Properties

Label 230.3.f.b.47.8
Level $230$
Weight $3$
Character 230.47
Analytic conductor $6.267$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.f (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.26704608029\)
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 47.8
Character \(\chi\) \(=\) 230.47
Dual form 230.3.f.b.93.8

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.74954 - 1.74954i) q^{3} +2.00000i q^{4} +(-3.63965 + 3.42826i) q^{5} +3.49907 q^{6} +(4.68530 + 4.68530i) q^{7} +(-2.00000 + 2.00000i) q^{8} +2.87825i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.74954 - 1.74954i) q^{3} +2.00000i q^{4} +(-3.63965 + 3.42826i) q^{5} +3.49907 q^{6} +(4.68530 + 4.68530i) q^{7} +(-2.00000 + 2.00000i) q^{8} +2.87825i q^{9} +(-7.06791 - 0.211383i) q^{10} +7.34415 q^{11} +(3.49907 + 3.49907i) q^{12} +(-0.802148 + 0.802148i) q^{13} +9.37061i q^{14} +(-0.369822 + 12.3656i) q^{15} -4.00000 q^{16} +(2.03445 + 2.03445i) q^{17} +(-2.87825 + 2.87825i) q^{18} +12.6979i q^{19} +(-6.85652 - 7.27929i) q^{20} +16.3942 q^{21} +(7.34415 + 7.34415i) q^{22} +(3.39116 - 3.39116i) q^{23} +6.99814i q^{24} +(1.49404 - 24.9553i) q^{25} -1.60430 q^{26} +(20.7814 + 20.7814i) q^{27} +(-9.37061 + 9.37061i) q^{28} -18.2947i q^{29} +(-12.7354 + 11.9957i) q^{30} +32.9458 q^{31} +(-4.00000 - 4.00000i) q^{32} +(12.8489 - 12.8489i) q^{33} +4.06891i q^{34} +(-33.1153 - 0.990394i) q^{35} -5.75651 q^{36} +(-22.1338 - 22.1338i) q^{37} +(-12.6979 + 12.6979i) q^{38} +2.80677i q^{39} +(0.422766 - 14.1358i) q^{40} -16.8120 q^{41} +(16.3942 + 16.3942i) q^{42} +(15.6643 - 15.6643i) q^{43} +14.6883i q^{44} +(-9.86741 - 10.4758i) q^{45} +6.78233 q^{46} +(-53.7739 - 53.7739i) q^{47} +(-6.99814 + 6.99814i) q^{48} -5.09584i q^{49} +(26.4494 - 23.4613i) q^{50} +7.11869 q^{51} +(-1.60430 - 1.60430i) q^{52} +(-15.1999 + 15.1999i) q^{53} +41.5628i q^{54} +(-26.7301 + 25.1777i) q^{55} -18.7412 q^{56} +(22.2155 + 22.2155i) q^{57} +(18.2947 - 18.2947i) q^{58} +8.32600i q^{59} +(-24.7311 - 0.739644i) q^{60} +16.1313 q^{61} +(32.9458 + 32.9458i) q^{62} +(-13.4855 + 13.4855i) q^{63} -8.00000i q^{64} +(0.169561 - 5.66951i) q^{65} +25.6977 q^{66} +(21.8813 + 21.8813i) q^{67} +(-4.06891 + 4.06891i) q^{68} -11.8659i q^{69} +(-32.1249 - 34.1057i) q^{70} -105.543 q^{71} +(-5.75651 - 5.75651i) q^{72} +(63.5112 - 63.5112i) q^{73} -44.2677i q^{74} +(-41.0463 - 46.2741i) q^{75} -25.3959 q^{76} +(34.4096 + 34.4096i) q^{77} +(-2.80677 + 2.80677i) q^{78} -19.7472i q^{79} +(14.5586 - 13.7130i) q^{80} +46.8114 q^{81} +(-16.8120 - 16.8120i) q^{82} +(105.262 - 105.262i) q^{83} +32.7884i q^{84} +(-14.3793 - 0.430049i) q^{85} +31.3285 q^{86} +(-32.0072 - 32.0072i) q^{87} +(-14.6883 + 14.6883i) q^{88} -131.803i q^{89} +(0.608414 - 20.3432i) q^{90} -7.51662 q^{91} +(6.78233 + 6.78233i) q^{92} +(57.6398 - 57.6398i) q^{93} -107.548i q^{94} +(-43.5319 - 46.2160i) q^{95} -13.9963 q^{96} +(101.232 + 101.232i) q^{97} +(5.09584 - 5.09584i) q^{98} +21.1383i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 1.74954 1.74954i 0.583178 0.583178i −0.352597 0.935775i \(-0.614701\pi\)
0.935775 + 0.352597i \(0.114701\pi\)
\(4\) 2.00000i 0.500000i
\(5\) −3.63965 + 3.42826i −0.727929 + 0.685652i
\(6\) 3.49907 0.583178
\(7\) 4.68530 + 4.68530i 0.669329 + 0.669329i 0.957561 0.288232i \(-0.0930673\pi\)
−0.288232 + 0.957561i \(0.593067\pi\)
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) 2.87825i 0.319806i
\(10\) −7.06791 0.211383i −0.706791 0.0211383i
\(11\) 7.34415 0.667650 0.333825 0.942635i \(-0.391660\pi\)
0.333825 + 0.942635i \(0.391660\pi\)
\(12\) 3.49907 + 3.49907i 0.291589 + 0.291589i
\(13\) −0.802148 + 0.802148i −0.0617037 + 0.0617037i −0.737285 0.675582i \(-0.763893\pi\)
0.675582 + 0.737285i \(0.263893\pi\)
\(14\) 9.37061i 0.669329i
\(15\) −0.369822 + 12.3656i −0.0246548 + 0.824370i
\(16\) −4.00000 −0.250000
\(17\) 2.03445 + 2.03445i 0.119674 + 0.119674i 0.764407 0.644734i \(-0.223032\pi\)
−0.644734 + 0.764407i \(0.723032\pi\)
\(18\) −2.87825 + 2.87825i −0.159903 + 0.159903i
\(19\) 12.6979i 0.668313i 0.942518 + 0.334156i \(0.108451\pi\)
−0.942518 + 0.334156i \(0.891549\pi\)
\(20\) −6.85652 7.27929i −0.342826 0.363965i
