Properties

Label 441.2.h.h.373.8
Level $441$
Weight $2$
Character 441.373
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.h (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 373.8
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.h.214.8

$q$-expansion

\(f(q)\) \(=\) \(q+0.0683740 q^{2} +(0.539550 + 1.64587i) q^{3} -1.99532 q^{4} +(-1.33190 - 2.30691i) q^{5} +(0.0368912 + 0.112535i) q^{6} -0.273176 q^{8} +(-2.41777 + 1.77606i) q^{9} +O(q^{10})\) \(q+0.0683740 q^{2} +(0.539550 + 1.64587i) q^{3} -1.99532 q^{4} +(-1.33190 - 2.30691i) q^{5} +(0.0368912 + 0.112535i) q^{6} -0.273176 q^{8} +(-2.41777 + 1.77606i) q^{9} +(-0.0910670 - 0.157733i) q^{10} +(0.799563 - 1.38488i) q^{11} +(-1.07658 - 3.28404i) q^{12} +(2.62690 - 4.54992i) q^{13} +(3.07825 - 3.43682i) q^{15} +3.97197 q^{16} +(-3.27360 - 5.67005i) q^{17} +(-0.165313 + 0.121436i) q^{18} +(0.950968 - 1.64713i) q^{19} +(2.65756 + 4.60304i) q^{20} +(0.0546693 - 0.0946900i) q^{22} +(1.53419 + 2.65729i) q^{23} +(-0.147392 - 0.449612i) q^{24} +(-1.04789 + 1.81500i) q^{25} +(0.179612 - 0.311096i) q^{26} +(-4.22767 - 3.02106i) q^{27} +(-3.19452 - 5.53306i) q^{29} +(0.210472 - 0.234989i) q^{30} -6.71923 q^{31} +0.817932 q^{32} +(2.71074 + 0.568763i) q^{33} +(-0.223829 - 0.387684i) q^{34} +(4.82424 - 3.54381i) q^{36} +(-2.11477 + 3.66290i) q^{37} +(0.0650215 - 0.112621i) q^{38} +(8.90592 + 1.86862i) q^{39} +(0.363842 + 0.630193i) q^{40} +(3.69648 - 6.40249i) q^{41} +(5.63176 + 9.75450i) q^{43} +(-1.59539 + 2.76329i) q^{44} +(7.31743 + 3.21206i) q^{45} +(0.104898 + 0.181689i) q^{46} -3.79918 q^{47} +(2.14308 + 6.53735i) q^{48} +(-0.0716485 + 0.124099i) q^{50} +(7.56589 - 8.44720i) q^{51} +(-5.24152 + 9.07858i) q^{52} +(-4.44931 - 7.70643i) q^{53} +(-0.289062 - 0.206562i) q^{54} -4.25974 q^{55} +(3.22405 + 0.676463i) q^{57} +(-0.218422 - 0.378317i) q^{58} +10.8928 q^{59} +(-6.14211 + 6.85757i) q^{60} -2.71386 q^{61} -0.459420 q^{62} -7.88802 q^{64} -13.9950 q^{65} +(0.185344 + 0.0388886i) q^{66} -3.32533 q^{67} +(6.53190 + 11.3136i) q^{68} +(-3.54578 + 3.95881i) q^{69} -12.3890 q^{71} +(0.660478 - 0.485177i) q^{72} +(1.09932 + 1.90407i) q^{73} +(-0.144596 + 0.250447i) q^{74} +(-3.55265 - 0.745409i) q^{75} +(-1.89749 + 3.28655i) q^{76} +(0.608933 + 0.127765i) q^{78} +0.813556 q^{79} +(-5.29025 - 9.16298i) q^{80} +(2.69124 - 8.58820i) q^{81} +(0.252743 - 0.437764i) q^{82} +(3.41842 + 5.92088i) q^{83} +(-8.72020 + 15.1038i) q^{85} +(0.385066 + 0.666954i) q^{86} +(7.38310 - 8.24312i) q^{87} +(-0.218422 + 0.378317i) q^{88} +(0.235286 - 0.407527i) q^{89} +(0.500321 + 0.219621i) q^{90} +(-3.06120 - 5.30216i) q^{92} +(-3.62536 - 11.0590i) q^{93} -0.259765 q^{94} -5.06636 q^{95} +(0.441315 + 1.34621i) q^{96} +(-2.57623 - 4.46216i) q^{97} +(0.526472 + 4.76840i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + 20q^{11} + 4q^{15} + 24q^{16} - 32q^{18} + 32q^{23} - 12q^{25} + 16q^{29} - 84q^{30} - 96q^{32} - 4q^{36} - 12q^{37} + 8q^{39} + 56q^{44} + 24q^{46} - 4q^{50} + 64q^{51} + 32q^{53} - 12q^{57} + 32q^{60} + 96q^{64} - 120q^{65} + 24q^{67} - 112q^{71} + 68q^{74} - 60q^{78} - 24q^{79} - 40q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 32q^{93} - 128q^{95} + 20q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0683740 0.0483477 0.0241739 0.999708i \(-0.492304\pi\)
0.0241739 + 0.999708i \(0.492304\pi\)
\(3\) 0.539550 + 1.64587i 0.311509 + 0.950243i
\(4\) −1.99532 −0.997662
\(5\) −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
\(9\) −2.41777 + 1.77606i −0.805924 + 0.592019i
\(10\) −0.0910670 0.157733i −0.0287979 0.0498794i
\(11\) 0.799563 1.38488i 0.241077 0.417558i −0.719944 0.694032i \(-0.755833\pi\)
0.961021 + 0.276474i \(0.0891659\pi\)
\(12\) −1.07658 3.28404i −0.310781 0.948022i
\(13\) 2.62690 4.54992i 0.728571 1.26192i −0.228916 0.973446i \(-0.573518\pi\)
0.957487 0.288476i \(-0.0931485\pi\)
\(14\) 0 0
\(15\) 3.07825 3.43682i 0.794801 0.887383i
\(16\) 3.97197 0.992993
\(17\) −3.27360 5.67005i −0.793966 1.37519i −0.923494 0.383613i \(-0.874680\pi\)
0.129528 0.991576i \(-0.458654\pi\)
\(18\) −0.165313 + 0.121436i −0.0389646 + 0.0286228i
\(19\) 0.950968 1.64713i 0.218167 0.377877i −0.736081 0.676894i \(-0.763326\pi\)
0.954248 + 0.299017i \(0.0966589\pi\)
\(20\) 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 \(0.729684\pi\)
\(24\) −0.147392 0.449612i −0.0300863 0.0917768i
\(25\) −1.04789 + 1.81500i −0.209578 + 0.363000i
\(26\) 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 \(-0.368805\pi\)
\(30\) 0.210472 0.234989i 0.0384268 0.0429029i
