Properties

Label 210.3.k.b.83.7
Level 210
Weight 3
Character 210.83
Analytic conductor 5.722
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 83.7
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.7

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-0.947561 - 2.84642i) q^{3} +2.00000i q^{4} +(-4.64638 - 1.84693i) q^{5} +(1.89886 - 3.79398i) q^{6} +(-3.13705 + 6.25771i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-7.20426 + 5.39432i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-0.947561 - 2.84642i) q^{3} +2.00000i q^{4} +(-4.64638 - 1.84693i) q^{5} +(1.89886 - 3.79398i) q^{6} +(-3.13705 + 6.25771i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-7.20426 + 5.39432i) q^{9} +(-2.79945 - 6.49331i) q^{10} -2.08576i q^{11} +(5.69285 - 1.89512i) q^{12} +(-8.39517 + 8.39517i) q^{13} +(-9.39476 + 3.12066i) q^{14} +(-0.854411 + 14.9756i) q^{15} -4.00000 q^{16} +(-4.96522 + 4.96522i) q^{17} +(-12.5986 - 1.80994i) q^{18} -17.3668 q^{19} +(3.69386 - 9.29276i) q^{20} +(20.7846 + 2.99982i) q^{21} +(2.08576 - 2.08576i) q^{22} +(-3.08467 + 3.08467i) q^{23} +(7.58797 + 3.79773i) q^{24} +(18.1777 + 17.1631i) q^{25} -16.7903 q^{26} +(22.1810 + 15.3949i) q^{27} +(-12.5154 - 6.27410i) q^{28} -39.1891 q^{29} +(-15.8301 + 14.1212i) q^{30} -42.3954i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-5.93696 + 1.97638i) q^{33} -9.93045 q^{34} +(26.1335 - 23.2818i) q^{35} +(-10.7886 - 14.4085i) q^{36} +(36.7464 - 36.7464i) q^{37} +(-17.3668 - 17.3668i) q^{38} +(31.8511 + 15.9413i) q^{39} +(12.9866 - 5.59891i) q^{40} -15.5827 q^{41} +(17.7848 + 23.7845i) q^{42} +(22.8274 + 22.8274i) q^{43} +4.17152 q^{44} +(43.4366 - 11.7583i) q^{45} -6.16934 q^{46} +(-33.4161 + 33.4161i) q^{47} +(3.79024 + 11.3857i) q^{48} +(-29.3178 - 39.2615i) q^{49} +(1.01465 + 35.3408i) q^{50} +(18.8380 + 9.42828i) q^{51} +(-16.7903 - 16.7903i) q^{52} +(59.7460 - 59.7460i) q^{53} +(6.78607 + 37.5759i) q^{54} +(-3.85225 + 9.69124i) q^{55} +(-6.24131 - 18.7895i) q^{56} +(16.4561 + 49.4332i) q^{57} +(-39.1891 - 39.1891i) q^{58} +48.9876i q^{59} +(-29.9513 - 1.70882i) q^{60} -82.9406i q^{61} +(42.3954 - 42.3954i) q^{62} +(-11.1560 - 62.0044i) q^{63} -8.00000i q^{64} +(54.5124 - 23.5019i) q^{65} +(-7.91334 - 3.96057i) q^{66} +(-54.8233 + 54.8233i) q^{67} +(-9.93045 - 9.93045i) q^{68} +(11.7032 + 5.85736i) q^{69} +(49.4153 + 2.85168i) q^{70} +74.9745i q^{71} +(3.61987 - 25.1972i) q^{72} +(-75.1938 + 75.1938i) q^{73} +73.4928 q^{74} +(31.6289 - 68.0045i) q^{75} -34.7336i q^{76} +(13.0521 + 6.54314i) q^{77} +(15.9099 + 47.7924i) q^{78} +3.61068i q^{79} +(18.5855 + 7.38771i) q^{80} +(22.8026 - 77.7241i) q^{81} +(-15.5827 - 15.5827i) q^{82} +(103.116 + 103.116i) q^{83} +(-5.99963 + 41.5693i) q^{84} +(32.2407 - 13.8999i) q^{85} +45.6547i q^{86} +(37.1340 + 111.549i) q^{87} +(4.17152 + 4.17152i) q^{88} +24.4427i q^{89} +(55.1950 + 31.6783i) q^{90} +(-26.1984 - 78.8706i) q^{91} +(-6.16934 - 6.16934i) q^{92} +(-120.675 + 40.1722i) q^{93} -66.8321 q^{94} +(80.6927 + 32.0752i) q^{95} +(-7.59545 + 15.1759i) q^{96} +(35.3616 + 35.3616i) q^{97} +(9.94368 - 68.5793i) q^{98} +(11.2513 + 15.0264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) −0.947561 2.84642i −0.315854 0.948808i
\(4\) 2.00000i 0.500000i
\(5\) −4.64638 1.84693i −0.929276 0.369386i
\(6\) 1.89886 3.79398i 0.316477 0.632331i
\(7\) −3.13705 + 6.25771i −0.448150 + 0.893958i
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) −7.20426 + 5.39432i −0.800473 + 0.599369i
\(10\) −2.79945 6.49331i −0.279945 0.649331i
\(11\) 2.08576i 0.189615i −0.995496 0.0948073i \(-0.969777\pi\)
0.995496 0.0948073i \(-0.0302235\pi\)
\(12\) 5.69285 1.89512i 0.474404 0.157927i
\(13\) −8.39517 + 8.39517i −0.645782 + 0.645782i −0.951971 0.306189i \(-0.900946\pi\)
0.306189 + 0.951971i \(0.400946\pi\)
\(14\) −9.39476 + 3.12066i −0.671054 + 0.222904i
\(15\) −0.854411 + 14.9756i −0.0569607 + 0.998376i
\(16\) −4.00000 −0.250000
\(17\) −4.96522 + 4.96522i −0.292072 + 0.292072i −0.837898 0.545826i \(-0.816216\pi\)
0.545826 + 0.837898i \(0.316216\pi\)
\(18\) −12.5986 1.80994i −0.699921 0.100552i
\(19\) −17.3668 −0.914041 −0.457021 0.889456i \(-0.651083\pi\)
−0.457021 + 0.889456i \(0.651083\pi\)
\(20\) 3.69386 9.29276i 0.184693 0.464638i
\(21\) 20.7846 + 2.99982i 0.989745 + 0.142848i
\(22\) 2.08576 2.08576i 0.0948073 0.0948073i
\(23\) −3.08467 + 3.08467i −0.134116 + 0.134116i −0.770978 0.636862i \(-0.780232\pi\)
0.636862 + 0.770978i \(0.280232\pi\)
\(24\) 7.58797 + 3.79773i 0.316165 + 0.158239i
\(25\) 18.1777 + 17.1631i 0.727109 + 0.686523i
\(26\) −16.7903 −0.645782
\(27\) 22.1810 + 15.3949i 0.821518 + 0.570182i
\(28\) −12.5154 6.27410i −0.446979 0.224075i
\(29\) −39.1891 −1.35135 −0.675674 0.737201i \(-0.736147\pi\)
−0.675674 + 0.737201i \(0.736147\pi\)
\(30\) −15.8301 + 14.1212i −0.527669 + 0.470708i
\(31\) 42.3954i 1.36759i −0.729673 0.683796i \(-0.760328\pi\)
0.729673 0.683796i \(-0.239672\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −5.93696 + 1.97638i −0.179908 + 0.0598905i
\(34\) −9.93045 −0.292072
\(35\) 26.1335 23.2818i 0.746671 0.665194i
\(36\) −10.7886 14.4085i −0.299684 0.400236i
\(37\) 36.7464 36.7464i 0.993146 0.993146i −0.00683066 0.999977i \(-0.502174\pi\)
0.999977 + 0.00683066i \(0.00217428\pi\)
\(38\) −17.3668 17.3668i −0.457021 0.457021i
\(39\) 31.8511 + 15.9413i 0.816696 + 0.408751i
\(40\) 12.9866 5.59891i 0.324665 0.139973i
\(41\) −15.5827 −0.380065 −0.190032 0.981778i \(-0.560859\pi\)
−0.190032 + 0.981778i \(0.560859\pi\)
\(42\) 17.7848 + 23.7845i 0.423448 + 0.566297i
\(43\) 22.8274 + 22.8274i 0.530869 + 0.530869i 0.920831 0.389962i \(-0.127512\pi\)
−0.389962 + 0.920831i \(0.627512\pi\)
\(44\) 4.17152 0.0948073
\(45\) 43.4366 11.7583i 0.965259 0.261296i
