Properties

Label 390.2.e.c.79.1
Level $390$
Weight $2$
Character 390.79
Analytic conductor $3.114$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 390.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.11416567883\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \(x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 79.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 390.79
Dual form 390.2.e.c.79.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} -2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +1.00000 q^{6} -2.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +(-1.00000 - 2.00000i) q^{10} +2.00000 q^{11} -1.00000i q^{12} -1.00000i q^{13} -2.00000 q^{14} +(1.00000 + 2.00000i) q^{15} +1.00000 q^{16} -2.00000i q^{17} +1.00000i q^{18} +4.00000 q^{19} +(-2.00000 + 1.00000i) q^{20} +2.00000 q^{21} -2.00000i q^{22} -1.00000 q^{24} +(3.00000 - 4.00000i) q^{25} -1.00000 q^{26} -1.00000i q^{27} +2.00000i q^{28} -4.00000 q^{29} +(2.00000 - 1.00000i) q^{30} +8.00000 q^{31} -1.00000i q^{32} +2.00000i q^{33} -2.00000 q^{34} +(-2.00000 - 4.00000i) q^{35} +1.00000 q^{36} -6.00000i q^{37} -4.00000i q^{38} +1.00000 q^{39} +(1.00000 + 2.00000i) q^{40} -6.00000 q^{41} -2.00000i q^{42} +4.00000i q^{43} -2.00000 q^{44} +(-2.00000 + 1.00000i) q^{45} +8.00000i q^{47} +1.00000i q^{48} +3.00000 q^{49} +(-4.00000 - 3.00000i) q^{50} +2.00000 q^{51} +1.00000i q^{52} +2.00000i q^{53} -1.00000 q^{54} +(4.00000 - 2.00000i) q^{55} +2.00000 q^{56} +4.00000i q^{57} +4.00000i q^{58} -10.0000 q^{59} +(-1.00000 - 2.00000i) q^{60} -14.0000 q^{61} -8.00000i q^{62} +2.00000i q^{63} -1.00000 q^{64} +(-1.00000 - 2.00000i) q^{65} +2.00000 q^{66} +16.0000i q^{67} +2.00000i q^{68} +(-4.00000 + 2.00000i) q^{70} -4.00000 q^{71} -1.00000i q^{72} +8.00000i q^{73} -6.00000 q^{74} +(4.00000 + 3.00000i) q^{75} -4.00000 q^{76} -4.00000i q^{77} -1.00000i q^{78} +8.00000 q^{79} +(2.00000 - 1.00000i) q^{80} +1.00000 q^{81} +6.00000i q^{82} +12.0000i q^{83} -2.00000 q^{84} +(-2.00000 - 4.00000i) q^{85} +4.00000 q^{86} -4.00000i q^{87} +2.00000i q^{88} -6.00000 q^{89} +(1.00000 + 2.00000i) q^{90} -2.00000 q^{91} +8.00000i q^{93} +8.00000 q^{94} +(8.00000 - 4.00000i) q^{95} +1.00000 q^{96} -12.0000i q^{97} -3.00000i q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} + 4q^{5} + 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} + 4q^{5} + 2q^{6} - 2q^{9} - 2q^{10} + 4q^{11} - 4q^{14} + 2q^{15} + 2q^{16} + 8q^{19} - 4q^{20} + 4q^{21} - 2q^{24} + 6q^{25} - 2q^{26} - 8q^{29} + 4q^{30} + 16q^{31} - 4q^{34} - 4q^{35} + 2q^{36} + 2q^{39} + 2q^{40} - 12q^{41} - 4q^{44} - 4q^{45} + 6q^{49} - 8q^{50} + 4q^{51} - 2q^{54} + 8q^{55} + 4q^{56} - 20q^{59} - 2q^{60} - 28q^{61} - 2q^{64} - 2q^{65} + 4q^{66} - 8q^{70} - 8q^{71} - 12q^{74} + 8q^{75} - 8q^{76} + 16q^{79} + 4q^{80} + 2q^{81} - 4q^{84} - 4q^{85} + 8q^{86} - 12q^{89} + 2q^{90} - 4q^{91} + 16q^{94} + 16q^{95} + 2q^{96} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).

\(n\) \(131\) \(157\) \(301\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) 1.00000 0.408248
\(7\) 2.00000i 0.755929i −0.925820 0.377964i \(-0.876624\pi\)
0.925820 0.377964i \(-0.123376\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −1.00000 2.00000i −0.316228 0.632456i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.00000i 0.277350i
\(14\) −2.00000 −0.534522
\(15\) 1.00000 + 2.00000i 0.258199 + 0.516398i
\(16\) 1.00000 0.250000
\(17\) 2.00000i 0.485071i −0.970143 0.242536i \(-0.922021\pi\)
0.970143 0.242536i \(-0.0779791\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) −2.00000 + 1.00000i −0.447214 + 0.223607i
\(21\) 2.00000 0.436436
\(22\) 2.00000i 0.426401i
\(23\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(24\) −1.00000 −0.204124
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) −1.00000 −0.196116
\(27\) 1.00000i 0.192450i
\(28\) 2.00000i 0.377964i
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 2.00000 1.00000i 0.365148 0.182574i
\(31\) 8.00000 1.43684 0.718421 0.695608i \(-0.244865\pi\)
0.718421 + 0.695608i \(0.244865\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 2.00000i 0.348155i
\(34\) −2.00000 −0.342997
\(35\) −2.00000 4.00000i −0.338062 0.676123i
\(36\) 1.00000 0.166667
\(37\) 6.00000i 0.986394i −0.869918 0.493197i \(-0.835828\pi\)
0.869918 0.493197i \(-0.164172\pi\)
\(38\) 4.00000i 0.648886i
