Properties

Label 570.2.c.d.569.1
Level $570$
Weight $2$
Character 570.569
Analytic conductor $4.551$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 569.1
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 570.569
Dual form 570.2.c.d.569.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.73205 q^{3} -1.00000 q^{4} +(-1.41421 - 1.73205i) q^{5} +1.73205i q^{6} -2.44949i q^{7} +1.00000i q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.73205 q^{3} -1.00000 q^{4} +(-1.41421 - 1.73205i) q^{5} +1.73205i q^{6} -2.44949i q^{7} +1.00000i q^{8} +3.00000 q^{9} +(-1.73205 + 1.41421i) q^{10} -3.46410i q^{11} +1.73205 q^{12} -2.44949 q^{14} +(2.44949 + 3.00000i) q^{15} +1.00000 q^{16} -7.07107 q^{17} -3.00000i q^{18} +(-1.00000 + 4.24264i) q^{19} +(1.41421 + 1.73205i) q^{20} +4.24264i q^{21} -3.46410 q^{22} +5.65685 q^{23} -1.73205i q^{24} +(-1.00000 + 4.89898i) q^{25} -5.19615 q^{27} +2.44949i q^{28} -4.89898 q^{29} +(3.00000 - 2.44949i) q^{30} +4.24264i q^{31} -1.00000i q^{32} +6.00000i q^{33} +7.07107i q^{34} +(-4.24264 + 3.46410i) q^{35} -3.00000 q^{36} -6.92820 q^{37} +(4.24264 + 1.00000i) q^{38} +(1.73205 - 1.41421i) q^{40} +2.44949 q^{41} +4.24264 q^{42} +9.79796i q^{43} +3.46410i q^{44} +(-4.24264 - 5.19615i) q^{45} -5.65685i q^{46} +2.82843 q^{47} -1.73205 q^{48} +1.00000 q^{49} +(4.89898 + 1.00000i) q^{50} +12.2474 q^{51} -12.0000i q^{53} +5.19615i q^{54} +(-6.00000 + 4.89898i) q^{55} +2.44949 q^{56} +(1.73205 - 7.34847i) q^{57} +4.89898i q^{58} -7.34847 q^{59} +(-2.44949 - 3.00000i) q^{60} -10.0000 q^{61} +4.24264 q^{62} -7.34847i q^{63} -1.00000 q^{64} +6.00000 q^{66} +13.8564 q^{67} +7.07107 q^{68} -9.79796 q^{69} +(3.46410 + 4.24264i) q^{70} -4.89898 q^{71} +3.00000i q^{72} -9.79796i q^{73} +6.92820i q^{74} +(1.73205 - 8.48528i) q^{75} +(1.00000 - 4.24264i) q^{76} -8.48528 q^{77} -4.24264i q^{79} +(-1.41421 - 1.73205i) q^{80} +9.00000 q^{81} -2.44949i q^{82} -1.41421 q^{83} -4.24264i q^{84} +(10.0000 + 12.2474i) q^{85} +9.79796 q^{86} +8.48528 q^{87} +3.46410 q^{88} -12.2474 q^{89} +(-5.19615 + 4.24264i) q^{90} -5.65685 q^{92} -7.34847i q^{93} -2.82843i q^{94} +(8.76268 - 4.26795i) q^{95} +1.73205i q^{96} +3.46410 q^{97} -1.00000i q^{98} -10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q - 8q^{4} + 24q^{9} + O(q^{10}) \) \( 8q - 8q^{4} + 24q^{9} + 8q^{16} - 8q^{19} - 8q^{25} + 24q^{30} - 24q^{36} + 8q^{49} - 48q^{55} - 80q^{61} - 8q^{64} + 48q^{66} + 8q^{76} + 72q^{81} + 80q^{85} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.73205 −1.00000
\(4\) −1.00000 −0.500000
\(5\) −1.41421 1.73205i −0.632456 0.774597i
\(6\) 1.73205i 0.707107i
\(7\) 2.44949i 0.925820i −0.886405 0.462910i \(-0.846805\pi\)
0.886405 0.462910i \(-0.153195\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 3.00000 1.00000
\(10\) −1.73205 + 1.41421i −0.547723 + 0.447214i
\(11\) 3.46410i 1.04447i −0.852803 0.522233i \(-0.825099\pi\)
0.852803 0.522233i \(-0.174901\pi\)
\(12\) 1.73205 0.500000
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −2.44949 −0.654654
\(15\) 2.44949 + 3.00000i 0.632456 + 0.774597i
\(16\) 1.00000 0.250000
\(17\) −7.07107 −1.71499 −0.857493 0.514496i \(-0.827979\pi\)
−0.857493 + 0.514496i \(0.827979\pi\)
\(18\) 3.00000i 0.707107i
\(19\) −1.00000 + 4.24264i −0.229416 + 0.973329i
\(20\) 1.41421 + 1.73205i 0.316228 + 0.387298i
\(21\) 4.24264i 0.925820i
\(22\) −3.46410 −0.738549
\(23\) 5.65685 1.17954 0.589768 0.807573i \(-0.299219\pi\)
0.589768 + 0.807573i \(0.299219\pi\)
\(24\) 1.73205i 0.353553i
\(25\) −1.00000 + 4.89898i −0.200000 + 0.979796i
\(26\) 0 0
\(27\) −5.19615 −1.00000
\(28\) 2.44949i 0.462910i
\(29\) −4.89898 −0.909718 −0.454859 0.890564i \(-0.650310\pi\)
−0.454859 + 0.890564i \(0.650310\pi\)
\(30\) 3.00000 2.44949i 0.547723 0.447214i
\(31\) 4.24264i 0.762001i 0.924575 + 0.381000i \(0.124420\pi\)
−0.924575 + 0.381000i \(0.875580\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 6.00000i 1.04447i
\(34\) 7.07107i 1.21268i
\(35\) −4.24264 + 3.46410i −0.717137 + 0.585540i
\(36\) −3.00000 −0.500000
\(37\) −6.92820 −1.13899 −0.569495 0.821995i \(-0.692861\pi\)
−0.569495 + 0.821995i \(0.692861\pi\)
\(38\) 4.24264 + 1.00000i 0.688247 + 0.162221i
\(39\) 0 0
\(40\) 1.73205 1.41421i 0.273861 0.223607i
\(41\) 2.44949 0.382546 0.191273 0.981537i \(-0.438738\pi\)
0.191273 + 0.981537i \(0.438738\pi\)
\(42\) 4.24264 0.654654
\(43\) 9.79796i 1.49417i 0.664726 + 0.747087i \(0.268548\pi\)
−0.664726 + 0.747087i \(0.731452\pi\)
