Properties

Label 637.2.g.i.263.1
Level $637$
Weight $2$
Character 637.263
Analytic conductor $5.086$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.100088711424.6
Defining polynomial: \(x^{8} - 13 x^{6} + 130 x^{4} - 507 x^{2} + 1521\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 263.1
Root \(2.49541 + 1.44073i\) of defining polynomial
Character \(\chi\) \(=\) 637.263
Dual form 637.2.g.i.373.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.15139 + 1.99426i) q^{2} -2.16731 q^{3} +(-1.65139 - 2.86029i) q^{4} +(1.08365 + 1.87694i) q^{5} +(2.49541 - 4.32218i) q^{6} +3.00000 q^{8} +1.69722 q^{9} +O(q^{10})\) \(q+(-1.15139 + 1.99426i) q^{2} -2.16731 q^{3} +(-1.65139 - 2.86029i) q^{4} +(1.08365 + 1.87694i) q^{5} +(2.49541 - 4.32218i) q^{6} +3.00000 q^{8} +1.69722 q^{9} -4.99082 q^{10} +4.90833 q^{11} +(3.57907 + 6.19912i) q^{12} +(1.41176 + 3.31767i) q^{13} +(-2.34861 - 4.06792i) q^{15} +(-0.151388 + 0.262211i) q^{16} +(3.57907 + 6.19912i) q^{17} +(-1.95416 + 3.38471i) q^{18} -2.16731 q^{19} +(3.57907 - 6.19912i) q^{20} +(-5.65139 + 9.78849i) q^{22} +(0.302776 - 0.524423i) q^{23} -6.50192 q^{24} +(0.151388 - 0.262211i) q^{25} +(-8.24179 - 1.00451i) q^{26} +2.82352 q^{27} +(1.15139 + 1.99426i) q^{29} +10.8167 q^{30} +(-3.57907 + 6.19912i) q^{31} +(2.65139 + 4.59234i) q^{32} -10.6379 q^{33} -16.4836 q^{34} +(-2.80278 - 4.85455i) q^{36} +(-4.30278 + 7.45263i) q^{37} +(2.49541 - 4.32218i) q^{38} +(-3.05971 - 7.19041i) q^{39} +(3.25096 + 5.63083i) q^{40} +(-4.99082 - 8.64436i) q^{41} +(6.25694 - 10.8373i) q^{43} +(-8.10555 - 14.0392i) q^{44} +(1.83920 + 3.18559i) q^{45} +(0.697224 + 1.20763i) q^{46} +(-0.755550 - 1.30865i) q^{47} +(0.328104 - 0.568293i) q^{48} +(0.348612 + 0.603814i) q^{50} +(-7.75694 - 13.4354i) q^{51} +(7.15813 - 9.51680i) q^{52} +(-1.19722 + 2.07365i) q^{53} +(-3.25096 + 5.63083i) q^{54} +(5.31893 + 9.21265i) q^{55} +4.69722 q^{57} -5.30278 q^{58} +(-1.41176 - 2.44524i) q^{59} +(-7.75694 + 13.4354i) q^{60} -4.33462 q^{61} +(-8.24179 - 14.2752i) q^{62} -12.8167 q^{64} +(-4.69722 + 6.24500i) q^{65} +(12.2483 - 21.2147i) q^{66} +1.00000 q^{67} +(11.8209 - 20.4743i) q^{68} +(-0.656208 + 1.13659i) q^{69} +(-2.00000 + 3.46410i) q^{71} +5.09167 q^{72} +(-2.16731 + 3.75389i) q^{73} +(-9.90833 - 17.1617i) q^{74} +(-0.328104 + 0.568293i) q^{75} +(3.57907 + 6.19912i) q^{76} +(17.8625 + 2.17708i) q^{78} +(3.30278 + 5.72058i) q^{79} -0.656208 q^{80} -11.2111 q^{81} +22.9855 q^{82} -2.82352 q^{83} +(-7.75694 + 13.4354i) q^{85} +(14.4083 + 24.9560i) q^{86} +(-2.49541 - 4.32218i) q^{87} +14.7250 q^{88} +(3.25096 - 5.63083i) q^{89} -8.47055 q^{90} -2.00000 q^{92} +(7.75694 - 13.4354i) q^{93} +3.47972 q^{94} +(-2.34861 - 4.06792i) q^{95} +(-5.74637 - 9.95301i) q^{96} +(-6.83003 + 11.8300i) q^{97} +8.33053 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 28 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{2} - 6 q^{4} + 24 q^{8} + 28 q^{9} - 4 q^{11} - 26 q^{15} + 6 q^{16} + 6 q^{18} - 38 q^{22} - 12 q^{23} - 6 q^{25} + 2 q^{29} + 14 q^{32} - 8 q^{36} - 20 q^{37} + 26 q^{39} + 14 q^{43} - 36 q^{44} + 20 q^{46} + 10 q^{50} - 26 q^{51} - 24 q^{53} + 52 q^{57} - 28 q^{58} - 26 q^{60} - 16 q^{64} - 52 q^{65} + 8 q^{67} - 16 q^{71} + 84 q^{72} - 36 q^{74} + 78 q^{78} + 12 q^{79} - 32 q^{81} - 26 q^{85} + 72 q^{86} - 12 q^{88} - 16 q^{92} + 26 q^{93} - 26 q^{95} - 92 q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15139 + 1.99426i −0.814154 + 1.41016i 0.0957796 + 0.995403i \(0.469466\pi\)
−0.909934 + 0.414754i \(0.863868\pi\)
\(3\) −2.16731 −1.25130 −0.625648 0.780106i \(-0.715165\pi\)
−0.625648 + 0.780106i \(0.715165\pi\)
\(4\) −1.65139 2.86029i −0.825694 1.43014i
\(5\) 1.08365 + 1.87694i 0.484625 + 0.839395i 0.999844 0.0176637i \(-0.00562281\pi\)
−0.515219 + 0.857058i \(0.672289\pi\)
\(6\) 2.49541 4.32218i 1.01875 1.76452i
\(7\) 0 0
\(8\) 3.00000 1.06066
\(9\) 1.69722 0.565741
\(10\) −4.99082 −1.57824
\(11\) 4.90833 1.47992 0.739958 0.672653i \(-0.234845\pi\)
0.739958 + 0.672653i \(0.234845\pi\)
\(12\) 3.57907 + 6.19912i 1.03319 + 1.78953i
\(13\) 1.41176 + 3.31767i 0.391551 + 0.920156i
\(14\) 0 0
\(15\) −2.34861 4.06792i −0.606409 1.05033i
\(16\) −0.151388 + 0.262211i −0.0378470 + 0.0655528i
\(17\) 3.57907 + 6.19912i 0.868051 + 1.50351i 0.863985 + 0.503517i \(0.167961\pi\)
0.00406561 + 0.999992i \(0.498706\pi\)
\(18\) −1.95416 + 3.38471i −0.460601 + 0.797784i
\(19\) −2.16731 −0.497215 −0.248607 0.968604i \(-0.579973\pi\)
−0.248607 + 0.968604i \(0.579973\pi\)
\(20\) 3.57907 6.19912i 0.800304 1.38617i
\(21\) 0 0
\(22\) −5.65139 + 9.78849i −1.20488 + 2.08691i
\(23\) 0.302776 0.524423i 0.0631331 0.109350i −0.832731 0.553677i \(-0.813224\pi\)
0.895864 + 0.444328i \(0.146557\pi\)
\(24\) −6.50192 −1.32720
\(25\) 0.151388 0.262211i 0.0302776 0.0524423i
\(26\) −8.24179 1.00451i −1.61635 0.197001i
\(27\) 2.82352 0.543386
\(28\) 0 0
\(29\) 1.15139 + 1.99426i 0.213807 + 0.370325i 0.952903 0.303275i \(-0.0980802\pi\)
−0.739096 + 0.673601i \(0.764747\pi\)
\(30\) 10.8167 1.97484
\(31\) −3.57907 + 6.19912i −0.642819 + 1.11340i 0.341981 + 0.939707i \(0.388902\pi\)
−0.984801 + 0.173689i \(0.944431\pi\)
\(32\) 2.65139 + 4.59234i 0.468704 + 0.811818i
\(33\) −10.6379 −1.85181
\(34\) −16.4836 −2.82691
\(35\) 0 0