\(39\) 1.00000 0.160128
\(40\) 1.00000 + 2.00000i 0.158114 + 0.316228i
\(41\) −6.00000 −0.937043 −0.468521 0.883452i \(-0.655213\pi\)
−0.468521 + 0.883452i \(0.655213\pi\)
\(42\) 2.00000i 0.308607i
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) −2.00000 −0.301511
\(45\) −2.00000 + 1.00000i −0.298142 + 0.149071i
\(46\) 0 0
\(47\) 8.00000i 1.16692i 0.812142 + 0.583460i \(0.198301\pi\)
−0.812142 + 0.583460i \(0.801699\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 3.00000 0.428571
\(50\) −4.00000 3.00000i −0.565685 0.424264i
\(51\) 2.00000 0.280056
\(52\) 1.00000i 0.138675i
\(53\) 2.00000i 0.274721i 0.990521 + 0.137361i \(0.0438619\pi\)
−0.990521 + 0.137361i \(0.956138\pi\)
\(54\) −1.00000 −0.136083
\(55\) 4.00000 2.00000i 0.539360 0.269680i
\(56\) 2.00000 0.267261
\(57\) 4.00000i 0.529813i
\(58\) 4.00000i 0.525226i
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) −1.00000 2.00000i −0.129099 0.258199i
\(61\) −14.0000 −1.79252 −0.896258 0.443533i \(-0.853725\pi\)
−0.896258 + 0.443533i \(0.853725\pi\)
\(62\) 8.00000i 1.01600i
\(63\) 2.00000i 0.251976i
\(64\) −1.00000 −0.125000
\(65\) −1.00000 2.00000i −0.124035 0.248069i
\(66\) 2.00000 0.246183
\(67\) 16.0000i 1.95471i 0.211604 + 0.977356i \(0.432131\pi\)
−0.211604 + 0.977356i \(0.567869\pi\)
\(68\) 2.00000i 0.242536i
\(69\) 0 0
\(70\) −4.00000 + 2.00000i −0.478091 + 0.239046i
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 8.00000i 0.936329i 0.883641 + 0.468165i \(0.155085\pi\)
−0.883641 + 0.468165i \(0.844915\pi\)
\(74\) −6.00000 −0.697486
\(75\) 4.00000 + 3.00000i 0.461880 + 0.346410i
\(76\) −4.00000 −0.458831
\(77\) 4.00000i 0.455842i
\(78\) 1.00000i 0.113228i
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 2.00000 1.00000i 0.223607 0.111803i
\(81\) 1.00000 0.111111
\(82\) 6.00000i 0.662589i
\(83\) 12.0000i 1.31717i 0.752506 + 0.658586i \(0.228845\pi\)
−0.752506 + 0.658586i \(0.771155\pi\)
\(84\) −2.00000 −0.218218
\(85\) −2.00000 4.00000i −0.216930 0.433861i
\(86\) 4.00000 0.431331
\(87\) 4.00000i 0.428845i
\(88\) 2.00000i 0.213201i
\(89\) −6.00000 −0.635999 −0.317999 0.948091i \(-0.603011\pi\)
−0.317999 + 0.948091i \(0.603011\pi\)
\(90\) 1.00000 + 2.00000i 0.105409 + 0.210819i
\(91\) −2.00000 −0.209657
\(92\) 0 0
\(93\) 8.00000i 0.829561i
\(94\) 8.00000 0.825137
\(95\) 8.00000 4.00000i 0.820783 0.410391i
\(96\) 1.00000 0.102062
\(97\) 12.0000i 1.21842i −0.793011 0.609208i \(-0.791488\pi\)
0.793011 0.609208i \(-0.208512\pi\)
\(98\) 3.00000i 0.303046i
\(99\) −2.00000 −0.201008
\(100\) −3.00000 + 4.00000i −0.300000 + 0.400000i
\(101\) 4.00000 0.398015 0.199007 0.979998i \(-0.436228\pi\)
0.199007 + 0.979998i \(0.436228\pi\)
\(102\) 2.00000i 0.198030i
\(103\) 6.00000i 0.591198i 0.955312 + 0.295599i \(0.0955191\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(104\) 1.00000 0.0980581
\(105\) 4.00000 2.00000i 0.390360 0.195180i
\(106\) 2.00000 0.194257
\(107\) 4.00000i 0.386695i 0.981130 + 0.193347i \(0.0619344\pi\)
−0.981130 + 0.193347i \(0.938066\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 18.0000 1.72409 0.862044 0.506834i \(-0.169184\pi\)
0.862044 + 0.506834i \(0.169184\pi\)
\(110\) −2.00000 4.00000i −0.190693 0.381385i
\(111\) 6.00000 0.569495
\(112\) 2.00000i 0.188982i
\(113\) 6.00000i 0.564433i 0.959351 + 0.282216i \(0.0910696\pi\)
−0.959351 + 0.282216i \(0.908930\pi\)
\(114\) 4.00000 0.374634
\(115\) 0 0
\(116\) 4.00000 0.371391
\(117\) 1.00000i 0.0924500i
\(118\) 10.0000i 0.920575i
\(119\) −4.00000 −0.366679
\(120\) −2.00000 + 1.00000i −0.182574 + 0.0912871i
\(121\) −7.00000 −0.636364
\(122\) 14.0000i 1.26750i
\(123\) 6.00000i 0.541002i
\(124\) −8.00000 −0.718421
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 2.00000 0.178174
\(127\) 6.00000i 0.532414i −0.963916 0.266207i \(-0.914230\pi\)
0.963916 0.266207i \(-0.0857705\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −4.00000 −0.352180
\(130\) −2.00000 + 1.00000i −0.175412 + 0.0877058i
\(131\) −6.00000 −0.524222 −0.262111 0.965038i \(-0.584419\pi\)
−0.262111 + 0.965038i \(0.584419\pi\)
\(132\) 2.00000i 0.174078i
\(133\) 8.00000i 0.693688i
\(134\) 16.0000 1.38219
\(135\) −1.00000 2.00000i −0.0860663 0.172133i
\(136\) 2.00000 0.171499
\(137\) 14.0000i 1.19610i 0.801459 + 0.598050i \(0.204058\pi\)
−0.801459 + 0.598050i \(0.795942\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 2.00000 + 4.00000i 0.169031 + 0.338062i
