Properties

Label 210.3.k.a.83.2
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 83.2
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-2.84642 - 0.947561i) q^{3} +2.00000i q^{4} +(-4.64638 - 1.84693i) q^{5} +(1.89886 + 3.79398i) q^{6} +(-6.25771 + 3.13705i) q^{7} +(2.00000 - 2.00000i) q^{8} +(7.20426 + 5.39432i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-2.84642 - 0.947561i) 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} +(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} +(20.7846 - 2.99982i) q^{21} +(2.08576 - 2.08576i) q^{22} +(3.08467 - 3.08467i) q^{23} +(-7.58797 + 3.79773i) q^{24} +(18.1777 + 17.1631i) q^{25} -16.7903 q^{26} +(-15.3949 - 22.1810i) q^{27} +(-6.27410 - 12.5154i) 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} +(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} +(-23.7845 - 17.7848i) 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} +(-62.0044 - 11.1560i) 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} +(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} +(-6.54314 - 13.0521i) 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} +(5.99963 + 41.5693i) 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} +(-68.5793 + 9.94368i) q^{98} +(-11.2513 + 15.0264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

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
\(7\) −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 \(0.0302235\pi\)
−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 −0.306189 0.951971i \(-0.599054\pi\)
0.951971 + 0.306189i \(0.0990538\pi\)
\(14\) 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 −0.837898 0.545826i \(-0.816216\pi\)
0.545826 + 0.837898i \(0.316216\pi\)
\(18\) −1.80994 12.5986i −0.100552 0.699921i
\(19\) 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
\(21\) 20.7846 2.99982i 0.989745 0.142848i
\(22\) 2.08576 2.08576i 0.0948073 0.0948073i
\(23\) 3.08467 3.08467i 0.134116 0.134116i −0.636862 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
\(28\) −6.27410 12.5154i −0.224075 0.446979i
\(29\) 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 \(0.239672\pi\)
−0.729673 + 0.683796i \(0.760328\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 1.97638 5.93696i 0.0598905 0.179908i
\(34\) 9.93045 0.292072
\(35\) 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 \(-0.560859\pi\)
−0.190032 + 0.981778i \(0.560859\pi\)
\(42\) −23.7845 17.7848i −0.566297 0.423448i
\(43\) 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 −0.966740 0.255760i \(-0.917674\pi\)
0.255760 + 0.966740i \(0.417674\pi\)
\(48\) 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 \(0.136270\pi\)
−0.909754 + 0.415149i \(0.863730\pi\)
\(60\) −19.3197 + 22.9510i −0.321996 + 0.382516i
\(61\) 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
\(63\) −62.0044 11.1560i −0.984197 0.177079i
\(64\) 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 \(-0.822946\pi\)
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 \(-0.490284\pi\)
0.999534 0.0305180i \(-0.00971569\pi\)
\(74\) −73.4928 −0.993146
\(75\) −35.4784 66.0778i −0.473046 0.881038i
\(76\) 34.7336i 0.457021i
\(77\) −6.54314 13.0521i −0.0849758 0.169508i
\(78\) 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 \(0.0914427\pi\)
0.283341 + 0.959019i \(0.408557\pi\)
\(84\) 5.99963 + 41.5693i 0.0714242 + 0.494872i
\(85\) 32.2407 13.8999i 0.379303 0.163528i
\(86\) 45.6547i 0.530869i
\(87\) −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 \(0.0438485\pi\)
−0.990527 + 0.137319i \(0.956152\pi\)
\(90\) −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 0.500933 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 \(-0.479513\pi\)
0.0643184 + 0.997929i \(0.479513\pi\)
\(102\) −28.2663 9.40970i −0.277120 0.0922520i
