Properties

Label 349.2.e.a.123.19
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 123.19
Character \(\chi\) = 349.123
Dual form 349.2.e.a.227.19

$q$-expansion

\(f(q)\) \(=\) \(q+(0.544820 - 0.314552i) q^{2} +(1.24137 - 2.15012i) q^{3} +(-0.802114 + 1.38930i) q^{4} +(-0.0260007 + 0.0450346i) q^{5} -1.56191i q^{6} +(3.86429 - 2.23105i) q^{7} +2.26743i q^{8} +(-1.58202 - 2.74014i) q^{9} +O(q^{10})\) \(q+(0.544820 - 0.314552i) q^{2} +(1.24137 - 2.15012i) q^{3} +(-0.802114 + 1.38930i) q^{4} +(-0.0260007 + 0.0450346i) q^{5} -1.56191i q^{6} +(3.86429 - 2.23105i) q^{7} +2.26743i q^{8} +(-1.58202 - 2.74014i) q^{9} +0.0327144i q^{10} -0.838293i q^{11} +(1.99145 + 3.44929i) q^{12} +(-0.282377 + 0.163031i) q^{13} +(1.40356 - 2.43104i) q^{14} +(0.0645533 + 0.111810i) q^{15} +(-0.891002 - 1.54326i) q^{16} -4.16708 q^{17} +(-1.72383 - 0.995254i) q^{18} +(1.06954 - 1.85249i) q^{19} +(-0.0417111 - 0.0722458i) q^{20} -11.0783i q^{21} +(-0.263687 - 0.456719i) q^{22} +(1.05574 + 1.82859i) q^{23} +(4.87526 + 2.81473i) q^{24} +(2.49865 + 4.32779i) q^{25} +(-0.102563 + 0.177645i) q^{26} -0.407259 q^{27} +7.15822i q^{28} +(0.848180 - 1.46909i) q^{29} +(0.0703399 + 0.0406107i) q^{30} -1.88493 q^{31} +(-4.89818 - 2.82797i) q^{32} +(-1.80243 - 1.04064i) q^{33} +(-2.27031 + 1.31076i) q^{34} +0.232036i q^{35} +5.07583 q^{36} -6.18873 q^{37} -1.34570i q^{38} +0.809528i q^{39} +(-0.102113 - 0.0589550i) q^{40} -9.18580 q^{41} +(-3.48469 - 6.03566i) q^{42} +(2.02422 + 1.16868i) q^{43} +(1.16464 + 0.672407i) q^{44} +0.164535 q^{45} +(1.15037 + 0.664169i) q^{46} +7.16739i q^{47} -4.42426 q^{48} +(6.45516 - 11.1807i) q^{49} +(2.72263 + 1.57191i) q^{50} +(-5.17290 + 8.95972i) q^{51} -0.523077i q^{52} +14.2776i q^{53} +(-0.221883 + 0.128104i) q^{54} +(0.0377522 + 0.0217963i) q^{55} +(5.05876 + 8.76203i) q^{56} +(-2.65539 - 4.59927i) q^{57} -1.06719i q^{58} +(9.70396 + 5.60259i) q^{59} -0.207116 q^{60} +6.56089i q^{61} +(-1.02695 + 0.592909i) q^{62} +(-12.2268 - 7.05912i) q^{63} +0.00583457 q^{64} -0.0169557i q^{65} -1.30934 q^{66} +1.28482 q^{67} +(3.34247 - 5.78933i) q^{68} +5.24226 q^{69} +(0.0729873 + 0.126418i) q^{70} +(-3.10180 + 1.79082i) q^{71} +(6.21308 - 3.58712i) q^{72} +(5.64929 - 9.78485i) q^{73} +(-3.37175 + 1.94668i) q^{74} +12.4070 q^{75} +(1.71578 + 2.97182i) q^{76} +(-1.87027 - 3.23941i) q^{77} +(0.254639 + 0.441047i) q^{78} +9.05345i q^{79} +0.0926668 q^{80} +(4.24049 - 7.34475i) q^{81} +(-5.00461 + 2.88941i) q^{82} +(-1.01912 - 1.76517i) q^{83} +(15.3911 + 8.88603i) q^{84} +(0.108347 - 0.187663i) q^{85} +1.47045 q^{86} +(-2.10582 - 3.64738i) q^{87} +1.90078 q^{88} +(-2.30329 - 1.32981i) q^{89} +(0.0896418 - 0.0517547i) q^{90} +(-0.727459 + 1.26000i) q^{91} -3.38729 q^{92} +(-2.33990 + 4.05283i) q^{93} +(2.25452 + 3.90494i) q^{94} +(0.0556175 + 0.0963323i) q^{95} +(-12.1610 + 7.02113i) q^{96} +(-12.9635 + 7.48450i) q^{97} -8.12194i q^{98} +(-2.29704 + 1.32619i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.544820 0.314552i 0.385246 0.222422i −0.294852 0.955543i \(-0.595270\pi\)
0.680098 + 0.733121i \(0.261937\pi\)
\(3\) 1.24137 2.15012i 0.716707 1.24137i −0.245590 0.969374i \(-0.578982\pi\)
0.962297 0.272000i \(-0.0876851\pi\)
\(4\) −0.802114 + 1.38930i −0.401057 + 0.694651i
\(5\) −0.0260007 + 0.0450346i −0.0116279 + 0.0201401i −0.871781 0.489896i \(-0.837035\pi\)
0.860153 + 0.510036i \(0.170368\pi\)
\(6\) 1.56191i 0.637646i
\(7\) 3.86429 2.23105i 1.46056 0.843257i 0.461527 0.887126i \(-0.347302\pi\)
0.999037 + 0.0438687i \(0.0139683\pi\)
\(8\) 2.26743i 0.801659i
\(9\) −1.58202 2.74014i −0.527339 0.913378i
\(10\) 0.0327144i 0.0103452i
\(11\) 0.838293i 0.252755i −0.991982 0.126377i \(-0.959665\pi\)
0.991982 0.126377i \(-0.0403351\pi\)
\(12\) 1.99145 + 3.44929i 0.574881 + 0.995723i
\(13\) −0.282377 + 0.163031i −0.0783174 + 0.0452166i −0.538647 0.842531i \(-0.681064\pi\)
0.460330 + 0.887748i \(0.347731\pi\)
\(14\) 1.40356 2.43104i 0.375118 0.649723i
\(15\) 0.0645533 + 0.111810i 0.0166676 + 0.0288691i
\(16\) −0.891002 1.54326i −0.222750 0.385815i
\(17\) −4.16708 −1.01066 −0.505332 0.862925i \(-0.668630\pi\)
−0.505332 + 0.862925i \(0.668630\pi\)
\(18\) −1.72383 0.995254i −0.406311 0.234584i
\(19\) 1.06954 1.85249i 0.245368 0.424991i −0.716867 0.697210i \(-0.754424\pi\)
0.962235 + 0.272220i \(0.0877577\pi\)
\(20\) −0.0417111 0.0722458i −0.00932689 0.0161547i
\(21\) 11.0783i 2.41748i
\(22\) −0.263687 0.456719i −0.0562182 0.0973728i
\(23\) 1.05574 + 1.82859i 0.220136 + 0.381287i 0.954849 0.297091i \(-0.0960164\pi\)
−0.734713 + 0.678378i \(0.762683\pi\)
\(24\) 4.87526 + 2.81473i 0.995159 + 0.574555i
\(25\) 2.49865 + 4.32779i 0.499730 + 0.865557i
\(26\) −0.102563 + 0.177645i −0.0201143 + 0.0348390i
\(27\) −0.407259 −0.0783770
\(28\) 7.15822i 1.35278i
\(29\) 0.848180 1.46909i 0.157503 0.272803i −0.776465 0.630161i \(-0.782989\pi\)
0.933968 + 0.357358i \(0.116322\pi\)
\(30\) 0.0703399 + 0.0406107i 0.0128422 + 0.00741447i
\(31\) −1.88493 −0.338543 −0.169272 0.985569i \(-0.554142\pi\)
−0.169272 + 0.985569i \(0.554142\pi\)
\(32\) −4.89818 2.82797i −0.865885 0.499919i
\(33\) −1.80243 1.04064i −0.313763 0.181151i
\(34\) −2.27031 + 1.31076i −0.389354 + 0.224794i
\(35\) 0.232036i 0.0392212i
\(36\) 5.07583 0.845972
\(37\) −6.18873 −1.01742 −0.508711 0.860937i \(-0.669878\pi\)
−0.508711 + 0.860937i \(0.669878\pi\)
\(38\) 1.34570i 0.218301i
\(39\) 0.809528i 0.129628i
\(40\) −0.102113 0.0589550i −0.0161455 0.00932160i
\(41\) −9.18580 −1.43458 −0.717290 0.696774i \(-0.754618\pi\)
−0.717290 + 0.696774i \(0.754618\pi\)
\(42\) −3.48469 6.03566i −0.537699 0.931323i
