Properties

Label 637.2.e.l.508.3
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 508.3
Root \(-0.827721 + 1.43366i\) of defining polynomial
Character \(\chi\) \(=\) 637.508
Dual form 637.2.e.l.79.3

$q$-expansion

\(f(q)\) \(=\) \(q+(1.32772 + 2.29968i) q^{2} +(1.19797 - 2.07494i) q^{3} +(-2.52569 + 4.37462i) q^{4} +(1.82772 + 3.16571i) q^{5} +6.36226 q^{6} -8.10275 q^{8} +(-1.37024 - 2.37333i) q^{9} +O(q^{10})\) \(q+(1.32772 + 2.29968i) q^{2} +(1.19797 - 2.07494i) q^{3} +(-2.52569 + 4.37462i) q^{4} +(1.82772 + 3.16571i) q^{5} +6.36226 q^{6} -8.10275 q^{8} +(-1.37024 - 2.37333i) q^{9} +(-4.85341 + 8.40635i) q^{10} +(-0.327721 + 0.567630i) q^{11} +(6.05137 + 10.4813i) q^{12} +1.00000 q^{13} +8.75819 q^{15} +(-5.70682 - 9.88450i) q^{16} +(1.19797 - 2.07494i) q^{17} +(3.63861 - 6.30225i) q^{18} +(-1.35341 - 2.34417i) q^{19} -18.4650 q^{20} -1.74049 q^{22} +(-3.68113 - 6.37590i) q^{23} +(-9.70682 + 16.8127i) q^{24} +(-4.18113 + 7.24193i) q^{25} +(1.32772 + 2.29968i) q^{26} +0.621770 q^{27} -0.208136 q^{29} +(11.6284 + 20.1410i) q^{30} +(-0.568211 + 0.984170i) q^{31} +(7.05137 - 12.2133i) q^{32} +(0.785198 + 1.36000i) q^{33} +6.36226 q^{34} +13.8432 q^{36} +(3.72365 + 6.44956i) q^{37} +(3.59390 - 6.22481i) q^{38} +(1.19797 - 2.07494i) q^{39} +(-14.8096 - 25.6509i) q^{40} +10.2055 q^{41} -3.10275 q^{43} +(-1.65544 - 2.86731i) q^{44} +(5.00885 - 8.67558i) q^{45} +(9.77503 - 16.9308i) q^{46} +(2.30203 + 3.98724i) q^{47} -27.3463 q^{48} -22.2055 q^{50} +(-2.87024 - 4.97141i) q^{51} +(-2.52569 + 4.37462i) q^{52} +(-2.62976 + 4.55487i) q^{53} +(0.825537 + 1.42987i) q^{54} -2.39593 q^{55} -6.48535 q^{57} +(-0.276347 - 0.478647i) q^{58} +(4.12976 - 7.15295i) q^{59} +(-22.1204 + 38.3137i) q^{60} +(-0.948626 - 1.64307i) q^{61} -3.01770 q^{62} +14.6218 q^{64} +(1.82772 + 3.16571i) q^{65} +(-2.08505 + 3.61141i) q^{66} +(6.44731 - 11.1671i) q^{67} +(6.05137 + 10.4813i) q^{68} -17.6395 q^{69} -6.75819 q^{71} +(11.1027 + 19.2305i) q^{72} +(6.26836 - 10.8571i) q^{73} +(-9.88795 + 17.1264i) q^{74} +(10.0177 + 17.3512i) q^{75} +13.6731 q^{76} +6.36226 q^{78} +(0.759511 + 1.31551i) q^{79} +(20.8609 - 36.1322i) q^{80} +(4.85559 - 8.41013i) q^{81} +(13.5501 + 23.4694i) q^{82} -15.7582 q^{83} +8.75819 q^{85} +(-4.11958 - 7.13533i) q^{86} +(-0.249340 + 0.431870i) q^{87} +(2.65544 - 4.59936i) q^{88} +(-7.40478 - 12.8255i) q^{89} +26.6014 q^{90} +37.1895 q^{92} +(1.36139 + 2.35800i) q^{93} +(-6.11292 + 10.5879i) q^{94} +(4.94731 - 8.56899i) q^{95} +(-16.8946 - 29.2623i) q^{96} +10.0177 q^{97} +1.79623 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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.32772 + 2.29968i 0.938841 + 1.62612i 0.767638 + 0.640884i \(0.221432\pi\)
0.171203 + 0.985236i \(0.445235\pi\)
\(3\) 1.19797 2.07494i 0.691646 1.19797i −0.279652 0.960101i \(-0.590219\pi\)
0.971298 0.237865i \(-0.0764475\pi\)
\(4\) −2.52569 + 4.37462i −1.26284 + 2.18731i
\(5\) 1.82772 + 3.16571i 0.817382 + 1.41575i 0.907605 + 0.419825i \(0.137909\pi\)
−0.0902232 + 0.995922i \(0.528758\pi\)
\(6\) 6.36226 2.59738
\(7\) 0 0
\(8\) −8.10275 −2.86475
\(9\) −1.37024 2.37333i −0.456748 0.791111i
\(10\) −4.85341 + 8.40635i −1.53478 + 2.65832i
\(11\) −0.327721 + 0.567630i −0.0988117 + 0.171147i −0.911193 0.411980i \(-0.864837\pi\)
0.812381 + 0.583126i \(0.198171\pi\)
\(12\) 6.05137 + 10.4813i 1.74688 + 3.02569i
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 8.75819 2.26136
\(16\) −5.70682 9.88450i −1.42670 2.47112i
\(17\) 1.19797 2.07494i 0.290549 0.503246i −0.683390 0.730053i \(-0.739495\pi\)
0.973940 + 0.226807i \(0.0728286\pi\)
\(18\) 3.63861 6.30225i 0.857628 1.48545i
\(19\) −1.35341 2.34417i −0.310493 0.537790i 0.667976 0.744183i \(-0.267161\pi\)
−0.978469 + 0.206393i \(0.933828\pi\)
\(20\) −18.4650 −4.12890
\(21\) 0 0
\(22\) −1.74049 −0.371074
\(23\) −3.68113 6.37590i −0.767569 1.32947i −0.938878 0.344250i \(-0.888133\pi\)
0.171309 0.985217i \(-0.445200\pi\)
\(24\) −9.70682 + 16.8127i −1.98140 + 3.43188i
\(25\) −4.18113 + 7.24193i −0.836226 + 1.44839i
\(26\) 1.32772 + 2.29968i 0.260388 + 0.451004i
\(27\) 0.621770 0.119660
\(28\) 0 0
\(29\) −0.208136 −0.0386499 −0.0193250 0.999813i \(-0.506152\pi\)
−0.0193250 + 0.999813i \(0.506152\pi\)
\(30\) 11.6284 + 20.1410i 2.12305 + 3.67723i
\(31\) −0.568211 + 0.984170i −0.102054 + 0.176762i −0.912531 0.409008i \(-0.865875\pi\)
0.810477 + 0.585771i \(0.199208\pi\)
\(32\) 7.05137 12.2133i 1.24652 2.15903i
\(33\) 0.785198 + 1.36000i 0.136685 + 0.236746i
\(34\) 6.36226 1.09112
\(35\) 0 0
\(36\) 13.8432 2.30721
\(37\) 3.72365 + 6.44956i 0.612165 + 1.06030i 0.990875 + 0.134785i \(0.0430344\pi\)
−0.378710 + 0.925515i \(0.623632\pi\)
\(38\) 3.59390 6.22481i 0.583007 1.00980i
\(39\) 1.19797 2.07494i 0.191828 0.332256i
\(40\) −14.8096 25.6509i −2.34160 4.05577i
\(41\) 10.2055 1.59383 0.796915 0.604091i \(-0.206464\pi\)
0.796915 + 0.604091i \(0.206464\pi\)
\(42\) 0 0
\(43\) −3.10275 −0.473165 −0.236582 0.971611i \(-0.576027\pi\)
−0.236582 + 0.971611i \(0.576027\pi\)
\(44\) −1.65544 2.86731i −0.249567 0.432263i
\(45\) 5.00885 8.67558i 0.746675 1.29328i
