Properties

Label 735.2.v.a.178.5
Level 735
Weight 2
Character 735.178
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 178.5
Character \(\chi\) \(=\) 735.178
Dual form 735.2.v.a.607.5

$q$-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 −0.773091 0.634295i \(-0.781291\pi\)
0.634295 + 0.773091i \(0.281291\pi\)
\(14\) 0 0
\(15\) 1.52092 1.63915i 0.392699 0.423226i
\(16\) 1.83411 + 3.17677i 0.458528 + 0.794194i
\(17\) −2.29273 + 0.614336i −0.556070 + 0.148998i −0.525900 0.850546i \(-0.676271\pi\)
−0.0301697 + 0.999545i \(0.509605\pi\)
\(18\) −0.228203 + 0.0611467i −0.0537879 + 0.0144124i
\(19\) −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
\(23\) −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 0.832198 0.554479i \(-0.187083\pi\)
−0.0640944 + 0.997944i \(0.520416\pi\)
\(32\) 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 \(0.203223\pi\)
−0.803024 + 0.595947i \(0.796777\pi\)
\(42\) 0 0
\(43\) 3.65191 + 3.65191i 0.556911 + 0.556911i 0.928427 0.371516i \(-0.121162\pi\)
−0.371516 + 0.928427i \(0.621162\pi\)
\(44\) 6.71132 3.87478i 1.01177 0.584145i
\(45\) −1.97694 1.04485i −0.294705 0.155757i
\(46\) −0.862019 + 1.49306i −0.127098 + 0.220140i
\(47\) 0.111749 0.417052i 0.0163002 0.0608333i −0.957297 0.289107i \(-0.906642\pi\)
0.973597 + 0.228274i \(0.0733082\pi\)
\(48\) 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 −0.595741 0.803176i \(-0.703142\pi\)
0.993442 + 0.114339i \(0.0364750\pi\)
\(60\) −4.15419 + 1.28138i −0.536304 + 0.165426i
\(61\) −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
\(65\) −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 0.929955 0.367674i \(-0.119846\pi\)
−0.989201 + 0.146562i \(0.953179\pi\)
\(74\) −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 \(-0.369315\pi\)
0.916898 0.399122i \(-0.130685\pi\)
\(84\) 0 0
\(85\) −3.89070 3.61007i −0.422006 0.391567i
\(86\) 0.610073 + 1.05668i 0.0657859 + 0.113944i
\(87\) 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 0.995404 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
\(93\) 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 0.220340 0.975423i \(-0.429283\pi\)
−0.975423 + 0.220340i \(0.929283\pi\)
\(98\) 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 0.746818 0.665028i \(-0.231581\pi\)
−0.202523 + 0.979278i \(0.564914\pi\)
\(102\) 0.145139 + 0.541665i 0.0143709 + 0.0536328i
\(103\) −17.1313 4.59031i −1.68799 0.452296i −0.718122 0.695917i \(-0.754998\pi\)
−0.969871 + 0.243620i \(0.921665\pi\)
\(104\) 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 0.426991 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
\(135\) −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 \(-0.494027\pi\)
0.0187636 + 0.999824i \(0.494027\pi\)
\(140\) 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 −0.665378 0.746507i \(-0.731729\pi\)
−0.202980 + 0.979183i \(0.565063\pi\)
\(158\) −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 0.504595 0.863356i \(-0.331642\pi\)
−0.863356 + 0.504595i \(0.831642\pi\)
\(168\) 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 0.127440 0.991846i \(-0.459324\pi\)
−0.385557 + 0.922684i \(0.625991\pi\)
\(174\) 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 \(0.102123\pi\)
−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
\(185\) −0.272425 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 −0.854890 0.518809i \(-0.826376\pi\)
0.876747 + 0.480953i \(0.159709\pi\)
\(200\) 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 −0.660279 0.751020i \(-0.729562\pi\)
0.751020 + 0.660279i \(0.229562\pi\)
\(224\) 0 0
\(225\) −0.373614 4.98602i −0.0249076 0.332401i
\(226\) −0.567410 0.982782i −0.0377435 0.0653737i
\(227\) 5.67498 1.52061i 0.376662 0.100926i −0.0655211 0.997851i \(-0.520871\pi\)
0.442183 + 0.896925i \(0.354204\pi\)
\(228\) 13.5559 3.63229i 0.897761 0.240554i
\(229\) 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
\(233\) −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 0.849485 0.527613i \(-0.176913\pi\)
−0.0321844 + 0.999482i \(0.510246\pi\)
\(242\) −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 \(0.232639\pi\)
−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
\(255\) −2.48007 + 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 \(-0.780699\pi\)
0.986360 0.164604i \(-0.0526348\pi\)
\(258\) 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 \(0.413802\pi\)
−0.968216 + 0.250116i \(0.919531\pi\)
\(270\) −0.246849 + 0.467057i −0.0150228 + 0.0284242i
\(271\) 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
\(275\) −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 \(-0.867741\pi\)
0.590513 0.807028i \(-0.298925\pi\)
\(284\) −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 −0.833098 0.553125i \(-0.813435\pi\)
0.553125 + 0.833098i \(0.313435\pi\)
\(294\) 0 0
\(295\) 13.6519 0.510768i 0.794845 0.0297381i
\(296\) 0.192580 + 0.333558i 0.0111935 + 0.0193876i
\(297\) −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 0.367728 0.929933i \(-0.380136\pi\)
−0.929933 + 0.367728i \(0.880136\pi\)
\(308\) 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 0.986947 0.161043i \(-0.0514858\pi\)
