Properties

Label 1512.2.c.g.757.22
Level 1512
Weight 2
Character 1512.757
Analytic conductor 12.073
Analytic rank 0
Dimension 24
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 1512.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.0733807856\)
Analytic rank: \(0\)
Dimension: \(24\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 757.22
Character \(\chi\) = 1512.757
Dual form 1512.2.c.g.757.21

$q$-expansion

\(f(q)\) \(=\) \(q+(1.35918 + 0.390688i) q^{2} +(1.69473 + 1.06203i) q^{4} -1.82986i q^{5} +1.00000 q^{7} +(1.88851 + 2.10559i) q^{8} +O(q^{10})\) \(q+(1.35918 + 0.390688i) q^{2} +(1.69473 + 1.06203i) q^{4} -1.82986i q^{5} +1.00000 q^{7} +(1.88851 + 2.10559i) q^{8} +(0.714906 - 2.48711i) q^{10} +3.75866i q^{11} +3.09942i q^{13} +(1.35918 + 0.390688i) q^{14} +(1.74419 + 3.59969i) q^{16} +3.61074 q^{17} +1.65297i q^{19} +(1.94337 - 3.10112i) q^{20} +(-1.46846 + 5.10869i) q^{22} -7.47934 q^{23} +1.65160 q^{25} +(-1.21090 + 4.21266i) q^{26} +(1.69473 + 1.06203i) q^{28} -2.38629i q^{29} +8.97301 q^{31} +(0.964311 + 5.57406i) q^{32} +(4.90764 + 1.41067i) q^{34} -1.82986i q^{35} -8.94392i q^{37} +(-0.645794 + 2.24668i) q^{38} +(3.85295 - 3.45572i) q^{40} +3.04284 q^{41} +1.82597i q^{43} +(-3.99180 + 6.36990i) q^{44} +(-10.1657 - 2.92209i) q^{46} +6.21697 q^{47} +1.00000 q^{49} +(2.24482 + 0.645259i) q^{50} +(-3.29167 + 5.25266i) q^{52} -3.21435i q^{53} +6.87784 q^{55} +(1.88851 + 2.10559i) q^{56} +(0.932294 - 3.24339i) q^{58} -12.4366i q^{59} +9.91962i q^{61} +(12.1959 + 3.50565i) q^{62} +(-0.867047 + 7.95288i) q^{64} +5.67151 q^{65} +8.73156i q^{67} +(6.11922 + 3.83471i) q^{68} +(0.714906 - 2.48711i) q^{70} -12.4229 q^{71} +9.79655 q^{73} +(3.49428 - 12.1564i) q^{74} +(-1.75550 + 2.80133i) q^{76} +3.75866i q^{77} -7.24388 q^{79} +(6.58695 - 3.19163i) q^{80} +(4.13577 + 1.18880i) q^{82} -8.99325i q^{83} -6.60717i q^{85} +(-0.713383 + 2.48181i) q^{86} +(-7.91421 + 7.09827i) q^{88} -1.54944 q^{89} +3.09942i q^{91} +(-12.6754 - 7.94327i) q^{92} +(8.44997 + 2.42890i) q^{94} +3.02470 q^{95} -10.2583 q^{97} +(1.35918 + 0.390688i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 6q^{4} + 24q^{7} + O(q^{10}) \) \( 24q + 6q^{4} + 24q^{7} - 16q^{10} + 2q^{16} + 16q^{22} - 24q^{25} + 6q^{28} + 8q^{31} + 22q^{34} + 26q^{46} + 24q^{49} - 6q^{52} + 16q^{55} - 58q^{58} + 6q^{64} - 16q^{70} + 60q^{76} + 8q^{79} - 28q^{82} + 12q^{88} + 36q^{94} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1081\) \(1135\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.35918 + 0.390688i 0.961084 + 0.276258i
\(3\) 0 0
\(4\) 1.69473 + 1.06203i 0.847363 + 0.531014i
\(5\) 1.82986i 0.818340i −0.912458 0.409170i \(-0.865818\pi\)
0.912458 0.409170i \(-0.134182\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.88851 + 2.10559i 0.667690 + 0.744440i
\(9\) 0 0
\(10\) 0.714906 2.48711i 0.226073 0.786493i
\(11\) 3.75866i 1.13328i 0.823966 + 0.566639i \(0.191757\pi\)
−0.823966 + 0.566639i \(0.808243\pi\)
\(12\) 0 0
\(13\) 3.09942i 0.859623i 0.902919 + 0.429812i \(0.141420\pi\)
−0.902919 + 0.429812i \(0.858580\pi\)
\(14\) 1.35918 + 0.390688i 0.363255 + 0.104416i
\(15\) 0 0
\(16\) 1.74419 + 3.59969i 0.436048 + 0.899923i
\(17\) 3.61074 0.875734 0.437867 0.899040i \(-0.355734\pi\)
0.437867 + 0.899040i \(0.355734\pi\)
\(18\) 0 0
\(19\) 1.65297i 0.379217i 0.981860 + 0.189608i \(0.0607218\pi\)
−0.981860 + 0.189608i \(0.939278\pi\)
\(20\) 1.94337 3.10112i 0.434550 0.693431i
\(21\) 0 0
\(22\) −1.46846 + 5.10869i −0.313077 + 1.08918i
\(23\) −7.47934 −1.55955 −0.779775 0.626060i \(-0.784666\pi\)
−0.779775 + 0.626060i \(0.784666\pi\)
\(24\) 0 0
\(25\) 1.65160 0.330320
\(26\) −1.21090 + 4.21266i −0.237478 + 0.826170i
\(27\) 0 0
\(28\) 1.69473 + 1.06203i 0.320273 + 0.200704i
\(29\) 2.38629i 0.443123i −0.975146 0.221561i \(-0.928885\pi\)
0.975146 0.221561i \(-0.0711153\pi\)
\(30\) 0 0
\(31\) 8.97301 1.61160 0.805800 0.592188i \(-0.201736\pi\)
0.805800 + 0.592188i \(0.201736\pi\)
\(32\) 0.964311 + 5.57406i 0.170468 + 0.985363i
\(33\) 0 0
\(34\) 4.90764 + 1.41067i 0.841653 + 0.241928i
\(35\) 1.82986i 0.309303i
\(36\) 0 0
\(37\) 8.94392i 1.47037i −0.677865 0.735186i \(-0.737095\pi\)
0.677865 0.735186i \(-0.262905\pi\)
\(38\) −0.645794 + 2.24668i −0.104762 + 0.364459i
\(39\) 0 0
\(40\) 3.85295 3.45572i 0.609205 0.546397i
\(41\) 3.04284 0.475212 0.237606 0.971362i \(-0.423637\pi\)
