Properties

Label 210.3.c.a.29.5
Level $210$
Weight $3$
Character 210.29
Analytic conductor $5.722$
Analytic rank $0$
Dimension $24$
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.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 29.5
Character \(\chi\) \(=\) 210.29
Dual form 210.3.c.a.29.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} +(-1.70910 - 2.46556i) q^{3} +2.00000 q^{4} +(-4.99890 - 0.104764i) q^{5} +(2.41703 + 3.48683i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(-3.15796 + 8.42777i) q^{9} +O(q^{10})\) \(q-1.41421 q^{2} +(-1.70910 - 2.46556i) q^{3} +2.00000 q^{4} +(-4.99890 - 0.104764i) q^{5} +(2.41703 + 3.48683i) q^{6} +2.64575i q^{7} -2.82843 q^{8} +(-3.15796 + 8.42777i) q^{9} +(7.06952 + 0.148158i) q^{10} -2.66621i q^{11} +(-3.41820 - 4.93112i) q^{12} +5.56242i q^{13} -3.74166i q^{14} +(8.28532 + 12.5041i) q^{15} +4.00000 q^{16} +18.5525 q^{17} +(4.46603 - 11.9187i) q^{18} +0.634999 q^{19} +(-9.99780 - 0.209527i) q^{20} +(6.52326 - 4.52185i) q^{21} +3.77058i q^{22} +15.6144 q^{23} +(4.83406 + 6.97365i) q^{24} +(24.9780 + 1.04741i) q^{25} -7.86645i q^{26} +(26.1764 - 6.61774i) q^{27} +5.29150i q^{28} +43.3517i q^{29} +(-11.7172 - 17.6835i) q^{30} +13.5411 q^{31} -5.65685 q^{32} +(-6.57369 + 4.55681i) q^{33} -26.2372 q^{34} +(0.277179 - 13.2259i) q^{35} +(-6.31593 + 16.8555i) q^{36} +35.0014i q^{37} -0.898024 q^{38} +(13.7145 - 9.50672i) q^{39} +(14.1390 + 0.296316i) q^{40} -15.6116i q^{41} +(-9.22528 + 6.39486i) q^{42} +64.4699i q^{43} -5.33241i q^{44} +(16.6693 - 41.7987i) q^{45} -22.0820 q^{46} +52.5576 q^{47} +(-6.83639 - 9.86224i) q^{48} -7.00000 q^{49} +(-35.3243 - 1.48126i) q^{50} +(-31.7081 - 45.7423i) q^{51} +11.1248i q^{52} -51.6056 q^{53} +(-37.0191 + 9.35890i) q^{54} +(-0.279321 + 13.3281i) q^{55} -7.48331i q^{56} +(-1.08528 - 1.56563i) q^{57} -61.3086i q^{58} -32.9384i q^{59} +(16.5706 + 25.0083i) q^{60} -104.197 q^{61} -19.1501 q^{62} +(-22.2978 - 8.35519i) q^{63} +8.00000 q^{64} +(0.582739 - 27.8060i) q^{65} +(9.29660 - 6.44430i) q^{66} +113.588i q^{67} +37.1050 q^{68} +(-26.6865 - 38.4981i) q^{69} +(-0.391990 + 18.7042i) q^{70} +36.8746i q^{71} +(8.93207 - 23.8373i) q^{72} -144.926i q^{73} -49.4995i q^{74} +(-40.1075 - 63.3750i) q^{75} +1.27000 q^{76} +7.05412 q^{77} +(-19.3952 + 13.4445i) q^{78} +57.9487 q^{79} +(-19.9956 - 0.419055i) q^{80} +(-61.0545 - 53.2292i) q^{81} +22.0781i q^{82} -45.0936 q^{83} +(13.0465 - 9.04370i) q^{84} +(-92.7422 - 1.94363i) q^{85} -91.1742i q^{86} +(106.886 - 74.0924i) q^{87} +7.54117i q^{88} +80.9733i q^{89} +(-23.5739 + 59.1124i) q^{90} -14.7168 q^{91} +31.2287 q^{92} +(-23.1432 - 33.3865i) q^{93} -74.3277 q^{94} +(-3.17430 - 0.0665248i) q^{95} +(9.66812 + 13.9473i) q^{96} +96.2255i q^{97} +9.89949 q^{98} +(22.4702 + 8.41978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 48 q^{4} + 44 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 48 q^{4} + 44 q^{9} + 16 q^{10} + 4 q^{15} + 96 q^{16} - 80 q^{19} - 28 q^{21} + 48 q^{25} - 56 q^{30} + 224 q^{31} + 128 q^{34} + 88 q^{36} - 92 q^{39} + 32 q^{40} - 72 q^{45} - 144 q^{46} - 168 q^{49} - 284 q^{51} - 144 q^{54} - 320 q^{55} + 8 q^{60} + 192 q^{64} + 224 q^{66} - 152 q^{69} - 56 q^{70} + 48 q^{75} - 160 q^{76} - 72 q^{79} - 212 q^{81} - 56 q^{84} - 64 q^{85} - 240 q^{90} + 168 q^{91} - 128 q^{94} - 876 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −0.707107
\(3\) −1.70910 2.46556i −0.569700 0.821853i
\(4\) 2.00000 0.500000
\(5\) −4.99890 0.104764i −0.999780 0.0209527i
\(6\) 2.41703 + 3.48683i 0.402838 + 0.581138i
\(7\) 2.64575i 0.377964i
\(8\) −2.82843 −0.353553
\(9\) −3.15796 + 8.42777i −0.350885 + 0.936419i
\(10\) 7.06952 + 0.148158i 0.706952 + 0.0148158i
\(11\) 2.66621i 0.242382i −0.992629 0.121191i \(-0.961329\pi\)
0.992629 0.121191i \(-0.0386714\pi\)
\(12\) −3.41820 4.93112i −0.284850 0.410927i
\(13\) 5.56242i 0.427878i 0.976847 + 0.213939i \(0.0686294\pi\)
−0.976847 + 0.213939i \(0.931371\pi\)
\(14\) 3.74166i 0.267261i
\(15\) 8.28532 + 12.5041i 0.552354 + 0.833609i
\(16\) 4.00000 0.250000
\(17\) 18.5525 1.09132 0.545662 0.838005i \(-0.316278\pi\)
0.545662 + 0.838005i \(0.316278\pi\)
\(18\) 4.46603 11.9187i 0.248113 0.662148i
\(19\) 0.634999 0.0334210 0.0167105 0.999860i \(-0.494681\pi\)
0.0167105 + 0.999860i \(0.494681\pi\)
\(20\) −9.99780 0.209527i −0.499890 0.0104764i
\(21\) 6.52326 4.52185i 0.310631 0.215326i
\(22\) 3.77058i 0.171390i
\(23\) 15.6144 0.678885 0.339442 0.940627i \(-0.389762\pi\)
0.339442 + 0.940627i \(0.389762\pi\)
\(24\) 4.83406 + 6.97365i 0.201419 + 0.290569i
\(25\) 24.9780 + 1.04741i 0.999122 + 0.0418963i
\(26\) 7.86645i 0.302556i
\(27\) 26.1764 6.61774i 0.969497 0.245101i
\(28\) 5.29150i 0.188982i
\(29\) 43.3517i 1.49489i 0.664325 + 0.747444i \(0.268719\pi\)
−0.664325 + 0.747444i \(0.731281\pi\)
\(30\) −11.7172 17.6835i −0.390574 0.589451i
\(31\) 13.5411 0.436811 0.218406 0.975858i \(-0.429914\pi\)
0.218406 + 0.975858i \(0.429914\pi\)
\(32\) −5.65685 −0.176777
\(33\) −6.57369 + 4.55681i −0.199203 + 0.138085i
\(34\) −26.2372 −0.771683
\(35\) 0.277179 13.2259i 0.00791939 0.377881i
\(36\) −6.31593 + 16.8555i −0.175442 + 0.468209i
\(37\) 35.0014i 0.945984i 0.881067 + 0.472992i \(0.156826\pi\)
−0.881067 + 0.472992i \(0.843174\pi\)
