Properties

Label 637.2.h.l.471.3
Level $637$
Weight $2$
Character 637.471
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.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \(x^{12} - x^{11} + 7 x^{10} - 2 x^{9} + 33 x^{8} - 11 x^{7} + 55 x^{6} + 17 x^{5} + 47 x^{4} + x^{3} + 8 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 471.3
Root \(0.756174 + 1.30973i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.l.165.3

$q$-expansion

\(f(q)\) \(=\) \(q-0.851125 q^{2} +(0.330612 - 0.572636i) q^{3} -1.27559 q^{4} +(1.72074 - 2.98041i) q^{5} +(-0.281392 + 0.487385i) q^{6} +2.78793 q^{8} +(1.28139 + 2.21944i) q^{9} +O(q^{10})\) \(q-0.851125 q^{2} +(0.330612 - 0.572636i) q^{3} -1.27559 q^{4} +(1.72074 - 2.98041i) q^{5} +(-0.281392 + 0.487385i) q^{6} +2.78793 q^{8} +(1.28139 + 2.21944i) q^{9} +(-1.46456 + 2.53670i) q^{10} +(0.448993 - 0.777679i) q^{11} +(-0.421723 + 0.730446i) q^{12} +(3.07517 - 1.88237i) q^{13} +(-1.13779 - 1.97071i) q^{15} +0.178289 q^{16} -1.93681 q^{17} +(-1.09063 - 1.88902i) q^{18} +(0.519020 + 0.898968i) q^{19} +(-2.19495 + 3.80177i) q^{20} +(-0.382150 + 0.661902i) q^{22} +5.65013 q^{23} +(0.921723 - 1.59647i) q^{24} +(-3.42189 - 5.92688i) q^{25} +(-2.61736 + 1.60213i) q^{26} +3.67824 q^{27} +(0.917969 + 1.58997i) q^{29} +(0.968404 + 1.67733i) q^{30} +(-4.56692 - 7.91014i) q^{31} -5.72761 q^{32} +(-0.296885 - 0.514219i) q^{33} +1.64847 q^{34} +(-1.63452 - 2.83108i) q^{36} -10.6000 q^{37} +(-0.441751 - 0.765135i) q^{38} +(-0.0612242 - 2.38329i) q^{39} +(4.79731 - 8.30918i) q^{40} +(-2.66571 - 4.61715i) q^{41} +(1.95732 - 3.39018i) q^{43} +(-0.572729 + 0.991996i) q^{44} +8.81977 q^{45} -4.80897 q^{46} +(3.59565 - 6.22784i) q^{47} +(0.0589445 - 0.102095i) q^{48} +(2.91246 + 5.04452i) q^{50} +(-0.640331 + 1.10909i) q^{51} +(-3.92265 + 2.40112i) q^{52} +(4.69324 + 8.12893i) q^{53} -3.13065 q^{54} +(-1.54520 - 2.67637i) q^{55} +0.686375 q^{57} +(-0.781307 - 1.35326i) q^{58} +0.510517 q^{59} +(1.45135 + 2.51382i) q^{60} +(0.718095 + 1.24378i) q^{61} +(3.88702 + 6.73252i) q^{62} +4.51834 q^{64} +(-0.318655 - 12.4043i) q^{65} +(0.252686 + 0.437665i) q^{66} +(4.22466 - 7.31732i) q^{67} +2.47057 q^{68} +(1.86800 - 3.23547i) q^{69} +(1.72419 - 2.98638i) q^{71} +(3.57244 + 6.18764i) q^{72} +(5.45026 + 9.44013i) q^{73} +9.02195 q^{74} -4.52526 q^{75} +(-0.662054 - 1.14671i) q^{76} +(0.0521095 + 2.02848i) q^{78} +(6.04589 - 10.4718i) q^{79} +(0.306789 - 0.531375i) q^{80} +(-2.62811 + 4.55201i) q^{81} +(2.26886 + 3.92977i) q^{82} -1.51669 q^{83} +(-3.33274 + 5.77248i) q^{85} +(-1.66593 + 2.88547i) q^{86} +1.21396 q^{87} +(1.25176 - 2.16812i) q^{88} -13.6078 q^{89} -7.50673 q^{90} -7.20722 q^{92} -6.03951 q^{93} +(-3.06035 + 5.30067i) q^{94} +3.57239 q^{95} +(-1.89362 + 3.27984i) q^{96} +(0.253120 - 0.438417i) q^{97} +2.30134 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} + O(q^{10}) \) \( 12q - 4q^{2} - q^{3} + 8q^{4} - q^{5} + 9q^{6} - 6q^{8} + 3q^{9} - 4q^{10} + 4q^{11} - 5q^{12} + 2q^{13} - 2q^{15} - 16q^{16} + 10q^{17} + 3q^{18} + q^{19} + q^{20} - 5q^{22} + 2q^{23} + 11q^{24} + 7q^{25} + 16q^{26} + 8q^{27} + 3q^{29} - 5q^{30} - 16q^{31} - 16q^{32} - 16q^{33} - 32q^{34} - 21q^{36} + 26q^{37} + 17q^{38} - 20q^{39} + 5q^{40} + 8q^{41} - 11q^{43} + 21q^{44} - 14q^{45} - 32q^{46} + q^{47} - 21q^{48} + 6q^{50} - 20q^{51} - 41q^{52} - 2q^{53} - 36q^{54} - 9q^{55} + 42q^{57} - 8q^{58} + 26q^{59} + 20q^{60} + 5q^{61} - 5q^{62} - 30q^{64} - 5q^{65} - 18q^{66} - 11q^{67} + 58q^{68} - 23q^{69} + 6q^{71} + 25q^{72} + 30q^{73} + 6q^{74} - 6q^{75} + 9q^{76} + 16q^{78} + 7q^{79} + 7q^{80} - 6q^{81} - q^{82} + 54q^{83} - q^{85} - 7q^{86} + 32q^{87} + 8q^{89} + 16q^{90} + 54q^{92} + 14q^{93} - 45q^{94} + 12q^{95} - 19q^{96} + 35q^{97} - 20q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.851125 −0.601837 −0.300918 0.953650i \(-0.597293\pi\)
−0.300918 + 0.953650i \(0.597293\pi\)
\(3\) 0.330612 0.572636i 0.190879 0.330612i −0.754663 0.656113i \(-0.772200\pi\)
0.945542 + 0.325501i \(0.105533\pi\)
\(4\) −1.27559 −0.637793
\(5\) 1.72074 2.98041i 0.769538 1.33288i −0.168276 0.985740i \(-0.553820\pi\)
0.937814 0.347139i \(-0.112847\pi\)
\(6\) −0.281392 + 0.487385i −0.114878 + 0.198974i
\(7\) 0 0
\(8\) 2.78793 0.985684
\(9\) 1.28139 + 2.21944i 0.427131 + 0.739812i
\(10\) −1.46456 + 2.53670i −0.463136 + 0.802175i
\(11\) 0.448993 0.777679i 0.135377 0.234479i −0.790365 0.612637i \(-0.790109\pi\)
0.925741 + 0.378158i \(0.123442\pi\)
\(12\) −0.421723 + 0.730446i −0.121741 + 0.210862i
\(13\) 3.07517 1.88237i 0.852900 0.522075i
\(14\) 0 0
\(15\) −1.13779 1.97071i −0.293777 0.508836i
\(16\) 0.178289 0.0445723
\(17\) −1.93681 −0.469745 −0.234873 0.972026i \(-0.575467\pi\)
−0.234873 + 0.972026i \(0.575467\pi\)
\(18\) −1.09063 1.88902i −0.257063 0.445246i
\(19\) 0.519020 + 0.898968i 0.119071 + 0.206237i 0.919400 0.393324i \(-0.128675\pi\)
−0.800329 + 0.599562i \(0.795342\pi\)
\(20\) −2.19495 + 3.80177i −0.490806 + 0.850101i
\(21\) 0 0
\(22\) −0.382150 + 0.661902i −0.0814745 + 0.141118i
\(23\) 5.65013 1.17813 0.589067 0.808084i \(-0.299496\pi\)
0.589067 + 0.808084i \(0.299496\pi\)
\(24\) 0.921723 1.59647i 0.188146 0.325878i
\(25\) −3.42189 5.92688i −0.684378 1.18538i
\(26\) −2.61736 + 1.60213i −0.513306 + 0.314204i
\(27\) 3.67824 0.707878
\(28\) 0 0
\(29\) 0.917969 + 1.58997i 0.170463 + 0.295250i 0.938582 0.345057i \(-0.112140\pi\)