\(21\) 16.3942 0.780677
\(22\) 7.34415 + 7.34415i 0.333825 + 0.333825i
\(23\) 3.39116 3.39116i 0.147442 0.147442i
\(24\) 6.99814i 0.291589i
\(25\) 1.49404 24.9553i 0.0597614 0.998213i
\(26\) −1.60430 −0.0617037
\(27\) 20.7814 + 20.7814i 0.769682 + 0.769682i
\(28\) −9.37061 + 9.37061i −0.334665 + 0.334665i
\(29\) 18.2947i 0.630851i −0.948950 0.315426i \(-0.897853\pi\)
0.948950 0.315426i \(-0.102147\pi\)
\(30\) −12.7354 + 11.9957i −0.424512 + 0.399858i
\(31\) 32.9458 1.06277 0.531384 0.847131i \(-0.321672\pi\)
0.531384 + 0.847131i \(0.321672\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 12.8489 12.8489i 0.389359 0.389359i
\(34\) 4.06891i 0.119674i
\(35\) −33.1153 0.990394i −0.946151 0.0282970i
\(36\) −5.75651 −0.159903
\(37\) −22.1338 22.1338i −0.598212 0.598212i 0.341625 0.939836i \(-0.389023\pi\)
−0.939836 + 0.341625i \(0.889023\pi\)
\(38\) −12.6979 + 12.6979i −0.334156 + 0.334156i
\(39\) 2.80677i 0.0719686i
\(40\) 0.422766 14.1358i 0.0105691 0.353395i
\(41\) −16.8120 −0.410049 −0.205024 0.978757i \(-0.565727\pi\)
−0.205024 + 0.978757i \(0.565727\pi\)
\(42\) 16.3942 + 16.3942i 0.390338 + 0.390338i
\(43\) 15.6643 15.6643i 0.364285 0.364285i −0.501103 0.865388i \(-0.667072\pi\)
0.865388 + 0.501103i \(0.167072\pi\)
\(44\) 14.6883i 0.333825i
\(45\) −9.86741 10.4758i −0.219276 0.232796i
\(46\) 6.78233 0.147442
\(47\) −53.7739 53.7739i −1.14412 1.14412i −0.987688 0.156437i \(-0.949999\pi\)
−0.156437 0.987688i \(-0.550001\pi\)
\(48\) −6.99814 + 6.99814i −0.145795 + 0.145795i
\(49\) 5.09584i 0.103997i
\(50\) 26.4494 23.4613i 0.528987 0.469226i
\(51\) 7.11869 0.139582
\(52\) −1.60430 1.60430i −0.0308519 0.0308519i
\(53\) −15.1999 + 15.1999i −0.286790 + 0.286790i −0.835809 0.549020i \(-0.815001\pi\)
0.549020 + 0.835809i \(0.315001\pi\)
\(54\) 41.5628i 0.769682i
\(55\) −26.7301 + 25.1777i −0.486002 + 0.457776i
\(56\) −18.7412 −0.334665
\(57\) 22.2155 + 22.2155i 0.389745 + 0.389745i
\(58\) 18.2947 18.2947i 0.315426 0.315426i
\(59\) 8.32600i 0.141119i 0.997508 + 0.0705593i \(0.0224784\pi\)
−0.997508 + 0.0705593i \(0.977522\pi\)
\(60\) −24.7311 0.739644i −0.412185 0.0123274i
\(61\) 16.1313 0.264448 0.132224 0.991220i \(-0.457788\pi\)
0.132224 + 0.991220i \(0.457788\pi\)
\(62\) 32.9458 + 32.9458i 0.531384 + 0.531384i
\(63\) −13.4855 + 13.4855i −0.214055 + 0.214055i
\(64\) 8.00000i 0.125000i
\(65\) 0.169561 5.66951i 0.00260862 0.0872233i
\(66\) 25.6977 0.389359
\(67\) 21.8813 + 21.8813i 0.326587 + 0.326587i 0.851287 0.524700i \(-0.175823\pi\)
−0.524700 + 0.851287i \(0.675823\pi\)
\(68\) −4.06891 + 4.06891i −0.0598368 + 0.0598368i
\(69\) 11.8659i 0.171970i
\(70\) −32.1249 34.1057i −0.458927 0.487224i
\(71\) −105.543 −1.48652 −0.743258 0.669005i \(-0.766721\pi\)
−0.743258 + 0.669005i \(0.766721\pi\)
\(72\) −5.75651 5.75651i −0.0799515 0.0799515i
\(73\) 63.5112 63.5112i 0.870017 0.870017i −0.122457 0.992474i \(-0.539077\pi\)
0.992474 + 0.122457i \(0.0390773\pi\)
\(74\) 44.2677i 0.598212i
\(75\) −41.0463 46.2741i −0.547285 0.616988i
\(76\) −25.3959 −0.334156
\(77\) 34.4096 + 34.4096i 0.446878 + 0.446878i
\(78\) −2.80677 + 2.80677i −0.0359843 + 0.0359843i
\(79\) 19.7472i 0.249964i −0.992159 0.124982i \(-0.960113\pi\)
0.992159 0.124982i \(-0.0398874\pi\)
\(80\) 14.5586 13.7130i 0.181982 0.171413i
\(81\) 46.8114 0.577918
\(82\) −16.8120 16.8120i −0.205024 0.205024i
\(83\) 105.262 105.262i 1.26822 1.26822i 0.321214 0.947007i \(-0.395909\pi\)
0.947007 0.321214i \(-0.104091\pi\)
\(84\) 32.7884i 0.390338i
\(85\) −14.3793 0.430049i −0.169169 0.00505940i
\(86\) 31.3285 0.364285
\(87\) −32.0072 32.0072i −0.367899 0.367899i
\(88\) −14.6883 + 14.6883i −0.166913 + 0.166913i
\(89\) 131.803i 1.48093i −0.672092 0.740467i \(-0.734604\pi\)
0.672092 0.740467i \(-0.265396\pi\)
\(90\) 0.608414 20.3432i 0.00676015 0.226036i
\(91\) −7.51662 −0.0826002
\(92\) 6.78233 + 6.78233i 0.0737210 + 0.0737210i
\(93\) 57.6398 57.6398i 0.619783 0.619783i
\(94\) 107.548i 1.14412i
\(95\) −43.5319 46.2160i −0.458230 0.486484i
\(96\) −13.9963 −0.145795
\(97\) 101.232 + 101.232i 1.04362 + 1.04362i 0.999004 + 0.0446199i \(0.0142077\pi\)
0.0446199 + 0.999004i \(0.485792\pi\)
\(98\) 5.09584 5.09584i 0.0519984 0.0519984i
