Properties

Label 882.2.f.q.295.1
Level $882$
Weight $2$
Character 882.295
Analytic conductor $7.043$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.1
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 882.295
Dual form 882.2.f.q.589.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.517638 + 0.896575i) q^{5} +(0.448288 - 1.67303i) q^{6} +1.00000 q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.517638 + 0.896575i) q^{5} +(0.448288 - 1.67303i) q^{6} +1.00000 q^{8} +(2.59808 - 1.50000i) q^{9} -1.03528 q^{10} +(0.133975 - 0.232051i) q^{11} +(1.22474 + 1.22474i) q^{12} +(-0.896575 - 1.55291i) q^{13} +(-1.26795 - 1.26795i) q^{15} +(-0.500000 + 0.866025i) q^{16} -6.83083 q^{17} +3.00000i q^{18} +4.38134 q^{19} +(0.517638 - 0.896575i) q^{20} +(0.133975 + 0.232051i) q^{22} +(-2.73205 - 4.73205i) q^{23} +(-1.67303 + 0.448288i) q^{24} +(1.96410 - 3.40192i) q^{25} +1.79315 q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.00000 - 3.46410i) q^{29} +(1.73205 - 0.464102i) q^{30} +(-3.34607 - 5.79555i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.120118 + 0.448288i) q^{33} +(3.41542 - 5.91567i) q^{34} +(-2.59808 - 1.50000i) q^{36} +7.46410 q^{37} +(-2.19067 + 3.79435i) q^{38} +(2.19615 + 2.19615i) q^{39} +(0.517638 + 0.896575i) q^{40} +(4.31199 + 7.46859i) q^{41} +(-0.133975 + 0.232051i) q^{43} -0.267949 q^{44} +(2.68973 + 1.55291i) q^{45} +5.46410 q^{46} +(-0.378937 + 0.656339i) q^{47} +(0.448288 - 1.67303i) q^{48} +(1.96410 + 3.40192i) q^{50} +(11.4282 - 3.06218i) q^{51} +(-0.896575 + 1.55291i) q^{52} +10.9282 q^{53} +(-1.34486 - 5.01910i) q^{54} +0.277401 q^{55} +(-7.33013 + 1.96410i) q^{57} +(2.00000 + 3.46410i) q^{58} +(0.637756 + 1.10463i) q^{59} +(-0.464102 + 1.73205i) q^{60} +(6.31319 - 10.9348i) q^{61} +6.69213 q^{62} +1.00000 q^{64} +(0.928203 - 1.60770i) q^{65} +(-0.328169 - 0.328169i) q^{66} +(-6.23205 - 10.7942i) q^{67} +(3.41542 + 5.91567i) q^{68} +(6.69213 + 6.69213i) q^{69} +9.46410 q^{71} +(2.59808 - 1.50000i) q^{72} +5.41662 q^{73} +(-3.73205 + 6.46410i) q^{74} +(-1.76097 + 6.57201i) q^{75} +(-2.19067 - 3.79435i) q^{76} +(-3.00000 + 0.803848i) q^{78} +(-4.46410 + 7.73205i) q^{79} -1.03528 q^{80} +(4.50000 - 7.79423i) q^{81} -8.62398 q^{82} +(-3.29530 + 5.70762i) q^{83} +(-3.53590 - 6.12436i) q^{85} +(-0.133975 - 0.232051i) q^{86} +(-1.79315 + 6.69213i) q^{87} +(0.133975 - 0.232051i) q^{88} +7.07107 q^{89} +(-2.68973 + 1.55291i) q^{90} +(-2.73205 + 4.73205i) q^{92} +(8.19615 + 8.19615i) q^{93} +(-0.378937 - 0.656339i) q^{94} +(2.26795 + 3.92820i) q^{95} +(1.22474 + 1.22474i) q^{96} +(9.07227 - 15.7136i) q^{97} -0.803848i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} + 8 q^{11} - 24 q^{15} - 4 q^{16} + 8 q^{22} - 8 q^{23} - 12 q^{25} + 16 q^{29} - 4 q^{32} + 32 q^{37} - 24 q^{39} - 8 q^{43} - 16 q^{44} + 16 q^{46} - 12 q^{50} + 36 q^{51} + 32 q^{53} - 24 q^{57} + 16 q^{58} + 24 q^{60} + 8 q^{64} - 48 q^{65} - 36 q^{67} + 48 q^{71} - 16 q^{74} - 24 q^{78} - 8 q^{79} + 36 q^{81} - 56 q^{85} - 8 q^{86} + 8 q^{88} - 8 q^{92} + 24 q^{93} + 32 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −1.67303 + 0.448288i −0.965926 + 0.258819i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.517638 + 0.896575i 0.231495 + 0.400961i 0.958248 0.285938i \(-0.0923050\pi\)
−0.726753 + 0.686898i \(0.758972\pi\)
\(6\) 0.448288 1.67303i 0.183013 0.683013i
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 2.59808 1.50000i 0.866025 0.500000i
\(10\) −1.03528 −0.327383
\(11\) 0.133975 0.232051i 0.0403949 0.0699660i −0.845121 0.534575i \(-0.820472\pi\)
0.885516 + 0.464609i \(0.153805\pi\)
\(12\) 1.22474 + 1.22474i 0.353553 + 0.353553i
\(13\) −0.896575 1.55291i −0.248665 0.430701i 0.714490 0.699645i \(-0.246659\pi\)
−0.963156 + 0.268944i \(0.913325\pi\)
\(14\) 0 0
\(15\) −1.26795 1.26795i −0.327383 0.327383i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −6.83083 −1.65672 −0.828360 0.560196i \(-0.810726\pi\)
−0.828360 + 0.560196i \(0.810726\pi\)
\(18\) 3.00000i 0.707107i
\(19\) 4.38134 1.00515 0.502574 0.864534i \(-0.332386\pi\)
0.502574 + 0.864534i \(0.332386\pi\)
\(20\) 0.517638 0.896575i 0.115747 0.200480i
\(21\) 0 0
\(22\) 0.133975 + 0.232051i 0.0285635 + 0.0494734i
\(23\) −2.73205 4.73205i −0.569672 0.986701i −0.996598 0.0824143i \(-0.973737\pi\)
0.426926 0.904286i \(-0.359596\pi\)
\(24\) −1.67303 + 0.448288i −0.341506 + 0.0915064i
\(25\) 1.96410 3.40192i 0.392820 0.680385i
\(26\) 1.79315 0.351666
\(27\) −3.67423 + 3.67423i −0.707107 + 0.707107i
\(28\) 0 0
\(29\) 2.00000 3.46410i 0.371391 0.643268i −0.618389 0.785872i \(-0.712214\pi\)
0.989780 + 0.142605i \(0.0455477\pi\)
\(30\) 1.73205 0.464102i 0.316228 0.0847330i
\(31\) −3.34607 5.79555i −0.600971 1.04091i −0.992674 0.120821i \(-0.961447\pi\)
0.391703 0.920092i \(-0.371886\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −0.120118 + 0.448288i −0.0209099 + 0.0780369i
\(34\) 3.41542 5.91567i 0.585739 1.01453i
\(35\) 0 0
\(36\) −2.59808 1.50000i −0.433013 0.250000i
\(37\) 7.46410 1.22709 0.613545 0.789659i \(-0.289743\pi\)
0.613545 + 0.789659i \(0.289743\pi\)
\(38\) −2.19067 + 3.79435i −0.355374 + 0.615525i
\(39\) 2.19615 + 2.19615i 0.351666 + 0.351666i
\(40\) 0.517638 + 0.896575i 0.0818458 + 0.141761i
\(41\) 4.31199 + 7.46859i 0.673420 + 1.16640i 0.976928 + 0.213569i \(0.0685087\pi\)
−0.303508 + 0.952829i \(0.598158\pi\)
