Properties

Label 735.2.v.a.313.4
Level 735
Weight 2
Character 735.313
Analytic conductor 5.869
Analytic rank 0
Dimension 32
CM no
Inner twists 8

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.v (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{12})\)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 313.4
Character \(\chi\) \(=\) 735.313
Dual form 735.2.v.a.472.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0611467 - 0.228203i) q^{2} +(0.965926 + 0.258819i) q^{3} +(1.68371 - 0.972092i) q^{4} +(1.04485 - 1.97694i) q^{5} -0.236253i q^{6} +(-0.658899 - 0.658899i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.0611467 - 0.228203i) q^{2} +(0.965926 + 0.258819i) q^{3} +(1.68371 - 0.972092i) q^{4} +(1.04485 - 1.97694i) q^{5} -0.236253i q^{6} +(-0.658899 - 0.658899i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-0.515032 - 0.117555i) q^{10} +(-1.99301 - 3.45200i) q^{11} +(1.87794 - 0.503192i) q^{12} +(-0.500437 + 0.500437i) q^{13} +(1.52092 - 1.63915i) q^{15} +(1.83411 - 3.17677i) q^{16} +(0.614336 - 2.29273i) q^{17} +(0.0611467 - 0.228203i) q^{18} +(-3.60925 + 6.25141i) q^{19} +(-0.162536 - 4.34429i) q^{20} +(-0.665888 + 0.665888i) q^{22} +(7.04878 - 1.88872i) q^{23} +(-0.465912 - 0.806983i) q^{24} +(-2.81657 - 4.13121i) q^{25} +(0.144801 + 0.0836010i) q^{26} +(0.707107 + 0.707107i) q^{27} +3.65191i q^{29} +(-0.467057 - 0.246849i) q^{30} +(-4.27662 + 2.46911i) q^{31} +(-2.63724 - 0.706647i) q^{32} +(-1.03166 - 3.85020i) q^{33} -0.560773 q^{34} +1.94418 q^{36} +(0.106980 + 0.399255i) q^{37} +(1.64728 + 0.441387i) q^{38} +(-0.612908 + 0.353863i) q^{39} +(-1.99105 + 0.614151i) q^{40} +7.63184i q^{41} +(3.65191 + 3.65191i) q^{43} +(-6.71132 - 3.87478i) q^{44} +(1.89334 - 1.18965i) q^{45} +(-0.862019 - 1.49306i) q^{46} +(-0.417052 + 0.111749i) q^{47} +(2.59383 - 2.59383i) q^{48} +(-0.770530 + 0.895358i) q^{50} +(1.18681 - 2.05561i) q^{51} +(-0.356122 + 1.32906i) q^{52} +(1.97527 - 7.37179i) q^{53} +(0.118126 - 0.204601i) q^{54} +(-8.90678 + 0.333235i) q^{55} +(-5.10425 + 5.10425i) q^{57} +(0.833375 - 0.223302i) q^{58} +(3.05480 + 5.29106i) q^{59} +(0.967387 - 4.23833i) q^{60} +(6.15784 + 3.55523i) q^{61} +(0.824957 + 0.824957i) q^{62} -6.69141i q^{64} +(0.466451 + 1.51222i) q^{65} +(-0.815543 + 0.470854i) q^{66} +(-1.28978 - 0.345596i) q^{67} +(-1.19438 - 4.45750i) q^{68} +7.29744 q^{69} +1.19297 q^{71} +(-0.241174 - 0.900073i) q^{72} +(1.88918 + 0.506205i) q^{73} +(0.0845694 - 0.0488262i) q^{74} +(-1.65136 - 4.71943i) q^{75} +14.0341i q^{76} +(0.118230 + 0.118230i) q^{78} +(7.48269 + 4.32013i) q^{79} +(-4.36391 - 6.94518i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.74161 - 0.466662i) q^{82} +(11.9895 - 11.9895i) q^{83} +(-3.89070 - 3.61007i) q^{85} +(0.610073 - 1.05668i) q^{86} +(-0.945184 + 3.52747i) q^{87} +(-0.961324 + 3.58771i) q^{88} +(3.91290 - 6.77735i) q^{89} +(-0.387253 - 0.359321i) q^{90} +(10.0321 - 10.0321i) q^{92} +(-4.76995 + 1.27810i) q^{93} +(0.0510027 + 0.0883393i) q^{94} +(8.58751 + 13.6671i) q^{95} +(-2.36449 - 1.36514i) q^{96} +(-7.43671 - 7.43671i) q^{97} -3.98602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 48q^{8} + O(q^{10}) \) \( 32q + 48q^{8} + 16q^{11} + 16q^{15} + 48q^{16} - 32q^{22} + 40q^{23} + 8q^{30} - 48q^{32} - 32q^{36} - 32q^{37} - 32q^{43} - 64q^{46} - 144q^{50} + 16q^{51} - 24q^{53} + 16q^{57} - 32q^{58} - 40q^{60} - 40q^{65} + 32q^{67} + 128q^{71} - 24q^{72} - 16q^{78} + 16q^{81} + 96q^{85} - 64q^{86} + 64q^{88} - 80q^{92} - 24q^{93} + 72q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{3}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0611467 0.228203i −0.0432372 0.161364i 0.940932 0.338596i \(-0.109952\pi\)
−0.984169 + 0.177233i \(0.943285\pi\)
\(3\) 0.965926 + 0.258819i 0.557678 + 0.149429i
\(4\) 1.68371 0.972092i 0.841857 0.486046i
\(5\) 1.04485 1.97694i 0.467272 0.884114i
\(6\) 0.236253i 0.0964497i
\(7\) 0 0
\(8\) −0.658899 0.658899i −0.232956 0.232956i
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) −0.515032 0.117555i −0.162867 0.0371740i
\(11\) −1.99301 3.45200i −0.600915 1.04082i −0.992683 0.120752i \(-0.961470\pi\)
0.391767 0.920064i \(-0.371864\pi\)
\(12\) 1.87794 0.503192i 0.542114 0.145259i
\(13\) −0.500437 + 0.500437i −0.138796 + 0.138796i −0.773091 0.634295i \(-0.781291\pi\)
0.634295 + 0.773091i \(0.281291\pi\)
\(14\) 0 0
\(15\) 1.52092 1.63915i 0.392699 0.423226i
\(16\) 1.83411 3.17677i 0.458528 0.794194i
\(17\) 0.614336 2.29273i 0.148998 0.556070i −0.850546 0.525900i \(-0.823729\pi\)
0.999545 0.0301697i \(-0.00960478\pi\)
\(18\) 0.0611467 0.228203i 0.0144124 0.0537879i
\(19\) −3.60925 + 6.25141i −0.828019 + 1.43417i 0.0715711 + 0.997435i \(0.477199\pi\)
−0.899590 + 0.436735i \(0.856135\pi\)
\(20\) −0.162536 4.34429i −0.0363441 0.971413i
\(21\) 0 0
\(22\) −0.665888 + 0.665888i −0.141968 + 0.141968i
\(23\) 7.04878 1.88872i 1.46977 0.393824i 0.566919 0.823773i \(-0.308135\pi\)
0.902853 + 0.429949i \(0.141468\pi\)
\(24\) −0.465912 0.806983i −0.0951039 0.164725i
\(25\) −2.81657 4.13121i −0.563314 0.826243i
\(26\) 0.144801 + 0.0836010i 0.0283978 + 0.0163955i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 0 0
\(29\) 3.65191i 0.678143i 0.940761 + 0.339071i \(0.110113\pi\)
−0.940761 + 0.339071i \(0.889887\pi\)
\(30\) −0.467057 0.246849i −0.0852725 0.0450683i
\(31\) −4.27662 + 2.46911i −0.768103 + 0.443465i −0.832198 0.554479i \(-0.812917\pi\)
0.0640944 + 0.997944i \(0.479584\pi\)
\(32\) −2.63724 0.706647i −0.466203 0.124919i
\(33\) −1.03166 3.85020i −0.179589 0.670234i
\(34\) −0.560773 −0.0961717
\(35\) 0 0
\(36\) 1.94418 0.324031
