Properties

Label 105.3.l.a.22.3
Level 105
Weight 3
Character 105.22
Analytic conductor 2.861
Analytic rank 0
Dimension 24
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.l (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 22.3
Character \(\chi\) \(=\) 105.22
Dual form 105.3.l.a.43.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.36784 - 1.36784i) q^{2} +(-1.22474 + 1.22474i) q^{3} -0.258033i q^{4} +(3.39663 + 3.66919i) q^{5} +3.35051 q^{6} +(1.87083 + 1.87083i) q^{7} +(-5.82430 + 5.82430i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.36784 - 1.36784i) q^{2} +(-1.22474 + 1.22474i) q^{3} -0.258033i q^{4} +(3.39663 + 3.66919i) q^{5} +3.35051 q^{6} +(1.87083 + 1.87083i) q^{7} +(-5.82430 + 5.82430i) q^{8} -3.00000i q^{9} +(0.372817 - 9.66489i) q^{10} +17.6130 q^{11} +(0.316024 + 0.316024i) q^{12} +(12.1245 - 12.1245i) q^{13} -5.11799i q^{14} +(-8.65382 - 0.333816i) q^{15} +14.9013 q^{16} +(13.8772 + 13.8772i) q^{17} +(-4.10352 + 4.10352i) q^{18} -18.3068i q^{19} +(0.946770 - 0.876441i) q^{20} -4.58258 q^{21} +(-24.0917 - 24.0917i) q^{22} +(-26.3956 + 26.3956i) q^{23} -14.2666i q^{24} +(-1.92585 + 24.9257i) q^{25} -33.1686 q^{26} +(3.67423 + 3.67423i) q^{27} +(0.482735 - 0.482735i) q^{28} -2.87815i q^{29} +(11.3804 + 12.2936i) q^{30} +16.1149 q^{31} +(2.91465 + 2.91465i) q^{32} +(-21.5714 + 21.5714i) q^{33} -37.9637i q^{34} +(-0.509912 + 13.2189i) q^{35} -0.774098 q^{36} +(2.52440 + 2.52440i) q^{37} +(-25.0408 + 25.0408i) q^{38} +29.6988i q^{39} +(-41.1534 - 1.58747i) q^{40} -1.89828 q^{41} +(6.26823 + 6.26823i) q^{42} +(-42.5974 + 42.5974i) q^{43} -4.54472i q^{44} +(11.0076 - 10.1899i) q^{45} +72.2098 q^{46} +(-57.7457 - 57.7457i) q^{47} +(-18.2503 + 18.2503i) q^{48} +7.00000i q^{49} +(36.7286 - 31.4601i) q^{50} -33.9922 q^{51} +(-3.12851 - 3.12851i) q^{52} +(66.5567 - 66.5567i) q^{53} -10.0515i q^{54} +(59.8247 + 64.6253i) q^{55} -21.7925 q^{56} +(22.4212 + 22.4212i) q^{57} +(-3.93685 + 3.93685i) q^{58} +16.4673i q^{59} +(-0.0861354 + 2.23297i) q^{60} -7.37026 q^{61} +(-22.0426 - 22.0426i) q^{62} +(5.61249 - 5.61249i) q^{63} -67.5787i q^{64} +(85.6692 + 3.30464i) q^{65} +59.0124 q^{66} +(-27.2024 - 27.2024i) q^{67} +(3.58078 - 3.58078i) q^{68} -64.6557i q^{69} +(18.7788 - 17.3839i) q^{70} -79.5984 q^{71} +(17.4729 + 17.4729i) q^{72} +(63.3051 - 63.3051i) q^{73} -6.90594i q^{74} +(-28.1690 - 32.8863i) q^{75} -4.72376 q^{76} +(32.9508 + 32.9508i) q^{77} +(40.6231 - 40.6231i) q^{78} +2.48684i q^{79} +(50.6141 + 54.6756i) q^{80} -9.00000 q^{81} +(2.59655 + 2.59655i) q^{82} +(-29.0421 + 29.0421i) q^{83} +1.18245i q^{84} +(-3.78237 + 98.0540i) q^{85} +116.533 q^{86} +(3.52500 + 3.52500i) q^{87} +(-102.583 + 102.583i) q^{88} +29.3345i q^{89} +(-28.9947 - 1.11845i) q^{90} +45.3656 q^{91} +(6.81092 + 6.81092i) q^{92} +(-19.7367 + 19.7367i) q^{93} +157.974i q^{94} +(67.1711 - 62.1814i) q^{95} -7.13941 q^{96} +(-89.1223 - 89.1223i) q^{97} +(9.57487 - 9.57487i) q^{98} -52.8389i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 16q^{5} + 24q^{6} - 48q^{8} - 40q^{10} - 48q^{12} + 64q^{13} - 184q^{16} + 24q^{17} + 24q^{18} + 72q^{20} + 8q^{22} + 8q^{23} - 136q^{25} - 80q^{26} + 96q^{30} + 96q^{31} + 56q^{32} - 72q^{33} + 168q^{36} + 8q^{37} + 56q^{38} + 232q^{40} + 320q^{41} - 112q^{43} - 72q^{45} + 320q^{46} + 64q^{47} + 192q^{48} - 256q^{50} - 192q^{51} + 96q^{52} - 72q^{53} - 80q^{55} - 336q^{56} + 48q^{57} - 512q^{58} - 192q^{60} - 496q^{61} - 776q^{62} + 312q^{65} - 192q^{66} - 192q^{67} + 568q^{68} + 112q^{70} - 144q^{71} + 144q^{72} + 224q^{73} + 144q^{75} + 416q^{76} + 112q^{77} - 216q^{78} - 528q^{80} - 216q^{81} + 352q^{82} - 32q^{83} + 24q^{85} + 240q^{86} + 384q^{87} + 216q^{88} - 24q^{90} + 1304q^{92} + 376q^{95} + 168q^{96} - 816q^{97} - 56q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.36784 1.36784i −0.683920 0.683920i 0.276961 0.960881i \(-0.410673\pi\)
−0.960881 + 0.276961i \(0.910673\pi\)
\(3\) −1.22474 + 1.22474i −0.408248 + 0.408248i
\(4\) 0.258033i 0.0645082i
\(5\) 3.39663 + 3.66919i 0.679325 + 0.733837i
\(6\) 3.35051 0.558418
\(7\) 1.87083 + 1.87083i 0.267261 + 0.267261i
\(8\) −5.82430 + 5.82430i −0.728038 + 0.728038i
\(9\) 3.00000i 0.333333i
\(10\) 0.372817 9.66489i 0.0372817 0.966489i
\(11\) 17.6130 1.60118 0.800589 0.599213i \(-0.204520\pi\)
0.800589 + 0.599213i \(0.204520\pi\)
\(12\) 0.316024 + 0.316024i 0.0263354 + 0.0263354i
\(13\) 12.1245 12.1245i 0.932651 0.932651i −0.0652196 0.997871i \(-0.520775\pi\)
0.997871 + 0.0652196i \(0.0207748\pi\)
\(14\) 5.11799i 0.365570i
\(15\) −8.65382 0.333816i −0.576921 0.0222544i
\(16\) 14.9013 0.931331
\(17\) 13.8772 + 13.8772i 0.816309 + 0.816309i 0.985571 0.169262i \(-0.0541385\pi\)
−0.169262 + 0.985571i \(0.554138\pi\)
\(18\) −4.10352 + 4.10352i −0.227973 + 0.227973i
\(19\) 18.3068i 0.963516i −0.876304 0.481758i \(-0.839998\pi\)
0.876304 0.481758i \(-0.160002\pi\)
\(20\) 0.946770 0.876441i 0.0473385 0.0438220i
\(21\) −4.58258 −0.218218
\(22\) −24.0917 24.0917i −1.09508 1.09508i
\(23\) −26.3956 + 26.3956i −1.14763 + 1.14763i −0.160617 + 0.987017i \(0.551348\pi\)
−0.987017 + 0.160617i \(0.948652\pi\)
\(24\) 14.2666i 0.594440i
\(25\) −1.92585 + 24.9257i −0.0770341 + 0.997028i
\(26\) −33.1686 −1.27572
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) 0.482735 0.482735i 0.0172405 0.0172405i
\(29\) 2.87815i 0.0992467i −0.998768 0.0496234i \(-0.984198\pi\)
0.998768 0.0496234i \(-0.0158021\pi\)
\(30\) 11.3804 + 12.2936i 0.379347 + 0.409788i
\(31\) 16.1149 0.519836 0.259918 0.965631i \(-0.416304\pi\)
