Properties

Label 210.3.k.b.83.10
Level 210
Weight 3
Character 210.83
Analytic conductor 5.722
Analytic rank 0
Dimension 32
CM no
Inner twists 4

Related objects

Downloads

Learn more about

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 83.10
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.10

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(0.947561 + 2.84642i) q^{3} +2.00000i q^{4} +(4.64638 + 1.84693i) q^{5} +(-1.89886 + 3.79398i) q^{6} +(-6.25771 + 3.13705i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-7.20426 + 5.39432i) q^{9} +O(q^{10})\) \(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} +(-6.25771 + 3.13705i) 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} +(-14.8589 - 14.8395i) 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} +(-6.27410 - 12.5154i) 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} +(-34.8696 + 3.01840i) 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} +(-0.0193943 - 29.6985i) 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} +(28.1599 - 56.3562i) 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} +(-37.8880 - 31.8512i) 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} +(6.54314 + 13.0521i) 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} +(29.6791 - 29.7179i) 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} +(68.5793 - 9.94368i) 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
\(7\) −6.25771 + 3.13705i −0.893958 + 0.448150i
\(8\) −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 −0.306189 0.951971i \(-0.599054\pi\)
0.951971 + 0.306189i \(0.0990538\pi\)
\(14\) −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 −0.545826 0.837898i \(-0.683784\pi\)
0.837898 + 0.545826i \(0.183784\pi\)
\(18\) −12.5986 1.80994i −0.699921 0.100552i
\(19\) 17.3668 0.914041 0.457021 0.889456i \(-0.348917\pi\)
0.457021 + 0.889456i \(0.348917\pi\)
\(20\) −3.69386 + 9.29276i −0.184693 + 0.464638i
\(21\) −14.8589 14.8395i −0.707568 0.706645i
\(22\) 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
\(28\) −6.27410 12.5154i −0.224075 0.446979i
\(29\) −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 \(0.239672\pi\)
−0.729673 + 0.683796i \(0.760328\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 5.93696 1.97638i 0.179908 0.0598905i
\(34\) 9.93045 0.292072
\(35\) −34.8696 + 3.01840i −0.996274 + 0.0862399i
\(36\) −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 \(-0.439141\pi\)
0.190032 + 0.981778i \(0.439141\pi\)
\(42\) −0.0193943 29.6985i −0.000461768 0.707107i
\(43\) 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 −0.255760 0.966740i \(-0.582326\pi\)
0.966740 + 0.255760i \(0.0823257\pi\)
\(48\) −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 \(-0.863730\pi\)
0.909754 0.415149i \(-0.136270\pi\)
\(60\) −29.9513 1.70882i −0.499188 0.0284804i
\(61\) 82.9406i 1.35968i 0.733360 + 0.679841i \(0.237951\pi\)
−0.733360 + 0.679841i \(0.762049\pi\)
\(62\) −42.3954 + 42.3954i −0.683796 + 0.683796i
\(63\) 28.1599 56.3562i 0.446982 0.894543i
\(64\) 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
\(70\) −37.8880 31.8512i −0.541257 0.455017i
\(71\) 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 \(-0.490284\pi\)
0.999534 0.0305180i \(-0.00971569\pi\)
\(74\) 73.4928 0.993146
\(75\) −31.6289 + 68.0045i −0.421718 + 0.906727i
\(76\) 34.7336i 0.457021i
\(77\) 6.54314 + 13.0521i 0.0849758 + 0.169508i
\(78\) 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 \(-0.908557\pi\)
−0.283341 0.959019i \(-0.591443\pi\)
\(84\) 29.6791 29.7179i 0.353322 0.353784i