\(36\) −2.80278 4.85455i −0.467129 0.809092i
\(37\) −4.30278 + 7.45263i −0.707372 + 1.22520i 0.258457 + 0.966023i \(0.416786\pi\)
−0.965829 + 0.259181i \(0.916547\pi\)
\(38\) 2.49541 4.32218i 0.404809 0.701150i
\(39\) −3.05971 7.19041i −0.489946 1.15139i
\(40\) 3.25096 + 5.63083i 0.514022 + 0.890313i
\(41\) −4.99082 8.64436i −0.779436 1.35002i −0.932267 0.361770i \(-0.882173\pi\)
0.152832 0.988252i \(-0.451161\pi\)
\(42\) 0 0
\(43\) 6.25694 10.8373i 0.954174 1.65268i 0.217928 0.975965i \(-0.430070\pi\)
0.736247 0.676713i \(-0.236596\pi\)
\(44\) −8.10555 14.0392i −1.22196 2.11649i
\(45\) 1.83920 + 3.18559i 0.274172 + 0.474880i
\(46\) 0.697224 + 1.20763i 0.102800 + 0.178055i
\(47\) −0.755550 1.30865i −0.110208 0.190886i 0.805646 0.592397i \(-0.201818\pi\)
−0.915854 + 0.401511i \(0.868485\pi\)
\(48\) 0.328104 0.568293i 0.0473577 0.0820260i
\(49\) 0 0
\(50\) 0.348612 + 0.603814i 0.0493012 + 0.0853922i
\(51\) −7.75694 13.4354i −1.08619 1.88133i
\(52\) 7.15813 9.51680i 0.992654 1.31974i
\(53\) −1.19722 + 2.07365i −0.164451 + 0.284838i −0.936460 0.350773i \(-0.885919\pi\)
0.772009 + 0.635612i \(0.219252\pi\)
\(54\) −3.25096 + 5.63083i −0.442400 + 0.766259i
\(55\) 5.31893 + 9.21265i 0.717204 + 1.24223i
\(56\) 0 0
\(57\) 4.69722 0.622163
\(58\) −5.30278 −0.696289
\(59\) −1.41176 2.44524i −0.183795 0.318343i 0.759375 0.650654i \(-0.225505\pi\)
−0.943170 + 0.332311i \(0.892172\pi\)
\(60\) −7.75694 + 13.4354i −1.00142 + 1.73450i
\(61\) −4.33462 −0.554991 −0.277495 0.960727i \(-0.589504\pi\)
−0.277495 + 0.960727i \(0.589504\pi\)
\(62\) −8.24179 14.2752i −1.04671 1.81295i
\(63\) 0 0
\(64\) −12.8167 −1.60208
\(65\) −4.69722 + 6.24500i −0.582619 + 0.774597i
\(66\) 12.2483 21.2147i 1.50766 2.61135i
\(67\) 1.00000 0.122169 0.0610847 0.998133i \(-0.480544\pi\)
0.0610847 + 0.998133i \(0.480544\pi\)
\(68\) 11.8209 20.4743i 1.43349 2.48288i
\(69\) −0.656208 + 1.13659i −0.0789982 + 0.136829i
\(70\) 0 0
\(71\) −2.00000 + 3.46410i −0.237356 + 0.411113i −0.959955 0.280155i \(-0.909614\pi\)
0.722599 + 0.691268i \(0.242948\pi\)
\(72\) 5.09167 0.600059
\(73\) −2.16731 + 3.75389i −0.253664 + 0.439359i −0.964532 0.263967i \(-0.914969\pi\)
0.710868 + 0.703326i \(0.248302\pi\)
\(74\) −9.90833 17.1617i −1.15182 1.99501i
\(75\) −0.328104 + 0.568293i −0.0378862 + 0.0656208i
\(76\) 3.57907 + 6.19912i 0.410547 + 0.711088i
\(77\) 0 0
\(78\) 17.8625 + 2.17708i 2.02253 + 0.246506i
\(79\) 3.30278 + 5.72058i 0.371591 + 0.643615i 0.989811 0.142391i \(-0.0454789\pi\)
−0.618219 + 0.786006i \(0.712146\pi\)
\(80\) −0.656208 −0.0733663
\(81\) −11.2111 −1.24568
\(82\) 22.9855 2.53832
\(83\) −2.82352 −0.309921 −0.154961 0.987921i \(-0.549525\pi\)
−0.154961 + 0.987921i \(0.549525\pi\)
\(84\) 0 0
\(85\) −7.75694 + 13.4354i −0.841358 + 1.45728i
\(86\) 14.4083 + 24.9560i 1.55369 + 2.69107i
\(87\) −2.49541 4.32218i −0.267536 0.463386i
\(88\) 14.7250 1.56969
\(89\) 3.25096 5.63083i 0.344601 0.596867i −0.640680 0.767808i \(-0.721347\pi\)
0.985281 + 0.170941i \(0.0546808\pi\)
\(90\) −8.47055 −0.892874
\(91\) 0 0
\(92\) −2.00000 −0.208514
\(93\) 7.75694 13.4354i 0.804357 1.39319i
\(94\) 3.47972 0.358906
\(95\) −2.34861 4.06792i −0.240963 0.417359i
\(96\) −5.74637 9.95301i −0.586487 1.01583i
\(97\) −6.83003 + 11.8300i −0.693484 + 1.20115i 0.277205 + 0.960811i \(0.410592\pi\)
−0.970689 + 0.240339i \(0.922741\pi\)
\(98\) 0 0
\(99\) 8.33053 0.837250
\(100\) −1.00000 −0.100000
\(101\) 6.50192 0.646966 0.323483 0.946234i \(-0.395146\pi\)
0.323483 + 0.946234i \(0.395146\pi\)
\(102\) 35.7250 3.53730
\(103\) 5.74637 + 9.95301i 0.566207 + 0.980699i 0.996936 + 0.0782182i \(0.0249231\pi\)
−0.430729 + 0.902481i \(0.641744\pi\)
\(104\) 4.23527 + 9.95301i 0.415303 + 0.975973i
\(105\) 0 0
\(106\) −2.75694 4.77516i −0.267778 0.463804i
\(107\) −2.84861 + 4.93394i −0.275386 + 0.476982i −0.970232 0.242176i \(-0.922139\pi\)
0.694847 + 0.719158i \(0.255472\pi\)
\(108\) −4.66272 8.07607i −0.448670 0.777120i
\(109\) −4.10555 + 7.11102i −0.393240 + 0.681113i −0.992875 0.119162i \(-0.961979\pi\)
0.599634 + 0.800274i \(0.295313\pi\)
\(110\) −24.4966 −2.33566
\(111\) 9.32544 16.1521i 0.885132 1.53309i
\(112\) 0 0
\(113\) −3.40833 + 5.90340i −0.320628 + 0.555345i −0.980618 0.195930i \(-0.937227\pi\)
0.659989 + 0.751275i \(0.270561\pi\)
\(114\) −5.40833 + 9.36750i −0.506536 + 0.877346i
\(115\) 1.31242 0.122383
\(116\) 3.80278 6.58660i 0.353079 0.611551i
\(117\) 2.39607 + 5.63083i 0.221517 + 0.520571i
\(118\) 6.50192 0.598551
\(119\) 0 0
\(120\) −7.04584 12.2037i −0.643194 1.11404i
\(121\) 13.0917 1.19015
\(122\) 4.99082 8.64436i 0.451848 0.782624i
\(123\) 10.8167 + 18.7350i 0.975305 + 1.68928i
\(124\) 23.6417 2.12309
\(125\) 11.4927 1.02794
\(126\) 0 0
\(127\) −3.95416 6.84881i −0.350875 0.607734i 0.635528 0.772078i \(-0.280783\pi\)
−0.986403 + 0.164344i \(0.947449\pi\)
\(128\) 9.45416 16.3751i 0.835638 1.44737i
\(129\) −13.5607 + 23.4878i −1.19395 + 2.06799i
\(130\) −7.04584 16.5579i −0.617961 1.45222i
\(131\) −5.31893 9.21265i −0.464717 0.804913i 0.534472 0.845186i \(-0.320511\pi\)
−0.999189 + 0.0402730i \(0.987177\pi\)
\(132\) 17.5672 + 30.4273i 1.52903 + 2.64836i
\(133\) 0 0
\(134\) −1.15139 + 1.99426i −0.0994648 + 0.172278i
\(135\) 3.05971 + 5.29958i 0.263338 + 0.456115i
\(136\) 10.7372 + 18.5974i 0.920707 + 1.59471i
