Properties

Label 216.2.d.c.109.1
Level $216$
Weight $2$
Character 216.109
Analytic conductor $1.725$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 216 = 2^{3} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 216.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.72476868366\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.629407744.1
Defining polynomial: \(x^{8} - 2 x^{6} + 2 x^{4} - 8 x^{2} + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 109.1
Root \(-1.38255 - 0.297594i\) of defining polynomial
Character \(\chi\) \(=\) 216.109
Dual form 216.2.d.c.109.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.38255 - 0.297594i) q^{2} +(1.82288 + 0.822876i) q^{4} -3.36028i q^{5} -2.64575 q^{7} +(-2.27533 - 1.68014i) q^{8} +O(q^{10})\) \(q+(-1.38255 - 0.297594i) q^{2} +(1.82288 + 0.822876i) q^{4} -3.36028i q^{5} -2.64575 q^{7} +(-2.27533 - 1.68014i) q^{8} +(-1.00000 + 4.64575i) q^{10} +2.16991i q^{11} -4.64575i q^{13} +(3.65788 + 0.787360i) q^{14} +(2.64575 + 3.00000i) q^{16} -4.55066 q^{17} -6.29150i q^{19} +(2.76510 - 6.12538i) q^{20} +(0.645751 - 3.00000i) q^{22} -0.979531 q^{23} -6.29150 q^{25} +(-1.38255 + 6.42297i) q^{26} +(-4.82288 - 2.17712i) q^{28} -4.33981i q^{29} +2.00000 q^{31} +(-2.76510 - 4.93500i) q^{32} +(6.29150 + 1.35425i) q^{34} +8.89047i q^{35} +1.35425i q^{37} +(-1.87231 + 8.69830i) q^{38} +(-5.64575 + 7.64575i) q^{40} +11.0604 q^{41} +3.29150i q^{43} +(-1.78556 + 3.95547i) q^{44} +(1.35425 + 0.291503i) q^{46} +10.0808 q^{47} +(8.69830 + 1.87231i) q^{50} +(3.82288 - 8.46863i) q^{52} -4.33981i q^{53} +7.29150 q^{55} +(6.01996 + 4.44524i) q^{56} +(-1.29150 + 6.00000i) q^{58} +11.2712i q^{59} +1.93725i q^{61} +(-2.76510 - 0.595188i) q^{62} +(2.35425 + 7.64575i) q^{64} -15.6110 q^{65} +3.00000i q^{67} +(-8.29529 - 3.74463i) q^{68} +(2.64575 - 12.2915i) q^{70} +11.5830 q^{73} +(0.403016 - 1.87231i) q^{74} +(5.17712 - 11.4686i) q^{76} -5.74103i q^{77} -8.64575 q^{79} +(10.0808 - 8.89047i) q^{80} +(-15.2915 - 3.29150i) q^{82} -2.38075i q^{83} +15.2915i q^{85} +(0.979531 - 4.55066i) q^{86} +(3.64575 - 4.93725i) q^{88} +4.55066 q^{89} +12.2915i q^{91} +(-1.78556 - 0.806032i) q^{92} +(-13.9373 - 3.00000i) q^{94} -21.1412 q^{95} +2.29150 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{4} + O(q^{10}) \) \( 8q + 4q^{4} - 8q^{10} - 16q^{22} - 8q^{25} - 28q^{28} + 16q^{31} + 8q^{34} - 24q^{40} + 32q^{46} + 20q^{52} + 16q^{55} + 32q^{58} + 40q^{64} + 8q^{73} + 52q^{76} - 48q^{79} - 80q^{82} + 8q^{88} - 48q^{94} - 24q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).

\(n\) \(55\) \(109\) \(137\)
\(\chi(n)\) \(1\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38255 0.297594i −0.977609 0.210431i
\(3\) 0 0
\(4\) 1.82288 + 0.822876i 0.911438 + 0.411438i
\(5\) 3.36028i 1.50276i −0.659867 0.751382i \(-0.729388\pi\)
0.659867 0.751382i \(-0.270612\pi\)
\(6\) 0 0
\(7\) −2.64575 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(8\) −2.27533 1.68014i −0.804450 0.594020i
\(9\) 0 0
\(10\) −1.00000 + 4.64575i −0.316228 + 1.46912i
\(11\) 2.16991i 0.654252i 0.944981 + 0.327126i \(0.106080\pi\)
−0.944981 + 0.327126i \(0.893920\pi\)
\(12\) 0 0
\(13\) 4.64575i 1.28850i −0.764815 0.644250i \(-0.777170\pi\)
0.764815 0.644250i \(-0.222830\pi\)
\(14\) 3.65788 + 0.787360i 0.977609 + 0.210431i
\(15\) 0 0
\(16\) 2.64575 + 3.00000i 0.661438 + 0.750000i
\(17\) −4.55066 −1.10370 −0.551848 0.833944i \(-0.686077\pi\)
−0.551848 + 0.833944i \(0.686077\pi\)
\(18\) 0 0
\(19\) 6.29150i 1.44337i −0.692222 0.721685i \(-0.743368\pi\)
0.692222 0.721685i \(-0.256632\pi\)
\(20\) 2.76510 6.12538i 0.618294 1.36968i
\(21\) 0 0
\(22\) 0.645751 3.00000i 0.137675 0.639602i
\(23\) −0.979531 −0.204246 −0.102123 0.994772i \(-0.532564\pi\)
−0.102123 + 0.994772i \(0.532564\pi\)
\(24\) 0 0
\(25\) −6.29150 −1.25830
\(26\) −1.38255 + 6.42297i −0.271140 + 1.25965i
\(27\) 0 0
\(28\) −4.82288 2.17712i −0.911438 0.411438i
\(29\) 4.33981i 0.805883i −0.915226 0.402942i \(-0.867988\pi\)
0.915226 0.402942i \(-0.132012\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −2.76510 4.93500i −0.488804 0.872393i
\(33\) 0 0
\(34\) 6.29150 + 1.35425i 1.07898 + 0.232252i
\(35\) 8.89047i 1.50276i
\(36\) 0 0
\(37\) 1.35425i 0.222637i 0.993785 + 0.111319i \(0.0355074\pi\)
−0.993785 + 0.111319i \(0.964493\pi\)
\(38\) −1.87231 + 8.69830i −0.303729 + 1.41105i
\(39\) 0 0
