Properties

Label 1950.2.bc.b.751.2
Level $1950$
Weight $2$
Character 1950.751
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.bc (of order \(6\), degree \(2\), 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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 390)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.b.901.2

$q$-expansion

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

Character values

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

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) −0.866025 0.500000i −0.353553 0.204124i
\(7\) 1.73205 + 1.00000i 0.654654 + 0.377964i 0.790237 0.612801i \(-0.209957\pi\)
−0.135583 + 0.990766i \(0.543291\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 5.59808 3.23205i 1.68788 0.974500i 0.731748 0.681575i \(-0.238705\pi\)
0.956136 0.292925i \(-0.0946285\pi\)
\(12\) −1.00000 −0.288675
\(13\) −1.00000 3.46410i −0.277350 0.960769i
\(14\) 2.00000 0.534522
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.00000 + 3.46410i −0.485071 + 0.840168i −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 6.46410 + 3.73205i 1.48297 + 0.856191i 0.999813 0.0193444i \(-0.00615788\pi\)
0.483154 + 0.875536i \(0.339491\pi\)
\(20\) 0 0
\(21\) 2.00000i 0.436436i
\(22\) 3.23205 5.59808i 0.689076 1.19351i
\(23\) 1.86603 + 3.23205i 0.389093 + 0.673929i 0.992328 0.123635i \(-0.0394551\pi\)
−0.603235 + 0.797564i \(0.706122\pi\)
\(24\) −0.866025 + 0.500000i −0.176777 + 0.102062i
\(25\) 0 0
\(26\) −2.59808 2.50000i −0.509525 0.490290i
\(27\) 1.00000 0.192450
\(28\) 1.73205 1.00000i 0.327327 0.188982i
\(29\) −0.133975 0.232051i −0.0248785 0.0430908i 0.853318 0.521391i \(-0.174587\pi\)
−0.878197 + 0.478300i \(0.841253\pi\)
\(30\) 0 0
\(31\) 1.73205i 0.311086i 0.987829 + 0.155543i \(0.0497126\pi\)
−0.987829 + 0.155543i \(0.950287\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −5.59808 3.23205i −0.974500 0.562628i
\(34\) 4.00000i 0.685994i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) −7.96410 + 4.59808i −1.30929 + 0.755919i −0.981978 0.188997i \(-0.939476\pi\)
−0.327313 + 0.944916i \(0.606143\pi\)
\(38\) 7.46410 1.21084
\(39\) −2.50000 + 2.59808i −0.400320 + 0.416025i
\(40\) 0 0
\(41\) 1.73205 1.00000i 0.270501 0.156174i −0.358614 0.933486i \(-0.616751\pi\)
0.629115 + 0.777312i \(0.283417\pi\)
\(42\) −1.00000 1.73205i −0.154303 0.267261i
\(43\) 5.96410 10.3301i 0.909517 1.57533i 0.0947805 0.995498i \(-0.469785\pi\)
0.814736 0.579831i \(-0.196882\pi\)
\(44\) 6.46410i 0.974500i
\(45\) 0 0
\(46\) 3.23205 + 1.86603i 0.476540 + 0.275130i
\(47\) 3.53590i 0.515764i −0.966176 0.257882i \(-0.916975\pi\)
0.966176 0.257882i \(-0.0830245\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −1.50000 2.59808i −0.214286 0.371154i
\(50\) 0 0
\(51\) 4.00000 0.560112
\(52\) −3.50000 0.866025i −0.485363 0.120096i
\(53\) −0.928203 −0.127499 −0.0637493 0.997966i \(-0.520306\pi\)
−0.0637493 + 0.997966i \(0.520306\pi\)
\(54\) 0.866025 0.500000i 0.117851 0.0680414i
\(55\) 0 0
\(56\) 1.00000 1.73205i 0.133631 0.231455i
\(57\) 7.46410i 0.988644i
\(58\) −0.232051 0.133975i −0.0304698 0.0175917i
\(59\) 7.33013 + 4.23205i 0.954301 + 0.550966i 0.894414 0.447239i \(-0.147593\pi\)
0.0598868 + 0.998205i \(0.480926\pi\)
\(60\) 0 0
\(61\) 5.19615 9.00000i 0.665299 1.15233i −0.313905 0.949454i \(-0.601637\pi\)
0.979204 0.202878i \(-0.0650293\pi\)
\(62\) 0.866025 + 1.50000i 0.109985 + 0.190500i
\(63\) −1.73205 + 1.00000i −0.218218 + 0.125988i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −6.46410 −0.795676
\(67\) 9.92820 5.73205i 1.21292 0.700281i 0.249528 0.968368i \(-0.419724\pi\)
0.963395 + 0.268086i \(0.0863912\pi\)
\(68\) 2.00000 + 3.46410i 0.242536 + 0.420084i
\(69\) 1.86603 3.23205i 0.224643 0.389093i
\(70\) 0 0
\(71\) −10.7321 6.19615i −1.27366 0.735348i −0.297985 0.954570i \(-0.596315\pi\)
−0.975675 + 0.219222i \(0.929648\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 2.00000i 0.234082i 0.993127 + 0.117041i \(0.0373409\pi\)
−0.993127 + 0.117041i \(0.962659\pi\)
\(74\) −4.59808 + 7.96410i −0.534516 + 0.925808i
\(75\) 0 0
\(76\) 6.46410 3.73205i 0.741483 0.428096i
\(77\) 12.9282 1.47331
\(78\) −0.866025 + 3.50000i −0.0980581 + 0.396297i
\(79\) −13.9282 −1.56705 −0.783523 0.621363i \(-0.786579\pi\)
−0.783523 + 0.621363i \(0.786579\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.00000 1.73205i 0.110432 0.191273i
\(83\) 8.92820i 0.979998i 0.871723 + 0.489999i \(0.163003\pi\)
−0.871723 + 0.489999i \(0.836997\pi\)
\(84\) −1.73205 1.00000i −0.188982 0.109109i
\(85\) 0 0
\(86\) 11.9282i 1.28625i
\(87\) −0.133975 + 0.232051i −0.0143636 + 0.0248785i
\(88\) −3.23205 5.59808i −0.344538 0.596757i