\(31\) −6.71923 −1.20681 −0.603405 0.797435i \(-0.706190\pi\)
−0.603405 + 0.797435i \(0.706190\pi\)
\(32\) 0.817932 0.144591
\(33\) 2.71074 + 0.568763i 0.471880 + 0.0990088i
\(34\) −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 −0.985835 0.167721i \(-0.946359\pi\)
0.638168 + 0.769897i \(0.279693\pi\)
\(38\) 0.0650215 0.112621i 0.0105479 0.0182695i
\(39\) 8.90592 + 1.86862i 1.42609 + 0.299219i
\(40\) 0.363842 + 0.630193i 0.0575285 + 0.0996423i
\(41\) 3.69648 6.40249i 0.577293 0.999901i −0.418495 0.908219i \(-0.637442\pi\)
0.995788 0.0916820i \(-0.0292243\pi\)
\(42\) 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
\(45\) 7.31743 + 3.21206i 1.09082 + 0.478826i
\(46\) 0.104898 + 0.181689i 0.0154664 + 0.0267887i
\(47\) −3.79918 −0.554167 −0.277083 0.960846i \(-0.589368\pi\)
−0.277083 + 0.960846i \(0.589368\pi\)
\(48\) 2.14308 + 6.53735i 0.309327 + 0.943585i
\(49\) 0 0
\(50\) −0.0716485 + 0.124099i −0.0101326 + 0.0175502i
\(51\) 7.56589 8.44720i 1.05944 1.18284i
\(52\) −5.24152 + 9.07858i −0.726868 + 1.25897i
\(53\) −4.44931 7.70643i −0.611160 1.05856i −0.991045 0.133527i \(-0.957370\pi\)
0.379885 0.925034i \(-0.375963\pi\)
\(54\) −0.289062 0.206562i −0.0393364 0.0281096i
\(55\) −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
\(59\) 10.8928 1.41812 0.709060 0.705148i \(-0.249120\pi\)
0.709060 + 0.705148i \(0.249120\pi\)
\(60\) −6.14211 + 6.85757i −0.792943 + 0.885309i
\(61\) −2.71386 −0.347475 −0.173737 0.984792i \(-0.555584\pi\)
−0.173737 + 0.984792i \(0.555584\pi\)
\(62\) −0.459420 −0.0583465
\(63\) 0 0
\(64\) −7.88802 −0.986002
\(65\) −13.9950 −1.73587
\(66\) 0.185344 + 0.0388886i 0.0228143 + 0.00478685i
\(67\) −3.32533 −0.406254 −0.203127 0.979152i \(-0.565110\pi\)
−0.203127 + 0.979152i \(0.565110\pi\)
\(68\) 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 \(0.762890\pi\)
\(72\) 0.660478 0.485177i 0.0778381 0.0571786i
\(73\) 1.09932 + 1.90407i 0.128665 + 0.222855i 0.923160 0.384417i \(-0.125597\pi\)
−0.794494 + 0.607271i \(0.792264\pi\)
\(74\) −0.144596 + 0.250447i −0.0168089 + 0.0291138i
\(75\) −3.55265 0.745409i −0.410224 0.0860724i
\(76\) −1.89749 + 3.28655i −0.217657 + 0.376993i
\(77\) 0 0
\(78\) 0.608933 + 0.127765i 0.0689481 + 0.0144666i
\(79\) 0.813556 0.0915322 0.0457661 0.998952i \(-0.485427\pi\)
0.0457661 + 0.998952i \(0.485427\pi\)
\(80\) −5.29025 9.16298i −0.591468 1.02445i
\(81\) 2.69124 8.58820i 0.299027 0.954245i
\(82\) 0.252743 0.437764i 0.0279108 0.0483429i
\(83\) 3.41842 + 5.92088i 0.375220 + 0.649901i 0.990360 0.138517i \(-0.0442337\pi\)
−0.615140 + 0.788418i \(0.710900\pi\)
\(84\) 0 0
\(85\) −8.72020 + 15.1038i −0.945838 + 1.63824i
\(86\) 0.385066 + 0.666954i 0.0415227 + 0.0719195i
\(87\) 7.38310 8.24312i 0.791551 0.883755i
\(88\) −0.218422 + 0.378317i −0.0232838 + 0.0403288i
\(89\) 0.235286 0.407527i 0.0249403 0.0431978i −0.853286 0.521443i \(-0.825394\pi\)
0.878226 + 0.478246i \(0.158727\pi\)
\(90\) 0.500321 + 0.219621i 0.0527385 + 0.0231501i
\(91\) 0 0
\(92\) −3.06120 5.30216i −0.319152 0.552788i
\(93\) −3.62536 11.0590i −0.375932 1.14676i
\(94\) −0.259765 −0.0267927
\(95\) −5.06636 −0.519798
\(96\) 0.441315 + 1.34621i 0.0450415 + 0.137397i
\(97\) −2.57623 4.46216i −0.261576 0.453064i 0.705085 0.709123i \(-0.250909\pi\)
−0.966661 + 0.256059i \(0.917576\pi\)
\(98\) 0 0
\(99\) 0.526472 + 4.76840i 0.0529125 + 0.479243i
\(100\) 2.09088 3.62152i 0.209088 0.362152i
\(101\) −0.922440 + 1.59771i −0.0917862 + 0.158978i −0.908263 0.418400i \(-0.862591\pi\)
0.816477 + 0.577379i \(0.195924\pi\)
\(102\) 0.517310 0.577569i 0.0512213 0.0571878i
\(103\) 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
\(107\) 8.47445 14.6782i 0.819256 1.41899i −0.0869755 0.996210i \(-0.527720\pi\)
0.906231 0.422782i \(-0.138946\pi\)
\(108\) 8.43557 + 6.02801i 0.811713 + 0.580045i
\(109\) 4.24996 + 7.36115i 0.407073 + 0.705070i 0.994560 0.104163i \(-0.0332163\pi\)
−0.587488 + 0.809233i \(0.699883\pi\)
\(110\) −0.291255 −0.0277701
\(111\) −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 \(0.225450\pi\)
\(114\) 0.220441 + 0.0462525i 0.0206462 + 0.00433194i
\(115\) 4.08675 7.07847i 0.381092 0.660070i
\(116\) 6.37410 + 11.0403i 0.591820 + 1.02506i
\(117\) 1.72968 + 15.6662i 0.159909 + 1.44834i
\(118\) 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
\(122\) −0.185558 −0.0167996
\(123\) 12.5321 + 2.62946i 1.12998 + 0.237090i
\(124\) 13.4070 1.20399
\(125\) −7.73623 −0.691949
\(126\) 0 0
\(127\) 10.9533 0.971946 0.485973 0.873974i \(-0.338465\pi\)
0.485973 + 0.873974i \(0.338465\pi\)
