Properties

Label 1470.2.g.a.589.1
Level $1470$
Weight $2$
Character 1470.589
Analytic conductor $11.738$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1470.g (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.7380090971\)
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: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 589.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1470.589
Dual form 1470.2.g.a.589.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} +(-2.00000 - 1.00000i) q^{5} +1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(-1.00000 + 2.00000i) q^{10} -5.00000 q^{11} -1.00000i q^{12} +1.00000i q^{13} +(1.00000 - 2.00000i) q^{15} +1.00000 q^{16} +2.00000i q^{17} +1.00000i q^{18} +7.00000 q^{19} +(2.00000 + 1.00000i) q^{20} +5.00000i q^{22} -3.00000i q^{23} -1.00000 q^{24} +(3.00000 + 4.00000i) q^{25} +1.00000 q^{26} -1.00000i q^{27} +(-2.00000 - 1.00000i) q^{30} +6.00000 q^{31} -1.00000i q^{32} -5.00000i q^{33} +2.00000 q^{34} +1.00000 q^{36} -5.00000i q^{37} -7.00000i q^{38} -1.00000 q^{39} +(1.00000 - 2.00000i) q^{40} +9.00000 q^{41} -10.0000i q^{43} +5.00000 q^{44} +(2.00000 + 1.00000i) q^{45} -3.00000 q^{46} +13.0000i q^{47} +1.00000i q^{48} +(4.00000 - 3.00000i) q^{50} -2.00000 q^{51} -1.00000i q^{52} +1.00000i q^{53} -1.00000 q^{54} +(10.0000 + 5.00000i) q^{55} +7.00000i q^{57} +4.00000 q^{59} +(-1.00000 + 2.00000i) q^{60} +2.00000 q^{61} -6.00000i q^{62} -1.00000 q^{64} +(1.00000 - 2.00000i) q^{65} -5.00000 q^{66} +6.00000i q^{67} -2.00000i q^{68} +3.00000 q^{69} -2.00000 q^{71} -1.00000i q^{72} +4.00000i q^{73} -5.00000 q^{74} +(-4.00000 + 3.00000i) q^{75} -7.00000 q^{76} +1.00000i q^{78} +14.0000 q^{79} +(-2.00000 - 1.00000i) q^{80} +1.00000 q^{81} -9.00000i q^{82} -10.0000i q^{83} +(2.00000 - 4.00000i) q^{85} -10.0000 q^{86} -5.00000i q^{88} +10.0000 q^{89} +(1.00000 - 2.00000i) q^{90} +3.00000i q^{92} +6.00000i q^{93} +13.0000 q^{94} +(-14.0000 - 7.00000i) q^{95} +1.00000 q^{96} -8.00000i q^{97} +5.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} - 4q^{5} + 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} - 4q^{5} + 2q^{6} - 2q^{9} - 2q^{10} - 10q^{11} + 2q^{15} + 2q^{16} + 14q^{19} + 4q^{20} - 2q^{24} + 6q^{25} + 2q^{26} - 4q^{30} + 12q^{31} + 4q^{34} + 2q^{36} - 2q^{39} + 2q^{40} + 18q^{41} + 10q^{44} + 4q^{45} - 6q^{46} + 8q^{50} - 4q^{51} - 2q^{54} + 20q^{55} + 8q^{59} - 2q^{60} + 4q^{61} - 2q^{64} + 2q^{65} - 10q^{66} + 6q^{69} - 4q^{71} - 10q^{74} - 8q^{75} - 14q^{76} + 28q^{79} - 4q^{80} + 2q^{81} + 4q^{85} - 20q^{86} + 20q^{89} + 2q^{90} + 26q^{94} - 28q^{95} + 2q^{96} + 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).

\(n\) \(491\) \(1081\) \(1177\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) −1.00000 + 2.00000i −0.316228 + 0.632456i
\(11\) −5.00000 −1.50756 −0.753778 0.657129i \(-0.771771\pi\)
−0.753778 + 0.657129i \(0.771771\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 1.00000i 0.277350i 0.990338 + 0.138675i \(0.0442844\pi\)
−0.990338 + 0.138675i \(0.955716\pi\)
\(14\) 0 0
\(15\) 1.00000 2.00000i 0.258199 0.516398i
\(16\) 1.00000 0.250000
\(17\) 2.00000i 0.485071i 0.970143 + 0.242536i \(0.0779791\pi\)
−0.970143 + 0.242536i \(0.922021\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 7.00000 1.60591 0.802955 0.596040i \(-0.203260\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) 2.00000 + 1.00000i 0.447214 + 0.223607i
\(21\) 0 0
\(22\) 5.00000i 1.06600i
\(23\) 3.00000i 0.625543i −0.949828 0.312772i \(-0.898743\pi\)
0.949828 0.312772i \(-0.101257\pi\)
\(24\) −1.00000 −0.204124
\(25\) 3.00000 + 4.00000i 0.600000 + 0.800000i
\(26\) 1.00000 0.196116
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) −2.00000 1.00000i −0.365148 0.182574i
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 5.00000i 0.870388i
\(34\) 2.00000 0.342997
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 5.00000i 0.821995i −0.911636 0.410997i \(-0.865181\pi\)
0.911636 0.410997i \(-0.134819\pi\)
\(38\) 7.00000i 1.13555i
\(39\) −1.00000 −0.160128
\(40\) 1.00000 2.00000i 0.158114 0.316228i
\(41\) 9.00000 1.40556 0.702782 0.711405i \(-0.251941\pi\)
0.702782 + 0.711405i \(0.251941\pi\)
