Properties

Label 637.2.e.o.508.1
Level $637$
Weight $2$
Character 637.508
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - 2 x^{11} + 9 x^{10} - 6 x^{9} + 34 x^{8} - 18 x^{7} + 85 x^{6} - 2 x^{5} + 92 x^{4} - 26 x^{3} + 43 x^{2} + 6 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 508.1
Root \(0.379209 + 0.656810i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.o.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.09161 - 1.89072i) q^{2} +(0.879209 - 1.52284i) q^{3} +(-1.38322 + 2.39581i) q^{4} +(1.05533 + 1.82788i) q^{5} -3.83901 q^{6} +1.67333 q^{8} +(-0.0460183 - 0.0797060i) q^{9} +O(q^{10})\) \(q+(-1.09161 - 1.89072i) q^{2} +(0.879209 - 1.52284i) q^{3} +(-1.38322 + 2.39581i) q^{4} +(1.05533 + 1.82788i) q^{5} -3.83901 q^{6} +1.67333 q^{8} +(-0.0460183 - 0.0797060i) q^{9} +(2.30401 - 3.99066i) q^{10} +(2.88445 - 4.99601i) q^{11} +(2.43229 + 4.21285i) q^{12} -1.00000 q^{13} +3.71141 q^{15} +(0.939830 + 1.62783i) q^{16} +(0.820411 - 1.42099i) q^{17} +(-0.100468 + 0.174016i) q^{18} +(-1.33538 - 2.31295i) q^{19} -5.83901 q^{20} -12.5948 q^{22} +(-3.21234 - 5.56394i) q^{23} +(1.47120 - 2.54820i) q^{24} +(0.272571 - 0.472106i) q^{25} +(1.09161 + 1.89072i) q^{26} +5.11342 q^{27} -6.04973 q^{29} +(-4.05142 - 7.01726i) q^{30} +(2.56101 - 4.43580i) q^{31} +(3.72518 - 6.45220i) q^{32} +(-5.07207 - 8.78508i) q^{33} -3.58227 q^{34} +0.254614 q^{36} +(-2.87386 - 4.97767i) q^{37} +(-2.91544 + 5.04968i) q^{38} +(-0.879209 + 1.52284i) q^{39} +(1.76591 + 3.05864i) q^{40} +7.14100 q^{41} -4.47061 q^{43} +(7.97967 + 13.8212i) q^{44} +(0.0971286 - 0.168232i) q^{45} +(-7.01325 + 12.1473i) q^{46} +(5.89550 + 10.2113i) q^{47} +3.30523 q^{48} -1.19016 q^{50} +(-1.44263 - 2.49870i) q^{51} +(1.38322 - 2.39581i) q^{52} +(-1.72480 + 2.98744i) q^{53} +(-5.58186 - 9.66806i) q^{54} +12.1761 q^{55} -4.69633 q^{57} +(6.60395 + 11.4384i) q^{58} +(6.59027 - 11.4147i) q^{59} +(-5.13372 + 8.89186i) q^{60} +(3.12333 + 5.40976i) q^{61} -11.1825 q^{62} -12.5065 q^{64} +(-1.05533 - 1.82788i) q^{65} +(-11.0734 + 19.1798i) q^{66} +(-3.87108 + 6.70491i) q^{67} +(2.26962 + 3.93111i) q^{68} -11.2973 q^{69} +13.6372 q^{71} +(-0.0770035 - 0.133374i) q^{72} +(-7.75204 + 13.4269i) q^{73} +(-6.27427 + 10.8673i) q^{74} +(-0.479293 - 0.830160i) q^{75} +7.38854 q^{76} +3.83901 q^{78} +(-0.561071 - 0.971803i) q^{79} +(-1.98366 + 3.43579i) q^{80} +(4.63382 - 8.02601i) q^{81} +(-7.79519 - 13.5017i) q^{82} -4.96925 q^{83} +3.46321 q^{85} +(4.88016 + 8.45269i) q^{86} +(-5.31898 + 9.21275i) q^{87} +(4.82662 - 8.35995i) q^{88} +(0.573148 + 0.992721i) q^{89} -0.424106 q^{90} +17.7736 q^{92} +(-4.50333 - 7.79999i) q^{93} +(12.8712 - 22.2935i) q^{94} +(2.81853 - 4.88184i) q^{95} +(-6.55043 - 11.3457i) q^{96} +6.97223 q^{97} -0.530949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 8q^{3} - 4q^{4} + 6q^{5} - 8q^{6} - 6q^{9} + O(q^{10}) \) \( 12q + 8q^{3} - 4q^{4} + 6q^{5} - 8q^{6} - 6q^{9} + 4q^{10} - 4q^{11} - 4q^{12} - 12q^{13} + 24q^{15} + 16q^{17} + 4q^{18} + 2q^{19} - 32q^{20} - 24q^{22} + 6q^{23} + 12q^{24} + 4q^{25} - 40q^{27} - 12q^{29} + 6q^{31} + 20q^{32} + 4q^{33} - 48q^{36} + 8q^{38} - 8q^{39} + 4q^{40} + 16q^{41} + 4q^{43} + 4q^{44} + 14q^{45} - 8q^{46} + 30q^{47} + 16q^{48} + 16q^{50} + 4q^{51} + 4q^{52} + 14q^{53} - 48q^{54} + 16q^{55} + 8q^{57} + 8q^{58} + 24q^{59} - 12q^{60} - 56q^{62} - 40q^{64} - 6q^{65} - 4q^{66} - 16q^{67} + 28q^{68} + 40q^{69} + 16q^{71} - 28q^{72} - 6q^{73} + 12q^{74} + 12q^{75} + 32q^{76} + 8q^{78} + 22q^{79} - 28q^{80} - 46q^{81} - 40q^{82} - 100q^{83} - 16q^{85} + 16q^{86} - 16q^{87} + 44q^{88} + 26q^{89} + 80q^{90} + 40q^{92} - 16q^{93} - 32q^{94} + 6q^{95} - 20q^{96} + 28q^{97} + 24q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.09161 1.89072i −0.771885 1.33694i −0.936529 0.350591i \(-0.885981\pi\)
0.164644 0.986353i \(-0.447352\pi\)
\(3\) 0.879209 1.52284i 0.507612 0.879209i −0.492349 0.870398i \(-0.663862\pi\)
0.999961 0.00881173i \(-0.00280490\pi\)
\(4\) −1.38322 + 2.39581i −0.691612 + 1.19791i
\(5\) 1.05533 + 1.82788i 0.471957 + 0.817453i 0.999485 0.0320846i \(-0.0102146\pi\)
−0.527529 + 0.849537i \(0.676881\pi\)
\(6\) −3.83901 −1.56727
\(7\) 0 0
\(8\) 1.67333 0.591610
\(9\) −0.0460183 0.0797060i −0.0153394 0.0265687i
\(10\) 2.30401 3.99066i 0.728592 1.26196i
\(11\) 2.88445 4.99601i 0.869694 1.50635i 0.00738342 0.999973i \(-0.497650\pi\)
0.862310 0.506381i \(-0.169017\pi\)
\(12\) 2.43229 + 4.21285i 0.702141 + 1.21614i
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 3.71141 0.958283
\(16\) 0.939830 + 1.62783i 0.234957 + 0.406958i
\(17\) 0.820411 1.42099i 0.198979 0.344642i −0.749219 0.662323i \(-0.769571\pi\)
0.948198 + 0.317681i \(0.102904\pi\)
\(18\) −0.100468 + 0.174016i −0.0236805 + 0.0410159i
\(19\) −1.33538 2.31295i −0.306358 0.530628i 0.671205 0.741272i \(-0.265777\pi\)
−0.977563 + 0.210644i \(0.932444\pi\)
\(20\) −5.83901 −1.30564
\(21\) 0 0
\(22\) −12.5948 −2.68521
\(23\) −3.21234 5.56394i −0.669820 1.16016i −0.977954 0.208820i \(-0.933038\pi\)
0.308134 0.951343i \(-0.400295\pi\)
\(24\) 1.47120 2.54820i 0.300308 0.520149i
\(25\) 0.272571 0.472106i 0.0545141 0.0944212i
\(26\) 1.09161 + 1.89072i 0.214082 + 0.370801i
\(27\) 5.11342 0.984078
\(28\) 0 0
\(29\) −6.04973 −1.12341 −0.561704 0.827338i \(-0.689854\pi\)
