Properties

Label 700.2.t.a.299.1
Level $700$
Weight $2$
Character 700.299
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 299.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 700.299
Dual form 700.2.t.a.199.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 + 0.366025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(1.73205 - 1.00000i) q^{4} +(1.73205 - 1.73205i) q^{6} +(-2.00000 + 1.73205i) q^{7} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(-1.36603 + 0.366025i) 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} +(2.09808 - 3.09808i) 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} +(1.26795 - 4.73205i) q^{24} +(-4.73205 + 1.26795i) q^{26} -5.19615i q^{27} +(-1.73205 + 5.00000i) q^{28} -4.00000 q^{29} +(0.866025 + 1.50000i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(0.866025 - 1.50000i) q^{33} +(1.73205 + 1.73205i) q^{34} +(-2.59808 - 1.50000i) q^{37} +(1.90192 - 7.09808i) q^{38} +(-5.19615 + 3.00000i) q^{39} -3.46410i q^{41} +(-0.464102 + 6.46410i) q^{42} +2.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(0.366025 - 1.36603i) 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} +(1.90192 + 7.09808i) q^{54} +(0.535898 - 7.46410i) q^{56} -9.00000i q^{57} +(5.46410 - 1.46410i) q^{58} +(-2.59808 - 4.50000i) q^{59} +(-4.50000 - 2.59808i) q^{61} +(-1.73205 - 1.73205i) q^{62} -8.00000i q^{64} +(-0.633975 + 2.36603i) 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} +(4.09808 + 1.09808i) 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} +(1.26795 + 4.73205i) q^{82} -13.8564i q^{83} +(-1.73205 - 9.00000i) q^{84} +(-2.73205 + 0.732051i) q^{86} +(6.00000 - 3.46410i) q^{87} +(0.732051 - 2.73205i) q^{88} +(-13.5000 - 7.79423i) q^{89} +(-6.92820 + 6.00000i) q^{91} +2.00000i q^{92} +(-2.59808 - 1.50000i) q^{93} +(11.8301 + 3.16987i) q^{94} +(-2.53590 - 9.46410i) q^{96} +17.3205 q^{97} +(1.16987 + 9.83013i) 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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 + 0.366025i −0.965926 + 0.258819i
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.500000\pi\)
\(4\) 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 \(-0.714837\pi\)
0.363727 + 0.931505i \(0.381504\pi\)
\(12\) −1.73205 + 3.00000i −0.500000 + 0.866025i
\(13\) 3.46410 0.960769 0.480384 0.877058i \(-0.340497\pi\)
0.480384 + 0.877058i \(0.340497\pi\)
\(14\) 2.09808 3.09808i 0.560734 0.827996i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −0.866025 1.50000i −0.210042 0.363803i 0.741685 0.670748i \(-0.234027\pi\)
−0.951727 + 0.306944i \(0.900693\pi\)
\(18\) 0 0
\(19\) −2.59808 + 4.50000i −0.596040 + 1.03237i 0.397360 + 0.917663i \(0.369927\pi\)
−0.993399 + 0.114708i \(0.963407\pi\)
\(20\) 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 −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 1.26795 4.73205i 0.258819 0.965926i
\(25\) 0 0
\(26\) −4.73205 + 1.26795i −0.928032 + 0.248665i
\(27\) 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 \(-0.116954\pi\)
−0.777714 + 0.628619i \(0.783621\pi\)
\(32\) −1.46410 + 5.46410i −0.258819 + 0.965926i
\(33\) 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 \(-0.412646\pi\)
−0.698119 + 0.715981i \(0.745980\pi\)
\(38\) 1.90192 7.09808i 0.308533 1.15146i
\(39\) −5.19615 + 3.00000i −0.832050 + 0.480384i
\(40\) 0 0
\(41\) 3.46410i 0.541002i −0.962720 0.270501i \(-0.912811\pi\)
0.962720 0.270501i \(-0.0871893\pi\)
\(42\) −0.464102 + 6.46410i −0.0716124 + 0.997433i
\(43\) 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