\(137\) −3.15139 5.45836i −0.269241 0.466339i 0.699425 0.714706i \(-0.253440\pi\)
−0.968666 + 0.248367i \(0.920106\pi\)
\(138\) −1.51110 2.61730i −0.128633 0.222800i
\(139\) −5.31893 + 9.21265i −0.451146 + 0.781407i −0.998457 0.0555216i \(-0.982318\pi\)
0.547312 + 0.836929i \(0.315651\pi\)
\(140\) 0 0
\(141\) 1.63751 + 2.83625i 0.137903 + 0.238855i
\(142\) −4.60555 7.97705i −0.386489 0.669419i
\(143\) 6.92937 + 16.2842i 0.579463 + 1.36175i
\(144\) −0.256939 + 0.445032i −0.0214116 + 0.0370860i
\(145\) −2.49541 + 4.32218i −0.207233 + 0.358938i
\(146\) −4.99082 8.64436i −0.413044 0.715412i
\(147\) 0 0
\(148\) 28.4222 2.33629
\(149\) −17.5139 −1.43479 −0.717396 0.696665i \(-0.754666\pi\)
−0.717396 + 0.696665i \(0.754666\pi\)
\(150\) −0.755550 1.30865i −0.0616904 0.106851i
\(151\) −4.10555 + 7.11102i −0.334105 + 0.578687i −0.983313 0.181924i \(-0.941767\pi\)
0.649207 + 0.760611i \(0.275101\pi\)
\(152\) −6.50192 −0.527376
\(153\) 6.07448 + 10.5213i 0.491092 + 0.850597i
\(154\) 0 0
\(155\) −15.5139 −1.24610
\(156\) −15.5139 + 20.6258i −1.24210 + 1.65139i
\(157\) −0.328104 + 0.568293i −0.0261856 + 0.0453547i −0.878821 0.477151i \(-0.841669\pi\)
0.852636 + 0.522506i \(0.175003\pi\)
\(158\) −15.2111 −1.21013
\(159\) 2.59475 4.49425i 0.205777 0.356417i
\(160\) −5.74637 + 9.95301i −0.454291 + 0.786855i
\(161\) 0 0
\(162\) 12.9083 22.3579i 1.01417 1.75660i
\(163\) −2.78890 −0.218443 −0.109222 0.994017i \(-0.534836\pi\)
−0.109222 + 0.994017i \(0.534836\pi\)
\(164\) −16.4836 + 28.5504i −1.28715 + 2.22941i
\(165\) −11.5278 19.9667i −0.897435 1.55440i
\(166\) 3.25096 5.63083i 0.252324 0.437037i
\(167\) 5.74637 + 9.95301i 0.444668 + 0.770187i 0.998029 0.0627542i \(-0.0199884\pi\)
−0.553361 + 0.832941i \(0.686655\pi\)
\(168\) 0 0
\(169\) −9.01388 + 9.36750i −0.693375 + 0.720577i
\(170\) −17.8625 30.9387i −1.36999 2.37289i
\(171\) −3.67841 −0.281295
\(172\) −41.3305 −3.15142
\(173\) −10.1803 −0.773996 −0.386998 0.922080i \(-0.626488\pi\)
−0.386998 + 0.922080i \(0.626488\pi\)
\(174\) 11.4927 0.871263
\(175\) 0 0
\(176\) −0.743061 + 1.28702i −0.0560103 + 0.0970127i
\(177\) 3.05971 + 5.29958i 0.229982 + 0.398341i
\(178\) 7.48624 + 12.9665i 0.561117 + 0.971883i
\(179\) 21.6056 1.61487 0.807437 0.589953i \(-0.200854\pi\)
0.807437 + 0.589953i \(0.200854\pi\)
\(180\) 6.07448 10.5213i 0.452765 0.784212i
\(181\) 24.2979 1.80605 0.903025 0.429588i \(-0.141341\pi\)
0.903025 + 0.429588i \(0.141341\pi\)
\(182\) 0 0
\(183\) 9.39445 0.694458
\(184\) 0.908327 1.57327i 0.0669627 0.115983i
\(185\) −18.6509 −1.37124
\(186\) 17.8625 + 30.9387i 1.30974 + 2.26854i
\(187\) 17.5672 + 30.4273i 1.28464 + 2.22507i
\(188\) −2.49541 + 4.32218i −0.181997 + 0.315227i
\(189\) 0 0
\(190\) 10.8167 0.784723
\(191\) 15.6972 1.13581 0.567906 0.823094i \(-0.307754\pi\)
0.567906 + 0.823094i \(0.307754\pi\)
\(192\) 27.7776 2.00468
\(193\) 19.8167 1.42643 0.713217 0.700943i \(-0.247237\pi\)
0.713217 + 0.700943i \(0.247237\pi\)
\(194\) −15.7280 27.2417i −1.12921 1.95584i
\(195\) 10.1803 13.5348i 0.729029 0.969250i
\(196\) 0 0
\(197\) 0.545837 + 0.945417i 0.0388892 + 0.0673581i 0.884815 0.465943i \(-0.154285\pi\)
−0.845926 + 0.533301i \(0.820951\pi\)
\(198\) −9.59167 + 16.6133i −0.681651 + 1.18065i
\(199\) −3.57907 6.19912i −0.253713 0.439444i 0.710832 0.703362i \(-0.248319\pi\)
−0.964545 + 0.263918i \(0.914985\pi\)
\(200\) 0.454163 0.786634i 0.0321142 0.0556234i
\(201\) −2.16731 −0.152870
\(202\) −7.48624 + 12.9665i −0.526730 + 0.912323i
\(203\) 0 0
\(204\) −25.6194 + 44.3742i −1.79372 + 3.10681i
\(205\) 10.8167 18.7350i 0.755468 1.30851i
\(206\) −26.4652 −1.84392
\(207\) 0.513878 0.890063i 0.0357170 0.0618637i
\(208\) −1.08365 0.132076i −0.0751379 0.00915781i
\(209\) −10.6379 −0.735836
\(210\) 0 0
\(211\) −7.50000 12.9904i −0.516321 0.894295i −0.999820 0.0189499i \(-0.993968\pi\)
0.483499 0.875345i \(-0.339366\pi\)
\(212\) 7.90833 0.543146
\(213\) 4.33462 7.50778i 0.297003 0.514424i
\(214\) −6.55971 11.3618i −0.448413 0.776674i
\(215\) 27.1214 1.84967
\(216\) 8.47055 0.576348
\(217\) 0 0
\(218\) −9.45416 16.3751i −0.640317 1.10906i
\(219\) 4.69722 8.13583i 0.317409 0.549769i
\(220\) 17.5672 30.4273i 1.18438 2.05141i
\(221\) −15.5139 + 20.6258i −1.04358 + 1.38744i
\(222\) 21.4744 + 37.1947i 1.44127 + 2.49635i
\(223\) −8.99734 15.5838i −0.602506 1.04357i −0.992440 0.122729i \(-0.960836\pi\)
0.389934 0.920843i \(-0.372498\pi\)
\(224\) 0 0
\(225\) 0.256939 0.445032i 0.0171293 0.0296688i
\(226\) −7.84861 13.5942i −0.522082 0.904272i
\(227\) −9.22610 15.9801i −0.612358 1.06063i −0.990842 0.135027i \(-0.956888\pi\)
0.378484 0.925608i \(-0.376445\pi\)
\(228\) −7.75694 13.4354i −0.513716 0.889782i
\(229\) −7.81434 13.5348i −0.516386 0.894407i −0.999819 0.0190256i \(-0.993944\pi\)
0.483433 0.875381i \(-0.339390\pi\)
\(230\) −1.51110 + 2.61730i −0.0996390 + 0.172580i
\(231\) 0 0
\(232\) 3.45416 + 5.98279i 0.226777 + 0.392789i
\(233\) 6.54584 + 11.3377i 0.428832 + 0.742759i 0.996770 0.0803127i \(-0.0255919\pi\)
−0.567938 + 0.823072i \(0.692259\pi\)
\(234\) −13.9882 1.70488i −0.914435 0.111451i
\(235\) 1.63751 2.83625i 0.106819 0.185017i
\(236\) −4.66272 + 8.07607i −0.303517 + 0.525707i
\(237\) −7.15813 12.3982i −0.464971 0.805353i
\(238\) 0 0
\(239\) 4.39445 0.284253 0.142127 0.989848i \(-0.454606\pi\)