\(37\) 0.106980 + 0.399255i 0.0175874 + 0.0656371i 0.974162 0.225851i \(-0.0725163\pi\)
−0.956574 + 0.291488i \(0.905850\pi\)
\(38\) 1.64728 + 0.441387i 0.267224 + 0.0716025i
\(39\) −0.612908 + 0.353863i −0.0981438 + 0.0566634i
\(40\) −1.99105 + 0.614151i −0.314813 + 0.0971058i
\(41\) 7.63184i 1.19189i 0.803024 + 0.595947i \(0.203223\pi\)
−0.803024 + 0.595947i \(0.796777\pi\)
\(42\) 0 0
\(43\) 3.65191 + 3.65191i 0.556911 + 0.556911i 0.928427 0.371516i \(-0.121162\pi\)
−0.371516 + 0.928427i \(0.621162\pi\)
\(44\) −6.71132 3.87478i −1.01177 0.584145i
\(45\) 1.89334 1.18965i 0.282242 0.177343i
\(46\) −0.862019 1.49306i −0.127098 0.220140i
\(47\) −0.417052 + 0.111749i −0.0608333 + 0.0163002i −0.289107 0.957297i \(-0.593358\pi\)
0.228274 + 0.973597i \(0.426692\pi\)
\(48\) 2.59383 2.59383i 0.374386 0.374386i
\(49\) 0 0
\(50\) −0.770530 + 0.895358i −0.108969 + 0.126623i
\(51\) 1.18681 2.05561i 0.166186 0.287843i
\(52\) −0.356122 + 1.32906i −0.0493852 + 0.184308i
\(53\) 1.97527 7.37179i 0.271324 1.01259i −0.686942 0.726713i \(-0.741047\pi\)
0.958265 0.285881i \(-0.0922861\pi\)
\(54\) 0.118126 0.204601i 0.0160750 0.0278426i
\(55\) −8.90678 + 0.333235i −1.20099 + 0.0449335i
\(56\) 0 0
\(57\) −5.10425 + 5.10425i −0.676075 + 0.676075i
\(58\) 0.833375 0.223302i 0.109428 0.0293210i
\(59\) 3.05480 + 5.29106i 0.397701 + 0.688838i 0.993442 0.114339i \(-0.0364750\pi\)
−0.595741 + 0.803176i \(0.703142\pi\)
\(60\) 0.967387 4.23833i 0.124889 0.547166i
\(61\) 6.15784 + 3.55523i 0.788431 + 0.455201i 0.839410 0.543499i \(-0.182901\pi\)
−0.0509788 + 0.998700i \(0.516234\pi\)
\(62\) 0.824957 + 0.824957i 0.104770 + 0.104770i
\(63\) 0 0
\(64\) 6.69141i 0.836426i
\(65\) 0.466451 + 1.51222i 0.0578561 + 0.187567i
\(66\) −0.815543 + 0.470854i −0.100386 + 0.0579581i
\(67\) −1.28978 0.345596i −0.157572 0.0422212i 0.179171 0.983818i \(-0.442659\pi\)
−0.336743 + 0.941597i \(0.609325\pi\)
\(68\) −1.19438 4.45750i −0.144840 0.540551i
\(69\) 7.29744 0.878508
\(70\) 0 0
\(71\) 1.19297 0.141579 0.0707897 0.997491i \(-0.477448\pi\)
0.0707897 + 0.997491i \(0.477448\pi\)
\(72\) −0.241174 0.900073i −0.0284226 0.106075i
\(73\) 1.88918 + 0.506205i 0.221112 + 0.0592469i 0.367674 0.929955i \(-0.380154\pi\)
−0.146562 + 0.989201i \(0.546821\pi\)
\(74\) 0.0845694 0.0488262i 0.00983100 0.00567593i
\(75\) −1.65136 4.71943i −0.190683 0.544953i
\(76\) 14.0341i 1.60982i
\(77\) 0 0
\(78\) 0.118230 + 0.118230i 0.0133869 + 0.0133869i
\(79\) 7.48269 + 4.32013i 0.841868 + 0.486053i 0.857899 0.513819i \(-0.171770\pi\)
−0.0160304 + 0.999872i \(0.505103\pi\)
\(80\) −4.36391 6.94518i −0.487900 0.776495i
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 1.74161 0.466662i 0.192328 0.0515342i
\(83\) 11.9895 11.9895i 1.31602 1.31602i 0.399122 0.916898i \(-0.369315\pi\)
0.916898 0.399122i \(-0.130685\pi\)
\(84\) 0 0
\(85\) −3.89070 3.61007i −0.422006 0.391567i
\(86\) 0.610073 1.05668i 0.0657859 0.113944i
\(87\) −0.945184 + 3.52747i −0.101334 + 0.378185i
\(88\) −0.961324 + 3.58771i −0.102477 + 0.382451i
\(89\) 3.91290 6.77735i 0.414767 0.718397i −0.580637 0.814163i \(-0.697196\pi\)
0.995404 + 0.0957652i \(0.0305298\pi\)
\(90\) −0.387253 0.359321i −0.0408201 0.0378758i
\(91\) 0 0
\(92\) 10.0321 10.0321i 1.04592 1.04592i
\(93\) −4.76995 + 1.27810i −0.494620 + 0.132533i
\(94\) 0.0510027 + 0.0883393i 0.00526053 + 0.00911150i
\(95\) 8.58751 + 13.6671i 0.881060 + 1.40221i
\(96\) −2.36449 1.36514i −0.241325 0.139329i
\(97\) −7.43671 7.43671i −0.755083 0.755083i 0.220340 0.975423i \(-0.429283\pi\)
−0.975423 + 0.220340i \(0.929283\pi\)
\(98\) 0 0
\(99\) 3.98602i 0.400610i
\(100\) −8.75822 4.21782i −0.875822 0.421782i
\(101\) −5.47010 + 3.15816i −0.544295 + 0.314249i −0.746818 0.665028i \(-0.768419\pi\)
0.202523 + 0.979278i \(0.435086\pi\)
\(102\) −0.541665 0.145139i −0.0536328 0.0143709i
\(103\) 4.59031 + 17.1313i 0.452296 + 1.68799i 0.695917 + 0.718122i \(0.254998\pi\)
−0.243620 + 0.969871i \(0.578335\pi\)
\(104\) 0.659476 0.0646669
\(105\) 0 0
\(106\) −1.80304 −0.175127
\(107\) 2.73794 + 10.2181i 0.264687 + 0.987825i 0.962442 + 0.271488i \(0.0875159\pi\)
−0.697755 + 0.716337i \(0.745817\pi\)
\(108\) 1.87794 + 0.503192i 0.180705 + 0.0484197i
\(109\) −0.578698 + 0.334112i −0.0554293 + 0.0320021i −0.527459 0.849581i \(-0.676855\pi\)
0.472029 + 0.881583i \(0.343522\pi\)
\(110\) 0.620666 + 2.01217i 0.0591781 + 0.191853i
\(111\) 0.413339i 0.0392324i
\(112\) 0 0
\(113\) −3.39653 3.39653i −0.319518 0.319518i 0.529064 0.848582i \(-0.322543\pi\)
−0.848582 + 0.529064i \(0.822543\pi\)
\(114\) 1.47691 + 0.852695i 0.138325 + 0.0798622i
\(115\) 3.63106 15.9084i 0.338598 1.48347i
\(116\) 3.54999 + 6.14877i 0.329609 + 0.570899i
\(117\) −0.683610 + 0.183173i −0.0631998 + 0.0169343i
\(118\) 1.02064 1.02064i 0.0939578 0.0939578i
\(119\) 0 0
\(120\) −2.08217 + 0.0779014i −0.190075 + 0.00711139i
\(121\) −2.44418 + 4.23345i −0.222199 + 0.384859i
\(122\) 0.434781 1.62263i 0.0393633 0.146906i
\(123\) −1.97527 + 7.37179i −0.178104 + 0.664692i
\(124\) −4.80040 + 8.31453i −0.431088 + 0.746667i
\(125\) −11.1101 + 1.25168i −0.993713 + 0.111953i
\(126\) 0 0
\(127\) −5.88837 + 5.88837i −0.522508 + 0.522508i −0.918328 0.395820i \(-0.870460\pi\)
0.395820 + 0.918328i \(0.370460\pi\)
\(128\) −6.80149 + 1.82245i −0.601172 + 0.161084i
\(129\) 2.58229 + 4.47266i 0.227358 + 0.393796i
\(130\) 0.316570 0.198912i 0.0277650 0.0174458i
\(131\) −16.2938 9.40722i −1.42359 0.821913i −0.426991 0.904256i \(-0.640426\pi\)
−0.996604 + 0.0823433i \(0.973760\pi\)
\(132\) −5.47977 5.47977i −0.476953 0.476953i
\(133\) 0 0
\(134\) 0.315463i 0.0272519i
\(135\) 2.13673 0.659085i 0.183900 0.0567250i
\(136\) −1.91547 + 1.10590i −0.164250 + 0.0948297i