\(46\) 0.366025 1.36603i 0.0539675 0.201409i
\(47\) −7.50000 4.33013i −1.09399 0.631614i −0.159352 0.987222i \(-0.550941\pi\)
−0.934635 + 0.355608i \(0.884274\pi\)
\(48\) 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 \(-0.644788\pi\)
0.558298 + 0.829640i \(0.311454\pi\)
\(54\) 1.90192 + 7.09808i 0.258819 + 0.965926i
\(55\) 0 0
\(56\) 0.535898 7.46410i 0.0716124 0.997433i
\(57\) 9.00000i 1.19208i
\(58\) 5.46410 1.46410i 0.717472 0.192246i
\(59\) −2.59808 4.50000i −0.338241 0.585850i 0.645861 0.763455i \(-0.276498\pi\)
−0.984102 + 0.177605i \(0.943165\pi\)
\(60\) 0 0
\(61\) −4.50000 2.59808i −0.576166 0.332650i 0.183442 0.983030i \(-0.441276\pi\)
−0.759608 + 0.650381i \(0.774609\pi\)
\(62\) −1.73205 1.73205i −0.219971 0.219971i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) −0.633975 + 2.36603i −0.0780369 + 0.291238i
\(67\) −1.50000 2.59808i −0.183254 0.317406i 0.759733 0.650236i \(-0.225330\pi\)
−0.942987 + 0.332830i \(0.891996\pi\)
\(68\) −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 −0.999969 0.00787336i \(-0.997494\pi\)
0.493166 0.869935i \(-0.335840\pi\)
\(74\) 4.09808 + 1.09808i 0.476392 + 0.127649i
\(75\) 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 \(-0.164350\pi\)
0.00727784 + 0.999974i \(0.497683\pi\)
\(80\) 0 0
\(81\) 4.50000 + 7.79423i 0.500000 + 0.866025i
\(82\) 1.26795 + 4.73205i 0.140022 + 0.522568i
\(83\) 13.8564i 1.52094i −0.649374 0.760469i \(-0.724969\pi\)
0.649374 0.760469i \(-0.275031\pi\)
\(84\) −1.73205 9.00000i −0.188982 0.981981i
\(85\) 0 0
\(86\) −2.73205 + 0.732051i −0.294605 + 0.0789391i
\(87\) 6.00000 3.46410i 0.643268 0.371391i
\(88\) 0.732051 2.73205i 0.0780369 0.291238i
\(89\) −13.5000 7.79423i −1.43100 0.826187i −0.433800 0.901009i \(-0.642828\pi\)
−0.997197 + 0.0748225i \(0.976161\pi\)
\(90\) 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
\(94\) 11.8301 + 3.16987i 1.22018 + 0.326947i
\(95\) 0 0
\(96\) −2.53590 9.46410i −0.258819 0.965926i
\(97\) 17.3205 1.75863 0.879316 0.476240i \(-0.158000\pi\)
0.879316 + 0.476240i \(0.158000\pi\)
\(98\) 1.16987 + 9.83013i 0.118175 + 0.992993i
\(99\) 0 0
\(100\) 0 0
\(101\) −7.50000 + 4.33013i −0.746278 + 0.430864i −0.824347 0.566084i \(-0.808458\pi\)
0.0780696 + 0.996948i \(0.475124\pi\)
\(102\) −4.09808 1.09808i −0.405770 0.108726i
\(103\) −7.50000 4.33013i −0.738997 0.426660i 0.0827075 0.996574i \(-0.473643\pi\)
−0.821705 + 0.569914i \(0.806977\pi\)
\(104\) −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 0.359498 + 0.933146i \(0.382948\pi\)
−0.987877 + 0.155238i \(0.950386\pi\)
\(108\) −5.19615 9.00000i −0.500000 0.866025i
\(109\) 4.50000 + 7.79423i 0.431022 + 0.746552i 0.996962 0.0778949i \(-0.0248199\pi\)
−0.565940 + 0.824447i \(0.691487\pi\)
\(110\) 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 \(0.728811\pi\)
\(114\) 3.29423 + 12.2942i 0.308533 + 1.15146i
\(115\) 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
\(122\) 7.09808 + 1.90192i 0.642630 + 0.172192i
\(123\) 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 \(0.585770\pi\)
\(128\) 2.92820 + 10.9282i 0.258819 + 0.965926i
\(129\) −3.00000 + 1.73205i −0.264135 + 0.152499i
\(130\) 0 0
\(131\) −2.59808 + 4.50000i −0.226995 + 0.393167i −0.956916 0.290365i \(-0.906223\pi\)
0.729921 + 0.683531i \(0.239557\pi\)
\(132\) 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
\(136\) 4.73205 + 1.26795i 0.405770 + 0.108726i
\(137\) 0.866025 0.500000i 0.0739895 0.0427179i −0.462549 0.886594i \(-0.653065\pi\)
0.536538 + 0.843876i \(0.319732\pi\)
\(138\) 0.633975 + 2.36603i 0.0539675 + 0.201409i