\(44\) 3.46410i 0.522233i
\(45\) −4.24264 5.19615i −0.632456 0.774597i
\(46\) 5.65685i 0.834058i
\(47\) 2.82843 0.412568 0.206284 0.978492i \(-0.433863\pi\)
0.206284 + 0.978492i \(0.433863\pi\)
\(48\) −1.73205 −0.250000
\(49\) 1.00000 0.142857
\(50\) 4.89898 + 1.00000i 0.692820 + 0.141421i
\(51\) 12.2474 1.71499
\(52\) 0 0
\(53\) 12.0000i 1.64833i −0.566352 0.824163i \(-0.691646\pi\)
0.566352 0.824163i \(-0.308354\pi\)
\(54\) 5.19615i 0.707107i
\(55\) −6.00000 + 4.89898i −0.809040 + 0.660578i
\(56\) 2.44949 0.327327
\(57\) 1.73205 7.34847i 0.229416 0.973329i
\(58\) 4.89898i 0.643268i
\(59\) −7.34847 −0.956689 −0.478345 0.878172i \(-0.658763\pi\)
−0.478345 + 0.878172i \(0.658763\pi\)
\(60\) −2.44949 3.00000i −0.316228 0.387298i
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 4.24264 0.538816
\(63\) 7.34847i 0.925820i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 6.00000 0.738549
\(67\) 13.8564 1.69283 0.846415 0.532524i \(-0.178756\pi\)
0.846415 + 0.532524i \(0.178756\pi\)
\(68\) 7.07107 0.857493
\(69\) −9.79796 −1.17954
\(70\) 3.46410 + 4.24264i 0.414039 + 0.507093i
\(71\) −4.89898 −0.581402 −0.290701 0.956814i \(-0.593888\pi\)
−0.290701 + 0.956814i \(0.593888\pi\)
\(72\) 3.00000i 0.353553i
\(73\) 9.79796i 1.14676i −0.819288 0.573382i \(-0.805631\pi\)
0.819288 0.573382i \(-0.194369\pi\)
\(74\) 6.92820i 0.805387i
\(75\) 1.73205 8.48528i 0.200000 0.979796i
\(76\) 1.00000 4.24264i 0.114708 0.486664i
\(77\) −8.48528 −0.966988
\(78\) 0 0
\(79\) 4.24264i 0.477334i −0.971101 0.238667i \(-0.923290\pi\)
0.971101 0.238667i \(-0.0767105\pi\)
\(80\) −1.41421 1.73205i −0.158114 0.193649i
\(81\) 9.00000 1.00000
\(82\) 2.44949i 0.270501i
\(83\) −1.41421 −0.155230 −0.0776151 0.996983i \(-0.524731\pi\)
−0.0776151 + 0.996983i \(0.524731\pi\)
\(84\) 4.24264i 0.462910i
\(85\) 10.0000 + 12.2474i 1.08465 + 1.32842i
\(86\) 9.79796 1.05654
\(87\) 8.48528 0.909718
\(88\) 3.46410 0.369274
\(89\) −12.2474 −1.29823 −0.649113 0.760692i \(-0.724860\pi\)
−0.649113 + 0.760692i \(0.724860\pi\)
\(90\) −5.19615 + 4.24264i −0.547723 + 0.447214i
\(91\) 0 0
\(92\) −5.65685 −0.589768
\(93\) 7.34847i 0.762001i
\(94\) 2.82843i 0.291730i
\(95\) 8.76268 4.26795i 0.899032 0.437882i
\(96\) 1.73205i 0.176777i
\(97\) 3.46410 0.351726 0.175863 0.984415i \(-0.443728\pi\)
0.175863 + 0.984415i \(0.443728\pi\)
\(98\) 1.00000i 0.101015i
\(99\) 10.3923i 1.04447i
\(100\) 1.00000 4.89898i 0.100000 0.489898i
\(101\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(102\) 12.2474i 1.21268i
\(103\) −3.46410 −0.341328 −0.170664 0.985329i \(-0.554591\pi\)
−0.170664 + 0.985329i \(0.554591\pi\)
\(104\) 0 0
\(105\) 7.34847 6.00000i 0.717137 0.585540i
\(106\) −12.0000 −1.16554
\(107\) 12.0000i 1.16008i 0.814587 + 0.580042i \(0.196964\pi\)
−0.814587 + 0.580042i \(0.803036\pi\)
\(108\) 5.19615 0.500000
\(109\) 12.7279i 1.21911i −0.792742 0.609557i \(-0.791347\pi\)
0.792742 0.609557i \(-0.208653\pi\)
\(110\) 4.89898 + 6.00000i 0.467099 + 0.572078i
\(111\) 12.0000 1.13899
\(112\) 2.44949i 0.231455i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) −7.34847 1.73205i −0.688247 0.162221i
\(115\) −8.00000 9.79796i −0.746004 0.913664i
\(116\) 4.89898 0.454859
\(117\) 0 0
\(118\) 7.34847i 0.676481i
\(119\) 17.3205i 1.58777i
\(120\) −3.00000 + 2.44949i −0.273861 + 0.223607i
\(121\) −1.00000 −0.0909091
\(122\) 10.0000i 0.905357i
\(123\) −4.24264 −0.382546
\(124\) 4.24264i 0.381000i
\(125\) 9.89949 5.19615i 0.885438 0.464758i
\(126\) −7.34847 −0.654654
\(127\) −3.46410 −0.307389 −0.153695 0.988118i \(-0.549117\pi\)
−0.153695 + 0.988118i \(0.549117\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 16.9706i 1.49417i
\(130\) 0 0
\(131\) 3.46410i 0.302660i −0.988483 0.151330i \(-0.951644\pi\)
0.988483 0.151330i \(-0.0483556\pi\)
\(132\) 6.00000i 0.522233i
\(133\) 10.3923 + 2.44949i 0.901127 + 0.212398i
\(134\) 13.8564i 1.19701i
\(135\) 7.34847 + 9.00000i 0.632456 + 0.774597i
\(136\) 7.07107i 0.606339i
\(137\) −7.07107 −0.604122 −0.302061 0.953289i \(-0.597675\pi\)
−0.302061 + 0.953289i \(0.597675\pi\)
\(138\) 9.79796i 0.834058i
\(139\) −10.0000 −0.848189 −0.424094 0.905618i \(-0.639408\pi\)
−0.424094 + 0.905618i \(0.639408\pi\)
\(140\) 4.24264 3.46410i 0.358569 0.292770i
\(141\) −4.89898 −0.412568
\(142\) 4.89898i 0.411113i
\(143\) 0 0
\(144\) 3.00000 0.250000
\(145\) 6.92820 + 8.48528i 0.575356 + 0.704664i
\(146\) −9.79796 −0.810885
\(147\) −1.73205 −0.142857
\(148\) 6.92820 0.569495
