Properties

Label 735.2.v.a.178.6
Level 735
Weight 2
Character 735.178
Analytic conductor 5.869
Analytic rank 0
Dimension 32
CM no
Inner twists 8

Related objects

Downloads

Learn more about

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 178.6
Character \(\chi\) \(=\) 735.178
Dual form 735.2.v.a.607.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.228203 + 0.0611467i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.68371 - 0.972092i) q^{4} +(-1.18965 - 1.89334i) q^{5} +0.236253i q^{6} +(-0.658899 - 0.658899i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(0.228203 + 0.0611467i) q^{2} +(0.258819 + 0.965926i) q^{3} +(-1.68371 - 0.972092i) q^{4} +(-1.18965 - 1.89334i) q^{5} +0.236253i q^{6} +(-0.658899 - 0.658899i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(-0.155711 - 0.504808i) q^{10} +(-1.99301 + 3.45200i) q^{11} +(0.503192 - 1.87794i) q^{12} +(0.500437 - 0.500437i) q^{13} +(1.52092 - 1.63915i) q^{15} +(1.83411 + 3.17677i) q^{16} +(2.29273 - 0.614336i) q^{17} +(-0.228203 + 0.0611467i) q^{18} +(3.60925 + 6.25141i) q^{19} +(0.162536 + 4.34429i) q^{20} +(-0.665888 + 0.665888i) q^{22} +(-1.88872 + 7.04878i) q^{23} +(0.465912 - 0.806983i) q^{24} +(-2.16945 + 4.50483i) q^{25} +(0.144801 - 0.0836010i) q^{26} +(-0.707107 - 0.707107i) q^{27} +3.65191i q^{29} +(0.447306 - 0.281059i) q^{30} +(-4.27662 - 2.46911i) q^{31} +(0.706647 + 2.63724i) q^{32} +(-3.85020 - 1.03166i) q^{33} +0.560773 q^{34} +1.94418 q^{36} +(-0.399255 - 0.106980i) q^{37} +(0.441387 + 1.64728i) q^{38} +(0.612908 + 0.353863i) q^{39} +(-0.463657 + 2.03138i) q^{40} -7.63184i q^{41} +(3.65191 + 3.65191i) q^{43} +(6.71132 - 3.87478i) q^{44} +(1.97694 + 1.04485i) q^{45} +(-0.862019 + 1.49306i) q^{46} +(-0.111749 + 0.417052i) q^{47} +(-2.59383 + 2.59383i) q^{48} +(-0.770530 + 0.895358i) q^{50} +(1.18681 + 2.05561i) q^{51} +(-1.32906 + 0.356122i) q^{52} +(-7.37179 + 1.97527i) q^{53} +(-0.118126 - 0.204601i) q^{54} +(8.90678 - 0.333235i) q^{55} +(-5.10425 + 5.10425i) q^{57} +(-0.223302 + 0.833375i) q^{58} +(-3.05480 + 5.29106i) q^{59} +(-4.15419 + 1.28138i) q^{60} +(6.15784 - 3.55523i) q^{61} +(-0.824957 - 0.824957i) q^{62} -6.69141i q^{64} +(-1.54284 - 0.352150i) q^{65} +(-0.815543 - 0.470854i) q^{66} +(0.345596 + 1.28978i) q^{67} +(-4.45750 - 1.19438i) q^{68} -7.29744 q^{69} +1.19297 q^{71} +(0.900073 + 0.241174i) q^{72} +(0.506205 + 1.88918i) q^{73} +(-0.0845694 - 0.0488262i) q^{74} +(-4.91283 - 0.929594i) q^{75} -14.0341i q^{76} +(0.118230 + 0.118230i) q^{78} +(-7.48269 + 4.32013i) q^{79} +(3.83275 - 7.25185i) q^{80} +(0.500000 - 0.866025i) q^{81} +(0.466662 - 1.74161i) q^{82} +(-11.9895 + 11.9895i) q^{83} +(-3.89070 - 3.61007i) q^{85} +(0.610073 + 1.05668i) q^{86} +(-3.52747 + 0.945184i) q^{87} +(3.58771 - 0.961324i) q^{88} +(-3.91290 - 6.77735i) q^{89} +(0.387253 + 0.359321i) q^{90} +(10.0321 - 10.0321i) q^{92} +(1.27810 - 4.76995i) q^{93} +(-0.0510027 + 0.0883393i) q^{94} +(7.54226 - 14.2705i) 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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.228203 + 0.0611467i 0.161364 + 0.0432372i 0.338596 0.940932i \(-0.390048\pi\)
−0.177233 + 0.984169i \(0.556715\pi\)
\(3\) 0.258819 + 0.965926i 0.149429 + 0.557678i
\(4\) −1.68371 0.972092i −0.841857 0.486046i
\(5\) −1.18965 1.89334i −0.532029 0.846726i
\(6\) 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
\(10\) −0.155711 0.504808i −0.0492400 0.159634i
\(11\) −1.99301 + 3.45200i −0.600915 + 1.04082i 0.391767 + 0.920064i \(0.371864\pi\)
−0.992683 + 0.120752i \(0.961470\pi\)
\(12\) 0.503192 1.87794i 0.145259 0.542114i
\(13\) 0.500437 0.500437i 0.138796 0.138796i −0.634295 0.773091i \(-0.718709\pi\)
0.773091 + 0.634295i \(0.218709\pi\)
\(14\) 0 0
\(15\) 1.52092 1.63915i 0.392699 0.423226i
\(16\) 1.83411 + 3.17677i 0.458528 + 0.794194i
\(17\) 2.29273 0.614336i 0.556070 0.148998i 0.0301697 0.999545i \(-0.490395\pi\)
0.525900 + 0.850546i \(0.323729\pi\)
\(18\) −0.228203 + 0.0611467i −0.0537879 + 0.0144124i
\(19\) 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
\(23\) −1.88872 + 7.04878i −0.393824 + 1.46977i 0.429949 + 0.902853i \(0.358532\pi\)
−0.823773 + 0.566919i \(0.808135\pi\)
\(24\) 0.465912 0.806983i 0.0951039 0.164725i
\(25\) −2.16945 + 4.50483i −0.433890 + 0.900966i
\(26\) 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 \(0.889887\pi\)
\(30\) 0.447306 0.281059i 0.0816665 0.0513141i
