Properties

Label 441.2.f.h.295.5
Level $441$
Weight $2$
Character 441.295
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.5
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.h.148.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0341870 + 0.0592136i) q^{2} +(-1.69514 + 0.355671i) q^{3} +(0.997662 + 1.72800i) q^{4} +(-1.33190 - 2.30691i) q^{5} +(0.0368912 - 0.112535i) q^{6} -0.273176 q^{8} +(2.74700 - 1.20582i) q^{9} +O(q^{10})\) \(q+(-0.0341870 + 0.0592136i) q^{2} +(-1.69514 + 0.355671i) q^{3} +(0.997662 + 1.72800i) q^{4} +(-1.33190 - 2.30691i) q^{5} +(0.0368912 - 0.112535i) q^{6} -0.273176 q^{8} +(2.74700 - 1.20582i) q^{9} +0.182134 q^{10} +(0.799563 - 1.38488i) q^{11} +(-2.30578 - 2.57437i) q^{12} +(2.62690 + 4.54992i) q^{13} +(3.07825 + 3.43682i) q^{15} +(-1.98599 + 3.43983i) q^{16} +6.54721 q^{17} +(-0.0225104 + 0.203883i) q^{18} -1.90194 q^{19} +(2.65756 - 4.60304i) q^{20} +(0.0546693 + 0.0946900i) q^{22} +(1.53419 + 2.65729i) q^{23} +(0.463072 - 0.0971608i) q^{24} +(-1.04789 + 1.81500i) q^{25} -0.359223 q^{26} +(-4.22767 + 3.02106i) q^{27} +(-3.19452 + 5.53306i) q^{29} +(-0.308743 + 0.0647797i) q^{30} +(3.35961 + 5.81902i) q^{31} +(-0.408966 - 0.708350i) q^{32} +(-0.862809 + 2.63195i) q^{33} +(-0.223829 + 0.387684i) q^{34} +(4.82424 + 3.54381i) q^{36} +4.22955 q^{37} +(0.0650215 - 0.112621i) q^{38} +(-6.07124 - 6.77845i) q^{39} +(0.363842 + 0.630193i) q^{40} +(3.69648 + 6.40249i) q^{41} +(5.63176 - 9.75450i) q^{43} +3.19078 q^{44} +(-6.44044 - 4.73105i) q^{45} -0.209797 q^{46} +(1.89959 - 3.29018i) q^{47} +(2.14308 - 6.53735i) q^{48} +(-0.0716485 - 0.124099i) q^{50} +(-11.0984 + 2.32865i) q^{51} +(-5.24152 + 9.07858i) q^{52} +8.89862 q^{53} +(-0.0343569 - 0.353616i) q^{54} -4.25974 q^{55} +(3.22405 - 0.676463i) q^{57} +(-0.218422 - 0.378317i) q^{58} +(-5.44639 - 9.43343i) q^{59} +(-2.86778 + 8.74801i) q^{60} +(1.35693 - 2.35027i) q^{61} -0.459420 q^{62} -7.88802 q^{64} +(6.99751 - 12.1200i) q^{65} +(-0.126351 - 0.141069i) q^{66} +(1.66267 + 2.87982i) q^{67} +(6.53190 + 11.3136i) q^{68} +(-3.54578 - 3.95881i) q^{69} -12.3890 q^{71} +(-0.750414 + 0.329402i) q^{72} -2.19863 q^{73} +(-0.144596 + 0.250447i) q^{74} +(1.13078 - 3.44939i) q^{75} +(-1.89749 - 3.28655i) q^{76} +(0.608933 - 0.127765i) q^{78} +(-0.406778 + 0.704560i) q^{79} +10.5805 q^{80} +(6.09198 - 6.62478i) q^{81} -0.505486 q^{82} +(3.41842 - 5.92088i) q^{83} +(-8.72020 - 15.1038i) q^{85} +(0.385066 + 0.666954i) q^{86} +(3.44720 - 10.5155i) q^{87} +(-0.218422 + 0.378317i) q^{88} -0.470572 q^{89} +(0.500321 - 0.219621i) q^{90} +(-3.06120 + 5.30216i) q^{92} +(-7.76467 - 8.66914i) q^{93} +(0.129882 + 0.224963i) q^{94} +(2.53318 + 4.38760i) q^{95} +(0.945194 + 1.05529i) q^{96} +(-2.57623 + 4.46216i) q^{97} +(0.526472 - 4.76840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + 20q^{11} + 4q^{15} - 12q^{16} + 4q^{18} + 32q^{23} - 12q^{25} + 16q^{29} + 48q^{32} - 4q^{36} + 24q^{37} + 32q^{39} - 112q^{44} - 48q^{46} - 4q^{50} - 56q^{51} - 64q^{53} - 12q^{57} - 88q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} + 168q^{72} + 68q^{74} - 60q^{78} + 12q^{79} + 80q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 80q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0341870 + 0.0592136i −0.0241739 + 0.0418703i −0.877859 0.478919i \(-0.841029\pi\)
0.853685 + 0.520789i \(0.174362\pi\)
\(3\) −1.69514 + 0.355671i −0.978689 + 0.205347i
\(4\) 0.997662 + 1.72800i 0.498831 + 0.864001i
\(5\) −1.33190 2.30691i −0.595642 1.03168i −0.993456 0.114216i \(-0.963564\pi\)
0.397814 0.917466i \(-0.369769\pi\)
\(6\) 0.0368912 0.112535i 0.0150608 0.0459421i
\(7\) 0 0
\(8\) −0.273176 −0.0965824
\(9\) 2.74700 1.20582i 0.915666 0.401941i
\(10\) 0.182134 0.0575958
\(11\) 0.799563 1.38488i 0.241077 0.417558i −0.719944 0.694032i \(-0.755833\pi\)
0.961021 + 0.276474i \(0.0891659\pi\)
\(12\) −2.30578 2.57437i −0.665620 0.743155i
\(13\) 2.62690 + 4.54992i 0.728571 + 1.26192i 0.957487 + 0.288476i \(0.0931485\pi\)
−0.228916 + 0.973446i \(0.573518\pi\)
\(14\) 0 0
\(15\) 3.07825 + 3.43682i 0.794801 + 0.887383i
\(16\) −1.98599 + 3.43983i −0.496496 + 0.859957i
\(17\) 6.54721 1.58793 0.793966 0.607963i \(-0.208013\pi\)
0.793966 + 0.607963i \(0.208013\pi\)
\(18\) −0.0225104 + 0.203883i −0.00530576 + 0.0480557i
\(19\) −1.90194 −0.436334 −0.218167 0.975911i \(-0.570008\pi\)
−0.218167 + 0.975911i \(0.570008\pi\)
\(20\) 2.65756 4.60304i 0.594249 1.02927i
\(21\) 0 0
\(22\) 0.0546693 + 0.0946900i 0.0116555 + 0.0201880i
\(23\) 1.53419 + 2.65729i 0.319900 + 0.554083i 0.980467 0.196684i \(-0.0630173\pi\)
−0.660567 + 0.750767i \(0.729684\pi\)
\(24\) 0.463072 0.0971608i 0.0945242 0.0198329i
\(25\) −1.04789 + 1.81500i −0.209578 + 0.363000i
\(26\) −0.359223 −0.0704495
\(27\) −4.22767 + 3.02106i −0.813615 + 0.581404i
\(28\) 0 0
\(29\) −3.19452 + 5.53306i −0.593207 + 1.02746i 0.400591 + 0.916257i \(0.368805\pi\)
−0.993797 + 0.111207i \(0.964528\pi\)
\(30\) −0.308743 + 0.0647797i −0.0563684 + 0.0118271i
\(31\) 3.35961 + 5.81902i 0.603405 + 1.04513i 0.992301 + 0.123846i \(0.0395229\pi\)
−0.388897 + 0.921281i \(0.627144\pi\)
\(32\) −0.408966 0.708350i −0.0722957 0.125220i
\(33\) −0.862809 + 2.63195i −0.150196 + 0.458164i
\(34\) −0.223829 + 0.387684i −0.0383864 + 0.0664872i
\(35\) 0 0
\(36\) 4.82424 + 3.54381i 0.804040 + 0.590635i
\(37\) 4.22955 0.695333 0.347667 0.937618i \(-0.386974\pi\)
0.347667 + 0.937618i \(0.386974\pi\)
\(38\) 0.0650215 0.112621i 0.0105479 0.0182695i
\(39\) −6.07124 6.77845i −0.972176 1.08542i
