Properties

Label 2646.2.h.d.667.1
Level $2646$
Weight $2$
Character 2646.667
Analytic conductor $21.128$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2646.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(21.1284163748\)
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 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 667.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.667
Dual form 2646.2.h.d.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +1.00000 q^{8} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +3.00000 q^{5} +1.00000 q^{8} +(-1.50000 - 2.59808i) q^{10} +3.00000 q^{11} +(-0.500000 - 0.866025i) q^{13} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(-3.50000 + 6.06218i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(-1.50000 - 2.59808i) q^{22} +9.00000 q^{23} +4.00000 q^{25} +(-0.500000 + 0.866025i) q^{26} +(1.50000 - 2.59808i) q^{29} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{34} +(0.500000 - 0.866025i) q^{37} +7.00000 q^{38} +3.00000 q^{40} +(-1.50000 - 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} +(-1.50000 + 2.59808i) q^{44} +(-4.50000 - 7.79423i) q^{46} +(-2.00000 - 3.46410i) q^{50} +1.00000 q^{52} +(1.50000 + 2.59808i) q^{53} +9.00000 q^{55} -3.00000 q^{58} +(1.00000 + 1.73205i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{65} +(2.00000 - 3.46410i) q^{67} +3.00000 q^{68} -12.0000 q^{71} +(5.50000 + 9.52628i) q^{73} -1.00000 q^{74} +(-3.50000 - 6.06218i) q^{76} +(8.00000 + 13.8564i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-1.50000 + 2.59808i) q^{82} +(4.50000 - 7.79423i) q^{83} +(-4.50000 - 7.79423i) q^{85} -1.00000 q^{86} +3.00000 q^{88} +(-1.50000 + 2.59808i) q^{89} +(-4.50000 + 7.79423i) q^{92} +(-10.5000 + 18.1865i) q^{95} +(-0.500000 + 0.866025i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{2} - q^{4} + 6 q^{5} + 2 q^{8} + O(q^{10}) \) \( 2 q - q^{2} - q^{4} + 6 q^{5} + 2 q^{8} - 3 q^{10} + 6 q^{11} - q^{13} - q^{16} - 3 q^{17} - 7 q^{19} - 3 q^{20} - 3 q^{22} + 18 q^{23} + 8 q^{25} - q^{26} + 3 q^{29} + 8 q^{31} - q^{32} - 3 q^{34} + q^{37} + 14 q^{38} + 6 q^{40} - 3 q^{41} + q^{43} - 3 q^{44} - 9 q^{46} - 4 q^{50} + 2 q^{52} + 3 q^{53} + 18 q^{55} - 6 q^{58} + 2 q^{61} - 16 q^{62} + 2 q^{64} - 3 q^{65} + 4 q^{67} + 6 q^{68} - 24 q^{71} + 11 q^{73} - 2 q^{74} - 7 q^{76} + 16 q^{79} - 3 q^{80} - 3 q^{82} + 9 q^{83} - 9 q^{85} - 2 q^{86} + 6 q^{88} - 3 q^{89} - 9 q^{92} - 21 q^{95} - q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 3.00000 1.34164 0.670820 0.741620i \(-0.265942\pi\)
0.670820 + 0.741620i \(0.265942\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) −1.50000 2.59808i −0.474342 0.821584i
\(11\) 3.00000 0.904534 0.452267 0.891883i \(-0.350615\pi\)
0.452267 + 0.891883i \(0.350615\pi\)
\(12\) 0 0
\(13\) −0.500000 0.866025i −0.138675 0.240192i 0.788320 0.615265i \(-0.210951\pi\)
−0.926995 + 0.375073i \(0.877618\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 0 0
\(19\) −3.50000 + 6.06218i −0.802955 + 1.39076i 0.114708 + 0.993399i \(0.463407\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −1.50000 + 2.59808i −0.335410 + 0.580948i
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) 9.00000 1.87663 0.938315 0.345782i \(-0.112386\pi\)
0.938315 + 0.345782i \(0.112386\pi\)
\(24\) 0 0
\(25\) 4.00000 0.800000
\(26\) −0.500000 + 0.866025i −0.0980581 + 0.169842i
\(27\) 0 0
\(28\) 0 0
\(29\) 1.50000 2.59808i 0.278543 0.482451i −0.692480 0.721437i \(-0.743482\pi\)
0.971023 + 0.238987i \(0.0768152\pi\)
\(30\) 0 0
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −1.50000 + 2.59808i −0.257248 + 0.445566i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.500000 0.866025i 0.0821995 0.142374i −0.821995 0.569495i \(-0.807139\pi\)
0.904194 + 0.427121i \(0.140472\pi\)
\(38\) 7.00000 1.13555
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) −1.50000 2.59808i −0.234261 0.405751i 0.724797 0.688963i \(-0.241934\pi\)
−0.959058 + 0.283211i \(0.908600\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) −1.50000 + 2.59808i −0.226134 + 0.391675i