\(141\) −8.00000 −0.673722
\(142\) 4.00000i 0.335673i
\(143\) 2.00000i 0.167248i
\(144\) −1.00000 −0.0833333
\(145\) −8.00000 + 4.00000i −0.664364 + 0.332182i
\(146\) 8.00000 0.662085
\(147\) 3.00000i 0.247436i
\(148\) 6.00000i 0.493197i
\(149\) −12.0000 −0.983078 −0.491539 0.870855i \(-0.663566\pi\)
−0.491539 + 0.870855i \(0.663566\pi\)
\(150\) 3.00000 4.00000i 0.244949 0.326599i
\(151\) −16.0000 −1.30206 −0.651031 0.759051i \(-0.725663\pi\)
−0.651031 + 0.759051i \(0.725663\pi\)
\(152\) 4.00000i 0.324443i
\(153\) 2.00000i 0.161690i
\(154\) −4.00000 −0.322329
\(155\) 16.0000 8.00000i 1.28515 0.642575i
\(156\) −1.00000 −0.0800641
\(157\) 10.0000i 0.798087i −0.916932 0.399043i \(-0.869342\pi\)
0.916932 0.399043i \(-0.130658\pi\)
\(158\) 8.00000i 0.636446i
\(159\) −2.00000 −0.158610
\(160\) −1.00000 2.00000i −0.0790569 0.158114i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 8.00000i 0.626608i −0.949653 0.313304i \(-0.898564\pi\)
0.949653 0.313304i \(-0.101436\pi\)
\(164\) 6.00000 0.468521
\(165\) 2.00000 + 4.00000i 0.155700 + 0.311400i
\(166\) 12.0000 0.931381
\(167\) 12.0000i 0.928588i −0.885681 0.464294i \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 2.00000i 0.154303i
\(169\) −1.00000 −0.0769231
\(170\) −4.00000 + 2.00000i −0.306786 + 0.153393i
\(171\) −4.00000 −0.305888
\(172\) 4.00000i 0.304997i
\(173\) 14.0000i 1.06440i 0.846619 + 0.532200i \(0.178635\pi\)
−0.846619 + 0.532200i \(0.821365\pi\)
\(174\) −4.00000 −0.303239
\(175\) −8.00000 6.00000i −0.604743 0.453557i
\(176\) 2.00000 0.150756
\(177\) 10.0000i 0.751646i
\(178\) 6.00000i 0.449719i
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) 2.00000 1.00000i 0.149071 0.0745356i
\(181\) −6.00000 −0.445976 −0.222988 0.974821i \(-0.571581\pi\)
−0.222988 + 0.974821i \(0.571581\pi\)
\(182\) 2.00000i 0.148250i
\(183\) 14.0000i 1.03491i
\(184\) 0 0
\(185\) −6.00000 12.0000i −0.441129 0.882258i
\(186\) 8.00000 0.586588
\(187\) 4.00000i 0.292509i
\(188\) 8.00000i 0.583460i
\(189\) −2.00000 −0.145479
\(190\) −4.00000 8.00000i −0.290191 0.580381i
\(191\) −12.0000 −0.868290 −0.434145 0.900843i \(-0.642949\pi\)
−0.434145 + 0.900843i \(0.642949\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(194\) −12.0000 −0.861550
\(195\) 2.00000 1.00000i 0.143223 0.0716115i
\(196\) −3.00000 −0.214286
\(197\) 10.0000i 0.712470i −0.934396 0.356235i \(-0.884060\pi\)
0.934396 0.356235i \(-0.115940\pi\)
\(198\) 2.00000i 0.142134i
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) 4.00000 + 3.00000i 0.282843 + 0.212132i
\(201\) −16.0000 −1.12855
\(202\) 4.00000i 0.281439i
\(203\) 8.00000i 0.561490i
\(204\) −2.00000 −0.140028
\(205\) −12.0000 + 6.00000i −0.838116 + 0.419058i
\(206\) 6.00000 0.418040
\(207\) 0 0
\(208\) 1.00000i 0.0693375i
\(209\) 8.00000 0.553372
\(210\) −2.00000 4.00000i −0.138013 0.276026i
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 2.00000i 0.137361i
\(213\) 4.00000i 0.274075i
\(214\) 4.00000 0.273434
\(215\) 4.00000 + 8.00000i 0.272798 + 0.545595i
\(216\) 1.00000 0.0680414
\(217\) 16.0000i 1.08615i
\(218\) 18.0000i 1.21911i
\(219\) −8.00000 −0.540590
\(220\) −4.00000 + 2.00000i −0.269680 + 0.134840i
\(221\) −2.00000 −0.134535
\(222\) 6.00000i 0.402694i
\(223\) 14.0000i 0.937509i −0.883328 0.468755i \(-0.844703\pi\)
0.883328 0.468755i \(-0.155297\pi\)
\(224\) −2.00000 −0.133631
\(225\) −3.00000 + 4.00000i −0.200000 + 0.266667i
\(226\) 6.00000 0.399114
\(227\) 12.0000i 0.796468i −0.917284 0.398234i \(-0.869623\pi\)
0.917284 0.398234i \(-0.130377\pi\)
\(228\) 4.00000i 0.264906i
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 4.00000 0.263181
\(232\) 4.00000i 0.262613i
\(233\) 14.0000i 0.917170i −0.888650 0.458585i \(-0.848356\pi\)
0.888650 0.458585i \(-0.151644\pi\)
\(234\) 1.00000 0.0653720
\(235\) 8.00000 + 16.0000i 0.521862 + 1.04372i
\(236\) 10.0000 0.650945
\(237\) 8.00000i 0.519656i
\(238\) 4.00000i 0.259281i
\(239\) 12.0000 0.776215 0.388108 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 1.00000 + 2.00000i 0.0645497 + 0.129099i
\(241\) −18.0000 −1.15948 −0.579741 0.814801i \(-0.696846\pi\)
−0.579741 + 0.814801i \(0.696846\pi\)
\(242\) 7.00000i 0.449977i
\(243\) 1.00000i 0.0641500i
\(244\) 14.0000 0.896258
\(245\) 6.00000 3.00000i 0.383326 0.191663i
\(246\) −6.00000 −0.382546
\(247\) 4.00000i 0.254514i
\(248\) 8.00000i 0.508001i
\(249\) −12.0000 −0.760469