\(89\) −0.464102 + 0.267949i −0.0491947 + 0.0284026i −0.524396 0.851475i \(-0.675709\pi\)
0.475201 + 0.879877i \(0.342375\pi\)
\(90\) 0 0
\(91\) 1.73205 7.00000i 0.181568 0.733799i
\(92\) 3.73205 0.389093
\(93\) 1.50000 0.866025i 0.155543 0.0898027i
\(94\) −1.76795 3.06218i −0.182350 0.315840i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −0.464102 0.267949i −0.0471224 0.0272061i 0.476254 0.879308i \(-0.341994\pi\)
−0.523376 + 0.852102i \(0.675328\pi\)
\(98\) −2.59808 1.50000i −0.262445 0.151523i
\(99\) 6.46410i 0.649667i
\(100\) 0 0
\(101\) −1.46410 2.53590i −0.145684 0.252331i 0.783944 0.620831i \(-0.213205\pi\)
−0.929628 + 0.368500i \(0.879871\pi\)
\(102\) 3.46410 2.00000i 0.342997 0.198030i
\(103\) 11.8564 1.16825 0.584123 0.811665i \(-0.301438\pi\)
0.584123 + 0.811665i \(0.301438\pi\)
\(104\) −3.46410 + 1.00000i −0.339683 + 0.0980581i
\(105\) 0 0
\(106\) −0.803848 + 0.464102i −0.0780766 + 0.0450775i
\(107\) −3.92820 6.80385i −0.379754 0.657753i 0.611273 0.791420i \(-0.290658\pi\)
−0.991026 + 0.133667i \(0.957325\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 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
\(112\) 2.00000i 0.188982i
\(113\) 0.401924 0.696152i 0.0378098 0.0654885i −0.846501 0.532387i \(-0.821295\pi\)
0.884311 + 0.466898i \(0.154629\pi\)
\(114\) −3.73205 6.46410i −0.349539 0.605419i
\(115\) 0 0
\(116\) −0.267949 −0.0248785
\(117\) 3.50000 + 0.866025i 0.323575 + 0.0800641i
\(118\) 8.46410 0.779184
\(119\) −6.92820 + 4.00000i −0.635107 + 0.366679i
\(120\) 0 0
\(121\) 15.3923 26.6603i 1.39930 2.42366i
\(122\) 10.3923i 0.940875i
\(123\) −1.73205 1.00000i −0.156174 0.0901670i
\(124\) 1.50000 + 0.866025i 0.134704 + 0.0777714i
\(125\) 0 0
\(126\) −1.00000 + 1.73205i −0.0890871 + 0.154303i
\(127\) −2.46410 4.26795i −0.218654 0.378719i 0.735743 0.677261i \(-0.236833\pi\)
−0.954397 + 0.298542i \(0.903500\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) −11.9282 −1.05022
\(130\) 0 0
\(131\) −18.6603 −1.63035 −0.815177 0.579212i \(-0.803360\pi\)
−0.815177 + 0.579212i \(0.803360\pi\)
\(132\) −5.59808 + 3.23205i −0.487250 + 0.281314i
\(133\) 7.46410 + 12.9282i 0.647220 + 1.12102i
\(134\) 5.73205 9.92820i 0.495174 0.857666i
\(135\) 0 0
\(136\) 3.46410 + 2.00000i 0.297044 + 0.171499i
\(137\) 2.13397 + 1.23205i 0.182318 + 0.105261i 0.588381 0.808584i \(-0.299765\pi\)
−0.406063 + 0.913845i \(0.633099\pi\)
\(138\) 3.73205i 0.317693i
\(139\) 6.46410 11.1962i 0.548278 0.949645i −0.450115 0.892971i \(-0.648617\pi\)
0.998393 0.0566745i \(-0.0180497\pi\)
\(140\) 0 0
\(141\) −3.06218 + 1.76795i −0.257882 + 0.148888i
\(142\) −12.3923 −1.03994
\(143\) −16.7942 16.1603i −1.40440 1.35139i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 1.00000 + 1.73205i 0.0827606 + 0.143346i
\(147\) −1.50000 + 2.59808i −0.123718 + 0.214286i
\(148\) 9.19615i 0.755919i
\(149\) −11.7224 6.76795i −0.960339 0.554452i −0.0640617 0.997946i \(-0.520405\pi\)
−0.896277 + 0.443494i \(0.853739\pi\)
\(150\) 0 0
\(151\) 10.3923i 0.845714i 0.906196 + 0.422857i \(0.138973\pi\)
−0.906196 + 0.422857i \(0.861027\pi\)
\(152\) 3.73205 6.46410i 0.302709 0.524308i
\(153\) −2.00000 3.46410i −0.161690 0.280056i
\(154\) 11.1962 6.46410i 0.902212 0.520892i
\(155\) 0 0
\(156\) 1.00000 + 3.46410i 0.0800641 + 0.277350i
\(157\) 5.00000 0.399043 0.199522 0.979893i \(-0.436061\pi\)
0.199522 + 0.979893i \(0.436061\pi\)
\(158\) −12.0622 + 6.96410i −0.959615 + 0.554034i
\(159\) 0.464102 + 0.803848i 0.0368057 + 0.0637493i
\(160\) 0 0
\(161\) 7.46410i 0.588254i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) −13.0359 7.52628i −1.02105 0.589504i −0.106642 0.994297i \(-0.534010\pi\)
−0.914408 + 0.404794i \(0.867343\pi\)
\(164\) 2.00000i 0.156174i
\(165\) 0 0
\(166\) 4.46410 + 7.73205i 0.346481 + 0.600124i
\(167\) −14.1340 + 8.16025i −1.09372 + 0.631459i −0.934564 0.355794i \(-0.884210\pi\)
−0.159155 + 0.987254i \(0.550877\pi\)
\(168\) −2.00000 −0.154303
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 0 0
\(171\) −6.46410 + 3.73205i −0.494322 + 0.285397i
\(172\) −5.96410 10.3301i −0.454758 0.787665i
\(173\) 5.46410 9.46410i 0.415428 0.719542i −0.580045 0.814584i \(-0.696965\pi\)
0.995473 + 0.0950419i \(0.0302985\pi\)
\(174\) 0.267949i 0.0203132i
\(175\) 0 0
\(176\) −5.59808 3.23205i −0.421971 0.243625i
\(177\) 8.46410i 0.636201i
\(178\) −0.267949 + 0.464102i −0.0200836 + 0.0347859i
\(179\) 9.86603 + 17.0885i 0.737421 + 1.27725i 0.953653 + 0.300909i \(0.0972901\pi\)
−0.216231 + 0.976342i \(0.569377\pi\)
\(180\) 0 0
\(181\) −2.92820 −0.217652 −0.108826 0.994061i \(-0.534709\pi\)
−0.108826 + 0.994061i \(0.534709\pi\)
\(182\) −2.00000 6.92820i −0.148250 0.513553i
