Properties

Label 637.2.e.l.79.2
Level $637$
Weight $2$
Character 637.79
Analytic conductor $5.086$
Analytic rank $0$
Dimension $6$
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: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.4406832.1
Defining polynomial: \(x^{6} - x^{5} + 6 x^{4} + 7 x^{3} + 24 x^{2} + 5 x + 1\)
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 79.2
Root \(-0.105378 - 0.182520i\) of defining polynomial
Character \(\chi\) \(=\) 637.79
Dual form 637.2.e.l.508.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.605378 - 1.04855i) q^{2} +(-0.872413 - 1.51106i) q^{3} +(0.267035 + 0.462518i) q^{4} +(1.10538 - 1.91457i) q^{5} -2.11256 q^{6} +3.06814 q^{8} +(-0.0222090 + 0.0384672i) q^{9} +O(q^{10})\) \(q+(0.605378 - 1.04855i) q^{2} +(-0.872413 - 1.51106i) q^{3} +(0.267035 + 0.462518i) q^{4} +(1.10538 - 1.91457i) q^{5} -2.11256 q^{6} +3.06814 q^{8} +(-0.0222090 + 0.0384672i) q^{9} +(-1.33834 - 2.31808i) q^{10} +(0.394622 + 0.683505i) q^{11} +(0.465930 - 0.807014i) q^{12} +1.00000 q^{13} -3.85738 q^{15} +(1.32331 - 2.29205i) q^{16} +(-0.872413 - 1.51106i) q^{17} +(0.0268897 + 0.0465743i) q^{18} +(2.16166 - 3.74410i) q^{19} +1.18070 q^{20} +0.955582 q^{22} +(0.556279 - 0.963504i) q^{23} +(-2.67669 - 4.63616i) q^{24} +(0.0562792 + 0.0974785i) q^{25} +(0.605378 - 1.04855i) q^{26} -5.15698 q^{27} -8.48965 q^{29} +(-2.33518 + 4.04464i) q^{30} +(2.85020 + 4.93670i) q^{31} +(1.46593 + 2.53906i) q^{32} +(0.688547 - 1.19260i) q^{33} -2.11256 q^{34} -0.0237224 q^{36} +(-1.13945 + 1.97358i) q^{37} +(-2.61724 - 4.53319i) q^{38} +(-0.872413 - 1.51106i) q^{39} +(3.39145 - 5.87417i) q^{40} -12.1363 q^{41} +8.06814 q^{43} +(-0.210756 + 0.365040i) q^{44} +(0.0490987 + 0.0850415i) q^{45} +(-0.673518 - 1.16657i) q^{46} +(4.37241 - 7.57324i) q^{47} -4.61791 q^{48} +0.136281 q^{50} +(-1.52221 + 2.63654i) q^{51} +(0.267035 + 0.462518i) q^{52} +(-3.97779 - 6.88974i) q^{53} +(-3.12192 + 5.40732i) q^{54} +1.74483 q^{55} -7.54343 q^{57} +(-5.13945 + 8.90179i) q^{58} +(5.47779 + 9.48781i) q^{59} +(-1.03006 - 1.78411i) q^{60} +(-6.53407 + 11.3173i) q^{61} +6.90180 q^{62} +8.84302 q^{64} +(1.10538 - 1.91457i) q^{65} +(-0.833662 - 1.44395i) q^{66} +(-3.27890 - 5.67921i) q^{67} +(0.465930 - 0.807014i) q^{68} -1.94122 q^{69} +5.85738 q^{71} +(-0.0681404 + 0.118023i) q^{72} +(4.00468 + 6.93631i) q^{73} +(1.37959 + 2.38953i) q^{74} +(0.0981974 - 0.170083i) q^{75} +2.30895 q^{76} -2.11256 q^{78} +(3.45558 - 5.98524i) q^{79} +(-2.92552 - 5.06716i) q^{80} +(4.56564 + 7.90792i) q^{81} +(-7.34704 + 12.7254i) q^{82} -3.14262 q^{83} -3.85738 q^{85} +(4.88427 - 8.45981i) q^{86} +(7.40648 + 12.8284i) q^{87} +(1.21076 + 2.09709i) q^{88} +(1.69573 - 2.93709i) q^{89} +0.118893 q^{90} +0.594184 q^{92} +(4.97311 - 8.61368i) q^{93} +(-5.29392 - 9.16935i) q^{94} +(-4.77890 - 8.27729i) q^{95} +(2.55779 - 4.43023i) q^{96} +0.0981974 q^{97} -0.0350567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{2} + 4q^{3} - 6q^{4} + 5q^{5} - 4q^{6} - 12q^{8} - 11q^{9} + O(q^{10}) \) \( 6q + 2q^{2} + 4q^{3} - 6q^{4} + 5q^{5} - 4q^{6} - 12q^{8} - 11q^{9} - 14q^{10} + 4q^{11} + 18q^{12} + 6q^{13} + 4q^{15} - 4q^{16} + 4q^{17} - 8q^{18} + 7q^{19} - 32q^{20} - 16q^{22} - q^{23} - 28q^{24} - 4q^{25} + 2q^{26} - 44q^{27} - 14q^{29} + 24q^{30} - 3q^{31} + 24q^{32} - 10q^{33} - 4q^{34} + 52q^{36} + 10q^{37} + 12q^{38} + 4q^{39} - 22q^{40} - 12q^{41} + 18q^{43} + 2q^{44} + 3q^{45} + 28q^{46} + 17q^{47} - 32q^{48} - 60q^{50} - 20q^{51} - 6q^{52} - 13q^{53} + 28q^{54} - 8q^{55} + 8q^{57} - 14q^{58} + 22q^{59} - 42q^{60} - 24q^{61} + 36q^{62} + 40q^{64} + 5q^{65} - 30q^{66} + 14q^{67} + 18q^{68} - 4q^{69} + 8q^{71} + 30q^{72} + 5q^{73} - 8q^{74} + 6q^{75} + 16q^{76} - 4q^{78} - q^{79} + 40q^{80} - 15q^{81} + 20q^{82} - 46q^{83} + 4q^{85} - 6q^{86} + 20q^{87} + 4q^{88} - 11q^{89} + 80q^{90} + 60q^{92} + 38q^{93} - 16q^{94} + 5q^{95} - 52q^{96} + 6q^{97} - 60q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.605378 1.04855i 0.428067 0.741434i −0.568635 0.822590i \(-0.692528\pi\)
0.996701 + 0.0811568i \(0.0258614\pi\)
\(3\) −0.872413 1.51106i −0.503688 0.872413i −0.999991 0.00426367i \(-0.998643\pi\)
0.496303 0.868149i \(-0.334691\pi\)
\(4\) 0.267035 + 0.462518i 0.133518 + 0.231259i
\(5\) 1.10538 1.91457i 0.494340 0.856222i −0.505639 0.862745i \(-0.668743\pi\)
0.999979 + 0.00652327i \(0.00207644\pi\)
\(6\) −2.11256 −0.862448
\(7\) 0 0
\(8\) 3.06814 1.08475
\(9\) −0.0222090 + 0.0384672i −0.00740301 + 0.0128224i
\(10\) −1.33834 2.31808i −0.423221 0.733041i
\(11\) 0.394622 + 0.683505i 0.118983 + 0.206085i 0.919365 0.393406i \(-0.128703\pi\)
−0.800382 + 0.599490i \(0.795370\pi\)
\(12\) 0.465930 0.807014i 0.134502 0.232965i
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −3.85738 −0.995972
\(16\) 1.32331 2.29205i 0.330829 0.573012i
\(17\) −0.872413 1.51106i −0.211591 0.366487i 0.740621 0.671923i \(-0.234531\pi\)
−0.952213 + 0.305436i \(0.901198\pi\)
\(18\) 0.0268897 + 0.0465743i 0.00633796 + 0.0109777i
\(19\) 2.16166 3.74410i 0.495918 0.858955i −0.504071 0.863662i \(-0.668165\pi\)
0.999989 + 0.00470690i \(0.00149826\pi\)
\(20\) 1.18070 0.264012
\(21\) 0 0
\(22\) 0.955582 0.203731
\(23\) 0.556279 0.963504i 0.115992 0.200904i −0.802184 0.597077i \(-0.796329\pi\)
0.918176 + 0.396173i \(0.129662\pi\)
\(24\) −2.67669 4.63616i −0.546376 0.946351i
