Properties

Label 115.2.b.a.24.1
Level $115$
Weight $2$
Character 115.24
Analytic conductor $0.918$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 115 = 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 115.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.918279623245\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 24.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 115.24
Dual form 115.2.b.a.24.2

$q$-expansion

\(f(q)\) \(=\) \(q-2.00000i q^{2} +2.00000i q^{3} -2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +4.00000 q^{6} -1.00000i q^{7} -1.00000 q^{9} +O(q^{10})\) \(q-2.00000i q^{2} +2.00000i q^{3} -2.00000 q^{4} +(2.00000 - 1.00000i) q^{5} +4.00000 q^{6} -1.00000i q^{7} -1.00000 q^{9} +(-2.00000 - 4.00000i) q^{10} -4.00000i q^{12} +2.00000i q^{13} -2.00000 q^{14} +(2.00000 + 4.00000i) q^{15} -4.00000 q^{16} +5.00000i q^{17} +2.00000i q^{18} -8.00000 q^{19} +(-4.00000 + 2.00000i) q^{20} +2.00000 q^{21} -1.00000i q^{23} +(3.00000 - 4.00000i) q^{25} +4.00000 q^{26} +4.00000i q^{27} +2.00000i q^{28} +5.00000 q^{29} +(8.00000 - 4.00000i) q^{30} -5.00000 q^{31} +8.00000i q^{32} +10.0000 q^{34} +(-1.00000 - 2.00000i) q^{35} +2.00000 q^{36} -7.00000i q^{37} +16.0000i q^{38} -4.00000 q^{39} -7.00000 q^{41} -4.00000i q^{42} +4.00000i q^{43} +(-2.00000 + 1.00000i) q^{45} -2.00000 q^{46} +2.00000i q^{47} -8.00000i q^{48} +6.00000 q^{49} +(-8.00000 - 6.00000i) q^{50} -10.0000 q^{51} -4.00000i q^{52} -1.00000i q^{53} +8.00000 q^{54} -16.0000i q^{57} -10.0000i q^{58} -3.00000 q^{59} +(-4.00000 - 8.00000i) q^{60} -6.00000 q^{61} +10.0000i q^{62} +1.00000i q^{63} +8.00000 q^{64} +(2.00000 + 4.00000i) q^{65} -13.0000i q^{67} -10.0000i q^{68} +2.00000 q^{69} +(-4.00000 + 2.00000i) q^{70} +13.0000 q^{71} +8.00000i q^{73} -14.0000 q^{74} +(8.00000 + 6.00000i) q^{75} +16.0000 q^{76} +8.00000i q^{78} +14.0000 q^{79} +(-8.00000 + 4.00000i) q^{80} -11.0000 q^{81} +14.0000i q^{82} -3.00000i q^{83} -4.00000 q^{84} +(5.00000 + 10.0000i) q^{85} +8.00000 q^{86} +10.0000i q^{87} +14.0000 q^{89} +(2.00000 + 4.00000i) q^{90} +2.00000 q^{91} +2.00000i q^{92} -10.0000i q^{93} +4.00000 q^{94} +(-16.0000 + 8.00000i) q^{95} -16.0000 q^{96} -14.0000i q^{97} -12.0000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{4} + 4 q^{5} + 8 q^{6} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{4} + 4 q^{5} + 8 q^{6} - 2 q^{9} - 4 q^{10} - 4 q^{14} + 4 q^{15} - 8 q^{16} - 16 q^{19} - 8 q^{20} + 4 q^{21} + 6 q^{25} + 8 q^{26} + 10 q^{29} + 16 q^{30} - 10 q^{31} + 20 q^{34} - 2 q^{35} + 4 q^{36} - 8 q^{39} - 14 q^{41} - 4 q^{45} - 4 q^{46} + 12 q^{49} - 16 q^{50} - 20 q^{51} + 16 q^{54} - 6 q^{59} - 8 q^{60} - 12 q^{61} + 16 q^{64} + 4 q^{65} + 4 q^{69} - 8 q^{70} + 26 q^{71} - 28 q^{74} + 16 q^{75} + 32 q^{76} + 28 q^{79} - 16 q^{80} - 22 q^{81} - 8 q^{84} + 10 q^{85} + 16 q^{86} + 28 q^{89} + 4 q^{90} + 4 q^{91} + 8 q^{94} - 32 q^{95} - 32 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000i 1.41421i −0.707107 0.707107i \(-0.750000\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(3\) 2.00000i 1.15470i 0.816497 + 0.577350i \(0.195913\pi\)
−0.816497 + 0.577350i \(0.804087\pi\)
\(4\) −2.00000 −1.00000
\(5\) 2.00000 1.00000i 0.894427 0.447214i
\(6\) 4.00000 1.63299
\(7\) 1.00000i 0.377964i −0.981981 0.188982i \(-0.939481\pi\)
0.981981 0.188982i \(-0.0605189\pi\)
\(8\) 0 0
\(9\) −1.00000 −0.333333
\(10\) −2.00000 4.00000i −0.632456 1.26491i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 4.00000i 1.15470i
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) −2.00000 −0.534522
\(15\) 2.00000 + 4.00000i 0.516398 + 1.03280i
\(16\) −4.00000 −1.00000
\(17\) 5.00000i 1.21268i 0.795206 + 0.606339i \(0.207363\pi\)
−0.795206 + 0.606339i \(0.792637\pi\)
\(18\) 2.00000i 0.471405i
\(19\) −8.00000 −1.83533 −0.917663 0.397360i \(-0.869927\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −4.00000 + 2.00000i −0.894427 + 0.447214i
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) 1.00000i 0.208514i
\(24\) 0 0
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 4.00000 0.784465
\(27\) 4.00000i 0.769800i
\(28\) 2.00000i 0.377964i
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 8.00000 4.00000i 1.46059 0.730297i
