Properties

Label 637.2.h.g.471.1
Level $637$
Weight $2$
Character 637.471
Analytic conductor $5.086$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
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 471.1
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.g.165.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.381966 q^{2} +(0.190983 - 0.330792i) q^{3} -1.85410 q^{4} +(-0.190983 + 0.330792i) q^{5} +(0.0729490 - 0.126351i) q^{6} -1.47214 q^{8} +(1.42705 + 2.47172i) q^{9} +O(q^{10})\) \(q+0.381966 q^{2} +(0.190983 - 0.330792i) q^{3} -1.85410 q^{4} +(-0.190983 + 0.330792i) q^{5} +(0.0729490 - 0.126351i) q^{6} -1.47214 q^{8} +(1.42705 + 2.47172i) q^{9} +(-0.0729490 + 0.126351i) q^{10} +(2.42705 - 4.20378i) q^{11} +(-0.354102 + 0.613323i) q^{12} +(-2.50000 - 2.59808i) q^{13} +(0.0729490 + 0.126351i) q^{15} +3.14590 q^{16} +7.47214 q^{17} +(0.545085 + 0.944115i) q^{18} +(-2.42705 - 4.20378i) q^{19} +(0.354102 - 0.613323i) q^{20} +(0.927051 - 1.60570i) q^{22} +4.47214 q^{23} +(-0.281153 + 0.486971i) q^{24} +(2.42705 + 4.20378i) q^{25} +(-0.954915 - 0.992377i) q^{26} +2.23607 q^{27} +(2.04508 + 3.54219i) q^{29} +(0.0278640 + 0.0482619i) q^{30} +(-4.35410 - 7.54153i) q^{31} +4.14590 q^{32} +(-0.927051 - 1.60570i) q^{33} +2.85410 q^{34} +(-2.64590 - 4.58283i) q^{36} +4.00000 q^{37} +(-0.927051 - 1.60570i) q^{38} +(-1.33688 + 0.330792i) q^{39} +(0.281153 - 0.486971i) q^{40} +(-2.61803 - 4.53457i) q^{41} +(3.78115 - 6.54915i) q^{43} +(-4.50000 + 7.79423i) q^{44} -1.09017 q^{45} +1.70820 q^{46} +(-1.11803 + 1.93649i) q^{47} +(0.600813 - 1.04064i) q^{48} +(0.927051 + 1.60570i) q^{50} +(1.42705 - 2.47172i) q^{51} +(4.63525 + 4.81710i) q^{52} +(-4.11803 - 7.13264i) q^{53} +0.854102 q^{54} +(0.927051 + 1.60570i) q^{55} -1.85410 q^{57} +(0.781153 + 1.35300i) q^{58} +2.23607 q^{59} +(-0.135255 - 0.234268i) q^{60} +(3.00000 + 5.19615i) q^{61} +(-1.66312 - 2.88061i) q^{62} -4.70820 q^{64} +(1.33688 - 0.330792i) q^{65} +(-0.354102 - 0.613323i) q^{66} +(-0.354102 + 0.613323i) q^{67} -13.8541 q^{68} +(0.854102 - 1.47935i) q^{69} +(-4.09017 + 7.08438i) q^{71} +(-2.10081 - 3.63871i) q^{72} +(1.00000 + 1.73205i) q^{73} +1.52786 q^{74} +1.85410 q^{75} +(4.50000 + 7.79423i) q^{76} +(-0.510643 + 0.126351i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(-0.600813 + 1.04064i) q^{80} +(-3.85410 + 6.67550i) q^{81} +(-1.00000 - 1.73205i) q^{82} -6.70820 q^{83} +(-1.42705 + 2.47172i) q^{85} +(1.44427 - 2.50155i) q^{86} +1.56231 q^{87} +(-3.57295 + 6.18853i) q^{88} +16.0902 q^{89} -0.416408 q^{90} -8.29180 q^{92} -3.32624 q^{93} +(-0.427051 + 0.739674i) q^{94} +1.85410 q^{95} +(0.791796 - 1.37143i) q^{96} +(-6.07295 + 10.5187i) q^{97} +13.8541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{2} + 3q^{3} + 6q^{4} - 3q^{5} + 7q^{6} + 12q^{8} - q^{9} + O(q^{10}) \) \( 4q + 6q^{2} + 3q^{3} + 6q^{4} - 3q^{5} + 7q^{6} + 12q^{8} - q^{9} - 7q^{10} + 3q^{11} + 12q^{12} - 10q^{13} + 7q^{15} + 26q^{16} + 12q^{17} - 9q^{18} - 3q^{19} - 12q^{20} - 3q^{22} + 19q^{24} + 3q^{25} - 15q^{26} - 3q^{29} + 18q^{30} - 4q^{31} + 30q^{32} + 3q^{33} - 2q^{34} - 24q^{36} + 16q^{37} + 3q^{38} - 21q^{39} - 19q^{40} - 6q^{41} - 5q^{43} - 18q^{44} + 18q^{45} - 20q^{46} + 27q^{48} - 3q^{50} - q^{51} - 15q^{52} - 12q^{53} - 10q^{54} - 3q^{55} + 6q^{57} - 17q^{58} + 33q^{60} + 12q^{61} + 9q^{62} + 8q^{64} + 21q^{65} + 12q^{66} + 12q^{67} - 42q^{68} - 10q^{69} + 6q^{71} - 33q^{72} + 4q^{73} + 24q^{74} - 6q^{75} + 18q^{76} - 49q^{78} - 8q^{79} - 27q^{80} - 2q^{81} - 4q^{82} + q^{85} - 30q^{86} - 34q^{87} - 21q^{88} + 42q^{89} + 52q^{90} - 60q^{92} + 18q^{93} + 5q^{94} - 6q^{95} + 30q^{96} - 31q^{97} + 42q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.381966 0.270091 0.135045 0.990839i \(-0.456882\pi\)
0.135045 + 0.990839i \(0.456882\pi\)
\(3\) 0.190983 0.330792i 0.110264 0.190983i −0.805613 0.592443i \(-0.798164\pi\)
0.915877 + 0.401460i \(0.131497\pi\)
\(4\) −1.85410 −0.927051
\(5\) −0.190983 + 0.330792i −0.0854102 + 0.147935i −0.905566 0.424206i \(-0.860553\pi\)
0.820156 + 0.572140i \(0.193887\pi\)
\(6\) 0.0729490 0.126351i 0.0297813 0.0515827i
\(7\) 0 0
\(8\) −1.47214 −0.520479
\(9\) 1.42705 + 2.47172i 0.475684 + 0.823908i
\(10\) −0.0729490 + 0.126351i −0.0230685 + 0.0399558i
\(11\) 2.42705 4.20378i 0.731783 1.26749i −0.224337 0.974512i \(-0.572022\pi\)
0.956120 0.292974i \(-0.0946451\pi\)
\(12\) −0.354102 + 0.613323i −0.102220 + 0.177051i
\(13\) −2.50000 2.59808i −0.693375 0.720577i
\(14\) 0 0
\(15\) 0.0729490 + 0.126351i 0.0188354 + 0.0326238i
\(16\) 3.14590 0.786475
\(17\) 7.47214 1.81226 0.906130 0.423000i \(-0.139023\pi\)
0.906130 + 0.423000i \(0.139023\pi\)
\(18\) 0.545085 + 0.944115i 0.128478 + 0.222530i
\(19\) −2.42705 4.20378i −0.556804 0.964412i −0.997761 0.0668841i \(-0.978694\pi\)
0.440957 0.897528i \(-0.354639\pi\)
\(20\) 0.354102 0.613323i 0.0791796 0.137143i
\(21\) 0 0
\(22\) 0.927051 1.60570i 0.197648 0.342336i
\(23\) 4.47214 0.932505 0.466252 0.884652i \(-0.345604\pi\)
0.466252 + 0.884652i \(0.345604\pi\)
\(24\) −0.281153 + 0.486971i −0.0573901 + 0.0994026i
\(25\) 2.42705 + 4.20378i 0.485410 + 0.840755i
\(26\) −0.954915 0.992377i −0.187274 0.194621i
\(27\) 2.23607 0.430331
\(28\) 0 0
\(29\) 2.04508 + 3.54219i 0.379763 + 0.657768i 0.991028 0.133658i \(-0.0426723\pi\)
−0.611265 + 0.791426i \(0.709339\pi\)
\(30\) 0.0278640 + 0.0482619i 0.00508726 + 0.00881138i
