Properties

Label 735.2.v.a.472.3
Level 735
Weight 2
Character 735.472
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 472.3
Character \(\chi\) \(=\) 735.472
Dual form 735.2.v.a.313.3

$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

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

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 −0.984169 0.177233i \(-0.943285\pi\)
0.940932 + 0.338596i \(0.109952\pi\)
\(3\) −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 0.391767 + 0.920064i \(0.371864\pi\)
−0.992683 + 0.120752i \(0.961470\pi\)
\(12\) −1.87794 0.503192i −0.542114 0.145259i
\(13\) 0.500437 + 0.500437i 0.138796 + 0.138796i 0.773091 0.634295i \(-0.218709\pi\)
−0.634295 + 0.773091i \(0.718709\pi\)
\(14\) 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 −0.999545 0.0301697i \(-0.990395\pi\)
0.850546 0.525900i \(-0.176271\pi\)
\(18\) 0.0611467 + 0.228203i 0.0144124 + 0.0537879i
\(19\) 3.60925 + 6.25141i 0.828019 + 1.43417i 0.899590 + 0.436735i \(0.143865\pi\)
−0.0715711 + 0.997435i \(0.522801\pi\)
\(20\) 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 0.902853 0.429949i \(-0.141468\pi\)
0.566919 + 0.823773i \(0.308135\pi\)
\(24\) 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 \(-0.889887\pi\)
0.940761 0.339071i \(-0.110113\pi\)
\(30\) −0.467057 + 0.246849i −0.0852725 + 0.0450683i
\(31\) 4.27662 + 2.46911i 0.768103 + 0.443465i 0.832198 0.554479i \(-0.187083\pi\)
−0.0640944 + 0.997944i \(0.520416\pi\)
\(32\) −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 −0.956574 0.291488i \(-0.905850\pi\)
0.974162 + 0.225851i \(0.0725163\pi\)
\(38\) −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 −0.371516 0.928427i \(-0.621162\pi\)
0.928427 + 0.371516i \(0.121162\pi\)
\(44\) −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 \(-0.406642\pi\)
−0.228274 + 0.973597i \(0.573308\pi\)
\(48\) −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 0.958265 + 0.285881i \(0.0922861\pi\)
−0.686942 + 0.726713i \(0.741047\pi\)
\(54\) −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 \(-0.963525\pi\)
0.595741 + 0.803176i \(0.296858\pi\)
\(60\) 0.967387 + 4.23833i 0.124889 + 0.547166i
\(61\) −6.15784 + 3.55523i −0.788431 + 0.455201i −0.839410 0.543499i \(-0.817099\pi\)
0.0509788 + 0.998700i \(0.483766\pi\)
\(62\) −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 −0.336743 0.941597i \(-0.609325\pi\)
0.179171 + 0.983818i \(0.442659\pi\)
\(68\) 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 \(-0.619846\pi\)
0.146562 + 0.989201i \(0.453179\pi\)
\(74\) 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 −0.0160304 0.999872i \(-0.505103\pi\)
0.857899 + 0.513819i \(0.171770\pi\)
\(80\) 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 −0.916898 0.399122i \(-0.869315\pi\)
−0.399122 0.916898i \(-0.630685\pi\)
\(84\) 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 \(-0.302804\pi\)
−0.995404 + 0.0957652i \(0.969470\pi\)
\(90\) 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 \(-0.570717\pi\)
0.975423 + 0.220340i \(0.0707167\pi\)
\(98\) 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 \(-0.231581\pi\)
−0.202523 + 0.979278i \(0.564914\pi\)
\(102\) −0.541665 + 0.145139i −0.0536328 + 0.0143709i
\(103\) −4.59031 + 17.1313i −0.452296 + 1.68799i 0.243620 + 0.969871i \(0.421665\pi\)
−0.695917 + 0.718122i \(0.745002\pi\)
\(104\) −0.659476 −0.0646669
\(105\) 0 0
