Properties

Label 105.3.o.b.44.5
Level 105
Weight 3
Character 105.44
Analytic conductor 2.861
Analytic rank 0
Dimension 40
CM no
Inner twists 8

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 44.5
Character \(\chi\) \(=\) 105.44
Dual form 105.3.o.b.74.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.949639 + 1.64482i) q^{2} +(-2.65035 - 1.40558i) q^{3} +(0.196373 + 0.340128i) q^{4} +(4.51617 - 2.14574i) q^{5} +(4.82880 - 3.02455i) q^{6} +(4.60961 + 5.26797i) q^{7} -8.34304 q^{8} +(5.04868 + 7.45056i) q^{9} +O(q^{10})\) \(q+(-0.949639 + 1.64482i) q^{2} +(-2.65035 - 1.40558i) q^{3} +(0.196373 + 0.340128i) q^{4} +(4.51617 - 2.14574i) q^{5} +(4.82880 - 3.02455i) q^{6} +(4.60961 + 5.26797i) q^{7} -8.34304 q^{8} +(5.04868 + 7.45056i) q^{9} +(-0.759373 + 9.46598i) q^{10} +(-8.35863 + 4.82586i) q^{11} +(-0.0423786 - 1.17748i) q^{12} +16.9521i q^{13} +(-13.0423 + 2.57932i) q^{14} +(-14.9854 - 0.660900i) q^{15} +(7.13738 - 12.3623i) q^{16} +(12.1835 + 21.1024i) q^{17} +(-17.0493 + 1.22884i) q^{18} +(6.95261 - 12.0423i) q^{19} +(1.61668 + 1.11471i) q^{20} +(-4.81249 - 20.4411i) q^{21} -18.3313i q^{22} +(0.354602 - 0.614188i) q^{23} +(22.1120 + 11.7268i) q^{24} +(15.7916 - 19.3810i) q^{25} +(-27.8832 - 16.0984i) q^{26} +(-2.90837 - 26.8429i) q^{27} +(-0.886581 + 2.60234i) q^{28} +16.5872i q^{29} +(15.3178 - 24.0208i) q^{30} +(7.12320 + 12.3377i) q^{31} +(-3.13021 - 5.42169i) q^{32} +(28.9364 - 1.04145i) q^{33} -46.2795 q^{34} +(32.1215 + 13.9000i) q^{35} +(-1.54272 + 3.18028i) q^{36} +(1.08578 + 0.626873i) q^{37} +(13.2049 + 22.8716i) q^{38} +(23.8276 - 44.9289i) q^{39} +(-37.6786 + 17.9020i) q^{40} -24.1024i q^{41} +(38.1922 + 11.4960i) q^{42} -57.6214i q^{43} +(-3.28282 - 1.89534i) q^{44} +(38.7876 + 22.8149i) q^{45} +(0.673487 + 1.16651i) q^{46} +(16.0840 - 27.8583i) q^{47} +(-36.2928 + 22.7322i) q^{48} +(-6.50303 + 48.5666i) q^{49} +(16.8821 + 44.3794i) q^{50} +(-2.62927 - 73.0534i) q^{51} +(-5.76588 + 3.32893i) q^{52} +(-8.67882 - 15.0322i) q^{53} +(46.9137 + 20.7073i) q^{54} +(-27.3940 + 39.7298i) q^{55} +(-38.4582 - 43.9509i) q^{56} +(-35.3532 + 22.1437i) q^{57} +(-27.2829 - 15.7518i) q^{58} +(-75.8739 + 43.8058i) q^{59} +(-2.71794 - 5.22675i) q^{60} +(52.2391 - 90.4808i) q^{61} -27.0578 q^{62} +(-15.9769 + 60.9404i) q^{63} +68.9894 q^{64} +(36.3748 + 76.5586i) q^{65} +(-25.7661 + 48.5843i) q^{66} +(-86.1690 + 49.7497i) q^{67} +(-4.78500 + 8.28786i) q^{68} +(-1.80311 + 1.12939i) q^{69} +(-53.3669 + 39.6341i) q^{70} -50.7518i q^{71} +(-42.1213 - 62.1603i) q^{72} +(81.5039 - 47.0563i) q^{73} +(-2.06219 + 1.19061i) q^{74} +(-69.0949 + 29.1701i) q^{75} +5.46122 q^{76} +(-63.9525 - 21.7877i) q^{77} +(51.2726 + 81.8584i) q^{78} +(-3.71265 + 6.43050i) q^{79} +(5.70736 - 71.1453i) q^{80} +(-30.0217 + 75.2310i) q^{81} +(39.6441 + 22.8885i) q^{82} +69.6382 q^{83} +(6.00756 - 5.65095i) q^{84} +(100.303 + 69.1594i) q^{85} +(94.7770 + 54.7196i) q^{86} +(23.3146 - 43.9617i) q^{87} +(69.7364 - 40.2623i) q^{88} +(78.3272 + 45.2223i) q^{89} +(-74.3607 + 42.1329i) q^{90} +(-89.3032 + 78.1425i) q^{91} +0.278537 q^{92} +(-1.53723 - 42.7115i) q^{93} +(30.5480 + 52.9107i) q^{94} +(5.55961 - 69.3035i) q^{95} +(0.675522 + 18.7691i) q^{96} +90.4517i q^{97} +(-73.7078 - 56.8170i) q^{98} +(-78.1554 - 37.9123i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + O(q^{10}) \) \( 40q - 44q^{4} + 80q^{6} + 12q^{9} + 62q^{10} + 84q^{15} - 116q^{16} - 56q^{19} + 36q^{21} - 12q^{24} - 6q^{25} - 20q^{30} - 444q^{31} + 256q^{34} - 688q^{36} + 168q^{39} + 54q^{40} - 40q^{45} + 304q^{46} + 156q^{49} + 156q^{51} - 140q^{54} - 500q^{55} - 130q^{60} + 288q^{61} + 472q^{64} + 340q^{66} - 272q^{69} + 710q^{70} - 524q^{75} + 400q^{76} - 340q^{79} + 496q^{84} + 896q^{85} + 1356q^{90} - 656q^{91} - 560q^{94} + 472q^{96} - 336q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.949639 + 1.64482i −0.474819 + 0.822411i −0.999584 0.0288361i \(-0.990820\pi\)
0.524765 + 0.851247i \(0.324153\pi\)
\(3\) −2.65035 1.40558i −0.883449 0.468527i
\(4\) 0.196373 + 0.340128i 0.0490932 + 0.0850320i
\(5\) 4.51617 2.14574i 0.903234 0.429148i
\(6\) 4.82880 3.02455i 0.804801 0.504092i
\(7\) 4.60961 + 5.26797i 0.658515 + 0.752567i
\(8\) −8.34304 −1.04288
\(9\) 5.04868 + 7.45056i 0.560964 + 0.827840i
\(10\) −0.759373 + 9.46598i −0.0759373 + 0.946598i
\(11\) −8.35863 + 4.82586i −0.759876 + 0.438714i −0.829251 0.558876i \(-0.811233\pi\)
0.0693754 + 0.997591i \(0.477899\pi\)
\(12\) −0.0423786 1.17748i −0.00353155 0.0981229i
\(13\) 16.9521i 1.30401i 0.758216 + 0.652004i \(0.226071\pi\)
−0.758216 + 0.652004i \(0.773929\pi\)
\(14\) −13.0423 + 2.57932i −0.931596 + 0.184237i
\(15\) −14.9854 0.660900i −0.999029 0.0440600i
\(16\) 7.13738 12.3623i 0.446086 0.772644i
\(17\) 12.1835 + 21.1024i 0.716674 + 1.24131i 0.962311 + 0.271953i \(0.0876696\pi\)
−0.245637 + 0.969362i \(0.578997\pi\)
\(18\) −17.0493 + 1.22884i −0.947182 + 0.0682687i
\(19\) 6.95261 12.0423i 0.365927 0.633804i −0.622997 0.782224i \(-0.714085\pi\)
0.988924 + 0.148420i \(0.0474187\pi\)
\(20\) 1.61668 + 1.11471i 0.0808340 + 0.0557355i
\(21\) −4.81249 20.4411i −0.229166 0.973387i
\(22\) 18.3313i 0.833240i
\(23\) 0.354602 0.614188i 0.0154175 0.0267038i −0.858214 0.513292i \(-0.828426\pi\)
0.873631 + 0.486589i \(0.161759\pi\)
\(24\) 22.1120 + 11.7268i 0.921331 + 0.488618i
\(25\) 15.7916 19.3810i 0.631665 0.775242i
\(26\) −27.8832 16.0984i −1.07243 0.619168i
\(27\) −2.90837 26.8429i −0.107717 0.994182i
\(28\) −0.886581 + 2.60234i −0.0316636 + 0.0929408i
\(29\) 16.5872i 0.571971i 0.958234 + 0.285986i \(0.0923209\pi\)
−0.958234 + 0.285986i \(0.907679\pi\)
\(30\) 15.3178 24.0208i 0.510594 0.800692i
\(31\) 7.12320 + 12.3377i 0.229781 + 0.397992i 0.957743 0.287625i \(-0.0928658\pi\)
−0.727962 + 0.685617i \(0.759532\pi\)
\(32\) −3.13021 5.42169i −0.0978192 0.169428i
\(33\) 28.9364 1.04145i 0.876861 0.0315592i
\(34\) −46.2795 −1.36116
\(35\) 32.1215 + 13.9000i 0.917756 + 0.397144i
\(36\) −1.54272 + 3.18028i −0.0428533 + 0.0883412i
