Properties

Label 475.2.e.c.201.1
Level $475$
Weight $2$
Character 475.201
Analytic conductor $3.793$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 475 = 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 475.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.79289409601\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 201.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 475.201
Dual form 475.2.e.c.26.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} +4.00000 q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.73205i) q^{2} +(-1.00000 - 1.73205i) q^{4} +4.00000 q^{7} +(1.50000 + 2.59808i) q^{9} -1.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(4.00000 - 6.92820i) q^{14} +(2.00000 - 3.46410i) q^{16} +(-1.00000 + 1.73205i) q^{17} +6.00000 q^{18} +(-3.50000 - 2.59808i) q^{19} +(-1.00000 + 1.73205i) q^{22} +(3.00000 + 5.19615i) q^{23} -4.00000 q^{26} +(-4.00000 - 6.92820i) q^{28} +(-4.50000 - 7.79423i) q^{29} -7.00000 q^{31} +(-4.00000 - 6.92820i) q^{32} +(2.00000 + 3.46410i) q^{34} +(3.00000 - 5.19615i) q^{36} -2.00000 q^{37} +(-8.00000 + 3.46410i) q^{38} +(-1.00000 + 1.73205i) q^{41} +(1.00000 - 1.73205i) q^{43} +(1.00000 + 1.73205i) q^{44} +12.0000 q^{46} +(3.00000 + 5.19615i) q^{47} +9.00000 q^{49} +(-2.00000 + 3.46410i) q^{52} +(2.00000 + 3.46410i) q^{53} -18.0000 q^{58} +(-4.50000 + 7.79423i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-7.00000 + 12.1244i) q^{62} +(6.00000 + 10.3923i) q^{63} -8.00000 q^{64} +(-5.00000 - 8.66025i) q^{67} +4.00000 q^{68} +(-0.500000 + 0.866025i) q^{71} +(5.00000 - 8.66025i) q^{73} +(-2.00000 + 3.46410i) q^{74} +(-1.00000 + 8.66025i) q^{76} -4.00000 q^{77} +(-0.500000 + 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(2.00000 + 3.46410i) q^{82} +6.00000 q^{83} +(-2.00000 - 3.46410i) q^{86} +(5.50000 + 9.52628i) q^{89} +(-4.00000 - 6.92820i) q^{91} +(6.00000 - 10.3923i) q^{92} +12.0000 q^{94} +(-3.00000 + 5.19615i) q^{97} +(9.00000 - 15.5885i) q^{98} +(-1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 2 q^{4} + 8 q^{7} + 3 q^{9} + O(q^{10}) \) \( 2 q + 2 q^{2} - 2 q^{4} + 8 q^{7} + 3 q^{9} - 2 q^{11} - 2 q^{13} + 8 q^{14} + 4 q^{16} - 2 q^{17} + 12 q^{18} - 7 q^{19} - 2 q^{22} + 6 q^{23} - 8 q^{26} - 8 q^{28} - 9 q^{29} - 14 q^{31} - 8 q^{32} + 4 q^{34} + 6 q^{36} - 4 q^{37} - 16 q^{38} - 2 q^{41} + 2 q^{43} + 2 q^{44} + 24 q^{46} + 6 q^{47} + 18 q^{49} - 4 q^{52} + 4 q^{53} - 36 q^{58} - 9 q^{59} + 7 q^{61} - 14 q^{62} + 12 q^{63} - 16 q^{64} - 10 q^{67} + 8 q^{68} - q^{71} + 10 q^{73} - 4 q^{74} - 2 q^{76} - 8 q^{77} - q^{79} - 9 q^{81} + 4 q^{82} + 12 q^{83} - 4 q^{86} + 11 q^{89} - 8 q^{91} + 12 q^{92} + 24 q^{94} - 6 q^{97} + 18 q^{98} - 3 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.73205i 0.707107 1.22474i −0.258819 0.965926i \(-0.583333\pi\)
0.965926 0.258819i \(-0.0833333\pi\)
\(3\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(4\) −1.00000 1.73205i −0.500000 0.866025i
\(5\) 0 0
\(6\) 0 0
\(7\) 4.00000 1.51186 0.755929 0.654654i \(-0.227186\pi\)
0.755929 + 0.654654i \(0.227186\pi\)
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 0 0
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) −1.00000 1.73205i −0.277350 0.480384i 0.693375 0.720577i \(-0.256123\pi\)
−0.970725 + 0.240192i \(0.922790\pi\)
\(14\) 4.00000 6.92820i 1.06904 1.85164i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 6.00000 1.41421
\(19\) −3.50000 2.59808i −0.802955 0.596040i
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) −4.00000 6.92820i −0.755929 1.30931i
\(29\) −4.50000 7.79423i −0.835629 1.44735i −0.893517 0.449029i \(-0.851770\pi\)
0.0578882 0.998323i \(-0.481563\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −4.00000 6.92820i −0.707107 1.22474i
\(33\) 0 0
\(34\) 2.00000 + 3.46410i 0.342997 + 0.594089i
\(35\) 0 0
\(36\) 3.00000 5.19615i 0.500000 0.866025i
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −8.00000 + 3.46410i −1.29777 + 0.561951i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.00000 + 1.73205i −0.156174 + 0.270501i −0.933486 0.358614i \(-0.883249\pi\)
0.777312 + 0.629115i \(0.216583\pi\)
\(42\) 0 0