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) 8.00000i 1.41421i
\(33\) 0 0
\(34\) 10.0000 1.71499
\(35\) −1.00000 2.00000i −0.169031 0.338062i
\(36\) 2.00000 0.333333
\(37\) 7.00000i 1.15079i −0.817875 0.575396i \(-0.804848\pi\)
0.817875 0.575396i \(-0.195152\pi\)
\(38\) 16.0000i 2.59554i
\(39\) −4.00000 −0.640513
\(40\) 0 0
\(41\) −7.00000 −1.09322 −0.546608 0.837389i \(-0.684081\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(42\) 4.00000i 0.617213i
\(43\) 4.00000i 0.609994i 0.952353 + 0.304997i \(0.0986555\pi\)
−0.952353 + 0.304997i \(0.901344\pi\)
\(44\) 0 0
\(45\) −2.00000 + 1.00000i −0.298142 + 0.149071i
\(46\) −2.00000 −0.294884
\(47\) 2.00000i 0.291730i 0.989305 + 0.145865i \(0.0465965\pi\)
−0.989305 + 0.145865i \(0.953403\pi\)
\(48\) 8.00000i 1.15470i
\(49\) 6.00000 0.857143
\(50\) −8.00000 6.00000i −1.13137 0.848528i
\(51\) −10.0000 −1.40028
\(52\) 4.00000i 0.554700i
\(53\) 1.00000i 0.137361i −0.997639 0.0686803i \(-0.978121\pi\)
0.997639 0.0686803i \(-0.0218788\pi\)
\(54\) 8.00000 1.08866
\(55\) 0 0
\(56\) 0 0
\(57\) 16.0000i 2.11925i
\(58\) 10.0000i 1.31306i
\(59\) −3.00000 −0.390567 −0.195283 0.980747i \(-0.562563\pi\)
−0.195283 + 0.980747i \(0.562563\pi\)
\(60\) −4.00000 8.00000i −0.516398 1.03280i
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 10.0000i 1.27000i
\(63\) 1.00000i 0.125988i
\(64\) 8.00000 1.00000
\(65\) 2.00000 + 4.00000i 0.248069 + 0.496139i
\(66\) 0 0
\(67\) 13.0000i 1.58820i −0.607785 0.794101i \(-0.707942\pi\)
0.607785 0.794101i \(-0.292058\pi\)
\(68\) 10.0000i 1.21268i
\(69\) 2.00000 0.240772
\(70\) −4.00000 + 2.00000i −0.478091 + 0.239046i
\(71\) 13.0000 1.54282 0.771408 0.636341i \(-0.219553\pi\)
0.771408 + 0.636341i \(0.219553\pi\)
\(72\) 0 0
\(73\) 8.00000i 0.936329i 0.883641 + 0.468165i \(0.155085\pi\)
−0.883641 + 0.468165i \(0.844915\pi\)
\(74\) −14.0000 −1.62747
\(75\) 8.00000 + 6.00000i 0.923760 + 0.692820i
\(76\) 16.0000 1.83533
\(77\) 0 0
\(78\) 8.00000i 0.905822i
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) −8.00000 + 4.00000i −0.894427 + 0.447214i
\(81\) −11.0000 −1.22222
\(82\) 14.0000i 1.54604i
\(83\) 3.00000i 0.329293i −0.986353 0.164646i \(-0.947352\pi\)
0.986353 0.164646i \(-0.0526483\pi\)
\(84\) −4.00000 −0.436436
\(85\) 5.00000 + 10.0000i 0.542326 + 1.08465i
\(86\) 8.00000 0.862662
\(87\) 10.0000i 1.07211i
\(88\) 0 0
\(89\) 14.0000 1.48400 0.741999 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 2.00000 + 4.00000i 0.210819 + 0.421637i
\(91\) 2.00000 0.209657
\(92\) 2.00000i 0.208514i
\(93\) 10.0000i 1.03695i
\(94\) 4.00000 0.412568
\(95\) −16.0000 + 8.00000i −1.64157 + 0.820783i
\(96\) −16.0000 −1.63299
\(97\) 14.0000i 1.42148i −0.703452 0.710742i \(-0.748359\pi\)
0.703452 0.710742i \(-0.251641\pi\)
\(98\) 12.0000i 1.21218i
\(99\) 0 0
\(100\) −6.00000 + 8.00000i −0.600000 + 0.800000i
\(101\) 15.0000 1.49256 0.746278 0.665635i \(-0.231839\pi\)
0.746278 + 0.665635i \(0.231839\pi\)
\(102\) 20.0000i 1.98030i
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0 0
\(105\) 4.00000 2.00000i 0.390360 0.195180i
\(106\) −2.00000 −0.194257
\(107\) 9.00000i 0.870063i −0.900415 0.435031i \(-0.856737\pi\)
0.900415 0.435031i \(-0.143263\pi\)
\(108\) 8.00000i 0.769800i
\(109\) −18.0000 −1.72409 −0.862044 0.506834i \(-0.830816\pi\)
−0.862044 + 0.506834i \(0.830816\pi\)
\(110\) 0 0
\(111\) 14.0000 1.32882
\(112\) 4.00000i 0.377964i
\(113\) 1.00000i 0.0940721i −0.998893 0.0470360i \(-0.985022\pi\)
0.998893 0.0470360i \(-0.0149776\pi\)
\(114\) −32.0000 −2.99707
\(115\) −1.00000 2.00000i −0.0932505 0.186501i
\(116\) −10.0000 −0.928477
\(117\) 2.00000i 0.184900i
\(118\) 6.00000i 0.552345i
\(119\) 5.00000 0.458349
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 12.0000i 1.08643i
\(123\) 14.0000i 1.26234i
\(124\) 10.0000 0.898027
\(125\) 2.00000 11.0000i 0.178885 0.983870i
\(126\) 2.00000 0.178174
\(127\) 20.0000i 1.77471i 0.461084 + 0.887357i \(0.347461\pi\)
−0.461084 + 0.887357i \(0.652539\pi\)
\(128\) 0 0
\(129\) −8.00000 −0.704361
\(130\) 8.00000 4.00000i 0.701646 0.350823i
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) 8.00000i 0.693688i
\(134\) −26.0000 −2.24606