\(37\) 1.08578 + 0.626873i 0.0293453 + 0.0169425i 0.514601 0.857430i \(-0.327940\pi\)
−0.485256 + 0.874372i \(0.661273\pi\)
\(38\) 13.2049 + 22.8716i 0.347498 + 0.601885i
\(39\) 23.8276 44.9289i 0.610963 1.15202i
\(40\) −37.6786 + 17.9020i −0.941965 + 0.447550i
\(41\) 24.1024i 0.587862i −0.955827 0.293931i \(-0.905036\pi\)
0.955827 0.293931i \(-0.0949637\pi\)
\(42\) 38.1922 + 11.4960i 0.909337 + 0.273714i
\(43\) 57.6214i 1.34003i −0.742346 0.670017i \(-0.766287\pi\)
0.742346 0.670017i \(-0.233713\pi\)
\(44\) −3.28282 1.89534i −0.0746095 0.0430758i
\(45\) 38.7876 + 22.8149i 0.861948 + 0.506997i
\(46\) 0.673487 + 1.16651i 0.0146410 + 0.0253590i
\(47\) 16.0840 27.8583i 0.342213 0.592730i −0.642630 0.766176i \(-0.722157\pi\)
0.984843 + 0.173446i \(0.0554903\pi\)
\(48\) −36.2928 + 22.7322i −0.756100 + 0.473588i
\(49\) −6.50303 + 48.5666i −0.132715 + 0.991154i
\(50\) 16.8821 + 44.3794i 0.337641 + 0.887588i
\(51\) −2.62927 73.0534i −0.0515544 1.43242i
\(52\) −5.76588 + 3.32893i −0.110882 + 0.0640180i
\(53\) −8.67882 15.0322i −0.163751 0.283625i 0.772460 0.635064i \(-0.219026\pi\)
−0.936211 + 0.351438i \(0.885693\pi\)
\(54\) 46.9137 + 20.7073i 0.868772 + 0.383469i
\(55\) −27.3940 + 39.7298i −0.498073 + 0.722361i
\(56\) −38.4582 43.9509i −0.686753 0.784838i
\(57\) −35.3532 + 22.1437i −0.620232 + 0.388487i
\(58\) −27.2829 15.7518i −0.470395 0.271583i
\(59\) −75.8739 + 43.8058i −1.28600 + 0.742471i −0.977938 0.208896i \(-0.933013\pi\)
−0.308060 + 0.951367i \(0.599680\pi\)
\(60\) −2.71794 5.22675i −0.0452990 0.0871124i
\(61\) 52.2391 90.4808i 0.856379 1.48329i −0.0189801 0.999820i \(-0.506042\pi\)
0.875359 0.483473i \(-0.160625\pi\)
\(62\) −27.0578 −0.436417
\(63\) −15.9769 + 60.9404i −0.253602 + 0.967309i
\(64\) 68.9894 1.07796
\(65\) 36.3748 + 76.5586i 0.559612 + 1.17782i
\(66\) −25.7661 + 48.5843i −0.390396 + 0.736125i
\(67\) −86.1690 + 49.7497i −1.28610 + 0.742533i −0.977957 0.208806i \(-0.933042\pi\)
−0.308147 + 0.951339i \(0.599709\pi\)
\(68\) −4.78500 + 8.28786i −0.0703676 + 0.121880i
\(69\) −1.80311 + 1.12939i −0.0261320 + 0.0163680i
\(70\) −53.3669 + 39.6341i −0.762384 + 0.566201i
\(71\) 50.7518i 0.714814i −0.933949 0.357407i \(-0.883661\pi\)
0.933949 0.357407i \(-0.116339\pi\)
\(72\) −42.1213 62.1603i −0.585018 0.863338i
\(73\) 81.5039 47.0563i 1.11649 0.644607i 0.175988 0.984392i \(-0.443688\pi\)
0.940503 + 0.339786i \(0.110355\pi\)
\(74\) −2.06219 + 1.19061i −0.0278674 + 0.0160893i
\(75\) −69.0949 + 29.1701i −0.921265 + 0.388934i
\(76\) 5.46122 0.0718582
\(77\) −63.9525 21.7877i −0.830552 0.282957i
\(78\) 51.2726 + 81.8584i 0.657340 + 1.04947i
\(79\) −3.71265 + 6.43050i −0.0469956 + 0.0813987i −0.888566 0.458748i \(-0.848298\pi\)
0.841571 + 0.540147i \(0.181631\pi\)
\(80\) 5.70736 71.1453i 0.0713420 0.889316i
\(81\) −30.0217 + 75.2310i −0.370639 + 0.928777i
\(82\) 39.6441 + 22.8885i 0.483465 + 0.279128i
\(83\) 69.6382 0.839015 0.419508 0.907752i \(-0.362203\pi\)
0.419508 + 0.907752i \(0.362203\pi\)
\(84\) 6.00756 5.65095i 0.0715185 0.0672732i
\(85\) 100.303 + 69.1594i 1.18003 + 0.813640i
\(86\) 94.7770 + 54.7196i 1.10206 + 0.636274i
\(87\) 23.3146 43.9617i 0.267984 0.505307i
\(88\) 69.7364 40.2623i 0.792459 0.457527i
\(89\) 78.3272 + 45.2223i 0.880081 + 0.508115i 0.870685 0.491841i \(-0.163676\pi\)
0.00939614 + 0.999956i \(0.497009\pi\)
\(90\) −74.3607 + 42.1329i −0.826230 + 0.468143i
\(91\) −89.3032 + 78.1425i −0.981354 + 0.858709i
\(92\) 0.278537 0.00302757
\(93\) −1.53723 42.7115i −0.0165294 0.459264i
\(94\) 30.5480 + 52.9107i 0.324979 + 0.562879i
\(95\) 5.55961 69.3035i 0.0585222 0.729510i
\(96\) 0.675522 + 18.7691i 0.00703669 + 0.195512i
\(97\) 90.4517i 0.932492i 0.884655 + 0.466246i \(0.154394\pi\)
−0.884655 + 0.466246i \(0.845606\pi\)
\(98\) −73.7078 56.8170i −0.752121 0.579765i
\(99\) −78.1554 37.9123i −0.789448 0.382953i
\(100\) 9.69308 + 1.56526i 0.0969308 + 0.0156526i
\(101\) 47.1698 27.2335i 0.467028 0.269638i −0.247967 0.968768i \(-0.579762\pi\)
0.714995 + 0.699130i \(0.246429\pi\)
\(102\) 122.657 + 65.0496i 1.20252 + 0.637742i
\(103\) −94.7932 54.7289i −0.920322 0.531348i −0.0365842 0.999331i \(-0.511648\pi\)
−0.883738 + 0.467982i \(0.844981\pi\)
\(104\) 141.432i 1.35992i
\(105\) −65.5954 81.9893i −0.624718 0.780851i
\(106\) 32.9670 0.311009
\(107\) 39.8017 68.9385i 0.371978 0.644285i −0.617892 0.786263i \(-0.712013\pi\)
0.989870 + 0.141978i \(0.0453462\pi\)
\(108\) 8.55889 6.26044i 0.0792490 0.0579670i
\(109\) −70.7849 122.603i −0.649402 1.12480i −0.983266 0.182176i \(-0.941686\pi\)
0.333864 0.942621i \(-0.391648\pi\)
\(110\) −39.3342 82.7873i −0.357583 0.752611i
\(111\) −1.99656 3.18758i −0.0179870 0.0287169i
\(112\) 98.0248 19.3859i 0.875222 0.173088i
\(113\) 99.6031 0.881443 0.440722 0.897644i \(-0.354723\pi\)
0.440722 + 0.897644i \(0.354723\pi\)
\(114\) −2.84972 79.1784i −0.0249975 0.694547i
\(115\) 0.283555 3.53466i 0.00246570 0.0307362i
\(116\) −5.64176 + 3.25727i −0.0486358 + 0.0280799i
\(117\) −126.303 + 85.5857i −1.07951 + 0.731502i
\(118\) 166.399i 1.41016i
\(119\) −55.0057 + 161.456i −0.462232 + 1.35677i
\(120\) 125.024 + 5.51392i 1.04187 + 0.0459493i
\(121\) −13.9222 + 24.1139i −0.115059 + 0.199288i
\(122\) 99.2166 + 171.848i 0.813251 + 1.40859i
\(123\) −33.8778 + 63.8796i −0.275430 + 0.519346i
\(124\) −2.79761 + 4.84560i −0.0225613 + 0.0390774i
\(125\) 29.7310 121.413i 0.237848 0.971302i
\(126\) −85.0639 84.1506i −0.675110 0.667862i
\(127\) 89.2383i 0.702663i −0.936251 0.351332i \(-0.885729\pi\)
0.936251 0.351332i \(-0.114271\pi\)
\(128\) −52.9941 + 91.7885i −0.414016 + 0.717097i
\(129\) −80.9917 + 152.717i −0.627843 + 1.18385i
\(130\) −160.468 12.8730i −1.23437 0.0990228i
\(131\) 96.9674 + 55.9841i 0.740209 + 0.427360i 0.822145 0.569278i \(-0.192777\pi\)
−0.0819364 + 0.996638i \(0.526110\pi\)
\(132\) 6.03656 + 9.63757i 0.0457315 + 0.0730119i
\(133\) 95.4872 18.8840i 0.717949 0.141985i
\(134\) 188.977i 1.41028i
\(135\) −70.7325 114.987i −0.523945 0.851752i