\(46\) 9.77503 16.9308i 1.44125 2.49632i
\(47\) 2.30203 + 3.98724i 0.335786 + 0.581599i 0.983636 0.180170i \(-0.0576647\pi\)
−0.647849 + 0.761768i \(0.724331\pi\)
\(48\) −27.3463 −3.94710
\(49\) 0 0
\(50\) −22.2055 −3.14033
\(51\) −2.87024 4.97141i −0.401915 0.696137i
\(52\) −2.52569 + 4.37462i −0.350250 + 0.606650i
\(53\) −2.62976 + 4.55487i −0.361225 + 0.625659i −0.988163 0.153410i \(-0.950975\pi\)
0.626938 + 0.779069i \(0.284308\pi\)
\(54\) 0.825537 + 1.42987i 0.112341 + 0.194581i
\(55\) −2.39593 −0.323067
\(56\) 0 0
\(57\) −6.48535 −0.859005
\(58\) −0.276347 0.478647i −0.0362861 0.0628494i
\(59\) 4.12976 7.15295i 0.537648 0.931234i −0.461382 0.887202i \(-0.652646\pi\)
0.999030 0.0440325i \(-0.0140205\pi\)
\(60\) −22.1204 + 38.3137i −2.85574 + 4.94628i
\(61\) −0.948626 1.64307i −0.121459 0.210373i 0.798884 0.601485i \(-0.205424\pi\)
−0.920343 + 0.391112i \(0.872091\pi\)
\(62\) −3.01770 −0.383248
\(63\) 0 0
\(64\) 14.6218 1.82772
\(65\) 1.82772 + 3.16571i 0.226701 + 0.392657i
\(66\) −2.08505 + 3.61141i −0.256652 + 0.444534i
\(67\) 6.44731 11.1671i 0.787664 1.36427i −0.139731 0.990190i \(-0.544624\pi\)
0.927395 0.374084i \(-0.122043\pi\)
\(68\) 6.05137 + 10.4813i 0.733837 + 1.27104i
\(69\) −17.6395 −2.12354
\(70\) 0 0
\(71\) −6.75819 −0.802050 −0.401025 0.916067i \(-0.631346\pi\)
−0.401025 + 0.916067i \(0.631346\pi\)
\(72\) 11.1027 + 19.2305i 1.30847 + 2.26634i
\(73\) 6.26836 10.8571i 0.733656 1.27073i −0.221654 0.975125i \(-0.571146\pi\)
0.955310 0.295604i \(-0.0955210\pi\)
\(74\) −9.88795 + 17.1264i −1.14945 + 1.99091i
\(75\) 10.0177 + 17.3512i 1.15674 + 2.00354i
\(76\) 13.6731 1.56842
\(77\) 0 0
\(78\) 6.36226 0.720384
\(79\) 0.759511 + 1.31551i 0.0854516 + 0.148007i 0.905584 0.424168i \(-0.139433\pi\)
−0.820132 + 0.572174i \(0.806100\pi\)
\(80\) 20.8609 36.1322i 2.33232 4.03970i
\(81\) 4.85559 8.41013i 0.539510 0.934459i
\(82\) 13.5501 + 23.4694i 1.49635 + 2.59176i
\(83\) −15.7582 −1.72969 −0.864843 0.502042i \(-0.832582\pi\)
−0.864843 + 0.502042i \(0.832582\pi\)
\(84\) 0 0
\(85\) 8.75819 0.949959
\(86\) −4.11958 7.13533i −0.444226 0.769422i
\(87\) −0.249340 + 0.431870i −0.0267321 + 0.0463013i
\(88\) 2.65544 4.59936i 0.283071 0.490294i
\(89\) −7.40478 12.8255i −0.784905 1.35950i −0.929056 0.369940i \(-0.879378\pi\)
0.144150 0.989556i \(-0.453955\pi\)
\(90\) 26.6014 2.80404
\(91\) 0 0
\(92\) 37.1895 3.87728
\(93\) 1.36139 + 2.35800i 0.141170 + 0.244514i
\(94\) −6.11292 + 10.5879i −0.630499 + 1.09206i
\(95\) 4.94731 8.56899i 0.507583 0.879159i
\(96\) −16.8946 29.2623i −1.72430 2.98657i
\(97\) 10.0177 1.01714 0.508572 0.861020i \(-0.330174\pi\)
0.508572 + 0.861020i \(0.330174\pi\)
\(98\) 0 0
\(99\) 1.79623 0.180528
\(100\) −21.1204 36.5817i −2.11204 3.65817i
\(101\) −1.50885 + 2.61341i −0.150136 + 0.260044i −0.931277 0.364311i \(-0.881305\pi\)
0.781141 + 0.624354i \(0.214638\pi\)
\(102\) 7.62177 13.2013i 0.754668 1.30712i
\(103\) −2.51902 4.36307i −0.248207 0.429906i 0.714822 0.699307i \(-0.246508\pi\)
−0.963028 + 0.269400i \(0.913174\pi\)
\(104\) −8.10275 −0.794540
\(105\) 0 0
\(106\) −13.9663 −1.35653
\(107\) −5.92162 10.2565i −0.572465 0.991538i −0.996312 0.0858041i \(-0.972654\pi\)
0.423848 0.905734i \(-0.360679\pi\)
\(108\) −1.57040 + 2.72000i −0.151111 + 0.261733i
\(109\) −1.77503 + 3.07444i −0.170017 + 0.294478i −0.938425 0.345482i \(-0.887716\pi\)
0.768409 + 0.639959i \(0.221049\pi\)
\(110\) −3.18113 5.50988i −0.303309 0.525346i
\(111\) 17.8432 1.69361
\(112\) 0 0
\(113\) −9.46501 −0.890393 −0.445197 0.895433i \(-0.646866\pi\)
−0.445197 + 0.895433i \(0.646866\pi\)
\(114\) −8.61073 14.9142i −0.806469 1.39685i
\(115\) 13.4562 23.3067i 1.25479 2.17337i
\(116\) 0.525687 0.910517i 0.0488088 0.0845394i
\(117\) −1.37024 2.37333i −0.126679 0.219415i
\(118\) 21.9327 2.01906
\(119\) 0 0
\(120\) −70.9654 −6.47823
\(121\) 5.28520 + 9.15423i 0.480473 + 0.832203i
\(122\) 2.51902 4.36307i 0.228061 0.395014i
\(123\) 12.2258 21.1758i 1.10237 1.90936i
\(124\) −2.87024 4.97141i −0.257756 0.446446i
\(125\) −12.2905 −1.09930
\(126\) 0 0
\(127\) 5.46765 0.485175 0.242588 0.970130i \(-0.422004\pi\)
0.242588 + 0.970130i \(0.422004\pi\)
\(128\) 5.31088 + 9.19872i 0.469420 + 0.813060i
\(129\) −3.71699 + 6.43801i −0.327262 + 0.566835i
\(130\) −4.85341 + 8.40635i −0.425672 + 0.737286i
\(131\) 4.91495 + 8.51295i 0.429421 + 0.743780i 0.996822 0.0796622i \(-0.0253842\pi\)
−0.567400 + 0.823442i \(0.692051\pi\)
\(132\) −7.93265 −0.690449
\(133\) 0 0
\(134\) 34.2409 2.95796
\(135\) 1.13642 + 1.96834i 0.0978076 + 0.169408i
\(136\) −9.70682 + 16.8127i −0.832353 + 1.44168i
\(137\) −8.77503 + 15.1988i −0.749701 + 1.29852i 0.198265 + 0.980149i \(0.436469\pi\)
−0.947966 + 0.318372i \(0.896864\pi\)
\(138\) −23.4203 40.5651i −1.99367 3.45313i
\(139\) 4.91495 0.416881 0.208440 0.978035i \(-0.433161\pi\)
0.208440 + 0.978035i \(0.433161\pi\)
\(140\) 0 0
\(141\) 11.0310 0.928981
\(142\) −8.97299 15.5417i −0.752997 1.30423i
\(143\) −0.327721 + 0.567630i −0.0274054 + 0.0474676i
\(144\) −15.6395 + 27.0884i −1.30329 + 2.25736i
\(145\) −0.380415 0.658898i −0.0315918 0.0547185i
\(146\) 33.2905 2.75515
\(147\) 0 0
