Properties

Label 637.2.f.c.393.2
Level $637$
Weight $2$
Character 637.393
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.f (of order \(3\), degree \(2\), 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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 393.2
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 637.393
Dual form 637.2.f.c.295.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.190983 - 0.330792i) q^{2} +(-0.190983 - 0.330792i) q^{3} +(0.927051 - 1.60570i) q^{4} -0.381966 q^{5} +(-0.0729490 + 0.126351i) q^{6} -1.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +O(q^{10})\) \(q+(-0.190983 - 0.330792i) q^{2} +(-0.190983 - 0.330792i) q^{3} +(0.927051 - 1.60570i) q^{4} -0.381966 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} -0.708204 q^{12} +(2.50000 + 2.59808i) q^{13} +(0.0729490 + 0.126351i) q^{15} +(-1.57295 - 2.72443i) q^{16} +(3.73607 - 6.47106i) q^{17} -1.09017 q^{18} +(2.42705 - 4.20378i) q^{19} +(-0.354102 + 0.613323i) q^{20} +(0.927051 - 1.60570i) q^{22} +(-2.23607 - 3.87298i) q^{23} +(0.281153 + 0.486971i) q^{24} -4.85410 q^{25} +(0.381966 - 1.32317i) q^{26} -2.23607 q^{27} +(2.04508 + 3.54219i) q^{29} +(0.0278640 - 0.0482619i) q^{30} -8.70820 q^{31} +(-2.07295 + 3.59045i) q^{32} +(0.927051 - 1.60570i) q^{33} -2.85410 q^{34} +(-2.64590 - 4.58283i) q^{36} +(-2.00000 - 3.46410i) q^{37} -1.85410 q^{38} +(0.381966 - 1.32317i) q^{39} +0.562306 q^{40} +(2.61803 + 4.53457i) q^{41} +(3.78115 - 6.54915i) q^{43} +9.00000 q^{44} +(-0.545085 + 0.944115i) q^{45} +(-0.854102 + 1.47935i) q^{46} -2.23607 q^{47} +(-0.600813 + 1.04064i) q^{48} +(0.927051 + 1.60570i) q^{50} -2.85410 q^{51} +(6.48936 - 1.60570i) q^{52} +8.23607 q^{53} +(0.427051 + 0.739674i) q^{54} +(-0.927051 - 1.60570i) q^{55} -1.85410 q^{57} +(0.781153 - 1.35300i) q^{58} +(1.11803 - 1.93649i) q^{59} +0.270510 q^{60} +(-3.00000 + 5.19615i) q^{61} +(1.66312 + 2.88061i) q^{62} -4.70820 q^{64} +(-0.954915 - 0.992377i) q^{65} -0.708204 q^{66} +(-0.354102 - 0.613323i) q^{67} +(-6.92705 - 11.9980i) q^{68} +(-0.854102 + 1.47935i) q^{69} +(-4.09017 + 7.08438i) q^{71} +(-2.10081 + 3.63871i) q^{72} +2.00000 q^{73} +(-0.763932 + 1.32317i) q^{74} +(0.927051 + 1.60570i) q^{75} +(-4.50000 - 7.79423i) q^{76} +(-0.510643 + 0.126351i) q^{78} +4.00000 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} -2.88854 q^{86} +(0.781153 - 1.35300i) q^{87} +(-3.57295 - 6.18853i) q^{88} +(8.04508 + 13.9345i) q^{89} +0.416408 q^{90} -8.29180 q^{92} +(1.66312 + 2.88061i) q^{93} +(0.427051 + 0.739674i) q^{94} +(-0.927051 + 1.60570i) q^{95} +1.58359 q^{96} +(6.07295 - 10.5187i) q^{97} +13.8541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 3q^{2} - 3q^{3} - 3q^{4} - 6q^{5} - 7q^{6} + 12q^{8} - q^{9} + O(q^{10}) \) \( 4q - 3q^{2} - 3q^{3} - 3q^{4} - 6q^{5} - 7q^{6} + 12q^{8} - q^{9} + 7q^{10} + 3q^{11} + 24q^{12} + 10q^{13} + 7q^{15} - 13q^{16} + 6q^{17} + 18q^{18} + 3q^{19} + 12q^{20} - 3q^{22} - 19q^{24} - 6q^{25} + 6q^{26} - 3q^{29} + 18q^{30} - 8q^{31} - 15q^{32} - 3q^{33} + 2q^{34} - 24q^{36} - 8q^{37} + 6q^{38} + 6q^{39} - 38q^{40} + 6q^{41} - 5q^{43} + 36q^{44} + 9q^{45} + 10q^{46} - 27q^{48} - 3q^{50} + 2q^{51} - 21q^{52} + 24q^{53} - 5q^{54} + 3q^{55} + 6q^{57} - 17q^{58} - 66q^{60} - 12q^{61} - 9q^{62} + 8q^{64} - 15q^{65} + 24q^{66} + 12q^{67} - 21q^{68} + 10q^{69} + 6q^{71} - 33q^{72} + 8q^{73} - 12q^{74} - 3q^{75} - 18q^{76} - 49q^{78} + 16q^{79} + 27q^{80} - 2q^{81} + 4q^{82} + q^{85} + 60q^{86} - 17q^{87} - 21q^{88} + 21q^{89} - 52q^{90} - 60q^{92} - 9q^{93} - 5q^{94} + 3q^{95} + 60q^{96} + 31q^{97} + 42q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.190983 0.330792i −0.135045 0.233905i 0.790569 0.612372i \(-0.209785\pi\)
−0.925615 + 0.378467i \(0.876451\pi\)
\(3\) −0.190983 0.330792i −0.110264 0.190983i 0.805613 0.592443i \(-0.201836\pi\)
−0.915877 + 0.401460i \(0.868503\pi\)
\(4\) 0.927051 1.60570i 0.463525 0.802850i
\(5\) −0.381966 −0.170820 −0.0854102 0.996346i \(-0.527220\pi\)
−0.0854102 + 0.996346i \(0.527220\pi\)
\(6\) −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 0.956120 + 0.292974i \(0.0946451\pi\)
−0.224337 + 0.974512i \(0.572022\pi\)
\(12\) −0.708204 −0.204441
\(13\) 2.50000 + 2.59808i 0.693375 + 0.720577i
\(14\) 0 0
\(15\) 0.0729490 + 0.126351i 0.0188354 + 0.0326238i
\(16\) −1.57295 2.72443i −0.393237 0.681107i
\(17\) 3.73607 6.47106i 0.906130 1.56946i 0.0867359 0.996231i \(-0.472356\pi\)
0.819394 0.573231i \(-0.194310\pi\)
\(18\) −1.09017 −0.256956