\(183\) −10.3923 −0.768221
\(184\) 3.23205 1.86603i 0.238270 0.137565i
\(185\) 0 0
\(186\) 0.866025 1.50000i 0.0635001 0.109985i
\(187\) 25.8564i 1.89081i
\(188\) −3.06218 1.76795i −0.223332 0.128941i
\(189\) 1.73205 + 1.00000i 0.125988 + 0.0727393i
\(190\) 0 0
\(191\) −10.7321 + 18.5885i −0.776544 + 1.34501i 0.157379 + 0.987538i \(0.449696\pi\)
−0.933923 + 0.357475i \(0.883638\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −9.80385 + 5.66025i −0.705696 + 0.407434i −0.809466 0.587167i \(-0.800243\pi\)
0.103769 + 0.994601i \(0.466910\pi\)
\(194\) −0.535898 −0.0384753
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −3.80385 + 2.19615i −0.271013 + 0.156469i −0.629348 0.777124i \(-0.716678\pi\)
0.358335 + 0.933593i \(0.383345\pi\)
\(198\) 3.23205 + 5.59808i 0.229692 + 0.397838i
\(199\) 2.53590 4.39230i 0.179765 0.311362i −0.762035 0.647536i \(-0.775800\pi\)
0.941800 + 0.336174i \(0.109133\pi\)
\(200\) 0 0
\(201\) −9.92820 5.73205i −0.700281 0.404308i
\(202\) −2.53590 1.46410i −0.178425 0.103014i
\(203\) 0.535898i 0.0376127i
\(204\) 2.00000 3.46410i 0.140028 0.242536i
\(205\) 0 0
\(206\) 10.2679 5.92820i 0.715402 0.413037i
\(207\) −3.73205 −0.259395
\(208\) −2.50000 + 2.59808i −0.173344 + 0.180144i
\(209\) 48.2487 3.33743
\(210\) 0 0
\(211\) 5.66025 + 9.80385i 0.389668 + 0.674925i 0.992405 0.123015i \(-0.0392564\pi\)
−0.602737 + 0.797940i \(0.705923\pi\)
\(212\) −0.464102 + 0.803848i −0.0318746 + 0.0552085i
\(213\) 12.3923i 0.849107i
\(214\) −6.80385 3.92820i −0.465101 0.268526i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) −1.73205 + 3.00000i −0.117579 + 0.203653i
\(218\) 7.92820 + 13.7321i 0.536966 + 0.930052i
\(219\) 1.73205 1.00000i 0.117041 0.0675737i
\(220\) 0 0
\(221\) 14.0000 + 3.46410i 0.941742 + 0.233021i
\(222\) 9.19615 0.617205
\(223\) 17.7846 10.2679i 1.19095 0.687593i 0.232424 0.972614i \(-0.425334\pi\)
0.958521 + 0.285022i \(0.0920008\pi\)
\(224\) −1.00000 1.73205i −0.0668153 0.115728i
\(225\) 0 0
\(226\) 0.803848i 0.0534711i
\(227\) 14.1962 + 8.19615i 0.942232 + 0.543998i 0.890659 0.454672i \(-0.150243\pi\)
0.0515725 + 0.998669i \(0.483577\pi\)
\(228\) −6.46410 3.73205i −0.428096 0.247161i
\(229\) 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
\(232\) −0.232051 + 0.133975i −0.0152349 + 0.00879586i
\(233\) −6.12436 −0.401220 −0.200610 0.979671i \(-0.564292\pi\)
−0.200610 + 0.979671i \(0.564292\pi\)
\(234\) 3.46410 1.00000i 0.226455 0.0653720i
\(235\) 0 0
\(236\) 7.33013 4.23205i 0.477151 0.275483i
\(237\) 6.96410 + 12.0622i 0.452367 + 0.783523i
\(238\) −4.00000 + 6.92820i −0.259281 + 0.449089i
\(239\) 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 0.905033 0.425341i \(-0.139846\pi\)
0.0841601 + 0.996452i \(0.473179\pi\)
\(242\) 30.7846i 1.97891i
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) −5.19615 9.00000i −0.332650 0.576166i
\(245\) 0 0
\(246\) −2.00000 −0.127515
\(247\) 6.46410 26.1244i 0.411301 1.66225i
\(248\) 1.73205 0.109985
\(249\) 7.73205 4.46410i 0.489999 0.282901i
\(250\) 0 0
\(251\) −7.86603 + 13.6244i −0.496499 + 0.859962i −0.999992 0.00403776i \(-0.998715\pi\)
0.503493 + 0.863999i \(0.332048\pi\)
\(252\) 2.00000i 0.125988i
\(253\) 20.8923 + 12.0622i 1.31349 + 0.758343i
\(254\) −4.26795 2.46410i −0.267795 0.154611i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −2.66987 4.62436i −0.166542 0.288459i 0.770660 0.637247i \(-0.219927\pi\)
−0.937202 + 0.348787i \(0.886593\pi\)
\(258\) −10.3301 + 5.96410i −0.643126 + 0.371309i
\(259\) −18.3923 −1.14284
\(260\) 0 0
\(261\) 0.267949 0.0165856
\(262\) −16.1603 + 9.33013i −0.998384 + 0.576417i
\(263\) 3.06218 + 5.30385i 0.188822 + 0.327049i 0.944858 0.327481i \(-0.106200\pi\)
−0.756036 + 0.654530i \(0.772866\pi\)
\(264\) −3.23205 + 5.59808i −0.198919 + 0.344538i
\(265\) 0 0
\(266\) 12.9282 + 7.46410i 0.792679 + 0.457653i
\(267\) 0.464102 + 0.267949i 0.0284026 + 0.0163982i
\(268\) 11.4641i 0.700281i
\(269\) −6.00000 + 10.3923i −0.365826 + 0.633630i −0.988908 0.148527i \(-0.952547\pi\)
0.623082 + 0.782157i \(0.285880\pi\)
\(270\) 0 0
\(271\) 1.03590 0.598076i 0.0629263 0.0363305i −0.468207 0.883619i \(-0.655100\pi\)
0.531133 + 0.847288i \(0.321766\pi\)
\(272\) 4.00000 0.242536
\(273\) −6.92820 + 2.00000i −0.419314 + 0.121046i
\(274\) 2.46410 0.148862
\(275\) 0 0
\(276\) −1.86603 3.23205i −0.112322 0.194547i
\(277\) −1.96410 + 3.40192i −0.118011 + 0.204402i −0.918980 0.394305i \(-0.870985\pi\)
0.800968 + 0.598707i \(0.204319\pi\)
\(278\) 12.9282i 0.775382i
\(279\) −1.50000 0.866025i −0.0898027 0.0518476i
\(280\) 0 0
\(281\) 8.92820i 0.532612i 0.963889 + 0.266306i \(0.0858032\pi\)
−0.963889 + 0.266306i \(0.914197\pi\)