\(43\) 2.02422 + 1.16868i 0.308691 + 0.178223i 0.646340 0.763049i \(-0.276299\pi\)
−0.337650 + 0.941272i \(0.609632\pi\)
\(44\) 1.16464 + 0.672407i 0.175576 + 0.101369i
\(45\) 0.164535 0.0245274
\(46\) 1.15037 + 0.664169i 0.169613 + 0.0979263i
\(47\) 7.16739i 1.04547i 0.852495 + 0.522736i \(0.175089\pi\)
−0.852495 + 0.522736i \(0.824911\pi\)
\(48\) −4.42426 −0.638588
\(49\) 6.45516 11.1807i 0.922166 1.59724i
\(50\) 2.72263 + 1.57191i 0.385038 + 0.222302i
\(51\) −5.17290 + 8.95972i −0.724351 + 1.25461i
\(52\) 0.523077i 0.0725377i
\(53\) 14.2776i 1.96119i 0.196055 + 0.980593i \(0.437187\pi\)
−0.196055 + 0.980593i \(0.562813\pi\)
\(54\) −0.221883 + 0.128104i −0.0301944 + 0.0174328i
\(55\) 0.0377522 + 0.0217963i 0.00509051 + 0.00293901i
\(56\) 5.05876 + 8.76203i 0.676005 + 1.17088i
\(57\) −2.65539 4.59927i −0.351715 0.609188i
\(58\) 1.06719i 0.140129i
\(59\) 9.70396 + 5.60259i 1.26335 + 0.729395i 0.973721 0.227745i \(-0.0731352\pi\)
0.289628 + 0.957139i \(0.406469\pi\)
\(60\) −0.207116 −0.0267386
\(61\) 6.56089i 0.840035i 0.907516 + 0.420018i \(0.137976\pi\)
−0.907516 + 0.420018i \(0.862024\pi\)
\(62\) −1.02695 + 0.592909i −0.130423 + 0.0752995i
\(63\) −12.2268 7.05912i −1.54043 0.889365i
\(64\) 0.00583457 0.000729322
\(65\) 0.0169557i 0.00210309i
\(66\) −1.30934 −0.161168
\(67\) 1.28482 0.156966 0.0784828 0.996915i \(-0.474992\pi\)
0.0784828 + 0.996915i \(0.474992\pi\)
\(68\) 3.34247 5.78933i 0.405334 0.702059i
\(69\) 5.24226 0.631094
\(70\) 0.0729873 + 0.126418i 0.00872366 + 0.0151098i
\(71\) −3.10180 + 1.79082i −0.368116 + 0.212532i −0.672635 0.739975i \(-0.734838\pi\)
0.304519 + 0.952506i \(0.401504\pi\)
\(72\) 6.21308 3.58712i 0.732218 0.422746i
\(73\) 5.64929 9.78485i 0.661199 1.14523i −0.319102 0.947720i \(-0.603381\pi\)
0.980301 0.197510i \(-0.0632855\pi\)
\(74\) −3.37175 + 1.94668i −0.391958 + 0.226297i
\(75\) 12.4070 1.43264
\(76\) 1.71578 + 2.97182i 0.196813 + 0.340891i
\(77\) −1.87027 3.23941i −0.213137 0.369165i
\(78\) 0.254639 + 0.441047i 0.0288321 + 0.0499387i
\(79\) 9.05345i 1.01859i 0.860591 + 0.509296i \(0.170094\pi\)
−0.860591 + 0.509296i \(0.829906\pi\)
\(80\) 0.0926668 0.0103605
\(81\) 4.24049 7.34475i 0.471166 0.816083i
\(82\) −5.00461 + 2.88941i −0.552666 + 0.319082i
\(83\) −1.01912 1.76517i −0.111863 0.193753i 0.804658 0.593738i \(-0.202349\pi\)
−0.916522 + 0.399985i \(0.869015\pi\)
\(84\) 15.3911 + 8.88603i 1.67930 + 0.969545i
\(85\) 0.108347 0.187663i 0.0117519 0.0203549i
\(86\) 1.47045 0.158562
\(87\) −2.10582 3.64738i −0.225767 0.391040i
\(88\) 1.90078 0.202623
\(89\) −2.30329 1.32981i −0.244149 0.140959i 0.372933 0.927858i \(-0.378352\pi\)
−0.617082 + 0.786899i \(0.711685\pi\)
\(90\) 0.0896418 0.0517547i 0.00944907 0.00545542i
\(91\) −0.727459 + 1.26000i −0.0762584 + 0.132083i
\(92\) −3.38729 −0.353149
\(93\) −2.33990 + 4.05283i −0.242637 + 0.420259i
\(94\) 2.25452 + 3.90494i 0.232536 + 0.402764i
\(95\) 0.0556175 + 0.0963323i 0.00570623 + 0.00988348i
\(96\) −12.1610 + 7.02113i −1.24117 + 0.716591i
\(97\) −12.9635 + 7.48450i −1.31625 + 0.759936i −0.983123 0.182947i \(-0.941436\pi\)
−0.333125 + 0.942883i \(0.608103\pi\)
\(98\) 8.12194i 0.820440i
\(99\) −2.29704 + 1.32619i −0.230861 + 0.133288i
\(100\) −8.01680 −0.801680
\(101\) 0.993439i 0.0988509i −0.998778 0.0494255i \(-0.984261\pi\)
0.998778 0.0494255i \(-0.0157390\pi\)
\(102\) 6.50858i 0.644446i
\(103\) 11.8142i 1.16409i −0.813158 0.582043i \(-0.802253\pi\)
0.813158 0.582043i \(-0.197747\pi\)
\(104\) −0.369661 0.640272i −0.0362483 0.0627839i
\(105\) 0.498905 + 0.288043i 0.0486882 + 0.0281101i
\(106\) 4.49106 + 7.77875i 0.436211 + 0.755539i
\(107\) −7.76733 + 4.48447i −0.750896 + 0.433530i −0.826017 0.563645i \(-0.809399\pi\)
0.0751217 + 0.997174i \(0.476065\pi\)
\(108\) 0.326668 0.565805i 0.0314336 0.0544446i
\(109\) 4.43496 7.68157i 0.424792 0.735761i −0.571609 0.820526i \(-0.693681\pi\)
0.996401 + 0.0847652i \(0.0270140\pi\)
\(110\) 0.0274242 0.00261480
\(111\) −7.68253 + 13.3065i −0.729194 + 1.26300i
\(112\) −6.88618 3.97574i −0.650683 0.375672i
\(113\) −1.96265 + 1.13314i −0.184631 + 0.106597i −0.589467 0.807793i \(-0.700662\pi\)
0.404836 + 0.914389i \(0.367329\pi\)
\(114\) −2.89342 1.67052i −0.270993 0.156458i
\(115\) −0.109800 −0.0102389
\(116\) 1.36067 + 2.35676i 0.126335 + 0.218819i
\(117\) 0.893452 + 0.515835i 0.0825997 + 0.0476889i
\(118\) 7.04922 0.648933
\(119\) −16.1028 + 9.29695i −1.47614 + 0.852250i
\(120\) −0.253521 + 0.146370i −0.0231432 + 0.0133617i
\(121\) 10.2973 0.936115
\(122\) 2.06374 + 3.57450i 0.186842 + 0.323620i
\(123\) −11.4030 + 19.7506i −1.02817 + 1.78085i
\(124\) 1.51193 2.61874i 0.135775 0.235170i
\(125\) −0.519874 −0.0464990
\(126\) −8.88184 −0.791257
\(127\) 14.8998i 1.32214i −0.750324 0.661071i \(-0.770102\pi\)
0.750324 0.661071i \(-0.229898\pi\)
\(128\) 9.79955 5.65777i 0.866166 0.500081i
\(129\) 5.02563 2.90155i 0.442482 0.255467i
\(130\) −0.00533344 0.00923779i −0.000467774 0.000810208i
\(131\) 15.6634i 1.36852i −0.729239 0.684259i \(-0.760126\pi\)
0.729239 0.684259i \(-0.239874\pi\)
\(132\) 2.89151 1.66942i 0.251674 0.145304i
\(133\) 9.54475i 0.827635i
\(134\) 0.699995 0.404142i 0.0604704 0.0349126i
\(135\) 0.0105890 0.0183407i 0.000911359 0.00157852i
\(136\) 9.44857i 0.810208i
\(137\) −11.1129 6.41602i −0.949437 0.548158i −0.0565311 0.998401i \(-0.518004\pi\)
−0.892906 + 0.450243i \(0.851337\pi\)
\(138\) 2.85609 1.64896i 0.243126 0.140369i
\(139\) −16.7768 −1.42299 −0.711495 0.702691i \(-0.751982\pi\)
−0.711495 + 0.702691i \(0.751982\pi\)
\(140\) −0.322368 0.186119i −0.0272451 0.0157299i