\(135\) 4.00000 + 8.00000i 0.344265 + 0.688530i
\(136\) 0 0
\(137\) 6.00000i 0.512615i −0.966595 0.256307i \(-0.917494\pi\)
0.966595 0.256307i \(-0.0825059\pi\)
\(138\) 4.00000i 0.340503i
\(139\) −9.00000 −0.763370 −0.381685 0.924292i \(-0.624656\pi\)
−0.381685 + 0.924292i \(0.624656\pi\)
\(140\) 2.00000 + 4.00000i 0.169031 + 0.338062i
\(141\) −4.00000 −0.336861
\(142\) 26.0000i 2.18187i
\(143\) 0 0
\(144\) 4.00000 0.333333
\(145\) 10.0000 5.00000i 0.830455 0.415227i
\(146\) 16.0000 1.32417
\(147\) 12.0000i 0.989743i
\(148\) 14.0000i 1.15079i
\(149\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(150\) 12.0000 16.0000i 0.979796 1.30639i
\(151\) 8.00000 0.651031 0.325515 0.945537i \(-0.394462\pi\)
0.325515 + 0.945537i \(0.394462\pi\)
\(152\) 0 0
\(153\) 5.00000i 0.404226i
\(154\) 0 0
\(155\) −10.0000 + 5.00000i −0.803219 + 0.401610i
\(156\) 8.00000 0.640513
\(157\) 3.00000i 0.239426i 0.992809 + 0.119713i \(0.0381975\pi\)
−0.992809 + 0.119713i \(0.961803\pi\)
\(158\) 28.0000i 2.22756i
\(159\) 2.00000 0.158610
\(160\) 8.00000 + 16.0000i 0.632456 + 1.26491i
\(161\) −1.00000 −0.0788110
\(162\) 22.0000i 1.72848i
\(163\) 24.0000i 1.87983i 0.341415 + 0.939913i \(0.389094\pi\)
−0.341415 + 0.939913i \(0.610906\pi\)
\(164\) 14.0000 1.09322
\(165\) 0 0
\(166\) −6.00000 −0.465690
\(167\) 16.0000i 1.23812i −0.785345 0.619059i \(-0.787514\pi\)
0.785345 0.619059i \(-0.212486\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) 20.0000 10.0000i 1.53393 0.766965i
\(171\) 8.00000 0.611775
\(172\) 8.00000i 0.609994i
\(173\) 6.00000i 0.456172i 0.973641 + 0.228086i \(0.0732467\pi\)
−0.973641 + 0.228086i \(0.926753\pi\)
\(174\) 20.0000 1.51620
\(175\) −4.00000 3.00000i −0.302372 0.226779i
\(176\) 0 0
\(177\) 6.00000i 0.450988i
\(178\) 28.0000i 2.09869i
\(179\) 4.00000 0.298974 0.149487 0.988764i \(-0.452238\pi\)
0.149487 + 0.988764i \(0.452238\pi\)
\(180\) 4.00000 2.00000i 0.298142 0.149071i
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) 4.00000i 0.296500i
\(183\) 12.0000i 0.887066i
\(184\) 0 0
\(185\) −7.00000 14.0000i −0.514650 1.02930i
\(186\) −20.0000 −1.46647
\(187\) 0 0
\(188\) 4.00000i 0.291730i
\(189\) 4.00000 0.290957
\(190\) 16.0000 + 32.0000i 1.16076 + 2.32152i
\(191\) −8.00000 −0.578860 −0.289430 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 16.0000i 1.15470i
\(193\) 12.0000i 0.863779i −0.901927 0.431889i \(-0.857847\pi\)
0.901927 0.431889i \(-0.142153\pi\)
\(194\) −28.0000 −2.01028
\(195\) −8.00000 + 4.00000i −0.572892 + 0.286446i
\(196\) −12.0000 −0.857143
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0 0
\(199\) −2.00000 −0.141776 −0.0708881 0.997484i \(-0.522583\pi\)
−0.0708881 + 0.997484i \(0.522583\pi\)
\(200\) 0 0
\(201\) 26.0000 1.83390
\(202\) 30.0000i 2.11079i
\(203\) 5.00000i 0.350931i
\(204\) 20.0000 1.40028
\(205\) −14.0000 + 7.00000i −0.977802 + 0.488901i
\(206\) 0 0
\(207\) 1.00000i 0.0695048i
\(208\) 8.00000i 0.554700i
\(209\) 0 0
\(210\) −4.00000 8.00000i −0.276026 0.552052i
\(211\) −9.00000 −0.619586 −0.309793 0.950804i \(-0.600260\pi\)
−0.309793 + 0.950804i \(0.600260\pi\)
\(212\) 2.00000i 0.137361i
\(213\) 26.0000i 1.78149i
\(214\) −18.0000 −1.23045
\(215\) 4.00000 + 8.00000i 0.272798 + 0.545595i
\(216\) 0 0
\(217\) 5.00000i 0.339422i
\(218\) 36.0000i 2.43823i
\(219\) −16.0000 −1.08118
\(220\) 0 0
\(221\) −10.0000 −0.672673
\(222\) 28.0000i 1.87924i
\(223\) 14.0000i 0.937509i −0.883328 0.468755i \(-0.844703\pi\)
0.883328 0.468755i \(-0.155297\pi\)
\(224\) 8.00000 0.534522
\(225\) −3.00000 + 4.00000i −0.200000 + 0.266667i
\(226\) −2.00000 −0.133038
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 32.0000i 2.11925i
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) −4.00000 + 2.00000i −0.263752 + 0.131876i
\(231\) 0 0
\(232\) 0 0
\(233\) 6.00000i 0.393073i 0.980497 + 0.196537i \(0.0629694\pi\)
−0.980497 + 0.196537i \(0.937031\pi\)
\(234\) −4.00000 −0.261488
\(235\) 2.00000 + 4.00000i 0.130466 + 0.260931i
\(236\) 6.00000 0.390567
\(237\) 28.0000i 1.81880i
\(238\) 10.0000i 0.648204i
\(239\) 1.00000 0.0646846 0.0323423 0.999477i \(-0.489703\pi\)
0.0323423 + 0.999477i \(0.489703\pi\)
\(240\) −8.00000 16.0000i −0.516398 1.03280i