\(148\) −37.6191 −3.09227
\(149\) 5.17096 + 8.95636i 0.423621 + 0.733734i 0.996291 0.0860527i \(-0.0274253\pi\)
−0.572669 + 0.819787i \(0.694092\pi\)
\(150\) −26.6014 + 46.0750i −2.17200 + 3.76201i
\(151\) −2.53586 + 4.39223i −0.206365 + 0.357435i −0.950567 0.310520i \(-0.899497\pi\)
0.744202 + 0.667955i \(0.232830\pi\)
\(152\) 10.9663 + 18.9942i 0.889487 + 1.54064i
\(153\) −6.56603 −0.530832
\(154\) 0 0
\(155\) −4.15412 −0.333667
\(156\) 6.05137 + 10.4813i 0.484498 + 0.839175i
\(157\) −6.30071 + 10.9132i −0.502852 + 0.870965i 0.497143 + 0.867669i \(0.334383\pi\)
−0.999995 + 0.00329606i \(0.998951\pi\)
\(158\) −2.01684 + 3.49326i −0.160451 + 0.277909i
\(159\) 6.30071 + 10.9132i 0.499679 + 0.865470i
\(160\) 51.5518 4.07553
\(161\) 0 0
\(162\) 25.7875 2.02606
\(163\) −1.60407 2.77833i −0.125640 0.217615i 0.796343 0.604846i \(-0.206765\pi\)
−0.921983 + 0.387230i \(0.873432\pi\)
\(164\) −25.7759 + 44.6452i −2.01276 + 3.48620i
\(165\) −2.87024 + 4.97141i −0.223448 + 0.387024i
\(166\) −20.9225 36.2388i −1.62390 2.81268i
\(167\) −8.12045 −0.628379 −0.314190 0.949360i \(-0.601733\pi\)
−0.314190 + 0.949360i \(0.601733\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 11.6284 + 20.1410i 0.891860 + 1.54475i
\(171\) −3.70900 + 6.42418i −0.283634 + 0.491269i
\(172\) 7.83657 13.5733i 0.597533 1.03496i
\(173\) −5.16429 8.94482i −0.392634 0.680062i 0.600162 0.799878i \(-0.295103\pi\)
−0.992796 + 0.119816i \(0.961769\pi\)
\(174\) −1.32422 −0.100389
\(175\) 0 0
\(176\) 7.48098 0.563900
\(177\) −9.89461 17.1380i −0.743725 1.28817i
\(178\) 19.6630 34.0573i 1.47380 2.55270i
\(179\) 1.18912 2.05961i 0.0888786 0.153942i −0.818159 0.574992i \(-0.805005\pi\)
0.907037 + 0.421050i \(0.138338\pi\)
\(180\) 25.3016 + 43.8236i 1.88587 + 3.26642i
\(181\) −21.8096 −1.62109 −0.810546 0.585675i \(-0.800830\pi\)
−0.810546 + 0.585675i \(0.800830\pi\)
\(182\) 0 0
\(183\) −4.54569 −0.336027
\(184\) 29.8273 + 51.6623i 2.19890 + 3.80860i
\(185\) −13.6116 + 23.5760i −1.00074 + 1.73334i
\(186\) −3.61510 + 6.26154i −0.265072 + 0.459119i
\(187\) 0.785198 + 1.36000i 0.0574193 + 0.0994532i
\(188\) −23.2569 −1.69618
\(189\) 0 0
\(190\) 26.2746 1.90616
\(191\) 12.5434 + 21.7258i 0.907608 + 1.57202i 0.817378 + 0.576102i \(0.195427\pi\)
0.0902297 + 0.995921i \(0.471240\pi\)
\(192\) 17.5164 30.3393i 1.26414 2.18955i
\(193\) −5.65544 + 9.79551i −0.407088 + 0.705096i −0.994562 0.104146i \(-0.966789\pi\)
0.587474 + 0.809243i \(0.300122\pi\)
\(194\) 13.3007 + 23.0375i 0.954936 + 1.65400i
\(195\) 8.75819 0.627187
\(196\) 0 0
\(197\) −16.7919 −1.19637 −0.598185 0.801358i \(-0.704111\pi\)
−0.598185 + 0.801358i \(0.704111\pi\)
\(198\) 2.38490 + 4.13076i 0.169487 + 0.293560i
\(199\) 10.2670 17.7830i 0.727811 1.26061i −0.229995 0.973192i \(-0.573871\pi\)
0.957806 0.287414i \(-0.0927957\pi\)
\(200\) 33.8786 58.6795i 2.39558 4.14927i
\(201\) −15.4473 26.7555i −1.08957 1.88719i
\(202\) −8.01333 −0.563816
\(203\) 0 0
\(204\) 28.9974 2.03022
\(205\) 18.6528 + 32.3076i 1.30277 + 2.25646i
\(206\) 6.68912 11.5859i 0.466053 0.807227i
\(207\) −10.0881 + 17.4731i −0.701171 + 1.21446i
\(208\) −5.70682 9.88450i −0.395697 0.685367i
\(209\) 1.77416 0.122721
\(210\) 0 0
\(211\) −15.7785 −1.08624 −0.543119 0.839655i \(-0.682757\pi\)
−0.543119 + 0.839655i \(0.682757\pi\)
\(212\) −13.2839 23.0084i −0.912340 1.58022i
\(213\) −8.09608 + 14.0228i −0.554734 + 0.960828i
\(214\) 15.7245 27.2357i 1.07491 1.86179i
\(215\) −5.67096 9.82239i −0.386756 0.669881i
\(216\) −5.03804 −0.342795
\(217\) 0 0
\(218\) −9.42697 −0.638475
\(219\) −15.0186 26.0129i −1.01486 1.75779i
\(220\) 6.05137 10.4813i 0.407984 0.706648i
\(221\) 1.19797 2.07494i 0.0805839 0.139575i
\(222\) 23.6908 + 41.0337i 1.59003 + 2.75400i
\(223\) 8.44731 0.565673 0.282837 0.959168i \(-0.408725\pi\)
0.282837 + 0.959168i \(0.408725\pi\)
\(224\) 0 0
\(225\) 22.9167 1.52778
\(226\) −12.5669 21.7665i −0.835937 1.44789i
\(227\) 3.34456 5.79294i 0.221986 0.384491i −0.733425 0.679771i \(-0.762079\pi\)
0.955411 + 0.295279i \(0.0954127\pi\)
\(228\) 16.3800 28.3709i 1.08479 1.87891i
\(229\) 4.31755 + 7.47822i 0.285312 + 0.494175i 0.972685 0.232130i \(-0.0745695\pi\)
−0.687373 + 0.726305i \(0.741236\pi\)
\(230\) 71.4641 4.71220
\(231\) 0 0
\(232\) 1.68648 0.110723
\(233\) 2.08373 + 3.60912i 0.136510 + 0.236441i 0.926173 0.377099i \(-0.123078\pi\)
−0.789664 + 0.613540i \(0.789745\pi\)
\(234\) 3.63861 6.30225i 0.237863 0.411991i
\(235\) −8.41495 + 14.5751i −0.548931 + 0.950776i
\(236\) 20.8609 + 36.1322i 1.35793 + 2.35201i
\(237\) 3.63947 0.236409
\(238\) 0 0
\(239\) −1.79450 −0.116077 −0.0580384 0.998314i \(-0.518485\pi\)
−0.0580384 + 0.998314i \(0.518485\pi\)
\(240\) −49.9814 86.5703i −3.22628 5.58809i
\(241\) 6.93047 12.0039i 0.446431 0.773241i −0.551720 0.834029i \(-0.686028\pi\)
0.998151 + 0.0607887i \(0.0193616\pi\)
\(242\) −14.0345 + 24.3085i −0.902174 + 1.56261i
\(243\) −10.7010 18.5347i −0.686470 1.18900i
\(244\) 9.58373 0.613535
\(245\) 0 0
\(246\) 64.9300 4.13979
\(247\) −1.35341 2.34417i −0.0861153 0.149156i
\(248\) 4.60407 7.97448i 0.292359 0.506380i
\(249\) −18.8778 + 32.6973i −1.19633 + 2.07211i