\(42\) 0 0
\(43\) 10.0000i 1.52499i −0.646997 0.762493i \(-0.723975\pi\)
0.646997 0.762493i \(-0.276025\pi\)
\(44\) 5.00000 0.753778
\(45\) 2.00000 + 1.00000i 0.298142 + 0.149071i
\(46\) −3.00000 −0.442326
\(47\) 13.0000i 1.89624i 0.317905 + 0.948122i \(0.397021\pi\)
−0.317905 + 0.948122i \(0.602979\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 0 0
\(50\) 4.00000 3.00000i 0.565685 0.424264i
\(51\) −2.00000 −0.280056
\(52\) 1.00000i 0.138675i
\(53\) 1.00000i 0.137361i 0.997639 + 0.0686803i \(0.0218788\pi\)
−0.997639 + 0.0686803i \(0.978121\pi\)
\(54\) −1.00000 −0.136083
\(55\) 10.0000 + 5.00000i 1.34840 + 0.674200i
\(56\) 0 0
\(57\) 7.00000i 0.927173i
\(58\) 0 0
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) −1.00000 + 2.00000i −0.129099 + 0.258199i
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 6.00000i 0.762001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.00000 2.00000i 0.124035 0.248069i
\(66\) −5.00000 −0.615457
\(67\) 6.00000i 0.733017i 0.930415 + 0.366508i \(0.119447\pi\)
−0.930415 + 0.366508i \(0.880553\pi\)
\(68\) 2.00000i 0.242536i
\(69\) 3.00000 0.361158
\(70\) 0 0
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 4.00000i 0.468165i 0.972217 + 0.234082i \(0.0752085\pi\)
−0.972217 + 0.234082i \(0.924791\pi\)
\(74\) −5.00000 −0.581238
\(75\) −4.00000 + 3.00000i −0.461880 + 0.346410i
\(76\) −7.00000 −0.802955
\(77\) 0 0
\(78\) 1.00000i 0.113228i
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) −2.00000 1.00000i −0.223607 0.111803i
\(81\) 1.00000 0.111111
\(82\) 9.00000i 0.993884i
\(83\) 10.0000i 1.09764i −0.835940 0.548821i \(-0.815077\pi\)
0.835940 0.548821i \(-0.184923\pi\)
\(84\) 0 0
\(85\) 2.00000 4.00000i 0.216930 0.433861i
\(86\) −10.0000 −1.07833
\(87\) 0 0
\(88\) 5.00000i 0.533002i
\(89\) 10.0000 1.06000 0.529999 0.847998i \(-0.322192\pi\)
0.529999 + 0.847998i \(0.322192\pi\)
\(90\) 1.00000 2.00000i 0.105409 0.210819i
\(91\) 0 0
\(92\) 3.00000i 0.312772i
\(93\) 6.00000i 0.622171i
\(94\) 13.0000 1.34085
\(95\) −14.0000 7.00000i −1.43637 0.718185i
\(96\) 1.00000 0.102062
\(97\) 8.00000i 0.812277i −0.913812 0.406138i \(-0.866875\pi\)
0.913812 0.406138i \(-0.133125\pi\)
\(98\) 0 0
\(99\) 5.00000 0.502519
\(100\) −3.00000 4.00000i −0.300000 0.400000i
\(101\) −8.00000 −0.796030 −0.398015 0.917379i \(-0.630301\pi\)
−0.398015 + 0.917379i \(0.630301\pi\)
\(102\) 2.00000i 0.198030i
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) 12.0000i 1.16008i 0.814587 + 0.580042i \(0.196964\pi\)
−0.814587 + 0.580042i \(0.803036\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 18.0000 1.72409 0.862044 0.506834i \(-0.169184\pi\)
0.862044 + 0.506834i \(0.169184\pi\)
\(110\) 5.00000 10.0000i 0.476731 0.953463i
\(111\) 5.00000 0.474579
\(112\) 0 0
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) 7.00000 0.655610
\(115\) −3.00000 + 6.00000i −0.279751 + 0.559503i
\(116\) 0 0
\(117\) 1.00000i 0.0924500i
\(118\) 4.00000i 0.368230i
\(119\) 0 0
\(120\) 2.00000 + 1.00000i 0.182574 + 0.0912871i
\(121\) 14.0000 1.27273
\(122\) 2.00000i 0.181071i
\(123\) 9.00000i 0.811503i
\(124\) −6.00000 −0.538816
\(125\) −2.00000 11.0000i −0.178885 0.983870i
\(126\) 0 0
\(127\) 9.00000i 0.798621i 0.916816 + 0.399310i \(0.130750\pi\)
−0.916816 + 0.399310i \(0.869250\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 10.0000 0.880451
\(130\) −2.00000 1.00000i −0.175412 0.0877058i
\(131\) 17.0000 1.48530 0.742648 0.669681i \(-0.233569\pi\)
0.742648 + 0.669681i \(0.233569\pi\)
\(132\) 5.00000i 0.435194i
\(133\) 0 0
\(134\) 6.00000 0.518321
\(135\) −1.00000 + 2.00000i −0.0860663 + 0.172133i
\(136\) −2.00000 −0.171499
\(137\) 4.00000i 0.341743i −0.985293 0.170872i \(-0.945342\pi\)
0.985293 0.170872i \(-0.0546583\pi\)
\(138\) 3.00000i 0.255377i
\(139\) −8.00000 −0.678551 −0.339276 0.940687i \(-0.610182\pi\)
−0.339276 + 0.940687i \(0.610182\pi\)
\(140\) 0 0
\(141\) −13.0000 −1.09480
\(142\) 2.00000i 0.167836i
\(143\) 5.00000i 0.418121i
\(144\) −1.00000 −0.0833333
\(145\) 0 0
\(146\) 4.00000 0.331042
\(147\) 0 0
\(148\) 5.00000i 0.410997i
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 3.00000 + 4.00000i 0.244949 + 0.326599i
