Properties

Label 882.2.l.a.509.5
Level $882$
Weight $2$
Character 882.509
Analytic conductor $7.043$
Analytic rank $0$
Dimension $16$
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.l (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} + 9 x^{12} + 54 x^{10} - 288 x^{8} + 486 x^{6} + 729 x^{4} - 4374 x^{2} + 6561\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 509.5
Root \(-0.0967785 + 1.72934i\) of defining polynomial
Character \(\chi\) \(=\) 882.509
Dual form 882.2.l.a.227.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000i q^{2} +(-1.54605 + 0.780860i) q^{3} -1.00000 q^{4} +(0.183299 + 0.317483i) q^{5} +(-0.780860 - 1.54605i) q^{6} -1.00000i q^{8} +(1.78052 - 2.41449i) q^{9} +O(q^{10})\) \(q+1.00000i q^{2} +(-1.54605 + 0.780860i) q^{3} -1.00000 q^{4} +(0.183299 + 0.317483i) q^{5} +(-0.780860 - 1.54605i) q^{6} -1.00000i q^{8} +(1.78052 - 2.41449i) q^{9} +(-0.317483 + 0.183299i) q^{10} +(-0.579764 - 0.334727i) q^{11} +(1.54605 - 0.780860i) q^{12} +(0.867380 + 0.500782i) q^{13} +(-0.531299 - 0.347713i) q^{15} +1.00000 q^{16} +(-2.49453 - 4.32065i) q^{17} +(2.41449 + 1.78052i) q^{18} +(-5.50552 - 3.17861i) q^{19} +(-0.183299 - 0.317483i) q^{20} +(0.334727 - 0.579764i) q^{22} +(6.66371 - 3.84729i) q^{23} +(0.780860 + 1.54605i) q^{24} +(2.43280 - 4.21374i) q^{25} +(-0.500782 + 0.867380i) q^{26} +(-0.867380 + 5.12325i) q^{27} +(1.58394 - 0.914490i) q^{29} +(0.347713 - 0.531299i) q^{30} +6.32588i q^{31} +1.00000i q^{32} +(1.15772 + 0.0647887i) q^{33} +(4.32065 - 2.49453i) q^{34} +(-1.78052 + 2.41449i) q^{36} +(2.58394 - 4.47552i) q^{37} +(3.17861 - 5.50552i) q^{38} +(-1.73205 - 0.0969299i) q^{39} +(0.317483 - 0.183299i) q^{40} +(2.15928 - 3.73998i) q^{41} +(2.24922 + 3.89576i) q^{43} +(0.579764 + 0.334727i) q^{44} +(1.09293 + 0.122710i) q^{45} +(3.84729 + 6.66371i) q^{46} +8.32901 q^{47} +(-1.54605 + 0.780860i) q^{48} +(4.21374 + 2.43280i) q^{50} +(7.23048 + 4.73205i) q^{51} +(-0.867380 - 0.500782i) q^{52} +(-5.12325 - 0.867380i) q^{54} -0.245420i q^{55} +(10.9938 + 0.615242i) q^{57} +(0.914490 + 1.58394i) q^{58} +8.72695 q^{59} +(0.531299 + 0.347713i) q^{60} +4.95771i q^{61} -6.32588 q^{62} -1.00000 q^{64} +0.367172i q^{65} +(-0.0647887 + 1.15772i) q^{66} -10.8907 q^{67} +(2.49453 + 4.32065i) q^{68} +(-7.29820 + 11.1515i) q^{69} +5.49843i q^{71} +(-2.41449 - 1.78052i) q^{72} +(-3.52744 + 2.03657i) q^{73} +(4.47552 + 2.58394i) q^{74} +(-0.470886 + 8.41431i) q^{75} +(5.50552 + 3.17861i) q^{76} +(0.0969299 - 1.73205i) q^{78} +8.35568 q^{79} +(0.183299 + 0.317483i) q^{80} +(-2.65953 - 8.59808i) q^{81} +(3.73998 + 2.15928i) q^{82} +(-8.50712 - 14.7348i) q^{83} +(0.914490 - 1.58394i) q^{85} +(-3.89576 + 2.24922i) q^{86} +(-1.73476 + 2.65068i) q^{87} +(-0.334727 + 0.579764i) q^{88} +(5.35566 - 9.27628i) q^{89} +(-0.122710 + 1.09293i) q^{90} +(-6.66371 + 3.84729i) q^{92} +(-4.93962 - 9.78010i) q^{93} +8.32901i q^{94} -2.33055i q^{95} +(-0.780860 - 1.54605i) q^{96} +(14.9093 - 8.60787i) q^{97} +(-1.84047 + 0.803848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 16 q^{4} - 12 q^{9} + O(q^{10}) \) \( 16 q - 16 q^{4} - 12 q^{9} + 12 q^{11} + 16 q^{16} + 12 q^{18} + 48 q^{23} - 8 q^{25} - 12 q^{29} + 12 q^{30} + 12 q^{36} + 4 q^{37} + 4 q^{43} - 12 q^{44} - 12 q^{46} + 60 q^{50} + 24 q^{51} + 48 q^{57} - 12 q^{58} - 16 q^{64} + 56 q^{67} - 12 q^{72} - 36 q^{74} - 24 q^{78} + 8 q^{79} - 12 q^{85} + 24 q^{86} - 48 q^{92} + 84 q^{93} - 72 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) −1.54605 + 0.780860i −0.892610 + 0.450830i
\(4\) −1.00000 −0.500000
\(5\) 0.183299 + 0.317483i 0.0819738 + 0.141983i 0.904098 0.427326i \(-0.140544\pi\)
−0.822124 + 0.569309i \(0.807211\pi\)
\(6\) −0.780860 1.54605i −0.318785 0.631171i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 1.78052 2.41449i 0.593505 0.804830i
\(10\) −0.317483 + 0.183299i −0.100397 + 0.0579643i
\(11\) −0.579764 0.334727i −0.174805 0.100924i 0.410044 0.912066i \(-0.365513\pi\)
−0.584850 + 0.811142i \(0.698847\pi\)
\(12\) 1.54605 0.780860i 0.446305 0.225415i
\(13\) 0.867380 + 0.500782i 0.240568 + 0.138892i 0.615438 0.788185i \(-0.288979\pi\)
−0.374870 + 0.927077i \(0.622313\pi\)
\(14\) 0 0
\(15\) −0.531299 0.347713i −0.137181 0.0897791i
\(16\) 1.00000 0.250000
\(17\) −2.49453 4.32065i −0.605013 1.04791i −0.992049 0.125848i \(-0.959835\pi\)
0.387037 0.922064i \(-0.373499\pi\)
\(18\) 2.41449 + 1.78052i 0.569101 + 0.419672i
\(19\) −5.50552 3.17861i −1.26305 0.729224i −0.289389 0.957212i \(-0.593452\pi\)
−0.973664 + 0.227988i \(0.926785\pi\)
\(20\) −0.183299 0.317483i −0.0409869 0.0709914i
\(21\) 0 0
\(22\) 0.334727 0.579764i 0.0713640 0.123606i
\(23\) 6.66371 3.84729i 1.38948 0.802216i 0.396223 0.918154i \(-0.370321\pi\)
0.993256 + 0.115938i \(0.0369875\pi\)
\(24\) 0.780860 + 1.54605i 0.159392 + 0.315585i
\(25\) 2.43280 4.21374i 0.486561 0.842748i
\(26\) −0.500782 + 0.867380i −0.0982115 + 0.170107i
\(27\) −0.867380 + 5.12325i −0.166927 + 0.985969i
\(28\) 0 0
\(29\) 1.58394 0.914490i 0.294131 0.169817i −0.345672 0.938355i \(-0.612349\pi\)
0.639803 + 0.768539i \(0.279016\pi\)
\(30\) 0.347713 0.531299i 0.0634834 0.0970014i
\(31\) 6.32588i 1.13616i 0.822973 + 0.568081i \(0.192314\pi\)
−0.822973 + 0.568081i \(0.807686\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 1.15772 + 0.0647887i 0.201532 + 0.0112783i
\(34\) 4.32065 2.49453i 0.740986 0.427809i
\(35\) 0 0
\(36\) −1.78052 + 2.41449i −0.296753 + 0.402415i
