Properties

Label 637.2.e.n.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.n.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 \(0.336138\pi\)
−0.999961 + 0.00881173i \(0.997195\pi\)
\(4\) −1.38322 + 2.39581i −0.691612 + 1.19791i
\(5\) −1.05533 1.82788i −0.471957 0.817453i 0.527529 0.849537i \(-0.323119\pi\)
−0.999485 + 0.0320846i \(0.989785\pi\)
\(6\) 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 −0.948198 0.317681i \(-0.897096\pi\)
0.749219 + 0.662323i \(0.230429\pi\)
\(18\) −0.100468 + 0.174016i −0.0236805 + 0.0410159i
\(19\) 1.33538 + 2.31295i 0.306358 + 0.530628i 0.977563 0.210644i \(-0.0675562\pi\)
−0.671205 + 0.741272i \(0.734223\pi\)
\(20\) 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 −0.998959 0.0456207i \(-0.985473\pi\)
0.538988 + 0.842313i \(0.318807\pi\)
\(32\) 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 \(-0.688285\pi\)
−0.557619 + 0.830097i \(0.688285\pi\)
\(42\) 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 \(-0.837163\pi\)
0.0120319 0.999928i \(-0.496170\pi\)
\(48\) −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 \(0.494948\pi\)
−0.873852 + 0.486192i \(0.838386\pi\)
\(60\) −5.13372 + 8.89186i −0.662760 + 1.14793i
\(61\) −3.12333 5.40976i −0.399901 0.692649i 0.593812 0.804604i \(-0.297622\pi\)
−0.993713 + 0.111954i \(0.964289\pi\)
\(62\) 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 \(-0.471467\pi\)
0.817789 0.575518i \(-0.195200\pi\)
\(74\) −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 \(-0.412076\pi\)
0.272723 + 0.962093i \(0.412076\pi\)
\(84\) 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 0.834049 0.551691i \(-0.186017\pi\)
−0.894802 + 0.446462i \(0.852684\pi\)
\(90\) 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 \(-0.615166\pi\)
−0.353961 + 0.935260i \(0.615166\pi\)
\(98\) 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 −0.657829 0.753167i \(-0.728525\pi\)
0.981176 + 0.193113i \(0.0618586\pi\)
\(102\) −3.14957 + 5.45521i −0.311854 + 0.540147i
\(103\) 0.289024 + 0.500604i 0.0284784 + 0.0493260i 0.879913 0.475134i \(-0.157600\pi\)
−0.851435 + 0.524460i \(0.824267\pi\)
\(104\) 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 0.572673 0.819784i \(-0.305906\pi\)
−0.996290 + 0.0860579i \(0.972573\pi\)
\(132\) −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 \(-0.447806\pi\)
0.163239 + 0.986587i \(0.447806\pi\)
\(140\) 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 −0.872651 0.488343i \(-0.837601\pi\)
0.859244 + 0.511567i \(0.170935\pi\)
\(158\) −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 \(-0.491764\pi\)
0.0258708 + 0.999665i \(0.491764\pi\)
\(168\) 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 \(-0.762697\pi\)
−0.220095 0.975478i \(-0.570637\pi\)
\(174\) −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 \(-0.361267\pi\)
0.422174 + 0.906515i \(0.361267\pi\)
\(182\) 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 −0.997227 0.0744219i \(-0.976289\pi\)
0.563065 + 0.826413i \(0.309622\pi\)
\(200\) 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 \(-0.410296\pi\)
0.278098 + 0.960553i \(0.410296\pi\)
\(224\) 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 −0.997771 0.0667264i \(-0.978745\pi\)
0.556672 + 0.830732i \(0.312078\pi\)
\(228\) 6.49607 11.2515i 0.430213 0.745151i
\(229\) −8.96033 15.5197i −0.592115 1.02557i −0.993947 0.109860i \(-0.964960\pi\)
0.401832 0.915714i \(-0.368374\pi\)
\(230\) 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 \(-0.611221\pi\)
0.984867 0.173309i \(-0.0554460\pi\)
\(242\) −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 \(-0.487721\pi\)
0.0385665 + 0.999256i \(0.487721\pi\)
\(252\) 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 \(0.0798763\pi\)
−0.269294 + 0.963058i \(0.586790\pi\)
\(258\) −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 \(-0.596637\pi\)
0.975896 0.218235i \(-0.0700299\pi\)
\(270\) 11.7814 20.4059i 0.716991 1.24187i
\(271\) 5.42116 + 9.38972i 0.329312 + 0.570385i 0.982375 0.186918i \(-0.0598499\pi\)
−0.653064 + 0.757303i \(0.726517\pi\)
\(272\) −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 −0.809363 0.587309i \(-0.800187\pi\)
0.913306 + 0.407275i \(0.133521\pi\)
\(284\) −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 \(-0.490653\pi\)
0.0293589 + 0.999569i \(0.490653\pi\)
\(294\) 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 \(-0.461229\pi\)
0.121501 + 0.992591i \(0.461229\pi\)
\(308\) 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 −0.750704 0.660639i \(-0.770286\pi\)
