Properties

Label 441.2.g.h.67.5
Level $441$
Weight $2$
Character 441.67
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.g (of order \(3\), degree \(2\), not 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 67.5
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.h.79.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0341870 + 0.0592136i) q^{2} +(-1.15559 + 1.29020i) q^{3} +(0.997662 + 1.72800i) q^{4} -2.66379 q^{5} +(-0.0368912 - 0.112535i) q^{6} -0.273176 q^{8} +(-0.329225 - 2.98188i) q^{9} +O(q^{10})\) \(q+(-0.0341870 + 0.0592136i) q^{2} +(-1.15559 + 1.29020i) q^{3} +(0.997662 + 1.72800i) q^{4} -2.66379 q^{5} +(-0.0368912 - 0.112535i) q^{6} -0.273176 q^{8} +(-0.329225 - 2.98188i) q^{9} +(0.0910670 - 0.157733i) q^{10} -1.59913 q^{11} +(-3.38235 - 0.709679i) q^{12} +(-2.62690 + 4.54992i) q^{13} +(3.07825 - 3.43682i) q^{15} +(-1.98599 + 3.43983i) q^{16} +(3.27360 - 5.67005i) q^{17} +(0.187823 + 0.0824469i) q^{18} +(-0.950968 - 1.64713i) q^{19} +(-2.65756 - 4.60304i) q^{20} +(0.0546693 - 0.0946900i) q^{22} -3.06837 q^{23} +(0.315680 - 0.352452i) q^{24} +2.09578 q^{25} +(-0.179612 - 0.311096i) q^{26} +(4.22767 + 3.02106i) q^{27} +(-3.19452 - 5.53306i) q^{29} +(0.0982704 + 0.299769i) q^{30} +(-3.35961 - 5.81902i) q^{31} +(-0.408966 - 0.708350i) q^{32} +(1.84793 - 2.06319i) q^{33} +(0.223829 + 0.387684i) q^{34} +(4.82424 - 3.54381i) q^{36} +(-2.11477 - 3.66290i) q^{37} +0.130043 q^{38} +(-2.83469 - 8.64707i) q^{39} +0.727684 q^{40} +(-3.69648 + 6.40249i) q^{41} +(5.63176 + 9.75450i) q^{43} +(-1.59539 - 2.76329i) q^{44} +(0.876986 + 7.94311i) q^{45} +(0.104898 - 0.181689i) q^{46} +(-1.89959 + 3.29018i) q^{47} +(-2.14308 - 6.53735i) q^{48} +(-0.0716485 + 0.124099i) q^{50} +(3.53255 + 10.7758i) q^{51} -10.4830 q^{52} +(-4.44931 + 7.70643i) q^{53} +(-0.323419 + 0.147054i) q^{54} +4.25974 q^{55} +(3.22405 + 0.676463i) q^{57} +0.436843 q^{58} +(5.44639 + 9.43343i) q^{59} +(9.00989 + 1.89044i) q^{60} +(-1.35693 + 2.35027i) q^{61} +0.459420 q^{62} -7.88802 q^{64} +(6.99751 - 12.1200i) q^{65} +(0.0589937 + 0.179957i) q^{66} +(1.66267 + 2.87982i) q^{67} +13.0638 q^{68} +(3.54578 - 3.95881i) q^{69} -12.3890 q^{71} +(0.0899364 + 0.814579i) q^{72} +(-1.09932 + 1.90407i) q^{73} +0.289191 q^{74} +(-2.42187 + 2.70398i) q^{75} +(1.89749 - 3.28655i) q^{76} +(0.608933 + 0.127765i) q^{78} +(-0.406778 + 0.704560i) q^{79} +(5.29025 - 9.16298i) q^{80} +(-8.78322 + 1.96342i) q^{81} +(-0.252743 - 0.437764i) q^{82} +(-3.41842 - 5.92088i) q^{83} +(-8.72020 + 15.1038i) q^{85} -0.770132 q^{86} +(10.8303 + 2.27239i) q^{87} +0.436843 q^{88} +(-0.235286 - 0.407527i) q^{89} +(-0.500321 - 0.219621i) q^{90} +(-3.06120 - 5.30216i) q^{92} +(11.3900 + 2.38983i) q^{93} +(-0.129882 - 0.224963i) q^{94} +(2.53318 + 4.38760i) q^{95} +(1.38651 + 0.290914i) q^{96} +(2.57623 + 4.46216i) q^{97} +(0.526472 + 4.76840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} - 40q^{11} + 4q^{15} - 12q^{16} + 28q^{18} - 64q^{23} + 24q^{25} + 16q^{29} + 84q^{30} + 48q^{32} - 4q^{36} - 12q^{37} - 40q^{39} + 56q^{44} + 24q^{46} - 4q^{50} - 8q^{51} + 32q^{53} - 12q^{57} + 56q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} - 168q^{72} - 136q^{74} - 60q^{78} + 12q^{79} - 40q^{81} + 12q^{85} - 152q^{86} + 16q^{92} + 112q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

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

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

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 \(0.174362\pi\)
\(3\) −1.15559 + 1.29020i −0.667180 + 0.744897i
\(4\) 0.997662 + 1.72800i 0.498831 + 0.864001i
\(5\) −2.66379 −1.19128 −0.595642 0.803250i \(-0.703102\pi\)
−0.595642 + 0.803250i \(0.703102\pi\)
\(6\) −0.0368912 0.112535i −0.0150608 0.0459421i
\(7\) 0 0
\(8\) −0.273176 −0.0965824
\(9\) −0.329225 2.98188i −0.109742 0.993960i
\(10\) 0.0910670 0.157733i 0.0287979 0.0498794i
\(11\) −1.59913 −0.482155 −0.241077 0.970506i \(-0.577501\pi\)
−0.241077 + 0.970506i \(0.577501\pi\)
\(12\) −3.38235 0.709679i −0.976402 0.204867i
\(13\) −2.62690 + 4.54992i −0.728571 + 1.26192i 0.228916 + 0.973446i \(0.426482\pi\)
−0.957487 + 0.288476i \(0.906852\pi\)
\(14\) 0 0
\(15\) 3.07825 3.43682i 0.794801 0.887383i
\(16\) −1.98599 + 3.43983i −0.496496 + 0.859957i
\(17\) 3.27360 5.67005i 0.793966 1.37519i −0.129528 0.991576i \(-0.541346\pi\)
0.923494 0.383613i \(-0.125320\pi\)
\(18\) 0.187823 + 0.0824469i 0.0442703 + 0.0194329i
\(19\) −0.950968 1.64713i −0.218167 0.377877i 0.736081 0.676894i \(-0.236674\pi\)
−0.954248 + 0.299017i \(0.903341\pi\)
\(20\) −2.65756 4.60304i −0.594249 1.02927i
\(21\) 0 0
\(22\) 0.0546693 0.0946900i 0.0116555 0.0201880i
\(23\) −3.06837 −0.639800 −0.319900 0.947451i \(-0.603649\pi\)
−0.319900 + 0.947451i \(0.603649\pi\)
\(24\) 0.315680 0.352452i 0.0644378 0.0719439i
\(25\) 2.09578 0.419157
\(26\) −0.179612 0.311096i −0.0352247 0.0610110i
\(27\) 4.22767 + 3.02106i 0.813615 + 0.581404i
\(28\) 0 0
\(29\) −3.19452 5.53306i −0.593207 1.02746i −0.993797 0.111207i \(-0.964528\pi\)
0.400591 0.916257i \(-0.368805\pi\)