\(25\) 0.0562792 + 0.0974785i 0.0112558 + 0.0194957i
\(26\) 0.605378 1.04855i 0.118724 0.205637i
\(27\) −5.15698 −0.992461
\(28\) 0 0
\(29\) −8.48965 −1.57649 −0.788244 0.615362i \(-0.789010\pi\)
−0.788244 + 0.615362i \(0.789010\pi\)
\(30\) −2.33518 + 4.04464i −0.426343 + 0.738447i
\(31\) 2.85020 + 4.93670i 0.511912 + 0.886657i 0.999905 + 0.0138096i \(0.00439586\pi\)
−0.487993 + 0.872848i \(0.662271\pi\)
\(32\) 1.46593 + 2.53906i 0.259142 + 0.448848i
\(33\) 0.688547 1.19260i 0.119861 0.207605i
\(34\) −2.11256 −0.362301
\(35\) 0 0
\(36\) −0.0237224 −0.00395373
\(37\) −1.13945 + 1.97358i −0.187324 + 0.324455i −0.944357 0.328922i \(-0.893315\pi\)
0.757033 + 0.653377i \(0.226648\pi\)
\(38\) −2.61724 4.53319i −0.424572 0.735381i
\(39\) −0.872413 1.51106i −0.139698 0.241964i
\(40\) 3.39145 5.87417i 0.536236 0.928788i
\(41\) −12.1363 −1.89537 −0.947684 0.319209i \(-0.896583\pi\)
−0.947684 + 0.319209i \(0.896583\pi\)
\(42\) 0 0
\(43\) 8.06814 1.23038 0.615190 0.788379i \(-0.289079\pi\)
0.615190 + 0.788379i \(0.289079\pi\)
\(44\) −0.210756 + 0.365040i −0.0317726 + 0.0550318i
\(45\) 0.0490987 + 0.0850415i 0.00731921 + 0.0126772i
\(46\) −0.673518 1.16657i −0.0993049 0.172001i
\(47\) 4.37241 7.57324i 0.637782 1.10467i −0.348136 0.937444i \(-0.613185\pi\)
0.985918 0.167227i \(-0.0534813\pi\)
\(48\) −4.61791 −0.666537
\(49\) 0 0
\(50\) 0.136281 0.0192730
\(51\) −1.52221 + 2.63654i −0.213152 + 0.369190i
\(52\) 0.267035 + 0.462518i 0.0370311 + 0.0641398i
\(53\) −3.97779 6.88974i −0.546392 0.946378i −0.998518 0.0544241i \(-0.982668\pi\)
0.452126 0.891954i \(-0.350666\pi\)
\(54\) −3.12192 + 5.40732i −0.424839 + 0.735844i
\(55\) 1.74483 0.235272
\(56\) 0 0
\(57\) −7.54343 −0.999152
\(58\) −5.13945 + 8.90179i −0.674843 + 1.16886i
\(59\) 5.47779 + 9.48781i 0.713148 + 1.23521i 0.963670 + 0.267097i \(0.0860644\pi\)
−0.250522 + 0.968111i \(0.580602\pi\)
\(60\) −1.03006 1.78411i −0.132980 0.230328i
\(61\) −6.53407 + 11.3173i −0.836602 + 1.44904i 0.0561175 + 0.998424i \(0.482128\pi\)
−0.892719 + 0.450613i \(0.851205\pi\)
\(62\) 6.90180 0.876530
\(63\) 0 0
\(64\) 8.84302 1.10538
\(65\) 1.10538 1.91457i 0.137105 0.237473i
\(66\) −0.833662 1.44395i −0.102617 0.177737i
\(67\) −3.27890 5.67921i −0.400581 0.693827i 0.593215 0.805044i \(-0.297858\pi\)
−0.993796 + 0.111217i \(0.964525\pi\)
\(68\) 0.465930 0.807014i 0.0565023 0.0978648i
\(69\) −1.94122 −0.233696
\(70\) 0 0
\(71\) 5.85738 0.695144 0.347572 0.937653i \(-0.387006\pi\)
0.347572 + 0.937653i \(0.387006\pi\)
\(72\) −0.0681404 + 0.118023i −0.00803042 + 0.0139091i
\(73\) 4.00468 + 6.93631i 0.468712 + 0.811834i 0.999360 0.0357585i \(-0.0113847\pi\)
−0.530648 + 0.847592i \(0.678051\pi\)
\(74\) 1.37959 + 2.38953i 0.160374 + 0.277777i
\(75\) 0.0981974 0.170083i 0.0113389 0.0196395i
\(76\) 2.30895 0.264855
\(77\) 0 0
\(78\) −2.11256 −0.239200
\(79\) 3.45558 5.98524i 0.388783 0.673393i −0.603503 0.797361i \(-0.706229\pi\)
0.992286 + 0.123968i \(0.0395621\pi\)
\(80\) −2.92552 5.06716i −0.327084 0.566525i
\(81\) 4.56564 + 7.90792i 0.507293 + 0.878658i
\(82\) −7.34704 + 12.7254i −0.811344 + 1.40529i
\(83\) −3.14262 −0.344947 −0.172473 0.985014i \(-0.555176\pi\)
−0.172473 + 0.985014i \(0.555176\pi\)
\(84\) 0 0
\(85\) −3.85738 −0.418392
\(86\) 4.88427 8.45981i 0.526685 0.912245i
\(87\) 7.40648 + 12.8284i 0.794058 + 1.37535i
\(88\) 1.21076 + 2.09709i 0.129067 + 0.223551i
\(89\) 1.69573 2.93709i 0.179747 0.311330i −0.762047 0.647522i \(-0.775806\pi\)
0.941794 + 0.336191i \(0.109139\pi\)
\(90\) 0.118893 0.0125324
\(91\) 0 0
\(92\) 0.594184 0.0619480
\(93\) 4.97311 8.61368i 0.515688 0.893197i
\(94\) −5.29392 9.16935i −0.546027 0.945746i
\(95\) −4.77890 8.27729i −0.490304 0.849232i
\(96\) 2.55779 4.43023i 0.261054 0.452158i
\(97\) 0.0981974 0.00997044 0.00498522 0.999988i \(-0.498413\pi\)
0.00498522 + 0.999988i \(0.498413\pi\)
\(98\) 0 0
\(99\) −0.0350567 −0.00352333
\(100\) −0.0300571 + 0.0520603i −0.00300571 + 0.00520603i
\(101\) 3.45090 + 5.97714i 0.343378 + 0.594747i 0.985058 0.172225i \(-0.0550956\pi\)
−0.641680 + 0.766972i \(0.721762\pi\)
\(102\) 1.84302 + 3.19221i 0.182487 + 0.316076i
\(103\) −7.91116 + 13.7025i −0.779510 + 1.35015i 0.152714 + 0.988270i \(0.451199\pi\)
−0.932224 + 0.361881i \(0.882135\pi\)
\(104\) 3.06814 0.300856
\(105\) 0 0
\(106\) −9.63227 −0.935569
\(107\) 1.01186 1.75259i 0.0978203 0.169430i −0.812962 0.582317i \(-0.802146\pi\)
0.910782 + 0.412887i \(0.135480\pi\)
\(108\) −1.37709 2.38520i −0.132511 0.229516i
\(109\) 8.67352 + 15.0230i 0.830772 + 1.43894i 0.897427 + 0.441164i \(0.145434\pi\)
−0.0666542 + 0.997776i \(0.521232\pi\)
\(110\) 1.05628 1.82953i 0.100712 0.174439i
\(111\) 3.97628 0.377412
\(112\) 0 0
\(113\) 10.1807 0.957720 0.478860 0.877891i \(-0.341050\pi\)
0.478860 + 0.877891i \(0.341050\pi\)
\(114\) −4.56663 + 7.90963i −0.427704 + 0.740805i
\(115\) −1.22980 2.13007i −0.114679 0.198630i
\(116\) −2.26704 3.92662i −0.210489 0.364578i
\(117\) −0.0222090 + 0.0384672i −0.00205322 + 0.00355629i
\(118\) 13.2645 1.22110
\(119\) 0 0
\(120\) −11.8350 −1.08038
\(121\) 5.18855 8.98683i 0.471686 0.816984i
\(122\) 7.91116 + 13.7025i 0.716243 + 1.24057i
\(123\) 10.5878 + 18.3387i 0.954674 + 1.65354i
\(124\) −1.52221 + 2.63654i −0.136698 + 0.236769i
\(125\) 11.3026 1.01094
\(126\) 0 0
\(127\) 16.4452 1.45928 0.729639 0.683832i \(-0.239688\pi\)
0.729639 + 0.683832i \(0.239688\pi\)
\(128\) 2.42151 4.19418i 0.214033 0.370717i