\(43\) 1.00000 1.73205i 0.152499 0.264135i −0.779647 0.626219i \(-0.784601\pi\)
0.932145 + 0.362084i \(0.117935\pi\)
\(44\) 1.00000 + 1.73205i 0.150756 + 0.261116i
\(45\) 0 0
\(46\) 12.0000 1.76930
\(47\) 3.00000 + 5.19615i 0.437595 + 0.757937i 0.997503 0.0706177i \(-0.0224970\pi\)
−0.559908 + 0.828554i \(0.689164\pi\)
\(48\) 0 0
\(49\) 9.00000 1.28571
\(50\) 0 0
\(51\) 0 0
\(52\) −2.00000 + 3.46410i −0.277350 + 0.480384i
\(53\) 2.00000 + 3.46410i 0.274721 + 0.475831i 0.970065 0.242846i \(-0.0780811\pi\)
−0.695344 + 0.718677i \(0.744748\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −18.0000 −2.36352
\(59\) −4.50000 + 7.79423i −0.585850 + 1.01472i 0.408919 + 0.912571i \(0.365906\pi\)
−0.994769 + 0.102151i \(0.967427\pi\)
\(60\) 0 0
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) −7.00000 + 12.1244i −0.889001 + 1.53979i
\(63\) 6.00000 + 10.3923i 0.755929 + 1.30931i
\(64\) −8.00000 −1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) −5.00000 8.66025i −0.610847 1.05802i −0.991098 0.133135i \(-0.957496\pi\)
0.380251 0.924883i \(-0.375838\pi\)
\(68\) 4.00000 0.485071
\(69\) 0 0
\(70\) 0 0
\(71\) −0.500000 + 0.866025i −0.0593391 + 0.102778i −0.894169 0.447730i \(-0.852233\pi\)
0.834830 + 0.550508i \(0.185566\pi\)
\(72\) 0 0
\(73\) 5.00000 8.66025i 0.585206 1.01361i −0.409644 0.912245i \(-0.634347\pi\)
0.994850 0.101361i \(-0.0323196\pi\)
\(74\) −2.00000 + 3.46410i −0.232495 + 0.402694i
\(75\) 0 0
\(76\) −1.00000 + 8.66025i −0.114708 + 0.993399i
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i \(-0.851249\pi\)
0.836527 + 0.547926i \(0.184582\pi\)
\(80\) 0 0
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 2.00000 + 3.46410i 0.220863 + 0.382546i
\(83\) 6.00000 0.658586 0.329293 0.944228i \(-0.393190\pi\)
0.329293 + 0.944228i \(0.393190\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 0 0
\(88\) 0 0
\(89\) 5.50000 + 9.52628i 0.582999 + 1.00978i 0.995122 + 0.0986553i \(0.0314541\pi\)
−0.412123 + 0.911128i \(0.635213\pi\)
\(90\) 0 0
\(91\) −4.00000 6.92820i −0.419314 0.726273i
\(92\) 6.00000 10.3923i 0.625543 1.08347i
\(93\) 0 0
\(94\) 12.0000 1.23771
\(95\) 0 0
\(96\) 0 0
\(97\) −3.00000 + 5.19615i −0.304604 + 0.527589i −0.977173 0.212445i \(-0.931857\pi\)
0.672569 + 0.740034i \(0.265191\pi\)
\(98\) 9.00000 15.5885i 0.909137 1.57467i
\(99\) −1.50000 2.59808i −0.150756 0.261116i
\(100\) 0 0
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 0 0
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) 10.0000 0.966736 0.483368 0.875417i \(-0.339413\pi\)
0.483368 + 0.875417i \(0.339413\pi\)
\(108\) 0 0
\(109\) −7.50000 + 12.9904i −0.718370 + 1.24425i 0.243276 + 0.969957i \(0.421778\pi\)
−0.961645 + 0.274296i \(0.911555\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 8.00000 13.8564i 0.755929 1.30931i
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −9.00000 + 15.5885i −0.835629 + 1.44735i
\(117\) 3.00000 5.19615i 0.277350 0.480384i
\(118\) 9.00000 + 15.5885i 0.828517 + 1.43503i
\(119\) −4.00000 + 6.92820i −0.366679 + 0.635107i
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 14.0000 1.26750
\(123\) 0 0
\(124\) 7.00000 + 12.1244i 0.628619 + 1.08880i
\(125\) 0 0
\(126\) 24.0000 2.13809
\(127\) −3.00000 5.19615i −0.266207 0.461084i 0.701672 0.712500i \(-0.252437\pi\)
−0.967879 + 0.251416i \(0.919104\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 0 0
\(133\) −14.0000 10.3923i −1.21395 0.901127i
\(134\) −20.0000 −1.72774
\(135\) 0 0
\(136\) 0 0
\(137\) 6.00000 + 10.3923i 0.512615 + 0.887875i 0.999893 + 0.0146279i \(0.00465636\pi\)
−0.487278 + 0.873247i \(0.662010\pi\)
\(138\) 0 0
\(139\) −10.0000 17.3205i −0.848189 1.46911i −0.882823 0.469706i \(-0.844360\pi\)
0.0346338 0.999400i \(-0.488974\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.00000 + 1.73205i 0.0839181 + 0.145350i
\(143\) 1.00000 + 1.73205i 0.0836242 + 0.144841i
\(144\) 12.0000 1.00000
\(145\) 0 0
\(146\) −10.0000 17.3205i −0.827606 1.43346i
\(147\) 0 0
\(148\) 2.00000 + 3.46410i 0.164399 + 0.284747i
\(149\) 0.500000 0.866025i 0.0409616 0.0709476i −0.844818 0.535054i \(-0.820291\pi\)
0.885779 + 0.464107i \(0.153625\pi\)
\(150\) 0 0