\(241\) 6.00000 0.386494 0.193247 0.981150i \(-0.438098\pi\)
0.193247 + 0.981150i \(0.438098\pi\)
\(242\) 22.0000i 1.41421i
\(243\) 10.0000i 0.641500i
\(244\) 12.0000 0.768221
\(245\) 12.0000 6.00000i 0.766652 0.383326i
\(246\) −28.0000 −1.78521
\(247\) 16.0000i 1.01806i
\(248\) 0 0
\(249\) 6.00000 0.380235
\(250\) −22.0000 4.00000i −1.39140 0.252982i
\(251\) 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
\(254\) 40.0000 2.50982
\(255\) −20.0000 + 10.0000i −1.25245 + 0.626224i
\(256\) 16.0000 1.00000
\(257\) 22.0000i 1.37232i −0.727450 0.686161i \(-0.759294\pi\)
0.727450 0.686161i \(-0.240706\pi\)
\(258\) 16.0000i 0.996116i
\(259\) −7.00000 −0.434959
\(260\) −4.00000 8.00000i −0.248069 0.496139i
\(261\) −5.00000 −0.309492
\(262\) 0 0
\(263\) 13.0000i 0.801614i −0.916162 0.400807i \(-0.868730\pi\)
0.916162 0.400807i \(-0.131270\pi\)
\(264\) 0 0
\(265\) −1.00000 2.00000i −0.0614295 0.122859i
\(266\) 16.0000 0.981023
\(267\) 28.0000i 1.71357i
\(268\) 26.0000i 1.58820i
\(269\) 15.0000 0.914566 0.457283 0.889321i \(-0.348823\pi\)
0.457283 + 0.889321i \(0.348823\pi\)
\(270\) 16.0000 8.00000i 0.973729 0.486864i
\(271\) −15.0000 −0.911185 −0.455593 0.890188i \(-0.650573\pi\)
−0.455593 + 0.890188i \(0.650573\pi\)
\(272\) 20.0000i 1.21268i
\(273\) 4.00000i 0.242091i
\(274\) −12.0000 −0.724947
\(275\) 0 0
\(276\) −4.00000 −0.240772
\(277\) 26.0000i 1.56219i 0.624413 + 0.781094i \(0.285338\pi\)
−0.624413 + 0.781094i \(0.714662\pi\)
\(278\) 18.0000i 1.07957i
\(279\) 5.00000 0.299342
\(280\) 0 0
\(281\) −12.0000 −0.715860 −0.357930 0.933748i \(-0.616517\pi\)
−0.357930 + 0.933748i \(0.616517\pi\)
\(282\) 8.00000i 0.476393i
\(283\) 11.0000i 0.653882i 0.945045 + 0.326941i \(0.106018\pi\)
−0.945045 + 0.326941i \(0.893982\pi\)
\(284\) −26.0000 −1.54282
\(285\) −16.0000 32.0000i −0.947758 1.89552i
\(286\) 0 0
\(287\) 7.00000i 0.413197i
\(288\) 8.00000i 0.471405i
\(289\) −8.00000 −0.470588
\(290\) −10.0000 20.0000i −0.587220 1.17444i
\(291\) 28.0000 1.64139
\(292\) 16.0000i 0.936329i
\(293\) 29.0000i 1.69420i 0.531435 + 0.847099i \(0.321653\pi\)
−0.531435 + 0.847099i \(0.678347\pi\)
\(294\) 24.0000 1.39971
\(295\) −6.00000 + 3.00000i −0.349334 + 0.174667i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.00000 0.115663
\(300\) −16.0000 12.0000i −0.923760 0.692820i
\(301\) 4.00000 0.230556
\(302\) 16.0000i 0.920697i
\(303\) 30.0000i 1.72345i
\(304\) 32.0000 1.83533
\(305\) −12.0000 + 6.00000i −0.687118 + 0.343559i
\(306\) −10.0000 −0.571662
\(307\) 14.0000i 0.799022i −0.916728 0.399511i \(-0.869180\pi\)
0.916728 0.399511i \(-0.130820\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 10.0000 + 20.0000i 0.567962 + 1.13592i
\(311\) 4.00000 0.226819 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) 0 0
\(313\) 21.0000i 1.18699i 0.804838 + 0.593495i \(0.202252\pi\)
−0.804838 + 0.593495i \(0.797748\pi\)
\(314\) 6.00000 0.338600
\(315\) 1.00000 + 2.00000i 0.0563436 + 0.112687i
\(316\) −28.0000 −1.57512
\(317\) 24.0000i 1.34797i 0.738743 + 0.673987i \(0.235420\pi\)
−0.738743 + 0.673987i \(0.764580\pi\)
\(318\) 4.00000i 0.224309i
\(319\) 0 0
\(320\) 16.0000 8.00000i 0.894427 0.447214i
\(321\) 18.0000 1.00466
\(322\) 2.00000i 0.111456i
\(323\) 40.0000i 2.22566i
\(324\) 22.0000 1.22222
\(325\) 8.00000 + 6.00000i 0.443760 + 0.332820i
\(326\) 48.0000 2.65847
\(327\) 36.0000i 1.99080i
\(328\) 0 0
\(329\) 2.00000 0.110264
\(330\) 0 0
\(331\) −5.00000 −0.274825 −0.137412 0.990514i \(-0.543879\pi\)
−0.137412 + 0.990514i \(0.543879\pi\)
\(332\) 6.00000i 0.329293i
\(333\) 7.00000i 0.383598i
\(334\) −32.0000 −1.75096
\(335\) −13.0000 26.0000i −0.710266 1.42053i
\(336\) −8.00000 −0.436436
\(337\) 26.0000i 1.41631i −0.706057 0.708155i \(-0.749528\pi\)
0.706057 0.708155i \(-0.250472\pi\)
\(338\) 18.0000i 0.979071i
\(339\) 2.00000 0.108625
\(340\) −10.0000 20.0000i −0.542326 1.08465i
\(341\) 0 0
\(342\) 16.0000i 0.865181i
\(343\) 13.0000i 0.701934i
\(344\) 0 0
\(345\) 4.00000 2.00000i 0.215353 0.107676i
\(346\) 12.0000 0.645124
\(347\) 8.00000i 0.429463i −0.976673 0.214731i \(-0.931112\pi\)
0.976673 0.214731i \(-0.0688876\pi\)
\(348\) 20.0000i 1.07211i
\(349\) −23.0000 −1.23116 −0.615581 0.788074i \(-0.711079\pi\)
−0.615581 + 0.788074i \(0.711079\pi\)
