Properties

Label 189.2.h.a.37.1
Level $189$
Weight $2$
Character 189.37
Analytic conductor $1.509$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 189.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.50917259820\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 189.37
Dual form 189.2.h.a.46.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +3.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 + 1.73205i) q^{7} +3.00000 q^{8} +(0.500000 + 0.866025i) q^{10} +(2.50000 - 4.33013i) q^{11} +(2.50000 - 4.33013i) q^{13} +(-2.00000 - 1.73205i) q^{14} -1.00000 q^{16} +(1.50000 + 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{19} +(0.500000 + 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +(1.50000 + 2.59808i) q^{23} +(2.00000 - 3.46410i) q^{25} +(-2.50000 + 4.33013i) q^{26} +(-2.00000 - 1.73205i) q^{28} +(-0.500000 - 0.866025i) q^{29} -5.00000 q^{32} +(-1.50000 - 2.59808i) q^{34} +(0.500000 - 2.59808i) q^{35} +(-1.50000 + 2.59808i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-2.50000 + 4.33013i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-2.50000 + 4.33013i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(1.00000 + 6.92820i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-2.50000 + 4.33013i) q^{52} +(-4.50000 - 7.79423i) q^{53} -5.00000 q^{55} +(6.00000 + 5.19615i) q^{56} +(0.500000 + 0.866025i) q^{58} -14.0000 q^{61} +7.00000 q^{64} -5.00000 q^{65} +4.00000 q^{67} +(-1.50000 - 2.59808i) q^{68} +(-0.500000 + 2.59808i) q^{70} +12.0000 q^{71} +(-1.50000 - 2.59808i) q^{73} +(1.50000 - 2.59808i) q^{74} +(0.500000 - 0.866025i) q^{76} +(12.5000 - 4.33013i) q^{77} +8.00000 q^{79} +(0.500000 + 0.866025i) q^{80} +(2.50000 - 4.33013i) q^{82} +(-4.50000 - 7.79423i) q^{83} +(1.50000 - 2.59808i) q^{85} +(-0.500000 - 0.866025i) q^{86} +(7.50000 - 12.9904i) q^{88} +(-6.50000 + 11.2583i) q^{89} +(12.5000 - 4.33013i) q^{91} +(-1.50000 - 2.59808i) q^{92} +1.00000 q^{95} +(4.50000 + 7.79423i) q^{97} +(-1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{2} - 2q^{4} - q^{5} + 4q^{7} + 6q^{8} + O(q^{10}) \) \( 2q - 2q^{2} - 2q^{4} - q^{5} + 4q^{7} + 6q^{8} + q^{10} + 5q^{11} + 5q^{13} - 4q^{14} - 2q^{16} + 3q^{17} - q^{19} + q^{20} - 5q^{22} + 3q^{23} + 4q^{25} - 5q^{26} - 4q^{28} - q^{29} - 10q^{32} - 3q^{34} + q^{35} - 3q^{37} + q^{38} - 3q^{40} - 5q^{41} + q^{43} - 5q^{44} - 3q^{46} + 2q^{49} - 4q^{50} - 5q^{52} - 9q^{53} - 10q^{55} + 12q^{56} + q^{58} - 28q^{61} + 14q^{64} - 10q^{65} + 8q^{67} - 3q^{68} - q^{70} + 24q^{71} - 3q^{73} + 3q^{74} + q^{76} + 25q^{77} + 16q^{79} + q^{80} + 5q^{82} - 9q^{83} + 3q^{85} - q^{86} + 15q^{88} - 13q^{89} + 25q^{91} - 3q^{92} + 2q^{95} + 9q^{97} - 2q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −0.500000 0.866025i −0.223607 0.387298i 0.732294 0.680989i \(-0.238450\pi\)
−0.955901 + 0.293691i \(0.905116\pi\)
\(6\) 0 0
\(7\) 2.00000 + 1.73205i 0.755929 + 0.654654i
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) 0.500000 + 0.866025i 0.158114 + 0.273861i
\(11\) 2.50000 4.33013i 0.753778 1.30558i −0.192201 0.981356i \(-0.561563\pi\)
0.945979 0.324227i \(-0.105104\pi\)
\(12\) 0 0
\(13\) 2.50000 4.33013i 0.693375 1.20096i −0.277350 0.960769i \(-0.589456\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) −2.00000 1.73205i −0.534522 0.462910i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 1.50000 + 2.59808i 0.363803 + 0.630126i 0.988583 0.150675i \(-0.0481447\pi\)
−0.624780 + 0.780801i \(0.714811\pi\)
\(18\) 0 0
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 0.500000 + 0.866025i 0.111803 + 0.193649i
\(21\) 0 0
\(22\) −2.50000 + 4.33013i −0.533002 + 0.923186i
\(23\) 1.50000 + 2.59808i 0.312772 + 0.541736i 0.978961 0.204046i \(-0.0654092\pi\)
−0.666190 + 0.745782i \(0.732076\pi\)
\(24\) 0 0
\(25\) 2.00000 3.46410i 0.400000 0.692820i
\(26\) −2.50000 + 4.33013i −0.490290 + 0.849208i
\(27\) 0 0
\(28\) −2.00000 1.73205i −0.377964 0.327327i
\(29\) −0.500000 0.866025i −0.0928477 0.160817i 0.815861 0.578249i \(-0.196264\pi\)
−0.908708 + 0.417432i \(0.862930\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) −1.50000 2.59808i −0.257248 0.445566i
\(35\) 0.500000 2.59808i 0.0845154 0.439155i
\(36\) 0 0
\(37\) −1.50000 + 2.59808i −0.246598 + 0.427121i −0.962580 0.270998i \(-0.912646\pi\)
0.715981 + 0.698119i \(0.245980\pi\)
\(38\) 0.500000 0.866025i 0.0811107 0.140488i
\(39\) 0 0