\(99\) 21.1383i 0.213519i
\(100\) 49.9106 + 2.98807i 0.499106 + 0.0298807i
\(101\) −33.1423 −0.328141 −0.164071 0.986449i \(-0.552463\pi\)
−0.164071 + 0.986449i \(0.552463\pi\)
\(102\) 7.11869 + 7.11869i 0.0697911 + 0.0697911i
\(103\) 63.5710 63.5710i 0.617194 0.617194i −0.327616 0.944811i \(-0.606245\pi\)
0.944811 + 0.327616i \(0.106245\pi\)
\(104\) 3.20859i 0.0308519i
\(105\) −59.6691 + 56.2037i −0.568277 + 0.535273i
\(106\) −30.3997 −0.286790
\(107\) 49.0182 + 49.0182i 0.458114 + 0.458114i 0.898036 0.439922i \(-0.144994\pi\)
−0.439922 + 0.898036i \(0.644994\pi\)
\(108\) −41.5628 + 41.5628i −0.384841 + 0.384841i
\(109\) 192.423i 1.76534i 0.469989 + 0.882672i \(0.344258\pi\)
−0.469989 + 0.882672i \(0.655742\pi\)
\(110\) −51.9078 1.55243i −0.471889 0.0141130i
\(111\) −77.4478 −0.697728
\(112\) −18.7412 18.7412i −0.167332 0.167332i
\(113\) 68.6393 68.6393i 0.607428 0.607428i −0.334845 0.942273i \(-0.608684\pi\)
0.942273 + 0.334845i \(0.108684\pi\)
\(114\) 44.4310i 0.389745i
\(115\) −0.716834 + 23.9684i −0.00623334 + 0.208421i
\(116\) 36.5894 0.315426
\(117\) −2.30879 2.30879i −0.0197332 0.0197332i
\(118\) −8.32600 + 8.32600i −0.0705593 + 0.0705593i
\(119\) 19.0641i 0.160202i
\(120\) −23.9915 25.4707i −0.199929 0.212256i
\(121\) −67.0634 −0.554243
\(122\) 16.1313 + 16.1313i 0.132224 + 0.132224i
\(123\) −29.4132 + 29.4132i −0.239131 + 0.239131i
\(124\) 65.8916i 0.531384i
\(125\) 80.1156 + 95.9504i 0.640925 + 0.767604i
\(126\) −26.9710 −0.214055
\(127\) 39.6115 + 39.6115i 0.311901 + 0.311901i 0.845646 0.533744i \(-0.179216\pi\)
−0.533744 + 0.845646i \(0.679216\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) 54.8103i 0.424886i
\(130\) 5.83907 5.49995i 0.0449159 0.0423073i
\(131\) −151.732 −1.15826 −0.579130 0.815236i \(-0.696607\pi\)
−0.579130 + 0.815236i \(0.696607\pi\)
\(132\) 25.6977 + 25.6977i 0.194680 + 0.194680i
\(133\) −59.4937 + 59.4937i −0.447321 + 0.447321i
\(134\) 43.7626i 0.326587i
\(135\) −146.881 4.39284i −1.08801 0.0325395i
\(136\) −8.13781 −0.0598368
\(137\) 115.031 + 115.031i 0.839642 + 0.839642i 0.988812 0.149169i \(-0.0476600\pi\)
−0.149169 + 0.988812i \(0.547660\pi\)
\(138\) 11.8659 11.8659i 0.0859850 0.0859850i
\(139\) 8.87351i 0.0638382i −0.999490 0.0319191i \(-0.989838\pi\)
0.999490 0.0319191i \(-0.0101619\pi\)
\(140\) 1.98079 66.2306i 0.0141485 0.473076i
\(141\) −188.159 −1.33446
\(142\) −105.543 105.543i −0.743258 0.743258i
\(143\) −5.89110 + 5.89110i −0.0411965 + 0.0411965i
\(144\) 11.5130i 0.0799515i
\(145\) 62.7190 + 66.5862i 0.432545 + 0.459215i
\(146\) 127.022 0.870017
\(147\) −8.91535 8.91535i −0.0606487 0.0606487i
\(148\) 44.2677 44.2677i 0.299106 0.299106i
\(149\) 98.3865i 0.660312i 0.943926 + 0.330156i \(0.107101\pi\)
−0.943926 + 0.330156i \(0.892899\pi\)
\(150\) 5.22773 87.3204i 0.0348516 0.582136i
\(151\) −74.3468 −0.492363 −0.246181 0.969224i \(-0.579176\pi\)
−0.246181 + 0.969224i \(0.579176\pi\)
\(152\) −25.3959 25.3959i −0.167078 0.167078i
\(153\) −5.85567 + 5.85567i −0.0382724 + 0.0382724i
\(154\) 68.8192i 0.446878i
\(155\) −119.911 + 112.947i −0.773620 + 0.728689i
\(156\) −5.61355 −0.0359843
\(157\) 102.456 + 102.456i 0.652587 + 0.652587i 0.953615 0.301028i \(-0.0973298\pi\)
−0.301028 + 0.953615i \(0.597330\pi\)
\(158\) 19.7472 19.7472i 0.124982 0.124982i
\(159\) 53.1853i 0.334499i
\(160\) 28.2716 + 0.845532i 0.176698 + 0.00528457i
\(161\) 31.7773 0.197374
\(162\) 46.8114 + 46.8114i 0.288959 + 0.288959i
\(163\) 69.6921 69.6921i 0.427559 0.427559i −0.460237 0.887796i \(-0.652236\pi\)
0.887796 + 0.460237i \(0.152236\pi\)
\(164\) 33.6240i 0.205024i
\(165\) −2.71603 + 90.8145i −0.0164608 + 0.550391i
\(166\) 210.525 1.26822
\(167\) −134.667 134.667i −0.806391 0.806391i 0.177695 0.984086i \(-0.443136\pi\)
−0.984086 + 0.177695i \(0.943136\pi\)
\(168\) −32.7884 + 32.7884i −0.195169 + 0.195169i
\(169\) 167.713i 0.992385i
\(170\) −13.9493 14.8094i −0.0820546 0.0871140i
\(171\) −36.5479 −0.213730
\(172\) 31.3285 + 31.3285i 0.182143 + 0.182143i
\(173\) −54.9807 + 54.9807i −0.317808 + 0.317808i −0.847925 0.530117i \(-0.822148\pi\)
0.530117 + 0.847925i \(0.322148\pi\)
\(174\) 64.0144i 0.367899i
\(175\) 123.923 109.923i 0.708133 0.628133i