0.237606 + 0.971362i \(0.423637\pi\)
\(42\) 0 0
\(43\) 1.82597i 0.278457i 0.990260 + 0.139229i \(0.0444623\pi\)
−0.990260 + 0.139229i \(0.955538\pi\)
\(44\) −3.99180 + 6.36990i −0.601787 + 0.960299i
\(45\) 0 0
\(46\) −10.1657 2.92209i −1.49886 0.430838i
\(47\) 6.21697 0.906838 0.453419 0.891297i \(-0.350204\pi\)
0.453419 + 0.891297i \(0.350204\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 2.24482 + 0.645259i 0.317465 + 0.0912535i
\(51\) 0 0
\(52\) −3.29167 + 5.25266i −0.456472 + 0.728413i
\(53\) 3.21435i 0.441525i −0.975328 0.220762i \(-0.929145\pi\)
0.975328 0.220762i \(-0.0708546\pi\)
\(54\) 0 0
\(55\) 6.87784 0.927407
\(56\) 1.88851 + 2.10559i 0.252363 + 0.281372i
\(57\) 0 0
\(58\) 0.932294 3.24339i 0.122416 0.425878i
\(59\) 12.4366i 1.61911i −0.587046 0.809554i \(-0.699709\pi\)
0.587046 0.809554i \(-0.300291\pi\)
\(60\) 0 0
\(61\) 9.91962i 1.27008i 0.772480 + 0.635039i \(0.219016\pi\)
−0.772480 + 0.635039i \(0.780984\pi\)
\(62\) 12.1959 + 3.50565i 1.54888 + 0.445218i
\(63\) 0 0
\(64\) −0.867047 + 7.95288i −0.108381 + 0.994109i
\(65\) 5.67151 0.703464
\(66\) 0 0
\(67\) 8.73156i 1.06673i 0.845885 + 0.533365i \(0.179073\pi\)
−0.845885 + 0.533365i \(0.820927\pi\)
\(68\) 6.11922 + 3.83471i 0.742064 + 0.465027i
\(69\) 0 0
\(70\) 0.714906 2.48711i 0.0854476 0.297266i
\(71\) −12.4229 −1.47432 −0.737161 0.675717i \(-0.763834\pi\)
−0.737161 + 0.675717i \(0.763834\pi\)
\(72\) 0 0
\(73\) 9.79655 1.14660 0.573300 0.819346i \(-0.305663\pi\)
0.573300 + 0.819346i \(0.305663\pi\)
\(74\) 3.49428 12.1564i 0.406202 1.41315i
\(75\) 0 0
\(76\) −1.75550 + 2.80133i −0.201369 + 0.321334i
\(77\) 3.75866i 0.428339i
\(78\) 0 0
\(79\) −7.24388 −0.815001 −0.407500 0.913205i \(-0.633599\pi\)
−0.407500 + 0.913205i \(0.633599\pi\)
\(80\) 6.58695 3.19163i 0.736443 0.356836i
\(81\) 0 0
\(82\) 4.13577 + 1.18880i 0.456719 + 0.131281i
\(83\) 8.99325i 0.987138i −0.869707 0.493569i \(-0.835692\pi\)
0.869707 0.493569i \(-0.164308\pi\)
\(84\) 0 0
\(85\) 6.60717i 0.716648i
\(86\) −0.713383 + 2.48181i −0.0769261 + 0.267621i
\(87\) 0 0
\(88\) −7.91421 + 7.09827i −0.843658 + 0.756679i
\(89\) −1.54944 −0.164240 −0.0821202 0.996622i \(-0.526169\pi\)
−0.0821202 + 0.996622i \(0.526169\pi\)
\(90\) 0 0
\(91\) 3.09942i 0.324907i
\(92\) −12.6754 7.94327i −1.32150 0.828143i
\(93\) 0 0
\(94\) 8.44997 + 2.42890i 0.871547 + 0.250521i
\(95\) 3.02470 0.310328
\(96\) 0 0
\(97\) −10.2583 −1.04158 −0.520788 0.853686i \(-0.674362\pi\)
−0.520788 + 0.853686i \(0.674362\pi\)
\(98\) 1.35918 + 0.390688i 0.137298 + 0.0394654i
\(99\) 0 0
\(100\) 2.79901 + 1.75404i 0.279901 + 0.175404i
\(101\) 5.97880i 0.594913i −0.954735 0.297456i \(-0.903862\pi\)
0.954735 0.297456i \(-0.0961383\pi\)
\(102\) 0 0
\(103\) −16.9060 −1.66579 −0.832896 0.553429i \(-0.813319\pi\)
−0.832896 + 0.553429i \(0.813319\pi\)
\(104\) −6.52611 + 5.85328i −0.639938 + 0.573962i
\(105\) 0 0
\(106\) 1.25581 4.36887i 0.121975 0.424342i
\(107\) 2.14315i 0.207186i 0.994620 + 0.103593i \(0.0330339\pi\)
−0.994620 + 0.103593i \(0.966966\pi\)
\(108\) 0 0
\(109\) 8.34775i 0.799569i −0.916609 0.399785i \(-0.869085\pi\)
0.916609 0.399785i \(-0.130915\pi\)
\(110\) 9.34820 + 2.68709i 0.891316 + 0.256204i
\(111\) 0 0
\(112\) 1.74419 + 3.59969i 0.164811 + 0.340139i
\(113\) −17.5901 −1.65474 −0.827369 0.561659i \(-0.810163\pi\)
−0.827369 + 0.561659i \(0.810163\pi\)
\(114\) 0 0
\(115\) 13.6862i 1.27624i
\(116\) 2.53431 4.04411i 0.235304 0.375486i
\(117\) 0 0
\(118\) 4.85883 16.9035i 0.447292 1.55610i
\(119\) 3.61074 0.330996
\(120\) 0 0
\(121\) −3.12753 −0.284321
\(122\) −3.87548 + 13.4825i −0.350869 + 1.22065i
\(123\) 0 0
\(124\) 15.2068 + 9.52959i 1.36561 + 0.855782i
\(125\) 12.1715i 1.08865i
\(126\) 0 0
\(127\) 9.73427 0.863777 0.431888 0.901927i \(-0.357847\pi\)
0.431888 + 0.901927i \(0.357847\pi\)
\(128\) −4.28556 + 10.4706i −0.378794 + 0.925481i
\(129\) 0 0
\(130\) 7.70859 + 2.21579i 0.676088 + 0.194338i
\(131\) 16.7317i 1.46185i 0.682456 + 0.730926i \(0.260912\pi\)
−0.682456 + 0.730926i \(0.739088\pi\)
\(132\) 0 0
\(133\) 1.65297i 0.143330i
\(134\) −3.41131 + 11.8677i −0.294693 + 1.02522i
\(135\) 0 0
\(136\) 6.81893 + 7.60275i 0.584718 + 0.651931i
\(137\) −15.1897 −1.29774 −0.648872 0.760897i \(-0.724759\pi\)
−0.648872 + 0.760897i \(0.724759\pi\)
\(138\) 0 0
\(139\) 9.32344i 0.790804i 0.918508 + 0.395402i \(0.129395\pi\)
−0.918508 + 0.395402i \(0.870605\pi\)
