Properties

Label 91.2.f.a.29.2
Level $91$
Weight $2$
Character 91.29
Analytic conductor $0.727$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
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: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 29.2
Root \(-0.309017 - 0.535233i\) of defining polynomial
Character \(\chi\) \(=\) 91.29
Dual form 91.2.f.a.22.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.190983 - 0.330792i) q^{2} +(0.190983 + 0.330792i) q^{3} +(0.927051 - 1.60570i) q^{4} +0.381966 q^{5} +(0.0729490 - 0.126351i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.47214 q^{8} +(1.42705 - 2.47172i) q^{9} +O(q^{10})\) \(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} +(-0.500000 + 0.866025i) q^{7} -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} +0.381966 q^{14} +(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} -0.381966 q^{21} +(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} +(0.927051 + 1.60570i) q^{28} +(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} +(-0.190983 + 0.330792i) q^{35} +(-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} +(0.0729490 + 0.126351i) q^{42} +(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} +(-0.500000 - 0.866025i) q^{49} +(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} +(0.736068 - 1.27491i) q^{56} -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} +(1.42705 + 2.47172i) q^{63} -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} +0.145898 q^{70} +(-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} -4.85410 q^{77} +(-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} +(-0.354102 + 0.613323i) q^{84} +(-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} +(3.50000 - 0.866025i) q^{91} -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} +(-0.190983 + 0.330792i) q^{98} +13.8541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 3q^{2} + 3q^{3} - 3q^{4} + 6q^{5} + 7q^{6} - 2q^{7} + 12q^{8} - q^{9} + O(q^{10}) \) \( 4q - 3q^{2} + 3q^{3} - 3q^{4} + 6q^{5} + 7q^{6} - 2q^{7} + 12q^{8} - q^{9} - 7q^{10} + 3q^{11} - 24q^{12} - 10q^{13} + 6q^{14} + 7q^{15} - 13q^{16} - 6q^{17} + 18q^{18} - 3q^{19} - 12q^{20} - 6q^{21} - 3q^{22} + 19q^{24} - 6q^{25} - 6q^{26} - 3q^{28} - 3q^{29} + 18q^{30} + 8q^{31} - 15q^{32} + 3q^{33} - 2q^{34} - 3q^{35} - 24q^{36} - 8q^{37} - 6q^{38} + 6q^{39} + 38q^{40} - 6q^{41} + 7q^{42} - 5q^{43} + 36q^{44} - 9q^{45} + 10q^{46} + 27q^{48} - 2q^{49} - 3q^{50} + 2q^{51} + 21q^{52} + 24q^{53} + 5q^{54} - 3q^{55} - 6q^{56} + 6q^{57} - 17q^{58} - 66q^{60} + 12q^{61} + 9q^{62} - q^{63} + 8q^{64} - 15q^{65} - 24q^{66} + 12q^{67} + 21q^{68} - 10q^{69} + 14q^{70} + 6q^{71} - 33q^{72} - 8q^{73} - 12q^{74} + 3q^{75} + 18q^{76} - 6q^{77} - 49q^{78} + 16q^{79} - 27q^{80} - 2q^{81} - 4q^{82} + 12q^{84} + q^{85} + 60q^{86} + 17q^{87} - 21q^{88} - 21q^{89} + 52q^{90} + 14q^{91} - 60q^{92} - 9q^{93} + 5q^{94} + 3q^{95} - 60q^{96} - 31q^{97} - 3q^{98} + 42q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 0.915877 0.401460i \(-0.131497\pi\)
−0.805613 + 0.592443i \(0.798164\pi\)
\(4\) 0.927051 1.60570i 0.463525 0.802850i
\(5\) 0.381966 0.170820 0.0854102 0.996346i \(-0.472780\pi\)
0.0854102 + 0.996346i \(0.472780\pi\)
\(6\) 0.0729490 0.126351i 0.0297813 0.0515827i
\(7\) −0.500000 + 0.866025i −0.188982 + 0.327327i
\(8\) −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
\(14\) 0.381966 0.102085
\(15\) 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 \(0.527644\pi\)
−0.819394 + 0.573231i \(0.805690\pi\)
\(18\) −1.09017 −0.256956
\(19\) −2.42705 + 4.20378i −0.556804 + 0.964412i 0.440957 + 0.897528i \(0.354639\pi\)
−0.997761 + 0.0668841i \(0.978694\pi\)
\(20\) 0.354102 0.613323i 0.0791796 0.137143i
