Properties

Label 150.2.e.b.143.4
Level $150$
Weight $2$
Character 150.143
Analytic conductor $1.198$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 150.e (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.19775603032\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 143.4
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 150.143
Dual form 150.2.e.b.107.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 + 0.707107i) q^{2} +(1.67303 - 0.448288i) q^{3} +1.00000i q^{4} +(1.50000 + 0.866025i) q^{6} +(-2.44949 + 2.44949i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(0.707107 + 0.707107i) q^{2} +(1.67303 - 0.448288i) q^{3} +1.00000i q^{4} +(1.50000 + 0.866025i) q^{6} +(-2.44949 + 2.44949i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.59808 - 1.50000i) q^{9} -5.19615i q^{11} +(0.448288 + 1.67303i) q^{12} -3.46410 q^{14} -1.00000 q^{16} +(-2.12132 - 2.12132i) q^{17} +(2.89778 + 0.776457i) q^{18} +1.00000i q^{19} +(-3.00000 + 5.19615i) q^{21} +(3.67423 - 3.67423i) q^{22} +(-4.24264 + 4.24264i) q^{23} +(-0.866025 + 1.50000i) q^{24} +(3.67423 - 3.67423i) q^{27} +(-2.44949 - 2.44949i) q^{28} -2.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.32937 - 8.69333i) q^{33} -3.00000i q^{34} +(1.50000 + 2.59808i) q^{36} +(2.44949 - 2.44949i) q^{37} +(-0.707107 + 0.707107i) q^{38} +5.19615i q^{41} +(-5.79555 + 1.55291i) q^{42} +(2.44949 + 2.44949i) q^{43} +5.19615 q^{44} -6.00000 q^{46} +(-1.67303 + 0.448288i) q^{48} -5.00000i q^{49} +(-4.50000 - 2.59808i) q^{51} +(4.24264 - 4.24264i) q^{53} +5.19615 q^{54} -3.46410i q^{56} +(0.448288 + 1.67303i) q^{57} -10.3923 q^{59} +14.0000 q^{61} +(-1.41421 - 1.41421i) q^{62} +(-2.68973 + 10.0382i) q^{63} -1.00000i q^{64} +(4.50000 - 7.79423i) q^{66} +(-3.67423 + 3.67423i) q^{67} +(2.12132 - 2.12132i) q^{68} +(-5.19615 + 9.00000i) q^{69} +(-0.776457 + 2.89778i) q^{72} +(6.12372 + 6.12372i) q^{73} +3.46410 q^{74} -1.00000 q^{76} +(12.7279 + 12.7279i) q^{77} +14.0000i q^{79} +(4.50000 - 7.79423i) q^{81} +(-3.67423 + 3.67423i) q^{82} +(2.12132 - 2.12132i) q^{83} +(-5.19615 - 3.00000i) q^{84} +3.46410i q^{86} +(3.67423 + 3.67423i) q^{88} +15.5885 q^{89} +(-4.24264 - 4.24264i) q^{92} +(-3.34607 + 0.896575i) q^{93} +(-1.50000 - 0.866025i) q^{96} +(-4.89898 + 4.89898i) q^{97} +(3.53553 - 3.53553i) q^{98} +(-7.79423 - 13.5000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 12q^{6} + O(q^{10}) \) \( 8q + 12q^{6} - 8q^{16} - 24q^{21} - 16q^{31} + 12q^{36} - 48q^{46} - 36q^{51} + 112q^{61} + 36q^{66} - 8q^{76} + 36q^{81} - 12q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/150\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 + 0.707107i 0.500000 + 0.500000i
\(3\) 1.67303 0.448288i 0.965926 0.258819i
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 1.50000 + 0.866025i 0.612372 + 0.353553i
\(7\) −2.44949 + 2.44949i −0.925820 + 0.925820i −0.997433 0.0716124i \(-0.977186\pi\)
0.0716124 + 0.997433i \(0.477186\pi\)
\(8\) −0.707107 + 0.707107i −0.250000 + 0.250000i
\(9\) 2.59808 1.50000i 0.866025 0.500000i
\(10\) 0 0
\(11\) 5.19615i 1.56670i −0.621582 0.783349i \(-0.713510\pi\)
0.621582 0.783349i \(-0.286490\pi\)
\(12\) 0.448288 + 1.67303i 0.129410 + 0.482963i
\(13\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(14\) −3.46410 −0.925820
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) −2.12132 2.12132i −0.514496 0.514496i 0.401405 0.915901i \(-0.368522\pi\)
−0.915901 + 0.401405i \(0.868522\pi\)
\(18\) 2.89778 + 0.776457i 0.683013 + 0.183013i
\(19\) 1.00000i 0.229416i 0.993399 + 0.114708i \(0.0365932\pi\)
−0.993399 + 0.114708i \(0.963407\pi\)
\(20\) 0 0
\(21\) −3.00000 + 5.19615i −0.654654 + 1.13389i
\(22\) 3.67423 3.67423i 0.783349 0.783349i
\(23\) −4.24264 + 4.24264i −0.884652 + 0.884652i −0.994003 0.109351i \(-0.965123\pi\)
0.109351 + 0.994003i \(0.465123\pi\)
\(24\) −0.866025 + 1.50000i −0.176777 + 0.306186i
\(25\) 0 0
\(26\) 0 0
\(27\) 3.67423 3.67423i 0.707107 0.707107i
\(28\) −2.44949 2.44949i −0.462910 0.462910i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) −0.707107 0.707107i −0.125000 0.125000i
\(33\) −2.32937 8.69333i −0.405492 1.51331i
\(34\) 3.00000i 0.514496i
\(35\) 0 0
\(36\) 1.50000 + 2.59808i 0.250000 + 0.433013i
\(37\) 2.44949 2.44949i 0.402694 0.402694i −0.476488 0.879181i \(-0.658090\pi\)
0.879181 + 0.476488i \(0.158090\pi\)
\(38\) −0.707107 + 0.707107i −0.114708 + 0.114708i
\(39\) 0 0
\(40\) 0 0
\(41\) 5.19615i 0.811503i 0.913984 + 0.405751i \(0.132990\pi\)
−0.913984 + 0.405751i \(0.867010\pi\)
\(42\) −5.79555 + 1.55291i −0.894274 + 0.239620i
\(43\) 2.44949 + 2.44949i 0.373544 + 0.373544i 0.868766 0.495222i \(-0.164913\pi\)
