Properties

Label 1170.2.bs.e.361.2
Level $1170$
Weight $2$
Character 1170.361
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 361.2
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1170.361
Dual form 1170.2.bs.e.901.2

$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).

\(n\) \(911\) \(937\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 0.135583 0.990766i \(-0.456709\pi\)
−0.790237 + 0.612801i \(0.790043\pi\)
\(8\) 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 −0.731748 + 0.681575i \(0.761295\pi\)
−0.956136 + 0.292925i \(0.905371\pi\)
\(12\) 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 −0.999853 0.0171533i \(-0.994540\pi\)
0.514782 + 0.857321i \(0.327873\pi\)
\(18\) 0 0
\(19\) 6.46410 + 3.73205i 1.48297 + 0.856191i 0.999813 0.0193444i \(-0.00615788\pi\)
0.483154 + 0.875536i \(0.339491\pi\)
\(20\) 0.866025 + 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 0.992328 0.123635i \(-0.0394551\pi\)
−0.603235 + 0.797564i \(0.706122\pi\)
\(24\) 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 0.878197 0.478300i \(-0.158747\pi\)
−0.853318 + 0.521391i \(0.825413\pi\)
\(30\) 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
\(33\) 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 0.327313 0.944916i \(-0.393857\pi\)
0.981978 + 0.188997i \(0.0605237\pi\)
\(38\) 7.46410 1.21084
\(39\) 0 0
\(40\) 1.00000 0.158114
\(41\) −1.73205 + 1.00000i −0.270501 + 0.156174i −0.629115 0.777312i \(-0.716583\pi\)
0.358614 + 0.933486i \(0.383249\pi\)
\(42\) 0 0
\(43\) −5.96410 + 10.3301i −0.909517 + 1.57533i −0.0947805 + 0.995498i \(0.530215\pi\)
−0.814736 + 0.579831i \(0.803118\pi\)
\(44\) 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 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 −0.0598868 0.998205i \(-0.519074\pi\)
−0.894414 + 0.447239i \(0.852407\pi\)
\(60\) 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
\(63\) 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 −0.963395 0.268086i \(-0.913609\pi\)
−0.249528 + 0.968368i \(0.580276\pi\)
\(68\) 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 0.975675 0.219222i \(-0.0703521\pi\)
0.297985 + 0.954570i \(0.403685\pi\)
\(72\) 0 0
\(73\) 2.00000i 0.234082i −0.993127 0.117041i \(-0.962659\pi\)
0.993127 0.117041i \(-0.0373409\pi\)
\(74\) 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 \(0.163003\pi\)
−0.871723 + 0.489999i \(0.836997\pi\)
\(84\) 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 −0.475201 0.879877i \(-0.657625\pi\)
0.524396 + 0.851475i \(0.324291\pi\)
\(90\) 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 0.523376 0.852102i \(-0.324672\pi\)
−0.476254 + 0.879308i \(0.658006\pi\)
\(98\) −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 0.929628 0.368500i \(-0.120129\pi\)
−0.783944 + 0.620831i \(0.786795\pi\)
\(102\) 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 0.611273 0.791420i \(-0.290658\pi\)
−0.991026 + 0.133667i \(0.957325\pi\)
\(108\) 0 0
\(109\) 15.8564i 1.51877i 0.650643 + 0.759384i \(0.274500\pi\)
−0.650643 + 0.759384i \(0.725500\pi\)
\(110\) −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 −0.846501 0.532387i \(-0.821295\pi\)
0.884311 + 0.466898i \(0.154629\pi\)
\(114\) 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 0.954397 0.298542i \(-0.0965002\pi\)
−0.735743 + 0.677261i \(0.763167\pi\)
\(128\) −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 0.588381 0.808584i \(-0.299765\pi\)
−0.406063 + 0.913845i \(0.633099\pi\)
\(138\) 0 0
\(139\) 6.46410 11.1962i 0.548278 0.949645i −0.450115 0.892971i \(-0.648617\pi\)
0.998393 0.0566745i \(-0.0180497\pi\)
\(140\) −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 0.896277 0.443494i \(-0.146261\pi\)
