Properties

Label 1710.2.l.f.1261.1
Level $1710$
Weight $2$
Character 1710.1261
Analytic conductor $13.654$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1710.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.6544187456\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 570)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 1261.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1710.1261
Dual form 1710.2.l.f.1531.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -1.00000 q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} -2.00000 q^{11} +(1.50000 - 2.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +(4.00000 + 1.73205i) q^{19} +1.00000 q^{20} +(-1.00000 - 1.73205i) q^{22} +(-3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +3.00000 q^{26} +(0.500000 - 0.866025i) q^{28} +(-5.00000 + 8.66025i) q^{29} +1.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{34} +(0.500000 + 0.866025i) q^{35} -5.00000 q^{37} +(0.500000 + 4.33013i) q^{38} +(0.500000 + 0.866025i) q^{40} +(1.00000 + 1.73205i) q^{41} +(2.50000 + 4.33013i) q^{43} +(1.00000 - 1.73205i) q^{44} -6.00000 q^{46} -6.00000 q^{49} -1.00000 q^{50} +(1.50000 + 2.59808i) q^{52} +(-6.00000 + 10.3923i) q^{53} +(1.00000 + 1.73205i) q^{55} +1.00000 q^{56} -10.0000 q^{58} +(-1.00000 - 1.73205i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(0.500000 + 0.866025i) q^{62} +1.00000 q^{64} -3.00000 q^{65} +(2.50000 - 4.33013i) q^{67} -4.00000 q^{68} +(-0.500000 + 0.866025i) q^{70} +(-5.50000 - 9.52628i) q^{73} +(-2.50000 - 4.33013i) q^{74} +(-3.50000 + 2.59808i) q^{76} +2.00000 q^{77} +(5.50000 + 9.52628i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-1.00000 + 1.73205i) q^{82} -2.00000 q^{83} +(2.00000 - 3.46410i) q^{85} +(-2.50000 + 4.33013i) q^{86} +2.00000 q^{88} +(-1.50000 + 2.59808i) q^{91} +(-3.00000 - 5.19615i) q^{92} +(-0.500000 - 4.33013i) q^{95} +(1.00000 + 1.73205i) q^{97} +(-3.00000 - 5.19615i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{4} - q^{5} - 2q^{7} - 2q^{8} + O(q^{10}) \) \( 2q + q^{2} - q^{4} - q^{5} - 2q^{7} - 2q^{8} + q^{10} - 4q^{11} + 3q^{13} - q^{14} - q^{16} + 4q^{17} + 8q^{19} + 2q^{20} - 2q^{22} - 6q^{23} - q^{25} + 6q^{26} + q^{28} - 10q^{29} + 2q^{31} + q^{32} - 4q^{34} + q^{35} - 10q^{37} + q^{38} + q^{40} + 2q^{41} + 5q^{43} + 2q^{44} - 12q^{46} - 12q^{49} - 2q^{50} + 3q^{52} - 12q^{53} + 2q^{55} + 2q^{56} - 20q^{58} - 2q^{59} - 5q^{61} + q^{62} + 2q^{64} - 6q^{65} + 5q^{67} - 8q^{68} - q^{70} - 11q^{73} - 5q^{74} - 7q^{76} + 4q^{77} + 11q^{79} - q^{80} - 2q^{82} - 4q^{83} + 4q^{85} - 5q^{86} + 4q^{88} - 3q^{91} - 6q^{92} - q^{95} + 2q^{97} - 6q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(1027\) \(1351\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 1.50000 2.59808i 0.416025 0.720577i −0.579510 0.814965i \(-0.696756\pi\)
0.995535 + 0.0943882i \(0.0300895\pi\)
\(14\) −0.500000 0.866025i −0.133631 0.231455i
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) 0 0
\(19\) 4.00000 + 1.73205i 0.917663 + 0.397360i
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) −1.00000 1.73205i −0.213201 0.369274i
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 3.00000 0.588348
\(27\) 0 0
\(28\) 0.500000 0.866025i 0.0944911 0.163663i
\(29\) −5.00000 + 8.66025i −0.928477 + 1.60817i −0.142605 + 0.989780i \(0.545548\pi\)
−0.785872 + 0.618389i \(0.787786\pi\)
\(30\) 0 0
\(31\) 1.00000 0.179605 0.0898027 0.995960i \(-0.471376\pi\)
0.0898027 + 0.995960i \(0.471376\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 0 0
\(34\) −2.00000 + 3.46410i −0.342997 + 0.594089i
\(35\) 0.500000 + 0.866025i 0.0845154 + 0.146385i
\(36\) 0 0
\(37\) −5.00000 −0.821995 −0.410997 0.911636i \(-0.634819\pi\)
−0.410997 + 0.911636i \(0.634819\pi\)
\(38\) 0.500000 + 4.33013i 0.0811107 + 0.702439i
\(39\) 0 0
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) 1.00000 + 1.73205i 0.156174 + 0.270501i 0.933486 0.358614i \(-0.116751\pi\)
−0.777312 + 0.629115i \(0.783417\pi\)
\(42\) 0 0
\(43\) 2.50000 + 4.33013i 0.381246 + 0.660338i 0.991241 0.132068i \(-0.0421616\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 1.00000 1.73205i 0.150756 0.261116i
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) −1.00000 −0.141421
\(51\) 0 0