\(137\) 1.10918 + 0.297204i 0.0947637 + 0.0253919i 0.305889 0.952067i \(-0.401046\pi\)
−0.211126 + 0.977459i \(0.567713\pi\)
\(138\) −0.446214 1.66529i −0.0379843 0.141759i
\(139\) 0.442439 0.0375272 0.0187636 0.999824i \(-0.494027\pi\)
0.0187636 + 0.999824i \(0.494027\pi\)
\(140\) 0 0
\(141\) −0.431764 −0.0363611
\(142\) −0.0729461 0.272239i −0.00612150 0.0228458i
\(143\) 2.72489 + 0.730131i 0.227866 + 0.0610566i
\(144\) 3.17677 1.83411i 0.264731 0.152843i
\(145\) 7.21960 + 3.81570i 0.599555 + 0.316877i
\(146\) 0.462070i 0.0382411i
\(147\) 0 0
\(148\) 0.568236 + 0.568236i 0.0467087 + 0.0467087i
\(149\) −2.72031 1.57057i −0.222856 0.128666i 0.384416 0.923160i \(-0.374403\pi\)
−0.607272 + 0.794494i \(0.707736\pi\)
\(150\) −0.976010 + 0.665422i −0.0796909 + 0.0543315i
\(151\) 7.36197 + 12.7513i 0.599109 + 1.03769i 0.992953 + 0.118509i \(0.0378116\pi\)
−0.393844 + 0.919177i \(0.628855\pi\)
\(152\) 6.49718 1.74091i 0.526991 0.141207i
\(153\) 1.67840 1.67840i 0.135690 0.135690i
\(154\) 0 0
\(155\) 0.412839 + 11.0345i 0.0331601 + 0.886309i
\(156\) −0.687974 + 1.19161i −0.0550820 + 0.0954049i
\(157\) 2.91542 10.8805i 0.232676 0.868358i −0.746507 0.665378i \(-0.768271\pi\)
0.979183 0.202980i \(-0.0650628\pi\)
\(158\) 0.528324 1.97173i 0.0420312 0.156862i
\(159\) 3.81592 6.60937i 0.302622 0.524157i
\(160\) −4.15253 + 4.47533i −0.328286 + 0.353806i
\(161\) 0 0
\(162\) 0.167056 0.167056i 0.0131251 0.0131251i
\(163\) −14.2681 + 3.82312i −1.11756 + 0.299450i −0.769897 0.638169i \(-0.779692\pi\)
−0.347666 + 0.937619i \(0.613026\pi\)
\(164\) 7.41885 + 12.8498i 0.579315 + 1.00340i
\(165\) −8.68954 1.98336i −0.676480 0.154405i
\(166\) −3.46916 2.00292i −0.269259 0.155457i
\(167\) −4.63621 4.63621i −0.358761 0.358761i 0.504595 0.863356i \(-0.331642\pi\)
−0.863356 + 0.504595i \(0.831642\pi\)
\(168\) 0 0
\(169\) 12.4991i 0.961471i
\(170\) −0.585924 + 1.10861i −0.0449383 + 0.0850267i
\(171\) −6.25141 + 3.60925i −0.478057 + 0.276006i
\(172\) 9.69876 + 2.59878i 0.739524 + 0.198155i
\(173\) 0.909686 + 3.39499i 0.0691621 + 0.258117i 0.991846 0.127440i \(-0.0406761\pi\)
−0.922684 + 0.385557i \(0.874009\pi\)
\(174\) 0.862773 0.0654067
\(175\) 0 0
\(176\) −14.6216 −1.10215
\(177\) 1.58128 + 5.90141i 0.118856 + 0.443577i
\(178\) −1.78587 0.478522i −0.133857 0.0358667i
\(179\) −19.1486 + 11.0554i −1.43123 + 0.826321i −0.997215 0.0745840i \(-0.976237\pi\)
−0.434016 + 0.900905i \(0.642904\pi\)
\(180\) 2.03138 3.84353i 0.151410 0.286480i
\(181\) 8.48528i 0.630706i 0.948974 + 0.315353i \(0.102123\pi\)
−0.948974 + 0.315353i \(0.897877\pi\)
\(182\) 0 0
\(183\) 5.02786 + 5.02786i 0.371670 + 0.371670i
\(184\) −5.88891 3.39996i −0.434136 0.250649i
\(185\) 0.901080 + 0.205669i 0.0662487 + 0.0151211i
\(186\) 0.583333 + 1.01036i 0.0427720 + 0.0740833i
\(187\) −9.13889 + 2.44876i −0.668302 + 0.179071i
\(188\) −0.593566 + 0.593566i −0.0432903 + 0.0432903i
\(189\) 0 0
\(190\) 2.59376 2.79539i 0.188171 0.202799i
\(191\) −7.64492 + 13.2414i −0.553167 + 0.958113i 0.444877 + 0.895592i \(0.353248\pi\)
−0.998044 + 0.0625216i \(0.980086\pi\)
\(192\) 1.73186 6.46341i 0.124987 0.466456i
\(193\) −3.26783 + 12.1957i −0.235223 + 0.877866i 0.742825 + 0.669486i \(0.233486\pi\)
−0.978048 + 0.208380i \(0.933181\pi\)
\(194\) −1.24235 + 2.15181i −0.0891952 + 0.154491i
\(195\) 0.0591665 + 1.58142i 0.00423700 + 0.113248i
\(196\) 0 0
\(197\) −2.68715 + 2.68715i −0.191451 + 0.191451i −0.796323 0.604872i \(-0.793224\pi\)
0.604872 + 0.796323i \(0.293224\pi\)
\(198\) −0.909620 + 0.243732i −0.0646439 + 0.0173213i
\(199\) 0.308318 + 0.534023i 0.0218561 + 0.0378559i 0.876747 0.480953i \(-0.159709\pi\)
−0.854890 + 0.518809i \(0.826376\pi\)
\(200\) −0.866218 + 4.57789i −0.0612509 + 0.323706i
\(201\) −1.15639 0.667639i −0.0815651 0.0470917i
\(202\) 1.05518 + 1.05518i 0.0742422 + 0.0742422i
\(203\) 0 0
\(204\) 4.61474i 0.323097i
\(205\) 15.0877 + 7.97414i 1.05377 + 0.556938i
\(206\) 3.62871 2.09504i 0.252825 0.145968i
\(207\) 7.04878 + 1.88872i 0.489924 + 0.131275i
\(208\) 0.671919 + 2.50763i 0.0465892 + 0.173873i
\(209\) 28.7731 1.99028
\(210\) 0 0
\(211\) 9.30849 0.640823 0.320411 0.947278i \(-0.396179\pi\)
0.320411 + 0.947278i \(0.396179\pi\)
\(212\) −3.84028 14.3321i −0.263752 0.984334i
\(213\) 1.15232 + 0.308763i 0.0789557 + 0.0211561i
\(214\) 2.16439 1.24961i 0.147955 0.0854217i
\(215\) 11.0353 3.40390i 0.752602 0.232144i
\(216\) 0.931824i 0.0634026i
\(217\) 0 0
\(218\) 0.111631 + 0.111631i 0.00756058 + 0.00756058i
\(219\) 1.69380 + 0.977914i 0.114456 + 0.0660813i
\(220\) −14.6725 + 9.21929i −0.989222 + 0.621564i
\(221\) 0.839933 + 1.45481i 0.0565000 + 0.0978609i
\(222\) 0.0943250 0.0252743i 0.00633068 0.00169630i
\(223\) 1.35505 1.35505i 0.0907407 0.0907407i −0.660279 0.751020i \(-0.729562\pi\)
0.751020 + 0.660279i \(0.229562\pi\)
\(224\) 0 0
\(225\) −0.373614 4.98602i −0.0249076 0.332401i
\(226\) −0.567410 + 0.982782i −0.0377435 + 0.0653737i
\(227\) −1.52061 + 5.67498i −0.100926 + 0.376662i −0.997851 0.0655211i \(-0.979129\pi\)
0.896925 + 0.442183i \(0.145796\pi\)
\(228\) −3.63229 + 13.5559i −0.240554 + 0.897761i
\(229\) 6.49500 11.2497i 0.429202 0.743399i −0.567601 0.823304i \(-0.692128\pi\)
0.996802 + 0.0799049i \(0.0254617\pi\)
\(230\) −3.85237 + 0.144131i −0.254018 + 0.00950374i
\(231\) 0 0
\(232\) 2.40624 2.40624i 0.157977 0.157977i
\(233\) 22.4901 6.02620i 1.47337 0.394790i 0.569288 0.822138i \(-0.307219\pi\)
0.904087 + 0.427349i \(0.140552\pi\)
\(234\) 0.0836010 + 0.144801i 0.00546517 + 0.00946595i
\(235\) −0.214837 + 0.941247i −0.0140144 + 0.0614002i
\(236\) 10.2868 + 5.93909i 0.669614 + 0.386602i
\(237\) 6.10959 + 6.10959i 0.396861 + 0.396861i