\(103\) 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
\(105\) −102.114 24.4494i −0.972512 0.232852i
\(106\) 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
\(112\) 25.0308 12.5482i 0.223490 0.112038i
\(113\) 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
\(126\) 50.8484 + 73.1604i 0.403559 + 0.580638i
\(127\) −104.552 + 104.552i −0.823247 + 0.823247i −0.986572 0.163325i \(-0.947778\pi\)
0.163325 + 0.986572i \(0.447778\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) −43.3460 86.6067i −0.336016 0.671370i
\(130\) 78.0143 + 31.0106i 0.600110 + 0.238543i
\(131\) −1.42804 −0.0109011 −0.00545054 0.999985i \(-0.501735\pi\)
−0.00545054 + 0.999985i \(0.501735\pi\)
\(132\) 11.8739 + 3.95277i 0.0899539 + 0.0299452i
\(133\) −108.676 + 54.4805i −0.817115 + 0.409628i
\(134\) 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 \(-0.413017\pi\)
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
\(147\) −120.654 + 83.9744i −0.820773 + 0.571255i
\(148\) 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 0.696311 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
\(162\) 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 −0.596886 0.802326i \(-0.703596\pi\)
0.802326 + 0.596886i \(0.203596\pi\)
\(168\) 35.5696 47.5689i 0.211724 0.283148i
\(169\) 28.0423i 0.165931i
\(170\) −46.1406 18.3408i −0.271416 0.107887i
\(171\) 125.115 + 93.6820i 0.731665 + 0.547848i
\(172\) −45.6547 + 45.6547i −0.265434 + 0.265434i
\(173\) 211.509 + 211.509i 1.22260 + 1.22260i 0.966706 + 0.255891i \(0.0823688\pi\)
0.255891 + 0.966706i \(0.417631\pi\)
\(174\) 74.4147 + 148.683i 0.427671 + 0.854499i
\(175\) −167.592 50.3770i −0.957670 0.287869i
\(176\) 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 \(-0.978617\pi\)
0.997744 0.0671264i \(-0.0213831\pi\)
\(182\) 105.069 52.6722i 0.577302 0.289407i
\(183\) 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
\(189\) 165.920 + 90.5075i 0.877883 + 0.478876i
\(190\) 48.6175 + 112.768i 0.255882 + 0.593515i
\(191\) 163.399i 0.855494i −0.903898 0.427747i \(-0.859307\pi\)
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 \(-0.435875\pi\)
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
\(207\) 38.8624 5.58305i 0.187741 0.0269713i
\(208\) −33.5807 + 33.5807i −0.161446 + 0.161446i
\(209\) 36.2230i 0.173316i
\(210\) 77.6643 + 126.563i 0.369830 + 0.602682i
\(211\) −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
\(217\) −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
\(222\) 209.192 + 69.6389i 0.942305 + 0.313689i
\(223\) −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
\(225\) 38.3738 + 221.704i 0.170550 + 0.985349i
\(226\) −278.787 −1.23357
\(227\) −70.0030 + 70.0030i −0.308383 + 0.308383i −0.844282 0.535899i \(-0.819973\pi\)
0.535899 + 0.844282i \(0.319973\pi\)
\(228\) 32.9122 98.8665i 0.144352 0.433625i
\(229\) −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
\(231\) 6.25690 + 43.3518i 0.0270861 + 0.187670i
\(232\) 78.3781 78.3781i 0.337837 0.337837i
\(233\) −199.347 + 199.347i −0.855568 + 0.855568i −0.990812 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
\(238\) −62.1418 + 31.1523i −0.261100 + 0.130892i
\(239\) −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 \(0.0432898\pi\)
−0.990766 + 0.135580i \(0.956710\pi\)
\(242\) −116.650 116.650i −0.482023 0.482023i
\(243\) 8.74241 242.843i 0.0359770 0.999353i
\(244\) −165.881 −0.679841
\(245\) −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 \(-0.410407\pi\)
0.277763 + 0.960650i \(0.410407\pi\)
\(252\) 22.3119 124.009i 0.0885394 0.492098i
\(253\) 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 \(0.599716\pi\)
−0.951332 + 0.308168i \(0.900284\pi\)
\(258\) −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 \(-0.740197\pi\)