\(139\) 6.92820 0.587643 0.293821 0.955860i \(-0.405073\pi\)
0.293821 + 0.955860i \(0.405073\pi\)
\(140\) 0 0
\(141\) 15.0000 1.26323
\(142\) 5.12436 + 19.1244i 0.430026 + 1.60488i
\(143\) −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 −0.844818 0.535054i \(-0.820291\pi\)
0.885779 + 0.464107i \(0.153625\pi\)
\(150\) 0 0
\(151\) 6.06218 3.50000i 0.493333 0.284826i −0.232623 0.972567i \(-0.574731\pi\)
0.725956 + 0.687741i \(0.241398\pi\)
\(152\) −3.80385 14.1962i −0.308533 1.15146i
\(153\) 0 0
\(154\) −0.267949 + 3.73205i −0.0215920 + 0.300737i
\(155\) 0 0
\(156\) −6.00000 + 10.3923i −0.480384 + 0.832050i
\(157\) 0.866025 + 1.50000i 0.0691164 + 0.119713i 0.898513 0.438948i \(-0.144649\pi\)
−0.829396 + 0.558661i \(0.811315\pi\)
\(158\) −12.2942 3.29423i −0.978076 0.262075i
\(159\) −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 0.0814491 + 0.996678i \(0.474045\pi\)
−0.903873 + 0.427802i \(0.859288\pi\)
\(164\) −3.46410 6.00000i −0.270501 0.468521i
\(165\) 0 0
\(166\) 5.07180 + 18.9282i 0.393648 + 1.46911i
\(167\) 17.3205i 1.34030i −0.742225 0.670151i \(-0.766230\pi\)
0.742225 0.670151i \(-0.233770\pi\)
\(168\) 5.66025 + 11.6603i 0.436698 + 0.899608i
\(169\) −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 \(-0.985806\pi\)
0.538107 + 0.842876i \(0.319140\pi\)
\(174\) −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
\(178\) 21.2942 + 5.70577i 1.59607 + 0.427666i
\(179\) −16.4545 + 9.50000i −1.22987 + 0.710063i −0.967002 0.254770i \(-0.918000\pi\)
−0.262864 + 0.964833i \(0.584667\pi\)
\(180\) 0 0
\(181\) 6.92820i 0.514969i 0.966282 + 0.257485i \(0.0828937\pi\)
−0.966282 + 0.257485i \(0.917106\pi\)
\(182\) 7.26795 10.7321i 0.538736 0.795513i
\(183\) 9.00000 0.665299
\(184\) −0.732051 2.73205i −0.0539675 0.201409i
\(185\) 0 0
\(186\) 4.09808 + 1.09808i 0.300486 + 0.0805149i
\(187\) 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 \(-0.321815\pi\)
−0.468341 + 0.883548i \(0.655148\pi\)
\(192\) 6.92820 + 12.0000i 0.500000 + 0.866025i
\(193\) 12.9904 7.50000i 0.935068 0.539862i 0.0466572 0.998911i \(-0.485143\pi\)
0.888411 + 0.459049i \(0.151810\pi\)
\(194\) −23.6603 + 6.33975i −1.69871 + 0.455167i
\(195\) 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 −0.920864 0.389885i \(-0.872515\pi\)
0.122782 0.992434i \(1.53918\pi\)
\(200\) 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
\(206\) 11.8301 + 3.16987i 0.824244 + 0.220856i
\(207\) 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
\(214\) 4.75833 17.7583i 0.325273 1.21393i
\(215\) 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
\(222\) −7.09808 + 1.90192i −0.476392 + 0.127649i
\(223\) 6.92820i 0.463947i −0.972722 0.231973i \(-0.925482\pi\)
0.972722 0.231973i \(-0.0745182\pi\)
\(224\) −6.53590 13.4641i −0.436698 0.899608i
\(225\) 0 0
\(226\) −5.85641 21.8564i −0.389562 1.45387i
\(227\) 16.5000 9.52628i 1.09514 0.632281i 0.160202 0.987084i \(-0.448785\pi\)
0.934941 + 0.354803i \(0.115452\pi\)
\(228\) −9.00000 15.5885i −0.596040 1.03237i
\(229\) 13.5000 + 7.79423i 0.892105 + 0.515057i 0.874630 0.484790i \(-0.161104\pi\)
0.0174746 + 0.999847i \(0.494437\pi\)
\(230\) 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 \(-0.406975\pi\)
−0.685252 + 0.728306i \(0.740308\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −9.00000 5.19615i −0.585850 0.338241i
\(237\) −15.5885 −1.01258
\(238\) −6.46410 0.464102i −0.419005 0.0300832i
\(239\) 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 −0.637883 0.770133i \(-0.720190\pi\)
0.348013 + 0.937490i \(0.386857\pi\)
