Properties

Label 105.3.o.b.44.16
Level 105
Weight 3
Character 105.44
Analytic conductor 2.861
Analytic rank 0
Dimension 40
CM no
Inner twists 8

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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 44.16
Character \(\chi\) \(=\) 105.44
Dual form 105.3.o.b.74.16

$q$-expansion

\(f(q)\) \(=\) \(q+(0.949639 - 1.64482i) q^{2} +(2.65035 + 1.40558i) q^{3} +(0.196373 + 0.340128i) q^{4} +(0.399822 + 4.98399i) q^{5} +(4.82880 - 3.02455i) q^{6} +(-4.60961 - 5.26797i) q^{7} +8.34304 q^{8} +(5.04868 + 7.45056i) q^{9} +O(q^{10})\) \(q+(0.949639 - 1.64482i) q^{2} +(2.65035 + 1.40558i) q^{3} +(0.196373 + 0.340128i) q^{4} +(0.399822 + 4.98399i) q^{5} +(4.82880 - 3.02455i) q^{6} +(-4.60961 - 5.26797i) q^{7} +8.34304 q^{8} +(5.04868 + 7.45056i) q^{9} +(8.57746 + 4.07535i) q^{10} +(-8.35863 + 4.82586i) q^{11} +(0.0423786 + 1.17748i) q^{12} -16.9521i q^{13} +(-13.0423 + 2.57932i) q^{14} +(-5.94574 + 13.7713i) 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} +(-24.6803 + 3.98542i) q^{25} +(-27.8832 - 16.0984i) q^{26} +(2.90837 + 26.8429i) q^{27} +(0.886581 - 2.60234i) q^{28} +16.5872i q^{29} +(17.0050 + 22.8574i) q^{30} +(7.12320 + 12.3377i) q^{31} +(3.13021 + 5.42169i) q^{32} +(-28.9364 + 1.04145i) q^{33} -46.2795 q^{34} +(24.4125 - 25.0805i) 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} +(3.33573 + 41.5816i) q^{40} -24.1024i q^{41} +(-38.1922 - 11.4960i) q^{42} +57.6214i q^{43} +(-3.28282 - 1.89534i) q^{44} +(-35.1149 + 28.1414i) 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} +(-5.85158 + 0.681995i) q^{60} +(52.2391 - 90.4808i) q^{61} +27.0578 q^{62} +(15.9769 - 60.9404i) q^{63} +68.9894 q^{64} +(84.4891 - 6.77782i) 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} +(-18.0699 - 63.9716i) q^{70} -50.7518i q^{71} +(42.1213 + 62.1603i) q^{72} +(-81.5039 + 47.0563i) q^{73} +(-2.06219 + 1.19061i) q^{74} +(-71.0131 - 24.1274i) q^{75} +5.46122 q^{76} +(63.9525 + 21.7877i) q^{77} +(-51.2726 - 81.8584i) q^{78} +(-3.71265 + 6.43050i) q^{79} +(64.4673 + 30.6299i) 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} +(12.9412 + 84.4820i) q^{90} +(-89.3032 + 78.1425i) q^{91} -0.278537 q^{92} +(1.53723 + 42.7115i) q^{93} +(30.5480 + 52.9107i) q^{94} +(62.7984 + 29.8370i) 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 −0.524765 0.851247i \(-0.675847\pi\)
0.999584 + 0.0288361i \(0.00918008\pi\)
\(3\) 2.65035 + 1.40558i 0.883449 + 0.468527i
\(4\) 0.196373 + 0.340128i 0.0490932 + 0.0850320i
\(5\) 0.399822 + 4.98399i 0.0799644 + 0.996798i
\(6\) 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
\(10\) 8.57746 + 4.07535i 0.857746 + 0.407535i
\(11\) −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 \(-0.773929\pi\)
0.758216 0.652004i \(-0.226071\pi\)
\(14\) −13.0423 + 2.57932i −0.931596 + 0.184237i
\(15\) −5.94574 + 13.7713i −0.396383 + 0.918085i
\(16\) 7.13738 12.3623i 0.446086 0.772644i
\(17\) −12.1835 21.1024i −0.716674 1.24131i −0.962311 0.271953i \(-0.912330\pi\)
0.245637 0.969362i \(-0.421003\pi\)
\(18\) 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 −0.873631 0.486589i \(-0.838241\pi\)
0.858214 + 0.513292i \(0.171574\pi\)
\(24\) 22.1120 + 11.7268i 0.921331 + 0.488618i
\(25\) −24.6803 + 3.98542i −0.987211 + 0.159417i