\(38\) −0.898024 −0.0236322
\(39\) 13.7145 9.50672i 0.351653 0.243762i
\(40\) 14.1390 + 0.296316i 0.353476 + 0.00740791i
\(41\) 15.6116i 0.380770i −0.981710 0.190385i \(-0.939026\pi\)
0.981710 0.190385i \(-0.0609736\pi\)
\(42\) −9.22528 + 6.39486i −0.219649 + 0.152259i
\(43\) 64.4699i 1.49930i 0.661835 + 0.749650i \(0.269778\pi\)
−0.661835 + 0.749650i \(0.730222\pi\)
\(44\) 5.33241i 0.121191i
\(45\) 16.6693 41.7987i 0.370428 0.928861i
\(46\) −22.0820 −0.480044
\(47\) 52.5576 1.11825 0.559124 0.829084i \(-0.311138\pi\)
0.559124 + 0.829084i \(0.311138\pi\)
\(48\) −6.83639 9.86224i −0.142425 0.205463i
\(49\) −7.00000 −0.142857
\(50\) −35.3243 1.48126i −0.706486 0.0296251i
\(51\) −31.7081 45.7423i −0.621727 0.896908i
\(52\) 11.1248i 0.213939i
\(53\) −51.6056 −0.973691 −0.486846 0.873488i \(-0.661853\pi\)
−0.486846 + 0.873488i \(0.661853\pi\)
\(54\) −37.0191 + 9.35890i −0.685538 + 0.173313i
\(55\) −0.279321 + 13.3281i −0.00507857 + 0.242329i
\(56\) 7.48331i 0.133631i
\(57\) −1.08528 1.56563i −0.0190399 0.0274672i
\(58\) 61.3086i 1.05705i
\(59\) 32.9384i 0.558277i −0.960251 0.279139i \(-0.909951\pi\)
0.960251 0.279139i \(-0.0900489\pi\)
\(60\) 16.5706 + 25.0083i 0.276177 + 0.416805i
\(61\) −104.197 −1.70815 −0.854077 0.520147i \(-0.825877\pi\)
−0.854077 + 0.520147i \(0.825877\pi\)
\(62\) −19.1501 −0.308872
\(63\) −22.2978 8.35519i −0.353933 0.132622i
\(64\) 8.00000 0.125000
\(65\) 0.582739 27.8060i 0.00896522 0.427784i
\(66\) 9.29660 6.44430i 0.140858 0.0976409i
\(67\) 113.588i 1.69535i 0.530519 + 0.847673i \(0.321997\pi\)
−0.530519 + 0.847673i \(0.678003\pi\)
\(68\) 37.1050 0.545662
\(69\) −26.6865 38.4981i −0.386760 0.557944i
\(70\) −0.391990 + 18.7042i −0.00559985 + 0.267203i
\(71\) 36.8746i 0.519361i 0.965695 + 0.259680i \(0.0836172\pi\)
−0.965695 + 0.259680i \(0.916383\pi\)
\(72\) 8.93207 23.8373i 0.124057 0.331074i
\(73\) 144.926i 1.98529i −0.121058 0.992645i \(-0.538629\pi\)
0.121058 0.992645i \(-0.461371\pi\)
\(74\) 49.4995i 0.668912i
\(75\) −40.1075 63.3750i −0.534767 0.845000i
\(76\) 1.27000 0.0167105
\(77\) 7.05412 0.0916119
\(78\) −19.3952 + 13.4445i −0.248656 + 0.172366i
\(79\) 57.9487 0.733528 0.366764 0.930314i \(-0.380466\pi\)
0.366764 + 0.930314i \(0.380466\pi\)
\(80\) −19.9956 0.419055i −0.249945 0.00523818i
\(81\) −61.0545 53.2292i −0.753760 0.657150i
\(82\) 22.0781i 0.269245i
\(83\) −45.0936 −0.543296 −0.271648 0.962397i \(-0.587569\pi\)
−0.271648 + 0.962397i \(0.587569\pi\)
\(84\) 13.0465 9.04370i 0.155316 0.107663i
\(85\) −92.7422 1.94363i −1.09109 0.0228662i
\(86\) 91.1742i 1.06016i
\(87\) 106.886 74.0924i 1.22858 0.851637i
\(88\) 7.54117i 0.0856951i
\(89\) 80.9733i 0.909813i 0.890539 + 0.454906i \(0.150327\pi\)
−0.890539 + 0.454906i \(0.849673\pi\)
\(90\) −23.5739 + 59.1124i −0.261932 + 0.656804i
\(91\) −14.7168 −0.161723
\(92\) 31.2287 0.339442
\(93\) −23.1432 33.3865i −0.248851 0.358995i
\(94\) −74.3277 −0.790720
\(95\) −3.17430 0.0665248i −0.0334137 0.000700261i
\(96\) 9.66812 + 13.9473i 0.100710 + 0.145284i
\(97\) 96.2255i 0.992016i 0.868318 + 0.496008i \(0.165201\pi\)
−0.868318 + 0.496008i \(0.834799\pi\)
\(98\) 9.89949 0.101015
\(99\) 22.4702 + 8.41978i 0.226971 + 0.0850483i
\(100\) 49.9561 + 2.09481i 0.499561 + 0.0209481i
\(101\) 91.9696i 0.910590i 0.890341 + 0.455295i \(0.150466\pi\)
−0.890341 + 0.455295i \(0.849534\pi\)
\(102\) 44.8420 + 64.6894i 0.439627 + 0.634210i
\(103\) 30.6043i 0.297129i 0.988903 + 0.148565i \(0.0474653\pi\)
−0.988903 + 0.148565i \(0.952535\pi\)
\(104\) 15.7329i 0.151278i
\(105\) −33.0828 + 21.9209i −0.315075 + 0.208770i
\(106\) 72.9814 0.688504
\(107\) 190.645 1.78173 0.890864 0.454270i \(-0.150100\pi\)
0.890864 + 0.454270i \(0.150100\pi\)
\(108\) 52.3529 13.2355i 0.484749 0.122551i
\(109\) 73.9965 0.678867 0.339433 0.940630i \(-0.389765\pi\)
0.339433 + 0.940630i \(0.389765\pi\)
\(110\) 0.395020 18.8488i 0.00359109 0.171353i
\(111\) 86.2980 59.8208i 0.777460 0.538927i
\(112\) 10.5830i 0.0944911i
\(113\) −128.861 −1.14037 −0.570183 0.821518i \(-0.693128\pi\)
−0.570183 + 0.821518i \(0.693128\pi\)
\(114\) 1.53481 + 2.21413i 0.0134633 + 0.0194222i
\(115\) −78.0546 1.63582i −0.678736 0.0142245i
\(116\) 86.7035i 0.747444i
\(117\) −46.8788 17.5659i −0.400673 0.150136i
\(118\) 46.5819i 0.394762i
\(119\) 49.0853i 0.412482i
\(120\) −23.4344 35.3671i −0.195287 0.294725i
\(121\) 113.891 0.941251
\(122\) 147.357 1.20785
\(123\) −38.4912 + 26.6817i −0.312937 + 0.216924i
\(124\) 27.0823 0.218406
\(125\) −124.753 7.85267i −0.998025 0.0628214i
\(126\) 31.5338 + 11.8160i 0.250268 + 0.0937779i
\(127\) 95.8035i 0.754358i 0.926140 + 0.377179i \(0.123106\pi\)
−0.926140 + 0.377179i \(0.876894\pi\)
\(128\) −11.3137 −0.0883883
\(129\) 158.954 110.185i 1.23220 0.854150i
\(130\) −0.824118 + 39.3236i −0.00633937 + 0.302489i
\(131\) 148.465i 1.13332i 0.823952 + 0.566660i \(0.191765\pi\)
−0.823952 + 0.566660i \(0.808235\pi\)
\(132\) −13.1474 + 9.11361i −0.0996013 + 0.0690425i
\(133\) 1.68005i 0.0126320i
\(134\) 160.638i 1.19879i
\(135\) −131.547 + 30.3391i −0.974420 + 0.224734i
\(136\) −52.4744 −0.385842
\(137\) −115.295 −0.841572 −0.420786 0.907160i \(-0.638246\pi\)
−0.420786 + 0.907160i \(0.638246\pi\)
\(138\) 37.7404 + 54.4445i 0.273481 + 0.394526i