−0.561704 + 0.827338i \(0.689854\pi\)
\(30\) −4.05142 7.01726i −0.739684 1.28117i
\(31\) 2.56101 4.43580i 0.459971 0.796693i −0.538988 0.842313i \(-0.681193\pi\)
0.998959 + 0.0456207i \(0.0145266\pi\)
\(32\) 3.72518 6.45220i 0.658525 1.14060i
\(33\) −5.07207 8.78508i −0.882933 1.52929i
\(34\) −3.58227 −0.614355
\(35\) 0 0
\(36\) 0.254614 0.0424357
\(37\) −2.87386 4.97767i −0.472460 0.818324i 0.527044 0.849838i \(-0.323300\pi\)
−0.999503 + 0.0315141i \(0.989967\pi\)
\(38\) −2.91544 + 5.04968i −0.472946 + 0.819167i
\(39\) −0.879209 + 1.52284i −0.140786 + 0.243849i
\(40\) 1.76591 + 3.05864i 0.279214 + 0.483613i
\(41\) 7.14100 1.11524 0.557619 0.830097i \(-0.311715\pi\)
0.557619 + 0.830097i \(0.311715\pi\)
\(42\) 0 0
\(43\) −4.47061 −0.681761 −0.340881 0.940107i \(-0.610725\pi\)
−0.340881 + 0.940107i \(0.610725\pi\)
\(44\) 7.97967 + 13.8212i 1.20298 + 2.08362i
\(45\) 0.0971286 0.168232i 0.0144791 0.0250785i
\(46\) −7.01325 + 12.1473i −1.03405 + 1.79102i
\(47\) 5.89550 + 10.2113i 0.859947 + 1.48947i 0.871979 + 0.489544i \(0.162837\pi\)
−0.0120319 + 0.999928i \(0.503830\pi\)
\(48\) 3.30523 0.477069
\(49\) 0 0
\(50\) −1.19016 −0.168314
\(51\) −1.44263 2.49870i −0.202008 0.349888i
\(52\) 1.38322 2.39581i 0.191819 0.332240i
\(53\) −1.72480 + 2.98744i −0.236919 + 0.410356i −0.959829 0.280587i \(-0.909471\pi\)
0.722910 + 0.690943i \(0.242804\pi\)
\(54\) −5.58186 9.66806i −0.759595 1.31566i
\(55\) 12.1761 1.64183
\(56\) 0 0
\(57\) −4.69633 −0.622044
\(58\) 6.60395 + 11.4384i 0.867141 + 1.50193i
\(59\) 6.59027 11.4147i 0.857981 1.48607i −0.0158712 0.999874i \(-0.505052\pi\)
0.873852 0.486192i \(-0.161614\pi\)
\(60\) −5.13372 + 8.89186i −0.662760 + 1.14793i
\(61\) 3.12333 + 5.40976i 0.399901 + 0.692649i 0.993713 0.111954i \(-0.0357111\pi\)
−0.593812 + 0.804604i \(0.702378\pi\)
\(62\) −11.1825 −1.42018
\(63\) 0 0
\(64\) −12.5065 −1.56331
\(65\) −1.05533 1.82788i −0.130897 0.226721i
\(66\) −11.0734 + 19.1798i −1.36305 + 2.36086i
\(67\) −3.87108 + 6.70491i −0.472928 + 0.819135i −0.999520 0.0309831i \(-0.990136\pi\)
0.526592 + 0.850118i \(0.323470\pi\)
\(68\) 2.26962 + 3.93111i 0.275232 + 0.476717i
\(69\) −11.2973 −1.36003
\(70\) 0 0
\(71\) 13.6372 1.61844 0.809221 0.587504i \(-0.199889\pi\)
0.809221 + 0.587504i \(0.199889\pi\)
\(72\) −0.0770035 0.133374i −0.00907495 0.0157183i
\(73\) −7.75204 + 13.4269i −0.907308 + 1.57150i −0.0895192 + 0.995985i \(0.528533\pi\)
−0.817789 + 0.575518i \(0.804800\pi\)
\(74\) −6.27427 + 10.8673i −0.729369 + 1.26330i
\(75\) −0.479293 0.830160i −0.0553440 0.0958586i
\(76\) 7.38854 0.847524
\(77\) 0 0
\(78\) 3.83901 0.434683
\(79\) −0.561071 0.971803i −0.0631254 0.109336i 0.832735 0.553671i \(-0.186773\pi\)
−0.895861 + 0.444335i \(0.853440\pi\)
\(80\) −1.98366 + 3.43579i −0.221779 + 0.384133i
\(81\) 4.63382 8.02601i 0.514869 0.891779i
\(82\) −7.79519 13.5017i −0.860835 1.49101i
\(83\) −4.96925 −0.545446 −0.272723 0.962093i \(-0.587924\pi\)
−0.272723 + 0.962093i \(0.587924\pi\)
\(84\) 0 0
\(85\) 3.46321 0.375638
\(86\) 4.88016 + 8.45269i 0.526241 + 0.911476i
\(87\) −5.31898 + 9.21275i −0.570255 + 0.987710i
\(88\) 4.82662 8.35995i 0.514519 0.891174i
\(89\) 0.573148 + 0.992721i 0.0607535 + 0.105228i 0.894802 0.446462i \(-0.147316\pi\)
−0.834049 + 0.551691i \(0.813983\pi\)
\(90\) −0.424106 −0.0447047
\(91\) 0 0
\(92\) 17.7736 1.85302
\(93\) −4.50333 7.79999i −0.466973 0.808821i
\(94\) 12.8712 22.2935i 1.32756 2.29940i
\(95\) 2.81853 4.88184i 0.289175 0.500866i
\(96\) −6.55043 11.3457i −0.668550 1.15796i
\(97\) 6.97223 0.707923 0.353961 0.935260i \(-0.384834\pi\)
0.353961 + 0.935260i \(0.384834\pi\)
\(98\) 0 0
\(99\) −0.530949 −0.0533624
\(100\) 0.754052 + 1.30606i 0.0754052 + 0.130606i
\(101\) −3.24960 + 5.62847i −0.323347 + 0.560053i −0.981176 0.193113i \(-0.938141\pi\)
0.657829 + 0.753167i \(0.271475\pi\)
\(102\) −3.14957 + 5.45521i −0.311854 + 0.540147i
\(103\) −0.289024 0.500604i −0.0284784 0.0493260i 0.851435 0.524460i \(-0.175733\pi\)
−0.879913 + 0.475134i \(0.842400\pi\)
\(104\) −1.67333 −0.164083
\(105\) 0 0
\(106\) 7.53122 0.731497
\(107\) 8.12863 + 14.0792i 0.785824 + 1.36109i 0.928505 + 0.371319i \(0.121094\pi\)
−0.142681 + 0.989769i \(0.545572\pi\)
\(108\) −7.07300 + 12.2508i −0.680600 + 1.17883i
\(109\) −0.890953 + 1.54318i −0.0853378 + 0.147809i −0.905535 0.424271i \(-0.860530\pi\)
0.820197 + 0.572081i \(0.193864\pi\)
\(110\) −13.2916 23.0217i −1.26730 2.19503i
\(111\) −10.1069 −0.959304
\(112\) 0 0
\(113\) −7.52215 −0.707624 −0.353812 0.935316i \(-0.615115\pi\)
−0.353812 + 0.935316i \(0.615115\pi\)
\(114\) 5.12656 + 8.87946i 0.480146 + 0.831638i
\(115\) 6.78015 11.7436i 0.632252 1.09509i
\(116\) 8.36814 14.4940i 0.776962 1.34574i
\(117\) 0.0460183 + 0.0797060i 0.00425439 + 0.00736882i
\(118\) −28.7760 −2.64905
\(119\) 0 0
\(120\) 6.21040 0.566930
\(121\) −11.1401 19.2952i −1.01273 1.75411i
\(122\) 6.81891 11.8107i 0.617355 1.06929i
\(123\) 6.27844 10.8746i 0.566108 0.980527i
\(124\) 7.08490 + 12.2714i 0.636243 + 1.10200i
\(125\) 11.7039 1.04683
\(126\) 0 0
\(127\) −19.3056 −1.71310 −0.856549 0.516067i \(-0.827396\pi\)
−0.856549 + 0.516067i \(0.827396\pi\)
\(128\) 6.20181 + 10.7418i 0.548168 + 0.949454i
\(129\) −3.93060 + 6.80800i −0.346070 + 0.599411i
\(130\) −2.30401 + 3.99066i −0.202075 + 0.350004i
\(131\) 4.84852 + 8.39788i 0.423617 + 0.733726i 0.996290 0.0860579i \(-0.0274270\pi\)