\(40\) −5.64575 + 7.64575i −0.892672 + 1.20890i
\(41\) 11.0604 1.72734 0.863671 0.504057i \(-0.168160\pi\)
0.863671 + 0.504057i \(0.168160\pi\)
\(42\) 0 0
\(43\) 3.29150i 0.501949i 0.967994 + 0.250975i \(0.0807511\pi\)
−0.967994 + 0.250975i \(0.919249\pi\)
\(44\) −1.78556 + 3.95547i −0.269184 + 0.596310i
\(45\) 0 0
\(46\) 1.35425 + 0.291503i 0.199673 + 0.0429797i
\(47\) 10.0808 1.47044 0.735222 0.677827i \(-0.237078\pi\)
0.735222 + 0.677827i \(0.237078\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 8.69830 + 1.87231i 1.23013 + 0.264785i
\(51\) 0 0
\(52\) 3.82288 8.46863i 0.530137 1.17439i
\(53\) 4.33981i 0.596119i −0.954547 0.298060i \(-0.903661\pi\)
0.954547 0.298060i \(-0.0963394\pi\)
\(54\) 0 0
\(55\) 7.29150 0.983186
\(56\) 6.01996 + 4.44524i 0.804450 + 0.594020i
\(57\) 0 0
\(58\) −1.29150 + 6.00000i −0.169583 + 0.787839i
\(59\) 11.2712i 1.46739i 0.679480 + 0.733694i \(0.262206\pi\)
−0.679480 + 0.733694i \(0.737794\pi\)
\(60\) 0 0
\(61\) 1.93725i 0.248040i 0.992280 + 0.124020i \(0.0395787\pi\)
−0.992280 + 0.124020i \(0.960421\pi\)
\(62\) −2.76510 0.595188i −0.351167 0.0755889i
\(63\) 0 0
\(64\) 2.35425 + 7.64575i 0.294281 + 0.955719i
\(65\) −15.6110 −1.93631
\(66\) 0 0
\(67\) 3.00000i 0.366508i 0.983066 + 0.183254i \(0.0586631\pi\)
−0.983066 + 0.183254i \(0.941337\pi\)
\(68\) −8.29529 3.74463i −1.00595 0.454103i
\(69\) 0 0
\(70\) 2.64575 12.2915i 0.316228 1.46912i
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 11.5830 1.35569 0.677844 0.735206i \(-0.262914\pi\)
0.677844 + 0.735206i \(0.262914\pi\)
\(74\) 0.403016 1.87231i 0.0468497 0.217652i
\(75\) 0 0
\(76\) 5.17712 11.4686i 0.593857 1.31554i
\(77\) 5.74103i 0.654252i
\(78\) 0 0
\(79\) −8.64575 −0.972723 −0.486362 0.873758i \(-0.661676\pi\)
−0.486362 + 0.873758i \(0.661676\pi\)
\(80\) 10.0808 8.89047i 1.12707 0.993985i
\(81\) 0 0
\(82\) −15.2915 3.29150i −1.68866 0.363486i
\(83\) 2.38075i 0.261321i −0.991427 0.130661i \(-0.958290\pi\)
0.991427 0.130661i \(-0.0417099\pi\)
\(84\) 0 0
\(85\) 15.2915i 1.65860i
\(86\) 0.979531 4.55066i 0.105626 0.490710i
\(87\) 0 0
\(88\) 3.64575 4.93725i 0.388638 0.526313i
\(89\) 4.55066 0.482369 0.241184 0.970479i \(-0.422464\pi\)
0.241184 + 0.970479i \(0.422464\pi\)
\(90\) 0 0
\(91\) 12.2915i 1.28850i
\(92\) −1.78556 0.806032i −0.186158 0.0840347i
\(93\) 0 0
\(94\) −13.9373 3.00000i −1.43752 0.309426i
\(95\) −21.1412 −2.16904
\(96\) 0 0
\(97\) 2.29150 0.232667 0.116333 0.993210i \(-0.462886\pi\)
0.116333 + 0.993210i \(0.462886\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −11.4686 5.17712i −1.14686 0.517712i
\(101\) 6.72057i 0.668721i 0.942445 + 0.334361i \(0.108520\pi\)
−0.942445 + 0.334361i \(0.891480\pi\)
\(102\) 0 0
\(103\) −5.35425 −0.527570 −0.263785 0.964582i \(-0.584971\pi\)
−0.263785 + 0.964582i \(0.584971\pi\)
\(104\) −7.80552 + 10.5706i −0.765394 + 1.03653i
\(105\) 0 0
\(106\) −1.29150 + 6.00000i −0.125442 + 0.582772i
\(107\) 17.9918i 1.73933i −0.493640 0.869666i \(-0.664334\pi\)
0.493640 0.869666i \(-0.335666\pi\)
\(108\) 0 0
\(109\) 15.2915i 1.46466i −0.680950 0.732330i \(-0.738433\pi\)
0.680950 0.732330i \(-0.261567\pi\)
\(110\) −10.0808 2.16991i −0.961171 0.206893i
\(111\) 0 0
\(112\) −7.00000 7.93725i −0.661438 0.750000i
\(113\) 6.50972 0.612383 0.306192 0.951970i \(-0.400945\pi\)
0.306192 + 0.951970i \(0.400945\pi\)
\(114\) 0 0
\(115\) 3.29150i 0.306934i
\(116\) 3.57113 7.91094i 0.331571 0.734513i
\(117\) 0 0
\(118\) 3.35425 15.5830i 0.308784 1.43453i
\(119\) 12.0399 1.10370
\(120\) 0 0
\(121\) 6.29150 0.571955
\(122\) 0.576515 2.67835i 0.0521952 0.242486i
\(123\) 0 0
\(124\) 3.64575 + 1.64575i 0.327398 + 0.147793i
\(125\) 4.33981i 0.388165i
\(126\) 0 0
\(127\) 5.29150 0.469545 0.234772 0.972050i \(-0.424565\pi\)
0.234772 + 0.972050i \(0.424565\pi\)
\(128\) −0.979531 11.2712i −0.0865792 0.996245i
\(129\) 0 0
\(130\) 21.5830 + 4.64575i 1.89295 + 0.407459i
\(131\) 15.4002i 1.34552i −0.739860 0.672761i \(-0.765108\pi\)
0.739860 0.672761i \(-0.234892\pi\)
\(132\) 0 0
\(133\) 16.6458i 1.44337i
\(134\) 0.892782 4.14764i 0.0771246 0.358302i
\(135\) 0 0
\(136\) 10.3542 + 7.64575i 0.887870 + 0.655618i
\(137\) −6.50972 −0.556163 −0.278082 0.960557i \(-0.589699\pi\)
−0.278082 + 0.960557i \(0.589699\pi\)
\(138\) 0 0
\(139\) 12.2915i 1.04255i −0.853388 0.521276i \(-0.825456\pi\)
0.853388 0.521276i \(-0.174544\pi\)
\(140\) −7.31575 + 16.2062i −0.618294 + 1.36968i
