Properties

Label 1950.2.y.c.199.2
Level $1950$
Weight $2$
Character 1950.199
Analytic conductor $15.571$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.y (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
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 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 199.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.199
Dual form 1950.2.y.c.49.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(5.59808 + 3.23205i) q^{11} -1.00000i q^{12} +(3.46410 + 1.00000i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.46410 - 2.00000i) q^{17} -1.00000 q^{18} +(-6.46410 + 3.73205i) q^{19} +2.00000i q^{21} +(-5.59808 + 3.23205i) q^{22} +(-3.23205 - 1.86603i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-2.59808 + 2.50000i) q^{26} +1.00000i q^{27} +(1.00000 - 1.73205i) q^{28} +(0.133975 - 0.232051i) q^{29} -1.73205i q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.23205 + 5.59808i) q^{33} +4.00000i q^{34} +(0.500000 - 0.866025i) q^{36} +(4.59808 - 7.96410i) q^{37} -7.46410i q^{38} +(2.50000 + 2.59808i) q^{39} +(1.73205 + 1.00000i) q^{41} +(-1.73205 - 1.00000i) q^{42} +(10.3301 - 5.96410i) q^{43} -6.46410i q^{44} +(3.23205 - 1.86603i) q^{46} -3.53590 q^{47} +(-0.866025 + 0.500000i) q^{48} +(1.50000 - 2.59808i) q^{49} +4.00000 q^{51} +(-0.866025 - 3.50000i) q^{52} +0.928203i q^{53} +(-0.866025 - 0.500000i) q^{54} +(1.00000 + 1.73205i) q^{56} -7.46410 q^{57} +(0.133975 + 0.232051i) q^{58} +(-7.33013 + 4.23205i) q^{59} +(5.19615 + 9.00000i) q^{61} +(1.50000 + 0.866025i) q^{62} +(-1.00000 + 1.73205i) q^{63} +1.00000 q^{64} -6.46410 q^{66} +(-5.73205 + 9.92820i) q^{67} +(-3.46410 - 2.00000i) q^{68} +(-1.86603 - 3.23205i) q^{69} +(-10.7321 + 6.19615i) q^{71} +(0.500000 + 0.866025i) q^{72} -2.00000 q^{73} +(4.59808 + 7.96410i) q^{74} +(6.46410 + 3.73205i) q^{76} +12.9282i q^{77} +(-3.50000 + 0.866025i) q^{78} +13.9282 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.73205 + 1.00000i) q^{82} -8.92820 q^{83} +(1.73205 - 1.00000i) q^{84} +11.9282i q^{86} +(0.232051 - 0.133975i) q^{87} +(5.59808 + 3.23205i) q^{88} +(0.464102 + 0.267949i) q^{89} +(1.73205 + 7.00000i) q^{91} +3.73205i q^{92} +(0.866025 - 1.50000i) q^{93} +(1.76795 - 3.06218i) q^{94} -1.00000i q^{96} +(-0.267949 - 0.464102i) q^{97} +(1.50000 + 2.59808i) q^{98} +6.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{4} + 4q^{7} + 4q^{8} + 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{4} + 4q^{7} + 4q^{8} + 2q^{9} + 12q^{11} - 8q^{14} - 2q^{16} - 4q^{18} - 12q^{19} - 12q^{22} - 6q^{23} + 4q^{28} + 4q^{29} - 2q^{32} + 6q^{33} + 2q^{36} + 8q^{37} + 10q^{39} + 24q^{43} + 6q^{46} - 28q^{47} + 6q^{49} + 16q^{51} + 4q^{56} - 16q^{57} + 4q^{58} - 12q^{59} + 6q^{62} - 4q^{63} + 4q^{64} - 12q^{66} - 16q^{67} - 4q^{69} - 36q^{71} + 2q^{72} - 8q^{73} + 8q^{74} + 12q^{76} - 14q^{78} + 28q^{79} - 2q^{81} - 8q^{83} - 6q^{87} + 12q^{88} - 12q^{89} + 14q^{94} - 8q^{97} + 6q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0
\(6\) −0.866025 + 0.500000i −0.353553 + 0.204124i
\(7\) 1.00000 + 1.73205i 0.377964 + 0.654654i 0.990766 0.135583i \(-0.0432908\pi\)
−0.612801 + 0.790237i \(0.709957\pi\)
\(8\) 1.00000 0.353553
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 5.59808 + 3.23205i 1.68788 + 0.974500i 0.956136 + 0.292925i \(0.0946285\pi\)
0.731748 + 0.681575i \(0.238705\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 3.46410 + 1.00000i 0.960769 + 0.277350i
\(14\) −2.00000 −0.534522
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.46410 2.00000i 0.840168 0.485071i −0.0171533 0.999853i \(-0.505460\pi\)
0.857321 + 0.514782i \(0.172127\pi\)
\(18\) −1.00000 −0.235702
\(19\) −6.46410 + 3.73205i −1.48297 + 0.856191i −0.999813 0.0193444i \(-0.993842\pi\)
−0.483154 + 0.875536i \(0.660509\pi\)
\(20\) 0 0
\(21\) 2.00000i 0.436436i
\(22\) −5.59808 + 3.23205i −1.19351 + 0.689076i
\(23\) −3.23205 1.86603i −0.673929 0.389093i 0.123635 0.992328i \(-0.460545\pi\)
−0.797564 + 0.603235i \(0.793878\pi\)
\(24\) 0.866025 + 0.500000i 0.176777 + 0.102062i
\(25\) 0 0
\(26\) −2.59808 + 2.50000i −0.509525 + 0.490290i
\(27\) 1.00000i 0.192450i
\(28\) 1.00000 1.73205i 0.188982 0.327327i
\(29\) 0.133975 0.232051i 0.0248785 0.0430908i −0.853318 0.521391i \(-0.825413\pi\)
0.878197 + 0.478300i \(0.158747\pi\)
\(30\) 0 0
\(31\) 1.73205i 0.311086i −0.987829 0.155543i \(-0.950287\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) 3.23205 + 5.59808i 0.562628 + 0.974500i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 0.866025i 0.0833333 0.144338i
\(37\) 4.59808 7.96410i 0.755919 1.30929i −0.188997 0.981978i \(-0.560524\pi\)
0.944916 0.327313i \(-0.106143\pi\)
\(38\) 7.46410i 1.21084i
\(39\) 2.50000 + 2.59808i 0.400320 + 0.416025i
\(40\) 0 0
\(41\) 1.73205 + 1.00000i 0.270501 + 0.156174i 0.629115 0.777312i \(-0.283417\pi\)
−0.358614 + 0.933486i \(0.616751\pi\)
\(42\) −1.73205 1.00000i −0.267261 0.154303i
\(43\) 10.3301 5.96410i 1.57533 0.909517i 0.579831 0.814736i \(-0.303118\pi\)
0.995498 0.0947805i \(-0.0302149\pi\)