\(149\) 13.8564i 1.13516i −0.823318 0.567581i \(-0.807880\pi\)
0.823318 0.567581i \(-0.192120\pi\)
\(150\) −8.48528 1.73205i −0.692820 0.141421i
\(151\) 12.7279i 1.03578i −0.855446 0.517892i \(-0.826717\pi\)
0.855446 0.517892i \(-0.173283\pi\)
\(152\) −4.24264 1.00000i −0.344124 0.0811107i
\(153\) −21.2132 −1.71499
\(154\) 8.48528i 0.683763i
\(155\) 7.34847 6.00000i 0.590243 0.481932i
\(156\) 0 0
\(157\) 7.34847i 0.586472i 0.956040 + 0.293236i \(0.0947321\pi\)
−0.956040 + 0.293236i \(0.905268\pi\)
\(158\) −4.24264 −0.337526
\(159\) 20.7846i 1.64833i
\(160\) −1.73205 + 1.41421i −0.136931 + 0.111803i
\(161\) 13.8564i 1.09204i
\(162\) 9.00000i 0.707107i
\(163\) 14.6969i 1.15115i −0.817748 0.575577i \(-0.804778\pi\)
0.817748 0.575577i \(-0.195222\pi\)
\(164\) −2.44949 −0.191273
\(165\) 10.3923 8.48528i 0.809040 0.660578i
\(166\) 1.41421i 0.109764i
\(167\) 18.0000i 1.39288i −0.717614 0.696441i \(-0.754766\pi\)
0.717614 0.696441i \(-0.245234\pi\)
\(168\) −4.24264 −0.327327
\(169\) −13.0000 −1.00000
\(170\) 12.2474 10.0000i 0.939336 0.766965i
\(171\) −3.00000 + 12.7279i −0.229416 + 0.973329i
\(172\) 9.79796i 0.747087i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 8.48528i 0.643268i
\(175\) 12.0000 + 2.44949i 0.907115 + 0.185164i
\(176\) 3.46410i 0.261116i
\(177\) 12.7279 0.956689
\(178\) 12.2474i 0.917985i
\(179\) −17.1464 −1.28158 −0.640792 0.767714i \(-0.721394\pi\)
−0.640792 + 0.767714i \(0.721394\pi\)
\(180\) 4.24264 + 5.19615i 0.316228 + 0.387298i
\(181\) 12.7279i 0.946059i 0.881047 + 0.473029i \(0.156840\pi\)
−0.881047 + 0.473029i \(0.843160\pi\)
\(182\) 0 0
\(183\) 17.3205 1.28037
\(184\) 5.65685i 0.417029i
\(185\) 9.79796 + 12.0000i 0.720360 + 0.882258i
\(186\) −7.34847 −0.538816
\(187\) 24.4949i 1.79124i
\(188\) −2.82843 −0.206284
\(189\) 12.7279i 0.925820i
\(190\) −4.26795 8.76268i −0.309630 0.635712i
\(191\) 17.3205i 1.25327i 0.779314 + 0.626634i \(0.215568\pi\)
−0.779314 + 0.626634i \(0.784432\pi\)
\(192\) 1.73205 0.125000
\(193\) −20.7846 −1.49611 −0.748054 0.663637i \(-0.769012\pi\)
−0.748054 + 0.663637i \(0.769012\pi\)
\(194\) 3.46410i 0.248708i
\(195\) 0 0
\(196\) −1.00000 −0.0714286
\(197\) −5.65685 −0.403034 −0.201517 0.979485i \(-0.564587\pi\)
−0.201517 + 0.979485i \(0.564587\pi\)
\(198\) −10.3923 −0.738549
\(199\) 20.0000 1.41776 0.708881 0.705328i \(-0.249200\pi\)
0.708881 + 0.705328i \(0.249200\pi\)
\(200\) −4.89898 1.00000i −0.346410 0.0707107i
\(201\) −24.0000 −1.69283
\(202\) 0 0
\(203\) 12.0000i 0.842235i
\(204\) −12.2474 −0.857493
\(205\) −3.46410 4.24264i −0.241943 0.296319i
\(206\) 3.46410i 0.241355i
\(207\) 16.9706 1.17954
\(208\) 0 0
\(209\) 14.6969 + 3.46410i 1.01661 + 0.239617i
\(210\) −6.00000 7.34847i −0.414039 0.507093i
\(211\) 25.4558i 1.75245i −0.481900 0.876226i \(-0.660053\pi\)
0.481900 0.876226i \(-0.339947\pi\)
\(212\) 12.0000i 0.824163i
\(213\) 8.48528 0.581402
\(214\) 12.0000 0.820303
\(215\) 16.9706 13.8564i 1.15738 0.944999i
\(216\) 5.19615i 0.353553i
\(217\) 10.3923 0.705476
\(218\) −12.7279 −0.862044
\(219\) 16.9706i 1.14676i
\(220\) 6.00000 4.89898i 0.404520 0.330289i
\(221\) 0 0
\(222\) 12.0000i 0.805387i
\(223\) −3.46410 −0.231973 −0.115987 0.993251i \(-0.537003\pi\)
−0.115987 + 0.993251i \(0.537003\pi\)
\(224\) −2.44949 −0.163663
\(225\) −3.00000 + 14.6969i −0.200000 + 0.979796i
\(226\) 6.00000 0.399114
\(227\) 12.0000i 0.796468i −0.917284 0.398234i \(-0.869623\pi\)
0.917284 0.398234i \(-0.130377\pi\)
\(228\) −1.73205 + 7.34847i −0.114708 + 0.486664i
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) −9.79796 + 8.00000i −0.646058 + 0.527504i
\(231\) 14.6969 0.966988
\(232\) 4.89898i 0.321634i
\(233\) −7.07107 −0.463241 −0.231621 0.972806i \(-0.574403\pi\)
−0.231621 + 0.972806i \(0.574403\pi\)
\(234\) 0 0
\(235\) −4.00000 4.89898i −0.260931 0.319574i
\(236\) 7.34847 0.478345
\(237\) 7.34847i 0.477334i
\(238\) 17.3205 1.12272
\(239\) 6.92820i 0.448148i 0.974572 + 0.224074i \(0.0719358\pi\)
−0.974572 + 0.224074i \(0.928064\pi\)
\(240\) 2.44949 + 3.00000i 0.158114 + 0.193649i
\(241\) 8.48528i 0.546585i 0.961931 + 0.273293i \(0.0881127\pi\)
−0.961931 + 0.273293i \(0.911887\pi\)
\(242\) 1.00000i 0.0642824i
\(243\) −15.5885 −1.00000
\(244\) 10.0000 0.640184
\(245\) −1.41421 1.73205i −0.0903508 0.110657i
\(246\) 4.24264i 0.270501i
\(247\) 0 0
\(248\) −4.24264 −0.269408
\(249\) 2.44949 0.155230
\(250\) −5.19615 9.89949i −0.328634 0.626099i
\(251\) 24.2487i 1.53057i 0.643695 + 0.765283i \(0.277401\pi\)