\(141\) 0 0
\(142\) 0 0
\(143\) 10.0808 0.843003
\(144\) 0 0
\(145\) −14.5830 −1.21105
\(146\) −16.0141 3.44703i −1.32533 0.285278i
\(147\) 0 0
\(148\) −1.11438 + 2.46863i −0.0916013 + 0.202920i
\(149\) 8.67963i 0.711063i 0.934664 + 0.355531i \(0.115700\pi\)
−0.934664 + 0.355531i \(0.884300\pi\)
\(150\) 0 0
\(151\) 12.6458 1.02910 0.514548 0.857461i \(-0.327960\pi\)
0.514548 + 0.857461i \(0.327960\pi\)
\(152\) −10.5706 + 14.3152i −0.857390 + 1.16112i
\(153\) 0 0
\(154\) −1.70850 + 7.93725i −0.137675 + 0.639602i
\(155\) 6.72057i 0.539809i
\(156\) 0 0
\(157\) 8.70850i 0.695014i −0.937677 0.347507i \(-0.887028\pi\)
0.937677 0.347507i \(-0.112972\pi\)
\(158\) 11.9532 + 2.57292i 0.950943 + 0.204691i
\(159\) 0 0
\(160\) −16.5830 + 9.29150i −1.31100 + 0.734558i
\(161\) 2.59160 0.204246
\(162\) 0 0
\(163\) 6.29150i 0.492789i 0.969170 + 0.246394i \(0.0792458\pi\)
−0.969170 + 0.246394i \(0.920754\pi\)
\(164\) 20.1617 + 9.10132i 1.57436 + 0.710694i
\(165\) 0 0
\(166\) −0.708497 + 3.29150i −0.0549901 + 0.255470i
\(167\) −19.1822 −1.48436 −0.742180 0.670200i \(-0.766208\pi\)
−0.742180 + 0.670200i \(0.766208\pi\)
\(168\) 0 0
\(169\) −8.58301 −0.660231
\(170\) 4.55066 21.1412i 0.349020 1.62146i
\(171\) 0 0
\(172\) −2.70850 + 6.00000i −0.206521 + 0.457496i
\(173\) 15.8219i 1.20292i 0.798905 + 0.601458i \(0.205413\pi\)
−0.798905 + 0.601458i \(0.794587\pi\)
\(174\) 0 0
\(175\) 16.6458 1.25830
\(176\) −6.50972 + 5.74103i −0.490689 + 0.432747i
\(177\) 0 0
\(178\) −6.29150 1.35425i −0.471568 0.101505i
\(179\) 4.76150i 0.355891i 0.984040 + 0.177946i \(0.0569452\pi\)
−0.984040 + 0.177946i \(0.943055\pi\)
\(180\) 0 0
\(181\) 16.6458i 1.23727i 0.785679 + 0.618634i \(0.212314\pi\)
−0.785679 + 0.618634i \(0.787686\pi\)
\(182\) 3.65788 16.9936i 0.271140 1.25965i
\(183\) 0 0
\(184\) 2.22876 + 1.64575i 0.164306 + 0.121326i
\(185\) 4.55066 0.334571
\(186\) 0 0
\(187\) 9.87451i 0.722096i
\(188\) 18.3761 + 8.29529i 1.34022 + 0.604996i
\(189\) 0 0
\(190\) 29.2288 + 6.29150i 2.12048 + 0.456434i
\(191\) −8.12179 −0.587672 −0.293836 0.955856i \(-0.594932\pi\)
−0.293836 + 0.955856i \(0.594932\pi\)
\(192\) 0 0
\(193\) −4.29150 −0.308909 −0.154455 0.988000i \(-0.549362\pi\)
−0.154455 + 0.988000i \(0.549362\pi\)
\(194\) −3.16811 0.681937i −0.227457 0.0489602i
\(195\) 0 0
\(196\) 0 0
\(197\) 7.70010i 0.548609i 0.961643 + 0.274305i \(0.0884477\pi\)
−0.961643 + 0.274305i \(0.911552\pi\)
\(198\) 0 0
\(199\) −18.5203 −1.31287 −0.656433 0.754384i \(-0.727936\pi\)
−0.656433 + 0.754384i \(0.727936\pi\)
\(200\) 14.3152 + 10.5706i 1.01224 + 0.747455i
\(201\) 0 0
\(202\) 2.00000 9.29150i 0.140720 0.653748i
\(203\) 11.4821i 0.805883i
\(204\) 0 0
\(205\) 37.1660i 2.59579i
\(206\) 7.40250 + 1.59339i 0.515757 + 0.111017i
\(207\) 0 0
\(208\) 13.9373 12.2915i 0.966375 0.852262i
\(209\) 13.6520 0.944327
\(210\) 0 0
\(211\) 0.291503i 0.0200679i 0.999950 + 0.0100339i \(0.00319395\pi\)
−0.999950 + 0.0100339i \(0.996806\pi\)
\(212\) 3.57113 7.91094i 0.245266 0.543326i
\(213\) 0 0
\(214\) −5.35425 + 24.8745i −0.366009 + 1.70039i
\(215\) 11.0604 0.754312
\(216\) 0 0
\(217\) −5.29150 −0.359211
\(218\) −4.55066 + 21.1412i −0.308210 + 1.43186i
\(219\) 0 0
\(220\) 13.2915 + 6.00000i 0.896113 + 0.404520i
\(221\) 21.1412i 1.42211i
\(222\) 0 0
\(223\) −10.0000 −0.669650 −0.334825 0.942280i \(-0.608677\pi\)
−0.334825 + 0.942280i \(0.608677\pi\)
\(224\) 7.31575 + 13.0568i 0.488804 + 0.872393i
\(225\) 0 0
\(226\) −9.00000 1.93725i −0.598671 0.128864i
\(227\) 13.4411i 0.892119i −0.895003 0.446060i \(-0.852827\pi\)
0.895003 0.446060i \(-0.147173\pi\)
\(228\) 0 0
\(229\) 13.1660i 0.870034i −0.900422 0.435017i \(-0.856742\pi\)
0.900422 0.435017i \(-0.143258\pi\)
\(230\) 0.979531 4.55066i 0.0645884 0.300062i
\(231\) 0 0
\(232\) −7.29150 + 9.87451i −0.478711 + 0.648293i
\(233\) −9.10132 −0.596247 −0.298124 0.954527i \(-0.596361\pi\)
−0.298124 + 0.954527i \(0.596361\pi\)
\(234\) 0 0
\(235\) 33.8745i 2.20973i
\(236\) −9.27482 + 20.5460i −0.603739 + 1.33743i
\(237\) 0 0
\(238\) −16.6458 3.58301i −1.07898 0.232252i
\(239\) 20.1617 1.30415 0.652076 0.758154i \(-0.273898\pi\)
0.652076 + 0.758154i \(0.273898\pi\)
\(240\) 0 0
\(241\) 26.8745 1.73114 0.865570 0.500789i \(-0.166957\pi\)
0.865570 + 0.500789i \(0.166957\pi\)
\(242\) −8.69830 1.87231i −0.559148 0.120357i
\(243\) 0 0
\(244\) −1.59412 + 3.53137i −0.102053 + 0.226073i
\(245\) 0 0