\(37\) 2.58394 4.47552i 0.424798 0.735771i −0.571604 0.820530i \(-0.693679\pi\)
0.996402 + 0.0847585i \(0.0270119\pi\)
\(38\) 3.17861 5.50552i 0.515639 0.893113i
\(39\) −1.73205 0.0969299i −0.277350 0.0155212i
\(40\) 0.317483 0.183299i 0.0501985 0.0289821i
\(41\) 2.15928 3.73998i 0.337223 0.584087i −0.646686 0.762756i \(-0.723846\pi\)
0.983909 + 0.178669i \(0.0571790\pi\)
\(42\) 0 0
\(43\) 2.24922 + 3.89576i 0.343002 + 0.594098i 0.984989 0.172618i \(-0.0552228\pi\)
−0.641986 + 0.766716i \(0.721889\pi\)
\(44\) 0.579764 + 0.334727i 0.0874027 + 0.0504619i
\(45\) 1.09293 + 0.122710i 0.162924 + 0.0182926i
\(46\) 3.84729 + 6.66371i 0.567252 + 0.982510i
\(47\) 8.32901 1.21491 0.607455 0.794354i \(-0.292190\pi\)
0.607455 + 0.794354i \(0.292190\pi\)
\(48\) −1.54605 + 0.780860i −0.223153 + 0.112707i
\(49\) 0 0
\(50\) 4.21374 + 2.43280i 0.595913 + 0.344050i
\(51\) 7.23048 + 4.73205i 1.01247 + 0.662620i
\(52\) −0.867380 0.500782i −0.120284 0.0694460i
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −5.12325 0.867380i −0.697185 0.118036i
\(55\) 0.245420i 0.0330925i
\(56\) 0 0
\(57\) 10.9938 + 0.615242i 1.45617 + 0.0814909i
\(58\) 0.914490 + 1.58394i 0.120078 + 0.207982i
\(59\) 8.72695 1.13615 0.568076 0.822976i \(-0.307688\pi\)
0.568076 + 0.822976i \(0.307688\pi\)
\(60\) 0.531299 + 0.347713i 0.0685904 + 0.0448895i
\(61\) 4.95771i 0.634770i 0.948297 + 0.317385i \(0.102805\pi\)
−0.948297 + 0.317385i \(0.897195\pi\)
\(62\) −6.32588 −0.803387
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.367172i 0.0455420i
\(66\) −0.0647887 + 1.15772i −0.00797493 + 0.142505i
\(67\) −10.8907 −1.33052 −0.665258 0.746614i \(-0.731678\pi\)
−0.665258 + 0.746614i \(0.731678\pi\)
\(68\) 2.49453 + 4.32065i 0.302506 + 0.523956i
\(69\) −7.29820 + 11.1515i −0.878600 + 1.34248i
\(70\) 0 0
\(71\) 5.49843i 0.652544i 0.945276 + 0.326272i \(0.105793\pi\)
−0.945276 + 0.326272i \(0.894207\pi\)
\(72\) −2.41449 1.78052i −0.284550 0.209836i
\(73\) −3.52744 + 2.03657i −0.412856 + 0.238363i −0.692016 0.721882i \(-0.743277\pi\)
0.279160 + 0.960245i \(0.409944\pi\)
\(74\) 4.47552 + 2.58394i 0.520269 + 0.300377i
\(75\) −0.470886 + 8.41431i −0.0543732 + 0.971601i
\(76\) 5.50552 + 3.17861i 0.631526 + 0.364612i
\(77\) 0 0
\(78\) 0.0969299 1.73205i 0.0109751 0.196116i
\(79\) 8.35568 0.940087 0.470044 0.882643i \(-0.344238\pi\)
0.470044 + 0.882643i \(0.344238\pi\)
\(80\) 0.183299 + 0.317483i 0.0204935 + 0.0354957i
\(81\) −2.65953 8.59808i −0.295503 0.955342i
\(82\) 3.73998 + 2.15928i 0.413012 + 0.238453i
\(83\) −8.50712 14.7348i −0.933778 1.61735i −0.776798 0.629750i \(-0.783158\pi\)
−0.156980 0.987602i \(-0.550176\pi\)
\(84\) 0 0
\(85\) 0.914490 1.58394i 0.0991904 0.171803i
\(86\) −3.89576 + 2.24922i −0.420090 + 0.242539i
\(87\) −1.73476 + 2.65068i −0.185986 + 0.284183i
\(88\) −0.334727 + 0.579764i −0.0356820 + 0.0618030i
\(89\) 5.35566 9.27628i 0.567699 0.983283i −0.429094 0.903260i \(-0.641167\pi\)
0.996793 0.0800234i \(-0.0254995\pi\)
\(90\) −0.122710 + 1.09293i −0.0129348 + 0.115205i
\(91\) 0 0
\(92\) −6.66371 + 3.84729i −0.694740 + 0.401108i
\(93\) −4.93962 9.78010i −0.512215 1.01415i
\(94\) 8.32901i 0.859071i
\(95\) 2.33055i 0.239109i
\(96\) −0.780860 1.54605i −0.0796962 0.157793i
\(97\) 14.9093 8.60787i 1.51381 0.873997i 0.513937 0.857828i \(-0.328186\pi\)
0.999869 0.0161687i \(-0.00514689\pi\)
\(98\) 0 0
\(99\) −1.84047 + 0.803848i −0.184974 + 0.0807897i
\(100\) −2.43280 + 4.21374i −0.243280 + 0.421374i
\(101\) 7.86586 13.6241i 0.782683 1.35565i −0.147691 0.989034i \(-0.547184\pi\)
0.930374 0.366613i \(-0.119483\pi\)
\(102\) −4.73205 + 7.23048i −0.468543 + 0.715925i
\(103\) −9.91124 + 5.72226i −0.976584 + 0.563831i −0.901237 0.433327i \(-0.857340\pi\)
−0.0753467 + 0.997157i \(0.524006\pi\)
\(104\) 0.500782 0.867380i 0.0491057 0.0850537i
\(105\) 0 0
\(106\) 0 0
\(107\) −9.57976 5.53088i −0.926111 0.534690i −0.0405313 0.999178i \(-0.512905\pi\)
−0.885579 + 0.464488i \(0.846238\pi\)
\(108\) 0.867380 5.12325i 0.0834637 0.492985i
\(109\) 5.28166 + 9.14811i 0.505891 + 0.876230i 0.999977 + 0.00681630i \(0.00216971\pi\)
−0.494085 + 0.869413i \(0.664497\pi\)
\(110\) 0.245420 0.0233999
\(111\) −0.500140 + 8.93706i −0.0474712 + 0.848268i
\(112\) 0 0
\(113\) 3.60226 + 2.07976i 0.338872 + 0.195648i 0.659773 0.751465i \(-0.270652\pi\)
−0.320901 + 0.947113i \(0.603986\pi\)
\(114\) −0.615242 + 10.9938i −0.0576227 + 1.02967i
\(115\) 2.44290 + 1.41041i 0.227802 + 0.131521i
\(116\) −1.58394 + 0.914490i −0.147065 + 0.0849083i
\(117\) 2.75352 1.20263i 0.254563 0.111183i
\(118\) 8.72695i 0.803381i
\(119\) 0 0
\(120\) −0.347713 + 0.531299i −0.0317417 + 0.0485007i
\(121\) −5.27592 9.13815i −0.479629 0.830741i
\(122\) −4.95771 −0.448850
\(123\) −0.417944 + 7.46828i −0.0376847 + 0.673392i
\(124\) 6.32588i 0.568081i
\(125\) 3.61671 0.323489
\(126\) 0 0
\(127\) −1.66945 −0.148140 −0.0740700 0.997253i \(-0.523599\pi\)
−0.0740700 + 0.997253i \(0.523599\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −6.51943 4.26670i −0.574004 0.375662i
\(130\) −0.367172 −0.0322031
\(131\) −6.76607 11.7192i −0.591154 1.02391i −0.994077 0.108675i \(-0.965339\pi\)
0.402923 0.915234i \(-0.367994\pi\)
\(132\) −1.15772 0.0647887i −0.100766 0.00563913i
\(133\) 0 0
\(134\) 10.8907i 0.940817i
\(135\) −1.78554 + 0.663707i −0.153674 + 0.0571228i
\(136\) −4.32065 + 2.49453i −0.370493 + 0.213904i
\(137\) −7.78428 4.49425i −0.665056 0.383970i 0.129145 0.991626i \(-0.458777\pi\)