0.142127 + 0.989848i \(0.454606\pi\)
\(240\) 1.42221 0.0918029
\(241\) −4.66272 8.07607i −0.300352 0.520225i 0.675863 0.737027i \(-0.263771\pi\)
−0.976216 + 0.216802i \(0.930438\pi\)
\(242\) −15.0736 + 26.1082i −0.968967 + 1.67830i
\(243\) 15.8274 1.01533
\(244\) 7.15813 + 12.3982i 0.458252 + 0.793717i
\(245\) 0 0
\(246\) −49.8167 −3.17619
\(247\) −3.05971 7.19041i −0.194685 0.457515i
\(248\) −10.7372 + 18.5974i −0.681813 + 1.18093i
\(249\) 6.11943 0.387803
\(250\) −13.2326 + 22.9196i −0.836904 + 1.44956i
\(251\) 14.9725 25.9331i 0.945054 1.63688i 0.189411 0.981898i \(-0.439342\pi\)
0.755643 0.654984i \(-0.227325\pi\)
\(252\) 0 0
\(253\) 1.48612 2.57404i 0.0934317 0.161828i
\(254\) 18.2111 1.14267
\(255\) 16.8117 29.1187i 1.05279 1.82348i
\(256\) 8.95416 + 15.5091i 0.559635 + 0.969317i
\(257\) 3.15162 5.45877i 0.196593 0.340508i −0.750829 0.660497i \(-0.770346\pi\)
0.947421 + 0.319988i \(0.103679\pi\)
\(258\) −31.2273 54.0872i −1.94413 3.36732i
\(259\) 0 0
\(260\) 25.6194 + 3.12250i 1.58885 + 0.193649i
\(261\) 1.95416 + 3.38471i 0.120960 + 0.209508i
\(262\) 24.4966 1.51340
\(263\) 15.4222 0.950974 0.475487 0.879723i \(-0.342272\pi\)
0.475487 + 0.879723i \(0.342272\pi\)
\(264\) −31.9136 −1.96414
\(265\) −5.18951 −0.318789
\(266\) 0 0
\(267\) −7.04584 + 12.2037i −0.431198 + 0.746857i
\(268\) −1.65139 2.86029i −0.100875 0.174720i
\(269\) −0.328104 0.568293i −0.0200049 0.0346494i 0.855850 0.517225i \(-0.173035\pi\)
−0.875855 + 0.482575i \(0.839702\pi\)
\(270\) −14.0917 −0.857592
\(271\) 7.25747 12.5703i 0.440860 0.763592i −0.556893 0.830584i \(-0.688007\pi\)
0.997754 + 0.0669918i \(0.0213401\pi\)
\(272\) −2.16731 −0.131412
\(273\) 0 0
\(274\) 14.5139 0.876815
\(275\) 0.743061 1.28702i 0.0448083 0.0776102i
\(276\) 4.33462 0.260913
\(277\) 0.105551 + 0.182820i 0.00634196 + 0.0109846i 0.869179 0.494498i \(-0.164648\pi\)
−0.862837 + 0.505482i \(0.831315\pi\)
\(278\) −12.2483 21.2147i −0.734604 1.27237i
\(279\) −6.07448 + 10.5213i −0.363670 + 0.629894i
\(280\) 0 0
\(281\) 23.8167 1.42078 0.710391 0.703807i \(-0.248518\pi\)
0.710391 + 0.703807i \(0.248518\pi\)
\(282\) −7.54163 −0.449098
\(283\) −18.6509 −1.10868 −0.554340 0.832290i \(-0.687029\pi\)
−0.554340 + 0.832290i \(0.687029\pi\)
\(284\) 13.2111 0.783935
\(285\) 5.09017 + 8.81643i 0.301515 + 0.522240i
\(286\) −40.4534 4.93046i −2.39206 0.291544i
\(287\) 0 0
\(288\) 4.50000 + 7.79423i 0.265165 + 0.459279i
\(289\) −17.1194 + 29.6517i −1.00703 + 1.74422i
\(290\) −5.74637 9.95301i −0.337439 0.584461i
\(291\) 14.8028 25.6392i 0.867754 1.50299i
\(292\) 14.3163 0.837796
\(293\) −14.3163 + 24.7965i −0.836365 + 1.44863i 0.0565490 + 0.998400i \(0.481990\pi\)
−0.892914 + 0.450227i \(0.851343\pi\)
\(294\) 0 0
\(295\) 3.05971 5.29958i 0.178143 0.308554i
\(296\) −12.9083 + 22.3579i −0.750281 + 1.29953i
\(297\) 13.8587 0.804166
\(298\) 20.1653 34.9273i 1.16814 2.02328i
\(299\) 2.16731 + 0.264152i 0.125339 + 0.0152763i
\(300\) 2.16731 0.125130
\(301\) 0 0
\(302\) −9.45416 16.3751i −0.544026 0.942281i
\(303\) −14.0917 −0.809545
\(304\) 0.328104 0.568293i 0.0188181 0.0325938i
\(305\) −4.69722 8.13583i −0.268962 0.465856i
\(306\) −27.9763 −1.59930
\(307\) −3.67841 −0.209938 −0.104969 0.994476i \(-0.533474\pi\)
−0.104969 + 0.994476i \(0.533474\pi\)
\(308\) 0 0
\(309\) −12.4542 21.5712i −0.708493 1.22715i
\(310\) 17.8625 30.9387i 1.01452 1.75720i
\(311\) 5.31893 9.21265i 0.301609 0.522402i −0.674892 0.737917i \(-0.735810\pi\)
0.976501 + 0.215515i \(0.0691430\pi\)
\(312\) −9.17914 21.5712i −0.519667 1.22123i
\(313\) −2.82352 4.89047i −0.159595 0.276426i 0.775128 0.631804i \(-0.217685\pi\)
−0.934723 + 0.355378i \(0.884352\pi\)
\(314\) −0.755550 1.30865i −0.0426382 0.0738514i
\(315\) 0 0
\(316\) 10.9083 18.8938i 0.613641 1.06286i
\(317\) 3.10555 + 5.37897i 0.174425 + 0.302113i 0.939962 0.341279i \(-0.110860\pi\)
−0.765537 + 0.643392i \(0.777527\pi\)
\(318\) 5.97514 + 10.3492i 0.335069 + 0.580357i
\(319\) 5.65139 + 9.78849i 0.316417 + 0.548050i
\(320\) −13.8888 24.0561i −0.776409 1.34478i
\(321\) 6.17382 10.6934i 0.344589 0.596846i
\(322\) 0 0
\(323\) −7.75694 13.4354i −0.431608 0.747566i
\(324\) 18.5139 + 32.0670i 1.02855 + 1.78150i
\(325\) 1.08365 + 0.132076i 0.0601103 + 0.00732625i
\(326\) 3.21110 5.56179i 0.177847 0.308039i
\(327\) 8.89799 15.4118i 0.492060 0.852273i
\(328\) −14.9725 25.9331i −0.826717 1.43192i
\(329\) 0 0
\(330\) 53.0917 2.92260
\(331\) 4.30278 0.236502 0.118251 0.992984i \(-0.462271\pi\)
0.118251 + 0.992984i \(0.462271\pi\)
\(332\) 4.66272 + 8.07607i 0.255900 + 0.443232i
\(333\) −7.30278 + 12.6488i −0.400190 + 0.693149i
\(334\) −26.4652 −1.44811
\(335\) 1.08365 + 1.87694i 0.0592063 + 0.102548i
\(336\) 0 0
\(337\) 18.1194 0.987028 0.493514 0.869738i \(-0.335712\pi\)
0.493514 + 0.869738i \(0.335712\pi\)
\(338\) −8.30278 28.7617i −0.451611 1.56443i
\(339\) 7.38689 12.7945i 0.401201 0.694901i
\(340\) 51.2389 2.77882
\(341\) −17.5672 + 30.4273i −0.951319 + 1.64773i
\(342\) 4.23527 7.33571i 0.229017 0.396670i
\(343\) 0 0
\(344\) 18.7708 32.5120i 1.01205 1.75293i
\(345\) −2.84441 −0.153138
\(346\) 11.7215 20.3023i 0.630152 1.09146i
\(347\) −7.60555 13.1732i −0.408287 0.707174i 0.586411 0.810014i \(-0.300541\pi\)
−0.994698 + 0.102839i \(0.967207\pi\)
\(348\) −8.24179 + 14.2752i −0.441806 + 0.765231i