−0.643695 + 0.765283i \(0.722599\pi\)
\(252\) 7.34847i 0.462910i
\(253\) 19.5959i 1.23198i
\(254\) 3.46410i 0.217357i
\(255\) −17.3205 21.2132i −1.08465 1.32842i
\(256\) 1.00000 0.0625000
\(257\) 6.00000i 0.374270i 0.982334 + 0.187135i \(0.0599201\pi\)
−0.982334 + 0.187135i \(0.940080\pi\)
\(258\) −16.9706 −1.05654
\(259\) 16.9706i 1.05450i
\(260\) 0 0
\(261\) −14.6969 −0.909718
\(262\) −3.46410 −0.214013
\(263\) 28.2843 1.74408 0.872041 0.489432i \(-0.162796\pi\)
0.872041 + 0.489432i \(0.162796\pi\)
\(264\) −6.00000 −0.369274
\(265\) −20.7846 + 16.9706i −1.27679 + 1.04249i
\(266\) 2.44949 10.3923i 0.150188 0.637193i
\(267\) 21.2132 1.29823
\(268\) −13.8564 −0.846415
\(269\) −19.5959 −1.19478 −0.597392 0.801949i \(-0.703796\pi\)
−0.597392 + 0.801949i \(0.703796\pi\)
\(270\) 9.00000 7.34847i 0.547723 0.447214i
\(271\) 28.0000 1.70088 0.850439 0.526073i \(-0.176336\pi\)
0.850439 + 0.526073i \(0.176336\pi\)
\(272\) −7.07107 −0.428746
\(273\) 0 0
\(274\) 7.07107i 0.427179i
\(275\) 16.9706 + 3.46410i 1.02336 + 0.208893i
\(276\) 9.79796 0.589768
\(277\) 12.2474i 0.735878i −0.929850 0.367939i \(-0.880064\pi\)
0.929850 0.367939i \(-0.119936\pi\)
\(278\) 10.0000i 0.599760i
\(279\) 12.7279i 0.762001i
\(280\) −3.46410 4.24264i −0.207020 0.253546i
\(281\) 31.8434 1.89962 0.949808 0.312833i \(-0.101278\pi\)
0.949808 + 0.312833i \(0.101278\pi\)
\(282\) 4.89898i 0.291730i
\(283\) 24.4949i 1.45607i −0.685540 0.728035i \(-0.740434\pi\)
0.685540 0.728035i \(-0.259566\pi\)
\(284\) 4.89898 0.290701
\(285\) −15.1774 + 7.39230i −0.899032 + 0.437882i
\(286\) 0 0
\(287\) 6.00000i 0.354169i
\(288\) 3.00000i 0.176777i
\(289\) 33.0000 1.94118
\(290\) 8.48528 6.92820i 0.498273 0.406838i
\(291\) −6.00000 −0.351726
\(292\) 9.79796i 0.573382i
\(293\) 6.00000i 0.350524i 0.984522 + 0.175262i \(0.0560772\pi\)
−0.984522 + 0.175262i \(0.943923\pi\)
\(294\) 1.73205i 0.101015i
\(295\) 10.3923 + 12.7279i 0.605063 + 0.741048i
\(296\) 6.92820i 0.402694i
\(297\) 18.0000i 1.04447i
\(298\) −13.8564 −0.802680
\(299\) 0 0
\(300\) −1.73205 + 8.48528i −0.100000 + 0.489898i
\(301\) 24.0000 1.38334
\(302\) −12.7279 −0.732410
\(303\) 0 0
\(304\) −1.00000 + 4.24264i −0.0573539 + 0.243332i
\(305\) 14.1421 + 17.3205i 0.809776 + 0.991769i
\(306\) 21.2132i 1.21268i
\(307\) −6.92820 −0.395413 −0.197707 0.980261i \(-0.563349\pi\)
−0.197707 + 0.980261i \(0.563349\pi\)
\(308\) 8.48528 0.483494
\(309\) 6.00000 0.341328
\(310\) −6.00000 7.34847i −0.340777 0.417365i
\(311\) 3.46410i 0.196431i 0.995165 + 0.0982156i \(0.0313135\pi\)
−0.995165 + 0.0982156i \(0.968687\pi\)
\(312\) 0 0
\(313\) 14.6969i 0.830720i 0.909657 + 0.415360i \(0.136344\pi\)
−0.909657 + 0.415360i \(0.863656\pi\)
\(314\) 7.34847 0.414698
\(315\) −12.7279 + 10.3923i −0.717137 + 0.585540i
\(316\) 4.24264i 0.238667i
\(317\) 6.00000i 0.336994i 0.985702 + 0.168497i \(0.0538913\pi\)
−0.985702 + 0.168497i \(0.946109\pi\)
\(318\) 20.7846 1.16554
\(319\) 16.9706i 0.950169i
\(320\) 1.41421 + 1.73205i 0.0790569 + 0.0968246i
\(321\) 20.7846i 1.16008i
\(322\) −13.8564 −0.772187
\(323\) 7.07107 30.0000i 0.393445 1.66924i
\(324\) −9.00000 −0.500000
\(325\) 0 0
\(326\) −14.6969 −0.813988
\(327\) 22.0454i 1.21911i
\(328\) 2.44949i 0.135250i
\(329\) 6.92820i 0.381964i
\(330\) −8.48528 10.3923i −0.467099 0.572078i
\(331\) 8.48528i 0.466393i 0.972430 + 0.233197i \(0.0749186\pi\)
−0.972430 + 0.233197i \(0.925081\pi\)
\(332\) 1.41421 0.0776151
\(333\) −20.7846 −1.13899
\(334\) −18.0000 −0.984916
\(335\) −19.5959 24.0000i −1.07064 1.31126i
\(336\) 4.24264i 0.231455i
\(337\) −20.7846 −1.13221 −0.566105 0.824333i \(-0.691550\pi\)
−0.566105 + 0.824333i \(0.691550\pi\)
\(338\) 13.0000i 0.707107i
\(339\) 10.3923i 0.564433i
\(340\) −10.0000 12.2474i −0.542326 0.664211i
\(341\) 14.6969 0.795884
\(342\) 12.7279 + 3.00000i 0.688247 + 0.162221i
\(343\) 19.5959i 1.05808i
\(344\) −9.79796 −0.528271
\(345\) 13.8564 + 16.9706i 0.746004 + 0.913664i
\(346\) 0 0
\(347\) −24.0416 −1.29062 −0.645311 0.763920i \(-0.723272\pi\)
−0.645311 + 0.763920i \(0.723272\pi\)
\(348\) −8.48528 −0.454859
\(349\) 2.00000 0.107058 0.0535288 0.998566i \(-0.482953\pi\)
0.0535288 + 0.998566i \(0.482953\pi\)
\(350\) 2.44949 12.0000i 0.130931 0.641427i
\(351\) 0 0
\(352\) −3.46410 −0.184637
\(353\) −15.5563 −0.827981 −0.413990 0.910281i \(-0.635865\pi\)
−0.413990 + 0.910281i \(0.635865\pi\)
\(354\) 12.7279i 0.676481i
\(355\) 6.92820 + 8.48528i 0.367711 + 0.450352i