\(141\) 15.4108 + 8.89741i 1.29782 + 0.749297i
\(142\) −1.12661 + 1.95135i −0.0945434 + 0.163754i
\(143\) 0.136667 + 0.236715i 0.0114287 + 0.0197951i
\(144\) −2.81916 + 4.88293i −0.234930 + 0.406911i
\(145\) 0.0441066 + 0.0763949i 0.00366286 + 0.00634425i
\(146\) 7.10798i 0.588261i
\(147\) −16.0265 27.7588i −1.32185 2.28951i
\(148\) 4.96407 8.59802i 0.408044 0.706753i
\(149\) −9.62437 + 5.55663i −0.788459 + 0.455217i −0.839420 0.543484i \(-0.817105\pi\)
0.0509609 + 0.998701i \(0.483772\pi\)
\(150\) 6.75960 3.90266i 0.551919 0.318650i
\(151\) −4.70094 + 8.14226i −0.382557 + 0.662608i −0.991427 0.130662i \(-0.958290\pi\)
0.608870 + 0.793270i \(0.291623\pi\)
\(152\) 4.20040 + 2.42510i 0.340698 + 0.196702i
\(153\) 6.59239 + 11.4183i 0.532963 + 0.923119i
\(154\) −2.03793 1.17660i −0.164221 0.0948129i
\(155\) 0.0490096 0.0848871i 0.00393655 0.00681830i
\(156\) −1.12468 0.649334i −0.0900464 0.0519883i
\(157\) 9.11212 15.7826i 0.727226 1.25959i −0.230825 0.972995i \(-0.574142\pi\)
0.958051 0.286597i \(-0.0925242\pi\)
\(158\) 2.84778 + 4.93250i 0.226557 + 0.392409i
\(159\) 30.6987 + 17.7239i 2.43456 + 1.40560i
\(160\) 0.254713 0.147059i 0.0201368 0.0116260i
\(161\) 8.15935 + 4.71080i 0.643047 + 0.371263i
\(162\) 5.33542i 0.419190i
\(163\) 3.76838i 0.295162i −0.989050 0.147581i \(-0.952851\pi\)
0.989050 0.147581i \(-0.0471488\pi\)
\(164\) 7.36806 12.7618i 0.575349 0.996533i
\(165\) 0.0937292 0.0541146i 0.00729681 0.00421282i
\(166\) −1.11048 0.641135i −0.0861898 0.0497617i
\(167\) 16.9359i 1.31054i −0.755395 0.655270i \(-0.772555\pi\)
0.755395 0.655270i \(-0.227445\pi\)
\(168\) 25.1192 1.93799
\(169\) −6.44684 + 11.1663i −0.495911 + 0.858943i
\(170\) 0.136323i 0.0104555i
\(171\) −6.76810 −0.517570
\(172\) −3.24731 + 1.87484i −0.247605 + 0.142955i
\(173\) −1.42916 + 0.825123i −0.108657 + 0.0627330i −0.553344 0.832953i \(-0.686648\pi\)
0.444687 + 0.895686i \(0.353315\pi\)
\(174\) −2.29458 1.32478i −0.173952 0.100431i
\(175\) 19.3110 + 11.1492i 1.45977 + 0.842801i
\(176\) −1.29370 + 0.746921i −0.0975167 + 0.0563013i
\(177\) 24.0925 13.9098i 1.81090 1.04553i
\(178\) −1.67317 −0.125410
\(179\) 12.9191i 0.965619i 0.875725 + 0.482810i \(0.160384\pi\)
−0.875725 + 0.482810i \(0.839616\pi\)
\(180\) −0.131975 + 0.228588i −0.00983687 + 0.0170380i
\(181\) 17.2917 1.28528 0.642641 0.766168i \(-0.277839\pi\)
0.642641 + 0.766168i \(0.277839\pi\)
\(182\) 0.915295i 0.0678461i
\(183\) 14.1067 + 8.14451i 1.04280 + 0.602060i
\(184\) −4.14621 + 2.39382i −0.305663 + 0.176474i
\(185\) 0.160912 0.278707i 0.0118305 0.0204910i
\(186\) 2.94409i 0.215871i
\(187\) 3.49323i 0.255450i
\(188\) −9.95767 5.74907i −0.726238 0.419294i
\(189\) −1.57377 + 0.908614i −0.114475 + 0.0660919i
\(190\) 0.0606030 + 0.0349892i 0.00439661 + 0.00253838i
\(191\) −13.7283 23.7781i −0.993345 1.72052i −0.596420 0.802673i \(-0.703411\pi\)
−0.396925 0.917851i \(-0.629923\pi\)
\(192\) 0.00724289 0.0125451i 0.000522710 0.000905361i
\(193\) 5.30524 + 3.06298i 0.381880 + 0.220478i 0.678636 0.734475i \(-0.262572\pi\)
−0.296756 + 0.954953i \(0.595905\pi\)
\(194\) −4.70853 + 8.15541i −0.338053 + 0.585525i
\(195\) −0.0364568 0.0210483i −0.00261072 0.00150730i
\(196\) 10.3555 + 17.9363i 0.739682 + 1.28117i
\(197\) −7.61910 4.39889i −0.542838 0.313408i 0.203390 0.979098i \(-0.434804\pi\)
−0.746228 + 0.665690i \(0.768137\pi\)
\(198\) −0.834315 + 1.44508i −0.0592922 + 0.102697i
\(199\) 18.6063 10.7423i 1.31896 0.761504i 0.335402 0.942075i \(-0.391128\pi\)
0.983562 + 0.180571i \(0.0577945\pi\)
\(200\) −9.81297 + 5.66552i −0.693882 + 0.400613i
\(201\) 1.59494 2.76252i 0.112498 0.194853i
\(202\) −0.312488 0.541246i −0.0219866 0.0380819i
\(203\) 7.56932i 0.531262i
\(204\) −8.29851 14.3734i −0.581012 1.00634i
\(205\) 0.238838 0.413679i 0.0166811 0.0288926i
\(206\) −3.71618 6.43661i −0.258918 0.448460i
\(207\) 3.34039 5.78572i 0.232173 0.402136i
\(208\) 0.503197 + 0.290521i 0.0348905 + 0.0201440i
\(209\) −1.55293 0.896585i −0.107418 0.0620181i
\(210\) 0.362418 0.0250092
\(211\) −18.2100 + 10.5136i −1.25363 + 0.723784i −0.971829 0.235689i \(-0.924265\pi\)
−0.281802 + 0.959473i \(0.590932\pi\)
\(212\) −19.8360 11.4523i −1.36234 0.786547i
\(213\) 8.89232i 0.609292i
\(214\) −2.82120 + 4.88646i −0.192853 + 0.334031i
\(215\) −0.105262 + 0.0607733i −0.00717884 + 0.00414470i
\(216\) 0.923432i 0.0628316i
\(217\) −7.28392 + 4.20537i −0.494465 + 0.285479i
\(218\) 5.58010i 0.377932i
\(219\) −14.0258 24.2933i −0.947773 1.64159i
\(220\) −0.0605632 + 0.0349662i −0.00408317 + 0.00235742i
\(221\) 1.17669 0.679361i 0.0791526 0.0456988i
\(222\) 9.66622i 0.648755i
\(223\) 14.6442 0.980651 0.490325 0.871539i \(-0.336878\pi\)
0.490325 + 0.871539i \(0.336878\pi\)
\(224\) −25.2373 −1.68624
\(225\) 7.90581 13.6933i 0.527054 0.912884i
\(226\) −0.712861 + 1.23471i −0.0474188 + 0.0821318i
\(227\) 5.45166 + 9.44255i 0.361839 + 0.626724i 0.988264 0.152758i \(-0.0488156\pi\)
−0.626424 + 0.779482i \(0.715482\pi\)
\(228\) 8.51970 0.564231
\(229\) 18.3776 10.6103i 1.21443 0.701150i 0.250707 0.968063i \(-0.419337\pi\)
0.963721 + 0.266913i \(0.0860037\pi\)
\(230\) −0.0598212 + 0.0345378i −0.00394449 + 0.00227735i
\(231\) −9.28683 −0.611029
\(232\) 3.33107 + 1.92319i 0.218695 + 0.126264i
\(233\) −1.79998 3.11766i −0.117921 0.204245i 0.801023 0.598634i \(-0.204290\pi\)
−0.918944 + 0.394389i \(0.870956\pi\)
\(234\) 0.649028 0.0424283
\(235\) −0.322781 0.186358i −0.0210559 0.0121566i
\(236\) −15.5674 + 8.98783i −1.01335 + 0.585058i
\(237\) 19.4660 + 11.2387i 1.26445 + 0.730033i
\(238\) −5.84875 + 10.1303i −0.379118 + 0.656652i
\(239\) 2.01095 0.130077 0.0650387 0.997883i \(-0.479283\pi\)
