Properties

Label 196.2.f.a.19.1
Level $196$
Weight $2$
Character 196.19
Analytic conductor $1.565$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 196 = 2^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 196.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.56506787962\)
Analytic rank: \(0\)
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 19.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 196.19
Dual form 196.2.f.a.31.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36603 + 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-2.00000 + 2.00000i) q^{8} +O(q^{10})\) \(q+(-1.36603 + 0.366025i) q^{2} +(-0.866025 - 1.50000i) q^{3} +(1.73205 - 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(1.73205 + 1.73205i) q^{6} +(-2.00000 + 2.00000i) q^{8} +(-2.36603 - 0.633975i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-3.00000 - 1.73205i) q^{12} -3.46410i q^{13} -3.00000i q^{15} +(2.00000 - 3.46410i) q^{16} +(1.50000 - 0.866025i) q^{17} +(2.59808 - 4.50000i) q^{19} +3.46410 q^{20} +(-1.00000 + 1.00000i) q^{22} +(0.866025 + 0.500000i) q^{23} +(4.73205 + 1.26795i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(1.26795 + 4.73205i) q^{26} -5.19615 q^{27} +4.00000 q^{29} +(1.09808 + 4.09808i) q^{30} +(0.866025 + 1.50000i) q^{31} +(-1.46410 + 5.46410i) q^{32} +(-1.50000 - 0.866025i) q^{33} +(-1.73205 + 1.73205i) q^{34} +(-1.50000 + 2.59808i) q^{37} +(-1.90192 + 7.09808i) q^{38} +(-5.19615 + 3.00000i) q^{39} +(-4.73205 + 1.26795i) q^{40} +3.46410i q^{41} -2.00000i q^{43} +(1.00000 - 1.73205i) q^{44} +(-1.36603 - 0.366025i) q^{46} +(-4.33013 + 7.50000i) q^{47} -6.92820 q^{48} +(2.00000 + 2.00000i) q^{50} +(-2.59808 - 1.50000i) q^{51} +(-3.46410 - 6.00000i) q^{52} +(0.500000 + 0.866025i) q^{53} +(7.09808 - 1.90192i) q^{54} +1.73205 q^{55} -9.00000 q^{57} +(-5.46410 + 1.46410i) q^{58} +(2.59808 + 4.50000i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(4.50000 + 2.59808i) q^{61} +(-1.73205 - 1.73205i) q^{62} -8.00000i q^{64} +(3.00000 - 5.19615i) q^{65} +(2.36603 + 0.633975i) q^{66} +(2.59808 - 1.50000i) q^{67} +(1.73205 - 3.00000i) q^{68} -1.73205i q^{69} +14.0000i q^{71} +(-7.50000 + 4.33013i) q^{73} +(1.09808 - 4.09808i) q^{74} +(-1.73205 + 3.00000i) q^{75} -10.3923i q^{76} +(6.00000 - 6.00000i) q^{78} +(7.79423 + 4.50000i) q^{79} +(6.00000 - 3.46410i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-1.26795 - 4.73205i) q^{82} +13.8564 q^{83} +3.00000 q^{85} +(0.732051 + 2.73205i) q^{86} +(-3.46410 - 6.00000i) q^{87} +(-0.732051 + 2.73205i) q^{88} +(-13.5000 - 7.79423i) q^{89} +2.00000 q^{92} +(1.50000 - 2.59808i) q^{93} +(3.16987 - 11.8301i) q^{94} +(7.79423 - 4.50000i) q^{95} +(9.46410 - 2.53590i) q^{96} +17.3205i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 6q^{5} - 8q^{8} + O(q^{10}) \) \( 4q - 2q^{2} + 6q^{5} - 8q^{8} - 6q^{10} - 12q^{12} + 8q^{16} + 6q^{17} - 4q^{22} + 12q^{24} - 4q^{25} + 12q^{26} + 16q^{29} - 6q^{30} + 8q^{32} - 6q^{33} - 6q^{37} - 18q^{38} - 12q^{40} + 4q^{44} - 2q^{46} + 8q^{50} + 2q^{53} + 18q^{54} - 36q^{57} - 8q^{58} - 12q^{60} + 18q^{61} + 12q^{65} + 6q^{66} - 30q^{73} - 6q^{74} + 24q^{78} + 24q^{80} + 18q^{81} - 12q^{82} + 12q^{85} - 4q^{86} + 4q^{88} - 54q^{89} + 8q^{92} + 6q^{93} + 30q^{94} + 24q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/196\mathbb{Z}\right)^\times\).

\(n\) \(99\) \(101\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36603 + 0.366025i −0.965926 + 0.258819i
\(3\) −0.866025 1.50000i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(1.00000\pi\)
\(4\) 1.73205 1.00000i 0.866025 0.500000i
\(5\) 1.50000 + 0.866025i 0.670820 + 0.387298i 0.796387 0.604787i \(-0.206742\pi\)
−0.125567 + 0.992085i \(0.540075\pi\)
\(6\) 1.73205 + 1.73205i 0.707107 + 0.707107i
\(7\) 0 0
\(8\) −2.00000 + 2.00000i −0.707107 + 0.707107i
\(9\) 0 0
\(10\) −2.36603 0.633975i −0.748203 0.200480i
\(11\) 0.866025 0.500000i 0.261116 0.150756i −0.363727 0.931505i \(-0.618496\pi\)
0.624844 + 0.780750i \(0.285163\pi\)
\(12\) −3.00000 1.73205i −0.866025 0.500000i
\(13\) 3.46410i 0.960769i −0.877058 0.480384i \(-0.840497\pi\)
0.877058 0.480384i \(-0.159503\pi\)
\(14\) 0 0
\(15\) 3.00000i 0.774597i
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 1.50000 0.866025i 0.363803 0.210042i −0.306944 0.951727i \(-0.599307\pi\)
0.670748 + 0.741685i \(0.265973\pi\)
\(18\) 0 0
\(19\) 2.59808 4.50000i 0.596040 1.03237i −0.397360 0.917663i \(-0.630073\pi\)
0.993399 0.114708i \(-0.0365932\pi\)
\(20\) 3.46410 0.774597
\(21\) 0 0
\(22\) −1.00000 + 1.00000i −0.213201 + 0.213201i
\(23\) 0.866025 + 0.500000i 0.180579 + 0.104257i 0.587565 0.809177i \(-0.300087\pi\)
−0.406986 + 0.913434i \(0.633420\pi\)
\(24\) 4.73205 + 1.26795i 0.965926 + 0.258819i
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 1.26795 + 4.73205i 0.248665 + 0.928032i
\(27\) −5.19615 −1.00000
\(28\) 0 0
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 1.09808 + 4.09808i 0.200480 + 0.748203i
