Properties

Label 637.2.u.h.361.2
Level $637$
Weight $2$
Character 637.361
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.u (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.2
Root \(1.40744 - 0.138282i\) of defining polynomial
Character \(\chi\) \(=\) 637.361
Dual form 637.2.u.h.30.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.10554 - 0.638282i) q^{2} -1.16793 q^{3} +(-0.185192 - 0.320762i) q^{4} +(-1.57173 + 0.907437i) q^{5} +(1.29118 + 0.745466i) q^{6} +3.02595i q^{8} -1.63595 q^{9} +O(q^{10})\) \(q+(-1.10554 - 0.638282i) q^{2} -1.16793 q^{3} +(-0.185192 - 0.320762i) q^{4} +(-1.57173 + 0.907437i) q^{5} +(1.29118 + 0.745466i) q^{6} +3.02595i q^{8} -1.63595 q^{9} +2.31680 q^{10} -2.77849i q^{11} +(0.216290 + 0.374626i) q^{12} +(-3.58305 - 0.402155i) q^{13} +(1.83566 - 1.05982i) q^{15} +(1.56102 - 2.70377i) q^{16} +(1.37198 + 2.37634i) q^{17} +(1.80860 + 1.04420i) q^{18} +5.86993i q^{19} +(0.582143 + 0.336100i) q^{20} +(-1.77346 + 3.07173i) q^{22} +(3.49955 - 6.06139i) q^{23} -3.53408i q^{24} +(-0.853117 + 1.47764i) q^{25} +(3.70451 + 2.73160i) q^{26} +5.41444 q^{27} +(1.75806 + 3.04505i) q^{29} -2.70585 q^{30} +(-1.79004 - 1.03348i) q^{31} +(1.78956 - 1.03320i) q^{32} +3.24507i q^{33} -3.50284i q^{34} +(0.302965 + 0.524751i) q^{36} +(-1.50950 - 0.871512i) q^{37} +(3.74667 - 6.48942i) q^{38} +(4.18474 + 0.469686i) q^{39} +(-2.74586 - 4.75596i) q^{40} +(5.51406 - 3.18355i) q^{41} +(4.55195 - 7.88422i) q^{43} +(-0.891235 + 0.514555i) q^{44} +(2.57127 - 1.48452i) q^{45} +(-7.73776 + 4.46740i) q^{46} +(5.76714 - 3.32966i) q^{47} +(-1.82316 + 3.15780i) q^{48} +(1.88631 - 1.08906i) q^{50} +(-1.60237 - 2.77539i) q^{51} +(0.534557 + 1.22378i) q^{52} +(5.24396 - 9.08280i) q^{53} +(-5.98587 - 3.45594i) q^{54} +(2.52131 + 4.36703i) q^{55} -6.85564i q^{57} -4.48855i q^{58} +(-2.66212 + 1.53698i) q^{59} +(-0.679899 - 0.392540i) q^{60} +1.08178 q^{61} +(1.31931 + 2.28511i) q^{62} -8.88199 q^{64} +(5.99651 - 2.61932i) q^{65} +(2.07127 - 3.58755i) q^{66} +5.01796i q^{67} +(0.508159 - 0.880158i) q^{68} +(-4.08721 + 7.07925i) q^{69} +(2.35453 + 1.35939i) q^{71} -4.95030i q^{72} +(6.64426 + 3.83607i) q^{73} +(1.11254 + 1.92698i) q^{74} +(0.996377 - 1.72578i) q^{75} +(1.88285 - 1.08706i) q^{76} +(-4.32659 - 3.19030i) q^{78} +(7.86993 + 13.6311i) q^{79} +5.66612i q^{80} -1.41581 q^{81} -8.12800 q^{82} +7.97408i q^{83} +(-4.31275 - 2.48997i) q^{85} +(-10.0647 + 5.81086i) q^{86} +(-2.05328 - 3.55639i) q^{87} +8.40757 q^{88} +(13.9118 + 8.03198i) q^{89} -3.79017 q^{90} -2.59235 q^{92} +(2.09064 + 1.20703i) q^{93} -8.50105 q^{94} +(-5.32659 - 9.22592i) q^{95} +(-2.09007 + 1.20670i) q^{96} +(-12.3209 - 7.11347i) q^{97} +4.54548i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29} - 16 q^{30} + 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} - 2 q^{38} - 10 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} + 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} + 26 q^{52} + 22 q^{53} - 12 q^{54} - 6 q^{55} - 18 q^{59} + 66 q^{60} - 28 q^{61} - 4 q^{62} - 52 q^{64} - 42 q^{65} + 26 q^{66} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 30 q^{73} + 6 q^{74} + 46 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} - 28 q^{82} - 48 q^{85} - 60 q^{86} - 2 q^{87} + 28 q^{88} + 12 q^{89} + 24 q^{90} + 24 q^{92} + 18 q^{93} - 8 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10554 0.638282i −0.781733 0.451334i 0.0553113 0.998469i \(-0.482385\pi\)
−0.837044 + 0.547136i \(0.815718\pi\)
\(3\) −1.16793 −0.674302 −0.337151 0.941451i \(-0.609463\pi\)
−0.337151 + 0.941451i \(0.609463\pi\)
\(4\) −0.185192 0.320762i −0.0925960 0.160381i
\(5\) −1.57173 + 0.907437i −0.702897 + 0.405818i −0.808426 0.588598i \(-0.799680\pi\)
0.105528 + 0.994416i \(0.466347\pi\)
\(6\) 1.29118 + 0.745466i 0.527124 + 0.304335i
\(7\) 0 0
\(8\) 3.02595i 1.06983i
\(9\) −1.63595 −0.545317
\(10\) 2.31680 0.732637
\(11\) 2.77849i 0.837747i −0.908045 0.418874i \(-0.862425\pi\)
0.908045 0.418874i \(-0.137575\pi\)
\(12\) 0.216290 + 0.374626i 0.0624377 + 0.108145i
\(13\) −3.58305 0.402155i −0.993760 0.111538i
\(14\) 0 0
\(15\) 1.83566 1.05982i 0.473965 0.273644i
\(16\) 1.56102 2.70377i 0.390256 0.675943i
\(17\) 1.37198 + 2.37634i 0.332754 + 0.576347i 0.983051 0.183334i \(-0.0586888\pi\)
−0.650297 + 0.759680i \(0.725355\pi\)
\(18\) 1.80860 + 1.04420i 0.426292 + 0.246120i
\(19\) 5.86993i 1.34665i 0.739345 + 0.673327i \(0.235135\pi\)
−0.739345 + 0.673327i \(0.764865\pi\)
\(20\) 0.582143 + 0.336100i 0.130171 + 0.0751543i
\(21\) 0 0
\(22\) −1.77346 + 3.07173i −0.378103 + 0.654894i
\(23\) 3.49955 6.06139i 0.729706 1.26389i −0.227302 0.973824i \(-0.572990\pi\)
0.957007 0.290063i \(-0.0936763\pi\)
\(24\) 3.53408i 0.721391i
\(25\) −0.853117 + 1.47764i −0.170623 + 0.295528i
\(26\) 3.70451 + 2.73160i 0.726514 + 0.535710i
\(27\) 5.41444 1.04201
\(28\) 0 0
\(29\) 1.75806 + 3.04505i 0.326463 + 0.565451i 0.981807 0.189879i \(-0.0608097\pi\)
−0.655344 + 0.755330i \(0.727476\pi\)
\(30\) −2.70585 −0.494019
\(31\) −1.79004 1.03348i −0.321501 0.185619i 0.330560 0.943785i \(-0.392762\pi\)
−0.652062 + 0.758166i \(0.726096\pi\)
\(32\) 1.78956 1.03320i 0.316352 0.182646i
\(33\) 3.24507i 0.564894i
\(34\) 3.50284i 0.600732i
\(35\) 0 0
\(36\) 0.302965 + 0.524751i 0.0504942 + 0.0874585i