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) −2.50000 + 4.33013i −0.390434 + 0.676252i −0.992507 0.122189i \(-0.961009\pi\)
0.602072 + 0.798441i \(0.294342\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) −2.50000 + 4.33013i −0.376889 + 0.652791i
\(45\) 0 0
\(46\) −1.50000 2.59808i −0.221163 0.383065i
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) 1.00000 + 6.92820i 0.142857 + 0.989743i
\(50\) −2.00000 + 3.46410i −0.282843 + 0.489898i
\(51\) 0 0
\(52\) −2.50000 + 4.33013i −0.346688 + 0.600481i
\(53\) −4.50000 7.79423i −0.618123 1.07062i −0.989828 0.142269i \(-0.954560\pi\)
0.371706 0.928351i \(-0.378773\pi\)
\(54\) 0 0
\(55\) −5.00000 −0.674200
\(56\) 6.00000 + 5.19615i 0.801784 + 0.694365i
\(57\) 0 0
\(58\) 0.500000 + 0.866025i 0.0656532 + 0.113715i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) −5.00000 −0.620174
\(66\) 0 0
\(67\) 4.00000 0.488678 0.244339 0.969690i \(-0.421429\pi\)
0.244339 + 0.969690i \(0.421429\pi\)
\(68\) −1.50000 2.59808i −0.181902 0.315063i
\(69\) 0 0
\(70\) −0.500000 + 2.59808i −0.0597614 + 0.310530i
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 0 0
\(73\) −1.50000 2.59808i −0.175562 0.304082i 0.764794 0.644275i \(-0.222841\pi\)
−0.940356 + 0.340193i \(0.889507\pi\)
\(74\) 1.50000 2.59808i 0.174371 0.302020i
\(75\) 0 0
\(76\) 0.500000 0.866025i 0.0573539 0.0993399i
\(77\) 12.5000 4.33013i 1.42451 0.493464i
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0.500000 + 0.866025i 0.0559017 + 0.0968246i
\(81\) 0 0
\(82\) 2.50000 4.33013i 0.276079 0.478183i
\(83\) −4.50000 7.79423i −0.493939 0.855528i 0.506036 0.862512i \(-0.331110\pi\)
−0.999976 + 0.00698436i \(0.997777\pi\)
\(84\) 0 0
\(85\) 1.50000 2.59808i 0.162698 0.281801i
\(86\) −0.500000 0.866025i −0.0539164 0.0933859i
\(87\) 0 0
\(88\) 7.50000 12.9904i 0.799503 1.38478i
\(89\) −6.50000 + 11.2583i −0.688999 + 1.19338i 0.283164 + 0.959072i \(0.408616\pi\)
−0.972162 + 0.234309i \(0.924717\pi\)
\(90\) 0 0
\(91\) 12.5000 4.33013i 1.31036 0.453921i
\(92\) −1.50000 2.59808i −0.156386 0.270868i
\(93\) 0 0
\(94\) 0 0
\(95\) 1.00000 0.102598
\(96\) 0 0
\(97\) 4.50000 + 7.79423i 0.456906 + 0.791384i 0.998796 0.0490655i \(-0.0156243\pi\)
−0.541890 + 0.840450i \(0.682291\pi\)
\(98\) −1.00000 6.92820i −0.101015 0.699854i
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) −8.50000 + 14.7224i −0.845782 + 1.46494i 0.0391591 + 0.999233i \(0.487532\pi\)
−0.884941 + 0.465704i \(0.845801\pi\)
\(102\) 0 0
\(103\) 0.500000 + 0.866025i 0.0492665 + 0.0853320i 0.889607 0.456727i \(-0.150978\pi\)
−0.840341 + 0.542059i \(0.817645\pi\)
\(104\) 7.50000 12.9904i 0.735436 1.27381i
\(105\) 0 0
\(106\) 4.50000 + 7.79423i 0.437079 + 0.757042i
\(107\) 8.50000 14.7224i 0.821726 1.42327i −0.0826699 0.996577i \(-0.526345\pi\)
0.904396 0.426694i \(-0.140322\pi\)
\(108\) 0 0
\(109\) 4.50000 + 7.79423i 0.431022 + 0.746552i 0.996962 0.0778949i \(-0.0248199\pi\)
−0.565940 + 0.824447i \(0.691487\pi\)
\(110\) 5.00000 0.476731
\(111\) 0 0
\(112\) −2.00000 1.73205i −0.188982 0.163663i
\(113\) −0.500000 + 0.866025i −0.0470360 + 0.0814688i −0.888585 0.458712i \(-0.848311\pi\)
0.841549 + 0.540181i \(0.181644\pi\)
\(114\) 0 0
\(115\) 1.50000 2.59808i 0.139876 0.242272i
\(116\) 0.500000 + 0.866025i 0.0464238 + 0.0804084i
\(117\) 0 0
\(118\) 0 0
\(119\) −1.50000 + 7.79423i −0.137505 + 0.714496i
\(120\) 0 0
\(121\) −7.00000 12.1244i −0.636364 1.10221i
\(122\) 14.0000 1.26750
\(123\) 0 0
\(124\) 0 0
\(125\) −9.00000 −0.804984
\(126\) 0 0
\(127\) −12.0000 −1.06483 −0.532414 0.846484i \(-0.678715\pi\)
−0.532414 + 0.846484i \(0.678715\pi\)
\(128\) 3.00000 0.265165
\(129\) 0 0
\(130\) 5.00000 0.438529
\(131\) −0.500000 0.866025i −0.0436852 0.0756650i 0.843356 0.537355i \(-0.180577\pi\)
−0.887041 + 0.461690i \(0.847243\pi\)
\(132\) 0 0
\(133\) −2.50000 + 0.866025i −0.216777 + 0.0750939i
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) 4.50000 + 7.79423i 0.385872 + 0.668350i
\(137\) −4.50000 + 7.79423i −0.384461 + 0.665906i −0.991694 0.128618i \(-0.958946\pi\)
0.607233 + 0.794524i \(0.292279\pi\)
\(138\) 0 0
\(139\) −4.50000 + 7.79423i −0.381685 + 0.661098i −0.991303 0.131597i \(-0.957989\pi\)
0.609618 + 0.792695i \(0.291323\pi\)
\(140\) −0.500000 + 2.59808i −0.0422577 + 0.219578i
\(141\) 0 0
\(142\) −12.0000 −1.00702
\(143\) −12.5000 21.6506i −1.04530 1.81052i
\(144\) 0 0
\(145\) −0.500000 + 0.866025i −0.0415227 + 0.0719195i
\(146\) 1.50000 + 2.59808i 0.124141 + 0.215018i