0.684998 0.728545i \(-0.259803\pi\)
\(270\) 100.931 162.059i 0.373817 0.600217i
\(271\) 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
\(273\) 149.307 199.675i 0.546911 0.731408i
\(274\) 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 \(0.0555558\pi\)
−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 \(-0.303659\pi\)
0.815720 0.578447i \(-0.196341\pi\)
\(284\) 149.949 0.527990
\(285\) 199.292 + 167.761i 0.699272 + 0.588635i
\(286\) 35.0206i 0.122450i
\(287\) 97.5118 48.8836i 0.339762 0.170326i
\(288\) 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 0.805294 0.592875i \(-0.202007\pi\)
−0.592875 + 0.805294i \(0.702007\pi\)
\(294\) 204.628 + 36.6792i 0.696014 + 0.124759i
\(295\) 90.4765 227.615i 0.306700 0.771576i
\(296\) 146.986i 0.496573i
\(297\) 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 0.565180 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 \(-0.304161\pi\)
0.577160 + 0.816631i \(0.304161\pi\)
\(312\) −31.8197 + 95.5848i −0.101986 + 0.306362i
\(313\) −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
\(315\) 267.492 + 166.352i 0.849180 + 0.528103i
\(316\) −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
\(322\) 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
\(327\) −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
\(336\) −83.1385 + 11.9993i −0.247436 + 0.0357121i
\(337\) −163.577 + 163.577i −0.485392 + 0.485392i −0.906848 0.421457i \(-0.861519\pi\)
0.421457 + 0.906848i \(0.361519\pi\)
\(338\) 28.0423 28.0423i 0.0829653 0.0829653i
\(339\) −528.856 + 264.689i −1.56005 + 0.780793i
\(340\) 27.7998 + 64.4815i 0.0817642 + 0.189651i
\(341\) −88.4266 −0.259315
\(342\) −31.4328 218.797i −0.0919087 0.639757i
\(343\) −60.2970 + 337.659i −0.175793 + 0.984427i
\(344\) 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 \(-0.434175\pi\)
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 0.378881 0.925445i \(-0.376309\pi\)
−0.925445 + 0.378881i \(0.876309\pi\)
\(354\) −185.858 + 93.0206i −0.525023 + 0.262770i
\(355\) −138.473 + 348.360i −0.390064 + 0.981296i
\(356\) −48.8855 −0.137319
\(357\) −88.3056 + 118.095i −0.247355 + 0.330799i
\(358\) 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 \(0.0261292\pi\)
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
\(372\) 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
\(378\) −75.4123 256.427i −0.199503 0.678379i
\(379\) 127.438i 0.336249i 0.985766 + 0.168124i \(0.0537710\pi\)
−0.985766 + 0.168124i \(0.946229\pi\)
\(380\) 64.1504 161.385i 0.168817 0.424698i
\(381\) 396.670 198.531i 1.04113 0.521078i
\(382\) −163.399 + 163.399i −0.427747 + 0.427747i
\(383\) −114.212 114.212i −0.298204 0.298204i 0.542106 0.840310i \(-0.317627\pi\)
−0.840310 + 0.542106i \(0.817627\pi\)
\(384\) 30.3519 15.1909i 0.0790413 0.0395596i
\(385\) 6.29565 + 72.7296i 0.0163523 + 0.188908i
\(386\) 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
\(392\) −19.8874 137.159i −0.0507330 0.349894i
\(393\) 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 \(0.142035\pi\)
0.431554 + 0.902087i \(0.357965\pi\)
\(398\) −79.6378 79.6378i −0.200095 0.200095i
\(399\) 360.962 52.0972i 0.904667 0.130569i
\(400\) −72.7109 68.6523i −0.181777 0.171631i
\(401\) 185.749i 0.463216i 0.972809 + 0.231608i \(0.0743986\pi\)
−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 \(-0.228842\pi\)
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
\(417\) −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 \(0.170462\pi\)
−0.860002 + 0.510290i \(0.829538\pi\)
\(420\) 48.8989 204.228i 0.116426 0.486256i
\(421\) −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
\(427\) −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 \(-0.674887\pi\)