\(128\) −2.17520 −0.192262
\(129\) −13.0160 + 14.5322i −1.14600 + 1.27949i
\(130\) −0.956896 −0.0839253
\(131\) −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
\(135\) −1.33852 + 13.7766i −0.115201 + 1.18570i
\(136\) 0.894271 + 1.54892i 0.0766831 + 0.132819i
\(137\) 9.76800 16.9187i 0.834537 1.44546i −0.0598699 0.998206i \(-0.519069\pi\)
0.894407 0.447254i \(-0.147598\pi\)
\(138\) −0.242439 + 0.270680i −0.0206378 + 0.0230418i
\(139\) 1.31540 2.27833i 0.111570 0.193246i −0.804833 0.593501i \(-0.797745\pi\)
0.916404 + 0.400256i \(0.131079\pi\)
\(140\) 0 0
\(141\) −2.04984 6.25295i −0.172628 0.526593i
\(142\) −0.847087 −0.0710860
\(143\) −4.20075 7.27590i −0.351284 0.608442i
\(144\) −9.60332 + 7.05445i −0.800277 + 0.587871i
\(145\) −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
\(149\) 4.40640 + 7.63212i 0.360987 + 0.625247i 0.988124 0.153662i \(-0.0491066\pi\)
−0.627137 + 0.778909i \(0.715773\pi\)
\(150\) −0.242908 0.0509666i −0.0198334 0.00416140i
\(151\) −2.33211 + 4.03933i −0.189784 + 0.328716i −0.945178 0.326555i \(-0.894112\pi\)
0.755394 + 0.655271i \(0.227446\pi\)
\(152\) −0.259782 + 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
\(156\) −17.7702 3.72851i −1.42276 0.298520i
\(157\) 4.07294 0.325056 0.162528 0.986704i \(-0.448035\pi\)
0.162528 + 0.986704i \(0.448035\pi\)
\(158\) 0.0556261 0.00442537
\(159\) 10.2832 11.4810i 0.815507 0.910502i
\(160\) −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 −0.524838 0.851202i \(-0.675874\pi\)
0.999582 + 0.0289220i \(0.00920745\pi\)
\(164\) −7.37568 + 12.7750i −0.575944 + 0.997564i
\(165\) −2.29834 7.01097i −0.178926 0.545804i
\(166\) 0.233731 + 0.404834i 0.0181410 + 0.0314212i
\(167\) −2.39951 + 4.15608i −0.185680 + 0.321607i −0.943805 0.330502i \(-0.892782\pi\)
0.758126 + 0.652109i \(0.226115\pi\)
\(168\) 0 0
\(169\) −7.30121 12.6461i −0.561631 0.972774i
\(170\) −0.596235 + 1.03271i −0.0457291 + 0.0792051i
\(171\) 0.626165 + 5.67135i 0.0478840 + 0.433699i
\(172\) −11.2372 19.4634i −0.856828 1.48407i
\(173\) −5.03171 −0.382554 −0.191277 0.981536i \(-0.561263\pi\)
−0.191277 + 0.981536i \(0.561263\pi\)
\(174\) 0.504812 0.563615i 0.0382697 0.0427275i
\(175\) 0 0
\(176\) 3.17584 5.50072i 0.239388 0.414632i
\(177\) 5.87720 + 17.9281i 0.441758 + 1.34756i
\(178\) 0.0160874 0.0278642i 0.00120580 0.00208851i
\(179\) 8.19896 + 14.2010i 0.612819 + 1.06143i 0.990763 + 0.135605i \(0.0432977\pi\)
−0.377944 + 0.925828i \(0.623369\pi\)
\(180\) −14.6006 6.40911i −1.08827 0.477707i
\(181\) 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
\(185\) 11.2666 0.828339
\(186\) −0.247880 0.756146i −0.0181755 0.0554433i
\(187\) −10.4698 −0.765629
\(188\) 7.58059 0.552871
\(189\) 0 0
\(190\) −0.346407 −0.0251310
\(191\) 2.84131 0.205590 0.102795 0.994703i \(-0.467221\pi\)
0.102795 + 0.994703i \(0.467221\pi\)
\(192\) −4.25598 12.9826i −0.307149 0.936942i
\(193\) 8.82886 0.635515 0.317758 0.948172i \(-0.397070\pi\)
0.317758 + 0.948172i \(0.397070\pi\)
\(194\) −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 \(0.434641\pi\)
\(198\) 0.0359970 + 0.326035i 0.00255820 + 0.0231703i
\(199\) −5.70752 9.88572i −0.404596 0.700780i 0.589679 0.807638i \(-0.299254\pi\)
−0.994274 + 0.106858i \(0.965921\pi\)
\(200\) 0.286259 0.495815i 0.0202416 0.0350594i
\(201\) −1.79418 5.47306i −0.126552 0.386040i
\(202\) −0.0630709 + 0.109242i −0.00443765 + 0.00768624i
\(203\) 0 0
\(204\) −15.0964 + 16.8549i −1.05696 + 1.18008i
\(205\) −19.6933 −1.37544
\(206\) 0.177021 + 0.306609i 0.0123336 + 0.0213625i
\(207\) −8.42881 3.69992i −0.585843 0.257162i
\(208\) 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 \(-0.0966486\pi\)
\(212\) 8.87782 + 15.3768i 0.609731 + 1.05609i
\(213\) −6.68450 20.3907i −0.458014 1.39715i
\(214\) 0.579432 1.00361i 0.0396091 0.0686050i
\(215\) 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
\(219\) −2.54072 + 2.83668i −0.171686 + 0.191685i
\(220\) 8.49956 0.573041
\(221\) −34.3977 −2.31384
\(222\) −0.490219 0.102857i −0.0329014 0.00690330i
\(223\) 3.58387 + 6.20744i 0.239994 + 0.415681i 0.960712 0.277547i \(-0.0895213\pi\)
−0.720719 + 0.693228i \(0.756188\pi\)
\(224\) 0 0
\(225\) −0.689984 6.24938i −0.0459989 0.416625i
\(226\) −0.133463 + 0.231165i −0.00887784 + 0.0153769i
\(227\) −6.89434 + 11.9413i −0.457593 + 0.792575i −0.998833 0.0482933i \(-0.984622\pi\)
0.541240 + 0.840868i \(0.317955\pi\)
\(228\) −6.43302 1.34976i −0.426037 0.0893903i
\(229\) −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
\(233\) 6.32230 10.9505i 0.414187 0.717394i −0.581155 0.813793i \(-0.697399\pi\)