\(37\) −1.50950 0.871512i −0.248161 0.143276i 0.370761 0.928728i \(-0.379097\pi\)
−0.618922 + 0.785453i \(0.712430\pi\)
\(38\) 3.74667 6.48942i 0.607790 1.05272i
\(39\) 4.18474 + 0.469686i 0.670094 + 0.0752100i
\(40\) −2.74586 4.75596i −0.434158 0.751984i
\(41\) 5.51406 3.18355i 0.861152 0.497186i −0.00324599 0.999995i \(-0.501033\pi\)
0.864398 + 0.502808i \(0.167700\pi\)
\(42\) 0 0
\(43\) 4.55195 7.88422i 0.694167 1.20233i −0.276294 0.961073i \(-0.589106\pi\)
0.970461 0.241259i \(-0.0775603\pi\)
\(44\) −0.891235 + 0.514555i −0.134359 + 0.0775721i
\(45\) 2.57127 1.48452i 0.383302 0.221299i
\(46\) −7.73776 + 4.46740i −1.14087 + 0.658681i
\(47\) 5.76714 3.32966i 0.841224 0.485681i −0.0164563 0.999865i \(-0.505238\pi\)
0.857680 + 0.514184i \(0.171905\pi\)
\(48\) −1.82316 + 3.15780i −0.263150 + 0.455790i
\(49\) 0 0
\(50\) 1.88631 1.08906i 0.266764 0.154016i
\(51\) −1.60237 2.77539i −0.224377 0.388632i
\(52\) 0.534557 + 1.22378i 0.0741297 + 0.169708i
\(53\) 5.24396 9.08280i 0.720313 1.24762i −0.240561 0.970634i \(-0.577331\pi\)
0.960874 0.276985i \(-0.0893352\pi\)
\(54\) −5.98587 3.45594i −0.814573 0.470294i
\(55\) 2.52131 + 4.36703i 0.339973 + 0.588850i
\(56\) 0 0
\(57\) 6.85564i 0.908052i
\(58\) 4.48855i 0.589375i
\(59\) −2.66212 + 1.53698i −0.346579 + 0.200097i −0.663177 0.748462i \(-0.730793\pi\)
0.316598 + 0.948560i \(0.397459\pi\)
\(60\) −0.679899 0.392540i −0.0877746 0.0506767i
\(61\) 1.08178 0.138508 0.0692541 0.997599i \(-0.477938\pi\)
0.0692541 + 0.997599i \(0.477938\pi\)
\(62\) 1.31931 + 2.28511i 0.167552 + 0.290209i
\(63\) 0 0
\(64\) −8.88199 −1.11025
\(65\) 5.99651 2.61932i 0.743775 0.324886i
\(66\) 2.07127 3.58755i 0.254956 0.441596i
\(67\) 5.01796i 0.613042i 0.951864 + 0.306521i \(0.0991649\pi\)
−0.951864 + 0.306521i \(0.900835\pi\)
\(68\) 0.508159 0.880158i 0.0616234 0.106735i
\(69\) −4.08721 + 7.07925i −0.492042 + 0.852242i
\(70\) 0 0
\(71\) 2.35453 + 1.35939i 0.279431 + 0.161330i 0.633166 0.774016i \(-0.281755\pi\)
−0.353735 + 0.935346i \(0.615088\pi\)
\(72\) 4.95030i 0.583399i
\(73\) 6.64426 + 3.83607i 0.777652 + 0.448978i 0.835598 0.549342i \(-0.185122\pi\)
−0.0579454 + 0.998320i \(0.518455\pi\)
\(74\) 1.11254 + 1.92698i 0.129330 + 0.224006i
\(75\) 0.996377 1.72578i 0.115052 0.199275i
\(76\) 1.88285 1.08706i 0.215978 0.124695i
\(77\) 0 0
\(78\) −4.32659 3.19030i −0.489890 0.361230i
\(79\) 7.86993 + 13.6311i 0.885436 + 1.53362i 0.845213 + 0.534430i \(0.179474\pi\)
0.0402236 + 0.999191i \(0.487193\pi\)
\(80\) 5.66612i 0.633492i
\(81\) −1.41581 −0.157313
\(82\) −8.12800 −0.897587
\(83\) 7.97408i 0.875269i 0.899153 + 0.437635i \(0.144184\pi\)
−0.899153 + 0.437635i \(0.855816\pi\)
\(84\) 0 0
\(85\) −4.31275 2.48997i −0.467784 0.270075i
\(86\) −10.0647 + 5.81086i −1.08531 + 0.626601i
\(87\) −2.05328 3.55639i −0.220135 0.381285i
\(88\) 8.40757 0.896250
\(89\) 13.9118 + 8.03198i 1.47465 + 0.851388i 0.999592 0.0285683i \(-0.00909482\pi\)
0.475055 + 0.879956i \(0.342428\pi\)
\(90\) −3.79017 −0.399519
\(91\) 0 0
\(92\) −2.59235 −0.270271
\(93\) 2.09064 + 1.20703i 0.216789 + 0.125163i
\(94\) −8.50105 −0.876816
\(95\) −5.32659 9.22592i −0.546497 0.946560i
\(96\) −2.09007 + 1.20670i −0.213317 + 0.123158i
\(97\) −12.3209 7.11347i −1.25100 0.722263i −0.279689 0.960091i \(-0.590231\pi\)
−0.971307 + 0.237827i \(0.923565\pi\)
\(98\) 0 0
\(99\) 4.54548i 0.456838i
\(100\) 0.631962 0.0631962
\(101\) 0.0731225 0.00727596 0.00363798 0.999993i \(-0.498842\pi\)
0.00363798 + 0.999993i \(0.498842\pi\)
\(102\) 4.09105i 0.405075i
\(103\) −6.45980 11.1887i −0.636503 1.10245i −0.986195 0.165590i \(-0.947047\pi\)
0.349692 0.936865i \(-0.386286\pi\)
\(104\) 1.21690 10.8421i 0.119327 1.06316i
\(105\) 0 0
\(106\) −11.5948 + 6.69425i −1.12618 + 0.650203i
\(107\) −2.00427 + 3.47150i −0.193761 + 0.335603i −0.946493 0.322723i \(-0.895402\pi\)
0.752733 + 0.658326i \(0.228735\pi\)
\(108\) −1.00271 1.73675i −0.0964860 0.167119i
\(109\) 1.71984 + 0.992947i 0.164730 + 0.0951071i 0.580099 0.814546i \(-0.303014\pi\)
−0.415368 + 0.909653i \(0.636347\pi\)
\(110\) 6.43722i 0.613765i
\(111\) 1.76299 + 1.01786i 0.167335 + 0.0966110i
\(112\) 0 0
\(113\) 5.28711 9.15754i 0.497369 0.861469i −0.502626 0.864504i \(-0.667633\pi\)
0.999995 + 0.00303506i \(0.000966090\pi\)
\(114\) −4.37583 + 7.57916i −0.409834 + 0.709854i
\(115\) 12.7025i 1.18451i
\(116\) 0.651157 1.12784i 0.0604584 0.104717i
\(117\) 5.86170 + 0.657905i 0.541914 + 0.0608233i
\(118\) 3.92410 0.361243
\(119\) 0 0
\(120\) 3.20695 + 5.55461i 0.292753 + 0.507064i
\(121\) 3.27998 0.298180
\(122\) −1.19595 0.690483i −0.108276 0.0625134i
\(123\) −6.44001 + 3.71814i −0.580676 + 0.335254i
\(124\) 0.765571i 0.0687503i
\(125\) 12.1710i 1.08860i
\(126\) 0 0
\(127\) 5.63478 + 9.75972i 0.500006 + 0.866035i 1.00000 6.53271e-6i \(2.07943e-6\pi\)
−0.499994 + 0.866029i \(0.666665\pi\)
\(128\) 6.24025 + 3.60281i 0.551566 + 0.318447i
\(129\) −5.31634 + 9.20818i −0.468078 + 0.810735i
\(130\) −8.30123 0.931713i −0.728066 0.0817166i
\(131\) −1.53241 2.65421i −0.133887 0.231899i 0.791285 0.611448i \(-0.209413\pi\)
−0.925172 + 0.379549i \(0.876079\pi\)
\(132\) 1.04090 0.600962i 0.0905984 0.0523070i
\(133\) 0 0
\(134\) 3.20288 5.54754i 0.276686 0.479235i
\(135\) −8.51002 + 4.91326i −0.732426 + 0.422867i
\(136\) −7.19067 + 4.15154i −0.616595 + 0.355991i