\(42\) 0 0
\(43\) −0.133975 + 0.232051i −0.0204309 + 0.0353874i −0.876060 0.482202i \(-0.839837\pi\)
0.855629 + 0.517589i \(0.173170\pi\)
\(44\) −0.267949 −0.0403949
\(45\) 2.68973 + 1.55291i 0.400961 + 0.231495i
\(46\) 5.46410 0.805638
\(47\) −0.378937 + 0.656339i −0.0552737 + 0.0957369i −0.892338 0.451367i \(-0.850936\pi\)
0.837065 + 0.547104i \(0.184270\pi\)
\(48\) 0.448288 1.67303i 0.0647048 0.241481i
\(49\) 0 0
\(50\) 1.96410 + 3.40192i 0.277766 + 0.481105i
\(51\) 11.4282 3.06218i 1.60027 0.428791i
\(52\) −0.896575 + 1.55291i −0.124333 + 0.215350i
\(53\) 10.9282 1.50110 0.750552 0.660811i \(-0.229788\pi\)
0.750552 + 0.660811i \(0.229788\pi\)
\(54\) −1.34486 5.01910i −0.183013 0.683013i
\(55\) 0.277401 0.0374048
\(56\) 0 0
\(57\) −7.33013 + 1.96410i −0.970899 + 0.260152i
\(58\) 2.00000 + 3.46410i 0.262613 + 0.454859i
\(59\) 0.637756 + 1.10463i 0.0830288 + 0.143810i 0.904550 0.426369i \(-0.140207\pi\)
−0.821521 + 0.570179i \(0.806874\pi\)
\(60\) −0.464102 + 1.73205i −0.0599153 + 0.223607i
\(61\) 6.31319 10.9348i 0.808322 1.40005i −0.105704 0.994398i \(-0.533710\pi\)
0.914026 0.405656i \(-0.132957\pi\)
\(62\) 6.69213 0.849901
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.928203 1.60770i 0.115129 0.199410i
\(66\) −0.328169 0.328169i −0.0403949 0.0403949i
\(67\) −6.23205 10.7942i −0.761366 1.31872i −0.942146 0.335201i \(-0.891196\pi\)
0.180780 0.983524i \(-0.442138\pi\)
\(68\) 3.41542 + 5.91567i 0.414180 + 0.717381i
\(69\) 6.69213 + 6.69213i 0.805638 + 0.805638i
\(70\) 0 0
\(71\) 9.46410 1.12318 0.561591 0.827415i \(-0.310189\pi\)
0.561591 + 0.827415i \(0.310189\pi\)
\(72\) 2.59808 1.50000i 0.306186 0.176777i
\(73\) 5.41662 0.633967 0.316984 0.948431i \(-0.397330\pi\)
0.316984 + 0.948431i \(0.397330\pi\)
\(74\) −3.73205 + 6.46410i −0.433842 + 0.751437i
\(75\) −1.76097 + 6.57201i −0.203339 + 0.758871i
\(76\) −2.19067 3.79435i −0.251287 0.435242i
\(77\) 0 0
\(78\) −3.00000 + 0.803848i −0.339683 + 0.0910178i
\(79\) −4.46410 + 7.73205i −0.502251 + 0.869924i 0.497746 + 0.867323i \(0.334161\pi\)
−0.999997 + 0.00260080i \(0.999172\pi\)
\(80\) −1.03528 −0.115747
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) −8.62398 −0.952360
\(83\) −3.29530 + 5.70762i −0.361706 + 0.626493i −0.988242 0.152900i \(-0.951139\pi\)
0.626536 + 0.779393i \(0.284472\pi\)
\(84\) 0 0
\(85\) −3.53590 6.12436i −0.383522 0.664280i
\(86\) −0.133975 0.232051i −0.0144469 0.0250227i
\(87\) −1.79315 + 6.69213i −0.192246 + 0.717472i
\(88\) 0.133975 0.232051i 0.0142817 0.0247367i
\(89\) 7.07107 0.749532 0.374766 0.927119i \(-0.377723\pi\)
0.374766 + 0.927119i \(0.377723\pi\)
\(90\) −2.68973 + 1.55291i −0.283522 + 0.163692i
\(91\) 0 0
\(92\) −2.73205 + 4.73205i −0.284836 + 0.493350i
\(93\) 8.19615 + 8.19615i 0.849901 + 0.849901i
\(94\) −0.378937 0.656339i −0.0390844 0.0676962i
\(95\) 2.26795 + 3.92820i 0.232687 + 0.403025i
\(96\) 1.22474 + 1.22474i 0.125000 + 0.125000i
\(97\) 9.07227 15.7136i 0.921149 1.59548i 0.123510 0.992343i \(-0.460585\pi\)
0.797640 0.603134i \(-0.206082\pi\)
\(98\) 0 0
\(99\) 0.803848i 0.0807897i
\(100\) −3.92820 −0.392820
\(101\) 2.44949 4.24264i 0.243733 0.422159i −0.718041 0.696000i \(-0.754961\pi\)
0.961775 + 0.273842i \(0.0882945\pi\)
\(102\) −3.06218 + 11.4282i −0.303201 + 1.13156i
\(103\) −6.17449 10.6945i −0.608391 1.05376i −0.991506 0.130063i \(-0.958482\pi\)
0.383115 0.923701i \(-0.374851\pi\)
\(104\) −0.896575 1.55291i −0.0879165 0.152276i
\(105\) 0 0
\(106\) −5.46410 + 9.46410i −0.530720 + 0.919235i
\(107\) −17.3923 −1.68138 −0.840689 0.541519i \(-0.817850\pi\)
−0.840689 + 0.541519i \(0.817850\pi\)
\(108\) 5.01910 + 1.34486i 0.482963 + 0.129410i
\(109\) 4.92820 0.472036 0.236018 0.971749i \(-0.424158\pi\)
0.236018 + 0.971749i \(0.424158\pi\)
\(110\) −0.138701 + 0.240237i −0.0132246 + 0.0229057i
\(111\) −12.4877 + 3.34607i −1.18528 + 0.317594i
\(112\) 0 0
\(113\) 3.46410 + 6.00000i 0.325875 + 0.564433i 0.981689 0.190490i \(-0.0610077\pi\)
−0.655814 + 0.754923i \(0.727674\pi\)
\(114\) 1.96410 7.33013i 0.183955 0.686529i
\(115\) 2.82843 4.89898i 0.263752 0.456832i
\(116\) −4.00000 −0.371391
\(117\) −4.65874 2.68973i −0.430701 0.248665i
\(118\) −1.27551 −0.117420
\(119\) 0 0
\(120\) −1.26795 1.26795i −0.115747 0.115747i
\(121\) 5.46410 + 9.46410i 0.496737 + 0.860373i
\(122\) 6.31319 + 10.9348i 0.571570 + 0.989988i
\(123\) −10.5622 10.5622i −0.952360 0.952360i
\(124\) −3.34607 + 5.79555i −0.300486 + 0.520456i
\(125\) 9.24316 0.826733
\(126\) 0 0
\(127\) 13.4641 1.19475 0.597373 0.801964i \(-0.296211\pi\)
0.597373 + 0.801964i \(0.296211\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) 0.120118 0.448288i 0.0105758 0.0394695i
\(130\) 0.928203 + 1.60770i 0.0814088 + 0.141004i
\(131\) −5.46739 9.46979i −0.477688 0.827379i 0.521985 0.852955i \(-0.325192\pi\)
−0.999673 + 0.0255752i \(0.991858\pi\)
\(132\) 0.448288 0.120118i 0.0390184 0.0104550i
\(133\) 0 0
\(134\) 12.4641 1.07673
\(135\) −5.19615 1.39230i −0.447214 0.119831i
\(136\) −6.83083 −0.585739
\(137\) −4.33013 + 7.50000i −0.369948 + 0.640768i −0.989557 0.144142i \(-0.953958\pi\)
0.619609 + 0.784910i \(0.287291\pi\)
\(138\) −9.14162 + 2.44949i −0.778186 + 0.208514i
\(139\) −0.397520 0.688524i −0.0337172 0.0583999i 0.848674 0.528916i \(-0.177401\pi\)
−0.882392 + 0.470516i \(0.844068\pi\)
\(140\) 0 0
\(141\) 0.339746 1.26795i 0.0286118 0.106781i
