Properties

Label 882.2.f.g.295.1
Level $882$
Weight $2$
Character 882.295
Analytic conductor $7.043$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
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 295.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 882.295
Dual form 882.2.f.g.589.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.73205i q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.50000 + 2.59808i) q^{5} +1.73205i q^{6} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +3.00000 q^{10} +(1.50000 - 2.59808i) q^{11} +(1.50000 + 0.866025i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-4.50000 - 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} -3.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} +7.00000 q^{19} +(1.50000 - 2.59808i) q^{20} +(-1.50000 - 2.59808i) q^{22} +(4.50000 + 7.79423i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-2.00000 + 3.46410i) q^{25} -1.00000 q^{26} +5.19615i q^{27} +(-1.50000 + 2.59808i) q^{29} +(-4.50000 + 2.59808i) q^{30} +(4.00000 + 6.92820i) q^{31} +(0.500000 + 0.866025i) q^{32} +5.19615i q^{33} +(-1.50000 + 2.59808i) q^{34} -3.00000 q^{36} -1.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +(1.50000 + 0.866025i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(1.50000 + 2.59808i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +9.00000 q^{45} +9.00000 q^{46} -1.73205i q^{48} +(2.00000 + 3.46410i) q^{50} +(4.50000 - 2.59808i) q^{51} +(-0.500000 + 0.866025i) q^{52} +3.00000 q^{53} +(4.50000 + 2.59808i) q^{54} +9.00000 q^{55} +(-10.5000 + 6.06218i) q^{57} +(1.50000 + 2.59808i) q^{58} +5.19615i q^{60} +(1.00000 - 1.73205i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(4.50000 + 2.59808i) q^{66} +(2.00000 + 3.46410i) q^{67} +(1.50000 + 2.59808i) q^{68} +(-13.5000 - 7.79423i) q^{69} +12.0000 q^{71} +(-1.50000 + 2.59808i) q^{72} -11.0000 q^{73} +(-0.500000 + 0.866025i) q^{74} -6.92820i q^{75} +(-3.50000 - 6.06218i) q^{76} +(1.50000 - 0.866025i) q^{78} +(8.00000 - 13.8564i) q^{79} -3.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} +3.00000 q^{82} +(-4.50000 + 7.79423i) q^{83} +(-4.50000 - 7.79423i) q^{85} +(-0.500000 - 0.866025i) q^{86} -5.19615i q^{87} +(-1.50000 + 2.59808i) q^{88} -3.00000 q^{89} +(4.50000 - 7.79423i) q^{90} +(4.50000 - 7.79423i) q^{92} +(-12.0000 - 6.92820i) q^{93} +(10.5000 + 18.1865i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(-0.500000 + 0.866025i) q^{97} +(-4.50000 - 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - 3q^{3} - q^{4} + 3q^{5} - 2q^{8} + 3q^{9} + O(q^{10}) \) \( 2q + q^{2} - 3q^{3} - q^{4} + 3q^{5} - 2q^{8} + 3q^{9} + 6q^{10} + 3q^{11} + 3q^{12} - q^{13} - 9q^{15} - q^{16} - 6q^{17} - 3q^{18} + 14q^{19} + 3q^{20} - 3q^{22} + 9q^{23} + 3q^{24} - 4q^{25} - 2q^{26} - 3q^{29} - 9q^{30} + 8q^{31} + q^{32} - 3q^{34} - 6q^{36} - 2q^{37} + 7q^{38} + 3q^{39} - 3q^{40} + 3q^{41} + q^{43} - 6q^{44} + 18q^{45} + 18q^{46} + 4q^{50} + 9q^{51} - q^{52} + 6q^{53} + 9q^{54} + 18q^{55} - 21q^{57} + 3q^{58} + 2q^{61} + 16q^{62} + 2q^{64} + 3q^{65} + 9q^{66} + 4q^{67} + 3q^{68} - 27q^{69} + 24q^{71} - 3q^{72} - 22q^{73} - q^{74} - 7q^{76} + 3q^{78} + 16q^{79} - 6q^{80} - 9q^{81} + 6q^{82} - 9q^{83} - 9q^{85} - q^{86} - 3q^{88} - 6q^{89} + 9q^{90} + 9q^{92} - 24q^{93} + 21q^{95} - 3q^{96} - q^{97} - 9q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(3\) −1.50000 + 0.866025i −0.866025 + 0.500000i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.50000 + 2.59808i 0.670820 + 1.16190i 0.977672 + 0.210138i \(0.0673912\pi\)
−0.306851 + 0.951757i \(0.599275\pi\)
\(6\) 1.73205i 0.707107i
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 3.00000 0.948683
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 1.50000 + 0.866025i 0.433013 + 0.250000i
\(13\) −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
\(15\) −4.50000 2.59808i −1.16190 0.670820i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) −1.50000 2.59808i −0.353553 0.612372i
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 1.50000 2.59808i 0.335410 0.580948i
\(21\) 0 0
\(22\) −1.50000 2.59808i −0.319801 0.553912i
\(23\) 4.50000 + 7.79423i 0.938315 + 1.62521i 0.768613 + 0.639713i \(0.220947\pi\)
0.169701 + 0.985496i \(0.445720\pi\)
\(24\) 1.50000 0.866025i 0.306186 0.176777i
\(25\) −2.00000 + 3.46410i −0.400000 + 0.692820i
\(26\) −1.00000 −0.196116
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) −4.50000 + 2.59808i −0.821584 + 0.474342i
\(31\) 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
