Properties

Label 637.2.f.c.295.2
Level $637$
Weight $2$
Character 637.295
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 295.2
Root \(-0.309017 + 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 637.295
Dual form 637.2.f.c.393.2

$q$-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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 7 q^{6} + 12 q^{8} - q^{9} + O(q^{10}) \) \( 4 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 6 q^{5} - 7 q^{6} + 12 q^{8} - q^{9} + 7 q^{10} + 3 q^{11} + 24 q^{12} + 10 q^{13} + 7 q^{15} - 13 q^{16} + 6 q^{17} + 18 q^{18} + 3 q^{19} + 12 q^{20} - 3 q^{22} - 19 q^{24} - 6 q^{25} + 6 q^{26} - 3 q^{29} + 18 q^{30} - 8 q^{31} - 15 q^{32} - 3 q^{33} + 2 q^{34} - 24 q^{36} - 8 q^{37} + 6 q^{38} + 6 q^{39} - 38 q^{40} + 6 q^{41} - 5 q^{43} + 36 q^{44} + 9 q^{45} + 10 q^{46} - 27 q^{48} - 3 q^{50} + 2 q^{51} - 21 q^{52} + 24 q^{53} - 5 q^{54} + 3 q^{55} + 6 q^{57} - 17 q^{58} - 66 q^{60} - 12 q^{61} - 9 q^{62} + 8 q^{64} - 15 q^{65} + 24 q^{66} + 12 q^{67} - 21 q^{68} + 10 q^{69} + 6 q^{71} - 33 q^{72} + 8 q^{73} - 12 q^{74} - 3 q^{75} - 18 q^{76} - 49 q^{78} + 16 q^{79} + 27 q^{80} - 2 q^{81} + 4 q^{82} + q^{85} + 60 q^{86} - 17 q^{87} - 21 q^{88} + 21 q^{89} - 52 q^{90} - 60 q^{92} - 9 q^{93} - 5 q^{94} + 3 q^{95} + 60 q^{96} + 31 q^{97} + 42 q^{99} + O(q^{100}) \)

Character values

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

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

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 −0.925615 0.378467i \(-0.876451\pi\)
0.790569 + 0.612372i \(0.209785\pi\)
\(3\) −0.190983 + 0.330792i −0.110264 + 0.190983i −0.915877 0.401460i \(-0.868503\pi\)
0.805613 + 0.592443i \(0.201836\pi\)
\(4\) 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 −0.224337 0.974512i \(-0.572022\pi\)
0.956120 0.292974i \(-0.0946451\pi\)
\(12\) −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 0.819394 + 0.573231i \(0.194310\pi\)
0.0867359 + 0.996231i \(0.472356\pi\)
\(18\) −1.09017 −0.256956
\(19\) 2.42705 + 4.20378i 0.556804 + 0.964412i 0.997761 + 0.0668841i \(0.0213058\pi\)
−0.440957 + 0.897528i \(0.645361\pi\)
\(20\) −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 −0.999257 0.0385394i \(-0.987729\pi\)
0.533005 + 0.846112i \(0.321063\pi\)
\(24\) 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 −0.611265 0.791426i \(-0.709339\pi\)
0.991028 + 0.133658i \(0.0426723\pi\)
\(30\) 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 −0.982274 0.187453i \(-0.939977\pi\)
0.653476 + 0.756948i \(0.273310\pi\)
\(38\) −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 −0.585895 0.810387i \(-0.699257\pi\)
0.994763 + 0.102206i \(0.0325902\pi\)
\(42\) 0 0
\(43\) 3.78115 + 6.54915i 0.576620 + 0.998736i 0.995864 + 0.0908618i \(0.0289622\pi\)
−0.419243 + 0.907874i \(0.637704\pi\)
\(44\) 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 0.929580 0.368620i \(-0.120170\pi\)
−0.784024 + 0.620730i \(0.786836\pi\)
\(60\) 0.270510 0.0349227
\(61\) −3.00000 5.19615i −0.384111 0.665299i 0.607535 0.794293i \(-0.292159\pi\)
−0.991645 + 0.128994i \(0.958825\pi\)
\(62\) 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 −0.886845 0.462067i \(-0.847108\pi\)
0.843584 + 0.536997i \(0.180441\pi\)
\(68\) −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 0.514446 0.857523i \(-0.327998\pi\)
−0.999860 + 0.0167615i \(0.994664\pi\)
\(72\) −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 −0.0259145 0.999664i \(-0.508250\pi\)
0.878692 0.477389i \(-0.158417\pi\)
\(90\) 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 0.990099 + 0.140371i \(0.0448296\pi\)