\(142\) −4.73205 + 8.19615i −0.397105 + 0.687806i
\(143\) −0.480473 −0.0401792
\(144\) 3.00000i 0.250000i
\(145\) 4.14110 0.343900
\(146\) −2.70831 + 4.69093i −0.224141 + 0.388224i
\(147\) 0 0
\(148\) −3.73205 6.46410i −0.306773 0.531346i
\(149\) −11.4641 19.8564i −0.939176 1.62670i −0.767013 0.641632i \(-0.778258\pi\)
−0.172163 0.985068i \(-0.555076\pi\)
\(150\) −4.81105 4.81105i −0.392820 0.392820i
\(151\) −9.19615 + 15.9282i −0.748372 + 1.29622i 0.200230 + 0.979749i \(0.435831\pi\)
−0.948603 + 0.316470i \(0.897502\pi\)
\(152\) 4.38134 0.355374
\(153\) −17.7470 + 10.2462i −1.43476 + 0.828360i
\(154\) 0 0
\(155\) 3.46410 6.00000i 0.278243 0.481932i
\(156\) 0.803848 3.00000i 0.0643593 0.240192i
\(157\) −4.76028 8.24504i −0.379912 0.658026i 0.611137 0.791524i \(-0.290712\pi\)
−0.991049 + 0.133498i \(0.957379\pi\)
\(158\) −4.46410 7.73205i −0.355145 0.615129i
\(159\) −18.2832 + 4.89898i −1.44996 + 0.388514i
\(160\) 0.517638 0.896575i 0.0409229 0.0708805i
\(161\) 0 0
\(162\) 4.50000 + 7.79423i 0.353553 + 0.612372i
\(163\) −13.3205 −1.04334 −0.521671 0.853147i \(-0.674691\pi\)
−0.521671 + 0.853147i \(0.674691\pi\)
\(164\) 4.31199 7.46859i 0.336710 0.583199i
\(165\) −0.464102 + 0.124356i −0.0361303 + 0.00968107i
\(166\) −3.29530 5.70762i −0.255765 0.442997i
\(167\) −0.757875 1.31268i −0.0586461 0.101578i 0.835212 0.549928i \(-0.185345\pi\)
−0.893858 + 0.448350i \(0.852012\pi\)
\(168\) 0 0
\(169\) 4.89230 8.47372i 0.376331 0.651825i
\(170\) 7.07180 0.542382
\(171\) 11.3831 6.57201i 0.870484 0.502574i
\(172\) 0.267949 0.0204309
\(173\) −3.34607 + 5.79555i −0.254397 + 0.440628i −0.964731 0.263236i \(-0.915210\pi\)
0.710335 + 0.703864i \(0.248544\pi\)
\(174\) −4.89898 4.89898i −0.371391 0.371391i
\(175\) 0 0
\(176\) 0.133975 + 0.232051i 0.0100987 + 0.0174915i
\(177\) −1.56218 1.56218i −0.117420 0.117420i
\(178\) −3.53553 + 6.12372i −0.264999 + 0.458993i
\(179\) 5.07180 0.379084 0.189542 0.981873i \(-0.439300\pi\)
0.189542 + 0.981873i \(0.439300\pi\)
\(180\) 3.10583i 0.231495i
\(181\) −16.9706 −1.26141 −0.630706 0.776022i \(-0.717235\pi\)
−0.630706 + 0.776022i \(0.717235\pi\)
\(182\) 0 0
\(183\) −5.66025 + 21.1244i −0.418418 + 1.56156i
\(184\) −2.73205 4.73205i −0.201409 0.348851i
\(185\) 3.86370 + 6.69213i 0.284065 + 0.492015i
\(186\) −11.1962 + 3.00000i −0.820942 + 0.219971i
\(187\) −0.915158 + 1.58510i −0.0669230 + 0.115914i
\(188\) 0.757875 0.0552737
\(189\) 0 0
\(190\) −4.53590 −0.329069
\(191\) −7.46410 + 12.9282i −0.540083 + 0.935452i 0.458815 + 0.888532i \(0.348274\pi\)
−0.998899 + 0.0469202i \(0.985059\pi\)
\(192\) −1.67303 + 0.448288i −0.120741 + 0.0323524i
\(193\) −7.52628 13.0359i −0.541753 0.938344i −0.998804 0.0489035i \(-0.984427\pi\)
0.457050 0.889441i \(-0.348906\pi\)
\(194\) 9.07227 + 15.7136i 0.651351 + 1.12817i
\(195\) −0.832204 + 3.10583i −0.0595954 + 0.222413i
\(196\) 0 0
\(197\) −16.9282 −1.20608 −0.603042 0.797709i \(-0.706045\pi\)
−0.603042 + 0.797709i \(0.706045\pi\)
\(198\) 0.696152 + 0.401924i 0.0494734 + 0.0285635i
\(199\) 26.2880 1.86351 0.931755 0.363087i \(-0.118277\pi\)
0.931755 + 0.363087i \(0.118277\pi\)
\(200\) 1.96410 3.40192i 0.138883 0.240552i
\(201\) 15.2653 + 15.2653i 1.07673 + 1.07673i
\(202\) 2.44949 + 4.24264i 0.172345 + 0.298511i
\(203\) 0 0
\(204\) −8.36603 8.36603i −0.585739 0.585739i
\(205\) −4.46410 + 7.73205i −0.311786 + 0.540030i
\(206\) 12.3490 0.860395
\(207\) −14.1962 8.19615i −0.986701 0.569672i
\(208\) 1.79315 0.124333
\(209\) 0.586988 1.01669i 0.0406028 0.0703262i
\(210\) 0 0
\(211\) −9.46410 16.3923i −0.651536 1.12849i −0.982750 0.184937i \(-0.940792\pi\)
0.331215 0.943555i \(-0.392542\pi\)
\(212\) −5.46410 9.46410i −0.375276 0.649997i
\(213\) −15.8338 + 4.24264i −1.08491 + 0.290701i
\(214\) 8.69615 15.0622i 0.594457 1.02963i
\(215\) −0.277401 −0.0189186
\(216\) −3.67423 + 3.67423i −0.250000 + 0.250000i
\(217\) 0 0
\(218\) −2.46410 + 4.26795i −0.166890 + 0.289062i
\(219\) −9.06218 + 2.42820i −0.612365 + 0.164083i
\(220\) −0.138701 0.240237i −0.00935120 0.0161968i
\(221\) 6.12436 + 10.6077i 0.411969 + 0.713551i
\(222\) 3.34607 12.4877i 0.224573 0.838119i
\(223\) 3.58630 6.21166i 0.240157 0.415963i −0.720602 0.693349i \(-0.756135\pi\)
0.960759 + 0.277385i \(0.0894679\pi\)
\(224\) 0 0
\(225\) 11.7846i 0.785641i
\(226\) −6.92820 −0.460857
\(227\) 13.8325 23.9587i 0.918098 1.59019i 0.115798 0.993273i \(-0.463057\pi\)
0.802300 0.596920i \(-0.203609\pi\)
\(228\) 5.36603 + 5.36603i 0.355374 + 0.355374i
\(229\) −0.240237 0.416102i −0.0158753 0.0274968i 0.857979 0.513685i \(-0.171720\pi\)
−0.873854 + 0.486189i \(0.838387\pi\)
\(230\) 2.82843 + 4.89898i 0.186501 + 0.323029i
\(231\) 0 0
\(232\) 2.00000 3.46410i 0.131306 0.227429i
\(233\) 0.124356 0.00814681 0.00407340 0.999992i \(-0.498703\pi\)
0.00407340 + 0.999992i \(0.498703\pi\)
\(234\) 4.65874 2.68973i 0.304552 0.175833i
\(235\) −0.784610 −0.0511823
\(236\) 0.637756 1.10463i 0.0415144 0.0719051i
\(237\) 4.00240 14.9372i 0.259984 0.970274i
\(238\) 0 0
\(239\) −0.464102 0.803848i −0.0300202 0.0519966i 0.850625 0.525773i \(-0.176224\pi\)
−0.880645 + 0.473776i \(0.842891\pi\)
\(240\) 1.73205 0.464102i 0.111803 0.0299576i
\(241\) −3.13801 + 5.43520i −0.202137 + 0.350112i −0.949217 0.314623i \(-0.898122\pi\)
0.747080 + 0.664735i \(0.231455\pi\)
\(242\) −10.9282 −0.702492
\(243\) −4.03459 + 15.0573i −0.258819 + 0.965926i