0.0650387 + 0.997883i \(0.479283\pi\)
\(240\) 0.115034 0.199245i 0.00742543 0.0128612i
\(241\) 2.67342 4.63049i 0.172210 0.298276i −0.766982 0.641668i \(-0.778243\pi\)
0.939192 + 0.343392i \(0.111576\pi\)
\(242\) 5.61016 3.23903i 0.360635 0.208212i
\(243\) −11.1390 19.2932i −0.714565 1.23766i
\(244\) −9.11505 5.26258i −0.583532 0.336902i
\(245\) 0.335678 + 0.581411i 0.0214457 + 0.0371450i
\(246\) 14.3474i 0.914754i
\(247\) 0.697469i 0.0443789i
\(248\) 4.27396i 0.271396i
\(249\) −5.06045 −0.320693
\(250\) −0.283238 + 0.163528i −0.0179135 + 0.0103424i
\(251\) 0.950211i 0.0599768i −0.999550 0.0299884i \(-0.990453\pi\)
0.999550 0.0299884i \(-0.00954703\pi\)
\(252\) 19.6145 11.3244i 1.23560 0.713372i
\(253\) 1.53290 0.885017i 0.0963723 0.0556406i
\(254\) −4.68675 8.11770i −0.294073 0.509350i
\(255\) −0.268998 0.465919i −0.0168453 0.0291770i
\(256\) 3.55349 6.15483i 0.222093 0.384677i
\(257\) −2.68835 −0.167694 −0.0838472 0.996479i \(-0.526721\pi\)
−0.0838472 + 0.996479i \(0.526721\pi\)
\(258\) 1.82538 3.16164i 0.113643 0.196835i
\(259\) −23.9151 + 13.8074i −1.48601 + 0.857948i
\(260\) 0.0235566 + 0.0136004i 0.00146092 + 0.000843460i
\(261\) −5.36734 −0.332230
\(262\) −4.92696 8.53374i −0.304388 0.527216i
\(263\) 2.82222 0.174026 0.0870129 0.996207i \(-0.472268\pi\)
0.0870129 + 0.996207i \(0.472268\pi\)
\(264\) 2.35957 4.08690i 0.145222 0.251531i
\(265\) −0.642988 0.371230i −0.0394985 0.0228045i
\(266\) −3.00232 5.20017i −0.184084 0.318843i
\(267\) −5.71850 + 3.30158i −0.349966 + 0.202053i
\(268\) −1.03057 + 1.78500i −0.0629521 + 0.109036i
\(269\) 7.22219 0.440345 0.220172 0.975461i \(-0.429338\pi\)
0.220172 + 0.975461i \(0.429338\pi\)
\(270\) 0.0133232i 0.000810824i
\(271\) 13.7444 + 23.8060i 0.834912 + 1.44611i 0.894102 + 0.447863i \(0.147815\pi\)
−0.0591901 + 0.998247i \(0.518852\pi\)
\(272\) 3.71287 + 6.43088i 0.225126 + 0.389929i
\(273\) 1.80610 + 3.12825i 0.109310 + 0.189330i
\(274\) −8.07269 −0.487689
\(275\) 3.62795 2.09460i 0.218774 0.126309i
\(276\) −4.20489 + 7.28308i −0.253105 + 0.438390i
\(277\) −5.16922 + 2.98445i −0.310589 + 0.179318i −0.647190 0.762329i \(-0.724056\pi\)
0.336601 + 0.941647i \(0.390723\pi\)
\(278\) −9.14035 + 5.27718i −0.548201 + 0.316504i
\(279\) 2.98199 + 5.16496i 0.178527 + 0.309218i
\(280\) −0.526126 −0.0314420
\(281\) 1.25346 2.17105i 0.0747750 0.129514i −0.826213 0.563357i \(-0.809509\pi\)
0.900988 + 0.433843i \(0.142843\pi\)
\(282\) 11.1948 0.666641
\(283\) 10.4991 0.624108 0.312054 0.950064i \(-0.398983\pi\)
0.312054 + 0.950064i \(0.398983\pi\)
\(284\) 5.74578i 0.340949i
\(285\) 0.276168 0.0163588
\(286\) 0.148918 + 0.0859781i 0.00880573 + 0.00508399i
\(287\) −35.4966 + 20.4940i −2.09530 + 1.20972i
\(288\) 17.8956i 1.05451i
\(289\) 0.364516 0.0214421
\(290\) 0.0480604 + 0.0277477i 0.00282220 + 0.00162940i
\(291\) 37.1643i 2.17861i
\(292\) 9.06275 + 15.6971i 0.530357 + 0.918605i
\(293\) 5.15367 + 8.92641i 0.301080 + 0.521487i 0.976381 0.216056i \(-0.0693194\pi\)
−0.675301 + 0.737543i \(0.735986\pi\)
\(294\) −17.4632 10.0824i −1.01847 0.588015i
\(295\) −0.504621 + 0.291343i −0.0293802 + 0.0169626i
\(296\) 14.0325i 0.815625i
\(297\) 0.341402i 0.0198102i
\(298\) −3.49570 + 6.05473i −0.202500 + 0.350741i
\(299\) −0.596232 0.344235i −0.0344810 0.0199076i
\(300\) −9.95185 + 17.2371i −0.574570 + 0.995185i
\(301\) 10.4296 0.601150
\(302\) 5.91476i 0.340356i
\(303\) −2.13602 1.23323i −0.122711 0.0708472i
\(304\) −3.81183 −0.218624
\(305\) −0.295467 0.170588i −0.0169184 0.00976784i
\(306\) 7.18333 + 4.14730i 0.410644 + 0.237085i
\(307\) −3.08985 5.35177i −0.176347 0.305442i 0.764280 0.644885i \(-0.223095\pi\)
−0.940627 + 0.339443i \(0.889761\pi\)
\(308\) 6.00069 0.341921
\(309\) −25.4020 14.6658i −1.44507 0.834310i
\(310\) 0.0616643i 0.00350230i
\(311\) 28.4283i 1.61202i −0.591902 0.806010i \(-0.701623\pi\)
0.591902 0.806010i \(-0.298377\pi\)
\(312\) −1.83555 −0.103918
\(313\) 25.4077 1.43613 0.718063 0.695978i \(-0.245029\pi\)
0.718063 + 0.695978i \(0.245029\pi\)
\(314\) 11.4649i 0.647004i
\(315\) 0.635809 0.367085i 0.0358238 0.0206829i
\(316\) −12.5780 7.26190i −0.707566 0.408514i
\(317\) 12.6132 + 7.28223i 0.708427 + 0.409011i 0.810478 0.585769i \(-0.199207\pi\)
−0.102051 + 0.994779i \(0.532541\pi\)
\(318\) 22.3004 1.25054
\(319\) −1.23153 0.711024i −0.0689524 0.0398097i
\(320\) −0.000151703 0 0.000262758i −8.48047e−6 0 1.46886e-5i
\(321\) 22.2676i 1.24286i
\(322\) 5.92717 0.330308
\(323\) −4.45684 + 7.71947i −0.247985 + 0.429523i
\(324\) 6.80272 + 11.7827i 0.377929 + 0.654592i
\(325\) −1.41112 0.814712i −0.0782750 0.0451921i
\(326\) −1.18535 2.05309i −0.0656506 0.113710i
\(327\) −11.0109 19.0714i −0.608903 1.05465i
\(328\) 20.8282i 1.15004i
\(329\) 15.9908 + 27.6969i 0.881602 + 1.52698i
\(330\) 0.0340437 0.0589654i 0.00187404 0.00324594i
\(331\) −18.9290 10.9287i −1.04043 0.600694i −0.120476 0.992716i \(-0.538442\pi\)
−0.919956 + 0.392023i \(0.871776\pi\)
\(332\) 3.26981 0.179454
\(333\) 9.79069 + 16.9580i 0.536526 + 0.929291i
\(334\) −5.32722 9.22702i −0.291493 0.504880i
\(335\) −0.0334062 + 0.0578613i −0.00182518 + 0.00316130i
\(336\) −17.0966 + 9.87075i −0.932698 + 0.538494i
\(337\) −13.5539 23.4761i −0.738331 1.27883i −0.953247 0.302193i \(-0.902281\pi\)
0.214916 0.976633i \(-0.431052\pi\)
\(338\) 8.11147i 0.441206i
\(339\) 5.62659i 0.305594i
\(340\) 0.173813 + 0.301054i 0.00942636 + 0.0163269i
\(341\) 1.58012i 0.0855685i
\(342\) −3.68740 + 2.12892i −0.199392 + 0.115119i
\(343\) 26.3724i 1.42398i
\(344\) −2.64991 + 4.58979i −0.142874 + 0.247465i