\(147\) 0 0
\(148\) 1.50000 2.59808i 0.123299 0.213561i
\(149\) 1.50000 + 2.59808i 0.122885 + 0.212843i 0.920904 0.389789i \(-0.127452\pi\)
−0.798019 + 0.602632i \(0.794119\pi\)
\(150\) 0 0
\(151\) −2.50000 + 4.33013i −0.203447 + 0.352381i −0.949637 0.313353i \(-0.898548\pi\)
0.746190 + 0.665733i \(0.231881\pi\)
\(152\) −1.50000 + 2.59808i −0.121666 + 0.210732i
\(153\) 0 0
\(154\) −12.5000 + 4.33013i −1.00728 + 0.348932i
\(155\) 0 0
\(156\) 0 0
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) −8.00000 −0.636446
\(159\) 0 0
\(160\) 2.50000 + 4.33013i 0.197642 + 0.342327i
\(161\) −1.50000 + 7.79423i −0.118217 + 0.614271i
\(162\) 0 0
\(163\) 5.50000 9.52628i 0.430793 0.746156i −0.566149 0.824303i \(-0.691567\pi\)
0.996942 + 0.0781474i \(0.0249005\pi\)
\(164\) 2.50000 4.33013i 0.195217 0.338126i
\(165\) 0 0
\(166\) 4.50000 + 7.79423i 0.349268 + 0.604949i
\(167\) −9.50000 + 16.4545i −0.735132 + 1.27329i 0.219533 + 0.975605i \(0.429547\pi\)
−0.954665 + 0.297681i \(0.903787\pi\)
\(168\) 0 0
\(169\) −6.00000 10.3923i −0.461538 0.799408i
\(170\) −1.50000 + 2.59808i −0.115045 + 0.199263i
\(171\) 0 0
\(172\) −0.500000 0.866025i −0.0381246 0.0660338i
\(173\) 14.0000 1.06440 0.532200 0.846619i \(-0.321365\pi\)
0.532200 + 0.846619i \(0.321365\pi\)
\(174\) 0 0
\(175\) 10.0000 3.46410i 0.755929 0.261861i
\(176\) −2.50000 + 4.33013i −0.188445 + 0.326396i
\(177\) 0 0
\(178\) 6.50000 11.2583i 0.487196 0.843848i
\(179\) 9.50000 + 16.4545i 0.710063 + 1.22987i 0.964833 + 0.262864i \(0.0846670\pi\)
−0.254770 + 0.967002i \(0.582000\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) −12.5000 + 4.33013i −0.926562 + 0.320970i
\(183\) 0 0
\(184\) 4.50000 + 7.79423i 0.331744 + 0.574598i
\(185\) 3.00000 0.220564
\(186\) 0 0
\(187\) 15.0000 1.09691
\(188\) 0 0
\(189\) 0 0
\(190\) −1.00000 −0.0725476
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 0 0
\(193\) −10.0000 −0.719816 −0.359908 0.932988i \(-0.617192\pi\)
−0.359908 + 0.932988i \(0.617192\pi\)
\(194\) −4.50000 7.79423i −0.323081 0.559593i
\(195\) 0 0
\(196\) −1.00000 6.92820i −0.0714286 0.494872i
\(197\) −2.00000 −0.142494 −0.0712470 0.997459i \(-0.522698\pi\)
−0.0712470 + 0.997459i \(0.522698\pi\)
\(198\) 0 0
\(199\) −1.50000 2.59808i −0.106332 0.184173i 0.807950 0.589252i \(-0.200577\pi\)
−0.914282 + 0.405079i \(0.867244\pi\)
\(200\) 6.00000 10.3923i 0.424264 0.734847i
\(201\) 0 0
\(202\) 8.50000 14.7224i 0.598058 1.03587i
\(203\) 0.500000 2.59808i 0.0350931 0.182349i
\(204\) 0 0
\(205\) 5.00000 0.349215
\(206\) −0.500000 0.866025i −0.0348367 0.0603388i
\(207\) 0 0
\(208\) −2.50000 + 4.33013i −0.173344 + 0.300240i
\(209\) 2.50000 + 4.33013i 0.172929 + 0.299521i
\(210\) 0 0
\(211\) −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i \(-0.981011\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 4.50000 + 7.79423i 0.309061 + 0.535310i
\(213\) 0 0
\(214\) −8.50000 + 14.7224i −0.581048 + 1.00640i
\(215\) 0.500000 0.866025i 0.0340997 0.0590624i
\(216\) 0 0
\(217\) 0 0
\(218\) −4.50000 7.79423i −0.304778 0.527892i
\(219\) 0 0
\(220\) 5.00000 0.337100
\(221\) 15.0000 1.00901
\(222\) 0 0
\(223\) −9.50000 16.4545i −0.636167 1.10187i −0.986267 0.165161i \(-0.947186\pi\)
0.350100 0.936713i \(-0.386148\pi\)
\(224\) −10.0000 8.66025i −0.668153 0.578638i
\(225\) 0 0
\(226\) 0.500000 0.866025i 0.0332595 0.0576072i
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) 0 0
\(229\) 0.500000 + 0.866025i 0.0330409 + 0.0572286i 0.882073 0.471113i \(-0.156147\pi\)
−0.849032 + 0.528341i \(0.822814\pi\)
\(230\) −1.50000 + 2.59808i −0.0989071 + 0.171312i
\(231\) 0 0
\(232\) −1.50000 2.59808i −0.0984798 0.170572i
\(233\) 1.50000 2.59808i 0.0982683 0.170206i −0.812700 0.582683i \(-0.802003\pi\)
0.910968 + 0.412477i \(0.135336\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 1.50000 7.79423i 0.0972306 0.505225i
\(239\) −7.50000 + 12.9904i −0.485135 + 0.840278i −0.999854 0.0170808i \(-0.994563\pi\)
0.514719 + 0.857359i \(0.327896\pi\)
\(240\) 0 0
\(241\) −5.50000 + 9.52628i −0.354286 + 0.613642i −0.986996 0.160748i \(-0.948609\pi\)
0.632709 + 0.774389i \(0.281943\pi\)
\(242\) 7.00000 + 12.1244i 0.449977 + 0.779383i
\(243\) 0 0
\(244\) 14.0000 0.896258
\(245\) 5.50000 4.33013i 0.351382 0.276642i
\(246\) 0 0
\(247\) 2.50000 + 4.33013i 0.159071 + 0.275519i
\(248\) 0 0
\(249\) 0 0
\(250\) 9.00000 0.569210
\(251\) 28.0000 1.76734 0.883672 0.468106i \(-0.155064\pi\)