\(238\) 0 0
\(239\) 5.48048i 0.354503i −0.984166 0.177251i \(-0.943279\pi\)
0.984166 0.177251i \(-0.0567205\pi\)
\(240\) −2.41767 7.83800i −0.156060 0.505940i
\(241\) −12.6879 + 7.32537i −0.817300 + 0.471868i −0.849485 0.527613i \(-0.823087\pi\)
0.0321844 + 0.999482i \(0.489754\pi\)
\(242\) 1.11554 + 0.298908i 0.0717095 + 0.0192145i
\(243\) 0.258819 + 0.965926i 0.0166032 + 0.0619642i
\(244\) 13.8241 0.884995
\(245\) 0 0
\(246\) 1.80304 0.114958
\(247\) −1.32223 4.93464i −0.0841317 0.313984i
\(248\) 4.44475 + 1.19097i 0.282242 + 0.0756265i
\(249\) 14.6841 8.47787i 0.930567 0.537263i
\(250\) 0.964979 + 2.45881i 0.0610306 + 0.155509i
\(251\) 21.1506i 1.33501i 0.744604 + 0.667507i \(0.232639\pi\)
−0.744604 + 0.667507i \(0.767361\pi\)
\(252\) 0 0
\(253\) −20.5681 20.5681i −1.29311 1.29311i
\(254\) 1.70380 + 0.983687i 0.106906 + 0.0617220i
\(255\) −2.82378 4.49405i −0.176832 0.281428i
\(256\) −5.85964 10.1492i −0.366227 0.634324i
\(257\) −12.8304 + 3.43788i −0.800336 + 0.214449i −0.635731 0.771910i \(-0.719301\pi\)
−0.164604 + 0.986360i \(0.552635\pi\)
\(258\) 0.862773 0.862773i 0.0537139 0.0537139i
\(259\) 0 0
\(260\) 2.25538 + 2.09271i 0.139873 + 0.129784i
\(261\) −1.82596 + 3.16265i −0.113024 + 0.195763i
\(262\) −1.15044 + 4.29350i −0.0710745 + 0.265254i
\(263\) 5.62869 21.0066i 0.347080 1.29532i −0.543083 0.839679i \(-0.682743\pi\)
0.890163 0.455642i \(-0.150590\pi\)
\(264\) −1.85714 + 3.21665i −0.114299 + 0.197971i
\(265\) −12.5097 11.6074i −0.768466 0.713037i
\(266\) 0 0
\(267\) 5.53368 5.53368i 0.338656 0.338656i
\(268\) −2.50757 + 0.671902i −0.153174 + 0.0410429i
\(269\) −11.4926 19.9057i −0.700714 1.21367i −0.968216 0.250116i \(-0.919531\pi\)
0.267501 0.963557i \(-0.413802\pi\)
\(270\) −0.281059 0.447306i −0.0171047 0.0272222i
\(271\) −13.6483 7.87982i −0.829072 0.478665i 0.0244625 0.999701i \(-0.492213\pi\)
−0.853535 + 0.521036i \(0.825546\pi\)
\(272\) −6.15674 6.15674i −0.373307 0.373307i
\(273\) 0 0
\(274\) 0.271291i 0.0163893i
\(275\) −8.64748 + 17.9563i −0.521463 + 1.08281i
\(276\) 12.2868 7.09378i 0.739578 0.426995i
\(277\) −6.56746 1.75975i −0.394600 0.105733i 0.0560621 0.998427i \(-0.482146\pi\)
−0.450662 + 0.892694i \(0.648812\pi\)
\(278\) −0.0270537 0.100966i −0.00162257 0.00605553i
\(279\) −4.93821 −0.295643
\(280\) 0 0
\(281\) −9.65658 −0.576063 −0.288032 0.957621i \(-0.593001\pi\)
−0.288032 + 0.957621i \(0.593001\pi\)
\(282\) 0.0264009 + 0.0985297i 0.00157215 + 0.00586736i
\(283\) 20.3668 + 5.45726i 1.21068 + 0.324400i 0.807028 0.590513i \(-0.201075\pi\)
0.403650 + 0.914913i \(0.367741\pi\)
\(284\) 2.00862 1.15968i 0.119190 0.0688141i
\(285\) 4.75760 + 15.4240i 0.281816 + 0.913637i
\(286\) 0.666471i 0.0394092i
\(287\) 0 0
\(288\) −1.93060 1.93060i −0.113761 0.113761i
\(289\) 9.84321 + 5.68298i 0.579012 + 0.334293i
\(290\) 0.429299 1.88085i 0.0252093 0.110447i
\(291\) −5.25855 9.10807i −0.308261 0.533924i
\(292\) 3.67292 0.984157i 0.214942 0.0575934i
\(293\) −4.79236 + 4.79236i −0.279973 + 0.279973i −0.833098 0.553125i \(-0.813435\pi\)
0.553125 + 0.833098i \(0.313435\pi\)
\(294\) 0 0
\(295\) 13.6519 0.510768i 0.794845 0.0297381i
\(296\) 0.192580 0.333558i 0.0111935 0.0193876i
\(297\) 1.03166 3.85020i 0.0598629 0.223411i
\(298\) −0.192070 + 0.716817i −0.0111263 + 0.0415241i
\(299\) −2.58229 + 4.47266i −0.149338 + 0.258660i
\(300\) −7.36814 6.34089i −0.425400 0.366091i
\(301\) 0 0
\(302\) 2.45972 2.45972i 0.141541 0.141541i
\(303\) −6.10111 + 1.63479i −0.350499 + 0.0939160i
\(304\) 13.2395 + 22.9316i 0.759340 + 1.31521i
\(305\) 13.4625 8.45899i 0.770861 0.484360i
\(306\) −0.485643 0.280386i −0.0277624 0.0160286i
\(307\) −9.85063 9.85063i −0.562205 0.562205i 0.367728 0.929933i \(-0.380136\pi\)
−0.929933 + 0.367728i \(0.880136\pi\)
\(308\) 0 0
\(309\) 17.7356i 1.00894i
\(310\) 2.49285 0.768932i 0.141584 0.0436724i
\(311\) −23.6480 + 13.6532i −1.34095 + 0.774200i −0.986947 0.161043i \(-0.948514\pi\)
−0.354006 + 0.935243i \(0.615181\pi\)
\(312\) 0.637004 + 0.170685i 0.0360633 + 0.00966313i
\(313\) −6.77439 25.2824i −0.382911 1.42904i −0.841434 0.540361i \(-0.818288\pi\)
0.458523 0.888683i \(-0.348379\pi\)
\(314\) −2.66123 −0.150182
\(315\) 0 0
\(316\) 16.7983 0.944977
\(317\) −8.00839 29.8877i −0.449796 1.67866i −0.702952 0.711237i \(-0.748135\pi\)
0.253156 0.967425i \(-0.418531\pi\)
\(318\) −1.74161 0.466662i −0.0976644 0.0261691i
\(319\) 12.6064 7.27830i 0.705822 0.407506i
\(320\) −13.2285 6.99153i −0.739496 0.390839i
\(321\) 10.5786i 0.590440i
\(322\) 0 0
\(323\) 12.1155 + 12.1155i 0.674126 + 0.674126i
\(324\) 1.68371 + 0.972092i 0.0935396 + 0.0540051i
\(325\) 3.47693 + 0.657897i 0.192865 + 0.0364936i
\(326\) 1.74489 + 3.02224i 0.0966406 + 0.167386i
\(327\) −0.645454 + 0.172949i −0.0356937 + 0.00956410i
\(328\) 5.02861 5.02861i 0.277659 0.277659i
\(329\) 0 0
\(330\) 0.0787277 + 2.10425i 0.00433382 + 0.115835i
\(331\) 8.34566 14.4551i 0.458719 0.794524i −0.540175 0.841553i \(-0.681642\pi\)
0.998894 + 0.0470286i \(0.0149752\pi\)
\(332\) 8.53199 31.8418i 0.468254 1.74755i
\(333\) −0.106980 + 0.399255i −0.00586246 + 0.0218790i
\(334\) −0.774506 + 1.34148i −0.0423791 + 0.0734027i
\(335\) −2.03085 + 2.18872i −0.110957 + 0.119583i
\(336\) 0 0
\(337\) 2.54028 2.54028i 0.138378 0.138378i −0.634525 0.772903i \(-0.718804\pi\)
0.772903 + 0.634525i \(0.218804\pi\)
\(338\) 2.85233 0.764280i 0.155146 0.0415714i
\(339\) −2.40171 4.15988i −0.130443 0.225934i
\(340\) −10.0602 2.29620i −0.545589 0.124529i
\(341\) 17.0467 + 9.84191i 0.923130 + 0.532969i
\(342\) 1.20589 + 1.20589i 0.0652072 + 0.0652072i
\(343\) 0 0
\(344\) 4.81248i 0.259472i
\(345\) 7.62474 14.4266i 0.410502 0.776701i