\(30\) 0.0982704 + 0.299769i 0.0179416 + 0.0547300i
\(31\) −3.35961 5.81902i −0.603405 1.04513i −0.992301 0.123846i \(-0.960477\pi\)
0.388897 0.921281i \(-0.372856\pi\)
\(32\) −0.408966 0.708350i −0.0722957 0.125220i
\(33\) 1.84793 2.06319i 0.321684 0.359155i
\(34\) 0.223829 + 0.387684i 0.0383864 + 0.0664872i
\(35\) 0 0
\(36\) 4.82424 3.54381i 0.804040 0.590635i
\(37\) −2.11477 3.66290i −0.347667 0.602176i 0.638168 0.769897i \(-0.279693\pi\)
−0.985835 + 0.167721i \(0.946359\pi\)
\(38\) 0.130043 0.0210958
\(39\) −2.83469 8.64707i −0.453913 1.38464i
\(40\) 0.727684 0.115057
\(41\) −3.69648 + 6.40249i −0.577293 + 0.999901i 0.418495 + 0.908219i \(0.362558\pi\)
−0.995788 + 0.0916820i \(0.970776\pi\)
\(42\) 0 0
\(43\) 5.63176 + 9.75450i 0.858836 + 1.48755i 0.873040 + 0.487648i \(0.162145\pi\)
−0.0142043 + 0.999899i \(0.504522\pi\)
\(44\) −1.59539 2.76329i −0.240514 0.416582i
\(45\) 0.876986 + 7.94311i 0.130733 + 1.18409i
\(46\) 0.104898 0.181689i 0.0154664 0.0267887i
\(47\) −1.89959 + 3.29018i −0.277083 + 0.479922i −0.970659 0.240462i \(-0.922701\pi\)
0.693575 + 0.720384i \(0.256034\pi\)
\(48\) −2.14308 6.53735i −0.309327 0.943585i
\(49\) 0 0
\(50\) −0.0716485 + 0.124099i −0.0101326 + 0.0175502i
\(51\) 3.53255 + 10.7758i 0.494655 + 1.50892i
\(52\) −10.4830 −1.45374
\(53\) −4.44931 + 7.70643i −0.611160 + 1.05856i 0.379885 + 0.925034i \(0.375963\pi\)
−0.991045 + 0.133527i \(0.957370\pi\)
\(54\) −0.323419 + 0.147054i −0.0440118 + 0.0200116i
\(55\) 4.25974 0.574383
\(56\) 0 0
\(57\) 3.22405 + 0.676463i 0.427036 + 0.0895997i
\(58\) 0.436843 0.0573604
\(59\) 5.44639 + 9.43343i 0.709060 + 1.22813i 0.965206 + 0.261490i \(0.0842138\pi\)
−0.256146 + 0.966638i \(0.582453\pi\)
\(60\) 9.00989 + 1.89044i 1.16317 + 0.244054i
\(61\) −1.35693 + 2.35027i −0.173737 + 0.300922i −0.939724 0.341935i \(-0.888918\pi\)
0.765986 + 0.642857i \(0.222251\pi\)
\(62\) 0.459420 0.0583465
\(63\) 0 0
\(64\) −7.88802 −0.986002
\(65\) 6.99751 12.1200i 0.867935 1.50331i
\(66\) 0.0589937 + 0.179957i 0.00726162 + 0.0221512i
\(67\) 1.66267 + 2.87982i 0.203127 + 0.351826i 0.949534 0.313663i \(-0.101556\pi\)
−0.746407 + 0.665489i \(0.768223\pi\)
\(68\) 13.0638 1.58422
\(69\) 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 \(0.762890\pi\)
\(72\) 0.0899364 + 0.814579i 0.0105991 + 0.0959990i
\(73\) −1.09932 + 1.90407i −0.128665 + 0.222855i −0.923160 0.384417i \(-0.874403\pi\)
0.794494 + 0.607271i \(0.207736\pi\)
\(74\) 0.289191 0.0336178
\(75\) −2.42187 + 2.70398i −0.279653 + 0.312228i
\(76\) 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 \(0.181240\pi\)
\(80\) 5.29025 9.16298i 0.591468 1.02445i
\(81\) −8.78322 + 1.96342i −0.975914 + 0.218158i
\(82\) −0.252743 0.437764i −0.0279108 0.0483429i
\(83\) −3.41842 5.92088i −0.375220 0.649901i 0.615140 0.788418i \(-0.289100\pi\)
−0.990360 + 0.138517i \(0.955766\pi\)
\(84\) 0 0
\(85\) −8.72020 + 15.1038i −0.945838 + 1.63824i
\(86\) −0.770132 −0.0830455
\(87\) 10.8303 + 2.27239i 1.16113 + 0.243626i
\(88\) 0.436843 0.0465677
\(89\) −0.235286 0.407527i −0.0249403 0.0431978i 0.853286 0.521443i \(-0.174606\pi\)
−0.878226 + 0.478246i \(0.841273\pi\)
\(90\) −0.500321 0.219621i −0.0527385 0.0231501i
\(91\) 0 0
\(92\) −3.06120 5.30216i −0.319152 0.552788i
\(93\) 11.3900 + 2.38983i 1.18109 + 0.247814i
\(94\) −0.129882 0.224963i −0.0133963 0.0232031i
\(95\) 2.53318 + 4.38760i 0.259899 + 0.450158i
\(96\) 1.38651 + 0.290914i 0.141510 + 0.0296913i
\(97\) 2.57623 + 4.46216i 0.261576 + 0.453064i 0.966661 0.256059i \(-0.0824243\pi\)
−0.705085 + 0.709123i \(0.749091\pi\)
\(98\) 0 0
\(99\) 0.526472 + 4.76840i 0.0529125 + 0.479243i
\(100\) 2.09088 + 3.62152i 0.209088 + 0.362152i
\(101\) −1.84488 −0.183572 −0.0917862 0.995779i \(-0.529258\pi\)
−0.0917862 + 0.995779i \(0.529258\pi\)
\(102\) −0.758844 0.159219i −0.0751368 0.0157650i
\(103\) 5.17802 0.510206 0.255103 0.966914i \(-0.417891\pi\)
0.255103 + 0.966914i \(0.417891\pi\)
\(104\) 0.717607 1.24293i 0.0703671 0.121879i
\(105\) 0 0
\(106\) −0.304217 0.526920i −0.0295482 0.0511790i
\(107\) 8.47445 + 14.6782i 0.819256 + 1.41899i 0.906231 + 0.422782i \(0.138946\pi\)
−0.0869755 + 0.996210i \(0.527720\pi\)
\(108\) −1.00262 + 10.3194i −0.0964773 + 0.992987i
\(109\) 4.24996 7.36115i 0.407073 0.705070i −0.587488 0.809233i \(-0.699883\pi\)
0.994560 + 0.104163i \(0.0332163\pi\)
\(110\) −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 −0.943112 0.332474i \(-0.892116\pi\)
0.759487 + 0.650522i \(0.225450\pi\)
\(114\) −0.150276 + 0.167781i −0.0140747 + 0.0157142i
\(115\) 8.17351 0.762183
\(116\) 6.37410 11.0403i 0.591820 1.02506i
\(117\) 14.4322 + 6.33515i 1.33425 + 0.585685i
\(118\) −0.744783 −0.0685628
\(119\) 0 0
\(120\) −0.840905 + 0.938858i −0.0767637 + 0.0857056i
\(121\) −8.44279 −0.767527
\(122\) −0.0927788 0.160698i −0.00839980 0.0145489i
\(123\) −3.98887 12.1678i −0.359664 1.09714i
\(124\) 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
\(129\) −19.0933 4.00611i −1.68107 0.352718i
\(130\) 0.478448 + 0.828696i 0.0419626 + 0.0726814i
\(131\) −4.45342 −0.389097 −0.194549 0.980893i \(-0.562324\pi\)