0.354006 + 0.935243i \(0.384819\pi\)
\(312\) −0.170685 0.637004i −0.00966313 0.0360633i
\(313\) 25.2824 + 6.77439i 1.42904 + 0.382911i 0.888683 0.458523i \(-0.151621\pi\)
0.540361 + 0.841434i \(0.318288\pi\)
\(314\) −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 \(-0.504333\pi\)
−0.0136124 + 0.999907i \(0.504333\pi\)
\(350\) 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 \(-0.948497\pi\)
0.774167 0.632982i \(-0.218169\pi\)
\(354\) −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 −0.244170 0.969732i \(-0.578516\pi\)
0.273408 + 0.961898i \(0.411849\pi\)
\(368\) −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 −0.110636 0.993861i \(-0.535289\pi\)
−0.592744 + 0.805391i \(0.701956\pi\)
\(384\) −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 −0.999841 0.0178380i \(-0.994322\pi\)
0.874807 + 0.484472i \(0.160988\pi\)
\(398\) 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 \(0.361099\pi\)
−0.996198 + 0.0871183i \(0.972234\pi\)
\(410\) −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 \(-0.603181\pi\)
−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 \(0.776802\pi\)
\(422\) 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 −0.0398028 0.999208i \(-0.512673\pi\)
0.999208 + 0.0398028i \(0.0126730\pi\)
\(434\) 0 0
\(435\) 5.98602 + 5.55426i 0.287008 + 0.266306i
\(436\) −0.649575 1.12510i −0.0311090 0.0538824i
\(437\) 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 \(0.0894430\pi\)
−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
\(443\) −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 \(-0.990365\pi\)
0.999542 0.0302636i \(-0.00963467\pi\)
\(462\) 0 0
\(463\) 16.5240 + 16.5240i 0.767934 + 0.767934i 0.977742 0.209809i \(-0.0672841\pi\)
−0.209809 + 0.977742i \(0.567284\pi\)
\(464\) −11.6013 + 6.69801i −0.538577 + 0.310947i
\(465\) 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 \(0.311812\pi\)
−0.897826 + 0.440350i \(0.854854\pi\)
\(468\) −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 −0.964408 0.264417i \(-0.914820\pi\)
0.711196 + 0.702994i \(0.248154\pi\)
\(480\) 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 −0.980357 0.197229i \(-0.936806\pi\)
0.197229 + 0.980357i \(0.436806\pi\)
\(504\) 0 0
\(505\) 0.528051 + 14.1139i 0.0234980 + 0.628059i
\(506\) −3.43603 5.95138i −0.152750 0.264571i
\(507\) 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 \(-0.954333\pi\)
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
\(513\) 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 −0.160216 0.987082i \(-0.551219\pi\)
−0.934946 + 0.354790i \(0.884552\pi\)
\(522\) −0.223302 0.833375i −0.00977367 0.0364758i
\(523\) −4.84539 1.29832i −0.211874 0.0567715i 0.151321 0.988485i \(-0.451647\pi\)
−0.363195 + 0.931713i \(0.618314\pi\)
\(524\) −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 \(0.220199\pi\)
−0.347985 + 0.937500i \(0.613134\pi\)
\(564\) 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 −0.146309 0.989239i \(-0.546739\pi\)
0.367912 + 0.929861i \(0.380073\pi\)
\(578\) −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 0.946420 0.322937i \(-0.104670\pi\)
−0.322937 + 0.946420i \(0.604670\pi\)
\(588\) 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 0.161318 0.986902i \(-0.448425\pi\)
−0.353745 + 0.935342i \(0.615092\pi\)
\(594\) −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 \(-0.713528\pi\)
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
\(605\) 5.10762 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 \(0.178792\pi\)
−0.999275 + 0.0380833i \(0.987875\pi\)
\(608\) 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 −0.956339 0.292261i \(-0.905593\pi\)
0.731274 + 0.682083i \(0.238926\pi\)
\(620\) 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 −0.893652 0.448761i \(-0.851866\pi\)
0.448761 + 0.893652i \(0.351866\pi\)
\(644\) 0 0
\(645\) 11.5403 0.431764i 0.454398 0.0170007i
\(646\) 2.02397 + 3.50562i 0.0796320 + 0.137927i
\(647\) −35.8439 + 9.60434i −1.40917 + 0.377586i −0.881628 0.471944i \(-0.843552\pi\)
−0.527540 + 0.849530i \(0.676886\pi\)
\(648\) −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 0.518421 0.855125i \(-0.326520\pi\)
−0.481350 + 0.876529i \(0.659853\pi\)
\(662\) 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 \(-0.683579\pi\)
0.891357 0.453302i \(-0.149754\pi\)
\(678\) −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 −0.690239 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
\(695\) 0.526349 + 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 \(0.135372\pi\)
−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
\(723\) 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 0.486254 0.873817i \(-0.338363\pi\)
−0.873817 + 0.486254i \(0.838363\pi\)
\(728\) 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 0.701223 0.712942i \(-0.252638\pi\)
0.250806 + 0.968037i \(0.419305\pi\)
\(734\) 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 −0.631563 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
\(765\) 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 \(-0.435168\pi\)
0.202271 +