Properties

Label 224.3.w.a.43.20
Level 224
Weight 3
Character 224.43
Analytic conductor 6.104
Analytic rank 0
Dimension 192
CM no
Inner twists 2

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 224 = 2^{5} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 224.w (of order \(8\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.10355792167\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(48\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 43.20
Character \(\chi\) \(=\) 224.43
Dual form 224.3.w.a.99.20

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.491313 + 1.93871i) q^{2} +(-1.80355 - 4.35417i) q^{3} +(-3.51722 - 1.90503i) q^{4} +(3.60551 - 8.70447i) q^{5} +(9.32759 - 1.35732i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(5.42137 - 5.88292i) q^{8} +(-9.34199 + 9.34199i) q^{9} +O(q^{10})\) \(q+(-0.491313 + 1.93871i) q^{2} +(-1.80355 - 4.35417i) q^{3} +(-3.51722 - 1.90503i) q^{4} +(3.60551 - 8.70447i) q^{5} +(9.32759 - 1.35732i) q^{6} +(-1.87083 + 1.87083i) q^{7} +(5.42137 - 5.88292i) q^{8} +(-9.34199 + 9.34199i) q^{9} +(15.1040 + 11.2667i) q^{10} +(-2.46245 + 5.94487i) q^{11} +(-1.95132 + 18.7504i) q^{12} +(-7.20061 - 17.3838i) q^{13} +(-2.70784 - 4.54616i) q^{14} -44.4035 q^{15} +(8.74170 + 13.4008i) q^{16} +23.3365i q^{17} +(-13.5216 - 22.7013i) q^{18} +(4.65002 - 1.92610i) q^{19} +(-29.2637 + 23.7469i) q^{20} +(11.5200 + 4.77176i) q^{21} +(-10.3156 - 7.69477i) q^{22} +(-8.77199 - 8.77199i) q^{23} +(-35.3929 - 12.9954i) q^{24} +(-45.0905 - 45.0905i) q^{25} +(37.2400 - 5.41902i) q^{26} +(18.3379 + 7.59580i) q^{27} +(10.1441 - 3.01613i) q^{28} +(13.2002 - 5.46770i) q^{29} +(21.8160 - 86.0856i) q^{30} +32.3111i q^{31} +(-30.2753 + 10.3636i) q^{32} +30.3261 q^{33} +(-45.2428 - 11.4655i) q^{34} +(9.53928 + 23.0299i) q^{35} +(50.6547 - 15.0611i) q^{36} +(13.3458 - 32.2195i) q^{37} +(1.44954 + 9.96137i) q^{38} +(-62.7053 + 62.7053i) q^{39} +(-31.6609 - 68.4011i) q^{40} +(41.1738 - 41.1738i) q^{41} +(-14.9110 + 19.9896i) q^{42} +(-23.3393 + 56.3461i) q^{43} +(19.9861 - 16.2184i) q^{44} +(47.6345 + 115.000i) q^{45} +(21.3162 - 12.6966i) q^{46} -12.8015 q^{47} +(42.5834 - 62.2320i) q^{48} -7.00000i q^{49} +(109.571 - 65.2639i) q^{50} +(101.611 - 42.0887i) q^{51} +(-7.79057 + 74.8601i) q^{52} +(-40.9010 - 16.9417i) q^{53} +(-23.7357 + 31.8200i) q^{54} +(42.8686 + 42.8686i) q^{55} +(0.863478 + 21.1484i) q^{56} +(-16.7731 - 16.7731i) q^{57} +(4.11487 + 28.2778i) q^{58} +(-52.4040 - 21.7064i) q^{59} +(156.177 + 84.5900i) q^{60} +(13.9505 - 5.77849i) q^{61} +(-62.6420 - 15.8749i) q^{62} -34.9545i q^{63} +(-5.21748 - 63.7870i) q^{64} -177.279 q^{65} +(-14.8996 + 58.7936i) q^{66} +(-41.9906 - 101.374i) q^{67} +(44.4568 - 82.0797i) q^{68} +(-22.3739 + 54.0154i) q^{69} +(-49.3351 + 7.17906i) q^{70} +(-19.4698 + 19.4698i) q^{71} +(4.31178 + 105.605i) q^{72} +(5.72991 - 5.72991i) q^{73} +(55.9075 + 41.7035i) q^{74} +(-115.008 + 277.654i) q^{75} +(-20.0244 - 2.08391i) q^{76} +(-6.51502 - 15.7286i) q^{77} +(-90.7596 - 152.375i) q^{78} +100.121 q^{79} +(148.166 - 27.7750i) q^{80} +25.3586i q^{81} +(59.5949 + 100.053i) q^{82} +(41.3037 - 17.1086i) q^{83} +(-31.4282 - 38.7294i) q^{84} +(203.132 + 84.1400i) q^{85} +(-97.7720 - 72.9318i) q^{86} +(-47.6146 - 47.6146i) q^{87} +(21.6234 + 46.7157i) q^{88} +(-37.4978 - 37.4978i) q^{89} +(-246.355 + 35.8487i) q^{90} +(45.9932 + 19.0510i) q^{91} +(14.1421 + 47.5639i) q^{92} +(140.688 - 58.2749i) q^{93} +(6.28956 - 24.8185i) q^{94} -47.4205i q^{95} +(99.7282 + 113.132i) q^{96} +43.9204 q^{97} +(13.5710 + 3.43919i) q^{98} +(-32.5328 - 78.5411i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192q + O(q^{10}) \) \( 192q + 80q^{10} + 96q^{12} - 20q^{16} - 60q^{18} - 260q^{22} + 64q^{23} - 144q^{24} - 200q^{26} + 192q^{27} - 40q^{30} + 40q^{32} + 120q^{34} + 464q^{36} + 504q^{38} - 384q^{39} + 360q^{40} - 96q^{43} + 52q^{44} + 64q^{46} - 104q^{48} - 312q^{50} - 384q^{51} - 320q^{52} + 160q^{53} - 576q^{54} - 512q^{55} - 196q^{56} - 360q^{58} - 872q^{60} + 128q^{61} - 408q^{62} + 832q^{66} + 160q^{67} + 856q^{68} - 384q^{69} + 336q^{70} + 1488q^{72} + 308q^{74} + 768q^{75} + 1024q^{76} - 224q^{77} - 408q^{78} + 1024q^{79} - 1040q^{80} - 240q^{82} - 1384q^{86} + 896q^{87} - 560q^{88} - 1320q^{90} - 380q^{92} - 936q^{94} - 1088q^{96} - 512q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(129\) \(197\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.491313 + 1.93871i −0.245657 + 0.969357i
\(3\) −1.80355 4.35417i −0.601185 1.45139i −0.872363 0.488859i \(-0.837413\pi\)
0.271178 0.962529i \(-0.412587\pi\)
\(4\) −3.51722 1.90503i −0.879306 0.476258i
\(5\) 3.60551 8.70447i 0.721102 1.74089i 0.0509141 0.998703i \(-0.483787\pi\)
0.670188 0.742191i \(-0.266213\pi\)
\(6\) 9.32759 1.35732i 1.55460 0.226219i
\(7\) −1.87083 + 1.87083i −0.267261 + 0.267261i
\(8\) 5.42137 5.88292i 0.677671 0.735365i
\(9\) −9.34199 + 9.34199i −1.03800 + 1.03800i
\(10\) 15.1040 + 11.2667i 1.51040 + 1.12667i
\(11\) −2.46245 + 5.94487i −0.223859 + 0.540443i −0.995408 0.0957273i \(-0.969482\pi\)
0.771549 + 0.636170i \(0.219482\pi\)
\(12\) −1.95132 + 18.7504i −0.162610 + 1.56253i
\(13\) −7.20061 17.3838i −0.553893 1.33722i −0.914533 0.404510i \(-0.867442\pi\)
0.360641 0.932705i \(-0.382558\pi\)
\(14\) −2.70784 4.54616i −0.193417 0.324726i
\(15\) −44.4035 −2.96023
\(16\) 8.74170 + 13.4008i 0.546357 + 0.837553i
\(17\) 23.3365i 1.37274i 0.727254 + 0.686368i \(0.240796\pi\)
−0.727254 + 0.686368i \(0.759204\pi\)
\(18\) −13.5216 22.7013i −0.751200 1.26118i
\(19\) 4.65002 1.92610i 0.244738 0.101374i −0.256943 0.966427i \(-0.582715\pi\)
0.501681 + 0.865053i \(0.332715\pi\)
\(20\) −29.2637 + 23.7469i −1.46318 + 1.18735i
\(21\) 11.5200 + 4.77176i 0.548573 + 0.227227i
\(22\) −10.3156 7.69477i −0.468889 0.349762i
\(23\) −8.77199 8.77199i −0.381391 0.381391i 0.490212 0.871603i \(-0.336919\pi\)
−0.871603 + 0.490212i \(0.836919\pi\)
\(24\) −35.3929 12.9954i −1.47471 0.541474i
\(25\) −45.0905 45.0905i −1.80362 1.80362i