\(31\) −4.27662 2.46911i −0.768103 0.443465i 0.0640944 0.997944i \(-0.479584\pi\)
−0.832198 + 0.554479i \(0.812917\pi\)
\(32\) 0.706647 + 2.63724i 0.124919 + 0.466203i
\(33\) −3.85020 1.03166i −0.670234 0.179589i
\(34\) 0.560773 0.0961717
\(35\) 0 0
\(36\) 1.94418 0.324031
\(37\) −0.399255 0.106980i −0.0656371 0.0175874i 0.225851 0.974162i \(-0.427484\pi\)
−0.291488 + 0.956574i \(0.594150\pi\)
\(38\) 0.441387 + 1.64728i 0.0716025 + 0.267224i
\(39\) 0.612908 + 0.353863i 0.0981438 + 0.0566634i
\(40\) −0.463657 + 2.03138i −0.0733106 + 0.321189i
\(41\) 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 0.928427 0.371516i \(-0.121162\pi\)
−0.371516 + 0.928427i \(0.621162\pi\)
\(44\) 6.71132 3.87478i 1.01177 0.584145i
\(45\) 1.97694 + 1.04485i 0.294705 + 0.155757i
\(46\) −0.862019 + 1.49306i −0.127098 + 0.220140i
\(47\) −0.111749 + 0.417052i −0.0163002 + 0.0608333i −0.973597 0.228274i \(-0.926692\pi\)
0.957297 + 0.289107i \(0.0933585\pi\)
\(48\) −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
\(52\) −1.32906 + 0.356122i −0.184308 + 0.0493852i
\(53\) −7.37179 + 1.97527i −1.01259 + 0.271324i −0.726713 0.686942i \(-0.758953\pi\)
−0.285881 + 0.958265i \(0.592286\pi\)
\(54\) −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
\(58\) −0.223302 + 0.833375i −0.0293210 + 0.109428i
\(59\) −3.05480 + 5.29106i −0.397701 + 0.688838i −0.993442 0.114339i \(-0.963525\pi\)
0.595741 + 0.803176i \(0.296858\pi\)
\(60\) −4.15419 + 1.28138i −0.536304 + 0.165426i
\(61\) 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
\(65\) −1.54284 0.352150i −0.191366 0.0436788i
\(66\) −0.815543 0.470854i −0.100386 0.0579581i
\(67\) 0.345596 + 1.28978i 0.0422212 + 0.157572i 0.983818 0.179171i \(-0.0573415\pi\)
−0.941597 + 0.336743i \(0.890675\pi\)
\(68\) −4.45750 1.19438i −0.540551 0.144840i
\(69\) −7.29744 −0.878508
\(70\) 0 0
\(71\) 1.19297 0.141579 0.0707897 0.997491i \(-0.477448\pi\)
0.0707897 + 0.997491i \(0.477448\pi\)
\(72\) 0.900073 + 0.241174i 0.106075 + 0.0284226i
\(73\) 0.506205 + 1.88918i 0.0592469 + 0.221112i 0.989201 0.146562i \(-0.0468208\pi\)
−0.929955 + 0.367674i \(0.880154\pi\)
\(74\) −0.0845694 0.0488262i −0.00983100 0.00567593i
\(75\) −4.91283 0.929594i −0.567284 0.107340i
\(76\) 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 \(-0.828230\pi\)
0.0160304 + 0.999872i \(0.494897\pi\)
\(80\) 3.83275 7.25185i 0.428514 0.810782i
\(81\) 0.500000 0.866025i 0.0555556 0.0962250i
\(82\) 0.466662 1.74161i 0.0515342 0.192328i
\(83\) −11.9895 + 11.9895i −1.31602 + 1.31602i −0.399122 + 0.916898i \(0.630685\pi\)
−0.916898 + 0.399122i \(0.869315\pi\)
\(84\) 0 0
\(85\) −3.89070 3.61007i −0.422006 0.391567i
\(86\) 0.610073 + 1.05668i 0.0657859 + 0.113944i
\(87\) −3.52747 + 0.945184i −0.378185 + 0.101334i
\(88\) 3.58771 0.961324i 0.382451 0.102477i
\(89\) −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
\(93\) 1.27810 4.76995i 0.132533 0.494620i
\(94\) −0.0510027 + 0.0883393i −0.00526053 + 0.00911150i
\(95\) 7.54226 14.2705i 0.773820 1.46413i
\(96\) −2.36449 + 1.36514i −0.241325 + 0.139329i
\(97\) 7.43671 + 7.43671i 0.755083 + 0.755083i 0.975423 0.220340i \(-0.0707167\pi\)
−0.220340 + 0.975423i \(0.570717\pi\)
\(98\) 0 0
\(99\) 3.98602i 0.400610i
\(100\) 8.03184 5.47593i 0.803184 0.547593i
\(101\) −5.47010 3.15816i −0.544295 0.314249i 0.202523 0.979278i \(-0.435086\pi\)
−0.746818 + 0.665028i \(0.768419\pi\)
\(102\) 0.145139 + 0.541665i 0.0143709 + 0.0536328i
\(103\) 17.1313 + 4.59031i 1.68799 + 0.452296i 0.969871 0.243620i \(-0.0783351\pi\)
0.718122 + 0.695917i \(0.245002\pi\)
\(104\) −0.659476 −0.0646669
\(105\) 0 0
\(106\) −1.80304 −0.175127
\(107\) −10.2181 2.73794i −0.987825 0.264687i −0.271488 0.962442i \(-0.587516\pi\)
−0.716337 + 0.697755i \(0.754183\pi\)
\(108\) 0.503192 + 1.87794i 0.0484197 + 0.180705i
\(109\) 0.578698 + 0.334112i 0.0554293 + 0.0320021i 0.527459 0.849581i \(-0.323145\pi\)
−0.472029 + 0.881583i \(0.656478\pi\)
\(110\) 2.05293 + 0.468575i 0.195739 + 0.0446769i
\(111\) 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
\(115\) 15.5926 4.80963i 1.45402 0.448500i
\(116\) 3.54999 6.14877i 0.329609 0.570899i
\(117\) −0.183173 + 0.683610i −0.0169343 + 0.0631998i
\(118\) −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
\(122\) 1.62263 0.434781i 0.146906 0.0393633i
\(123\) 7.37179 1.97527i 0.664692 0.178104i
\(124\) 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 \(0.370460\pi\)