\(250\) −16.3184 28.2643i −1.03207 1.78759i
\(251\) −14.7449 −0.930687 −0.465344 0.885130i \(-0.654069\pi\)
−0.465344 + 0.885130i \(0.654069\pi\)
\(252\) 0 0
\(253\) 4.82554 0.303379
\(254\) 7.25951 + 12.5738i 0.455502 + 0.788953i
\(255\) 10.4920 18.1727i 0.657035 1.13802i
\(256\) 0.519021 0.898971i 0.0324388 0.0561857i
\(257\) 11.8534 + 20.5307i 0.739395 + 1.28067i 0.952768 + 0.303699i \(0.0982218\pi\)
−0.213373 + 0.976971i \(0.568445\pi\)
\(258\) −19.7405 −1.22899
\(259\) 0 0
\(260\) −18.4650 −1.14515
\(261\) 0.285198 + 0.493977i 0.0176533 + 0.0305764i
\(262\) −13.0514 + 22.6056i −0.806317 + 1.39658i
\(263\) −5.68780 + 9.85155i −0.350725 + 0.607473i −0.986377 0.164503i \(-0.947398\pi\)
0.635652 + 0.771976i \(0.280731\pi\)
\(264\) −6.36226 11.0198i −0.391570 0.678219i
\(265\) −19.2258 −1.18103
\(266\) 0 0
\(267\) −35.4827 −2.17151
\(268\) 32.5678 + 56.4090i 1.98939 + 3.44573i
\(269\) −5.55269 + 9.61755i −0.338554 + 0.586392i −0.984161 0.177277i \(-0.943271\pi\)
0.645607 + 0.763670i \(0.276604\pi\)
\(270\) −3.01770 + 5.22681i −0.183651 + 0.318094i
\(271\) −6.36226 11.0198i −0.386480 0.669402i 0.605494 0.795850i \(-0.292976\pi\)
−0.991973 + 0.126448i \(0.959642\pi\)
\(272\) −27.3463 −1.65811
\(273\) 0 0
\(274\) −46.6032 −2.81540
\(275\) −2.74049 4.74667i −0.165258 0.286235i
\(276\) 44.5518 77.1660i 2.68170 4.64484i
\(277\) 1.50000 2.59808i 0.0901263 0.156103i −0.817438 0.576017i \(-0.804606\pi\)
0.907564 + 0.419914i \(0.137940\pi\)
\(278\) 6.52569 + 11.3028i 0.391385 + 0.677898i
\(279\) 3.11435 0.186451
\(280\) 0 0
\(281\) 3.44731 0.205649 0.102825 0.994700i \(-0.467212\pi\)
0.102825 + 0.994700i \(0.467212\pi\)
\(282\) 14.6461 + 25.3679i 0.872165 + 1.51063i
\(283\) −6.23917 + 10.8066i −0.370880 + 0.642383i −0.989701 0.143149i \(-0.954277\pi\)
0.618821 + 0.785532i \(0.287611\pi\)
\(284\) 17.0691 29.5645i 1.01286 1.75433i
\(285\) −11.8534 20.5307i −0.702135 1.21613i
\(286\) −1.74049 −0.102917
\(287\) 0 0
\(288\) −38.6484 −2.27738
\(289\) 5.62976 + 9.75102i 0.331162 + 0.573590i
\(290\) 1.01017 1.74967i 0.0593192 0.102744i
\(291\) 12.0009 20.7861i 0.703503 1.21850i
\(292\) 31.6638 + 54.8434i 1.85299 + 3.20947i
\(293\) 13.5341 0.790670 0.395335 0.918537i \(-0.370629\pi\)
0.395335 + 0.918537i \(0.370629\pi\)
\(294\) 0 0
\(295\) 30.1922 1.75786
\(296\) −30.1718 52.2591i −1.75370 3.03750i
\(297\) −0.203767 + 0.352935i −0.0118238 + 0.0204794i
\(298\) −13.7312 + 23.7831i −0.795426 + 1.37772i
\(299\) −3.68113 6.37590i −0.212885 0.368728i
\(300\) −101.206 −5.84315
\(301\) 0 0
\(302\) −13.4676 −0.774976
\(303\) 3.61510 + 6.26154i 0.207682 + 0.359716i
\(304\) −15.4473 + 26.7555i −0.885964 + 1.53453i
\(305\) 3.46765 6.00614i 0.198557 0.343911i
\(306\) −8.71785 15.0998i −0.498366 0.863196i
\(307\) −28.2365 −1.61154 −0.805772 0.592226i \(-0.798249\pi\)
−0.805772 + 0.592226i \(0.798249\pi\)
\(308\) 0 0
\(309\) −12.0708 −0.686684
\(310\) −5.51552 9.55316i −0.313260 0.542583i
\(311\) −12.3521 + 21.3944i −0.700423 + 1.21317i 0.267895 + 0.963448i \(0.413672\pi\)
−0.968318 + 0.249720i \(0.919662\pi\)
\(312\) −9.70682 + 16.8127i −0.549540 + 0.951832i
\(313\) −10.4061 18.0239i −0.588188 1.01877i −0.994470 0.105023i \(-0.966508\pi\)
0.406282 0.913748i \(-0.366825\pi\)
\(314\) −33.4624 −1.88839
\(315\) 0 0
\(316\) −7.67314 −0.431648
\(317\) −13.0691 22.6363i −0.734032 1.27138i −0.955147 0.296134i \(-0.904303\pi\)
0.221114 0.975248i \(-0.429031\pi\)
\(318\) −16.7312 + 28.9793i −0.938238 + 1.62508i
\(319\) 0.0682107 0.118144i 0.00381906 0.00661481i
\(320\) 26.7245 + 46.2882i 1.49395 + 2.58759i
\(321\) −28.3756 −1.58377
\(322\) 0 0
\(323\) −6.48535 −0.360854
\(324\) 24.5274 + 42.4827i 1.36263 + 2.36015i
\(325\) −4.18113 + 7.24193i −0.231927 + 0.401710i
\(326\) 4.25951 7.37769i 0.235912 0.408612i
\(327\) 4.25284 + 7.36614i 0.235183 + 0.407349i
\(328\) −82.6926 −4.56593
\(329\) 0 0
\(330\) −15.2435 −0.839129
\(331\) 12.0691 + 20.9043i 0.663376 + 1.14900i 0.979723 + 0.200358i \(0.0642105\pi\)
−0.316346 + 0.948644i \(0.602456\pi\)
\(332\) 39.8003 68.9361i 2.18432 3.78336i
\(333\) 10.2046 17.6749i 0.559210 0.968581i
\(334\) −10.7817 18.6744i −0.589948 1.02182i
\(335\) 47.1355 2.57529
\(336\) 0 0
\(337\) −30.5297 −1.66306 −0.831530 0.555480i \(-0.812534\pi\)
−0.831530 + 0.555480i \(0.812534\pi\)
\(338\) 1.32772 + 2.29968i 0.0722185 + 0.125086i
\(339\) −11.3388 + 19.6393i −0.615837 + 1.06666i
\(340\) −22.1204 + 38.3137i −1.19965 + 2.07785i
\(341\) −0.372429 0.645067i −0.0201682 0.0349323i
\(342\) −19.6981 −1.06515
\(343\) 0 0
\(344\) 25.1408 1.35550
\(345\) −32.2400 55.8414i −1.73575 3.00640i
\(346\) 13.7135 23.7524i 0.737241 1.27694i
\(347\) 12.4987 21.6483i 0.670964 1.16214i −0.306667 0.951817i \(-0.599214\pi\)
0.977631 0.210327i \(-0.0674530\pi\)
\(348\) −1.25951 2.18154i −0.0675169 0.116943i
\(349\) 1.83887 0.0984324 0.0492162 0.998788i \(-0.484328\pi\)
0.0492162 + 0.998788i \(0.484328\pi\)
\(350\) 0 0
\(351\) 0.621770 0.0331876
\(352\) 4.62177 + 8.00514i 0.246341 + 0.426675i
\(353\) −11.6284 + 20.1410i −0.618919 + 1.07200i 0.370764 + 0.928727i \(0.379096\pi\)
−0.989683 + 0.143272i \(0.954238\pi\)