0.0640617 + 0.997946i \(0.479595\pi\)
\(150\) 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
\(153\) 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 0.914408 0.404794i \(-0.132657\pi\)
0.106642 + 0.994297i \(0.465990\pi\)
\(164\) 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 \(0.550877\pi\)
\(168\) 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 −0.580045 0.814584i \(-0.696965\pi\)
0.995473 + 0.0950419i \(0.0302985\pi\)
\(174\) 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 −0.953653 0.300909i \(-0.902710\pi\)
0.216231 0.976342i \(-0.430623\pi\)
\(180\) 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 −0.157379 0.987538i \(-0.550304\pi\)
0.933923 0.357475i \(-0.116362\pi\)
\(192\) 0 0
\(193\) 9.80385 5.66025i 0.705696 0.407434i −0.103769 0.994601i \(-0.533090\pi\)
0.809466 + 0.587167i \(0.199757\pi\)
\(194\) 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 \(0.383345\pi\)
\(198\) 0 0
\(199\) 2.53590 4.39230i 0.179765 0.311362i −0.762035 0.647536i \(-0.775800\pi\)
0.941800 + 0.336174i \(0.109133\pi\)
\(200\) 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 0.992405 0.123015i \(-0.0392564\pi\)
−0.602737 + 0.797940i \(0.705923\pi\)
\(212\) −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 −0.958521 0.285022i \(-0.907999\pi\)
−0.232424 + 0.972614i \(0.574666\pi\)
\(224\) 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 \(0.483577\pi\)
\(228\) 0 0
\(229\) 7.85641i 0.519166i 0.965721 + 0.259583i \(0.0835851\pi\)
−0.965721 + 0.259583i \(0.916415\pi\)
\(230\) −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 \(-0.822130\pi\)
0.847894 0.530165i \(-0.177870\pi\)
\(240\) 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 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 −0.503493 0.863999i \(-0.667952\pi\)
0.999992 + 0.00403776i \(0.00128526\pi\)
\(252\) 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 0.770660 0.637247i \(-0.219927\pi\)
−0.937202 + 0.348787i \(0.886593\pi\)
\(258\) 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 0.944858 0.327481i \(-0.106200\pi\)
−0.756036 + 0.654530i \(0.772866\pi\)
\(264\) 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 −0.623082 0.782157i \(-0.714120\pi\)
0.988908 + 0.148527i \(0.0474530\pi\)
\(270\) 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
\(273\) 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 −0.800968 0.598707i \(-0.795681\pi\)
0.918980 + 0.394305i \(0.129015\pi\)
\(278\) 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 \(-0.914197\pi\)
0.963889 0.266306i \(-0.0858032\pi\)
\(282\) 0 0
\(283\) 4.96410 + 8.59808i 0.295085 + 0.511103i 0.975005 0.222184i \(-0.0713186\pi\)
−0.679920 + 0.733287i \(0.737985\pi\)
\(284\) 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 0.988968 + 0.148128i \(0.0473247\pi\)
0.622767 + 0.782408i \(0.286009\pi\)
\(294\) 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 \(-0.812551\pi\)
0.831558 0.555437i \(-0.187449\pi\)
\(308\) 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 \(0.133846\pi\)
−0.912889 + 0.408209i \(0.866154\pi\)
\(318\) 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 0.0441440 0.999025i \(-0.485944\pi\)
−0.843109 + 0.537742i \(0.819277\pi\)
\(332\) 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 −0.843642 0.536906i \(-0.819593\pi\)
0.886795 + 0.462163i \(0.152926\pi\)
\(348\) 0 0
\(349\) 18.5885 10.7321i 0.995017 0.574474i 0.0882471 0.996099i \(-0.471873\pi\)
0.906770 + 0.421625i \(0.138540\pi\)
\(350\) 2.00000 0.106904
\(351\) 0 0
\(352\) 6.46410 0.344538
\(353\) −1.73205 + 1.00000i −0.0921878 + 0.0532246i −0.545385 0.838186i \(-0.683617\pi\)
0.453197 + 0.891410i \(0.350283\pi\)
