Properties

Label 1170.2.bs.e.901.2
Level $1170$
Weight $2$
Character 1170.901
Analytic conductor $9.342$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1170.bs (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.34249703649\)
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 901.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1170.901
Dual form 1170.2.bs.e.361.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} -1.00000i q^{5} +(-1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{10} +(-5.59808 - 3.23205i) q^{11} +(1.00000 - 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +(6.46410 - 3.73205i) q^{19} +(0.866025 - 0.500000i) q^{20} +(-3.23205 - 5.59808i) q^{22} +(1.86603 - 3.23205i) q^{23} -1.00000 q^{25} +(2.59808 - 2.50000i) q^{26} +(-1.73205 - 1.00000i) q^{28} +(0.133975 - 0.232051i) q^{29} -1.73205i q^{31} +(-0.866025 + 0.500000i) q^{32} -4.00000i q^{34} +(1.00000 + 1.73205i) q^{35} +(7.96410 + 4.59808i) q^{37} +7.46410 q^{38} +1.00000 q^{40} +(-1.73205 - 1.00000i) q^{41} +(-5.96410 - 10.3301i) q^{43} -6.46410i q^{44} +(3.23205 - 1.86603i) q^{46} +3.53590i q^{47} +(-1.50000 + 2.59808i) q^{49} +(-0.866025 - 0.500000i) q^{50} +(3.50000 - 0.866025i) q^{52} -0.928203 q^{53} +(-3.23205 + 5.59808i) q^{55} +(-1.00000 - 1.73205i) q^{56} +(0.232051 - 0.133975i) q^{58} +(-7.33013 + 4.23205i) q^{59} +(5.19615 + 9.00000i) q^{61} +(0.866025 - 1.50000i) q^{62} -1.00000 q^{64} +(-3.46410 - 1.00000i) q^{65} +(-9.92820 - 5.73205i) q^{67} +(2.00000 - 3.46410i) q^{68} +2.00000i q^{70} +(10.7321 - 6.19615i) q^{71} +2.00000i q^{73} +(4.59808 + 7.96410i) q^{74} +(6.46410 + 3.73205i) q^{76} +12.9282 q^{77} -13.9282 q^{79} +(0.866025 + 0.500000i) q^{80} +(-1.00000 - 1.73205i) q^{82} -8.92820i q^{83} +(-3.46410 + 2.00000i) q^{85} -11.9282i q^{86} +(3.23205 - 5.59808i) q^{88} +(0.464102 + 0.267949i) q^{89} +(1.73205 + 7.00000i) q^{91} +3.73205 q^{92} +(-1.76795 + 3.06218i) q^{94} +(-3.73205 - 6.46410i) q^{95} +(0.464102 - 0.267949i) q^{97} +(-2.59808 + 1.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{4} + O(q^{10}) \) \( 4q + 2q^{4} + 2q^{10} - 12q^{11} + 4q^{13} - 8q^{14} - 2q^{16} - 8q^{17} + 12q^{19} - 6q^{22} + 4q^{23} - 4q^{25} + 4q^{29} + 4q^{35} + 18q^{37} + 16q^{38} + 4q^{40} - 10q^{43} + 6q^{46} - 6q^{49} + 14q^{52} + 24q^{53} - 6q^{55} - 4q^{56} - 6q^{58} - 12q^{59} - 4q^{64} - 12q^{67} + 8q^{68} + 36q^{71} + 8q^{74} + 12q^{76} + 24q^{77} - 28q^{79} - 4q^{82} + 6q^{88} - 12q^{89} + 8q^{92} - 14q^{94} - 8q^{95} - 12q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0 0
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.00000i 0.447214i
\(6\) 0 0
\(7\) −1.73205 + 1.00000i −0.654654 + 0.377964i −0.790237 0.612801i \(-0.790043\pi\)
0.135583 + 0.990766i \(0.456709\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −5.59808 3.23205i −1.68788 0.974500i −0.956136 0.292925i \(-0.905371\pi\)
−0.731748 0.681575i \(-0.761295\pi\)
\(12\) 0 0
\(13\) 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 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 0 0
\(19\) 6.46410 3.73205i 1.48297 0.856191i 0.483154 0.875536i \(-0.339491\pi\)
0.999813 + 0.0193444i \(0.00615788\pi\)
\(20\) 0.866025 0.500000i 0.193649 0.111803i
\(21\) 0 0
\(22\) −3.23205 5.59808i −0.689076 1.19351i
\(23\) 1.86603 3.23205i 0.389093 0.673929i −0.603235 0.797564i \(-0.706122\pi\)
0.992328 + 0.123635i \(0.0394551\pi\)
\(24\) 0 0
\(25\) −1.00000 −0.200000
\(26\) 2.59808 2.50000i 0.509525 0.490290i
\(27\) 0 0
\(28\) −1.73205 1.00000i −0.327327 0.188982i
\(29\) 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 \(-0.0497126\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 4.00000i 0.685994i
\(35\) 1.00000 + 1.73205i 0.169031 + 0.292770i
\(36\) 0 0
\(37\) 7.96410 + 4.59808i 1.30929 + 0.755919i 0.981978 0.188997i \(-0.0605237\pi\)
0.327313 + 0.944916i \(0.393857\pi\)
\(38\) 7.46410 1.21084