−0.794201 + 0.607656i \(0.792110\pi\)
\(138\) −11.1515 7.29820i −0.949280 0.621264i
\(139\) 8.05336 + 4.64961i 0.683077 + 0.394375i 0.801014 0.598646i \(-0.204294\pi\)
−0.117936 + 0.993021i \(0.537628\pi\)
\(140\) 0 0
\(141\) −12.8770 + 6.50379i −1.08444 + 0.547718i
\(142\) −5.49843 −0.461418
\(143\) −0.335250 0.580671i −0.0280351 0.0485581i
\(144\) 1.78052 2.41449i 0.148376 0.201208i
\(145\) 0.580671 + 0.335250i 0.0482221 + 0.0278410i
\(146\) −2.03657 3.52744i −0.168548 0.291933i
\(147\) 0 0
\(148\) −2.58394 + 4.47552i −0.212399 + 0.367886i
\(149\) 2.45268 1.41606i 0.200931 0.116008i −0.396158 0.918182i \(-0.629657\pi\)
0.597090 + 0.802174i \(0.296324\pi\)
\(150\) −8.41431 0.470886i −0.687026 0.0384477i
\(151\) 8.27592 14.3343i 0.673484 1.16651i −0.303425 0.952855i \(-0.598130\pi\)
0.976909 0.213654i \(-0.0685365\pi\)
\(152\) −3.17861 + 5.50552i −0.257820 + 0.446556i
\(153\) −14.8737 1.66997i −1.20247 0.135009i
\(154\) 0 0
\(155\) −2.00836 + 1.15953i −0.161315 + 0.0931355i
\(156\) 1.73205 + 0.0969299i 0.138675 + 0.00776060i
\(157\) 2.83456i 0.226222i 0.993582 + 0.113111i \(0.0360816\pi\)
−0.993582 + 0.113111i \(0.963918\pi\)
\(158\) 8.35568i 0.664742i
\(159\) 0 0
\(160\) −0.317483 + 0.183299i −0.0250993 + 0.0144911i
\(161\) 0 0
\(162\) 8.59808 2.65953i 0.675529 0.208952i
\(163\) −12.3640 + 21.4151i −0.968426 + 1.67736i −0.268313 + 0.963332i \(0.586466\pi\)
−0.700113 + 0.714032i \(0.746867\pi\)
\(164\) −2.15928 + 3.73998i −0.168611 + 0.292044i
\(165\) 0.191639 + 0.379431i 0.0149191 + 0.0295387i
\(166\) 14.7348 8.50712i 1.14364 0.660281i
\(167\) 9.67422 16.7562i 0.748614 1.29664i −0.199874 0.979822i \(-0.564053\pi\)
0.948487 0.316815i \(-0.102614\pi\)
\(168\) 0 0
\(169\) −5.99843 10.3896i −0.461418 0.799199i
\(170\) 1.58394 + 0.914490i 0.121483 + 0.0701382i
\(171\) −17.4774 + 7.63345i −1.33653 + 0.583745i
\(172\) −2.24922 3.89576i −0.171501 0.297049i
\(173\) −4.83654 −0.367715 −0.183858 0.982953i \(-0.558859\pi\)
−0.183858 + 0.982953i \(0.558859\pi\)
\(174\) −2.65068 1.73476i −0.200948 0.131512i
\(175\) 0 0
\(176\) −0.579764 0.334727i −0.0437013 0.0252310i
\(177\) −13.4923 + 6.81453i −1.01414 + 0.512211i
\(178\) 9.27628 + 5.35566i 0.695286 + 0.401424i
\(179\) 3.16789 1.82898i 0.236779 0.136704i −0.376916 0.926247i \(-0.623016\pi\)
0.613695 + 0.789543i \(0.289682\pi\)
\(180\) −1.09293 0.122710i −0.0814620 0.00914628i
\(181\) 5.66796i 0.421296i −0.977562 0.210648i \(-0.932443\pi\)
0.977562 0.210648i \(-0.0675574\pi\)
\(182\) 0 0
\(183\) −3.87128 7.66485i −0.286173 0.566602i
\(184\) −3.84729 6.66371i −0.283626 0.491255i
\(185\) 1.89454 0.139289
\(186\) 9.78010 4.93962i 0.717111 0.362191i
\(187\) 3.33994i 0.244241i
\(188\) −8.32901 −0.607455
\(189\) 0 0
\(190\) 2.33055 0.169076
\(191\) 27.3777i 1.98098i 0.137587 + 0.990490i \(0.456065\pi\)
−0.137587 + 0.990490i \(0.543935\pi\)
\(192\) 1.54605 0.780860i 0.111576 0.0563537i
\(193\) −10.0283 −0.721850 −0.360925 0.932595i \(-0.617539\pi\)
−0.360925 + 0.932595i \(0.617539\pi\)
\(194\) 8.60787 + 14.9093i 0.618009 + 1.07042i
\(195\) −0.286710 0.567664i −0.0205317 0.0406513i
\(196\) 0 0
\(197\) 18.8258i 1.34129i −0.741780 0.670643i \(-0.766018\pi\)
0.741780 0.670643i \(-0.233982\pi\)
\(198\) −0.803848 1.84047i −0.0571270 0.130797i
\(199\) 4.64541 2.68203i 0.329305 0.190124i −0.326228 0.945291i \(-0.605778\pi\)
0.655532 + 0.755167i \(0.272444\pi\)
\(200\) −4.21374 2.43280i −0.297956 0.172025i
\(201\) 16.8376 8.50414i 1.18763 0.599836i
\(202\) 13.6241 + 7.86586i 0.958587 + 0.553440i
\(203\) 0 0
\(204\) −7.23048 4.73205i −0.506235 0.331310i
\(205\) 1.58318 0.110574
\(206\) −5.72226 9.91124i −0.398689 0.690549i
\(207\) 2.57558 22.9396i 0.179015 1.59441i
\(208\) 0.867380 + 0.500782i 0.0601420 + 0.0347230i
\(209\) 2.12793 + 3.68569i 0.147192 + 0.254944i
\(210\) 0 0
\(211\) −0.828981 + 1.43584i −0.0570694 + 0.0988471i −0.893149 0.449762i \(-0.851509\pi\)
0.836079 + 0.548609i \(0.184842\pi\)
\(212\) 0 0
\(213\) −4.29351 8.50083i −0.294186 0.582467i
\(214\) 5.53088 9.57976i 0.378083 0.654859i
\(215\) −0.824559 + 1.42818i −0.0562344 + 0.0974009i
\(216\) 5.12325 + 0.867380i 0.348593 + 0.0590178i
\(217\) 0 0
\(218\) −9.14811 + 5.28166i −0.619588 + 0.357719i
\(219\) 3.86331 5.90307i 0.261059 0.398893i
\(220\) 0.245420i 0.0165462i
\(221\) 4.99687i 0.336126i
\(222\) −8.93706 0.500140i −0.599816 0.0335672i
\(223\) −14.7546 + 8.51860i −0.988044 + 0.570448i −0.904689 0.426072i \(-0.859897\pi\)
−0.0833551 + 0.996520i \(0.526564\pi\)
\(224\) 0 0
\(225\) −5.84239 13.3766i −0.389492 0.891774i
\(226\) −2.07976 + 3.60226i −0.138344 + 0.239619i
\(227\) −2.55512 + 4.42560i −0.169589 + 0.293737i −0.938276 0.345889i \(-0.887577\pi\)
0.768686 + 0.639626i \(0.220911\pi\)
\(228\) −10.9938 0.615242i −0.728084 0.0407454i
\(229\) −13.2215 + 7.63345i −0.873703 + 0.504433i −0.868577 0.495554i \(-0.834965\pi\)
−0.00512595 + 0.999987i \(0.501632\pi\)
\(230\) −1.41041 + 2.44290i −0.0929997 + 0.161080i
\(231\) 0 0
\(232\) −0.914490 1.58394i −0.0600392 0.103991i
\(233\) −8.82741 5.09651i −0.578303 0.333883i 0.182156 0.983270i \(-0.441693\pi\)
−0.760459 + 0.649386i \(0.775026\pi\)
\(234\) 1.20263 + 2.75352i 0.0786184 + 0.180003i
\(235\) 1.52670 + 2.64432i 0.0995909 + 0.172496i
\(236\) −8.72695 −0.568076
\(237\) −12.9183 + 6.52461i −0.839131 + 0.423819i
\(238\) 0 0
\(239\) −16.6117 9.59076i −1.07452 0.620375i −0.145108 0.989416i \(-0.546353\pi\)
−0.929413 + 0.369041i \(0.879686\pi\)
