Properties

Label 637.2.e.k.508.2
Level $637$
Weight $2$
Character 637.508
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 508.2
Root \(-0.105378 + 0.182520i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.k.79.2

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9} + O(q^{10}) \) \( 6 q + 2 q^{2} - 4 q^{3} - 6 q^{4} - 5 q^{5} + 4 q^{6} - 12 q^{8} - 11 q^{9} + 14 q^{10} + 4 q^{11} - 18 q^{12} - 6 q^{13} + 4 q^{15} - 4 q^{16} - 4 q^{17} - 8 q^{18} - 7 q^{19} + 32 q^{20} - 16 q^{22} - q^{23} + 28 q^{24} - 4 q^{25} - 2 q^{26} + 44 q^{27} - 14 q^{29} + 24 q^{30} + 3 q^{31} + 24 q^{32} + 10 q^{33} + 4 q^{34} + 52 q^{36} + 10 q^{37} - 12 q^{38} + 4 q^{39} + 22 q^{40} + 12 q^{41} + 18 q^{43} + 2 q^{44} - 3 q^{45} + 28 q^{46} - 17 q^{47} + 32 q^{48} - 60 q^{50} - 20 q^{51} + 6 q^{52} - 13 q^{53} - 28 q^{54} + 8 q^{55} + 8 q^{57} - 14 q^{58} - 22 q^{59} - 42 q^{60} + 24 q^{61} - 36 q^{62} + 40 q^{64} + 5 q^{65} + 30 q^{66} + 14 q^{67} - 18 q^{68} + 4 q^{69} + 8 q^{71} + 30 q^{72} - 5 q^{73} - 8 q^{74} - 6 q^{75} - 16 q^{76} - 4 q^{78} - q^{79} - 40 q^{80} - 15 q^{81} - 20 q^{82} + 46 q^{83} + 4 q^{85} - 6 q^{86} - 20 q^{87} + 4 q^{88} + 11 q^{89} - 80 q^{90} + 60 q^{92} + 38 q^{93} + 16 q^{94} + 5 q^{95} + 52 q^{96} - 6 q^{97} - 60 q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.605378 + 1.04855i 0.428067 + 0.741434i 0.996701 0.0811568i \(-0.0258614\pi\)
−0.568635 + 0.822590i \(0.692528\pi\)
\(3\) 0.872413 1.51106i 0.503688 0.872413i −0.496303 0.868149i \(-0.665309\pi\)
0.999991 0.00426367i \(-0.00135717\pi\)
\(4\) 0.267035 0.462518i 0.133518 0.231259i
\(5\) −1.10538 1.91457i −0.494340 0.856222i 0.505639 0.862745i \(-0.331257\pi\)
−0.999979 + 0.00652327i \(0.997924\pi\)
\(6\) 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 −0.800382 0.599490i \(-0.795370\pi\)
0.919365 + 0.393406i \(0.128703\pi\)
\(12\) −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 \(-0.765469\pi\)
0.952213 + 0.305436i \(0.0988021\pi\)
\(18\) 0.0268897 0.0465743i 0.00633796 0.0109777i
\(19\) −2.16166 3.74410i −0.495918 0.858955i 0.504071 0.863662i \(-0.331835\pi\)
−0.999989 + 0.00470690i \(0.998502\pi\)
\(20\) −1.18070 −0.264012
\(21\) 0 0
\(22\) 0.955582 0.203731
\(23\) 0.556279 + 0.963504i 0.115992 + 0.200904i 0.918176 0.396173i \(-0.129662\pi\)
−0.802184 + 0.597077i \(0.796329\pi\)
\(24\) 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 0.487993 + 0.872848i \(0.337729\pi\)
−0.999905 + 0.0138096i \(0.995604\pi\)
\(32\) 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 0.757033 0.653377i \(-0.226648\pi\)
−0.944357 + 0.328922i \(0.893315\pi\)
\(38\) 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 \(-0.103417\pi\)
0.947684 + 0.319209i \(0.103417\pi\)
\(42\) 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 −0.985918 0.167227i \(-0.946519\pi\)
0.348136 0.937444i \(-0.386815\pi\)
\(48\) 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 0.452126 + 0.891954i \(0.350666\pi\)
−0.998518 + 0.0544241i \(0.982668\pi\)
\(54\) 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 0.250522 + 0.968111i \(0.419398\pi\)
−0.963670 + 0.267097i \(0.913936\pi\)
\(60\) −1.03006 + 1.78411i −0.132980 + 0.230328i
\(61\) 6.53407 + 11.3173i 0.836602 + 1.44904i 0.892719 + 0.450613i \(0.148795\pi\)
−0.0561175 + 0.998424i \(0.517872\pi\)
\(62\) −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 −0.993796 0.111217i \(-0.964525\pi\)