0.259918 + 0.965631i \(0.416304\pi\)
\(32\) 2.91465 + 2.91465i 0.0910828 + 0.0910828i
\(33\) −21.5714 + 21.5714i −0.653679 + 0.653679i
\(34\) 37.9637i 1.11658i
\(35\) −0.509912 + 13.2189i −0.0145689 + 0.377684i
\(36\) −0.774098 −0.0215027
\(37\) 2.52440 + 2.52440i 0.0682270 + 0.0682270i 0.740397 0.672170i \(-0.234638\pi\)
−0.672170 + 0.740397i \(0.734638\pi\)
\(38\) −25.0408 + 25.0408i −0.658968 + 0.658968i
\(39\) 29.6988i 0.761507i
\(40\) −41.1534 1.58747i −1.02884 0.0396867i
\(41\) −1.89828 −0.0462996 −0.0231498 0.999732i \(-0.507369\pi\)
−0.0231498 + 0.999732i \(0.507369\pi\)
\(42\) 6.26823 + 6.26823i 0.149243 + 0.149243i
\(43\) −42.5974 + 42.5974i −0.990637 + 0.990637i −0.999957 0.00931954i \(-0.997033\pi\)
0.00931954 + 0.999957i \(0.497033\pi\)
\(44\) 4.54472i 0.103289i
\(45\) 11.0076 10.1899i 0.244612 0.226442i
\(46\) 72.2098 1.56978
\(47\) −57.7457 57.7457i −1.22863 1.22863i −0.964482 0.264150i \(-0.914909\pi\)
−0.264150 0.964482i \(-0.585091\pi\)
\(48\) −18.2503 + 18.2503i −0.380214 + 0.380214i
\(49\) 7.00000i 0.142857i
\(50\) 36.7286 31.4601i 0.734572 0.629202i
\(51\) −33.9922 −0.666513
\(52\) −3.12851 3.12851i −0.0601636 0.0601636i
\(53\) 66.5567 66.5567i 1.25579 1.25579i 0.302701 0.953086i \(-0.402112\pi\)
0.953086 0.302701i \(-0.0978883\pi\)
\(54\) 10.0515i 0.186139i
\(55\) 59.8247 + 64.6253i 1.08772 + 1.17500i
\(56\) −21.7925 −0.389153
\(57\) 22.4212 + 22.4212i 0.393354 + 0.393354i
\(58\) −3.93685 + 3.93685i −0.0678768 + 0.0678768i
\(59\) 16.4673i 0.279107i 0.990215 + 0.139554i \(0.0445668\pi\)
−0.990215 + 0.139554i \(0.955433\pi\)
\(60\) −0.0861354 + 2.23297i −0.00143559 + 0.0372161i
\(61\) −7.37026 −0.120824 −0.0604119 0.998174i \(-0.519241\pi\)
−0.0604119 + 0.998174i \(0.519241\pi\)
\(62\) −22.0426 22.0426i −0.355526 0.355526i
\(63\) 5.61249 5.61249i 0.0890871 0.0890871i
\(64\) 67.5787i 1.05592i
\(65\) 85.6692 + 3.30464i 1.31799 + 0.0508406i
\(66\) 59.0124 0.894127
\(67\) −27.2024 27.2024i −0.406006 0.406006i 0.474337 0.880343i \(-0.342688\pi\)
−0.880343 + 0.474337i \(0.842688\pi\)
\(68\) 3.58078 3.58078i 0.0526586 0.0526586i
\(69\) 64.6557i 0.937039i
\(70\) 18.7788 17.3839i 0.268269 0.248341i
\(71\) −79.5984 −1.12110 −0.560552 0.828119i \(-0.689411\pi\)
−0.560552 + 0.828119i \(0.689411\pi\)
\(72\) 17.4729 + 17.4729i 0.242679 + 0.242679i
\(73\) 63.3051 63.3051i 0.867193 0.867193i −0.124968 0.992161i \(-0.539883\pi\)
0.992161 + 0.124968i \(0.0398827\pi\)
\(74\) 6.90594i 0.0933235i
\(75\) −28.1690 32.8863i −0.375586 0.438484i
\(76\) −4.72376 −0.0621547
\(77\) 32.9508 + 32.9508i 0.427933 + 0.427933i
\(78\) 40.6231 40.6231i 0.520809 0.520809i
\(79\) 2.48684i 0.0314790i 0.999876 + 0.0157395i \(0.00501024\pi\)
−0.999876 + 0.0157395i \(0.994990\pi\)
\(80\) 50.6141 + 54.6756i 0.632676 + 0.683445i
\(81\) −9.00000 −0.111111
\(82\) 2.59655 + 2.59655i 0.0316652 + 0.0316652i
\(83\) −29.0421 + 29.0421i −0.349905 + 0.349905i −0.860074 0.510169i \(-0.829583\pi\)
0.510169 + 0.860074i \(0.329583\pi\)
\(84\) 1.18245i 0.0140768i
\(85\) −3.78237 + 98.0540i −0.0444985 + 1.15358i
\(86\) 116.533 1.35503
\(87\) 3.52500 + 3.52500i 0.0405173 + 0.0405173i
\(88\) −102.583 + 102.583i −1.16572 + 1.16572i
\(89\) 29.3345i 0.329601i 0.986327 + 0.164800i \(0.0526980\pi\)
−0.986327 + 0.164800i \(0.947302\pi\)
\(90\) −28.9947 1.11845i −0.322163 0.0124272i
\(91\) 45.3656 0.498523
\(92\) 6.81092 + 6.81092i 0.0740318 + 0.0740318i
\(93\) −19.7367 + 19.7367i −0.212222 + 0.212222i
\(94\) 157.974i 1.68057i
\(95\) 67.1711 62.1814i 0.707064 0.654541i
\(96\) −7.13941 −0.0743688
\(97\) −89.1223 89.1223i −0.918786 0.918786i 0.0781549 0.996941i \(-0.475097\pi\)
−0.996941 + 0.0781549i \(0.975097\pi\)
\(98\) 9.57487 9.57487i 0.0977028 0.0977028i
\(99\) 52.8389i 0.533726i
\(100\) 6.43165 + 0.496933i 0.0643165 + 0.00496933i
\(101\) −87.3306 −0.864660 −0.432330 0.901716i \(-0.642308\pi\)
−0.432330 + 0.901716i \(0.642308\pi\)
\(102\) 46.4958 + 46.4958i 0.455841 + 0.455841i
\(103\) 36.7417 36.7417i 0.356715 0.356715i −0.505885 0.862601i \(-0.668834\pi\)
0.862601 + 0.505885i \(0.168834\pi\)
\(104\) 141.233i 1.35801i
\(105\) −15.5653 16.8143i −0.148241 0.160136i
\(106\) −182.078 −1.71771
\(107\) −91.9855 91.9855i −0.859677 0.859677i 0.131622 0.991300i \(-0.457981\pi\)
−0.991300 + 0.131622i \(0.957981\pi\)
\(108\) 0.948073 0.948073i 0.00877845 0.00877845i
\(109\) 144.628i 1.32686i 0.748237 + 0.663432i \(0.230901\pi\)
−0.748237 + 0.663432i \(0.769099\pi\)
\(110\) 6.56642 170.227i 0.0596947 1.54752i
\(111\) −6.18349 −0.0557071
\(112\) 27.8778 + 27.8778i 0.248909 + 0.248909i
\(113\) 28.6801 28.6801i 0.253806 0.253806i −0.568723 0.822529i \(-0.692562\pi\)
0.822529 + 0.568723i \(0.192562\pi\)
\(114\) 61.3371i 0.538045i
\(115\) −186.506 7.19436i −1.62179 0.0625597i
\(116\) −0.742658 −0.00640222
\(117\) −36.3734 36.3734i −0.310884 0.310884i
\(118\) 22.5247 22.5247i 0.190887 0.190887i
\(119\) 51.9239i 0.436335i
\(120\) 52.3467 48.4582i 0.436223 0.403818i
\(121\) 189.217 1.56377
\(122\) 10.0813 + 10.0813i 0.0826338 + 0.0826338i
\(123\) 2.32491 2.32491i 0.0189017 0.0189017i
\(124\) 4.15818i 0.0335337i
\(125\) −97.9985 + 77.5970i −0.783988 + 0.620776i
\(126\) −15.3540 −0.121857
\(127\) 12.2062 + 12.2062i 0.0961116 + 0.0961116i 0.753528 0.657416i \(-0.228351\pi\)
−0.657416 + 0.753528i \(0.728351\pi\)
\(128\) −80.7782 + 80.7782i −0.631080 + 0.631080i
\(129\) 104.342i 0.808852i
\(130\) −112.661 121.702i −0.866627 0.936169i
\(131\) −23.2249 −0.177290 −0.0886448 0.996063i \(-0.528254\pi\)
−0.0886448 + 0.996063i \(0.528254\pi\)