\(151\) 9.00000 0.732410 0.366205 0.930534i \(-0.380657\pi\)
0.366205 + 0.930534i \(0.380657\pi\)
\(152\) 0 0
\(153\) −6.00000 −0.485071
\(154\) −4.00000 + 6.92820i −0.322329 + 0.558291i
\(155\) 0 0
\(156\) 0 0
\(157\) 2.00000 3.46410i 0.159617 0.276465i −0.775113 0.631822i \(-0.782307\pi\)
0.934731 + 0.355357i \(0.115641\pi\)
\(158\) 1.00000 + 1.73205i 0.0795557 + 0.137795i
\(159\) 0 0
\(160\) 0 0
\(161\) 12.0000 + 20.7846i 0.945732 + 1.63806i
\(162\) 9.00000 + 15.5885i 0.707107 + 1.22474i
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 4.00000 0.312348
\(165\) 0 0
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 0 0
\(169\) 4.50000 7.79423i 0.346154 0.599556i
\(170\) 0 0
\(171\) 1.50000 12.9904i 0.114708 0.993399i
\(172\) −4.00000 −0.304997
\(173\) −12.0000 + 20.7846i −0.912343 + 1.58022i −0.101598 + 0.994826i \(0.532395\pi\)
−0.810745 + 0.585399i \(0.800938\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.00000 + 3.46410i −0.150756 + 0.261116i
\(177\) 0 0
\(178\) 22.0000 1.64897
\(179\) 15.0000 1.12115 0.560576 0.828103i \(-0.310580\pi\)
0.560576 + 0.828103i \(0.310580\pi\)
\(180\) 0 0
\(181\) 3.00000 + 5.19615i 0.222988 + 0.386227i 0.955714 0.294297i \(-0.0950855\pi\)
−0.732726 + 0.680524i \(0.761752\pi\)
\(182\) −16.0000 −1.18600
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1.00000 1.73205i 0.0731272 0.126660i
\(188\) 6.00000 10.3923i 0.437595 0.757937i
\(189\) 0 0
\(190\) 0 0
\(191\) −3.00000 −0.217072 −0.108536 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) 0 0
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) 6.00000 + 10.3923i 0.430775 + 0.746124i
\(195\) 0 0
\(196\) −9.00000 15.5885i −0.642857 1.11346i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −6.00000 −0.426401
\(199\) −6.50000 11.2583i −0.460773 0.798082i 0.538227 0.842800i \(-0.319094\pi\)
−0.999000 + 0.0447181i \(0.985761\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −30.0000 −2.11079
\(203\) −18.0000 31.1769i −1.26335 2.18819i
\(204\) 0 0
\(205\) 0 0
\(206\) −16.0000 + 27.7128i −1.11477 + 1.93084i
\(207\) −9.00000 + 15.5885i −0.625543 + 1.08347i
\(208\) −8.00000 −0.554700
\(209\) 3.50000 + 2.59808i 0.242100 + 0.179713i
\(210\) 0 0
\(211\) −2.50000 + 4.33013i −0.172107 + 0.298098i −0.939156 0.343490i \(-0.888391\pi\)
0.767049 + 0.641588i \(0.221724\pi\)
\(212\) 4.00000 6.92820i 0.274721 0.475831i
\(213\) 0 0
\(214\) 10.0000 17.3205i 0.683586 1.18401i
\(215\) 0 0
\(216\) 0 0
\(217\) −28.0000 −1.90076
\(218\) 15.0000 + 25.9808i 1.01593 + 1.75964i
\(219\) 0 0
\(220\) 0 0
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) −1.00000 + 1.73205i −0.0669650 + 0.115987i −0.897564 0.440884i \(-0.854665\pi\)
0.830599 + 0.556871i \(0.187998\pi\)
\(224\) −16.0000 27.7128i −1.06904 1.85164i
\(225\) 0 0
\(226\) 12.0000 20.7846i 0.798228 1.38257i
\(227\) −14.0000 −0.929213 −0.464606 0.885517i \(-0.653804\pi\)
−0.464606 + 0.885517i \(0.653804\pi\)
\(228\) 0 0
\(229\) 17.0000 1.12339 0.561696 0.827344i \(-0.310149\pi\)
0.561696 + 0.827344i \(0.310149\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −4.00000 + 6.92820i −0.262049 + 0.453882i −0.966786 0.255586i \(-0.917731\pi\)
0.704737 + 0.709468i \(0.251065\pi\)
\(234\) −6.00000 10.3923i −0.392232 0.679366i
\(235\) 0 0
\(236\) 18.0000 1.17170
\(237\) 0 0
\(238\) 8.00000 + 13.8564i 0.518563 + 0.898177i
\(239\) −19.0000 −1.22901 −0.614504 0.788914i \(-0.710644\pi\)
−0.614504 + 0.788914i \(0.710644\pi\)
\(240\) 0 0
\(241\) −0.500000 0.866025i −0.0322078 0.0557856i 0.849472 0.527633i \(-0.176921\pi\)
−0.881680 + 0.471848i \(0.843587\pi\)
\(242\) −10.0000 + 17.3205i −0.642824 + 1.11340i
\(243\) 0 0
\(244\) 7.00000 12.1244i 0.448129 0.776182i
\(245\) 0 0
\(246\) 0 0
\(247\) −1.00000 + 8.66025i −0.0636285 + 0.551039i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −6.50000 11.2583i −0.410276 0.710620i 0.584643 0.811290i \(-0.301234\pi\)
−0.994920 + 0.100671i \(0.967901\pi\)
\(252\) 12.0000 20.7846i 0.755929 1.30931i
\(253\) −3.00000 5.19615i −0.188608 0.326679i
\(254\) −12.0000 −0.752947
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −3.00000 5.19615i −0.187135 0.324127i 0.757159 0.653231i \(-0.226587\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(258\) 0 0