−0.768119 + 0.640307i \(0.778807\pi\)
\(30\) 0.968404 + 1.67733i 0.176806 + 0.306236i
\(31\) −4.56692 7.91014i −0.820244 1.42070i −0.905501 0.424345i \(-0.860505\pi\)
0.0852573 0.996359i \(-0.472829\pi\)
\(32\) −5.72761 −1.01251
\(33\) −0.296885 0.514219i −0.0516810 0.0895141i
\(34\) 1.64847 0.282710
\(35\) 0 0
\(36\) −1.63452 2.83108i −0.272421 0.471847i
\(37\) −10.6000 −1.74263 −0.871316 0.490722i \(-0.836733\pi\)
−0.871316 + 0.490722i \(0.836733\pi\)
\(38\) −0.441751 0.765135i −0.0716614 0.124121i
\(39\) −0.0612242 2.38329i −0.00980372 0.381631i
\(40\) 4.79731 8.30918i 0.758521 1.31380i
\(41\) −2.66571 4.61715i −0.416314 0.721078i 0.579251 0.815149i \(-0.303345\pi\)
−0.995565 + 0.0940715i \(0.970012\pi\)
\(42\) 0 0
\(43\) 1.95732 3.39018i 0.298489 0.516998i −0.677302 0.735706i \(-0.736851\pi\)
0.975790 + 0.218708i \(0.0701841\pi\)
\(44\) −0.572729 + 0.991996i −0.0863422 + 0.149549i
\(45\) 8.81977 1.31477
\(46\) −4.80897 −0.709044
\(47\) 3.59565 6.22784i 0.524479 0.908424i −0.475115 0.879924i \(-0.657593\pi\)
0.999594 0.0285004i \(-0.00907317\pi\)
\(48\) 0.0589445 0.102095i 0.00850791 0.0147361i
\(49\) 0 0
\(50\) 2.91246 + 5.04452i 0.411883 + 0.713403i
\(51\) −0.640331 + 1.10909i −0.0896643 + 0.155303i
\(52\) −3.92265 + 2.40112i −0.543973 + 0.332976i
\(53\) 4.69324 + 8.12893i 0.644666 + 1.11659i 0.984378 + 0.176065i \(0.0563370\pi\)
−0.339712 + 0.940529i \(0.610330\pi\)
\(54\) −3.13065 −0.426027
\(55\) −1.54520 2.67637i −0.208355 0.360881i
\(56\) 0 0
\(57\) 0.686375 0.0909127
\(58\) −0.781307 1.35326i −0.102591 0.177692i
\(59\) 0.510517 0.0664637 0.0332318 0.999448i \(-0.489420\pi\)
0.0332318 + 0.999448i \(0.489420\pi\)
\(60\) 1.45135 + 2.51382i 0.187369 + 0.324532i
\(61\) 0.718095 + 1.24378i 0.0919426 + 0.159249i 0.908328 0.418258i \(-0.137359\pi\)
−0.816386 + 0.577507i \(0.804026\pi\)
\(62\) 3.88702 + 6.73252i 0.493653 + 0.855031i
\(63\) 0 0
\(64\) 4.51834 0.564792
\(65\) −0.318655 12.4043i −0.0395242 1.53857i
\(66\) 0.252686 + 0.437665i 0.0311035 + 0.0538729i
\(67\) 4.22466 7.31732i 0.516124 0.893953i −0.483701 0.875233i \(-0.660708\pi\)
0.999825 0.0187197i \(-0.00595900\pi\)
\(68\) 2.47057 0.299600
\(69\) 1.86800 3.23547i 0.224881 0.389504i
\(70\) 0 0
\(71\) 1.72419 2.98638i 0.204623 0.354418i −0.745389 0.666629i \(-0.767736\pi\)
0.950013 + 0.312211i \(0.101070\pi\)
\(72\) 3.57244 + 6.18764i 0.421016 + 0.729221i
\(73\) 5.45026 + 9.44013i 0.637905 + 1.10488i 0.985892 + 0.167384i \(0.0535320\pi\)
−0.347987 + 0.937499i \(0.613135\pi\)
\(74\) 9.02195 1.04878
\(75\) −4.52526 −0.522532
\(76\) −0.662054 1.14671i −0.0759428 0.131537i
\(77\) 0 0
\(78\) 0.0521095 + 2.02848i 0.00590024 + 0.229680i
\(79\) 6.04589 10.4718i 0.680216 1.17817i −0.294699 0.955590i \(-0.595219\pi\)
0.974915 0.222578i \(-0.0714472\pi\)
\(80\) 0.306789 0.531375i 0.0343001 0.0594095i
\(81\) −2.62811 + 4.55201i −0.292012 + 0.505779i
\(82\) 2.26886 + 3.92977i 0.250553 + 0.433971i
\(83\) −1.51669 −0.166479 −0.0832393 0.996530i \(-0.526527\pi\)
−0.0832393 + 0.996530i \(0.526527\pi\)
\(84\) 0 0
\(85\) −3.33274 + 5.77248i −0.361487 + 0.626113i
\(86\) −1.66593 + 2.88547i −0.179642 + 0.311148i
\(87\) 1.21396 0.130151
\(88\) 1.25176 2.16812i 0.133438 0.231122i
\(89\) −13.6078 −1.44243 −0.721213 0.692714i \(-0.756415\pi\)
−0.721213 + 0.692714i \(0.756415\pi\)
\(90\) −7.50673 −0.791279
\(91\) 0 0
\(92\) −7.20722 −0.751405
\(93\) −6.03951 −0.626268
\(94\) −3.06035 + 5.30067i −0.315651 + 0.546723i
\(95\) 3.57239 0.366519
\(96\) −1.89362 + 3.27984i −0.193266 + 0.334747i
\(97\) 0.253120 0.438417i 0.0257005 0.0445145i −0.852889 0.522092i \(-0.825152\pi\)
0.878590 + 0.477578i \(0.158485\pi\)
\(98\) 0 0
\(99\) 2.30134 0.231294
\(100\) 4.36491 + 7.56025i 0.436491 + 0.756025i
\(101\) −2.99327 + 5.18450i −0.297842 + 0.515877i −0.975642 0.219369i \(-0.929600\pi\)
0.677800 + 0.735246i \(0.262933\pi\)
\(102\) 0.545002 0.943972i 0.0539633 0.0934671i
\(103\) −2.06651 + 3.57930i −0.203619 + 0.352679i −0.949692 0.313186i \(-0.898604\pi\)
0.746073 + 0.665865i \(0.231937\pi\)
\(104\) 8.57338 5.24792i 0.840689 0.514601i
\(105\) 0 0
\(106\) −3.99454 6.91874i −0.387984 0.672008i
\(107\) −14.1234 −1.36536 −0.682679 0.730718i \(-0.739185\pi\)
−0.682679 + 0.730718i \(0.739185\pi\)
\(108\) −4.69191 −0.451479
\(109\) 2.10119 + 3.63936i 0.201257 + 0.348588i 0.948934 0.315475i \(-0.102164\pi\)
−0.747677 + 0.664063i \(0.768831\pi\)
\(110\) 1.31516 + 2.27792i 0.125396 + 0.217191i
\(111\) −3.50449 + 6.06995i −0.332631 + 0.576135i
\(112\) 0 0
\(113\) −6.88472 + 11.9247i −0.647660 + 1.12178i 0.336020 + 0.941855i \(0.390919\pi\)
−0.983680 + 0.179926i \(0.942414\pi\)
\(114\) −0.584192 −0.0547146
\(115\) 9.72240 16.8397i 0.906618 1.57031i
\(116\) −1.17095 2.02814i −0.108720 0.188308i
\(117\) 8.11830 + 4.41310i 0.750537 + 0.407991i
\(118\) −0.434514 −0.0400003
\(119\) 0 0
\(120\) −3.17209 5.49422i −0.289571 0.501552i
\(121\) 5.09681 + 8.82793i 0.463346 + 0.802539i
\(122\) −0.611189 1.05861i −0.0553344 0.0958420i
\(123\) −3.52526 −0.317862
\(124\) 5.82550 + 10.0901i 0.523145 + 0.906114i
\(125\) −6.34531 −0.567542
\(126\) 0 0
\(127\) −0.972482 1.68439i −0.0862938 0.149465i 0.819648 0.572868i \(-0.194169\pi\)
−0.905942 + 0.423402i \(0.860836\pi\)
\(128\) 7.60956 0.672596
\(129\) −1.29423 2.24167i −0.113950 0.197368i
\(130\) 0.271215 + 10.5576i 0.0237871 + 0.925967i