\(350\) −6.00000 + 8.00000i −0.320713 + 0.427618i
\(351\) −8.00000 −0.427008
\(352\) 0 0
\(353\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(354\) −12.0000 −0.637793
\(355\) 26.0000 13.0000i 1.37994 0.689968i
\(356\) −28.0000 −1.48400
\(357\) 10.0000i 0.529256i
\(358\) 8.00000i 0.422813i
\(359\) 6.00000 0.316668 0.158334 0.987386i \(-0.449388\pi\)
0.158334 + 0.987386i \(0.449388\pi\)
\(360\) 0 0
\(361\) 45.0000 2.36842
\(362\) 28.0000i 1.47165i
\(363\) 22.0000i 1.15470i
\(364\) −4.00000 −0.209657
\(365\) 8.00000 + 16.0000i 0.418739 + 0.837478i
\(366\) −24.0000 −1.25450
\(367\) 13.0000i 0.678594i 0.940679 + 0.339297i \(0.110189\pi\)
−0.940679 + 0.339297i \(0.889811\pi\)
\(368\) 4.00000i 0.208514i
\(369\) 7.00000 0.364405
\(370\) −28.0000 + 14.0000i −1.45565 + 0.727825i
\(371\) −1.00000 −0.0519174
\(372\) 20.0000i 1.03695i
\(373\) 6.00000i 0.310668i −0.987862 0.155334i \(-0.950355\pi\)
0.987862 0.155334i \(-0.0496454\pi\)
\(374\) 0 0
\(375\) 22.0000 + 4.00000i 1.13608 + 0.206559i
\(376\) 0 0
\(377\) 10.0000i 0.515026i
\(378\) 8.00000i 0.411476i
\(379\) −6.00000 −0.308199 −0.154100 0.988055i \(-0.549248\pi\)
−0.154100 + 0.988055i \(0.549248\pi\)
\(380\) 32.0000 16.0000i 1.64157 0.820783i
\(381\) −40.0000 −2.04926
\(382\) 16.0000i 0.818631i
\(383\) 3.00000i 0.153293i 0.997058 + 0.0766464i \(0.0244213\pi\)
−0.997058 + 0.0766464i \(0.975579\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −24.0000 −1.22157
\(387\) 4.00000i 0.203331i
\(388\) 28.0000i 1.42148i
\(389\) −22.0000 −1.11544 −0.557722 0.830028i \(-0.688325\pi\)
−0.557722 + 0.830028i \(0.688325\pi\)
\(390\) 8.00000 + 16.0000i 0.405096 + 0.810191i
\(391\) 5.00000 0.252861
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 28.0000 14.0000i 1.40883 0.704416i
\(396\) 0 0
\(397\) 16.0000i 0.803017i −0.915855 0.401508i \(-0.868486\pi\)
0.915855 0.401508i \(-0.131514\pi\)
\(398\) 4.00000i 0.200502i
\(399\) −16.0000 −0.801002
\(400\) −12.0000 + 16.0000i −0.600000 + 0.800000i
\(401\) 2.00000 0.0998752 0.0499376 0.998752i \(-0.484098\pi\)
0.0499376 + 0.998752i \(0.484098\pi\)
\(402\) 52.0000i 2.59352i
\(403\) 10.0000i 0.498135i
\(404\) −30.0000 −1.49256
\(405\) −22.0000 + 11.0000i −1.09319 + 0.546594i
\(406\) −10.0000 −0.496292
\(407\) 0 0
\(408\) 0 0
\(409\) 19.0000 0.939490 0.469745 0.882802i \(-0.344346\pi\)
0.469745 + 0.882802i \(0.344346\pi\)
\(410\) 14.0000 + 28.0000i 0.691411 + 1.38282i
\(411\) 12.0000 0.591916
\(412\) 0 0
\(413\) 3.00000i 0.147620i
\(414\) 2.00000 0.0982946
\(415\) −3.00000 6.00000i −0.147264 0.294528i
\(416\) −16.0000 −0.784465
\(417\) 18.0000i 0.881464i
\(418\) 0 0
\(419\) 2.00000 0.0977064 0.0488532 0.998806i \(-0.484443\pi\)
0.0488532 + 0.998806i \(0.484443\pi\)
\(420\) −8.00000 + 4.00000i −0.390360 + 0.195180i
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 18.0000i 0.876226i
\(423\) 2.00000i 0.0972433i
\(424\) 0 0
\(425\) 20.0000 + 15.0000i 0.970143 + 0.727607i
\(426\) 52.0000 2.51941
\(427\) 6.00000i 0.290360i
\(428\) 18.0000i 0.870063i
\(429\) 0 0
\(430\) 16.0000 8.00000i 0.771589 0.385794i
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 16.0000i 0.769800i
\(433\) 19.0000i 0.913082i 0.889702 + 0.456541i \(0.150912\pi\)
−0.889702 + 0.456541i \(0.849088\pi\)
\(434\) 10.0000 0.480015
\(435\) 10.0000 + 20.0000i 0.479463 + 0.958927i
\(436\) 36.0000 1.72409
\(437\) 8.00000i 0.382692i
\(438\) 32.0000i 1.52902i
\(439\) 28.0000 1.33637 0.668184 0.743996i \(-0.267072\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) 20.0000i 0.951303i
\(443\) 24.0000i 1.14027i −0.821549 0.570137i \(-0.806890\pi\)
0.821549 0.570137i \(-0.193110\pi\)
\(444\) −28.0000 −1.32882
\(445\) 28.0000 14.0000i 1.32733 0.663664i
\(446\) −28.0000 −1.32584
\(447\) 0 0
\(448\) 8.00000i 0.377964i
\(449\) −15.0000 −0.707894 −0.353947 0.935266i \(-0.615161\pi\)
−0.353947 + 0.935266i \(0.615161\pi\)
\(450\) 8.00000 + 6.00000i 0.377124 + 0.282843i
\(451\) 0 0
\(452\) 2.00000i 0.0940721i
\(453\) 16.0000i 0.751746i
\(454\) 0 0
\(455\) 4.00000 2.00000i 0.187523 0.0937614i
\(456\) 0 0
\(457\) 1.00000i 0.0467780i −0.999726 0.0233890i \(-0.992554\pi\)
0.999726 0.0233890i \(-0.00744563\pi\)
\(458\) 8.00000i 0.373815i