\(40\) 0.363842 + 0.630193i 0.0575285 + 0.0996423i
\(41\) 3.69648 + 6.40249i 0.577293 + 0.999901i 0.995788 + 0.0916820i \(0.0292243\pi\)
−0.418495 + 0.908219i \(0.637442\pi\)
\(42\) 0 0
\(43\) 5.63176 9.75450i 0.858836 1.48755i −0.0142043 0.999899i \(-0.504522\pi\)
0.873040 0.487648i \(-0.162145\pi\)
\(44\) 3.19078 0.481028
\(45\) −6.44044 4.73105i −0.960084 0.705263i
\(46\) −0.209797 −0.0309329
\(47\) 1.89959 3.29018i 0.277083 0.479922i −0.693575 0.720384i \(-0.743966\pi\)
0.970659 + 0.240462i \(0.0772989\pi\)
\(48\) 2.14308 6.53735i 0.309327 0.943585i
\(49\) 0 0
\(50\) −0.0716485 0.124099i −0.0101326 0.0175502i
\(51\) −11.0984 + 2.32865i −1.55409 + 0.326076i
\(52\) −5.24152 + 9.07858i −0.726868 + 1.25897i
\(53\) 8.89862 1.22232 0.611160 0.791507i \(-0.290703\pi\)
0.611160 + 0.791507i \(0.290703\pi\)
\(54\) −0.0343569 0.353616i −0.00467539 0.0481211i
\(55\) −4.25974 −0.574383
\(56\) 0 0
\(57\) 3.22405 0.676463i 0.427036 0.0895997i
\(58\) −0.218422 0.378317i −0.0286802 0.0496755i
\(59\) −5.44639 9.43343i −0.709060 1.22813i −0.965206 0.261490i \(-0.915786\pi\)
0.256146 0.966638i \(-0.417547\pi\)
\(60\) −2.86778 + 8.74801i −0.370228 + 1.12936i
\(61\) 1.35693 2.35027i 0.173737 0.300922i −0.765986 0.642857i \(-0.777749\pi\)
0.939724 + 0.341935i \(0.111082\pi\)
\(62\) −0.459420 −0.0583465
\(63\) 0 0
\(64\) −7.88802 −0.986002
\(65\) 6.99751 12.1200i 0.867935 1.50331i
\(66\) −0.126351 0.141069i −0.0155527 0.0173643i
\(67\) 1.66267 + 2.87982i 0.203127 + 0.351826i 0.949534 0.313663i \(-0.101556\pi\)
−0.746407 + 0.665489i \(0.768223\pi\)
\(68\) 6.53190 + 11.3136i 0.792110 + 1.37197i
\(69\) −3.54578 3.95881i −0.426862 0.476585i
\(70\) 0 0
\(71\) −12.3890 −1.47031 −0.735154 0.677900i \(-0.762890\pi\)
−0.735154 + 0.677900i \(0.762890\pi\)
\(72\) −0.750414 + 0.329402i −0.0884372 + 0.0388204i
\(73\) −2.19863 −0.257331 −0.128665 0.991688i \(-0.541069\pi\)
−0.128665 + 0.991688i \(0.541069\pi\)
\(74\) −0.144596 + 0.250447i −0.0168089 + 0.0291138i
\(75\) 1.13078 3.44939i 0.130571 0.398301i
\(76\) −1.89749 3.28655i −0.217657 0.376993i
\(77\) 0 0
\(78\) 0.608933 0.127765i 0.0689481 0.0144666i
\(79\) −0.406778 + 0.704560i −0.0457661 + 0.0792692i −0.888001 0.459841i \(-0.847906\pi\)
0.842235 + 0.539111i \(0.181240\pi\)
\(80\) 10.5805 1.18294
\(81\) 6.09198 6.62478i 0.676887 0.736087i
\(82\) −0.505486 −0.0558216
\(83\) 3.41842 5.92088i 0.375220 0.649901i −0.615140 0.788418i \(-0.710900\pi\)
0.990360 + 0.138517i \(0.0442337\pi\)
\(84\) 0 0
\(85\) −8.72020 15.1038i −0.945838 1.63824i
\(86\) 0.385066 + 0.666954i 0.0415227 + 0.0719195i
\(87\) 3.44720 10.5155i 0.369579 1.12738i
\(88\) −0.218422 + 0.378317i −0.0232838 + 0.0403288i
\(89\) −0.470572 −0.0498805 −0.0249403 0.999689i \(-0.507940\pi\)
−0.0249403 + 0.999689i \(0.507940\pi\)
\(90\) 0.500321 0.219621i 0.0527385 0.0231501i
\(91\) 0 0
\(92\) −3.06120 + 5.30216i −0.319152 + 0.552788i
\(93\) −7.76467 8.66914i −0.805159 0.898948i
\(94\) 0.129882 + 0.224963i 0.0133963 + 0.0232031i
\(95\) 2.53318 + 4.38760i 0.259899 + 0.450158i
\(96\) 0.945194 + 1.05529i 0.0964684 + 0.107706i
\(97\) −2.57623 + 4.46216i −0.261576 + 0.453064i −0.966661 0.256059i \(-0.917576\pi\)
0.705085 + 0.709123i \(0.250909\pi\)
\(98\) 0 0
\(99\) 0.526472 4.76840i 0.0529125 0.479243i
\(100\) −4.18177 −0.418177
\(101\) −0.922440 + 1.59771i −0.0917862 + 0.158978i −0.908263 0.418400i \(-0.862591\pi\)
0.816477 + 0.577379i \(0.195924\pi\)
\(102\) 0.241534 0.736788i 0.0239155 0.0729529i
\(103\) 2.58901 + 4.48430i 0.255103 + 0.441851i 0.964923 0.262531i \(-0.0845573\pi\)
−0.709821 + 0.704383i \(0.751224\pi\)
\(104\) −0.717607 1.24293i −0.0703671 0.121879i
\(105\) 0 0
\(106\) −0.304217 + 0.526920i −0.0295482 + 0.0511790i
\(107\) −16.9489 −1.63851 −0.819256 0.573428i \(-0.805613\pi\)
−0.819256 + 0.573428i \(0.805613\pi\)
\(108\) −9.43819 4.29141i −0.908190 0.412942i
\(109\) −8.49992 −0.814145 −0.407073 0.913396i \(-0.633450\pi\)
−0.407073 + 0.913396i \(0.633450\pi\)
\(110\) 0.145628 0.252235i 0.0138851 0.0240496i
\(111\) −7.16967 + 1.50433i −0.680515 + 0.142784i
\(112\) 0 0
\(113\) −1.95196 3.38089i −0.183625 0.318048i 0.759487 0.650522i \(-0.225450\pi\)
−0.943112 + 0.332474i \(0.892116\pi\)
\(114\) −0.0701647 + 0.214034i −0.00657152 + 0.0200461i
\(115\) 4.08675 7.07847i 0.381092 0.660070i
\(116\) −12.7482 −1.18364
\(117\) 12.7025 + 9.33105i 1.17435 + 0.862656i
\(118\) 0.744783 0.0685628
\(119\) 0 0
\(120\) −0.840905 0.938858i −0.0767637 0.0857056i
\(121\) 4.22140 + 7.31167i 0.383763 + 0.664698i
\(122\) 0.0927788 + 0.160698i 0.00839980 + 0.0145489i
\(123\) −8.54323 9.53838i −0.770317 0.860047i
\(124\) −6.70352 + 11.6108i −0.601994 + 1.04268i
\(125\) −7.73623 −0.691949
\(126\) 0 0
\(127\) 10.9533 0.971946 0.485973 0.873974i \(-0.338465\pi\)
0.485973 + 0.873974i \(0.338465\pi\)
\(128\) 1.08760 1.88378i 0.0961311 0.166504i
\(129\) −6.07724 + 18.5383i −0.535071 + 1.63221i
\(130\) 0.478448 + 0.828696i 0.0419626 + 0.0726814i
\(131\) −2.22671 3.85678i −0.194549 0.336968i 0.752204 0.658931i \(-0.228991\pi\)
−0.946752 + 0.321962i \(0.895658\pi\)
\(132\) −5.40881 + 1.13487i −0.470777 + 0.0987774i
\(133\) 0 0
\(134\) −0.227366 −0.0196414
\(135\) 12.6001 + 5.72911i 1.08445 + 0.493083i
\(136\) −1.78854 −0.153366
\(137\) 9.76800 16.9187i 0.834537 1.44546i −0.0598699 0.998206i \(-0.519069\pi\)
0.894407 0.447254i \(-0.147598\pi\)
\(138\) 0.355635 0.0746186i 0.0302737 0.00635196i
\(139\) 1.31540 + 2.27833i 0.111570 + 0.193246i 0.916404 0.400256i \(-0.131079\pi\)