\(346\) 0.719122 0.415185i 0.0386602 0.0223205i
\(347\) −18.7118 5.01382i −1.00450 0.269156i −0.281173 0.959657i \(-0.590723\pi\)
−0.723331 + 0.690501i \(0.757390\pi\)
\(348\) 1.83761 + 6.85806i 0.0985063 + 0.367631i
\(349\) −0.508601 −0.0272248 −0.0136124 0.999907i \(-0.504333\pi\)
−0.0136124 + 0.999907i \(0.504333\pi\)
\(350\) 0 0
\(351\) −0.707725 −0.0377756
\(352\) 2.81671 + 10.5121i 0.150131 + 0.560297i
\(353\) 14.9193 + 3.99763i 0.794077 + 0.212772i 0.632982 0.774167i \(-0.281831\pi\)
0.161095 + 0.986939i \(0.448497\pi\)
\(354\) 1.25003 0.721704i 0.0664382 0.0383581i
\(355\) 1.24648 2.35843i 0.0661561 0.125172i
\(356\) 15.2148i 0.806383i
\(357\) 0 0
\(358\) 3.69375 + 3.69375i 0.195221 + 0.195221i
\(359\) −13.8443 7.99301i −0.730674 0.421855i 0.0879945 0.996121i \(-0.471954\pi\)
−0.818669 + 0.574266i \(0.805288\pi\)
\(360\) −2.03138 0.463657i −0.107063 0.0244369i
\(361\) −16.5534 28.6713i −0.871231 1.50902i
\(362\) 1.93636 0.518847i 0.101773 0.0272700i
\(363\) −3.45660 + 3.45660i −0.181424 + 0.181424i
\(364\) 0 0
\(365\) 2.97465 3.20589i 0.155701 0.167804i
\(366\) 0.839933 1.45481i 0.0439040 0.0760440i
\(367\) −0.150084 + 0.560120i −0.00783431 + 0.0292380i −0.969732 0.244170i \(-0.921484\pi\)
0.961898 + 0.273408i \(0.0881510\pi\)
\(368\) 6.92823 25.8565i 0.361159 1.34786i
\(369\) −3.81592 + 6.60937i −0.198649 + 0.344070i
\(370\) −0.00816384 0.218205i −0.000424418 0.0113439i
\(371\) 0 0
\(372\) −6.78879 + 6.78879i −0.351982 + 0.351982i
\(373\) 4.70591 1.26094i 0.243663 0.0652892i −0.134921 0.990856i \(-0.543078\pi\)
0.378583 + 0.925567i \(0.376411\pi\)
\(374\) 1.11763 + 1.93578i 0.0577911 + 0.100097i
\(375\) −11.0554 1.66647i −0.570901 0.0860559i
\(376\) 0.348426 + 0.201164i 0.0179687 + 0.0103742i
\(377\) −1.82755 1.82755i −0.0941237 0.0941237i
\(378\) 0 0
\(379\) 12.9179i 0.663547i 0.943359 + 0.331773i \(0.107647\pi\)
−0.943359 + 0.331773i \(0.892353\pi\)
\(380\) 27.7445 + 14.6636i 1.42327 + 0.752224i
\(381\) −7.21175 + 4.16371i −0.369469 + 0.213313i
\(382\) 3.48918 + 0.934923i 0.178522 + 0.0478348i
\(383\) 3.68844 + 13.7654i 0.188470 + 0.703381i 0.993861 + 0.110636i \(0.0352889\pi\)
−0.805391 + 0.592744i \(0.798044\pi\)
\(384\) −7.04142 −0.359331
\(385\) 0 0
\(386\) 2.98291 0.151826
\(387\) 1.33669 + 4.98860i 0.0679479 + 0.253585i
\(388\) −19.7504 5.29212i −1.00268 0.268666i
\(389\) −21.0704 + 12.1650i −1.06831 + 0.616791i −0.927720 0.373277i \(-0.878234\pi\)
−0.140593 + 0.990068i \(0.544901\pi\)
\(390\) 0.357265 0.110200i 0.0180908 0.00558021i
\(391\) 17.3213i 0.875976i
\(392\) 0 0
\(393\) −13.3038 13.3038i −0.671089 0.671089i
\(394\) 0.777524 + 0.448904i 0.0391711 + 0.0226154i
\(395\) 16.3589 10.2789i 0.823108 0.517189i
\(396\) −3.87478 6.71132i −0.194715 0.337256i
\(397\) 9.29762 2.49129i 0.466634 0.125034i −0.0178380 0.999841i \(-0.505678\pi\)
0.484472 + 0.874807i \(0.339012\pi\)
\(398\) 0.103013 0.103013i 0.00516356 0.00516356i
\(399\) 0 0
\(400\) −18.2898 + 1.37050i −0.914492 + 0.0685249i
\(401\) 4.41545 7.64778i 0.220497 0.381912i −0.734462 0.678650i \(-0.762565\pi\)
0.954959 + 0.296738i \(0.0958987\pi\)
\(402\) −0.0816479 + 0.304714i −0.00407223 + 0.0151978i
\(403\) 0.904546 3.37581i 0.0450587 0.168161i
\(404\) −6.14006 + 10.6349i −0.305479 + 0.529105i
\(405\) 2.23450 0.0836010i 0.111033 0.00415417i
\(406\) 0 0
\(407\) 1.16501 1.16501i 0.0577476 0.0577476i
\(408\) −2.13643 + 0.572453i −0.105769 + 0.0283407i
\(409\) −11.5992 20.0905i −0.573546 0.993410i −0.996198 0.0871183i \(-0.972234\pi\)
0.422652 0.906292i \(-0.361099\pi\)
\(410\) 0.897158 3.93064i 0.0443075 0.194120i
\(411\) 0.994464 + 0.574154i 0.0490533 + 0.0283209i
\(412\) 24.3819 + 24.3819i 1.20121 + 1.20121i
\(413\) 0 0
\(414\) 1.72404i 0.0847319i
\(415\) −11.1753 36.2298i −0.548572 1.77845i
\(416\) 1.67341 0.966143i 0.0820456 0.0473690i
\(417\) 0.427364 + 0.114512i 0.0209281 + 0.00560766i
\(418\) −1.75938 6.56610i −0.0860541 0.321158i
\(419\) −13.0393 −0.637009 −0.318505 0.947921i \(-0.603181\pi\)
−0.318505 + 0.947921i \(0.603181\pi\)
\(420\) 0 0
\(421\) −31.3549 −1.52814 −0.764071 0.645132i \(-0.776802\pi\)
−0.764071 + 0.645132i \(0.776802\pi\)
\(422\) −0.569183 2.12422i −0.0277074 0.103405i
\(423\) −0.417052 0.111749i −0.0202778 0.00543341i
\(424\) −6.15877 + 3.55577i −0.299096 + 0.172683i
\(425\) −11.2021 + 3.91969i −0.543382 + 0.190133i
\(426\) 0.281842i 0.0136553i
\(427\) 0 0
\(428\) 14.5429 + 14.5429i 0.702957 + 0.702957i
\(429\) 2.44307 + 1.41050i 0.117952 + 0.0680998i
\(430\) −1.45155 2.31015i −0.0700000 0.111405i
\(431\) 11.2779 + 19.5339i 0.543238 + 0.940915i 0.998716 + 0.0506681i \(0.0161351\pi\)
−0.455478 + 0.890247i \(0.650532\pi\)
\(432\) 3.54323 0.949406i 0.170474 0.0456783i
\(433\) 19.9639 19.9639i 0.959405 0.959405i −0.0398028 0.999208i \(-0.512673\pi\)
0.999208 + 0.0398028i \(0.0126730\pi\)
\(434\) 0 0
\(435\) 5.98602 + 5.55426i 0.287008 + 0.266306i
\(436\) −0.649575 + 1.12510i −0.0311090 + 0.0538824i
\(437\) −13.6337 + 50.8816i −0.652188 + 2.43400i
\(438\) 0.119592 0.446325i 0.00571435 0.0213262i
\(439\) 15.0972 26.1490i 0.720548 1.24803i −0.240232 0.970715i \(-0.577224\pi\)
0.960780 0.277310i \(-0.0894430\pi\)
\(440\) 6.08824 + 5.64910i 0.290246 + 0.269310i
\(441\) 0 0
\(442\) 0.280632 0.280632i 0.0133483 0.0133483i
\(443\) 17.4063 4.66400i 0.826997 0.221593i 0.179594 0.983741i \(-0.442522\pi\)
0.647403 + 0.762148i \(0.275855\pi\)
\(444\) 0.401803 + 0.695944i 0.0190687 + 0.0330280i
\(445\) −9.30999 14.8169i −0.441336 0.702388i
\(446\) −0.392082 0.226369i −0.0185656 0.0107189i
\(447\) −2.22112 2.22112i −0.105056 0.105056i
\(448\) 0 0
\(449\) 30.4170i 1.43547i −0.696318 0.717734i \(-0.745180\pi\)