\(129\) −7.03875 12.1915i −0.619727 1.07340i
\(130\) −1.33834 2.31808i −0.117380 0.203309i
\(131\) 6.16634 10.6804i 0.538755 0.933152i −0.460216 0.887807i \(-0.652228\pi\)
0.998971 0.0453448i \(-0.0144386\pi\)
\(132\) 0.735465 0.0640140
\(133\) 0 0
\(134\) −7.93989 −0.685902
\(135\) −5.70041 + 9.87340i −0.490613 + 0.849767i
\(136\) −2.67669 4.63616i −0.229524 0.397547i
\(137\) 1.67352 + 2.89862i 0.142978 + 0.247646i 0.928617 0.371040i \(-0.120999\pi\)
−0.785639 + 0.618686i \(0.787665\pi\)
\(138\) −1.17517 + 2.03546i −0.100037 + 0.173270i
\(139\) 6.16634 0.523022 0.261511 0.965201i \(-0.415779\pi\)
0.261511 + 0.965201i \(0.415779\pi\)
\(140\) 0 0
\(141\) −15.2582 −1.28497
\(142\) 3.54593 6.14173i 0.297568 0.515403i
\(143\) 0.394622 + 0.683505i 0.0330000 + 0.0571576i
\(144\) 0.0587790 + 0.101808i 0.00489825 + 0.00848402i
\(145\) −9.38427 + 16.2540i −0.779322 + 1.34982i
\(146\) 9.69738 0.802561
\(147\) 0 0
\(148\) −1.21709 −0.100044
\(149\) −9.41834 + 16.3131i −0.771581 + 1.33642i 0.165115 + 0.986274i \(0.447200\pi\)
−0.936696 + 0.350143i \(0.886133\pi\)
\(150\) −0.118893 0.205929i −0.00970758 0.0168140i
\(151\) −10.0950 17.4851i −0.821522 1.42292i −0.904549 0.426370i \(-0.859792\pi\)
0.0830268 0.996547i \(-0.473541\pi\)
\(152\) 6.63227 11.4874i 0.537948 0.931753i
\(153\) 0.0775018 0.00626565
\(154\) 0 0
\(155\) 12.6022 1.01223
\(156\) 0.465930 0.807014i 0.0373042 0.0646128i
\(157\) 6.94055 + 12.0214i 0.553916 + 0.959411i 0.997987 + 0.0634196i \(0.0202006\pi\)
−0.444070 + 0.895992i \(0.646466\pi\)
\(158\) −4.18387 7.24667i −0.332851 0.576514i
\(159\) −6.94055 + 12.0214i −0.550422 + 0.953358i
\(160\) 6.48163 0.512418
\(161\) 0 0
\(162\) 11.0558 0.868622
\(163\) −5.74483 + 9.95033i −0.449970 + 0.779370i −0.998383 0.0568369i \(-0.981898\pi\)
0.548414 + 0.836207i \(0.315232\pi\)
\(164\) −3.24081 5.61325i −0.253065 0.438321i
\(165\) −1.52221 2.63654i −0.118504 0.205255i
\(166\) −1.90247 + 3.29517i −0.147660 + 0.255755i
\(167\) 12.9699 1.00364 0.501822 0.864971i \(-0.332663\pi\)
0.501822 + 0.864971i \(0.332663\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −2.33518 + 4.04464i −0.179100 + 0.310210i
\(171\) 0.0960166 + 0.166306i 0.00734257 + 0.0127177i
\(172\) 2.15448 + 3.73166i 0.164277 + 0.284537i
\(173\) 1.24015 2.14799i 0.0942865 0.163309i −0.815024 0.579427i \(-0.803276\pi\)
0.909311 + 0.416118i \(0.136610\pi\)
\(174\) 17.9349 1.35964
\(175\) 0 0
\(176\) 2.08884 0.157452
\(177\) 9.55779 16.5546i 0.718408 1.24432i
\(178\) −2.05311 3.55609i −0.153887 0.266541i
\(179\) 4.07849 + 7.06415i 0.304841 + 0.527999i 0.977226 0.212202i \(-0.0680635\pi\)
−0.672385 + 0.740201i \(0.734730\pi\)
\(180\) −0.0262222 + 0.0454181i −0.00195448 + 0.00338527i
\(181\) −3.60855 −0.268221 −0.134111 0.990966i \(-0.542818\pi\)
−0.134111 + 0.990966i \(0.542818\pi\)
\(182\) 0 0
\(183\) 22.8016 1.68555
\(184\) 1.70674 2.95617i 0.125823 0.217931i
\(185\) 2.51904 + 4.36311i 0.185204 + 0.320782i
\(186\) −6.02122 10.4291i −0.441497 0.764696i
\(187\) 0.688547 1.19260i 0.0503515 0.0872114i
\(188\) 4.67035 0.340620
\(189\) 0 0
\(190\) −11.5722 −0.839532
\(191\) −0.168838 + 0.292435i −0.0122167 + 0.0211599i −0.872069 0.489383i \(-0.837222\pi\)
0.859852 + 0.510543i \(0.170555\pi\)
\(192\) −7.71477 13.3624i −0.556765 0.964346i
\(193\) −4.21076 7.29324i −0.303097 0.524979i 0.673739 0.738969i \(-0.264687\pi\)
−0.976836 + 0.213990i \(0.931354\pi\)
\(194\) 0.0594466 0.102964i 0.00426801 0.00739242i
\(195\) −3.85738 −0.276233
\(196\) 0 0
\(197\) −8.51035 −0.606337 −0.303169 0.952937i \(-0.598045\pi\)
−0.303169 + 0.952937i \(0.598045\pi\)
\(198\) −0.0212225 + 0.0367585i −0.00150822 + 0.00261231i
\(199\) −7.30829 12.6583i −0.518071 0.897325i −0.999780 0.0209934i \(-0.993317\pi\)
0.481709 0.876331i \(-0.340016\pi\)
\(200\) 0.172673 + 0.299078i 0.0122098 + 0.0211480i
\(201\) −5.72110 + 9.90924i −0.403536 + 0.698944i
\(202\) 8.35640 0.587954
\(203\) 0 0
\(204\) −1.62593 −0.113838
\(205\) −13.4152 + 23.2358i −0.936957 + 1.62286i
\(206\) 9.57849 + 16.5904i 0.667365 + 1.15591i
\(207\) 0.0247088 + 0.0427970i 0.00171738 + 0.00297459i
\(208\) 1.32331 2.29205i 0.0917553 0.158925i
\(209\) 3.41215 0.236023
\(210\) 0 0
\(211\) −23.8667 −1.64305 −0.821527 0.570169i \(-0.806878\pi\)
−0.821527 + 0.570169i \(0.806878\pi\)
\(212\) 2.12442 3.67960i 0.145906 0.252716i
\(213\) −5.11006 8.85088i −0.350135 0.606452i
\(214\) −1.22512 2.12196i −0.0837473 0.145055i
\(215\) 8.91834 15.4470i 0.608226 1.05348i
\(216\) −15.8223 −1.07657
\(217\) 0 0
\(218\) 21.0030 1.42250
\(219\) 6.98747 12.1027i 0.472170 0.817822i
\(220\) 0.465930 + 0.807014i 0.0314130 + 0.0544089i
\(221\) −0.872413 1.51106i −0.0586849 0.101645i
\(222\) 2.40715 4.16931i 0.161557 0.279826i
\(223\) −1.27890 −0.0856412 −0.0428206 0.999083i \(-0.513634\pi\)
−0.0428206 + 0.999083i \(0.513634\pi\)
\(224\) 0 0
\(225\) −0.00499963 −0.000333308
\(226\) 6.16317 10.6749i 0.409968 0.710085i
\(227\) 4.78924 + 8.29521i 0.317873 + 0.550573i 0.980044 0.198780i \(-0.0636980\pi\)
−0.662171 + 0.749353i \(0.730365\pi\)
\(228\) −2.01436 3.48898i −0.133404 0.231063i
\(229\) −6.75669 + 11.7029i −0.446494 + 0.773351i −0.998155 0.0607177i \(-0.980661\pi\)
0.551661 + 0.834069i \(0.313994\pi\)
\(230\) −2.97797 −0.196361
\(231\) 0 0
\(232\) −26.0474 −1.71010
\(233\) −14.4793 + 25.0789i −0.948571 + 1.64297i −0.200132 + 0.979769i \(0.564137\pi\)
