Properties

Label 700.2.t.a.199.2
Level $700$
Weight $2$
Character 700.199
Analytic conductor $5.590$
Analytic rank $1$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.t (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.58952814149\)
Analytic rank: \(1\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 700.199
Dual form 700.2.t.a.299.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.366025 - 1.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.73205 + 1.73205i) q^{6} +(-2.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(0.366025 - 1.36603i) q^{2} +(-1.50000 - 0.866025i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-1.73205 + 1.73205i) q^{6} +(-2.00000 - 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(0.866025 + 0.500000i) q^{11} +(1.73205 + 3.00000i) q^{12} -3.46410 q^{13} +(-3.09808 + 2.09808i) q^{14} +(2.00000 + 3.46410i) q^{16} +(0.866025 - 1.50000i) q^{17} +(2.59808 + 4.50000i) q^{19} +(1.50000 + 4.33013i) q^{21} +(1.00000 - 1.00000i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(4.73205 - 1.26795i) q^{24} +(-1.26795 + 4.73205i) q^{26} +5.19615i q^{27} +(1.73205 + 5.00000i) q^{28} -4.00000 q^{29} +(-0.866025 + 1.50000i) q^{31} +(5.46410 - 1.46410i) q^{32} +(-0.866025 - 1.50000i) q^{33} +(-1.73205 - 1.73205i) q^{34} +(2.59808 - 1.50000i) q^{37} +(7.09808 - 1.90192i) q^{38} +(5.19615 + 3.00000i) q^{39} +3.46410i q^{41} +(6.46410 - 0.464102i) q^{42} +2.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} +(-1.36603 + 0.366025i) q^{46} +(-7.50000 + 4.33013i) q^{47} -6.92820i q^{48} +(1.00000 + 6.92820i) q^{49} +(-2.59808 + 1.50000i) q^{51} +(6.00000 + 3.46410i) q^{52} +(-0.866025 - 0.500000i) q^{53} +(7.09808 + 1.90192i) q^{54} +(7.46410 - 0.535898i) q^{56} -9.00000i q^{57} +(-1.46410 + 5.46410i) q^{58} +(2.59808 - 4.50000i) q^{59} +(-4.50000 + 2.59808i) q^{61} +(1.73205 + 1.73205i) q^{62} -8.00000i q^{64} +(-2.36603 + 0.633975i) q^{66} +(-1.50000 + 2.59808i) q^{67} +(-3.00000 + 1.73205i) q^{68} +1.73205i q^{69} -14.0000i q^{71} +(4.33013 - 7.50000i) q^{73} +(-1.09808 - 4.09808i) q^{74} -10.3923i q^{76} +(-0.866025 - 2.50000i) q^{77} +(6.00000 - 6.00000i) q^{78} +(-7.79423 + 4.50000i) q^{79} +(4.50000 - 7.79423i) q^{81} +(4.73205 + 1.26795i) q^{82} +13.8564i q^{83} +(1.73205 - 9.00000i) q^{84} +(0.732051 - 2.73205i) q^{86} +(6.00000 + 3.46410i) q^{87} +(-2.73205 + 0.732051i) q^{88} +(-13.5000 + 7.79423i) q^{89} +(6.92820 + 6.00000i) q^{91} +2.00000i q^{92} +(2.59808 - 1.50000i) q^{93} +(3.16987 + 11.8301i) q^{94} +(-9.46410 - 2.53590i) q^{96} -17.3205 q^{97} +(9.83013 + 1.16987i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 6q^{3} - 8q^{7} - 8q^{8} + O(q^{10}) \) \( 4q - 2q^{2} - 6q^{3} - 8q^{7} - 8q^{8} - 2q^{14} + 8q^{16} + 6q^{21} + 4q^{22} - 2q^{23} + 12q^{24} - 12q^{26} - 16q^{29} + 8q^{32} + 18q^{38} + 12q^{42} + 8q^{43} - 4q^{44} - 2q^{46} - 30q^{47} + 4q^{49} + 24q^{52} + 18q^{54} + 16q^{56} + 8q^{58} - 18q^{61} - 6q^{66} - 6q^{67} - 12q^{68} + 6q^{74} + 24q^{78} + 18q^{81} + 12q^{82} - 4q^{86} + 24q^{87} - 4q^{88} - 54q^{89} + 30q^{94} - 24q^{96} + 22q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.366025 1.36603i 0.258819 0.965926i
\(3\) −1.50000 0.866025i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) 0 0
\(6\) −1.73205 + 1.73205i −0.707107 + 0.707107i
\(7\) −2.00000 1.73205i −0.755929 0.654654i
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) 0 0
\(10\) 0 0
\(11\) 0.866025 + 0.500000i 0.261116 + 0.150756i 0.624844 0.780750i \(-0.285163\pi\)
−0.363727 + 0.931505i \(0.618496\pi\)
\(12\) 1.73205 + 3.00000i 0.500000 + 0.866025i
\(13\) −3.46410 −0.960769 −0.480384 0.877058i \(-0.659503\pi\)
−0.480384 + 0.877058i \(0.659503\pi\)
\(14\) −3.09808 + 2.09808i −0.827996 + 0.560734i
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 0.866025 1.50000i 0.210042 0.363803i −0.741685 0.670748i \(-0.765973\pi\)
0.951727 + 0.306944i \(0.0993066\pi\)
\(18\) 0 0
\(19\) 2.59808 + 4.50000i 0.596040 + 1.03237i 0.993399 + 0.114708i \(0.0365932\pi\)
−0.397360 + 0.917663i \(0.630073\pi\)
\(20\) 0 0
\(21\) 1.50000 + 4.33013i 0.327327 + 0.944911i
\(22\) 1.00000 1.00000i 0.213201 0.213201i
\(23\) −0.500000 0.866025i −0.104257 0.180579i 0.809177 0.587565i \(-0.199913\pi\)
−0.913434 + 0.406986i \(0.866580\pi\)
\(24\) 4.73205 1.26795i 0.965926 0.258819i
\(25\) 0 0
\(26\) −1.26795 + 4.73205i −0.248665 + 0.928032i
\(27\) 5.19615i 1.00000i
\(28\) 1.73205 + 5.00000i 0.327327 + 0.944911i
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) −0.866025 + 1.50000i −0.155543 + 0.269408i −0.933257 0.359211i \(-0.883046\pi\)
0.777714 + 0.628619i \(0.216379\pi\)
\(32\) 5.46410 1.46410i 0.965926 0.258819i
\(33\) −0.866025 1.50000i −0.150756 0.261116i
\(34\) −1.73205 1.73205i −0.297044 0.297044i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.59808 1.50000i 0.427121 0.246598i −0.270998 0.962580i \(-0.587354\pi\)
0.698119 + 0.715981i \(0.254020\pi\)
\(38\) 7.09808 1.90192i 1.15146 0.308533i
\(39\) 5.19615 + 3.00000i 0.832050 + 0.480384i
\(40\) 0 0