\(33\) 5.19615i 0.904534i
\(34\) −1.50000 + 2.59808i −0.257248 + 0.445566i
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 3.50000 6.06218i 0.567775 0.983415i
\(39\) 1.50000 + 0.866025i 0.240192 + 0.138675i
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) 1.50000 + 2.59808i 0.234261 + 0.405751i 0.959058 0.283211i \(-0.0913998\pi\)
−0.724797 + 0.688963i \(0.758066\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) −3.00000 −0.452267
\(45\) 9.00000 1.34164
\(46\) 9.00000 1.32698
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 1.73205i 0.250000i
\(49\) 0 0
\(50\) 2.00000 + 3.46410i 0.282843 + 0.489898i
\(51\) 4.50000 2.59808i 0.630126 0.363803i
\(52\) −0.500000 + 0.866025i −0.0693375 + 0.120096i
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 4.50000 + 2.59808i 0.612372 + 0.353553i
\(55\) 9.00000 1.21356
\(56\) 0 0
\(57\) −10.5000 + 6.06218i −1.39076 + 0.802955i
\(58\) 1.50000 + 2.59808i 0.196960 + 0.341144i
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 5.19615i 0.670820i
\(61\) 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
\(66\) 4.50000 + 2.59808i 0.553912 + 0.319801i
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) 1.50000 + 2.59808i 0.181902 + 0.315063i
\(69\) −13.5000 7.79423i −1.62521 0.938315i
\(70\) 0 0
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) −11.0000 −1.28745 −0.643726 0.765256i \(-0.722612\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(74\) −0.500000 + 0.866025i −0.0581238 + 0.100673i
\(75\) 6.92820i 0.800000i
\(76\) −3.50000 6.06218i −0.401478 0.695379i
\(77\) 0 0
\(78\) 1.50000 0.866025i 0.169842 0.0980581i
\(79\) 8.00000 13.8564i 0.900070 1.55897i 0.0726692 0.997356i \(-0.476848\pi\)
0.827401 0.561611i \(-0.189818\pi\)
\(80\) −3.00000 −0.335410
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 3.00000 0.331295
\(83\) −4.50000 + 7.79423i −0.493939 + 0.855528i −0.999976 0.00698436i \(-0.997777\pi\)
0.506036 + 0.862512i \(0.331110\pi\)
\(84\) 0 0
\(85\) −4.50000 7.79423i −0.488094 0.845403i
\(86\) −0.500000 0.866025i −0.0539164 0.0933859i
\(87\) 5.19615i 0.557086i
\(88\) −1.50000 + 2.59808i −0.159901 + 0.276956i
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 4.50000 7.79423i 0.474342 0.821584i
\(91\) 0 0
\(92\) 4.50000 7.79423i 0.469157 0.812605i
\(93\) −12.0000 6.92820i −1.24434 0.718421i
\(94\) 0 0
\(95\) 10.5000 + 18.1865i 1.07728 + 1.86590i
\(96\) −1.50000 0.866025i −0.153093 0.0883883i
\(97\) −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
\(99\) −4.50000 7.79423i −0.452267 0.783349i
\(100\) 4.00000 0.400000
\(101\) 1.50000 2.59808i 0.149256 0.258518i −0.781697 0.623658i \(-0.785646\pi\)
0.930953 + 0.365140i \(0.118979\pi\)
\(102\) 5.19615i 0.514496i
\(103\) −6.50000 11.2583i −0.640464 1.10932i −0.985329 0.170664i \(-0.945409\pi\)
0.344865 0.938652i \(-0.387925\pi\)
\(104\) 0.500000 + 0.866025i 0.0490290 + 0.0849208i
\(105\) 0 0
\(106\) 1.50000 2.59808i 0.145693 0.252347i
\(107\) 9.00000 0.870063 0.435031 0.900415i \(-0.356737\pi\)
0.435031 + 0.900415i \(0.356737\pi\)
\(108\) 4.50000 2.59808i 0.433013 0.250000i
\(109\) −13.0000 −1.24517 −0.622587 0.782551i \(-0.713918\pi\)
−0.622587 + 0.782551i \(0.713918\pi\)
\(110\) 4.50000 7.79423i 0.429058 0.743151i
\(111\) 1.50000 0.866025i 0.142374 0.0821995i
\(112\) 0 0
\(113\) 4.50000 + 7.79423i 0.423324 + 0.733219i 0.996262 0.0863794i \(-0.0275297\pi\)
−0.572938 + 0.819599i \(0.694196\pi\)
\(114\) 12.1244i 1.13555i
\(115\) −13.5000 + 23.3827i −1.25888 + 2.18045i
\(116\) 3.00000 0.278543
\(117\) −3.00000 −0.277350
\(118\) 0 0
\(119\) 0 0
\(120\) 4.50000 + 2.59808i 0.410792 + 0.237171i
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −1.00000 1.73205i −0.0905357 0.156813i
\(123\) −4.50000 2.59808i −0.405751 0.234261i
\(124\) 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
\(129\) 1.73205i 0.152499i
\(130\) −1.50000 2.59808i −0.131559 0.227866i
\(131\) 7.50000 + 12.9904i 0.655278 + 1.13497i 0.981824 + 0.189794i \(0.0607819\pi\)
−0.326546 + 0.945181i \(0.605885\pi\)
\(132\) 4.50000 2.59808i 0.391675 0.226134i
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) −13.5000 + 7.79423i −1.16190 + 0.670820i
\(136\) 3.00000 0.257248
\(137\) 4.50000 7.79423i 0.384461 0.665906i −0.607233 0.794524i \(-0.707721\pi\)
0.991694 + 0.128618i \(0.0410540\pi\)
\(138\) −13.5000 + 7.79423i −1.14920 + 0.663489i
\(139\) −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
\(143\) −3.00000 −0.250873