\(356\) 12.2474 0.649113
\(357\) 30.0000i 1.58777i
\(358\) 17.1464i 0.906217i
\(359\) 13.8564i 0.731313i 0.930750 + 0.365657i \(0.119156\pi\)
−0.930750 + 0.365657i \(0.880844\pi\)
\(360\) 5.19615 4.24264i 0.273861 0.223607i
\(361\) −17.0000 8.48528i −0.894737 0.446594i
\(362\) 12.7279 0.668965
\(363\) 1.73205 0.0909091
\(364\) 0 0
\(365\) −16.9706 + 13.8564i −0.888280 + 0.725277i
\(366\) 17.3205i 0.905357i
\(367\) 7.34847i 0.383587i 0.981435 + 0.191793i \(0.0614304\pi\)
−0.981435 + 0.191793i \(0.938570\pi\)
\(368\) 5.65685 0.294884
\(369\) 7.34847 0.382546
\(370\) 12.0000 9.79796i 0.623850 0.509372i
\(371\) −29.3939 −1.52605
\(372\) 7.34847i 0.381000i
\(373\) −6.92820 −0.358729 −0.179364 0.983783i \(-0.557404\pi\)
−0.179364 + 0.983783i \(0.557404\pi\)
\(374\) 24.4949 1.26660
\(375\) −17.1464 + 9.00000i −0.885438 + 0.464758i
\(376\) 2.82843i 0.145865i
\(377\) 0 0
\(378\) 12.7279 0.654654
\(379\) 25.4558i 1.30758i −0.756677 0.653789i \(-0.773178\pi\)
0.756677 0.653789i \(-0.226822\pi\)
\(380\) −8.76268 + 4.26795i −0.449516 + 0.218941i
\(381\) 6.00000 0.307389
\(382\) 17.3205 0.886194
\(383\) 24.0000i 1.22634i −0.789950 0.613171i \(-0.789894\pi\)
0.789950 0.613171i \(-0.210106\pi\)
\(384\) 1.73205i 0.0883883i
\(385\) 12.0000 + 14.6969i 0.611577 + 0.749025i
\(386\) 20.7846i 1.05791i
\(387\) 29.3939i 1.49417i
\(388\) −3.46410 −0.175863
\(389\) 13.8564i 0.702548i 0.936273 + 0.351274i \(0.114251\pi\)
−0.936273 + 0.351274i \(0.885749\pi\)
\(390\) 0 0
\(391\) −40.0000 −2.02289
\(392\) 1.00000i 0.0505076i
\(393\) 6.00000i 0.302660i
\(394\) 5.65685i 0.284988i
\(395\) −7.34847 + 6.00000i −0.369742 + 0.301893i
\(396\) 10.3923i 0.522233i
\(397\) 26.9444i 1.35230i −0.736764 0.676150i \(-0.763647\pi\)
0.736764 0.676150i \(-0.236353\pi\)
\(398\) 20.0000i 1.00251i
\(399\) −18.0000 4.24264i −0.901127 0.212398i
\(400\) −1.00000 + 4.89898i −0.0500000 + 0.244949i
\(401\) −17.1464 −0.856252 −0.428126 0.903719i \(-0.640826\pi\)
−0.428126 + 0.903719i \(0.640826\pi\)
\(402\) 24.0000i 1.19701i
\(403\) 0 0
\(404\) 0 0
\(405\) −12.7279 15.5885i −0.632456 0.774597i
\(406\) 12.0000 0.595550
\(407\) 24.0000i 1.18964i
\(408\) 12.2474i 0.606339i
\(409\) 33.9411i 1.67828i −0.543915 0.839140i \(-0.683059\pi\)
0.543915 0.839140i \(-0.316941\pi\)
\(410\) −4.24264 + 3.46410i −0.209529 + 0.171080i
\(411\) 12.2474 0.604122
\(412\) 3.46410 0.170664
\(413\) 18.0000i 0.885722i
\(414\) 16.9706i 0.834058i
\(415\) 2.00000 + 2.44949i 0.0981761 + 0.120241i
\(416\) 0 0
\(417\) 17.3205 0.848189
\(418\) 3.46410 14.6969i 0.169435 0.718851i
\(419\) 31.1769i 1.52309i −0.648111 0.761546i \(-0.724441\pi\)
0.648111 0.761546i \(-0.275559\pi\)
\(420\) −7.34847 + 6.00000i −0.358569 + 0.292770i
\(421\) 4.24264i 0.206774i −0.994641 0.103387i \(-0.967032\pi\)
0.994641 0.103387i \(-0.0329680\pi\)
\(422\) −25.4558 −1.23917
\(423\) 8.48528 0.412568
\(424\) 12.0000 0.582772
\(425\) 7.07107 34.6410i 0.342997 1.68034i
\(426\) 8.48528i 0.411113i
\(427\) 24.4949i 1.18539i
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) −13.8564 16.9706i −0.668215 0.818393i
\(431\) −9.79796 −0.471951 −0.235976 0.971759i \(-0.575829\pi\)
−0.235976 + 0.971759i \(0.575829\pi\)
\(432\) −5.19615 −0.250000
\(433\) 20.7846 0.998845 0.499422 0.866359i \(-0.333546\pi\)
0.499422 + 0.866359i \(0.333546\pi\)
\(434\) 10.3923i 0.498847i
\(435\) −12.0000 14.6969i −0.575356 0.704664i
\(436\) 12.7279i 0.609557i
\(437\) −5.65685 + 24.0000i −0.270604 + 1.14808i
\(438\) 16.9706 0.810885
\(439\) 12.7279i 0.607471i 0.952756 + 0.303735i \(0.0982338\pi\)
−0.952756 + 0.303735i \(0.901766\pi\)
\(440\) −4.89898 6.00000i −0.233550 0.286039i
\(441\) 3.00000 0.142857
\(442\) 0 0
\(443\) −15.5563 −0.739104 −0.369552 0.929210i \(-0.620489\pi\)
−0.369552 + 0.929210i \(0.620489\pi\)
\(444\) −12.0000 −0.569495
\(445\) 17.3205 + 21.2132i 0.821071 + 1.00560i
\(446\) 3.46410i 0.164030i
\(447\) 24.0000i 1.13516i
\(448\) 2.44949i 0.115728i
\(449\) 22.0454 1.04039 0.520194 0.854048i \(-0.325860\pi\)
0.520194 + 0.854048i \(0.325860\pi\)
\(450\) 14.6969 + 3.00000i 0.692820 + 0.141421i
\(451\) 8.48528i 0.399556i
\(452\) 6.00000i 0.282216i
\(453\) 22.0454i 1.03578i
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) 7.34847 + 1.73205i 0.344124 + 0.0811107i
\(457\) 9.79796i 0.458329i −0.973388 0.229165i \(-0.926401\pi\)
0.973388 0.229165i \(-0.0735994\pi\)
\(458\) 22.0000i 1.02799i
\(459\) 36.7423 1.71499
\(460\) 8.00000 + 9.79796i 0.373002 + 0.456832i