\(19\) 2.42705 4.20378i 0.556804 0.964412i −0.440957 0.897528i \(-0.645361\pi\)
0.997761 0.0668841i \(-0.0213058\pi\)
\(20\) −0.354102 + 0.613323i −0.0791796 + 0.137143i
\(21\) 0 0
\(22\) 0.927051 1.60570i 0.197648 0.342336i
\(23\) −2.23607 3.87298i −0.466252 0.807573i 0.533005 0.846112i \(-0.321063\pi\)
−0.999257 + 0.0385394i \(0.987729\pi\)
\(24\) 0.281153 + 0.486971i 0.0573901 + 0.0994026i
\(25\) −4.85410 −0.970820
\(26\) 0.381966 1.32317i 0.0749097 0.259495i
\(27\) −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
\(31\) −8.70820 −1.56404 −0.782020 0.623254i \(-0.785810\pi\)
−0.782020 + 0.623254i \(0.785810\pi\)
\(32\) −2.07295 + 3.59045i −0.366449 + 0.634708i
\(33\) 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
\(37\) −2.00000 3.46410i −0.328798 0.569495i 0.653476 0.756948i \(-0.273310\pi\)
−0.982274 + 0.187453i \(0.939977\pi\)
\(38\) −1.85410 −0.300775
\(39\) 0.381966 1.32317i 0.0611635 0.211877i
\(40\) 0.562306 0.0889084
\(41\) 2.61803 + 4.53457i 0.408868 + 0.708181i 0.994763 0.102206i \(-0.0325902\pi\)
−0.585895 + 0.810387i \(0.699257\pi\)
\(42\) 0 0
\(43\) 3.78115 6.54915i 0.576620 0.998736i −0.419243 0.907874i \(-0.637704\pi\)
0.995864 0.0908618i \(-0.0289622\pi\)
\(44\) 9.00000 1.35680
\(45\) −0.545085 + 0.944115i −0.0812565 + 0.140740i
\(46\) −0.854102 + 1.47935i −0.125930 + 0.218118i
\(47\) −2.23607 −0.326164 −0.163082 0.986613i \(-0.552144\pi\)
−0.163082 + 0.986613i \(0.552144\pi\)
\(48\) −0.600813 + 1.04064i −0.0867199 + 0.150203i
\(49\) 0 0
\(50\) 0.927051 + 1.60570i 0.131105 + 0.227080i
\(51\) −2.85410 −0.399654
\(52\) 6.48936 1.60570i 0.899912 0.222670i
\(53\) 8.23607 1.13131 0.565655 0.824642i \(-0.308623\pi\)
0.565655 + 0.824642i \(0.308623\pi\)
\(54\) 0.427051 + 0.739674i 0.0581143 + 0.100657i
\(55\) −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
\(59\) 1.11803 1.93649i 0.145556 0.252110i −0.784024 0.620730i \(-0.786836\pi\)
0.929580 + 0.368620i \(0.120170\pi\)
\(60\) 0.270510 0.0349227
\(61\) −3.00000 + 5.19615i −0.384111 + 0.665299i −0.991645 0.128994i \(-0.958825\pi\)
0.607535 + 0.794293i \(0.292159\pi\)
\(62\) 1.66312 + 2.88061i 0.211216 + 0.365837i
\(63\) 0 0
\(64\) −4.70820 −0.588525
\(65\) −0.954915 0.992377i −0.118443 0.123089i
\(66\) −0.708204 −0.0871739
\(67\) −0.354102 0.613323i −0.0432604 0.0749293i 0.843584 0.536997i \(-0.180441\pi\)
−0.886845 + 0.462067i \(0.847108\pi\)
\(68\) −6.92705 11.9980i −0.840028 1.45497i
\(69\) −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
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) −0.763932 + 1.32317i −0.0888053 + 0.153815i
\(75\) 0.927051 + 1.60570i 0.107047 + 0.185410i
\(76\) −4.50000 7.79423i −0.516185 0.894059i
\(77\) 0 0
\(78\) −0.510643 + 0.126351i −0.0578189 + 0.0143065i
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 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 \(-0.379988\pi\)
0.368161 + 0.929762i \(0.379988\pi\)
\(84\) 0 0
\(85\) −1.42705 + 2.47172i −0.154785 + 0.268096i
\(86\) −2.88854 −0.311480
\(87\) 0.781153 1.35300i 0.0837484 0.145056i
\(88\) −3.57295 6.18853i −0.380878 0.659699i
\(89\) 8.04508 + 13.9345i 0.852777 + 1.47705i 0.878692 + 0.477389i \(0.158417\pi\)
−0.0259145 + 0.999664i \(0.508250\pi\)
\(90\) 0.416408 0.0438932
\(91\) 0 0
\(92\) −8.29180 −0.864479
\(93\) 1.66312 + 2.88061i 0.172457 + 0.298705i
\(94\) 0.427051 + 0.739674i 0.0440469 + 0.0762915i
\(95\) −0.927051 + 1.60570i −0.0951134 + 0.164741i
\(96\) 1.58359 0.161625
\(97\) 6.07295 10.5187i 0.616615 1.06801i −0.373484 0.927636i \(-0.621837\pi\)
0.990099 0.140371i \(-0.0448296\pi\)
\(98\) 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 \(-0.0265923\pi\)
−0.570522 + 0.821283i \(0.693259\pi\)
\(102\) 0.545085 + 0.944115i 0.0539715 + 0.0934813i
\(103\) −4.70820 −0.463913 −0.231957 0.972726i \(-0.574513\pi\)
−0.231957 + 0.972726i \(0.574513\pi\)
\(104\) −3.68034 3.82472i −0.360887 0.375045i
\(105\) 0 0
\(106\) −1.57295 2.72443i −0.152778 0.264620i
\(107\) 2.80902 + 4.86536i 0.271558 + 0.470352i 0.969261 0.246035i \(-0.0791278\pi\)
−0.697703 + 0.716387i \(0.745794\pi\)
\(108\) −2.07295 + 3.59045i −0.199470 + 0.345492i
\(109\) 10.7082 1.02566 0.512830 0.858490i \(-0.328597\pi\)
0.512830 + 0.858490i \(0.328597\pi\)
\(110\) −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 \(0.0523521\pi\)
\(114\) 0.354102 + 0.613323i 0.0331647 + 0.0574429i
\(115\) 0.854102 + 1.47935i 0.0796454 + 0.137950i
\(116\) 7.58359 0.704119
\(117\) 9.98936 2.47172i 0.923516 0.228511i
\(118\) −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
