Properties

Label 735.2.v.a.472.4
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 472.4
Character \(\chi\) \(=\) 735.472
Dual form 735.2.v.a.313.4

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

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

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 0.634295 0.773091i \(-0.281291\pi\)
−0.773091 + 0.634295i \(0.781291\pi\)
\(14\) 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 \(0.00960478\pi\)
−0.850546 + 0.525900i \(0.823729\pi\)
\(18\) 0.0611467 + 0.228203i 0.0144124 + 0.0537879i
\(19\) −3.60925 6.25141i −0.828019 1.43417i −0.899590 0.436735i \(-0.856135\pi\)
0.0715711 0.997435i \(-0.477199\pi\)
\(20\) −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 0.0640944 0.997944i \(-0.479584\pi\)
−0.832198 + 0.554479i \(0.812917\pi\)
\(32\) −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 \(-0.796777\pi\)
0.803024 0.595947i \(-0.203223\pi\)
\(42\) 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 0.228274 0.973597i \(-0.426692\pi\)
−0.289107 + 0.957297i \(0.593358\pi\)
\(48\) 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 −0.595741 0.803176i \(-0.703142\pi\)
0.993442 + 0.114339i \(0.0364750\pi\)
\(60\) 0.967387 + 4.23833i 0.124889 + 0.547166i
\(61\) 6.15784 3.55523i 0.788431 0.455201i −0.0509788 0.998700i \(-0.516234\pi\)
0.839410 + 0.543499i \(0.182901\pi\)
\(62\) 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 −0.146562 0.989201i \(-0.546821\pi\)
0.367674 + 0.929955i \(0.380154\pi\)
\(74\) 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 \(0.130685\pi\)
0.399122 + 0.916898i \(0.369315\pi\)
\(84\) 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 0.995404 0.0957652i \(-0.0305298\pi\)
−0.580637 + 0.814163i \(0.697196\pi\)
\(90\) −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 −0.975423 0.220340i \(-0.929283\pi\)
0.220340 + 0.975423i \(0.429283\pi\)
\(98\) 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 0.202523 0.979278i \(-0.435086\pi\)
−0.746818 + 0.665028i \(0.768419\pi\)
\(102\) −0.541665 + 0.145139i −0.0536328 + 0.0143709i
\(103\) 4.59031 17.1313i 0.452296 1.68799i −0.243620 0.969871i \(-0.578335\pi\)
0.695917 0.718122i \(-0.254998\pi\)
\(104\) 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 −0.996604 0.0823433i \(-0.973760\pi\)
−0.426991 + 0.904256i \(0.640426\pi\)
\(132\) −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 \(-0.494027\pi\)
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 −0.607272 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 \(0.0650628\pi\)
−0.746507 + 0.665378i \(0.768271\pi\)
\(158\) 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 −0.863356 0.504595i \(-0.831642\pi\)
0.504595 + 0.863356i \(0.331642\pi\)
\(168\) 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 −0.922684 0.385557i \(-0.874009\pi\)
0.991846 + 0.127440i \(0.0406761\pi\)
\(174\) 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 \(-0.897877\pi\)
0.948974 0.315353i \(-0.102123\pi\)
\(182\) 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 −0.854890 0.518809i \(-0.826376\pi\)
0.876747 + 0.480953i \(0.159709\pi\)
\(200\) −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 0.751020 0.660279i \(-0.229562\pi\)
−0.660279 + 0.751020i \(0.729562\pi\)
\(224\) 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 0.896925 0.442183i \(-0.145796\pi\)
−0.997851 + 0.0655211i \(0.979129\pi\)
\(228\) −3.63229 13.5559i −0.240554 0.897761i
\(229\) 6.49500 + 11.2497i 0.429202 + 0.743399i 0.996802 0.0799049i \(-0.0254617\pi\)
−0.567601 + 0.823304i \(0.692128\pi\)
\(230\) −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 0.0321844 0.999482i \(-0.489754\pi\)
−0.849485 + 0.527613i \(0.823087\pi\)
\(242\) 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 \(-0.767361\pi\)
0.744604 0.667507i \(-0.232639\pi\)
\(252\) 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 −0.164604 0.986360i \(-0.552635\pi\)
−0.635731 + 0.771910i \(0.719301\pi\)
\(258\) 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 \(0.413802\pi\)
−0.968216 + 0.250116i \(0.919531\pi\)
\(270\) −0.281059 + 0.447306i −0.0171047 + 0.0272222i
\(271\) −13.6483 + 7.87982i −0.829072 + 0.478665i −0.853535 0.521036i \(-0.825546\pi\)
0.0244625 + 0.999701i \(0.492213\pi\)
\(272\) −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 0.403650 0.914913i \(-0.367741\pi\)
0.807028 + 0.590513i \(0.201075\pi\)
\(284\) 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 0.553125 0.833098i \(-0.313435\pi\)
−0.833098 + 0.553125i \(0.813435\pi\)
\(294\) 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 −0.929933 0.367728i \(-0.880136\pi\)