−0.373484 + 0.927636i \(0.621837\pi\)
\(98\) 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 −0.570522 0.821283i \(-0.693259\pi\)
0.996512 + 0.0834451i \(0.0265923\pi\)
\(102\) 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 −0.697703 0.716387i \(-0.745794\pi\)
0.969261 + 0.246035i \(0.0791278\pi\)
\(108\) −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 0.986505 0.163728i \(-0.0523521\pi\)
−0.635046 + 0.772475i \(0.719019\pi\)
\(114\) 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 −0.360405 0.932796i \(-0.617361\pi\)
0.988027 0.154278i \(-0.0493053\pi\)
\(128\) 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 0.874069 0.485803i \(-0.161473\pi\)
−0.857752 + 0.514064i \(0.828139\pi\)
\(138\) 0.652476 0.0555424
\(139\) −7.78115 13.4774i −0.659989 1.14313i −0.980618 0.195929i \(-0.937228\pi\)
0.320629 0.947205i \(-0.396106\pi\)
\(140\) 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 0.948150 0.317823i \(-0.102952\pi\)
−0.749318 + 0.662210i \(0.769619\pi\)
\(150\) 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 0.610888 0.791717i \(-0.290812\pi\)
−0.991091 + 0.133186i \(0.957479\pi\)
\(164\) 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 −0.612961 0.790113i \(-0.710022\pi\)
0.990739 + 0.135783i \(0.0433550\pi\)
\(168\) 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 0.642699 0.766119i \(-0.277815\pi\)
−0.984828 + 0.173534i \(0.944481\pi\)
\(174\) −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 −0.647397 0.762153i \(-0.724142\pi\)
0.983742 + 0.179585i \(0.0574756\pi\)
\(180\) 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 −0.877135 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 \(0.0973836\pi\)
\(194\) −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 −0.970839 0.239732i \(-0.922940\pi\)
0.693034 + 0.720905i \(0.256274\pi\)
\(198\) −2.64590 + 4.58283i −0.188036 + 0.325688i
\(199\) 1.20820 + 2.09267i 0.0856473 + 0.148345i 0.905667 0.423990i \(-0.139371\pi\)
−0.820020 + 0.572336i \(0.806038\pi\)
\(200\) 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 −0.676330 0.736599i \(-0.736430\pi\)
0.976078 + 0.217419i \(0.0697638\pi\)
\(212\) 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 −0.998005 0.0631310i \(-0.979891\pi\)
0.553676 + 0.832732i \(0.313225\pi\)
\(224\) 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 0.714991 0.699133i \(-0.246431\pi\)
−0.962963 + 0.269634i \(0.913097\pi\)
\(228\) −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 0.928598 0.371087i \(-0.121015\pi\)
−0.785670 + 0.618646i \(0.787681\pi\)
\(242\) 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 0.936744 0.350016i \(-0.113824\pi\)
−0.771495 + 0.636236i \(0.780491\pi\)
\(252\) 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 0.114815 + 0.993387i \(0.463373\pi\)
−0.917706 + 0.397261i \(0.869961\pi\)
\(258\) 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 −0.970758 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
\(268\) −1.31308 −0.0802093
\(269\) 6.87132 + 11.9015i 0.418952 + 0.725646i 0.995834 0.0911812i \(-0.0290642\pi\)
−0.576882 + 0.816827i \(0.695731\pi\)
\(270\) −0.163119 + 0.282530i −0.00992710 + 0.0171942i
\(271\) 9.20820 15.9491i 0.559359 0.968837i −0.438192 0.898882i \(-0.644381\pi\)
0.997550 0.0699558i \(-0.0222858\pi\)
\(272\) −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 0.931305 0.364241i \(-0.118672\pi\)
−0.781094 + 0.624413i \(0.785338\pi\)
\(278\) 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 −0.993573 0.113190i \(-0.963893\pi\)
0.594812 + 0.803865i \(0.297226\pi\)
\(284\) 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 0.653947 0.756540i \(-0.273112\pi\)