\(26\) 37.2400 5.41902i 1.43231 0.208424i
\(27\) 18.3379 + 7.59580i 0.679181 + 0.281326i
\(28\) 10.1441 3.01613i 0.362290 0.107719i
\(29\) 13.2002 5.46770i 0.455179 0.188541i −0.143301 0.989679i \(-0.545772\pi\)
0.598480 + 0.801138i \(0.295772\pi\)
\(30\) 21.8160 86.0856i 0.727200 2.86952i
\(31\) 32.3111i 1.04229i 0.853467 + 0.521147i \(0.174496\pi\)
−0.853467 + 0.521147i \(0.825504\pi\)
\(32\) −30.2753 + 10.3636i −0.946104 + 0.323864i
\(33\) 30.3261 0.918973
\(34\) −45.2428 11.4655i −1.33067 0.337222i
\(35\) 9.53928 + 23.0299i 0.272551 + 0.657996i
\(36\) 50.6547 15.0611i 1.40707 0.418363i
\(37\) 13.3458 32.2195i 0.360697 0.870799i −0.634502 0.772921i \(-0.718795\pi\)
0.995198 0.0978773i \(-0.0312053\pi\)
\(38\) 1.44954 + 9.96137i 0.0381458 + 0.262141i
\(39\) −62.7053 + 62.7053i −1.60783 + 1.60783i
\(40\) −31.6609 68.4011i −0.791522 1.71003i
\(41\) 41.1738 41.1738i 1.00424 1.00424i 0.00424762 0.999991i \(-0.498648\pi\)
0.999991 0.00424762i \(-0.00135206\pi\)
\(42\) −14.9110 + 19.9896i −0.355024 + 0.475944i
\(43\) −23.3393 + 56.3461i −0.542774 + 1.31037i 0.379983 + 0.924993i \(0.375930\pi\)
−0.922758 + 0.385380i \(0.874070\pi\)
\(44\) 19.9861 16.2184i 0.454230 0.368600i
\(45\) 47.6345 + 115.000i 1.05854 + 2.55555i
\(46\) 21.3162 12.6966i 0.463395 0.276013i
\(47\) −12.8015 −0.272373 −0.136186 0.990683i \(-0.543485\pi\)
−0.136186 + 0.990683i \(0.543485\pi\)
\(48\) 42.5834 62.2320i 0.887153 1.29650i
\(49\) 7.00000i 0.142857i
\(50\) 109.571 65.2639i 2.19142 1.30528i
\(51\) 101.611 42.0887i 1.99237 0.825268i
\(52\) −7.79057 + 74.8601i −0.149819 + 1.43962i
\(53\) −40.9010 16.9417i −0.771716 0.319655i −0.0381489 0.999272i \(-0.512146\pi\)
−0.733567 + 0.679617i \(0.762146\pi\)
\(54\) −23.7357 + 31.8200i −0.439550 + 0.589259i
\(55\) 42.8686 + 42.8686i 0.779429 + 0.779429i
\(56\) 0.863478 + 21.1484i 0.0154193 + 0.377650i
\(57\) −16.7731 16.7731i −0.294265 0.294265i
\(58\) 4.11487 + 28.2778i 0.0709461 + 0.487548i
\(59\) −52.4040 21.7064i −0.888203 0.367906i −0.108530 0.994093i \(-0.534614\pi\)
−0.779672 + 0.626188i \(0.784614\pi\)
\(60\) 156.177 + 84.5900i 2.60295 + 1.40983i
\(61\) 13.9505 5.77849i 0.228697 0.0947293i −0.265393 0.964140i \(-0.585502\pi\)
0.494089 + 0.869411i \(0.335502\pi\)
\(62\) −62.6420 15.8749i −1.01036 0.256047i
\(63\) 34.9545i 0.554834i
\(64\) −5.21748 63.7870i −0.0815231 0.996671i
\(65\) −177.279 −2.72736
\(66\) −14.8996 + 58.7936i −0.225752 + 0.890813i
\(67\) −41.9906 101.374i −0.626725 1.51305i −0.843668 0.536865i \(-0.819609\pi\)
0.216943 0.976184i \(-0.430391\pi\)
\(68\) 44.4568 82.0797i 0.653777 1.20705i
\(69\) −22.3739 + 54.0154i −0.324260 + 0.782833i
\(70\) −49.3351 + 7.17906i −0.704787 + 0.102558i
\(71\) −19.4698 + 19.4698i −0.274222 + 0.274222i −0.830797 0.556575i \(-0.812115\pi\)
0.556575 + 0.830797i \(0.312115\pi\)
\(72\) 4.31178 + 105.605i 0.0598859 + 1.46673i
\(73\) 5.72991 5.72991i 0.0784919 0.0784919i −0.666771 0.745263i \(-0.732324\pi\)
0.745263 + 0.666771i \(0.232324\pi\)
\(74\) 55.9075 + 41.7035i 0.755507 + 0.563561i
\(75\) −115.008 + 277.654i −1.53344 + 3.70206i
\(76\) −20.0244 2.08391i −0.263479 0.0274199i
\(77\) −6.51502 15.7286i −0.0846106 0.204268i
\(78\) −90.7596 152.375i −1.16358 1.95353i
\(79\) 100.121 1.26736 0.633678 0.773597i \(-0.281544\pi\)
0.633678 + 0.773597i \(0.281544\pi\)
\(80\) 148.166 27.7750i 1.85207 0.347188i
\(81\) 25.3586i 0.313069i
\(82\) 59.5949 + 100.053i 0.726768 + 1.22016i
\(83\) 41.3037 17.1086i 0.497635 0.206127i −0.119726 0.992807i \(-0.538202\pi\)
0.617361 + 0.786680i \(0.288202\pi\)
\(84\) −31.4282 38.7294i −0.374145 0.461064i
\(85\) 203.132 + 84.1400i 2.38979 + 0.989883i
\(86\) −97.7720 72.9318i −1.13688 0.848044i
\(87\) −47.6146 47.6146i −0.547294 0.547294i
\(88\) 21.6234 + 46.7157i 0.245720 + 0.530860i
\(89\) −37.4978 37.4978i −0.421323 0.421323i 0.464336 0.885659i \(-0.346293\pi\)
−0.885659 + 0.464336i \(0.846293\pi\)
\(90\) −246.355 + 35.8487i −2.73728 + 0.398318i
\(91\) 45.9932 + 19.0510i 0.505420 + 0.209352i
\(92\) 14.1421 + 47.5639i 0.153719 + 0.516999i
\(93\) 140.688 58.2749i 1.51277 0.626612i
\(94\) 6.28956 24.8185i 0.0669102 0.264026i
\(95\) 47.4205i 0.499164i
\(96\) 99.7282 + 113.132i 1.03884 + 1.17846i
\(97\) 43.9204 0.452787 0.226394 0.974036i \(-0.427306\pi\)
0.226394 + 0.974036i \(0.427306\pi\)
\(98\) 13.5710 + 3.43919i 0.138480 + 0.0350938i
\(99\) −32.5328 78.5411i −0.328614 0.793344i
\(100\) 72.6944 + 244.492i 0.726944 + 2.44492i
\(101\) 34.7369 83.8624i 0.343930 0.830321i −0.653380 0.757030i \(-0.726650\pi\)
0.997311 0.0732910i \(-0.0233502\pi\)
\(102\) 31.6750 + 217.673i 0.310539 + 2.13405i
\(103\) 97.3266 97.3266i 0.944918 0.944918i −0.0536421 0.998560i \(-0.517083\pi\)
0.998560 + 0.0536421i \(0.0170830\pi\)
\(104\) −141.305 51.8834i −1.35870 0.498879i
\(105\) 83.0712 83.0712i 0.791155 0.791155i
\(106\) 52.9404 70.9716i 0.499437 0.669543i
\(107\) −5.11430 + 12.3470i −0.0477972 + 0.115393i −0.945975 0.324240i \(-0.894891\pi\)
0.898178 + 0.439633i \(0.144891\pi\)
\(108\) −50.0281 61.6503i −0.463224 0.570837i
\(109\) 38.7115 + 93.4579i 0.355152 + 0.857412i 0.995967 + 0.0897173i \(0.0285964\pi\)
−0.640815 + 0.767695i \(0.721404\pi\)
\(110\) −104.172 + 62.0480i −0.947016 + 0.564073i
\(111\) −164.359 −1.48071
\(112\) −41.4249 8.71645i −0.369865 0.0778255i
\(113\) 51.9120i 0.459398i −0.973262 0.229699i \(-0.926226\pi\)
0.973262 0.229699i \(-0.0737742\pi\)
\(114\) 40.7591 24.2774i 0.357536 0.212960i
\(115\) −107.983 + 44.7280i −0.938983 + 0.388939i
\(116\) −56.8442 5.91568i −0.490036 0.0509973i
\(117\) 229.667 + 95.1313i 1.96297 + 0.813088i
\(118\) 67.8293 90.9316i 0.574825 0.770607i
\(119\) −43.6586 43.6586i −0.366879 0.366879i
\(120\) −240.728 + 261.222i −2.00606 + 2.17685i
\(121\) 56.2821 + 56.2821i 0.465141 + 0.465141i
\(122\) 4.34876 + 29.8851i 0.0356456 + 0.244960i
\(123\) −253.537 105.018i −2.06127 0.853807i
\(124\) 61.5537 113.645i 0.496401 0.916495i
\(125\) −337.451 + 139.777i −2.69961 + 1.11821i
\(126\) 67.7668 + 17.1736i 0.537832 + 0.136299i