\(85\) 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 \(-0.956152\pi\)
0.990527 0.137319i \(-0.0438485\pi\)
\(90\) −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 0.500933 0.865486i \(-0.332990\pi\)
−0.865486 + 0.500933i \(0.832990\pi\)
\(98\) 68.5793 9.94368i 0.699789 0.101466i
\(99\) 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 \(-0.520487\pi\)
−0.0643184 + 0.997929i \(0.520487\pi\)
\(102\) 9.40970 + 28.2663i 0.0922520 + 0.277120i
\(103\) 45.5816 45.5816i 0.442540 0.442540i −0.450325 0.892865i \(-0.648692\pi\)
0.892865 + 0.450325i \(0.148692\pi\)
\(104\) 33.5807i 0.322891i
\(105\) −41.6327 96.3936i −0.396502 0.918034i
\(106\) 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
\(112\) 25.0308 12.5482i 0.223490 0.112038i
\(113\) −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
\(126\) 84.5161 28.1963i 0.670763 0.223780i
\(127\) −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 \(-0.498265\pi\)
0.00545054 + 0.999985i \(0.498265\pi\)
\(132\) 3.95277 + 11.8739i 0.0299452 + 0.0899539i
\(133\) −108.676 + 54.4805i −0.817115 + 0.409628i
\(134\) −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 \(-0.413017\pi\)
0.269876 + 0.962895i \(0.413017\pi\)
\(140\) −6.03679 69.7392i −0.0431200 0.498137i
\(141\) 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
\(147\) 139.535 + 46.2483i 0.949220 + 0.314614i
\(148\) 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 0.696311 0.717740i \(-0.254823\pi\)
−0.717740 + 0.696311i \(0.754823\pi\)
\(158\) −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 −0.802326 0.596886i \(-0.796404\pi\)
0.596886 + 0.802326i \(0.296404\pi\)
\(168\) 59.3970 0.0387885i 0.353553 0.000230884i
\(169\) 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 \(-0.917631\pi\)
−0.255891 0.966706i \(-0.582369\pi\)
\(174\) 74.4147 148.683i 0.427671 0.854499i
\(175\) −167.592 50.3770i −0.957670 0.287869i
\(176\) 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 \(-0.978617\pi\)
0.997744 0.0671264i \(-0.0213831\pi\)
\(182\) −105.069 + 52.6722i −0.577302 + 0.289407i
\(183\) −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
\(189\) 187.097 + 26.7540i 0.989930 + 0.141556i
\(190\) 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 \(-0.435875\pi\)
0.200095 + 0.979776i \(0.435875\pi\)
\(200\) −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
\(203\) 245.234 122.938i 1.20805 0.605607i
\(204\) −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
\(210\) 54.7608 138.026i 0.260766 0.657268i
\(211\) −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
\(217\) −132.996 265.298i −0.612887 1.22257i
\(218\) 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 −0.999975 0.00711229i \(-0.997736\pi\)
0.00711229 + 0.999975i \(0.497736\pi\)
\(224\) 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 −0.535899 0.844282i \(-0.680027\pi\)
0.844282 + 0.535899i \(0.180027\pi\)
\(228\) −98.8665 + 32.9122i −0.433625 + 0.144352i
\(229\) −287.075 −1.25360 −0.626802 0.779178i \(-0.715637\pi\)
−0.626802 + 0.779178i \(0.715637\pi\)
\(230\) −28.6651 11.3943i −0.124631 0.0495405i
\(231\) −30.9517 + 30.9922i −0.133990 + 0.134165i
\(232\) 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
\(238\) −62.1418 + 31.1523i −0.261100 + 0.130892i
\(239\) 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 \(0.0432898\pi\)
−0.990766 + 0.135580i \(0.956710\pi\)
\(242\) 116.650 + 116.650i 0.482023 + 0.482023i
\(243\) 242.843 8.74241i 0.999353 0.0359770i
\(244\) −165.881 −0.679841
\(245\) 208.735 128.276i 0.851979 0.523575i
\(246\) −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 \(-0.589593\pi\)