\(354\) 26.2746 45.5089i 1.39648 2.41877i
\(355\) −12.3521 21.3944i −0.655581 1.13550i
\(356\) 74.8087 3.96485
\(357\) 0 0
\(358\) 6.31525 0.333772
\(359\) 10.7237 + 18.5739i 0.565973 + 0.980294i 0.996958 + 0.0779348i \(0.0248326\pi\)
−0.430986 + 0.902359i \(0.641834\pi\)
\(360\) −40.5855 + 70.2961i −2.13904 + 3.70493i
\(361\) 5.83657 10.1092i 0.307188 0.532065i
\(362\) −28.9570 50.1550i −1.52195 2.63609i
\(363\) 25.3259 1.32927
\(364\) 0 0
\(365\) 45.8273 2.39871
\(366\) −6.03540 10.4536i −0.315476 0.546420i
\(367\) −0.560225 + 0.970338i −0.0292435 + 0.0506512i −0.880277 0.474461i \(-0.842643\pi\)
0.851033 + 0.525112i \(0.175976\pi\)
\(368\) −42.0151 + 72.7722i −2.19019 + 3.79351i
\(369\) −13.9840 24.2210i −0.727979 1.26090i
\(370\) −72.2896 −3.75816
\(371\) 0 0
\(372\) −13.7538 −0.713102
\(373\) −7.80290 13.5150i −0.404019 0.699781i 0.590188 0.807266i \(-0.299054\pi\)
−0.994207 + 0.107485i \(0.965720\pi\)
\(374\) −2.08505 + 3.61141i −0.107815 + 0.186741i
\(375\) −14.7237 + 25.5021i −0.760326 + 1.31692i
\(376\) −18.6528 32.3076i −0.961945 1.66614i
\(377\) −0.208136 −0.0107196
\(378\) 0 0
\(379\) 12.7849 0.656714 0.328357 0.944554i \(-0.393505\pi\)
0.328357 + 0.944554i \(0.393505\pi\)
\(380\) 24.9907 + 43.2852i 1.28200 + 2.22048i
\(381\) 6.55005 11.3450i 0.335569 0.581223i
\(382\) −33.3082 + 57.6916i −1.70420 + 2.95176i
\(383\) 17.0177 + 29.4755i 0.869564 + 1.50613i 0.862443 + 0.506154i \(0.168933\pi\)
0.00712095 + 0.999975i \(0.497733\pi\)
\(384\) 25.4490 1.29869
\(385\) 0 0
\(386\) −30.0354 −1.52876
\(387\) 4.25152 + 7.36386i 0.216117 + 0.374326i
\(388\) −25.3016 + 43.8236i −1.28449 + 2.22481i
\(389\) 12.3353 21.3653i 0.625422 1.08326i −0.363037 0.931775i \(-0.618260\pi\)
0.988459 0.151488i \(-0.0484065\pi\)
\(390\) 11.6284 + 20.1410i 0.588829 + 1.01988i
\(391\) −17.6395 −0.892066
\(392\) 0 0
\(393\) 23.5518 1.18803
\(394\) −22.2949 38.6159i −1.12320 1.94544i
\(395\) −2.77635 + 4.80877i −0.139693 + 0.241956i
\(396\) −4.53672 + 7.85783i −0.227979 + 0.394871i
\(397\) −2.48983 4.31251i −0.124961 0.216439i 0.796757 0.604300i \(-0.206547\pi\)
−0.921718 + 0.387861i \(0.873214\pi\)
\(398\) 54.5271 2.73320
\(399\) 0 0
\(400\) 95.4438 4.77219
\(401\) −0.344558 0.596791i −0.0172064 0.0298023i 0.857294 0.514827i \(-0.172144\pi\)
−0.874500 + 0.485025i \(0.838811\pi\)
\(402\) 41.0194 71.0477i 2.04586 3.54354i
\(403\) −0.568211 + 0.984170i −0.0283046 + 0.0490250i
\(404\) −7.62177 13.2013i −0.379197 0.656789i
\(405\) 35.4987 1.76394
\(406\) 0 0
\(407\) −4.88128 −0.241956
\(408\) 23.2569 + 40.2821i 1.15139 + 1.99426i
\(409\) 9.98851 17.3006i 0.493900 0.855460i −0.506075 0.862489i \(-0.668904\pi\)
0.999975 + 0.00702937i \(0.00223754\pi\)
\(410\) −49.5314 + 85.7910i −2.44618 + 4.23691i
\(411\) 21.0244 + 36.4153i 1.03706 + 1.79623i
\(412\) 25.4490 1.25378
\(413\) 0 0
\(414\) −53.5767 −2.63315
\(415\) −28.8016 49.8858i −1.41381 2.44880i
\(416\) 7.05137 12.2133i 0.345722 0.598808i
\(417\) 5.88795 10.1982i 0.288334 0.499409i
\(418\) 2.35559 + 4.08001i 0.115216 + 0.199560i
\(419\) −19.6661 −0.960754 −0.480377 0.877062i \(-0.659500\pi\)
−0.480377 + 0.877062i \(0.659500\pi\)
\(420\) 0 0
\(421\) 14.9283 0.727560 0.363780 0.931485i \(-0.381486\pi\)
0.363780 + 0.931485i \(0.381486\pi\)
\(422\) −20.9495 36.2856i −1.01981 1.76635i
\(423\) 6.30870 10.9270i 0.306739 0.531288i
\(424\) 21.3082 36.9070i 1.03482 1.79236i
\(425\) 10.0177 + 17.3512i 0.485930 + 0.841655i
\(426\) −42.9974 −2.08323
\(427\) 0 0
\(428\) 59.8246 2.89173
\(429\) 0.785198 + 1.36000i 0.0379097 + 0.0656615i
\(430\) 15.0589 26.0828i 0.726205 1.25782i
\(431\) 16.3419 28.3050i 0.787163 1.36341i −0.140536 0.990076i \(-0.544883\pi\)
0.927699 0.373330i \(-0.121784\pi\)
\(432\) −3.54832 6.14588i −0.170719 0.295694i
\(433\) 8.96196 0.430684 0.215342 0.976539i \(-0.430913\pi\)
0.215342 + 0.976539i \(0.430913\pi\)
\(434\) 0 0
\(435\) −1.82290 −0.0874012
\(436\) −8.96633 15.5301i −0.429409 0.743759i
\(437\) −9.96414 + 17.2584i −0.476650 + 0.825581i
\(438\) 39.8809 69.0758i 1.90558 3.30057i
\(439\) −3.96633 6.86988i −0.189302 0.327881i 0.755715 0.654900i \(-0.227289\pi\)
−0.945018 + 0.327019i \(0.893956\pi\)
\(440\) 19.4136 0.925509
\(441\) 0 0
\(442\) 6.36226 0.302622
\(443\) 4.45529 + 7.71679i 0.211677 + 0.366636i 0.952240 0.305352i \(-0.0987741\pi\)
−0.740562 + 0.671988i \(0.765441\pi\)
\(444\) −45.0664 + 78.0574i −2.13876 + 3.70444i
\(445\) 27.0678 46.8827i 1.28313 2.22245i
\(446\) 11.2157 + 19.4261i 0.531077 + 0.919853i
\(447\) 24.7785 1.17198
\(448\) 0 0
\(449\) −8.45168 −0.398859 −0.199430 0.979912i \(-0.563909\pi\)
−0.199430 + 0.979912i \(0.563909\pi\)
\(450\) 30.4270 + 52.7010i 1.43434 + 2.48435i
\(451\) −3.34456 + 5.79294i −0.157489 + 0.272779i
\(452\) 23.9056 41.4058i 1.12443 1.94756i
\(453\) 6.07574 + 10.5235i 0.285463 + 0.494437i
\(454\) 17.7626 0.833638
\(455\) 0 0
\(456\) 52.5491 2.46084
\(457\) −11.5846 20.0651i −0.541904 0.938606i −0.998795 0.0490829i \(-0.984370\pi\)
0.456890 0.889523i \(-0.348963\pi\)
\(458\) −11.4650 + 19.8580i −0.535725 + 0.927902i
\(459\) 0.744859 1.29013i 0.0347670 0.0602183i
\(460\) 67.9721 + 117.731i 3.16921 + 5.48924i
