Properties

Label 349.2.e.a.123.20
Level 349
Weight 2
Character 349.123
Analytic conductor 2.787
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 349.e (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.78677903054\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 123.20
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.20

$q$-expansion

\(f(q)\) \(=\) \(q+(0.831968 - 0.480337i) q^{2} +(-1.62465 + 2.81397i) q^{3} +(-0.538552 + 0.932800i) q^{4} +(-1.69786 + 2.94079i) q^{5} +3.12152i q^{6} +(3.20576 - 1.85085i) q^{7} +2.95610i q^{8} +(-3.77897 - 6.54537i) q^{9} +O(q^{10})\) \(q+(0.831968 - 0.480337i) q^{2} +(-1.62465 + 2.81397i) q^{3} +(-0.538552 + 0.932800i) q^{4} +(-1.69786 + 2.94079i) q^{5} +3.12152i q^{6} +(3.20576 - 1.85085i) q^{7} +2.95610i q^{8} +(-3.77897 - 6.54537i) q^{9} +3.26219i q^{10} -2.98370i q^{11} +(-1.74992 - 3.03095i) q^{12} +(-3.77890 + 2.18175i) q^{13} +(1.77806 - 3.07969i) q^{14} +(-5.51687 - 9.55550i) q^{15} +(0.342818 + 0.593778i) q^{16} +6.34956 q^{17} +(-6.28797 - 3.63036i) q^{18} +(-0.995395 + 1.72407i) q^{19} +(-1.82878 - 3.16754i) q^{20} +12.0279i q^{21} +(-1.43318 - 2.48235i) q^{22} +(1.30287 + 2.25663i) q^{23} +(-8.31838 - 4.80262i) q^{24} +(-3.26549 - 5.65599i) q^{25} +(-2.09595 + 3.63029i) q^{26} +14.8101 q^{27} +3.98711i q^{28} +(-3.93778 + 6.82043i) q^{29} +(-9.17972 - 5.29991i) q^{30} -3.57639 q^{31} +(-4.54968 - 2.62676i) q^{32} +(8.39607 + 4.84747i) q^{33} +(5.28263 - 3.04993i) q^{34} +12.5700i q^{35} +8.14069 q^{36} +1.15990 q^{37} +1.91250i q^{38} -14.1783i q^{39} +(-8.69325 - 5.01905i) q^{40} -1.68052 q^{41} +(5.77745 + 10.0068i) q^{42} +(1.19553 + 0.690240i) q^{43} +(2.78320 + 1.60688i) q^{44} +25.6647 q^{45} +(2.16789 + 1.25163i) q^{46} +8.06563i q^{47} -2.22783 q^{48} +(3.35128 - 5.80458i) q^{49} +(-5.43357 - 3.13707i) q^{50} +(-10.3158 + 17.8675i) q^{51} -4.69995i q^{52} -4.74099i q^{53} +(12.3215 - 7.11384i) q^{54} +(8.77444 + 5.06593i) q^{55} +(5.47128 + 9.47654i) q^{56} +(-3.23433 - 5.60203i) q^{57} +7.56584i q^{58} +(6.75038 + 3.89733i) q^{59} +11.8845 q^{60} -11.6094i q^{61} +(-2.97545 + 1.71787i) q^{62} +(-24.2290 - 13.9886i) q^{63} -6.41819 q^{64} -14.8173i q^{65} +9.31368 q^{66} -8.07146 q^{67} +(-3.41957 + 5.92287i) q^{68} -8.46681 q^{69} +(6.03782 + 10.4578i) q^{70} +(-5.22205 + 3.01495i) q^{71} +(19.3487 - 11.1710i) q^{72} +(0.280564 - 0.485951i) q^{73} +(0.965003 - 0.557145i) q^{74} +21.2211 q^{75} +(-1.07214 - 1.85701i) q^{76} +(-5.52238 - 9.56505i) q^{77} +(-6.81037 - 11.7959i) q^{78} +9.98474i q^{79} -2.32823 q^{80} +(-12.7243 + 22.0392i) q^{81} +(-1.39814 + 0.807217i) q^{82} +(8.50963 + 14.7391i) q^{83} +(-11.2196 - 6.47766i) q^{84} +(-10.7807 + 18.6727i) q^{85} +1.32619 q^{86} +(-12.7950 - 22.1616i) q^{87} +8.82011 q^{88} +(14.0692 + 8.12287i) q^{89} +(21.3522 - 12.3277i) q^{90} +(-8.07617 + 13.9883i) q^{91} -2.80665 q^{92} +(5.81038 - 10.0639i) q^{93} +(3.87422 + 6.71035i) q^{94} +(-3.38009 - 5.85449i) q^{95} +(14.7833 - 8.53512i) q^{96} +(-1.72586 + 0.996423i) q^{97} -6.43897i q^{98} +(-19.5294 + 11.2753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} + O(q^{10}) \) \( 58q - 3q^{2} + 27q^{4} + 2q^{5} - 29q^{9} - q^{12} - 3q^{13} - 10q^{14} + q^{15} - 29q^{16} - 10q^{17} + 15q^{18} - 9q^{19} - 3q^{22} - 17q^{23} - 48q^{24} - 29q^{25} - 4q^{26} + 18q^{27} - 2q^{29} + 9q^{30} + 32q^{31} + 9q^{32} - 12q^{33} - 63q^{34} + 24q^{36} - 16q^{37} + 54q^{40} - 10q^{41} - 15q^{42} - 45q^{43} + 18q^{44} - 2q^{45} + 27q^{46} + 6q^{48} + 35q^{49} + 6q^{50} - 14q^{51} + 27q^{54} + 24q^{55} + 11q^{56} - 29q^{57} - 18q^{59} + 116q^{60} - 9q^{62} - 21q^{63} - 132q^{64} + 130q^{66} + 58q^{67} + 42q^{69} + 40q^{70} - 24q^{71} + 72q^{72} - 6q^{73} + 30q^{74} - 58q^{75} + 37q^{76} - 4q^{77} - 33q^{78} - 40q^{80} - 81q^{81} + 21q^{82} + 12q^{83} + 18q^{84} - 11q^{85} - 126q^{86} - 42q^{87} - 50q^{88} + 3q^{89} - 12q^{90} - 28q^{91} - 120q^{92} + 31q^{93} + 29q^{94} + 60q^{95} - 120q^{96} - 15q^{97} + 39q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/349\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.831968 0.480337i 0.588290 0.339650i −0.176131 0.984367i \(-0.556358\pi\)
0.764421 + 0.644717i \(0.223025\pi\)
\(3\) −1.62465 + 2.81397i −0.937992 + 1.62465i −0.168781 + 0.985654i \(0.553983\pi\)
−0.769210 + 0.638996i \(0.779350\pi\)
\(4\) −0.538552 + 0.932800i −0.269276 + 0.466400i
\(5\) −1.69786 + 2.94079i −0.759308 + 1.31516i 0.183896 + 0.982946i \(0.441129\pi\)
−0.943204 + 0.332215i \(0.892204\pi\)
\(6\) 3.12152i 1.27435i
\(7\) 3.20576 1.85085i 1.21166 0.699555i 0.248543 0.968621i \(-0.420048\pi\)
0.963122 + 0.269066i \(0.0867150\pi\)
\(8\) 2.95610i 1.04514i
\(9\) −3.77897 6.54537i −1.25966 2.18179i
\(10\) 3.26219i 1.03160i
\(11\) 2.98370i 0.899621i −0.893124 0.449810i \(-0.851492\pi\)
0.893124 0.449810i \(-0.148508\pi\)
\(12\) −1.74992 3.03095i −0.505158 0.874959i
\(13\) −3.77890 + 2.18175i −1.04808 + 0.605108i −0.922111 0.386926i \(-0.873537\pi\)
−0.125968 + 0.992034i \(0.540204\pi\)
\(14\) 1.77806 3.07969i 0.475207 0.823083i
\(15\) −5.51687 9.55550i −1.42445 2.46722i
\(16\) 0.342818 + 0.593778i 0.0857044 + 0.148444i
\(17\) 6.34956 1.53999 0.769997 0.638048i \(-0.220258\pi\)
0.769997 + 0.638048i \(0.220258\pi\)
\(18\) −6.28797 3.63036i −1.48209 0.855684i
\(19\) −0.995395 + 1.72407i −0.228359 + 0.395530i −0.957322 0.289024i \(-0.906669\pi\)
0.728963 + 0.684553i \(0.240003\pi\)
\(20\) −1.82878 3.16754i −0.408927 0.708283i
\(21\) 12.0279i 2.62471i
\(22\) −1.43318 2.48235i −0.305556 0.529238i
\(23\) 1.30287 + 2.25663i 0.271667 + 0.470541i 0.969289 0.245925i \(-0.0790918\pi\)