\(259\) −8.00000 −0.497096
\(260\) 0 0
\(261\) 13.5000 23.3827i 0.835629 1.44735i
\(262\) 12.0000 + 20.7846i 0.741362 + 1.28408i
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −32.0000 + 13.8564i −1.96205 + 0.849591i
\(267\) 0 0
\(268\) −10.0000 + 17.3205i −0.610847 + 1.05802i
\(269\) −1.50000 + 2.59808i −0.0914566 + 0.158408i −0.908124 0.418701i \(-0.862486\pi\)
0.816668 + 0.577108i \(0.195819\pi\)
\(270\) 0 0
\(271\) −1.50000 + 2.59808i −0.0911185 + 0.157822i −0.907982 0.419009i \(-0.862378\pi\)
0.816864 + 0.576831i \(0.195711\pi\)
\(272\) 4.00000 + 6.92820i 0.242536 + 0.420084i
\(273\) 0 0
\(274\) 24.0000 1.44989
\(275\) 0 0
\(276\) 0 0
\(277\) 28.0000 1.68236 0.841178 0.540758i \(-0.181862\pi\)
0.841178 + 0.540758i \(0.181862\pi\)
\(278\) −40.0000 −2.39904
\(279\) −10.5000 18.1865i −0.628619 1.08880i
\(280\) 0 0
\(281\) −5.00000 8.66025i −0.298275 0.516627i 0.677466 0.735554i \(-0.263078\pi\)
−0.975741 + 0.218926i \(0.929745\pi\)
\(282\) 0 0
\(283\) 7.00000 12.1244i 0.416107 0.720718i −0.579437 0.815017i \(-0.696728\pi\)
0.995544 + 0.0942988i \(0.0300609\pi\)
\(284\) 2.00000 0.118678
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) −4.00000 + 6.92820i −0.236113 + 0.408959i
\(288\) 12.0000 20.7846i 0.707107 1.22474i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) 0 0
\(291\) 0 0
\(292\) −20.0000 −1.17041
\(293\) −4.00000 −0.233682 −0.116841 0.993151i \(-0.537277\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −1.00000 1.73205i −0.0579284 0.100335i
\(299\) 6.00000 10.3923i 0.346989 0.601003i
\(300\) 0 0
\(301\) 4.00000 6.92820i 0.230556 0.399335i
\(302\) 9.00000 15.5885i 0.517892 0.897015i
\(303\) 0 0
\(304\) −16.0000 + 6.92820i −0.917663 + 0.397360i
\(305\) 0 0
\(306\) −6.00000 + 10.3923i −0.342997 + 0.594089i
\(307\) 8.00000 13.8564i 0.456584 0.790827i −0.542194 0.840254i \(-0.682406\pi\)
0.998778 + 0.0494267i \(0.0157394\pi\)
\(308\) 4.00000 + 6.92820i 0.227921 + 0.394771i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 15.0000 + 25.9808i 0.847850 + 1.46852i 0.883123 + 0.469142i \(0.155437\pi\)
−0.0352727 + 0.999378i \(0.511230\pi\)
\(314\) −4.00000 6.92820i −0.225733 0.390981i
\(315\) 0 0
\(316\) 2.00000 0.112509
\(317\) −1.00000 1.73205i −0.0561656 0.0972817i 0.836576 0.547852i \(-0.184554\pi\)
−0.892741 + 0.450570i \(0.851221\pi\)
\(318\) 0 0
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 0 0
\(321\) 0 0
\(322\) 48.0000 2.67494
\(323\) 8.00000 3.46410i 0.445132 0.192748i
\(324\) 18.0000 1.00000
\(325\) 0 0
\(326\) −4.00000 + 6.92820i −0.221540 + 0.383718i
\(327\) 0 0
\(328\) 0 0
\(329\) 12.0000 + 20.7846i 0.661581 + 1.14589i
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) −6.00000 10.3923i −0.329293 0.570352i
\(333\) −3.00000 5.19615i −0.164399 0.284747i
\(334\) −24.0000 −1.31322
\(335\) 0 0
\(336\) 0 0
\(337\) 17.0000 29.4449i 0.926049 1.60396i 0.136184 0.990684i \(-0.456516\pi\)
0.789865 0.613280i \(-0.210150\pi\)
\(338\) −9.00000 15.5885i −0.489535 0.847900i
\(339\) 0 0
\(340\) 0 0
\(341\) 7.00000 0.379071
\(342\) −21.0000 15.5885i −1.13555 0.842927i
\(343\) 8.00000 0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 24.0000 + 41.5692i 1.29025 + 2.23478i
\(347\) −6.00000 + 10.3923i −0.322097 + 0.557888i −0.980921 0.194409i \(-0.937721\pi\)
0.658824 + 0.752297i \(0.271054\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.00000 + 6.92820i 0.213201 + 0.369274i
\(353\) 8.00000 0.425797 0.212899 0.977074i \(-0.431710\pi\)
0.212899 + 0.977074i \(0.431710\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 11.0000 19.0526i 0.582999 1.00978i
\(357\) 0 0
\(358\) 15.0000 25.9808i 0.792775 1.37313i
\(359\) 10.0000 17.3205i 0.527780 0.914141i −0.471696 0.881761i \(-0.656358\pi\)
0.999476 0.0323801i \(-0.0103087\pi\)
\(360\) 0 0
\(361\) 5.50000 + 18.1865i 0.289474 + 0.957186i
\(362\) 12.0000 0.630706
\(363\) 0 0
\(364\) −8.00000 + 13.8564i −0.419314 + 0.726273i
\(365\) 0 0
\(366\) 0 0
\(367\) −8.00000 13.8564i −0.417597 0.723299i 0.578101 0.815966i \(-0.303794\pi\)
−0.995697 + 0.0926670i \(0.970461\pi\)
\(368\) 24.0000 1.25109