\(459\) −20.0000 −0.933520
\(460\) 2.00000 + 4.00000i 0.0932505 + 0.186501i
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 4.00000i 0.185896i −0.995671 0.0929479i \(-0.970371\pi\)
0.995671 0.0929479i \(-0.0296290\pi\)
\(464\) −20.0000 −0.928477
\(465\) −10.0000 20.0000i −0.463739 0.927478i
\(466\) 12.0000 0.555889
\(467\) 27.0000i 1.24941i 0.780860 + 0.624705i \(0.214781\pi\)
−0.780860 + 0.624705i \(0.785219\pi\)
\(468\) 4.00000i 0.184900i
\(469\) −13.0000 −0.600284
\(470\) 8.00000 4.00000i 0.369012 0.184506i
\(471\) −6.00000 −0.276465
\(472\) 0 0
\(473\) 0 0
\(474\) 56.0000 2.57217
\(475\) −24.0000 + 32.0000i −1.10120 + 1.46826i
\(476\) −10.0000 −0.458349
\(477\) 1.00000i 0.0457869i
\(478\) 2.00000i 0.0914779i
\(479\) 28.0000 1.27935 0.639676 0.768644i \(-0.279068\pi\)
0.639676 + 0.768644i \(0.279068\pi\)
\(480\) −32.0000 + 16.0000i −1.46059 + 0.730297i
\(481\) 14.0000 0.638345
\(482\) 12.0000i 0.546585i
\(483\) 2.00000i 0.0910032i
\(484\) 22.0000 1.00000
\(485\) −14.0000 28.0000i −0.635707 1.27141i
\(486\) −20.0000 −0.907218
\(487\) 32.0000i 1.45006i 0.688718 + 0.725029i \(0.258174\pi\)
−0.688718 + 0.725029i \(0.741826\pi\)
\(488\) 0 0
\(489\) −48.0000 −2.17064
\(490\) −12.0000 24.0000i −0.542105 1.08421i
\(491\) −31.0000 −1.39901 −0.699505 0.714628i \(-0.746596\pi\)
−0.699505 + 0.714628i \(0.746596\pi\)
\(492\) 28.0000i 1.26234i
\(493\) 25.0000i 1.12594i
\(494\) −32.0000 −1.43975
\(495\) 0 0
\(496\) 20.0000 0.898027
\(497\) 13.0000i 0.583130i
\(498\) 12.0000i 0.537733i
\(499\) 11.0000 0.492428 0.246214 0.969216i \(-0.420813\pi\)
0.246214 + 0.969216i \(0.420813\pi\)
\(500\) −4.00000 + 22.0000i −0.178885 + 0.983870i
\(501\) 32.0000 1.42965
\(502\) 36.0000i 1.60676i
\(503\) 9.00000i 0.401290i −0.979664 0.200645i \(-0.935696\pi\)
0.979664 0.200645i \(-0.0643038\pi\)
\(504\) 0 0
\(505\) 30.0000 15.0000i 1.33498 0.667491i
\(506\) 0 0
\(507\) 18.0000i 0.799408i
\(508\) 40.0000i 1.77471i
\(509\) −26.0000 −1.15243 −0.576215 0.817298i \(-0.695471\pi\)
−0.576215 + 0.817298i \(0.695471\pi\)
\(510\) 20.0000 + 40.0000i 0.885615 + 1.77123i
\(511\) 8.00000 0.353899
\(512\) 32.0000i 1.41421i
\(513\) 32.0000i 1.41283i
\(514\) −44.0000 −1.94076
\(515\) 0 0
\(516\) 16.0000 0.704361
\(517\) 0 0
\(518\) 14.0000i 0.615125i
\(519\) −12.0000 −0.526742
\(520\) 0 0
\(521\) −20.0000 −0.876216 −0.438108 0.898922i \(-0.644351\pi\)
−0.438108 + 0.898922i \(0.644351\pi\)
\(522\) 10.0000i 0.437688i
\(523\) 28.0000i 1.22435i −0.790721 0.612177i \(-0.790294\pi\)
0.790721 0.612177i \(-0.209706\pi\)
\(524\) 0 0
\(525\) 6.00000 8.00000i 0.261861 0.349149i
\(526\) −26.0000 −1.13365
\(527\) 25.0000i 1.08902i
\(528\) 0 0
\(529\) −1.00000 −0.0434783
\(530\) −4.00000 + 2.00000i −0.173749 + 0.0868744i
\(531\) 3.00000 0.130189
\(532\) 16.0000i 0.693688i
\(533\) 14.0000i 0.606407i
\(534\) 56.0000 2.42336
\(535\) −9.00000 18.0000i −0.389104 0.778208i
\(536\) 0 0
\(537\) 8.00000i 0.345225i
\(538\) 30.0000i 1.29339i
\(539\) 0 0
\(540\) −8.00000 16.0000i −0.344265 0.688530i
\(541\) 14.0000 0.601907 0.300954 0.953639i \(-0.402695\pi\)
0.300954 + 0.953639i \(0.402695\pi\)
\(542\) 30.0000i 1.28861i
\(543\) 28.0000i 1.20160i
\(544\) −40.0000 −1.71499
\(545\) −36.0000 + 18.0000i −1.54207 + 0.771035i
\(546\) 8.00000 0.342368
\(547\) 4.00000i 0.171028i 0.996337 + 0.0855138i \(0.0272532\pi\)
−0.996337 + 0.0855138i \(0.972747\pi\)
\(548\) 12.0000i 0.512615i
\(549\) 6.00000 0.256074
\(550\) 0 0
\(551\) −40.0000 −1.70406
\(552\) 0 0
\(553\) 14.0000i 0.595341i
\(554\) 52.0000 2.20927
\(555\) 28.0000 14.0000i 1.18853 0.594267i
\(556\) 18.0000 0.763370
\(557\) 33.0000i 1.39825i 0.714997 + 0.699127i \(0.246428\pi\)
−0.714997 + 0.699127i \(0.753572\pi\)
\(558\) 10.0000i 0.423334i
\(559\) −8.00000 −0.338364
\(560\) 4.00000 + 8.00000i 0.169031 + 0.338062i
\(561\) 0 0
\(562\) 24.0000i 1.01238i
\(563\) 25.0000i 1.05362i −0.849982 0.526812i \(-0.823387\pi\)
0.849982 0.526812i \(-0.176613\pi\)
\(564\) 8.00000 0.336861
\(565\) −1.00000 2.00000i −0.0420703 0.0841406i
\(566\) 22.0000 0.924729
\(567\) 11.0000i 0.461957i
\(568\) 0 0
\(569\) 12.0000 0.503066 0.251533 0.967849i \(-0.419065\pi\)
0.251533 + 0.967849i \(0.419065\pi\)
\(570\) −64.0000 + 32.0000i −2.68067 + 1.34033i