\(26\) −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 \(0.907679\pi\)
\(30\) 17.0050 + 22.8574i 0.566834 + 0.761914i
\(31\) 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
\(35\) 24.4125 25.0805i 0.697500 0.716585i
\(36\) −1.54272 + 3.18028i −0.0428533 + 0.0883412i
\(37\) −1.08578 0.626873i −0.0293453 0.0169425i 0.485256 0.874372i \(-0.338727\pi\)
−0.514601 + 0.857430i \(0.672060\pi\)
\(38\) −13.2049 22.8716i −0.347498 0.601885i
\(39\) 23.8276 44.9289i 0.610963 1.15202i
\(40\) 3.33573 + 41.5816i 0.0833933 + 1.03954i
\(41\) 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 \(0.233713\pi\)
−0.742346 + 0.670017i \(0.766287\pi\)
\(44\) −3.28282 1.89534i −0.0746095 0.0430758i
\(45\) −35.1149 + 28.1414i −0.780332 + 0.625365i
\(46\) 0.673487 + 1.16651i 0.0146410 + 0.0253590i
\(47\) −16.0840 + 27.8583i −0.342213 + 0.592730i −0.984843 0.173446i \(-0.944510\pi\)
0.642630 + 0.766176i \(0.277843\pi\)
\(48\) 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 0.936211 0.351438i \(-0.114307\pi\)
−0.772460 + 0.635064i \(0.780974\pi\)
\(54\) 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 \(0.599680\pi\)
\(60\) −5.85158 + 0.681995i −0.0975263 + 0.0113666i
\(61\) 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
\(65\) 84.4891 6.77782i 1.29983 0.104274i
\(66\) −25.7661 + 48.5843i −0.390396 + 0.736125i
\(67\) 86.1690 49.7497i 1.28610 0.742533i 0.308147 0.951339i \(-0.400291\pi\)
0.977957 + 0.208806i \(0.0669577\pi\)
\(68\) 4.78500 8.28786i 0.0703676 0.121880i
\(69\) −1.80311 + 1.12939i −0.0261320 + 0.0163680i
\(70\) −18.0699 63.9716i −0.258141 0.913880i
\(71\) 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 −0.940503 0.339786i \(-0.889645\pi\)
−0.175988 + 0.984392i \(0.556312\pi\)
\(74\) −2.06219 + 1.19061i −0.0278674 + 0.0160893i
\(75\) −71.0131 24.1274i −0.946842 0.321699i
\(76\) 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 \(0.181631\pi\)
\(80\) 64.4673 + 30.6299i 0.805841 + 0.382874i
\(81\) −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 \(-0.637797\pi\)
−0.419508 + 0.907752i \(0.637797\pi\)
\(84\) 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 \(0.497009\pi\)
\(90\) 12.9412 + 84.4820i 0.143791 + 0.938689i
\(91\) −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
\(95\) 62.7984 + 29.8370i 0.661036 + 0.314073i
\(96\) 0.675522 + 18.7691i 0.00703669 + 0.195512i
\(97\) 90.4517i 0.932492i −0.884655 0.466246i \(-0.845606\pi\)
0.884655 0.466246i \(-0.154394\pi\)
\(98\) 73.7078 + 56.8170i 0.752121 + 0.579765i
\(99\) −78.1554 37.9123i −0.789448 0.382953i
\(100\) −6.20209 7.61183i −0.0620209 0.0761183i
\(101\) 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 0.883738 0.467982i \(-0.155019\pi\)
0.0365842 + 0.999331i \(0.488352\pi\)
\(104\) 141.432i 1.35992i
\(105\) 99.9542 32.1582i 0.951945 0.306269i
\(106\) 32.9670 0.311009
\(107\) −39.8017 + 68.9385i −0.371978 + 0.644285i −0.989870 0.141978i \(-0.954654\pi\)
0.617892 + 0.786263i \(0.287987\pi\)
\(108\) −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 \(-0.391648\pi\)
\(110\) −91.3629 + 7.32925i −0.830572 + 0.0666295i
\(111\) −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 \(-0.645277\pi\)
−0.440722 + 0.897644i \(0.645277\pi\)
\(114\) −2.84972 79.1784i −0.0249975 0.694547i