\(240\) −0.531299 0.347713i −0.0342952 0.0224448i
\(241\) 17.9140 + 10.3426i 1.15394 + 0.666227i 0.949844 0.312724i \(-0.101241\pi\)
0.204095 + 0.978951i \(0.434575\pi\)
\(242\) 9.13815 5.27592i 0.587423 0.339149i
\(243\) 10.8256 + 11.2163i 0.694465 + 0.719526i
\(244\) 4.95771i 0.317385i
\(245\) 0 0
\(246\) −7.46828 0.417944i −0.476160 0.0266471i
\(247\) −3.18359 5.51413i −0.202567 0.350856i
\(248\) 6.32588 0.401694
\(249\) 24.6582 + 16.1378i 1.56265 + 1.02269i
\(250\) 3.61671i 0.228741i
\(251\) 1.81200 0.114373 0.0571864 0.998364i \(-0.481787\pi\)
0.0571864 + 0.998364i \(0.481787\pi\)
\(252\) 0 0
\(253\) −5.15117 −0.323851
\(254\) 1.66945i 0.104751i
\(255\) −0.177006 + 3.16294i −0.0110845 + 0.198071i
\(256\) 1.00000 0.0625000
\(257\) −3.22773 5.59059i −0.201340 0.348731i 0.747620 0.664126i \(-0.231196\pi\)
−0.948960 + 0.315395i \(0.897863\pi\)
\(258\) 4.26670 6.51943i 0.265633 0.405882i
\(259\) 0 0
\(260\) 0.367172i 0.0227710i
\(261\) 0.612209 5.45268i 0.0378948 0.337513i
\(262\) 11.7192 6.76607i 0.724013 0.418009i
\(263\) 7.63888 + 4.41031i 0.471034 + 0.271951i 0.716672 0.697410i \(-0.245664\pi\)
−0.245639 + 0.969361i \(0.578998\pi\)
\(264\) 0.0647887 1.15772i 0.00398747 0.0712525i
\(265\) 0 0
\(266\) 0 0
\(267\) −1.03663 + 18.5236i −0.0634404 + 1.13362i
\(268\) 10.8907 0.665258
\(269\) 7.13267 + 12.3541i 0.434886 + 0.753245i 0.997286 0.0736199i \(-0.0234552\pi\)
−0.562400 + 0.826865i \(0.690122\pi\)
\(270\) −0.663707 1.78554i −0.0403919 0.108664i
\(271\) 2.64381 + 1.52641i 0.160600 + 0.0927226i 0.578146 0.815933i \(-0.303776\pi\)
−0.417546 + 0.908656i \(0.637110\pi\)
\(272\) −2.49453 4.32065i −0.151253 0.261978i
\(273\) 0 0
\(274\) 4.49425 7.78428i 0.271508 0.470265i
\(275\) −2.82090 + 1.62865i −0.170107 + 0.0982112i
\(276\) 7.29820 11.1515i 0.439300 0.671242i
\(277\) −0.632828 + 1.09609i −0.0380230 + 0.0658577i −0.884411 0.466710i \(-0.845439\pi\)
0.846388 + 0.532567i \(0.178773\pi\)
\(278\) −4.64961 + 8.05336i −0.278865 + 0.483009i
\(279\) 15.2738 + 11.2633i 0.914417 + 0.674318i
\(280\) 0 0
\(281\) 9.11639 5.26335i 0.543838 0.313985i −0.202795 0.979221i \(-0.565002\pi\)
0.746633 + 0.665236i \(0.231669\pi\)
\(282\) −6.50379 12.8770i −0.387295 0.766816i
\(283\) 19.8718i 1.18125i −0.806945 0.590627i \(-0.798881\pi\)
0.806945 0.590627i \(-0.201119\pi\)
\(284\) 5.49843i 0.326272i
\(285\) 1.81983 + 3.60313i 0.107797 + 0.213431i
\(286\) 0.580671 0.335250i 0.0343358 0.0198238i
\(287\) 0 0
\(288\) 2.41449 + 1.78052i 0.142275 + 0.104918i
\(289\) −3.94537 + 6.83358i −0.232081 + 0.401975i
\(290\) −0.335250 + 0.580671i −0.0196866 + 0.0340982i
\(291\) −16.3289 + 24.9502i −0.957215 + 1.46261i
\(292\) 3.52744 2.03657i 0.206428 0.119181i
\(293\) −6.70606 + 11.6152i −0.391772 + 0.678569i −0.992683 0.120747i \(-0.961471\pi\)
0.600911 + 0.799316i \(0.294804\pi\)
\(294\) 0 0
\(295\) 1.59964 + 2.77066i 0.0931348 + 0.161314i
\(296\) −4.47552 2.58394i −0.260134 0.150189i
\(297\) 2.21776 2.67994i 0.128688 0.155506i
\(298\) 1.41606 + 2.45268i 0.0820299 + 0.142080i
\(299\) 7.70663 0.445686
\(300\) 0.470886 8.41431i 0.0271866 0.485800i
\(301\) 0 0
\(302\) 14.3343 + 8.27592i 0.824847 + 0.476225i
\(303\) −1.52249 + 27.2056i −0.0874649 + 1.56292i
\(304\) −5.50552 3.17861i −0.315763 0.182306i
\(305\) −1.57399 + 0.908744i −0.0901265 + 0.0520346i
\(306\) 1.66997 14.8737i 0.0954660 0.850275i
\(307\) 0.653728i 0.0373102i −0.999826 0.0186551i \(-0.994062\pi\)
0.999826 0.0186551i \(-0.00593845\pi\)
\(308\) 0 0
\(309\) 10.8550 16.5862i 0.617517 0.943554i
\(310\) −1.15953 2.00836i −0.0658567 0.114067i
\(311\) 9.24493 0.524232 0.262116 0.965036i \(-0.415580\pi\)
0.262116 + 0.965036i \(0.415580\pi\)
\(312\) −0.0969299 + 1.73205i −0.00548757 + 0.0980581i
\(313\) 6.16414i 0.348418i 0.984709 + 0.174209i \(0.0557368\pi\)
−0.984709 + 0.174209i \(0.944263\pi\)
\(314\) −2.83456 −0.159963
\(315\) 0 0
\(316\) −8.35568 −0.470044
\(317\) 20.6548i 1.16009i −0.814584 0.580045i \(-0.803035\pi\)
0.814584 0.580045i \(-0.196965\pi\)
\(318\) 0 0
\(319\) −1.22442 −0.0685542
\(320\) −0.183299 0.317483i −0.0102467 0.0177479i
\(321\) 19.1296 + 1.07054i 1.06771 + 0.0597517i
\(322\) 0 0
\(323\) 31.7166i 1.76476i
\(324\) 2.65953 + 8.59808i 0.147752 + 0.477671i
\(325\) 4.22033 2.43661i 0.234102 0.135159i
\(326\) −21.4151 12.3640i −1.18608 0.684781i
\(327\) −15.3091 10.0192i −0.846594 0.554061i
\(328\) −3.73998 2.15928i −0.206506 0.119226i
\(329\) 0 0
\(330\) −0.379431 + 0.191639i −0.0208870 + 0.0105494i
\(331\) 10.7114 0.588750 0.294375 0.955690i \(-0.404889\pi\)
0.294375 + 0.955690i \(0.404889\pi\)
\(332\) 8.50712 + 14.7348i 0.466889 + 0.808676i
\(333\) −6.20535 14.2076i −0.340051 0.778574i
\(334\) 16.7562 + 9.67422i 0.916861 + 0.529350i
\(335\) −1.99626 3.45763i −0.109067 0.188910i
\(336\) 0 0
\(337\) 3.77592 6.54008i 0.205687 0.356261i −0.744664 0.667439i \(-0.767390\pi\)
0.950351 + 0.311179i \(0.100724\pi\)
\(338\) 10.3896 5.99843i 0.565119 0.326272i
\(339\) −7.19326 0.402553i −0.390684 0.0218637i
\(340\) −0.914490 + 1.58394i −0.0495952 + 0.0859014i
\(341\) 2.11744 3.66751i 0.114666 0.198607i
\(342\) −7.63345 17.4774i −0.412770 0.945069i
\(343\) 0 0
\(344\) 3.89576 2.24922i 0.210045 0.121270i
\(345\) −4.87817 0.272995i −0.262632 0.0146975i
\(346\) 4.83654i 0.260014i
\(347\) 10.9320i 0.586859i 0.955981 + 0.293430i \(0.0947967\pi\)
−0.955981 + 0.293430i \(0.905203\pi\)
\(348\) 1.73476 2.65068i 0.0929929 0.142091i