\(345\) −0.136303 + 0.236083i −0.00733829 + 0.0127103i
\(346\) −0.519089 + 0.899088i −0.0279064 + 0.0483353i
\(347\) −3.66980 + 2.11876i −0.197005 + 0.113741i −0.595258 0.803535i \(-0.702950\pi\)
0.398252 + 0.917276i \(0.369617\pi\)
\(348\) 6.75642 0.362182
\(349\) 18.6774 0.394140i 0.999777 0.0210978i
\(350\) 14.0280 0.749830
\(351\) 0.115001 0.0663956i 0.00613828 0.00354394i
\(352\) −2.37067 + 4.10611i −0.126357 + 0.218857i
\(353\) −12.2739 + 21.2590i −0.653274 + 1.13150i 0.329049 + 0.944313i \(0.393272\pi\)
−0.982323 + 0.187191i \(0.940062\pi\)
\(354\) 8.75072 15.1567i 0.465095 0.805569i
\(355\) 0.186251i 0.00988518i
\(356\) 3.69501 2.13331i 0.195835 0.113065i
\(357\) 46.1640i 2.44326i
\(358\) 4.06373 + 7.03859i 0.214775 + 0.372001i
\(359\) 28.8960i 1.52507i −0.646945 0.762537i \(-0.723954\pi\)
0.646945 0.762537i \(-0.276046\pi\)
\(360\) 0.373071i 0.0196626i
\(361\) 7.21219 + 12.4919i 0.379589 + 0.657467i
\(362\) 9.42086 5.43914i 0.495150 0.285875i
\(363\) 12.7828 22.1404i 0.670921 1.16207i
\(364\) −1.16701 2.02132i −0.0611679 0.105946i
\(365\) 0.293771 + 0.508827i 0.0153767 + 0.0266332i
\(366\) 10.2475 0.535645
\(367\) 0.496327 + 0.286554i 0.0259080 + 0.0149580i 0.512898 0.858450i \(-0.328572\pi\)
−0.486990 + 0.873408i \(0.661905\pi\)
\(368\) 1.88133 3.25855i 0.0980710 0.169864i
\(369\) 14.5321 + 25.1703i 0.756511 + 1.31031i
\(370\) 0.202460i 0.0105254i
\(371\) 31.8541 + 55.1730i 1.65378 + 2.86444i
\(372\) −3.75374 6.50166i −0.194622 0.337096i
\(373\) 25.6106 + 14.7863i 1.32607 + 0.765606i 0.984689 0.174319i \(-0.0557724\pi\)
0.341380 + 0.939925i \(0.389106\pi\)
\(374\) 1.09880 + 1.90318i 0.0568178 + 0.0984112i
\(375\) −0.645358 + 1.11779i −0.0333262 + 0.0577226i
\(376\) −16.2516 −0.838112
\(377\) 0.553117i 0.0284870i
\(378\) −0.571613 + 0.990063i −0.0294006 + 0.0509233i
\(379\) 20.1059 + 11.6082i 1.03277 + 0.596271i 0.917778 0.397095i \(-0.129982\pi\)
0.114995 + 0.993366i \(0.463315\pi\)
\(380\) −0.178446 −0.00915410
\(381\) −32.0363 18.4962i −1.64127 0.947588i
\(382\) −14.9589 8.63653i −0.765364 0.441883i
\(383\) −27.6765 + 15.9790i −1.41420 + 0.816489i −0.995781 0.0917642i \(-0.970749\pi\)
−0.418420 + 0.908254i \(0.637416\pi\)
\(384\) 28.0936i 1.43365i
\(385\) 0.194514 0.00991335
\(386\) 3.85387 0.196157
\(387\) 7.39551i 0.375935i
\(388\) 24.0137i 1.21911i
\(389\) 25.2730 + 14.5914i 1.28139 + 0.739811i 0.977103 0.212769i \(-0.0682481\pi\)
0.304288 + 0.952580i \(0.401581\pi\)
\(390\) −0.0264832 −0.00134103
\(391\) −4.39934 7.61987i −0.222484 0.385354i
\(392\) 25.3514 + 14.6367i 1.28044 + 0.739263i
\(393\) −33.6782 19.4441i −1.69884 0.980827i
\(394\) −5.53472 −0.278835
\(395\) −0.407719 0.235396i −0.0205145 0.0118441i
\(396\) 4.25504i 0.213824i
\(397\) −27.2834 −1.36931 −0.684657 0.728865i \(-0.740048\pi\)
−0.684657 + 0.728865i \(0.740048\pi\)
\(398\) 6.75805 11.7053i 0.338750 0.586733i
\(399\) −20.5224 11.8486i −1.02740 0.593172i
\(400\) 4.45260 7.71213i 0.222630 0.385606i
\(401\) 2.62003i 0.130838i −0.997858 0.0654191i \(-0.979162\pi\)
0.997858 0.0654191i \(-0.0208384\pi\)
\(402\) 2.00677i 0.100088i
\(403\) 0.532262 0.307301i 0.0265138 0.0153078i
\(404\) 1.38019 + 0.796852i 0.0686669 + 0.0396449i
\(405\) 0.220512 + 0.381938i 0.0109573 + 0.0189786i
\(406\) −2.38095 4.12392i −0.118164 0.204667i
\(407\) 5.18797i 0.257158i
\(408\) −20.3156 11.7292i −1.00577 0.580682i
\(409\) −19.5189 −0.965150 −0.482575 0.875855i \(-0.660298\pi\)
−0.482575 + 0.875855i \(0.660298\pi\)
\(410\) 0.300507i 0.0148410i
\(411\) −27.5905 + 15.9294i −1.36094 + 0.785738i
\(412\) 16.4135 + 9.47633i 0.808634 + 0.466865i
\(413\) 49.9986 2.46027
\(414\) 4.20291i 0.206562i
\(415\) 0.105992 0.00520294
\(416\) 1.84418 0.0904184
\(417\) −20.8263 + 36.0722i −1.01987 + 1.76646i
\(418\) −1.12809 −0.0551767
\(419\) 2.60493 + 4.51186i 0.127259 + 0.220419i 0.922614 0.385725i \(-0.126049\pi\)
−0.795355 + 0.606144i \(0.792715\pi\)
\(420\) −0.800358 + 0.462087i −0.0390535 + 0.0225475i
\(421\) −19.3409 + 11.1665i −0.942616 + 0.544220i −0.890779 0.454436i \(-0.849841\pi\)
−0.0518367 + 0.998656i \(0.516508\pi\)
\(422\) −6.61413 + 11.4560i −0.321971 + 0.557670i
\(423\) 19.6396 11.3389i 0.954911 0.551318i
\(424\) −32.3736 −1.57220
\(425\) −10.4121 18.0342i −0.505059 0.874787i
\(426\) 2.79710 + 4.84472i 0.135520 + 0.234727i
\(427\) 14.6377 + 25.3532i 0.708366 + 1.22693i
\(428\) 14.3882i 0.695481i
\(429\) 0.678622 0.0327642
\(430\) −0.0382327 + 0.0662210i −0.00184375 + 0.00319346i
\(431\) 6.11969 3.53320i 0.294775 0.170188i −0.345318 0.938486i \(-0.612229\pi\)
0.640093 + 0.768297i \(0.278896\pi\)
\(432\) 0.362868 + 0.628506i 0.0174585 + 0.0302390i
\(433\) −7.98319 4.60910i −0.383648 0.221499i 0.295757 0.955263i \(-0.404428\pi\)
−0.679404 + 0.733764i \(0.737762\pi\)
\(434\) −2.64562 + 4.58234i −0.126994 + 0.219959i
\(435\) 0.219011 0.0105008
\(436\) 7.11468 + 12.3230i 0.340731 + 0.590164i
\(437\) 4.51660 0.216058
\(438\) −15.2830 8.82366i −0.730251 0.421611i
\(439\) 4.09463 2.36404i 0.195426 0.112829i −0.399094 0.916910i \(-0.630675\pi\)
0.594520 + 0.804081i \(0.297342\pi\)
\(440\) −0.0494216 + 0.0856007i −0.00235608 + 0.00408085i
\(441\) −40.8487 −1.94518
\(442\) 0.427389 0.740259i 0.0203288 0.0352105i
\(443\) 9.97339 + 17.2744i 0.473850 + 0.820733i 0.999552 0.0299365i \(-0.00953050\pi\)
−0.525702 + 0.850669i \(0.676197\pi\)
\(444\) −12.3245 21.3467i −0.584896 1.01307i
\(445\) 0.119775 0.0691520i 0.00567787 0.00327812i
\(446\) 7.97848 4.60638i 0.377792 0.218118i
\(447\) 27.5914i 1.30503i
\(448\) 0.0225465 0.0130172i 0.00106522 0.000615006i
\(449\) −7.24079 −0.341714 −0.170857 0.985296i \(-0.554654\pi\)
