Properties

Label 210.3.k.a.83.15
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 83.15
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.15

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(2.84642 + 0.947561i) q^{3} +2.00000i q^{4} +(4.64638 + 1.84693i) q^{5} +(-1.89886 - 3.79398i) q^{6} +(-3.13705 + 6.25771i) q^{7} +(2.00000 - 2.00000i) q^{8} +(7.20426 + 5.39432i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(2.84642 + 0.947561i) 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} +(-1.89512 + 5.69285i) q^{12} +(-8.39517 + 8.39517i) q^{13} +(9.39476 - 3.12066i) q^{14} +(11.4755 + 9.65987i) q^{15} -4.00000 q^{16} +(4.96522 - 4.96522i) q^{17} +(-1.80994 - 12.5986i) 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} +(15.3949 + 22.1810i) q^{27} +(-12.5154 - 6.27410i) q^{28} +39.1891 q^{29} +(-1.81562 - 21.1354i) q^{30} -42.3954i q^{31} +(4.00000 + 4.00000i) q^{32} +(-1.97638 + 5.93696i) 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} +(29.6985 + 0.0193943i) q^{42} +(22.8274 + 22.8274i) q^{43} -4.17152 q^{44} +(23.5108 + 38.3698i) q^{45} -6.16934 q^{46} +(33.4161 - 33.4161i) q^{47} +(-11.3857 - 3.79024i) 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} +(-49.4332 - 16.4561i) q^{57} +(-39.1891 - 39.1891i) q^{58} -48.9876i q^{59} +(-19.3197 + 22.9510i) q^{60} -82.9406i q^{61} +(-42.3954 + 42.3954i) q^{62} +(-56.3562 + 28.1599i) 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} +(25.1972 - 3.61987i) q^{72} +(-75.1938 + 75.1938i) q^{73} -73.4928 q^{74} +(35.4784 + 66.0778i) q^{75} -34.7336i q^{76} +(-13.0521 - 6.54314i) q^{77} +(47.7924 + 15.9099i) 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} +(111.549 + 37.1340i) q^{87} +(4.17152 + 4.17152i) q^{88} -24.4427i q^{89} +(14.8590 - 61.8806i) q^{90} +(-26.1984 - 78.8706i) q^{91} +(6.16934 + 6.16934i) q^{92} +(40.1722 - 120.675i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

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
\(3\) 2.84642 + 0.947561i 0.948808 + 0.315854i
\(4\) 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 \(0.0302235\pi\)
−0.995496 + 0.0948073i \(0.969777\pi\)
\(12\) −1.89512 + 5.69285i −0.157927 + 0.474404i
\(13\) −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
\(15\) 11.4755 + 9.65987i 0.765033 + 0.643991i
\(16\) −4.00000 −0.250000
\(17\) 4.96522 4.96522i 0.292072 0.292072i −0.545826 0.837898i \(-0.683784\pi\)
0.837898 + 0.545826i \(0.183784\pi\)
\(18\) −1.80994 12.5986i −0.100552 0.699921i
\(19\) −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
\(21\) −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 −0.636862 0.770978i \(-0.719768\pi\)
0.770978 + 0.636862i \(0.219768\pi\)
\(24\) 7.58797 3.79773i 0.316165 0.158239i
\(25\) 18.1777 + 17.1631i 0.727109 + 0.686523i
\(26\) 16.7903 0.645782
\(27\) 15.3949 + 22.1810i 0.570182 + 0.821518i
\(28\) −12.5154 6.27410i −0.446979 0.224075i
\(29\) 39.1891 1.35135 0.675674 0.737201i \(-0.263853\pi\)
0.675674 + 0.737201i \(0.263853\pi\)
\(30\) −1.81562 21.1354i −0.0605208 0.704512i
\(31\) 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
\(33\) −1.97638 + 5.93696i −0.0598905 + 0.179908i