\(122\) 2.29180 0.207489
\(123\) 1.00000 1.73205i 0.0901670 0.156174i
\(124\) −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 \(0.617361\pi\)
\(128\) 5.04508 + 8.73834i 0.445927 + 0.772368i
\(129\) −2.88854 −0.254322
\(130\) −0.145898 + 0.505406i −0.0127961 + 0.0443270i
\(131\) −0.326238 −0.0285035 −0.0142518 0.999898i \(-0.504537\pi\)
−0.0142518 + 0.999898i \(0.504537\pi\)
\(132\) −1.71885 2.97713i −0.149606 0.259126i
\(133\) 0 0
\(134\) −0.135255 + 0.234268i −0.0116842 + 0.0202377i
\(135\) 0.854102 0.0735094
\(136\) −5.50000 + 9.52628i −0.471621 + 0.816872i
\(137\) 0.190983 0.330792i 0.0163168 0.0282615i −0.857752 0.514064i \(-0.828139\pi\)
0.874069 + 0.485803i \(0.161473\pi\)
\(138\) 0.652476 0.0555424
\(139\) −7.78115 + 13.4774i −0.659989 + 1.14313i 0.320629 + 0.947205i \(0.396106\pi\)
−0.980618 + 0.195929i \(0.937228\pi\)
\(140\) 0 0
\(141\) 0.427051 + 0.739674i 0.0359642 + 0.0622918i
\(142\) 3.12461 0.262212
\(143\) −4.85410 + 16.8151i −0.405920 + 1.40615i
\(144\) −8.97871 −0.748226
\(145\) −0.781153 1.35300i −0.0648712 0.112360i
\(146\) −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 −0.749318 0.662210i \(-0.769619\pi\)
0.948150 + 0.317823i \(0.102952\pi\)
\(150\) 0.354102 0.613323i 0.0289123 0.0500776i
\(151\) −14.7082 −1.19694 −0.598468 0.801146i \(-0.704224\pi\)
−0.598468 + 0.801146i \(0.704224\pi\)
\(152\) −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
\(156\) −1.77051 1.83997i −0.141754 0.147315i
\(157\) −8.14590 −0.650113 −0.325057 0.945695i \(-0.605383\pi\)
−0.325057 + 0.945695i \(0.605383\pi\)
\(158\) −0.763932 1.32317i −0.0607752 0.105266i
\(159\) −1.57295 2.72443i −0.124743 0.216061i
\(160\) 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 −0.991091 0.133186i \(-0.957479\pi\)
0.610888 + 0.791717i \(0.290812\pi\)
\(164\) 9.70820 0.758083
\(165\) −0.354102 + 0.613323i −0.0275668 + 0.0477471i
\(166\) −1.28115 2.21902i −0.0994368 0.172230i
\(167\) 4.88197 + 8.45581i 0.377778 + 0.654330i 0.990739 0.135783i \(-0.0433550\pi\)
−0.612961 + 0.790113i \(0.710022\pi\)
\(168\) 0 0
\(169\) −0.500000 + 12.9904i −0.0384615 + 0.999260i
\(170\) 1.09017 0.0836122
\(171\) −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 \(-0.944481\pi\)
0.642699 + 0.766119i \(0.277815\pi\)
\(174\) −0.596748 −0.0452393
\(175\) 0 0
\(176\) 7.63525 13.2246i 0.575529 0.996845i
\(177\) −0.854102 −0.0641982
\(178\) 3.07295 5.32250i 0.230327 0.398939i
\(179\) 4.50000 + 7.79423i 0.336346 + 0.582568i 0.983742 0.179585i \(-0.0574756\pi\)
−0.647397 + 0.762153i \(0.724142\pi\)
\(180\) 1.01064 + 1.75049i 0.0753289 + 0.130473i
\(181\) 3.70820 0.275629 0.137814 0.990458i \(-0.455992\pi\)
0.137814 + 0.990458i \(0.455992\pi\)
\(182\) 0 0
\(183\) 2.29180 0.169414
\(184\) 3.29180 + 5.70156i 0.242674 + 0.420324i
\(185\) 0.763932 + 1.32317i 0.0561654 + 0.0972813i
\(186\) 0.635255 1.10029i 0.0465792 0.0806775i
\(187\) 36.2705 2.65236
\(188\) −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 0.0226649 + 0.999743i \(0.492785\pi\)
−0.877135 + 0.480243i \(0.840548\pi\)
\(192\) 0.899187 + 1.55744i 0.0648932 + 0.112398i
\(193\) 3.00000 + 5.19615i 0.215945 + 0.374027i 0.953564 0.301189i \(-0.0973836\pi\)
−0.737620 + 0.675216i \(0.764050\pi\)
\(194\) −4.63932 −0.333084
\(195\) −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 \(0.922940\pi\)
\(198\) −2.64590 4.58283i −0.188036 0.325688i
\(199\) 1.20820 2.09267i 0.0856473 0.148345i −0.820020 0.572336i \(-0.806038\pi\)
0.905667 + 0.423990i \(0.139371\pi\)
\(200\) 7.14590 0.505291
\(201\) −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
\(205\) −1.00000 1.73205i −0.0698430 0.120972i
\(206\) 0.899187 + 1.55744i 0.0626493 + 0.108512i
\(207\) −12.7639 −0.887155
\(208\) 3.14590 10.8977i 0.218129 0.755620i
\(209\) 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
\(213\) 3.12461 0.214095
\(214\) 1.07295 1.85840i 0.0733453 0.127038i
\(215\) −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
\(219\) −0.381966 0.661585i −0.0258109 0.0447057i
\(220\) −3.43769 −0.231769
\(221\) 26.1525 6.47106i 1.75921 0.435291i
\(222\) 0.583592 0.0391681
\(223\) −6.63525 11.4926i −0.444330 0.769601i 0.553676 0.832732i \(-0.313225\pi\)
−0.998005 + 0.0631310i \(0.979891\pi\)
\(224\) 0 0
\(225\) −6.92705 + 11.9980i −0.461803 + 0.799867i
\(226\) −2.85410 −0.189852
\(227\) −3.73607 + 6.47106i −0.247972 + 0.429499i −0.962963 0.269634i \(-0.913097\pi\)
0.714991 + 0.699133i \(0.246431\pi\)
\(228\) −1.71885 + 2.97713i −0.113833 + 0.197165i