\(242\) 3.66025 13.6603i 0.235290 0.878114i
\(243\) 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
\(248\) −4.73205 1.26795i −0.300486 0.0805149i
\(249\) 12.0000 + 20.7846i 0.760469 + 1.31717i
\(250\) 0 0
\(251\) −3.46410 −0.218652 −0.109326 0.994006i \(-0.534869\pi\)
−0.109326 + 0.994006i \(0.534869\pi\)
\(252\) 0 0
\(253\) 1.00000i 0.0628695i
\(254\) 8.19615 2.19615i 0.514272 0.137799i
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −2.59808 + 4.50000i −0.162064 + 0.280702i −0.935609 0.353039i \(-0.885148\pi\)
0.773545 + 0.633741i \(0.218482\pi\)
\(258\) 3.46410 3.46410i 0.215666 0.215666i
\(259\) 7.79423 1.50000i 0.484310 0.0932055i
\(260\) 0 0
\(261\) 0 0
\(262\) 1.90192 7.09808i 0.117501 0.438521i
\(263\) 11.5000 + 19.9186i 0.709120 + 1.22823i 0.965184 + 0.261573i \(0.0842411\pi\)
−0.256063 + 0.966660i \(0.582426\pi\)
\(264\) 1.26795 + 4.73205i 0.0780369 + 0.291238i
\(265\) 0 0
\(266\) 8.49038 + 17.4904i 0.520579 + 1.07240i
\(267\) 27.0000 1.65237
\(268\) −5.19615 3.00000i −0.317406 0.183254i
\(269\) −19.5000 + 11.2583i −1.18894 + 0.686433i −0.958065 0.286552i \(-0.907491\pi\)
−0.230871 + 0.972984i \(0.574158\pi\)
\(270\) 0 0
\(271\) 7.79423 13.5000i 0.473466 0.820067i −0.526073 0.850439i \(-0.676336\pi\)
0.999539 + 0.0303728i \(0.00966946\pi\)
\(272\) −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 \(-0.794381\pi\)
0.122068 + 0.992522i \(0.461047\pi\)
\(278\) −9.46410 + 2.53590i −0.567619 + 0.152093i
\(279\) 0 0
\(280\) 0 0
\(281\) −4.00000 −0.238620 −0.119310 0.992857i \(-0.538068\pi\)
−0.119310 + 0.992857i \(0.538068\pi\)
\(282\) −20.4904 + 5.49038i −1.22018 + 0.326947i
\(283\) −10.5000 + 6.06218i −0.624160 + 0.360359i −0.778487 0.627661i \(-0.784012\pi\)
0.154327 + 0.988020i \(0.450679\pi\)
\(284\) −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 \(-0.707677\pi\)
−0.607125 + 0.794606i \(0.707677\pi\)
\(294\) −10.2679 13.7321i −0.598839 0.800869i
\(295\) 0 0
\(296\) 8.19615 2.19615i 0.476392 0.127649i
\(297\) 2.59808 + 4.50000i 0.150756 + 0.261116i
\(298\) −0.366025 + 1.36603i −0.0212033 + 0.0791317i
\(299\) −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 \(0.202104\pi\)
−0.805114 + 0.593120i \(0.797896\pi\)
\(308\) −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 \(-0.245632\pi\)
−0.962283 + 0.272050i \(0.912298\pi\)
\(312\) 4.39230 16.3923i 0.248665 0.928032i
\(313\) 0.866025 1.50000i 0.0489506 0.0847850i −0.840512 0.541793i \(-0.817746\pi\)
0.889463 + 0.457008i \(0.151079\pi\)
\(314\) −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 \(-0.433298\pi\)
−0.743070 + 0.669214i \(0.766631\pi\)
\(318\) 0.633975 2.36603i 0.0355515 0.132680i
\(319\) 3.46410 2.00000i 0.193952 0.111979i
\(320\) 0 0
\(321\) 22.5167i 1.25676i
\(322\) 1.63397 + 3.36603i 0.0910578 + 0.187581i
\(323\) 9.00000 0.500773
\(324\) 15.5885 + 9.00000i 0.866025 + 0.500000i
\(325\) 0 0
\(326\) 7.68653 28.6865i 0.425718 1.58880i
\(327\) −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 \(-0.271714\pi\)
−0.324057 + 0.946038i \(0.605047\pi\)
\(332\) −13.8564 24.0000i −0.760469 1.31717i
\(333\) 0 0
\(334\) 6.33975 + 23.6603i 0.346895 + 1.29463i
\(335\) 0 0
\(336\) −12.0000 13.8564i −0.654654 0.755929i
\(337\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(338\) 1.36603 0.366025i 0.0743020 0.0199092i
\(339\) −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
\(346\) 4.43782 16.5622i 0.238579 0.890388i
\(347\) 6.50000 + 11.2583i 0.348938 + 0.604379i 0.986061 0.166383i \(-0.0532089\pi\)
−0.637123 + 0.770762i \(0.719876\pi\)