−0.748439 + 0.663204i \(0.769196\pi\)
\(234\) 0.0268897 + 0.0465743i 0.00175783 + 0.00304466i
\(235\) −9.66634 16.7426i −0.630562 1.09217i
\(236\) −2.92552 + 5.06716i −0.190435 + 0.329844i
\(237\) −12.0588 −0.783302
\(238\) 0 0
\(239\) −24.1363 −1.56125 −0.780623 0.625002i \(-0.785098\pi\)
−0.780623 + 0.625002i \(0.785098\pi\)
\(240\) −5.10453 + 8.84131i −0.329496 + 0.570704i
\(241\) −4.96276 8.59576i −0.319680 0.553701i 0.660742 0.750614i \(-0.270242\pi\)
−0.980421 + 0.196912i \(0.936909\pi\)
\(242\) −6.28206 10.8809i −0.403826 0.699448i
\(243\) 0.230784 0.399730i 0.0148048 0.0256427i
\(244\) −6.97930 −0.446804
\(245\) 0 0
\(246\) 25.6386 1.63466
\(247\) 2.16166 3.74410i 0.137543 0.238231i
\(248\) 8.74483 + 15.1465i 0.555297 + 0.961803i
\(249\) 2.74166 + 4.74869i 0.173746 + 0.300936i
\(250\) 6.84236 11.8513i 0.432749 0.749543i
\(251\) −18.4990 −1.16765 −0.583824 0.811880i \(-0.698444\pi\)
−0.583824 + 0.811880i \(0.698444\pi\)
\(252\) 0 0
\(253\) 0.878080 0.0552044
\(254\) 9.95558 17.2436i 0.624669 1.08196i
\(255\) 3.36523 + 5.82875i 0.210739 + 0.365011i
\(256\) 5.91116 + 10.2384i 0.369448 + 0.639902i
\(257\) 8.33834 14.4424i 0.520132 0.900894i −0.479595 0.877490i \(-0.659216\pi\)
0.999726 0.0234040i \(-0.00745042\pi\)
\(258\) −17.0444 −1.06114
\(259\) 0 0
\(260\) 1.18070 0.0732238
\(261\) 0.188547 0.326573i 0.0116708 0.0202143i
\(262\) −7.46593 12.9314i −0.461247 0.798903i
\(263\) 6.73448 + 11.6645i 0.415266 + 0.719261i 0.995456 0.0952194i \(-0.0303553\pi\)
−0.580191 + 0.814481i \(0.697022\pi\)
\(264\) 2.11256 3.65906i 0.130019 0.225199i
\(265\) −17.5878 −1.08041
\(266\) 0 0
\(267\) −5.91750 −0.362145
\(268\) 1.75116 3.03310i 0.106969 0.185276i
\(269\) −15.2789 26.4638i −0.931571 1.61353i −0.780638 0.624984i \(-0.785106\pi\)
−0.150933 0.988544i \(-0.548228\pi\)
\(270\) 6.90180 + 11.9543i 0.420030 + 0.727514i
\(271\) 2.11256 3.65906i 0.128329 0.222272i −0.794700 0.607002i \(-0.792372\pi\)
0.923029 + 0.384730i \(0.125705\pi\)
\(272\) −4.61791 −0.280002
\(273\) 0 0
\(274\) 4.05244 0.244817
\(275\) −0.0444180 + 0.0769343i −0.00267851 + 0.00463931i
\(276\) −0.518374 0.897850i −0.0312025 0.0540442i
\(277\) 1.50000 + 2.59808i 0.0901263 + 0.156103i 0.907564 0.419914i \(-0.137940\pi\)
−0.817438 + 0.576017i \(0.804606\pi\)
\(278\) 3.73296 6.46568i 0.223888 0.387786i
\(279\) −0.253201 −0.0151587
\(280\) 0 0
\(281\) −6.27890 −0.374568 −0.187284 0.982306i \(-0.559968\pi\)
−0.187284 + 0.982306i \(0.559968\pi\)
\(282\) −9.23698 + 15.9989i −0.550054 + 0.952722i
\(283\) 11.7685 + 20.3837i 0.699568 + 1.21169i 0.968616 + 0.248560i \(0.0799573\pi\)
−0.269049 + 0.963127i \(0.586709\pi\)
\(284\) 1.56413 + 2.70915i 0.0928139 + 0.160758i
\(285\) −8.33834 + 14.4424i −0.493921 + 0.855496i
\(286\) 0.955582 0.0565047
\(287\) 0 0
\(288\) −0.130227 −0.00767373
\(289\) 6.97779 12.0859i 0.410458 0.710935i
\(290\) 11.3621 + 19.6797i 0.667203 + 1.15563i
\(291\) −0.0856687 0.148383i −0.00502199 0.00869834i
\(292\) −2.13878 + 3.70448i −0.125163 + 0.216788i
\(293\) −21.6166 −1.26285 −0.631427 0.775435i \(-0.717530\pi\)
−0.631427 + 0.775435i \(0.717530\pi\)
\(294\) 0 0
\(295\) 24.2201 1.41015
\(296\) −3.49599 + 6.05523i −0.203200 + 0.351953i
\(297\) −2.03506 3.52482i −0.118086 0.204531i
\(298\) 11.4033 + 19.7511i 0.660576 + 1.14415i
\(299\) 0.556279 0.963504i 0.0321705 0.0557209i
\(300\) 0.104889 0.00605575
\(301\) 0 0
\(302\) −24.4452 −1.40667
\(303\) 6.02122 10.4291i 0.345910 0.599134i
\(304\) −5.72110 9.90924i −0.328128 0.568334i
\(305\) 14.4452 + 25.0199i 0.827132 + 1.43263i
\(306\) 0.0469179 0.0812641i 0.00268212 0.00464556i
\(307\) 20.3945 1.16397 0.581987 0.813198i \(-0.302275\pi\)
0.581987 + 0.813198i \(0.302275\pi\)
\(308\) 0 0
\(309\) 27.6072 1.57052
\(310\) 7.62910 13.2140i 0.433304 0.750504i
\(311\) 6.47462 + 11.2144i 0.367142 + 0.635909i 0.989117 0.147128i \(-0.0470029\pi\)
−0.621975 + 0.783037i \(0.713670\pi\)
\(312\) −2.67669 4.63616i −0.151537 0.262471i
\(313\) −16.6172 + 28.7819i −0.939262 + 1.62685i −0.172410 + 0.985025i \(0.555155\pi\)
−0.766852 + 0.641824i \(0.778178\pi\)
\(314\) 16.8066 0.948453
\(315\) 0 0
\(316\) 3.69105 0.207638
\(317\) 2.43587 4.21906i 0.136812 0.236966i −0.789476 0.613781i \(-0.789648\pi\)
0.926288 + 0.376816i \(0.122981\pi\)
\(318\) 8.40332 + 14.5550i 0.471235 + 0.816202i
\(319\) −3.35020 5.80272i −0.187575 0.324890i
\(320\) 9.77488 16.9306i 0.546433 0.946449i
\(321\) −3.53104 −0.197084
\(322\) 0 0
\(323\) −7.54343 −0.419728
\(324\) −2.43837 + 4.22339i −0.135465 + 0.234633i
\(325\) 0.0562792 + 0.0974785i 0.00312181 + 0.00540713i
\(326\) 6.95558 + 12.0474i 0.385234 + 0.667245i
\(327\) 15.1338 26.2125i 0.836900 1.44955i
\(328\) −37.2358 −2.05600
\(329\) 0 0
\(330\) −3.68605 −0.202910
\(331\) −3.43587 + 5.95111i −0.188853 + 0.327102i −0.944868 0.327452i \(-0.893810\pi\)
0.756015 + 0.654554i \(0.227144\pi\)
\(332\) −0.839189 1.45352i −0.0460565 0.0797721i
\(333\) −0.0506121 0.0876626i −0.00277352 0.00480388i
\(334\) 7.85172 13.5996i 0.429627 0.744136i
\(335\) −14.4977 −0.792093
\(336\) 0 0
\(337\) 11.0712 0.603085 0.301542 0.953453i \(-0.402499\pi\)
0.301542 + 0.953453i \(0.402499\pi\)
\(338\) 0.605378 1.04855i 0.0329282 0.0570333i
\(339\) −8.88177 15.3837i −0.482392 0.835527i
\(340\) −1.03006 1.78411i −0.0558627 0.0967570i
\(341\) −2.24951 + 3.89626i −0.121818 + 0.210994i
\(342\) 0.232505 0.0125724
\(343\) 0 0