\(127\) 211.601i 1.66615i −0.553163 0.833073i \(-0.686579\pi\)
0.553163 0.833073i \(-0.313421\pi\)
\(128\) 126.228 + 21.2242i 0.986157 + 0.165814i
\(129\) 287.434 2.22817
\(130\) 87.0994 343.693i 0.669995 2.64379i
\(131\) −90.8373 219.301i −0.693415 1.67405i −0.737785 0.675036i \(-0.764128\pi\)
0.0443698 0.999015i \(-0.485872\pi\)
\(132\) −106.664 57.7722i −0.808058 0.437668i
\(133\) −5.09598 + 12.3028i −0.0383157 + 0.0925022i
\(134\) 217.166 31.6012i 1.62064 0.235830i
\(135\) 132.235 132.235i 0.979517 0.979517i
\(136\) 137.287 + 126.516i 1.00946 + 0.930264i
\(137\) 65.8765 65.8765i 0.480851 0.480851i −0.424553 0.905403i \(-0.639569\pi\)
0.905403 + 0.424553i \(0.139569\pi\)
\(138\) −93.7279 69.9152i −0.679188 0.506632i
\(139\) −8.41859 + 20.3243i −0.0605654 + 0.146218i −0.951265 0.308374i \(-0.900215\pi\)
0.890700 + 0.454592i \(0.150215\pi\)
\(140\) 10.3209 99.1738i 0.0737204 0.708384i
\(141\) 23.0882 + 55.7399i 0.163746 + 0.395319i
\(142\) −28.1805 47.3121i −0.198455 0.333184i
\(143\) 121.076 0.846682
\(144\) −206.855 43.5256i −1.43650 0.302261i
\(145\) 134.615i 0.928377i
\(146\) 8.29347 + 13.9238i 0.0568046 + 0.0953687i
\(147\) −30.4792 + 12.6249i −0.207341 + 0.0858836i
\(148\) −108.319 + 87.8992i −0.731887 + 0.593913i
\(149\) −200.786 83.1682i −1.34756 0.558176i −0.411944 0.911209i \(-0.635150\pi\)
−0.935611 + 0.353033i \(0.885150\pi\)
\(150\) −481.787 359.383i −3.21192 2.39589i
\(151\) −28.6272 28.6272i −0.189584 0.189584i 0.605932 0.795516i \(-0.292800\pi\)
−0.795516 + 0.605932i \(0.792800\pi\)
\(152\) 13.8784 37.7978i 0.0913051 0.248670i
\(153\) −218.009 218.009i −1.42490 1.42490i
\(154\) 33.6943 4.90306i 0.218794 0.0318381i
\(155\) 281.251 + 116.498i 1.81452 + 0.751601i
\(156\) 340.004 101.093i 2.17951 0.648031i
\(157\) 46.6535 19.3245i 0.297156 0.123086i −0.229124 0.973397i \(-0.573586\pi\)
0.526280 + 0.850311i \(0.323586\pi\)
\(158\) −49.1908 + 194.106i −0.311334 + 1.22852i
\(159\) 208.645i 1.31223i
\(160\) −18.9479 + 300.897i −0.118424 + 1.88061i
\(161\) 32.8218 0.203862
\(162\) −49.1630 12.4590i −0.303475 0.0769074i
\(163\) 56.9905 + 137.587i 0.349635 + 0.844093i 0.996663 + 0.0816271i \(0.0260116\pi\)
−0.647028 + 0.762466i \(0.723988\pi\)
\(164\) −223.255 + 66.3800i −1.36131 + 0.404756i
\(165\) 109.341 263.973i 0.662673 1.59983i
\(166\) 12.8755 + 88.4818i 0.0775635 + 0.533023i
\(167\) 60.7860 60.7860i 0.363988 0.363988i −0.501291 0.865279i \(-0.667141\pi\)
0.865279 + 0.501291i \(0.167141\pi\)
\(168\) 90.5263 41.9020i 0.538847 0.249417i
\(169\) −130.847 + 130.847i −0.774241 + 0.774241i
\(170\) −262.925 + 352.476i −1.54662 + 2.07339i
\(171\) −25.4468 + 61.4340i −0.148812 + 0.359263i
\(172\) 189.431 153.719i 1.10134 0.893718i
\(173\) −75.6636 182.668i −0.437362 1.05588i −0.976857 0.213895i \(-0.931385\pi\)
0.539495 0.841989i \(-0.318615\pi\)
\(174\) 115.705 68.9173i 0.664969 0.396077i
\(175\) 168.713 0.964075
\(176\) −101.192 + 18.9694i −0.574956 + 0.107781i
\(177\) 267.324i 1.51031i
\(178\) 91.1206 54.2743i 0.511913 0.304912i
\(179\) −133.751 + 55.4016i −0.747213 + 0.309506i −0.723604 0.690215i \(-0.757516\pi\)
−0.0236094 + 0.999721i \(0.507516\pi\)
\(180\) 51.5373 495.225i 0.286318 2.75125i
\(181\) 241.619 + 100.082i 1.33491 + 0.552939i 0.932053 0.362323i \(-0.118016\pi\)
0.402860 + 0.915262i \(0.368016\pi\)
\(182\) −59.5315 + 79.8077i −0.327096 + 0.438504i
\(183\) −50.3210 50.3210i −0.274978 0.274978i
\(184\) −99.1611 + 4.04870i −0.538919 + 0.0220038i
\(185\) −232.336 232.336i −1.25587 1.25587i
\(186\) 43.8564 + 301.385i 0.235787 + 1.62035i
\(187\) −138.733 57.4649i −0.741885 0.307299i
\(188\) 45.0258 + 24.3873i 0.239499 + 0.129720i
\(189\) −48.5175 + 20.0966i −0.256706 + 0.106331i
\(190\) 91.9348 + 23.2983i 0.483868 + 0.122623i
\(191\) 21.1617i 0.110794i −0.998464 0.0553972i \(-0.982357\pi\)
0.998464 0.0553972i \(-0.0176425\pi\)
\(192\) −268.329 + 137.761i −1.39755 + 0.717505i
\(193\) −219.372 −1.13664 −0.568321 0.822807i \(-0.692407\pi\)
−0.568321 + 0.822807i \(0.692407\pi\)
\(194\) −21.5787 + 85.1491i −0.111230 + 0.438913i
\(195\) 319.732 + 771.901i 1.63965 + 3.95847i
\(196\) −13.3352 + 24.6206i −0.0680369 + 0.125615i
\(197\) −61.0242 + 147.325i −0.309767 + 0.747845i 0.689945 + 0.723862i \(0.257635\pi\)
−0.999712 + 0.0239829i \(0.992365\pi\)
\(198\) 168.252 24.4835i 0.849760 0.123654i
\(199\) 22.8141 22.8141i 0.114644 0.114644i −0.647458 0.762101i \(-0.724168\pi\)
0.762101 + 0.647458i \(0.224168\pi\)
\(200\) −509.716 + 20.8114i −2.54858 + 0.104057i
\(201\) −365.668 + 365.668i −1.81924 + 1.81924i
\(202\) 145.518 + 108.548i 0.720388 + 0.537365i
\(203\) −14.4662 + 34.9244i −0.0712620 + 0.172042i
\(204\) −437.569 45.5371i −2.14495 0.223221i
\(205\) −209.944 506.849i −1.02411 2.47243i
\(206\) 140.871 + 236.506i 0.683837 + 1.14809i
\(207\) 163.896 0.791766
\(208\) 170.012 248.458i 0.817365 1.19451i
\(209\) 32.3867i 0.154960i
\(210\) 120.237 + 201.865i 0.572559 + 0.961264i
\(211\) −161.852 + 67.0412i −0.767070 + 0.317731i −0.731685 0.681643i \(-0.761266\pi\)
−0.0353851 + 0.999374i \(0.511266\pi\)
\(212\) 111.583 + 137.505i 0.526336 + 0.648611i
\(213\) 119.889 + 49.6598i 0.562861 + 0.233145i
\(214\) −21.4246 15.9814i −0.100115 0.0746795i
\(215\) 406.313 + 406.313i 1.88983 + 1.88983i
\(216\) 144.102 66.7006i 0.667138 0.308799i
\(217\) −60.4486 60.4486i −0.278565 0.278565i
\(218\) −200.208 + 29.1335i −0.918384 + 0.133640i
\(219\) −35.2832 14.6148i −0.161110 0.0667341i
\(220\) −69.1123 232.444i −0.314147 1.05657i
\(221\) 405.677 168.037i 1.83564 0.760348i
\(222\) 80.7518 318.645i 0.363747 1.43534i
\(223\) 17.9463i 0.0804769i 0.999190 + 0.0402384i \(0.0128118\pi\)
−0.999190 + 0.0402384i \(0.987188\pi\)
\(224\) 37.2513 76.0285i 0.166301 0.339413i
\(225\) 842.469 3.74431
\(226\) 100.643 + 25.5051i 0.445321 + 0.112854i
\(227\) −162.297 391.819i −0.714963 1.72607i −0.687209 0.726460i \(-0.741164\pi\)
−0.0277544 0.999615i \(-0.508836\pi\)
\(228\) 27.0415 + 90.9481i 0.118603 + 0.398895i
\(229\) −149.017 + 359.758i −0.650727 + 1.57099i 0.160998 + 0.986955i \(0.448529\pi\)
