i 1.20199 1.70307i
\(393\) −18.7190 −0.944251
\(394\) 41.7168 2.10166
\(395\) 10.4621i 0.526404i
\(396\) 4.91348i 0.246911i
\(397\) 27.5109i 1.38073i 0.723460 + 0.690366i \(0.242550\pi\)
−0.723460 + 0.690366i \(0.757450\pi\)
\(398\) 23.3731 1.17159
\(399\) 1.37772 + 2.65868i 0.0689724 + 0.133100i
\(400\) −21.6878 −1.08439
\(401\) 15.1679i 0.757450i −0.925509 0.378725i \(-0.876363\pi\)
0.925509 0.378725i \(-0.123637\pi\)
\(402\) 9.19615 0.458662
\(403\) −3.55460 −0.177067
\(404\) 38.5661i 1.91874i
\(405\) 1.21729 0.0604878
\(406\) 12.8772 6.67296i 0.639085 0.331173i
\(407\) 11.5422 0.572124
\(408\) 18.0733i 0.894760i
\(409\) 23.2861i 1.15142i −0.817653 0.575711i \(-0.804725\pi\)
0.817653 0.575711i \(-0.195275\pi\)
\(410\) 15.3269i 0.756943i
\(411\) −12.3027 −0.606849
\(412\) 49.9293 2.45984
\(413\) −0.244491 0.471809i −0.0120306 0.0232162i
\(414\) 0.859523 + 12.0462i 0.0422433 + 0.592040i
\(415\) −14.1580 −0.694990
\(416\) 1.93364i 0.0948046i
\(417\) 13.7794 0.674781
\(418\) 3.22569i 0.157774i
\(419\) 5.31385 0.259598 0.129799 0.991540i \(-0.458567\pi\)
0.129799 + 0.991540i \(0.458567\pi\)
\(420\) −6.43298 12.4141i −0.313897 0.605747i
\(421\) 16.1136i 0.785329i 0.919682 + 0.392664i \(0.128447\pi\)
−0.919682 + 0.392664i \(0.871553\pi\)
\(422\) 20.0539 0.976210
\(423\) 4.21327i 0.204856i
\(424\) 31.9233i 1.55033i
\(425\) −10.7846 −0.523132
\(426\) 5.45052i 0.264078i
\(427\) −14.6025 + 7.56702i −0.706667 + 0.366194i
\(428\) 11.6307i 0.562193i
\(429\) 0.586493i 0.0283162i
\(430\) 20.5910i 0.992986i
\(431\) 11.4274i 0.550441i −0.961381 0.275220i \(-0.911249\pi\)
0.961381 0.275220i \(-0.0887508\pi\)
\(432\) 6.16445i 0.296587i
\(433\) −13.5351 −0.650458 −0.325229 0.945635i \(-0.605441\pi\)
−0.325229 + 0.945635i \(0.605441\pi\)
\(434\) 21.0271 + 40.5772i 1.00933 + 1.94777i
\(435\) 2.64989i 0.127053i
\(436\) 77.0428i 3.68968i
\(437\) 0.386309 + 5.41412i 0.0184796 + 0.258992i
\(438\) −25.7481 −1.23029
\(439\) 36.0415i 1.72017i −0.510153 0.860084i \(-0.670411\pi\)
0.510153 0.860084i \(-0.329589\pi\)
\(440\) 8.12294i 0.387246i
\(441\) −4.03640 + 5.71905i −0.192209 + 0.272336i
\(442\) 4.00010i 0.190266i
\(443\) −32.8034 −1.55854 −0.779268 0.626691i \(-0.784409\pi\)
−0.779268 + 0.626691i \(0.784409\pi\)
\(444\) −44.2734 −2.10112
\(445\) 6.22482 0.295085
\(446\) 53.1259i 2.51558i
\(447\) 8.46473 0.400368
\(448\) 6.88826 3.56949i 0.325440 0.168643i
\(449\) −20.7430 −0.978924 −0.489462 0.872025i \(-0.662807\pi\)
−0.489462 + 0.872025i \(0.662807\pi\)
\(450\) 8.85952 0.417642
\(451\) 5.65896 0.266470
\(452\) 9.63461i 0.453174i
\(453\) 17.5786i 0.825913i
\(454\) 62.6506 2.94034
\(455\) 0.767868 + 1.48180i 0.0359982 + 0.0694679i
\(456\) 6.67296i 0.312490i
\(457\) 3.13887i 0.146830i 0.997301 + 0.0734152i \(0.0233898\pi\)