\(34\) −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 \(-0.439141\pi\)
0.190032 + 0.981778i \(0.439141\pi\)
\(42\) 29.6985 + 0.0193943i 0.707107 + 0.000461768i
\(43\) 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
\(45\) 23.5108 + 38.3698i 0.522462 + 0.852662i
\(46\) −6.16934 −0.134116
\(47\) 33.4161 33.4161i 0.710980 0.710980i −0.255760 0.966740i \(-0.582326\pi\)
0.966740 + 0.255760i \(0.0823257\pi\)
\(48\) −11.3857 3.79024i −0.237202 0.0789634i
\(49\) −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 \(0.543638\pi\)
−0.990617 + 0.136665i \(0.956362\pi\)
\(54\) 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
\(57\) −49.4332 16.4561i −0.867250 0.288703i
\(58\) −39.1891 39.1891i −0.675674 0.675674i
\(59\) 48.9876i 0.830298i −0.909754 0.415149i \(-0.863730\pi\)
0.909754 0.415149i \(-0.136270\pi\)
\(60\) −19.3197 + 22.9510i −0.321996 + 0.382516i
\(61\) 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
\(63\) −56.3562 + 28.1599i −0.894543 + 0.446982i
\(64\) 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 \(-0.822946\pi\)
0.849251 0.527990i \(-0.177054\pi\)
\(72\) 25.1972 3.61987i 0.349960 0.0502760i
\(73\) −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
\(75\) 35.4784 + 66.0778i 0.473046 + 0.881038i
\(76\) 34.7336i 0.457021i
\(77\) −13.0521 6.54314i −0.169508 0.0849758i
\(78\) 47.7924 + 15.9099i 0.612723 + 0.203973i
\(79\) 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
\(87\) 111.549 + 37.1340i 1.28217 + 0.426828i
\(88\) 4.17152 + 4.17152i 0.0474036 + 0.0474036i
\(89\) 24.4427i 0.274637i −0.990527 0.137319i \(-0.956152\pi\)
0.990527 0.137319i \(-0.0438485\pi\)
\(90\) 14.8590 61.8806i 0.165100 0.687562i
\(91\) −26.1984 78.8706i −0.287895 0.866710i
\(92\) 6.16934 + 6.16934i 0.0670580 + 0.0670580i
\(93\) 40.1722 120.675i 0.431959 1.29758i
\(94\) −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 \(-0.520487\pi\)
−0.0643184 + 0.997929i \(0.520487\pi\)
\(102\) −28.2663 9.40970i −0.277120 0.0922520i
\(103\) −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
\(105\) −96.4478 + 41.5068i −0.918551 + 0.395303i
\(106\) 119.492 1.12728
\(107\) 49.5198 + 49.5198i 0.462802 + 0.462802i 0.899573 0.436771i \(-0.143878\pi\)
−0.436771 + 0.899573i \(0.643878\pi\)
\(108\) −44.3620 + 30.7898i −0.410759 + 0.285091i
\(109\) 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 \(-0.412650\pi\)
0.962583 0.270986i \(-0.0873496\pi\)
\(114\) 32.9771 + 65.8893i 0.289273 + 0.577976i
\(115\) 20.0297 8.63538i 0.174171 0.0750903i
\(116\) 78.3781i 0.675674i
\(117\) −105.767 + 15.1947i −0.903993 + 0.129869i
\(118\) −48.9876 + 48.9876i −0.415149 + 0.415149i
\(119\) 15.4948 + 46.6471i 0.130208 + 0.391992i
\(120\) 42.2707 3.63125i 0.352256 0.0302604i
\(121\) 116.650 0.964046
\(122\) −82.9406 + 82.9406i −0.679841 + 0.679841i
\(123\) 44.3549 + 14.7655i 0.360609 + 0.120045i
\(124\) 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 \(0.498265\pi\)
\(132\) −11.8739 3.95277i −0.0899539 0.0299452i
\(133\) 54.4805 108.676i 0.409628 0.817115i
\(134\) 109.647 0.818258
\(135\) 30.5640 + 131.495i 0.226400 + 0.974034i
\(136\) 19.8609i 0.146036i
\(137\) 152.451 + 152.451i 1.11278 + 1.11278i 0.992773 + 0.120010i \(0.0382925\pi\)