−0.811725 + 0.584040i \(0.801471\pi\)
\(230\) −33.6613 231.324i −0.146354 1.00575i
\(231\) −56.7349 + 56.7349i −0.245606 + 0.245606i
\(232\) 39.3971 107.298i 0.169815 0.462492i
\(233\) −35.1721 + 35.1721i −0.150953 + 0.150953i −0.778544 0.627590i \(-0.784041\pi\)
0.627590 + 0.778544i \(0.284041\pi\)
\(234\) −297.271 + 398.520i −1.27039 + 1.70308i
\(235\) −46.1560 + 111.430i −0.196409 + 0.474172i
\(236\) 142.965 + 176.178i 0.605784 + 0.746515i
\(237\) −180.574 435.944i −0.761915 1.83943i
\(238\) 106.092 63.1915i 0.445763 0.265510i
\(239\) 117.082 0.489883 0.244941 0.969538i \(-0.421231\pi\)
0.244941 + 0.969538i \(0.421231\pi\)
\(240\) −388.162 595.044i −1.61734 2.47935i
\(241\) 117.733i 0.488520i 0.969710 + 0.244260i \(0.0785450\pi\)
−0.969710 + 0.244260i \(0.921455\pi\)
\(242\) −136.767 + 81.4627i −0.565153 + 0.336623i
\(243\) 275.456 114.098i 1.13356 0.469538i
\(244\) −60.0752 6.25193i −0.246210 0.0256227i
\(245\) −60.9313 25.2386i −0.248699 0.103015i
\(246\) 328.166 439.938i 1.33401 1.78837i
\(247\) −66.9659 66.9659i −0.271117 0.271117i
\(248\) 190.084 + 175.171i 0.766467 + 0.706333i
\(249\) −148.987 148.987i −0.598342 0.598342i
\(250\) −105.193 722.895i −0.420772 2.89158i
\(251\) 76.5109 + 31.6918i 0.304824 + 0.126262i 0.529852 0.848090i \(-0.322247\pi\)
−0.225028 + 0.974352i \(0.572247\pi\)
\(252\) −66.5895 + 122.943i −0.264244 + 0.487868i
\(253\) 73.7489 30.5478i 0.291497 0.120742i
\(254\) 410.233 + 103.962i 1.61509 + 0.409300i
\(255\) 1036.22i 4.06361i
\(256\) −103.165 + 234.292i −0.402989 + 0.915205i
\(257\) −221.809 −0.863070 −0.431535 0.902096i \(-0.642028\pi\)
−0.431535 + 0.902096i \(0.642028\pi\)
\(258\) −141.220 + 557.252i −0.547365 + 2.15989i
\(259\) 35.3096 + 85.2449i 0.136330 + 0.329131i
\(260\) 623.528 + 337.722i 2.39819 + 1.29893i
\(261\) −72.2369 + 174.395i −0.276770 + 0.668182i
\(262\) 469.791 68.3622i 1.79310 0.260924i
\(263\) 74.8796 74.8796i 0.284713 0.284713i −0.550272 0.834985i \(-0.685476\pi\)
0.834985 + 0.550272i \(0.185476\pi\)
\(264\) 164.409 178.406i 0.622762 0.675780i
\(265\) −294.938 + 294.938i −1.11297 + 1.11297i
\(266\) −21.3479 15.9242i −0.0802551 0.0598653i
\(267\) −95.6422 + 230.901i −0.358211 + 0.864797i
\(268\) −45.4310 + 436.549i −0.169519 + 1.62892i
\(269\) 53.8442 + 129.991i 0.200164 + 0.483239i 0.991807 0.127745i \(-0.0407739\pi\)
−0.791643 + 0.610984i \(0.790774\pi\)
\(270\) 191.397 + 321.334i 0.708877 + 1.19013i
\(271\) 265.989 0.981508 0.490754 0.871298i \(-0.336721\pi\)
0.490754 + 0.871298i \(0.336721\pi\)
\(272\) −312.729 + 204.001i −1.14974 + 0.750003i
\(273\) 234.622i 0.859420i
\(274\) 95.3497 + 160.082i 0.347992 + 0.584240i
\(275\) 379.090 157.024i 1.37851 0.570997i
\(276\) 181.595 147.361i 0.657954 0.533918i
\(277\) 163.495 + 67.7219i 0.590235 + 0.244483i 0.657752 0.753235i \(-0.271508\pi\)
−0.0675165 + 0.997718i \(0.521508\pi\)
\(278\) −35.2668 26.3068i −0.126859 0.0946289i
\(279\) −301.850 301.850i −1.08190 1.08190i
\(280\) 187.199 + 68.7346i 0.668567 + 0.245481i
\(281\) 305.589 + 305.589i 1.08751 + 1.08751i 0.995785 + 0.0917210i \(0.0292368\pi\)
0.0917210 + 0.995785i \(0.470763\pi\)
\(282\) −119.407 + 17.3757i −0.423430 + 0.0616160i
\(283\) 76.8193 + 31.8196i 0.271446 + 0.112437i 0.514255 0.857638i \(-0.328069\pi\)
−0.242808 + 0.970074i \(0.578069\pi\)
\(284\) 105.570 31.3890i 0.371725 0.110525i
\(285\) −206.477 + 85.5255i −0.724480 + 0.300090i
\(286\) −59.4860 + 234.731i −0.207993 + 0.820737i
\(287\) 154.058i 0.536788i
\(288\) 186.015 379.649i 0.645884 1.31823i
\(289\) −255.593 −0.884404
\(290\) 260.979 + 66.1380i 0.899928 + 0.228062i
\(291\) −79.2128 191.237i −0.272209 0.657171i
\(292\) −31.0690 + 9.23770i −0.106401 + 0.0316360i
\(293\) −106.243 + 256.494i −0.362605 + 0.875405i 0.632313 + 0.774713i \(0.282106\pi\)
−0.994918 + 0.100692i \(0.967894\pi\)
\(294\) −9.50121 65.2931i −0.0323170 0.222086i
\(295\) −377.886 + 377.886i −1.28097 + 1.28097i
\(296\) −117.193 253.186i −0.395921 0.855359i
\(297\) −90.3120 + 90.3120i −0.304081 + 0.304081i
\(298\) 259.888 348.404i 0.872107 1.16914i
\(299\) −89.3269 + 215.654i −0.298752 + 0.721251i
\(300\) 933.450 757.478i 3.11150 2.52493i
\(301\) −61.7500 149.078i −0.205149 0.495275i
\(302\) 69.5648 41.4350i 0.230347 0.137202i
\(303\) −427.801 −1.41188
\(304\) 66.4605 + 45.4768i 0.218620 + 0.149595i
\(305\) 142.266i 0.466446i
\(306\) 529.769 315.547i 1.73127 1.03120i
\(307\) 286.704 118.757i 0.933891 0.386830i 0.136738 0.990607i \(-0.456338\pi\)
0.797153 + 0.603777i \(0.206338\pi\)
\(308\) −7.04881 + 67.7325i −0.0228857 + 0.219911i
\(309\) −599.310 248.242i −1.93951 0.803373i
\(310\) −364.039 + 488.029i −1.17432 + 1.57429i
\(311\) −12.1983 12.1983i −0.0392228 0.0392228i 0.687223 0.726446i \(-0.258829\pi\)
−0.726446 + 0.687223i \(0.758829\pi\)
\(312\) 28.9415 + 708.838i 0.0927613 + 2.27192i
\(313\) 31.3024 + 31.3024i 0.100008 + 0.100008i 0.755340 0.655333i \(-0.227472\pi\)
−0.655333 + 0.755340i \(0.727472\pi\)
\(314\) 14.5432 + 99.9423i 0.0463160 + 0.318287i
\(315\) −304.261 126.029i −0.965907 0.400092i
\(316\) −352.148 190.734i −1.11439 0.603588i
\(317\) 393.794 163.115i 1.24225 0.514558i 0.337835 0.941205i \(-0.390305\pi\)
0.904418 + 0.426647i \(0.140305\pi\)
\(318\) −404.503 102.510i −1.27202 0.322359i
\(319\) 91.9374i 0.288205i
\(320\) −574.044 184.569i −1.79389 0.576779i
\(321\) 62.9849 0.196215
\(322\) −16.1258 + 63.6320i −0.0500801 + 0.197615i
\(323\) 44.9485 + 108.515i 0.139159 + 0.335960i
\(324\) 48.3089 89.1917i 0.149101 0.275283i
\(325\) −459.165 + 1108.52i −1.41282 + 3.41084i
\(326\) −294.742 + 42.8898i −0.904118 + 0.131564i
\(327\) 337.113 337.113i 1.03093 1.03093i
\(328\) −19.0037 465.440i −0.0579381 1.41903i
\(329\) 23.9494 23.9494i 0.0727947 0.0727947i
\(330\) 458.047 + 341.674i 1.38802 + 1.03538i
\(331\) 120.382 290.627i 0.363691 0.878028i −0.631063 0.775732i \(-0.717381\pi\)
0.994754 0.102296i \(-0.0326190\pi\)
\(332\) −177.867 18.5103i −0.535743 0.0557540i
\(333\) 176.319 + 425.671i 0.529485 + 1.27829i