\(44\) 6.46410i 0.974500i
\(45\) 0 0
\(46\) 3.23205 1.86603i 0.476540 0.275130i
\(47\) −3.53590 −0.515764 −0.257882 0.966176i \(-0.583025\pi\)
−0.257882 + 0.966176i \(0.583025\pi\)
\(48\) −0.866025 + 0.500000i −0.125000 + 0.0721688i
\(49\) 1.50000 2.59808i 0.214286 0.371154i
\(50\) 0 0
\(51\) 4.00000 0.560112
\(52\) −0.866025 3.50000i −0.120096 0.485363i
\(53\) 0.928203i 0.127499i 0.997966 + 0.0637493i \(0.0203058\pi\)
−0.997966 + 0.0637493i \(0.979694\pi\)
\(54\) −0.866025 0.500000i −0.117851 0.0680414i
\(55\) 0 0
\(56\) 1.00000 + 1.73205i 0.133631 + 0.231455i
\(57\) −7.46410 −0.988644
\(58\) 0.133975 + 0.232051i 0.0175917 + 0.0304698i
\(59\) −7.33013 + 4.23205i −0.954301 + 0.550966i −0.894414 0.447239i \(-0.852407\pi\)
−0.0598868 + 0.998205i \(0.519074\pi\)
\(60\) 0 0
\(61\) 5.19615 + 9.00000i 0.665299 + 1.15233i 0.979204 + 0.202878i \(0.0650293\pi\)
−0.313905 + 0.949454i \(0.601637\pi\)
\(62\) 1.50000 + 0.866025i 0.190500 + 0.109985i
\(63\) −1.00000 + 1.73205i −0.125988 + 0.218218i
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −6.46410 −0.795676
\(67\) −5.73205 + 9.92820i −0.700281 + 1.21292i 0.268086 + 0.963395i \(0.413609\pi\)
−0.968368 + 0.249528i \(0.919724\pi\)
\(68\) −3.46410 2.00000i −0.420084 0.242536i
\(69\) −1.86603 3.23205i −0.224643 0.389093i
\(70\) 0 0
\(71\) −10.7321 + 6.19615i −1.27366 + 0.735348i −0.975675 0.219222i \(-0.929648\pi\)
−0.297985 + 0.954570i \(0.596315\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −2.00000 −0.234082 −0.117041 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) 4.59808 + 7.96410i 0.534516 + 0.925808i
\(75\) 0 0
\(76\) 6.46410 + 3.73205i 0.741483 + 0.428096i
\(77\) 12.9282i 1.47331i
\(78\) −3.50000 + 0.866025i −0.396297 + 0.0980581i
\(79\) 13.9282 1.56705 0.783523 0.621363i \(-0.213421\pi\)
0.783523 + 0.621363i \(0.213421\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.73205 + 1.00000i −0.191273 + 0.110432i
\(83\) −8.92820 −0.979998 −0.489999 0.871723i \(-0.663003\pi\)
−0.489999 + 0.871723i \(0.663003\pi\)
\(84\) 1.73205 1.00000i 0.188982 0.109109i
\(85\) 0 0
\(86\) 11.9282i 1.28625i
\(87\) 0.232051 0.133975i 0.0248785 0.0143636i
\(88\) 5.59808 + 3.23205i 0.596757 + 0.344538i
\(89\) 0.464102 + 0.267949i 0.0491947 + 0.0284026i 0.524396 0.851475i \(-0.324291\pi\)
−0.475201 + 0.879877i \(0.657625\pi\)
\(90\) 0 0
\(91\) 1.73205 + 7.00000i 0.181568 + 0.733799i
\(92\) 3.73205i 0.389093i
\(93\) 0.866025 1.50000i 0.0898027 0.155543i
\(94\) 1.76795 3.06218i 0.182350 0.315840i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −0.267949 0.464102i −0.0272061 0.0471224i 0.852102 0.523376i \(-0.175328\pi\)
−0.879308 + 0.476254i \(0.841994\pi\)
\(98\) 1.50000 + 2.59808i 0.151523 + 0.262445i
\(99\) 6.46410i 0.649667i
\(100\) 0 0
\(101\) −1.46410 + 2.53590i −0.145684 + 0.252331i −0.929628 0.368500i \(-0.879871\pi\)
0.783944 + 0.620831i \(0.213205\pi\)
\(102\) −2.00000 + 3.46410i −0.198030 + 0.342997i
\(103\) 11.8564i 1.16825i −0.811665 0.584123i \(-0.801438\pi\)
0.811665 0.584123i \(-0.198562\pi\)
\(104\) 3.46410 + 1.00000i 0.339683 + 0.0980581i
\(105\) 0 0
\(106\) −0.803848 0.464102i −0.0780766 0.0450775i
\(107\) −6.80385 3.92820i −0.657753 0.379754i 0.133667 0.991026i \(-0.457325\pi\)
−0.791420 + 0.611273i \(0.790658\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 15.8564i 1.51877i 0.650643 + 0.759384i \(0.274500\pi\)
−0.650643 + 0.759384i \(0.725500\pi\)
\(110\) 0 0
\(111\) 7.96410 4.59808i 0.755919 0.436430i
\(112\) −2.00000 −0.188982
\(113\) 0.696152 0.401924i 0.0654885 0.0378098i −0.466898 0.884311i \(-0.654629\pi\)
0.532387 + 0.846501i \(0.321295\pi\)
\(114\) 3.73205 6.46410i 0.349539 0.605419i
\(115\) 0 0
\(116\) −0.267949 −0.0248785
\(117\) 0.866025 + 3.50000i 0.0800641 + 0.323575i
\(118\) 8.46410i 0.779184i
\(119\) 6.92820 + 4.00000i 0.635107 + 0.366679i
\(120\) 0 0
\(121\) 15.3923 + 26.6603i 1.39930 + 2.42366i
\(122\) −10.3923 −0.940875
\(123\) 1.00000 + 1.73205i 0.0901670 + 0.156174i
\(124\) −1.50000 + 0.866025i −0.134704 + 0.0777714i
\(125\) 0 0
\(126\) −1.00000 1.73205i −0.0890871 0.154303i
\(127\) −4.26795 2.46410i −0.378719 0.218654i 0.298542 0.954397i \(-0.403500\pi\)
−0.677261 + 0.735743i \(0.736833\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 11.9282 1.05022
\(130\) 0 0
\(131\) −18.6603 −1.63035 −0.815177 0.579212i \(-0.803360\pi\)
−0.815177 + 0.579212i \(0.803360\pi\)
\(132\) 3.23205 5.59808i 0.281314 0.487250i
\(133\) −12.9282 7.46410i −1.12102 0.647220i
\(134\) −5.73205 9.92820i −0.495174 0.857666i
\(135\) 0 0
\(136\) 3.46410 2.00000i 0.297044 0.171499i
\(137\) 1.23205 + 2.13397i 0.105261 + 0.182318i 0.913845 0.406063i \(-0.133099\pi\)
−0.808584 + 0.588381i \(0.799765\pi\)
\(138\) 3.73205 0.317693
\(139\) −6.46410 11.1962i −0.548278 0.949645i −0.998393 0.0566745i \(-0.981950\pi\)
0.450115 0.892971i \(-0.351383\pi\)
\(140\) 0 0
\(141\) −3.06218 1.76795i −0.257882 0.148888i
\(142\) 12.3923i 1.03994i
\(143\) 16.1603 + 16.7942i 1.35139 + 1.40440i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 1.00000 1.73205i 0.0827606 0.143346i