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) −1.73205 1.00000i −0.270501 0.156174i 0.358614 0.933486i \(-0.383249\pi\)
−0.629115 + 0.777312i \(0.716583\pi\)
\(42\) 0 0
\(43\) −5.96410 10.3301i −0.909517 1.57533i −0.814736 0.579831i \(-0.803118\pi\)
−0.0947805 0.995498i \(-0.530215\pi\)
\(44\) 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 \(0.0830245\pi\)
−0.966176 + 0.257882i \(0.916975\pi\)
\(48\) 0 0
\(49\) −1.50000 + 2.59808i −0.214286 + 0.371154i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) 0 0
\(52\) 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 0
\(55\) −3.23205 + 5.59808i −0.435810 + 0.754844i
\(56\) −1.00000 1.73205i −0.133631 0.231455i
\(57\) 0 0
\(58\) 0.232051 0.133975i 0.0304698 0.0175917i
\(59\) −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 \(0.601637\pi\)
\(62\) 0.866025 1.50000i 0.109985 0.190500i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −3.46410 1.00000i −0.429669 0.124035i
\(66\) 0 0
\(67\) −9.92820 5.73205i −1.21292 0.700281i −0.249528 0.968368i \(-0.580276\pi\)
−0.963395 + 0.268086i \(0.913609\pi\)
\(68\) 2.00000 3.46410i 0.242536 0.420084i
\(69\) 0 0
\(70\) 2.00000i 0.239046i
\(71\) 10.7321 6.19615i 1.27366 0.735348i 0.297985 0.954570i \(-0.403685\pi\)
0.975675 + 0.219222i \(0.0703521\pi\)
\(72\) 0 0
\(73\) 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 0
\(79\) −13.9282 −1.56705 −0.783523 0.621363i \(-0.786579\pi\)
−0.783523 + 0.621363i \(0.786579\pi\)
\(80\) 0.866025 + 0.500000i 0.0968246 + 0.0559017i
\(81\) 0 0
\(82\) −1.00000 1.73205i −0.110432 0.191273i
\(83\) 8.92820i 0.979998i −0.871723 0.489999i \(-0.836997\pi\)
0.871723 0.489999i \(-0.163003\pi\)
\(84\) 0 0
\(85\) −3.46410 + 2.00000i −0.375735 + 0.216930i
\(86\) 11.9282i 1.28625i
\(87\) 0 0
\(88\) 3.23205 5.59808i 0.344538 0.596757i
\(89\) 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
\(92\) 3.73205 0.389093
\(93\) 0 0
\(94\) −1.76795 + 3.06218i −0.182350 + 0.315840i
\(95\) −3.73205 6.46410i −0.382900 0.663203i
\(96\) 0 0
\(97\) 0.464102 0.267949i 0.0471224 0.0272061i −0.476254 0.879308i \(-0.658006\pi\)
0.523376 + 0.852102i \(0.324672\pi\)
\(98\) −2.59808 + 1.50000i −0.262445 + 0.151523i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 1.46410 2.53590i 0.145684 0.252331i −0.783944 0.620831i \(-0.786795\pi\)
0.929628 + 0.368500i \(0.120129\pi\)
\(102\) 0 0
\(103\) −11.8564 −1.16825 −0.584123 0.811665i \(-0.698562\pi\)
−0.584123 + 0.811665i \(0.698562\pi\)
\(104\) 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 −0.991026 0.133667i \(-0.957325\pi\)
0.611273 + 0.791420i \(0.290658\pi\)
\(108\) 0 0
\(109\) 15.8564i 1.51877i −0.650643 0.759384i \(-0.725500\pi\)
0.650643 0.759384i \(-0.274500\pi\)
\(110\) −5.59808 + 3.23205i −0.533756 + 0.308164i
\(111\) 0 0
\(112\) 2.00000i 0.188982i
\(113\) 0.401924 + 0.696152i 0.0378098 + 0.0654885i 0.884311 0.466898i \(-0.154629\pi\)
−0.846501 + 0.532387i \(0.821295\pi\)
\(114\) 0 0
\(115\) −3.23205 1.86603i −0.301390 0.174008i
\(116\) 0.267949 0.0248785
\(117\) 0 0
\(118\) −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
\(123\) 0 0
\(124\) 1.50000 0.866025i 0.134704 0.0777714i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 2.46410 4.26795i 0.218654 0.378719i −0.735743 0.677261i \(-0.763167\pi\)
0.954397 + 0.298542i \(0.0965002\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 0 0
\(130\) −2.50000 2.59808i −0.219265 0.227866i
\(131\) 18.6603 1.63035 0.815177 0.579212i \(-0.196640\pi\)
0.815177 + 0.579212i \(0.196640\pi\)
\(132\) 0 0
\(133\) −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 −0.406063 0.913845i \(-0.633099\pi\)
0.588381 + 0.808584i \(0.299765\pi\)
\(138\) 0 0
\(139\) 6.46410 + 11.1962i 0.548278 + 0.949645i 0.998393 + 0.0566745i \(0.0180497\pi\)
−0.450115 + 0.892971i \(0.648617\pi\)
\(140\) −1.00000 + 1.73205i −0.0845154 + 0.146385i
\(141\) 0 0