0.120010 + 0.992773i \(0.461707\pi\)
\(138\) −17.5605 5.84582i −0.127250 0.0423610i
\(139\) −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
\(147\) −46.2483 139.535i −0.314614 0.949220i
\(148\) 73.4928 + 73.4928i 0.496573 + 0.496573i
\(149\) 183.297 1.23018 0.615091 0.788456i \(-0.289119\pi\)
0.615091 + 0.788456i \(0.289119\pi\)
\(150\) 30.5994 101.556i 0.203996 0.677042i
\(151\) −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
\(153\) 62.5547 8.98674i 0.408855 0.0587369i
\(154\) 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
\(162\) 54.9215 100.527i 0.339022 0.620536i
\(163\) 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
\(165\) −20.1482 + 23.9351i −0.122110 + 0.145061i
\(166\) 206.232i 1.24236i
\(167\) −34.3084 + 34.3084i −0.205439 + 0.205439i −0.802326 0.596886i \(-0.796404\pi\)
0.596886 + 0.802326i \(0.296404\pi\)
\(168\) −0.0387885 + 59.3970i −0.000230884 + 0.353553i
\(169\) 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
\(175\) −164.426 + 59.9094i −0.939576 + 0.342340i
\(176\) 8.34304i 0.0474036i
\(177\) 46.4187 139.439i 0.262253 0.787793i
\(178\) −24.4427 + 24.4427i −0.137319 + 0.137319i
\(179\) −110.880 −0.619440 −0.309720 0.950828i \(-0.600235\pi\)
−0.309720 + 0.950828i \(0.600235\pi\)
\(180\) −76.7396 + 47.0216i −0.426331 + 0.261231i
\(181\) 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
\(183\) 78.5913 236.084i 0.429460 1.29008i
\(184\) 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 \(-0.859307\pi\)
0.903898 0.427747i \(-0.140693\pi\)
\(192\) 7.58049 22.7714i 0.0394817 0.118601i
\(193\) −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
\(195\) −177.435 + 15.2425i −0.909923 + 0.0781665i
\(196\) 78.5230 58.6356i 0.400628 0.299161i
\(197\) −19.3286 19.3286i −0.0981145 0.0981145i 0.656346 0.754460i \(-0.272101\pi\)
−0.754460 + 0.656346i \(0.772101\pi\)
\(198\) 26.2776 3.77509i 0.132715 0.0190661i
\(199\) −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
\(207\) 38.8624 5.58305i 0.187741 0.0269713i
\(208\) 33.5807 33.5807i 0.161446 0.161446i
\(209\) 36.2230i 0.173316i
\(210\) 137.955 + 54.9411i 0.656927 + 0.261624i
\(211\) −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
\(213\) 71.0429 213.409i 0.333535 1.00192i
\(214\) 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
\(222\) −209.192 69.6389i −0.942305 0.313689i
\(223\) 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
\(225\) 38.3738 + 221.704i 0.170550 + 0.985349i
\(226\) −278.787 −1.23357
\(227\) 70.0030 70.0030i 0.308383 0.308383i −0.535899 0.844282i \(-0.680027\pi\)
0.844282 + 0.535899i \(0.180027\pi\)
\(228\) 32.9122 98.8665i 0.144352 0.433625i
\(229\) 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
\(231\) −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 −0.990812 0.135245i \(-0.956818\pi\)
0.135245 + 0.990812i \(0.456818\pi\)
\(234\) 120.962 + 90.5725i 0.516931 + 0.387062i
\(235\) 216.981 93.5467i 0.923323 0.398071i
\(236\) 97.9751 0.415149
\(237\) −3.42134 + 10.2775i −0.0144360 + 0.0433651i
\(238\) 31.1523 62.1418i 0.130892 0.261100i
\(239\) −46.3651 −0.193996 −0.0969982 0.995285i \(-0.530924\pi\)
−0.0969982 + 0.995285i \(0.530924\pi\)