0.696318 0.717734i \(-0.254820\pi\)
\(450\) −1.11498 + 0.390138i −0.0525605 + 0.0183913i
\(451\) 26.3451 15.2103i 1.24054 0.716227i
\(452\) −9.02051 2.41704i −0.424289 0.113688i
\(453\) 3.81084 + 14.2222i 0.179049 + 0.668219i
\(454\) 1.38802 0.0651432
\(455\) 0 0
\(456\) 6.72637 0.314991
\(457\) 0.481493 + 1.79696i 0.0225233 + 0.0840581i 0.976273 0.216545i \(-0.0694788\pi\)
−0.953749 + 0.300603i \(0.902812\pi\)
\(458\) −2.96435 0.794295i −0.138515 0.0371150i
\(459\) 2.05561 1.18681i 0.0959476 0.0553954i
\(460\) −9.35081 30.3150i −0.435984 1.41344i
\(461\) 1.29957i 0.0605272i −0.999542 0.0302636i \(-0.990365\pi\)
0.999542 0.0302636i \(-0.00963467\pi\)
\(462\) 0 0
\(463\) 16.5240 + 16.5240i 0.767934 + 0.767934i 0.977742 0.209809i \(-0.0672841\pi\)
−0.209809 + 0.977742i \(0.567284\pi\)
\(464\) 11.6013 + 6.69801i 0.538577 + 0.310947i
\(465\) −2.45716 + 10.7653i −0.113948 + 0.499230i
\(466\) −2.75039 4.76381i −0.127409 0.220679i
\(467\) 27.4583 7.35742i 1.27062 0.340461i 0.440350 0.897826i \(-0.354854\pi\)
0.830267 + 0.557365i \(0.188188\pi\)
\(468\) −0.972943 + 0.972943i −0.0449743 + 0.0449743i
\(469\) 0 0
\(470\) 0.227932 0.00852775i 0.0105137 0.000393356i
\(471\) 5.63216 9.75519i 0.259516 0.449495i
\(472\) 1.47347 5.49908i 0.0678221 0.253116i
\(473\) 5.32808 19.8847i 0.244986 0.914298i
\(474\) 1.02064 1.76781i 0.0468797 0.0811980i
\(475\) 35.9916 2.69693i 1.65141 0.123744i
\(476\) 0 0
\(477\) 5.39653 5.39653i 0.247090 0.247090i
\(478\) −1.25066 + 0.335113i −0.0572038 + 0.0153277i
\(479\) −5.54182 9.59872i −0.253212 0.438577i 0.711196 0.702994i \(-0.248154\pi\)
−0.964408 + 0.264417i \(0.914820\pi\)
\(480\) −5.16933 + 3.24808i −0.235947 + 0.148254i
\(481\) −0.253339 0.146265i −0.0115513 0.00666912i
\(482\) 2.44749 + 2.44749i 0.111480 + 0.111480i
\(483\) 0 0
\(484\) 9.50389i 0.431995i
\(485\) −22.4722 + 6.93165i −1.02041 + 0.314750i
\(486\) 0.204601 0.118126i 0.00928088 0.00535832i
\(487\) 18.6489 + 4.99695i 0.845060 + 0.226433i 0.655273 0.755392i \(-0.272554\pi\)
0.189787 + 0.981825i \(0.439220\pi\)
\(488\) −1.71486 6.39994i −0.0776280 0.289712i
\(489\) −14.7714 −0.667986
\(490\) 0 0
\(491\) 32.1155 1.44935 0.724677 0.689089i \(-0.241989\pi\)
0.724677 + 0.689089i \(0.241989\pi\)
\(492\) 3.84028 + 14.3321i 0.173133 + 0.646142i
\(493\) 8.37286 + 2.24350i 0.377095 + 0.101042i
\(494\) −1.04525 + 0.603474i −0.0470279 + 0.0271516i
\(495\) −7.88012 4.16480i −0.354185 0.187194i
\(496\) 18.1145i 0.813364i
\(497\) 0 0
\(498\) −2.83255 2.83255i −0.126930 0.126930i
\(499\) 3.70166 + 2.13715i 0.165709 + 0.0956722i 0.580561 0.814217i \(-0.302833\pi\)
−0.414852 + 0.909889i \(0.636167\pi\)
\(500\) −17.4894 + 12.9075i −0.782150 + 0.577239i
\(501\) −3.27830 5.67818i −0.146463 0.253682i
\(502\) 4.82662 1.29329i 0.215423 0.0577223i
\(503\) −17.5637 + 17.5637i −0.783128 + 0.783128i −0.980357 0.197229i \(-0.936806\pi\)
0.197229 + 0.980357i \(0.436806\pi\)
\(504\) 0 0
\(505\) 0.528051 + 14.1139i 0.0234980 + 0.628059i
\(506\) −3.43603 + 5.95138i −0.152750 + 0.264571i
\(507\) −3.23501 + 12.0732i −0.143672 + 0.536191i
\(508\) −4.19029 + 15.6384i −0.185914 + 0.693840i
\(509\) −13.9581 + 24.1762i −0.618682 + 1.07159i 0.371044 + 0.928615i \(0.379000\pi\)
−0.989726 + 0.142974i \(0.954333\pi\)
\(510\) −0.852889 + 0.919189i −0.0377666 + 0.0407024i
\(511\) 0 0
\(512\) −11.9158 + 11.9158i −0.526611 + 0.526611i
\(513\) −6.97254 + 1.86829i −0.307845 + 0.0824868i
\(514\) 1.56907 + 2.71771i 0.0692086 + 0.119873i
\(515\) 38.6636 + 8.82487i 1.70372 + 0.388870i
\(516\) 8.69567 + 5.02045i 0.382806 + 0.221013i
\(517\) 1.21695 + 1.21695i 0.0535212 + 0.0535212i
\(518\) 0 0
\(519\) 3.51476i 0.154281i
\(520\) 0.689054 1.30374i 0.0302170 0.0571729i
\(521\) 24.9975 14.4323i 1.09516 0.632292i 0.160216 0.987082i \(-0.448781\pi\)
0.934946 + 0.354790i \(0.115448\pi\)
\(522\) 0.833375 + 0.223302i 0.0364758 + 0.00977367i
\(523\) 1.29832 + 4.84539i 0.0567715 + 0.211874i 0.988485 0.151321i \(-0.0483526\pi\)
−0.931713 + 0.363195i \(0.881686\pi\)
\(524\) −36.5788 −1.59795
\(525\) 0 0
\(526\) −5.13793 −0.224024
\(527\) 3.03372 + 11.3220i 0.132151 + 0.493195i
\(528\) −14.1234 3.78435i −0.614642 0.164693i
\(529\) 26.1995 15.1263i 1.13911 0.657665i
\(530\) −1.88391 + 3.56450i −0.0818319 + 0.154832i
\(531\) 6.10959i 0.265134i
\(532\) 0 0
\(533\) −3.81926 3.81926i −0.165430 0.165430i
\(534\) −1.60117 0.924434i −0.0692892 0.0400042i
\(535\) 23.0614 + 5.26370i 0.997031 + 0.227570i
\(536\) 0.622122 + 1.07755i 0.0268716 + 0.0465430i
\(537\) −21.3574 + 5.72271i −0.921642 + 0.246953i
\(538\) −3.83980 + 3.83980i −0.165546 + 0.165546i
\(539\) 0 0
\(540\) 2.95695 3.18681i 0.127247 0.137138i
\(541\) 2.04349 3.53943i 0.0878565 0.152172i −0.818748 0.574153i \(-0.805332\pi\)
0.906605 + 0.421981i \(0.138665\pi\)
\(542\) −0.963650 + 3.59639i −0.0413923 + 0.154478i
\(543\) −2.19615 + 8.19615i −0.0942459 + 0.351731i
\(544\) −3.24031 + 5.61238i −0.138927 + 0.240629i
\(545\) 0.0558641 + 1.49315i 0.00239296 + 0.0639594i
\(546\) 0 0
\(547\) 28.2200 28.2200i 1.20660 1.20660i 0.234482 0.972121i \(-0.424661\pi\)
0.972121 0.234482i \(-0.0753392\pi\)
\(548\) 2.15645 0.577820i 0.0921191 0.0246832i
\(549\) 3.55523 + 6.15784i 0.151734 + 0.262810i
\(550\) 4.62645 + 0.875407i 0.197272 + 0.0373275i
\(551\) −22.8296 13.1807i −0.972572 0.561515i
\(552\) −4.80827 4.80827i −0.204654 0.204654i
\(553\) 0 0
\(554\) 1.60631i 0.0682457i
\(555\) 0.817145 + 0.431878i 0.0346859 + 0.0183322i
\(556\) 0.744941 0.430092i 0.0315925 0.0182400i
\(557\) −38.4695 10.3079i −1.63000 0.436758i −0.676086 0.736823i \(-0.736325\pi\)
−0.953919 + 0.300065i \(0.902992\pi\)