\(461\) −2.27284 −0.105857 −0.0529284 0.998598i \(-0.516856\pi\)
−0.0529284 + 0.998598i \(0.516856\pi\)
\(462\) 0 0
\(463\) −4.10976 −0.190997 −0.0954983 0.995430i \(-0.530444\pi\)
−0.0954983 + 0.995430i \(0.530444\pi\)
\(464\) 1.18780 + 2.05732i 0.0551420 + 0.0955088i
\(465\) −4.97650 + 8.61955i −0.230780 + 0.399722i
\(466\) −5.53322 + 9.58381i −0.256321 + 0.443962i
\(467\) 16.4575 + 28.5052i 0.761561 + 1.31906i 0.942046 + 0.335485i \(0.108900\pi\)
−0.180484 + 0.983578i \(0.557767\pi\)
\(468\) 13.8432 0.639904
\(469\) 0 0
\(470\) −44.6908 −2.06143
\(471\) 15.0961 + 26.1472i 0.695591 + 1.20480i
\(472\) −33.4624 + 57.9585i −1.54023 + 2.66776i
\(473\) 1.01684 1.76121i 0.0467542 0.0809806i
\(474\) 4.83220 + 8.36962i 0.221950 + 0.384429i
\(475\) 22.6351 1.03857
\(476\) 0 0
\(477\) 14.4136 0.659955
\(478\) −2.38260 4.12678i −0.108978 0.188755i
\(479\) −4.65763 + 8.06725i −0.212812 + 0.368602i −0.952594 0.304246i \(-0.901596\pi\)
0.739781 + 0.672847i \(0.234929\pi\)
\(480\) 61.7573 106.967i 2.81882 4.88234i
\(481\) 3.72365 + 6.44956i 0.169784 + 0.294074i
\(482\) 36.8069 1.67651
\(483\) 0 0
\(484\) −53.3950 −2.42705
\(485\) 18.3096 + 31.7131i 0.831395 + 1.44002i
\(486\) 28.4159 49.2178i 1.28897 2.23257i
\(487\) −10.1204 + 17.5291i −0.458601 + 0.794321i −0.998887 0.0471606i \(-0.984983\pi\)
0.540286 + 0.841481i \(0.318316\pi\)
\(488\) 7.68648 + 13.3134i 0.347950 + 0.602668i
\(489\) −7.68648 −0.347594
\(490\) 0 0
\(491\) −4.36226 −0.196866 −0.0984330 0.995144i \(-0.531383\pi\)
−0.0984330 + 0.995144i \(0.531383\pi\)
\(492\) 61.7573 + 106.967i 2.78423 + 4.82243i
\(493\) −0.249340 + 0.431870i −0.0112297 + 0.0194504i
\(494\) 3.59390 6.22481i 0.161697 0.280068i
\(495\) 3.28301 + 5.68635i 0.147560 + 0.255582i
\(496\) 12.9707 0.582401
\(497\) 0 0
\(498\) −100.258 −4.49265
\(499\) −4.84674 8.39480i −0.216970 0.375803i 0.736910 0.675991i \(-0.236284\pi\)
−0.953880 + 0.300188i \(0.902951\pi\)
\(500\) 31.0421 53.7664i 1.38824 2.40451i
\(501\) −9.72802 + 16.8494i −0.434616 + 0.752777i
\(502\) −19.5771 33.9085i −0.873767 1.51341i
\(503\) −2.64843 −0.118088 −0.0590439 0.998255i \(-0.518805\pi\)
−0.0590439 + 0.998255i \(0.518805\pi\)
\(504\) 0 0
\(505\) −11.0310 −0.490875
\(506\) 6.40697 + 11.0972i 0.284824 + 0.493330i
\(507\) 1.19797 2.07494i 0.0532035 0.0921512i
\(508\) −13.8096 + 23.9189i −0.612700 + 1.06123i
\(509\) −6.97081 12.0738i −0.308976 0.535162i 0.669163 0.743116i \(-0.266653\pi\)
−0.978139 + 0.207954i \(0.933319\pi\)
\(510\) 55.7219 2.46741
\(511\) 0 0
\(512\) 24.0000 1.06066
\(513\) −0.841508 1.45753i −0.0371535 0.0643517i
\(514\) −31.4760 + 54.5181i −1.38835 + 2.40469i
\(515\) 9.20814 15.9490i 0.405759 0.702795i
\(516\) −18.7759 32.5208i −0.826563 1.43165i
\(517\) −3.01770 −0.132718
\(518\) 0 0
\(519\) −24.7466 −1.08625
\(520\) −14.8096 25.6509i −0.649442 1.12487i
\(521\) −7.31088 + 12.6628i −0.320296 + 0.554768i −0.980549 0.196275i \(-0.937116\pi\)
0.660253 + 0.751043i \(0.270449\pi\)
\(522\) −0.757326 + 1.31173i −0.0331473 + 0.0574127i
\(523\) 8.25951 + 14.3059i 0.361163 + 0.625553i 0.988153 0.153475i \(-0.0490464\pi\)
−0.626989 + 0.779028i \(0.715713\pi\)
\(524\) −49.6545 −2.16917
\(525\) 0 0
\(526\) −30.2072 −1.31710
\(527\) 1.36139 + 2.35800i 0.0593033 + 0.102716i
\(528\) 8.96196 15.5226i 0.390019 0.675533i
\(529\) −15.6014 + 27.0225i −0.678323 + 1.17489i
\(530\) −25.5266 44.2133i −1.10880 1.92050i
\(531\) −22.6351 −0.982280
\(532\) 0 0
\(533\) 10.2055 0.442049
\(534\) −47.1111 81.5989i −2.03870 3.53113i
\(535\) 21.6461 37.4922i 0.935844 1.62093i
\(536\) −52.2409 + 90.4839i −2.25646 + 3.90831i
\(537\) −2.84904 4.93468i −0.122945 0.212947i
\(538\) −29.4897 −1.27139
\(539\) 0 0
\(540\) −11.4810 −0.494063
\(541\) 21.5509 + 37.3273i 0.926546 + 1.60483i 0.789055 + 0.614322i \(0.210571\pi\)
0.137491 + 0.990503i \(0.456096\pi\)
\(542\) 16.8946 29.2623i 0.725686 1.25692i
\(543\) −26.1271 + 45.2535i −1.12122 + 1.94201i
\(544\) −16.8946 29.2623i −0.724351 1.25461i
\(545\) −12.9770 −0.555874
\(546\) 0 0
\(547\) −13.5057 −0.577462 −0.288731 0.957410i \(-0.593233\pi\)
−0.288731 + 0.957410i \(0.593233\pi\)
\(548\) −44.3259 76.7748i −1.89351 3.27966i
\(549\) −2.59970 + 4.50281i −0.110952 + 0.192175i
\(550\) 7.27721 12.6045i 0.310301 0.537458i
\(551\) 0.281693 + 0.487907i 0.0120005 + 0.0207855i
\(552\) 142.928 6.08343
\(553\) 0 0
\(554\) 7.96633 0.338457
\(555\) 32.6125 + 56.4864i 1.38432 + 2.39772i
\(556\) −12.4136 + 21.5010i −0.526455 + 0.911847i
\(557\) −0.675783 + 1.17049i −0.0286338 + 0.0495953i −0.879987 0.474997i \(-0.842449\pi\)
0.851353 + 0.524593i \(0.175782\pi\)
\(558\) 4.13499 + 7.16201i 0.175048 + 0.303192i
\(559\) −3.10275 −0.131232
\(560\) 0 0
\(561\) 3.76256 0.158855
\(562\) 4.57706 + 7.92770i 0.193072 + 0.334410i
\(563\) 15.8813 27.5072i 0.669316 1.15929i −0.308779 0.951134i \(-0.599921\pi\)
0.978096 0.208156i \(-0.0667462\pi\)
\(564\) −27.8609 + 48.2566i −1.17316 + 2.03197i
\(565\) −17.2994 29.9634i −0.727791 1.26057i
\(566\) −33.1355 −1.39279
\(567\) 0 0
\(568\) 54.7599 2.29768
\(569\) −15.1865 26.3037i −0.636650 1.10271i −0.986163 0.165779i \(-0.946986\pi\)