−0.697622 + 0.716466i \(0.745758\pi\)
\(24\) −8.31838 4.80262i −1.69798 0.980330i
\(25\) −3.26549 5.65599i −0.653098 1.13120i
\(26\) −2.09595 + 3.63029i −0.411050 + 0.711959i
\(27\) 14.8101 2.85021
\(28\) 3.98711i 0.753494i
\(29\) −3.93778 + 6.82043i −0.731227 + 1.26652i 0.225132 + 0.974328i \(0.427719\pi\)
−0.956359 + 0.292194i \(0.905615\pi\)
\(30\) −9.17972 5.29991i −1.67598 0.967628i
\(31\) −3.57639 −0.642339 −0.321170 0.947022i \(-0.604076\pi\)
−0.321170 + 0.947022i \(0.604076\pi\)
\(32\) −4.54968 2.62676i −0.804278 0.464350i
\(33\) 8.39607 + 4.84747i 1.46157 + 0.843836i
\(34\) 5.28263 3.04993i 0.905964 0.523058i
\(35\) 12.5700i 2.12471i
\(36\) 8.14069 1.35678
\(37\) 1.15990 0.190687 0.0953434 0.995444i \(-0.469605\pi\)
0.0953434 + 0.995444i \(0.469605\pi\)
\(38\) 1.91250i 0.310249i
\(39\) 14.1783i 2.27035i
\(40\) −8.69325 5.01905i −1.37452 0.793582i
\(41\) −1.68052 −0.262453 −0.131227 0.991352i \(-0.541892\pi\)
−0.131227 + 0.991352i \(0.541892\pi\)
\(42\) 5.77745 + 10.0068i 0.891480 + 1.54409i
\(43\) 1.19553 + 0.690240i 0.182317 + 0.105261i 0.588381 0.808584i \(-0.299766\pi\)
−0.406064 + 0.913845i \(0.633099\pi\)
\(44\) 2.78320 + 1.60688i 0.419583 + 0.242246i
\(45\) 25.6647 3.82587
\(46\) 2.16789 + 1.25163i 0.319638 + 0.184543i
\(47\) 8.06563i 1.17649i 0.808681 + 0.588247i \(0.200182\pi\)
−0.808681 + 0.588247i \(0.799818\pi\)
\(48\) −2.22783 −0.321560
\(49\) 3.35128 5.80458i 0.478754 0.829226i
\(50\) −5.43357 3.13707i −0.768422 0.443649i
\(51\) −10.3158 + 17.8675i −1.44450 + 2.50195i
\(52\) 4.69995i 0.651765i
\(53\) 4.74099i 0.651225i −0.945503 0.325613i \(-0.894429\pi\)
0.945503 0.325613i \(-0.105571\pi\)
\(54\) 12.3215 7.11384i 1.67675 0.968071i
\(55\) 8.77444 + 5.06593i 1.18315 + 0.683089i
\(56\) 5.47128 + 9.47654i 0.731131 + 1.26636i
\(57\) −3.23433 5.60203i −0.428398 0.742007i
\(58\) 7.56584i 0.993444i
\(59\) 6.75038 + 3.89733i 0.878825 + 0.507390i 0.870271 0.492574i \(-0.163944\pi\)
0.00855397 + 0.999963i \(0.497277\pi\)
\(60\) 11.8845 1.53428
\(61\) 11.6094i 1.48643i −0.669053 0.743215i \(-0.733300\pi\)
0.669053 0.743215i \(-0.266700\pi\)
\(62\) −2.97545 + 1.71787i −0.377882 + 0.218170i
\(63\) −24.2290 13.9886i −3.05256 1.76240i
\(64\) −6.41819 −0.802274
\(65\) 14.8173i 1.83786i
\(66\) 9.31368 1.14644
\(67\) −8.07146 −0.986086 −0.493043 0.870005i \(-0.664115\pi\)
−0.493043 + 0.870005i \(0.664115\pi\)
\(68\) −3.41957 + 5.92287i −0.414684 + 0.718253i
\(69\) −8.46681 −1.01928
\(70\) 6.03782 + 10.4578i 0.721657 + 1.24995i
\(71\) −5.22205 + 3.01495i −0.619743 + 0.357809i −0.776769 0.629786i \(-0.783143\pi\)
0.157026 + 0.987594i \(0.449809\pi\)
\(72\) 19.3487 11.1710i 2.28027 1.31651i
\(73\) 0.280564 0.485951i 0.0328376 0.0568763i −0.849140 0.528169i \(-0.822879\pi\)
0.881977 + 0.471292i \(0.156212\pi\)
\(74\) 0.965003 0.557145i 0.112179 0.0647667i
\(75\) 21.2211 2.45040
\(76\) −1.07214 1.85701i −0.122983 0.213014i
\(77\) −5.52238 9.56505i −0.629334 1.09004i
\(78\) −6.81037 11.7959i −0.771122 1.33562i
\(79\) 9.98474i 1.12337i 0.827351 + 0.561685i \(0.189847\pi\)
−0.827351 + 0.561685i \(0.810153\pi\)
\(80\) −2.32823 −0.260304
\(81\) −12.7243 + 22.0392i −1.41381 + 2.44880i
\(82\) −1.39814 + 0.807217i −0.154399 + 0.0891422i
\(83\) 8.50963 + 14.7391i 0.934054 + 1.61783i 0.776313 + 0.630348i \(0.217088\pi\)
0.157741 + 0.987481i \(0.449579\pi\)
\(84\) −11.2196 6.47766i −1.22416 0.706771i
\(85\) −10.7807 + 18.6727i −1.16933 + 2.02534i
\(86\) 1.32619 0.143007
\(87\) −12.7950 22.1616i −1.37177 2.37597i
\(88\) 8.82011 0.940227
\(89\) 14.0692 + 8.12287i 1.49134 + 0.861023i 0.999951 0.00992010i \(-0.00315772\pi\)
0.491384 + 0.870943i \(0.336491\pi\)
\(90\) 21.3522 12.3277i 2.25072 1.29946i
\(91\) −8.07617 + 13.9883i −0.846613 + 1.46638i
\(92\) −2.80665 −0.292614
\(93\) 5.81038 10.0639i 0.602509 1.04358i
\(94\) 3.87422 + 6.71035i 0.399596 + 0.692120i
\(95\) −3.38009 5.85449i −0.346790 0.600658i
\(96\) 14.7833 8.53512i 1.50881 0.871113i
\(97\) −1.72586 + 0.996423i −0.175234 + 0.101171i −0.585052 0.810996i \(-0.698926\pi\)
0.409817 + 0.912168i \(0.365592\pi\)
\(98\) 6.43897i 0.650434i
\(99\) −19.5294 + 11.2753i −1.96278 + 1.13321i
\(100\) 7.03455 0.703455
\(101\) 6.98452i 0.694986i −0.937683 0.347493i \(-0.887033\pi\)
0.937683 0.347493i \(-0.112967\pi\)
\(102\) 19.8203i 1.96250i
\(103\) 6.03173i 0.594324i −0.954827 0.297162i \(-0.903960\pi\)
0.954827 0.297162i \(-0.0960402\pi\)
\(104\) −6.44946 11.1708i −0.632422 1.09539i
\(105\) −35.3715 20.4218i −3.45191 1.99296i
\(106\) −2.27727 3.94435i −0.221188 0.383110i
\(107\) 12.3967 7.15725i 1.19844 0.691917i 0.238229 0.971209i \(-0.423433\pi\)
0.960206 + 0.279292i \(0.0900997\pi\)
\(108\) −7.97602 + 13.8149i −0.767493 + 1.32934i
\(109\) −1.77911 + 3.08150i −0.170407 + 0.295154i −0.938562 0.345110i \(-0.887842\pi\)
0.768155 + 0.640264i \(0.221175\pi\)
\(110\) 9.73341 0.928044
\(111\) −1.88444 + 3.26394i −0.178863 + 0.309799i
\(112\) 2.19798 + 1.26901i 0.207690 + 0.119910i
\(113\) 3.07564 1.77572i 0.289332 0.167046i −0.348309 0.937380i \(-0.613244\pi\)
0.637640 + 0.770334i \(0.279911\pi\)
\(114\) −5.38173 3.10714i −0.504045 0.291011i
\(115\) −8.84837 −0.825115
\(116\) −4.24140 7.34632i −0.393804 0.682088i
\(117\) 28.5607 + 16.4895i 2.64044 + 1.52446i
\(118\) 7.48814 0.689339
\(119\) 20.3552 11.7521i 1.86596 1.07731i
\(120\) 28.2470 16.3084i 2.57858 1.48875i
\(121\) 2.09751 0.190683
\(122\) −5.57642 9.65864i −0.504865 0.874452i
\(123\) 2.73026 4.72894i 0.246179 0.426394i
\(124\) 1.92607 3.33606i 0.172967 0.299587i
\(125\) 5.19879 0.464994
\(126\) −26.8770 −2.39439
\(127\) 9.40171i 0.834267i −0.908845 0.417133i \(-0.863035\pi\)