\(41\) 3.46410i 0.541002i 0.962720 + 0.270501i \(0.0871893\pi\)
−0.962720 + 0.270501i \(0.912811\pi\)
\(42\) 6.46410 0.464102i 0.997433 0.0716124i
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) 0 0
\(46\) −1.36603 + 0.366025i −0.201409 + 0.0539675i
\(47\) −7.50000 + 4.33013i −1.09399 + 0.631614i −0.934635 0.355608i \(-0.884274\pi\)
−0.159352 + 0.987222i \(0.550941\pi\)
\(48\) 6.92820i 1.00000i
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) 0 0
\(51\) −2.59808 + 1.50000i −0.363803 + 0.210042i
\(52\) 6.00000 + 3.46410i 0.832050 + 0.480384i
\(53\) −0.866025 0.500000i −0.118958 0.0686803i 0.439340 0.898321i \(-0.355212\pi\)
−0.558298 + 0.829640i \(0.688546\pi\)
\(54\) 7.09808 + 1.90192i 0.965926 + 0.258819i
\(55\) 0 0
\(56\) 7.46410 0.535898i 0.997433 0.0716124i
\(57\) 9.00000i 1.19208i
\(58\) −1.46410 + 5.46410i −0.192246 + 0.717472i
\(59\) 2.59808 4.50000i 0.338241 0.585850i −0.645861 0.763455i \(-0.723502\pi\)
0.984102 + 0.177605i \(0.0568349\pi\)
\(60\) 0 0
\(61\) −4.50000 + 2.59808i −0.576166 + 0.332650i −0.759608 0.650381i \(-0.774609\pi\)
0.183442 + 0.983030i \(0.441276\pi\)
\(62\) 1.73205 + 1.73205i 0.219971 + 0.219971i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) −2.36603 + 0.633975i −0.291238 + 0.0780369i
\(67\) −1.50000 + 2.59808i −0.183254 + 0.317406i −0.942987 0.332830i \(-0.891996\pi\)
0.759733 + 0.650236i \(0.225330\pi\)
\(68\) −3.00000 + 1.73205i −0.363803 + 0.210042i
\(69\) 1.73205i 0.208514i
\(70\) 0 0
\(71\) 14.0000i 1.66149i −0.556650 0.830747i \(-0.687914\pi\)
0.556650 0.830747i \(-0.312086\pi\)
\(72\) 0 0
\(73\) 4.33013 7.50000i 0.506803 0.877809i −0.493166 0.869935i \(-0.664160\pi\)
0.999969 0.00787336i \(-0.00250619\pi\)
\(74\) −1.09808 4.09808i −0.127649 0.476392i
\(75\) 0 0
\(76\) 10.3923i 1.19208i
\(77\) −0.866025 2.50000i −0.0986928 0.284901i
\(78\) 6.00000 6.00000i 0.679366 0.679366i
\(79\) −7.79423 + 4.50000i −0.876919 + 0.506290i −0.869641 0.493684i \(-0.835650\pi\)
−0.00727784 + 0.999974i \(0.502317\pi\)
\(80\) 0 0
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) 4.73205 + 1.26795i 0.522568 + 0.140022i
\(83\) 13.8564i 1.52094i 0.649374 + 0.760469i \(0.275031\pi\)
−0.649374 + 0.760469i \(0.724969\pi\)
\(84\) 1.73205 9.00000i 0.188982 0.981981i
\(85\) 0 0
\(86\) 0.732051 2.73205i 0.0789391 0.294605i
\(87\) 6.00000 + 3.46410i 0.643268 + 0.371391i
\(88\) −2.73205 + 0.732051i −0.291238 + 0.0780369i
\(89\) −13.5000 + 7.79423i −1.43100 + 0.826187i −0.997197 0.0748225i \(-0.976161\pi\)
−0.433800 + 0.901009i \(0.642828\pi\)
\(90\) 0 0
\(91\) 6.92820 + 6.00000i 0.726273 + 0.628971i
\(92\) 2.00000i 0.208514i
\(93\) 2.59808 1.50000i 0.269408 0.155543i
\(94\) 3.16987 + 11.8301i 0.326947 + 1.22018i
\(95\) 0 0
\(96\) −9.46410 2.53590i −0.965926 0.258819i
\(97\) −17.3205 −1.75863 −0.879316 0.476240i \(-0.842000\pi\)
−0.879316 + 0.476240i \(0.842000\pi\)
\(98\) 9.83013 + 1.16987i 0.992993 + 0.118175i
\(99\) 0 0
\(100\) 0 0
\(101\) −7.50000 4.33013i −0.746278 0.430864i 0.0780696 0.996948i \(-0.475124\pi\)
−0.824347 + 0.566084i \(0.808458\pi\)
\(102\) 1.09808 + 4.09808i 0.108726 + 0.405770i
\(103\) −7.50000 + 4.33013i −0.738997 + 0.426660i −0.821705 0.569914i \(-0.806977\pi\)
0.0827075 + 0.996574i \(0.473643\pi\)
\(104\) 6.92820 6.92820i 0.679366 0.679366i
\(105\) 0 0
\(106\) −1.00000 + 1.00000i −0.0971286 + 0.0971286i
\(107\) −6.50000 11.2583i −0.628379 1.08838i −0.987877 0.155238i \(-0.950386\pi\)
0.359498 0.933146i \(1.61705\pi\)
\(108\) 5.19615 9.00000i 0.500000 0.866025i
\(109\) 4.50000 7.79423i 0.431022 0.746552i −0.565940 0.824447i \(-0.691487\pi\)
0.996962 + 0.0778949i \(0.0248199\pi\)
\(110\) 0 0
\(111\) −5.19615 −0.493197
\(112\) 2.00000 10.3923i 0.188982 0.981981i
\(113\) 16.0000i 1.50515i 0.658505 + 0.752577i \(0.271189\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) −12.2942 3.29423i −1.15146 0.308533i
\(115\) 0 0
\(116\) 6.92820 + 4.00000i 0.643268 + 0.371391i
\(117\) 0 0
\(118\) −5.19615 5.19615i −0.478345 0.478345i
\(119\) −4.33013 + 1.50000i −0.396942 + 0.137505i
\(120\) 0 0
\(121\) −5.00000 8.66025i −0.454545 0.787296i
\(122\) 1.90192 + 7.09808i 0.172192 + 0.642630i
\(123\) 3.00000 5.19615i 0.270501 0.468521i
\(124\) 3.00000 1.73205i 0.269408 0.155543i
\(125\) 0 0
\(126\) 0 0
\(127\) −6.00000 −0.532414 −0.266207 0.963916i \(-0.585770\pi\)
−0.266207 + 0.963916i \(0.585770\pi\)
\(128\) −10.9282 2.92820i −0.965926 0.258819i
\(129\) −3.00000 1.73205i −0.264135 0.152499i
\(130\) 0 0
\(131\) 2.59808 + 4.50000i 0.226995 + 0.393167i 0.956916 0.290365i \(-0.0937766\pi\)
−0.729921 + 0.683531i \(0.760443\pi\)
\(132\) 3.46410i 0.301511i
\(133\) 2.59808 13.5000i 0.225282 1.17060i
\(134\) 3.00000 + 3.00000i 0.259161 + 0.259161i
\(135\) 0 0
\(136\) 1.26795 + 4.73205i 0.108726 + 0.405770i
\(137\) −0.866025 0.500000i −0.0739895 0.0427179i 0.462549 0.886594i \(-0.346935\pi\)
−0.536538 + 0.843876i \(0.680268\pi\)
\(138\) 2.36603 + 0.633975i 0.201409 + 0.0539675i
\(139\) −6.92820 −0.587643 −0.293821 0.955860i \(-0.594927\pi\)
−0.293821 + 0.955860i \(0.594927\pi\)
\(140\) 0 0