\(31\) −4.35410 7.54153i −0.782020 1.35450i −0.930763 0.365622i \(-0.880856\pi\)
0.148744 0.988876i \(-0.452477\pi\)
\(32\) 4.14590 0.732898
\(33\) −0.927051 1.60570i −0.161379 0.279516i
\(34\) 2.85410 0.489474
\(35\) 0 0
\(36\) −2.64590 4.58283i −0.440983 0.763805i
\(37\) 4.00000 0.657596 0.328798 0.944400i \(-0.393356\pi\)
0.328798 + 0.944400i \(0.393356\pi\)
\(38\) −0.927051 1.60570i −0.150388 0.260479i
\(39\) −1.33688 + 0.330792i −0.214072 + 0.0529692i
\(40\) 0.281153 0.486971i 0.0444542 0.0769969i
\(41\) −2.61803 4.53457i −0.408868 0.708181i 0.585895 0.810387i \(-0.300743\pi\)
−0.994763 + 0.102206i \(0.967410\pi\)
\(42\) 0 0
\(43\) 3.78115 6.54915i 0.576620 0.998736i −0.419243 0.907874i \(-0.637704\pi\)
0.995864 0.0908618i \(-0.0289622\pi\)
\(44\) −4.50000 + 7.79423i −0.678401 + 1.17502i
\(45\) −1.09017 −0.162513
\(46\) 1.70820 0.251861
\(47\) −1.11803 + 1.93649i −0.163082 + 0.282466i −0.935973 0.352073i \(-0.885477\pi\)
0.772890 + 0.634539i \(0.218810\pi\)
\(48\) 0.600813 1.04064i 0.0867199 0.150203i
\(49\) 0 0
\(50\) 0.927051 + 1.60570i 0.131105 + 0.227080i
\(51\) 1.42705 2.47172i 0.199827 0.346111i
\(52\) 4.63525 + 4.81710i 0.642794 + 0.668011i
\(53\) −4.11803 7.13264i −0.565655 0.979744i −0.996988 0.0775512i \(-0.975290\pi\)
0.431333 0.902193i \(-0.358043\pi\)
\(54\) 0.854102 0.116229
\(55\) 0.927051 + 1.60570i 0.125004 + 0.216512i
\(56\) 0 0
\(57\) −1.85410 −0.245582
\(58\) 0.781153 + 1.35300i 0.102570 + 0.177657i
\(59\) 2.23607 0.291111 0.145556 0.989350i \(-0.453503\pi\)
0.145556 + 0.989350i \(0.453503\pi\)
\(60\) −0.135255 0.234268i −0.0174613 0.0302439i
\(61\) 3.00000 + 5.19615i 0.384111 + 0.665299i 0.991645 0.128994i \(-0.0411748\pi\)
−0.607535 + 0.794293i \(0.707841\pi\)
\(62\) −1.66312 2.88061i −0.211216 0.365837i
\(63\) 0 0
\(64\) −4.70820 −0.588525
\(65\) 1.33688 0.330792i 0.165820 0.0410297i
\(66\) −0.354102 0.613323i −0.0435869 0.0754948i
\(67\) −0.354102 + 0.613323i −0.0432604 + 0.0749293i −0.886845 0.462067i \(-0.847108\pi\)
0.843584 + 0.536997i \(0.180441\pi\)
\(68\) −13.8541 −1.68006
\(69\) 0.854102 1.47935i 0.102822 0.178093i
\(70\) 0 0
\(71\) −4.09017 + 7.08438i −0.485414 + 0.840761i −0.999860 0.0167615i \(-0.994664\pi\)
0.514446 + 0.857523i \(0.327998\pi\)
\(72\) −2.10081 3.63871i −0.247583 0.428827i
\(73\) 1.00000 + 1.73205i 0.117041 + 0.202721i 0.918594 0.395203i \(-0.129326\pi\)
−0.801553 + 0.597924i \(0.795992\pi\)
\(74\) 1.52786 0.177611
\(75\) 1.85410 0.214093
\(76\) 4.50000 + 7.79423i 0.516185 + 0.894059i
\(77\) 0 0
\(78\) −0.510643 + 0.126351i −0.0578189 + 0.0143065i
\(79\) −2.00000 + 3.46410i −0.225018 + 0.389742i −0.956325 0.292306i \(-0.905577\pi\)
0.731307 + 0.682048i \(0.238911\pi\)
\(80\) −0.600813 + 1.04064i −0.0671729 + 0.116347i
\(81\) −3.85410 + 6.67550i −0.428234 + 0.741722i
\(82\) −1.00000 1.73205i −0.110432 0.191273i
\(83\) −6.70820 −0.736321 −0.368161 0.929762i \(-0.620012\pi\)
−0.368161 + 0.929762i \(0.620012\pi\)
\(84\) 0 0
\(85\) −1.42705 + 2.47172i −0.154785 + 0.268096i
\(86\) 1.44427 2.50155i 0.155740 0.269749i
\(87\) 1.56231 0.167497
\(88\) −3.57295 + 6.18853i −0.380878 + 0.659699i
\(89\) 16.0902 1.70555 0.852777 0.522275i \(-0.174916\pi\)
0.852777 + 0.522275i \(0.174916\pi\)
\(90\) −0.416408 −0.0438932
\(91\) 0 0
\(92\) −8.29180 −0.864479
\(93\) −3.32624 −0.344915
\(94\) −0.427051 + 0.739674i −0.0440469 + 0.0762915i
\(95\) 1.85410 0.190227
\(96\) 0.791796 1.37143i 0.0808123 0.139971i
\(97\) −6.07295 + 10.5187i −0.616615 + 1.06801i 0.373484 + 0.927636i \(0.378163\pi\)
−0.990099 + 0.140371i \(0.955170\pi\)
\(98\) 0 0
\(99\) 13.8541 1.39239
\(100\) −4.50000 7.79423i −0.450000 0.779423i
\(101\) −4.28115 + 7.41517i −0.425991 + 0.737837i −0.996512 0.0834451i \(-0.973408\pi\)
0.570522 + 0.821283i \(0.306741\pi\)
\(102\) 0.545085 0.944115i 0.0539715 0.0934813i
\(103\) −2.35410 + 4.07742i −0.231957 + 0.401761i −0.958384 0.285483i \(-0.907846\pi\)
0.726427 + 0.687243i \(0.241179\pi\)
\(104\) 3.68034 + 3.82472i 0.360887 + 0.375045i
\(105\) 0 0
\(106\) −1.57295 2.72443i −0.152778 0.264620i
\(107\) −5.61803 −0.543116 −0.271558 0.962422i \(-0.587539\pi\)
−0.271558 + 0.962422i \(0.587539\pi\)
\(108\) −4.14590 −0.398939
\(109\) −5.35410 9.27358i −0.512830 0.888248i −0.999889 0.0148787i \(-0.995264\pi\)
0.487059 0.873369i \(-0.338070\pi\)
\(110\) 0.354102 + 0.613323i 0.0337623 + 0.0584780i
\(111\) 0.763932 1.32317i 0.0725092 0.125590i
\(112\) 0 0
\(113\) 3.73607 6.47106i 0.351460 0.608746i −0.635046 0.772475i \(-0.719019\pi\)
0.986505 + 0.163728i \(0.0523521\pi\)
\(114\) −0.708204 −0.0663294
\(115\) −0.854102 + 1.47935i −0.0796454 + 0.137950i
\(116\) −3.79180 6.56758i −0.352059 0.609785i
\(117\) 2.85410 9.88690i 0.263862 0.914044i
\(118\) 0.854102 0.0786265
\(119\) 0 0
\(120\) −0.107391 0.186006i −0.00980340 0.0169800i
\(121\) −6.28115 10.8793i −0.571014 0.989025i
\(122\) 1.14590 + 1.98475i 0.103745 + 0.179691i
\(123\) −2.00000 −0.180334
\(124\) 8.07295 + 13.9828i 0.724972 + 1.25569i
\(125\) −3.76393 −0.336656
\(126\) 0 0
\(127\) 7.07295 + 12.2507i 0.627623 + 1.08707i 0.988027 + 0.154278i \(0.0493053\pi\)
−0.360405 + 0.932796i \(0.617361\pi\)
\(128\) −10.0902 −0.891853
\(129\) −1.44427 2.50155i −0.127161 0.220249i
\(130\) 0.510643 0.126351i 0.0447864 0.0110818i
\(131\) −0.163119 + 0.282530i −0.0142518 + 0.0246848i −0.873063 0.487607i \(-0.837870\pi\)
0.858812 + 0.512292i \(0.171203\pi\)
