Properties

Label 1110.2.u.e.401.1
Level $1110$
Weight $2$
Character 1110.401
Analytic conductor $8.863$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.u (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.1
Character \(\chi\) \(=\) 1110.401
Dual form 1110.2.u.e.191.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.73082 - 0.0652635i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.27002 - 1.17773i) q^{6} -5.10391 q^{7} +(0.707107 + 0.707107i) q^{8} +(2.99148 + 0.225919i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.73082 - 0.0652635i) q^{3} -1.00000i q^{4} +(-0.707107 - 0.707107i) q^{5} +(1.27002 - 1.17773i) q^{6} -5.10391 q^{7} +(0.707107 + 0.707107i) q^{8} +(2.99148 + 0.225919i) q^{9} +1.00000 q^{10} -2.52188 q^{11} +(-0.0652635 + 1.73082i) q^{12} +(4.82201 - 4.82201i) q^{13} +(3.60901 - 3.60901i) q^{14} +(1.17773 + 1.27002i) q^{15} -1.00000 q^{16} +(-2.16139 - 2.16139i) q^{17} +(-2.27505 + 1.95555i) q^{18} +(2.84634 - 2.84634i) q^{19} +(-0.707107 + 0.707107i) q^{20} +(8.83396 + 0.333099i) q^{21} +(1.78324 - 1.78324i) q^{22} +(-1.47717 - 1.47717i) q^{23} +(-1.17773 - 1.27002i) q^{24} +1.00000i q^{25} +6.81935i q^{26} +(-5.16297 - 0.586260i) q^{27} +5.10391i q^{28} +(-4.98506 + 4.98506i) q^{29} +(-1.73082 - 0.0652635i) q^{30} +(-2.75008 - 2.75008i) q^{31} +(0.707107 - 0.707107i) q^{32} +(4.36492 + 0.164587i) q^{33} +3.05666 q^{34} +(3.60901 + 3.60901i) q^{35} +(0.225919 - 2.99148i) q^{36} +(-5.45849 - 2.68420i) q^{37} +4.02534i q^{38} +(-8.66073 + 8.03133i) q^{39} -1.00000i q^{40} +4.87039 q^{41} +(-6.48209 + 6.01102i) q^{42} +(-6.39822 + 6.39822i) q^{43} +2.52188i q^{44} +(-1.95555 - 2.27505i) q^{45} +2.08904 q^{46} -0.0691642i q^{47} +(1.73082 + 0.0652635i) q^{48} +19.0499 q^{49} +(-0.707107 - 0.707107i) q^{50} +(3.59991 + 3.88203i) q^{51} +(-4.82201 - 4.82201i) q^{52} +4.54376i q^{53} +(4.06532 - 3.23623i) q^{54} +(1.78324 + 1.78324i) q^{55} +(-3.60901 - 3.60901i) q^{56} +(-5.11228 + 4.74075i) q^{57} -7.04993i q^{58} +(9.35679 + 9.35679i) q^{59} +(1.27002 - 1.17773i) q^{60} +(4.43926 + 4.43926i) q^{61} +3.88920 q^{62} +(-15.2683 - 1.15307i) q^{63} +1.00000i q^{64} -6.81935 q^{65} +(-3.20284 + 2.97008i) q^{66} +14.1658i q^{67} +(-2.16139 + 2.16139i) q^{68} +(2.46032 + 2.65313i) q^{69} -5.10391 q^{70} -1.36435i q^{71} +(1.95555 + 2.27505i) q^{72} +12.8981i q^{73} +(5.75775 - 1.96172i) q^{74} +(0.0652635 - 1.73082i) q^{75} +(-2.84634 - 2.84634i) q^{76} +12.8714 q^{77} +(0.445055 - 11.8031i) q^{78} +(-3.36382 + 3.36382i) q^{79} +(0.707107 + 0.707107i) q^{80} +(8.89792 + 1.35166i) q^{81} +(-3.44389 + 3.44389i) q^{82} -9.73857i q^{83} +(0.333099 - 8.83396i) q^{84} +3.05666i q^{85} -9.04844i q^{86} +(8.95358 - 8.30290i) q^{87} +(-1.78324 - 1.78324i) q^{88} +(7.24712 - 7.24712i) q^{89} +(2.99148 + 0.225919i) q^{90} +(-24.6111 + 24.6111i) q^{91} +(-1.47717 + 1.47717i) q^{92} +(4.58042 + 4.93938i) q^{93} +(0.0489065 + 0.0489065i) q^{94} -4.02534 q^{95} +(-1.27002 + 1.17773i) q^{96} +(-4.90712 + 4.90712i) q^{97} +(-13.4703 + 13.4703i) q^{98} +(-7.54415 - 0.569740i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 24q^{7} - 8q^{9} + O(q^{10}) \) \( 40q - 24q^{7} - 8q^{9} + 40q^{10} - 8q^{12} - 16q^{13} - 40q^{16} + 8q^{18} + 16q^{19} - 24q^{31} + 24q^{33} - 8q^{34} + 16q^{39} - 20q^{42} - 32q^{43} - 8q^{45} + 72q^{46} + 96q^{49} + 20q^{51} + 16q^{52} + 24q^{54} - 16q^{57} + 40q^{61} - 24q^{63} - 44q^{66} - 24q^{70} + 8q^{72} + 8q^{75} - 16q^{76} + 48q^{79} + 24q^{81} - 56q^{82} - 8q^{84} + 12q^{87} - 8q^{90} - 64q^{91} + 12q^{93} + 24q^{94} + 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −1.73082 0.0652635i −0.999290 0.0376799i
\(4\) 1.00000i 0.500000i
\(5\) −0.707107 0.707107i −0.316228 0.316228i
\(6\) 1.27002 1.17773i 0.518485 0.480805i
\(7\) −5.10391 −1.92910 −0.964549 0.263904i \(-0.914990\pi\)
−0.964549 + 0.263904i \(0.914990\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 2.99148 + 0.225919i 0.997160 + 0.0753063i
\(10\) 1.00000 0.316228
\(11\) −2.52188 −0.760375 −0.380187 0.924909i \(-0.624141\pi\)
−0.380187 + 0.924909i \(0.624141\pi\)
\(12\) −0.0652635 + 1.73082i −0.0188400 + 0.499645i
\(13\) 4.82201 4.82201i 1.33738 1.33738i 0.438798 0.898586i \(-0.355404\pi\)
0.898586 0.438798i \(-0.144596\pi\)
\(14\) 3.60901 3.60901i 0.964549 0.964549i
\(15\) 1.17773 + 1.27002i 0.304088 + 0.327919i
\(16\) −1.00000 −0.250000
\(17\) −2.16139 2.16139i −0.524213 0.524213i 0.394628 0.918841i \(-0.370873\pi\)
−0.918841 + 0.394628i \(0.870873\pi\)
\(18\) −2.27505 + 1.95555i −0.536233 + 0.460927i
\(19\) 2.84634 2.84634i 0.652996 0.652996i −0.300717 0.953713i \(-0.597226\pi\)
0.953713 + 0.300717i \(0.0972260\pi\)
\(20\) −0.707107 + 0.707107i −0.158114 + 0.158114i
\(21\) 8.83396 + 0.333099i 1.92773 + 0.0726883i
\(22\) 1.78324 1.78324i 0.380187 0.380187i
\(23\) −1.47717 1.47717i −0.308012 0.308012i 0.536126 0.844138i \(-0.319887\pi\)
−0.844138 + 0.536126i \(0.819887\pi\)
\(24\) −1.17773 1.27002i −0.240402 0.259242i
\(25\) 1.00000i 0.200000i
\(26\) 6.81935i 1.33738i
\(27\) −5.16297 0.586260i −0.993615 0.112826i
\(28\) 5.10391i 0.964549i
\(29\) −4.98506 + 4.98506i −0.925702 + 0.925702i −0.997425 0.0717228i \(-0.977150\pi\)
0.0717228 + 0.997425i \(0.477150\pi\)
\(30\) −1.73082 0.0652635i −0.316003 0.0119154i
\(31\) −2.75008 2.75008i −0.493929 0.493929i 0.415613 0.909542i \(-0.363567\pi\)
−0.909542 + 0.415613i \(0.863567\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 4.36492 + 0.164587i 0.759835 + 0.0286509i
\(34\) 3.05666 0.524213
\(35\) 3.60901 + 3.60901i 0.610034 + 0.610034i
\(36\) 0.225919 2.99148i 0.0376532 0.498580i
\(37\) −5.45849 2.68420i −0.897370 0.441279i
\(38\) 4.02534i 0.652996i