\(106\) −1.80304 −0.175127
\(107\) 2.73794 10.2181i 0.264687 0.987825i −0.697755 0.716337i \(-0.745817\pi\)
0.962442 0.271488i \(-0.0875159\pi\)
\(108\) −1.87794 + 0.503192i −0.180705 + 0.0484197i
\(109\) −0.578698 0.334112i −0.0554293 0.0320021i 0.472029 0.881583i \(-0.343522\pi\)
−0.527459 + 0.849581i \(0.676855\pi\)
\(110\) −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 −0.848582 0.529064i \(-0.822543\pi\)
0.529064 + 0.848582i \(0.322543\pi\)
\(114\) 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 0.395820 0.918328i \(-0.370460\pi\)
−0.918328 + 0.395820i \(0.870460\pi\)
\(128\) −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 \(-0.359574\pi\)
0.996604 + 0.0823433i \(0.0262404\pi\)
\(132\) 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 −0.211126 0.977459i \(-0.567713\pi\)
0.305889 + 0.952067i \(0.401046\pi\)
\(138\) 0.446214 1.66529i 0.0379843 0.141759i
\(139\) −0.442439 −0.0375272 −0.0187636 0.999824i \(-0.505973\pi\)
−0.0187636 + 0.999824i \(0.505973\pi\)
\(140\) 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 −0.607272 0.794494i \(-0.707736\pi\)
0.384416 + 0.923160i \(0.374403\pi\)
\(150\) 0.976010 + 0.665422i 0.0796909 + 0.0543315i
\(151\) 7.36197 12.7513i 0.599109 1.03769i −0.393844 0.919177i \(-0.628855\pi\)
0.992953 0.118509i \(-0.0378116\pi\)
\(152\) −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 −0.979183 0.202980i \(-0.934937\pi\)
0.746507 0.665378i \(-0.231729\pi\)
\(158\) 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 −0.347666 0.937619i \(-0.613026\pi\)
−0.769897 + 0.638169i \(0.779692\pi\)
\(164\) −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 \(-0.668358\pi\)
0.863356 + 0.504595i \(0.168358\pi\)
\(168\) 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 \(-0.959324\pi\)
0.922684 + 0.385557i \(0.125991\pi\)
\(174\) −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 −0.434016 0.900905i \(-0.642904\pi\)
−0.997215 + 0.0745840i \(0.976237\pi\)
\(180\) −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 −0.998044 0.0625216i \(-0.980086\pi\)
0.444877 0.895592i \(-0.353248\pi\)
\(192\) −1.73186 6.46341i −0.124987 0.466456i
\(193\) −3.26783 12.1957i −0.235223 0.877866i −0.978048 0.208380i \(-0.933181\pi\)
0.742825 0.669486i \(-0.233486\pi\)
\(194\) 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 0.604872 0.796323i \(-0.293224\pi\)
−0.796323 + 0.604872i \(0.793224\pi\)
\(198\) −0.909620 0.243732i −0.0646439 0.0173213i
\(199\) −0.308318 + 0.534023i −0.0218561 + 0.0378559i −0.876747 0.480953i \(-0.840291\pi\)
0.854890 + 0.518809i \(0.173624\pi\)
\(200\) −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 \(-0.270438\pi\)
−0.751020 + 0.660279i \(0.770438\pi\)
\(224\) 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 \(-0.0208710\pi\)
−0.896925 + 0.442183i \(0.854204\pi\)
\(228\) −3.63229 13.5559i −0.240554 0.897761i
\(229\) −6.49500 11.2497i −0.429202 0.743399i 0.567601 0.823304i \(-0.307872\pi\)
−0.996802 + 0.0799049i \(0.974538\pi\)
\(230\) 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 0.904087 0.427349i \(-0.140552\pi\)
0.569288 + 0.822138i \(0.307219\pi\)
\(234\) −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 \(0.0567205\pi\)
−0.984166 + 0.177251i \(0.943279\pi\)
\(240\) −2.41767 + 7.83800i −0.156060 + 0.505940i
\(241\) 12.6879 + 7.32537i 0.817300 + 0.471868i 0.849485 0.527613i \(-0.176913\pi\)