\(128\) 1.82245 6.80149i 0.161084 0.601172i
\(129\) −2.58229 + 4.47266i −0.227358 + 0.393796i
\(130\) −0.330548 0.174701i −0.0289910 0.0153223i
\(131\) −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
\(135\) −0.497580 + 2.18000i −0.0428249 + 0.187625i
\(136\) −1.91547 1.10590i −0.164250 0.0948297i
\(137\) −0.297204 1.10918i −0.0253919 0.0947637i 0.952067 0.305889i \(-0.0989538\pi\)
−0.977459 + 0.211126i \(0.932287\pi\)
\(138\) −1.66529 0.446214i −0.141759 0.0379843i
\(139\) −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
\(142\) 0.272239 + 0.0729461i 0.0228458 + 0.00612150i
\(143\) 0.730131 + 2.72489i 0.0610566 + 0.227866i
\(144\) −3.17677 1.83411i −0.264731 0.152843i
\(145\) 6.91430 4.34451i 0.574201 0.360792i
\(146\) 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 \(-0.625597\pi\)
0.607272 + 0.794494i \(0.292264\pi\)
\(150\) −1.06428 0.512539i −0.0868979 0.0418486i
\(151\) 7.36197 12.7513i 0.599109 1.03769i −0.393844 0.919177i \(-0.628855\pi\)
0.992953 0.118509i \(-0.0378116\pi\)
\(152\) 1.74091 6.49718i 0.141207 0.526991i
\(153\) −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
\(157\) 10.8805 2.91542i 0.868358 0.232676i 0.202980 0.979183i \(-0.434937\pi\)
0.665378 + 0.746507i \(0.268271\pi\)
\(158\) −1.97173 + 0.528324i −0.156862 + 0.0420312i
\(159\) −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
\(163\) 3.82312 14.2681i 0.299450 1.11756i −0.638169 0.769897i \(-0.720308\pi\)
0.937619 0.347666i \(-0.113026\pi\)
\(164\) −7.41885 + 12.8498i −0.579315 + 1.00340i
\(165\) 2.62713 + 8.51705i 0.204521 + 0.663051i
\(166\) −3.46916 + 2.00292i −0.269259 + 0.155457i
\(167\) 4.63621 + 4.63621i 0.358761 + 0.358761i 0.863356 0.504595i \(-0.168358\pi\)
−0.504595 + 0.863356i \(0.668358\pi\)
\(168\) 0 0
\(169\) 12.4991i 0.961471i
\(170\) −0.667125 1.06173i −0.0511661 0.0814311i
\(171\) −6.25141 3.60925i −0.478057 0.276006i
\(172\) −2.59878 9.69876i −0.198155 0.739524i
\(173\) 3.39499 + 0.909686i 0.258117 + 0.0691621i 0.385557 0.922684i \(-0.374009\pi\)
−0.127440 + 0.991846i \(0.540676\pi\)
\(174\) −0.862773 −0.0654067
\(175\) 0 0
\(176\) −14.6216 −1.10215
\(177\) −5.90141 1.58128i −0.443577 0.118856i
\(178\) −0.478522 1.78587i −0.0358667 0.133857i
\(179\) 19.1486 + 11.0554i 1.43123 + 0.826321i 0.997215 0.0745840i \(-0.0237629\pi\)
0.434016 + 0.900905i \(0.357096\pi\)
\(180\) −2.31290 3.68100i −0.172394 0.274365i
\(181\) 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
\(185\) 0.272425 + 0.883193i 0.0200291 + 0.0649336i
\(186\) 0.583333 1.01036i 0.0427720 0.0740833i
\(187\) −2.44876 + 9.13889i −0.179071 + 0.668302i
\(188\) 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 \(-0.353248\pi\)
\(192\) 6.46341 1.73186i 0.466456 0.124987i
\(193\) 12.1957 3.26783i 0.877866 0.235223i 0.208380 0.978048i \(-0.433181\pi\)
0.669486 + 0.742825i \(0.266514\pi\)
\(194\) 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 \(0.293224\pi\)
\(198\) 0.243732 0.909620i 0.0173213 0.0646439i
\(199\) −0.308318 + 0.534023i −0.0218561 + 0.0378559i −0.876747 0.480953i \(-0.840291\pi\)
0.854890 + 0.518809i \(0.173624\pi\)
\(200\) 4.39768 1.53878i 0.310963 0.108808i
\(201\) −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
\(205\) −14.4496 + 9.07924i −1.00921 + 0.634122i
\(206\) 3.62871 + 2.09504i 0.252825 + 0.145968i
\(207\) −1.88872 7.04878i −0.131275 0.489924i
\(208\) 2.50763 + 0.671919i 0.173873 + 0.0465892i
\(209\) −28.7731 −1.99028
\(210\) 0 0
\(211\) 9.30849 0.640823 0.320411 0.947278i \(-0.396179\pi\)
0.320411 + 0.947278i \(0.396179\pi\)
\(212\) 14.3321 + 3.84028i 0.984334 + 0.263752i
\(213\) 0.308763 + 1.15232i 0.0211561 + 0.0789557i
\(214\) −2.16439 1.24961i −0.147955 0.0854217i
\(215\) 2.56979 11.2588i 0.175258 0.767844i
\(216\) 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
\(220\) −15.3204 8.09714i −1.03290 0.545909i
\(221\) 0.839933 1.45481i 0.0565000 0.0978609i
\(222\) 0.0252743 0.0943250i 0.00169630 0.00633068i
\(223\) −1.35505 + 1.35505i −0.0907407 + 0.0907407i −0.751020 0.660279i \(-0.770438\pi\)
0.660279 + 0.751020i \(0.270438\pi\)
\(224\) 0 0
\(225\) −0.373614 4.98602i −0.0249076 0.332401i
\(226\) −0.567410 0.982782i −0.0377435 0.0653737i
\(227\) −5.67498 + 1.52061i −0.376662 + 0.100926i −0.442183 0.896925i \(-0.645796\pi\)
0.0655211 + 0.997851i \(0.479129\pi\)
\(228\) 13.5559 3.63229i 0.897761 0.240554i
\(229\) −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