−0.572673 + 0.819784i \(0.694094\pi\)
\(132\) 28.0632 2.44259
\(133\) 0 0
\(134\) 16.9028 1.46018
\(135\) 5.39633 + 9.34671i 0.464442 + 0.804437i
\(136\) 1.37281 2.37778i 0.117718 0.203893i
\(137\) 7.72467 13.3795i 0.659963 1.14309i −0.320662 0.947194i \(-0.603905\pi\)
0.980625 0.195895i \(-0.0627613\pi\)
\(138\) 12.3322 + 21.3601i 1.04979 + 1.81829i
\(139\) −3.84912 −0.326478 −0.163239 0.986587i \(-0.552194\pi\)
−0.163239 + 0.986587i \(0.552194\pi\)
\(140\) 0 0
\(141\) 20.7335 1.74608
\(142\) −14.8865 25.7842i −1.24925 2.16377i
\(143\) −2.88445 + 4.99601i −0.241210 + 0.417787i
\(144\) 0.0864987 0.149820i 0.00720822 0.0124850i
\(145\) −6.38445 11.0582i −0.530199 0.918332i
\(146\) 33.8488 2.80135
\(147\) 0 0
\(148\) 15.9008 1.30704
\(149\) 0.520140 + 0.900909i 0.0426115 + 0.0738054i 0.886545 0.462643i \(-0.153099\pi\)
−0.843933 + 0.536449i \(0.819766\pi\)
\(150\) −1.04640 + 1.81242i −0.0854384 + 0.147984i
\(151\) 2.17168 3.76146i 0.176729 0.306104i −0.764029 0.645182i \(-0.776782\pi\)
0.940758 + 0.339078i \(0.110115\pi\)
\(152\) −2.23453 3.87032i −0.181244 0.313925i
\(153\) −0.151016 −0.0122089
\(154\) 0 0
\(155\) 10.8108 0.868345
\(156\) −2.43229 4.21285i −0.194739 0.337298i
\(157\) 0.168000 0.290985i 0.0134079 0.0232231i −0.859244 0.511567i \(-0.829065\pi\)
0.872651 + 0.488343i \(0.162399\pi\)
\(158\) −1.22494 + 2.12166i −0.0974511 + 0.168790i
\(159\) 3.03291 + 5.25316i 0.240526 + 0.416603i
\(160\) 15.7251 1.24318
\(161\) 0 0
\(162\) −20.2333 −1.58968
\(163\) −3.39959 5.88827i −0.266277 0.461205i 0.701621 0.712551i \(-0.252460\pi\)
−0.967897 + 0.251346i \(0.919127\pi\)
\(164\) −9.87761 + 17.1085i −0.771312 + 1.33595i
\(165\) 10.7054 18.5423i 0.833412 1.44351i
\(166\) 5.42448 + 9.39548i 0.421022 + 0.729231i
\(167\) −0.668649 −0.0517416 −0.0258708 0.999665i \(-0.508236\pi\)
−0.0258708 + 0.999665i \(0.508236\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −3.78047 6.54797i −0.289949 0.502206i
\(171\) −0.122904 + 0.212876i −0.00939871 + 0.0162790i
\(172\) 6.18385 10.7107i 0.471514 0.816687i
\(173\) 12.5589 + 21.7527i 0.954837 + 1.65383i 0.734741 + 0.678347i \(0.237303\pi\)
0.220095 + 0.975478i \(0.429363\pi\)
\(174\) 23.2250 1.76068
\(175\) 0 0
\(176\) 10.8436 0.817364
\(177\) −11.5885 20.0718i −0.871042 1.50869i
\(178\) 1.25131 2.16733i 0.0937895 0.162448i
\(179\) 0.947633 1.64135i 0.0708294 0.122680i −0.828436 0.560084i \(-0.810769\pi\)
0.899265 + 0.437404i \(0.144102\pi\)
\(180\) 0.268701 + 0.465404i 0.0200278 + 0.0346892i
\(181\) −11.3595 −0.844347 −0.422174 0.906515i \(-0.638733\pi\)
−0.422174 + 0.906515i \(0.638733\pi\)
\(182\) 0 0
\(183\) 10.9842 0.811978
\(184\) −5.37530 9.31029i −0.396272 0.686364i
\(185\) 6.06572 10.5061i 0.445961 0.772427i
\(186\) −9.83175 + 17.0291i −0.720899 + 1.24863i
\(187\) −4.73286 8.19756i −0.346101 0.599465i
\(188\) −32.6192 −2.37900
\(189\) 0 0
\(190\) −12.3070 −0.892840
\(191\) 11.7203 + 20.3002i 0.848055 + 1.46887i 0.882942 + 0.469482i \(0.155559\pi\)
−0.0348873 + 0.999391i \(0.511107\pi\)
\(192\) −10.9958 + 19.0453i −0.793553 + 1.37447i
\(193\) 0.926048 1.60396i 0.0666584 0.115456i −0.830770 0.556616i \(-0.812100\pi\)
0.897428 + 0.441160i \(0.145433\pi\)
\(194\) −7.61095 13.1826i −0.546435 0.946453i
\(195\) −3.71141 −0.265780
\(196\) 0 0
\(197\) −9.87082 −0.703267 −0.351634 0.936138i \(-0.614374\pi\)
−0.351634 + 0.936138i \(0.614374\pi\)
\(198\) 0.579589 + 1.00388i 0.0411896 + 0.0713425i
\(199\) 6.12461 10.6081i 0.434162 0.751991i −0.563065 0.826413i \(-0.690378\pi\)
0.997227 + 0.0744219i \(0.0237111\pi\)
\(200\) 0.456099 0.789987i 0.0322511 0.0558605i
\(201\) 6.80698 + 11.7900i 0.480127 + 0.831605i
\(202\) 14.1892 0.998347
\(203\) 0 0
\(204\) 7.98190 0.558845
\(205\) 7.53609 + 13.0529i 0.526343 + 0.911654i
\(206\) −0.631003 + 1.09293i −0.0439640 + 0.0761480i
\(207\) −0.295653 + 0.512086i −0.0205493 + 0.0355924i
\(208\) −0.939830 1.62783i −0.0651655 0.112870i
\(209\) −15.4074 −1.06575
\(210\) 0 0
\(211\) −0.739899 −0.0509368 −0.0254684 0.999676i \(-0.508108\pi\)
−0.0254684 + 0.999676i \(0.508108\pi\)
\(212\) −4.77156 8.26459i −0.327712 0.567614i
\(213\) 11.9900 20.7673i 0.821540 1.42295i
\(214\) 17.7466 30.7380i 1.21313 2.10121i
\(215\) −4.71795 8.17173i −0.321762 0.557308i
\(216\) 8.55641 0.582190
\(217\) 0 0
\(218\) 3.89029 0.263484
\(219\) 13.6313 + 23.6102i 0.921120 + 1.59543i
\(220\) −16.8423 + 29.1718i −1.13551 + 1.96676i
\(221\) −0.820411 + 1.42099i −0.0551868 + 0.0955864i
\(222\) 11.0328 + 19.1094i 0.740472 + 1.28254i
\(223\) −8.30577 −0.556196 −0.278098 0.960553i \(-0.589704\pi\)
−0.278098 + 0.960553i \(0.589704\pi\)
\(224\) 0 0
\(225\) −0.0501729 −0.00334486
\(226\) 8.21125 + 14.2223i 0.546205 + 0.946054i
\(227\) 6.64583 11.5109i 0.441099 0.764006i −0.556672 0.830732i \(-0.687922\pi\)
0.997771 + 0.0667264i \(0.0212555\pi\)
\(228\) 6.49607 11.2515i 0.430213 0.745151i
\(229\) 8.96033 + 15.5197i 0.592115 + 1.02557i 0.993947 + 0.109860i \(0.0350404\pi\)
−0.401832 + 0.915714i \(0.631626\pi\)
\(230\) −29.6051 −1.95210
\(231\) 0 0
\(232\) −10.1232 −0.664619
\(233\) −3.14984 5.45568i −0.206353 0.357413i 0.744210 0.667946i \(-0.232826\pi\)
−0.950563 + 0.310532i \(0.899493\pi\)
\(234\) 0.100468 0.174016i 0.00656780 0.0113758i
\(235\) −12.4434 + 21.5525i −0.811715 + 1.40593i