\(115\) −3.20288 1.52176i −0.0278512 0.0132327i
\(116\) −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
\(120\) −49.6056 + 114.894i −0.413380 + 0.957453i
\(121\) −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 \(0.114271\pi\)
−0.936251 + 0.351332i \(0.885729\pi\)
\(128\) 52.9941 91.7885i 0.414016 0.717097i
\(129\) −80.9917 + 152.717i −0.627843 + 1.18385i
\(130\) 69.0858 145.406i 0.531429 1.11851i
\(131\) 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
\(135\) −132.622 + 25.2277i −0.982384 + 0.186871i
\(136\) −101.647 176.058i −0.747405 1.29454i
\(137\) 44.2662 + 76.6714i 0.323111 + 0.559645i 0.981128 0.193358i \(-0.0619379\pi\)
−0.658017 + 0.753003i \(0.728605\pi\)
\(138\) 0.145343 + 4.03831i 0.00105321 + 0.0292631i
\(139\) −5.87121 −0.0422389 −0.0211195 0.999777i \(-0.506723\pi\)
−0.0211195 + 0.999777i \(0.506723\pi\)
\(140\) 13.3245 + 3.37824i 0.0951752 + 0.0241303i
\(141\) −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
\(145\) −82.6702 + 6.63191i −0.570139 + 0.0457373i
\(146\) 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 \(0.672814\pi\)
\(150\) −107.122 + 93.8917i −0.714148 + 0.625944i
\(151\) 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 −0.00154383 0.999999i \(-0.500491\pi\)
0.865252 + 0.501336i \(0.167158\pi\)
\(158\) 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 0.492021 0.870583i \(-0.336258\pi\)
−0.507937 + 0.861394i \(0.669592\pi\)
\(164\) 8.19788 4.73305i 0.0499871 0.0288601i
\(165\) −16.7600 143.802i −0.101576 0.871530i
\(166\) −66.1312 + 114.543i −0.398381 + 0.690015i
\(167\) −201.798 −1.20837 −0.604186 0.796844i \(-0.706501\pi\)
−0.604186 + 0.796844i \(0.706501\pi\)
\(168\) −40.1508 170.541i −0.238993 1.01513i
\(169\) −118.374 −0.700436
\(170\) −18.5036 230.656i −0.108844 1.35680i
\(171\) 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 −0.842658 0.538449i \(-0.819010\pi\)
0.887640 + 0.460539i \(0.152344\pi\)
\(174\) 50.1688 + 80.0962i 0.288326 + 0.460323i
\(175\) 134.761 + 111.644i 0.770066 + 0.637965i
\(176\) 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 \(0.305416\pi\)
\(180\) −16.4673 6.41735i −0.0914851 0.0356520i
\(181\) 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
\(185\) 2.69021 5.66213i 0.0145417 0.0306061i
\(186\) 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 −0.538187 0.842825i \(-0.680891\pi\)
0.460814 + 0.887497i \(0.347557\pi\)
\(194\) −148.777 85.8964i −0.766891 0.442765i
\(195\) 233.452 + 100.793i 1.19719 + 0.516886i
\(196\) −17.7959 + 7.32530i −0.0907952 + 0.0373740i
\(197\) 354.243 1.79819 0.899094 0.437755i \(-0.144226\pi\)
0.899094 + 0.437755i \(0.144226\pi\)
\(198\) −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 \(0.820928\pi\)
\(200\) −205.909 + 33.2505i −1.02954 + 0.166252i
\(201\) 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
\(205\) 120.126 9.63665i 0.585980 0.0470080i
\(206\) 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
\(210\) 42.0258 194.946i 0.200123 0.928313i
\(211\) −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
\(215\) −287.185 + 23.0383i −1.33574 + 0.107155i
\(216\) 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
\(220\) 8.13379 17.1193i 0.0369718 0.0778151i
\(221\) −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 \(0.0909782\pi\)