\(176\) −29.3766 −0.166913
\(177\) 14.5666 + 14.5666i 0.0822974 + 0.0822974i
\(178\) 131.803 131.803i 0.740467 0.740467i
\(179\) 151.781i 0.847941i 0.905676 + 0.423970i \(0.139364\pi\)
−0.905676 + 0.423970i \(0.860636\pi\)
\(180\) 20.9516 19.7348i 0.116398 0.109638i
\(181\) −13.6959 −0.0756682 −0.0378341 0.999284i \(-0.512046\pi\)
−0.0378341 + 0.999284i \(0.512046\pi\)
\(182\) −7.51662 7.51662i −0.0413001 0.0413001i
\(183\) 28.2223 28.2223i 0.154220 0.154220i
\(184\) 13.5647i 0.0737210i
\(185\) 156.440 + 4.67871i 0.845621 + 0.0252903i
\(186\) 115.280 0.619783
\(187\) 14.9413 + 14.9413i 0.0799002 + 0.0799002i
\(188\) 107.548 107.548i 0.572062 0.572062i
\(189\) 194.735i 1.03034i
\(190\) 2.68413 89.7479i 0.0141270 0.472357i
\(191\) −222.336 −1.16406 −0.582032 0.813166i \(-0.697742\pi\)
−0.582032 + 0.813166i \(0.697742\pi\)
\(192\) −13.9963 13.9963i −0.0728973 0.0728973i
\(193\) 107.725 107.725i 0.558158 0.558158i −0.370625 0.928783i \(-0.620856\pi\)
0.928783 + 0.370625i \(0.120856\pi\)
\(194\) 202.463i 1.04362i
\(195\) −9.62236 10.2157i −0.0493454 0.0523880i
\(196\) 10.1917 0.0519984
\(197\) −5.03748 5.03748i −0.0255709 0.0255709i 0.694206 0.719777i \(-0.255756\pi\)
−0.719777 + 0.694206i \(0.755756\pi\)
\(198\) −21.1383 + 21.1383i −0.106759 + 0.106759i
\(199\) 127.303i 0.639711i 0.947466 + 0.319856i \(0.103634\pi\)
−0.947466 + 0.319856i \(0.896366\pi\)
\(200\) 46.9226 + 52.8987i 0.234613 + 0.264494i
\(201\) 76.5642 0.380916
\(202\) −33.1423 33.1423i −0.164071 0.164071i
\(203\) 85.7162 85.7162i 0.422247 0.422247i
\(204\) 14.2374i 0.0697911i
\(205\) 61.1897 57.6359i 0.298486 0.281151i
\(206\) 127.142 0.617194
\(207\) 9.76063 + 9.76063i 0.0471528 + 0.0471528i
\(208\) 3.20859 3.20859i 0.0154259 0.0154259i
\(209\) 93.2556i 0.446199i
\(210\) −115.873 3.46546i −0.551775 0.0165022i
\(211\) 9.59463 0.0454722 0.0227361 0.999742i \(-0.492762\pi\)
0.0227361 + 0.999742i \(0.492762\pi\)
\(212\) −30.3997 30.3997i −0.143395 0.143395i
\(213\) −184.651 + 184.651i −0.866904 + 0.866904i
\(214\) 98.0363i 0.458114i
\(215\) −3.31116 + 110.714i −0.0154007 + 0.514947i
\(216\) −83.1257 −0.384841
\(217\) 154.361 + 154.361i 0.711342 + 0.711342i
\(218\) −192.423 + 192.423i −0.882672 + 0.882672i
\(219\) 222.230i 1.01475i
\(220\) −50.3554 53.4602i −0.228888 0.243001i
\(221\) −3.26387 −0.0147686
\(222\) −77.4478 77.4478i −0.348864 0.348864i
\(223\) 231.304 231.304i 1.03724 1.03724i 0.0379566 0.999279i \(-0.487915\pi\)
0.999279 0.0379566i \(-0.0120849\pi\)
\(224\) 37.4824i 0.167332i
\(225\) 71.8277 + 4.30021i 0.319234 + 0.0191121i
\(226\) 137.279 0.607428
\(227\) −295.186 295.186i −1.30038 1.30038i −0.928134 0.372247i \(-0.878588\pi\)
−0.372247 0.928134i \(-0.621412\pi\)
\(228\) −44.4310 + 44.4310i −0.194873 + 0.194873i
\(229\) 441.791i 1.92922i −0.263687 0.964608i \(-0.584939\pi\)
0.263687 0.964608i \(-0.415061\pi\)
\(230\) −24.6853 + 23.2516i −0.107327 + 0.101094i
\(231\) 120.402 0.521219
\(232\) 36.5894 + 36.5894i 0.157713 + 0.157713i
\(233\) −142.357 + 142.357i −0.610974 + 0.610974i −0.943200 0.332226i \(-0.892200\pi\)
0.332226 + 0.943200i \(0.392200\pi\)
\(234\) 4.61757i 0.0197332i
\(235\) 380.069 + 11.3669i 1.61731 + 0.0483697i
\(236\) −16.6520 −0.0705593
\(237\) −34.5484 34.5484i −0.145774 0.145774i
\(238\) −19.0641 + 19.0641i −0.0801011 + 0.0801011i
\(239\) 103.472i 0.432938i 0.976289 + 0.216469i \(0.0694541\pi\)
−0.976289 + 0.216469i \(0.930546\pi\)
\(240\) 1.47929 49.4622i 0.00616370 0.206093i
\(241\) 11.4659 0.0475762 0.0237881 0.999717i \(-0.492427\pi\)
0.0237881 + 0.999717i \(0.492427\pi\)
\(242\) −67.0634 67.0634i −0.277122 0.277122i
\(243\) −105.135 + 105.135i −0.432653 + 0.432653i
\(244\) 32.2626i 0.132224i
\(245\) 17.4699 + 18.5471i 0.0713056 + 0.0757023i
\(246\) −58.8263 −0.239131
\(247\) −10.1856 10.1856i −0.0412374 0.0412374i
\(248\) −65.8916 + 65.8916i −0.265692 + 0.265692i
\(249\) 368.320i 1.47920i
\(250\) −15.8348 + 176.066i −0.0633393 + 0.704264i
\(251\) 46.6849 0.185996 0.0929978 0.995666i \(-0.470355\pi\)
0.0929978 + 0.995666i \(0.470355\pi\)
\(252\) −26.9710 26.9710i −0.107028 0.107028i
\(253\) 24.9052 24.9052i 0.0984397 0.0984397i
\(254\) 79.2229i 0.311901i