\(147\) 2.59808 1.50000i 0.214286 0.123718i
\(148\) −9.19615 −0.755919
\(149\) 11.7224 6.76795i 0.960339 0.554452i 0.0640617 0.997946i \(-0.479595\pi\)
0.896277 + 0.443494i \(0.146261\pi\)
\(150\) 0 0
\(151\) 10.3923i 0.845714i −0.906196 0.422857i \(-0.861027\pi\)
0.906196 0.422857i \(-0.138973\pi\)
\(152\) −6.46410 + 3.73205i −0.524308 + 0.302709i
\(153\) 3.46410 + 2.00000i 0.280056 + 0.161690i
\(154\) −11.1962 6.46410i −0.902212 0.520892i
\(155\) 0 0
\(156\) 1.00000 3.46410i 0.0800641 0.277350i
\(157\) 5.00000i 0.399043i 0.979893 + 0.199522i \(0.0639388\pi\)
−0.979893 + 0.199522i \(0.936061\pi\)
\(158\) −6.96410 + 12.0622i −0.554034 + 0.959615i
\(159\) −0.464102 + 0.803848i −0.0368057 + 0.0637493i
\(160\) 0 0
\(161\) 7.46410i 0.588254i
\(162\) −0.500000 0.866025i −0.0392837 0.0680414i
\(163\) 7.52628 + 13.0359i 0.589504 + 1.02105i 0.994297 + 0.106642i \(0.0340100\pi\)
−0.404794 + 0.914408i \(0.632657\pi\)
\(164\) 2.00000i 0.156174i
\(165\) 0 0
\(166\) 4.46410 7.73205i 0.346481 0.600124i
\(167\) 8.16025 14.1340i 0.631459 1.09372i −0.355794 0.934564i \(-0.615790\pi\)
0.987254 0.159155i \(-0.0508771\pi\)
\(168\) 2.00000i 0.154303i
\(169\) 11.0000 + 6.92820i 0.846154 + 0.532939i
\(170\) 0 0
\(171\) −6.46410 3.73205i −0.494322 0.285397i
\(172\) −10.3301 5.96410i −0.787665 0.454758i
\(173\) 9.46410 5.46410i 0.719542 0.415428i −0.0950419 0.995473i \(-0.530299\pi\)
0.814584 + 0.580045i \(0.196965\pi\)
\(174\) 0.267949i 0.0203132i
\(175\) 0 0
\(176\) −5.59808 + 3.23205i −0.421971 + 0.243625i
\(177\) −8.46410 −0.636201
\(178\) −0.464102 + 0.267949i −0.0347859 + 0.0200836i
\(179\) −9.86603 + 17.0885i −0.737421 + 1.27725i 0.216231 + 0.976342i \(0.430623\pi\)
−0.953653 + 0.300909i \(0.902710\pi\)
\(180\) 0 0
\(181\) −2.92820 −0.217652 −0.108826 0.994061i \(-0.534709\pi\)
−0.108826 + 0.994061i \(0.534709\pi\)
\(182\) −6.92820 2.00000i −0.513553 0.148250i
\(183\) 10.3923i 0.768221i
\(184\) −3.23205 1.86603i −0.238270 0.137565i
\(185\) 0 0
\(186\) 0.866025 + 1.50000i 0.0635001 + 0.109985i
\(187\) 25.8564 1.89081
\(188\) 1.76795 + 3.06218i 0.128941 + 0.223332i
\(189\) −1.73205 + 1.00000i −0.125988 + 0.0727393i
\(190\) 0 0
\(191\) −10.7321 18.5885i −0.776544 1.34501i −0.933923 0.357475i \(-0.883638\pi\)
0.157379 0.987538i \(-0.449696\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) −5.66025 + 9.80385i −0.407434 + 0.705696i −0.994601 0.103769i \(-0.966910\pi\)
0.587167 + 0.809466i \(0.300243\pi\)
\(194\) 0.535898 0.0384753
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 2.19615 3.80385i 0.156469 0.271013i −0.777124 0.629348i \(-0.783322\pi\)
0.933593 + 0.358335i \(0.116655\pi\)
\(198\) −5.59808 3.23205i −0.397838 0.229692i
\(199\) −2.53590 4.39230i −0.179765 0.311362i 0.762035 0.647536i \(-0.224200\pi\)
−0.941800 + 0.336174i \(0.890867\pi\)
\(200\) 0 0
\(201\) −9.92820 + 5.73205i −0.700281 + 0.404308i
\(202\) −1.46410 2.53590i −0.103014 0.178425i
\(203\) 0.535898 0.0376127
\(204\) −2.00000 3.46410i −0.140028 0.242536i
\(205\) 0 0
\(206\) 10.2679 + 5.92820i 0.715402 + 0.413037i
\(207\) 3.73205i 0.259395i
\(208\) −2.59808 + 2.50000i −0.180144 + 0.173344i
\(209\) −48.2487 −3.33743
\(210\) 0 0
\(211\) 5.66025 9.80385i 0.389668 0.674925i −0.602737 0.797940i \(-0.705923\pi\)
0.992405 + 0.123015i \(0.0392564\pi\)
\(212\) 0.803848 0.464102i 0.0552085 0.0318746i
\(213\) −12.3923 −0.849107
\(214\) 6.80385 3.92820i 0.465101 0.268526i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 3.00000 1.73205i 0.203653 0.117579i
\(218\) −13.7321 7.92820i −0.930052 0.536966i
\(219\) −1.73205 1.00000i −0.117041 0.0675737i
\(220\) 0 0
\(221\) 14.0000 3.46410i 0.941742 0.233021i
\(222\) 9.19615i 0.617205i
\(223\) 10.2679 17.7846i 0.687593 1.19095i −0.285022 0.958521i \(-0.592001\pi\)
0.972614 0.232424i \(-0.0746659\pi\)
\(224\) 1.00000 1.73205i 0.0668153 0.115728i
\(225\) 0 0
\(226\) 0.803848i 0.0534711i
\(227\) 8.19615 + 14.1962i 0.543998 + 0.942232i 0.998669 + 0.0515725i \(0.0164233\pi\)
−0.454672 + 0.890659i \(0.650243\pi\)
\(228\) 3.73205 + 6.46410i 0.247161 + 0.428096i
\(229\) 7.85641i 0.519166i 0.965721 + 0.259583i \(0.0835851\pi\)
−0.965721 + 0.259583i \(0.916415\pi\)
\(230\) 0 0
\(231\) −6.46410 + 11.1962i −0.425307 + 0.736653i
\(232\) 0.133975 0.232051i 0.00879586 0.0152349i
\(233\) 6.12436i 0.401220i 0.979671 + 0.200610i \(0.0642924\pi\)
−0.979671 + 0.200610i \(0.935708\pi\)
\(234\) −3.46410 1.00000i −0.226455 0.0653720i
\(235\) 0 0
\(236\) 7.33013 + 4.23205i 0.477151 + 0.275483i
\(237\) 12.0622 + 6.96410i 0.783523 + 0.452367i
\(238\) −6.92820 + 4.00000i −0.449089 + 0.259281i
\(239\) 16.3923i 1.06033i 0.847894 + 0.530165i \(0.177870\pi\)
−0.847894 + 0.530165i \(0.822130\pi\)
\(240\) 0 0
\(241\) 15.3564 8.86603i 0.989193 0.571111i 0.0841601 0.996452i \(-0.473179\pi\)
0.905033 + 0.425341i \(0.139846\pi\)
\(242\) −30.7846 −1.97891
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 5.19615 9.00000i 0.332650 0.576166i
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) −26.1244 + 6.46410i −1.66225 + 0.411301i
