Properties

Label 825.2.k.d.782.2
Level $825$
Weight $2$
Character 825.782
Analytic conductor $6.588$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{6})\)
Defining polynomial: \(x^{4} + 9\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 782.2
Root \(1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 825.782
Dual form 825.2.k.d.518.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.22474 - 1.22474i) q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000i q^{4} +3.00000i q^{6} +(-2.44949 - 2.44949i) q^{7} +(1.22474 + 1.22474i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(1.22474 - 1.22474i) q^{2} +(-1.22474 + 1.22474i) q^{3} -1.00000i q^{4} +3.00000i q^{6} +(-2.44949 - 2.44949i) q^{7} +(1.22474 + 1.22474i) q^{8} -3.00000i q^{9} +1.00000i q^{11} +(1.22474 + 1.22474i) q^{12} +(2.44949 - 2.44949i) q^{13} -6.00000 q^{14} +5.00000 q^{16} +(4.89898 - 4.89898i) q^{17} +(-3.67423 - 3.67423i) q^{18} +2.00000i q^{19} +6.00000 q^{21} +(1.22474 + 1.22474i) q^{22} +(-4.89898 - 4.89898i) q^{23} -3.00000 q^{24} -6.00000i q^{26} +(3.67423 + 3.67423i) q^{27} +(-2.44949 + 2.44949i) q^{28} +6.00000 q^{29} +4.00000 q^{31} +(3.67423 - 3.67423i) q^{32} +(-1.22474 - 1.22474i) q^{33} -12.0000i q^{34} -3.00000 q^{36} +(2.44949 + 2.44949i) q^{38} +6.00000i q^{39} -6.00000i q^{41} +(7.34847 - 7.34847i) q^{42} +(7.34847 - 7.34847i) q^{43} +1.00000 q^{44} -12.0000 q^{46} +(-4.89898 + 4.89898i) q^{47} +(-6.12372 + 6.12372i) q^{48} +5.00000i q^{49} +12.0000i q^{51} +(-2.44949 - 2.44949i) q^{52} +(-4.89898 - 4.89898i) q^{53} +9.00000 q^{54} -6.00000i q^{56} +(-2.44949 - 2.44949i) q^{57} +(7.34847 - 7.34847i) q^{58} +2.00000 q^{61} +(4.89898 - 4.89898i) q^{62} +(-7.34847 + 7.34847i) q^{63} +1.00000i q^{64} -3.00000 q^{66} +(-2.44949 - 2.44949i) q^{67} +(-4.89898 - 4.89898i) q^{68} +12.0000 q^{69} +12.0000i q^{71} +(3.67423 - 3.67423i) q^{72} +(-2.44949 + 2.44949i) q^{73} +2.00000 q^{76} +(2.44949 - 2.44949i) q^{77} +(7.34847 + 7.34847i) q^{78} +10.0000i q^{79} -9.00000 q^{81} +(-7.34847 - 7.34847i) q^{82} +(-7.34847 - 7.34847i) q^{83} -6.00000i q^{84} -18.0000i q^{86} +(-7.34847 + 7.34847i) q^{87} +(-1.22474 + 1.22474i) q^{88} -12.0000 q^{89} -12.0000 q^{91} +(-4.89898 + 4.89898i) q^{92} +(-4.89898 + 4.89898i) q^{93} +12.0000i q^{94} +9.00000i q^{96} +(9.79796 + 9.79796i) q^{97} +(6.12372 + 6.12372i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + O(q^{10}) \) \( 4 q - 24 q^{14} + 20 q^{16} + 24 q^{21} - 12 q^{24} + 24 q^{29} + 16 q^{31} - 12 q^{36} + 4 q^{44} - 48 q^{46} + 36 q^{54} + 8 q^{61} - 12 q^{66} + 48 q^{69} + 8 q^{76} - 36 q^{81} - 48 q^{89} - 48 q^{91} + 12 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.22474 1.22474i 0.866025 0.866025i −0.126004 0.992030i \(-0.540215\pi\)
0.992030 + 0.126004i \(0.0402153\pi\)
\(3\) −1.22474 + 1.22474i −0.707107 + 0.707107i
\(4\) 1.00000i 0.500000i
\(5\) 0 0
\(6\) 3.00000i 1.22474i
\(7\) −2.44949 2.44949i −0.925820 0.925820i 0.0716124 0.997433i \(-0.477186\pi\)
−0.997433 + 0.0716124i \(0.977186\pi\)
\(8\) 1.22474 + 1.22474i 0.433013 + 0.433013i
\(9\) 3.00000i 1.00000i
\(10\) 0 0
\(11\) 1.00000i 0.301511i
\(12\) 1.22474 + 1.22474i 0.353553 + 0.353553i
\(13\) 2.44949 2.44949i 0.679366 0.679366i −0.280491 0.959857i \(-0.590497\pi\)
0.959857 + 0.280491i \(0.0904971\pi\)
\(14\) −6.00000 −1.60357
\(15\) 0 0
\(16\) 5.00000 1.25000
\(17\) 4.89898 4.89898i 1.18818 1.18818i 0.210606 0.977571i \(-0.432456\pi\)
0.977571 0.210606i \(-0.0675437\pi\)
\(18\) −3.67423 3.67423i −0.866025 0.866025i
\(19\) 2.00000i 0.458831i 0.973329 + 0.229416i \(0.0736815\pi\)
−0.973329 + 0.229416i \(0.926318\pi\)
\(20\) 0 0
\(21\) 6.00000 1.30931
\(22\) 1.22474 + 1.22474i 0.261116 + 0.261116i
\(23\) −4.89898 4.89898i −1.02151 1.02151i −0.999764 0.0217443i \(-0.993078\pi\)
−0.0217443 0.999764i \(-0.506922\pi\)
\(24\) −3.00000 −0.612372
\(25\) 0 0
\(26\) 6.00000i 1.17670i
\(27\) 3.67423 + 3.67423i 0.707107 + 0.707107i
\(28\) −2.44949 + 2.44949i −0.462910 + 0.462910i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) 4.00000 0.718421 0.359211 0.933257i \(-0.383046\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) 3.67423 3.67423i 0.649519 0.649519i
\(33\) −1.22474 1.22474i −0.213201 0.213201i
\(34\) 12.0000i 2.05798i
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) 2.44949 + 2.44949i 0.397360 + 0.397360i
\(39\) 6.00000i 0.960769i
\(40\) 0 0