\(334\) 87.9816 + 147.712i 0.263418 + 0.442250i
\(335\) −1033.81 −3.08599
\(336\) 36.7592 + 196.092i 0.109402 + 0.583606i
\(337\) 526.534i 1.56242i −0.624271 0.781208i \(-0.714604\pi\)
0.624271 0.781208i \(-0.285396\pi\)
\(338\) −189.388 317.961i −0.560318 0.940713i
\(339\) −226.033 + 93.6261i −0.666765 + 0.276183i
\(340\) −554.171 682.912i −1.62991 2.00857i
\(341\) −192.085 79.5644i −0.563300 0.233327i
\(342\) −106.601 79.5175i −0.311698 0.232507i
\(343\) 13.0958 + 13.0958i 0.0381802 + 0.0381802i
\(344\) 204.948 + 442.776i 0.595780 + 1.28714i
\(345\) 389.507 + 389.507i 1.12900 + 1.12900i
\(346\) 391.315 56.9427i 1.13097 0.164574i
\(347\) 265.259 + 109.874i 0.764434 + 0.316639i 0.730616 0.682789i \(-0.239233\pi\)
0.0338187 + 0.999428i \(0.489233\pi\)
\(348\) 76.7637 + 258.178i 0.220585 + 0.741892i
\(349\) 587.614 243.398i 1.68371 0.697414i 0.684215 0.729280i \(-0.260145\pi\)
0.999492 + 0.0318660i \(0.0101450\pi\)
\(350\) −82.8910 + 327.086i −0.236831 + 0.934532i
\(351\) 373.476i 1.06403i
\(352\) 12.9408 205.503i 0.0367636 0.583815i
\(353\) −67.4312 −0.191023 −0.0955116 0.995428i \(-0.530449\pi\)
−0.0955116 + 0.995428i \(0.530449\pi\)
\(354\) −518.265 131.340i −1.46403 0.371017i
\(355\) 99.2756 + 239.673i 0.279650 + 0.675134i
\(356\) 60.4535 + 203.322i 0.169813 + 0.571130i
\(357\) −111.356 + 268.838i −0.311922 + 0.753046i
\(358\) −41.6940 286.525i −0.116464 0.800349i
\(359\) −215.758 + 215.758i −0.600999 + 0.600999i −0.940578 0.339579i \(-0.889715\pi\)
0.339579 + 0.940578i \(0.389715\pi\)
\(360\) 934.778 + 343.227i 2.59661 + 0.953407i
\(361\) −237.353 + 237.353i −0.657487 + 0.657487i
\(362\) −312.741 + 419.259i −0.863925 + 1.15817i
\(363\) 143.554 346.569i 0.395465 0.954737i
\(364\) −125.476 154.625i −0.344713 0.424794i
\(365\) −29.2166 70.5351i −0.0800454 0.193247i
\(366\) 122.281 72.8346i 0.334102 0.199002i
\(367\) −50.8475 −0.138549 −0.0692745 0.997598i \(-0.522068\pi\)
−0.0692745 + 0.997598i \(0.522068\pi\)
\(368\) 40.8699 194.234i 0.111060 0.527810i
\(369\) 769.290i 2.08480i
\(370\) 564.582 336.283i 1.52590 0.908873i
\(371\) 108.214 44.8236i 0.291681 0.120818i
\(372\) −605.847 63.0495i −1.62862 0.169488i
\(373\) 392.031 + 162.384i 1.05102 + 0.435347i 0.840256 0.542190i \(-0.182405\pi\)
0.210764 + 0.977537i \(0.432405\pi\)
\(374\) 179.569 240.729i 0.480131 0.643661i
\(375\) 1217.22 + 1217.22i 3.24593 + 3.24593i
\(376\) −69.4018 + 75.3103i −0.184579 + 0.200293i
\(377\) −190.099 190.099i −0.504241 0.504241i
\(378\) −15.1243 103.935i −0.0400113 0.274961i
\(379\) −342.373 141.816i −0.903360 0.374184i −0.117849 0.993032i \(-0.537600\pi\)
−0.785511 + 0.618848i \(0.787600\pi\)
\(380\) −90.3376 + 166.789i −0.237731 + 0.438917i
\(381\) −921.344 + 381.633i −2.41823 + 1.00166i
\(382\) 41.0265 + 10.3970i 0.107399 + 0.0272174i
\(383\) 325.117i 0.848870i 0.905458 + 0.424435i \(0.139527\pi\)
−0.905458 + 0.424435i \(0.860473\pi\)
\(384\) −135.246 587.897i −0.352202 1.53098i
\(385\) −160.400 −0.416622
\(386\) 107.780 425.299i 0.279224 1.10181i
\(387\) −308.349 744.420i −0.796767 1.92357i
\(388\) −154.478 83.6698i −0.398139 0.215644i
\(389\) 175.565 423.851i 0.451323 1.08959i −0.520496 0.853864i \(-0.674253\pi\)
0.971819 0.235726i \(-0.0757469\pi\)
\(390\) −1653.58 + 240.623i −4.23996 + 0.616982i
\(391\) 204.708 204.708i 0.523549 0.523549i
\(392\) −41.1804 37.9496i −0.105052 0.0968102i
\(393\) −791.042 + 791.042i −2.01283 + 2.01283i
\(394\) −255.640 190.691i −0.648832 0.483988i
\(395\) 360.988 871.501i 0.913893 2.20633i
\(396\) −35.1983 + 338.222i −0.0888845 + 0.854097i
\(397\) 299.686 + 723.506i 0.754877 + 1.82243i 0.529875 + 0.848076i \(0.322239\pi\)
0.225002 + 0.974358i \(0.427761\pi\)
\(398\) 33.0211 + 55.4388i 0.0829675 + 0.139293i
\(399\) 62.7593 0.157291
\(400\) 210.083 998.418i 0.525207 2.49604i
\(401\) 117.073i 0.291951i 0.989288 + 0.145976i \(0.0466321\pi\)
−0.989288 + 0.145976i \(0.953368\pi\)
\(402\) −529.268 888.583i −1.31659 2.21041i
\(403\) 561.690 232.660i 1.39377 0.577319i
\(404\) −281.938 + 228.788i −0.697867 + 0.566306i
\(405\) 220.733 + 91.4305i 0.545019 + 0.225754i
\(406\) −60.6011 45.2046i −0.149264 0.111341i
\(407\) 158.678 + 158.678i 0.389872 + 0.389872i
\(408\) 303.267 825.948i 0.743301 2.02438i
\(409\) −103.371 103.371i −0.252741 0.252741i 0.569352 0.822094i \(-0.307194\pi\)
−0.822094 + 0.569352i \(0.807194\pi\)
\(410\) 1085.78 157.999i 2.64825 0.385363i
\(411\) −405.649 168.025i −0.986981 0.408821i
\(412\) −527.729 + 156.909i −1.28090 + 0.380847i
\(413\) 138.648 57.4298i 0.335709 0.139055i
\(414\) −80.5241 + 317.747i −0.194503 + 0.767504i
\(415\) 421.212i 1.01497i
\(416\) 398.160 + 451.675i 0.957116 + 1.08576i
\(417\) 103.679 0.248630
\(418\) −62.7885 15.9120i −0.150212 0.0380670i
\(419\) 49.7864 + 120.195i 0.118822 + 0.286861i 0.972089 0.234613i \(-0.0753822\pi\)
−0.853267 + 0.521474i \(0.825382\pi\)
\(420\) −450.433 + 133.927i −1.07246 + 0.318873i
\(421\) 134.779 325.386i 0.320141 0.772889i −0.679104 0.734042i \(-0.737631\pi\)
0.999245 0.0388471i \(-0.0123685\pi\)
\(422\) −50.4538 346.723i −0.119559 0.821617i
\(423\) 119.592 119.592i 0.282723 0.282723i
\(424\) −321.406 + 148.770i −0.758033 + 0.350872i
\(425\) 1052.25 1052.25i 2.47589 2.47589i
\(426\) −155.179 + 208.033i −0.364271 + 0.488340i
\(427\) −15.2884 + 36.9096i −0.0358043 + 0.0864393i
\(428\) 41.5096 33.6843i 0.0969850 0.0787016i
\(429\) −218.366 527.183i −0.509012 1.22886i
\(430\) −987.351 + 588.097i −2.29616 + 1.36767i
\(431\) −746.935 −1.73303 −0.866514 0.499152i \(-0.833645\pi\)
−0.866514 + 0.499152i \(0.833645\pi\)
\(432\) 58.5142 + 312.143i 0.135450 + 0.722554i
\(433\) 500.959i 1.15695i −0.815701 0.578474i \(-0.803648\pi\)
0.815701 0.578474i \(-0.196352\pi\)
\(434\) 146.892 87.4933i 0.338460 0.201597i
\(435\) −586.134 + 242.785i −1.34744 + 0.558126i
\(436\) 41.8833 402.459i 0.0960626 0.923071i
\(437\) −57.6856 23.8942i −0.132004 0.0546777i
\(438\) 45.6690 61.2235i 0.104267 0.139780i
\(439\) 346.502 + 346.502i 0.789297 + 0.789297i 0.981379 0.192082i \(-0.0615238\pi\)