0.349513 0.936932i \(-0.386347\pi\)
\(570\) 31.4760 54.5181i 1.31839 2.28351i
\(571\) 0.216122 0.374334i 0.00904442 0.0156654i −0.861468 0.507812i \(-0.830454\pi\)
0.870512 + 0.492147i \(0.163788\pi\)
\(572\) −1.65544 2.86731i −0.0692175 0.119888i
\(573\) 60.1062 2.51097
\(574\) 0 0
\(575\) 61.5651 2.56744
\(576\) −20.0354 34.7023i −0.834808 1.44593i
\(577\) 9.06908 15.7081i 0.377551 0.653937i −0.613155 0.789963i \(-0.710100\pi\)
0.990705 + 0.136026i \(0.0434331\pi\)
\(578\) −14.9495 + 25.8933i −0.621817 + 1.07702i
\(579\) 13.5501 + 23.4694i 0.563121 + 0.975354i
\(580\) 3.84324 0.159582
\(581\) 0 0
\(582\) 63.7352 2.64191
\(583\) −1.72365 2.98545i −0.0713864 0.123645i
\(584\) −50.7910 + 87.9725i −2.10174 + 3.64033i
\(585\) 5.00885 8.67558i 0.207090 0.358691i
\(586\) 17.9695 + 31.1241i 0.742313 + 1.28572i
\(587\) −19.3065 −0.796865 −0.398433 0.917198i \(-0.630446\pi\)
−0.398433 + 0.917198i \(0.630446\pi\)
\(588\) 0 0
\(589\) 3.07608 0.126748
\(590\) 40.0868 + 69.4323i 1.65035 + 2.85848i
\(591\) −20.1161 + 34.8421i −0.827465 + 1.43321i
\(592\) 42.5004 73.6129i 1.74676 3.02547i
\(593\) 4.10056 + 7.10238i 0.168390 + 0.291660i 0.937854 0.347030i \(-0.112810\pi\)
−0.769464 + 0.638690i \(0.779477\pi\)
\(594\) −1.08218 −0.0444025
\(595\) 0 0
\(596\) −52.2409 −2.13987
\(597\) −24.5991 42.6069i −1.00678 1.74379i
\(598\) 9.77503 16.9308i 0.399731 0.692354i
\(599\) −11.7392 + 20.3328i −0.479649 + 0.830777i −0.999728 0.0233415i \(-0.992570\pi\)
0.520078 + 0.854119i \(0.325903\pi\)
\(600\) −81.1709 140.592i −3.31379 5.73965i
\(601\) 8.96196 0.365566 0.182783 0.983153i \(-0.441489\pi\)
0.182783 + 0.983153i \(0.441489\pi\)
\(602\) 0 0
\(603\) −35.3375 −1.43906
\(604\) −12.8096 22.1868i −0.521214 0.902769i
\(605\) −19.3197 + 33.4628i −0.785459 + 1.36045i
\(606\) −9.59970 + 16.6272i −0.389961 + 0.675432i
\(607\) 21.7320 + 37.6410i 0.882077 + 1.52780i 0.849028 + 0.528348i \(0.177188\pi\)
0.0330487 + 0.999454i \(0.489478\pi\)
\(608\) −38.1736 −1.54814
\(609\) 0 0
\(610\) 18.4163 0.745653
\(611\) 2.30203 + 3.98724i 0.0931303 + 0.161306i
\(612\) 16.5837 28.7239i 0.670357 1.16109i
\(613\) 10.7245 18.5754i 0.433159 0.750254i −0.563984 0.825786i \(-0.690732\pi\)
0.997143 + 0.0755318i \(0.0240655\pi\)
\(614\) −37.4902 64.9350i −1.51298 2.62056i
\(615\) 89.3817 3.60422
\(616\) 0 0
\(617\) −12.1294 −0.488312 −0.244156 0.969736i \(-0.578511\pi\)
−0.244156 + 0.969736i \(0.578511\pi\)
\(618\) −16.0267 27.7590i −0.644687 1.11663i
\(619\) 6.36226 11.0198i 0.255721 0.442921i −0.709370 0.704836i \(-0.751021\pi\)
0.965091 + 0.261915i \(0.0843539\pi\)
\(620\) 10.4920 18.1727i 0.421369 0.729833i
\(621\) −2.28881 3.96434i −0.0918469 0.159084i
\(622\) −65.6005 −2.63034
\(623\) 0 0
\(624\) −27.3463 −1.09473
\(625\) −1.55804 2.69860i −0.0623216 0.107944i
\(626\) 27.6328 47.8614i 1.10443 1.91293i
\(627\) 2.12539 3.68128i 0.0848797 0.147016i
\(628\) −31.8273 55.1264i −1.27005 2.19978i
\(629\) 17.8432 0.711456
\(630\) 0 0
\(631\) −11.7538 −0.467912 −0.233956 0.972247i \(-0.575167\pi\)
−0.233956 + 0.972247i \(0.575167\pi\)
\(632\) −6.15412 10.6593i −0.244798 0.424002i
\(633\) −18.9021 + 32.7395i −0.751293 + 1.30128i
\(634\) 34.7042 60.1094i 1.37828 2.38725i
\(635\) 9.99333 + 17.3090i 0.396573 + 0.686885i
\(636\) −63.6545 −2.52407
\(637\) 0 0
\(638\) 0.362259 0.0143420
\(639\) 9.26038 + 16.0394i 0.366335 + 0.634510i
\(640\) −19.4136 + 33.6254i −0.767391 + 1.32916i
\(641\) −2.34324 + 4.05861i −0.0925523 + 0.160305i −0.908584 0.417701i \(-0.862836\pi\)
0.816032 + 0.578007i \(0.196169\pi\)
\(642\) −37.6749 65.2548i −1.48691 2.57540i
\(643\) 0.751182 0.0296237 0.0148119 0.999890i \(-0.495285\pi\)
0.0148119 + 0.999890i \(0.495285\pi\)
\(644\) 0 0
\(645\) −27.1745 −1.06999
\(646\) −8.61073 14.9142i −0.338785 0.586792i
\(647\) 20.4238 35.3751i 0.802943 1.39074i −0.114729 0.993397i \(-0.536600\pi\)
0.917671 0.397340i \(-0.130067\pi\)
\(648\) −39.3436 + 68.1452i −1.54556 + 2.67700i
\(649\) 2.70682 + 4.68834i 0.106252 + 0.184034i
\(650\) −22.2055 −0.870971
\(651\) 0 0
\(652\) 16.2055 0.634656
\(653\) 23.2392 + 40.2514i 0.909419 + 1.57516i 0.814873 + 0.579639i \(0.196807\pi\)
0.0945459 + 0.995521i \(0.469860\pi\)
\(654\) −11.2932 + 19.5604i −0.441598 + 0.764871i
\(655\) −17.9663 + 31.1186i −0.702002 + 1.21590i
\(656\) −58.2409 100.876i −2.27393 3.93855i
\(657\) −34.3568 −1.34038
\(658\) 0 0
\(659\) 30.3596 1.18264 0.591321 0.806436i \(-0.298606\pi\)
0.591321 + 0.806436i \(0.298606\pi\)
\(660\) −14.4987 25.1125i −0.564360 0.977501i
\(661\) −0.0535589 + 0.0927667i −0.00208320 + 0.00360820i −0.867065 0.498195i \(-0.833996\pi\)
0.864982 + 0.501803i \(0.167330\pi\)
\(662\) −32.0487 + 55.5100i −1.24561 + 2.15746i
\(663\) −2.87024 4.97141i −0.111471 0.193074i
\(664\) 127.685 4.95513
\(665\) 0 0
\(666\) 54.1956 2.10004
\(667\) 0.766177 + 1.32706i 0.0296665 + 0.0513838i
\(668\) 20.5097 35.5239i 0.793545 1.37446i
\(669\) 10.1196 17.5276i 0.391246 0.677658i
\(670\) 62.5828 + 108.397i 2.41779 + 4.18773i
\(671\) 1.24354 0.0480063
\(672\) 0 0
\(673\) 38.5385 1.48555 0.742774 0.669542i \(-0.233510\pi\)
0.742774 + 0.669542i \(0.233510\pi\)