0.995343 + 0.0963989i \(0.0307324\pi\)
\(234\) 0.118265 + 1.07116i 0.00773124 + 0.0700240i
\(235\) 5.06010 + 8.76436i 0.330085 + 0.571724i
\(236\) −21.7346 −1.41481
\(237\) 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 \(0.000318696\pi\)
\(240\) 12.2267 13.6510i 0.789231 0.881165i
\(241\) 0.589942 1.02181i 0.0380015 0.0658205i −0.846399 0.532549i \(-0.821234\pi\)
0.884401 + 0.466729i \(0.154568\pi\)
\(242\) 0.288634 + 0.499928i 0.0185541 + 0.0321366i
\(243\) 15.5871 0.204333i 0.999914 0.0131080i
\(244\) 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
\(248\) 1.83553 0.116557
\(249\) −7.90059 + 8.82089i −0.500679 + 0.559001i
\(250\) −0.528957 −0.0334542
\(251\) −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
\(254\) 0.748919 0.0469913
\(255\) −29.5639 6.20304i −1.85136 0.388449i
\(256\) 15.6273 0.976707
\(257\) 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
\(261\) 17.5506 + 7.70404i 1.08636 + 0.476868i
\(262\) −0.152249 0.263703i −0.00940598 0.0162916i
\(263\) −5.96612 + 10.3336i −0.367887 + 0.637199i −0.989235 0.146336i \(-0.953252\pi\)
0.621348 + 0.783535i \(0.286585\pi\)
\(264\) −0.740511 0.155372i −0.0455753 0.00956251i
\(265\) −11.8520 + 20.5283i −0.728065 + 1.26105i
\(266\) 0 0
\(267\) 0.797685 + 0.167369i 0.0488175 + 0.0102428i
\(268\) 6.63512 0.405304
\(269\) 14.9824 + 25.9503i 0.913494 + 1.58222i 0.809092 + 0.587682i \(0.199959\pi\)
0.104401 + 0.994535i \(0.466707\pi\)
\(270\) −0.0915197 + 0.941960i −0.00556971 + 0.0573259i
\(271\) −3.54825 + 6.14575i −0.215541 + 0.373328i −0.953440 0.301584i \(-0.902485\pi\)
0.737899 + 0.674911i \(0.235818\pi\)
\(272\) −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
\(276\) 7.07499 7.89912i 0.425864 0.475471i
\(277\) 4.91175 8.50741i 0.295119 0.511161i −0.679894 0.733311i \(-0.737974\pi\)
0.975013 + 0.222150i \(0.0713075\pi\)
\(278\) 0.0899388 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 \(0.581026\pi\)
\(282\) −0.140156 0.427539i −0.00834617 0.0254596i
\(283\) 3.01595 0.179280 0.0896399 0.995974i \(-0.471428\pi\)
0.0896399 + 0.995974i \(0.471428\pi\)
\(284\) 24.7201 1.46687
\(285\) −2.73356 8.33857i −0.161922 0.493934i
\(286\) −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
\(290\) −0.581830 + 1.00776i −0.0341662 + 0.0591776i
\(291\) 5.95413 6.64770i 0.349037 0.389695i
\(292\) −2.19350 3.79925i −0.128365 0.222334i
\(293\) 8.52913 14.7729i 0.498277 0.863041i −0.501721 0.865030i \(-0.667300\pi\)
0.999998 + 0.00198814i \(0.000632845\pi\)
\(294\) 0 0
\(295\) −14.5081 25.1287i −0.844692 1.46305i
\(296\) 0.577706 1.00062i 0.0335785 0.0581596i
\(297\) −7.56411 + 3.43930i −0.438914 + 0.199568i
\(298\) 0.301283 + 0.521838i 0.0174529 + 0.0302293i
\(299\) 16.1206 0.932280
\(300\) 7.08868 + 1.48733i 0.409265 + 0.0858712i
\(301\) 0 0
\(302\) −0.159456 + 0.276185i −0.00917564 + 0.0158927i
\(303\) −3.12733 0.656170i −0.179660 0.0376960i
\(304\) 3.77722 6.54234i 0.216638 0.375229i
\(305\) 3.61458 + 6.26064i 0.206970 + 0.358483i
\(306\) 1.22972 + 0.539797i 0.0702982 + 0.0308582i
\(307\) −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
\(311\) −1.79093 −0.101555 −0.0507773 0.998710i \(-0.516170\pi\)
−0.0507773 + 0.998710i \(0.516170\pi\)
\(312\) −2.43289 0.510463i −0.137735 0.0288993i
\(313\) −4.60917 −0.260526 −0.130263 0.991480i \(-0.541582\pi\)
−0.130263 + 0.991480i \(0.541582\pi\)
\(314\) 0.278483 0.0157157
\(315\) 0 0
\(316\) −1.62331 −0.0913183
\(317\) −25.8841 −1.45380 −0.726898 0.686745i \(-0.759039\pi\)
−0.726898 + 0.686745i \(0.759039\pi\)
\(318\) 0.703100 0.785001i 0.0394279 0.0440207i
\(319\) −10.2169 −0.572035
\(320\) 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
\(324\) −5.36990 + 17.1363i −0.298328 + 0.952014i
\(325\) 5.50541 + 9.53566i 0.305385 + 0.528943i
\(326\) 0.414423 0.717802i 0.0229528 0.0397554i
\(327\) −9.82242 + 10.9666i −0.543181 + 0.606454i
\(328\) −1.00979 + 1.74901i −0.0557563 + 0.0965728i
\(329\) 0 0
\(330\) −0.157147 0.479368i −0.00865065 0.0263884i
\(331\) 0.161323 0.00886714 0.00443357 0.999990i \(-0.498589\pi\)
0.00443357 + 0.999990i \(0.498589\pi\)
\(332\) −6.82086 11.8141i −0.374343 0.648382i
\(333\) −1.39247 12.6120i −0.0763070 0.691134i
\(334\) −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 \(0.0873572\pi\)
\(338\) −0.499213 0.864662i −0.0271536 0.0470314i
\(339\) −6.61769 1.38851i −0.359423 0.0754135i
\(340\) 17.3996 30.1370i 0.943627 1.63441i
\(341\) −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
\(345\) 13.8552 + 2.90708i 0.745941 + 0.156512i