\(137\) −18.9512 + 10.9415i −1.61911 + 0.934796i −0.631965 + 0.774997i \(0.717751\pi\)
−0.987150 + 0.159799i \(0.948915\pi\)
\(138\) 9.03712 5.21758i 0.769291 0.444150i
\(139\) −5.53535 + 9.58750i −0.469502 + 0.813201i −0.999392 0.0348652i \(-0.988900\pi\)
0.529890 + 0.848066i \(0.322233\pi\)
\(140\) 0 0
\(141\) −6.73559 + 3.88879i −0.567239 + 0.327495i
\(142\) −1.73534 3.00570i −0.145627 0.252233i
\(143\) −1.11738 + 9.95549i −0.0934403 + 0.832520i
\(144\) −2.55376 + 4.42324i −0.212813 + 0.368603i
\(145\) −5.52637 3.19065i −0.458940 0.264969i
\(146\) −4.89699 8.48183i −0.405277 0.701961i
\(147\) 0 0
\(148\) 0.645588i 0.0530670i
\(149\) 2.30737i 0.189027i 0.995524 + 0.0945136i \(0.0301296\pi\)
−0.995524 + 0.0945136i \(0.969870\pi\)
\(150\) −2.20306 + 1.27194i −0.179879 + 0.103853i
\(151\) 17.8538 + 10.3079i 1.45292 + 0.838845i 0.998646 0.0520168i \(-0.0165649\pi\)
0.454275 + 0.890861i \(0.349898\pi\)
\(152\) −17.7621 −1.44070
\(153\) −2.24449 3.88757i −0.181456 0.314292i
\(154\) 0 0
\(155\) 3.75128 0.301310
\(156\) −0.624323 1.42929i −0.0499858 0.114435i
\(157\) −1.44824 + 2.50843i −0.115582 + 0.200194i −0.918012 0.396552i \(-0.870207\pi\)
0.802430 + 0.596746i \(0.203540\pi\)
\(158\) 20.0929i 1.59851i
\(159\) −6.12455 + 10.6080i −0.485709 + 0.841272i
\(160\) −1.87513 + 3.24782i −0.148242 + 0.256763i
\(161\) 0 0
\(162\) 1.56523 + 0.903688i 0.122976 + 0.0710004i
\(163\) 23.4339i 1.83549i 0.397175 + 0.917743i \(0.369990\pi\)
−0.397175 + 0.917743i \(0.630010\pi\)
\(164\) −2.04232 1.17913i −0.159478 0.0920750i
\(165\) −2.94470 5.10037i −0.229244 0.397063i
\(166\) 5.08971 8.81564i 0.395038 0.684226i
\(167\) 6.58349 3.80098i 0.509446 0.294129i −0.223160 0.974782i \(-0.571637\pi\)
0.732606 + 0.680653i \(0.238304\pi\)
\(168\) 0 0
\(169\) 12.6765 + 2.88188i 0.975119 + 0.221683i
\(170\) 3.17861 + 5.50551i 0.243788 + 0.422253i
\(171\) 9.60292i 0.734353i
\(172\) −3.37194 −0.257108
\(173\) −5.39721 −0.410343 −0.205171 0.978726i \(-0.565775\pi\)
−0.205171 + 0.978726i \(0.565775\pi\)
\(174\) 5.24229i 0.397417i
\(175\) 0 0
\(176\) −7.51241 4.33729i −0.566269 0.326936i
\(177\) 3.10916 1.79508i 0.233699 0.134926i
\(178\) −10.2533 17.7593i −0.768520 1.33112i
\(179\) 12.2914 0.918704 0.459352 0.888254i \(-0.348082\pi\)
0.459352 + 0.888254i \(0.348082\pi\)
\(180\) −0.952357 0.549843i −0.0709845 0.0409829i
\(181\) −21.8525 −1.62428 −0.812140 0.583463i \(-0.801697\pi\)
−0.812140 + 0.583463i \(0.801697\pi\)
\(182\) 0 0
\(183\) −1.26344 −0.0933964
\(184\) 18.3415 + 10.5894i 1.35215 + 0.780664i
\(185\) 3.16337 0.232575
\(186\) −1.54085 2.66883i −0.112981 0.195688i
\(187\) 6.60264 3.81204i 0.482833 0.278764i
\(188\) −2.13606 1.23325i −0.155788 0.0899442i
\(189\) 0 0
\(190\) 13.5995i 0.986609i
\(191\) 2.75716 0.199501 0.0997507 0.995012i \(-0.468195\pi\)
0.0997507 + 0.995012i \(0.468195\pi\)
\(192\) 10.3735 0.748643
\(193\) 12.9893i 0.934993i 0.883995 + 0.467497i \(0.154844\pi\)
−0.883995 + 0.467497i \(0.845156\pi\)
\(194\) 9.08080 + 15.7284i 0.651963 + 1.12923i
\(195\) −7.00347 + 3.05917i −0.501529 + 0.219071i
\(196\) 0 0
\(197\) 16.4772 9.51312i 1.17395 0.677781i 0.219344 0.975648i \(-0.429608\pi\)
0.954608 + 0.297866i \(0.0962749\pi\)
\(198\) 2.90130 5.02519i 0.206186 0.357125i
\(199\) −10.0159 17.3480i −0.710006 1.22977i −0.964854 0.262786i \(-0.915359\pi\)
0.254848 0.966981i \(-0.417975\pi\)
\(200\) −4.47127 2.58149i −0.316166 0.182539i
\(201\) 5.86061i 0.413375i
\(202\) −0.0808396 0.0466728i −0.00568785 0.00328388i
\(203\) 0 0
\(204\) −0.593492 + 1.02796i −0.0415528 + 0.0719715i
\(205\) −5.77773 + 10.0073i −0.403534 + 0.698942i
\(206\) 16.4927i 1.14910i
\(207\) −5.72509 + 9.91614i −0.397921 + 0.689219i
\(208\) −6.68057 + 9.05999i −0.463214 + 0.628197i
\(209\) 16.3096 1.12816
\(210\) 0 0
\(211\) −5.00015 8.66052i −0.344225 0.596215i 0.640988 0.767551i \(-0.278525\pi\)
−0.985213 + 0.171336i \(0.945192\pi\)
\(212\) −3.88456 −0.266793
\(213\) −2.74991 1.58766i −0.188421 0.108785i
\(214\) 4.43160 2.55858i 0.302938 0.174901i
\(215\) 16.5224i 1.12682i
\(216\) 16.3838i 1.11478i
\(217\) 0 0
\(218\) −1.26756 2.19548i −0.0858501 0.148697i
\(219\) −7.76000 4.48024i −0.524372 0.302747i
\(220\) 0.933852 1.61748i 0.0629603 0.109050i
\(221\) −3.96022 9.06629i −0.266393 0.609865i
\(222\) −1.29936 2.25056i −0.0872076 0.151048i
\(223\) 7.25954 4.19130i 0.486135 0.280670i −0.236835 0.971550i \(-0.576110\pi\)
0.722970 + 0.690880i \(0.242777\pi\)
\(224\) 0 0
\(225\) 1.39566 2.41735i 0.0930439 0.161157i
\(226\) −11.6902 + 6.74933i −0.777620 + 0.448959i
\(227\) 0.796500 0.459860i 0.0528656 0.0305220i −0.473334 0.880883i \(-0.656950\pi\)
0.526200 + 0.850361i \(0.323616\pi\)
\(228\) −2.19903 + 1.26961i −0.145634 + 0.0840820i
\(229\) 21.3222 12.3104i 1.40901 0.813494i 0.413719 0.910404i \(-0.364229\pi\)
0.995293 + 0.0969108i \(0.0308962\pi\)
\(230\) 8.10776 14.0430i 0.534610 0.925971i
\(231\) 0 0
\(232\) −9.21415 + 5.31979i −0.604939 + 0.349261i
\(233\) −8.63847 14.9623i −0.565925 0.980211i −0.996963 0.0778773i \(-0.975186\pi\)
0.431038 0.902334i \(-0.358148\pi\)
\(234\) −6.06040 4.46876i −0.396180 0.292132i
\(235\) −6.04291 + 10.4666i −0.394196 + 0.682767i
\(236\) 0.986008 + 0.569272i 0.0641837 + 0.0370565i
\(237\) −9.19149 15.9201i −0.597051 1.03412i
\(238\) 0 0
\(239\) 14.4828i 0.936816i 0.883512 + 0.468408i \(0.155172\pi\)
