Properties

Label 637.2.h.l.165.3
Level $637$
Weight $2$
Character 637.165
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 165.3
Root \(0.756174 - 1.30973i\) of defining polynomial
Character \(\chi\) \(=\) 637.165
Dual form 637.2.h.l.471.3

$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 0.945542 0.325501i \(-0.105533\pi\)
−0.754663 + 0.656113i \(0.772200\pi\)
\(4\) −1.27559 −0.637793
\(5\) 1.72074 + 2.98041i 0.769538 + 1.33288i 0.937814 + 0.347139i \(0.112847\pi\)
−0.168276 + 0.985740i \(0.553820\pi\)
\(6\) −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 0.925741 0.378158i \(-0.123442\pi\)
−0.790365 + 0.612637i \(0.790109\pi\)
\(12\) −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 −0.800329 0.599562i \(-0.795342\pi\)
0.919400 + 0.393324i \(0.128675\pi\)
\(20\) −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 −0.768119 0.640307i \(-0.778807\pi\)
0.938582 + 0.345057i \(0.112140\pi\)
\(30\) 0.968404 1.67733i 0.176806 0.306236i
\(31\) −4.56692 + 7.91014i −0.820244 + 1.42070i 0.0852573 + 0.996359i \(0.472829\pi\)
−0.905501 + 0.424345i \(0.860505\pi\)
\(32\) −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 −0.995565 0.0940715i \(-0.970012\pi\)
0.579251 + 0.815149i \(0.303345\pi\)
\(42\) 0 0
\(43\) 1.95732 + 3.39018i 0.298489 + 0.516998i 0.975790 0.218708i \(-0.0701841\pi\)
−0.677302 + 0.735706i \(0.736851\pi\)
\(44\) −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 0.999594 + 0.0285004i \(0.00907317\pi\)
−0.475115 + 0.879924i \(0.657593\pi\)
\(48\) 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 −0.339712 0.940529i \(-0.610330\pi\)
0.984378 0.176065i \(-0.0563370\pi\)
\(54\) −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 −0.816386 0.577507i \(-0.804026\pi\)
0.908328 + 0.418258i \(0.137359\pi\)
\(62\) 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 0.999825 + 0.0187197i \(0.00595900\pi\)
−0.483701 + 0.875233i \(0.660708\pi\)
\(68\) 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 0.950013 0.312211i \(-0.101070\pi\)
−0.745389 + 0.666629i \(0.767736\pi\)
\(72\) 3.57244 6.18764i 0.421016 0.729221i
\(73\) 5.45026 9.44013i 0.637905 1.10488i −0.347987 0.937499i \(-0.613135\pi\)
0.985892 0.167384i \(-0.0535320\pi\)
\(74\) 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 0.974915 + 0.222578i \(0.0714472\pi\)
−0.294699 + 0.955590i \(0.595219\pi\)
\(80\) 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 0.878590 0.477578i \(-0.158485\pi\)
−0.852889 + 0.522092i \(0.825152\pi\)
\(98\) 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 0.677800 0.735246i \(-0.262933\pi\)
−0.975642 + 0.219369i \(0.929600\pi\)
\(102\) 0.545002 + 0.943972i 0.0539633 + 0.0934671i
\(103\) −2.06651 3.57930i −0.203619 0.352679i 0.746073 0.665865i \(-0.231937\pi\)
−0.949692 + 0.313186i \(0.898604\pi\)
\(104\) 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 −0.747677 0.664063i \(-0.768831\pi\)
0.948934 + 0.315475i \(0.102164\pi\)
\(110\) 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 −0.983680 0.179926i \(-0.942414\pi\)
0.336020 0.941855i \(-0.390919\pi\)
\(114\) −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 −0.905942 0.423402i \(-0.860836\pi\)
0.819648 + 0.572868i \(0.194169\pi\)
\(128\) 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 −0.999549 0.0300158i \(-0.990444\pi\)
0.473780 0.880643i \(-0.342889\pi\)
\(132\) 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 0.941418 0.337241i \(-0.109494\pi\)
−0.762769 + 0.646672i \(0.776160\pi\)
\(140\) 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 −0.960781 0.277310i \(-0.910557\pi\)
0.720548 + 0.693406i \(0.243891\pi\)
\(150\) 3.85157 0.314479
\(151\) 8.42840 14.5984i 0.685893 1.18800i −0.287262 0.957852i \(-0.592745\pi\)
0.973155 0.230150i \(-0.0739216\pi\)
\(152\) 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 −0.902116 0.431493i \(-0.857987\pi\)
0.824742 + 0.565509i \(0.191320\pi\)
\(158\) −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 −0.533360 0.845888i \(-0.679071\pi\)
0.999241 + 0.0389590i \(0.0124042\pi\)
\(164\) 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 −0.343787 0.939048i \(-0.611710\pi\)
0.985133 0.171796i \(-0.0549569\pi\)
\(168\) 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 −0.991009 0.133798i \(-0.957283\pi\)
0.611377 + 0.791340i \(0.290616\pi\)
\(174\) −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 0.642033 0.766677i \(-0.278091\pi\)
−0.984978 + 0.172679i \(0.944758\pi\)