\(236\) 18.2317 + 31.5782i 1.18678 + 2.05556i
\(237\) −1.97320 −0.128173
\(238\) 0 0
\(239\) 9.41783 0.609189 0.304594 0.952482i \(-0.401479\pi\)
0.304594 + 0.952482i \(0.401479\pi\)
\(240\) 3.48810 + 6.04156i 0.225156 + 0.389981i
\(241\) −9.97465 + 17.2766i −0.642524 + 1.11288i 0.342344 + 0.939575i \(0.388779\pi\)
−0.984867 + 0.173309i \(0.944554\pi\)
\(242\) −24.3212 + 42.1256i −1.56343 + 2.70794i
\(243\) −0.478069 0.828039i −0.0306681 0.0531187i
\(244\) −17.2811 −1.10631
\(245\) 0 0
\(246\) −27.4144 −1.74788
\(247\) 1.33538 + 2.31295i 0.0849684 + 0.147170i
\(248\) 4.28540 7.42253i 0.272123 0.471331i
\(249\) −4.36901 + 7.56735i −0.276875 + 0.479561i
\(250\) −12.7761 22.1288i −0.808029 1.39955i
\(251\) −1.22202 −0.0771330 −0.0385665 0.999256i \(-0.512279\pi\)
−0.0385665 + 0.999256i \(0.512279\pi\)
\(252\) 0 0
\(253\) −37.0633 −2.33015
\(254\) 21.0742 + 36.5016i 1.32231 + 2.29031i
\(255\) 3.04488 5.27389i 0.190678 0.330264i
\(256\) 1.03346 1.79000i 0.0645911 0.111875i
\(257\) −11.2120 19.4198i −0.699386 1.21137i −0.968680 0.248313i \(-0.920124\pi\)
0.269294 0.963058i \(-0.413210\pi\)
\(258\) 17.1627 1.06850
\(259\) 0 0
\(260\) 5.83901 0.362120
\(261\) 0.278398 + 0.482200i 0.0172324 + 0.0298474i
\(262\) 10.5854 18.3344i 0.653967 1.13270i
\(263\) −4.49524 + 7.78598i −0.277188 + 0.480104i −0.970685 0.240356i \(-0.922736\pi\)
0.693497 + 0.720460i \(0.256069\pi\)
\(264\) −8.48722 14.7003i −0.522352 0.904740i
\(265\) −7.28090 −0.447262
\(266\) 0 0
\(267\) 2.01567 0.123357
\(268\) −10.7091 18.5488i −0.654165 1.13305i
\(269\) −11.1027 + 19.2305i −0.676945 + 1.17250i 0.298951 + 0.954268i \(0.403363\pi\)
−0.975896 + 0.218235i \(0.929970\pi\)
\(270\) 11.7814 20.4059i 0.716991 1.24187i
\(271\) −5.42116 9.38972i −0.329312 0.570385i 0.653064 0.757303i \(-0.273483\pi\)
−0.982375 + 0.186918i \(0.940150\pi\)
\(272\) 3.08419 0.187006
\(273\) 0 0
\(274\) −33.7293 −2.03766
\(275\) −1.57243 2.72353i −0.0948211 0.164235i
\(276\) 15.6267 27.0662i 0.940616 1.62920i
\(277\) −2.94414 + 5.09940i −0.176896 + 0.306393i −0.940816 0.338918i \(-0.889939\pi\)
0.763920 + 0.645311i \(0.223272\pi\)
\(278\) 4.20173 + 7.27762i 0.252003 + 0.436482i
\(279\) −0.471413 −0.0282227
\(280\) 0 0
\(281\) 26.9071 1.60514 0.802572 0.596556i \(-0.203465\pi\)
0.802572 + 0.596556i \(0.203465\pi\)
\(282\) −22.6329 39.2013i −1.34777 2.33441i
\(283\) −1.74859 + 3.02864i −0.103943 + 0.180034i −0.913306 0.407275i \(-0.866479\pi\)
0.809363 + 0.587309i \(0.199813\pi\)
\(284\) −18.8634 + 32.6723i −1.11933 + 1.93874i
\(285\) −4.95616 8.58432i −0.293578 0.508491i
\(286\) 12.5948 0.744744
\(287\) 0 0
\(288\) −0.685705 −0.0404056
\(289\) 7.15385 + 12.3908i 0.420815 + 0.728873i
\(290\) −13.9387 + 24.1425i −0.818506 + 1.41769i
\(291\) 6.13005 10.6176i 0.359350 0.622412i
\(292\) −21.4456 37.1449i −1.25501 2.17374i
\(293\) −1.00509 −0.0587179 −0.0293589 0.999569i \(-0.509347\pi\)
−0.0293589 + 0.999569i \(0.509347\pi\)
\(294\) 0 0
\(295\) 27.8196 1.61972
\(296\) −4.80890 8.32926i −0.279512 0.484129i
\(297\) 14.7494 25.5467i 0.855846 1.48237i
\(298\) 1.13558 1.96688i 0.0657824 0.113938i
\(299\) 3.21234 + 5.56394i 0.185775 + 0.321771i
\(300\) 2.65188 0.153106
\(301\) 0 0
\(302\) −9.48252 −0.545657
\(303\) 5.71415 + 9.89720i 0.328270 + 0.568579i
\(304\) 2.51007 4.34756i 0.143962 0.249350i
\(305\) −6.59227 + 11.4181i −0.377472 + 0.653801i
\(306\) 0.164850 + 0.285529i 0.00942385 + 0.0163226i
\(307\) −4.25772 −0.243001 −0.121501 0.992591i \(-0.538771\pi\)
−0.121501 + 0.992591i \(0.538771\pi\)
\(308\) 0 0
\(309\) −1.01645 −0.0578238
\(310\) −11.8012 20.4402i −0.670262 1.16093i
\(311\) −3.47022 + 6.01059i −0.196778 + 0.340829i −0.947482 0.319809i \(-0.896381\pi\)
0.750704 + 0.660639i \(0.229714\pi\)
\(312\) −1.47120 + 2.54820i −0.0832905 + 0.144263i
\(313\) −4.98150 8.62820i −0.281571 0.487695i 0.690201 0.723618i \(-0.257522\pi\)
−0.971772 + 0.235923i \(0.924189\pi\)
\(314\) −0.733563 −0.0413973
\(315\) 0 0
\(316\) 3.10435 0.174633
\(317\) −1.87673 3.25058i −0.105407 0.182571i 0.808497 0.588500i \(-0.200281\pi\)
−0.913905 + 0.405929i \(0.866948\pi\)
\(318\) 6.62152 11.4688i 0.371316 0.643139i
\(319\) −17.4501 + 30.2245i −0.977020 + 1.69225i
\(320\) −13.1984 22.8603i −0.737813 1.27793i
\(321\) 28.5871 1.59557
\(322\) 0 0
\(323\) −4.38225 −0.243835
\(324\) 12.8192 + 22.2035i 0.712179 + 1.23353i
\(325\) −0.272571 + 0.472106i −0.0151195 + 0.0261877i
\(326\) −7.42206 + 12.8554i −0.411070 + 0.711994i
\(327\) 1.56667 + 2.71355i 0.0866370 + 0.150060i
\(328\) 11.9492 0.659785
\(329\) 0 0
\(330\) −46.7444 −2.57319
\(331\) 9.99061 + 17.3043i 0.549134 + 0.951128i 0.998334 + 0.0576966i \(0.0183756\pi\)
−0.449200 + 0.893431i \(0.648291\pi\)
\(332\) 6.87359 11.9054i 0.377237 0.653394i
\(333\) −0.264500 + 0.458128i −0.0144945 + 0.0251052i
\(334\) 0.729904 + 1.26423i 0.0399385 + 0.0691756i
\(335\) −16.3410 −0.892805
\(336\) 0 0
\(337\) 18.4887 1.00714 0.503571 0.863954i \(-0.332019\pi\)
0.503571 + 0.863954i \(0.332019\pi\)
\(338\) −1.09161 1.89072i −0.0593757 0.102842i
\(339\) −6.61355 + 11.4550i −0.359198 + 0.622150i
\(340\) −4.79039 + 8.29720i −0.259795 + 0.449979i
\(341\) −14.7742 25.5896i −0.800067 1.38576i
\(342\) 0.536653 0.0290189
\(343\) 0 0
\(344\) −7.48078 −0.403337
\(345\) −11.9223 20.6501i −0.641877 1.11176i
\(346\) 27.4189 47.4909i 1.47405 2.55313i