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) −9.00000 −0.747409
\(146\) −5.50000 + 9.52628i −0.455183 + 0.788400i
\(147\) 0 0
\(148\) 0.500000 + 0.866025i 0.0410997 + 0.0711868i
\(149\) 4.50000 + 7.79423i 0.368654 + 0.638528i 0.989355 0.145519i \(-0.0464853\pi\)
−0.620701 + 0.784047i \(0.713152\pi\)
\(150\) −6.00000 3.46410i −0.489898 0.282843i
\(151\) 3.50000 6.06218i 0.284826 0.493333i −0.687741 0.725956i \(-0.741398\pi\)
0.972567 + 0.232623i \(0.0747309\pi\)
\(152\) −7.00000 −0.567775
\(153\) −4.50000 + 7.79423i −0.363803 + 0.630126i
\(154\) 0 0
\(155\) −12.0000 + 20.7846i −0.963863 + 1.66946i
\(156\) 1.73205i 0.138675i
\(157\) −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
\(159\) −4.50000 + 2.59808i −0.356873 + 0.206041i
\(160\) −1.50000 + 2.59808i −0.118585 + 0.205396i
\(161\) 0 0
\(162\) −9.00000 −0.707107
\(163\) −19.0000 −1.48819 −0.744097 0.668071i \(-0.767120\pi\)
−0.744097 + 0.668071i \(0.767120\pi\)
\(164\) 1.50000 2.59808i 0.117130 0.202876i
\(165\) −13.5000 + 7.79423i −1.05097 + 0.606780i
\(166\) 4.50000 + 7.79423i 0.349268 + 0.604949i
\(167\) −7.50000 12.9904i −0.580367 1.00523i −0.995436 0.0954356i \(-0.969576\pi\)
0.415068 0.909790i \(-0.363758\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) −9.00000 −0.690268
\(171\) 10.5000 18.1865i 0.802955 1.39076i
\(172\) −1.00000 −0.0762493
\(173\) −3.00000 + 5.19615i −0.228086 + 0.395056i −0.957241 0.289292i \(-0.906580\pi\)
0.729155 + 0.684349i \(0.239913\pi\)
\(174\) −4.50000 2.59808i −0.341144 0.196960i
\(175\) 0 0
\(176\) 1.50000 + 2.59808i 0.113067 + 0.195837i
\(177\) 0 0
\(178\) −1.50000 + 2.59808i −0.112430 + 0.194734i
\(179\) −21.0000 −1.56961 −0.784807 0.619740i \(-0.787238\pi\)
−0.784807 + 0.619740i \(0.787238\pi\)
\(180\) −4.50000 7.79423i −0.335410 0.580948i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 3.46410i 0.256074i
\(184\) −4.50000 7.79423i −0.331744 0.574598i
\(185\) −1.50000 2.59808i −0.110282 0.191014i
\(186\) −12.0000 + 6.92820i −0.879883 + 0.508001i
\(187\) −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 \(0.166667\pi\)
\(192\) −1.50000 + 0.866025i −0.108253 + 0.0625000i
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 0.500000 + 0.866025i 0.0358979 + 0.0621770i
\(195\) 5.19615i 0.372104i
\(196\) 0 0
\(197\) 18.0000 1.28245 0.641223 0.767354i \(-0.278427\pi\)
0.641223 + 0.767354i \(0.278427\pi\)
\(198\) −9.00000 −0.639602
\(199\) 25.0000 1.77220 0.886102 0.463491i \(-0.153403\pi\)
0.886102 + 0.463491i \(0.153403\pi\)
\(200\) 2.00000 3.46410i 0.141421 0.244949i
\(201\) −6.00000 3.46410i −0.423207 0.244339i
\(202\) −1.50000 2.59808i −0.105540 0.182800i
\(203\) 0 0
\(204\) −4.50000 2.59808i −0.315063 0.181902i
\(205\) −4.50000 + 7.79423i −0.314294 + 0.544373i
\(206\) −13.0000 −0.905753
\(207\) 27.0000 1.87663
\(208\) 1.00000 0.0693375
\(209\) 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 \(0.888391\pi\)
\(212\) −1.50000 2.59808i −0.103020 0.178437i
\(213\) −18.0000 + 10.3923i −1.23334 + 0.712069i
\(214\) 4.50000 7.79423i 0.307614 0.532803i
\(215\) 3.00000 0.204598
\(216\) 5.19615i 0.353553i
\(217\) 0 0
\(218\) −6.50000 + 11.2583i −0.440236 + 0.762510i
\(219\) 16.5000 9.52628i 1.11497 0.643726i
\(220\) −4.50000 7.79423i −0.303390 0.525487i
\(221\) 1.50000 + 2.59808i 0.100901 + 0.174766i
\(222\) 1.73205i 0.116248i
\(223\) −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
\(225\) 6.00000 + 10.3923i 0.400000 + 0.692820i
\(226\) 9.00000 0.598671
\(227\) −1.50000 + 2.59808i −0.0995585 + 0.172440i −0.911502 0.411296i \(-0.865076\pi\)
0.811943 + 0.583736i \(0.198410\pi\)
\(228\) 10.5000 + 6.06218i 0.695379 + 0.401478i
\(229\) −6.50000 11.2583i −0.429532 0.743971i 0.567300 0.823511i \(-0.307988\pi\)
−0.996832 + 0.0795401i \(0.974655\pi\)
\(230\) 13.5000 + 23.3827i 0.890164 + 1.54181i
\(231\) 0 0
\(232\) 1.50000 2.59808i 0.0984798 0.170572i
\(233\) 3.00000 0.196537 0.0982683 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) −1.50000 + 2.59808i −0.0980581 + 0.169842i
\(235\) 0 0
\(236\) 0 0
\(237\) 27.7128i 1.80014i
\(238\) 0 0
\(239\) 1.50000 + 2.59808i 0.0970269 + 0.168056i 0.910453 0.413613i \(-0.135733\pi\)
−0.813426 + 0.581669i \(0.802400\pi\)
\(240\) 4.50000 2.59808i 0.290474 0.167705i
\(241\) −6.50000 + 11.2583i −0.418702 + 0.725213i −0.995809 0.0914555i \(-0.970848\pi\)
0.577107 + 0.816668i \(0.304181\pi\)
\(242\) 2.00000 0.128565
\(243\) 13.5000 + 7.79423i 0.866025 + 0.500000i
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) −4.50000 + 2.59808i −0.286910 + 0.165647i