−0.0321844 + 0.999482i \(0.510246\pi\)
\(242\) 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 \(-0.280699\pi\)
0.164604 + 0.986360i \(0.447365\pi\)
\(258\) −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 0.890163 + 0.455642i \(0.150590\pi\)
−0.543083 + 0.839679i \(0.682743\pi\)
\(264\) 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 −0.267501 0.963557i \(-0.586198\pi\)
0.968216 0.250116i \(-0.0804686\pi\)
\(270\) −0.281059 + 0.447306i −0.0171047 + 0.0272222i
\(271\) 13.6483 7.87982i 0.829072 0.478665i −0.0244625 0.999701i \(-0.507787\pi\)
0.853535 + 0.521036i \(0.174454\pi\)
\(272\) 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 −0.450662 0.892694i \(-0.648812\pi\)
0.0560621 + 0.998427i \(0.482146\pi\)
\(278\) 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 \(-0.798925\pi\)
−0.403650 + 0.914913i \(0.632259\pi\)
\(284\) 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 \(-0.186565\pi\)
−0.553125 + 0.833098i \(0.686565\pi\)
\(294\) 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 \(-0.619864\pi\)
0.929933 + 0.367728i \(0.119864\pi\)
\(308\) 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 \(-0.0514858\pi\)
0.354006 + 0.935243i \(0.384819\pi\)
\(312\) 0.637004 0.170685i 0.0360633 0.00966313i
\(313\) 6.77439 25.2824i 0.382911 1.42904i −0.458523 0.888683i \(-0.651621\pi\)
0.841434 0.540361i \(-0.181712\pi\)
\(314\) 2.66123 0.150182
\(315\) 0 0
\(316\) 16.7983 0.944977
\(317\) −8.00839 + 29.8877i −0.449796 + 1.67866i 0.253156 + 0.967425i \(0.418531\pi\)
−0.702952 + 0.711237i \(0.748135\pi\)
\(318\) 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 0.998894 0.0470286i \(-0.0149752\pi\)
−0.540175 + 0.841553i \(0.681642\pi\)
\(332\) −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 0.772903 0.634525i \(-0.218804\pi\)
−0.634525 + 0.772903i \(0.718804\pi\)
\(338\) 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 −0.723331 0.690501i \(-0.757390\pi\)
−0.281173 + 0.959657i \(0.590723\pi\)
\(348\) −1.83761 + 6.85806i −0.0985063 + 0.367631i
\(349\) 0.508601 0.0272248 0.0136124 0.999907i \(-0.495667\pi\)
0.0136124 + 0.999907i \(0.495667\pi\)
\(350\) 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 \(-0.718169\pi\)
−0.161095 + 0.986939i \(0.551503\pi\)
\(354\) 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 −0.818669 0.574266i \(-0.805288\pi\)
0.0879945 + 0.996121i \(0.471954\pi\)
\(360\) 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 \(-0.0785156\pi\)
−0.961898 + 0.273408i \(0.911849\pi\)
\(368\) 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 0.378583 0.925567i \(-0.376411\pi\)
−0.134921 + 0.990856i \(0.543078\pi\)
\(374\) −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 \(-0.892353\pi\)
0.943359 0.331773i \(-0.107647\pi\)
\(380\) 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 0.805391 + 0.592744i \(0.201956\pi\)
−0.993861 + 0.110636i \(0.964711\pi\)
\(384\) 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 −0.140593 0.990068i \(-0.544901\pi\)
−0.927720 + 0.373277i \(0.878234\pi\)
\(390\) −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 \(-0.494322\pi\)
−0.484472 + 0.874807i \(0.660988\pi\)
\(398\) −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 0.954959 0.296738i \(-0.0958987\pi\)
−0.734462 + 0.678650i \(0.762565\pi\)
\(402\) 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 −0.422652 0.906292i \(-0.638901\pi\)