\(141\) 15.0000 1.26323
\(142\) −19.1244 5.12436i −1.60488 0.430026i
\(143\) −3.00000 1.73205i −0.250873 0.144841i
\(144\) 0 0
\(145\) 0 0
\(146\) −8.66025 8.66025i −0.716728 0.716728i
\(147\) 4.50000 11.2583i 0.371154 0.928571i
\(148\) −6.00000 −0.493197
\(149\) 0.500000 + 0.866025i 0.0409616 + 0.0709476i 0.885779 0.464107i \(-0.153625\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(150\) 0 0
\(151\) −6.06218 3.50000i −0.493333 0.284826i 0.232623 0.972567i \(-0.425269\pi\)
−0.725956 + 0.687741i \(0.758602\pi\)
\(152\) −14.1962 3.80385i −1.15146 0.308533i
\(153\) 0 0
\(154\) −3.73205 + 0.267949i −0.300737 + 0.0215920i
\(155\) 0 0
\(156\) −6.00000 10.3923i −0.480384 0.832050i
\(157\) −0.866025 + 1.50000i −0.0691164 + 0.119713i −0.898513 0.438948i \(-0.855351\pi\)
0.829396 + 0.558661i \(0.188685\pi\)
\(158\) 3.29423 + 12.2942i 0.262075 + 0.978076i
\(159\) 0.866025 + 1.50000i 0.0686803 + 0.118958i
\(160\) 0 0
\(161\) −0.500000 + 2.59808i −0.0394055 + 0.204757i
\(162\) −9.00000 9.00000i −0.707107 0.707107i
\(163\) −10.5000 18.1865i −0.822423 1.42448i −0.903873 0.427802i \(-0.859288\pi\)
0.0814491 0.996678i \(1.52595\pi\)
\(164\) 3.46410 6.00000i 0.270501 0.468521i
\(165\) 0 0
\(166\) 18.9282 + 5.07180i 1.46911 + 0.393648i
\(167\) 17.3205i 1.34030i 0.742225 + 0.670151i \(0.233770\pi\)
−0.742225 + 0.670151i \(0.766230\pi\)
\(168\) −11.6603 5.66025i −0.899608 0.436698i
\(169\) −1.00000 −0.0769231
\(170\) 0 0
\(171\) 0 0
\(172\) −3.46410 2.00000i −0.264135 0.152499i
\(173\) 6.06218 + 10.5000i 0.460899 + 0.798300i 0.999006 0.0445762i \(-0.0141938\pi\)
−0.538107 + 0.842876i \(0.680860\pi\)
\(174\) 6.92820 6.92820i 0.525226 0.525226i
\(175\) 0 0
\(176\) 4.00000i 0.301511i
\(177\) −7.79423 + 4.50000i −0.585850 + 0.338241i
\(178\) 5.70577 + 21.2942i 0.427666 + 1.59607i
\(179\) 16.4545 + 9.50000i 1.22987 + 0.710063i 0.967002 0.254770i \(-0.0819996\pi\)
0.262864 + 0.964833i \(0.415333\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i −0.966282 0.257485i \(-0.917106\pi\)
0.966282 0.257485i \(-0.0828937\pi\)
\(182\) 10.7321 7.26795i 0.795513 0.538736i
\(183\) 9.00000 0.665299
\(184\) 2.73205 + 0.732051i 0.201409 + 0.0539675i
\(185\) 0 0
\(186\) −1.09808 4.09808i −0.0805149 0.300486i
\(187\) 1.50000 0.866025i 0.109691 0.0633300i
\(188\) 17.3205 1.26323
\(189\) 9.00000 10.3923i 0.654654 0.755929i
\(190\) 0 0
\(191\) −0.866025 + 0.500000i −0.0626634 + 0.0361787i −0.531004 0.847369i \(-0.678185\pi\)
0.468341 + 0.883548i \(0.344852\pi\)
\(192\) −6.92820 + 12.0000i −0.500000 + 0.866025i
\(193\) −12.9904 7.50000i −0.935068 0.539862i −0.0466572 0.998911i \(-0.514857\pi\)
−0.888411 + 0.459049i \(0.848190\pi\)
\(194\) −6.33975 + 23.6603i −0.455167 + 1.69871i
\(195\) 0 0
\(196\) 5.19615 13.0000i 0.371154 0.928571i
\(197\) 16.0000i 1.13995i 0.821661 + 0.569976i \(0.193048\pi\)
−0.821661 + 0.569976i \(0.806952\pi\)
\(198\) 0 0
\(199\) 11.2583 19.5000i 0.798082 1.38232i −0.122782 0.992434i \(-0.539182\pi\)
0.920864 0.389885i \(-0.127485\pi\)
\(200\) 0 0
\(201\) 4.50000 2.59808i 0.317406 0.183254i
\(202\) −8.66025 + 8.66025i −0.609333 + 0.609333i
\(203\) 8.00000 + 6.92820i 0.561490 + 0.486265i
\(204\) 6.00000 0.420084
\(205\) 0 0
\(206\) 3.16987 + 11.8301i 0.220856 + 0.824244i
\(207\) 0 0
\(208\) −6.92820 12.0000i −0.480384 0.832050i
\(209\) 5.19615i 0.359425i
\(210\) 0 0
\(211\) 10.0000i 0.688428i 0.938891 + 0.344214i \(0.111855\pi\)
−0.938891 + 0.344214i \(0.888145\pi\)
\(212\) 1.00000 + 1.73205i 0.0686803 + 0.118958i
\(213\) −12.1244 + 21.0000i −0.830747 + 1.43890i
\(214\) −17.7583 + 4.75833i −1.21393 + 0.325273i
\(215\) 0 0
\(216\) −10.3923 10.3923i −0.707107 0.707107i
\(217\) 4.33013 1.50000i 0.293948 0.101827i
\(218\) −9.00000 9.00000i −0.609557 0.609557i
\(219\) −12.9904 + 7.50000i −0.877809 + 0.506803i
\(220\) 0 0
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) −1.90192 + 7.09808i −0.127649 + 0.476392i
\(223\) 6.92820i 0.463947i 0.972722 + 0.231973i \(0.0745182\pi\)
−0.972722 + 0.231973i \(0.925482\pi\)
\(224\) −13.4641 6.53590i −0.899608 0.436698i
\(225\) 0 0
\(226\) 21.8564 + 5.85641i 1.45387 + 0.389562i
\(227\) 16.5000 + 9.52628i 1.09514 + 0.632281i 0.934941 0.354803i \(-0.115452\pi\)
0.160202 + 0.987084i \(0.448785\pi\)
\(228\) −9.00000 + 15.5885i −0.596040 + 1.03237i
\(229\) 13.5000 7.79423i 0.892105 0.515057i 0.0174746 0.999847i \(-0.494437\pi\)
0.874630 + 0.484790i \(0.161104\pi\)
\(230\) 0 0
\(231\) −0.866025 + 4.50000i −0.0569803 + 0.296078i
\(232\) 8.00000 8.00000i 0.525226 0.525226i
\(233\) 6.06218 3.50000i 0.397146 0.229293i −0.288106 0.957599i \(-0.593025\pi\)
0.685252 + 0.728306i \(0.259692\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −9.00000 + 5.19615i −0.585850 + 0.338241i
\(237\) 15.5885 1.01258
\(238\) 0.464102 + 6.46410i 0.0300832 + 0.419005i
\(239\) 20.0000i 1.29369i −0.762620 0.646846i \(-0.776088\pi\)
0.762620 0.646846i \(-0.223912\pi\)
\(240\) 0 0
\(241\) −4.50000 2.59808i −0.289870 0.167357i 0.348013 0.937490i \(-0.386857\pi\)
−0.637883 + 0.770133i \(0.720190\pi\)
\(242\) −13.6603 + 3.66025i −0.878114 + 0.235290i