\(250\) −11.0000 2.00000i −0.695701 0.126491i
\(251\) 18.0000 1.13615 0.568075 0.822977i \(-0.307688\pi\)
0.568075 + 0.822977i \(0.307688\pi\)
\(252\) 2.00000i 0.125988i
\(253\) 0 0
\(254\) −6.00000 −0.376473
\(255\) 4.00000 2.00000i 0.250490 0.125245i
\(256\) 1.00000 0.0625000
\(257\) 18.0000i 1.12281i 0.827541 + 0.561405i \(0.189739\pi\)
−0.827541 + 0.561405i \(0.810261\pi\)
\(258\) 4.00000i 0.249029i
\(259\) −12.0000 −0.745644
\(260\) 1.00000 + 2.00000i 0.0620174 + 0.124035i
\(261\) 4.00000 0.247594
\(262\) 6.00000i 0.370681i
\(263\) 8.00000i 0.493301i −0.969104 0.246651i \(-0.920670\pi\)
0.969104 0.246651i \(-0.0793300\pi\)
\(264\) −2.00000 −0.123091
\(265\) 2.00000 + 4.00000i 0.122859 + 0.245718i
\(266\) −8.00000 −0.490511
\(267\) 6.00000i 0.367194i
\(268\) 16.0000i 0.977356i
\(269\) 20.0000 1.21942 0.609711 0.792624i \(-0.291286\pi\)
0.609711 + 0.792624i \(0.291286\pi\)
\(270\) −2.00000 + 1.00000i −0.121716 + 0.0608581i
\(271\) 16.0000 0.971931 0.485965 0.873978i \(-0.338468\pi\)
0.485965 + 0.873978i \(0.338468\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 2.00000i 0.121046i
\(274\) 14.0000 0.845771
\(275\) 6.00000 8.00000i 0.361814 0.482418i
\(276\) 0 0
\(277\) 2.00000i 0.120168i 0.998193 + 0.0600842i \(0.0191369\pi\)
−0.998193 + 0.0600842i \(0.980863\pi\)
\(278\) 4.00000i 0.239904i
\(279\) −8.00000 −0.478947
\(280\) 4.00000 2.00000i 0.239046 0.119523i
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 8.00000i 0.476393i
\(283\) 16.0000i 0.951101i 0.879688 + 0.475551i \(0.157751\pi\)
−0.879688 + 0.475551i \(0.842249\pi\)
\(284\) 4.00000 0.237356
\(285\) 4.00000 + 8.00000i 0.236940 + 0.473879i
\(286\) −2.00000 −0.118262
\(287\) 12.0000i 0.708338i
\(288\) 1.00000i 0.0589256i
\(289\) 13.0000 0.764706
\(290\) 4.00000 + 8.00000i 0.234888 + 0.469776i
\(291\) 12.0000 0.703452
\(292\) 8.00000i 0.468165i
\(293\) 26.0000i 1.51894i 0.650545 + 0.759468i \(0.274541\pi\)
−0.650545 + 0.759468i \(0.725459\pi\)
\(294\) 3.00000 0.174964
\(295\) −20.0000 + 10.0000i −1.16445 + 0.582223i
\(296\) 6.00000 0.348743
\(297\) 2.00000i 0.116052i
\(298\) 12.0000i 0.695141i
\(299\) 0 0
\(300\) −4.00000 3.00000i −0.230940 0.173205i
\(301\) 8.00000 0.461112
\(302\) 16.0000i 0.920697i
\(303\) 4.00000i 0.229794i
\(304\) 4.00000 0.229416
\(305\) −28.0000 + 14.0000i −1.60328 + 0.801638i
\(306\) 2.00000 0.114332
\(307\) 28.0000i 1.59804i 0.601302 + 0.799022i \(0.294649\pi\)
−0.601302 + 0.799022i \(0.705351\pi\)
\(308\) 4.00000i 0.227921i
\(309\) −6.00000 −0.341328
\(310\) −8.00000 16.0000i −0.454369 0.908739i
\(311\) 20.0000 1.13410 0.567048 0.823685i \(-0.308085\pi\)
0.567048 + 0.823685i \(0.308085\pi\)
\(312\) 1.00000i 0.0566139i
\(313\) 20.0000i 1.13047i −0.824931 0.565233i \(-0.808786\pi\)
0.824931 0.565233i \(-0.191214\pi\)
\(314\) −10.0000 −0.564333
\(315\) 2.00000 + 4.00000i 0.112687 + 0.225374i
\(316\) −8.00000 −0.450035
\(317\) 18.0000i 1.01098i 0.862832 + 0.505490i \(0.168688\pi\)
−0.862832 + 0.505490i \(0.831312\pi\)
\(318\) 2.00000i 0.112154i
\(319\) −8.00000 −0.447914
\(320\) −2.00000 + 1.00000i −0.111803 + 0.0559017i
\(321\) −4.00000 −0.223258
\(322\) 0 0
\(323\) 8.00000i 0.445132i
\(324\) −1.00000 −0.0555556
\(325\) −4.00000 3.00000i −0.221880 0.166410i
\(326\) −8.00000 −0.443079
\(327\) 18.0000i 0.995402i
\(328\) 6.00000i 0.331295i
\(329\) 16.0000 0.882109
\(330\) 4.00000 2.00000i 0.220193 0.110096i
\(331\) −12.0000 −0.659580 −0.329790 0.944054i \(-0.606978\pi\)
−0.329790 + 0.944054i \(0.606978\pi\)
\(332\) 12.0000i 0.658586i
\(333\) 6.00000i 0.328798i
\(334\) −12.0000 −0.656611
\(335\) 16.0000 + 32.0000i 0.874173 + 1.74835i
\(336\) 2.00000 0.109109
\(337\) 20.0000i 1.08947i −0.838608 0.544735i \(-0.816630\pi\)
0.838608 0.544735i \(-0.183370\pi\)
\(338\) 1.00000i 0.0543928i
\(339\) −6.00000 −0.325875
\(340\) 2.00000 + 4.00000i 0.108465 + 0.216930i
\(341\) 16.0000 0.866449
\(342\) 4.00000i 0.216295i
\(343\) 20.0000i 1.07990i
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) 14.0000 0.752645
\(347\) 12.0000i 0.644194i −0.946707 0.322097i \(-0.895612\pi\)
0.946707 0.322097i \(-0.104388\pi\)
\(348\) 4.00000i 0.214423i
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) −6.00000 + 8.00000i −0.320713 + 0.427618i
\(351\) −1.00000 −0.0533761
\(352\) 2.00000i 0.106600i
\(353\) 34.0000i 1.80964i −0.425797 0.904819i \(-0.640006\pi\)
0.425797 0.904819i \(-0.359994\pi\)