\(461\) 17.3205i 0.806696i −0.915047 0.403348i \(-0.867846\pi\)
0.915047 0.403348i \(-0.132154\pi\)
\(462\) 14.6969i 0.683763i
\(463\) 12.2474i 0.569187i −0.958648 0.284594i \(-0.908141\pi\)
0.958648 0.284594i \(-0.0918587\pi\)
\(464\) −4.89898 −0.227429
\(465\) −12.7279 + 10.3923i −0.590243 + 0.481932i
\(466\) 7.07107i 0.327561i
\(467\) −26.8701 −1.24340 −0.621699 0.783256i \(-0.713557\pi\)
−0.621699 + 0.783256i \(0.713557\pi\)
\(468\) 0 0
\(469\) 33.9411i 1.56726i
\(470\) −4.89898 + 4.00000i −0.225973 + 0.184506i
\(471\) 12.7279i 0.586472i
\(472\) 7.34847i 0.338241i
\(473\) 33.9411 1.56061
\(474\) 7.34847 0.337526
\(475\) −19.7846 9.14162i −0.907780 0.419446i
\(476\) 17.3205i 0.793884i
\(477\) 36.0000i 1.64833i
\(478\) 6.92820 0.316889
\(479\) 10.3923i 0.474837i −0.971408 0.237418i \(-0.923699\pi\)
0.971408 0.237418i \(-0.0763012\pi\)
\(480\) 3.00000 2.44949i 0.136931 0.111803i
\(481\) 0 0
\(482\) 8.48528 0.386494
\(483\) 24.0000i 1.09204i
\(484\) 1.00000 0.0454545
\(485\) −4.89898 6.00000i −0.222451 0.272446i
\(486\) 15.5885i 0.707107i
\(487\) 3.46410 0.156973 0.0784867 0.996915i \(-0.474991\pi\)
0.0784867 + 0.996915i \(0.474991\pi\)
\(488\) 10.0000i 0.452679i
\(489\) 25.4558i 1.15115i
\(490\) −1.73205 + 1.41421i −0.0782461 + 0.0638877i
\(491\) 10.3923i 0.468998i −0.972116 0.234499i \(-0.924655\pi\)
0.972116 0.234499i \(-0.0753450\pi\)
\(492\) 4.24264 0.191273
\(493\) 34.6410 1.56015
\(494\) 0 0
\(495\) −18.0000 + 14.6969i −0.809040 + 0.660578i
\(496\) 4.24264i 0.190500i
\(497\) 12.0000i 0.538274i
\(498\) 2.44949i 0.109764i
\(499\) 14.0000 0.626726 0.313363 0.949633i \(-0.398544\pi\)
0.313363 + 0.949633i \(0.398544\pi\)
\(500\) −9.89949 + 5.19615i −0.442719 + 0.232379i
\(501\) 31.1769i 1.39288i
\(502\) 24.2487 1.08227
\(503\) −5.65685 −0.252227 −0.126113 0.992016i \(-0.540250\pi\)
−0.126113 + 0.992016i \(0.540250\pi\)
\(504\) 7.34847 0.327327
\(505\) 0 0
\(506\) −19.5959 −0.871145
\(507\) 22.5167 1.00000
\(508\) 3.46410 0.153695
\(509\) 24.4949 1.08572 0.542859 0.839824i \(-0.317342\pi\)
0.542859 + 0.839824i \(0.317342\pi\)
\(510\) −21.2132 + 17.3205i −0.939336 + 0.766965i
\(511\) −24.0000 −1.06170
\(512\) 1.00000i 0.0441942i
\(513\) 5.19615 22.0454i 0.229416 0.973329i
\(514\) 6.00000 0.264649
\(515\) 4.89898 + 6.00000i 0.215875 + 0.264392i
\(516\) 16.9706i 0.747087i
\(517\) 9.79796i 0.430914i
\(518\) 16.9706 0.745644
\(519\) 0 0
\(520\) 0 0
\(521\) −22.0454 −0.965827 −0.482913 0.875668i \(-0.660421\pi\)
−0.482913 + 0.875668i \(0.660421\pi\)
\(522\) 14.6969i 0.643268i
\(523\) −13.8564 −0.605898 −0.302949 0.953007i \(-0.597971\pi\)
−0.302949 + 0.953007i \(0.597971\pi\)
\(524\) 3.46410i 0.151330i
\(525\) −20.7846 4.24264i −0.907115 0.185164i
\(526\) 28.2843i 1.23325i
\(527\) 30.0000i 1.30682i
\(528\) 6.00000i 0.261116i
\(529\) 9.00000 0.391304
\(530\) 16.9706 + 20.7846i 0.737154 + 0.902826i
\(531\) −22.0454 −0.956689
\(532\) −10.3923 2.44949i −0.450564 0.106199i
\(533\) 0 0
\(534\) 21.2132i 0.917985i
\(535\) 20.7846 16.9706i 0.898597 0.733701i
\(536\) 13.8564i 0.598506i
\(537\) 29.6985 1.28158
\(538\) 19.5959i 0.844840i
\(539\) 3.46410i 0.149209i
\(540\) −7.34847 9.00000i −0.316228 0.387298i
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) 28.0000i 1.20270i
\(543\) 22.0454i 0.946059i
\(544\) 7.07107i 0.303170i
\(545\) −22.0454 + 18.0000i −0.944322 + 0.771035i
\(546\) 0 0
\(547\) 34.6410 1.48114 0.740571 0.671978i \(-0.234555\pi\)
0.740571 + 0.671978i \(0.234555\pi\)
\(548\) 7.07107 0.302061
\(549\) −30.0000 −1.28037
\(550\) 3.46410 16.9706i 0.147710 0.723627i
\(551\) 4.89898 20.7846i 0.208704 0.885454i
\(552\) 9.79796i 0.417029i
\(553\) −10.3923 −0.441926
\(554\) −12.2474 −0.520344
\(555\) −16.9706 20.7846i −0.720360 0.882258i
\(556\) 10.0000 0.424094
\(557\) −5.65685 −0.239689 −0.119844 0.992793i \(-0.538240\pi\)
−0.119844 + 0.992793i \(0.538240\pi\)
\(558\) 12.7279 0.538816
\(559\) 0 0
\(560\) −4.24264 + 3.46410i −0.179284 + 0.146385i
\(561\) 42.4264i 1.79124i
\(562\) 31.8434i 1.34323i
\(563\) 12.0000i 0.505740i −0.967500 0.252870i \(-0.918626\pi\)
0.967500 0.252870i \(-0.0813744\pi\)
\(564\) 4.89898 0.206284
\(565\) 10.3923 8.48528i 0.437208 0.356978i
\(566\) −24.4949 −1.02960
\(567\) 22.0454i 0.925820i
\(568\) 4.89898i 0.205557i
\(569\) −2.44949 −0.102688 −0.0513440 0.998681i \(-0.516350\pi\)
−0.0513440 + 0.998681i \(0.516350\pi\)
\(570\) 7.39230 + 15.1774i 0.309630 + 0.635712i
\(571\) 4.00000 0.167395 0.0836974 0.996491i \(-0.473327\pi\)