\(349\) 5.09017 + 8.81643i 0.272470 + 0.471932i 0.969494 0.245116i \(-0.0788260\pi\)
−0.697023 + 0.717048i \(0.745493\pi\)
\(350\) 0 0
\(351\) 3.98612 + 9.36750i 0.212763 + 0.500000i
\(352\) 13.0139 + 22.5407i 0.693642 + 1.20142i
\(353\) 26.4652 1.40860 0.704301 0.709902i \(-0.251261\pi\)
0.704301 + 0.709902i \(0.251261\pi\)
\(354\) −14.0917 −0.748964
\(355\) −8.66923 −0.460115
\(356\) −21.4744 −1.13814
\(357\) 0 0
\(358\) −24.8764 + 43.0871i −1.31476 + 2.27723i
\(359\) 6.04584 + 10.4717i 0.319087 + 0.552675i 0.980298 0.197525i \(-0.0632904\pi\)
−0.661211 + 0.750200i \(0.729957\pi\)
\(360\) 5.51761 + 9.55678i 0.290804 + 0.503687i
\(361\) −14.3028 −0.752778
\(362\) −27.9763 + 48.4564i −1.47040 + 2.54681i
\(363\) −28.3737 −1.48923
\(364\) 0 0
\(365\) −9.39445 −0.491728
\(366\) −10.8167 + 18.7350i −0.565396 + 0.979294i
\(367\) −25.6103 −1.33685 −0.668424 0.743780i \(-0.733031\pi\)
−0.668424 + 0.743780i \(0.733031\pi\)
\(368\) 0.0916731 + 0.158782i 0.00477879 + 0.00827711i
\(369\) −8.47055 14.6714i −0.440959 0.763764i
\(370\) 21.4744 37.1947i 1.11640 1.93366i
\(371\) 0 0
\(372\) −51.2389 −2.65661
\(373\) −12.6972 −0.657437 −0.328719 0.944428i \(-0.606617\pi\)
−0.328719 + 0.944428i \(0.606617\pi\)
\(374\) −80.9068 −4.18359
\(375\) −24.9083 −1.28626
\(376\) −2.26665 3.92595i −0.116894 0.202466i
\(377\) −4.99082 + 6.63534i −0.257041 + 0.341737i
\(378\) 0 0
\(379\) 6.05971 + 10.4957i 0.311267 + 0.539130i 0.978637 0.205596i \(-0.0659134\pi\)
−0.667370 + 0.744726i \(0.732580\pi\)
\(380\) −7.75694 + 13.4354i −0.397923 + 0.689222i
\(381\) 8.56989 + 14.8435i 0.439049 + 0.760455i
\(382\) −18.0736 + 31.3044i −0.924725 + 1.60167i
\(383\) 22.3293 1.14097 0.570487 0.821307i \(-0.306755\pi\)
0.570487 + 0.821307i \(0.306755\pi\)
\(384\) −20.4901 + 35.4899i −1.04563 + 1.81108i
\(385\) 0 0
\(386\) −22.8167 + 39.5196i −1.16134 + 2.01149i
\(387\) 10.6194 18.3934i 0.539816 0.934989i
\(388\) 45.1161 2.29042
\(389\) −14.5139 + 25.1388i −0.735883 + 1.27459i 0.218452 + 0.975848i \(0.429899\pi\)
−0.954335 + 0.298739i \(0.903434\pi\)
\(390\) 15.2705 + 35.8861i 0.773252 + 1.81716i
\(391\) 4.33462 0.219211
\(392\) 0 0
\(393\) 11.5278 + 19.9667i 0.581498 + 1.00718i
\(394\) −2.51388 −0.126647
\(395\) −7.15813 + 12.3982i −0.360165 + 0.623824i
\(396\) −13.7569 23.8277i −0.691312 1.19739i
\(397\) −4.33462 −0.217548 −0.108774 0.994066i \(-0.534693\pi\)
−0.108774 + 0.994066i \(0.534693\pi\)
\(398\) 16.4836 0.826247
\(399\) 0 0
\(400\) 0.0458365 + 0.0793912i 0.00229183 + 0.00396956i
\(401\) 5.05971 8.76368i 0.252670 0.437637i −0.711590 0.702595i \(-0.752025\pi\)
0.964260 + 0.264958i \(0.0853579\pi\)
\(402\) 2.49541 4.32218i 0.124460 0.215571i
\(403\) −25.6194 3.12250i −1.27619 0.155543i
\(404\) −10.7372 18.5974i −0.534196 0.925254i
\(405\) −12.1490 21.0426i −0.603687 1.04562i
\(406\) 0 0
\(407\) −21.1194 + 36.5799i −1.04685 + 1.81320i
\(408\) −23.2708 40.3062i −1.15208 1.99546i
\(409\) 1.73986 + 3.01353i 0.0860306 + 0.149009i 0.905830 0.423642i \(-0.139248\pi\)
−0.819799 + 0.572651i \(0.805915\pi\)
\(410\) 24.9083 + 43.1425i 1.23013 + 2.13066i
\(411\) 6.83003 + 11.8300i 0.336900 + 0.583529i
\(412\) 18.9790 32.8726i 0.935027 1.61952i
\(413\) 0 0
\(414\) 1.18335 + 2.04962i 0.0581583 + 0.100733i
\(415\) −3.05971 5.29958i −0.150195 0.260146i
\(416\) −11.4927 + 15.2797i −0.563478 + 0.749149i
\(417\) 11.5278 19.9667i 0.564517 0.977772i
\(418\) 12.2483 21.2147i 0.599084 1.03764i
\(419\) −8.56989 14.8435i −0.418667 0.725152i 0.577139 0.816646i \(-0.304169\pi\)
−0.995806 + 0.0914942i \(0.970836\pi\)
\(420\) 0 0
\(421\) 5.02776 0.245038 0.122519 0.992466i \(-0.460903\pi\)
0.122519 + 0.992466i \(0.460903\pi\)
\(422\) 34.5416 1.68146
\(423\) −1.28234 2.22107i −0.0623494 0.107992i
\(424\) −3.59167 + 6.22096i −0.174427 + 0.302117i
\(425\) 2.16731 0.105130
\(426\) 9.98165 + 17.2887i 0.483612 + 0.837641i
\(427\) 0 0
\(428\) 18.8167 0.909537
\(429\) −15.0181 35.2929i −0.725080 1.70396i
\(430\) −31.2273 + 54.0872i −1.50591 + 2.60832i
\(431\) −20.9361 −1.00846 −0.504228 0.863571i \(-0.668223\pi\)
−0.504228 + 0.863571i \(0.668223\pi\)
\(432\) −0.427446 + 0.740358i −0.0205655 + 0.0356205i
\(433\) 8.56989 14.8435i 0.411843 0.713332i −0.583249 0.812294i \(-0.698219\pi\)
0.995091 + 0.0989613i \(0.0315520\pi\)
\(434\) 0 0
\(435\) 5.40833 9.36750i 0.259309 0.449137i
\(436\) 27.1194 1.29879
\(437\) −0.656208 + 1.13659i −0.0313907 + 0.0543703i
\(438\) 10.8167 + 18.7350i 0.516840 + 0.895193i
\(439\) −1.83920 + 3.18559i −0.0877804 + 0.152040i −0.906573 0.422050i \(-0.861311\pi\)
0.818792 + 0.574090i \(0.194644\pi\)
\(440\) 15.9568 + 27.6380i 0.760710 + 1.31759i
\(441\) 0 0
\(442\) −23.2708 54.6871i −1.10688 2.60120i
\(443\) 10.1194 + 17.5274i 0.480789 + 0.832750i 0.999757 0.0220431i \(-0.00701711\pi\)
−0.518968 + 0.854793i \(0.673684\pi\)
\(444\) −61.5997 −2.92339
\(445\) 14.0917 0.668009
\(446\) 41.4377 1.96213
\(447\) 37.9580 1.79535
\(448\) 0 0
\(449\) 10.2111 17.6861i 0.481892 0.834661i −0.517892 0.855446i \(-0.673283\pi\)
0.999784 + 0.0207849i \(0.00661652\pi\)
\(450\) 0.591673 + 1.02481i 0.0278917 + 0.0483099i
\(451\) −24.4966 42.4294i −1.15350 1.99792i
\(452\) 22.5139 1.05896
\(453\) 8.89799 15.4118i 0.418064 0.724109i
\(454\) 42.4913 1.99421
\(455\) 0 0