\(21\) −0.381966 −0.0833518
\(22\) 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
\(28\) 0.927051 + 1.60570i 0.175196 + 0.303449i
\(29\) 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 \(-0.214190\pi\)
0.782020 + 0.623254i \(0.214190\pi\)
\(32\) −2.07295 + 3.59045i −0.366449 + 0.634708i
\(33\) −0.927051 + 1.60570i −0.161379 + 0.279516i
\(34\) 2.85410 0.489474
\(35\) −0.190983 + 0.330792i −0.0322820 + 0.0559141i
\(36\) −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 0.585895 0.810387i \(-0.300743\pi\)
−0.994763 + 0.102206i \(0.967410\pi\)
\(42\) 0.0729490 + 0.126351i 0.0112563 + 0.0194964i
\(43\) 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 \(-0.447856\pi\)
0.163082 + 0.986613i \(0.447856\pi\)
\(48\) 0.600813 1.04064i 0.0867199 0.150203i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) 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
\(56\) 0.736068 1.27491i 0.0983612 0.170367i
\(57\) −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 \(-0.879830\pi\)
0.784024 + 0.620730i \(0.213164\pi\)
\(60\) 0.270510 0.0349227
\(61\) 3.00000 5.19615i 0.384111 0.665299i −0.607535 0.794293i \(-0.707841\pi\)
0.991645 + 0.128994i \(0.0411748\pi\)
\(62\) −1.66312 2.88061i −0.211216 0.365837i
\(63\) 1.42705 + 2.47172i 0.179792 + 0.311408i
\(64\) −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
\(70\) 0.145898 0.0174382
\(71\) −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 \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −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
\(77\) −4.85410 −0.553176
\(78\) −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 \(-0.620012\pi\)
−0.368161 + 0.929762i \(0.620012\pi\)
\(84\) −0.354102 + 0.613323i −0.0386357 + 0.0669190i
\(85\) −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 \(-0.841583\pi\)
0.0259145 0.999664i \(-0.491750\pi\)
\(90\) −0.416408 −0.0438932
\(91\) 3.50000 0.866025i 0.366900 0.0907841i
\(92\) −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 \(0.378163\pi\)
−0.990099 + 0.140371i \(0.955170\pi\)
\(98\) −0.190983 + 0.330792i −0.0192922 + 0.0334151i
\(99\) 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 \(-0.306741\pi\)
−0.996512 + 0.0834451i \(0.973408\pi\)
\(102\) 0.545085 + 0.944115i 0.0539715 + 0.0934813i
\(103\) 4.70820 0.463913 0.231957 0.972726i \(-0.425487\pi\)
0.231957 + 0.972726i \(0.425487\pi\)
\(104\) 3.68034 + 3.82472i 0.360887 + 0.375045i
\(105\) −0.145898 −0.0142382
\(106\) −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
\(112\) 3.14590 0.297259
\(113\) 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
\(119\) −3.73607 6.47106i −0.342485 0.593201i
\(120\) −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
\(126\) 0.545085 0.944115i 0.0485600 0.0841084i
\(127\) 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 \(-0.495463\pi\)
0.0142518 + 0.999898i \(0.495463\pi\)
\(132\) 1.71885 + 2.97713i 0.149606 + 0.259126i
\(133\) −2.42705 4.20378i −0.210452 0.364514i
\(134\) −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 \(-0.603894\pi\)
0.980618 0.195929i \(-0.0627723\pi\)
\(140\) 0.354102 + 0.613323i 0.0299271 + 0.0518352i
\(141\) 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
\(147\) 0.190983 0.330792i 0.0157520 0.0272833i
\(148\) −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
\(154\) 0.927051 + 1.60570i 0.0747039 + 0.129391i
\(155\) 3.32624 0.267170
\(156\) −1.77051 1.83997i −0.141754 0.147315i
\(157\) 8.14590 0.650113 0.325057 0.945695i \(-0.394617\pi\)
0.325057 + 0.945695i \(0.394617\pi\)
\(158\) −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
\(161\) 4.47214 0.352454
\(162\) −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 0.612961 0.790113i \(-0.289978\pi\)