−0.883512 + 0.468408i \(0.844828\pi\)
\(240\) 6.61760i 0.427165i
\(241\) 7.30441 4.21720i 0.470518 0.271654i −0.245938 0.969285i \(-0.579096\pi\)
0.716457 + 0.697632i \(0.245763\pi\)
\(242\) −3.62614 2.09355i −0.233097 0.134579i
\(243\) −14.5898 −0.935934
\(244\) −0.200338 0.346995i −0.0128253 0.0222141i
\(245\) 0 0
\(246\) 9.49290 0.605245
\(247\) 2.36062 21.0323i 0.150203 1.33825i
\(248\) 3.12726 5.41658i 0.198581 0.343953i
\(249\) 9.31313i 0.590196i
\(250\) −7.76851 + 13.4555i −0.491324 + 0.850998i
\(251\) −7.33631 + 12.7069i −0.463064 + 0.802050i −0.999112 0.0421373i \(-0.986583\pi\)
0.536048 + 0.844188i \(0.319917\pi\)
\(252\) 0 0
\(253\) −16.8415 9.72346i −1.05882 0.611309i
\(254\) 14.3863i 0.902677i
\(255\) 5.03697 + 2.90810i 0.315427 + 0.182112i
\(256\) 4.28277 + 7.41797i 0.267673 + 0.463623i
\(257\) 14.6643 25.3993i 0.914733 1.58436i 0.107441 0.994211i \(-0.465734\pi\)
0.807292 0.590152i \(-0.200932\pi\)
\(258\) 11.7548 6.78665i 0.731824 0.422519i
\(259\) 0 0
\(260\) −1.95068 1.43838i −0.120976 0.0892043i
\(261\) −2.87610 4.98155i −0.178026 0.308350i
\(262\) 3.91243i 0.241711i
\(263\) 19.9149 1.22801 0.614004 0.789303i \(-0.289558\pi\)
0.614004 + 0.789303i \(0.289558\pi\)
\(264\) −9.81942 −0.604343
\(265\) 19.0342i 1.16926i
\(266\) 0 0
\(267\) −16.2479 9.38075i −0.994357 0.574092i
\(268\) 1.60957 0.929287i 0.0983203 0.0567652i
\(269\) 11.1625 + 19.3340i 0.680589 + 1.17881i 0.974801 + 0.223074i \(0.0716093\pi\)
−0.294213 + 0.955740i \(0.595057\pi\)
\(270\) 12.5442 0.763415
\(271\) 8.14054 + 4.69994i 0.494502 + 0.285501i 0.726440 0.687230i \(-0.241173\pi\)
−0.231938 + 0.972731i \(0.574507\pi\)
\(272\) 8.56677 0.519437
\(273\) 0 0
\(274\) 27.9351 1.68762
\(275\) 4.10562 + 2.37038i 0.247578 + 0.142939i
\(276\) 3.02767 0.182245
\(277\) −7.17133 12.4211i −0.430883 0.746312i 0.566066 0.824360i \(-0.308465\pi\)
−0.996950 + 0.0780478i \(0.975131\pi\)
\(278\) 12.2391 7.06622i 0.734050 0.423804i
\(279\) 2.92842 + 1.69073i 0.175320 + 0.101221i
\(280\) 0 0
\(281\) 0.0988416i 0.00589640i 0.999996 + 0.00294820i \(0.000938442\pi\)
−0.999996 + 0.00294820i \(0.999062\pi\)
\(282\) 9.92859 0.591239
\(283\) 0.620673 0.0368952 0.0184476 0.999830i \(-0.494128\pi\)
0.0184476 + 0.999830i \(0.494128\pi\)
\(284\) 1.00699i 0.0597539i
\(285\) 6.22106 + 10.7752i 0.368504 + 0.638267i
\(286\) 7.58972 10.2930i 0.448789 0.608635i
\(287\) 0 0
\(288\) −2.92763 + 1.69027i −0.172512 + 0.0995998i
\(289\) 4.73534 8.20186i 0.278550 0.482462i
\(290\) 4.07307 + 7.05477i 0.239179 + 0.414270i
\(291\) 14.3899 + 8.30800i 0.843549 + 0.487023i
\(292\) 2.84164i 0.166294i
\(293\) 21.5586 + 12.4469i 1.25947 + 0.727153i 0.972971 0.230928i \(-0.0741762\pi\)
0.286496 + 0.958082i \(0.407510\pi\)
\(294\) 0 0
\(295\) 2.78942 4.83142i 0.162406 0.281296i
\(296\) 2.63715 4.56767i 0.153281 0.265491i
\(297\) 15.0440i 0.872941i
\(298\) 1.47275 2.55088i 0.0853143 0.147769i
\(299\) −14.9767 + 20.3109i −0.866124 + 1.17461i
\(300\) −0.738085 −0.0426133
\(301\) 0 0
\(302\) −13.1587 22.7915i −0.757197 1.31150i
\(303\) −0.0854016 −0.00490619
\(304\) 15.8710 + 9.16310i 0.910262 + 0.525540i
\(305\) −1.70027 + 0.981651i −0.0973571 + 0.0562091i
\(306\) 5.73047i 0.327589i
\(307\) 9.89767i 0.564890i 0.959284 + 0.282445i \(0.0911455\pi\)
−0.959284 + 0.282445i \(0.908855\pi\)
\(308\) 0 0
\(309\) 7.54456 + 13.0676i 0.429195 + 0.743387i
\(310\) −4.14718 2.39437i −0.235544 0.135991i
\(311\) 3.61895 6.26820i 0.205212 0.355437i −0.744988 0.667077i \(-0.767545\pi\)
0.950200 + 0.311640i \(0.100878\pi\)
\(312\) −1.42125 + 12.6628i −0.0804622 + 0.716890i
\(313\) −16.3303 28.2849i −0.923043 1.59876i −0.794678 0.607031i \(-0.792360\pi\)
−0.128365 0.991727i \(-0.540973\pi\)
\(314\) 3.20217 1.84877i 0.180709 0.104332i
\(315\) 0 0
\(316\) 2.91490 5.04875i 0.163976 0.284014i
\(317\) 14.8734 8.58718i 0.835375 0.482304i −0.0203143 0.999794i \(-0.506467\pi\)
0.855690 + 0.517489i \(0.173133\pi\)
\(318\) 13.5418 7.81838i 0.759388 0.438433i
\(319\) 8.46064 4.88475i 0.473705 0.273494i
\(320\) 13.9601 8.05984i 0.780391 0.450559i
\(321\) 2.34084 4.05446i 0.130653 0.226298i
\(322\) 0 0
\(323\) −13.9489 + 8.05342i −0.776140 + 0.448105i
\(324\) 0.262197 + 0.454139i 0.0145665 + 0.0252299i
\(325\) 3.65101 4.95139i 0.202521 0.274654i
\(326\) 14.9574 25.9071i 0.828416 1.43486i
\(327\) −2.00864 1.15969i −0.111078 0.0641309i
\(328\) 9.63324 + 16.6853i 0.531907 + 0.921289i
\(329\) 0 0
\(330\) 7.51819i 0.413863i
\(331\) 19.9340i 1.09567i −0.836587 0.547835i \(-0.815452\pi\)
0.836587 0.547835i \(-0.184548\pi\)
\(332\) 2.55778 1.47674i 0.140377 0.0810465i
\(333\) 2.46947 + 1.42575i 0.135326 + 0.0781306i
\(334\) −9.70438 −0.531000
\(335\) −4.55348 7.88687i −0.248783 0.430905i
\(336\) 0 0
\(337\) 1.27189 0.0692842 0.0346421 0.999400i \(-0.488971\pi\)
0.0346421 + 0.999400i \(0.488971\pi\)
\(338\) −12.1749 11.2772i −0.662229 0.613401i
\(339\) −6.17495 + 10.6953i −0.335377 + 0.580890i
\(340\) 1.84449i 0.100032i
\(341\) −2.87152 + 4.97363i −0.155502 + 0.269337i
\(342\) −6.12937 + 10.6164i −0.331438 + 0.574068i
\(343\) 0 0
\(344\) 23.8572 + 13.7740i 1.28630 + 0.742643i
\(345\) 14.8355i 0.798718i
\(346\) 5.96682 + 3.44494i 0.320778 + 0.185201i
\(347\) −12.9417 22.4156i −0.694744 1.20333i −0.970267 0.242038i \(-0.922184\pi\)
0.275522 0.961295i \(-0.411149\pi\)