\(344\) 24.7542 1.33466
\(345\) −2.14578 + 3.71660i −0.115525 + 0.200095i
\(346\) −1.50151 2.60070i −0.0807219 0.139814i
\(347\) −2.81297 4.87220i −0.151008 0.261553i 0.780590 0.625043i \(-0.214919\pi\)
−0.931598 + 0.363490i \(0.881585\pi\)
\(348\) −3.95558 + 6.85127i −0.212041 + 0.367267i
\(349\) −18.4783 −0.989122 −0.494561 0.869143i \(-0.664671\pi\)
−0.494561 + 0.869143i \(0.664671\pi\)
\(350\) 0 0
\(351\) −5.15698 −0.275259
\(352\) −1.15698 + 2.00394i −0.0616671 + 0.106810i
\(353\) 2.33518 + 4.04464i 0.124289 + 0.215275i 0.921455 0.388486i \(-0.127002\pi\)
−0.797166 + 0.603760i \(0.793668\pi\)
\(354\) −11.5722 20.0436i −0.615053 1.06530i
\(355\) 6.47462 11.2144i 0.343637 0.595197i
\(356\) 1.81127 0.0959974
\(357\) 0 0
\(358\) 9.87611 0.521968
\(359\) 5.86055 10.1508i 0.309308 0.535737i −0.668903 0.743350i \(-0.733236\pi\)
0.978211 + 0.207612i \(0.0665692\pi\)
\(360\) 0.150642 + 0.260919i 0.00793952 + 0.0137516i
\(361\) 0.154477 + 0.267561i 0.00813035 + 0.0140822i
\(362\) −2.18453 + 3.78372i −0.114817 + 0.198868i
\(363\) −18.1062 −0.950330
\(364\) 0 0
\(365\) 17.7067 0.926813
\(366\) 13.8036 23.9085i 0.721526 1.24972i
\(367\) 9.98497 + 17.2945i 0.521211 + 0.902764i 0.999696 + 0.0246684i \(0.00785298\pi\)
−0.478484 + 0.878096i \(0.658814\pi\)
\(368\) −1.47226 2.55004i −0.0767471 0.132930i
\(369\) 0.269535 0.466848i 0.0140314 0.0243031i
\(370\) 6.09989 0.317118
\(371\) 0 0
\(372\) 5.31198 0.275413
\(373\) 2.21326 3.83347i 0.114598 0.198490i −0.803021 0.595951i \(-0.796775\pi\)
0.917619 + 0.397461i \(0.130109\pi\)
\(374\) −0.833662 1.44395i −0.0431076 0.0746646i
\(375\) −9.86055 17.0790i −0.509197 0.881955i
\(376\) 13.4152 23.2358i 0.691835 1.19829i
\(377\) −8.48965 −0.437239
\(378\) 0 0
\(379\) −32.5702 −1.67302 −0.836509 0.547953i \(-0.815407\pi\)
−0.836509 + 0.547953i \(0.815407\pi\)
\(380\) 2.55227 4.42065i 0.130928 0.226775i
\(381\) −14.3470 24.8498i −0.735021 1.27309i
\(382\) 0.204421 + 0.354068i 0.0104591 + 0.0181157i
\(383\) 7.09820 12.2944i 0.362701 0.628216i −0.625703 0.780061i \(-0.715188\pi\)
0.988404 + 0.151845i \(0.0485213\pi\)
\(384\) −8.45023 −0.431224
\(385\) 0 0
\(386\) −10.1964 −0.518983
\(387\) −0.179185 + 0.310358i −0.00910851 + 0.0157764i
\(388\) 0.0262222 + 0.0454181i 0.00133123 + 0.00230576i
\(389\) −8.65849 14.9969i −0.439003 0.760375i 0.558610 0.829430i \(-0.311335\pi\)
−0.997613 + 0.0690552i \(0.978002\pi\)
\(390\) −2.33518 + 4.04464i −0.118246 + 0.204808i
\(391\) −1.94122 −0.0981718
\(392\) 0 0
\(393\) −21.5184 −1.08546
\(394\) −5.15198 + 8.92349i −0.259553 + 0.449559i
\(395\) −7.63945 13.2319i −0.384382 0.665770i
\(396\) −0.00936136 0.0162144i −0.000470426 0.000814802i
\(397\) 7.86207 13.6175i 0.394586 0.683443i −0.598462 0.801151i \(-0.704221\pi\)
0.993048 + 0.117708i \(0.0375548\pi\)
\(398\) −17.6971 −0.887075
\(399\) 0 0
\(400\) 0.297900 0.0148950
\(401\) −1.78924 + 3.09906i −0.0893506 + 0.154760i −0.907237 0.420620i \(-0.861812\pi\)
0.817886 + 0.575380i \(0.195146\pi\)
\(402\) 6.92686 + 11.9977i 0.345480 + 0.598390i
\(403\) 2.85020 + 4.93670i 0.141979 + 0.245914i
\(404\) −1.84302 + 3.19221i −0.0916938 + 0.158818i
\(405\) 20.1870 1.00310
\(406\) 0 0
\(407\) −1.79861 −0.0891536
\(408\) −4.67035 + 8.08929i −0.231217 + 0.400479i
\(409\) −15.6750 27.1500i −0.775080 1.34248i −0.934749 0.355308i \(-0.884376\pi\)
0.159669 0.987171i \(-0.448957\pi\)
\(410\) 16.2425 + 28.1328i 0.802160 + 1.38938i
\(411\) 2.92000 5.05759i 0.144033 0.249472i
\(412\) −8.45023 −0.416313
\(413\) 0 0
\(414\) 0.0598327 0.00294062
\(415\) −3.47378 + 6.01676i −0.170521 + 0.295351i
\(416\) 1.46593 + 2.53906i 0.0718731 + 0.124488i
\(417\) −5.37959 9.31773i −0.263440 0.456291i
\(418\) 2.06564 3.57779i 0.101034 0.174996i
\(419\) 28.7716 1.40558 0.702792 0.711396i \(-0.251937\pi\)
0.702792 + 0.711396i \(0.251937\pi\)
\(420\) 0 0
\(421\) −0.190060 −0.00926297 −0.00463148 0.999989i \(-0.501474\pi\)
−0.00463148 + 0.999989i \(0.501474\pi\)
\(422\) −14.4484 + 25.0254i −0.703337 + 1.21822i
\(423\) 0.194214 + 0.336389i 0.00944301 + 0.0163558i
\(424\) −12.2044 21.1387i −0.592699 1.02658i
\(425\) 0.0981974 0.170083i 0.00476328 0.00825024i
\(426\) −12.3741 −0.599526
\(427\) 0 0
\(428\) 1.08081 0.0522429
\(429\) 0.688547 1.19260i 0.0332434 0.0575792i
\(430\) −10.7979 18.7026i −0.520723 0.901918i
\(431\) −12.8367 22.2338i −0.618322 1.07096i −0.989792 0.142520i \(-0.954480\pi\)
0.371470 0.928445i \(-0.378854\pi\)
\(432\) −6.82430 + 11.8200i −0.328334 + 0.568692i
\(433\) −1.82233 −0.0875755 −0.0437877 0.999041i \(-0.513943\pi\)
−0.0437877 + 0.999041i \(0.513943\pi\)
\(434\) 0 0
\(435\) 32.7479 1.57014
\(436\) −4.63227 + 8.02332i −0.221845 + 0.384247i
\(437\) −2.40497 4.16553i −0.115045 0.199264i
\(438\) −8.46012 14.6534i −0.404240 0.700165i
\(439\) 0.367732 0.636931i 0.0175509 0.0303991i −0.857117 0.515123i \(-0.827746\pi\)
0.874667 + 0.484723i \(0.161080\pi\)
\(440\) 5.35337 0.255212
\(441\) 0 0
\(442\) −2.11256 −0.100484
\(443\) 1.85587 3.21446i 0.0881751 0.152724i −0.818565 0.574414i \(-0.805230\pi\)
0.906740 + 0.421691i \(0.138563\pi\)
\(444\) 1.06181 + 1.83910i 0.0503911 + 0.0872799i
\(445\) −3.74884 6.49318i −0.177712 0.307806i
\(446\) −0.774216 + 1.34098i −0.0366602 + 0.0634973i
\(447\) 32.8667 1.55454
\(448\) 0 0
\(449\) −5.17570 −0.244256 −0.122128 0.992514i \(-0.538972\pi\)
−0.122128 + 0.992514i \(0.538972\pi\)