\(244\) −12.6264 −0.808322
\(245\) 0 0
\(246\) 14.4282 3.86603i 0.919909 0.246489i
\(247\) −3.92820 6.80385i −0.249946 0.432918i
\(248\) −3.34607 5.79555i −0.212475 0.368018i
\(249\) 2.95448 11.0263i 0.187233 0.698762i
\(250\) −4.62158 + 8.00481i −0.292294 + 0.506269i
\(251\) 0.795040 0.0501824 0.0250912 0.999685i \(-0.492012\pi\)
0.0250912 + 0.999685i \(0.492012\pi\)
\(252\) 0 0
\(253\) −1.46410 −0.0920473
\(254\) −6.73205 + 11.6603i −0.422406 + 0.731629i
\(255\) 8.66115 + 8.66115i 0.542382 + 0.542382i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −5.01910 8.69333i −0.313083 0.542275i 0.665945 0.746001i \(-0.268028\pi\)
−0.979028 + 0.203725i \(0.934695\pi\)
\(258\) 0.328169 + 0.328169i 0.0204309 + 0.0204309i
\(259\) 0 0
\(260\) −1.85641 −0.115129
\(261\) 12.0000i 0.742781i
\(262\) 10.9348 0.675552
\(263\) 4.26795 7.39230i 0.263173 0.455829i −0.703910 0.710289i \(-0.748564\pi\)
0.967083 + 0.254460i \(0.0818977\pi\)
\(264\) −0.120118 + 0.448288i −0.00739277 + 0.0275902i
\(265\) 5.65685 + 9.79796i 0.347498 + 0.601884i
\(266\) 0 0
\(267\) −11.8301 + 3.16987i −0.723992 + 0.193993i
\(268\) −6.23205 + 10.7942i −0.380683 + 0.659362i
\(269\) −5.65685 −0.344904 −0.172452 0.985018i \(-0.555169\pi\)
−0.172452 + 0.985018i \(0.555169\pi\)
\(270\) 3.80385 3.80385i 0.231495 0.231495i
\(271\) 13.1069 0.796185 0.398093 0.917345i \(-0.369672\pi\)
0.398093 + 0.917345i \(0.369672\pi\)
\(272\) 3.41542 5.91567i 0.207090 0.358690i
\(273\) 0 0
\(274\) −4.33013 7.50000i −0.261593 0.453092i
\(275\) −0.526279 0.911543i −0.0317358 0.0549681i
\(276\) 2.44949 9.14162i 0.147442 0.550261i
\(277\) −15.7321 + 27.2487i −0.945247 + 1.63722i −0.189992 + 0.981786i \(0.560846\pi\)
−0.755255 + 0.655431i \(0.772487\pi\)
\(278\) 0.795040 0.0476833
\(279\) −17.3867 10.0382i −1.04091 0.600971i
\(280\) 0 0
\(281\) −8.92820 + 15.4641i −0.532612 + 0.922511i 0.466663 + 0.884435i \(0.345456\pi\)
−0.999275 + 0.0380757i \(0.987877\pi\)
\(282\) 0.928203 + 0.928203i 0.0552737 + 0.0552737i
\(283\) 7.53794 + 13.0561i 0.448084 + 0.776104i 0.998261 0.0589437i \(-0.0187732\pi\)
−0.550177 + 0.835048i \(0.685440\pi\)
\(284\) −4.73205 8.19615i −0.280796 0.486352i
\(285\) −5.55532 5.55532i −0.329069 0.329069i
\(286\) 0.240237 0.416102i 0.0142055 0.0246046i
\(287\) 0 0
\(288\) −2.59808 1.50000i −0.153093 0.0883883i
\(289\) 29.6603 1.74472
\(290\) −2.07055 + 3.58630i −0.121587 + 0.210595i
\(291\) −8.13397 + 30.3564i −0.476822 + 1.77952i
\(292\) −2.70831 4.69093i −0.158492 0.274516i
\(293\) 4.62158 + 8.00481i 0.269995 + 0.467646i 0.968860 0.247608i \(-0.0796445\pi\)
−0.698865 + 0.715254i \(0.746311\pi\)
\(294\) 0 0
\(295\) −0.660254 + 1.14359i −0.0384415 + 0.0665826i
\(296\) 7.46410 0.433842
\(297\) 0.360355 + 1.34486i 0.0209099 + 0.0780369i
\(298\) 22.9282 1.32820
\(299\) −4.89898 + 8.48528i −0.283315 + 0.490716i
\(300\) 6.57201 1.76097i 0.379435 0.101669i
\(301\) 0 0
\(302\) −9.19615 15.9282i −0.529179 0.916565i
\(303\) −2.19615 + 8.19615i −0.126166 + 0.470857i
\(304\) −2.19067 + 3.79435i −0.125644 + 0.217621i
\(305\) 13.0718 0.748489
\(306\) 20.4925i 1.17148i
\(307\) 1.17398 0.0670024 0.0335012 0.999439i \(-0.489334\pi\)
0.0335012 + 0.999439i \(0.489334\pi\)
\(308\) 0 0
\(309\) 15.1244 + 15.1244i 0.860395 + 0.860395i
\(310\) 3.46410 + 6.00000i 0.196748 + 0.340777i
\(311\) 3.72500 + 6.45189i 0.211226 + 0.365853i 0.952098 0.305792i \(-0.0989212\pi\)
−0.740873 + 0.671645i \(0.765588\pi\)
\(312\) 2.19615 + 2.19615i 0.124333 + 0.124333i
\(313\) −3.13801 + 5.43520i −0.177371 + 0.307216i −0.940979 0.338464i \(-0.890093\pi\)
0.763608 + 0.645680i \(0.223426\pi\)
\(314\) 9.52056 0.537276
\(315\) 0 0
\(316\) 8.92820 0.502251
\(317\) 13.0000 22.5167i 0.730153 1.26466i −0.226665 0.973973i \(-0.572782\pi\)
0.956818 0.290689i \(-0.0938844\pi\)
\(318\) 4.89898 18.2832i 0.274721 1.02527i
\(319\) −0.535898 0.928203i −0.0300045 0.0519694i
\(320\) 0.517638 + 0.896575i 0.0289368 + 0.0501201i
\(321\) 29.0979 7.79676i 1.62409 0.435173i
\(322\) 0 0
\(323\) −29.9282 −1.66525
\(324\) −9.00000 −0.500000
\(325\) −7.04386 −0.390723
\(326\) 6.66025 11.5359i 0.368877 0.638914i
\(327\) −8.24504 + 2.20925i −0.455952 + 0.122172i
\(328\) 4.31199 + 7.46859i 0.238090 + 0.412384i
\(329\) 0 0
\(330\) 0.124356 0.464102i 0.00684555 0.0255480i
\(331\) 5.73205 9.92820i 0.315062 0.545703i −0.664389 0.747387i \(-0.731308\pi\)
0.979451 + 0.201684i \(0.0646413\pi\)
\(332\) 6.59059 0.361706
\(333\) 19.3923 11.1962i 1.06269 0.613545i
\(334\) 1.51575 0.0829381
\(335\) 6.45189 11.1750i 0.352505 0.610556i
\(336\) 0 0
\(337\) 3.50000 + 6.06218i 0.190657 + 0.330228i 0.945468 0.325714i \(-0.105605\pi\)
−0.754811 + 0.655942i \(0.772271\pi\)
\(338\) 4.89230 + 8.47372i 0.266106 + 0.460910i
\(339\) −8.48528 8.48528i −0.460857 0.460857i
\(340\) −3.53590 + 6.12436i −0.191761 + 0.332140i
\(341\) −1.79315 −0.0971046
\(342\) 13.1440i 0.710747i
\(343\) 0 0
\(344\) −0.133975 + 0.232051i −0.00722343 + 0.0125113i
\(345\) −2.53590 + 9.46410i −0.136528 + 0.509530i
\(346\) −3.34607 5.79555i −0.179886 0.311571i
\(347\) 4.79423 + 8.30385i 0.257368 + 0.445774i 0.965536 0.260270i \(-0.0838115\pi\)
−0.708168 + 0.706044i \(0.750478\pi\)
\(348\) 6.69213 1.79315i 0.358736 0.0961230i
\(349\) 4.00240 6.93237i 0.214244 0.371081i −0.738795 0.673931i \(-0.764605\pi\)
0.953038 + 0.302850i \(0.0979380\pi\)
\(350\) 0 0
\(351\) 9.00000 + 2.41154i 0.480384 + 0.128719i