0.593215 + 0.805044i \(0.297858\pi\)
\(68\) −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 \(-0.988615\pi\)
0.530648 + 0.847592i \(0.321949\pi\)
\(74\) 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 0.992286 0.123968i \(-0.0395621\pi\)
−0.603503 + 0.797361i \(0.706229\pi\)
\(80\) 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 \(-0.444824\pi\)
0.172473 + 0.985014i \(0.444824\pi\)
\(84\) 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 \(-0.224194\pi\)
−0.941794 + 0.336191i \(0.890861\pi\)
\(90\) −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 \(-0.501587\pi\)
−0.00498522 + 0.999988i \(0.501587\pi\)
\(98\) 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 \(-0.944904\pi\)
0.641680 + 0.766972i \(0.278238\pi\)
\(102\) 1.84302 3.19221i 0.182487 0.316076i
\(103\) 7.91116 + 13.7025i 0.779510 + 1.35015i 0.932224 + 0.361881i \(0.117865\pi\)
−0.152714 + 0.988270i \(0.548801\pi\)
\(104\) −3.06814 −0.300856
\(105\) 0 0
\(106\) −9.63227 −0.935569
\(107\) 1.01186 + 1.75259i 0.0978203 + 0.169430i 0.910782 0.412887i \(-0.135480\pi\)
−0.812962 + 0.582317i \(0.802146\pi\)
\(108\) 1.37709 2.38520i 0.132511 0.229516i
\(109\) 8.67352 15.0230i 0.830772 1.43894i −0.0666542 0.997776i \(-0.521232\pi\)
0.897427 0.441164i \(-0.145434\pi\)
\(110\) −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 −0.998971 0.0453448i \(-0.985561\pi\)
0.460216 0.887807i \(-0.347772\pi\)
\(132\) −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 −0.785639 0.618686i \(-0.787665\pi\)
0.928617 + 0.371040i \(0.120999\pi\)
\(138\) 1.17517 + 2.03546i 0.100037 + 0.173270i
\(139\) −6.16634 −0.523022 −0.261511 0.965201i \(-0.584221\pi\)
−0.261511 + 0.965201i \(0.584221\pi\)
\(140\) 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 −0.936696 0.350143i \(-0.886133\pi\)
0.165115 0.986274i \(-0.447200\pi\)
\(150\) 0.118893 0.205929i 0.00970758 0.0168140i
\(151\) −10.0950 + 17.4851i −0.821522 + 1.42292i 0.0830268 + 0.996547i \(0.473541\pi\)
−0.904549 + 0.426370i \(0.859792\pi\)
\(152\) −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 0.444070 + 0.895992i \(0.353534\pi\)
−0.997987 + 0.0634196i \(0.979799\pi\)
\(158\) −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 0.548414 0.836207i \(-0.315232\pi\)
−0.998383 + 0.0568369i \(0.981898\pi\)
\(164\) 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 \(-0.667337\pi\)
−0.501822 + 0.864971i \(0.667337\pi\)
\(168\) 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 \(-0.196724\pi\)
−0.909311 + 0.416118i \(0.863390\pi\)
\(174\) −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 −0.672385 0.740201i \(-0.734730\pi\)
0.977226 + 0.212202i \(0.0680635\pi\)
\(180\) 0.0262222 + 0.0454181i 0.00195448 + 0.00338527i
\(181\) 3.60855 0.268221 0.134111 0.990966i \(-0.457182\pi\)
0.134111 + 0.990966i \(0.457182\pi\)
\(182\) 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 0.859852 0.510543i \(-0.170555\pi\)
−0.872069 + 0.489383i \(0.837222\pi\)
\(192\) 7.71477 13.3624i 0.556765 0.964346i
\(193\) −4.21076 + 7.29324i −0.303097 + 0.524979i −0.976836 0.213990i \(-0.931354\pi\)
0.673739 + 0.738969i \(0.264687\pi\)
\(194\) −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 −0.481709 0.876331i \(-0.659984\pi\)
0.999780 0.0209934i \(-0.00668290\pi\)
\(200\) 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 \(-0.486366\pi\)