\(229\) −27.1246 −1.79244 −0.896222 0.443605i \(-0.853699\pi\)
−0.896222 + 0.443605i \(0.853699\pi\)
\(230\) 0.326238 0.565061i 0.0215115 0.0372590i
\(231\) 0 0
\(232\) −3.01064 5.21459i −0.197658 0.342354i
\(233\) 0.381966 0.0250234 0.0125117 0.999922i \(-0.496017\pi\)
0.0125117 + 0.999922i \(0.496017\pi\)
\(234\) −2.72542 2.83234i −0.178167 0.185156i
\(235\) 0.854102 0.0557155
\(236\) −2.07295 3.59045i −0.134937 0.233719i
\(237\) −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
\(241\) 2.21885 3.84316i 0.142929 0.247559i −0.785670 0.618646i \(-0.787681\pi\)
0.928598 + 0.371087i \(0.121015\pi\)
\(242\) 4.79837 0.308451
\(243\) −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
\(247\) 16.9894 4.20378i 1.08101 0.267480i
\(248\) 12.8197 0.814049
\(249\) −1.28115 2.21902i −0.0811898 0.140625i
\(250\) −0.718847 1.24508i −0.0454639 0.0787457i
\(251\) 2.61803 4.53457i 0.165249 0.286219i −0.771495 0.636236i \(-0.780491\pi\)
0.936744 + 0.350016i \(0.113824\pi\)
\(252\) 0 0
\(253\) 10.8541 18.7999i 0.682392 1.18194i
\(254\) 2.70163 4.67935i 0.169515 0.293609i
\(255\) 1.09017 0.0682691
\(256\) −2.78115 + 4.81710i −0.173822 + 0.301069i
\(257\) −12.8713 22.2938i −0.802891 1.39065i −0.917706 0.397261i \(-0.869961\pi\)
0.114815 0.993387i \(-0.463373\pi\)
\(258\) 0.551663 + 0.955508i 0.0343450 + 0.0594873i
\(259\) 0 0
\(260\) −2.47871 + 0.613323i −0.153723 + 0.0380367i
\(261\) 11.6738 0.722588
\(262\) 0.0623059 + 0.107917i 0.00384927 + 0.00666713i
\(263\) −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i \(-0.256167\pi\)
−0.970758 + 0.240059i \(0.922833\pi\)
\(264\) −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
\(268\) −1.31308 −0.0802093
\(269\) 6.87132 11.9015i 0.418952 0.725646i −0.576882 0.816827i \(-0.695731\pi\)
0.995834 + 0.0911812i \(0.0290642\pi\)
\(270\) −0.163119 0.282530i −0.00992710 0.0171942i
\(271\) 9.20820 + 15.9491i 0.559359 + 0.968837i 0.997550 + 0.0699558i \(0.0222858\pi\)
−0.438192 + 0.898882i \(0.644381\pi\)
\(272\) −23.5066 −1.42530
\(273\) 0 0
\(274\) −0.145898 −0.00881402
\(275\) −11.7812 20.4056i −0.710430 1.23050i
\(276\) 1.58359 + 2.74286i 0.0953210 + 0.165101i
\(277\) 2.50000 4.33013i 0.150210 0.260172i −0.781094 0.624413i \(-0.785338\pi\)
0.931305 + 0.364241i \(0.118672\pi\)
\(278\) 5.94427 0.356514
\(279\) −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 \(-0.297226\pi\)
−0.993573 + 0.113190i \(0.963893\pi\)
\(284\) 7.58359 + 13.1352i 0.450003 + 0.779429i
\(285\) 0.708204 0.0419504
\(286\) 6.48936 1.60570i 0.383724 0.0949470i
\(287\) 0 0
\(288\) 5.91641 + 10.2475i 0.348628 + 0.603841i
\(289\) −19.4164 33.6302i −1.14214 1.97825i
\(290\) −0.298374 + 0.516799i −0.0175211 + 0.0303475i
\(291\) −4.63932 −0.271962
\(292\) 1.85410 3.21140i 0.108503 0.187933i
\(293\) −5.61803 + 9.73072i −0.328209 + 0.568475i −0.982157 0.188065i \(-0.939778\pi\)
0.653947 + 0.756540i \(0.273112\pi\)
\(294\) 0 0
\(295\) −0.427051 + 0.739674i −0.0248639 + 0.0430655i
\(296\) 2.94427 + 5.09963i 0.171132 + 0.296410i
\(297\) −5.42705 9.39993i −0.314909 0.545439i
\(298\) −1.85410 −0.107405
\(299\) 4.47214 15.4919i 0.258630 0.895922i
\(300\) 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
\(304\) −15.2705 −0.875824
\(305\) 1.14590 1.98475i 0.0656139 0.113647i
\(306\) −4.07295 + 7.05455i −0.232835 + 0.403282i
\(307\) −1.85410 −0.105819 −0.0529096 0.998599i \(-0.516850\pi\)
−0.0529096 + 0.998599i \(0.516850\pi\)
\(308\) 0 0
\(309\) 0.899187 + 1.55744i 0.0511530 + 0.0885995i
\(310\) −0.635255 1.10029i −0.0360801 0.0624925i
\(311\) 12.3262 0.698957 0.349478 0.936944i \(-0.386359\pi\)
0.349478 + 0.936944i \(0.386359\pi\)
\(312\) −0.562306 + 1.94788i −0.0318343 + 0.110277i
\(313\) 15.1246 0.854894 0.427447 0.904041i \(-0.359413\pi\)
0.427447 + 0.904041i \(0.359413\pi\)
\(314\) 1.55573 + 2.69460i 0.0877948 + 0.152065i
\(315\) 0 0
\(316\) 3.70820 6.42280i 0.208603 0.361311i
\(317\) 21.7639 1.22238 0.611192 0.791482i \(-0.290690\pi\)
0.611192 + 0.791482i \(0.290690\pi\)
\(318\) −0.600813 + 1.04064i −0.0336919 + 0.0583561i
\(319\) −9.92705 + 17.1942i −0.555808 + 0.962688i
\(320\) 1.79837 0.100532
\(321\) 1.07295 1.85840i 0.0598862 0.103726i
\(322\) 0 0
\(323\) −18.1353 31.4112i −1.00907 1.74776i
\(324\) −14.2918 −0.793989
\(325\) −12.1353 12.6113i −0.673143 0.699551i
\(326\) 3.70820 0.205378
\(327\) −2.04508 3.54219i −0.113093 0.195884i
\(328\) −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 −0.535925 0.844265i \(-0.680037\pi\)
0.999118 + 0.0419923i \(0.0133705\pi\)
\(332\) 6.21885 10.7714i 0.341304 0.591155i