\(240\) −45.9020 38.6395i −0.191258 0.160998i
\(241\) 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
\(243\) −8.74241 + 242.843i −0.0359770 + 0.999353i
\(244\) 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 \(-0.589593\pi\)
−0.277763 + 0.960650i \(0.589593\pi\)
\(252\) −56.3198 112.712i −0.223491 0.447271i
\(253\) 6.43388 + 6.43388i 0.0254304 + 0.0254304i
\(254\) 209.105 0.823247
\(255\) 104.942 9.01497i 0.411536 0.0353528i
\(256\) 16.0000 0.0625000
\(257\) 323.691 323.691i 1.25950 1.25950i 0.308168 0.951332i \(-0.400284\pi\)
0.951332 0.308168i \(-0.0997158\pi\)
\(258\) 43.2606 129.953i 0.167677 0.503693i
\(259\) 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 −0.918456 0.395523i \(-0.870563\pi\)
0.395523 + 0.918456i \(0.370563\pi\)
\(264\) 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
\(267\) 23.1610 69.5744i 0.0867452 0.260578i
\(268\) −109.647 109.647i −0.409129 0.409129i
\(269\) 391.957i 1.45709i 0.684998 + 0.728545i \(0.259803\pi\)
−0.684998 + 0.728545i \(0.740197\pi\)
\(270\) 100.931 162.059i 0.373817 0.600217i
\(271\) 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
\(273\) 0.162818 249.324i 0.000596403 0.913274i
\(274\) 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 \(0.0555558\pi\)
−0.984808 + 0.173649i \(0.944444\pi\)
\(282\) −190.233 63.3275i −0.674584 0.224566i
\(283\) −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
\(285\) −199.292 167.761i −0.699272 0.588635i
\(286\) 35.0206i 0.122450i
\(287\) −48.8836 + 97.5118i −0.170326 + 0.339762i
\(288\) 7.23975 + 50.3943i 0.0251380 + 0.174980i
\(289\) 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
\(297\) −46.2642 + 32.1101i −0.155772 + 0.108115i
\(298\) −183.297 183.297i −0.615091 0.615091i
\(299\) 51.7926i 0.173220i
\(300\) −132.156 + 70.9568i −0.440519 + 0.236523i
\(301\) −214.458 + 71.2364i −0.712484 + 0.236666i
\(302\) 203.889 + 203.889i 0.675130 + 0.675130i
\(303\) −36.9817 12.3110i −0.122052 0.0406304i
\(304\) 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 \(-0.695839\pi\)
−0.577160 + 0.816631i \(0.695839\pi\)
\(312\) −31.8197 + 95.5848i −0.101986 + 0.306362i
\(313\) 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
\(315\) −313.862 + 26.7557i −0.996386 + 0.0849386i
\(316\) −7.22137 −0.0228524
\(317\) −46.3542 46.3542i −0.146228 0.146228i 0.630203 0.776431i \(-0.282972\pi\)
−0.776431 + 0.630203i \(0.782972\pi\)
\(318\) 340.125 + 113.226i 1.06957 + 0.356056i
\(319\) 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
\(327\) 161.487 485.098i 0.493844 1.48348i
\(328\) 31.1653 31.1653i 0.0950162 0.0950162i
\(329\) 104.280 + 313.936i 0.316961 + 0.954213i
\(330\) 44.0833 3.78695i 0.133586 0.0114756i
\(331\) 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
\(333\) 462.952 66.5087i 1.39025 0.199726i
\(334\) 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
\(342\) 31.4328 + 218.797i 0.0919087 + 0.639757i
\(343\) 337.659 60.2970i 0.984427 0.175793i
\(344\) 91.3095 0.265434
\(345\) 65.1956 5.60060i 0.188973 0.0162336i
\(346\) 423.018i 1.22260i
\(347\) 231.964 + 231.964i 0.668483 + 0.668483i 0.957365 0.288882i \(-0.0932835\pi\)
−0.288882 + 0.957365i \(0.593284\pi\)