\(674\) −40.5349 70.2086i −1.56135 2.70433i
\(675\) −2.59970 + 4.50281i −0.100062 + 0.173313i
\(676\) −2.52569 + 4.37462i −0.0971418 + 0.168255i
\(677\) −10.3901 17.9962i −0.399325 0.691651i 0.594318 0.804230i \(-0.297422\pi\)
−0.993643 + 0.112579i \(0.964089\pi\)
\(678\) −60.2188 −2.31269
\(679\) 0 0
\(680\) −70.9654 −2.72140
\(681\) −8.01333 13.8795i −0.307072 0.531864i
\(682\) 0.988965 1.71294i 0.0378694 0.0655918i
\(683\) −13.7919 + 23.8882i −0.527731 + 0.914057i 0.471746 + 0.881734i \(0.343624\pi\)
−0.999477 + 0.0323227i \(0.989710\pi\)
\(684\) −18.7356 32.4509i −0.716372 1.24079i
\(685\) −64.1532 −2.45117
\(686\) 0 0
\(687\) 20.6891 0.789339
\(688\) 17.7068 + 30.6691i 0.675066 + 1.16925i
\(689\) −2.62976 + 4.55487i −0.100186 + 0.173527i
\(690\) 85.6116 148.284i 3.25918 5.64506i
\(691\) 21.8388 + 37.8258i 0.830785 + 1.43896i 0.897416 + 0.441185i \(0.145442\pi\)
−0.0666308 + 0.997778i \(0.521225\pi\)
\(692\) 52.1736 1.98334
\(693\) 0 0
\(694\) 66.3791 2.51971
\(695\) 8.98316 + 15.5593i 0.340751 + 0.590198i
\(696\) 2.02034 3.49933i 0.0765808 0.132642i
\(697\) 12.2258 21.1758i 0.463087 0.802090i
\(698\) 2.44150 + 4.22881i 0.0924123 + 0.160063i
\(699\) 9.98494 0.377665
\(700\) 0 0
\(701\) −20.8973 −0.789278 −0.394639 0.918836i \(-0.629130\pi\)
−0.394639 + 0.918836i \(0.629130\pi\)
\(702\) 0.825537 + 1.42987i 0.0311579 + 0.0539670i
\(703\) 10.0792 17.4578i 0.380146 0.658432i
\(704\) −4.79186 + 8.29975i −0.180600 + 0.312809i
\(705\) 20.1617 + 34.9210i 0.759332 + 1.31520i
\(706\) −61.7573 −2.32427
\(707\) 0 0
\(708\) 99.9628 3.75683
\(709\) −4.96983 8.60800i −0.186646 0.323280i 0.757484 0.652854i \(-0.226428\pi\)
−0.944130 + 0.329574i \(0.893095\pi\)
\(710\) 32.8003 56.8117i 1.23097 2.13211i
\(711\) 2.08143 3.60514i 0.0780597 0.135203i
\(712\) 59.9991 + 103.921i 2.24856 + 3.89462i
\(713\) 8.36663 0.313333
\(714\) 0 0
\(715\) −2.39593 −0.0896028
\(716\) 6.00667 + 10.4039i 0.224480 + 0.388810i
\(717\) −2.14975 + 3.72348i −0.0802840 + 0.139056i
\(718\) −28.4760 + 49.3220i −1.06272 + 1.84068i
\(719\) −5.98983 10.3747i −0.223383 0.386911i 0.732450 0.680821i \(-0.238377\pi\)
−0.955833 + 0.293910i \(0.905043\pi\)
\(720\) −114.338 −4.26114
\(721\) 0 0
\(722\) 30.9974 1.15360
\(723\) −16.6049 28.7606i −0.617544 1.06962i
\(724\) 55.0841 95.4085i 2.04719 3.54583i
\(725\) 0.870245 1.50731i 0.0323201 0.0559800i
\(726\) 33.6258 + 58.2416i 1.24797 + 2.16155i
\(727\) −24.1736 −0.896547 −0.448274 0.893896i \(-0.647961\pi\)
−0.448274 + 0.893896i \(0.647961\pi\)
\(728\) 0 0
\(729\) −22.1443 −0.820157
\(730\) 60.8458 + 105.388i 2.25201 + 3.90059i
\(731\) −3.71699 + 6.43801i −0.137478 + 0.238118i
\(732\) 11.4810 19.8856i 0.424349 0.734994i
\(733\) −18.2237 31.5643i −0.673106 1.16585i −0.977019 0.213154i \(-0.931626\pi\)
0.303913 0.952700i \(-0.401707\pi\)
\(734\) −2.97529 −0.109820
\(735\) 0 0
\(736\) −103.828 −3.82715
\(737\) 4.22584 + 7.31937i 0.155661 + 0.269612i
\(738\) 37.1338 64.3176i 1.36691 2.36756i
\(739\) −21.6386 + 37.4792i −0.795989 + 1.37869i 0.126220 + 0.992002i \(0.459715\pi\)
−0.922209 + 0.386691i \(0.873618\pi\)
\(740\) −68.7573 119.091i −2.52757 4.37788i
\(741\) −6.48535 −0.238245
\(742\) 0 0
\(743\) 22.6572 0.831211 0.415606 0.909545i \(-0.363570\pi\)
0.415606 + 0.909545i \(0.363570\pi\)
\(744\) −11.0310 19.1063i −0.404417 0.700471i
\(745\) −18.9021 + 32.7395i −0.692521 + 1.19948i
\(746\) 20.7201 35.8884i 0.758619 1.31397i
\(747\) 21.5926 + 37.3994i 0.790031 + 1.36837i
\(748\) −7.93265 −0.290047
\(749\) 0 0
\(750\) −78.1956 −2.85530
\(751\) −14.9340 25.8664i −0.544948 0.943878i −0.998610 0.0527044i \(-0.983216\pi\)
0.453662 0.891174i \(-0.350117\pi\)
\(752\) 26.2746 45.5089i 0.958135 1.65954i
\(753\) −17.6638 + 30.5947i −0.643706 + 1.11493i
\(754\) −0.276347 0.478647i −0.0100640 0.0174313i
\(755\) −18.5394 −0.674716
\(756\) 0 0
\(757\) 2.55706 0.0929380 0.0464690 0.998920i \(-0.485203\pi\)
0.0464690 + 0.998920i \(0.485203\pi\)
\(758\) 16.9747 + 29.4011i 0.616550 + 1.06790i
\(759\) 5.78083 10.0127i 0.209831 0.363438i
\(760\) −40.0868 + 69.4323i −1.45410 + 2.51858i
\(761\) 7.36444 + 12.7556i 0.266961 + 0.462390i 0.968075 0.250659i \(-0.0806472\pi\)
−0.701115 + 0.713049i \(0.747314\pi\)
\(762\) 34.7866 1.26019
\(763\) 0 0
\(764\) −126.723 −4.58467
\(765\) −12.0009 20.7861i −0.433892 0.751523i
\(766\) −45.1895 + 78.2706i −1.63276 + 2.82803i
\(767\) 4.12976 7.15295i 0.149117 0.258278i
\(768\) −1.24354 2.15387i −0.0448724 0.0777212i
\(769\) 36.1692 1.30429 0.652147 0.758092i \(-0.273868\pi\)
0.652147 + 0.758092i \(0.273868\pi\)
\(770\) 0 0
\(771\) 56.7999 2.04560
\(772\) −28.5678 49.4808i −1.02818 1.78085i
\(773\) 19.4783 33.7375i 0.700587 1.21345i −0.267673 0.963510i \(-0.586255\pi\)
0.968261 0.249943i \(-0.0804118\pi\)
\(774\) −11.2897 + 19.5543i −0.405799 + 0.702865i
\(775\) −4.75152 8.22988i −0.170680 0.295626i
\(776\) −81.1709 −2.91387
\(777\) 0 0
\(778\) 65.5111 2.34869
\(779\) −13.8122 23.9234i −0.494874 0.857146i
\(780\) −22.1204 + 38.3137i −0.792039 + 1.37185i
\(781\) 2.21480 3.83615i 0.0792519 0.137268i
\(782\) −23.4203 40.5651i −0.837508 1.45061i
\(783\) −0.129413