\(246\) 0 0
\(247\) −29.2288 −1.85978
\(248\) −4.55066 3.36028i −0.288967 0.213378i
\(249\) 0 0
\(250\) 1.29150 6.00000i 0.0816818 0.379473i
\(251\) 24.5015i 1.54652i −0.634088 0.773261i \(-0.718624\pi\)
0.634088 0.773261i \(-0.281376\pi\)
\(252\) 0 0
\(253\) 2.12549i 0.133629i
\(254\) −7.31575 1.57472i −0.459031 0.0988067i
\(255\) 0 0
\(256\) −2.00000 + 15.8745i −0.125000 + 0.992157i
\(257\) 20.1617 1.25765 0.628826 0.777546i \(-0.283536\pi\)
0.628826 + 0.777546i \(0.283536\pi\)
\(258\) 0 0
\(259\) 3.58301i 0.222637i
\(260\) −28.4570 12.8459i −1.76483 0.796672i
\(261\) 0 0
\(262\) −4.58301 + 21.2915i −0.283139 + 1.31539i
\(263\) −1.95906 −0.120801 −0.0604005 0.998174i \(-0.519238\pi\)
−0.0604005 + 0.998174i \(0.519238\pi\)
\(264\) 0 0
\(265\) −14.5830 −0.895827
\(266\) 4.95368 23.0135i 0.303729 1.41105i
\(267\) 0 0
\(268\) −2.46863 + 5.46863i −0.150795 + 0.334050i
\(269\) 5.74103i 0.350037i 0.984565 + 0.175019i \(0.0559985\pi\)
−0.984565 + 0.175019i \(0.944001\pi\)
\(270\) 0 0
\(271\) −21.2288 −1.28956 −0.644778 0.764370i \(-0.723050\pi\)
−0.644778 + 0.764370i \(0.723050\pi\)
\(272\) −12.0399 13.6520i −0.730027 0.827773i
\(273\) 0 0
\(274\) 9.00000 + 1.93725i 0.543710 + 0.117034i
\(275\) 13.6520i 0.823245i
\(276\) 0 0
\(277\) 8.70850i 0.523243i 0.965171 + 0.261621i \(0.0842572\pi\)
−0.965171 + 0.261621i \(0.915743\pi\)
\(278\) −3.65788 + 16.9936i −0.219385 + 1.01921i
\(279\) 0 0
\(280\) 14.9373 20.2288i 0.892672 1.20890i
\(281\) −20.1617 −1.20275 −0.601373 0.798968i \(-0.705379\pi\)
−0.601373 + 0.798968i \(0.705379\pi\)
\(282\) 0 0
\(283\) 27.2915i 1.62231i 0.584830 + 0.811156i \(0.301161\pi\)
−0.584830 + 0.811156i \(0.698839\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) −13.9373 3.00000i −0.824127 0.177394i
\(287\) −29.2630 −1.72734
\(288\) 0 0
\(289\) 3.70850 0.218147
\(290\) 20.1617 + 4.33981i 1.18394 + 0.254843i
\(291\) 0 0
\(292\) 21.1144 + 9.53137i 1.23563 + 0.557781i
\(293\) 14.4207i 0.842464i −0.906953 0.421232i \(-0.861598\pi\)
0.906953 0.421232i \(-0.138402\pi\)
\(294\) 0 0
\(295\) 37.8745 2.20514
\(296\) 2.27533 3.08136i 0.132251 0.179101i
\(297\) 0 0
\(298\) 2.58301 12.0000i 0.149629 0.695141i
\(299\) 4.55066i 0.263171i
\(300\) 0 0
\(301\) 8.70850i 0.501949i
\(302\) −17.4834 3.76330i −1.00605 0.216554i
\(303\) 0 0
\(304\) 18.8745 16.6458i 1.08253 0.954699i
\(305\) 6.50972 0.372746
\(306\) 0 0
\(307\) 9.87451i 0.563568i 0.959478 + 0.281784i \(0.0909261\pi\)
−0.959478 + 0.281784i \(0.909074\pi\)
\(308\) 4.72416 10.4652i 0.269184 0.596310i
\(309\) 0 0
\(310\) −2.00000 + 9.29150i −0.113592 + 0.527722i
\(311\) −0.979531 −0.0555441 −0.0277721 0.999614i \(-0.508841\pi\)
−0.0277721 + 0.999614i \(0.508841\pi\)
\(312\) 0 0
\(313\) 14.8745 0.840757 0.420378 0.907349i \(-0.361897\pi\)
0.420378 + 0.907349i \(0.361897\pi\)
\(314\) −2.59160 + 12.0399i −0.146252 + 0.679452i
\(315\) 0 0
\(316\) −15.7601 7.11438i −0.886577 0.400215i
\(317\) 20.5834i 1.15608i −0.816009 0.578039i \(-0.803818\pi\)
0.816009 0.578039i \(-0.196182\pi\)
\(318\) 0 0
\(319\) 9.41699 0.527250
\(320\) 25.6919 7.91094i 1.43622 0.442235i
\(321\) 0 0
\(322\) −3.58301 0.771243i −0.199673 0.0429797i
\(323\) 28.6305i 1.59304i
\(324\) 0 0
\(325\) 29.2288i 1.62132i
\(326\) 1.87231 8.69830i 0.103698 0.481754i
\(327\) 0 0
\(328\) −25.1660 18.5830i −1.38956 1.02607i
\(329\) −26.6714 −1.47044
\(330\) 0 0
\(331\) 5.70850i 0.313767i −0.987617 0.156884i \(-0.949855\pi\)
0.987617 0.156884i \(-0.0501448\pi\)
\(332\) 1.95906 4.33981i 0.107518 0.238178i
\(333\) 0 0
\(334\) 26.5203 + 5.70850i 1.45112 + 0.312355i
\(335\) 10.0808 0.550776
\(336\) 0 0
\(337\) 2.29150 0.124826 0.0624131 0.998050i \(-0.480120\pi\)
0.0624131 + 0.998050i \(0.480120\pi\)
\(338\) 11.8664 + 2.55425i 0.645448 + 0.138933i
\(339\) 0 0
\(340\) −12.5830 + 27.8745i −0.682409 + 1.51171i
\(341\) 4.33981i 0.235014i
\(342\) 0 0
\(343\) 18.5203 1.00000
\(344\) 5.53019 7.48925i 0.298168 0.403793i
\(345\) 0 0
\(346\) 4.70850 21.8745i 0.253130 1.17598i
\(347\) 0.421689i 0.0226375i −0.999936 0.0113187i \(-0.996397\pi\)
0.999936 0.0113187i \(-0.00360294\pi\)
\(348\) 0 0
\(349\) 10.6458i 0.569854i −0.958549 0.284927i \(-0.908031\pi\)
0.958549 0.284927i \(-0.0919694\pi\)
\(350\) −23.0135 4.95368i −1.23013 0.264785i
\(351\) 0 0
\(352\) 10.7085 6.00000i 0.570765 0.319801i
\(353\) 13.0194 0.692955 0.346478 0.938058i \(-0.387378\pi\)