\(354\) −10.0000 −0.531494
\(355\) −8.00000 + 4.00000i −0.424596 + 0.212298i
\(356\) 6.00000 0.317999
\(357\) 4.00000i 0.211702i
\(358\) 18.0000i 0.951330i
\(359\) −32.0000 −1.68890 −0.844448 0.535638i \(-0.820071\pi\)
−0.844448 + 0.535638i \(0.820071\pi\)
\(360\) −1.00000 2.00000i −0.0527046 0.105409i
\(361\) −3.00000 −0.157895
\(362\) 6.00000i 0.315353i
\(363\) 7.00000i 0.367405i
\(364\) 2.00000 0.104828
\(365\) 8.00000 + 16.0000i 0.418739 + 0.837478i
\(366\) −14.0000 −0.731792
\(367\) 10.0000i 0.521996i 0.965339 + 0.260998i \(0.0840516\pi\)
−0.965339 + 0.260998i \(0.915948\pi\)
\(368\) 0 0
\(369\) 6.00000 0.312348
\(370\) −12.0000 + 6.00000i −0.623850 + 0.311925i
\(371\) 4.00000 0.207670
\(372\) 8.00000i 0.414781i
\(373\) 22.0000i 1.13912i −0.821951 0.569558i \(-0.807114\pi\)
0.821951 0.569558i \(-0.192886\pi\)
\(374\) −4.00000 −0.206835
\(375\) 11.0000 + 2.00000i 0.568038 + 0.103280i
\(376\) −8.00000 −0.412568
\(377\) 4.00000i 0.206010i
\(378\) 2.00000i 0.102869i
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) −8.00000 + 4.00000i −0.410391 + 0.205196i
\(381\) 6.00000 0.307389
\(382\) 12.0000i 0.613973i
\(383\) 24.0000i 1.22634i 0.789950 + 0.613171i \(0.210106\pi\)
−0.789950 + 0.613171i \(0.789894\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −4.00000 8.00000i −0.203859 0.407718i
\(386\) 0 0
\(387\) 4.00000i 0.203331i
\(388\) 12.0000i 0.609208i
\(389\) −16.0000 −0.811232 −0.405616 0.914044i \(-0.632943\pi\)
−0.405616 + 0.914044i \(0.632943\pi\)
\(390\) −1.00000 2.00000i −0.0506370 0.101274i
\(391\) 0 0
\(392\) 3.00000i 0.151523i
\(393\) 6.00000i 0.302660i
\(394\) −10.0000 −0.503793
\(395\) 16.0000 8.00000i 0.805047 0.402524i
\(396\) 2.00000 0.100504
\(397\) 18.0000i 0.903394i 0.892171 + 0.451697i \(0.149181\pi\)
−0.892171 + 0.451697i \(0.850819\pi\)
\(398\) 24.0000i 1.20301i
\(399\) 8.00000 0.400501
\(400\) 3.00000 4.00000i 0.150000 0.200000i
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 16.0000i 0.798007i
\(403\) 8.00000i 0.398508i
\(404\) −4.00000 −0.199007
\(405\) 2.00000 1.00000i 0.0993808 0.0496904i
\(406\) 8.00000 0.397033
\(407\) 12.0000i 0.594818i
\(408\) 2.00000i 0.0990148i
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 6.00000 + 12.0000i 0.296319 + 0.592638i
\(411\) −14.0000 −0.690569
\(412\) 6.00000i 0.295599i
\(413\) 20.0000i 0.984136i
\(414\) 0 0
\(415\) 12.0000 + 24.0000i 0.589057 + 1.17811i
\(416\) −1.00000 −0.0490290
\(417\) 4.00000i 0.195881i
\(418\) 8.00000i 0.391293i
\(419\) 14.0000 0.683945 0.341972 0.939710i \(-0.388905\pi\)
0.341972 + 0.939710i \(0.388905\pi\)
\(420\) −4.00000 + 2.00000i −0.195180 + 0.0975900i
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 4.00000i 0.194717i
\(423\) 8.00000i 0.388973i
\(424\) −2.00000 −0.0971286
\(425\) −8.00000 6.00000i −0.388057 0.291043i
\(426\) −4.00000 −0.193801
\(427\) 28.0000i 1.35501i
\(428\) 4.00000i 0.193347i
\(429\) 2.00000 0.0965609
\(430\) 8.00000 4.00000i 0.385794 0.192897i
\(431\) 16.0000 0.770693 0.385346 0.922772i \(-0.374082\pi\)
0.385346 + 0.922772i \(0.374082\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 12.0000i 0.576683i 0.957528 + 0.288342i \(0.0931039\pi\)
−0.957528 + 0.288342i \(0.906896\pi\)
\(434\) −16.0000 −0.768025
\(435\) −4.00000 8.00000i −0.191785 0.383571i
\(436\) −18.0000 −0.862044
\(437\) 0 0
\(438\) 8.00000i 0.382255i
\(439\) −32.0000 −1.52728 −0.763638 0.645644i \(-0.776589\pi\)
−0.763638 + 0.645644i \(0.776589\pi\)
\(440\) 2.00000 + 4.00000i 0.0953463 + 0.190693i
\(441\) −3.00000 −0.142857
\(442\) 2.00000i 0.0951303i
\(443\) 4.00000i 0.190046i 0.995475 + 0.0950229i \(0.0302924\pi\)
−0.995475 + 0.0950229i \(0.969708\pi\)
\(444\) −6.00000 −0.284747
\(445\) −12.0000 + 6.00000i −0.568855 + 0.284427i
\(446\) −14.0000 −0.662919
\(447\) 12.0000i 0.567581i
\(448\) 2.00000i 0.0944911i
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 4.00000 + 3.00000i 0.188562 + 0.141421i
\(451\) −12.0000 −0.565058
\(452\) 6.00000i 0.282216i
\(453\) 16.0000i 0.751746i
\(454\) −12.0000 −0.563188
\(455\) −4.00000 + 2.00000i −0.187523 + 0.0937614i
\(456\) −4.00000 −0.187317
\(457\) 28.0000i 1.30978i 0.755722 + 0.654892i \(0.227286\pi\)
−0.755722 + 0.654892i \(0.772714\pi\)
\(458\) 22.0000i 1.02799i
\(459\) −2.00000 −0.0933520
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 4.00000i 0.186097i