\(131\) −6.01770 + 10.4230i −0.525769 + 0.910659i 0.473780 + 0.880643i \(0.342889\pi\)
−0.999549 + 0.0300158i \(0.990444\pi\)
\(132\) 0.378702 + 0.655931i 0.0329618 + 0.0570914i
\(133\) 0 0
\(134\) −3.59571 + 6.22796i −0.310622 + 0.538014i
\(135\) 6.32930 10.9627i 0.544739 0.943516i
\(136\) −5.39970 −0.463020
\(137\) 8.71715 0.744756 0.372378 0.928081i \(-0.378543\pi\)
0.372378 + 0.928081i \(0.378543\pi\)
\(138\) −1.58990 + 2.75379i −0.135341 + 0.234418i
\(139\) 2.10625 3.64813i 0.178650 0.309430i −0.762769 0.646672i \(-0.776160\pi\)
0.941418 + 0.337241i \(0.109494\pi\)
\(140\) 0 0
\(141\) −2.37752 4.11799i −0.200224 0.346798i
\(142\) −1.46750 + 2.54178i −0.123150 + 0.213302i
\(143\) −0.0831467 3.23667i −0.00695307 0.270664i
\(144\) 0.228459 + 0.395702i 0.0190382 + 0.0329751i
\(145\) 6.31834 0.524710
\(146\) −4.63885 8.03473i −0.383914 0.664959i
\(147\) 0 0
\(148\) 13.5212 1.11144
\(149\) −2.93242 5.07910i −0.240233 0.416096i 0.720548 0.693406i \(-0.243891\pi\)
−0.960781 + 0.277310i \(0.910557\pi\)
\(150\) 3.85157 0.314479
\(151\) 8.42840 + 14.5984i 0.685893 + 1.18800i 0.973155 + 0.230150i \(0.0739216\pi\)
−0.287262 + 0.957852i \(0.592745\pi\)
\(152\) 1.44699 + 2.50626i 0.117367 + 0.203285i
\(153\) −2.48181 4.29862i −0.200643 0.347523i
\(154\) 0 0
\(155\) −31.4339 −2.52483
\(156\) 0.0780967 + 3.04009i 0.00625274 + 0.243402i
\(157\) −0.969500 1.67922i −0.0773746 0.134017i 0.824742 0.565509i \(-0.191320\pi\)
−0.902116 + 0.431493i \(0.857987\pi\)
\(158\) −5.14581 + 8.91280i −0.409379 + 0.709065i
\(159\) 6.20656 0.492212
\(160\) −9.85573 + 17.0706i −0.779164 + 1.34955i
\(161\) 0 0
\(162\) 2.23685 3.87433i 0.175743 0.304396i
\(163\) 5.94797 + 10.3022i 0.465881 + 0.806929i 0.999241 0.0389590i \(-0.0124042\pi\)
−0.533360 + 0.845888i \(0.679071\pi\)
\(164\) 3.40035 + 5.88957i 0.265522 + 0.459898i
\(165\) −2.04344 −0.159082
\(166\) 1.29090 0.100193
\(167\) 8.28801 + 14.3553i 0.641346 + 1.11084i 0.985133 + 0.171796i \(0.0549569\pi\)
−0.343787 + 0.939048i \(0.611710\pi\)
\(168\) 0 0
\(169\) 5.91338 11.5772i 0.454875 0.890555i
\(170\) 2.83658 4.91310i 0.217556 0.376818i
\(171\) −1.33013 + 2.30386i −0.101718 + 0.176181i
\(172\) −2.49673 + 4.32447i −0.190374 + 0.329738i
\(173\) −4.99328 8.64862i −0.379632 0.657542i 0.611377 0.791340i \(-0.290616\pi\)
−0.991009 + 0.133798i \(0.957283\pi\)
\(174\) −1.03324 −0.0783295
\(175\) 0 0
\(176\) 0.0800507 0.138652i 0.00603405 0.0104513i
\(177\) 0.168783 0.292341i 0.0126865 0.0219737i
\(178\) 11.5820 0.868105
\(179\) −4.58829 + 7.94715i −0.342945 + 0.593998i −0.984978 0.172679i \(-0.944758\pi\)
0.642033 + 0.766677i \(0.278091\pi\)
\(180\) −11.2504 −0.838553
\(181\) −6.00489 −0.446340 −0.223170 0.974780i \(-0.571640\pi\)
−0.223170 + 0.974780i \(0.571640\pi\)
\(182\) 0 0
\(183\) 0.949642 0.0701995
\(184\) 15.7522 1.16127
\(185\) −18.2399 + 31.5924i −1.34102 + 2.32272i
\(186\) 5.14038 0.376911
\(187\) −0.869614 + 1.50622i −0.0635925 + 0.110145i
\(188\) −4.58655 + 7.94415i −0.334509 + 0.579386i
\(189\) 0 0
\(190\) −3.04055 −0.220585
\(191\) −0.658061 1.13980i −0.0476156 0.0824727i 0.841235 0.540669i \(-0.181829\pi\)
−0.888851 + 0.458197i \(0.848496\pi\)
\(192\) 1.49382 2.58736i 0.107807 0.186727i
\(193\) 8.21270 14.2248i 0.591163 1.02392i −0.402913 0.915238i \(-0.632002\pi\)
0.994076 0.108686i \(-0.0346643\pi\)
\(194\) −0.215437 + 0.373148i −0.0154675 + 0.0267905i
\(195\) −7.20852 3.91854i −0.516213 0.280613i
\(196\) 0 0
\(197\) 12.7938 + 22.1594i 0.911517 + 1.57879i 0.811922 + 0.583766i \(0.198421\pi\)
0.0995951 + 0.995028i \(0.468245\pi\)
\(198\) −1.95873 −0.139201
\(199\) 25.3788 1.79906 0.899528 0.436864i \(-0.143911\pi\)
0.899528 + 0.436864i \(0.143911\pi\)
\(200\) −9.54000 16.5238i −0.674580 1.16841i
\(201\) −2.79344 4.83838i −0.197034 0.341273i
\(202\) 2.54765 4.41266i 0.179252 0.310473i
\(203\) 0 0
\(204\) 0.816797 1.41473i 0.0571873 0.0990512i
\(205\) −18.3480 −1.28148
\(206\) 1.75886 3.04643i 0.122546 0.212255i
\(207\) 7.24003 + 12.5401i 0.503217 + 0.871597i
\(208\) 0.548271 0.335606i 0.0380157 0.0232701i
\(209\) 0.932145 0.0644778
\(210\) 0 0
\(211\) 2.84824 + 4.93330i 0.196081 + 0.339622i 0.947254 0.320483i \(-0.103845\pi\)
−0.751173 + 0.660105i \(0.770512\pi\)
\(212\) −5.98663 10.3691i −0.411164 0.712156i
\(213\) −1.14007 1.97466i −0.0781165 0.135302i
\(214\) 12.0208 0.821723
\(215\) −6.73608 11.6672i −0.459397 0.795699i
\(216\) 10.2547 0.697744
\(217\) 0 0
\(218\) −1.78837 3.09755i −0.121124 0.209793i
\(219\) 7.20768 0.487050
\(220\) 1.97104 + 3.41393i 0.132887 + 0.230167i
\(221\) −5.95602 + 3.64579i −0.400645 + 0.245242i
\(222\) 2.98276 5.16629i 0.200190 0.346739i
\(223\) 1.17906 + 2.04219i 0.0789558 + 0.136755i 0.902800 0.430061i \(-0.141508\pi\)
−0.823844 + 0.566817i \(0.808175\pi\)
\(224\) 0 0
\(225\) 8.76956 15.1893i 0.584637 1.01262i
\(226\) 5.85976 10.1494i 0.389786 0.675129i
\(227\) −26.2926 −1.74510 −0.872551 0.488523i \(-0.837536\pi\)
−0.872551 + 0.488523i \(0.837536\pi\)
\(228\) −0.875531 −0.0579834
\(229\) 0.0342777 0.0593708i 0.00226514 0.00392333i −0.864891 0.501960i \(-0.832612\pi\)
0.867156 + 0.498037i \(0.165946\pi\)
\(230\) −8.27498 + 14.3327i −0.545636 + 0.945069i
\(231\) 0 0
\(232\) 2.55924 + 4.43273i 0.168022 + 0.291023i
\(233\) −7.33514 + 12.7048i −0.480541 + 0.832322i −0.999751 0.0223253i \(-0.992893\pi\)
0.519210 + 0.854647i \(0.326226\pi\)
\(234\) −6.90969 3.75610i −0.451701 0.245544i
