Properties

Label 2646.2.h.d.361.1
Level $2646$
Weight $2$
Character 2646.361
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: \( x^{2} - x + 1 \) Copy content Toggle raw display
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 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 2646.361
Dual form 2646.2.h.d.667.1

$q$-expansion

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

Character values

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

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

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 −0.926995 0.375073i \(-0.877618\pi\)
0.788320 + 0.615265i \(0.210951\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.50000 + 2.59808i −0.363803 + 0.630126i −0.988583 0.150675i \(-0.951855\pi\)
0.624780 + 0.780801i \(0.285189\pi\)
\(18\) 0 0
\(19\) −3.50000 6.06218i −0.802955 1.39076i −0.917663 0.397360i \(-0.869927\pi\)
0.114708 0.993399i \(-0.463407\pi\)
\(20\) −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 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 0 0
\(31\) 4.00000 + 6.92820i 0.718421 + 1.24434i 0.961625 + 0.274367i \(0.0884683\pi\)
−0.243204 + 0.969975i \(0.578198\pi\)
\(32\) −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 0.904194 0.427121i \(-0.140472\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 7.00000 1.13555
\(39\) 0 0
\(40\) 3.00000 0.474342
\(41\) −1.50000 + 2.59808i −0.234261 + 0.405751i −0.959058 0.283211i \(-0.908600\pi\)
0.724797 + 0.688963i \(0.241934\pi\)
\(42\) 0 0
\(43\) 0.500000 + 0.866025i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 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 −0.744423 0.667708i \(-0.767275\pi\)
0.950464 + 0.310835i \(0.100609\pi\)
\(54\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) 1.00000 1.73205i 0.128037 0.221766i −0.794879 0.606768i \(-0.792466\pi\)
0.922916 + 0.385002i \(0.125799\pi\)
\(62\) −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 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 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 −0.340868 0.940111i \(-0.610721\pi\)
0.984594 0.174855i \(-0.0559458\pi\)
\(74\) −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 0.0726692 0.997356i \(-0.476848\pi\)
0.827401 0.561611i \(-0.189818\pi\)
\(80\) −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 0.999976 0.00698436i \(-0.00222321\pi\)
−0.506036 + 0.862512i \(0.668890\pi\)
\(84\) 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 0.775509 0.631337i \(-0.217494\pi\)
−0.934508 + 0.355942i \(0.884160\pi\)
\(90\) 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 0.839525 0.543321i \(-0.182833\pi\)
−0.890292 + 0.455389i \(0.849500\pi\)
\(98\) 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 0.997298 0.0734594i \(-0.0234039\pi\)
−0.562267 + 0.826956i \(0.690071\pi\)
\(108\) 0 0
\(109\) 6.50000 11.2583i 0.622587 1.07835i −0.366415 0.930451i \(-0.619415\pi\)
0.989002 0.147901i \(-0.0472517\pi\)
\(110\) −4.50000 + 7.79423i −0.429058 + 0.743151i
\(111\) 0 0
\(112\) 0 0
\(113\) −4.50000 + 7.79423i −0.423324 + 0.733219i −0.996262 0.0863794i \(-0.972470\pi\)
0.572938 + 0.819599i \(0.305804\pi\)
\(114\) 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 −0.975417 0.220366i \(-0.929275\pi\)
0.678551 + 0.734553i \(0.262608\pi\)
\(140\) 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 −0.853646 0.520854i \(-0.825614\pi\)
−0.0242497 0.999706i \(-0.507720\pi\)
\(158\) 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 0.950615 + 0.310372i \(0.100454\pi\)
−0.206518 + 0.978443i \(0.566213\pi\)
\(164\) 3.00000 0.234261
\(165\) 0 0
\(166\) −9.00000 −0.698535
\(167\) 7.50000 12.9904i 0.580367 1.00523i −0.415068 0.909790i \(-0.636242\pi\)
0.995436 0.0954356i \(-0.0304244\pi\)
\(168\) 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 −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 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 0.144308 + 0.989533i \(0.453905\pi\)
−0.929114 + 0.369792i \(0.879429\pi\)
\(180\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) 0 0
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 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 −0.0416556 + 0.999132i \(0.513263\pi\)
−0.844446 + 0.535641i \(0.820070\pi\)