\(348\) −0.760503 + 1.31723i −0.0407672 + 0.0706109i
\(349\) −14.9967 + 8.65837i −0.802757 + 0.463472i −0.844434 0.535659i \(-0.820063\pi\)
0.0416774 + 0.999131i \(0.486730\pi\)
\(350\) 0 0
\(351\) −19.4002 2.17744i −1.03551 0.116223i
\(352\) −2.87074 4.97227i −0.153011 0.265023i
\(353\) 25.3495i 1.34922i −0.738176 0.674608i \(-0.764313\pi\)
0.738176 0.674608i \(-0.235687\pi\)
\(354\) −4.58306 −0.243587
\(355\) −4.93423 −0.261882
\(356\) 5.94983i 0.315341i
\(357\) 0 0
\(358\) −13.5886 7.84539i −0.718181 0.414642i
\(359\) −4.56434 + 2.63522i −0.240897 + 0.139082i −0.615589 0.788068i \(-0.711082\pi\)
0.374692 + 0.927149i \(0.377748\pi\)
\(360\) 4.49208 + 7.78052i 0.236754 + 0.410069i
\(361\) −15.4561 −0.813478
\(362\) 24.1587 + 13.9480i 1.26975 + 0.733092i
\(363\) −3.83077 −0.201063
\(364\) 0 0
\(365\) −13.9240 −0.728813
\(366\) 1.39678 + 0.806433i 0.0730110 + 0.0421529i
\(367\) 25.3176 1.32157 0.660783 0.750577i \(-0.270224\pi\)
0.660783 + 0.750577i \(0.270224\pi\)
\(368\) −10.9257 18.9240i −0.569544 0.986479i
\(369\) −9.02073 + 5.20812i −0.469601 + 0.271124i
\(370\) −3.49722 2.01912i −0.181812 0.104969i
\(371\) 0 0
\(372\) 0.894130i 0.0463585i
\(373\) −6.78782 −0.351460 −0.175730 0.984438i \(-0.556229\pi\)
−0.175730 + 0.984438i \(0.556229\pi\)
\(374\) −9.73261 −0.503262
\(375\) 14.2148i 0.734048i
\(376\) 10.0754 + 17.4511i 0.519598 + 0.899970i
\(377\) −5.07464 11.6176i −0.261357 0.598336i
\(378\) 0 0
\(379\) 10.6717 6.16130i 0.548168 0.316485i −0.200215 0.979752i \(-0.564164\pi\)
0.748383 + 0.663267i \(0.230831\pi\)
\(380\) −1.97288 + 3.41714i −0.101207 + 0.175295i
\(381\) −6.58100 11.3986i −0.337155 0.583969i
\(382\) −3.04815 1.75985i −0.155957 0.0900417i
\(383\) 7.25917i 0.370926i 0.982651 + 0.185463i \(0.0593785\pi\)
−0.982651 + 0.185463i \(0.940621\pi\)
\(384\) −7.28815 4.20782i −0.371922 0.214729i
\(385\) 0 0
\(386\) 8.29086 14.3602i 0.421994 0.730915i
\(387\) −7.44677 + 12.8982i −0.378541 + 0.655652i
\(388\) 5.26943i 0.267515i
\(389\) −3.57406 + 6.19045i −0.181212 + 0.313868i −0.942293 0.334788i \(-0.891335\pi\)
0.761082 + 0.648656i \(0.224669\pi\)
\(390\) 9.69521 + 1.08817i 0.490936 + 0.0551017i
\(391\) 19.2052 0.971250
\(392\) 0 0
\(393\) 1.78974 + 3.09991i 0.0902802 + 0.156370i
\(394\) −24.2882 −1.22362
\(395\) −24.7388 14.2829i −1.24474 0.718652i
\(396\) 1.45802 0.841786i 0.0732681 0.0423014i
\(397\) 22.4612i 1.12729i 0.826016 + 0.563647i \(0.190602\pi\)
−0.826016 + 0.563647i \(0.809398\pi\)
\(398\) 25.5718i 1.28180i
\(399\) 0 0
\(400\) 2.66347 + 4.61327i 0.133174 + 0.230663i
\(401\) 2.64547 + 1.52736i 0.132108 + 0.0762729i 0.564598 0.825366i \(-0.309031\pi\)
−0.432489 + 0.901639i \(0.642365\pi\)
\(402\) −3.74072 + 6.47912i −0.186570 + 0.323149i
\(403\) 5.99820 + 4.42290i 0.298792 + 0.220320i
\(404\) −0.0135417 0.0234549i −0.000673725 0.00116693i
\(405\) 2.22527 1.28476i 0.110575 0.0638403i
\(406\) 0 0
\(407\) −2.42149 + 4.19414i −0.120029 + 0.207896i
\(408\) 8.39817 4.84869i 0.415771 0.240046i
\(409\) −4.85482 + 2.80293i −0.240055 + 0.138596i −0.615202 0.788369i \(-0.710926\pi\)
0.375147 + 0.926965i \(0.377592\pi\)
\(410\) 12.7750 7.37564i 0.630912 0.364257i
\(411\) 22.1336 12.7789i 1.09177 0.630335i
\(412\) −2.39261 + 4.14412i −0.117875 + 0.204166i
\(413\) 0 0
\(414\) 12.6586 7.30844i 0.622136 0.359190i
\(415\) −7.23597 12.5331i −0.355200 0.615224i
\(416\) −6.82758 + 2.98233i −0.334750 + 0.146221i
\(417\) 6.46487 11.1975i 0.316586 0.548343i
\(418\) −18.0308 10.4101i −0.881916 0.509175i
\(419\) −3.06969 5.31687i −0.149964 0.259746i 0.781250 0.624219i \(-0.214583\pi\)
−0.931214 + 0.364473i \(0.881249\pi\)
\(420\) 0 0
\(421\) 1.92589i 0.0938622i −0.998898 0.0469311i \(-0.985056\pi\)
0.998898 0.0469311i \(-0.0149441\pi\)
\(422\) 12.7660i 0.621441i
\(423\) −9.43475 + 5.44716i −0.458733 + 0.264850i
\(424\) 27.4841 + 15.8679i 1.33475 + 0.770615i
\(425\) −4.68184 −0.227102
\(426\) 2.02675 + 3.51044i 0.0981965 + 0.170081i
\(427\) 0 0
\(428\) 1.48470 0.0717658
\(429\) 1.30502 11.6273i 0.0630070 0.561370i
\(430\) 10.5460 18.2662i 0.508572 0.880873i
\(431\) 10.7494i 0.517779i 0.965907 + 0.258890i \(0.0833566\pi\)
−0.965907 + 0.258890i \(0.916643\pi\)
\(432\) 8.45207 14.6394i 0.406651 0.704340i
\(433\) 20.1328 34.8710i 0.967520 1.67579i 0.264835 0.964294i \(-0.414682\pi\)
0.702685 0.711501i \(-0.251984\pi\)
\(434\) 0 0
\(435\) 6.45439 + 3.72644i 0.309464 + 0.178669i
\(436\) 0.735544i 0.0352262i
\(437\) 35.5799 + 20.5421i 1.70202 + 0.982662i
\(438\) 5.71931 + 9.90614i 0.273279 + 0.473334i
\(439\) −10.9754 + 19.0099i −0.523826 + 0.907294i 0.475789 + 0.879560i \(0.342163\pi\)
−0.999615 + 0.0277345i \(0.991171\pi\)
\(440\) −13.2144 + 7.62934i −0.629972 + 0.363715i
\(441\) 0 0
\(442\) −1.40868 + 12.5509i −0.0670042 + 0.596984i
\(443\) 13.9482 + 24.1589i 0.662697 + 1.14783i 0.979904 + 0.199469i \(0.0639217\pi\)
−0.317207 + 0.948356i \(0.602745\pi\)
\(444\) 0.753999i 0.0357832i
\(445\) −29.1540 −1.38203
\(446\) −10.7009 −0.506703
\(447\) 2.69484i 0.127461i
\(448\) 0 0
\(449\) 19.1056 + 11.0306i 0.901648 + 0.520567i 0.877734 0.479147i \(-0.159054\pi\)
0.0239134 + 0.999714i \(0.492387\pi\)
\(450\) −3.08590 + 1.78165i −0.145471 + 0.0839876i
\(451\) −8.84546 15.3208i −0.416516 0.721427i
\(452\) −3.91652 −0.184218
\(453\) −20.8519 12.0389i −0.979708 0.565635i
\(454\) −1.17408 −0.0551023