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 −0.714177 0.699965i \(-0.753199\pi\)
0.699965 + 0.714177i \(0.253199\pi\)
\(434\) −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 \(-0.794761\pi\)
−0.799235 + 0.601019i \(0.794761\pi\)
\(440\) −11.6780 27.0870i −0.0265409 0.0615613i
\(441\) 423.002 124.700i 0.959189 0.282767i
\(442\) 83.3678 83.3678i 0.188615 0.188615i
\(443\) −176.482 + 176.482i −0.398379 + 0.398379i −0.877661 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
\(448\) 25.0964 + 50.0617i 0.0560188 + 0.111745i
\(449\) −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
\(455\) 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 \(-0.801079\pi\)
−0.811005 + 0.585040i \(0.801079\pi\)
\(462\) 37.0949 49.6087i 0.0802919 0.107378i
\(463\) −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 −0.625294 0.780389i \(-0.715021\pi\)
0.780389 + 0.625294i \(0.215021\pi\)
\(468\) 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 \(-0.983605\pi\)
0.998674 0.0514822i \(-0.0163945\pi\)
\(480\) 7.26249 + 84.5414i 0.0151302 + 0.176128i
\(481\) 616.985i 1.28271i
\(482\) 65.3496 65.3496i 0.135580 0.135580i
\(483\) 54.8603 73.3672i 0.113582 0.151899i
\(484\) 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 \(0.232752\pi\)
−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
\(497\) 235.199 + 469.169i 0.473237 + 0.944002i
\(498\) −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 0.838330 0.545163i \(-0.183532\pi\)
−0.545163 + 0.838330i \(0.683532\pi\)
\(504\) −146.321 + 101.697i −0.290319 + 0.201779i
\(505\) −60.3673 23.9959i −0.119539 0.0475166i
\(506\) 12.8678i 0.0254304i
\(507\) 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 \(-0.816521\pi\)
0.838421 0.545024i \(-0.183479\pi\)
\(510\) 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
\(518\) 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 \(-0.501142\pi\)
−0.00358632 + 0.999994i \(0.501142\pi\)
\(522\) −70.9297 493.727i −0.135881 0.945836i
\(523\) 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
\(525\) 429.303 + 302.198i 0.817720 + 0.575616i
\(526\) 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
\(532\) −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
\(537\) 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
\(546\) −348.981 + 50.3679i −0.639160 + 0.0922490i
\(547\) 400.474 400.474i 0.732129 0.732129i −0.238913 0.971041i \(-0.576791\pi\)
0.971041 + 0.238913i \(0.0767909\pi\)
\(548\) −304.902 + 304.902i −0.556391 + 0.556391i
\(549\) −447.408 + 597.525i −0.814951 + 1.08839i
\(550\) 73.7124 2.11631i 0.134023 0.00384784i
\(551\) 680.588 1.23519
\(552\) −11.6916 + 35.1211i −0.0211805 + 0.0636252i
\(553\) −11.3269 22.5946i −0.0204826 0.0408582i
\(554\) −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
\(560\) −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 \(-0.992612\pi\)
−0.0232074 0.999731i \(-0.507388\pi\)
\(564\) 126.905 + 253.560i 0.225009 + 0.449575i
\(565\) −905.124 + 390.225i −1.60199 + 0.690664i
\(566\) −789.098 −1.39417
\(567\) −386.517 414.842i −0.681687 0.731644i
\(568\) −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 0.903793 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
\(582\) 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 −0.131595 0.991304i \(-0.542010\pi\)
0.991304 + 0.131595i \(0.0420098\pi\)
\(588\) −167.949 241.307i −0.285627 0.410386i
\(589\) 736.271i 1.25004i
\(590\) −318.091 + 137.138i −0.539138 + 0.232438i
\(591\) 36.7023 + 73.3322i 0.0621020 + 0.124082i
\(592\) −146.986 + 146.986i −0.248287 + 0.248287i
\(593\) 615.151 + 615.151i 1.03735 + 1.03735i 0.999275 + 0.0380802i \(0.0121242\pi\)
0.0380802 + 0.999275i \(0.487876\pi\)
\(594\) −78.3743 14.1541i −0.131943 0.0238285i
\(595\) −158.148 + 188.122i −0.265796 + 0.316172i