\(200\) 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 −0.939156 0.343490i \(-0.888391\pi\)
0.767049 + 0.641588i \(0.221724\pi\)
\(212\) −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 0.848799 0.528716i \(-0.177326\pi\)
−0.882281 + 0.470723i \(0.843993\pi\)
\(224\) 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 0.910968 0.412477i \(-0.135336\pi\)
−0.812700 + 0.582683i \(0.802003\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.50000 + 2.59808i −0.0970269 + 0.168056i −0.910453 0.413613i \(-0.864267\pi\)
0.813426 + 0.581669i \(0.197600\pi\)
\(240\) 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 −0.998816 0.0486418i \(-0.984511\pi\)
0.541533 + 0.840679i \(0.317844\pi\)
\(270\) 0 0
\(271\) 2.50000 + 4.33013i 0.151864 + 0.263036i 0.931913 0.362682i \(-0.118139\pi\)
−0.780049 + 0.625719i \(0.784806\pi\)
\(272\) −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 −0.988273 0.152699i \(-0.951204\pi\)
0.361895 0.932219i \(-0.382130\pi\)
\(282\) 0 0
\(283\) −2.00000 3.46410i −0.118888 0.205919i 0.800439 0.599414i \(-0.204600\pi\)
−0.919327 + 0.393494i \(0.871266\pi\)
\(284\) 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 −0.704117 0.710084i \(-0.748657\pi\)
0.967009 + 0.254741i \(0.0819901\pi\)
\(294\) 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 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) 0 0
\(313\) −5.00000 + 8.66025i −0.282617 + 0.489506i −0.972028 0.234863i \(-0.924536\pi\)
0.689412 + 0.724370i \(0.257869\pi\)
\(314\) 22.0000 1.24153
\(315\) 0 0
\(316\) −16.0000 −0.900070
\(317\) 9.00000 15.5885i 0.505490 0.875535i −0.494489 0.869184i \(-0.664645\pi\)
0.999980 0.00635137i \(-0.00202172\pi\)
\(318\) 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 −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) 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 −0.632882 0.774248i \(-0.718128\pi\)
0.986960 + 0.160968i \(0.0514616\pi\)
\(338\) −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 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 0 0
\(349\) 11.5000 + 19.9186i 0.615581 + 1.06622i 0.990282 + 0.139072i \(0.0444119\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 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 0.959997 0.280012i \(-0.0903384\pi\)
−0.722496 + 0.691375i \(0.757005\pi\)
\(360\) 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 0.655534 0.755166i \(-0.272444\pi\)
−0.981760 + 0.190126i \(0.939110\pi\)
\(398\) −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 −0.889392 0.457146i \(-0.848872\pi\)
0.0487958 0.998809i \(-0.484462\pi\)
\(410\) −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 −0.954759 0.297382i \(-0.903887\pi\)
0.734919 + 0.678155i \(0.237220\pi\)
\(420\) 0 0
\(421\) −17.5000 30.3109i −0.852898 1.47726i −0.878582 0.477592i \(-0.841510\pi\)
0.0256838 0.999670i \(-0.491824\pi\)
\(422\) −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 −0.332785 0.943003i \(-0.607988\pi\)
0.983057 0.183301i \(-0.0586785\pi\)
\(432\) 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 −0.754642 0.656136i \(-0.772190\pi\)
0.945552 + 0.325471i \(0.105523\pi\)
\(440\) 9.00000 0.429058
\(441\) 0 0
\(442\) 3.00000 0.142695
\(443\) 18.0000 31.1769i 0.855206 1.48126i −0.0212481 0.999774i \(-0.506764\pi\)
0.876454 0.481486i \(-0.159903\pi\)
\(444\) 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 −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) −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 0.951584 0.307388i \(-0.0994551\pi\)
−0.741998 + 0.670402i \(0.766122\pi\)
\(462\) 0 0
\(463\) −20.5000 + 35.5070i −0.952716 + 1.65015i −0.213205 + 0.977007i \(0.568390\pi\)
−0.739511 + 0.673145i \(0.764943\pi\)
\(464\) −3.00000 −0.139272
\(465\) 0 0
\(466\) −3.00000 −0.138972
\(467\) 1.50000 + 2.59808i 0.0694117 + 0.120225i 0.898642 0.438682i \(-0.144554\pi\)
−0.829231 + 0.558906i \(0.811221\pi\)
\(468\) 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 −0.430486 0.902597i \(-0.641658\pi\)
0.996915 0.0784867i \(-0.0250088\pi\)
\(488\) 1.00000 1.73205i 0.0452679 0.0784063i
\(489\) 0 0
\(490\) 0 0
\(491\) 10.5000 18.1865i 0.473858 0.820747i −0.525694 0.850674i \(-0.676194\pi\)
0.999552 + 0.0299272i \(0.00952753\pi\)
\(492\) 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 −0.897011 0.442007i \(-0.854267\pi\)
0.831295 + 0.555831i \(0.187600\pi\)