0.0428206 + 0.999083i \(0.486366\pi\)
\(224\) 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 \(-0.936302\pi\)
0.662171 + 0.749353i \(0.269635\pi\)
\(228\) −2.01436 + 3.48898i −0.133404 + 0.231063i
\(229\) 6.75669 + 11.7029i 0.446494 + 0.773351i 0.998155 0.0607177i \(-0.0193389\pi\)
−0.551661 + 0.834069i \(0.686006\pi\)
\(230\) 2.97797 0.196361
\(231\) 0 0
\(232\) −26.0474 −1.71010
\(233\) −14.4793 25.0789i −0.948571 1.64297i −0.748439 0.663204i \(-0.769196\pi\)
−0.200132 0.979769i \(-0.564137\pi\)
\(234\) −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 \(-0.729758\pi\)
0.980421 + 0.196912i \(0.0630914\pi\)
\(242\) −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 \(-0.301556\pi\)
0.583824 + 0.811880i \(0.301556\pi\)
\(252\) 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 −0.999726 0.0234040i \(-0.992550\pi\)
0.479595 0.877490i \(-0.340784\pi\)
\(258\) 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 −0.580191 0.814481i \(-0.697022\pi\)
0.995456 + 0.0952194i \(0.0303553\pi\)
\(264\) −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 0.150933 0.988544i \(-0.451772\pi\)
0.780638 0.624984i \(-0.214894\pi\)
\(270\) 6.90180 11.9543i 0.420030 0.727514i
\(271\) −2.11256 3.65906i −0.128329 0.222272i 0.794700 0.607002i \(-0.207628\pi\)
−0.923029 + 0.384730i \(0.874295\pi\)
\(272\) 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 −0.817438 0.576017i \(-0.804606\pi\)
0.907564 + 0.419914i \(0.137940\pi\)
\(278\) −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 0.269049 + 0.963127i \(0.413291\pi\)
−0.968616 + 0.248560i \(0.920043\pi\)
\(284\) 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 \(-0.282470\pi\)
0.631427 + 0.775435i \(0.282470\pi\)
\(294\) 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 \(-0.697725\pi\)
−0.581987 + 0.813198i \(0.697725\pi\)
\(308\) 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 \(-0.952997\pi\)
0.621975 + 0.783037i \(0.286330\pi\)
\(312\) −2.67669 + 4.63616i −0.151537 + 0.262471i
\(313\) 16.6172 + 28.7819i 0.939262 + 1.62685i 0.766852 + 0.641824i \(0.221822\pi\)
0.172410 + 0.985025i \(0.444845\pi\)
\(314\) −16.8066 −0.948453
\(315\) 0 0
\(316\) 3.69105 0.207638
\(317\) 2.43587 + 4.21906i 0.136812 + 0.236966i 0.926288 0.376816i \(-0.122981\pi\)
−0.789476 + 0.613781i \(0.789648\pi\)
\(318\) −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 0.756015 0.654554i \(-0.227144\pi\)
−0.944868 + 0.327452i \(0.893810\pi\)
\(332\) 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 −0.931598 0.363490i \(-0.881585\pi\)
0.780590 + 0.625043i \(0.214919\pi\)
\(348\) 3.95558 + 6.85127i 0.212041 + 0.367267i
\(349\) 18.4783 0.989122 0.494561 0.869143i \(-0.335329\pi\)
0.494561 + 0.869143i \(0.335329\pi\)
\(350\) 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 \(-0.872998\pi\)
0.797166 + 0.603760i \(0.206332\pi\)
\(354\) −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 0.978211 0.207612i \(-0.0665692\pi\)
−0.668903 + 0.743350i \(0.733236\pi\)
\(360\) −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 0.478484 + 0.878096i \(0.341186\pi\)
−0.999696 + 0.0246684i \(0.992147\pi\)
\(368\) −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 0.917619 0.397461i \(-0.130109\pi\)
−0.803021 + 0.595951i \(0.796775\pi\)
\(374\) 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 \(-0.284812\pi\)