\(136\) −101.647 176.058i −0.747405 1.29454i
\(137\) −44.2662 76.6714i −0.323111 0.559645i 0.658017 0.753003i \(-0.271395\pi\)
−0.981128 + 0.193358i \(0.938062\pi\)
\(138\) −0.145343 4.03831i −0.00105321 0.0292631i
\(139\) −5.87121 −0.0422389 −0.0211195 0.999777i \(-0.506723\pi\)
−0.0211195 + 0.999777i \(0.506723\pi\)
\(140\) 1.57999 + 13.6550i 0.0112857 + 0.0975357i
\(141\) −81.7853 + 51.2268i −0.580038 + 0.363311i
\(142\) 83.4777 + 48.1959i 0.587871 + 0.339408i
\(143\) −81.8085 141.696i −0.572087 0.990884i
\(144\) 128.140 9.23580i 0.889865 0.0641375i
\(145\) 35.5917 + 74.9105i 0.245460 + 0.516624i
\(146\) 178.746i 1.22429i
\(147\) 85.4996 119.578i 0.581630 0.813454i
\(148\) 0.492404i 0.00332705i
\(149\) −4.98359 2.87728i −0.0334469 0.0193106i 0.483183 0.875519i \(-0.339480\pi\)
−0.516630 + 0.856209i \(0.672814\pi\)
\(150\) 17.6356 141.350i 0.117571 0.942333i
\(151\) 131.443 + 227.666i 0.870482 + 1.50772i 0.861498 + 0.507760i \(0.169526\pi\)
0.00898406 + 0.999960i \(0.497140\pi\)
\(152\) −58.0059 + 100.469i −0.381618 + 0.660982i
\(153\) −95.7141 + 197.313i −0.625582 + 1.28962i
\(154\) 96.5687 84.5001i 0.627069 0.548702i
\(155\) 58.6431 + 40.4348i 0.378343 + 0.260870i
\(156\) 19.9607 0.718407i 0.127953 0.00460517i
\(157\) −135.602 + 78.2900i −0.863709 + 0.498662i −0.865252 0.501336i \(-0.832842\pi\)
0.00154383 + 0.999999i \(0.499509\pi\)
\(158\) −7.05135 12.2133i −0.0446288 0.0772994i
\(159\) 1.87295 + 52.0392i 0.0117795 + 0.327291i
\(160\) −25.7701 17.7687i −0.161063 0.111054i
\(161\) 4.87010 0.963135i 0.0302491 0.00598221i
\(162\) −95.2318 120.823i −0.587850 0.745819i
\(163\) 2.59424 + 1.49779i 0.0159156 + 0.00918887i 0.507937 0.861394i \(-0.330408\pi\)
−0.492021 + 0.870583i \(0.663742\pi\)
\(164\) 8.19788 4.73305i 0.0499871 0.0288601i
\(165\) 128.447 66.7934i 0.778468 0.404808i
\(166\) −66.1312 + 114.543i −0.398381 + 0.690015i
\(167\) 201.798 1.20837 0.604186 0.796844i \(-0.293499\pi\)
0.604186 + 0.796844i \(0.293499\pi\)
\(168\) 40.1508 + 170.541i 0.238993 + 1.01513i
\(169\) −118.374 −0.700436
\(170\) −209.006 + 99.3037i −1.22945 + 0.584139i
\(171\) 124.823 8.99671i 0.729960 0.0526123i
\(172\) 19.5987 11.3153i 0.113946 0.0657866i
\(173\) −7.78179 + 13.4785i −0.0449814 + 0.0779101i −0.887640 0.460539i \(-0.847656\pi\)
0.842658 + 0.538449i \(0.180990\pi\)
\(174\) 50.1688 + 80.0962i 0.288326 + 0.460323i
\(175\) 174.892 6.14927i 0.999382 0.0351387i
\(176\) 137.776i 0.782818i
\(177\) 262.665 9.45359i 1.48398 0.0534101i
\(178\) −148.765 + 85.8896i −0.835759 + 0.482526i
\(179\) 27.1566 15.6789i 0.151713 0.0875916i −0.422222 0.906493i \(-0.638750\pi\)
0.573935 + 0.818901i \(0.305416\pi\)
\(180\) −0.143131 + 17.6730i −0.000795173 + 0.0981832i
\(181\) 125.301 0.692273 0.346137 0.938184i \(-0.387493\pi\)
0.346137 + 0.938184i \(0.387493\pi\)
\(182\) −43.7249 221.095i −0.240246 1.21481i
\(183\) −265.630 + 166.379i −1.45153 + 0.909176i
\(184\) −2.95846 + 5.12420i −0.0160786 + 0.0278489i
\(185\) 6.24866 + 0.501275i 0.0337765 + 0.00270959i
\(186\) 71.7127 + 38.0320i 0.385552 + 0.204473i
\(187\) −203.674 117.591i −1.08917 0.628830i
\(188\) 12.6339 0.0672013
\(189\) 128.001 139.056i 0.677255 0.735748i
\(190\) 108.712 + 74.9578i 0.572170 + 0.394515i
\(191\) 42.0451 + 24.2747i 0.220131 + 0.127093i 0.606011 0.795456i \(-0.292769\pi\)
−0.385880 + 0.922549i \(0.626102\pi\)
\(192\) −182.846 96.9702i −0.952322 0.505053i
\(193\) 14.9330 8.62156i 0.0773730 0.0446713i −0.460814 0.887497i \(-0.652443\pi\)
0.538187 + 0.842825i \(0.319109\pi\)
\(194\) −148.777 85.8964i −0.766891 0.442765i
\(195\) 11.2036 254.035i 0.0574546 1.30274i
\(196\) −17.7959 + 7.32530i −0.0907952 + 0.0373740i
\(197\) −354.243 −1.79819 −0.899094 0.437755i \(-0.855774\pi\)
−0.899094 + 0.437755i \(0.855774\pi\)
\(198\) 136.578 92.5488i 0.689790 0.467418i
\(199\) 7.75382 + 13.4300i 0.0389639 + 0.0674875i 0.884850 0.465877i \(-0.154261\pi\)
−0.845886 + 0.533364i \(0.820928\pi\)
\(200\) −131.750 + 161.697i −0.658750 + 0.808484i
\(201\) 298.305 10.7363i 1.48410 0.0534146i
\(202\) 103.448i 0.512118i
\(203\) −87.3807 + 76.4603i −0.430447 + 0.376652i
\(204\) 24.3312 15.2400i 0.119270 0.0747059i
\(205\) −51.7174 108.850i −0.252280 0.530977i
\(206\) 180.039 103.945i 0.873973 0.504589i
\(207\) 6.36631 0.458856i 0.0307551 0.00221669i
\(208\) 209.567 + 120.994i 1.00753 + 0.581700i
\(209\) 134.209i 0.642150i
\(210\) 197.150 30.0325i 0.938808 0.143012i
\(211\) −355.817 −1.68634 −0.843169 0.537649i \(-0.819313\pi\)
−0.843169 + 0.537649i \(0.819313\pi\)
\(212\) 3.40857 5.90381i 0.0160782 0.0278482i
\(213\) −71.3359 + 134.510i −0.334910 + 0.631502i
\(214\) 75.5944 + 130.933i 0.353245 + 0.611838i
\(215\) −123.641 260.228i −0.575072 1.21036i
\(216\) 24.2646 + 223.951i 0.112336 + 1.03681i
\(217\) −32.1597 + 94.3969i −0.148201 + 0.435009i
\(218\) 268.880 1.23340
\(219\) −282.155 + 10.1551i −1.28838 + 0.0463702i
\(220\) −18.8927 1.51559i −0.0858758 0.00688906i
\(221\) −357.729 + 206.535i −1.61868 + 0.934548i
\(222\) 7.13901 0.256941i 0.0321577 0.00115739i
\(223\) 125.746i 0.563882i −0.959432 0.281941i \(-0.909022\pi\)
0.959432 0.281941i \(-0.0909782\pi\)
\(224\) 14.1322 41.4817i 0.0630904 0.185186i
\(225\) 224.126 + 19.8077i 0.996117 + 0.0880344i
\(226\) −94.5869 + 163.829i −0.418526 + 0.724909i
\(227\) 195.808 + 339.150i 0.862591 + 1.49405i 0.869420 + 0.494074i \(0.164493\pi\)
−0.00682884 + 0.999977i \(0.502174\pi\)
\(228\) −14.4741 7.67619i −0.0634830 0.0336675i
\(229\) 63.3517 109.728i 0.276645 0.479163i −0.693904 0.720068i \(-0.744111\pi\)
0.970549 + 0.240904i \(0.0774441\pi\)
\(230\) 5.54461 + 3.82305i 0.0241070 + 0.0166219i
\(231\) 138.872 + 147.636i 0.601177 + 0.639115i
\(232\) 138.387i 0.596497i
\(233\) −187.050 + 323.979i −0.802788 + 1.39047i 0.114986 + 0.993367i \(0.463318\pi\)
−0.917774 + 0.397103i \(0.870016\pi\)
\(234\) −20.8313 289.021i −0.0890229 1.23513i
\(235\) 12.8615 160.325i 0.0547297 0.682234i
\(236\) −29.7991 17.2045i −0.126268 0.0729006i
\(237\) 18.8784 11.8246i 0.0796557 0.0498929i
