Properties

Label 570.2.d.a.229.1
Level $570$
Weight $2$
Character 570.229
Analytic conductor $4.551$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
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 229.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 570.229
Dual form 570.2.d.a.229.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -1.00000 q^{6} +1.00000i q^{8} -1.00000 q^{9} +(2.00000 + 1.00000i) q^{10} -4.00000 q^{11} +1.00000i q^{12} +2.00000i q^{13} +(2.00000 + 1.00000i) q^{15} +1.00000 q^{16} +6.00000i q^{17} +1.00000i q^{18} +1.00000 q^{19} +(1.00000 - 2.00000i) q^{20} +4.00000i q^{22} +6.00000i q^{23} +1.00000 q^{24} +(-3.00000 - 4.00000i) q^{25} +2.00000 q^{26} +1.00000i q^{27} +2.00000 q^{29} +(1.00000 - 2.00000i) q^{30} -6.00000 q^{31} -1.00000i q^{32} +4.00000i q^{33} +6.00000 q^{34} +1.00000 q^{36} +10.0000i q^{37} -1.00000i q^{38} +2.00000 q^{39} +(-2.00000 - 1.00000i) q^{40} -6.00000i q^{43} +4.00000 q^{44} +(1.00000 - 2.00000i) q^{45} +6.00000 q^{46} -6.00000i q^{47} -1.00000i q^{48} +7.00000 q^{49} +(-4.00000 + 3.00000i) q^{50} +6.00000 q^{51} -2.00000i q^{52} +10.0000i q^{53} +1.00000 q^{54} +(4.00000 - 8.00000i) q^{55} -1.00000i q^{57} -2.00000i q^{58} -2.00000 q^{59} +(-2.00000 - 1.00000i) q^{60} -6.00000 q^{61} +6.00000i q^{62} -1.00000 q^{64} +(-4.00000 - 2.00000i) q^{65} +4.00000 q^{66} -8.00000i q^{67} -6.00000i q^{68} +6.00000 q^{69} -12.0000 q^{71} -1.00000i q^{72} -16.0000i q^{73} +10.0000 q^{74} +(-4.00000 + 3.00000i) q^{75} -1.00000 q^{76} -2.00000i q^{78} +14.0000 q^{79} +(-1.00000 + 2.00000i) q^{80} +1.00000 q^{81} +12.0000i q^{83} +(-12.0000 - 6.00000i) q^{85} -6.00000 q^{86} -2.00000i q^{87} -4.00000i q^{88} -4.00000 q^{89} +(-2.00000 - 1.00000i) q^{90} -6.00000i q^{92} +6.00000i q^{93} -6.00000 q^{94} +(-1.00000 + 2.00000i) q^{95} -1.00000 q^{96} +10.0000i q^{97} -7.00000i q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 2q^{4} - 2q^{5} - 2q^{6} - 2q^{9} + O(q^{10}) \) \( 2q - 2q^{4} - 2q^{5} - 2q^{6} - 2q^{9} + 4q^{10} - 8q^{11} + 4q^{15} + 2q^{16} + 2q^{19} + 2q^{20} + 2q^{24} - 6q^{25} + 4q^{26} + 4q^{29} + 2q^{30} - 12q^{31} + 12q^{34} + 2q^{36} + 4q^{39} - 4q^{40} + 8q^{44} + 2q^{45} + 12q^{46} + 14q^{49} - 8q^{50} + 12q^{51} + 2q^{54} + 8q^{55} - 4q^{59} - 4q^{60} - 12q^{61} - 2q^{64} - 8q^{65} + 8q^{66} + 12q^{69} - 24q^{71} + 20q^{74} - 8q^{75} - 2q^{76} + 28q^{79} - 2q^{80} + 2q^{81} - 24q^{85} - 12q^{86} - 8q^{89} - 4q^{90} - 12q^{94} - 2q^{95} - 2q^{96} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) −1.00000 −0.408248
\(7\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 2.00000 + 1.00000i 0.632456 + 0.316228i
\(11\) −4.00000 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 2.00000i 0.554700i 0.960769 + 0.277350i \(0.0894562\pi\)
−0.960769 + 0.277350i \(0.910544\pi\)
\(14\) 0 0
\(15\) 2.00000 + 1.00000i 0.516398 + 0.258199i
\(16\) 1.00000 0.250000
\(17\) 6.00000i 1.45521i 0.685994 + 0.727607i \(0.259367\pi\)
−0.685994 + 0.727607i \(0.740633\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 1.00000 0.229416
\(20\) 1.00000 2.00000i 0.223607 0.447214i
\(21\) 0 0
\(22\) 4.00000i 0.852803i
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 1.00000 0.204124
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 2.00000 0.392232
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 1.00000 2.00000i 0.182574 0.365148i
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 4.00000i 0.696311i
\(34\) 6.00000 1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 10.0000i 1.64399i 0.569495 + 0.821995i \(0.307139\pi\)
−0.569495 + 0.821995i \(0.692861\pi\)
\(38\) 1.00000i 0.162221i
\(39\) 2.00000 0.320256
\(40\) −2.00000 1.00000i −0.316228 0.158114i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 6.00000i 0.914991i −0.889212 0.457496i \(-0.848747\pi\)
0.889212 0.457496i \(-0.151253\pi\)
\(44\) 4.00000 0.603023
\(45\) 1.00000 2.00000i 0.149071 0.298142i
\(46\) 6.00000 0.884652
\(47\) 6.00000i 0.875190i −0.899172 0.437595i \(-0.855830\pi\)
0.899172 0.437595i \(-0.144170\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 7.00000 1.00000
