Properties

Label 150.2.e.b.143.2
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 143.2
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 150.143
Dual form 150.2.e.b.107.2

$q$-expansion

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

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
\(3\) −0.448288 + 1.67303i −0.258819 + 0.965926i
\(4\) 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 \(0.286490\pi\)
−0.621582 + 0.783349i \(0.713510\pi\)
\(12\) −1.67303 0.448288i −0.482963 0.129410i
\(13\) 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 0.915901 0.401405i \(-0.131478\pi\)
−0.401405 + 0.915901i \(0.631478\pi\)
\(18\) 0.776457 + 2.89778i 0.183013 + 0.683013i
\(19\) 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 −0.109351 0.994003i \(-0.534877\pi\)
0.994003 + 0.109351i \(0.0348774\pi\)
\(24\) 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
\(33\) −8.69333 2.32937i −1.51331 0.405492i
\(34\) 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 \(-0.867010\pi\)
0.913984 0.405751i \(-0.132990\pi\)
\(42\) −1.55291 + 5.79555i −0.239620 + 0.894274i
\(43\) 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 \(0.750000\pi\)
\(48\) 0.448288 1.67303i 0.0647048 0.241481i
\(49\) 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 −0.935664 0.352892i \(-0.885198\pi\)
0.352892 + 0.935664i \(0.385198\pi\)
\(54\) −5.19615 −0.707107
\(55\) 0 0
\(56\) 3.46410i 0.462910i
\(57\) −1.67303 0.448288i −0.221599 0.0593772i
\(58\) 0 0
\(59\) 10.3923 1.35296 0.676481 0.736460i \(-0.263504\pi\)
0.676481 + 0.736460i \(0.263504\pi\)
\(60\) 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
\(63\) 10.0382 2.68973i 1.26469 0.338874i
\(64\) 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 \(\pi\)
\(72\) −2.89778 + 0.776457i −0.341506 + 0.0915064i
\(73\) 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 −0.813879 0.581034i \(-0.802648\pi\)
0.581034 + 0.813879i \(0.302648\pi\)
\(84\) 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 \(-0.809494\pi\)
−0.826187 + 0.563397i \(0.809494\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 4.24264 + 4.24264i 0.442326 + 0.442326i
\(93\) 0.896575 3.34607i 0.0929705 0.346971i
\(94\) 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 \(-0.827035\pi\)
0.855963 0.517036i \(-0.172965\pi\)
\(102\) 5.01910 + 1.34486i 0.496965 + 0.133161i
\(103\) −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 0.944303 0.329076i \(-0.106737\pi\)
−0.329076 + 0.944303i \(0.606737\pi\)
\(108\) 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 −0.939959 0.341288i \(-0.889137\pi\)
0.341288 + 0.939959i \(0.389137\pi\)
\(114\) 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
\(123\) 8.69333 + 2.32937i 0.783851 + 0.210032i
\(124\) 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 \(-0.850000\pi\)
0.891007 0.453990i \(-0.150000\pi\)
\(132\) 2.32937 8.69333i 0.202746 0.756657i
\(133\) −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 \(0.104313\pi\)
0.321874 + 0.946783i \(0.395687\pi\)
\(138\) 2.68973 10.0382i 0.228965 0.854508i
\(139\) 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
\(147\) 8.36516 + 2.24144i 0.689947 + 0.184871i
\(148\) 2.44949 + 2.44949i 0.201347 + 0.201347i
\(149\) 20.7846 1.70274 0.851371 0.524564i \(-0.175772\pi\)
0.851371 + 0.524564i \(0.175772\pi\)
\(150\) 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