\(349\) −1.02562 + 0.592145i −0.0549004 + 0.0316968i −0.527199 0.849742i \(-0.676758\pi\)
0.472299 + 0.881439i \(0.343424\pi\)
\(350\) 0 0
\(351\) −3.31798 + 4.00943i −0.177101 + 0.214008i
\(352\) 0.334727 0.579764i 0.0178410 0.0309015i
\(353\) −16.7912 + 29.0832i −0.893706 + 1.54794i −0.0583086 + 0.998299i \(0.518571\pi\)
−0.835398 + 0.549646i \(0.814763\pi\)
\(354\) −6.81453 13.4923i −0.362188 0.717106i
\(355\) −1.74566 + 1.00786i −0.0926501 + 0.0534915i
\(356\) −5.35566 + 9.27628i −0.283849 + 0.491642i
\(357\) 0 0
\(358\) 1.82898 + 3.16789i 0.0966646 + 0.167428i
\(359\) 8.77122 + 5.06407i 0.462927 + 0.267271i 0.713274 0.700885i \(-0.247211\pi\)
−0.250347 + 0.968156i \(0.580545\pi\)
\(360\) 0.122710 1.09293i 0.00646739 0.0576023i
\(361\) 10.7072 + 18.5453i 0.563534 + 0.976070i
\(362\) 5.66796 0.297901
\(363\) 15.2924 + 10.0083i 0.802644 + 0.525297i
\(364\) 0 0
\(365\) −1.29315 0.746603i −0.0676868 0.0390790i
\(366\) 7.66485 3.87128i 0.400648 0.202355i
\(367\) −15.5903 9.00104i −0.813805 0.469850i 0.0344706 0.999406i \(-0.489025\pi\)
−0.848275 + 0.529555i \(0.822359\pi\)
\(368\) 6.66371 3.84729i 0.347370 0.200554i
\(369\) −5.18552 11.8727i −0.269947 0.618066i
\(370\) 1.89454i 0.0984923i
\(371\) 0 0
\(372\) 4.93962 + 9.78010i 0.256108 + 0.507074i
\(373\) −8.20451 14.2106i −0.424814 0.735799i 0.571589 0.820540i \(-0.306327\pi\)
−0.996403 + 0.0847411i \(0.972994\pi\)
\(374\) −3.33994 −0.172704
\(375\) −5.59160 + 2.82415i −0.288749 + 0.145838i
\(376\) 8.32901i 0.429536i
\(377\) 1.83184 0.0943447
\(378\) 0 0
\(379\) −2.91372 −0.149668 −0.0748339 0.997196i \(-0.523843\pi\)
−0.0748339 + 0.997196i \(0.523843\pi\)
\(380\) 2.33055i 0.119555i
\(381\) 2.58105 1.30361i 0.132231 0.0667859i
\(382\) −27.3777 −1.40076
\(383\) 4.28721 + 7.42567i 0.219066 + 0.379434i 0.954523 0.298138i \(-0.0963655\pi\)
−0.735456 + 0.677572i \(0.763032\pi\)
\(384\) 0.780860 + 1.54605i 0.0398481 + 0.0788963i
\(385\) 0 0
\(386\) 10.0283i 0.510425i
\(387\) 13.4110 + 1.50575i 0.681721 + 0.0765414i
\(388\) −14.9093 + 8.60787i −0.756903 + 0.436998i
\(389\) 30.7906 + 17.7770i 1.56115 + 0.901328i 0.997142 + 0.0755559i \(0.0240731\pi\)
0.564004 + 0.825772i \(0.309260\pi\)
\(390\) 0.567664 0.286710i 0.0287448 0.0145181i
\(391\) −33.2456 19.1944i −1.68130 0.970702i
\(392\) 0 0
\(393\) 19.6117 + 12.8350i 0.989279 + 0.647442i
\(394\) 18.8258 0.948433
\(395\) 1.53159 + 2.65279i 0.0770626 + 0.133476i
\(396\) 1.84047 0.803848i 0.0924872 0.0403949i
\(397\) −3.10066 1.79017i −0.155618 0.0898460i 0.420169 0.907446i \(-0.361971\pi\)
−0.575787 + 0.817600i \(0.695304\pi\)
\(398\) 2.68203 + 4.64541i 0.134438 + 0.232853i
\(399\) 0 0
\(400\) 2.43280 4.21374i 0.121640 0.210687i
\(401\) −0.165300 + 0.0954357i −0.00825467 + 0.00476583i −0.504122 0.863633i \(-0.668184\pi\)
0.495867 + 0.868398i \(0.334850\pi\)
\(402\) 8.50414 + 16.8376i 0.424148 + 0.839782i
\(403\) −3.16789 + 5.48694i −0.157804 + 0.273324i
\(404\) −7.86586 + 13.6241i −0.391341 + 0.677823i
\(405\) 2.24226 2.42037i 0.111419 0.120269i
\(406\) 0 0
\(407\) −2.99615 + 1.72983i −0.148514 + 0.0857445i
\(408\) 4.73205 7.23048i 0.234271 0.357962i
\(409\) 3.47371i 0.171764i −0.996305 0.0858819i \(-0.972629\pi\)
0.996305 0.0858819i \(-0.0273708\pi\)
\(410\) 1.58318i 0.0781875i
\(411\) 15.5442 + 0.869894i 0.766740 + 0.0429087i
\(412\) 9.91124 5.72226i 0.488292 0.281915i
\(413\) 0 0
\(414\) 22.9396 + 2.57558i 1.12742 + 0.126583i
\(415\) 3.11870 5.40174i 0.153091 0.265161i
\(416\) −0.500782 + 0.867380i −0.0245529 + 0.0425268i
\(417\) −16.0816 0.899965i −0.787518 0.0440715i
\(418\) −3.68569 + 2.12793i −0.180273 + 0.104081i
\(419\) −0.703955 + 1.21929i −0.0343905 + 0.0595660i −0.882708 0.469921i \(-0.844282\pi\)
0.848318 + 0.529487i \(0.177616\pi\)
\(420\) 0 0
\(421\) 15.1930 + 26.3151i 0.740463 + 1.28252i 0.952285 + 0.305211i \(0.0987268\pi\)
−0.211822 + 0.977308i \(0.567940\pi\)
\(422\) −1.43584 0.828981i −0.0698954 0.0403541i
\(423\) 14.8299 20.1103i 0.721056 0.977797i
\(424\) 0 0
\(425\) −24.2748 −1.17750
\(426\) 8.50083 4.29351i 0.411867 0.208021i
\(427\) 0 0
\(428\) 9.57976 + 5.53088i 0.463055 + 0.267345i
\(429\) 0.971735 + 0.635960i 0.0469158 + 0.0307044i
\(430\) −1.42818 0.824559i −0.0688728 0.0397638i
\(431\) −23.6206 + 13.6373i −1.13776 + 0.656888i −0.945876 0.324529i \(-0.894794\pi\)
−0.191887 + 0.981417i \(0.561461\pi\)
\(432\) −0.867380 + 5.12325i −0.0417319 + 0.246492i
\(433\) 8.15047i 0.391686i −0.980635 0.195843i \(-0.937256\pi\)
0.980635 0.195843i \(-0.0627444\pi\)
\(434\) 0 0
\(435\) −1.15953 0.0648900i −0.0555951 0.00311124i
\(436\) −5.28166 9.14811i −0.252946 0.438115i
\(437\) −48.9162 −2.33998
\(438\) 5.90307 + 3.86331i 0.282060 + 0.184596i
\(439\) 12.2404i 0.584203i −0.956387 0.292101i \(-0.905646\pi\)
0.956387 0.292101i \(-0.0943545\pi\)
\(440\) −0.245420 −0.0117000
\(441\) 0 0
\(442\) 4.99687 0.237677
\(443\) 8.00836i 0.380489i 0.981737 + 0.190244i \(0.0609280\pi\)
−0.981737 + 0.190244i \(0.939072\pi\)
\(444\) 0.500140 8.93706i 0.0237356 0.424134i
\(445\) 3.92675 0.186146
\(446\) −8.51860 14.7546i −0.403367 0.698653i
\(447\) −2.68622 + 4.10449i −0.127054 + 0.194136i
\(448\) 0 0
\(449\) 14.5183i 0.685163i 0.939488 + 0.342581i \(0.111301\pi\)
−0.939488 + 0.342581i \(0.888699\pi\)
\(450\) 13.3766 5.84239i 0.630579 0.275413i
\(451\) −2.50374 + 1.44554i −0.117897 + 0.0680677i
\(452\) −3.60226 2.07976i −0.169436 0.0978239i
\(453\) −1.60186 + 28.6238i −0.0752620 + 1.34486i
\(454\) −4.42560 2.55512i −0.207704 0.119918i