\(238\) −213.330 243.799i −0.896346 1.02437i
\(239\) 82.1964i 0.343918i 0.985104 + 0.171959i \(0.0550097\pi\)
−0.985104 + 0.171959i \(0.944990\pi\)
\(240\) −115.127 + 180.537i −0.479696 + 0.752240i
\(241\) −104.237 180.543i −0.432517 0.749141i 0.564572 0.825384i \(-0.309041\pi\)
−0.997089 + 0.0762423i \(0.975708\pi\)
\(242\) −26.4421 45.7990i −0.109265 0.189252i
\(243\) 185.311 157.190i 0.762598 0.646873i
\(244\) 41.0334 0.168170
\(245\) 74.8423 + 233.289i 0.305479 + 0.952199i
\(246\) −72.8989 116.386i −0.296337 0.473112i
\(247\) 204.142 + 117.861i 0.826486 + 0.477172i
\(248\) −59.4291 102.934i −0.239634 0.415058i
\(249\) −184.566 97.8823i −0.741227 0.393102i
\(250\) 171.469 + 164.200i 0.685875 + 0.656802i
\(251\) 279.326i 1.11285i −0.830897 0.556427i \(-0.812172\pi\)
0.830897 0.556427i \(-0.187828\pi\)
\(252\) −23.8650 + 6.53286i −0.0947023 + 0.0259240i
\(253\) 6.84503i 0.0270555i
\(254\) 146.781 + 84.7441i 0.577878 + 0.333638i
\(255\) −168.628 324.280i −0.661285 1.27169i
\(256\) 37.3282 + 64.6544i 0.145813 + 0.252556i
\(257\) 80.6774 139.737i 0.313920 0.543725i −0.665288 0.746587i \(-0.731691\pi\)
0.979207 + 0.202862i \(0.0650244\pi\)
\(258\) −174.279 278.243i −0.675501 1.07846i
\(259\) 1.70265 + 8.60947i 0.00657395 + 0.0332412i
\(260\) −18.8967 + 27.4061i −0.0726796 + 0.105408i
\(261\) −123.584 + 83.7432i −0.473501 + 0.320855i
\(262\) −184.168 + 106.329i −0.702931 + 0.405837i
\(263\) −15.5086 26.8617i −0.0589680 0.102136i 0.835034 0.550198i \(-0.185448\pi\)
−0.894002 + 0.448062i \(0.852114\pi\)
\(264\) −241.418 + 8.68889i −0.914461 + 0.0329125i
\(265\) −71.4501 49.2653i −0.269623 0.185907i
\(266\) −59.6175 + 174.992i −0.224126 + 0.657866i
\(267\) −144.031 229.950i −0.539441 0.861236i
\(268\) −33.8425 19.5390i −0.126278 0.0729067i
\(269\) 271.904 156.984i 1.01080 0.583583i 0.0993714 0.995050i \(-0.468317\pi\)
0.911425 + 0.411467i \(0.134983\pi\)
\(270\) 256.303 7.14678i 0.949270 0.0264695i
\(271\) 128.076 221.834i 0.472604 0.818574i −0.526905 0.849924i \(-0.676648\pi\)
0.999508 + 0.0313506i \(0.00998084\pi\)
\(272\) 347.832 1.27879
\(273\) 346.520 81.5819i 1.26930 0.298835i
\(274\) 168.148 0.613678
\(275\) −38.4661 + 238.207i −0.139877 + 0.866208i
\(276\) −0.738219 0.391506i −0.00267471 0.00141850i
\(277\) 283.178 163.493i 1.02230 0.590226i 0.107532 0.994202i \(-0.465705\pi\)
0.914770 + 0.403975i \(0.132372\pi\)
\(278\) 5.57553 9.65710i 0.0200559 0.0347378i
\(279\) −55.9604 + 115.361i −0.200575 + 0.413481i
\(280\) −267.991 115.969i −0.957110 0.414174i
\(281\) 405.760i 1.44399i −0.691900 0.721993i \(-0.743226\pi\)
0.691900 0.721993i \(-0.256774\pi\)
\(282\) −6.59247 183.169i −0.0233775 0.649537i
\(283\) 393.833 227.380i 1.39164 0.803462i 0.398140 0.917325i \(-0.369656\pi\)
0.993496 + 0.113863i \(0.0363224\pi\)
\(284\) 17.2621 9.96628i 0.0607821 0.0350926i
\(285\) −112.147 + 175.864i −0.393497 + 0.617066i
\(286\) 310.754 1.08655
\(287\) 126.971 111.102i 0.442406 0.387116i
\(288\) 24.5912 50.6942i 0.0853861 0.176022i
\(289\) −152.373 + 263.918i −0.527242 + 0.913210i
\(290\) −157.014 12.5958i −0.541426 0.0434339i
\(291\) 127.137 239.728i 0.436898 0.823809i
\(292\) 32.0103 + 18.4812i 0.109624 + 0.0632916i
\(293\) 141.910 0.484333 0.242166 0.970235i \(-0.422142\pi\)
0.242166 + 0.970235i \(0.422142\pi\)
\(294\) 115.490 + 254.187i 0.392824 + 0.864582i
\(295\) −248.664 + 360.640i −0.842928 + 1.22251i
\(296\) −9.05867 5.23003i −0.0306036 0.0176690i
\(297\) 153.850 + 210.335i 0.518014 + 0.708197i
\(298\) 9.46522 5.46474i 0.0317625 0.0183381i
\(299\) 10.4118 + 6.01124i 0.0348220 + 0.0201045i
\(300\) −23.4899 17.7729i −0.0782998 0.0592430i
\(301\) 303.548 265.612i 1.00847 0.882433i
\(302\) −499.293 −1.65329
\(303\) −163.295 + 5.87717i −0.538928 + 0.0193966i
\(304\) −99.2469 171.901i −0.326470 0.565463i
\(305\) 41.7727 520.719i 0.136960 1.70727i
\(306\) −233.650 344.808i −0.763563 1.12682i
\(307\) 187.823i 0.611801i −0.952063 0.305901i \(-0.901042\pi\)
0.952063 0.305901i \(-0.0989575\pi\)
\(308\) −5.14793 26.0305i −0.0167141 0.0845148i
\(309\) 174.309 + 278.290i 0.564106 + 0.900615i
\(310\) −122.198 + 58.0591i −0.394187 + 0.187287i
\(311\) −233.836 + 135.005i −0.751885 + 0.434101i −0.826375 0.563121i \(-0.809601\pi\)
0.0744894 + 0.997222i \(0.476267\pi\)
\(312\) −198.794 + 374.844i −0.637162 + 1.20142i
\(313\) 55.2832 + 31.9177i 0.176623 + 0.101974i 0.585705 0.810524i \(-0.300818\pi\)
−0.409082 + 0.912498i \(0.634151\pi\)
\(314\) 297.389i 0.947098i
\(315\) 58.6078 + 309.500i 0.186056 + 0.982539i
\(316\) −2.91626 −0.00922866
\(317\) −99.2398 + 171.888i −0.313059 + 0.542235i −0.979023 0.203749i \(-0.934687\pi\)
0.665964 + 0.745984i \(0.268021\pi\)
\(318\) −87.3739 46.3378i −0.274761 0.145716i
\(319\) −80.0473 138.646i −0.250932 0.434627i
\(320\) 311.568 148.033i 0.973649 0.462603i
\(321\) −202.387 + 126.766i −0.630489 + 0.394911i
\(322\) −3.04065 + 8.92508i −0.00944301 + 0.0277176i
\(323\) 338.827 1.04900
\(324\) −31.4836 + 4.56210i −0.0971716 + 0.0140805i
\(325\) 328.549 + 267.701i 1.01092 + 0.823695i
\(326\) −4.92718 + 2.84471i −0.0151141 + 0.00872611i
\(327\) 15.2759 + 424.434i 0.0467152 + 1.29796i
\(328\) 201.087i 0.613070i
\(329\) 220.898 43.6858i 0.671422 0.132784i
\(330\) −12.1151 + 274.702i −0.0367126 + 0.832431i
\(331\) 27.5811 47.7719i 0.0833266 0.144326i −0.821350 0.570424i \(-0.806779\pi\)
0.904677 + 0.426098i \(0.140112\pi\)
\(332\) 13.6751 + 23.6859i 0.0411900 + 0.0713431i
\(333\) 0.811176 + 11.2545i 0.00243596 + 0.0337974i
\(334\) −191.635 + 331.922i −0.573758 + 0.993778i
\(335\) −282.404 + 409.574i −0.842998 + 1.22261i
\(336\) −287.048 86.4027i −0.854310 0.257151i
\(337\) 300.345i 0.891232i 0.895224 + 0.445616i \(0.147015\pi\)
−0.895224 + 0.445616i \(0.852985\pi\)
\(338\) 112.412 194.704i 0.332581 0.576047i
\(339\) −263.983 140.000i −0.778710 0.412980i
\(340\) −3.82629 + 47.6968i −0.0112538 + 0.140285i
\(341\) −119.080 68.7511i −0.349209 0.201616i
\(342\) −103.739 + 213.856i −0.303330 + 0.625309i