\(45\) 0 0
\(46\) −4.50000 7.79423i −0.663489 1.14920i
\(47\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.00000 3.46410i −0.282843 0.489898i
\(51\) 0 0
\(52\) 1.00000 0.138675
\(53\) 1.50000 + 2.59808i 0.206041 + 0.356873i 0.950464 0.310835i \(-0.100609\pi\)
−0.744423 + 0.667708i \(0.767275\pi\)
\(54\) 0 0
\(55\) 9.00000 1.21356
\(56\) 0 0
\(57\) 0 0
\(58\) −3.00000 −0.393919
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 1.00000 + 1.73205i 0.128037 + 0.221766i 0.922916 0.385002i \(-0.125799\pi\)
−0.794879 + 0.606768i \(0.792466\pi\)
\(62\) −8.00000 −1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −1.50000 2.59808i −0.186052 0.322252i
\(66\) 0 0
\(67\) 2.00000 3.46410i 0.244339 0.423207i −0.717607 0.696449i \(-0.754762\pi\)
0.961946 + 0.273241i \(0.0880957\pi\)
\(68\) 3.00000 0.363803
\(69\) 0 0
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 5.50000 + 9.52628i 0.643726 + 1.11497i 0.984594 + 0.174855i \(0.0559458\pi\)
−0.340868 + 0.940111i \(0.610721\pi\)
\(74\) −1.00000 −0.116248
\(75\) 0 0
\(76\) −3.50000 6.06218i −0.401478 0.695379i
\(77\) 0 0
\(78\) 0 0
\(79\) 8.00000 + 13.8564i 0.900070 + 1.55897i 0.827401 + 0.561611i \(0.189818\pi\)
0.0726692 + 0.997356i \(0.476848\pi\)
\(80\) −1.50000 2.59808i −0.167705 0.290474i
\(81\) 0 0
\(82\) −1.50000 + 2.59808i −0.165647 + 0.286910i
\(83\) 4.50000 7.79423i 0.493939 0.855528i −0.506036 0.862512i \(-0.668890\pi\)
0.999976 + 0.00698436i \(0.00222321\pi\)
\(84\) 0 0
\(85\) −4.50000 7.79423i −0.488094 0.845403i
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) 3.00000 0.319801
\(89\) −1.50000 + 2.59808i −0.159000 + 0.275396i −0.934508 0.355942i \(-0.884160\pi\)
0.775509 + 0.631337i \(0.217494\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −4.50000 + 7.79423i −0.469157 + 0.812605i
\(93\) 0 0
\(94\) 0 0
\(95\) −10.5000 + 18.1865i −1.07728 + 1.86590i
\(96\) 0 0
\(97\) −0.500000 + 0.866025i −0.0507673 + 0.0879316i −0.890292 0.455389i \(-0.849500\pi\)
0.839525 + 0.543321i \(0.182833\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 + 3.46410i −0.200000 + 0.346410i
\(101\) 3.00000 0.298511 0.149256 0.988799i \(-0.452312\pi\)
0.149256 + 0.988799i \(0.452312\pi\)
\(102\) 0 0
\(103\) 13.0000 1.28093 0.640464 0.767988i \(-0.278742\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) −0.500000 0.866025i −0.0490290 0.0849208i
\(105\) 0 0
\(106\) 1.50000 2.59808i 0.145693 0.252347i
\(107\) 4.50000 7.79423i 0.435031 0.753497i −0.562267 0.826956i \(-0.690071\pi\)
0.997298 + 0.0734594i \(0.0234039\pi\)
\(108\) 0 0
\(109\) 6.50000 + 11.2583i 0.622587 + 1.07835i 0.989002 + 0.147901i \(0.0472517\pi\)
−0.366415 + 0.930451i \(0.619415\pi\)
\(110\) −4.50000 7.79423i −0.429058 0.743151i
\(111\) 0 0
\(112\) 0 0
\(113\) −4.50000 7.79423i −0.423324 0.733219i 0.572938 0.819599i \(-0.305804\pi\)
−0.996262 + 0.0863794i \(0.972470\pi\)
\(114\) 0 0
\(115\) 27.0000 2.51776
\(116\) 1.50000 + 2.59808i 0.139272 + 0.241225i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.00000 −0.181818
\(122\) 1.00000 1.73205i 0.0905357 0.156813i
\(123\) 0 0
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) −3.00000 −0.268328
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) −1.50000 + 2.59808i −0.131559 + 0.227866i
\(131\) 15.0000 1.31056 0.655278 0.755388i \(-0.272551\pi\)
0.655278 + 0.755388i \(0.272551\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −4.00000 −0.345547
\(135\) 0 0
\(136\) −1.50000 2.59808i −0.128624 0.222783i
\(137\) 9.00000 0.768922 0.384461 0.923141i \(-0.374387\pi\)
0.384461 + 0.923141i \(0.374387\pi\)
\(138\) 0 0
\(139\) −3.50000 6.06218i −0.296866 0.514187i 0.678551 0.734553i \(-0.262608\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 6.00000 + 10.3923i 0.503509 + 0.872103i
\(143\) −1.50000 2.59808i −0.125436 0.217262i
\(144\) 0 0
\(145\) 4.50000 7.79423i 0.373705 0.647275i
\(146\) 5.50000 9.52628i 0.455183 0.788400i
\(147\) 0 0
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) 9.00000 0.737309 0.368654 0.929567i \(-0.379819\pi\)
0.368654 + 0.929567i \(0.379819\pi\)
\(150\) 0 0