0.908845 0.417133i \(-0.136965\pi\)
\(128\) 3.75963 2.17062i 0.332307 0.191858i
\(129\) −3.88464 + 2.24280i −0.342023 + 0.197467i
\(130\) −7.11728 12.3275i −0.624227 1.08119i
\(131\) 5.17156i 0.451842i 0.974146 + 0.225921i \(0.0725391\pi\)
−0.974146 + 0.225921i \(0.927461\pi\)
\(132\) −9.04344 + 5.22124i −0.787131 + 0.454450i
\(133\) 7.36930i 0.638999i
\(134\) −6.71520 + 3.87702i −0.580105 + 0.334924i
\(135\) −25.1456 + 43.5534i −2.16418 + 3.74848i
\(136\) 18.7699i 1.60951i
\(137\) 5.02311 + 2.90009i 0.429153 + 0.247772i 0.698986 0.715136i \(-0.253635\pi\)
−0.269833 + 0.962907i \(0.586968\pi\)
\(138\) −7.04412 + 4.06692i −0.599635 + 0.346200i
\(139\) 7.79745 0.661371 0.330686 0.943741i \(-0.392720\pi\)
0.330686 + 0.943741i \(0.392720\pi\)
\(140\) −11.7253 6.76958i −0.990965 0.572134i
\(141\) −22.6965 13.1038i −1.91139 1.10354i
\(142\) −2.89638 + 5.01668i −0.243059 + 0.420991i
\(143\) 6.50969 + 11.2751i 0.544368 + 0.942873i
\(144\) 2.59100 4.48774i 0.215916 0.373978i
\(145\) −13.3716 23.1603i −1.11045 1.92336i
\(146\) 0.539062i 0.0446131i
\(147\) 10.8893 + 18.8608i 0.898134 + 1.55561i
\(148\) −0.624669 + 1.08196i −0.0513474 + 0.0889364i
\(149\) 14.5454 8.39778i 1.19160 0.687973i 0.232934 0.972493i \(-0.425167\pi\)
0.958670 + 0.284519i \(0.0918340\pi\)
\(150\) 17.6553 10.1933i 1.44155 0.832278i
\(151\) −2.57957 + 4.46794i −0.209922 + 0.363596i −0.951690 0.307061i \(-0.900654\pi\)
0.741768 + 0.670657i \(0.233988\pi\)
\(152\) −5.09653 2.94248i −0.413383 0.238667i
\(153\) −23.9948 41.5602i −1.93986 3.35994i
\(154\) −9.18889 5.30521i −0.740462 0.427506i
\(155\) 6.07223 10.5174i 0.487733 0.844779i
\(156\) 13.2255 + 7.63576i 1.05889 + 0.611350i
\(157\) −2.00905 + 3.47977i −0.160339 + 0.277716i −0.934990 0.354673i \(-0.884592\pi\)
0.774651 + 0.632389i \(0.217926\pi\)
\(158\) 4.79604 + 8.30698i 0.381552 + 0.660868i
\(159\) 13.3410 + 7.70245i 1.05801 + 0.610844i
\(160\) 15.4495 8.91976i 1.22139 0.705169i
\(161\) 8.35337 + 4.82282i 0.658338 + 0.380092i
\(162\) 24.4478i 1.92080i
\(163\) 3.05996i 0.239674i 0.992794 + 0.119837i \(0.0382372\pi\)
−0.992794 + 0.119837i \(0.961763\pi\)
\(164\) 0.905048 1.56759i 0.0706724 0.122408i
\(165\) −28.5108 + 16.4607i −2.21956 + 1.28146i
\(166\) 14.1595 + 8.17499i 1.09899 + 0.634502i
\(167\) 17.7853i 1.37627i 0.725582 + 0.688135i \(0.241570\pi\)
−0.725582 + 0.688135i \(0.758430\pi\)
\(168\) −35.5557 −2.74318
\(169\) 3.02006 5.23090i 0.232312 0.402377i
\(170\) 20.7135i 1.58865i
\(171\) 15.0463 1.15062
\(172\) −1.28771 + 0.743461i −0.0981871 + 0.0566884i
\(173\) 2.60333 1.50303i 0.197927 0.114273i −0.397761 0.917489i \(-0.630213\pi\)
0.595688 + 0.803216i \(0.296879\pi\)
\(174\) −21.2901 12.2918i −1.61400 0.931842i
\(175\) −20.9368 12.0878i −1.58267 0.913755i
\(176\) 1.77166 1.02287i 0.133544 0.0771015i
\(177\) −21.9340 + 12.6636i −1.64866 + 0.951854i
\(178\) 15.6069 1.16978
\(179\) 1.30236i 0.0973426i −0.998815 0.0486713i \(-0.984501\pi\)
0.998815 0.0486713i \(-0.0154987\pi\)
\(180\) −13.8218 + 23.9401i −1.03022 + 1.78439i
\(181\) 4.32195 0.321248 0.160624 0.987016i \(-0.448649\pi\)
0.160624 + 0.987016i \(0.448649\pi\)
\(182\) 15.5171i 1.15021i
\(183\) 32.6685 + 18.8612i 2.41493 + 1.39426i
\(184\) −6.67082 + 3.85140i −0.491780 + 0.283929i
\(185\) −1.96936 + 3.41103i −0.144790 + 0.250784i
\(186\) 11.1638i 0.818567i
\(187\) 18.9452i 1.38541i
\(188\) −7.52362 4.34377i −0.548717 0.316802i
\(189\) 47.4777 27.4113i 3.45349 1.99388i
\(190\) −5.62426 3.24717i −0.408027 0.235574i
\(191\) 7.32468 + 12.6867i 0.529995 + 0.917979i 0.999388 + 0.0349890i \(0.0111396\pi\)
−0.469392 + 0.882990i \(0.655527\pi\)
\(192\) 10.4273 18.0606i 0.752526 1.30341i
\(193\) 0.826017 + 0.476901i 0.0594580 + 0.0343281i 0.529434 0.848351i \(-0.322404\pi\)
−0.469976 + 0.882679i \(0.655738\pi\)
\(194\) −0.957238 + 1.65799i −0.0687257 + 0.119036i
\(195\) 41.6954 + 24.0729i 2.98587 + 1.72389i
\(196\) 3.60968 + 6.25214i 0.257834 + 0.446581i
\(197\) −14.6402 8.45255i −1.04307 0.602219i −0.122372 0.992484i \(-0.539050\pi\)
−0.920703 + 0.390265i \(0.872383\pi\)
\(198\) −10.8319 + 18.7614i −0.769791 + 1.33332i
\(199\) 7.82396 4.51717i 0.554626 0.320213i −0.196360 0.980532i \(-0.562912\pi\)
0.750986 + 0.660318i \(0.229579\pi\)
\(200\) 16.7197 9.65310i 1.18226 0.682577i
\(201\) 13.1133 22.7129i 0.924940 1.60204i
\(202\) −3.35493 5.81090i −0.236052 0.408854i
\(203\) 29.1529i 2.04613i
\(204\) −11.1112 19.2452i −0.777940 1.34743i
\(205\) 2.85330 4.94206i 0.199283 0.345168i
\(206\) −2.89726 5.01821i −0.201862 0.349635i
\(207\) 9.84700 17.0555i 0.684414 1.18544i
\(208\) −2.59095 1.49588i −0.179650 0.103721i
\(209\) 5.14413 + 2.96996i 0.355827 + 0.205437i
\(210\) −39.2373 −2.70763
\(211\) −0.269404 + 0.155540i −0.0185465 + 0.0107078i −0.509245 0.860622i \(-0.670075\pi\)
0.490698 + 0.871330i \(0.336742\pi\)
\(212\) 4.42240 + 2.55327i 0.303732 + 0.175359i
\(213\) 19.5929i 1.34249i
\(214\) 6.87578 11.9092i 0.470019 0.814097i
\(215\) −4.05970 + 2.34387i −0.276869 + 0.159850i
\(216\) 43.7801i 2.97886i
\(217\) −11.4651 + 6.61936i −0.778299 + 0.449351i
\(218\) 3.41828i 0.231515i
\(219\) 0.911637 + 1.57900i 0.0616027 + 0.106699i
\(220\) −9.45099 + 5.45653i −0.637186 + 0.367879i
\(221\) −23.9943 + 13.8531i −1.61403 + 0.931863i
\(222\) 3.62066i 0.243003i
\(223\) −2.03911 −0.136549 −0.0682745 0.997667i \(-0.521749\pi\)
−0.0682745 + 0.997667i \(0.521749\pi\)
\(224\) −19.4469 −1.29935
\(225\) −24.6804 + 42.7477i −1.64536 + 2.84984i
\(226\) 1.70589 2.95468i 0.113474 0.196543i
\(227\) 3.19713 + 5.53759i 0.212201 + 0.367543i 0.952403 0.304842i \(-0.0986035\pi\)