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 6.00000 0.840168
\(52\) 2.00000i 0.277350i
\(53\) 10.0000i 1.37361i 0.726844 + 0.686803i \(0.240986\pi\)
−0.726844 + 0.686803i \(0.759014\pi\)
\(54\) 1.00000 0.136083
\(55\) 4.00000 8.00000i 0.539360 1.07872i
\(56\) 0 0
\(57\) 1.00000i 0.132453i
\(58\) 2.00000i 0.262613i
\(59\) −2.00000 −0.260378 −0.130189 0.991489i \(-0.541558\pi\)
−0.130189 + 0.991489i \(0.541558\pi\)
\(60\) −2.00000 1.00000i −0.258199 0.129099i
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 6.00000i 0.762001i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −4.00000 2.00000i −0.496139 0.248069i
\(66\) 4.00000 0.492366
\(67\) 8.00000i 0.977356i −0.872464 0.488678i \(-0.837479\pi\)
0.872464 0.488678i \(-0.162521\pi\)
\(68\) 6.00000i 0.727607i
\(69\) 6.00000 0.722315
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 16.0000i 1.87266i −0.351123 0.936329i \(-0.614200\pi\)
0.351123 0.936329i \(-0.385800\pi\)
\(74\) 10.0000 1.16248
\(75\) −4.00000 + 3.00000i −0.461880 + 0.346410i
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 2.00000i 0.226455i
\(79\) 14.0000 1.57512 0.787562 0.616236i \(-0.211343\pi\)
0.787562 + 0.616236i \(0.211343\pi\)
\(80\) −1.00000 + 2.00000i −0.111803 + 0.223607i
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.0000i 1.31717i 0.752506 + 0.658586i \(0.228845\pi\)
−0.752506 + 0.658586i \(0.771155\pi\)
\(84\) 0 0
\(85\) −12.0000 6.00000i −1.30158 0.650791i
\(86\) −6.00000 −0.646997
\(87\) 2.00000i 0.214423i
\(88\) 4.00000i 0.426401i
\(89\) −4.00000 −0.423999 −0.212000 0.977270i \(-0.567998\pi\)
−0.212000 + 0.977270i \(0.567998\pi\)
\(90\) −2.00000 1.00000i −0.210819 0.105409i
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) 6.00000i 0.622171i
\(94\) −6.00000 −0.618853
\(95\) −1.00000 + 2.00000i −0.102598 + 0.205196i
\(96\) −1.00000 −0.102062
\(97\) 10.0000i 1.01535i 0.861550 + 0.507673i \(0.169494\pi\)
−0.861550 + 0.507673i \(0.830506\pi\)
\(98\) 7.00000i 0.707107i
\(99\) 4.00000 0.402015
\(100\) 3.00000 + 4.00000i 0.300000 + 0.400000i
\(101\) −18.0000 −1.79107 −0.895533 0.444994i \(-0.853206\pi\)
−0.895533 + 0.444994i \(0.853206\pi\)
\(102\) 6.00000i 0.594089i
\(103\) 8.00000i 0.788263i 0.919054 + 0.394132i \(0.128955\pi\)
−0.919054 + 0.394132i \(0.871045\pi\)
\(104\) −2.00000 −0.196116
\(105\) 0 0
\(106\) 10.0000 0.971286
\(107\) 4.00000i 0.386695i 0.981130 + 0.193347i \(0.0619344\pi\)
−0.981130 + 0.193347i \(0.938066\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) −8.00000 4.00000i −0.762770 0.381385i
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) 2.00000i 0.188144i 0.995565 + 0.0940721i \(0.0299884\pi\)
−0.995565 + 0.0940721i \(0.970012\pi\)
\(114\) −1.00000 −0.0936586
\(115\) −12.0000 6.00000i −1.11901 0.559503i
\(116\) −2.00000 −0.185695
\(117\) 2.00000i 0.184900i
\(118\) 2.00000i 0.184115i
\(119\) 0 0
\(120\) −1.00000 + 2.00000i −0.0912871 + 0.182574i
\(121\) 5.00000 0.454545
\(122\) 6.00000i 0.543214i
\(123\) 0 0
\(124\) 6.00000 0.538816
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 8.00000i 0.709885i −0.934888 0.354943i \(-0.884500\pi\)
0.934888 0.354943i \(-0.115500\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −6.00000 −0.528271
\(130\) −2.00000 + 4.00000i −0.175412 + 0.350823i
\(131\) −8.00000 −0.698963 −0.349482 0.936943i \(-0.613642\pi\)
−0.349482 + 0.936943i \(0.613642\pi\)
\(132\) 4.00000i 0.348155i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) −2.00000 1.00000i −0.172133 0.0860663i
\(136\) −6.00000 −0.514496
\(137\) 6.00000i 0.512615i −0.966595 0.256307i \(-0.917494\pi\)
0.966595 0.256307i \(-0.0825059\pi\)
\(138\) 6.00000i 0.510754i
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 12.0000i 1.00702i
\(143\) 8.00000i 0.668994i
\(144\) −1.00000 −0.0833333
\(145\) −2.00000 + 4.00000i −0.166091 + 0.332182i
\(146\) −16.0000 −1.32417
\(147\) 7.00000i 0.577350i
\(148\) 10.0000i 0.821995i
\(149\) 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
\(151\) 10.0000 0.813788 0.406894 0.913475i \(-0.366612\pi\)