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) 8.00000 + 13.8564i 0.415339 + 0.719389i
\(372\) 0 0
\(373\) 12.0000 0.621336 0.310668 0.950518i \(-0.399447\pi\)
0.310668 + 0.950518i \(0.399447\pi\)
\(374\) −2.00000 3.46410i −0.103418 0.179124i
\(375\) 0 0
\(376\) 0 0
\(377\) −9.00000 + 15.5885i −0.463524 + 0.802846i
\(378\) 0 0
\(379\) −29.0000 −1.48963 −0.744815 0.667271i \(-0.767462\pi\)
−0.744815 + 0.667271i \(0.767462\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −3.00000 + 5.19615i −0.153493 + 0.265858i
\(383\) 3.00000 5.19615i 0.153293 0.265511i −0.779143 0.626846i \(-0.784346\pi\)
0.932436 + 0.361335i \(0.117679\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −16.0000 27.7128i −0.814379 1.41055i
\(387\) 6.00000 0.304997
\(388\) 12.0000 0.609208
\(389\) 16.5000 + 28.5788i 0.836583 + 1.44900i 0.892735 + 0.450582i \(0.148784\pi\)
−0.0561516 + 0.998422i \(0.517883\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 0 0
\(393\) 0 0
\(394\) 18.0000 31.1769i 0.906827 1.57067i
\(395\) 0 0
\(396\) −3.00000 + 5.19615i −0.150756 + 0.261116i
\(397\) −4.00000 + 6.92820i −0.200754 + 0.347717i −0.948772 0.315963i \(-0.897673\pi\)
0.748017 + 0.663679i \(0.231006\pi\)
\(398\) −26.0000 −1.30326
\(399\) 0 0
\(400\) 0 0
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 0 0
\(403\) 7.00000 + 12.1244i 0.348695 + 0.603957i
\(404\) −15.0000 + 25.9808i −0.746278 + 1.29259i
\(405\) 0 0
\(406\) −72.0000 −3.57330
\(407\) 2.00000 0.0991363
\(408\) 0 0
\(409\) 2.50000 + 4.33013i 0.123617 + 0.214111i 0.921192 0.389109i \(-0.127217\pi\)
−0.797574 + 0.603220i \(0.793884\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 16.0000 + 27.7128i 0.788263 + 1.36531i
\(413\) −18.0000 + 31.1769i −0.885722 + 1.53412i
\(414\) 18.0000 + 31.1769i 0.884652 + 1.53226i
\(415\) 0 0
\(416\) −8.00000 + 13.8564i −0.392232 + 0.679366i
\(417\) 0 0
\(418\) 8.00000 3.46410i 0.391293 0.169435i
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 0 0
\(421\) 7.50000 12.9904i 0.365528 0.633112i −0.623333 0.781956i \(-0.714222\pi\)
0.988861 + 0.148844i \(0.0475552\pi\)
\(422\) 5.00000 + 8.66025i 0.243396 + 0.421575i
\(423\) −9.00000 + 15.5885i −0.437595 + 0.757937i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 14.0000 + 24.2487i 0.677507 + 1.17348i
\(428\) −10.0000 17.3205i −0.483368 0.837218i
\(429\) 0 0
\(430\) 0 0
\(431\) −10.5000 18.1865i −0.505767 0.876014i −0.999978 0.00667224i \(-0.997876\pi\)
0.494211 0.869342i \(-0.335457\pi\)
\(432\) 0 0
\(433\) −2.00000 3.46410i −0.0961139 0.166474i 0.813959 0.580922i \(-0.197308\pi\)
−0.910073 + 0.414448i \(0.863975\pi\)
\(434\) −28.0000 + 48.4974i −1.34404 + 2.32795i
\(435\) 0 0
\(436\) 30.0000 1.43674
\(437\) 3.00000 25.9808i 0.143509 1.24283i
\(438\) 0 0
\(439\) 6.50000 11.2583i 0.310228 0.537331i −0.668184 0.743996i \(-0.732928\pi\)
0.978412 + 0.206666i \(0.0662612\pi\)
\(440\) 0 0
\(441\) 13.5000 + 23.3827i 0.642857 + 1.11346i
\(442\) 4.00000 6.92820i 0.190261 0.329541i
\(443\) 2.00000 + 3.46410i 0.0950229 + 0.164584i 0.909618 0.415445i \(-0.136374\pi\)
−0.814595 + 0.580030i \(0.803041\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 2.00000 + 3.46410i 0.0947027 + 0.164030i
\(447\) 0 0
\(448\) −32.0000 −1.51186
\(449\) 31.0000 1.46298 0.731490 0.681852i \(-0.238825\pi\)
0.731490 + 0.681852i \(0.238825\pi\)
\(450\) 0 0
\(451\) 1.00000 1.73205i 0.0470882 0.0815591i
\(452\) −12.0000 20.7846i −0.564433 0.977626i
\(453\) 0 0
\(454\) −14.0000 + 24.2487i −0.657053 + 1.13805i
\(455\) 0 0
\(456\) 0 0
\(457\) −34.0000 −1.59045 −0.795226 0.606313i \(-0.792648\pi\)
−0.795226 + 0.606313i \(0.792648\pi\)
\(458\) 17.0000 29.4449i 0.794358 1.37587i
\(459\) 0 0
\(460\) 0 0
\(461\) 12.5000 21.6506i 0.582183 1.00837i −0.413037 0.910714i \(-0.635532\pi\)
0.995220 0.0976564i \(-0.0311346\pi\)
\(462\) 0 0
\(463\) 4.00000 0.185896 0.0929479 0.995671i \(-0.470371\pi\)
0.0929479 + 0.995671i \(0.470371\pi\)
\(464\) −36.0000 −1.67126
\(465\) 0 0
\(466\) 8.00000 + 13.8564i 0.370593 + 0.641886i
\(467\) −10.0000 −0.462745 −0.231372 0.972865i \(-0.574322\pi\)
−0.231372 + 0.972865i \(0.574322\pi\)
\(468\) −12.0000 −0.554700