−0.740202 + 0.672384i \(0.765270\pi\)
\(228\) 6.96743 0.461430
\(229\) −11.4865 + 6.63171i −0.759047 + 0.438236i −0.828953 0.559318i \(-0.811063\pi\)
0.0699067 + 0.997554i \(0.477730\pi\)
\(230\) −7.36157 + 4.25020i −0.485407 + 0.280250i
\(231\) 35.8877 2.36124
\(232\) −20.1618 11.6404i −1.32369 0.764233i
\(233\) −11.4434 19.8206i −0.749684 1.29849i −0.947974 0.318347i \(-0.896872\pi\)
0.198291 0.980143i \(-0.436461\pi\)
\(234\) 31.6821 2.07113
\(235\) −23.7193 13.6944i −1.54728 0.893321i
\(236\) −7.27087 + 4.19784i −0.473293 + 0.273256i
\(237\) −28.0968 16.2217i −1.82508 1.05371i
\(238\) 11.2899 19.5547i 0.731816 1.26754i
\(239\) −12.5876 −0.814223 −0.407112 0.913378i \(-0.633464\pi\)
−0.407112 + 0.913378i \(0.633464\pi\)
\(240\) 3.78256 6.55159i 0.244163 0.422903i
\(241\) 5.74335 9.94777i 0.369961 0.640792i −0.619598 0.784920i \(-0.712704\pi\)
0.989559 + 0.144128i \(0.0460376\pi\)
\(242\) 1.74506 1.00751i 0.112177 0.0647654i
\(243\) −19.1299 33.1340i −1.22719 2.12555i
\(244\) 10.8292 + 6.25226i 0.693271 + 0.400260i
\(245\) 11.3800 + 19.7108i 0.727043 + 1.25928i
\(246\) 5.24577i 0.334458i
\(247\) 8.68681i 0.552728i
\(248\) 10.5722i 0.671333i
\(249\) −55.3007 −3.50454
\(250\) 4.32523 2.49717i 0.273551 0.157935i
\(251\) 3.82701i 0.241559i −0.992679 0.120779i \(-0.961461\pi\)
0.992679 0.120779i \(-0.0385393\pi\)
\(252\) 26.0971 15.0672i 1.64396 0.949143i
\(253\) 6.73313 3.88737i 0.423308 0.244397i
\(254\) −4.51599 7.82192i −0.283358 0.490791i
\(255\) −35.0297 60.6732i −2.19364 3.79950i
\(256\) 8.50345 14.7284i 0.531466 0.920526i
\(257\) −3.10779 −0.193859 −0.0969294 0.995291i \(-0.530902\pi\)
−0.0969294 + 0.995291i \(0.530902\pi\)
\(258\) −2.15460 + 3.73187i −0.134139 + 0.232336i
\(259\) 3.71837 2.14680i 0.231049 0.133396i
\(260\) 13.8215 + 7.97987i 0.857176 + 0.494891i
\(261\) 59.5230 3.68438
\(262\) 2.48409 + 4.30258i 0.153468 + 0.265814i
\(263\) 10.4265 0.642928 0.321464 0.946922i \(-0.395825\pi\)
0.321464 + 0.946922i \(0.395825\pi\)
\(264\) −14.3296 + 24.8196i −0.881925 + 1.52754i
\(265\) 13.9423 + 8.04956i 0.856466 + 0.494481i
\(266\) 3.53975 + 6.13102i 0.217036 + 0.375917i
\(267\) −45.7151 + 26.3936i −2.79772 + 1.61526i
\(268\) 4.34690 7.52906i 0.265529 0.459910i
\(269\) 6.35180 0.387276 0.193638 0.981073i \(-0.437971\pi\)
0.193638 + 0.981073i \(0.437971\pi\)
\(270\) 48.3134i 2.94026i
\(271\) −1.66974 2.89207i −0.101429 0.175681i 0.810844 0.585262i \(-0.199008\pi\)
−0.912274 + 0.409581i \(0.865675\pi\)
\(272\) 2.17674 + 3.77023i 0.131984 + 0.228603i
\(273\) −26.2419 45.4523i −1.58823 2.75090i
\(274\) 5.57209 0.336622
\(275\) −16.8758 + 9.74325i −1.01765 + 0.587540i
\(276\) 4.55982 7.89784i 0.274469 0.475394i
\(277\) 27.1710 15.6872i 1.63255 0.942552i 0.649243 0.760581i \(-0.275086\pi\)
0.983304 0.181971i \(-0.0582477\pi\)
\(278\) 6.48723 3.74541i 0.389078 0.224635i
\(279\) 13.5151 + 23.4088i 0.809127 + 1.40145i
\(280\) −37.1580 −2.22061
\(281\) 8.19792 14.1992i 0.489047 0.847054i −0.510874 0.859656i \(-0.670678\pi\)
0.999921 + 0.0126016i \(0.00401133\pi\)
\(282\) −25.1770 −1.49927
\(283\) −11.4878 −0.682882 −0.341441 0.939903i \(-0.610915\pi\)
−0.341441 + 0.939903i \(0.610915\pi\)
\(284\) 6.49483i 0.385397i
\(285\) 21.9658 1.30114
\(286\) 10.8317 + 6.25370i 0.640493 + 0.369789i
\(287\) −5.38735 + 3.11039i −0.318005 + 0.183600i
\(288\) 39.7058i 2.33969i
\(289\) 23.3169 1.37158
\(290\) −22.2495 12.8458i −1.30654 0.754330i
\(291\) 6.47535i 0.379592i
\(292\) 0.302197 + 0.523421i 0.0176847 + 0.0306309i
\(293\) 5.68234 + 9.84210i 0.331966 + 0.574982i 0.982897 0.184155i \(-0.0589548\pi\)
−0.650931 + 0.759137i \(0.725621\pi\)
\(294\) 18.1191 + 10.4611i 1.05673 + 0.610102i
\(295\) −22.9225 + 13.2343i −1.33460 + 0.770530i
\(296\) 3.42878i 0.199294i
\(297\) 44.1890i 2.56410i
\(298\) 8.06753 13.9734i 0.467340 0.809456i
\(299\) −9.84682 5.68506i −0.569456 0.328776i
\(300\) −11.4287 + 19.7950i −0.659835 + 1.14287i
\(301\) 5.11012 0.294542
\(302\) 4.95624i 0.285200i
\(303\) 19.6543 + 11.3474i 1.12911 + 0.651891i
\(304\) −1.36496 −0.0782856
\(305\) 34.1407 + 19.7112i 1.95489 + 1.12866i
\(306\) −39.9258 23.0512i −2.28241 1.31775i
\(307\) −11.5361 19.9810i −0.658397 1.14038i −0.981031 0.193853i \(-0.937901\pi\)
0.322633 0.946524i \(-0.395432\pi\)
\(308\) 11.8964 0.677858
\(309\) 16.9731 + 9.79945i 0.965568 + 0.557471i
\(310\) 11.6669i 0.662634i
\(311\) 5.79075i 0.328363i 0.986430 + 0.164182i \(0.0524983\pi\)
−0.986430 + 0.164182i \(0.947502\pi\)
\(312\) 41.9124 2.37282
\(313\) −20.9591 −1.18468 −0.592338 0.805689i \(-0.701795\pi\)
−0.592338 + 0.805689i \(0.701795\pi\)
\(314\) 3.86008i 0.217837i
\(315\) 82.2750 47.5015i 4.63567 2.67641i
\(316\) −9.31376 5.37730i −0.523940 0.302497i
\(317\) 23.3255 + 13.4670i 1.31009 + 0.756380i 0.982111 0.188305i \(-0.0602993\pi\)
0.327978 + 0.944685i \(0.393633\pi\)
\(318\) 14.7991 0.829892
\(319\) 20.3501 + 11.7492i 1.13939 + 0.657827i
\(320\) 10.8972 18.8745i 0.609173 1.05512i
\(321\) 46.5121i 2.59605i
\(322\) 9.26632 0.516392
\(323\) −6.32031 + 10.9471i −0.351672 + 0.609113i
\(324\) −13.7054 23.7385i −0.761412 1.31880i
\(325\) 24.6799 + 14.2490i 1.36900 + 0.790390i
\(326\) 1.46981 + 2.54579i 0.0814053 + 0.140998i
\(327\) −5.78085 10.0127i −0.319682 0.553705i
\(328\) 4.96778i 0.274300i
\(329\) 14.9283 + 25.8565i 0.823022 + 1.42552i
\(330\) −15.8134 + 27.3896i −0.870498 + 1.50775i
\(331\) 9.09716 + 5.25225i 0.500025 + 0.288690i 0.728724 0.684807i \(-0.240114\pi\)
−0.228699 + 0.973497i \(0.573447\pi\)
\(332\) −18.3315 −1.00607
\(333\) −4.38324 7.59199i −0.240200 0.416039i
\(334\) 8.54296 + 14.7968i 0.467450 + 0.809647i