\(450\) −0.00302666 + 0.00524233i −0.000142678 + 0.000247126i
\(451\) −4.78924 8.29521i −0.225517 0.390606i
\(452\) 2.71860 + 4.70876i 0.127872 + 0.221481i
\(453\) −17.6141 + 30.5085i −0.827581 + 1.43341i
\(454\) 11.5972 0.544284
\(455\) 0 0
\(456\) −23.1443 −1.08383
\(457\) 17.0650 29.5574i 0.798266 1.38264i −0.122479 0.992471i \(-0.539084\pi\)
0.920745 0.390166i \(-0.127582\pi\)
\(458\) 8.18070 + 14.1694i 0.382259 + 0.662092i
\(459\) 4.49901 + 7.79252i 0.209996 + 0.363724i
\(460\) 0.656798 1.13761i 0.0306234 0.0530412i
\(461\) 11.4008 0.530989 0.265494 0.964112i \(-0.414465\pi\)
0.265494 + 0.964112i \(0.414465\pi\)
\(462\) 0 0
\(463\) −30.0124 −1.39479 −0.697397 0.716685i \(-0.745659\pi\)
−0.697397 + 0.716685i \(0.745659\pi\)
\(464\) −11.2345 + 19.4587i −0.521548 + 0.903347i
\(465\) −10.9943 19.0427i −0.509850 0.883086i
\(466\) 17.5309 + 30.3644i 0.812103 + 1.40660i
\(467\) 17.0832 29.5889i 0.790515 1.36921i −0.135134 0.990827i \(-0.543146\pi\)
0.925649 0.378384i \(-0.123520\pi\)
\(468\) −0.0237224 −0.00109657
\(469\) 0 0
\(470\) −23.4072 −1.07969
\(471\) 12.1101 20.9752i 0.558002 0.966488i
\(472\) 16.8066 + 29.1099i 0.773588 + 1.33989i
\(473\) 3.18387 + 5.51462i 0.146394 + 0.253562i
\(474\) −7.30012 + 12.6442i −0.335306 + 0.580766i
\(475\) 0.486625 0.0223279
\(476\) 0 0
\(477\) 0.353371 0.0161798
\(478\) −14.6116 + 25.3080i −0.668318 + 1.15756i
\(479\) −6.43805 11.1510i −0.294162 0.509504i 0.680627 0.732630i \(-0.261707\pi\)
−0.974790 + 0.223126i \(0.928374\pi\)
\(480\) −5.65465 9.79415i −0.258099 0.447040i
\(481\) −1.13945 + 1.97358i −0.0519544 + 0.0899876i
\(482\) −12.0174 −0.547377
\(483\) 0 0
\(484\) 5.54210 0.251913
\(485\) 0.108545 0.188006i 0.00492879 0.00853691i
\(486\) −0.279423 0.483975i −0.0126749 0.0219536i
\(487\) 10.9699 + 19.0005i 0.497096 + 0.860995i 0.999994 0.00335051i \(-0.00106650\pi\)
−0.502899 + 0.864345i \(0.667733\pi\)
\(488\) −20.0474 + 34.7232i −0.907505 + 1.57185i
\(489\) 20.0474 0.906577
\(490\) 0 0
\(491\) 4.11256 0.185597 0.0927986 0.995685i \(-0.470419\pi\)
0.0927986 + 0.995685i \(0.470419\pi\)
\(492\) −5.65465 + 9.79415i −0.254932 + 0.441554i
\(493\) 7.40648 + 12.8284i 0.333571 + 0.577762i
\(494\) −2.61724 4.53319i −0.117755 0.203958i
\(495\) −0.0387509 + 0.0671185i −0.00174172 + 0.00301675i
\(496\) 15.0869 0.677420
\(497\) 0 0
\(498\) 6.63896 0.297499
\(499\) −9.51654 + 16.4831i −0.426019 + 0.737886i −0.996515 0.0834139i \(-0.973418\pi\)
0.570496 + 0.821300i \(0.306751\pi\)
\(500\) 3.01820 + 5.22767i 0.134978 + 0.233788i
\(501\) −11.3151 19.5984i −0.505524 0.875592i
\(502\) −11.1989 + 19.3971i −0.499831 + 0.865733i
\(503\) 35.8698 1.59935 0.799677 0.600430i \(-0.205004\pi\)
0.799677 + 0.600430i \(0.205004\pi\)
\(504\) 0 0
\(505\) 15.2582 0.678981
\(506\) 0.531570 0.920707i 0.0236312 0.0409304i
\(507\) −0.872413 1.51106i −0.0387452 0.0671087i
\(508\) 4.39145 + 7.60622i 0.194839 + 0.337472i
\(509\) 8.77323 15.1957i 0.388867 0.673537i −0.603431 0.797415i \(-0.706200\pi\)
0.992297 + 0.123879i \(0.0395334\pi\)
\(510\) 8.14895 0.360842
\(511\) 0 0
\(512\) 24.0000 1.06066
\(513\) −11.1476 + 19.3082i −0.492179 + 0.852479i
\(514\) −10.0957 17.4863i −0.445302 0.771286i
\(515\) 17.4897 + 30.2930i 0.770686 + 1.33487i
\(516\) 3.75919 6.51110i 0.165489 0.286635i
\(517\) 6.90180 0.303541
\(518\) 0 0
\(519\) −4.32768 −0.189964
\(520\) 3.39145 5.87417i 0.148725 0.257599i
\(521\) −4.42151 7.65828i −0.193710 0.335515i 0.752767 0.658287i \(-0.228719\pi\)
−0.946477 + 0.322772i \(0.895385\pi\)
\(522\) −0.228284 0.395400i −0.00999173 0.0173062i
\(523\) 10.9556 18.9756i 0.479054 0.829746i −0.520657 0.853766i \(-0.674313\pi\)
0.999711 + 0.0240196i \(0.00764641\pi\)
\(524\) 6.58651 0.287733
\(525\) 0 0
\(526\) 16.3076 0.711046
\(527\) 4.97311 8.61368i 0.216632 0.375218i
\(528\) −1.82233 3.15636i −0.0793066 0.137363i
\(529\) 10.8811 + 18.8466i 0.473092 + 0.819419i
\(530\) −10.6473 + 18.4417i −0.462489 + 0.801054i
\(531\) −0.486625 −0.0211177
\(532\) 0 0
\(533\) −12.1363 −0.525681
\(534\) −3.58232 + 6.20477i −0.155022 + 0.268506i
\(535\) −2.23698 3.87456i −0.0967130 0.167512i
\(536\) −10.0601 17.4246i −0.434531 0.752629i
\(537\) 7.11625 12.3257i 0.307089 0.531894i
\(538\) −36.9980 −1.59510
\(539\) 0 0
\(540\) −6.08884 −0.262022
\(541\) −11.4327 + 19.8020i −0.491530 + 0.851356i −0.999952 0.00975240i \(-0.996896\pi\)
0.508422 + 0.861108i \(0.330229\pi\)
\(542\) −2.55779 4.43023i −0.109867 0.190295i
\(543\) 3.14814 + 5.45274i 0.135100 + 0.234000i
\(544\) 2.55779 4.43023i 0.109664 0.189944i
\(545\) 38.3501 1.64274
\(546\) 0 0
\(547\) −35.2676 −1.50793 −0.753966 0.656913i \(-0.771862\pi\)
−0.753966 + 0.656913i \(0.771862\pi\)
\(548\) −0.893776 + 1.54807i −0.0381802 + 0.0661301i
\(549\) −0.290231 0.502694i −0.0123867 0.0214545i
\(550\) 0.0537794 + 0.0931487i 0.00229316 + 0.00397187i
\(551\) −18.3517 + 31.7861i −0.781809 + 1.35413i
\(552\) −5.95594 −0.253502
\(553\) 0 0
\(554\) 3.63227 0.154320
\(555\) 4.39529 7.61286i 0.186570 0.323148i
\(556\) 1.64663 + 2.85204i 0.0698326 + 0.120954i
\(557\) −19.9349 34.5282i −0.844668 1.46301i −0.885909 0.463859i \(-0.846464\pi\)
0.0412408 0.999149i \(-0.486869\pi\)
\(558\) −0.153282 + 0.265493i −0.00648896 + 0.0112392i
\(559\) 8.06814 0.341246
\(560\) 0 0
\(561\) −2.40279 −0.101446
\(562\) −3.80111 + 6.58371i −0.160340 + 0.277717i
\(563\) 12.7986 + 22.1678i 0.539397 + 0.934263i 0.998937 + 0.0461056i \(0.0146811\pi\)