0.406894 + 0.913475i \(0.366612\pi\)
\(152\) 1.00000i 0.0811107i
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 6.00000 12.0000i 0.481932 0.963863i
\(156\) −2.00000 −0.160128
\(157\) 18.0000i 1.43656i 0.695756 + 0.718278i \(0.255069\pi\)
−0.695756 + 0.718278i \(0.744931\pi\)
\(158\) 14.0000i 1.11378i
\(159\) 10.0000 0.793052
\(160\) 2.00000 + 1.00000i 0.158114 + 0.0790569i
\(161\) 0 0
\(162\) 1.00000i 0.0785674i
\(163\) 10.0000i 0.783260i −0.920123 0.391630i \(-0.871911\pi\)
0.920123 0.391630i \(-0.128089\pi\)
\(164\) 0 0
\(165\) −8.00000 4.00000i −0.622799 0.311400i
\(166\) 12.0000 0.931381
\(167\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) −6.00000 + 12.0000i −0.460179 + 0.920358i
\(171\) −1.00000 −0.0764719
\(172\) 6.00000i 0.457496i
\(173\) 14.0000i 1.06440i −0.846619 0.532200i \(-0.821365\pi\)
0.846619 0.532200i \(-0.178635\pi\)
\(174\) −2.00000 −0.151620
\(175\) 0 0
\(176\) −4.00000 −0.301511
\(177\) 2.00000i 0.150329i
\(178\) 4.00000i 0.299813i
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) −1.00000 + 2.00000i −0.0745356 + 0.149071i
\(181\) −4.00000 −0.297318 −0.148659 0.988889i \(-0.547496\pi\)
−0.148659 + 0.988889i \(0.547496\pi\)
\(182\) 0 0
\(183\) 6.00000i 0.443533i
\(184\) −6.00000 −0.442326
\(185\) −20.0000 10.0000i −1.47043 0.735215i
\(186\) 6.00000 0.439941
\(187\) 24.0000i 1.75505i
\(188\) 6.00000i 0.437595i
\(189\) 0 0
\(190\) 2.00000 + 1.00000i 0.145095 + 0.0725476i
\(191\) 24.0000 1.73658 0.868290 0.496058i \(-0.165220\pi\)
0.868290 + 0.496058i \(0.165220\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 14.0000i 1.00774i 0.863779 + 0.503871i \(0.168091\pi\)
−0.863779 + 0.503871i \(0.831909\pi\)
\(194\) 10.0000 0.717958
\(195\) −2.00000 + 4.00000i −0.143223 + 0.286446i
\(196\) −7.00000 −0.500000
\(197\) 8.00000i 0.569976i −0.958531 0.284988i \(-0.908010\pi\)
0.958531 0.284988i \(-0.0919897\pi\)
\(198\) 4.00000i 0.284268i
\(199\) 16.0000 1.13421 0.567105 0.823646i \(-0.308063\pi\)
0.567105 + 0.823646i \(0.308063\pi\)
\(200\) 4.00000 3.00000i 0.282843 0.212132i
\(201\) −8.00000 −0.564276
\(202\) 18.0000i 1.26648i
\(203\) 0 0
\(204\) −6.00000 −0.420084
\(205\) 0 0
\(206\) 8.00000 0.557386
\(207\) 6.00000i 0.417029i
\(208\) 2.00000i 0.138675i
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 10.0000i 0.686803i
\(213\) 12.0000i 0.822226i
\(214\) 4.00000 0.273434
\(215\) 12.0000 + 6.00000i 0.818393 + 0.409197i
\(216\) −1.00000 −0.0680414
\(217\) 0 0
\(218\) 4.00000i 0.270914i
\(219\) −16.0000 −1.08118
\(220\) −4.00000 + 8.00000i −0.269680 + 0.539360i
\(221\) −12.0000 −0.807207
\(222\) 10.0000i 0.671156i
\(223\) 8.00000i 0.535720i −0.963458 0.267860i \(-0.913684\pi\)
0.963458 0.267860i \(-0.0863164\pi\)
\(224\) 0 0
\(225\) 3.00000 + 4.00000i 0.200000 + 0.266667i
\(226\) 2.00000 0.133038
\(227\) 12.0000i 0.796468i 0.917284 + 0.398234i \(0.130377\pi\)
−0.917284 + 0.398234i \(0.869623\pi\)
\(228\) 1.00000i 0.0662266i
\(229\) 10.0000 0.660819 0.330409 0.943838i \(-0.392813\pi\)
0.330409 + 0.943838i \(0.392813\pi\)
\(230\) −6.00000 + 12.0000i −0.395628 + 0.791257i
\(231\) 0 0
\(232\) 2.00000i 0.131306i
\(233\) 14.0000i 0.917170i 0.888650 + 0.458585i \(0.151644\pi\)
−0.888650 + 0.458585i \(0.848356\pi\)
\(234\) −2.00000 −0.130744
\(235\) 12.0000 + 6.00000i 0.782794 + 0.391397i
\(236\) 2.00000 0.130189
\(237\) 14.0000i 0.909398i
\(238\) 0 0
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 2.00000 + 1.00000i 0.129099 + 0.0645497i
\(241\) −10.0000 −0.644157 −0.322078 0.946713i \(-0.604381\pi\)
−0.322078 + 0.946713i \(0.604381\pi\)
\(242\) 5.00000i 0.321412i
\(243\) 1.00000i 0.0641500i
\(244\) 6.00000 0.384111
\(245\) −7.00000 + 14.0000i −0.447214 + 0.894427i
\(246\) 0 0
\(247\) 2.00000i 0.127257i
\(248\) 6.00000i 0.381000i
\(249\) 12.0000 0.760469
\(250\) −2.00000 11.0000i −0.126491 0.695701i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 24.0000i 1.50887i
\(254\) −8.00000 −0.501965
\(255\) −6.00000 + 12.0000i −0.375735 + 0.751469i
\(256\) 1.00000 0.0625000
\(257\) 22.0000i 1.37232i −0.727450 0.686161i \(-0.759294\pi\)