\(142\) 12.3923 1.03994
\(143\) −16.7942 + 16.1603i −1.40440 + 1.35139i
\(144\) 0 0
\(145\) −0.232051 0.133975i −0.0192708 0.0111260i
\(146\) −1.00000 + 1.73205i −0.0827606 + 0.143346i
\(147\) 0 0
\(148\) 9.19615i 0.755919i
\(149\) 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 \(-0.138973\pi\)
\(152\) 3.73205 + 6.46410i 0.302709 + 0.524308i
\(153\) 0 0
\(154\) 11.1962 + 6.46410i 0.902212 + 0.520892i
\(155\) −1.73205 −0.139122
\(156\) 0 0
\(157\) −5.00000 −0.399043 −0.199522 0.979893i \(-0.563939\pi\)
−0.199522 + 0.979893i \(0.563939\pi\)
\(158\) −12.0622 6.96410i −0.959615 0.554034i
\(159\) 0 0
\(160\) 0.500000 + 0.866025i 0.0395285 + 0.0684653i
\(161\) 7.46410i 0.588254i
\(162\) 0 0
\(163\) 13.0359 7.52628i 1.02105 0.589504i 0.106642 0.994297i \(-0.465990\pi\)
0.914408 + 0.404794i \(0.132657\pi\)
\(164\) 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 −0.159155 0.987254i \(-0.550877\pi\)
−0.934564 + 0.355794i \(0.884210\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) −4.00000 −0.306786
\(171\) 0 0
\(172\) 5.96410 10.3301i 0.454758 0.787665i
\(173\) 5.46410 + 9.46410i 0.415428 + 0.719542i 0.995473 0.0950419i \(-0.0302985\pi\)
−0.580045 + 0.814584i \(0.696965\pi\)
\(174\) 0 0
\(175\) 1.73205 1.00000i 0.130931 0.0755929i
\(176\) 5.59808 3.23205i 0.421971 0.243625i
\(177\) 0 0
\(178\) 0.267949 + 0.464102i 0.0200836 + 0.0347859i
\(179\) −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 \(0.534709\pi\)
\(182\) −2.00000 + 6.92820i −0.148250 + 0.513553i
\(183\) 0 0
\(184\) 3.23205 + 1.86603i 0.238270 + 0.137565i
\(185\) 4.59808 7.96410i 0.338057 0.585532i
\(186\) 0 0
\(187\) 25.8564i 1.89081i
\(188\) −3.06218 + 1.76795i −0.223332 + 0.128941i
\(189\) 0 0
\(190\) 7.46410i 0.541503i
\(191\) 10.7321 + 18.5885i 0.776544 + 1.34501i 0.933923 + 0.357475i \(0.116362\pi\)
−0.157379 + 0.987538i \(0.550304\pi\)
\(192\) 0 0
\(193\) 9.80385 + 5.66025i 0.705696 + 0.407434i 0.809466 0.587167i \(-0.199757\pi\)
−0.103769 + 0.994601i \(0.533090\pi\)
\(194\) 0.535898 0.0384753
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) −3.80385 2.19615i −0.271013 0.156469i 0.358335 0.933593i \(-0.383345\pi\)
−0.629348 + 0.777124i \(0.716678\pi\)
\(198\) 0 0
\(199\) 2.53590 + 4.39230i 0.179765 + 0.311362i 0.941800 0.336174i \(-0.109133\pi\)
−0.762035 + 0.647536i \(0.775800\pi\)
\(200\) 1.00000i 0.0707107i
\(201\) 0 0
\(202\) 2.53590 1.46410i 0.178425 0.103014i
\(203\) 0.535898i 0.0376127i
\(204\) 0 0
\(205\) −1.00000 + 1.73205i −0.0698430 + 0.120972i
\(206\) −10.2679 5.92820i −0.715402 0.413037i
\(207\) 0 0
\(208\) 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 −0.602737 0.797940i \(-0.705923\pi\)
0.992405 + 0.123015i \(0.0392564\pi\)
\(212\) −0.464102 0.803848i −0.0318746 0.0552085i
\(213\) 0 0
\(214\) −6.80385 + 3.92820i −0.465101 + 0.268526i
\(215\) −10.3301 + 5.96410i −0.704509 + 0.406748i
\(216\) 0 0
\(217\) 1.73205 + 3.00000i 0.117579 + 0.203653i
\(218\) 7.92820 13.7321i 0.536966 0.930052i
\(219\) 0 0
\(220\) −6.46410 −0.435810
\(221\) −14.0000 + 3.46410i −0.941742 + 0.233021i
\(222\) 0 0
\(223\) −17.7846 10.2679i −1.19095 0.687593i −0.232424 0.972614i \(-0.574666\pi\)
−0.958521 + 0.285022i \(0.907999\pi\)
\(224\) 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 0.0515725 0.998669i \(-0.483577\pi\)
0.890659 + 0.454672i \(0.150243\pi\)
\(228\) 0 0
\(229\) 7.85641i 0.519166i −0.965721 0.259583i \(-0.916415\pi\)
0.965721 0.259583i \(-0.0835851\pi\)
\(230\) −1.86603 3.23205i −0.123042 0.213115i
\(231\) 0 0
\(232\) 0.232051 + 0.133975i 0.0152349 + 0.00879586i
\(233\) −6.12436 −0.401220 −0.200610 0.979671i \(-0.564292\pi\)
−0.200610 + 0.979671i \(0.564292\pi\)
\(234\) 0 0
\(235\) 3.53590 0.230657
\(236\) −7.33013 4.23205i −0.477151 0.275483i
\(237\) 0 0
\(238\) 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 0.0841601 0.996452i \(-0.473179\pi\)
0.905033 + 0.425341i \(0.139846\pi\)