0.367728 + 0.929933i \(0.380136\pi\)
\(308\) 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 −0.354006 0.935243i \(-0.615181\pi\)
−0.986947 + 0.161043i \(0.948514\pi\)
\(312\) 0.637004 0.170685i 0.0360633 0.00966313i
\(313\) −6.77439 + 25.2824i −0.382911 + 1.42904i 0.458523 + 0.888683i \(0.348379\pi\)
−0.841434 + 0.540361i \(0.818288\pi\)
\(314\) −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 \(-0.504333\pi\)
−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 0.161095 0.986939i \(-0.448497\pi\)
0.632982 + 0.774167i \(0.281831\pi\)
\(354\) 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 0.961898 0.273408i \(-0.0881510\pi\)
−0.969732 + 0.244170i \(0.921484\pi\)
\(368\) 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 \(-0.798044\pi\)
0.993861 0.110636i \(-0.0352889\pi\)
\(384\) −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 0.484472 0.874807i \(-0.339012\pi\)
−0.0178380 + 0.999841i \(0.505678\pi\)
\(398\) 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 \(0.361099\pi\)
−0.996198 + 0.0871183i \(0.972234\pi\)
\(410\) 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 −0.455478 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 0.999208 0.0398028i \(-0.0126730\pi\)
−0.0398028 + 0.999208i \(0.512673\pi\)
\(434\) 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 \(0.0894430\pi\)
−0.240232 + 0.970715i \(0.577224\pi\)
\(440\) 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 \(0.00963467\pi\)
−0.999542 + 0.0302636i \(0.990365\pi\)
\(462\) 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 0.830267 0.557365i \(-0.188188\pi\)
0.440350 + 0.897826i \(0.354854\pi\)
\(468\) −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 −0.964408 0.264417i \(-0.914820\pi\)
0.711196 + 0.702994i \(0.248154\pi\)
\(480\) −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 0.197229 0.980357i \(-0.436806\pi\)
−0.980357 + 0.197229i \(0.936806\pi\)
\(504\) 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 \(-0.954333\pi\)
0.371044 0.928615i \(-0.379000\pi\)
\(510\) −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 0.934946 0.354790i \(-0.115448\pi\)
0.160216 + 0.987082i \(0.448781\pi\)
\(522\) 0.833375 0.223302i 0.0364758 0.00977367i
\(523\) 1.29832 4.84539i 0.0567715 0.211874i −0.931713 0.363195i \(-0.881686\pi\)
0.988485 + 0.151321i \(0.0483526\pi\)
\(524\) −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 −0.937500 0.347985i \(-0.886866\pi\)
−0.637906 + 0.770114i \(0.720199\pi\)
\(564\) −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 0.929861 0.367912i \(-0.119927\pi\)
−0.989239 + 0.146309i \(0.953261\pi\)
\(578\) 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 −0.322937 0.946420i \(-0.604670\pi\)
0.946420 + 0.322937i \(0.104670\pi\)
\(588\) 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 −0.935342 0.353745i \(-0.884908\pi\)
0.986902 + 0.161318i \(0.0515746\pi\)
\(594\) −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 \(0.286472\pi\)
−0.621628 + 0.783313i \(0.713528\pi\)
\(602\) 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 0.532618 0.846356i \(-0.321208\pi\)
0.0380833 + 0.999275i \(0.487875\pi\)
\(608\) 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 −0.956339 0.292261i \(-0.905593\pi\)
0.731274 + 0.682083i \(0.238926\pi\)
\(620\) 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 0.448761 0.893652i \(-0.351866\pi\)
−0.893652 + 0.448761i \(0.851866\pi\)
\(644\) 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 \(0.176886\pi\)
−0.471944 + 0.881628i \(0.656448\pi\)
\(648\) 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 0.481350 0.876529i \(-0.340147\pi\)
−0.518421 + 0.855125i \(0.673480\pi\)
\(662\) −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 −0.453302 0.891357i \(-0.649754\pi\)
−0.838249 + 0.545287i \(0.816421\pi\)
\(678\) −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 −0.281521 0.959555i \(-0.590839\pi\)
0.690239 + 0.723582i \(0.257505\pi\)
\(692\) 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 \(0.135372\pi\)
−0.0981578 + 0.995171i \(0.531295\pi\)
\(720\) −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 −0.873817 0.486254i \(-0.838363\pi\)
0.486254 + 0.873817i \(0.338363\pi\)
\(728\) 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 \(0.247362\pi\)
−0.968037 + 0.250806i \(0.919305\pi\)
\(734\) 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 −0.355670 0.934612i \(-0.615747\pi\)
0.631563 + 0.775325i \(0.282414\pi\)
\(762\) 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 \(0.435168\pi\)