0.727450 0.686161i \(-0.240706\pi\)
\(258\) 6.00000i 0.373544i
\(259\) 0 0
\(260\) 4.00000 + 2.00000i 0.248069 + 0.124035i
\(261\) −2.00000 −0.123797
\(262\) 8.00000i 0.494242i
\(263\) 2.00000i 0.123325i −0.998097 0.0616626i \(-0.980360\pi\)
0.998097 0.0616626i \(-0.0196403\pi\)
\(264\) −4.00000 −0.246183
\(265\) −20.0000 10.0000i −1.22859 0.614295i
\(266\) 0 0
\(267\) 4.00000i 0.244796i
\(268\) 8.00000i 0.488678i
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) −1.00000 + 2.00000i −0.0608581 + 0.121716i
\(271\) 32.0000 1.94386 0.971931 0.235267i \(-0.0755965\pi\)
0.971931 + 0.235267i \(0.0755965\pi\)
\(272\) 6.00000i 0.363803i
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) 12.0000 + 16.0000i 0.723627 + 0.964836i
\(276\) −6.00000 −0.361158
\(277\) 26.0000i 1.56219i 0.624413 + 0.781094i \(0.285338\pi\)
−0.624413 + 0.781094i \(0.714662\pi\)
\(278\) 12.0000i 0.719712i
\(279\) 6.00000 0.359211
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 6.00000i 0.357295i
\(283\) 22.0000i 1.30776i 0.756596 + 0.653882i \(0.226861\pi\)
−0.756596 + 0.653882i \(0.773139\pi\)
\(284\) 12.0000 0.712069
\(285\) 2.00000 + 1.00000i 0.118470 + 0.0592349i
\(286\) −8.00000 −0.473050
\(287\) 0 0
\(288\) 1.00000i 0.0589256i
\(289\) −19.0000 −1.11765
\(290\) 4.00000 + 2.00000i 0.234888 + 0.117444i
\(291\) 10.0000 0.586210
\(292\) 16.0000i 0.936329i
\(293\) 2.00000i 0.116841i 0.998292 + 0.0584206i \(0.0186065\pi\)
−0.998292 + 0.0584206i \(0.981394\pi\)
\(294\) −7.00000 −0.408248
\(295\) 2.00000 4.00000i 0.116445 0.232889i
\(296\) −10.0000 −0.581238
\(297\) 4.00000i 0.232104i
\(298\) 6.00000i 0.347571i
\(299\) −12.0000 −0.693978
\(300\) 4.00000 3.00000i 0.230940 0.173205i
\(301\) 0 0
\(302\) 10.0000i 0.575435i
\(303\) 18.0000i 1.03407i
\(304\) 1.00000 0.0573539
\(305\) 6.00000 12.0000i 0.343559 0.687118i
\(306\) −6.00000 −0.342997
\(307\) 12.0000i 0.684876i 0.939540 + 0.342438i \(0.111253\pi\)
−0.939540 + 0.342438i \(0.888747\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) −12.0000 6.00000i −0.681554 0.340777i
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 2.00000i 0.113228i
\(313\) 28.0000i 1.58265i 0.611393 + 0.791327i \(0.290609\pi\)
−0.611393 + 0.791327i \(0.709391\pi\)
\(314\) 18.0000 1.01580
\(315\) 0 0
\(316\) −14.0000 −0.787562
\(317\) 6.00000i 0.336994i −0.985702 0.168497i \(-0.946109\pi\)
0.985702 0.168497i \(-0.0538913\pi\)
\(318\) 10.0000i 0.560772i
\(319\) −8.00000 −0.447914
\(320\) 1.00000 2.00000i 0.0559017 0.111803i
\(321\) 4.00000 0.223258
\(322\) 0 0
\(323\) 6.00000i 0.333849i
\(324\) −1.00000 −0.0555556
\(325\) 8.00000 6.00000i 0.443760 0.332820i
\(326\) −10.0000 −0.553849
\(327\) 4.00000i 0.221201i
\(328\) 0 0
\(329\) 0 0
\(330\) −4.00000 + 8.00000i −0.220193 + 0.440386i
\(331\) −4.00000 −0.219860 −0.109930 0.993939i \(-0.535063\pi\)
−0.109930 + 0.993939i \(0.535063\pi\)
\(332\) 12.0000i 0.658586i
\(333\) 10.0000i 0.547997i
\(334\) 0 0
\(335\) 16.0000 + 8.00000i 0.874173 + 0.437087i
\(336\) 0 0
\(337\) 6.00000i 0.326841i −0.986557 0.163420i \(-0.947747\pi\)
0.986557 0.163420i \(-0.0522527\pi\)
\(338\) 9.00000i 0.489535i
\(339\) 2.00000 0.108625
\(340\) 12.0000 + 6.00000i 0.650791 + 0.325396i
\(341\) 24.0000 1.29967
\(342\) 1.00000i 0.0540738i
\(343\) 0 0
\(344\) 6.00000 0.323498
\(345\) −6.00000 + 12.0000i −0.323029 + 0.646058i
\(346\) −14.0000 −0.752645
\(347\) 20.0000i 1.07366i −0.843692 0.536828i \(-0.819622\pi\)
0.843692 0.536828i \(-0.180378\pi\)
\(348\) 2.00000i 0.107211i
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) −2.00000 −0.106752
\(352\) 4.00000i 0.213201i
\(353\) 2.00000i 0.106449i −0.998583 0.0532246i \(-0.983050\pi\)
0.998583 0.0532246i \(-0.0169499\pi\)
\(354\) 2.00000 0.106299
\(355\) 12.0000 24.0000i 0.636894 1.27379i
\(356\) 4.00000 0.212000
\(357\) 0 0
\(358\) 18.0000i 0.951330i
\(359\) 8.00000 0.422224 0.211112 0.977462i \(-0.432292\pi\)
0.211112 + 0.977462i \(0.432292\pi\)
\(360\) 2.00000 + 1.00000i 0.105409 + 0.0527046i
\(361\) 1.00000 0.0526316
\(362\) 4.00000i 0.210235i
\(363\) 5.00000i 0.262432i
\(364\) 0 0