\(243\) 0 0
\(244\) 10.3923 0.665299
\(245\) 0 0
\(246\) −6.00000 6.00000i −0.382546 0.382546i
\(247\) −9.00000 15.5885i −0.572656 0.991870i
\(248\) −1.26795 4.73205i −0.0805149 0.300486i
\(249\) 12.0000 20.7846i 0.760469 1.31717i
\(250\) 0 0
\(251\) 3.46410 0.218652 0.109326 0.994006i \(-0.465131\pi\)
0.109326 + 0.994006i \(0.465131\pi\)
\(252\) 0 0
\(253\) 1.00000i 0.0628695i
\(254\) −2.19615 + 8.19615i −0.137799 + 0.514272i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 2.59808 + 4.50000i 0.162064 + 0.280702i 0.935609 0.353039i \(-0.114852\pi\)
−0.773545 + 0.633741i \(0.781518\pi\)
\(258\) −3.46410 + 3.46410i −0.215666 + 0.215666i
\(259\) −7.79423 1.50000i −0.484310 0.0932055i
\(260\) 0 0
\(261\) 0 0
\(262\) 7.09808 1.90192i 0.438521 0.117501i
\(263\) 11.5000 19.9186i 0.709120 1.22823i −0.256063 0.966660i \(-0.582426\pi\)
0.965184 0.261573i \(-0.0842411\pi\)
\(264\) 4.73205 + 1.26795i 0.291238 + 0.0780369i
\(265\) 0 0
\(266\) −17.4904 8.49038i −1.07240 0.520579i
\(267\) 27.0000 1.65237
\(268\) 5.19615 3.00000i 0.317406 0.183254i
\(269\) −19.5000 11.2583i −1.18894 0.686433i −0.230871 0.972984i \(-0.574158\pi\)
−0.958065 + 0.286552i \(0.907491\pi\)
\(270\) 0 0
\(271\) −7.79423 13.5000i −0.473466 0.820067i 0.526073 0.850439i \(-0.323664\pi\)
−0.999539 + 0.0303728i \(0.990331\pi\)
\(272\) 6.92820 0.420084
\(273\) −5.19615 15.0000i −0.314485 0.907841i
\(274\) −1.00000 + 1.00000i −0.0604122 + 0.0604122i
\(275\) 0 0
\(276\) 1.73205 3.00000i 0.104257 0.180579i
\(277\) 11.2583 + 6.50000i 0.676448 + 0.390547i 0.798515 0.601975i \(-0.205619\pi\)
−0.122068 + 0.992522i \(0.538953\pi\)
\(278\) −2.53590 + 9.46410i −0.152093 + 0.567619i
\(279\) 0 0
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) 5.49038 20.4904i 0.326947 1.22018i
\(283\) −10.5000 6.06218i −0.624160 0.360359i 0.154327 0.988020i \(-0.450679\pi\)
−0.778487 + 0.627661i \(0.784012\pi\)
\(284\) −14.0000 + 24.2487i −0.830747 + 1.43890i
\(285\) 0 0
\(286\) −3.46410 + 3.46410i −0.204837 + 0.204837i
\(287\) 6.00000 6.92820i 0.354169 0.408959i
\(288\) 0 0
\(289\) 7.00000 + 12.1244i 0.411765 + 0.713197i
\(290\) 0 0
\(291\) 25.9808 + 15.0000i 1.52302 + 0.879316i
\(292\) −15.0000 + 8.66025i −0.877809 + 0.506803i
\(293\) 20.7846 1.21425 0.607125 0.794606i \(-0.292323\pi\)
0.607125 + 0.794606i \(0.292323\pi\)
\(294\) −13.7321 10.2679i −0.800869 0.598839i
\(295\) 0 0
\(296\) −2.19615 + 8.19615i −0.127649 + 0.476392i
\(297\) −2.59808 + 4.50000i −0.150756 + 0.261116i
\(298\) 1.36603 0.366025i 0.0791317 0.0212033i
\(299\) 1.73205 + 3.00000i 0.100167 + 0.173494i
\(300\) 0 0
\(301\) −4.00000 3.46410i −0.230556 0.199667i
\(302\) −7.00000 + 7.00000i −0.402805 + 0.402805i
\(303\) 7.50000 + 12.9904i 0.430864 + 0.746278i
\(304\) −10.3923 + 18.0000i −0.596040 + 1.03237i
\(305\) 0 0
\(306\) 0 0
\(307\) 20.7846i 1.18624i −0.805114 0.593120i \(-0.797896\pi\)
0.805114 0.593120i \(-0.202104\pi\)
\(308\) −1.00000 + 5.19615i −0.0569803 + 0.296078i
\(309\) 15.0000 0.853320
\(310\) 0 0
\(311\) 4.33013 7.50000i 0.245539 0.425286i −0.716744 0.697336i \(-0.754368\pi\)
0.962283 + 0.272050i \(0.0877017\pi\)
\(312\) −16.3923 + 4.39230i −0.928032 + 0.248665i
\(313\) −0.866025 1.50000i −0.0489506 0.0847850i 0.840512 0.541793i \(-0.182254\pi\)
−0.889463 + 0.457008i \(0.848921\pi\)
\(314\) 1.73205 + 1.73205i 0.0977453 + 0.0977453i
\(315\) 0 0
\(316\) 18.0000 1.01258
\(317\) 9.52628 5.50000i 0.535049 0.308911i −0.208021 0.978124i \(-0.566702\pi\)
0.743070 + 0.669214i \(0.233369\pi\)
\(318\) 2.36603 0.633975i 0.132680 0.0355515i
\(319\) −3.46410 2.00000i −0.193952 0.111979i
\(320\) 0 0
\(321\) 22.5167i 1.25676i
\(322\) 3.36603 + 1.63397i 0.187581 + 0.0910578i
\(323\) 9.00000 0.500773
\(324\) −15.5885 + 9.00000i −0.866025 + 0.500000i
\(325\) 0 0
\(326\) −28.6865 + 7.68653i −1.58880 + 0.425718i
\(327\) −13.5000 + 7.79423i −0.746552 + 0.431022i
\(328\) −6.92820 6.92820i −0.382546 0.382546i
\(329\) 22.5000 + 4.33013i 1.24047 + 0.238728i
\(330\) 0 0
\(331\) −6.06218 + 3.50000i −0.333207 + 0.192377i −0.657264 0.753660i \(-0.728286\pi\)
0.324057 + 0.946038i \(0.394953\pi\)
\(332\) 13.8564 24.0000i 0.760469 1.31717i
\(333\) 0 0
\(334\) 23.6603 + 6.33975i 1.29463 + 0.346895i
\(335\) 0 0
\(336\) −12.0000 + 13.8564i −0.654654 + 0.755929i
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) −0.366025 + 1.36603i −0.0199092 + 0.0743020i
\(339\) 13.8564 24.0000i 0.752577 1.30350i
\(340\) 0 0
\(341\) −1.50000 + 0.866025i −0.0812296 + 0.0468979i
\(342\) 0 0
\(343\) 10.0000 15.5885i 0.539949 0.841698i
\(344\) −4.00000 + 4.00000i −0.215666 + 0.215666i
\(345\) 0 0
\(346\) 16.5622 4.43782i 0.890388 0.238579i
\(347\) 6.50000 11.2583i 0.348938 0.604379i −0.637123 0.770762i \(-0.719876\pi\)
0.986061 + 0.166383i \(0.0532089\pi\)
\(348\) −6.92820 12.0000i −0.371391 0.643268i
\(349\) 10.3923i 0.556287i 0.960539 + 0.278144i \(0.0897191\pi\)
−0.960539 + 0.278144i \(0.910281\pi\)
\(350\) 0 0
\(351\) 18.0000i 0.960769i
\(352\) 5.46410 + 1.46410i 0.291238 + 0.0780369i