−0.194549 + 0.980893i \(0.562324\pi\)
\(132\) 5.40881 + 1.13487i 0.470777 + 0.0987774i
\(133\) 0 0
\(134\) −0.227366 −0.0196414
\(135\) −11.2616 8.04749i −0.969246 0.692617i
\(136\) −0.894271 + 1.54892i −0.0766831 + 0.132819i
\(137\) −19.5360 −1.66907 −0.834537 0.550952i \(-0.814265\pi\)
−0.834537 + 0.550952i \(0.814265\pi\)
\(138\) 0.113196 + 0.345298i 0.00963588 + 0.0293937i
\(139\) −1.31540 + 2.27833i −0.111570 + 0.193246i −0.916404 0.400256i \(-0.868921\pi\)
0.804833 + 0.593501i \(0.202255\pi\)
\(140\) 0 0
\(141\) −2.04984 6.25295i −0.172628 0.526593i
\(142\) 0.423544 0.733599i 0.0355430 0.0615623i
\(143\) 4.20075 7.27590i 0.351284 0.608442i
\(144\) 10.9110 + 4.78950i 0.909249 + 0.399125i
\(145\) 8.50952 + 14.7389i 0.706677 + 1.22400i
\(146\) −0.0751647 0.130189i −0.00622067 0.0107745i
\(147\) 0 0
\(148\) 4.21966 7.30867i 0.346854 0.600769i
\(149\) −8.81281 −0.721973 −0.360987 0.932571i \(-0.617560\pi\)
−0.360987 + 0.932571i \(0.617560\pi\)
\(150\) −0.0773159 0.235848i −0.00631282 0.0192569i
\(151\) 4.66422 0.379569 0.189784 0.981826i \(-0.439221\pi\)
0.189784 + 0.981826i \(0.439221\pi\)
\(152\) 0.259782 + 0.449956i 0.0210711 + 0.0364962i
\(153\) −17.9852 7.89478i −1.45401 0.638255i
\(154\) 0 0
\(155\) 8.94931 + 15.5007i 0.718826 + 1.24504i
\(156\) 12.1141 13.5252i 0.969904 1.08288i
\(157\) 2.03647 + 3.52727i 0.162528 + 0.281506i 0.935775 0.352599i \(-0.114702\pi\)
−0.773247 + 0.634105i \(0.781369\pi\)
\(158\) −0.0278130 0.0481736i −0.00221269 0.00383249i
\(159\) −4.80125 14.6460i −0.380764 1.16150i
\(160\) 1.08940 + 1.88690i 0.0861246 + 0.149172i
\(161\) 0 0
\(162\) 0.184011 0.587210i 0.0144573 0.0461355i
\(163\) 6.06112 + 10.4982i 0.474744 + 0.822280i 0.999582 0.0289220i \(-0.00920745\pi\)
−0.524838 + 0.851202i \(0.675874\pi\)
\(164\) −14.7514 −1.15189
\(165\) −4.92251 + 5.49591i −0.383217 + 0.427856i
\(166\) 0.467462 0.0362821
\(167\) 2.39951 4.15608i 0.185680 0.321607i −0.758126 0.652109i \(-0.773885\pi\)
0.943805 + 0.330502i \(0.107218\pi\)
\(168\) 0 0
\(169\) −7.30121 12.6461i −0.561631 0.972774i
\(170\) −0.596235 1.03271i −0.0457291 0.0792051i
\(171\) −4.59845 + 3.37795i −0.351652 + 0.258318i
\(172\) −11.2372 + 19.4634i −0.856828 + 1.48407i
\(173\) −2.51585 + 4.35759i −0.191277 + 0.331301i −0.945674 0.325118i \(-0.894596\pi\)
0.754397 + 0.656419i \(0.227929\pi\)
\(174\) −0.504812 + 0.563615i −0.0382697 + 0.0427275i
\(175\) 0 0
\(176\) 3.17584 5.50072i 0.239388 0.414632i
\(177\) −18.4648 3.87425i −1.38790 0.291206i
\(178\) 0.0321749 0.00241161
\(179\) 8.19896 14.2010i 0.612819 1.06143i −0.377944 0.925828i \(-0.623369\pi\)
0.990763 0.135605i \(-0.0432977\pi\)
\(180\) −12.8508 + 9.43997i −0.957840 + 0.703614i
\(181\) −14.4345 −1.07291 −0.536454 0.843930i \(-0.680237\pi\)
−0.536454 + 0.843930i \(0.680237\pi\)
\(182\) 0 0
\(183\) −1.46426 4.46666i −0.108242 0.330185i
\(184\) 0.838207 0.0617934
\(185\) 5.63332 + 9.75719i 0.414170 + 0.717363i
\(186\) −0.530902 + 0.592744i −0.0389276 + 0.0434621i
\(187\) −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 \(0.199445\pi\)
\(192\) 9.11531 10.1771i 0.657841 0.734470i
\(193\) −4.41443 7.64601i −0.317758 0.550372i 0.662262 0.749272i \(-0.269596\pi\)
−0.980020 + 0.198900i \(0.936263\pi\)
\(194\) −0.352294 −0.0252932
\(195\) 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 \(0.434641\pi\)
\(198\) −0.300353 0.131843i −0.0213452 0.00936968i
\(199\) 5.70752 9.88572i 0.404596 0.700780i −0.589679 0.807638i \(-0.700746\pi\)
0.994274 + 0.106858i \(0.0340789\pi\)
\(200\) −0.572518 −0.0404832
\(201\) −5.63690 1.18272i −0.397596 0.0834229i
\(202\) 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
\(206\) −0.177021 + 0.306609i −0.0123336 + 0.0213625i
\(207\) 1.01019 + 9.14952i 0.0702127 + 0.635936i
\(208\) −10.4340 18.0722i −0.723466 1.25308i
\(209\) 1.52072 + 2.63396i 0.105190 + 0.182195i
\(210\) 0 0
\(211\) 10.6919 18.5189i 0.736059 1.27489i −0.218199 0.975904i \(-0.570018\pi\)
0.954257 0.298986i \(-0.0966486\pi\)
\(212\) −17.7556 −1.21946
\(213\) 14.3166 15.9843i 0.980960 1.09523i
\(214\) −1.15886 −0.0792183
\(215\) −15.0018 25.9840i −1.02312 1.77209i
\(216\) −1.15490 0.825283i −0.0785809 0.0561534i
\(217\) 0 0
\(218\) 0.290587 + 0.503311i 0.0196810 + 0.0340885i
\(219\) −1.18627 3.61867i −0.0801609 0.244527i
\(220\) 4.24978 + 7.36084i 0.286520 + 0.496268i
\(221\) 17.1989 + 29.7893i 1.15692 + 2.00385i
\(222\) −0.334186 + 0.373114i −0.0224291 + 0.0250418i
\(223\) −3.58387 6.20744i −0.239994 0.415681i 0.720719 0.693228i \(-0.243812\pi\)
−0.960712 + 0.277547i \(0.910479\pi\)
\(224\) 0 0
\(225\) −0.689984 6.24938i −0.0459989 0.416625i
\(226\) −0.133463 0.231165i −0.00887784 0.0153769i
\(227\) −13.7887 −0.915187 −0.457593 0.889162i \(-0.651288\pi\)
−0.457593 + 0.889162i \(0.651288\pi\)
\(228\) 2.04758 + 6.24604i 0.135604 + 0.413654i
\(229\) −26.3943 −1.74418 −0.872092 0.489341i \(-0.837237\pi\)
−0.872092 + 0.489341i \(0.837237\pi\)
\(230\) −0.279428 + 0.483983i −0.0184249 + 0.0319129i
\(231\) 0 0
\(232\) 0.872666 + 1.51150i 0.0572933 + 0.0992349i