\(455\) 0 0
\(456\) 0.615242 10.9938i 0.0288114 0.514833i
\(457\) 9.95501 0.465676 0.232838 0.972516i \(-0.425199\pi\)
0.232838 + 0.972516i \(0.425199\pi\)
\(458\) −7.63345 13.2215i −0.356688 0.617801i
\(459\) 24.2995 9.03245i 1.13420 0.421598i
\(460\) −2.44290 1.41041i −0.113901 0.0657607i
\(461\) 16.1635 + 27.9960i 0.752810 + 1.30391i 0.946456 + 0.322834i \(0.104636\pi\)
−0.193645 + 0.981072i \(0.562031\pi\)
\(462\) 0 0
\(463\) −4.72516 + 8.18421i −0.219597 + 0.380353i −0.954685 0.297619i \(-0.903807\pi\)
0.735088 + 0.677972i \(0.237141\pi\)
\(464\) 1.58394 0.914490i 0.0735327 0.0424541i
\(465\) 2.19959 3.36093i 0.102003 0.155859i
\(466\) 5.09651 8.82741i 0.236091 0.408922i
\(467\) 10.3312 17.8941i 0.478069 0.828039i −0.521615 0.853181i \(-0.674670\pi\)
0.999684 + 0.0251414i \(0.00800361\pi\)
\(468\) −2.75352 + 1.20263i −0.127281 + 0.0555916i
\(469\) 0 0
\(470\) −2.64432 + 1.52670i −0.121973 + 0.0704214i
\(471\) −2.21339 4.38235i −0.101988 0.201928i
\(472\) 8.72695i 0.401691i
\(473\) 3.01149i 0.138469i
\(474\) −6.52461 12.9183i −0.299685 0.593356i
\(475\) −26.7877 + 15.4659i −1.22910 + 0.709623i
\(476\) 0 0
\(477\) 0 0
\(478\) 9.59076 16.6117i 0.438671 0.759801i
\(479\) 5.08042 8.79955i 0.232131 0.402062i −0.726304 0.687373i \(-0.758764\pi\)
0.958435 + 0.285311i \(0.0920970\pi\)
\(480\) 0.347713 0.531299i 0.0158708 0.0242504i
\(481\) 4.48252 2.58799i 0.204386 0.118002i
\(482\) −10.3426 + 17.9140i −0.471094 + 0.815958i
\(483\) 0 0
\(484\) 5.27592 + 9.13815i 0.239814 + 0.415371i
\(485\) 5.46571 + 3.15563i 0.248185 + 0.143290i
\(486\) −11.2163 + 10.8256i −0.508782 + 0.491061i
\(487\) 15.6148 + 27.0457i 0.707575 + 1.22556i 0.965754 + 0.259459i \(0.0835443\pi\)
−0.258179 + 0.966097i \(0.583122\pi\)
\(488\) 4.95771 0.224425
\(489\) 2.39315 42.7634i 0.108222 1.93383i
\(490\) 0 0
\(491\) 17.8314 + 10.2950i 0.804720 + 0.464605i 0.845119 0.534578i \(-0.179529\pi\)
−0.0403987 + 0.999184i \(0.512863\pi\)
\(492\) 0.417944 7.46828i 0.0188424 0.336696i
\(493\) −7.90239 4.56245i −0.355906 0.205482i
\(494\) 5.51413 3.18359i 0.248093 0.143236i
\(495\) −0.592565 0.436975i −0.0266338 0.0196406i
\(496\) 6.32588i 0.284040i
\(497\) 0 0
\(498\) −16.1378 + 24.6582i −0.723150 + 1.10496i
\(499\) 12.5766 + 21.7834i 0.563007 + 0.975157i 0.997232 + 0.0743527i \(0.0236891\pi\)
−0.434225 + 0.900805i \(0.642978\pi\)
\(500\) −3.61671 −0.161744
\(501\) −1.87251 + 33.4601i −0.0836577 + 1.49489i
\(502\) 1.81200i 0.0808737i
\(503\) 31.1553 1.38915 0.694574 0.719421i \(-0.255593\pi\)
0.694574 + 0.719421i \(0.255593\pi\)
\(504\) 0 0
\(505\) 5.76722 0.256638
\(506\) 5.15117i 0.228997i
\(507\) 17.3867 + 11.3789i 0.772169 + 0.505352i
\(508\) 1.66945 0.0740700
\(509\) 2.41674 + 4.18591i 0.107120 + 0.185537i 0.914602 0.404354i \(-0.132504\pi\)
−0.807482 + 0.589892i \(0.799170\pi\)
\(510\) −3.16294 0.177006i −0.140057 0.00783796i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 21.0602 25.4491i 0.929830 1.12360i
\(514\) 5.59059 3.22773i 0.246590 0.142369i
\(515\) −3.63344 2.09777i −0.160109 0.0924387i
\(516\) 6.51943 + 4.26670i 0.287002 + 0.187831i
\(517\) −4.82886 2.78794i −0.212373 0.122613i
\(518\) 0 0
\(519\) 7.47751 3.77666i 0.328226 0.165777i
\(520\) 0.367172 0.0161015
\(521\) 8.76611 + 15.1834i 0.384050 + 0.665195i 0.991637 0.129059i \(-0.0411956\pi\)
−0.607587 + 0.794253i \(0.707862\pi\)
\(522\) 5.45268 + 0.612209i 0.238657 + 0.0267956i
\(523\) −16.5427 9.55094i −0.723362 0.417633i 0.0926268 0.995701i \(-0.470474\pi\)
−0.815989 + 0.578068i \(0.803807\pi\)
\(524\) 6.76607 + 11.7192i 0.295577 + 0.511955i
\(525\) 0 0
\(526\) −4.41031 + 7.63888i −0.192299 + 0.333071i
\(527\) 27.3319 15.7801i 1.19060 0.687392i
\(528\) 1.15772 + 0.0647887i 0.0503831 + 0.00281957i
\(529\) 18.1033 31.3559i 0.787101 1.36330i
\(530\) 0 0
\(531\) 15.5385 21.0711i 0.674312 0.914410i
\(532\) 0 0
\(533\) 3.74584 2.16266i 0.162250 0.0936752i
\(534\) −18.5236 1.03663i −0.801593 0.0448592i
\(535\) 4.05522i 0.175322i
\(536\) 10.8907i 0.470408i
\(537\) −3.46952 + 5.30136i −0.149721 + 0.228771i
\(538\) −12.3541 + 7.13267i −0.532625 + 0.307511i
\(539\) 0 0
\(540\) 1.78554 0.663707i 0.0768372 0.0285614i
\(541\) −6.83211 + 11.8336i −0.293735 + 0.508765i −0.974690 0.223561i \(-0.928232\pi\)
0.680954 + 0.732326i \(0.261565\pi\)
\(542\) −1.52641 + 2.64381i −0.0655648 + 0.113562i
\(543\) 4.42588 + 8.76293i 0.189933 + 0.376053i
\(544\) 4.32065 2.49453i 0.185247 0.106952i
\(545\) −1.93625 + 3.35368i −0.0829397 + 0.143656i
\(546\) 0 0
\(547\) 4.94380 + 8.56292i 0.211382 + 0.366124i 0.952147 0.305640i \(-0.0988703\pi\)
−0.740765 + 0.671764i \(0.765537\pi\)
\(548\) 7.78428 + 4.49425i 0.332528 + 0.191985i
\(549\) 11.9704 + 8.82729i 0.510882 + 0.376739i
\(550\) −1.62865 2.82090i −0.0694458 0.120284i
\(551\) −11.6272 −0.495337
\(552\) 11.1515 + 7.29820i 0.474640 + 0.310632i
\(553\) 0 0
\(554\) −1.09609 0.632828i −0.0465684 0.0268863i
\(555\) −2.92904 + 1.47937i −0.124331 + 0.0627957i
\(556\) −8.05336 4.64961i −0.341539 0.197187i
\(557\) −10.8946 + 6.29002i −0.461621 + 0.266517i −0.712725 0.701443i \(-0.752539\pi\)
0.251105 + 0.967960i \(0.419206\pi\)
\(558\) −11.2633 + 15.2738i −0.476815 + 0.646590i
\(559\) 4.50547i 0.190561i
\(560\) 0 0
\(561\) −2.60803 5.16371i −0.110111 0.218012i
\(562\) 5.26335 + 9.11639i 0.222021 + 0.384552i
\(563\) 24.3333 1.02553 0.512763 0.858530i \(-0.328622\pi\)
0.512763 + 0.858530i \(0.328622\pi\)
\(564\) 12.8770 6.50379i 0.542221 0.273859i