\(31\) 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
\(33\) −1.50000 0.866025i −0.261116 0.150756i
\(34\) −1.73205 + 1.73205i −0.297044 + 0.297044i
\(35\) 0 0
\(36\) 0 0
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) −1.90192 + 7.09808i −0.308533 + 1.15146i
\(39\) −5.19615 + 3.00000i −0.832050 + 0.480384i
\(40\) −4.73205 + 1.26795i −0.748203 + 0.200480i
\(41\) 3.46410i 0.541002i 0.962720 + 0.270501i \(0.0871893\pi\)
−0.962720 + 0.270501i \(0.912811\pi\)
\(42\) 0 0
\(43\) 2.00000i 0.304997i −0.988304 0.152499i \(-0.951268\pi\)
0.988304 0.152499i \(-0.0487319\pi\)
\(44\) 1.00000 1.73205i 0.150756 0.261116i
\(45\) 0 0
\(46\) −1.36603 0.366025i −0.201409 0.0539675i
\(47\) −4.33013 + 7.50000i −0.631614 + 1.09399i 0.355608 + 0.934635i \(0.384274\pi\)
−0.987222 + 0.159352i \(0.949059\pi\)
\(48\) −6.92820 −1.00000
\(49\) 0 0
\(50\) 2.00000 + 2.00000i 0.282843 + 0.282843i
\(51\) −2.59808 1.50000i −0.363803 0.210042i
\(52\) −3.46410 6.00000i −0.480384 0.832050i
\(53\) 0.500000 + 0.866025i 0.0686803 + 0.118958i 0.898321 0.439340i \(-0.144788\pi\)
−0.829640 + 0.558298i \(0.811454\pi\)
\(54\) 7.09808 1.90192i 0.965926 0.258819i
\(55\) 1.73205 0.233550
\(56\) 0 0
\(57\) −9.00000 −1.19208
\(58\) −5.46410 + 1.46410i −0.717472 + 0.192246i
\(59\) 2.59808 + 4.50000i 0.338241 + 0.585850i 0.984102 0.177605i \(-0.0568349\pi\)
−0.645861 + 0.763455i \(0.723502\pi\)
\(60\) −3.00000 5.19615i −0.387298 0.670820i
\(61\) 4.50000 + 2.59808i 0.576166 + 0.332650i 0.759608 0.650381i \(-0.225391\pi\)
−0.183442 + 0.983030i \(0.558724\pi\)
\(62\) −1.73205 1.73205i −0.219971 0.219971i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 3.00000 5.19615i 0.372104 0.644503i
\(66\) 2.36603 + 0.633975i 0.291238 + 0.0780369i
\(67\) 2.59808 1.50000i 0.317406 0.183254i −0.332830 0.942987i \(-0.608004\pi\)
0.650236 + 0.759733i \(0.274670\pi\)
\(68\) 1.73205 3.00000i 0.210042 0.363803i
\(69\) 1.73205i 0.208514i
\(70\) 0 0
\(71\) 14.0000i 1.66149i 0.556650 + 0.830747i \(0.312086\pi\)
−0.556650 + 0.830747i \(0.687914\pi\)
\(72\) 0 0
\(73\) −7.50000 + 4.33013i −0.877809 + 0.506803i −0.869935 0.493166i \(-0.835840\pi\)
−0.00787336 + 0.999969i \(0.502506\pi\)
\(74\) 1.09808 4.09808i 0.127649 0.476392i
\(75\) −1.73205 + 3.00000i −0.200000 + 0.346410i
\(76\) 10.3923i 1.19208i
\(77\) 0 0
\(78\) 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 \(0.497683\pi\)
\(80\) 6.00000 3.46410i 0.670820 0.387298i
\(81\) 4.50000 + 7.79423i 0.500000 + 0.866025i
\(82\) −1.26795 4.73205i −0.140022 0.522568i
\(83\) 13.8564 1.52094 0.760469 0.649374i \(-0.224969\pi\)
0.760469 + 0.649374i \(0.224969\pi\)
\(84\) 0 0
\(85\) 3.00000 0.325396
\(86\) 0.732051 + 2.73205i 0.0789391 + 0.294605i
\(87\) −3.46410 6.00000i −0.371391 0.643268i
\(88\) −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
\(91\) 0 0
\(92\) 2.00000 0.208514
\(93\) 1.50000 2.59808i 0.155543 0.269408i
\(94\) 3.16987 11.8301i 0.326947 1.22018i
\(95\) 7.79423 4.50000i 0.799671 0.461690i
\(96\) 9.46410 2.53590i 0.965926 0.258819i
\(97\) 17.3205i 1.75863i 0.476240 + 0.879316i \(0.342000\pi\)
−0.476240 + 0.879316i \(0.658000\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.46410 2.00000i −0.346410 0.200000i
\(101\) 7.50000 4.33013i 0.746278 0.430864i −0.0780696 0.996948i \(-0.524876\pi\)
0.824347 + 0.566084i \(0.191542\pi\)
\(102\) 4.09808 + 1.09808i 0.405770 + 0.108726i
\(103\) 4.33013 7.50000i 0.426660 0.738997i −0.569914 0.821705i \(-0.693023\pi\)
0.996574 + 0.0827075i \(0.0263567\pi\)
\(104\) 6.92820 + 6.92820i 0.679366 + 0.679366i
\(105\) 0 0
\(106\) −1.00000 1.00000i −0.0971286 0.0971286i
\(107\) −11.2583 6.50000i −1.08838 0.628379i −0.155238 0.987877i \(-0.549614\pi\)
−0.933146 + 0.359498i \(0.882948\pi\)
\(108\) −9.00000 + 5.19615i −0.866025 + 0.500000i
\(109\) −4.50000 7.79423i −0.431022 0.746552i 0.565940 0.824447i \(-0.308513\pi\)
−0.996962 + 0.0778949i \(0.975180\pi\)
\(110\) −2.36603 + 0.633975i −0.225592 + 0.0604471i
\(111\) 5.19615 0.493197
\(112\) 0 0
\(113\) −16.0000 −1.50515 −0.752577 0.658505i \(-0.771189\pi\)
−0.752577 + 0.658505i \(0.771189\pi\)
\(114\) 12.2942 3.29423i 1.15146 0.308533i
\(115\) 0.866025 + 1.50000i 0.0807573 + 0.139876i
\(116\) 6.92820 4.00000i 0.643268 0.371391i
\(117\) 0 0
\(118\) −5.19615 5.19615i −0.478345 0.478345i
\(119\) 0 0
\(120\) 6.00000 + 6.00000i 0.547723 + 0.547723i
\(121\) −5.00000 + 8.66025i −0.454545 + 0.787296i
\(122\) −7.09808 1.90192i −0.642630 0.172192i
\(123\) 5.19615 3.00000i 0.468521 0.270501i
\(124\) 3.00000 + 1.73205i 0.269408 + 0.155543i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) 6.00000i 0.532414i −0.963916 0.266207i \(-0.914230\pi\)
0.963916 0.266207i \(-0.0857705\pi\)
\(128\) 2.92820 + 10.9282i 0.258819 + 0.965926i
\(129\) −3.00000 + 1.73205i −0.264135 + 0.152499i
\(130\) −2.19615 + 8.19615i −0.192615 + 0.718850i
\(131\) −2.59808 + 4.50000i −0.226995 + 0.393167i −0.956916 0.290365i \(-0.906223\pi\)