0.883672 + 0.468106i \(0.155064\pi\)
\(252\) 0 0
\(253\) 15.0000 0.943042
\(254\) 12.0000 0.752947
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) −14.5000 25.1147i −0.904485 1.56661i −0.821607 0.570055i \(-0.806922\pi\)
−0.0828783 0.996560i \(-0.526411\pi\)
\(258\) 0 0
\(259\) −7.50000 + 2.59808i −0.466027 + 0.161437i
\(260\) 5.00000 0.310087
\(261\) 0 0
\(262\) 0.500000 + 0.866025i 0.0308901 + 0.0535032i
\(263\) 2.50000 4.33013i 0.154157 0.267007i −0.778595 0.627527i \(-0.784067\pi\)
0.932752 + 0.360520i \(0.117401\pi\)
\(264\) 0 0
\(265\) −4.50000 + 7.79423i −0.276433 + 0.478796i
\(266\) 2.50000 0.866025i 0.153285 0.0530994i
\(267\) 0 0
\(268\) −4.00000 −0.244339
\(269\) 1.50000 + 2.59808i 0.0914566 + 0.158408i 0.908124 0.418701i \(-0.137514\pi\)
−0.816668 + 0.577108i \(0.804181\pi\)
\(270\) 0 0
\(271\) −0.500000 + 0.866025i −0.0303728 + 0.0526073i −0.880812 0.473466i \(-0.843003\pi\)
0.850439 + 0.526073i \(0.176336\pi\)
\(272\) −1.50000 2.59808i −0.0909509 0.157532i
\(273\) 0 0
\(274\) 4.50000 7.79423i 0.271855 0.470867i
\(275\) −10.0000 17.3205i −0.603023 1.04447i
\(276\) 0 0
\(277\) −9.50000 + 16.4545i −0.570800 + 0.988654i 0.425684 + 0.904872i \(0.360033\pi\)
−0.996484 + 0.0837823i \(0.973300\pi\)
\(278\) 4.50000 7.79423i 0.269892 0.467467i
\(279\) 0 0
\(280\) 1.50000 7.79423i 0.0896421 0.465794i
\(281\) −14.5000 25.1147i −0.864997 1.49822i −0.867050 0.498222i \(-0.833987\pi\)
0.00205220 0.999998i \(-0.499347\pi\)
\(282\) 0 0
\(283\) 28.0000 1.66443 0.832214 0.554455i \(-0.187073\pi\)
0.832214 + 0.554455i \(0.187073\pi\)
\(284\) −12.0000 −0.712069
\(285\) 0 0
\(286\) 12.5000 + 21.6506i 0.739140 + 1.28023i
\(287\) −12.5000 + 4.33013i −0.737852 + 0.255599i
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) 0.500000 0.866025i 0.0293610 0.0508548i
\(291\) 0 0
\(292\) 1.50000 + 2.59808i 0.0877809 + 0.152041i
\(293\) −2.50000 + 4.33013i −0.146052 + 0.252969i −0.929765 0.368154i \(-0.879990\pi\)
0.783713 + 0.621123i \(0.213323\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −4.50000 + 7.79423i −0.261557 + 0.453030i
\(297\) 0 0
\(298\) −1.50000 2.59808i −0.0868927 0.150503i
\(299\) 15.0000 0.867472
\(300\) 0 0
\(301\) −0.500000 + 2.59808i −0.0288195 + 0.149751i
\(302\) 2.50000 4.33013i 0.143859 0.249171i
\(303\) 0 0
\(304\) 0.500000 0.866025i 0.0286770 0.0496700i
\(305\) 7.00000 + 12.1244i 0.400819 + 0.694239i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) −12.5000 + 4.33013i −0.712254 + 0.246732i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 14.0000 0.791327 0.395663 0.918396i \(-0.370515\pi\)
0.395663 + 0.918396i \(0.370515\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) 6.00000 0.336994 0.168497 0.985702i \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) 0 0
\(319\) −5.00000 −0.279946
\(320\) −3.50000 6.06218i −0.195656 0.338886i
\(321\) 0 0
\(322\) 1.50000 7.79423i 0.0835917 0.434355i
\(323\) −3.00000 −0.166924
\(324\) 0 0
\(325\) −10.0000 17.3205i −0.554700 0.960769i
\(326\) −5.50000 + 9.52628i −0.304617 + 0.527612i
\(327\) 0 0
\(328\) −7.50000 + 12.9904i −0.414118 + 0.717274i
\(329\) 0 0
\(330\) 0 0
\(331\) 8.00000 0.439720 0.219860 0.975531i \(-0.429440\pi\)
0.219860 + 0.975531i \(0.429440\pi\)
\(332\) 4.50000 + 7.79423i 0.246970 + 0.427764i
\(333\) 0 0
\(334\) 9.50000 16.4545i 0.519817 0.900349i
\(335\) −2.00000 3.46410i −0.109272 0.189264i
\(336\) 0 0
\(337\) 14.5000 25.1147i 0.789865 1.36809i −0.136184 0.990684i \(-0.543484\pi\)
0.926049 0.377403i \(-0.123183\pi\)
\(338\) 6.00000 + 10.3923i 0.326357 + 0.565267i
\(339\) 0 0
\(340\) −1.50000 + 2.59808i −0.0813489 + 0.140900i
\(341\) 0 0
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 1.50000 + 2.59808i 0.0808746 + 0.140079i
\(345\) 0 0
\(346\) −14.0000 −0.752645
\(347\) −4.00000 −0.214731 −0.107366 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) 0 0
\(349\) −9.50000 16.4545i −0.508523 0.880788i −0.999951 0.00987003i \(-0.996858\pi\)
0.491428 0.870918i \(-0.336475\pi\)
\(350\) −10.0000 + 3.46410i −0.534522 + 0.185164i
\(351\) 0 0
\(352\) −12.5000 + 21.6506i −0.666252 + 1.15398i
\(353\) 5.50000 9.52628i 0.292735 0.507033i −0.681720 0.731613i \(-0.738768\pi\)
0.974456 + 0.224580i \(0.0721011\pi\)
\(354\) 0 0
\(355\) −6.00000 10.3923i −0.318447 0.551566i
\(356\) 6.50000 11.2583i 0.344499 0.596690i
\(357\) 0 0
\(358\) −9.50000 16.4545i −0.502091 0.869646i