−0.459540 + 0.888157i \(0.651986\pi\)
\(564\) −4.07448 7.05720i −0.171566 0.297162i
\(565\) 11.2535 19.4917i 0.473439 0.820021i
\(566\) 28.4977 1.19785
\(567\) 0 0
\(568\) 17.9713 0.754058
\(569\) 12.5474 21.7328i 0.526016 0.911087i −0.473524 0.880781i \(-0.657018\pi\)
0.999541 0.0303062i \(-0.00964823\pi\)
\(570\) 10.0957 + 17.4863i 0.422862 + 0.732419i
\(571\) 15.6244 + 27.0623i 0.653862 + 1.13252i 0.982178 + 0.187954i \(0.0601855\pi\)
−0.328316 + 0.944568i \(0.606481\pi\)
\(572\) −0.210756 + 0.365040i −0.00881215 + 0.0152631i
\(573\) 0.589185 0.0246135
\(574\) 0 0
\(575\) 0.125228 0.00522236
\(576\) −0.196395 + 0.340166i −0.00818312 + 0.0141736i
\(577\) −6.43587 11.1473i −0.267929 0.464066i 0.700398 0.713753i \(-0.253006\pi\)
−0.968327 + 0.249686i \(0.919673\pi\)
\(578\) −8.44840 14.6331i −0.351407 0.608655i
\(579\) −7.34704 + 12.7254i −0.305332 + 0.528851i
\(580\) −10.0237 −0.416212
\(581\) 0 0
\(582\) −0.207448 −0.00859899
\(583\) 3.13945 5.43768i 0.130023 0.225206i
\(584\) 12.2869 + 21.2816i 0.508436 + 0.880638i
\(585\) 0.0490987 + 0.0850415i 0.00202998 + 0.00351603i
\(586\) −13.0862 + 22.6660i −0.540586 + 0.936322i
\(587\) −9.96692 −0.411379 −0.205689 0.978617i \(-0.565944\pi\)
−0.205689 + 0.978617i \(0.565944\pi\)
\(588\) 0 0
\(589\) 24.6447 1.01547
\(590\) 14.6623 25.3959i 0.603638 1.04553i
\(591\) 7.42454 + 12.8597i 0.305405 + 0.528976i
\(592\) 3.01570 + 5.22334i 0.123944 + 0.214678i
\(593\) −10.2954 + 17.8322i −0.422783 + 0.732282i −0.996211 0.0869747i \(-0.972280\pi\)
0.573428 + 0.819256i \(0.305613\pi\)
\(594\) −4.92791 −0.202195
\(595\) 0 0
\(596\) −10.0601 −0.412078
\(597\) −12.7517 + 22.0866i −0.521892 + 0.903943i
\(598\) −0.673518 1.16657i −0.0275422 0.0477045i
\(599\) 6.26855 + 10.8574i 0.256126 + 0.443623i 0.965201 0.261510i \(-0.0842205\pi\)
−0.709075 + 0.705133i \(0.750887\pi\)
\(600\) 0.301284 0.521838i 0.0122998 0.0213040i
\(601\) −1.82233 −0.0743343 −0.0371672 0.999309i \(-0.511833\pi\)
−0.0371672 + 0.999309i \(0.511833\pi\)
\(602\) 0 0
\(603\) 0.291284 0.0118620
\(604\) 5.39145 9.33827i 0.219375 0.379969i
\(605\) −11.4706 19.8677i −0.466347 0.807736i
\(606\) −7.29023 12.6270i −0.296145 0.512939i
\(607\) −15.4890 + 26.8277i −0.628678 + 1.08890i 0.359139 + 0.933284i \(0.383071\pi\)
−0.987817 + 0.155619i \(0.950263\pi\)
\(608\) 12.6754 0.514053
\(609\) 0 0
\(610\) 34.9793 1.41627
\(611\) 4.37241 7.57324i 0.176889 0.306381i
\(612\) 0.0206957 + 0.0358460i 0.000836574 + 0.00144899i
\(613\) −6.22512 10.7822i −0.251430 0.435490i 0.712490 0.701683i \(-0.247568\pi\)
−0.963920 + 0.266193i \(0.914234\pi\)
\(614\) 12.3464 21.3845i 0.498259 0.863010i
\(615\) 46.8143 1.88773
\(616\) 0 0
\(617\) 31.7809 1.27945 0.639726 0.768603i \(-0.279048\pi\)
0.639726 + 0.768603i \(0.279048\pi\)
\(618\) 16.7128 28.9474i 0.672287 1.16444i
\(619\) −2.11256 3.65906i −0.0849109 0.147070i 0.820442 0.571729i \(-0.193727\pi\)
−0.905353 + 0.424659i \(0.860394\pi\)
\(620\) 3.36523 + 5.82875i 0.135151 + 0.234088i
\(621\) −2.86872 + 4.96877i −0.115118 + 0.199390i
\(622\) 15.6784 0.628646
\(623\) 0 0
\(624\) −4.61791 −0.184864
\(625\) 12.2123 21.1523i 0.488491 0.846091i
\(626\) 20.1194 + 34.8479i 0.804134 + 1.39280i
\(627\) −2.97680 5.15598i −0.118882 0.205910i
\(628\) −3.70674 + 6.42027i −0.147915 + 0.256197i
\(629\) 3.97628 0.158545
\(630\) 0 0
\(631\) 7.31198 0.291085 0.145543 0.989352i \(-0.453507\pi\)
0.145543 + 0.989352i \(0.453507\pi\)
\(632\) 10.6022 18.3636i 0.421733 0.730463i
\(633\) 20.8217 + 36.0642i 0.827587 + 1.43342i
\(634\) −2.94925 5.10825i −0.117130 0.202874i
\(635\) 18.1782 31.4856i 0.721380 1.24947i
\(636\) −7.41349 −0.293964
\(637\) 0 0
\(638\) −8.11256 −0.321179
\(639\) −0.130087 + 0.225317i −0.00514615 + 0.00891340i
\(640\) −5.35337 9.27231i −0.211611 0.366520i
\(641\) 11.5237 + 19.9597i 0.455160 + 0.788360i 0.998697 0.0510251i \(-0.0162488\pi\)
−0.543538 + 0.839385i \(0.682916\pi\)
\(642\) −2.13762 + 3.70246i −0.0843650 + 0.146124i
\(643\) −48.9379 −1.92992 −0.964961 0.262392i \(-0.915489\pi\)
−0.964961 + 0.262392i \(0.915489\pi\)
\(644\) 0 0
\(645\) −31.1219 −1.22542
\(646\) −4.56663 + 7.90963i −0.179672 + 0.311200i
\(647\) 16.7154 + 28.9520i 0.657152 + 1.13822i 0.981350 + 0.192231i \(0.0615722\pi\)
−0.324198 + 0.945989i \(0.605094\pi\)
\(648\) 14.0080 + 24.2626i 0.550287 + 0.953125i
\(649\) −4.32331 + 7.48820i −0.169705 + 0.293938i
\(650\) 0.136281 0.00534537
\(651\) 0 0
\(652\) −6.13628 −0.240315
\(653\) 5.23145 9.06114i 0.204723 0.354590i −0.745322 0.666705i \(-0.767704\pi\)
0.950044 + 0.312115i \(0.101037\pi\)
\(654\) −18.3233 31.7369i −0.716498 1.24101i
\(655\) −13.6323 23.6118i −0.532657 0.922589i
\(656\) −16.0601 + 27.8169i −0.627042 + 1.08607i
\(657\) −0.355760 −0.0138795
\(658\) 0 0
\(659\) −8.73849 −0.340403 −0.170202 0.985409i \(-0.554442\pi\)
−0.170202 + 0.985409i \(0.554442\pi\)
\(660\) 0.812966 1.40810i 0.0316447 0.0548102i
\(661\) 2.30677 + 3.99545i 0.0897230 + 0.155405i 0.907394 0.420281i \(-0.138068\pi\)
−0.817671 + 0.575686i \(0.804735\pi\)
\(662\) 4.16000 + 7.20534i 0.161683 + 0.280043i
\(663\) −1.52221 + 2.63654i −0.0591177 + 0.102395i
\(664\) −9.64199 −0.374182
\(665\) 0 0
\(666\) −0.122558 −0.00474901
\(667\) −4.72262 + 8.17981i −0.182860 + 0.316724i
\(668\) 3.46343 + 5.99884i 0.134004 + 0.232102i
\(669\) 1.11573 + 1.93249i 0.0431365 + 0.0747145i