\(347\) 0.398050 0.689443i 0.0213684 0.0370112i −0.855143 0.518391i \(-0.826531\pi\)
0.876512 + 0.481380i \(0.159864\pi\)
\(348\) −14.7147 25.4866i −0.788790 1.36622i
\(349\) 11.3725 0.608754 0.304377 0.952552i \(-0.401552\pi\)
0.304377 + 0.952552i \(0.401552\pi\)
\(350\) 0 0
\(351\) −5.11342 −0.272934
\(352\) −21.4902 37.2221i −1.14543 1.98394i
\(353\) 12.0534 20.8771i 0.641537 1.11117i −0.343553 0.939133i \(-0.611631\pi\)
0.985090 0.172041i \(-0.0550361\pi\)
\(354\) −25.3002 + 43.8212i −1.34469 + 2.32907i
\(355\) 14.3917 + 24.9272i 0.763834 + 1.32300i
\(356\) −3.17117 −0.168072
\(357\) 0 0
\(358\) −4.13778 −0.218689
\(359\) −4.53591 7.85642i −0.239396 0.414646i 0.721145 0.692784i \(-0.243616\pi\)
−0.960541 + 0.278138i \(0.910283\pi\)
\(360\) 0.162528 0.281506i 0.00856597 0.0148367i
\(361\) 5.93350 10.2771i 0.312289 0.540901i
\(362\) 12.4002 + 21.4777i 0.651739 + 1.12884i
\(363\) −39.1778 −2.05630
\(364\) 0 0
\(365\) −32.7238 −1.71284
\(366\) −11.9905 20.7682i −0.626754 1.08557i
\(367\) −15.7754 + 27.3237i −0.823467 + 1.42629i 0.0796176 + 0.996825i \(0.474630\pi\)
−0.903085 + 0.429462i \(0.858703\pi\)
\(368\) 6.03811 10.4583i 0.314758 0.545178i
\(369\) −0.328617 0.569181i −0.0171071 0.0296304i
\(370\) −26.4856 −1.37692
\(371\) 0 0
\(372\) 24.9164 1.29186
\(373\) 8.02905 + 13.9067i 0.415728 + 0.720063i 0.995505 0.0947130i \(-0.0301933\pi\)
−0.579776 + 0.814776i \(0.696860\pi\)
\(374\) −10.3329 + 17.8971i −0.534301 + 0.925436i
\(375\) 10.2902 17.8231i 0.531381 0.920379i
\(376\) 9.86509 + 17.0868i 0.508753 + 0.881186i
\(377\) 6.04973 0.311577
\(378\) 0 0
\(379\) −5.36895 −0.275785 −0.137892 0.990447i \(-0.544033\pi\)
−0.137892 + 0.990447i \(0.544033\pi\)
\(380\) 7.79733 + 13.5054i 0.399994 + 0.692811i
\(381\) −16.9737 + 29.3993i −0.869588 + 1.50617i
\(382\) 25.5881 44.3199i 1.30920 2.26760i
\(383\) 17.2537 + 29.8843i 0.881625 + 1.52702i 0.849534 + 0.527534i \(0.176883\pi\)
0.0320905 + 0.999485i \(0.489784\pi\)
\(384\) 21.8108 1.11303
\(385\) 0 0
\(386\) −4.04353 −0.205810
\(387\) 0.205730 + 0.356334i 0.0104578 + 0.0181135i
\(388\) −9.64416 + 16.7042i −0.489608 + 0.848026i
\(389\) −11.4605 + 19.8501i −0.581070 + 1.00644i 0.414283 + 0.910148i \(0.364032\pi\)
−0.995353 + 0.0962942i \(0.969301\pi\)
\(390\) 4.05142 + 7.01726i 0.205151 + 0.355333i
\(391\) −10.5418 −0.533120
\(392\) 0 0
\(393\) 17.0514 0.860131
\(394\) 10.7751 + 18.6630i 0.542841 + 0.940228i
\(395\) 1.18423 2.05114i 0.0595849 0.103204i
\(396\) 0.734421 1.27206i 0.0369061 0.0639232i
\(397\) 5.41468 + 9.37850i 0.271755 + 0.470694i 0.969311 0.245836i \(-0.0790626\pi\)
−0.697556 + 0.716530i \(0.745729\pi\)
\(398\) −26.7427 −1.34049
\(399\) 0 0
\(400\) 1.02468 0.0512340
\(401\) −18.7708 32.5119i −0.937367 1.62357i −0.770357 0.637613i \(-0.779922\pi\)
−0.167010 0.985955i \(-0.553411\pi\)
\(402\) 14.8611 25.7402i 0.741206 1.28381i
\(403\) −2.56101 + 4.43580i −0.127573 + 0.220963i
\(404\) −8.98984 15.5709i −0.447261 0.774680i
\(405\) 19.5608 0.971983
\(406\) 0 0
\(407\) −33.1580 −1.64358
\(408\) −2.41398 4.18114i −0.119510 0.206997i
\(409\) −10.2363 + 17.7299i −0.506155 + 0.876686i 0.493820 + 0.869564i \(0.335600\pi\)
−0.999975 + 0.00712174i \(0.997733\pi\)
\(410\) 16.4529 28.4973i 0.812553 1.40738i
\(411\) −13.5832 23.5268i −0.670010 1.16049i
\(412\) 1.59914 0.0787840
\(413\) 0 0
\(414\) 1.29095 0.0634468
\(415\) −5.24418 9.08319i −0.257427 0.445876i
\(416\) −3.72518 + 6.45220i −0.182642 + 0.316345i
\(417\) −3.38418 + 5.86157i −0.165724 + 0.287042i
\(418\) 16.8188 + 29.1311i 0.822637 + 1.42485i
\(419\) 15.4980 0.757127 0.378564 0.925575i \(-0.376418\pi\)
0.378564 + 0.925575i \(0.376418\pi\)
\(420\) 0 0
\(421\) 17.9390 0.874293 0.437147 0.899390i \(-0.355989\pi\)
0.437147 + 0.899390i \(0.355989\pi\)
\(422\) 0.807681 + 1.39894i 0.0393173 + 0.0680996i
\(423\) 0.542601 0.939813i 0.0263822 0.0456953i
\(424\) −2.88615 + 4.99895i −0.140164 + 0.242771i
\(425\) −0.447240 0.774642i −0.0216943 0.0375757i
\(426\) −52.3535 −2.53654
\(427\) 0 0
\(428\) −44.9749 −2.17394
\(429\) 5.07207 + 8.78508i 0.244882 + 0.424147i
\(430\) −10.3003 + 17.8407i −0.496726 + 0.860354i
\(431\) −10.7219 + 18.5709i −0.516456 + 0.894529i 0.483361 + 0.875421i \(0.339416\pi\)
−0.999817 + 0.0191077i \(0.993917\pi\)
\(432\) 4.80574 + 8.32379i 0.231216 + 0.400479i
\(433\) 14.9365 0.717800 0.358900 0.933376i \(-0.383152\pi\)
0.358900 + 0.933376i \(0.383152\pi\)
\(434\) 0 0
\(435\) −22.4531 −1.07654
\(436\) −2.46478 4.26912i −0.118041 0.204454i
\(437\) −8.57943 + 14.8600i −0.410410 + 0.710850i
\(438\) 29.7602 51.5462i 1.42200 2.46297i
\(439\) −1.79661 3.11182i −0.0857476 0.148519i 0.819962 0.572418i \(-0.193995\pi\)
−0.905710 + 0.423899i \(0.860661\pi\)
\(440\) 20.3746 0.971323
\(441\) 0 0
\(442\) 3.58227 0.170391
\(443\) 6.82672 + 11.8242i 0.324347 + 0.561786i 0.981380 0.192076i \(-0.0615221\pi\)
−0.657033 + 0.753862i \(0.728189\pi\)
\(444\) 13.9801 24.2143i 0.663466 1.14916i
\(445\) −1.20972 + 2.09529i −0.0573461 + 0.0993263i
\(446\) 9.06666 + 15.7039i 0.429319 + 0.743602i
\(447\) 1.82925 0.0865205
\(448\) 0 0
\(449\) −8.72412 −0.411717 −0.205858 0.978582i \(-0.565999\pi\)
−0.205858 + 0.978582i \(0.565999\pi\)
\(450\) 0.0547692 + 0.0948631i 0.00258185 + 0.00447189i
\(451\) 20.5978 35.6765i 0.969915 1.67994i