−0.959432 + 0.281941i \(0.909022\pi\)
\(224\) 14.1322 41.4817i 0.0630904 0.185186i
\(225\) −154.296 163.761i −0.685762 0.727826i
\(226\) −94.5869 + 163.829i −0.418526 + 0.724909i
\(227\) −195.808 339.150i −0.862591 1.49405i −0.869420 0.494074i \(-0.835507\pi\)
0.00682884 0.999977i \(-0.497826\pi\)
\(228\) 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 \(-0.536682\pi\)
0.917774 0.397103i \(-0.129984\pi\)
\(234\) −20.8313 289.021i −0.0890229 1.23513i
\(235\) −145.276 69.0241i −0.618197 0.293720i
\(236\) −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 \(0.944990\pi\)
\(240\) 127.808 + 171.794i 0.532533 + 0.715808i
\(241\) −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
\(245\) −244.655 12.9930i −0.998593 0.0530328i
\(246\) −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
\(250\) −227.936 66.3961i −0.911745 0.265584i
\(251\) 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
\(255\) 363.046 42.3126i 1.42371 0.165932i
\(256\) 37.3282 + 64.6544i 0.145813 + 0.252556i
\(257\) −80.6774 + 139.737i −0.313920 + 0.543725i −0.979207 0.202862i \(-0.934976\pi\)
0.665288 + 0.746587i \(0.268309\pi\)
\(258\) 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 0.894002 0.448062i \(-0.147886\pi\)
−0.835034 + 0.550198i \(0.814552\pi\)
\(264\) −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 \(0.134983\pi\)
\(270\) −84.4479 + 242.097i −0.312770 + 0.896654i
\(271\) 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
\(275\) 187.060 152.416i 0.680220 0.554241i
\(276\) −0.738219 0.391506i −0.00267471 0.00141850i
\(277\) −283.178 + 163.493i −1.02230 + 0.590226i −0.914770 0.403975i \(-0.867628\pi\)
−0.107532 + 0.994202i \(0.534295\pi\)
\(278\) −5.57553 + 9.65710i −0.0200559 + 0.0347378i
\(279\) −55.9604 + 115.361i −0.200575 + 0.413481i
\(280\) 203.674 209.248i 0.727409 0.747313i
\(281\) 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 −0.993496 0.113863i \(-0.963678\pi\)
−0.398140 + 0.917325i \(0.630344\pi\)
\(284\) 17.2621 9.96628i 0.0607821 0.0350926i
\(285\) 124.499 + 167.347i 0.436839 + 0.587181i
\(286\) 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
\(290\) −67.5985 + 142.276i −0.233098 + 0.490606i
\(291\) 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 \(-0.577858\pi\)
−0.242166 + 0.970235i \(0.577858\pi\)
\(294\) 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
\(300\) −5.73864 28.8915i −0.0191288 0.0963051i
\(301\) 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
\(305\) 471.842 + 224.183i 1.54702 + 0.735026i
\(306\) −233.650 344.808i −0.763563 1.12682i
\(307\) 187.823i 0.611801i 0.952063 + 0.305901i \(0.0989575\pi\)
−0.952063 + 0.305901i \(0.901042\pi\)
\(308\) 5.14793 + 26.0305i 0.0167141 + 0.0845148i
\(309\) 174.309 + 278.290i 0.564106 + 0.900615i
\(310\) 10.8183 + 134.856i 0.0348978 + 0.435019i
\(311\) −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 0.409082 0.912498i \(-0.365849\pi\)
−0.585705 + 0.810524i \(0.699182\pi\)
\(314\) 297.389i 0.947098i
\(315\) 310.114 + 55.2634i 0.984490 + 0.175440i
\(316\) −2.91626 −0.00922866
\(317\) 99.2398 171.888i 0.313059 0.542235i −0.665964 0.745984i \(-0.731979\pi\)
0.979023 + 0.203749i \(0.0653128\pi\)
\(318\) 87.3739 + 46.3378i 0.274761 + 0.145716i
\(319\) −80.0473 138.646i −0.250932 0.434627i