\(46\) −6.16934 −0.134116
\(47\) −33.4161 + 33.4161i −0.710980 + 0.710980i −0.966740 0.255760i \(-0.917674\pi\)
0.255760 + 0.966740i \(0.417674\pi\)
\(48\) 3.79024 + 11.3857i 0.0789634 + 0.237202i
\(49\) −29.3178 39.2615i −0.598323 0.801255i
\(50\) 1.01465 + 35.3408i 0.0202930 + 0.706816i
\(51\) 18.8380 + 9.42828i 0.369372 + 0.184868i
\(52\) −16.7903 16.7903i −0.322891 0.322891i
\(53\) 59.7460 59.7460i 1.12728 1.12728i 0.136665 0.990617i \(-0.456362\pi\)
0.990617 0.136665i \(-0.0436385\pi\)
\(54\) 6.78607 + 37.5759i 0.125668 + 0.695850i
\(55\) −3.85225 + 9.69124i −0.0700409 + 0.176204i
\(56\) −6.24131 18.7895i −0.111452 0.335527i
\(57\) 16.4561 + 49.4332i 0.288703 + 0.867250i
\(58\) −39.1891 39.1891i −0.675674 0.675674i
\(59\) 48.9876i 0.830298i 0.909754 + 0.415149i \(0.136270\pi\)
−0.909754 + 0.415149i \(0.863730\pi\)
\(60\) −29.9513 1.70882i −0.499188 0.0284804i
\(61\) 82.9406i 1.35968i −0.733360 0.679841i \(-0.762049\pi\)
0.733360 0.679841i \(-0.237951\pi\)
\(62\) 42.3954 42.3954i 0.683796 0.683796i
\(63\) −11.1560 62.0044i −0.177079 0.984197i
\(64\) 8.00000i 0.125000i
\(65\) 54.5124 23.5019i 0.838653 0.361567i
\(66\) −7.91334 3.96057i −0.119899 0.0600087i
\(67\) −54.8233 + 54.8233i −0.818258 + 0.818258i −0.985855 0.167598i \(-0.946399\pi\)
0.167598 + 0.985855i \(0.446399\pi\)
\(68\) −9.93045 9.93045i −0.146036 0.146036i
\(69\) 11.7032 + 5.85736i 0.169611 + 0.0848893i
\(70\) 49.4153 + 2.85168i 0.705932 + 0.0407383i
\(71\) 74.9745i 1.05598i 0.849251 + 0.527990i \(0.177054\pi\)
−0.849251 + 0.527990i \(0.822946\pi\)
\(72\) 3.61987 25.1972i 0.0502760 0.349960i
\(73\) −75.1938 + 75.1938i −1.03005 + 1.03005i −0.0305180 + 0.999534i \(0.509716\pi\)
−0.999534 + 0.0305180i \(0.990284\pi\)
\(74\) 73.4928 0.993146
\(75\) 31.6289 68.0045i 0.421718 0.906727i
\(76\) 34.7336i 0.457021i
\(77\) 13.0521 + 6.54314i 0.169508 + 0.0849758i
\(78\) 15.9099 + 47.7924i 0.203973 + 0.612723i
\(79\) 3.61068i 0.0457048i 0.999739 + 0.0228524i \(0.00727479\pi\)
−0.999739 + 0.0228524i \(0.992725\pi\)
\(80\) 18.5855 + 7.38771i 0.232319 + 0.0923464i
\(81\) 22.8026 77.7241i 0.281514 0.959557i
\(82\) −15.5827 15.5827i −0.190032 0.190032i
\(83\) 103.116 + 103.116i 1.24236 + 1.24236i 0.959019 + 0.283341i \(0.0914427\pi\)
0.283341 + 0.959019i \(0.408557\pi\)
\(84\) −5.99963 + 41.5693i −0.0714242 + 0.494872i
\(85\) 32.2407 13.8999i 0.379303 0.163528i
\(86\) 45.6547i 0.530869i
\(87\) 37.1340 + 111.549i 0.426828 + 1.28217i
\(88\) 4.17152 + 4.17152i 0.0474036 + 0.0474036i
\(89\) 24.4427i 0.274637i 0.990527 + 0.137319i \(0.0438485\pi\)
−0.990527 + 0.137319i \(0.956152\pi\)
\(90\) 55.1950 + 31.6783i 0.613277 + 0.351981i
\(91\) −26.1984 78.8706i −0.287895 0.866710i
\(92\) −6.16934 6.16934i −0.0670580 0.0670580i
\(93\) −120.675 + 40.1722i −1.29758 + 0.431959i
\(94\) −66.8321 −0.710980
\(95\) 80.6927 + 32.0752i 0.849397 + 0.337634i
\(96\) −7.59545 + 15.1759i −0.0791193 + 0.158083i
\(97\) 35.3616 + 35.3616i 0.364553 + 0.364553i 0.865486 0.500933i \(-0.167010\pi\)
−0.500933 + 0.865486i \(0.667010\pi\)
\(98\) 9.94368 68.5793i 0.101466 0.699789i
\(99\) 11.2513 + 15.0264i 0.113649 + 0.151781i
\(100\) −34.3261 + 36.3554i −0.343261 + 0.363554i
\(101\) 12.9923 0.128637 0.0643184 0.997929i \(-0.479513\pi\)
0.0643184 + 0.997929i \(0.479513\pi\)
\(102\) 9.40970 + 28.2663i 0.0922520 + 0.277120i
\(103\) −45.5816 + 45.5816i −0.442540 + 0.442540i −0.892865 0.450325i \(-0.851308\pi\)
0.450325 + 0.892865i \(0.351308\pi\)
\(104\) 33.5807i 0.322891i
\(105\) −91.0329 52.3260i −0.866980 0.498343i
\(106\) 119.492 1.12728
\(107\) −49.5198 49.5198i −0.462802 0.462802i 0.436771 0.899573i \(-0.356122\pi\)
−0.899573 + 0.436771i \(0.856122\pi\)
\(108\) −30.7898 + 44.3620i −0.285091 + 0.410759i
\(109\) 170.424i 1.56352i −0.623579 0.781760i \(-0.714322\pi\)
0.623579 0.781760i \(-0.285678\pi\)
\(110\) −13.5435 + 5.83899i −0.123123 + 0.0530817i
\(111\) −139.415 69.7764i −1.25599 0.628616i
\(112\) 12.5482 25.0308i 0.112038 0.223490i
\(113\) −139.393 + 139.393i −1.23357 + 1.23357i −0.270986 + 0.962583i \(0.587350\pi\)
−0.962583 + 0.270986i \(0.912650\pi\)
\(114\) −32.9771 + 65.8893i −0.289273 + 0.577976i
\(115\) 20.0297 8.63538i 0.174171 0.0750903i
\(116\) 78.3781i 0.675674i
\(117\) 15.1947 105.767i 0.129869 0.903993i
\(118\) −48.9876 + 48.9876i −0.415149 + 0.415149i
\(119\) −15.4948 46.6471i −0.130208 0.391992i
\(120\) −28.2425 31.6601i −0.235354 0.263834i
\(121\) 116.650 0.964046
\(122\) 82.9406 82.9406i 0.679841 0.679841i
\(123\) 14.7655 + 44.3549i 0.120045 + 0.360609i
\(124\) 84.7907 0.683796
\(125\) −52.7616 113.319i −0.422093 0.906553i
\(126\) 50.8484 73.1604i 0.403559 0.580638i
\(127\) −104.552 + 104.552i −0.823247 + 0.823247i −0.986572 0.163325i \(-0.947778\pi\)
0.163325 + 0.986572i \(0.447778\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 43.3460 86.6067i 0.336016 0.671370i
\(130\) 78.0143 + 31.0106i 0.600110 + 0.238543i
\(131\) −1.42804 −0.0109011 −0.00545054 0.999985i \(-0.501735\pi\)
−0.00545054 + 0.999985i \(0.501735\pi\)
\(132\) −3.95277 11.8739i −0.0299452 0.0899539i
\(133\) 54.4805 108.676i 0.409628 0.817115i
\(134\) −109.647 −0.818258
\(135\) −74.6280 112.497i −0.552800 0.833314i
\(136\) 19.8609i 0.146036i
\(137\) −152.451 152.451i −1.11278 1.11278i −0.992773 0.120010i \(-0.961707\pi\)
−0.120010 0.992773i \(-0.538293\pi\)
\(138\) 5.84582 + 17.5605i 0.0423610 + 0.127250i
\(139\) −75.0255 −0.539752 −0.269876 0.962895i \(-0.586983\pi\)
−0.269876 + 0.962895i \(0.586983\pi\)
\(140\) 46.5636 + 52.2669i 0.332597 + 0.373335i
\(141\) 126.780 + 63.4525i 0.899149 + 0.450018i
\(142\) −74.9745 + 74.9745i −0.527990 + 0.527990i
\(143\) 17.5103 + 17.5103i 0.122450 + 0.122450i
\(144\) 28.8170 21.5773i 0.200118 0.149842i