\(463\) 6.00000i 0.278844i 0.990233 + 0.139422i \(0.0445244\pi\)
−0.990233 + 0.139422i \(0.955476\pi\)
\(464\) −4.00000 −0.185695
\(465\) 8.00000 + 16.0000i 0.370991 + 0.741982i
\(466\) −14.0000 −0.648537
\(467\) 28.0000i 1.29569i −0.761774 0.647843i \(-0.775671\pi\)
0.761774 0.647843i \(-0.224329\pi\)
\(468\) 1.00000i 0.0462250i
\(469\) 32.0000 1.47762
\(470\) 16.0000 8.00000i 0.738025 0.369012i
\(471\) 10.0000 0.460776
\(472\) 10.0000i 0.460287i
\(473\) 8.00000i 0.367840i
\(474\) 8.00000 0.367452
\(475\) 12.0000 16.0000i 0.550598 0.734130i
\(476\) 4.00000 0.183340
\(477\) 2.00000i 0.0915737i
\(478\) 12.0000i 0.548867i
\(479\) −36.0000 −1.64488 −0.822441 0.568850i \(-0.807388\pi\)
−0.822441 + 0.568850i \(0.807388\pi\)
\(480\) 2.00000 1.00000i 0.0912871 0.0456435i
\(481\) −6.00000 −0.273576
\(482\) 18.0000i 0.819878i
\(483\) 0 0
\(484\) 7.00000 0.318182
\(485\) −12.0000 24.0000i −0.544892 1.08978i
\(486\) 1.00000 0.0453609
\(487\) 26.0000i 1.17817i 0.808070 + 0.589086i \(0.200512\pi\)
−0.808070 + 0.589086i \(0.799488\pi\)
\(488\) 14.0000i 0.633750i
\(489\) 8.00000 0.361773
\(490\) −3.00000 6.00000i −0.135526 0.271052i
\(491\) −22.0000 −0.992846 −0.496423 0.868081i \(-0.665354\pi\)
−0.496423 + 0.868081i \(0.665354\pi\)
\(492\) 6.00000i 0.270501i
\(493\) 8.00000i 0.360302i
\(494\) −4.00000 −0.179969
\(495\) −4.00000 + 2.00000i −0.179787 + 0.0898933i
\(496\) 8.00000 0.359211
\(497\) 8.00000i 0.358849i
\(498\) 12.0000i 0.537733i
\(499\) −36.0000 −1.61158 −0.805791 0.592200i \(-0.798259\pi\)
−0.805791 + 0.592200i \(0.798259\pi\)
\(500\) −2.00000 + 11.0000i −0.0894427 + 0.491935i
\(501\) 12.0000 0.536120
\(502\) 18.0000i 0.803379i
\(503\) 36.0000i 1.60516i −0.596544 0.802580i \(-0.703460\pi\)
0.596544 0.802580i \(-0.296540\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 8.00000 4.00000i 0.355995 0.177998i
\(506\) 0 0
\(507\) 1.00000i 0.0444116i
\(508\) 6.00000i 0.266207i
\(509\) 40.0000 1.77297 0.886484 0.462758i \(-0.153140\pi\)
0.886484 + 0.462758i \(0.153140\pi\)
\(510\) −2.00000 4.00000i −0.0885615 0.177123i
\(511\) 16.0000 0.707798
\(512\) 1.00000i 0.0441942i
\(513\) 4.00000i 0.176604i
\(514\) 18.0000 0.793946
\(515\) 6.00000 + 12.0000i 0.264392 + 0.528783i
\(516\) 4.00000 0.176090
\(517\) 16.0000i 0.703679i
\(518\) 12.0000i 0.527250i
\(519\) −14.0000 −0.614532
\(520\) 2.00000 1.00000i 0.0877058 0.0438529i
\(521\) −10.0000 −0.438108 −0.219054 0.975713i \(-0.570297\pi\)
−0.219054 + 0.975713i \(0.570297\pi\)
\(522\) 4.00000i 0.175075i
\(523\) 16.0000i 0.699631i 0.936819 + 0.349816i \(0.113756\pi\)
−0.936819 + 0.349816i \(0.886244\pi\)
\(524\) 6.00000 0.262111
\(525\) 6.00000 8.00000i 0.261861 0.349149i
\(526\) −8.00000 −0.348817
\(527\) 16.0000i 0.696971i
\(528\) 2.00000i 0.0870388i
\(529\) 23.0000 1.00000
\(530\) 4.00000 2.00000i 0.173749 0.0868744i
\(531\) 10.0000 0.433963
\(532\) 8.00000i 0.346844i
\(533\) 6.00000i 0.259889i
\(534\) −6.00000 −0.259645
\(535\) 4.00000 + 8.00000i 0.172935 + 0.345870i
\(536\) −16.0000 −0.691095
\(537\) 18.0000i 0.776757i
\(538\) 20.0000i 0.862261i
\(539\) 6.00000 0.258438
\(540\) 1.00000 + 2.00000i 0.0430331 + 0.0860663i
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 16.0000i 0.687259i
\(543\) 6.00000i 0.257485i
\(544\) −2.00000 −0.0857493
\(545\) 36.0000 18.0000i 1.54207 0.771035i
\(546\) −2.00000 −0.0855921
\(547\) 20.0000i 0.855138i 0.903983 + 0.427569i \(0.140630\pi\)
−0.903983 + 0.427569i \(0.859370\pi\)
\(548\) 14.0000i 0.598050i
\(549\) 14.0000 0.597505
\(550\) −8.00000 6.00000i −0.341121 0.255841i
\(551\) −16.0000 −0.681623
\(552\) 0 0
\(553\) 16.0000i 0.680389i
\(554\) 2.00000 0.0849719
\(555\) 12.0000 6.00000i 0.509372 0.254686i
\(556\) 4.00000 0.169638
\(557\) 14.0000i 0.593199i 0.955002 + 0.296600i \(0.0958526\pi\)
−0.955002 + 0.296600i \(0.904147\pi\)
\(558\) 8.00000i 0.338667i
\(559\) 4.00000 0.169182
\(560\) −2.00000 4.00000i −0.0845154 0.169031i
\(561\) 4.00000 0.168880
\(562\) 18.0000i 0.759284i
\(563\) 44.0000i 1.85438i −0.374593 0.927189i \(-0.622217\pi\)
0.374593 0.927189i \(-0.377783\pi\)
\(564\) 8.00000 0.336861
\(565\) 6.00000 + 12.0000i 0.252422 + 0.504844i
\(566\) 16.0000 0.672530
\(567\) 2.00000i 0.0839921i
\(568\) 4.00000i 0.167836i
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 8.00000 4.00000i 0.335083 0.167542i
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 2.00000i 0.0836242i
\(573\) 12.0000i 0.501307i