0.729921 + 0.683531i \(0.239557\pi\)
\(132\) −3.46410 −0.301511
\(133\) 0 0
\(134\) −3.00000 + 3.00000i −0.259161 + 0.259161i
\(135\) −7.79423 4.50000i −0.670820 0.387298i
\(136\) −1.26795 + 4.73205i −0.108726 + 0.405770i
\(137\) −0.500000 0.866025i −0.0427179 0.0739895i 0.843876 0.536538i \(-0.180268\pi\)
−0.886594 + 0.462549i \(0.846935\pi\)
\(138\) 0.633975 + 2.36603i 0.0539675 + 0.201409i
\(139\) −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
\(142\) −5.12436 19.1244i −0.430026 1.60488i
\(143\) −1.73205 3.00000i −0.144841 0.250873i
\(144\) 0 0
\(145\) 6.00000 + 3.46410i 0.498273 + 0.287678i
\(146\) 8.66025 8.66025i 0.716728 0.716728i
\(147\) 0 0
\(148\) 6.00000i 0.493197i
\(149\) −0.500000 + 0.866025i −0.0409616 + 0.0709476i −0.885779 0.464107i \(-0.846375\pi\)
0.844818 + 0.535054i \(0.179709\pi\)
\(150\) 1.26795 4.73205i 0.103528 0.386370i
\(151\) −6.06218 + 3.50000i −0.493333 + 0.284826i −0.725956 0.687741i \(-0.758602\pi\)
0.232623 + 0.972567i \(0.425269\pi\)
\(152\) 3.80385 + 14.1962i 0.308533 + 1.15146i
\(153\) 0 0
\(154\) 0 0
\(155\) 3.00000i 0.240966i
\(156\) −6.00000 + 10.3923i −0.480384 + 0.832050i
\(157\) −1.50000 + 0.866025i −0.119713 + 0.0691164i −0.558661 0.829396i \(-0.688685\pi\)
0.438948 + 0.898513i \(0.355351\pi\)
\(158\) −12.2942 3.29423i −0.978076 0.262075i
\(159\) 0.866025 1.50000i 0.0686803 0.118958i
\(160\) −6.92820 + 6.92820i −0.547723 + 0.547723i
\(161\) 0 0
\(162\) −9.00000 9.00000i −0.707107 0.707107i
\(163\) 18.1865 + 10.5000i 1.42448 + 0.822423i 0.996678 0.0814491i \(-0.0259548\pi\)
0.427802 + 0.903873i \(0.359288\pi\)
\(164\) 3.46410 + 6.00000i 0.270501 + 0.468521i
\(165\) −1.50000 2.59808i −0.116775 0.202260i
\(166\) −18.9282 + 5.07180i −1.46911 + 0.393648i
\(167\) −17.3205 −1.34030 −0.670151 0.742225i \(-0.733770\pi\)
−0.670151 + 0.742225i \(0.733770\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −4.09808 + 1.09808i −0.314308 + 0.0842186i
\(171\) 0 0
\(172\) −2.00000 3.46410i −0.152499 0.264135i
\(173\) 10.5000 + 6.06218i 0.798300 + 0.460899i 0.842876 0.538107i \(-0.180860\pi\)
−0.0445762 + 0.999006i \(0.514194\pi\)
\(174\) 6.92820 + 6.92820i 0.525226 + 0.525226i
\(175\) 0 0
\(176\) 4.00000i 0.301511i
\(177\) 4.50000 7.79423i 0.338241 0.585850i
\(178\) 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 \(-0.917106\pi\)
0.966282 0.257485i \(-0.0828937\pi\)
\(182\) 0 0
\(183\) 9.00000i 0.665299i
\(184\) −2.73205 + 0.732051i −0.201409 + 0.0539675i
\(185\) −4.50000 + 2.59808i −0.330847 + 0.191014i
\(186\) −1.09808 + 4.09808i −0.0805149 + 0.300486i
\(187\) 0.866025 1.50000i 0.0633300 0.109691i
\(188\) 17.3205i 1.26323i
\(189\) 0 0
\(190\) −9.00000 + 9.00000i −0.652929 + 0.652929i
\(191\) −0.866025 0.500000i −0.0626634 0.0361787i 0.468341 0.883548i \(-0.344852\pi\)
−0.531004 + 0.847369i \(0.678185\pi\)
\(192\) −12.0000 + 6.92820i −0.866025 + 0.500000i
\(193\) 7.50000 + 12.9904i 0.539862 + 0.935068i 0.998911 + 0.0466572i \(0.0148568\pi\)
−0.459049 + 0.888411i \(0.651810\pi\)
\(194\) −6.33975 23.6603i −0.455167 1.69871i
\(195\) −10.3923 −0.744208
\(196\) 0 0
\(197\) 16.0000 1.13995 0.569976 0.821661i \(-0.306952\pi\)
0.569976 + 0.821661i \(0.306952\pi\)
\(198\) 0 0
\(199\) 11.2583 + 19.5000i 0.798082 + 1.38232i 0.920864 + 0.389885i \(0.127485\pi\)
−0.122782 + 0.992434i \(0.539182\pi\)
\(200\) 5.46410 + 1.46410i 0.386370 + 0.103528i
\(201\) −4.50000 2.59808i −0.317406 0.183254i
\(202\) −8.66025 + 8.66025i −0.609333 + 0.609333i
\(203\) 0 0
\(204\) −6.00000 −0.420084
\(205\) −3.00000 + 5.19615i −0.209529 + 0.362915i
\(206\) −3.16987 + 11.8301i −0.220856 + 0.824244i
\(207\) 0 0
\(208\) −12.0000 6.92820i −0.832050 0.480384i
\(209\) 5.19615i 0.359425i
\(210\) 0 0
\(211\) 10.0000i 0.688428i −0.938891 0.344214i \(-0.888145\pi\)
0.938891 0.344214i \(-0.111855\pi\)
\(212\) 1.73205 + 1.00000i 0.118958 + 0.0686803i
\(213\) 21.0000 12.1244i 1.43890 0.830747i
\(214\) 17.7583 + 4.75833i 1.21393 + 0.325273i
\(215\) 1.73205 3.00000i 0.118125 0.204598i
\(216\) 10.3923 10.3923i 0.707107 0.707107i
\(217\) 0 0
\(218\) 9.00000 + 9.00000i 0.609557 + 0.609557i
\(219\) 12.9904 + 7.50000i 0.877809 + 0.506803i
\(220\) 3.00000 1.73205i 0.202260 0.116775i
\(221\) −3.00000 5.19615i −0.201802 0.349531i
\(222\) −7.09808 + 1.90192i −0.476392 + 0.127649i
\(223\) 6.92820 0.463947 0.231973 0.972722i \(-0.425482\pi\)
0.231973 + 0.972722i \(0.425482\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 21.8564 5.85641i 1.45387 0.389562i
\(227\) −9.52628 16.5000i −0.632281 1.09514i −0.987084 0.160202i \(-0.948785\pi\)
0.354803 0.934941i \(1.61545\pi\)
\(228\) −15.5885 + 9.00000i −1.03237 + 0.596040i
\(229\) 13.5000 + 7.79423i 0.892105 + 0.515057i 0.874630 0.484790i \(-0.161104\pi\)
0.0174746 + 0.999847i \(0.494437\pi\)
\(230\) −1.73205 1.73205i −0.114208 0.114208i
\(231\) 0 0
\(232\) −8.00000 + 8.00000i −0.525226 + 0.525226i
\(233\) 3.50000 6.06218i 0.229293 0.397146i −0.728306 0.685252i \(-0.759692\pi\)