\(365\) 32.0000 + 16.0000i 1.67496 + 0.837478i
\(366\) 6.00000 0.313625
\(367\) 12.0000i 0.626395i −0.949688 0.313197i \(-0.898600\pi\)
0.949688 0.313197i \(-0.101400\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 0 0
\(370\) −10.0000 + 20.0000i −0.519875 + 1.03975i
\(371\) 0 0
\(372\) 6.00000i 0.311086i
\(373\) 6.00000i 0.310668i 0.987862 + 0.155334i \(0.0496454\pi\)
−0.987862 + 0.155334i \(0.950355\pi\)
\(374\) −24.0000 −1.24101
\(375\) −2.00000 11.0000i −0.103280 0.568038i
\(376\) 6.00000 0.309426
\(377\) 4.00000i 0.206010i
\(378\) 0 0
\(379\) −24.0000 −1.23280 −0.616399 0.787434i \(-0.711409\pi\)
−0.616399 + 0.787434i \(0.711409\pi\)
\(380\) 1.00000 2.00000i 0.0512989 0.102598i
\(381\) −8.00000 −0.409852
\(382\) 24.0000i 1.22795i
\(383\) 36.0000i 1.83951i 0.392488 + 0.919757i \(0.371614\pi\)
−0.392488 + 0.919757i \(0.628386\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 6.00000i 0.304997i
\(388\) 10.0000i 0.507673i
\(389\) −38.0000 −1.92668 −0.963338 0.268290i \(-0.913542\pi\)
−0.963338 + 0.268290i \(0.913542\pi\)
\(390\) 4.00000 + 2.00000i 0.202548 + 0.101274i
\(391\) −36.0000 −1.82060
\(392\) 7.00000i 0.353553i
\(393\) 8.00000i 0.403547i
\(394\) −8.00000 −0.403034
\(395\) −14.0000 + 28.0000i −0.704416 + 1.40883i
\(396\) −4.00000 −0.201008
\(397\) 30.0000i 1.50566i 0.658217 + 0.752828i \(0.271311\pi\)
−0.658217 + 0.752828i \(0.728689\pi\)
\(398\) 16.0000i 0.802008i
\(399\) 0 0
\(400\) −3.00000 4.00000i −0.150000 0.200000i
\(401\) 16.0000 0.799002 0.399501 0.916733i \(-0.369183\pi\)
0.399501 + 0.916733i \(0.369183\pi\)
\(402\) 8.00000i 0.399004i
\(403\) 12.0000i 0.597763i
\(404\) 18.0000 0.895533
\(405\) −1.00000 + 2.00000i −0.0496904 + 0.0993808i
\(406\) 0 0
\(407\) 40.0000i 1.98273i
\(408\) 6.00000i 0.297044i
\(409\) −26.0000 −1.28562 −0.642809 0.766027i \(-0.722231\pi\)
−0.642809 + 0.766027i \(0.722231\pi\)
\(410\) 0 0
\(411\) −6.00000 −0.295958
\(412\) 8.00000i 0.394132i
\(413\) 0 0
\(414\) −6.00000 −0.294884
\(415\) −24.0000 12.0000i −1.17811 0.589057i
\(416\) 2.00000 0.0980581
\(417\) 12.0000i 0.587643i
\(418\) 4.00000i 0.195646i
\(419\) −8.00000 −0.390826 −0.195413 0.980721i \(-0.562605\pi\)
−0.195413 + 0.980721i \(0.562605\pi\)
\(420\) 0 0
\(421\) 16.0000 0.779792 0.389896 0.920859i \(-0.372511\pi\)
0.389896 + 0.920859i \(0.372511\pi\)
\(422\) 8.00000i 0.389434i
\(423\) 6.00000i 0.291730i
\(424\) −10.0000 −0.485643
\(425\) 24.0000 18.0000i 1.16417 0.873128i
\(426\) 12.0000 0.581402
\(427\) 0 0
\(428\) 4.00000i 0.193347i
\(429\) −8.00000 −0.386244
\(430\) 6.00000 12.0000i 0.289346 0.578691i
\(431\) −24.0000 −1.15604 −0.578020 0.816023i \(-0.696174\pi\)
−0.578020 + 0.816023i \(0.696174\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 6.00000i 0.288342i 0.989553 + 0.144171i \(0.0460515\pi\)
−0.989553 + 0.144171i \(0.953949\pi\)
\(434\) 0 0
\(435\) 4.00000 + 2.00000i 0.191785 + 0.0958927i
\(436\) 4.00000 0.191565
\(437\) 6.00000i 0.287019i
\(438\) 16.0000i 0.764510i
\(439\) 14.0000 0.668184 0.334092 0.942541i \(-0.391570\pi\)
0.334092 + 0.942541i \(0.391570\pi\)
\(440\) 8.00000 + 4.00000i 0.381385 + 0.190693i
\(441\) −7.00000 −0.333333
\(442\) 12.0000i 0.570782i
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) −10.0000 −0.474579
\(445\) 4.00000 8.00000i 0.189618 0.379236i
\(446\) −8.00000 −0.378811
\(447\) 6.00000i 0.283790i
\(448\) 0 0
\(449\) −4.00000 −0.188772 −0.0943858 0.995536i \(-0.530089\pi\)
−0.0943858 + 0.995536i \(0.530089\pi\)
\(450\) 4.00000 3.00000i 0.188562 0.141421i
\(451\) 0 0
\(452\) 2.00000i 0.0940721i
\(453\) 10.0000i 0.469841i
\(454\) 12.0000 0.563188
\(455\) 0 0
\(456\) 1.00000 0.0468293
\(457\) 16.0000i 0.748448i −0.927338 0.374224i \(-0.877909\pi\)
0.927338 0.374224i \(-0.122091\pi\)
\(458\) 10.0000i 0.467269i
\(459\) −6.00000 −0.280056
\(460\) 12.0000 + 6.00000i 0.559503 + 0.279751i
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) 8.00000i 0.371792i −0.982569 0.185896i \(-0.940481\pi\)
0.982569 0.185896i \(-0.0595187\pi\)
\(464\) 2.00000 0.0928477
\(465\) −12.0000 6.00000i −0.556487 0.278243i
\(466\) 14.0000 0.648537