\(282\) −1.76795 + 3.06218i −0.105280 + 0.182350i
\(283\) −4.96410 8.59808i −0.295085 0.511103i 0.679920 0.733287i \(-0.262015\pi\)
−0.975005 + 0.222184i \(0.928681\pi\)
\(284\) −10.7321 + 6.19615i −0.636830 + 0.367674i
\(285\) 0 0
\(286\) −22.6244 5.59808i −1.33781 0.331021i
\(287\) 4.00000 0.236113
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) 0.500000 + 0.866025i 0.0294118 + 0.0509427i
\(290\) 0 0
\(291\) 0.535898i 0.0314149i
\(292\) 1.73205 + 1.00000i 0.101361 + 0.0585206i
\(293\) 27.5885 + 15.9282i 1.61173 + 0.930536i 0.988968 + 0.148128i \(0.0473247\pi\)
0.622767 + 0.782408i \(0.286009\pi\)
\(294\) 3.00000i 0.174964i
\(295\) 0 0
\(296\) 4.59808 + 7.96410i 0.267258 + 0.462904i
\(297\) 5.59808 3.23205i 0.324833 0.187543i
\(298\) −13.5359 −0.784114
\(299\) 9.33013 9.69615i 0.539575 0.560743i
\(300\) 0 0
\(301\) 20.6603 11.9282i 1.19084 0.687530i
\(302\) 5.19615 + 9.00000i 0.299005 + 0.517892i
\(303\) −1.46410 + 2.53590i −0.0841104 + 0.145684i
\(304\) 7.46410i 0.428096i
\(305\) 0 0
\(306\) −3.46410 2.00000i −0.198030 0.114332i
\(307\) 19.4641i 1.11087i 0.831558 + 0.555437i \(0.187449\pi\)
−0.831558 + 0.555437i \(0.812551\pi\)
\(308\) 6.46410 11.1962i 0.368326 0.637960i
\(309\) −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 \(0.797829\pi\)
\(312\) 2.59808 + 2.50000i 0.147087 + 0.141535i
\(313\) 28.0000 1.58265 0.791327 0.611393i \(-0.209391\pi\)
0.791327 + 0.611393i \(0.209391\pi\)
\(314\) 4.33013 2.50000i 0.244363 0.141083i
\(315\) 0 0
\(316\) −6.96410 + 12.0622i −0.391761 + 0.678551i
\(317\) 14.5359i 0.816417i 0.912889 + 0.408209i \(0.133846\pi\)
−0.912889 + 0.408209i \(0.866154\pi\)
\(318\) 0.803848 + 0.464102i 0.0450775 + 0.0260255i
\(319\) −1.50000 0.866025i −0.0839839 0.0484881i
\(320\) 0 0
\(321\) −3.92820 + 6.80385i −0.219251 + 0.379754i
\(322\) 3.73205 + 6.46410i 0.207979 + 0.360230i
\(323\) −25.8564 + 14.9282i −1.43869 + 0.830627i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −15.0526 −0.833684
\(327\) 13.7321 7.92820i 0.759384 0.438431i
\(328\) −1.00000 1.73205i −0.0552158 0.0956365i
\(329\) 3.53590 6.12436i 0.194940 0.337647i
\(330\) 0 0
\(331\) −14.5359 8.39230i −0.798965 0.461283i 0.0441440 0.999025i \(-0.485944\pi\)
−0.843109 + 0.537742i \(0.819277\pi\)
\(332\) 7.73205 + 4.46410i 0.424351 + 0.244999i
\(333\) 9.19615i 0.503946i
\(334\) −8.16025 + 14.1340i −0.446509 + 0.773377i
\(335\) 0 0
\(336\) −1.73205 + 1.00000i −0.0944911 + 0.0545545i
\(337\) −9.32051 −0.507720 −0.253860 0.967241i \(-0.581700\pi\)
−0.253860 + 0.967241i \(0.581700\pi\)
\(338\) −6.06218 + 11.5000i −0.329739 + 0.625518i
\(339\) −0.803848 −0.0436590
\(340\) 0 0
\(341\) 5.59808 + 9.69615i 0.303153 + 0.525076i
\(342\) −3.73205 + 6.46410i −0.201806 + 0.349539i
\(343\) 20.0000i 1.07990i
\(344\) −10.3301 5.96410i −0.556963 0.321563i
\(345\) 0 0
\(346\) 10.9282i 0.587504i
\(347\) 0.803848 1.39230i 0.0431528 0.0747428i −0.843642 0.536906i \(-0.819593\pi\)
0.886795 + 0.462163i \(0.152926\pi\)
\(348\) 0.133975 + 0.232051i 0.00718179 + 0.0124392i
\(349\) 18.5885 10.7321i 0.995017 0.574474i 0.0882471 0.996099i \(-0.471873\pi\)
0.906770 + 0.421625i \(0.138540\pi\)
\(350\) 0 0
\(351\) −1.00000 3.46410i −0.0533761 0.184900i
\(352\) −6.46410 −0.344538
\(353\) −1.73205 + 1.00000i −0.0921878 + 0.0532246i −0.545385 0.838186i \(-0.683617\pi\)
0.453197 + 0.891410i \(0.350283\pi\)
\(354\) −4.23205 7.33013i −0.224931 0.389592i
\(355\) 0 0
\(356\) 0.535898i 0.0284026i
\(357\) 6.92820 + 4.00000i 0.366679 + 0.211702i
\(358\) 17.0885 + 9.86603i 0.903153 + 0.521436i
\(359\) 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
\(362\) −2.53590 + 1.46410i −0.133284 + 0.0769515i
\(363\) −30.7846 −1.61577
\(364\) −5.19615 5.00000i −0.272352 0.262071i
\(365\) 0 0
\(366\) −9.00000 + 5.19615i −0.470438 + 0.271607i
\(367\) 7.80385 + 13.5167i 0.407358 + 0.705564i 0.994593 0.103852i \(-0.0331170\pi\)
−0.587235 + 0.809416i \(0.699784\pi\)
\(368\) 1.86603 3.23205i 0.0972733 0.168482i
\(369\) 2.00000i 0.104116i
\(370\) 0 0
\(371\) −1.60770 0.928203i −0.0834674 0.0481899i
\(372\) 1.73205i 0.0898027i
\(373\) −7.89230 + 13.6699i −0.408648 + 0.707799i −0.994739 0.102446i \(-0.967333\pi\)
0.586090 + 0.810246i \(0.300666\pi\)
\(374\) 12.9282 + 22.3923i 0.668501 + 1.15788i
\(375\) 0 0
\(376\) −3.53590 −0.182350
\(377\) −0.669873 + 0.696152i −0.0345002 + 0.0358537i
\(378\) 2.00000 0.102869
\(379\) 24.1244 13.9282i 1.23918 0.715444i 0.270257 0.962788i \(-0.412891\pi\)
0.968928 + 0.247344i \(0.0795579\pi\)
\(380\) 0 0
\(381\) −2.46410 + 4.26795i −0.126240 + 0.218654i
\(382\) 21.4641i 1.09820i
\(383\) −21.9904 12.6962i −1.12366 0.648743i −0.181324 0.983423i \(-0.558038\pi\)