\(353\) −14.7224 + 25.5000i −0.783596 + 1.35723i 0.146238 + 0.989249i \(0.453283\pi\)
−0.929834 + 0.367979i \(0.880050\pi\)
\(354\) 3.29423 + 12.2942i 0.175086 + 0.653431i
\(355\) 0 0
\(356\) 31.1769 1.65237
\(357\) 7.79423 + 1.50000i 0.412514 + 0.0793884i
\(358\) 19.0000 19.0000i 1.00418 1.00418i
\(359\) −19.9186 + 11.5000i −1.05126 + 0.606947i −0.923003 0.384794i \(-0.874273\pi\)
−0.128260 + 0.991741i \(0.540939\pi\)
\(360\) 0 0
\(361\) −4.00000 + 6.92820i −0.210526 + 0.364642i
\(362\) −9.46410 2.53590i −0.497422 0.133284i
\(363\) 17.3205i 0.909091i
\(364\) −6.00000 17.3205i −0.314485 0.907841i
\(365\) 0 0
\(366\) 3.29423 12.2942i 0.172192 0.642630i
\(367\) 1.50000 + 0.866025i 0.0782994 + 0.0452062i 0.538639 0.842537i \(-0.318939\pi\)
−0.460339 + 0.887743i \(0.652272\pi\)
\(368\) 2.00000 3.46410i 0.104257 0.180579i
\(369\) 0 0
\(370\) 0 0
\(371\) 0.866025 + 2.50000i 0.0449618 + 0.129794i
\(372\) −6.00000 −0.311086
\(373\) 25.1147 14.5000i 1.30039 0.750782i 0.319921 0.947444i \(-0.396344\pi\)
0.980471 + 0.196663i \(0.0630104\pi\)
\(374\) −0.633975 2.36603i −0.0327820 0.122344i
\(375\) 0 0
\(376\) 6.33975 23.6603i 0.326947 1.22018i
\(377\) 13.8564 0.713641
\(378\) −10.9019 16.0981i −0.560734 0.827996i
\(379\) 8.00000i 0.410932i 0.978664 + 0.205466i \(0.0658711\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(380\) 0 0
\(381\) 9.00000 + 5.19615i 0.461084 + 0.266207i
\(382\) 0.366025 + 1.36603i 0.0187275 + 0.0698919i
\(383\) −4.50000 + 2.59808i −0.229939 + 0.132755i −0.610544 0.791982i \(-0.709049\pi\)
0.380605 + 0.924738i \(0.375716\pi\)
\(384\) 13.8564 + 13.8564i 0.707107 + 0.707107i
\(385\) 0 0
\(386\) −15.0000 + 15.0000i −0.763480 + 0.763480i
\(387\) 0 0
\(388\) 30.0000 + 17.3205i 1.52302 + 0.879316i
\(389\) −9.50000 + 16.4545i −0.481669 + 0.834275i −0.999779 0.0210389i \(-0.993303\pi\)
0.518110 + 0.855314i \(0.326636\pi\)
\(390\) 0 0
\(391\) −1.73205 −0.0875936
\(392\) −15.8564 11.8564i −0.800869 0.598839i
\(393\) 9.00000i 0.453990i
\(394\) 21.8564 + 5.85641i 1.10111 + 0.295041i
\(395\) 0 0
\(396\) 0 0
\(397\) 9.52628 + 16.5000i 0.478110 + 0.828111i 0.999685 0.0250943i \(-0.00798860\pi\)
−0.521575 + 0.853206i \(0.674655\pi\)
\(398\) −22.5167 22.5167i −1.12866 1.12866i
\(399\) −15.5885 + 18.0000i −0.780399 + 0.901127i
\(400\) 0 0
\(401\) 11.5000 + 19.9186i 0.574283 + 0.994687i 0.996119 + 0.0880147i \(0.0280523\pi\)
−0.421837 + 0.906672i \(0.638614\pi\)
\(402\) −1.90192 7.09808i −0.0948593 0.354020i
\(403\) 3.00000 5.19615i 0.149441 0.258839i
\(404\) 8.66025 + 15.0000i 0.430864 + 0.746278i
\(405\) 0 0
\(406\) 12.3923 8.39230i 0.615020 0.416503i
\(407\) 3.00000 0.148704
\(408\) 2.19615 8.19615i 0.108726 0.405770i
\(409\) −22.5000 12.9904i −1.11255 0.642333i −0.173064 0.984911i \(-0.555367\pi\)
−0.939490 + 0.342578i \(0.888700\pi\)
\(410\) 0 0
\(411\) 0.866025 + 1.50000i 0.0427179 + 0.0739895i
\(412\) 17.3205 0.853320
\(413\) −12.9904 + 4.50000i −0.639215 + 0.221431i
\(414\) 0 0
\(415\) 0 0
\(416\) −18.9282 + 5.07180i −0.928032 + 0.248665i
\(417\) 10.3923 + 6.00000i 0.508913 + 0.293821i
\(418\) 7.09808 + 1.90192i 0.347178 + 0.0930261i
\(419\) −20.7846 −1.01539 −0.507697 0.861536i \(-0.669503\pi\)
−0.507697 + 0.861536i \(0.669503\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 13.6603 + 3.66025i 0.664971 + 0.178178i
\(423\) 0 0
\(424\) 2.73205 0.732051i 0.132680 0.0355515i
\(425\) 0 0
\(426\) 24.2487 + 24.2487i 1.17485 + 1.17485i
\(427\) 13.5000 + 2.59808i 0.653311 + 0.125730i
\(428\) 26.0000i 1.25676i
\(429\) 3.00000 + 5.19615i 0.144841 + 0.250873i
\(430\) 0 0
\(431\) −19.9186 11.5000i −0.959444 0.553936i −0.0634424 0.997985i \(-0.520208\pi\)
−0.896002 + 0.444050i \(0.853541\pi\)
\(432\) −18.0000 + 10.3923i −0.866025 + 0.500000i
\(433\) 10.3923 0.499422 0.249711 0.968320i \(-0.419664\pi\)
0.249711 + 0.968320i \(0.419664\pi\)
\(434\) −0.464102 6.46410i −0.0222776 0.310287i
\(435\) 0 0
\(436\) −15.5885 + 9.00000i −0.746552 + 0.431022i
\(437\) 2.59808 4.50000i 0.124283 0.215264i
\(438\) 5.49038 + 20.4904i 0.262341 + 0.979068i
\(439\) −11.2583 19.5000i −0.537331 0.930684i −0.999047 0.0436563i \(-0.986099\pi\)
0.461716 0.887028i \(1.65277\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 6.00000 + 6.00000i 0.285391 + 0.285391i
\(443\) 8.50000 + 14.7224i 0.403847 + 0.699484i 0.994187 0.107671i \(-0.0343394\pi\)
−0.590339 + 0.807155i \(0.701006\pi\)
\(444\) 9.00000 + 5.19615i 0.427121 + 0.246598i
\(445\) 0 0
\(446\) 9.46410 + 2.53590i 0.448138 + 0.120078i
\(447\) 1.73205i 0.0819232i
\(448\) −13.8564 + 16.0000i −0.654654 + 0.755929i
\(449\) −8.00000 −0.377543 −0.188772 0.982021i \(-0.560451\pi\)
−0.188772 + 0.982021i \(0.560451\pi\)
\(450\) 0 0
\(451\) −1.73205 + 3.00000i −0.0815591 + 0.141264i
\(452\) 16.0000 27.7128i 0.752577 1.30350i
\(453\) 6.06218 + 10.5000i 0.284826 + 0.493333i
\(454\) 19.0526 19.0526i 0.894181 0.894181i
\(455\) 0 0
\(456\) 18.0000 + 18.0000i 0.842927 + 0.842927i
\(457\) 12.9904 7.50000i 0.607664 0.350835i −0.164386 0.986396i \(-0.552564\pi\)
0.772051 + 0.635561i \(0.219231\pi\)
\(458\) −5.70577 21.2942i −0.266613 0.995014i