\(153\) −2.32937 8.69333i −0.188319 0.702814i
\(154\) 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
\(162\) 2.32937 8.69333i 0.183013 0.683013i
\(163\) −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 0.297966 0.954577i \(-0.403692\pi\)
−0.954577 + 0.297966i \(0.903692\pi\)
\(168\) −5.79555 1.55291i −0.447137 0.119810i
\(169\) 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 −0.306687 0.951811i \(-0.599220\pi\)
0.951811 + 0.306687i \(0.0992203\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 5.19615i 0.391675i
\(177\) −4.65874 + 17.3867i −0.350173 + 1.30686i
\(178\) 11.0227 + 11.0227i 0.826187 + 0.826187i
\(179\) −15.5885 −1.16514 −0.582568 0.812782i \(-0.697952\pi\)
−0.582568 + 0.812782i \(0.697952\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) −6.27603 + 23.4225i −0.463937 + 1.73144i
\(184\) 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 \(0.122694\pi\)
−0.926628 + 0.375980i \(0.877306\pi\)
\(192\) 1.67303 + 0.448288i 0.120741 + 0.0323524i
\(193\) 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 0.841904 0.539628i \(-0.181435\pi\)
−0.539628 + 0.841904i \(0.681435\pi\)
\(198\) −15.0573 + 4.03459i −1.07008 + 0.286726i
\(199\) 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
\(207\) −17.3867 + 4.65874i −1.20846 + 0.323805i
\(208\) 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
\(222\) 1.55291 5.79555i 0.104225 0.388972i
\(223\) −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 0.367024 0.930212i \(-0.380377\pi\)
−0.930212 + 0.367024i \(0.880377\pi\)
\(228\) 0.448288 1.67303i 0.0296886 0.110799i
\(229\) 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 −0.154205 0.988039i \(-0.549282\pi\)
0.988039 + 0.154205i \(0.0492816\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 10.3923i 0.676481i
\(237\) −23.4225 6.27603i −1.52145 0.407672i
\(238\) 7.34847 + 7.34847i 0.476331 + 0.476331i
\(239\) 20.7846 1.34444 0.672222 0.740349i \(-0.265340\pi\)
0.672222 + 0.740349i \(0.265340\pi\)
\(240\) 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
\(243\) −15.0573 + 4.03459i −0.965926 + 0.258819i
\(244\) 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 \(0.0524362\pi\)
−0.986462 + 0.163989i \(0.947564\pi\)
\(252\) 2.68973 + 10.0382i 0.169437 + 0.632347i
\(253\) 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 0.562291 0.826940i \(-0.309920\pi\)
−0.826940 + 0.562291i \(0.809920\pi\)
\(258\) 5.79555 + 1.55291i 0.360815 + 0.0966802i
\(259\) 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 −0.980643 0.195805i \(-0.937268\pi\)
0.195805 + 0.980643i \(0.437268\pi\)
\(264\) −7.79423 + 4.50000i −0.479702 + 0.276956i
\(265\) 0 0
\(266\) 3.46410i 0.212398i
\(267\) 6.98811 26.0800i 0.427666 1.59607i
\(268\) −3.67423 3.67423i −0.224440 0.224440i
\(269\) 20.7846 1.26726 0.633630 0.773636i \(-0.281564\pi\)
0.633630 + 0.773636i \(0.281564\pi\)
\(270\) 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 \(0.212848\pi\)
−0.784639 + 0.619953i \(0.787152\pi\)
\(282\) 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
\(288\) −0.776457 2.89778i −0.0457532 0.170753i
\(289\) 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 \(-0.409998\pi\)
0.960292 0.278996i \(-0.0900018\pi\)
\(294\) −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
\(303\) 17.3867 + 4.65874i 0.998838 + 0.267638i
\(304\) 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 \(-0.654881\pi\)
0.467600 0.883940i \(-0.345119\pi\)