\(348\) 6.92820 12.0000i 0.371391 0.643268i
\(349\) 10.3923i 0.556287i −0.960539 0.278144i \(-0.910281\pi\)
0.960539 0.278144i \(-0.0897191\pi\)
\(350\) 0 0
\(351\) 18.0000i 0.960769i
\(352\) −1.46410 5.46410i −0.0780369 0.291238i
\(353\) 14.7224 + 25.5000i 0.783596 + 1.35723i 0.929834 + 0.367979i \(0.119950\pi\)
−0.146238 + 0.989249i \(0.546717\pi\)
\(354\) −12.2942 3.29423i −0.653431 0.175086i
\(355\) 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 \(-0.125727\pi\)
0.128260 + 0.991741i \(0.459061\pi\)
\(360\) 0 0
\(361\) −4.00000 6.92820i −0.210526 0.364642i
\(362\) −2.53590 9.46410i −0.133284 0.497422i
\(363\) 17.3205i 0.909091i
\(364\) −6.00000 + 17.3205i −0.314485 + 0.907841i
\(365\) 0 0
\(366\) −12.2942 + 3.29423i −0.642630 + 0.172192i
\(367\) 1.50000 0.866025i 0.0782994 0.0452062i −0.460339 0.887743i \(-0.652272\pi\)
0.538639 + 0.842537i \(0.318939\pi\)
\(368\) 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 \(-0.603656\pi\)
−0.980471 + 0.196663i \(0.936990\pi\)
\(374\) −2.36603 0.633975i −0.122344 0.0327820i
\(375\) 0 0
\(376\) 23.6603 6.33975i 1.22018 0.326947i
\(377\) −13.8564 −0.713641
\(378\) −16.0981 10.9019i −0.827996 0.560734i
\(379\) 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
\(382\) −1.36603 0.366025i −0.0698919 0.0187275i
\(383\) −4.50000 2.59808i −0.229939 0.132755i 0.380605 0.924738i \(-0.375716\pi\)
−0.610544 + 0.791982i \(0.709049\pi\)
\(384\) −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 0.518110 0.855314i \(-0.326636\pi\)
−0.999779 + 0.0210389i \(0.993303\pi\)
\(390\) 0 0
\(391\) 1.73205 0.0875936
\(392\) 11.8564 + 15.8564i 0.598839 + 0.800869i
\(393\) 9.00000i 0.453990i
\(394\) −5.85641 21.8564i −0.295041 1.10111i
\(395\) 0 0
\(396\) 0 0
\(397\) −9.52628 + 16.5000i −0.478110 + 0.828111i −0.999685 0.0250943i \(-0.992011\pi\)
0.521575 + 0.853206i \(0.325345\pi\)
\(398\) 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 −0.421837 0.906672i \(-0.638614\pi\)
0.996119 0.0880147i \(-0.0280523\pi\)
\(402\) −7.09808 1.90192i −0.354020 0.0948593i
\(403\) 3.00000 + 5.19615i 0.149441 + 0.258839i
\(404\) −8.66025 + 15.0000i −0.430864 + 0.746278i
\(405\) 0 0
\(406\) −8.39230 + 12.3923i −0.416503 + 0.615020i
\(407\) 3.00000 0.148704
\(408\) −8.19615 + 2.19615i −0.405770 + 0.108726i
\(409\) −22.5000 + 12.9904i −1.11255 + 0.642333i −0.939490 0.342578i \(-0.888700\pi\)
−0.173064 + 0.984911i \(0.555367\pi\)
\(410\) 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
\(416\) −5.07180 + 18.9282i −0.248665 + 0.928032i
\(417\) −10.3923 + 6.00000i −0.508913 + 0.293821i
\(418\) 1.90192 + 7.09808i 0.0930261 + 0.347178i
\(419\) 20.7846 1.01539 0.507697 0.861536i \(-0.330497\pi\)
0.507697 + 0.861536i \(0.330497\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) −3.66025 13.6603i −0.178178 0.664971i
\(423\) 0 0
\(424\) −0.732051 + 2.73205i −0.0355515 + 0.132680i
\(425\) 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 \(-0.479792\pi\)
0.896002 + 0.444050i \(0.146459\pi\)
\(432\) −18.0000 10.3923i −0.866025 0.500000i
\(433\) −10.3923 −0.499422 −0.249711 0.968320i \(-0.580336\pi\)
−0.249711 + 0.968320i \(0.580336\pi\)
\(434\) 6.46410 + 0.464102i 0.310287 + 0.0222776i
\(435\) 0 0
\(436\) 15.5885 + 9.00000i 0.746552 + 0.431022i
\(437\) −2.59808 4.50000i −0.124283 0.215264i
\(438\) −20.4904 5.49038i −0.979068 0.262341i
\(439\) 11.2583 19.5000i 0.537331 0.930684i −0.461716 0.887028i \(-0.652766\pi\)
0.999047 0.0436563i \(-0.0139007\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 6.00000 + 6.00000i 0.285391 + 0.285391i