−0.982157 + 0.188065i \(0.939778\pi\)
\(294\) 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 0.999118 0.0419923i \(-0.0133705\pi\)
−0.535925 + 0.844265i \(0.680037\pi\)
\(332\) 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 −0.754171 0.656679i \(-0.771961\pi\)
−0.191615 0.981470i \(-0.561373\pi\)
\(348\) −1.44834 + 2.50859i −0.0776390 + 0.134475i
\(349\) 3.64590 6.31488i 0.195160 0.338028i −0.751793 0.659400i \(-0.770811\pi\)
0.946953 + 0.321372i \(0.104144\pi\)
\(350\) 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 −0.170839 0.985299i \(-0.554648\pi\)
0.938713 0.344699i \(-0.112019\pi\)
\(354\) 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 −0.316364 0.948638i \(-0.602462\pi\)
0.979726 0.200340i \(-0.0642047\pi\)
\(368\) −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 0.871636 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
\(376\) 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 −0.652403 0.757872i \(-0.726239\pi\)
0.982538 + 0.186061i \(0.0595722\pi\)
\(380\) 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 0.985833 + 0.167732i \(0.0536443\pi\)
−0.347656 + 0.937622i \(0.613022\pi\)
\(384\) 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 −0.985913 0.167258i \(-0.946509\pi\)
0.348107 0.937455i \(-0.386825\pi\)
\(398\) −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 −0.489291 0.872121i \(-0.662744\pi\)
0.999924 0.0123222i \(-0.00392237\pi\)
\(402\) 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 0.877110 + 0.480290i \(0.159468\pi\)
−0.0226119 + 0.999744i \(0.507198\pi\)
\(410\) −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 −0.784249 0.620447i \(-0.786951\pi\)
0.929447 + 0.368956i \(0.120285\pi\)
\(420\) 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 −0.589697 0.807624i \(-0.700753\pi\)
0.994272 + 0.106881i \(0.0340863\pi\)
\(432\) 3.51722 6.09201i 0.169222 0.293102i
\(433\) 0.500000 + 0.866025i 0.0240285 + 0.0416185i 0.877790 0.479046i \(-0.159017\pi\)
−0.853761 + 0.520665i \(0.825684\pi\)
\(434\) 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 −0.752310 0.658810i \(-0.771060\pi\)
0.946701 + 0.322114i \(0.104394\pi\)
\(440\) 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 −0.977381 0.211484i \(-0.932170\pi\)
0.305540 0.952179i \(-0.401163\pi\)
\(450\) 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 −0.701072 0.713091i \(-0.747295\pi\)
0.968090 + 0.250601i \(0.0806282\pi\)
\(458\) 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 0.809505 + 0.587113i \(0.199736\pi\)
0.103702 + 0.994608i \(0.466931\pi\)
\(462\) 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 0.497880 + 0.867246i \(0.334112\pi\)
−0.999997 + 0.00244569i \(0.999222\pi\)
\(480\) −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 0.991726 0.128372i \(-0.0409752\pi\)
−0.607037 + 0.794674i \(0.707642\pi\)
\(488\) 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 −0.982482 0.186357i \(-0.940332\pi\)
0.652631 + 0.757676i \(0.273665\pi\)
\(492\) −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 0.998695 + 0.0510624i \(0.0162607\pi\)
−0.455126 + 0.890427i \(0.650406\pi\)
\(504\) 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 −0.297467 0.954732i \(-0.596142\pi\)
0.975556 0.219752i \(-0.0705247\pi\)
\(510\) −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 0.0208736 + 0.999782i \(0.493355\pi\)
−0.876274 + 0.481814i \(0.839978\pi\)
\(524\) −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 −0.993976 0.109594i \(-0.965045\pi\)
0.591899 + 0.806012i \(0.298378\pi\)