\(52\) 1.50000 + 2.59808i 0.208013 + 0.360288i
\(53\) −6.00000 + 10.3923i −0.824163 + 1.42749i 0.0783936 + 0.996922i \(0.475021\pi\)
−0.902557 + 0.430570i \(0.858312\pi\)
\(54\) 0 0
\(55\) 1.00000 + 1.73205i 0.134840 + 0.233550i
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −10.0000 −1.31306
\(59\) −1.00000 1.73205i −0.130189 0.225494i 0.793560 0.608492i \(-0.208225\pi\)
−0.923749 + 0.382998i \(0.874892\pi\)
\(60\) 0 0
\(61\) −2.50000 + 4.33013i −0.320092 + 0.554416i −0.980507 0.196485i \(-0.937047\pi\)
0.660415 + 0.750901i \(0.270381\pi\)
\(62\) 0.500000 + 0.866025i 0.0635001 + 0.109985i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −3.00000 −0.372104
\(66\) 0 0
\(67\) 2.50000 4.33013i 0.305424 0.529009i −0.671932 0.740613i \(-0.734535\pi\)
0.977356 + 0.211604i \(0.0678686\pi\)
\(68\) −4.00000 −0.485071
\(69\) 0 0
\(70\) −0.500000 + 0.866025i −0.0597614 + 0.103510i
\(71\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(72\) 0 0
\(73\) −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) −2.50000 4.33013i −0.290619 0.503367i
\(75\) 0 0
\(76\) −3.50000 + 2.59808i −0.401478 + 0.298020i
\(77\) 2.00000 0.227921
\(78\) 0 0
\(79\) 5.50000 + 9.52628i 0.618798 + 1.07179i 0.989705 + 0.143120i \(0.0457135\pi\)
−0.370907 + 0.928670i \(0.620953\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) −1.00000 + 1.73205i −0.110432 + 0.191273i
\(83\) −2.00000 −0.219529 −0.109764 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) 0 0
\(85\) 2.00000 3.46410i 0.216930 0.375735i
\(86\) −2.50000 + 4.33013i −0.269582 + 0.466930i
\(87\) 0 0
\(88\) 2.00000 0.213201
\(89\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) −1.50000 + 2.59808i −0.157243 + 0.272352i
\(92\) −3.00000 5.19615i −0.312772 0.541736i
\(93\) 0 0
\(94\) 0 0
\(95\) −0.500000 4.33013i −0.0512989 0.444262i
\(96\) 0 0
\(97\) 1.00000 + 1.73205i 0.101535 + 0.175863i 0.912317 0.409484i \(-0.134291\pi\)
−0.810782 + 0.585348i \(0.800958\pi\)
\(98\) −3.00000 5.19615i −0.303046 0.524891i
\(99\) 0 0
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 3.00000 5.19615i 0.298511 0.517036i −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 0 0
\(103\) 19.0000 1.87213 0.936063 0.351833i \(-0.114441\pi\)
0.936063 + 0.351833i \(0.114441\pi\)
\(104\) −1.50000 + 2.59808i −0.147087 + 0.254762i
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) 4.00000 0.386695 0.193347 0.981130i \(-0.438066\pi\)
0.193347 + 0.981130i \(0.438066\pi\)
\(108\) 0 0
\(109\) 9.00000 + 15.5885i 0.862044 + 1.49310i 0.869953 + 0.493135i \(0.164149\pi\)
−0.00790932 + 0.999969i \(0.502518\pi\)
\(110\) −1.00000 + 1.73205i −0.0953463 + 0.165145i
\(111\) 0 0
\(112\) 0.500000 + 0.866025i 0.0472456 + 0.0818317i
\(113\) −14.0000 −1.31701 −0.658505 0.752577i \(-0.728811\pi\)
−0.658505 + 0.752577i \(0.728811\pi\)
\(114\) 0 0
\(115\) 6.00000 0.559503
\(116\) −5.00000 8.66025i −0.464238 0.804084i
\(117\) 0 0
\(118\) 1.00000 1.73205i 0.0920575 0.159448i
\(119\) −2.00000 3.46410i −0.183340 0.317554i
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) −5.00000 −0.452679
\(123\) 0 0
\(124\) −0.500000 + 0.866025i −0.0449013 + 0.0777714i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −8.00000 + 13.8564i −0.709885 + 1.22956i 0.255014 + 0.966937i \(0.417920\pi\)
−0.964899 + 0.262620i \(0.915413\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −1.50000 2.59808i −0.131559 0.227866i
\(131\) −3.00000 5.19615i −0.262111 0.453990i 0.704692 0.709514i \(-0.251085\pi\)
−0.966803 + 0.255524i \(0.917752\pi\)
\(132\) 0 0
\(133\) −4.00000 1.73205i −0.346844 0.150188i
\(134\) 5.00000 0.431934
\(135\) 0 0
\(136\) −2.00000 3.46410i −0.171499 0.297044i
\(137\) −1.00000 + 1.73205i −0.0854358 + 0.147979i −0.905577 0.424182i \(-0.860562\pi\)
0.820141 + 0.572161i \(0.193895\pi\)
\(138\) 0 0
\(139\) 4.50000 7.79423i 0.381685 0.661098i −0.609618 0.792695i \(-0.708677\pi\)
0.991303 + 0.131597i \(0.0420106\pi\)
\(140\) −1.00000 −0.0845154
\(141\) 0 0
\(142\) 0 0
\(143\) −3.00000 + 5.19615i −0.250873 + 0.434524i
\(144\) 0 0
\(145\) 10.0000 0.830455
\(146\) 5.50000 9.52628i 0.455183 0.788400i
\(147\) 0 0
\(148\) 2.50000 4.33013i 0.205499 0.355934i
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −4.00000 1.73205i −0.324443 0.140488i
\(153\) 0 0
\(154\) 1.00000 + 1.73205i 0.0805823 + 0.139573i