\(233\) −6.02620 + 22.4901i −0.394790 + 1.47337i 0.427349 + 0.904087i \(0.359448\pi\)
−0.822138 + 0.569288i \(0.807219\pi\)
\(234\) −0.0836010 + 0.144801i −0.00546517 + 0.00946595i
\(235\) 0.922563 0.284569i 0.0601813 0.0185632i
\(236\) 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 \(-0.0567205\pi\)
\(240\) 7.99674 + 1.82523i 0.516187 + 0.117818i
\(241\) −12.6879 7.32537i −0.817300 0.471868i 0.0321844 0.999482i \(-0.489754\pi\)
−0.849485 + 0.527613i \(0.823087\pi\)
\(242\) −0.298908 1.11554i −0.0192145 0.0717095i
\(243\) 0.965926 + 0.258819i 0.0619642 + 0.0166032i
\(244\) −13.8241 −0.884995
\(245\) 0 0
\(246\) 1.80304 0.114958
\(247\) 4.93464 + 1.32223i 0.313984 + 0.0841317i
\(248\) 1.19097 + 4.44475i 0.0756265 + 0.282242i
\(249\) −14.6841 8.47787i −0.930567 0.537263i
\(250\) 2.61188 + 0.393707i 0.165190 + 0.0249002i
\(251\) 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
\(255\) 2.48007 4.69249i 0.155308 0.293855i
\(256\) −5.85964 + 10.1492i −0.366227 + 0.634324i
\(257\) −3.43788 + 12.8304i −0.214449 + 0.800336i 0.771910 + 0.635731i \(0.219301\pi\)
−0.986360 + 0.164604i \(0.947365\pi\)
\(258\) −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
\(262\) −4.29350 + 1.15044i −0.265254 + 0.0710745i
\(263\) −21.0066 + 5.62869i −1.29532 + 0.347080i −0.839679 0.543083i \(-0.817257\pi\)
−0.455642 + 0.890163i \(0.650590\pi\)
\(264\) 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
\(268\) 0.671902 2.50757i 0.0410429 0.153174i
\(269\) 11.4926 19.9057i 0.700714 1.21367i −0.267501 0.963557i \(-0.586198\pi\)
0.968216 0.250116i \(-0.0804686\pi\)
\(270\) −0.246849 + 0.467057i −0.0150228 + 0.0284242i
\(271\) −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
\(275\) −11.2269 16.4671i −0.677008 0.993004i
\(276\) 12.2868 + 7.09378i 0.739578 + 0.426995i
\(277\) 1.75975 + 6.56746i 0.105733 + 0.394600i 0.998427 0.0560621i \(-0.0178545\pi\)
−0.892694 + 0.450662i \(0.851188\pi\)
\(278\) −0.100966 0.0270537i −0.00605553 0.00162257i
\(279\) 4.93821 0.295643
\(280\) 0 0
\(281\) −9.65658 −0.576063 −0.288032 0.957621i \(-0.593001\pi\)
−0.288032 + 0.957621i \(0.593001\pi\)
\(282\) −0.0985297 0.0264009i −0.00586736 0.00157215i
\(283\) 5.45726 + 20.3668i 0.324400 + 1.21068i 0.914913 + 0.403650i \(0.132259\pi\)
−0.590513 + 0.807028i \(0.701075\pi\)
\(284\) −2.00862 1.15968i −0.119190 0.0688141i
\(285\) 15.7364 + 3.59178i 0.932141 + 0.212759i
\(286\) 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
\(290\) 1.84351 0.568641i 0.108255 0.0333917i
\(291\) −5.25855 + 9.10807i −0.308261 + 0.533924i
\(292\) 0.984157 3.67292i 0.0575934 0.214942i
\(293\) 4.79236 4.79236i 0.279973 0.279973i −0.553125 0.833098i \(-0.686565\pi\)
0.833098 + 0.553125i \(0.186565\pi\)
\(294\) 0 0
\(295\) 13.6519 0.510768i 0.794845 0.0297381i
\(296\) 0.192580 + 0.333558i 0.0111935 + 0.0193876i
\(297\) 3.85020 1.03166i 0.223411 0.0598629i
\(298\) 0.716817 0.192070i 0.0415241 0.0111263i
\(299\) 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
\(303\) 1.63479 6.10111i 0.0939160 0.350499i
\(304\) −13.2395 + 22.9316i −0.759340 + 1.31521i
\(305\) −14.0570 7.42938i −0.804899 0.425405i
\(306\) −0.485643 + 0.280386i −0.0277624 + 0.0160286i
\(307\) 9.85063 + 9.85063i 0.562205 + 0.562205i 0.929933 0.367728i \(-0.119864\pi\)
−0.367728 + 0.929933i \(0.619864\pi\)
\(308\) 0 0
\(309\) 17.7356i 1.00894i
\(310\) −0.580510 + 2.54334i −0.0329707 + 0.144452i
\(311\) −23.6480 13.6532i −1.34095 0.774200i −0.354006 0.935243i \(-0.615181\pi\)
−0.986947 + 0.161043i \(0.948514\pi\)
\(312\) −0.170685 0.637004i −0.00966313 0.0360633i
\(313\) −25.2824 6.77439i −1.42904 0.382911i −0.540361 0.841434i \(-0.681712\pi\)
−0.888683 + 0.458523i \(0.848379\pi\)
\(314\) 2.66123 0.150182
\(315\) 0 0
\(316\) 16.7983 0.944977
\(317\) 29.8877 + 8.00839i 1.67866 + 0.449796i 0.967425 0.253156i \(-0.0814687\pi\)
0.711237 + 0.702952i \(0.248135\pi\)
\(318\) −0.466662 1.74161i −0.0261691 0.0976644i
\(319\) −12.6064 7.27830i −0.705822 0.407506i
\(320\) −12.6691 + 7.96046i −0.708224 + 0.445003i
\(321\) 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
\(325\) 1.16871 + 3.34006i 0.0648283 + 0.185273i
\(326\) 1.74489 3.02224i 0.0966406 0.167386i
\(327\) −0.172949 + 0.645454i −0.00956410 + 0.0356937i
\(328\) −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 \(0.681642\pi\)
\(332\) 31.8418 8.53199i 1.74755 0.468254i
\(333\) 0.399255 0.106980i 0.0218790 0.00586246i