\(242\) 30.7846i 1.97891i
\(243\) 0 0
\(244\) −5.19615 + 9.00000i −0.332650 + 0.576166i
\(245\) 2.59808 + 1.50000i 0.165985 + 0.0958315i
\(246\) 0 0
\(247\) −6.46410 26.1244i −0.411301 1.66225i
\(248\) 1.73205 0.109985
\(249\) 0 0
\(250\) −0.500000 + 0.866025i −0.0316228 + 0.0547723i
\(251\) 7.86603 + 13.6244i 0.496499 + 0.859962i 0.999992 0.00403776i \(-0.00128526\pi\)
−0.503493 + 0.863999i \(0.667952\pi\)
\(252\) 0 0
\(253\) −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 −0.937202 0.348787i \(-0.886593\pi\)
0.770660 + 0.637247i \(0.219927\pi\)
\(258\) 0 0
\(259\) −18.3923 −1.14284
\(260\) −0.866025 3.50000i −0.0537086 0.217061i
\(261\) 0 0
\(262\) 16.1603 + 9.33013i 0.998384 + 0.576417i
\(263\) 3.06218 5.30385i 0.188822 0.327049i −0.756036 0.654530i \(-0.772866\pi\)
0.944858 + 0.327481i \(0.106200\pi\)
\(264\) 0 0
\(265\) 0.928203i 0.0570191i
\(266\) −12.9282 + 7.46410i −0.792679 + 0.457653i
\(267\) 0 0
\(268\) 11.4641i 0.700281i
\(269\) 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 \(0.655100\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) 2.46410 0.148862
\(275\) 5.59808 + 3.23205i 0.337577 + 0.194900i
\(276\) 0 0
\(277\) 1.96410 + 3.40192i 0.118011 + 0.204402i 0.918980 0.394305i \(-0.129015\pi\)
−0.800968 + 0.598707i \(0.795681\pi\)
\(278\) 12.9282i 0.775382i
\(279\) 0 0
\(280\) −1.73205 + 1.00000i −0.103510 + 0.0597614i
\(281\) 8.92820i 0.532612i 0.963889 + 0.266306i \(0.0858032\pi\)
−0.963889 + 0.266306i \(0.914197\pi\)
\(282\) 0 0
\(283\) 4.96410 8.59808i 0.295085 0.511103i −0.679920 0.733287i \(-0.737985\pi\)
0.975005 + 0.222184i \(0.0713186\pi\)
\(284\) 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 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) −0.133975 0.232051i −0.00786726 0.0136265i
\(291\) 0 0
\(292\) −1.73205 + 1.00000i −0.101361 + 0.0585206i
\(293\) 27.5885 15.9282i 1.61173 0.930536i 0.622767 0.782408i \(-0.286009\pi\)
0.988968 0.148128i \(-0.0473247\pi\)
\(294\) 0 0
\(295\) 4.23205 + 7.33013i 0.246400 + 0.426776i
\(296\) −4.59808 + 7.96410i −0.267258 + 0.462904i
\(297\) 0 0
\(298\) 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
\(303\) 0 0
\(304\) 7.46410i 0.428096i
\(305\) 9.00000 5.19615i 0.515339 0.297531i
\(306\) 0 0
\(307\) 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
\(309\) 0 0
\(310\) −1.50000 0.866025i −0.0851943 0.0491869i
\(311\) 28.3923 1.60998 0.804990 0.593288i \(-0.202171\pi\)
0.804990 + 0.593288i \(0.202171\pi\)
\(312\) 0 0
\(313\) −28.0000 −1.58265 −0.791327 0.611393i \(-0.790609\pi\)
−0.791327 + 0.611393i \(0.790609\pi\)
\(314\) −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 \(-0.866154\pi\)
0.912889 0.408209i \(-0.133846\pi\)
\(318\) 0 0
\(319\) −1.50000 + 0.866025i −0.0839839 + 0.0484881i
\(320\) 1.00000i 0.0559017i
\(321\) 0 0
\(322\) −3.73205 + 6.46410i −0.207979 + 0.360230i
\(323\) −25.8564 14.9282i −1.43869 0.830627i
\(324\) 0 0
\(325\) −1.00000 + 3.46410i −0.0554700 + 0.192154i
\(326\) 15.0526 0.833684
\(327\) 0 0
\(328\) 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 −0.843109 0.537742i \(-0.819277\pi\)
0.0441440 + 0.999025i \(0.485944\pi\)
\(332\) 7.73205 4.46410i 0.424351 0.244999i
\(333\) 0 0
\(334\) −8.16025 14.1340i −0.446509 0.773377i
\(335\) −5.73205 + 9.92820i −0.313175 + 0.542436i
\(336\) 0 0
\(337\) 9.32051 0.507720 0.253860 0.967241i \(-0.418300\pi\)
0.253860 + 0.967241i \(0.418300\pi\)
\(338\) −6.06218 11.5000i −0.329739 0.625518i
\(339\) 0 0
\(340\) −3.46410 2.00000i −0.187867 0.108465i
\(341\) −5.59808 + 9.69615i −0.303153 + 0.525076i
\(342\) 0 0
\(343\) 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 0.886795 0.462163i \(-0.152926\pi\)
−0.843642 + 0.536906i \(0.819593\pi\)
\(348\) 0 0
\(349\) 18.5885 + 10.7321i 0.995017 + 0.574474i 0.906770 0.421625i \(-0.138540\pi\)
0.0882471 + 0.996099i \(0.471873\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) 6.46410 0.344538