\(155\) −0.500000 0.866025i −0.0401610 0.0695608i
\(156\) 0 0
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) −5.50000 + 9.52628i −0.437557 + 0.757870i
\(159\) 0 0
\(160\) −1.00000 −0.0790569
\(161\) 3.00000 5.19615i 0.236433 0.409514i
\(162\) 0 0
\(163\) −17.0000 −1.33154 −0.665771 0.746156i \(-0.731897\pi\)
−0.665771 + 0.746156i \(0.731897\pi\)
\(164\) −2.00000 −0.156174
\(165\) 0 0
\(166\) −1.00000 1.73205i −0.0776151 0.134433i
\(167\) 7.00000 12.1244i 0.541676 0.938211i −0.457132 0.889399i \(-0.651123\pi\)
0.998808 0.0488118i \(-0.0155435\pi\)
\(168\) 0 0
\(169\) 2.00000 + 3.46410i 0.153846 + 0.266469i
\(170\) 4.00000 0.306786
\(171\) 0 0
\(172\) −5.00000 −0.381246
\(173\) −13.0000 22.5167i −0.988372 1.71191i −0.625871 0.779926i \(-0.715256\pi\)
−0.362500 0.931984i \(-0.618077\pi\)
\(174\) 0 0
\(175\) 0.500000 0.866025i 0.0377964 0.0654654i
\(176\) 1.00000 + 1.73205i 0.0753778 + 0.130558i
\(177\) 0 0
\(178\) 0 0
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 0 0
\(181\) 3.00000 5.19615i 0.222988 0.386227i −0.732726 0.680524i \(-0.761752\pi\)
0.955714 + 0.294297i \(0.0950855\pi\)
\(182\) −3.00000 −0.222375
\(183\) 0 0
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) 2.50000 + 4.33013i 0.183804 + 0.318357i
\(186\) 0 0
\(187\) −4.00000 6.92820i −0.292509 0.506640i
\(188\) 0 0
\(189\) 0 0
\(190\) 3.50000 2.59808i 0.253917 0.188484i
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 0 0
\(193\) −12.5000 21.6506i −0.899770 1.55845i −0.827788 0.561041i \(-0.810401\pi\)
−0.0719816 0.997406i \(-0.522932\pi\)
\(194\) −1.00000 + 1.73205i −0.0717958 + 0.124354i
\(195\) 0 0
\(196\) 3.00000 5.19615i 0.214286 0.371154i
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) 0 0
\(199\) −2.50000 + 4.33013i −0.177220 + 0.306955i −0.940927 0.338608i \(-0.890044\pi\)
0.763707 + 0.645563i \(0.223377\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) 0 0
\(202\) 6.00000 0.422159
\(203\) 5.00000 8.66025i 0.350931 0.607831i
\(204\) 0 0
\(205\) 1.00000 1.73205i 0.0698430 0.120972i
\(206\) 9.50000 + 16.4545i 0.661896 + 1.14644i
\(207\) 0 0
\(208\) −3.00000 −0.208013
\(209\) −8.00000 3.46410i −0.553372 0.239617i
\(210\) 0 0
\(211\) 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i \(-0.111609\pi\)
−0.767049 + 0.641588i \(0.778276\pi\)
\(212\) −6.00000 10.3923i −0.412082 0.713746i
\(213\) 0 0
\(214\) 2.00000 + 3.46410i 0.136717 + 0.236801i
\(215\) 2.50000 4.33013i 0.170499 0.295312i
\(216\) 0 0
\(217\) −1.00000 −0.0678844
\(218\) −9.00000 + 15.5885i −0.609557 + 1.05578i
\(219\) 0 0
\(220\) −2.00000 −0.134840
\(221\) 12.0000 0.807207
\(222\) 0 0
\(223\) 0.500000 + 0.866025i 0.0334825 + 0.0579934i 0.882281 0.470723i \(-0.156007\pi\)
−0.848799 + 0.528716i \(0.822674\pi\)
\(224\) −0.500000 + 0.866025i −0.0334077 + 0.0578638i
\(225\) 0 0
\(226\) −7.00000 12.1244i −0.465633 0.806500i
\(227\) 18.0000 1.19470 0.597351 0.801980i \(-0.296220\pi\)
0.597351 + 0.801980i \(0.296220\pi\)
\(228\) 0 0
\(229\) −5.00000 −0.330409 −0.165205 0.986259i \(-0.552828\pi\)
−0.165205 + 0.986259i \(0.552828\pi\)
\(230\) 3.00000 + 5.19615i 0.197814 + 0.342624i
\(231\) 0 0
\(232\) 5.00000 8.66025i 0.328266 0.568574i
\(233\) −2.00000 3.46410i −0.131024 0.226941i 0.793047 0.609160i \(-0.208493\pi\)
−0.924072 + 0.382219i \(0.875160\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 2.00000 0.130189
\(237\) 0 0
\(238\) 2.00000 3.46410i 0.129641 0.224544i
\(239\) 18.0000 1.16432 0.582162 0.813073i \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 0 0
\(241\) −2.50000 + 4.33013i −0.161039 + 0.278928i −0.935242 0.354010i \(-0.884818\pi\)
0.774202 + 0.632938i \(0.218151\pi\)
\(242\) −3.50000 6.06218i −0.224989 0.389692i
\(243\) 0 0
\(244\) −2.50000 4.33013i −0.160046 0.277208i
\(245\) 3.00000 + 5.19615i 0.191663 + 0.331970i
\(246\) 0 0
\(247\) 10.5000 7.79423i 0.668099 0.495935i
\(248\) −1.00000 −0.0635001
\(249\) 0 0
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) −1.00000 + 1.73205i −0.0631194 + 0.109326i −0.895858 0.444340i \(-0.853438\pi\)
0.832739 + 0.553666i \(0.186772\pi\)
\(252\) 0 0
\(253\) 6.00000 10.3923i 0.377217 0.653359i
\(254\) −16.0000 −1.00393
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 0 0
\(259\) 5.00000 0.310685