0.947482 + 0.319809i \(0.103619\pi\)
\(312\) −1.47120 + 2.54820i −0.0832905 + 0.144263i
\(313\) 4.98150 + 8.62820i 0.281571 + 0.487695i 0.971772 0.235923i \(-0.0758112\pi\)
−0.690201 + 0.723618i \(0.742478\pi\)
\(314\) 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 \(-0.598448\pi\)
−0.304377 + 0.952552i \(0.598448\pi\)
\(350\) 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 \(0.388369\pi\)
−0.985090 + 0.172041i \(0.944964\pi\)
\(354\) −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 \(-0.525370\pi\)
0.903085 0.429462i \(-0.141297\pi\)
\(368\) 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 \(-0.823117\pi\)
−0.0320905 0.999485i \(-0.510216\pi\)
\(384\) −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 0.697556 0.716530i \(-0.254271\pi\)
−0.969311 + 0.245836i \(0.920937\pi\)
\(398\) 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 \(-0.664400\pi\)
0.999975 0.00712174i \(-0.00226694\pi\)
\(410\) 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 \(-0.623582\pi\)
−0.378564 + 0.925575i \(0.623582\pi\)
\(420\) 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 \(-0.616848\pi\)
−0.358900 + 0.933376i \(0.616848\pi\)
\(434\) 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 0.905710 0.423899i \(-0.139339\pi\)
−0.819962 + 0.572418i \(0.806005\pi\)
\(440\) −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 \(-0.461191\pi\)
0.121619 + 0.992577i \(0.461191\pi\)
\(462\) 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 0.846041 0.533118i \(-0.178980\pi\)
−0.884714 + 0.466134i \(0.845647\pi\)
\(468\) 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 −0.961614 0.274404i \(-0.911519\pi\)
0.718448 + 0.695581i \(0.244853\pi\)
\(480\) 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 \(-0.266029\pi\)
0.670617 + 0.741803i \(0.266029\pi\)
\(504\) 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 \(-0.902328\pi\)
0.215059 0.976601i \(-0.431006\pi\)
\(510\) 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 \(0.421562\pi\)
−0.961831 + 0.273643i \(0.911771\pi\)
\(522\) 0.607805 1.05275i 0.0266029 0.0460775i
\(523\) −12.6308 21.8772i −0.552307 0.956623i −0.998108 0.0614909i \(-0.980414\pi\)
0.445801 0.895132i \(-0.352919\pi\)
\(524\) 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 \(0.489348\pi\)
−0.882270 + 0.470743i \(0.843986\pi\)
\(564\) −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 \(-0.567420\pi\)
0.951785 0.306766i \(-0.0992469\pi\)
\(578\) 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 \(-0.472721\pi\)
0.0855938 + 0.996330i \(0.472721\pi\)
\(588\) 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 0.999986 0.00521562i \(-0.00166019\pi\)
−0.504510 + 0.863406i \(0.668327\pi\)
\(594\) 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 \(-0.736837\pi\)
−0.677270 + 0.735735i \(0.736837\pi\)
\(602\) 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 0.997860 0.0653815i \(-0.0208264\pi\)
−0.555552 + 0.831482i \(0.687493\pi\)
\(608\) 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 \(-0.486231\pi\)
0.843594 0.536981i \(-0.180435\pi\)
\(620\) −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 \(-0.340379\pi\)
0.480711 + 0.876879i \(0.340379\pi\)
\(644\) 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 \(-0.573771\pi\)
0.957716 0.287715i \(-0.0928955\pi\)
\(648\) 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 −0.603762 0.797165i \(-0.706332\pi\)
0.992246 + 0.124291i \(0.0396655\pi\)
\(662\) 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 \(0.0969764\pi\)
−0.217194 + 0.976129i \(0.569690\pi\)
\(678\) −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 \(0.117254\pi\)
−0.154611 + 0.987975i \(0.549412\pi\)
\(692\) 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 0.744491 0.667633i \(-0.232692\pi\)
−0.950432 + 0.310931i \(0.899359\pi\)
\(720\) −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 \(-0.479529\pi\)
0.0642672 + 0.997933i \(0.479529\pi\)
\(728\) 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 \(0.0134673\pi\)
−0.462923 + 0.886398i \(0.653199\pi\)
\(734\) −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 \(0.102846\pi\)
−0.199158 + 0.979967i \(0.563821\pi\)
\(762\) −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 \(-0.269511\pi\)
0.662464 + 0.749094i \(0.269511\pi\)
\(770\) 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 −0.565942 0.824445i \(-0.691487\pi\)
0.996961 + 0.0778972i \(0.0248206\pi\)
\(774\) 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