\(353\) −1.73205 1.00000i −0.0921878 0.0532246i 0.453197 0.891410i \(-0.350283\pi\)
−0.545385 + 0.838186i \(0.683617\pi\)
\(354\) 0 0
\(355\) −6.19615 10.7321i −0.328858 0.569598i
\(356\) 0.535898i 0.0284026i
\(357\) 0 0
\(358\) −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
\(363\) 0 0
\(364\) −5.19615 + 5.00000i −0.272352 + 0.262071i
\(365\) 2.00000 0.104685
\(366\) 0 0
\(367\) −7.80385 + 13.5167i −0.407358 + 0.705564i −0.994593 0.103852i \(-0.966883\pi\)
0.587235 + 0.809416i \(0.300216\pi\)
\(368\) 1.86603 + 3.23205i 0.0972733 + 0.168482i
\(369\) 0 0
\(370\) 7.96410 4.59808i 0.414034 0.239043i
\(371\) 1.60770 0.928203i 0.0834674 0.0481899i
\(372\) 0 0
\(373\) 7.89230 + 13.6699i 0.408648 + 0.707799i 0.994739 0.102446i \(-0.0326670\pi\)
−0.586090 + 0.810246i \(0.699334\pi\)
\(374\) −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
\(378\) 0 0
\(379\) 24.1244 + 13.9282i 1.23918 + 0.715444i 0.968928 0.247344i \(-0.0795579\pi\)
0.270257 + 0.962788i \(0.412891\pi\)
\(380\) 3.73205 6.46410i 0.191450 0.331601i
\(381\) 0 0
\(382\) 21.4641i 1.09820i
\(383\) −21.9904 + 12.6962i −1.12366 + 0.648743i −0.942332 0.334680i \(-0.891372\pi\)
−0.181324 + 0.983423i \(0.558038\pi\)
\(384\) 0 0
\(385\) 12.9282i 0.658882i
\(386\) 5.66025 + 9.80385i 0.288099 + 0.499003i
\(387\) 0 0
\(388\) 0.464102 + 0.267949i 0.0235612 + 0.0136031i
\(389\) 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
\(392\) −2.59808 1.50000i −0.131223 0.0757614i
\(393\) 0 0
\(394\) −2.19615 3.80385i −0.110641 0.191635i
\(395\) 13.9282i 0.700804i
\(396\) 0 0
\(397\) 10.5000 6.06218i 0.526980 0.304252i −0.212806 0.977095i \(-0.568260\pi\)
0.739786 + 0.672843i \(0.234927\pi\)
\(398\) 5.07180i 0.254226i
\(399\) 0 0
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 27.7128 + 16.0000i 1.38391 + 0.799002i 0.992620 0.121265i \(-0.0386950\pi\)
0.391292 + 0.920267i \(0.372028\pi\)
\(402\) 0 0
\(403\) −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
\(408\) 0 0
\(409\) 3.46410 2.00000i 0.171289 0.0988936i −0.411905 0.911227i \(-0.635136\pi\)
0.583193 + 0.812333i \(0.301803\pi\)
\(410\) −1.73205 + 1.00000i −0.0855399 + 0.0493865i
\(411\) 0 0
\(412\) −5.92820 10.2679i −0.292062 0.505866i
\(413\) 8.46410 14.6603i 0.416491 0.721384i
\(414\) 0 0
\(415\) −8.92820 −0.438268
\(416\) 0.866025 + 3.50000i 0.0424604 + 0.171602i
\(417\) 0 0
\(418\) −41.7846 24.1244i −2.04375 1.17996i
\(419\) 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 \(0.965865\pi\)
\(422\) 9.80385 5.66025i 0.477244 0.275537i
\(423\) 0 0
\(424\) 0.928203i 0.0450775i
\(425\) 2.00000 + 3.46410i 0.0970143 + 0.168034i
\(426\) 0 0
\(427\) −18.0000 10.3923i −0.871081 0.502919i
\(428\) −7.85641 −0.379754
\(429\) 0 0
\(430\) −11.9282 −0.575229
\(431\) −24.5885 14.1962i −1.18438 0.683805i −0.227360 0.973811i \(-0.573009\pi\)
−0.957025 + 0.290006i \(0.906343\pi\)
\(432\) 0 0
\(433\) −9.66025 16.7321i −0.464242 0.804091i 0.534925 0.844900i \(-0.320340\pi\)
−0.999167 + 0.0408086i \(0.987007\pi\)
\(434\) 3.46410i 0.166282i
\(435\) 0 0
\(436\) 13.7321 7.92820i 0.657646 0.379692i
\(437\) 27.8564i 1.33255i
\(438\) 0 0
\(439\) 8.92820 15.4641i 0.426120 0.738061i −0.570404 0.821364i \(-0.693214\pi\)
0.996524 + 0.0833027i \(0.0265468\pi\)
\(440\) −5.59808 3.23205i −0.266878 0.154082i
\(441\) 0 0
\(442\) −13.8564 4.00000i −0.659082 0.190261i
\(443\) −16.3923 −0.778822 −0.389411 0.921064i \(-0.627321\pi\)
−0.389411 + 0.921064i \(0.627321\pi\)
\(444\) 0 0
\(445\) 0.267949 0.464102i 0.0127020 0.0220005i
\(446\) −10.2679 17.7846i −0.486201 0.842126i
\(447\) 0 0
\(448\) 1.73205 1.00000i 0.0818317 0.0472456i
\(449\) 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
\(452\) −0.401924 + 0.696152i −0.0189049 + 0.0327443i
\(453\) 0 0
\(454\) 16.3923 0.769329
\(455\) 7.00000 1.73205i 0.328165 0.0811998i
\(456\) 0 0