\(247\) −3.50000 6.06218i −0.222700 0.385727i
\(248\) −4.00000 6.92820i −0.254000 0.439941i
\(249\) 15.5885i 0.987878i
\(250\) 1.50000 2.59808i 0.0948683 0.164317i
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) −2.00000 + 3.46410i −0.125491 + 0.217357i
\(255\) 13.5000 + 7.79423i 0.845403 + 0.488094i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −10.5000 18.1865i −0.654972 1.13444i −0.981901 0.189396i \(-0.939347\pi\)
0.326929 0.945049i \(-0.393986\pi\)
\(258\) 1.50000 + 0.866025i 0.0933859 + 0.0539164i
\(259\) 0 0
\(260\) −3.00000 −0.186052
\(261\) 4.50000 + 7.79423i 0.278543 + 0.482451i
\(262\) 15.0000 0.926703
\(263\) −4.50000 + 7.79423i −0.277482 + 0.480613i −0.970758 0.240059i \(-0.922833\pi\)
0.693276 + 0.720672i \(0.256167\pi\)
\(264\) 5.19615i 0.319801i
\(265\) 4.50000 + 7.79423i 0.276433 + 0.478796i
\(266\) 0 0
\(267\) 4.50000 2.59808i 0.275396 0.159000i
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) −15.0000 −0.914566 −0.457283 0.889321i \(-0.651177\pi\)
−0.457283 + 0.889321i \(0.651177\pi\)
\(270\) 15.5885i 0.948683i
\(271\) −5.00000 −0.303728 −0.151864 0.988401i \(-0.548528\pi\)
−0.151864 + 0.988401i \(0.548528\pi\)
\(272\) 1.50000 2.59808i 0.0909509 0.157532i
\(273\) 0 0
\(274\) −4.50000 7.79423i −0.271855 0.470867i
\(275\) 6.00000 + 10.3923i 0.361814 + 0.626680i
\(276\) 15.5885i 0.938315i
\(277\) 0.500000 0.866025i 0.0300421 0.0520344i −0.850613 0.525792i \(-0.823769\pi\)
0.880656 + 0.473757i \(0.157103\pi\)
\(278\) −7.00000 −0.419832
\(279\) 24.0000 1.43684
\(280\) 0 0
\(281\) 10.5000 18.1865i 0.626377 1.08492i −0.361895 0.932219i \(-0.617870\pi\)
0.988273 0.152699i \(-0.0487965\pi\)
\(282\) 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
\(285\) −31.5000 18.1865i −1.86590 1.07728i
\(286\) −1.50000 + 2.59808i −0.0886969 + 0.153627i
\(287\) 0 0
\(288\) 3.00000 0.176777
\(289\) −8.00000 −0.470588
\(290\) −4.50000 + 7.79423i −0.264249 + 0.457693i
\(291\) 1.73205i 0.101535i
\(292\) 5.50000 + 9.52628i 0.321863 + 0.557483i
\(293\) −4.50000 7.79423i −0.262893 0.455344i 0.704117 0.710084i \(-0.251343\pi\)
−0.967009 + 0.254741i \(0.918010\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 0.0581238
\(297\) 13.5000 + 7.79423i 0.783349 + 0.452267i
\(298\) 9.00000 0.521356
\(299\) 4.50000 7.79423i 0.260242 0.450752i
\(300\) −6.00000 + 3.46410i −0.346410 + 0.200000i
\(301\) 0 0
\(302\) −3.50000 6.06218i −0.201402 0.348839i
\(303\) 5.19615i 0.298511i
\(304\) −3.50000 + 6.06218i −0.200739 + 0.347690i
\(305\) 6.00000 0.343559
\(306\) 4.50000 + 7.79423i 0.257248 + 0.445566i
\(307\) 28.0000 1.59804 0.799022 0.601302i \(-0.205351\pi\)
0.799022 + 0.601302i \(0.205351\pi\)
\(308\) 0 0
\(309\) 19.5000 + 11.2583i 1.10932 + 0.640464i
\(310\) 12.0000 + 20.7846i 0.681554 + 1.18049i
\(311\) −12.0000 20.7846i −0.680458 1.17859i −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) −1.50000 0.866025i −0.0849208 0.0490290i
\(313\) −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 \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 5.19615i 0.291386i
\(319\) 4.50000 + 7.79423i 0.251952 + 0.436393i
\(320\) 1.50000 + 2.59808i 0.0838525 + 0.145237i
\(321\) −13.5000 + 7.79423i −0.753497 + 0.435031i
\(322\) 0 0
\(323\) −21.0000 −1.16847
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) 4.00000 0.221880
\(326\) −9.50000 + 16.4545i −0.526156 + 0.911330i
\(327\) 19.5000 11.2583i 1.07835 0.622587i
\(328\) −1.50000 2.59808i −0.0828236 0.143455i
\(329\) 0 0
\(330\) 15.5885i 0.858116i
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) 9.00000 0.493939
\(333\) −1.50000 + 2.59808i −0.0821995 + 0.142374i
\(334\) −15.0000 −0.820763
\(335\) −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 \(0.718128\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) −13.5000 7.79423i −0.733219 0.423324i
\(340\) −4.50000 + 7.79423i −0.244047 + 0.422701i
\(341\) 24.0000 1.29967
\(342\) −10.5000 18.1865i −0.567775 0.983415i
\(343\) 0 0
\(344\) −0.500000 + 0.866025i −0.0269582 + 0.0466930i
\(345\) 46.7654i 2.51776i
\(346\) 3.00000 + 5.19615i 0.161281 + 0.279347i
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) −4.50000 + 2.59808i −0.241225 + 0.139272i
\(349\) 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
\(351\) 4.50000 2.59808i 0.240192 0.138675i
\(352\) 3.00000 0.159901
\(353\) 1.50000 2.59808i 0.0798369 0.138282i −0.823343 0.567545i \(-0.807893\pi\)
0.903179 + 0.429263i \(0.141227\pi\)
\(354\) 0 0
\(355\) 18.0000 + 31.1769i 0.955341 + 1.65470i