\(456\) 14.0917 0.659903
\(457\) −10.3028 + 17.8449i −0.481944 + 0.834751i −0.999785 0.0207258i \(-0.993402\pi\)
0.517842 + 0.855476i \(0.326736\pi\)
\(458\) 35.9893 1.68167
\(459\) 10.1056 + 17.5033i 0.471687 + 0.816985i
\(460\) −2.16731 3.75389i −0.101051 0.175026i
\(461\) −12.5764 + 21.7830i −0.585741 + 1.01453i 0.409041 + 0.912516i \(0.365863\pi\)
−0.994783 + 0.102018i \(0.967470\pi\)
\(462\) 0 0
\(463\) −13.7889 −0.640824 −0.320412 0.947278i \(-0.603821\pi\)
−0.320412 + 0.947278i \(0.603821\pi\)
\(464\) −0.697224 −0.0323678
\(465\) 33.6234 1.55925
\(466\) −30.1472 −1.39654
\(467\) 6.40258 + 11.0896i 0.296276 + 0.513165i 0.975281 0.220968i \(-0.0709218\pi\)
−0.679005 + 0.734134i \(0.737588\pi\)
\(468\) 12.1490 16.1521i 0.561586 0.746633i
\(469\) 0 0
\(470\) 3.77082 + 6.53125i 0.173935 + 0.301264i
\(471\) 0.711103 1.23167i 0.0327659 0.0567522i
\(472\) −4.23527 7.33571i −0.194944 0.337653i
\(473\) 30.7111 53.1932i 1.41210 2.44583i
\(474\) 32.9671 1.51423
\(475\) −0.328104 + 0.568293i −0.0150544 + 0.0260751i
\(476\) 0 0
\(477\) −2.03196 + 3.51946i −0.0930370 + 0.161145i
\(478\) −5.05971 + 8.76368i −0.231426 + 0.400842i
\(479\) 16.4836 0.753154 0.376577 0.926385i \(-0.377101\pi\)
0.376577 + 0.926385i \(0.377101\pi\)
\(480\) 12.4542 21.5712i 0.568452 0.984588i
\(481\) −30.7998 3.75389i −1.40435 0.171163i
\(482\) 21.4744 0.978132
\(483\) 0 0
\(484\) −21.6194 37.4460i −0.982701 1.70209i
\(485\) −29.6056 −1.34432
\(486\) −18.2234 + 31.5639i −0.826632 + 1.43177i
\(487\) 15.6514 + 27.1090i 0.709232 + 1.22843i 0.965142 + 0.261725i \(0.0842915\pi\)
−0.255910 + 0.966701i \(0.582375\pi\)
\(488\) −13.0038 −0.588657
\(489\) 6.04440 0.273337
\(490\) 0 0
\(491\) −9.86249 17.0823i −0.445088 0.770915i 0.552970 0.833201i \(-0.313494\pi\)
−0.998058 + 0.0622859i \(0.980161\pi\)
\(492\) 35.7250 61.8775i 1.61061 2.78965i
\(493\) −8.24179 + 14.2752i −0.371191 + 0.642922i
\(494\) 17.8625 + 2.17708i 0.803671 + 0.0979516i
\(495\) 9.02741 + 15.6359i 0.405752 + 0.702783i
\(496\) −1.08365 1.87694i −0.0486575 0.0842773i
\(497\) 0 0
\(498\) −7.04584 + 12.2037i −0.315731 + 0.546863i
\(499\) 4.16527 + 7.21445i 0.186463 + 0.322963i 0.944069 0.329749i \(-0.106964\pi\)
−0.757606 + 0.652713i \(0.773631\pi\)
\(500\) −18.9790 32.8726i −0.848766 1.47011i
\(501\) −12.4542 21.5712i −0.556411 0.963732i
\(502\) 34.4782 + 59.7181i 1.53884 + 2.66535i
\(503\) −9.75289 + 16.8925i −0.434860 + 0.753199i −0.997284 0.0736495i \(-0.976535\pi\)
0.562424 + 0.826849i \(0.309869\pi\)
\(504\) 0 0
\(505\) 7.04584 + 12.2037i 0.313536 + 0.543060i
\(506\) 3.42221 + 5.92743i 0.152136 + 0.263507i
\(507\) 19.5359 20.3023i 0.867618 0.901655i
\(508\) −13.0597 + 22.6201i −0.579431 + 1.00360i
\(509\) 10.7372 18.5974i 0.475918 0.824314i −0.523701 0.851902i \(-0.675449\pi\)
0.999619 + 0.0275878i \(0.00878258\pi\)
\(510\) 38.7135 + 67.0538i 1.71426 + 2.96919i
\(511\) 0 0
\(512\) −3.42221 −0.151242
\(513\) −6.11943 −0.270179
\(514\) 7.25747 + 12.5703i 0.320113 + 0.554453i
\(515\) −12.4542 + 21.5712i −0.548796 + 0.950543i
\(516\) 89.5760 3.94336
\(517\) −3.70849 6.42329i −0.163099 0.282496i
\(518\) 0 0
\(519\) 22.0639 0.968498
\(520\) −14.0917 + 18.7350i −0.617961 + 0.821584i
\(521\) −10.8365 + 18.7694i −0.474757 + 0.822304i −0.999582 0.0289063i \(-0.990798\pi\)
0.524825 + 0.851210i \(0.324131\pi\)
\(522\) −9.00000 −0.393919
\(523\) 12.1490 21.0426i 0.531237 0.920129i −0.468099 0.883676i \(-0.655061\pi\)
0.999335 0.0364529i \(-0.0116059\pi\)
\(524\) −17.5672 + 30.4273i −0.767428 + 1.32922i
\(525\) 0 0
\(526\) −17.7569 + 30.7559i −0.774239 + 1.34102i
\(527\) −51.2389 −2.23200
\(528\) 1.61044 2.78937i 0.0700855 0.121392i
\(529\) 11.3167 + 19.6010i 0.492028 + 0.852218i
\(530\) 5.97514 10.3492i 0.259543 0.449542i
\(531\) −2.39607 4.15012i −0.103981 0.180100i
\(532\) 0 0
\(533\) 21.6333 28.7617i 0.937043 1.24581i
\(534\) −16.2250 28.1025i −0.702124 1.21611i
\(535\) −12.3476 −0.533835
\(536\) 3.00000 0.129580
\(537\) −46.8259 −2.02069
\(538\) 1.51110 0.0651481
\(539\) 0 0
\(540\) 10.1056 17.5033i 0.434874 0.753223i
\(541\) −13.9680 24.1934i −0.600533 1.04015i −0.992740 0.120277i \(-0.961622\pi\)
0.392207 0.919877i \(-0.371712\pi\)
\(542\) 16.7123 + 28.9466i 0.717856 + 1.24336i
\(543\) −52.6611 −2.25990
\(544\) −18.9790 + 32.8726i −0.813717 + 1.40940i
\(545\) −17.7960 −0.762296
\(546\) 0 0
\(547\) 29.0000 1.23995 0.619975 0.784621i \(-0.287143\pi\)
0.619975 + 0.784621i \(0.287143\pi\)
\(548\) −10.4083 + 18.0278i −0.444622 + 0.770107i
\(549\) −7.35682 −0.313981
\(550\) 1.71110 + 2.96372i 0.0729617 + 0.126373i
\(551\) −2.49541 4.32218i −0.106308 0.184131i
\(552\) −1.96862 + 3.40976i −0.0837902 + 0.145129i
\(553\) 0 0
\(554\) −0.486122 −0.0206533
\(555\) 40.4222 1.71583
\(556\) 35.1345 1.49003
\(557\) 6.09167 0.258112 0.129056 0.991637i \(-0.458805\pi\)
0.129056 + 0.991637i \(0.458805\pi\)
\(558\) −13.9882 24.2282i −0.592166 1.02566i
\(559\) 44.7880 + 5.45877i 1.89433 + 0.230881i
\(560\) 0 0
\(561\) −38.0736 65.9454i −1.60747 2.78422i
\(562\) −27.4222 + 47.4967i −1.15674 + 2.00353i
\(563\) 0.656208 + 1.13659i 0.0276559 + 0.0479014i 0.879522 0.475858i \(-0.157862\pi\)
−0.851866 + 0.523759i \(0.824529\pi\)
\(564\) 5.40833 9.36750i 0.227732 0.394443i
\(565\) −14.7738 −0.621538
\(566\) 21.4744 37.1947i 0.902636 1.56341i