\(312\) 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 0.427456 0.904036i \(-0.359410\pi\)
−0.904036 + 0.427456i \(0.859410\pi\)
\(318\) −2.68973 + 10.0382i −0.150832 + 0.562914i
\(319\) 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
\(327\) 16.7303 + 4.48288i 0.925189 + 0.247904i
\(328\) −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
\(333\) −10.0382 + 2.68973i −0.550090 + 0.147396i
\(334\) 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
\(342\) −2.89778 + 0.776457i −0.156694 + 0.0419860i
\(343\) −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 0.515347 0.856982i \(-0.327663\pi\)
−0.856982 + 0.515347i \(0.827663\pi\)
\(348\) 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 −0.959420 0.281981i \(-0.909008\pi\)
0.281981 + 0.959420i \(0.409008\pi\)
\(354\) 15.5885 9.00000i 0.828517 0.478345i
\(355\) 0 0
\(356\) 15.5885i 0.826187i
\(357\) 4.65874 17.3867i 0.246567 0.920200i
\(358\) 11.0227 + 11.0227i 0.582568 + 0.582568i
\(359\) −10.3923 −0.548485 −0.274242 0.961661i \(-0.588427\pi\)
−0.274242 + 0.961661i \(0.588427\pi\)
\(360\) 0 0
\(361\) 18.0000 0.947368
\(362\) 1.41421 + 1.41421i 0.0743294 + 0.0743294i
\(363\) 7.17260 26.7685i 0.376464 1.40498i
\(364\) 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
\(372\) 3.34607 + 0.896575i 0.173485 + 0.0464853i
\(373\) −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 −0.807144 0.590355i \(-0.798988\pi\)
0.590355 + 0.807144i \(0.298988\pi\)
\(384\) −0.866025 1.50000i −0.0441942 0.0765466i
\(385\) 0 0
\(386\) 8.66025i 0.440795i
\(387\) −2.68973 10.0382i −0.136726 0.510270i
\(388\) −4.89898 4.89898i −0.248708 0.248708i
\(389\) −10.3923 −0.526911 −0.263455 0.964672i \(-0.584862\pi\)
−0.263455 + 0.964672i \(0.584862\pi\)
\(390\) 0 0
\(391\) 18.0000 0.910299
\(392\) −3.53553 3.53553i −0.178571 0.178571i
\(393\) 17.3867 + 4.65874i 0.877041 + 0.235002i
\(394\) 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 \(0.0414148\pi\)
−0.991548 + 0.129742i \(0.958585\pi\)
\(402\) −2.32937 + 8.69333i −0.116178 + 0.433584i
\(403\) 0 0
\(404\) 10.3923 0.517036
\(405\) 0 0
\(406\) 0 0
\(407\) 12.7279 + 12.7279i 0.630900 + 0.630900i
\(408\) −1.34486 + 5.01910i −0.0665807 + 0.248482i
\(409\) 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
\(417\) −11.7112 3.13801i −0.573501 0.153669i
\(418\) 3.67423 + 3.67423i 0.179713 + 0.179713i
\(419\) −25.9808 −1.26924 −0.634622 0.772823i \(-0.718844\pi\)
−0.634622 + 0.772823i \(0.718844\pi\)
\(420\) 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 \(0.0805259\pi\)
−0.968171 + 0.250290i \(0.919474\pi\)
\(432\) −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
\(438\) 14.4889 + 3.88229i 0.692306 + 0.185503i
\(439\) 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 −0.260079 0.965587i \(-0.583748\pi\)
0.965587 + 0.260079i \(0.0837485\pi\)
\(444\) −5.19615 + 3.00000i −0.246598 + 0.142374i
\(445\) 0 0
\(446\) 13.8564i 0.656120i
\(447\) −9.31749 + 34.7733i −0.440702 + 1.64472i
\(448\) 2.44949 + 2.44949i 0.115728 + 0.115728i
\(449\) −25.9808 −1.22611 −0.613054 0.790041i \(-0.710059\pi\)
−0.613054 + 0.790041i \(0.710059\pi\)
\(450\) 0 0
\(451\) 27.0000 1.27138
\(452\) −6.36396 6.36396i −0.299336 0.299336i
\(453\) 6.27603 23.4225i 0.294874 1.10048i
\(454\) 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 \(\pi\)
\(462\) −30.1146 8.06918i −1.40106 0.375412i