\(558\) 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 −0.905197 0.424992i \(-0.860277\pi\)
0.0845442 0.996420i \(-0.473057\pi\)
\(564\) 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 −0.833517 0.552494i \(-0.813676\pi\)
0.895232 + 0.445600i \(0.147010\pi\)
\(570\) −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 0.343458 + 0.939168i \(0.388402\pi\)
−0.985072 + 0.172141i \(0.944932\pi\)
\(588\) 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 0.293535 + 0.955948i \(0.405168\pi\)
−0.974643 + 0.223765i \(0.928165\pi\)
\(602\) 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 0.532509 0.846424i \(-0.321249\pi\)
−0.999279 + 0.0379540i \(0.987916\pi\)
\(608\) 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 −0.974180 0.225771i \(-0.927510\pi\)
0.682614 + 0.730779i \(0.260843\pi\)
\(614\) 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 0.626955 0.779056i \(-0.284301\pi\)
−0.988159 + 0.153431i \(0.950968\pi\)
\(618\) 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 0.929507 + 0.368804i \(0.120233\pi\)
−0.145360 + 0.989379i \(0.546434\pi\)
\(632\) −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 0.944411 0.328768i \(-0.106633\pi\)
−0.756927 + 0.653500i \(0.773300\pi\)
\(642\) −0.819660 −0.0323494
\(643\) −3.50000 6.06218i −0.138027 0.239069i 0.788723 0.614749i \(-0.210743\pi\)
−0.926750 + 0.375680i \(0.877409\pi\)
\(644\) 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 \(-0.638454\pi\)
0.996075 0.0885157i \(-0.0282123\pi\)
\(648\) 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 −0.839275 0.543706i \(-0.817021\pi\)
0.890501 + 0.454981i \(0.150354\pi\)
\(654\) −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 0.726710 0.686944i \(-0.241048\pi\)
−0.958266 + 0.285877i \(0.907715\pi\)
\(660\) 0.656541 1.13716i 0.0255558 0.0442640i
\(661\) 9.27051 16.0570i 0.360581 0.624545i −0.627476 0.778636i \(-0.715912\pi\)
0.988057 + 0.154092i \(0.0492451\pi\)
\(662\) −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 0.127806 + 0.991799i \(0.459207\pi\)
−0.922826 + 0.385216i \(0.874127\pi\)
\(674\) −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 0.928609 0.371060i \(-0.121006\pi\)
−0.785652 + 0.618669i \(0.787672\pi\)
\(684\) −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 −0.857788 0.514003i \(-0.828162\pi\)
0.874034 + 0.485865i \(0.161495\pi\)
\(692\) 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 0.831943 0.554861i \(-0.187229\pi\)
−0.896495 + 0.443053i \(0.853895\pi\)
\(710\) −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 −0.992966 0.118403i \(-0.962222\pi\)
0.393943 0.919135i \(-0.371111\pi\)
\(720\) 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 0.00145790 0.999999i \(-0.499536\pi\)
0.865296 0.501262i \(-0.167131\pi\)
\(740\) 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 −0.997234 0.0743213i \(-0.976321\pi\)
0.562981 + 0.826470i \(0.309654\pi\)
\(744\) −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 −0.938255 0.345944i \(-0.887559\pi\)
0.768724 + 0.639581i \(0.220892\pi\)
\(752\) 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 0.491109 + 0.871098i \(0.336592\pi\)
−0.999948 + 0.0102362i \(0.996742\pi\)
\(758\) 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 0.592500 0.805570i \(-0.298141\pi\)
−0.993894 + 0.110335i \(0.964808\pi\)
\(762\) −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 −0.780120 0.625630i \(-0.784842\pi\)
0.931872 + 0.362788i \(0.118175\pi\)
\(770\) 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 0.637748 0.770245i \(-0.279866\pi\)
−0.985926 + 0.167184i \(0.946533\pi\)
\(774\) −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