\(180\) −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 −0.888851 0.458197i \(-0.848496\pi\)
0.841235 + 0.540669i \(0.181829\pi\)
\(192\) 1.49382 + 2.58736i 0.107807 + 0.186727i
\(193\) 8.21270 + 14.2248i 0.591163 + 1.02392i 0.994076 + 0.108686i \(0.0346643\pi\)
−0.402913 + 0.915238i \(0.632002\pi\)
\(194\) −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 0.0995951 0.995028i \(-0.468245\pi\)
0.811922 0.583766i \(-0.198421\pi\)
\(198\) −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 −0.751173 0.660105i \(-0.770512\pi\)
0.947254 + 0.320483i \(0.103845\pi\)
\(212\) −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 −0.823844 0.566817i \(-0.808175\pi\)
0.902800 + 0.430061i \(0.141508\pi\)
\(224\) 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 0.867156 0.498037i \(-0.165946\pi\)
−0.864891 + 0.501960i \(0.832612\pi\)
\(230\) −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 0.519210 0.854647i \(-0.326226\pi\)
−0.999751 + 0.0223253i \(0.992893\pi\)
\(234\) −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 0.975280 + 0.220975i \(0.0709238\pi\)
−0.296270 + 0.955104i \(0.595743\pi\)
\(252\) 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 0.970406 0.241480i \(-0.0776327\pi\)
−0.694330 + 0.719656i \(0.744299\pi\)
\(264\) −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 0.998612 0.0526775i \(-0.0167755\pi\)
−0.544926 + 0.838484i \(0.683442\pi\)
\(284\) −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 0.766142 0.642671i \(-0.222174\pi\)
−0.939641 + 0.342163i \(0.888841\pi\)
\(294\) 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 −0.692091 0.721811i \(-0.743310\pi\)
0.971152 + 0.238463i \(0.0766435\pi\)
\(312\) −0.170689 + 6.64445i −0.00966337 + 0.376168i
\(313\) −10.4563 18.1108i −0.591023 1.02368i −0.994095 0.108513i \(-0.965391\pi\)
0.403072 0.915168i \(-0.367942\pi\)
\(314\) 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 0.964034 + 0.265778i \(0.0856288\pi\)
−0.251847 + 0.967767i \(0.581038\pi\)
\(318\) −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 −0.889484 0.456967i \(-0.848936\pi\)
0.840487 + 0.541832i \(0.182269\pi\)
\(332\) 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 −0.0874885 0.996166i \(-0.527884\pi\)
0.906449 0.422315i \(-0.138783\pi\)
\(350\) 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 0.851013 0.525145i \(-0.175989\pi\)
−0.880295 + 0.474426i \(0.842656\pi\)
\(354\) −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 0.965685 0.259716i \(-0.0836288\pi\)
−0.707763 + 0.706450i \(0.750295\pi\)
\(360\) 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 0.683092 0.730333i \(-0.260635\pi\)
−0.974033 + 0.226408i \(0.927302\pi\)
\(368\) 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 −0.126902 0.991915i \(-0.540504\pi\)
0.922475 0.386057i \(-0.126163\pi\)
\(374\) 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 0.413341 + 0.910576i \(0.364362\pi\)
−0.995253 + 0.0973246i \(0.968972\pi\)
\(380\) −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 −0.873455 0.486905i \(-0.838126\pi\)
0.858400 + 0.512981i \(0.171459\pi\)
\(384\) 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 −0.929181 0.369624i \(-0.879486\pi\)
0.784695 + 0.619883i \(0.212820\pi\)
\(390\) 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 0.344682 + 0.938720i \(0.387987\pi\)
−0.985296 + 0.170857i \(0.945346\pi\)
\(398\) −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 −0.648853 0.760914i \(-0.724751\pi\)
0.983397 + 0.181466i \(0.0580844\pi\)
\(420\) 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 −0.999071 0.0430997i \(-0.986277\pi\)
0.462210 0.886771i \(-0.347057\pi\)
\(432\) 0.655791 0.0315518
\(433\) −12.9481 22.4268i −0.622247 1.07776i −0.989066 0.147472i \(-0.952886\pi\)
0.366819 0.930292i \(-0.380447\pi\)
\(434\) 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 −0.926641 0.375947i \(-0.877317\pi\)
0.137741 0.990468i \(-0.456016\pi\)
\(444\) 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 0.534651 0.845073i \(-0.320443\pi\)
−0.999180 + 0.0404845i \(0.987110\pi\)
\(450\) −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 −0.936209 0.351445i \(-0.885691\pi\)
0.163744 0.986503i \(-0.447643\pi\)
\(462\) 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 −0.973433 0.228973i \(-0.926463\pi\)
0.288420 0.957504i \(-0.406870\pi\)
\(468\) −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 0.980881 0.194606i \(-0.0623429\pi\)