\(443\) 8.50000 14.7224i 0.403847 0.699484i −0.590339 0.807155i \(-0.701006\pi\)
0.994187 + 0.107671i \(0.0343394\pi\)
\(444\) 9.00000 5.19615i 0.427121 0.246598i
\(445\) 0 0
\(446\) 2.53590 + 9.46410i 0.120078 + 0.448138i
\(447\) 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 \(-0.447436\pi\)
−0.772051 + 0.635561i \(0.780769\pi\)
\(458\) −21.2942 5.70577i −0.995014 0.266613i
\(459\) −7.79423 + 4.50000i −0.363803 + 0.210042i
\(460\) 0 0
\(461\) 17.3205i 0.806696i −0.915047 0.403348i \(-0.867846\pi\)
0.915047 0.403348i \(-0.132154\pi\)
\(462\) −2.83013 5.83013i −0.131669 0.271242i
\(463\) −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
\(466\) 9.56218 + 2.56218i 0.442959 + 0.118691i
\(467\) 7.50000 + 4.33013i 0.347059 + 0.200374i 0.663389 0.748275i \(-0.269117\pi\)
−0.316330 + 0.948649i \(0.602451\pi\)
\(468\) 0 0
\(469\) 7.50000 + 2.59808i 0.346318 + 0.119968i
\(470\) 0 0
\(471\) −2.59808 1.50000i −0.119713 0.0691164i
\(472\) 14.1962 + 3.80385i 0.653431 + 0.175086i
\(473\) −1.73205 + 1.00000i −0.0796398 + 0.0459800i
\(474\) 21.2942 5.70577i 0.978076 0.262075i
\(475\) 0 0
\(476\) 9.00000 1.73205i 0.412514 0.0793884i
\(477\) 0 0
\(478\) 7.32051 + 27.3205i 0.334832 + 1.24961i
\(479\) −6.06218 10.5000i −0.276988 0.479757i 0.693647 0.720315i \(-0.256003\pi\)
−0.970635 + 0.240558i \(0.922670\pi\)
\(480\) 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 −0.967632 0.252367i \(-0.918791\pi\)
0.265260 0.964177i \(1.58546\pi\)
\(488\) 14.1962 3.80385i 0.642630 0.172192i
\(489\) 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
\(494\) 6.58846 24.5885i 0.296429 1.10629i
\(495\) 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 \(-0.619854\pi\)
−0.989205 + 0.146538i \(0.953187\pi\)
\(500\) 0 0
\(501\) 15.0000 + 25.9808i 0.670151 + 1.16073i
\(502\) 4.73205 1.26795i 0.211202 0.0565913i
\(503\) 6.92820i 0.308913i 0.988000 + 0.154457i \(0.0493627\pi\)
−0.988000 + 0.154457i \(0.950637\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0.366025 + 1.36603i 0.0162718 + 0.0607272i
\(507\) 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 0.248910 0.968527i \(-0.419928\pi\)
−0.714314 + 0.699825i \(0.753261\pi\)
\(510\) 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
\(514\) 1.90192 7.09808i 0.0838903 0.313083i
\(515\) 0 0
\(516\) −3.46410 + 6.00000i −0.152499 + 0.264135i
\(517\) 8.66025 0.380878
\(518\) −10.0981 + 4.90192i −0.443684 + 0.215378i
\(519\) 21.0000i 0.921798i
\(520\) 0 0
\(521\) 1.50000 0.866025i 0.0657162 0.0379413i −0.466782 0.884372i \(-0.654587\pi\)
0.532498 + 0.846431i \(0.321253\pi\)
\(522\) 0 0
\(523\) −22.5000 12.9904i −0.983856 0.568030i −0.0804241 0.996761i \(-0.525627\pi\)
−0.903432 + 0.428731i \(0.858961\pi\)
\(524\) 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
\(534\) −36.8827 + 9.88269i −1.59607 + 0.427666i
\(535\) 0 0
\(536\) 8.19615 + 2.19615i 0.354020 + 0.0948593i
\(537\) 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 −0.586278 0.810110i \(-0.699407\pi\)
0.994715 + 0.102677i \(0.0327407\pi\)
\(542\) −5.70577 + 21.2942i −0.245084 + 0.914665i
\(543\) −6.00000 10.3923i −0.257485 0.445976i
\(544\) 9.46410 2.53590i 0.405770 0.108726i
\(545\) 0 0
\(546\) −1.60770 + 22.3923i −0.0688030 + 0.958302i
\(547\) 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 \(-0.379909\pi\)
0.989314 + 0.145802i \(0.0465761\pi\)
\(558\) 0 0
\(559\) 6.92820 0.293032
\(560\) 0 0
\(561\) −3.00000 −0.126660
\(562\) 5.46410 1.46410i 0.230489 0.0617594i
\(563\) −19.5000 + 11.2583i −0.821827 + 0.474482i −0.851046 0.525091i \(-0.824031\pi\)