\(145\) 182.087 + 72.3794i 1.25577 + 0.499168i
\(146\) −150.388 −1.03005
\(147\) −83.9744 + 120.654i −0.571255 + 0.820773i
\(148\) 73.4928 + 73.4928i 0.496573 + 0.496573i
\(149\) −183.297 −1.23018 −0.615091 0.788456i \(-0.710881\pi\)
−0.615091 + 0.788456i \(0.710881\pi\)
\(150\) 99.6334 36.3757i 0.664223 0.242504i
\(151\) −203.889 −1.35026 −0.675130 0.737699i \(-0.735913\pi\)
−0.675130 + 0.737699i \(0.735913\pi\)
\(152\) 34.7336 34.7336i 0.228510 0.228510i
\(153\) 8.98674 62.5547i 0.0587369 0.408855i
\(154\) 6.50894 + 19.5952i 0.0422659 + 0.127242i
\(155\) −78.3012 + 196.985i −0.505169 + 1.27087i
\(156\) −31.8826 + 63.7023i −0.204375 + 0.408348i
\(157\) 3.36424 + 3.36424i 0.0214283 + 0.0214283i 0.717740 0.696311i \(-0.245177\pi\)
−0.696311 + 0.717740i \(0.745177\pi\)
\(158\) −3.61068 + 3.61068i −0.0228524 + 0.0228524i
\(159\) −226.675 113.449i −1.42563 0.713518i
\(160\) 11.1978 + 25.9732i 0.0699863 + 0.162333i
\(161\) −9.62619 28.9797i −0.0597900 0.179998i
\(162\) 100.527 54.9215i 0.620536 0.339022i
\(163\) 105.247 + 105.247i 0.645690 + 0.645690i 0.951948 0.306259i \(-0.0990772\pi\)
−0.306259 + 0.951948i \(0.599077\pi\)
\(164\) 31.1653i 0.190032i
\(165\) 31.2356 + 1.78210i 0.189307 + 0.0108006i
\(166\) 206.232i 1.24236i
\(167\) 34.3084 34.3084i 0.205439 0.205439i −0.596886 0.802326i \(-0.703596\pi\)
0.802326 + 0.596886i \(0.203596\pi\)
\(168\) −47.5689 + 35.5696i −0.283148 + 0.211724i
\(169\) 28.0423i 0.165931i
\(170\) 46.1406 + 18.3408i 0.271416 + 0.107887i
\(171\) 125.115 93.6820i 0.731665 0.547848i
\(172\) −45.6547 + 45.6547i −0.265434 + 0.265434i
\(173\) 211.509 + 211.509i 1.22260 + 1.22260i 0.966706 + 0.255891i \(0.0823688\pi\)
0.255891 + 0.966706i \(0.417631\pi\)
\(174\) −74.4147 + 148.683i −0.427671 + 0.854499i
\(175\) −164.426 + 59.9094i −0.939576 + 0.342340i
\(176\) 8.34304i 0.0474036i
\(177\) 139.439 46.4187i 0.787793 0.262253i
\(178\) −24.4427 + 24.4427i −0.137319 + 0.137319i
\(179\) 110.880 0.619440 0.309720 0.950828i \(-0.399765\pi\)
0.309720 + 0.950828i \(0.399765\pi\)
\(180\) 23.5166 + 86.8733i 0.130648 + 0.482629i
\(181\) 24.2997i 0.134253i 0.997744 + 0.0671264i \(0.0213831\pi\)
−0.997744 + 0.0671264i \(0.978617\pi\)
\(182\) 52.6722 105.069i 0.289407 0.577302i
\(183\) −236.084 + 78.5913i −1.29008 + 0.429460i
\(184\) 12.3387i 0.0670580i
\(185\) −238.606 + 102.870i −1.28976 + 0.556053i
\(186\) −160.847 80.5030i −0.864771 0.432812i
\(187\) 10.3563 + 10.3563i 0.0553811 + 0.0553811i
\(188\) −66.8321 66.8321i −0.355490 0.355490i
\(189\) −165.920 + 90.5075i −0.877883 + 0.478876i
\(190\) 48.6175 + 112.768i 0.255882 + 0.593515i
\(191\) 163.399i 0.855494i 0.903898 + 0.427747i \(0.140693\pi\)
−0.903898 + 0.427747i \(0.859307\pi\)
\(192\) −22.7714 + 7.58049i −0.118601 + 0.0394817i
\(193\) −36.3745 36.3745i −0.188469 0.188469i 0.606565 0.795034i \(-0.292547\pi\)
−0.795034 + 0.606565i \(0.792547\pi\)
\(194\) 70.7233i 0.364553i
\(195\) −118.550 132.896i −0.607950 0.681518i
\(196\) 78.5230 58.6356i 0.400628 0.299161i
\(197\) 19.3286 + 19.3286i 0.0981145 + 0.0981145i 0.754460 0.656346i \(-0.227899\pi\)
−0.656346 + 0.754460i \(0.727899\pi\)
\(198\) −3.77509 + 26.2776i −0.0190661 + 0.132715i
\(199\) −79.6378 −0.400190 −0.200095 0.979776i \(-0.564125\pi\)
−0.200095 + 0.979776i \(0.564125\pi\)
\(200\) −70.6816 + 2.02930i −0.353408 + 0.0101465i
\(201\) 207.999 + 104.102i 1.03482 + 0.517920i
\(202\) 12.9923 + 12.9923i 0.0643184 + 0.0643184i
\(203\) 122.938 245.234i 0.605607 1.20805i
\(204\) −18.8566 + 37.6760i −0.0924341 + 0.184686i
\(205\) 72.4030 + 28.7801i 0.353185 + 0.140391i
\(206\) −91.1632 −0.442540
\(207\) 5.58305 38.8624i 0.0269713 0.187741i
\(208\) 33.5807 33.5807i 0.161446 0.161446i
\(209\) 36.2230i 0.173316i
\(210\) −38.7069 143.359i −0.184318 0.682661i
\(211\) −146.466 −0.694152 −0.347076 0.937837i \(-0.612825\pi\)
−0.347076 + 0.937837i \(0.612825\pi\)
\(212\) 119.492 + 119.492i 0.563641 + 0.563641i
\(213\) 213.409 71.0429i 1.00192 0.333535i
\(214\) 99.0397i 0.462802i
\(215\) −63.9041 148.225i −0.297229 0.689419i
\(216\) −75.1518 + 13.5721i −0.347925 + 0.0628340i
\(217\) 265.298 + 132.996i 1.22257 + 0.612887i
\(218\) 170.424 170.424i 0.781760 0.781760i
\(219\) 285.284 + 142.783i 1.30267 + 0.651976i
\(220\) −19.3825 7.70450i −0.0881022 0.0350204i
\(221\) 83.3678i 0.377230i
\(222\) −69.6389 209.192i −0.313689 0.942305i
\(223\) 221.408 221.408i 0.992862 0.992862i −0.00711229 0.999975i \(-0.502264\pi\)
0.999975 + 0.00711229i \(0.00226393\pi\)
\(224\) 37.5790 12.4826i 0.167764 0.0557260i
\(225\) −223.540 25.5907i −0.993511 0.113737i
\(226\) −278.787 −1.23357
\(227\) −70.0030 + 70.0030i −0.308383 + 0.308383i −0.844282 0.535899i \(-0.819973\pi\)
0.535899 + 0.844282i \(0.319973\pi\)
\(228\) −98.8665 + 32.9122i −0.433625 + 0.144352i
\(229\) 287.075 1.25360 0.626802 0.779178i \(-0.284363\pi\)
0.626802 + 0.779178i \(0.284363\pi\)
\(230\) 28.6651 + 11.3943i 0.124631 + 0.0495405i
\(231\) 6.25690 43.3518i 0.0270861 0.187670i
\(232\) 78.3781 78.3781i 0.337837 0.337837i
\(233\) 199.347 199.347i 0.855568 0.855568i −0.135245 0.990812i \(-0.543182\pi\)
0.990812 + 0.135245i \(0.0431820\pi\)
\(234\) 120.962 90.5725i 0.516931 0.387062i
\(235\) 216.981 93.5467i 0.923323 0.398071i
\(236\) −97.9751 −0.415149
\(237\) 10.2775 3.42134i 0.0433651 0.0144360i
\(238\) 31.1523 62.1418i 0.130892 0.261100i
\(239\) 46.3651 0.193996 0.0969982 0.995285i \(-0.469076\pi\)
0.0969982 + 0.995285i \(0.469076\pi\)
\(240\) 3.41764 59.9026i 0.0142402 0.249594i
\(241\) 65.3496i 0.271160i −0.990766 0.135580i \(-0.956710\pi\)
0.990766 0.135580i \(-0.0432898\pi\)
\(242\) 116.650 + 116.650i 0.482023 + 0.482023i
\(243\) −242.843 + 8.74241i −0.999353 + 0.0359770i
\(244\) 165.881 0.679841