\(140\) 1.94337 3.10112i 0.164244 0.262092i
\(141\) 0 0
\(142\) −16.8849 4.85346i −1.41695 0.407293i
\(143\) −11.6497 −0.974193
\(144\) 0 0
\(145\) −4.36658 −0.362625
\(146\) 13.3152 + 3.82739i 1.10198 + 0.316757i
\(147\) 0 0
\(148\) 9.49870 15.1575i 0.780788 1.24594i
\(149\) 3.32322i 0.272248i −0.990692 0.136124i \(-0.956535\pi\)
0.990692 0.136124i \(-0.0434646\pi\)
\(150\) 0 0
\(151\) 12.3757 1.00712 0.503561 0.863960i \(-0.332023\pi\)
0.503561 + 0.863960i \(0.332023\pi\)
\(152\) −3.48048 + 3.12165i −0.282304 + 0.253199i
\(153\) 0 0
\(154\) −1.46846 + 5.10869i −0.118332 + 0.411670i
\(155\) 16.4194i 1.31884i
\(156\) 0 0
\(157\) 12.9811i 1.03601i −0.855378 0.518004i \(-0.826675\pi\)
0.855378 0.518004i \(-0.173325\pi\)
\(158\) −9.84572 2.83010i −0.783284 0.225150i
\(159\) 0 0
\(160\) 10.1998 1.76456i 0.806362 0.139500i
\(161\) −7.47934 −0.589454
\(162\) 0 0
\(163\) 6.17108i 0.483356i 0.970356 + 0.241678i \(0.0776978\pi\)
−0.970356 + 0.241678i \(0.922302\pi\)
\(164\) 5.15679 + 3.23159i 0.402677 + 0.252345i
\(165\) 0 0
\(166\) 3.51355 12.2234i 0.272705 0.948722i
\(167\) −5.75113 −0.445036 −0.222518 0.974929i \(-0.571428\pi\)
−0.222518 + 0.974929i \(0.571428\pi\)
\(168\) 0 0
\(169\) 3.39362 0.261048
\(170\) 2.58134 8.98031i 0.197980 0.688758i
\(171\) 0 0
\(172\) −1.93923 + 3.09451i −0.147865 + 0.235954i
\(173\) 8.09698i 0.615602i −0.951451 0.307801i \(-0.900407\pi\)
0.951451 0.307801i \(-0.0995931\pi\)
\(174\) 0 0
\(175\) 1.65160 0.124849
\(176\) −13.5300 + 6.55583i −1.01986 + 0.494164i
\(177\) 0 0
\(178\) −2.10596 0.605347i −0.157849 0.0453727i
\(179\) 15.4128i 1.15201i −0.817447 0.576003i \(-0.804611\pi\)
0.817447 0.576003i \(-0.195389\pi\)
\(180\) 0 0
\(181\) 6.06823i 0.451048i −0.974238 0.225524i \(-0.927591\pi\)
0.974238 0.225524i \(-0.0724095\pi\)
\(182\) −1.21090 + 4.21266i −0.0897582 + 0.312263i
\(183\) 0 0
\(184\) −14.1248 15.7484i −1.04130 1.16099i
\(185\) −16.3662 −1.20326
\(186\) 0 0
\(187\) 13.5716i 0.992450i
\(188\) 10.5361 + 6.60260i 0.768421 + 0.481544i
\(189\) 0 0
\(190\) 4.11111 + 1.18172i 0.298251 + 0.0857306i
\(191\) −2.76632 −0.200164 −0.100082 0.994979i \(-0.531910\pi\)
−0.100082 + 0.994979i \(0.531910\pi\)
\(192\) 0 0
\(193\) −17.9782 −1.29410 −0.647048 0.762449i \(-0.723997\pi\)
−0.647048 + 0.762449i \(0.723997\pi\)
\(194\) −13.9429 4.00781i −1.00104 0.287744i
\(195\) 0 0
\(196\) 1.69473 + 1.06203i 0.121052 + 0.0758592i
\(197\) 10.5179i 0.749369i −0.927152 0.374684i \(-0.877751\pi\)
0.927152 0.374684i \(-0.122249\pi\)
\(198\) 0 0
\(199\) 4.09973 0.290622 0.145311 0.989386i \(-0.453582\pi\)
0.145311 + 0.989386i \(0.453582\pi\)
\(200\) 3.11906 + 3.47759i 0.220551 + 0.245903i
\(201\) 0 0
\(202\) 2.33584 8.12625i 0.164349 0.571761i
\(203\) 2.38629i 0.167485i
\(204\) 0 0
\(205\) 5.56799i 0.388885i
\(206\) −22.9782 6.60495i −1.60097 0.460189i
\(207\) 0 0
\(208\) −11.1569 + 5.40598i −0.773595 + 0.374837i
\(209\) −6.21294 −0.429758
\(210\) 0 0
\(211\) 21.1789i 1.45802i 0.684504 + 0.729009i \(0.260019\pi\)
−0.684504 + 0.729009i \(0.739981\pi\)
\(212\) 3.41373 5.44744i 0.234456 0.374132i
\(213\) 0 0
\(214\) −0.837301 + 2.91292i −0.0572367 + 0.199123i
\(215\) 3.34127 0.227873
\(216\) 0 0
\(217\) 8.97301 0.609128
\(218\) 3.26136 11.3461i 0.220887 0.768453i
\(219\) 0 0
\(220\) 11.6560 + 7.30446i 0.785851 + 0.492466i
\(221\) 11.1912i 0.752801i
\(222\) 0 0
\(223\) −2.30718 −0.154500 −0.0772502 0.997012i \(-0.524614\pi\)
−0.0772502 + 0.997012i \(0.524614\pi\)
\(224\) 0.964311 + 5.57406i 0.0644307 + 0.372432i
\(225\) 0 0
\(226\) −23.9081 6.87224i −1.59034 0.457134i
\(227\) 2.69006i 0.178545i −0.996007 0.0892727i \(-0.971546\pi\)
0.996007 0.0892727i \(-0.0284543\pi\)
\(228\) 0 0
\(229\) 15.3215i 1.01247i −0.862394 0.506237i \(-0.831036\pi\)
0.862394 0.506237i \(-0.168964\pi\)
\(230\) −5.34702 + 18.6019i −0.352572 + 1.22657i
\(231\) 0 0
\(232\) 5.02455 4.50653i 0.329878 0.295868i
\(233\) 21.3885 1.40121 0.700605 0.713549i \(-0.252914\pi\)
0.700605 + 0.713549i \(0.252914\pi\)
\(234\) 0 0
\(235\) 11.3762i 0.742102i
\(236\) 13.2080 21.0766i 0.859769 1.37197i
\(237\) 0 0
\(238\) 4.90764 + 1.41067i 0.318115 + 0.0914404i
\(239\) −7.04548 −0.455734 −0.227867 0.973692i \(-0.573175\pi\)
−0.227867 + 0.973692i \(0.573175\pi\)
\(240\) 0 0
\(241\) −0.343612 −0.0221340 −0.0110670 0.999939i \(-0.503523\pi\)
−0.0110670 + 0.999939i \(0.503523\pi\)
\(242\) −4.25087 1.22189i −0.273256 0.0785460i