0.957599 + 0.288106i \(0.0930254\pi\)
\(234\) 0 0
\(235\) −12.9904 + 7.50000i −0.847399 + 0.489246i
\(236\) 9.00000 + 5.19615i 0.585850 + 0.338241i
\(237\) 15.5885i 1.01258i
\(238\) 0 0
\(239\) 20.0000i 1.29369i −0.762620 0.646846i \(-0.776088\pi\)
0.762620 0.646846i \(-0.223912\pi\)
\(240\) −10.3923 6.00000i −0.670820 0.387298i
\(241\) 4.50000 2.59808i 0.289870 0.167357i −0.348013 0.937490i \(-0.613143\pi\)
0.637883 + 0.770133i \(0.279810\pi\)
\(242\) 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
\(247\) −15.5885 9.00000i −0.991870 0.572656i
\(248\) −4.73205 1.26795i −0.300486 0.0805149i
\(249\) −12.0000 20.7846i −0.760469 1.31717i
\(250\) 4.43782 + 16.5622i 0.280673 + 1.04748i
\(251\) −3.46410 −0.218652 −0.109326 0.994006i \(-0.534869\pi\)
−0.109326 + 0.994006i \(0.534869\pi\)
\(252\) 0 0
\(253\) 1.00000 0.0628695
\(254\) 2.19615 + 8.19615i 0.137799 + 0.514272i
\(255\) −2.59808 4.50000i −0.162698 0.281801i
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −4.50000 2.59808i −0.280702 0.162064i 0.353039 0.935609i \(-0.385148\pi\)
−0.633741 + 0.773545i \(0.718482\pi\)
\(258\) 3.46410 3.46410i 0.215666 0.215666i
\(259\) 0 0
\(260\) 12.0000i 0.744208i
\(261\) 0 0
\(262\) 1.90192 7.09808i 0.117501 0.438521i
\(263\) 19.9186 11.5000i 1.22823 0.709120i 0.261573 0.965184i \(-0.415759\pi\)
0.966660 + 0.256063i \(0.0824256\pi\)
\(264\) 4.73205 1.26795i 0.291238 0.0780369i
\(265\) 1.73205i 0.106399i
\(266\) 0 0
\(267\) 27.0000i 1.65237i
\(268\) 3.00000 5.19615i 0.183254 0.317406i
\(269\) −19.5000 + 11.2583i −1.18894 + 0.686433i −0.958065 0.286552i \(-0.907491\pi\)
−0.230871 + 0.972984i \(0.574158\pi\)
\(270\) 12.2942 + 3.29423i 0.748203 + 0.200480i
\(271\) 7.79423 13.5000i 0.473466 0.820067i −0.526073 0.850439i \(-0.676336\pi\)
0.999539 + 0.0303728i \(0.00966946\pi\)
\(272\) 6.92820i 0.420084i
\(273\) 0 0
\(274\) 1.00000 + 1.00000i 0.0604122 + 0.0604122i
\(275\) −1.73205 1.00000i −0.104447 0.0603023i
\(276\) −1.73205 3.00000i −0.104257 0.180579i
\(277\) 6.50000 + 11.2583i 0.390547 + 0.676448i 0.992522 0.122068i \(-0.0389525\pi\)
−0.601975 + 0.798515i \(0.705619\pi\)
\(278\) 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
\(283\) −6.06218 10.5000i −0.360359 0.624160i 0.627661 0.778487i \(-0.284012\pi\)
−0.988020 + 0.154327i \(0.950679\pi\)
\(284\) 14.0000 + 24.2487i 0.830747 + 1.43890i
\(285\) −13.5000 7.79423i −0.799671 0.461690i
\(286\) 3.46410 + 3.46410i 0.204837 + 0.204837i
\(287\) 0 0
\(288\) 0 0
\(289\) −7.00000 + 12.1244i −0.411765 + 0.713197i
\(290\) −9.46410 2.53590i −0.555751 0.148913i
\(291\) 25.9808 15.0000i 1.52302 0.879316i
\(292\) −8.66025 + 15.0000i −0.506803 + 0.877809i
\(293\) 20.7846i 1.21425i 0.794606 + 0.607125i \(0.207677\pi\)
−0.794606 + 0.607125i \(0.792323\pi\)
\(294\) 0 0
\(295\) 9.00000i 0.524000i
\(296\) −2.19615 8.19615i −0.127649 0.476392i
\(297\) −4.50000 + 2.59808i −0.261116 + 0.150756i
\(298\) 0.366025 1.36603i 0.0212033 0.0791317i
\(299\) 1.73205 3.00000i 0.100167 0.173494i
\(300\) 6.92820i 0.400000i
\(301\) 0 0
\(302\) 7.00000 7.00000i 0.402805 0.402805i
\(303\) −12.9904 7.50000i −0.746278 0.430864i
\(304\) −10.3923 18.0000i −0.596040 1.03237i
\(305\) 4.50000 + 7.79423i 0.257669 + 0.446296i
\(306\) 0 0
\(307\) 20.7846 1.18624 0.593120 0.805114i \(-0.297896\pi\)
0.593120 + 0.805114i \(0.297896\pi\)
\(308\) 0 0
\(309\) −15.0000 −0.853320
\(310\) −1.09808 4.09808i −0.0623665 0.232755i
\(311\) −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
\(313\) −1.50000 0.866025i −0.0847850 0.0489506i 0.457008 0.889463i \(-0.348921\pi\)
−0.541793 + 0.840512i \(0.682254\pi\)
\(314\) 1.73205 1.73205i 0.0977453 0.0977453i
\(315\) 0 0
\(316\) 18.0000 1.01258
\(317\) −5.50000 + 9.52628i −0.308911 + 0.535049i −0.978124 0.208021i \(-0.933298\pi\)
0.669214 + 0.743070i \(0.266631\pi\)
\(318\) −0.633975 + 2.36603i −0.0355515 + 0.132680i
\(319\) 3.46410 2.00000i 0.193952 0.111979i
\(320\) 6.92820 12.0000i 0.387298 0.670820i
\(321\) 22.5167i 1.25676i
\(322\) 0 0
\(323\) 9.00000i 0.500773i
\(324\) 15.5885 + 9.00000i 0.866025 + 0.500000i
\(325\) −6.00000 + 3.46410i −0.332820 + 0.192154i
\(326\) −28.6865 7.68653i −1.58880 0.425718i
\(327\) −7.79423 + 13.5000i −0.431022 + 0.746552i
\(328\) −6.92820 6.92820i −0.382546 0.382546i
\(329\) 0 0
\(330\) 3.00000 + 3.00000i 0.165145 + 0.165145i
\(331\) −6.06218 3.50000i −0.333207 0.192377i 0.324057 0.946038i \(-0.394953\pi\)
−0.657264 + 0.753660i \(0.728286\pi\)
\(332\) 24.0000 13.8564i 1.31717 0.760469i
\(333\) 0 0
\(334\) 23.6603 6.33975i 1.29463 0.346895i
\(335\) 5.19615 0.283896
\(336\) 0 0
\(337\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) −1.36603 + 0.366025i −0.0743020 + 0.0199092i
\(339\) 13.8564 + 24.0000i 0.752577 + 1.30350i
\(340\) 5.19615 3.00000i 0.281801 0.162698i
\(341\) 1.50000 + 0.866025i 0.0812296 + 0.0468979i
\(342\) 0 0
\(343\) 0 0
\(344\) 4.00000 + 4.00000i 0.215666 + 0.215666i