\(132\) 5.56613 + 5.56613i 0.0421676 + 0.0421676i
\(133\) 34.2489 34.2489i 0.257511 0.257511i
\(134\) 74.4170i 0.555351i
\(135\) −1.00145 + 25.9615i −0.00741813 + 0.192307i
\(136\) −161.651 −1.18861
\(137\) −17.2588 17.2588i −0.125977 0.125977i 0.641307 0.767284i \(-0.278392\pi\)
−0.767284 + 0.641307i \(0.778392\pi\)
\(138\) −88.4386 + 88.4386i −0.640859 + 0.640859i
\(139\) 29.4799i 0.212085i −0.994362 0.106043i \(-0.966182\pi\)
0.994362 0.106043i \(-0.0338180\pi\)
\(140\) 3.41092 + 0.131574i 0.0243637 + 0.000939814i
\(141\) 141.447 1.00317
\(142\) 108.878 + 108.878i 0.766745 + 0.766745i
\(143\) 213.548 213.548i 1.49334 1.49334i
\(144\) 44.7039i 0.310444i
\(145\) 10.5605 9.77602i 0.0728309 0.0674208i
\(146\) −173.182 −1.18618
\(147\) −8.57321 8.57321i −0.0583212 0.0583212i
\(148\) 0.651377 0.651377i 0.00440120 0.00440120i
\(149\) 14.3848i 0.0965421i −0.998834 0.0482710i \(-0.984629\pi\)
0.998834 0.0482710i \(-0.0153711\pi\)
\(150\) −6.45259 + 83.5138i −0.0430172 + 0.556759i
\(151\) 15.3569 0.101701 0.0508506 0.998706i \(-0.483807\pi\)
0.0508506 + 0.998706i \(0.483807\pi\)
\(152\) 106.624 + 106.624i 0.701476 + 0.701476i
\(153\) 41.6317 41.6317i 0.272103 0.272103i
\(154\) 90.1429i 0.585344i
\(155\) 54.7364 + 59.1286i 0.353138 + 0.381475i
\(156\) 7.66325 0.0491234
\(157\) 63.2769 + 63.2769i 0.403037 + 0.403037i 0.879302 0.476265i \(-0.158010\pi\)
−0.476265 + 0.879302i \(0.658010\pi\)
\(158\) 3.40160 3.40160i 0.0215291 0.0215291i
\(159\) 163.030i 1.02535i
\(160\) −0.794415 + 20.5944i −0.00496509 + 0.128715i
\(161\) −98.7632 −0.613436
\(162\) 12.3106 + 12.3106i 0.0759911 + 0.0759911i
\(163\) −121.254 + 121.254i −0.743890 + 0.743890i −0.973324 0.229434i \(-0.926312\pi\)
0.229434 + 0.973324i \(0.426312\pi\)
\(164\) 0.489819i 0.00298670i
\(165\) −152.419 5.87948i −0.923754 0.0356332i
\(166\) 79.4498 0.478613
\(167\) −51.2223 51.2223i −0.306720 0.306720i 0.536916 0.843636i \(-0.319589\pi\)
−0.843636 + 0.536916i \(0.819589\pi\)
\(168\) 26.6903 26.6903i 0.158871 0.158871i
\(169\) 125.005i 0.739677i
\(170\) 139.296 128.948i 0.819387 0.758520i
\(171\) −54.9204 −0.321172
\(172\) 10.9915 + 10.9915i 0.0639042 + 0.0639042i
\(173\) 78.5418 78.5418i 0.453999 0.453999i −0.442681 0.896679i \(-0.645972\pi\)
0.896679 + 0.442681i \(0.145972\pi\)
\(174\) 9.64328i 0.0554211i
\(175\) −50.2347 + 43.0288i −0.287055 + 0.245879i
\(176\) 262.456 1.49123
\(177\) −20.1683 20.1683i −0.113945 0.113945i
\(178\) 40.1248 40.1248i 0.225420 0.225420i
\(179\) 162.375i 0.907125i 0.891224 + 0.453563i \(0.149847\pi\)
−0.891224 + 0.453563i \(0.850153\pi\)
\(180\) −2.62932 2.84031i −0.0146073 0.0157795i
\(181\) 257.224 1.42113 0.710564 0.703633i \(-0.248440\pi\)
0.710564 + 0.703633i \(0.248440\pi\)
\(182\) −62.0528 62.0528i −0.340950 0.340950i
\(183\) 9.02668 9.02668i 0.0493261 0.0493261i
\(184\) 307.472i 1.67104i
\(185\) −0.688048 + 17.8369i −0.00371918 + 0.0964158i
\(186\) 53.9932 0.290286
\(187\) 244.420 + 244.420i 1.30706 + 1.30706i
\(188\) −14.9003 + 14.9003i −0.0792568 + 0.0792568i
\(189\) 13.7477i 0.0727393i
\(190\) −176.933 6.82510i −0.931228 0.0359216i
\(191\) −334.101 −1.74922 −0.874610 0.484827i \(-0.838883\pi\)
−0.874610 + 0.484827i \(0.838883\pi\)
\(192\) 82.7667 + 82.7667i 0.431076 + 0.431076i
\(193\) 19.9582 19.9582i 0.103410 0.103410i −0.653509 0.756919i \(-0.726704\pi\)
0.756919 + 0.653509i \(0.226704\pi\)
\(194\) 243.810i 1.25675i
\(195\) −108.970 + 100.876i −0.558822 + 0.517311i
\(196\) 1.80623 0.00921545
\(197\) 36.5252 + 36.5252i 0.185407 + 0.185407i 0.793707 0.608300i \(-0.208148\pi\)
−0.608300 + 0.793707i \(0.708148\pi\)
\(198\) −72.2751 + 72.2751i −0.365026 + 0.365026i
\(199\) 187.619i 0.942810i −0.881917 0.471405i \(-0.843747\pi\)
0.881917 0.471405i \(-0.156253\pi\)
\(200\) −133.958 156.392i −0.669791 0.781958i
\(201\) 66.6320 0.331502
\(202\) 119.454 + 119.454i 0.591358 + 0.591358i
\(203\) 5.38453 5.38453i 0.0265248 0.0265248i
\(204\) 8.77110i 0.0429956i
\(205\) −6.44776 6.96516i −0.0314525 0.0339764i
\(206\) −100.513 −0.487929
\(207\) 79.1867 + 79.1867i 0.382545 + 0.382545i
\(208\) 180.670 180.670i 0.868607 0.868607i
\(209\) 322.437i 1.54276i
\(210\) −1.70846 + 44.2901i −0.00813554 + 0.210905i
\(211\) −73.6409 −0.349009 −0.174505 0.984656i \(-0.555832\pi\)
−0.174505 + 0.984656i \(0.555832\pi\)
\(212\) −17.1738 17.1738i −0.0810085 0.0810085i
\(213\) 97.4878 97.4878i 0.457689 0.457689i
\(214\) 251.643i 1.17590i
\(215\) −300.985 11.6103i −1.39993 0.0540015i
\(216\) −42.7997 −0.198147
\(217\) 30.1483 + 30.1483i 0.138932 + 0.138932i
\(218\) 197.828 197.828i 0.907468 0.907468i
\(219\) 155.065i 0.708060i
\(220\) 16.6754 15.4367i 0.0757974 0.0701669i
\(221\) 336.509 1.52266
\(222\) 8.45801 + 8.45801i 0.0380992 + 0.0380992i
\(223\) 258.221 258.221i 1.15794 1.15794i 0.173025 0.984917i \(-0.444646\pi\)
0.984917 0.173025i \(-0.0553542\pi\)
\(224\) 10.9056i 0.0486858i
\(225\) 74.7771 + 5.77756i 0.332343 + 0.0256780i
\(226\) −78.4596 −0.347166
\(227\) −9.72923 9.72923i −0.0428601 0.0428601i 0.685352 0.728212i \(-0.259648\pi\)
−0.728212 + 0.685352i \(0.759648\pi\)
\(228\) 5.78540 5.78540i 0.0253745 0.0253745i
\(229\) 108.047i 0.471822i −0.971775 0.235911i \(-0.924193\pi\)
0.971775 0.235911i \(-0.0758074\pi\)
\(230\) 245.270 + 264.951i 1.06639 + 1.15196i
\(231\) −80.7128 −0.349406
\(232\) 16.7632 + 16.7632i 0.0722554 + 0.0722554i
\(233\) −2.47323 + 2.47323i −0.0106147 + 0.0106147i −0.712394 0.701779i \(-0.752389\pi\)
0.701779 + 0.712394i \(0.252389\pi\)
\(234\) 99.5059i 0.425239i
\(235\) 15.7391 408.020i 0.0669750 1.73626i