\(455\) 0 0
\(456\) 20.7448 0.971464
\(457\) −4.77724 2.75814i −0.223470 0.129020i 0.384086 0.923297i \(-0.374517\pi\)
−0.607556 + 0.794277i \(0.707850\pi\)
\(458\) −31.4300 −1.46863
\(459\) 7.42851 + 12.8665i 0.346733 + 0.600559i
\(460\) 4.07447 2.35240i 0.189973 0.109681i
\(461\) 25.0092 + 14.4391i 1.16479 + 0.672494i 0.952448 0.304700i \(-0.0985562\pi\)
0.212346 + 0.977195i \(0.431890\pi\)
\(462\) 0 0
\(463\) 14.2284i 0.661251i 0.943762 + 0.330625i \(0.107260\pi\)
−0.943762 + 0.330625i \(0.892740\pi\)
\(464\) 10.9775 0.509617
\(465\) −4.38121 −0.203174
\(466\) 22.0551i 1.02168i
\(467\) −2.27163 3.93457i −0.105118 0.182070i 0.808668 0.588265i \(-0.200189\pi\)
−0.913787 + 0.406195i \(0.866855\pi\)
\(468\) −0.874509 2.00205i −0.0404242 0.0925448i
\(469\) 0 0
\(470\) 13.3613 7.71416i 0.616312 0.355828i
\(471\) 1.69144 2.92966i 0.0779374 0.134992i
\(472\) −4.65081 8.05545i −0.214071 0.370782i
\(473\) −21.9062 12.6476i −1.00725 0.581536i
\(474\) 23.4671i 1.07788i
\(475\) −8.67366 5.00774i −0.397975 0.229771i
\(476\) 0 0
\(477\) −8.57886 + 14.8590i −0.392799 + 0.680348i
\(478\) 9.24413 16.0113i 0.422817 0.732340i
\(479\) 1.66553i 0.0760999i −0.999276 0.0380499i \(-0.987885\pi\)
0.999276 0.0380499i \(-0.0121146\pi\)
\(480\) 2.19001 3.79321i 0.0999598 0.173135i
\(481\) 5.05815 + 3.72973i 0.230632 + 0.170061i
\(482\) −10.7671 −0.490426
\(483\) 0 0
\(484\) −0.607426 1.05209i −0.0276103 0.0478224i
\(485\) 25.8201 1.17243
\(486\) 16.1295 + 9.31239i 0.731650 + 0.422418i
\(487\) 1.28598 0.742463i 0.0582735 0.0336442i −0.470580 0.882357i \(-0.655955\pi\)
0.528854 + 0.848713i \(0.322622\pi\)
\(488\) 3.27342i 0.148181i
\(489\) 27.3691i 1.23767i
\(490\) 0 0
\(491\) 7.99791 + 13.8528i 0.360941 + 0.625167i 0.988116 0.153711i \(-0.0491224\pi\)
−0.627175 + 0.778878i \(0.715789\pi\)
\(492\) 2.38528 + 1.37714i 0.107537 + 0.0620863i
\(493\) −4.82404 + 8.35548i −0.217264 + 0.376312i
\(494\) −16.0343 + 21.7452i −0.721416 + 0.978363i
\(495\) −4.12473 7.14425i −0.185393 0.321110i
\(496\) −5.58860 + 3.22658i −0.250936 + 0.144878i
\(497\) 0 0
\(498\) −5.94440 + 10.2960i −0.266375 + 0.461375i
\(499\) −15.3459 + 8.85997i −0.686977 + 0.396627i −0.802479 0.596681i \(-0.796486\pi\)
0.115501 + 0.993307i \(0.463153\pi\)
\(500\) −3.90398 + 2.25397i −0.174591 + 0.100800i
\(501\) −7.68902 + 4.43926i −0.343520 + 0.198331i
\(502\) 16.2211 9.36527i 0.723984 0.417993i
\(503\) 0.598451 1.03655i 0.0266836 0.0462174i −0.852375 0.522931i \(-0.824839\pi\)
0.879059 + 0.476713i \(0.158172\pi\)
\(504\) 0 0
\(505\) −0.114929 + 0.0663540i −0.00511425 + 0.00295272i
\(506\) 12.4126 + 21.4993i 0.551809 + 0.955760i
\(507\) −14.8053 3.36582i −0.657524 0.149481i
\(508\) 2.08703 3.61485i 0.0925971 0.160383i
\(509\) −5.44396 3.14307i −0.241299 0.139314i 0.374474 0.927237i \(-0.377823\pi\)
−0.615774 + 0.787923i \(0.711156\pi\)
\(510\) −3.71237 6.43002i −0.164387 0.284726i
\(511\) 0 0
\(512\) 25.3457i 1.12013i
\(513\) 31.7824i 1.40323i
\(514\) −32.4238 + 18.7199i −1.43015 + 0.825699i
\(515\) 20.3061 + 11.7237i 0.894792 + 0.516608i
\(516\) 3.93818 0.173369
\(517\) −9.25143 16.0240i −0.406878 0.704733i
\(518\) 0 0
\(519\) 6.30354 0.276695
\(520\) 7.92592 + 18.1451i 0.347574 + 0.795716i
\(521\) 5.42367 9.39407i 0.237615 0.411562i −0.722414 0.691460i \(-0.756968\pi\)
0.960029 + 0.279899i \(0.0903010\pi\)
\(522\) 7.34304i 0.321396i
\(523\) −0.673629 + 1.16676i −0.0294557 + 0.0510188i −0.880377 0.474274i \(-0.842711\pi\)
0.850922 + 0.525292i \(0.176044\pi\)
\(524\) −0.567579 + 0.983076i −0.0247948 + 0.0429459i
\(525\) 0 0
\(526\) −22.0167 12.7113i −0.959974 0.554241i
\(527\) 5.67167i 0.247062i
\(528\) 8.77394 + 5.06563i 0.381837 + 0.220453i
\(529\) −12.9936 22.5057i −0.564941 0.978507i
\(530\) 12.1492 21.0431i 0.527728 0.914052i
\(531\) 4.35510 2.51442i 0.188995 0.109117i
\(532\) 0 0
\(533\) −21.0375 + 9.18931i −0.911233 + 0.398033i
\(534\) 11.9751 + 20.7415i 0.518214 + 0.897574i
\(535\) 7.27501i 0.314526i
\(536\) −15.1841 −0.655853
\(537\) −14.3555 −0.619484
\(538\) 28.4993i 1.22869i
\(539\) 0 0
\(540\) 3.15198 + 1.81980i 0.135640 + 0.0783115i
\(541\) −17.4565 + 10.0785i −0.750516 + 0.433310i −0.825880 0.563846i \(-0.809321\pi\)
0.0753646 + 0.997156i \(0.475988\pi\)
\(542\) −5.99978 10.3919i −0.257712 0.446371i
\(543\) 25.5220 1.09526
\(544\) 4.91047 + 2.83506i 0.210535 + 0.121552i
\(545\) −3.60415 −0.154385
\(546\) 0 0
\(547\) −3.42286 −0.146351 −0.0731755 0.997319i \(-0.523313\pi\)
−0.0731755 + 0.997319i \(0.523313\pi\)
\(548\) 7.01924 + 4.05256i 0.299847 + 0.173117i
\(549\) −1.76975 −0.0755309
\(550\) −3.02594 5.24109i −0.129027 0.223481i
\(551\) −17.8742 + 10.3197i −0.761467 + 0.439633i
\(552\) −21.4214 12.3677i −0.911757 0.526403i
\(553\) 0 0
\(554\) 18.3093i 0.777889i
\(555\) −3.69458 −0.156826
\(556\) 4.10041 0.173896
\(557\) 23.6654i 1.00273i −0.865234 0.501367i \(-0.832830\pi\)
0.865234 0.501367i \(-0.167170\pi\)
\(558\) −2.15832 3.73832i −0.0913690 0.158256i
\(559\) −19.4806 + 26.4190i −0.823940 + 1.11740i
\(560\) 0 0
\(561\) −7.71139 + 4.45217i −0.325575 + 0.187971i
\(562\) 0.0630888 0.109273i 0.00266124 0.00460941i
\(563\) 14.4037 + 24.9480i 0.607045 + 1.05143i 0.991725 + 0.128382i \(0.0409784\pi\)
−0.384680 + 0.923050i \(0.625688\pi\)
\(564\) 2.49475 + 1.44035i 0.105048 + 0.0606496i
\(565\) 19.1909i 0.807366i