−0.804833 + 0.593501i \(0.797745\pi\)
\(140\) 0 0
\(141\) −2.04984 + 6.25295i −0.172628 + 0.526593i
\(142\) 0.423544 0.733599i 0.0355430 0.0615623i
\(143\) 8.40149 0.702568
\(144\) −1.30767 + 11.8439i −0.108973 + 0.986995i
\(145\) 17.0190 1.41335
\(146\) 0.0751647 0.130189i 0.00622067 0.0107745i
\(147\) 0 0
\(148\) 4.21966 + 7.30867i 0.346854 + 0.600769i
\(149\) 4.40640 + 7.63212i 0.360987 + 0.625247i 0.988124 0.153662i \(-0.0491066\pi\)
−0.627137 + 0.778909i \(0.715773\pi\)
\(150\) 0.165593 + 0.184882i 0.0135206 + 0.0150955i
\(151\) −2.33211 + 4.03933i −0.189784 + 0.328716i −0.945178 0.326555i \(-0.894112\pi\)
0.755394 + 0.655271i \(0.227446\pi\)
\(152\) 0.519564 0.0421422
\(153\) 17.9852 7.89478i 1.45401 0.638255i
\(154\) 0 0
\(155\) 8.94931 15.5007i 0.718826 1.24504i
\(156\) 5.65612 17.2537i 0.452852 1.38140i
\(157\) −2.03647 3.52727i −0.162528 0.281506i 0.773247 0.634105i \(-0.218631\pi\)
−0.935775 + 0.352599i \(0.885298\pi\)
\(158\) −0.0278130 0.0481736i −0.00221269 0.00383249i
\(159\) −15.0844 + 3.16498i −1.19627 + 0.250999i
\(160\) −1.08940 + 1.88690i −0.0861246 + 0.149172i
\(161\) 0 0
\(162\) 0.184011 + 0.587210i 0.0144573 + 0.0461355i
\(163\) −12.1222 −0.949487 −0.474744 0.880124i \(-0.657459\pi\)
−0.474744 + 0.880124i \(0.657459\pi\)
\(164\) −7.37568 + 12.7750i −0.575944 + 0.997564i
\(165\) 7.22085 1.51506i 0.562143 0.117948i
\(166\) 0.233731 + 0.404834i 0.0181410 + 0.0314212i
\(167\) −2.39951 4.15608i −0.185680 0.321607i 0.758126 0.652109i \(-0.226115\pi\)
−0.943805 + 0.330502i \(0.892782\pi\)
\(168\) 0 0
\(169\) −7.30121 + 12.6461i −0.561631 + 0.972774i
\(170\) 1.19247 0.0914582
\(171\) −5.22461 + 2.29340i −0.399536 + 0.175381i
\(172\) 22.4744 1.71366
\(173\) 2.51585 4.35759i 0.191277 0.331301i −0.754397 0.656419i \(-0.772071\pi\)
0.945674 + 0.325118i \(0.105404\pi\)
\(174\) 0.504812 + 0.563615i 0.0382697 + 0.0427275i
\(175\) 0 0
\(176\) 3.17584 + 5.50072i 0.239388 + 0.414632i
\(177\) 12.5876 + 14.0539i 0.946141 + 1.05635i
\(178\) 0.0160874 0.0278642i 0.00120580 0.00208851i
\(179\) −16.3979 −1.22564 −0.612819 0.790224i \(-0.709964\pi\)
−0.612819 + 0.790224i \(0.709964\pi\)
\(180\) 1.74987 15.8491i 0.130428 1.18132i
\(181\) 14.4345 1.07291 0.536454 0.843930i \(-0.319763\pi\)
0.536454 + 0.843930i \(0.319763\pi\)
\(182\) 0 0
\(183\) −1.46426 + 4.46666i −0.108242 + 0.330185i
\(184\) −0.419103 0.725908i −0.0308967 0.0535147i
\(185\) −5.63332 9.75719i −0.414170 0.717363i
\(186\) 0.778782 0.163402i 0.0571031 0.0119812i
\(187\) 5.23491 9.06713i 0.382814 0.663054i
\(188\) 7.58059 0.552871
\(189\) 0 0
\(190\) −0.346407 −0.0251310
\(191\) −1.42066 + 2.46065i −0.102795 + 0.178046i −0.912835 0.408328i \(-0.866112\pi\)
0.810040 + 0.586374i \(0.199445\pi\)
\(192\) 13.3713 2.80554i 0.964990 0.202472i
\(193\) −4.41443 7.64601i −0.317758 0.550372i 0.662262 0.749272i \(-0.269596\pi\)
−0.980020 + 0.198900i \(0.936263\pi\)
\(194\) −0.176147 0.305096i −0.0126466 0.0219046i
\(195\) −7.55102 + 23.0340i −0.540739 + 1.64950i
\(196\) 0 0
\(197\) 5.72354 0.407785 0.203893 0.978993i \(-0.434641\pi\)
0.203893 + 0.978993i \(0.434641\pi\)
\(198\) 0.264356 + 0.194192i 0.0187870 + 0.0138006i
\(199\) 11.4150 0.809191 0.404596 0.914496i \(-0.367412\pi\)
0.404596 + 0.914496i \(0.367412\pi\)
\(200\) 0.286259 0.495815i 0.0202416 0.0350594i
\(201\) −3.84272 4.29034i −0.271044 0.302617i
\(202\) −0.0630709 0.109242i −0.00443765 0.00768624i
\(203\) 0 0
\(204\) −15.0964 16.8549i −1.05696 1.18008i
\(205\) 9.84665 17.0549i 0.687720 1.19117i
\(206\) −0.354042 −0.0246673
\(207\) 7.41863 + 5.44961i 0.515630 + 0.378774i
\(208\) −20.8679 −1.44693
\(209\) −1.52072 + 2.63396i −0.105190 + 0.182195i
\(210\) 0 0
\(211\) 10.6919 + 18.5189i 0.736059 + 1.27489i 0.954257 + 0.298986i \(0.0966486\pi\)
−0.218199 + 0.975904i \(0.570018\pi\)
\(212\) 8.87782 + 15.3768i 0.609731 + 1.05609i
\(213\) 21.0011 4.40642i 1.43897 0.301923i
\(214\) 0.579432 1.00361i 0.0396091 0.0686050i
\(215\) −30.0037 −2.04623
\(216\) 1.15490 0.825283i 0.0785809 0.0561534i
\(217\) 0 0
\(218\) 0.290587 0.503311i 0.0196810 0.0340885i
\(219\) 3.72699 0.781990i 0.251847 0.0528420i
\(220\) −4.24978 7.36084i −0.286520 0.496268i
\(221\) 17.1989 + 29.7893i 1.15692 + 2.00385i
\(222\) 0.156033 0.475971i 0.0104722 0.0319451i
\(223\) 3.58387 6.20744i 0.239994 0.415681i −0.720719 0.693228i \(-0.756188\pi\)
0.960712 + 0.277547i \(0.0895213\pi\)
\(224\) 0 0
\(225\) −0.689984 + 6.24938i −0.0459989 + 0.416625i
\(226\) 0.266926 0.0177557
\(227\) −6.89434 + 11.9413i −0.457593 + 0.792575i −0.998833 0.0482933i \(-0.984622\pi\)
0.541240 + 0.840868i \(0.317955\pi\)
\(228\) 4.38544 + 4.89628i 0.290433 + 0.324264i
\(229\) −13.1972 22.8581i −0.872092 1.51051i −0.859828 0.510584i \(-0.829429\pi\)
−0.0122645 0.999925i \(-0.503904\pi\)
\(230\) 0.279428 + 0.483983i 0.0184249 + 0.0319129i
\(231\) 0 0
\(232\) 0.872666 1.51150i 0.0572933 0.0992349i
\(233\) −12.6446 −0.828375 −0.414187 0.910192i \(-0.635934\pi\)
−0.414187 + 0.910192i \(0.635934\pi\)
\(234\) −0.986785 + 0.433160i −0.0645081 + 0.0283165i
\(235\) −10.1202 −0.660170
\(236\) 10.8673 18.8228i 0.707403 1.22526i
\(237\) 0.438954 1.33901i 0.0285131 0.0869779i
\(238\) 0 0
\(239\) 7.71640 + 13.3652i 0.499133 + 0.864523i 0.999999 0.00100121i \(-0.000318696\pi\)
−0.500867 + 0.865524i \(0.666985\pi\)
\(240\) −17.9354 + 3.76318i −1.15773 + 0.242912i
\(241\) 0.589942 1.02181i 0.0380015 0.0658205i −0.846399 0.532549i \(-0.821234\pi\)
0.884401 + 0.466729i \(0.154568\pi\)
\(242\) −0.577267 −0.0371082