\(132\) 1.71885 + 2.97713i 0.149606 + 0.259126i
\(133\) 0 0
\(134\) −0.135255 + 0.234268i −0.0116842 + 0.0202377i
\(135\) −0.427051 + 0.739674i −0.0367547 + 0.0636610i
\(136\) −11.0000 −0.943242
\(137\) −0.381966 −0.0326336 −0.0163168 0.999867i \(-0.505194\pi\)
−0.0163168 + 0.999867i \(0.505194\pi\)
\(138\) 0.326238 0.565061i 0.0277712 0.0481012i
\(139\) 7.78115 13.4774i 0.659989 1.14313i −0.320629 0.947205i \(-0.603894\pi\)
0.980618 0.195929i \(-0.0627723\pi\)
\(140\) 0 0
\(141\) 0.427051 + 0.739674i 0.0359642 + 0.0622918i
\(142\) −1.56231 + 2.70599i −0.131106 + 0.227082i
\(143\) −16.9894 + 4.20378i −1.42072 + 0.351537i
\(144\) 4.48936 + 7.77579i 0.374113 + 0.647983i
\(145\) −1.56231 −0.129742
\(146\) 0.381966 + 0.661585i 0.0316117 + 0.0547531i
\(147\) 0 0
\(148\) −7.41641 −0.609625
\(149\) 2.42705 + 4.20378i 0.198832 + 0.344387i 0.948150 0.317823i \(-0.102952\pi\)
−0.749318 + 0.662210i \(0.769619\pi\)
\(150\) 0.708204 0.0578246
\(151\) 7.35410 + 12.7377i 0.598468 + 1.03658i 0.993047 + 0.117716i \(0.0375571\pi\)
−0.394579 + 0.918862i \(0.629110\pi\)
\(152\) 3.57295 + 6.18853i 0.289804 + 0.501956i
\(153\) 10.6631 + 18.4691i 0.862062 + 1.49314i
\(154\) 0 0
\(155\) 3.32624 0.267170
\(156\) 2.47871 0.613323i 0.198456 0.0491051i
\(157\) −4.07295 7.05455i −0.325057 0.563015i 0.656467 0.754355i \(-0.272050\pi\)
−0.981524 + 0.191340i \(0.938717\pi\)
\(158\) −0.763932 + 1.32317i −0.0607752 + 0.105266i
\(159\) −3.14590 −0.249486
\(160\) −0.791796 + 1.37143i −0.0625970 + 0.108421i
\(161\) 0 0
\(162\) −1.47214 + 2.54981i −0.115662 + 0.200332i
\(163\) −4.85410 8.40755i −0.380203 0.658530i 0.610888 0.791717i \(-0.290812\pi\)
−0.991091 + 0.133186i \(0.957479\pi\)
\(164\) 4.85410 + 8.40755i 0.379042 + 0.656519i
\(165\) 0.708204 0.0551336
\(166\) −2.56231 −0.198874
\(167\) −4.88197 8.45581i −0.377778 0.654330i 0.612961 0.790113i \(-0.289978\pi\)
−0.990739 + 0.135783i \(0.956645\pi\)
\(168\) 0 0
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) −0.545085 + 0.944115i −0.0418061 + 0.0724103i
\(171\) 6.92705 11.9980i 0.529725 0.917510i
\(172\) −7.01064 + 12.1428i −0.534557 + 0.925879i
\(173\) 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) 0.596748 0.0452393
\(175\) 0 0
\(176\) 7.63525 13.2246i 0.575529 0.996845i
\(177\) 0.427051 0.739674i 0.0320991 0.0555973i
\(178\) 6.14590 0.460655
\(179\) 4.50000 7.79423i 0.336346 0.582568i −0.647397 0.762153i \(-0.724142\pi\)
0.983742 + 0.179585i \(0.0574756\pi\)
\(180\) 2.02129 0.150658
\(181\) −3.70820 −0.275629 −0.137814 0.990458i \(-0.544008\pi\)
−0.137814 + 0.990458i \(0.544008\pi\)
\(182\) 0 0
\(183\) 2.29180 0.169414
\(184\) −6.58359 −0.485349
\(185\) −0.763932 + 1.32317i −0.0561654 + 0.0972813i
\(186\) −1.27051 −0.0931583
\(187\) 18.1353 31.4112i 1.32618 2.29701i
\(188\) 2.07295 3.59045i 0.151185 0.261861i
\(189\) 0 0
\(190\) 0.708204 0.0513785
\(191\) −11.8090 20.4538i −0.854470 1.47999i −0.877135 0.480243i \(-0.840548\pi\)
0.0226649 0.999743i \(-0.492785\pi\)
\(192\) −0.899187 + 1.55744i −0.0648932 + 0.112398i
\(193\) 3.00000 5.19615i 0.215945 0.374027i −0.737620 0.675216i \(-0.764050\pi\)
0.953564 + 0.301189i \(0.0973836\pi\)
\(194\) −2.31966 + 4.01777i −0.166542 + 0.288459i
\(195\) 0.145898 0.505406i 0.0104480 0.0361928i
\(196\) 0 0
\(197\) −3.89919 6.75359i −0.277806 0.481173i 0.693034 0.720905i \(-0.256274\pi\)
−0.970839 + 0.239732i \(0.922940\pi\)
\(198\) 5.29180 0.376072
\(199\) 2.41641 0.171295 0.0856473 0.996326i \(-0.472704\pi\)
0.0856473 + 0.996326i \(0.472704\pi\)
\(200\) −3.57295 6.18853i −0.252646 0.437595i
\(201\) 0.135255 + 0.234268i 0.00954015 + 0.0165240i
\(202\) −1.63525 + 2.83234i −0.115056 + 0.199283i
\(203\) 0 0
\(204\) −2.64590 + 4.58283i −0.185250 + 0.320862i
\(205\) 2.00000 0.139686
\(206\) −0.899187 + 1.55744i −0.0626493 + 0.108512i
\(207\) 6.38197 + 11.0539i 0.443577 + 0.768298i
\(208\) −7.86475 8.17328i −0.545322 0.566715i
\(209\) −23.5623 −1.62984
\(210\) 0 0
\(211\) 4.35410 + 7.54153i 0.299749 + 0.519180i 0.976078 0.217419i \(-0.0697638\pi\)
−0.676330 + 0.736599i \(0.736430\pi\)
\(212\) 7.63525 + 13.2246i 0.524391 + 0.908273i
\(213\) 1.56231 + 2.70599i 0.107047 + 0.185412i
\(214\) −2.14590 −0.146691
\(215\) 1.44427 + 2.50155i 0.0984985 + 0.170604i
\(216\) −3.29180 −0.223978
\(217\) 0 0
\(218\) −2.04508 3.54219i −0.138511 0.239907i
\(219\) 0.763932 0.0516217
\(220\) −1.71885 2.97713i −0.115885 0.200718i
\(221\) −18.6803 19.4132i −1.25658 1.30587i
\(222\) 0.291796 0.505406i 0.0195841 0.0339206i
\(223\) 6.63525 + 11.4926i 0.444330 + 0.769601i 0.998005 0.0631310i \(-0.0201086\pi\)
−0.553676 + 0.832732i \(0.686775\pi\)
\(224\) 0 0
\(225\) −6.92705 + 11.9980i −0.461803 + 0.799867i
\(226\) 1.42705 2.47172i 0.0949260 0.164417i
\(227\) −7.47214 −0.495943 −0.247972 0.968767i \(-0.579764\pi\)
−0.247972 + 0.968767i \(0.579764\pi\)
\(228\) 3.43769 0.227667
\(229\) −13.5623 + 23.4906i −0.896222 + 1.55230i −0.0639380 + 0.997954i \(0.520366\pi\)
−0.832284 + 0.554349i \(0.812967\pi\)
\(230\) −0.326238 + 0.565061i −0.0215115 + 0.0372590i
\(231\) 0 0
\(232\) −3.01064 5.21459i −0.197658 0.342354i
\(233\) −0.190983 + 0.330792i −0.0125117 + 0.0216709i −0.872213 0.489125i \(-0.837316\pi\)
0.859702 + 0.510796i \(0.170649\pi\)
\(234\) 1.09017 3.77646i 0.0712666 0.246875i
\(235\) −0.427051 0.739674i −0.0278577 0.0482510i
\(236\) −4.14590 −0.269875
\(237\) 0.763932 + 1.32317i 0.0496227 + 0.0859491i