\(151\) −7.00000 −0.569652 −0.284826 0.958579i \(-0.591936\pi\)
−0.284826 + 0.958579i \(0.591936\pi\)
\(152\) −3.50000 + 6.06218i −0.283887 + 0.491708i
\(153\) 0 0
\(154\) 0 0
\(155\) 12.0000 20.7846i 0.963863 1.66946i
\(156\) 0 0
\(157\) −11.0000 + 19.0526i −0.877896 + 1.52056i −0.0242497 + 0.999706i \(0.507720\pi\)
−0.853646 + 0.520854i \(0.825614\pi\)
\(158\) 8.00000 13.8564i 0.636446 1.10236i
\(159\) 0 0
\(160\) −1.50000 + 2.59808i −0.118585 + 0.205396i
\(161\) 0 0
\(162\) 0 0
\(163\) 9.50000 16.4545i 0.744097 1.28881i −0.206518 0.978443i \(-0.566213\pi\)
0.950615 0.310372i \(-0.100454\pi\)
\(164\) 3.00000 0.234261
\(165\) 0 0
\(166\) −9.00000 −0.698535
\(167\) 7.50000 + 12.9904i 0.580367 + 1.00523i 0.995436 + 0.0954356i \(0.0304244\pi\)
−0.415068 + 0.909790i \(0.636242\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) −4.50000 + 7.79423i −0.345134 + 0.597790i
\(171\) 0 0
\(172\) 0.500000 + 0.866025i 0.0381246 + 0.0660338i
\(173\) 3.00000 + 5.19615i 0.228086 + 0.395056i 0.957241 0.289292i \(-0.0934200\pi\)
−0.729155 + 0.684349i \(0.760087\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.50000 2.59808i −0.113067 0.195837i
\(177\) 0 0
\(178\) 3.00000 0.224860
\(179\) −10.5000 18.1865i −0.784807 1.35933i −0.929114 0.369792i \(-0.879429\pi\)
0.144308 0.989533i \(-0.453905\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 9.00000 0.663489
\(185\) 1.50000 2.59808i 0.110282 0.191014i
\(186\) 0 0
\(187\) −4.50000 7.79423i −0.329073 0.569970i
\(188\) 0 0
\(189\) 0 0
\(190\) 21.0000 1.52350
\(191\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 0 0
\(193\) −7.00000 + 12.1244i −0.503871 + 0.872730i 0.496119 + 0.868255i \(0.334758\pi\)
−0.999990 + 0.00447566i \(0.998575\pi\)
\(194\) 1.00000 0.0717958
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −12.5000 21.6506i −0.886102 1.53477i −0.844446 0.535641i \(-0.820070\pi\)
−0.0416556 0.999132i \(-0.513263\pi\)
\(200\) 4.00000 0.282843
\(201\) 0 0
\(202\) −1.50000 2.59808i −0.105540 0.182800i
\(203\) 0 0
\(204\) 0 0
\(205\) −4.50000 7.79423i −0.314294 0.544373i
\(206\) −6.50000 11.2583i −0.452876 0.784405i
\(207\) 0 0
\(208\) −0.500000 + 0.866025i −0.0346688 + 0.0600481i
\(209\) −10.5000 + 18.1865i −0.726300 + 1.25799i
\(210\) 0 0
\(211\) −2.50000 4.33013i −0.172107 0.298098i 0.767049 0.641588i \(-0.221724\pi\)
−0.939156 + 0.343490i \(0.888391\pi\)
\(212\) −3.00000 −0.206041
\(213\) 0 0
\(214\) −9.00000 −0.615227
\(215\) 1.50000 2.59808i 0.102299 0.177187i
\(216\) 0 0
\(217\) 0 0
\(218\) 6.50000 11.2583i 0.440236 0.762510i
\(219\) 0 0
\(220\) −4.50000 + 7.79423i −0.303390 + 0.525487i
\(221\) −1.50000 + 2.59808i −0.100901 + 0.174766i
\(222\) 0 0
\(223\) −0.500000 + 0.866025i −0.0334825 + 0.0579934i −0.882281 0.470723i \(-0.843993\pi\)
0.848799 + 0.528716i \(0.177326\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −4.50000 + 7.79423i −0.299336 + 0.518464i
\(227\) −3.00000 −0.199117 −0.0995585 0.995032i \(-0.531743\pi\)
−0.0995585 + 0.995032i \(0.531743\pi\)
\(228\) 0 0
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) −13.5000 23.3827i −0.890164 1.54181i
\(231\) 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
\(238\) 0 0
\(239\) −1.50000 2.59808i −0.0970269 0.168056i 0.813426 0.581669i \(-0.197600\pi\)
−0.910453 + 0.413613i \(0.864267\pi\)
\(240\) 0 0
\(241\) 13.0000 0.837404 0.418702 0.908124i \(-0.362485\pi\)
0.418702 + 0.908124i \(0.362485\pi\)
\(242\) 1.00000 + 1.73205i 0.0642824 + 0.111340i
\(243\) 0 0
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) 0 0
\(247\) 7.00000 0.445399
\(248\) 4.00000 6.92820i 0.254000 0.439941i
\(249\) 0 0
\(250\) 1.50000 + 2.59808i 0.0948683 + 0.164317i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) 2.00000 + 3.46410i 0.125491 + 0.217357i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −21.0000 −1.30994 −0.654972 0.755653i \(-0.727320\pi\)
−0.654972 + 0.755653i \(0.727320\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 3.00000 0.186052
\(261\) 0 0
\(262\) −7.50000 12.9904i −0.463352 0.802548i
\(263\) −9.00000 −0.554964 −0.277482 0.960731i \(-0.589500\pi\)