\(452\) 10.4048 18.0217i 0.489402 0.847668i
\(453\) −3.81873 6.61423i −0.179419 0.310763i
\(454\) −29.0186 −1.36191
\(455\) 0 0
\(456\) −7.85848 −0.368007
\(457\) 15.2330 + 26.3843i 0.712568 + 1.23420i 0.963890 + 0.266300i \(0.0858013\pi\)
−0.251322 + 0.967904i \(0.580865\pi\)
\(458\) 19.5624 33.8830i 0.914090 1.58325i
\(459\) 4.19510 7.26613i 0.195811 0.339154i
\(460\) 18.7569 + 32.4879i 0.874546 + 1.51476i
\(461\) −5.22253 −0.243237 −0.121619 0.992577i \(-0.538809\pi\)
−0.121619 + 0.992577i \(0.538809\pi\)
\(462\) 0 0
\(463\) 20.6220 0.958386 0.479193 0.877709i \(-0.340929\pi\)
0.479193 + 0.877709i \(0.340929\pi\)
\(464\) −5.68572 9.84796i −0.263953 0.457180i
\(465\) 9.50496 16.4631i 0.440782 0.763457i
\(466\) −6.87679 + 11.9109i −0.318561 + 0.551764i
\(467\) 0.835745 + 1.44755i 0.0386737 + 0.0669848i 0.884714 0.466134i \(-0.154353\pi\)
−0.846041 + 0.533118i \(0.821020\pi\)
\(468\) −0.254614 −0.0117696
\(469\) 0 0
\(470\) 54.3332 2.50620
\(471\) −0.295415 0.511673i −0.0136120 0.0235767i
\(472\) 11.0277 19.1005i 0.507590 0.879171i
\(473\) −12.8952 + 22.3352i −0.592923 + 1.02697i
\(474\) 2.15396 + 3.73077i 0.0989346 + 0.171360i
\(475\) −1.45595 −0.0668034
\(476\) 0 0
\(477\) 0.317489 0.0145368
\(478\) −10.2806 17.8065i −0.470224 0.814451i
\(479\) 5.32196 9.21790i 0.243166 0.421177i −0.718448 0.695581i \(-0.755147\pi\)
0.961614 + 0.274404i \(0.0884806\pi\)
\(480\) 13.8257 23.9468i 0.631053 1.09302i
\(481\) 2.87386 + 4.97767i 0.131037 + 0.226962i
\(482\) 43.5537 1.98382
\(483\) 0 0
\(484\) 61.6369 2.80168
\(485\) 7.35798 + 12.7444i 0.334109 + 0.578693i
\(486\) −1.04373 + 1.80779i −0.0473445 + 0.0820031i
\(487\) 15.9156 27.5667i 0.721206 1.24916i −0.239311 0.970943i \(-0.576922\pi\)
0.960517 0.278222i \(-0.0897450\pi\)
\(488\) 5.22635 + 9.05230i 0.236586 + 0.409778i
\(489\) −11.9558 −0.540661
\(490\) 0 0
\(491\) 6.87077 0.310074 0.155037 0.987909i \(-0.450450\pi\)
0.155037 + 0.987909i \(0.450450\pi\)
\(492\) 17.3690 + 30.0839i 0.783054 + 1.35629i
\(493\) −4.96327 + 8.59663i −0.223534 + 0.387173i
\(494\) 2.91544 5.04968i 0.131172 0.227196i
\(495\) −0.560325 0.970511i −0.0251847 0.0436212i
\(496\) 9.62765 0.432294
\(497\) 0 0
\(498\) 19.0770 0.854862
\(499\) −0.172167 0.298203i −0.00770727 0.0133494i 0.862146 0.506660i \(-0.169120\pi\)
−0.869853 + 0.493310i \(0.835787\pi\)
\(500\) −16.1891 + 28.0403i −0.723998 + 1.25400i
\(501\) −0.587882 + 1.01824i −0.0262646 + 0.0454917i
\(502\) 1.33397 + 2.31050i 0.0595378 + 0.103122i
\(503\) −30.0808 −1.34123 −0.670617 0.741803i \(-0.733971\pi\)
−0.670617 + 0.741803i \(0.733971\pi\)
\(504\) 0 0
\(505\) −13.7175 −0.610423
\(506\) 40.4587 + 70.0766i 1.79861 + 3.11528i
\(507\) 0.879209 1.52284i 0.0390471 0.0676315i
\(508\) 26.7040 46.2527i 1.18480 2.05213i
\(509\) 16.6553 + 28.8478i 0.738232 + 1.27865i 0.953291 + 0.302054i \(0.0976722\pi\)
−0.215059 + 0.976601i \(0.568994\pi\)
\(510\) −13.2953 −0.588726
\(511\) 0 0
\(512\) 20.2947 0.896908
\(513\) −6.82838 11.8271i −0.301480 0.522179i
\(514\) −24.4783 + 42.3976i −1.07969 + 1.87008i
\(515\) 0.610029 1.05660i 0.0268811 0.0465594i
\(516\) −10.8738 18.8340i −0.478693 0.829120i
\(517\) 68.0210 2.99156
\(518\) 0 0
\(519\) 44.1677 1.93875
\(520\) −1.76591 3.05864i −0.0774401 0.134130i
\(521\) 16.3863 28.3819i 0.717897 1.24343i −0.243934 0.969792i \(-0.578438\pi\)
0.961831 0.273643i \(-0.0882286\pi\)
\(522\) 0.607805 1.05275i 0.0266029 0.0460775i
\(523\) 12.6308 + 21.8772i 0.552307 + 0.956623i 0.998108 + 0.0614909i \(0.0195855\pi\)
−0.445801 + 0.895132i \(0.647081\pi\)
\(524\) −26.8263 −1.17191
\(525\) 0 0
\(526\) 19.6282 0.855830
\(527\) −4.20216 7.27835i −0.183049 0.317050i
\(528\) 9.53376 16.5130i 0.414904 0.718634i
\(529\) −9.13831 + 15.8280i −0.397318 + 0.688175i
\(530\) 7.94790 + 13.7662i 0.345235 + 0.597964i
\(531\) −1.21309 −0.0526437
\(532\) 0 0
\(533\) −7.14100 −0.309311
\(534\) −2.20032 3.81107i −0.0952173 0.164921i
\(535\) −17.1567 + 29.7163i −0.741750 + 1.28475i
\(536\) −6.47758 + 11.2195i −0.279789 + 0.484608i
\(537\) −1.66634 2.88618i −0.0719077 0.124548i
\(538\) 48.4794 2.09009
\(539\) 0 0
\(540\) −29.8573 −1.28485
\(541\) −6.58148 11.3995i −0.282960 0.490101i 0.689152 0.724616i \(-0.257983\pi\)
−0.972112 + 0.234515i \(0.924650\pi\)
\(542\) −11.8356 + 20.4998i −0.508382 + 0.880543i
\(543\) −9.98740 + 17.2987i −0.428601 + 0.742358i
\(544\) −6.11236 10.5869i −0.262065 0.453910i
\(545\) −3.76099 −0.161103
\(546\) 0 0
\(547\) −2.79349 −0.119441 −0.0597204 0.998215i \(-0.519021\pi\)
−0.0597204 + 0.998215i \(0.519021\pi\)
\(548\) 21.3699 + 37.0137i 0.912877 + 1.58115i
\(549\) 0.287460 0.497896i 0.0122685 0.0212497i
\(550\) −3.43296 + 5.94606i −0.146382 + 0.253541i
\(551\) 8.07872 + 13.9927i 0.344165 + 0.596111i
\(552\) −18.9040 −0.804610
\(553\) 0 0
\(554\) 12.8554 0.546174
\(555\) −10.6661 18.4742i −0.452750 0.784186i
\(556\) 5.32419 9.22177i 0.225796 0.391090i
\(557\) 2.30642 3.99484i 0.0977262 0.169267i −0.813017 0.582240i \(-0.802176\pi\)
0.910743 + 0.412973i \(0.135510\pi\)
\(558\) 0.514599 + 0.891311i 0.0217847 + 0.0377322i
\(559\) 4.47061 0.189087
\(560\) 0 0
\(561\) −16.6447 −0.702740
\(562\) −29.3721 50.8739i −1.23899 2.14599i
\(563\) 20.1403 34.8840i 0.848811 1.47018i −0.0334593 0.999440i \(-0.510652\pi\)
0.882270 0.470743i \(-0.156014\pi\)
\(564\) −28.6791 + 49.6736i −1.20761 + 2.09164i