\(346\) −0.344038 −0.0184956
\(347\) −5.81968 −0.312417 −0.156208 0.987724i \(-0.549927\pi\)
−0.156208 + 0.987724i \(0.549927\pi\)
\(348\) −14.7317 + 16.4477i −0.789701 + 0.881689i
\(349\) 13.6310 + 23.6095i 0.729648 + 1.26379i 0.957032 + 0.289983i \(0.0936496\pi\)
−0.227384 + 0.973805i \(0.573017\pi\)
\(350\) 0 0
\(351\) −24.8513 + 11.2995i −1.32646 + 0.603124i
\(352\) 0.653988 1.13274i 0.0348577 0.0603753i
\(353\) −12.0948 + 20.9488i −0.643741 + 1.11499i 0.340850 + 0.940118i \(0.389285\pi\)
−0.984591 + 0.174874i \(0.944048\pi\)
\(354\) 0.401848 + 1.22582i 0.0213580 + 0.0651514i
\(355\) 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
\(359\) 10.5188 18.2191i 0.555161 0.961567i −0.442730 0.896655i \(-0.645990\pi\)
0.997891 0.0649124i \(-0.0206768\pi\)
\(360\) −1.99895 0.877459i −0.105354 0.0462461i
\(361\) 7.69132 + 13.3218i 0.404806 + 0.701145i
\(362\) 0.986944 0.0518726
\(363\) −9.75641 + 10.8929i −0.512079 + 0.571728i
\(364\) 0 0
\(365\) 2.92835 5.07205i 0.153277 0.265483i
\(366\) −0.100118 0.305404i −0.00523323 0.0159637i
\(367\) 17.5190 30.3438i 0.914485 1.58393i 0.106831 0.994277i \(-0.465930\pi\)
0.807654 0.589657i \(-0.200737\pi\)
\(368\) 6.09375 + 10.5547i 0.317659 + 0.550201i
\(369\) 2.43395 + 22.0449i 0.126706 + 1.14761i
\(370\) 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 \(0.842635\pi\)
\(374\) −0.715863 −0.0370164
\(375\) −4.17408 12.7328i −0.215549 0.657520i
\(376\) 1.03784 0.0535227
\(377\) −33.5667 −1.72877
\(378\) 0 0
\(379\) −21.9619 −1.12811 −0.564054 0.825738i \(-0.690759\pi\)
−0.564054 + 0.825738i \(0.690759\pi\)
\(380\) 10.1090 0.518583
\(381\) 5.90984 + 18.0277i 0.302770 + 0.923585i
\(382\) 0.194272 0.00993981
\(383\) −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
\(387\) −30.9409 13.5818i −1.57281 0.690403i
\(388\) 5.14042 + 8.90346i 0.260965 + 0.452005i
\(389\) −7.88753 + 13.6616i −0.399914 + 0.692671i −0.993715 0.111941i \(-0.964293\pi\)
0.593801 + 0.804612i \(0.297627\pi\)
\(390\) −0.516293 1.57493i −0.0261435 0.0797494i
\(391\) 10.0446 17.3978i 0.507979 0.879846i
\(392\) 0 0
\(393\) 5.14633 5.74580i 0.259598 0.289837i
\(394\) 0.391341 0.0197155
\(395\) −1.08357 1.87680i −0.0545204 0.0944321i
\(396\) −1.05048 9.51452i −0.0527888 0.478122i
\(397\) 8.25277 14.2942i 0.414195 0.717406i −0.581149 0.813797i \(-0.697397\pi\)
0.995344 + 0.0963911i \(0.0307300\pi\)
\(398\) −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 \(-0.348554\pi\)
\(402\) −0.122675 0.374215i −0.00611849 0.0186641i
\(403\) −17.6507 + 30.5720i −0.879246 + 1.52290i
\(404\) 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
\(408\) −2.06682 + 2.30757i −0.102323 + 0.114242i
\(409\) 30.5721 1.51169 0.755846 0.654750i \(-0.227226\pi\)
0.755846 + 0.654750i \(0.227226\pi\)
\(410\) −1.34651 −0.0664993
\(411\) 33.1163 + 6.94839i 1.63350 + 0.342739i
\(412\) −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
\(416\) 2.14863 3.72153i 0.105345 0.182463i
\(417\) 4.45956 + 0.935695i 0.218385 + 0.0458212i
\(418\) −0.103978 0.180094i −0.00508571 0.00880871i
\(419\) −10.8081 + 18.7202i −0.528011 + 0.914542i 0.471456 + 0.881890i \(0.343729\pi\)
−0.999467 + 0.0326524i \(0.989605\pi\)
\(420\) 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
\(423\) 9.18554 6.74755i 0.446616 0.328077i
\(424\) 1.21545 + 2.10521i 0.0590273 + 0.102238i
\(425\) 13.7215 0.665592
\(426\) −0.457046 1.39419i −0.0221439 0.0675490i
\(427\) 0 0
\(428\) −16.9093 + 29.2877i −0.817341 + 1.41568i
\(429\) 9.70868 10.8396i 0.468739 0.523340i
\(430\) 1.02574 1.77663i 0.0494654 0.0856765i
\(431\) −4.09843 7.09869i −0.197415 0.341932i 0.750275 0.661126i \(-0.229921\pi\)
−0.947689 + 0.319194i \(0.896588\pi\)
\(432\) −16.7922 11.9996i −0.807914 0.577330i
\(433\) −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
\(437\) 5.83585 0.279167
\(438\) −0.173719 + 0.193955i −0.00830062 + 0.00926752i
\(439\) −6.58831 −0.314443 −0.157221 0.987563i \(-0.550254\pi\)
−0.157221 + 0.987563i \(0.550254\pi\)
\(440\) 1.16366 0.0554753
\(441\) 0 0
\(442\) −2.35191 −0.111869
\(443\) 28.6912 1.36316 0.681581 0.731743i \(-0.261293\pi\)
0.681581 + 0.731743i \(0.261293\pi\)
\(444\) 14.3058 + 3.00162i 0.678925 + 0.142451i
\(445\) −1.25350 −0.0594218
\(446\) 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 \(0.496562\pi\)
\(450\) −0.0471770 0.427295i −0.00222394 0.0201429i
\(451\) −5.91114 10.2384i −0.278345 0.482107i
\(452\) 3.89479 6.74598i 0.183196 0.317304i
\(453\) −7.90650 1.65893i −0.371480 0.0779431i
\(454\) −0.471393 + 0.816477i −0.0221236 + 0.0383192i
\(455\) 0 0