\(243\) −7.97052 + 13.3967i −0.511309 + 0.859397i
\(244\) 5.41504 0.346662
\(245\) 0 0
\(246\) 0.856869 0.179787i 0.0546320 0.0114628i
\(247\) −4.99620 8.65367i −0.317900 0.550620i
\(248\) −0.917767 1.58962i −0.0582783 0.100941i
\(249\) −3.68882 + 11.2525i −0.233769 + 0.713101i
\(250\) 0.264478 0.458090i 0.0167271 0.0289721i
\(251\) −5.54970 −0.350294 −0.175147 0.984542i \(-0.556040\pi\)
−0.175147 + 0.984542i \(0.556040\pi\)
\(252\) 0 0
\(253\) 4.90672 0.308483
\(254\) −0.374459 + 0.648583i −0.0234957 + 0.0406957i
\(255\) 20.1539 + 22.5016i 1.26209 + 1.40910i
\(256\) −7.81365 13.5336i −0.488353 0.845853i
\(257\) 4.91538 + 8.51369i 0.306613 + 0.531069i 0.977619 0.210382i \(-0.0674709\pi\)
−0.671006 + 0.741452i \(0.734138\pi\)
\(258\) −0.889957 0.993623i −0.0554063 0.0618603i
\(259\) 0 0
\(260\) 27.9246 1.73181
\(261\) −2.10343 + 19.0513i −0.130199 + 1.17925i
\(262\) 0.304498 0.0188120
\(263\) −5.96612 + 10.3336i −0.367887 + 0.637199i −0.989235 0.146336i \(-0.953252\pi\)
0.621348 + 0.783535i \(0.286585\pi\)
\(264\) 0.235699 0.718987i 0.0145063 0.0442506i
\(265\) −11.8520 20.5283i −0.728065 1.26105i
\(266\) 0 0
\(267\) 0.797685 0.167369i 0.0488175 0.0102428i
\(268\) −3.31756 + 5.74618i −0.202652 + 0.351004i
\(269\) −29.9648 −1.82699 −0.913494 0.406853i \(-0.866626\pi\)
−0.913494 + 0.406853i \(0.866626\pi\)
\(270\) −0.770002 + 0.550239i −0.0468608 + 0.0334865i
\(271\) 7.09650 0.431082 0.215541 0.976495i \(-0.430849\pi\)
0.215541 + 0.976495i \(0.430849\pi\)
\(272\) −13.0027 + 22.5213i −0.788402 + 1.36555i
\(273\) 0 0
\(274\) 0.667877 + 1.15680i 0.0403479 + 0.0698847i
\(275\) 1.67571 + 2.90242i 0.101049 + 0.175022i
\(276\) 3.30334 10.0767i 0.198838 0.606545i
\(277\) 4.91175 8.50741i 0.295119 0.511161i −0.679894 0.733311i \(-0.737974\pi\)
0.975013 + 0.222150i \(0.0713075\pi\)
\(278\) −0.179878 −0.0107883
\(279\) 16.2456 + 11.9337i 0.972596 + 0.714454i
\(280\) 0 0
\(281\) 11.9389 20.6787i 0.712213 1.23359i −0.251812 0.967776i \(-0.581026\pi\)
0.964025 0.265813i \(-0.0856403\pi\)
\(282\) −0.300181 0.335148i −0.0178755 0.0199578i
\(283\) −1.50798 2.61189i −0.0896399 0.155261i 0.817719 0.575618i \(-0.195238\pi\)
−0.907359 + 0.420357i \(0.861905\pi\)
\(284\) −12.3601 21.4083i −0.733435 1.27035i
\(285\) −5.85464 6.53661i −0.346799 0.387196i
\(286\) −0.287222 + 0.497483i −0.0169838 + 0.0294168i
\(287\) 0 0
\(288\) −1.97757 1.45269i −0.116530 0.0856008i
\(289\) 25.8659 1.52153
\(290\) −0.581830 + 1.00776i −0.0341662 + 0.0591776i
\(291\) 2.78001 8.48027i 0.162967 0.497123i
\(292\) −2.19350 3.79925i −0.128365 0.222334i
\(293\) 8.52913 + 14.7729i 0.498277 + 0.863041i 0.999998 0.00198814i \(-0.000632845\pi\)
−0.501721 + 0.865030i \(0.667300\pi\)
\(294\) 0 0
\(295\) −14.5081 + 25.1287i −0.844692 + 1.46305i
\(296\) −1.15541 −0.0671570
\(297\) 0.803538 + 8.27036i 0.0466260 + 0.479895i
\(298\) −0.602567 −0.0349058
\(299\) −8.06031 + 13.9609i −0.466140 + 0.807378i
\(300\) 7.08868 1.48733i 0.409265 0.0858712i
\(301\) 0 0
\(302\) −0.159456 0.276185i −0.00917564 0.0158927i
\(303\) 0.995404 3.03643i 0.0571845 0.174438i
\(304\) 3.77722 6.54234i 0.216638 0.375229i
\(305\) −7.22917 −0.413941
\(306\) −0.147380 + 1.33486i −0.00842518 + 0.0763091i
\(307\) −23.2178 −1.32511 −0.662554 0.749014i \(-0.730527\pi\)
−0.662554 + 0.749014i \(0.730527\pi\)
\(308\) 0 0
\(309\) −5.98367 6.68068i −0.340399 0.380050i
\(310\) 0.611900 + 1.05984i 0.0347536 + 0.0601950i
\(311\) 0.895467 + 1.55100i 0.0507773 + 0.0879489i 0.890297 0.455381i \(-0.150497\pi\)
−0.839520 + 0.543329i \(0.817163\pi\)
\(312\) 1.65852 + 1.85171i 0.0938951 + 0.104832i
\(313\) 2.30458 3.99166i 0.130263 0.225622i −0.793515 0.608551i \(-0.791751\pi\)
0.923778 + 0.382929i \(0.125085\pi\)
\(314\) 0.278483 0.0157157
\(315\) 0 0
\(316\) −1.62331 −0.0913183
\(317\) 12.9421 22.4163i 0.726898 1.25902i −0.231290 0.972885i \(-0.574295\pi\)
0.958188 0.286140i \(-0.0923721\pi\)
\(318\) 0.328281 1.00140i 0.0184091 0.0561559i
\(319\) 5.10843 + 8.84807i 0.286017 + 0.495397i
\(320\) 10.5060 + 18.1970i 0.587304 + 1.01724i
\(321\) 28.7307 6.02823i 1.60359 0.336463i
\(322\) 0 0
\(323\) −12.4524 −0.692869
\(324\) 17.5254 + 3.91766i 0.973632 + 0.217648i
\(325\) −11.0108 −0.610771
\(326\) 0.414423 0.717802i 0.0229528 0.0397554i
\(327\) 14.4086 3.02317i 0.796795 0.167182i
\(328\) −1.00979 1.74901i −0.0557563 0.0965728i
\(329\) 0 0
\(330\) −0.157147 + 0.479368i −0.00865065 + 0.0263884i
\(331\) −0.0806617 + 0.139710i −0.00443357 + 0.00767917i −0.868234 0.496156i \(-0.834745\pi\)
0.863800 + 0.503835i \(0.168078\pi\)
\(332\) 13.6417 0.748687
\(333\) 11.6186 5.10009i 0.636693 0.279483i
\(334\) 0.328128 0.0179544
\(335\) 4.42899 7.67124i 0.241982 0.419125i
\(336\) 0 0
\(337\) 4.52675 + 7.84057i 0.246588 + 0.427103i 0.962577 0.271009i \(-0.0873572\pi\)
−0.715989 + 0.698112i \(0.754024\pi\)
\(338\) −0.499213 0.864662i −0.0271536 0.0470314i
\(339\) 4.51133 + 5.03683i 0.245022 + 0.273563i
\(340\) 17.3996 30.1370i 0.943627 1.63441i
\(341\) 10.7449 0.581869
\(342\) 0.0428134 0.387773i 0.00231508 0.0209683i
\(343\) 0 0
\(344\) −1.53846 + 2.66470i −0.0829484 + 0.143671i
\(345\) −4.41002 + 13.4525i −0.237427 + 0.724260i
\(346\) 0.172019 + 0.297945i 0.00924779 + 0.0160176i
\(347\) 2.90984 + 5.03999i 0.156208 + 0.270561i 0.933498 0.358582i \(-0.116740\pi\)
−0.777290 + 0.629142i \(0.783406\pi\)
\(348\) 21.6100 4.53416i 1.15842 0.243056i
\(349\) 13.6310 23.6095i 0.729648 1.26379i −0.227384 0.973805i \(-0.573017\pi\)
0.957032 0.289983i \(-0.0936496\pi\)
\(350\) 0 0