\(233\) 6.32230 + 10.9505i 0.414187 + 0.717394i 0.995343 0.0963989i \(-0.0307324\pi\)
−0.581155 + 0.813793i \(0.697399\pi\)
\(234\) −0.868520 + 0.638001i −0.0567769 + 0.0417074i
\(235\) 5.06010 8.76436i 0.330085 0.571724i
\(236\) −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 −0.500867 0.865524i \(-0.666985\pi\)
0.999999 + 0.00100121i \(0.000318696\pi\)
\(240\) 5.70871 + 17.4141i 0.368496 + 1.12408i
\(241\) 1.17988 0.0760029 0.0380015 0.999278i \(-0.487901\pi\)
0.0380015 + 0.999278i \(0.487901\pi\)
\(242\) 0.288634 0.499928i 0.0185541 0.0321366i
\(243\) 7.61660 13.6010i 0.488605 0.872505i
\(244\) −5.41504 −0.346662
\(245\) 0 0
\(246\) 0.856869 + 0.179787i 0.0546320 + 0.0114628i
\(247\) 9.99240 0.635801
\(248\) 0.917767 + 1.58962i 0.0582783 + 0.100941i
\(249\) 11.5894 + 2.43166i 0.734449 + 0.154101i
\(250\) −0.264478 + 0.458090i −0.0167271 + 0.0289721i
\(251\) 5.54970 0.350294 0.175147 0.984542i \(-0.443960\pi\)
0.175147 + 0.984542i \(0.443960\pi\)
\(252\) 0 0
\(253\) 4.90672 0.308483
\(254\) −0.374459 + 0.648583i −0.0234957 + 0.0406957i
\(255\) −9.40996 28.7046i −0.589275 1.79755i
\(256\) −7.81365 13.5336i −0.488353 0.845853i
\(257\) 9.83076 0.613226 0.306613 0.951834i \(-0.400804\pi\)
0.306613 + 0.951834i \(0.400804\pi\)
\(258\) 0.889957 0.993623i 0.0554063 0.0618603i
\(259\) 0 0
\(260\) 27.9246 1.73181
\(261\) −15.4472 + 11.3473i −0.956159 + 0.702379i
\(262\) 0.152249 0.263703i 0.00940598 0.0162916i
\(263\) 11.9322 0.735774 0.367887 0.929870i \(-0.380081\pi\)
0.367887 + 0.929870i \(0.380081\pi\)
\(264\) −0.504812 + 0.563615i −0.0310690 + 0.0346881i
\(265\) 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
\(269\) −14.9824 + 25.9503i −0.913494 + 1.58222i −0.104401 + 0.994535i \(0.533293\pi\)
−0.809092 + 0.587682i \(0.800041\pi\)
\(270\) 0.861522 0.391722i 0.0524305 0.0238394i
\(271\) 3.54825 + 6.14575i 0.215541 + 0.373328i 0.953440 0.301584i \(-0.0975152\pi\)
−0.737899 + 0.674911i \(0.764182\pi\)
\(272\) 13.0027 + 22.5213i 0.788402 + 1.36555i
\(273\) 0 0
\(274\) 0.667877 1.15680i 0.0403479 0.0698847i
\(275\) −3.35142 −0.202098
\(276\) 10.3783 + 2.17756i 0.624702 + 0.131074i
\(277\) −9.82351 −0.590237 −0.295119 0.955461i \(-0.595359\pi\)
−0.295119 + 0.955461i \(0.595359\pi\)
\(278\) −0.0899388 0.155779i −0.00539417 0.00934298i
\(279\) −16.2456 + 11.9337i −0.972596 + 0.714454i
\(280\) 0 0
\(281\) 11.9389 + 20.6787i 0.712213 + 1.23359i 0.964025 + 0.265813i \(0.0856403\pi\)
−0.251812 + 0.967776i \(0.581026\pi\)
\(282\) 0.440337 + 0.0923907i 0.0262217 + 0.00550179i
\(283\) 1.50798 + 2.61189i 0.0896399 + 0.155261i 0.907359 0.420357i \(-0.138095\pi\)
−0.817719 + 0.575618i \(0.804762\pi\)
\(284\) −12.3601 21.4083i −0.733435 1.27035i
\(285\) −8.58819 1.80196i −0.508721 0.106739i
\(286\) 0.287222 + 0.497483i 0.0169838 + 0.0294168i
\(287\) 0 0
\(288\) −1.97757 + 1.45269i −0.116530 + 0.0856008i
\(289\) −12.9330 22.4006i −0.760763 1.31768i
\(290\) −1.16366 −0.0683324
\(291\) −8.73414 1.83258i −0.512004 0.107428i
\(292\) −4.38699 −0.256729
\(293\) −8.52913 + 14.7729i −0.498277 + 0.863041i −0.999998 0.00198814i \(-0.999367\pi\)
0.501721 + 0.865030i \(0.332700\pi\)
\(294\) 0 0
\(295\) −14.5081 25.1287i −0.844692 1.46305i
\(296\) 0.577706 + 1.00062i 0.0335785 + 0.0581596i
\(297\) −6.76057 4.83107i −0.392288 0.280327i
\(298\) 0.301283 0.521838i 0.0174529 0.0302293i
\(299\) 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
\(303\) 2.13192 2.38026i 0.122476 0.136742i
\(304\) 7.55444 0.433277
\(305\) 3.61458 6.26064i 0.206970 0.358483i
\(306\) 1.08234 0.795068i 0.0618731 0.0454510i
\(307\) 23.2178 1.32511 0.662554 0.749014i \(-0.269473\pi\)
0.662554 + 0.749014i \(0.269473\pi\)
\(308\) 0 0
\(309\) −5.98367 + 6.68068i −0.340399 + 0.380050i
\(310\) −1.22380 −0.0695072
\(311\) −0.895467 1.55100i −0.0507773 0.0879489i 0.839520 0.543329i \(-0.182837\pi\)
−0.890297 + 0.455381i \(0.849503\pi\)
\(312\) 0.774369 + 2.36217i 0.0438400 + 0.133732i
\(313\) −2.30458 + 3.99166i −0.130263 + 0.225622i −0.923778 0.382929i \(-0.874915\pi\)
0.793515 + 0.608551i \(0.208249\pi\)
\(314\) −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 \(-0.0923721\pi\)
\(318\) 1.03138 + 0.216402i 0.0578370 + 0.0121352i
\(319\) 5.10843 + 8.84807i 0.286017 + 0.495397i
\(320\) 21.0120 1.17461
\(321\) −28.7307 6.02823i −1.60359 0.336463i
\(322\) 0 0
\(323\) −12.4524 −0.692869
\(324\) −12.1555 13.2186i −0.675305 0.734367i
\(325\) −5.50541 + 9.53566i −0.305385 + 0.528943i
\(326\) −0.828846 −0.0459055
\(327\) 4.58613 + 13.9898i 0.253614 + 0.773636i
\(328\) 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 \(0.168078\pi\)
\(332\) 6.82086 11.8141i 0.374343 0.648382i
\(333\) −10.2261 + 7.51192i −0.560386 + 0.411651i
\(334\) 0.164064 + 0.284168i 0.00897719 + 0.0155490i
\(335\) −4.42899 7.67124i −0.241982 0.419125i
\(336\) 0 0
\(337\) 4.52675 7.84057i 0.246588 0.427103i −0.715989 0.698112i \(-0.754024\pi\)
0.962577 + 0.271009i \(0.0873572\pi\)
\(338\) 0.998425 0.0543072
\(339\) −2.10636 6.42534i −0.114402 0.348976i
\(340\) −34.7993 −1.88725