\(260\) 1.50000 2.59808i 0.0930261 0.161126i
\(261\) 0 0
\(262\) 3.00000 5.19615i 0.185341 0.321019i
\(263\) −5.00000 8.66025i −0.308313 0.534014i 0.669680 0.742650i \(-0.266431\pi\)
−0.977993 + 0.208635i \(0.933098\pi\)
\(264\) 0 0
\(265\) 12.0000 0.737154
\(266\) −0.500000 4.33013i −0.0306570 0.265497i
\(267\) 0 0
\(268\) 2.50000 + 4.33013i 0.152712 + 0.264505i
\(269\) 5.00000 + 8.66025i 0.304855 + 0.528025i 0.977229 0.212187i \(-0.0680585\pi\)
−0.672374 + 0.740212i \(0.734725\pi\)
\(270\) 0 0
\(271\) 4.00000 + 6.92820i 0.242983 + 0.420858i 0.961563 0.274586i \(-0.0885408\pi\)
−0.718580 + 0.695444i \(0.755208\pi\)
\(272\) 2.00000 3.46410i 0.121268 0.210042i
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 1.00000 1.73205i 0.0603023 0.104447i
\(276\) 0 0
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) 9.00000 0.539784
\(279\) 0 0
\(280\) −0.500000 0.866025i −0.0298807 0.0517549i
\(281\) −15.0000 + 25.9808i −0.894825 + 1.54988i −0.0608039 + 0.998150i \(0.519366\pi\)
−0.834021 + 0.551733i \(0.813967\pi\)
\(282\) 0 0
\(283\) −4.00000 6.92820i −0.237775 0.411839i 0.722300 0.691580i \(-0.243085\pi\)
−0.960076 + 0.279741i \(0.909752\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −6.00000 −0.354787
\(287\) −1.00000 1.73205i −0.0590281 0.102240i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 5.00000 + 8.66025i 0.293610 + 0.508548i
\(291\) 0 0
\(292\) 11.0000 0.643726
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) 0 0
\(295\) −1.00000 + 1.73205i −0.0582223 + 0.100844i
\(296\) 5.00000 0.290619
\(297\) 0 0
\(298\) −9.00000 + 15.5885i −0.521356 + 0.903015i
\(299\) 9.00000 + 15.5885i 0.520483 + 0.901504i
\(300\) 0 0
\(301\) −2.50000 4.33013i −0.144098 0.249584i
\(302\) 0 0
\(303\) 0 0
\(304\) −0.500000 4.33013i −0.0286770 0.248350i
\(305\) 5.00000 0.286299
\(306\) 0 0
\(307\) −2.00000 3.46410i −0.114146 0.197707i 0.803292 0.595585i \(-0.203080\pi\)
−0.917438 + 0.397879i \(0.869747\pi\)
\(308\) −1.00000 + 1.73205i −0.0569803 + 0.0986928i
\(309\) 0 0
\(310\) 0.500000 0.866025i 0.0283981 0.0491869i
\(311\) 10.0000 0.567048 0.283524 0.958965i \(-0.408496\pi\)
0.283524 + 0.958965i \(0.408496\pi\)
\(312\) 0 0
\(313\) −9.00000 + 15.5885i −0.508710 + 0.881112i 0.491239 + 0.871025i \(0.336544\pi\)
−0.999949 + 0.0100869i \(0.996789\pi\)
\(314\) −6.50000 + 11.2583i −0.366816 + 0.635344i
\(315\) 0 0
\(316\) −11.0000 −0.618798
\(317\) 15.0000 25.9808i 0.842484 1.45922i −0.0453045 0.998973i \(-0.514426\pi\)
0.887788 0.460252i \(-0.152241\pi\)
\(318\) 0 0
\(319\) 10.0000 17.3205i 0.559893 0.969762i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 0 0
\(322\) 6.00000 0.334367
\(323\) 2.00000 + 17.3205i 0.111283 + 0.963739i
\(324\) 0 0
\(325\) 1.50000 + 2.59808i 0.0832050 + 0.144115i
\(326\) −8.50000 14.7224i −0.470771 0.815400i
\(327\) 0 0
\(328\) −1.00000 1.73205i −0.0552158 0.0956365i
\(329\) 0 0
\(330\) 0 0
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) 1.00000 1.73205i 0.0548821 0.0950586i
\(333\) 0 0
\(334\) 14.0000 0.766046
\(335\) −5.00000 −0.273179
\(336\) 0 0
\(337\) −11.5000 19.9186i −0.626445 1.08503i −0.988260 0.152784i \(-0.951176\pi\)
0.361815 0.932250i \(-0.382157\pi\)
\(338\) −2.00000 + 3.46410i −0.108786 + 0.188422i
\(339\) 0 0
\(340\) 2.00000 + 3.46410i 0.108465 + 0.187867i
\(341\) −2.00000 −0.108306
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) −2.50000 4.33013i −0.134791 0.233465i
\(345\) 0 0
\(346\) 13.0000 22.5167i 0.698884 1.21050i
\(347\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) 0 0
\(349\) 17.0000 0.909989 0.454995 0.890494i \(-0.349641\pi\)
0.454995 + 0.890494i \(0.349641\pi\)
\(350\) 1.00000 0.0534522
\(351\) 0 0
\(352\) −1.00000 + 1.73205i −0.0533002 + 0.0923186i
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 5.00000 + 8.66025i 0.264258 + 0.457709i
\(359\) −1.00000 1.73205i −0.0527780 0.0914141i 0.838429 0.545010i \(-0.183474\pi\)
−0.891207 + 0.453596i \(0.850141\pi\)
\(360\) 0 0
\(361\) 13.0000 + 13.8564i 0.684211 + 0.729285i
\(362\) 6.00000 0.315353
\(363\) 0 0
\(364\) −1.50000 2.59808i −0.0786214 0.136176i
\(365\) −5.50000 + 9.52628i −0.287883 + 0.498628i
\(366\) 0 0
\(367\) 3.50000 6.06218i 0.182699 0.316443i −0.760100 0.649806i \(-0.774850\pi\)
0.942799 + 0.333363i \(0.108183\pi\)