\(351\) −24.8513 11.2995i −1.32646 0.603124i
\(352\) −1.30798 −0.0697154
\(353\) −12.0948 + 20.9488i −0.643741 + 1.11499i 0.340850 + 0.940118i \(0.389285\pi\)
−0.984591 + 0.174874i \(0.944048\pi\)
\(354\) −1.26251 + 0.264898i −0.0671017 + 0.0140791i
\(355\) 16.5009 + 28.5804i 0.875777 + 1.51689i
\(356\) −0.469472 0.813149i −0.0248820 0.0430968i
\(357\) 0 0
\(358\) 0.560595 0.970979i 0.0296284 0.0513179i
\(359\) −21.0376 −1.11032 −0.555161 0.831743i \(-0.687343\pi\)
−0.555161 + 0.831743i \(0.687343\pi\)
\(360\) 1.75938 + 1.29241i 0.0927272 + 0.0681160i
\(361\) −15.3826 −0.809612
\(362\) −0.493472 + 0.854719i −0.0259363 + 0.0449230i
\(363\) −9.75641 10.8929i −0.512079 0.571728i
\(364\) 0 0
\(365\) 2.92835 + 5.07205i 0.153277 + 0.265483i
\(366\) −0.214428 0.239406i −0.0112084 0.0125140i
\(367\) 17.5190 30.3438i 0.914485 1.58393i 0.106831 0.994277i \(-0.465930\pi\)
0.807654 0.589657i \(-0.200737\pi\)
\(368\) −12.1875 −0.635317
\(369\) 17.8745 + 13.1303i 0.930509 + 0.683537i
\(370\) 0.770345 0.0400483
\(371\) 0 0
\(372\) 7.23377 22.0662i 0.375054 1.14408i
\(373\) −0.564310 0.977414i −0.0292189 0.0506086i 0.851046 0.525091i \(-0.175969\pi\)
−0.880265 + 0.474482i \(0.842635\pi\)
\(374\) 0.357931 + 0.619955i 0.0185082 + 0.0320571i
\(375\) 13.1140 2.75155i 0.677203 0.142089i
\(376\) −0.518922 + 0.898800i −0.0267614 + 0.0463521i
\(377\) −33.5667 −1.72877
\(378\) 0 0
\(379\) −21.9619 −1.12811 −0.564054 0.825738i \(-0.690759\pi\)
−0.564054 + 0.825738i \(0.690759\pi\)
\(380\) −5.05452 + 8.75468i −0.259291 + 0.449106i
\(381\) −18.5673 + 3.89576i −0.951233 + 0.199586i
\(382\) −0.0971359 0.168244i −0.00496991 0.00860813i
\(383\) −11.5200 19.9533i −0.588647 1.01957i −0.994410 0.105588i \(-0.966328\pi\)
0.405763 0.913978i \(-0.367006\pi\)
\(384\) −1.17363 + 3.58009i −0.0598915 + 0.182696i
\(385\) 0 0
\(386\) 0.603664 0.0307257
\(387\) 3.70823 33.5865i 0.188500 1.70730i
\(388\) −10.2808 −0.521930
\(389\) −7.88753 + 13.6616i −0.399914 + 0.692671i −0.993715 0.111941i \(-0.964293\pi\)
0.593801 + 0.804612i \(0.297627\pi\)
\(390\) −1.10578 1.23459i −0.0559933 0.0625157i
\(391\) 10.0446 + 17.3978i 0.507979 + 0.879846i
\(392\) 0 0
\(393\) 5.14633 + 5.74580i 0.259598 + 0.289837i
\(394\) −0.195671 + 0.338912i −0.00985774 + 0.0170741i
\(395\) 2.16714 0.109041
\(396\) 8.76505 3.84751i 0.440461 0.193345i
\(397\) −16.5055 −0.828389 −0.414195 0.910188i \(-0.635937\pi\)
−0.414195 + 0.910188i \(0.635937\pi\)
\(398\) −0.390246 + 0.675926i −0.0195613 + 0.0338811i
\(399\) 0 0
\(400\) −4.16220 7.20914i −0.208110 0.360457i
\(401\) −10.8300 18.7581i −0.540823 0.936733i −0.998857 0.0477986i \(-0.984779\pi\)
0.458034 0.888935i \(-0.348554\pi\)
\(402\) 0.385417 0.0808675i 0.0192229 0.00403330i
\(403\) −17.6507 + 30.5720i −0.879246 + 1.52290i
\(404\) −3.68113 −0.183143
\(405\) −23.3967 5.23014i −1.16259 0.259888i
\(406\) 0 0
\(407\) 3.38179 5.85743i 0.167629 0.290342i
\(408\) 3.03183 0.636132i 0.150098 0.0314932i
\(409\) −15.2860 26.4762i −0.755846 1.30916i −0.944953 0.327207i \(-0.893893\pi\)
0.189107 0.981956i \(-0.439441\pi\)
\(410\) 0.673255 + 1.16611i 0.0332497 + 0.0575901i
\(411\) −10.5407 + 32.1537i −0.519932 + 1.58603i
\(412\) −5.16592 + 8.94763i −0.254507 + 0.440818i
\(413\) 0 0
\(414\) −0.576311 + 0.252978i −0.0283242 + 0.0124332i
\(415\) −18.2119 −0.893988
\(416\) 2.14863 3.72153i 0.105345 0.182463i
\(417\) −3.04011 3.39424i −0.148875 0.166217i
\(418\) −0.103978 0.180094i −0.00508571 0.00880871i
\(419\) −10.8081 18.7202i −0.528011 0.914542i −0.999467 0.0326524i \(-0.989605\pi\)
0.471456 0.881890i \(-0.343729\pi\)
\(420\) 0 0
\(421\) 13.6217 23.5935i 0.663881 1.14988i −0.315706 0.948857i \(-0.602241\pi\)
0.979587 0.201019i \(-0.0644252\pi\)
\(422\) −1.46209 −0.0711735
\(423\) 1.25078 11.3287i 0.0608152 0.550820i
\(424\) −2.43089 −0.118055
\(425\) −6.86077 + 11.8832i −0.332796 + 0.576420i
\(426\) −0.457046 + 1.39419i −0.0221439 + 0.0675490i
\(427\) 0 0
\(428\) −16.9093 29.2877i −0.817341 1.41568i
\(429\) −14.2417 + 2.98816i −0.687596 + 0.144270i
\(430\) 1.02574 1.77663i 0.0494654 0.0856765i
\(431\) 8.19687 0.394829 0.197415 0.980320i \(-0.436745\pi\)
0.197415 + 0.980320i \(0.436745\pi\)
\(432\) −1.99586 20.5422i −0.0960258 0.988339i
\(433\) −3.41468 −0.164099 −0.0820494 0.996628i \(-0.526147\pi\)
−0.0820494 + 0.996628i \(0.526147\pi\)
\(434\) 0 0
\(435\) −28.8497 + 6.05318i −1.38324 + 0.290228i
\(436\) −8.48005 14.6879i −0.406121 0.703422i
\(437\) −2.91793 5.05400i −0.139583 0.241765i
\(438\) −0.0811102 + 0.247423i −0.00387560 + 0.0118223i
\(439\) 3.29416 5.70564i 0.157221 0.272316i −0.776644 0.629939i \(-0.783080\pi\)
0.933866 + 0.357624i \(0.116413\pi\)
\(440\) 1.16366 0.0554753
\(441\) 0 0
\(442\) −2.35191 −0.111869
\(443\) −14.3456 + 24.8473i −0.681581 + 1.18053i 0.292917 + 0.956138i \(0.405374\pi\)
−0.974498 + 0.224395i \(0.927959\pi\)
\(444\) −9.75240 10.8884i −0.462828 0.516741i
\(445\) 0.626752 + 1.08557i 0.0297109 + 0.0514608i
\(446\) 0.245043 + 0.424428i 0.0116031 + 0.0200972i
\(447\) −10.1840 11.3703i −0.481686 0.537796i
\(448\) 0 0
\(449\) 0.457724 0.0216013 0.0108007 0.999942i \(-0.496562\pi\)
0.0108007 + 0.999942i \(0.496562\pi\)
\(450\) −0.346460 0.254504i −0.0163323 0.0119974i
\(451\) 11.8223 0.556689
\(452\) 3.89479 6.74598i 0.183196 0.317304i
\(453\) 2.51658 7.67669i 0.118239 0.360683i
\(454\) −0.471393 0.816477i −0.0221236 0.0383192i
\(455\) 0 0
\(456\) −0.880733 + 0.184794i −0.0412441 + 0.00865376i
\(457\) −10.1105 + 17.5119i −0.472950 + 0.819173i −0.999521 0.0309581i \(-0.990144\pi\)