\(238\) 0 0
\(239\) −11.2918 −0.730406 −0.365203 0.930928i \(-0.619000\pi\)
−0.365203 + 0.930928i \(0.619000\pi\)
\(240\) 0.229490 + 0.397489i 0.0148135 + 0.0256578i
\(241\) 4.43769 0.285857 0.142929 0.989733i \(-0.454348\pi\)
0.142929 + 0.989733i \(0.454348\pi\)
\(242\) −2.39919 4.15551i −0.154226 0.267127i
\(243\) 4.82624 + 8.35929i 0.309603 + 0.536249i
\(244\) −5.56231 9.63420i −0.356090 0.616766i
\(245\) 0 0
\(246\) −0.763932 −0.0487065
\(247\) −4.85410 + 16.8151i −0.308859 + 1.06992i
\(248\) 6.40983 + 11.1022i 0.407025 + 0.704987i
\(249\) −1.28115 + 2.21902i −0.0811898 + 0.140625i
\(250\) −1.43769 −0.0909278
\(251\) −2.61803 + 4.53457i −0.165249 + 0.286219i −0.936744 0.350016i \(-0.886176\pi\)
0.771495 + 0.636236i \(0.219509\pi\)
\(252\) 0 0
\(253\) 10.8541 18.7999i 0.682392 1.18194i
\(254\) 2.70163 + 4.67935i 0.169515 + 0.293609i
\(255\) 0.545085 + 0.944115i 0.0341345 + 0.0591228i
\(256\) 5.56231 0.347644
\(257\) −25.7426 −1.60578 −0.802891 0.596126i \(-0.796706\pi\)
−0.802891 + 0.596126i \(0.796706\pi\)
\(258\) −0.551663 0.955508i −0.0343450 0.0594873i
\(259\) 0 0
\(260\) −2.47871 + 0.613323i −0.153723 + 0.0380367i
\(261\) −5.83688 + 10.1098i −0.361294 + 0.625779i
\(262\) −0.0623059 + 0.107917i −0.00384927 + 0.00666713i
\(263\) −4.50000 + 7.79423i −0.277482 + 0.480613i −0.970758 0.240059i \(-0.922833\pi\)
0.693276 + 0.720672i \(0.256167\pi\)
\(264\) 1.36475 + 2.36381i 0.0839943 + 0.145482i
\(265\) 3.14590 0.193251
\(266\) 0 0
\(267\) 3.07295 5.32250i 0.188061 0.325732i
\(268\) 0.656541 1.13716i 0.0401046 0.0694633i
\(269\) 13.7426 0.837904 0.418952 0.908008i \(-0.362398\pi\)
0.418952 + 0.908008i \(0.362398\pi\)
\(270\) −0.163119 + 0.282530i −0.00992710 + 0.0171942i
\(271\) 18.4164 1.11872 0.559359 0.828926i \(-0.311048\pi\)
0.559359 + 0.828926i \(0.311048\pi\)
\(272\) 23.5066 1.42530
\(273\) 0 0
\(274\) −0.145898 −0.00881402
\(275\) 23.5623 1.42086
\(276\) −1.58359 + 2.74286i −0.0953210 + 0.165101i
\(277\) −5.00000 −0.300421 −0.150210 0.988654i \(-0.547995\pi\)
−0.150210 + 0.988654i \(0.547995\pi\)
\(278\) 2.97214 5.14789i 0.178257 0.308750i
\(279\) 12.4271 21.5243i 0.743988 1.28863i
\(280\) 0 0
\(281\) −2.18034 −0.130068 −0.0650341 0.997883i \(-0.520716\pi\)
−0.0650341 + 0.997883i \(0.520716\pi\)
\(282\) 0.163119 + 0.282530i 0.00971359 + 0.0168244i
\(283\) 6.70820 11.6190i 0.398761 0.690675i −0.594812 0.803865i \(-0.702774\pi\)
0.993573 + 0.113190i \(0.0361069\pi\)
\(284\) 7.58359 13.1352i 0.450003 0.779429i
\(285\) 0.354102 0.613323i 0.0209752 0.0363301i
\(286\) −6.48936 + 1.60570i −0.383724 + 0.0949470i
\(287\) 0 0
\(288\) 5.91641 + 10.2475i 0.348628 + 0.603841i
\(289\) 38.8328 2.28428
\(290\) −0.596748 −0.0350422
\(291\) 2.31966 + 4.01777i 0.135981 + 0.235526i
\(292\) −1.85410 3.21140i −0.108503 0.187933i
\(293\) 5.61803 9.73072i 0.328209 0.568475i −0.653947 0.756540i \(-0.726888\pi\)
0.982157 + 0.188065i \(0.0602216\pi\)
\(294\) 0 0
\(295\) −0.427051 + 0.739674i −0.0248639 + 0.0430655i
\(296\) −5.88854 −0.342265
\(297\) 5.42705 9.39993i 0.314909 0.545439i
\(298\) 0.927051 + 1.60570i 0.0537026 + 0.0930157i
\(299\) −11.1803 11.6190i −0.646576 0.671941i
\(300\) −3.43769 −0.198475
\(301\) 0 0
\(302\) 2.80902 + 4.86536i 0.161641 + 0.279970i
\(303\) 1.63525 + 2.83234i 0.0939429 + 0.162714i
\(304\) −7.63525 13.2246i −0.437912 0.758486i
\(305\) −2.29180 −0.131228
\(306\) 4.07295 + 7.05455i 0.232835 + 0.403282i
\(307\) 1.85410 0.105819 0.0529096 0.998599i \(-0.483150\pi\)
0.0529096 + 0.998599i \(0.483150\pi\)
\(308\) 0 0
\(309\) 0.899187 + 1.55744i 0.0511530 + 0.0885995i
\(310\) 1.27051 0.0721601
\(311\) 6.16312 + 10.6748i 0.349478 + 0.605314i 0.986157 0.165815i \(-0.0530255\pi\)
−0.636678 + 0.771129i \(0.719692\pi\)
\(312\) 1.96807 0.486971i 0.111420 0.0275693i
\(313\) 7.56231 13.0983i 0.427447 0.740360i −0.569199 0.822200i \(-0.692746\pi\)
0.996645 + 0.0818405i \(0.0260798\pi\)
\(314\) −1.55573 2.69460i −0.0877948 0.152065i
\(315\) 0 0
\(316\) 3.70820 6.42280i 0.208603 0.361311i
\(317\) −10.8820 + 18.8481i −0.611192 + 1.05862i 0.379848 + 0.925049i \(0.375976\pi\)
−0.991040 + 0.133567i \(0.957357\pi\)
\(318\) −1.20163 −0.0673838
\(319\) 19.8541 1.11162
\(320\) 0.899187 1.55744i 0.0502661 0.0870634i
\(321\) −1.07295 + 1.85840i −0.0598862 + 0.103726i
\(322\) 0 0
\(323\) −18.1353 31.4112i −1.00907 1.74776i
\(324\) 7.14590 12.3771i 0.396994 0.687614i
\(325\) 4.85410 16.8151i 0.269257 0.932734i
\(326\) −1.85410 3.21140i −0.102689 0.177863i
\(327\) −4.09017 −0.226187
\(328\) 3.85410 + 6.67550i 0.212807 + 0.368593i
\(329\) 0 0
\(330\) 0.270510 0.0148911
\(331\) 8.42705 + 14.5961i 0.463193 + 0.802273i 0.999118 0.0419923i \(-0.0133705\pi\)
−0.535925 + 0.844265i \(0.680037\pi\)
\(332\) 12.4377 0.682607
\(333\) 5.70820 + 9.88690i 0.312808 + 0.541799i
\(334\) −1.86475 3.22983i −0.102034 0.176729i
\(335\) −0.135255 0.234268i −0.00738977 0.0127994i
\(336\) 0 0
\(337\) 8.56231 0.466419 0.233209 0.972427i \(-0.425077\pi\)
0.233209 + 0.972427i \(0.425077\pi\)
\(338\) −0.190983 + 4.96188i −0.0103881 + 0.269891i
\(339\) −1.42705 2.47172i −0.0775068 0.134246i
\(340\) 2.64590 4.58283i 0.143494 0.248539i
\(341\) −42.2705 −2.28908
\(342\) 2.64590 4.58283i 0.143074 0.247811i
\(343\) 0 0
\(344\) −5.56637 + 9.64124i −0.300119 + 0.519821i
\(345\) 0.326238 + 0.565061i 0.0175641 + 0.0304218i
\(346\) 1.71885 + 2.97713i 0.0924058 + 0.160052i