\(522\) 0 0
\(523\) −3.50000 6.06218i −0.153044 0.265081i 0.779301 0.626650i \(-0.215574\pi\)
−0.932345 + 0.361569i \(0.882241\pi\)
\(524\) −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 0.723234 0.690604i \(-0.242655\pi\)
−0.959697 + 0.281037i \(0.909322\pi\)
\(542\) −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 0.724157 0.689635i \(-0.242229\pi\)
−0.959320 + 0.282321i \(0.908896\pi\)
\(548\) −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 −0.945473 0.325701i \(-0.894400\pi\)
0.754802 + 0.655953i \(0.227733\pi\)
\(558\) 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 0.711445 0.702742i \(-0.248041\pi\)
−0.964315 + 0.264758i \(0.914708\pi\)
\(564\) 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 −0.990668 0.136295i \(-0.956481\pi\)
0.613369 + 0.789797i \(0.289814\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 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 0.479337 + 0.877631i \(0.340877\pi\)
−0.999719 + 0.0236970i \(0.992456\pi\)
\(578\) −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 0.833408 0.552658i \(-0.186386\pi\)
−0.895320 + 0.445424i \(0.853053\pi\)
\(588\) 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 −0.919111 0.394000i \(-0.871091\pi\)
0.118342 0.992973i \(-0.462242\pi\)
\(594\) 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 0.509631 0.860393i \(-0.329782\pi\)
−0.999938 + 0.0111569i \(0.996449\pi\)
\(600\) 0 0
\(601\) −12.5000 21.6506i −0.509886 0.883148i −0.999934 0.0114528i \(-0.996354\pi\)
0.490049 0.871695i \(-0.336979\pi\)
\(602\) 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 −0.999178 0.0405396i \(-0.987092\pi\)
0.534697 + 0.845044i \(0.320426\pi\)
\(614\) −14.0000 + 24.2487i −0.564994 + 0.978598i
\(615\) 0 0
\(616\) 0 0
\(617\) −22.5000 + 38.9711i −0.905816 + 1.56892i −0.0859976 + 0.996295i \(0.527408\pi\)
−0.819818 + 0.572624i \(0.805926\pi\)
\(618\) 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 −0.424555 0.905402i \(-0.639569\pi\)
0.996379 0.0850262i \(-0.0270974\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −10.5000 + 18.1865i −0.413117 + 0.715540i
\(647\) 10.5000 18.1865i 0.412798 0.714986i −0.582397 0.812905i \(-0.697885\pi\)
0.995194 + 0.0979182i \(0.0312184\pi\)
\(648\) 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 0.893762 0.448542i \(-0.148057\pi\)
−0.835330 + 0.549749i \(0.814723\pi\)
\(660\) 0 0
\(661\) −11.0000 19.0526i −0.427850 0.741059i 0.568831 0.822454i \(-0.307396\pi\)
−0.996682 + 0.0813955i \(0.974062\pi\)
\(662\) −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 −0.976593 0.215096i \(-0.930993\pi\)
0.302017 0.953302i \(-0.402340\pi\)
\(674\) 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 −0.419380 0.907811i \(-0.637753\pi\)
0.995877 0.0907112i \(-0.0289140\pi\)
\(678\) 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 −0.939184 0.343413i \(-0.888417\pi\)
0.766997 + 0.641651i \(0.221750\pi\)
\(684\) 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 −0.0555386 0.998457i \(-0.517688\pi\)
0.892458 0.451130i \(-0.148979\pi\)
\(692\) −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 −0.999908 0.0135434i \(-0.995689\pi\)
0.511683 + 0.859174i \(0.329022\pi\)
\(710\) 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 0.971311 0.237814i \(-0.0764307\pi\)
−0.691608 + 0.722273i \(0.743097\pi\)
\(720\) 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 0.719948 0.694028i \(-0.244166\pi\)
−0.961020 + 0.276479i \(0.910832\pi\)
\(728\) 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 −0.996235 0.0866983i \(-0.972368\pi\)
0.573200 + 0.819415i \(0.305702\pi\)
\(740\) 1.50000 2.59808i 0.0551411 0.0955072i
\(741\) 0 0
\(742\) 0 0
\(743\) 10.5000 18.1865i 0.385208 0.667199i −0.606590 0.795015i \(-0.707463\pi\)
0.991798 + 0.127815i \(0.0407965\pi\)
\(744\) 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 −0.580696 0.814120i \(-0.697220\pi\)
0.995397 + 0.0958377i \(0.0305530\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) −13.5000 + 23.3827i −0.485561 + 0.841017i −0.999862 0.0165929i \(-0.994718\pi\)
0.514301 + 0.857610i \(0.328051\pi\)
\(774\) 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 0.500953 0.865474i \(-0.332983\pi\)
−0.999999 + 0.00110111i \(0.999650\pi\)
\(788\) 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