\(359\) −5.50000 + 9.52628i −0.290279 + 0.502778i −0.973876 0.227082i \(-0.927081\pi\)
0.683597 + 0.729860i \(0.260415\pi\)
\(360\) 0 0
\(361\) 9.00000 + 15.5885i 0.473684 + 0.820445i
\(362\) 14.0000 0.735824
\(363\) 0 0
\(364\) −12.5000 + 4.33013i −0.655178 + 0.226960i
\(365\) −1.50000 + 2.59808i −0.0785136 + 0.135990i
\(366\) 0 0
\(367\) 1.50000 2.59808i 0.0782994 0.135618i −0.824217 0.566274i \(-0.808384\pi\)
0.902516 + 0.430656i \(0.141718\pi\)
\(368\) −1.50000 2.59808i −0.0781929 0.135434i
\(369\) 0 0
\(370\) −3.00000 −0.155963
\(371\) 4.50000 23.3827i 0.233628 1.21397i
\(372\) 0 0
\(373\) 12.5000 + 21.6506i 0.647225 + 1.12103i 0.983783 + 0.179364i \(0.0574041\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) −15.0000 −0.775632
\(375\) 0 0
\(376\) 0 0
\(377\) −5.00000 −0.257513
\(378\) 0 0
\(379\) −12.0000 −0.616399 −0.308199 0.951322i \(-0.599726\pi\)
−0.308199 + 0.951322i \(0.599726\pi\)
\(380\) −1.00000 −0.0512989
\(381\) 0 0
\(382\) 8.00000 0.409316
\(383\) 13.5000 + 23.3827i 0.689818 + 1.19480i 0.971897 + 0.235408i \(0.0756427\pi\)
−0.282079 + 0.959391i \(0.591024\pi\)
\(384\) 0 0
\(385\) −10.0000 8.66025i −0.509647 0.441367i
\(386\) 10.0000 0.508987
\(387\) 0 0
\(388\) −4.50000 7.79423i −0.228453 0.395692i
\(389\) −4.50000 + 7.79423i −0.228159 + 0.395183i −0.957263 0.289220i \(-0.906604\pi\)
0.729103 + 0.684403i \(0.239937\pi\)
\(390\) 0 0
\(391\) −4.50000 + 7.79423i −0.227575 + 0.394171i
\(392\) 3.00000 + 20.7846i 0.151523 + 1.04978i
\(393\) 0 0
\(394\) 2.00000 0.100759
\(395\) −4.00000 6.92820i −0.201262 0.348596i
\(396\) 0 0
\(397\) −7.50000 + 12.9904i −0.376414 + 0.651969i −0.990538 0.137241i \(-0.956176\pi\)
0.614123 + 0.789210i \(0.289510\pi\)
\(398\) 1.50000 + 2.59808i 0.0751882 + 0.130230i
\(399\) 0 0
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) 1.50000 + 2.59808i 0.0749064 + 0.129742i 0.901046 0.433724i \(-0.142801\pi\)
−0.826139 + 0.563466i \(0.809468\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 8.50000 14.7224i 0.422891 0.732468i
\(405\) 0 0
\(406\) −0.500000 + 2.59808i −0.0248146 + 0.128940i
\(407\) 7.50000 + 12.9904i 0.371761 + 0.643909i
\(408\) 0 0
\(409\) 14.0000 0.692255 0.346128 0.938187i \(-0.387496\pi\)
0.346128 + 0.938187i \(0.387496\pi\)
\(410\) −5.00000 −0.246932
\(411\) 0 0
\(412\) −0.500000 0.866025i −0.0246332 0.0426660i
\(413\) 0 0
\(414\) 0 0
\(415\) −4.50000 + 7.79423i −0.220896 + 0.382604i
\(416\) −12.5000 + 21.6506i −0.612863 + 1.06151i
\(417\) 0 0
\(418\) −2.50000 4.33013i −0.122279 0.211793i
\(419\) 4.50000 7.79423i 0.219839 0.380773i −0.734919 0.678155i \(-0.762780\pi\)
0.954759 + 0.297382i \(0.0961133\pi\)
\(420\) 0 0
\(421\) 0.500000 + 0.866025i 0.0243685 + 0.0422075i 0.877952 0.478748i \(-0.158909\pi\)
−0.853584 + 0.520955i \(0.825576\pi\)
\(422\) 6.50000 11.2583i 0.316415 0.548047i
\(423\) 0 0
\(424\) −13.5000 23.3827i −0.655618 1.13556i
\(425\) 12.0000 0.582086
\(426\) 0 0
\(427\) −28.0000 24.2487i −1.35501 1.17348i
\(428\) −8.50000 + 14.7224i −0.410863 + 0.711636i
\(429\) 0 0
\(430\) −0.500000 + 0.866025i −0.0241121 + 0.0417635i
\(431\) −4.50000 7.79423i −0.216757 0.375435i 0.737057 0.675830i \(-0.236215\pi\)
−0.953815 + 0.300395i \(0.902881\pi\)
\(432\) 0 0
\(433\) −14.0000 −0.672797 −0.336399 0.941720i \(-0.609209\pi\)
−0.336399 + 0.941720i \(0.609209\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −4.50000 7.79423i −0.215511 0.373276i
\(437\) −3.00000 −0.143509
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) −15.0000 −0.715097
\(441\) 0 0
\(442\) −15.0000 −0.713477
\(443\) −36.0000 −1.71041 −0.855206 0.518289i \(-0.826569\pi\)
−0.855206 + 0.518289i \(0.826569\pi\)
\(444\) 0 0
\(445\) 13.0000 0.616259
\(446\) 9.50000 + 16.4545i 0.449838 + 0.779142i
\(447\) 0 0
\(448\) 14.0000 + 12.1244i 0.661438 + 0.572822i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 0 0
\(451\) 12.5000 + 21.6506i 0.588602 + 1.01949i
\(452\) 0.500000 0.866025i 0.0235180 0.0407344i
\(453\) 0 0
\(454\) 1.50000 2.59808i 0.0703985 0.121934i
\(455\) −10.0000 8.66025i −0.468807 0.405999i
\(456\) 0 0
\(457\) 22.0000 1.02912 0.514558 0.857455i \(-0.327956\pi\)
0.514558 + 0.857455i \(0.327956\pi\)
\(458\) −0.500000 0.866025i −0.0233635 0.0404667i
\(459\) 0 0
\(460\) −1.50000 + 2.59808i −0.0699379 + 0.121136i
\(461\) 9.50000 + 16.4545i 0.442459 + 0.766362i 0.997871 0.0652135i \(-0.0207728\pi\)
−0.555412 + 0.831575i \(0.687440\pi\)
\(462\) 0 0