\(352\) −0.267949 −0.0142817
\(353\) −12.5063 + 21.6615i −0.665641 + 1.15292i 0.313470 + 0.949598i \(0.398509\pi\)
−0.979111 + 0.203327i \(0.934825\pi\)
\(354\) 2.13397 0.571797i 0.113419 0.0303907i
\(355\) 4.89898 + 8.48528i 0.260011 + 0.450352i
\(356\) −3.53553 6.12372i −0.187383 0.324557i
\(357\) 0 0
\(358\) −2.53590 + 4.39230i −0.134026 + 0.232141i
\(359\) 7.46410 0.393940 0.196970 0.980409i \(-0.436890\pi\)
0.196970 + 0.980409i \(0.436890\pi\)
\(360\) 2.68973 + 1.55291i 0.141761 + 0.0818458i
\(361\) 0.196152 0.0103238
\(362\) 8.48528 14.6969i 0.445976 0.772454i
\(363\) −13.3843 13.3843i −0.702492 0.702492i
\(364\) 0 0
\(365\) 2.80385 + 4.85641i 0.146760 + 0.254196i
\(366\) −15.4641 15.4641i −0.808322 0.808322i
\(367\) −9.28032 + 16.0740i −0.484429 + 0.839055i −0.999840 0.0178877i \(-0.994306\pi\)
0.515411 + 0.856943i \(0.327639\pi\)
\(368\) 5.46410 0.284836
\(369\) 22.4058 + 12.9360i 1.16640 + 0.673420i
\(370\) −7.72741 −0.401729
\(371\) 0 0
\(372\) 3.00000 11.1962i 0.155543 0.580493i
\(373\) 5.39230 + 9.33975i 0.279203 + 0.483594i 0.971187 0.238319i \(-0.0765964\pi\)
−0.691984 + 0.721913i \(0.743263\pi\)
\(374\) −0.915158 1.58510i −0.0473217 0.0819636i
\(375\) −15.4641 + 4.14359i −0.798563 + 0.213974i
\(376\) −0.378937 + 0.656339i −0.0195422 + 0.0338481i
\(377\) −7.17260 −0.369408
\(378\) 0 0
\(379\) 13.5885 0.697992 0.348996 0.937124i \(-0.386523\pi\)
0.348996 + 0.937124i \(0.386523\pi\)
\(380\) 2.26795 3.92820i 0.116343 0.201513i
\(381\) −22.5259 + 6.03579i −1.15404 + 0.309223i
\(382\) −7.46410 12.9282i −0.381897 0.661464i
\(383\) −13.6617 23.6627i −0.698078 1.20911i −0.969132 0.246543i \(-0.920705\pi\)
0.271054 0.962564i \(-0.412628\pi\)
\(384\) 0.448288 1.67303i 0.0228766 0.0853766i
\(385\) 0 0
\(386\) 15.0526 0.766155
\(387\) 0.803848i 0.0408619i
\(388\) −18.1445 −0.921149
\(389\) −4.00000 + 6.92820i −0.202808 + 0.351274i −0.949432 0.313972i \(-0.898340\pi\)
0.746624 + 0.665246i \(0.231673\pi\)
\(390\) −2.27362 2.27362i −0.115129 0.115129i
\(391\) 18.6622 + 32.3238i 0.943787 + 1.63469i
\(392\) 0 0
\(393\) 13.3923 + 13.3923i 0.675552 + 0.675552i
\(394\) 8.46410 14.6603i 0.426415 0.738573i
\(395\) −9.24316 −0.465074
\(396\) −0.696152 + 0.401924i −0.0349830 + 0.0201974i
\(397\) 13.1069 0.657814 0.328907 0.944362i \(-0.393320\pi\)
0.328907 + 0.944362i \(0.393320\pi\)
\(398\) −13.1440 + 22.7661i −0.658850 + 1.14116i
\(399\) 0 0
\(400\) 1.96410 + 3.40192i 0.0982051 + 0.170096i
\(401\) 11.8923 + 20.5981i 0.593873 + 1.02862i 0.993705 + 0.112030i \(0.0357353\pi\)
−0.399831 + 0.916589i \(0.630931\pi\)
\(402\) −20.8528 + 5.58750i −1.04005 + 0.278679i
\(403\) −6.00000 + 10.3923i −0.298881 + 0.517678i
\(404\) −4.89898 −0.243733
\(405\) 9.31749 0.462990
\(406\) 0 0
\(407\) 1.00000 1.73205i 0.0495682 0.0858546i
\(408\) 11.4282 3.06218i 0.565780 0.151600i
\(409\) −2.24144 3.88229i −0.110832 0.191967i 0.805274 0.592903i \(-0.202018\pi\)
−0.916106 + 0.400936i \(0.868685\pi\)
\(410\) −4.46410 7.73205i −0.220466 0.381859i
\(411\) 3.88229 14.4889i 0.191499 0.714684i
\(412\) −6.17449 + 10.6945i −0.304195 + 0.526882i
\(413\) 0 0
\(414\) 14.1962 8.19615i 0.697703 0.402819i
\(415\) −6.82309 −0.334932
\(416\) −0.896575 + 1.55291i −0.0439582 + 0.0761379i
\(417\) 0.973721 + 0.973721i 0.0476833 + 0.0476833i
\(418\) 0.586988 + 1.01669i 0.0287105 + 0.0497281i
\(419\) −18.0938 31.3393i −0.883939 1.53103i −0.846925 0.531712i \(-0.821549\pi\)
−0.0370132 0.999315i \(-0.511784\pi\)
\(420\) 0 0
\(421\) −3.80385 + 6.58846i −0.185388 + 0.321102i −0.943707 0.330782i \(-0.892688\pi\)
0.758319 + 0.651884i \(0.226021\pi\)
\(422\) 18.9282 0.921411
\(423\) 2.27362i 0.110547i
\(424\) 10.9282 0.530720
\(425\) −13.4164 + 23.2380i −0.650793 + 1.12721i
\(426\) 4.24264 15.8338i 0.205557 0.767148i
\(427\) 0 0
\(428\) 8.69615 + 15.0622i 0.420344 + 0.728058i
\(429\) 0.803848 0.215390i 0.0388101 0.0103991i
\(430\) 0.138701 0.240237i 0.00668874 0.0115852i
\(431\) −10.1436 −0.488600 −0.244300 0.969700i \(-0.578558\pi\)
−0.244300 + 0.969700i \(0.578558\pi\)
\(432\) −1.34486 5.01910i −0.0647048 0.241481i
\(433\) −19.8362 −0.953265 −0.476632 0.879103i \(-0.658143\pi\)
−0.476632 + 0.879103i \(0.658143\pi\)
\(434\) 0 0
\(435\) −6.92820 + 1.85641i −0.332182 + 0.0890079i
\(436\) −2.46410 4.26795i −0.118009 0.204398i
\(437\) −11.9700 20.7327i −0.572605 0.991781i
\(438\) 2.42820 9.06218i 0.116024 0.433008i
\(439\) −9.79796 + 16.9706i −0.467631 + 0.809961i −0.999316 0.0369815i \(-0.988226\pi\)
0.531685 + 0.846942i \(0.321559\pi\)
\(440\) 0.277401 0.0132246
\(441\) 0 0
\(442\) −12.2487 −0.582612
\(443\) −8.16025 + 14.1340i −0.387705 + 0.671525i −0.992140 0.125129i \(-0.960066\pi\)
0.604435 + 0.796654i \(0.293399\pi\)
\(444\) 9.14162 + 9.14162i 0.433842 + 0.433842i
\(445\) 3.66025 + 6.33975i 0.173513 + 0.300533i
\(446\) 3.58630 + 6.21166i 0.169816 + 0.294130i
\(447\) 28.0812 + 28.0812i 1.32820 + 1.32820i
\(448\) 0 0
\(449\) 23.7846 1.12247 0.561233 0.827658i \(-0.310327\pi\)
0.561233 + 0.827658i \(0.310327\pi\)
\(450\) 10.2058 + 5.89230i 0.481105 + 0.277766i
\(451\) 2.31079 0.108811
\(452\) 3.46410 6.00000i 0.162938 0.282216i
\(453\) 8.24504 30.7709i 0.387386 1.44574i
\(454\) 13.8325 + 23.9587i 0.649194 + 1.12444i
\(455\) 0 0
\(456\) −7.33013 + 1.96410i −0.343265 + 0.0919775i
\(457\) 15.5263 26.8923i 0.726289 1.25797i −0.232153 0.972679i \(-0.574577\pi\)