\(243\) 0 0
\(244\) −10.5349 + 16.8110i −0.674429 + 1.07622i
\(245\) 1.82986i 0.116906i
\(246\) 0 0
\(247\) −5.12323 −0.325983
\(248\) 16.9456 + 18.8935i 1.07605 + 1.19974i
\(249\) 0 0
\(250\) 4.75526 16.5433i 0.300749 1.04629i
\(251\) 7.65363i 0.483093i −0.970389 0.241546i \(-0.922345\pi\)
0.970389 0.241546i \(-0.0776546\pi\)
\(252\) 0 0
\(253\) 28.1123i 1.76740i
\(254\) 13.2306 + 3.80306i 0.830162 + 0.238625i
\(255\) 0 0
\(256\) −9.91558 + 12.5571i −0.619724 + 0.784820i
\(257\) 7.01134 0.437356 0.218678 0.975797i \(-0.429826\pi\)
0.218678 + 0.975797i \(0.429826\pi\)
\(258\) 0 0
\(259\) 8.94392i 0.555748i
\(260\) 9.61165 + 6.02330i 0.596089 + 0.373549i
\(261\) 0 0
\(262\) −6.53686 + 22.7413i −0.403849 + 1.40496i
\(263\) 24.0879 1.48532 0.742661 0.669667i \(-0.233563\pi\)
0.742661 + 0.669667i \(0.233563\pi\)
\(264\) 0 0
\(265\) −5.88182 −0.361317
\(266\) −0.645794 + 2.24668i −0.0395962 + 0.137753i
\(267\) 0 0
\(268\) −9.27316 + 14.7976i −0.566449 + 0.903907i
\(269\) 14.4906i 0.883507i −0.897136 0.441753i \(-0.854357\pi\)
0.897136 0.441753i \(-0.145643\pi\)
\(270\) 0 0
\(271\) 28.3057 1.71945 0.859726 0.510756i \(-0.170635\pi\)
0.859726 + 0.510756i \(0.170635\pi\)
\(272\) 6.29783 + 12.9976i 0.381862 + 0.788093i
\(273\) 0 0
\(274\) −20.6455 5.93444i −1.24724 0.358512i
\(275\) 6.20780i 0.374344i
\(276\) 0 0
\(277\) 9.70296i 0.582994i −0.956572 0.291497i \(-0.905847\pi\)
0.956572 0.291497i \(-0.0941534\pi\)
\(278\) −3.64256 + 12.6722i −0.218466 + 0.760029i
\(279\) 0 0
\(280\) 3.85295 3.45572i 0.230258 0.206519i
\(281\) −16.0412 −0.956937 −0.478469 0.878105i \(-0.658808\pi\)
−0.478469 + 0.878105i \(0.658808\pi\)
\(282\) 0 0
\(283\) 11.0326i 0.655818i 0.944709 + 0.327909i \(0.106344\pi\)
−0.944709 + 0.327909i \(0.893656\pi\)
\(284\) −21.0533 13.1934i −1.24929 0.782886i
\(285\) 0 0
\(286\) −15.8339 4.55138i −0.936281 0.269129i
\(287\) 3.04284 0.179613
\(288\) 0 0
\(289\) −3.96254 −0.233091
\(290\) −5.93496 1.70597i −0.348513 0.100178i
\(291\) 0 0
\(292\) 16.6025 + 10.4042i 0.971586 + 0.608860i
\(293\) 10.9744i 0.641131i 0.947226 + 0.320566i \(0.103873\pi\)
−0.947226 + 0.320566i \(0.896127\pi\)
\(294\) 0 0
\(295\) −22.7573 −1.32498
\(296\) 18.8323 16.8907i 1.09460 0.981752i
\(297\) 0 0
\(298\) 1.29834 4.51684i 0.0752108 0.261653i
\(299\) 23.1816i 1.34062i
\(300\) 0 0
\(301\) 1.82597i 0.105247i
\(302\) 16.8208 + 4.83504i 0.967928 + 0.278225i
\(303\) 0 0
\(304\) −5.95018 + 2.88309i −0.341266 + 0.165357i
\(305\) 18.1516 1.03936
\(306\) 0 0
\(307\) 28.2184i 1.61051i −0.592931 0.805254i \(-0.702029\pi\)
0.592931 0.805254i \(-0.297971\pi\)
\(308\) −3.99180 + 6.36990i −0.227454 + 0.362959i
\(309\) 0 0
\(310\) 6.41485 22.3169i 0.364339 1.26751i
\(311\) −24.3156 −1.37881 −0.689407 0.724375i \(-0.742129\pi\)
−0.689407 + 0.724375i \(0.742129\pi\)
\(312\) 0 0
\(313\) −8.29548 −0.468889 −0.234444 0.972130i \(-0.575327\pi\)
−0.234444 + 0.972130i \(0.575327\pi\)
\(314\) 5.07157 17.6437i 0.286205 0.995690i
\(315\) 0 0
\(316\) −12.2764 7.69321i −0.690601 0.432777i
\(317\) 0.906822i 0.0509322i −0.999676 0.0254661i \(-0.991893\pi\)
0.999676 0.0254661i \(-0.00810699\pi\)
\(318\) 0 0
\(319\) 8.96925 0.502182
\(320\) 14.5527 + 1.58658i 0.813519 + 0.0886924i
\(321\) 0 0
\(322\) −10.1657 2.92209i −0.566515 0.162841i
\(323\) 5.96844i 0.332093i
\(324\) 0 0
\(325\) 5.11899i 0.283950i
\(326\) −2.41096 + 8.38759i −0.133531 + 0.464546i
\(327\) 0 0
\(328\) 5.74645 + 6.40699i 0.317295 + 0.353767i
\(329\) 6.21697 0.342753
\(330\) 0 0
\(331\) 31.7662i 1.74603i −0.487697 0.873013i \(-0.662163\pi\)
0.487697 0.873013i \(-0.337837\pi\)
\(332\) 9.55109 15.2411i 0.524184 0.836464i
\(333\) 0 0
\(334\) −7.81681 2.24690i −0.427717 0.122945i
\(335\) 15.9776 0.872948
\(336\) 0 0
\(337\) −34.4231 −1.87515 −0.937573 0.347788i \(-0.886933\pi\)
−0.937573 + 0.347788i \(0.886933\pi\)
\(338\) 4.61253 + 1.32585i 0.250889 + 0.0721166i
\(339\) 0 0
\(340\) 7.01700 11.1973i 0.380550 0.607261i
\(341\) 33.7265i 1.82639i
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −3.84474 + 3.44836i −0.207295 + 0.185923i
\(345\) 0 0
\(346\) 3.16339 11.0052i 0.170065 0.591645i
\(347\) 23.5611i 1.26483i 0.774630 + 0.632414i \(0.217936\pi\)
−0.774630 + 0.632414i \(0.782064\pi\)
\(348\) 0 0
\(349\) 28.6095i 1.53143i −0.643179 0.765716i \(-0.722385\pi\)
0.643179 0.765716i \(-0.277615\pi\)
\(350\) 2.24482 + 0.645259i 0.119990 + 0.0344906i