\(139\) 95.1005 0.684176 0.342088 0.939668i \(-0.388866\pi\)
0.342088 + 0.939668i \(0.388866\pi\)
\(140\) 0.554357 26.4517i 0.00395969 0.188941i
\(141\) −89.8262 129.584i −0.637065 0.919035i
\(142\) 52.1486i 0.367244i
\(143\) 14.8305 0.103710
\(144\) −12.6319 + 33.7111i −0.0877212 + 0.234105i
\(145\) 4.54169 216.711i 0.0313220 1.49456i
\(146\) 204.957i 1.40381i
\(147\) 11.9637 + 17.2589i 0.0813857 + 0.117408i
\(148\) 70.0028i 0.472992i
\(149\) 179.342i 1.20364i 0.798632 + 0.601820i \(0.205558\pi\)
−0.798632 + 0.601820i \(0.794442\pi\)
\(150\) 56.7206 + 89.6258i 0.378137 + 0.597505i
\(151\) 45.6621 0.302398 0.151199 0.988503i \(-0.451687\pi\)
0.151199 + 0.988503i \(0.451687\pi\)
\(152\) −1.79605 −0.0118161
\(153\) −58.5882 + 156.356i −0.382929 + 1.02194i
\(154\) −9.97603 −0.0647794
\(155\) −67.6909 1.41862i −0.436715 0.00915238i
\(156\) 27.4289 19.0134i 0.175827 0.121881i
\(157\) 223.977i 1.42661i −0.700856 0.713303i \(-0.747198\pi\)
0.700856 0.713303i \(-0.252802\pi\)
\(158\) −81.9518 −0.518683
\(159\) 88.1991 + 127.237i 0.554711 + 0.800231i
\(160\) 28.2781 + 0.592633i 0.176738 + 0.00370395i
\(161\) 41.3117i 0.256594i
\(162\) 86.3441 + 75.2774i 0.532989 + 0.464675i
\(163\) 300.309i 1.84239i −0.389102 0.921195i \(-0.627215\pi\)
0.389102 0.921195i \(-0.372785\pi\)
\(164\) 31.2231i 0.190385i
\(165\) 33.3386 22.0904i 0.202052 0.133881i
\(166\) 63.7719 0.384168
\(167\) 125.443 0.751158 0.375579 0.926790i \(-0.377444\pi\)
0.375579 + 0.926790i \(0.377444\pi\)
\(168\) −18.4506 + 12.7897i −0.109825 + 0.0761293i
\(169\) 138.060 0.816920
\(170\) 131.157 + 2.74871i 0.771514 + 0.0161689i
\(171\) −2.00530 + 5.35163i −0.0117269 + 0.0312961i
\(172\) 128.940i 0.749650i
\(173\) 195.635 1.13084 0.565419 0.824804i \(-0.308714\pi\)
0.565419 + 0.824804i \(0.308714\pi\)
\(174\) −151.160 + 104.782i −0.868736 + 0.602198i
\(175\) −2.77118 + 66.0857i −0.0158353 + 0.377633i
\(176\) 10.6648i 0.0605956i
\(177\) −81.2115 + 56.2949i −0.458822 + 0.318050i
\(178\) 114.514i 0.643335i
\(179\) 164.110i 0.916815i −0.888742 0.458408i \(-0.848420\pi\)
0.888742 0.458408i \(-0.151580\pi\)
\(180\) 33.3386 83.5975i 0.185214 0.464431i
\(181\) 113.029 0.624468 0.312234 0.950005i \(-0.398923\pi\)
0.312234 + 0.950005i \(0.398923\pi\)
\(182\) 20.8127 0.114355
\(183\) 178.084 + 256.905i 0.973135 + 1.40385i
\(184\) −44.1641 −0.240022
\(185\) 3.66687 174.969i 0.0198209 0.945776i
\(186\) 32.7294 + 47.2156i 0.175964 + 0.253847i
\(187\) 49.4648i 0.264518i
\(188\) 105.115 0.559124
\(189\) 17.5089 + 69.2563i 0.0926397 + 0.366436i
\(190\) 4.48914 + 0.0940803i 0.0236270 + 0.000495160i
\(191\) 196.398i 1.02826i 0.857711 + 0.514132i \(0.171886\pi\)
−0.857711 + 0.514132i \(0.828114\pi\)
\(192\) −13.6728 19.7245i −0.0712124 0.102732i
\(193\) 282.304i 1.46272i −0.681994 0.731358i \(-0.738887\pi\)
0.681994 0.731358i \(-0.261113\pi\)
\(194\) 136.083i 0.701461i
\(195\) −69.5533 + 46.0864i −0.356683 + 0.236340i
\(196\) −14.0000 −0.0714286
\(197\) −286.761 −1.45564 −0.727821 0.685767i \(-0.759467\pi\)
−0.727821 + 0.685767i \(0.759467\pi\)
\(198\) −31.7776 11.9074i −0.160493 0.0601382i
\(199\) −74.9133 −0.376449 −0.188224 0.982126i \(-0.560273\pi\)
−0.188224 + 0.982126i \(0.560273\pi\)
\(200\) −70.6486 2.96251i −0.353243 0.0148126i
\(201\) 280.058 194.133i 1.39333 0.965838i
\(202\) 130.065i 0.643884i
\(203\) −114.698 −0.565014
\(204\) −63.4162 91.4847i −0.310864 0.448454i
\(205\) −1.63552 + 78.0406i −0.00797816 + 0.380686i
\(206\) 43.2810i 0.210102i
\(207\) −49.3096 + 131.594i −0.238210 + 0.635720i
\(208\) 22.2497i 0.106970i
\(209\) 1.69304i 0.00810066i
\(210\) 46.7862 31.0008i 0.222791 0.147623i
\(211\) −136.746 −0.648083 −0.324042 0.946043i \(-0.605042\pi\)
−0.324042 + 0.946043i \(0.605042\pi\)
\(212\) −103.211 −0.486846
\(213\) 90.9166 63.0224i 0.426838 0.295880i
\(214\) −269.613 −1.25987
\(215\) 6.75410 322.279i 0.0314144 1.49897i
\(216\) −74.0381 + 18.7178i −0.342769 + 0.0866565i
\(217\) 35.8265i 0.165099i
\(218\) −104.647 −0.480031
\(219\) −357.324 + 247.693i −1.63162 + 1.13102i
\(220\) −0.558643 + 26.6562i −0.00253929 + 0.121165i
\(221\) 103.197i 0.466954i
\(222\) −122.044 + 84.5994i −0.549747 + 0.381079i
\(223\) 25.8662i 0.115992i 0.998317 + 0.0579959i \(0.0184710\pi\)
−0.998317 + 0.0579959i \(0.981529\pi\)
\(224\) 14.9666i 0.0668153i
\(225\) −87.7071 + 207.202i −0.389809 + 0.920896i
\(226\) 182.238 0.806361
\(227\) 24.3393 0.107222 0.0536109 0.998562i \(-0.482927\pi\)
0.0536109 + 0.998562i \(0.482927\pi\)
\(228\) −2.17055 3.13126i −0.00951997 0.0137336i
\(229\) −241.018 −1.05248 −0.526239 0.850336i \(-0.676398\pi\)
−0.526239 + 0.850336i \(0.676398\pi\)
\(230\) 110.386 + 2.31339i 0.479939 + 0.0100582i
\(231\) −12.0562 17.3923i −0.0521913 0.0752915i
\(232\) 122.617i 0.528523i
\(233\) 24.9582 0.107117 0.0535584 0.998565i \(-0.482944\pi\)
0.0535584 + 0.998565i \(0.482944\pi\)
\(234\) 66.2966 + 24.8420i 0.283319 + 0.106162i
\(235\) −262.731 5.50613i −1.11800 0.0234303i
\(236\) 65.8767i 0.279139i
\(237\) −99.0401 142.876i −0.417891 0.602852i
\(238\) 69.4172i 0.291669i
\(239\) 240.780i 1.00745i −0.863864 0.503725i \(-0.831963\pi\)
0.863864 0.503725i \(-0.168037\pi\)
\(240\) 33.1413 + 50.0166i 0.138089 + 0.208402i