\(469\) −20.0000 34.6410i −0.923514 1.59957i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.00000 + 1.73205i −0.0459800 + 0.0796398i
\(474\) 0 0
\(475\) 0 0
\(476\) 16.0000 0.733359
\(477\) −6.00000 + 10.3923i −0.274721 + 0.475831i
\(478\) −19.0000 + 32.9090i −0.869040 + 1.50522i
\(479\) −7.50000 12.9904i −0.342684 0.593546i 0.642246 0.766498i \(-0.278003\pi\)
−0.984930 + 0.172953i \(0.944669\pi\)
\(480\) 0 0
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) −2.00000 −0.0910975
\(483\) 0 0
\(484\) 10.0000 + 17.3205i 0.454545 + 0.787296i
\(485\) 0 0
\(486\) 0 0
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.50000 + 11.2583i −0.293341 + 0.508081i −0.974598 0.223963i \(-0.928100\pi\)
0.681257 + 0.732045i \(0.261434\pi\)
\(492\) 0 0
\(493\) 18.0000 0.810679
\(494\) 14.0000 + 10.3923i 0.629890 + 0.467572i
\(495\) 0 0
\(496\) −14.0000 + 24.2487i −0.628619 + 1.08880i
\(497\) −2.00000 + 3.46410i −0.0897123 + 0.155386i
\(498\) 0 0
\(499\) −14.0000 + 24.2487i −0.626726 + 1.08552i 0.361478 + 0.932381i \(0.382272\pi\)
−0.988204 + 0.153141i \(0.951061\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −26.0000 −1.16044
\(503\) −13.0000 22.5167i −0.579641 1.00397i −0.995520 0.0945483i \(-0.969859\pi\)
0.415879 0.909420i \(-0.363474\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −12.0000 −0.533465
\(507\) 0 0
\(508\) −6.00000 + 10.3923i −0.266207 + 0.461084i
\(509\) −9.00000 15.5885i −0.398918 0.690946i 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113020i \(0.963948\pi\)
\(510\) 0 0
\(511\) 20.0000 34.6410i 0.884748 1.53243i
\(512\) −32.0000 −1.41421
\(513\) 0 0
\(514\) −12.0000 −0.529297
\(515\) 0 0
\(516\) 0 0
\(517\) −3.00000 5.19615i −0.131940 0.228527i
\(518\) −8.00000 + 13.8564i −0.351500 + 0.608816i
\(519\) 0 0
\(520\) 0 0
\(521\) 15.0000 0.657162 0.328581 0.944476i \(-0.393430\pi\)
0.328581 + 0.944476i \(0.393430\pi\)
\(522\) −27.0000 46.7654i −1.18176 2.04686i
\(523\) 8.00000 + 13.8564i 0.349816 + 0.605898i 0.986216 0.165460i \(-0.0529109\pi\)
−0.636401 + 0.771358i \(0.719578\pi\)
\(524\) 24.0000 1.04844
\(525\) 0 0
\(526\) 0 0
\(527\) 7.00000 12.1244i 0.304925 0.528145i
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) −27.0000 −1.17170
\(532\) −4.00000 + 34.6410i −0.173422 + 1.50188i
\(533\) 4.00000 0.173259
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 3.00000 + 5.19615i 0.129339 + 0.224022i
\(539\) −9.00000 −0.387657
\(540\) 0 0
\(541\) −11.5000 19.9186i −0.494424 0.856367i 0.505556 0.862794i \(-0.331288\pi\)
−0.999979 + 0.00642713i \(0.997954\pi\)
\(542\) 3.00000 + 5.19615i 0.128861 + 0.223194i
\(543\) 0 0
\(544\) 16.0000 0.685994
\(545\) 0 0
\(546\) 0 0
\(547\) 11.0000 + 19.0526i 0.470326 + 0.814629i 0.999424 0.0339321i \(-0.0108030\pi\)
−0.529098 + 0.848561i \(0.677470\pi\)
\(548\) 12.0000 20.7846i 0.512615 0.887875i
\(549\) −10.5000 + 18.1865i −0.448129 + 0.776182i
\(550\) 0 0
\(551\) −4.50000 + 38.9711i −0.191706 + 1.66023i
\(552\) 0 0
\(553\) −2.00000 + 3.46410i −0.0850487 + 0.147309i
\(554\) 28.0000 48.4974i 1.18961 2.06046i
\(555\) 0 0
\(556\) −20.0000 + 34.6410i −0.848189 + 1.46911i
\(557\) 7.00000 + 12.1244i 0.296600 + 0.513725i 0.975356 0.220638i \(-0.0708140\pi\)
−0.678756 + 0.734364i \(0.737481\pi\)
\(558\) −42.0000 −1.77800
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 0 0
\(562\) −20.0000 −0.843649
\(563\) 24.0000 1.01148 0.505740 0.862686i \(-0.331220\pi\)
0.505740 + 0.862686i \(0.331220\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −14.0000 24.2487i −0.588464 1.01925i
\(567\) −18.0000 + 31.1769i −0.755929 + 1.30931i
\(568\) 0 0
\(569\) 15.0000 0.628833 0.314416 0.949285i \(-0.398191\pi\)
0.314416 + 0.949285i \(0.398191\pi\)
\(570\) 0 0
\(571\) 13.0000 0.544033 0.272017 0.962293i \(-0.412309\pi\)
0.272017 + 0.962293i \(0.412309\pi\)
\(572\) 2.00000 3.46410i 0.0836242 0.144841i
\(573\) 0 0
\(574\) 8.00000 + 13.8564i 0.333914 + 0.578355i
\(575\) 0 0
\(576\) −12.0000 20.7846i −0.500000 0.866025i
\(577\) −6.00000 −0.249783 −0.124892 0.992170i \(-0.539858\pi\)
−0.124892 + 0.992170i \(0.539858\pi\)
\(578\) 26.0000 1.08146
\(579\) 0 0
\(580\) 0 0
\(581\) 24.0000 0.995688
\(582\) 0 0