\(457\) 21.2487 + 12.2679i 0.993973 + 0.573870i 0.906459 0.422293i \(-0.138775\pi\)
0.0875134 + 0.996163i \(0.472108\pi\)
\(458\) 3.92820 6.80385i 0.183553 0.317923i
\(459\) 0 0
\(460\) 3.73205i 0.174008i
\(461\) −0.401924 + 0.232051i −0.0187195 + 0.0108077i −0.509331 0.860571i \(-0.670107\pi\)
0.490611 + 0.871379i \(0.336774\pi\)
\(462\) 0 0
\(463\) 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 \(0.380428\pi\)
\(468\) 0 0
\(469\) 22.9282 1.05873
\(470\) 3.06218 + 1.76795i 0.141248 + 0.0815494i
\(471\) 0 0
\(472\) −4.23205 7.33013i −0.194796 0.337396i
\(473\) 77.1051i 3.54530i
\(474\) 0 0
\(475\) −6.46410 + 3.73205i −0.296593 + 0.171238i
\(476\) 8.00000i 0.366679i
\(477\) 0 0
\(478\) −8.19615 + 14.1962i −0.374883 + 0.649317i
\(479\) −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
\(482\) 17.7321 0.807673
\(483\) 0 0
\(484\) −15.3923 + 26.6603i −0.699650 + 1.21183i
\(485\) −0.267949 0.464102i −0.0121669 0.0210738i
\(486\) 0 0
\(487\) 20.0718 11.5885i 0.909540 0.525123i 0.0292568 0.999572i \(-0.490686\pi\)
0.880283 + 0.474449i \(0.157353\pi\)
\(488\) −9.00000 + 5.19615i −0.407411 + 0.235219i
\(489\) 0 0
\(490\) 1.50000 + 2.59808i 0.0677631 + 0.117369i
\(491\) −8.66025 + 15.0000i −0.390832 + 0.676941i −0.992559 0.121761i \(-0.961146\pi\)
0.601728 + 0.798701i \(0.294479\pi\)
\(492\) 0 0
\(493\) −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
\(498\) 0 0
\(499\) 6.53590i 0.292587i 0.989241 + 0.146293i \(0.0467344\pi\)
−0.989241 + 0.146293i \(0.953266\pi\)
\(500\) −0.866025 + 0.500000i −0.0387298 + 0.0223607i
\(501\) 0 0
\(502\) 15.7321i 0.702156i
\(503\) −15.5885 27.0000i −0.695055 1.20387i −0.970162 0.242457i \(-0.922047\pi\)
0.275107 0.961414i \(-0.411287\pi\)
\(504\) 0 0
\(505\) −2.53590 1.46410i −0.112846 0.0651517i
\(506\) −24.1244 −1.07246
\(507\) 0 0
\(508\) 4.92820 0.218654
\(509\) −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
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −4.62436 + 2.66987i −0.203972 + 0.117763i
\(515\) 11.8564i 0.522456i
\(516\) 0 0
\(517\) 11.4282 19.7942i 0.502612 0.870549i
\(518\) −15.9282 9.19615i −0.699845 0.404056i
\(519\) 0 0
\(520\) 1.00000 3.46410i 0.0438529 0.151911i
\(521\) 17.3205 0.758825 0.379413 0.925228i \(-0.376126\pi\)
0.379413 + 0.925228i \(0.376126\pi\)
\(522\) 0 0
\(523\) −5.89230 + 10.2058i −0.257653 + 0.446267i −0.965613 0.259985i \(-0.916282\pi\)
0.707960 + 0.706252i \(0.249616\pi\)
\(524\) 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
\(528\) 0 0
\(529\) 4.53590 + 7.85641i 0.197213 + 0.341583i
\(530\) −0.464102 + 0.803848i −0.0201593 + 0.0349169i
\(531\) 0 0
\(532\) −14.9282 −0.647220
\(533\) −5.19615 + 5.00000i −0.225070 + 0.216574i
\(534\) 0 0
\(535\) 6.80385 + 3.92820i 0.294156 + 0.169831i
\(536\) 5.73205 9.92820i 0.247587 0.428833i
\(537\) 0 0
\(538\) 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 \(0.196505\pi\)
−0.815422 + 0.578867i \(0.803495\pi\)
\(542\) 0.598076 + 1.03590i 0.0256896 + 0.0444956i
\(543\) 0 0
\(544\) 3.46410 + 2.00000i 0.148522 + 0.0857493i
\(545\) −15.8564 −0.679214
\(546\) 0 0
\(547\) 22.9282 0.980339 0.490170 0.871627i \(-0.336935\pi\)
0.490170 + 0.871627i \(0.336935\pi\)
\(548\) 2.13397 + 1.23205i 0.0911589 + 0.0526306i
\(549\) 0 0
\(550\) 3.23205 + 5.59808i 0.137815 + 0.238703i
\(551\) 2.00000i 0.0852029i
\(552\) 0 0
\(553\) 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 0.138477 0.990366i \(-0.455779\pi\)
−0.788443 + 0.615108i \(0.789113\pi\)
\(558\) 0 0
\(559\) −41.7487 + 10.3301i −1.76578 + 0.436918i
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) −4.46410 + 7.73205i −0.188307 + 0.326157i
\(563\) −2.33975 4.05256i −0.0986085 0.170795i 0.812500 0.582961i \(-0.198106\pi\)
−0.911109 + 0.412166i \(0.864772\pi\)
\(564\) 0 0
\(565\) 0.696152 0.401924i 0.0292874 0.0169091i
\(566\) 8.59808 4.96410i 0.361404 0.208657i
\(567\) 0 0
\(568\) 6.19615 + 10.7321i 0.259985 + 0.450307i