\(235\) −12.3743 21.4330i −0.807213 1.39813i
\(236\) −0.651208 −0.0423901
\(237\) −3.99768 6.92419i −0.259677 0.449774i
\(238\) 0 0
\(239\) 3.35434 0.216974 0.108487 0.994098i \(-0.465399\pi\)
0.108487 + 0.994098i \(0.465399\pi\)
\(240\) −0.202856 0.351357i −0.0130943 0.0226800i
\(241\) 8.57978 0.552672 0.276336 0.961061i \(-0.410880\pi\)
0.276336 + 0.961061i \(0.410880\pi\)
\(242\) −4.33802 7.51368i −0.278859 0.482998i
\(243\) 7.25513 + 12.5662i 0.465417 + 0.806125i
\(244\) −0.915991 1.58654i −0.0586403 0.101568i
\(245\) 0 0
\(246\) 3.00044 0.191301
\(247\) 3.28826 + 1.78750i 0.209227 + 0.113736i
\(248\) −12.7323 22.0530i −0.808501 1.40036i
\(249\) −0.501436 + 0.868513i −0.0317772 + 0.0550398i
\(250\) 5.40066 0.341568
\(251\) 10.7575 18.6326i 0.679010 1.17608i −0.296270 0.955104i \(-0.595743\pi\)
0.975280 0.220975i \(-0.0709238\pi\)
\(252\) 0 0
\(253\) 2.53687 4.39399i 0.159492 0.276248i
\(254\) 0.827704 + 1.43363i 0.0519348 + 0.0899537i
\(255\) 2.20369 + 3.81690i 0.138000 + 0.239023i
\(256\) −15.5134 −0.969585
\(257\) −4.93792 −0.308019 −0.154010 0.988069i \(-0.549219\pi\)
−0.154010 + 0.988069i \(0.549219\pi\)
\(258\) 1.10155 + 1.90794i 0.0685795 + 0.118783i
\(259\) 0 0
\(260\) 0.406471 + 15.8228i 0.0252083 + 0.981288i
\(261\) −2.35256 + 4.07475i −0.145620 + 0.252221i
\(262\) 5.12182 8.87125i 0.316427 0.548068i
\(263\) 4.47719 7.75473i 0.276076 0.478177i −0.694330 0.719656i \(-0.744299\pi\)
0.970406 + 0.241480i \(0.0776327\pi\)
\(264\) −0.827695 1.43361i −0.0509411 0.0882326i
\(265\) 32.3034 1.98438
\(266\) 0 0
\(267\) −4.49890 + 7.79233i −0.275328 + 0.476883i
\(268\) −5.38891 + 9.33387i −0.329180 + 0.570157i
\(269\) 4.82345 0.294091 0.147045 0.989130i \(-0.453024\pi\)
0.147045 + 0.989130i \(0.453024\pi\)
\(270\) −5.38702 + 9.33060i −0.327844 + 0.567842i
\(271\) 7.42144 0.450820 0.225410 0.974264i \(-0.427628\pi\)
0.225410 + 0.974264i \(0.427628\pi\)
\(272\) −0.345312 −0.0209376
\(273\) 0 0
\(274\) −7.41938 −0.448221
\(275\) −6.14562 −0.370595
\(276\) −2.38279 + 4.12712i −0.143427 + 0.248423i
\(277\) 3.81631 0.229300 0.114650 0.993406i \(-0.463425\pi\)
0.114650 + 0.993406i \(0.463425\pi\)
\(278\) −1.79268 + 3.10502i −0.107518 + 0.186226i
\(279\) 11.7040 20.2720i 0.700702 1.21365i
\(280\) 0 0
\(281\) 8.54978 0.510037 0.255019 0.966936i \(-0.417918\pi\)
0.255019 + 0.966936i \(0.417918\pi\)
\(282\) 2.02357 + 3.50493i 0.120502 + 0.208715i
\(283\) 7.63217 13.2193i 0.453686 0.785807i −0.544926 0.838484i \(-0.683442\pi\)
0.998612 + 0.0526775i \(0.0167755\pi\)
\(284\) −2.19935 + 3.80938i −0.130507 + 0.226045i
\(285\) 1.18107 2.04568i 0.0699607 0.121176i
\(286\) 0.0707683 + 2.75481i 0.00418461 + 0.162895i
\(287\) 0 0
\(288\) −7.33932 12.7121i −0.432474 0.749066i
\(289\) −13.2488 −0.779340
\(290\) −5.37770 −0.315790
\(291\) −0.167369 0.289892i −0.00981135 0.0169938i
\(292\) −6.95227 12.0417i −0.406851 0.704687i
\(293\) −2.96982 + 5.14388i −0.173499 + 0.300509i −0.939641 0.342163i \(-0.888841\pi\)
0.766142 + 0.642671i \(0.222174\pi\)
\(294\) 0 0
\(295\) 0.878467 1.52155i 0.0511463 0.0885881i
\(296\) −29.5522 −1.71768
\(297\) 1.65151 2.86049i 0.0958301 0.165983i
\(298\) 2.49586 + 4.32295i 0.144581 + 0.250422i
\(299\) 17.3751 10.6356i 1.00483 0.615074i
\(300\) 5.77236 0.333267
\(301\) 0 0
\(302\) −7.17362 12.4251i −0.412796 0.714983i
\(303\) 1.97922 + 3.42811i 0.113703 + 0.196940i
\(304\) 0.0925356 + 0.160276i 0.00530728 + 0.00919248i
\(305\) 4.94262 0.283013
\(306\) 2.11233 + 3.65867i 0.120754 + 0.209152i
\(307\) −22.2133 −1.26778 −0.633891 0.773422i \(-0.718543\pi\)
−0.633891 + 0.773422i \(0.718543\pi\)
\(308\) 0 0
\(309\) 1.36642 + 2.36672i 0.0777332 + 0.134638i
\(310\) 26.7542 1.51954
\(311\) 4.92130 + 8.52394i 0.279061 + 0.483348i 0.971152 0.238463i \(-0.0766435\pi\)
−0.692091 + 0.721811i \(0.743310\pi\)
\(312\) −0.170689 6.64445i −0.00966337 0.376168i
\(313\) −10.4563 + 18.1108i −0.591023 + 1.02368i 0.403072 + 0.915168i \(0.367942\pi\)
−0.994095 + 0.108513i \(0.965391\pi\)
\(314\) 0.825166 + 1.42923i 0.0465668 + 0.0806561i
\(315\) 0 0
\(316\) −7.71205 + 13.3577i −0.433837 + 0.751427i
\(317\) 12.6801 21.9626i 0.712188 1.23355i −0.251847 0.967767i \(-0.581038\pi\)
0.964034 0.265778i \(-0.0856288\pi\)
\(318\) −5.28256 −0.296231
\(319\) 1.64865 0.0923065
\(320\) 7.77489 13.4665i 0.434629 0.752800i
\(321\) −4.66935 + 8.08755i −0.260618 + 0.451403i
\(322\) 0 0
\(323\) −1.00524 1.74113i −0.0559331 0.0968790i
\(324\) 3.35237 5.80648i 0.186243 0.322582i
\(325\) −21.6795 11.7849i −1.20256 0.653711i
\(326\) −5.06247 8.76845i −0.280384 0.485640i
\(327\) 2.77871 0.153663
\(328\) −7.43183 12.8723i −0.410354 0.710755i
\(329\) 0 0
\(330\) 1.73923 0.0957413
\(331\) −0.891417 1.54398i −0.0489967 0.0848648i 0.840487 0.541832i \(-0.182269\pi\)
−0.889484 + 0.456967i \(0.848936\pi\)
\(332\) 1.93467 0.106179
\(333\) −13.5828 23.5261i −0.744332 1.28922i
\(334\) −7.05414 12.2181i −0.385985 0.668546i
\(335\) −14.5391 25.1824i −0.794354 1.37586i
\(336\) 0 0
\(337\) 9.56149 0.520848 0.260424 0.965494i \(-0.416138\pi\)
0.260424 + 0.965494i \(0.416138\pi\)
\(338\) −5.03303 + 9.85366i −0.273761 + 0.535969i
\(339\) 4.55234 + 7.88488i 0.247249 + 0.428248i
\(340\) 4.25120 7.36329i 0.230554 0.399331i
\(341\) −8.20207 −0.444167
\(342\) 1.13211 1.96087i 0.0612176 0.106032i
\(343\) 0 0
\(344\) 5.45689 9.45160i 0.294216 0.509596i
\(345\) −6.42867 11.1348i −0.346108 0.599477i