\(356\) 1.50000 + 2.59808i 0.0794998 + 0.137698i
\(357\) 0 0
\(358\) −10.5000 + 18.1865i −0.554942 + 0.961188i
\(359\) 9.00000 0.475002 0.237501 0.971387i \(-0.423672\pi\)
0.237501 + 0.971387i \(0.423672\pi\)
\(360\) −9.00000 −0.474342
\(361\) 30.0000 1.57895
\(362\) −1.00000 + 1.73205i −0.0525588 + 0.0910346i
\(363\) −3.00000 1.73205i −0.157459 0.0909091i
\(364\) 0 0
\(365\) −16.5000 28.5788i −0.863649 1.49588i
\(366\) 3.00000 + 1.73205i 0.156813 + 0.0905357i
\(367\) 8.50000 14.7224i 0.443696 0.768505i −0.554264 0.832341i \(-0.687000\pi\)
0.997960 + 0.0638362i \(0.0203335\pi\)
\(368\) −9.00000 −0.469157
\(369\) 9.00000 0.468521
\(370\) −3.00000 −0.155963
\(371\) 0 0
\(372\) 13.8564i 0.718421i
\(373\) 6.50000 + 11.2583i 0.336557 + 0.582934i 0.983783 0.179364i \(-0.0574041\pi\)
−0.647225 + 0.762299i \(0.724071\pi\)
\(374\) 4.50000 + 7.79423i 0.232689 + 0.403030i
\(375\) −4.50000 + 2.59808i −0.232379 + 0.134164i
\(376\) 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
\(381\) 6.00000 3.46410i 0.307389 0.177471i
\(382\) 0 0
\(383\) 7.50000 + 12.9904i 0.383232 + 0.663777i 0.991522 0.129937i \(-0.0414776\pi\)
−0.608290 + 0.793715i \(0.708144\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) −1.50000 2.59808i −0.0762493 0.132068i
\(388\) 1.00000 0.0507673
\(389\) −13.5000 + 23.3827i −0.684477 + 1.18555i 0.289124 + 0.957292i \(0.406636\pi\)
−0.973601 + 0.228257i \(0.926697\pi\)
\(390\) 4.50000 + 2.59808i 0.227866 + 0.131559i
\(391\) −13.5000 23.3827i −0.682724 1.18251i
\(392\) 0 0
\(393\) −22.5000 12.9904i −1.13497 0.655278i
\(394\) 9.00000 15.5885i 0.453413 0.785335i
\(395\) 48.0000 2.41514
\(396\) −4.50000 + 7.79423i −0.226134 + 0.391675i
\(397\) 13.0000 0.652451 0.326226 0.945292i \(-0.394223\pi\)
0.326226 + 0.945292i \(0.394223\pi\)
\(398\) 12.5000 21.6506i 0.626568 1.08525i
\(399\) 0 0
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −13.5000 23.3827i −0.674158 1.16768i −0.976714 0.214544i \(-0.931173\pi\)
0.302556 0.953131i \(-0.402160\pi\)
\(402\) −6.00000 + 3.46410i −0.299253 + 0.172774i
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) −3.00000 −0.149256
\(405\) 13.5000 23.3827i 0.670820 1.16190i
\(406\) 0 0
\(407\) −1.50000 + 2.59808i −0.0743522 + 0.128782i
\(408\) −4.50000 + 2.59808i −0.222783 + 0.128624i
\(409\) −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
\(411\) 15.5885i 0.768922i
\(412\) −6.50000 + 11.2583i −0.320232 + 0.554658i
\(413\) 0 0
\(414\) 13.5000 23.3827i 0.663489 1.14920i
\(415\) −27.0000 −1.32538
\(416\) 0.500000 0.866025i 0.0245145 0.0424604i
\(417\) 10.5000 + 6.06218i 0.514187 + 0.296866i
\(418\) −10.5000 18.1865i −0.513572 0.889532i
\(419\) 4.50000 + 7.79423i 0.219839 + 0.380773i 0.954759 0.297382i \(-0.0961133\pi\)
−0.734919 + 0.678155i \(0.762780\pi\)
\(420\) 0 0
\(421\) −17.5000 + 30.3109i −0.852898 + 1.47726i 0.0256838 + 0.999670i \(0.491824\pi\)
−0.878582 + 0.477592i \(0.841510\pi\)
\(422\) −5.00000 −0.243396
\(423\) 0 0
\(424\) −3.00000 −0.145693
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) 20.7846i 1.00702i
\(427\) 0 0
\(428\) −4.50000 7.79423i −0.217516 0.376748i
\(429\) 4.50000 2.59808i 0.217262 0.125436i
\(430\) 1.50000 2.59808i 0.0723364 0.125290i
\(431\) 27.0000 1.30054 0.650272 0.759701i \(-0.274655\pi\)
0.650272 + 0.759701i \(0.274655\pi\)
\(432\) −4.50000 2.59808i −0.216506 0.125000i
\(433\) −2.00000 −0.0961139 −0.0480569 0.998845i \(-0.515303\pi\)
−0.0480569 + 0.998845i \(0.515303\pi\)
\(434\) 0 0
\(435\) 13.5000 7.79423i 0.647275 0.373705i
\(436\) 6.50000 + 11.2583i 0.311294 + 0.539176i
\(437\) 31.5000 + 54.5596i 1.50685 + 2.60994i
\(438\) 19.0526i 0.910366i
\(439\) 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 \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) −1.50000 0.866025i −0.0711868 0.0410997i
\(445\) −4.50000 7.79423i −0.213320 0.369482i
\(446\) 0.500000 + 0.866025i 0.0236757 + 0.0410075i
\(447\) −13.5000 7.79423i −0.638528 0.368654i
\(448\) 0 0
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 12.0000 0.565685
\(451\) 9.00000 0.423793
\(452\) 4.50000 7.79423i 0.211662 0.366610i
\(453\) 12.1244i 0.569652i
\(454\) 1.50000 + 2.59808i 0.0703985 + 0.121934i
\(455\) 0 0
\(456\) 10.5000 6.06218i 0.491708 0.283887i
\(457\) 5.00000 8.66025i 0.233890 0.405110i −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) −13.0000 −0.607450
\(459\) 15.5885i 0.727607i
\(460\) 27.0000 1.25888
\(461\) −4.50000 + 7.79423i −0.209586 + 0.363013i −0.951584 0.307388i \(-0.900545\pi\)
0.741998 + 0.670402i \(0.233878\pi\)