\(459\) 7.79423 + 4.50000i 0.363803 + 0.210042i
\(460\) 0 0
\(461\) 17.3205i 0.806696i 0.915047 + 0.403348i \(0.132154\pi\)
−0.915047 + 0.403348i \(0.867846\pi\)
\(462\) 5.83013 + 2.83013i 0.271242 + 0.131669i
\(463\) −30.0000 −1.39422 −0.697109 0.716965i \(-0.745531\pi\)
−0.697109 + 0.716965i \(0.745531\pi\)
\(464\) −8.00000 13.8564i −0.371391 0.643268i
\(465\) 0 0
\(466\) −2.56218 9.56218i −0.118691 0.442959i
\(467\) 7.50000 4.33013i 0.347059 0.200374i −0.316330 0.948649i \(-0.602451\pi\)
0.663389 + 0.748275i \(0.269117\pi\)
\(468\) 0 0
\(469\) 7.50000 2.59808i 0.346318 0.119968i
\(470\) 0 0
\(471\) 2.59808 1.50000i 0.119713 0.0691164i
\(472\) 3.80385 + 14.1962i 0.175086 + 0.653431i
\(473\) 1.73205 + 1.00000i 0.0796398 + 0.0459800i
\(474\) 5.70577 21.2942i 0.262075 0.978076i
\(475\) 0 0
\(476\) 9.00000 + 1.73205i 0.412514 + 0.0793884i
\(477\) 0 0
\(478\) −27.3205 7.32051i −1.24961 0.334832i
\(479\) 6.06218 10.5000i 0.276988 0.479757i −0.693647 0.720315i \(-0.743997\pi\)
0.970635 + 0.240558i \(0.0773304\pi\)
\(480\) 0 0
\(481\) −9.00000 + 5.19615i −0.410365 + 0.236924i
\(482\) −5.19615 + 5.19615i −0.236678 + 0.236678i
\(483\) 3.00000 3.46410i 0.136505 0.157622i
\(484\) 20.0000i 0.909091i
\(485\) 0 0
\(486\) 0 0
\(487\) −15.5000 + 26.8468i −0.702372 + 1.21654i 0.265260 + 0.964177i \(0.414542\pi\)
−0.967632 + 0.252367i \(0.918791\pi\)
\(488\) 3.80385 14.1962i 0.172192 0.642630i
\(489\) 36.3731i 1.64485i
\(490\) 0 0
\(491\) 32.0000i 1.44414i 0.691820 + 0.722070i \(0.256809\pi\)
−0.691820 + 0.722070i \(0.743191\pi\)
\(492\) −10.3923 + 6.00000i −0.468521 + 0.270501i
\(493\) −3.46410 + 6.00000i −0.156015 + 0.270226i
\(494\) −24.5885 + 6.58846i −1.10629 + 0.296429i
\(495\) 0 0
\(496\) −6.92820 −0.311086
\(497\) −24.2487 + 28.0000i −1.08770 + 1.25597i
\(498\) −24.0000 24.0000i −1.07547 1.07547i
\(499\) 30.3109 17.5000i 1.35690 0.783408i 0.367697 0.929946i \(-0.380146\pi\)
0.989205 + 0.146538i \(0.0468131\pi\)
\(500\) 0 0
\(501\) 15.0000 25.9808i 0.670151 1.16073i
\(502\) 1.26795 4.73205i 0.0565913 0.211202i
\(503\) 6.92820i 0.308913i −0.988000 0.154457i \(-0.950637\pi\)
0.988000 0.154457i \(-0.0493627\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −1.36603 0.366025i −0.0607272 0.0162718i
\(507\) 1.50000 + 0.866025i 0.0666173 + 0.0384615i
\(508\) 10.3923 + 6.00000i 0.461084 + 0.266207i
\(509\) −10.5000 + 6.06218i −0.465404 + 0.268701i −0.714314 0.699825i \(-0.753261\pi\)
0.248910 + 0.968527i \(0.419928\pi\)
\(510\) 0 0
\(511\) −21.6506 + 7.50000i −0.957768 + 0.331780i
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) −23.3827 + 13.5000i −1.03237 + 0.596040i
\(514\) 7.09808 1.90192i 0.313083 0.0838903i
\(515\) 0 0
\(516\) 3.46410 + 6.00000i 0.152499 + 0.264135i
\(517\) −8.66025 −0.380878
\(518\) −4.90192 + 10.0981i −0.215378 + 0.443684i
\(519\) 21.0000i 0.921798i
\(520\) 0 0
\(521\) 1.50000 + 0.866025i 0.0657162 + 0.0379413i 0.532498 0.846431i \(-0.321253\pi\)
−0.466782 + 0.884372i \(0.654587\pi\)
\(522\) 0 0
\(523\) −22.5000 + 12.9904i −0.983856 + 0.568030i −0.903432 0.428731i \(-0.858961\pi\)
−0.0804241 + 0.996761i \(0.525627\pi\)
\(524\) 10.3923i 0.453990i
\(525\) 0 0
\(526\) −23.0000 23.0000i −1.00285 1.00285i
\(527\) 1.50000 + 2.59808i 0.0653410 + 0.113174i
\(528\) 3.46410 6.00000i 0.150756 0.261116i
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) 0 0
\(531\) 0 0
\(532\) −18.0000 + 20.7846i −0.780399 + 0.901127i
\(533\) 12.0000i 0.519778i
\(534\) 9.88269 36.8827i 0.427666 1.59607i
\(535\) 0 0
\(536\) −2.19615 8.19615i −0.0948593 0.354020i
\(537\) −16.4545 28.5000i −0.710063 1.22987i
\(538\) −22.5167 + 22.5167i −0.970762 + 0.970762i
\(539\) −2.59808 + 6.50000i −0.111907 + 0.279975i
\(540\) 0 0
\(541\) 9.50000 + 16.4545i 0.408437 + 0.707433i 0.994715 0.102677i \(-0.0327407\pi\)
−0.586278 + 0.810110i \(0.699407\pi\)
\(542\) −21.2942 + 5.70577i −0.914665 + 0.245084i
\(543\) −6.00000 + 10.3923i −0.257485 + 0.445976i
\(544\) 2.53590 9.46410i 0.108726 0.405770i
\(545\) 0 0
\(546\) −22.3923 + 1.60770i −0.958302 + 0.0688030i
\(547\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(548\) 1.00000 + 1.73205i 0.0427179 + 0.0739895i
\(549\) 0 0
\(550\) 0 0
\(551\) −10.3923 18.0000i −0.442727 0.766826i
\(552\) −3.46410 3.46410i −0.147442 0.147442i
\(553\) 23.3827 + 4.50000i 0.994333 + 0.191359i
\(554\) 13.0000 13.0000i 0.552317 0.552317i
\(555\) 0 0
\(556\) 12.0000 + 6.92820i 0.508913 + 0.293821i
\(557\) −32.0429 18.5000i −1.35770 0.783870i −0.368389 0.929672i \(-0.620091\pi\)
−0.989314 + 0.145802i \(0.953424\pi\)
\(558\) 0 0
\(559\) −6.92820 −0.293032
\(560\) 0 0
\(561\) −3.00000 −0.126660
\(562\) −1.46410 + 5.46410i −0.0617594 + 0.230489i
\(563\) −19.5000 11.2583i −0.821827 0.474482i 0.0292191 0.999573i \(-0.490698\pi\)
−0.851046 + 0.525091i \(0.824031\pi\)
\(564\) −25.9808 15.0000i −1.09399 0.631614i
\(565\) 0 0
\(566\) −12.1244 + 12.1244i −0.509625 + 0.509625i
\(567\) −22.5000 + 7.79423i −0.944911 + 0.327327i
\(568\) 28.0000 + 28.0000i 1.17485 + 1.17485i
\(569\) −6.50000 11.2583i −0.272494 0.471974i 0.697006 0.717066i \(-0.254515\pi\)