\(567\) 0 0
\(568\) −6.00000 + 10.3923i −0.251754 + 0.436051i
\(569\) 17.3028 29.9693i 0.725370 1.25638i −0.233451 0.972368i \(-0.575002\pi\)
0.958822 0.284009i \(-0.0916647\pi\)
\(570\) −23.4430 −0.981920
\(571\) 5.36249 9.28811i 0.224413 0.388695i −0.731730 0.681595i \(-0.761287\pi\)
0.956143 + 0.292899i \(0.0946201\pi\)
\(572\) 35.1345 46.7115i 1.46905 1.95311i
\(573\) −34.0207 −1.42124
\(574\) 0 0
\(575\) −0.0916731 0.158782i −0.00382303 0.00662169i
\(576\) −21.7527 −0.906364
\(577\) 16.5829 28.7225i 0.690356 1.19573i −0.281366 0.959601i \(-0.590787\pi\)
0.971721 0.236131i \(-0.0758793\pi\)
\(578\) −39.4222 68.2813i −1.63975 2.84013i
\(579\) −42.9488 −1.78489
\(580\) 16.4836 0.684443
\(581\) 0 0
\(582\) 34.0875 + 59.0412i 1.41297 + 2.44734i
\(583\) −5.87637 + 10.1782i −0.243374 + 0.421537i
\(584\) −6.50192 + 11.2617i −0.269052 + 0.466011i
\(585\) −7.97224 + 10.5992i −0.329612 + 0.438221i
\(586\) −32.9671 57.1008i −1.36186 2.35881i
\(587\) 0.984312 + 1.70488i 0.0406269 + 0.0703679i 0.885624 0.464403i \(-0.153731\pi\)
−0.844997 + 0.534771i \(0.820398\pi\)
\(588\) 0 0
\(589\) 7.75694 13.4354i 0.319619 0.553597i
\(590\) 7.04584 + 12.2037i 0.290072 + 0.502420i
\(591\) −1.18300 2.04901i −0.0486620 0.0842850i
\(592\) −1.30278 2.25647i −0.0535437 0.0927405i
\(593\) 3.15162 + 5.45877i 0.129422 + 0.224165i 0.923453 0.383712i \(-0.125355\pi\)
−0.794031 + 0.607877i \(0.792021\pi\)
\(594\) −15.9568 + 27.6380i −0.654715 + 1.13400i
\(595\) 0 0
\(596\) 28.9222 + 50.0947i 1.18470 + 2.05196i
\(597\) 7.75694 + 13.4354i 0.317470 + 0.549875i
\(598\) −3.02220 + 4.01804i −0.123587 + 0.164310i
\(599\) 5.25694 9.10529i 0.214793 0.372032i −0.738416 0.674346i \(-0.764426\pi\)
0.953208 + 0.302314i \(0.0977591\pi\)
\(600\) −0.984312 + 1.70488i −0.0401844 + 0.0696014i
\(601\) 4.56338 + 7.90400i 0.186144 + 0.322411i 0.943961 0.330056i \(-0.107068\pi\)
−0.757817 + 0.652467i \(0.773734\pi\)
\(602\) 0 0
\(603\) 1.69722 0.0691163
\(604\) 27.1194 1.10347
\(605\) 14.1868 + 24.5723i 0.576777 + 0.999008i
\(606\) 16.2250 28.1025i 0.659095 1.14159i
\(607\) −38.8129 −1.57537 −0.787683 0.616081i \(-0.788719\pi\)
−0.787683 + 0.616081i \(0.788719\pi\)
\(608\) −5.74637 9.95301i −0.233046 0.403648i
\(609\) 0 0
\(610\) 21.6333 0.875907
\(611\) 3.27502 4.35416i 0.132493 0.176151i
\(612\) 20.0626 34.7495i 0.810984 1.40467i
\(613\) 31.9083 1.28877 0.644383 0.764703i \(-0.277114\pi\)
0.644383 + 0.764703i \(0.277114\pi\)
\(614\) 4.23527 7.33571i 0.170922 0.296045i
\(615\) −23.4430 + 40.6045i −0.945314 + 1.63733i
\(616\) 0 0
\(617\) −7.92221 + 13.7217i −0.318936 + 0.552413i −0.980266 0.197681i \(-0.936659\pi\)
0.661330 + 0.750095i \(0.269992\pi\)
\(618\) 57.3583 2.30729
\(619\) −14.9725 + 25.9331i −0.601794 + 1.04234i 0.390755 + 0.920495i \(0.372214\pi\)
−0.992549 + 0.121844i \(0.961119\pi\)
\(620\) 25.6194 + 44.3742i 1.02890 + 1.78211i
\(621\) 0.854892 1.48072i 0.0343056 0.0594191i
\(622\) 12.2483 + 21.2147i 0.491112 + 0.850631i
\(623\) 0 0
\(624\) 2.34861 + 0.286249i 0.0940197 + 0.0114591i
\(625\) 11.6972 + 20.2602i 0.467889 + 0.810407i
\(626\) 13.0038 0.519738
\(627\) 23.0555 0.920748
\(628\) 2.16731 0.0864850
\(629\) −61.5997 −2.45614
\(630\) 0 0
\(631\) −11.4542 + 19.8392i −0.455983 + 0.789786i −0.998744 0.0501013i \(-0.984046\pi\)
0.542761 + 0.839887i \(0.317379\pi\)
\(632\) 9.90833 + 17.1617i 0.394132 + 0.682657i
\(633\) 16.2548 + 28.1542i 0.646071 + 1.11903i
\(634\) −14.3028 −0.568036
\(635\) 8.56989 14.8435i 0.340086 0.589046i
\(636\) −17.1398 −0.679637
\(637\) 0 0
\(638\) −26.0278 −1.03045
\(639\) −3.39445 + 5.87936i −0.134282 + 0.232584i
\(640\) 40.9802 1.61988
\(641\) 7.25694 + 12.5694i 0.286632 + 0.496461i 0.973004 0.230790i \(-0.0741310\pi\)
−0.686372 + 0.727251i \(0.740798\pi\)
\(642\) 14.2169 + 24.6244i 0.561097 + 0.971849i
\(643\) 8.56989 14.8435i 0.337963 0.585370i −0.646086 0.763265i \(-0.723595\pi\)
0.984050 + 0.177895i \(0.0569286\pi\)
\(644\) 0 0
\(645\) −58.7805 −2.31448
\(646\) 35.7250 1.40558
\(647\) 32.9671 1.29607 0.648036 0.761610i \(-0.275591\pi\)
0.648036 + 0.761610i \(0.275591\pi\)
\(648\) −33.6333 −1.32124
\(649\) −6.92937 12.0020i −0.272002 0.471121i
\(650\) −1.51110 + 2.00902i −0.0592702 + 0.0788002i
\(651\) 0 0
\(652\) 4.60555 + 7.97705i 0.180367 + 0.312405i
\(653\) 23.3764 40.4891i 0.914788 1.58446i 0.107577 0.994197i \(-0.465691\pi\)
0.807211 0.590262i \(-0.200976\pi\)
\(654\) 20.4901 + 35.4899i 0.801226 + 1.38776i
\(655\) 11.5278 19.9667i 0.450427 0.780162i
\(656\) 3.02220 0.117997
\(657\) −3.67841 + 6.37119i −0.143508 + 0.248564i
\(658\) 0 0
\(659\) 9.81665 17.0029i 0.382403 0.662341i −0.609003 0.793168i \(-0.708430\pi\)
0.991405 + 0.130828i \(0.0417634\pi\)
\(660\) −38.0736 + 65.9454i −1.48201 + 2.56692i
\(661\) 22.9855 0.894032 0.447016 0.894526i \(-0.352487\pi\)
0.447016 + 0.894526i \(0.352487\pi\)
\(662\) −4.95416 + 8.58086i −0.192549 + 0.333505i
\(663\) 33.6234 44.7025i 1.30582 1.73610i
\(664\) −8.47055 −0.328721
\(665\) 0 0
\(666\) −16.8167 29.1273i −0.651632 1.12866i
\(667\) 1.39445 0.0539933
\(668\) 18.9790 32.8726i 0.734319 1.27188i
\(669\) 19.5000 + 33.7750i 0.753914 + 1.30582i
\(670\) −4.99082 −0.192812
\(671\) −21.2757 −0.821340
\(672\) 0 0
\(673\) 1.10555 + 1.91487i 0.0426159 + 0.0738129i 0.886547 0.462639i \(-0.153098\pi\)