\(151\) −22.0000 −1.79033 −0.895167 0.445730i \(-0.852944\pi\)
−0.895167 + 0.445730i \(0.852944\pi\)
\(152\) 7.00000i 0.567775i
\(153\) 2.00000i 0.161690i
\(154\) 0 0
\(155\) −12.0000 6.00000i −0.963863 0.481932i
\(156\) 1.00000 0.0800641
\(157\) 13.0000i 1.03751i −0.854922 0.518756i \(-0.826395\pi\)
0.854922 0.518756i \(-0.173605\pi\)
\(158\) 14.0000i 1.11378i
\(159\) −1.00000 −0.0793052
\(160\) −1.00000 + 2.00000i −0.0790569 + 0.158114i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 12.0000i 0.939913i 0.882690 + 0.469956i \(0.155730\pi\)
−0.882690 + 0.469956i \(0.844270\pi\)
\(164\) −9.00000 −0.702782
\(165\) −5.00000 + 10.0000i −0.389249 + 0.778499i
\(166\) −10.0000 −0.776151
\(167\) 19.0000i 1.47026i 0.677924 + 0.735132i \(0.262880\pi\)
−0.677924 + 0.735132i \(0.737120\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) −4.00000 2.00000i −0.306786 0.153393i
\(171\) −7.00000 −0.535303
\(172\) 10.0000i 0.762493i
\(173\) 7.00000i 0.532200i 0.963945 + 0.266100i \(0.0857352\pi\)
−0.963945 + 0.266100i \(0.914265\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −5.00000 −0.376889
\(177\) 4.00000i 0.300658i
\(178\) 10.0000i 0.749532i
\(179\) 11.0000 0.822179 0.411089 0.911595i \(-0.365148\pi\)
0.411089 + 0.911595i \(0.365148\pi\)
\(180\) −2.00000 1.00000i −0.149071 0.0745356i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) 3.00000 0.221163
\(185\) −5.00000 + 10.0000i −0.367607 + 0.735215i
\(186\) 6.00000 0.439941
\(187\) 10.0000i 0.731272i
\(188\) 13.0000i 0.948122i
\(189\) 0 0
\(190\) −7.00000 + 14.0000i −0.507833 + 1.01567i
\(191\) −16.0000 −1.15772 −0.578860 0.815427i \(-0.696502\pi\)
−0.578860 + 0.815427i \(0.696502\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 18.0000i 1.29567i 0.761781 + 0.647834i \(0.224325\pi\)
−0.761781 + 0.647834i \(0.775675\pi\)
\(194\) −8.00000 −0.574367
\(195\) 2.00000 + 1.00000i 0.143223 + 0.0716115i
\(196\) 0 0
\(197\) 27.0000i 1.92367i −0.273629 0.961835i \(-0.588224\pi\)
0.273629 0.961835i \(-0.411776\pi\)
\(198\) 5.00000i 0.355335i
\(199\) −14.0000 −0.992434 −0.496217 0.868199i \(-0.665278\pi\)
−0.496217 + 0.868199i \(0.665278\pi\)
\(200\) −4.00000 + 3.00000i −0.282843 + 0.212132i
\(201\) −6.00000 −0.423207
\(202\) 8.00000i 0.562878i
\(203\) 0 0
\(204\) 2.00000 0.140028
\(205\) −18.0000 9.00000i −1.25717 0.628587i
\(206\) 0 0
\(207\) 3.00000i 0.208514i
\(208\) 1.00000i 0.0693375i
\(209\) −35.0000 −2.42100
\(210\) 0 0
\(211\) 19.0000 1.30801 0.654007 0.756489i \(-0.273087\pi\)
0.654007 + 0.756489i \(0.273087\pi\)
\(212\) 1.00000i 0.0686803i
\(213\) 2.00000i 0.137038i
\(214\) 12.0000 0.820303
\(215\) −10.0000 + 20.0000i −0.681994 + 1.36399i
\(216\) 1.00000 0.0680414
\(217\) 0 0
\(218\) 18.0000i 1.21911i
\(219\) −4.00000 −0.270295
\(220\) −10.0000 5.00000i −0.674200 0.337100i
\(221\) −2.00000 −0.134535
\(222\) 5.00000i 0.335578i
\(223\) 16.0000i 1.07144i 0.844396 + 0.535720i \(0.179960\pi\)
−0.844396 + 0.535720i \(0.820040\pi\)
\(224\) 0 0
\(225\) −3.00000 4.00000i −0.200000 0.266667i
\(226\) −6.00000 −0.399114
\(227\) 14.0000i 0.929213i −0.885517 0.464606i \(-0.846196\pi\)
0.885517 0.464606i \(-0.153804\pi\)
\(228\) 7.00000i 0.463586i
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) 6.00000 + 3.00000i 0.395628 + 0.197814i
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) −1.00000 −0.0653720
\(235\) 13.0000 26.0000i 0.848026 1.69605i
\(236\) −4.00000 −0.260378
\(237\) 14.0000i 0.909398i
\(238\) 0 0
\(239\) −20.0000 −1.29369 −0.646846 0.762620i \(-0.723912\pi\)
−0.646846 + 0.762620i \(0.723912\pi\)
\(240\) 1.00000 2.00000i 0.0645497 0.129099i
\(241\) 1.00000 0.0644157 0.0322078 0.999481i \(-0.489746\pi\)
0.0322078 + 0.999481i \(0.489746\pi\)
\(242\) 14.0000i 0.899954i
\(243\) 1.00000i 0.0641500i
\(244\) −2.00000 −0.128037
\(245\) 0 0
\(246\) 9.00000 0.573819
\(247\) 7.00000i 0.445399i
\(248\) 6.00000i 0.381000i
\(249\) 10.0000 0.633724
\(250\) −11.0000 + 2.00000i −0.695701 + 0.126491i
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 0 0
\(253\) 15.0000i 0.943042i
\(254\) 9.00000 0.564710
\(255\) 4.00000 + 2.00000i 0.250490 + 0.125245i
\(256\) 1.00000 0.0625000
\(257\) 10.0000i 0.623783i 0.950118 + 0.311891i \(0.100963\pi\)