\(347\) 35.2361 1.89157 0.945786 0.324792i \(-0.105294\pi\)
0.945786 + 0.324792i \(0.105294\pi\)
\(348\) −2.89667 −0.155278
\(349\) −3.64590 6.31488i −0.195160 0.338028i 0.751793 0.659400i \(-0.229189\pi\)
−0.946953 + 0.321372i \(0.895856\pi\)
\(350\) 0 0
\(351\) −5.59017 5.80948i −0.298381 0.310087i
\(352\) 10.0623 17.4284i 0.536323 0.928938i
\(353\) −14.4271 + 24.9884i −0.767874 + 1.33000i 0.170839 + 0.985299i \(0.445352\pi\)
−0.938713 + 0.344699i \(0.887981\pi\)
\(354\) 0.163119 0.282530i 0.00866967 0.0150163i
\(355\) −1.56231 2.70599i −0.0829186 0.143619i
\(356\) −29.8328 −1.58114
\(357\) 0 0
\(358\) 1.71885 2.97713i 0.0908439 0.157346i
\(359\) 5.45492 9.44819i 0.287899 0.498656i −0.685409 0.728159i \(-0.740376\pi\)
0.973308 + 0.229502i \(0.0737098\pi\)
\(360\) 1.60488 0.0845845
\(361\) −2.28115 + 3.95107i −0.120061 + 0.207951i
\(362\) −1.41641 −0.0744447
\(363\) −4.79837 −0.251849
\(364\) 0 0
\(365\) −0.763932 −0.0399860
\(366\) 0.875388 0.0457573
\(367\) −12.7082 + 22.0113i −0.663363 + 1.14898i 0.316364 + 0.948638i \(0.397538\pi\)
−0.979726 + 0.200340i \(0.935795\pi\)
\(368\) 14.0689 0.733391
\(369\) 7.47214 12.9421i 0.388984 0.673740i
\(370\) −0.291796 + 0.505406i −0.0151698 + 0.0262748i
\(371\) 0 0
\(372\) 6.16718 0.319754
\(373\) 0.218847 + 0.379054i 0.0113315 + 0.0196267i 0.871636 0.490155i \(-0.163060\pi\)
−0.860304 + 0.509781i \(0.829726\pi\)
\(374\) 6.92705 11.9980i 0.358189 0.620402i
\(375\) −0.718847 + 1.24508i −0.0371211 + 0.0642956i
\(376\) 1.64590 2.85078i 0.0848807 0.147018i
\(377\) 4.09017 14.1688i 0.210654 0.729728i
\(378\) 0 0
\(379\) 6.42705 + 11.1320i 0.330135 + 0.571811i 0.982538 0.186061i \(-0.0595722\pi\)
−0.652403 + 0.757872i \(0.726239\pi\)
\(380\) −3.43769 −0.176350
\(381\) 5.40325 0.276817
\(382\) −4.51064 7.81266i −0.230785 0.399731i
\(383\) −12.4894 21.6322i −0.638176 1.10535i −0.985833 0.167732i \(-0.946356\pi\)
0.347656 0.937622i \(-0.386978\pi\)
\(384\) −1.92705 + 3.33775i −0.0983394 + 0.170329i
\(385\) 0 0
\(386\) 1.14590 1.98475i 0.0583247 0.101021i
\(387\) 21.5836 1.09716
\(388\) 11.2599 19.5027i 0.571633 0.990098i
\(389\) −11.9443 20.6881i −0.605599 1.04893i −0.991957 0.126579i \(-0.959600\pi\)
0.386358 0.922349i \(-0.373733\pi\)
\(390\) 0.0557281 0.193048i 0.00282190 0.00977535i
\(391\) 33.4164 1.68994
\(392\) 0 0
\(393\) 0.0623059 + 0.107917i 0.00314292 + 0.00544369i
\(394\) −1.48936 2.57964i −0.0750327 0.129960i
\(395\) −0.763932 1.32317i −0.0384376 0.0665759i
\(396\) −25.6869 −1.29082
\(397\) 12.7082 + 22.0113i 0.637806 + 1.10471i 0.985913 + 0.167258i \(0.0534914\pi\)
−0.348107 + 0.937455i \(0.613175\pi\)
\(398\) 0.922986 0.0462651
\(399\) 0 0
\(400\) 7.63525 + 13.2246i 0.381763 + 0.661232i
\(401\) −20.4508 −1.02127 −0.510633 0.859799i \(-0.670589\pi\)
−0.510633 + 0.859799i \(0.670589\pi\)
\(402\) 0.0516628 + 0.0894826i 0.00257671 + 0.00446298i
\(403\) −8.70820 + 30.1661i −0.433787 + 1.50268i
\(404\) 7.93769 13.7485i 0.394915 0.684013i
\(405\) −1.47214 2.54981i −0.0731510 0.126701i
\(406\) 0 0
\(407\) 9.70820 16.8151i 0.481218 0.833494i
\(408\) −2.10081 + 3.63871i −0.104006 + 0.180143i
\(409\) 34.5623 1.70900 0.854498 0.519455i \(-0.173865\pi\)
0.854498 + 0.519455i \(0.173865\pi\)
\(410\) 0.763932 0.0377279
\(411\) −0.0729490 + 0.126351i −0.00359831 + 0.00623246i
\(412\) 4.36475 7.55996i 0.215036 0.372453i
\(413\) 0 0
\(414\) 2.43769 + 4.22221i 0.119806 + 0.207510i
\(415\) 1.28115 2.21902i 0.0628893 0.108928i
\(416\) −10.3647 10.7714i −0.508173 0.528109i
\(417\) −2.97214 5.14789i −0.145546 0.252093i
\(418\) −9.00000 −0.440204
\(419\) −2.97214 5.14789i −0.145198 0.251491i 0.784249 0.620447i \(-0.213049\pi\)
−0.929447 + 0.368956i \(0.879715\pi\)
\(420\) 0 0
\(421\) −25.4164 −1.23872 −0.619360 0.785107i \(-0.712608\pi\)
−0.619360 + 0.785107i \(0.712608\pi\)
\(422\) 1.66312 + 2.88061i 0.0809594 + 0.140226i
\(423\) −6.38197 −0.310302
\(424\) 6.06231 + 10.5002i 0.294412 + 0.509936i
\(425\) 18.1353 + 31.4112i 0.879689 + 1.52367i
\(426\) 0.596748 + 1.03360i 0.0289125 + 0.0500780i
\(427\) 0 0
\(428\) 10.4164 0.503496
\(429\) −1.85410 + 6.42280i −0.0895169 + 0.310096i
\(430\) 0.551663 + 0.955508i 0.0266035 + 0.0460787i
\(431\) 8.39919 14.5478i 0.404575 0.700744i −0.589697 0.807624i \(-0.700753\pi\)
0.994272 + 0.106881i \(0.0340863\pi\)
\(432\) 7.03444 0.338445
\(433\) −0.500000 + 0.866025i −0.0240285 + 0.0416185i −0.877790 0.479046i \(-0.840983\pi\)
0.853761 + 0.520665i \(0.174316\pi\)
\(434\) 0 0
\(435\) −0.298374 + 0.516799i −0.0143059 + 0.0247786i
\(436\) 9.92705 + 17.1942i 0.475420 + 0.823451i
\(437\) −10.8541 18.7999i −0.519222 0.899319i
\(438\) 0.291796 0.0139426
\(439\) 8.14590 0.388783 0.194391 0.980924i \(-0.437727\pi\)
0.194391 + 0.980924i \(0.437727\pi\)
\(440\) −1.36475 2.36381i −0.0650617 0.112690i
\(441\) 0 0
\(442\) −7.13525 7.41517i −0.339389 0.352704i
\(443\) 0.381966 0.661585i 0.0181478 0.0314328i −0.856809 0.515634i \(-0.827556\pi\)
0.874957 + 0.484201i \(0.160890\pi\)
\(444\) −1.41641 + 2.45329i −0.0672197 + 0.116428i
\(445\) −3.07295 + 5.32250i −0.145672 + 0.252311i
\(446\) 2.53444 + 4.38978i 0.120009 + 0.207862i
\(447\) 1.85410 0.0876960
\(448\) 0 0
\(449\) −14.2361 + 24.6576i −0.671842 + 1.16366i 0.305540 + 0.952179i \(0.401163\pi\)
−0.977381 + 0.211484i \(0.932170\pi\)
\(450\) −2.64590 + 4.58283i −0.124729 + 0.216037i
\(451\) −25.4164 −1.19681
\(452\) −6.92705 + 11.9980i −0.325821 + 0.564339i