0.526571 + 0.850131i \(0.323477\pi\)
\(458\) 1.80468 0.0843273
\(459\) −27.6794 + 19.7795i −1.29196 + 0.923230i
\(460\) 16.3088 0.760402
\(461\) 12.1036 20.9640i 0.563719 0.976390i −0.433449 0.901178i \(-0.642703\pi\)
0.997168 0.0752117i \(-0.0239633\pi\)
\(462\) 0 0
\(463\) 2.40242 + 4.16111i 0.111650 + 0.193383i 0.916436 0.400182i \(-0.131053\pi\)
−0.804786 + 0.593565i \(0.797720\pi\)
\(464\) −12.6885 21.9772i −0.589050 1.02026i
\(465\) −9.65720 + 29.4588i −0.447842 + 1.36612i
\(466\) 0.432281 0.748732i 0.0200250 0.0346843i
\(467\) 27.2456 1.26078 0.630389 0.776279i \(-0.282895\pi\)
0.630389 + 0.776279i \(0.282895\pi\)
\(468\) −3.45128 + 31.2592i −0.159535 + 1.44496i
\(469\) 0 0
\(470\) 0.345979 0.599254i 0.0159588 0.0276415i
\(471\) 4.70664 + 5.25490i 0.216871 + 0.242133i
\(472\) 1.48783 + 2.57699i 0.0684827 + 0.118616i
\(473\) −9.00590 15.5987i −0.414092 0.717228i
\(474\) 0.0642809 + 0.0717687i 0.00295252 + 0.00329644i
\(475\) 1.99302 3.45202i 0.0914462 0.158389i
\(476\) 0 0
\(477\) 24.4445 10.7302i 1.11924 0.491301i
\(478\) −1.05520 −0.0482638
\(479\) 10.2628 17.7756i 0.468917 0.812188i −0.530452 0.847715i \(-0.677978\pi\)
0.999369 + 0.0355269i \(0.0113109\pi\)
\(480\) 1.17557 3.58602i 0.0536572 0.163679i
\(481\) 11.1106 + 19.2441i 0.506600 + 0.877457i
\(482\) 0.0403366 + 0.0698651i 0.00183728 + 0.00318227i
\(483\) 0 0
\(484\) −8.42306 + 14.5892i −0.382866 + 0.663144i
\(485\) 13.7251 0.623224
\(486\) −0.520777 0.929955i −0.0236229 0.0421836i
\(487\) 25.8449 1.17114 0.585571 0.810621i \(-0.300870\pi\)
0.585571 + 0.810621i \(0.300870\pi\)
\(488\) −0.370682 + 0.642039i −0.0167800 + 0.0290638i
\(489\) 20.5489 4.31153i 0.929253 0.194974i
\(490\) 0 0
\(491\) −7.80775 13.5234i −0.352359 0.610303i 0.634303 0.773084i \(-0.281287\pi\)
−0.986662 + 0.162781i \(0.947954\pi\)
\(492\) 7.95909 24.2788i 0.358824 1.09457i
\(493\) −20.9152 + 36.2261i −0.941971 + 1.63154i
\(494\) 0.683220 0.0307395
\(495\) −11.7015 + 5.13649i −0.525943 + 0.230868i
\(496\) −26.6886 −1.19835
\(497\) 0 0
\(498\) −0.540194 0.603119i −0.0242067 0.0270264i
\(499\) −10.6345 18.4195i −0.476066 0.824571i 0.523558 0.851990i \(-0.324604\pi\)
−0.999624 + 0.0274192i \(0.991271\pi\)
\(500\) −7.71814 13.3682i −0.345166 0.597845i
\(501\) 5.54570 + 6.19170i 0.247764 + 0.276625i
\(502\) 0.189728 0.328618i 0.00846795 0.0146669i
\(503\) 16.3298 0.728110 0.364055 0.931377i \(-0.381392\pi\)
0.364055 + 0.931377i \(0.381392\pi\)
\(504\) 0 0
\(505\) 4.91437 0.218687
\(506\) −0.167746 + 0.290544i −0.00745722 + 0.0129163i
\(507\) 7.87873 24.0337i 0.349907 1.06737i
\(508\) 10.9277 + 18.9273i 0.484837 + 0.839762i
\(509\) −6.73089 11.6582i −0.298342 0.516743i 0.677415 0.735601i \(-0.263100\pi\)
−0.975757 + 0.218858i \(0.929767\pi\)
\(510\) −2.02140 + 0.424126i −0.0895092 + 0.0187806i
\(511\) 0 0
\(512\) 5.41890 0.239484
\(513\) 8.04076 5.74587i 0.355008 0.253687i
\(514\) −0.672168 −0.0296481
\(515\) 6.89659 11.9452i 0.303900 0.526370i
\(516\) −38.0972 + 7.99349i −1.67714 + 0.351894i
\(517\) −3.03768 5.26142i −0.133597 0.231397i
\(518\) 0 0
\(519\) −2.71486 + 8.28153i −0.119169 + 0.363519i
\(520\) −1.91155 + 3.31091i −0.0838272 + 0.145193i
\(521\) 1.42619 0.0624826 0.0312413 0.999512i \(-0.490054\pi\)
0.0312413 + 0.999512i \(0.490054\pi\)
\(522\) −1.05619 0.775859i −0.0462281 0.0339584i
\(523\) 7.71060 0.337161 0.168581 0.985688i \(-0.446082\pi\)
0.168581 + 0.985688i \(0.446082\pi\)
\(524\) 4.44301 7.69553i 0.194094 0.336181i
\(525\) 0 0
\(526\) −0.407928 0.706551i −0.0177865 0.0308071i
\(527\) 21.9961 + 38.0984i 0.958165 + 1.65959i
\(528\) −7.33994 8.19494i −0.319430 0.356639i
\(529\) 6.79254 11.7650i 0.295328 0.511523i
\(530\) 1.62074 0.0704005
\(531\) −26.3363 19.3462i −1.14290 0.839554i
\(532\) 0 0
\(533\) −19.4206 + 33.6374i −0.841198 + 1.45700i
\(534\) −0.0173599 + 0.0529556i −0.000751238 + 0.00229161i
\(535\) 22.5742 + 39.0996i 0.975966 + 1.69042i
\(536\) −0.454201 0.786699i −0.0196185 0.0339802i
\(537\) 27.7967 5.83226i 1.19952 0.251680i
\(538\) 1.02441 1.77432i 0.0441653 0.0764966i
\(539\) 0 0
\(540\) 2.67078 + 27.4888i 0.114932 + 1.18293i
\(541\) 28.0456 1.20577 0.602886 0.797827i \(-0.294017\pi\)
0.602886 + 0.797827i \(0.294017\pi\)
\(542\) −0.242608 + 0.420209i −0.0104209 + 0.0180495i
\(543\) −24.4685 + 5.13393i −1.05004 + 0.220318i
\(544\) −2.67759 4.63771i −0.114801 0.198840i
\(545\) 11.3210 + 19.6086i 0.484939 + 0.839939i
\(546\) 0 0
\(547\) 17.7305 30.7101i 0.758101 1.31307i −0.185717 0.982603i \(-0.559461\pi\)
0.943818 0.330466i \(-0.107206\pi\)
\(548\) 38.9807 1.66517
\(549\) 0.893471 8.09242i 0.0381324 0.345376i
\(550\) −0.229150 −0.00977099
\(551\) 6.07577 10.5235i 0.258836 0.448318i
\(552\) 0.968623 + 1.08145i 0.0412273 + 0.0460297i
\(553\) 0 0
\(554\) 0.335836 + 0.581685i 0.0142683 + 0.0247134i
\(555\) 13.0196 + 14.5362i 0.552651 + 0.617027i
\(556\) −2.62464 + 4.54601i −0.111310 + 0.192794i
\(557\) 35.0419 1.48477 0.742386 0.669972i \(-0.233694\pi\)
0.742386 + 0.669972i \(0.233694\pi\)
\(558\) −1.26203 + 0.553980i −0.0534258 + 0.0234518i
\(559\) 59.1763 2.50289
\(560\) 0 0
\(561\) −5.64899 + 17.2319i −0.238500 + 0.727533i
\(562\) 0.816308 + 1.41389i 0.0344339 + 0.0596412i
\(563\) 8.01311 + 13.8791i 0.337712 + 0.584935i 0.984002 0.178157i \(-0.0570135\pi\)
−0.646290 + 0.763092i \(0.723680\pi\)
\(564\) −12.8502 + 2.69619i −0.541089 + 0.113530i
\(565\) −5.19961 + 9.00599i −0.218749 + 0.378885i
\(566\) 0.206213 0.00866776
\(567\) 0 0
\(568\) 3.38439 0.142006