\(346\) 4.24991 + 7.36106i 0.228477 + 0.395733i
\(347\) 0.633389 0.0340021 0.0170010 0.999855i \(-0.494588\pi\)
0.0170010 + 0.999855i \(0.494588\pi\)
\(348\) −1.54852 −0.0830092
\(349\) 15.2994 + 26.4994i 0.818960 + 1.41848i 0.906449 + 0.422315i \(0.138783\pi\)
−0.0874885 + 0.996166i \(0.527884\pi\)
\(350\) 0 0
\(351\) 11.3112 6.92381i 0.603749 0.369565i
\(352\) −2.57166 + 4.45425i −0.137070 + 0.237412i
\(353\) −0.550173 + 0.952928i −0.0292828 + 0.0507192i −0.880295 0.474426i \(-0.842656\pi\)
0.851013 + 0.525145i \(0.175989\pi\)
\(354\) −0.143655 + 0.248819i −0.00763520 + 0.0132246i
\(355\) −5.93375 10.2776i −0.314931 0.545476i
\(356\) 17.3579 0.919969
\(357\) 0 0
\(358\) 3.90521 6.76402i 0.206397 0.357489i
\(359\) 4.88693 8.46441i 0.257922 0.446734i −0.707763 0.706450i \(-0.750295\pi\)
0.965685 + 0.259716i \(0.0836288\pi\)
\(360\) 24.5889 1.29595
\(361\) 8.96124 15.5213i 0.471644 0.816912i
\(362\) 5.11091 0.268624
\(363\) 6.74026 0.353772
\(364\) 0 0
\(365\) 37.5139 1.96357
\(366\) −0.808264 −0.0422487
\(367\) −5.57363 + 9.65381i −0.290941 + 0.503925i −0.974033 0.226408i \(-0.927302\pi\)
0.683092 + 0.730333i \(0.260635\pi\)
\(368\) 1.00736 0.0525121
\(369\) 6.83165 11.8328i 0.355641 0.615989i
\(370\) 15.5244 26.8891i 0.807076 1.39790i
\(371\) 0 0
\(372\) 7.70391 0.399429
\(373\) 15.3651 + 26.6131i 0.795573 + 1.37797i 0.922475 + 0.386057i \(0.126163\pi\)
−0.126902 + 0.991915i \(0.540504\pi\)
\(374\) 0.740150 1.28198i 0.0382723 0.0662895i
\(375\) −2.09783 + 3.63355i −0.108332 + 0.187636i
\(376\) 10.0244 17.3628i 0.516970 0.895419i
\(377\) 5.81582 + 3.16147i 0.299530 + 0.162824i
\(378\) 0 0
\(379\) −11.3286 19.6217i −0.581912 1.00790i −0.995253 0.0973246i \(-0.968972\pi\)
0.413341 0.910576i \(-0.364362\pi\)
\(380\) −4.55689 −0.233763
\(381\) −1.28606 −0.0658866
\(382\) 0.560093 + 0.970109i 0.0286568 + 0.0496351i
\(383\) −0.294631 0.510317i −0.0150550 0.0260760i 0.858400 0.512981i \(-0.171459\pi\)
−0.873455 + 0.486905i \(0.838126\pi\)
\(384\) 2.51581 4.35751i 0.128384 0.222368i
\(385\) 0 0
\(386\) −6.99004 + 12.1071i −0.355783 + 0.616235i
\(387\) 10.0324 0.509975
\(388\) −0.322877 + 0.559239i −0.0163916 + 0.0283910i
\(389\) −2.84973 4.93587i −0.144487 0.250259i 0.784695 0.619883i \(-0.212820\pi\)
−0.929181 + 0.369624i \(0.879486\pi\)
\(390\) 6.13536 + 3.33517i 0.310676 + 0.168883i
\(391\) −10.9432 −0.553422
\(392\) 0 0
\(393\) 3.97904 + 6.89191i 0.200716 + 0.347651i
\(394\) −10.8891 18.8605i −0.548584 0.950176i
\(395\) −20.8068 36.0384i −1.04690 1.81329i
\(396\) −2.93556 −0.147518
\(397\) −12.7641 22.1082i −0.640614 1.10958i −0.985296 0.170857i \(-0.945346\pi\)
0.344682 0.938720i \(-0.387987\pi\)
\(398\) −21.6005 −1.08274
\(399\) 0 0
\(400\) −0.610086 1.05670i −0.0305043 0.0528350i
\(401\) 25.5011 1.27347 0.636733 0.771085i \(-0.280286\pi\)
0.636733 + 0.771085i \(0.280286\pi\)
\(402\) 2.37757 + 4.11807i 0.118582 + 0.205391i
\(403\) −28.9339 15.7284i −1.44130 0.783489i
\(404\) 3.81817 6.61327i 0.189961 0.329022i
\(405\) 9.04457 + 15.6657i 0.449428 + 0.778433i
\(406\) 0 0
\(407\) −4.75934 + 8.24341i −0.235912 + 0.408611i
\(408\) −1.78520 + 3.09206i −0.0883807 + 0.153080i
\(409\) −0.146988 −0.00726807 −0.00363403 0.999993i \(-0.501157\pi\)
−0.00363403 + 0.999993i \(0.501157\pi\)
\(410\) 15.6164 0.771241
\(411\) 2.88199 4.99175i 0.142158 0.246225i
\(412\) 2.63601 4.56570i 0.129867 0.224936i
\(413\) 0 0
\(414\) −6.16217 10.6732i −0.302854 0.524559i
\(415\) −2.60983 + 4.52036i −0.128112 + 0.221896i
\(416\) −17.6134 + 10.7815i −0.863568 + 0.528606i
\(417\) −1.39270 2.41223i −0.0682008 0.118127i
\(418\) −0.793372 −0.0388051
\(419\) 6.84795 + 11.8610i 0.334544 + 0.579447i 0.983397 0.181466i \(-0.0580844\pi\)
−0.648853 + 0.760914i \(0.724751\pi\)
\(420\) 0 0
\(421\) 3.44169 0.167738 0.0838688 0.996477i \(-0.473272\pi\)
0.0838688 + 0.996477i \(0.473272\pi\)
\(422\) −2.42421 4.19885i −0.118009 0.204397i
\(423\) 18.4297 0.896084
\(424\) 13.0844 + 22.6629i 0.635437 + 1.10061i
\(425\) 6.62754 + 11.4792i 0.321483 + 0.556825i
\(426\) 0.970345 + 1.68069i 0.0470134 + 0.0814295i
\(427\) 0 0
\(428\) 18.0156 0.870816
\(429\) −1.88092 1.02247i −0.0908118 0.0493652i
\(430\) 5.73325 + 9.93028i 0.276482 + 0.478881i
\(431\) −11.1455 + 19.3046i −0.536861 + 0.929870i 0.462210 + 0.886771i \(0.347057\pi\)
−0.999071 + 0.0430997i \(0.986277\pi\)
\(432\) 0.655791 0.0315518
\(433\) −12.9481 + 22.4268i −0.622247 + 1.07776i 0.366819 + 0.930292i \(0.380447\pi\)
−0.989066 + 0.147472i \(0.952886\pi\)
\(434\) 0 0
\(435\) 2.08892 3.61811i 0.100156 0.173475i
\(436\) −2.68024 4.64232i −0.128360 0.222327i
\(437\) 2.93253 + 5.07929i 0.140282 + 0.242975i
\(438\) −6.13464 −0.293124
\(439\) 27.9838 1.33560 0.667798 0.744343i \(-0.267237\pi\)
0.667798 + 0.744343i \(0.267237\pi\)
\(440\) −4.30792 7.46153i −0.205372 0.355715i
\(441\) 0 0
\(442\) 5.06932 3.10302i 0.241123 0.147596i
\(443\) −16.6044 + 28.7597i −0.788900 + 1.36642i 0.137741 + 0.990468i \(0.456016\pi\)
−0.926641 + 0.375947i \(0.877317\pi\)
\(444\) 4.47028 7.74275i 0.212150 0.367454i
\(445\) −23.4155 + 40.5568i −1.11000 + 1.92258i
\(446\) −1.00353 1.73816i −0.0475185 0.0823044i
\(447\) −3.87796 −0.183421
\(448\) 0 0
\(449\) −9.84320 + 17.0489i −0.464529 + 0.804589i −0.999180 0.0404845i \(-0.987110\pi\)
0.534651 + 0.845073i \(0.320443\pi\)
\(450\) −7.46399 + 12.9280i −0.351856 + 0.609433i
\(451\) −4.78755 −0.225437