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 2.00000i 0.0924500i
\(469\) 0 0
\(470\) 6.00000 12.0000i 0.276759 0.553519i
\(471\) 18.0000 0.829396
\(472\) 2.00000i 0.0920575i
\(473\) 24.0000i 1.10352i
\(474\) −14.0000 −0.643041
\(475\) −3.00000 4.00000i −0.137649 0.183533i
\(476\) 0 0
\(477\) 10.0000i 0.457869i
\(478\) 8.00000i 0.365911i
\(479\) 16.0000 0.731059 0.365529 0.930800i \(-0.380888\pi\)
0.365529 + 0.930800i \(0.380888\pi\)
\(480\) 1.00000 2.00000i 0.0456435 0.0912871i
\(481\) −20.0000 −0.911922
\(482\) 10.0000i 0.455488i
\(483\) 0 0
\(484\) −5.00000 −0.227273
\(485\) −20.0000 10.0000i −0.908153 0.454077i
\(486\) −1.00000 −0.0453609
\(487\) 24.0000i 1.08754i −0.839233 0.543772i \(-0.816996\pi\)
0.839233 0.543772i \(-0.183004\pi\)
\(488\) 6.00000i 0.271607i
\(489\) −10.0000 −0.452216
\(490\) 14.0000 + 7.00000i 0.632456 + 0.316228i
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) 12.0000i 0.540453i
\(494\) 2.00000 0.0899843
\(495\) −4.00000 + 8.00000i −0.179787 + 0.359573i
\(496\) −6.00000 −0.269408
\(497\) 0 0
\(498\) 12.0000i 0.537733i
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) −11.0000 + 2.00000i −0.491935 + 0.0894427i
\(501\) 0 0
\(502\) 12.0000i 0.535586i
\(503\) 14.0000i 0.624229i −0.950044 0.312115i \(-0.898963\pi\)
0.950044 0.312115i \(-0.101037\pi\)
\(504\) 0 0
\(505\) 18.0000 36.0000i 0.800989 1.60198i
\(506\) −24.0000 −1.06693
\(507\) 9.00000i 0.399704i
\(508\) 8.00000i 0.354943i
\(509\) −6.00000 −0.265945 −0.132973 0.991120i \(-0.542452\pi\)
−0.132973 + 0.991120i \(0.542452\pi\)
\(510\) 12.0000 + 6.00000i 0.531369 + 0.265684i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 1.00000i 0.0441511i
\(514\) −22.0000 −0.970378
\(515\) −16.0000 8.00000i −0.705044 0.352522i
\(516\) 6.00000 0.264135
\(517\) 24.0000i 1.05552i
\(518\) 0 0
\(519\) −14.0000 −0.614532
\(520\) 2.00000 4.00000i 0.0877058 0.175412i
\(521\) −24.0000 −1.05146 −0.525730 0.850652i \(-0.676208\pi\)
−0.525730 + 0.850652i \(0.676208\pi\)
\(522\) 2.00000i 0.0875376i
\(523\) 36.0000i 1.57417i 0.616844 + 0.787085i \(0.288411\pi\)
−0.616844 + 0.787085i \(0.711589\pi\)
\(524\) 8.00000 0.349482
\(525\) 0 0
\(526\) −2.00000 −0.0872041
\(527\) 36.0000i 1.56818i
\(528\) 4.00000i 0.174078i
\(529\) −13.0000 −0.565217
\(530\) −10.0000 + 20.0000i −0.434372 + 0.868744i
\(531\) 2.00000 0.0867926
\(532\) 0 0
\(533\) 0 0
\(534\) 4.00000 0.173097
\(535\) −8.00000 4.00000i −0.345870 0.172935i
\(536\) 8.00000 0.345547
\(537\) 18.0000i 0.776757i
\(538\) 14.0000i 0.603583i
\(539\) −28.0000 −1.20605
\(540\) 2.00000 + 1.00000i 0.0860663 + 0.0430331i
\(541\) 38.0000 1.63375 0.816874 0.576816i \(-0.195705\pi\)
0.816874 + 0.576816i \(0.195705\pi\)
\(542\) 32.0000i 1.37452i
\(543\) 4.00000i 0.171656i
\(544\) 6.00000 0.257248
\(545\) 4.00000 8.00000i 0.171341 0.342682i
\(546\) 0 0
\(547\) 36.0000i 1.53925i 0.638497 + 0.769624i \(0.279557\pi\)
−0.638497 + 0.769624i \(0.720443\pi\)
\(548\) 6.00000i 0.256307i
\(549\) 6.00000 0.256074
\(550\) 16.0000 12.0000i 0.682242 0.511682i
\(551\) 2.00000 0.0852029
\(552\) 6.00000i 0.255377i
\(553\) 0 0
\(554\) 26.0000 1.10463
\(555\) −10.0000 + 20.0000i −0.424476 + 0.848953i
\(556\) 12.0000 0.508913
\(557\) 24.0000i 1.01691i −0.861088 0.508456i \(-0.830216\pi\)
0.861088 0.508456i \(-0.169784\pi\)
\(558\) 6.00000i 0.254000i
\(559\) 12.0000 0.507546
\(560\) 0 0
\(561\) −24.0000 −1.01328
\(562\) 0 0
\(563\) 12.0000i 0.505740i −0.967500 0.252870i \(-0.918626\pi\)
0.967500 0.252870i \(-0.0813744\pi\)
\(564\) 6.00000 0.252646
\(565\) −4.00000 2.00000i −0.168281 0.0841406i
\(566\) 22.0000 0.924729
\(567\) 0 0
\(568\) 12.0000i 0.503509i
\(569\) 28.0000 1.17382 0.586911 0.809652i \(-0.300344\pi\)
0.586911 + 0.809652i \(0.300344\pi\)
\(570\) 1.00000 2.00000i 0.0418854 0.0837708i
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 8.00000i 0.334497i
\(573\) 24.0000i 1.00261i
\(574\) 0 0
\(575\) 24.0000 18.0000i 1.00087 0.750652i
\(576\) 1.00000 0.0416667
\(577\) 8.00000i 0.333044i 0.986038 + 0.166522i \(0.0532537\pi\)
−0.986038 + 0.166522i \(0.946746\pi\)