−0.950118 + 0.311891i \(0.899037\pi\)
\(258\) 10.0000i 0.622573i
\(259\) 0 0
\(260\) −1.00000 + 2.00000i −0.0620174 + 0.124035i
\(261\) 0 0
\(262\) 17.0000i 1.05026i
\(263\) 24.0000i 1.47990i −0.672660 0.739952i \(-0.734848\pi\)
0.672660 0.739952i \(-0.265152\pi\)
\(264\) 5.00000 0.307729
\(265\) 1.00000 2.00000i 0.0614295 0.122859i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) 6.00000i 0.366508i
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 2.00000 + 1.00000i 0.121716 + 0.0608581i
\(271\) −8.00000 −0.485965 −0.242983 0.970031i \(-0.578126\pi\)
−0.242983 + 0.970031i \(0.578126\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) −4.00000 −0.241649
\(275\) −15.0000 20.0000i −0.904534 1.20605i
\(276\) −3.00000 −0.180579
\(277\) 2.00000i 0.120168i 0.998193 + 0.0600842i \(0.0191369\pi\)
−0.998193 + 0.0600842i \(0.980863\pi\)
\(278\) 8.00000i 0.479808i
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) −11.0000 −0.656205 −0.328102 0.944642i \(-0.606409\pi\)
−0.328102 + 0.944642i \(0.606409\pi\)
\(282\) 13.0000i 0.774139i
\(283\) 26.0000i 1.54554i 0.634686 + 0.772770i \(0.281129\pi\)
−0.634686 + 0.772770i \(0.718871\pi\)
\(284\) 2.00000 0.118678
\(285\) 7.00000 14.0000i 0.414644 0.829288i
\(286\) −5.00000 −0.295656
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) 13.0000 0.764706
\(290\) 0 0
\(291\) 8.00000 0.468968
\(292\) 4.00000i 0.234082i
\(293\) 1.00000i 0.0584206i 0.999573 + 0.0292103i \(0.00929925\pi\)
−0.999573 + 0.0292103i \(0.990701\pi\)
\(294\) 0 0
\(295\) −8.00000 4.00000i −0.465778 0.232889i
\(296\) 5.00000 0.290619
\(297\) 5.00000i 0.290129i
\(298\) 6.00000i 0.347571i
\(299\) 3.00000 0.173494
\(300\) 4.00000 3.00000i 0.230940 0.173205i
\(301\) 0 0
\(302\) 22.0000i 1.26596i
\(303\) 8.00000i 0.459588i
\(304\) 7.00000 0.401478
\(305\) −4.00000 2.00000i −0.229039 0.114520i
\(306\) −2.00000 −0.114332
\(307\) 2.00000i 0.114146i −0.998370 0.0570730i \(-0.981823\pi\)
0.998370 0.0570730i \(-0.0181768\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −6.00000 + 12.0000i −0.340777 + 0.681554i
\(311\) 26.0000 1.47432 0.737162 0.675716i \(-0.236165\pi\)
0.737162 + 0.675716i \(0.236165\pi\)
\(312\) 1.00000i 0.0566139i
\(313\) 10.0000i 0.565233i −0.959233 0.282617i \(-0.908798\pi\)
0.959233 0.282617i \(-0.0912024\pi\)
\(314\) −13.0000 −0.733632
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) 2.00000i 0.112331i 0.998421 + 0.0561656i \(0.0178875\pi\)
−0.998421 + 0.0561656i \(0.982113\pi\)
\(318\) 1.00000i 0.0560772i
\(319\) 0 0
\(320\) 2.00000 + 1.00000i 0.111803 + 0.0559017i
\(321\) −12.0000 −0.669775
\(322\) 0 0
\(323\) 14.0000i 0.778981i
\(324\) −1.00000 −0.0555556
\(325\) −4.00000 + 3.00000i −0.221880 + 0.166410i
\(326\) 12.0000 0.664619
\(327\) 18.0000i 0.995402i
\(328\) 9.00000i 0.496942i
\(329\) 0 0
\(330\) 10.0000 + 5.00000i 0.550482 + 0.275241i
\(331\) −15.0000 −0.824475 −0.412237 0.911077i \(-0.635253\pi\)
−0.412237 + 0.911077i \(0.635253\pi\)
\(332\) 10.0000i 0.548821i
\(333\) 5.00000i 0.273998i
\(334\) 19.0000 1.03963
\(335\) 6.00000 12.0000i 0.327815 0.655630i
\(336\) 0 0
\(337\) 14.0000i 0.762629i −0.924445 0.381314i \(-0.875472\pi\)
0.924445 0.381314i \(-0.124528\pi\)
\(338\) 12.0000i 0.652714i
\(339\) 6.00000 0.325875
\(340\) −2.00000 + 4.00000i −0.108465 + 0.216930i
\(341\) −30.0000 −1.62459
\(342\) 7.00000i 0.378517i
\(343\) 0 0
\(344\) 10.0000 0.539164
\(345\) −6.00000 3.00000i −0.323029 0.161515i
\(346\) 7.00000 0.376322
\(347\) 16.0000i 0.858925i −0.903085 0.429463i \(-0.858703\pi\)
0.903085 0.429463i \(-0.141297\pi\)
\(348\) 0 0
\(349\) −24.0000 −1.28469 −0.642345 0.766415i \(-0.722038\pi\)
−0.642345 + 0.766415i \(0.722038\pi\)
\(350\) 0 0
\(351\) 1.00000 0.0533761
\(352\) 5.00000i 0.266501i
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) 4.00000 0.212598
\(355\) 4.00000 + 2.00000i 0.212298 + 0.106149i
\(356\) −10.0000 −0.529999
\(357\) 0 0
\(358\) 11.0000i 0.581368i
\(359\) 28.0000 1.47778 0.738892 0.673824i \(-0.235349\pi\)
0.738892 + 0.673824i \(0.235349\pi\)
\(360\) −1.00000 + 2.00000i −0.0527046 + 0.105409i
\(361\) 30.0000 1.57895
\(362\) 2.00000i 0.105118i
\(363\) 14.0000i 0.734809i