−0.495222 + 0.868766i \(0.664913\pi\)
\(44\) 5.19615 0.783349
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(48\) −1.67303 + 0.448288i −0.241481 + 0.0647048i
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) −4.50000 2.59808i −0.630126 0.363803i
\(52\) 0 0
\(53\) 4.24264 4.24264i 0.582772 0.582772i −0.352892 0.935664i \(-0.614802\pi\)
0.935664 + 0.352892i \(0.114802\pi\)
\(54\) 5.19615 0.707107
\(55\) 0 0
\(56\) 3.46410i 0.462910i
\(57\) 0.448288 + 1.67303i 0.0593772 + 0.221599i
\(58\) 0 0
\(59\) −10.3923 −1.35296 −0.676481 0.736460i \(-0.736496\pi\)
−0.676481 + 0.736460i \(0.736496\pi\)
\(60\) 0 0
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) −1.41421 1.41421i −0.179605 0.179605i
\(63\) −2.68973 + 10.0382i −0.338874 + 1.26469i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) 4.50000 7.79423i 0.553912 0.959403i
\(67\) −3.67423 + 3.67423i −0.448879 + 0.448879i −0.894982 0.446103i \(-0.852812\pi\)
0.446103 + 0.894982i \(0.352812\pi\)
\(68\) 2.12132 2.12132i 0.257248 0.257248i
\(69\) −5.19615 + 9.00000i −0.625543 + 1.08347i
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −0.776457 + 2.89778i −0.0915064 + 0.341506i
\(73\) 6.12372 + 6.12372i 0.716728 + 0.716728i 0.967934 0.251206i \(-0.0808271\pi\)
−0.251206 + 0.967934i \(0.580827\pi\)
\(74\) 3.46410 0.402694
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) 12.7279 + 12.7279i 1.45048 + 1.45048i
\(78\) 0 0
\(79\) 14.0000i 1.57512i 0.616236 + 0.787562i \(0.288657\pi\)
−0.616236 + 0.787562i \(0.711343\pi\)
\(80\) 0 0
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) −3.67423 + 3.67423i −0.405751 + 0.405751i
\(83\) 2.12132 2.12132i 0.232845 0.232845i −0.581034 0.813879i \(-0.697352\pi\)
0.813879 + 0.581034i \(0.197352\pi\)
\(84\) −5.19615 3.00000i −0.566947 0.327327i
\(85\) 0 0
\(86\) 3.46410i 0.373544i
\(87\) 0 0
\(88\) 3.67423 + 3.67423i 0.391675 + 0.391675i
\(89\) 15.5885 1.65237 0.826187 0.563397i \(-0.190506\pi\)
0.826187 + 0.563397i \(0.190506\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −4.24264 4.24264i −0.442326 0.442326i
\(93\) −3.34607 + 0.896575i −0.346971 + 0.0929705i
\(94\) 0 0
\(95\) 0 0
\(96\) −1.50000 0.866025i −0.153093 0.0883883i
\(97\) −4.89898 + 4.89898i −0.497416 + 0.497416i −0.910633 0.413217i \(-0.864405\pi\)
0.413217 + 0.910633i \(0.364405\pi\)
\(98\) 3.53553 3.53553i 0.357143 0.357143i
\(99\) −7.79423 13.5000i −0.783349 1.35680i
\(100\) 0 0
\(101\) 10.3923i 1.03407i 0.855963 + 0.517036i \(0.172965\pi\)
−0.855963 + 0.517036i \(0.827035\pi\)
\(102\) −1.34486 5.01910i −0.133161 0.496965i
\(103\) −9.79796 9.79796i −0.965422 0.965422i 0.0340002 0.999422i \(-0.489175\pi\)
−0.999422 + 0.0340002i \(0.989175\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −6.36396 6.36396i −0.615227 0.615227i 0.329076 0.944303i \(-0.393263\pi\)
−0.944303 + 0.329076i \(0.893263\pi\)
\(108\) 3.67423 + 3.67423i 0.353553 + 0.353553i
\(109\) 10.0000i 0.957826i −0.877862 0.478913i \(-0.841031\pi\)
0.877862 0.478913i \(-0.158969\pi\)
\(110\) 0 0
\(111\) 3.00000 5.19615i 0.284747 0.493197i
\(112\) 2.44949 2.44949i 0.231455 0.231455i
\(113\) 6.36396 6.36396i 0.598671 0.598671i −0.341288 0.939959i \(-0.610863\pi\)
0.939959 + 0.341288i \(0.110863\pi\)
\(114\) −0.866025 + 1.50000i −0.0811107 + 0.140488i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −7.34847 7.34847i −0.676481 0.676481i
\(119\) 10.3923 0.952661
\(120\) 0 0
\(121\) −16.0000 −1.45455
\(122\) 9.89949 + 9.89949i 0.896258 + 0.896258i
\(123\) 2.32937 + 8.69333i 0.210032 + 0.783851i
\(124\) 2.00000i 0.179605i
\(125\) 0 0
\(126\) −9.00000 + 5.19615i −0.801784 + 0.462910i
\(127\) 7.34847 7.34847i 0.652071 0.652071i −0.301420 0.953491i \(-0.597461\pi\)
0.953491 + 0.301420i \(0.0974607\pi\)
\(128\) 0.707107 0.707107i 0.0625000 0.0625000i
\(129\) 5.19615 + 3.00000i 0.457496 + 0.264135i
\(130\) 0 0
\(131\) 10.3923i 0.907980i 0.891007 + 0.453990i \(0.150000\pi\)
−0.891007 + 0.453990i \(0.850000\pi\)
\(132\) 8.69333 2.32937i 0.756657 0.202746i
\(133\) −2.44949 2.44949i −0.212398 0.212398i
\(134\) −5.19615 −0.448879
\(135\) 0 0
\(136\) 3.00000 0.257248
\(137\) −14.8492 14.8492i −1.26866 1.26866i −0.946783 0.321874i \(-0.895687\pi\)
−0.321874 0.946783i \(-0.604313\pi\)
\(138\) −10.0382 + 2.68973i −0.854508 + 0.228965i
\(139\) 7.00000i 0.593732i 0.954919 + 0.296866i \(0.0959415\pi\)
−0.954919 + 0.296866i \(0.904058\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −2.59808 + 1.50000i −0.216506 + 0.125000i
\(145\) 0 0
\(146\) 8.66025i 0.716728i
\(147\) −2.24144 8.36516i −0.184871 0.689947i