−0.277763 + 0.960650i \(0.589593\pi\)
\(252\) 112.712 + 56.3198i 0.447271 + 0.223491i
\(253\) 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 \(-0.400284\pi\)
0.951332 0.308168i \(-0.0997158\pi\)
\(258\) −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 \(0.259803\pi\)
−0.684998 + 0.728545i \(0.740197\pi\)
\(270\) 37.8693 187.125i 0.140257 0.693057i
\(271\) 327.322i 1.20783i −0.797049 0.603914i \(-0.793607\pi\)
0.797049 0.603914i \(-0.206393\pi\)
\(272\) −19.8609 + 19.8609i −0.0730180 + 0.0730180i
\(273\) −249.324 + 0.162818i −0.913274 + 0.000596403i
\(274\) 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
\(280\) 63.7024 75.7760i 0.227509 0.270629i
\(281\) 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 \(-0.303659\pi\)
0.815720 0.578447i \(-0.196341\pi\)
\(284\) −149.949 −0.527990
\(285\) −14.8384 + 260.079i −0.0520645 + 0.912557i
\(286\) 35.0206i 0.122450i
\(287\) −97.5118 + 48.8836i −0.339762 + 0.170326i
\(288\) 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 0.592875 0.805294i \(-0.297993\pi\)
−0.805294 + 0.592875i \(0.797993\pi\)
\(294\) 93.2870 + 185.784i 0.317303 + 0.631917i
\(295\) 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 0.565180 0.824967i \(-0.308807\pi\)
−0.824967 + 0.565180i \(0.808807\pi\)
\(308\) −26.1042 + 13.0863i −0.0847538 + 0.0424879i
\(309\) 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 \(-0.695839\pi\)
−0.577160 + 0.816631i \(0.695839\pi\)
\(312\) −95.5848 + 31.8197i −0.306362 + 0.101986i
\(313\) −309.220 + 309.220i −0.987922 + 0.987922i −0.999928 0.0120057i \(-0.996178\pi\)
0.0120057 + 0.999928i \(0.496178\pi\)
\(314\) 6.72848i 0.0214283i
\(315\) 234.927 209.843i 0.745801 0.666169i
\(316\) −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
\(322\) 38.6059 19.3535i 0.119894 0.0601041i
\(323\) 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
\(336\) 59.4357 + 59.3582i 0.176892 + 0.176661i
\(337\) −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
\(343\) −60.2970 + 337.659i −0.175793 + 0.984427i
\(344\) −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 \(-0.434175\pi\)
0.205323 + 0.978694i \(0.434175\pi\)
\(350\) −117.215 217.969i −0.334901 0.622769i
\(351\) −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 0.925445 0.378881i \(-0.123691\pi\)
−0.378881 + 0.925445i \(0.623691\pi\)
\(354\) 185.858 + 93.0206i 0.525023 + 0.262770i
\(355\) −138.473 + 348.360i −0.390064 + 0.981296i
\(356\) 48.8855 0.137319
\(357\) −147.460 + 0.0962968i −0.413052 + 0.000269739i
\(358\) 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 \(0.0261292\pi\)
0.0819951 + 0.996633i \(0.473871\pi\)
\(368\) 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
\(378\) 160.343 + 213.851i 0.424187 + 0.565743i
\(379\) 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 0.840310 0.542106i \(-0.182373\pi\)
−0.542106 + 0.840310i \(0.682373\pi\)
\(384\) 30.3519 + 15.1909i 0.0790413 + 0.0395596i
\(385\) 6.29565 + 72.7296i 0.0163523 + 0.188908i
\(386\) 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
\(392\) 19.8874 + 137.159i 0.0507330 + 0.349894i
\(393\) 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 \(0.142035\pi\)
0.431554 + 0.902087i \(0.357965\pi\)
\(398\) 79.6378 + 79.6378i 0.200095 + 0.200095i
\(399\) −258.052 257.715i −0.646747 0.645903i
\(400\) −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 \(-0.228842\pi\)
0.752511 + 0.658579i \(0.228842\pi\)
\(410\) 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
\(413\) 153.676 + 306.550i 0.372098 + 0.742251i