\(248\) 1.73205i 0.109985i
\(249\) −7.73205 4.46410i −0.489999 0.282901i
\(250\) 0 0
\(251\) −7.86603 13.6244i −0.496499 0.859962i 0.503493 0.863999i \(-0.332048\pi\)
−0.999992 + 0.00403776i \(0.998715\pi\)
\(252\) 2.00000 0.125988
\(253\) −12.0622 20.8923i −0.758343 1.31349i
\(254\) 4.26795 2.46410i 0.267795 0.154611i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −4.62436 2.66987i −0.288459 0.166542i 0.348787 0.937202i \(-0.386593\pi\)
−0.637247 + 0.770660i \(0.719927\pi\)
\(258\) −5.96410 + 10.3301i −0.371309 + 0.643126i
\(259\) 18.3923 1.14284
\(260\) 0 0
\(261\) 0.267949 0.0165856
\(262\) 9.33013 16.1603i 0.576417 0.998384i
\(263\) −5.30385 3.06218i −0.327049 0.188822i 0.327481 0.944858i \(-0.393800\pi\)
−0.654530 + 0.756036i \(0.727134\pi\)
\(264\) 3.23205 + 5.59808i 0.198919 + 0.344538i
\(265\) 0 0
\(266\) 12.9282 7.46410i 0.792679 0.457653i
\(267\) 0.267949 + 0.464102i 0.0163982 + 0.0284026i
\(268\) 11.4641 0.700281
\(269\) 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i \(-0.0474530\pi\)
−0.623082 + 0.782157i \(0.714120\pi\)
\(270\) 0 0
\(271\) 1.03590 + 0.598076i 0.0629263 + 0.0363305i 0.531133 0.847288i \(-0.321766\pi\)
−0.468207 + 0.883619i \(0.655100\pi\)
\(272\) 4.00000i 0.242536i
\(273\) −2.00000 + 6.92820i −0.121046 + 0.419314i
\(274\) −2.46410 −0.148862
\(275\) 0 0
\(276\) −1.86603 + 3.23205i −0.112322 + 0.194547i
\(277\) 3.40192 1.96410i 0.204402 0.118011i −0.394305 0.918980i \(-0.629015\pi\)
0.598707 + 0.800968i \(0.295681\pi\)
\(278\) 12.9282 0.775382
\(279\) 1.50000 0.866025i 0.0898027 0.0518476i
\(280\) 0 0
\(281\) 8.92820i 0.532612i −0.963889 0.266306i \(-0.914197\pi\)
0.963889 0.266306i \(-0.0858032\pi\)
\(282\) 3.06218 1.76795i 0.182350 0.105280i
\(283\) 8.59808 + 4.96410i 0.511103 + 0.295085i 0.733287 0.679920i \(-0.237985\pi\)
−0.222184 + 0.975005i \(0.571319\pi\)
\(284\) 10.7321 + 6.19615i 0.636830 + 0.367674i
\(285\) 0 0
\(286\) −22.6244 + 5.59808i −1.33781 + 0.331021i
\(287\) 4.00000i 0.236113i
\(288\) 0.500000 0.866025i 0.0294628 0.0510310i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 0.535898i 0.0314149i
\(292\) 1.00000 + 1.73205i 0.0585206 + 0.101361i
\(293\) −15.9282 27.5885i −0.930536 1.61173i −0.782408 0.622767i \(-0.786009\pi\)
−0.148128 0.988968i \(-0.547325\pi\)
\(294\) 3.00000i 0.174964i
\(295\) 0 0
\(296\) 4.59808 7.96410i 0.267258 0.462904i
\(297\) −3.23205 + 5.59808i −0.187543 + 0.324833i
\(298\) 13.5359i 0.784114i
\(299\) −9.33013 9.69615i −0.539575 0.560743i
\(300\) 0 0
\(301\) 20.6603 + 11.9282i 1.19084 + 0.687530i
\(302\) 9.00000 + 5.19615i 0.517892 + 0.299005i
\(303\) −2.53590 + 1.46410i −0.145684 + 0.0841104i
\(304\) 7.46410i 0.428096i
\(305\) 0 0
\(306\) −3.46410 + 2.00000i −0.198030 + 0.114332i
\(307\) 19.4641 1.11087 0.555437 0.831558i \(-0.312551\pi\)
0.555437 + 0.831558i \(0.312551\pi\)
\(308\) 11.1962 6.46410i 0.637960 0.368326i
\(309\) 5.92820 10.2679i 0.337244 0.584123i
\(310\) 0 0
\(311\) −28.3923 −1.60998 −0.804990 0.593288i \(-0.797829\pi\)
−0.804990 + 0.593288i \(0.797829\pi\)
\(312\) 2.50000 + 2.59808i 0.141535 + 0.147087i
\(313\) 28.0000i 1.58265i −0.611393 0.791327i \(-0.709391\pi\)
0.611393 0.791327i \(-0.290609\pi\)
\(314\) −4.33013 2.50000i −0.244363 0.141083i
\(315\) 0 0
\(316\) −6.96410 12.0622i −0.391761 0.678551i
\(317\) 14.5359 0.816417 0.408209 0.912889i \(-0.366154\pi\)
0.408209 + 0.912889i \(0.366154\pi\)
\(318\) −0.464102 0.803848i −0.0260255 0.0450775i
\(319\) 1.50000 0.866025i 0.0839839 0.0484881i
\(320\) 0 0
\(321\) −3.92820 6.80385i −0.219251 0.379754i
\(322\) 6.46410 + 3.73205i 0.360230 + 0.207979i
\(323\) −14.9282 + 25.8564i −0.830627 + 1.43869i
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) −15.0526 −0.833684
\(327\) −7.92820 + 13.7321i −0.438431 + 0.759384i
\(328\) 1.73205 + 1.00000i 0.0956365 + 0.0552158i
\(329\) −3.53590 6.12436i −0.194940 0.337647i
\(330\) 0 0
\(331\) −14.5359 + 8.39230i −0.798965 + 0.461283i −0.843109 0.537742i \(-0.819277\pi\)
0.0441440 + 0.999025i \(0.485944\pi\)
\(332\) 4.46410 + 7.73205i 0.244999 + 0.424351i
\(333\) 9.19615 0.503946
\(334\) 8.16025 + 14.1340i 0.446509 + 0.773377i
\(335\) 0 0
\(336\) −1.73205 1.00000i −0.0944911 0.0545545i
\(337\) 9.32051i 0.507720i −0.967241 0.253860i \(-0.918300\pi\)
0.967241 0.253860i \(-0.0817003\pi\)
\(338\) −11.5000 + 6.06218i −0.625518 + 0.329739i
\(339\) 0.803848 0.0436590
\(340\) 0 0
\(341\) 5.59808 9.69615i 0.303153 0.525076i
\(342\) 6.46410 3.73205i 0.349539 0.201806i
\(343\) 20.0000 1.07990
\(344\) 10.3301 5.96410i 0.556963 0.321563i
\(345\) 0 0
\(346\) 10.9282i 0.587504i
\(347\) −1.39230 + 0.803848i −0.0747428 + 0.0431528i −0.536906 0.843642i \(-0.680407\pi\)
0.462163 + 0.886795i \(0.347074\pi\)
\(348\) −0.232051 0.133975i −0.0124392 0.00718179i
\(349\) −18.5885 10.7321i −0.995017 0.574474i −0.0882471 0.996099i \(-0.528127\pi\)
−0.906770 + 0.421625i \(0.861460\pi\)
\(350\) 0 0
\(351\) −1.00000 + 3.46410i −0.0533761 + 0.184900i
\(352\) 6.46410i 0.344538i
\(353\) −1.00000 + 1.73205i −0.0532246 + 0.0921878i −0.891410 0.453197i \(-0.850283\pi\)