\(348\) −74.2681 + 223.097i −0.213414 + 0.641085i
\(349\) −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 0.925445 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
\(357\) −0.0962968 + 147.460i −0.000269739 + 0.413052i
\(358\) 110.880 + 110.880i 0.309720 + 0.309720i
\(359\) 424.811 1.18332 0.591659 0.806189i \(-0.298473\pi\)
0.591659 + 0.806189i \(0.298473\pi\)
\(360\) 123.761 + 29.7180i 0.343781 + 0.0825501i
\(361\) −59.3948 −0.164528
\(362\) 24.2997 24.2997i 0.0671264 0.0671264i
\(363\) 332.034 + 110.533i 0.914695 + 0.304498i
\(364\) 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
\(372\) 241.350 + 80.3444i 0.648791 + 0.215980i
\(373\) 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
\(375\) 42.8052 + 372.549i 0.114147 + 0.993464i
\(376\) 133.664i 0.355490i
\(377\) −328.999 + 328.999i −0.872676 + 0.872676i
\(378\) 213.851 + 160.343i 0.565743 + 0.424187i
\(379\) 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
\(385\) −48.5602 54.5082i −0.126130 0.141580i
\(386\) 72.7491i 0.188469i
\(387\) 41.3161 + 287.592i 0.106760 + 0.743133i
\(388\) −70.7233 + 70.7233i −0.182277 + 0.182277i
\(389\) 365.324 0.939136 0.469568 0.882896i \(-0.344410\pi\)
0.469568 + 0.882896i \(0.344410\pi\)
\(390\) 192.677 + 162.192i 0.494045 + 0.415878i
\(391\) 30.6321i 0.0783431i
\(392\) −137.159 19.8874i −0.349894 0.0507330i
\(393\) 4.06481 + 1.35316i 0.0103430 + 0.00344315i
\(394\) 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
\(399\) 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 \(0.0743986\pi\)
−0.972809 + 0.231608i \(0.925601\pi\)
\(402\) 312.101 + 103.897i 0.776369 + 0.258450i
\(403\) 355.916 + 355.916i 0.883167 + 0.883167i
\(404\) 25.9847i 0.0643184i
\(405\) −37.6012 + 403.251i −0.0928425 + 0.995681i
\(406\) 368.172 122.296i 0.906827 0.301221i
\(407\) 76.6442 + 76.6442i 0.188315 + 0.188315i
\(408\) 18.8194 56.5325i 0.0461260 0.138560i
\(409\) −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
\(417\) −213.554 71.0913i −0.512121 0.170483i
\(418\) −36.2230 + 36.2230i −0.0866578 + 0.0866578i
\(419\) 427.623i 1.02058i −0.860002 0.510290i \(-0.829538\pi\)
0.860002 0.510290i \(-0.170462\pi\)
\(420\) −83.0136 192.896i −0.197651 0.459275i
\(421\) −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
\(423\) 420.995 60.4810i 0.995260 0.142981i
\(424\) 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 \(-0.674887\pi\)
0.522197 0.852825i \(-0.325113\pi\)
\(432\) −61.5797 88.7240i −0.142546 0.205380i
\(433\) 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
\(435\) 449.714 + 378.561i 1.03383 + 0.870256i
\(436\) 340.847 0.781760
\(437\) −53.5708 + 53.5708i −0.122588 + 0.122588i
\(438\) 428.067 + 142.501i 0.977322 + 0.325346i
\(439\) 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
\(441\) 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 −0.877661 0.479282i \(-0.840897\pi\)
0.479282 + 0.877661i \(0.340897\pi\)
\(444\) 139.553 + 278.831i 0.314308 + 0.627997i
\(445\) 45.1440 113.570i 0.101447 0.255214i
\(446\) −442.817 −0.992862
\(447\) 521.741 + 173.685i 1.16721 + 0.388557i
\(448\) 50.0617 + 25.0964i 0.111745 + 0.0560188i
\(449\) −521.716 −1.16195 −0.580976 0.813921i \(-0.697329\pi\)