\(320\) 27.5835 + 343.842i 0.0861983 + 1.07451i
\(321\) −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
\(325\) 67.5612 + 418.383i 0.207880 + 1.28733i
\(326\) −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
\(330\) −252.445 108.993i −0.764986 0.330282i
\(331\) 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 \(-0.852985\pi\)
0.895224 0.445616i \(-0.147015\pi\)
\(338\) −112.412 + 194.704i −0.332581 + 0.576047i
\(339\) −263.983 140.000i −0.778710 0.412980i
\(340\) 43.2198 + 20.5347i 0.127117 + 0.0603962i
\(341\) −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
\(345\) −6.34979 8.53512i −0.0184052 0.0247395i
\(346\) −14.7798 25.5993i −0.0427161 0.0739865i
\(347\) −71.3734 123.622i −0.205687 0.356260i 0.744664 0.667439i \(-0.232610\pi\)
−0.950351 + 0.311179i \(0.899276\pi\)
\(348\) −19.5310 + 0.702941i −0.0561235 + 0.00201995i
\(349\) 46.0748 0.132020 0.0660098 0.997819i \(-0.478973\pi\)
0.0660098 + 0.997819i \(0.478973\pi\)
\(350\) 311.609 115.637i 0.890311 0.330393i
\(351\) 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 0.999068 0.0431618i \(-0.0137431\pi\)
−0.536913 + 0.843637i \(0.680410\pi\)
\(354\) −233.887 + 441.014i −0.660698 + 1.24580i
\(355\) 252.947 20.2917i 0.712525 0.0571597i
\(356\) 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 \(0.626363\pi\)
\(360\) −292.965 + 234.785i −0.813793 + 0.652181i
\(361\) 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 −0.110187 0.993911i \(-0.535145\pi\)
0.805658 + 0.592380i \(0.201812\pi\)
\(368\) 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 0.546430 0.837505i \(-0.315986\pi\)
−0.452085 + 0.891975i \(0.649320\pi\)
\(374\) 386.833 223.338i 1.03431 0.597161i
\(375\) 91.8583 363.575i 0.244955 0.969534i
\(376\) −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 \(0.513524\pi\)
\(380\) 2.18351 + 27.2187i 0.00574609 + 0.0716280i
\(381\) −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 −0.654242 0.756285i \(-0.727012\pi\)
0.982083 + 0.188448i \(0.0603456\pi\)
\(384\) 269.469 168.784i 0.701742 0.439541i
\(385\) −83.0201 + 327.450i −0.215637 + 0.850519i
\(386\) 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 \(0.344750\pi\)
\(390\) 387.481 288.271i 0.993542 0.739155i
\(391\) 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
\(395\) −33.5339 15.9328i −0.0848961 0.0403361i
\(396\) −2.45257 34.0278i −0.00619336 0.0859287i
\(397\) 281.690 + 162.634i 0.709546 + 0.409657i 0.810893 0.585195i \(-0.198982\pi\)
−0.101347 + 0.994851i \(0.532315\pi\)
\(398\) 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
\(405\) −386.954 119.549i −0.955441 0.295183i
\(406\) −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 \(0.661296\pi\)
\(410\) 98.2256 206.737i 0.239575 0.504237i
\(411\) 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
\(415\) −27.8429 347.076i −0.0670913 0.836328i
\(416\) 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 \(0.805208\pi\)
\(420\) 30.5662 + 27.6822i 0.0727767 + 0.0659100i
\(421\) −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
\(425\) 384.793 + 472.256i 0.905395 + 1.11119i
\(426\) −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
\(430\) −234.828 + 494.246i −0.546111 + 1.14941i
\(431\) 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 \(-0.931725\pi\)