−0.988404 + 0.151845i \(0.951479\pi\)
\(384\) 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 −0.997613 0.0690552i \(-0.978002\pi\)
0.558610 + 0.829430i \(0.311335\pi\)
\(390\) 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 \(-0.295779\pi\)
−0.993048 + 0.117708i \(0.962445\pi\)
\(398\) 17.6971 0.887075
\(399\) 0 0
\(400\) 0.297900 0.0148950
\(401\) −1.78924 3.09906i −0.0893506 0.154760i 0.817886 0.575380i \(-0.195146\pi\)
−0.907237 + 0.420620i \(0.861812\pi\)
\(402\) −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 −0.159669 0.987171i \(-0.551043\pi\)
0.934749 0.355308i \(-0.115624\pi\)
\(410\) 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 \(-0.748063\pi\)
−0.702792 + 0.711396i \(0.748063\pi\)
\(420\) 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 0.371470 + 0.928445i \(0.378854\pi\)
−0.989792 + 0.142520i \(0.954480\pi\)
\(432\) 6.82430 + 11.8200i 0.328334 + 0.568692i
\(433\) 1.82233 0.0875755 0.0437877 0.999041i \(-0.486057\pi\)
0.0437877 + 0.999041i \(0.486057\pi\)
\(434\) 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 \(-0.172254\pi\)
−0.874667 + 0.484723i \(0.838920\pi\)
\(440\) −5.35337 −0.255212
\(441\) 0 0
\(442\) −2.11256 −0.100484
\(443\) 1.85587 + 3.21446i 0.0881751 + 0.152724i 0.906740 0.421691i \(-0.138563\pi\)
−0.818565 + 0.574414i \(0.805230\pi\)
\(444\) −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 0.920745 + 0.390166i \(0.127582\pi\)
−0.122479 + 0.992471i \(0.539084\pi\)
\(458\) −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 \(-0.585535\pi\)
−0.265494 + 0.964112i \(0.585535\pi\)
\(462\) 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 −0.925649 0.378384i \(-0.876480\pi\)
0.135134 0.990827i \(-0.456854\pi\)
\(468\) 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 \(-0.738293\pi\)
0.974790 + 0.223126i \(0.0716261\pi\)
\(480\) −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 −0.502899 0.864345i \(-0.667733\pi\)
0.999994 + 0.00335051i \(0.00106650\pi\)
\(488\) 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 0.570496 0.821300i \(-0.306751\pi\)
−0.996515 + 0.0834139i \(0.973418\pi\)
\(500\) −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 \(-0.794996\pi\)
−0.799677 + 0.600430i \(0.794996\pi\)
\(504\) 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 \(-0.293800\pi\)
−0.992297 + 0.123879i \(0.960467\pi\)
\(510\) −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 \(-0.771281\pi\)
0.946477 + 0.322772i \(0.104615\pi\)
\(522\) −0.228284 + 0.395400i −0.00999173 + 0.0173062i
\(523\) −10.9556 18.9756i −0.479054 0.829746i 0.520657 0.853766i \(-0.325687\pi\)
−0.999711 + 0.0240196i \(0.992354\pi\)
\(524\) −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 0.508422 0.861108i \(-0.330229\pi\)
−0.999952 + 0.00975240i \(0.996896\pi\)
\(542\) 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 0.0412408 + 0.999149i \(0.486869\pi\)
−0.885909 + 0.463859i \(0.846464\pi\)
\(558\) 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 0.459540 + 0.888157i \(0.348014\pi\)
−0.998937 + 0.0461056i \(0.985319\pi\)
\(564\) −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 0.999541 + 0.0303062i \(0.00964823\pi\)
−0.473524 + 0.880781i \(0.657018\pi\)
\(570\) −10.0957 + 17.4863i −0.422862 + 0.732419i
\(571\) 15.6244 27.0623i 0.653862 1.13252i −0.328316 0.944568i \(-0.606481\pi\)