\(354\) 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 \(0.0427307\pi\)
−0.991003 + 0.133840i \(0.957269\pi\)
\(360\) 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 0.587235 0.809416i \(-0.300216\pi\)
−0.994593 + 0.103852i \(0.966883\pi\)
\(368\) 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 −0.586090 0.810246i \(-0.699334\pi\)
0.994739 + 0.102446i \(0.0326670\pi\)
\(374\) −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 0.270257 0.962788i \(-0.412891\pi\)
0.968928 + 0.247344i \(0.0795579\pi\)
\(380\) 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 −0.181324 0.983423i \(-0.558038\pi\)
−0.942332 + 0.334680i \(0.891372\pi\)
\(384\) 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 0.739786 0.672843i \(-0.234927\pi\)
−0.212806 + 0.977095i \(0.568260\pi\)
\(398\) 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 0.391292 0.920267i \(-0.372028\pi\)
0.992620 + 0.121265i \(0.0386950\pi\)
\(402\) 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 0.583193 0.812333i \(-0.301803\pi\)
−0.411905 + 0.911227i \(0.635136\pi\)
\(410\) −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 0.998480 + 0.0551112i \(0.0175513\pi\)
−0.451512 + 0.892265i \(0.649115\pi\)
\(420\) 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
\(423\) 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 −0.957025 0.290006i \(-0.906343\pi\)
−0.227360 + 0.973811i \(0.573009\pi\)
\(432\) 0 0
\(433\) −9.66025 + 16.7321i −0.464242 + 0.804091i −0.999167 0.0408086i \(-0.987007\pi\)
0.534925 + 0.844900i \(0.320340\pi\)
\(434\) 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 0.996524 0.0833027i \(-0.0265468\pi\)
−0.570404 + 0.821364i \(0.693214\pi\)
\(440\) −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 0.785456 0.618917i \(-0.212428\pi\)
−0.143270 + 0.989684i \(0.545762\pi\)
\(450\) 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 0.0875134 0.996163i \(-0.472108\pi\)
0.906459 + 0.422293i \(0.138775\pi\)
\(458\) 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 0.490611 0.871379i \(-0.336774\pi\)
−0.509331 + 0.860571i \(0.670107\pi\)
\(462\) 0 0
\(463\) 7.07180i 0.328654i −0.986406 0.164327i \(-0.947455\pi\)
0.986406 0.164327i \(-0.0525453\pi\)
\(464\) 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 −0.604195 0.796836i \(-0.706505\pi\)
0.387983 + 0.921667i \(0.373172\pi\)
\(480\) 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 0.880283 0.474449i \(-0.157353\pi\)
0.0292568 + 0.999572i \(0.490686\pi\)
\(488\) −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 0.601728 0.798701i \(-0.294479\pi\)
−0.992559 + 0.121761i \(0.961146\pi\)
\(492\) 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 \(-0.953266\pi\)
0.989241 0.146293i \(-0.0467344\pi\)
\(500\) −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 0.275107 + 0.961414i \(0.411287\pi\)
−0.970162 + 0.242457i \(0.922047\pi\)
\(504\) 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 −0.526484 0.850185i \(-0.676490\pi\)
0.473039 + 0.881041i \(0.343157\pi\)
\(510\) 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 0.707960 0.706252i \(-0.249616\pi\)
−0.965613 + 0.259985i \(0.916282\pi\)
\(524\) 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 \(-0.803495\pi\)
0.815422 0.578867i \(-0.196505\pi\)
\(542\) 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 −0.788443 0.615108i \(-0.789113\pi\)
0.138477 + 0.990366i \(0.455779\pi\)
\(558\) 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 −0.911109 0.412166i \(-0.864772\pi\)
0.812500 + 0.582961i \(0.198106\pi\)
\(564\) 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 0.990456 + 0.137827i \(0.0440118\pi\)
−0.375867 + 0.926674i \(0.622655\pi\)