\(241\) −147.382 −0.611543 −0.305771 0.952105i \(-0.598914\pi\)
−0.305771 + 0.952105i \(0.598914\pi\)
\(242\) −161.067 −0.665565
\(243\) −26.8914 + 241.507i −0.110664 + 0.993858i
\(244\) −208.395 −0.854077
\(245\) 34.9923 + 0.733345i 0.142826 + 0.00299325i
\(246\) 54.4348 37.7336i 0.221280 0.153389i
\(247\) 3.53213i 0.0143001i
\(248\) −38.3001 −0.154436
\(249\) 77.0693 + 111.181i 0.309515 + 0.446509i
\(250\) 176.428 + 11.1054i 0.705710 + 0.0444214i
\(251\) 387.525i 1.54393i −0.635668 0.771963i \(-0.719275\pi\)
0.635668 0.771963i \(-0.280725\pi\)
\(252\) −44.5956 16.7104i −0.176966 0.0663110i
\(253\) 41.6311i 0.164550i
\(254\) 135.487i 0.533412i
\(255\) 153.713 + 231.983i 0.602798 + 0.909738i
\(256\) 16.0000 0.0625000
\(257\) −11.2525 −0.0437839 −0.0218919 0.999760i \(-0.506969\pi\)
−0.0218919 + 0.999760i \(0.506969\pi\)
\(258\) −224.795 + 155.826i −0.871300 + 0.603975i
\(259\) −92.6050 −0.357548
\(260\) 1.16548 55.6120i 0.00448261 0.213892i
\(261\) −365.358 136.903i −1.39984 0.524533i
\(262\) 209.961i 0.801378i
\(263\) 308.658 1.17361 0.586803 0.809730i \(-0.300386\pi\)
0.586803 + 0.809730i \(0.300386\pi\)
\(264\) 18.5932 12.8886i 0.0704288 0.0488204i
\(265\) 257.971 + 5.40639i 0.973477 + 0.0204015i
\(266\) 2.37595i 0.00893214i
\(267\) 199.644 138.391i 0.747732 0.518320i
\(268\) 227.176i 0.847673i
\(269\) 198.926i 0.739503i −0.929131 0.369751i \(-0.879443\pi\)
0.929131 0.369751i \(-0.120557\pi\)
\(270\) 186.035 42.9060i 0.689019 0.158911i
\(271\) −176.341 −0.650706 −0.325353 0.945593i \(-0.605483\pi\)
−0.325353 + 0.945593i \(0.605483\pi\)
\(272\) 74.2101 0.272831
\(273\) 25.1524 + 36.2851i 0.0921334 + 0.132912i
\(274\) 163.052 0.595082
\(275\) 2.79260 66.5966i 0.0101549 0.242169i
\(276\) −53.3729 76.9962i −0.193380 0.278972i
\(277\) 433.093i 1.56351i 0.623583 + 0.781757i \(0.285676\pi\)
−0.623583 + 0.781757i \(0.714324\pi\)
\(278\) −134.492 −0.483786
\(279\) −42.7624 + 114.122i −0.153270 + 0.409038i
\(280\) −0.783979 + 37.4084i −0.00279993 + 0.133601i
\(281\) 281.134i 1.00048i 0.865887 + 0.500239i \(0.166754\pi\)
−0.865887 + 0.500239i \(0.833246\pi\)
\(282\) 127.033 + 183.259i 0.450473 + 0.649856i
\(283\) 113.795i 0.402101i 0.979581 + 0.201050i \(0.0644355\pi\)
−0.979581 + 0.201050i \(0.935565\pi\)
\(284\) 73.7492i 0.259680i
\(285\) 5.26117 + 7.94012i 0.0184602 + 0.0278601i
\(286\) −20.9736 −0.0733341
\(287\) 41.3043 0.143917
\(288\) 17.8641 47.6747i 0.0620283 0.165537i
\(289\) 55.1959 0.190989
\(290\) −6.42291 + 306.476i −0.0221480 + 1.05681i
\(291\) 237.250 164.459i 0.815291 0.565151i
\(292\) 289.852i 0.992645i
\(293\) 355.330 1.21273 0.606365 0.795187i \(-0.292627\pi\)
0.606365 + 0.795187i \(0.292627\pi\)
\(294\) −16.9192 24.4078i −0.0575483 0.0830197i
\(295\) −3.45074 + 164.656i −0.0116974 + 0.558155i
\(296\) 98.9989i 0.334456i
\(297\) −17.6443 69.7917i −0.0594083 0.234989i
\(298\) 253.628i 0.851102i
\(299\) 86.8535i 0.290480i
\(300\) −80.2150 126.750i −0.267383 0.422500i
\(301\) −170.571 −0.566682
\(302\) −64.5759 −0.213828
\(303\) 226.756 157.185i 0.748371 0.518763i
\(304\) 2.54000 0.00835525
\(305\) 520.873 + 10.9161i 1.70778 + 0.0357905i
\(306\) 82.8562 221.121i 0.270772 0.722618i
\(307\) 404.490i 1.31756i −0.752337 0.658778i \(-0.771074\pi\)
0.752337 0.658778i \(-0.228926\pi\)
\(308\) 14.1082 0.0458059
\(309\) 75.4567 52.3058i 0.244196 0.169274i
\(310\) 95.7293 + 2.00623i 0.308804 + 0.00647171i
\(311\) 530.330i 1.70524i 0.522530 + 0.852621i \(0.324988\pi\)
−0.522530 + 0.852621i \(0.675012\pi\)
\(312\) −38.7904 + 26.8891i −0.124328 + 0.0861829i
\(313\) 561.172i 1.79288i 0.443165 + 0.896440i \(0.353856\pi\)
−0.443165 + 0.896440i \(0.646144\pi\)
\(314\) 316.751i 1.00876i
\(315\) 110.589 + 44.1028i 0.351076 + 0.140009i
\(316\) 115.897 0.366764
\(317\) −264.560 −0.834574 −0.417287 0.908775i \(-0.637019\pi\)
−0.417287 + 0.908775i \(0.637019\pi\)
\(318\) −124.732 179.940i −0.392240 0.565849i
\(319\) 115.585 0.362334
\(320\) −39.9912 0.838109i −0.124973 0.00261909i
\(321\) −325.831 470.046i −1.01505 1.46432i
\(322\) 58.4236i 0.181440i
\(323\) 11.7808 0.0364732
\(324\) −122.109 106.458i −0.376880 0.328575i
\(325\) −5.82611 + 138.938i −0.0179265 + 0.427503i
\(326\) 424.702i 1.30277i
\(327\) −126.467 182.443i −0.386750 0.557929i
\(328\) 44.1561i 0.134622i
\(329\) 139.054i 0.422658i
\(330\) −47.1479 + 31.2405i −0.142872 + 0.0946681i
\(331\) 540.436 1.63274 0.816369 0.577530i \(-0.195984\pi\)
0.816369 + 0.577530i \(0.195984\pi\)
\(332\) −90.1871 −0.271648
\(333\) −294.984 110.533i −0.885837 0.331931i
\(334\) −177.404 −0.531149
\(335\) 11.8999 567.816i 0.0355221 1.69497i
\(336\) 26.0930 18.0874i 0.0776578 0.0538315i
\(337\) 444.323i 1.31847i −0.751939 0.659233i \(-0.770881\pi\)
0.751939 0.659233i \(-0.229119\pi\)
\(338\) −195.246 −0.577650
\(339\) 220.237 + 317.715i 0.649666 + 0.937214i
\(340\) −185.484 3.88726i −0.545543 0.0114331i
\(341\) 36.1035i 0.105875i
\(342\) 2.83593 7.56834i 0.00829219 0.0221297i
\(343\) 18.5203i 0.0539949i
\(344\) 182.348i 0.530082i
\(345\) 129.370 + 195.244i 0.374985 + 0.565925i
\(346\) −276.670 −0.799624
\(347\) −253.956 −0.731861 −0.365931 0.930642i \(-0.619249\pi\)
−0.365931 + 0.930642i \(0.619249\pi\)
\(348\) 213.773 148.185i 0.614289 0.425818i
\(349\) 415.627 1.19091 0.595454 0.803389i \(-0.296972\pi\)