−0.170857 + 0.985296i \(0.554654\pi\)
\(450\) 9.94716i 0.468913i
\(451\) 7.70039i 0.362597i
\(452\) 3.63562i 0.171005i
\(453\) 11.6712 + 20.2152i 0.548363 + 0.949792i
\(454\) 5.94035 + 3.42966i 0.278794 + 0.160962i
\(455\) −0.0378289 0.0655217i −0.00177345 0.00307170i
\(456\) 10.4285 6.02092i 0.488361 0.281955i
\(457\) −0.100682 + 0.174386i −0.00470969 + 0.00815742i −0.868371 0.495916i \(-0.834832\pi\)
0.863661 + 0.504073i \(0.168166\pi\)
\(458\) 6.67500 11.5614i 0.311902 0.540230i
\(459\) 1.69708 0.0792128
\(460\) 0.0880720 0.152545i 0.00410638 0.00711245i
\(461\) −26.7717 15.4567i −1.24688 0.719889i −0.276398 0.961043i \(-0.589141\pi\)
−0.970487 + 0.241154i \(0.922474\pi\)
\(462\) −5.05965 + 2.92119i −0.235396 + 0.135906i
\(463\) −30.6441 17.6924i −1.42415 0.822235i −0.427503 0.904014i \(-0.640607\pi\)
−0.996651 + 0.0817788i \(0.973940\pi\)
\(464\) −3.02292 −0.140335
\(465\) −0.121678 0.210753i −0.00564270 0.00977345i
\(466\) −1.96133 1.13238i −0.0908570 0.0524563i
\(467\) −15.0983 −0.698665 −0.349333 0.936999i \(-0.613592\pi\)
−0.349333 + 0.936999i \(0.613592\pi\)
\(468\) −1.43330 + 0.827516i −0.0662543 + 0.0382520i
\(469\) 4.96491 2.86649i 0.229258 0.132362i
\(470\) −0.234477 −0.0108156
\(471\) −22.6231 39.1843i −1.04242 1.80552i
\(472\) −12.7035 + 22.0031i −0.584726 + 1.01278i
\(473\) 0.979700 1.69689i 0.0450466 0.0780231i
\(474\) 14.1406 0.649501
\(475\) 10.6896 0.490471
\(476\) 29.8289i 1.36720i
\(477\) 39.1227 22.5875i 1.79130 1.03421i
\(478\) 1.09561 0.632548i 0.0501118 0.0289321i
\(479\) 20.3259 + 35.2054i 0.928712 + 1.60858i 0.785479 + 0.618888i \(0.212417\pi\)
0.143233 + 0.989689i \(0.454250\pi\)
\(480\) 0.730219i 0.0333298i
\(481\) 1.74756 1.00895i 0.0796818 0.0460043i
\(482\) 3.36372i 0.153213i
\(483\) 20.2576 11.6957i 0.921753 0.532174i
\(484\) −8.25958 + 14.3060i −0.375435 + 0.650273i
\(485\) 0.778411i 0.0353458i
\(486\) −12.1375 7.00757i −0.550566 0.317870i
\(487\) 13.9993 8.08252i 0.634371 0.366254i −0.148072 0.988977i \(-0.547307\pi\)
0.782443 + 0.622722i \(0.213973\pi\)
\(488\) −14.8764 −0.673422
\(489\) −8.10248 4.67797i −0.366407 0.211545i
\(490\) 0.365768 + 0.211176i 0.0165237 + 0.00953998i
\(491\) 11.6073 20.1045i 0.523832 0.907303i −0.475783 0.879563i \(-0.657835\pi\)
0.999615 0.0277409i \(-0.00883133\pi\)
\(492\) −18.2930 31.6844i −0.824713 1.42845i
\(493\) −3.53443 + 6.12181i −0.159183 + 0.275713i
\(494\) 0.219390 + 0.379995i 0.00987083 + 0.0170968i
\(495\) 0.137928i 0.00619941i
\(496\) 1.67948 + 2.90894i 0.0754107 + 0.130615i
\(497\) −7.99083 + 13.8405i −0.358438 + 0.620832i
\(498\) −2.75704 + 1.59178i −0.123546 + 0.0713292i
\(499\) 7.66362 4.42460i 0.343071 0.198072i −0.318558 0.947903i \(-0.603199\pi\)
0.661629 + 0.749831i \(0.269865\pi\)
\(500\) 0.416998 0.722263i 0.0186487 0.0323006i
\(501\) −36.4143 21.0238i −1.62687 0.939273i
\(502\) −0.298891 0.517694i −0.0133401 0.0231058i
\(503\) −3.81141 2.20052i −0.169942 0.0981162i 0.412616 0.910905i \(-0.364615\pi\)
−0.582559 + 0.812789i \(0.697948\pi\)
\(504\) 16.0061 27.7234i 0.712968 1.23490i
\(505\) 0.0447392 + 0.0258302i 0.00199087 + 0.00114943i
\(506\) 0.556768 0.964351i 0.0247514 0.0428706i
\(507\) 16.0059 + 27.7230i 0.710846 + 1.23122i
\(508\) 20.7003 + 11.9513i 0.918427 + 0.530254i
\(509\) 36.6026 21.1325i 1.62238 0.936682i 0.636099 0.771607i \(-0.280547\pi\)
0.986281 0.165075i \(-0.0527865\pi\)
\(510\) −0.293112 0.169228i −0.0129792 0.00749354i
\(511\) 50.4154i 2.23024i
\(512\) 18.1600i 0.802568i
\(513\) −0.435578 + 0.754443i −0.0192312 + 0.0333095i
\(514\) −1.46467 + 0.845625i −0.0646036 + 0.0372989i
\(515\) 0.532047 + 0.307178i 0.0234448 + 0.0135359i
\(516\) 9.30948i 0.409827i
\(517\) 6.00838 0.264248
\(518\) −8.68627 + 15.0451i −0.381653 + 0.661042i
\(519\) 4.09715i 0.179845i
\(520\) 0.0384459 0.00168596
\(521\) 16.6240 9.59789i 0.728312 0.420491i −0.0894923 0.995988i \(-0.528524\pi\)
0.817804 + 0.575496i \(0.195191\pi\)
\(522\) −2.92424 + 1.68831i −0.127990 + 0.0738953i
\(523\) −11.1541 6.43983i −0.487735 0.281594i 0.235899 0.971778i \(-0.424196\pi\)
−0.723634 + 0.690183i \(0.757530\pi\)
\(524\) 21.7612 + 12.5638i 0.950643 + 0.548854i
\(525\) 47.9443 27.6807i 2.09246 1.20808i
\(526\) 1.53760 0.887736i 0.0670427 0.0387071i
\(527\) 7.85465 0.342154
\(528\) 3.70883i 0.161406i
\(529\) 9.27084 16.0576i 0.403080 0.698155i
\(530\) −0.467084 −0.0202888
\(531\) 35.4536i 1.53855i
\(532\) 13.2605 + 7.65598i 0.574917 + 0.331929i
\(533\) 2.59386 1.49757i 0.112353 0.0648668i
\(534\) −2.07704 + 3.59753i −0.0898821 + 0.155680i
\(535\) 0.466398i 0.0201641i
\(536\) 2.91324i 0.125833i
\(537\) 27.7777 + 16.0374i 1.19869 + 0.692067i
\(538\) 3.93479 2.27175i 0.169641 0.0979423i
\(539\) −9.37268 5.41132i −0.403710 0.233082i
\(540\) 0.0169872 + 0.0294227i 0.000731013 + 0.00126615i
\(541\) 11.7562 20.3624i 0.505440 0.875447i −0.494541 0.869155i \(-0.664664\pi\)
0.999980 0.00629250i \(-0.00200298\pi\)
\(542\) 14.9764 + 8.64665i 0.643293 + 0.371405i
\(543\) 21.4655 37.1793i 0.921171 1.59551i
\(544\) 20.4111 + 11.7844i 0.875119 + 0.505250i
\(545\) 0.230624 + 0.399453i 0.00987886 + 0.0171107i
\(546\) 1.96800 + 1.13622i 0.0842224 + 0.0486258i
\(547\) −18.9302 + 32.7881i −0.809398 + 1.40192i 0.103883 + 0.994590i \(0.466873\pi\)
−0.913281 + 0.407329i \(0.866460\pi\)
\(548\) 17.8276 10.2928i 0.761557 0.439685i
\(549\) 17.9777 10.3794i 0.767270 0.442984i
\(550\) 1.31772 2.28236i 0.0561878 0.0973202i
\(551\) −1.81432 3.14249i −0.0772925 0.133875i
\(552\) 11.8865i 0.505922i
\(553\) 20.1987 + 34.9852i 0.858936 + 1.48772i
\(554\) −1.87753 + 3.25198i −0.0797687 + 0.138163i