\(245\) 63.7086 + 236.572i 0.260035 + 0.965599i
\(246\) −29.5893 + 59.1204i −0.120282 + 0.240327i
\(247\) 145.797 145.797i 0.590272 0.590272i
\(248\) 84.7907 + 84.7907i 0.341898 + 0.341898i
\(249\) 195.803 391.220i 0.786357 1.57116i
\(250\) 60.5574 166.081i 0.242230 0.664323i
\(251\) 139.437 0.555525 0.277763 0.960650i \(-0.410407\pi\)
0.277763 + 0.960650i \(0.410407\pi\)
\(252\) 124.009 22.3119i 0.492098 0.0885394i
\(253\) 6.43388 + 6.43388i 0.0254304 + 0.0254304i
\(254\) −209.105 −0.823247
\(255\) −70.1151 78.5998i −0.274961 0.308234i
\(256\) 16.0000 0.0625000
\(257\) −323.691 + 323.691i −1.25950 + 1.25950i −0.308168 + 0.951332i \(0.599716\pi\)
−0.951332 + 0.308168i \(0.900284\pi\)
\(258\) 129.953 43.2606i 0.503693 0.167677i
\(259\) 114.673 + 345.224i 0.442753 + 1.33291i
\(260\) 47.0038 + 109.025i 0.180784 + 0.419326i
\(261\) 282.328 211.398i 1.08172 0.809956i
\(262\) −1.42804 1.42804i −0.00545054 0.00545054i
\(263\) 137.531 137.531i 0.522933 0.522933i −0.395523 0.918456i \(-0.629437\pi\)
0.918456 + 0.395523i \(0.129437\pi\)
\(264\) 7.92115 15.8267i 0.0300043 0.0599496i
\(265\) −387.949 + 167.256i −1.46396 + 0.631155i
\(266\) 163.157 54.1958i 0.613371 0.203744i
\(267\) 69.5744 23.1610i 0.260578 0.0867452i
\(268\) −109.647 109.647i −0.409129 0.409129i
\(269\) 391.957i 1.45709i −0.684998 0.728545i \(-0.740197\pi\)
0.684998 0.728545i \(-0.259803\pi\)
\(270\) 37.8693 187.125i 0.140257 0.693057i
\(271\) 327.322i 1.20783i 0.797049 + 0.603914i \(0.206393\pi\)
−0.797049 + 0.603914i \(0.793607\pi\)
\(272\) 19.8609 19.8609i 0.0730180 0.0730180i
\(273\) −199.675 + 149.307i −0.731408 + 0.546911i
\(274\) 304.902i 1.11278i
\(275\) 35.7980 37.9144i 0.130175 0.137870i
\(276\) −11.7147 + 23.4064i −0.0424447 + 0.0848057i
\(277\) 38.0116 38.0116i 0.137226 0.137226i −0.635157 0.772383i \(-0.719065\pi\)
0.772383 + 0.635157i \(0.219065\pi\)
\(278\) −75.0255 75.0255i −0.269876 0.269876i
\(279\) 228.694 + 305.427i 0.819692 + 1.09472i
\(280\) −5.70337 + 98.8305i −0.0203692 + 0.352966i
\(281\) 97.5907i 0.347298i −0.984808 0.173649i \(-0.944444\pi\)
0.984808 0.173649i \(-0.0555558\pi\)
\(282\) 63.3275 + 190.233i 0.224566 + 0.674584i
\(283\) −394.549 + 394.549i −1.39417 + 1.39417i −0.578447 + 0.815720i \(0.696341\pi\)
−0.815720 + 0.578447i \(0.803659\pi\)
\(284\) −149.949 −0.527990
\(285\) 14.8384 260.079i 0.0520645 0.912557i
\(286\) 35.0206i 0.122450i
\(287\) 48.8836 97.5118i 0.170326 0.339762i
\(288\) 50.3943 + 7.23975i 0.174980 + 0.0251380i
\(289\) 239.693i 0.829388i
\(290\) 109.708 + 254.467i 0.378303 + 0.877472i
\(291\) 67.1469 134.162i 0.230745 0.461036i
\(292\) −150.388 150.388i −0.515026 0.515026i
\(293\) 62.2388 + 62.2388i 0.212419 + 0.212419i 0.805294 0.592875i \(-0.202007\pi\)
−0.592875 + 0.805294i \(0.702007\pi\)
\(294\) −204.628 + 36.6792i −0.696014 + 0.124759i
\(295\) 90.4765 227.615i 0.306700 0.771576i
\(296\) 146.986i 0.496573i
\(297\) 32.1101 46.2642i 0.108115 0.155772i
\(298\) −183.297 183.297i −0.615091 0.615091i
\(299\) 51.7926i 0.173220i
\(300\) 136.009 + 63.2577i 0.453363 + 0.210859i
\(301\) −214.458 + 71.2364i −0.712484 + 0.236666i
\(302\) −203.889 203.889i −0.675130 0.675130i
\(303\) −12.3110 36.9817i −0.0406304 0.122052i
\(304\) 69.4671 0.228510
\(305\) −153.185 + 385.374i −0.502247 + 1.26352i
\(306\) 71.5415 53.5680i 0.233796 0.175059i
\(307\) 79.7547 + 79.7547i 0.259787 + 0.259787i 0.824967 0.565180i \(-0.191193\pi\)
−0.565180 + 0.824967i \(0.691193\pi\)
\(308\) −13.0863 + 26.1042i −0.0424879 + 0.0847538i
\(309\) 172.936 + 86.5532i 0.559663 + 0.280107i
\(310\) −275.286 + 118.684i −0.888020 + 0.382851i
\(311\) 358.994 1.15432 0.577160 0.816631i \(-0.304161\pi\)
0.577160 + 0.816631i \(0.304161\pi\)
\(312\) −95.5848 + 31.8197i −0.306362 + 0.101986i
\(313\) 309.220 309.220i 0.987922 0.987922i −0.0120057 0.999928i \(-0.503822\pi\)
0.999928 + 0.0120057i \(0.00382162\pi\)
\(314\) 6.72848i 0.0214283i
\(315\) −62.6828 + 308.700i −0.198993 + 0.980001i
\(316\) −7.22137 −0.0228524
\(317\) 46.3542 + 46.3542i 0.146228 + 0.146228i 0.776431 0.630203i \(-0.217028\pi\)
−0.630203 + 0.776431i \(0.717028\pi\)
\(318\) −113.226 340.125i −0.356056 1.06957i
\(319\) 81.7390i 0.256235i
\(320\) −14.7754 + 37.1710i −0.0461732 + 0.116160i
\(321\) −94.0314 + 187.877i −0.292933 + 0.585288i
\(322\) 19.3535 38.6059i 0.0601041 0.119894i
\(323\) 86.2300 86.2300i 0.266966 0.266966i
\(324\) 155.448 + 45.6053i 0.479779 + 0.140757i
\(325\) −296.692 + 8.51815i −0.912898 + 0.0262097i
\(326\) 210.495i 0.645690i
\(327\) −485.098 + 161.487i −1.48348 + 0.493844i
\(328\) 31.1653 31.1653i 0.0950162 0.0950162i
\(329\) −104.280 313.936i −0.316961 0.954213i
\(330\) 29.4535 + 33.0177i 0.0892531 + 0.100054i
\(331\) 373.528 1.12848 0.564242 0.825609i \(-0.309168\pi\)
0.564242 + 0.825609i \(0.309168\pi\)
\(332\) −206.232 + 206.232i −0.621180 + 0.621180i
\(333\) −66.5087 + 462.952i −0.199726 + 1.39025i
\(334\) 68.6168 0.205439
\(335\) 355.984 153.475i 1.06264 0.458135i
\(336\) −83.1385 11.9993i −0.247436 0.0357121i
\(337\) −163.577 + 163.577i −0.485392 + 0.485392i −0.906848 0.421457i \(-0.861519\pi\)
0.421457 + 0.906848i \(0.361519\pi\)
\(338\) −28.0423 + 28.0423i −0.0829653 + 0.0829653i
\(339\) 528.856 + 264.689i 1.56005 + 0.780793i
\(340\) 27.7998 + 64.4815i 0.0817642 + 0.189651i
\(341\) −88.4266 −0.259315
\(342\) 218.797 + 31.4328i 0.639757 + 0.0919087i
\(343\) 337.659 60.2970i 0.984427 0.175793i
\(344\) −91.3095 −0.265434
\(345\) −43.5593 48.8305i −0.126259 0.141538i
\(346\) 423.018i 1.22260i
\(347\) −231.964 231.964i −0.668483 0.668483i 0.288882 0.957365i \(-0.406716\pi\)
−0.957365 + 0.288882i \(0.906716\pi\)
\(348\) −223.097 + 74.2681i −0.641085 + 0.213414i
\(349\) −143.315 −0.410646 −0.205323 0.978694i \(-0.565825\pi\)