0.346478 + 0.938058i \(0.387378\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 8.29529 + 3.74463i 0.439649 + 0.198465i
\(357\) 0 0
\(358\) 1.41699 6.58301i 0.0748905 0.347923i
\(359\) −21.1412 −1.11579 −0.557896 0.829911i \(-0.688391\pi\)
−0.557896 + 0.829911i \(0.688391\pi\)
\(360\) 0 0
\(361\) −20.5830 −1.08332
\(362\) 4.95368 23.0135i 0.260359 1.20956i
\(363\) 0 0
\(364\) −10.1144 + 22.4059i −0.530137 + 1.17439i
\(365\) 38.9222i 2.03728i
\(366\) 0 0
\(367\) 4.52026 0.235956 0.117978 0.993016i \(-0.462359\pi\)
0.117978 + 0.993016i \(0.462359\pi\)
\(368\) −2.59160 2.93859i −0.135096 0.153185i
\(369\) 0 0
\(370\) −6.29150 1.35425i −0.327080 0.0704040i
\(371\) 11.4821i 0.596119i
\(372\) 0 0
\(373\) 38.5203i 1.99450i 0.0740880 + 0.997252i \(0.476395\pi\)
−0.0740880 + 0.997252i \(0.523605\pi\)
\(374\) −2.93859 + 13.6520i −0.151951 + 0.705927i
\(375\) 0 0
\(376\) −22.9373 16.9373i −1.18290 0.873472i
\(377\) −20.1617 −1.03838
\(378\) 0 0
\(379\) 21.5830i 1.10864i 0.832302 + 0.554322i \(0.187022\pi\)
−0.832302 + 0.554322i \(0.812978\pi\)
\(380\) −38.5378 17.3966i −1.97695 0.892427i
\(381\) 0 0
\(382\) 11.2288 + 2.41699i 0.574513 + 0.123664i
\(383\) 20.1617 1.03021 0.515107 0.857126i \(-0.327752\pi\)
0.515107 + 0.857126i \(0.327752\pi\)
\(384\) 0 0
\(385\) −19.2915 −0.983186
\(386\) 5.93321 + 1.27713i 0.301992 + 0.0650040i
\(387\) 0 0
\(388\) 4.17712 + 1.88562i 0.212061 + 0.0957279i
\(389\) 5.31935i 0.269702i −0.990866 0.134851i \(-0.956944\pi\)
0.990866 0.134851i \(-0.0430555\pi\)
\(390\) 0 0
\(391\) 4.45751 0.225426
\(392\) 0 0
\(393\) 0 0
\(394\) 2.29150 10.6458i 0.115444 0.536325i
\(395\) 29.0522i 1.46177i
\(396\) 0 0
\(397\) 15.2915i 0.767459i −0.923446 0.383729i \(-0.874640\pi\)
0.923446 0.383729i \(-0.125360\pi\)
\(398\) 25.6051 + 5.51152i 1.28347 + 0.276267i
\(399\) 0 0
\(400\) −16.6458 18.8745i −0.832288 0.943725i
\(401\) −13.0194 −0.650160 −0.325080 0.945687i \(-0.605391\pi\)
−0.325080 + 0.945687i \(0.605391\pi\)
\(402\) 0 0
\(403\) 9.29150i 0.462843i
\(404\) −5.53019 + 12.2508i −0.275137 + 0.609498i
\(405\) 0 0
\(406\) 3.41699 15.8745i 0.169583 0.787839i
\(407\) −2.93859 −0.145661
\(408\) 0 0
\(409\) 8.29150 0.409988 0.204994 0.978763i \(-0.434282\pi\)
0.204994 + 0.978763i \(0.434282\pi\)
\(410\) −11.0604 + 51.3838i −0.546233 + 2.53766i
\(411\) 0 0
\(412\) −9.76013 4.40588i −0.480847 0.217062i
\(413\) 29.8209i 1.46739i
\(414\) 0 0
\(415\) −8.00000 −0.392705
\(416\) −22.9268 + 12.8459i −1.12408 + 0.629824i
\(417\) 0 0
\(418\) −18.8745 4.06275i −0.923182 0.198715i
\(419\) 2.16991i 0.106007i 0.998594 + 0.0530035i \(0.0168794\pi\)
−0.998594 + 0.0530035i \(0.983121\pi\)
\(420\) 0 0
\(421\) 22.6458i 1.10369i 0.833948 + 0.551843i \(0.186075\pi\)
−0.833948 + 0.551843i \(0.813925\pi\)
\(422\) 0.0867494 0.403016i 0.00422290 0.0196185i
\(423\) 0 0
\(424\) −7.29150 + 9.87451i −0.354107 + 0.479548i
\(425\) 28.6305 1.38878
\(426\) 0 0
\(427\) 5.12549i 0.248040i
\(428\) 14.8050 32.7968i 0.715627 1.58529i
\(429\) 0 0
\(430\) −15.2915 3.29150i −0.737422 0.158730i
\(431\) 30.2425 1.45673 0.728366 0.685188i \(-0.240280\pi\)
0.728366 + 0.685188i \(0.240280\pi\)
\(432\) 0 0
\(433\) −0.125492 −0.00603077 −0.00301538 0.999995i \(-0.500960\pi\)
−0.00301538 + 0.999995i \(0.500960\pi\)
\(434\) 7.31575 + 1.57472i 0.351167 + 0.0755889i
\(435\) 0 0
\(436\) 12.5830 27.8745i 0.602617 1.33495i
\(437\) 6.16272i 0.294803i
\(438\) 0 0
\(439\) −11.1660 −0.532925 −0.266462 0.963845i \(-0.585855\pi\)
−0.266462 + 0.963845i \(0.585855\pi\)
\(440\) −16.5906 12.2508i −0.790924 0.584032i
\(441\) 0 0
\(442\) 6.29150 29.2288i 0.299256 1.39027i
\(443\) 28.8413i 1.37029i 0.728405 + 0.685146i \(0.240262\pi\)
−0.728405 + 0.685146i \(0.759738\pi\)
\(444\) 0 0
\(445\) 15.2915i 0.724887i
\(446\) 13.8255 + 2.97594i 0.654655 + 0.140915i
\(447\) 0 0
\(448\) −6.22876 20.2288i −0.294281 0.955719i
\(449\) 19.5292 0.921638 0.460819 0.887494i \(-0.347556\pi\)
0.460819 + 0.887494i \(0.347556\pi\)
\(450\) 0 0
\(451\) 24.0000i 1.13012i
\(452\) 11.8664 + 5.35669i 0.558149 + 0.251958i
\(453\) 0 0
\(454\) −4.00000 + 18.5830i −0.187729 + 0.872144i
\(455\) 41.3029 1.93631
\(456\) 0 0
\(457\) 23.8745 1.11680 0.558401 0.829571i \(-0.311415\pi\)
0.558401 + 0.829571i \(0.311415\pi\)
\(458\) −3.91813 + 18.2026i −0.183082 + 0.850553i
\(459\) 0 0
\(460\) −2.70850 + 6.00000i −0.126284 + 0.279751i