\(565\) −7.93833 13.7496i −0.333968 0.578449i
\(566\) 7.63510 0.320927
\(567\) 0 0
\(568\) 22.8195 0.957486
\(569\) −3.59934 6.23425i −0.150892 0.261353i 0.780663 0.624952i \(-0.214881\pi\)
−0.931556 + 0.363598i \(0.881548\pi\)
\(570\) −10.8204 + 18.7415i −0.453216 + 0.784993i
\(571\) −5.69101 + 9.85712i −0.238161 + 0.412508i −0.960187 0.279359i \(-0.909878\pi\)
0.722025 + 0.691867i \(0.243211\pi\)
\(572\) −7.97967 13.8212i −0.333647 0.577893i
\(573\) 41.2186 1.72193
\(574\) 0 0
\(575\) −3.50236 −0.146059
\(576\) 0.575525 + 0.996839i 0.0239802 + 0.0415350i
\(577\) −17.8129 + 30.8528i −0.741560 + 1.28442i 0.210225 + 0.977653i \(0.432580\pi\)
−0.951785 + 0.306766i \(0.900753\pi\)
\(578\) 15.6184 27.0519i 0.649641 1.12521i
\(579\) −1.62838 2.82044i −0.0676732 0.117213i
\(580\) 35.3245 1.46677
\(581\) 0 0
\(582\) −26.7665 −1.10951
\(583\) 9.95017 + 17.2342i 0.412094 + 0.713768i
\(584\) −12.9717 + 22.4676i −0.536772 + 0.929717i
\(585\) −0.0971286 + 0.168232i −0.00401577 + 0.00695552i
\(586\) 1.09716 + 1.90034i 0.0453234 + 0.0785025i
\(587\) −4.14755 −0.171188 −0.0855938 0.996330i \(-0.527279\pi\)
−0.0855938 + 0.996330i \(0.527279\pi\)
\(588\) 0 0
\(589\) −13.6797 −0.563663
\(590\) −30.3681 52.5991i −1.25024 2.16547i
\(591\) −8.67852 + 15.0316i −0.356987 + 0.618319i
\(592\) 5.40188 9.35633i 0.222016 0.384543i
\(593\) −12.0656 20.8983i −0.495476 0.858190i 0.504510 0.863406i \(-0.331673\pi\)
−0.999986 + 0.00521562i \(0.998340\pi\)
\(594\) −64.4023 −2.64246
\(595\) 0 0
\(596\) −2.87788 −0.117883
\(597\) −10.7696 18.6535i −0.440772 0.763439i
\(598\) 7.01325 12.1473i 0.286793 0.496741i
\(599\) 24.2803 42.0548i 0.992068 1.71831i 0.387172 0.922007i \(-0.373452\pi\)
0.604896 0.796305i \(-0.293215\pi\)
\(600\) −0.802014 1.38913i −0.0327421 0.0567109i
\(601\) 33.2069 1.35454 0.677270 0.735735i \(-0.263163\pi\)
0.677270 + 0.735735i \(0.263163\pi\)
\(602\) 0 0
\(603\) 0.712562 0.0290178
\(604\) 6.00785 + 10.4059i 0.244456 + 0.423410i
\(605\) 23.5128 40.7254i 0.955932 1.65572i
\(606\) 12.4753 21.6078i 0.506772 0.877756i
\(607\) −10.8973 18.8747i −0.442308 0.766100i 0.555552 0.831482i \(-0.312507\pi\)
−0.997860 + 0.0653815i \(0.979174\pi\)
\(608\) −19.8982 −0.806978
\(609\) 0 0
\(610\) 28.7847 1.16546
\(611\) −5.89550 10.2113i −0.238506 0.413105i
\(612\) 0.208888 0.361805i 0.00844381 0.0146251i
\(613\) 11.3995 19.7446i 0.460423 0.797476i −0.538559 0.842588i \(-0.681031\pi\)
0.998982 + 0.0451115i \(0.0143643\pi\)
\(614\) 4.64777 + 8.05018i 0.187569 + 0.324879i
\(615\) 26.5032 1.06871
\(616\) 0 0
\(617\) −42.5433 −1.71273 −0.856364 0.516373i \(-0.827282\pi\)
−0.856364 + 0.516373i \(0.827282\pi\)
\(618\) 1.10957 + 1.92183i 0.0446333 + 0.0773072i
\(619\) −22.0642 + 38.2164i −0.886836 + 1.53605i −0.0432419 + 0.999065i \(0.513769\pi\)
−0.843594 + 0.536981i \(0.819565\pi\)
\(620\) −14.9538 + 25.9007i −0.600558 + 1.04020i
\(621\) −16.4261 28.4508i −0.659155 1.14169i
\(622\) 15.1525 0.607559
\(623\) 0 0
\(624\) −3.30523 −0.132315
\(625\) 10.9886 + 19.0327i 0.439542 + 0.761310i
\(626\) −10.8757 + 18.8373i −0.434680 + 0.752889i
\(627\) −13.5463 + 23.4629i −0.540987 + 0.937018i
\(628\) 0.464764 + 0.804995i 0.0185461 + 0.0321228i
\(629\) −9.43098 −0.376038
\(630\) 0 0
\(631\) 9.09226 0.361957 0.180979 0.983487i \(-0.442074\pi\)
0.180979 + 0.983487i \(0.442074\pi\)
\(632\) −0.938854 1.62614i −0.0373456 0.0646845i
\(633\) −0.650526 + 1.12674i −0.0258561 + 0.0447841i
\(634\) −4.09730 + 7.09674i −0.162725 + 0.281847i
\(635\) −20.3737 35.2884i −0.808507 1.40038i
\(636\) −16.7808 −0.665402
\(637\) 0 0
\(638\) 76.1950 3.01659
\(639\) −0.627562 1.08697i −0.0248260 0.0429998i
\(640\) −13.0899 + 22.6723i −0.517423 + 0.896202i
\(641\) 11.3321 19.6278i 0.447591 0.775250i −0.550638 0.834744i \(-0.685615\pi\)
0.998229 + 0.0594943i \(0.0189488\pi\)
\(642\) −31.2059 54.0503i −1.23160 2.13319i
\(643\) −24.3792 −0.961422 −0.480711 0.876879i \(-0.659621\pi\)
−0.480711 + 0.876879i \(0.659621\pi\)
\(644\) 0 0
\(645\) −16.5923 −0.653320
\(646\) 4.78371 + 8.28563i 0.188213 + 0.325994i
\(647\) −18.5182 + 32.0745i −0.728026 + 1.26098i 0.229690 + 0.973264i \(0.426229\pi\)
−0.957716 + 0.287715i \(0.907105\pi\)
\(648\) 7.75389 13.4301i 0.304601 0.527585i
\(649\) −38.0186 65.8501i −1.49236 2.58484i
\(650\) 1.19016 0.0466820
\(651\) 0 0
\(652\) 18.8096 0.736641
\(653\) −9.36705 16.2242i −0.366561 0.634902i 0.622464 0.782648i \(-0.286132\pi\)
−0.989025 + 0.147746i \(0.952798\pi\)
\(654\) 3.42038 5.92428i 0.133748 0.231658i
\(655\) −10.2335 + 17.7250i −0.399857 + 0.692573i
\(656\) 6.71133 + 11.6244i 0.262033 + 0.453855i
\(657\) 1.42694 0.0556703
\(658\) 0 0
\(659\) −28.5206 −1.11100 −0.555502 0.831515i \(-0.687474\pi\)
−0.555502 + 0.831515i \(0.687474\pi\)
\(660\) 29.6159 + 51.2962i 1.15280 + 1.99670i
\(661\) −9.98790 + 17.2995i −0.388484 + 0.672874i −0.992246 0.124291i \(-0.960335\pi\)
0.603762 + 0.797165i \(0.293668\pi\)
\(662\) 21.8117 37.7790i 0.847736 1.46832i
\(663\) 1.44263 + 2.49870i 0.0560270 + 0.0970415i
\(664\) −8.31517 −0.322691
\(665\) 0 0
\(666\) 1.15492 0.0447524
\(667\) 19.4338 + 33.6604i 0.752481 + 1.30334i
\(668\) 0.924891 1.60196i 0.0357851 0.0619816i
\(669\) −7.30251 + 12.6483i −0.282331 + 0.489012i
\(670\) 17.8380 + 30.8964i 0.689143 + 1.19363i
\(671\) 36.0363 1.39117
\(672\) 0 0