−0.997301 + 0.0734152i \(0.976610\pi\)
\(458\) −49.1275 −2.29558
\(459\) 3.06538i 0.143080i
\(460\) −1.80379 25.2801i −0.0841019 1.17869i
\(461\) 39.0094i 1.81685i −0.418051 0.908423i \(-0.637287\pi\)
0.418051 0.908423i \(-0.362713\pi\)
\(462\) −6.69507 + 3.46938i −0.311483 + 0.161410i
\(463\) −20.2299 −0.940165 −0.470082 0.882623i \(-0.655776\pi\)
−0.470082 + 0.882623i \(0.655776\pi\)
\(464\) −13.4192 −0.622972
\(465\) 8.35005 0.387224
\(466\) −21.0051 −0.973043
\(467\) −12.4617 −0.576660 −0.288330 0.957531i \(-0.593100\pi\)
−0.288330 + 0.957531i \(0.593100\pi\)
\(468\) 2.24967i 0.103991i
\(469\) 4.44540 + 8.57857i 0.205270 + 0.396122i
\(470\) 12.9153i 0.595738i
\(471\) 18.6337i 0.858595i
\(472\) 1.18418i 0.0545065i
\(473\) −7.60254 −0.349565
\(474\) −21.6428 −0.994085
\(475\) 3.98187 0.182701
\(476\) −31.2612 + 16.1995i −1.43286 + 0.742504i
\(477\) 5.41447i 0.247912i
\(478\) −53.8334 −2.46228
\(479\) −25.2363 −1.15307 −0.576537 0.817071i \(-0.695596\pi\)
−0.576537 + 0.817071i \(0.695596\pi\)
\(480\) 4.54229i 0.207326i
\(481\) 5.28466 0.240960
\(482\) 22.3268 1.01696
\(483\) −10.8218 + 6.62493i −0.492407 + 0.301445i
\(484\) 42.1935 1.91789
\(485\) −22.1083 −1.00389
\(486\) 2.51820i 0.114228i
\(487\) −19.0531 −0.863377 −0.431688 0.902023i \(-0.642082\pi\)
−0.431688 + 0.902023i \(0.642082\pi\)
\(488\) 36.6506 1.65910
\(489\) 7.23725i 0.327280i
\(490\) 12.3731 17.5311i 0.558960 0.791973i
\(491\) −12.8471 −0.579782 −0.289891 0.957060i \(-0.593619\pi\)
−0.289891 + 0.957060i \(0.593619\pi\)
\(492\) −21.7066 −0.978610
\(493\) −6.67296 −0.300535
\(494\) 1.47691i 0.0664492i
\(495\) 1.37772i 0.0619240i
\(496\) 42.2852i 1.89866i
\(497\) −5.08448 + 2.63477i −0.228070 + 0.118186i
\(498\) 29.2885i 1.31245i
\(499\) −8.62228 −0.385986 −0.192993 0.981200i \(-0.561819\pi\)
−0.192993 + 0.981200i \(0.561819\pi\)
\(500\) −45.0158 −2.01317
\(501\) −17.8282 −0.796507
\(502\) −32.9696 −1.47150
\(503\) 3.30988 0.147580 0.0737900 0.997274i \(-0.476491\pi\)
0.0737900 + 0.997274i \(0.476491\pi\)
\(504\) 13.8500 7.17706i 0.616929 0.319692i
\(505\) 10.8138i 0.481208i
\(506\) −13.6338 + 0.972802i −0.606098 + 0.0432463i
\(507\) 12.7315i 0.565424i
\(508\) −11.8582 −0.526122
\(509\) 8.92077i 0.395406i −0.980262 0.197703i \(-0.936652\pi\)
0.980262 0.197703i \(-0.0633482\pi\)
\(510\) 9.39658i 0.416088i
\(511\) −12.4466 24.0190i −0.550605 1.06254i
\(512\) −49.6878 −2.19591
\(513\) 1.13179i 0.0499698i
\(514\) 35.0218i 1.54474i
\(515\) 14.0000 0.616914
\(516\) 29.1618 1.28378
\(517\) −4.76855 −0.209720
\(518\) −31.2612 60.3267i −1.37354 2.65060i
\(519\) −20.2248 −0.887771
\(520\) 3.71914i 0.163095i
\(521\) 42.6255 1.86746 0.933729 0.357980i \(-0.116535\pi\)
0.933729 + 0.357980i \(0.116535\pi\)
\(522\) 5.48180 0.239932