\(463\) −6.50000 + 11.2583i −0.302081 + 0.523219i −0.976607 0.215032i \(-0.931015\pi\)
0.674526 + 0.738251i \(0.264348\pi\)
\(464\) 0.500000 + 0.866025i 0.0232119 + 0.0402042i
\(465\) 0 0
\(466\) −1.50000 + 2.59808i −0.0694862 + 0.120354i
\(467\) −13.5000 + 23.3827i −0.624705 + 1.08202i 0.363892 + 0.931441i \(0.381448\pi\)
−0.988598 + 0.150581i \(0.951886\pi\)
\(468\) 0 0
\(469\) 8.00000 + 6.92820i 0.369406 + 0.319915i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 5.00000 0.229900
\(474\) 0 0
\(475\) 2.00000 + 3.46410i 0.0917663 + 0.158944i
\(476\) 1.50000 7.79423i 0.0687524 0.357248i
\(477\) 0 0
\(478\) 7.50000 12.9904i 0.343042 0.594166i
\(479\) 12.5000 21.6506i 0.571140 0.989243i −0.425310 0.905048i \(-0.639835\pi\)
0.996449 0.0841949i \(-0.0268318\pi\)
\(480\) 0 0
\(481\) 7.50000 + 12.9904i 0.341971 + 0.592310i
\(482\) 5.50000 9.52628i 0.250518 0.433910i
\(483\) 0 0
\(484\) 7.00000 + 12.1244i 0.318182 + 0.551107i
\(485\) 4.50000 7.79423i 0.204334 0.353918i
\(486\) 0 0
\(487\) −9.50000 16.4545i −0.430486 0.745624i 0.566429 0.824110i \(-0.308325\pi\)
−0.996915 + 0.0784867i \(0.974991\pi\)
\(488\) −42.0000 −1.90125
\(489\) 0 0
\(490\) −5.50000 + 4.33013i −0.248465 + 0.195615i
\(491\) 6.50000 11.2583i 0.293341 0.508081i −0.681257 0.732045i \(-0.738566\pi\)
0.974598 + 0.223963i \(0.0718996\pi\)
\(492\) 0 0
\(493\) 1.50000 2.59808i 0.0675566 0.117011i
\(494\) −2.50000 4.33013i −0.112480 0.194822i
\(495\) 0 0
\(496\) 0 0
\(497\) 24.0000 + 20.7846i 1.07655 + 0.932317i
\(498\) 0 0
\(499\) −15.5000 26.8468i −0.693875 1.20183i −0.970558 0.240866i \(-0.922569\pi\)
0.276683 0.960961i \(-0.410765\pi\)
\(500\) 9.00000 0.402492
\(501\) 0 0
\(502\) −28.0000 −1.24970
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 17.0000 0.756490
\(506\) −15.0000 −0.666831
\(507\) 0 0
\(508\) 12.0000 0.532414
\(509\) −14.5000 25.1147i −0.642701 1.11319i −0.984827 0.173537i \(-0.944480\pi\)
0.342126 0.939654i \(-0.388853\pi\)
\(510\) 0 0
\(511\) 1.50000 7.79423i 0.0663561 0.344796i
\(512\) 11.0000 0.486136
\(513\) 0 0
\(514\) 14.5000 + 25.1147i 0.639568 + 1.10776i
\(515\) 0.500000 0.866025i 0.0220326 0.0381616i
\(516\) 0 0
\(517\) 0 0
\(518\) 7.50000 2.59808i 0.329531 0.114153i
\(519\) 0 0
\(520\) −15.0000 −0.657794
\(521\) 1.50000 + 2.59808i 0.0657162 + 0.113824i 0.897011 0.442007i \(-0.145733\pi\)
−0.831295 + 0.555831i \(0.812400\pi\)
\(522\) 0 0
\(523\) −0.500000 + 0.866025i −0.0218635 + 0.0378686i −0.876750 0.480946i \(-0.840293\pi\)
0.854887 + 0.518815i \(0.173627\pi\)
\(524\) 0.500000 + 0.866025i 0.0218426 + 0.0378325i
\(525\) 0 0
\(526\) −2.50000 + 4.33013i −0.109005 + 0.188803i
\(527\) 0 0
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 4.50000 7.79423i 0.195468 0.338560i
\(531\) 0 0
\(532\) 2.50000 0.866025i 0.108389 0.0375470i
\(533\) 12.5000 + 21.6506i 0.541435 + 0.937793i
\(534\) 0 0
\(535\) −17.0000 −0.734974
\(536\) 12.0000 0.518321
\(537\) 0 0
\(538\) −1.50000 2.59808i −0.0646696 0.112011i
\(539\) 32.5000 + 12.9904i 1.39987 + 0.559535i
\(540\) 0 0
\(541\) 12.5000 21.6506i 0.537417 0.930834i −0.461625 0.887075i \(-0.652733\pi\)
0.999042 0.0437584i \(-0.0139332\pi\)
\(542\) 0.500000 0.866025i 0.0214768 0.0371990i
\(543\) 0 0
\(544\) −7.50000 12.9904i −0.321560 0.556958i
\(545\) 4.50000 7.79423i 0.192759 0.333868i
\(546\) 0 0
\(547\) 14.5000 + 25.1147i 0.619975 + 1.07383i 0.989490 + 0.144604i \(0.0461907\pi\)
−0.369514 + 0.929225i \(0.620476\pi\)
\(548\) 4.50000 7.79423i 0.192230 0.332953i
\(549\) 0 0
\(550\) 10.0000 + 17.3205i 0.426401 + 0.738549i
\(551\) 1.00000 0.0426014
\(552\) 0 0
\(553\) 16.0000 + 13.8564i 0.680389 + 0.589234i
\(554\) 9.50000 16.4545i 0.403616 0.699084i
\(555\) 0 0
\(556\) 4.50000 7.79423i 0.190843 0.330549i
\(557\) −18.5000 32.0429i −0.783870 1.35770i −0.929672 0.368389i \(-0.879909\pi\)
0.145802 0.989314i \(-0.453424\pi\)
\(558\) 0 0
\(559\) 5.00000 0.211477
\(560\) −0.500000 + 2.59808i −0.0211289 + 0.109789i
\(561\) 0 0
\(562\) 14.5000 + 25.1147i 0.611646 + 1.05940i
\(563\) 28.0000 1.18006 0.590030 0.807382i \(-0.299116\pi\)
0.590030 + 0.807382i \(0.299116\pi\)
\(564\) 0 0
\(565\) 1.00000 0.0420703
\(566\) −28.0000 −1.17693
\(567\) 0 0
\(568\) 36.0000 1.51053
\(569\) 34.0000 1.42535 0.712677 0.701492i \(-0.247483\pi\)
0.712677 + 0.701492i \(0.247483\pi\)
\(570\) 0 0
\(571\) 32.0000 1.33916 0.669579 0.742741i \(-0.266474\pi\)
0.669579 + 0.742741i \(0.266474\pi\)