\(334\) 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 \(0.218804\pi\)
\(338\) −0.764280 + 2.85233i −0.0415714 + 0.155146i
\(339\) 2.40171 4.15988i 0.130443 0.225934i
\(340\) 3.04151 + 9.86045i 0.164949 + 0.534758i
\(341\) 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
\(345\) 8.68142 + 13.8165i 0.467392 + 0.743856i
\(346\) 0.719122 + 0.415185i 0.0386602 + 0.0223205i
\(347\) 5.01382 + 18.7118i 0.269156 + 1.00450i 0.959657 + 0.281173i \(0.0907233\pi\)
−0.690501 + 0.723331i \(0.742610\pi\)
\(348\) 6.85806 + 1.83761i 0.367631 + 0.0985063i
\(349\) 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
\(352\) −10.5121 2.81671i −0.560297 0.150131i
\(353\) 3.99763 + 14.9193i 0.212772 + 0.794077i 0.986939 + 0.161095i \(0.0515025\pi\)
−0.774167 + 0.632982i \(0.781831\pi\)
\(354\) −1.25003 0.721704i −0.0664382 0.0383581i
\(355\) −1.41922 2.25869i −0.0753244 0.119879i
\(356\) 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 \(-0.528046\pi\)
0.818669 + 0.574266i \(0.194712\pi\)
\(360\) −0.614151 1.99105i −0.0323686 0.104938i
\(361\) −16.5534 + 28.6713i −0.871231 + 1.50902i
\(362\) 0.518847 1.93636i 0.0272700 0.101773i
\(363\) 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
\(367\) −0.560120 + 0.150084i −0.0292380 + 0.00783431i −0.273408 0.961898i \(-0.588151\pi\)
0.244170 + 0.969732i \(0.421484\pi\)
\(368\) −25.8565 + 6.92823i −1.34786 + 0.361159i
\(369\) 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
\(373\) −1.26094 + 4.70591i −0.0652892 + 0.243663i −0.990856 0.134921i \(-0.956922\pi\)
0.925567 + 0.378583i \(0.123589\pi\)
\(374\) −1.11763 + 1.93578i −0.0577911 + 0.100097i
\(375\) 4.08452 + 10.4075i 0.210924 + 0.537443i
\(376\) 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 \(0.892353\pi\)
\(380\) −26.5713 + 16.6957i −1.36308 + 0.856472i
\(381\) −7.21175 4.16371i −0.369469 0.213313i
\(382\) −0.934923 3.48918i −0.0478348 0.178522i
\(383\) 13.7654 + 3.68844i 0.703381 + 0.188470i 0.592744 0.805391i \(-0.298044\pi\)
0.110636 + 0.993861i \(0.464711\pi\)
\(384\) 7.04142 0.359331
\(385\) 0 0
\(386\) 2.98291 0.151826
\(387\) −4.98860 1.33669i −0.253585 0.0679479i
\(388\) −5.29212 19.7504i −0.268666 1.00268i
\(389\) 21.0704 + 12.1650i 1.06831 + 0.616791i 0.927720 0.373277i \(-0.121766\pi\)
0.140593 + 0.990068i \(0.455099\pi\)
\(390\) 0.0831964 0.364501i 0.00421281 0.0184572i
\(391\) 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
\(395\) 17.0813 + 9.02780i 0.859452 + 0.454238i
\(396\) −3.87478 + 6.71132i −0.194715 + 0.337256i
\(397\) 2.49129 9.29762i 0.125034 0.466634i −0.874807 0.484472i \(-0.839012\pi\)
0.999841 + 0.0178380i \(0.00567832\pi\)
\(398\) −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 \(0.762565\pi\)
\(402\) −0.304714 + 0.0816479i −0.0151978 + 0.00407223i
\(403\) −3.37581 + 0.904546i −0.168161 + 0.0450587i
\(404\) 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
\(408\) 0.572453 2.13643i 0.0283407 0.105769i
\(409\) 11.5992 20.0905i 0.573546 0.993410i −0.422652 0.906292i \(-0.638901\pi\)
0.996198 0.0871183i \(-0.0277658\pi\)
\(410\) −3.85261 + 1.18836i −0.190267 + 0.0586888i
\(411\) 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
\(415\) 36.9635 + 8.43683i 1.81447 + 0.414148i
\(416\) 1.67341 + 0.966143i 0.0820456 + 0.0473690i
\(417\) −0.114512 0.427364i −0.00560766 0.0209281i
\(418\) −6.56610 1.75938i −0.321158 0.0860541i
\(419\) 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 \(0.776802\pi\)
\(422\) 2.12422 + 0.569183i 0.103405 + 0.0277074i
\(423\) −0.111749 0.417052i −0.00543341 0.0202778i
\(424\) 6.15877 + 3.55577i 0.299096 + 0.172683i
\(425\) −2.20650 + 11.6611i −0.107031 + 0.565649i
\(426\) 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
\(430\) 1.27487 2.41215i 0.0614798 0.116324i
\(431\) 11.2779 19.5339i 0.543238 0.940915i −0.455478 0.890247i \(-0.650532\pi\)
0.998716 0.0506681i \(-0.0161351\pi\)
\(432\) 0.949406 3.54323i 0.0456783 0.170474i
\(433\) −19.9639 + 19.9639i −0.959405 + 0.959405i −0.999208 0.0398028i \(-0.987327\pi\)
0.0398028 + 0.999208i \(0.487327\pi\)
\(434\) 0 0
\(435\) 5.98602 + 5.55426i 0.287008 + 0.266306i
\(436\) −0.649575 1.12510i −0.0311090 0.0538824i
\(437\) −50.8816 + 13.6337i −2.43400 + 0.652188i
\(438\) −0.446325 + 0.119592i −0.0213262 + 0.00571435i
\(439\) −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
\(443\) −4.66400 + 17.4063i −0.221593 + 0.826997i 0.762148 + 0.647403i \(0.224145\pi\)
−0.983741 + 0.179594i \(0.942522\pi\)