\(596\) 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 \(0.310057\pi\)
−0.561936 + 0.827180i \(0.689943\pi\)
\(602\) 143.221 + 285.694i 0.237909 + 0.474575i
\(603\) −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 0.750602 0.660755i \(-0.229764\pi\)
−0.660755 + 0.750602i \(0.729764\pi\)
\(608\) 69.4671 + 69.4671i 0.114255 + 0.114255i
\(609\) 814.531 117.560i 1.33749 0.193038i
\(610\) −538.559 + 232.188i −0.882883 + 0.380636i
\(611\) 561.067i 0.918277i
\(612\) −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 \(-0.547067\pi\)
−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
\(627\) 34.3235 103.106i 0.0547423 0.164443i
\(628\) 6.72848 6.72848i 0.0107141 0.0107141i
\(629\) 364.908i 0.580140i
\(630\) −101.139 433.844i −0.160539 0.688642i
\(631\) 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
\(637\) −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 \(-0.958005\pi\)
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 −0.726503 0.687163i \(-0.758856\pi\)
0.687163 + 0.726503i \(0.258856\pi\)
\(644\) −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 −0.715703 0.698405i \(-0.753894\pi\)
0.698405 + 0.715703i \(0.253894\pi\)
\(648\) 201.054 + 109.843i 0.310268 + 0.169511i
\(649\) −102.176 −0.157437
\(650\) −305.210 288.174i −0.469554 0.443344i
\(651\) 127.178 + 881.172i 0.195358 + 1.35357i
\(652\) −210.495 + 210.495i −0.322845 + 0.322845i
\(653\) 319.932 319.932i 0.489941 0.489941i −0.418346 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
\(658\) −418.216 + 209.656i −0.635587 + 0.318626i
\(659\) 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 \(-0.853578\pi\)
0.896053 0.443947i \(-0.146422\pi\)
\(662\) −373.528 373.528i −0.564242 0.564242i
\(663\) 78.9961 237.300i 0.119149 0.357919i
\(664\) 412.464 0.621180
\(665\) 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
\(672\) 95.1378 + 71.1393i 0.141574 + 0.105862i
\(673\) 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 −0.280727 0.959788i \(-0.590575\pi\)
0.959788 + 0.280727i \(0.0905755\pi\)
\(678\) 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 \(-0.997362\pi\)
0.999966 0.00828695i \(-0.00263785\pi\)
\(692\) −423.018 + 423.018i −0.611298 + 0.611298i
\(693\) 23.2687 129.326i 0.0335767 0.186618i
\(694\) 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 \(0.149678\pi\)
−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
\(707\) −81.3022 + 40.7576i −0.114996 + 0.0576486i
\(708\) 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
\(714\) 206.401 29.7895i 0.289077 0.0417220i
\(715\) −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 \(-0.896977\pi\)
0.948079 0.318034i \(-0.103023\pi\)
\(720\) 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 \(-0.836096\pi\)
−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
\(732\) 472.168 + 157.183i 0.645038 + 0.214730i
\(733\) 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
\(735\) 715.697 167.339i 0.973738 0.227672i
\(736\) 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
\(742\) −747.746 + 374.852i −1.00774 + 0.505192i
\(743\) 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
\(756\) −181.015 + 331.840i −0.239438 + 0.438941i
\(757\) 39.6428 39.6428i 0.0523684 0.0523684i −0.680438 0.732806i \(-0.738210\pi\)
0.732806 + 0.680438i \(0.238210\pi\)
\(758\) 127.438 127.438i 0.168124 0.168124i
\(759\) −12.2171 24.4100i −0.0160962 0.0321608i
\(760\) −225.536 + 97.2350i −0.296758 + 0.127941i
\(761\) −1032.38 −1.35661 −0.678307 0.734778i \(-0.737286\pi\)
−0.678307 + 0.734778i \(0.737286\pi\)
\(762\) −595.201 198.139i −0.781103 0.260026i
\(763\) 534.628 + 1066.46i 0.700692 + 1.39772i
\(764\) 326.799 0.427747
\(765\) 307.251 + 73.7783i 0.401635 + 0.0964422i
\(766\) 228.424i 0.298204i
\(767\) 411.259