0.595454 + 0.803389i \(0.296972\pi\)
\(350\) 3.91904 93.4593i 0.0111972 0.267027i
\(351\) 36.8106 + 145.604i 0.104874 + 0.414827i
\(352\) 15.0823i 0.0428475i
\(353\) −278.041 −0.787652 −0.393826 0.919185i \(-0.628849\pi\)
−0.393826 + 0.919185i \(0.628849\pi\)
\(354\) 114.850 79.6130i 0.324436 0.224895i
\(355\) 3.86312 184.333i 0.0108820 0.519247i
\(356\) 161.947i 0.454906i
\(357\) 121.023 83.8917i 0.339000 0.234991i
\(358\) 232.086i 0.648286i
\(359\) 81.6150i 0.227340i −0.993519 0.113670i \(-0.963739\pi\)
0.993519 0.113670i \(-0.0362606\pi\)
\(360\) −47.1478 + 118.225i −0.130966 + 0.328402i
\(361\) −360.597 −0.998883
\(362\) −159.847 −0.441565
\(363\) −194.652 280.806i −0.536230 0.773570i
\(364\) −29.4335 −0.0808614
\(365\) −15.1830 + 724.472i −0.0415973 + 1.98485i
\(366\) −251.848 363.318i −0.688110 0.992673i
\(367\) 514.501i 1.40191i 0.713206 + 0.700955i \(0.247242\pi\)
−0.713206 + 0.700955i \(0.752758\pi\)
\(368\) 62.4574 0.169721
\(369\) 131.571 + 49.3007i 0.356560 + 0.133606i
\(370\) −5.18574 + 247.443i −0.0140155 + 0.668765i
\(371\) 136.536i 0.368021i
\(372\) −46.2863 66.7730i −0.124426 0.179497i
\(373\) 80.1359i 0.214842i −0.994214 0.107421i \(-0.965741\pi\)
0.994214 0.107421i \(-0.0342592\pi\)
\(374\) 69.9538i 0.187042i
\(375\) 193.854 + 321.007i 0.516944 + 0.856019i
\(376\) −148.655 −0.395360
\(377\) −241.140 −0.639630
\(378\) −24.7613 97.9432i −0.0655061 0.259109i
\(379\) 706.877 1.86511 0.932556 0.361026i \(-0.117573\pi\)
0.932556 + 0.361026i \(0.117573\pi\)
\(380\) −6.34860 0.133050i −0.0167068 0.000350131i
\(381\) 236.209 163.738i 0.619972 0.429758i
\(382\) 277.749i 0.727092i
\(383\) 49.2802 0.128669 0.0643345 0.997928i \(-0.479508\pi\)
0.0643345 + 0.997928i \(0.479508\pi\)
\(384\) 19.3362 + 27.8946i 0.0503548 + 0.0726422i
\(385\) −35.2628 0.739015i −0.0915918 0.00191952i
\(386\) 399.238i 1.03430i
\(387\) −543.337 203.594i −1.40397 0.526081i
\(388\) 192.451i 0.496008i
\(389\) 2.68340i 0.00689821i 0.999994 + 0.00344911i \(0.00109789\pi\)
−0.999994 + 0.00344911i \(0.998902\pi\)
\(390\) 98.3632 65.1760i 0.252213 0.167118i
\(391\) 289.686 0.740884
\(392\) 19.7990 0.0505076
\(393\) 366.049 253.741i 0.931423 0.645652i
\(394\) 405.542 1.02929
\(395\) −289.680 6.07092i −0.733367 0.0153694i
\(396\) 44.9403 + 16.8396i 0.113486 + 0.0425241i
\(397\) 372.015i 0.937065i 0.883446 + 0.468532i \(0.155217\pi\)
−0.883446 + 0.468532i \(0.844783\pi\)
\(398\) 105.943 0.266190
\(399\) 4.14226 2.87137i 0.0103816 0.00719642i
\(400\) 99.9122 + 4.18963i 0.249780 + 0.0104741i
\(401\) 119.122i 0.297062i 0.988908 + 0.148531i \(0.0474545\pi\)
−0.988908 + 0.148531i \(0.952545\pi\)
\(402\) −396.062 + 274.546i −0.985230 + 0.682950i
\(403\) 75.3215i 0.186902i
\(404\) 183.939i 0.455295i
\(405\) 299.629 + 272.484i 0.739825 + 0.672799i
\(406\) 162.207 0.399525
\(407\) 93.3209 0.229290
\(408\) 89.6840 + 129.379i 0.219814 + 0.317105i
\(409\) 198.033 0.484189 0.242095 0.970253i \(-0.422166\pi\)
0.242095 + 0.970253i \(0.422166\pi\)
\(410\) 2.31298 110.366i 0.00564141 0.269186i
\(411\) 197.051 + 284.268i 0.479443 + 0.691649i
\(412\) 61.2086i 0.148565i
\(413\) 87.1467 0.211009
\(414\) 69.7342 186.102i 0.168440 0.449522i
\(415\) 225.418 + 4.72416i 0.543177 + 0.0113835i
\(416\) 31.4658i 0.0756389i
\(417\) −162.536 234.476i −0.389775 0.562292i
\(418\) 2.39432i 0.00572803i
\(419\) 229.736i 0.548295i 0.961688 + 0.274148i \(0.0883957\pi\)
−0.961688 + 0.274148i \(0.911604\pi\)
\(420\) −66.1657 + 43.8418i −0.157537 + 0.104385i
\(421\) −590.500 −1.40261 −0.701306 0.712860i \(-0.747399\pi\)
−0.701306 + 0.712860i \(0.747399\pi\)
\(422\) 193.387 0.458264
\(423\) −165.975 + 442.944i −0.392376 + 1.04715i
\(424\) 145.963 0.344252
\(425\) 463.406 + 19.4320i 1.09037 + 0.0457224i
\(426\) −128.575 + 89.1271i −0.301820 + 0.209219i
\(427\) 275.680i 0.645622i
\(428\) 381.290 0.890864
\(429\) −25.3469 36.5656i −0.0590836 0.0852345i
\(430\) −9.55174 + 455.771i −0.0222133 + 1.05993i
\(431\) 414.879i 0.962597i −0.876557 0.481298i \(-0.840165\pi\)
0.876557 0.481298i \(-0.159835\pi\)
\(432\) 104.706 26.4710i 0.242374 0.0612754i
\(433\) 219.764i 0.507538i 0.967265 + 0.253769i \(0.0816703\pi\)
−0.967265 + 0.253769i \(0.918330\pi\)
\(434\) 50.6663i 0.116743i
\(435\) −542.076 + 359.183i −1.24615 + 0.825708i
\(436\) 147.993 0.339433
\(437\) 9.91510 0.0226890
\(438\) 505.333 350.291i 1.15373 0.799751i
\(439\) −638.375 −1.45416 −0.727079 0.686554i \(-0.759123\pi\)
−0.727079 + 0.686554i \(0.759123\pi\)
\(440\) 0.790040 37.6976i 0.00179555 0.0856763i
\(441\) 22.1057 58.9944i 0.0501264 0.133774i
\(442\) 145.942i 0.330186i
\(443\) −299.160 −0.675305 −0.337652 0.941271i \(-0.609633\pi\)
−0.337652 + 0.941271i \(0.609633\pi\)
\(444\) 172.596 119.642i 0.388730 0.269463i
\(445\) 8.48306 404.778i 0.0190631 0.909613i
\(446\) 36.5803i 0.0820185i
\(447\) 442.179 306.514i 0.989216 0.685713i
\(448\) 21.1660i 0.0472456i
\(449\) 580.653i 1.29321i −0.762823 0.646607i \(-0.776187\pi\)
0.762823 0.646607i \(-0.223813\pi\)
\(450\) 124.037 293.027i 0.275637 0.651172i
\(451\) −41.6236 −0.0922918
\(452\) −257.723 −0.570183
\(453\) −78.0410 112.583i −0.172276 0.248527i
\(454\) −34.4210 −0.0758172
\(455\) 73.5677 + 1.54178i 0.161687 + 0.00338853i