\(368\) 6.00000 0.312772
\(369\) 0 0
\(370\) −2.50000 + 4.33013i −0.129969 + 0.225113i
\(371\) 6.00000 10.3923i 0.311504 0.539542i
\(372\) 0 0
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 4.00000 6.92820i 0.206835 0.358249i
\(375\) 0 0
\(376\) 0 0
\(377\) 15.0000 + 25.9808i 0.772539 + 1.33808i
\(378\) 0 0
\(379\) −11.0000 −0.565032 −0.282516 0.959263i \(-0.591169\pi\)
−0.282516 + 0.959263i \(0.591169\pi\)
\(380\) 4.00000 + 1.73205i 0.205196 + 0.0888523i
\(381\) 0 0
\(382\) −8.00000 13.8564i −0.409316 0.708955i
\(383\) −18.0000 31.1769i −0.919757 1.59307i −0.799783 0.600289i \(-0.795052\pi\)
−0.119974 0.992777i \(-0.538281\pi\)
\(384\) 0 0
\(385\) −1.00000 1.73205i −0.0509647 0.0882735i
\(386\) 12.5000 21.6506i 0.636233 1.10199i
\(387\) 0 0
\(388\) −2.00000 −0.101535
\(389\) −5.00000 + 8.66025i −0.253510 + 0.439092i −0.964490 0.264120i \(-0.914918\pi\)
0.710980 + 0.703213i \(0.248252\pi\)
\(390\) 0 0
\(391\) −24.0000 −1.21373
\(392\) 6.00000 0.303046
\(393\) 0 0
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) 5.50000 9.52628i 0.276735 0.479319i
\(396\) 0 0
\(397\) 0.500000 + 0.866025i 0.0250943 + 0.0434646i 0.878300 0.478110i \(-0.158678\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −5.00000 −0.250627
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −19.0000 32.9090i −0.948815 1.64340i −0.747927 0.663781i \(-0.768951\pi\)
−0.200888 0.979614i \(-0.564383\pi\)
\(402\) 0 0
\(403\) 1.50000 2.59808i 0.0747203 0.129419i
\(404\) 3.00000 + 5.19615i 0.149256 + 0.258518i
\(405\) 0 0
\(406\) 10.0000 0.496292
\(407\) 10.0000 0.495682
\(408\) 0 0
\(409\) 15.0000 25.9808i 0.741702 1.28467i −0.210017 0.977698i \(-0.567352\pi\)
0.951720 0.306968i \(-0.0993146\pi\)
\(410\) 2.00000 0.0987730
\(411\) 0 0
\(412\) −9.50000 + 16.4545i −0.468031 + 0.810654i
\(413\) 1.00000 + 1.73205i 0.0492068 + 0.0852286i
\(414\) 0 0
\(415\) 1.00000 + 1.73205i 0.0490881 + 0.0850230i
\(416\) −1.50000 2.59808i −0.0735436 0.127381i
\(417\) 0 0
\(418\) −1.00000 8.66025i −0.0489116 0.423587i
\(419\) 24.0000 1.17248 0.586238 0.810139i \(-0.300608\pi\)
0.586238 + 0.810139i \(0.300608\pi\)
\(420\) 0 0
\(421\) 7.00000 + 12.1244i 0.341159 + 0.590905i 0.984648 0.174550i \(-0.0558472\pi\)
−0.643489 + 0.765455i \(0.722514\pi\)
\(422\) −2.50000 + 4.33013i −0.121698 + 0.210787i
\(423\) 0 0
\(424\) 6.00000 10.3923i 0.291386 0.504695i
\(425\) −4.00000 −0.194029
\(426\) 0 0
\(427\) 2.50000 4.33013i 0.120983 0.209550i
\(428\) −2.00000 + 3.46410i −0.0966736 + 0.167444i
\(429\) 0 0
\(430\) 5.00000 0.241121
\(431\) −10.0000 + 17.3205i −0.481683 + 0.834300i −0.999779 0.0210230i \(-0.993308\pi\)
0.518096 + 0.855323i \(0.326641\pi\)
\(432\) 0 0
\(433\) −14.5000 + 25.1147i −0.696826 + 1.20694i 0.272736 + 0.962089i \(0.412071\pi\)
−0.969561 + 0.244848i \(0.921262\pi\)
\(434\) −0.500000 0.866025i −0.0240008 0.0415705i
\(435\) 0 0
\(436\) −18.0000 −0.862044
\(437\) −21.0000 + 15.5885i −1.00457 + 0.745697i
\(438\) 0 0
\(439\) 20.5000 + 35.5070i 0.978412 + 1.69466i 0.668184 + 0.743996i \(0.267072\pi\)
0.310228 + 0.950662i \(0.399595\pi\)
\(440\) −1.00000 1.73205i −0.0476731 0.0825723i
\(441\) 0 0
\(442\) 6.00000 + 10.3923i 0.285391 + 0.494312i
\(443\) 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −0.500000 + 0.866025i −0.0236757 + 0.0410075i
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) −28.0000 −1.32140 −0.660701 0.750649i \(-0.729741\pi\)
−0.660701 + 0.750649i \(0.729741\pi\)
\(450\) 0 0
\(451\) −2.00000 3.46410i −0.0941763 0.163118i
\(452\) 7.00000 12.1244i 0.329252 0.570282i
\(453\) 0 0
\(454\) 9.00000 + 15.5885i 0.422391 + 0.731603i
\(455\) 3.00000 0.140642
\(456\) 0 0
\(457\) 23.0000 1.07589 0.537947 0.842978i \(-0.319200\pi\)
0.537947 + 0.842978i \(0.319200\pi\)
\(458\) −2.50000 4.33013i −0.116817 0.202334i
\(459\) 0 0
\(460\) −3.00000 + 5.19615i −0.139876 + 0.242272i
\(461\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(462\) 0 0
\(463\) 1.00000 0.0464739 0.0232370 0.999730i \(-0.492603\pi\)
0.0232370 + 0.999730i \(0.492603\pi\)
\(464\) 10.0000 0.464238
\(465\) 0 0
\(466\) 2.00000 3.46410i 0.0926482 0.160471i
\(467\) −30.0000 −1.38823 −0.694117 0.719862i \(-0.744205\pi\)
−0.694117 + 0.719862i \(0.744205\pi\)
\(468\) 0 0
\(469\) −2.50000 + 4.33013i −0.115439 + 0.199947i
\(470\) 0 0