\(578\) 19.0000i 0.790296i
\(579\) 14.0000 0.581820
\(580\) 2.00000 4.00000i 0.0830455 0.166091i
\(581\) 0 0
\(582\) 10.0000i 0.414513i
\(583\) 40.0000i 1.65663i
\(584\) 16.0000 0.662085
\(585\) 4.00000 + 2.00000i 0.165380 + 0.0826898i
\(586\) 2.00000 0.0826192
\(587\) 28.0000i 1.15568i 0.816149 + 0.577842i \(0.196105\pi\)
−0.816149 + 0.577842i \(0.803895\pi\)
\(588\) 7.00000i 0.288675i
\(589\) −6.00000 −0.247226
\(590\) −4.00000 2.00000i −0.164677 0.0823387i
\(591\) −8.00000 −0.329076
\(592\) 10.0000i 0.410997i
\(593\) 46.0000i 1.88899i −0.328521 0.944497i \(-0.606550\pi\)
0.328521 0.944497i \(-0.393450\pi\)
\(594\) −4.00000 −0.164122
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) 16.0000i 0.654836i
\(598\) 12.0000i 0.490716i
\(599\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(600\) −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
\(603\) 8.00000i 0.325785i
\(604\) −10.0000 −0.406894
\(605\) −5.00000 + 10.0000i −0.203279 + 0.406558i
\(606\) 18.0000 0.731200
\(607\) 24.0000i 0.974130i 0.873366 + 0.487065i \(0.161933\pi\)
−0.873366 + 0.487065i \(0.838067\pi\)
\(608\) 1.00000i 0.0405554i
\(609\) 0 0
\(610\) −12.0000 6.00000i −0.485866 0.242933i
\(611\) 12.0000 0.485468
\(612\) 6.00000i 0.242536i
\(613\) 22.0000i 0.888572i −0.895885 0.444286i \(-0.853457\pi\)
0.895885 0.444286i \(-0.146543\pi\)
\(614\) 12.0000 0.484281
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000i 0.724653i 0.932051 + 0.362326i \(0.118017\pi\)
−0.932051 + 0.362326i \(0.881983\pi\)
\(618\) 8.00000i 0.321807i
\(619\) −44.0000 −1.76851 −0.884255 0.467005i \(-0.845333\pi\)
−0.884255 + 0.467005i \(0.845333\pi\)
\(620\) −6.00000 + 12.0000i −0.240966 + 0.481932i
\(621\) −6.00000 −0.240772
\(622\) 24.0000i 0.962312i
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 28.0000 1.11911
\(627\) 4.00000i 0.159745i
\(628\) 18.0000i 0.718278i
\(629\) −60.0000 −2.39236
\(630\) 0 0
\(631\) −20.0000 −0.796187 −0.398094 0.917345i \(-0.630328\pi\)
−0.398094 + 0.917345i \(0.630328\pi\)
\(632\) 14.0000i 0.556890i
\(633\) 8.00000i 0.317971i
\(634\) −6.00000 −0.238290
\(635\) 16.0000 + 8.00000i 0.634941 + 0.317470i
\(636\) −10.0000 −0.396526
\(637\) 14.0000i 0.554700i
\(638\) 8.00000i 0.316723i
\(639\) 12.0000 0.474713
\(640\) −2.00000 1.00000i −0.0790569 0.0395285i
\(641\) 48.0000 1.89589 0.947943 0.318440i \(-0.103159\pi\)
0.947943 + 0.318440i \(0.103159\pi\)
\(642\) 4.00000i 0.157867i
\(643\) 26.0000i 1.02534i −0.858586 0.512670i \(-0.828656\pi\)
0.858586 0.512670i \(-0.171344\pi\)
\(644\) 0 0
\(645\) 6.00000 12.0000i 0.236250 0.472500i
\(646\) 6.00000 0.236067
\(647\) 6.00000i 0.235884i −0.993020 0.117942i \(-0.962370\pi\)
0.993020 0.117942i \(-0.0376297\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 8.00000 0.314027
\(650\) −6.00000 8.00000i −0.235339 0.313786i
\(651\) 0 0
\(652\) 10.0000i 0.391630i
\(653\) 48.0000i 1.87839i 0.343391 + 0.939193i \(0.388424\pi\)
−0.343391 + 0.939193i \(0.611576\pi\)
\(654\) 4.00000 0.156412
\(655\) 8.00000 16.0000i 0.312586 0.625172i
\(656\) 0 0
\(657\) 16.0000i 0.624219i
\(658\) 0 0
\(659\) −46.0000 −1.79191 −0.895953 0.444149i \(-0.853506\pi\)
−0.895953 + 0.444149i \(0.853506\pi\)
\(660\) 8.00000 + 4.00000i 0.311400 + 0.155700i
\(661\) −8.00000 −0.311164 −0.155582 0.987823i \(-0.549725\pi\)
−0.155582 + 0.987823i \(0.549725\pi\)
\(662\) 4.00000i 0.155464i
\(663\) 12.0000i 0.466041i
\(664\) −12.0000 −0.465690
\(665\) 0 0
\(666\) −10.0000 −0.387492
\(667\) 12.0000i 0.464642i
\(668\) 0 0
\(669\) −8.00000 −0.309298
\(670\) 8.00000 16.0000i 0.309067 0.618134i
\(671\) 24.0000 0.926510
\(672\) 0 0
\(673\) 26.0000i 1.00223i 0.865382 + 0.501113i \(0.167076\pi\)
−0.865382 + 0.501113i \(0.832924\pi\)
\(674\) −6.00000 −0.231111
\(675\) 4.00000 3.00000i 0.153960 0.115470i
\(676\) −9.00000 −0.346154
\(677\) 6.00000i 0.230599i 0.993331 + 0.115299i \(0.0367827\pi\)
−0.993331 + 0.115299i \(0.963217\pi\)
\(678\) 2.00000i 0.0768095i
\(679\) 0 0
\(680\) 6.00000 12.0000i 0.230089 0.460179i
\(681\) 12.0000 0.459841
\(682\) 24.0000i 0.919007i