\(343\) −285.824 + 189.615i −0.833305 + 0.552814i
\(344\) 480.738i 1.39749i
\(345\) −5.71978 + 8.96952i −0.0165791 + 0.0259986i
\(346\) −14.7798 25.5993i −0.0427161 0.0739865i
\(347\) 71.3734 + 123.622i 0.205687 + 0.356260i 0.950351 0.311179i \(-0.100724\pi\)
−0.744664 + 0.667439i \(0.767390\pi\)
\(348\) 19.5310 0.702941i 0.0561235 0.00201995i
\(349\) 46.0748 0.132020 0.0660098 0.997819i \(-0.478973\pi\)
0.0660098 + 0.997819i \(0.478973\pi\)
\(350\) −155.970 + 293.506i −0.445628 + 0.838588i
\(351\) 455.044 49.3029i 1.29642 0.140464i
\(352\) 52.3286 + 30.2119i 0.148661 + 0.0858294i
\(353\) −163.141 282.568i −0.462155 0.800476i 0.536913 0.843637i \(-0.319590\pi\)
−0.999068 + 0.0431618i \(0.986257\pi\)
\(354\) −233.887 + 441.014i −0.660698 + 1.24580i
\(355\) −108.900 229.204i −0.306761 0.645645i
\(356\) 35.5217i 0.0997801i
\(357\) 372.723 350.598i 1.04404 0.982069i
\(358\) 59.5571i 0.166361i
\(359\) 78.5207 + 45.3340i 0.218721 + 0.126278i 0.605358 0.795954i \(-0.293030\pi\)
−0.386637 + 0.922232i \(0.626363\pi\)
\(360\) −323.607 190.345i −0.898908 0.528737i
\(361\) 83.8224 + 145.185i 0.232195 + 0.402173i
\(362\) −118.991 + 206.099i −0.328705 + 0.569333i
\(363\) 70.7926 44.3414i 0.195021 0.122153i
\(364\) −44.1152 15.0294i −0.121196 0.0412896i
\(365\) 267.115 387.400i 0.731822 1.06137i
\(366\) −21.4116 594.914i −0.0585017 1.62545i
\(367\) −255.238 + 147.362i −0.695471 + 0.401531i −0.805658 0.592380i \(-0.798188\pi\)
0.110187 + 0.993911i \(0.464855\pi\)
\(368\) −5.06186 8.76739i −0.0137550 0.0238244i
\(369\) 179.576 121.685i 0.486656 0.329770i
\(370\) −6.75847 + 9.80190i −0.0182661 + 0.0264916i
\(371\) 39.1830 115.012i 0.105615 0.310006i
\(372\) 14.2255 8.91024i 0.0382406 0.0239523i
\(373\) −35.1907 20.3173i −0.0943450 0.0544701i 0.452085 0.891975i \(-0.350680\pi\)
−0.546430 + 0.837505i \(0.684014\pi\)
\(374\) 386.833 223.338i 1.03431 0.597161i
\(375\) −249.453 + 279.997i −0.665208 + 0.746658i
\(376\) −134.190 + 232.423i −0.356887 + 0.618147i
\(377\) −281.187 −0.745855
\(378\) 107.168 + 342.593i 0.283514 + 0.906330i
\(379\) −32.1947 −0.0849463 −0.0424732 0.999098i \(-0.513524\pi\)
−0.0424732 + 0.999098i \(0.513524\pi\)
\(380\) 24.6638 11.7183i 0.0649047 0.0308378i
\(381\) −125.432 + 236.512i −0.329217 + 0.620767i
\(382\) −79.8553 + 46.1045i −0.209045 + 0.120692i
\(383\) −125.563 + 217.482i −0.327841 + 0.567838i −0.982083 0.188448i \(-0.939654\pi\)
0.654242 + 0.756285i \(0.272988\pi\)
\(384\) 269.469 168.784i 0.701742 0.439541i
\(385\) −335.571 + 38.8283i −0.871614 + 0.100853i
\(386\) 32.7495i 0.0848432i
\(387\) 429.312 290.912i 1.10933 0.751711i
\(388\) −30.7651 + 17.7623i −0.0792916 + 0.0457790i
\(389\) −24.1611 + 13.9494i −0.0621108 + 0.0358597i −0.530734 0.847539i \(-0.678084\pi\)
0.468623 + 0.883398i \(0.344750\pi\)
\(390\) 407.202 + 259.669i 1.04411 + 0.665818i
\(391\) 17.2811 0.0441971
\(392\) 54.2550 405.193i 0.138406 1.03366i
\(393\) −178.307 284.673i −0.453707 0.724359i
\(394\) 336.403 582.667i 0.853815 1.47885i
\(395\) −2.96880 + 37.0076i −0.00751594 + 0.0936902i
\(396\) −2.45257 34.0278i −0.00619336 0.0859287i
\(397\) −281.690 162.634i −0.709546 0.409657i 0.101347 0.994851i \(-0.467685\pi\)
−0.810893 + 0.585195i \(0.801018\pi\)
\(398\) −29.4533 −0.0740033
\(399\) −279.617 84.1659i −0.700795 0.210942i
\(400\) −126.884 333.551i −0.317209 0.833877i
\(401\) −324.443 187.317i −0.809084 0.467125i 0.0375536 0.999295i \(-0.488044\pi\)
−0.846638 + 0.532170i \(0.821377\pi\)
\(402\) −265.623 + 500.854i −0.660753 + 1.24591i
\(403\) −209.151 + 120.753i −0.518984 + 0.299636i
\(404\) 18.5257 + 10.6958i 0.0458558 + 0.0264748i
\(405\) 25.8427 + 404.175i 0.0638091 + 0.997962i
\(406\) −42.7836 216.335i −0.105378 0.532846i
\(407\) −12.1008 −0.0297317
\(408\) 21.9361 + 609.488i 0.0537650 + 1.49384i
\(409\) 210.447 + 364.506i 0.514541 + 0.891212i 0.999858 + 0.0168731i \(0.00537114\pi\)
−0.485316 + 0.874339i \(0.661296\pi\)
\(410\) 228.152 + 18.3027i 0.556469 + 0.0446407i
\(411\) 9.55296 + 265.426i 0.0232432 + 0.645804i
\(412\) 42.9891i 0.104342i
\(413\) −580.516 197.774i −1.40561 0.478871i
\(414\) −5.29096 + 10.9072i −0.0127801 + 0.0263459i
\(415\) 314.498 149.425i 0.757827 0.360061i
\(416\) 91.9090 53.0637i 0.220935 0.127557i
\(417\) 15.5608 + 8.25247i 0.0373160 + 0.0197901i
\(418\) −220.750 127.450i −0.528111 0.304905i
\(419\) 481.407i 1.14894i 0.818524 + 0.574472i \(0.194792\pi\)
−0.818524 + 0.574472i \(0.805208\pi\)
\(420\) 15.0057 38.4113i 0.0357278 0.0914555i
\(421\) −125.377 −0.297807 −0.148904 0.988852i \(-0.547574\pi\)
−0.148904 + 0.988852i \(0.547574\pi\)
\(422\) 337.898 585.256i 0.800706 1.38686i
\(423\) 288.763 20.8128i 0.682655 0.0492027i
\(424\) 72.4077 + 125.414i 0.170773 + 0.295787i
\(425\) 601.382 + 97.1122i 1.41502 + 0.228499i
\(426\) −153.502 245.071i −0.360333 0.575283i
\(427\) 717.452 141.887i 1.68022 0.332288i
\(428\) 31.2639 0.0730465
\(429\) 17.6548 + 490.533i 0.0411534 + 1.14343i
\(430\) 545.443 + 43.7561i 1.26847 + 0.101758i
\(431\) 294.379 169.960i 0.683013 0.394338i −0.117976 0.993016i \(-0.537641\pi\)
0.800989 + 0.598678i \(0.204307\pi\)
\(432\) −352.598 155.634i −0.816200 0.360264i
\(433\) 184.329i 0.425703i 0.977085 + 0.212852i \(0.0682751\pi\)
−0.977085 + 0.212852i \(0.931725\pi\)
\(434\) −124.726 142.540i −0.287387 0.328433i
\(435\) 10.9625 248.566i 0.0252010 0.571416i
\(436\) 27.8005 48.1518i 0.0637625 0.110440i
\(437\) −4.93081 8.54042i −0.0112833 0.0195433i
\(438\) 251.242 473.738i 0.573612 1.08159i
\(439\) −62.0405 + 107.457i −0.141322 + 0.244777i −0.927995 0.372593i \(-0.878469\pi\)
0.786673 + 0.617371i \(0.211802\pi\)
\(440\) 228.549 331.468i 0.519430 0.753336i
\(441\) −394.680 + 196.746i −0.894966 + 0.446135i
\(442\) 784.535i 1.77497i
\(443\) 280.029 485.025i 0.632121 1.09487i −0.354997 0.934868i \(-0.615518\pi\)
0.987117 0.159998i \(-0.0511486\pi\)
\(444\) 0.692114 1.30504i 0.00155881 0.00293928i
\(445\) 450.774 + 36.1617i 1.01298 + 0.0812622i