\(236\) 4.24911 0.0180047
\(237\) −3.04574 3.04574i −0.0128512 0.0128512i
\(238\) 71.0236 71.0236i 0.298418 0.298418i
\(239\) 230.974i 0.966417i 0.875505 + 0.483209i \(0.160529\pi\)
−0.875505 + 0.483209i \(0.839471\pi\)
\(240\) −128.953 4.97428i −0.537304 0.0207262i
\(241\) −280.404 −1.16350 −0.581752 0.813366i \(-0.697633\pi\)
−0.581752 + 0.813366i \(0.697633\pi\)
\(242\) −258.818 258.818i −1.06950 1.06950i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 1.90177i 0.00779413i
\(245\) −25.6843 + 23.7764i −0.104834 + 0.0970465i
\(246\) −6.36022 −0.0258545
\(247\) −221.960 221.960i −0.898625 0.898625i
\(248\) −93.8582 + 93.8582i −0.378460 + 0.378460i
\(249\) 71.1383i 0.285696i
\(250\) 240.186 + 27.9059i 0.960746 + 0.111624i
\(251\) 53.4737 0.213043 0.106521 0.994310i \(-0.466029\pi\)
0.106521 + 0.994310i \(0.466029\pi\)
\(252\) −1.44821 1.44821i −0.00574685 0.00574685i
\(253\) −464.904 + 464.904i −1.83757 + 1.83757i
\(254\) 33.3921i 0.131465i
\(255\) −115.459 124.724i −0.452779 0.489112i
\(256\) −49.3317 −0.192702
\(257\) 78.9368 + 78.9368i 0.307147 + 0.307147i 0.843802 0.536655i \(-0.180312\pi\)
−0.536655 + 0.843802i \(0.680312\pi\)
\(258\) −142.723 + 142.723i −0.553189 + 0.553189i
\(259\) 9.44543i 0.0364688i
\(260\) 0.852705 22.1055i 0.00327963 0.0850210i
\(261\) −8.63446 −0.0330822
\(262\) 31.7680 + 31.7680i 0.121252 + 0.121252i
\(263\) −323.863 + 323.863i −1.23142 + 1.23142i −0.268002 + 0.963418i \(0.586363\pi\)
−0.963418 + 0.268002i \(0.913637\pi\)
\(264\) 251.277i 0.951806i
\(265\) 470.277 + 18.1406i 1.77463 + 0.0684553i
\(266\) −93.6940 −0.352233
\(267\) −35.9272 35.9272i −0.134559 0.134559i
\(268\) −7.01911 + 7.01911i −0.0261907 + 0.0261907i
\(269\) 119.052i 0.442573i 0.975209 + 0.221286i \(0.0710256\pi\)
−0.975209 + 0.221286i \(0.928974\pi\)
\(270\) 36.8809 34.1413i 0.136596 0.126449i
\(271\) 380.174 1.40286 0.701429 0.712740i \(-0.252546\pi\)
0.701429 + 0.712740i \(0.252546\pi\)
\(272\) 206.789 + 206.789i 0.760253 + 0.760253i
\(273\) −55.5613 + 55.5613i −0.203521 + 0.203521i
\(274\) 47.2146i 0.172316i
\(275\) −33.9200 + 439.016i −0.123345 + 1.59642i
\(276\) −16.6833 −0.0604467
\(277\) −374.455 374.455i −1.35182 1.35182i −0.883624 0.468198i \(-0.844903\pi\)
−0.468198 0.883624i \(-0.655097\pi\)
\(278\) −40.3237 + 40.3237i −0.145049 + 0.145049i
\(279\) 48.3448i 0.173279i
\(280\) −74.0212 79.9609i −0.264361 0.285575i
\(281\) −300.844 −1.07062 −0.535309 0.844656i \(-0.679805\pi\)
−0.535309 + 0.844656i \(0.679805\pi\)
\(282\) −193.477 193.477i −0.686090 0.686090i
\(283\) −137.166 + 137.166i −0.484686 + 0.484686i −0.906624 0.421938i \(-0.861350\pi\)
0.421938 + 0.906624i \(0.361350\pi\)
\(284\) 20.5390i 0.0723204i
\(285\) −6.11110 + 158.424i −0.0214425 + 0.555873i
\(286\) −584.198 −2.04265
\(287\) −3.55136 3.55136i −0.0123741 0.0123741i
\(288\) 8.74395 8.74395i 0.0303609 0.0303609i
\(289\) 96.1561i 0.332720i
\(290\) −27.8171 1.07303i −0.0959209 0.00370009i
\(291\) 218.304 0.750186
\(292\) −16.3348 16.3348i −0.0559411 0.0559411i
\(293\) 193.498 193.498i 0.660403 0.660403i −0.295072 0.955475i \(-0.595344\pi\)
0.955475 + 0.295072i \(0.0953436\pi\)
\(294\) 23.4536i 0.0797740i
\(295\) −60.4217 + 55.9334i −0.204819 + 0.189605i
\(296\) −29.4057 −0.0993436
\(297\) 64.7142 + 64.7142i 0.217893 + 0.217893i
\(298\) −19.6761 + 19.6761i −0.0660270 + 0.0660270i
\(299\) 640.065i 2.14068i
\(300\) −8.48575 + 7.26851i −0.0282858 + 0.0242284i
\(301\) −159.385 −0.529518
\(302\) −21.0057 21.0057i −0.0695554 0.0695554i
\(303\) 106.958 106.958i 0.352996 0.352996i
\(304\) 272.795i 0.897352i
\(305\) −25.0340 27.0428i −0.0820787 0.0886650i
\(306\) −113.891 −0.372193
\(307\) 122.528 + 122.528i 0.399115 + 0.399115i 0.877921 0.478806i \(-0.158930\pi\)
−0.478806 + 0.877921i \(0.658930\pi\)
\(308\) 8.50240 8.50240i 0.0276052 0.0276052i
\(309\) 89.9984i 0.291257i
\(310\) 6.00792 155.749i 0.0193804 0.502416i
\(311\) 118.050 0.379582 0.189791 0.981825i \(-0.439219\pi\)
0.189791 + 0.981825i \(0.439219\pi\)
\(312\) −172.975 172.975i −0.554406 0.554406i
\(313\) −289.482 + 289.482i −0.924861 + 0.924861i −0.997368 0.0725069i \(-0.976900\pi\)
0.0725069 + 0.997368i \(0.476900\pi\)
\(314\) 173.105i 0.551290i
\(315\) 39.6568 + 1.52974i 0.125895 + 0.00485630i
\(316\) 0.641686 0.00203065
\(317\) −292.255 292.255i −0.921942 0.921942i 0.0752250 0.997167i \(-0.476032\pi\)
−0.997167 + 0.0752250i \(0.976032\pi\)
\(318\) 222.999 222.999i 0.701254 0.701254i
\(319\) 50.6928i 0.158912i
\(320\) 247.959 229.540i 0.774871 0.717311i
\(321\) 225.318 0.701924
\(322\) 135.092 + 135.092i 0.419541 + 0.419541i
\(323\) 254.048 254.048i 0.786527 0.786527i
\(324\) 2.32229i 0.00716758i
\(325\) 278.861 + 325.561i 0.858034 + 1.00173i
\(326\) 331.712 1.01752
\(327\) −177.133 177.133i −0.541690 0.541690i
\(328\) 11.0562 11.0562i 0.0337079 0.0337079i
\(329\) 216.065i 0.656731i
\(330\) 200.443 + 216.527i 0.607403 + 0.656144i
\(331\) 580.718 1.75443 0.877217 0.480093i \(-0.159397\pi\)
0.877217 + 0.480093i \(0.159397\pi\)
\(332\) 7.49381 + 7.49381i 0.0225717 + 0.0225717i
\(333\) 7.57319 7.57319i 0.0227423 0.0227423i
\(334\) 140.128i 0.419544i
\(335\) 7.41427 192.207i 0.0221321 0.573752i
\(336\) −68.2863 −0.203233
\(337\) 253.637 + 253.637i 0.752631 + 0.752631i 0.974970 0.222339i \(-0.0713690\pi\)
−0.222339 + 0.974970i \(0.571369\pi\)
\(338\) −170.987 + 170.987i −0.505880 + 0.505880i
\(339\) 70.2516i 0.207232i
\(340\) 25.3012 + 0.975976i 0.0744152 + 0.00287052i
\(341\) 283.832 0.832351
\(342\) 75.1223 + 75.1223i 0.219656 + 0.219656i