\(574\) 12.0000 0.500870
\(575\) 0 0
\(576\) 1.00000 0.0416667
\(577\) 28.0000i 1.16566i −0.812596 0.582828i \(-0.801946\pi\)
0.812596 0.582828i \(-0.198054\pi\)
\(578\) 13.0000i 0.540729i
\(579\) 0 0
\(580\) 8.00000 4.00000i 0.332182 0.166091i
\(581\) 24.0000 0.995688
\(582\) 12.0000i 0.497416i
\(583\) 4.00000i 0.165663i
\(584\) −8.00000 −0.331042
\(585\) 1.00000 + 2.00000i 0.0413449 + 0.0826898i
\(586\) 26.0000 1.07405
\(587\) 36.0000i 1.48588i −0.669359 0.742940i \(-0.733431\pi\)
0.669359 0.742940i \(-0.266569\pi\)
\(588\) 3.00000i 0.123718i
\(589\) 32.0000 1.31854
\(590\) 10.0000 + 20.0000i 0.411693 + 0.823387i
\(591\) 10.0000 0.411345
\(592\) 6.00000i 0.246598i
\(593\) 34.0000i 1.39621i 0.715994 + 0.698106i \(0.245974\pi\)
−0.715994 + 0.698106i \(0.754026\pi\)
\(594\) −2.00000 −0.0820610
\(595\) −8.00000 + 4.00000i −0.327968 + 0.163984i
\(596\) 12.0000 0.491539
\(597\) 24.0000i 0.982255i
\(598\) 0 0
\(599\) −32.0000 −1.30748 −0.653742 0.756717i \(-0.726802\pi\)
−0.653742 + 0.756717i \(0.726802\pi\)
\(600\) −3.00000 + 4.00000i −0.122474 + 0.163299i
\(601\) −46.0000 −1.87638 −0.938190 0.346122i \(-0.887498\pi\)
−0.938190 + 0.346122i \(0.887498\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 16.0000i 0.651570i
\(604\) 16.0000 0.651031
\(605\) −14.0000 + 7.00000i −0.569181 + 0.284590i
\(606\) 4.00000 0.162489
\(607\) 18.0000i 0.730597i −0.930890 0.365299i \(-0.880967\pi\)
0.930890 0.365299i \(-0.119033\pi\)
\(608\) 4.00000i 0.162221i
\(609\) −8.00000 −0.324176
\(610\) 14.0000 + 28.0000i 0.566843 + 1.13369i
\(611\) 8.00000 0.323645
\(612\) 2.00000i 0.0808452i
\(613\) 2.00000i 0.0807792i −0.999184 0.0403896i \(-0.987140\pi\)
0.999184 0.0403896i \(-0.0128599\pi\)
\(614\) 28.0000 1.12999
\(615\) −6.00000 12.0000i −0.241943 0.483887i
\(616\) 4.00000 0.161165
\(617\) 46.0000i 1.85189i −0.377658 0.925945i \(-0.623271\pi\)
0.377658 0.925945i \(-0.376729\pi\)
\(618\) 6.00000i 0.241355i
\(619\) 24.0000 0.964641 0.482321 0.875995i \(-0.339794\pi\)
0.482321 + 0.875995i \(0.339794\pi\)
\(620\) −16.0000 + 8.00000i −0.642575 + 0.321288i
\(621\) 0 0
\(622\) 20.0000i 0.801927i
\(623\) 12.0000i 0.480770i
\(624\) 1.00000 0.0400320
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) −20.0000 −0.799361
\(627\) 8.00000i 0.319489i
\(628\) 10.0000i 0.399043i
\(629\) −12.0000 −0.478471
\(630\) 4.00000 2.00000i 0.159364 0.0796819i
\(631\) −8.00000 −0.318475 −0.159237 0.987240i \(-0.550904\pi\)
−0.159237 + 0.987240i \(0.550904\pi\)
\(632\) 8.00000i 0.318223i
\(633\) 4.00000i 0.158986i
\(634\) 18.0000 0.714871
\(635\) −6.00000 12.0000i −0.238103 0.476205i
\(636\) 2.00000 0.0793052
\(637\) 3.00000i 0.118864i
\(638\) 8.00000i 0.316723i
\(639\) 4.00000 0.158238
\(640\) 1.00000 + 2.00000i 0.0395285 + 0.0790569i
\(641\) −38.0000 −1.50091 −0.750455 0.660922i \(-0.770166\pi\)
−0.750455 + 0.660922i \(0.770166\pi\)
\(642\) 4.00000i 0.157867i
\(643\) 32.0000i 1.26196i 0.775800 + 0.630978i \(0.217346\pi\)
−0.775800 + 0.630978i \(0.782654\pi\)
\(644\) 0 0
\(645\) −8.00000 + 4.00000i −0.315000 + 0.157500i
\(646\) −8.00000 −0.314756
\(647\) 36.0000i 1.41531i −0.706560 0.707653i \(-0.749754\pi\)
0.706560 0.707653i \(-0.250246\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −20.0000 −0.785069
\(650\) −3.00000 + 4.00000i −0.117670 + 0.156893i
\(651\) 16.0000 0.627089
\(652\) 8.00000i 0.313304i
\(653\) 34.0000i 1.33052i −0.746611 0.665261i \(-0.768320\pi\)
0.746611 0.665261i \(-0.231680\pi\)
\(654\) 18.0000 0.703856
\(655\) −12.0000 + 6.00000i −0.468879 + 0.234439i
\(656\) −6.00000 −0.234261
\(657\) 8.00000i 0.312110i
\(658\) 16.0000i 0.623745i
\(659\) −10.0000 −0.389545 −0.194772 0.980848i \(-0.562397\pi\)
−0.194772 + 0.980848i \(0.562397\pi\)
\(660\) −2.00000 4.00000i −0.0778499 0.155700i
\(661\) 30.0000 1.16686 0.583432 0.812162i \(-0.301709\pi\)
0.583432 + 0.812162i \(0.301709\pi\)
\(662\) 12.0000i 0.466393i
\(663\) 2.00000i 0.0776736i
\(664\) −12.0000 −0.465690
\(665\) −8.00000 16.0000i −0.310227 0.620453i
\(666\) 6.00000 0.232495
\(667\) 0 0
\(668\) 12.0000i 0.464294i
\(669\) 14.0000 0.541271
\(670\) 32.0000 16.0000i 1.23627 0.618134i
\(671\) −28.0000 −1.08093
\(672\) 2.00000i 0.0771517i
\(673\) 36.0000i 1.38770i −0.720121 0.693849i \(-0.755914\pi\)
0.720121 0.693849i \(-0.244086\pi\)
\(674\) −20.0000 −0.770371
\(675\) −4.00000 3.00000i −0.153960 0.115470i
\(676\) 1.00000 0.0384615