\(572\) 12.5000 + 21.6506i 0.522651 + 0.905259i
\(573\) 0 0
\(574\) 12.5000 4.33013i 0.521740 0.180736i
\(575\) 12.0000 0.500435
\(576\) 0 0
\(577\) −15.5000 26.8468i −0.645273 1.11765i −0.984238 0.176847i \(-0.943410\pi\)
0.338965 0.940799i \(-0.389923\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) 0 0
\(580\) 0.500000 0.866025i 0.0207614 0.0359597i
\(581\) 4.50000 23.3827i 0.186691 0.970077i
\(582\) 0 0
\(583\) −45.0000 −1.86371
\(584\) −4.50000 7.79423i −0.186211 0.322527i
\(585\) 0 0
\(586\) 2.50000 4.33013i 0.103274 0.178876i
\(587\) −18.5000 32.0429i −0.763577 1.32255i −0.940996 0.338418i \(-0.890108\pi\)
0.177419 0.984135i \(-0.443225\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.50000 2.59808i 0.0616496 0.106780i
\(593\) 7.50000 12.9904i 0.307988 0.533451i −0.669934 0.742421i \(-0.733678\pi\)
0.977922 + 0.208970i \(0.0670110\pi\)
\(594\) 0 0
\(595\) 7.50000 2.59808i 0.307470 0.106511i
\(596\) −1.50000 2.59808i −0.0614424 0.106421i
\(597\) 0 0
\(598\) −15.0000 −0.613396
\(599\) 24.0000 0.980613 0.490307 0.871550i \(-0.336885\pi\)
0.490307 + 0.871550i \(0.336885\pi\)
\(600\) 0 0
\(601\) 4.50000 + 7.79423i 0.183559 + 0.317933i 0.943090 0.332538i \(-0.107905\pi\)
−0.759531 + 0.650471i \(0.774572\pi\)
\(602\) 0.500000 2.59808i 0.0203785 0.105890i
\(603\) 0 0
\(604\) 2.50000 4.33013i 0.101724 0.176190i
\(605\) −7.00000 + 12.1244i −0.284590 + 0.492925i
\(606\) 0 0
\(607\) 0.500000 + 0.866025i 0.0202944 + 0.0351509i 0.875994 0.482322i \(-0.160206\pi\)
−0.855700 + 0.517472i \(0.826873\pi\)
\(608\) 2.50000 4.33013i 0.101388 0.175610i
\(609\) 0 0
\(610\) −7.00000 12.1244i −0.283422 0.490901i
\(611\) 0 0
\(612\) 0 0
\(613\) −9.50000 16.4545i −0.383701 0.664590i 0.607887 0.794024i \(-0.292017\pi\)
−0.991588 + 0.129433i \(0.958684\pi\)
\(614\) −28.0000 −1.12999
\(615\) 0 0
\(616\) 37.5000 12.9904i 1.51092 0.523397i
\(617\) 13.5000 23.3827i 0.543490 0.941351i −0.455211 0.890384i \(-0.650436\pi\)
0.998700 0.0509678i \(-0.0162306\pi\)
\(618\) 0 0
\(619\) −12.5000 + 21.6506i −0.502417 + 0.870212i 0.497579 + 0.867419i \(0.334223\pi\)
−0.999996 + 0.00279365i \(0.999111\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −32.5000 + 11.2583i −1.30209 + 0.451055i
\(624\) 0 0
\(625\) −5.50000 9.52628i −0.220000 0.381051i
\(626\) −14.0000 −0.559553
\(627\) 0 0
\(628\) 14.0000 0.558661
\(629\) −9.00000 −0.358854
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 24.0000 0.954669
\(633\) 0 0
\(634\) −6.00000 −0.238290
\(635\) 6.00000 + 10.3923i 0.238103 + 0.412406i
\(636\) 0 0
\(637\) 32.5000 + 12.9904i 1.28770 + 0.514698i
\(638\) 5.00000 0.197952
\(639\) 0 0
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) −4.50000 + 7.79423i −0.177739 + 0.307854i −0.941106 0.338112i \(-0.890212\pi\)
0.763367 + 0.645966i \(0.223545\pi\)
\(642\) 0 0
\(643\) 9.50000 16.4545i 0.374643 0.648901i −0.615630 0.788035i \(-0.711098\pi\)
0.990274 + 0.139134i \(0.0444318\pi\)
\(644\) 1.50000 7.79423i 0.0591083 0.307136i
\(645\) 0 0
\(646\) 3.00000 0.118033
\(647\) 15.5000 + 26.8468i 0.609368 + 1.05546i 0.991345 + 0.131284i \(0.0419101\pi\)
−0.381977 + 0.924172i \(0.624757\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 10.0000 + 17.3205i 0.392232 + 0.679366i
\(651\) 0 0
\(652\) −5.50000 + 9.52628i −0.215397 + 0.373078i
\(653\) 1.50000 + 2.59808i 0.0586995 + 0.101671i 0.893882 0.448303i \(-0.147971\pi\)
−0.835182 + 0.549973i \(0.814638\pi\)
\(654\) 0 0
\(655\) −0.500000 + 0.866025i −0.0195366 + 0.0338384i
\(656\) 2.50000 4.33013i 0.0976086 0.169063i
\(657\) 0 0
\(658\) 0 0
\(659\) 13.5000 + 23.3827i 0.525885 + 0.910860i 0.999545 + 0.0301523i \(0.00959924\pi\)
−0.473660 + 0.880708i \(0.657067\pi\)
\(660\) 0 0
\(661\) −14.0000 −0.544537 −0.272268 0.962221i \(-0.587774\pi\)
−0.272268 + 0.962221i \(0.587774\pi\)
\(662\) −8.00000 −0.310929
\(663\) 0 0
\(664\) −13.5000 23.3827i −0.523902 0.907424i
\(665\) 2.00000 + 1.73205i 0.0775567 + 0.0671660i
\(666\) 0 0
\(667\) 1.50000 2.59808i 0.0580802 0.100598i
\(668\) 9.50000 16.4545i 0.367566 0.636643i
\(669\) 0 0
\(670\) 2.00000 + 3.46410i 0.0772667 + 0.133830i
\(671\) −35.0000 + 60.6218i −1.35116 + 2.34028i
\(672\) 0 0
\(673\) 14.5000 + 25.1147i 0.558934 + 0.968102i 0.997586 + 0.0694449i \(0.0221228\pi\)
−0.438652 + 0.898657i \(0.644544\pi\)
\(674\) −14.5000 + 25.1147i −0.558519 + 0.967384i
\(675\) 0 0
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) −42.0000 −1.61419 −0.807096 0.590421i \(-0.798962\pi\)