\(683\) 36.0000i 1.37750i −0.724998 0.688751i \(-0.758159\pi\)
0.724998 0.688751i \(-0.241841\pi\)
\(684\) 1.00000 0.0382360
\(685\) 12.0000 + 6.00000i 0.458496 + 0.229248i
\(686\) 0 0
\(687\) 10.0000i 0.381524i
\(688\) 6.00000i 0.228748i
\(689\) −20.0000 −0.761939
\(690\) 12.0000 + 6.00000i 0.456832 + 0.228416i
\(691\) 44.0000 1.67384 0.836919 0.547326i \(-0.184354\pi\)
0.836919 + 0.547326i \(0.184354\pi\)
\(692\) 14.0000i 0.532200i
\(693\) 0 0
\(694\) −20.0000 −0.759190
\(695\) 12.0000 24.0000i 0.455186 0.910372i
\(696\) 2.00000 0.0758098
\(697\) 0 0
\(698\) 26.0000i 0.984115i
\(699\) 14.0000 0.529529
\(700\) 0 0
\(701\) −22.0000 −0.830929 −0.415464 0.909610i \(-0.636381\pi\)
−0.415464 + 0.909610i \(0.636381\pi\)
\(702\) 2.00000i 0.0754851i
\(703\) 10.0000i 0.377157i
\(704\) 4.00000 0.150756
\(705\) 6.00000 12.0000i 0.225973 0.451946i
\(706\) −2.00000 −0.0752710
\(707\) 0 0
\(708\) 2.00000i 0.0751646i
\(709\) 2.00000 0.0751116 0.0375558 0.999295i \(-0.488043\pi\)
0.0375558 + 0.999295i \(0.488043\pi\)
\(710\) −24.0000 12.0000i −0.900704 0.450352i
\(711\) −14.0000 −0.525041
\(712\) 4.00000i 0.149906i
\(713\) 36.0000i 1.34821i
\(714\) 0 0
\(715\) 16.0000 + 8.00000i 0.598366 + 0.299183i
\(716\) −18.0000 −0.672692
\(717\) 8.00000i 0.298765i
\(718\) 8.00000i 0.298557i
\(719\) −48.0000 −1.79010 −0.895049 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 1.00000 2.00000i 0.0372678 0.0745356i
\(721\) 0 0
\(722\) 1.00000i 0.0372161i
\(723\) 10.0000i 0.371904i
\(724\) 4.00000 0.148659
\(725\) −6.00000 8.00000i −0.222834 0.297113i
\(726\) −5.00000 −0.185567
\(727\) 28.0000i 1.03846i 0.854634 + 0.519231i \(0.173782\pi\)
−0.854634 + 0.519231i \(0.826218\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 16.0000 32.0000i 0.592187 1.18437i
\(731\) 36.0000 1.33151
\(732\) 6.00000i 0.221766i
\(733\) 46.0000i 1.69905i 0.527549 + 0.849524i \(0.323111\pi\)
−0.527549 + 0.849524i \(0.676889\pi\)
\(734\) −12.0000 −0.442928
\(735\) 14.0000 + 7.00000i 0.516398 + 0.258199i
\(736\) 6.00000 0.221163
\(737\) 32.0000i 1.17874i
\(738\) 0 0
\(739\) −20.0000 −0.735712 −0.367856 0.929883i \(-0.619908\pi\)
−0.367856 + 0.929883i \(0.619908\pi\)
\(740\) 20.0000 + 10.0000i 0.735215 + 0.367607i
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) 8.00000i 0.293492i −0.989174 0.146746i \(-0.953120\pi\)
0.989174 0.146746i \(-0.0468799\pi\)
\(744\) −6.00000 −0.219971
\(745\) −6.00000 + 12.0000i −0.219823 + 0.439646i
\(746\) 6.00000 0.219676
\(747\) 12.0000i 0.439057i
\(748\) 24.0000i 0.877527i
\(749\) 0 0
\(750\) −11.0000 + 2.00000i −0.401663 + 0.0730297i
\(751\) −26.0000 −0.948753 −0.474377 0.880322i \(-0.657327\pi\)
−0.474377 + 0.880322i \(0.657327\pi\)
\(752\) 6.00000i 0.218797i
\(753\) 12.0000i 0.437304i
\(754\) 4.00000 0.145671
\(755\) −10.0000 + 20.0000i −0.363937 + 0.727875i
\(756\) 0 0
\(757\) 2.00000i 0.0726912i 0.999339 + 0.0363456i \(0.0115717\pi\)
−0.999339 + 0.0363456i \(0.988428\pi\)
\(758\) 24.0000i 0.871719i
\(759\) −24.0000 −0.871145
\(760\) −2.00000 1.00000i −0.0725476 0.0362738i
\(761\) 30.0000 1.08750 0.543750 0.839248i \(-0.317004\pi\)
0.543750 + 0.839248i \(0.317004\pi\)
\(762\) 8.00000i 0.289809i
\(763\) 0 0
\(764\) −24.0000 −0.868290
\(765\) 12.0000 + 6.00000i 0.433861 + 0.216930i
\(766\) 36.0000 1.30073
\(767\) 4.00000i 0.144432i
\(768\) 1.00000i 0.0360844i
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) −22.0000 −0.792311
\(772\) 14.0000i 0.503871i
\(773\) 50.0000i 1.79838i −0.437564 0.899188i \(-0.644158\pi\)
0.437564 0.899188i \(-0.355842\pi\)
\(774\) 6.00000 0.215666
\(775\) 18.0000 + 24.0000i 0.646579 + 0.862105i
\(776\) −10.0000 −0.358979
\(777\) 0 0
\(778\) 38.0000i 1.36237i
\(779\) 0 0
\(780\) 2.00000 4.00000i 0.0716115 0.143223i
\(781\) 48.0000 1.71758
\(782\) 36.0000i 1.28736i
\(783\) 2.00000i 0.0714742i
\(784\) 7.00000 0.250000
\(785\) −36.0000 18.0000i −1.28490 0.642448i
\(786\) 8.00000 0.285351
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 8.00000i 0.284988i
\(789\) −2.00000 −0.0712019
\(790\) 28.0000 + 14.0000i 0.996195 + 0.498098i
\(791\) 0 0
\(792\) 4.00000i 0.142134i