\(461\) 18.7605i 0.873763i 0.899519 + 0.436881i \(0.143917\pi\)
−0.899519 + 0.436881i \(0.856083\pi\)
\(462\) 0 0
\(463\) 31.2288 1.45132 0.725662 0.688052i \(-0.241534\pi\)
0.725662 + 0.688052i \(0.241534\pi\)
\(464\) 13.0194 11.4821i 0.604412 0.533042i
\(465\) 0 0
\(466\) 12.5830 + 2.70850i 0.582896 + 0.125469i
\(467\) 0.210845i 0.00975672i 0.999988 + 0.00487836i \(0.00155284\pi\)
−0.999988 + 0.00487836i \(0.998447\pi\)
\(468\) 0 0
\(469\) 7.93725i 0.366508i
\(470\) −10.0808 + 46.8331i −0.464995 + 2.16025i
\(471\) 0 0
\(472\) 18.9373 25.6458i 0.871658 1.18044i
\(473\) −7.14226 −0.328401
\(474\) 0 0
\(475\) 39.5830i 1.81619i
\(476\) 21.9473 + 9.90735i 1.00595 + 0.454103i
\(477\) 0 0
\(478\) −27.8745 6.00000i −1.27495 0.274434i
\(479\) −35.1402 −1.60560 −0.802798 0.596250i \(-0.796657\pi\)
−0.802798 + 0.596250i \(0.796657\pi\)
\(480\) 0 0
\(481\) 6.29150 0.286868
\(482\) −37.1553 7.99769i −1.69238 0.364285i
\(483\) 0 0
\(484\) 11.4686 + 5.17712i 0.521301 + 0.235324i
\(485\) 7.70010i 0.349643i
\(486\) 0 0
\(487\) 6.06275 0.274729 0.137365 0.990521i \(-0.456137\pi\)
0.137365 + 0.990521i \(0.456137\pi\)
\(488\) 3.25486 4.40789i 0.147341 0.199536i
\(489\) 0 0
\(490\) 0 0
\(491\) 4.12897i 0.186338i 0.995650 + 0.0931689i \(0.0296997\pi\)
−0.995650 + 0.0931689i \(0.970300\pi\)
\(492\) 0 0
\(493\) 19.7490i 0.889451i
\(494\) 40.4101 + 8.69830i 1.81814 + 0.391355i
\(495\) 0 0
\(496\) 5.29150 + 6.00000i 0.237595 + 0.269408i
\(497\) 0 0
\(498\) 0 0
\(499\) 43.7490i 1.95847i −0.202717 0.979237i \(-0.564977\pi\)
0.202717 0.979237i \(-0.435023\pi\)
\(500\) −3.57113 + 7.91094i −0.159706 + 0.353788i
\(501\) 0 0
\(502\) −7.29150 + 33.8745i −0.325436 + 1.51189i
\(503\) −2.93859 −0.131025 −0.0655127 0.997852i \(-0.520868\pi\)
−0.0655127 + 0.997852i \(0.520868\pi\)
\(504\) 0 0
\(505\) 22.5830 1.00493
\(506\) −0.632534 + 2.93859i −0.0281196 + 0.130636i
\(507\) 0 0
\(508\) 9.64575 + 4.35425i 0.427961 + 0.193189i
\(509\) 33.0450i 1.46469i 0.680932 + 0.732347i \(0.261575\pi\)
−0.680932 + 0.732347i \(0.738425\pi\)
\(510\) 0 0
\(511\) −30.6458 −1.35569
\(512\) 7.48925 21.3521i 0.330981 0.943637i
\(513\) 0 0
\(514\) −27.8745 6.00000i −1.22949 0.264649i
\(515\) 17.9918i 0.792813i
\(516\) 0 0
\(517\) 21.8745i 0.962040i
\(518\) −1.06628 + 4.95368i −0.0468497 + 0.217652i
\(519\) 0 0
\(520\) 35.5203 + 26.2288i 1.55767 + 1.15021i
\(521\) 13.6520 0.598104 0.299052 0.954237i \(-0.403330\pi\)
0.299052 + 0.954237i \(0.403330\pi\)
\(522\) 0 0
\(523\) 0.874508i 0.0382396i 0.999817 + 0.0191198i \(0.00608639\pi\)
−0.999817 + 0.0191198i \(0.993914\pi\)
\(524\) 12.6724 28.0726i 0.553598 1.22636i
\(525\) 0 0
\(526\) 2.70850 + 0.583005i 0.118096 + 0.0254202i
\(527\) −9.10132 −0.396460
\(528\) 0 0
\(529\) −22.0405 −0.958283
\(530\) 20.1617 + 4.33981i 0.875768 + 0.188509i
\(531\) 0 0
\(532\) −13.6974 + 30.3431i −0.593857 + 1.31554i
\(533\) 51.3838i 2.22568i
\(534\) 0 0
\(535\) −60.4575 −2.61381
\(536\) 5.04042 6.82599i 0.217713 0.294838i
\(537\) 0 0
\(538\) 1.70850 7.93725i 0.0736586 0.342199i
\(539\) 0 0
\(540\) 0 0
\(541\) 26.5203i 1.14019i −0.821577 0.570097i \(-0.806905\pi\)
0.821577 0.570097i \(-0.193095\pi\)
\(542\) 29.3498 + 6.31755i 1.26068 + 0.271362i
\(543\) 0 0
\(544\) 12.5830 + 22.4575i 0.539492 + 0.962858i
\(545\) −51.3838 −2.20104
\(546\) 0 0
\(547\) 9.58301i 0.409740i 0.978789 + 0.204870i \(0.0656771\pi\)
−0.978789 + 0.204870i \(0.934323\pi\)
\(548\) −11.8664 5.35669i −0.506908 0.228827i
\(549\) 0 0
\(550\) −4.06275 + 18.8745i −0.173236 + 0.804812i
\(551\) −27.3040 −1.16319
\(552\) 0 0
\(553\) 22.8745 0.972723
\(554\) 2.59160 12.0399i 0.110106 0.511527i
\(555\) 0 0
\(556\) 10.1144 22.4059i 0.428945 0.950221i
\(557\) 1.40122i 0.0593716i −0.999559 0.0296858i \(-0.990549\pi\)
0.999559 0.0296858i \(-0.00945067\pi\)
\(558\) 0 0
\(559\) 15.2915 0.646762
\(560\) −26.6714 + 23.5220i −1.12707 + 0.993985i
\(561\) 0 0
\(562\) 27.8745 + 6.00000i 1.17582 + 0.253095i
\(563\) 41.8608i 1.76422i 0.471042 + 0.882111i \(0.343878\pi\)
−0.471042 + 0.882111i \(0.656122\pi\)
\(564\) 0 0
\(565\) 21.8745i 0.920267i
\(566\) 8.12179 37.7318i 0.341384 1.58599i
\(567\) 0 0
\(568\) 0 0
\(569\) 26.6714 1.11812 0.559062 0.829126i \(-0.311161\pi\)
0.559062 + 0.829126i \(0.311161\pi\)
\(570\) 0 0
\(571\) 5.70850i 0.238893i 0.992841 + 0.119447i \(0.0381120\pi\)
−0.992841 + 0.119447i \(0.961888\pi\)
\(572\) 18.3761 + 8.29529i 0.768345 + 0.346843i