\(453\) 5.61803 0.263958
\(454\) −2.85410 −0.133950
\(455\) 0 0
\(456\) 2.72949 0.127820
\(457\) −11.4164 −0.534037 −0.267019 0.963691i \(-0.586038\pi\)
−0.267019 + 0.963691i \(0.586038\pi\)
\(458\) −5.18034 + 8.97261i −0.242061 + 0.419263i
\(459\) 16.7082 0.779872
\(460\) 1.58359 2.74286i 0.0738354 0.127887i
\(461\) −19.6074 + 33.9610i −0.913207 + 1.58172i −0.103702 + 0.994608i \(0.533069\pi\)
−0.809505 + 0.587113i \(0.800264\pi\)
\(462\) 0 0
\(463\) −6.70820 −0.311757 −0.155878 0.987776i \(-0.549821\pi\)
−0.155878 + 0.987776i \(0.549821\pi\)
\(464\) 6.43363 + 11.1434i 0.298674 + 0.517318i
\(465\) 0.635255 1.10029i 0.0294592 0.0510249i
\(466\) −0.0729490 + 0.126351i −0.00337930 + 0.00585312i
\(467\) −16.8262 + 29.1439i −0.778625 + 1.34862i 0.154109 + 0.988054i \(0.450749\pi\)
−0.932734 + 0.360565i \(0.882584\pi\)
\(468\) −5.29180 + 18.3313i −0.244613 + 0.847366i
\(469\) 0 0
\(470\) −0.163119 0.282530i −0.00752412 0.0130322i
\(471\) −3.11146 −0.143368
\(472\) −3.29180 −0.151517
\(473\) −18.3541 31.7902i −0.843923 1.46172i
\(474\) 0.291796 + 0.505406i 0.0134026 + 0.0232140i
\(475\) 11.7812 20.4056i 0.540556 0.936271i
\(476\) 0 0
\(477\) 11.7533 20.3573i 0.538146 0.932096i
\(478\) −4.31308 −0.197276
\(479\) 10.9894 19.0341i 0.502117 0.869691i −0.497880 0.867246i \(-0.665888\pi\)
0.999997 0.00244569i \(-0.000778487\pi\)
\(480\) 0.302439 + 0.523840i 0.0138044 + 0.0239099i
\(481\) −10.0000 10.3923i −0.455961 0.473848i
\(482\) 1.69505 0.0772073
\(483\) 0 0
\(484\) 11.6459 + 20.1713i 0.529359 + 0.916877i
\(485\) −2.31966 4.01777i −0.105330 0.182438i
\(486\) 1.84346 + 3.19296i 0.0836210 + 0.144836i
\(487\) −16.9787 −0.769379 −0.384689 0.923046i \(-0.625691\pi\)
−0.384689 + 0.923046i \(0.625691\pi\)
\(488\) −4.41641 7.64944i −0.199921 0.346274i
\(489\) −3.70820 −0.167691
\(490\) 0 0
\(491\) −7.30902 12.6596i −0.329851 0.571319i 0.652631 0.757676i \(-0.273665\pi\)
−0.982482 + 0.186357i \(0.940332\pi\)
\(492\) 3.70820 0.167179
\(493\) 15.2812 + 26.4677i 0.688229 + 1.19205i
\(494\) −1.85410 + 6.42280i −0.0834200 + 0.288975i
\(495\) −2.64590 + 4.58283i −0.118924 + 0.205983i
\(496\) −13.6976 23.7249i −0.615039 1.06528i
\(497\) 0 0
\(498\) −0.489357 + 0.847591i −0.0219286 + 0.0379815i
\(499\) −4.07295 + 7.05455i −0.182330 + 0.315805i −0.942674 0.333716i \(-0.891697\pi\)
0.760343 + 0.649521i \(0.225031\pi\)
\(500\) 6.97871 0.312098
\(501\) −3.72949 −0.166621
\(502\) −1.00000 + 1.73205i −0.0446322 + 0.0773052i
\(503\) −12.1910 + 21.1154i −0.543569 + 0.941489i 0.455126 + 0.890427i \(0.349594\pi\)
−0.998695 + 0.0510624i \(0.983739\pi\)
\(504\) 0 0
\(505\) −1.63525 2.83234i −0.0727679 0.126038i
\(506\) 4.14590 7.18091i 0.184308 0.319230i
\(507\) 4.20163 + 2.64634i 0.186601 + 0.117528i
\(508\) −13.1140 22.7141i −0.581838 1.00777i
\(509\) 30.5967 1.35618 0.678089 0.734980i \(-0.262809\pi\)
0.678089 + 0.734980i \(0.262809\pi\)
\(510\) 0.208204 + 0.360620i 0.00921943 + 0.0159685i
\(511\) 0 0
\(512\) 22.3050 0.985749
\(513\) −5.42705 9.39993i −0.239610 0.415017i
\(514\) −9.83282 −0.433707
\(515\) −0.899187 1.55744i −0.0396229 0.0686289i
\(516\) 2.67783 + 4.63813i 0.117885 + 0.204182i
\(517\) 5.42705 + 9.39993i 0.238681 + 0.413408i
\(518\) 0 0
\(519\) 3.43769 0.150898
\(520\) −1.96807 + 0.486971i −0.0863056 + 0.0213551i
\(521\) 6.32624 + 10.9574i 0.277158 + 0.480051i 0.970677 0.240387i \(-0.0772743\pi\)
−0.693520 + 0.720438i \(0.743941\pi\)
\(522\) −2.22949 + 3.86159i −0.0975821 + 0.169017i
\(523\) −39.1246 −1.71080 −0.855400 0.517968i \(-0.826689\pi\)
−0.855400 + 0.517968i \(0.826689\pi\)
\(524\) 0.302439 0.523840i 0.0132121 0.0228841i
\(525\) 0 0
\(526\) −1.71885 + 2.97713i −0.0749453 + 0.129809i
\(527\) −32.5344 56.3513i −1.41722 2.45470i
\(528\) −2.91641 5.05137i −0.126920 0.219833i
\(529\) −3.00000 −0.130435
\(530\) 1.20163 0.0521953
\(531\) 3.19098 + 5.52694i 0.138477 + 0.239849i
\(532\) 0 0
\(533\) −5.23607 + 18.1383i −0.226799 + 0.785656i
\(534\) 1.17376 2.03302i 0.0507937 0.0879772i
\(535\) 1.07295 1.85840i 0.0463876 0.0803457i
\(536\) 0.521286 0.902894i 0.0225161 0.0389991i
\(537\) −1.71885 2.97713i −0.0741737 0.128473i
\(538\) 5.24922 0.226310
\(539\) 0 0
\(540\) 0.791796 1.37143i 0.0340735 0.0590170i
\(541\) −0.864745 + 1.49778i −0.0371783 + 0.0643947i −0.884016 0.467457i \(-0.845170\pi\)
0.846838 + 0.531852i \(0.178504\pi\)
\(542\) 7.03444 0.302155
\(543\) −0.708204 + 1.22665i −0.0303919 + 0.0526404i
\(544\) 30.9787 1.32820
\(545\) 4.09017 0.175204
\(546\) 0 0
\(547\) −3.00000 −0.128271 −0.0641354 0.997941i \(-0.520429\pi\)
−0.0641354 + 0.997941i \(0.520429\pi\)
\(548\) 0.708204 0.0302530
\(549\) −8.56231 + 14.8303i −0.365430 + 0.632944i
\(550\) 9.00000 0.383761
\(551\) 9.92705 17.1942i 0.422907 0.732496i
\(552\) −1.25735 + 2.17780i −0.0535165 + 0.0926934i
\(553\) 0 0
\(554\) −1.90983 −0.0811409
\(555\) 0.291796 + 0.505406i 0.0123861 + 0.0214533i
\(556\) −14.4271 + 24.9884i −0.611843 + 1.05974i
\(557\) −9.48936 + 16.4360i −0.402077 + 0.696418i −0.993976 0.109594i \(-0.965045\pi\)
0.591899 + 0.806012i \(0.298378\pi\)
\(558\) 4.74671 8.22154i 0.200944 0.348046i
\(559\) −26.4681 + 6.54915i −1.11948 + 0.276999i
\(560\) 0 0
\(561\) −6.92705 11.9980i −0.292460 0.506556i
\(562\) −0.832816 −0.0351302
\(563\) −38.9443 −1.64131 −0.820653 0.571427i \(-0.806390\pi\)
−0.820653 + 0.571427i \(0.806390\pi\)
\(564\) −0.791796 1.37143i −0.0333406 0.0577477i