\(351\) 0 0
\(352\) −20.9510 + 3.62452i −1.11669 + 0.193187i
\(353\) −7.03843 −0.374618 −0.187309 0.982301i \(-0.559976\pi\)
−0.187309 + 0.982301i \(0.559976\pi\)
\(354\) 0 0
\(355\) 22.7321i 1.20650i
\(356\) −2.62588 1.64555i −0.139171 0.0872139i
\(357\) 0 0
\(358\) 6.02159 20.9487i 0.318251 1.10717i
\(359\) −13.2261 −0.698046 −0.349023 0.937114i \(-0.613487\pi\)
−0.349023 + 0.937114i \(0.613487\pi\)
\(360\) 0 0
\(361\) 16.2677 0.856195
\(362\) 2.37079 8.24781i 0.124606 0.433495i
\(363\) 0 0
\(364\) −3.29167 + 5.25266i −0.172530 + 0.275314i
\(365\) 17.9263i 0.938308i
\(366\) 0 0
\(367\) 11.6530 0.608281 0.304140 0.952627i \(-0.401631\pi\)
0.304140 + 0.952627i \(0.401631\pi\)
\(368\) −13.0454 26.9233i −0.680039 1.40347i
\(369\) 0 0
\(370\) −22.2445 6.39406i −1.15644 0.332411i
\(371\) 3.21435i 0.166881i
\(372\) 0 0
\(373\) 9.85547i 0.510297i −0.966902 0.255148i \(-0.917876\pi\)
0.966902 0.255148i \(-0.0821243\pi\)
\(374\) −5.30224 + 18.4462i −0.274172 + 0.953828i
\(375\) 0 0
\(376\) 11.7408 + 13.0904i 0.605487 + 0.675087i
\(377\) 7.39610 0.380919
\(378\) 0 0
\(379\) 34.5581i 1.77513i 0.460684 + 0.887564i \(0.347604\pi\)
−0.460684 + 0.887564i \(0.652396\pi\)
\(380\) 5.12605 + 3.21232i 0.262961 + 0.164789i
\(381\) 0 0
\(382\) −3.75992 1.08077i −0.192374 0.0552968i
\(383\) 11.4073 0.582884 0.291442 0.956589i \(-0.405865\pi\)
0.291442 + 0.956589i \(0.405865\pi\)
\(384\) 0 0
\(385\) 6.87784 0.350527
\(386\) −24.4355 7.02385i −1.24373 0.357504i
\(387\) 0 0
\(388\) −17.3851 10.8946i −0.882593 0.553092i
\(389\) 37.3093i 1.89166i 0.324667 + 0.945828i \(0.394748\pi\)
−0.324667 + 0.945828i \(0.605252\pi\)
\(390\) 0 0
\(391\) −27.0060 −1.36575
\(392\) 1.88851 + 2.10559i 0.0953842 + 0.106349i
\(393\) 0 0
\(394\) 4.10921 14.2957i 0.207019 0.720206i
\(395\) 13.2553i 0.666947i
\(396\) 0 0
\(397\) 10.8903i 0.546567i 0.961934 + 0.273283i \(0.0881097\pi\)
−0.961934 + 0.273283i \(0.911890\pi\)
\(398\) 5.57226 + 1.60171i 0.279312 + 0.0802867i
\(399\) 0 0
\(400\) 2.88071 + 5.94525i 0.144035 + 0.297262i
\(401\) 20.6784 1.03263 0.516316 0.856398i \(-0.327303\pi\)
0.516316 + 0.856398i \(0.327303\pi\)
\(402\) 0 0
\(403\) 27.8111i 1.38537i
\(404\) 6.34965 10.1324i 0.315907 0.504107i
\(405\) 0 0
\(406\) 0.932294 3.24339i 0.0462690 0.160967i
\(407\) 33.6172 1.66634
\(408\) 0 0
\(409\) −16.1209 −0.797129 −0.398565 0.917140i \(-0.630492\pi\)
−0.398565 + 0.917140i \(0.630492\pi\)
\(410\) 2.17535 7.56789i 0.107433 0.373751i
\(411\) 0 0
\(412\) −28.6510 17.9546i −1.41153 0.884559i
\(413\) 12.4366i 0.611965i
\(414\) 0 0
\(415\) −16.4564 −0.807814
\(416\) −17.2763 + 2.98880i −0.847041 + 0.146538i
\(417\) 0 0
\(418\) −8.44449 2.42732i −0.413034 0.118724i
\(419\) 26.5958i 1.29929i 0.760237 + 0.649645i \(0.225083\pi\)
−0.760237 + 0.649645i \(0.774917\pi\)
\(420\) 0 0
\(421\) 27.2198i 1.32661i −0.748348 0.663307i \(-0.769153\pi\)
0.748348 0.663307i \(-0.230847\pi\)
\(422\) −8.27435 + 28.7859i −0.402789 + 1.40128i
\(423\) 0 0
\(424\) 6.76811 6.07034i 0.328689 0.294802i
\(425\) 5.96350 0.289272
\(426\) 0 0
\(427\) 9.91962i 0.480044i
\(428\) −2.27608 + 3.63205i −0.110019 + 0.175562i
\(429\) 0 0
\(430\) 4.54138 + 1.30539i 0.219005 + 0.0629517i
\(431\) 4.58135 0.220676 0.110338 0.993894i \(-0.464807\pi\)
0.110338 + 0.993894i \(0.464807\pi\)
\(432\) 0 0
\(433\) 4.43085 0.212933 0.106466 0.994316i \(-0.466046\pi\)
0.106466 + 0.994316i \(0.466046\pi\)
\(434\) 12.1959 + 3.50565i 0.585423 + 0.168276i
\(435\) 0 0
\(436\) 8.86554 14.1471i 0.424582 0.677525i
\(437\) 12.3631i 0.591407i
\(438\) 0 0
\(439\) −11.2867 −0.538685 −0.269343 0.963044i \(-0.586806\pi\)
−0.269343 + 0.963044i \(0.586806\pi\)
\(440\) 12.9889 + 14.4819i 0.619220 + 0.690399i
\(441\) 0 0
\(442\) −4.37226 + 15.2108i −0.207967 + 0.723505i
\(443\) 3.69129i 0.175378i 0.996148 + 0.0876892i \(0.0279482\pi\)
−0.996148 + 0.0876892i \(0.972052\pi\)
\(444\) 0 0
\(445\) 2.83526i 0.134404i
\(446\) −3.13587 0.901388i −0.148488 0.0426820i
\(447\) 0 0
\(448\) −0.867047 + 7.95288i −0.0409641 + 0.375738i
\(449\) −18.0692 −0.852737 −0.426368 0.904550i \(-0.640207\pi\)
−0.426368 + 0.904550i \(0.640207\pi\)
\(450\) 0 0
\(451\) 11.4370i 0.538548i
\(452\) −29.8104 18.6812i −1.40216 0.878689i
\(453\) 0 0
\(454\) 1.05097 3.65626i 0.0493246 0.171597i
\(455\) 5.67151 0.265884
\(456\) 0 0
\(457\) −21.4880 −1.00517 −0.502583 0.864529i \(-0.667617\pi\)