\(343\) −13.0958 + 13.0958i −0.0381802 + 0.0381802i
\(344\) 496.200i 1.44244i
\(345\) 237.234 219.611i 0.687634 0.636554i
\(346\) −214.865 −0.620997
\(347\) 60.2580 + 60.2580i 0.173654 + 0.173654i 0.788583 0.614929i \(-0.210815\pi\)
−0.614929 + 0.788583i \(0.710815\pi\)
\(348\) 0.909567 0.909567i 0.00261370 0.00261370i
\(349\) 348.191i 0.997681i 0.866694 + 0.498841i \(0.166241\pi\)
−0.866694 + 0.498841i \(0.833759\pi\)
\(350\) 127.569 + 9.85649i 0.364484 + 0.0281614i
\(351\) 89.0963 0.253836
\(352\) 51.3356 + 51.3356i 0.145840 + 0.145840i
\(353\) 113.128 113.128i 0.320476 0.320476i −0.528474 0.848950i \(-0.677235\pi\)
0.848950 + 0.528474i \(0.177235\pi\)
\(354\) 55.1740i 0.155859i
\(355\) −270.366 292.061i −0.761595 0.822708i
\(356\) 7.56925 0.0212619
\(357\) −63.5935 63.5935i −0.178133 0.178133i
\(358\) 222.103 222.103i 0.620401 0.620401i
\(359\) 105.651i 0.294293i 0.989115 + 0.147147i \(0.0470089\pi\)
−0.989115 + 0.147147i \(0.952991\pi\)
\(360\) −4.76241 + 123.460i −0.0132289 + 0.342945i
\(361\) 25.8608 0.0716365
\(362\) −351.841 351.841i −0.971937 0.971937i
\(363\) −231.742 + 231.742i −0.638408 + 0.638408i
\(364\) 11.7058i 0.0321588i
\(365\) 447.302 + 17.2544i 1.22548 + 0.0472723i
\(366\) −24.6941 −0.0674702
\(367\) −230.168 230.168i −0.627161 0.627161i 0.320191 0.947353i \(-0.396253\pi\)
−0.947353 + 0.320191i \(0.896253\pi\)
\(368\) −393.328 + 393.328i −1.06883 + 1.06883i
\(369\) 5.69485i 0.0154332i
\(370\) 25.3392 23.4569i 0.0684843 0.0633970i
\(371\) 249.032 0.671246
\(372\) 5.09271 + 5.09271i 0.0136901 + 0.0136901i
\(373\) −211.456 + 211.456i −0.566906 + 0.566906i −0.931260 0.364355i \(-0.881290\pi\)
0.364355 + 0.931260i \(0.381290\pi\)
\(374\) 668.653i 1.78784i
\(375\) 24.9866 215.060i 0.0666309 0.573493i
\(376\) 672.657 1.78898
\(377\) −34.8961 34.8961i −0.0925626 0.0925626i
\(378\) 18.8047 18.8047i 0.0497478 0.0497478i
\(379\) 132.280i 0.349024i −0.984655 0.174512i \(-0.944165\pi\)
0.984655 0.174512i \(-0.0558347\pi\)
\(380\) −16.0448 17.3323i −0.0422233 0.0456114i
\(381\) −29.8989 −0.0784748
\(382\) 456.997 + 456.997i 1.19633 + 1.19633i
\(383\) 149.538 149.538i 0.390438 0.390438i −0.484406 0.874844i \(-0.660964\pi\)
0.874844 + 0.484406i \(0.160964\pi\)
\(384\) 197.865i 0.515274i
\(385\) −8.98106 + 232.825i −0.0233274 + 0.604739i
\(386\) −54.5991 −0.141448
\(387\) 127.792 + 127.792i 0.330212 + 0.330212i
\(388\) −22.9965 + 22.9965i −0.0592692 + 0.0592692i
\(389\) 289.081i 0.743140i −0.928405 0.371570i \(-0.878820\pi\)
0.928405 0.371570i \(-0.121180\pi\)
\(390\) 287.035 + 11.0722i 0.735988 + 0.0283903i
\(391\) −732.596 −1.87365
\(392\) −40.7701 40.7701i −0.104005 0.104005i
\(393\) 28.4446 28.4446i 0.0723781 0.0723781i
\(394\) 99.9213i 0.253607i
\(395\) −9.12468 + 8.44687i −0.0231005 + 0.0213845i
\(396\) −13.6342 −0.0344297
\(397\) −502.891 502.891i −1.26673 1.26673i −0.947768 0.318961i \(-0.896666\pi\)
−0.318961 0.947768i \(-0.603334\pi\)
\(398\) −256.633 + 256.633i −0.644806 + 0.644806i
\(399\) 83.8923i 0.210256i
\(400\) −28.6977 + 371.425i −0.0717442 + 0.928563i
\(401\) 405.912 1.01225 0.506125 0.862460i \(-0.331078\pi\)
0.506125 + 0.862460i \(0.331078\pi\)
\(402\) −91.1418 91.1418i −0.226721 0.226721i
\(403\) 195.385 195.385i 0.484826 0.484826i
\(404\) 22.5342i 0.0557776i
\(405\) −30.5696 33.0227i −0.0754806 0.0815375i
\(406\) −14.7304 −0.0362817
\(407\) 44.4621 + 44.4621i 0.109244 + 0.109244i
\(408\) 197.981 197.981i 0.485247 0.485247i
\(409\) 505.400i 1.23570i 0.786297 + 0.617849i \(0.211996\pi\)
−0.786297 + 0.617849i \(0.788004\pi\)
\(410\) −0.707713 + 18.3467i −0.00172613 + 0.0447481i
\(411\) 42.2753 0.102860
\(412\) −9.48056 9.48056i −0.0230111 0.0230111i
\(413\) −30.8076 + 30.8076i −0.0745946 + 0.0745946i
\(414\) 216.629i 0.523259i
\(415\) −205.206 7.91569i −0.494472 0.0190740i
\(416\) 70.6772 0.169897
\(417\) 36.1053 + 36.1053i 0.0865834 + 0.0865834i
\(418\) −441.042 + 441.042i −1.05512 + 1.05512i
\(419\) 553.591i 1.32122i −0.750729 0.660610i \(-0.770298\pi\)
0.750729 0.660610i \(-0.229702\pi\)
\(420\) −4.33865 + 4.01636i −0.0103301 + 0.00956275i
\(421\) −320.444 −0.761150 −0.380575 0.924750i \(-0.624274\pi\)
−0.380575 + 0.924750i \(0.624274\pi\)
\(422\) 100.729 + 100.729i 0.238694 + 0.238694i
\(423\) −173.237 + 173.237i −0.409544 + 0.409544i
\(424\) 775.293i 1.82852i
\(425\) −372.626 + 319.175i −0.876767 + 0.750999i
\(426\) −266.695 −0.626045
\(427\) −13.7885 13.7885i −0.0322915 0.0322915i
\(428\) −23.7353 + 23.7353i −0.0554562 + 0.0554562i
\(429\) 523.083i 1.21931i
\(430\) 395.818 + 427.580i 0.920508 + 0.994373i
\(431\) 221.870 0.514780 0.257390 0.966308i \(-0.417138\pi\)
0.257390 + 0.966308i \(0.417138\pi\)
\(432\) 54.7508 + 54.7508i 0.126738 + 0.126738i
\(433\) −162.133 + 162.133i −0.374440 + 0.374440i −0.869091 0.494651i \(-0.835296\pi\)
0.494651 + 0.869091i \(0.335296\pi\)
\(434\) 82.4759i 0.190037i
\(435\) −0.960773 + 24.9070i −0.00220867 + 0.0572575i
\(436\) 37.3188 0.0855936
\(437\) 483.219 + 483.219i 1.10576 + 1.10576i
\(438\) 212.104 212.104i 0.484256 0.484256i
\(439\) 606.504i 1.38156i −0.723066 0.690779i \(-0.757268\pi\)
0.723066 0.690779i \(-0.242732\pi\)
\(440\) −724.834 27.9600i −1.64735 0.0635455i
\(441\) 21.0000 0.0476190
\(442\) −460.289 460.289i −1.04138 1.04138i
\(443\) −9.75385 + 9.75385i −0.0220177 + 0.0220177i −0.718030 0.696012i \(-0.754956\pi\)
0.696012 + 0.718030i \(0.254956\pi\)
\(444\) 1.59554i 0.00359356i
\(445\) −107.634 + 99.6382i −0.241873 + 0.223906i
\(446\) −706.410 −1.58388
\(447\) 17.6177 + 17.6177i 0.0394131 + 0.0394131i
\(448\) 126.428 126.428i 0.282206 0.282206i