\(463\) 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 0.482980 0.875632i \(-0.339555\pi\)
−0.875632 + 0.482980i \(0.839555\pi\)
\(468\) 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
\(477\) 17.3867 4.65874i 0.796081 0.213309i
\(478\) −14.6969 14.6969i −0.672222 0.672222i
\(479\) 10.3923 0.474837 0.237418 0.971408i \(-0.423699\pi\)
0.237418 + 0.971408i \(0.423699\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0.707107 + 0.707107i 0.0322078 + 0.0322078i
\(483\) −34.7733 9.31749i −1.58224 0.423960i
\(484\) 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 \(0.248379\pi\)
−0.710698 + 0.703497i \(0.751621\pi\)
\(492\) −2.32937 + 8.69333i −0.105016 + 0.391926i
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 0 0
\(498\) −1.34486 + 5.01910i −0.0602648 + 0.224911i
\(499\) 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 −0.870503 0.492163i \(-0.836206\pi\)
0.492163 + 0.870503i \(0.336206\pi\)
\(504\) 5.19615 9.00000i 0.231455 0.400892i
\(505\) 0 0
\(506\) 31.1769i 1.38598i
\(507\) 21.7494 + 5.82774i 0.965926 + 0.258819i
\(508\) 7.34847 + 7.34847i 0.326036 + 0.326036i
\(509\) −10.3923 −0.460631 −0.230315 0.973116i \(-0.573976\pi\)
−0.230315 + 0.973116i \(0.573976\pi\)
\(510\) 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 \(-0.706542\pi\)
0.604287 0.796766i \(-0.293458\pi\)
\(522\) 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
\(528\) 8.69333 + 2.32937i 0.378329 + 0.101373i
\(529\) 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
\(537\) 6.98811 26.0800i 0.301559 1.12543i
\(538\) −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
\(543\) 0.896575 3.34607i 0.0384757 0.143593i
\(544\) 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
\(552\) 10.0382 + 2.68973i 0.427254 + 0.114482i
\(553\) −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 \(0.750000\pi\)
\(558\) −1.55291 5.79555i −0.0657401 0.245345i
\(559\) 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
\(567\) −30.1146 8.06918i −1.26469 0.338874i
\(568\) 0 0
\(569\) 25.9808 1.08917 0.544585 0.838706i \(-0.316687\pi\)
0.544585 + 0.838706i \(0.316687\pi\)
\(570\) 0 0
\(571\) 20.0000 0.836974 0.418487 0.908223i \(-0.362561\pi\)
0.418487 + 0.908223i \(0.362561\pi\)
\(572\) 0 0
\(573\) −17.3867 4.65874i −0.726338 0.194622i
\(574\) 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
\(582\) −3.10583 + 11.5911i −0.128741 + 0.480467i
\(583\) −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 0.943699 0.330805i \(-0.107320\pi\)
−0.330805 + 0.943699i \(0.607320\pi\)
\(588\) −2.24144 + 8.36516i −0.0924354 + 0.344974i
\(589\) 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 −0.0409281 0.999162i \(-0.513031\pi\)
0.999162 + 0.0409281i \(0.0130314\pi\)
\(594\) 27.0000i 1.10782i
\(595\) 0 0
\(596\) 20.7846i 0.851371i
\(597\) 26.7685 + 7.17260i 1.09556 + 0.293555i
\(598\) 0 0
\(599\) −10.3923 −0.424618 −0.212309 0.977203i \(-0.568098\pi\)
−0.212309 + 0.977203i \(0.568098\pi\)
\(600\) 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
\(603\) 15.0573 4.03459i 0.613180 0.164301i
\(604\) 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
\(612\) 8.69333 2.32937i 0.351407 0.0941593i
\(613\) −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 0.990624 0.136613i \(-0.0436217\pi\)
−0.136613 + 0.990624i \(0.543622\pi\)
\(618\) −23.1822 6.21166i −0.932526 0.249869i
\(619\) 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