−0.502583 + 0.864529i \(0.667617\pi\)
\(458\) 5.98593 20.8247i 0.279704 0.973073i
\(459\) 0 0
\(460\) −14.5351 + 23.1943i −0.677702 + 1.08144i
\(461\) 16.7622i 0.780695i −0.920668 0.390348i \(-0.872355\pi\)
0.920668 0.390348i \(-0.127645\pi\)
\(462\) 0 0
\(463\) −9.74065 −0.452686 −0.226343 0.974048i \(-0.572677\pi\)
−0.226343 + 0.974048i \(0.572677\pi\)
\(464\) 8.58991 4.16215i 0.398776 0.193223i
\(465\) 0 0
\(466\) 29.0708 + 8.35624i 1.34668 + 0.387096i
\(467\) 33.8683i 1.56724i 0.621241 + 0.783620i \(0.286629\pi\)
−0.621241 + 0.783620i \(0.713371\pi\)
\(468\) 0 0
\(469\) 8.73156i 0.403186i
\(470\) 4.44455 15.4623i 0.205012 0.713222i
\(471\) 0 0
\(472\) 26.1864 23.4867i 1.20533 1.08106i
\(473\) −6.86319 −0.315570
\(474\) 0 0
\(475\) 2.73004i 0.125263i
\(476\) 6.11922 + 3.83471i 0.280474 + 0.175764i
\(477\) 0 0
\(478\) −9.57606 2.75258i −0.437999 0.125900i
\(479\) −12.0611 −0.551084 −0.275542 0.961289i \(-0.588857\pi\)
−0.275542 + 0.961289i \(0.588857\pi\)
\(480\) 0 0
\(481\) 27.7209 1.26397
\(482\) −0.467030 0.134245i −0.0212726 0.00611470i
\(483\) 0 0
\(484\) −5.30031 3.32153i −0.240923 0.150978i
\(485\) 18.7714i 0.852364i
\(486\) 0 0
\(487\) −11.5752 −0.524522 −0.262261 0.964997i \(-0.584468\pi\)
−0.262261 + 0.964997i \(0.584468\pi\)
\(488\) −20.8867 + 18.7333i −0.945496 + 0.848018i
\(489\) 0 0
\(490\) 0.714906 2.48711i 0.0322961 0.112356i
\(491\) 40.0965i 1.80953i −0.425911 0.904765i \(-0.640046\pi\)
0.425911 0.904765i \(-0.359954\pi\)
\(492\) 0 0
\(493\) 8.61627i 0.388057i
\(494\) −6.96338 2.00158i −0.313297 0.0900556i
\(495\) 0 0
\(496\) 15.6507 + 32.3001i 0.702735 + 1.45032i
\(497\) −12.4229 −0.557241
\(498\) 0 0
\(499\) 33.2035i 1.48639i −0.669073 0.743197i \(-0.733309\pi\)
0.669073 0.743197i \(-0.266691\pi\)
\(500\) 12.9265 20.6274i 0.578090 0.922485i
\(501\) 0 0
\(502\) 2.99018 10.4026i 0.133458 0.464292i
\(503\) 4.46295 0.198993 0.0994967 0.995038i \(-0.468277\pi\)
0.0994967 + 0.995038i \(0.468277\pi\)
\(504\) 0 0
\(505\) −10.9404 −0.486841
\(506\) 10.9831 38.2096i 0.488260 1.69862i
\(507\) 0 0
\(508\) 16.4969 + 10.3381i 0.731933 + 0.458678i
\(509\) 28.2457i 1.25197i 0.779837 + 0.625983i \(0.215302\pi\)
−0.779837 + 0.625983i \(0.784698\pi\)
\(510\) 0 0
\(511\) 9.79655 0.433374
\(512\) −18.3830 + 13.1935i −0.812419 + 0.583074i
\(513\) 0 0
\(514\) 9.52966 + 2.73925i 0.420335 + 0.120823i
\(515\) 30.9356i 1.36318i
\(516\) 0 0
\(517\) 23.3675i 1.02770i
\(518\) 3.49428 12.1564i 0.153530 0.534121i
\(519\) 0 0
\(520\) 10.7107 + 11.9419i 0.469696 + 0.523687i
\(521\) 30.4655 1.33472 0.667359 0.744737i \(-0.267425\pi\)
0.667359 + 0.744737i \(0.267425\pi\)
\(522\) 0 0
\(523\) 36.5909i 1.60001i −0.599994 0.800004i \(-0.704831\pi\)
0.599994 0.800004i \(-0.295169\pi\)
\(524\) −17.7695 + 28.3556i −0.776264 + 1.23872i
\(525\) 0 0
\(526\) 32.7397 + 9.41085i 1.42752 + 0.410332i
\(527\) 32.3992 1.41133
\(528\) 0 0
\(529\) 32.9405 1.43219
\(530\) −7.99444 2.29796i −0.347256 0.0998169i
\(531\) 0 0
\(532\) −1.75550 + 2.80133i −0.0761105 + 0.121453i
\(533\) 9.43104i 0.408504i
\(534\) 0 0
\(535\) 3.92167 0.169548
\(536\) −18.3851 + 16.4897i −0.794116 + 0.712245i
\(537\) 0 0
\(538\) 5.66130 19.6953i 0.244076 0.849124i
\(539\) 3.75866i 0.161897i
\(540\) 0 0
\(541\) 42.8045i 1.84031i −0.391556 0.920154i \(-0.628063\pi\)
0.391556 0.920154i \(-0.371937\pi\)
\(542\) 38.4725 + 11.0587i 1.65254 + 0.475012i
\(543\) 0 0
\(544\) 3.48188 + 20.1265i 0.149284 + 0.862916i
\(545\) −15.2752 −0.654319
\(546\) 0 0
\(547\) 6.57128i 0.280968i −0.990083 0.140484i \(-0.955134\pi\)
0.990083 0.140484i \(-0.0448658\pi\)
\(548\) −25.7424 16.1319i −1.09966 0.689121i
\(549\) 0 0
\(550\) −2.42531 + 8.43750i −0.103416 + 0.359776i
\(551\) 3.94446 0.168040
\(552\) 0 0
\(553\) −7.24388 −0.308041
\(554\) 3.79083 13.1880i 0.161057 0.560306i
\(555\) 0 0
\(556\) −9.90176 + 15.8007i −0.419928 + 0.670098i
\(557\) 31.2762i 1.32521i 0.748967 + 0.662607i \(0.230550\pi\)
−0.748967 + 0.662607i \(0.769450\pi\)
\(558\) 0 0
\(559\) −5.65943 −0.239368
\(560\) 6.58695 3.19163i 0.278349 0.134871i
\(561\) 0 0
\(562\) −21.8028 6.26710i −0.919697 0.264362i
\(563\) 3.69436i 0.155699i −0.996965 0.0778493i \(-0.975195\pi\)
0.996965 0.0778493i \(-0.0248053\pi\)
\(564\) 0 0
\(565\) 32.1875i 1.35414i
\(566\) −4.31029 + 14.9952i −0.181175 + 0.630296i
\(567\) 0 0
\(568\) −23.4607 26.1575i −0.984390 1.09754i