−0.277482 + 0.960731i \(0.589500\pi\)
\(264\) 0 0
\(265\) 4.50000 + 7.79423i 0.276433 + 0.478796i
\(266\) 0 0
\(267\) 0 0
\(268\) 2.00000 + 3.46410i 0.122169 + 0.211604i
\(269\) −7.50000 12.9904i −0.457283 0.792038i 0.541533 0.840679i \(-0.317844\pi\)
−0.998816 + 0.0486418i \(0.984511\pi\)
\(270\) 0 0
\(271\) 2.50000 4.33013i 0.151864 0.263036i −0.780049 0.625719i \(-0.784806\pi\)
0.931913 + 0.362682i \(0.118139\pi\)
\(272\) −1.50000 + 2.59808i −0.0909509 + 0.157532i
\(273\) 0 0
\(274\) −4.50000 7.79423i −0.271855 0.470867i
\(275\) 12.0000 0.723627
\(276\) 0 0
\(277\) −1.00000 −0.0600842 −0.0300421 0.999549i \(-0.509564\pi\)
−0.0300421 + 0.999549i \(0.509564\pi\)
\(278\) −3.50000 + 6.06218i −0.209916 + 0.363585i
\(279\) 0 0
\(280\) 0 0
\(281\) −10.5000 + 18.1865i −0.626377 + 1.08492i 0.361895 + 0.932219i \(0.382130\pi\)
−0.988273 + 0.152699i \(0.951204\pi\)
\(282\) 0 0
\(283\) −2.00000 + 3.46410i −0.118888 + 0.205919i −0.919327 0.393494i \(-0.871266\pi\)
0.800439 + 0.599414i \(0.204600\pi\)
\(284\) 6.00000 10.3923i 0.356034 0.616670i
\(285\) 0 0
\(286\) −1.50000 + 2.59808i −0.0886969 + 0.153627i
\(287\) 0 0
\(288\) 0 0
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) −9.00000 −0.528498
\(291\) 0 0
\(292\) −11.0000 −0.643726
\(293\) 4.50000 + 7.79423i 0.262893 + 0.455344i 0.967009 0.254741i \(-0.0819901\pi\)
−0.704117 + 0.710084i \(0.748657\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.500000 0.866025i 0.0290619 0.0503367i
\(297\) 0 0
\(298\) −4.50000 7.79423i −0.260678 0.451508i
\(299\) −4.50000 7.79423i −0.260242 0.450752i
\(300\) 0 0
\(301\) 0 0
\(302\) 3.50000 + 6.06218i 0.201402 + 0.348839i
\(303\) 0 0
\(304\) 7.00000 0.401478
\(305\) 3.00000 + 5.19615i 0.171780 + 0.297531i
\(306\) 0 0
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −24.0000 −1.36311
\(311\) 12.0000 20.7846i 0.680458 1.17859i −0.294384 0.955687i \(-0.595114\pi\)
0.974841 0.222900i \(-0.0715523\pi\)
\(312\) 0 0
\(313\) −5.00000 8.66025i −0.282617 0.489506i 0.689412 0.724370i \(-0.257869\pi\)
−0.972028 + 0.234863i \(0.924536\pi\)
\(314\) 22.0000 1.24153
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) 9.00000 + 15.5885i 0.505490 + 0.875535i 0.999980 + 0.00635137i \(0.00202172\pi\)
−0.494489 + 0.869184i \(0.664645\pi\)
\(318\) 0 0
\(319\) 4.50000 7.79423i 0.251952 0.436393i
\(320\) 3.00000 0.167705
\(321\) 0 0
\(322\) 0 0
\(323\) 21.0000 1.16847
\(324\) 0 0
\(325\) −2.00000 3.46410i −0.110940 0.192154i
\(326\) −19.0000 −1.05231
\(327\) 0 0
\(328\) −1.50000 2.59808i −0.0828236 0.143455i
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 6.92820i −0.219860 0.380808i 0.734905 0.678170i \(-0.237227\pi\)
−0.954765 + 0.297361i \(0.903893\pi\)
\(332\) 4.50000 + 7.79423i 0.246970 + 0.427764i
\(333\) 0 0
\(334\) 7.50000 12.9904i 0.410382 0.710802i
\(335\) 6.00000 10.3923i 0.327815 0.567792i
\(336\) 0 0
\(337\) 6.50000 + 11.2583i 0.354078 + 0.613280i 0.986960 0.160968i \(-0.0514616\pi\)
−0.632882 + 0.774248i \(0.718128\pi\)
\(338\) −12.0000 −0.652714
\(339\) 0 0
\(340\) 9.00000 0.488094
\(341\) 12.0000 20.7846i 0.649836 1.12555i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.500000 0.866025i 0.0269582 0.0466930i
\(345\) 0 0
\(346\) 3.00000 5.19615i 0.161281 0.279347i
\(347\) 6.00000 10.3923i 0.322097 0.557888i −0.658824 0.752297i \(-0.728946\pi\)
0.980921 + 0.194409i \(0.0622790\pi\)
\(348\) 0 0
\(349\) 11.5000 19.9186i 0.615581 1.06622i −0.374701 0.927146i \(-0.622255\pi\)
0.990282 0.139072i \(-0.0444119\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.50000 + 2.59808i −0.0799503 + 0.138478i
\(353\) 3.00000 0.159674 0.0798369 0.996808i \(-0.474560\pi\)
0.0798369 + 0.996808i \(0.474560\pi\)
\(354\) 0 0
\(355\) −36.0000 −1.91068
\(356\) −1.50000 2.59808i −0.0794998 0.137698i
\(357\) 0 0
\(358\) −10.5000 + 18.1865i −0.554942 + 0.961188i
\(359\) 4.50000 7.79423i 0.237501 0.411364i −0.722496 0.691375i \(-0.757005\pi\)
0.959997 + 0.280012i \(0.0903384\pi\)
\(360\) 0 0
\(361\) −15.0000 25.9808i −0.789474 1.36741i
\(362\) 1.00000 + 1.73205i 0.0525588 + 0.0910346i