\(565\) 1.52487i 0.0641520i
\(566\) 19.8718 0.835272
\(567\) 0 0
\(568\) 5.49843 0.230709
\(569\) 9.45406i 0.396335i −0.980168 0.198167i \(-0.936501\pi\)
0.980168 0.198167i \(-0.0634990\pi\)
\(570\) −3.60313 + 1.81983i −0.150919 + 0.0762243i
\(571\) −31.5686 −1.32110 −0.660551 0.750781i \(-0.729677\pi\)
−0.660551 + 0.750781i \(0.729677\pi\)
\(572\) 0.335250 + 0.580671i 0.0140175 + 0.0242791i
\(573\) −21.3781 42.3272i −0.893084 1.76824i
\(574\) 0 0
\(575\) 37.4388i 1.56131i
\(576\) −1.78052 + 2.41449i −0.0741882 + 0.100604i
\(577\) 29.0806 16.7897i 1.21064 0.698964i 0.247742 0.968826i \(-0.420312\pi\)
0.962899 + 0.269862i \(0.0869782\pi\)
\(578\) −6.83358 3.94537i −0.284239 0.164106i
\(579\) 15.5042 7.83067i 0.644331 0.325432i
\(580\) −0.580671 0.335250i −0.0241110 0.0139205i
\(581\) 0 0
\(582\) −24.9502 16.3289i −1.03422 0.676853i
\(583\) 0 0
\(584\) 2.03657 + 3.52744i 0.0842739 + 0.145967i
\(585\) 0.886533 + 0.653755i 0.0366536 + 0.0270294i
\(586\) −11.6152 6.70606i −0.479821 0.277025i
\(587\) 9.65855 + 16.7291i 0.398651 + 0.690484i 0.993560 0.113310i \(-0.0361452\pi\)
−0.594909 + 0.803793i \(0.702812\pi\)
\(588\) 0 0
\(589\) 20.1075 34.8272i 0.828516 1.43503i
\(590\) −2.77066 + 1.59964i −0.114066 + 0.0658562i
\(591\) 14.7003 + 29.1056i 0.604692 + 1.19725i
\(592\) 2.58394 4.47552i 0.106199 0.183943i
\(593\) 0.366598 0.634967i 0.0150544 0.0260750i −0.858400 0.512981i \(-0.828541\pi\)
0.873454 + 0.486906i \(0.161875\pi\)
\(594\) 2.67994 + 2.21776i 0.109959 + 0.0909959i
\(595\) 0 0
\(596\) −2.45268 + 1.41606i −0.100466 + 0.0580039i
\(597\) −5.08773 + 7.77396i −0.208227 + 0.318167i
\(598\) 7.70663i 0.315147i
\(599\) 30.7783i 1.25757i −0.777580 0.628785i \(-0.783553\pi\)
0.777580 0.628785i \(-0.216447\pi\)
\(600\) 8.41431 + 0.470886i 0.343513 + 0.0192238i
\(601\) 0.786931 0.454335i 0.0320996 0.0185327i −0.483864 0.875143i \(-0.660767\pi\)
0.515964 + 0.856610i \(0.327434\pi\)
\(602\) 0 0
\(603\) −19.3911 + 26.2956i −0.789668 + 1.07084i
\(604\) −8.27592 + 14.3343i −0.336742 + 0.583255i
\(605\) 1.93414 3.35003i 0.0786340 0.136198i
\(606\) −27.2056 1.52249i −1.10515 0.0618470i
\(607\) 38.7783 22.3887i 1.57396 0.908728i 0.578287 0.815833i \(-0.303721\pi\)
0.995676 0.0928949i \(-0.0296121\pi\)
\(608\) 3.17861 5.50552i 0.128910 0.223278i
\(609\) 0 0
\(610\) −0.908744 1.57399i −0.0367940 0.0637290i
\(611\) 7.22442 + 4.17102i 0.292269 + 0.168741i
\(612\) 14.8737 + 1.66997i 0.601235 + 0.0675046i
\(613\) −9.07402 15.7167i −0.366496 0.634790i 0.622519 0.782605i \(-0.286109\pi\)
−0.989015 + 0.147815i \(0.952776\pi\)
\(614\) 0.653728 0.0263823
\(615\) −2.44766 + 1.23624i −0.0986993 + 0.0498500i
\(616\) 0 0
\(617\) −19.7393 11.3965i −0.794674 0.458805i 0.0469315 0.998898i \(-0.485056\pi\)
−0.841605 + 0.540093i \(0.818389\pi\)
\(618\) 16.5862 + 10.8550i 0.667193 + 0.436650i
\(619\) −38.4228 22.1834i −1.54434 0.891626i −0.998557 0.0537011i \(-0.982898\pi\)
−0.545785 0.837925i \(-0.683768\pi\)
\(620\) 2.00836 1.15953i 0.0806577 0.0465677i
\(621\) 13.9307 + 37.4769i 0.559018 + 1.50390i
\(622\) 9.24493i 0.370688i
\(623\) 0 0
\(624\) −1.73205 0.0969299i −0.0693375 0.00388030i
\(625\) −11.5011 19.9204i −0.460043 0.796818i
\(626\) −6.16414 −0.246368
\(627\) −6.16789 4.03663i −0.246322 0.161207i
\(628\) 2.83456i 0.113111i
\(629\) −25.7829 −1.02803
\(630\) 0 0
\(631\) −32.5707 −1.29662 −0.648310 0.761377i \(-0.724524\pi\)
−0.648310 + 0.761377i \(0.724524\pi\)
\(632\) 8.35568i 0.332371i
\(633\) 0.160455 2.86719i 0.00637751 0.113960i
\(634\) 20.6548 0.820308
\(635\) −0.306009 0.530024i −0.0121436 0.0210333i
\(636\) 0 0
\(637\) 0 0
\(638\) 1.22442i 0.0484751i
\(639\) 13.2759 + 9.79005i 0.525187 + 0.387288i
\(640\) 0.317483 0.183299i 0.0125496 0.00724553i
\(641\) 10.2270 + 5.90456i 0.403942 + 0.233216i 0.688184 0.725537i \(-0.258408\pi\)
−0.284241 + 0.958753i \(0.591742\pi\)
\(642\) −1.07054 + 19.1296i −0.0422508 + 0.754985i
\(643\) −25.3714 14.6482i −1.00055 0.577668i −0.0921392 0.995746i \(-0.529370\pi\)
−0.908411 + 0.418078i \(0.862704\pi\)
\(644\) 0 0
\(645\) 0.159599 2.85189i 0.00628421 0.112293i
\(646\) −31.7166 −1.24787
\(647\) −14.0841 24.3945i −0.553705 0.959045i −0.998003 0.0631660i \(-0.979880\pi\)
0.444298 0.895879i \(-0.353453\pi\)
\(648\) −8.59808 + 2.65953i −0.337764 + 0.104476i
\(649\) −5.05957 2.92114i −0.198605 0.114665i
\(650\) 2.43661 + 4.22033i 0.0955717 + 0.165535i
\(651\) 0 0
\(652\) 12.3640 21.4151i 0.484213 0.838682i
\(653\) −39.0555 + 22.5487i −1.52836 + 0.882399i −0.528929 + 0.848666i \(0.677406\pi\)
−0.999431 + 0.0337326i \(0.989261\pi\)
\(654\) 10.0192 15.3091i 0.391780 0.598632i
\(655\) 2.48043 4.29623i 0.0969184 0.167868i
\(656\) 2.15928 3.73998i 0.0843057 0.146022i
\(657\) −1.36339 + 12.1431i −0.0531909 + 0.473748i
\(658\) 0 0
\(659\) 27.5435 15.9022i 1.07294 0.619463i 0.143958 0.989584i \(-0.454017\pi\)
0.928984 + 0.370121i \(0.120684\pi\)
\(660\) −0.191639 0.379431i −0.00745953 0.0147693i
\(661\) 19.7724i 0.769056i 0.923113 + 0.384528i \(0.125636\pi\)
−0.923113 + 0.384528i \(0.874364\pi\)
\(662\) 10.7114i 0.416309i
\(663\) 3.90185 + 7.72539i 0.151535 + 0.300029i
\(664\) −14.7348 + 8.50712i −0.571820 + 0.330140i
\(665\) 0 0
\(666\) 14.2076 6.20535i 0.550535 0.240452i
\(667\) 7.03663 12.1878i 0.272459 0.471913i
\(668\) −9.67422 + 16.7562i −0.374307 + 0.648318i
\(669\) 16.1595 24.6915i 0.624763 0.954627i
\(670\) 3.45763 1.99626i 0.133580 0.0771223i
\(671\) 1.65948 2.87430i 0.0640635 0.110961i