\(523\) 20.5553 0.898819 0.449410 0.893326i \(-0.351634\pi\)
0.449410 + 0.893326i \(0.351634\pi\)
\(524\) 81.2655i 3.55010i
\(525\) 4.28268 + 8.26455i 0.186911 + 0.360694i
\(526\) 59.9121i 2.61229i
\(527\) 21.0271i 0.915954i
\(528\) 6.97688 0.303630
\(529\) −22.7670 + 3.26557i −0.989869 + 0.141981i
\(530\) 16.5974i 0.720946i
\(531\) 0.200848i 0.00871606i
\(532\) 11.5422 5.98114i 0.500417 0.259315i
\(533\) 2.59099 0.112228
\(534\) 12.8772i 0.557252i
\(535\) 3.26122i 0.140995i
\(536\) 21.5312i 0.930005i
\(537\) 10.4141i 0.449402i
\(538\) 14.5118i 0.625646i
\(539\) −6.47277 4.56836i −0.278802 0.196773i
\(540\) 5.28466i 0.227416i
\(541\) 5.98027 0.257112 0.128556 0.991702i \(-0.458966\pi\)
0.128556 + 0.991702i \(0.458966\pi\)
\(542\) 29.0655i 1.24847i
\(543\) 14.0653i 0.603601i
\(544\) 11.4384 0.490417
\(545\) 21.6025i 0.925351i
\(546\) −3.06538 + 1.58848i −0.131186 + 0.0679806i
\(547\) 4.06037 0.173609 0.0868045 0.996225i \(-0.472334\pi\)
0.0868045 + 0.996225i \(0.472334\pi\)
\(548\) 53.4102i 2.28157i
\(549\) −6.21627 −0.265304
\(550\) 10.0271i 0.427559i
\(551\) 2.46377 0.104960
\(552\) 28.2041 2.01242i 1.20045 0.0856544i
\(553\) −10.4621 20.1893i −0.444892 0.858536i
\(554\) 61.8753 2.62883
\(555\) −12.4141 −0.526950
\(556\) 59.8209i 2.53697i
\(557\) 2.49295i 0.105630i −0.998604 0.0528149i \(-0.983181\pi\)
0.998604 0.0528149i \(-0.0168193\pi\)
\(558\) 17.2736i 0.731252i
\(559\) −3.48088 −0.147225
\(560\) −17.6274 + 9.13449i −0.744893 + 0.386003i
\(561\) 3.46938 0.146477
\(562\) 42.0542i 1.77395i
\(563\) 0.846107 0.0356592 0.0178296 0.999841i \(-0.494324\pi\)
0.0178296 + 0.999841i \(0.494324\pi\)
\(564\) 18.2912 0.770198
\(565\) 2.70151i 0.113653i
\(566\) −30.7654 −1.29317
\(567\) −2.34908 + 1.21729i −0.0986523 + 0.0511215i
\(568\) 12.7614 0.535458
\(569\) 40.2916i 1.68911i −0.535469 0.844555i \(-0.679865\pi\)
0.535469 0.844555i \(-0.320135\pi\)
\(570\) 3.46938i 0.145316i
\(571\) 38.1275i 1.59559i 0.602930 + 0.797794i \(0.294000\pi\)
−0.602930 + 0.797794i \(0.706000\pi\)
\(572\) −2.54616 −0.106460
\(573\) −12.3319 −0.515173
\(574\) −15.3269 29.5773i −0.639733 1.23453i
\(575\) 1.20085 + 16.8299i 0.0500788 + 0.701855i
\(576\) 2.93232 0.122180
\(577\) 23.7918i 0.990467i 0.868760 + 0.495234i \(0.164918\pi\)
−0.868760 + 0.495234i \(0.835082\pi\)
\(578\) −19.1469 −0.796407
\(579\) 3.17687i 0.132026i
\(580\) −11.5040 −0.477679
\(581\) 27.3216 14.1580i 1.13349 0.587373i
\(582\) 45.7352i 1.89579i
\(583\) 6.12805 0.253798
\(584\) 60.2847i 2.49460i
\(585\) 0.630799i 0.0260803i
\(586\) −55.5470 −2.29463
\(587\) 16.3049i 0.672976i −0.941688 0.336488i \(-0.890761\pi\)
0.941688 0.336488i \(-0.109239\pi\)
\(588\) 24.8282 + 17.5233i 1.02390 + 0.722649i
\(589\) 7.76355i 0.319892i
\(590\) 0.615677i 0.0253470i