\(41\) 6.00000i 0.937043i −0.883452 0.468521i \(-0.844787\pi\)
0.883452 0.468521i \(-0.155213\pi\)
\(42\) 7.34847 7.34847i 1.13389 1.13389i
\(43\) 7.34847 7.34847i 1.12063 1.12063i 0.128984 0.991647i \(-0.458828\pi\)
0.991647 0.128984i \(-0.0411717\pi\)
\(44\) 1.00000 0.150756
\(45\) 0 0
\(46\) −12.0000 −1.76930
\(47\) −4.89898 + 4.89898i −0.714590 + 0.714590i −0.967492 0.252902i \(-0.918615\pi\)
0.252902 + 0.967492i \(0.418615\pi\)
\(48\) −6.12372 + 6.12372i −0.883883 + 0.883883i
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) 12.0000i 1.68034i
\(52\) −2.44949 2.44949i −0.339683 0.339683i
\(53\) −4.89898 4.89898i −0.672927 0.672927i 0.285463 0.958390i \(-0.407853\pi\)
−0.958390 + 0.285463i \(0.907853\pi\)
\(54\) 9.00000 1.22474
\(55\) 0 0
\(56\) 6.00000i 0.801784i
\(57\) −2.44949 2.44949i −0.324443 0.324443i
\(58\) 7.34847 7.34847i 0.964901 0.964901i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 4.89898 4.89898i 0.622171 0.622171i
\(63\) −7.34847 + 7.34847i −0.925820 + 0.925820i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −3.00000 −0.369274
\(67\) −2.44949 2.44949i −0.299253 0.299253i 0.541468 0.840721i \(-0.317869\pi\)
−0.840721 + 0.541468i \(0.817869\pi\)
\(68\) −4.89898 4.89898i −0.594089 0.594089i
\(69\) 12.0000 1.44463
\(70\) 0 0
\(71\) 12.0000i 1.42414i 0.702109 + 0.712069i \(0.252242\pi\)
−0.702109 + 0.712069i \(0.747758\pi\)
\(72\) 3.67423 3.67423i 0.433013 0.433013i
\(73\) −2.44949 + 2.44949i −0.286691 + 0.286691i −0.835770 0.549079i \(-0.814979\pi\)
0.549079 + 0.835770i \(0.314979\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) 2.44949 2.44949i 0.279145 0.279145i
\(78\) 7.34847 + 7.34847i 0.832050 + 0.832050i
\(79\) 10.0000i 1.12509i 0.826767 + 0.562544i \(0.190177\pi\)
−0.826767 + 0.562544i \(0.809823\pi\)
\(80\) 0 0
\(81\) −9.00000 −1.00000
\(82\) −7.34847 7.34847i −0.811503 0.811503i
\(83\) −7.34847 7.34847i −0.806599 0.806599i 0.177518 0.984118i \(-0.443193\pi\)
−0.984118 + 0.177518i \(0.943193\pi\)
\(84\) 6.00000i 0.654654i
\(85\) 0 0
\(86\) 18.0000i 1.94099i
\(87\) −7.34847 + 7.34847i −0.787839 + 0.787839i
\(88\) −1.22474 + 1.22474i −0.130558 + 0.130558i
\(89\) −12.0000 −1.27200 −0.635999 0.771690i \(-0.719412\pi\)
−0.635999 + 0.771690i \(0.719412\pi\)
\(90\) 0 0
\(91\) −12.0000 −1.25794
\(92\) −4.89898 + 4.89898i −0.510754 + 0.510754i
\(93\) −4.89898 + 4.89898i −0.508001 + 0.508001i
\(94\) 12.0000i 1.23771i
\(95\) 0 0
\(96\) 9.00000i 0.918559i
\(97\) 9.79796 + 9.79796i 0.994832 + 0.994832i 0.999987 0.00515471i \(-0.00164080\pi\)
−0.00515471 + 0.999987i \(0.501641\pi\)
\(98\) 6.12372 + 6.12372i 0.618590 + 0.618590i
\(99\) 3.00000 0.301511
\(100\) 0 0
\(101\) 18.0000i 1.79107i −0.444994 0.895533i \(-0.646794\pi\)
0.444994 0.895533i \(-0.353206\pi\)
\(102\) 14.6969 + 14.6969i 1.45521 + 1.45521i
\(103\) 2.44949 2.44949i 0.241355 0.241355i −0.576055 0.817411i \(-0.695409\pi\)
0.817411 + 0.576055i \(0.195409\pi\)
\(104\) 6.00000 0.588348
\(105\) 0 0
\(106\) −12.0000 −1.16554
\(107\) −2.44949 + 2.44949i −0.236801 + 0.236801i −0.815524 0.578723i \(-0.803551\pi\)
0.578723 + 0.815524i \(0.303551\pi\)
\(108\) 3.67423 3.67423i 0.353553 0.353553i
\(109\) 10.0000i 0.957826i 0.877862 + 0.478913i \(0.158969\pi\)
−0.877862 + 0.478913i \(0.841031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −12.2474 12.2474i −1.15728 1.15728i
\(113\) 4.89898 + 4.89898i 0.460857 + 0.460857i 0.898936 0.438079i \(-0.144341\pi\)
−0.438079 + 0.898936i \(0.644341\pi\)
\(114\) −6.00000 −0.561951
\(115\) 0 0
\(116\) 6.00000i 0.557086i
\(117\) −7.34847 7.34847i −0.679366 0.679366i
\(118\) 0 0
\(119\) −24.0000 −2.20008
\(120\) 0 0
\(121\) −1.00000 −0.0909091
\(122\) 2.44949 2.44949i 0.221766 0.221766i
\(123\) 7.34847 + 7.34847i 0.662589 + 0.662589i
\(124\) 4.00000i 0.359211i
\(125\) 0 0
\(126\) 18.0000i 1.60357i
\(127\) 2.44949 + 2.44949i 0.217357 + 0.217357i 0.807384 0.590027i \(-0.200883\pi\)
−0.590027 + 0.807384i \(0.700883\pi\)
\(128\) 8.57321 + 8.57321i 0.757772 + 0.757772i
\(129\) 18.0000i 1.58481i
\(130\) 0 0
\(131\) 12.0000i 1.04844i 0.851581 + 0.524222i \(0.175644\pi\)
−0.851581 + 0.524222i \(0.824356\pi\)
\(132\) −1.22474 + 1.22474i −0.106600 + 0.106600i
\(133\) 4.89898 4.89898i 0.424795 0.424795i
\(134\) −6.00000 −0.518321
\(135\) 0 0
\(136\) 12.0000 1.02899
\(137\) −9.79796 + 9.79796i −0.837096 + 0.837096i −0.988476 0.151380i \(-0.951628\pi\)
0.151380 + 0.988476i \(0.451628\pi\)