−0.192082 + 0.981379i \(0.561524\pi\)
\(440\) 484.599 19.7859i 1.10136 0.0449680i
\(441\) 65.3939 + 65.3939i 0.148286 + 0.148286i
\(442\) 126.461 + 869.051i 0.286111 + 1.96618i
\(443\) 277.762 + 115.053i 0.627003 + 0.259713i 0.673479 0.739206i \(-0.264799\pi\)
−0.0464760 + 0.998919i \(0.514799\pi\)
\(444\) 578.087 + 313.109i 1.30200 + 0.705201i
\(445\) −461.597 + 191.200i −1.03730 + 0.429662i
\(446\) −34.7928 8.81728i −0.0780108 0.0197697i
\(447\) 1024.25i 2.29139i
\(448\) 129.096 + 109.573i 0.288160 + 0.244584i
\(449\) 37.0427 0.0825004 0.0412502 0.999149i \(-0.486866\pi\)
0.0412502 + 0.999149i \(0.486866\pi\)
\(450\) −413.916 + 1633.31i −0.919814 + 3.62957i
\(451\) 143.385 + 346.161i 0.317926 + 0.767541i
\(452\) −98.8940 + 182.586i −0.218792 + 0.403951i
\(453\) −73.0168 + 176.278i −0.161185 + 0.389135i
\(454\) 839.363 122.141i 1.84882 0.269033i
\(455\) 331.658 331.658i 0.728919 0.728919i
\(456\) −189.608 + 7.74161i −0.415808 + 0.0169772i
\(457\) 158.269 158.269i 0.346321 0.346321i −0.512416 0.858737i \(-0.671249\pi\)
0.858737 + 0.512416i \(0.171249\pi\)
\(458\) −624.253 465.654i −1.36300 1.01671i
\(459\) −177.259 + 427.942i −0.386186 + 0.932336i
\(460\) 465.009 + 48.3927i 1.01089 + 0.105202i
\(461\) 39.2781 + 94.8256i 0.0852018 + 0.205695i 0.960738 0.277457i \(-0.0894916\pi\)
−0.875536 + 0.483153i \(0.839492\pi\)
\(462\) −82.1182 137.867i −0.177745 0.298414i
\(463\) −150.322 −0.324669 −0.162335 0.986736i \(-0.551902\pi\)
−0.162335 + 0.986736i \(0.551902\pi\)
\(464\) 188.664 + 129.097i 0.406604 + 0.278226i
\(465\) 1434.73i 3.08543i
\(466\) −50.9081 85.4692i −0.109245 0.183410i
\(467\) −58.8057 + 24.3581i −0.125922 + 0.0521587i −0.444755 0.895652i \(-0.646709\pi\)
0.318833 + 0.947811i \(0.396709\pi\)
\(468\) −626.563 772.122i −1.33881 1.64983i
\(469\) 268.211 + 111.097i 0.571879 + 0.236880i
\(470\) −193.355 144.231i −0.411393 0.306874i
\(471\) −168.284 168.284i −0.357292 0.357292i
\(472\) −411.799 + 190.610i −0.872454 + 0.403834i
\(473\) −277.498 277.498i −0.586677 0.586677i
\(474\) 933.889 135.896i 1.97023 0.286700i
\(475\) −296.520 122.823i −0.624253 0.258574i
\(476\) 70.3860 + 236.728i 0.147870 + 0.497328i
\(477\) 540.366 223.827i 1.13284 0.469239i
\(478\) −57.5240 + 226.988i −0.120343 + 0.474871i
\(479\) 444.681i 0.928352i 0.885743 + 0.464176i \(0.153650\pi\)
−0.885743 + 0.464176i \(0.846350\pi\)
\(480\) 1344.33 460.182i 2.80068 0.958712i
\(481\) −656.196 −1.36423
\(482\) −228.251 57.8439i −0.473550 0.120008i
\(483\) −59.1959 142.911i −0.122559 0.295883i
\(484\) −90.7374 305.176i −0.187474 0.630528i
\(485\) 158.355 382.304i 0.326506 0.788255i
\(486\) 85.8674 + 590.088i 0.176682 + 1.21417i
\(487\) 366.301 366.301i 0.752158 0.752158i −0.222723 0.974882i \(-0.571495\pi\)
0.974882 + 0.222723i \(0.0714947\pi\)
\(488\) 41.6365 113.397i 0.0853206 0.232371i
\(489\) 496.292 496.292i 1.01491 1.01491i
\(490\) 78.8667 105.728i 0.160953 0.215772i
\(491\) −102.872 + 248.354i −0.209514 + 0.505813i −0.993347 0.115160i \(-0.963262\pi\)
0.783833 + 0.620972i \(0.213262\pi\)
\(492\) 691.681 + 852.368i 1.40586 + 1.73246i
\(493\) 127.597 + 308.047i 0.258818 + 0.624841i
\(494\) 162.729 96.9265i 0.329411 0.196207i
\(495\) −800.956 −1.61809
\(496\) −432.996 + 282.454i −0.872977 + 0.569464i
\(497\) 72.8492i 0.146578i
\(498\) 362.043 215.644i 0.726993 0.433020i
\(499\) 95.6052 39.6010i 0.191594 0.0793606i −0.284824 0.958580i \(-0.591935\pi\)
0.476417 + 0.879219i \(0.341935\pi\)
\(500\) 1453.17 + 151.229i 2.90634 + 0.302458i
\(501\) −374.303 155.041i −0.747112 0.309464i
\(502\) −99.0322 + 132.762i −0.197275 + 0.264466i
\(503\) 7.48609 + 7.48609i 0.0148829 + 0.0148829i 0.714509 0.699626i \(-0.246650\pi\)
−0.699626 + 0.714509i \(0.746650\pi\)
\(504\) −205.635 189.501i −0.408005 0.375995i
\(505\) −604.733 604.733i −1.19749 1.19749i
\(506\) 22.9896 + 157.986i 0.0454340 + 0.312226i
\(507\) 805.718 + 333.739i 1.58919 + 0.658263i
\(508\) −403.106 + 744.246i −0.793516 + 1.46505i
\(509\) 508.353 210.567i 0.998730 0.413687i 0.177398 0.984139i \(-0.443232\pi\)
0.821331 + 0.570452i \(0.193232\pi\)
\(510\) 2008.94 + 509.110i 3.93909 + 0.998254i
\(511\) 21.4394i 0.0419557i
\(512\) −403.540 315.119i −0.788163 0.615466i
\(513\) 99.9017 0.194740
\(514\) 108.978 430.024i 0.212019 0.836622i
\(515\) −496.264 1198.09i −0.963620 2.32639i
\(516\) −1010.97 547.571i −1.95924 1.06118i
\(517\) 31.5230 76.1034i 0.0609730 0.147202i
\(518\) −182.614 + 26.5732i −0.352536 + 0.0512997i
\(519\) −658.903 + 658.903i −1.26956 + 1.26956i
\(520\) −961.093 + 1042.92i −1.84826 + 2.00561i
\(521\) −442.255 + 442.255i −0.848857 + 0.848857i −0.989991 0.141133i \(-0.954925\pi\)
0.141133 + 0.989991i \(0.454925\pi\)
\(522\) −302.612 225.730i −0.579716 0.432432i
\(523\) 260.027 627.760i 0.497183 1.20031i −0.453812 0.891098i \(-0.649936\pi\)
0.950994 0.309208i \(-0.100064\pi\)
\(524\) −98.2799 + 944.377i −0.187557 + 1.80225i
\(525\) −304.283 734.605i −0.579587 1.39925i
\(526\) 108.381 + 181.959i 0.206047 + 0.345930i
\(527\) −754.029 −1.43080
\(528\) 265.102 + 406.395i 0.502087 + 0.769688i
\(529\) 375.104i 0.709082i
\(530\) −426.893 716.707i −0.805458 1.35228i
\(531\) 692.339 286.776i 1.30384 0.540068i
\(532\) 41.3609 33.5636i 0.0777461 0.0630896i
\(533\) −1012.23 419.281i −1.89912 0.786643i
\(534\) −400.660 298.868i −0.750300 0.559677i
\(535\) 89.0346 + 89.0346i 0.166420 + 0.166420i
\(536\) −824.023 302.560i −1.53736 0.564478i
\(537\) 482.455 + 482.455i 0.898427 + 0.898427i
\(538\) −278.470 + 40.5220i −0.517603 + 0.0753196i
\(539\) 41.6141 + 17.2371i 0.0772061 + 0.0319798i
\(540\) −717.011 + 213.188i −1.32780 + 0.394792i
\(541\) 216.194 89.5506i 0.399620 0.165528i −0.173817 0.984778i \(-0.555610\pi\)
0.573436 + 0.819250i \(0.305610\pi\)
\(542\) −130.684 + 515.676i −0.241114 + 0.951431i
\(543\) 1232.55i 2.26990i
\(544\) −241.851 706.520i −0.444580 1.29875i
\(545\) 953.077 1.74876
\(546\) 454.864 + 115.273i 0.833085 + 0.211122i
\(547\) −41.5068 100.206i −0.0758807 0.183192i 0.881387 0.472394i \(-0.156610\pi\)