0.838186 + 0.545385i \(0.183617\pi\)
\(354\) 4.23205 7.33013i 0.224931 0.389592i
\(355\) 0 0
\(356\) 0.535898i 0.0284026i
\(357\) 4.00000 + 6.92820i 0.211702 + 0.366679i
\(358\) −9.86603 17.0885i −0.521436 0.903153i
\(359\) 5.07180i 0.267679i −0.991003 0.133840i \(-0.957269\pi\)
0.991003 0.133840i \(-0.0427307\pi\)
\(360\) 0 0
\(361\) 18.3564 31.7942i 0.966127 1.67338i
\(362\) 1.46410 2.53590i 0.0769515 0.133284i
\(363\) 30.7846i 1.61577i
\(364\) 5.19615 5.00000i 0.272352 0.262071i
\(365\) 0 0
\(366\) −9.00000 5.19615i −0.470438 0.271607i
\(367\) 13.5167 + 7.80385i 0.705564 + 0.407358i 0.809416 0.587235i \(-0.199784\pi\)
−0.103852 + 0.994593i \(0.533117\pi\)
\(368\) 3.23205 1.86603i 0.168482 0.0972733i
\(369\) 2.00000i 0.104116i
\(370\) 0 0
\(371\) −1.60770 + 0.928203i −0.0834674 + 0.0481899i
\(372\) −1.73205 −0.0898027
\(373\) −13.6699 + 7.89230i −0.707799 + 0.408648i −0.810246 0.586090i \(-0.800666\pi\)
0.102446 + 0.994739i \(0.467333\pi\)
\(374\) −12.9282 + 22.3923i −0.668501 + 1.15788i
\(375\) 0 0
\(376\) −3.53590 −0.182350
\(377\) 0.696152 0.669873i 0.0358537 0.0345002i
\(378\) 2.00000i 0.102869i
\(379\) −24.1244 13.9282i −1.23918 0.715444i −0.270257 0.962788i \(-0.587109\pi\)
−0.968928 + 0.247344i \(0.920442\pi\)
\(380\) 0 0
\(381\) −2.46410 4.26795i −0.126240 0.218654i
\(382\) 21.4641 1.09820
\(383\) 12.6962 + 21.9904i 0.648743 + 1.12366i 0.983423 + 0.181324i \(0.0580383\pi\)
−0.334680 + 0.942332i \(0.608628\pi\)
\(384\) −0.866025 + 0.500000i −0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) −5.66025 9.80385i −0.288099 0.499003i
\(387\) 10.3301 + 5.96410i 0.525110 + 0.303172i
\(388\) −0.267949 + 0.464102i −0.0136031 + 0.0235612i
\(389\) 23.7321 1.20326 0.601631 0.798774i \(-0.294518\pi\)
0.601631 + 0.798774i \(0.294518\pi\)
\(390\) 0 0
\(391\) −14.9282 −0.754952
\(392\) 1.50000 2.59808i 0.0757614 0.131223i
\(393\) −16.1603 9.33013i −0.815177 0.470643i
\(394\) 2.19615 + 3.80385i 0.110641 + 0.191635i
\(395\) 0 0
\(396\) 5.59808 3.23205i 0.281314 0.162417i
\(397\) −6.06218 10.5000i −0.304252 0.526980i 0.672843 0.739786i \(-0.265073\pi\)
−0.977095 + 0.212806i \(0.931740\pi\)
\(398\) 5.07180 0.254226
\(399\) −7.46410 12.9282i −0.373672 0.647220i
\(400\) 0 0
\(401\) −27.7128 16.0000i −1.38391 0.799002i −0.391292 0.920267i \(-0.627972\pi\)
−0.992620 + 0.121265i \(0.961305\pi\)
\(402\) 11.4641i 0.571777i
\(403\) 1.73205 6.00000i 0.0862796 0.298881i
\(404\) 2.92820 0.145684
\(405\) 0 0
\(406\) −0.267949 + 0.464102i −0.0132981 + 0.0230330i
\(407\) 51.4808 29.7224i 2.55181 1.47329i
\(408\) 4.00000 0.198030
\(409\) −3.46410 + 2.00000i −0.171289 + 0.0988936i −0.583193 0.812333i \(-0.698197\pi\)
0.411905 + 0.911227i \(0.364864\pi\)
\(410\) 0 0
\(411\) 2.46410i 0.121545i
\(412\) −10.2679 + 5.92820i −0.505866 + 0.292062i
\(413\) −14.6603 8.46410i −0.721384 0.416491i
\(414\) 3.23205 + 1.86603i 0.158847 + 0.0917101i
\(415\) 0 0
\(416\) −0.866025 3.50000i −0.0424604 0.171602i
\(417\) 12.9282i 0.633097i
\(418\) 24.1244 41.7846i 1.17996 2.04375i
\(419\) 11.1962 19.3923i 0.546968 0.947376i −0.451512 0.892265i \(-0.649115\pi\)
0.998480 0.0551112i \(-0.0175513\pi\)
\(420\) 0 0
\(421\) 4.39230i 0.214068i 0.994255 + 0.107034i \(0.0341353\pi\)
−0.994255 + 0.107034i \(0.965865\pi\)
\(422\) 5.66025 + 9.80385i 0.275537 + 0.477244i
\(423\) −1.76795 3.06218i −0.0859606 0.148888i
\(424\) 0.928203i 0.0450775i
\(425\) 0 0
\(426\) 6.19615 10.7321i 0.300205 0.519970i
\(427\) −10.3923 + 18.0000i −0.502919 + 0.871081i
\(428\) 7.85641i 0.379754i
\(429\) 5.59808 + 22.6244i 0.270278 + 1.09231i
\(430\) 0 0
\(431\) 24.5885 + 14.1962i 1.18438 + 0.683805i 0.957025 0.290006i \(-0.0936574\pi\)
0.227360 + 0.973811i \(0.426991\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 16.7321 9.66025i 0.804091 0.464242i −0.0408086 0.999167i \(-0.512993\pi\)
0.844900 + 0.534925i \(0.179660\pi\)
\(434\) 3.46410i 0.166282i
\(435\) 0 0
\(436\) 13.7321 7.92820i 0.657646 0.379692i
\(437\) 27.8564 1.33255
\(438\) 1.73205 1.00000i 0.0827606 0.0477818i
\(439\) −8.92820 + 15.4641i −0.426120 + 0.738061i −0.996524 0.0833027i \(-0.973453\pi\)
0.570404 + 0.821364i \(0.306786\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) −4.00000 + 13.8564i −0.190261 + 0.659082i
\(443\) 16.3923i 0.778822i 0.921064 + 0.389411i \(0.127321\pi\)
−0.921064 + 0.389411i \(0.872679\pi\)
\(444\) −7.96410 4.59808i −0.377960 0.218215i
\(445\) 0 0
\(446\) 10.2679 + 17.7846i 0.486201 + 0.842126i
\(447\) 13.5359 0.640226
\(448\) 1.00000 + 1.73205i 0.0472456 + 0.0818317i
\(449\) 13.6077 7.85641i 0.642187 0.370767i −0.143270 0.989684i \(-0.545762\pi\)
0.785456 + 0.618917i \(0.212428\pi\)
\(450\) 0 0
\(451\) 6.46410 + 11.1962i 0.304383 + 0.527206i
\(452\) −0.696152 0.401924i −0.0327443 0.0189049i
\(453\) 5.19615 9.00000i 0.244137 0.422857i
\(454\) −16.3923 −0.769329
\(455\) 0 0
\(456\) −7.46410 −0.349539
\(457\) 12.2679 21.2487i 0.573870 0.993973i −0.422293 0.906459i \(-0.638775\pi\)
0.996163 0.0875134i \(-0.0278920\pi\)
\(458\) −6.80385 3.92820i −0.317923 0.183553i