\(333\) −11.4164 −0.625615
\(334\) 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 \(0.425077\pi\)
\(338\) 4.39261 2.31555i 0.238926 0.125949i
\(339\) −2.85410 −0.155014
\(340\) 2.64590 + 4.58283i 0.143494 + 0.248539i
\(341\) −21.1353 36.6073i −1.14454 1.98240i
\(342\) −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
\(346\) 3.43769 0.184812
\(347\) −17.6180 + 30.5153i −0.945786 + 1.63815i −0.191615 + 0.981470i \(0.561373\pi\)
−0.754171 + 0.656679i \(0.771961\pi\)
\(348\) −1.44834 2.50859i −0.0776390 0.134475i
\(349\) 3.64590 + 6.31488i 0.195160 + 0.338028i 0.946953 0.321372i \(-0.104144\pi\)
−0.751793 + 0.659400i \(0.770811\pi\)
\(350\) 0 0
\(351\) −5.59017 5.80948i −0.298381 0.310087i
\(352\) −20.1246 −1.07265
\(353\) 14.4271 + 24.9884i 0.767874 + 1.33000i 0.938713 + 0.344699i \(0.112019\pi\)
−0.170839 + 0.985299i \(0.554648\pi\)
\(354\) 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
\(359\) −10.9098 −0.575799 −0.287899 0.957661i \(-0.592957\pi\)
−0.287899 + 0.957661i \(0.592957\pi\)
\(360\) 0.802439 1.38987i 0.0422923 0.0732523i
\(361\) −2.28115 3.95107i −0.120061 0.207951i
\(362\) −0.708204 1.22665i −0.0372224 0.0644710i
\(363\) 4.79837 0.251849
\(364\) 0 0
\(365\) −0.763932 −0.0399860
\(366\) −0.437694 0.758108i −0.0228786 0.0396270i
\(367\) 12.7082 + 22.0113i 0.663363 + 1.14898i 0.979726 + 0.200340i \(0.0642047\pi\)
−0.316364 + 0.948638i \(0.602462\pi\)
\(368\) −7.03444 + 12.1840i −0.366696 + 0.635135i
\(369\) 14.9443 0.777968
\(370\) 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 −0.860304 0.509781i \(-0.829726\pi\)
0.871636 + 0.490155i \(0.163060\pi\)
\(374\) −6.92705 11.9980i −0.358189 0.620402i
\(375\) −0.718847 1.24508i −0.0371211 0.0642956i
\(376\) 3.29180 0.169761
\(377\) −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 \(0.726239\pi\)
\(380\) 1.71885 + 2.97713i 0.0881750 + 0.152724i
\(381\) 2.70163 4.67935i 0.138408 0.239731i
\(382\) 9.02129 0.461569
\(383\) 12.4894 21.6322i 0.638176 1.10535i −0.347656 0.937622i \(-0.613022\pi\)
0.985833 0.167732i \(-0.0536443\pi\)
\(384\) 1.92705 3.33775i 0.0983394 0.170329i
\(385\) 0 0
\(386\) 1.14590 1.98475i 0.0583247 0.101021i
\(387\) −10.7918 18.6919i −0.548578 0.950165i
\(388\) −11.2599 19.5027i −0.571633 0.990098i
\(389\) 23.8885 1.21120 0.605599 0.795770i \(-0.292934\pi\)
0.605599 + 0.795770i \(0.292934\pi\)
\(390\) 0.195048 0.0482619i 0.00987666 0.00244384i
\(391\) −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
\(395\) −1.52786 −0.0768752
\(396\) 12.8435 22.2455i 0.645408 1.11788i
\(397\) −12.7082 + 22.0113i −0.637806 + 1.10471i 0.348107 + 0.937455i \(0.386825\pi\)
−0.985913 + 0.167258i \(0.946509\pi\)
\(398\) −0.922986 −0.0462651
\(399\) 0 0
\(400\) 7.63525 + 13.2246i 0.381763 + 0.661232i
\(401\) 10.2254 + 17.7110i 0.510633 + 0.884443i 0.999924 + 0.0123222i \(0.00392237\pi\)
−0.489291 + 0.872121i \(0.662744\pi\)
\(402\) 0.103326 0.00515341
\(403\) −21.7705 22.6246i −1.08447 1.12701i
\(404\) 15.8754 0.789830
\(405\) 1.47214 + 2.54981i 0.0731510 + 0.126701i
\(406\) 0 0
\(407\) 9.70820 16.8151i 0.481218 0.833494i
\(408\) 4.20163 0.208011
\(409\) 17.2812 29.9318i 0.854498 1.48003i −0.0226119 0.999744i \(-0.507198\pi\)
0.877110 0.480290i \(-0.159468\pi\)
\(410\) −0.381966 + 0.661585i −0.0188640 + 0.0326733i
\(411\) −0.145898 −0.00719662
\(412\) −4.36475 + 7.55996i −0.215036 + 0.372453i
\(413\) 0 0
\(414\) 2.43769 + 4.22221i 0.119806 + 0.207510i
\(415\) −2.56231 −0.125779
\(416\) −14.5106 + 3.59045i −0.711443 + 0.176036i
\(417\) 5.94427 0.291092
\(418\) −4.50000 7.79423i −0.220102 0.381228i
\(419\) 2.97214 + 5.14789i 0.145198 + 0.251491i 0.929447 0.368956i \(-0.120285\pi\)
−0.784249 + 0.620447i \(0.786951\pi\)
\(420\) 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
\(423\) −3.19098 + 5.52694i −0.155151 + 0.268729i
\(424\) −12.1246 −0.588823
\(425\) −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
\(429\) 6.48936 1.60570i 0.313309 0.0775239i
\(430\) 1.10333 0.0532071
\(431\) 8.39919 + 14.5478i 0.404575 + 0.700744i 0.994272 0.106881i \(-0.0340863\pi\)
−0.589697 + 0.807624i \(0.700753\pi\)
\(432\) 3.51722 + 6.09201i 0.169222 + 0.293102i
\(433\) 0.500000 0.866025i 0.0240285 0.0416185i −0.853761 0.520665i \(-0.825684\pi\)
0.877790 + 0.479046i \(0.159017\pi\)
\(434\) 0 0
\(435\) −0.298374 + 0.516799i −0.0143059 + 0.0247786i
\(436\) 9.92705 17.1942i 0.475420 0.823451i
\(437\) −21.7082 −1.03844
\(438\) −0.145898 + 0.252703i −0.00697128 + 0.0120746i