−0.580976 + 0.813921i \(0.697329\pi\)
\(450\) 183.330 260.077i 0.407399 0.577950i
\(451\) 32.5017i 0.0720659i
\(452\) 278.787 + 278.787i 0.616785 + 0.616785i
\(453\) −580.355 193.198i −1.28114 0.426485i
\(454\) −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 \(-0.198921\pi\)
0.811005 + 0.585040i \(0.198921\pi\)
\(462\) −0.0404518 + 61.9439i −8.75580e−5 + 0.134078i
\(463\) −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
\(465\) 409.534 486.508i 0.880718 1.04625i
\(466\) 398.695 0.855568
\(467\) −72.4294 + 72.4294i −0.155095 + 0.155095i −0.780389 0.625294i \(-0.784979\pi\)
0.625294 + 0.780389i \(0.284979\pi\)
\(468\) −30.3894 211.534i −0.0649347 0.451997i
\(469\) −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
\(477\) −752.714 + 108.136i −1.57802 + 0.226701i
\(478\) 46.3651 + 46.3651i 0.0969982 + 0.0969982i
\(479\) 49.3199i 0.102964i 0.998674 + 0.0514822i \(0.0163945\pi\)
−0.998674 + 0.0514822i \(0.983605\pi\)
\(480\) 7.26249 + 84.5414i 0.0151302 + 0.176128i
\(481\) 616.985i 1.28271i
\(482\) −65.3496 + 65.3496i −0.135580 + 0.135580i
\(483\) −0.0598249 + 91.6100i −0.000123861 + 0.189669i
\(484\) 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 \(0.232752\pi\)
−0.744366 + 0.667771i \(0.767248\pi\)
\(492\) −29.5310 + 88.7097i −0.0600225 + 0.180304i
\(493\) 194.583 194.583i 0.394691 0.394691i
\(494\) −291.594 −0.590272
\(495\) −80.0302 + 49.0379i −0.161677 + 0.0990664i
\(496\) 169.581i 0.341898i
\(497\) 469.169 + 235.199i 0.944002 + 0.473237i
\(498\) −195.417 + 587.023i −0.392404 + 1.17876i
\(499\) 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
\(507\) −26.5717 + 79.8201i −0.0524098 + 0.157436i
\(508\) −209.105 209.105i −0.411623 0.411623i
\(509\) 554.834i 1.09005i 0.838421 + 0.545024i \(0.183479\pi\)
−0.838421 + 0.545024i \(0.816521\pi\)
\(510\) −113.957 95.9268i −0.223445 0.188092i
\(511\) −234.654 706.428i −0.459206 1.38244i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −267.360 385.213i −0.521170 0.750902i
\(514\) −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 \(-0.498858\pi\)
0.00358632 + 0.999994i \(0.498858\pi\)
\(522\) −70.9297 493.727i −0.135881 0.945836i
\(523\) −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
\(525\) −524.793 + 14.7241i −0.999607 + 0.0280458i
\(526\) 275.063 0.522933
\(527\) −210.502 210.502i −0.399435 0.399435i
\(528\) 7.90554 23.7478i 0.0149726 0.0449770i
\(529\) 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
\(537\) −315.611 105.065i −0.587730 0.195652i
\(538\) 391.957 391.957i 0.728545 0.728545i
\(539\) 81.8901 61.1499i 0.151930 0.113451i
\(540\) −262.989 + 61.1279i −0.487017 + 0.113200i
\(541\) −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
\(543\) −23.0255 + 69.1674i −0.0424042 + 0.127380i
\(544\) 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
\(552\) 11.6916 35.1211i 0.0211805 0.0636252i
\(553\) −22.5946 11.3269i −0.0408582 0.0204826i
\(554\) −76.0232 −0.137226
\(555\) 776.649 66.7176i 1.39937 0.120212i
\(556\) 150.051i 0.269876i
\(557\) −545.370 545.370i −0.979121 0.979121i 0.0206659 0.999786i \(-0.493421\pi\)
−0.999786 + 0.0206659i \(0.993421\pi\)
\(558\) −534.121 + 76.7329i −0.957207 + 0.137514i