\(558\) 0.301955 + 1.12691i 0.0127828 + 0.0477060i
\(559\) −3.65510 −0.154594
\(560\) 0 0
\(561\) −9.46128 −0.399455
\(562\) 0.590468 + 2.20366i 0.0249074 + 0.0929556i
\(563\) −37.3806 10.0161i −1.57541 0.422129i −0.637906 0.770114i \(-0.720199\pi\)
−0.937500 + 0.347985i \(0.886866\pi\)
\(564\) −0.726967 + 0.419715i −0.0306108 + 0.0176732i
\(565\) −10.2636 + 3.16586i −0.431792 + 0.133189i
\(566\) 4.98144i 0.209386i
\(567\) 0 0
\(568\) −0.786047 0.786047i −0.0329818 0.0329818i
\(569\) −15.3951 8.88837i −0.645396 0.372620i 0.141294 0.989968i \(-0.454874\pi\)
−0.786690 + 0.617348i \(0.788207\pi\)
\(570\) 3.22888 2.02882i 0.135243 0.0849780i
\(571\) 8.44331 + 14.6242i 0.353342 + 0.612005i 0.986833 0.161744i \(-0.0517120\pi\)
−0.633491 + 0.773750i \(0.718379\pi\)
\(572\) 5.29768 1.41951i 0.221507 0.0593527i
\(573\) −10.8116 + 10.8116i −0.451659 + 0.451659i
\(574\) 0 0
\(575\) −27.6561 23.8003i −1.15334 0.992543i
\(576\) 3.34571 5.79493i 0.139404 0.241456i
\(577\) −1.42632 + 5.32309i −0.0593784 + 0.221603i −0.989239 0.146309i \(-0.953261\pi\)
0.929861 + 0.367912i \(0.119927\pi\)
\(578\) 0.694991 2.59374i 0.0289078 0.107885i
\(579\) −6.31296 + 10.9344i −0.262358 + 0.454417i
\(580\) 15.8650 0.593566i 0.658756 0.0246465i
\(581\) 0 0
\(582\) −1.75694 + 1.75694i −0.0728276 + 0.0728276i
\(583\) −29.3841 + 7.87345i −1.21697 + 0.326085i
\(584\) −0.911244 1.57832i −0.0377075 0.0653114i
\(585\) −0.352150 + 1.54284i −0.0145596 + 0.0637887i
\(586\) 1.38667 + 0.800592i 0.0572826 + 0.0330721i
\(587\) 15.1058 + 15.1058i 0.623484 + 0.623484i 0.946420 0.322937i \(-0.104670\pi\)
−0.322937 + 0.946420i \(0.604670\pi\)
\(588\) 0 0
\(589\) 35.6465i 1.46879i
\(590\) −0.951328 3.08417i −0.0391655 0.126973i
\(591\) −3.29107 + 1.90010i −0.135377 + 0.0781597i
\(592\) 1.46456 + 0.392426i 0.0601928 + 0.0161286i
\(593\) 1.25558 + 4.68590i 0.0515606 + 0.192427i 0.986902 0.161318i \(-0.0515746\pi\)
−0.935342 + 0.353745i \(0.884908\pi\)
\(594\) −0.941708 −0.0386388
\(595\) 0 0
\(596\) −6.10696 −0.250151
\(597\) 0.159597 + 0.595625i 0.00653188 + 0.0243773i
\(598\) 1.17857 + 0.315797i 0.0481953 + 0.0129139i
\(599\) −8.74769 + 5.05048i −0.357421 + 0.206357i −0.667949 0.744207i \(-0.732827\pi\)
0.310528 + 0.950564i \(0.399494\pi\)
\(600\) −2.02155 + 4.19771i −0.0825293 + 0.171371i
\(601\) 38.4063i 1.56663i −0.621628 0.783313i \(-0.713528\pi\)
0.621628 0.783313i \(-0.286472\pi\)
\(602\) 0 0
\(603\) −0.944185 0.944185i −0.0384502 0.0384502i
\(604\) 24.7909 + 14.3130i 1.00873 + 0.582389i
\(605\) 5.81546 + 9.25533i 0.236432 + 0.376283i
\(606\) 0.746125 + 1.29233i 0.0303093 + 0.0524972i
\(607\) 14.0606 3.76752i 0.570702 0.152919i 0.0380833 0.999275i \(-0.487875\pi\)
0.532618 + 0.846356i \(0.321208\pi\)
\(608\) 13.9360 13.9360i 0.565180 0.565180i
\(609\) 0 0
\(610\) −2.75355 2.55494i −0.111488 0.103447i
\(611\) 0.152785 0.264632i 0.00618103 0.0107059i
\(612\) 1.19438 4.45750i 0.0482801 0.180184i
\(613\) −5.27642 + 19.6919i −0.213113 + 0.795347i 0.773710 + 0.633540i \(0.218399\pi\)
−0.986822 + 0.161807i \(0.948268\pi\)
\(614\) −1.64560 + 2.85027i −0.0664112 + 0.115028i
\(615\) 12.5097 + 11.6074i 0.504440 + 0.468056i
\(616\) 0 0
\(617\) −25.4196 + 25.4196i −1.02336 + 1.02336i −0.0236346 + 0.999721i \(0.507524\pi\)
−0.999721 + 0.0236346i \(0.992476\pi\)
\(618\) 4.04731 1.08447i 0.162807 0.0436239i
\(619\) −5.59953 9.69868i −0.225064 0.389823i 0.731274 0.682083i \(-0.238926\pi\)
−0.956339 + 0.292261i \(0.905593\pi\)
\(620\) 11.4216 + 18.1775i 0.458703 + 0.730028i
\(621\) 6.31977 + 3.64872i 0.253603 + 0.146418i
\(622\) 4.56168 + 4.56168i 0.182907 + 0.182907i
\(623\) 0 0
\(624\) 2.59609i 0.103927i
\(625\) −9.13387 + 23.2717i −0.365355 + 0.930868i
\(626\) −5.35527 + 3.09186i −0.214040 + 0.123576i
\(627\) 27.7927 + 7.44703i 1.10993 + 0.297406i
\(628\) −5.66812 21.1537i −0.226182 0.844124i
\(629\) 0.981107 0.0391193
\(630\) 0 0
\(631\) 21.2015 0.844020 0.422010 0.906591i \(-0.361325\pi\)
0.422010 + 0.906591i \(0.361325\pi\)
\(632\) −2.08381 7.77687i −0.0828894 0.309347i
\(633\) 8.99131 + 2.40921i 0.357373 + 0.0957577i
\(634\) −6.33077 + 3.65507i −0.251427 + 0.145161i
\(635\) 5.48847 + 17.7934i 0.217803 + 0.706110i
\(636\) 14.8377i 0.588353i
\(637\) 0 0
\(638\) −2.43176 2.43176i −0.0962745 0.0962745i
\(639\) 1.03314 + 0.596485i 0.0408705 + 0.0235966i
\(640\) −3.50367 + 15.3503i −0.138495 + 0.606774i
\(641\) 14.9484 + 25.8915i 0.590428 + 1.02265i 0.994175 + 0.107781i \(0.0343745\pi\)
−0.403746 + 0.914871i \(0.632292\pi\)
\(642\) 2.41406 0.646846i 0.0952755 0.0255290i
\(643\) −11.2813 + 11.2813i −0.444891 + 0.444891i −0.893652 0.448761i \(-0.851866\pi\)
0.448761 + 0.893652i \(0.351866\pi\)
\(644\) 0 0
\(645\) 11.5403 0.431764i 0.454398 0.0170007i
\(646\) 2.02397 3.50562i 0.0796320 0.137927i
\(647\) 9.60434 35.8439i 0.377586 1.40917i −0.471944 0.881628i \(-0.656448\pi\)
0.849530 0.527540i \(-0.176886\pi\)
\(648\) 0.241174 0.900073i 0.00947420 0.0353582i
\(649\) 12.1765 21.0903i 0.477969 0.827866i
\(650\) −0.0624689 0.833673i −0.00245023 0.0326993i
\(651\) 0 0
\(652\) −20.3069 + 20.3069i −0.795281 + 0.795281i
\(653\) 2.69982 0.723414i 0.105652 0.0283094i −0.205606 0.978635i \(-0.565916\pi\)
0.311258 + 0.950326i \(0.399250\pi\)
\(654\) 0.0789348 + 0.136719i 0.00308659 + 0.00534614i
\(655\) −35.6221 + 22.3827i −1.39187 + 0.874563i
\(656\) 24.2446 + 13.9976i 0.946594 + 0.546516i
\(657\) 1.38298 + 1.38298i 0.0539552 + 0.0539552i
\(658\) 0 0
\(659\) 15.1044i 0.588385i 0.955746 + 0.294193i \(0.0950507\pi\)
−0.955746 + 0.294193i \(0.904949\pi\)
\(660\) −16.5587 + 5.10762i −0.644547 + 0.198814i
\(661\) −0.953098 + 0.550272i −0.0370712 + 0.0214031i −0.518421 0.855125i \(-0.673480\pi\)