\(456\) −0.880733 0.184794i −0.0412441 0.00865376i
\(457\) 20.2210 0.945900 0.472950 0.881089i \(-0.343189\pi\)
0.472950 + 0.881089i \(0.343189\pi\)
\(458\) −0.902342 1.56290i −0.0421637 0.0730296i
\(459\) −3.28988 + 33.8608i −0.153558 + 1.58049i
\(460\) −8.15440 + 14.1238i −0.380201 + 0.658527i
\(461\) 12.1036 + 20.9640i 0.563719 + 0.976390i 0.997168 + 0.0752117i \(0.0239633\pi\)
−0.433449 + 0.901178i \(0.642703\pi\)
\(462\) 0 0
\(463\) 2.40242 4.16111i 0.111650 0.193383i −0.804786 0.593565i \(-0.797720\pi\)
0.916436 + 0.400182i \(0.131053\pi\)
\(464\) −12.6885 21.9772i −0.589050 1.02026i
\(465\) −20.6835 + 23.0928i −0.959173 + 1.07090i
\(466\) 0.432281 0.748732i 0.0200250 0.0346843i
\(467\) −13.6228 + 23.5954i −0.630389 + 1.09187i 0.357083 + 0.934073i \(0.383771\pi\)
−0.987472 + 0.157793i \(0.949562\pi\)
\(468\) −3.45128 31.2592i −0.159535 1.44496i
\(469\) 0 0
\(470\) 0.345979 + 0.599254i 0.0159588 + 0.0276415i
\(471\) 2.19755 + 6.70352i 0.101258 + 0.308882i
\(472\) −2.97565 −0.136965
\(473\) 18.0118 0.828184
\(474\) 0.0300130 + 0.0915532i 0.00137854 + 0.00420518i
\(475\) 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
\(479\) 10.2628 17.7756i 0.468917 0.812188i −0.530452 0.847715i \(-0.677978\pi\)
0.999369 + 0.0355269i \(0.0113109\pi\)
\(480\) 2.51780 2.81108i 0.114921 0.128308i
\(481\) 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
\(485\) −6.86254 + 11.8863i −0.311612 + 0.539727i
\(486\) 1.06575 0.0139711i 0.0483435 0.000633742i
\(487\) −12.9224 22.3823i −0.585571 1.01424i −0.994804 0.101809i \(-0.967537\pi\)
0.409233 0.912430i \(-0.365796\pi\)
\(488\) 0.741363 0.0335599
\(489\) 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 \(0.281287\pi\)
\(492\) −25.0056 5.24663i −1.12734 0.236536i
\(493\) −20.9152 + 36.2261i −0.941971 + 1.63154i
\(494\) −0.341610 0.591686i −0.0153698 0.0266212i
\(495\) 10.2991 7.56554i 0.462909 0.340046i
\(496\) −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 \(0.991271\pi\)
\(500\) 15.4363 0.690332
\(501\) −8.13502 1.70687i −0.363446 0.0762574i
\(502\) −0.379455 −0.0169359
\(503\) 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
\(506\) 0.335492 0.0149144
\(507\) 16.8744 18.8400i 0.749418 0.836714i
\(508\) −21.8553 −0.969674
\(509\) −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
\(513\) −8.99645 + 4.09056i −0.397203 + 0.180603i
\(514\) 0.336084 + 0.582115i 0.0148240 + 0.0256760i
\(515\) 6.89659 11.9452i 0.303900 0.526370i
\(516\) 25.9712 28.9964i 1.14332 1.27650i
\(517\) −3.03768 + 5.26142i −0.133597 + 0.231397i
\(518\) 0 0
\(519\) −2.71486 8.28153i −0.119169 0.363519i
\(520\) 3.82311 0.167654
\(521\) −0.713095 1.23512i −0.0312413 0.0541115i 0.849982 0.526812i \(-0.176613\pi\)
−0.881223 + 0.472700i \(0.843279\pi\)
\(522\) 1.20001 + 0.526756i 0.0525229 + 0.0230555i
\(523\) −3.85530 + 6.67758i −0.168581 + 0.291990i −0.937921 0.346849i \(-0.887252\pi\)
0.769340 + 0.638839i \(0.220585\pi\)
\(524\) 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
\(528\) 10.7670 + 2.25911i 0.468573 + 0.0983151i
\(529\) 6.79254 11.7650i 0.295328 0.511523i
\(530\) −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
\(534\) 0.0545409 + 0.0114437i 0.00236021 + 0.000495215i
\(535\) −45.1483 −1.95193
\(536\) 0.908402 0.0392370
\(537\) −18.9493 + 21.1566i −0.817721 + 0.912973i
\(538\) 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 0.389495 + 0.921028i \(0.372649\pi\)
−0.992382 + 0.123201i \(0.960684\pi\)
\(542\) −0.242608 + 0.420209i −0.0104209 + 0.0180495i
\(543\) 7.78813 + 23.7573i 0.334221 + 1.01952i
\(544\) −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 0.943818 + 0.330466i \(0.107206\pi\)
−0.185717 + 0.982603i \(0.559461\pi\)
\(548\) −19.4903 + 33.7583i −0.832586 + 1.44208i
\(549\) 6.56150 4.81998i 0.280038 0.205712i
\(550\) 0.114575 + 0.198450i 0.00488550 + 0.00846193i
\(551\) −12.1515 −0.517673
\(552\) 0.968623 1.08145i 0.0412273 0.0460297i
\(553\) 0 0
\(554\) 0.335836 0.581685i 0.0142683 0.0247134i
\(555\) 6.07891 + 18.5434i 0.258035 + 0.787124i
\(556\) −2.62464 + 4.54601i −0.111310 + 0.192794i
\(557\) −17.5209 30.3472i −0.742386 1.28585i −0.951406 0.307940i \(-0.900361\pi\)
0.209019 0.977911i \(-0.432973\pi\)
\(558\) 1.11077 0.815957i 0.0470228 0.0345422i
\(559\) 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
\(563\) −16.0262 −0.675425 −0.337712 0.941249i \(-0.609653\pi\)
−0.337712 + 0.941249i \(0.609653\pi\)
\(564\) 4.09011 + 12.4767i 0.172225 + 0.525362i
\(565\) 10.3992 0.437499
\(566\) 0.206213 0.00866776
\(567\) 0 0
\(568\) 3.38439 0.142006