\(363\) 0 0
\(364\) 0 0
\(365\) 16.5000 + 28.5788i 0.863649 + 1.49588i
\(366\) 0 0
\(367\) −17.0000 −0.887393 −0.443696 0.896177i \(-0.646333\pi\)
−0.443696 + 0.896177i \(0.646333\pi\)
\(368\) −4.50000 7.79423i −0.234579 0.406302i
\(369\) 0 0
\(370\) −3.00000 −0.155963
\(371\) 0 0
\(372\) 0 0
\(373\) −13.0000 −0.673114 −0.336557 0.941663i \(-0.609263\pi\)
−0.336557 + 0.941663i \(0.609263\pi\)
\(374\) −4.50000 + 7.79423i −0.232689 + 0.403030i
\(375\) 0 0
\(376\) 0 0
\(377\) −3.00000 −0.154508
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) −10.5000 18.1865i −0.538639 0.932949i
\(381\) 0 0
\(382\) 0 0
\(383\) 15.0000 0.766464 0.383232 0.923652i \(-0.374811\pi\)
0.383232 + 0.923652i \(0.374811\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 0 0
\(388\) −0.500000 0.866025i −0.0253837 0.0439658i
\(389\) −27.0000 −1.36895 −0.684477 0.729034i \(-0.739969\pi\)
−0.684477 + 0.729034i \(0.739969\pi\)
\(390\) 0 0
\(391\) −13.5000 23.3827i −0.682724 1.18251i
\(392\) 0 0
\(393\) 0 0
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) 24.0000 + 41.5692i 1.20757 + 2.09157i
\(396\) 0 0
\(397\) −6.50000 + 11.2583i −0.326226 + 0.565039i −0.981760 0.190126i \(-0.939110\pi\)
0.655534 + 0.755166i \(0.272444\pi\)
\(398\) −12.5000 + 21.6506i −0.626568 + 1.08525i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −27.0000 −1.34832 −0.674158 0.738587i \(-0.735493\pi\)
−0.674158 + 0.738587i \(0.735493\pi\)
\(402\) 0 0
\(403\) −8.00000 −0.398508
\(404\) −1.50000 + 2.59808i −0.0746278 + 0.129259i
\(405\) 0 0
\(406\) 0 0
\(407\) 1.50000 2.59808i 0.0743522 0.128782i
\(408\) 0 0
\(409\) −17.0000 + 29.4449i −0.840596 + 1.45595i 0.0487958 + 0.998809i \(0.484462\pi\)
−0.889392 + 0.457146i \(0.848872\pi\)
\(410\) −4.50000 + 7.79423i −0.222239 + 0.384930i
\(411\) 0 0
\(412\) −6.50000 + 11.2583i −0.320232 + 0.554658i
\(413\) 0 0
\(414\) 0 0
\(415\) 13.5000 23.3827i 0.662689 1.14781i
\(416\) 1.00000 0.0490290
\(417\) 0 0
\(418\) 21.0000 1.02714
\(419\) −4.50000 7.79423i −0.219839 0.380773i 0.734919 0.678155i \(-0.237220\pi\)
−0.954759 + 0.297382i \(0.903887\pi\)
\(420\) 0 0
\(421\) −17.5000 + 30.3109i −0.852898 + 1.47726i 0.0256838 + 0.999670i \(0.491824\pi\)
−0.878582 + 0.477592i \(0.841510\pi\)
\(422\) −2.50000 + 4.33013i −0.121698 + 0.210787i
\(423\) 0 0
\(424\) 1.50000 + 2.59808i 0.0728464 + 0.126174i
\(425\) −6.00000 10.3923i −0.291043 0.504101i
\(426\) 0 0
\(427\) 0 0
\(428\) 4.50000 + 7.79423i 0.217516 + 0.376748i
\(429\) 0 0
\(430\) −3.00000 −0.144673
\(431\) 13.5000 + 23.3827i 0.650272 + 1.12630i 0.983057 + 0.183301i \(0.0586785\pi\)
−0.332785 + 0.943003i \(0.607988\pi\)
\(432\) 0 0
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −13.0000 −0.622587
\(437\) −31.5000 + 54.5596i −1.50685 + 2.60994i
\(438\) 0 0
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) 9.00000 0.429058
\(441\) 0 0
\(442\) 3.00000 0.142695
\(443\) 18.0000 + 31.1769i 0.855206 + 1.48126i 0.876454 + 0.481486i \(0.159903\pi\)
−0.0212481 + 0.999774i \(0.506764\pi\)
\(444\) 0 0
\(445\) −4.50000 + 7.79423i −0.213320 + 0.369482i
\(446\) 1.00000 0.0473514
\(447\) 0 0
\(448\) 0 0
\(449\) −6.00000 −0.283158 −0.141579 0.989927i \(-0.545218\pi\)
−0.141579 + 0.989927i \(0.545218\pi\)
\(450\) 0 0
\(451\) −4.50000 7.79423i −0.211897 0.367016i
\(452\) 9.00000 0.423324
\(453\) 0 0
\(454\) 1.50000 + 2.59808i 0.0703985 + 0.121934i
\(455\) 0 0
\(456\) 0 0
\(457\) 5.00000 + 8.66025i 0.233890 + 0.405110i 0.958950 0.283577i \(-0.0915211\pi\)
−0.725059 + 0.688686i \(0.758188\pi\)
\(458\) −6.50000 11.2583i −0.303725 0.526067i
\(459\) 0 0
\(460\) −13.5000 + 23.3827i −0.629441 + 1.09022i
\(461\) 4.50000 7.79423i 0.209586 0.363013i −0.741998 0.670402i \(-0.766122\pi\)
0.951584 + 0.307388i \(0.0994551\pi\)
\(462\) 0 0
\(463\) −20.5000 35.5070i −0.952716 1.65015i −0.739511 0.673145i \(-0.764943\pi\)
−0.213205 0.977007i \(-0.568390\pi\)
\(464\) −3.00000 −0.139272
\(465\) 0 0
\(466\) −3.00000 −0.138972
\(467\) 1.50000 2.59808i 0.0694117 0.120225i −0.829231 0.558906i \(-0.811221\pi\)