\(672\) 0 0
\(673\) −0.945369 1.63743i −0.0364413 0.0631182i 0.847230 0.531227i \(-0.178269\pi\)
−0.883671 + 0.468109i \(0.844936\pi\)
\(674\) 6.54008 + 3.77592i 0.251914 + 0.145443i
\(675\) 19.4779 + 16.1188i 0.749703 + 0.620411i
\(676\) 5.99843 + 10.3896i 0.230709 + 0.399600i
\(677\) 21.1322 0.812175 0.406088 0.913834i \(-0.366893\pi\)
0.406088 + 0.913834i \(0.366893\pi\)
\(678\) 0.402553 7.19326i 0.0154599 0.276255i
\(679\) 0 0
\(680\) −1.58394 0.914490i −0.0607415 0.0350691i
\(681\) 0.494561 8.83737i 0.0189516 0.338649i
\(682\) 3.66751 + 2.11744i 0.140436 + 0.0810810i
\(683\) −7.55150 + 4.35986i −0.288950 + 0.166825i −0.637468 0.770477i \(-0.720018\pi\)
0.348518 + 0.937302i \(0.386685\pi\)
\(684\) 17.4774 7.63345i 0.668265 0.291872i
\(685\) 3.29517i 0.125902i
\(686\) 0 0
\(687\) 14.4804 22.1258i 0.552463 0.844153i
\(688\) 2.24922 + 3.89576i 0.0857506 + 0.148524i
\(689\) 0 0
\(690\) 0.272995 4.87817i 0.0103927 0.185709i
\(691\) 18.1370i 0.689964i 0.938609 + 0.344982i \(0.112115\pi\)
−0.938609 + 0.344982i \(0.887885\pi\)
\(692\) 4.83654 0.183858
\(693\) 0 0
\(694\) −10.9320 −0.414972
\(695\) 3.40908i 0.129314i
\(696\) 2.65068 + 1.73476i 0.100474 + 0.0657559i
\(697\) −21.5456 −0.816097
\(698\) −0.592145 1.02562i −0.0224130 0.0388205i
\(699\) 17.6272 + 0.986465i 0.666724 + 0.0373115i
\(700\) 0 0
\(701\) 35.6167i 1.34523i 0.739995 + 0.672613i \(0.234828\pi\)
−0.739995 + 0.672613i \(0.765172\pi\)
\(702\) −4.00943 3.31798i −0.151326 0.125229i
\(703\) −28.4519 + 16.4267i −1.07308 + 0.619545i
\(704\) 0.579764 + 0.334727i 0.0218507 + 0.0126155i
\(705\) −4.42519 2.89610i −0.166662 0.109074i
\(706\) −29.0832 16.7912i −1.09456 0.631946i
\(707\) 0 0
\(708\) 13.4923 6.81453i 0.507071 0.256106i
\(709\) −3.60770 −0.135490 −0.0677449 0.997703i \(-0.521580\pi\)
−0.0677449 + 0.997703i \(0.521580\pi\)
\(710\) −1.00786 1.74566i −0.0378242 0.0655135i
\(711\) 14.8774 20.1747i 0.557947 0.756611i
\(712\) −9.27628 5.35566i −0.347643 0.200712i
\(713\) 24.3375 + 42.1538i 0.911447 + 1.57867i
\(714\) 0 0
\(715\) 0.122902 0.212873i 0.00459628 0.00796099i
\(716\) −3.16789 + 1.82898i −0.118390 + 0.0683522i
\(717\) 33.1715 + 1.85636i 1.23881 + 0.0693270i
\(718\) −5.06407 + 8.77122i −0.188989 + 0.327339i
\(719\) −12.8915 + 22.3287i −0.480770 + 0.832718i −0.999757 0.0220642i \(-0.992976\pi\)
0.518986 + 0.854782i \(0.326310\pi\)
\(720\) 1.09293 + 0.122710i 0.0407310 + 0.00457314i
\(721\) 0 0
\(722\) −18.5453 + 10.7072i −0.690186 + 0.398479i
\(723\) −35.7719 2.00189i −1.33037 0.0744510i
\(724\) 5.66796i 0.210648i
\(725\) 8.89910i 0.330504i
\(726\) −10.0083 + 15.2924i −0.371441 + 0.567555i
\(727\) −1.32423 + 0.764544i −0.0491129 + 0.0283554i −0.524355 0.851499i \(-0.675694\pi\)
0.475242 + 0.879855i \(0.342360\pi\)
\(728\) 0 0
\(729\) −25.4953 8.88761i −0.944270 0.329171i
\(730\) 0.746603 1.29315i 0.0276330 0.0478618i
\(731\) 11.2215 19.4362i 0.415042 0.718873i
\(732\) 3.87128 + 7.66485i 0.143087 + 0.283301i
\(733\) −17.9908 + 10.3870i −0.664504 + 0.383651i −0.793991 0.607930i \(-0.792000\pi\)
0.129487 + 0.991581i \(0.458667\pi\)
\(734\) 9.00104 15.5903i 0.332234 0.575447i
\(735\) 0 0
\(736\) 3.84729 + 6.66371i 0.141813 + 0.245628i
\(737\) 6.31405 + 3.64542i 0.232581 + 0.134281i
\(738\) 11.8727 5.18552i 0.437039 0.190882i
\(739\) 5.93544 + 10.2805i 0.218339 + 0.378174i 0.954300 0.298850i \(-0.0966029\pi\)
−0.735961 + 0.677023i \(0.763270\pi\)
\(740\) −1.89454 −0.0696446
\(741\) 9.22773 + 6.03917i 0.338989 + 0.221854i
\(742\) 0 0
\(743\) −37.5906 21.7029i −1.37907 0.796204i −0.387019 0.922072i \(-0.626495\pi\)
−0.992047 + 0.125868i \(0.959828\pi\)
\(744\) −9.78010 + 4.93962i −0.358556 + 0.181095i
\(745\) 0.899148 + 0.519124i 0.0329422 + 0.0190192i
\(746\) 14.2106 8.20451i 0.520288 0.300389i
\(747\) −50.7240 5.69512i −1.85590 0.208374i
\(748\) 3.33994i 0.122120i
\(749\) 0 0
\(750\) −2.82415 5.59160i −0.103123 0.204176i
\(751\) −1.15691 2.00383i −0.0422164 0.0731209i 0.844145 0.536115i \(-0.180109\pi\)
−0.886362 + 0.462994i \(0.846775\pi\)
\(752\) 8.32901 0.303728
\(753\) −2.80144 + 1.41492i −0.102090 + 0.0515626i
\(754\) 1.83184i 0.0667118i
\(755\) 6.06787 0.220832
\(756\) 0 0
\(757\) −15.0946 −0.548624 −0.274312 0.961641i \(-0.588450\pi\)
−0.274312 + 0.961641i \(0.588450\pi\)
\(758\) 2.91372i 0.105831i
\(759\) 7.96394 4.02234i 0.289073 0.146002i
\(760\) −2.33055 −0.0845378
\(761\) −11.6690 20.2112i −0.422999 0.732656i 0.573232 0.819393i \(-0.305689\pi\)
−0.996231 + 0.0867370i \(0.972356\pi\)
\(762\) 1.30361 + 2.58105i 0.0472248 + 0.0935016i
\(763\) 0 0
\(764\) 27.3777i 0.990490i
\(765\) −2.19615 5.02826i −0.0794021 0.181797i
\(766\) −7.42567 + 4.28721i −0.268300 + 0.154903i
\(767\) 7.56959 + 4.37030i 0.273322 + 0.157803i
\(768\) −1.54605 + 0.780860i −0.0557881 + 0.0281769i
\(769\) 15.8266 + 9.13748i 0.570721 + 0.329506i 0.757437 0.652908i \(-0.226451\pi\)
−0.186716 + 0.982414i \(0.559784\pi\)
\(770\) 0 0
\(771\) 9.35568 + 6.12290i 0.336937 + 0.220511i
\(772\) 10.0283 0.360925
\(773\) −0.219254 0.379758i −0.00788600 0.0136590i 0.862055 0.506814i \(-0.169177\pi\)
−0.869941 + 0.493155i \(0.835844\pi\)
\(774\) −1.50575 + 13.4110i −0.0541229 + 0.482050i
\(775\) 26.6556 + 15.3896i 0.957497 + 0.552811i
\(776\) −8.60787 14.9093i −0.309004 0.535211i
\(777\) 0 0
\(778\) −17.7770 + 30.7906i −0.637335 + 1.10390i
\(779\) −23.7759 + 13.7270i −0.851861 + 0.491822i
\(780\) 0.286710 + 0.567664i 0.0102659 + 0.0203256i