\(255\) −25.9095 + 24.4047i −0.101606 + 0.0957049i
\(256\) 16.0000 0.0625000
\(257\) −309.876 309.876i −1.20574 1.20574i −0.972393 0.233351i \(-0.925031\pi\)
−0.233351 0.972393i \(-0.574969\pi\)
\(258\) 54.8103 54.8103i 0.212443 0.212443i
\(259\) 207.407i 0.800801i
\(260\) 11.3390 + 0.339121i 0.0436116 + 0.00130431i
\(261\) 52.6567 0.201750
\(262\) −151.732 151.732i −0.579130 0.579130i
\(263\) −45.9507 + 45.9507i −0.174718 + 0.174718i −0.789048 0.614331i \(-0.789426\pi\)
0.614331 + 0.789048i \(0.289426\pi\)
\(264\) 51.3954i 0.194680i
\(265\) 3.21299 107.431i 0.0121245 0.405401i
\(266\) −118.987 −0.447321
\(267\) −230.594 230.594i −0.863649 0.863649i
\(268\) −43.7626 + 43.7626i −0.163293 + 0.163293i
\(269\) 138.967i 0.516606i −0.966064 0.258303i \(-0.916837\pi\)
0.966064 0.258303i \(-0.0831632\pi\)
\(270\) −142.488 151.274i −0.527735 0.560274i
\(271\) −373.516 −1.37829 −0.689143 0.724625i \(-0.742013\pi\)
−0.689143 + 0.724625i \(0.742013\pi\)
\(272\) −8.13781 8.13781i −0.0299184 0.0299184i
\(273\) −13.1506 + 13.1506i −0.0481707 + 0.0481707i
\(274\) 230.062i 0.839642i
\(275\) 10.9724 183.276i 0.0398997 0.666457i
\(276\) 23.7318 0.0859850
\(277\) 329.820 + 329.820i 1.19069 + 1.19069i 0.976875 + 0.213813i \(0.0685882\pi\)
0.213813 + 0.976875i \(0.431412\pi\)
\(278\) 8.87351 8.87351i 0.0319191 0.0319191i
\(279\) 94.8264i 0.339880i
\(280\) 68.2114 64.2498i 0.243612 0.229464i
\(281\) 433.168 1.54152 0.770761 0.637124i \(-0.219876\pi\)
0.770761 + 0.637124i \(0.219876\pi\)
\(282\) −188.159 188.159i −0.667229 0.667229i
\(283\) −112.199 + 112.199i −0.396462 + 0.396462i −0.876983 0.480521i \(-0.840448\pi\)
0.480521 + 0.876983i \(0.340448\pi\)
\(284\) 211.085i 0.743258i
\(285\) −157.017 4.69598i −0.550937 0.0164771i
\(286\) −11.7822 −0.0411965
\(287\) −78.7693 78.7693i −0.274457 0.274457i
\(288\) 11.5130 11.5130i 0.0399757 0.0399757i
\(289\) 280.722i 0.971356i
\(290\) −3.86719 + 129.305i −0.0133351 + 0.445880i
\(291\) 354.216 1.21724
\(292\) 127.022 + 127.022i 0.435008 + 0.435008i
\(293\) −157.692 + 157.692i −0.538196 + 0.538196i −0.922999 0.384803i \(-0.874270\pi\)
0.384803 + 0.922999i \(0.374270\pi\)
\(294\) 17.8307i 0.0606487i
\(295\) −28.5437 30.3037i −0.0967584 0.102724i
\(296\) 88.5353 0.299106
\(297\) 152.622 + 152.622i 0.513879 + 0.513879i
\(298\) −98.3865 + 98.3865i −0.330156 + 0.330156i
\(299\) 5.44044i 0.0181954i
\(300\) 92.5481 82.0927i 0.308494 0.273642i
\(301\) 146.784 0.487653
\(302\) −74.3468 74.3468i −0.246181 0.246181i
\(303\) −57.9836 + 57.9836i −0.191365 + 0.191365i
\(304\) 50.7918i 0.167078i
\(305\) −58.7122 + 55.3023i −0.192499 + 0.181319i
\(306\) −11.7113 −0.0382724
\(307\) 157.847 + 157.847i 0.514159 + 0.514159i 0.915798 0.401639i \(-0.131559\pi\)
−0.401639 + 0.915798i \(0.631559\pi\)
\(308\) −68.8192 + 68.8192i −0.223439 + 0.223439i
\(309\) 222.440i 0.719869i
\(310\) −232.858 6.96418i −0.751155 0.0224651i
\(311\) −543.283 −1.74689 −0.873445 0.486923i \(-0.838119\pi\)
−0.873445 + 0.486923i \(0.838119\pi\)
\(312\) −5.61355 5.61355i −0.0179921 0.0179921i
\(313\) 30.7142 30.7142i 0.0981286 0.0981286i −0.656338 0.754467i \(-0.727896\pi\)
0.754467 + 0.656338i \(0.227896\pi\)
\(314\) 204.912i 0.652587i
\(315\) 2.85060 95.3142i 0.00904954 0.302585i
\(316\) 39.4944 0.124982
\(317\) −370.911 370.911i −1.17007 1.17007i −0.982193 0.187873i \(-0.939841\pi\)
−0.187873 0.982193i \(-0.560159\pi\)
\(318\) −53.1853 + 53.1853i −0.167250 + 0.167250i
\(319\) 134.359i 0.421188i
\(320\) 27.4261 + 29.1172i 0.0857066 + 0.0909911i
\(321\) 171.518 0.534324
\(322\) 31.7773 + 31.7773i 0.0986872 + 0.0986872i
\(323\) −25.8334 + 25.8334i −0.0799794 + 0.0799794i
\(324\) 93.6228i 0.288959i
\(325\) 18.8194 + 21.2163i 0.0579059 + 0.0652809i
\(326\) 139.384 0.427559
\(327\) 336.650 + 336.650i 1.02951 + 1.02951i
\(328\) 33.6240 33.6240i 0.102512 0.102512i
\(329\) 503.894i 1.53159i
\(330\) −93.5305 + 88.0985i −0.283426 + 0.266965i
\(331\) −334.223 −1.00974 −0.504869 0.863196i \(-0.668459\pi\)
−0.504869 + 0.863196i \(0.668459\pi\)
\(332\) 210.525 + 210.525i 0.634110 + 0.634110i
\(333\) 63.7068 63.7068i 0.191312 0.191312i
\(334\) 269.335i 0.806391i
\(335\) −154.655 4.62533i −0.461657 0.0138070i
\(336\) −65.5768 −0.195169