\(341\) 5.37245 + 9.30535i 0.290934 + 0.503913i
\(342\) −0.0428134 0.387773i −0.00231508 0.0209683i
\(343\) 0 0
\(344\) −1.53846 2.66470i −0.0829484 0.143671i
\(345\) −9.44522 + 10.5454i −0.508514 + 0.567748i
\(346\) −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 \(0.783406\pi\)
\(348\) 6.87829 + 20.9819i 0.368715 + 1.12475i
\(349\) −13.6310 23.6095i −0.729648 1.26379i −0.957032 0.289983i \(-0.906350\pi\)
0.227384 0.973805i \(-0.426983\pi\)
\(350\) 0 0
\(351\) −24.8513 + 11.2995i −1.32646 + 0.603124i
\(352\) 0.653988 + 1.13274i 0.0348577 + 0.0603753i
\(353\) −24.1896 −1.28748 −0.643741 0.765244i \(-0.722618\pi\)
−0.643741 + 0.765244i \(0.722618\pi\)
\(354\) 0.860664 0.960918i 0.0457438 0.0510722i
\(355\) 33.0018 1.75155
\(356\) 0.469472 0.813149i 0.0248820 0.0430968i
\(357\) 0 0
\(358\) 0.560595 + 0.970979i 0.0296284 + 0.0513179i
\(359\) 10.5188 + 18.2191i 0.555161 + 0.961567i 0.997891 + 0.0649124i \(0.0206768\pi\)
−0.442730 + 0.896655i \(0.645990\pi\)
\(360\) −0.239572 2.16987i −0.0126265 0.114362i
\(361\) 7.69132 13.3218i 0.404806 0.701145i
\(362\) 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
\(366\) 0.314546 + 0.0659974i 0.0164416 + 0.00344974i
\(367\) 35.0380 1.82897 0.914485 0.404620i \(-0.132596\pi\)
0.914485 + 0.404620i \(0.132596\pi\)
\(368\) 6.09375 10.5547i 0.317659 0.550201i
\(369\) 20.3084 + 8.91460i 1.05721 + 0.464076i
\(370\) −0.770345 −0.0400483
\(371\) 0 0
\(372\) 7.23377 + 22.0662i 0.375054 + 1.14408i
\(373\) 1.12862 0.0584377 0.0292189 0.999573i \(-0.490698\pi\)
0.0292189 + 0.999573i \(0.490698\pi\)
\(374\) −0.357931 0.619955i −0.0185082 0.0320571i
\(375\) −8.93990 + 9.98127i −0.461655 + 0.515431i
\(376\) 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
\(381\) −12.6575 + 14.1319i −0.648463 + 0.723999i
\(382\) −0.0971359 0.168244i −0.00496991 0.00860813i
\(383\) −23.0401 −1.17729 −0.588647 0.808390i \(-0.700339\pi\)
−0.588647 + 0.808390i \(0.700339\pi\)
\(384\) 1.17363 + 3.58009i 0.0598915 + 0.182696i
\(385\) 0 0
\(386\) 0.603664 0.0307257
\(387\) 27.2326 20.0047i 1.38431 1.01689i
\(388\) −5.14042 + 8.90346i −0.260965 + 0.452005i
\(389\) 15.7751 0.799828 0.399914 0.916553i \(-0.369040\pi\)
0.399914 + 0.916553i \(0.369040\pi\)
\(390\) −1.62207 0.340340i −0.0821368 0.0172338i
\(391\) −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
\(395\) 1.08357 1.87680i 0.0545204 0.0944321i
\(396\) −7.71457 + 5.66700i −0.387672 + 0.284778i
\(397\) −8.25277 14.2942i −0.414195 0.717406i 0.581149 0.813797i \(-0.302603\pi\)
−0.995344 + 0.0963911i \(0.969270\pi\)
\(398\) 0.390246 + 0.675926i 0.0195613 + 0.0338811i
\(399\) 0 0
\(400\) −4.16220 + 7.20914i −0.208110 + 0.360457i
\(401\) 21.6600 1.08165 0.540823 0.841136i \(-0.318113\pi\)
0.540823 + 0.841136i \(0.318113\pi\)
\(402\) 0.262742 0.293347i 0.0131044 0.0146308i
\(403\) 35.3015 1.75849
\(404\) −1.84057 3.18796i −0.0915716 0.158607i
\(405\) 23.3967 5.23014i 1.16259 0.259888i
\(406\) 0 0
\(407\) 3.38179 + 5.85743i 0.167629 + 0.290342i
\(408\) −0.965008 2.94371i −0.0477750 0.145735i
\(409\) 15.2860 + 26.4762i 0.755846 + 1.30916i 0.944953 + 0.327207i \(0.106107\pi\)
−0.189107 + 0.981956i \(0.560559\pi\)
\(410\) 0.673255 + 1.16611i 0.0332497 + 0.0575901i
\(411\) 22.5756 25.2053i 1.11357 1.24329i
\(412\) 5.16592 + 8.94763i 0.254507 + 0.440818i
\(413\) 0 0
\(414\) −0.576311 0.252978i −0.0283242 0.0124332i
\(415\) 9.10596 + 15.7720i 0.446994 + 0.774216i
\(416\) 4.29725 0.210690
\(417\) −1.41944 4.32994i −0.0695104 0.212038i
\(418\) −0.207955 −0.0101714
\(419\) 10.8081 18.7202i 0.528011 0.914542i −0.471456 0.881890i \(-0.656271\pi\)
0.999467 0.0326524i \(-0.0103954\pi\)
\(420\) 0 0
\(421\) 13.6217 + 23.5935i 0.663881 + 1.14988i 0.979587 + 0.201019i \(0.0644252\pi\)
−0.315706 + 0.948857i \(0.602241\pi\)
\(422\) 0.731046 + 1.26621i 0.0355867 + 0.0616380i
\(423\) 10.4363 + 4.58113i 0.507431 + 0.222742i
\(424\) 1.21545 2.10521i 0.0590273 0.102238i
\(425\) 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
\(429\) 4.53302 + 13.8278i 0.218856 + 0.667610i
\(430\) 2.05147 0.0989307
\(431\) −4.09843 + 7.09869i −0.197415 + 0.341932i −0.947689 0.319194i \(-0.896588\pi\)
0.750275 + 0.661126i \(0.229921\pi\)
\(432\) −18.7880 + 8.54266i −0.903940 + 0.411009i
\(433\) 3.41468 0.164099 0.0820494 0.996628i \(-0.473853\pi\)
0.0820494 + 0.996628i \(0.473853\pi\)
\(434\) 0 0
\(435\) −28.8497 6.05318i −1.38324 0.290228i
\(436\) 16.9601 0.812242
\(437\) 2.91793 + 5.05400i 0.139583 + 0.241765i
\(438\) 0.254829 + 0.0534678i 0.0121762 + 0.00255479i
\(439\) −3.29416 + 5.70564i −0.157221 + 0.272316i −0.933866 0.357624i \(-0.883587\pi\)
0.776644 + 0.629939i \(0.216920\pi\)
\(440\) −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 \(0.927959\pi\)
\(444\) 4.55344 + 13.8900i 0.216097 + 0.659191i
\(445\) 0.626752 + 1.08557i 0.0297109 + 0.0514608i
\(446\) 0.490087 0.0232063
\(447\) 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 \(0.496562\pi\)
\(450\) 0.393636 + 0.172791i 0.0185562 + 0.00814544i
\(451\) 5.91114 10.2384i 0.278345 0.482107i
\(452\) −7.78958 −0.366391