\(439\) 4.07295 + 7.05455i 0.194391 + 0.336696i 0.946701 0.322114i \(-0.104394\pi\)
−0.752310 + 0.658810i \(0.771060\pi\)
\(440\) 1.36475 + 2.36381i 0.0650617 + 0.112690i
\(441\) 0 0
\(442\) −7.13525 7.41517i −0.339389 0.352704i
\(443\) −0.763932 −0.0362955 −0.0181478 0.999835i \(-0.505777\pi\)
−0.0181478 + 0.999835i \(0.505777\pi\)
\(444\) 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 \(0.932170\pi\)
\(450\) 5.29180 0.249458
\(451\) −12.7082 + 22.0113i −0.598406 + 1.03647i
\(452\) −6.92705 11.9980i −0.325821 0.564339i
\(453\) 2.80902 + 4.86536i 0.131979 + 0.228595i
\(454\) 2.85410 0.133950
\(455\) 0 0
\(456\) 2.72949 0.127820
\(457\) 5.70820 + 9.88690i 0.267019 + 0.462490i 0.968090 0.250601i \(-0.0806282\pi\)
−0.701072 + 0.713091i \(0.747295\pi\)
\(458\) 5.18034 + 8.97261i 0.242061 + 0.419263i
\(459\) −8.35410 + 14.4697i −0.389936 + 0.675389i
\(460\) 3.16718 0.147671
\(461\) 19.6074 33.9610i 0.913207 1.58172i 0.103702 0.994608i \(-0.466931\pi\)
0.809505 0.587113i \(-0.199736\pi\)
\(462\) 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
\(467\) −33.6525 −1.55725 −0.778625 0.627489i \(-0.784083\pi\)
−0.778625 + 0.627489i \(0.784083\pi\)
\(468\) 5.29180 18.3313i 0.244613 0.847366i
\(469\) 0 0
\(470\) −0.163119 0.282530i −0.00752412 0.0130322i
\(471\) 1.55573 + 2.69460i 0.0716842 + 0.124161i
\(472\) −1.64590 + 2.85078i −0.0757586 + 0.131218i
\(473\) 36.7082 1.68785
\(474\) −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
\(478\) 2.15654 + 3.73524i 0.0986379 + 0.170846i
\(479\) −10.9894 19.0341i −0.502117 0.869691i −0.999997 0.00244569i \(-0.999222\pi\)
0.497880 0.867246i \(-0.334112\pi\)
\(480\) −0.604878 −0.0276088
\(481\) 4.00000 13.8564i 0.182384 0.631798i
\(482\) −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
\(486\) 3.68692 0.167242
\(487\) 8.48936 14.7040i 0.384689 0.666302i −0.607037 0.794674i \(-0.707642\pi\)
0.991726 + 0.128372i \(0.0409752\pi\)
\(488\) 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 \(0.940332\pi\)
\(492\) −1.85410 3.21140i −0.0835894 0.144781i
\(493\) 30.5623 1.37646
\(494\) −4.63525 4.81710i −0.208550 0.216731i
\(495\) −5.29180 −0.237849
\(496\) 13.6976 + 23.7249i 0.615039 + 1.06528i
\(497\) 0 0
\(498\) −0.489357 + 0.847591i −0.0219286 + 0.0379815i
\(499\) 8.14590 0.364660 0.182330 0.983237i \(-0.441636\pi\)
0.182330 + 0.983237i \(0.441636\pi\)
\(500\) 3.48936 6.04374i 0.156049 0.270284i
\(501\) 1.86475 3.22983i 0.0833107 0.144298i
\(502\) −2.00000 −0.0892644
\(503\) 12.1910 21.1154i 0.543569 0.941489i −0.455126 0.890427i \(-0.650406\pi\)
0.998695 0.0510624i \(-0.0162607\pi\)
\(504\) 0 0
\(505\) −1.63525 2.83234i −0.0727679 0.126038i
\(506\) −8.29180 −0.368615
\(507\) 4.39261 2.31555i 0.195083 0.102837i
\(508\) 26.2279 1.16368
\(509\) 15.2984 + 26.4976i 0.678089 + 1.17448i 0.975556 + 0.219752i \(0.0705247\pi\)
−0.297467 + 0.954732i \(0.596142\pi\)
\(510\) −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
\(514\) −4.91641 + 8.51547i −0.216853 + 0.375601i
\(515\) 1.79837 0.0792458
\(516\) −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
\(520\) 1.40576 + 1.46091i 0.0616469 + 0.0640653i
\(521\) 12.6525 0.554315 0.277158 0.960824i \(-0.410608\pi\)
0.277158 + 0.960824i \(0.410608\pi\)
\(522\) −2.22949 3.86159i −0.0975821 0.169017i
\(523\) −19.5623 33.8829i −0.855400 1.48160i −0.876274 0.481814i \(-0.839978\pi\)
0.0208736 0.999782i \(-0.493355\pi\)
\(524\) −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
\(528\) −5.83282 −0.253841
\(529\) 1.50000 2.59808i 0.0652174 0.112960i
\(530\) 0.600813 + 1.04064i 0.0260977 + 0.0452025i
\(531\) −3.19098 5.52694i −0.138477 0.239849i
\(532\) 0 0
\(533\) −5.23607 + 18.1383i −0.226799 + 0.785656i
\(534\) −2.34752 −0.101587
\(535\) −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
\(541\) 1.72949 0.0743566 0.0371783 0.999309i \(-0.488163\pi\)
0.0371783 + 0.999309i \(0.488163\pi\)
\(542\) 3.51722 6.09201i 0.151078 0.261674i
\(543\) −0.708204 1.22665i −0.0303919 0.0526404i
\(544\) 15.4894 + 26.8284i 0.664101 + 1.15026i
\(545\) −4.09017 −0.175204
\(546\) 0 0
\(547\) −3.00000 −0.128271 −0.0641354 0.997941i \(-0.520429\pi\)
−0.0641354 + 0.997941i \(0.520429\pi\)
\(548\) −0.354102 0.613323i −0.0151265 0.0261998i
\(549\) 8.56231 + 14.8303i 0.365430 + 0.632944i
\(550\) −4.50000 + 7.79423i −0.191881 + 0.332347i
\(551\) 19.8541 0.845813
\(552\) 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 0.591899 0.806012i \(-0.298378\pi\)
−0.993976 + 0.109594i \(0.965045\pi\)
\(558\) 9.49342 0.401889
\(559\) 26.4681 6.54915i 1.11948 0.276999i