0.898642 + 0.438682i \(0.144554\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.50000 2.59808i 0.0689701 0.119460i
\(474\) 0 0
\(475\) −14.0000 + 24.2487i −0.642364 + 1.11261i
\(476\) 0 0
\(477\) 0 0
\(478\) −1.50000 + 2.59808i −0.0686084 + 0.118833i
\(479\) −3.00000 −0.137073 −0.0685367 0.997649i \(-0.521833\pi\)
−0.0685367 + 0.997649i \(0.521833\pi\)
\(480\) 0 0
\(481\) −1.00000 −0.0455961
\(482\) −6.50000 11.2583i −0.296067 0.512803i
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) −1.50000 + 2.59808i −0.0681115 + 0.117973i
\(486\) 0 0
\(487\) 12.5000 + 21.6506i 0.566429 + 0.981084i 0.996915 + 0.0784867i \(0.0250088\pi\)
−0.430486 + 0.902597i \(0.641658\pi\)
\(488\) 1.00000 + 1.73205i 0.0452679 + 0.0784063i
\(489\) 0 0
\(490\) 0 0
\(491\) 10.5000 + 18.1865i 0.473858 + 0.820747i 0.999552 0.0299272i \(-0.00952753\pi\)
−0.525694 + 0.850674i \(0.676194\pi\)
\(492\) 0 0
\(493\) −9.00000 −0.405340
\(494\) −3.50000 6.06218i −0.157472 0.272750i
\(495\) 0 0
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) −25.0000 −1.11915 −0.559577 0.828778i \(-0.689036\pi\)
−0.559577 + 0.828778i \(0.689036\pi\)
\(500\) 1.50000 2.59808i 0.0670820 0.116190i
\(501\) 0 0
\(502\) −6.00000 10.3923i −0.267793 0.463831i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) −13.5000 23.3827i −0.600148 1.03949i
\(507\) 0 0
\(508\) 2.00000 3.46410i 0.0887357 0.153695i
\(509\) −9.00000 −0.398918 −0.199459 0.979906i \(-0.563918\pi\)
−0.199459 + 0.979906i \(0.563918\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 10.5000 + 18.1865i 0.463135 + 0.802174i
\(515\) 39.0000 1.71855
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) −1.50000 2.59808i −0.0657794 0.113933i
\(521\) −1.50000 2.59808i −0.0657162 0.113824i 0.831295 0.555831i \(-0.187600\pi\)
−0.897011 + 0.442007i \(0.854267\pi\)
\(522\) 0 0
\(523\) −3.50000 + 6.06218i −0.153044 + 0.265081i −0.932345 0.361569i \(-0.882241\pi\)
0.779301 + 0.626650i \(0.215574\pi\)
\(524\) −7.50000 + 12.9904i −0.327639 + 0.567487i
\(525\) 0 0
\(526\) 4.50000 + 7.79423i 0.196209 + 0.339845i
\(527\) −24.0000 −1.04546
\(528\) 0 0
\(529\) 58.0000 2.52174
\(530\) 4.50000 7.79423i 0.195468 0.338560i
\(531\) 0 0
\(532\) 0 0
\(533\) −1.50000 + 2.59808i −0.0649722 + 0.112535i
\(534\) 0 0
\(535\) 13.5000 23.3827i 0.583656 1.01092i
\(536\) 2.00000 3.46410i 0.0863868 0.149626i
\(537\) 0 0
\(538\) −7.50000 + 12.9904i −0.323348 + 0.560055i
\(539\) 0 0
\(540\) 0 0
\(541\) −5.50000 + 9.52628i −0.236463 + 0.409567i −0.959697 0.281037i \(-0.909322\pi\)
0.723234 + 0.690604i \(0.242655\pi\)
\(542\) −5.00000 −0.214768
\(543\) 0 0
\(544\) 3.00000 0.128624
\(545\) 19.5000 + 33.7750i 0.835288 + 1.44676i
\(546\) 0 0
\(547\) −5.50000 + 9.52628i −0.235163 + 0.407314i −0.959320 0.282321i \(-0.908896\pi\)
0.724157 + 0.689635i \(0.242229\pi\)
\(548\) −4.50000 + 7.79423i −0.192230 + 0.332953i
\(549\) 0 0
\(550\) −6.00000 10.3923i −0.255841 0.443129i
\(551\) 10.5000 + 18.1865i 0.447315 + 0.774772i
\(552\) 0 0
\(553\) 0 0
\(554\) 0.500000 + 0.866025i 0.0212430 + 0.0367939i
\(555\) 0 0
\(556\) 7.00000 0.296866
\(557\) −4.50000 7.79423i −0.190671 0.330252i 0.754802 0.655953i \(-0.227733\pi\)
−0.945473 + 0.325701i \(0.894400\pi\)
\(558\) 0 0
\(559\) −1.00000 −0.0422955
\(560\) 0 0
\(561\) 0 0
\(562\) 21.0000 0.885832
\(563\) −6.00000 + 10.3923i −0.252870 + 0.437983i −0.964315 0.264758i \(-0.914708\pi\)
0.711445 + 0.702742i \(0.248041\pi\)
\(564\) 0 0
\(565\) −13.5000 23.3827i −0.567949 0.983717i
\(566\) 4.00000 0.168133
\(567\) 0 0
\(568\) −12.0000 −0.503509
\(569\) −9.00000 15.5885i −0.377300 0.653502i 0.613369 0.789797i \(-0.289814\pi\)
−0.990668 + 0.136295i \(0.956481\pi\)
\(570\) 0 0
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) 3.00000 0.125436
\(573\) 0 0
\(574\) 0 0
\(575\) 36.0000 1.50130
\(576\) 0 0
\(577\) −12.5000 21.6506i −0.520382 0.901328i −0.999719 0.0236970i \(-0.992456\pi\)
0.479337 0.877631i \(-0.340877\pi\)
\(578\) −8.00000 −0.332756
\(579\) 0 0
\(580\) 4.50000 + 7.79423i 0.186852 + 0.323638i
\(581\) 0 0
\(582\) 0 0
\(583\) 4.50000 + 7.79423i 0.186371 + 0.322804i