\(39\) −8.66073 + 8.03133i −1.38683 + 1.28604i
\(40\) 1.00000i 0.158114i
\(41\) 4.87039 0.760627 0.380314 0.924858i \(-0.375816\pi\)
0.380314 + 0.924858i \(0.375816\pi\)
\(42\) −6.48209 + 6.01102i −1.00021 + 0.927520i
\(43\) −6.39822 + 6.39822i −0.975719 + 0.975719i −0.999712 0.0239935i \(-0.992362\pi\)
0.0239935 + 0.999712i \(0.492362\pi\)
\(44\) 2.52188i 0.380187i
\(45\) −1.95555 2.27505i −0.291516 0.339144i
\(46\) 2.08904 0.308012
\(47\) 0.0691642i 0.0100886i −0.999987 0.00504432i \(-0.998394\pi\)
0.999987 0.00504432i \(-0.00160566\pi\)
\(48\) 1.73082 + 0.0652635i 0.249822 + 0.00941998i
\(49\) 19.0499 2.72142
\(50\) −0.707107 0.707107i −0.100000 0.100000i
\(51\) 3.59991 + 3.88203i 0.504088 + 0.543593i
\(52\) −4.82201 4.82201i −0.668692 0.668692i
\(53\) 4.54376i 0.624133i 0.950060 + 0.312067i \(0.101021\pi\)
−0.950060 + 0.312067i \(0.898979\pi\)
\(54\) 4.06532 3.23623i 0.553220 0.440395i
\(55\) 1.78324 + 1.78324i 0.240452 + 0.240452i
\(56\) −3.60901 3.60901i −0.482274 0.482274i
\(57\) −5.11228 + 4.74075i −0.677137 + 0.627928i
\(58\) 7.04993i 0.925702i
\(59\) 9.35679 + 9.35679i 1.21815 + 1.21815i 0.968279 + 0.249871i \(0.0803882\pi\)
0.249871 + 0.968279i \(0.419612\pi\)
\(60\) 1.27002 1.17773i 0.163959 0.152044i
\(61\) 4.43926 + 4.43926i 0.568389 + 0.568389i 0.931677 0.363288i \(-0.118346\pi\)
−0.363288 + 0.931677i \(0.618346\pi\)
\(62\) 3.88920 0.493929
\(63\) −15.2683 1.15307i −1.92362 0.145273i
\(64\) 1.00000i 0.125000i
\(65\) −6.81935 −0.845836
\(66\) −3.20284 + 2.97008i −0.394243 + 0.365592i
\(67\) 14.1658i 1.73063i 0.501232 + 0.865313i \(0.332880\pi\)
−0.501232 + 0.865313i \(0.667120\pi\)
\(68\) −2.16139 + 2.16139i −0.262106 + 0.262106i
\(69\) 2.46032 + 2.65313i 0.296187 + 0.319399i
\(70\) −5.10391 −0.610034
\(71\) 1.36435i 0.161918i −0.996717 0.0809590i \(-0.974202\pi\)
0.996717 0.0809590i \(-0.0257983\pi\)
\(72\) 1.95555 + 2.27505i 0.230464 + 0.268117i
\(73\) 12.8981i 1.50961i 0.655948 + 0.754806i \(0.272269\pi\)
−0.655948 + 0.754806i \(0.727731\pi\)
\(74\) 5.75775 1.96172i 0.669325 0.228045i
\(75\) 0.0652635 1.73082i 0.00753598 0.199858i
\(76\) −2.84634 2.84634i −0.326498 0.326498i
\(77\) 12.8714 1.46684
\(78\) 0.445055 11.8031i 0.0503925 1.33643i
\(79\) −3.36382 + 3.36382i −0.378459 + 0.378459i −0.870546 0.492087i \(-0.836234\pi\)
0.492087 + 0.870546i \(0.336234\pi\)
\(80\) 0.707107 + 0.707107i 0.0790569 + 0.0790569i
\(81\) 8.89792 + 1.35166i 0.988658 + 0.150185i
\(82\) −3.44389 + 3.44389i −0.380314 + 0.380314i
\(83\) 9.73857i 1.06895i −0.845185 0.534474i \(-0.820510\pi\)
0.845185 0.534474i \(-0.179490\pi\)
\(84\) 0.333099 8.83396i 0.0363441 0.963864i
\(85\) 3.05666i 0.331541i
\(86\) 9.04844i 0.975719i
\(87\) 8.95358 8.30290i 0.959925 0.890164i
\(88\) −1.78324 1.78324i −0.190094 0.190094i
\(89\) 7.24712 7.24712i 0.768193 0.768193i −0.209595 0.977788i \(-0.567215\pi\)
0.977788 + 0.209595i \(0.0672146\pi\)
\(90\) 2.99148 + 0.225919i 0.315330 + 0.0238140i
\(91\) −24.6111 + 24.6111i −2.57994 + 2.57994i
\(92\) −1.47717 + 1.47717i −0.154006 + 0.154006i
\(93\) 4.58042 + 4.93938i 0.474967 + 0.512190i
\(94\) 0.0489065 + 0.0489065i 0.00504432 + 0.00504432i
\(95\) −4.02534 −0.412991
\(96\) −1.27002 + 1.17773i −0.129621 + 0.120201i
\(97\) −4.90712 + 4.90712i −0.498242 + 0.498242i −0.910890 0.412648i \(-0.864604\pi\)
0.412648 + 0.910890i \(0.364604\pi\)
\(98\) −13.4703 + 13.4703i −1.36071 + 1.36071i
\(99\) −7.54415 0.569740i −0.758216 0.0572610i
\(100\) 1.00000 0.100000
\(101\) −17.0003 −1.69159 −0.845796 0.533507i \(-0.820874\pi\)
−0.845796 + 0.533507i \(0.820874\pi\)
\(102\) −5.29053 0.199488i −0.523841 0.0197523i
\(103\) −4.76900 4.76900i −0.469904 0.469904i 0.431980 0.901883i \(-0.357815\pi\)
−0.901883 + 0.431980i \(0.857815\pi\)
\(104\) 6.81935 0.668692
\(105\) −6.01102 6.48209i −0.586615 0.632587i
\(106\) −3.21292 3.21292i −0.312067 0.312067i
\(107\) 17.6140i 1.70280i −0.524513 0.851402i \(-0.675753\pi\)
0.524513 0.851402i \(-0.324247\pi\)
\(108\) −0.586260 + 5.16297i −0.0564129 + 0.496807i
\(109\) −1.38209 + 1.38209i −0.132380 + 0.132380i −0.770192 0.637812i \(-0.779840\pi\)
0.637812 + 0.770192i \(0.279840\pi\)
\(110\) −2.52188 −0.240452
\(111\) 9.27248 + 5.00211i 0.880105 + 0.474779i
\(112\) 5.10391 0.482274
\(113\) −4.81041 + 4.81041i −0.452526 + 0.452526i −0.896192 0.443666i \(-0.853678\pi\)
0.443666 + 0.896192i \(0.353678\pi\)
\(114\) 0.262708 6.96714i 0.0246049 0.652533i
\(115\) 2.08904i 0.194804i
\(116\) 4.98506 + 4.98506i 0.462851 + 0.462851i
\(117\) 15.5143 13.3356i 1.43430 1.23287i
\(118\) −13.2325 −1.21815
\(119\) 11.0315 + 11.0315i 1.01126 + 1.01126i
\(120\) −0.0652635 + 1.73082i −0.00595772 + 0.158002i
\(121\) −4.64013 −0.421830
\(122\) −6.27806 −0.568389
\(123\) −8.42977 0.317859i −0.760087 0.0286604i
\(124\) −2.75008 + 2.75008i −0.246965 + 0.246965i
\(125\) 0.707107 0.707107i 0.0632456 0.0632456i
\(126\) 11.6116 9.98095i 1.03445 0.889173i
\(127\) 13.6854 1.21438 0.607190 0.794557i \(-0.292297\pi\)
0.607190 + 0.794557i \(0.292297\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 11.4917 10.6566i 1.01179 0.938261i
\(130\) 4.82201 4.82201i 0.422918 0.422918i
\(131\) 1.16781 1.16781i 0.102032 0.102032i −0.654248 0.756280i \(-0.727015\pi\)
0.756280 + 0.654248i \(0.227015\pi\)
\(132\) 0.164587 4.36492i 0.0143254 0.379917i
\(133\) −14.5275 + 14.5275i −1.25969 + 1.25969i
\(134\) −10.0167 10.0167i −0.865313 0.865313i
\(135\) 3.23623 + 4.06532i 0.278530 + 0.349887i
\(136\) 3.05666i 0.262106i
\(137\) 9.28520i 0.793288i 0.917973 + 0.396644i \(0.129825\pi\)
−0.917973 + 0.396644i \(0.870175\pi\)
\(138\) −3.61575 0.136338i −0.307793 0.0116059i
\(139\) 5.21169i 0.442050i −0.975268 0.221025i \(-0.929060\pi\)