\(559\) −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 \(0.00738780\pi\)
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
\(567\) −557.908 101.132i −0.983965 0.178364i
\(568\) −149.949 149.949i −0.263995 0.263995i
\(569\) −524.362 −0.921549 −0.460775 0.887517i \(-0.652428\pi\)
−0.460775 + 0.887517i \(0.652428\pi\)
\(570\) 31.5315 + 367.053i 0.0553185 + 0.643953i
\(571\) 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
\(573\) 154.831 465.104i 0.270211 0.811700i
\(574\) 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
\(582\) 67.0146 201.308i 0.115145 0.345891i
\(583\) −124.616 124.616i −0.213749 0.213749i
\(584\) 300.775i 0.515026i
\(585\) −519.498 124.744i −0.888031 0.213237i
\(586\) 124.478i 0.212419i
\(587\) −504.649 + 504.649i −0.859709 + 0.859709i −0.991304 0.131595i \(-0.957990\pi\)
0.131595 + 0.991304i \(0.457990\pi\)
\(588\) 279.071 92.4966i 0.474610 0.157307i
\(589\) 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
\(595\) −14.1592 + 245.358i −0.0237971 + 0.412366i
\(596\) 366.594i 0.615091i
\(597\) −226.683 75.4617i −0.379703 0.126401i
\(598\) 51.7926 51.7926i 0.0866098 0.0866098i
\(599\) 103.401 0.172623 0.0863115 0.996268i \(-0.472492\pi\)
0.0863115 + 0.996268i \(0.472492\pi\)
\(600\) 203.113 + 61.1988i 0.338521 + 0.101998i
\(601\) 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
\(603\) −690.695 + 99.2266i −1.14543 + 0.164555i
\(604\) 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
\(609\) −582.308 + 581.548i −0.956171 + 0.954923i
\(610\) −538.559 + 232.188i −0.882883 + 0.380636i
\(611\) 561.067i 0.918277i
\(612\) 17.9735 + 125.109i 0.0293684 + 0.204427i
\(613\) 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
\(615\) 178.819 + 150.526i 0.290762 + 0.244759i
\(616\) −39.1904 + 13.0179i −0.0636208 + 0.0211329i
\(617\) −37.9474 37.9474i −0.0615032 0.0615032i 0.675686 0.737189i \(-0.263847\pi\)
−0.737189 + 0.675686i \(0.763847\pi\)
\(618\) 259.489 + 86.3827i 0.419885 + 0.139778i
\(619\) 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
\(627\) 34.3235 103.106i 0.0547423 0.164443i
\(628\) −6.72848 + 6.72848i −0.0107141 + 0.0107141i
\(629\) 364.908i 0.580140i
\(630\) 340.617 + 287.106i 0.540662 + 0.455724i
\(631\) 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
\(633\) −416.904 138.785i −0.658617 0.219250i
\(634\) 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 \(-0.958005\pi\)
0.991310 0.131548i \(-0.0419946\pi\)
\(642\) 93.8461 281.909i 0.146178 0.439110i
\(643\) 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
\(645\) 41.4459 + 482.465i 0.0642572 + 0.748007i
\(646\) 172.460 0.266966
\(647\) 11.1919 11.1919i 0.0172981 0.0172981i −0.698405 0.715703i \(-0.746106\pi\)
0.715703 + 0.698405i \(0.246106\pi\)
\(648\) 201.054 + 109.843i 0.310268 + 0.169511i
\(649\) 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 −0.418346 0.908288i \(-0.637390\pi\)
0.908288 + 0.418346i \(0.137390\pi\)
\(654\) −646.585 + 323.611i −0.988662 + 0.494818i
\(655\) 6.63522 + 2.63749i 0.0101301 + 0.00402670i
\(656\) −62.3307 −0.0950162
\(657\) −947.335 + 136.096i −1.44191 + 0.207148i
\(658\) 209.656 418.216i 0.318626 0.635587i