\(569\) 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 \(0.617024\pi\)
\(572\) −22.3923 6.46410i −0.936269 0.270278i
\(573\) 0 0
\(574\) 3.46410 + 2.00000i 0.144589 + 0.0834784i
\(575\) −1.86603 + 3.23205i −0.0778186 + 0.134786i
\(576\) 0 0
\(577\) 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
\(579\) 0 0
\(580\) 0.267949i 0.0111260i
\(581\) 8.92820 + 15.4641i 0.370404 + 0.641559i
\(582\) 0 0
\(583\) 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 0.542146 0.840284i \(-0.317612\pi\)
−0.456634 + 0.889655i \(0.650945\pi\)
\(588\) 0 0
\(589\) −6.46410 11.1962i −0.266349 0.461329i
\(590\) 8.46410i 0.348462i
\(591\) 0 0
\(592\) −7.96410 + 4.59808i −0.327323 + 0.188980i
\(593\) 45.1051i 1.85225i −0.377223 0.926123i \(-0.623121\pi\)
0.377223 0.926123i \(-0.376879\pi\)
\(594\) 0 0
\(595\) 4.00000 6.92820i 0.163984 0.284029i
\(596\) 11.7224 + 6.76795i 0.480170 + 0.277226i
\(597\) 0 0
\(598\) −3.23205 13.0622i −0.132168 0.534152i
\(599\) 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 \(0.0344548\pi\)
\(602\) 11.9282 + 20.6603i 0.486157 + 0.842049i
\(603\) 0 0
\(604\) 9.00000 5.19615i 0.366205 0.211428i
\(605\) 26.6603 15.3923i 1.08389 0.625786i
\(606\) 0 0
\(607\) 9.58846 + 16.6077i 0.389183 + 0.674086i 0.992340 0.123537i \(-0.0394239\pi\)
−0.603156 + 0.797623i \(0.706091\pi\)
\(608\) −3.73205 + 6.46410i −0.151355 + 0.262154i
\(609\) 0 0
\(610\) 10.3923 0.420772
\(611\) 12.2487 + 3.53590i 0.495530 + 0.143047i
\(612\) 0 0
\(613\) −33.8205 19.5263i −1.36600 0.788659i −0.375583 0.926789i \(-0.622558\pi\)
−0.990414 + 0.138130i \(0.955891\pi\)
\(614\) −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 −0.0543580 0.998522i \(-0.517311\pi\)
0.837566 + 0.546336i \(0.183978\pi\)
\(618\) 0 0
\(619\) 24.2487i 0.974638i −0.873224 0.487319i \(-0.837975\pi\)
0.873224 0.487319i \(-0.162025\pi\)
\(620\) −0.866025 1.50000i −0.0347804 0.0602414i
\(621\) 0 0
\(622\) 24.5885 + 14.1962i 0.985907 + 0.569214i
\(623\) −1.07180 −0.0429406
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −24.2487 14.0000i −0.969173 0.559553i
\(627\) 0 0
\(628\) −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 0.152579 0.988291i \(-0.451242\pi\)
0.932175 + 0.362008i \(0.117909\pi\)
\(632\) 13.9282i 0.554034i
\(633\) 0 0
\(634\) 7.26795 12.5885i 0.288647 0.499952i
\(635\) −4.26795 2.46410i −0.169368 0.0977849i
\(636\) 0 0
\(637\) 7.50000 + 7.79423i 0.297161 + 0.308819i
\(638\) −1.73205 −0.0685725
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) 0.0717968 + 0.124356i 0.00283580 + 0.00491175i 0.867440 0.497542i \(-0.165764\pi\)
−0.864604 + 0.502454i \(0.832431\pi\)
\(642\) 0 0
\(643\) −17.7846 + 10.2679i −0.701357 + 0.404928i −0.807852 0.589385i \(-0.799370\pi\)
0.106496 + 0.994313i \(0.466037\pi\)
\(644\) −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 −0.966731 0.255794i \(-0.917663\pi\)
0.704890 + 0.709317i \(0.250996\pi\)
\(648\) 0 0
\(649\) 54.7128 2.14767
\(650\) −2.59808 + 2.50000i −0.101905 + 0.0980581i
\(651\) 0 0
\(652\) 13.0359 + 7.52628i 0.510525 + 0.294752i
\(653\) 2.12436 3.67949i 0.0831325 0.143990i −0.821461 0.570264i \(-0.806841\pi\)
0.904594 + 0.426274i \(0.140174\pi\)
\(654\) 0 0
\(655\) 18.6603i 0.729116i
\(656\) 1.73205 1.00000i 0.0676252 0.0390434i
\(657\) 0 0
\(658\) 7.07180i 0.275687i
\(659\) −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 \(0.720655\pi\)
\(662\) −16.7846 −0.652352
\(663\) 0 0
\(664\) 8.92820 0.346481
\(665\) 12.9282 + 7.46410i 0.501334 + 0.289445i
\(666\) 0 0
\(667\) −0.500000 0.866025i −0.0193601 0.0335326i
\(668\) 16.3205i 0.631459i
\(669\) 0 0
\(670\) −9.92820 + 5.73205i −0.383560 + 0.221448i
\(671\) 67.1769i 2.59334i
\(672\) 0 0
\(673\) −16.0000 + 27.7128i −0.616755 + 1.06825i 0.373319 + 0.927703i \(0.378220\pi\)
−0.990074 + 0.140548i \(0.955114\pi\)
\(674\) 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 0