\(335\) 13.7042 23.7364i 0.748743 1.29686i
\(336\) −7.14191 + 4.12338i −0.389623 + 0.224949i
\(337\) −5.17173 8.95770i −0.281722 0.487957i 0.690087 0.723727i \(-0.257572\pi\)
−0.971809 + 0.235769i \(0.924239\pi\)
\(338\) 5.80259i 0.315619i
\(339\) 11.5397i 0.626750i
\(340\) −11.6119 20.1125i −0.629745 1.09075i
\(341\) 10.6709i 0.577861i
\(342\) 12.5180 7.22728i 0.676897 0.390807i
\(343\) 1.10106i 0.0594519i
\(344\) −2.04042 + 3.53410i −0.110012 + 0.190546i
\(345\) 14.3755 24.8991i 0.773951 1.34052i
\(346\) 1.44392 2.50095i 0.0776258 0.134452i
\(347\) 1.49467 0.862948i 0.0802381 0.0463255i −0.459344 0.888258i \(-0.651916\pi\)
0.539582 + 0.841933i \(0.318582\pi\)
\(348\) 27.5631 1.47754
\(349\) −10.1115 + 15.7085i −0.541259 + 0.840856i
\(350\) −23.2250 −1.24143
\(351\) −55.9659 + 32.3119i −2.98724 + 1.72468i
\(352\) −7.83747 + 13.5749i −0.417739 + 0.723545i
\(353\) 13.3888 23.1901i 0.712614 1.23428i −0.251258 0.967920i \(-0.580844\pi\)
0.963873 0.266364i \(-0.0858223\pi\)
\(354\) −12.1656 + 21.0714i −0.646594 + 1.11993i
\(355\) 20.4759i 1.08675i
\(356\) −15.1540 + 8.74919i −0.803162 + 0.463706i
\(357\) 76.3719i 4.04203i
\(358\) −0.625570 1.08352i −0.0330624 0.0572657i
\(359\) 30.2865i 1.59846i −0.601026 0.799229i \(-0.705241\pi\)
0.601026 0.799229i \(-0.294759\pi\)
\(360\) 75.8674i 3.99856i
\(361\) 7.51838 + 13.0222i 0.395704 + 0.685380i
\(362\) 3.59572 2.07599i 0.188987 0.109112i
\(363\) −3.40772 + 5.90235i −0.178859 + 0.309793i
\(364\) −8.69888 15.0669i −0.455945 0.789721i
\(365\) 0.952720 + 1.65016i 0.0498676 + 0.0863733i
\(366\) 36.2389 1.89424
\(367\) 15.7055 + 9.06760i 0.819823 + 0.473325i 0.850355 0.526209i \(-0.176387\pi\)
−0.0305324 + 0.999534i \(0.509720\pi\)
\(368\) −0.893292 + 1.54723i −0.0465661 + 0.0806548i
\(369\) 6.35064 + 10.9996i 0.330601 + 0.572618i
\(370\) 3.78382i 0.196712i
\(371\) −8.77485 15.1985i −0.455568 0.789066i
\(372\) 6.25839 + 10.8399i 0.324482 + 0.562020i
\(373\) −10.6345 6.13986i −0.550636 0.317910i 0.198742 0.980052i \(-0.436314\pi\)
−0.749379 + 0.662142i \(0.769648\pi\)
\(374\) −9.10008 15.7618i −0.470554 0.815023i
\(375\) −8.44621 + 14.6293i −0.436160 + 0.755452i
\(376\) −23.8428 −1.22960
\(377\) 34.3650i 1.76989i
\(378\) 26.3333 45.6106i 1.35444 2.34596i
\(379\) 29.5899 + 17.0838i 1.51993 + 0.877534i 0.999724 + 0.0234946i \(0.00747925\pi\)
0.520209 + 0.854039i \(0.325854\pi\)
\(380\) 7.28142 0.373529
\(381\) 26.4562 + 15.2745i 1.35539 + 0.782535i
\(382\) 12.1878 + 7.03663i 0.623582 + 0.360025i
\(383\) 11.2066 6.47014i 0.572631 0.330609i −0.185568 0.982631i \(-0.559413\pi\)
0.758200 + 0.652023i \(0.226079\pi\)
\(384\) 14.1060i 0.719844i
\(385\) 37.5050 1.91143
\(386\) 0.916293 0.0466381
\(387\) 10.4336i 0.530369i
\(388\) 2.14650i 0.108972i
\(389\) −29.6740 17.1323i −1.50453 0.868641i −0.999986 0.00525450i \(-0.998327\pi\)
−0.504544 0.863386i \(-0.668339\pi\)
\(390\) 46.2523 2.34208
\(391\) 8.27263 + 14.3286i 0.418365 + 0.724630i
\(392\) 17.1589 + 9.90669i 0.866655 + 0.500363i
\(393\) −14.5527 8.40198i −0.734084 0.423824i
\(394\) −16.2403 −0.818174
\(395\) −29.3630 16.9527i −1.47741 0.852984i
\(396\) 24.2894i 1.22059i
\(397\) 0.348649 0.0174982 0.00874911 0.999962i \(-0.497215\pi\)
0.00874911 + 0.999962i \(0.497215\pi\)
\(398\) 4.33953 7.51628i 0.217521 0.376757i
\(399\) −20.7370 11.9725i −1.03815 0.599376i
\(400\) 2.23894 3.87795i 0.111947 0.193897i
\(401\) 39.5725i 1.97615i 0.153958 + 0.988077i \(0.450798\pi\)
−0.153958 + 0.988077i \(0.549202\pi\)
\(402\) 25.1952i 1.25662i
\(403\) 13.5148 7.80279i 0.673222 0.388685i
\(404\) 6.51516 + 3.76153i 0.324141 + 0.187143i
\(405\) −43.2083 74.8390i −2.14704 3.71878i
\(406\) 14.0032 + 24.2543i 0.694968 + 1.20372i
\(407\) 3.46081i 0.171546i
\(408\) −52.8180 30.4945i −2.61488 1.50970i
\(409\) 25.1943 1.24578 0.622890 0.782309i \(-0.285958\pi\)
0.622890 + 0.782309i \(0.285958\pi\)
\(410\) 5.48218i 0.270745i
\(411\) −16.3216 + 9.42327i −0.805084 + 0.464815i
\(412\) 5.62640 + 3.24840i 0.277193 + 0.160037i
\(413\) 28.8535 1.41979
\(414\) 18.9195i 0.929843i
\(415\) −57.7928 −2.83694
\(416\) 22.9237 1.12393
\(417\) −12.6681 + 21.9418i −0.620361 + 1.07450i
\(418\) 5.70633 0.279106
\(419\) 7.16294 + 12.4066i 0.349932 + 0.606100i 0.986237 0.165337i \(-0.0528713\pi\)
−0.636305 + 0.771438i \(0.719538\pi\)
\(420\) 38.0989 21.9964i 1.85903 1.07331i
\(421\) 8.46539 4.88749i 0.412578 0.238202i −0.279319 0.960198i \(-0.590109\pi\)
0.691897 + 0.721997i \(0.256775\pi\)
\(422\) −0.149424 + 0.258809i −0.00727383 + 0.0125986i
\(423\) 52.7925 30.4798i 2.56686 1.48198i
\(424\) 14.0148 0.680620
\(425\) −20.7344 35.9130i −1.00577 1.74204i
\(426\) −9.41122 16.3007i −0.455975 0.789772i
\(427\) −21.4872 37.2169i −1.03984 1.80105i
\(428\) 15.4182i 0.745267i
\(429\) −42.3039 −2.04245
\(430\) −2.25169 + 3.90005i −0.108586 + 0.188077i
\(431\) −10.0912 + 5.82613i −0.486074 + 0.280635i −0.722944 0.690906i \(-0.757212\pi\)
0.236870 + 0.971541i \(0.423878\pi\)
\(432\) 5.07717 + 8.79391i 0.244275 + 0.423097i
\(433\) −30.4483 17.5793i −1.46325 0.844809i −0.464092 0.885787i \(-0.653619\pi\)
−0.999160 + 0.0409780i \(0.986953\pi\)
\(434\) −6.35905 + 11.0142i −0.305244 + 0.528698i
\(435\) 86.8968 4.16638
\(436\) −1.91628 3.31910i −0.0917734 0.158956i
\(437\) −5.18747 −0.248150
\(438\) 1.51691 + 0.875786i 0.0724806 + 0.0418467i
\(439\) −24.1970 + 13.9701i −1.15486 + 0.666758i −0.950067 0.312047i \(-0.898985\pi\)
−0.204792 + 0.978805i \(0.565652\pi\)
\(440\) −14.9754 + 25.9381i −0.713922 + 1.23655i
\(441\) −50.6575 −2.41226
\(442\) −13.3084 + 23.0507i −0.633014 + 1.09641i