\(452\) 8.78205 15.2110i 0.413073 0.715464i
\(453\) 11.1461 0.523690
\(454\) 22.3783 1.05027
\(455\) 0 0
\(456\) 1.91357 0.0896111
\(457\) −0.746942 −0.0349405 −0.0174702 0.999847i \(-0.505561\pi\)
−0.0174702 + 0.999847i \(0.505561\pi\)
\(458\) −0.0291746 + 0.0505320i −0.00136324 + 0.00236120i
\(459\) −7.12405 −0.332522
\(460\) −12.4017 + 21.4805i −0.578235 + 1.00153i
\(461\) −16.5855 + 28.7269i −0.772464 + 1.33795i 0.163744 + 0.986503i \(0.447643\pi\)
−0.936209 + 0.351445i \(0.885691\pi\)
\(462\) 0 0
\(463\) −30.7521 −1.42917 −0.714586 0.699548i \(-0.753385\pi\)
−0.714586 + 0.699548i \(0.753385\pi\)
\(464\) 0.163664 + 0.283475i 0.00759792 + 0.0131600i
\(465\) −10.3924 + 18.0002i −0.481937 + 0.834740i
\(466\) 6.24313 10.8134i 0.289207 0.500922i
\(467\) −14.8033 + 25.6400i −0.685013 + 1.18648i 0.288420 + 0.957504i \(0.406870\pi\)
−0.973433 + 0.228973i \(0.926463\pi\)
\(468\) −10.3556 5.62928i −0.478687 0.260214i
\(469\) 0 0
\(470\) 10.5321 + 18.2422i 0.485810 + 0.841448i
\(471\) −1.28211 −0.0590766
\(472\) 1.42329 0.0655122
\(473\) −1.75765 3.04434i −0.0808168 0.139979i
\(474\) 3.40253 + 5.89335i 0.156283 + 0.270691i
\(475\) 3.55205 6.15234i 0.162979 0.282289i
\(476\) 0 0
\(477\) −12.0278 + 20.8327i −0.550714 + 0.953864i
\(478\) −2.85496 −0.130583
\(479\) 7.04527 12.2028i 0.321907 0.557559i −0.658975 0.752165i \(-0.729010\pi\)
0.980881 + 0.194606i \(0.0623429\pi\)
\(480\) 6.51684 + 11.2875i 0.297452 + 0.515201i
\(481\) −32.5969 + 19.9531i −1.48629 + 0.909785i
\(482\) −7.30247 −0.332618
\(483\) 0 0
\(484\) −6.50142 11.2608i −0.295519 0.511854i
\(485\) −0.871108 1.50880i −0.0395550 0.0685112i
\(486\) −6.17502 10.6955i −0.280105 0.485156i
\(487\) −16.7955 −0.761075 −0.380537 0.924766i \(-0.624261\pi\)
−0.380537 + 0.924766i \(0.624261\pi\)
\(488\) 2.00200 + 3.46757i 0.0906263 + 0.156969i
\(489\) 7.86587 0.355707
\(490\) 0 0
\(491\) −10.8345 18.7659i −0.488954 0.846893i 0.510965 0.859601i \(-0.329288\pi\)
−0.999919 + 0.0127081i \(0.995955\pi\)
\(492\) 4.49677 0.202730
\(493\) −1.77793 3.07947i −0.0800740 0.138692i
\(494\) −2.79873 1.52138i −0.125921 0.0684503i
\(495\) 3.96001 6.85895i 0.177989 0.308287i
\(496\) −0.814234 1.41029i −0.0365602 0.0633241i
\(497\) 0 0
\(498\) 0.426785 0.739213i 0.0191247 0.0331249i
\(499\) 11.6524 20.1825i 0.521633 0.903495i −0.478051 0.878332i \(-0.658656\pi\)
0.999683 0.0251622i \(-0.00801023\pi\)
\(500\) 8.09399 0.361974
\(501\) 10.9605 0.489677
\(502\) −9.15601 + 15.8587i −0.408653 + 0.707807i
\(503\) −21.9415 + 38.0037i −0.978322 + 1.69450i −0.309816 + 0.950796i \(0.600268\pi\)
−0.668506 + 0.743707i \(0.733066\pi\)
\(504\) 0 0
\(505\) 10.3013 + 17.8423i 0.458401 + 0.793974i
\(506\) −2.15919 + 3.73983i −0.0959879 + 0.166256i
\(507\) −4.67450 7.21378i −0.207602 0.320375i
\(508\) 1.24048 + 2.14858i 0.0550376 + 0.0953279i
\(509\) −19.9242 −0.883125 −0.441563 0.897230i \(-0.645576\pi\)
−0.441563 + 0.897230i \(0.645576\pi\)
\(510\) −1.87561 3.24866i −0.0830536 0.143853i
\(511\) 0 0
\(512\) −2.01529 −0.0890641
\(513\) 1.90908 + 3.30662i 0.0842879 + 0.145991i
\(514\) 4.20279 0.185377
\(515\) 7.11185 + 12.3181i 0.313386 + 0.542800i
\(516\) 1.65090 + 2.85944i 0.0726767 + 0.125880i
\(517\) −3.22884 5.59252i −0.142004 0.245959i
\(518\) 0 0
\(519\) −6.60335 −0.289855
\(520\) −0.888388 34.5825i −0.0389584 1.51654i
\(521\) −8.26204 14.3103i −0.361967 0.626944i 0.626318 0.779568i \(-0.284561\pi\)
−0.988284 + 0.152623i \(0.951228\pi\)
\(522\) 2.00232 3.46812i 0.0876392 0.151796i
\(523\) 11.9962 0.524556 0.262278 0.964992i \(-0.415526\pi\)
0.262278 + 0.964992i \(0.415526\pi\)
\(524\) 7.67609 13.2954i 0.335332 0.580812i
\(525\) 0 0
\(526\) −3.81065 + 6.60024i −0.166152 + 0.287784i
\(527\) 8.84526 + 15.3204i 0.385305 + 0.667369i
\(528\) −0.0529314 0.0916798i −0.00230354 0.00398985i
\(529\) 8.92395 0.387998
\(530\) −27.4942 −1.19427
\(531\) 0.654173 + 1.13306i 0.0283887 + 0.0491706i
\(532\) 0 0
\(533\) −16.8887 9.18068i −0.731531 0.397660i
\(534\) 3.82913 6.63225i 0.165703 0.287005i
\(535\) −24.3026 + 42.0934i −1.05070 + 1.81986i
\(536\) 11.7781 20.4002i 0.508735 0.881155i
\(537\) 3.03388 + 5.25484i 0.130922 + 0.226763i
\(538\) −4.10536 −0.176995
\(539\) 0 0
\(540\) −8.07356 + 13.9838i −0.347431 + 0.601767i
\(541\) −18.1158 + 31.3775i −0.778860 + 1.34903i 0.153739 + 0.988112i \(0.450869\pi\)
−0.932599 + 0.360914i \(0.882465\pi\)
\(542\) −6.31658 −0.271320
\(543\) −1.98529 + 3.43862i −0.0851968 + 0.147565i
\(544\) 11.0933 0.475621
\(545\) 14.4624 0.619500
\(546\) 0 0
\(547\) −7.34857 −0.314202 −0.157101 0.987583i \(-0.550215\pi\)
−0.157101 + 0.987583i \(0.550215\pi\)
\(548\) −11.1195 −0.475000
\(549\) −1.84032 + 3.18753i −0.0785430 + 0.136040i
\(550\) 5.23069 0.223037
\(551\) −0.952888 + 1.65045i −0.0405944 + 0.0703115i
\(552\) 5.20786 9.02027i 0.221661 0.383928i
\(553\) 0 0
\(554\) −3.24816 −0.138001
\(555\) 12.0606 + 20.8896i 0.511945 + 0.886715i
\(556\) −2.68670 + 4.65350i −0.113941 + 0.197352i
\(557\) −5.41399 + 9.37731i −0.229398 + 0.397329i −0.957630 0.288002i \(-0.907009\pi\)
0.728232 + 0.685331i \(0.240342\pi\)
\(558\) −9.96160 + 17.2540i −0.421708 + 0.730420i
\(559\) −0.362466 14.1098i −0.0153307 0.596781i
\(560\) 0 0
\(561\) 0.575009 + 0.995945i 0.0242769 + 0.0420488i
\(562\) −7.27694 −0.306959
\(563\) 13.8599 0.584127 0.292064 0.956399i \(-0.405658\pi\)
0.292064 + 0.956399i \(0.405658\pi\)
\(564\) 3.03274 + 5.25285i 0.127701 + 0.221185i