\(453\) −5.38992 + 6.01777i −0.253241 + 0.282739i
\(454\) 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 \(0.323477\pi\)
\(458\) 0.902342 1.56290i 0.0421637 0.0730296i
\(459\) 30.9693 14.0813i 1.44552 0.657259i
\(460\) 8.15440 + 14.1238i 0.380201 + 0.658527i
\(461\) −12.1036 20.9640i −0.563719 0.976390i −0.997168 0.0752117i \(-0.976037\pi\)
0.433449 0.901178i \(-0.357297\pi\)
\(462\) 0 0
\(463\) 2.40242 4.16111i 0.111650 0.193383i −0.804786 0.593565i \(-0.797720\pi\)
0.916436 + 0.400182i \(0.131053\pi\)
\(464\) 25.3770 1.17810
\(465\) −30.3407 6.36602i −1.40701 0.295217i
\(466\) −0.864561 −0.0400500
\(467\) 13.6228 + 23.5954i 0.630389 + 1.09187i 0.987472 + 0.157793i \(0.0504379\pi\)
−0.357083 + 0.934073i \(0.616229\pi\)
\(468\) 3.45128 + 31.2592i 0.159535 + 1.44496i
\(469\) 0 0
\(470\) 0.345979 + 0.599254i 0.0159588 + 0.0276415i
\(471\) −6.90420 1.44862i −0.318129 0.0667491i
\(472\) −1.48783 2.57699i −0.0684827 0.118616i
\(473\) −9.00590 15.5987i −0.414092 0.717228i
\(474\) 0.0942940 + 0.0197846i 0.00433107 + 0.000908735i
\(475\) −1.99302 3.45202i −0.0914462 0.158389i
\(476\) 0 0
\(477\) 24.4445 + 10.7302i 1.11924 + 0.491301i
\(478\) 0.527601 + 0.913832i 0.0241319 + 0.0417977i
\(479\) 20.5255 0.937834 0.468917 0.883242i \(-0.344644\pi\)
0.468917 + 0.883242i \(0.344644\pi\)
\(480\) −3.69337 0.774935i −0.168579 0.0353708i
\(481\) 22.2212 1.01320
\(482\) −0.0403366 + 0.0698651i −0.00183728 + 0.00318227i
\(483\) 0 0
\(484\) −8.42306 14.5892i −0.382866 0.663144i
\(485\) −6.86254 11.8863i −0.311612 0.539727i
\(486\) 0.544976 + 0.915984i 0.0247206 + 0.0415499i
\(487\) −12.9224 + 22.3823i −0.585571 + 1.01424i 0.409233 + 0.912430i \(0.365796\pi\)
−0.994804 + 0.101809i \(0.967537\pi\)
\(488\) 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 −0.986662 0.162781i \(-0.947954\pi\)
0.634303 + 0.773084i \(0.281287\pi\)
\(492\) 17.0465 19.0322i 0.768516 0.858037i
\(493\) −41.8303 −1.88394
\(494\) −0.341610 + 0.591686i −0.0153698 + 0.0266212i
\(495\) −1.40241 12.7020i −0.0630337 0.570914i
\(496\) 26.6886 1.19835
\(497\) 0 0
\(498\) −0.540194 + 0.603119i −0.0242067 + 0.0270264i
\(499\) 21.2690 0.952133 0.476066 0.879409i \(-0.342062\pi\)
0.476066 + 0.879409i \(0.342062\pi\)
\(500\) 7.71814 + 13.3682i 0.345166 + 0.597845i
\(501\) 2.58931 + 7.89857i 0.115682 + 0.352882i
\(502\) −0.189728 + 0.328618i −0.00846795 + 0.0146669i
\(503\) −16.3298 −0.728110 −0.364055 0.931377i \(-0.618608\pi\)
−0.364055 + 0.931377i \(0.618608\pi\)
\(504\) 0 0
\(505\) 4.91437 0.218687
\(506\) −0.167746 + 0.290544i −0.00745722 + 0.0129163i
\(507\) 24.7531 + 5.19365i 1.09933 + 0.230658i
\(508\) 10.9277 + 18.9273i 0.484837 + 0.839762i
\(509\) −13.4618 −0.596683 −0.298342 0.954459i \(-0.596433\pi\)
−0.298342 + 0.954459i \(0.596433\pi\)
\(510\) 2.02140 + 0.424126i 0.0895092 + 0.0187806i
\(511\) 0 0
\(512\) 5.41890 0.239484
\(513\) 0.955696 9.83644i 0.0421950 0.434289i
\(514\) −0.336084 + 0.582115i −0.0148240 + 0.0256760i
\(515\) −13.7932 −0.607800
\(516\) −12.1261 36.9899i −0.533820 1.62839i
\(517\) 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
\(521\) 0.713095 1.23512i 0.0312413 0.0541115i −0.849982 0.526812i \(-0.823387\pi\)
0.881223 + 0.472700i \(0.156721\pi\)
\(522\) −0.143820 1.30261i −0.00629482 0.0570139i
\(523\) 3.85530 + 6.67758i 0.168581 + 0.291990i 0.937921 0.346849i \(-0.112748\pi\)
−0.769340 + 0.638839i \(0.779415\pi\)
\(524\) −4.44301 7.69553i −0.194094 0.336181i
\(525\) 0 0
\(526\) −0.407928 + 0.706551i −0.0177865 + 0.0308071i
\(527\) −43.9922 −1.91633
\(528\) 3.42705 + 10.4540i 0.149143 + 0.454954i
\(529\) −13.5851 −0.590656
\(530\) 0.810371 + 1.40360i 0.0352003 + 0.0609686i
\(531\) 26.3363 19.3462i 1.14290 0.839554i
\(532\) 0 0
\(533\) −19.4206 33.6374i −0.841198 1.45700i
\(534\) −0.0371809 + 0.0415120i −0.00160898 + 0.00179640i
\(535\) −22.5742 39.0996i −0.975966 1.69042i
\(536\) −0.454201 0.786699i −0.0196185 0.0339802i
\(537\) 8.84749 + 26.9888i 0.381797 + 1.16465i
\(538\) −1.02441 1.77432i −0.0441653 0.0764966i
\(539\) 0 0
\(540\) 2.67078 27.4888i 0.114932 1.18293i
\(541\) −14.0228 24.2882i −0.602886 1.04423i −0.992382 0.123201i \(-0.960684\pi\)
0.389495 0.921028i \(-0.372649\pi\)
\(542\) −0.485216 −0.0208418
\(543\) 16.6804 18.6234i 0.715823 0.799205i
\(544\) −5.35517 −0.229601
\(545\) −11.3210 + 19.6086i −0.484939 + 0.839939i
\(546\) 0 0
\(547\) 17.7305 + 30.7101i 0.758101 + 1.31307i 0.943818 + 0.330466i \(0.107206\pi\)
−0.185717 + 0.982603i \(0.559461\pi\)
\(548\) −19.4903 33.7583i −0.832586 1.44208i
\(549\) 7.45497 + 3.27244i 0.318171 + 0.139664i
\(550\) 0.114575 0.198450i 0.00488550 0.00846193i
\(551\) −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
\(555\) −19.0985 4.00721i −0.810687 0.170097i
\(556\) −5.24928 −0.222619
\(557\) −17.5209 + 30.3472i −0.742386 + 1.28585i 0.209019 + 0.977911i \(0.432973\pi\)
−0.951406 + 0.307940i \(0.900361\pi\)
\(558\) −0.151253 1.36994i −0.00640303 0.0579940i
\(559\) −59.1763 −2.50289
\(560\) 0 0
\(561\) −5.64899 17.2319i −0.238500 0.727533i
\(562\) −1.63262 −0.0688677