\(345\) 1.50000 2.59808i 0.0807573 0.139876i
\(346\) −16.5622 4.43782i −0.890388 0.238579i
\(347\) −11.2583 + 6.50000i −0.604379 + 0.348938i −0.770762 0.637123i \(-0.780124\pi\)
0.166383 + 0.986061i \(0.446791\pi\)
\(348\) −12.0000 6.92820i −0.643268 0.371391i
\(349\) 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
\(353\) 25.5000 14.7224i 1.35723 0.783596i 0.367979 0.929834i \(-0.380050\pi\)
0.989249 + 0.146238i \(0.0467166\pi\)
\(354\) −3.29423 + 12.2942i −0.175086 + 0.653431i
\(355\) −12.1244 + 21.0000i −0.643494 + 1.11456i
\(356\) −31.1769 −1.65237
\(357\) 0 0
\(358\) 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
\(363\) 17.3205 0.909091
\(364\) 0 0
\(365\) −15.0000 −0.785136
\(366\) 3.29423 + 12.2942i 0.172192 + 0.642630i
\(367\) −0.866025 1.50000i −0.0452062 0.0782994i 0.842537 0.538639i \(-0.181061\pi\)
−0.887743 + 0.460339i \(0.847728\pi\)
\(368\) 3.46410 2.00000i 0.180579 0.104257i
\(369\) 0 0
\(370\) 5.19615 5.19615i 0.270135 0.270135i
\(371\) 0 0
\(372\) 6.00000i 0.311086i
\(373\) 14.5000 25.1147i 0.750782 1.30039i −0.196663 0.980471i \(-0.563010\pi\)
0.947444 0.319921i \(-0.103656\pi\)
\(374\) −0.633975 + 2.36603i −0.0327820 + 0.122344i
\(375\) −18.1865 + 10.5000i −0.939149 + 0.542218i
\(376\) −6.33975 23.6603i −0.326947 1.22018i
\(377\) 13.8564i 0.713641i
\(378\) 0 0
\(379\) 8.00000i 0.410932i 0.978664 + 0.205466i \(0.0658711\pi\)
−0.978664 + 0.205466i \(0.934129\pi\)
\(380\) 9.00000 15.5885i 0.461690 0.799671i
\(381\) −9.00000 + 5.19615i −0.461084 + 0.266207i
\(382\) 1.36603 + 0.366025i 0.0698919 + 0.0187275i
\(383\) 2.59808 4.50000i 0.132755 0.229939i −0.791982 0.610544i \(-0.790951\pi\)
0.924738 + 0.380605i \(0.124284\pi\)
\(384\) 13.8564 13.8564i 0.707107 0.707107i
\(385\) 0 0
\(386\) −15.0000 15.0000i −0.763480 0.763480i
\(387\) 0 0
\(388\) 17.3205 + 30.0000i 0.879316 + 1.52302i
\(389\) 9.50000 + 16.4545i 0.481669 + 0.834275i 0.999779 0.0210389i \(-0.00669738\pi\)
−0.518110 + 0.855314i \(0.673364\pi\)
\(390\) 14.1962 3.80385i 0.718850 0.192615i
\(391\) 1.73205 0.0875936
\(392\) 0 0
\(393\) 9.00000 0.453990
\(394\) −21.8564 + 5.85641i −1.10111 + 0.295041i
\(395\) 7.79423 + 13.5000i 0.392170 + 0.679259i
\(396\) 0 0
\(397\) −16.5000 9.52628i −0.828111 0.478110i 0.0250943 0.999685i \(-0.492011\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −22.5167 22.5167i −1.12866 1.12866i
\(399\) 0 0
\(400\) −8.00000 −0.400000
\(401\) 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
\(403\) 5.19615 3.00000i 0.258839 0.149441i
\(404\) 8.66025 15.0000i 0.430864 0.746278i
\(405\) 15.5885i 0.774597i
\(406\) 0 0
\(407\) 3.00000i 0.148704i
\(408\) 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 \(0.555367\pi\)
\(410\) 2.19615 8.19615i 0.108460 0.404779i
\(411\) −0.866025 + 1.50000i −0.0427179 + 0.0739895i
\(412\) 17.3205i 0.853320i
\(413\) 0 0
\(414\) 0 0
\(415\) 20.7846 + 12.0000i 1.02028 + 0.589057i
\(416\) 18.9282 + 5.07180i 0.928032 + 0.248665i
\(417\) 6.00000 + 10.3923i 0.293821 + 0.508913i
\(418\) 1.90192 + 7.09808i 0.0930261 + 0.347178i
\(419\) −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 \(0.662044\pi\)
\(422\) 3.66025 + 13.6603i 0.178178 + 0.664971i
\(423\) 0 0
\(424\) −2.73205 0.732051i −0.132680 0.0355515i
\(425\) −3.00000 1.73205i −0.145521 0.0840168i
\(426\) −24.2487 + 24.2487i −1.17485 + 1.17485i
\(427\) 0 0
\(428\) −26.0000 −1.25676
\(429\) −3.00000 + 5.19615i −0.144841 + 0.250873i
\(430\) −1.26795 + 4.73205i −0.0611459 + 0.228200i
\(431\) −19.9186 + 11.5000i −0.959444 + 0.553936i −0.896002 0.444050i \(-0.853541\pi\)
−0.0634424 + 0.997985i \(0.520208\pi\)
\(432\) −10.3923 + 18.0000i −0.500000 + 0.866025i
\(433\) 10.3923i 0.499422i 0.968320 + 0.249711i \(0.0803357\pi\)
−0.968320 + 0.249711i \(0.919664\pi\)
\(434\) 0 0
\(435\) 12.0000i 0.575356i
\(436\) −15.5885 9.00000i −0.746552 0.431022i
\(437\) 4.50000 2.59808i 0.215264 0.124283i
\(438\) −20.4904 5.49038i −0.979068 0.262341i
\(439\) −11.2583 + 19.5000i −0.537331 + 0.930684i 0.461716 + 0.887028i \(0.347234\pi\)
−0.999047 + 0.0436563i \(0.986099\pi\)
\(440\) −3.46410 + 3.46410i −0.165145 + 0.165145i
\(441\) 0 0
\(442\) 6.00000 + 6.00000i 0.285391 + 0.285391i
\(443\) −14.7224 8.50000i −0.699484 0.403847i 0.107671 0.994187i \(-0.465661\pi\)
−0.807155 + 0.590339i \(0.798994\pi\)
\(444\) 9.00000 5.19615i 0.427121 0.246598i
\(445\) −13.5000 23.3827i −0.639961 1.10845i
\(446\) −9.46410 + 2.53590i −0.448138 + 0.120078i
\(447\) 1.73205 0.0819232
\(448\) 0 0
\(449\) 8.00000 0.377543 0.188772 0.982021i \(-0.439549\pi\)
0.188772 + 0.982021i \(0.439549\pi\)
\(450\) 0 0
\(451\) 1.73205 + 3.00000i 0.0815591 + 0.141264i
\(452\) −27.7128 + 16.0000i −1.30350 + 0.752577i
\(453\) 10.5000 + 6.06218i 0.493333 + 0.284826i
\(454\) 19.0526 + 19.0526i 0.894181 + 0.894181i
\(455\) 0 0
\(456\) 18.0000 18.0000i 0.842927 0.842927i
\(457\) −7.50000 + 12.9904i −0.350835 + 0.607664i −0.986396 0.164386i \(-0.947436\pi\)