\(138\) 14.6969 14.6969i 1.25109 1.25109i
\(139\) 22.0000i 1.86602i −0.359856 0.933008i \(-0.617174\pi\)
0.359856 0.933008i \(-0.382826\pi\)
\(140\) 0 0
\(141\) 12.0000i 1.01058i
\(142\) 14.6969 + 14.6969i 1.23334 + 1.23334i
\(143\) 2.44949 + 2.44949i 0.204837 + 0.204837i
\(144\) 15.0000i 1.25000i
\(145\) 0 0
\(146\) 6.00000i 0.496564i
\(147\) −6.12372 6.12372i −0.505076 0.505076i
\(148\) 0 0
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) 0 0
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) −2.44949 + 2.44949i −0.198680 + 0.198680i
\(153\) −14.6969 14.6969i −1.18818 1.18818i
\(154\) 6.00000i 0.483494i
\(155\) 0 0
\(156\) 6.00000 0.480384
\(157\) 9.79796 + 9.79796i 0.781962 + 0.781962i 0.980162 0.198199i \(-0.0635094\pi\)
−0.198199 + 0.980162i \(0.563509\pi\)
\(158\) 12.2474 + 12.2474i 0.974355 + 0.974355i
\(159\) 12.0000 0.951662
\(160\) 0 0
\(161\) 24.0000i 1.89146i
\(162\) −11.0227 + 11.0227i −0.866025 + 0.866025i
\(163\) −12.2474 + 12.2474i −0.959294 + 0.959294i −0.999203 0.0399091i \(-0.987293\pi\)
0.0399091 + 0.999203i \(0.487293\pi\)
\(164\) −6.00000 −0.468521
\(165\) 0 0
\(166\) −18.0000 −1.39707
\(167\) −2.44949 + 2.44949i −0.189547 + 0.189547i −0.795500 0.605953i \(-0.792792\pi\)
0.605953 + 0.795500i \(0.292792\pi\)
\(168\) 7.34847 + 7.34847i 0.566947 + 0.566947i
\(169\) 1.00000i 0.0769231i
\(170\) 0 0
\(171\) 6.00000 0.458831
\(172\) −7.34847 7.34847i −0.560316 0.560316i
\(173\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(174\) 18.0000i 1.36458i
\(175\) 0 0
\(176\) 5.00000i 0.376889i
\(177\) 0 0
\(178\) −14.6969 + 14.6969i −1.10158 + 1.10158i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 10.0000 0.743294 0.371647 0.928374i \(-0.378793\pi\)
0.371647 + 0.928374i \(0.378793\pi\)
\(182\) −14.6969 + 14.6969i −1.08941 + 1.08941i
\(183\) −2.44949 + 2.44949i −0.181071 + 0.181071i
\(184\) 12.0000i 0.884652i
\(185\) 0 0
\(186\) 12.0000i 0.879883i
\(187\) 4.89898 + 4.89898i 0.358249 + 0.358249i
\(188\) 4.89898 + 4.89898i 0.357295 + 0.357295i
\(189\) 18.0000i 1.30931i
\(190\) 0 0
\(191\) 24.0000i 1.73658i −0.496058 0.868290i \(-0.665220\pi\)
0.496058 0.868290i \(-0.334780\pi\)
\(192\) −1.22474 1.22474i −0.0883883 0.0883883i
\(193\) −7.34847 + 7.34847i −0.528954 + 0.528954i −0.920261 0.391306i \(-0.872023\pi\)
0.391306 + 0.920261i \(0.372023\pi\)
\(194\) 24.0000 1.72310
\(195\) 0 0
\(196\) 5.00000 0.357143
\(197\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(198\) 3.67423 3.67423i 0.261116 0.261116i
\(199\) 4.00000i 0.283552i 0.989899 + 0.141776i \(0.0452813\pi\)
−0.989899 + 0.141776i \(0.954719\pi\)
\(200\) 0 0
\(201\) 6.00000 0.423207
\(202\) −22.0454 22.0454i −1.55111 1.55111i
\(203\) −14.6969 14.6969i −1.03152 1.03152i
\(204\) 12.0000 0.840168
\(205\) 0 0
\(206\) 6.00000i 0.418040i
\(207\) −14.6969 + 14.6969i −1.02151 + 1.02151i
\(208\) 12.2474 12.2474i 0.849208 0.849208i
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) 26.0000 1.78991 0.894957 0.446153i \(-0.147206\pi\)
0.894957 + 0.446153i \(0.147206\pi\)
\(212\) −4.89898 + 4.89898i −0.336463 + 0.336463i
\(213\) −14.6969 14.6969i −1.00702 1.00702i
\(214\) 6.00000i 0.410152i
\(215\) 0 0
\(216\) 9.00000i 0.612372i
\(217\) −9.79796 9.79796i −0.665129 0.665129i
\(218\) 12.2474 + 12.2474i 0.829502 + 0.829502i
\(219\) 6.00000i 0.405442i
\(220\) 0 0
\(221\) 24.0000i 1.61441i
\(222\) 0 0
\(223\) 17.1464 17.1464i 1.14821 1.14821i 0.161305 0.986905i \(-0.448430\pi\)
0.986905 0.161305i \(-0.0515703\pi\)
\(224\) −18.0000 −1.20268
\(225\) 0 0
\(226\) 12.0000 0.798228
\(227\) −12.2474 + 12.2474i −0.812892 + 0.812892i −0.985066 0.172175i \(-0.944921\pi\)
0.172175 + 0.985066i \(0.444921\pi\)
\(228\) −2.44949 + 2.44949i −0.162221 + 0.162221i
\(229\) 10.0000i 0.660819i −0.943838 0.330409i \(-0.892813\pi\)
0.943838 0.330409i \(-0.107187\pi\)
\(230\) 0 0
\(231\) 6.00000i 0.394771i
\(232\) 7.34847 + 7.34847i 0.482451 + 0.482451i
\(233\) 4.89898 + 4.89898i 0.320943 + 0.320943i 0.849129 0.528186i \(-0.177128\pi\)
−0.528186 + 0.849129i \(0.677128\pi\)
\(234\) −18.0000 −1.17670
\(235\) 0 0
\(236\) 0 0
\(237\) −12.2474 12.2474i −0.795557 0.795557i
\(238\) −29.3939 + 29.3939i −1.90532 + 1.90532i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) −1.22474 + 1.22474i −0.0787296 + 0.0787296i
\(243\) 11.0227 11.0227i 0.707107 0.707107i
\(244\) 2.00000i 0.128037i
\(245\) 0 0
\(246\) 18.0000 1.14764
\(247\) 4.89898 + 4.89898i 0.311715 + 0.311715i