0.975268 0.221025i \(-0.0709403\pi\)
\(140\) 3.60901 3.60901i 0.305017 0.305017i
\(141\) −0.00451390 + 0.119711i −0.000380139 + 0.0100815i
\(142\) 0.964738 + 0.964738i 0.0809590 + 0.0809590i
\(143\) −12.1605 + 12.1605i −1.01691 + 1.01691i
\(144\) −2.99148 0.225919i −0.249290 0.0188266i
\(145\) 7.04993 0.585465
\(146\) −9.12036 9.12036i −0.754806 0.754806i
\(147\) −32.9720 1.24327i −2.71949 0.102543i
\(148\) −2.68420 + 5.45849i −0.220640 + 0.448685i
\(149\) 4.53764i 0.371738i 0.982575 + 0.185869i \(0.0595100\pi\)
−0.982575 + 0.185869i \(0.940490\pi\)
\(150\) 1.17773 + 1.27002i 0.0961610 + 0.103697i
\(151\) 4.08345i 0.332307i 0.986100 + 0.166153i \(0.0531347\pi\)
−0.986100 + 0.166153i \(0.946865\pi\)
\(152\) 4.02534 0.326498
\(153\) −5.97745 6.95404i −0.483248 0.562201i
\(154\) −9.10149 + 9.10149i −0.733419 + 0.733419i
\(155\) 3.88920i 0.312388i
\(156\) 8.03133 + 8.66073i 0.643021 + 0.693413i
\(157\) 0.162952 0.0130050 0.00650250 0.999979i \(-0.497930\pi\)
0.00650250 + 0.999979i \(0.497930\pi\)
\(158\) 4.75715i 0.378459i
\(159\) 0.296542 7.86443i 0.0235173 0.623690i
\(160\) −1.00000 −0.0790569
\(161\) 7.53936 + 7.53936i 0.594185 + 0.594185i
\(162\) −7.24755 + 5.33601i −0.569421 + 0.419236i
\(163\) 6.42172 + 6.42172i 0.502988 + 0.502988i 0.912365 0.409377i \(-0.134254\pi\)
−0.409377 + 0.912365i \(0.634254\pi\)
\(164\) 4.87039i 0.380314i
\(165\) −2.97008 3.20284i −0.231221 0.249341i
\(166\) 6.88621 + 6.88621i 0.534474 + 0.534474i
\(167\) 13.7065 + 13.7065i 1.06064 + 1.06064i 0.998038 + 0.0626045i \(0.0199407\pi\)
0.0626045 + 0.998038i \(0.480059\pi\)
\(168\) 6.01102 + 6.48209i 0.463760 + 0.500104i
\(169\) 33.5035i 2.57719i
\(170\) −2.16139 2.16139i −0.165771 0.165771i
\(171\) 9.15783 7.87174i 0.700317 0.601967i
\(172\) 6.39822 + 6.39822i 0.487859 + 0.487859i
\(173\) 12.3062 0.935621 0.467810 0.883829i \(-0.345043\pi\)
0.467810 + 0.883829i \(0.345043\pi\)
\(174\) −0.460104 + 12.2022i −0.0348804 + 0.925044i
\(175\) 5.10391i 0.385820i
\(176\) 2.52188 0.190094
\(177\) −15.5843 16.8056i −1.17139 1.26318i
\(178\) 10.2490i 0.768193i
\(179\) −3.97415 + 3.97415i −0.297042 + 0.297042i −0.839854 0.542812i \(-0.817360\pi\)
0.542812 + 0.839854i \(0.317360\pi\)
\(180\) −2.27505 + 1.95555i −0.169572 + 0.145758i
\(181\) −13.8542 −1.02978 −0.514888 0.857258i \(-0.672166\pi\)
−0.514888 + 0.857258i \(0.672166\pi\)
\(182\) 34.8053i 2.57994i
\(183\) −7.39384 7.97328i −0.546568 0.589402i
\(184\) 2.08904i 0.154006i
\(185\) 1.96172 + 5.75775i 0.144228 + 0.423318i
\(186\) −6.73151 0.253823i −0.493578 0.0186112i
\(187\) 5.45075 + 5.45075i 0.398598 + 0.398598i
\(188\) −0.0691642 −0.00504432
\(189\) 26.3514 + 2.99222i 1.91678 + 0.217652i
\(190\) 2.84634 2.84634i 0.206496 0.206496i
\(191\) 15.5800 + 15.5800i 1.12733 + 1.12733i 0.990610 + 0.136716i \(0.0436547\pi\)
0.136716 + 0.990610i \(0.456345\pi\)
\(192\) 0.0652635 1.73082i 0.00470999 0.124911i
\(193\) 10.1951 10.1951i 0.733858 0.733858i −0.237524 0.971382i \(-0.576336\pi\)
0.971382 + 0.237524i \(0.0763358\pi\)
\(194\) 6.93971i 0.498242i
\(195\) 11.8031 + 0.445055i 0.845235 + 0.0318710i
\(196\) 19.0499i 1.36071i
\(197\) 18.6163i 1.32636i −0.748462 0.663178i \(-0.769207\pi\)
0.748462 0.663178i \(-0.230793\pi\)
\(198\) 5.73739 4.93165i 0.407738 0.350477i
\(199\) 11.0077 + 11.0077i 0.780313 + 0.780313i 0.979883 0.199571i \(-0.0639547\pi\)
−0.199571 + 0.979883i \(0.563955\pi\)
\(200\) −0.707107 + 0.707107i −0.0500000 + 0.0500000i
\(201\) 0.924509 24.5184i 0.0652099 1.72940i
\(202\) 12.0210 12.0210i 0.845796 0.845796i
\(203\) 25.4433 25.4433i 1.78577 1.78577i
\(204\) 3.88203 3.59991i 0.271797 0.252044i
\(205\) −3.44389 3.44389i −0.240531 0.240531i
\(206\) 6.74438 0.469904
\(207\) −4.08521 4.75265i −0.283942 0.330332i
\(208\) −4.82201 + 4.82201i −0.334346 + 0.334346i
\(209\) −7.17814 + 7.17814i −0.496522 + 0.496522i
\(210\) 8.83396 + 0.333099i 0.609601 + 0.0229860i
\(211\) 5.42872 0.373728 0.186864 0.982386i \(-0.440168\pi\)
0.186864 + 0.982386i \(0.440168\pi\)
\(212\) 4.54376 0.312067
\(213\) −0.0890421 + 2.36144i −0.00610106 + 0.161803i
\(214\) 12.4549 + 12.4549i 0.851402 + 0.851402i
\(215\) 9.04844 0.617099
\(216\) −3.23623 4.06532i −0.220197 0.276610i
\(217\) 14.0362 + 14.0362i 0.952837 + 0.952837i
\(218\) 1.95457i 0.132380i
\(219\) 0.841778 22.3244i 0.0568821 1.50854i
\(220\) 1.78324 1.78324i 0.120226 0.120226i
\(221\) −20.8444 −1.40215
\(222\) −10.0937 + 3.01961i −0.677442 + 0.202663i
\(223\) 0.585115 0.0391822 0.0195911 0.999808i \(-0.493764\pi\)
0.0195911 + 0.999808i \(0.493764\pi\)
\(224\) −3.60901 + 3.60901i −0.241137 + 0.241137i
\(225\) −0.225919 + 2.99148i −0.0150613 + 0.199432i
\(226\) 6.80295i 0.452526i
\(227\) 9.42921 + 9.42921i 0.625838 + 0.625838i 0.947018 0.321180i \(-0.104079\pi\)
−0.321180 + 0.947018i \(0.604079\pi\)
\(228\) 4.74075 + 5.11228i 0.313964 + 0.338569i
\(229\) −10.8504 −0.717016 −0.358508 0.933527i \(-0.616714\pi\)
−0.358508 + 0.933527i \(0.616714\pi\)
\(230\) −1.47717 1.47717i −0.0974019 0.0974019i
\(231\) −22.2782 0.840036i −1.46580 0.0552703i
\(232\) −7.04993 −0.462851
\(233\) 7.44823 0.487950 0.243975 0.969782i \(-0.421549\pi\)
0.243975 + 0.969782i \(0.421549\pi\)
\(234\) −1.54062 + 20.3999i −0.100713 + 1.33359i
\(235\) −0.0489065 + 0.0489065i −0.00319031 + 0.00319031i
\(236\) 9.35679 9.35679i 0.609075 0.609075i
\(237\) 6.04170 5.60263i 0.392450 0.363930i
\(238\) −15.6009 −1.01126
\(239\) −19.5319 19.5319i −1.26341 1.26341i −0.949429 0.313982i \(-0.898337\pi\)
−0.313982 0.949429i \(-0.601663\pi\)
\(240\) −1.17773 1.27002i −0.0760219 0.0819797i
\(241\) −16.7350 + 16.7350i −1.07799 + 1.07799i −0.0813043 + 0.996689i \(0.525909\pi\)
−0.996689 + 0.0813043i \(0.974091\pi\)