\(571\) 18.0000 0.753277 0.376638 0.926360i \(-0.377080\pi\)
0.376638 + 0.926360i \(0.377080\pi\)
\(572\) 0 0
\(573\) 16.0000i 0.668410i
\(574\) 14.0000 0.584349
\(575\) −4.00000 3.00000i −0.166812 0.125109i
\(576\) −8.00000 −0.333333
\(577\) 22.0000i 0.915872i −0.888985 0.457936i \(-0.848589\pi\)
0.888985 0.457936i \(-0.151411\pi\)
\(578\) 16.0000i 0.665512i
\(579\) 24.0000 0.997406
\(580\) −20.0000 + 10.0000i −0.830455 + 0.415227i
\(581\) −3.00000 −0.124461
\(582\) 56.0000i 2.32127i
\(583\) 0 0
\(584\) 0 0
\(585\) −2.00000 4.00000i −0.0826898 0.165380i
\(586\) 58.0000 2.39596
\(587\) 12.0000i 0.495293i 0.968850 + 0.247647i \(0.0796572\pi\)
−0.968850 + 0.247647i \(0.920343\pi\)
\(588\) 24.0000i 0.989743i
\(589\) 40.0000 1.64817
\(590\) 6.00000 + 12.0000i 0.247016 + 0.494032i
\(591\) 0 0
\(592\) 28.0000i 1.15079i
\(593\) 30.0000i 1.23195i 0.787765 + 0.615976i \(0.211238\pi\)
−0.787765 + 0.615976i \(0.788762\pi\)
\(594\) 0 0
\(595\) 10.0000 5.00000i 0.409960 0.204980i
\(596\) 0 0
\(597\) 4.00000i 0.163709i
\(598\) 4.00000i 0.163572i
\(599\) 48.0000 1.96123 0.980613 0.195952i \(-0.0627798\pi\)
0.980613 + 0.195952i \(0.0627798\pi\)
\(600\) 0 0
\(601\) −25.0000 −1.01977 −0.509886 0.860242i \(-0.670312\pi\)
−0.509886 + 0.860242i \(0.670312\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 13.0000i 0.529401i
\(604\) −16.0000 −0.651031
\(605\) −22.0000 + 11.0000i −0.894427 + 0.447214i
\(606\) 60.0000 2.43733
\(607\) 38.0000i 1.54237i 0.636610 + 0.771186i \(0.280336\pi\)
−0.636610 + 0.771186i \(0.719664\pi\)
\(608\) 64.0000i 2.59554i
\(609\) 10.0000 0.405220
\(610\) 12.0000 + 24.0000i 0.485866 + 0.971732i
\(611\) −4.00000 −0.161823
\(612\) 10.0000i 0.404226i
\(613\) 6.00000i 0.242338i 0.992632 + 0.121169i \(0.0386643\pi\)
−0.992632 + 0.121169i \(0.961336\pi\)
\(614\) −28.0000 −1.12999
\(615\) −14.0000 28.0000i −0.564534 1.12907i
\(616\) 0 0
\(617\) 47.0000i 1.89215i 0.323949 + 0.946074i \(0.394989\pi\)
−0.323949 + 0.946074i \(0.605011\pi\)
\(618\) 0 0
\(619\) 10.0000 0.401934 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(620\) 20.0000 10.0000i 0.803219 0.401610i
\(621\) 4.00000 0.160514
\(622\) 8.00000i 0.320771i
\(623\) 14.0000i 0.560898i
\(624\) 16.0000 0.640513
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 42.0000 1.67866
\(627\) 0 0
\(628\) 6.00000i 0.239426i
\(629\) 35.0000 1.39554
\(630\) 4.00000 2.00000i 0.159364 0.0796819i
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 0 0
\(633\) 18.0000i 0.715436i
\(634\) 48.0000 1.90632
\(635\) 20.0000 + 40.0000i 0.793676 + 1.58735i
\(636\) −4.00000 −0.158610
\(637\) 12.0000i 0.475457i
\(638\) 0 0
\(639\) −13.0000 −0.514272
\(640\) 0 0
\(641\) −24.0000 −0.947943 −0.473972 0.880540i \(-0.657180\pi\)
−0.473972 + 0.880540i \(0.657180\pi\)
\(642\) 36.0000i 1.42081i
\(643\) 37.0000i 1.45914i 0.683907 + 0.729569i \(0.260279\pi\)
−0.683907 + 0.729569i \(0.739721\pi\)
\(644\) 2.00000 0.0788110
\(645\) −16.0000 + 8.00000i −0.629999 + 0.315000i
\(646\) −80.0000 −3.14756
\(647\) 18.0000i 0.707653i 0.935311 + 0.353827i \(0.115120\pi\)
−0.935311 + 0.353827i \(0.884880\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 12.0000 16.0000i 0.470679 0.627572i
\(651\) −10.0000 −0.391931
\(652\) 48.0000i 1.87983i
\(653\) 2.00000i 0.0782660i 0.999234 + 0.0391330i \(0.0124596\pi\)
−0.999234 + 0.0391330i \(0.987540\pi\)
\(654\) −72.0000 −2.81542
\(655\) 0 0
\(656\) 28.0000 1.09322
\(657\) 8.00000i 0.312110i
\(658\) 4.00000i 0.155936i
\(659\) −22.0000 −0.856998 −0.428499 0.903542i \(-0.640958\pi\)
−0.428499 + 0.903542i \(0.640958\pi\)
\(660\) 0 0
\(661\) −16.0000 −0.622328 −0.311164 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) 10.0000i 0.388661i
\(663\) 20.0000i 0.776736i
\(664\) 0 0
\(665\) 8.00000 + 16.0000i 0.310227 + 0.620453i
\(666\) 14.0000 0.542489
\(667\) 5.00000i 0.193601i
\(668\) 32.0000i 1.23812i
\(669\) 28.0000 1.08254
\(670\) −52.0000 + 26.0000i −2.00894 + 1.00447i
\(671\) 0 0
\(672\) 16.0000i 0.617213i
\(673\) 24.0000i 0.925132i 0.886585 + 0.462566i \(0.153071\pi\)
−0.886585 + 0.462566i \(0.846929\pi\)
\(674\) −52.0000 −2.00297
\(675\) 16.0000 + 12.0000i 0.615840 + 0.461880i
\(676\) −18.0000 −0.692308