\(148\) 2.44949 + 2.44949i 0.201347 + 0.201347i
\(149\) −20.7846 −1.70274 −0.851371 0.524564i \(-0.824228\pi\)
−0.851371 + 0.524564i \(0.824228\pi\)
\(150\) 0 0
\(151\) −14.0000 −1.13930 −0.569652 0.821886i \(-0.692922\pi\)
−0.569652 + 0.821886i \(0.692922\pi\)
\(152\) −0.707107 0.707107i −0.0573539 0.0573539i
\(153\) −8.69333 2.32937i −0.702814 0.188319i
\(154\) 18.0000i 1.45048i
\(155\) 0 0
\(156\) 0 0
\(157\) 12.2474 12.2474i 0.977453 0.977453i −0.0222985 0.999751i \(-0.507098\pi\)
0.999751 + 0.0222985i \(0.00709843\pi\)
\(158\) −9.89949 + 9.89949i −0.787562 + 0.787562i
\(159\) 5.19615 9.00000i 0.412082 0.713746i
\(160\) 0 0
\(161\) 20.7846i 1.63806i
\(162\) 8.69333 2.32937i 0.683013 0.183013i
\(163\) −3.67423 3.67423i −0.287788 0.287788i 0.548417 0.836205i \(-0.315231\pi\)
−0.836205 + 0.548417i \(0.815231\pi\)
\(164\) −5.19615 −0.405751
\(165\) 0 0
\(166\) 3.00000 0.232845
\(167\) 8.48528 + 8.48528i 0.656611 + 0.656611i 0.954577 0.297966i \(-0.0963081\pi\)
−0.297966 + 0.954577i \(0.596308\pi\)
\(168\) −1.55291 5.79555i −0.119810 0.447137i
\(169\) 13.0000i 1.00000i
\(170\) 0 0
\(171\) 1.50000 + 2.59808i 0.114708 + 0.198680i
\(172\) −2.44949 + 2.44949i −0.186772 + 0.186772i
\(173\) −8.48528 + 8.48528i −0.645124 + 0.645124i −0.951811 0.306687i \(-0.900780\pi\)
0.306687 + 0.951811i \(0.400780\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.19615i 0.391675i
\(177\) −17.3867 + 4.65874i −1.30686 + 0.350173i
\(178\) 11.0227 + 11.0227i 0.826187 + 0.826187i
\(179\) 15.5885 1.16514 0.582568 0.812782i \(-0.302048\pi\)
0.582568 + 0.812782i \(0.302048\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) 23.4225 6.27603i 1.73144 0.463937i
\(184\) 6.00000i 0.442326i
\(185\) 0 0
\(186\) −3.00000 1.73205i −0.219971 0.127000i
\(187\) −11.0227 + 11.0227i −0.806060 + 0.806060i
\(188\) 0 0
\(189\) 18.0000i 1.30931i
\(190\) 0 0
\(191\) 10.3923i 0.751961i −0.926628 0.375980i \(-0.877306\pi\)
0.926628 0.375980i \(-0.122694\pi\)
\(192\) −0.448288 1.67303i −0.0323524 0.120741i
\(193\) 6.12372 + 6.12372i 0.440795 + 0.440795i 0.892279 0.451484i \(-0.149105\pi\)
−0.451484 + 0.892279i \(0.649105\pi\)
\(194\) −6.92820 −0.497416
\(195\) 0 0
\(196\) 5.00000 0.357143
\(197\) −4.24264 4.24264i −0.302276 0.302276i 0.539628 0.841904i \(-0.318565\pi\)
−0.841904 + 0.539628i \(0.818565\pi\)
\(198\) 4.03459 15.0573i 0.286726 1.07008i
\(199\) 16.0000i 1.13421i −0.823646 0.567105i \(-0.808063\pi\)
0.823646 0.567105i \(-0.191937\pi\)
\(200\) 0 0
\(201\) −4.50000 + 7.79423i −0.317406 + 0.549762i
\(202\) −7.34847 + 7.34847i −0.517036 + 0.517036i
\(203\) 0 0
\(204\) 2.59808 4.50000i 0.181902 0.315063i
\(205\) 0 0
\(206\) 13.8564i 0.965422i
\(207\) −4.65874 + 17.3867i −0.323805 + 1.20846i
\(208\) 0 0
\(209\) 5.19615 0.359425
\(210\) 0 0
\(211\) 23.0000 1.58339 0.791693 0.610920i \(-0.209200\pi\)
0.791693 + 0.610920i \(0.209200\pi\)
\(212\) 4.24264 + 4.24264i 0.291386 + 0.291386i
\(213\) 0 0
\(214\) 9.00000i 0.615227i
\(215\) 0 0
\(216\) 5.19615i 0.353553i
\(217\) 4.89898 4.89898i 0.332564 0.332564i
\(218\) 7.07107 7.07107i 0.478913 0.478913i
\(219\) 12.9904 + 7.50000i 0.877809 + 0.506803i
\(220\) 0 0
\(221\) 0 0
\(222\) 5.79555 1.55291i 0.388972 0.104225i
\(223\) −9.79796 9.79796i −0.656120 0.656120i 0.298340 0.954460i \(-0.403567\pi\)
−0.954460 + 0.298340i \(0.903567\pi\)
\(224\) 3.46410 0.231455
\(225\) 0 0
\(226\) 9.00000 0.598671
\(227\) 8.48528 + 8.48528i 0.563188 + 0.563188i 0.930212 0.367024i \(-0.119623\pi\)
−0.367024 + 0.930212i \(0.619623\pi\)
\(228\) −1.67303 + 0.448288i −0.110799 + 0.0296886i
\(229\) 16.0000i 1.05731i 0.848837 + 0.528655i \(0.177303\pi\)
−0.848837 + 0.528655i \(0.822697\pi\)
\(230\) 0 0
\(231\) 27.0000 + 15.5885i 1.77647 + 1.02565i
\(232\) 0 0
\(233\) −12.7279 + 12.7279i −0.833834 + 0.833834i −0.988039 0.154205i \(-0.950718\pi\)
0.154205 + 0.988039i \(0.450718\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 10.3923i 0.676481i
\(237\) 6.27603 + 23.4225i 0.407672 + 1.52145i
\(238\) 7.34847 + 7.34847i 0.476331 + 0.476331i
\(239\) −20.7846 −1.34444 −0.672222 0.740349i \(-0.734660\pi\)
−0.672222 + 0.740349i \(0.734660\pi\)
\(240\) 0 0
\(241\) −1.00000 −0.0644157 −0.0322078 0.999481i \(-0.510254\pi\)
−0.0322078 + 0.999481i \(0.510254\pi\)
\(242\) −11.3137 11.3137i −0.727273 0.727273i
\(243\) 4.03459 15.0573i 0.258819 0.965926i
\(244\) 14.0000i 0.896258i
\(245\) 0 0
\(246\) −4.50000 + 7.79423i −0.286910 + 0.496942i
\(247\) 0 0
\(248\) 1.41421 1.41421i 0.0898027 0.0898027i
\(249\) 2.59808 4.50000i 0.164646 0.285176i
\(250\) 0 0
\(251\) 5.19615i 0.327978i −0.986462 0.163989i \(-0.947564\pi\)
0.986462 0.163989i \(-0.0524362\pi\)