\(414\) 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 \(-0.829538\pi\)
0.860002 0.510290i \(-0.170462\pi\)
\(420\) 192.787 83.2654i 0.459017 0.198251i
\(421\) −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
\(427\) −260.189 519.018i −0.609342 1.21550i
\(428\) 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 −0.714177 0.699965i \(-0.753199\pi\)
0.699965 + 0.714177i \(0.253199\pi\)
\(434\) 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 \(-0.794761\pi\)
−0.799235 + 0.601019i \(0.794761\pi\)
\(440\) 11.6780 + 27.0870i 0.0265409 + 0.0615613i
\(441\) 0.575980 + 441.000i 0.00130608 + 0.999999i
\(442\) 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
\(448\) 25.0964 + 50.0617i 0.0560188 + 0.111745i
\(449\) 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
\(455\) −267.396 + 318.076i −0.587684 + 0.699069i
\(456\) −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 \(-0.198921\pi\)
0.811005 + 0.585040i \(0.198921\pi\)
\(462\) −61.9439 + 0.0404518i −0.134078 + 8.75580e-5i
\(463\) −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 −0.780389 0.625294i \(-0.784979\pi\)
0.625294 + 0.780389i \(0.284979\pi\)
\(468\) −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 \(0.0163945\pi\)
−0.998674 + 0.0514822i \(0.983605\pi\)
\(480\) 63.3202 56.4849i 0.131917 0.117677i
\(481\) 616.985i 1.28271i
\(482\) −65.3496 + 65.3496i −0.135580 + 0.135580i
\(483\) 91.6100 0.0598249i 0.189669 0.000123861i
\(484\) 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
\(490\) 337.011 + 80.4590i 0.687777 + 0.164202i
\(491\) 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
\(497\) −235.199 469.169i −0.473237 0.944002i
\(498\) 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 0.545163 0.838330i \(-0.316468\pi\)
−0.838330 + 0.545163i \(0.816468\pi\)
\(504\) 56.3926 + 169.032i 0.111890 + 0.335381i
\(505\) −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 \(0.183479\pi\)
−0.838421 + 0.545024i \(0.816521\pi\)
\(510\) −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
\(518\) −459.897 + 230.551i −0.887831 + 0.445079i
\(519\) 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 \(-0.498858\pi\)
0.00358632 + 0.999994i \(0.498858\pi\)
\(522\) 493.727 + 70.9297i 0.945836 + 0.135881i
\(523\) 638.273 638.273i 1.22041 1.22041i 0.252921 0.967487i \(-0.418609\pi\)
0.967487 0.252921i \(-0.0813912\pi\)
\(524\) 2.85608i 0.00545054i
\(525\) −15.4095 524.774i −0.0293514 0.999569i
\(526\) 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
\(532\) −108.961 217.353i −0.204814 0.408557i
\(533\) 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
\(546\) −249.487 249.161i −0.456935 0.456339i
\(547\) 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
\(553\) −11.3269 22.5946i −0.0204826 0.0408582i
\(554\) 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
\(560\) 139.478 12.0736i 0.249069 0.0215600i
\(561\) 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 \(0.00738780\pi\)
0.0232074 + 0.999731i \(0.492612\pi\)
\(564\) −126.905 + 253.560i −0.225009 + 0.449575i
\(565\) −905.124 + 390.225i −1.60199 + 0.690664i
\(566\) 789.098 1.39417
\(567\) 101.132 + 557.908i 0.178364 + 0.983965i
\(568\) −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 0.903793 0.427970i \(-0.140771\pi\)
−0.427970 + 0.903793i \(0.640771\pi\)
\(578\) −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 −0.991304 0.131595i \(-0.957990\pi\)
0.131595 + 0.991304i \(0.457990\pi\)
\(588\) −92.4966 + 279.071i −0.157307 + 0.474610i
\(589\) 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 \(-0.987876\pi\)
−0.0380802 0.999275i \(-0.512124\pi\)