−0.990739 + 0.135783i \(0.956645\pi\)
\(168\) 0.562306 0.0433828
\(169\) −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 \(-0.722185\pi\)
0.984828 + 0.173534i \(0.0555188\pi\)
\(174\) 0.596748 0.0452393
\(175\) 2.42705 4.20378i 0.183468 0.317776i
\(176\) 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 \(-0.544008\pi\)
−0.137814 + 0.990458i \(0.544008\pi\)
\(182\) −0.954915 0.992377i −0.0707830 0.0735599i
\(183\) 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
\(189\) −1.11803 + 1.93649i −0.0813250 + 0.140859i
\(190\) 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
\(196\) −1.85410 −0.132436
\(197\) −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 −0.905667 0.423990i \(-0.860629\pi\)
0.820020 + 0.572336i \(0.193962\pi\)
\(200\) 7.14590 0.505291
\(201\) 0.135255 0.234268i 0.00954015 0.0165240i
\(202\) −1.63525 + 2.83234i −0.115056 + 0.199283i
\(203\) −4.09017 −0.287074
\(204\) −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
\(210\) 0.0278640 + 0.0482619i 0.00192280 + 0.00333039i
\(211\) 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
\(217\) −4.35410 + 7.54153i −0.295576 + 0.511952i
\(218\) −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 \(-0.0201086\pi\)
−0.553676 + 0.832732i \(0.686775\pi\)
\(224\) −2.07295 3.59045i −0.138505 0.239897i
\(225\) −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 \(-0.753569\pi\)
0.962963 + 0.269634i \(0.0869027\pi\)
\(228\) −1.71885 + 2.97713i −0.113833 + 0.197165i
\(229\) 27.1246 1.79244 0.896222 0.443605i \(-0.146301\pi\)
0.896222 + 0.443605i \(0.146301\pi\)
\(230\) −0.326238 + 0.565061i −0.0215115 + 0.0372590i
\(231\) −0.927051 1.60570i −0.0609955 0.105647i
\(232\) −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
\(238\) −1.42705 + 2.47172i −0.0925020 + 0.160218i
\(239\) −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 \(-0.878985\pi\)
0.785670 + 0.618646i \(0.212319\pi\)
\(242\) 4.79837 0.308451
\(243\) 4.82624 8.35929i 0.309603 0.536249i
\(244\) −5.56231 9.63420i −0.356090 0.616766i
\(245\) −0.190983 0.330792i −0.0122015 0.0211335i
\(246\) −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 \(-0.886176\pi\)
0.771495 + 0.636236i \(0.219509\pi\)
\(252\) 5.29180 0.333352
\(253\) 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 \(0.130039\pi\)
−0.114815 + 0.993387i \(0.536627\pi\)
\(258\) −0.551663 0.955508i −0.0343450 0.0594873i
\(259\) 4.00000 0.248548
\(260\) −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
\(266\) −0.927051 + 1.60570i −0.0568411 + 0.0984517i
\(267\) 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 \(-0.970936\pi\)
0.576882 + 0.816827i \(0.304269\pi\)
\(270\) −0.163119 0.282530i −0.00992710 0.0171942i
\(271\) −9.20820 15.9491i −0.559359 0.968837i −0.997550 0.0699558i \(-0.977714\pi\)
0.438192 0.898882i \(-0.355619\pi\)
\(272\) 23.5066 1.42530
\(273\) 0.954915 + 0.992377i 0.0577941 + 0.0600614i
\(274\) −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
\(280\) 0.281153 0.486971i 0.0168021 0.0291021i
\(281\) −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 \(-0.0361069\pi\)
−0.594812 + 0.803865i \(0.702774\pi\)
\(284\) 7.58359 + 13.1352i 0.450003 + 0.779429i
\(285\) −0.708204 −0.0419504
\(286\) −6.48936 + 1.60570i −0.383724 + 0.0949470i
\(287\) 5.23607 0.309075
\(288\) 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 \(-0.726888\pi\)
0.982157 + 0.188065i \(0.0602216\pi\)
\(294\) −0.145898 −0.00850895
\(295\) −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
\(301\) 3.78115 + 6.54915i 0.217942 + 0.377487i
\(302\) 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 \(-0.483150\pi\)
0.0529096 + 0.998599i \(0.483150\pi\)