\(563\) −8.01311 13.8791i −0.337712 0.584935i 0.646290 0.763092i \(-0.276320\pi\)
−0.984002 + 0.178157i \(0.942986\pi\)
\(564\) 8.76005 9.78047i 0.368865 0.411832i
\(565\) 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 \(0.169144\pi\)
\(570\) 0.400305 0.446934i 0.0167669 0.0187200i
\(571\) −14.6152 25.3142i −0.611626 1.05937i −0.990966 0.134110i \(-0.957182\pi\)
0.379340 0.925257i \(-0.376151\pi\)
\(572\) 16.7637 0.700926
\(573\) −1.53303 4.67643i −0.0640432 0.195361i
\(574\) 0 0
\(575\) −6.43065 −0.268177
\(576\) 2.59693 + 23.5211i 0.108205 + 0.980047i
\(577\) 7.52852 13.0398i 0.313417 0.542853i −0.665683 0.746235i \(-0.731860\pi\)
0.979100 + 0.203381i \(0.0651930\pi\)
\(578\) 1.76856 0.0735623
\(579\) 14.9661 + 3.14017i 0.621972 + 0.130501i
\(580\) −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
\(584\) 0.300307 0.520148i 0.0124268 0.0215239i
\(585\) −38.4443 16.8755i −1.58948 0.697717i
\(586\) −0.583171 1.01008i −0.0240906 0.0417261i
\(587\) −0.835901 1.44782i −0.0345013 0.0597580i 0.848259 0.529581i \(-0.177651\pi\)
−0.882760 + 0.469823i \(0.844318\pi\)
\(588\) 0 0
\(589\) −6.38977 + 11.0674i −0.263286 + 0.456025i
\(590\) 1.98395 0.0816778
\(591\) −6.61407 + 7.38451i −0.272066 + 0.303758i
\(592\) 16.7996 0.690461
\(593\) 5.40871 + 9.36816i 0.222109 + 0.384704i 0.955448 0.295159i \(-0.0953726\pi\)
−0.733339 + 0.679863i \(0.762039\pi\)
\(594\) 0.517188 0.235158i 0.0212205 0.00964867i
\(595\) 0 0
\(596\) −8.79221 15.2286i −0.360143 0.623786i
\(597\) 6.15899 + 18.7877i 0.252071 + 0.768929i
\(598\) 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 \(0.943743\pi\)
\(600\) 0.661596 0.738662i 0.0270096 0.0301558i
\(601\) 12.9011 + 22.3453i 0.526246 + 0.911485i 0.999532 + 0.0305765i \(0.00973432\pi\)
−0.473286 + 0.880909i \(0.656932\pi\)
\(602\) 0 0
\(603\) 8.03989 5.90598i 0.327410 0.240510i
\(604\) 4.65332 + 8.05978i 0.189341 + 0.327948i
\(605\) 22.4898 0.914342
\(606\) 0.0680598 + 0.207613i 0.00276474 + 0.00843369i
\(607\) −37.8049 −1.53445 −0.767227 0.641376i \(-0.778364\pi\)
−0.767227 + 0.641376i \(0.778364\pi\)
\(608\) −0.777828 + 1.34724i −0.0315451 + 0.0546377i
\(609\) 0 0
\(610\) 0.247143 + 0.428065i 0.0100065 + 0.0173318i
\(611\) −9.98005 17.2860i −0.403750 0.699315i
\(612\) −4.30093 38.9547i −0.173855 1.57465i
\(613\) 6.47719 11.2188i 0.261611 0.453124i −0.705059 0.709149i \(-0.749080\pi\)
0.966670 + 0.256025i \(0.0824129\pi\)
\(614\) −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 −0.329393 0.944193i \(-0.606844\pi\)
0.982391 0.186834i \(-0.0598227\pi\)
\(618\) −0.191023 0.582707i −0.00768409 0.0234399i
\(619\) −33.1974 −1.33431 −0.667157 0.744917i \(-0.732489\pi\)
−0.667157 + 0.744917i \(0.732489\pi\)
\(620\) −17.8568 + 30.9289i −0.717146 + 1.24213i
\(621\) −12.9721 9.26976i −0.520551 0.371983i
\(622\) 0.122453 0.00490993
\(623\) 0 0
\(624\) 35.3741 + 7.42212i 1.41610 + 0.297122i
\(625\) −31.0866 −1.24346
\(626\) −0.157574 0.272925i −0.00629791 0.0109083i
\(627\) −5.15566 1.08175i −0.205897 0.0432009i
\(628\) −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
\(633\) 11.5376 + 35.1948i 0.458578 + 1.39887i
\(634\) 0.884900 + 1.53269i 0.0351439 + 0.0608709i
\(635\) −29.1772 −1.15786
\(636\) 20.5182 22.9083i 0.813601 0.908374i
\(637\) 0 0
\(638\) −0.698568 −0.0276566
\(639\) 4.07878 + 36.9426i 0.161354 + 1.46143i
\(640\) −2.89714 + 5.01799i −0.114519 + 0.198353i
\(641\) 43.0814 1.70161 0.850806 0.525480i \(-0.176114\pi\)
0.850806 + 0.525480i \(0.176114\pi\)
\(642\) 1.33917 1.49516i 0.0528528 0.0590094i
\(643\) 3.20088 5.54409i 0.126230 0.218638i −0.795983 0.605319i \(-0.793045\pi\)
0.922213 + 0.386682i \(0.126379\pi\)
\(644\) 0 0
\(645\) 50.8604 + 10.6714i 2.00263 + 0.420187i
\(646\) 0.425709 0.737350i 0.0167493 0.0290107i
\(647\) 1.94403 3.36716i 0.0764278 0.132377i −0.825278 0.564726i \(-0.808982\pi\)
0.901706 + 0.432349i \(0.142315\pi\)
\(648\) 2.39937 0.536359i 0.0942561 0.0210702i
\(649\) −8.70947 15.0852i −0.341877 0.592148i
\(650\) −0.376427 0.651991i −0.0147647 0.0255732i
\(651\) 0 0
\(652\) −12.0939 + 20.9473i −0.473634 + 0.820358i
\(653\) 15.1035 0.591044 0.295522 0.955336i \(-0.404506\pi\)
0.295522 + 0.955336i \(0.404506\pi\)
\(654\) −0.985170 0.206706i −0.0385232 0.00808286i
\(655\) 11.8630 0.463525
\(656\) −14.6823 25.4305i −0.573248 0.992895i
\(657\) 6.03964 + 2.65116i 0.235629 + 0.103432i
\(658\) 0 0
\(659\) −7.13002 12.3496i −0.277746 0.481070i 0.693078 0.720862i \(-0.256254\pi\)
−0.970824 + 0.239792i \(0.922921\pi\)
\(660\) −14.4079 3.02305i −0.560829 0.117672i
\(661\) −9.70965 16.8176i −0.377662 0.654129i 0.613060 0.790036i \(-0.289938\pi\)
−0.990722 + 0.135907i \(0.956605\pi\)
\(662\) −0.00551516 0.00955254i −0.000214353 0.000371270i
\(663\) −58.3089 12.2343i −2.26453 0.475139i
\(664\) 0.933832 + 1.61744i 0.0362397 + 0.0627690i
\(665\) 0 0
\(666\) −0.0952089 0.862333i −0.00368927 0.0334147i
\(667\) 9.80197 + 16.9775i 0.379534 + 0.657372i
\(668\) 9.57561 0.370492
\(669\) 12.1503 + 2.54936i 0.469758 + 0.0985638i
\(670\) 0.605656 0.0233985
\(671\) 2.16991 3.75839i 0.0837683 0.145091i