0.0292191 + 0.999573i \(0.490698\pi\)
\(564\) 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 −0.969500 0.245092i \(-0.921182\pi\)
0.697006 + 0.717066i \(0.254515\pi\)
\(570\) 0 0
\(571\) −18.1865 + 10.5000i −0.761083 + 0.439411i −0.829684 0.558233i \(-0.811480\pi\)
0.0686016 + 0.997644i \(0.478146\pi\)
\(572\) −3.46410 + 6.00000i −0.144841 + 0.250873i
\(573\) −1.73205 −0.0723575
\(574\) −10.7321 7.26795i −0.447947 0.303358i
\(575\) 0 0
\(576\) 0 0
\(577\) −16.4545 28.5000i −0.685009 1.18647i −0.973434 0.228968i \(-0.926465\pi\)
0.288425 0.957503i \(-0.406868\pi\)
\(578\) −5.12436 + 19.1244i −0.213145 + 0.795468i
\(579\) −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
\(584\) 23.6603 + 6.33975i 0.979068 + 0.262341i
\(585\) 0 0
\(586\) 28.3923 7.60770i 1.17288 0.314271i
\(587\) 6.92820i 0.285958i 0.989726 + 0.142979i \(0.0456681\pi\)
−0.989726 + 0.142979i \(0.954332\pi\)
\(588\) 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 \(-0.937040\pi\)
0.660432 + 0.750886i \(0.270373\pi\)
\(594\) −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
\(598\) 1.26795 4.73205i 0.0518503 0.193508i
\(599\) −14.7224 + 8.50000i −0.601542 + 0.347301i −0.769648 0.638468i \(-0.779568\pi\)
0.168106 + 0.985769i \(0.446235\pi\)
\(600\) 0 0
\(601\) 38.1051i 1.55434i 0.629291 + 0.777170i \(0.283346\pi\)
−0.629291 + 0.777170i \(0.716654\pi\)
\(602\) 4.19615 6.19615i 0.171022 0.252536i
\(603\) 0 0
\(604\) 7.00000 12.1244i 0.284826 0.493333i
\(605\) 0 0
\(606\) −5.49038 + 20.4904i −0.223031 + 0.832365i
\(607\) −13.5000 7.79423i −0.547948 0.316358i 0.200346 0.979725i \(-0.435793\pi\)
−0.748294 + 0.663367i \(0.769127\pi\)
\(608\) −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 \(-0.451342\pi\)
0.932062 + 0.362300i \(0.118008\pi\)
\(614\) −7.60770 28.3923i −0.307022 1.14582i
\(615\) 0 0
\(616\) 3.26795 + 6.73205i 0.131669 + 0.271242i
\(617\) 20.0000i 0.805170i 0.915383 + 0.402585i \(0.131888\pi\)
−0.915383 + 0.402585i \(0.868112\pi\)
\(618\) −20.4904 + 5.49038i −0.824244 + 0.220856i
\(619\) 7.79423 + 13.5000i 0.313276 + 0.542611i 0.979070 0.203526i \(-0.0652400\pi\)
−0.665793 + 0.746136i \(0.731907\pi\)
\(620\) 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
\(626\) −0.633975 + 2.36603i −0.0253387 + 0.0945654i
\(627\) 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 \(0.796303\pi\)
\(632\) −24.5885 + 6.58846i −0.978076 + 0.262075i
\(633\) −8.66025 15.0000i −0.344214 0.596196i
\(634\) 15.0263 + 4.02628i 0.596770 + 0.159904i
\(635\) 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 0.965365 0.260902i \(-0.0840201\pi\)
−0.708631 + 0.705580i \(0.750687\pi\)
\(642\) 8.24167 + 30.7583i 0.325273 + 1.21393i
\(643\) 13.8564i 0.546443i 0.961951 + 0.273222i \(0.0880892\pi\)
−0.961951 + 0.273222i \(0.911911\pi\)
\(644\) −3.46410 4.00000i −0.136505 0.157622i
\(645\) 0 0
\(646\) −12.2942 + 3.29423i −0.483710 + 0.129610i
\(647\) −28.5000 + 16.4545i −1.12045 + 0.646892i −0.941516 0.336968i \(-0.890598\pi\)
−0.178935 + 0.983861i \(0.557265\pi\)
\(648\) −24.5885 6.58846i −0.965926 0.258819i
\(649\) 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 \(-0.125882\pi\)
0.127780 + 0.991803i \(0.459215\pi\)
\(654\) 21.2942 + 5.70577i 0.832670 + 0.223113i
\(655\) 0 0
\(656\) −12.0000 6.92820i −0.468521 0.270501i
\(657\) 0 0
\(658\) −29.1506 + 14.1506i −1.13641 + 0.551649i
\(659\) 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 −0.987085 0.160196i \(-0.948788\pi\)
−0.354809 + 0.934939i \(0.615454\pi\)
\(662\) −9.56218 2.56218i −0.371645 0.0995819i