0.977085 0.212852i \(-0.0682751\pi\)
\(434\) −124.726 142.540i −0.287387 0.328433i
\(435\) −228.426 98.6229i −0.525118 0.226719i
\(436\) 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 \(0.384482\pi\)
−0.987117 + 0.159998i \(0.948851\pi\)
\(444\) 0.692114 1.30504i 0.00155881 0.00293928i
\(445\) −194.070 + 408.463i −0.436113 + 0.917894i
\(446\) 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 \(-0.145875\pi\)
\(450\) −415.883 + 98.2764i −0.924185 + 0.218392i
\(451\) 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
\(455\) −425.167 413.843i −0.934433 0.909545i
\(456\) 294.954 184.746i 0.646828 0.405145i
\(457\) 608.910 + 351.555i 1.33241 + 0.769266i 0.985668 0.168695i \(-0.0539554\pi\)
0.346740 + 0.937961i \(0.387289\pi\)
\(458\) −120.322 208.405i −0.262713 0.455032i
\(459\) 531.014 388.413i 1.15689 0.846215i
\(460\) −0.111365 1.38822i −0.000242098 0.00301788i
\(461\) 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 \(-0.599850\pi\)
0.308570 0.951202i \(-0.400150\pi\)
\(464\) 205.056 + 118.389i 0.441930 + 0.255149i
\(465\) −212.259 + 24.7386i −0.456471 + 0.0532012i
\(466\) −355.259 615.327i −0.762359 1.32044i
\(467\) 25.2777 43.7822i 0.0541278 0.0937521i −0.837692 0.546143i \(-0.816095\pi\)
0.891820 + 0.452391i \(0.149429\pi\)
\(468\) 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 \(0.573503\pi\)
\(480\) −93.2751 + 10.8711i −0.194323 + 0.0226481i
\(481\) −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
\(485\) 450.810 36.1646i 0.929505 0.0745661i
\(486\) 82.5711 + 454.078i 0.169899 + 0.934317i
\(487\) 701.394 404.950i 1.44023 0.831520i 0.442370 0.896833i \(-0.354138\pi\)
0.997865 + 0.0653129i \(0.0208045\pi\)
\(488\) 435.833 754.886i 0.893101 1.54690i
\(489\) −4.77038 7.61607i −0.00975537 0.0155748i
\(490\) −253.705 + 390.076i −0.517766 + 0.796073i
\(491\) 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
\(495\) 157.706 404.684i 0.318599 0.817543i
\(496\) 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 \(-0.0731230\pi\)
\(500\) 35.4575 33.9545i 0.0709150 0.0679090i
\(501\) −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 \(-0.404900\pi\)
0.294341 + 0.955701i \(0.404900\pi\)
\(504\) 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 \(0.972614\pi\)
\(510\) 275.166 637.328i 0.539541 1.24966i
\(511\) 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
\(515\) −234.868 + 494.330i −0.456054 + 0.959864i
\(516\) −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
\(520\) 704.896 56.5476i 1.35557 0.108745i
\(521\) −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 0.301131 0.953583i \(-0.402636\pi\)
−0.675261 + 0.737579i \(0.735969\pi\)
\(524\) 43.9751i 0.0839219i
\(525\) 200.240 + 485.313i 0.381410 + 0.924406i
\(526\) 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
\(530\) 13.1809 + 164.307i 0.0248696 + 0.310013i
\(531\) −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
\(535\) −359.502 170.808i −0.671967 0.319267i
\(536\) 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
\(540\) −34.6240 40.1544i −0.0641185 0.0743600i
\(541\) −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 \(0.0886141\pi\)
−0.961499 + 0.274807i \(0.911386\pi\)
\(548\) −17.3854 + 30.1124i −0.0317251 + 0.0549496i
\(549\) 937.872 67.5976i 1.70833 0.123129i