−0.205323 + 0.978694i \(0.565825\pi\)
\(350\) −224.335 104.516i −0.640958 0.298618i
\(351\) −315.456 + 56.9702i −0.898735 + 0.162308i
\(352\) −8.34304 + 8.34304i −0.0237018 + 0.0237018i
\(353\) −192.937 192.937i −0.546564 0.546564i 0.378881 0.925445i \(-0.376309\pi\)
−0.925445 + 0.378881i \(0.876309\pi\)
\(354\) 185.858 + 93.0206i 0.525023 + 0.262770i
\(355\) 138.473 348.360i 0.390064 0.981296i
\(356\) −48.8855 −0.137319
\(357\) −118.095 + 88.3056i −0.330799 + 0.247355i
\(358\) 110.880 + 110.880i 0.309720 + 0.309720i
\(359\) −424.811 −1.18332 −0.591659 0.806189i \(-0.701527\pi\)
−0.591659 + 0.806189i \(0.701527\pi\)
\(360\) −63.3566 + 110.390i −0.175991 + 0.306639i
\(361\) −59.3948 −0.164528
\(362\) −24.2997 + 24.2997i −0.0671264 + 0.0671264i
\(363\) −110.533 332.034i −0.304498 0.914695i
\(364\) 157.741 52.3969i 0.433355 0.143948i
\(365\) 488.257 210.502i 1.33769 0.576717i
\(366\) −314.675 157.493i −0.859769 0.430308i
\(367\) −395.856 395.856i −1.07863 1.07863i −0.996633 0.0819951i \(-0.973871\pi\)
−0.0819951 0.996633i \(-0.526129\pi\)
\(368\) 12.3387 12.3387i 0.0335290 0.0335290i
\(369\) 112.262 84.0579i 0.304232 0.227799i
\(370\) −341.476 135.736i −0.922907 0.366854i
\(371\) 186.447 + 561.299i 0.502552 + 1.51294i
\(372\) −80.3444 241.350i −0.215980 0.648791i
\(373\) 184.517 + 184.517i 0.494683 + 0.494683i 0.909778 0.415095i \(-0.136252\pi\)
−0.415095 + 0.909778i \(0.636252\pi\)
\(374\) 20.7125i 0.0553811i
\(375\) −272.559 + 257.559i −0.726825 + 0.686823i
\(376\) 133.664i 0.355490i
\(377\) 328.999 328.999i 0.872676 0.872676i
\(378\) −256.427 75.4123i −0.678379 0.199503i
\(379\) 127.438i 0.336249i 0.985766 + 0.168124i \(0.0537710\pi\)
−0.985766 + 0.168124i \(0.946229\pi\)
\(380\) −64.1504 + 161.385i −0.168817 + 0.424698i
\(381\) 396.670 + 198.531i 1.04113 + 0.521078i
\(382\) −163.399 + 163.399i −0.427747 + 0.427747i
\(383\) −114.212 114.212i −0.298204 0.298204i 0.542106 0.840310i \(-0.317627\pi\)
−0.840310 + 0.542106i \(0.817627\pi\)
\(384\) −30.3519 15.1909i −0.0790413 0.0395596i
\(385\) −48.5602 54.5082i −0.126130 0.141580i
\(386\) 72.7491i 0.188469i
\(387\) −287.592 41.3161i −0.743133 0.106760i
\(388\) −70.7233 + 70.7233i −0.182277 + 0.182277i
\(389\) −365.324 −0.939136 −0.469568 0.882896i \(-0.655590\pi\)
−0.469568 + 0.882896i \(0.655590\pi\)
\(390\) 14.3459 251.446i 0.0367842 0.644734i
\(391\) 30.6321i 0.0783431i
\(392\) 137.159 + 19.8874i 0.349894 + 0.0507330i
\(393\) 1.35316 + 4.06481i 0.00344315 + 0.0103430i
\(394\) 38.6571i 0.0981145i
\(395\) 6.66867 16.7766i 0.0168827 0.0424724i
\(396\) −30.0527 + 22.5025i −0.0758907 + 0.0568245i
\(397\) −529.456 529.456i −1.33364 1.33364i −0.902087 0.431554i \(-0.857965\pi\)
−0.431554 0.902087i \(-0.642035\pi\)
\(398\) −79.6378 79.6378i −0.200095 0.200095i
\(399\) −360.962 52.0972i −0.904667 0.130569i
\(400\) −72.7109 68.6523i −0.181777 0.171631i
\(401\) 185.749i 0.463216i −0.972809 0.231608i \(-0.925601\pi\)
0.972809 0.231608i \(-0.0743986\pi\)
\(402\) 103.897 + 312.101i 0.258450 + 0.776369i
\(403\) 355.916 + 355.916i 0.883167 + 0.883167i
\(404\) 25.9847i 0.0643184i
\(405\) −249.501 + 319.021i −0.616051 + 0.787706i
\(406\) 368.172 122.296i 0.906827 0.301221i
\(407\) −76.6442 76.6442i −0.188315 0.188315i
\(408\) −56.5325 + 18.8194i −0.138560 + 0.0461260i
\(409\) −615.554 −1.50502 −0.752511 0.658579i \(-0.771158\pi\)
−0.752511 + 0.658579i \(0.771158\pi\)
\(410\) 43.6229 + 101.183i 0.106397 + 0.246788i
\(411\) −289.484 + 578.397i −0.704340 + 1.40729i
\(412\) −91.1632 91.1632i −0.221270 0.221270i
\(413\) −306.550 153.676i −0.742251 0.372098i
\(414\) 44.4455 33.2794i 0.107356 0.0803850i
\(415\) −288.668 669.563i −0.695586 1.61341i
\(416\) 67.1614 0.161446
\(417\) 71.0913 + 213.554i 0.170483 + 0.512121i
\(418\) −36.2230 + 36.2230i −0.0866578 + 0.0866578i
\(419\) 427.623i 1.02058i 0.860002 + 0.510290i \(0.170462\pi\)
−0.860002 + 0.510290i \(0.829538\pi\)
\(420\) 104.652 182.066i 0.249172 0.433490i
\(421\) −294.683 −0.699959 −0.349980 0.936757i \(-0.613811\pi\)
−0.349980 + 0.936757i \(0.613811\pi\)
\(422\) −146.466 146.466i −0.347076 0.347076i
\(423\) 60.4810 420.995i 0.142981 0.995260i
\(424\) 238.984i 0.563641i
\(425\) −175.475 + 5.03796i −0.412882 + 0.0118540i
\(426\) 284.452 + 142.366i 0.667728 + 0.334193i
\(427\) 519.018 + 260.189i 1.21550 + 0.609342i
\(428\) 99.0397 99.0397i 0.231401 0.231401i
\(429\) 33.2497 66.4339i 0.0775051 0.154857i
\(430\) 84.3210 212.129i 0.196095 0.493324i
\(431\) 735.135i 1.70565i 0.522197 + 0.852825i \(0.325113\pi\)
−0.522197 + 0.852825i \(0.674887\pi\)
\(432\) −88.7240 61.5797i −0.205380 0.142546i
\(433\) 6.15401 6.15401i 0.0142125 0.0142125i −0.699965 0.714177i \(-0.746801\pi\)
0.714177 + 0.699965i \(0.246801\pi\)
\(434\) 132.301 + 398.294i 0.304842 + 0.917729i
\(435\) 33.4836 586.882i 0.0769738 1.34915i
\(436\) 340.847 0.781760
\(437\) 53.5708 53.5708i 0.122588 0.122588i
\(438\) 142.501 + 428.067i 0.325346 + 0.977322i
\(439\) 701.728 1.59847 0.799235 0.601019i \(-0.205239\pi\)
0.799235 + 0.601019i \(0.205239\pi\)
\(440\) −11.6780 27.0870i −0.0265409 0.0615613i
\(441\) 423.002 + 124.700i 0.959189 + 0.282767i
\(442\) 83.3678 83.3678i 0.188615 0.188615i
\(443\) 176.482 176.482i 0.398379 0.398379i −0.479282 0.877661i \(-0.659103\pi\)
0.877661 + 0.479282i \(0.159103\pi\)
\(444\) 139.553 278.831i 0.314308 0.627997i
\(445\) 45.1440 113.570i 0.101447 0.255214i
\(446\) 442.817 0.992862
\(447\) 173.685 + 521.741i 0.388557 + 1.16721i
\(448\) 50.0617 + 25.0964i 0.111745 + 0.0560188i
\(449\) 521.716 1.16195 0.580976 0.813921i \(-0.302671\pi\)
0.580976 + 0.813921i \(0.302671\pi\)
\(450\) −197.949 249.131i −0.439887 0.553624i
\(451\) 32.5017i 0.0720659i
\(452\) −278.787 278.787i −0.616785 0.616785i