\(248\) 4.89898 + 4.89898i 0.311086 + 0.311086i
\(249\) 18.0000 1.14070
\(250\) 0 0
\(251\) 12.0000i 0.757433i −0.925513 0.378717i \(-0.876365\pi\)
0.925513 0.378717i \(-0.123635\pi\)
\(252\) 7.34847 + 7.34847i 0.462910 + 0.462910i
\(253\) 4.89898 4.89898i 0.307996 0.307996i
\(254\) 6.00000 0.376473
\(255\) 0 0
\(256\) 19.0000 1.18750
\(257\) 9.79796 9.79796i 0.611180 0.611180i −0.332074 0.943253i \(-0.607748\pi\)
0.943253 + 0.332074i \(0.107748\pi\)
\(258\) 22.0454 + 22.0454i 1.37249 + 1.37249i
\(259\) 0 0
\(260\) 0 0
\(261\) 18.0000i 1.11417i
\(262\) 14.6969 + 14.6969i 0.907980 + 0.907980i
\(263\) 17.1464 + 17.1464i 1.05729 + 1.05729i 0.998256 + 0.0590383i \(0.0188034\pi\)
0.0590383 + 0.998256i \(0.481197\pi\)
\(264\) 3.00000i 0.184637i
\(265\) 0 0
\(266\) 12.0000i 0.735767i
\(267\) 14.6969 14.6969i 0.899438 0.899438i
\(268\) −2.44949 + 2.44949i −0.149626 + 0.149626i
\(269\) 24.0000 1.46331 0.731653 0.681677i \(-0.238749\pi\)
0.731653 + 0.681677i \(0.238749\pi\)
\(270\) 0 0
\(271\) 2.00000 0.121491 0.0607457 0.998153i \(-0.480652\pi\)
0.0607457 + 0.998153i \(0.480652\pi\)
\(272\) 24.4949 24.4949i 1.48522 1.48522i
\(273\) 14.6969 14.6969i 0.889499 0.889499i
\(274\) 24.0000i 1.44989i
\(275\) 0 0
\(276\) 12.0000i 0.722315i
\(277\) 12.2474 + 12.2474i 0.735878 + 0.735878i 0.971777 0.235900i \(-0.0758036\pi\)
−0.235900 + 0.971777i \(0.575804\pi\)
\(278\) −26.9444 26.9444i −1.61602 1.61602i
\(279\) 12.0000i 0.718421i
\(280\) 0 0
\(281\) 30.0000i 1.78965i 0.446417 + 0.894825i \(0.352700\pi\)
−0.446417 + 0.894825i \(0.647300\pi\)
\(282\) −14.6969 14.6969i −0.875190 0.875190i
\(283\) −12.2474 + 12.2474i −0.728035 + 0.728035i −0.970228 0.242193i \(-0.922133\pi\)
0.242193 + 0.970228i \(0.422133\pi\)
\(284\) 12.0000 0.712069
\(285\) 0 0
\(286\) 6.00000 0.354787
\(287\) −14.6969 + 14.6969i −0.867533 + 0.867533i
\(288\) −11.0227 11.0227i −0.649519 0.649519i
\(289\) 31.0000i 1.82353i
\(290\) 0 0
\(291\) −24.0000 −1.40690
\(292\) 2.44949 + 2.44949i 0.143346 + 0.143346i
\(293\) −9.79796 9.79796i −0.572403 0.572403i 0.360396 0.932799i \(-0.382641\pi\)
−0.932799 + 0.360396i \(0.882641\pi\)
\(294\) −15.0000 −0.874818
\(295\) 0 0
\(296\) 0 0
\(297\) −3.67423 + 3.67423i −0.213201 + 0.213201i
\(298\) −7.34847 + 7.34847i −0.425685 + 0.425685i
\(299\) −24.0000 −1.38796
\(300\) 0 0
\(301\) −36.0000 −2.07501
\(302\) 12.2474 12.2474i 0.704761 0.704761i
\(303\) 22.0454 + 22.0454i 1.26648 + 1.26648i
\(304\) 10.0000i 0.573539i
\(305\) 0 0
\(306\) −36.0000 −2.05798
\(307\) 17.1464 + 17.1464i 0.978598 + 0.978598i 0.999776 0.0211774i \(-0.00674148\pi\)
−0.0211774 + 0.999776i \(0.506741\pi\)
\(308\) −2.44949 2.44949i −0.139573 0.139573i
\(309\) 6.00000i 0.341328i
\(310\) 0 0
\(311\) 24.0000i 1.36092i −0.732787 0.680458i \(-0.761781\pi\)
0.732787 0.680458i \(-0.238219\pi\)
\(312\) −7.34847 + 7.34847i −0.416025 + 0.416025i
\(313\) 4.89898 4.89898i 0.276907 0.276907i −0.554966 0.831873i \(-0.687269\pi\)
0.831873 + 0.554966i \(0.187269\pi\)
\(314\) 24.0000 1.35440
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 4.89898 4.89898i 0.275154 0.275154i −0.556017 0.831171i \(-0.687671\pi\)
0.831171 + 0.556017i \(0.187671\pi\)
\(318\) 14.6969 14.6969i 0.824163 0.824163i
\(319\) 6.00000i 0.335936i
\(320\) 0 0
\(321\) 6.00000i 0.334887i
\(322\) 29.3939 + 29.3939i 1.63806 + 1.63806i
\(323\) 9.79796 + 9.79796i 0.545173 + 0.545173i
\(324\) 9.00000i 0.500000i
\(325\) 0 0
\(326\) 30.0000i 1.66155i
\(327\) −12.2474 12.2474i −0.677285 0.677285i
\(328\) 7.34847 7.34847i 0.405751 0.405751i
\(329\) 24.0000 1.32316
\(330\) 0 0
\(331\) −28.0000 −1.53902 −0.769510 0.638635i \(-0.779499\pi\)
−0.769510 + 0.638635i \(0.779499\pi\)
\(332\) −7.34847 + 7.34847i −0.403300 + 0.403300i
\(333\) 0 0
\(334\) 6.00000i 0.328305i
\(335\) 0 0
\(336\) 30.0000 1.63663
\(337\) −22.0454 22.0454i −1.20089 1.20089i −0.973896 0.226994i \(-0.927110\pi\)
−0.226994 0.973896i \(-0.572890\pi\)
\(338\) 1.22474 + 1.22474i 0.0666173 + 0.0666173i
\(339\) −12.0000 −0.651751
\(340\) 0 0
\(341\) 4.00000i 0.216612i
\(342\) 7.34847 7.34847i 0.397360 0.397360i
\(343\) −4.89898 + 4.89898i −0.264520 + 0.264520i
\(344\) 18.0000 0.970495
\(345\) 0 0
\(346\) 0 0
\(347\) −12.2474 + 12.2474i −0.657477 + 0.657477i −0.954783 0.297305i \(-0.903912\pi\)
0.297305 + 0.954783i \(0.403912\pi\)
\(348\) 7.34847 + 7.34847i 0.393919 + 0.393919i
\(349\) 2.00000i 0.107058i 0.998566 + 0.0535288i \(0.0170469\pi\)