−0.658975 + 0.752165i \(0.729010\pi\)
\(480\) 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 −0.999919 0.0127081i \(-0.995955\pi\)
0.510965 + 0.859601i \(0.329288\pi\)
\(492\) 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 0.999683 + 0.0251622i \(0.00801023\pi\)
−0.478051 + 0.878332i \(0.658656\pi\)
\(500\) 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 −0.668506 0.743707i \(-0.733066\pi\)
−0.309816 0.950796i \(-0.600268\pi\)
\(504\) 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 −0.988284 0.152623i \(-0.951228\pi\)
0.626318 + 0.779568i \(0.284561\pi\)
\(522\) 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 −0.932599 0.360914i \(-0.882465\pi\)
0.153739 0.988112i \(-0.450869\pi\)
\(542\) −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 0.728232 0.685331i \(-0.240342\pi\)
−0.957630 + 0.288002i \(0.907009\pi\)
\(558\) −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 −0.863844 0.503760i \(-0.831950\pi\)
0.868191 + 0.496230i \(0.165283\pi\)
\(572\) 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 −0.898568 0.438833i \(-0.855392\pi\)
0.829325 + 0.558766i \(0.188725\pi\)
\(578\) 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 −0.978629 0.205634i \(-0.934074\pi\)
0.667399 + 0.744701i \(0.267408\pi\)
\(588\) 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 0.999356 + 0.0358751i \(0.0114218\pi\)
−0.468609 + 0.883405i \(0.655245\pi\)
\(594\) −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 −0.232274 0.972650i \(-0.574617\pi\)
0.958477 0.285170i \(-0.0920501\pi\)
\(600\) −12.6161 −0.515052
\(601\) −13.6474 + 23.6379i −0.556688 + 0.964212i 0.441082 + 0.897467i \(0.354595\pi\)
−0.997770 + 0.0667449i \(0.978739\pi\)
\(602\) 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 0.136006 + 0.990708i \(0.456574\pi\)
−0.925981 + 0.377570i \(0.876760\pi\)
\(608\) −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 0.856934 0.515427i \(-0.172367\pi\)
−0.874839 + 0.484413i \(0.839033\pi\)
\(614\) 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 −0.968371 0.249515i \(-0.919729\pi\)
0.268099 0.963391i \(-0.413605\pi\)
\(618\) −1.16300 + 2.01437i −0.0467827 + 0.0810300i
\(619\) 1.02781 1.78021i 0.0413111 0.0715529i −0.844631 0.535350i \(-0.820180\pi\)
0.885942 + 0.463797i \(0.153513\pi\)
\(620\) 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 0.827023 + 0.562168i \(0.190033\pi\)
0.0733401 + 0.997307i \(0.476634\pi\)
\(632\) 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 0.743268 0.668994i \(-0.233275\pi\)
−0.951000 + 0.309192i \(0.899942\pi\)
\(644\) 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 0.524658 0.851313i \(-0.324193\pi\)
−0.999588 + 0.0287105i \(0.990860\pi\)
\(648\) −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 0.904030 0.427469i \(-0.140595\pi\)
−0.822214 + 0.569178i \(0.807261\pi\)
\(660\) 2.60659 0.101461
\(661\) 8.83631 + 15.3049i 0.343693 + 0.595293i 0.985115 0.171894i \(-0.0549888\pi\)
−0.641423 + 0.767188i \(0.721655\pi\)
\(662\) 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 −0.596149 0.802874i \(-0.703303\pi\)
0.993384 + 0.114843i \(0.0366366\pi\)
\(674\) −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 0.585374 0.810763i \(-0.300948\pi\)
−0.994829 + 0.101567i \(0.967614\pi\)
\(678\) −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 −0.819113 0.573632i \(-0.805534\pi\)
0.906336 + 0.422557i \(0.138867\pi\)
\(710\) 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 −0.402105 0.915594i \(-0.631721\pi\)
0.993980 0.109564i \(-0.0349453\pi\)
\(720\) 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 0.787251 0.616633i \(-0.211504\pi\)
−0.927645 + 0.373463i \(0.878170\pi\)
\(734\) 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 0.990428 + 0.138033i \(0.0440781\pi\)
−0.375673 + 0.926752i \(0.622589\pi\)
\(740\) 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 −0.837818 0.545949i \(-0.816169\pi\)
0.891715 + 0.452597i \(0.149503\pi\)
\(744\) −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 −0.951661 0.307150i \(-0.900625\pi\)
0.741830 + 0.670588i \(0.233958\pi\)
\(758\) 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 −0.359921 0.932983i \(-0.617197\pi\)
0.987947 0.154790i \(-0.0494702\pi\)
\(762\) 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 −0.919006 0.394245i \(-0.871006\pi\)
0.800929 + 0.598760i \(0.204340\pi\)
\(770\) 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