\(449\) 448.959i 0.999908i −0.866052 0.499954i \(-0.833350\pi\)
0.866052 0.499954i \(-0.166650\pi\)
\(450\) −94.3803 110.186i −0.209734 0.244857i
\(451\) −33.4344 −0.0741340
\(452\) −7.40041 7.40041i −0.0163726 0.0163726i
\(453\) −18.8083 + 18.8083i −0.0415193 + 0.0415193i
\(454\) 26.6161i 0.0586257i
\(455\) 154.090 + 166.455i 0.338659 + 0.365835i
\(456\) −261.175 −0.572753
\(457\) 368.860 + 368.860i 0.807133 + 0.807133i 0.984199 0.177066i \(-0.0566606\pi\)
−0.177066 + 0.984199i \(0.556661\pi\)
\(458\) −147.791 + 147.791i −0.322688 + 0.322688i
\(459\) 101.977i 0.222171i
\(460\) −1.85638 + 48.1247i −0.00403561 + 0.104619i
\(461\) −507.955 −1.10186 −0.550928 0.834553i \(-0.685726\pi\)
−0.550928 + 0.834553i \(0.685726\pi\)
\(462\) 110.402 + 110.402i 0.238966 + 0.238966i
\(463\) 255.428 255.428i 0.551681 0.551681i −0.375245 0.926926i \(-0.622441\pi\)
0.926926 + 0.375245i \(0.122441\pi\)
\(464\) 42.8882i 0.0924315i
\(465\) −139.456 5.37941i −0.299904 0.0115686i
\(466\) 6.76597 0.0145192
\(467\) 408.350 + 408.350i 0.874411 + 0.874411i 0.992950 0.118538i \(-0.0378208\pi\)
−0.118538 + 0.992950i \(0.537821\pi\)
\(468\) −9.38553 + 9.38553i −0.0200545 + 0.0200545i
\(469\) 101.782i 0.217019i
\(470\) −579.635 + 536.577i −1.23326 + 1.14165i
\(471\) −154.996 −0.329079
\(472\) −95.9108 95.9108i −0.203201 0.203201i
\(473\) −750.267 + 750.267i −1.58619 + 1.58619i
\(474\) 8.33218i 0.0175784i
\(475\) 456.310 + 35.2562i 0.960653 + 0.0742236i
\(476\) 13.3981 0.0281472
\(477\) −199.670 199.670i −0.418595 0.418595i
\(478\) 315.935 315.935i 0.660952 0.660952i
\(479\) 664.740i 1.38777i −0.720087 0.693883i \(-0.755898\pi\)
0.720087 0.693883i \(-0.244102\pi\)
\(480\) −24.2499 26.1958i −0.0505206 0.0545746i
\(481\) 61.2140 0.127264
\(482\) 383.548 + 383.548i 0.795743 + 0.795743i
\(483\) 120.960 120.960i 0.250434 0.250434i
\(484\) 48.8241i 0.100876i
\(485\) 24.2911 629.721i 0.0500848 1.29839i
\(486\) −30.1546 −0.0620464
\(487\) −334.715 334.715i −0.687300 0.687300i 0.274334 0.961634i \(-0.411543\pi\)
−0.961634 + 0.274334i \(0.911543\pi\)
\(488\) 42.9266 42.9266i 0.0879643 0.0879643i
\(489\) 297.010i 0.607383i
\(490\) 67.6543 + 2.60972i 0.138070 + 0.00532596i
\(491\) −312.255 −0.635958 −0.317979 0.948098i \(-0.603004\pi\)
−0.317979 + 0.948098i \(0.603004\pi\)
\(492\) −0.599904 0.599904i −0.00121932 0.00121932i
\(493\) 39.9409 39.9409i 0.0810160 0.0810160i
\(494\) 607.212i 1.22917i
\(495\) 193.876 179.474i 0.391668 0.362574i
\(496\) 240.133 0.484139
\(497\) −148.915 148.915i −0.299628 0.299628i
\(498\) −97.3057 + 97.3057i −0.195393 + 0.195393i
\(499\) 89.3669i 0.179092i 0.995983 + 0.0895460i \(0.0285416\pi\)
−0.995983 + 0.0895460i \(0.971458\pi\)
\(500\) 20.0226 + 25.2868i 0.0400451 + 0.0505736i
\(501\) 125.469 0.250436
\(502\) −73.1434 73.1434i −0.145704 0.145704i
\(503\) 627.521 627.521i 1.24756 1.24756i 0.290761 0.956796i \(-0.406092\pi\)
0.956796 0.290761i \(-0.0939085\pi\)
\(504\) 65.3776i 0.129718i
\(505\) −296.630 320.432i −0.587385 0.634520i
\(506\) 1271.83 2.51350
\(507\) 153.100 + 153.100i 0.301972 + 0.301972i
\(508\) 3.14959 3.14959i 0.00619998 0.00619998i
\(509\) 556.945i 1.09420i −0.837069 0.547098i \(-0.815733\pi\)
0.837069 0.547098i \(-0.184267\pi\)
\(510\) −12.6729 + 328.531i −0.0248488 + 0.644178i
\(511\) 236.866 0.463534
\(512\) 390.591 + 390.591i 0.762872 + 0.762872i
\(513\) 67.2635 67.2635i 0.131118 0.131118i
\(514\) 215.946i 0.420128i
\(515\) 259.610 + 10.0143i 0.504097 + 0.0194452i
\(516\) −26.9236 −0.0521776
\(517\) −1017.07 1017.07i −1.96726 1.96726i
\(518\) 12.9198 12.9198i 0.0249418 0.0249418i
\(519\) 192.387i 0.370688i
\(520\) −518.211 + 479.716i −0.996559 + 0.922531i
\(521\) −64.5705 −0.123936 −0.0619679 0.998078i \(-0.519738\pi\)
−0.0619679 + 0.998078i \(0.519738\pi\)
\(522\) 11.8106 + 11.8106i 0.0226256 + 0.0226256i
\(523\) −431.531 + 431.531i −0.825107 + 0.825107i −0.986835 0.161728i \(-0.948293\pi\)
0.161728 + 0.986835i \(0.448293\pi\)
\(524\) 5.99279i 0.0114366i
\(525\) 8.82537 114.224i 0.0168102 0.217569i
\(526\) 885.986 1.68438
\(527\) 223.631 + 223.631i 0.424347 + 0.424347i
\(528\) −321.442 + 321.442i −0.608791 + 0.608791i
\(529\) 864.452i 1.63413i
\(530\) −618.450 668.077i −1.16689 1.26052i
\(531\) 49.4020 0.0930358
\(532\) −8.83734 8.83734i −0.0166115 0.0166115i
\(533\) −23.0157 + 23.0157i −0.0431814 + 0.0431814i
\(534\) 98.2854i 0.184055i
\(535\) 25.0715 649.952i 0.0468626 1.21486i
\(536\) 316.870 0.591175
\(537\) −198.868 198.868i −0.370332 0.370332i
\(538\) 162.844 162.844i 0.302684 0.302684i
\(539\) 123.291i 0.228740i
\(540\) 6.69891 + 0.258406i 0.0124054 + 0.000478530i
\(541\) −571.616 −1.05659 −0.528295 0.849061i \(-0.677169\pi\)
−0.528295 + 0.849061i \(0.677169\pi\)
\(542\) −520.017 520.017i −0.959441 0.959441i
\(543\) −315.034 + 315.034i −0.580173 + 0.580173i
\(544\) 80.8946i 0.148703i
\(545\) −530.667 + 491.248i −0.973702 + 0.901372i
\(546\) 151.998 0.278384
\(547\) 259.835 + 259.835i 0.475017 + 0.475017i 0.903534 0.428516i \(-0.140964\pi\)
−0.428516 + 0.903534i \(0.640964\pi\)
\(548\) −4.45334 + 4.45334i −0.00812653 + 0.00812653i
\(549\) 22.1108i 0.0402746i
\(550\) 646.900 554.106i 1.17618 1.00747i
\(551\) −52.6898 −0.0956258
\(552\) 376.574 + 376.574i 0.682200 + 0.682200i
\(553\) −4.65245 + 4.65245i −0.00841311 + 0.00841311i
\(554\) 1024.39i 1.84907i
\(555\) −21.0030 22.6884i −0.0378432 0.0408799i
\(556\) −7.60677 −0.0136812
\(557\) 503.660 + 503.660i 0.904237 + 0.904237i 0.995799 0.0915625i \(-0.0291861\pi\)
−0.0915625 + 0.995799i \(0.529186\pi\)