\(337\) −280.330 280.330i −0.831841 0.831841i 0.155927 0.987769i \(-0.450163\pi\)
−0.987769 + 0.155927i \(0.950163\pi\)
\(338\) −167.713 + 167.713i −0.496193 + 0.496193i
\(339\) 240.174i 0.708477i
\(340\) 0.860097 28.7586i 0.00252970 0.0845843i
\(341\) 241.959 0.709557
\(342\) −36.5479 36.5479i −0.106865 0.106865i
\(343\) 253.455 253.455i 0.738937 0.738937i
\(344\) 62.6570i 0.182143i
\(345\) 40.6795 + 43.1878i 0.117912 + 0.125182i
\(346\) −109.961 −0.317808
\(347\) 433.965 + 433.965i 1.25062 + 1.25062i 0.955443 + 0.295176i \(0.0953782\pi\)
0.295176 + 0.955443i \(0.404622\pi\)
\(348\) 64.0144 64.0144i 0.183949 0.183949i
\(349\) 221.072i 0.633443i −0.948519 0.316721i \(-0.897418\pi\)
0.948519 0.316721i \(-0.102582\pi\)
\(350\) 233.847 + 14.0000i 0.668133 + 0.0400001i
\(351\) −33.3396 −0.0949845
\(352\) −29.3766 29.3766i −0.0834563 0.0834563i
\(353\) −10.4152 + 10.4152i −0.0295049 + 0.0295049i −0.721705 0.692200i \(-0.756641\pi\)
0.692200 + 0.721705i \(0.256641\pi\)
\(354\) 29.1333i 0.0822974i
\(355\) 384.138 361.828i 1.08208 1.01923i
\(356\) 263.606 0.740467
\(357\) 33.3532 + 33.3532i 0.0934265 + 0.0934265i
\(358\) −151.781 + 151.781i −0.423970 + 0.423970i
\(359\) 92.8731i 0.258699i 0.991599 + 0.129350i \(0.0412890\pi\)
−0.991599 + 0.129350i \(0.958711\pi\)
\(360\) 40.6865 + 1.21683i 0.113018 + 0.00338008i
\(361\) 199.762 0.553358
\(362\) −13.6959 13.6959i −0.0378341 0.0378341i
\(363\) −117.330 + 117.330i −0.323223 + 0.323223i
\(364\) 15.0332i 0.0413001i
\(365\) −13.4252 + 448.892i −0.0367814 + 1.22984i
\(366\) 56.4446 0.154220
\(367\) −42.3293 42.3293i −0.115339 0.115339i 0.647082 0.762421i \(-0.275989\pi\)
−0.762421 + 0.647082i \(0.775989\pi\)
\(368\) −13.5647 + 13.5647i −0.0368605 + 0.0368605i
\(369\) 48.3892i 0.131136i
\(370\) 151.761 + 161.119i 0.410165 + 0.435456i
\(371\) −142.432 −0.383913
\(372\) 115.280 + 115.280i 0.309892 + 0.309892i
\(373\) −99.0976 + 99.0976i −0.265677 + 0.265677i −0.827356 0.561678i \(-0.810156\pi\)
0.561678 + 0.827356i \(0.310156\pi\)
\(374\) 29.8827i 0.0799002i
\(375\) 308.034 + 27.7036i 0.821423 + 0.0738763i
\(376\) 215.095 0.572062
\(377\) 14.6751 + 14.6751i 0.0389259 + 0.0389259i
\(378\) −194.735 + 194.735i −0.515171 + 0.515171i
\(379\) 267.871i 0.706784i 0.935475 + 0.353392i \(0.114972\pi\)
−0.935475 + 0.353392i \(0.885028\pi\)
\(380\) 92.4320 87.0637i 0.243242 0.229115i
\(381\) 138.603 0.363788
\(382\) −222.336 222.336i −0.582032 0.582032i
\(383\) 193.931 193.931i 0.506347 0.506347i −0.407056 0.913403i \(-0.633445\pi\)
0.913403 + 0.407056i \(0.133445\pi\)
\(384\) 27.9926i 0.0728973i
\(385\) −243.204 7.27360i −0.631698 0.0188925i
\(386\) 215.449 0.558158
\(387\) 45.0857 + 45.0857i 0.116501 + 0.116501i
\(388\) −202.463 + 202.463i −0.521812 + 0.521812i
\(389\) 582.596i 1.49768i 0.662753 + 0.748838i \(0.269388\pi\)
−0.662753 + 0.748838i \(0.730612\pi\)
\(390\) 0.593304 19.8380i 0.00152129 0.0508667i
\(391\) 13.7983 0.0352898
\(392\) 10.1917 + 10.1917i 0.0259992 + 0.0259992i
\(393\) −265.460 + 265.460i −0.675472 + 0.675472i
\(394\) 10.0750i 0.0255709i
\(395\) 67.6985 + 71.8728i 0.171389 + 0.181956i
\(396\) −42.2767 −0.106759
\(397\) 325.494 + 325.494i 0.819885 + 0.819885i 0.986091 0.166206i \(-0.0531518\pi\)
−0.166206 + 0.986091i \(0.553152\pi\)
\(398\) −127.303 + 127.303i −0.319856 + 0.319856i
\(399\) 208.173i 0.521736i
\(400\) −5.97614 + 99.8213i −0.0149404 + 0.249553i
\(401\) 101.242 0.252474 0.126237 0.992000i \(-0.459710\pi\)
0.126237 + 0.992000i \(0.459710\pi\)
\(402\) 76.5642 + 76.5642i 0.190458 + 0.190458i
\(403\) −26.4274 + 26.4274i −0.0655767 + 0.0655767i
\(404\) 66.2845i 0.164071i
\(405\) −170.377 + 160.482i −0.420683 + 0.396251i
\(406\) 171.432 0.422247
\(407\) −162.554 162.554i −0.399396 0.399396i
\(408\) −14.2374 + 14.2374i −0.0348956 + 0.0348956i
\(409\) 348.881i 0.853011i −0.904485 0.426505i \(-0.859745\pi\)
0.904485 0.426505i \(-0.140255\pi\)
\(410\) 118.826 + 3.55377i 0.289819 + 0.00866773i
\(411\) 402.501 0.979322
\(412\) 127.142 + 127.142i 0.308597 + 0.308597i
\(413\) −39.0098 + 39.0098i −0.0944548 + 0.0944548i
\(414\) 19.5213i 0.0471528i
\(415\) −22.2507 + 743.984i −0.0536161 + 1.79273i
\(416\) 6.41719 0.0154259