\(569\) 0.371302 0.0155658 0.00778290 0.999970i \(-0.497523\pi\)
0.00778290 + 0.999970i \(0.497523\pi\)
\(570\) −0.186904 0.570141i −0.00782855 0.0238806i
\(571\) 29.2304 1.22325 0.611626 0.791147i \(-0.290516\pi\)
0.611626 + 0.791147i \(0.290516\pi\)
\(572\) 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
\(576\) 19.0714 14.0096i 0.794643 0.583732i
\(577\) −7.52852 13.0398i −0.313417 0.542853i 0.665683 0.746235i \(-0.268140\pi\)
−0.979100 + 0.203381i \(0.934807\pi\)
\(578\) −0.884279 + 1.53162i −0.0367811 + 0.0637068i
\(579\) 4.76361 + 14.5311i 0.197969 + 0.603894i
\(580\) 16.9793 29.4089i 0.705025 1.22114i
\(581\) 0 0
\(582\) 0.407107 0.454529i 0.0168751 0.0188408i
\(583\) −14.2300 −0.589347
\(584\) −0.300307 0.520148i −0.0124268 0.0215239i
\(585\) 33.8368 24.8560i 1.39898 1.02767i
\(586\) 0.583171 1.01008i 0.0240906 0.0417261i
\(587\) 0.835901 + 1.44782i 0.0345013 + 0.0597580i 0.882760 0.469823i \(-0.155682\pi\)
−0.848259 + 0.529581i \(0.822349\pi\)
\(588\) 0 0
\(589\) −6.38977 + 11.0674i −0.263286 + 0.456025i
\(590\) −0.991973 1.71815i −0.0408389 0.0707350i
\(591\) 3.08814 + 9.42020i 0.127029 + 0.387495i
\(592\) −8.39982 + 14.5489i −0.345231 + 0.597957i
\(593\) −5.40871 + 9.36816i −0.222109 + 0.384704i −0.955448 0.295159i \(-0.904627\pi\)
0.733339 + 0.679863i \(0.237961\pi\)
\(594\) −0.517188 + 0.235158i −0.0212205 + 0.00964867i
\(595\) 0 0
\(596\) −8.79221 15.2286i −0.360143 0.623786i
\(597\) 13.1911 14.7277i 0.539876 0.602764i
\(598\) 1.10223 0.0450736
\(599\) 16.6401 0.679898 0.339949 0.940444i \(-0.389590\pi\)
0.339949 + 0.940444i \(0.389590\pi\)
\(600\) 0.970498 + 0.203628i 0.0396204 + 0.00831308i
\(601\) −12.9011 22.3453i −0.526246 0.911485i −0.999532 0.0305765i \(-0.990266\pi\)
0.473286 0.880909i \(-0.343068\pi\)
\(602\) 0 0
\(603\) 8.03989 5.90598i 0.327410 0.240510i
\(604\) 4.65332 8.05978i 0.189341 0.327948i
\(605\) 11.2449 19.4768i 0.457171 0.791843i
\(606\) −0.213828 0.0448649i −0.00868616 0.00182251i
\(607\) −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
\(611\) −9.98005 + 17.2860i −0.403750 + 0.699315i
\(612\) −35.8862 15.7526i −1.45062 0.636763i
\(613\) 6.47719 + 11.2188i 0.261611 + 0.453124i 0.966670 0.256025i \(-0.0824129\pi\)
−0.705059 + 0.709149i \(0.749080\pi\)
\(614\) −1.58749 −0.0640659
\(615\) −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 \(-0.0598227\pi\)
\(618\) −0.409127 + 0.456784i −0.0164575 + 0.0183746i
\(619\) −16.5987 + 28.7498i −0.667157 + 1.15555i 0.311538 + 0.950234i \(0.399156\pi\)
−0.978696 + 0.205317i \(0.934178\pi\)
\(620\) −17.8568 30.9289i −0.717146 1.24213i
\(621\) 1.54181 15.8690i 0.0618708 0.636802i
\(622\) −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
\(626\) −0.315147 −0.0125958
\(627\) 3.51465 3.92406i 0.140362 0.156712i
\(628\) −8.12683 −0.324296
\(629\) 27.6917 1.10414
\(630\) 0 0
\(631\) 32.2773 1.28494 0.642470 0.766311i \(-0.277910\pi\)
0.642470 + 0.766311i \(0.277910\pi\)
\(632\) −0.222244 −0.00884040
\(633\) 36.2484 + 7.60557i 1.44075 + 0.302294i
\(634\) −1.76980 −0.0702877
\(635\) −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
\(639\) 29.9538 22.0036i 1.18496 0.870450i
\(640\) 2.89714 + 5.01799i 0.114519 + 0.198353i
\(641\) −21.5407 + 37.3096i −0.850806 + 1.47364i 0.0296762 + 0.999560i \(0.490552\pi\)
−0.880482 + 0.474079i \(0.842781\pi\)
\(642\) 1.96444 + 0.412174i 0.0775301 + 0.0162672i
\(643\) −3.20088 + 5.54409i −0.126230 + 0.218638i −0.922213 0.386682i \(-0.873621\pi\)
0.795983 + 0.605319i \(0.206955\pi\)
\(644\) 0 0
\(645\) 50.8604 + 10.6714i 2.00263 + 0.420187i
\(646\) −0.851419 −0.0334986
\(647\) −1.94403 3.36716i −0.0764278 0.132377i 0.825278 0.564726i \(-0.191018\pi\)
−0.901706 + 0.432349i \(0.857685\pi\)
\(648\) −0.735183 + 2.34609i −0.0288807 + 0.0921632i
\(649\) 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
\(653\) −7.55174 13.0800i −0.295522 0.511860i 0.679584 0.733598i \(-0.262160\pi\)
−0.975106 + 0.221738i \(0.928827\pi\)
\(654\) −0.671598 + 0.749829i −0.0262616 + 0.0293206i
\(655\) −5.93150 + 10.2737i −0.231763 + 0.401425i
\(656\) 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 \(0.922921\pi\)
\(660\) 4.58594 + 13.9892i 0.178507 + 0.544528i
\(661\) −19.4193 −0.755323 −0.377662 0.925944i \(-0.623272\pi\)
−0.377662 + 0.925944i \(0.623272\pi\)
\(662\) 0.0110303 0.000428706
\(663\) −18.5593 56.6142i −0.720783 2.19871i
\(664\) −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
\(668\) 4.78781 8.29273i 0.185246 0.320855i
\(669\) −8.28297 + 9.24781i −0.320238 + 0.357541i