−0.969500 + 0.245092i \(0.921182\pi\)
\(570\) 0 0
\(571\) 18.1865 + 10.5000i 0.761083 + 0.439411i 0.829684 0.558233i \(-0.188520\pi\)
−0.0686016 + 0.997644i \(0.521854\pi\)
\(572\) 3.46410 + 6.00000i 0.144841 + 0.250873i
\(573\) 1.73205 0.0723575
\(574\) −7.26795 10.7321i −0.303358 0.447947i
\(575\) 0 0
\(576\) 0 0
\(577\) 16.4545 28.5000i 0.685009 1.18647i −0.288425 0.957503i \(-0.593132\pi\)
0.973434 0.228968i \(-0.0735351\pi\)
\(578\) 19.1244 5.12436i 0.795468 0.213145i
\(579\) 12.9904 + 22.5000i 0.539862 + 0.935068i
\(580\) 0 0
\(581\) 24.0000 27.7128i 0.995688 1.14972i
\(582\) 30.0000 30.0000i 1.24354 1.24354i
\(583\) −0.500000 0.866025i −0.0207079 0.0358671i
\(584\) 6.33975 + 23.6603i 0.262341 + 0.979068i
\(585\) 0 0
\(586\) 7.60770 28.3923i 0.314271 1.17288i
\(587\) 6.92820i 0.285958i −0.989726 0.142979i \(-0.954332\pi\)
0.989726 0.142979i \(-0.0456681\pi\)
\(588\) −19.0526 + 15.0000i −0.785714 + 0.618590i
\(589\) −9.00000 −0.370839
\(590\) 0 0
\(591\) 13.8564 24.0000i 0.569976 0.987228i
\(592\) 10.3923 + 6.00000i 0.427121 + 0.246598i
\(593\) 7.79423 + 13.5000i 0.320071 + 0.554379i 0.980502 0.196508i \(-0.0629600\pi\)
−0.660432 + 0.750886i \(0.729627\pi\)
\(594\) 5.19615 + 5.19615i 0.213201 + 0.213201i
\(595\) 0 0
\(596\) 2.00000i 0.0819232i
\(597\) −33.7750 + 19.5000i −1.38232 + 0.798082i
\(598\) 4.73205 1.26795i 0.193508 0.0518503i
\(599\) 14.7224 + 8.50000i 0.601542 + 0.347301i 0.769648 0.638468i \(-0.220432\pi\)
−0.168106 + 0.985769i \(0.553765\pi\)
\(600\) 0 0
\(601\) 38.1051i 1.55434i −0.629291 0.777170i \(-0.716654\pi\)
0.629291 0.777170i \(-0.283346\pi\)
\(602\) −6.19615 + 4.19615i −0.252536 + 0.171022i
\(603\) 0 0
\(604\) 7.00000 + 12.1244i 0.284826 + 0.493333i
\(605\) 0 0
\(606\) 20.4904 5.49038i 0.832365 0.223031i
\(607\) −13.5000 + 7.79423i −0.547948 + 0.316358i −0.748294 0.663367i \(-0.769127\pi\)
0.200346 + 0.979725i \(0.435793\pi\)
\(608\) 20.7846 + 20.7846i 0.842927 + 0.842927i
\(609\) −6.00000 17.3205i −0.243132 0.701862i
\(610\) 0 0
\(611\) 25.9808 15.0000i 1.05107 0.606835i
\(612\) 0 0
\(613\) −26.8468 15.5000i −1.08433 0.626039i −0.152270 0.988339i \(-0.548658\pi\)
−0.932062 + 0.362300i \(0.881992\pi\)
\(614\) −28.3923 7.60770i −1.14582 0.307022i
\(615\) 0 0
\(616\) 6.73205 + 3.26795i 0.271242 + 0.131669i
\(617\) 20.0000i 0.805170i 0.915383 + 0.402585i \(0.131888\pi\)
−0.915383 + 0.402585i \(0.868112\pi\)
\(618\) 5.49038 20.4904i 0.220856 0.824244i
\(619\) −7.79423 + 13.5000i −0.313276 + 0.542611i −0.979070 0.203526i \(-0.934760\pi\)
0.665793 + 0.746136i \(0.268093\pi\)
\(620\) 0 0
\(621\) 4.50000 2.59808i 0.180579 0.104257i
\(622\) −8.66025 8.66025i −0.347245 0.347245i
\(623\) 40.5000 + 7.79423i 1.62260 + 0.312269i
\(624\) 24.0000i 0.960769i
\(625\) 0 0
\(626\) −2.36603 + 0.633975i −0.0945654 + 0.0253387i
\(627\) 4.50000 7.79423i 0.179713 0.311272i
\(628\) 3.00000 1.73205i 0.119713 0.0691164i
\(629\) 5.19615i 0.207184i
\(630\) 0 0
\(631\) 30.0000i 1.19428i 0.802137 + 0.597141i \(0.203697\pi\)
−0.802137 + 0.597141i \(0.796303\pi\)
\(632\) 6.58846 24.5885i 0.262075 0.978076i
\(633\) 8.66025 15.0000i 0.344214 0.596196i
\(634\) −4.02628 15.0263i −0.159904 0.596770i
\(635\) 0 0
\(636\) 3.46410i 0.137361i
\(637\) −3.46410 24.0000i −0.137253 0.950915i
\(638\) −4.00000 + 4.00000i −0.158362 + 0.158362i
\(639\) 0 0
\(640\) 0 0
\(641\) 6.50000 11.2583i 0.256735 0.444677i −0.708631 0.705580i \(-0.750687\pi\)
0.965365 + 0.260902i \(0.0840201\pi\)
\(642\) 30.7583 + 8.24167i 1.21393 + 0.325273i
\(643\) 13.8564i 0.546443i −0.961951 0.273222i \(-0.911911\pi\)
0.961951 0.273222i \(-0.0880892\pi\)
\(644\) 3.46410 4.00000i 0.136505 0.157622i
\(645\) 0 0
\(646\) 3.29423 12.2942i 0.129610 0.483710i
\(647\) −28.5000 16.4545i −1.12045 0.646892i −0.178935 0.983861i \(-0.557265\pi\)
−0.941516 + 0.336968i \(0.890598\pi\)
\(648\) 6.58846 + 24.5885i 0.258819 + 0.965926i
\(649\) 4.50000 2.59808i 0.176640 0.101983i
\(650\) 0 0
\(651\) −7.79423 1.50000i −0.305480 0.0587896i
\(652\) 42.0000i 1.64485i
\(653\) −26.8468 + 15.5000i −1.05060 + 0.606562i −0.922816 0.385241i \(-0.874118\pi\)
−0.127780 + 0.991803i \(0.540785\pi\)
\(654\) 5.70577 + 21.2942i 0.223113 + 0.832670i
\(655\) 0 0
\(656\) −12.0000 + 6.92820i −0.468521 + 0.270501i
\(657\) 0 0
\(658\) 14.1506 29.1506i 0.551649 1.13641i
\(659\) 38.0000i 1.48027i 0.672458 + 0.740135i \(0.265238\pi\)
−0.672458 + 0.740135i \(0.734762\pi\)
\(660\) 0 0
\(661\) −34.5000 19.9186i −1.34189 0.774743i −0.354809 0.934939i \(-0.615454\pi\)
−0.987085 + 0.160196i \(0.948788\pi\)
\(662\) 2.56218 + 9.56218i 0.0995819 + 0.371645i
\(663\) 9.00000 5.19615i 0.349531 0.201802i
\(664\) −27.7128 27.7128i −1.07547 1.07547i
\(665\) 0 0
\(666\) 0 0
\(667\) 2.00000 + 3.46410i 0.0774403 + 0.134131i
\(668\) 17.3205 30.0000i 0.670151 1.16073i
\(669\) 6.00000 10.3923i 0.231973 0.401790i
\(670\) 0 0
\(671\) −5.19615 −0.200595
\(672\) 14.5359 + 21.4641i 0.560734 + 0.827996i
\(673\) 24.0000i 0.925132i −0.886585 0.462566i \(-0.846929\pi\)