0.958441 0.285290i \(-0.0920898\pi\)
\(458\) 0.480473 0.0224510
\(459\) 25.0981 25.0981i 1.17148 1.17148i
\(460\) −5.65685 −0.263752
\(461\) 5.51815 9.55772i 0.257006 0.445148i −0.708432 0.705779i \(-0.750597\pi\)
0.965438 + 0.260631i \(0.0839306\pi\)
\(462\) 0 0
\(463\) 15.3205 + 26.5359i 0.712004 + 1.23323i 0.964104 + 0.265526i \(0.0855457\pi\)
−0.252099 + 0.967701i \(0.581121\pi\)
\(464\) 2.00000 + 3.46410i 0.0928477 + 0.160817i
\(465\) −3.10583 + 11.5911i −0.144029 + 0.537525i
\(466\) −0.0621778 + 0.107695i −0.00288033 + 0.00498888i
\(467\) 9.17878 0.424744 0.212372 0.977189i \(-0.431881\pi\)
0.212372 + 0.977189i \(0.431881\pi\)
\(468\) 5.37945i 0.248665i
\(469\) 0 0
\(470\) 0.392305 0.679492i 0.0180957 0.0313426i
\(471\) 11.6603 + 11.6603i 0.537276 + 0.537276i
\(472\) 0.637756 + 1.10463i 0.0293551 + 0.0508446i
\(473\) 0.0358984 + 0.0621778i 0.00165061 + 0.00285894i
\(474\) 10.9348 + 10.9348i 0.502251 + 0.502251i
\(475\) 8.60540 14.9050i 0.394843 0.683888i
\(476\) 0 0
\(477\) 28.3923 16.3923i 1.29999 0.750552i
\(478\) 0.928203 0.0424550
\(479\) 2.07055 3.58630i 0.0946060 0.163862i −0.814838 0.579689i \(-0.803174\pi\)
0.909444 + 0.415826i \(0.136508\pi\)
\(480\) −0.464102 + 1.73205i −0.0211832 + 0.0790569i
\(481\) −6.69213 11.5911i −0.305135 0.528509i
\(482\) −3.13801 5.43520i −0.142933 0.247567i
\(483\) 0 0
\(484\) 5.46410 9.46410i 0.248368 0.430186i
\(485\) 18.7846 0.852965
\(486\) −11.0227 11.0227i −0.500000 0.500000i
\(487\) −2.78461 −0.126183 −0.0630914 0.998008i \(-0.520096\pi\)
−0.0630914 + 0.998008i \(0.520096\pi\)
\(488\) 6.31319 10.9348i 0.285785 0.494994i
\(489\) 22.2856 5.97142i 1.00779 0.270037i
\(490\) 0 0
\(491\) −9.69615 16.7942i −0.437581 0.757913i 0.559921 0.828546i \(-0.310831\pi\)
−0.997502 + 0.0706330i \(0.977498\pi\)
\(492\) −3.86603 + 14.4282i −0.174294 + 0.650474i
\(493\) −13.6617 + 23.6627i −0.615290 + 1.06571i
\(494\) 7.85641 0.353476
\(495\) 0.720710 0.416102i 0.0323935 0.0187024i
\(496\) 6.69213 0.300486
\(497\) 0 0
\(498\) 8.07180 + 8.07180i 0.361706 + 0.361706i
\(499\) −16.6962 28.9186i −0.747422 1.29457i −0.949054 0.315112i \(-0.897958\pi\)
0.201632 0.979461i \(-0.435376\pi\)
\(500\) −4.62158 8.00481i −0.206683 0.357986i
\(501\) 1.85641 + 1.85641i 0.0829381 + 0.0829381i
\(502\) −0.397520 + 0.688524i −0.0177422 + 0.0307303i
\(503\) −12.3490 −0.550614 −0.275307 0.961356i \(-0.588780\pi\)
−0.275307 + 0.961356i \(0.588780\pi\)
\(504\) 0 0
\(505\) 5.07180 0.225692
\(506\) 0.732051 1.26795i 0.0325436 0.0563672i
\(507\) −4.38632 + 16.3700i −0.194803 + 0.727016i
\(508\) −6.73205 11.6603i −0.298686 0.517340i
\(509\) −10.7961 18.6993i −0.478527 0.828834i 0.521169 0.853453i \(-0.325496\pi\)
−0.999697 + 0.0246194i \(0.992163\pi\)
\(510\) −11.8313 + 3.17020i −0.523901 + 0.140379i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) −16.0981 + 16.0981i −0.710747 + 0.710747i
\(514\) 10.0382 0.442766
\(515\) 6.39230 11.0718i 0.281679 0.487882i
\(516\) −0.448288 + 0.120118i −0.0197348 + 0.00528791i
\(517\) 0.101536 + 0.175865i 0.00446555 + 0.00773455i
\(518\) 0 0
\(519\) 3.00000 11.1962i 0.131685 0.491457i
\(520\) 0.928203 1.60770i 0.0407044 0.0705021i
\(521\) −33.7752 −1.47972 −0.739860 0.672761i \(-0.765108\pi\)
−0.739860 + 0.672761i \(0.765108\pi\)
\(522\) 10.3923 + 6.00000i 0.454859 + 0.262613i
\(523\) 20.7327 0.906579 0.453289 0.891363i \(-0.350250\pi\)
0.453289 + 0.891363i \(0.350250\pi\)
\(524\) −5.46739 + 9.46979i −0.238844 + 0.413690i
\(525\) 0 0
\(526\) 4.26795 + 7.39230i 0.186091 + 0.322320i
\(527\) 22.8564 + 39.5885i 0.995641 + 1.72450i
\(528\) −0.328169 0.328169i −0.0142817 0.0142817i
\(529\) −3.42820 + 5.93782i −0.149052 + 0.258166i
\(530\) −11.3137 −0.491436
\(531\) 3.31388 + 1.91327i 0.143810 + 0.0830288i
\(532\) 0 0
\(533\) 7.73205 13.3923i 0.334912 0.580085i
\(534\) 3.16987 11.8301i 0.137174 0.511940i
\(535\) −9.00292 15.5935i −0.389230 0.674166i
\(536\) −6.23205 10.7942i −0.269184 0.466240i
\(537\) −8.48528 + 2.27362i −0.366167 + 0.0981141i
\(538\) 2.82843 4.89898i 0.121942 0.211210i
\(539\) 0 0
\(540\) 1.39230 + 5.19615i 0.0599153 + 0.223607i
\(541\) 15.3205 0.658680 0.329340 0.944211i \(-0.393174\pi\)
0.329340 + 0.944211i \(0.393174\pi\)
\(542\) −6.55343 + 11.3509i −0.281494 + 0.487562i
\(543\) 28.3923 7.60770i 1.21843 0.326477i
\(544\) 3.41542 + 5.91567i 0.146435 + 0.253632i
\(545\) 2.55103 + 4.41851i 0.109274 + 0.189268i
\(546\) 0 0
\(547\) −17.1865 + 29.7679i −0.734843 + 1.27279i 0.219949 + 0.975511i \(0.429411\pi\)
−0.954792 + 0.297274i \(0.903922\pi\)
\(548\) 8.66025 0.369948
\(549\) 37.8792i 1.61664i
\(550\) 1.05256 0.0448813
\(551\) 8.76268 15.1774i 0.373303 0.646579i
\(552\) 6.69213 + 6.69213i 0.284836 + 0.284836i
\(553\) 0 0
\(554\) −15.7321 27.2487i −0.668391 1.15769i
\(555\) −9.46410 9.46410i −0.401729 0.401729i
\(556\) −0.397520 + 0.688524i −0.0168586 + 0.0291999i
\(557\) −6.92820 −0.293557 −0.146779 0.989169i \(-0.546891\pi\)
−0.146779 + 0.989169i \(0.546891\pi\)
\(558\) 17.3867 10.0382i 0.736036 0.424951i
\(559\) 0.480473 0.0203219
\(560\) 0 0
\(561\) 0.820508 3.06218i 0.0346419 0.129285i
\(562\) −8.92820 15.4641i −0.376614 0.652314i
\(563\) 9.12304 + 15.8016i 0.384490 + 0.665957i 0.991698 0.128586i \(-0.0410439\pi\)
−0.607208 + 0.794543i \(0.707711\pi\)
\(564\) −1.26795 + 0.339746i −0.0533903 + 0.0143059i
\(565\) −3.58630 + 6.21166i −0.150877 + 0.261326i