−0.957268 + 0.289202i \(0.906610\pi\)
\(548\) −357.199 + 106.205i −0.651824 + 0.193806i
\(549\) −76.3429 + 184.308i −0.139058 + 0.335716i
\(550\) 118.173 + 812.094i 0.214860 + 1.47654i
\(551\) 50.8498 50.8498i 0.0922864 0.0922864i
\(552\) 196.471 + 424.462i 0.355926 + 0.768953i
\(553\) −187.309 + 187.309i −0.338715 + 0.338715i
\(554\) −211.621 + 283.698i −0.381987 + 0.512090i
\(555\) −592.598 + 1430.66i −1.06774 + 2.57776i
\(556\) 68.3285 55.4473i 0.122893 0.0997254i
\(557\) −137.966 333.080i −0.247696 0.597990i 0.750312 0.661084i \(-0.229903\pi\)
−0.998008 + 0.0630938i \(0.979903\pi\)
\(558\) 733.504 436.898i 1.31452 0.782972i
\(559\) 1147.57 2.05289
\(560\) −225.230 + 329.155i −0.402197 + 0.587776i
\(561\) 707.705i 1.26151i
\(562\) −742.590 + 442.310i −1.32133 + 0.787028i
\(563\) 583.901 241.860i 1.03712 0.429591i 0.201845 0.979417i \(-0.435306\pi\)
0.835279 + 0.549827i \(0.185306\pi\)
\(564\) 24.9799 240.034i 0.0442906 0.425591i
\(565\) −451.867 187.169i −0.799764 0.331273i
\(566\) −99.4314 + 133.297i −0.175674 + 0.235507i
\(567\) −47.4415 47.4415i −0.0836711 0.0836711i
\(568\) 8.98624 + 220.092i 0.0158209 + 0.387486i
\(569\) 443.205 + 443.205i 0.778919 + 0.778919i 0.979647 0.200728i \(-0.0643307\pi\)
−0.200728 + 0.979647i \(0.564331\pi\)
\(570\) −64.3646 442.319i −0.112920 0.775999i
\(571\) 218.856 + 90.6529i 0.383285 + 0.158762i 0.566002 0.824404i \(-0.308489\pi\)
−0.182717 + 0.983165i \(0.558489\pi\)
\(572\) −425.849 230.653i −0.744492 0.403239i
\(573\) −92.1417 + 38.1663i −0.160806 + 0.0666079i
\(574\) −298.675 75.6909i −0.520339 0.131866i
\(575\) 791.066i 1.37577i
\(576\) 644.639 + 547.156i 1.11916 + 0.949923i
\(577\) 893.147 1.54792 0.773958 0.633237i \(-0.218274\pi\)
0.773958 + 0.633237i \(0.218274\pi\)
\(578\) 125.576 495.521i 0.217260 0.857303i
\(579\) 395.649 + 955.181i 0.683332 + 1.64971i
\(580\) −256.445 + 473.470i −0.442147 + 0.816327i
\(581\) −45.2650 + 109.279i −0.0779088 + 0.188088i
\(582\) 409.671 59.6138i 0.703903 0.102429i
\(583\) 201.433 201.433i 0.345511 0.345511i
\(584\) −2.64463 64.7726i −0.00452848 0.110912i
\(585\) 1656.14 1656.14i 2.83100 2.83100i
\(586\) −445.069 331.994i −0.759504 0.566543i
\(587\) 368.197 888.907i 0.627253 1.51432i −0.215771 0.976444i \(-0.569226\pi\)
0.843023 0.537877i \(-0.180774\pi\)
\(588\) 131.253 + 13.6593i 0.223219 + 0.0232300i
\(589\) 62.2345 + 150.247i 0.105661 + 0.255089i
\(590\) −546.952 918.273i −0.927038 1.55640i
\(591\) 751.540 1.27164
\(592\) 548.434 102.809i 0.926409 0.173664i
\(593\) 417.572i 0.704169i 0.935968 + 0.352084i \(0.114527\pi\)
−0.935968 + 0.352084i \(0.885473\pi\)
\(594\) −130.718 219.461i −0.220063 0.369462i
\(595\) −537.437 + 222.614i −0.903255 + 0.374141i
\(596\) 547.770 + 675.024i 0.919077 + 1.13259i
\(597\) −140.483 58.1898i −0.235314 0.0974704i
\(598\) −374.204 279.133i −0.625759 0.466778i
\(599\) 438.516 + 438.516i 0.732081 + 0.732081i 0.971032 0.238951i \(-0.0768035\pi\)
−0.238951 + 0.971032i \(0.576803\pi\)
\(600\) 1009.92 + 2181.85i 1.68319 + 3.63642i
\(601\) 727.159 + 727.159i 1.20991 + 1.20991i 0.971054 + 0.238861i \(0.0767739\pi\)
0.238861 + 0.971054i \(0.423226\pi\)
\(602\) 319.358 46.4717i 0.530494 0.0771955i
\(603\) 1339.31 + 554.762i 2.22108 + 0.920003i
\(604\) 46.1524 + 155.224i 0.0764113 + 0.256993i
\(605\) 692.831 286.980i 1.14518 0.474347i
\(606\) 210.184 829.383i 0.346839 1.36862i
\(607\) 21.8287i 0.0359616i −0.999838 0.0179808i \(-0.994276\pi\)
0.999838 0.0179808i \(-0.00572378\pi\)
\(608\) −120.819 + 106.504i −0.198716 + 0.175172i
\(609\) 178.157 0.292541
\(610\) 275.813 + 69.8973i 0.452153 + 0.114586i
\(611\) 92.1787 + 222.539i 0.150865 + 0.364221i
\(612\) 351.473 + 1182.10i 0.574302 + 1.93154i
\(613\) −265.781 + 641.653i −0.433575 + 1.04674i 0.544551 + 0.838728i \(0.316700\pi\)
−0.978126 + 0.208015i \(0.933300\pi\)
\(614\) 89.3739 + 614.185i 0.145560 + 1.00030i
\(615\) −1828.26 + 1828.26i −2.97278 + 2.97278i
\(616\) −127.851 46.9435i −0.207550 0.0762070i
\(617\) −21.3499 + 21.3499i −0.0346027 + 0.0346027i −0.724196 0.689594i \(-0.757789\pi\)
0.689594 + 0.724196i \(0.257789\pi\)
\(618\) 775.720 1039.93i 1.25521 1.68273i
\(619\) −135.806 + 327.865i −0.219396 + 0.529668i −0.994806 0.101790i \(-0.967543\pi\)
0.775410 + 0.631458i \(0.217543\pi\)
\(620\) −767.291 945.543i −1.23757 1.52507i
\(621\) −94.2294 227.490i −0.151738 0.366328i
\(622\) 29.6421 17.6558i 0.0476562 0.0283855i
\(623\) 140.304 0.225207
\(624\) −1388.45 292.153i −2.22509 0.468193i
\(625\) 1847.11i 2.95538i
\(626\) −76.0657 + 45.3071i −0.121511 + 0.0723756i
\(627\) 141.017 58.4111i 0.224907 0.0931597i
\(628\) −200.905 20.9078i −0.319912 0.0332927i
\(629\) 751.892 + 311.444i 1.19538 + 0.495141i
\(630\) 393.821 527.955i 0.625113 0.838023i
\(631\) 496.809 + 496.809i 0.787335 + 0.787335i 0.981057 0.193721i \(-0.0620558\pi\)
−0.193721 + 0.981057i \(0.562056\pi\)
\(632\) 542.794 589.004i 0.858851 0.931969i
\(633\) 583.817 + 583.817i 0.922302 + 0.922302i
\(634\) 122.757 + 843.595i 0.193623 + 1.33059i
\(635\) −1841.87 762.928i −2.90059 1.20146i
\(636\) 397.475 733.851i 0.624961 1.15385i
\(637\) −121.687 + 50.4042i −0.191031 + 0.0791275i
\(638\) −178.240 45.1701i −0.279373 0.0707995i
\(639\) 363.773i 0.569284i
\(640\) 639.862 1022.22i 0.999785 1.59723i
\(641\) −420.798 −0.656472 −0.328236 0.944596i \(-0.606454\pi\)
−0.328236 + 0.944596i \(0.606454\pi\)
\(642\) −30.9453 + 122.110i −0.0482014 + 0.190202i
\(643\) −272.220 657.196i −0.423359 1.02208i −0.981350 0.192231i \(-0.938428\pi\)
0.557991 0.829847i \(-0.311572\pi\)
\(644\) −115.441 62.5265i −0.179257 0.0970909i
\(645\) 1036.35 2501.96i 1.60674 3.87901i
\(646\) −232.464 + 33.8272i −0.359851 + 0.0523642i
\(647\) 130.560 130.560i 0.201792 0.201792i −0.598975 0.800768i \(-0.704425\pi\)
0.800768 + 0.598975i \(0.204425\pi\)
\(648\) 149.182 + 137.478i 0.230220 + 0.212158i
\(649\) 258.084 258.084i 0.397664 0.397664i
\(650\) −1923.51 1434.82i −2.95925 2.20742i
\(651\) −154.181 + 372.226i −0.236837 + 0.571775i