\(584\) 5.50000 + 9.52628i 0.227592 + 0.394200i
\(585\) 0 0
\(586\) 4.50000 7.79423i 0.185893 0.321977i
\(587\) −1.50000 + 2.59808i −0.0619116 + 0.107234i −0.895320 0.445424i \(-0.853053\pi\)
0.833408 + 0.552658i \(0.186386\pi\)
\(588\) 0 0
\(589\) 28.0000 + 48.4974i 1.15372 + 1.99830i
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 −0.0410997
\(593\) −19.5000 + 33.7750i −0.800769 + 1.38697i 0.118342 + 0.992973i \(0.462242\pi\)
−0.919111 + 0.394000i \(0.871091\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −4.50000 + 7.79423i −0.184327 + 0.319264i
\(597\) 0 0
\(598\) −4.50000 + 7.79423i −0.184019 + 0.318730i
\(599\) −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i \(-0.996449\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(600\) 0 0
\(601\) −12.5000 + 21.6506i −0.509886 + 0.883148i 0.490049 + 0.871695i \(0.336979\pi\)
−0.999934 + 0.0114528i \(0.996354\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 3.50000 6.06218i 0.142413 0.246667i
\(605\) −6.00000 −0.243935
\(606\) 0 0
\(607\) 13.0000 0.527654 0.263827 0.964570i \(-0.415015\pi\)
0.263827 + 0.964570i \(0.415015\pi\)
\(608\) −3.50000 6.06218i −0.141944 0.245854i
\(609\) 0 0
\(610\) 3.00000 5.19615i 0.121466 0.210386i
\(611\) 0 0
\(612\) 0 0
\(613\) −11.5000 19.9186i −0.464481 0.804504i 0.534697 0.845044i \(-0.320426\pi\)
−0.999178 + 0.0405396i \(0.987092\pi\)
\(614\) −14.0000 24.2487i −0.564994 0.978598i
\(615\) 0 0
\(616\) 0 0
\(617\) −22.5000 38.9711i −0.905816 1.56892i −0.819818 0.572624i \(-0.805926\pi\)
−0.0859976 0.996295i \(-0.527408\pi\)
\(618\) 0 0
\(619\) −17.0000 −0.683288 −0.341644 0.939829i \(-0.610984\pi\)
−0.341644 + 0.939829i \(0.610984\pi\)
\(620\) 12.0000 + 20.7846i 0.481932 + 0.834730i
\(621\) 0 0
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) 0 0
\(625\) −29.0000 −1.16000
\(626\) −5.00000 + 8.66025i −0.199840 + 0.346133i
\(627\) 0 0
\(628\) −11.0000 19.0526i −0.438948 0.760280i
\(629\) −3.00000 −0.119618
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 8.00000 + 13.8564i 0.318223 + 0.551178i
\(633\) 0 0
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) −12.0000 −0.476205
\(636\) 0 0
\(637\) 0 0
\(638\) −9.00000 −0.356313
\(639\) 0 0
\(640\) −1.50000 2.59808i −0.0592927 0.102698i
\(641\) 33.0000 1.30342 0.651711 0.758468i \(-0.274052\pi\)
0.651711 + 0.758468i \(0.274052\pi\)
\(642\) 0 0
\(643\) 14.5000 + 25.1147i 0.571824 + 0.990429i 0.996379 + 0.0850262i \(0.0270974\pi\)
−0.424555 + 0.905402i \(0.639569\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −10.5000 18.1865i −0.413117 0.715540i
\(647\) 10.5000 + 18.1865i 0.412798 + 0.714986i 0.995194 0.0979182i \(-0.0312184\pi\)
−0.582397 + 0.812905i \(0.697885\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −2.00000 + 3.46410i −0.0784465 + 0.135873i
\(651\) 0 0
\(652\) 9.50000 + 16.4545i 0.372049 + 0.644407i
\(653\) −15.0000 −0.586995 −0.293498 0.955960i \(-0.594819\pi\)
−0.293498 + 0.955960i \(0.594819\pi\)
\(654\) 0 0
\(655\) 45.0000 1.75830
\(656\) −1.50000 + 2.59808i −0.0585652 + 0.101438i
\(657\) 0 0
\(658\) 0 0
\(659\) 1.50000 2.59808i 0.0584317 0.101207i −0.835330 0.549749i \(-0.814723\pi\)
0.893762 + 0.448542i \(0.148057\pi\)
\(660\) 0 0
\(661\) −11.0000 + 19.0526i −0.427850 + 0.741059i −0.996682 0.0813955i \(-0.974062\pi\)
0.568831 + 0.822454i \(0.307396\pi\)
\(662\) −4.00000 + 6.92820i −0.155464 + 0.269272i
\(663\) 0 0
\(664\) 4.50000 7.79423i 0.174634 0.302475i
\(665\) 0 0
\(666\) 0 0
\(667\) 13.5000 23.3827i 0.522722 0.905381i
\(668\) −15.0000 −0.580367
\(669\) 0 0
\(670\) −12.0000 −0.463600
\(671\) 3.00000 + 5.19615i 0.115814 + 0.200595i
\(672\) 0 0
\(673\) −17.5000 + 30.3109i −0.674575 + 1.16840i 0.302017 + 0.953302i \(0.402340\pi\)
−0.976593 + 0.215096i \(0.930993\pi\)
\(674\) 6.50000 11.2583i 0.250371 0.433655i
\(675\) 0 0
\(676\) 6.00000 + 10.3923i 0.230769 + 0.399704i
\(677\) 15.0000 + 25.9808i 0.576497 + 0.998522i 0.995877 + 0.0907112i \(0.0289140\pi\)
−0.419380 + 0.907811i \(0.637753\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −4.50000 7.79423i −0.172567 0.298895i
\(681\) 0 0