−0.843931 + 0.536452i \(0.819764\pi\)
\(674\) −20.8625 + 36.1349i −0.803593 + 1.39186i
\(675\) 0.427446 0.740358i 0.0164524 0.0284964i
\(676\) 41.6791 + 10.3129i 1.60304 + 0.396651i
\(677\) −13.2326 22.9196i −0.508571 0.880870i −0.999951 0.00992485i \(-0.996841\pi\)
0.491380 0.870945i \(-0.336493\pi\)
\(678\) 17.0104 + 29.4628i 0.653279 + 1.13151i
\(679\) 0 0
\(680\) −23.2708 + 40.3062i −0.892395 + 1.54567i
\(681\) 19.9958 + 34.6337i 0.766241 + 1.32717i
\(682\) −40.4534 70.0673i −1.54904 2.68302i
\(683\) 1.80278 + 3.12250i 0.0689813 + 0.119479i 0.898453 0.439069i \(-0.144692\pi\)
−0.829472 + 0.558549i \(0.811358\pi\)
\(684\) 6.07448 + 10.5213i 0.232263 + 0.402292i
\(685\) 6.83003 11.8300i 0.260962 0.451999i
\(686\) 0 0
\(687\) 16.9361 + 29.3342i 0.646152 + 1.11917i
\(688\) 1.89445 + 3.28128i 0.0722252 + 0.125098i
\(689\) −8.56989 1.04450i −0.326487 0.0397923i
\(690\) 3.27502 5.67250i 0.124678 0.215948i
\(691\) −18.8796 + 32.7005i −0.718215 + 1.24399i 0.243491 + 0.969903i \(0.421707\pi\)
−0.961706 + 0.274082i \(0.911626\pi\)
\(692\) 16.8117 + 29.1187i 0.639084 + 1.10693i
\(693\) 0 0
\(694\) 35.0278 1.32964
\(695\) −23.0555 −0.874545
\(696\) −7.48624 12.9665i −0.283765 0.491495i
\(697\) 35.7250 61.8775i 1.35318 2.34378i
\(698\) −23.4430 −0.887331
\(699\) −14.1868 24.5723i −0.536596 0.929411i
\(700\) 0 0
\(701\) 9.02776 0.340974 0.170487 0.985360i \(-0.445466\pi\)
0.170487 + 0.985360i \(0.445466\pi\)
\(702\) −23.2708 2.83625i −0.878300 0.107047i
\(703\) 9.32544 16.1521i 0.351716 0.609189i
\(704\) −62.9083 −2.37095
\(705\) −3.54899 + 6.14703i −0.133663 + 0.231510i
\(706\) −30.4717 + 52.7786i −1.14682 + 1.98635i
\(707\) 0 0
\(708\) 10.1056 17.5033i 0.379790 0.657815i
\(709\) 32.7250 1.22901 0.614506 0.788912i \(-0.289355\pi\)
0.614506 + 0.788912i \(0.289355\pi\)
\(710\) 9.98165 17.2887i 0.374605 0.648834i
\(711\) 5.60555 + 9.70910i 0.210225 + 0.364120i
\(712\) 9.75289 16.8925i 0.365505 0.633073i
\(713\) 2.16731 + 3.75389i 0.0811663 + 0.140584i
\(714\) 0 0
\(715\) −23.0555 + 30.6525i −0.862227 + 1.14634i
\(716\) −35.6791 61.7981i −1.33339 2.30950i
\(717\) −9.52412 −0.355685
\(718\) −27.8444 −1.03914
\(719\) 22.7868 0.849805 0.424902 0.905239i \(-0.360308\pi\)
0.424902 + 0.905239i \(0.360308\pi\)
\(720\) −1.11373 −0.0415064
\(721\) 0 0
\(722\) 16.4680 28.5235i 0.612877 1.06153i
\(723\) 10.1056 + 17.5033i 0.375829 + 0.650956i
\(724\) −40.1253 69.4990i −1.49124 2.58291i
\(725\) 0.697224 0.0258943
\(726\) 32.6691 56.5846i 1.21246 2.10005i
\(727\) −37.1031 −1.37608 −0.688038 0.725674i \(-0.741528\pi\)
−0.688038 + 0.725674i \(0.741528\pi\)
\(728\) 0 0
\(729\) −0.669468 −0.0247951
\(730\) 10.8167 18.7350i 0.400342 0.693413i
\(731\) 89.5760 3.31309
\(732\) −15.5139 26.8708i −0.573409 0.993174i
\(733\) −3.35030 5.80290i −0.123746 0.214335i 0.797496 0.603324i \(-0.206158\pi\)
−0.921242 + 0.388990i \(0.872824\pi\)
\(734\) 29.4874 51.0737i 1.08840 1.88517i
\(735\) 0 0
\(736\) 3.21110 0.118363
\(737\) 4.90833 0.180801
\(738\) 39.0115 1.43603
\(739\) −33.2111 −1.22169 −0.610845 0.791750i \(-0.709170\pi\)
−0.610845 + 0.791750i \(0.709170\pi\)
\(740\) 30.7998 + 53.3469i 1.13222 + 1.96107i
\(741\) 6.63134 + 15.5838i 0.243609 + 0.572487i
\(742\) 0 0
\(743\) 20.6514 + 35.7693i 0.757626 + 1.31225i 0.944058 + 0.329779i \(0.106974\pi\)
−0.186432 + 0.982468i \(0.559692\pi\)
\(744\) 23.2708 40.3062i 0.853150 1.47770i
\(745\) −18.9790 32.8726i −0.695336 1.20436i
\(746\) 14.6194 25.3216i 0.535255 0.927089i
\(747\) −4.79214 −0.175335
\(748\) 58.0206 100.495i 2.12144 3.67445i
\(749\) 0 0
\(750\) 28.6791 49.6737i 1.04721 1.81383i
\(751\) 5.80278 10.0507i 0.211746 0.366755i −0.740515 0.672040i \(-0.765418\pi\)
0.952261 + 0.305285i \(0.0987516\pi\)
\(752\) 0.457524 0.0166842
\(753\) −32.4500 + 56.2050i −1.18254 + 2.04822i
\(754\) −7.48624 17.5929i −0.272633 0.640694i
\(755\) −17.7960 −0.647662
\(756\) 0 0
\(757\) −3.11943 5.40301i −0.113378 0.196376i 0.803752 0.594964i \(-0.202834\pi\)
−0.917130 + 0.398588i \(0.869500\pi\)
\(758\) −27.9083 −1.01368
\(759\) −3.22088 + 5.57873i −0.116911 + 0.202495i
\(760\) −7.04584 12.2037i −0.255579 0.442676i
\(761\) 42.2926 1.53311 0.766553 0.642182i \(-0.221971\pi\)
0.766553 + 0.642182i \(0.221971\pi\)
\(762\) −39.4691 −1.42981
\(763\) 0 0
\(764\) −25.9222 44.8986i −0.937832 1.62437i
\(765\) −13.1653 + 22.8029i −0.475991 + 0.824441i
\(766\) −25.7097 + 44.5305i −0.928928 + 1.60895i
\(767\) 6.11943 8.13583i 0.220960 0.293768i
\(768\) −19.4064 33.6129i −0.700269 1.21290i
\(769\) 23.5424 + 40.7766i 0.848959 + 1.47044i 0.882138 + 0.470991i \(0.156104\pi\)
−0.0331785 + 0.999449i \(0.510563\pi\)
\(770\) 0 0
\(771\) −6.83053 + 11.8308i −0.245996 + 0.426077i
\(772\) −32.7250 56.6813i −1.17780 2.04001i
\(773\) 14.2169 + 24.6244i 0.511347 + 0.885679i 0.999914 + 0.0131525i \(0.00418670\pi\)
−0.488566 + 0.872527i \(0.662480\pi\)
\(774\) 24.4542 + 42.3559i 0.878987 + 1.52245i
\(775\) 1.08365 + 1.87694i 0.0389260 + 0.0674218i
\(776\) −20.4901 + 35.4899i −0.735551 + 1.27401i
\(777\) 0 0
\(778\) −33.4222 57.8890i −1.19824 2.07542i
\(779\) 10.8167 + 18.7350i 0.387547 + 0.671251i
\(780\) −55.5252 6.76742i −1.98812 0.242312i
\(781\) −9.81665 + 17.0029i −0.351267 + 0.608413i
\(782\) −4.99082 + 8.64436i −0.178472 + 0.309122i
\(783\) 3.25096 +