0.996198 0.0871183i \(-0.0277658\pi\)
\(410\) 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 \(-0.396819\pi\)
0.318505 + 0.947921i \(0.396819\pi\)
\(420\) 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 −0.455478 0.890247i \(-0.650532\pi\)
0.998716 0.0506681i \(-0.0161351\pi\)
\(432\) −3.54323 0.949406i −0.170474 0.0456783i
\(433\) −19.9639 19.9639i −0.959405 0.959405i 0.0398028 0.999208i \(-0.487327\pi\)
−0.999208 + 0.0398028i \(0.987327\pi\)
\(434\) 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 −0.960780 0.277310i \(-0.910557\pi\)
0.240232 0.970715i \(-0.422776\pi\)
\(440\) −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 0.647403 0.762148i \(-0.275855\pi\)
0.179594 + 0.983741i \(0.442522\pi\)
\(444\) −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 \(0.254820\pi\)
−0.696318 + 0.717734i \(0.745180\pi\)
\(450\) −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 −0.953749 0.300603i \(-0.902812\pi\)
0.976273 + 0.216545i \(0.0694788\pi\)
\(458\) 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 −0.209809 0.977742i \(-0.567284\pi\)
0.977742 + 0.209809i \(0.0672841\pi\)
\(464\) 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 \(-0.645146\pi\)
−0.830267 + 0.557365i \(0.811812\pi\)
\(468\) 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 \(-0.751846\pi\)
0.964408 + 0.264417i \(0.0851795\pi\)
\(480\) −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 0.189787 0.981825i \(-0.439220\pi\)
0.655273 + 0.755392i \(0.272554\pi\)
\(488\) 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 −0.414852 0.909889i \(-0.636167\pi\)
0.580561 + 0.814217i \(0.302833\pi\)
\(500\) 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 \(-0.0631943\pi\)
−0.197229 + 0.980357i \(0.563194\pi\)
\(504\) 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 0.989726 + 0.142974i \(0.0456666\pi\)
−0.371044 + 0.928615i \(0.621000\pi\)
\(510\) 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 \(-0.551219\pi\)
−0.934946 + 0.354790i \(0.884552\pi\)
\(522\) 0.833375 0.223302i 0.0364758 0.00977367i
\(523\) −1.29832 + 4.84539i −0.0567715 + 0.211874i −0.988485 0.151321i \(-0.951647\pi\)
0.931713 + 0.363195i \(0.118314\pi\)
\(524\) 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 0.906605 0.421981i \(-0.138665\pi\)
−0.818748 + 0.574153i \(0.805332\pi\)
\(542\) 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 0.972121 + 0.234482i \(0.0753392\pi\)
0.234482 + 0.972121i \(0.424661\pi\)
\(548\) 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 −0.953919 0.300065i \(-0.902992\pi\)
−0.676086 + 0.736823i \(0.736325\pi\)
\(558\) −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 \(-0.279801\pi\)
0.937500 + 0.347985i \(0.113134\pi\)
\(564\) −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 −0.786690 0.617348i \(-0.788207\pi\)
0.141294 + 0.989968i \(0.454874\pi\)
\(570\) −3.22888 2.02882i −0.135243 0.0849780i
\(571\) 8.44331 14.6242i 0.353342 0.612005i −0.633491 0.773750i \(-0.718379\pi\)
0.986833 + 0.161744i \(0.0517120\pi\)
\(572\) −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 \(-0.0467394\pi\)
−0.929861 + 0.367912i \(0.880073\pi\)
\(578\) 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 \(-0.895330\pi\)
0.322937 + 0.946420i \(0.395330\pi\)
\(588\) 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 \(-0.948425\pi\)
0.935342 + 0.353745i \(0.115092\pi\)