\(594\) −78.3743 + 14.1541i −0.131943 + 0.0238285i
\(595\) −158.148 + 188.122i −0.265796 + 0.316172i
\(596\) 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 \(0.310057\pi\)
−0.561936 + 0.827180i \(0.689943\pi\)
\(602\) −143.221 285.694i −0.237909 0.474575i
\(603\) 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 0.750602 0.660755i \(-0.229764\pi\)
−0.660755 + 0.750602i \(0.729764\pi\)
\(608\) −69.4671 69.4671i −0.114255 0.114255i
\(609\) 582.308 + 581.548i 0.956171 + 0.954923i
\(610\) −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 \(-0.547067\pi\)
−0.147326 + 0.989088i \(0.547067\pi\)
\(620\) −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
\(623\) 76.6781 + 152.955i 0.123079 + 0.245514i
\(624\) −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
\(630\) 444.770 + 25.0843i 0.705985 + 0.0398163i
\(631\) 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
\(637\) −83.4789 575.735i −0.131050 0.903823i
\(638\) −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 −0.726503 0.687163i \(-0.758856\pi\)
0.687163 + 0.726503i \(0.258856\pi\)
\(644\) 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 −0.698405 0.715703i \(-0.746106\pi\)
0.715703 + 0.698405i \(0.246106\pi\)
\(648\) 109.843 + 201.054i 0.169511 + 0.310268i
\(649\) −102.176 −0.157437
\(650\) 305.210 + 288.174i 0.469554 + 0.443344i
\(651\) 629.128 629.950i 0.966402 0.967665i
\(652\) −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
\(658\) −418.216 + 209.656i −0.635587 + 0.318626i
\(659\) −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 \(-0.853578\pi\)
0.896053 0.443947i \(-0.146422\pi\)
\(662\) 373.528 + 373.528i 0.564242 + 0.564242i
\(663\) 237.300 78.9961i 0.357919 0.119149i
\(664\) 412.464 0.621180
\(665\) −605.573 + 52.4199i −0.910636 + 0.0788268i
\(666\) −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
\(672\) 0.0775770 + 118.794i 0.000115442 + 0.176777i
\(673\) 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 −0.959788 0.280727i \(-0.909425\pi\)
0.280727 + 0.959788i \(0.409425\pi\)
\(678\) −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 \(-0.997362\pi\)
0.999966 0.00828695i \(-0.00263785\pi\)
\(692\) 423.018 423.018i 0.611298 0.611298i
\(693\) −117.546 58.7348i −0.169618 0.0847543i
\(694\) 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
\(700\) 100.754 335.184i 0.143934 0.478835i
\(701\) 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
\(707\) 81.3022 40.7576i 0.114996 0.0576486i
\(708\) 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
\(714\) −147.556 147.363i −0.206661 0.206391i
\(715\) −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 \(0.103023\pi\)
−0.948079 + 0.318034i \(0.896977\pi\)
\(720\) 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 \(-0.836096\pi\)
−0.492464 0.870333i \(-0.663904\pi\)
\(728\) −105.344 210.138i −0.144704 0.288651i
\(729\) 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 −0.337077 0.941477i \(-0.609438\pi\)
0.941477 + 0.337077i \(0.109438\pi\)
\(734\) 791.713i 1.07863i
\(735\) 562.917 + 472.599i 0.765873 + 0.642992i
\(736\) 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
\(742\) −747.746 + 374.852i −1.00774 + 0.505192i
\(743\) −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
\(756\) −53.5080 + 374.194i −0.0707778 + 0.494965i
\(757\) 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 \(-0.262714\pi\)
0.678307 + 0.734778i \(0.262714\pi\)
\(762\) −198.139 595.201i −0.260026 0.781103i
\(763\) 534.628 + 1066.46i 0.700692 + 1.39772i
\(764\) −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