\(583\) −2.00000 3.46410i −0.0828315 0.143468i
\(584\) 0 0
\(585\) 0 0
\(586\) −4.00000 + 6.92820i −0.165238 + 0.286201i
\(587\) −12.0000 + 20.7846i −0.495293 + 0.857873i −0.999985 0.00542667i \(-0.998273\pi\)
0.504692 + 0.863299i \(0.331606\pi\)
\(588\) 0 0
\(589\) 24.5000 + 18.1865i 1.00950 + 0.749363i
\(590\) 0 0
\(591\) 0 0
\(592\) −4.00000 + 6.92820i −0.164399 + 0.284747i
\(593\) −16.0000 27.7128i −0.657041 1.13803i −0.981378 0.192087i \(-0.938474\pi\)
0.324337 0.945942i \(-0.394859\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −2.00000 −0.0819232
\(597\) 0 0
\(598\) −12.0000 20.7846i −0.490716 0.849946i
\(599\) 6.00000 + 10.3923i 0.245153 + 0.424618i 0.962175 0.272433i \(-0.0878284\pi\)
−0.717021 + 0.697051i \(0.754495\pi\)
\(600\) 0 0
\(601\) 17.0000 0.693444 0.346722 0.937968i \(-0.387295\pi\)
0.346722 + 0.937968i \(0.387295\pi\)
\(602\) −8.00000 13.8564i −0.326056 0.564745i
\(603\) 15.0000 25.9808i 0.610847 1.05802i
\(604\) −9.00000 15.5885i −0.366205 0.634285i
\(605\) 0 0
\(606\) 0 0
\(607\) 14.0000 0.568242 0.284121 0.958788i \(-0.408298\pi\)
0.284121 + 0.958788i \(0.408298\pi\)
\(608\) −4.00000 + 34.6410i −0.162221 + 1.40488i
\(609\) 0 0
\(610\) 0 0
\(611\) 6.00000 10.3923i 0.242734 0.420428i
\(612\) 6.00000 + 10.3923i 0.242536 + 0.420084i
\(613\) 12.0000 20.7846i 0.484675 0.839482i −0.515170 0.857088i \(-0.672271\pi\)
0.999845 + 0.0176058i \(0.00560439\pi\)
\(614\) −16.0000 27.7128i −0.645707 1.11840i
\(615\) 0 0
\(616\) 0 0
\(617\) 9.00000 + 15.5885i 0.362326 + 0.627568i 0.988343 0.152242i \(-0.0486493\pi\)
−0.626017 + 0.779809i \(0.715316\pi\)
\(618\) 0 0
\(619\) 4.00000 0.160774 0.0803868 0.996764i \(-0.474384\pi\)
0.0803868 + 0.996764i \(0.474384\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 22.0000 + 38.1051i 0.881411 + 1.52665i
\(624\) 0 0
\(625\) 0 0
\(626\) 60.0000 2.39808
\(627\) 0 0
\(628\) −8.00000 −0.319235
\(629\) 2.00000 3.46410i 0.0797452 0.138123i
\(630\) 0 0
\(631\) −0.500000 0.866025i −0.0199047 0.0344759i 0.855901 0.517139i \(-0.173003\pi\)
−0.875806 + 0.482663i \(0.839670\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −4.00000 −0.158860
\(635\) 0 0
\(636\) 0 0
\(637\) −9.00000 15.5885i −0.356593 0.617637i
\(638\) 18.0000 0.712627
\(639\) −3.00000 −0.118678
\(640\) 0 0
\(641\) −10.5000 + 18.1865i −0.414725 + 0.718325i −0.995400 0.0958109i \(-0.969456\pi\)
0.580674 + 0.814136i \(0.302789\pi\)
\(642\) 0 0
\(643\) −23.0000 + 39.8372i −0.907031 + 1.57102i −0.0888646 + 0.996044i \(0.528324\pi\)
−0.818167 + 0.574981i \(0.805009\pi\)
\(644\) 24.0000 41.5692i 0.945732 1.63806i
\(645\) 0 0
\(646\) 2.00000 17.3205i 0.0786889 0.681466i
\(647\) 6.00000 0.235884 0.117942 0.993020i \(-0.462370\pi\)
0.117942 + 0.993020i \(0.462370\pi\)
\(648\) 0 0
\(649\) 4.50000 7.79423i 0.176640 0.305950i
\(650\) 0 0
\(651\) 0 0
\(652\) 4.00000 + 6.92820i 0.156652 + 0.271329i
\(653\) −10.0000 −0.391330 −0.195665 0.980671i \(-0.562687\pi\)
−0.195665 + 0.980671i \(0.562687\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 4.00000 + 6.92820i 0.156174 + 0.270501i
\(657\) 30.0000 1.17041
\(658\) 48.0000 1.87123
\(659\) −10.0000 17.3205i −0.389545 0.674711i 0.602844 0.797859i \(-0.294034\pi\)
−0.992388 + 0.123148i \(0.960701\pi\)
\(660\) 0 0
\(661\) 7.50000 + 12.9904i 0.291716 + 0.505267i 0.974216 0.225619i \(-0.0724404\pi\)
−0.682499 + 0.730886i \(0.739107\pi\)
\(662\) 20.0000 34.6410i 0.777322 1.34636i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −12.0000 −0.464991
\(667\) 27.0000 46.7654i 1.04544 1.81076i
\(668\) −12.0000 + 20.7846i −0.464294 + 0.804181i
\(669\) 0 0
\(670\) 0 0
\(671\) −3.50000 6.06218i −0.135116 0.234028i
\(672\) 0 0
\(673\) 20.0000 0.770943 0.385472 0.922720i \(-0.374039\pi\)
0.385472 + 0.922720i \(0.374039\pi\)
\(674\) −34.0000 58.8897i −1.30963 2.26835i
\(675\) 0 0
\(676\) −18.0000 −0.692308
\(677\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(678\) 0 0
\(679\) −12.0000 + 20.7846i −0.460518 + 0.797640i
\(680\) 0 0
\(681\) 0 0
\(682\) 7.00000 12.1244i 0.268044 0.464266i
\(683\) −30.0000 −1.14792 −0.573959 0.818884i \(-0.694593\pi\)
−0.573959 + 0.818884i \(0.694593\pi\)
\(684\) −24.0000 + 10.3923i −0.917663 + 0.397360i