\(566\) −15.0759 −0.633686
\(567\) 0 0
\(568\) 9.46410 0.397105
\(569\) 12.8923 22.3301i 0.540474 0.936128i −0.458403 0.888744i \(-0.651578\pi\)
0.998877 0.0473833i \(-0.0150882\pi\)
\(570\) 7.58871 2.03339i 0.317856 0.0851692i
\(571\) 16.5263 + 28.6244i 0.691603 + 1.19789i 0.971312 + 0.237807i \(0.0764286\pi\)
−0.279709 + 0.960085i \(0.590238\pi\)
\(572\) 0.240237 + 0.416102i 0.0100448 + 0.0173981i
\(573\) 6.69213 24.9754i 0.279568 1.04336i
\(574\) 0 0
\(575\) −21.4641 −0.895115
\(576\) 2.59808 1.50000i 0.108253 0.0625000i
\(577\) −27.4892 −1.14439 −0.572196 0.820117i \(-0.693908\pi\)
−0.572196 + 0.820117i \(0.693908\pi\)
\(578\) −14.8301 + 25.6865i −0.616852 + 1.06842i
\(579\) 18.4355 + 18.4355i 0.766155 + 0.766155i
\(580\) −2.07055 3.58630i −0.0859750 0.148913i
\(581\) 0 0
\(582\) −22.2224 22.2224i −0.921149 0.921149i
\(583\) 1.46410 2.53590i 0.0606369 0.105026i
\(584\) 5.41662 0.224141
\(585\) 5.56922i 0.230259i
\(586\) −9.24316 −0.381831
\(587\) 20.9408 36.2705i 0.864319 1.49704i −0.00340370 0.999994i \(-0.501083\pi\)
0.867722 0.497049i \(-0.165583\pi\)
\(588\) 0 0
\(589\) −14.6603 25.3923i −0.604065 1.04627i
\(590\) −0.660254 1.14359i −0.0271822 0.0470810i
\(591\) 28.3214 7.58871i 1.16499 0.312158i
\(592\) −3.73205 + 6.46410i −0.153386 + 0.265673i
\(593\) 16.8690 0.692728 0.346364 0.938100i \(-0.387416\pi\)
0.346364 + 0.938100i \(0.387416\pi\)
\(594\) −1.34486 0.360355i −0.0551804 0.0147855i
\(595\) 0 0
\(596\) −11.4641 + 19.8564i −0.469588 + 0.813350i
\(597\) −43.9808 + 11.7846i −1.80001 + 0.482312i
\(598\) −4.89898 8.48528i −0.200334 0.346989i
\(599\) −2.39230 4.14359i −0.0977469 0.169303i 0.813005 0.582257i \(-0.197830\pi\)
−0.910752 + 0.412954i \(0.864497\pi\)
\(600\) −1.76097 + 6.57201i −0.0718911 + 0.268301i
\(601\) 1.67303 2.89778i 0.0682444 0.118203i −0.829884 0.557936i \(-0.811594\pi\)
0.898129 + 0.439733i \(0.144927\pi\)
\(602\) 0 0
\(603\) −32.3827 18.6962i −1.31872 0.761366i
\(604\) 18.3923 0.748372
\(605\) −5.65685 + 9.79796i −0.229984 + 0.398344i
\(606\) −6.00000 6.00000i −0.243733 0.243733i
\(607\) 1.13681 + 1.96902i 0.0461418 + 0.0799199i 0.888174 0.459507i \(-0.151974\pi\)
−0.842032 + 0.539427i \(0.818641\pi\)
\(608\) −2.19067 3.79435i −0.0888434 0.153881i
\(609\) 0 0
\(610\) −6.53590 + 11.3205i −0.264631 + 0.458354i
\(611\) 1.35898 0.0549786
\(612\) 17.7470 + 10.2462i 0.717381 + 0.414180i
\(613\) 24.9282 1.00684 0.503420 0.864042i \(-0.332075\pi\)
0.503420 + 0.864042i \(0.332075\pi\)
\(614\) −0.586988 + 1.01669i −0.0236889 + 0.0410304i
\(615\) 4.00240 14.9372i 0.161393 0.602325i
\(616\) 0 0
\(617\) 1.57180 + 2.72243i 0.0632782 + 0.109601i 0.895929 0.444197i \(-0.146511\pi\)
−0.832651 + 0.553798i \(0.813178\pi\)
\(618\) −20.6603 + 5.53590i −0.831077 + 0.222686i
\(619\) 15.8523 27.4570i 0.637159 1.10359i −0.348894 0.937162i \(-0.613443\pi\)
0.986053 0.166430i \(-0.0532239\pi\)
\(620\) −6.92820 −0.278243
\(621\) 27.4249 + 7.34847i 1.10052 + 0.294884i
\(622\) −7.45001 −0.298718
\(623\) 0 0
\(624\) −3.00000 + 0.803848i −0.120096 + 0.0321797i
\(625\) −5.03590 8.72243i −0.201436 0.348897i
\(626\) −3.13801 5.43520i −0.125420 0.217234i
\(627\) −0.526279 + 1.96410i −0.0210176 + 0.0784387i
\(628\) −4.76028 + 8.24504i −0.189956 + 0.329013i
\(629\) −50.9860 −2.03295
\(630\) 0 0
\(631\) −19.7128 −0.784755 −0.392377 0.919804i \(-0.628347\pi\)
−0.392377 + 0.919804i \(0.628347\pi\)
\(632\) −4.46410 + 7.73205i −0.177572 + 0.307564i
\(633\) 23.1822 + 23.1822i 0.921411 + 0.921411i
\(634\) 13.0000 + 22.5167i 0.516296 + 0.894251i
\(635\) 6.96953 + 12.0716i 0.276577 + 0.479046i
\(636\) 13.3843 + 13.3843i 0.530720 + 0.530720i
\(637\) 0 0
\(638\) 1.07180 0.0424328
\(639\) 24.5885 14.1962i 0.972704 0.561591i
\(640\) −1.03528 −0.0409229
\(641\) −2.03590 + 3.52628i −0.0804132 + 0.139280i −0.903427 0.428741i \(-0.858957\pi\)
0.823014 + 0.568021i \(0.192291\pi\)
\(642\) −7.79676 + 29.0979i −0.307713 + 1.14840i
\(643\) 22.4565 + 38.8959i 0.885599 + 1.53390i 0.845025 + 0.534726i \(0.179585\pi\)
0.0405737 + 0.999177i \(0.487081\pi\)
\(644\) 0 0
\(645\) 0.464102 0.124356i 0.0182740 0.00489650i
\(646\) 14.9641 25.9186i 0.588755 1.01975i
\(647\) 21.8695 0.859780 0.429890 0.902881i \(-0.358552\pi\)
0.429890 + 0.902881i \(0.358552\pi\)
\(648\) 4.50000 7.79423i 0.176777 0.306186i
\(649\) 0.341773 0.0134157
\(650\) 3.52193 6.10016i 0.138141 0.239268i
\(651\) 0 0
\(652\) 6.66025 + 11.5359i 0.260836 + 0.451781i
\(653\) −3.00000 5.19615i −0.117399 0.203341i 0.801337 0.598213i \(-0.204122\pi\)
−0.918736 + 0.394872i \(0.870789\pi\)
\(654\) 2.20925 8.24504i 0.0863886 0.322407i
\(655\) 5.66025 9.80385i 0.221164 0.383068i
\(656\) −8.62398 −0.336710
\(657\) 14.0728 8.12493i 0.549032 0.316984i
\(658\) 0 0
\(659\) 24.1244 41.7846i 0.939751 1.62770i 0.173818 0.984778i \(-0.444390\pi\)
0.765934 0.642919i \(-0.222277\pi\)
\(660\) 0.339746 + 0.339746i 0.0132246 + 0.0132246i
\(661\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(662\) 5.73205 + 9.92820i 0.222782 + 0.385871i
\(663\) −15.0015 15.0015i −0.582612 0.582612i
\(664\) −3.29530 + 5.70762i −0.127882 + 0.221499i
\(665\) 0 0
\(666\) 22.3923i 0.867684i
\(667\) −21.8564 −0.846283
\(668\) −0.757875 + 1.31268i −0.0293231 + 0.0507890i
\(669\) −3.21539 + 12.0000i −0.124314 + 0.463947i
\(670\) 6.45189 + 11.1750i 0.249258 + 0.431728i
\(671\) −1.69161 2.92996i −0.0653041 0.113110i