\(308\) −4.50000 + 7.79423i −0.256411 + 0.444117i
\(309\) 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 \(-0.613641\pi\)
−0.349478 + 0.936944i \(0.613641\pi\)
\(312\) −0.562306 + 1.94788i −0.0318343 + 0.110277i
\(313\) −15.1246 −0.854894 −0.427447 0.904041i \(-0.640587\pi\)
−0.427447 + 0.904041i \(0.640587\pi\)
\(314\) −1.55573 2.69460i −0.0877948 0.152065i
\(315\) 0.545085 + 0.944115i 0.0307121 + 0.0531948i
\(316\) 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
\(322\) −0.854102 1.47935i −0.0475972 0.0824408i
\(323\) −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
\(329\) −1.11803 + 1.93649i −0.0616392 + 0.106762i
\(330\) 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
\(336\) 0.600813 + 1.04064i 0.0327770 + 0.0567715i
\(337\) 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
\(343\) 1.00000 0.0539949
\(344\) −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 0.751793 0.659400i \(-0.229189\pi\)
−0.946953 + 0.321372i \(0.895856\pi\)
\(350\) −1.85410 −0.0991059
\(351\) −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 \(-0.887981\pi\)
0.170839 0.985299i \(-0.445352\pi\)
\(354\) 0.163119 + 0.282530i 0.00866967 + 0.0150163i
\(355\) −1.56231 + 2.70599i −0.0829186 + 0.143619i
\(356\) −29.8328 −1.58114
\(357\) 1.42705 2.47172i 0.0755275 0.130818i
\(358\) 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
\(364\) 1.85410 6.42280i 0.0971813 0.336646i
\(365\) −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 \(-0.935795\pi\)
0.316364 0.948638i \(-0.397538\pi\)
\(368\) −7.03444 + 12.1840i −0.366696 + 0.635135i
\(369\) −14.9443 −0.777968
\(370\) −0.291796 + 0.505406i −0.0151698 + 0.0262748i
\(371\) −4.11803 + 7.13264i −0.213798 + 0.370308i
\(372\) 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
\(378\) 0.854102 0.0439303
\(379\) 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 \(0.386978\pi\)
−0.985833 + 0.167732i \(0.946356\pi\)
\(384\) −1.92705 + 3.33775i −0.0983394 + 0.170329i
\(385\) −1.85410 −0.0944938
\(386\) 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
\(392\) 0.736068 + 1.27491i 0.0371770 + 0.0643925i
\(393\) 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 \(-0.613175\pi\)
0.985913 0.167258i \(-0.0534914\pi\)
\(398\) 0.922986 0.0462651
\(399\) 0.927051 1.60570i 0.0464106 0.0803855i
\(400\) 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
\(406\) 0.781153 + 1.35300i 0.0387680 + 0.0671481i
\(407\) 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 \(0.492802\pi\)
−0.877110 + 0.480290i \(0.840532\pi\)
\(410\) −0.381966 + 0.661585i −0.0188640 + 0.0326733i
\(411\) 0.145898 0.00719662
\(412\) 4.36475 7.55996i 0.215036 0.372453i
\(413\) −1.11803 1.93649i −0.0550149 0.0952885i
\(414\) 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 \(-0.213049\pi\)
−0.929447 + 0.368956i \(0.879715\pi\)
\(420\) −0.135255 + 0.234268i −0.00659976 + 0.0114311i
\(421\) −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
\(427\) 3.00000 + 5.19615i 0.145180 + 0.251459i
\(428\) 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 −0.877790 0.479046i \(-0.840983\pi\)
0.853761 + 0.520665i \(0.174316\pi\)
\(434\) 3.32624 0.159665
\(435\) −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 \(-0.228940\pi\)
−0.946701 + 0.322114i \(0.895606\pi\)
\(440\) −1.36475 2.36381i −0.0650617 0.112690i
\(441\) −2.85410 −0.135910
\(442\) −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
\(448\) 2.35410 4.07742i 0.111221 0.192640i
\(449\) −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
\(455\) 1.33688 0.330792i 0.0626739 0.0155078i
\(456\) 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 \(0.533069\pi\)
−0.809505 + 0.587113i \(0.800264\pi\)
\(462\) −0.354102 + 0.613323i −0.0164743 + 0.0285343i