\(659\) 692.273 1.05049 0.525245 0.850951i \(-0.323974\pi\)
0.525245 + 0.850951i \(0.323974\pi\)
\(660\) −47.8703 40.2963i −0.0725307 0.0610551i
\(661\) 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
\(663\) −78.9961 + 237.300i −0.119149 + 0.357919i
\(664\) −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
\(672\) −118.794 0.0775770i −0.176777 0.000115442i
\(673\) 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
\(675\) −100.849 + 667.424i −0.149406 + 0.988776i
\(676\) −56.0845 −0.0829653
\(677\) −459.724 + 459.724i −0.679061 + 0.679061i −0.959788 0.280727i \(-0.909425\pi\)
0.280727 + 0.959788i \(0.409425\pi\)
\(678\) −793.545 264.167i −1.17042 0.389627i
\(679\) −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 −0.754222 0.656619i \(-0.771986\pi\)
0.656619 + 0.754222i \(0.271986\pi\)
\(684\) 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
\(687\) 817.138 + 272.021i 1.18943 + 0.395956i
\(688\) −91.3095 91.3095i −0.132717 0.132717i
\(689\) 1003.16i 1.45596i
\(690\) −70.7962 59.5950i −0.102603 0.0863696i
\(691\) 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
\(693\) −58.7348 117.546i −0.0847543 0.169618i
\(694\) 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 \(0.149678\pi\)
−0.891465 + 0.453089i \(0.850322\pi\)
\(702\) 258.486 + 372.426i 0.368214 + 0.530522i
\(703\) −638.167 + 638.167i −0.907777 + 0.907777i
\(704\) 16.6861 0.0237018
\(705\) 706.261 60.6710i 1.00179 0.0860581i
\(706\) 385.875i 0.546564i
\(707\) 40.7576 81.3022i 0.0576486 0.114996i
\(708\) 278.879 + 92.8374i 0.393896 + 0.131126i
\(709\) 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
\(717\) −131.975 43.9338i −0.184065 0.0612745i
\(718\) −424.811 424.811i −0.591659 0.591659i
\(719\) 457.334i 0.636069i 0.948079 + 0.318034i \(0.103023\pi\)
−0.948079 + 0.318034i \(0.896977\pi\)
\(720\) −94.0432 153.479i −0.130616 0.213166i
\(721\) −142.245 428.228i −0.197288 0.593936i
\(722\) 59.3948 + 59.3948i 0.0822642 + 0.0822642i
\(723\) 61.9228 186.013i 0.0856470 0.257279i
\(724\) −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
\(732\) 472.168 + 157.183i 0.645038 + 0.214730i
\(733\) −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
\(735\) 42.8245 733.751i 0.0582647 0.998301i
\(736\) 24.6773 0.0335290
\(737\) −114.348 114.348i −0.155154 0.155154i
\(738\) −28.2036 196.319i −0.0382163 0.266015i
\(739\) 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 \(-0.463291\pi\)
0.993357 0.115071i \(-0.0367095\pi\)
\(744\) −161.006 321.695i −0.216406 0.432385i
\(745\) 851.668 + 338.536i 1.14318 + 0.454411i
\(746\) 369.034i 0.494683i
\(747\) −186.633 1299.11i −0.249844 1.73911i
\(748\) −20.7125 + 20.7125i −0.0276905 + 0.0276905i
\(749\) −465.227 + 154.534i −0.621131 + 0.206321i
\(750\) 329.744 415.354i 0.439658 0.553806i
\(751\) −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
\(753\) −396.896 132.125i −0.527087 0.175465i
\(754\) 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 \(0.262714\pi\)
\(762\) 595.201 + 198.139i 0.781103 + 0.260026i
\(763\) 1066.46 + 534.628i 1.39772 + 0.700692i
\(764\) 326.799 0.427747
\(765\) 307.251 + 73.7783i 0.401635 + 0.0964422i
\(766\) 228.424i 0.298204i
\(767\) 411.259