\(364\) 0 0
\(365\) 4.00000 8.00000i 0.209370 0.418739i
\(366\) 2.00000 0.104542
\(367\) 37.0000i 1.93138i 0.259690 + 0.965692i \(0.416380\pi\)
−0.259690 + 0.965692i \(0.583620\pi\)
\(368\) 3.00000i 0.156386i
\(369\) −9.00000 −0.468521
\(370\) 10.0000 + 5.00000i 0.519875 + 0.259938i
\(371\) 0 0
\(372\) 6.00000i 0.311086i
\(373\) 6.00000i 0.310668i −0.987862 0.155334i \(-0.950355\pi\)
0.987862 0.155334i \(-0.0496454\pi\)
\(374\) −10.0000 −0.517088
\(375\) 11.0000 2.00000i 0.568038 0.103280i
\(376\) −13.0000 −0.670424
\(377\) 0 0
\(378\) 0 0
\(379\) 1.00000 0.0513665 0.0256833 0.999670i \(-0.491824\pi\)
0.0256833 + 0.999670i \(0.491824\pi\)
\(380\) 14.0000 + 7.00000i 0.718185 + 0.359092i
\(381\) −9.00000 −0.461084
\(382\) 16.0000i 0.818631i
\(383\) 9.00000i 0.459879i −0.973205 0.229939i \(-0.926147\pi\)
0.973205 0.229939i \(-0.0738528\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) 18.0000 0.916176
\(387\) 10.0000i 0.508329i
\(388\) 8.00000i 0.406138i
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 1.00000 2.00000i 0.0506370 0.101274i
\(391\) 6.00000 0.303433
\(392\) 0 0
\(393\) 17.0000i 0.857537i
\(394\) −27.0000 −1.36024
\(395\) −28.0000 14.0000i −1.40883 0.704416i
\(396\) −5.00000 −0.251259
\(397\) 2.00000i 0.100377i 0.998740 + 0.0501886i \(0.0159822\pi\)
−0.998740 + 0.0501886i \(0.984018\pi\)
\(398\) 14.0000i 0.701757i
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) −27.0000 −1.34832 −0.674158 0.738587i \(-0.735493\pi\)
−0.674158 + 0.738587i \(0.735493\pi\)
\(402\) 6.00000i 0.299253i
\(403\) 6.00000i 0.298881i
\(404\) 8.00000 0.398015
\(405\) −2.00000 1.00000i −0.0993808 0.0496904i
\(406\) 0 0
\(407\) 25.0000i 1.23920i
\(408\) 2.00000i 0.0990148i
\(409\) 10.0000 0.494468 0.247234 0.968956i \(-0.420478\pi\)
0.247234 + 0.968956i \(0.420478\pi\)
\(410\) −9.00000 + 18.0000i −0.444478 + 0.888957i
\(411\) 4.00000 0.197305
\(412\) 0 0
\(413\) 0 0
\(414\) 3.00000 0.147442
\(415\) −10.0000 + 20.0000i −0.490881 + 0.981761i
\(416\) 1.00000 0.0490290
\(417\) 8.00000i 0.391762i
\(418\) 35.0000i 1.71191i
\(419\) 3.00000 0.146560 0.0732798 0.997311i \(-0.476653\pi\)
0.0732798 + 0.997311i \(0.476653\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 19.0000i 0.924906i
\(423\) 13.0000i 0.632082i
\(424\) −1.00000 −0.0485643
\(425\) −8.00000 + 6.00000i −0.388057 + 0.291043i
\(426\) −2.00000 −0.0969003
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) 5.00000 0.241402
\(430\) 20.0000 + 10.0000i 0.964486 + 0.482243i
\(431\) 18.0000 0.867029 0.433515 0.901146i \(-0.357273\pi\)
0.433515 + 0.901146i \(0.357273\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 4.00000i 0.192228i 0.995370 + 0.0961139i \(0.0306413\pi\)
−0.995370 + 0.0961139i \(0.969359\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −18.0000 −0.862044
\(437\) 21.0000i 1.00457i
\(438\) 4.00000i 0.191127i
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) −5.00000 + 10.0000i −0.238366 + 0.476731i
\(441\) 0 0
\(442\) 2.00000i 0.0951303i
\(443\) 6.00000i 0.285069i 0.989790 + 0.142534i \(0.0455251\pi\)
−0.989790 + 0.142534i \(0.954475\pi\)
\(444\) −5.00000 −0.237289
\(445\) −20.0000 10.0000i −0.948091 0.474045i
\(446\) 16.0000 0.757622
\(447\) 6.00000i 0.283790i
\(448\) 0 0
\(449\) −9.00000 −0.424736 −0.212368 0.977190i \(-0.568118\pi\)
−0.212368 + 0.977190i \(0.568118\pi\)
\(450\) −4.00000 + 3.00000i −0.188562 + 0.141421i
\(451\) −45.0000 −2.11897
\(452\) 6.00000i 0.282216i
\(453\) 22.0000i 1.03365i
\(454\) −14.0000 −0.657053
\(455\) 0 0
\(456\) −7.00000 −0.327805
\(457\) 38.0000i 1.77757i −0.458329 0.888783i \(-0.651552\pi\)
0.458329 0.888783i \(-0.348448\pi\)
\(458\) 4.00000i 0.186908i
\(459\) 2.00000 0.0933520
\(460\) 3.00000 6.00000i 0.139876 0.279751i
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 15.0000i 0.697109i 0.937288 + 0.348555i \(0.113327\pi\)
−0.937288 + 0.348555i \(0.886673\pi\)
\(464\) 0 0
\(465\) 6.00000 12.0000i 0.278243 0.556487i
\(466\) 0 0
\(467\) 2.00000i 0.0925490i −0.998929 0.0462745i \(-0.985265\pi\)
0.998929 0.0462745i \(-0.0147349\pi\)
\(468\) 1.00000i 0.0462250i
\(469\) 0 0
\(470\) −26.0000 13.0000i −1.19929 0.599645i
\(471\) 13.0000 0.599008