\(242\) 3.28107 3.28107i 0.210915 0.210915i
\(243\) −15.3125 2.92020i −0.982297 0.187331i
\(244\) 4.43926 4.43926i 0.284194 0.284194i
\(245\) −13.4703 13.4703i −0.860588 0.860588i
\(246\) 6.18551 5.73599i 0.394374 0.365713i
\(247\) 27.4502i 1.74661i
\(248\) 3.88920i 0.246965i
\(249\) −0.635574 + 16.8557i −0.0402779 + 1.06819i
\(250\) 1.00000i 0.0632456i
\(251\) 0.817495 0.817495i 0.0515998 0.0515998i −0.680836 0.732436i \(-0.738383\pi\)
0.732436 + 0.680836i \(0.238383\pi\)
\(252\) −1.15307 + 15.2683i −0.0726366 + 0.961810i
\(253\) 3.72525 + 3.72525i 0.234204 + 0.234204i
\(254\) −9.67701 + 9.67701i −0.607190 + 0.607190i
\(255\) 0.199488 5.29053i 0.0124925 0.331306i
\(256\) 1.00000 0.0625000
\(257\) −5.87353 5.87353i −0.366381 0.366381i 0.499775 0.866156i \(-0.333416\pi\)
−0.866156 + 0.499775i \(0.833416\pi\)
\(258\) −0.590533 + 15.6612i −0.0367650 + 0.975026i
\(259\) 27.8596 + 13.6999i 1.73111 + 0.851271i
\(260\) 6.81935i 0.422918i
\(261\) −16.0389 + 13.7865i −0.992784 + 0.853362i
\(262\) 1.65153i 0.102032i
\(263\) 23.1214 1.42572 0.712862 0.701304i \(-0.247399\pi\)
0.712862 + 0.701304i \(0.247399\pi\)
\(264\) 2.97008 + 3.20284i 0.182796 + 0.197121i
\(265\) 3.21292 3.21292i 0.197368 0.197368i
\(266\) 20.5450i 1.25969i
\(267\) −13.0164 + 12.0705i −0.796593 + 0.738702i
\(268\) 14.1658 0.865313
\(269\) 7.67575i 0.467999i −0.972237 0.233999i \(-0.924819\pi\)
0.972237 0.233999i \(-0.0751813\pi\)
\(270\) −5.16297 0.586260i −0.314209 0.0356786i
\(271\) −7.78777 −0.473074 −0.236537 0.971623i \(-0.576012\pi\)
−0.236537 + 0.971623i \(0.576012\pi\)
\(272\) 2.16139 + 2.16139i 0.131053 + 0.131053i
\(273\) 44.2036 40.9912i 2.67532 2.48090i
\(274\) −6.56563 6.56563i −0.396644 0.396644i
\(275\) 2.52188i 0.152075i
\(276\) 2.65313 2.46032i 0.159699 0.148094i
\(277\) 0.279231 + 0.279231i 0.0167774 + 0.0167774i 0.715446 0.698668i \(-0.246224\pi\)
−0.698668 + 0.715446i \(0.746224\pi\)
\(278\) 3.68522 + 3.68522i 0.221025 + 0.221025i
\(279\) −7.60552 8.84811i −0.455331 0.529723i
\(280\) 5.10391i 0.305017i
\(281\) 8.56400 + 8.56400i 0.510885 + 0.510885i 0.914798 0.403912i \(-0.132350\pi\)
−0.403912 + 0.914798i \(0.632350\pi\)
\(282\) −0.0814565 0.0878401i −0.00485066 0.00523080i
\(283\) −7.11377 7.11377i −0.422870 0.422870i 0.463321 0.886191i \(-0.346658\pi\)
−0.886191 + 0.463321i \(0.846658\pi\)
\(284\) −1.36435 −0.0809590
\(285\) 6.96714 + 0.262708i 0.412698 + 0.0155615i
\(286\) 17.1976i 1.01691i
\(287\) −24.8580 −1.46732
\(288\) 2.27505 1.95555i 0.134058 0.115232i
\(289\) 7.65683i 0.450402i
\(290\) −4.98506 + 4.98506i −0.292733 + 0.292733i
\(291\) 8.81360 8.17309i 0.516662 0.479115i
\(292\) 12.8981 0.754806
\(293\) 22.3923i 1.30817i 0.756421 + 0.654085i \(0.226946\pi\)
−0.756421 + 0.654085i \(0.773054\pi\)
\(294\) 24.1939 22.4356i 1.41101 1.30847i
\(295\) 13.2325i 0.770426i
\(296\) −1.96172 5.75775i −0.114023 0.334662i
\(297\) 13.0204 + 1.47848i 0.755520 + 0.0857899i
\(298\) −3.20860 3.20860i −0.185869 0.185869i
\(299\) −14.2459 −0.823860
\(300\) −1.73082 0.0652635i −0.0999290 0.00376799i
\(301\) 32.6559 32.6559i 1.88226 1.88226i
\(302\) −2.88744 2.88744i −0.166153 0.166153i
\(303\) 29.4244 + 1.10950i 1.69039 + 0.0637390i
\(304\) −2.84634 + 2.84634i −0.163249 + 0.163249i
\(305\) 6.27806i 0.359481i
\(306\) 9.14394 + 0.690558i 0.522724 + 0.0394766i
\(307\) 14.5985i 0.833180i 0.909095 + 0.416590i \(0.136775\pi\)
−0.909095 + 0.416590i \(0.863225\pi\)
\(308\) 12.8714i 0.733419i
\(309\) 7.94304 + 8.56553i 0.451864 + 0.487276i
\(310\) −2.75008 2.75008i −0.156194 0.156194i
\(311\) −14.7246 + 14.7246i −0.834955 + 0.834955i −0.988190 0.153234i \(-0.951031\pi\)
0.153234 + 0.988190i \(0.451031\pi\)
\(312\) −11.8031 0.445055i −0.668217 0.0251963i
\(313\) 0.123805 0.123805i 0.00699787 0.00699787i −0.703599 0.710597i \(-0.748425\pi\)
0.710597 + 0.703599i \(0.248425\pi\)
\(314\) −0.115225 + 0.115225i −0.00650250 + 0.00650250i
\(315\) 9.98095 + 11.6116i 0.562363 + 0.654241i
\(316\) 3.36382 + 3.36382i 0.189229 + 0.189229i
\(317\) 14.8309 0.832987 0.416493 0.909139i \(-0.363259\pi\)
0.416493 + 0.909139i \(0.363259\pi\)
\(318\) 5.35131 + 5.77068i 0.300086 + 0.323604i
\(319\) 12.5717 12.5717i 0.703880 0.703880i
\(320\) 0.707107 0.707107i 0.0395285 0.0395285i
\(321\) −1.14955 + 30.4866i −0.0641616 + 1.70160i
\(322\) −10.6623 −0.594185
\(323\) −12.3041 −0.684618
\(324\) 1.35166 8.89792i 0.0750925 0.494329i
\(325\) 4.82201 + 4.82201i 0.267477 + 0.267477i
\(326\) −9.08168 −0.502988
\(327\) 2.48235 2.30195i 0.137274 0.127298i
\(328\) 3.44389 + 3.44389i 0.190157 + 0.190157i
\(329\) 0.353008i 0.0194620i
\(330\) 4.36492 + 0.164587i 0.240281 + 0.00906020i
\(331\) −0.578555 + 0.578555i −0.0318003 + 0.0318003i −0.722828 0.691028i \(-0.757158\pi\)
0.691028 + 0.722828i \(0.257158\pi\)
\(332\) −9.73857 −0.534474
\(333\) −15.7226 9.26290i −0.861590 0.507604i
\(334\) −19.3840 −1.06064
\(335\) 10.0167 10.0167i 0.547272 0.547272i
\(336\) −8.83396 0.333099i −0.481932 0.0181721i
\(337\) 33.2306i 1.81019i 0.425212 + 0.905094i \(0.360200\pi\)
−0.425212 + 0.905094i \(0.639800\pi\)
\(338\) 23.6905 + 23.6905i 1.28860 + 1.28860i
\(339\) 8.63991 8.01202i 0.469255 0.435153i
\(340\) 3.05666 0.165771
\(341\) 6.93537 + 6.93537i 0.375571 + 0.375571i
\(342\) −0.909401 + 12.0417i −0.0491748 + 0.651142i
\(343\) −61.5018 −3.32078
\(344\) −9.04844 −0.487859
\(345\) 0.136338 3.61575i 0.00734019 0.194665i
\(346\) −8.70178 + 8.70178i −0.467810 + 0.467810i
\(347\) 4.41151 4.41151i 0.236822 0.236822i −0.578711 0.815533i \(-0.696444\pi\)
0.815533 + 0.578711i \(0.196444\pi\)
\(348\) −8.30290 8.95358i −0.445082 0.479962i
\(349\) 14.9035 0.797766 0.398883 0.917002i \(-0.369398\pi\)
0.398883 + 0.917002i \(0.369398\pi\)