\(443\) −0.141711 0.245450i −0.00673288 0.0116617i 0.862639 0.505820i \(-0.168810\pi\)
−0.869372 + 0.494158i \(0.835476\pi\)
\(444\) −2.02973 3.51560i −0.0963269 0.166843i
\(445\) −47.7753 + 27.5831i −2.26477 + 1.30756i
\(446\) −1.69648 + 0.979461i −0.0803305 + 0.0463788i
\(447\) 54.5738i 2.58125i
\(448\) −20.5752 + 11.8791i −0.972087 + 0.561235i
\(449\) 11.3534 0.535798 0.267899 0.963447i \(-0.413671\pi\)
0.267899 + 0.963447i \(0.413671\pi\)
\(450\) 47.4196i 2.23538i
\(451\) 5.01418i 0.236108i
\(452\) 3.82527i 0.179926i
\(453\) −8.38178 14.5177i −0.393810 0.682099i
\(454\) 5.31982 + 3.07140i 0.249672 + 0.144148i
\(455\) −27.4245 47.5006i −1.28568 2.22686i
\(456\) 16.5601 9.56100i 0.775500 0.447735i
\(457\) 18.3179 31.7275i 0.856873 1.48415i −0.0180234 0.999838i \(-0.505737\pi\)
0.874896 0.484310i \(-0.160929\pi\)
\(458\) −6.37091 + 11.0347i −0.297693 + 0.515620i
\(459\) 94.0376 4.38930
\(460\) 4.76531 8.25376i 0.222184 0.384834i
\(461\) −20.9069 12.0706i −0.973733 0.562185i −0.0733611 0.997305i \(-0.523373\pi\)
−0.900372 + 0.435120i \(0.856706\pi\)
\(462\) 29.8575 17.2382i 1.38909 0.801994i
\(463\) −8.71155 5.02961i −0.404860 0.233746i 0.283719 0.958908i \(-0.408432\pi\)
−0.688579 + 0.725161i \(0.741765\pi\)
\(464\) −5.39976 −0.250678
\(465\) 19.7305 + 34.1742i 0.914979 + 1.58479i
\(466\) −19.0411 10.9934i −0.882064 0.509260i
\(467\) 23.7954 1.10112 0.550560 0.834796i \(-0.314414\pi\)
0.550560 + 0.834796i \(0.314414\pi\)
\(468\) −30.7629 + 17.7610i −1.42201 + 0.821000i
\(469\) −25.8752 + 14.9390i −1.19480 + 0.689821i
\(470\) −26.3116 −1.21367
\(471\) −6.52799 11.3068i −0.300794 0.520990i
\(472\) −11.5209 + 19.9548i −0.530292 + 0.918493i
\(473\) 2.05947 3.56711i 0.0946946 0.164016i
\(474\) −31.1675 −1.43157
\(475\) 13.0018 0.596564
\(476\) 25.3164i 1.16038i
\(477\) −31.0315 + 17.9161i −1.42084 + 0.820320i
\(478\) −10.4725 + 6.04628i −0.479000 + 0.276551i
\(479\) 11.6470 + 20.1731i 0.532163 + 0.921733i 0.999295 + 0.0375455i \(0.0119539\pi\)
−0.467132 + 0.884188i \(0.654713\pi\)
\(480\) 57.9659i 2.64577i
\(481\) −4.38316 + 2.53062i −0.199855 + 0.115386i
\(482\) 11.0350i 0.502629i
\(483\) −27.1426 + 15.6708i −1.23503 + 0.713045i
\(484\) −1.12962 + 1.95656i −0.0513464 + 0.0889345i
\(485\) 6.76717i 0.307281i
\(486\) −31.8310 18.3776i −1.44388 0.833627i
\(487\) 5.95323 3.43710i 0.269767 0.155750i −0.359015 0.933332i \(-0.616887\pi\)
0.628782 + 0.777582i \(0.283554\pi\)
\(488\) 34.3185 1.55352
\(489\) −8.61064 4.97136i −0.389387 0.224812i
\(490\) 18.9356 + 10.9325i 0.855425 + 0.493880i
\(491\) 12.7193 22.0305i 0.574014 0.994221i −0.422134 0.906533i \(-0.638719\pi\)
0.996148 0.0876877i \(-0.0279477\pi\)
\(492\) 2.94077 + 5.09357i 0.132580 + 0.229636i
\(493\) −25.0031 + 43.3067i −1.12608 + 1.95044i
\(494\) −4.17260 7.22715i −0.187734 0.325165i
\(495\) 76.5759i 3.44183i
\(496\) −1.22605 2.12358i −0.0550513 0.0953517i
\(497\) −11.1604 + 19.3304i −0.500613 + 0.867088i
\(498\) −46.0084 + 26.5630i −2.06169 + 1.19032i
\(499\) 0.433526 0.250296i 0.0194073 0.0112048i −0.490265 0.871573i \(-0.663100\pi\)
0.509672 + 0.860369i \(0.329767\pi\)
\(500\) −2.79982 + 4.84943i −0.125212 + 0.216873i
\(501\) −50.0475 28.8949i −2.23596 1.29093i
\(502\) −1.83825 3.18395i −0.0820453 0.142107i
\(503\) −23.0760 13.3229i −1.02891 0.594039i −0.112235 0.993682i \(-0.535801\pi\)
−0.916671 + 0.399643i \(0.869134\pi\)
\(504\) 41.3516 71.6231i 1.84195 3.19035i
\(505\) 20.5400 + 11.8588i 0.914018 + 0.527708i
\(506\) 3.73450 6.46834i 0.166019 0.287553i
\(507\) 9.81308 + 16.9967i 0.435814 + 0.754852i
\(508\) 8.76992 + 5.06331i 0.389102 + 0.224648i
\(509\) −6.15381 + 3.55291i −0.272763 + 0.157480i −0.630143 0.776479i \(-0.717004\pi\)
0.357380 + 0.933959i \(0.383670\pi\)
\(510\) −58.2872 33.6521i −2.58100 1.49014i
\(511\) 2.07713i 0.0918867i
\(512\) 7.65561i 0.338333i
\(513\) −14.7419 + 25.5337i −0.650871 + 1.12734i
\(514\) −2.58559 + 1.49279i −0.114045 + 0.0658441i
\(515\) 17.7380 + 10.2411i 0.781632 + 0.451275i
\(516\) 4.83145i 0.212693i
\(517\) 24.0655 1.05840
\(518\) 2.06238 3.57215i 0.0906158 0.156951i
\(519\) 9.76760i 0.428750i
\(520\) 43.8012 1.92081
\(521\) 15.1960 8.77343i 0.665750 0.384371i −0.128714 0.991682i \(-0.541085\pi\)
0.794464 + 0.607311i \(0.207752\pi\)
\(522\) 49.5212 28.5911i 2.16748 1.25140i
\(523\) −22.7497 13.1345i −0.994774 0.574333i −0.0880764 0.996114i \(-0.528072\pi\)
−0.906698 + 0.421780i \(0.861405\pi\)
\(524\) −4.82404 2.78516i −0.210739 0.121670i
\(525\) 68.0298 39.2770i 2.96906 1.71419i
\(526\) 8.67455 5.00825i 0.378228 0.218370i
\(527\) −22.7085 −0.989198
\(528\) 6.64720i 0.289282i
\(529\) 8.10507 14.0384i 0.352394 0.610365i
\(530\) 15.4660 0.671801
\(531\) 58.9116i 2.55655i
\(532\) −6.87408 3.96875i −0.298029 0.172067i
\(533\) 6.35052 3.66648i 0.275072 0.158813i
\(534\) −25.3557 + 43.9173i −1.09725 + 1.90049i
\(535\) 48.6081i 2.10151i
\(536\) 23.8600i 1.03060i
\(537\) 3.66480 + 2.11587i 0.158148 + 0.0913066i
\(538\) 5.28450 3.05101i 0.227831 0.131538i
\(539\) −17.3191 9.99921i −0.745988 0.430697i
\(540\) −27.0844 46.9116i −1.16553 2.01875i
\(541\) 17.3275 30.0120i 0.744965 1.29032i −0.205246 0.978710i \(-0.565799\pi\)
0.950211 0.311607i \(-0.100867\pi\)
\(542\) −2.77834 1.60407i −0.119340 0.0689009i
\(543\) −7.02164 + 12.1618i −0.301328 + 0.521915i
\(544\) −28.8885 16.6788i −1.23858 0.715096i
\(545\) −6.04136 10.4639i −0.258784 0.448226i
\(546\) −43.6648 25.2099i −1.86868 1.07888i
\(547\) −0.436650 + 0.756300i −0.0186698 + 0.0323370i −0.875209 0.483744i \(-0.839276\pi\)
0.856540 + 0.516081i \(0.172610\pi\)
\(548\) −5.41041 + 3.12370i −0.231121 + 0.133438i
\(549\) −75.9877 + 43.8715i −3.24308 + 1.87239i