0.982178 0.187954i \(-0.0601855\pi\)
\(572\) 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 \(-0.746994\pi\)
0.968327 + 0.249686i \(0.0803274\pi\)
\(578\) −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 \(-0.434056\pi\)
0.205689 + 0.978617i \(0.434056\pi\)
\(588\) 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 \(-0.0277199\pi\)
−0.573428 + 0.819256i \(0.694387\pi\)
\(594\) 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 −0.709075 0.705133i \(-0.750887\pi\)
0.965201 + 0.261510i \(0.0842205\pi\)
\(600\) −0.301284 0.521838i −0.0122998 0.0213040i
\(601\) 1.82233 0.0743343 0.0371672 0.999309i \(-0.488167\pi\)
0.0371672 + 0.999309i \(0.488167\pi\)
\(602\) 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 0.987817 + 0.155619i \(0.0497372\pi\)
−0.359139 + 0.933284i \(0.616929\pi\)
\(608\) −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 −0.963920 0.266193i \(-0.914234\pi\)
0.712490 + 0.701683i \(0.247568\pi\)
\(614\) −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 \(-0.806273\pi\)
0.905353 + 0.424659i \(0.139606\pi\)
\(620\) 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 −0.543538 0.839385i \(-0.682916\pi\)
0.998697 + 0.0510251i \(0.0162488\pi\)
\(642\) 2.13762 + 3.70246i 0.0843650 + 0.146124i
\(643\) 48.9379 1.92992 0.964961 0.262392i \(-0.0845113\pi\)
0.964961 + 0.262392i \(0.0845113\pi\)
\(644\) 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 0.324198 + 0.945989i \(0.394906\pi\)
−0.981350 + 0.192231i \(0.938428\pi\)
\(648\) 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 0.950044 0.312115i \(-0.101037\pi\)
−0.745322 + 0.666705i \(0.767704\pi\)
\(654\) 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 \(-0.861932\pi\)
0.817671 + 0.575686i \(0.195265\pi\)
\(662\) 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 \(-0.137907\pi\)
−0.817378 + 0.576102i \(0.804573\pi\)
\(678\) 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 −0.951980 0.306160i \(-0.900956\pi\)
0.741132 + 0.671359i \(0.234289\pi\)
\(684\) 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 −0.953699 0.300762i \(-0.902759\pi\)
0.216382 0.976309i \(-0.430574\pi\)
\(692\) −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 −0.960983 0.276606i \(-0.910790\pi\)
0.240944 0.970539i \(-0.422543\pi\)
\(710\) 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 \(-0.218680\pi\)
−0.935828 + 0.352457i \(0.885346\pi\)
\(720\) −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 \(-0.664710\pi\)
−0.494667 + 0.869083i \(0.664710\pi\)
\(728\) 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 \(-0.00239009\pi\)
−0.506489 + 0.862247i \(0.669057\pi\)
\(734\) −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 0.316659 + 0.948539i \(0.397439\pi\)
−0.979789 + 0.200035i \(0.935894\pi\)
\(740\) 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 −0.927570 0.373648i \(-0.878107\pi\)
0.140196 0.990124i \(-0.455227\pi\)
\(752\) 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 \(-0.191092\pi\)
−0.901807 + 0.432140i \(0.857759\pi\)
\(762\) 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 \(-0.375586\pi\)
0.380983 + 0.924582i \(0.375586\pi\)
\(770\) 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 −0.398777 0.917048i \(-0.630565\pi\)
0.993575 0.113173i \(-0.0361013\pi\)
\(774\) 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
\(782\)