\(350\) 3.60901 + 3.60901i 0.192910 + 0.192910i
\(351\) −27.7228 + 22.0689i −1.47974 + 1.17795i
\(352\) −1.78324 + 1.78324i −0.0950469 + 0.0950469i
\(353\) −18.6335 + 18.6335i −0.991762 + 0.991762i −0.999966 0.00820423i \(-0.997388\pi\)
0.00820423 + 0.999966i \(0.497388\pi\)
\(354\) 22.9031 + 0.863600i 1.21729 + 0.0458998i
\(355\) −0.964738 + 0.964738i −0.0512030 + 0.0512030i
\(356\) −7.24712 7.24712i −0.384097 0.384097i
\(357\) −18.3736 19.8135i −0.972436 1.04864i
\(358\) 5.62030i 0.297042i
\(359\) 9.49276i 0.501009i −0.968115 0.250504i \(-0.919404\pi\)
0.968115 0.250504i \(-0.0805964\pi\)
\(360\) 0.225919 2.99148i 0.0119070 0.157665i
\(361\) 2.79664i 0.147192i
\(362\) 9.79640 9.79640i 0.514888 0.514888i
\(363\) 8.03123 + 0.302831i 0.421530 + 0.0158945i
\(364\) 24.6111 + 24.6111i 1.28997 + 1.28997i
\(365\) 9.12036 9.12036i 0.477381 0.477381i
\(366\) 10.8662 + 0.409728i 0.567985 + 0.0214168i
\(367\) −5.07778 −0.265058 −0.132529 0.991179i \(-0.542310\pi\)
−0.132529 + 0.991179i \(0.542310\pi\)
\(368\) 1.47717 + 1.47717i 0.0770029 + 0.0770029i
\(369\) 14.5697 + 1.10031i 0.758467 + 0.0572800i
\(370\) −5.45849 2.68420i −0.283773 0.139545i
\(371\) 23.1909i 1.20401i
\(372\) 4.93938 4.58042i 0.256095 0.237484i
\(373\) 2.58217i 0.133700i −0.997763 0.0668499i \(-0.978705\pi\)
0.997763 0.0668499i \(-0.0212949\pi\)
\(374\) −7.70853 −0.398598
\(375\) −1.27002 + 1.17773i −0.0655837 + 0.0608176i
\(376\) 0.0489065 0.0489065i 0.00252216 0.00252216i
\(377\) 48.0759i 2.47604i
\(378\) −20.7491 + 16.5174i −1.06722 + 0.849564i
\(379\) 10.7934 0.554419 0.277209 0.960810i \(-0.410590\pi\)
0.277209 + 0.960810i \(0.410590\pi\)
\(380\) 4.02534i 0.206496i
\(381\) −23.6869 0.893155i −1.21352 0.0457577i
\(382\) −22.0334 −1.12733
\(383\) 5.75655 + 5.75655i 0.294146 + 0.294146i 0.838716 0.544570i \(-0.183307\pi\)
−0.544570 + 0.838716i \(0.683307\pi\)
\(384\) 1.17773 + 1.27002i 0.0601006 + 0.0648106i
\(385\) −9.10149 9.10149i −0.463855 0.463855i
\(386\) 14.4180i 0.733858i
\(387\) −20.5856 + 17.6947i −1.04643 + 0.899470i
\(388\) 4.90712 + 4.90712i 0.249121 + 0.249121i
\(389\) −23.0070 23.0070i −1.16650 1.16650i −0.983024 0.183478i \(-0.941264\pi\)
−0.183478 0.983024i \(-0.558736\pi\)
\(390\) −8.66073 + 8.03133i −0.438553 + 0.406682i
\(391\) 6.38548i 0.322927i
\(392\) 13.4703 + 13.4703i 0.680355 + 0.680355i
\(393\) −2.09748 + 1.94505i −0.105804 + 0.0981150i
\(394\) 13.1637 + 13.1637i 0.663178 + 0.663178i
\(395\) 4.75715 0.239358
\(396\) −0.569740 + 7.54415i −0.0286305 + 0.379108i
\(397\) 8.20919i 0.412008i 0.978551 + 0.206004i \(0.0660459\pi\)
−0.978551 + 0.206004i \(0.933954\pi\)
\(398\) −15.5672 −0.780313
\(399\) 26.0926 24.1964i 1.30626 1.21133i
\(400\) 1.00000i 0.0500000i
\(401\) −5.94884 + 5.94884i −0.297071 + 0.297071i −0.839866 0.542795i \(-0.817366\pi\)
0.542795 + 0.839866i \(0.317366\pi\)
\(402\) 16.6834 + 17.9909i 0.832094 + 0.897304i
\(403\) −26.5218 −1.32115
\(404\) 17.0003i 0.845796i
\(405\) −5.33601 7.24755i −0.265148 0.360134i
\(406\) 35.9823i 1.78577i
\(407\) 13.7656 + 6.76922i 0.682337 + 0.335538i
\(408\) −0.199488 + 5.29053i −0.00987615 + 0.261920i
\(409\) 17.8854 + 17.8854i 0.884374 + 0.884374i 0.993976 0.109601i \(-0.0349574\pi\)
−0.109601 + 0.993976i \(0.534957\pi\)
\(410\) 4.87039 0.240531
\(411\) 0.605985 16.0710i 0.0298910 0.792724i
\(412\) −4.76900 + 4.76900i −0.234952 + 0.234952i
\(413\) −47.7562 47.7562i −2.34993 2.34993i
\(414\) 6.24932 + 0.471953i 0.307137 + 0.0231952i
\(415\) −6.88621 + 6.88621i −0.338031 + 0.338031i
\(416\) 6.81935i 0.334346i
\(417\) −0.340134 + 9.02051i −0.0166564 + 0.441736i
\(418\) 10.1514i 0.496522i
\(419\) 16.3639i 0.799429i 0.916640 + 0.399714i \(0.130891\pi\)
−0.916640 + 0.399714i \(0.869109\pi\)
\(420\) −6.48209 + 6.01102i −0.316294 + 0.293308i
\(421\) −1.58888 1.58888i −0.0774373 0.0774373i 0.667327 0.744765i \(-0.267438\pi\)
−0.744765 + 0.667327i \(0.767438\pi\)
\(422\) −3.83868 + 3.83868i −0.186864 + 0.186864i
\(423\) 0.0156255 0.206903i 0.000759738 0.0100600i
\(424\) −3.21292 + 3.21292i −0.156033 + 0.156033i
\(425\) 2.16139 2.16139i 0.104843 0.104843i
\(426\) −1.60683 1.73275i −0.0778510 0.0839521i
\(427\) −22.6576 22.6576i −1.09648 1.09648i
\(428\) −17.6140 −0.851402
\(429\) 21.8413 20.2540i 1.05451 0.977874i
\(430\) −6.39822 + 6.39822i −0.308549 + 0.308549i
\(431\) −12.8119 + 12.8119i −0.617127 + 0.617127i −0.944793 0.327666i \(-0.893738\pi\)
0.327666 + 0.944793i \(0.393738\pi\)
\(432\) 5.16297 + 0.586260i 0.248404 + 0.0282064i
\(433\) 10.0976 0.485259 0.242629 0.970119i \(-0.421990\pi\)
0.242629 + 0.970119i \(0.421990\pi\)
\(434\) −19.8501 −0.952837
\(435\) −12.2022 0.460104i −0.585049 0.0220603i
\(436\) 1.38209 + 1.38209i 0.0661900 + 0.0661900i
\(437\) −8.40908 −0.402261
\(438\) 15.1905 + 16.3809i 0.725829 + 0.782711i
\(439\) 0.758341 + 0.758341i 0.0361937 + 0.0361937i 0.724972 0.688778i \(-0.241853\pi\)
−0.688778 + 0.724972i \(0.741853\pi\)
\(440\) 2.52188i 0.120226i
\(441\) 56.9875 + 4.30374i 2.71369 + 0.204940i
\(442\) 14.7392 14.7392i 0.701074 0.701074i
\(443\) 26.5884 1.26325 0.631626 0.775273i \(-0.282388\pi\)
0.631626 + 0.775273i \(0.282388\pi\)
\(444\) 5.00211 9.27248i 0.237389 0.440053i
\(445\) −10.2490 −0.485848
\(446\) −0.413739 + 0.413739i −0.0195911 + 0.0195911i
\(447\) 0.296143 7.85385i 0.0140071 0.371474i
\(448\) 5.10391i 0.241137i
\(449\) 12.5200 + 12.5200i 0.590854 + 0.590854i 0.937862 0.347008i \(-0.112802\pi\)
−0.347008 + 0.937862i \(0.612802\pi\)
\(450\) −1.95555 2.27505i −0.0921854 0.107247i
\(451\) −12.2825 −0.578362
\(452\) 4.81041 + 4.81041i 0.226263 + 0.226263i
\(453\) 0.266501 7.06772i 0.0125213 0.332071i
\(454\) −13.3349 −0.625838
\(455\) 34.8053 1.63170