0.635561 + 0.772051i \(0.280769\pi\)
\(458\) −21.2942 5.70577i −0.995014 0.266613i
\(459\) −7.79423 + 4.50000i −0.363803 + 0.210042i
\(460\) 3.00000 + 1.73205i 0.139876 + 0.0807573i
\(461\) 17.3205i 0.806696i 0.915047 + 0.403348i \(0.132154\pi\)
−0.915047 + 0.403348i \(0.867846\pi\)
\(462\) 0 0
\(463\) 30.0000i 1.39422i 0.716965 + 0.697109i \(0.245531\pi\)
−0.716965 + 0.697109i \(0.754469\pi\)
\(464\) 8.00000 13.8564i 0.371391 0.643268i
\(465\) 4.50000 2.59808i 0.208683 0.120483i
\(466\) −2.56218 + 9.56218i −0.118691 + 0.442959i
\(467\) 4.33013 7.50000i 0.200374 0.347059i −0.748275 0.663389i \(-0.769117\pi\)
0.948649 + 0.316330i \(0.102451\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 15.0000 15.0000i 0.691898 0.691898i
\(471\) 2.59808 + 1.50000i 0.119713 + 0.0691164i
\(472\) −14.1962 3.80385i −0.653431 0.175086i
\(473\) −1.00000 1.73205i −0.0459800 0.0796398i
\(474\) 5.70577 + 21.2942i 0.262075 + 0.978076i
\(475\) −10.3923 −0.476832
\(476\) 0 0
\(477\) 0 0
\(478\) 7.32051 + 27.3205i 0.334832 + 1.24961i
\(479\) 6.06218 + 10.5000i 0.276988 + 0.479757i 0.970635 0.240558i \(-0.0773304\pi\)
−0.693647 + 0.720315i \(0.743997\pi\)
\(480\) 16.3923 + 4.39230i 0.748203 + 0.200480i
\(481\) 9.00000 + 5.19615i 0.410365 + 0.236924i
\(482\) −5.19615 + 5.19615i −0.236678 + 0.236678i
\(483\) 0 0
\(484\) 20.0000i 0.909091i
\(485\) −15.0000 + 25.9808i −0.681115 + 1.17973i
\(486\) 0 0
\(487\) 26.8468 15.5000i 1.21654 0.702372i 0.252367 0.967632i \(-0.418791\pi\)
0.964177 + 0.265260i \(0.0854576\pi\)
\(488\) −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 \(-0.743191\pi\)
0.691820 0.722070i \(-0.256809\pi\)
\(492\) 6.00000 10.3923i 0.270501 0.468521i
\(493\) 6.00000 3.46410i 0.270226 0.156015i
\(494\) 24.5885 + 6.58846i 1.10629 + 0.296429i
\(495\) 0 0
\(496\) 6.92820 0.311086
\(497\) 0 0
\(498\) 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 \(0.953187\pi\)
\(500\) −12.1244 21.0000i −0.542218 0.939149i
\(501\) 15.0000 + 25.9808i 0.670151 + 1.16073i
\(502\) 4.73205 1.26795i 0.211202 0.0565913i
\(503\) −6.92820 −0.308913 −0.154457 0.988000i \(-0.549363\pi\)
−0.154457 + 0.988000i \(0.549363\pi\)
\(504\) 0 0
\(505\) 15.0000 0.667491
\(506\) −1.36603 + 0.366025i −0.0607272 + 0.0162718i
\(507\) −0.866025 1.50000i −0.0384615 0.0666173i
\(508\) −6.00000 10.3923i −0.266207 0.461084i
\(509\) −10.5000 6.06218i −0.465404 0.268701i 0.248910 0.968527i \(-0.419928\pi\)
−0.714314 + 0.699825i \(0.753261\pi\)
\(510\) 5.19615 + 5.19615i 0.230089 + 0.230089i
\(511\) 0 0
\(512\) 16.0000 + 16.0000i 0.707107 + 0.707107i
\(513\) −13.5000 + 23.3827i −0.596040 + 1.03237i
\(514\) 7.09808 + 1.90192i 0.313083 + 0.0838903i
\(515\) 12.9904 7.50000i 0.572425 0.330489i
\(516\) −3.46410 + 6.00000i −0.152499 + 0.264135i
\(517\) 8.66025i 0.380878i
\(518\) 0 0
\(519\) 21.0000i 0.921798i
\(520\) 4.39230 + 16.3923i 0.192615 + 0.718850i
\(521\) −1.50000 + 0.866025i −0.0657162 + 0.0379413i −0.532498 0.846431i \(-0.678747\pi\)
0.466782 + 0.884372i \(0.345413\pi\)
\(522\) 0 0
\(523\) 12.9904 22.5000i 0.568030 0.983856i −0.428731 0.903432i \(-0.641039\pi\)
0.996761 0.0804241i \(-0.0256275\pi\)
\(524\) 10.3923i 0.453990i
\(525\) 0 0
\(526\) −23.0000 + 23.0000i −1.00285 + 1.00285i
\(527\) 2.59808 + 1.50000i 0.113174 + 0.0653410i
\(528\) −6.00000 + 3.46410i −0.261116 + 0.150756i
\(529\) −11.0000 19.0526i −0.478261 0.828372i
\(530\) −0.633975 2.36603i −0.0275381 0.102774i
\(531\) 0 0
\(532\) 0 0
\(533\) 12.0000 0.519778
\(534\) −9.88269 36.8827i −0.427666 1.59607i
\(535\) −11.2583 19.5000i −0.486740 0.843059i
\(536\) −2.19615 + 8.19615i −0.0948593 + 0.354020i
\(537\) 28.5000 + 16.4545i 1.22987 + 0.710063i
\(538\) 22.5167 22.5167i 0.970762 0.970762i
\(539\) 0 0
\(540\) −18.0000 −0.774597
\(541\) 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
\(543\) −10.3923 + 6.00000i −0.445976 + 0.257485i
\(544\) 2.53590 + 9.46410i 0.108726 + 0.405770i
\(545\) 15.5885i 0.667736i
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) −1.73205 1.00000i −0.0739895 0.0427179i
\(549\) 0 0
\(550\) 2.73205 + 0.732051i 0.116495 + 0.0312148i
\(551\) 10.3923 18.0000i 0.442727 0.766826i
\(552\) 3.46410 + 3.46410i 0.147442 + 0.147442i
\(553\) 0 0
\(554\) −13.0000 13.0000i −0.552317 0.552317i
\(555\) 7.79423 + 4.50000i 0.330847 + 0.191014i
\(556\) −12.0000 + 6.92820i −0.508913 + 0.293821i
\(557\) −18.5000 32.0429i −0.783870 1.35770i −0.929672 0.368389i \(-0.879909\pi\)
0.145802 0.989314i \(-0.453424\pi\)
\(558\) 0 0
\(559\) −6.92820 −0.293032
\(560\) 0 0
\(561\) −3.00000 −0.126660
\(562\) 5.46410 1.46410i 0.230489 0.0617594i
\(563\) −11.2583 19.5000i −0.474482 0.821827i 0.525091 0.851046i \(-0.324031\pi\)
−0.999573 + 0.0292191i \(0.990698\pi\)
\(564\) 25.9808 15.0000i 1.09399 0.631614i
\(565\) −24.0000 13.8564i −1.00969 0.582943i
\(566\) 12.1244 + 12.1244i 0.509625 + 0.509625i
\(567\) 0 0
\(568\) −28.0000 28.0000i −1.17485 1.17485i