\(252\) −10.0382 2.68973i −0.632347 0.169437i
\(253\) 22.0454 + 22.0454i 1.38598 + 1.38598i
\(254\) 10.3923 0.652071
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 4.24264 + 4.24264i 0.264649 + 0.264649i 0.826940 0.562291i \(-0.190080\pi\)
−0.562291 + 0.826940i \(0.690080\pi\)
\(258\) 1.55291 + 5.79555i 0.0966802 + 0.360815i
\(259\) 12.0000i 0.745644i
\(260\) 0 0
\(261\) 0 0
\(262\) −7.34847 + 7.34847i −0.453990 + 0.453990i
\(263\) 12.7279 12.7279i 0.784837 0.784837i −0.195805 0.980643i \(-0.562732\pi\)
0.980643 + 0.195805i \(0.0627321\pi\)
\(264\) 7.79423 + 4.50000i 0.479702 + 0.276956i
\(265\) 0 0
\(266\) 3.46410i 0.212398i
\(267\) 26.0800 6.98811i 1.59607 0.427666i
\(268\) −3.67423 3.67423i −0.224440 0.224440i
\(269\) −20.7846 −1.26726 −0.633630 0.773636i \(-0.718436\pi\)
−0.633630 + 0.773636i \(0.718436\pi\)
\(270\) 0 0
\(271\) −10.0000 −0.607457 −0.303728 0.952759i \(-0.598232\pi\)
−0.303728 + 0.952759i \(0.598232\pi\)
\(272\) 2.12132 + 2.12132i 0.128624 + 0.128624i
\(273\) 0 0
\(274\) 21.0000i 1.26866i
\(275\) 0 0
\(276\) −9.00000 5.19615i −0.541736 0.312772i
\(277\) 9.79796 9.79796i 0.588702 0.588702i −0.348578 0.937280i \(-0.613335\pi\)
0.937280 + 0.348578i \(0.113335\pi\)
\(278\) −4.94975 + 4.94975i −0.296866 + 0.296866i
\(279\) −5.19615 + 3.00000i −0.311086 + 0.179605i
\(280\) 0 0
\(281\) 20.7846i 1.23991i −0.784639 0.619953i \(-0.787152\pi\)
0.784639 0.619953i \(-0.212848\pi\)
\(282\) 0 0
\(283\) −6.12372 6.12372i −0.364018 0.364018i 0.501272 0.865290i \(-0.332866\pi\)
−0.865290 + 0.501272i \(0.832866\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −12.7279 12.7279i −0.751305 0.751305i
\(288\) −2.89778 0.776457i −0.170753 0.0457532i
\(289\) 8.00000i 0.470588i
\(290\) 0 0
\(291\) −6.00000 + 10.3923i −0.351726 + 0.609208i
\(292\) −6.12372 + 6.12372i −0.358364 + 0.358364i
\(293\) −21.2132 + 21.2132i −1.23929 + 1.23929i −0.278996 + 0.960292i \(0.590002\pi\)
−0.960292 + 0.278996i \(0.909998\pi\)
\(294\) 4.33013 7.50000i 0.252538 0.437409i
\(295\) 0 0
\(296\) 3.46410i 0.201347i
\(297\) −19.0919 19.0919i −1.10782 1.10782i
\(298\) −14.6969 14.6969i −0.851371 0.851371i
\(299\) 0 0
\(300\) 0 0
\(301\) −12.0000 −0.691669
\(302\) −9.89949 9.89949i −0.569652 0.569652i
\(303\) 4.65874 + 17.3867i 0.267638 + 0.998838i
\(304\) 1.00000i 0.0573539i
\(305\) 0 0
\(306\) −4.50000 7.79423i −0.257248 0.445566i
\(307\) 1.22474 1.22474i 0.0698999 0.0698999i −0.671293 0.741192i \(-0.734261\pi\)
0.741192 + 0.671293i \(0.234261\pi\)
\(308\) −12.7279 + 12.7279i −0.725241 + 0.725241i
\(309\) −20.7846 12.0000i −1.18240 0.682656i
\(310\) 0 0
\(311\) 31.1769i 1.76788i 0.467600 + 0.883940i \(0.345119\pi\)
−0.467600 + 0.883940i \(0.654881\pi\)
\(312\) 0 0
\(313\) −14.6969 14.6969i −0.830720 0.830720i 0.156895 0.987615i \(-0.449852\pi\)
−0.987615 + 0.156895i \(0.949852\pi\)
\(314\) 17.3205 0.977453
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) 8.48528 + 8.48528i 0.476581 + 0.476581i 0.904036 0.427456i \(-0.140590\pi\)
−0.427456 + 0.904036i \(0.640590\pi\)
\(318\) 10.0382 2.68973i 0.562914 0.150832i
\(319\) 0 0
\(320\) 0 0
\(321\) −13.5000 7.79423i −0.753497 0.435031i
\(322\) 14.6969 14.6969i 0.819028 0.819028i
\(323\) 2.12132 2.12132i 0.118033 0.118033i
\(324\) 7.79423 + 4.50000i 0.433013 + 0.250000i
\(325\) 0 0
\(326\) 5.19615i 0.287788i
\(327\) −4.48288 16.7303i −0.247904 0.925189i
\(328\) −3.67423 3.67423i −0.202876 0.202876i
\(329\) 0 0
\(330\) 0 0
\(331\) −13.0000 −0.714545 −0.357272 0.934000i \(-0.616293\pi\)
−0.357272 + 0.934000i \(0.616293\pi\)
\(332\) 2.12132 + 2.12132i 0.116423 + 0.116423i
\(333\) 2.68973 10.0382i 0.147396 0.550090i
\(334\) 12.0000i 0.656611i
\(335\) 0 0
\(336\) 3.00000 5.19615i 0.163663 0.283473i
\(337\) −3.67423 + 3.67423i −0.200148 + 0.200148i −0.800064 0.599915i \(-0.795201\pi\)
0.599915 + 0.800064i \(0.295201\pi\)
\(338\) 9.19239 9.19239i 0.500000 0.500000i
\(339\) 7.79423 13.5000i 0.423324 0.733219i
\(340\) 0 0
\(341\) 10.3923i 0.562775i
\(342\) −0.776457 + 2.89778i −0.0419860 + 0.156694i
\(343\) −4.89898 4.89898i −0.264520 0.264520i
\(344\) −3.46410 −0.186772
\(345\) 0 0
\(346\) −12.0000 −0.645124
\(347\) 6.36396 + 6.36396i 0.341635 + 0.341635i 0.856982 0.515347i \(-0.172337\pi\)
−0.515347 + 0.856982i \(0.672337\pi\)
\(348\) 0 0
\(349\) 22.0000i 1.17763i 0.808267 + 0.588817i \(0.200406\pi\)
−0.808267 + 0.588817i \(0.799594\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −3.67423 + 3.67423i −0.195837 + 0.195837i
\(353\) 12.7279 12.7279i 0.677439 0.677439i −0.281981 0.959420i \(-0.590992\pi\)
0.959420 + 0.281981i \(0.0909915\pi\)