\(456\) −6.96714 0.262708i −0.326266 0.0123024i
\(457\) 7.21832 7.21832i 0.337659 0.337659i −0.517827 0.855485i \(-0.673259\pi\)
0.855485 + 0.517827i \(0.173259\pi\)
\(458\) 7.67241 7.67241i 0.358508 0.358508i
\(459\) 9.89204 + 12.4263i 0.461721 + 0.580010i
\(460\) 2.08904 0.0974019
\(461\) −18.4973 18.4973i −0.861506 0.861506i 0.130007 0.991513i \(-0.458500\pi\)
−0.991513 + 0.130007i \(0.958500\pi\)
\(462\) 16.3470 15.1590i 0.760533 0.705263i
\(463\) −20.2551 + 20.2551i −0.941333 + 0.941333i −0.998372 0.0570389i \(-0.981834\pi\)
0.0570389 + 0.998372i \(0.481834\pi\)
\(464\) 4.98506 4.98506i 0.231425 0.231425i
\(465\) 0.253823 6.73151i 0.0117708 0.312166i
\(466\) −5.26670 + 5.26670i −0.243975 + 0.243975i
\(467\) −26.7256 26.7256i −1.23671 1.23671i −0.961337 0.275374i \(-0.911198\pi\)
−0.275374 0.961337i \(-0.588802\pi\)
\(468\) −13.3356 15.5143i −0.616436 0.717150i
\(469\) 72.3009i 3.33855i
\(470\) 0.0691642i 0.00319031i
\(471\) −0.282041 0.0106348i −0.0129958 0.000490027i
\(472\) 13.2325i 0.609075i
\(473\) 16.1355 16.1355i 0.741912 0.741912i
\(474\) −0.310469 + 8.23378i −0.0142603 + 0.378190i
\(475\) 2.84634 + 2.84634i 0.130599 + 0.130599i
\(476\) 11.0315 11.0315i 0.505629 0.505629i
\(477\) −1.02652 + 13.5926i −0.0470012 + 0.622361i
\(478\) 27.6222 1.26341
\(479\) −4.24011 4.24011i −0.193736 0.193736i 0.603572 0.797308i \(-0.293743\pi\)
−0.797308 + 0.603572i \(0.793743\pi\)
\(480\) 1.73082 + 0.0652635i 0.0790008 + 0.00297886i
\(481\) −39.2641 + 13.3776i −1.79029 + 0.609968i
\(482\) 23.6668i 1.07799i
\(483\) −12.5572 13.5413i −0.571374 0.616152i
\(484\) 4.64013i 0.210915i
\(485\) 6.93971 0.315116
\(486\) 12.8925 8.76267i 0.584814 0.397483i
\(487\) −15.4326 + 15.4326i −0.699319 + 0.699319i −0.964264 0.264944i \(-0.914646\pi\)
0.264944 + 0.964264i \(0.414646\pi\)
\(488\) 6.27806i 0.284194i
\(489\) −10.6957 11.5339i −0.483678 0.521583i
\(490\) 19.0499 0.860588
\(491\) 4.62335i 0.208649i −0.994543 0.104324i \(-0.966732\pi\)
0.994543 0.104324i \(-0.0332680\pi\)
\(492\) −0.317859 + 8.42977i −0.0143302 + 0.380044i
\(493\) 21.5493 0.970530
\(494\) 19.4102 + 19.4102i 0.873307 + 0.873307i
\(495\) 4.93165 + 5.73739i 0.221661 + 0.257876i
\(496\) 2.75008 + 2.75008i 0.123482 + 0.123482i
\(497\) 6.96350i 0.312356i
\(498\) −11.4694 12.3682i −0.513955 0.554233i
\(499\) 6.56428 + 6.56428i 0.293858 + 0.293858i 0.838602 0.544744i \(-0.183373\pi\)
−0.544744 + 0.838602i \(0.683373\pi\)
\(500\) −0.707107 0.707107i −0.0316228 0.0316228i
\(501\) −22.8290 24.6181i −1.01992 1.09985i
\(502\) 1.15611i 0.0515998i
\(503\) 2.11670 + 2.11670i 0.0943789 + 0.0943789i 0.752720 0.658341i \(-0.228741\pi\)
−0.658341 + 0.752720i \(0.728741\pi\)
\(504\) −9.98095 11.6116i −0.444587 0.517223i
\(505\) 12.0210 + 12.0210i 0.534928 + 0.534928i
\(506\) −5.26830 −0.234204
\(507\) −2.18656 + 57.9885i −0.0971083 + 2.57536i
\(508\) 13.6854i 0.607190i
\(509\) 2.11394 0.0936987 0.0468493 0.998902i \(-0.485082\pi\)
0.0468493 + 0.998902i \(0.485082\pi\)
\(510\) 3.59991 + 3.88203i 0.159407 + 0.171899i
\(511\) 65.8309i 2.91219i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −16.3643 + 13.0269i −0.722502 + 0.575152i
\(514\) 8.30643 0.366381
\(515\) 6.74438i 0.297193i
\(516\) −10.6566 11.4917i −0.469130 0.505895i
\(517\) 0.174424i 0.00767114i
\(518\) −29.3870 + 10.0124i −1.29119 + 0.439921i
\(519\) −21.2998 0.803144i −0.934956 0.0352541i
\(520\) −4.82201 4.82201i −0.211459 0.211459i
\(521\) 32.2201 1.41159 0.705794 0.708417i \(-0.250590\pi\)
0.705794 + 0.708417i \(0.250590\pi\)
\(522\) 1.59271 21.0897i 0.0697112 0.923073i
\(523\) 6.90482 6.90482i 0.301927 0.301927i −0.539841 0.841767i \(-0.681515\pi\)
0.841767 + 0.539841i \(0.181515\pi\)
\(524\) −1.16781 1.16781i −0.0510160 0.0510160i
\(525\) −0.333099 + 8.83396i −0.0145377 + 0.385546i
\(526\) −16.3493 + 16.3493i −0.712862 + 0.712862i
\(527\) 11.8880i 0.517848i
\(528\) −4.36492 0.164587i −0.189959 0.00716272i
\(529\) 18.6359i 0.810258i
\(530\) 4.54376i 0.197368i
\(531\) 25.8768 + 30.1045i 1.12296 + 1.30643i
\(532\) 14.5275 + 14.5275i 0.629847 + 0.629847i
\(533\) 23.4850 23.4850i 1.01725 1.01725i
\(534\) 0.668884 17.7391i 0.0289455 0.767647i
\(535\) −12.4549 + 12.4549i −0.538474 + 0.538474i
\(536\) −10.0167 + 10.0167i −0.432657 + 0.432657i
\(537\) 7.13791 6.61917i 0.308023 0.285638i
\(538\) 5.42757 + 5.42757i 0.233999 + 0.233999i
\(539\) −48.0416 −2.06930
\(540\) 4.06532 3.23623i 0.174944 0.139265i
\(541\) 12.0638 12.0638i 0.518663 0.518663i −0.398504 0.917167i \(-0.630470\pi\)
0.917167 + 0.398504i \(0.130470\pi\)
\(542\) 5.50679 5.50679i 0.236537 0.236537i
\(543\) 23.9791 + 0.904175i 1.02904 + 0.0388018i
\(544\) −3.05666 −0.131053
\(545\) 1.95457 0.0837244
\(546\) −2.27152 + 60.2418i −0.0972121 + 2.57811i
\(547\) −20.2713 20.2713i −0.866737 0.866737i 0.125373 0.992110i \(-0.459987\pi\)
−0.992110 + 0.125373i \(0.959987\pi\)
\(548\) 9.28520 0.396644
\(549\) 12.2770 + 14.2829i 0.523971 + 0.609578i
\(550\) 1.78324 + 1.78324i 0.0760375 + 0.0760375i
\(551\) 28.3784i 1.20896i
\(552\) −0.136338 + 3.61575i −0.00580293 + 0.153896i
\(553\) 17.1686 17.1686i 0.730084 0.730084i
\(554\) −0.394892 −0.0167774
\(555\) −3.01961 10.0937i −0.128175 0.428452i
\(556\) −5.21169 −0.221025
\(557\) 3.36050 3.36050i 0.142389 0.142389i −0.632319 0.774708i \(-0.717897\pi\)
0.774708 + 0.632319i \(0.217897\pi\)
\(558\) 11.6345 + 0.878644i 0.492527 + 0.0371960i
\(559\) 61.7045i 2.60982i
\(560\) −3.60901 3.60901i −0.152509 0.152509i
\(561\) −9.07854 9.79001i −0.383296 0.413334i
\(562\) −12.1113 −0.510885
\(563\) −4.35089 4.35089i −0.183368 0.183368i 0.609454 0.792822i \(-0.291389\pi\)
−0.792822 + 0.609454i \(0.791389\pi\)
\(564\) 0.119711 + 0.00451390i 0.00504073 + 0.000190069i