\(463\) −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 \(-0.215917\pi\)
0.778625 + 0.627489i \(0.215917\pi\)
\(468\) −5.29180 + 18.3313i −0.244613 + 0.847366i
\(469\) 0.708204 0.0327018
\(470\) −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
\(476\) −13.8541 −0.635002
\(477\) 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 \(0.000778487\pi\)
−0.497880 + 0.867246i \(0.665888\pi\)
\(480\) −0.604878 −0.0276088
\(481\) −4.00000 + 13.8564i −0.182384 + 0.631798i
\(482\) 1.69505 0.0772073
\(483\) 0.854102 + 1.47935i 0.0388630 + 0.0673127i
\(484\) 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
\(490\) −0.0729490 + 0.126351i −0.00329550 + 0.00570797i
\(491\) −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
\(497\) −4.09017 7.08438i −0.183469 0.317778i
\(498\) −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 \(0.349594\pi\)
−0.998695 + 0.0510624i \(0.983739\pi\)
\(504\) −2.10081 3.63871i −0.0935777 0.162081i
\(505\) −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 \(-0.929475\pi\)
0.297467 0.954732i \(-0.403858\pi\)
\(510\) 0.208204 + 0.360620i 0.00921943 + 0.0159685i
\(511\) 1.00000 1.73205i 0.0442374 0.0766214i
\(512\) 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
\(518\) −0.763932 1.32317i −0.0335652 0.0581367i
\(519\) 3.43769 0.150898
\(520\) 1.40576 + 1.46091i 0.0616469 + 0.0640653i
\(521\) −12.6525 −0.554315 −0.277158 0.960824i \(-0.589392\pi\)
−0.277158 + 0.960824i \(0.589392\pi\)
\(522\) −2.22949 3.86159i −0.0975821 0.169017i
\(523\) 19.5623 + 33.8829i 0.855400 + 1.48160i 0.876274 + 0.481814i \(0.160022\pi\)
−0.0208736 + 0.999782i \(0.506645\pi\)
\(524\) 0.302439 0.523840i 0.0132121 0.0228841i
\(525\) 1.85410 0.0809196
\(526\) −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
\(532\) −9.00000 −0.390199
\(533\) −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
\(539\) 2.42705 4.20378i 0.104540 0.181069i
\(540\) 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
\(546\) 0.145898 0.505406i 0.00624386 0.0216294i
\(547\) −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
\(553\) −2.00000 + 3.46410i −0.0850487 + 0.147309i
\(554\) −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
\(560\) 1.20163 0.0507780
\(561\) −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 \(-0.526943\pi\)
0.905197 0.424992i \(-0.139723\pi\)
\(564\) 1.58359 0.0666813
\(565\) 1.42705 2.47172i 0.0600365 0.103986i
\(566\) 2.56231 4.43804i 0.107702 0.186545i
\(567\) 7.70820 0.323714
\(568\) 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
\(574\) −1.00000 1.73205i −0.0417392 0.0722944i
\(575\) 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 \(-0.434387\pi\)
0.204673 + 0.978830i \(0.434387\pi\)
\(578\) −7.41641 + 12.8456i −0.308482 + 0.534306i
\(579\) −1.14590 + 1.98475i −0.0476219 + 0.0824835i
\(580\) 2.89667 0.120278
\(581\) 3.35410 5.80948i 0.139152 0.241018i
\(582\) 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 \(0.0550683\pi\)
−0.343458 + 0.939168i \(0.611598\pi\)
\(588\) −0.354102 0.613323i −0.0146029 0.0252930i
\(589\) −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 \(-0.371002\pi\)
0.394258 + 0.919000i \(0.371002\pi\)
\(594\) 2.07295 3.59045i 0.0850541 0.147318i
\(595\) −1.42705 2.47172i −0.0585034 0.101331i
\(596\) −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 \(0.0718348\pi\)
−0.293535 + 0.955948i \(0.594832\pi\)
\(602\) 1.44427 2.50155i 0.0588641 0.101956i
\(603\) −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 \(-0.678751\pi\)
0.999279 + 0.0379540i \(0.0120840\pi\)
\(608\) −10.0623 17.4284i −0.408080 0.706816i
\(609\) −0.781153 1.35300i −0.0316539 0.0548262i
\(610\) −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