\(472\) 4.00000i 0.184115i
\(473\) 50.0000i 2.29900i
\(474\) 14.0000 0.643041
\(475\) 21.0000 + 28.0000i 0.963546 + 1.28473i
\(476\) 0 0
\(477\) 1.00000i 0.0457869i
\(478\) 20.0000i 0.914779i
\(479\) 8.00000 0.365529 0.182765 0.983157i \(-0.441495\pi\)
0.182765 + 0.983157i \(0.441495\pi\)
\(480\) −2.00000 1.00000i −0.0912871 0.0456435i
\(481\) 5.00000 0.227980
\(482\) 1.00000i 0.0455488i
\(483\) 0 0
\(484\) −14.0000 −0.636364
\(485\) −8.00000 + 16.0000i −0.363261 + 0.726523i
\(486\) 1.00000 0.0453609
\(487\) 24.0000i 1.08754i 0.839233 + 0.543772i \(0.183004\pi\)
−0.839233 + 0.543772i \(0.816996\pi\)
\(488\) 2.00000i 0.0905357i
\(489\) −12.0000 −0.542659
\(490\) 0 0
\(491\) 24.0000 1.08310 0.541552 0.840667i \(-0.317837\pi\)
0.541552 + 0.840667i \(0.317837\pi\)
\(492\) 9.00000i 0.405751i
\(493\) 0 0
\(494\) 7.00000 0.314945
\(495\) −10.0000 5.00000i −0.449467 0.224733i
\(496\) 6.00000 0.269408
\(497\) 0 0
\(498\) 10.0000i 0.448111i
\(499\) 28.0000 1.25345 0.626726 0.779240i \(-0.284395\pi\)
0.626726 + 0.779240i \(0.284395\pi\)
\(500\) 2.00000 + 11.0000i 0.0894427 + 0.491935i
\(501\) −19.0000 −0.848857
\(502\) 3.00000i 0.133897i
\(503\) 24.0000i 1.07011i 0.844818 + 0.535054i \(0.179709\pi\)
−0.844818 + 0.535054i \(0.820291\pi\)
\(504\) 0 0
\(505\) 16.0000 + 8.00000i 0.711991 + 0.355995i
\(506\) 15.0000 0.666831
\(507\) 12.0000i 0.532939i
\(508\) 9.00000i 0.399310i
\(509\) 14.0000 0.620539 0.310270 0.950649i \(-0.399581\pi\)
0.310270 + 0.950649i \(0.399581\pi\)
\(510\) 2.00000 4.00000i 0.0885615 0.177123i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 7.00000i 0.309058i
\(514\) 10.0000 0.441081
\(515\) 0 0
\(516\) −10.0000 −0.440225
\(517\) 65.0000i 2.85870i
\(518\) 0 0
\(519\) −7.00000 −0.307266
\(520\) 2.00000 + 1.00000i 0.0877058 + 0.0438529i
\(521\) 15.0000 0.657162 0.328581 0.944476i \(-0.393430\pi\)
0.328581 + 0.944476i \(0.393430\pi\)
\(522\) 0 0
\(523\) 12.0000i 0.524723i 0.964970 + 0.262362i \(0.0845013\pi\)
−0.964970 + 0.262362i \(0.915499\pi\)
\(524\) −17.0000 −0.742648
\(525\) 0 0
\(526\) −24.0000 −1.04645
\(527\) 12.0000i 0.522728i
\(528\) 5.00000i 0.217597i
\(529\) 14.0000 0.608696
\(530\) −2.00000 1.00000i −0.0868744 0.0434372i
\(531\) −4.00000 −0.173585
\(532\) 0 0
\(533\) 9.00000i 0.389833i
\(534\) 10.0000 0.432742
\(535\) 12.0000 24.0000i 0.518805 1.03761i
\(536\) −6.00000 −0.259161
\(537\) 11.0000i 0.474685i
\(538\) 14.0000i 0.603583i
\(539\) 0 0
\(540\) 1.00000 2.00000i 0.0430331 0.0860663i
\(541\) 4.00000 0.171973 0.0859867 0.996296i \(-0.472596\pi\)
0.0859867 + 0.996296i \(0.472596\pi\)
\(542\) 8.00000i 0.343629i
\(543\) 2.00000i 0.0858282i
\(544\) 2.00000 0.0857493
\(545\) −36.0000 18.0000i −1.54207 0.771035i
\(546\) 0 0
\(547\) 14.0000i 0.598597i −0.954160 0.299298i \(-0.903247\pi\)
0.954160 0.299298i \(-0.0967526\pi\)
\(548\) 4.00000i 0.170872i
\(549\) −2.00000 −0.0853579
\(550\) −20.0000 + 15.0000i −0.852803 + 0.639602i
\(551\) 0 0
\(552\) 3.00000i 0.127688i
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) −10.0000 5.00000i −0.424476 0.212238i
\(556\) 8.00000 0.339276
\(557\) 39.0000i 1.65248i −0.563316 0.826242i \(-0.690475\pi\)
0.563316 0.826242i \(-0.309525\pi\)
\(558\) 6.00000i 0.254000i
\(559\) 10.0000 0.422955
\(560\) 0 0
\(561\) 10.0000 0.422200
\(562\) 11.0000i 0.464007i
\(563\) 30.0000i 1.26435i 0.774826 + 0.632175i \(0.217837\pi\)
−0.774826 + 0.632175i \(0.782163\pi\)
\(564\) 13.0000 0.547399
\(565\) −6.00000 + 12.0000i −0.252422 + 0.504844i
\(566\) 26.0000 1.09286
\(567\) 0 0
\(568\) 2.00000i 0.0839181i
\(569\) 3.00000 0.125767 0.0628833 0.998021i \(-0.479970\pi\)
0.0628833 + 0.998021i \(0.479970\pi\)
\(570\) −14.0000 7.00000i −0.586395 0.293198i
\(571\) −8.00000 −0.334790 −0.167395 0.985890i \(-0.553535\pi\)
−0.167395 + 0.985890i \(0.553535\pi\)
\(572\) 5.00000i 0.209061i
\(573\) 16.0000i 0.668410i
\(574\) 0 0
\(575\) 12.0000 9.00000i 0.500435 0.375326i
\(576\) 1.00000 0.0416667
\(577\) 24.0000i 0.999133i −0.866276 0.499567i \(-0.833493\pi\)
0.866276 0.499567i \(-0.166507\pi\)
\(578\) 13.0000i 0.540729i
\(579\) −18.0000 −0.748054
\(580\) 0 0
\(581\) 0 0
\(582\) 8.00000i 0.331611i
\(583\) 5.00000i 0.207079i
\(584\) −4.00000 −0.165521