\(354\) −15.5885 9.00000i −0.828517 0.478345i
\(355\) 0 0
\(356\) 15.5885i 0.826187i
\(357\) 17.3867 4.65874i 0.920200 0.246567i
\(358\) 11.0227 + 11.0227i 0.582568 + 0.582568i
\(359\) 10.3923 0.548485 0.274242 0.961661i \(-0.411573\pi\)
0.274242 + 0.961661i \(0.411573\pi\)
\(360\) 0 0
\(361\) 18.0000 0.947368
\(362\) −1.41421 1.41421i −0.0743294 0.0743294i
\(363\) −26.7685 + 7.17260i −1.40498 + 0.376464i
\(364\) 0 0
\(365\) 0 0
\(366\) 21.0000 + 12.1244i 1.09769 + 0.633750i
\(367\) 14.6969 14.6969i 0.767174 0.767174i −0.210434 0.977608i \(-0.567488\pi\)
0.977608 + 0.210434i \(0.0674877\pi\)
\(368\) 4.24264 4.24264i 0.221163 0.221163i
\(369\) 7.79423 + 13.5000i 0.405751 + 0.702782i
\(370\) 0 0
\(371\) 20.7846i 1.07908i
\(372\) −0.896575 3.34607i −0.0464853 0.173485i
\(373\) −2.44949 2.44949i −0.126830 0.126830i 0.640843 0.767672i \(-0.278585\pi\)
−0.767672 + 0.640843i \(0.778585\pi\)
\(374\) −15.5885 −0.806060
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) −12.7279 + 12.7279i −0.654654 + 0.654654i
\(379\) 11.0000i 0.565032i −0.959263 0.282516i \(-0.908831\pi\)
0.959263 0.282516i \(-0.0911690\pi\)
\(380\) 0 0
\(381\) 9.00000 15.5885i 0.461084 0.798621i
\(382\) 7.34847 7.34847i 0.375980 0.375980i
\(383\) 4.24264 4.24264i 0.216789 0.216789i −0.590355 0.807144i \(-0.701012\pi\)
0.807144 + 0.590355i \(0.201012\pi\)
\(384\) 0.866025 1.50000i 0.0441942 0.0765466i
\(385\) 0 0
\(386\) 8.66025i 0.440795i
\(387\) 10.0382 + 2.68973i 0.510270 + 0.136726i
\(388\) −4.89898 4.89898i −0.248708 0.248708i
\(389\) 10.3923 0.526911 0.263455 0.964672i \(-0.415138\pi\)
0.263455 + 0.964672i \(0.415138\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) 3.53553 + 3.53553i 0.178571 + 0.178571i
\(393\) 4.65874 + 17.3867i 0.235002 + 0.877041i
\(394\) 6.00000i 0.302276i
\(395\) 0 0
\(396\) 13.5000 7.79423i 0.678401 0.391675i
\(397\) −19.5959 + 19.5959i −0.983491 + 0.983491i −0.999866 0.0163750i \(-0.994787\pi\)
0.0163750 + 0.999866i \(0.494787\pi\)
\(398\) 11.3137 11.3137i 0.567105 0.567105i
\(399\) −5.19615 3.00000i −0.260133 0.150188i
\(400\) 0 0
\(401\) 5.19615i 0.259483i −0.991548 0.129742i \(-0.958585\pi\)
0.991548 0.129742i \(-0.0414148\pi\)
\(402\) −8.69333 + 2.32937i −0.433584 + 0.116178i
\(403\) 0 0
\(404\) −10.3923 −0.517036
\(405\) 0 0
\(406\) 0 0
\(407\) −12.7279 12.7279i −0.630900 0.630900i
\(408\) 5.01910 1.34486i 0.248482 0.0665807i
\(409\) 5.00000i 0.247234i −0.992330 0.123617i \(-0.960551\pi\)
0.992330 0.123617i \(-0.0394494\pi\)
\(410\) 0 0
\(411\) −31.5000 18.1865i −1.55378 0.897076i
\(412\) 9.79796 9.79796i 0.482711 0.482711i
\(413\) 25.4558 25.4558i 1.25260 1.25260i
\(414\) −15.5885 + 9.00000i −0.766131 + 0.442326i
\(415\) 0 0
\(416\) 0 0
\(417\) 3.13801 + 11.7112i 0.153669 + 0.573501i
\(418\) 3.67423 + 3.67423i 0.179713 + 0.179713i
\(419\) 25.9808 1.26924 0.634622 0.772823i \(-0.281156\pi\)
0.634622 + 0.772823i \(0.281156\pi\)
\(420\) 0 0
\(421\) 4.00000 0.194948 0.0974740 0.995238i \(-0.468924\pi\)
0.0974740 + 0.995238i \(0.468924\pi\)
\(422\) 16.2635 + 16.2635i 0.791693 + 0.791693i
\(423\) 0 0
\(424\) 6.00000i 0.291386i
\(425\) 0 0
\(426\) 0 0
\(427\) −34.2929 + 34.2929i −1.65955 + 1.65955i
\(428\) 6.36396 6.36396i 0.307614 0.307614i
\(429\) 0 0
\(430\) 0 0
\(431\) 10.3923i 0.500580i −0.968171 0.250290i \(-0.919474\pi\)
0.968171 0.250290i \(-0.0805259\pi\)
\(432\) −3.67423 + 3.67423i −0.176777 + 0.176777i
\(433\) 15.9217 + 15.9217i 0.765147 + 0.765147i 0.977248 0.212101i \(-0.0680304\pi\)
−0.212101 + 0.977248i \(0.568030\pi\)
\(434\) 6.92820 0.332564
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) −4.24264 4.24264i −0.202953 0.202953i
\(438\) 3.88229 + 14.4889i 0.185503 + 0.692306i
\(439\) 4.00000i 0.190910i −0.995434 0.0954548i \(-0.969569\pi\)
0.995434 0.0954548i \(-0.0304305\pi\)
\(440\) 0 0
\(441\) −7.50000 12.9904i −0.357143 0.618590i
\(442\) 0 0
\(443\) −14.8492 + 14.8492i −0.705509 + 0.705509i −0.965587 0.260079i \(-0.916252\pi\)
0.260079 + 0.965587i \(0.416252\pi\)
\(444\) 5.19615 + 3.00000i 0.246598 + 0.142374i
\(445\) 0 0
\(446\) 13.8564i 0.656120i
\(447\) −34.7733 + 9.31749i −1.64472 + 0.440702i
\(448\) 2.44949 + 2.44949i 0.115728 + 0.115728i
\(449\) 25.9808 1.22611 0.613054 0.790041i \(-0.289941\pi\)
0.613054 + 0.790041i \(0.289941\pi\)
\(450\) 0 0
\(451\) 27.0000 1.27138
\(452\) 6.36396 + 6.36396i 0.299336 + 0.299336i
\(453\) −23.4225 + 6.27603i −1.10048 + 0.294874i
\(454\) 12.0000i 0.563188i
\(455\) 0 0
\(456\) −1.50000 0.866025i −0.0702439 0.0405554i
\(457\) −18.3712 + 18.3712i −0.859367 + 0.859367i −0.991264 0.131896i \(-0.957893\pi\)
0.131896 + 0.991264i \(0.457893\pi\)