\(616\) 7.14590 0.287916
\(617\) −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 \(-0.613823\pi\)
−0.350012 + 0.936745i \(0.613823\pi\)
\(620\) 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
\(623\) 16.0902 0.644639
\(624\) −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
\(630\) 0.208204 0.360620i 0.00829504 0.0143674i
\(631\) 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
\(637\) −1.00000 + 3.46410i −0.0396214 + 0.137253i
\(638\) 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 −0.788723 0.614749i \(-0.789257\pi\)
0.926750 + 0.375680i \(0.122591\pi\)
\(644\) 4.14590 7.18091i 0.163371 0.282967i
\(645\) 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 \(-0.971788\pi\)
0.421381 0.906884i \(-0.361546\pi\)
\(648\) 5.67376 + 9.82724i 0.222886 + 0.386051i
\(649\) −10.8541 −0.426061
\(650\) 1.85410 6.42280i 0.0727239 0.251923i
\(651\) −3.32624 −0.130366
\(652\) 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
\(658\) 0.854102 0.0332964
\(659\) −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 0.627476 0.778636i \(-0.284088\pi\)
−0.988057 + 0.154092i \(0.950755\pi\)
\(662\) −6.43769 −0.250208
\(663\) 7.13525 + 7.41517i 0.277110 + 0.287982i
\(664\) 9.87539 0.383239
\(665\) −0.927051 1.60570i −0.0359495 0.0622664i
\(666\) 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
\(672\) 0.791796 1.37143i 0.0305442 0.0529041i
\(673\) −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 \(-0.492308\pi\)
0.0241620 + 0.999708i \(0.492308\pi\)
\(678\) −0.545085 0.944115i −0.0209339 0.0362585i
\(679\) −6.07295 10.5187i −0.233058 0.403669i
\(680\) 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
\(686\) −0.190983 0.330792i −0.00729177 0.0126297i
\(687\) 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 \(-0.171838\pi\)
−0.874034 + 0.485865i \(0.838505\pi\)
\(692\) −8.34346 14.4513i −0.317171 0.549356i
\(693\) −6.92705 + 11.9980i −0.263137 + 0.455766i
\(694\) 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
\(700\) −4.50000 7.79423i −0.170084 0.294594i
\(701\) 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
\(707\) 8.56231 0.322019
\(708\) −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
\(714\) −1.09017 −0.0407986
\(715\) 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 \(-0.628889\pi\)
0.992966 0.118403i \(-0.0377775\pi\)
\(720\) −3.42956 −0.127812
\(721\) −2.35410 + 4.07742i −0.0876713 + 0.151851i
\(722\) −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 \(-0.603904\pi\)
−0.320659 + 0.947195i \(0.603904\pi\)
\(728\) −5.15248 + 1.27491i −0.190963 + 0.0472512i
\(729\) −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 \(-0.492531\pi\)
0.0234637 + 0.999725i \(0.492531\pi\)
\(734\) −4.85410 + 8.40755i −0.179168 + 0.310328i
\(735\) 0.0729490 0.126351i 0.00269077 0.00466054i
\(736\) 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
\(742\) 3.14590 0.115490
\(743\) −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
\(749\) −5.61803 −0.205278
\(750\) −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
\(756\) 2.07295 + 3.59045i 0.0753924 + 0.130584i
\(757\) −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 −0.592500 0.805570i \(-0.701859\pi\)
0.993894 + 0.110335i \(0.0351925\pi\)
\(762\) 2.06386 0.0747657
\(763\) −5.35410 + 9.27358i −0.193832 + 0.335726i
\(764\) 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 \(-0.215158\pi\)
−0.931872 + 0.362788i \(0.881825\pi\)
\(770\) 0.354102 + 0.613323i 0.0127609 + 0.0221026i
\(771\) −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 \(-0.720134\pi\)
0.985926 + 0.167184i \(0.0534673\pi\)
\(774\) −4.12210 + 7.13969i −0.148166 + 0.256631i
\(775\) −42.2705 −1.51840
\(776\) 8.94021