\(585\) −1.00000 + 2.00000i −0.0413449 + 0.0826898i
\(586\) 1.00000 0.0413096
\(587\) 2.00000i 0.0825488i −0.999148 0.0412744i \(-0.986858\pi\)
0.999148 0.0412744i \(-0.0131418\pi\)
\(588\) 0 0
\(589\) 42.0000 1.73058
\(590\) −4.00000 + 8.00000i −0.164677 + 0.329355i
\(591\) 27.0000 1.11063
\(592\) 5.00000i 0.205499i
\(593\) 34.0000i 1.39621i −0.715994 0.698106i \(-0.754026\pi\)
0.715994 0.698106i \(-0.245974\pi\)
\(594\) 5.00000 0.205152
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 14.0000i 0.572982i
\(598\) 3.00000i 0.122679i
\(599\) 28.0000 1.14405 0.572024 0.820237i \(-0.306158\pi\)
0.572024 + 0.820237i \(0.306158\pi\)
\(600\) −3.00000 4.00000i −0.122474 0.163299i
\(601\) 30.0000 1.22373 0.611863 0.790964i \(-0.290420\pi\)
0.611863 + 0.790964i \(0.290420\pi\)
\(602\) 0 0
\(603\) 6.00000i 0.244339i
\(604\) 22.0000 0.895167
\(605\) −28.0000 14.0000i −1.13836 0.569181i
\(606\) −8.00000 −0.324978
\(607\) 13.0000i 0.527654i −0.964570 0.263827i \(-0.915015\pi\)
0.964570 0.263827i \(-0.0849848\pi\)
\(608\) 7.00000i 0.283887i
\(609\) 0 0
\(610\) −2.00000 + 4.00000i −0.0809776 + 0.161955i
\(611\) −13.0000 −0.525924
\(612\) 2.00000i 0.0808452i
\(613\) 19.0000i 0.767403i −0.923457 0.383701i \(-0.874649\pi\)
0.923457 0.383701i \(-0.125351\pi\)
\(614\) −2.00000 −0.0807134
\(615\) 9.00000 18.0000i 0.362915 0.725830i
\(616\) 0 0
\(617\) 30.0000i 1.20775i 0.797077 + 0.603877i \(0.206378\pi\)
−0.797077 + 0.603877i \(0.793622\pi\)
\(618\) 0 0
\(619\) 15.0000 0.602901 0.301450 0.953482i \(-0.402529\pi\)
0.301450 + 0.953482i \(0.402529\pi\)
\(620\) 12.0000 + 6.00000i 0.481932 + 0.240966i
\(621\) −3.00000 −0.120386
\(622\) 26.0000i 1.04251i
\(623\) 0 0
\(624\) −1.00000 −0.0400320
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) −10.0000 −0.399680
\(627\) 35.0000i 1.39777i
\(628\) 13.0000i 0.518756i
\(629\) 10.0000 0.398726
\(630\) 0 0
\(631\) 18.0000 0.716569 0.358284 0.933613i \(-0.383362\pi\)
0.358284 + 0.933613i \(0.383362\pi\)
\(632\) 14.0000i 0.556890i
\(633\) 19.0000i 0.755182i
\(634\) 2.00000 0.0794301
\(635\) 9.00000 18.0000i 0.357154 0.714308i
\(636\) 1.00000 0.0396526
\(637\) 0 0
\(638\) 0 0
\(639\) 2.00000 0.0791188
\(640\) 1.00000 2.00000i 0.0395285 0.0790569i
\(641\) −33.0000 −1.30342 −0.651711 0.758468i \(-0.725948\pi\)
−0.651711 + 0.758468i \(0.725948\pi\)
\(642\) 12.0000i 0.473602i
\(643\) 38.0000i 1.49857i 0.662246 + 0.749287i \(0.269604\pi\)
−0.662246 + 0.749287i \(0.730396\pi\)
\(644\) 0 0
\(645\) −20.0000 10.0000i −0.787499 0.393750i
\(646\) 14.0000 0.550823
\(647\) 1.00000i 0.0393141i 0.999807 + 0.0196570i \(0.00625743\pi\)
−0.999807 + 0.0196570i \(0.993743\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) −20.0000 −0.785069
\(650\) 3.00000 + 4.00000i 0.117670 + 0.156893i
\(651\) 0 0
\(652\) 12.0000i 0.469956i
\(653\) 5.00000i 0.195665i −0.995203 0.0978326i \(-0.968809\pi\)
0.995203 0.0978326i \(-0.0311910\pi\)
\(654\) 18.0000 0.703856
\(655\) −34.0000 17.0000i −1.32849 0.664245i
\(656\) 9.00000 0.351391
\(657\) 4.00000i 0.156055i
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 5.00000 10.0000i 0.194625 0.389249i
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) 15.0000i 0.582992i
\(663\) 2.00000i 0.0776736i
\(664\) 10.0000 0.388075
\(665\) 0 0
\(666\) 5.00000 0.193746
\(667\) 0 0
\(668\) 19.0000i 0.735132i
\(669\) −16.0000 −0.618596
\(670\) −12.0000 6.00000i −0.463600 0.231800i
\(671\) −10.0000 −0.386046
\(672\) 0 0
\(673\) 36.0000i 1.38770i −0.720121 0.693849i \(-0.755914\pi\)
0.720121 0.693849i \(-0.244086\pi\)
\(674\) −14.0000 −0.539260
\(675\) 4.00000 3.00000i 0.153960 0.115470i
\(676\) −12.0000 −0.461538
\(677\) 33.0000i 1.26829i −0.773213 0.634147i \(-0.781352\pi\)
0.773213 0.634147i \(-0.218648\pi\)
\(678\) 6.00000i 0.230429i
\(679\) 0 0
\(680\) 4.00000 + 2.00000i 0.153393 + 0.0766965i
\(681\) 14.0000 0.536481
\(682\) 30.0000i 1.14876i
\(683\) 4.00000i 0.153056i 0.997067 + 0.0765279i \(0.0243834\pi\)
−0.997067 + 0.0765279i \(0.975617\pi\)
\(684\) 7.00000 0.267652
\(685\) −4.00000 + 8.00000i −0.152832 + 0.305664i
\(686\) 0 0
\(687\) 4.00000i 0.152610i
\(688\) 10.0000i 0.381246i
\(689\) −1.00000 −0.0380970