\(591\) 16.5661i 0.681440i
\(592\) 62.8659i 2.58377i
\(593\) 3.57346i 0.146744i −0.997305 0.0733721i \(-0.976624\pi\)
0.997305 0.0733721i \(-0.0233761\pi\)
\(594\) −2.85008 −0.116940
\(595\) −8.76554 + 4.54229i −0.359352 + 0.186216i
\(596\) 36.7481i 1.50526i
\(597\) 9.28165i 0.379873i
\(598\) −6.24234 + 0.445404i −0.255268 + 0.0182139i
\(599\) −16.3100 −0.666410 −0.333205 0.942854i \(-0.608130\pi\)
−0.333205 + 0.942854i \(0.608130\pi\)
\(600\) 20.7430i 0.846830i
\(601\) 21.8771i 0.892384i 0.894937 + 0.446192i \(0.147220\pi\)
−0.894937 + 0.446192i \(0.852780\pi\)
\(602\) 20.5910 + 39.7357i 0.839226 + 1.61951i
\(603\) 3.65188i 0.148716i
\(604\) 76.3143 3.10518
\(605\) 11.8309 0.480995
\(606\) −22.3704 −0.908736
\(607\) 17.8355i 0.723923i −0.932193 0.361961i \(-0.882107\pi\)
0.932193 0.361961i \(-0.117893\pi\)
\(608\) −4.22325 −0.171275
\(609\) 2.64989 + 5.11366i 0.107379 + 0.207216i
\(610\) 19.0553 0.771525
\(611\) −2.18331 −0.0883273
\(612\) −13.3078 −0.537937
\(613\) 28.6488i 1.15711i −0.815642 0.578557i \(-0.803616\pi\)
0.815642 0.578557i \(-0.196384\pi\)
\(614\) 50.4059i 2.03422i
\(615\) −6.08646 −0.245430
\(616\) 8.12294 + 15.6753i 0.327283 + 0.631577i
\(617\) 30.6387i 1.23347i 0.787171 + 0.616734i \(0.211545\pi\)
−0.787171 + 0.616734i \(0.788455\pi\)
\(618\) 28.9616i 1.16501i
\(619\) 27.1135 1.08979 0.544893 0.838506i \(-0.316570\pi\)
0.544893 + 0.838506i \(0.316570\pi\)
\(620\) 36.2503i 1.45585i
\(621\) −4.78367 + 0.341325i −0.191962 + 0.0136969i
\(622\) 39.6441i 1.58958i
\(623\) −12.0124 + 6.22482i −0.481268 + 0.249392i
\(624\) 3.19441 0.127879
\(625\) 4.96872 0.198749
\(626\) 21.3159 0.851954
\(627\) −1.28095 −0.0511563
\(628\) 80.8949 3.22806
\(629\) 31.2612i 1.24647i
\(630\) 7.20085 3.73147i 0.286889 0.148665i
\(631\) 39.5904i 1.57607i −0.615631 0.788034i \(-0.711099\pi\)
0.615631 0.788034i \(-0.288901\pi\)
\(632\) 50.6727i 2.01565i
\(633\) 7.96360i 0.316525i
\(634\) 70.7823 2.81113
\(635\) −3.32500 −0.131949
\(636\) −23.5060 −0.932072
\(637\) −2.96360 2.09166i −0.117422 0.0828744i
\(638\) 6.20426i 0.245629i
\(639\) −2.16445 −0.0856243
\(640\) −18.0733 −0.714409
\(641\) 27.2725i 1.07720i 0.842562 + 0.538600i \(0.181047\pi\)
−0.842562 + 0.538600i \(0.818953\pi\)
\(642\) 6.74645 0.266261
\(643\) −32.3127 −1.27429 −0.637144 0.770745i \(-0.719884\pi\)
−0.637144 + 0.770745i \(0.719884\pi\)
\(644\) 28.7610 + 46.9807i 1.13334 + 1.85130i
\(645\) 8.17687 0.321964
\(646\) −8.73658 −0.343736
\(647\) 1.89168i 0.0743696i 0.999308 + 0.0371848i \(0.0118390\pi\)
−0.999308 + 0.0371848i \(0.988161\pi\)
\(648\) 5.89592 0.231614
\(649\) 0.227318 0.00892302
\(650\) 4.59099i 0.180074i
\(651\) −16.1136 + 8.35005i −0.631542 + 0.327264i
\(652\) 31.4192 1.23047
\(653\) 39.2903 1.53755 0.768774 0.639520i \(-0.220867\pi\)