\(453\) 193.198 + 580.355i 0.426485 + 1.28114i
\(454\) −140.006 −0.308383
\(455\) −23.9404 + 414.849i −0.0526162 + 0.911757i
\(456\) −131.779 65.9543i −0.288988 0.144637i
\(457\) 34.8065 34.8065i 0.0761631 0.0761631i −0.667999 0.744162i \(-0.732849\pi\)
0.744162 + 0.667999i \(0.232849\pi\)
\(458\) 287.075 + 287.075i 0.626802 + 0.626802i
\(459\) −186.573 + 33.6944i −0.406477 + 0.0734082i
\(460\) 17.2708 + 40.0594i 0.0375451 + 0.0870857i
\(461\) −747.746 −1.62201 −0.811005 0.585040i \(-0.801079\pi\)
−0.811005 + 0.585040i \(0.801079\pi\)
\(462\) 49.6087 37.0949i 0.107378 0.0802919i
\(463\) −629.053 629.053i −1.35865 1.35865i −0.875590 0.483055i \(-0.839527\pi\)
−0.483055 0.875590i \(-0.660473\pi\)
\(464\) 156.756 0.337837
\(465\) 634.898 + 36.2231i 1.36537 + 0.0778991i
\(466\) 398.695 0.855568
\(467\) 72.4294 72.4294i 0.155095 0.155095i −0.625294 0.780389i \(-0.715021\pi\)
0.780389 + 0.625294i \(0.215021\pi\)
\(468\) 211.534 + 30.3894i 0.451997 + 0.0649347i
\(469\) −171.085 515.051i −0.364786 1.09819i
\(470\) 310.528 + 123.434i 0.660697 + 0.262626i
\(471\) 6.38823 12.7639i 0.0135631 0.0270995i
\(472\) −97.9751 97.9751i −0.207574 0.207574i
\(473\) 47.6124 47.6124i 0.100660 0.100660i
\(474\) 13.6989 + 6.85619i 0.0289006 + 0.0144645i
\(475\) −315.688 298.067i −0.664607 0.627510i
\(476\) 93.2942 30.9895i 0.195996 0.0651040i
\(477\) −108.136 + 752.714i −0.226701 + 1.57802i
\(478\) 46.3651 + 46.3651i 0.0969982 + 0.0969982i
\(479\) 49.3199i 0.102964i −0.998674 0.0514822i \(-0.983605\pi\)
0.998674 0.0514822i \(-0.0163945\pi\)
\(480\) 63.3202 56.4849i 0.131917 0.117677i
\(481\) 616.985i 1.28271i
\(482\) 65.3496 65.3496i 0.135580 0.135580i
\(483\) −73.3672 + 54.8603i −0.151899 + 0.113582i
\(484\) 233.299i 0.482023i
\(485\) −98.9933 229.614i −0.204110 0.473431i
\(486\) −251.585 234.100i −0.517665 0.481688i
\(487\) 83.8584 83.8584i 0.172194 0.172194i −0.615749 0.787943i \(-0.711146\pi\)
0.787943 + 0.615749i \(0.211146\pi\)
\(488\) 165.881 + 165.881i 0.339920 + 0.339920i
\(489\) 199.850 399.307i 0.408692 0.816579i
\(490\) −172.863 + 300.280i −0.352782 + 0.612817i
\(491\) 655.752i 1.33554i −0.744366 0.667771i \(-0.767248\pi\)
0.744366 0.667771i \(-0.232752\pi\)
\(492\) −88.7097 + 29.5310i −0.180304 + 0.0600225i
\(493\) 194.583 194.583i 0.394691 0.394691i
\(494\) 291.594 0.590272
\(495\) −24.5250 90.5984i −0.0495455 0.183027i
\(496\) 169.581i 0.341898i
\(497\) −469.169 235.199i −0.944002 0.473237i
\(498\) 587.023 195.417i 1.17876 0.392404i
\(499\) 433.348i 0.868433i −0.900809 0.434216i \(-0.857025\pi\)
0.900809 0.434216i \(-0.142975\pi\)
\(500\) 226.638 105.523i 0.453276 0.211047i
\(501\) −130.165 65.1469i −0.259811 0.130034i
\(502\) 139.437 + 139.437i 0.277763 + 0.277763i
\(503\) 147.463 + 147.463i 0.293167 + 0.293167i 0.838330 0.545163i \(-0.183532\pi\)
−0.545163 + 0.838330i \(0.683532\pi\)
\(504\) 146.321 + 101.697i 0.290319 + 0.201779i
\(505\) −60.3673 23.9959i −0.119539 0.0475166i
\(506\) 12.8678i 0.0254304i
\(507\) 79.8201 26.5717i 0.157436 0.0524098i
\(508\) −209.105 209.105i −0.411623 0.411623i
\(509\) 554.834i 1.09005i −0.838421 0.545024i \(-0.816521\pi\)
0.838421 0.545024i \(-0.183479\pi\)
\(510\) 8.48468 148.715i 0.0166366 0.291598i
\(511\) −234.654 706.428i −0.459206 1.38244i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −385.213 267.360i −0.750902 0.521170i
\(514\) −647.383 −1.25950
\(515\) 295.975 127.604i 0.574709 0.247774i
\(516\) 173.213 + 86.6921i 0.335685 + 0.168008i
\(517\) 69.6979 + 69.6979i 0.134812 + 0.134812i
\(518\) −230.551 + 459.897i −0.445079 + 0.887831i
\(519\) 401.627 802.463i 0.773848 1.54617i
\(520\) −62.0211 + 156.029i −0.119271 + 0.300055i
\(521\) −3.73694 −0.00717263 −0.00358632 0.999994i \(-0.501142\pi\)
−0.00358632 + 0.999994i \(0.501142\pi\)
\(522\) 493.727 + 70.9297i 0.945836 + 0.135881i
\(523\) −638.273 + 638.273i −1.22041 + 1.22041i −0.252921 + 0.967487i \(0.581391\pi\)
−0.967487 + 0.252921i \(0.918609\pi\)
\(524\) 2.85608i 0.00545054i
\(525\) 326.331 + 411.258i 0.621583 + 0.783348i
\(526\) 275.063 0.522933
\(527\) 210.502 + 210.502i 0.399435 + 0.399435i
\(528\) 23.7478 7.90554i 0.0449770 0.0149726i
\(529\) 509.970i 0.964026i
\(530\) −555.205 220.693i −1.04756 0.416402i
\(531\) −264.255 352.919i −0.497655 0.664631i
\(532\) 217.353 + 108.961i 0.408557 + 0.204814i
\(533\) 130.819 130.819i 0.245439 0.245439i
\(534\) 92.7354 + 46.4134i 0.173662 + 0.0869165i
\(535\) 138.628 + 321.548i 0.259119 + 0.601024i
\(536\) 219.293i 0.409129i
\(537\) −105.065 315.611i −0.195652 0.587730i
\(538\) 391.957 391.957i 0.728545 0.728545i
\(539\) −81.8901 + 61.1499i −0.151930 + 0.113451i
\(540\) 224.995 149.256i 0.416657 0.276400i
\(541\) −967.493 −1.78834 −0.894171 0.447725i \(-0.852234\pi\)
−0.894171 + 0.447725i \(0.852234\pi\)
\(542\) −327.322 + 327.322i −0.603914 + 0.603914i
\(543\) 69.1674 23.0255i 0.127380 0.0424042i
\(544\) 39.7218 0.0730180
\(545\) −314.760 + 791.854i −0.577542 + 1.45294i
\(546\) −348.981 50.3679i −0.639160 0.0922490i
\(547\) 400.474 400.474i 0.732129 0.732129i −0.238913 0.971041i \(-0.576791\pi\)
0.971041 + 0.238913i \(0.0767909\pi\)
\(548\) 304.902 304.902i 0.556391 0.556391i
\(549\) 447.408 + 597.525i 0.814951 + 1.08839i
\(550\) 73.7124 2.11631i 0.134023 0.00384784i
\(551\) 680.588 1.23519
\(552\) −35.1211 + 11.6916i −0.0636252 + 0.0211805i
\(553\) −22.5946 11.3269i −0.0408582 0.0204826i
\(554\) 76.0232 0.137226
\(555\) 518.905 + 581.698i 0.934963 + 1.04810i
\(556\) 150.051i 0.269876i
\(557\) 545.370 + 545.370i 0.979121 + 0.979121i 0.999786 0.0206659i \(-0.00657863\pi\)
−0.0206659 + 0.999786i \(0.506579\pi\)
\(558\) −76.7329 + 534.121i −0.137514 + 0.957207i
\(559\) −383.279 −0.685652