\(550\) −73.0578 452.421i −0.132832 0.822584i
\(551\) 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
\(555\) 15.0886 11.2253i 0.0271866 0.0202258i
\(556\) −1.15295 1.99696i −0.00207365 0.00359166i
\(557\) −217.246 376.281i −0.390028 0.675549i 0.602425 0.798176i \(-0.294201\pi\)
−0.992453 + 0.122627i \(0.960868\pi\)
\(558\) 136.606 + 201.596i 0.244814 + 0.361283i
\(559\) 976.805 1.74741
\(560\) −135.811 480.804i −0.242521 0.858578i
\(561\) 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 0.994262 0.106970i \(-0.0341150\pi\)
−0.589770 + 0.807571i \(0.700782\pi\)
\(564\) −33.4841 17.7579i −0.0593690 0.0314857i
\(565\) −39.8235 496.421i −0.0704840 0.878620i
\(566\) 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 \(0.790900\pi\)
\(570\) 393.485 45.8602i 0.690324 0.0804565i
\(571\) −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 −0.336228 0.941780i \(-0.609151\pi\)
0.647492 + 0.762073i \(0.275818\pi\)
\(578\) 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
\(585\) 477.057 + 595.272i 0.815481 + 1.01756i
\(586\) −134.763 + 233.416i −0.229971 + 0.398321i
\(587\) 473.066 0.805905 0.402953 0.915221i \(-0.367984\pi\)
0.402953 + 0.915221i \(0.367984\pi\)
\(588\) −57.4615 5.59897i −0.0977237 0.00952206i
\(589\) 198.099 0.336332
\(590\) −829.329 + 66.5298i −1.40564 + 0.112762i
\(591\) 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 −0.989895 0.141799i \(-0.954711\pi\)
0.617749 + 0.786375i \(0.288045\pi\)
\(594\) −492.065 + 53.3141i −0.828392 + 0.0897544i
\(595\) −826.686 209.594i −1.38939 0.352259i
\(596\) 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 \(0.302971\pi\)
\(600\) −592.466 201.296i −0.987443 0.335494i
\(601\) −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
\(605\) −125.750 59.7467i −0.207851 0.0987548i
\(606\) 145.405 274.173i 0.239941 0.452430i
\(607\) −187.998 108.541i −0.309716 0.178815i 0.337083 0.941475i \(-0.390560\pi\)
−0.646800 + 0.762660i \(0.723893\pi\)
\(608\) 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 −0.466438 0.884554i \(-0.654463\pi\)
0.532827 + 0.846224i \(0.321130\pi\)
\(614\) 308.935 + 178.364i 0.503152 + 0.290495i
\(615\) 331.920 + 143.306i 0.539708 + 0.233018i
\(616\) 533.558 + 181.776i 0.866166 + 0.295091i
\(617\) 140.650 0.227958 0.113979 0.993483i \(-0.463640\pi\)
0.113979 + 0.993483i \(0.463640\pi\)
\(618\) 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 \(0.812015\pi\)
\(620\) −25.2689 12.0059i −0.0407563 0.0193643i
\(621\) −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
\(625\) 593.233 196.722i 0.949173 0.314756i
\(626\) −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
\(630\) 385.395 457.603i 0.611738 0.726354i
\(631\) 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
\(635\) −444.762 + 35.6794i −0.700413 + 0.0561880i
\(636\) −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
\(640\) 478.661 + 227.423i 0.747908 + 0.355348i
\(641\) 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 \(0.177733\pi\)
−0.848122 + 0.529801i \(0.822267\pi\)
\(644\) 1.28394 + 1.46732i 0.00199370 + 0.00227845i
\(645\) −793.521 342.602i −1.23027 0.531166i
\(646\) −321.763 + 557.311i −0.498086 + 0.862710i
\(647\) 76.8005 + 133.022i 0.118702 + 0.205599i 0.919254 0.393666i \(-0.128793\pi\)