\(444\) −0.401803 + 0.695944i −0.0190687 + 0.0330280i
\(445\) −8.17681 + 15.4711i −0.387618 + 0.733402i
\(446\) −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 \(-0.254820\pi\)
\(450\) 0.219619 1.16067i 0.0103529 0.0547144i
\(451\) 26.3451 + 15.2103i 1.24054 + 0.716227i
\(452\) 2.41704 + 9.02051i 0.113688 + 0.424289i
\(453\) 14.2222 + 3.81084i 0.668219 + 0.179049i
\(454\) −1.38802 −0.0651432
\(455\) 0 0
\(456\) 6.72637 0.314991
\(457\) −1.79696 0.481493i −0.0840581 0.0225233i 0.216545 0.976273i \(-0.430521\pi\)
−0.300603 + 0.953749i \(0.597188\pi\)
\(458\) −0.794295 2.96435i −0.0371150 0.138515i
\(459\) −2.05561 1.18681i −0.0959476 0.0553954i
\(460\) −30.9289 7.05945i −1.44207 0.329148i
\(461\) 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 0.977742 0.209809i \(-0.0672841\pi\)
−0.209809 + 0.977742i \(0.567284\pi\)
\(464\) −11.6013 + 6.69801i −0.538577 + 0.310947i
\(465\) −10.5516 + 3.25470i −0.489320 + 0.150933i
\(466\) −2.75039 + 4.76381i −0.127409 + 0.220679i
\(467\) 7.35742 27.4583i 0.340461 1.27062i −0.557365 0.830267i \(-0.688188\pi\)
0.897826 0.440350i \(-0.145146\pi\)
\(468\) 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
\(472\) 5.49908 1.47347i 0.253116 0.0678221i
\(473\) −19.8847 + 5.32808i −0.914298 + 0.244986i
\(474\) −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
\(478\) 0.335113 1.25066i 0.0153277 0.0572038i
\(479\) 5.54182 9.59872i 0.253212 0.438577i −0.711196 0.702994i \(-0.751846\pi\)
0.964408 + 0.264417i \(0.0851795\pi\)
\(480\) 5.39759 + 2.85273i 0.246365 + 0.130209i
\(481\) −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
\(485\) 5.23309 22.9273i 0.237623 1.04107i
\(486\) 0.204601 + 0.118126i 0.00928088 + 0.00535832i
\(487\) −4.99695 18.6489i −0.226433 0.845060i −0.981825 0.189787i \(-0.939220\pi\)
0.755392 0.655273i \(-0.227446\pi\)
\(488\) −6.39994 1.71486i −0.289712 0.0776280i
\(489\) 14.7714 0.667986
\(490\) 0 0
\(491\) 32.1155 1.44935 0.724677 0.689089i \(-0.241989\pi\)
0.724677 + 0.689089i \(0.241989\pi\)
\(492\) −14.3321 3.84028i −0.646142 0.173133i
\(493\) 2.24350 + 8.37286i 0.101042 + 0.377095i
\(494\) 1.04525 + 0.603474i 0.0470279 + 0.0271516i
\(495\) −7.54688 + 4.74198i −0.339207 + 0.213136i
\(496\) 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 \(-0.697167\pi\)
0.414852 + 0.909889i \(0.363833\pi\)
\(500\) −19.9229 8.69253i −0.890979 0.388742i
\(501\) −3.27830 + 5.67818i −0.146463 + 0.253682i
\(502\) 1.29329 4.82662i 0.0577223 0.215423i
\(503\) 17.5637 17.5637i 0.783128 0.783128i −0.197229 0.980357i \(-0.563194\pi\)
0.980357 + 0.197229i \(0.0631943\pi\)
\(504\) 0 0
\(505\) 0.528051 + 14.1139i 0.0234980 + 0.628059i
\(506\) −3.43603 5.95138i −0.152750 0.264571i
\(507\) −12.0732 + 3.23501i −0.536191 + 0.143672i
\(508\) 15.6384 4.19029i 0.693840 0.185914i
\(509\) 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
\(513\) 1.86829 6.97254i 0.0824868 0.307845i
\(514\) −1.56907 + 2.71771i −0.0692086 + 0.119873i
\(515\) −11.6893 37.8961i −0.515090 1.66990i
\(516\) 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
\(520\) 0.784547 + 1.24861i 0.0344047 + 0.0547552i
\(521\) 24.9975 + 14.4323i 1.09516 + 0.632292i 0.934946 0.354790i \(-0.115448\pi\)
0.160216 + 0.987082i \(0.448781\pi\)
\(522\) −0.223302 0.833375i −0.00977367 0.0364758i
\(523\) 4.84539 + 1.29832i 0.211874 + 0.0567715i 0.363195 0.931713i \(-0.381686\pi\)
−0.151321 + 0.988485i \(0.548353\pi\)
\(524\) 36.5788 1.59795
\(525\) 0 0
\(526\) −5.13793 −0.224024
\(527\) −11.3220 3.03372i −0.493195 0.132151i
\(528\) −3.78435 14.1234i −0.164693 0.614642i
\(529\) −26.1995 15.1263i −1.13911 0.657665i
\(530\) 2.14499 + 3.41377i 0.0931726 + 0.148285i
\(531\) 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
\(535\) 6.97219 + 22.6036i 0.301434 + 0.977239i
\(536\) 0.622122 1.07755i 0.0268716 0.0465430i
\(537\) −5.72271 + 21.3574i −0.246953 + 0.921642i
\(538\) 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 \(0.805332\pi\)
\(542\) −3.59639 + 0.963650i −0.154478 + 0.0413923i
\(543\) 8.19615 2.19615i 0.351731 0.0942459i
\(544\) 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 \(-0.0753392\pi\)
\(548\) −0.577820 + 2.15645i −0.0246832 + 0.0921191i
\(549\) −3.55523 + 6.15784i −0.151734 + 0.262810i
\(550\) −1.55510 4.44433i −0.0663097 0.189507i
\(551\) −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
\(555\) −0.782590 + 0.491730i −0.0332191 + 0.0208728i