\(682\) −24.0000 −0.919007
\(683\) −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
\(685\) 27.0000 1.03162
\(686\) 0 0
\(687\) 0 0
\(688\) −1.00000 −0.0381246
\(689\) 1.50000 2.59808i 0.0571454 0.0989788i
\(690\) 0 0
\(691\) 22.0000 + 38.1051i 0.836919 + 1.44959i 0.892458 + 0.451130i \(0.148979\pi\)
−0.0555386 + 0.998457i \(0.517688\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) −10.5000 18.1865i −0.398288 0.689855i
\(696\) 0 0
\(697\) −4.50000 + 7.79423i −0.170450 + 0.295227i
\(698\) −23.0000 −0.870563
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 0 0
\(703\) 3.50000 + 6.06218i 0.132005 + 0.228639i
\(704\) 3.00000 0.113067
\(705\) 0 0
\(706\) −1.50000 2.59808i −0.0564532 0.0977799i
\(707\) 0 0
\(708\) 0 0
\(709\) −13.0000 22.5167i −0.488225 0.845631i 0.511683 0.859174i \(-0.329022\pi\)
−0.999908 + 0.0135434i \(0.995689\pi\)
\(710\) 18.0000 + 31.1769i 0.675528 + 1.17005i
\(711\) 0 0
\(712\) −1.50000 + 2.59808i −0.0562149 + 0.0973670i
\(713\) 36.0000 62.3538i 1.34821 2.33517i
\(714\) 0 0
\(715\) −4.50000 7.79423i −0.168290 0.291488i
\(716\) 21.0000 0.784807
\(717\) 0 0
\(718\) −9.00000 −0.335877
\(719\) 7.50000 12.9904i 0.279703 0.484459i −0.691608 0.722273i \(-0.743097\pi\)
0.971311 + 0.237814i \(0.0764307\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −15.0000 + 25.9808i −0.558242 + 0.966904i
\(723\) 0 0
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) 6.00000 10.3923i 0.222834 0.385961i
\(726\) 0 0
\(727\) −6.50000 + 11.2583i −0.241072 + 0.417548i −0.961020 0.276479i \(-0.910832\pi\)
0.719948 + 0.694028i \(0.244166\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 16.5000 28.5788i 0.610692 1.05775i
\(731\) −3.00000 −0.110959
\(732\) 0 0
\(733\) 1.00000 0.0369358 0.0184679 0.999829i \(-0.494121\pi\)
0.0184679 + 0.999829i \(0.494121\pi\)
\(734\) 8.50000 + 14.7224i 0.313741 + 0.543415i
\(735\) 0 0
\(736\) −4.50000 + 7.79423i −0.165872 + 0.287299i
\(737\) 6.00000 10.3923i 0.221013 0.382805i
\(738\) 0 0
\(739\) −11.5000 19.9186i −0.423034 0.732717i 0.573200 0.819415i \(-0.305702\pi\)
−0.996235 + 0.0866983i \(0.972368\pi\)
\(740\) 1.50000 + 2.59808i 0.0551411 + 0.0955072i
\(741\) 0 0
\(742\) 0 0
\(743\) 10.5000 + 18.1865i 0.385208 + 0.667199i 0.991798 0.127815i \(-0.0407965\pi\)
−0.606590 + 0.795015i \(0.707463\pi\)
\(744\) 0 0
\(745\) 27.0000 0.989203
\(746\) 6.50000 + 11.2583i 0.237982 + 0.412197i
\(747\) 0 0
\(748\) 9.00000 0.329073
\(749\) 0 0
\(750\) 0 0
\(751\) −13.0000 −0.474377 −0.237188 0.971464i \(-0.576226\pi\)
−0.237188 + 0.971464i \(0.576226\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 1.50000 + 2.59808i 0.0546268 + 0.0946164i
\(755\) −21.0000 −0.764268
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 14.0000 + 24.2487i 0.508503 + 0.880753i
\(759\) 0 0
\(760\) −10.5000 + 18.1865i −0.380875 + 0.659695i
\(761\) −45.0000 −1.63125 −0.815624 0.578582i \(-0.803606\pi\)
−0.815624 + 0.578582i \(0.803606\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) −7.50000 12.9904i −0.270986 0.469362i
\(767\) 0 0
\(768\) 0 0
\(769\) 11.5000 + 19.9186i 0.414701 + 0.718283i 0.995397 0.0958377i \(-0.0305530\pi\)
−0.580696 + 0.814120i \(0.697220\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.00000 12.1244i −0.251936 0.436365i
\(773\) −13.5000 23.3827i −0.485561 0.841017i 0.514301 0.857610i \(-0.328051\pi\)
−0.999862 + 0.0165929i \(0.994718\pi\)
\(774\) 0 0
\(775\) 16.0000 27.7128i 0.574737 0.995474i
\(776\) −0.500000 + 0.866025i −0.0179490 + 0.0310885i
\(777\) 0 0
\(778\) 13.5000 + 23.3827i 0.483998 + 0.838310i
\(779\) 21.0000 0.752403
\(780\) 0 0
\(781\) −36.0000 −1.28818
\(782\) −13.5000 + 23.3827i −0.482759 + 0.836163i
\(783\) 0 0
\(784\) 0 0
\(785\) −33.0000 + 57.1577i −1.17782 + 2.04004i
\(786\) 0 0
\(787\) −14.0000 + 24.2487i −0.499046 + 0.864373i −0.999999 0.00110111i \(-0.999650\pi\)
0.500953 + 0.865474i \(0.332983\pi\)
\(788\) 9.00000 15.5885i 0.320612 0.555316i
\(789\) 0 0
\(790\) 24.0000 41.5692i 0.853882 1.47897i
\(791\) 0 0
\(792\) 0 0
\(793\) 1.00000 1.73205i 0.0355110 0.0615069i
\(794\) 13.0000 0.461353