\(570\) 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 \(0.0667451\pi\)
−0.978096 + 0.208153i \(0.933255\pi\)
\(578\) 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 −0.456634 0.889655i \(-0.650945\pi\)
0.542146 + 0.840284i \(0.317612\pi\)
\(588\) 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 \(0.376879\pi\)
−0.377223 + 0.926123i \(0.623121\pi\)
\(594\) 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 0.994147 0.108032i \(-0.0344548\pi\)
−0.590632 + 0.806941i \(0.701121\pi\)
\(602\) 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 −0.603156 0.797623i \(-0.706091\pi\)
0.992340 + 0.123537i \(0.0394239\pi\)
\(608\) −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 −0.990414 0.138130i \(-0.955891\pi\)
−0.375583 + 0.926789i \(0.622558\pi\)
\(614\) −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 \(0.517311\pi\)
\(618\) 0 0
\(619\) 24.2487i 0.974638i 0.873224 + 0.487319i \(0.162025\pi\)
−0.873224 + 0.487319i \(0.837975\pi\)
\(620\) −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 0.932175 0.362008i \(-0.117909\pi\)
0.152579 + 0.988291i \(0.451242\pi\)
\(632\) 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 −0.864604 0.502454i \(-0.832431\pi\)
0.867440 + 0.497542i \(0.165764\pi\)
\(642\) 0 0
\(643\) −17.7846 10.2679i −0.701357 0.404928i 0.106496 0.994313i \(-0.466037\pi\)
−0.807852 + 0.589385i \(0.799370\pi\)
\(644\) −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 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 0.904594 0.426274i \(-0.140174\pi\)
−0.821461 + 0.570264i \(0.806841\pi\)
\(654\) 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 −0.868623 0.495473i \(-0.834995\pi\)
0.863404 + 0.504513i \(0.168328\pi\)
\(660\) 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
\(663\) 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 −0.990074 0.140548i \(-0.955114\pi\)
0.373319 0.927703i \(-0.378220\pi\)
\(674\) 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 0.988460 0.151483i \(-0.0484049\pi\)
0.363042 + 0.931773i \(0.381738\pi\)
\(684\) 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 −0.875688 0.482877i \(-0.839592\pi\)
−0.0196598 + 0.999807i \(0.506258\pi\)
\(692\) −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 0.0784234 0.996920i \(-0.475011\pi\)
−0.824146 + 0.566377i \(0.808345\pi\)
\(710\) 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 0.338136 + 0.941097i \(0.390204\pi\)
−0.984082 + 0.177714i \(0.943130\pi\)
\(720\) 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 \(0.389678\pi\)
−0.339688 + 0.940538i \(0.610322\pi\)
\(734\) −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 −0.775114 0.631821i \(-0.782308\pi\)
0.159616 + 0.987179i \(0.448974\pi\)
\(740\) 9.19615 0.338057
\(741\) 0 0
\(742\) 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 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 0.708624 0.705586i \(-0.249316\pi\)
−0.965368 + 0.260893i \(0.915983\pi\)
\(752\) −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 0.981937 0.189207i \(-0.0605917\pi\)
−0.654827 + 0.755779i \(0.727258\pi\)
\(758\) 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 0.418272 0.908322i \(-0.362636\pi\)
−0.577493 + 0.816395i \(0.695969\pi\)
\(762\) 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 −0.669916 0.742437i \(-0.733670\pi\)
0.308012 + 0.951383i \(0.400336\pi\)
\(770\) 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 0.00186926 0.999998i \(-0.499405\pi\)
−0.865089 + 0.501618i \(0.832738\pi\)
\(774\) 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 0.526496 0.850177i \(-0.323505\pi\)
−0.473027 + 0.881048i \(0.656839\pi\)
\(788\) 4.39230i 0.156469i
\(789\)