−0.942332 + 0.334680i \(0.891372\pi\)
\(384\) 0.866025 + 0.500000i 0.0441942 + 0.0255155i
\(385\) 0 0
\(386\) −5.66025 + 9.80385i −0.288099 + 0.499003i
\(387\) 5.96410 + 10.3301i 0.303172 + 0.525110i
\(388\) −0.464102 + 0.267949i −0.0235612 + 0.0136031i
\(389\) −23.7321 −1.20326 −0.601631 0.798774i \(-0.705482\pi\)
−0.601631 + 0.798774i \(0.705482\pi\)
\(390\) 0 0
\(391\) −14.9282 −0.754952
\(392\) −2.59808 + 1.50000i −0.131223 + 0.0757614i
\(393\) 9.33013 + 16.1603i 0.470643 + 0.815177i
\(394\) −2.19615 + 3.80385i −0.110641 + 0.191635i
\(395\) 0 0
\(396\) 5.59808 + 3.23205i 0.281314 + 0.162417i
\(397\) −10.5000 6.06218i −0.526980 0.304252i 0.212806 0.977095i \(-0.431740\pi\)
−0.739786 + 0.672843i \(0.765073\pi\)
\(398\) 5.07180i 0.254226i
\(399\) 7.46410 12.9282i 0.373672 0.647220i
\(400\) 0 0
\(401\) −27.7128 + 16.0000i −1.38391 + 0.799002i −0.992620 0.121265i \(-0.961305\pi\)
−0.391292 + 0.920267i \(0.627972\pi\)
\(402\) −11.4641 −0.571777
\(403\) 6.00000 1.73205i 0.298881 0.0862796i
\(404\) −2.92820 −0.145684
\(405\) 0 0
\(406\) −0.267949 0.464102i −0.0132981 0.0230330i
\(407\) −29.7224 + 51.4808i −1.47329 + 2.55181i
\(408\) 4.00000i 0.198030i
\(409\) 3.46410 + 2.00000i 0.171289 + 0.0988936i 0.583193 0.812333i \(-0.301803\pi\)
−0.411905 + 0.911227i \(0.635136\pi\)
\(410\) 0 0
\(411\) 2.46410i 0.121545i
\(412\) 5.92820 10.2679i 0.292062 0.505866i
\(413\) 8.46410 + 14.6603i 0.416491 + 0.721384i
\(414\) −3.23205 + 1.86603i −0.158847 + 0.0917101i
\(415\) 0 0
\(416\) −0.866025 + 3.50000i −0.0424604 + 0.171602i
\(417\) −12.9282 −0.633097
\(418\) 41.7846 24.1244i 2.04375 1.17996i
\(419\) −11.1962 19.3923i −0.546968 0.947376i −0.998480 0.0551112i \(-0.982449\pi\)
0.451512 0.892265i \(-0.350885\pi\)
\(420\) 0 0
\(421\) 4.39230i 0.214068i −0.994255 0.107034i \(-0.965865\pi\)
0.994255 0.107034i \(-0.0341353\pi\)
\(422\) 9.80385 + 5.66025i 0.477244 + 0.275537i
\(423\) 3.06218 + 1.76795i 0.148888 + 0.0859606i
\(424\) 0.928203i 0.0450775i
\(425\) 0 0
\(426\) 6.19615 + 10.7321i 0.300205 + 0.519970i
\(427\) 18.0000 10.3923i 0.871081 0.502919i
\(428\) −7.85641 −0.379754
\(429\) −5.59808 + 22.6244i −0.270278 + 1.09231i
\(430\) 0 0
\(431\) 24.5885 14.1962i 1.18438 0.683805i 0.227360 0.973811i \(-0.426991\pi\)
0.957025 + 0.290006i \(0.0936574\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 9.66025 16.7321i 0.464242 0.804091i −0.534925 0.844900i \(-0.679660\pi\)
0.999167 + 0.0408086i \(0.0129934\pi\)
\(434\) 3.46410i 0.166282i
\(435\) 0 0
\(436\) 13.7321 + 7.92820i 0.657646 + 0.379692i
\(437\) 27.8564i 1.33255i
\(438\) 1.00000 1.73205i 0.0477818 0.0827606i
\(439\) 8.92820 + 15.4641i 0.426120 + 0.738061i 0.996524 0.0833027i \(-0.0265468\pi\)
−0.570404 + 0.821364i \(0.693214\pi\)
\(440\) 0 0
\(441\) 3.00000 0.142857
\(442\) 13.8564 4.00000i 0.659082 0.190261i
\(443\) −16.3923 −0.778822 −0.389411 0.921064i \(-0.627321\pi\)
−0.389411 + 0.921064i \(0.627321\pi\)
\(444\) 7.96410 4.59808i 0.377960 0.218215i
\(445\) 0 0
\(446\) 10.2679 17.7846i 0.486201 0.842126i
\(447\) 13.5359i 0.640226i
\(448\) −1.73205 1.00000i −0.0818317 0.0472456i
\(449\) −13.6077 7.85641i −0.642187 0.370767i 0.143270 0.989684i \(-0.454238\pi\)
−0.785456 + 0.618917i \(0.787572\pi\)
\(450\) 0 0
\(451\) 6.46410 11.1962i 0.304383 0.527206i
\(452\) −0.401924 0.696152i −0.0189049 0.0327443i
\(453\) 9.00000 5.19615i 0.422857 0.244137i
\(454\) 16.3923 0.769329
\(455\) 0 0
\(456\) −7.46410 −0.349539
\(457\) −21.2487 + 12.2679i −0.993973 + 0.573870i −0.906459 0.422293i \(-0.861225\pi\)
−0.0875134 + 0.996163i \(0.527892\pi\)
\(458\) 3.92820 + 6.80385i 0.183553 + 0.317923i
\(459\) −2.00000 + 3.46410i −0.0933520 + 0.161690i
\(460\) 0 0
\(461\) 0.401924 + 0.232051i 0.0187195 + 0.0108077i 0.509331 0.860571i \(-0.329893\pi\)
−0.490611 + 0.871379i \(0.663226\pi\)
\(462\) −11.1962 6.46410i −0.520892 0.300737i
\(463\) 7.07180i 0.328654i 0.986406 + 0.164327i \(0.0525453\pi\)
−0.986406 + 0.164327i \(0.947455\pi\)
\(464\) −0.133975 + 0.232051i −0.00621961 + 0.0107727i
\(465\) 0 0
\(466\) −5.30385 + 3.06218i −0.245696 + 0.141853i
\(467\) 15.8564 0.733747 0.366873 0.930271i \(-0.380428\pi\)
0.366873 + 0.930271i \(0.380428\pi\)
\(468\) 2.50000 2.59808i 0.115563 0.120096i
\(469\) 22.9282 1.05873
\(470\) 0 0
\(471\) −2.50000 4.33013i −0.115194 0.199522i
\(472\) 4.23205 7.33013i 0.194796 0.337396i
\(473\) 77.1051i 3.54530i
\(474\) 12.0622 + 6.96410i 0.554034 + 0.319872i
\(475\) 0 0
\(476\) 8.00000i 0.366679i
\(477\) 0.464102 0.803848i 0.0212498 0.0368057i
\(478\) 8.19615 + 14.1962i 0.374883 + 0.649317i
\(479\) 4.73205 2.73205i 0.216213 0.124831i −0.387983 0.921667i \(-0.626828\pi\)