\(565\) 23.6936 + 41.0386i 0.996798 + 1.72651i
\(566\) −6.49594 + 11.2513i −0.273045 + 0.472927i
\(567\) 0 0
\(568\) 4.80692 8.32583i 0.201694 0.349344i
\(569\) 27.4120 1.14917 0.574586 0.818444i \(-0.305163\pi\)
0.574586 + 0.818444i \(0.305163\pi\)
\(570\) −1.00524 + 1.74113i −0.0421049 + 0.0729279i
\(571\) 0.103879 + 0.179923i 0.00434719 + 0.00752956i 0.868191 0.496230i \(-0.165283\pi\)
−0.863844 + 0.503760i \(0.831950\pi\)
\(572\) 0.106061 + 4.12865i 0.00443462 + 0.172627i
\(573\) −0.870251 −0.0363552
\(574\) 0 0
\(575\) −19.3341 33.4876i −0.806288 1.39653i
\(576\) 5.78976 + 10.0282i 0.241240 + 0.417840i
\(577\) −1.66328 2.88089i −0.0692434 0.119933i 0.829325 0.558766i \(-0.188725\pi\)
−0.898568 + 0.438833i \(0.855392\pi\)
\(578\) 11.2764 0.469035
\(579\) −5.43043 9.40577i −0.225681 0.390891i
\(580\) −8.05959 −0.334656
\(581\) 0 0
\(582\) 0.142452 + 0.246734i 0.00590483 + 0.0102275i
\(583\) 8.42893 0.349091
\(584\) 15.1950 + 26.3185i 0.628772 + 1.08907i
\(585\) 27.1223 16.6020i 1.12137 0.686410i
\(586\) 2.52769 4.37809i 0.104418 0.180857i
\(587\) −7.54051 13.0606i −0.311230 0.539067i 0.667399 0.744701i \(-0.267408\pi\)
−0.978629 + 0.205634i \(0.934074\pi\)
\(588\) 0 0
\(589\) 4.74064 8.21104i 0.195335 0.338330i
\(590\) −0.747686 + 1.29503i −0.0307817 + 0.0533155i
\(591\) 16.9191 0.695957
\(592\) −1.88987 −0.0776732
\(593\) 12.9245 22.3859i 0.530747 0.919281i −0.468609 0.883405i \(-0.655245\pi\)
0.999356 0.0358751i \(-0.0114218\pi\)
\(594\) −1.40564 + 2.43464i −0.0576740 + 0.0998944i
\(595\) 0 0
\(596\) 3.74055 + 6.47882i 0.153219 + 0.265383i
\(597\) 8.39052 14.5328i 0.343401 0.594788i
\(598\) −14.7884 + 9.05225i −0.604743 + 0.370174i
\(599\) 17.7734 + 30.7845i 0.726203 + 1.25782i 0.958477 + 0.285170i \(0.0920501\pi\)
−0.232274 + 0.972650i \(0.574617\pi\)
\(600\) −12.6161 −0.515052
\(601\) −13.6474 23.6379i −0.556688 0.964212i −0.997770 0.0667449i \(-0.978739\pi\)
0.441082 0.897467i \(-0.354595\pi\)
\(602\) 0 0
\(603\) 21.6538 0.881810
\(604\) −10.7511 18.6215i −0.437458 0.757699i
\(605\) 35.0811 1.42625
\(606\) −1.68456 2.91775i −0.0684308 0.118526i
\(607\) −19.4629 33.7108i −0.789976 1.36828i −0.925981 0.377570i \(-0.876760\pi\)
0.136006 0.990708i \(-0.456574\pi\)
\(608\) −2.97274 5.14894i −0.120561 0.208817i
\(609\) 0 0
\(610\) −4.20679 −0.170328
\(611\) −0.665859 25.9200i −0.0269378 1.04861i
\(612\) 3.16576 + 5.48326i 0.127968 + 0.221648i
\(613\) −0.443322 + 0.767857i −0.0179056 + 0.0310135i −0.874839 0.484413i \(-0.839033\pi\)
0.856934 + 0.515427i \(0.172367\pi\)
\(614\) 18.9063 0.762997
\(615\) −6.06606 + 10.5067i −0.244607 + 0.423672i
\(616\) 0 0
\(617\) −17.3944 + 30.1280i −0.700272 + 1.21291i 0.268099 + 0.963391i \(0.413605\pi\)
−0.968371 + 0.249515i \(0.919729\pi\)
\(618\) −1.16300 2.01437i −0.0467827 0.0810300i
\(619\) 1.02781 + 1.78021i 0.0413111 + 0.0715529i 0.885942 0.463797i \(-0.153513\pi\)
−0.844631 + 0.535350i \(0.820180\pi\)
\(620\) 40.0967 1.61032
\(621\) 20.7825 0.833975
\(622\) −4.18864 7.25494i −0.167949 0.290897i
\(623\) 0 0
\(624\) −0.0109156 0.424915i −0.000436975 0.0170102i
\(625\) 6.19081 10.7228i 0.247632 0.428912i
\(626\) 8.89959 15.4145i 0.355699 0.616089i
\(627\) 0.308178 0.533780i 0.0123074 0.0213171i
\(628\) 1.23668 + 2.14199i 0.0493489 + 0.0854749i
\(629\) 20.5302 0.818593
\(630\) 0 0
\(631\) 22.6169 39.1736i 0.900363 1.55947i 0.0733401 0.997307i \(-0.476634\pi\)
0.827023 0.562168i \(-0.190033\pi\)
\(632\) 16.8555 29.1946i 0.670477 1.16130i
\(633\) 3.76665 0.149711
\(634\) −10.7924 + 18.6930i −0.428621 + 0.742393i
\(635\) −6.69355 −0.265625
\(636\) −7.91700 −0.313929
\(637\) 0 0
\(638\) −1.40321 −0.0555534
\(639\) 8.83744 0.349604
\(640\) 13.0941 22.6796i 0.517588 0.896489i
\(641\) −19.0619 −0.752902 −0.376451 0.926437i \(-0.622856\pi\)
−0.376451 + 0.926437i \(0.622856\pi\)
\(642\) 3.97420 6.88352i 0.156849 0.271671i
\(643\) −5.26755 + 9.12367i −0.207732 + 0.359802i −0.951000 0.309192i \(-0.899942\pi\)
0.743268 + 0.668994i \(0.233275\pi\)
\(644\) 0 0
\(645\) −8.90811 −0.350756
\(646\) 0.855587 + 1.48192i 0.0336626 + 0.0583053i
\(647\) −12.0804 + 20.9239i −0.474930 + 0.822603i −0.999588 0.0287105i \(-0.990860\pi\)
0.524658 + 0.851313i \(0.324193\pi\)
\(648\) −7.32699 + 12.6907i −0.287831 + 0.498538i
\(649\) 0.229219 0.397019i 0.00899762 0.0155843i
\(650\) 18.4520 + 10.0305i 0.723745 + 0.393427i
\(651\) 0 0
\(652\) −7.58714 13.1413i −0.297135 0.514654i
\(653\) −33.6890 −1.31835 −0.659176 0.751988i \(-0.729095\pi\)
−0.659176 + 0.751988i \(0.729095\pi\)
\(654\) −2.36503 −0.0924799
\(655\) 20.7098 + 35.8704i 0.809199 + 1.40157i
\(656\) −0.475268 0.823189i −0.0185561 0.0321401i
\(657\) −13.9678 + 24.1930i −0.544937 + 0.943859i
\(658\) 0 0
\(659\) 2.10030 3.63782i 0.0818159 0.141709i −0.822214 0.569178i \(-0.807261\pi\)
0.904030 + 0.427469i \(0.140595\pi\)
\(660\) 2.60659 0.101461
\(661\) 8.83631 15.3049i 0.343693 0.595293i −0.641423 0.767188i \(-0.721655\pi\)
0.985115 + 0.171894i \(0.0549888\pi\)
\(662\) 0.758708 + 1.31412i 0.0294880 + 0.0510748i
\(663\) 0.118580 + 4.61597i 0.00460525 + 0.179270i
\(664\) −4.22844 −0.164095
\(665\) 0 0
\(666\) 11.5607 + 20.0236i 0.447966 + 0.775900i
\(667\) 5.18664 + 8.98353i 0.200828 + 0.347844i
\(668\) −10.5721 18.3114i −0.409046 0.708488i
\(669\) 1.55925 0.0602839
\(670\) 12.3746 + 21.4334i 0.478071 + 0.828044i
\(671\) 1.28968 0.0497875