\(458\) −11.3137 + 11.3137i −0.528655 + 0.528655i
\(459\) −15.5885 −0.727607
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) 8.06918 + 30.1146i 0.375412 + 1.40106i
\(463\) 24.4949 + 24.4949i 1.13837 + 1.13837i 0.988742 + 0.149633i \(0.0478091\pi\)
0.149633 + 0.988742i \(0.452191\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −18.0000 −0.833834
\(467\) 8.48528 + 8.48528i 0.392652 + 0.392652i 0.875632 0.482980i \(-0.160445\pi\)
−0.482980 + 0.875632i \(0.660445\pi\)
\(468\) 0 0
\(469\) 18.0000i 0.831163i
\(470\) 0 0
\(471\) 15.0000 25.9808i 0.691164 1.19713i
\(472\) 7.34847 7.34847i 0.338241 0.338241i
\(473\) 12.7279 12.7279i 0.585230 0.585230i
\(474\) −12.1244 + 21.0000i −0.556890 + 0.964562i
\(475\) 0 0
\(476\) 10.3923i 0.476331i
\(477\) 4.65874 17.3867i 0.213309 0.796081i
\(478\) −14.6969 14.6969i −0.672222 0.672222i
\(479\) −10.3923 −0.474837 −0.237418 0.971408i \(-0.576301\pi\)
−0.237418 + 0.971408i \(0.576301\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.707107 0.707107i −0.0322078 0.0322078i
\(483\) −9.31749 34.7733i −0.423960 1.58224i
\(484\) 16.0000i 0.727273i
\(485\) 0 0
\(486\) 13.5000 7.79423i 0.612372 0.353553i
\(487\) 22.0454 22.0454i 0.998973 0.998973i −0.00102669 0.999999i \(-0.500327\pi\)
0.999999 + 0.00102669i \(0.000326807\pi\)
\(488\) −9.89949 + 9.89949i −0.448129 + 0.448129i
\(489\) −7.79423 4.50000i −0.352467 0.203497i
\(490\) 0 0
\(491\) 31.1769i 1.40699i −0.710698 0.703497i \(-0.751621\pi\)
0.710698 0.703497i \(-0.248379\pi\)
\(492\) −8.69333 + 2.32937i −0.391926 + 0.105016i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) 5.01910 1.34486i 0.224911 0.0602648i
\(499\) 20.0000i 0.895323i 0.894203 + 0.447661i \(0.147743\pi\)
−0.894203 + 0.447661i \(0.852257\pi\)
\(500\) 0 0
\(501\) 18.0000 + 10.3923i 0.804181 + 0.464294i
\(502\) 3.67423 3.67423i 0.163989 0.163989i
\(503\) 8.48528 8.48528i 0.378340 0.378340i −0.492163 0.870503i \(-0.663794\pi\)
0.870503 + 0.492163i \(0.163794\pi\)
\(504\) −5.19615 9.00000i −0.231455 0.400892i
\(505\) 0 0
\(506\) 31.1769i 1.38598i
\(507\) −5.82774 21.7494i −0.258819 0.965926i
\(508\) 7.34847 + 7.34847i 0.326036 + 0.326036i
\(509\) 10.3923 0.460631 0.230315 0.973116i \(-0.426024\pi\)
0.230315 + 0.973116i \(0.426024\pi\)
\(510\) 0 0
\(511\) −30.0000 −1.32712
\(512\) 0.707107 + 0.707107i 0.0312500 + 0.0312500i
\(513\) 3.67423 + 3.67423i 0.162221 + 0.162221i
\(514\) 6.00000i 0.264649i
\(515\) 0 0
\(516\) −3.00000 + 5.19615i −0.132068 + 0.228748i
\(517\) 0 0
\(518\) −8.48528 + 8.48528i −0.372822 + 0.372822i
\(519\) −10.3923 + 18.0000i −0.456172 + 0.790112i
\(520\) 0 0
\(521\) 36.3731i 1.59353i 0.604287 + 0.796766i \(0.293458\pi\)
−0.604287 + 0.796766i \(0.706542\pi\)
\(522\) 0 0
\(523\) 30.6186 + 30.6186i 1.33886 + 1.33886i 0.897167 + 0.441692i \(0.145622\pi\)
0.441692 + 0.897167i \(0.354378\pi\)
\(524\) −10.3923 −0.453990
\(525\) 0 0
\(526\) 18.0000 0.784837
\(527\) 4.24264 + 4.24264i 0.184812 + 0.184812i
\(528\) 2.32937 + 8.69333i 0.101373 + 0.378329i
\(529\) 13.0000i 0.565217i
\(530\) 0 0
\(531\) −27.0000 + 15.5885i −1.17170 + 0.676481i
\(532\) 2.44949 2.44949i 0.106199 0.106199i
\(533\) 0 0
\(534\) 23.3827 + 13.5000i 1.01187 + 0.584202i
\(535\) 0 0
\(536\) 5.19615i 0.224440i
\(537\) 26.0800 6.98811i 1.12543 0.301559i
\(538\) −14.6969 14.6969i −0.633630 0.633630i
\(539\) −25.9808 −1.11907
\(540\) 0 0
\(541\) 8.00000 0.343947 0.171973 0.985102i \(-0.444986\pi\)
0.171973 + 0.985102i \(0.444986\pi\)
\(542\) −7.07107 7.07107i −0.303728 0.303728i
\(543\) −3.34607 + 0.896575i −0.143593 + 0.0384757i
\(544\) 3.00000i 0.128624i
\(545\) 0 0
\(546\) 0 0
\(547\) 8.57321 8.57321i 0.366564 0.366564i −0.499658 0.866223i \(-0.666541\pi\)
0.866223 + 0.499658i \(0.166541\pi\)
\(548\) 14.8492 14.8492i 0.634328 0.634328i
\(549\) 36.3731 21.0000i 1.55236 0.896258i
\(550\) 0 0
\(551\) 0 0
\(552\) −2.68973 10.0382i −0.114482 0.427254i
\(553\) −34.2929 34.2929i −1.45828 1.45828i
\(554\) 13.8564 0.588702
\(555\) 0 0
\(556\) −7.00000 −0.296866
\(557\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(558\) −5.79555 1.55291i −0.245345 0.0657401i
\(559\) 0 0
\(560\) 0 0
\(561\) −13.5000 + 23.3827i −0.569970 + 0.987218i
\(562\) 14.6969 14.6969i 0.619953 0.619953i
\(563\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 8.66025i 0.364018i
\(567\) 8.06918 + 30.1146i 0.338874 + 1.26469i
\(568\) 0 0
\(569\) −25.9808 −1.08917 −0.544585 0.838706i \(-0.683313\pi\)
−0.544585 + 0.838706i \(0.683313\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) −4.65874 17.3867i −0.194622 0.726338i
\(574\) 18.0000i 0.751305i
\(575\) 0 0