0.604195 + 0.796836i \(0.293495\pi\)
\(480\) 0 0
\(481\) 23.8923 + 22.9904i 1.08940 + 1.04827i
\(482\) 17.7321 0.807673
\(483\) 6.46410 3.73205i 0.294127 0.169814i
\(484\) −15.3923 26.6603i −0.699650 1.21183i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) −20.0718 11.5885i −0.909540 0.525123i −0.0292568 0.999572i \(-0.509314\pi\)
−0.880283 + 0.474449i \(0.842647\pi\)
\(488\) −9.00000 5.19615i −0.407411 0.235219i
\(489\) 15.0526i 0.680700i
\(490\) 0 0
\(491\) 8.66025 + 15.0000i 0.390832 + 0.676941i 0.992559 0.121761i \(-0.0388541\pi\)
−0.601728 + 0.798701i \(0.705521\pi\)
\(492\) −1.73205 + 1.00000i −0.0780869 + 0.0450835i
\(493\) 1.07180 0.0482713
\(494\) −7.46410 25.8564i −0.335826 1.16333i
\(495\) 0 0
\(496\) 1.50000 0.866025i 0.0673520 0.0388857i
\(497\) −12.3923 21.4641i −0.555871 0.962797i
\(498\) 4.46410 7.73205i 0.200041 0.346481i
\(499\) 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
\(502\) 15.7321i 0.702156i
\(503\) −15.5885 + 27.0000i −0.695055 + 1.20387i 0.275107 + 0.961414i \(0.411287\pi\)
−0.970162 + 0.242457i \(0.922047\pi\)
\(504\) 1.00000 + 1.73205i 0.0445435 + 0.0771517i
\(505\) 0 0
\(506\) 24.1244 1.07246
\(507\) 11.5000 + 6.06218i 0.510733 + 0.269231i
\(508\) −4.92820 −0.218654
\(509\) 1.20577 0.696152i 0.0534449 0.0308564i −0.473039 0.881041i \(-0.656843\pi\)
0.526484 + 0.850185i \(0.323510\pi\)
\(510\) 0 0
\(511\) −2.00000 + 3.46410i −0.0884748 + 0.153243i
\(512\) 1.00000i 0.0441942i
\(513\) 6.46410 + 3.73205i 0.285397 + 0.164774i
\(514\) −4.62436 2.66987i −0.203972 0.117763i
\(515\) 0 0
\(516\) −5.96410 + 10.3301i −0.262555 + 0.454758i
\(517\) −11.4282 19.7942i −0.502612 0.870549i
\(518\) −15.9282 + 9.19615i −0.699845 + 0.404056i
\(519\) −10.9282 −0.479695
\(520\) 0 0
\(521\) −17.3205 −0.758825 −0.379413 0.925228i \(-0.623874\pi\)
−0.379413 + 0.925228i \(0.623874\pi\)
\(522\) 0.232051 0.133975i 0.0101566 0.00586391i
\(523\) 5.89230 + 10.2058i 0.257653 + 0.446267i 0.965613 0.259985i \(-0.0837177\pi\)
−0.707960 + 0.706252i \(0.750384\pi\)
\(524\) −9.33013 + 16.1603i −0.407588 + 0.705964i
\(525\) 0 0
\(526\) 5.30385 + 3.06218i 0.231259 + 0.133517i
\(527\) −6.00000 3.46410i −0.261364 0.150899i
\(528\) 6.46410i 0.281314i
\(529\) 4.53590 7.85641i 0.197213 0.341583i
\(530\) 0 0
\(531\) −7.33013 + 4.23205i −0.318100 + 0.183655i
\(532\) 14.9282 0.647220
\(533\) −5.19615 5.00000i −0.225070 0.216574i
\(534\) 0.535898 0.0231906
\(535\) 0 0
\(536\) −5.73205 9.92820i −0.247587 0.428833i
\(537\) 9.86603 17.0885i 0.425750 0.737421i
\(538\) 12.0000i 0.517357i
\(539\) −16.7942 9.69615i −0.723379 0.417643i
\(540\) 0 0
\(541\) 26.9282i 1.15773i −0.815422 0.578867i \(-0.803495\pi\)
0.815422 0.578867i \(-0.196505\pi\)
\(542\) 0.598076 1.03590i 0.0256896 0.0444956i
\(543\) 1.46410 + 2.53590i 0.0628306 + 0.108826i
\(544\) 3.46410 2.00000i 0.148522 0.0857493i
\(545\) 0 0
\(546\) −5.00000 + 5.19615i −0.213980 + 0.222375i
\(547\) −22.9282 −0.980339 −0.490170 0.871627i \(-0.663065\pi\)
−0.490170 + 0.871627i \(0.663065\pi\)
\(548\) 2.13397 1.23205i 0.0911589 0.0526306i
\(549\) 5.19615 + 9.00000i 0.221766 + 0.384111i
\(550\) 0 0
\(551\) 2.00000i 0.0852029i
\(552\) −3.23205 1.86603i −0.137565 0.0794233i
\(553\) −24.1244 13.9282i −1.02587 0.592287i
\(554\) 3.92820i 0.166893i
\(555\) 0 0
\(556\) −6.46410 11.1962i −0.274139 0.474823i
\(557\) −15.3397 + 8.85641i −0.649966 + 0.375258i −0.788443 0.615108i \(-0.789113\pi\)
0.138477 + 0.990366i \(0.455779\pi\)
\(558\) −1.73205 −0.0733236
\(559\) −41.7487 10.3301i −1.76578 0.436918i
\(560\) 0 0
\(561\) 22.3923 12.9282i 0.945404 0.545829i
\(562\) 4.46410 + 7.73205i 0.188307 + 0.326157i
\(563\) −2.33975 + 4.05256i −0.0986085 + 0.170795i −0.911109 0.412166i \(-0.864772\pi\)
0.812500 + 0.582961i \(0.198106\pi\)
\(564\) 3.53590i 0.148888i
\(565\) 0 0
\(566\) −8.59808 4.96410i −0.361404 0.208657i
\(567\) 2.00000i 0.0839921i
\(568\) −6.19615 + 10.7321i −0.259985 + 0.450307i
\(569\) −14.6603 25.3923i −0.614590 1.06450i −0.990456 0.137827i \(-0.955988\pi\)
0.375867 0.926674i \(-0.377345\pi\)
\(570\) 0 0
\(571\) −17.1769 −0.718832 −0.359416 0.933178i \(-0.617024\pi\)
−0.359416 + 0.933178i \(0.617024\pi\)
\(572\) −22.3923 + 6.46410i −0.936269 + 0.270278i
\(573\) 21.4641 0.896676
\(574\) 3.46410 2.00000i 0.144589 0.0834784i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 10.0000i 0.416305i −0.978096 0.208153i \(-0.933255\pi\)
0.978096 0.208153i \(-0.0667451\pi\)
\(578\) 0.866025 + 0.500000i 0.0360219 + 0.0207973i
\(579\) 9.80385 + 5.66025i 0.407434 + 0.235232i
\(580\) 0 0
\(581\) −8.92820 + 15.4641i −0.370404 + 0.641559i
\(582\) 0.267949 + 0.464102i 0.0111069 + 0.0192376i
\(583\) −5.19615 + 3.00000i −0.215203 + 0.124247i