\(555\) −0.399503 0.691960i −0.0169580 0.0293721i
\(556\) 13.4569 23.3081i 0.570700 0.988482i
\(557\) 16.8207 + 9.71146i 0.712717 + 0.411488i 0.812066 0.583565i \(-0.198343\pi\)
−0.0993489 + 0.995053i \(0.531676\pi\)
\(558\) 3.24930 + 1.87598i 0.137554 + 0.0794167i
\(559\) −0.762125 −0.0322345
\(560\) 0.358092 0.206744i 0.0151321 0.00873654i
\(561\) 7.51087 + 4.33641i 0.317109 + 0.183083i
\(562\) 1.57711i 0.0665264i
\(563\) −5.66902 + 9.81903i −0.238921 + 0.413823i −0.960405 0.278608i \(-0.910127\pi\)
0.721484 + 0.692431i \(0.243460\pi\)
\(564\) −24.7224 + 14.2735i −1.04100 + 0.601022i
\(565\) 0.117850i 0.00495797i
\(566\) 5.72013 3.30252i 0.240435 0.138815i
\(567\) 37.8430i 1.58926i
\(568\) −4.06058 7.03312i −0.170378 0.295103i
\(569\) 17.7025 10.2205i 0.742125 0.428466i −0.0807162 0.996737i \(-0.525721\pi\)
0.822842 + 0.568271i \(0.192387\pi\)
\(570\) 0.150462 0.0868693i 0.00630216 0.00363856i
\(571\) 7.55195i 0.316039i 0.987436 + 0.158020i \(0.0505110\pi\)
−0.987436 + 0.158020i \(0.949489\pi\)
\(572\) −0.438492 −0.0183343
\(573\) −68.1678 −2.84775
\(574\) −12.8928 + 22.3311i −0.538137 + 0.932080i
\(575\) −5.27583 + 9.13801i −0.220017 + 0.381081i
\(576\) −0.00923040 0.0159875i −0.000384600 0.000666147i
\(577\) −19.9515 −0.830592 −0.415296 0.909686i \(-0.636322\pi\)
−0.415296 + 0.909686i \(0.636322\pi\)
\(578\) 0.198596 0.114659i 0.00826049 0.00476919i
\(579\) 13.1716 7.60461i 0.547392 0.316037i
\(580\) −0.141514 −0.00587606
\(581\) −7.87638 4.54743i −0.326767 0.188659i
\(582\) 11.6901 + 20.2478i 0.484570 + 0.839300i
\(583\) 11.9689 0.495699
\(584\) 22.1865 + 12.8094i 0.918085 + 0.530056i
\(585\) −0.0464608 + 0.0268242i −0.00192092 + 0.00110904i
\(586\) 5.61564 + 3.24219i 0.231980 + 0.133934i
\(587\) −3.17013 + 5.49082i −0.130845 + 0.226630i −0.924003 0.382386i \(-0.875102\pi\)
0.793157 + 0.609017i \(0.208436\pi\)
\(588\) 51.4204 2.12054
\(589\) −2.01600 + 3.49182i −0.0830679 + 0.143878i
\(590\) −0.183285 + 0.317459i −0.00754572 + 0.0130696i
\(591\) −18.9163 + 10.9213i −0.778112 + 0.449243i
\(592\) 5.51417 + 9.55083i 0.226631 + 0.392537i
\(593\) −18.0690 10.4322i −0.742006 0.428397i 0.0807922 0.996731i \(-0.474255\pi\)
−0.822798 + 0.568334i \(0.807588\pi\)
\(594\) 0.107389 + 0.186003i 0.00440621 + 0.00763179i
\(595\) 0.966911i 0.0396395i
\(596\) 17.8282i 0.730272i
\(597\) 53.3410i 2.18310i
\(598\) −0.433119 −0.0177116
\(599\) −17.5193 + 10.1148i −0.715819 + 0.413278i −0.813212 0.581968i \(-0.802283\pi\)
0.0973928 + 0.995246i \(0.468950\pi\)
\(600\) 28.1321i 1.14849i
\(601\) 11.7124 6.76218i 0.477761 0.275835i −0.241722 0.970345i \(-0.577712\pi\)
0.719483 + 0.694510i \(0.244379\pi\)
\(602\) 5.68224 3.28064i 0.231591 0.133709i
\(603\) −2.03261 3.52058i −0.0827741 0.143369i
\(604\) −7.54137 13.0620i −0.306854 0.531487i
\(605\) −0.267737 + 0.463733i −0.0108850 + 0.0188534i
\(606\) −1.55166 −0.0630319
\(607\) −5.42069 + 9.38891i −0.220019 + 0.381084i −0.954813 0.297206i \(-0.903945\pi\)
0.734795 + 0.678290i \(0.237279\pi\)
\(608\) −10.4776 + 6.04923i −0.424921 + 0.245329i
\(609\) −16.2750 9.39636i −0.659495 0.380760i
\(610\) −0.214635 −0.00869032
\(611\) −1.16850 2.02391i −0.0472726 0.0818786i
\(612\) −21.1514 −0.854994
\(613\) 13.9271 24.1225i 0.562511 0.974298i −0.434765 0.900544i \(-0.643169\pi\)
0.997276 0.0737539i \(-0.0234979\pi\)
\(614\) −3.36682 1.94383i −0.135874 0.0784468i
\(615\) −0.592974 1.02706i −0.0239110 0.0414151i
\(616\) 7.34515 4.24072i 0.295944 0.170864i
\(617\) 15.5591 26.9492i 0.626386 1.08493i −0.361885 0.932223i \(-0.617867\pi\)
0.988271 0.152710i \(-0.0488000\pi\)
\(618\) −18.4527 −0.742275
\(619\) 33.1492i 1.33238i 0.745782 + 0.666190i \(0.232076\pi\)
−0.745782 + 0.666190i \(0.767924\pi\)
\(620\) 0.0786226 + 0.136178i 0.00315756 + 0.00546905i
\(621\) −0.429958 0.744709i −0.0172536 0.0298842i
\(622\) −8.94217 15.4883i −0.358548 0.621024i
\(623\) −11.8675 −0.475460
\(624\) 1.24931 0.721291i 0.0500125 0.0288747i
\(625\) −12.4797 + 21.6155i −0.499189 + 0.864621i
\(626\) 13.8426 7.99204i 0.553262 0.319426i
\(627\) −3.85553 + 2.22599i −0.153975 + 0.0888976i
\(628\) 14.6179 + 25.3190i 0.583318 + 1.01034i
\(629\) 25.7889 1.02827
\(630\) 0.230935 0.399990i 0.00920065 0.0159360i
\(631\) −37.3977 −1.48878 −0.744390 0.667745i \(-0.767260\pi\)
−0.744390 + 0.667745i \(0.767260\pi\)
\(632\) −20.5281 −0.816564
\(633\) 52.2051i 2.07496i
\(634\) 9.16256 0.363892
\(635\) 0.671006 + 0.387405i 0.0266280 + 0.0153737i
\(636\) −49.2477 + 28.4332i −1.95280 + 1.12745i
\(637\) 4.20956i 0.166789i
\(638\) −0.894616 −0.0354182
\(639\) 9.81420 + 5.66623i 0.388244 + 0.224153i
\(640\) 0.588425i 0.0232595i
\(641\) −19.6888 34.1021i −0.777662 1.34695i −0.933286 0.359134i \(-0.883072\pi\)
0.155624 0.987816i \(-0.450261\pi\)
\(642\) 7.00432 + 12.1318i 0.276438 + 0.478806i
\(643\) −34.7095 20.0395i −1.36881 0.790282i −0.378033 0.925792i \(-0.623400\pi\)
−0.990776 + 0.135510i \(0.956733\pi\)
\(644\) −13.0895 + 7.55720i −0.515797 + 0.297795i
\(645\) 0.301770i 0.0118822i
\(646\) 5.60763i 0.220629i
\(647\) 21.7277 37.6334i 0.854202 1.47952i −0.0231806 0.999731i \(-0.507379\pi\)
0.877383 0.479791i \(-0.159287\pi\)
\(648\) 16.6537 + 9.61504i 0.654221 + 0.377714i
\(649\) 4.69661 8.13477i 0.184358 0.319318i
\(650\) −1.02508 −0.0402069
\(651\) 20.8818i 0.818420i
\(652\) 5.23542 + 3.02267i 0.205035 + 0.118377i
\(653\) 2.24051 0.0876778 0.0438389 0.999039i \(-0.486041\pi\)
0.0438389 + 0.999039i \(0.486041\pi\)
\(654\) −11.9979 6.92699i −0.469155 0.270867i
\(655\) 0.705396 + 0.407260i 0.0275621 + 0.0159130i
\(656\) 8.18456 + 14.1761i 0.319553 + 0.553483i