\(594\) 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 0.310528 0.950564i \(-0.399494\pi\)
−0.667949 + 0.744207i \(0.732827\pi\)
\(600\) 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 \(-0.512125\pi\)
−0.532618 + 0.846356i \(0.678792\pi\)
\(608\) −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 −0.986822 0.161807i \(-0.948268\pi\)
0.773710 0.633540i \(-0.218399\pi\)
\(614\) 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 −0.999721 0.0236346i \(-0.992476\pi\)
−0.0236346 0.999721i \(-0.507524\pi\)
\(618\) 4.04731 + 1.08447i 0.162807 + 0.0436239i
\(619\) 5.59953 9.69868i 0.225064 0.389823i −0.731274 0.682083i \(-0.761074\pi\)
0.956339 + 0.292261i \(0.0944075\pi\)
\(620\) 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 −0.403746 0.914871i \(-0.632292\pi\)
0.994175 0.107781i \(-0.0343745\pi\)
\(642\) −2.41406 0.646846i −0.0952755 0.0255290i
\(643\) 11.2813 + 11.2813i 0.444891 + 0.444891i 0.893652 0.448761i \(-0.148134\pi\)
−0.448761 + 0.893652i \(0.648134\pi\)
\(644\) 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 −0.849530 0.527540i \(-0.823114\pi\)
0.471944 0.881628i \(-0.343552\pi\)
\(648\) 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 0.311258 0.950326i \(-0.399250\pi\)
−0.205606 + 0.978635i \(0.565916\pi\)
\(654\) −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 \(-0.904949\pi\)
0.955746 0.294193i \(-0.0950507\pi\)
\(660\) −16.5587 5.10762i −0.644547 0.198814i
\(661\) 0.953098 + 0.550272i 0.0370712 + 0.0214031i 0.518421 0.855125i \(-0.326520\pi\)
−0.481350 + 0.876529i \(0.659853\pi\)
\(662\) −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 −0.892316 0.451411i \(-0.850921\pi\)
0.451411 + 0.892316i \(0.350921\pi\)
\(674\) −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 \(-0.183579\pi\)
0.453302 + 0.891357i \(0.350246\pi\)
\(678\) 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 −0.992474 0.122452i \(-0.960924\pi\)
0.798282 0.602284i \(-0.205742\pi\)
\(684\) 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 \(-0.742495\pi\)
0.281521 + 0.959555i \(0.409161\pi\)
\(692\) −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 −0.583262 + 0.812284i \(0.698224\pi\)
−0.995090 + 0.0989781i \(0.968443\pi\)
\(710\) 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 −0.910922 0.412578i \(-0.864628\pi\)
0.0981578 0.995171i \(-0.468705\pi\)
\(720\) 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 \(-0.661637\pi\)
0.873817 + 0.486254i \(0.161637\pi\)
\(728\) 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 −0.712942 0.701223i \(-0.752638\pi\)
0.968037 0.250806i \(-0.0806955\pi\)
\(734\) −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 0.127311 0.991863i \(-0.459366\pi\)
−0.795323 + 0.606186i \(0.792699\pi\)
\(740\) −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 −0.518208 0.855255i \(-0.673401\pi\)
0.855255 + 0.518208i \(0.173401\pi\)
\(744\) 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 0.745617 0.666375i \(-0.232155\pi\)
−0.949906 + 0.312535i \(0.898822\pi\)
\(752\) 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 0.407031 0.913414i \(-0.366564\pi\)
−0.913414 + 0.407031i \(0.866564\pi\)
\(758\) 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 \(-0.717586\pi\)
0.355670 + 0.934612i \(0.384253\pi\)
\(762\) −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 \(-0.564832\pi\)
−0.202271 + 0.979330i \(0.564832\pi\)
\(770\) 0 0