\(569\) 6.50000 11.2583i 0.272494 0.471974i −0.697006 0.717066i \(-0.745485\pi\)
0.969500 + 0.245092i \(0.0788181\pi\)
\(570\) 21.2942 + 5.70577i 0.891917 + 0.238988i
\(571\) 18.1865 10.5000i 0.761083 0.439411i −0.0686016 0.997644i \(-0.521854\pi\)
0.829684 + 0.558233i \(0.188520\pi\)
\(572\) −6.00000 3.46410i −0.250873 0.144841i
\(573\) 1.73205i 0.0723575i
\(574\) 0 0
\(575\) 2.00000i 0.0834058i
\(576\) 0 0
\(577\) 28.5000 16.4545i 1.18647 0.685009i 0.228968 0.973434i \(-0.426465\pi\)
0.957503 + 0.288425i \(0.0931316\pi\)
\(578\) 5.12436 19.1244i 0.213145 0.795468i
\(579\) 12.9904 22.5000i 0.539862 0.935068i
\(580\) 13.8564 0.575356
\(581\) 0 0
\(582\) −30.0000 + 30.0000i −1.24354 + 1.24354i
\(583\) 0.866025 + 0.500000i 0.0358671 + 0.0207079i
\(584\) 6.33975 23.6603i 0.262341 0.979068i
\(585\) 0 0
\(586\) −7.60770 28.3923i −0.314271 1.17288i
\(587\) 6.92820 0.285958 0.142979 0.989726i \(-0.454332\pi\)
0.142979 + 0.989726i \(0.454332\pi\)
\(588\) 0 0
\(589\) 9.00000 0.370839
\(590\) −3.29423 12.2942i −0.135621 0.506145i
\(591\) −13.8564 24.0000i −0.569976 0.987228i
\(592\) 6.00000 + 10.3923i 0.246598 + 0.427121i
\(593\) 13.5000 + 7.79423i 0.554379 + 0.320071i 0.750886 0.660432i \(-0.229627\pi\)
−0.196508 + 0.980502i \(0.562960\pi\)
\(594\) 5.19615 5.19615i 0.213201 0.213201i
\(595\) 0 0
\(596\) 2.00000i 0.0819232i
\(597\) 19.5000 33.7750i 0.798082 1.38232i
\(598\) −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 \(0.446235\pi\)
\(600\) −2.53590 9.46410i −0.103528 0.386370i
\(601\) 38.1051i 1.55434i −0.629291 0.777170i \(-0.716654\pi\)
0.629291 0.777170i \(-0.283346\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −7.00000 + 12.1244i −0.284826 + 0.493333i
\(605\) −15.0000 + 8.66025i −0.609837 + 0.352089i
\(606\) 20.4904 + 5.49038i 0.832365 + 0.223031i
\(607\) −7.79423 + 13.5000i −0.316358 + 0.547948i −0.979725 0.200346i \(-0.935793\pi\)
0.663367 + 0.748294i \(0.269127\pi\)
\(608\) 20.7846 + 20.7846i 0.842927 + 0.842927i
\(609\) 0 0
\(610\) −9.00000 9.00000i −0.364399 0.364399i
\(611\) 25.9808 + 15.0000i 1.05107 + 0.606835i
\(612\) 0 0
\(613\) 15.5000 + 26.8468i 0.626039 + 1.08433i 0.988339 + 0.152270i \(0.0486583\pi\)
−0.362300 + 0.932062i \(0.618008\pi\)
\(614\) −28.3923 + 7.60770i −1.14582 + 0.307022i
\(615\) 10.3923 0.419058
\(616\) 0 0
\(617\) 20.0000 0.805170 0.402585 0.915383i \(-0.368112\pi\)
0.402585 + 0.915383i \(0.368112\pi\)
\(618\) 20.4904 5.49038i 0.824244 0.220856i
\(619\) −7.79423 13.5000i −0.313276 0.542611i 0.665793 0.746136i \(-0.268093\pi\)
−0.979070 + 0.203526i \(0.934760\pi\)
\(620\) 3.00000 + 5.19615i 0.120483 + 0.208683i
\(621\) −4.50000 2.59808i −0.180579 0.104257i
\(622\) 8.66025 + 8.66025i 0.347245 + 0.347245i
\(623\) 0 0
\(624\) 24.0000i 0.960769i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 2.36603 + 0.633975i 0.0945654 + 0.0253387i
\(627\) −7.79423 + 4.50000i −0.311272 + 0.179713i
\(628\) −1.73205 + 3.00000i −0.0691164 + 0.119713i
\(629\) 5.19615i 0.207184i
\(630\) 0 0
\(631\) 30.0000i 1.19428i −0.802137 0.597141i \(-0.796303\pi\)
0.802137 0.597141i \(-0.203697\pi\)
\(632\) −24.5885 + 6.58846i −0.978076 + 0.262075i
\(633\) −15.0000 + 8.66025i −0.596196 + 0.344214i
\(634\) 4.02628 15.0263i 0.159904 0.596770i
\(635\) 5.19615 9.00000i 0.206203 0.357154i
\(636\) 3.46410i 0.137361i
\(637\) 0 0
\(638\) −4.00000 + 4.00000i −0.158362 + 0.158362i
\(639\) 0 0
\(640\) −5.07180 + 18.9282i −0.200480 + 0.748203i
\(641\) 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
\(643\) −13.8564 −0.546443 −0.273222 0.961951i \(-0.588089\pi\)
−0.273222 + 0.961951i \(0.588089\pi\)
\(644\) 0 0
\(645\) −6.00000 −0.236250
\(646\) 3.29423 + 12.2942i 0.129610 + 0.483710i
\(647\) 16.4545 + 28.5000i 0.646892 + 1.12045i 0.983861 + 0.178935i \(0.0572651\pi\)
−0.336968 + 0.941516i \(0.609402\pi\)
\(648\) −24.5885 6.58846i −0.965926 0.258819i
\(649\) 4.50000 + 2.59808i 0.176640 + 0.101983i
\(650\) 6.92820 6.92820i 0.271746 0.271746i
\(651\) 0 0
\(652\) 42.0000 1.64485
\(653\) −15.5000 + 26.8468i −0.606562 + 1.05060i 0.385241 + 0.922816i \(0.374118\pi\)
−0.991803 + 0.127780i \(0.959215\pi\)
\(654\) 5.70577 21.2942i 0.223113 0.832670i
\(655\) −7.79423 + 4.50000i −0.304546 + 0.175830i
\(656\) 12.0000 + 6.92820i 0.468521 + 0.270501i
\(657\) 0 0
\(658\) 0 0
\(659\) 38.0000i 1.48027i 0.672458 + 0.740135i \(0.265238\pi\)
−0.672458 + 0.740135i \(0.734762\pi\)
\(660\) −5.19615 3.00000i −0.202260 0.116775i
\(661\) 34.5000 19.9186i 1.34189 0.774743i 0.354809 0.934939i \(-0.384546\pi\)
0.987085 + 0.160196i \(0.0512125\pi\)
\(662\) 9.56218 + 2.56218i 0.371645 + 0.0995819i
\(663\) −5.19615 + 9.00000i −0.201802 + 0.349531i
\(664\) −27.7128 + 27.7128i −1.07547 + 1.07547i
\(665\) 0 0
\(666\) 0 0
\(667\) 3.46410 + 2.00000i 0.134131 + 0.0774403i
\(668\) −30.0000 + 17.3205i −1.16073 + 0.670151i
\(669\) −6.00000 10.3923i −0.231973 0.401790i
\(670\) −7.09808 + 1.90192i −0.274223 + 0.0734777i
\(671\) 5.19615 0.200595
\(672\) 0 0