\(471\) 0 0
\(472\) 1.00000 + 1.73205i 0.0460287 + 0.0797241i
\(473\) −5.00000 8.66025i −0.229900 0.398199i
\(474\) 0 0
\(475\) −3.50000 + 2.59808i −0.160591 + 0.119208i
\(476\) 4.00000 0.183340
\(477\) 0 0
\(478\) 9.00000 + 15.5885i 0.411650 + 0.712999i
\(479\) 21.0000 36.3731i 0.959514 1.66193i 0.235833 0.971794i \(-0.424218\pi\)
0.723681 0.690134i \(-0.242449\pi\)
\(480\) 0 0
\(481\) −7.50000 + 12.9904i −0.341971 + 0.592310i
\(482\) −5.00000 −0.227744
\(483\) 0 0
\(484\) 3.50000 6.06218i 0.159091 0.275554i
\(485\) 1.00000 1.73205i 0.0454077 0.0786484i
\(486\) 0 0
\(487\) 16.0000 0.725029 0.362515 0.931978i \(-0.381918\pi\)
0.362515 + 0.931978i \(0.381918\pi\)
\(488\) 2.50000 4.33013i 0.113170 0.196016i
\(489\) 0 0
\(490\) −3.00000 + 5.19615i −0.135526 + 0.234738i
\(491\) 14.0000 + 24.2487i 0.631811 + 1.09433i 0.987181 + 0.159603i \(0.0510215\pi\)
−0.355370 + 0.934726i \(0.615645\pi\)
\(492\) 0 0
\(493\) −40.0000 −1.80151
\(494\) 12.0000 + 5.19615i 0.539906 + 0.233786i
\(495\) 0 0
\(496\) −0.500000 0.866025i −0.0224507 0.0388857i
\(497\) 0 0
\(498\) 0 0
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) 0 0
\(502\) −2.00000 −0.0892644
\(503\) 22.0000 38.1051i 0.980932 1.69902i 0.322151 0.946688i \(-0.395594\pi\)
0.658781 0.752335i \(-0.271072\pi\)
\(504\) 0 0
\(505\) −6.00000 −0.266996
\(506\) 12.0000 0.533465
\(507\) 0 0
\(508\) −8.00000 13.8564i −0.354943 0.614779i
\(509\) −4.00000 + 6.92820i −0.177297 + 0.307087i −0.940954 0.338535i \(-0.890069\pi\)
0.763657 + 0.645622i \(0.223402\pi\)
\(510\) 0 0
\(511\) 5.50000 + 9.52628i 0.243306 + 0.421418i
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −6.00000 −0.264649
\(515\) −9.50000 16.4545i −0.418620 0.725071i
\(516\) 0 0
\(517\) 0 0
\(518\) 2.50000 + 4.33013i 0.109844 + 0.190255i
\(519\) 0 0
\(520\) 3.00000 0.131559
\(521\) −8.00000 −0.350486 −0.175243 0.984525i \(-0.556071\pi\)
−0.175243 + 0.984525i \(0.556071\pi\)
\(522\) 0 0
\(523\) 5.50000 9.52628i 0.240498 0.416555i −0.720358 0.693602i \(-0.756023\pi\)
0.960856 + 0.277047i \(0.0893559\pi\)
\(524\) 6.00000 0.262111
\(525\) 0 0
\(526\) 5.00000 8.66025i 0.218010 0.377605i
\(527\) 2.00000 + 3.46410i 0.0871214 + 0.150899i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) 6.00000 + 10.3923i 0.260623 + 0.451413i
\(531\) 0 0
\(532\) 3.50000 2.59808i 0.151744 0.112641i
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) −2.00000 3.46410i −0.0864675 0.149766i
\(536\) −2.50000 + 4.33013i −0.107984 + 0.187033i
\(537\) 0 0
\(538\) −5.00000 + 8.66025i −0.215565 + 0.373370i
\(539\) 12.0000 0.516877
\(540\) 0 0
\(541\) 4.50000 7.79423i 0.193470 0.335100i −0.752928 0.658103i \(-0.771359\pi\)
0.946398 + 0.323003i \(0.104692\pi\)
\(542\) −4.00000 + 6.92820i −0.171815 + 0.297592i
\(543\) 0 0
\(544\) 4.00000 0.171499
\(545\) 9.00000 15.5885i 0.385518 0.667736i
\(546\) 0 0
\(547\) 4.50000 7.79423i 0.192406 0.333257i −0.753641 0.657286i \(-0.771704\pi\)
0.946047 + 0.324029i \(0.105038\pi\)
\(548\) −1.00000 1.73205i −0.0427179 0.0739895i
\(549\) 0 0
\(550\) 2.00000 0.0852803
\(551\) −35.0000 + 25.9808i −1.49105 + 1.10682i
\(552\) 0 0
\(553\) −5.50000 9.52628i −0.233884 0.405099i
\(554\) −5.00000 8.66025i −0.212430 0.367939i
\(555\) 0 0
\(556\) 4.50000 + 7.79423i 0.190843 + 0.330549i
\(557\) −6.00000 + 10.3923i −0.254228 + 0.440336i −0.964686 0.263404i \(-0.915155\pi\)
0.710457 + 0.703740i \(0.248488\pi\)
\(558\) 0 0
\(559\) 15.0000 0.634432
\(560\) 0.500000 0.866025i 0.0211289 0.0365963i
\(561\) 0 0
\(562\) −30.0000 −1.26547
\(563\) −22.0000 −0.927189 −0.463595 0.886047i \(-0.653441\pi\)
−0.463595 + 0.886047i \(0.653441\pi\)
\(564\) 0 0
\(565\) 7.00000 + 12.1244i 0.294492 + 0.510075i
\(566\) 4.00000 6.92820i 0.168133 0.291214i
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 39.0000 1.63210 0.816050 0.577982i \(-0.196160\pi\)
0.816050 + 0.577982i \(0.196160\pi\)
\(572\) −3.00000 5.19615i −0.125436 0.217262i
\(573\) 0 0
\(574\) 1.00000 1.73205i 0.0417392 0.0722944i
\(575\) −3.00000 5.19615i −0.125109 0.216695i
\(576\) 0 0
\(577\) −18.0000 −0.749350 −0.374675 0.927156i \(-0.622246\pi\)
−0.374675 + 0.927156i \(0.622246\pi\)
\(578\) 1.00000 0.0415945
\(579\) 0 0
\(580\) −5.00000 + 8.66025i −0.207614 + 0.359597i
\(581\) 2.00000 0.0829740
\(582\) 0 0