\(550\) −9.36009 + 16.2122i −0.399116 + 0.691289i
\(551\) −7.83928 13.5780i −0.333965 0.578444i
\(552\) 25.0287i 1.06529i
\(553\) 18.4802 + 32.0087i 0.785859 + 1.36115i
\(554\) 15.0703 26.1025i 0.640275 1.10899i
\(555\) −6.39903 11.0835i −0.271624 0.470466i
\(556\) −4.19934 + 7.27346i −0.178092 + 0.308464i
\(557\) 15.5561 + 8.98130i 0.659132 + 0.380550i 0.791946 0.610591i \(-0.209068\pi\)
−0.132814 + 0.991141i \(0.542401\pi\)
\(558\) 22.4882 + 12.9836i 0.952003 + 0.549639i
\(559\) −6.02372 −0.254776
\(560\) −7.46376 + 4.30920i −0.315401 + 0.182097i
\(561\) 53.3113 + 30.7793i 2.25080 + 1.29950i
\(562\) 15.7511i 0.664419i
\(563\) −12.3469 + 21.3855i −0.520361 + 0.901291i 0.479359 + 0.877619i \(0.340869\pi\)
−0.999720 + 0.0236722i \(0.992464\pi\)
\(564\) 24.4465 14.1142i 1.02938 0.594315i
\(565\) 12.0597i 0.507356i
\(566\) −9.55753 + 5.51804i −0.401733 + 0.231941i
\(567\) 94.2031i 3.95616i
\(568\) −8.91248 15.4369i −0.373959 0.647716i
\(569\) −36.1856 + 20.8918i −1.51698 + 0.875828i −0.517178 + 0.855878i \(0.673017\pi\)
−0.999801 + 0.0199500i \(0.993649\pi\)
\(570\) 18.2749 10.5510i 0.765451 0.441933i
\(571\) 2.67483i 0.111938i 0.998432 + 0.0559692i \(0.0178249\pi\)
−0.998432 + 0.0559692i \(0.982175\pi\)
\(572\) −14.0232 −0.586341
\(573\) −47.6001 −1.98852
\(574\) −2.98807 + 5.17549i −0.124720 + 0.216021i
\(575\) 8.50900 14.7380i 0.354850 0.614618i
\(576\) 24.2542 + 42.0094i 1.01059 + 1.75039i
\(577\) 35.0719 1.46006 0.730032 0.683413i \(-0.239505\pi\)
0.730032 + 0.683413i \(0.239505\pi\)
\(578\) 19.3989 11.2000i 0.806888 0.465857i
\(579\) −2.68397 + 1.54959i −0.111542 + 0.0643989i
\(580\) 28.8053 1.19607
\(581\) 54.5597 + 31.5001i 2.26352 + 1.30684i
\(582\) −3.11035 5.38729i −0.128928 0.223310i
\(583\) −14.1457 −0.585856
\(584\) 1.43652 + 0.829375i 0.0594436 + 0.0343198i
\(585\) −96.9844 + 55.9940i −4.00981 + 2.31507i
\(586\) 9.45506 + 5.45888i 0.390585 + 0.225504i
\(587\) 16.2924 28.2192i 0.672458 1.16473i −0.304747 0.952433i \(-0.598572\pi\)
0.977205 0.212298i \(-0.0680946\pi\)
\(588\) −23.4578 −0.967384
\(589\) 3.55992 6.16597i 0.146684 0.254064i
\(590\) −12.7138 + 22.0210i −0.523421 + 0.906591i
\(591\) 47.5705 27.4649i 1.95679 1.12975i
\(592\) 0.397635 + 0.688725i 0.0163427 + 0.0283064i
\(593\) −24.7074 14.2648i −1.01461 0.585786i −0.102073 0.994777i \(-0.532548\pi\)
−0.912539 + 0.408991i \(0.865881\pi\)
\(594\) −21.2256 36.7638i −0.870897 1.50844i
\(595\) 79.8137i 3.27204i
\(596\) 18.0906i 0.741019i
\(597\) 29.3552i 1.20143i
\(598\) −10.9230 −0.446674
\(599\) −16.9273 + 9.77299i −0.691631 + 0.399314i −0.804223 0.594328i \(-0.797418\pi\)
0.112592 + 0.993641i \(0.464085\pi\)
\(600\) 62.7316i 2.56101i
\(601\) −7.76060 + 4.48058i −0.316561 + 0.182767i −0.649859 0.760055i \(-0.725172\pi\)
0.333298 + 0.942822i \(0.391839\pi\)
\(602\) 4.25146 2.45458i 0.173276 0.100041i
\(603\) 30.5018 + 52.8307i 1.24213 + 2.15143i
\(604\) −2.77846 4.81244i −0.113054 0.195815i
\(605\) −3.56129 + 6.16834i −0.144787 + 0.250779i
\(606\) 21.8023 0.885658
\(607\) 21.0945 36.5368i 0.856200 1.48298i −0.0193267 0.999813i \(-0.506152\pi\)
0.875527 0.483169i \(-0.160514\pi\)
\(608\) 9.05746 5.22932i 0.367328 0.212077i
\(609\) −82.0355 47.3632i −3.32425 1.91926i
\(610\) 37.8720 1.53339
\(611\) −17.5972 30.4792i −0.711906 1.23306i
\(612\) 51.6898 2.08944
\(613\) 9.88310 17.1180i 0.399175 0.691391i −0.594450 0.804133i \(-0.702630\pi\)
0.993624 + 0.112742i \(0.0359634\pi\)
\(614\) −19.1953 11.0824i −0.774658 0.447249i
\(615\) 9.27121 + 16.0582i 0.373851 + 0.647530i
\(616\) 28.2752 16.3247i 1.13924 0.657740i
\(617\) −16.9140 + 29.2958i −0.680930 + 1.17941i 0.293767 + 0.955877i \(0.405091\pi\)
−0.974697 + 0.223529i \(0.928242\pi\)
\(618\) 18.8282 0.757379
\(619\) 36.0964i 1.45084i 0.688309 + 0.725418i \(0.258353\pi\)
−0.688309 + 0.725418i \(0.741647\pi\)
\(620\) 6.54043 + 11.3284i 0.262670 + 0.454958i
\(621\) 19.2956 + 33.4210i 0.774306 + 1.34114i
\(622\) 2.78151 + 4.81772i 0.111528 + 0.193173i
\(623\) 60.1368 2.40933
\(624\) 8.41876 4.86058i 0.337020 0.194579i
\(625\) 7.50061 12.9914i 0.300024 0.519657i
\(626\) −17.4373 + 10.0674i −0.696934 + 0.402375i
\(627\) −16.7148 + 9.65030i −0.667525 + 0.385396i
\(628\) −2.16395 3.74808i −0.0863512 0.149565i
\(629\) 7.36487 0.293657
\(630\) 45.6335 79.0395i 1.81808 3.14901i
\(631\) −11.9846 −0.477099 −0.238550 0.971130i \(-0.576672\pi\)
−0.238550 + 0.971130i \(0.576672\pi\)
\(632\) −29.5158 −1.17408
\(633\) 1.01079i 0.0401755i
\(634\) 25.8747 1.02762
\(635\) 27.6484 + 15.9628i 1.09719 + 0.633466i
\(636\) −14.3697 + 8.29634i −0.569795 + 0.328971i
\(637\) 29.2466i 1.15879i
\(638\) 22.5742 0.893722
\(639\) 39.4679 + 22.7868i 1.56133 + 0.901432i
\(640\) 14.7417i 0.582717i
\(641\) 6.97274 + 12.0771i 0.275407 + 0.477018i 0.970238 0.242155i \(-0.0778541\pi\)
−0.694831 + 0.719173i \(0.744521\pi\)
\(642\) 22.3415 + 38.6966i 0.881747 + 1.52723i
\(643\) 11.7058 + 6.75834i 0.461631 + 0.266523i 0.712730 0.701439i \(-0.247459\pi\)
−0.251099 + 0.967961i \(0.580792\pi\)
\(644\) −8.99746 + 5.19468i −0.354549 + 0.204699i
\(645\) 15.2319i 0.599754i
\(646\) 12.1435i 0.477781i
\(647\) −13.9277 + 24.1234i −0.547553 + 0.948390i 0.450888 + 0.892580i \(0.351107\pi\)
−0.998441 + 0.0558096i \(0.982226\pi\)
\(648\) −65.1499 37.6143i −2.55933 1.47763i
\(649\) 11.6285 20.1411i 0.456458 0.790609i
\(650\) 27.3772 1.07382
\(651\) 43.0165i 1.68595i
\(652\) −2.85433 1.64795i −0.111784 0.0645386i
\(653\) −23.1161 −0.904603 −0.452301 0.891865i \(-0.649397\pi\)
−0.452301 + 0.891865i \(0.649397\pi\)
\(654\) −9.61896 5.55351i −0.376131 0.217159i