\(573\) 0 0
\(574\) 40.4575 + 8.70850i 1.68866 + 0.363486i
\(575\) 6.16272 0.257003
\(576\) 0 0
\(577\) 23.5830 0.981773 0.490887 0.871223i \(-0.336673\pi\)
0.490887 + 0.871223i \(0.336673\pi\)
\(578\) −5.12717 1.10363i −0.213262 0.0459048i
\(579\) 0 0
\(580\) −26.5830 12.0000i −1.10380 0.498273i
\(581\) 6.29888i 0.261321i
\(582\) 0 0
\(583\) 9.41699 0.390012
\(584\) −26.3552 19.4611i −1.09058 0.805306i
\(585\) 0 0
\(586\) −4.29150 + 19.9373i −0.177280 + 0.823600i
\(587\) 21.9099i 0.904319i −0.891937 0.452160i \(-0.850654\pi\)
0.891937 0.452160i \(-0.149346\pi\)
\(588\) 0 0
\(589\) 12.5830i 0.518474i
\(590\) −52.3633 11.2712i −2.15576 0.464029i
\(591\) 0 0
\(592\) −4.06275 + 3.58301i −0.166978 + 0.147261i
\(593\) −33.1811 −1.36259 −0.681293 0.732011i \(-0.738582\pi\)
−0.681293 + 0.732011i \(0.738582\pi\)
\(594\) 0 0
\(595\) 40.4575i 1.65860i
\(596\) −7.14226 + 15.8219i −0.292558 + 0.648090i
\(597\) 0 0
\(598\) 1.35425 6.29150i 0.0553793 0.257279i
\(599\) 35.1402 1.43579 0.717895 0.696151i \(-0.245106\pi\)
0.717895 + 0.696151i \(0.245106\pi\)
\(600\) 0 0
\(601\) −31.8745 −1.30019 −0.650094 0.759854i \(-0.725271\pi\)
−0.650094 + 0.759854i \(0.725271\pi\)
\(602\) −2.59160 + 12.0399i −0.105626 + 0.490710i
\(603\) 0 0
\(604\) 23.0516 + 10.4059i 0.937958 + 0.423409i
\(605\) 21.1412i 0.859513i
\(606\) 0 0
\(607\) 33.3542 1.35381 0.676904 0.736072i \(-0.263321\pi\)
0.676904 + 0.736072i \(0.263321\pi\)
\(608\) −31.0486 + 17.3966i −1.25919 + 0.705525i
\(609\) 0 0
\(610\) −9.00000 1.93725i −0.364399 0.0784371i
\(611\) 46.8331i 1.89467i
\(612\) 0 0
\(613\) 21.1033i 0.852353i −0.904640 0.426176i \(-0.859860\pi\)
0.904640 0.426176i \(-0.140140\pi\)
\(614\) 2.93859 13.6520i 0.118592 0.550949i
\(615\) 0 0
\(616\) −9.64575 + 13.0627i −0.388638 + 0.526313i
\(617\) −17.5701 −0.707346 −0.353673 0.935369i \(-0.615067\pi\)
−0.353673 + 0.935369i \(0.615067\pi\)
\(618\) 0 0
\(619\) 39.0000i 1.56754i −0.621050 0.783771i \(-0.713294\pi\)
0.621050 0.783771i \(-0.286706\pi\)
\(620\) 5.53019 12.2508i 0.222098 0.492002i
\(621\) 0 0
\(622\) 1.35425 + 0.291503i 0.0543004 + 0.0116882i
\(623\) −12.0399 −0.482369
\(624\) 0 0
\(625\) −16.8745 −0.674980
\(626\) −20.5647 4.42656i −0.821931 0.176921i
\(627\) 0 0
\(628\) 7.16601 15.8745i 0.285955 0.633462i
\(629\) 6.16272i 0.245724i
\(630\) 0 0
\(631\) 19.2288 0.765485 0.382742 0.923855i \(-0.374980\pi\)
0.382742 + 0.923855i \(0.374980\pi\)
\(632\) 19.6719 + 14.5261i 0.782507 + 0.577817i
\(633\) 0 0
\(634\) −6.12549 + 28.4575i −0.243274 + 1.13019i
\(635\) 17.7809i 0.705615i
\(636\) 0 0
\(637\) 0 0
\(638\) −13.0194 2.80244i −0.515445 0.110950i
\(639\) 0 0
\(640\) −37.8745 + 3.29150i −1.49712 + 0.130108i
\(641\) 22.1208 0.873718 0.436859 0.899530i \(-0.356091\pi\)
0.436859 + 0.899530i \(0.356091\pi\)
\(642\) 0 0
\(643\) 27.2915i 1.07627i 0.842858 + 0.538136i \(0.180871\pi\)
−0.842858 + 0.538136i \(0.819129\pi\)
\(644\) 4.72416 + 2.13256i 0.186158 + 0.0840347i
\(645\) 0 0
\(646\) 8.52026 39.5830i 0.335225 1.55737i
\(647\) 33.1811 1.30449 0.652243 0.758010i \(-0.273828\pi\)
0.652243 + 0.758010i \(0.273828\pi\)
\(648\) 0 0
\(649\) −24.4575 −0.960041
\(650\) 8.69830 40.4101i 0.341175 1.58502i
\(651\) 0 0
\(652\) −5.17712 + 11.4686i −0.202752 + 0.449146i
\(653\) 24.5015i 0.958818i −0.877592 0.479409i \(-0.840851\pi\)
0.877592 0.479409i \(-0.159149\pi\)
\(654\) 0 0
\(655\) −51.7490 −2.02200
\(656\) 29.2630 + 33.1811i 1.14253 + 1.29551i
\(657\) 0 0
\(658\) 36.8745 + 7.93725i 1.43752 + 0.309426i
\(659\) 11.4821i 0.447278i −0.974672 0.223639i \(-0.928206\pi\)
0.974672 0.223639i \(-0.0717937\pi\)
\(660\) 0 0
\(661\) 14.5203i 0.564773i −0.959301 0.282386i \(-0.908874\pi\)
0.959301 0.282386i \(-0.0911260\pi\)
\(662\) −1.69881 + 7.89227i −0.0660263 + 0.306742i
\(663\) 0 0
\(664\) −4.00000 + 5.41699i −0.155230 + 0.210220i
\(665\) 55.9344 2.16904
\(666\) 0 0
\(667\) 4.25098i 0.164599i
\(668\) −34.9667 15.7845i −1.35290 0.610722i
\(669\) 0 0
\(670\) −13.9373 3.00000i −0.538443 0.115900i
\(671\) −4.20366 −0.162281
\(672\) 0 0
\(673\) −40.8745 −1.57560 −0.787798 0.615933i \(-0.788779\pi\)
−0.787798 + 0.615933i \(0.788779\pi\)
\(674\) −3.16811 0.681937i −0.122031 0.0262672i
\(675\) 0 0
\(676\) −15.6458 7.06275i −0.601760 0.271644i
\(677\) 31.7799i 1.22140i 0.791861 + 0.610701i \(0.209112\pi\)
−0.791861 + 0.610701i \(0.790888\pi\)
\(678\) 0 0
\(679\) −6.06275 −0.232667