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) 31.8564 1.31598
\(587\) 2.07180 1.19615i 0.0855122 0.0493705i −0.456634 0.889655i \(-0.650945\pi\)
0.542146 + 0.840284i \(0.317612\pi\)
\(588\) 1.50000 + 2.59808i 0.0618590 + 0.107143i
\(589\) −6.46410 + 11.1962i −0.266349 + 0.461329i
\(590\) 0 0
\(591\) 3.80385 + 2.19615i 0.156469 + 0.0903376i
\(592\) 7.96410 + 4.59808i 0.327323 + 0.188980i
\(593\) 45.1051i 1.85225i 0.377223 + 0.926123i \(0.376879\pi\)
−0.377223 + 0.926123i \(0.623121\pi\)
\(594\) 3.23205 5.59808i 0.132613 0.229692i
\(595\) 0 0
\(596\) −11.7224 + 6.76795i −0.480170 + 0.277226i
\(597\) −5.07180 −0.207575
\(598\) 3.23205 13.0622i 0.132168 0.534152i
\(599\) −10.3923 −0.424618 −0.212309 0.977203i \(-0.568098\pi\)
−0.212309 + 0.977203i \(0.568098\pi\)
\(600\) 0 0
\(601\) 9.89230 + 17.1340i 0.403516 + 0.698909i 0.994147 0.108032i \(-0.0344548\pi\)
−0.590632 + 0.806941i \(0.701121\pi\)
\(602\) 11.9282 20.6603i 0.486157 0.842049i
\(603\) 11.4641i 0.466854i
\(604\) 9.00000 + 5.19615i 0.366205 + 0.211428i
\(605\) 0 0
\(606\) 2.92820i 0.118950i
\(607\) −9.58846 + 16.6077i −0.389183 + 0.674086i −0.992340 0.123537i \(-0.960576\pi\)
0.603156 + 0.797623i \(0.293909\pi\)
\(608\) −3.73205 6.46410i −0.151355 0.262154i
\(609\) −0.464102 + 0.267949i −0.0188063 + 0.0108578i
\(610\) 0 0
\(611\) −12.2487 + 3.53590i −0.495530 + 0.143047i
\(612\) −4.00000 −0.161690
\(613\) 33.8205 19.5263i 1.36600 0.788659i 0.375583 0.926789i \(-0.377442\pi\)
0.990414 + 0.138130i \(0.0441091\pi\)
\(614\) 9.73205 + 16.8564i 0.392754 + 0.680269i
\(615\) 0 0
\(616\) 12.9282i 0.520892i
\(617\) 19.4545 + 11.2321i 0.783208 + 0.452185i 0.837566 0.546336i \(-0.183978\pi\)
−0.0543580 + 0.998522i \(0.517311\pi\)
\(618\) −10.2679 5.92820i −0.413037 0.238467i
\(619\) 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
\(622\) −24.5885 + 14.1962i −0.985907 + 0.569214i
\(623\) −1.07180 −0.0429406
\(624\) 3.50000 + 0.866025i 0.140112 + 0.0346688i
\(625\) 0 0
\(626\) 24.2487 14.0000i 0.969173 0.559553i
\(627\) −24.1244 41.7846i −0.963434 1.66872i
\(628\) 2.50000 4.33013i 0.0997609 0.172791i
\(629\) 36.7846i 1.46670i
\(630\) 0 0
\(631\) 27.2487 + 15.7321i 1.08475 + 0.626283i 0.932175 0.362008i \(-0.117909\pi\)
0.152579 + 0.988291i \(0.451242\pi\)
\(632\) 13.9282i 0.554034i
\(633\) 5.66025 9.80385i 0.224975 0.389668i
\(634\) 7.26795 + 12.5885i 0.288647 + 0.499952i
\(635\) 0 0
\(636\) 0.928203 0.0368057
\(637\) −7.50000 + 7.79423i −0.297161 + 0.308819i
\(638\) −1.73205 −0.0685725
\(639\) 10.7321 6.19615i 0.424553 0.245116i
\(640\) 0 0
\(641\) −0.0717968 + 0.124356i −0.00283580 + 0.00491175i −0.867440 0.497542i \(-0.834236\pi\)
0.864604 + 0.502454i \(0.167569\pi\)
\(642\) 7.85641i 0.310068i
\(643\) 17.7846 + 10.2679i 0.701357 + 0.404928i 0.807852 0.589385i \(-0.200630\pi\)
−0.106496 + 0.994313i \(0.533963\pi\)
\(644\) 6.46410 + 3.73205i 0.254721 + 0.147063i
\(645\) 0 0
\(646\) −14.9282 + 25.8564i −0.587342 + 1.01731i
\(647\) −6.66025 11.5359i −0.261842 0.453523i 0.704890 0.709317i \(-0.250996\pi\)
−0.966731 + 0.255794i \(0.917663\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 54.7128 2.14767
\(650\) 0 0
\(651\) 3.46410 0.135769
\(652\) −13.0359 + 7.52628i −0.510525 + 0.294752i
\(653\) 2.12436 + 3.67949i 0.0831325 + 0.143990i 0.904594 0.426274i \(-0.140174\pi\)
−0.821461 + 0.570264i \(0.806841\pi\)
\(654\) 7.92820 13.7321i 0.310017 0.536966i
\(655\) 0 0
\(656\) −1.73205 1.00000i −0.0676252 0.0390434i
\(657\) −1.73205 1.00000i −0.0675737 0.0390137i
\(658\) 7.07180i 0.275687i
\(659\) 0.133975 0.232051i 0.00521891 0.00903942i −0.863404 0.504513i \(-0.831672\pi\)
0.868623 + 0.495473i \(0.165005\pi\)
\(660\) 0 0
\(661\) −7.51666 + 4.33975i −0.292364 + 0.168797i −0.639008 0.769200i \(-0.720655\pi\)
0.346643 + 0.937997i \(0.387321\pi\)
\(662\) −16.7846 −0.652352
\(663\) −4.00000 13.8564i −0.155347 0.538138i
\(664\) 8.92820 0.346481
\(665\) 0 0
\(666\) −4.59808 7.96410i −0.178172 0.308603i
\(667\) 0.500000 0.866025i 0.0193601 0.0335326i
\(668\) 16.3205i 0.631459i
\(669\) −17.7846 10.2679i −0.687593 0.396982i
\(670\) 0 0
\(671\) 67.1769i 2.59334i
\(672\) −1.00000 + 1.73205i −0.0385758 + 0.0668153i
\(673\) 16.0000 + 27.7128i 0.616755 + 1.06825i 0.990074 + 0.140548i \(0.0448863\pi\)
−0.373319 + 0.927703i \(0.621780\pi\)
\(674\) −8.07180 + 4.66025i −0.310914 + 0.179506i
\(675\) 0 0
\(676\) 0.500000 + 12.9904i 0.0192308 + 0.499630i
\(677\) −32.3923 −1.24494 −0.622469 0.782645i \(-0.713870\pi\)
−0.622469 + 0.782645i \(0.713870\pi\)
\(678\) −0.696152 + 0.401924i −0.0267356 + 0.0154358i
\(679\) −0.535898 0.928203i −0.0205659 0.0356212i
\(680\) 0 0