\(583\) 12.0000 20.7846i 0.496989 0.860811i
\(584\) 5.50000 + 9.52628i 0.227592 + 0.394200i
\(585\) 0 0
\(586\) 13.0000 + 22.5167i 0.537025 + 0.930155i
\(587\) 9.00000 + 15.5885i 0.371470 + 0.643404i 0.989792 0.142520i \(-0.0455206\pi\)
−0.618322 + 0.785925i \(0.712187\pi\)
\(588\) 0 0
\(589\) 4.00000 + 1.73205i 0.164817 + 0.0713679i
\(590\) −2.00000 −0.0823387
\(591\) 0 0
\(592\) 2.50000 + 4.33013i 0.102749 + 0.177967i
\(593\) 14.0000 24.2487i 0.574911 0.995775i −0.421140 0.906996i \(-0.638370\pi\)
0.996051 0.0887797i \(-0.0282967\pi\)
\(594\) 0 0
\(595\) −2.00000 + 3.46410i −0.0819920 + 0.142014i
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) −9.00000 + 15.5885i −0.368037 + 0.637459i
\(599\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 0 0
\(601\) 7.00000 0.285536 0.142768 0.989756i \(-0.454400\pi\)
0.142768 + 0.989756i \(0.454400\pi\)
\(602\) 2.50000 4.33013i 0.101892 0.176483i
\(603\) 0 0
\(604\) 0 0
\(605\) 3.50000 + 6.06218i 0.142295 + 0.246463i
\(606\) 0 0
\(607\) −9.00000 −0.365299 −0.182649 0.983178i \(-0.558467\pi\)
−0.182649 + 0.983178i \(0.558467\pi\)
\(608\) 3.50000 2.59808i 0.141944 0.105366i
\(609\) 0 0
\(610\) 2.50000 + 4.33013i 0.101222 + 0.175322i
\(611\) 0 0
\(612\) 0 0
\(613\) 11.0000 + 19.0526i 0.444286 + 0.769526i 0.998002 0.0631797i \(-0.0201241\pi\)
−0.553716 + 0.832705i \(0.686791\pi\)
\(614\) 2.00000 3.46410i 0.0807134 0.139800i
\(615\) 0 0
\(616\) −2.00000 −0.0805823
\(617\) 12.0000 20.7846i 0.483102 0.836757i −0.516710 0.856161i \(-0.672843\pi\)
0.999812 + 0.0194037i \(0.00617676\pi\)
\(618\) 0 0
\(619\) −29.0000 −1.16561 −0.582804 0.812613i \(-0.698045\pi\)
−0.582804 + 0.812613i \(0.698045\pi\)
\(620\) 1.00000 0.0401610
\(621\) 0 0
\(622\) 5.00000 + 8.66025i 0.200482 + 0.347245i
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) −18.0000 −0.719425
\(627\) 0 0
\(628\) −13.0000 −0.518756
\(629\) −10.0000 17.3205i −0.398726 0.690614i
\(630\) 0 0
\(631\) 21.5000 37.2391i 0.855901 1.48246i −0.0199047 0.999802i \(-0.506336\pi\)
0.875806 0.482663i \(-0.160330\pi\)
\(632\) −5.50000 9.52628i −0.218778 0.378935i
\(633\) 0 0
\(634\) 30.0000 1.19145
\(635\) 16.0000 0.634941
\(636\) 0 0
\(637\) −9.00000 + 15.5885i −0.356593 + 0.617637i
\(638\) 20.0000 0.791808
\(639\) 0 0
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 12.0000 + 20.7846i 0.473972 + 0.820943i 0.999556 0.0297987i \(-0.00948663\pi\)
−0.525584 + 0.850741i \(0.676153\pi\)
\(642\) 0 0
\(643\) −20.5000 35.5070i −0.808441 1.40026i −0.913943 0.405842i \(-0.866978\pi\)
0.105502 0.994419i \(-0.466355\pi\)
\(644\) 3.00000 + 5.19615i 0.118217 + 0.204757i
\(645\) 0 0
\(646\) −14.0000 + 10.3923i −0.550823 + 0.408880i
\(647\) −46.0000 −1.80845 −0.904223 0.427060i \(-0.859549\pi\)
−0.904223 + 0.427060i \(0.859549\pi\)
\(648\) 0 0
\(649\) 2.00000 + 3.46410i 0.0785069 + 0.135978i
\(650\) −1.50000 + 2.59808i −0.0588348 + 0.101905i
\(651\) 0 0
\(652\) 8.50000 14.7224i 0.332886 0.576575i
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 0 0
\(655\) −3.00000 + 5.19615i −0.117220 + 0.203030i
\(656\) 1.00000 1.73205i 0.0390434 0.0676252i
\(657\) 0 0
\(658\) 0 0
\(659\) 9.00000 15.5885i 0.350590 0.607240i −0.635763 0.771885i \(-0.719314\pi\)
0.986353 + 0.164644i \(0.0526477\pi\)
\(660\) 0 0
\(661\) −23.0000 + 39.8372i −0.894596 + 1.54949i −0.0602929 + 0.998181i \(0.519203\pi\)
−0.834303 + 0.551306i \(0.814130\pi\)
\(662\) 2.50000 + 4.33013i 0.0971653 + 0.168295i
\(663\) 0 0
\(664\) 2.00000 0.0776151
\(665\) 0.500000 + 4.33013i 0.0193892 + 0.167915i
\(666\) 0 0
\(667\) −30.0000 51.9615i −1.16160 2.01196i
\(668\) 7.00000 + 12.1244i 0.270838 + 0.469105i
\(669\) 0 0
\(670\) −2.50000 4.33013i −0.0965834 0.167287i
\(671\) 5.00000 8.66025i 0.193023 0.334325i
\(672\) 0 0
\(673\) −23.0000 −0.886585 −0.443292 0.896377i \(-0.646190\pi\)
−0.443292 + 0.896377i \(0.646190\pi\)
\(674\) 11.5000 19.9186i 0.442963 0.767235i
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) −48.0000 −1.84479 −0.922395 0.386248i \(-0.873771\pi\)
−0.922395 + 0.386248i \(0.873771\pi\)
\(678\) 0 0
\(679\) −1.00000 1.73205i −0.0383765 0.0664700i
\(680\) −2.00000 + 3.46410i −0.0766965 + 0.132842i
\(681\) 0 0
\(682\) −1.00000 1.73205i −0.0382920 0.0663237i
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 2.00000 0.0764161