0.0836974 + 0.996491i \(0.473327\pi\)
\(572\) 0 0
\(573\) 30.0000i 1.25327i
\(574\) −6.00000 −0.250435
\(575\) −5.65685 + 27.7128i −0.235907 + 1.15570i
\(576\) −3.00000 −0.125000
\(577\) 4.89898i 0.203947i −0.994787 0.101974i \(-0.967484\pi\)
0.994787 0.101974i \(-0.0325157\pi\)
\(578\) 33.0000i 1.37262i
\(579\) 36.0000 1.49611
\(580\) −6.92820 8.48528i −0.287678 0.352332i
\(581\) 3.46410i 0.143715i
\(582\) 6.00000i 0.248708i
\(583\) −41.5692 −1.72162
\(584\) 9.79796 0.405442
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) −9.89949 −0.408596 −0.204298 0.978909i \(-0.565491\pi\)
−0.204298 + 0.978909i \(0.565491\pi\)
\(588\) 1.73205 0.0714286
\(589\) −18.0000 4.24264i −0.741677 0.174815i
\(590\) 12.7279 10.3923i 0.524000 0.427844i
\(591\) 9.79796 0.403034
\(592\) −6.92820 −0.284747
\(593\) −18.3848 −0.754972 −0.377486 0.926015i \(-0.623211\pi\)
−0.377486 + 0.926015i \(0.623211\pi\)
\(594\) 18.0000 0.738549
\(595\) 30.0000 24.4949i 1.22988 1.00419i
\(596\) 13.8564i 0.567581i
\(597\) −34.6410 −1.41776
\(598\) 0 0
\(599\) 39.1918 1.60134 0.800668 0.599109i \(-0.204478\pi\)
0.800668 + 0.599109i \(0.204478\pi\)
\(600\) 8.48528 + 1.73205i 0.346410 + 0.0707107i
\(601\) 25.4558i 1.03837i −0.854663 0.519183i \(-0.826236\pi\)
0.854663 0.519183i \(-0.173764\pi\)
\(602\) 24.0000i 0.978167i
\(603\) 41.5692 1.69283
\(604\) 12.7279i 0.517892i
\(605\) 1.41421 + 1.73205i 0.0574960 + 0.0704179i
\(606\) 0 0
\(607\) −10.3923 −0.421811 −0.210905 0.977506i \(-0.567641\pi\)
−0.210905 + 0.977506i \(0.567641\pi\)
\(608\) 4.24264 + 1.00000i 0.172062 + 0.0405554i
\(609\) 20.7846i 0.842235i
\(610\) 17.3205 14.1421i 0.701287 0.572598i
\(611\) 0 0
\(612\) 21.2132 0.857493
\(613\) 2.44949i 0.0989340i 0.998776 + 0.0494670i \(0.0157523\pi\)
−0.998776 + 0.0494670i \(0.984248\pi\)
\(614\) 6.92820i 0.279600i
\(615\) 6.00000 + 7.34847i 0.241943 + 0.296319i
\(616\) 8.48528i 0.341882i
\(617\) 1.41421 0.0569341 0.0284670 0.999595i \(-0.490937\pi\)
0.0284670 + 0.999595i \(0.490937\pi\)
\(618\) 6.00000i 0.241355i
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) −7.34847 + 6.00000i −0.295122 + 0.240966i
\(621\) −29.3939 −1.17954
\(622\) 3.46410 0.138898
\(623\) 30.0000i 1.20192i
\(624\) 0 0
\(625\) −23.0000 9.79796i −0.920000 0.391918i
\(626\) 14.6969 0.587408
\(627\) −25.4558 6.00000i −1.01661 0.239617i
\(628\) 7.34847i 0.293236i
\(629\) 48.9898 1.95335
\(630\) 10.3923 + 12.7279i 0.414039 + 0.507093i
\(631\) −4.00000 −0.159237 −0.0796187 0.996825i \(-0.525370\pi\)
−0.0796187 + 0.996825i \(0.525370\pi\)
\(632\) 4.24264 0.168763
\(633\) 44.0908i 1.75245i
\(634\) 6.00000 0.238290
\(635\) 4.89898 + 6.00000i 0.194410 + 0.238103i
\(636\) 20.7846i 0.824163i
\(637\) 0 0
\(638\) 16.9706 0.671871
\(639\) −14.6969 −0.581402
\(640\) 1.73205 1.41421i 0.0684653 0.0559017i
\(641\) 17.1464 0.677243 0.338622 0.940923i \(-0.390039\pi\)
0.338622 + 0.940923i \(0.390039\pi\)
\(642\) −20.7846 −0.820303
\(643\) 34.2929i 1.35238i 0.736728 + 0.676189i \(0.236370\pi\)
−0.736728 + 0.676189i \(0.763630\pi\)
\(644\) 13.8564i 0.546019i
\(645\) −29.3939 + 24.0000i −1.15738 + 0.944999i
\(646\) −30.0000 7.07107i −1.18033 0.278207i
\(647\) −11.3137 −0.444788 −0.222394 0.974957i \(-0.571387\pi\)
−0.222394 + 0.974957i \(0.571387\pi\)
\(648\) 9.00000i 0.353553i
\(649\) 25.4558i 0.999229i
\(650\) 0 0
\(651\) −18.0000 −0.705476
\(652\) 14.6969i 0.575577i
\(653\) 36.7696 1.43890 0.719452 0.694542i \(-0.244393\pi\)
0.719452 + 0.694542i \(0.244393\pi\)
\(654\) 22.0454 0.862044
\(655\) −6.00000 + 4.89898i −0.234439 + 0.191419i
\(656\) 2.44949 0.0956365
\(657\) 29.3939i 1.14676i
\(658\) −6.92820 −0.270089
\(659\) −2.44949 −0.0954186 −0.0477093 0.998861i \(-0.515192\pi\)
−0.0477093 + 0.998861i \(0.515192\pi\)
\(660\) −10.3923 + 8.48528i −0.404520 + 0.330289i
\(661\) 38.1838i 1.48518i 0.669748 + 0.742588i \(0.266402\pi\)
−0.669748 + 0.742588i \(0.733598\pi\)
\(662\) 8.48528 0.329790
\(663\) 0 0
\(664\) 1.41421i 0.0548821i
\(665\) −10.4543 21.4641i −0.405400 0.832342i
\(666\) 20.7846i 0.805387i
\(667\) −27.7128 −1.07304
\(668\) 18.0000i 0.696441i
\(669\) 6.00000 0.231973
\(670\) −24.0000 + 19.5959i −0.927201 + 0.757056i
\(671\) 34.6410i 1.33730i
\(672\) 4.24264 0.163663
\(673\) 38.1051 1.46884 0.734422 0.678693i \(-0.237453\pi\)
0.734422 + 0.678693i \(0.237453\pi\)
\(674\) 20.7846i 0.800593i
\(675\) 5.19615 25.4558i 0.200000 0.979796i
\(676\) 13.0000 0.500000
\(677\) 42.0000i 1.61419i 0.590421 + 0.807096i \(0.298962\pi\)