\(417\) −15.5245 15.5245i −0.0372291 0.0372291i
\(418\) −93.2556 + 93.2556i −0.223100 + 0.223100i
\(419\) 120.421i 0.287401i 0.989621 + 0.143700i \(0.0459002\pi\)
−0.989621 + 0.143700i \(0.954100\pi\)
\(420\) −112.407 119.338i −0.267636 0.284139i
\(421\) −703.519 −1.67107 −0.835534 0.549439i \(-0.814841\pi\)
−0.835534 + 0.549439i \(0.814841\pi\)
\(422\) 9.59463 + 9.59463i 0.0227361 + 0.0227361i
\(423\) 154.775 154.775i 0.365898 0.365898i
\(424\) 60.7994i 0.143395i
\(425\) 53.8100 47.7309i 0.126612 0.112308i
\(426\) −369.301 −0.866904
\(427\) 75.5801 + 75.5801i 0.177002 + 0.177002i
\(428\) −98.0363 + 98.0363i −0.229057 + 0.229057i
\(429\) 20.6134i 0.0480498i
\(430\) −114.025 + 107.402i −0.265174 + 0.249773i
\(431\) −309.307 −0.717650 −0.358825 0.933405i \(-0.616823\pi\)
−0.358825 + 0.933405i \(0.616823\pi\)
\(432\) −83.1257 83.1257i −0.192421 0.192421i
\(433\) −88.2644 + 88.2644i −0.203844 + 0.203844i −0.801645 0.597801i \(-0.796041\pi\)
0.597801 + 0.801645i \(0.296041\pi\)
\(434\) 308.722i 0.711342i
\(435\) 226.224 + 6.76578i 0.520055 + 0.0155535i
\(436\) −384.845 −0.882672
\(437\) 43.0608 + 43.0608i 0.0985373 + 0.0985373i
\(438\) 222.230 222.230i 0.507375 0.507375i
\(439\) 231.130i 0.526492i 0.964729 + 0.263246i \(0.0847931\pi\)
−0.964729 + 0.263246i \(0.915207\pi\)
\(440\) 3.10486 103.816i 0.00705649 0.235945i
\(441\) 14.6671 0.0332588
\(442\) −3.26387 3.26387i −0.00738431 0.00738431i
\(443\) −572.899 + 572.899i −1.29322 + 1.29322i −0.360444 + 0.932781i \(0.617375\pi\)
−0.932781 + 0.360444i \(0.882625\pi\)
\(444\) 154.896i 0.348864i
\(445\) 451.856 + 479.717i 1.01541 + 1.07802i
\(446\) 462.607 1.03724
\(447\) 172.131 + 172.131i 0.385080 + 0.385080i
\(448\) 37.4824 37.4824i 0.0836662 0.0836662i
\(449\) 58.7939i 0.130944i −0.997854 0.0654721i \(-0.979145\pi\)
0.997854 0.0654721i \(-0.0208553\pi\)
\(450\) 67.5275 + 76.1279i 0.150061 + 0.169173i
\(451\) −123.470 −0.273769
\(452\) 137.279 + 137.279i 0.303714 + 0.303714i
\(453\) −130.072 + 130.072i −0.287135 + 0.287135i
\(454\) 590.373i 1.30038i
\(455\) 27.3578 25.7689i 0.0601271 0.0566350i
\(456\) −88.8620 −0.194873
\(457\) −146.469 146.469i −0.320501 0.320501i 0.528458 0.848959i \(-0.322770\pi\)
−0.848959 + 0.528458i \(0.822770\pi\)
\(458\) 441.791 441.791i 0.964608 0.964608i
\(459\) 84.5576i 0.184221i
\(460\) −47.9369 1.43367i −0.104211 0.00311667i
\(461\) 532.088 1.15420 0.577102 0.816672i \(-0.304183\pi\)
0.577102 + 0.816672i \(0.304183\pi\)
\(462\) 120.402 + 120.402i 0.260609 + 0.260609i
\(463\) −97.3256 + 97.3256i −0.210206 + 0.210206i −0.804355 0.594149i \(-0.797489\pi\)
0.594149 + 0.804355i \(0.297489\pi\)
\(464\) 73.1788i 0.157713i
\(465\) −12.1841 + 407.393i −0.0262023 + 0.876114i
\(466\) −284.714 −0.610974
\(467\) −648.867 648.867i −1.38944 1.38944i −0.826501 0.562935i \(-0.809672\pi\)
−0.562935 0.826501i \(-0.690328\pi\)
\(468\) 4.61757 4.61757i 0.00986661 0.00986661i
\(469\) 205.041i 0.437188i
\(470\) 368.702 + 391.436i 0.784472 + 0.832842i
\(471\) 358.501 0.761149
\(472\) −16.6520 16.6520i −0.0352797 0.0352797i
\(473\) 115.041 115.041i 0.243215 0.243215i
\(474\) 69.0968i 0.145774i
\(475\) 316.881 + 18.9712i 0.667118 + 0.0399393i
\(476\) −38.1281 −0.0801011
\(477\) −43.7490 43.7490i −0.0917170 0.0917170i
\(478\) −103.472 + 103.472i −0.216469 + 0.216469i
\(479\) 67.3465i 0.140598i −0.997526 0.0702991i \(-0.977605\pi\)
0.997526 0.0702991i \(-0.0223954\pi\)
\(480\) 50.9415 47.9829i 0.106128 0.0999644i
\(481\) 35.5092 0.0738238
\(482\) 11.4659 + 11.4659i 0.0237881 + 0.0237881i
\(483\) 55.5955 55.5955i 0.115104 0.115104i
\(484\) 134.127i 0.277122i
\(485\) −715.495 21.3986i −1.47525 0.0441209i
\(486\) −210.269 −0.432653
\(487\) 74.4495 + 74.4495i 0.152874 + 0.152874i 0.779400 0.626526i \(-0.215524\pi\)
−0.626526 + 0.779400i \(0.715524\pi\)
\(488\) −32.2626 + 32.2626i −0.0661119 + 0.0661119i
\(489\) 243.858i 0.498687i
\(490\) −1.07717 + 36.0169i −0.00219831 + 0.0735039i
\(491\) 767.159 1.56244 0.781221 0.624255i \(-0.214597\pi\)
0.781221 + 0.624255i \(0.214597\pi\)
\(492\) −58.8263 58.8263i −0.119566 0.119566i
\(493\) 37.2197 37.2197i 0.0754963 0.0754963i
\(494\) 20.3713i 0.0412374i
\(495\) −72.4678 76.9360i −0.146399 0.155426i