\(569\) −11.6082 −0.486641 −0.243320 0.969946i \(-0.578237\pi\)
−0.243320 + 0.969946i \(0.578237\pi\)
\(570\) 0 0
\(571\) 26.8739i 1.12464i 0.826920 + 0.562319i \(0.190091\pi\)
−0.826920 + 0.562319i \(0.809909\pi\)
\(572\) −19.7430 12.3723i −0.825495 0.517310i
\(573\) 0 0
\(574\) 4.13577 + 1.18880i 0.172624 + 0.0496197i
\(575\) −12.3529 −0.515150
\(576\) 0 0
\(577\) 10.2051 0.424843 0.212421 0.977178i \(-0.431865\pi\)
0.212421 + 0.977178i \(0.431865\pi\)
\(578\) −5.38580 1.54812i −0.224020 0.0643932i
\(579\) 0 0
\(580\) −7.40016 4.63743i −0.307275 0.192559i
\(581\) 8.99325i 0.373103i
\(582\) 0 0
\(583\) 12.0817 0.500371
\(584\) 18.5009 + 20.6275i 0.765573 + 0.853574i
\(585\) 0 0
\(586\) −4.28756 + 14.9162i −0.177118 + 0.616181i
\(587\) 25.0075i 1.03217i −0.856538 0.516085i \(-0.827389\pi\)
0.856538 0.516085i \(-0.172611\pi\)
\(588\) 0 0
\(589\) 14.8321i 0.611146i
\(590\) −30.9312 8.89100i −1.27342 0.366037i
\(591\) 0 0
\(592\) 32.1954 15.5999i 1.32322 0.641153i
\(593\) 43.4040 1.78239 0.891195 0.453620i \(-0.149868\pi\)
0.891195 + 0.453620i \(0.149868\pi\)
\(594\) 0 0
\(595\) 6.60717i 0.270867i
\(596\) 3.52935 5.63194i 0.144568 0.230693i
\(597\) 0 0
\(598\) 9.05676 31.5079i 0.370358 1.28845i
\(599\) −2.47057 −0.100945 −0.0504724 0.998725i \(-0.516073\pi\)
−0.0504724 + 0.998725i \(0.516073\pi\)
\(600\) 0 0
\(601\) −13.2142 −0.539018 −0.269509 0.962998i \(-0.586861\pi\)
−0.269509 + 0.962998i \(0.586861\pi\)
\(602\) −0.713383 + 2.48181i −0.0290753 + 0.101151i
\(603\) 0 0
\(604\) 20.9734 + 13.1434i 0.853397 + 0.534795i
\(605\) 5.72296i 0.232671i
\(606\) 0 0
\(607\) 29.4562 1.19559 0.597796 0.801649i \(-0.296043\pi\)
0.597796 + 0.801649i \(0.296043\pi\)
\(608\) −9.21373 + 1.59397i −0.373666 + 0.0646442i
\(609\) 0 0
\(610\) 24.6712 + 7.09159i 0.998907 + 0.287130i
\(611\) 19.2690i 0.779539i
\(612\) 0 0
\(613\) 16.9457i 0.684429i 0.939622 + 0.342215i \(0.111177\pi\)
−0.939622 + 0.342215i \(0.888823\pi\)
\(614\) 11.0246 38.3538i 0.444916 1.54783i
\(615\) 0 0
\(616\) −7.91421 + 7.09827i −0.318873 + 0.285998i
\(617\) 42.1917 1.69858 0.849288 0.527930i \(-0.177032\pi\)
0.849288 + 0.527930i \(0.177032\pi\)
\(618\) 0 0
\(619\) 47.7508i 1.91927i 0.281256 + 0.959633i \(0.409249\pi\)
−0.281256 + 0.959633i \(0.590751\pi\)
\(620\) 17.4379 27.8264i 0.700321 1.11753i
\(621\) 0 0
\(622\) −33.0493 9.49982i −1.32515 0.380908i
\(623\) −1.54944 −0.0620770
\(624\) 0 0
\(625\) −14.0142 −0.560569
\(626\) −11.2750 3.24095i −0.450641 0.129534i
\(627\) 0 0
\(628\) 13.7863 21.9995i 0.550135 0.877875i
\(629\) 32.2942i 1.28765i
\(630\) 0 0
\(631\) 29.3539 1.16856 0.584279 0.811553i \(-0.301377\pi\)
0.584279 + 0.811553i \(0.301377\pi\)
\(632\) −13.6802 15.2527i −0.544167 0.606719i
\(633\) 0 0
\(634\) 0.354284 1.23253i 0.0140704 0.0489501i
\(635\) 17.8124i 0.706863i
\(636\) 0 0
\(637\) 3.09942i 0.122803i
\(638\) 12.1908 + 3.50418i 0.482638 + 0.138732i
\(639\) 0 0
\(640\) 19.1598 + 7.84200i 0.757358 + 0.309982i
\(641\) 15.2796 0.603509 0.301754 0.953386i \(-0.402428\pi\)
0.301754 + 0.953386i \(0.402428\pi\)
\(642\) 0 0
\(643\) 26.8547i 1.05905i −0.848295 0.529524i \(-0.822371\pi\)
0.848295 0.529524i \(-0.177629\pi\)
\(644\) −12.6754 7.94327i −0.499482 0.313008i
\(645\) 0 0
\(646\) −2.33180 + 8.11217i −0.0917433 + 0.319169i
\(647\) −13.6808 −0.537850 −0.268925 0.963161i \(-0.586668\pi\)
−0.268925 + 0.963161i \(0.586668\pi\)
\(648\) 0 0
\(649\) 46.7450 1.83490
\(650\) −1.99993 + 6.95762i −0.0784436 + 0.272900i
\(651\) 0 0
\(652\) −6.55386 + 10.4583i −0.256669 + 0.409578i
\(653\) 5.65064i 0.221127i −0.993869 0.110563i \(-0.964734\pi\)
0.993869 0.110563i \(-0.0352655\pi\)
\(654\) 0 0
\(655\) 30.6167 1.19629
\(656\) 5.30731 + 10.9533i 0.207216 + 0.427655i
\(657\) 0 0
\(658\) 8.44997 + 2.42890i 0.329414 + 0.0946882i
\(659\) 24.7127i 0.962669i 0.876537 + 0.481334i \(0.159848\pi\)
−0.876537 + 0.481334i \(0.840152\pi\)
\(660\) 0 0
\(661\) 20.1467i 0.783615i −0.920047 0.391807i \(-0.871850\pi\)
0.920047 0.391807i \(-0.128150\pi\)
\(662\) 12.4106 43.1758i 0.482354 1.67808i
\(663\) 0 0
\(664\) 18.9361 16.9839i 0.734865 0.659102i
\(665\) 3.02470 0.117293
\(666\) 0 0
\(667\) 17.8479i 0.691072i
\(668\) −9.74659 6.10786i −0.377107 0.236320i
\(669\) 0 0
\(670\) 21.7163 + 6.24224i 0.838976 + 0.241159i
\(671\) −37.2845 −1.43935
\(672\) 0 0
\(673\) −23.0926 −0.890155 −0.445077 0.895492i \(-0.646824\pi\)
−0.445077 + 0.895492i \(0.646824\pi\)