0.886585 0.462566i \(-0.153071\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 1.73205 + 1.00000i 0.0666173 + 0.0384615i
\(677\) −21.6506 37.5000i −0.832102 1.44124i −0.896369 0.443309i \(-0.853804\pi\)
0.0642672 0.997933i \(-0.479529\pi\)
\(678\) −27.7128 27.7128i −1.06430 1.06430i
\(679\) 34.6410 + 30.0000i 1.32940 + 1.15129i
\(680\) 0 0
\(681\) −16.5000 28.5788i −0.632281 1.09514i
\(682\) 0.633975 + 2.36603i 0.0242761 + 0.0905998i
\(683\) 12.5000 21.6506i 0.478299 0.828439i −0.521391 0.853318i \(-0.674587\pi\)
0.999690 + 0.0248792i \(0.00792011\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −17.6340 19.3660i −0.673268 0.739398i
\(687\) −27.0000 −1.03011
\(688\) 4.00000 + 6.92820i 0.152499 + 0.264135i
\(689\) 3.00000 + 1.73205i 0.114291 + 0.0659859i
\(690\) 0 0
\(691\) 6.06218 + 10.5000i 0.230616 + 0.399439i 0.957990 0.286803i \(-0.0925925\pi\)
−0.727373 + 0.686242i \(0.759259\pi\)
\(692\) 24.2487i 0.921798i
\(693\) 0 0
\(694\) −13.0000 13.0000i −0.493473 0.493473i
\(695\) 0 0
\(696\) −18.9282 + 5.07180i −0.717472 + 0.192246i
\(697\) 5.19615 + 3.00000i 0.196818 + 0.113633i
\(698\) 14.1962 + 3.80385i 0.537332 + 0.143978i
\(699\) −12.1244 −0.458585
\(700\) 0 0
\(701\) −26.0000 −0.982006 −0.491003 0.871158i \(-0.663370\pi\)
−0.491003 + 0.871158i \(0.663370\pi\)
\(702\) −24.5885 6.58846i −0.928032 0.248665i
\(703\) 13.5000 + 7.79423i 0.509162 + 0.293965i
\(704\) 4.00000 6.92820i 0.150756 0.261116i
\(705\) 0 0
\(706\) 29.4449 + 29.4449i 1.10817 + 1.10817i
\(707\) 7.50000 + 21.6506i 0.282067 + 0.814256i
\(708\) 18.0000 0.676481
\(709\) −4.50000 7.79423i −0.169001 0.292718i 0.769068 0.639167i \(-0.220721\pi\)
−0.938069 + 0.346449i \(0.887387\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 11.4115 42.5885i 0.427666 1.59607i
\(713\) 1.73205 0.0648658
\(714\) 4.90192 10.0981i 0.183450 0.377911i
\(715\) 0 0
\(716\) −19.0000 32.9090i −0.710063 1.22987i
\(717\) −17.3205 + 30.0000i −0.646846 + 1.12037i
\(718\) 8.41858 + 31.4186i 0.314179 + 1.17253i
\(719\) −12.9904 22.5000i −0.484459 0.839108i 0.515381 0.856961i \(-0.327650\pi\)
−0.999841 + 0.0178527i \(0.994317\pi\)
\(720\) 0 0
\(721\) 22.5000 + 4.33013i 0.837944 + 0.161262i
\(722\) 8.00000 + 8.00000i 0.297729 + 0.297729i
\(723\) 4.50000 + 7.79423i 0.167357 + 0.289870i
\(724\) −6.92820 + 12.0000i −0.257485 + 0.445976i
\(725\) 0 0
\(726\) 23.6603 + 6.33975i 0.878114 + 0.235290i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) −25.8564 + 1.85641i −0.958302 + 0.0688030i
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) 1.73205 3.00000i 0.0640622 0.110959i
\(732\) −15.5885 9.00000i −0.576166 0.332650i
\(733\) −21.6506 37.5000i −0.799684 1.38509i −0.919822 0.392337i \(-0.871667\pi\)
0.120137 0.992757i \(-0.461667\pi\)
\(734\) 1.73205 1.73205i 0.0639312 0.0639312i
\(735\) 0 0
\(736\) −4.00000 4.00000i −0.147442 0.147442i
\(737\) −2.59808 + 1.50000i −0.0957014 + 0.0552532i
\(738\) 0 0
\(739\) 44.1673 + 25.5000i 1.62472 + 0.938033i 0.985634 + 0.168898i \(0.0540208\pi\)
0.639087 + 0.769135i \(0.279313\pi\)
\(740\) 0 0
\(741\) 31.1769i 1.14531i
\(742\) 3.73205 0.267949i 0.137008 0.00983672i
\(743\) −34.0000 −1.24734 −0.623670 0.781688i \(-0.714359\pi\)
−0.623670 + 0.781688i \(0.714359\pi\)
\(744\) −2.19615 + 8.19615i −0.0805149 + 0.300486i
\(745\) 0 0
\(746\) −10.6147 39.6147i −0.388633 1.45040i
\(747\) 0 0
\(748\) −3.46410 −0.126660
\(749\) −6.50000 + 33.7750i −0.237505 + 1.23411i
\(750\) 0 0
\(751\) −21.6506 + 12.5000i −0.790043 + 0.456131i −0.839978 0.542621i \(-0.817432\pi\)
0.0499348 + 0.998752i \(0.484099\pi\)
\(752\) −30.0000 17.3205i −1.09399 0.631614i
\(753\) −5.19615 3.00000i −0.189358 0.109326i
\(754\) 5.07180 18.9282i 0.184704 0.689325i
\(755\) 0 0
\(756\) −25.9808 + 9.00000i −0.944911 + 0.327327i
\(757\) 48.0000i 1.74459i −0.488980 0.872295i \(-0.662631\pi\)
0.488980 0.872295i \(-0.337369\pi\)
\(758\) 10.9282 + 2.92820i 0.396930 + 0.106357i
\(759\) −0.866025 + 1.50000i −0.0314347 + 0.0544466i
\(760\) 0 0
\(761\) 16.5000 9.52628i 0.598125 0.345327i −0.170179 0.985413i \(-0.554435\pi\)
0.768303 + 0.640086i \(0.221101\pi\)
\(762\) 10.3923 10.3923i 0.376473 0.376473i
\(763\) −22.5000 + 7.79423i −0.814555 + 0.282170i
\(764\) 2.00000 0.0723575
\(765\) 0 0
\(766\) 1.90192 + 7.09808i 0.0687193 + 0.256464i
\(767\) −9.00000 + 15.5885i −0.324971 + 0.562867i
\(768\) 24.0000 13.8564i 0.866025 0.500000i
\(769\) 3.46410i 0.124919i −0.998048 0.0624593i \(-0.980106\pi\)
0.998048 0.0624593i \(-0.0198944\pi\)
\(770\) 0 0
\(771\) 9.00000i 0.324127i
\(772\) 15.0000 + 25.9808i 0.539862 + 0.935068i
\(773\) 12.9904 22.5000i 0.467232 0.809269i −0.532068 0.846702i \(-0.678585\pi\)
0.999299 + 0.0374331i \(0.0119181\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 34.6410 34.6410i 1.24354 1.24354i
\(777\) 10.3923 + 9.00000i 0.372822 + 0.322873i
\(778\) 19.0000 + 19.0000i 0.681183 + 0.681183i
\(779\) −15.5885 + 9.00000i −0.558514 + 0.322458i
\(780\) 0 0
\(781\) 7.00000 12.1244i 0.250480 0.433844i
\(782\) −0.633975 + 2.36603i −0.0226709 + 0.0846089i
\(783\) 20.7846i 0.742781i
\(784\) −22.0000 +