\(663\) 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
\(672\) 21.4641 + 14.5359i 0.827996 + 0.560734i
\(673\) 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 −0.0642672 0.997933i \(-0.520471\pi\)
0.896369 0.443309i \(-0.146196\pi\)
\(678\) 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
\(682\) 2.36603 + 0.633975i 0.0905998 + 0.0242761i
\(683\) 12.5000 + 21.6506i 0.478299 + 0.828439i 0.999690 0.0248792i \(-0.00792011\pi\)
−0.521391 + 0.853318i \(0.674587\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −19.3660 17.6340i −0.739398 0.673268i
\(687\) −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 \(-0.907407\pi\)
0.727373 + 0.686242i \(0.240741\pi\)
\(692\) 24.2487i 0.921798i
\(693\) 0 0
\(694\) −13.0000 13.0000i −0.493473 0.493473i
\(695\) 0 0
\(696\) −5.07180 + 18.9282i −0.192246 + 0.717472i
\(697\) −5.19615 + 3.00000i −0.196818 + 0.113633i
\(698\) 3.80385 + 14.1962i 0.143978 + 0.537332i
\(699\) 12.1244 0.458585
\(700\) 0 0
\(701\) −26.0000 −0.982006 −0.491003 0.871158i \(-0.663370\pi\)
−0.491003 + 0.871158i \(0.663370\pi\)
\(702\) 6.58846 + 24.5885i 0.248665 + 0.928032i
\(703\) 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 −0.938069 0.346449i \(-0.887387\pi\)
0.769068 + 0.639167i \(0.220721\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 42.5885 11.4115i 1.59607 0.427666i
\(713\) −1.73205 −0.0648658
\(714\) 10.0981 4.90192i 0.377911 0.183450i
\(715\) 0 0
\(716\) −19.0000 + 32.9090i −0.710063 + 1.22987i
\(717\) 17.3205 + 30.0000i 0.646846 + 1.12037i
\(718\) −31.4186 8.41858i −1.17253 0.314179i
\(719\) 12.9904 22.5000i 0.484459 0.839108i −0.515381 0.856961i \(-0.672350\pi\)
0.999841 + 0.0178527i \(0.00568298\pi\)
\(720\) 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
\(726\) 6.33975 + 23.6603i 0.235290 + 0.878114i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 1.85641 25.8564i 0.0688030 0.958302i
\(729\) −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 −0.120137 0.992757i \(-0.538333\pi\)
0.919822 0.392337i \(-0.128333\pi\)
\(734\) −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 −0.639087 + 0.769135i \(0.720687\pi\)
−0.985634 + 0.168898i \(0.945979\pi\)
\(740\) 0 0
\(741\) 31.1769i 1.14531i
\(742\) 0.267949 3.73205i 0.00983672 0.137008i
\(743\) −34.0000 −1.24734 −0.623670 0.781688i \(-0.714359\pi\)
−0.623670 + 0.781688i \(0.714359\pi\)
\(744\) 8.19615 2.19615i 0.300486 0.0805149i
\(745\) 0 0
\(746\) 39.6147 + 10.6147i 1.45040 + 0.388633i
\(747\) 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 \(-0.182568\pi\)
−0.0499348 + 0.998752i \(0.515901\pi\)
\(752\) −30.0000 + 17.3205i −1.09399 + 0.631614i
\(753\) 5.19615 3.00000i 0.189358 0.109326i
\(754\) 18.9282 5.07180i 0.689325 0.184704i
\(755\) 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 \(-0.337369\pi\)
\(758\) −2.92820 10.9282i −0.106357 0.396930i
\(759\) 0.866025 + 1.50000i 0.0314347 + 0.0544466i
\(760\) 0 0
\(761\) 16.5000 + 9.52628i 0.598125 + 0.345327i 0.768303 0.640086i \(-0.221101\pi\)
−0.170179 + 0.985413i \(0.554435\pi\)
\(762\) −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
\(766\) 7.09808 + 1.90192i 0.256464 + 0.0687193i
\(767\) −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 \(0.0198944\pi\)
−0.998048 + 0.0624593i \(0.980106\pi\)
\(770\) 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 \(-0.321415\pi\)
−0.999299 + 0.0374331i \(0.988082\pi\)
\(774\) 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
\(782\) −2.36603 + 0.633975i −0.0846089 + 0.0226709i
\(783\) 20.7846i 0.742781i
\(784\) −22.0000 17.3205i