\(569\) −0.185651 + 0.321557i −0.00778290 + 0.0134804i −0.869891 0.493245i \(-0.835811\pi\)
0.862108 + 0.506725i \(0.169144\pi\)
\(570\) 0.587209 0.123207i 0.0245955 0.00516057i
\(571\) −14.6152 25.3142i −0.611626 1.05937i −0.990966 0.134110i \(-0.957182\pi\)
0.379340 0.925257i \(-0.376151\pi\)
\(572\) 8.38185 + 14.5178i 0.350463 + 0.607019i
\(573\) 1.53303 4.67643i 0.0640432 0.195361i
\(574\) 0 0
\(575\) −6.43065 −0.268177
\(576\) −21.6684 + 9.51155i −0.902848 + 0.396315i
\(577\) 15.0570 0.626833 0.313417 0.949616i \(-0.398526\pi\)
0.313417 + 0.949616i \(0.398526\pi\)
\(578\) −0.884279 + 1.53162i −0.0367811 + 0.0637068i
\(579\) 10.2025 + 11.3910i 0.424003 + 0.473393i
\(580\) 16.9793 + 29.4089i 0.705025 + 1.22114i
\(581\) 0 0
\(582\) 0.407107 + 0.454529i 0.0168751 + 0.0188408i
\(583\) 7.11501 12.3236i 0.294674 0.510390i
\(584\) 0.600615 0.0248536
\(585\) 4.60751 41.7315i 0.190497 1.72538i
\(586\) −1.16634 −0.0481811
\(587\) 0.835901 1.44782i 0.0345013 0.0597580i −0.848259 0.529581i \(-0.822349\pi\)
0.882760 + 0.469823i \(0.155682\pi\)
\(588\) 0 0
\(589\) −6.38977 11.0674i −0.263286 0.456025i
\(590\) −0.991973 1.71815i −0.0408389 0.0707350i
\(591\) −9.70220 + 2.03570i −0.399095 + 0.0837374i
\(592\) −8.39982 + 14.5489i −0.345231 + 0.597957i
\(593\) 10.8174 0.444218 0.222109 0.975022i \(-0.428706\pi\)
0.222109 + 0.975022i \(0.428706\pi\)
\(594\) −0.517188 0.235158i −0.0212205 0.00964867i
\(595\) 0 0
\(596\) −8.79221 + 15.2286i −0.360143 + 0.623786i
\(597\) −19.3501 + 4.06000i −0.791947 + 0.166165i
\(598\) −0.551116 0.954560i −0.0225368 0.0390349i
\(599\) −8.32007 14.4108i −0.339949 0.588809i 0.644474 0.764626i \(-0.277076\pi\)
−0.984423 + 0.175817i \(0.943743\pi\)
\(600\) −0.308902 + 0.942290i −0.0126109 + 0.0384688i
\(601\) −12.9011 + 22.3453i −0.526246 + 0.911485i 0.473286 + 0.880909i \(0.343068\pi\)
−0.999532 + 0.0305765i \(0.990266\pi\)
\(602\) 0 0
\(603\) 8.03989 + 5.90598i 0.327410 + 0.240510i
\(604\) −9.30663 −0.378681
\(605\) 11.2449 19.4768i 0.457171 0.791843i
\(606\) 0.145768 + 0.162748i 0.00592142 + 0.00661118i
\(607\) −18.9025 32.7400i −0.767227 1.32888i −0.939061 0.343750i \(-0.888303\pi\)
0.171834 0.985126i \(-0.445031\pi\)
\(608\) 0.777828 + 1.34724i 0.0315451 + 0.0546377i
\(609\) 0 0
\(610\) 0.247143 0.428065i 0.0100065 0.0173318i
\(611\) 19.9601 0.807499
\(612\) 31.5853 + 23.2021i 1.27676 + 0.937888i
\(613\) −12.9544 −0.523222 −0.261611 0.965173i \(-0.584254\pi\)
−0.261611 + 0.965173i \(0.584254\pi\)
\(614\) 0.793745 1.37481i 0.0320330 0.0554827i
\(615\) −10.6255 + 32.4126i −0.428462 + 1.30700i
\(616\) 0 0
\(617\) 16.2202 + 28.0941i 0.652999 + 1.13103i 0.982391 + 0.186834i \(0.0598227\pi\)
−0.329393 + 0.944193i \(0.606844\pi\)
\(618\) 0.600151 0.125922i 0.0241416 0.00506534i
\(619\) −16.5987 + 28.7498i −0.667157 + 1.15555i 0.311538 + 0.950234i \(0.399156\pi\)
−0.978696 + 0.205317i \(0.934178\pi\)
\(620\) 35.7136 1.43429
\(621\) −14.5139 6.59926i −0.582422 0.264819i
\(622\) −0.122453 −0.00490993
\(623\) 0 0
\(624\) 35.3741 7.42212i 1.41610 0.297122i
\(625\) 15.5433 + 26.9218i 0.621732 + 1.07687i
\(626\) 0.157574 + 0.272925i 0.00629791 + 0.0109083i
\(627\) 1.64101 5.00581i 0.0655355 0.199913i
\(628\) 4.06342 7.03804i 0.162148 0.280848i
\(629\) 27.6917 1.10414
\(630\) 0 0
\(631\) 32.2773 1.28494 0.642470 0.766311i \(-0.277910\pi\)
0.642470 + 0.766311i \(0.277910\pi\)
\(632\) 0.111122 0.192469i 0.00442020 0.00765601i
\(633\) −24.7108 27.5893i −0.982167 1.09657i
\(634\) 0.884900 + 1.53269i 0.0351439 + 0.0608709i
\(635\) −14.5886 25.2682i −0.578931 1.00274i
\(636\) −20.5182 22.9083i −0.813601 0.908374i
\(637\) 0 0
\(638\) −0.698568 −0.0276566
\(639\) −34.0326 + 14.9390i −1.34631 + 0.590977i
\(640\) −5.79428 −0.229039
\(641\) −21.5407 + 37.3096i −0.850806 + 1.47364i 0.0296762 + 0.999560i \(0.490552\pi\)
−0.880482 + 0.474079i \(0.842781\pi\)
\(642\) −0.625265 + 1.90734i −0.0246772 + 0.0752766i
\(643\) −3.20088 5.54409i −0.126230 0.218638i 0.795983 0.605319i \(-0.206955\pi\)
−0.922213 + 0.386682i \(0.873621\pi\)
\(644\) 0 0
\(645\) 50.8604 10.6714i 2.00263 0.420187i
\(646\) 0.425709 0.737350i 0.0167493 0.0290107i
\(647\) 3.88807 0.152856 0.0764278 0.997075i \(-0.475649\pi\)
0.0764278 + 0.997075i \(0.475649\pi\)
\(648\) −1.66418 + 1.80973i −0.0653753 + 0.0710931i
\(649\) −17.4189 −0.683753
\(650\) 0.376427 0.651991i 0.0147647 0.0255732i
\(651\) 0 0
\(652\) −12.0939 20.9473i −0.473634 0.820358i
\(653\) −7.55174 13.0800i −0.295522 0.511860i 0.679584 0.733598i \(-0.262160\pi\)
−0.975106 + 0.221738i \(0.928827\pi\)
\(654\) −0.313572 + 0.956536i −0.0122616 + 0.0374035i
\(655\) −5.93150 + 10.2737i −0.231763 + 0.401425i
\(656\) −29.3646 −1.14650
\(657\) −6.03964 + 2.65116i −0.235629 + 0.103432i
\(658\) 0 0
\(659\) −7.13002 + 12.3496i −0.277746 + 0.481070i −0.970824 0.239792i \(-0.922921\pi\)
0.693078 + 0.720862i \(0.256254\pi\)
\(660\) 9.82201 + 10.9661i 0.382321 + 0.426856i
\(661\) 9.70965 + 16.8176i 0.377662 + 0.654129i 0.990722 0.135907i \(-0.0433949\pi\)
−0.613060 + 0.790036i \(0.710062\pi\)
\(662\) −0.00551516 0.00955254i −0.000214353 0.000371270i
\(663\) −39.7497 44.3799i −1.54375 1.72357i
\(664\) −0.933832 + 1.61744i −0.0362397 + 0.0627690i
\(665\) 0 0
\(666\) −0.0952089 + 0.862333i −0.00368927 + 0.0334147i
\(667\) −19.6039 −0.759067
\(668\) 4.78781 8.29273i 0.185246 0.320855i
\(669\) −3.86735 + 11.7972i −0.149521 + 0.456105i
\(670\) 0.302828 + 0.524513i 0.0116993 + 0.0202637i
\(671\) −2.16991 3.75839i −0.0837683 0.145091i