\(686\) 6.50000 + 11.2583i 0.248171 + 0.429845i
\(687\) 0 0
\(688\) 2.50000 4.33013i 0.0953116 0.165085i
\(689\) 18.0000 + 31.1769i 0.685745 + 1.18775i
\(690\) 0 0
\(691\) 4.00000 0.152167 0.0760836 0.997101i \(-0.475758\pi\)
0.0760836 + 0.997101i \(0.475758\pi\)
\(692\) 26.0000 0.988372
\(693\) 0 0
\(694\) 0 0
\(695\) −9.00000 −0.341389
\(696\) 0 0
\(697\) −4.00000 + 6.92820i −0.151511 + 0.262424i
\(698\) 8.50000 + 14.7224i 0.321730 + 0.557252i
\(699\) 0 0
\(700\) 0.500000 + 0.866025i 0.0188982 + 0.0327327i
\(701\) 14.0000 + 24.2487i 0.528773 + 0.915861i 0.999437 + 0.0335489i \(0.0106809\pi\)
−0.470664 + 0.882312i \(0.655986\pi\)
\(702\) 0 0
\(703\) −20.0000 8.66025i −0.754314 0.326628i
\(704\) −2.00000 −0.0753778
\(705\) 0 0
\(706\) 3.00000 + 5.19615i 0.112906 + 0.195560i
\(707\) −3.00000 + 5.19615i −0.112827 + 0.195421i
\(708\) 0 0
\(709\) −9.50000 + 16.4545i −0.356780 + 0.617961i −0.987421 0.158114i \(-0.949459\pi\)
0.630641 + 0.776075i \(0.282792\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −3.00000 + 5.19615i −0.112351 + 0.194597i
\(714\) 0 0
\(715\) 6.00000 0.224387
\(716\) −5.00000 + 8.66025i −0.186859 + 0.323649i
\(717\) 0 0
\(718\) 1.00000 1.73205i 0.0373197 0.0646396i
\(719\) 13.0000 + 22.5167i 0.484818 + 0.839730i 0.999848 0.0174426i \(-0.00555244\pi\)
−0.515030 + 0.857172i \(0.672219\pi\)
\(720\) 0 0
\(721\) −19.0000 −0.707597
\(722\) −5.50000 + 18.1865i −0.204689 + 0.676833i
\(723\) 0 0
\(724\) 3.00000 + 5.19615i 0.111494 + 0.193113i
\(725\) −5.00000 8.66025i −0.185695 0.321634i
\(726\) 0 0
\(727\) 22.5000 + 38.9711i 0.834479 + 1.44536i 0.894454 + 0.447160i \(0.147564\pi\)
−0.0599753 + 0.998200i \(0.519102\pi\)
\(728\) 1.50000 2.59808i 0.0555937 0.0962911i
\(729\) 0 0
\(730\) −11.0000 −0.407128
\(731\) −10.0000 + 17.3205i −0.369863 + 0.640622i
\(732\) 0 0
\(733\) −34.0000 −1.25582 −0.627909 0.778287i \(-0.716089\pi\)
−0.627909 + 0.778287i \(0.716089\pi\)
\(734\) 7.00000 0.258375
\(735\) 0 0
\(736\) 3.00000 + 5.19615i 0.110581 + 0.191533i
\(737\) −5.00000 + 8.66025i −0.184177 + 0.319005i
\(738\) 0 0
\(739\) −0.500000 0.866025i −0.0183928 0.0318573i 0.856683 0.515844i \(-0.172522\pi\)
−0.875075 + 0.483987i \(0.839188\pi\)
\(740\) −5.00000 −0.183804
\(741\) 0 0
\(742\) 12.0000 0.440534
\(743\) 3.00000 + 5.19615i 0.110059 + 0.190628i 0.915794 0.401648i \(-0.131563\pi\)
−0.805735 + 0.592277i \(0.798229\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) −11.0000 19.0526i −0.402739 0.697564i
\(747\) 0 0
\(748\) 8.00000 0.292509
\(749\) −4.00000 −0.146157
\(750\) 0 0
\(751\) 23.5000 40.7032i 0.857527 1.48528i −0.0167534 0.999860i \(-0.505333\pi\)
0.874281 0.485421i \(-0.161334\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −15.0000 + 25.9808i −0.546268 + 0.946164i
\(755\) 0 0
\(756\) 0 0
\(757\) 3.50000 + 6.06218i 0.127210 + 0.220334i 0.922595 0.385771i \(-0.126065\pi\)
−0.795385 + 0.606105i \(0.792731\pi\)
\(758\) −5.50000 9.52628i −0.199769 0.346010i
\(759\) 0 0
\(760\) 0.500000 + 4.33013i 0.0181369 + 0.157070i
\(761\) −10.0000 −0.362500 −0.181250 0.983437i \(-0.558014\pi\)
−0.181250 + 0.983437i \(0.558014\pi\)
\(762\) 0 0
\(763\) −9.00000 15.5885i −0.325822 0.564340i
\(764\) 8.00000 13.8564i 0.289430 0.501307i
\(765\) 0 0
\(766\) 18.0000 31.1769i 0.650366 1.12647i
\(767\) −6.00000 −0.216647
\(768\) 0 0
\(769\) 16.5000 28.5788i 0.595005 1.03058i −0.398541 0.917151i \(-0.630483\pi\)
0.993546 0.113429i \(-0.0361834\pi\)
\(770\) 1.00000 1.73205i 0.0360375 0.0624188i
\(771\) 0 0
\(772\) 25.0000 0.899770
\(773\) −3.00000 + 5.19615i −0.107903 + 0.186893i −0.914920 0.403634i \(-0.867747\pi\)
0.807018 + 0.590527i \(0.201080\pi\)
\(774\) 0 0
\(775\) −0.500000 + 0.866025i −0.0179605 + 0.0311086i
\(776\) −1.00000 1.73205i −0.0358979 0.0621770i
\(777\) 0 0
\(778\) −10.0000 −0.358517
\(779\) 1.00000 + 8.66025i 0.0358287 + 0.310286i
\(780\) 0 0
\(781\) 0 0
\(782\) −12.0000 20.7846i −0.429119 0.743256i
\(783\) 0 0
\(784\) 3.00000 + 5.19615i 0.107143 + 0.185577i
\(785\) 6.50000 11.2583i 0.231995 0.401827i
\(786\) 0 0
\(787\) −23.0000 −0.819861 −0.409931 0.912117i \(-0.634447\pi\)
−0.409931 + 0.912117i \(0.634447\pi\)
\(788\) −9.00000 + 15.5885i −0.320612 + 0.555316i
\(789\) 0 0
\(790\) 11.0000 0.391362
\(791\) 14.0000 0.497783
\(792\) 0