\(670\) 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 0.803190 0.595723i \(-0.203135\pi\)
−0.917506 + 0.397721i \(0.869801\pi\)
\(674\) 0.309512 0.536091i 0.0119220 0.0206494i
\(675\) 9.91337 4.50747i 0.381566 0.173493i
\(676\) 14.5683 + 25.2330i 0.560318 + 0.970500i
\(677\) 36.9826 1.42136 0.710678 0.703518i \(-0.248388\pi\)
0.710678 + 0.703518i \(0.248388\pi\)
\(678\) −0.452477 0.0949379i −0.0173773 0.00364607i
\(679\) 0 0
\(680\) 2.38215 4.12601i 0.0913513 0.158225i
\(681\) −23.3737 4.90423i −0.895683 0.187930i
\(682\) −0.367336 + 0.636244i −0.0140660 + 0.0243630i
\(683\) −6.56800 11.3761i −0.251317 0.435294i 0.712571 0.701600i \(-0.247530\pi\)
−0.963889 + 0.266305i \(0.914197\pi\)
\(684\) −1.24940 11.3162i −0.0477721 0.432685i
\(685\) −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
\(689\) −46.7516 −1.78109
\(690\) 0.947338 + 0.198768i 0.0360645 + 0.00756699i
\(691\) 14.7658 0.561719 0.280860 0.959749i \(-0.409380\pi\)
0.280860 + 0.959749i \(0.409380\pi\)
\(692\) 10.0399 0.381659
\(693\) 0 0
\(694\) −0.397915 −0.0151046
\(695\) −7.00788 −0.265824
\(696\) −2.01689 + 2.25182i −0.0764499 + 0.0853552i
\(697\) −48.4032 −1.83340
\(698\) 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 \(0.695107\pi\)
\(702\) −1.69918 + 0.772594i −0.0641314 + 0.0291597i
\(703\) 4.02217 + 6.96660i 0.151699 + 0.262750i
\(704\) −6.30697 + 10.9240i −0.237703 + 0.411713i
\(705\) −11.6948 + 13.0571i −0.440452 + 0.491758i
\(706\) −0.826969 + 1.43235i −0.0311234 + 0.0539073i
\(707\) 0 0
\(708\) −11.7269 35.7724i −0.440725 1.34441i
\(709\) 14.1030 0.529650 0.264825 0.964296i \(-0.414686\pi\)
0.264825 + 0.964296i \(0.414686\pi\)
\(710\) 1.12823 + 1.95415i 0.0423418 + 0.0733381i
\(711\) −1.96699 + 1.44492i −0.0737680 + 0.0541888i
\(712\) −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
\(716\) −16.3596 28.3356i −0.611386 1.05895i
\(717\) 26.1608 + 5.48900i 0.976992 + 0.204990i
\(718\) 0.719212 1.24571i 0.0268408 0.0464896i
\(719\) −7.49790 + 12.9867i −0.279624 + 0.484324i −0.971291 0.237893i \(-0.923543\pi\)
0.691667 + 0.722217i \(0.256877\pi\)
\(720\) 29.0646 + 12.7582i 1.08317 + 0.475471i
\(721\) 0 0
\(722\) 0.525886 + 0.910861i 0.0195715 + 0.0338987i
\(723\) 2.00007 + 0.419650i 0.0743833 + 0.0156069i
\(724\) −28.8015 −1.07040
\(725\) 13.3900 0.497293
\(726\) −0.667084 + 0.744790i −0.0247578 + 0.0276417i
\(727\) −13.0527 22.6080i −0.484099 0.838485i 0.515734 0.856749i \(-0.327519\pi\)
−0.999833 + 0.0182642i \(0.994186\pi\)
\(728\) 0 0
\(729\) 8.74633 + 25.5441i 0.323938 + 0.946078i
\(730\) 0.200223 0.346796i 0.00741059 0.0128355i
\(731\) 36.8723 63.8648i 1.36377 2.36212i
\(732\) 2.92168 + 8.91245i 0.107989 + 0.329414i
\(733\) −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
\(737\) −2.65881 + 4.60520i −0.0979386 + 0.169635i
\(738\) 0.166419 + 1.50730i 0.00612595 + 0.0554844i
\(739\) −23.2933 40.3451i −0.856857 1.48412i −0.874912 0.484282i \(-0.839081\pi\)
0.0180552 0.999837i \(-0.494253\pi\)
\(740\) −22.4806 −0.826403
\(741\) 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 \(0.168646\pi\)
\(744\) 0.990362 + 3.02105i 0.0363084 + 0.110757i
\(745\) 11.7377 20.3304i 0.430038 0.744847i
\(746\) −0.0385841 0.0668297i −0.00141267 0.00244681i
\(747\) −18.7808 8.24402i −0.687153 0.301633i
\(748\) 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 \(0.602399\pi\)
\(752\) −15.0902 −0.550284
\(753\) −2.99434 9.13408i −0.109120 0.332864i
\(754\) −2.29509 −0.0835822
\(755\) 12.4245 0.452174
\(756\) 0 0
\(757\) −27.4703 −0.998424 −0.499212 0.866480i \(-0.666377\pi\)
−0.499212 + 0.866480i \(0.666377\pi\)
\(758\) −1.50162 −0.0545415
\(759\) 2.64742 + 8.07582i 0.0960952 + 0.293134i
\(760\) 1.38401 0.0502033
\(761\) −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
\(765\) −5.74181 52.0052i −0.207596 1.88025i
\(766\) −0.787671 1.36429i −0.0284597 0.0492937i
\(767\) 28.6143 49.5614i 1.03320 1.78956i
\(768\) 8.43171 + 25.7205i 0.304253 + 0.928109i
\(769\) −1.28876 + 2.23219i −0.0464738 + 0.0804949i −0.888327 0.459212i \(-0.848132\pi\)
0.841853 + 0.539707i \(0.181465\pi\)
\(770\) 0 0
\(771\) −11.3603 + 12.6836i −0.409132 + 0.456790i
\(772\) −17.6164 −0.634030
\(773\) −3.36486 5.82811i −0.121026 0.209623i 0.799147 0.601136i \(-0.205285\pi\)
−0.920172 + 0.391513i \(0.871952\pi\)
\(774\) −2.11555 0.928643i −0.0760419 0.0333794i
\(775\) 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
\(779\) −7.03047 12.1771i −0.251893 0.436291i
\(780\) 15.0667 + 45.9603i 0.539475 + 1.64564i
\(781\) −9.90581 + 17.1574i −0.354458 + 0.613939i
\(782\)