\(672\) 0 0
\(673\) −20.7846 + 36.0000i −0.801188 + 1.38770i 0.117647 + 0.993055i \(0.462465\pi\)
−0.918835 + 0.394643i \(0.870868\pi\)
\(674\) −7.00000 −0.269630
\(675\) 5.28290 + 19.7160i 0.203339 + 0.758871i
\(676\) −9.78461 −0.376331
\(677\) 2.68973 4.65874i 0.103375 0.179050i −0.809698 0.586846i \(-0.800369\pi\)
0.913073 + 0.407796i \(0.133703\pi\)
\(678\) 11.5911 3.10583i 0.445154 0.119279i
\(679\) 0 0
\(680\) −3.53590 6.12436i −0.135596 0.234858i
\(681\) −12.4019 + 46.2846i −0.475243 + 1.77363i
\(682\) 0.896575 1.55291i 0.0343316 0.0594642i
\(683\) −38.3205 −1.46629 −0.733147 0.680070i \(-0.761949\pi\)
−0.733147 + 0.680070i \(0.761949\pi\)
\(684\) −11.3831 6.57201i −0.435242 0.251287i
\(685\) −8.96575 −0.342564
\(686\) 0 0
\(687\) 0.588457 + 0.588457i 0.0224510 + 0.0224510i
\(688\) −0.133975 0.232051i −0.00510773 0.00884685i
\(689\) −9.79796 16.9706i −0.373273 0.646527i
\(690\) −6.92820 6.92820i −0.263752 0.263752i
\(691\) −12.1595 + 21.0609i −0.462570 + 0.801194i −0.999088 0.0426942i \(-0.986406\pi\)
0.536518 + 0.843889i \(0.319739\pi\)
\(692\) 6.69213 0.254397
\(693\) 0 0
\(694\) −9.58846 −0.363973
\(695\) 0.411543 0.712813i 0.0156107 0.0270385i
\(696\) −1.79315 + 6.69213i −0.0679692 + 0.253665i
\(697\) −29.4545 51.0167i −1.11567 1.93239i
\(698\) 4.00240 + 6.93237i 0.151493 + 0.262394i
\(699\) −0.208051 + 0.0557471i −0.00786921 + 0.00210855i
\(700\) 0 0
\(701\) −20.7846 −0.785024 −0.392512 0.919747i \(-0.628394\pi\)
−0.392512 + 0.919747i \(0.628394\pi\)
\(702\) −6.58846 + 6.58846i −0.248665 + 0.248665i
\(703\) 32.7028 1.23341
\(704\) 0.133975 0.232051i 0.00504936 0.00874574i
\(705\) 1.31268 0.351731i 0.0494383 0.0132470i
\(706\) −12.5063 21.6615i −0.470680 0.815241i
\(707\) 0 0
\(708\) −0.571797 + 2.13397i −0.0214894 + 0.0801997i
\(709\) 6.19615 10.7321i 0.232701 0.403051i −0.725901 0.687799i \(-0.758577\pi\)
0.958602 + 0.284749i \(0.0919102\pi\)
\(710\) −9.79796 −0.367711
\(711\) 26.7846i 1.00450i
\(712\) 7.07107 0.264999
\(713\) −18.2832 + 31.6675i −0.684713 + 1.18596i
\(714\) 0 0
\(715\) −0.248711 0.430781i −0.00930128 0.0161103i
\(716\) −2.53590 4.39230i −0.0947710 0.164148i
\(717\) 1.13681 + 1.13681i 0.0424550 + 0.0424550i
\(718\) −3.73205 + 6.46410i −0.139279 + 0.241238i
\(719\) −49.6733 −1.85250 −0.926251 0.376906i \(-0.876988\pi\)
−0.926251 + 0.376906i \(0.876988\pi\)
\(720\) −2.68973 + 1.55291i −0.100240 + 0.0578737i
\(721\) 0 0
\(722\) −0.0980762 + 0.169873i −0.00365002 + 0.00632202i
\(723\) 2.81347 10.5000i 0.104634 0.390499i
\(724\) 8.48528 + 14.6969i 0.315353 + 0.546207i
\(725\) −7.85641 13.6077i −0.291780 0.505377i
\(726\) 18.2832 4.89898i 0.678555 0.181818i
\(727\) −16.3514 + 28.3214i −0.606439 + 1.05038i 0.385383 + 0.922757i \(0.374069\pi\)
−0.991822 + 0.127627i \(0.959264\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) −5.60770 −0.207550
\(731\) 0.915158 1.58510i 0.0338483 0.0586270i
\(732\) 21.1244 5.66025i 0.780779 0.209209i
\(733\) −4.00240 6.93237i −0.147832 0.256053i 0.782594 0.622533i \(-0.213896\pi\)
−0.930426 + 0.366480i \(0.880563\pi\)
\(734\) −9.28032 16.0740i −0.342543 0.593302i
\(735\) 0 0
\(736\) −2.73205 + 4.73205i −0.100705 + 0.174426i
\(737\) −3.33975 −0.123021
\(738\) −22.4058 + 12.9360i −0.824768 + 0.476180i
\(739\) 6.12436 0.225288 0.112644 0.993635i \(-0.464068\pi\)
0.112644 + 0.993635i \(0.464068\pi\)
\(740\) 3.86370 6.69213i 0.142033 0.246008i
\(741\) 9.62209 + 9.62209i 0.353476 + 0.353476i
\(742\) 0 0
\(743\) 15.7846 + 27.3397i 0.579081 + 1.00300i 0.995585 + 0.0938641i \(0.0299219\pi\)
−0.416504 + 0.909134i \(0.636745\pi\)
\(744\) 8.19615 + 8.19615i 0.300486 + 0.300486i
\(745\) 11.8685 20.5569i 0.434829 0.753145i
\(746\) −10.7846 −0.394853
\(747\) 19.7718i 0.723412i
\(748\) 1.83032 0.0669230
\(749\) 0 0
\(750\) 4.14359 15.4641i 0.151303 0.564669i
\(751\) −17.3923 30.1244i −0.634654 1.09925i −0.986588 0.163229i \(-0.947809\pi\)
0.351934 0.936025i \(-0.385524\pi\)
\(752\) −0.378937 0.656339i −0.0138184 0.0239342i
\(753\) −1.33013 + 0.356406i −0.0484725 + 0.0129882i
\(754\) 3.58630 6.21166i 0.130605 0.226215i
\(755\) −19.0411 −0.692977
\(756\) 0 0
\(757\) 19.3205 0.702216 0.351108 0.936335i \(-0.385805\pi\)
0.351108 + 0.936335i \(0.385805\pi\)
\(758\) −6.79423 + 11.7679i −0.246777 + 0.427431i
\(759\) 2.44949 0.656339i 0.0889108 0.0238236i
\(760\) 2.26795 + 3.92820i 0.0822672 + 0.142491i
\(761\) 20.1272 + 34.8613i 0.729609 + 1.26372i 0.957049 + 0.289928i \(0.0936312\pi\)
−0.227440 + 0.973792i \(0.573035\pi\)
\(762\) 6.03579 22.5259i 0.218654 0.816027i
\(763\) 0 0
\(764\) 14.9282 0.540083
\(765\) −18.3731 10.6077i −0.664280 0.383522i
\(766\) 27.3233 0.987232
\(767\) 1.14359 1.98076i 0.0412928 0.0715212i
\(768\) 1.22474 + 1.22474i 0.0441942 + 0.0441942i
\(769\) −19.0919 33.0681i −0.688471 1.19247i −0.972332 0.233601i \(-0.924949\pi\)
0.283862 0.958865i \(-0.408384\pi\)
\(770\) 0 0
\(771\) 12.2942 + 12.2942i 0.442766 + 0.442766i
\(772\) −7.52628 + 13.0359i −0.270877 + 0.469172i
\(773\) 39.3949 1.41694 0.708468 0.705743i \(-0.249387\pi\)
0.708468 + 0.705743i \(0.249387\pi\)
\(774\) −0.696152 0.401924i −0.0250227 0.0144469i
\(775\) −26.2880 −0.944295
\(776\) 9.07227 15.7136i 0.325676 0.564087i
\(777\) 0 0
\(778\) −4.00000 6.92820i −0.143407 0.248388i
\(779\) 18.8923 + 32.7224i 0.676887 + 1.17240i
\(780\) 3.10583 0.832204i 0.111207 0.0297977i