\(446\) 206.829 + 119.413i 0.463742 + 0.267742i
\(447\) 9.16399 + 14.6306i 0.0205011 + 0.0327307i
\(448\) 318.014 + 363.434i 0.709852 + 0.811236i
\(449\) 397.281i 0.884814i −0.896814 0.442407i \(-0.854125\pi\)
0.896814 0.442407i \(-0.145875\pi\)
\(450\) −245.419 + 349.838i −0.545376 + 0.777418i
\(451\) 116.315 + 201.463i 0.257904 + 0.446702i
\(452\) 19.5593 + 33.8778i 0.0432729 + 0.0749508i
\(453\) −28.3663 788.147i −0.0626187 1.73984i
\(454\) −743.788 −1.63830
\(455\) −235.635 + 544.526i −0.517879 + 1.19676i
\(456\) 294.954 184.746i 0.646828 0.405145i
\(457\) −608.910 351.555i −1.33241 0.769266i −0.346740 0.937961i \(-0.612711\pi\)
−0.985668 + 0.168695i \(0.946045\pi\)
\(458\) 120.322 + 208.405i 0.262713 + 0.455032i
\(459\) 531.014 388.413i 1.15689 0.846215i
\(460\) 1.25792 0.597667i 0.00273461 0.00129928i
\(461\) 780.964i 1.69406i −0.531542 0.847032i \(-0.678387\pi\)
0.531542 0.847032i \(-0.321613\pi\)
\(462\) −374.712 + 88.2192i −0.811066 + 0.190951i
\(463\) 880.813i 1.90240i 0.308570 + 0.951202i \(0.400150\pi\)
−0.308570 + 0.951202i \(0.599850\pi\)
\(464\) 205.056 + 118.389i 0.441930 + 0.255149i
\(465\) −98.5902 189.594i −0.212022 0.407729i
\(466\) −355.259 615.327i −0.762359 1.32044i
\(467\) −25.2777 + 43.7822i −0.0541278 + 0.0937521i −0.891820 0.452391i \(-0.850571\pi\)
0.837692 + 0.546143i \(0.183905\pi\)
\(468\) −53.9125 26.1523i −0.115198 0.0558811i
\(469\) −659.285 224.609i −1.40573 0.478911i
\(470\) 251.492 + 173.406i 0.535090 + 0.368948i
\(471\) 469.436 16.8955i 0.996679 0.0358716i
\(472\) 633.019 365.474i 1.34114 0.774309i
\(473\) 278.073 + 481.637i 0.587892 + 1.01826i
\(474\) 1.52173 + 42.2807i 0.00321040 + 0.0891999i
\(475\) −123.599 324.916i −0.260208 0.684033i
\(476\) −65.7172 + 12.9966i −0.138061 + 0.0273037i
\(477\) 68.1814 140.555i 0.142938 0.294664i
\(478\) −135.198 78.0569i −0.282842 0.163299i
\(479\) −568.259 + 328.084i −1.18634 + 0.684936i −0.957474 0.288521i \(-0.906836\pi\)
−0.228870 + 0.973457i \(0.573503\pi\)
\(480\) 43.3244 + 83.3151i 0.0902592 + 0.173573i
\(481\) −10.6268 + 18.4062i −0.0220932 + 0.0382665i
\(482\) 395.948 0.821469
\(483\) −14.2612 4.29268i −0.0295263 0.00888754i
\(484\) −10.9357 −0.0225945
\(485\) 194.086 + 408.495i 0.400177 + 0.842258i
\(486\) 82.5711 + 454.078i 0.169899 + 0.934317i
\(487\) −701.394 + 404.950i −1.44023 + 0.831520i −0.997865 0.0653129i \(-0.979195\pi\)
−0.442370 + 0.896833i \(0.645862\pi\)
\(488\) −435.833 + 754.886i −0.893101 + 1.54690i
\(489\) −4.77038 7.61607i −0.00975537 0.0155748i
\(490\) −454.792 98.4376i −0.928146 0.200893i
\(491\) 406.082i 0.827051i 0.910492 + 0.413526i \(0.135703\pi\)
−0.910492 + 0.413526i \(0.864297\pi\)
\(492\) −28.3799 + 1.02142i −0.0576828 + 0.00207607i
\(493\) −350.028 + 202.089i −0.709996 + 0.409917i
\(494\) −387.722 + 223.851i −0.784863 + 0.453141i
\(495\) −434.313 3.51744i −0.877400 0.00710594i
\(496\) 203.364 0.410008
\(497\) 267.359 233.946i 0.537946 0.470716i
\(498\) 336.270 210.625i 0.675240 0.422941i
\(499\) 341.349 591.233i 0.684065 1.18484i −0.289664 0.957128i \(-0.593544\pi\)
0.973730 0.227708i \(-0.0731230\pi\)
\(500\) 47.1342 13.7299i 0.0942685 0.0274597i
\(501\) −534.835 283.644i −1.06753 0.566155i
\(502\) 459.442 + 265.259i 0.915223 + 0.528404i
\(503\) −296.107 −0.588682 −0.294341 0.955701i \(-0.595100\pi\)
−0.294341 + 0.955701i \(0.595100\pi\)
\(504\) 133.296 508.429i 0.264476 1.00879i
\(505\) 154.591 224.205i 0.306121 0.443971i
\(506\) −11.2589 6.50030i −0.0222507 0.0128465i
\(507\) 313.731 + 166.384i 0.618800 + 0.328174i
\(508\) 30.3524 17.5240i 0.0597489 0.0344960i
\(509\) −722.798 417.308i −1.42004 0.819858i −0.423735 0.905786i \(-0.639281\pi\)
−0.996301 + 0.0859284i \(0.972614\pi\)
\(510\) 693.518 + 30.5861i 1.35984 + 0.0599728i
\(511\) 623.592 + 212.449i 1.22034 + 0.415751i
\(512\) −565.746 −1.10497
\(513\) −343.470 151.605i −0.669533 0.295526i
\(514\) 153.229 + 265.400i 0.298110 + 0.516342i
\(515\) −545.536 43.7636i −1.05929 0.0849778i
\(516\) −67.8478 + 2.44192i −0.131488 + 0.00473240i
\(517\) 310.477i 0.600535i
\(518\) −15.7780 5.37533i −0.0304594 0.0103771i
\(519\) 39.5695 24.7846i 0.0762418 0.0477546i
\(520\) −303.476 638.732i −0.583608 1.22833i
\(521\) −619.025 + 357.394i −1.18815 + 0.685977i −0.957885 0.287152i \(-0.907292\pi\)
−0.230262 + 0.973129i \(0.573958\pi\)
\(522\) −20.3829 282.799i −0.0390477 0.541760i
\(523\) 195.670 + 112.970i 0.374130 + 0.216004i 0.675261 0.737579i \(-0.264031\pi\)
−0.301131 + 0.953583i \(0.597364\pi\)
\(524\) 43.9751i 0.0839219i
\(525\) −472.168 229.527i −0.899367 0.437195i
\(526\) 58.9102 0.111997
\(527\) −173.570 + 300.632i −0.329355 + 0.570460i
\(528\) 193.656 365.154i 0.366772 0.691580i
\(529\) 264.249 + 457.692i 0.499525 + 0.865202i
\(530\) 148.884 70.7385i 0.280914 0.133469i
\(531\) −709.440 344.142i −1.33605 0.648101i
\(532\) 25.1741 + 28.7695i 0.0473197 + 0.0540781i
\(533\) 408.586 0.766577
\(534\) 515.004 18.5356i 0.964427 0.0347108i
\(535\) 31.8272 396.742i 0.0594900 0.741574i
\(536\) 718.912 415.064i 1.34125 0.774373i
\(537\) −94.0125 + 3.38361i −0.175070 + 0.00630096i
\(538\) 596.312i 1.10839i
\(539\) −180.019 437.333i −0.333987 0.811378i
\(540\) 25.2202 46.6384i 0.0467040 0.0863673i
\(541\) −315.187 + 545.919i −0.582600 + 1.00909i 0.412570 + 0.910926i \(0.364631\pi\)
−0.995170 + 0.0981672i \(0.968702\pi\)
\(542\) 243.251 + 421.323i 0.448803 + 0.777349i
\(543\) −332.092 176.121i −0.611588 0.324349i
\(544\) 76.2736 132.110i 0.140209 0.242849i
\(545\) −582.750 401.810i −1.06927 0.737267i
\(546\) −194.881 + 647.437i −0.356925 + 1.18578i
\(547\) 300.639i 0.549615i −0.961499 0.274807i \(-0.911386\pi\)
0.961499 0.274807i \(-0.0886141\pi\)
\(548\) 17.3854 30.1124i 0.0317251 0.0549496i
\(549\) 937.872 67.5976i 1.70833 0.123129i
\(550\) −355.280 289.481i −0.645963 0.526328i
\(551\) 199.747 + 115.324i 0.362518 + 0.209300i
\(552\) 15.0434 9.42254i 0.0272526 0.0170698i
\(553\) −50.9896 + 10.0839i −0.0922053 + 0.0182350i
\(554\) 621.036i 1.12100i