\(560\) 0 0
\(561\) −6.92705 11.9980i −0.292460 0.506556i
\(562\) 0.416408 + 0.721240i 0.0175651 + 0.0304237i
\(563\) −19.4721 + 33.7267i −0.820653 + 1.42141i 0.0845442 + 0.996420i \(0.473057\pi\)
−0.905197 + 0.424992i \(0.860277\pi\)
\(564\) 1.58359 0.0666813
\(565\) −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
\(569\) 1.47214 + 2.54981i 0.0617151 + 0.106894i 0.895232 0.445600i \(-0.147010\pi\)
−0.833517 + 0.552494i \(0.813676\pi\)
\(570\) −0.135255 0.234268i −0.00566521 0.00981242i
\(571\) −35.6869 −1.49345 −0.746726 0.665132i \(-0.768375\pi\)
−0.746726 + 0.665132i \(0.768375\pi\)
\(572\) 22.5000 + 23.3827i 0.940772 + 0.977679i
\(573\) 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
\(577\) −9.83282 −0.409345 −0.204673 0.978830i \(-0.565613\pi\)
−0.204673 + 0.978830i \(0.565613\pi\)
\(578\) −7.41641 + 12.8456i −0.308482 + 0.534306i
\(579\) 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
\(583\) 19.9894 + 34.6226i 0.827875 + 1.43392i
\(584\) −2.94427 −0.121835
\(585\) −3.81559 + 0.944115i −0.157755 + 0.0390343i
\(586\) 4.29180 0.177292
\(587\) −15.5451 26.9249i −0.641614 1.11131i −0.985072 0.172141i \(-0.944932\pi\)
0.343458 0.939168i \(-0.388402\pi\)
\(588\) 0 0
\(589\) −21.1353 + 36.6073i −0.870863 + 1.50838i
\(590\) 0.326238 0.0134310
\(591\) −1.48936 + 2.57964i −0.0612640 + 0.106112i
\(592\) −6.29180 + 10.8977i −0.258591 + 0.447893i
\(593\) −19.2016 −0.788516 −0.394258 0.919000i \(-0.628998\pi\)
−0.394258 + 0.919000i \(0.628998\pi\)
\(594\) −2.07295 + 3.59045i −0.0850541 + 0.147318i
\(595\) 0 0
\(596\) −4.50000 7.79423i −0.184327 0.319264i
\(597\) −0.922986 −0.0377753
\(598\) −5.97871 + 1.47935i −0.244488 + 0.0604950i
\(599\) −8.50658 −0.347569 −0.173785 0.984784i \(-0.555600\pi\)
−0.173785 + 0.984784i \(0.555600\pi\)
\(600\) −1.36475 2.36381i −0.0557155 0.0965021i
\(601\) −16.6976 28.9210i −0.681108 1.17971i −0.974643 0.223765i \(-0.928165\pi\)
0.293535 0.955948i \(-0.405168\pi\)
\(602\) 0 0
\(603\) −2.02129 −0.0823131
\(604\) −13.6353 + 23.6170i −0.554811 + 0.960960i
\(605\) 2.39919 4.15551i 0.0975408 0.168946i
\(606\) −1.24922 −0.0507462
\(607\) −11.5000 + 19.9186i −0.466771 + 0.808470i −0.999279 0.0379540i \(-0.987916\pi\)
0.532509 + 0.846424i \(0.321249\pi\)
\(608\) 10.0623 + 17.4284i 0.408080 + 0.706816i
\(609\) 0 0
\(610\) −0.875388 −0.0354434
\(611\) −5.59017 5.80948i −0.226154 0.235026i
\(612\) −39.5410 −1.59835
\(613\) −7.21885 12.5034i −0.291566 0.505008i 0.682614 0.730779i \(-0.260843\pi\)
−0.974180 + 0.225771i \(0.927510\pi\)
\(614\) 0.354102 + 0.613323i 0.0142904 + 0.0247517i
\(615\) −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
\(619\) 17.4164 0.700025 0.350012 0.936745i \(-0.386177\pi\)
0.350012 + 0.936745i \(0.386177\pi\)
\(620\) 3.08359 5.34094i 0.123840 0.214497i
\(621\) 5.00000 + 8.66025i 0.200643 + 0.347524i
\(622\) −2.35410 4.07742i −0.0943909 0.163490i
\(623\) 0 0
\(624\) −4.20569 + 1.04064i −0.168362 + 0.0416589i
\(625\) 22.8328 0.913313
\(626\) −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 \(-0.120233\pi\)
\(632\) −5.88854 −0.234234
\(633\) 1.66312 2.88061i 0.0661030 0.114494i
\(634\) −4.15654 7.19934i −0.165077 0.285922i
\(635\) −2.70163 4.67935i −0.107211 0.185694i
\(636\) −5.83282 −0.231286
\(637\) 0 0
\(638\) 7.58359 0.300237
\(639\) 11.6738 + 20.2195i 0.461807 + 0.799873i
\(640\) −1.92705 3.33775i −0.0761734 0.131936i
\(641\) 4.74671 8.22154i 0.187484 0.324731i −0.756927 0.653500i \(-0.773300\pi\)
0.944411 + 0.328768i \(0.106633\pi\)
\(642\) −0.819660 −0.0323494
\(643\) −3.50000 + 6.06218i −0.138027 + 0.239069i −0.926750 0.375680i \(-0.877409\pi\)
0.788723 + 0.614749i \(0.210743\pi\)
\(644\) 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 0.996075 + 0.0885157i \(0.0282123\pi\)
−0.421381 + 0.906884i \(0.638454\pi\)
\(648\) 5.67376 + 9.82724i 0.222886 + 0.386051i
\(649\) 10.8541 0.426061
\(650\) −1.85410 + 6.42280i −0.0727239 + 0.251923i
\(651\) 0 0
\(652\) 9.00000 + 15.5885i 0.352467 + 0.610491i
\(653\) 1.30902 + 2.26728i 0.0512258 + 0.0887257i 0.890501 0.454981i \(-0.150354\pi\)
−0.839275 + 0.543706i \(0.817021\pi\)
\(654\) −0.781153 + 1.35300i −0.0305455 + 0.0529064i
\(655\) 0.124612 0.00486899
\(656\) 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 \(0.241048\pi\)
\(660\) 0.656541 + 1.13716i 0.0255558 + 0.0442640i
\(661\) 9.27051 + 16.0570i 0.360581 + 0.624545i 0.988057 0.154092i \(-0.0492451\pi\)
−0.627476 + 0.778636i \(0.715912\pi\)
\(662\) −6.43769 −0.250208
\(663\) −7.13525 7.41517i −0.277110 0.287982i