\(456\) 3.06962 + 4.42826i 0.00673163 + 0.00971111i
\(457\) 563.314i 1.23264i 0.787498 + 0.616318i \(0.211376\pi\)
−0.787498 + 0.616318i \(0.788624\pi\)
\(458\) 340.850 0.744215
\(459\) 485.639 122.776i 1.05804 0.267485i
\(460\) −156.109 3.27163i −0.339368 0.00711224i
\(461\) 138.227i 0.299842i 0.988698 + 0.149921i \(0.0479020\pi\)
−0.988698 + 0.149921i \(0.952098\pi\)
\(462\) 17.0500 + 24.5965i 0.0369048 + 0.0532391i
\(463\) 154.802i 0.334346i −0.985928 0.167173i \(-0.946536\pi\)
0.985928 0.167173i \(-0.0534638\pi\)
\(464\) 173.407i 0.373722i
\(465\) 112.193 + 169.320i 0.241275 + 0.364130i
\(466\) −35.2963 −0.0757431
\(467\) −462.873 −0.991162 −0.495581 0.868562i \(-0.665045\pi\)
−0.495581 + 0.868562i \(0.665045\pi\)
\(468\) −93.7575 35.1318i −0.200337 0.0750680i
\(469\) −300.526 −0.640781
\(470\) 371.557 + 7.78684i 0.790547 + 0.0165678i
\(471\) −552.229 + 382.799i −1.17246 + 0.812737i
\(472\) 93.1637i 0.197381i
\(473\) 171.890 0.363404
\(474\) 140.064 + 202.057i 0.295493 + 0.426281i
\(475\) 15.8610 + 0.665102i 0.0333917 + 0.00140022i
\(476\) 98.1707i 0.206241i
\(477\) 162.969 434.920i 0.341653 0.911782i
\(478\) 340.515i 0.712374i
\(479\) 836.942i 1.74727i −0.486582 0.873635i \(-0.661757\pi\)
0.486582 0.873635i \(-0.338243\pi\)
\(480\) −46.8688 70.7341i −0.0976434 0.147363i
\(481\) −194.692 −0.404766
\(482\) 208.429 0.432426
\(483\) 101.856 70.6058i 0.210883 0.146182i
\(484\) 227.783 0.470625
\(485\) 10.0809 481.022i 0.0207854 0.991798i
\(486\) 38.0302 341.543i 0.0782515 0.702764i
\(487\) 212.042i 0.435405i −0.976015 0.217703i \(-0.930144\pi\)
0.976015 0.217703i \(-0.0698563\pi\)
\(488\) 294.715 0.603924
\(489\) −740.431 + 513.258i −1.51417 + 1.04961i
\(490\) −49.4866 1.03711i −0.100993 0.00211655i
\(491\) 79.1998i 0.161303i −0.996742 0.0806516i \(-0.974300\pi\)
0.996742 0.0806516i \(-0.0257001\pi\)
\(492\) −76.9824 + 53.3634i −0.156468 + 0.108462i
\(493\) 804.284i 1.63141i
\(494\) 4.99519i 0.0101117i
\(495\) −111.444 44.4437i −0.225139 0.0897853i
\(496\) 54.1646 0.109203
\(497\) −97.5611 −0.196300
\(498\) −108.992 157.233i −0.218860 0.315730i
\(499\) −259.432 −0.519905 −0.259952 0.965621i \(-0.583707\pi\)
−0.259952 + 0.965621i \(0.583707\pi\)
\(500\) −249.506 15.7053i −0.499012 0.0314107i
\(501\) −214.395 309.288i −0.427934 0.617341i
\(502\) 548.044i 1.09172i
\(503\) −175.890 −0.349683 −0.174841 0.984597i \(-0.555941\pi\)
−0.174841 + 0.984597i \(0.555941\pi\)
\(504\) 63.0676 + 23.6320i 0.125134 + 0.0468890i
\(505\) 9.63507 459.747i 0.0190793 0.910390i
\(506\) 58.8752i 0.116354i
\(507\) −235.957 340.394i −0.465399 0.671388i
\(508\) 191.607i 0.377179i
\(509\) 577.094i 1.13378i 0.823794 + 0.566890i \(0.191853\pi\)
−0.823794 + 0.566890i \(0.808147\pi\)
\(510\) −217.384 328.074i −0.426243 0.643282i
\(511\) 383.439 0.750369
\(512\) −22.6274 −0.0441942
\(513\) 16.6220 4.20226i 0.0324016 0.00819154i
\(514\) 15.9134 0.0309599
\(515\) 3.20622 152.988i 0.00622566 0.297064i
\(516\) 317.909 220.371i 0.616102 0.427075i
\(517\) 140.129i 0.271043i
\(518\) 130.963 0.252825
\(519\) −334.360 482.350i −0.644238 0.929383i
\(520\) −1.64824 + 78.6472i −0.00316968 + 0.151245i
\(521\) 198.309i 0.380631i −0.981723 0.190316i \(-0.939049\pi\)
0.981723 0.190316i \(-0.0609512\pi\)
\(522\) 516.695 + 193.610i 0.989837 + 0.370901i
\(523\) 307.722i 0.588378i −0.955747 0.294189i \(-0.904951\pi\)
0.955747 0.294189i \(-0.0950495\pi\)
\(524\) 296.930i 0.566660i
\(525\) 167.674 106.114i 0.319380 0.202123i
\(526\) −436.509 −0.829864
\(527\) 251.222 0.476703
\(528\) −26.2947 + 18.2272i −0.0498007 + 0.0345213i
\(529\) −285.192 −0.539115
\(530\) −364.827 7.64579i −0.688352 0.0144260i
\(531\) 277.597 + 104.018i 0.522781 + 0.195891i
\(532\) 3.36010i 0.00631598i
\(533\) 86.8380 0.162923
\(534\) −282.340 + 195.715i −0.528726 + 0.366507i
\(535\) −953.015 19.9727i −1.78134 0.0373321i
\(536\) 321.276i 0.599395i
\(537\) −404.623 + 280.480i −0.753487 + 0.522309i
\(538\) 281.324i 0.522907i
\(539\) 18.6634i 0.0346260i
\(540\) −263.093 + 60.6782i −0.487210 + 0.112367i
\(541\) 229.692 0.424569 0.212284 0.977208i \(-0.431910\pi\)
0.212284 + 0.977208i \(0.431910\pi\)
\(542\) 249.384 0.460118
\(543\) −193.177 278.679i −0.355759 0.513221i
\(544\) −104.949 −0.192921
\(545\) −369.901 7.75214i −0.678718 0.0142241i
\(546\) −35.5709 51.3148i −0.0651482 0.0939832i
\(547\) 296.031i 0.541191i 0.962693 + 0.270596i \(0.0872206\pi\)
−0.962693 + 0.270596i \(0.912779\pi\)
\(548\) −230.591 −0.420786
\(549\) 329.052 878.151i 0.599365 1.59955i
\(550\) −3.94933 + 94.1818i −0.00718061 + 0.171240i
\(551\) 27.5283i 0.0499606i
\(552\) 75.4807 + 108.889i 0.136740 + 0.197263i
\(553\) 153.318i 0.277247i
\(554\) 612.487i 1.10557i
\(555\) −437.662 + 289.998i −0.788581 + 0.522518i
\(556\) 190.201 0.342088
\(557\) 659.047 1.18321 0.591604 0.806228i \(-0.298495\pi\)
0.591604 + 0.806228i \(0.298495\pi\)
\(558\) 60.4752 161.392i 0.108379 0.289234i
\(559\) −358.608 −0.641518
\(560\) 1.10871 52.9034i 0.00197985 0.0944704i
\(561\) −121.958 + 84.5403i −0.217395 + 0.150696i
\(562\) 397.584i 0.707444i
\(563\) −1041.64 −1.85016 −0.925079 0.379774i \(-0.876002\pi\)
−0.925079 + 0.379774i \(0.876002\pi\)
\(564\) −179.652 259.168i −0.318533 0.459518i
\(565\) 644.166 + 13.5000i 1.14012 + 0.0238938i