−0.800551 + 0.599264i \(0.795460\pi\)
\(648\) −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 −0.944428 0.328720i \(-0.893383\pi\)
0.756893 + 0.653538i \(0.226716\pi\)
\(654\) −712.626 377.933i −1.08964 0.577879i
\(655\) −240.255 + 505.668i −0.366801 + 0.772012i
\(656\) −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 \(-0.195273\pi\)
\(660\) 45.6200 33.9394i 0.0691212 0.0514234i
\(661\) −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
\(665\) −132.296 468.357i −0.198941 0.704296i
\(666\) −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
\(670\) 941.859 75.5571i 1.40576 0.112772i
\(671\) 1008.39i 1.50282i
\(672\) 95.7613 90.0770i 0.142502 0.134043i
\(673\) 1101.01i 1.63598i 0.575235 + 0.817988i \(0.304911\pi\)
−0.575235 + 0.817988i \(0.695089\pi\)
\(674\) −494.014 285.219i −0.732959 0.423174i
\(675\) −178.759 650.899i −0.264829 0.964295i
\(676\) −23.2454 40.2622i −0.0343867 0.0595595i
\(677\) −68.0959 + 117.946i −0.100585 + 0.174218i −0.911926 0.410355i \(-0.865405\pi\)
0.811341 + 0.584573i \(0.198738\pi\)
\(678\) −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 \(-0.818028\pi\)
−0.0480644 0.998844i \(-0.515305\pi\)
\(684\) 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
\(690\) −20.0688 + 2.33899i −0.0290852 + 0.00338984i
\(691\) −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
\(695\) −2.34744 29.2621i −0.00337761 0.0421037i
\(696\) −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
\(700\) −11.5097 + 67.7600i −0.0164424 + 0.0967999i
\(701\) 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
\(705\) −288.013 387.136i −0.408530 0.549129i
\(706\) 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 \(0.975853\pi\)
\(710\) 206.832 435.322i 0.291312 0.613129i
\(711\) −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 \(0.482877\pi\)
\(720\) 97.2645 + 634.958i 0.135090 + 0.881886i
\(721\) −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
\(725\) −66.1067 409.376i −0.0911817 0.564656i
\(726\) 5.70638 + 158.550i 0.00786002 + 0.218388i
\(727\) 579.070i 0.796520i −0.917273 0.398260i \(-0.869614\pi\)
0.917273 0.398260i \(-0.130386\pi\)
\(728\) −745.060 + 651.947i −1.02343 + 0.895531i
\(729\) −712.083 + 156.138i −0.976794 + 0.214181i
\(730\) −890.867 + 71.4665i −1.22037 + 0.0978993i
\(731\) 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 0.0397023 0.999212i \(-0.487359\pi\)
−0.845491 + 0.533989i \(0.820692\pi\)
\(734\) 559.762i 0.762618i
\(735\) −630.158 378.319i −0.857358 0.514720i
\(736\) −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 \(-0.369611\pi\)
\(740\) 2.45413 0.196874i 0.00331640 0.000266046i
\(741\) −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 \(-0.516501\pi\)
−0.0518171 + 0.998657i \(0.516501\pi\)
\(744\) 12.8252 + 356.344i 0.0172382 + 0.478957i
\(745\) 12.3478 25.9885i 0.0165742 0.0348840i
\(746\) 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
\(750\) −510.785 496.356i −0.681046 0.661808i
\(751\) −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 \(0.0837803\pi\)
−0.965561 + 0.260175i \(0.916220\pi\)
\(758\) −30.5733 + 52.9545i −0.0403342 + 0.0698608i
\(759\) 9.62125 18.1417i 0.0126762 0.0239021i
\(760\) 523.930 + 248.931i 0.689381 + 0.327541i
\(761\) −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
\(765\)