\(670\) −8.77657 + 15.2015i −0.339069 + 0.587284i
\(671\) −10.3140 −0.398166
\(672\) 0 0
\(673\) 9.83802 0.379228 0.189614 0.981859i \(-0.439276\pi\)
0.189614 + 0.981859i \(0.439276\pi\)
\(674\) 6.70224 11.6086i 0.258161 0.447147i
\(675\) −0.290231 0.502694i −0.0111710 0.0193487i
\(676\) 0.267035 + 0.462518i 0.0102706 + 0.0177892i
\(677\) −2.34770 + 4.06634i −0.0902296 + 0.156282i −0.907608 0.419819i \(-0.862093\pi\)
0.817378 + 0.576102i \(0.195427\pi\)
\(678\) −21.5073 −0.825984
\(679\) 0 0
\(680\) −11.8350 −0.453851
\(681\) 8.35640 14.4737i 0.320218 0.554634i
\(682\) 2.72360 + 4.71742i 0.104292 + 0.180639i
\(683\) −5.51035 9.54420i −0.210848 0.365199i 0.741132 0.671359i \(-0.234289\pi\)
−0.951980 + 0.306160i \(0.900956\pi\)
\(684\) −0.0512796 + 0.0888189i −0.00196072 + 0.00339607i
\(685\) 7.39948 0.282720
\(686\) 0 0
\(687\) 23.5785 0.899575
\(688\) 10.6767 18.4926i 0.407045 0.705022i
\(689\) −3.97779 6.88974i −0.151542 0.262478i
\(690\) 2.59802 + 4.49990i 0.0989049 + 0.171308i
\(691\) 19.3818 33.5702i 0.737317 1.27707i −0.216382 0.976309i \(-0.569426\pi\)
0.953699 0.300762i \(-0.0972411\pi\)
\(692\) 1.32465 0.0503556
\(693\) 0 0
\(694\) −6.81163 −0.258566
\(695\) 6.81613 11.8059i 0.258551 0.447823i
\(696\) 22.7241 + 39.3593i 0.861356 + 1.49191i
\(697\) 10.5878 + 18.3387i 0.401043 + 0.694628i
\(698\) −11.1864 + 19.3754i −0.423410 + 0.733368i
\(699\) 50.5277 1.91113
\(700\) 0 0
\(701\) −32.0681 −1.21120 −0.605598 0.795770i \(-0.707066\pi\)
−0.605598 + 0.795770i \(0.707066\pi\)
\(702\) −3.12192 + 5.40732i −0.117829 + 0.204086i
\(703\) 4.92619 + 8.53242i 0.185795 + 0.321806i
\(704\) 3.48965 + 6.04425i 0.131521 + 0.227801i
\(705\) −16.8661 + 29.2129i −0.635213 + 1.10022i
\(706\) 5.65465 0.212816
\(707\) 0 0
\(708\) 10.2091 0.383680
\(709\) −19.1725 + 33.2078i −0.720040 + 1.24715i 0.240944 + 0.970539i \(0.422543\pi\)
−0.960983 + 0.276606i \(0.910790\pi\)
\(710\) −7.83919 13.5779i −0.294200 0.509568i
\(711\) 0.153490 + 0.265853i 0.00575633 + 0.00997026i
\(712\) 5.20273 9.01139i 0.194981 0.337716i
\(713\) 6.34204 0.237511
\(714\) 0 0
\(715\) 1.74483 0.0652528
\(716\) −2.17820 + 3.77275i −0.0814031 + 0.140994i
\(717\) 21.0568 + 36.4715i 0.786381 + 1.36205i
\(718\) −7.09570 12.2901i −0.264809 0.458663i
\(719\) 4.36207 7.55532i 0.162678 0.281766i −0.773151 0.634223i \(-0.781320\pi\)
0.935828 + 0.352457i \(0.114654\pi\)
\(720\) 0.259892 0.00968561
\(721\) 0 0
\(722\) 0.374067 0.0139213
\(723\) −8.65916 + 14.9981i −0.322038 + 0.557785i
\(724\) −0.963608 1.66902i −0.0358122 0.0620286i
\(725\) −0.477791 0.827558i −0.0177447 0.0307347i
\(726\) −10.9611 + 18.9852i −0.406805 + 0.704607i
\(727\) 26.6754 0.989334 0.494667 0.869083i \(-0.335290\pi\)
0.494667 + 0.869083i \(0.335290\pi\)
\(728\) 0 0
\(729\) 26.5885 0.984759
\(730\) 10.7193 18.5663i 0.396738 0.687170i
\(731\) −7.03875 12.1915i −0.260338 0.450918i
\(732\) 6.08884 + 10.5462i 0.225050 + 0.389798i
\(733\) −13.3606 + 23.1412i −0.493483 + 0.854738i −0.999972 0.00750863i \(-0.997610\pi\)
0.506489 + 0.862247i \(0.330943\pi\)
\(734\) 24.1787 0.892453
\(735\) 0 0
\(736\) 3.26187 0.120234
\(737\) 2.58785 4.48229i 0.0953247 0.165107i
\(738\) −0.326341 0.565239i −0.0120128 0.0208067i
\(739\) −18.0269 31.2235i −0.663130 1.14857i −0.979789 0.200035i \(-0.935894\pi\)
0.316659 0.948539i \(-0.397439\pi\)
\(740\) −1.34535 + 2.33021i −0.0494559 + 0.0856601i
\(741\) −7.54343 −0.277115
\(742\) 0 0
\(743\) −2.96058 −0.108613 −0.0543066 0.998524i \(-0.517295\pi\)
−0.0543066 + 0.998524i \(0.517295\pi\)
\(744\) 15.2582 26.4280i 0.559393 0.968897i
\(745\) 20.8217 + 36.0642i 0.762847 + 1.32129i
\(746\) −2.67971 4.64140i −0.0981112 0.169934i
\(747\) 0.0697944 0.120887i 0.00255364 0.00442304i
\(748\) 0.735465 0.0268913
\(749\) 0 0
\(750\) −23.8774 −0.871881
\(751\) −21.5775 + 37.3733i −0.787374 + 1.36377i 0.140196 + 0.990124i \(0.455227\pi\)
−0.927570 + 0.373648i \(0.878107\pi\)
\(752\) −11.5722 20.0436i −0.421993 0.730913i
\(753\) 16.1388 + 27.9532i 0.588130 + 1.01867i
\(754\) −5.13945 + 8.90179i −0.187168 + 0.324184i
\(755\) −44.6353 −1.62444
\(756\) 0 0
\(757\) 18.7335 0.680880 0.340440 0.940266i \(-0.389424\pi\)
0.340440 + 0.940266i \(0.389424\pi\)
\(758\) −19.7173 + 34.1513i −0.716163 + 1.24043i
\(759\) −0.766049 1.32684i −0.0278058 0.0481611i
\(760\) −14.6623 25.3959i −0.531858 0.921206i
\(761\) 2.11474 3.66284i 0.0766592 0.132778i −0.825147 0.564918i \(-0.808908\pi\)
0.901807 + 0.432140i \(0.142241\pi\)
\(762\) −34.7415 −1.25855
\(763\) 0 0
\(764\) −0.180342 −0.00652456
\(765\) 0.0856687 0.148383i 0.00309736 0.00536478i
\(766\) −8.59418 14.8856i −0.310521 0.537837i
\(767\) 5.47779 + 9.48781i 0.197792 + 0.342585i
\(768\) 10.3140 17.8643i 0.372173 0.644622i
\(769\) −21.1299 −0.761965 −0.380983 0.924582i \(-0.624414\pi\)
−0.380983 + 0.924582i \(0.624414\pi\)
\(770\) 0 0
\(771\) −29.0979 −1.04794
\(772\) 2.24884 3.89510i 0.0809375 0.140188i
\(773\) −16.5371 28.6431i −0.594798 1.03022i −0.993575 0.113173i \(-0.963899\pi\)
0.398777 0.917048i \(-0.369435\pi\)
\(774\) 0.216950 + 0.375768i 0.00779810 + 0.0135067i
\(775\) −0.320815 + 0.555667i −0.0115240 + 0.0199601i
\(776\) 0.301284 0.0108154
\(777\) 0 0
\(778\) −20.9666 −0.751690
\(779\) −26.2345 + 45.4394i −0.939948 + 1.62804i
\(780\) −1.03006 1.78411i −0.0368820 0.0638814i
\(781\) 2.31145 + 4.00355i 0.0827103 + 0.143258i
\(782\) −1.17517 + 2.03546i −0.0420241 + 0.0727878i