\(556\) 0.744941 + 0.430092i 0.0315925 + 0.0182400i
\(557\) 10.3079 + 38.4695i 0.436758 + 1.63000i 0.736823 + 0.676086i \(0.236325\pi\)
−0.300065 + 0.953919i \(0.597008\pi\)
\(558\) 1.12691 + 0.301955i 0.0477060 + 0.0127828i
\(559\) 3.65510 0.154594
\(560\) 0 0
\(561\) −9.46128 −0.399455
\(562\) −2.20366 0.590468i −0.0929556 0.0249074i
\(563\) −10.0161 37.3806i −0.422129 1.57541i −0.770114 0.637906i \(-0.779801\pi\)
0.347985 0.937500i \(-0.386866\pi\)
\(564\) 0.726967 + 0.419715i 0.0306108 + 0.0176732i
\(565\) −2.39008 + 10.4715i −0.100552 + 0.440537i
\(566\) 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 \(-0.545126\pi\)
0.786690 + 0.617348i \(0.211793\pi\)
\(570\) 3.37145 + 1.78188i 0.141215 + 0.0746347i
\(571\) 8.44331 14.6242i 0.353342 0.612005i −0.633491 0.773750i \(-0.718379\pi\)
0.986833 + 0.161744i \(0.0517120\pi\)
\(572\) 1.41951 5.29768i 0.0593527 0.221507i
\(573\) 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
\(577\) −5.32309 + 1.42632i −0.221603 + 0.0593784i −0.367912 0.929861i \(-0.619927\pi\)
0.146309 + 0.989239i \(0.453261\pi\)
\(578\) −2.59374 + 0.694991i −0.107885 + 0.0289078i
\(579\) 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
\(583\) 7.87345 29.3841i 0.326085 1.21697i
\(584\) 0.911244 1.57832i 0.0377075 0.0653114i
\(585\) 1.51222 0.466451i 0.0625225 0.0192854i
\(586\) 1.38667 0.800592i 0.0572826 0.0330721i
\(587\) −15.1058 15.1058i −0.623484 0.623484i 0.322937 0.946420i \(-0.395330\pi\)
−0.946420 + 0.322937i \(0.895330\pi\)
\(588\) 0 0
\(589\) 35.6465i 1.46879i
\(590\) 3.14663 + 0.718211i 0.129545 + 0.0295683i
\(591\) −3.29107 1.90010i −0.135377 0.0781597i
\(592\) −0.392426 1.46456i −0.0161286 0.0601928i
\(593\) 4.68590 + 1.25558i 0.192427 + 0.0515606i 0.353745 0.935342i \(-0.384908\pi\)
−0.161318 + 0.986902i \(0.551575\pi\)
\(594\) 0.941708 0.0386388
\(595\) 0 0
\(596\) −6.10696 −0.250151
\(597\) −0.595625 0.159597i −0.0243773 0.00653188i
\(598\) 0.315797 + 1.17857i 0.0129139 + 0.0481953i
\(599\) 8.74769 + 5.05048i 0.357421 + 0.206357i 0.667949 0.744207i \(-0.267173\pi\)
−0.310528 + 0.950564i \(0.600506\pi\)
\(600\) 2.62455 + 3.84957i 0.107147 + 0.157158i
\(601\) 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
\(605\) −5.10762 + 9.66400i −0.207654 + 0.392898i
\(606\) 0.746125 1.29233i 0.0303093 0.0524972i
\(607\) 3.76752 14.0606i 0.152919 0.570702i −0.846356 0.532618i \(-0.821208\pi\)
0.999275 0.0380833i \(-0.0121252\pi\)
\(608\) −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
\(612\) 4.45750 1.19438i 0.180184 0.0482801i
\(613\) 19.6919 5.27642i 0.795347 0.213113i 0.161807 0.986822i \(-0.448268\pi\)
0.633540 + 0.773710i \(0.281601\pi\)
\(614\) 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 \(0.992476\pi\)
\(618\) −1.08447 + 4.04731i −0.0436239 + 0.162807i
\(619\) 5.59953 9.69868i 0.225064 0.389823i −0.731274 0.682083i \(-0.761074\pi\)
0.956339 + 0.292261i \(0.0944075\pi\)
\(620\) 10.0314 18.9802i 0.402871 0.762262i
\(621\) 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
\(625\) −15.5870 19.5460i −0.623478 0.781841i
\(626\) −5.35527 3.09186i −0.214040 0.123576i
\(627\) −7.44703 27.7927i −0.297406 1.10993i
\(628\) −21.1537 5.66812i −0.844124 0.226182i
\(629\) −0.981107 −0.0391193
\(630\) 0 0
\(631\) 21.2015 0.844020 0.422010 0.906591i \(-0.361325\pi\)
0.422010 + 0.906591i \(0.361325\pi\)
\(632\) 7.77687 + 2.08381i 0.309347 + 0.0828894i
\(633\) 2.40921 + 8.99131i 0.0957577 + 0.357373i
\(634\) 6.33077 + 3.65507i 0.251427 + 0.145161i
\(635\) 18.1538 + 4.14355i 0.720411 + 0.164432i
\(636\) 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
\(640\) −15.0456 + 4.64089i −0.594729 + 0.183447i
\(641\) 14.9484 25.8915i 0.590428 1.02265i −0.403746 0.914871i \(-0.632292\pi\)
0.994175 0.107781i \(-0.0343745\pi\)
\(642\) 0.646846 2.41406i 0.0255290 0.0952755i
\(643\) 11.2813 11.2813i 0.444891 0.444891i −0.448761 0.893652i \(-0.648134\pi\)
0.893652 + 0.448761i \(0.148134\pi\)
\(644\) 0 0
\(645\) 11.5403 0.431764i 0.454398 0.0170007i
\(646\) 2.02397 + 3.50562i 0.0796320 + 0.137927i
\(647\) 35.8439 9.60434i 1.40917 0.377586i 0.527540 0.849530i \(-0.323114\pi\)
0.881628 + 0.471944i \(0.156448\pi\)
\(648\) −0.900073 + 0.241174i −0.0353582 + 0.00947420i
\(649\) −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
\(653\) −0.723414 + 2.69982i −0.0283094 + 0.105652i −0.978635 0.205606i \(-0.934084\pi\)
0.950326 + 0.311258i \(0.100750\pi\)