\(576\) −1.50000 2.59808i −0.0625000 0.108253i
\(577\) 13.4722 13.4722i 0.560855 0.560855i −0.368695 0.929550i \(-0.620195\pi\)
0.929550 + 0.368695i \(0.120195\pi\)
\(578\) 5.65685 5.65685i 0.235294 0.235294i
\(579\) 12.9904 + 7.50000i 0.539862 + 0.311689i
\(580\) 0 0
\(581\) 10.3923i 0.431145i
\(582\) −11.5911 + 3.10583i −0.480467 + 0.128741i
\(583\) −22.0454 22.0454i −0.913027 0.913027i
\(584\) −8.66025 −0.358364
\(585\) 0 0
\(586\) −30.0000 −1.23929
\(587\) −14.8492 14.8492i −0.612894 0.612894i 0.330805 0.943699i \(-0.392680\pi\)
−0.943699 + 0.330805i \(0.892680\pi\)
\(588\) 8.36516 2.24144i 0.344974 0.0924354i
\(589\) 2.00000i 0.0824086i
\(590\) 0 0
\(591\) −9.00000 5.19615i −0.370211 0.213741i
\(592\) −2.44949 + 2.44949i −0.100673 + 0.100673i
\(593\) −23.3345 + 23.3345i −0.958234 + 0.958234i −0.999162 0.0409281i \(-0.986969\pi\)
0.0409281 + 0.999162i \(0.486969\pi\)
\(594\) 27.0000i 1.10782i
\(595\) 0 0
\(596\) 20.7846i 0.851371i
\(597\) −7.17260 26.7685i −0.293555 1.09556i
\(598\) 0 0
\(599\) 10.3923 0.424618 0.212309 0.977203i \(-0.431902\pi\)
0.212309 + 0.977203i \(0.431902\pi\)
\(600\) 0 0
\(601\) −5.00000 −0.203954 −0.101977 0.994787i \(-0.532517\pi\)
−0.101977 + 0.994787i \(0.532517\pi\)
\(602\) −8.48528 8.48528i −0.345834 0.345834i
\(603\) −4.03459 + 15.0573i −0.164301 + 0.613180i
\(604\) 14.0000i 0.569652i
\(605\) 0 0
\(606\) −9.00000 + 15.5885i −0.365600 + 0.633238i
\(607\) −4.89898 + 4.89898i −0.198843 + 0.198843i −0.799504 0.600661i \(-0.794904\pi\)
0.600661 + 0.799504i \(0.294904\pi\)
\(608\) 0.707107 0.707107i 0.0286770 0.0286770i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 2.32937 8.69333i 0.0941593 0.351407i
\(613\) −17.1464 17.1464i −0.692538 0.692538i 0.270252 0.962790i \(-0.412893\pi\)
−0.962790 + 0.270252i \(0.912893\pi\)
\(614\) 1.73205 0.0698999
\(615\) 0 0
\(616\) −18.0000 −0.725241
\(617\) −21.2132 21.2132i −0.854011 0.854011i 0.136613 0.990624i \(-0.456378\pi\)
−0.990624 + 0.136613i \(0.956378\pi\)
\(618\) −6.21166 23.1822i −0.249869 0.932526i
\(619\) 4.00000i 0.160774i −0.996764 0.0803868i \(-0.974384\pi\)
0.996764 0.0803868i \(-0.0256155\pi\)
\(620\) 0 0
\(621\) 31.1769i 1.25109i
\(622\) −22.0454 + 22.0454i −0.883940 + 0.883940i
\(623\) −38.1838 + 38.1838i −1.52980 + 1.52980i
\(624\) 0 0
\(625\) 0 0
\(626\) 20.7846i 0.830720i
\(627\) 8.69333 2.32937i 0.347178 0.0930261i
\(628\) 12.2474 + 12.2474i 0.488726 + 0.488726i
\(629\) −10.3923 −0.414368
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) −9.89949 9.89949i −0.393781 0.393781i
\(633\) 38.4797 10.3106i 1.52943 0.409810i
\(634\) 12.0000i 0.476581i
\(635\) 0 0
\(636\) 9.00000 + 5.19615i 0.356873 + 0.206041i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 20.7846i 0.820943i 0.911873 + 0.410471i \(0.134636\pi\)
−0.911873 + 0.410471i \(0.865364\pi\)
\(642\) −4.03459 15.0573i −0.159233 0.594264i
\(643\) 22.0454 + 22.0454i 0.869386 + 0.869386i 0.992404 0.123018i \(-0.0392574\pi\)
−0.123018 + 0.992404i \(0.539257\pi\)
\(644\) 20.7846 0.819028
\(645\) 0 0
\(646\) 3.00000 0.118033
\(647\) 33.9411 + 33.9411i 1.33436 + 1.33436i 0.901422 + 0.432941i \(0.142524\pi\)
0.432941 + 0.901422i \(0.357476\pi\)
\(648\) 2.32937 + 8.69333i 0.0915064 + 0.341506i
\(649\) 54.0000i 2.11969i
\(650\) 0 0
\(651\) 6.00000 10.3923i 0.235159 0.407307i
\(652\) 3.67423 3.67423i 0.143894 0.143894i
\(653\) 4.24264 4.24264i 0.166027 0.166027i −0.619203 0.785231i \(-0.712544\pi\)
0.785231 + 0.619203i \(0.212544\pi\)
\(654\) 8.66025 15.0000i 0.338643 0.586546i
\(655\) 0 0
\(656\) 5.19615i 0.202876i
\(657\) 25.0955 + 6.72432i 0.979068 + 0.262341i
\(658\) 0 0
\(659\) −25.9808 −1.01207 −0.506033 0.862514i \(-0.668889\pi\)
−0.506033 + 0.862514i \(0.668889\pi\)
\(660\) 0 0
\(661\) −20.0000 −0.777910 −0.388955 0.921257i \(-0.627164\pi\)
−0.388955 + 0.921257i \(0.627164\pi\)
\(662\) −9.19239 9.19239i −0.357272 0.357272i
\(663\) 0 0
\(664\) 3.00000i 0.116423i
\(665\) 0 0
\(666\) 9.00000 5.19615i 0.348743 0.201347i
\(667\) 0 0
\(668\) −8.48528 + 8.48528i −0.328305 + 0.328305i
\(669\) −20.7846 12.0000i −0.803579 0.463947i
\(670\) 0 0
\(671\) 72.7461i 2.80833i
\(672\) 5.79555 1.55291i 0.223568 0.0599050i
\(673\) −4.89898 4.89898i −0.188842 0.188842i 0.606353 0.795195i \(-0.292632\pi\)
−0.795195 + 0.606353i \(0.792632\pi\)
\(674\) −5.19615 −0.200148
\(675\) 0 0
\(676\) 13.0000 0.500000
\(677\) 25.4558 + 25.4558i 0.978348 + 0.978348i 0.999771 0.0214229i \(-0.00681965\pi\)
−0.0214229 + 0.999771i \(0.506820\pi\)
\(678\) 15.0573 4.03459i 0.578272 0.154947i
\(679\) 24.0000i 0.921035i
\(680\) 0 0
\(681\) 18.0000 + 10.3923i 0.689761 + 0.398234i