\(655\) −15.2085 8.78062i −0.594244 0.343087i
\(656\) −0.576112 0.997856i −0.0224934 0.0389597i
\(657\) −4.24097 −0.165456
\(658\) 24.8397 + 14.3412i 0.968352 + 0.559078i
\(659\) 23.1935i 0.903490i 0.892147 + 0.451745i \(0.149198\pi\)
−0.892147 + 0.451745i \(0.850802\pi\)
\(660\) 35.4598i 1.38027i
\(661\) 42.5075 1.65335 0.826676 0.562679i \(-0.190229\pi\)
0.826676 + 0.562679i \(0.190229\pi\)
\(662\) 10.0914 0.392214
\(663\) 90.0260i 3.49632i
\(664\) −43.5702 + 25.1553i −1.69085 + 0.976215i
\(665\) −21.6715 12.5121i −0.840386 0.485197i
\(666\) −7.29343 4.21086i −0.282615 0.163168i
\(667\) −20.5216 −0.794600
\(668\) −16.5902 9.57834i −0.641893 0.370597i
\(669\) 3.31284 5.73801i 0.128082 0.221844i
\(670\) 26.3306i 1.01724i
\(671\) −34.6390 −1.33722
\(672\) 31.5944 54.7232i 1.21878 2.11099i
\(673\) −6.59063 11.4153i −0.254050 0.440028i 0.710587 0.703609i \(-0.248430\pi\)
−0.964637 + 0.263582i \(0.915096\pi\)
\(674\) −8.60543 4.96835i −0.331469 0.191374i
\(675\) −48.3622 83.7658i −1.86146 3.22415i
\(676\) 3.25292 + 5.63423i 0.125112 + 0.216701i
\(677\) 10.9116i 0.419365i 0.977769 + 0.209683i \(0.0672431\pi\)
−0.977769 + 0.209683i \(0.932757\pi\)
\(678\) 5.54294 + 9.60065i 0.212875 + 0.368711i
\(679\) −3.68846 + 6.38859i −0.141550 + 0.245172i
\(680\) −55.1983 31.8687i −2.11676 1.22211i
\(681\) −20.7769 −0.796171
\(682\) 5.12563 + 8.87785i 0.196270 + 0.339950i
\(683\) −23.1676 40.1274i −0.886482 1.53543i −0.844006 0.536334i \(-0.819809\pi\)
−0.0424761 0.999097i \(-0.513525\pi\)
\(684\) −8.10320 + 14.0352i −0.309834 + 0.536648i
\(685\) −17.0571 + 9.84793i −0.651719 + 0.376270i
\(686\) 0.528882 + 0.916051i 0.0201928 + 0.0349750i
\(687\) 43.0968i 1.64425i
\(688\) 0.946506i 0.0360852i
\(689\) 10.3437 + 17.9157i 0.394062 + 0.682535i
\(690\) 27.6204i 1.05149i
\(691\) 37.7196 21.7774i 1.43492 0.828452i 0.437430 0.899252i \(-0.355889\pi\)
0.997491 + 0.0708002i \(0.0225553\pi\)
\(692\) 3.23785i 0.123084i
\(693\) −41.7378 + 72.2920i −1.58549 + 2.74615i
\(694\) 0.829012 1.43589i 0.0314689 0.0545057i
\(695\) −13.2390 + 22.9307i −0.502185 + 0.869809i
\(696\) 65.5118 37.8233i 2.48322 1.43369i
\(697\) −10.6706 −0.404176
\(698\) −0.867119 + 17.9259i −0.0328209 + 0.678506i
\(699\) 74.3662 2.81279
\(700\) 22.5511 13.0199i 0.852351 0.492105i
\(701\) −7.92471 + 13.7260i −0.299312 + 0.518424i −0.975979 0.217866i \(-0.930090\pi\)
0.676667 + 0.736289i \(0.263424\pi\)
\(702\) −31.0412 + 53.7650i −1.17158 + 2.02923i
\(703\) −1.15456 + 1.99976i −0.0435451 + 0.0754223i
\(704\) 19.1500i 0.721742i
\(705\) 77.0711 44.4970i 2.90267 1.67586i
\(706\) 25.7246i 0.968157i
\(707\) −12.9273 22.3907i −0.486181 0.842090i
\(708\) 27.2801i 1.02525i
\(709\) 7.36494i 0.276596i 0.990391 + 0.138298i \(0.0441632\pi\)
−0.990391 + 0.138298i \(0.955837\pi\)
\(710\) −9.83534 17.0353i −0.369114 0.639324i
\(711\) 65.3538 37.7320i 2.45096 1.41506i
\(712\) −24.0120 + 41.5900i −0.899887 + 1.55865i
\(713\) −4.65957 8.07061i −0.174502 0.302247i
\(714\) 36.6843 + 63.5390i 1.37287 + 2.37789i
\(715\) −44.2103 −1.65337
\(716\) 1.21484 + 0.701387i 0.0454006 + 0.0262121i
\(717\) 20.4504 35.4211i 0.763734 1.32283i
\(718\) −14.5477 25.1974i −0.542916 0.940358i
\(719\) 15.7013i 0.585559i −0.956180 0.292780i \(-0.905420\pi\)
0.956180 0.292780i \(-0.0945803\pi\)
\(720\) 8.79832 + 15.2391i 0.327894 + 0.567929i
\(721\) −11.1638 19.3363i −0.415762 0.720121i
\(722\) 12.5101 + 7.22271i 0.465578 + 0.268802i
\(723\) 18.6618 + 32.3233i 0.694041 + 1.20211i
\(724\) −2.32759 + 4.03151i −0.0865044 + 0.149830i
\(725\) 51.4351 1.91025
\(726\) 6.54742i 0.242998i
\(727\) −25.0980 + 43.4711i −0.930835 + 1.61225i −0.148937 + 0.988847i \(0.547585\pi\)
−0.781898 + 0.623406i \(0.785748\pi\)
\(728\) −41.3509 23.8739i −1.53257 0.884827i
\(729\) 47.9719 1.77674
\(730\) 1.58527 + 0.915254i 0.0586733 + 0.0338751i
\(731\) 7.59109 + 4.38272i 0.280767 + 0.162101i
\(732\) −35.1874 + 20.3155i −1.30056 + 0.750881i
\(733\) 38.5458i 1.42372i −0.702321 0.711861i \(-0.747853\pi\)
0.702321 0.711861i \(-0.252147\pi\)
\(734\) 17.4220 0.643059
\(735\) −73.9542 −2.72784
\(736\) 13.6893i 0.504594i
\(737\) 24.0828i 0.887103i
\(738\) 10.5671 + 6.10089i 0.388979 + 0.224577i
\(739\) −43.6269 −1.60484 −0.802421 0.596759i \(-0.796455\pi\)
−0.802421 + 0.596759i \(0.796455\pi\)
\(740\) −2.12121 3.67404i −0.0779771 0.135060i
\(741\) 24.4445 + 14.1130i 0.897990 + 0.518455i
\(742\) −14.6008 8.42978i −0.536012 0.309467i
\(743\) −9.29924 −0.341156 −0.170578 0.985344i \(-0.554563\pi\)
−0.170578 + 0.985344i \(0.554563\pi\)
\(744\) 29.7498 + 17.1760i 1.09068 + 0.629704i
\(745\) 57.0332i 2.08953i
\(746\) −11.7968 −0.431912
\(747\) 64.3153 111.397i 2.35317 4.07582i
\(748\) 17.6721 + 10.2030i 0.646155 + 0.373058i
\(749\) 26.4939 45.8889i 0.968068 1.67674i
\(750\) 16.2281i 0.592567i
\(751\) 13.1443i 0.479641i 0.970817 + 0.239821i \(0.0770886\pi\)
−0.970817 + 0.239821i \(0.922911\pi\)
\(752\) −4.78919 + 2.76504i −0.174644 + 0.100831i
\(753\) 10.7691 + 6.21755i 0.392448 + 0.226580i
\(754\) −16.5068 28.5906i −0.601141 1.04121i
\(755\) −8.75951 15.1719i −0.318791 0.552162i
\(756\) 59.0496i 2.14761i
\(757\) −26.7459 15.4418i −0.972097 0.561240i −0.0722219 0.997389i \(-0.523009\pi\)
−0.899875 + 0.436148i \(0.856342\pi\)
\(758\) 32.8239 1.19222
\(759\) 25.2625i 0.916969i
\(760\) 17.3064 9.99187i 0.627770 0.362443i
\(761\) 17.2188 + 9.94126i 0.624180 + 0.360370i 0.778494 0.627651i \(-0.215984\pi\)
−0.154315 + 0.988022i \(0.549317\pi\)
\(762\) 29.3476 1.06315
\(763\) 13.1714i 0.476837i
\(764\) −15.7789 −0.570860
\(765\) 162.960 5.89182
\(766\) 6.21570 10.7659i 0.224582 0.388988i
\(767\) −34.0120