\(555\) −15.8565 10.1116i −0.0285703 0.0182190i
\(556\) −1.15295 1.99696i −0.00207365 0.00359166i
\(557\) 217.246 + 376.281i 0.390028 + 0.675549i 0.992453 0.122627i \(-0.0391319\pi\)
−0.602425 + 0.798176i \(0.705799\pi\)
\(558\) −136.606 201.596i −0.244814 0.361283i
\(559\) 976.805 1.74741
\(560\) 401.100 297.886i 0.716250 0.531939i
\(561\) 374.523 + 597.938i 0.667598 + 1.06584i
\(562\) 667.404 + 385.326i 1.18755 + 0.685633i
\(563\) −227.729 394.438i −0.404492 0.700601i 0.589770 0.807571i \(-0.299218\pi\)
−0.994262 + 0.106970i \(0.965885\pi\)
\(564\) −33.4841 17.7579i −0.0593690 0.0314857i
\(565\) 449.825 213.722i 0.796150 0.378269i
\(566\) 863.714i 1.52600i
\(567\) −534.703 + 188.632i −0.943038 + 0.332684i
\(568\) 423.425i 0.745466i
\(569\) −374.954 216.480i −0.658970 0.380457i 0.132914 0.991128i \(-0.457566\pi\)
−0.791884 + 0.610671i \(0.790900\pi\)
\(570\) −182.766 351.468i −0.320642 0.616611i
\(571\) −107.252 185.766i −0.187832 0.325335i 0.756695 0.653768i \(-0.226813\pi\)
−0.944527 + 0.328433i \(0.893479\pi\)
\(572\) 32.1299 55.6507i 0.0561712 0.0972914i
\(573\) −77.3139 123.434i −0.134928 0.215418i
\(574\) 62.1676 + 314.351i 0.108306 + 0.547650i
\(575\) −6.30387 16.5716i −0.0109633 0.0288201i
\(576\) 348.305 + 514.009i 0.604696 + 0.892377i
\(577\) −179.599 + 103.691i −0.311263 + 0.179708i −0.647492 0.762073i \(-0.724182\pi\)
0.336228 + 0.941780i \(0.390849\pi\)
\(578\) −289.398 501.253i −0.500689 0.867219i
\(579\) −51.6959 + 1.86059i −0.0892848 + 0.00321346i
\(580\) −18.4899 + 26.8161i −0.0318791 + 0.0462347i
\(581\) 321.005 + 366.852i 0.552504 + 0.631415i
\(582\) 273.576 + 436.774i 0.470062 + 0.750470i
\(583\) 145.086 + 83.7655i 0.248861 + 0.143680i
\(584\) −679.990 + 392.593i −1.16437 + 0.672247i
\(585\) −386.760 + 657.532i −0.661128 + 1.12399i
\(586\) −134.763 + 233.416i −0.229971 + 0.398321i
\(587\) −473.066 −0.805905 −0.402953 0.915221i \(-0.632016\pi\)
−0.402953 + 0.915221i \(0.632016\pi\)
\(588\) 57.4615 + 5.59897i 0.0977237 + 0.00952206i
\(589\) 198.099 0.336332
\(590\) −357.048 751.485i −0.605166 1.27370i
\(591\) 938.867 + 497.918i 1.58861 + 0.842501i
\(592\) 15.4992 8.94847i 0.0261811 0.0151157i
\(593\) 220.683 382.234i 0.372146 0.644576i −0.617749 0.786375i \(-0.711955\pi\)
0.989895 + 0.141799i \(0.0452887\pi\)
\(594\) −492.065 + 53.3141i −0.828392 + 0.0897544i
\(595\) 98.0266 + 847.189i 0.164751 + 1.42385i
\(596\) 2.26008i 0.00379207i
\(597\) −1.67333 46.4928i −0.00280290 0.0778774i
\(598\) −19.7749 + 11.4170i −0.0330683 + 0.0190920i
\(599\) 98.8142 57.0504i 0.164965 0.0952427i −0.415244 0.909710i \(-0.636304\pi\)
0.580210 + 0.814467i \(0.302971\pi\)
\(600\) 576.462 243.367i 0.960770 0.405612i
\(601\) −1061.91 −1.76691 −0.883454 0.468518i \(-0.844788\pi\)
−0.883454 + 0.468518i \(0.844788\pi\)
\(602\) 148.624 + 751.518i 0.246884 + 1.24837i
\(603\) −805.703 390.837i −1.33616 0.648155i
\(604\) −51.6236 + 89.4148i −0.0854696 + 0.148038i
\(605\) −11.1328 + 138.776i −0.0184013 + 0.229382i
\(606\) 145.405 274.173i 0.239941 0.452430i
\(607\) 187.998 + 108.541i 0.309716 + 0.178815i 0.646800 0.762660i \(-0.276107\pi\)
−0.337083 + 0.941475i \(0.609440\pi\)
\(608\) −87.0527 −0.143179
\(609\) 339.060 79.8256i 0.556749 0.131077i
\(610\) 816.821 + 563.203i 1.33905 + 0.923284i
\(611\) 472.257 + 272.658i 0.772925 + 0.446248i
\(612\) −85.9071 + 6.19181i −0.140371 + 0.0101173i
\(613\) −40.6966 + 23.4962i −0.0663893 + 0.0383299i −0.532827 0.846224i \(-0.678870\pi\)
0.466438 + 0.884554i \(0.345537\pi\)
\(614\) 308.935 + 178.364i 0.503152 + 0.290495i
\(615\) −15.9292 + 361.184i −0.0259012 + 0.587291i
\(616\) 533.558 + 181.776i 0.866166 + 0.295091i
\(617\) −140.650 −0.227958 −0.113979 0.993483i \(-0.536360\pi\)
−0.113979 + 0.993483i \(0.536360\pi\)
\(618\) −623.268 + 22.4321i −1.00852 + 0.0362979i
\(619\) 41.4260 + 71.7519i 0.0669241 + 0.115916i 0.897546 0.440921i \(-0.145348\pi\)
−0.830622 + 0.556837i \(0.812015\pi\)
\(620\) −2.23709 + 27.8865i −0.00360821 + 0.0449782i
\(621\) −17.5179 7.73225i −0.0282092 0.0124513i
\(622\) 512.826i 0.824479i
\(623\) 122.828 + 621.082i 0.197156 + 0.996922i
\(624\) −385.359 615.239i −0.617563 0.985960i
\(625\) −126.250 612.116i −0.202000 0.979386i
\(626\) −104.998 + 60.6206i −0.167728 + 0.0968381i
\(627\) 188.642 355.701i 0.300865 0.567307i
\(628\) −53.2572 30.7481i −0.0848045 0.0489619i
\(629\) 30.5499i 0.0485690i
\(630\) −564.728 197.514i −0.896394 0.313514i
\(631\) 243.800 0.386371 0.193186 0.981162i \(-0.438118\pi\)
0.193186 + 0.981162i \(0.438118\pi\)
\(632\) 30.9748 53.6499i 0.0490108 0.0848891i
\(633\) 943.039 + 500.130i 1.48979 + 0.790095i
\(634\) −188.484 326.464i −0.297293 0.514927i
\(635\) −191.482 403.015i −0.301546 0.634670i
\(636\) −17.3322 + 10.8561i −0.0272519 + 0.0170694i
\(637\) −823.305 110.240i −1.29247 0.173061i
\(638\) 304.064 0.476589
\(639\) 378.130 256.230i 0.591752 0.400985i
\(640\) −42.3764 + 528.244i −0.0662131 + 0.825381i
\(641\) 115.942 66.9392i 0.180877 0.104429i −0.406828 0.913505i \(-0.633365\pi\)
0.587705 + 0.809076i \(0.300032\pi\)
\(642\) −16.3138 453.273i −0.0254109 0.706033i
\(643\) 681.323i 1.05960i −0.848122 0.529801i \(-0.822267\pi\)
0.848122 0.529801i \(-0.177733\pi\)
\(644\) 1.28394 + 1.46732i 0.00199370 + 0.00227845i
\(645\) −38.0820 + 863.482i −0.0590419 + 1.33873i
\(646\) −321.763 + 557.311i −0.498086 + 0.862710i
\(647\) −76.8005 133.022i −0.118702 0.205599i 0.800551 0.599264i \(-0.204540\pi\)
−0.919254 + 0.393666i \(0.871207\pi\)
\(648\) 250.473 627.655i 0.386532 0.968603i
\(649\) 422.801 732.313i 0.651466 1.12837i
\(650\) −752.324 + 286.186i −1.15742 + 0.440287i
\(651\) 217.917 204.981i 0.334742 0.314872i
\(652\) 1.17650i 0.00180445i
\(653\) 122.460 212.107i 0.187534 0.324819i −0.756893 0.653538i \(-0.773284\pi\)
0.944428 + 0.328720i \(0.106617\pi\)
\(654\) −712.626 377.933i −1.08964 0.577879i
\(655\) 558.049 + 44.7674i 0.851983 + 0.0683471i
\(656\) −297.961 172.028i −0.454209 0.262237i
\(657\) 762.082 + 369.678i 1.15994 + 0.562675i