\(690\) −3.00000 + 6.00000i −0.114208 + 0.228416i
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 7.00000i 0.266100i
\(693\) 0 0
\(694\) −16.0000 −0.607352
\(695\) 16.0000 + 8.00000i 0.606915 + 0.303457i
\(696\) 0 0
\(697\) 18.0000i 0.681799i
\(698\) 24.0000i 0.908413i
\(699\) 0 0
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) 1.00000i 0.0377426i
\(703\) 35.0000i 1.32005i
\(704\) 5.00000 0.188445
\(705\) 26.0000 + 13.0000i 0.979217 + 0.489608i
\(706\) 0 0
\(707\) 0 0
\(708\) 4.00000i 0.150329i
\(709\) −16.0000 −0.600893 −0.300446 0.953799i \(-0.597136\pi\)
−0.300446 + 0.953799i \(0.597136\pi\)
\(710\) 2.00000 4.00000i 0.0750587 0.150117i
\(711\) −14.0000 −0.525041
\(712\) 10.0000i 0.374766i
\(713\) 18.0000i 0.674105i
\(714\) 0 0
\(715\) −5.00000 + 10.0000i −0.186989 + 0.373979i
\(716\) −11.0000 −0.411089
\(717\) 20.0000i 0.746914i
\(718\) 28.0000i 1.04495i
\(719\) −2.00000 −0.0745874 −0.0372937 0.999304i \(-0.511874\pi\)
−0.0372937 + 0.999304i \(0.511874\pi\)
\(720\) 2.00000 + 1.00000i 0.0745356 + 0.0372678i
\(721\) 0 0
\(722\) 30.0000i 1.11648i
\(723\) 1.00000i 0.0371904i
\(724\) −2.00000 −0.0743294
\(725\) 0 0
\(726\) 14.0000 0.519589
\(727\) 53.0000i 1.96566i −0.184510 0.982831i \(-0.559070\pi\)
0.184510 0.982831i \(-0.440930\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) −8.00000 4.00000i −0.296093 0.148047i
\(731\) 20.0000 0.739727
\(732\) 2.00000i 0.0739221i
\(733\) 21.0000i 0.775653i −0.921732 0.387826i \(-0.873226\pi\)
0.921732 0.387826i \(-0.126774\pi\)
\(734\) 37.0000 1.36569
\(735\) 0 0
\(736\) −3.00000 −0.110581
\(737\) 30.0000i 1.10506i
\(738\) 9.00000i 0.331295i
\(739\) −47.0000 −1.72892 −0.864461 0.502699i \(-0.832340\pi\)
−0.864461 + 0.502699i \(0.832340\pi\)
\(740\) 5.00000 10.0000i 0.183804 0.367607i
\(741\) −7.00000 −0.257151
\(742\) 0 0
\(743\) 31.0000i 1.13728i 0.822587 + 0.568640i \(0.192530\pi\)
−0.822587 + 0.568640i \(0.807470\pi\)
\(744\) −6.00000 −0.219971
\(745\) −12.0000 6.00000i −0.439646 0.219823i
\(746\) −6.00000 −0.219676
\(747\) 10.0000i 0.365881i
\(748\) 10.0000i 0.365636i
\(749\) 0 0
\(750\) −2.00000 11.0000i −0.0730297 0.401663i
\(751\) 4.00000 0.145962 0.0729810 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) 13.0000i 0.474061i
\(753\) 3.00000i 0.109326i
\(754\) 0 0
\(755\) 44.0000 + 22.0000i 1.60132 + 0.800662i
\(756\) 0 0
\(757\) 26.0000i 0.944986i −0.881334 0.472493i \(-0.843354\pi\)
0.881334 0.472493i \(-0.156646\pi\)
\(758\) 1.00000i 0.0363216i
\(759\) −15.0000 −0.544466
\(760\) 7.00000 14.0000i 0.253917 0.507833i
\(761\) 3.00000 0.108750 0.0543750 0.998521i \(-0.482683\pi\)
0.0543750 + 0.998521i \(0.482683\pi\)
\(762\) 9.00000i 0.326036i
\(763\) 0 0
\(764\) 16.0000 0.578860
\(765\) −2.00000 + 4.00000i −0.0723102 + 0.144620i
\(766\) −9.00000 −0.325183
\(767\) 4.00000i 0.144432i
\(768\) 1.00000i 0.0360844i
\(769\) 51.0000 1.83911 0.919554 0.392965i \(-0.128551\pi\)
0.919554 + 0.392965i \(0.128551\pi\)
\(770\) 0 0
\(771\) −10.0000 −0.360141
\(772\) 18.0000i 0.647834i
\(773\) 37.0000i 1.33080i −0.746488 0.665399i \(-0.768262\pi\)
0.746488 0.665399i \(-0.231738\pi\)
\(774\) 10.0000 0.359443
\(775\) 18.0000 + 24.0000i 0.646579 + 0.862105i
\(776\) 8.00000 0.287183
\(777\) 0 0
\(778\) 6.00000i 0.215110i
\(779\) 63.0000 2.25721
\(780\) −2.00000 1.00000i −0.0716115 0.0358057i
\(781\) 10.0000 0.357828
\(782\) 6.00000i 0.214560i
\(783\) 0 0
\(784\) 0 0
\(785\) −13.0000 + 26.0000i −0.463990 + 0.927980i
\(786\) 17.0000 0.606370
\(787\) 38.0000i 1.35455i −0.735728 0.677277i \(-0.763160\pi\)
0.735728 0.677277i \(-0.236840\pi\)
\(788\) 27.0000i 0.961835i
\(789\) 24.0000 0.854423
\(790\) −14.0000 + 28.0000i −0.498098 + 0.996195i
\(791\) 0 0
\(792\) 5.00000i 0.177667i
\(793\) 2.00000i 0.0710221i
\(794\) 2.00000 0.0709773
\(795\) 2.00000 + 1.00000i 0.0709327 + 0.0354663i
\(796\) 14.0000 0.496217
\(797\) 30.0000i 1.06265i 0.847167 + 0.531327i \(0.178307\pi\)
−0.847167 + 0.531327i \(0.821693\pi\)
\(798\) 0 0
\(799\) −26.0000 −0.919814
\(800\) 4.00000 3.00000i 0.141421 0.106066i
\(801\) −10.0000 −0.353333
\(802\) 27.0000i 0.953403i
\(803\) 20.0000i 0.705785i
\(804\) 6.00000 0.211604
\(805\) 0 0
\(806\) 6.00000 0.211341