\(672\) 0 0
\(673\) 10.3052 + 17.8491i 0.397235 + 0.688031i 0.993384 0.114843i \(-0.0366366\pi\)
−0.596149 + 0.802874i \(0.703303\pi\)
\(674\) −8.13803 −0.313465
\(675\) −12.5865 21.8005i −0.484456 0.839102i
\(676\) −7.54302 + 14.7677i −0.290116 + 0.567990i
\(677\) −10.6537 + 18.4527i −0.409455 + 0.709196i −0.994829 0.101567i \(-0.967614\pi\)
0.585374 + 0.810763i \(0.300948\pi\)
\(678\) −3.87461 6.71102i −0.148804 0.257735i
\(679\) 0 0
\(680\) −9.29147 + 16.0933i −0.356312 + 0.617150i
\(681\) −8.69264 + 15.0561i −0.333103 + 0.576951i
\(682\) 6.98099 0.267316
\(683\) −6.69757 −0.256275 −0.128138 0.991756i \(-0.540900\pi\)
−0.128138 + 0.991756i \(0.540900\pi\)
\(684\) 1.69670 2.93877i 0.0648750 0.112367i
\(685\) 14.9999 25.9806i 0.573118 0.992670i
\(686\) 0 0
\(687\) −0.0226652 0.0392573i −0.000864732 0.00149776i
\(688\) 0.348970 0.604433i 0.0133043 0.0230438i
\(689\) 29.7342 + 16.1635i 1.13278 + 0.615779i
\(690\) 5.47161 + 9.47710i 0.208301 + 0.360787i
\(691\) 24.9263 0.948242 0.474121 0.880460i \(-0.342766\pi\)
0.474121 + 0.880460i \(0.342766\pi\)
\(692\) 6.36936 + 11.0321i 0.242127 + 0.419376i
\(693\) 0 0
\(694\) −0.539093 −0.0204637
\(695\) −7.24861 12.5550i −0.274955 0.476237i
\(696\) 3.38445 0.128287
\(697\) 5.16298 + 8.94254i 0.195562 + 0.338723i
\(698\) −13.0217 22.5543i −0.492880 0.853694i
\(699\) 4.85017 + 8.40073i 0.183450 + 0.317745i
\(700\) 0 0
\(701\) −4.94583 −0.186801 −0.0934007 0.995629i \(-0.529774\pi\)
−0.0934007 + 0.995629i \(0.529774\pi\)
\(702\) −9.62728 + 5.89303i −0.363358 + 0.222418i
\(703\) −5.50162 9.52908i −0.207497 0.359396i
\(704\) 2.02870 3.51382i 0.0764597 0.132432i
\(705\) −16.3644 −0.616319
\(706\) 0.468266 0.811061i 0.0176234 0.0305247i
\(707\) 0 0
\(708\) −0.215297 + 0.372905i −0.00809136 + 0.0140146i
\(709\) 2.32249 + 4.02267i 0.0872228 + 0.151074i 0.906336 0.422557i \(-0.138867\pi\)
−0.819113 + 0.573632i \(0.805534\pi\)
\(710\) 5.05037 + 8.74749i 0.189537 + 0.328288i
\(711\) 30.9886 1.16216
\(712\) −37.9377 −1.42178
\(713\) −25.8037 44.6933i −0.966356 1.67378i
\(714\) 0 0
\(715\) −9.78966 5.32165i −0.366113 0.199018i
\(716\) 5.85275 10.1373i 0.218728 0.378847i
\(717\) 1.10898 1.92082i 0.0414157 0.0717342i
\(718\) −4.15939 + 7.20427i −0.155227 + 0.268861i
\(719\) 15.8706 + 27.4887i 0.591875 + 1.02516i 0.993980 + 0.109564i \(0.0349453\pi\)
−0.402105 + 0.915594i \(0.631721\pi\)
\(720\) 1.57247 0.0586025
\(721\) 0 0
\(722\) −7.62714 + 13.2106i −0.283853 + 0.491647i
\(723\) 2.83658 4.91309i 0.105493 0.182720i
\(724\) 7.65975 0.284672
\(725\) 6.28237 10.8814i 0.233322 0.404125i
\(726\) −5.73681 −0.212913
\(727\) −47.8755 −1.77560 −0.887801 0.460227i \(-0.847768\pi\)
−0.887801 + 0.460227i \(0.847768\pi\)
\(728\) 0 0
\(729\) −6.17412 −0.228671
\(730\) −31.9290 −1.18175
\(731\) −3.79096 + 6.56613i −0.140214 + 0.242857i
\(732\) −1.21135 −0.0447728
\(733\) −3.80104 + 6.58359i −0.140395 + 0.243171i −0.927645 0.373463i \(-0.878170\pi\)
0.787251 + 0.616633i \(0.211504\pi\)
\(734\) 4.74386 8.21660i 0.175099 0.303280i
\(735\) 0 0
\(736\) −32.3618 −1.19287
\(737\) −3.79368 6.57086i −0.139742 0.242041i
\(738\) −5.81459 + 10.0712i −0.214038 + 0.370725i
\(739\) 16.7118 28.9457i 0.614754 1.06479i −0.375673 0.926752i \(-0.622589\pi\)
0.990428 0.138033i \(-0.0440781\pi\)
\(740\) 23.2665 40.2988i 0.855294 1.48141i
\(741\) 2.11072 1.29201i 0.0775394 0.0474632i
\(742\) 0 0
\(743\) 1.46912 + 2.54458i 0.0538966 + 0.0933517i 0.891715 0.452597i \(-0.149503\pi\)
−0.837818 + 0.545949i \(0.816169\pi\)
\(744\) −16.8378 −0.617302
\(745\) −20.1837 −0.739474
\(746\) −13.0776 22.6511i −0.478805 0.829314i
\(747\) −1.94348 3.36620i −0.0711081 0.123163i
\(748\) 1.10927 1.92131i 0.0405588 0.0702499i
\(749\) 0 0
\(750\) 1.78552 3.09261i 0.0651980 0.112926i
\(751\) 1.19678 0.0436711 0.0218355 0.999762i \(-0.493049\pi\)
0.0218355 + 0.999762i \(0.493049\pi\)
\(752\) 0.641065 1.11036i 0.0233773 0.0404906i
\(753\) −7.11313 12.3203i −0.259217 0.448977i
\(754\) −4.94999 2.69081i −0.180268 0.0979936i
\(755\) 58.0123 2.11128
\(756\) 0 0
\(757\) −5.77321 9.99950i −0.209831 0.363438i 0.741830 0.670588i \(-0.233958\pi\)
−0.951661 + 0.307150i \(0.900625\pi\)
\(758\) 9.64207 + 16.7006i 0.350216 + 0.606592i
\(759\) −1.67744 2.90541i −0.0608871 0.105460i
\(760\) 9.95959 0.361272
\(761\) 17.3249 + 30.0075i 0.628026 + 1.08777i 0.987947 + 0.154790i \(0.0494702\pi\)
−0.359921 + 0.932983i \(0.617197\pi\)
\(762\) 1.09459 0.0396530
\(763\) 0 0
\(764\) 0.839413 + 1.45391i 0.0303689 + 0.0526005i
\(765\) −17.0822 −0.617608
\(766\) 0.250768 + 0.434344i 0.00906063 + 0.0156935i
\(767\) 1.56993 0.960982i 0.0566869 0.0346990i
\(768\) −5.12890 + 8.88351i −0.185073 + 0.320556i
\(769\) −3.27437 5.67138i −0.118077 0.204515i 0.800929 0.598760i \(-0.204340\pi\)
−0.919006 + 0.394245i \(0.871006\pi\)
\(770\) 0 0
\(771\) −1.63253 + 2.82763i −0.0587943 + 0.101835i
\(772\) −10.4760 + 18.1450i −0.377039 + 0.653051i
\(773\) −33.9275 −1.22029 −0.610143 0.792291i \(-0.708888\pi\)
−0.610143 + 0.792291i \(0.708888\pi\)
\(774\) −8.53882 −0.306922
\(775\) −31.2550 + 54.1352i −1.12271 + 1.94459i
\(776\) 0.705683 1.22228i 0.0253325 0.0438772i
\(777\) 0 0
\(778\) 2.42547 + 4.20104i 0.0869575 + 0.150615i
\(779\) 2.76711 4.79278i 0.0991422 0.171719i
\(780\) 9.19508 + 4.99844i 0.329237 + 0.178973i
\(781\) −1.54830 2.68173i −0.0554024 0.0959598i
\(782\) 9.31405 0.333070
\(783\) 3.37651 + 5