−0.998566 + 0.0535288i \(0.982953\pi\)
\(350\) 0 0
\(351\) 18.0000 0.960769
\(352\) 3.67423 + 3.67423i 0.195837 + 0.195837i
\(353\) −24.4949 24.4949i −1.30373 1.30373i −0.925856 0.377875i \(-0.876655\pi\)
−0.377875 0.925856i \(-0.623345\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 12.0000i 0.635999i
\(357\) 29.3939 29.3939i 1.55569 1.55569i
\(358\) 0 0
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) 15.0000 0.789474
\(362\) 12.2474 12.2474i 0.643712 0.643712i
\(363\) 1.22474 1.22474i 0.0642824 0.0642824i
\(364\) 12.0000i 0.628971i
\(365\) 0 0
\(366\) 6.00000i 0.313625i
\(367\) −2.44949 2.44949i −0.127862 0.127862i 0.640280 0.768142i \(-0.278818\pi\)
−0.768142 + 0.640280i \(0.778818\pi\)
\(368\) −24.4949 24.4949i −1.27688 1.27688i
\(369\) −18.0000 −0.937043
\(370\) 0 0
\(371\) 24.0000i 1.24602i
\(372\) 4.89898 + 4.89898i 0.254000 + 0.254000i
\(373\) −17.1464 + 17.1464i −0.887808 + 0.887808i −0.994312 0.106504i \(-0.966034\pi\)
0.106504 + 0.994312i \(0.466034\pi\)
\(374\) 12.0000 0.620505
\(375\) 0 0
\(376\) −12.0000 −0.618853
\(377\) 14.6969 14.6969i 0.756931 0.756931i
\(378\) −22.0454 22.0454i −1.13389 1.13389i
\(379\) 20.0000i 1.02733i 0.857991 + 0.513665i \(0.171713\pi\)
−0.857991 + 0.513665i \(0.828287\pi\)
\(380\) 0 0
\(381\) −6.00000 −0.307389
\(382\) −29.3939 29.3939i −1.50392 1.50392i
\(383\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(384\) −21.0000 −1.07165
\(385\) 0 0
\(386\) 18.0000i 0.916176i
\(387\) −22.0454 22.0454i −1.12063 1.12063i
\(388\) 9.79796 9.79796i 0.497416 0.497416i
\(389\) −12.0000 −0.608424 −0.304212 0.952604i \(-0.598393\pi\)
−0.304212 + 0.952604i \(0.598393\pi\)
\(390\) 0 0
\(391\) −48.0000 −2.42746
\(392\) −6.12372 + 6.12372i −0.309295 + 0.309295i
\(393\) −14.6969 14.6969i −0.741362 0.741362i
\(394\) 0 0
\(395\) 0 0
\(396\) 3.00000i 0.150756i
\(397\) −4.89898 4.89898i −0.245873 0.245873i 0.573402 0.819274i \(-0.305623\pi\)
−0.819274 + 0.573402i \(0.805623\pi\)
\(398\) 4.89898 + 4.89898i 0.245564 + 0.245564i
\(399\) 12.0000i 0.600751i
\(400\) 0 0
\(401\) 24.0000i 1.19850i 0.800561 + 0.599251i \(0.204535\pi\)
−0.800561 + 0.599251i \(0.795465\pi\)
\(402\) 7.34847 7.34847i 0.366508 0.366508i
\(403\) 9.79796 9.79796i 0.488071 0.488071i
\(404\) −18.0000 −0.895533
\(405\) 0 0
\(406\) −36.0000 −1.78665
\(407\) 0 0
\(408\) −14.6969 + 14.6969i −0.727607 + 0.727607i
\(409\) 10.0000i 0.494468i −0.968956 0.247234i \(-0.920478\pi\)
0.968956 0.247234i \(-0.0795217\pi\)
\(410\) 0 0
\(411\) 24.0000i 1.18383i
\(412\) −2.44949 2.44949i −0.120678 0.120678i
\(413\) 0 0
\(414\) 36.0000i 1.76930i
\(415\) 0 0
\(416\) 18.0000i 0.882523i
\(417\) 26.9444 + 26.9444i 1.31947 + 1.31947i
\(418\) −2.44949 + 2.44949i −0.119808 + 0.119808i
\(419\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 31.8434 31.8434i 1.55011 1.55011i
\(423\) 14.6969 + 14.6969i 0.714590 + 0.714590i
\(424\) 12.0000i 0.582772i
\(425\) 0 0
\(426\) −36.0000 −1.74421
\(427\) −4.89898 4.89898i −0.237078 0.237078i
\(428\) 2.44949 + 2.44949i 0.118401 + 0.118401i
\(429\) −6.00000 −0.289683
\(430\) 0 0
\(431\) 24.0000i 1.15604i 0.816023 + 0.578020i \(0.196174\pi\)
−0.816023 + 0.578020i \(0.803826\pi\)
\(432\) 18.3712 + 18.3712i 0.883883 + 0.883883i
\(433\) −19.5959 + 19.5959i −0.941720 + 0.941720i −0.998393 0.0566731i \(-0.981951\pi\)
0.0566731 + 0.998393i \(0.481951\pi\)
\(434\) −24.0000 −1.15204
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) 9.79796 9.79796i 0.468700 0.468700i
\(438\) −7.34847 7.34847i −0.351123 0.351123i
\(439\) 26.0000i 1.24091i −0.784241 0.620456i \(-0.786947\pi\)
0.784241 0.620456i \(-0.213053\pi\)
\(440\) 0 0
\(441\) 15.0000 0.714286
\(442\) −29.3939 29.3939i −1.39812 1.39812i
\(443\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 42.0000i 1.98876i
\(447\) 7.34847 7.34847i 0.347571 0.347571i
\(448\) 2.44949 2.44949i 0.115728 0.115728i
\(449\) −12.0000 −0.566315 −0.283158 0.959073i \(-0.591382\pi\)
−0.283158 + 0.959073i \(0.591382\pi\)
\(450\) 0 0
\(451\) 6.00000 0.282529
\(452\) 4.89898 4.89898i 0.230429 0.230429i
\(453\) −12.2474 + 12.2474i −0.575435 + 0.575435i
\(454\) 30.0000i 1.40797i
\(455\) 0 0
\(456\) 6.00000i 0.280976i
\(457\) 22.0454 + 22.0454i 1.03124 + 1.03124i 0.999496 + 0.0317447i \(0.0101063\pi\)
0.0317447 + 0.999496i \(0.489894\pi\)
\(458\) −12.2474 12.2474i −0.572286 0.572286i
\(459\) 36.0000 1.68034
\(460\) 0 0
\(461\) 6.00000i 0.279448i 0.990190 + 0.139724i \(0.0446215\pi\)