0.768774 + 0.639520i \(0.220867\pi\)
\(654\) 44.6889 1.74748
\(655\) 22.7866i 0.890344i
\(656\) 30.8223i 1.20341i
\(657\) 10.2248i 0.398908i
\(658\) 12.9153 + 24.9234i 0.503491 + 0.971617i
\(659\) 22.8600i 0.890501i −0.895406 0.445251i \(-0.853115\pi\)
0.895406 0.445251i \(-0.146885\pi\)
\(660\) 5.98114 0.232816
\(661\) 46.0209 1.79001 0.895003 0.446060i \(-0.147173\pi\)
0.895003 + 0.446060i \(0.147173\pi\)
\(662\) −23.2299 −0.902857
\(663\) 1.58848 0.0616914
\(664\) −68.5739 −2.66118
\(665\) 3.23639 1.67709i 0.125502 0.0650348i
\(666\) 25.6809i 0.995116i
\(667\) 0.743021 + 10.4134i 0.0287699 + 0.403210i
\(668\) 77.3982i 2.99463i
\(669\) 21.0968 0.815648
\(670\) 11.1944i 0.432478i
\(671\) 7.03552i 0.271603i
\(672\) −4.54229 8.76554i −0.175223 0.338138i
\(673\) −11.6347 −0.448485 −0.224242 0.974533i \(-0.571991\pi\)
−0.224242 + 0.974533i \(0.571991\pi\)
\(674\) 35.4547i 1.36566i
\(675\) 3.51820i 0.135416i
\(676\) 55.2714 2.12582
\(677\) 36.8519 1.41633 0.708166 0.706046i \(-0.249523\pi\)
0.708166 + 0.706046i \(0.249523\pi\)
\(678\) −5.58858 −0.214628
\(679\) 42.6638 22.1083i 1.63729 0.848439i
\(680\) 22.0005 0.843679
\(681\) 24.8791i 0.953371i
\(682\) −19.5502 −0.748615
\(683\) −20.6034 −0.788368 −0.394184 0.919032i \(-0.628973\pi\)
−0.394184 + 0.919032i \(0.628973\pi\)
\(684\) 4.91348 0.187871
\(685\) 14.9760i 0.572205i
\(686\) −6.34608 + 46.2039i −0.242294 + 1.76407i
\(687\) 19.5090i 0.744314i
\(688\) 41.4082i 1.57867i
\(689\) 2.80577 0.106891
\(690\) 14.6638 1.04629i 0.558241 0.0398316i
\(691\) 27.9314i 1.06256i 0.847196 + 0.531281i \(0.178289\pi\)
−0.847196 + 0.531281i \(0.821711\pi\)
\(692\) 87.8025i 3.33775i
\(693\) −1.37772 2.65868i −0.0523353 0.100995i
\(694\) −11.3464 −0.430705
\(695\) 16.7736i 0.636258i
\(696\) 12.8347i 0.486497i
\(697\) 15.3269i 0.580549i
\(698\) 29.8462i 1.12970i
\(699\) 8.34132i 0.315498i
\(700\) 35.8791 18.5925i 1.35610 0.702730i
\(701\) 45.7180i 1.72675i 0.504566 + 0.863373i \(0.331653\pi\)
−0.504566 + 0.863373i \(0.668347\pi\)
\(702\) −1.30493 −0.0492513
\(703\) 11.5422i 0.435321i
\(704\) 3.31877i 0.125081i
\(705\) 5.12878 0.193161
\(706\) 60.4787i 2.27615i
\(707\) −10.8138 20.8681i −0.406695 0.784825i
\(708\) −0.871947 −0.0327698
\(709\) 15.4536i 0.580373i 0.956970 + 0.290186i \(0.0937173\pi\)
−0.956970 + 0.290186i \(0.906283\pi\)
\(710\) 6.63487 0.249002
\(711\) 8.59454i 0.322320i
\(712\) 30.1497 1.12991
\(713\) −32.8137 + 2.34132i −1.22888 + 0.0876833i
\(714\) −9.39658 18.1332i −0.351658 0.678617i
\(715\) −0.713934 −0.0266996
\(716\) −45.2111 −1.68962
\(717\) 21.3777i 0.798366i
\(718\) 3.06538i 0.114399i
\(719\) 23.3820i 0.872000i 0.899947 + 0.436000i \(0.143605\pi\)
−0.899947 + 0.436000i \(0.856395\pi\)
\(720\) −7.50394 −0.279655