\(685\) 0 0
\(686\) 8.00000 13.8564i 0.305441 0.529040i
\(687\) 0 0
\(688\) −4.00000 6.92820i −0.152499 0.264135i
\(689\) 4.00000 6.92820i 0.152388 0.263944i
\(690\) 0 0
\(691\) 3.00000 0.114125 0.0570627 0.998371i \(-0.481827\pi\)
0.0570627 + 0.998371i \(0.481827\pi\)
\(692\) 48.0000 1.82469
\(693\) −6.00000 10.3923i −0.227921 0.394771i
\(694\) 12.0000 + 20.7846i 0.455514 + 0.788973i
\(695\) 0 0
\(696\) 0 0
\(697\) −2.00000 3.46410i −0.0757554 0.131212i
\(698\) 14.0000 24.2487i 0.529908 0.917827i
\(699\) 0 0
\(700\) 0 0
\(701\) −3.00000 + 5.19615i −0.113308 + 0.196256i −0.917102 0.398652i \(-0.869478\pi\)
0.803794 + 0.594908i \(0.202811\pi\)
\(702\) 0 0
\(703\) 7.00000 + 5.19615i 0.264010 + 0.195977i
\(704\) 8.00000 0.301511
\(705\) 0 0
\(706\) 8.00000 13.8564i 0.301084 0.521493i
\(707\) −30.0000 51.9615i −1.12827 1.95421i
\(708\) 0 0
\(709\) −12.5000 21.6506i −0.469447 0.813107i 0.529943 0.848034i \(-0.322213\pi\)
−0.999390 + 0.0349269i \(0.988880\pi\)
\(710\) 0 0
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) −21.0000 36.3731i −0.786456 1.36218i
\(714\) 0 0
\(715\) 0 0
\(716\) −15.0000 25.9808i −0.560576 0.970947i
\(717\) 0 0
\(718\) −20.0000 34.6410i −0.746393 1.29279i
\(719\) 10.5000 18.1865i 0.391584 0.678243i −0.601075 0.799193i \(-0.705261\pi\)
0.992659 + 0.120950i \(0.0385939\pi\)
\(720\) 0 0
\(721\) −64.0000 −2.38348
\(722\) 37.0000 + 8.66025i 1.37700 + 0.322301i
\(723\) 0 0
\(724\) 6.00000 10.3923i 0.222988 0.386227i
\(725\) 0 0
\(726\) 0 0
\(727\) 4.00000 6.92820i 0.148352 0.256953i −0.782267 0.622944i \(-0.785937\pi\)
0.930618 + 0.365991i \(0.119270\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 2.00000 + 3.46410i 0.0739727 + 0.128124i
\(732\) 0 0
\(733\) 6.00000 0.221615 0.110808 0.993842i \(-0.464656\pi\)
0.110808 + 0.993842i \(0.464656\pi\)
\(734\) −32.0000 −1.18114
\(735\) 0 0
\(736\) 24.0000 41.5692i 0.884652 1.53226i
\(737\) 5.00000 + 8.66025i 0.184177 + 0.319005i
\(738\) −6.00000 + 10.3923i −0.220863 + 0.382546i
\(739\) 14.5000 25.1147i 0.533391 0.923861i −0.465848 0.884865i \(-0.654251\pi\)
0.999239 0.0389959i \(-0.0124159\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 32.0000 1.17476
\(743\) 25.0000 43.3013i 0.917161 1.58857i 0.113455 0.993543i \(-0.463808\pi\)
0.803706 0.595026i \(-0.202858\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 12.0000 20.7846i 0.439351 0.760979i
\(747\) 9.00000 + 15.5885i 0.329293 + 0.570352i
\(748\) −4.00000 −0.146254
\(749\) 40.0000 1.46157
\(750\) 0 0
\(751\) −20.5000 35.5070i −0.748056 1.29567i −0.948753 0.316017i \(-0.897654\pi\)
0.200698 0.979653i \(-0.435679\pi\)
\(752\) 24.0000 0.875190
\(753\) 0 0
\(754\) 18.0000 + 31.1769i 0.655521 + 1.13540i
\(755\) 0 0
\(756\) 0 0
\(757\) 13.0000 22.5167i 0.472493 0.818382i −0.527011 0.849858i \(-0.676688\pi\)
0.999505 + 0.0314762i \(0.0100208\pi\)
\(758\) −29.0000 + 50.2295i −1.05333 + 1.82442i
\(759\) 0 0
\(760\) 0 0
\(761\) −18.0000 −0.652499 −0.326250 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) 0 0
\(763\) −30.0000 + 51.9615i −1.08607 + 1.88113i
\(764\) 3.00000 + 5.19615i 0.108536 + 0.187990i
\(765\) 0 0
\(766\) −6.00000 10.3923i −0.216789 0.375489i
\(767\) 18.0000 0.649942
\(768\) 0 0
\(769\) −2.50000 4.33013i −0.0901523 0.156148i 0.817423 0.576038i \(-0.195402\pi\)
−0.907575 + 0.419890i \(0.862069\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −32.0000 −1.15171
\(773\) 17.0000 + 29.4449i 0.611448 + 1.05906i 0.990997 + 0.133887i \(0.0427458\pi\)
−0.379549 + 0.925172i \(0.623921\pi\)
\(774\) 6.00000 10.3923i 0.215666 0.373544i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 66.0000 2.36621
\(779\) 8.00000 3.46410i 0.286630 0.124114i
\(780\) 0 0
\(781\) 0.500000 0.866025i 0.0178914 0.0309888i
\(782\) −12.0000 + 20.7846i −0.429119 + 0.743256i
\(783\) 0 0
\(784\) 18.0000 31.1769i 0.642857 1.11346i
\(785\) 0 0
\(786\) 0 0
\(787\) −22.0000 −0.784215 −0.392108 0.919919i \(-0.628254\pi\)
−0.392108 + 0.919919i \(0.628254\pi\)
\(788\) −18.0000 31.1769i −0.641223 1.11063i
\(789\) 0 0
\(790\) 0 0
\(791\) 48.0000 1.70668
\(792\) 0 0
\(793\) 7.00000 12.1244i 0.248577 0.430548i
\(794\)