\(459\) 2.00000 + 3.46410i 0.0933520 + 0.161690i
\(460\) 0 0
\(461\) 0.401924 0.232051i 0.0187195 0.0108077i −0.490611 0.871379i \(-0.663226\pi\)
0.509331 + 0.860571i \(0.329893\pi\)
\(462\) −6.46410 11.1962i −0.300737 0.520892i
\(463\) −7.07180 −0.328654 −0.164327 0.986406i \(-0.552545\pi\)
−0.164327 + 0.986406i \(0.552545\pi\)
\(464\) 0.133975 + 0.232051i 0.00621961 + 0.0107727i
\(465\) 0 0
\(466\) −5.30385 3.06218i −0.245696 0.141853i
\(467\) 15.8564i 0.733747i 0.930271 + 0.366873i \(0.119572\pi\)
−0.930271 + 0.366873i \(0.880428\pi\)
\(468\) 2.59808 2.50000i 0.120096 0.115563i
\(469\) −22.9282 −1.05873
\(470\) 0 0
\(471\) −2.50000 + 4.33013i −0.115194 + 0.199522i
\(472\) −7.33013 + 4.23205i −0.337396 + 0.194796i
\(473\) 77.1051 3.54530
\(474\) −12.0622 + 6.96410i −0.554034 + 0.319872i
\(475\) 0 0
\(476\) 8.00000i 0.366679i
\(477\) −0.803848 + 0.464102i −0.0368057 + 0.0212498i
\(478\) −14.1962 8.19615i −0.649317 0.374883i
\(479\) −4.73205 2.73205i −0.216213 0.124831i 0.387983 0.921667i \(-0.373172\pi\)
−0.604195 + 0.796836i \(0.706505\pi\)
\(480\) 0 0
\(481\) 23.8923 22.9904i 1.08940 1.04827i
\(482\) 17.7321i 0.807673i
\(483\) 3.73205 6.46410i 0.169814 0.294127i
\(484\) 15.3923 26.6603i 0.699650 1.21183i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −11.5885 20.0718i −0.525123 0.909540i −0.999572 0.0292568i \(-0.990686\pi\)
0.474449 0.880283i \(-0.342647\pi\)
\(488\) 5.19615 + 9.00000i 0.235219 + 0.407411i
\(489\) 15.0526i 0.680700i
\(490\) 0 0
\(491\) 8.66025 15.0000i 0.390832 0.676941i −0.601728 0.798701i \(-0.705521\pi\)
0.992559 + 0.121761i \(0.0388541\pi\)
\(492\) 1.00000 1.73205i 0.0450835 0.0780869i
\(493\) 1.07180i 0.0482713i
\(494\) 7.46410 25.8564i 0.335826 1.16333i
\(495\) 0 0
\(496\) 1.50000 + 0.866025i 0.0673520 + 0.0388857i
\(497\) −21.4641 12.3923i −0.962797 0.555871i
\(498\) 7.73205 4.46410i 0.346481 0.200041i
\(499\) 6.53590i 0.292587i −0.989241 0.146293i \(-0.953266\pi\)
0.989241 0.146293i \(-0.0467344\pi\)
\(500\) 0 0
\(501\) 14.1340 8.16025i 0.631459 0.364573i
\(502\) 15.7321 0.702156
\(503\) −27.0000 + 15.5885i −1.20387 + 0.695055i −0.961414 0.275107i \(-0.911287\pi\)
−0.242457 + 0.970162i \(0.577953\pi\)
\(504\) −1.00000 + 1.73205i −0.0445435 + 0.0771517i
\(505\) 0 0
\(506\) 24.1244 1.07246
\(507\) 6.06218 + 11.5000i 0.269231 + 0.510733i
\(508\) 4.92820i 0.218654i
\(509\) −1.20577 0.696152i −0.0534449 0.0308564i 0.473039 0.881041i \(-0.343157\pi\)
−0.526484 + 0.850185i \(0.676490\pi\)
\(510\) 0 0
\(511\) −2.00000 3.46410i −0.0884748 0.153243i
\(512\) 1.00000 0.0441942
\(513\) −3.73205 6.46410i −0.164774 0.285397i
\(514\) 4.62436 2.66987i 0.203972 0.117763i
\(515\) 0 0
\(516\) −5.96410 10.3301i −0.262555 0.454758i
\(517\) −19.7942 11.4282i −0.870549 0.502612i
\(518\) −9.19615 + 15.9282i −0.404056 + 0.699845i
\(519\) 10.9282 0.479695
\(520\) 0 0
\(521\) −17.3205 −0.758825 −0.379413 0.925228i \(-0.623874\pi\)
−0.379413 + 0.925228i \(0.623874\pi\)
\(522\) −0.133975 + 0.232051i −0.00586391 + 0.0101566i
\(523\) −10.2058 5.89230i −0.446267 0.257653i 0.259985 0.965613i \(-0.416282\pi\)
−0.706252 + 0.707960i \(0.749616\pi\)
\(524\) 9.33013 + 16.1603i 0.407588 + 0.705964i
\(525\) 0 0
\(526\) 5.30385 3.06218i 0.231259 0.133517i
\(527\) −3.46410 6.00000i −0.150899 0.261364i
\(528\) −6.46410 −0.281314
\(529\) −4.53590 7.85641i −0.197213 0.341583i
\(530\) 0 0
\(531\) −7.33013 4.23205i −0.318100 0.183655i
\(532\) 14.9282i 0.647220i
\(533\) 5.00000 + 5.19615i 0.216574 + 0.225070i
\(534\) −0.535898 −0.0231906
\(535\) 0 0
\(536\) −5.73205 + 9.92820i −0.247587 + 0.428833i
\(537\) −17.0885 + 9.86603i −0.737421 + 0.425750i
\(538\) −12.0000 −0.517357
\(539\) 16.7942 9.69615i 0.723379 0.417643i
\(540\) 0 0
\(541\) 26.9282i 1.15773i 0.815422 + 0.578867i \(0.196505\pi\)
−0.815422 + 0.578867i \(0.803495\pi\)
\(542\) −1.03590 + 0.598076i −0.0444956 + 0.0256896i
\(543\) −2.53590 1.46410i −0.108826 0.0628306i
\(544\) −3.46410 2.00000i −0.148522 0.0857493i
\(545\) 0 0
\(546\) −5.00000 5.19615i −0.213980 0.222375i
\(547\) 22.9282i 0.980339i −0.871627 0.490170i \(-0.836935\pi\)
0.871627 0.490170i \(-0.163065\pi\)
\(548\) 1.23205 2.13397i 0.0526306 0.0911589i
\(549\) −5.19615 + 9.00000i −0.221766 + 0.384111i
\(550\) 0 0
\(551\) 2.00000i 0.0852029i
\(552\) −1.86603 3.23205i −0.0794233 0.137565i
\(553\) 13.9282 + 24.1244i 0.592287 + 1.02587i
\(554\) 3.92820i 0.166893i
\(555\) 0 0
\(556\) −6.46410 + 11.1962i −0.274139 + 0.474823i
\(557\) 8.85641 15.3397i 0.375258 0.649966i −0.615108 0.788443i \(-0.710887\pi\)
0.990366 + 0.138477i \(0.0442208\pi\)
\(558\) 1.73205i 0.0733236i
\(559\) 41.7487 10.3301i 1.76578 0.436918i
\(560\) 0 0
\(561\) 22.3923 + 12.9282i 0.945404 + 0.545829i
\(562\) 7.73205 + 4.46410i 0.326157 + 0.188307i
\(563\) −4.05256 + 2.33975i −0.170795 + 0.0986085i −0.582961 0.812500i \(-0.698106\pi\)
0.412166 + 0.911109i \(0.364772\pi\)
\(564\) 3.53590i 0.148888i
\(565\) 0 0
\(566\) −8.59808 + 4.96410i −0.361404 + 0.208657i
\(567\) −2.00000 −0.0839921
\(568\) −10.7321 + 6.19615i −0.450307 + 0.259985i