\(560\) −104.534 + 93.1272i −0.186668 + 0.166298i
\(561\) 19.6651 39.2915i 0.0350537 0.0700383i
\(562\) 97.5907 97.5907i 0.173649 0.173649i
\(563\) −575.914 575.914i −1.02294 1.02294i −0.999731 0.0232074i \(-0.992612\pi\)
−0.0232074 0.999731i \(-0.507388\pi\)
\(564\) −126.905 + 253.560i −0.225009 + 0.449575i
\(565\) 905.124 390.225i 1.60199 0.690664i
\(566\) −789.098 −1.39417
\(567\) 414.842 + 386.517i 0.731644 + 0.681687i
\(568\) −149.949 149.949i −0.263995 0.263995i
\(569\) 524.362 0.921549 0.460775 0.887517i \(-0.347572\pi\)
0.460775 + 0.887517i \(0.347572\pi\)
\(570\) 274.917 245.240i 0.482311 0.430246i
\(571\) 607.181 1.06337 0.531683 0.846944i \(-0.321560\pi\)
0.531683 + 0.846944i \(0.321560\pi\)
\(572\) −35.0206 + 35.0206i −0.0612249 + 0.0612249i
\(573\) 465.104 154.831i 0.811700 0.270211i
\(574\) 146.395 48.6281i 0.255044 0.0847180i
\(575\) −109.015 + 3.12986i −0.189591 + 0.00544323i
\(576\) 43.1546 + 57.6341i 0.0749211 + 0.100059i
\(577\) −274.550 274.550i −0.475823 0.475823i 0.427970 0.903793i \(-0.359229\pi\)
−0.903793 + 0.427970i \(0.859229\pi\)
\(578\) −239.693 + 239.693i −0.414694 + 0.414694i
\(579\) −69.0702 + 138.004i −0.119292 + 0.238350i
\(580\) −144.759 + 364.175i −0.249584 + 0.627887i
\(581\) −968.749 + 321.789i −1.66738 + 0.553854i
\(582\) 201.308 67.0146i 0.345891 0.115145i
\(583\) −124.616 124.616i −0.213749 0.213749i
\(584\) 300.775i 0.515026i
\(585\) −265.945 + 463.371i −0.454607 + 0.792087i
\(586\) 124.478i 0.212419i
\(587\) 504.649 504.649i 0.859709 0.859709i −0.131595 0.991304i \(-0.542010\pi\)
0.991304 + 0.131595i \(0.0420098\pi\)
\(588\) −241.307 167.949i −0.410386 0.285627i
\(589\) 736.271i 1.25004i
\(590\) 318.091 137.138i 0.539138 0.232438i
\(591\) 36.7023 73.3322i 0.0621020 0.124082i
\(592\) −146.986 + 146.986i −0.248287 + 0.248287i
\(593\) 615.151 + 615.151i 1.03735 + 1.03735i 0.999275 + 0.0380802i \(0.0121242\pi\)
0.0380802 + 0.999275i \(0.487876\pi\)
\(594\) 78.3743 14.1541i 0.131943 0.0238285i
\(595\) −14.1592 + 245.358i −0.0237971 + 0.412366i
\(596\) 366.594i 0.615091i
\(597\) 75.4617 + 226.683i 0.126401 + 0.379703i
\(598\) 51.7926 51.7926i 0.0866098 0.0866098i
\(599\) −103.401 −0.172623 −0.0863115 0.996268i \(-0.527508\pi\)
−0.0863115 + 0.996268i \(0.527508\pi\)
\(600\) 72.7513 + 199.267i 0.121252 + 0.332111i
\(601\) 994.271i 1.65436i −0.561936 0.827180i \(-0.689943\pi\)
0.561936 0.827180i \(-0.310057\pi\)
\(602\) −285.694 143.221i −0.474575 0.237909i
\(603\) 99.2266 690.695i 0.164555 1.14543i
\(604\) 407.779i 0.675130i
\(605\) −541.999 215.443i −0.895865 0.356105i
\(606\) 24.6706 49.2927i 0.0407106 0.0813411i
\(607\) −54.5368 54.5368i −0.0898464 0.0898464i 0.660755 0.750602i \(-0.270236\pi\)
−0.750602 + 0.660755i \(0.770236\pi\)
\(608\) 69.4671 + 69.4671i 0.114255 + 0.114255i
\(609\) −814.531 117.560i −1.33749 0.193038i
\(610\) −538.559 + 232.188i −0.882883 + 0.380636i
\(611\) 561.067i 0.918277i
\(612\) 125.109 + 17.9735i 0.204427 + 0.0293684i
\(613\) 23.2311 + 23.2311i 0.0378975 + 0.0378975i 0.725802 0.687904i \(-0.241469\pi\)
−0.687904 + 0.725802i \(0.741469\pi\)
\(614\) 159.509i 0.259787i
\(615\) 13.3140 233.360i 0.0216488 0.379448i
\(616\) −39.1904 + 13.0179i −0.0636208 + 0.0211329i
\(617\) 37.9474 + 37.9474i 0.0615032 + 0.0615032i 0.737189 0.675686i \(-0.236153\pi\)
−0.675686 + 0.737189i \(0.736153\pi\)
\(618\) 86.3827 + 259.489i 0.139778 + 0.419885i
\(619\) 182.389 0.294651 0.147326 0.989088i \(-0.452933\pi\)
0.147326 + 0.989088i \(0.452933\pi\)
\(620\) −393.970 156.602i −0.635436 0.252585i
\(621\) −115.909 + 20.9328i −0.186649 + 0.0337082i
\(622\) 358.994 + 358.994i 0.577160 + 0.577160i
\(623\) −152.955 76.6781i −0.245514 0.123079i
\(624\) −127.405 63.7651i −0.204174 0.102188i
\(625\) 35.8585 + 623.970i 0.0573736 + 0.998353i
\(626\) 618.439 0.987922
\(627\) 103.106 34.3235i 0.164443 0.0547423i
\(628\) −6.72848 + 6.72848i −0.0107141 + 0.0107141i
\(629\) 364.908i 0.580140i
\(630\) −371.383 + 246.017i −0.589497 + 0.390504i
\(631\) 165.153 0.261732 0.130866 0.991400i \(-0.458224\pi\)
0.130866 + 0.991400i \(0.458224\pi\)
\(632\) −7.22137 7.22137i −0.0114262 0.0114262i
\(633\) 138.785 + 416.904i 0.219250 + 0.658617i
\(634\) 92.7084i 0.146228i
\(635\) 678.891 292.689i 1.06912 0.460928i
\(636\) 226.899 453.351i 0.356759 0.712815i
\(637\) 575.735 + 83.4789i 0.903823 + 0.131050i
\(638\) −81.7390 + 81.7390i −0.128118 + 0.128118i
\(639\) −404.437 540.136i −0.632921 0.845283i
\(640\) −51.9465 + 22.3956i −0.0811664 + 0.0349932i
\(641\) 168.644i 0.263095i 0.991310 + 0.131548i \(0.0419946\pi\)
−0.991310 + 0.131548i \(0.958005\pi\)
\(642\) −281.909 + 93.8461i −0.439110 + 0.146178i
\(643\) 25.2955 25.2955i 0.0393398 0.0393398i −0.687163 0.726503i \(-0.741144\pi\)
0.726503 + 0.687163i \(0.241144\pi\)
\(644\) 57.9594 19.2524i 0.0899991 0.0298950i
\(645\) −361.359 + 322.351i −0.560246 + 0.499768i
\(646\) 172.460 0.266966
\(647\) −11.1919 + 11.1919i −0.0172981 + 0.0172981i −0.715703 0.698405i \(-0.753894\pi\)
0.698405 + 0.715703i \(0.253894\pi\)
\(648\) 109.843 + 201.054i 0.169511 + 0.310268i
\(649\) 102.176 0.157437
\(650\) −305.210 288.174i −0.469554 0.443344i
\(651\) 127.178 881.172i 0.195358 1.35357i
\(652\) −210.495 + 210.495i −0.322845 + 0.322845i
\(653\) −319.932 + 319.932i −0.489941 + 0.489941i −0.908288 0.418346i \(-0.862610\pi\)
0.418346 + 0.908288i \(0.362610\pi\)
\(654\) −646.585 323.611i −0.988662 0.494818i
\(655\) 6.63522 + 2.63749i 0.0101301 + 0.00402670i
\(656\) 62.3307 0.0950162
\(657\) 136.096 947.335i 0.207148 1.44191i
\(658\) 209.656 418.216i 0.318626 0.635587i
\(659\) −692.273 −1.05049 −0.525245 0.850951i \(-0.676026\pi\)
−0.525245 + 0.850951i \(0.676026\pi\)
\(660\) −3.56419 + 62.4712i −0.00540029 + 0.0946534i