\(462\) 0 0
\(463\) −20.5000 35.5070i −0.952716 1.65015i −0.739511 0.673145i \(-0.764943\pi\)
−0.213205 0.977007i \(-0.568390\pi\)
\(464\) −1.50000 2.59808i −0.0696358 0.120613i
\(465\) 41.5692i 1.92773i
\(466\) 1.50000 2.59808i 0.0694862 0.120354i
\(467\) 3.00000 0.138823 0.0694117 0.997588i \(-0.477888\pi\)
0.0694117 + 0.997588i \(0.477888\pi\)
\(468\) 1.50000 + 2.59808i 0.0693375 + 0.120096i
\(469\) 0 0
\(470\) 0 0
\(471\) 33.0000 + 19.0526i 1.52056 + 0.877896i
\(472\) 0 0
\(473\) −1.50000 2.59808i −0.0689701 0.119460i
\(474\) 24.0000 + 13.8564i 1.10236 + 0.636446i
\(475\) −14.0000 + 24.2487i −0.642364 + 1.11261i
\(476\) 0 0
\(477\) 4.50000 7.79423i 0.206041 0.356873i
\(478\) 3.00000 0.137217
\(479\) −1.50000 + 2.59808i −0.0685367 + 0.118709i −0.898257 0.439470i \(-0.855166\pi\)
0.829721 + 0.558179i \(0.188500\pi\)
\(480\) 5.19615i 0.237171i
\(481\) 0.500000 + 0.866025i 0.0227980 + 0.0394874i
\(482\) 6.50000 + 11.2583i 0.296067 + 0.512803i
\(483\) 0 0
\(484\) 1.00000 1.73205i 0.0454545 0.0787296i
\(485\) −3.00000 −0.136223
\(486\) 13.5000 7.79423i 0.612372 0.353553i
\(487\) −25.0000 −1.13286 −0.566429 0.824110i \(-0.691675\pi\)
−0.566429 + 0.824110i \(0.691675\pi\)
\(488\) −1.00000 + 1.73205i −0.0452679 + 0.0784063i
\(489\) 28.5000 16.4545i 1.28881 0.744097i
\(490\) 0 0
\(491\) −10.5000 18.1865i −0.473858 0.820747i 0.525694 0.850674i \(-0.323806\pi\)
−0.999552 + 0.0299272i \(0.990472\pi\)
\(492\) 5.19615i 0.234261i
\(493\) 4.50000 7.79423i 0.202670 0.351034i
\(494\) −7.00000 −0.314945
\(495\) 13.5000 23.3827i 0.606780 1.05097i
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) −13.5000 7.79423i −0.604949 0.349268i
\(499\) 12.5000 + 21.6506i 0.559577 + 0.969216i 0.997532 + 0.0702185i \(0.0223697\pi\)
−0.437955 + 0.898997i \(0.644297\pi\)
\(500\) −1.50000 2.59808i −0.0670820 0.116190i
\(501\) 22.5000 + 12.9904i 1.00523 + 0.580367i
\(502\) −6.00000 + 10.3923i −0.267793 + 0.463831i
\(503\) 24.0000 1.07011 0.535054 0.844818i \(-0.320291\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(504\) 0 0
\(505\) 9.00000 0.400495
\(506\) 13.5000 23.3827i 0.600148 1.03949i
\(507\) 20.7846i 0.923077i
\(508\) 2.00000 + 3.46410i 0.0887357 + 0.153695i
\(509\) −4.50000 7.79423i −0.199459 0.345473i 0.748894 0.662690i \(-0.230585\pi\)
−0.948353 + 0.317217i \(0.897252\pi\)
\(510\) 13.5000 7.79423i 0.597790 0.345134i
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 36.3731i 1.60591i
\(514\) −21.0000 −0.926270
\(515\) 19.5000 33.7750i 0.859273 1.48830i
\(516\) 1.50000 0.866025i 0.0660338 0.0381246i
\(517\) 0 0
\(518\) 0 0
\(519\) 10.3923i 0.456172i
\(520\) −1.50000 + 2.59808i −0.0657794 + 0.113933i
\(521\) −3.00000 −0.131432 −0.0657162 0.997838i \(-0.520933\pi\)
−0.0657162 + 0.997838i \(0.520933\pi\)
\(522\) 9.00000 0.393919
\(523\) 7.00000 0.306089 0.153044 0.988219i \(-0.451092\pi\)
0.153044 + 0.988219i \(0.451092\pi\)
\(524\) 7.50000 12.9904i 0.327639 0.567487i
\(525\) 0 0
\(526\) 4.50000 + 7.79423i 0.196209 + 0.339845i
\(527\) −12.0000 20.7846i −0.522728 0.905392i
\(528\) −4.50000 2.59808i −0.195837 0.113067i
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) 9.00000 0.390935
\(531\) 0 0
\(532\) 0 0
\(533\) 1.50000 2.59808i 0.0649722 0.112535i
\(534\) 5.19615i 0.224860i
\(535\) 13.5000 + 23.3827i 0.583656 + 1.01092i
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) 31.5000 18.1865i 1.35933 0.784807i
\(538\) −7.50000 + 12.9904i −0.323348 + 0.560055i
\(539\) 0 0
\(540\) 13.5000 + 7.79423i 0.580948 + 0.335410i
\(541\) 11.0000 0.472927 0.236463 0.971640i \(-0.424012\pi\)
0.236463 + 0.971640i \(0.424012\pi\)
\(542\) −2.50000 + 4.33013i −0.107384 + 0.185995i
\(543\) 3.00000 1.73205i 0.128742 0.0743294i
\(544\) −1.50000 2.59808i −0.0643120 0.111392i
\(545\) −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 \(0.242229\pi\)
\(548\) −9.00000 −0.384461
\(549\) −3.00000 5.19615i −0.128037 0.221766i
\(550\) 12.0000 0.511682
\(551\) −10.5000 + 18.1865i −0.447315 + 0.774772i
\(552\) 13.5000 + 7.79423i 0.574598 + 0.331744i
\(553\) 0 0
\(554\) −0.500000 0.866025i −0.0212430 0.0367939i
\(555\) 4.50000 + 2.59808i 0.191014 + 0.110282i
\(556\) −3.50000 + 6.06218i −0.148433 + 0.257094i
\(557\) −9.00000 −0.381342 −0.190671 0.981654i \(-0.561066\pi\)
−0.190671 + 0.981654i \(0.561066\pi\)
\(558\) 12.0000 20.7846i 0.508001 0.879883i
\(559\) −1.00000 −0.0422955
\(560\) 0 0
\(561\) 15.5885i 0.658145i
\(562\) −10.5000 18.1865i −0.442916 0.767153i