\(566\) −0.686177 0.396164i −0.0288422 0.0166520i
\(567\) 0 0
\(568\) −4.11343 + 7.12467i −0.172596 + 0.298945i
\(569\) −13.8361 + 23.9648i −0.580040 + 1.00466i 0.415434 + 0.909623i \(0.363630\pi\)
−0.995474 + 0.0950353i \(0.969704\pi\)
\(570\) 15.8832i 0.665272i
\(571\) 6.48273 11.2284i 0.271294 0.469895i −0.697899 0.716196i \(-0.745882\pi\)
0.969193 + 0.246301i \(0.0792151\pi\)
\(572\) 3.40027 1.48526i 0.142173 0.0621020i
\(573\) −3.22016 −0.134524
\(574\) 0 0
\(575\) 5.97105 + 10.3422i 0.249010 + 0.431298i
\(576\) 14.5305 0.605437
\(577\) 8.19301 + 4.73023i 0.341079 + 0.196922i 0.660749 0.750607i \(-0.270239\pi\)
−0.319670 + 0.947529i \(0.603572\pi\)
\(578\) −10.4702 + 6.04497i −0.435503 + 0.251438i
\(579\) 15.1706i 0.630468i
\(580\) 2.36354i 0.0981405i
\(581\) 0 0
\(582\) −10.6057 18.3696i −0.439620 0.761444i
\(583\) −25.2365 14.5703i −1.04519 0.603440i
\(584\) −11.6077 + 20.1052i −0.480332 + 0.831959i
\(585\) −9.80999 + 4.28507i −0.405593 + 0.177166i
\(586\) −15.8892 27.5209i −0.656377 1.13688i
\(587\) −18.6673 + 10.7776i −0.770481 + 0.444837i −0.833046 0.553204i \(-0.813405\pi\)
0.0625654 + 0.998041i \(0.480072\pi\)
\(588\) 0 0
\(589\) 6.06647 10.5074i 0.249965 0.432951i
\(590\) −6.16761 + 3.56087i −0.253917 + 0.146599i
\(591\) −19.2441 + 11.1106i −0.791598 + 0.457029i
\(592\) −4.71274 + 2.72090i −0.193692 + 0.111828i
\(593\) −3.44015 + 1.98617i −0.141270 + 0.0815622i −0.568969 0.822359i \(-0.692658\pi\)
0.427699 + 0.903921i \(0.359324\pi\)
\(594\) −9.60231 + 16.6317i −0.393988 + 0.682407i
\(595\) 0 0
\(596\) 0.740117 0.427307i 0.0303164 0.0175032i
\(597\) 11.6978 + 20.2612i 0.478759 + 0.829234i
\(598\) 29.5214 12.8951i 1.20722 0.527322i
\(599\) 9.75246 16.8918i 0.398475 0.690179i −0.595063 0.803679i \(-0.702873\pi\)
0.993538 + 0.113500i \(0.0362063\pi\)
\(600\) 5.22211 + 3.01498i 0.213192 + 0.123086i
\(601\) 13.4368 + 23.2733i 0.548100 + 0.949336i 0.998405 + 0.0564616i \(0.0179818\pi\)
−0.450305 + 0.892875i \(0.648685\pi\)
\(602\) 0 0
\(603\) 8.20914i 0.334302i
\(604\) 7.63576i 0.310695i
\(605\) −5.15523 + 2.97637i −0.209590 + 0.121007i
\(606\) 0.0944146 + 0.0545103i 0.00383533 + 0.00221433i
\(607\) 25.0203 1.01554 0.507772 0.861491i \(-0.330469\pi\)
0.507772 + 0.861491i \(0.330469\pi\)
\(608\) 6.06482 + 10.5046i 0.245961 + 0.426016i
\(609\) 0 0
\(610\) 2.50628 0.101476
\(611\) −22.0030 + 9.61106i −0.890146 + 0.388822i
\(612\) −0.831324 + 1.43990i −0.0336043 + 0.0582043i
\(613\) 21.3585i 0.862663i −0.902194 0.431332i \(-0.858044\pi\)
0.902194 0.431332i \(-0.141956\pi\)
\(614\) 6.31751 10.9422i 0.254954 0.441593i
\(615\) 6.74796 11.6878i 0.272104 0.471298i
\(616\) 0 0
\(617\) −28.5425 16.4790i −1.14908 0.663420i −0.200415 0.979711i \(-0.564229\pi\)
−0.948662 + 0.316291i \(0.897562\pi\)
\(618\) 19.2622i 0.774840i
\(619\) −42.3588 24.4559i −1.70254 0.982965i −0.943170 0.332311i \(-0.892172\pi\)
−0.759375 0.650654i \(-0.774495\pi\)
\(620\) −0.694707 1.20327i −0.0279001 0.0483244i
\(621\) 18.9481 32.8191i 0.760361 1.31698i
\(622\) −8.00176 + 4.61982i −0.320841 + 0.185238i
\(623\) 0 0
\(624\) 7.80240 10.5814i 0.312346 0.423595i
\(625\) 6.77880 + 11.7412i 0.271152 + 0.469649i
\(626\) 41.6934i 1.66640i
\(627\) −19.0483 −0.760718
\(628\) 1.07281 0.0428099
\(629\) 4.78278i 0.190702i
\(630\) 0 0
\(631\) 4.65076 + 2.68512i 0.185144 + 0.106893i 0.589707 0.807617i \(-0.299243\pi\)
−0.404563 + 0.914510i \(0.632576\pi\)
\(632\) −41.2470 + 23.8140i −1.64072 + 0.947270i
\(633\) 5.83981 + 10.1148i 0.232111 + 0.402029i
\(634\) −21.9242 −0.870720
\(635\) −17.7127 10.2264i −0.702905 0.405823i
\(636\) 4.53687 0.179899
\(637\) 0 0
\(638\) −12.4714 −0.493747
\(639\) −3.85189 2.22389i −0.152378 0.0879757i
\(640\) −13.0773 −0.516926
\(641\) 19.8510 + 34.3829i 0.784066 + 1.35804i 0.929555 + 0.368683i \(0.120191\pi\)
−0.145489 + 0.989360i \(0.546475\pi\)
\(642\) −5.17578 + 2.98824i −0.204272 + 0.117936i
\(643\) 27.8388 + 16.0727i 1.09785 + 0.633847i 0.935657 0.352911i \(-0.114808\pi\)
0.162198 + 0.986758i \(0.448142\pi\)
\(644\) 0 0
\(645\) 19.2970i 0.759818i
\(646\) 20.5614 0.808978
\(647\) 19.8500 0.780385 0.390193 0.920733i \(-0.372408\pi\)
0.390193 + 0.920733i \(0.372408\pi\)
\(648\) 4.28417i 0.168298i
\(649\) 4.27048 + 7.39669i 0.167631 + 0.290346i
\(650\) −7.19670 + 3.14357i −0.282278 + 0.123301i
\(651\) 0 0
\(652\) 7.51671 4.33977i 0.294377 0.169959i
\(653\) 9.50024 16.4549i 0.371773 0.643930i −0.618065 0.786127i \(-0.712083\pi\)
0.989838 + 0.142197i \(0.0454165\pi\)
\(654\) 1.48042 + 2.56416i 0.0578889 + 0.100266i
\(655\) 4.81705 + 2.78112i 0.188218 + 0.108667i
\(656\) 19.8784i 0.776120i
\(657\) −10.8697 6.27562i −0.424067 0.244835i
\(658\) 0 0
\(659\) 3.60729 6.24801i 0.140520 0.243388i −0.787173 0.616733i \(-0.788456\pi\)
0.927693 + 0.373345i \(0.121789\pi\)
\(660\) −1.09067 + 1.88909i −0.0424542 + 0.0735329i
\(661\) 16.7510i 0.651537i 0.945450 + 0.325769i \(0.105623\pi\)
−0.945450 + 0.325769i \(0.894377\pi\)
\(662\) −12.7235 + 22.0377i −0.494512 + 0.856520i
\(663\) 4.62524 + 10.5888i 0.179629 + 0.411233i
\(664\) −24.1291 −0.936393
\(665\) 0 0
\(666\) −1.82006 3.15244i −0.0705259 0.122155i
\(667\) 24.6096 0.952889
\(668\) −2.43842 1.40782i −0.0943453 0.0544703i
\(669\) −8.47860 + 4.89512i −0.327802 + 0.189256i
\(670\) 11.6256i 0.449137i
\(671\) 3.00573i 0.116035i
\(672\) 0 0