0.481350 + 0.876529i \(0.340147\pi\)
\(662\) −3.80900 1.02062i −0.148041 0.0396675i
\(663\) 0.434781 + 1.62263i 0.0168855 + 0.0630176i
\(664\) −15.7998 −0.613150
\(665\) 0 0
\(666\) 0.0976524 0.00378395
\(667\) 6.89742 + 25.7415i 0.267069 + 0.996716i
\(668\) −12.3129 3.29923i −0.476399 0.127651i
\(669\) 1.65959 0.958163i 0.0641633 0.0370447i
\(670\) 0.623651 + 0.329612i 0.0240937 + 0.0127340i
\(671\) 28.3425i 1.09415i
\(672\) 0 0
\(673\) −11.4381 11.4381i −0.440906 0.440906i 0.451411 0.892316i \(-0.350921\pi\)
−0.892316 + 0.451411i \(0.850921\pi\)
\(674\) −0.735028 0.424369i −0.0283122 0.0163461i
\(675\) 0.929594 4.91283i 0.0357801 0.189095i
\(676\) 12.1503 + 21.0449i 0.467319 + 0.809421i
\(677\) −33.6052 + 9.00447i −1.29155 + 0.346070i −0.838249 0.545287i \(-0.816421\pi\)
−0.453302 + 0.891357i \(0.649754\pi\)
\(678\) −0.802438 + 0.802438i −0.0308175 + 0.0308175i
\(679\) 0 0
\(680\) 0.184908 + 4.94226i 0.00709089 + 0.189527i
\(681\) −2.93759 + 5.08805i −0.112569 + 0.194974i
\(682\) 1.20360 4.49190i 0.0460882 0.172004i
\(683\) −5.07507 + 18.9404i −0.194192 + 0.724736i 0.798282 + 0.602284i \(0.205742\pi\)
−0.992474 + 0.122452i \(0.960924\pi\)
\(684\) −7.01705 + 12.1539i −0.268304 + 0.464715i
\(685\) 1.74648 1.88225i 0.0667297 0.0719170i
\(686\) 0 0
\(687\) 9.18531 9.18531i 0.350442 0.350442i
\(688\) 18.2993 4.90328i 0.697655 0.186936i
\(689\) 2.70062 + 4.67762i 0.102886 + 0.178203i
\(690\) −3.75841 0.857847i −0.143080 0.0326577i
\(691\) 10.7439 + 6.20301i 0.408718 + 0.235974i 0.690239 0.723582i \(-0.257505\pi\)
−0.281521 + 0.959555i \(0.590839\pi\)
\(692\) 4.83190 + 4.83190i 0.183681 + 0.183681i
\(693\) 0 0
\(694\) 4.57667i 0.173728i
\(695\) 0.462284 0.874675i 0.0175354 0.0331783i
\(696\) 2.94703 1.70147i 0.111707 0.0644940i
\(697\) 17.4978 + 4.68852i 0.662776 + 0.177590i
\(698\) 0.0310993 + 0.116064i 0.00117713 + 0.00439309i
\(699\) 23.2835 0.880661
\(700\) 0 0
\(701\) 1.45193 0.0548388 0.0274194 0.999624i \(-0.491271\pi\)
0.0274194 + 0.999624i \(0.491271\pi\)
\(702\) 0.0432751 + 0.161505i 0.00163331 + 0.00609560i
\(703\) −2.88202 0.772235i −0.108697 0.0291254i
\(704\) −23.0987 + 13.3361i −0.870566 + 0.502622i
\(705\) −0.451129 + 0.853571i −0.0169905 + 0.0321473i
\(706\) 3.64907i 0.137335i
\(707\) 0 0
\(708\) 8.39914 + 8.39914i 0.315659 + 0.315659i
\(709\) −42.0269 24.2642i −1.57835 0.911262i −0.995090 0.0989781i \(-0.968443\pi\)
−0.583262 0.812284i \(-0.698224\pi\)
\(710\) −0.614417 0.140239i −0.0230587 0.00526308i
\(711\) 4.32013 + 7.48269i 0.162018 + 0.280623i
\(712\) −7.04380 + 1.88738i −0.263977 + 0.0707325i
\(713\) −25.4815 + 25.4815i −0.954290 + 0.954290i
\(714\) 0 0
\(715\) 4.29052 4.62405i 0.160457 0.172930i
\(716\) −21.4938 + 37.2283i −0.803261 + 1.39129i
\(717\) 1.41845 5.29373i 0.0529730 0.197698i
\(718\) −0.977492 + 3.64805i −0.0364797 + 0.136144i
\(719\) 21.7936 37.7476i 0.812764 1.40775i −0.0981578 0.995171i \(-0.531295\pi\)
0.910922 0.412578i \(-0.135372\pi\)
\(720\) −0.306667 8.19666i −0.0114288 0.305472i
\(721\) 0 0
\(722\) −5.53068 + 5.53068i −0.205831 + 0.205831i
\(723\) −14.1515 + 3.79189i −0.526301 + 0.141022i
\(724\) 8.24848 + 14.2868i 0.306552 + 0.530964i
\(725\) 15.0868 10.2859i 0.560311 0.382007i
\(726\) 1.00016 + 0.577445i 0.0371196 + 0.0214310i
\(727\) −10.4498 10.4498i −0.387563 0.387563i 0.486254 0.873817i \(-0.338363\pi\)
−0.873817 + 0.486254i \(0.838363\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) −0.913483 0.482794i −0.0338095 0.0178690i
\(731\) 10.6164 6.12936i 0.392660 0.226703i
\(732\) 13.3530 + 3.57793i 0.493542 + 0.132244i
\(733\) −6.90644 25.7752i −0.255095 0.952028i −0.968037 0.250806i \(-0.919305\pi\)
0.712942 0.701223i \(-0.247362\pi\)
\(734\) 0.136998 0.00505669
\(735\) 0 0
\(736\) −19.9240 −0.734409
\(737\) 1.37755 + 5.14109i 0.0507428 + 0.189375i
\(738\) 1.74161 + 0.466662i 0.0641094 + 0.0171781i
\(739\) −18.1596 + 10.4845i −0.668013 + 0.385677i −0.795323 0.606186i \(-0.792699\pi\)
0.127311 + 0.991863i \(0.459366\pi\)
\(740\) 1.71709 0.529645i 0.0631215 0.0194701i
\(741\) 5.10872i 0.187673i
\(742\) 0 0
\(743\) 9.18724 + 9.18724i 0.337047 + 0.337047i 0.855255 0.518208i \(-0.173401\pi\)
−0.518208 + 0.855255i \(0.673401\pi\)
\(744\) 3.98506 + 2.30077i 0.146099 + 0.0843504i
\(745\) −5.94724 + 3.73687i −0.217890 + 0.136908i
\(746\) −0.575501 0.996797i −0.0210706 0.0364953i
\(747\) 16.3780 4.38847i 0.599239 0.160566i
\(748\) −13.0069 + 13.0069i −0.475578 + 0.475578i
\(749\) 0 0
\(750\) 0.295712 + 2.62478i 0.0107979 + 0.0958434i
\(751\) −5.59843 + 9.69676i −0.204290 + 0.353840i −0.949906 0.312535i \(-0.898822\pi\)
0.745617 + 0.666375i \(0.232155\pi\)
\(752\) −0.409919 + 1.52984i −0.0149482 + 0.0557875i
\(753\) −5.47418 + 20.4299i −0.199490 + 0.744507i
\(754\) −0.305303 + 0.528801i −0.0111185 + 0.0192578i
\(755\) 32.9007 1.23094i 1.19738 0.0447984i
\(756\) 0 0
\(757\) −13.9324 + 13.9324i −0.506383 + 0.506383i −0.913414 0.407031i \(-0.866564\pi\)
0.407031 + 0.913414i \(0.366564\pi\)
\(758\) 2.94789 0.789886i 0.107072 0.0286899i
\(759\) −14.5439 25.1907i −0.527909 0.914365i
\(760\) 3.34691 14.6635i 0.121405 0.531902i
\(761\) 7.61085 + 4.39412i 0.275893 + 0.159287i 0.631563 0.775325i \(-0.282414\pi\)
−0.355670 + 0.934612i \(0.615747\pi\)
\(762\) 1.39114 + 1.39114i 0.0503958 + 0.0503958i
\(763\) 0 0
\(764\) 29.7263i 1.07546i
\(765\) −1.56441 5.07177i −0.0565615 0.183370i
\(766\) 2.91577 1.68342i 0.105351 0.0608245i
\(767\) −4.17658 1.11911i −0.150808 0.0404088i
\(768\) −3.03317 11.3199i −0.109450 0.408473i
\(769\) 11.2183 0.404543 0.202271 0.979330i \(-0.435168\pi\)
0.202271 + 0.979330i \(0.435168\pi\)
\(770\)