\(563\) 6.00000 + 10.3923i 0.252870 + 0.437983i 0.964315 0.264758i \(-0.0852922\pi\)
−0.711445 + 0.702742i \(0.751959\pi\)
\(564\) 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 \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) −31.5000 + 18.1865i −1.31939 + 0.761750i
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 1.50000 + 2.59808i 0.0627182 + 0.108631i
\(573\) 0 0
\(574\) 0 0
\(575\) −36.0000 −1.50130
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) 25.0000 1.04076 0.520382 0.853934i \(-0.325790\pi\)
0.520382 + 0.853934i \(0.325790\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) 21.0000 + 12.1244i 0.872730 + 0.503871i
\(580\) 4.50000 + 7.79423i 0.186852 + 0.323638i
\(581\) 0 0
\(582\) −1.50000 0.866025i −0.0621770 0.0358979i
\(583\) 4.50000 7.79423i 0.186371 0.322804i
\(584\) 11.0000 0.455183
\(585\) −4.50000 7.79423i −0.186052 0.322252i
\(586\) −9.00000 −0.371787
\(587\) 1.50000 2.59808i 0.0619116 0.107234i −0.833408 0.552658i \(-0.813614\pi\)
0.895320 + 0.445424i \(0.146947\pi\)
\(588\) 0 0
\(589\) 28.0000 + 48.4974i 1.15372 + 1.99830i
\(590\) 0 0
\(591\) −27.0000 + 15.5885i −1.11063 + 0.641223i
\(592\) 0.500000 0.866025i 0.0205499 0.0355934i
\(593\) −39.0000 −1.60154 −0.800769 0.598973i \(-0.795576\pi\)
−0.800769 + 0.598973i \(0.795576\pi\)
\(594\) 13.5000 7.79423i 0.553912 0.319801i
\(595\) 0 0
\(596\) 4.50000 7.79423i 0.184327 0.319264i
\(597\) −37.5000 + 21.6506i −1.53477 + 0.886102i
\(598\) −4.50000 7.79423i −0.184019 0.318730i
\(599\) 12.0000 + 20.7846i 0.490307 + 0.849236i 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) 6.92820i 0.282843i
\(601\) −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
\(603\) 12.0000 0.488678
\(604\) −7.00000 −0.284826
\(605\) −3.00000 + 5.19615i −0.121967 + 0.211254i
\(606\) 4.50000 + 2.59808i 0.182800 + 0.105540i
\(607\) −6.50000 11.2583i −0.263827 0.456962i 0.703429 0.710766i \(-0.251651\pi\)
−0.967256 + 0.253804i \(0.918318\pi\)
\(608\) 3.50000 + 6.06218i 0.141944 + 0.245854i
\(609\) 0 0
\(610\) 3.00000 5.19615i 0.121466 0.210386i
\(611\) 0 0
\(612\) 9.00000 0.363803
\(613\) 23.0000 0.928961 0.464481 0.885583i \(-0.346241\pi\)
0.464481 + 0.885583i \(0.346241\pi\)
\(614\) 14.0000 24.2487i 0.564994 0.978598i
\(615\) 15.5885i 0.628587i
\(616\) 0 0
\(617\) 22.5000 + 38.9711i 0.905816 + 1.56892i 0.819818 + 0.572624i \(0.194074\pi\)
0.0859976 + 0.996295i \(0.472592\pi\)
\(618\) 19.5000 11.2583i 0.784405 0.452876i
\(619\) 8.50000 14.7224i 0.341644 0.591744i −0.643094 0.765787i \(-0.722350\pi\)
0.984738 + 0.174042i \(0.0556830\pi\)
\(620\) 24.0000 0.963863
\(621\) −40.5000 + 23.3827i −1.62521 + 0.938315i
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) −1.50000 + 0.866025i −0.0600481 + 0.0346688i
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 5.00000 + 8.66025i 0.199840 + 0.346133i
\(627\) 36.3731i 1.45260i
\(628\) −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
\(633\) 7.50000 + 4.33013i 0.298098 + 0.172107i
\(634\) 9.00000 + 15.5885i 0.357436 + 0.619097i
\(635\) −6.00000 10.3923i −0.238103 0.412406i
\(636\) 4.50000 + 2.59808i 0.178437 + 0.103020i
\(637\) 0 0
\(638\) 9.00000 0.356313
\(639\) 18.0000 31.1769i 0.712069 1.23334i
\(640\) 3.00000 0.118585
\(641\) 16.5000 28.5788i 0.651711 1.12880i −0.330997 0.943632i \(-0.607385\pi\)
0.982708 0.185164i \(-0.0592817\pi\)
\(642\) 15.5885i 0.615227i
\(643\) 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
\(645\) −4.50000 + 2.59808i −0.177187 + 0.102299i
\(646\) −10.5000 + 18.1865i −0.413117 + 0.715540i
\(647\) 21.0000 0.825595 0.412798 0.910823i \(-0.364552\pi\)
0.412798 + 0.910823i \(0.364552\pi\)
\(648\) 4.50000 + 7.79423i 0.176777 + 0.306186i
\(649\) 0 0
\(650\) 2.00000 3.46410i 0.0784465 0.135873i
\(651\) 0 0
\(652\) 9.50000 + 16.4545i 0.372049 + 0.644407i
\(653\) −7.50000 12.9904i −0.293498 0.508353i 0.681137 0.732156i \(-0.261486\pi\)
−0.974634 + 0.223803i \(0.928153\pi\)
\(654\) 22.5167i 0.880471i
\(655\) −22.5000 + 38.9711i −0.879148 + 1.52273i
\(656\) −3.00000 −0.117130
\(657\) −16.5000 + 28.5788i −0.643726 + 1.11497i
\(658\) 0 0
\(659\) −1.50000 + 2.59808i −0.0584317 + 0.101207i −0.893762 0.448542i \(-0.851943\pi\)
0.835330 + 0.549749i \(0.185277\pi\)
\(660\) 13.5000 + 7.79423i 0.525487 + 0.303390i
\(661\) −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
\(663\) −4.50000 2.59808i −0.174766 0.100901i
\(664\) 4.50000 7.79423i 0.174634 0.302475i
\(665\) 0 0
\(666\) 1.50000 + 2.59808i 0.0581238 + 0.100673i
\(667\) −27.0000 −1.04544
\(668\) −7.50000 + 12.9904i −0.290184 + 0.502613i