\(558\) −66.1278 + 66.1278i −0.118509 + 0.118509i
\(559\) 1032.94i 1.84784i
\(560\) −7.59834 + 196.979i −0.0135685 + 0.351748i
\(561\) −598.703 −1.06721
\(562\) 411.506 + 411.506i 0.732216 + 0.732216i
\(563\) −405.076 + 405.076i −0.719495 + 0.719495i −0.968502 0.249007i \(-0.919896\pi\)
0.249007 + 0.968502i \(0.419896\pi\)
\(564\) 36.4981i 0.0647129i
\(565\) 202.648 + 7.81703i 0.358670 + 0.0138355i
\(566\) 375.242 0.662972
\(567\) −16.8375 16.8375i −0.0296957 0.0296957i
\(568\) 463.605 463.605i 0.816207 0.816207i
\(569\) 674.447i 1.18532i 0.805453 + 0.592660i \(0.201922\pi\)
−0.805453 + 0.592660i \(0.798078\pi\)
\(570\) 225.057 208.339i 0.394837 0.365507i
\(571\) 825.137 1.44507 0.722537 0.691333i \(-0.242976\pi\)
0.722537 + 0.691333i \(0.242976\pi\)
\(572\) −55.1023 55.1023i −0.0963328 0.0963328i
\(573\) 409.189 409.189i 0.714116 0.714116i
\(574\) 9.71539i 0.0169258i
\(575\) −607.094 708.762i −1.05582 1.23263i
\(576\) −202.736 −0.351972
\(577\) 532.596 + 532.596i 0.923043 + 0.923043i 0.997243 0.0742001i \(-0.0236403\pi\)
−0.0742001 + 0.997243i \(0.523640\pi\)
\(578\) 131.526 131.526i 0.227554 0.227554i
\(579\) 48.8873i 0.0844340i
\(580\) −2.52253 2.72495i −0.00434919 0.00469819i
\(581\) −108.666 −0.187032
\(582\) −298.605 298.605i −0.513067 0.513067i
\(583\) 1172.26 1172.26i 2.01074 2.01074i
\(584\) 737.416i 1.26270i
\(585\) 9.91391 257.008i 0.0169469 0.439329i
\(586\) −529.349 −0.903325
\(587\) 800.352 + 800.352i 1.36346 + 1.36346i 0.869463 + 0.493999i \(0.164465\pi\)
0.493999 + 0.869463i \(0.335535\pi\)
\(588\) −2.21217 + 2.21217i −0.00376219 + 0.00376219i
\(589\) 295.013i 0.500871i
\(590\) 159.155 + 6.13931i 0.269754 + 0.0104056i
\(591\) −89.4682 −0.151384
\(592\) 37.6168 + 37.6168i 0.0635419 + 0.0635419i
\(593\) 254.908 254.908i 0.429862 0.429862i −0.458719 0.888581i \(-0.651692\pi\)
0.888581 + 0.458719i \(0.151692\pi\)
\(594\) 177.037i 0.298042i
\(595\) −190.518 + 176.366i −0.320199 + 0.296414i
\(596\) −3.71174 −0.00622775
\(597\) 229.786 + 229.786i 0.384900 + 0.384900i
\(598\) 875.505 875.505i 1.46406 1.46406i
\(599\) 661.029i 1.10355i −0.833991 0.551777i \(-0.813950\pi\)
0.833991 0.551777i \(-0.186050\pi\)
\(600\) 355.604 + 27.4753i 0.592674 + 0.0457922i
\(601\) −410.580 −0.683162 −0.341581 0.939852i \(-0.610962\pi\)
−0.341581 + 0.939852i \(0.610962\pi\)
\(602\) 218.013 + 218.013i 0.362148 + 0.362148i
\(603\) −81.6072 + 81.6072i −0.135335 + 0.135335i
\(604\) 3.96258i 0.00656056i
\(605\) 642.698 + 694.271i 1.06231 + 1.14756i
\(606\) −292.602 −0.482842
\(607\) −604.297 604.297i −0.995548 0.995548i 0.00444263 0.999990i \(-0.498586\pi\)
−0.999990 + 0.00444263i \(0.998586\pi\)
\(608\) 53.3579 53.3579i 0.0877598 0.0877598i
\(609\) 13.1894i 0.0216574i
\(610\) −2.74776 + 71.2327i −0.00450452 + 0.116775i
\(611\) −1400.27 −2.29177
\(612\) −10.7424 10.7424i −0.0175529 0.0175529i
\(613\) −61.4626 + 61.4626i −0.100265 + 0.100265i −0.755460 0.655195i \(-0.772587\pi\)
0.655195 + 0.755460i \(0.272587\pi\)
\(614\) 335.198i 0.545926i
\(615\) 16.4274 + 0.633677i 0.0267112 + 0.00103037i
\(616\) −383.831 −0.623103
\(617\) −509.151 509.151i −0.825204 0.825204i 0.161645 0.986849i \(-0.448320\pi\)
−0.986849 + 0.161645i \(0.948320\pi\)
\(618\) 123.103 123.103i 0.199196 0.199196i
\(619\) 735.555i 1.18830i 0.804356 + 0.594148i \(0.202511\pi\)
−0.804356 + 0.594148i \(0.797489\pi\)
\(620\) 15.2571 14.1238i 0.0246083 0.0227803i
\(621\) −193.967 −0.312346
\(622\) −161.473 161.473i −0.259603 0.259603i
\(623\) −54.8798 + 54.8798i −0.0880895 + 0.0880895i
\(624\) 442.550i 0.709214i
\(625\) −617.582 96.0065i −0.988131 0.153610i
\(626\) 791.928 1.26506
\(627\) 394.903 + 394.903i 0.629830 + 0.629830i
\(628\) 16.3275 16.3275i 0.0259992 0.0259992i
\(629\) 70.0634i 0.111389i
\(630\) −52.1517 56.3365i −0.0827804 0.0894230i
\(631\) 649.002 1.02853 0.514265 0.857631i \(-0.328065\pi\)
0.514265 + 0.857631i \(0.328065\pi\)
\(632\) −14.4841 14.4841i −0.0229179 0.0229179i
\(633\) 90.1914 90.1914i 0.142482 0.142482i
\(634\) 799.517i 1.26107i
\(635\) −3.32691 + 86.2465i −0.00523922 + 0.135821i
\(636\) 42.0671 0.0661432
\(637\) 84.8713 + 84.8713i 0.133236 + 0.133236i
\(638\) −69.3396 + 69.3396i −0.108683 + 0.108683i
\(639\) 238.795i 0.373702i
\(640\) −570.763 22.0168i −0.891818 0.0344013i
\(641\) −103.576 −0.161585 −0.0807925 0.996731i \(-0.525745\pi\)
−0.0807925 + 0.996731i \(0.525745\pi\)
\(642\) −308.198 308.198i −0.480059 0.480059i
\(643\) 504.926 504.926i 0.785266 0.785266i −0.195448 0.980714i \(-0.562616\pi\)
0.980714 + 0.195448i \(0.0626160\pi\)
\(644\) 25.4841i 0.0395716i
\(645\) 382.850 354.410i 0.593566 0.549473i
\(646\) −694.994 −1.07584
\(647\) 134.888 + 134.888i 0.208482 + 0.208482i 0.803622 0.595140i \(-0.202903\pi\)
−0.595140 + 0.803622i \(0.702903\pi\)
\(648\) 52.4187 52.4187i 0.0808931 0.0808931i
\(649\) 290.039i 0.446901i
\(650\) 63.8779 826.752i 0.0982738 1.27193i
\(651\) −73.8478 −0.113438
\(652\) 31.2875 + 31.2875i 0.0479870 + 0.0479870i
\(653\) −123.054 + 123.054i −0.188444 + 0.188444i −0.795023 0.606579i \(-0.792541\pi\)
0.606579 + 0.795023i \(0.292541\pi\)
\(654\) 484.578i 0.740944i
\(655\) −78.8864 85.2166i −0.120437 0.130102i
\(656\) −28.2869 −0.0431202
\(657\) −189.915 189.915i −0.289064 0.289064i
\(658\) −295.542 + 295.542i −0.449151 + 0.449151i
\(659\) 811.814i 1.23189i 0.787790 + 0.615944i \(0.211225\pi\)
−0.787790 + 0.615944i \(0.788775\pi\)
\(660\) −1.51710 + 39.3292i −0.00229864 + 0.0595897i
\(661\) 979.510 1.48186 0.740930 0.671582i \(-0.234385\pi\)
0.740930 + 0.671582i \(0.234385\pi\)