−0.990190 + 0.139724i \(0.955378\pi\)
\(462\) 7.34847 + 7.34847i 0.341882 + 0.341882i
\(463\) 2.44949 2.44949i 0.113837 0.113837i −0.647893 0.761731i \(-0.724350\pi\)
0.761731 + 0.647893i \(0.224350\pi\)
\(464\) 30.0000 1.39272
\(465\) 0 0
\(466\) 12.0000 0.555889
\(467\) −24.4949 + 24.4949i −1.13349 + 1.13349i −0.143896 + 0.989593i \(0.545963\pi\)
−0.989593 + 0.143896i \(0.954037\pi\)
\(468\) −7.34847 + 7.34847i −0.339683 + 0.339683i
\(469\) 12.0000i 0.554109i
\(470\) 0 0
\(471\) −24.0000 −1.10586
\(472\) 0 0
\(473\) 7.34847 + 7.34847i 0.337883 + 0.337883i
\(474\) −30.0000 −1.37795
\(475\) 0 0
\(476\) 24.0000i 1.10004i
\(477\) −14.6969 + 14.6969i −0.672927 + 0.672927i
\(478\) 0 0
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −12.2474 + 12.2474i −0.557856 + 0.557856i
\(483\) −29.3939 29.3939i −1.33747 1.33747i
\(484\) 1.00000i 0.0454545i
\(485\) 0 0
\(486\) 27.0000i 1.22474i
\(487\) 17.1464 + 17.1464i 0.776979 + 0.776979i 0.979316 0.202337i \(-0.0648537\pi\)
−0.202337 + 0.979316i \(0.564854\pi\)
\(488\) 2.44949 + 2.44949i 0.110883 + 0.110883i
\(489\) 30.0000i 1.35665i
\(490\) 0 0
\(491\) 12.0000i 0.541552i −0.962642 0.270776i \(-0.912720\pi\)
0.962642 0.270776i \(-0.0872803\pi\)
\(492\) 7.34847 7.34847i 0.331295 0.331295i
\(493\) 29.3939 29.3939i 1.32383 1.32383i
\(494\) 12.0000 0.539906
\(495\) 0 0
\(496\) 20.0000 0.898027
\(497\) 29.3939 29.3939i 1.31850 1.31850i
\(498\) 22.0454 22.0454i 0.987878 0.987878i
\(499\) 16.0000i 0.716258i 0.933672 + 0.358129i \(0.116585\pi\)
−0.933672 + 0.358129i \(0.883415\pi\)
\(500\) 0 0
\(501\) 6.00000i 0.268060i
\(502\) −14.6969 14.6969i −0.655956 0.655956i
\(503\) 17.1464 + 17.1464i 0.764521 + 0.764521i 0.977136 0.212615i \(-0.0681979\pi\)
−0.212615 + 0.977136i \(0.568198\pi\)
\(504\) −18.0000 −0.801784
\(505\) 0 0
\(506\) 12.0000i 0.533465i
\(507\) −1.22474 1.22474i −0.0543928 0.0543928i
\(508\) 2.44949 2.44949i 0.108679 0.108679i
\(509\) 24.0000 1.06378 0.531891 0.846813i \(-0.321482\pi\)
0.531891 + 0.846813i \(0.321482\pi\)
\(510\) 0 0
\(511\) 12.0000 0.530849
\(512\) 6.12372 6.12372i 0.270633 0.270633i
\(513\) −7.34847 + 7.34847i −0.324443 + 0.324443i
\(514\) 24.0000i 1.05859i
\(515\) 0 0
\(516\) 18.0000 0.792406
\(517\) −4.89898 4.89898i −0.215457 0.215457i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 24.0000i 1.05146i 0.850652 + 0.525730i \(0.176208\pi\)
−0.850652 + 0.525730i \(0.823792\pi\)
\(522\) −22.0454 22.0454i −0.964901 0.964901i
\(523\) −7.34847 + 7.34847i −0.321326 + 0.321326i −0.849276 0.527950i \(-0.822961\pi\)
0.527950 + 0.849276i \(0.322961\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 42.0000 1.83129
\(527\) 19.5959 19.5959i 0.853612 0.853612i
\(528\) −6.12372 6.12372i −0.266501 0.266501i
\(529\) 25.0000i 1.08696i
\(530\) 0 0
\(531\) 0 0
\(532\) −4.89898 4.89898i −0.212398 0.212398i
\(533\) −14.6969 14.6969i −0.636595 0.636595i
\(534\) 36.0000i 1.55787i
\(535\) 0 0
\(536\) 6.00000i 0.259161i
\(537\) 0 0
\(538\) 29.3939 29.3939i 1.26726 1.26726i
\(539\) −5.00000 −0.215365
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 2.44949 2.44949i 0.105215 0.105215i
\(543\) −12.2474 + 12.2474i −0.525588 + 0.525588i
\(544\) 36.0000i 1.54349i
\(545\) 0 0
\(546\) 36.0000i 1.54066i
\(547\) 12.2474 + 12.2474i 0.523663 + 0.523663i 0.918676 0.395013i \(-0.129260\pi\)
−0.395013 + 0.918676i \(0.629260\pi\)
\(548\) 9.79796 + 9.79796i 0.418548 + 0.418548i
\(549\) 6.00000i 0.256074i
\(550\) 0 0
\(551\) 12.0000i 0.511217i
\(552\) 14.6969 + 14.6969i 0.625543 + 0.625543i
\(553\) 24.4949 24.4949i 1.04163 1.04163i
\(554\) 30.0000 1.27458
\(555\) 0 0
\(556\) −22.0000 −0.933008
\(557\) 19.5959 19.5959i 0.830306 0.830306i −0.157253 0.987558i \(-0.550264\pi\)
0.987558 + 0.157253i \(0.0502637\pi\)
\(558\) −14.6969 14.6969i −0.622171 0.622171i
\(559\) 36.0000i 1.52264i
\(560\) 0 0
\(561\) −12.0000 −0.506640
\(562\) 36.7423 + 36.7423i 1.54988 + 1.54988i
\(563\) −7.34847 7.34847i −0.309701 0.309701i 0.535092 0.844794i \(-0.320277\pi\)
−0.844794 + 0.535092i \(0.820277\pi\)
\(564\) −12.0000 −0.505291
\(565\) 0 0
\(566\) 30.0000i 1.26099i
\(567\) 22.0454 + 22.0454i 0.925820 + 0.925820i
\(568\) −14.6969 + 14.6969i −0.616670 + 0.616670i
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) 0 0
\(571\) 14.0000 0.585882 0.292941 0.956131i \(-0.405366\pi\)
0.292941 + 0.956131i \(0.405366\pi\)
\(572\) 2.44949 2.44949i 0.102418 0.102418i