−0.590421 + 0.807096i \(0.701038\pi\)
\(678\) −10.3923 −0.399114
\(679\) 8.48528i 0.325635i
\(680\) −12.2474 + 10.0000i −0.469668 + 0.383482i
\(681\) 20.7846i 0.796468i
\(682\) 14.6969i 0.562775i
\(683\) 24.0000i 0.918334i 0.888350 + 0.459167i \(0.151852\pi\)
−0.888350 + 0.459167i \(0.848148\pi\)
\(684\) 3.00000 12.7279i 0.114708 0.486664i
\(685\) 10.0000 + 12.2474i 0.382080 + 0.467951i
\(686\) −19.5959 −0.748176
\(687\) 38.1051 1.45380
\(688\) 9.79796i 0.373544i
\(689\) 0 0
\(690\) 16.9706 13.8564i 0.646058 0.527504i
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 0 0
\(693\) −25.4558 −0.966988
\(694\) 24.0416i 0.912608i
\(695\) 14.1421 + 17.3205i 0.536442 + 0.657004i
\(696\) 8.48528i 0.321634i
\(697\) −17.3205 −0.656061
\(698\) 2.00000i 0.0757011i
\(699\) 12.2474 0.463241
\(700\) −12.0000 2.44949i −0.453557 0.0925820i
\(701\) 31.1769i 1.17754i −0.808302 0.588768i \(-0.799613\pi\)
0.808302 0.588768i \(-0.200387\pi\)
\(702\) 0 0
\(703\) 6.92820 29.3939i 0.261302 1.10861i
\(704\) 3.46410i 0.130558i
\(705\) 6.92820 + 8.48528i 0.260931 + 0.319574i
\(706\) 15.5563i 0.585471i
\(707\) 0 0
\(708\) −12.7279 −0.478345
\(709\) −22.0000 −0.826227 −0.413114 0.910679i \(-0.635559\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) 8.48528 6.92820i 0.318447 0.260011i
\(711\) 12.7279i 0.477334i
\(712\) 12.2474i 0.458993i
\(713\) 24.0000i 0.898807i
\(714\) −30.0000 −1.12272
\(715\) 0 0
\(716\) 17.1464 0.640792
\(717\) 12.0000i 0.448148i
\(718\) 13.8564 0.517116
\(719\) 13.8564i 0.516757i −0.966044 0.258378i \(-0.916812\pi\)
0.966044 0.258378i \(-0.0831881\pi\)
\(720\) −4.24264 5.19615i −0.158114 0.193649i
\(721\) 8.48528i 0.316008i
\(722\) −8.48528 + 17.0000i −0.315789 + 0.632674i
\(723\) 14.6969i 0.546585i
\(724\) 12.7279i 0.473029i
\(725\) 4.89898 24.0000i 0.181944 0.891338i
\(726\) 1.73205i 0.0642824i
\(727\) 41.6413i 1.54439i 0.635385 + 0.772196i \(0.280841\pi\)
−0.635385 + 0.772196i \(0.719159\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 13.8564 + 16.9706i 0.512849 + 0.628109i
\(731\) 69.2820i 2.56249i
\(732\) −17.3205 −0.640184
\(733\) 22.0454i 0.814266i 0.913369 + 0.407133i \(0.133471\pi\)
−0.913369 + 0.407133i \(0.866529\pi\)
\(734\) 7.34847 0.271237
\(735\) 2.44949 + 3.00000i 0.0903508 + 0.110657i
\(736\) 5.65685i 0.208514i
\(737\) 48.0000i 1.76810i
\(738\) 7.34847i 0.270501i
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) −9.79796 12.0000i −0.360180 0.441129i
\(741\) 0 0
\(742\) 29.3939i 1.07908i
\(743\) 18.0000i 0.660356i 0.943919 + 0.330178i \(0.107109\pi\)
−0.943919 + 0.330178i \(0.892891\pi\)
\(744\) 7.34847 0.269408
\(745\) −24.0000 + 19.5959i −0.879292 + 0.717939i
\(746\) 6.92820i 0.253660i
\(747\) −4.24264 −0.155230
\(748\) 24.4949i 0.895622i
\(749\) 29.3939 1.07403
\(750\) 9.00000 + 17.1464i 0.328634 + 0.626099i
\(751\) 21.2132i 0.774081i 0.922063 + 0.387040i \(0.126503\pi\)
−0.922063 + 0.387040i \(0.873497\pi\)
\(752\) 2.82843 0.103142
\(753\) 42.0000i 1.53057i
\(754\) 0 0
\(755\) −22.0454 + 18.0000i −0.802315 + 0.655087i
\(756\) 12.7279i 0.462910i
\(757\) 17.1464i 0.623198i −0.950214 0.311599i \(-0.899136\pi\)
0.950214 0.311599i \(-0.100864\pi\)
\(758\) −25.4558 −0.924598
\(759\) 33.9411i 1.23198i
\(760\) 4.26795 + 8.76268i 0.154815 + 0.317856i
\(761\) 48.4974i 1.75803i 0.476794 + 0.879015i \(0.341799\pi\)
−0.476794 + 0.879015i \(0.658201\pi\)
\(762\) 6.00000i 0.217357i
\(763\) −31.1769 −1.12868
\(764\) 17.3205i 0.626634i
\(765\) 30.0000 + 36.7423i 1.08465 + 1.32842i
\(766\) −24.0000 −0.867155
\(767\) 0 0
\(768\) −1.73205 −0.0625000
\(769\) −4.00000 −0.144244 −0.0721218 0.997396i \(-0.522977\pi\)
−0.0721218 + 0.997396i \(0.522977\pi\)
\(770\) 14.6969 12.0000i 0.529641 0.432450i
\(771\) 10.3923i 0.374270i
\(772\) 20.7846 0.748054
\(773\) 24.0000i 0.863220i −0.902060 0.431610i \(-0.857946\pi\)
0.902060 0.431610i \(-0.142054\pi\)
\(774\) 29.3939 1.05654
\(775\) −20.7846 4.24264i −0.746605 0.152400i
\(776\) 3.46410i 0.124354i
\(777\) 29.3939i 1.05450i
\(778\) 13.8564 0.496776
\(779\) −2.44949 + 10.3923i −0.0877621 + 0.372343i
\(780\) 0 0
\(781\) 16.9706i 0.607254i
\(782\) 40.0000i 1.43040i
\(783\) 25.4558 0.909718
\(784\) 1.00000 0.0357143
\(785\) 12.7279 10.3923i 0.454279 0.370917i
\(786\) 6.00000 0.214013
\(787\) 24.2487 0.864373 0.432187 0.901784i \(-0.357742\pi\)
0.432187 + 0.901784i \(0.357742\pi\)
\(788\) 5.65685 0.201517
\(789\) −48.9898 −1.74408
\(790\) 6.00000 + 7.34847i 0.213470