\(566\) 160.930i 0.284328i
\(567\) 140.831 161.535i 0.248379 0.284894i
\(568\) 104.297i 0.183622i
\(569\) 143.782i 0.252692i 0.991986 + 0.126346i \(0.0403250\pi\)
−0.991986 + 0.126346i \(0.959675\pi\)
\(570\) −7.44042 11.2290i −0.0130534 0.0197000i
\(571\) 198.901 0.348337 0.174169 0.984716i \(-0.444276\pi\)
0.174169 + 0.984716i \(0.444276\pi\)
\(572\) 29.6611 0.0518551
\(573\) 484.232 335.664i 0.845082 0.585801i
\(574\) −58.4131 −0.101765
\(575\) 390.016 + 16.3546i 0.678289 + 0.0284427i
\(576\) −25.2637 + 67.4221i −0.0438606 + 0.117052i
\(577\) 55.7825i 0.0966767i 0.998831 + 0.0483384i \(0.0153926\pi\)
−0.998831 + 0.0483384i \(0.984607\pi\)
\(578\) −78.0588 −0.135050
\(579\) −696.037 + 482.486i −1.20214 + 0.833308i
\(580\) 9.08337 433.422i 0.0156610 0.747280i
\(581\) 119.306i 0.205347i
\(582\) −335.522 + 232.580i −0.576498 + 0.399622i
\(583\) 137.591i 0.236005i
\(584\) 409.913i 0.701906i
\(585\) 232.502 + 92.7215i 0.397439 + 0.158498i
\(586\) −502.512 −0.857529
\(587\) −679.045 −1.15681 −0.578403 0.815751i \(-0.696324\pi\)
−0.578403 + 0.815751i \(0.696324\pi\)
\(588\) 23.9274 + 34.5178i 0.0406928 + 0.0587038i
\(589\) 8.59862 0.0145987
\(590\) 4.88009 232.858i 0.00827133 0.394675i
\(591\) 490.104 + 707.027i 0.829278 + 1.19632i
\(592\) 140.006i 0.236496i
\(593\) −794.933 −1.34053 −0.670264 0.742123i \(-0.733819\pi\)
−0.670264 + 0.742123i \(0.733819\pi\)
\(594\) 24.9527 + 98.7004i 0.0420080 + 0.166162i
\(595\) 5.14236 245.373i 0.00864262 0.412391i
\(596\) 358.685i 0.601820i
\(597\) 128.034 + 184.703i 0.214463 + 0.309386i
\(598\) 122.829i 0.205400i
\(599\) 525.925i 0.878004i −0.898486 0.439002i \(-0.855332\pi\)
0.898486 0.439002i \(-0.144668\pi\)
\(600\) 113.441 + 179.252i 0.189069 + 0.298753i
\(601\) 169.552 0.282116 0.141058 0.990001i \(-0.454950\pi\)
0.141058 + 0.990001i \(0.454950\pi\)
\(602\) 241.224 0.400705
\(603\) −957.295 358.707i −1.58755 0.594871i
\(604\) 91.3242 0.151199
\(605\) −569.332 11.9317i −0.941044 0.0197218i
\(606\) −320.682 + 222.293i −0.529178 + 0.366821i
\(607\) 29.1399i 0.0480064i 0.999712 + 0.0240032i \(0.00764119\pi\)
−0.999712 + 0.0240032i \(0.992359\pi\)
\(608\) −3.59210 −0.00590806
\(609\) 196.030 + 282.794i 0.321888 + 0.464359i
\(610\) −736.625 15.4377i −1.20758 0.0253077i
\(611\) 292.348i 0.478474i
\(612\) −117.176 + 312.713i −0.191465 + 0.510968i
\(613\) 167.118i 0.272623i 0.990666 + 0.136311i \(0.0435247\pi\)
−0.990666 + 0.136311i \(0.956475\pi\)
\(614\) 572.035i 0.931653i
\(615\) 195.209 129.347i 0.317413 0.210320i
\(616\) −19.9521 −0.0323897
\(617\) 872.471 1.41405 0.707027 0.707187i \(-0.250036\pi\)
0.707027 + 0.707187i \(0.250036\pi\)
\(618\) −106.712 + 73.9715i −0.172673 + 0.119695i
\(619\) −852.170 −1.37669 −0.688344 0.725384i \(-0.741662\pi\)
−0.688344 + 0.725384i \(0.741662\pi\)
\(620\) −135.382 2.83724i −0.218358 0.00457619i
\(621\) 408.728 103.332i 0.658177 0.166396i
\(622\) 750.000i 1.20579i
\(623\) −214.235 −0.343877
\(624\) 54.8579 38.0269i 0.0879133 0.0609405i
\(625\) 622.806 + 52.3243i 0.996489 + 0.0837189i
\(626\) 793.616i 1.26776i
\(627\) −4.17429 + 2.89357i −0.00665755 + 0.00461494i
\(628\) 447.954i 0.713303i
\(629\) 649.364i 1.03238i
\(630\) −156.397 62.3707i −0.248249 0.0990011i
\(631\) 550.448 0.872343 0.436171 0.899864i \(-0.356334\pi\)
0.436171 + 0.899864i \(0.356334\pi\)
\(632\) −163.904 −0.259341
\(633\) 233.712 + 337.154i 0.369213 + 0.532629i
\(634\) 374.144 0.590133
\(635\) 10.0367 478.912i 0.0158059 0.754193i
\(636\) 176.398 + 254.473i 0.277356 + 0.400115i
\(637\) 38.9369i 0.0611255i
\(638\) −163.461 −0.256209
\(639\) −310.771 116.449i −0.486339 0.182236i
\(640\) 56.5561 + 1.18527i 0.0883689 + 0.00185198i
\(641\) 56.3780i 0.0879532i 0.999033 + 0.0439766i \(0.0140027\pi\)
−0.999033 + 0.0439766i \(0.985997\pi\)
\(642\) 460.795 + 664.746i 0.717749 + 1.03543i
\(643\) 934.856i 1.45390i −0.686692 0.726948i \(-0.740938\pi\)
0.686692 0.726948i \(-0.259062\pi\)
\(644\) 82.6234i 0.128297i
\(645\) −806.140 + 534.153i −1.24983 + 0.828145i
\(646\) −16.6606 −0.0257904
\(647\) 523.120 0.808532 0.404266 0.914641i \(-0.367527\pi\)
0.404266 + 0.914641i \(0.367527\pi\)
\(648\) 172.688 + 150.555i 0.266494 + 0.232338i
\(649\) −87.8204 −0.135316
\(650\) 8.23937 196.488i 0.0126759 0.302290i
\(651\) 88.3324 61.2310i 0.135687 0.0940569i
\(652\) 600.619i 0.921195i
\(653\) 629.201 0.963554 0.481777 0.876294i \(-0.339992\pi\)
0.481777 + 0.876294i \(0.339992\pi\)
\(654\) 178.852 + 258.013i 0.273474 + 0.394515i
\(655\) 15.5537 742.162i 0.0237461 1.13307i
\(656\) 62.4462i 0.0951924i
\(657\) 1221.40 + 457.672i 1.85906 + 0.696608i
\(658\) 196.653i 0.298864i
\(659\) 1205.86i 1.82983i −0.403644 0.914916i \(-0.632257\pi\)
0.403644 0.914916i \(-0.367743\pi\)
\(660\) 66.6772 44.1807i 0.101026 0.0669405i
\(661\) 421.451 0.637596 0.318798 0.947823i \(-0.396721\pi\)
0.318798 + 0.947823i \(0.396721\pi\)
\(662\) −764.292 −1.15452
\(663\) 254.438 176.374i 0.383768 0.266024i
\(664\) 127.544 0.192084
\(665\) 0.176008 8.39840i 0.000264674 0.0126292i
\(666\) 417.170 + 156.317i 0.626381 + 0.234711i
\(667\) 676.909i 1.01486i
\(668\) 250.887 0.375579
\(669\) 63.7745 44.2078i 0.0953281 0.0660804i
\(670\) −16.8290 + 803.013i −0.0251179 + 1.19853i
\(671\) 277.812i 0.414026i