\(565\) 6.80295 0.286202
\(566\) 10.0604 0.422870
\(567\) −45.4142 6.89878i −1.90722 0.289722i
\(568\) 0.964738 0.964738i 0.0404795 0.0404795i
\(569\) −25.7059 + 25.7059i −1.07765 + 1.07765i −0.0809257 + 0.996720i \(0.525788\pi\)
−0.996720 + 0.0809257i \(0.974212\pi\)
\(570\) −5.11228 + 4.74075i −0.214130 + 0.198568i
\(571\) −24.4214 −1.02200 −0.511001 0.859580i \(-0.670725\pi\)
−0.511001 + 0.859580i \(0.670725\pi\)
\(572\) 12.1605 + 12.1605i 0.508456 + 0.508456i
\(573\) −25.9493 27.9829i −1.08405 1.16900i
\(574\) 17.5773 17.5773i 0.733662 0.733662i
\(575\) 1.47717 1.47717i 0.0616023 0.0616023i
\(576\) −0.225919 + 2.99148i −0.00941329 + 0.124645i
\(577\) 4.61472 4.61472i 0.192113 0.192113i −0.604495 0.796609i \(-0.706625\pi\)
0.796609 + 0.604495i \(0.206625\pi\)
\(578\) 5.41419 + 5.41419i 0.225201 + 0.225201i
\(579\) −18.3112 + 16.9805i −0.760989 + 0.705685i
\(580\) 7.04993i 0.292733i
\(581\) 49.7048i 2.06210i
\(582\) −0.452910 + 12.0114i −0.0187737 + 0.497888i
\(583\) 11.4588i 0.474575i
\(584\) −9.12036 + 9.12036i −0.377403 + 0.377403i
\(585\) −20.3999 1.54062i −0.843434 0.0636968i
\(586\) −15.8337 15.8337i −0.654085 0.654085i
\(587\) 3.92406 3.92406i 0.161963 0.161963i −0.621473 0.783436i \(-0.713465\pi\)
0.783436 + 0.621473i \(0.213465\pi\)
\(588\) −1.24327 + 32.9720i −0.0512714 + 1.35974i
\(589\) −15.6554 −0.645068
\(590\) 9.35679 + 9.35679i 0.385213 + 0.385213i
\(591\) −1.21497 + 32.2215i −0.0499770 + 1.32541i
\(592\) 5.45849 + 2.68420i 0.224342 + 0.110320i
\(593\) 32.5461i 1.33651i 0.743934 + 0.668253i \(0.232958\pi\)
−0.743934 + 0.668253i \(0.767042\pi\)
\(594\) −10.2522 + 8.16137i −0.420655 + 0.334865i
\(595\) 15.6009i 0.639576i
\(596\) 4.53764 0.185869
\(597\) −18.3339 19.7707i −0.750357 0.809161i
\(598\) 10.0733 10.0733i 0.411930 0.411930i
\(599\) 15.7962i 0.645415i 0.946499 + 0.322707i \(0.104593\pi\)
−0.946499 + 0.322707i \(0.895407\pi\)
\(600\) 1.27002 1.17773i 0.0518485 0.0480805i
\(601\) 21.8320 0.890546 0.445273 0.895395i \(-0.353107\pi\)
0.445273 + 0.895395i \(0.353107\pi\)
\(602\) 46.1825i 1.88226i
\(603\) −3.20032 + 42.3767i −0.130327 + 1.72571i
\(604\) 4.08345 0.166153
\(605\) 3.28107 + 3.28107i 0.133394 + 0.133394i
\(606\) −21.5908 + 20.0217i −0.877064 + 0.813325i
\(607\) 25.8401 + 25.8401i 1.04882 + 1.04882i 0.998746 + 0.0500729i \(0.0159454\pi\)
0.0500729 + 0.998746i \(0.484055\pi\)
\(608\) 4.02534i 0.163249i
\(609\) −45.6983 + 42.3773i −1.85179 + 1.71721i
\(610\) 4.43926 + 4.43926i 0.179740 + 0.179740i
\(611\) −0.333510 0.333510i −0.0134924 0.0134924i
\(612\) −6.95404 + 5.97745i −0.281100 + 0.241624i
\(613\) 21.7834i 0.879822i 0.898041 + 0.439911i \(0.144990\pi\)
−0.898041 + 0.439911i \(0.855010\pi\)
\(614\) −10.3227 10.3227i −0.416590 0.416590i
\(615\) 5.73599 + 6.18551i 0.231297 + 0.249424i
\(616\) 9.10149 + 9.10149i 0.366709 + 0.366709i
\(617\) −10.9168 −0.439496 −0.219748 0.975557i \(-0.570523\pi\)
−0.219748 + 0.975557i \(0.570523\pi\)
\(618\) −11.6733 0.440162i −0.469570 0.0177059i
\(619\) 38.1104i 1.53179i −0.642968 0.765893i \(-0.722297\pi\)
0.642968 0.765893i \(-0.277703\pi\)
\(620\) 3.88920 0.156194
\(621\) 6.76060 + 8.49261i 0.271293 + 0.340797i
\(622\) 20.8237i 0.834955i
\(623\) −36.9887 + 36.9887i −1.48192 + 1.48192i
\(624\) 8.66073 8.03133i 0.346707 0.321510i
\(625\) −1.00000 −0.0400000
\(626\) 0.175087i 0.00699787i
\(627\) 12.8925 11.9556i 0.514878 0.477461i
\(628\) 0.162952i 0.00650250i
\(629\) 5.99631 + 17.5995i 0.239088 + 0.701737i
\(630\) −15.2683 1.15307i −0.608302 0.0459394i
\(631\) −17.9394 17.9394i −0.714158 0.714158i 0.253244 0.967402i \(-0.418502\pi\)
−0.967402 + 0.253244i \(0.918502\pi\)
\(632\) −4.75715 −0.189229
\(633\) −9.39613 0.354297i −0.373463 0.0140820i
\(634\) −10.4870 + 10.4870i −0.416493 + 0.416493i
\(635\) −9.67701 9.67701i −0.384020 0.384020i
\(636\) −7.86443 0.296542i −0.311845 0.0117586i
\(637\) 91.8588 91.8588i 3.63958 3.63958i
\(638\) 17.7791i 0.703880i
\(639\) 0.308232 4.08142i 0.0121935 0.161458i
\(640\) 1.00000i 0.0395285i
\(641\) 17.7585i 0.701418i 0.936484 + 0.350709i \(0.114059\pi\)
−0.936484 + 0.350709i \(0.885941\pi\)
\(642\) −20.7444 22.3701i −0.818717 0.882879i
\(643\) 10.8079 + 10.8079i 0.426221 + 0.426221i 0.887339 0.461118i \(-0.152551\pi\)
−0.461118 + 0.887339i \(0.652551\pi\)
\(644\) 7.53936 7.53936i 0.297092 0.297092i
\(645\) −15.6612 0.590533i −0.616660 0.0232522i
\(646\) 8.70031 8.70031i 0.342309 0.342309i
\(647\) −22.9188 + 22.9188i −0.901032 + 0.901032i −0.995525 0.0944933i \(-0.969877\pi\)
0.0944933 + 0.995525i \(0.469877\pi\)
\(648\) 5.33601 + 7.24755i 0.209618 + 0.284711i
\(649\) −23.5967 23.5967i −0.926251 0.926251i
\(650\) −6.81935 −0.267477
\(651\) −23.3780 25.2101i −0.916258 0.988064i
\(652\) 6.42172 6.42172i 0.251494 0.251494i
\(653\) −8.84098 + 8.84098i −0.345974 + 0.345974i −0.858608 0.512633i \(-0.828670\pi\)
0.512633 + 0.858608i \(0.328670\pi\)
\(654\) −0.127562 + 3.38300i −0.00498807 + 0.132286i
\(655\) −1.65153 −0.0645307
\(656\) −4.87039 −0.190157
\(657\) −2.91393 + 38.5845i −0.113683 + 1.50533i
\(658\) −0.249614 0.249614i −0.00973098 0.00973098i
\(659\) −19.8111 −0.771732 −0.385866 0.922555i \(-0.626097\pi\)
−0.385866 + 0.922555i \(0.626097\pi\)
\(660\) −3.20284 + 2.97008i −0.124671 + 0.115610i
\(661\) −12.4769 12.4769i −0.485294 0.485294i 0.421523 0.906818i \(-0.361496\pi\)
−0.906818 + 0.421523i \(0.861496\pi\)
\(662\) 0.818200i 0.0318003i
\(663\) 36.0780 + 1.36038i 1.40115 + 0.0528328i
\(664\) 6.88621 6.88621i 0.267237 0.267237i
\(665\) 20.5450 0.796700
\(666\) 17.6674 4.56766i 0.684597 0.176993i
\(667\) 14.7276 0.570254
\(668\) 13.7065 13.7065i 0.530321 0.530321i