\(679\) −0.535898 + 0.928203i −0.0205659 + 0.0356212i
\(680\) −2.00000 3.46410i −0.0766965 0.132842i
\(681\) 0 0
\(682\) −9.69615 + 5.59808i −0.371285 + 0.214361i
\(683\) 35.3205 20.3923i 1.35150 0.780290i 0.363042 0.931773i \(-0.381738\pi\)
0.988460 + 0.151483i \(0.0484049\pi\)
\(684\) 0 0
\(685\) −1.23205 2.13397i −0.0470742 0.0815350i
\(686\) 10.0000 17.3205i 0.381802 0.661300i
\(687\) 0 0
\(688\) 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 −0.0196598 0.999807i \(-0.506258\pi\)
−0.875688 + 0.482877i \(0.839592\pi\)
\(692\) −5.46410 + 9.46410i −0.207714 + 0.359771i
\(693\) 0 0
\(694\) 1.60770i 0.0610273i
\(695\) 11.1962 6.46410i 0.424694 0.245197i
\(696\) 0 0
\(697\) 8.00000i 0.303022i
\(698\) 10.7321 + 18.5885i 0.406214 + 0.703583i
\(699\) 0 0
\(700\) 1.73205 + 1.00000i 0.0654654 + 0.0377964i
\(701\) 0.267949 0.0101203 0.00506015 0.999987i \(-0.498389\pi\)
0.00506015 + 0.999987i \(0.498389\pi\)
\(702\) 0 0
\(703\) 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
\(708\) 0 0
\(709\) −19.8564 + 11.4641i −0.745723 + 0.430543i −0.824146 0.566377i \(-0.808345\pi\)
0.0784234 + 0.996920i \(0.475011\pi\)
\(710\) 12.3923i 0.465075i
\(711\) 0 0
\(712\) −0.267949 + 0.464102i −0.0100418 + 0.0173929i
\(713\) −5.59808 3.23205i −0.209650 0.121041i
\(714\) 0 0
\(715\) 16.1603 + 16.7942i 0.604359 + 0.628069i
\(716\) −19.7321 −0.737421
\(717\) 0 0
\(718\) 2.53590 4.39230i 0.0946389 0.163919i
\(719\) −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
\(722\) 31.7942 18.3564i 1.18326 0.683155i
\(723\) 0 0
\(724\) −1.46410 2.53590i −0.0544129 0.0942459i
\(725\) −0.133975 + 0.232051i −0.00497569 + 0.00861815i
\(726\) 0 0
\(727\) −31.7128 −1.17616 −0.588082 0.808802i \(-0.700117\pi\)
−0.588082 + 0.808802i \(0.700117\pi\)
\(728\) −7.00000 + 1.73205i −0.259437 + 0.0641941i
\(729\) 0 0
\(730\) 1.73205 + 1.00000i 0.0641061 + 0.0370117i
\(731\) −23.8564 + 41.3205i −0.882361 + 1.52829i
\(732\) 0 0
\(733\) 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
\(738\) 0 0
\(739\) −16.7321 9.66025i −0.615498 0.355358i 0.159616 0.987179i \(-0.448974\pi\)
−0.775114 + 0.631821i \(0.782308\pi\)
\(740\) 9.19615 0.338057
\(741\) 0 0
\(742\) 1.85641 0.0681508
\(743\) 35.0429 + 20.2321i 1.28560 + 0.742242i 0.977866 0.209230i \(-0.0670958\pi\)
0.307734 + 0.951472i \(0.400429\pi\)
\(744\) 0 0
\(745\) −6.76795 11.7224i −0.247958 0.429477i
\(746\) 15.7846i 0.577916i
\(747\) 0 0
\(748\) −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 −0.965368 0.260893i \(-0.915983\pi\)
0.708624 + 0.705586i \(0.249316\pi\)
\(752\) −3.06218 1.76795i −0.111666 0.0644705i
\(753\) 0 0
\(754\) −0.232051 0.937822i −0.00845079 0.0341535i
\(755\) −10.3923 −0.378215
\(756\) 0 0
\(757\) 9.00000 15.5885i 0.327111 0.566572i −0.654827 0.755779i \(-0.727258\pi\)
0.981937 + 0.189207i \(0.0605917\pi\)
\(758\) 13.9282 + 24.1244i 0.505895 + 0.876236i
\(759\) 0 0
\(760\) 6.46410 3.73205i 0.234478 0.135376i
\(761\) −4.39230 + 2.53590i −0.159221 + 0.0919262i −0.577493 0.816395i \(-0.695969\pi\)
0.418272 + 0.908322i \(0.362636\pi\)
\(762\) 0 0
\(763\) 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
\(768\) 0 0
\(769\) −10.0359 5.79423i −0.361904 0.208945i 0.308012 0.951383i \(-0.400336\pi\)
−0.669916 + 0.742437i \(0.733670\pi\)
\(770\) 6.46410 11.1962i 0.232950 0.403481i
\(771\) 0 0
\(772\) 11.3205i 0.407434i
\(773\) −24.0000 + 13.8564i −0.863220 + 0.498380i −0.865089 0.501618i \(-0.832738\pi\)
0.00186926 + 0.999998i \(0.499405\pi\)
\(774\) 0 0
\(775\) 1.73205i 0.0622171i
\(776\) 0.267949 + 0.464102i 0.00961882 + 0.0166603i
\(777\) 0 0
\(778\) 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 0
\(784\) −1.50000 2.59808i −0.0535714 0.0927884i
\(785\) 5.00000i 0.178458i
\(786\) 0 0
\(787\) 1.50000 0.866025i 0.0534692 0.0308705i −0.473027 0.881048i \(-0.656839\pi\)
0.526496 + 0.850177i \(0.323505\pi\)
\(788\) 4.39230i 0.156469i
\(789\)