\(681\) 16.3923i 0.628154i
\(682\) 9.69615 + 5.59808i 0.371285 + 0.214361i
\(683\) 35.3205 + 20.3923i 1.35150 + 0.780290i 0.988460 0.151483i \(-0.0484049\pi\)
0.363042 + 0.931773i \(0.381738\pi\)
\(684\) 7.46410i 0.285397i
\(685\) 0 0
\(686\) −10.0000 17.3205i −0.381802 0.661300i
\(687\) 6.80385 3.92820i 0.259583 0.149870i
\(688\) −11.9282 −0.454758
\(689\) 0.928203 + 3.21539i 0.0353617 + 0.122497i
\(690\) 0 0
\(691\) −23.5359 + 13.5885i −0.895348 + 0.516929i −0.875688 0.482877i \(-0.839592\pi\)
−0.0196598 + 0.999807i \(0.506258\pi\)
\(692\) −5.46410 9.46410i −0.207714 0.359771i
\(693\) −6.46410 + 11.1962i −0.245551 + 0.425307i
\(694\) 1.60770i 0.0610273i
\(695\) 0 0
\(696\) 0.232051 + 0.133975i 0.00879586 + 0.00507829i
\(697\) 8.00000i 0.303022i
\(698\) 10.7321 18.5885i 0.406214 0.703583i
\(699\) 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 \(0.501611\pi\)
\(702\) −2.59808 2.50000i −0.0980581 0.0943564i
\(703\) −68.6410 −2.58884
\(704\) −5.59808 + 3.23205i −0.210985 + 0.121812i
\(705\) 0 0
\(706\) −1.00000 + 1.73205i −0.0376355 + 0.0651866i
\(707\) 5.85641i 0.220253i
\(708\) −7.33013 4.23205i −0.275483 0.159050i
\(709\) −19.8564 11.4641i −0.745723 0.430543i 0.0784234 0.996920i \(-0.475011\pi\)
−0.824146 + 0.566377i \(0.808345\pi\)
\(710\) 0 0
\(711\) 6.96410 12.0622i 0.261174 0.452367i
\(712\) 0.267949 + 0.464102i 0.0100418 + 0.0173929i
\(713\) −5.59808 + 3.23205i −0.209650 + 0.121041i
\(714\) 8.00000 0.299392
\(715\) 0 0
\(716\) 19.7321 0.737421
\(717\) 14.1962 8.19615i 0.530165 0.306091i
\(718\) −2.53590 4.39230i −0.0946389 0.163919i
\(719\) 17.3205 30.0000i 0.645946 1.11881i −0.338136 0.941097i \(-0.609796\pi\)
0.984082 0.177714i \(-0.0568702\pi\)
\(720\) 0 0
\(721\) 20.5359 + 11.8564i 0.764797 + 0.441556i
\(722\) 31.7942 + 18.3564i 1.18326 + 0.683155i
\(723\) 17.7321i 0.659462i
\(724\) −1.46410 + 2.53590i −0.0544129 + 0.0942459i
\(725\) 0 0
\(726\) −26.6603 + 15.3923i −0.989455 + 0.571262i
\(727\) 31.7128 1.17616 0.588082 0.808802i \(-0.299883\pi\)
0.588082 + 0.808802i \(0.299883\pi\)
\(728\) −7.00000 1.73205i −0.259437 0.0641941i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 23.8564 + 41.3205i 0.882361 + 1.52829i
\(732\) −5.19615 + 9.00000i −0.192055 + 0.332650i
\(733\) 50.9282i 1.88108i −0.339688 0.940538i \(-0.610322\pi\)
0.339688 0.940538i \(-0.389678\pi\)
\(734\) 13.5167 + 7.80385i 0.498909 + 0.288045i
\(735\) 0 0
\(736\) 3.73205i 0.137565i
\(737\) 37.0526 64.1769i 1.36485 2.36399i
\(738\) 1.00000 + 1.73205i 0.0368105 + 0.0637577i
\(739\) −16.7321 + 9.66025i −0.615498 + 0.355358i −0.775114 0.631821i \(-0.782308\pi\)
0.159616 + 0.987179i \(0.448974\pi\)
\(740\) 0 0
\(741\) −25.8564 + 7.46410i −0.949859 + 0.274201i
\(742\) −1.85641 −0.0681508
\(743\) 35.0429 20.2321i 1.28560 0.742242i 0.307734 0.951472i \(-0.400429\pi\)
0.977866 + 0.209230i \(0.0670958\pi\)
\(744\) −0.866025 1.50000i −0.0317500 0.0549927i
\(745\) 0 0
\(746\) 15.7846i 0.577916i
\(747\) −7.73205 4.46410i −0.282901 0.163333i
\(748\) 22.3923 + 12.9282i 0.818744 + 0.472702i
\(749\) 15.7128i 0.574134i
\(750\) 0 0
\(751\) −7.03590 12.1865i −0.256744 0.444693i 0.708624 0.705586i \(-0.249316\pi\)
−0.965368 + 0.260893i \(0.915983\pi\)
\(752\) −3.06218 + 1.76795i −0.111666 + 0.0644705i
\(753\) 15.7321 0.573308
\(754\) −0.232051 + 0.937822i −0.00845079 + 0.0341535i
\(755\) 0 0
\(756\) 1.73205 1.00000i 0.0629941 0.0363696i
\(757\) −9.00000 15.5885i −0.327111 0.566572i 0.654827 0.755779i \(-0.272742\pi\)
−0.981937 + 0.189207i \(0.939408\pi\)
\(758\) 13.9282 24.1244i 0.505895 0.876236i
\(759\) 24.1244i 0.875659i
\(760\) 0 0
\(761\) 4.39230 + 2.53590i 0.159221 + 0.0919262i 0.577493 0.816395i \(-0.304031\pi\)
−0.418272 + 0.908322i \(0.637364\pi\)
\(762\) 4.92820i 0.178530i
\(763\) −15.8564 + 27.4641i −0.574040 + 0.994267i
\(764\) 10.7321 + 18.5885i 0.388272 + 0.672507i
\(765\) 0 0
\(766\) −25.3923 −0.917461
\(767\) 7.33013 29.6244i 0.264676 1.06967i
\(768\) 1.00000 0.0360844
\(769\) −10.0359 + 5.79423i −0.361904 + 0.208945i −0.669916 0.742437i \(-0.733670\pi\)
0.308012 + 0.951383i \(0.400336\pi\)
\(770\) 0 0
\(771\) −2.66987 + 4.62436i −0.0961531 + 0.166542i
\(772\) 11.3205i 0.407434i
\(773\) −24.0000 13.8564i −0.863220 0.498380i 0.00186926 0.999998i \(-0.499405\pi\)
−0.865089 + 0.501618i \(0.832738\pi\)
\(774\) 10.3301 + 5.96410i 0.371309 + 0.214375i
\(775\) 0 0
\(776\) −0.267949 + 0.464102i −0.00961882 + 0.0166603i
\(777\) 9.19615 + 15.9282i 0.329910 + 0.571421i
\(778\) −20.5526 + 11.8660i −0.736845 + 0.425418i
\(779\) 14.9282 0.534858
\(780\) 0 0
\(781\) −80.1051 −2.86639
\(782\) −12.9282 + 7.46410i −0.462312 + 0.266916i
\(783\) −0.133975 0.232051i −0.00478786