\(672\) −36.9011 + 25.5794i −0.0549124 + 0.0380647i
\(673\) 208.482i 0.309779i −0.987932 0.154890i \(-0.950498\pi\)
0.987932 0.154890i \(-0.0495022\pi\)
\(674\) 628.368i 0.932297i
\(675\) 660.768 137.881i 0.978915 0.204268i
\(676\) 276.119 0.408460
\(677\) 1253.11 1.85097 0.925485 0.378784i \(-0.123658\pi\)
0.925485 + 0.378784i \(0.123658\pi\)
\(678\) −311.462 449.317i −0.459383 0.662710i
\(679\) −254.589 −0.374947
\(680\) 262.315 + 5.49741i 0.385757 + 0.00808443i
\(681\) −41.5983 60.0101i −0.0610842 0.0881205i
\(682\) 51.0580i 0.0748651i
\(683\) 982.114 1.43794 0.718971 0.695041i \(-0.244614\pi\)
0.718971 + 0.695041i \(0.244614\pi\)
\(684\) −4.01061 + 10.7033i −0.00586346 + 0.0156480i
\(685\) 576.350 + 12.0788i 0.841388 + 0.0176332i
\(686\) 26.1916i 0.0381802i
\(687\) 411.923 + 594.243i 0.599597 + 0.864983i
\(688\) 257.880i 0.374825i
\(689\) 287.052i 0.416621i
\(690\) −182.957 276.117i −0.265154 0.400169i
\(691\) 204.605 0.296099 0.148050 0.988980i \(-0.452700\pi\)
0.148050 + 0.988980i \(0.452700\pi\)
\(692\) 391.270 0.565419
\(693\) −22.2766 + 59.4504i −0.0321452 + 0.0857871i
\(694\) 359.148 0.517504
\(695\) −475.398 9.96307i −0.684026 0.0143354i
\(696\) −302.320 + 209.565i −0.434368 + 0.301099i
\(697\) 289.634i 0.415543i
\(698\) −587.785 −0.842099
\(699\) −42.6561 61.5360i −0.0610244 0.0880343i
\(700\) −5.54235 + 132.171i −0.00791765 + 0.188816i
\(701\) 330.503i 0.471473i 0.971817 + 0.235736i \(0.0757502\pi\)
−0.971817 + 0.235736i \(0.924250\pi\)
\(702\) −52.0581 205.915i −0.0741568 0.293327i
\(703\) 22.2259i 0.0316157i
\(704\) 21.3296i 0.0302978i
\(705\) 435.457 + 657.188i 0.617669 + 0.932182i
\(706\) 393.210 0.556954
\(707\) −243.329 −0.344171
\(708\) −162.423 + 112.590i −0.229411 + 0.159025i
\(709\) 265.328 0.374229 0.187114 0.982338i \(-0.440086\pi\)
0.187114 + 0.982338i \(0.440086\pi\)
\(710\) −5.46328 + 260.686i −0.00769476 + 0.367163i
\(711\) −183.000 + 488.378i −0.257384 + 0.686889i
\(712\) 229.027i 0.321667i
\(713\) 211.436 0.296544
\(714\) −171.152 + 118.641i −0.239709 + 0.166164i
\(715\) −74.1364 1.55370i −0.103687 0.00217301i
\(716\) 328.220i 0.458408i
\(717\) −593.658 + 411.517i −0.827975 + 0.573943i
\(718\) 115.421i 0.160754i
\(719\) 994.084i 1.38259i 0.722572 + 0.691296i \(0.242960\pi\)
−0.722572 + 0.691296i \(0.757040\pi\)
\(720\) 66.6771 167.195i 0.0926071 0.232215i
\(721\) −80.9713 −0.112304
\(722\) 509.961 0.706317
\(723\) 251.890 + 363.379i 0.348396 + 0.502598i
\(724\) 226.057 0.312234
\(725\) −45.4069 + 1082.84i −0.0626302 + 1.49357i
\(726\) 275.279 + 397.119i 0.379172 + 0.546996i
\(727\) 1244.89i 1.71236i 0.516674 + 0.856182i \(0.327170\pi\)
−0.516674 + 0.856182i \(0.672830\pi\)
\(728\) 41.6253 0.0571776
\(729\) 641.411 346.458i 0.879851 0.475251i
\(730\) 21.4720 1024.56i 0.0294137 1.40350i
\(731\) 1196.08i 1.63622i
\(732\) 356.167 + 513.810i 0.486567 + 0.701926i
\(733\) 822.707i 1.12238i −0.827686 0.561192i \(-0.810343\pi\)
0.827686 0.561192i \(-0.189657\pi\)
\(734\) 727.614i 0.991300i
\(735\) −57.9972 87.5290i −0.0789078 0.119087i
\(736\) −88.3281 −0.120011
\(737\) 302.849 0.410922
\(738\) −186.069 69.7217i −0.252126 0.0944739i
\(739\) −550.154 −0.744458 −0.372229 0.928141i \(-0.621406\pi\)
−0.372229 + 0.928141i \(0.621406\pi\)
\(740\) 7.33375 349.937i 0.00991047 0.472888i
\(741\) 8.70868 6.03676i 0.0117526 0.00814677i
\(742\) 193.091i 0.260230i
\(743\) 356.858 0.480293 0.240147 0.970737i \(-0.422805\pi\)
0.240147 + 0.970737i \(0.422805\pi\)
\(744\) 65.4587 + 94.4313i 0.0879821 + 0.126924i
\(745\) 18.7886 896.515i 0.0252196 1.20338i
\(746\) 113.329i 0.151916i
\(747\) 142.404 380.038i 0.190634 0.508752i
\(748\) 98.9296i 0.132259i
\(749\) 504.399i 0.673430i
\(750\) −274.151 453.973i −0.365535 0.605297i
\(751\) 1027.14 1.36770 0.683850 0.729623i \(-0.260304\pi\)
0.683850 + 0.729623i \(0.260304\pi\)
\(752\) 210.231 0.279562
\(753\) −955.467 + 662.319i −1.26888 + 0.879574i
\(754\) 341.024 0.452287
\(755\) −228.260 4.78373i −0.302332 0.00633606i
\(756\) 35.0178 + 138.513i 0.0463198 + 0.183218i
\(757\) 799.336i 1.05593i 0.849267 + 0.527963i \(0.177044\pi\)
−0.849267 + 0.527963i \(0.822956\pi\)
\(758\) −999.675 −1.31883
\(759\) −102.644 + 71.1516i −0.135236 + 0.0937439i
\(760\) 8.97827 + 0.188161i 0.0118135 + 0.000247580i
\(761\) 799.993i 1.05124i −0.850720 0.525619i \(-0.823834\pi\)
0.850720 0.525619i \(-0.176166\pi\)
\(762\) −334.050 + 231.560i −0.438386 + 0.303884i
\(763\) 195.776i 0.256588i
\(764\) 392.797i 0.514132i
\(765\) 309.257 775.472i 0.404258 1.01369i
\(766\) −69.6927 −0.0909827
\(767\) 183.217 0.238875
\(768\) −27.3456 39.4489i −0.0356062 0.0513658i
\(769\) −1066.44 −1.38679 −0.693393 0.720560i \(-0.743885\pi\)
−0.693393 + 0.720560i \(0.743885\pi\)
\(770\) 49.8692 + 1.04512i 0.0647652 + 0.00135730i
\(771\) 19.2315 + 27.7436i 0.0249436 + 0.0359839i
\(772\) 564.608i 0.731358i
\(773\) −10.9234 −0.0141311 −0.00706557 0.999975i \(-0.502249\pi\)
−0.00706557 + 0.999975i \(0.502249\pi\)
\(774\) 768.395 + 287.925i 0.992758 + 0.371996i
\(775\) 338.231 + 14.1831i 0.436428 + 0.0183008i
\(776\) 272.167i 0.350731i
\(777\) 158.271 + 228.323i 0.203695 + 0.293852i
\(778\) 3.79491i 0.00487777i
\(779\) 9.91332i 0.0127257i
\(780\) −139.107 + 92.1728i −0.178342 + 0.118170i