\(664\) −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
\(668\) 18.1033 0.700439
\(669\) −2.53444 + 4.38978i −0.0979872 + 0.169719i
\(670\) 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 \(-0.459207\pi\)
\(674\) −1.63525 2.83234i −0.0629877 0.109098i
\(675\) 10.8541 0.417775
\(676\) 20.3951 + 12.8456i 0.784428 + 0.494061i
\(677\) −1.25735 −0.0483240 −0.0241620 0.999708i \(-0.507692\pi\)
−0.0241620 + 0.999708i \(0.507692\pi\)
\(678\) 0.545085 + 0.944115i 0.0209339 + 0.0362585i
\(679\) 0 0
\(680\) 2.10081 3.63871i 0.0805625 0.139538i
\(681\) 2.85410 0.109369
\(682\) −8.07295 + 13.9828i −0.309129 + 0.535427i
\(683\) 3.73607 6.47106i 0.142957 0.247608i −0.785652 0.618669i \(-0.787672\pi\)
0.928609 + 0.371060i \(0.121006\pi\)
\(684\) −25.6869 −0.982164
\(685\) −0.0729490 + 0.126351i −0.00278724 + 0.00482764i
\(686\) 0 0
\(687\) 5.18034 + 8.97261i 0.197642 + 0.342326i
\(688\) −23.7902 −0.906995
\(689\) 20.5902 + 21.3979i 0.784423 + 0.815196i
\(690\) −0.249224 −0.00948778
\(691\) 0.427051 + 0.739674i 0.0162458 + 0.0281385i 0.874034 0.485865i \(-0.161495\pi\)
−0.857788 + 0.514003i \(0.828162\pi\)
\(692\) 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
\(696\) −1.14996 + 1.99179i −0.0435892 + 0.0754988i
\(697\) 39.1246 1.48195
\(698\) 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 \(0.459229\pi\)
\(702\) −0.854102 + 2.95870i −0.0322360 + 0.111669i
\(703\) −19.4164 −0.732304
\(704\) −11.4271 19.7922i −0.430673 0.745948i
\(705\) −0.163119 0.282530i −0.00614342 0.0106407i
\(706\) 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 −0.896495 0.443053i \(-0.853895\pi\)
0.831943 + 0.554861i \(0.187229\pi\)
\(710\) −1.19350 −0.0447911
\(711\) 5.70820 9.88690i 0.214074 0.370788i
\(712\) −11.8435 20.5135i −0.443852 0.768775i
\(713\) 19.4721 + 33.7267i 0.729237 + 1.26308i
\(714\) 0 0
\(715\) 1.85410 6.42280i 0.0693395 0.240199i
\(716\) 16.6869 0.623619
\(717\) 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 0.393943 + 0.919135i \(0.371111\pi\)
−0.992966 + 0.118403i \(0.962222\pi\)
\(720\) 3.42956 0.127812
\(721\) 0 0
\(722\) −0.871323 + 1.50918i −0.0324273 + 0.0561657i
\(723\) −1.69505 −0.0630395
\(724\) 3.43769 5.95426i 0.127761 0.221288i
\(725\) −9.92705 17.1942i −0.368681 0.638575i
\(726\) −0.916408 1.58726i −0.0340111 0.0589089i
\(727\) 17.2918 0.641317 0.320659 0.947195i \(-0.396096\pi\)
0.320659 + 0.947195i \(0.396096\pi\)
\(728\) 0 0
\(729\) −19.4377 −0.719915
\(730\) 0.145898 + 0.252703i 0.00539993 + 0.00935295i
\(731\) −28.2533 48.9361i −1.04499 1.80997i
\(732\) 2.12461 3.67994i 0.0785279 0.136014i
\(733\) −1.27051 −0.0469274 −0.0234637 0.999725i \(-0.507469\pi\)
−0.0234637 + 0.999725i \(0.507469\pi\)
\(734\) 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 0.865296 + 0.501262i \(0.167131\pi\)
0.00145790 + 0.999999i \(0.499536\pi\)
\(740\) 2.83282 0.104136
\(741\) −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 \(0.976321\pi\)
\(744\) −2.44834 4.24064i −0.0897604 0.155470i
\(745\) −0.927051 + 1.60570i −0.0339645 + 0.0588283i
\(746\) −0.167184 −0.00612105
\(747\) 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
\(751\) −4.64590 8.04693i −0.169531 0.293637i 0.768724 0.639581i \(-0.220892\pi\)
−0.938255 + 0.345944i \(0.887559\pi\)
\(752\) 3.51722 + 6.09201i 0.128260 + 0.222153i
\(753\) −2.00000 −0.0728841
\(754\) 5.46807 1.35300i 0.199135 0.0492732i
\(755\) 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
\(759\) −8.29180 −0.300973
\(760\) 1.36475 2.36381i 0.0495045 0.0857443i
\(761\) −11.0729 + 19.1789i −0.401394 + 0.695235i −0.993894 0.110335i \(-0.964808\pi\)
0.592500 + 0.805570i \(0.298141\pi\)
\(762\) −2.06386 −0.0747657
\(763\) 0 0
\(764\) 21.8951 + 37.9235i 0.792138 + 1.37202i
\(765\) 4.07295 + 7.05455i 0.147258 + 0.255058i
\(766\) −9.54102 −0.344731
\(767\) 7.82624 1.93649i 0.282589 0.0699227i
\(768\) 2.12461 0.0766653
\(769\) 4.20820 + 7.28882i 0.151752 + 0.262842i 0.931872 0.362788i \(-0.118175\pi\)
−0.780120 + 0.625630i \(0.784842\pi\)
\(770\) 0 0
\(771\) −4.91641 + 8.51547i −0.177060 + 0.306677i
\(772\) 11.1246 0.400384
\(773\) −9.68034 + 16.7668i −0.348178 + 0.603061i −0.985926 0.167184i \(-0.946533\pi\)
0.637748 + 0.770245i \(0.279866\pi\)
\(774\) −4.12210 + 7.13969i −0.148166 + 0.256631i
\(775\) 42.2705 1.51840
\(776\) −8.94021 + 15.4849i −0.320935 + 0.555875i
\(777\) 0 0
\(778\) −4.56231 7.90215i −0.163567 0.283306i
\(779\) 25.4164 0.910637
\(780\) 0.676275 + 0.702805i 0.0242145 + 0.0251645i
\(781\) −39.7082