\(657\) −35.7491 −1.39471
\(658\) 17.4242 + 10.0599i 0.679267 + 0.392175i
\(659\) 37.7584i 1.47086i −0.677601 0.735429i \(-0.736980\pi\)
0.677601 0.735429i \(-0.263020\pi\)
\(660\) 0.173624i 0.00675832i
\(661\) −11.6017 −0.451255 −0.225628 0.974214i \(-0.572443\pi\)
−0.225628 + 0.974214i \(0.572443\pi\)
\(662\) −13.7505 −0.534430
\(663\) 3.37336i 0.131011i
\(664\) 4.00242 2.31080i 0.155324 0.0896763i
\(665\) 0.429844 + 0.248171i 0.0166686 + 0.00962364i
\(666\) 10.6683 + 6.15936i 0.413389 + 0.238670i
\(667\) 3.58182 0.138689
\(668\) 23.5291 + 13.5845i 0.910367 + 0.525601i
\(669\) 18.1790 31.4869i 0.702840 1.21735i
\(670\) 0.0420320i 0.00162384i
\(671\) 5.49995 0.212323
\(672\) −31.3290 + 54.2634i −1.20854 + 2.09325i
\(673\) −21.2388 36.7867i −0.818696 1.41802i −0.906644 0.421898i \(-0.861364\pi\)
0.0879477 0.996125i \(-0.471969\pi\)
\(674\) −14.7689 8.52684i −0.568878 0.328442i
\(675\) −1.01760 1.76253i −0.0391673 0.0678397i
\(676\) −10.3422 17.9132i −0.397777 0.688970i
\(677\) 15.5899i 0.599168i 0.954070 + 0.299584i \(0.0968479\pi\)
−0.954070 + 0.299584i \(0.903152\pi\)
\(678\) 1.76985 + 3.06548i 0.0679708 + 0.117729i
\(679\) −33.3966 + 57.8446i −1.28164 + 2.21987i
\(680\) 0.425513 + 0.245670i 0.0163177 + 0.00942101i
\(681\) 27.0702 1.03733
\(682\) 0.497031 + 0.860884i 0.0190323 + 0.0329649i
\(683\) 19.4385 + 33.6684i 0.743792 + 1.28829i 0.950757 + 0.309937i \(0.100308\pi\)
−0.206965 + 0.978348i \(0.566359\pi\)
\(684\) 5.42879 9.40294i 0.207575 0.359530i
\(685\) 0.577886 0.333643i 0.0220799 0.0127478i
\(686\) −8.29550 14.3682i −0.316724 0.548582i
\(687\) 52.6855i 2.01008i
\(688\) 4.16520i 0.158797i
\(689\) −2.32769 4.03168i −0.0886781 0.153595i
\(690\) 0.171497i 0.00652878i
\(691\) −12.7362 + 7.35326i −0.484509 + 0.279731i −0.722294 0.691587i \(-0.756912\pi\)
0.237785 + 0.971318i \(0.423579\pi\)
\(692\) 2.64737i 0.100638i
\(693\) −5.91761 + 10.2496i −0.224791 + 0.389350i
\(694\) −1.33292 + 2.30869i −0.0505970 + 0.0876366i
\(695\) 0.436210 0.755537i 0.0165464 0.0286592i
\(696\) 8.27020 4.77480i 0.313481 0.180988i
\(697\) 38.2779 1.44988
\(698\) 10.0518 6.08974i 0.380468 0.230500i
\(699\) −8.93781 −0.338059
\(700\) −30.9793 + 17.8859i −1.17091 + 0.676023i
\(701\) −25.3870 + 43.9716i −0.958854 + 1.66078i −0.233562 + 0.972342i \(0.575038\pi\)
−0.725292 + 0.688442i \(0.758295\pi\)
\(702\) 0.0417698 0.0723474i 0.00157650 0.00273058i
\(703\) −6.61907 + 11.4646i −0.249643 + 0.432395i
\(704\) 0.00489108i 0.000184340i
\(705\) −0.801383 + 0.462679i −0.0301818 + 0.0174255i
\(706\) 15.4431i 0.581210i
\(707\) −2.21641 3.83894i −0.0833568 0.144378i
\(708\) 44.6290i 1.67726i
\(709\) 41.1266i 1.54454i 0.635293 + 0.772271i \(0.280879\pi\)
−0.635293 + 0.772271i \(0.719121\pi\)
\(710\) −0.0585856 0.101473i −0.00219868 0.00380823i
\(711\) 24.8077 14.3227i 0.930360 0.537144i
\(712\) 3.01525 5.22257i 0.113001 0.195724i
\(713\) −1.98999 3.44677i −0.0745257 0.129082i
\(714\) 14.5210 + 25.1511i 0.543434 + 0.941255i
\(715\) −0.0142138 −0.000531567
\(716\) −17.9485 10.3626i −0.670768 0.387268i
\(717\) 2.49634 4.32379i 0.0932275 0.161475i
\(718\) −9.08931 15.7431i −0.339210 0.587529i
\(719\) 50.0836i 1.86780i 0.357531 + 0.933901i \(0.383619\pi\)
−0.357531 + 0.933901i \(0.616381\pi\)
\(720\) −0.146601 0.253920i −0.00546348 0.00946303i
\(721\) −26.3580 45.6535i −0.981625 1.70022i
\(722\) 7.85869 + 4.53722i 0.292470 + 0.168858i
\(723\) −6.63742 11.4963i −0.246848 0.427554i
\(724\) −13.8699 + 24.0234i −0.515471 + 0.892822i
\(725\) 8.47721 0.314836
\(726\) 16.0834i 0.596910i
\(727\) 10.8890 18.8603i 0.403850 0.699489i −0.590337 0.807157i \(-0.701005\pi\)
0.994187 + 0.107668i \(0.0343385\pi\)
\(728\) −2.85696 1.64947i −0.105886 0.0611332i
\(729\) −29.8675 −1.10620
\(730\) 0.320105 + 0.184813i 0.0118476 + 0.00684023i
\(731\) −8.43508 4.86999i −0.311983 0.180123i
\(732\) −22.6304 + 13.0657i −0.836443 + 0.482921i
\(733\) 4.93529i 0.182289i 0.995838 + 0.0911446i \(0.0290525\pi\)
−0.995838 + 0.0911446i \(0.970947\pi\)
\(734\) 0.360545 0.0133080
\(735\) 1.66681 0.0614811
\(736\) 11.9424i 0.440201i
\(737\) 1.07705i 0.0396738i
\(738\) 15.8348 + 9.14220i 0.582885 + 0.336529i
\(739\) 8.44918 0.310808 0.155404 0.987851i \(-0.450332\pi\)
0.155404 + 0.987851i \(0.450332\pi\)
\(740\) 0.258139 + 0.447110i 0.00948938 + 0.0164361i
\(741\) 1.49964 + 0.865819i 0.0550908 + 0.0318067i
\(742\) 34.7096 + 20.0396i 1.27423 + 0.735676i
\(743\) 4.08079 0.149710 0.0748548 0.997194i \(-0.476151\pi\)
0.0748548 + 0.997194i \(0.476151\pi\)
\(744\) −9.18953 5.30558i −0.336904 0.194512i
\(745\) 0.577906i 0.0211728i
\(746\) 18.6043 0.681150
\(747\) −3.22454 + 5.58507i −0.117980 + 0.204347i
\(748\) −4.85315 2.80197i −0.177449 0.102450i
\(749\) −20.0101 + 34.6586i −0.731154 + 1.26640i
\(750\) 0.811995i 0.0296499i
\(751\) 14.8663i 0.542477i 0.962512 + 0.271239i \(0.0874333\pi\)
−0.962512 + 0.271239i \(0.912567\pi\)
\(752\) 11.0612 6.38616i 0.403359 0.232879i
\(753\) −2.04307 1.17957i −0.0744536 0.0429858i
\(754\) 0.173984 + 0.301349i 0.00633613 + 0.0109745i
\(755\) −0.244456 0.423410i −0.00889666 0.0154095i
\(756\) 2.91525i 0.106027i
\(757\) −21.7159 12.5377i −0.789278 0.455690i 0.0504304 0.998728i \(-0.483941\pi\)
−0.839708 + 0.543038i \(0.817274\pi\)
\(758\) 14.6055 0.530495
\(759\) 4.39455i 0.159512i
\(760\) −0.218427 + 0.126109i −0.00792319 + 0.00457445i
\(761\) −42.8741 24.7534i −1.55418 0.897309i −0.997794 0.0663877i \(-0.978853\pi\)
−0.556390 0.830921i \(-0.687814\pi\)
\(762\) −23.2721 −0.843058
\(763\) 39.5784i 1.43283i
\(764\) 44.0466 1.59355
\(765\) −0.685628 −0.0247889
\(766\)