\(669\) −1.01273 0.0381867i −0.0391544 0.00147638i
\(670\) 14.1658i 0.547272i
\(671\) −11.1953 11.1953i −0.432188 0.432188i
\(672\) 6.48209 6.01102i 0.250052 0.231880i
\(673\) 17.8938 0.689754 0.344877 0.938648i \(-0.387921\pi\)
0.344877 + 0.938648i \(0.387921\pi\)
\(674\) −23.4976 23.4976i −0.905094 0.905094i
\(675\) 0.586260 5.16297i 0.0225652 0.198723i
\(676\) −33.5035 −1.28860
\(677\) −1.54229 −0.0592751 −0.0296375 0.999561i \(-0.509435\pi\)
−0.0296375 + 0.999561i \(0.509435\pi\)
\(678\) −0.443985 + 11.7747i −0.0170511 + 0.452204i
\(679\) 25.0455 25.0455i 0.961158 0.961158i
\(680\) −2.16139 + 2.16139i −0.0828853 + 0.0828853i
\(681\) −15.7049 16.9356i −0.601812 0.648976i
\(682\) −9.80809 −0.375571
\(683\) −8.13767 8.13767i −0.311379 0.311379i 0.534064 0.845444i \(-0.320664\pi\)
−0.845444 + 0.534064i \(0.820664\pi\)
\(684\) −7.87174 9.15783i −0.300984 0.350158i
\(685\) 6.56563 6.56563i 0.250860 0.250860i
\(686\) 43.4883 43.4883i 1.66039 1.66039i
\(687\) 18.7801 + 0.708137i 0.716507 + 0.0270171i
\(688\) 6.39822 6.39822i 0.243930 0.243930i
\(689\) 21.9100 + 21.9100i 0.834705 + 0.834705i
\(690\) 2.46032 + 2.65313i 0.0936626 + 0.101003i
\(691\) 32.6581i 1.24237i 0.783663 + 0.621187i \(0.213349\pi\)
−0.783663 + 0.621187i \(0.786651\pi\)
\(692\) 12.3062i 0.467810i
\(693\) 38.5047 + 2.90790i 1.46267 + 0.110462i
\(694\) 6.23882i 0.236822i
\(695\) −3.68522 + 3.68522i −0.139789 + 0.139789i
\(696\) 12.2022 + 0.460104i 0.462522 + 0.0174402i
\(697\) −10.5268 10.5268i −0.398731 0.398731i
\(698\) −10.5384 + 10.5384i −0.398883 + 0.398883i
\(699\) −12.8916 0.486098i −0.487603 0.0183859i
\(700\) −5.10391 −0.192910
\(701\) −14.4490 14.4490i −0.545732 0.545732i 0.379472 0.925203i \(-0.376106\pi\)
−0.925203 + 0.379472i \(0.876106\pi\)
\(702\) 3.99791 35.2081i 0.150891 1.32884i
\(703\) −23.1769 + 7.89658i −0.874133 + 0.297825i
\(704\) 2.52188i 0.0950469i
\(705\) 0.0878401 0.0814565i 0.00330825 0.00306783i
\(706\) 26.3518i 0.991762i
\(707\) 86.7680 3.26324
\(708\) −16.8056 + 15.5843i −0.631592 + 0.585693i
\(709\) −15.5170 + 15.5170i −0.582752 + 0.582752i −0.935659 0.352906i \(-0.885193\pi\)
0.352906 + 0.935659i \(0.385193\pi\)
\(710\) 1.36435i 0.0512030i
\(711\) −10.8227 + 9.30284i −0.405885 + 0.348884i
\(712\) 10.2490 0.384097
\(713\) 8.12469i 0.304272i
\(714\) 27.0024 + 1.01817i 1.01054 + 0.0381041i
\(715\) 17.1976 0.643152
\(716\) 3.97415 + 3.97415i 0.148521 + 0.148521i
\(717\) 32.5314 + 35.0809i 1.21491 + 1.31012i
\(718\) 6.71239 + 6.71239i 0.250504 + 0.250504i
\(719\) 29.0910i 1.08491i −0.840085 0.542455i \(-0.817495\pi\)
0.840085 0.542455i \(-0.182505\pi\)
\(720\) 1.95555 + 2.27505i 0.0728790 + 0.0847859i
\(721\) 24.3406 + 24.3406i 0.906490 + 0.906490i
\(722\) −1.97752 1.97752i −0.0735958 0.0735958i
\(723\) 30.0574 27.8730i 1.11785 1.03661i
\(724\) 13.8542i 0.514888i
\(725\) −4.98506 4.98506i −0.185140 0.185140i
\(726\) −5.89307 + 5.46481i −0.218712 + 0.202818i
\(727\) −16.8955 16.8955i −0.626620 0.626620i 0.320596 0.947216i \(-0.396117\pi\)
−0.947216 + 0.320596i \(0.896117\pi\)
\(728\) −34.8053 −1.28997
\(729\) 26.3126 + 6.05369i 0.974541 + 0.224211i
\(730\) 12.8981i 0.477381i
\(731\) 27.6580 1.02297
\(732\) −7.97328 + 7.39384i −0.294701 + 0.273284i
\(733\) 1.93766i 0.0715691i −0.999360 0.0357845i \(-0.988607\pi\)
0.999360 0.0357845i \(-0.0113930\pi\)
\(734\) 3.59053 3.59053i 0.132529 0.132529i
\(735\) 22.4356 + 24.1939i 0.827550 + 0.892404i
\(736\) −2.08904 −0.0770029
\(737\) 35.7244i 1.31592i
\(738\) −11.0804 + 9.52428i −0.407874 + 0.350594i
\(739\) 20.9810i 0.771800i 0.922541 + 0.385900i \(0.126109\pi\)
−0.922541 + 0.385900i \(0.873891\pi\)
\(740\) 5.75775 1.96172i 0.211659 0.0721142i
\(741\) −1.79150 + 47.5113i −0.0658122 + 1.74537i
\(742\) 16.3985 + 16.3985i 0.602007 + 0.602007i
\(743\) −20.4459 −0.750088 −0.375044 0.927007i \(-0.622372\pi\)
−0.375044 + 0.927007i \(0.622372\pi\)
\(744\) −0.253823 + 6.73151i −0.00930560 + 0.246789i
\(745\) 3.20860 3.20860i 0.117554 0.117554i
\(746\) 1.82587 + 1.82587i 0.0668499 + 0.0668499i
\(747\) 2.20013 29.1328i 0.0804985 1.06591i
\(748\) 5.45075 5.45075i 0.199299 0.199299i
\(749\) 89.9001i 3.28488i
\(750\) 0.0652635 1.73082i 0.00238309 0.0632006i
\(751\) 6.66294i 0.243134i −0.992583 0.121567i \(-0.961208\pi\)
0.992583 0.121567i \(-0.0387920\pi\)
\(752\) 0.0691642i 0.00252216i
\(753\) −1.46829 + 1.36159i −0.0535075 + 0.0496189i
\(754\) −33.9948 33.9948i −1.23802 1.23802i
\(755\) 2.88744 2.88744i 0.105085 0.105085i
\(756\) 2.99222 26.3514i 0.108826 0.958390i
\(757\) −25.6892 + 25.6892i −0.933692 + 0.933692i −0.997934 0.0642427i \(-0.979537\pi\)
0.0642427 + 0.997934i \(0.479537\pi\)
\(758\) −7.63207 + 7.63207i −0.277209 + 0.277209i
\(759\) −6.20462 6.69086i −0.225213 0.242863i
\(760\) −2.84634 2.84634i −0.103248 0.103248i
\(761\) −32.0342 −1.16124 −0.580619 0.814175i \(-0.697190\pi\)
−0.580619 + 0.814175i \(0.697190\pi\)
\(762\) 17.3807 16.1176i 0.629637 0.583880i
\(763\) 7.05405 7.05405i 0.255374 0.255374i
\(764\) 15.5800 15.5800i 0.563663 0.563663i
\(765\) −0.690558 + 9.14394i −0.0249672 + 0.330600i
\(766\) −8.14100 −0.294146
\(767\) 90.2370 3.25827
\(768\) −1.73082 0.0652635i −0.0624556 0.00235500i
\(769\) −4.95008 4.95008i −0.178504 0.178504i 0.612199 0.790704i \(-0.290285\pi\)
−0.790704 + 0.612199i \(0.790285\pi\)
\(770\) 12.8714 0.463855
\(771\) 9.78271 + 10.5494i 0.352316 + 0.379926i
\(772\) −10.1951 10.1951i −0.366929 0.366929i
\(773\) 24.3133i 0.874489i −0.899343 0.437245i \(-0.855954\pi\)
0.899343 0.437245i \(-0.144046\pi\)
\(774\) 2.04421 27.0682i 0.0734778 0.972948i
\(775\) 2.75008 2.75008i 0.0987858 0.0987858i
\(776\) −6.93971 −0.249121
\(777\) −47.3259 25.5303i −1.69781 0.915895i
\(778\) 32.5368 1.16650