\(673\) −4.18849 −0.161454 −0.0807272 0.996736i \(-0.525724\pi\)
−0.0807272 + 0.996736i \(0.525724\pi\)
\(674\) −20.1824 34.9570i −0.777398 1.34649i
\(675\) 1.39377 2.41408i 0.0536461 0.0929178i
\(676\) −1.38322 + 2.39581i −0.0532009 + 0.0921467i
\(677\) −19.1698 33.2031i −0.736755 1.27610i −0.953949 0.299969i \(-0.903024\pi\)
0.217194 0.976129i \(-0.430310\pi\)
\(678\) 28.8776 1.10904
\(679\) 0 0
\(680\) 5.79507 0.222231
\(681\) −11.6861 20.2410i −0.447814 0.775637i
\(682\) −32.2553 + 55.8678i −1.23512 + 2.13929i
\(683\) 1.30604 2.26212i 0.0499741 0.0865577i −0.839956 0.542654i \(-0.817419\pi\)
0.889930 + 0.456096i \(0.150753\pi\)
\(684\) −0.340008 0.588911i −0.0130005 0.0225176i
\(685\) 32.6082 1.24589
\(686\) 0 0
\(687\) 31.5120 1.20226
\(688\) −4.20161 7.27740i −0.160185 0.277448i
\(689\) 1.72480 2.98744i 0.0657095 0.113812i
\(690\) −26.0291 + 45.0837i −0.990910 + 1.71631i
\(691\) −20.4592 35.4365i −0.778307 1.34807i −0.932917 0.360091i \(-0.882746\pi\)
0.154611 0.987975i \(-0.450588\pi\)
\(692\) −69.4872 −2.64151
\(693\) 0 0
\(694\) −1.73806 −0.0659759
\(695\) −4.06208 7.03572i −0.154083 0.266880i
\(696\) −8.90039 + 15.4159i −0.337368 + 0.584339i
\(697\) 5.85856 10.1473i 0.221909 0.384357i
\(698\) −12.4143 21.5022i −0.469888 0.813870i
\(699\) −11.0775 −0.418988
\(700\) 0 0
\(701\) −0.762896 −0.0288142 −0.0144071 0.999896i \(-0.504586\pi\)
−0.0144071 + 0.999896i \(0.504586\pi\)
\(702\) 5.58186 + 9.66806i 0.210674 + 0.364897i
\(703\) −7.67541 + 13.2942i −0.289484 + 0.501400i
\(704\) −36.0742 + 62.4824i −1.35960 + 2.35489i
\(705\) 21.8806 + 37.8984i 0.824072 + 1.42733i
\(706\) −52.6304 −1.98077
\(707\) 0 0
\(708\) 64.1178 2.40969
\(709\) −1.32641 2.29740i −0.0498142 0.0862807i 0.840043 0.542520i \(-0.182530\pi\)
−0.889857 + 0.456239i \(0.849196\pi\)
\(710\) 31.4203 54.4216i 1.17918 2.04241i
\(711\) −0.0516390 + 0.0894414i −0.00193661 + 0.00335432i
\(712\) 0.959063 + 1.66115i 0.0359424 + 0.0622541i
\(713\) −32.9074 −1.23239
\(714\) 0 0
\(715\) −12.1761 −0.455362
\(716\) 2.62158 + 4.54070i 0.0979729 + 0.169694i
\(717\) 8.28025 14.3418i 0.309231 0.535605i
\(718\) −9.90288 + 17.1523i −0.369572 + 0.640118i
\(719\) 5.52216 + 9.56465i 0.205942 + 0.356701i 0.950432 0.310931i \(-0.100641\pi\)
−0.744491 + 0.667633i \(0.767308\pi\)
\(720\) 0.365138 0.0136079
\(721\) 0 0
\(722\) −25.9083 −0.964206
\(723\) 17.5396 + 30.3795i 0.652305 + 1.12983i
\(724\) 15.7128 27.2153i 0.583961 1.01145i
\(725\) −1.64898 + 2.85612i −0.0612416 + 0.106074i
\(726\) 42.7669 + 74.0744i 1.58723 + 2.74916i
\(727\) −3.46566 −0.128534 −0.0642672 0.997933i \(-0.520471\pi\)
−0.0642672 + 0.997933i \(0.520471\pi\)
\(728\) 0 0
\(729\) 26.1216 0.967468
\(730\) 35.7216 + 61.8716i 1.32211 + 2.28997i
\(731\) −3.66774 + 6.35270i −0.135656 + 0.234963i
\(732\) −15.1937 + 26.3162i −0.561574 + 0.972675i
\(733\) −14.5166 25.1435i −0.536182 0.928695i −0.999105 0.0422961i \(-0.986533\pi\)
0.462923 0.886398i \(-0.346801\pi\)
\(734\) 68.8822 2.54249
\(735\) 0 0
\(736\) −47.8663 −1.76437
\(737\) 22.3319 + 38.6799i 0.822605 + 1.42479i
\(738\) −0.717442 + 1.24265i −0.0264094 + 0.0457424i
\(739\) −23.7761 + 41.1814i −0.874618 + 1.51488i −0.0174482 + 0.999848i \(0.505554\pi\)
−0.857169 + 0.515034i \(0.827779\pi\)
\(740\) 16.7805 + 29.0647i 0.616864 + 1.06844i
\(741\) 4.69633 0.172524
\(742\) 0 0
\(743\) 12.6122 0.462697 0.231349 0.972871i \(-0.425686\pi\)
0.231349 + 0.972871i \(0.425686\pi\)
\(744\) −7.53553 13.0519i −0.276266 0.478507i
\(745\) −1.09784 + 1.90151i −0.0402216 + 0.0696658i
\(746\) 17.5292 30.3614i 0.641789 1.11161i
\(747\) 0.228676 + 0.396079i 0.00836683 + 0.0144918i
\(748\) 26.1864 0.957471
\(749\) 0 0
\(750\) −44.9313 −1.64066
\(751\) 3.85390 + 6.67516i 0.140631 + 0.243580i 0.927734 0.373241i \(-0.121754\pi\)
−0.787103 + 0.616821i \(0.788420\pi\)
\(752\) −11.0815 + 19.1938i −0.404102 + 0.699925i
\(753\) −1.07441 + 1.86093i −0.0391536 + 0.0678161i
\(754\) −6.60395 11.4384i −0.240502 0.416561i
\(755\) 9.16734 0.333633
\(756\) 0 0
\(757\) 2.39454 0.0870311 0.0435156 0.999053i \(-0.486144\pi\)
0.0435156 + 0.999053i \(0.486144\pi\)
\(758\) 5.86080 + 10.1512i 0.212874 + 0.368708i
\(759\) −32.5864 + 56.4414i −1.18281 + 2.04869i
\(760\) 4.71632 8.16891i 0.171079 0.296318i
\(761\) −20.6648 35.7925i −0.749098 1.29748i −0.948255 0.317508i \(-0.897154\pi\)
0.199158 0.979967i \(-0.436179\pi\)
\(762\) 74.1146 2.68489
\(763\) 0 0
\(764\) −64.8475 −2.34610
\(765\) −0.159371 0.276038i −0.00576206 0.00998018i
\(766\) 37.6687 65.2441i 1.36103 2.35736i
\(767\) −6.59027 + 11.4147i −0.237961 + 0.412161i
\(768\) −1.81725 3.14757i −0.0655744 0.113578i
\(769\) −36.7414 −1.32493 −0.662464 0.749094i \(-0.730489\pi\)
−0.662464 + 0.749094i \(0.730489\pi\)
\(770\) 0 0
\(771\) −39.4308 −1.42007
\(772\) 2.56186 + 4.43728i 0.0922035 + 0.159701i
\(773\) −11.9836 + 20.7562i −0.431020 + 0.746548i −0.996961 0.0778972i \(-0.975179\pi\)
0.565942 + 0.824445i \(0.308513\pi\)
\(774\) 0.449153 0.777956i 0.0161445 0.0279630i
\(775\) −1.39611 2.41814i −0.0501498 0.0868620i
\(776\) 11.6668 0.418814
\(777\) 0 0
\(778\) 50.0415 1.79408
\(779\) −9.53598 16.5168i −0.341662 0.591776i
\(780\) 5.13372 8.89186i 0.183817 0.318380i
\(781\) 39.3359 68.1318i 1.40755 2.43795i
\(782\) 11.5075 + 19.9316i 0.411507 + 0.712752i
\(783\) −30.9348 −1.10552
\(784\) 0 0
\(785\)