\(662\) −794.329 794.329i −1.19989 1.19989i
\(663\) −412.137 + 412.137i −0.621625 + 0.621625i
\(664\) 338.300i 0.509488i
\(665\) 241.996 + 9.33486i 0.363904 + 0.0140374i
\(666\) −20.7178 −0.0311078
\(667\) 75.9705 + 75.9705i 0.113899 + 0.113899i
\(668\) −13.2170 + 13.2170i −0.0197860 + 0.0197860i
\(669\) 632.510i 0.945456i
\(670\) −273.050 + 252.767i −0.407537 + 0.377264i
\(671\) −129.812 −0.193461
\(672\) −13.3566 13.3566i −0.0198759 0.0198759i
\(673\) −327.449 + 327.449i −0.486552 + 0.486552i −0.907216 0.420664i \(-0.861797\pi\)
0.420664 + 0.907216i \(0.361797\pi\)
\(674\) 693.868i 1.02948i
\(675\) −98.6589 + 84.5069i −0.146161 + 0.125195i
\(676\) −32.2555 −0.0477152
\(677\) 463.677 + 463.677i 0.684900 + 0.684900i 0.961100 0.276200i \(-0.0890754\pi\)
−0.276200 + 0.961100i \(0.589075\pi\)
\(678\) 96.0929 96.0929i 0.141730 0.141730i
\(679\) 333.465i 0.491112i
\(680\) −549.067 593.126i −0.807451 0.872244i
\(681\) 23.8317 0.0349951
\(682\) −388.236 388.236i −0.569261 0.569261i
\(683\) 667.534 667.534i 0.977356 0.977356i −0.0223933 0.999749i \(-0.507129\pi\)
0.999749 + 0.0223933i \(0.00712859\pi\)
\(684\) 14.1713i 0.0207182i
\(685\) 4.70405 121.948i 0.00686723 0.178026i
\(686\) 35.8259 0.0522243
\(687\) 132.330 + 132.330i 0.192621 + 0.192621i
\(688\) −634.756 + 634.756i −0.922610 + 0.922610i
\(689\) 1613.93i 2.34242i
\(690\) −624.890 24.1048i −0.905638 0.0349344i
\(691\) −622.518 −0.900895 −0.450447 0.892803i \(-0.648736\pi\)
−0.450447 + 0.892803i \(0.648736\pi\)
\(692\) −20.2663 20.2663i −0.0292866 0.0292866i
\(693\) 98.8525 98.8525i 0.142644 0.142644i
\(694\) 164.846i 0.237531i
\(695\) 108.167 100.132i 0.155636 0.144075i
\(696\) −41.0614 −0.0589963
\(697\) −26.3430 26.3430i −0.0377948 0.0377948i
\(698\) 476.269 476.269i 0.682334 0.682334i
\(699\) 6.05816i 0.00866689i
\(700\) 11.1028 + 12.9622i 0.0158612 + 0.0185174i
\(701\) −821.585 −1.17202 −0.586009 0.810304i \(-0.699302\pi\)
−0.586009 + 0.810304i \(0.699302\pi\)
\(702\) −121.869 121.869i −0.173603 0.173603i
\(703\) 46.2137 46.2137i 0.0657378 0.0657378i
\(704\) 1190.26i 1.69071i
\(705\) 480.444 + 518.997i 0.681481 + 0.736166i
\(706\) −309.482 −0.438359
\(707\) −163.381 163.381i −0.231090 0.231090i
\(708\) −5.20408 + 5.20408i −0.00735039 + 0.00735039i
\(709\) 1124.01i 1.58535i 0.609647 + 0.792673i \(0.291311\pi\)
−0.609647 + 0.792673i \(0.708689\pi\)
\(710\) −29.6757 + 769.310i −0.0417967 + 1.08354i
\(711\) 7.46052 0.0104930
\(712\) −170.853 170.853i −0.239962 0.239962i
\(713\) −425.363 + 425.363i −0.596581 + 0.596581i
\(714\) 173.971i 0.243658i
\(715\) 1508.89 + 58.2045i 2.11033 + 0.0814048i
\(716\) 41.8982 0.0585170
\(717\) −282.884 282.884i −0.394538 0.394538i
\(718\) 144.514 144.514i 0.201273 0.201273i
\(719\) 826.757i 1.14987i 0.818199 + 0.574936i \(0.194973\pi\)
−0.818199 + 0.574936i \(0.805027\pi\)
\(720\) 164.027 151.842i 0.227815 0.210892i
\(721\) 137.475 0.190672
\(722\) −35.3734 35.3734i −0.0489936 0.0489936i
\(723\) 343.424 343.424i 0.474998 0.474998i
\(724\) 66.3722i 0.0916744i
\(725\) 71.7400 + 5.54290i 0.0989518 + 0.00764538i
\(726\) 633.972 0.873239
\(727\) 829.278 + 829.278i 1.14069 + 1.14069i 0.988325 + 0.152360i \(0.0486874\pi\)
0.152360 + 0.988325i \(0.451313\pi\)
\(728\) −264.223 + 264.223i −0.362944 + 0.362944i
\(729\) 27.0000i 0.0370370i
\(730\) −588.236 635.438i −0.805803 0.870463i
\(731\) −1182.27 −1.61733
\(732\) −2.32918 2.32918i −0.00318194 0.00318194i
\(733\) −306.100 + 306.100i −0.417599 + 0.417599i −0.884375 0.466776i \(-0.845415\pi\)
0.466776 + 0.884375i \(0.345415\pi\)
\(734\) 629.666i 0.857856i
\(735\) 2.33671 60.5767i 0.00317920 0.0824173i
\(736\) −153.868 −0.209059
\(737\) −479.115 479.115i −0.650088 0.650088i
\(738\) 7.78964 7.78964i 0.0105551 0.0105551i
\(739\) 1152.24i 1.55919i 0.626283 + 0.779596i \(0.284575\pi\)
−0.626283 + 0.779596i \(0.715425\pi\)
\(740\) 4.60251 + 0.177539i 0.00621961 + 0.000239918i
\(741\) 543.689 0.733724
\(742\) −340.636 340.636i −0.459078 0.459078i
\(743\) −87.8428 + 87.8428i −0.118227 + 0.118227i −0.763745 0.645518i \(-0.776642\pi\)
0.645518 + 0.763745i \(0.276642\pi\)
\(744\) 229.905i 0.309012i
\(745\) 52.7804 48.8597i 0.0708462 0.0655835i
\(746\) 578.475 0.775436
\(747\) 87.1263 + 87.1263i 0.116635 + 0.116635i
\(748\) 63.0682 63.0682i 0.0843158 0.0843158i
\(749\) 344.178i 0.459517i
\(750\) −328.345 + 259.989i −0.437793 + 0.346653i
\(751\) −601.083 −0.800377 −0.400189 0.916433i \(-0.631055\pi\)
−0.400189 + 0.916433i \(0.631055\pi\)
\(752\) −860.485 860.485i −1.14426 1.14426i
\(753\) −65.4916 + 65.4916i −0.0869743 + 0.0869743i
\(754\) 95.4645i 0.126611i
\(755\) 52.1616 + 56.3472i 0.0690882 + 0.0746321i
\(756\) 3.54736 0.00469228
\(757\) 650.454 + 650.454i 0.859252 + 0.859252i 0.991250 0.131998i \(-0.0421393\pi\)
−0.131998 + 0.991250i \(0.542139\pi\)
\(758\) −180.938 + 180.938i −0.238704 + 0.238704i
\(759\) 1138.78i 1.50037i
\(760\) −29.0615 + 753.388i −0.0382388 + 0.991300i
\(761\) 344.833 0.453131 0.226566 0.973996i \(-0.427250\pi\)
0.226566 + 0.973996i \(0.427250\pi\)
\(762\) 40.8969 + 40.8969i 0.0536704 + 0.0536704i
\(763\) −270.574 + 270.574i −0.354619 + 0.354619i
\(764\) 86.2090i 0.112839i
\(765\) 294.162 + 11.3471i 0.384526 + 0.0148328i
\(766\) −409.087 −0.534056
\(767\) 199.658 + 199.658i 0.260310 + 0.260310i
\(768\) 60.4187 60.4187i 0.0786702 0.0786702i
\(769\) 953.105i 1.23941i 0.784836 + 0.619704i \(0.212747\pi\)
−0.784836 + 0.619704i \(0.787253\pi\)
\(770\) 330.751 306.182i 0.429547 0.397639i
\(771\) −193.355 −0.250785
\(772\) −5.14986 5.14986i −0.00667080