\(654\) −0.0789348 + 0.136719i −0.00308659 + 0.00534614i
\(655\) 37.1950 + 19.6583i 1.45333 + 0.768113i
\(656\) 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 \(0.904949\pi\)
\(660\) 3.85603 16.8941i 0.150096 0.657601i
\(661\) −0.953098 0.550272i −0.0370712 0.0214031i 0.481350 0.876529i \(-0.340147\pi\)
−0.518421 + 0.855125i \(0.673480\pi\)
\(662\) 1.02062 + 3.80900i 0.0396675 + 0.148041i
\(663\) 1.62263 + 0.434781i 0.0630176 + 0.0168855i
\(664\) 15.7998 0.613150
\(665\) 0 0
\(666\) 0.0976524 0.00378395
\(667\) −25.7415 6.89742i −0.996716 0.267069i
\(668\) −3.29923 12.3129i −0.127651 0.476399i
\(669\) −1.65959 0.958163i −0.0641633 0.0370447i
\(670\) 0.597278 0.375292i 0.0230749 0.0144988i
\(671\) 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
\(675\) 4.71943 1.65136i 0.181651 0.0635609i
\(676\) 12.1503 21.0449i 0.467319 0.809421i
\(677\) −9.00447 + 33.6052i −0.346070 + 1.29155i 0.545287 + 0.838249i \(0.316421\pi\)
−0.891357 + 0.453302i \(0.850246\pi\)
\(678\) 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
\(682\) 4.49190 1.20360i 0.172004 0.0460882i
\(683\) 18.9404 5.07507i 0.724736 0.194192i 0.122452 0.992474i \(-0.460924\pi\)
0.602284 + 0.798282i \(0.294258\pi\)
\(684\) 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
\(688\) −4.90328 + 18.2993i −0.186936 + 0.697655i
\(689\) −2.70062 + 4.67762i −0.102886 + 0.178203i
\(690\) 1.13629 + 3.68380i 0.0432577 + 0.140240i
\(691\) 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
\(695\) 0.526349 + 0.837687i 0.0199656 + 0.0317753i
\(696\) 2.94703 + 1.70147i 0.111707 + 0.0644940i
\(697\) −4.68852 17.4978i −0.177590 0.662776i
\(698\) 0.116064 + 0.0310993i 0.00439309 + 0.00117713i
\(699\) −23.2835 −0.880661
\(700\) 0 0
\(701\) 1.45193 0.0548388 0.0274194 0.999624i \(-0.491271\pi\)
0.0274194 + 0.999624i \(0.491271\pi\)
\(702\) −0.161505 0.0432751i −0.00609560 0.00163331i
\(703\) −0.772235 2.88202i −0.0291254 0.108697i
\(704\) 23.0987 + 13.3361i 0.870566 + 0.502622i
\(705\) 0.513649 + 0.817475i 0.0193452 + 0.0307879i
\(706\) 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 \(-0.301776\pi\)
0.995090 0.0989781i \(-0.0315574\pi\)
\(710\) −0.185758 0.602220i −0.00697137 0.0226009i
\(711\) 4.32013 7.48269i 0.162018 0.280623i
\(712\) −1.88738 + 7.04380i −0.0707325 + 0.263977i
\(713\) 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
\(717\) 5.29373 1.41845i 0.197698 0.0529730i
\(718\) 3.64805 0.977492i 0.136144 0.0364797i
\(719\) −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
\(723\) 3.79189 14.1515i 0.141022 0.526301i
\(724\) −8.24848 + 14.2868i −0.306552 + 0.530964i
\(725\) −16.4512 7.92264i −0.610983 0.294240i
\(726\) 1.00016 0.577445i 0.0371196 0.0214310i
\(727\) 10.4498 + 10.4498i 0.387563 + 0.387563i 0.873817 0.486254i \(-0.161637\pi\)
−0.486254 + 0.873817i \(0.661637\pi\)
\(728\) 0 0
\(729\) 1.00000i 0.0370370i
\(730\) 0.874853 0.549702i 0.0323798 0.0203454i
\(731\) 10.6164 + 6.12936i 0.392660 + 0.226703i
\(732\) −3.57793 13.3530i −0.132244 0.493542i
\(733\) −25.7752 6.90644i −0.952028 0.255095i −0.250806 0.968037i \(-0.580695\pi\)
−0.701223 + 0.712942i \(0.747362\pi\)
\(734\) −0.136998 −0.00505669
\(735\) 0 0
\(736\) −19.9240 −0.734409
\(737\) −5.14109 1.37755i −0.189375 0.0507428i
\(738\) 0.466662 + 1.74161i 0.0171781 + 0.0641094i
\(739\) 18.1596 + 10.4845i 0.668013 + 0.385677i 0.795323 0.606186i \(-0.207301\pi\)
−0.127311 + 0.991863i \(0.540634\pi\)
\(740\) 0.399859 1.75187i 0.0146991 0.0643999i
\(741\) 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
\(745\) −6.20984 3.28203i −0.227511 0.120244i
\(746\) −0.575501 + 0.996797i −0.0210706 + 0.0364953i
\(747\) 4.38847 16.3780i 0.160566 0.599239i
\(748\) 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 \(0.898822\pi\)
\(752\) −1.52984 + 0.409919i −0.0557875 + 0.0149482i
\(753\) 20.4299 5.47418i 0.744507 0.199490i
\(754\) 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 \(0.366564\pi\)
\(758\) −0.789886 + 2.94789i −0.0286899 + 0.107072i
\(759\) 14.5439 25.1907i 0.527909 0.914365i
\(760\) −14.3724 + 4.43325i −0.521343 + 0.160811i
\(761\) 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
\(765\) 5.17449 + 1.18106i 0.187084 + 0.0427014i
\(766\) 2.91577 + 1.68342i 0.105351 + 0.0608245i
\(767\) 1.11911 + 4.17658i 0.0404088 + 0.150808i
\(768\) −11.3199 3.03317i −0.408473 0.109450i
\(769\) −11.2183 −0.404543 −0.202271 0.979330i \(-0.564832\pi\)
−0.202271 + 0.979330i \(0.564832\pi\)