\(569\) 14.6603 25.3923i 0.614590 1.06450i −0.375867 0.926674i \(-0.622655\pi\)
0.990456 0.137827i \(-0.0440118\pi\)
\(570\) 0 0
\(571\) −17.1769 −0.718832 −0.359416 0.933178i \(-0.617024\pi\)
−0.359416 + 0.933178i \(0.617024\pi\)
\(572\) 6.46410 22.3923i 0.270278 0.936269i
\(573\) 21.4641i 0.896676i
\(574\) −3.46410 2.00000i −0.144589 0.0834784i
\(575\) 0 0
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) −0.500000 0.866025i −0.0207973 0.0360219i
\(579\) −9.80385 + 5.66025i −0.407434 + 0.235232i
\(580\) 0 0
\(581\) −8.92820 15.4641i −0.370404 0.641559i
\(582\) 0.464102 + 0.267949i 0.0192376 + 0.0111069i
\(583\) −3.00000 + 5.19615i −0.124247 + 0.215203i
\(584\) −2.00000 −0.0827606
\(585\) 0 0
\(586\) 31.8564 1.31598
\(587\) −1.19615 + 2.07180i −0.0493705 + 0.0855122i −0.889655 0.456634i \(-0.849055\pi\)
0.840284 + 0.542146i \(0.182388\pi\)
\(588\) −2.59808 1.50000i −0.107143 0.0618590i
\(589\) 6.46410 + 11.1962i 0.266349 + 0.461329i
\(590\) 0 0
\(591\) 3.80385 2.19615i 0.156469 0.0903376i
\(592\) 4.59808 + 7.96410i 0.188980 + 0.327323i
\(593\) −45.1051 −1.85225 −0.926123 0.377223i \(-0.876879\pi\)
−0.926123 + 0.377223i \(0.876879\pi\)
\(594\) −3.23205 5.59808i −0.132613 0.229692i
\(595\) 0 0
\(596\) −11.7224 6.76795i −0.480170 0.277226i
\(597\) 5.07180i 0.207575i
\(598\) 13.0622 3.23205i 0.534152 0.132168i
\(599\) 10.3923 0.424618 0.212309 0.977203i \(-0.431902\pi\)
0.212309 + 0.977203i \(0.431902\pi\)
\(600\) 0 0
\(601\) 9.89230 17.1340i 0.403516 0.698909i −0.590632 0.806941i \(-0.701121\pi\)
0.994147 + 0.108032i \(0.0344548\pi\)
\(602\) −20.6603 + 11.9282i −0.842049 + 0.486157i
\(603\) −11.4641 −0.466854
\(604\) −9.00000 + 5.19615i −0.366205 + 0.211428i
\(605\) 0 0
\(606\) 2.92820i 0.118950i
\(607\) 16.6077 9.58846i 0.674086 0.389183i −0.123537 0.992340i \(-0.539424\pi\)
0.797623 + 0.603156i \(0.206091\pi\)
\(608\) 6.46410 + 3.73205i 0.262154 + 0.151355i
\(609\) 0.464102 + 0.267949i 0.0188063 + 0.0108578i
\(610\) 0 0
\(611\) −12.2487 3.53590i −0.495530 0.143047i
\(612\) 4.00000i 0.161690i
\(613\) 19.5263 33.8205i 0.788659 1.36600i −0.138130 0.990414i \(-0.544109\pi\)
0.926789 0.375583i \(-0.122558\pi\)
\(614\) −9.73205 + 16.8564i −0.392754 + 0.680269i
\(615\) 0 0
\(616\) 12.9282i 0.520892i
\(617\) 11.2321 + 19.4545i 0.452185 + 0.783208i 0.998522 0.0543580i \(-0.0173112\pi\)
−0.546336 + 0.837566i \(0.683978\pi\)
\(618\) 5.92820 + 10.2679i 0.238467 + 0.413037i
\(619\) 24.2487i 0.974638i 0.873224 + 0.487319i \(0.162025\pi\)
−0.873224 + 0.487319i \(0.837975\pi\)
\(620\) 0 0
\(621\) 1.86603 3.23205i 0.0748810 0.129698i
\(622\) 14.1962 24.5885i 0.569214 0.985907i
\(623\) 1.07180i 0.0429406i
\(624\) −3.50000 + 0.866025i −0.140112 + 0.0346688i
\(625\) 0 0
\(626\) 24.2487 + 14.0000i 0.969173 + 0.559553i
\(627\) −41.7846 24.1244i −1.66872 0.963434i
\(628\) 4.33013 2.50000i 0.172791 0.0997609i
\(629\) 36.7846i 1.46670i
\(630\) 0 0
\(631\) 27.2487 15.7321i 1.08475 0.626283i 0.152579 0.988291i \(-0.451242\pi\)
0.932175 + 0.362008i \(0.117909\pi\)
\(632\) 13.9282 0.554034
\(633\) 9.80385 5.66025i 0.389668 0.224975i
\(634\) −7.26795 + 12.5885i −0.288647 + 0.499952i
\(635\) 0 0
\(636\) 0.928203 0.0368057
\(637\) 7.79423 7.50000i 0.308819 0.297161i
\(638\) 1.73205i 0.0685725i
\(639\) −10.7321 6.19615i −0.424553 0.245116i
\(640\) 0 0
\(641\) −0.0717968 0.124356i −0.00283580 0.00491175i 0.864604 0.502454i \(-0.167569\pi\)
−0.867440 + 0.497542i \(0.834236\pi\)
\(642\) 7.85641 0.310068
\(643\) −10.2679 17.7846i −0.404928 0.701357i 0.589385 0.807852i \(-0.299370\pi\)
−0.994313 + 0.106496i \(0.966037\pi\)
\(644\) −6.46410 + 3.73205i −0.254721 + 0.147063i
\(645\) 0 0
\(646\) −14.9282 25.8564i −0.587342 1.01731i
\(647\) −11.5359 6.66025i −0.453523 0.261842i 0.255794 0.966731i \(-0.417663\pi\)
−0.709317 + 0.704890i \(0.750996\pi\)
\(648\) −0.500000 + 0.866025i −0.0196419 + 0.0340207i
\(649\) −54.7128 −2.14767
\(650\) 0 0
\(651\) 3.46410 0.135769
\(652\) 7.52628 13.0359i 0.294752 0.510525i
\(653\) −3.67949 2.12436i −0.143990 0.0831325i 0.426274 0.904594i \(-0.359826\pi\)
−0.570264 + 0.821461i \(0.693159\pi\)
\(654\) −7.92820 13.7321i −0.310017 0.536966i
\(655\) 0 0
\(656\) −1.73205 + 1.00000i −0.0676252 + 0.0390434i
\(657\) −1.00000 1.73205i −0.0390137 0.0675737i
\(658\) 7.07180 0.275687
\(659\) −0.133975 0.232051i −0.00521891 0.00903942i 0.863404 0.504513i \(-0.168328\pi\)
−0.868623 + 0.495473i \(0.834995\pi\)
\(660\) 0 0
\(661\) −7.51666 4.33975i −0.292364 0.168797i 0.346643 0.937997i \(-0.387321\pi\)
−0.639008 + 0.769200i \(0.720655\pi\)
\(662\) 16.7846i 0.652352i
\(663\) 13.8564 + 4.00000i 0.538138 + 0.155347i
\(664\) −8.92820 −0.346481
\(665\) 0 0
\(666\) −4.59808 + 7.96410i −0.178172 + 0.308603i
\(667\) −0.866025 + 0.500000i −0.0335326 + 0.0193601i
\(668\) −16.3205 −0.631459
\(669\) 17.7846 10.2679i 0.687593 0.396982i
\(670\) 0 0
\(671\) 67.1769i 2.59334i
\(672\) 1.73205 1.00000i 0.0668153 0.0385758i
\(673\) −27.7128 16.0000i −1.06825 0.616755i −0.140548 0.990074i \(-0.544886\pi\)
−0.927703 + 0.373319i \(0.878220\pi\)
\(674\) 8.07180 + 4.66025i 0.310914 + 0.179506i