\(672\) 0 0
\(673\) −2.96563 5.13663i −0.114317 0.198002i 0.803190 0.595723i \(-0.203135\pi\)
−0.917506 + 0.397721i \(0.869801\pi\)
\(674\) 0.309512 + 0.536091i 0.0119220 + 0.0206494i
\(675\) 8.86027 + 6.33150i 0.341032 + 0.243699i
\(676\) 14.5683 25.2330i 0.560318 0.970500i
\(677\) 18.4913 32.0278i 0.710678 1.23093i −0.253925 0.967224i \(-0.581722\pi\)
0.964603 0.263706i \(-0.0849449\pi\)
\(678\) 0.452477 + 0.0949379i 0.0173773 + 0.00364607i
\(679\) 0 0
\(680\) 2.38215 4.12601i 0.0913513 0.158225i
\(681\) 15.9341 17.7901i 0.610594 0.681719i
\(682\) −0.734671 −0.0281320
\(683\) −6.56800 + 11.3761i −0.251317 + 0.435294i −0.963889 0.266305i \(-0.914197\pi\)
0.712571 + 0.701600i \(0.247530\pi\)
\(684\) −10.4248 4.57608i −0.398602 0.174971i
\(685\) 52.0398 1.98834
\(686\) 0 0
\(687\) 30.5010 34.0539i 1.16369 1.29924i
\(688\) −44.7384 −1.70564
\(689\) −23.3758 40.4881i −0.890547 1.54247i
\(690\) −0.301530 0.919803i −0.0114791 0.0350163i
\(691\) 7.38292 12.7876i 0.280860 0.486463i −0.690737 0.723106i \(-0.742714\pi\)
0.971597 + 0.236643i \(0.0760472\pi\)
\(692\) −10.0399 −0.381659
\(693\) 0 0
\(694\) −0.397915 −0.0151046
\(695\) 3.50394 6.06900i 0.132912 0.230210i
\(696\) −2.95858 0.620763i −0.112145 0.0235300i
\(697\) 24.2016 + 41.9184i 0.916702 + 1.58777i
\(698\) 1.86401 0.0705536
\(699\) −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 \(0.695107\pi\)
\(702\) 0.180504 1.85783i 0.00681270 0.0701193i
\(703\) −4.02217 + 6.96660i −0.151699 + 0.262750i
\(704\) 12.6139 0.475406
\(705\) 5.46036 + 16.6565i 0.205649 + 0.627322i
\(706\) 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 \(0.251981\pi\)
\(710\) −1.12823 + 1.95415i −0.0423418 + 0.0733381i
\(711\) 2.23484 + 0.981005i 0.0838129 + 0.0367906i
\(712\) 0.0642745 + 0.111327i 0.00240879 + 0.00417215i
\(713\) 10.3086 + 17.8549i 0.386058 + 0.668673i
\(714\) 0 0
\(715\) −11.1899 + 19.3815i −0.418479 + 0.724827i
\(716\) 32.7192 1.22277
\(717\) 8.32677 + 25.4004i 0.310969 + 0.948595i
\(718\) −1.43842 −0.0536815
\(719\) 7.49790 + 12.9867i 0.279624 + 0.484324i 0.971291 0.237893i \(-0.0764567\pi\)
−0.691667 + 0.722217i \(0.743123\pi\)
\(720\) −29.0646 12.7582i −1.08317 0.475471i
\(721\) 0 0
\(722\) 0.525886 + 0.910861i 0.0195715 + 0.0338987i
\(723\) −1.36346 + 1.52228i −0.0507076 + 0.0566143i
\(724\) −14.4008 24.9429i −0.535200 0.926994i
\(725\) −6.69501 11.5961i −0.248646 0.430668i
\(726\) 0.311465 + 0.950107i 0.0115595 + 0.0352618i
\(727\) 13.0527 + 22.6080i 0.484099 + 0.838485i 0.999833 0.0182642i \(-0.00581399\pi\)
−0.515734 + 0.856749i \(0.672481\pi\)
\(728\) 0 0
\(729\) 8.74633 + 25.5441i 0.323938 + 0.946078i
\(730\) 0.200223 + 0.346796i 0.00741059 + 0.0128355i
\(731\) 73.7447 2.72754
\(732\) 6.25756 6.98648i 0.231286 0.258228i
\(733\) −28.3821 −1.04832 −0.524159 0.851621i \(-0.675620\pi\)
−0.524159 + 0.851621i \(0.675620\pi\)
\(734\) −1.19784 + 2.07473i −0.0442132 + 0.0765796i
\(735\) 0 0
\(736\) 1.25486 + 2.17348i 0.0462548 + 0.0801156i
\(737\) −2.65881 4.60520i −0.0979386 0.169635i
\(738\) −1.22215 + 0.897772i −0.0449880 + 0.0330474i
\(739\) −23.2933 + 40.3451i −0.856857 + 1.48412i 0.0180552 + 0.999837i \(0.494253\pi\)
−0.874912 + 0.484282i \(0.839081\pi\)
\(740\) −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 −0.869118 0.494605i \(-0.835313\pi\)
0.862899 + 0.505376i \(0.168646\pi\)
\(744\) −3.11149 0.652846i −0.114073 0.0239345i
\(745\) 23.4755 0.860075
\(746\) −0.0385841 + 0.0668297i −0.00141267 + 0.00244681i
\(747\) −16.5299 + 12.1426i −0.604798 + 0.444275i
\(748\) −20.8907 −0.763839
\(749\) 0 0
\(750\) −0.285398 0.870593i −0.0104213 0.0317896i
\(751\) −36.3662 −1.32702 −0.663510 0.748168i \(-0.730934\pi\)
−0.663510 + 0.748168i \(0.730934\pi\)
\(752\) −7.54511 13.0685i −0.275142 0.476560i
\(753\) −6.41318 + 7.16022i −0.233709 + 0.260933i
\(754\) −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
\(759\) −5.67015 + 6.33064i −0.205814 + 0.229788i
\(760\) −0.692005 1.19859i −0.0251017 0.0434773i
\(761\) −33.0357 −1.19754 −0.598771 0.800920i \(-0.704344\pi\)
−0.598771 + 0.800920i \(0.704344\pi\)
\(762\) −0.404079 1.23262i −0.0146382 0.0446532i
\(763\) 0 0
\(764\) −5.66934 −0.205110
\(765\) 47.9087 + 21.0300i 1.73214 + 0.760342i
\(766\) 0.787671 1.36429i 0.0284597 0.0492937i
\(767\) −57.2285 −2.06640
\(768\) 26.4905 + 5.55818i 0.955893 + 0.200563i
\(769\) 1.28876 2.23219i 0.0464738 0.0804949i −0.841853 0.539707i \(-0.818535\pi\)
0.888327 + 0.459212i \(0.151868\pi\)
\(770\) 0 0
\(771\) −11.3603 + 12.6836i −0.409132 + 0.456790i
\(772\) 8.80822 15.2563i 0.317015 0.549086i
\(773\) 3.36486 5.82811i 0.121026 0.209623i −0.799147 0.601136i \(-0.794715\pi\)
0.920172 + 0.391513i \(0.128048\pi\)
\(774\) 0.253547 + 2.29644i 0.00911355 + 0.0825439i
\(775\) −7.04102 12.1954i −0.252921 0.438072i
\(776\) −0.703765 1.21896i −0.0252637 0.0437580i
\(777\) 0 0
\(778\) −0.539302 + 0.934099i −0.0193349 + 0.0334891i
\(779\) 14.0609 0.503785
\(780\) −32.2694 + 36.0283i −1.15543 + 1.29002i
\(781\) 19.8116 0.708916
\(782\) −0.686792 1.18956i −0.0245596 0.0425385i