\(652\) 61.6598 592.493i 0.0945703 0.908732i
\(653\) −15.1294 36.5256i −0.0231690 0.0559350i 0.911872 0.410476i \(-0.134637\pi\)
−0.935041 + 0.354541i \(0.884637\pi\)
\(654\) 487.937 + 819.194i 0.746082 + 1.25259i
\(655\) −2236.41 −3.41437
\(656\) 911.692 + 191.834i 1.38978 + 0.292430i
\(657\) 107.058i 0.162949i
\(658\) 34.6644 + 58.1978i 0.0526815 + 0.0884465i
\(659\) −445.466 + 184.518i −0.675973 + 0.279997i −0.694143 0.719838i \(-0.744216\pi\)
0.0181692 + 0.999835i \(0.494216\pi\)
\(660\) −887.453 + 720.152i −1.34463 + 1.09114i
\(661\) 1.00741 + 0.417284i 0.00152407 + 0.000631291i 0.383445 0.923564i \(-0.374737\pi\)
−0.381921 + 0.924195i \(0.624737\pi\)
\(662\) 504.298 + 376.175i 0.761779 + 0.568240i
\(663\) −1463.32 1463.32i −2.20712 2.20712i
\(664\) 123.275 335.738i 0.185654 0.505630i
\(665\) 88.7157 + 88.7157i 0.133407 + 0.133407i
\(666\) −911.882 + 132.694i −1.36919 + 0.199240i
\(667\) −163.755 67.8294i −0.245509 0.101693i
\(668\) −329.597 + 97.9985i −0.493409 + 0.146704i
\(669\) 78.1414 32.3672i 0.116803 0.0483815i
\(670\) 507.923 2004.26i 0.758094 2.99143i
\(671\) 97.1631i 0.144803i
\(672\) −398.226 25.0768i −0.592598 0.0373167i
\(673\) 461.465 0.685683 0.342842 0.939393i \(-0.388611\pi\)
0.342842 + 0.939393i \(0.388611\pi\)
\(674\) 1020.80 + 258.693i 1.51454 + 0.383818i
\(675\) −484.365 1169.36i −0.717578 1.73239i
\(676\) 709.484 210.950i 1.04953 0.312056i
\(677\) 175.931 424.735i 0.259869 0.627379i −0.739061 0.673639i \(-0.764730\pi\)
0.998929 + 0.0462603i \(0.0147304\pi\)
\(678\) −70.4610 484.214i −0.103925 0.714180i
\(679\) −82.1675 + 82.1675i −0.121013 + 0.121013i
\(680\) 1596.24 738.855i 2.34742 1.08655i
\(681\) −1413.33 + 1413.33i −2.07538 + 2.07538i
\(682\) 248.627 333.308i 0.364555 0.488721i
\(683\) −479.662 + 1158.01i −0.702286 + 1.69547i 0.0161437 + 0.999870i \(0.494861\pi\)
−0.718430 + 0.695599i \(0.755139\pi\)
\(684\) 206.536 167.600i 0.301953 0.245030i
\(685\) −335.902 810.939i −0.490368 1.18385i
\(686\) −31.8232 + 18.9549i −0.0463894 + 0.0276310i
\(687\) 1835.20 2.67133
\(688\) −959.110 + 179.794i −1.39406 + 0.261329i
\(689\) 833.005i 1.20901i
\(690\) −946.511 + 563.772i −1.37176 + 0.817061i
\(691\) 454.875 188.415i 0.658285 0.272670i −0.0284318 0.999596i \(-0.509051\pi\)
0.686717 + 0.726925i \(0.259051\pi\)
\(692\) −81.8629 + 786.625i −0.118299 + 1.13674i
\(693\) 207.800 + 86.0736i 0.299856 + 0.124204i
\(694\) −343.339 + 460.278i −0.494725 + 0.663225i
\(695\) 146.559 + 146.559i 0.210876 + 0.210876i
\(696\) −538.249 + 21.9764i −0.773346 + 0.0315753i
\(697\) 960.852 + 960.852i 1.37855 + 1.37855i
\(698\) 183.176 + 1258.80i 0.262429 + 1.80344i
\(699\) 216.580 + 89.7104i 0.309843 + 0.128341i
\(700\) −593.401 321.404i −0.847716 0.459148i
\(701\) −89.0006 + 36.8653i −0.126962 + 0.0525895i −0.445260 0.895401i \(-0.646889\pi\)
0.318298 + 0.947991i \(0.396889\pi\)
\(702\) 724.064 + 183.494i 1.03143 + 0.261387i
\(703\) 175.527i 0.249683i
\(704\) 392.053 + 126.055i 0.556893 + 0.179055i
\(705\) 568.432 0.806286
\(706\) 33.1298 130.730i 0.0469261 0.185170i
\(707\) 91.9053 + 221.879i 0.129993 + 0.313832i
\(708\) 509.261 940.239i 0.719296 1.32802i
\(709\) 153.858 371.447i 0.217007 0.523902i −0.777462 0.628930i \(-0.783493\pi\)
0.994469 + 0.105028i \(0.0334932\pi\)
\(710\) −513.432 + 74.7127i −0.723143 + 0.105229i
\(711\) −935.330 + 935.330i −1.31551 + 1.31551i
\(712\) −423.886 + 17.3070i −0.595345 + 0.0243076i
\(713\) 283.433 283.433i 0.397521 0.397521i
\(714\) −466.488 347.971i −0.653345 0.487355i
\(715\) 436.539 1053.90i 0.610544 1.47398i
\(716\) 575.974 + 59.9407i 0.804434 + 0.0837161i
\(717\) −211.164 509.794i −0.294510 0.711010i
\(718\) −312.289 524.299i −0.434943 0.730221i
\(719\) −122.268 −0.170052 −0.0850261 0.996379i \(-0.527097\pi\)
−0.0850261 + 0.996379i \(0.527097\pi\)
\(720\) −1124.69 + 1643.64i −1.56207 + 2.28283i
\(721\) 364.163i 0.505080i
\(722\) −343.544 576.774i −0.475823 0.798855i
\(723\) 512.630 212.338i 0.709032 0.293691i
\(724\) −659.169 812.303i −0.910455 1.12197i
\(725\) −841.744 348.662i −1.16103 0.480913i
\(726\) 601.369 + 448.584i 0.828332 + 0.617884i
\(727\) −798.915 798.915i −1.09892 1.09892i −0.994537 0.104383i \(-0.966713\pi\)
−0.104383 0.994537i \(-0.533287\pi\)
\(728\) 361.422 167.292i 0.496459 0.229796i
\(729\) −832.220 832.220i −1.14159 1.14159i
\(730\) 151.102 21.9878i 0.206989 0.0301202i
\(731\) −1314.92 544.658i −1.79880 0.745086i
\(732\) 81.1270 + 272.853i 0.110829 + 0.372750i
\(733\) −1271.79 + 526.791i −1.73504 + 0.718678i −0.735908 + 0.677081i \(0.763244\pi\)
−0.999134 + 0.0415967i \(0.986756\pi\)
\(734\) 24.9821 98.5787i 0.0340355 0.134303i
\(735\) 310.824i 0.422890i
\(736\) 356.485 + 174.665i 0.484354 + 0.237316i
\(737\) 706.056 0.958014
\(738\) −1491.43 377.963i −2.02091 0.512144i
\(739\) 175.530 + 423.766i 0.237523 + 0.573432i 0.997025 0.0770728i \(-0.0245574\pi\)
−0.759502 + 0.650505i \(0.774557\pi\)
\(740\) 374.570 + 1259.78i 0.506175 + 1.70241i
\(741\) −170.804 + 412.357i −0.230505 + 0.556488i
\(742\) 33.7333 + 231.818i 0.0454626 + 0.312423i
\(743\) 72.2027 72.2027i 0.0971773 0.0971773i −0.656847 0.754024i \(-0.728110\pi\)
0.754024 + 0.656847i \(0.228110\pi\)
\(744\) 419.895 1143.59i 0.564376 1.53708i
\(745\) −1447.87 + 1447.87i −1.94345 + 1.94345i
\(746\) −507.427 + 680.253i −0.680197 + 0.911868i
\(747\) −226.031 + 545.687i −0.302585 + 0.730505i
\(748\) 378.481 + 466.407i 0.505990 + 0.623538i
\(749\) −13.5312 32.6671i −0.0180656 0.0436143i
\(750\) −2957.88 + 1761.81i −3.94384 + 2.34908i
\(751\) −639.410 −0.851412 −0.425706 0.904862i \(-0.639974\pi\)
−0.425706 + 0.904862i \(0.639974\pi\)
\(752\) −111.907 171.551i −0.148813 0.228127i
\(753\) 390.299i 0.518325i
\(754\) 461.945 275.149i 0.612660 0.364919i
\(755\) −352.400 + 145.969i −0.466755 + 0.193336i
\(756\) 208.931 + 21.7431i 0.276364 + 0.0287608i
\(757\) 934.715 + 387.172i 1.23476 + 0.511455i 0.902074 0.431582i \(-0.142044\pi\)
0.332688 + 0.943037i \(0.392044\pi\)
\(758\) 443.153 594.088i 0.584634 0.783757i
\(759\) −266.020 266.020i </