\(627\) 2.32937 8.69333i 0.0930261 0.347178i
\(628\) 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
\(633\) −10.3106 + 38.4797i −0.409810 + 1.52943i
\(634\) 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 \(-0.865364\pi\)
0.911873 0.410471i \(-0.134636\pi\)
\(642\) 15.0573 + 4.03459i 0.594264 + 0.159233i
\(643\) 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 \(-0.857476\pi\)
−0.432941 0.901422i \(-0.642524\pi\)
\(648\) 8.69333 + 2.32937i 0.341506 + 0.0915064i
\(649\) 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 −0.785231 0.619203i \(-0.787456\pi\)
0.619203 + 0.785231i \(0.287456\pi\)
\(654\) −8.66025 15.0000i −0.338643 0.586546i
\(655\) 0 0
\(656\) 5.19615i 0.202876i
\(657\) −6.72432 25.0955i −0.262341 0.979068i
\(658\) 0 0
\(659\) 25.9808 1.01207 0.506033 0.862514i \(-0.331111\pi\)
0.506033 + 0.862514i \(0.331111\pi\)
\(660\) 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
\(672\) 1.55291 5.79555i 0.0599050 0.223568i
\(673\) −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 0.0214229 0.999771i \(-0.493180\pi\)
−0.999771 + 0.0214229i \(0.993180\pi\)
\(678\) −4.03459 + 15.0573i −0.154947 + 0.578272i
\(679\) 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 −0.363431 0.931621i \(-0.618395\pi\)
0.931621 + 0.363431i \(0.118395\pi\)
\(684\) 2.59808 + 1.50000i 0.0993399 + 0.0573539i
\(685\) 0 0
\(686\) 6.92820i 0.264520i
\(687\) −26.7685 7.17260i −1.02128 0.273652i
\(688\) −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
\(693\) 13.9762 + 52.1600i 0.530913 + 1.98139i
\(694\) 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 \(0.128394\pi\)
−0.919747 + 0.392512i \(0.871606\pi\)
\(702\) 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
\(708\) −17.3867 4.65874i −0.653431 0.175086i
\(709\) 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
\(717\) −9.31749 + 34.7733i −0.347968 + 1.29863i
\(718\) 7.34847 + 7.34847i 0.274242 + 0.274242i
\(719\) 31.1769 1.16270 0.581351 0.813653i \(-0.302524\pi\)
0.581351 + 0.813653i \(0.302524\pi\)
\(720\) 0 0
\(721\) 48.0000 1.78761
\(722\) −12.7279 12.7279i −0.473684 0.473684i
\(723\) 0.448288 1.67303i 0.0166720 0.0622208i
\(724\) 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
\(732\) −23.4225 6.27603i −0.865719 0.231969i
\(733\) −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
\(738\) 15.0573 4.03459i 0.554267 0.148515i
\(739\) 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 −0.900922 0.433980i \(-0.857109\pi\)
0.433980 + 0.900922i \(0.357109\pi\)
\(744\) −1.73205 3.00000i −0.0635001 0.109985i
\(745\) 0 0
\(746\) 3.46410i 0.126830i
\(747\) 8.69333 2.32937i 0.318072 0.0852272i
\(748\) −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
\(753\) −8.69333 2.32937i −0.316803 0.0848870i
\(754\) 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 \(-0.969977\pi\)
0.995555 0.0941802i \(-0.0300230\pi\)
\(762\) 4.65874 17.3867i 0.168768 0.629852i
\(763\) 24.4949 + 24.4949i 0.886775 + 0.886775i
\(764\) −10.3923 −0.375980
\(765\) 0 0
\(766\) 6.00000 0.216789
\(767\) 0 0
\(768\) −0.448288 + 1.67303i −0.0161762 + 0.0603704i
\(769\) 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 −0.843042 0.537848i \(-0.819238\pi\)
0.537848 + 0.843042i \(0.319238\pi\)
\(774\) −5.19615 + 9.00000i −0.186772 + 0.323498i
\(775\) 0 0
\(776\) 6.92820i 0.248708i
\(777\) −20.0764 5.37945i −0.720237 0.192987i
\(778\) 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