\(573\) 29.3939 + 29.3939i 1.22795 + 1.22795i
\(574\) 36.0000i 1.50261i
\(575\) 0 0
\(576\) 3.00000 0.125000
\(577\) −14.6969 14.6969i −0.611842 0.611842i 0.331584 0.943426i \(-0.392417\pi\)
−0.943426 + 0.331584i \(0.892417\pi\)
\(578\) −37.9671 37.9671i −1.57922 1.57922i
\(579\) 18.0000i 0.748054i
\(580\) 0 0
\(581\) 36.0000i 1.49353i
\(582\) −29.3939 + 29.3939i −1.21842 + 1.21842i
\(583\) 4.89898 4.89898i 0.202895 0.202895i
\(584\) −6.00000 −0.248282
\(585\) 0 0
\(586\) −24.0000 −0.991431
\(587\) −4.89898 + 4.89898i −0.202203 + 0.202203i −0.800943 0.598741i \(-0.795668\pi\)
0.598741 + 0.800943i \(0.295668\pi\)
\(588\) −6.12372 + 6.12372i −0.252538 + 0.252538i
\(589\) 8.00000i 0.329634i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 14.6969 + 14.6969i 0.603531 + 0.603531i 0.941248 0.337717i \(-0.109655\pi\)
−0.337717 + 0.941248i \(0.609655\pi\)
\(594\) 9.00000i 0.369274i
\(595\) 0 0
\(596\) 6.00000i 0.245770i
\(597\) −4.89898 4.89898i −0.200502 0.200502i
\(598\) −29.3939 + 29.3939i −1.20201 + 1.20201i
\(599\) 12.0000 0.490307 0.245153 0.969484i \(-0.421162\pi\)
0.245153 + 0.969484i \(0.421162\pi\)
\(600\) 0 0
\(601\) 22.0000 0.897399 0.448699 0.893683i \(-0.351887\pi\)
0.448699 + 0.893683i \(0.351887\pi\)
\(602\) −44.0908 + 44.0908i −1.79701 + 1.79701i
\(603\) −7.34847 + 7.34847i −0.299253 + 0.299253i
\(604\) 10.0000i 0.406894i
\(605\) 0 0
\(606\) 54.0000 2.19360
\(607\) −12.2474 12.2474i −0.497109 0.497109i 0.413428 0.910537i \(-0.364331\pi\)
−0.910537 + 0.413428i \(0.864331\pi\)
\(608\) 7.34847 + 7.34847i 0.298020 + 0.298020i
\(609\) 36.0000 1.45879
\(610\) 0 0
\(611\) 24.0000i 0.970936i
\(612\) −14.6969 + 14.6969i −0.594089 + 0.594089i
\(613\) 2.44949 2.44949i 0.0989340 0.0989340i −0.655907 0.754841i \(-0.727714\pi\)
0.754841 + 0.655907i \(0.227714\pi\)
\(614\) 42.0000 1.69498
\(615\) 0 0
\(616\) 6.00000 0.241747
\(617\) 14.6969 14.6969i 0.591676 0.591676i −0.346408 0.938084i \(-0.612599\pi\)
0.938084 + 0.346408i \(0.112599\pi\)
\(618\) 7.34847 + 7.34847i 0.295599 + 0.295599i
\(619\) 4.00000i 0.160774i 0.996764 + 0.0803868i \(0.0256155\pi\)
−0.996764 + 0.0803868i \(0.974384\pi\)
\(620\) 0 0
\(621\) 36.0000i 1.44463i
\(622\) −29.3939 29.3939i −1.17859 1.17859i
\(623\) 29.3939 + 29.3939i 1.17764 + 1.17764i
\(624\) 30.0000i 1.20096i
\(625\) 0 0
\(626\) 12.0000i 0.479616i
\(627\) 2.44949 2.44949i 0.0978232 0.0978232i
\(628\) 9.79796 9.79796i 0.390981 0.390981i
\(629\) 0 0
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −12.2474 + 12.2474i −0.487177 + 0.487177i
\(633\) −31.8434 + 31.8434i −1.26566 + 1.26566i
\(634\) 12.0000i 0.476581i
\(635\) 0 0
\(636\) 12.0000i 0.475831i
\(637\) 12.2474 + 12.2474i 0.485262 + 0.485262i
\(638\) 7.34847 + 7.34847i 0.290929 + 0.290929i
\(639\) 36.0000 1.42414
\(640\) 0 0
\(641\) 12.0000i 0.473972i 0.971513 + 0.236986i \(0.0761595\pi\)
−0.971513 + 0.236986i \(0.923841\pi\)
\(642\) −7.34847 7.34847i −0.290021 0.290021i
\(643\) −12.2474 + 12.2474i −0.482992 + 0.482992i −0.906086 0.423094i \(-0.860944\pi\)
0.423094 + 0.906086i \(0.360944\pi\)
\(644\) 24.0000 0.945732
\(645\) 0 0
\(646\) 24.0000 0.944267
\(647\) 19.5959 19.5959i 0.770395 0.770395i −0.207780 0.978175i \(-0.566624\pi\)
0.978175 + 0.207780i \(0.0666240\pi\)
\(648\) −11.0227 11.0227i −0.433013 0.433013i
\(649\) 0 0
\(650\) 0 0
\(651\) 24.0000 0.940634
\(652\) 12.2474 + 12.2474i 0.479647 + 0.479647i
\(653\) 29.3939 + 29.3939i 1.15027 + 1.15027i 0.986498 + 0.163773i \(0.0523666\pi\)
0.163773 + 0.986498i \(0.447633\pi\)
\(654\) −30.0000 −1.17309
\(655\) 0 0
\(656\) 30.0000i 1.17130i
\(657\) 7.34847 + 7.34847i 0.286691 + 0.286691i
\(658\) 29.3939 29.3939i 1.14589 1.14589i
\(659\) −12.0000 −0.467454 −0.233727 0.972302i \(-0.575092\pi\)
−0.233727 + 0.972302i \(0.575092\pi\)
\(660\) 0 0
\(661\) 34.0000 1.32245 0.661223 0.750189i \(-0.270038\pi\)
0.661223 + 0.750189i \(0.270038\pi\)
\(662\) −34.2929 + 34.2929i −1.33283 + 1.33283i
\(663\) 29.3939 + 29.3939i 1.14156 + 1.14156i
\(664\) 18.0000i 0.698535i
\(665\) 0 0
\(666\) 0 0
\(667\) −29.3939 29.3939i −1.13814 1.13814i
\(668\) 2.44949 + 2.44949i 0.0947736 + 0.0947736i
\(669\) 42.0000i 1.62381i
\(670\) 0 0
\(671\) 2.00000i 0.0772091i
\(672\) 22.0454 22.0454i 0.850420 0.850420i
\(673\) −2.44949 + 2.44949i −0.0944209 + 0.0944209i −0.752739 0.658319i \(-0.771268\pi\)
0.658319 + 0.752739i \(0.271268\pi\)
\(674\) −54.0000 −2.08000
\(675\) 0 0