\(677\) 10.0000i 0.384331i 0.981363 + 0.192166i \(0.0615511\pi\)
−0.981363 + 0.192166i \(0.938449\pi\)
\(678\) 6.00000i 0.230429i
\(679\) −24.0000 −0.921035
\(680\) 4.00000 2.00000i 0.153393 0.0766965i
\(681\) 12.0000 0.459841
\(682\) 16.0000i 0.612672i
\(683\) 12.0000i 0.459167i 0.973289 + 0.229584i \(0.0737364\pi\)
−0.973289 + 0.229584i \(0.926264\pi\)
\(684\) 4.00000 0.152944
\(685\) 14.0000 + 28.0000i 0.534913 + 1.06983i
\(686\) −20.0000 −0.763604
\(687\) 22.0000i 0.839352i
\(688\) 4.00000i 0.152499i
\(689\) 2.00000 0.0761939
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 14.0000i 0.532200i
\(693\) 4.00000i 0.151947i
\(694\) −12.0000 −0.455514
\(695\) −8.00000 + 4.00000i −0.303457 + 0.151729i
\(696\) 4.00000 0.151620
\(697\) 12.0000i 0.454532i
\(698\) 14.0000i 0.529908i
\(699\) 14.0000 0.529529
\(700\) 8.00000 + 6.00000i 0.302372 + 0.226779i
\(701\) 12.0000 0.453234 0.226617 0.973984i \(-0.427233\pi\)
0.226617 + 0.973984i \(0.427233\pi\)
\(702\) 1.00000i 0.0377426i
\(703\) 24.0000i 0.905177i
\(704\) −2.00000 −0.0753778
\(705\) −16.0000 + 8.00000i −0.602595 + 0.301297i
\(706\) −34.0000 −1.27961
\(707\) 8.00000i 0.300871i
\(708\) 10.0000i 0.375823i
\(709\) −34.0000 −1.27690 −0.638448 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) 4.00000 + 8.00000i 0.150117 + 0.300235i
\(711\) −8.00000 −0.300023
\(712\) 6.00000i 0.224860i
\(713\) 0 0
\(714\) −4.00000 −0.149696
\(715\) −2.00000 4.00000i −0.0747958 0.149592i
\(716\) −18.0000 −0.672692
\(717\) 12.0000i 0.448148i
\(718\) 32.0000i 1.19423i
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) −2.00000 + 1.00000i −0.0745356 + 0.0372678i
\(721\) 12.0000 0.446903
\(722\) 3.00000i 0.111648i
\(723\) 18.0000i 0.669427i
\(724\) 6.00000 0.222988
\(725\) −12.0000 + 16.0000i −0.445669 + 0.594225i
\(726\) −7.00000 −0.259794
\(727\) 34.0000i 1.26099i −0.776193 0.630495i \(-0.782852\pi\)
0.776193 0.630495i \(-0.217148\pi\)
\(728\) 2.00000i 0.0741249i
\(729\) −1.00000 −0.0370370
\(730\) 16.0000 8.00000i 0.592187 0.296093i
\(731\) 8.00000 0.295891
\(732\) 14.0000i 0.517455i
\(733\) 14.0000i 0.517102i 0.965998 + 0.258551i \(0.0832450\pi\)
−0.965998 + 0.258551i \(0.916755\pi\)
\(734\) 10.0000 0.369107
\(735\) 3.00000 + 6.00000i 0.110657 + 0.221313i
\(736\) 0 0
\(737\) 32.0000i 1.17874i
\(738\) 6.00000i 0.220863i
\(739\) −28.0000 −1.03000 −0.514998 0.857191i \(-0.672207\pi\)
−0.514998 + 0.857191i \(0.672207\pi\)
\(740\) 6.00000 + 12.0000i 0.220564 + 0.441129i
\(741\) 4.00000 0.146944
\(742\) 4.00000i 0.146845i
\(743\) 16.0000i 0.586983i 0.955962 + 0.293492i \(0.0948173\pi\)
−0.955962 + 0.293492i \(0.905183\pi\)
\(744\) −8.00000 −0.293294
\(745\) −24.0000 + 12.0000i −0.879292 + 0.439646i
\(746\) −22.0000 −0.805477
\(747\) 12.0000i 0.439057i
\(748\) 4.00000i 0.146254i
\(749\) 8.00000 0.292314
\(750\) 2.00000 11.0000i 0.0730297 0.401663i
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 18.0000i 0.655956i
\(754\) 4.00000 0.145671
\(755\) −32.0000 + 16.0000i −1.16460 + 0.582300i
\(756\) 2.00000 0.0727393
\(757\) 26.0000i 0.944986i 0.881334 + 0.472493i \(0.156646\pi\)
−0.881334 + 0.472493i \(0.843354\pi\)
\(758\) 8.00000i 0.290573i
\(759\) 0 0
\(760\) 4.00000 + 8.00000i 0.145095 + 0.290191i
\(761\) 38.0000 1.37750 0.688749 0.724999i \(-0.258160\pi\)
0.688749 + 0.724999i \(0.258160\pi\)
\(762\) 6.00000i 0.217357i
\(763\) 36.0000i 1.30329i
\(764\) 12.0000 0.434145
\(765\) 2.00000 + 4.00000i 0.0723102 + 0.144620i
\(766\) 24.0000 0.867155
\(767\) 10.0000i 0.361079i
\(768\) 1.00000i 0.0360844i
\(769\) −2.00000 −0.0721218 −0.0360609 0.999350i \(-0.511481\pi\)
−0.0360609 + 0.999350i \(0.511481\pi\)
\(770\) −8.00000 + 4.00000i −0.288300 + 0.144150i
\(771\) −18.0000 −0.648254
\(772\) 0 0
\(773\) 22.0000i 0.791285i 0.918405 + 0.395643i \(0.129478\pi\)
−0.918405 + 0.395643i \(0.870522\pi\)
\(774\) −4.00000 −0.143777
\(775\) 24.0000 32.0000i 0.862105 1.14947i
\(776\) 12.0000 0.430775
\(777\) 12.0000i 0.430498i
\(778\) 16.0000i 0.573628i
\(779\) −24.0000 −0.859889
\(780\) −2.00000 + 1.00000i −0.0716115 + 0.0358057i
\(781\) −8.00000 −0.286263
\(782\) 0 0
\(783\) 4.00000i 0.142948i
\(784\) 3.00000 0.107143
\(785\) −10.0000 20.0000i −0.356915 0.713831i
\(786\) −6.00000 −0.214013
\(787\) 8.00000i 0.285169i 0.989783 + 0.142585i \(0.0455413\pi\)
−0.989783 + 0.142585i \(0.954459\pi\)
\(788\) 10.0000i 0.356235i
\(789\) 8.00000