\(674\) −46.7871 13.4487i −1.80217 0.518024i
\(675\) 0 0
\(676\) 5.75126 + 3.60412i 0.221202 + 0.138620i
\(677\) 5.41515i 0.208121i −0.994571 0.104061i \(-0.966816\pi\)
0.994571 0.104061i \(-0.0331836\pi\)
\(678\) 0 0
\(679\) −10.2583 −0.393679
\(680\) 13.9120 12.4777i 0.533501 0.478498i
\(681\) 0 0
\(682\) −13.1765 + 45.8403i −0.504556 + 1.75532i
\(683\) 16.5403i 0.632898i 0.948609 + 0.316449i \(0.102491\pi\)
−0.948609 + 0.316449i \(0.897509\pi\)
\(684\) 0 0
\(685\) 27.7951i 1.06200i
\(686\) 1.35918 + 0.390688i 0.0518936 + 0.0149165i
\(687\) 0 0
\(688\) −6.57292 + 3.18484i −0.250590 + 0.121421i
\(689\) 9.96261 0.379545
\(690\) 0 0
\(691\) 17.8893i 0.680542i −0.940327 0.340271i \(-0.889481\pi\)
0.940327 0.340271i \(-0.110519\pi\)
\(692\) 8.59922 13.7222i 0.326893 0.521638i
\(693\) 0 0
\(694\) −9.20505 + 32.0238i −0.349419 + 1.21561i
\(695\) 17.0606 0.647147
\(696\) 0 0
\(697\) 10.9869 0.416160
\(698\) 11.1774 38.8854i 0.423070 1.47183i
\(699\) 0 0
\(700\) 2.79901 + 1.75404i 0.105793 + 0.0662966i
\(701\) 28.6956i 1.08382i 0.840437 + 0.541909i \(0.182298\pi\)
−0.840437 + 0.541909i \(0.817702\pi\)
\(702\) 0 0
\(703\) 14.7840 0.557590
\(704\) −29.8922 3.25894i −1.12660 0.122826i
\(705\) 0 0
\(706\) −9.56647 2.74983i −0.360039 0.103491i
\(707\) 5.97880i 0.224856i
\(708\) 0 0
\(709\) 43.2083i 1.62272i 0.584546 + 0.811360i \(0.301272\pi\)
−0.584546 + 0.811360i \(0.698728\pi\)
\(710\) −8.88117 + 30.8970i −0.333304 + 1.15954i
\(711\) 0 0
\(712\) −2.92614 3.26249i −0.109662 0.122267i
\(713\) −67.1122 −2.51337
\(714\) 0 0
\(715\) 21.3173i 0.797221i
\(716\) 16.3688 26.1205i 0.611732 0.976168i
\(717\) 0 0
\(718\) −17.9766 5.16727i −0.670881 0.192841i
\(719\) −40.7179 −1.51852 −0.759261 0.650786i \(-0.774440\pi\)
−0.759261 + 0.650786i \(0.774440\pi\)
\(720\) 0 0
\(721\) −16.9060 −0.629611
\(722\) 22.1107 + 6.35559i 0.822875 + 0.236531i
\(723\) 0 0
\(724\) 6.44463 10.2840i 0.239513 0.382202i
\(725\) 3.94119i 0.146372i
\(726\) 0 0
\(727\) −1.96551 −0.0728967 −0.0364483 0.999336i \(-0.511604\pi\)
−0.0364483 + 0.999336i \(0.511604\pi\)
\(728\) −6.52611 + 5.85328i −0.241874 + 0.216937i
\(729\) 0 0
\(730\) 7.00361 24.3651i 0.259215 0.901792i
\(731\) 6.59310i 0.243854i
\(732\) 0 0
\(733\) 39.1211i 1.44497i 0.691386 + 0.722486i \(0.257001\pi\)
−0.691386 + 0.722486i \(0.742999\pi\)
\(734\) 15.8385 + 4.55268i 0.584609 + 0.168042i
\(735\) 0 0
\(736\) −7.21240 41.6902i −0.265853 1.53672i
\(737\) −32.8190 −1.20890
\(738\) 0 0
\(739\) 36.1851i 1.33109i 0.746357 + 0.665546i \(0.231801\pi\)
−0.746357 + 0.665546i \(0.768199\pi\)
\(740\) −27.7362 17.3813i −1.01960 0.638950i
\(741\) 0 0
\(742\) 1.25581 4.36887i 0.0461021 0.160386i
\(743\) −20.1222 −0.738210 −0.369105 0.929388i \(-0.620336\pi\)
−0.369105 + 0.929388i \(0.620336\pi\)
\(744\) 0 0
\(745\) −6.08103 −0.222792
\(746\) 3.85041 13.3953i 0.140974 0.490438i
\(747\) 0 0
\(748\) −14.4134 + 23.0001i −0.527005 + 0.840966i
\(749\) 2.14315i 0.0783089i
\(750\) 0 0
\(751\) −36.2627 −1.32324 −0.661622 0.749838i \(-0.730131\pi\)
−0.661622 + 0.749838i \(0.730131\pi\)
\(752\) 10.8436 + 22.3792i 0.395425 + 0.816085i
\(753\) 0 0
\(754\) 10.0526 + 2.88957i 0.366095 + 0.105232i
\(755\) 22.6459i 0.824167i
\(756\) 0 0
\(757\) 53.6865i 1.95127i −0.219401 0.975635i \(-0.570410\pi\)
0.219401 0.975635i \(-0.429590\pi\)
\(758\) −13.5014 + 46.9705i −0.490393 + 1.70605i
\(759\) 0 0
\(760\) 5.71219 + 6.36880i 0.207203 + 0.231021i
\(761\) 37.3332 1.35333 0.676664 0.736292i \(-0.263425\pi\)
0.676664 + 0.736292i \(0.263425\pi\)
\(762\) 0 0
\(763\) 8.34775i 0.302209i
\(764\) −4.68815 2.93791i −0.169611 0.106290i
\(765\) 0 0
\(766\) 15.5045 + 4.45668i 0.560200 + 0.161026i
\(767\) 38.5462 1.39182
\(768\) 0 0
\(769\) 15.5423 0.560469 0.280235 0.959932i \(-0.409588\pi\)
0.280235 + 0.959932i \(0.409588\pi\)
\(770\) 9.34820 + 2.68709i 0.336886 + 0.0968359i
\(771\) 0 0
\(772\) −30.4680 19.0933i −1.09657 0.687183i
\(773\) 39.0073i 1.40299i −0.712672 0.701497i \(-0.752515\pi\)
0.712672 0.701497i \(-0.247485\pi\)
\(774\) 0 0
\(775\) 14.8198 0.532343
\(776\) −19.3730 21.5999i −0.695450 0.775391i
\(777\) 0 0
\(778\) −14.5763 + 50.7100i −0.522585 + 1.81804i
\(779\) 5.02972i 0.180209i
\(780\) 0 0
\(781\) 46.6933i 1.67082i
\(782\) −36.7059 10.5509i −1.31260 0.377299i
\(783\) 0 0
\(784\) 1.74419 + 3.59969i 0.0622926 + 0.128560i
\(785\) −23.7537 −0.847807
\(786\) 0 0