\(673\) −18.6684 32.3346i −0.719614 1.24641i −0.961153 0.276016i \(-0.910986\pi\)
0.241539 0.970391i \(-0.422348\pi\)
\(674\) −1.40612 0.811824i −0.0541618 0.0312703i
\(675\) −4.61916 + 8.00061i −0.177791 + 0.307944i
\(676\) −1.42320 4.59986i −0.0547383 0.176918i
\(677\) −14.0671 24.3649i −0.540641 0.936418i −0.998867 0.0475826i \(-0.984848\pi\)
0.458226 0.888836i \(-0.348485\pi\)
\(678\) 13.6533 7.88271i 0.524350 0.302734i
\(679\) 0 0
\(680\) 7.53452 13.0502i 0.288935 0.500451i
\(681\) −0.930253 + 0.537082i −0.0356474 + 0.0205810i
\(682\) 6.34915 3.66568i 0.243122 0.140366i
\(683\) 1.79295 1.03516i 0.0686053 0.0396093i −0.465305 0.885150i \(-0.654055\pi\)
0.533910 + 0.845541i \(0.320722\pi\)
\(684\) −3.08025 + 1.77838i −0.117776 + 0.0679982i
\(685\) 19.8574 34.3941i 0.758714 1.31413i
\(686\) 0 0
\(687\) −24.9028 + 14.3776i −0.950100 + 0.548540i
\(688\) −14.2114 24.6149i −0.541805 0.938434i
\(689\) −22.4421 + 30.4353i −0.854975 + 1.15949i
\(690\) −9.46925 + 16.4012i −0.360488 + 0.624384i
\(691\) −31.0542 17.9291i −1.18136 0.682057i −0.225029 0.974352i \(-0.572248\pi\)
−0.956328 + 0.292295i \(0.905581\pi\)
\(692\) 0.999521 + 1.73122i 0.0379961 + 0.0658112i
\(693\) 0 0
\(694\) 33.0417i 1.25425i
\(695\) 20.0919i 0.762129i
\(696\) 10.7614 6.21312i 0.407911 0.235508i
\(697\) 15.1304 + 8.73552i 0.573103 + 0.330881i
\(698\) 22.1059 0.836722
\(699\) 10.0891 + 17.4748i 0.381604 + 0.660958i
\(700\) 0 0
\(701\) −44.8940 −1.69562 −0.847812 0.530297i \(-0.822081\pi\)
−0.847812 + 0.530297i \(0.822081\pi\)
\(702\) 20.0579 + 14.7901i 0.757035 + 0.558215i
\(703\) 5.11571 8.86067i 0.192943 0.334187i
\(704\) 24.6785i 0.930107i
\(705\) 7.05767 12.2242i 0.265807 0.460391i
\(706\) −16.1801 + 28.0248i −0.608947 + 1.05473i
\(707\) 0 0
\(708\) −1.15158 0.664867i −0.0432792 0.0249872i
\(709\) 16.2656i 0.610866i 0.952213 + 0.305433i \(0.0988013\pi\)
−0.952213 + 0.305433i \(0.901199\pi\)
\(710\) 5.45497 + 3.14943i 0.204721 + 0.118196i
\(711\) −12.8748 22.2998i −0.482843 0.836309i
\(712\) −24.3043 + 42.0963i −0.910843 + 1.57763i
\(713\) −12.5287 + 7.23344i −0.469203 + 0.270894i
\(714\) 0 0
\(715\) −7.27775 16.6613i −0.272173 0.623096i
\(716\) −2.27627 3.94262i −0.0850683 0.147343i
\(717\) 16.9149i 0.631697i
\(718\) 6.72806 0.251089
\(719\) 10.0149 0.373492 0.186746 0.982408i \(-0.440206\pi\)
0.186746 + 0.982408i \(0.440206\pi\)
\(720\) 9.26949i 0.345454i
\(721\) 0 0
\(722\) 17.0873 + 9.86534i 0.635922 + 0.367150i
\(723\) −8.53100 + 4.92538i −0.317271 + 0.183177i
\(724\) 4.04690 + 7.00944i 0.150402 + 0.260504i
\(725\) −5.99932 −0.222809
\(726\) 4.23506 + 2.44511i 0.157178 + 0.0907466i
\(727\) 34.5299 1.28064 0.640322 0.768106i \(-0.278801\pi\)
0.640322 + 0.768106i \(0.278801\pi\)
\(728\) 0 0
\(729\) 21.2872 0.788415
\(730\) 15.3934 + 8.88741i 0.569737 + 0.328938i
\(731\) 24.9808 0.923947
\(732\) 0.233980 + 0.405265i 0.00864814 + 0.0149790i
\(733\) 28.6966 16.5680i 1.05993 0.611953i 0.134520 0.990911i \(-0.457051\pi\)
0.925414 + 0.378958i \(0.123717\pi\)
\(734\) −27.9895 16.1598i −1.03311 0.596468i
\(735\) 0 0
\(736\) 14.4629i 0.533111i
\(737\) 13.9424 0.513574
\(738\) 13.2970 0.489470
\(739\) 4.01567i 0.147719i −0.997269 0.0738594i \(-0.976468\pi\)
0.997269 0.0738594i \(-0.0235316\pi\)
\(740\) −0.585830 1.01469i −0.0215356 0.0373007i
\(741\) −2.75703 + 24.5641i −0.101282 + 0.902386i
\(742\) 0 0
\(743\) 10.8361 6.25622i 0.397538 0.229519i −0.287883 0.957666i \(-0.592952\pi\)
0.685421 + 0.728147i \(0.259618\pi\)
\(744\) −3.65241 + 6.32616i −0.133904 + 0.231928i
\(745\) −2.09379 3.62656i −0.0767107 0.132867i
\(746\) 7.50418 + 4.33254i 0.274748 + 0.158626i
\(747\) 13.0452i 0.477299i
\(748\) −2.44551 1.41192i −0.0894168 0.0516248i
\(749\) 0 0
\(750\) 9.07304 15.7150i 0.331300 0.573829i
\(751\) 18.7579 32.4896i 0.684486 1.18556i −0.289112 0.957295i \(-0.593360\pi\)
0.973598 0.228269i \(-0.0733065\pi\)
\(752\) 20.7907i 0.758159i
\(753\) 8.56826 14.8407i 0.312245 0.540824i
\(754\) −1.80509 + 16.0827i −0.0657375 + 0.585698i
\(755\) −37.4150 −1.36167
\(756\) 0 0
\(757\) 17.5223 + 30.3496i 0.636860 + 1.10307i 0.986118 + 0.166047i \(0.0531004\pi\)
−0.349258 + 0.937027i \(0.613566\pi\)
\(758\) −15.7306 −0.571361
\(759\) 19.6697 + 11.3563i 0.713963 + 0.412207i
\(760\) 27.9172 16.1180i 1.01266 0.584661i
\(761\) 4.30225i 0.155956i 0.996955 + 0.0779782i \(0.0248465\pi\)
−0.996955 + 0.0779782i \(0.975154\pi\)
\(762\) 16.8021i 0.608677i
\(763\) 0 0
\(764\) −0.510605 0.884394i −0.0184730 0.0319962i
\(765\) 7.05545 + 4.07347i 0.255090 + 0.147277i
\(766\) 4.63340 8.02528i 0.167411 0.289965i
\(767\) 10.1566 4.43649i 0.366735 0.160192i
\(768\) −5.00195 8.66363i −0.180492 0.312622i
\(769\) 10.6146 6.12834i 0.382772 0.220994i −0.296251 0.955110i \(-0.595737\pi\)
0.679024 + 0.734116i \(0.262403\pi\)
\(770\) 0 0
\(771\) −17.1268 + 29.6645i −0.616806 + 1.06834i
\(772\) 4.16649 2.40552i 0.149955 0.0865767i
\(773\) 3.29372 1.90163i 0.118467 0.0683970i −0.439596 0.898196i \(-0.644878\pi\)
0.558063 + 0.829799i \(0.311545\pi\)
\(774\) 16.4654 9.50628i 0.591835 0.341696i
\(775\) 3.05424 1.76336i 0.109711 0.0633419i
\(776\) 21.5250 37.2824i 0.772702 1.33836i
\(777\) 0 0
\(778\) 7.90250 4.56251i 0.283318 0.163574i
\(779\) 18.6872 + 32.3672i 0.669538 + 1.15967i
\(780\) 2.27825 + 1.67992i 0.0815745 + 0.0601506i
\(781\)