\(672\) 0 0
\(673\) −2.96563 + 5.13663i −0.114317 + 0.198002i −0.917506 0.397721i \(-0.869801\pi\)
0.803190 + 0.595723i \(0.203135\pi\)
\(674\) −0.619024 −0.0238439
\(675\) −1.05310 10.8390i −0.0405339 0.417192i
\(676\) −29.1366 −1.12064
\(677\) −18.4913 + 32.0278i −0.710678 + 1.23093i 0.253925 + 0.967224i \(0.418278\pi\)
−0.964603 + 0.263706i \(0.915055\pi\)
\(678\) −0.452477 + 0.0949379i −0.0173773 + 0.00364607i
\(679\) 0 0
\(680\) 2.38215 + 4.12601i 0.0913513 + 0.158225i
\(681\) 7.43968 22.6944i 0.285089 0.869650i
\(682\) −0.367336 + 0.636244i −0.0140660 + 0.0243630i
\(683\) 13.1360 0.502635 0.251317 0.967905i \(-0.419136\pi\)
0.251317 + 0.967905i \(0.419136\pi\)
\(684\) −9.17540 6.74011i −0.350830 0.257714i
\(685\) −52.0398 −1.98834
\(686\) 0 0
\(687\) 30.5010 + 34.0539i 1.16369 + 1.29924i
\(688\) 22.3692 + 38.7446i 0.852818 + 1.47712i
\(689\) 23.3758 + 40.4881i 0.890547 + 1.54247i
\(690\) −0.645807 0.721034i −0.0245855 0.0274493i
\(691\) −7.38292 + 12.7876i −0.280860 + 0.486463i −0.971597 0.236643i \(-0.923953\pi\)
0.690737 + 0.723106i \(0.257286\pi\)
\(692\) 10.0399 0.381659
\(693\) 0 0
\(694\) −0.397915 −0.0151046
\(695\) 3.50394 6.06900i 0.132912 0.230210i
\(696\) −0.941693 + 2.87259i −0.0356948 + 0.108885i
\(697\) 24.2016 + 41.9184i 0.916702 + 1.58777i
\(698\) 0.932003 + 1.61428i 0.0352768 + 0.0611012i
\(699\) 21.4344 4.49731i 0.810722 0.170104i
\(700\) 0 0
\(701\) −30.4627 −1.15056 −0.575281 0.817956i \(-0.695107\pi\)
−0.575281 + 0.817956i \(0.695107\pi\)
\(702\) 1.51868 1.08524i 0.0573187 0.0409596i
\(703\) −8.04433 −0.303398
\(704\) −6.30697 + 10.9240i −0.237703 + 0.411713i
\(705\) 17.1552 3.59946i 0.646101 0.135564i
\(706\) −0.826969 1.43235i −0.0311234 0.0539073i
\(707\) 0 0
\(708\) −11.7269 + 35.7724i −0.440725 + 1.34441i
\(709\) −7.05152 + 12.2136i −0.264825 + 0.458691i −0.967518 0.252803i \(-0.918648\pi\)
0.702693 + 0.711494i \(0.251981\pi\)
\(710\) −2.25646 −0.0846836
\(711\) −0.267843 + 2.42593i −0.0100449 + 0.0909794i
\(712\) 0.128549 0.00481758
\(713\) −10.3086 + 17.8549i −0.386058 + 0.668673i
\(714\) 0 0
\(715\) −11.1899 19.3815i −0.418479 0.724827i
\(716\) −16.3596 28.3356i −0.611386 1.05895i
\(717\) −17.8340 19.9114i −0.666023 0.743604i
\(718\) 0.719212 1.24571i 0.0268408 0.0464896i
\(719\) 14.9958 0.559249 0.279624 0.960109i \(-0.409790\pi\)
0.279624 + 0.960109i \(0.409790\pi\)
\(720\) 29.0646 12.7582i 1.08317 0.475471i
\(721\) 0 0
\(722\) 0.525886 0.910861i 0.0195715 0.0338987i
\(723\) −0.636606 + 1.94193i −0.0236756 + 0.0722213i
\(724\) 14.4008 + 24.9429i 0.535200 + 0.926994i
\(725\) −6.69501 11.5961i −0.248646 0.430668i
\(726\) 0.978549 0.205317i 0.0363174 0.00762003i
\(727\) −13.0527 + 22.6080i −0.484099 + 0.838485i −0.999833 0.0182642i \(-0.994186\pi\)
0.515734 + 0.856749i \(0.327519\pi\)
\(728\) 0 0
\(729\) 8.74633 25.5441i 0.323938 0.946078i
\(730\) −0.400446 −0.0148212
\(731\) 36.8723 63.8648i 1.36377 2.36212i
\(732\) −9.17925 + 1.92597i −0.339275 + 0.0711859i
\(733\) −14.1911 24.5796i −0.524159 0.907869i −0.999604 0.0281244i \(-0.991047\pi\)
0.475446 0.879745i \(-0.342287\pi\)
\(734\) 1.19784 + 2.07473i 0.0442132 + 0.0765796i
\(735\) 0 0
\(736\) 1.25486 2.17348i 0.0462548 0.0801156i
\(737\) 5.31763 0.195877
\(738\) −1.38857 + 0.609527i −0.0511139 + 0.0224370i
\(739\) 46.5865 1.71371 0.856857 0.515555i \(-0.172414\pi\)
0.856857 + 0.515555i \(0.172414\pi\)
\(740\) 11.2403 19.4688i 0.413202 0.715686i
\(741\) 11.5471 + 12.8922i 0.424194 + 0.473606i
\(742\) 0 0
\(743\) −0.169513 0.293606i −0.00621884 0.0107713i 0.862899 0.505376i \(-0.168646\pi\)
−0.869118 + 0.494605i \(0.835313\pi\)
\(744\) 2.12112 + 2.36820i 0.0777642 + 0.0868225i
\(745\) 11.7377 20.3304i 0.430038 0.744847i
\(746\) 0.0771683 0.00282533
\(747\) 2.25086 20.3866i 0.0823546 0.745908i
\(748\) 20.8907 0.763839
\(749\) 0 0
\(750\) −0.285398 + 0.870593i −0.0104213 + 0.0317896i
\(751\) 18.1831 + 31.4940i 0.663510 + 1.14923i 0.979687 + 0.200533i \(0.0642673\pi\)
−0.316177 + 0.948700i \(0.602399\pi\)
\(752\) 7.54511 + 13.0685i 0.275142 + 0.476560i
\(753\) 9.40752 1.97387i 0.342829 0.0719317i
\(754\) 1.14754 1.98760i 0.0417911 0.0723843i
\(755\) 12.4245 0.452174
\(756\) 0 0
\(757\) −27.4703 −0.998424 −0.499212 0.866480i \(-0.666377\pi\)
−0.499212 + 0.866480i \(0.666377\pi\)
\(758\) 0.750812 1.30044i 0.0272707 0.0472343i
\(759\) −8.31757 + 1.74518i −0.301909 + 0.0633459i
\(760\) −0.692005 1.19859i −0.0251017 0.0434773i
\(761\) −16.5178 28.6097i −0.598771 1.03710i −0.993003 0.118091i \(-0.962323\pi\)
0.394232 0.919011i \(-0.371011\pi\)
\(762\) 0.404079 1.23262i 0.0146382 0.0446532i
\(763\) 0 0
\(764\) −5.66934 −0.205110
\(765\) −42.1669 30.9751i −1.52455 1.11991i
\(766\) 1.57534 0.0569194
\(767\) 28.6143 49.5614i 1.03320 1.78956i
\(768\) 18.0588 + 20.1623i 0.651639 + 0.727546i
\(769\) −1.28876 2.23219i −0.0464738 0.0804949i 0.841853 0.539707i \(-0.181465\pi\)
−0.888327 + 0.459212i \(0.848132\pi\)
\(770\) 0 0
\(771\) −11.3603 12.6836i −0.409132 0.456790i
\(772\) 8.80822 15.2563i 0.317015 0.549086i
\(773\) 6.72973 0.242051 0.121026 0.992649i \(-0.461382\pi\)
0.121026 + 0.992649i \(0.461382\pi\)
\(774\) 1.86200 + 1.36780i 0.0669283 + 0.0491645i
\(775\) −14.0820 −0.505842
\(776\) 0.703765 1.21896i 0.0252637 0.0437580i
\(777\) 0 0
\(778\) −0.539302 0.934099i −0.0193349 0.0334891i
\(779\) −7.03047 12.1771i −0.251893 0.436291i
\(780\) −47.3361 + 9.93197i −1.69491 + 0.355622i
\(781\) −9.90581 + 17.1574i −0.354458 + 0.613939i
\(782\) −1.37358 −0.0491193
\(783\) &