\(673\) 24.0000 0.925132 0.462566 0.886585i \(-0.346929\pi\)
0.462566 + 0.886585i \(0.346929\pi\)
\(674\) 0 0
\(675\) 5.19615 + 9.00000i 0.200000 + 0.346410i
\(676\) 1.73205 1.00000i 0.0666173 0.0384615i
\(677\) 37.5000 + 21.6506i 1.44124 + 0.832102i 0.997933 0.0642672i \(-0.0204710\pi\)
0.443309 + 0.896369i \(0.353804\pi\)
\(678\) −27.7128 27.7128i −1.06430 1.06430i
\(679\) 0 0
\(680\) −6.00000 + 6.00000i −0.230089 + 0.230089i
\(681\) −16.5000 + 28.5788i −0.632281 + 1.09514i
\(682\) −2.36603 0.633975i −0.0905998 0.0242761i
\(683\) 21.6506 12.5000i 0.828439 0.478299i −0.0248792 0.999690i \(-0.507920\pi\)
0.853318 + 0.521391i \(0.174587\pi\)
\(684\) 0 0
\(685\) 1.73205i 0.0661783i
\(686\) 0 0
\(687\) 27.0000i 1.03011i
\(688\) −6.92820 4.00000i −0.264135 0.152499i
\(689\) 3.00000 1.73205i 0.114291 0.0659859i
\(690\) −1.09808 + 4.09808i −0.0418030 + 0.156011i
\(691\) −6.06218 + 10.5000i −0.230616 + 0.399439i −0.957990 0.286803i \(-0.907407\pi\)
0.727373 + 0.686242i \(0.240741\pi\)
\(692\) 24.2487 0.921798
\(693\) 0 0
\(694\) 13.0000 13.0000i 0.493473 0.493473i
\(695\) −10.3923 6.00000i −0.394203 0.227593i
\(696\) 18.9282 + 5.07180i 0.717472 + 0.192246i
\(697\) 3.00000 + 5.19615i 0.113633 + 0.196818i
\(698\) 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
\(703\) 7.79423 + 13.5000i 0.293965 + 0.509162i
\(704\) −4.00000 6.92820i −0.150756 0.261116i
\(705\) 22.5000 + 12.9904i 0.847399 + 0.489246i
\(706\) −29.4449 + 29.4449i −1.10817 + 1.10817i
\(707\) 0 0
\(708\) 18.0000i 0.676481i
\(709\) 4.50000 7.79423i 0.169001 0.292718i −0.769068 0.639167i \(-0.779279\pi\)
0.938069 + 0.346449i \(0.112613\pi\)
\(710\) 8.87564 33.1244i 0.333097 1.24313i
\(711\) 0 0
\(712\) 42.5885 11.4115i 1.59607 0.427666i
\(713\) 1.73205i 0.0648658i
\(714\) 0 0
\(715\) 6.00000i 0.224387i
\(716\) −19.0000 + 32.9090i −0.710063 + 1.22987i
\(717\) −30.0000 + 17.3205i −1.12037 + 0.646846i
\(718\) −31.4186 8.41858i −1.17253 0.314179i
\(719\) −12.9904 + 22.5000i −0.484459 + 0.839108i −0.999841 0.0178527i \(-0.994317\pi\)
0.515381 + 0.856961i \(0.327650\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 8.00000 + 8.00000i 0.297729 + 0.297729i
\(723\) −7.79423 4.50000i −0.289870 0.167357i
\(724\) −6.92820 12.0000i −0.257485 0.445976i
\(725\) −4.00000 6.92820i −0.148556 0.257307i
\(726\) −23.6603 + 6.33975i −0.878114 + 0.235290i
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 20.4904 5.49038i 0.758383 0.203208i
\(731\) −1.73205 3.00000i −0.0640622 0.110959i
\(732\) −9.00000 15.5885i −0.332650 0.576166i
\(733\) −37.5000 21.6506i −1.38509 0.799684i −0.392337 0.919822i \(-0.628333\pi\)
−0.992757 + 0.120137i \(0.961667\pi\)
\(734\) 1.73205 + 1.73205i 0.0639312 + 0.0639312i
\(735\) 0 0
\(736\) −4.00000 + 4.00000i −0.147442 + 0.147442i
\(737\) 1.50000 2.59808i 0.0552532 0.0957014i
\(738\) 0 0
\(739\) −44.1673 + 25.5000i −1.62472 + 0.938033i −0.639087 + 0.769135i \(0.720687\pi\)
−0.985634 + 0.168898i \(0.945979\pi\)
\(740\) −5.19615 + 9.00000i −0.191014 + 0.330847i
\(741\) 31.1769i 1.14531i
\(742\) 0 0
\(743\) 34.0000i 1.24734i 0.781688 + 0.623670i \(0.214359\pi\)
−0.781688 + 0.623670i \(0.785641\pi\)
\(744\) 2.19615 + 8.19615i 0.0805149 + 0.300486i
\(745\) −1.50000 + 0.866025i −0.0549557 + 0.0317287i
\(746\) −10.6147 + 39.6147i −0.388633 + 1.45040i
\(747\) 0 0
\(748\) 3.46410i 0.126660i
\(749\) 0 0
\(750\) 21.0000 21.0000i 0.766812 0.766812i
\(751\) −21.6506 12.5000i −0.790043 0.456131i 0.0499348 0.998752i \(-0.484099\pi\)
−0.839978 + 0.542621i \(0.817432\pi\)
\(752\) 17.3205 + 30.0000i 0.631614 + 1.09399i
\(753\) 3.00000 + 5.19615i 0.109326 + 0.189358i
\(754\) 5.07180 + 18.9282i 0.184704 + 0.689325i
\(755\) −12.1244 −0.441250
\(756\) 0 0
\(757\) −48.0000 −1.74459 −0.872295 0.488980i \(-0.837369\pi\)
−0.872295 + 0.488980i \(0.837369\pi\)
\(758\) −2.92820 10.9282i −0.106357 0.396930i
\(759\) −0.866025 1.50000i −0.0314347 0.0544466i
\(760\) −6.58846 + 24.5885i −0.238988 + 0.891917i
\(761\) −16.5000 9.52628i −0.598125 0.345327i 0.170179 0.985413i \(-0.445565\pi\)
−0.768303 + 0.640086i \(0.778899\pi\)
\(762\) 10.3923 10.3923i 0.376473 0.376473i
\(763\) 0 0
\(764\) −2.00000 −0.0723575
\(765\) 0 0
\(766\) −1.90192 + 7.09808i −0.0687193 + 0.256464i
\(767\) 15.5885 9.00000i 0.562867 0.324971i
\(768\) −13.8564 + 24.0000i −0.500000 + 0.866025i
\(769\) 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
\(772\) 25.9808 + 15.0000i 0.935068 + 0.539862i
\(773\) −22.5000 + 12.9904i −0.809269 + 0.467232i −0.846702 0.532068i \(-0.821415\pi\)
0.0374331 + 0.999299i \(0.488082\pi\)
\(774\) 0 0
\(775\) 1.73205 3.00000i 0.0622171 0.107763i
\(776\) −34.6410 34.6410i −1.24354 1.24354i
\(777\) 0 0
\(778\) −19.0000 19.0000i −0.681183 0.681183i
\(779\) 15.5885 + 9.00000i 0.558514 + 0.322458i
\(780\) −18.0000 + 10.3923i −0.644503 + 0.372104i
\(781\) 7.00000 + 12.1244i 0.250480 + 0.433844i
\(782\) −2.36603 + 0.633975i −0.0846089 + 0.0226709i
\(783\) −20.7846 −0.742781