\(565\) 1.42705 + 2.47172i 0.0600365 + 0.103986i
\(566\) 2.56231 4.43804i 0.107702 0.186545i
\(567\) 0 0
\(568\) 6.02129 10.4292i 0.252648 0.437598i
\(569\) −2.94427 −0.123430 −0.0617151 0.998094i \(-0.519657\pi\)
−0.0617151 + 0.998094i \(0.519657\pi\)
\(570\) 0.135255 0.234268i 0.00566521 0.00981242i
\(571\) 17.8435 + 30.9058i 0.746726 + 1.29337i 0.949384 + 0.314117i \(0.101708\pi\)
−0.202659 + 0.979249i \(0.564958\pi\)
\(572\) 31.5000 7.79423i 1.31708 0.325893i
\(573\) −9.02129 −0.376870
\(574\) 0 0
\(575\) 10.8541 + 18.7999i 0.452647 + 0.784008i
\(576\) −6.71885 11.6374i −0.279952 0.484891i
\(577\) −4.91641 8.51547i −0.204673 0.354504i 0.745356 0.666667i \(-0.232280\pi\)
−0.950028 + 0.312163i \(0.898946\pi\)
\(578\) 14.8328 0.616964
\(579\) −1.14590 1.98475i −0.0476219 0.0824835i
\(580\) 2.89667 0.120278
\(581\) 0 0
\(582\) 0.886031 + 1.53465i 0.0367272 + 0.0636133i
\(583\) −39.9787 −1.65575
\(584\) −1.47214 2.54981i −0.0609174 0.105512i
\(585\) 2.72542 + 2.83234i 0.112682 + 0.117103i
\(586\) 2.14590 3.71680i 0.0886462 0.153540i
\(587\) 15.5451 + 26.9249i 0.641614 + 1.11131i 0.985072 + 0.172141i \(0.0550683\pi\)
−0.343458 + 0.939168i \(0.611598\pi\)
\(588\) 0 0
\(589\) −21.1353 + 36.6073i −0.870863 + 1.50838i
\(590\) −0.163119 + 0.282530i −0.00671550 + 0.0116316i
\(591\) −2.97871 −0.122528
\(592\) 12.5836 0.517182
\(593\) −9.60081 + 16.6291i −0.394258 + 0.682875i −0.993006 0.118062i \(-0.962332\pi\)
0.598748 + 0.800937i \(0.295665\pi\)
\(594\) 2.07295 3.59045i 0.0850541 0.147318i
\(595\) 0 0
\(596\) −4.50000 7.79423i −0.184327 0.319264i
\(597\) 0.461493 0.799329i 0.0188876 0.0327144i
\(598\) −4.27051 4.43804i −0.174634 0.181485i
\(599\) 4.25329 + 7.36691i 0.173785 + 0.301004i 0.939740 0.341890i \(-0.111067\pi\)
−0.765955 + 0.642894i \(0.777734\pi\)
\(600\) −2.72949 −0.111431
\(601\) 16.6976 + 28.9210i 0.681108 + 1.17971i 0.974643 + 0.223765i \(0.0718348\pi\)
−0.293535 + 0.955948i \(0.594832\pi\)
\(602\) 0 0
\(603\) −2.02129 −0.0823131
\(604\) −13.6353 23.6170i −0.554811 0.960960i
\(605\) 4.79837 0.195082
\(606\) 0.624612 + 1.08186i 0.0253731 + 0.0439475i
\(607\) 11.5000 + 19.9186i 0.466771 + 0.808470i 0.999279 0.0379540i \(-0.0120840\pi\)
−0.532509 + 0.846424i \(0.678751\pi\)
\(608\) −10.0623 17.4284i −0.408080 0.706816i
\(609\) 0 0
\(610\) −0.875388 −0.0354434
\(611\) 7.82624 1.93649i 0.316616 0.0783421i
\(612\) −19.7705 34.2435i −0.799175 1.38421i
\(613\) −7.21885 + 12.5034i −0.291566 + 0.505008i −0.974180 0.225771i \(-0.927510\pi\)
0.682614 + 0.730779i \(0.260843\pi\)
\(614\) 0.708204 0.0285808
\(615\) 0.381966 0.661585i 0.0154024 0.0266777i
\(616\) 0 0
\(617\) −8.97214 + 15.5402i −0.361205 + 0.625625i −0.988159 0.153431i \(-0.950968\pi\)
0.626955 + 0.779056i \(0.284301\pi\)
\(618\) 0.343459 + 0.594888i 0.0138159 + 0.0239299i
\(619\) 8.70820 + 15.0831i 0.350012 + 0.606239i 0.986251 0.165253i \(-0.0528441\pi\)
−0.636239 + 0.771492i \(0.719511\pi\)
\(620\) −6.16718 −0.247680
\(621\) 10.0000 0.401286
\(622\) 2.35410 + 4.07742i 0.0943909 + 0.163490i
\(623\) 0 0
\(624\) −4.20569 + 1.04064i −0.168362 + 0.0416589i
\(625\) −11.4164 + 19.7738i −0.456656 + 0.790952i
\(626\) 2.88854 5.00310i 0.115449 0.199964i
\(627\) −4.50000 + 7.79423i −0.179713 + 0.311272i
\(628\) 7.55166 + 13.0799i 0.301344 + 0.521943i
\(629\) 29.8885 1.19173
\(630\) 0 0
\(631\) 19.6976 34.1172i 0.784148 1.35818i −0.145360 0.989379i \(-0.546434\pi\)
0.929507 0.368804i \(-0.120233\pi\)
\(632\) 2.94427 5.09963i 0.117117 0.202852i
\(633\) 3.32624 0.132206
\(634\) −4.15654 + 7.19934i −0.165077 + 0.285922i
\(635\) −5.40325 −0.214422
\(636\) 5.83282 0.231286
\(637\) 0 0
\(638\) 7.58359 0.300237
\(639\) −23.3475 −0.923614
\(640\) 1.92705 3.33775i 0.0761734 0.131936i
\(641\) −9.49342 −0.374968 −0.187484 0.982268i \(-0.560033\pi\)
−0.187484 + 0.982268i \(0.560033\pi\)
\(642\) −0.409830 + 0.709846i −0.0161747 + 0.0280154i
\(643\) 3.50000 6.06218i 0.138027 0.239069i −0.788723 0.614749i \(-0.789257\pi\)
0.926750 + 0.375680i \(0.122591\pi\)
\(644\) 0 0
\(645\) 1.10333 0.0434434
\(646\) −6.92705 11.9980i −0.272541 0.472055i
\(647\) −14.6180 + 25.3192i −0.574694 + 0.995400i 0.421381 + 0.906884i \(0.361546\pi\)
−0.996075 + 0.0885157i \(0.971788\pi\)
\(648\) 5.67376 9.82724i 0.222886 0.386051i
\(649\) 5.42705 9.39993i 0.213030 0.368979i
\(650\) 1.85410 6.42280i 0.0727239 0.251923i
\(651\) 0 0
\(652\) 9.00000 + 15.5885i 0.352467 + 0.610491i
\(653\) −2.61803 −0.102452 −0.0512258 0.998687i \(-0.516313\pi\)
−0.0512258 + 0.998687i \(0.516313\pi\)
\(654\) −1.56231 −0.0610910
\(655\) −0.0623059 0.107917i −0.00243449 0.00421667i
\(656\) −8.23607 14.2653i −0.321564 0.556966i
\(657\) −2.85410 + 4.94345i −0.111349 + 0.192862i
\(658\) 0 0
\(659\) −5.94427 + 10.2958i −0.231556 + 0.401067i −0.958266 0.285877i \(-0.907715\pi\)
0.726710 + 0.686944i \(0.241048\pi\)
\(660\) −1.31308 −0.0511117
\(661\) −9.27051 + 16.0570i −0.360581 + 0.624545i −0.988057 0.154092i \(-0.950755\pi\)
0.627476 + 0.778636i \(0.284088\pi\)
\(662\) 3.21885 + 5.57521i 0.125104 + 0.216687i
\(663\) −9.98936 + 2.47172i −0.387954 + 0.0959938i
\(664\) 9.87539 0.383239
\(665\) 0 0
\(666\) 2.18034 + 3.77646i 0.0844865 + 0.146335i
\(667\) 9.14590 + 15.8412i 0.354131 + 0.613372i
\(668\) 9.05166 + 15.6779i 0.350219 + 0.606598i
\(669\) 5.06888 0.195974
\(670\) −0.0516628 0.0894826i −0.00199591 0.00345701i
\(671\) 29.1246 1.12434