\(658\) −137.918 + 404.823i −0.209601 + 0.615233i
\(659\) 758.783i 1.15142i −0.817655 0.575708i \(-0.804727\pi\)
0.817655 0.575708i \(-0.195273\pi\)
\(660\) 47.9418 + 30.5720i 0.0726391 + 0.0463213i
\(661\) −495.701 858.579i −0.749926 1.29891i −0.947858 0.318694i \(-0.896756\pi\)
0.197932 0.980216i \(-0.436578\pi\)
\(662\) 52.3842 + 90.7321i 0.0791302 + 0.137058i
\(663\) 1238.41 44.5717i 1.86789 0.0672273i
\(664\) −580.995 −0.874992
\(665\) 390.716 290.174i 0.587543 0.436352i
\(666\) −19.2820 9.35348i −0.0289520 0.0140443i
\(667\) 10.1876 + 5.88183i 0.0152738 + 0.00881834i
\(668\) 39.6277 + 68.6371i 0.0593228 + 0.102750i
\(669\) −176.746 + 333.269i −0.264194 + 0.498161i
\(670\) −405.495 853.452i −0.605217 1.27381i
\(671\) 1008.39i 1.50282i
\(672\) −95.7613 + 90.0770i −0.142502 + 0.134043i
\(673\) 1101.01i 1.63598i −0.575235 0.817988i \(-0.695089\pi\)
0.575235 0.817988i \(-0.304911\pi\)
\(674\) −494.014 285.219i −0.732959 0.423174i
\(675\) −566.171 367.526i −0.838772 0.544482i
\(676\) −23.2454 40.2622i −0.0343867 0.0595595i
\(677\) 68.0959 117.946i 0.100585 0.174218i −0.811341 0.584573i \(-0.801262\pi\)
0.911926 + 0.410355i \(0.134595\pi\)
\(678\) 480.964 301.255i 0.709386 0.444329i
\(679\) −476.497 + 416.947i −0.701763 + 0.614060i
\(680\) −836.830 576.999i −1.23063 0.848529i
\(681\) −42.2567 1174.09i −0.0620510 1.72407i
\(682\) 226.167 130.577i 0.331623 0.191462i
\(683\) 607.226 + 1051.75i 0.889057 + 1.53989i 0.840992 + 0.541047i \(0.181972\pi\)
0.0480644 + 0.998844i \(0.484695\pi\)
\(684\) 27.5719 + 40.6892i 0.0403098 + 0.0594871i
\(685\) −364.431 251.277i −0.532015 0.366828i
\(686\) −40.4539 650.195i −0.0589707 0.947806i
\(687\) −322.136 + 201.772i −0.468903 + 0.293700i
\(688\) −712.334 411.266i −1.03537 0.597771i
\(689\) 254.827 147.124i 0.369850 0.213533i
\(690\) −9.32154 17.9258i −0.0135095 0.0259794i
\(691\) −580.261 + 1005.04i −0.839741 + 1.45447i 0.0503694 + 0.998731i \(0.483960\pi\)
−0.890111 + 0.455744i \(0.849373\pi\)
\(692\) −6.11253 −0.00883314
\(693\) −160.545 586.481i −0.231666 0.846293i
\(694\) −271.116 −0.390657
\(695\) −26.5154 + 12.5981i −0.0381517 + 0.0181267i
\(696\) −194.515 + 366.775i −0.279475 + 0.526975i
\(697\) 508.616 293.650i 0.729722 0.421305i
\(698\) −43.7545 + 75.7849i −0.0626855 + 0.108574i
\(699\) 951.126 595.744i 1.36070 0.852281i
\(700\) 36.4356 + 58.2781i 0.0520508 + 0.0832544i
\(701\) 1106.20i 1.57803i 0.614373 + 0.789016i \(0.289409\pi\)
−0.614373 + 0.789016i \(0.710591\pi\)
\(702\) −351.032 + 795.286i −0.500046 + 1.13289i
\(703\) 15.0980 8.71681i 0.0214765 0.0123994i
\(704\) −576.657 + 332.933i −0.819115 + 0.472916i
\(705\) −259.437 + 406.839i −0.367996 + 0.577077i
\(706\) 619.699 0.877760
\(707\) 360.899 + 122.953i 0.510466 + 0.173909i
\(708\) 54.7957 + 87.4832i 0.0773950 + 0.123564i
\(709\) −400.014 + 692.845i −0.564195 + 0.977214i 0.432929 + 0.901428i \(0.357480\pi\)
−0.997124 + 0.0757864i \(0.975853\pi\)
\(710\) 480.416 + 38.5395i 0.676642 + 0.0542810i
\(711\) −66.6548 + 4.80418i −0.0937480 + 0.00675694i
\(712\) −653.488 377.291i −0.917820 0.529903i
\(713\) 10.1036 0.0141705
\(714\) 222.720 + 946.005i 0.311933 + 1.32494i
\(715\) −673.504 464.386i −0.941964 0.649491i
\(716\) 10.6657 + 6.15782i 0.0148962 + 0.00860031i
\(717\) 115.534 217.849i 0.161135 0.303834i
\(718\) −149.133 + 86.1018i −0.207706 + 0.119919i
\(719\) 679.759 + 392.459i 0.945423 + 0.545840i 0.891656 0.452714i \(-0.149544\pi\)
0.0537665 + 0.998554i \(0.482877\pi\)
\(720\) 558.887 316.666i 0.776232 0.439815i
\(721\) −148.649 751.646i −0.206171 1.04251i
\(722\) −318.404 −0.441002
\(723\) 22.4950 + 625.015i 0.0311134 + 0.864474i
\(724\) 24.6058 + 42.6185i 0.0339859 + 0.0588653i
\(725\) 321.477 + 261.938i 0.443416 + 0.361294i
\(726\) 5.70638 + 158.550i 0.00786002 + 0.218388i
\(727\) 579.070i 0.796520i 0.917273 + 0.398260i \(0.130386\pi\)
−0.917273 + 0.398260i \(0.869614\pi\)
\(728\) 745.060 651.947i 1.02343 0.895531i
\(729\) −712.083 + 156.138i −0.976794 + 0.214181i
\(730\) 383.542 + 807.247i 0.525400 + 1.10582i
\(731\) 1215.95 702.028i 1.66340 0.960367i
\(732\) −108.753 57.6758i −0.148569 0.0787921i
\(733\) 590.643 + 341.008i 0.805789 + 0.465223i 0.845491 0.533989i \(-0.179308\pi\)
−0.0397023 + 0.999212i \(0.512641\pi\)
\(734\) 559.762i 0.762618i
\(735\) 129.548 723.493i 0.176256 0.984344i
\(736\) −4.43992 −0.00603249
\(737\) 480.170 831.679i 0.651520 1.12847i
\(738\) 29.6178 + 410.928i 0.0401326 + 0.556812i
\(739\) −439.884 761.902i −0.595243 1.03099i −0.993513 0.113722i \(-0.963723\pi\)
0.398270 0.917268i \(-0.369611\pi\)
\(740\) 1.05657 + 2.22378i 0.00142780 + 0.00300511i
\(741\) −375.383 599.312i −0.506590 0.808788i
\(742\) 151.965 + 173.669i 0.204804 + 0.234055i
\(743\) 77.0002 0.103634 0.0518171 0.998657i \(-0.483499\pi\)
0.0518171 + 0.998657i \(0.483499\pi\)
\(744\) 12.8252 + 356.344i 0.0172382 + 0.478957i
\(745\) −28.6806 2.30080i −0.0384975 0.00308832i
\(746\) 66.8368 38.5883i 0.0895936 0.0517269i
\(747\) 351.581 + 518.844i 0.470657 + 0.694570i
\(748\) 92.3669i 0.123485i
\(749\) 546.636 108.106i 0.729821 0.144333i
\(750\) −223.655 676.202i −0.298206 0.901602i
\(751\) −399.639 + 692.195i −0.532142 + 0.921697i 0.467154 + 0.884176i \(0.345279\pi\)
−0.999296 + 0.0375212i \(0.988054\pi\)
\(752\) −229.595 397.671i −0.305313 0.528818i
\(753\) −392.616 + 740.311i −0.521402 + 0.983149i
\(754\) 267.026 462.503i 0.354146 0.613399i
\(755\) 1082.13 + 746.135i 1.43328 + 0.988259i
\(756\) 72.4329 + 16.2298i 0.0958108 + 0.0214681i
\(757\) 393.905i 0.520350i −0.965561 0.260175i \(-0.916220\pi\)
0.965561 0.260175i \(-0.0837803\pi\)
\(758\) 30.5733 52.9545i 0.0403342 0.0698608i
\(759\) 9.62125 18.1417i 0.0126762 0.0239021i
\(760\) −46.3841 + 578.202i −0.0610317 + 0.760792i
\(761\) −654.465 377.855i −0.860006 0.496525i 0.00400819 0.999992i \(-0.498724\pi\)
−0.864014 + 0.503467i \(0.832057\pi\)
\(762\) −269.906 430.914i −0.354207 0.565504i
\(763\) 319.578 938.044i 0.418845 1.22942i
\(764\) 19.0676i 0.0249576i
\(765\) −8.88020