−0.807096 + 0.590421i \(0.798962\pi\)
\(678\) 0 0
\(679\) −4.50000 + 23.3827i −0.172694 + 0.897345i
\(680\) 4.50000 7.79423i 0.172567 0.298895i
\(681\) 0 0
\(682\) 0 0
\(683\) −4.50000 7.79423i −0.172188 0.298238i 0.766997 0.641651i \(-0.221750\pi\)
−0.939184 + 0.343413i \(0.888417\pi\)
\(684\) 0 0
\(685\) 9.00000 0.343872
\(686\) 10.0000 15.5885i 0.381802 0.595170i
\(687\) 0 0
\(688\) −0.500000 0.866025i −0.0190623 0.0330169i
\(689\) −45.0000 −1.71436
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) −14.0000 −0.532200
\(693\) 0 0
\(694\) 4.00000 0.151838
\(695\) 9.00000 0.341389
\(696\) 0 0
\(697\) −15.0000 −0.568166
\(698\) 9.50000 + 16.4545i 0.359580 + 0.622811i
\(699\) 0 0
\(700\) −10.0000 + 3.46410i −0.377964 + 0.130931i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) −1.50000 2.59808i −0.0565736 0.0979883i
\(704\) 17.5000 30.3109i 0.659556 1.14238i
\(705\) 0 0
\(706\) −5.50000 + 9.52628i −0.206995 + 0.358526i
\(707\) −42.5000 + 14.7224i −1.59838 + 0.553694i
\(708\) 0 0
\(709\) −6.00000 −0.225335 −0.112667 0.993633i \(-0.535939\pi\)
−0.112667 + 0.993633i \(0.535939\pi\)
\(710\) 6.00000 + 10.3923i 0.225176 + 0.390016i
\(711\) 0 0
\(712\) −19.5000 + 33.7750i −0.730793 + 1.26577i
\(713\) 0 0
\(714\) 0 0
\(715\) −12.5000 + 21.6506i −0.467473 + 0.809688i
\(716\) −9.50000 16.4545i −0.355032 0.614933i
\(717\) 0 0
\(718\) 5.50000 9.52628i 0.205258 0.355518i
\(719\) −13.5000 + 23.3827i −0.503465 + 0.872027i 0.496527 + 0.868021i \(0.334608\pi\)
−0.999992 + 0.00400572i \(0.998725\pi\)
\(720\) 0 0
\(721\) −0.500000 + 2.59808i −0.0186210 + 0.0967574i
\(722\) −9.00000 15.5885i −0.334945 0.580142i
\(723\) 0 0
\(724\) 14.0000 0.520306
\(725\) −4.00000 −0.148556
\(726\) 0 0
\(727\) −23.5000 40.7032i −0.871567 1.50960i −0.860376 0.509661i \(-0.829771\pi\)
−0.0111912 0.999937i \(-0.503562\pi\)
\(728\) 37.5000 12.9904i 1.38984 0.481456i
\(729\) 0 0
\(730\) 1.50000 2.59808i 0.0555175 0.0961591i
\(731\) −1.50000 + 2.59808i −0.0554795 + 0.0960933i
\(732\) 0 0
\(733\) −13.5000 23.3827i −0.498634 0.863659i 0.501365 0.865236i \(-0.332831\pi\)
−0.999999 + 0.00157675i \(0.999498\pi\)
\(734\) −1.50000 + 2.59808i −0.0553660 + 0.0958967i
\(735\) 0 0
\(736\) −7.50000 12.9904i −0.276454 0.478832i
\(737\) 10.0000 17.3205i 0.368355 0.638009i
\(738\) 0 0
\(739\) 4.50000 + 7.79423i 0.165535 + 0.286715i 0.936845 0.349744i \(-0.113732\pi\)
−0.771310 + 0.636460i \(0.780398\pi\)
\(740\) −3.00000 −0.110282
\(741\) 0 0
\(742\) −4.50000 + 23.3827i −0.165200 + 0.858405i
\(743\) −7.50000 + 12.9904i −0.275148 + 0.476571i −0.970173 0.242415i \(-0.922060\pi\)
0.695024 + 0.718986i \(0.255394\pi\)
\(744\) 0 0
\(745\) 1.50000 2.59808i 0.0549557 0.0951861i
\(746\) −12.5000 21.6506i −0.457658 0.792686i
\(747\) 0 0
\(748\) −15.0000 −0.548454
\(749\) 42.5000 14.7224i 1.55292 0.537946i
\(750\) 0 0
\(751\) −15.5000 26.8468i −0.565603 0.979653i −0.996993 0.0774878i \(-0.975310\pi\)
0.431390 0.902165i \(-0.358023\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 5.00000 0.182089
\(755\) 5.00000 0.181969
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) 12.0000 0.435860
\(759\) 0 0
\(760\) 3.00000 0.108821
\(761\) 13.5000 + 23.3827i 0.489375 + 0.847622i 0.999925 0.0122260i \(-0.00389175\pi\)
−0.510551 + 0.859848i \(0.670558\pi\)
\(762\) 0 0
\(763\) −4.50000 + 23.3827i −0.162911 + 0.846510i
\(764\) 8.00000 0.289430
\(765\) 0 0
\(766\) −13.5000 23.3827i −0.487775 0.844851i
\(767\) 0 0
\(768\) 0 0
\(769\) −11.5000 + 19.9186i −0.414701 + 0.718283i −0.995397 0.0958377i \(-0.969447\pi\)
0.580696 + 0.814120i \(0.302780\pi\)
\(770\) 10.0000 + 8.66025i 0.360375 + 0.312094i
\(771\) 0 0
\(772\) 10.0000 0.359908
\(773\) 15.5000 + 26.8468i 0.557496 + 0.965612i 0.997705 + 0.0677162i \(0.0215712\pi\)
−0.440208 + 0.897896i \(0.645095\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 13.5000 + 23.3827i 0.484622 + 0.839390i
\(777\) 0 0
\(778\) 4.50000 7.79423i 0.161333 0.279437i
\(779\) −2.50000 4.33013i −0.0895718 0.155143i
\(780\) 0 0
\(781\) 30.0000 51.9615i 1.07348 1.85933i
\(782\) 4.50000 7.79423i 0.160920 0.278721i
\(783\) 0 0
\(784\) −1.00000 6.92820i −0.0357143 0.247436i
\(785\) 7.00000 + 12.1244i 0.249841 + 0.432737i
\(786\) 0 0
\(787\) 28.0000 0.998092 0.499046 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) 2.00000 0.0712470
\(789\) 0 0
\(790\) 4.00000 + 6.92820i 0.142314 + 0.246494i
\(791\) −2.50000 +