\(721\) −27.0167 + 14.0000i −1.00615 + 0.521387i
\(722\) −44.6201 −1.66059
\(723\) 8.86616i 0.329736i
\(724\) −61.0621 −2.26936
\(725\) 7.65868 0.284436
\(726\) 24.4745i 0.908334i
\(727\) −0.447787 −0.0166075 −0.00830376 0.999966i \(-0.502643\pi\)
−0.00830376 + 0.999966i \(0.502643\pi\)
\(728\) 3.71914 + 7.17706i 0.137841 + 0.266000i
\(729\) −1.00000 −0.0370370
\(730\) 31.3430i 1.16006i
\(731\) 20.5910i 0.761585i
\(732\) 26.9868i 0.997463i
\(733\) 19.9959 0.738566 0.369283 0.929317i \(-0.379603\pi\)
0.369283 + 0.929317i \(0.379603\pi\)
\(734\) −27.0541 −0.998585
\(735\) 6.96175 + 4.91348i 0.256788 + 0.181236i
\(736\) −1.27364 17.8501i −0.0469471 0.657964i
\(737\) −4.13317 −0.152247
\(738\) 12.5910i 0.463481i
\(739\) −18.8449 −0.693221 −0.346610 0.938009i \(-0.612667\pi\)
−0.346610 + 0.938009i \(0.612667\pi\)
\(740\) 53.8937i 1.98117i
\(741\) −0.586493 −0.0215454
\(742\) −16.5974 32.0291i −0.609311 1.17582i
\(743\) 4.81285i 0.176566i −0.996095 0.0882832i \(-0.971862\pi\)
0.996095 0.0882832i \(-0.0281381\pi\)
\(744\) 40.4432 1.48272
\(745\) 10.3041i 0.377511i
\(746\) 71.3427i 2.61204i
\(747\) 11.6307 0.425546
\(748\) 15.0617i 0.550710i
\(749\) 3.26122 + 6.29338i 0.119162 + 0.229955i
\(750\) 26.1116i 0.953459i
\(751\) 40.5772i 1.48068i −0.672230 0.740342i \(-0.734663\pi\)
0.672230 0.740342i \(-0.265337\pi\)
\(752\) 25.9725i 0.947120i
\(753\) 13.0925i 0.477118i
\(754\) 2.84066i 0.103451i
\(755\) 21.3983 0.778763
\(756\) 5.28466 + 10.1981i 0.192201 + 0.370903i
\(757\) 39.0471i 1.41919i −0.704609 0.709596i \(-0.748877\pi\)
0.704609 0.709596i \(-0.251123\pi\)
\(758\) 12.2615i 0.445359i
\(759\) −0.386309 5.41412i −0.0140221 0.196520i
\(760\) −8.12294 −0.294650
\(761\) 40.8959i 1.48248i −0.671242 0.741238i \(-0.734239\pi\)
0.671242 0.741238i \(-0.265761\pi\)
\(762\) 6.87838i 0.249178i
\(763\) 21.6025 + 41.6878i 0.782065 + 1.50920i
\(764\) 53.5369i 1.93690i
\(765\) −3.73147 −0.134912
\(766\) 87.2118 3.15109
\(767\) 0.104079 0.00375808
\(768\) 31.5233i 1.13750i
\(769\) −28.8730 −1.04119 −0.520594 0.853804i \(-0.674289\pi\)
−0.520594 + 0.853804i \(0.674289\pi\)
\(770\) 4.22325 + 8.14986i 0.152195 + 0.293701i
\(771\) 13.9075 0.500865
\(772\) −13.7918 −0.496379
\(773\) −23.7213 −0.853195 −0.426598 0.904442i \(-0.640288\pi\)
−0.426598 + 0.904442i \(0.640288\pi\)
\(774\) 16.9154i 0.608012i
\(775\) 24.1332i 0.866889i
\(776\) −107.081 −3.84398
\(777\) 23.9563 12.4141i 0.859427 0.445354i
\(778\) 29.2885i 1.05004i
\(779\) 5.65896i 0.202753i
\(780\) 2.73851 0.0980542
\(781\) 2.44971i 0.0876574i
\(782\) −2.63477 36.9263i −0.0942192 1.32048i
\(783\) 2.17687i 0.0777951i
\(784\) 24.8822 35.2548i 0.888649 1.25910i
\(785\) 22.6826 0.809578
\(786\) −47.1383 −1.68137
\(787\) −33.2615 −1.18564 −0.592822 0.805334i \(-0.701986\pi\)