\(661\) 586.898i 0.887894i 0.896053 + 0.443947i \(0.146422\pi\)
−0.896053 + 0.443947i \(0.853578\pi\)
\(662\) 373.528 + 373.528i 0.564242 + 0.564242i
\(663\) −237.300 + 78.9961i −0.357919 + 0.119149i
\(664\) −412.464 −0.621180
\(665\) −453.854 + 404.330i −0.682488 + 0.608015i
\(666\) −529.461 + 396.444i −0.794987 + 0.595261i
\(667\) 120.885 120.885i 0.181237 0.181237i
\(668\) 68.6168 + 68.6168i 0.102720 + 0.102720i
\(669\) −840.020 420.424i −1.25563 0.628437i
\(670\) 509.460 + 202.509i 0.760387 + 0.302253i
\(671\) −172.994 −0.257815
\(672\) −71.1393 95.1378i −0.105862 0.141574i
\(673\) 419.099 + 419.099i 0.622732 + 0.622732i 0.946229 0.323497i \(-0.104859\pi\)
−0.323497 + 0.946229i \(0.604859\pi\)
\(674\) −327.154 −0.485392
\(675\) 138.976 + 660.538i 0.205890 + 0.978575i
\(676\) −56.0845 −0.0829653
\(677\) 459.724 459.724i 0.679061 0.679061i −0.280727 0.959788i \(-0.590575\pi\)
0.959788 + 0.280727i \(0.0905755\pi\)
\(678\) 264.167 + 793.545i 0.389627 + 1.17042i
\(679\) −332.214 + 110.352i −0.489270 + 0.162521i
\(680\) −36.6816 + 92.2813i −0.0539436 + 0.135708i
\(681\) 265.590 + 132.926i 0.390000 + 0.195192i
\(682\) −88.4266 88.4266i −0.129658 0.129658i
\(683\) 66.6626 66.6626i 0.0976027 0.0976027i −0.656619 0.754222i \(-0.728014\pi\)
0.754222 + 0.656619i \(0.228014\pi\)
\(684\) 187.364 + 250.230i 0.273924 + 0.365833i
\(685\) 426.780 + 989.913i 0.623036 + 1.44513i
\(686\) 397.956 + 277.361i 0.580110 + 0.404317i
\(687\) −272.021 817.138i −0.395956 1.18943i
\(688\) −91.3095 91.3095i −0.132717 0.132717i
\(689\) 1003.16i 1.45596i
\(690\) 5.27115 92.3898i 0.00763935 0.133898i
\(691\) 11.4526i 0.0165739i 0.999966 + 0.00828695i \(0.00263785\pi\)
−0.999966 + 0.00828695i \(0.997362\pi\)
\(692\) −423.018 + 423.018i −0.611298 + 0.611298i
\(693\) −129.326 + 23.2687i −0.186618 + 0.0335767i
\(694\) 463.927i 0.668483i
\(695\) 348.597 + 138.567i 0.501579 + 0.199377i
\(696\) −297.365 148.829i −0.427249 0.213835i
\(697\) 77.3714 77.3714i 0.111006 0.111006i
\(698\) −143.315 143.315i −0.205323 0.205323i
\(699\) −756.321 378.533i −1.08200 0.541535i
\(700\) −119.819 328.852i −0.171170 0.469788i
\(701\) 635.231i 0.906178i −0.891465 0.453089i \(-0.850322\pi\)
0.891465 0.453089i \(-0.149678\pi\)
\(702\) −372.426 258.486i −0.530522 0.368214i
\(703\) −638.167 + 638.167i −0.907777 + 0.907777i
\(704\) −16.6861 −0.0237018
\(705\) −471.876 528.978i −0.669328 0.750324i
\(706\) 385.875i 0.546564i
\(707\) −40.7576 + 81.3022i −0.0576486 + 0.114996i
\(708\) 92.8374 + 278.879i 0.131126 + 0.393896i
\(709\) 68.9098i 0.0971930i −0.998818 0.0485965i \(-0.984525\pi\)
0.998818 0.0485965i \(-0.0154748\pi\)
\(710\) 486.833 209.888i 0.685680 0.295616i
\(711\) −19.4772 26.0123i −0.0273941 0.0365855i
\(712\) −48.8855 48.8855i −0.0686594 0.0686594i
\(713\) 130.776 + 130.776i 0.183416 + 0.183416i
\(714\) −206.401 29.7895i −0.289077 0.0417220i
\(715\) −49.0193 113.700i −0.0685584 0.159021i
\(716\) 221.760i 0.309720i
\(717\) −43.9338 131.975i −0.0612745 0.184065i
\(718\) −424.811 424.811i −0.591659 0.591659i
\(719\) 457.334i 0.636069i −0.948079 0.318034i \(-0.896977\pi\)
0.948079 0.318034i \(-0.103023\pi\)
\(720\) −173.747 + 47.0333i −0.241315 + 0.0653240i
\(721\) −142.245 428.228i −0.197288 0.593936i
\(722\) −59.3948 59.3948i −0.0822642 0.0822642i
\(723\) −186.013 + 61.9228i −0.257279 + 0.0856470i
\(724\) −48.5995 −0.0671264
\(725\) −712.368 672.605i −0.982576 0.927730i
\(726\) 221.502 442.567i 0.305099 0.609596i
\(727\) 990.753 + 990.753i 1.36280 + 1.36280i 0.870333 + 0.492464i \(0.163904\pi\)
0.492464 + 0.870333i \(0.336096\pi\)
\(728\) 210.138 + 105.344i 0.288651 + 0.144704i
\(729\) 254.993 + 682.949i 0.349784 + 0.936830i
\(730\) 698.758 + 277.755i 0.957203 + 0.380486i
\(731\) −226.686 −0.310104
\(732\) −157.183 472.168i −0.214730 0.645038i
\(733\) −443.025 + 443.025i −0.604400 + 0.604400i −0.941477 0.337077i \(-0.890562\pi\)
0.337077 + 0.941477i \(0.390562\pi\)
\(734\) 791.713i 1.07863i
\(735\) 613.016 405.508i 0.834035 0.551711i
\(736\) 24.6773 0.0335290
\(737\) 114.348 + 114.348i 0.155154 + 0.155154i
\(738\) 196.319 + 28.2036i 0.266015 + 0.0382163i
\(739\) 1424.55i 1.92768i 0.266488 + 0.963838i \(0.414137\pi\)
−0.266488 + 0.963838i \(0.585863\pi\)
\(740\) −205.740 477.212i −0.278027 0.644880i
\(741\) −553.152 276.849i −0.746494 0.373615i
\(742\) −374.852 + 747.746i −0.505192 + 1.00774i
\(743\) −823.562 + 823.562i −1.10843 + 1.10843i −0.115071 + 0.993357i \(0.536709\pi\)
−0.993357 + 0.115071i \(0.963291\pi\)
\(744\) 161.006 321.695i 0.216406 0.432385i
\(745\) 851.668 + 338.536i 1.14318 + 0.454411i
\(746\) 369.034i 0.494683i
\(747\) −1299.11 186.633i −1.73911 0.249844i
\(748\) −20.7125 + 20.7125i −0.0276905 + 0.0276905i
\(749\) 465.227 154.534i 0.621131 0.206321i
\(750\) −530.118 15.0005i −0.706824 0.0200007i
\(751\) −436.270 −0.580919 −0.290459 0.956887i \(-0.593808\pi\)
−0.290459 + 0.956887i \(0.593808\pi\)
\(752\) 133.664 133.664i 0.177745 0.177745i
\(753\) −132.125 396.896i −0.175465 0.527087i
\(754\) 657.998 0.872676
\(755\) 947.348 + 376.569i 1.25476 + 0.498767i
\(756\) −181.015 331.840i −0.239438 0.438941i
\(757\) 39.6428 39.6428i 0.0523684 0.0523684i −0.680438 0.732806i \(-0.738210\pi\)
0.732806 + 0.680438i \(0.238210\pi\)
\(758\) −127.438 + 127.438i −0.168124 + 0.168124i
\(759\) 12.2171 24.4100i 0.0160962 0.0321608i
\(760\) −225.536 + 97.2350i −0.296758 + 0.127941i
\(761\) −1032.38 −1.35661 −0.678307 0.734778i \(-0.737286\pi\)
−0.678307 + 0.734778i \(0.737286\pi\)
\(762\) 198.139 + 595.201i 0.260026 + 0.781103i
\(763\) 1066.46 + 534.628i 1.39772 + 0.700692i
\(764\) −326.799 −0.427747
\(765\) −157.290 + 274.055i −0.205608 + 0.358242i
\(766\) 228.424i 0.298204i
\(767\) −411.259 411.259i −0.536191 0.536191i
\(768\)