\(682\) −7.34847 + 7.34847i −0.281387 + 0.281387i
\(683\) −14.8492 + 14.8492i −0.568190 + 0.568190i −0.931621 0.363431i \(-0.881605\pi\)
0.363431 + 0.931621i \(0.381605\pi\)
\(684\) −2.59808 + 1.50000i −0.0993399 + 0.0573539i
\(685\) 0 0
\(686\) 6.92820i 0.264520i
\(687\) 7.17260 + 26.7685i 0.273652 + 1.02128i
\(688\) −2.44949 2.44949i −0.0933859 0.0933859i
\(689\) 0 0
\(690\) 0 0
\(691\) 37.0000 1.40755 0.703773 0.710425i \(-0.251497\pi\)
0.703773 + 0.710425i \(0.251497\pi\)
\(692\) −8.48528 8.48528i −0.322562 0.322562i
\(693\) 52.1600 + 13.9762i 1.98139 + 0.530913i
\(694\) 9.00000i 0.341635i
\(695\) 0 0
\(696\) 0 0
\(697\) 11.0227 11.0227i 0.417515 0.417515i
\(698\) −15.5563 + 15.5563i −0.588817 + 0.588817i
\(699\) −15.5885 + 27.0000i −0.589610 + 1.02123i
\(700\) 0 0
\(701\) 20.7846i 0.785024i −0.919747 0.392512i \(-0.871606\pi\)
0.919747 0.392512i \(-0.128394\pi\)
\(702\) 0 0
\(703\) 2.44949 + 2.44949i 0.0923843 + 0.0923843i
\(704\) −5.19615 −0.195837
\(705\) 0 0
\(706\) 18.0000 0.677439
\(707\) −25.4558 25.4558i −0.957366 0.957366i
\(708\) −4.65874 17.3867i −0.175086 0.653431i
\(709\) 40.0000i 1.50223i 0.660171 + 0.751116i \(0.270484\pi\)
−0.660171 + 0.751116i \(0.729516\pi\)
\(710\) 0 0
\(711\) 21.0000 + 36.3731i 0.787562 + 1.36410i
\(712\) −11.0227 + 11.0227i −0.413093 + 0.413093i
\(713\) 8.48528 8.48528i 0.317776 0.317776i
\(714\) 15.5885 + 9.00000i 0.583383 + 0.336817i
\(715\) 0 0
\(716\) 15.5885i 0.582568i
\(717\) −34.7733 + 9.31749i −1.29863 + 0.347968i
\(718\) 7.34847 + 7.34847i 0.274242 + 0.274242i
\(719\) −31.1769 −1.16270 −0.581351 0.813653i \(-0.697476\pi\)
−0.581351 + 0.813653i \(0.697476\pi\)
\(720\) 0 0
\(721\) 48.0000 1.78761
\(722\) 12.7279 + 12.7279i 0.473684 + 0.473684i
\(723\) −1.67303 + 0.448288i −0.0622208 + 0.0166720i
\(724\) 2.00000i 0.0743294i
\(725\) 0 0
\(726\) −24.0000 13.8564i −0.890724 0.514259i
\(727\) 4.89898 4.89898i 0.181693 0.181693i −0.610400 0.792093i \(-0.708991\pi\)
0.792093 + 0.610400i \(0.208991\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 10.3923i 0.384373i
\(732\) 6.27603 + 23.4225i 0.231969 + 0.865719i
\(733\) −14.6969 14.6969i −0.542844 0.542844i 0.381518 0.924362i \(-0.375402\pi\)
−0.924362 + 0.381518i \(0.875402\pi\)
\(734\) 20.7846 0.767174
\(735\) 0 0
\(736\) 6.00000 0.221163
\(737\) 19.0919 + 19.0919i 0.703259 + 0.703259i
\(738\) −4.03459 + 15.0573i −0.148515 + 0.554267i
\(739\) 20.0000i 0.735712i −0.929883 0.367856i \(-0.880092\pi\)
0.929883 0.367856i \(-0.119908\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −14.6969 + 14.6969i −0.539542 + 0.539542i
\(743\) 12.7279 12.7279i 0.466942 0.466942i −0.433980 0.900922i \(-0.642891\pi\)
0.900922 + 0.433980i \(0.142891\pi\)
\(744\) 1.73205 3.00000i 0.0635001 0.109985i
\(745\) 0 0
\(746\) 3.46410i 0.126830i
\(747\) 2.32937 8.69333i 0.0852272 0.318072i
\(748\) −11.0227 11.0227i −0.403030 0.403030i
\(749\) 31.1769 1.13918
\(750\) 0 0
\(751\) −20.0000 −0.729810 −0.364905 0.931045i \(-0.618899\pi\)
−0.364905 + 0.931045i \(0.618899\pi\)
\(752\) 0 0
\(753\) −2.32937 8.69333i −0.0848870 0.316803i
\(754\) 0 0
\(755\) 0 0
\(756\) −18.0000 −0.654654
\(757\) −24.4949 + 24.4949i −0.890282 + 0.890282i −0.994549 0.104267i \(-0.966750\pi\)
0.104267 + 0.994549i \(0.466750\pi\)
\(758\) 7.77817 7.77817i 0.282516 0.282516i
\(759\) 46.7654 + 27.0000i 1.69748 + 0.980038i
\(760\) 0 0
\(761\) 5.19615i 0.188360i 0.995555 + 0.0941802i \(0.0300230\pi\)
−0.995555 + 0.0941802i \(0.969977\pi\)
\(762\) 17.3867 4.65874i 0.629852 0.168768i
\(763\) 24.4949 + 24.4949i 0.886775 + 0.886775i
\(764\) 10.3923 0.375980
\(765\) 0 0
\(766\) 6.00000 0.216789
\(767\) 0 0
\(768\) 1.67303 0.448288i 0.0603704 0.0161762i
\(769\) 13.0000i 0.468792i −0.972141 0.234396i \(-0.924689\pi\)
0.972141 0.234396i \(-0.0753112\pi\)
\(770\) 0 0
\(771\) 9.00000 + 5.19615i 0.324127 + 0.187135i
\(772\) −6.12372 + 6.12372i −0.220398 + 0.220398i
\(773\) 8.48528 8.48528i 0.305194 0.305194i −0.537848 0.843042i \(-0.680762\pi\)
0.843042 + 0.537848i \(0.180762\pi\)
\(774\) 5.19615 + 9.00000i 0.186772 + 0.323498i
\(775\) 0 0
\(776\) 6.92820i 0.248708i
\(777\) 5.37945 + 20.0764i 0.192987 + 0.720237i
\(778\) 7.34847 + 7.34847i 0.263455 + 0.263455i
\(779\) −5.19615 −0.186171
\(780\) 0 0
\(781\) 0 0
\(782\) 12.7279 + 12.7279i 0.455150 + 0.455150i
\(783\) 0 0
\(784\) 5.00000i 0.178571i
\(785\) 0 0
\(786\) −9.00000 + 15.5885i −0.321019 + 0.556022i
\(787\) −17.1464 + 17.1464i −0.611204 + 0.611204i −0.943260 0.332056i \(-0.892258\pi\)
0.332056 + 0.943260i \(0.392258\pi\)
\(788\) 4.24264 4.24264i 0.151138 0.151138i
\(789\) 15.5885 27.0000i 0.554964 0.961225i