\(675\) 0 0
\(676\) 0.500000 12.9904i 0.0192308 0.499630i
\(677\) 32.3923i 1.24494i −0.782645 0.622469i \(-0.786130\pi\)
0.782645 0.622469i \(-0.213870\pi\)
\(678\) −0.401924 + 0.696152i −0.0154358 + 0.0267356i
\(679\) 0.535898 0.928203i 0.0205659 0.0356212i
\(680\) 0 0
\(681\) 16.3923i 0.628154i
\(682\) 5.59808 + 9.69615i 0.214361 + 0.371285i
\(683\) −20.3923 35.3205i −0.780290 1.35150i −0.931773 0.363042i \(-0.881738\pi\)
0.151483 0.988460i \(-0.451595\pi\)
\(684\) 7.46410i 0.285397i
\(685\) 0 0
\(686\) −10.0000 + 17.3205i −0.381802 + 0.661300i
\(687\) −3.92820 + 6.80385i −0.149870 + 0.259583i
\(688\) 11.9282i 0.454758i
\(689\) −0.928203 + 3.21539i −0.0353617 + 0.122497i
\(690\) 0 0
\(691\) −23.5359 13.5885i −0.895348 0.516929i −0.0196598 0.999807i \(-0.506258\pi\)
−0.875688 + 0.482877i \(0.839592\pi\)
\(692\) −9.46410 5.46410i −0.359771 0.207714i
\(693\) −11.1962 + 6.46410i −0.425307 + 0.245551i
\(694\) 1.60770i 0.0610273i
\(695\) 0 0
\(696\) 0.232051 0.133975i 0.00879586 0.00507829i
\(697\) 8.00000 0.303022
\(698\) 18.5885 10.7321i 0.703583 0.406214i
\(699\) −3.06218 + 5.30385i −0.115822 + 0.200610i
\(700\) 0 0
\(701\) −0.267949 −0.0101203 −0.00506015 0.999987i \(-0.501611\pi\)
−0.00506015 + 0.999987i \(0.501611\pi\)
\(702\) −2.50000 2.59808i −0.0943564 0.0980581i
\(703\) 68.6410i 2.58884i
\(704\) 5.59808 + 3.23205i 0.210985 + 0.121812i
\(705\) 0 0
\(706\) −1.00000 1.73205i −0.0376355 0.0651866i
\(707\) −5.85641 −0.220253
\(708\) 4.23205 + 7.33013i 0.159050 + 0.275483i
\(709\) 19.8564 11.4641i 0.745723 0.430543i −0.0784234 0.996920i \(-0.524989\pi\)
0.824146 + 0.566377i \(0.191655\pi\)
\(710\) 0 0
\(711\) 6.96410 + 12.0622i 0.261174 + 0.452367i
\(712\) 0.464102 + 0.267949i 0.0173929 + 0.0100418i
\(713\) −3.23205 + 5.59808i −0.121041 + 0.209650i
\(714\) −8.00000 −0.299392
\(715\) 0 0
\(716\) 19.7321 0.737421
\(717\) −8.19615 + 14.1962i −0.306091 + 0.530165i
\(718\) 4.39230 + 2.53590i 0.163919 + 0.0946389i
\(719\) −17.3205 30.0000i −0.645946 1.11881i −0.984082 0.177714i \(-0.943130\pi\)
0.338136 0.941097i \(-0.390204\pi\)
\(720\) 0 0
\(721\) 20.5359 11.8564i 0.764797 0.441556i
\(722\) 18.3564 + 31.7942i 0.683155 + 1.18326i
\(723\) 17.7321 0.659462
\(724\) 1.46410 + 2.53590i 0.0544129 + 0.0942459i
\(725\) 0 0
\(726\) −26.6603 15.3923i −0.989455 0.571262i
\(727\) 31.7128i 1.17616i 0.808802 + 0.588082i \(0.200117\pi\)
−0.808802 + 0.588082i \(0.799883\pi\)
\(728\) 1.73205 + 7.00000i 0.0641941 + 0.259437i
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) 23.8564 41.3205i 0.882361 1.52829i
\(732\) 9.00000 5.19615i 0.332650 0.192055i
\(733\) 50.9282 1.88108 0.940538 0.339688i \(-0.110322\pi\)
0.940538 + 0.339688i \(0.110322\pi\)
\(734\) −13.5167 + 7.80385i −0.498909 + 0.288045i
\(735\) 0 0
\(736\) 3.73205i 0.137565i
\(737\) −64.1769 + 37.0526i −2.36399 + 1.36485i
\(738\) −1.73205 1.00000i −0.0637577 0.0368105i
\(739\) 16.7321 + 9.66025i 0.615498 + 0.355358i 0.775114 0.631821i \(-0.217692\pi\)
−0.159616 + 0.987179i \(0.551026\pi\)
\(740\) 0 0
\(741\) −25.8564 7.46410i −0.949859 0.274201i
\(742\) 1.85641i 0.0681508i
\(743\) 20.2321 35.0429i 0.742242 1.28560i −0.209230 0.977866i \(-0.567096\pi\)
0.951472 0.307734i \(-0.0995708\pi\)
\(744\) 0.866025 1.50000i 0.0317500 0.0549927i
\(745\) 0 0
\(746\) 15.7846i 0.577916i
\(747\) −4.46410 7.73205i −0.163333 0.282901i
\(748\) −12.9282 22.3923i −0.472702 0.818744i
\(749\) 15.7128i 0.574134i
\(750\) 0 0
\(751\) −7.03590 + 12.1865i −0.256744 + 0.444693i −0.965368 0.260893i \(-0.915983\pi\)
0.708624 + 0.705586i \(0.249316\pi\)
\(752\) 1.76795 3.06218i 0.0644705 0.111666i
\(753\) 15.7321i 0.573308i
\(754\) 0.232051 + 0.937822i 0.00845079 + 0.0341535i
\(755\) 0 0
\(756\) 1.73205 + 1.00000i 0.0629941 + 0.0363696i
\(757\) −15.5885 9.00000i −0.566572 0.327111i 0.189207 0.981937i \(-0.439408\pi\)
−0.755779 + 0.654827i \(0.772742\pi\)
\(758\) 24.1244 13.9282i 0.876236 0.505895i
\(759\) 24.1244i 0.875659i
\(760\) 0 0
\(761\) 4.39230 2.53590i 0.159221 0.0919262i −0.418272 0.908322i \(-0.637364\pi\)
0.577493 + 0.816395i \(0.304031\pi\)
\(762\) 4.92820 0.178530
\(763\) −27.4641 + 15.8564i −0.994267 + 0.574040i
\(764\) −10.7321 + 18.5885i −0.388272 + 0.672507i
\(765\) 0 0
\(766\) −25.3923 −0.917461
\(767\) −29.6244 + 7.33013i −1.06967 + 0.264676i
\(768\) 1.00000i 0.0360844i
\(769\) 10.0359 + 5.79423i 0.361904 + 0.208945i 0.669916 0.742437i \(-0.266330\pi\)
−0.308012 + 0.951383i \(0.599664\pi\)
\(770\) 0 0
\(771\) −2.66987 4.62436i −0.0961531 0.166542i
\(772\) 11.3205 0.407434
\(773\) 13.8564 + 24.0000i 0.498380 + 0.863220i 0.999998 0.00186926i \(-0.000595004\pi\)
−0.501618 + 0.865089i \(0.667262\pi\)
\(774\) −10.3301 + 5.96410i −0.371309 + 0.214375i
\(775\) 0 0
\(776\) −0.267949 0.464102i −0.00961882 0.0166603i
\(777\) 15.9282 + 9.19615i 0.571421 + 0.329910i
\(778\) −11.8660 + 20.5526i −0.425418 + 0.736845i
\(779\) −14.9282 −0.534858
\(780\) 0 0
\(781\) −80.1051 −2.86639
\(782\) 7.46410 12.9282i 0.266916 0.462312i
\(783\) 0.232051 + 0.133975i 0.00829282 + 0.00478786i