\(672\) 0 0
\(673\) −20.6246 35.7229i −0.795020 1.37702i −0.922826 0.385216i \(-0.874127\pi\)
0.127806 0.991799i \(-0.459207\pi\)
\(674\) 3.27051 0.125975
\(675\) 5.42705 + 9.39993i 0.208887 + 0.361803i
\(676\) 0.927051 24.0855i 0.0356558 0.926365i
\(677\) −0.628677 + 1.08890i −0.0241620 + 0.0418499i −0.877854 0.478929i \(-0.841025\pi\)
0.853692 + 0.520779i \(0.174358\pi\)
\(678\) −0.545085 0.944115i −0.0209339 0.0362585i
\(679\) 0 0
\(680\) 2.10081 3.63871i 0.0805625 0.139538i
\(681\) −1.42705 + 2.47172i −0.0546847 + 0.0947167i
\(682\) −16.1459 −0.618258
\(683\) −7.47214 −0.285913 −0.142957 0.989729i \(-0.545661\pi\)
−0.142957 + 0.989729i \(0.545661\pi\)
\(684\) −12.8435 + 22.2455i −0.491082 + 0.850579i
\(685\) 0.0729490 0.126351i 0.00278724 0.00482764i
\(686\) 0 0
\(687\) 5.18034 + 8.97261i 0.197642 + 0.342326i
\(688\) 11.8951 20.6030i 0.453497 0.785480i
\(689\) −8.23607 + 28.5306i −0.313769 + 1.08693i
\(690\) 0.124612 + 0.215834i 0.00474389 + 0.00821666i
\(691\) 0.854102 0.0324916 0.0162458 0.999868i \(-0.494829\pi\)
0.0162458 + 0.999868i \(0.494829\pi\)
\(692\) −8.34346 14.4513i −0.317171 0.549356i
\(693\) 0 0
\(694\) 13.4590 0.510896
\(695\) 2.97214 + 5.14789i 0.112740 + 0.195271i
\(696\) −2.29993 −0.0871785
\(697\) −19.5623 33.8829i −0.740975 1.28341i
\(698\) −1.39261 2.41207i −0.0527110 0.0912982i
\(699\) 0.0729490 + 0.126351i 0.00275919 + 0.00477905i
\(700\) 0 0
\(701\) 6.76393 0.255470 0.127735 0.991808i \(-0.459229\pi\)
0.127735 + 0.991808i \(0.459229\pi\)
\(702\) −2.13525 2.21902i −0.0805900 0.0837516i
\(703\) −9.70820 16.8151i −0.366152 0.634194i
\(704\) −11.4271 + 19.7922i −0.430673 + 0.745948i
\(705\) −0.326238 −0.0122868
\(706\) −5.51064 + 9.54471i −0.207396 + 0.359220i
\(707\) 0 0
\(708\) −0.791796 + 1.37143i −0.0297575 + 0.0515415i
\(709\) −1.71885 2.97713i −0.0645527 0.111808i 0.831943 0.554861i \(-0.187229\pi\)
−0.896495 + 0.443053i \(0.853895\pi\)
\(710\) −0.596748 1.03360i −0.0223955 0.0387902i
\(711\) −11.4164 −0.428149
\(712\) −23.6869 −0.887705
\(713\) −19.4721 33.7267i −0.729237 1.26308i
\(714\) 0 0
\(715\) 1.85410 6.42280i 0.0693395 0.240199i
\(716\) −8.34346 + 14.4513i −0.311810 + 0.540070i
\(717\) −2.15654 + 3.73524i −0.0805375 + 0.139495i
\(718\) 2.08359 3.60889i 0.0777590 0.134682i
\(719\) 16.0623 + 27.8207i 0.599023 + 1.03754i 0.992966 + 0.118403i \(0.0377775\pi\)
−0.393943 + 0.919135i \(0.628889\pi\)
\(720\) −3.42956 −0.127812
\(721\) 0 0
\(722\) −0.871323 + 1.50918i −0.0324273 + 0.0561657i
\(723\) 0.847524 1.46795i 0.0315198 0.0545938i
\(724\) 6.87539 0.255522
\(725\) −9.92705 + 17.1942i −0.368681 + 0.638575i
\(726\) −1.83282 −0.0680222
\(727\) −17.2918 −0.641317 −0.320659 0.947195i \(-0.603904\pi\)
−0.320659 + 0.947195i \(0.603904\pi\)
\(728\) 0 0
\(729\) −19.4377 −0.719915
\(730\) −0.291796 −0.0107999
\(731\) 28.2533 48.9361i 1.04499 1.80997i
\(732\) −4.24922 −0.157056
\(733\) −0.635255 + 1.10029i −0.0234637 + 0.0406403i −0.877519 0.479542i \(-0.840803\pi\)
0.854055 + 0.520182i \(0.174136\pi\)
\(734\) −4.85410 + 8.40755i −0.179168 + 0.310328i
\(735\) 0 0
\(736\) 18.5410 0.683431
\(737\) 1.71885 + 2.97713i 0.0633145 + 0.109664i
\(738\) 2.85410 4.94345i 0.105061 0.181971i
\(739\) 23.5623 40.8111i 0.866753 1.50126i 0.00145790 0.999999i \(-0.499536\pi\)
0.865296 0.501262i \(-0.167131\pi\)
\(740\) 1.41641 2.45329i 0.0520682 0.0901847i
\(741\) 4.63525 + 4.81710i 0.170280 + 0.176961i
\(742\) 0 0
\(743\) −11.8369 20.5021i −0.434253 0.752148i 0.562981 0.826470i \(-0.309654\pi\)
−0.997234 + 0.0743213i \(0.976321\pi\)
\(744\) 4.89667 0.179521
\(745\) −1.85410 −0.0679290
\(746\) 0.0835921 + 0.144786i 0.00306053 + 0.00530099i
\(747\) −9.57295 16.5808i −0.350256 0.606661i
\(748\) −33.6246 + 58.2395i −1.22944 + 2.12945i
\(749\) 0 0
\(750\) −0.274575 + 0.475578i −0.0100261 + 0.0173657i
\(751\) 9.29180 0.339062 0.169531 0.985525i \(-0.445775\pi\)
0.169531 + 0.985525i \(0.445775\pi\)
\(752\) −3.51722 + 6.09201i −0.128260 + 0.222153i
\(753\) 1.00000 + 1.73205i 0.0364420 + 0.0631194i
\(754\) 1.56231 5.41199i 0.0568958 0.197093i
\(755\) −5.61803 −0.204461
\(756\) 0 0
\(757\) −14.0000 24.2487i −0.508839 0.881334i −0.999948 0.0102362i \(-0.996742\pi\)
0.491109 0.871098i \(-0.336592\pi\)
\(758\) 2.45492 + 4.25204i 0.0891665 + 0.154441i
\(759\) −4.14590 7.18091i −0.150487 0.260650i
\(760\) −2.72949 −0.0990090
\(761\) 11.0729 + 19.1789i 0.401394 + 0.695235i 0.993894 0.110335i \(-0.0351925\pi\)
−0.592500 + 0.805570i \(0.701859\pi\)
\(762\) 2.06386 0.0747657
\(763\) 0 0
\(764\) 21.8951 + 37.9235i 0.792138 + 1.37202i
\(765\) −8.14590 −0.294516
\(766\) −4.77051 8.26277i −0.172366 0.298546i
\(767\) −5.59017 5.80948i −0.201849 0.209768i
\(768\) 1.06231 1.83997i 0.0383327 0.0663941i
\(769\) −4.20820 7.28882i −0.151752 0.262842i 0.780120 0.625630i \(-0.215158\pi\)
−0.931872 + 0.362788i \(0.881825\pi\)
\(770\) 0 0
\(771\) −4.91641 + 8.51547i −0.177060 + 0.306677i
\(772\) −5.56231 + 9.63420i −0.200192 + 0.346742i
\(773\) −19.3607 −0.696355 −0.348178 0.937429i \(-0.613199\pi\)
−0.348178 + 0.937429i \(0.613199\pi\)
\(774\) 8.24420 0.296332
\(775\) 21.1353 36.6073i 0.759201 1.31497i
\(776\) 8.94021 15.4849i 0.320935 0.555875i
\(777\) 0 0
\(778\) −4.56231 7.90215i −0.163567 0.283306i
\(779\) −12.7082 + 22.0113i −0.455319 + 0.788635i
\(780\) −0.270510 + 0.937074i −0.00968581 + 0.0335526i
\(781\) 19.8541 + 34.3883i 0.710436 +