\(677\) 3.00000i 0.115299i 0.998337 + 0.0576497i \(0.0183606\pi\)
−0.998337 + 0.0576497i \(0.981639\pi\)
\(678\) 4.00000i 0.153619i
\(679\) −14.0000 −0.537271
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 46.0000i 1.76014i 0.474843 + 0.880071i \(0.342505\pi\)
−0.474843 + 0.880071i \(0.657495\pi\)
\(684\) −16.0000 −0.611775
\(685\) −6.00000 12.0000i −0.229248 0.458496i
\(686\) −26.0000 −0.992685
\(687\) 8.00000i 0.305219i
\(688\) 16.0000i 0.609994i
\(689\) 2.00000 0.0761939
\(690\) −4.00000 8.00000i −0.152277 0.304555i
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 12.0000i 0.456172i
\(693\) 0 0
\(694\) −16.0000 −0.607352
\(695\) −18.0000 + 9.00000i −0.682779 + 0.341389i
\(696\) 0 0
\(697\) 35.0000i 1.32572i
\(698\) 46.0000i 1.74113i
\(699\) −12.0000 −0.453882
\(700\) 8.00000 + 6.00000i 0.302372 + 0.226779i
\(701\) −28.0000 −1.05755 −0.528773 0.848763i \(-0.677348\pi\)
−0.528773 + 0.848763i \(0.677348\pi\)
\(702\) 16.0000i 0.603881i
\(703\) 56.0000i 2.11208i
\(704\) 0 0
\(705\) −8.00000 + 4.00000i −0.301297 + 0.150649i
\(706\) 0 0
\(707\) 15.0000i 0.564133i
\(708\) 12.0000i 0.450988i
\(709\) −4.00000 −0.150223 −0.0751116 0.997175i \(-0.523931\pi\)
−0.0751116 + 0.997175i \(0.523931\pi\)
\(710\) −26.0000 52.0000i −0.975763 1.95153i
\(711\) −14.0000 −0.525041
\(712\) 0 0
\(713\) 5.00000i 0.187251i
\(714\) 20.0000 0.748481
\(715\) 0 0
\(716\) −8.00000 −0.298974
\(717\) 2.00000i 0.0746914i
\(718\) 12.0000i 0.447836i
\(719\) 45.0000 1.67822 0.839108 0.543964i \(-0.183077\pi\)
0.839108 + 0.543964i \(0.183077\pi\)
\(720\) 8.00000 4.00000i 0.298142 0.149071i
\(721\) 0 0
\(722\) 90.0000i 3.34945i
\(723\) 12.0000i 0.446285i
\(724\) 28.0000 1.04061
\(725\) 15.0000 20.0000i 0.557086 0.742781i
\(726\) −44.0000 −1.63299
\(727\) 27.0000i 1.00137i −0.865628 0.500687i \(-0.833081\pi\)
0.865628 0.500687i \(-0.166919\pi\)
\(728\) 0 0
\(729\) −13.0000 −0.481481
\(730\) 32.0000 16.0000i 1.18437 0.592187i
\(731\) −20.0000 −0.739727
\(732\) 24.0000i 0.887066i
\(733\) 7.00000i 0.258551i 0.991609 + 0.129275i \(0.0412651\pi\)
−0.991609 + 0.129275i \(0.958735\pi\)
\(734\) 26.0000 0.959678
\(735\) 12.0000 + 24.0000i 0.442627 + 0.885253i
\(736\) 8.00000 0.294884
\(737\) 0 0
\(738\) 14.0000i 0.515347i
\(739\) −7.00000 −0.257499 −0.128750 0.991677i \(-0.541096\pi\)
−0.128750 + 0.991677i \(0.541096\pi\)
\(740\) 14.0000 + 28.0000i 0.514650 + 1.02930i
\(741\) 32.0000 1.17555
\(742\) 2.00000i 0.0734223i
\(743\) 32.0000i 1.17397i −0.809599 0.586983i \(-0.800316\pi\)
0.809599 0.586983i \(-0.199684\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −12.0000 −0.439351
\(747\) 3.00000i 0.109764i
\(748\) 0 0
\(749\) −9.00000 −0.328853
\(750\) 8.00000 44.0000i 0.292119 1.60665i
\(751\) 14.0000 0.510867 0.255434 0.966827i \(-0.417782\pi\)
0.255434 + 0.966827i \(0.417782\pi\)
\(752\) 8.00000i 0.291730i
\(753\) 36.0000i 1.31191i
\(754\) 20.0000 0.728357
\(755\) 16.0000 8.00000i 0.582300 0.291150i
\(756\) −8.00000 −0.290957
\(757\) 35.0000i 1.27210i 0.771649 + 0.636048i \(0.219432\pi\)
−0.771649 + 0.636048i \(0.780568\pi\)
\(758\) 12.0000i 0.435860i
\(759\) 0 0
\(760\) 0 0
\(761\) 25.0000 0.906249 0.453125 0.891447i \(-0.350309\pi\)
0.453125 + 0.891447i \(0.350309\pi\)
\(762\) 80.0000i 2.89809i
\(763\) 18.0000i 0.651644i
\(764\) 16.0000 0.578860
\(765\) −5.00000 10.0000i −0.180775 0.361551i
\(766\) 6.00000 0.216789
\(767\) 6.00000i 0.216647i
\(768\) 32.0000i 1.15470i
\(769\) −10.0000 −0.360609 −0.180305 0.983611i \(-0.557708\pi\)
−0.180305 + 0.983611i \(0.557708\pi\)
\(770\) 0 0
\(771\) 44.0000 1.58462
\(772\) 24.0000i 0.863779i
\(773\) 42.0000i 1.51064i −0.655359 0.755318i \(-0.727483\pi\)
0.655359 0.755318i \(-0.272517\pi\)
\(774\) −8.00000 −0.287554
\(775\) −15.0000 + 20.0000i −0.538816 + 0.718421i
\(776\) 0 0
\(777\) 14.0000i 0.502247i
\(778\) 44.0000i 1.57748i
\(779\) 56.0000 2.00641
\(780\) 16.0000 8.00000i 0.572892 0.286446i
\(781\) 0 0
\(782\) 10.0000i 0.357599i
\(783\) 20.0000i 0.714742i
\(784\) −24.0000 −0.857143
\(785\) 3.00000 + 6.00000i 0.107075 + 0.214149i
\(786\) 0 0
\(787\) 17.0000i 0.605985i −0.952993 0.302992i \(-0.902014\pi\)
0.952993 0.302992i \(-0.0979856\pi\)
\(788\) 0 0
\(789\) 26.0000 0.925625
\(790\)