\(669\) 1.73205i 0.0669650i
\(670\) 6.00000 + 10.3923i 0.231800 + 0.401490i
\(671\) −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 \(0.930993\pi\)
\(674\) 13.0000 0.500741
\(675\) −18.0000 10.3923i −0.692820 0.400000i
\(676\) −12.0000 −0.461538
\(677\) −15.0000 + 25.9808i −0.576497 + 0.998522i 0.419380 + 0.907811i \(0.362247\pi\)
−0.995877 + 0.0907112i \(0.971086\pi\)
\(678\) −13.5000 + 7.79423i −0.518464 + 0.299336i
\(679\) 0 0
\(680\) 4.50000 + 7.79423i 0.172567 + 0.298895i
\(681\) 5.19615i 0.199117i
\(682\) 12.0000 20.7846i 0.459504 0.795884i
\(683\) −9.00000 −0.344375 −0.172188 0.985064i \(-0.555084\pi\)
−0.172188 + 0.985064i \(0.555084\pi\)
\(684\) −21.0000 −0.802955
\(685\) 27.0000 1.03162
\(686\) 0 0
\(687\) 19.5000 + 11.2583i 0.743971 + 0.429532i
\(688\) 0.500000 + 0.866025i 0.0190623 + 0.0330169i
\(689\) −1.50000 2.59808i −0.0571454 0.0989788i
\(690\) −40.5000 23.3827i −1.54181 0.890164i
\(691\) 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
\(696\) 5.19615i 0.196960i
\(697\) −4.50000 7.79423i −0.170450 0.295227i
\(698\) −11.5000 19.9186i −0.435281 0.753930i
\(699\) −4.50000 + 2.59808i −0.170206 + 0.0982683i
\(700\) 0 0
\(701\) −18.0000 −0.679851 −0.339925 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 5.19615i 0.196116i
\(703\) −7.00000 −0.264010
\(704\) 1.50000 2.59808i 0.0565334 0.0979187i
\(705\) 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 \(0.329022\pi\)
\(710\) 36.0000 1.35106
\(711\) −24.0000 41.5692i −0.900070 1.55897i
\(712\) 3.00000 0.112430
\(713\) −36.0000 + 62.3538i −1.34821 + 2.33517i
\(714\) 0 0
\(715\) −4.50000 7.79423i −0.168290 0.291488i
\(716\) 10.5000 + 18.1865i 0.392403 + 0.679663i
\(717\) −4.50000 2.59808i −0.168056 0.0970269i
\(718\) 4.50000 7.79423i 0.167939 0.290878i
\(719\) 15.0000 0.559406 0.279703 0.960087i \(-0.409764\pi\)
0.279703 + 0.960087i \(0.409764\pi\)
\(720\) −4.50000 + 7.79423i −0.167705 + 0.290474i
\(721\) 0 0
\(722\) 15.0000 25.9808i 0.558242 0.966904i
\(723\) 22.5167i 0.837404i
\(724\) 1.00000 + 1.73205i 0.0371647 + 0.0643712i
\(725\) −6.00000 10.3923i −0.222834 0.385961i
\(726\) −3.00000 + 1.73205i −0.111340 + 0.0642824i
\(727\) −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
\(729\) −27.0000 −1.00000
\(730\) −33.0000 −1.22138
\(731\) −1.50000 + 2.59808i −0.0554795 + 0.0960933i
\(732\) 3.00000 1.73205i 0.110883 0.0640184i
\(733\) −0.500000 0.866025i −0.0184679 0.0319874i 0.856644 0.515908i \(-0.172546\pi\)
−0.875112 + 0.483921i \(0.839212\pi\)
\(734\) −8.50000 14.7224i −0.313741 0.543415i
\(735\) 0 0
\(736\) −4.50000 + 7.79423i −0.165872 + 0.287299i
\(737\) 12.0000 0.442026
\(738\) 4.50000 7.79423i 0.165647 0.286910i
\(739\) 23.0000 0.846069 0.423034 0.906114i \(-0.360965\pi\)
0.423034 + 0.906114i \(0.360965\pi\)
\(740\) −1.50000 + 2.59808i −0.0551411 + 0.0955072i
\(741\) 10.5000 + 6.06218i 0.385727 + 0.222700i
\(742\) 0 0
\(743\) −10.5000 18.1865i −0.385208 0.667199i 0.606590 0.795015i \(-0.292537\pi\)
−0.991798 + 0.127815i \(0.959204\pi\)
\(744\) 12.0000 + 6.92820i 0.439941 + 0.254000i
\(745\) −13.5000 + 23.3827i −0.494602 + 0.856675i
\(746\) 13.0000 0.475964
\(747\) 13.5000 + 23.3827i 0.493939 + 0.855528i
\(748\) 9.00000 0.329073
\(749\) 0 0
\(750\) 5.19615i 0.189737i
\(751\) 6.50000 + 11.2583i 0.237188 + 0.410822i 0.959906 0.280321i \(-0.0904408\pi\)
−0.722718 + 0.691143i \(0.757107\pi\)
\(752\) 0 0
\(753\) 18.0000 10.3923i 0.655956 0.378717i
\(754\) 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
\(759\) −40.5000 + 23.3827i −1.47006 + 0.848738i
\(760\) −10.5000 18.1865i −0.380875 0.659695i
\(761\) −22.5000 38.9711i −0.815624 1.41270i −0.908879 0.417061i \(-0.863060\pi\)
0.0932544 0.995642i \(-0.470273\pi\)
\(762\) 6.92820i 0.250982i
\(763\) 0 0
\(764\) 0 0
\(765\) −27.0000 −0.976187
\(766\) 15.0000 0.541972
\(767\) 0 0
\(768\) 1.50000 + 0.866025i 0.0541266 + 0.0312500i
\(769\) 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
\(771\) 31.5000 + 18.1865i 1.13444 + 0.654972i
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) −27.0000 −0.971123 −0.485561 0.874203i \(-0.661385\pi\)
−0.485561 + 0.874203i \(0.661385\pi\)
\(774\) −3.00000 −0.107833
\(775\) −32.0000 −1.14947
\(776\) 0.500000 0.866025i 0.0179490 0.0310885i
\(777\) 0 0
\(778\) 13.5000 + 23.3827i 0.483998 + 0.838310i
\(779\) 10.5000 + 18.1865i 0.376202 + 0.651600i
\(780\) 4.50000 2.59808i 0.161126 0.0930261i
\(781\) 18.0000 31.1769i 0.644091 1.11560i
\(782\) −27.0000 −0.965518
\(783\) −13.5000 &min