\(680\) 25.6919 34.7932i 0.985239 1.33426i
\(681\) 0 0
\(682\) 1.29150 6.00000i 0.0494542 0.229752i
\(683\) 17.7809i 0.680369i 0.940359 + 0.340185i \(0.110490\pi\)
−0.940359 + 0.340185i \(0.889510\pi\)
\(684\) 0 0
\(685\) 21.8745i 0.835782i
\(686\) −25.6051 5.51152i −0.977609 0.210431i
\(687\) 0 0
\(688\) −9.87451 + 8.70850i −0.376462 + 0.332008i
\(689\) −20.1617 −0.768100
\(690\) 0 0
\(691\) 27.2915i 1.03822i −0.854708 0.519109i \(-0.826264\pi\)
0.854708 0.519109i \(-0.173736\pi\)
\(692\) −13.0194 + 28.8413i −0.494925 + 1.09638i
\(693\) 0 0
\(694\) −0.125492 + 0.583005i −0.00476362 + 0.0221306i
\(695\) −41.3029 −1.56671
\(696\) 0 0
\(697\) −50.3320 −1.90646
\(698\) −3.16811 + 14.7183i −0.119915 + 0.557094i
\(699\) 0 0
\(700\) 30.3431 + 13.6974i 1.14686 + 0.517712i
\(701\) 16.8014i 0.634581i 0.948328 + 0.317290i \(0.102773\pi\)
−0.948328 + 0.317290i \(0.897227\pi\)
\(702\) 0 0
\(703\) 8.52026 0.321348
\(704\) −16.5906 + 5.10850i −0.625281 + 0.192534i
\(705\) 0 0
\(706\) −18.0000 3.87451i −0.677439 0.145819i
\(707\) 17.7809i 0.668721i
\(708\) 0 0
\(709\) 3.47974i 0.130684i −0.997863 0.0653422i \(-0.979186\pi\)
0.997863 0.0653422i \(-0.0208139\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −10.3542 7.64575i −0.388042 0.286537i
\(713\) −1.95906 −0.0733675
\(714\) 0 0
\(715\) 33.8745i 1.26683i
\(716\) −3.91813 + 8.67963i −0.146427 + 0.324373i
\(717\) 0 0
\(718\) 29.2288 + 6.29150i 1.09081 + 0.234797i
\(719\) −51.3838 −1.91629 −0.958146 0.286281i \(-0.907581\pi\)
−0.958146 + 0.286281i \(0.907581\pi\)
\(720\) 0 0
\(721\) 14.1660 0.527570
\(722\) 28.4570 + 6.12538i 1.05906 + 0.227963i
\(723\) 0 0
\(724\) −13.6974 + 30.3431i −0.509059 + 1.12769i
\(725\) 27.3040i 1.01404i
\(726\) 0 0
\(727\) 44.5830 1.65349 0.826746 0.562575i \(-0.190189\pi\)
0.826746 + 0.562575i \(0.190189\pi\)
\(728\) 20.6515 27.9672i 0.765394 1.03653i
\(729\) 0 0
\(730\) −11.5830 + 53.8118i −0.428706 + 1.99166i
\(731\) 14.9785i 0.554000i
\(732\) 0 0
\(733\) 28.4575i 1.05110i −0.850762 0.525551i \(-0.823859\pi\)
0.850762 0.525551i \(-0.176141\pi\)
\(734\) −6.24947 1.34520i −0.230672 0.0496523i
\(735\) 0 0
\(736\) 2.70850 + 4.83399i 0.0998365 + 0.178183i
\(737\) −6.50972 −0.239789
\(738\) 0 0
\(739\) 40.4575i 1.48825i −0.668038 0.744127i \(-0.732866\pi\)
0.668038 0.744127i \(-0.267134\pi\)
\(740\) 8.29529 + 3.74463i 0.304941 + 0.137655i
\(741\) 0 0
\(742\) 3.41699 15.8745i 0.125442 0.582772i
\(743\) −25.0594 −0.919339 −0.459669 0.888090i \(-0.652032\pi\)
−0.459669 + 0.888090i \(0.652032\pi\)
\(744\) 0 0
\(745\) 29.1660 1.06856
\(746\) 11.4634 53.2561i 0.419705 1.94984i
\(747\) 0 0
\(748\) 8.12549 18.0000i 0.297097 0.658145i
\(749\) 47.6018i 1.73933i
\(750\) 0 0
\(751\) 24.0627 0.878062 0.439031 0.898472i \(-0.355322\pi\)
0.439031 + 0.898472i \(0.355322\pi\)
\(752\) 26.6714 + 30.2425i 0.972607 + 1.10283i
\(753\) 0 0
\(754\) 27.8745 + 6.00000i 1.01513 + 0.218507i
\(755\) 42.4933i 1.54649i
\(756\) 0 0
\(757\) 13.9373i 0.506558i 0.967393 + 0.253279i \(0.0815091\pi\)
−0.967393 + 0.253279i \(0.918491\pi\)
\(758\) 6.42297 29.8395i 0.233293 1.08382i
\(759\) 0 0
\(760\) 48.1033 + 35.5203i 1.74489 + 1.28846i
\(761\) 9.73385 0.352852 0.176426 0.984314i \(-0.443546\pi\)
0.176426 + 0.984314i \(0.443546\pi\)
\(762\) 0 0
\(763\) 40.4575i 1.46466i
\(764\) −14.8050 6.68322i −0.535626 0.241790i
\(765\) 0 0
\(766\) −27.8745 6.00000i −1.00715 0.216789i
\(767\) 52.3633 1.89073
\(768\) 0 0
\(769\) 36.1660 1.30418 0.652090 0.758142i \(-0.273892\pi\)
0.652090 + 0.758142i \(0.273892\pi\)
\(770\) 26.6714 + 5.74103i 0.961171 + 0.206893i
\(771\) 0 0
\(772\) −7.82288 3.53137i −0.281551 0.127097i
\(773\) 6.29888i 0.226555i −0.993563 0.113277i \(-0.963865\pi\)
0.993563 0.113277i \(-0.0361349\pi\)
\(774\) 0 0
\(775\) −12.5830 −0.451995
\(776\) −5.21392 3.85005i −0.187169 0.138209i
\(777\) 0 0
\(778\) −1.58301 + 7.35425i −0.0567535 + 0.263663i
\(779\) 69.5864i 2.49319i
\(780\) 0 0
\(781\) 0 0
\(782\) −6.16272 1.32653i −0.220379 0.0474366i
\(783\) 0 0
\(784\) 0 0
\(785\) −29.2630 −1.04444
\(786\) 0 0
\(787\) 50.6235i 1.80453i 0.431178 + 0.902267i \(0.358098\pi\)
−0.431178 + 0.902267i \(0.641902\pi\)
\(788\) −6.33622 + 14.0363i −0.225719 + 0.500023i
\(789\) 0 0
\(790\) 8.64575 40.1660i 0.307602 1.42904i
\(791\) −17.2231 −0.612383
\(792\) 0 0
\(793\) 9.00000 0.319599
\(794\) −4.55066 + 21.1412i −0.161497 + 0.750274i
\(795\)