\(676\) 1.00000 0.0384615
\(677\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(678\) −14.6969 + 14.6969i −0.564433 + 0.564433i
\(679\) 48.0000i 1.84207i
\(680\) 0 0
\(681\) 30.0000i 1.14960i
\(682\) 4.89898 + 4.89898i 0.187592 + 0.187592i
\(683\) 14.6969 + 14.6969i 0.562363 + 0.562363i 0.929978 0.367615i \(-0.119826\pi\)
−0.367615 + 0.929978i \(0.619826\pi\)
\(684\) 6.00000i 0.229416i
\(685\) 0 0
\(686\) 12.0000i 0.458162i
\(687\) 12.2474 + 12.2474i 0.467269 + 0.467269i
\(688\) 36.7423 36.7423i 1.40079 1.40079i
\(689\) −24.0000 −0.914327
\(690\) 0 0
\(691\) 28.0000 1.06517 0.532585 0.846376i \(-0.321221\pi\)
0.532585 + 0.846376i \(0.321221\pi\)
\(692\) 0 0
\(693\) −7.34847 7.34847i −0.279145 0.279145i
\(694\) 30.0000i 1.13878i
\(695\) 0 0
\(696\) −18.0000 −0.682288
\(697\) −29.3939 29.3939i −1.11337 1.11337i
\(698\) 2.44949 + 2.44949i 0.0927146 + 0.0927146i
\(699\) −12.0000 −0.453882
\(700\) 0 0
\(701\) 18.0000i 0.679851i −0.940452 0.339925i \(-0.889598\pi\)
0.940452 0.339925i \(-0.110402\pi\)
\(702\) 22.0454 22.0454i 0.832050 0.832050i
\(703\) 0 0
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) −60.0000 −2.25813
\(707\) −44.0908 + 44.0908i −1.65821 + 1.65821i
\(708\) 0 0
\(709\) 46.0000i 1.72757i −0.503864 0.863783i \(-0.668089\pi\)
0.503864 0.863783i \(-0.331911\pi\)
\(710\) 0 0
\(711\) 30.0000 1.12509
\(712\) −14.6969 14.6969i −0.550791 0.550791i
\(713\) −19.5959 19.5959i −0.733873 0.733873i
\(714\) 72.0000i 2.69453i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) −29.3939 + 29.3939i −1.09697 + 1.09697i
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 0 0
\(721\) −12.0000 −0.446903
\(722\) 18.3712 18.3712i 0.683704 0.683704i
\(723\) 12.2474 12.2474i 0.455488 0.455488i
\(724\) 10.0000i 0.371647i
\(725\) 0 0
\(726\) 3.00000i 0.111340i
\(727\) −22.0454 22.0454i −0.817619 0.817619i 0.168144 0.985763i \(-0.446223\pi\)
−0.985763 + 0.168144i \(0.946223\pi\)
\(728\) −14.6969 14.6969i −0.544705 0.544705i
\(729\) 27.0000i 1.00000i
\(730\) 0 0
\(731\) 72.0000i 2.66302i
\(732\) 2.44949 + 2.44949i 0.0905357 + 0.0905357i
\(733\) 22.0454 22.0454i 0.814266 0.814266i −0.171005 0.985270i \(-0.554701\pi\)
0.985270 + 0.171005i \(0.0547013\pi\)
\(734\) −6.00000 −0.221464
\(735\) 0 0
\(736\) −36.0000 −1.32698
\(737\) 2.44949 2.44949i 0.0902281 0.0902281i
\(738\) −22.0454 + 22.0454i −0.811503 + 0.811503i
\(739\) 38.0000i 1.39785i 0.715194 + 0.698926i \(0.246338\pi\)
−0.715194 + 0.698926i \(0.753662\pi\)
\(740\) 0 0
\(741\) −12.0000 −0.440831
\(742\) 29.3939 + 29.3939i 1.07908 + 1.07908i
\(743\) −12.2474 12.2474i −0.449315 0.449315i 0.445812 0.895127i \(-0.352915\pi\)
−0.895127 + 0.445812i \(0.852915\pi\)
\(744\) −12.0000 −0.439941
\(745\) 0 0
\(746\) 42.0000i 1.53773i
\(747\) −22.0454 + 22.0454i −0.806599 + 0.806599i
\(748\) 4.89898 4.89898i 0.179124 0.179124i
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) −24.4949 + 24.4949i −0.893237 + 0.893237i
\(753\) 14.6969 + 14.6969i 0.535586 + 0.535586i
\(754\) 36.0000i 1.31104i
\(755\) 0 0
\(756\) −18.0000 −0.654654
\(757\) −9.79796 9.79796i −0.356113 0.356113i 0.506265 0.862378i \(-0.331026\pi\)
−0.862378 + 0.506265i \(0.831026\pi\)
\(758\) 24.4949 + 24.4949i 0.889695 + 0.889695i
\(759\) 12.0000i 0.435572i
\(760\) 0 0
\(761\) 42.0000i 1.52250i 0.648459 + 0.761249i \(0.275414\pi\)
−0.648459 + 0.761249i \(0.724586\pi\)
\(762\) −7.34847 + 7.34847i −0.266207 + 0.266207i
\(763\) 24.4949 24.4949i 0.886775 0.886775i
\(764\) −24.0000 −0.868290
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −23.2702 + 23.2702i −0.839689 + 0.839689i
\(769\) 22.0000i 0.793340i 0.917961 + 0.396670i \(0.129834\pi\)
−0.917961 + 0.396670i \(0.870166\pi\)
\(770\) 0 0
\(771\) 24.0000i 0.864339i
\(772\) 7.34847 + 7.34847i 0.264477 + 0.264477i
\(773\) −19.5959 19.5959i −0.704816 0.704816i 0.260624 0.965440i \(-0.416072\pi\)
−0.965440 + 0.260624i \(0.916072\pi\)
\(774\) −54.0000 −1.94099
\(775\) 0 0
\(776\) 24.0000i 0.861550i
\(777\) 0 0
\(778\) −14.6969 + 14.6969i −0.526911 + 0.526911i
\(779\) 12.0000 0.429945
\(780\) 0 0
\(781\) −12.0000 −0.429394
\(782\) −58.7878 + 58.7878i −2.10225 + 2.10225i
\(783\) 22.0454 + 22.0454i 0.787839 + 0.787839i
\(784\) 25.0000i 0.892857i
\(785\) 0 0
\(786\) −36.0000 −1.28408
\(787\) 2.44949 + 2.44949i 0.0873149 + 0.0873149i 0.749415 0.662100i \(-0.230335\pi\)
−0.662100 + 0.749415i \(0.730335\pi\)
\(788\) 0 0
\(789\) −42.0000 −1.49524
\(790\)