\(496\) −131.783 −0.265692
\(497\) −494.500 494.500i −0.994969 0.994969i
\(498\) 368.320 368.320i 0.739599 0.739599i
\(499\) 530.092i 1.06231i −0.847275 0.531154i \(-0.821759\pi\)
0.847275 0.531154i \(-0.178241\pi\)
\(500\) −191.901 + 160.231i −0.383802 + 0.320462i
\(501\) −471.210 −0.940539
\(502\) 46.6849 + 46.6849i 0.0929978 + 0.0929978i
\(503\) −145.546 + 145.546i −0.289355 + 0.289355i −0.836825 0.547470i \(-0.815591\pi\)
0.547470 + 0.836825i \(0.315591\pi\)
\(504\) 53.9420i 0.107028i
\(505\) 120.626 113.620i 0.238864 0.224991i
\(506\) 49.8105 0.0984397
\(507\) 293.420 + 293.420i 0.578738 + 0.578738i
\(508\) −79.2229 + 79.2229i −0.155951 + 0.155951i
\(509\) 771.820i 1.51635i −0.652054 0.758173i \(-0.726092\pi\)
0.652054 0.758173i \(-0.273908\pi\)
\(510\) −50.3143 1.50477i −0.0986554 0.00295053i
\(511\) 595.139 1.16466
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −263.881 + 263.881i −0.514388 + 0.514388i
\(514\) 619.752i 1.20574i
\(515\) −13.4378 + 449.314i −0.0260929 + 0.872455i
\(516\) 109.621 0.212443
\(517\) −394.923 394.923i −0.763875 0.763875i
\(518\) 207.407 207.407i 0.400400 0.400400i
\(519\) 192.381i 0.370677i
\(520\) 10.9999 + 11.6781i 0.0211537 + 0.0224580i
\(521\) −61.1677 −0.117404 −0.0587022 0.998276i \(-0.518696\pi\)
−0.0587022 + 0.998276i \(0.518696\pi\)
\(522\) 52.6567 + 52.6567i 0.100875 + 0.100875i
\(523\) 471.652 471.652i 0.901819 0.901819i −0.0937741 0.995593i \(-0.529893\pi\)
0.995593 + 0.0937741i \(0.0298932\pi\)
\(524\) 303.464i 0.579130i
\(525\) 24.4935 409.123i 0.0466543 0.779281i
\(526\) −91.9014 −0.174718
\(527\) 67.0267 + 67.0267i 0.127185 + 0.127185i
\(528\) −51.3954 + 51.3954i −0.0973398 + 0.0973398i
\(529\) 23.0000i 0.0434783i
\(530\) 110.644 104.218i 0.208763 0.196638i
\(531\) −23.9643 −0.0451306
\(532\) −118.987 118.987i −0.223661 0.223661i
\(533\) 13.4857 13.4857i 0.0253015 0.0253015i
\(534\) 461.189i 0.863649i
\(535\) −346.456 10.3616i −0.647581 0.0193675i
\(536\) −87.5252 −0.163293
\(537\) 265.547 + 265.547i 0.494501 + 0.494501i
\(538\) 138.967 138.967i 0.258303 0.258303i
\(539\) 37.4246i 0.0694335i
\(540\) 8.78568 293.762i 0.0162698 0.544004i
\(541\) −721.465 −1.33358 −0.666789 0.745247i \(-0.732332\pi\)
−0.666789 + 0.745247i \(0.732332\pi\)
\(542\) −373.516 373.516i −0.689143 0.689143i
\(543\) −23.9615 + 23.9615i −0.0441280 + 0.0441280i
\(544\) 16.2756i 0.0299184i
\(545\) −659.675 700.350i −1.21041 1.28505i
\(546\) −26.3012 −0.0481707
\(547\) −574.163 574.163i −1.04966 1.04966i −0.998701 0.0509573i \(-0.983773\pi\)
−0.0509573 0.998701i \(-0.516227\pi\)
\(548\) −230.062 + 230.062i −0.419821 + 0.419821i
\(549\) 46.4300i 0.0845719i
\(550\) 194.248 172.303i 0.353178 0.313279i
\(551\) 232.305 0.421606
\(552\) 23.7318 + 23.7318i 0.0429925 + 0.0429925i
\(553\) 92.5216 92.5216i 0.167308 0.167308i
\(554\) 659.641i 1.19069i
\(555\) 281.883 265.511i 0.507897 0.478399i
\(556\) 17.7470 0.0319191
\(557\) −337.658 337.658i −0.606209 0.606209i 0.335744 0.941953i \(-0.391012\pi\)
−0.941953 + 0.335744i \(0.891012\pi\)
\(558\) −94.8264 + 94.8264i −0.169940 + 0.169940i
\(559\) 25.1301i 0.0449555i
\(560\) 132.461 + 3.96157i 0.236538 + 0.00707424i
\(561\) 52.2808 0.0931921
\(562\) 433.168 + 433.168i 0.770761 + 0.770761i
\(563\) −42.8665 + 42.8665i −0.0761394 + 0.0761394i −0.744151 0.668012i \(-0.767146\pi\)
0.668012 + 0.744151i \(0.267146\pi\)
\(564\) 376.317i 0.667229i
\(565\) −14.5092 + 485.136i −0.0256800 + 0.858648i
\(566\) −224.398 −0.396462
\(567\) 219.326 + 219.326i 0.386818 + 0.386818i
\(568\) 211.085 211.085i 0.371629 0.371629i
\(569\) 428.539i 0.753145i 0.926387 + 0.376572i \(0.122897\pi\)
−0.926387 + 0.376572i \(0.877103\pi\)
\(570\) −152.321 161.713i −0.267230 0.283707i
\(571\) −1067.35 −1.86926 −0.934628 0.355626i \(-0.884268\pi\)
−0.934628 + 0.355626i \(0.884268\pi\)
\(572\) −11.7822 11.7822i −0.0205983 0.0205983i
\(573\) −388.985 + 388.985i −0.678857 + 0.678857i
\(574\) 157.539i 0.274457i
\(575\) −79.5611 89.6941i −0.138367 0.155990i
\(576\) 23.0260 0.0399757
\(577\) −308.950 308.950i −0.535442 0.535442i 0.386745 0.922187i \(-0.373599\pi\)
−0.922187 + 0.386745i \(0.873599\pi\)
\(578\) 280.722 280.722i 0.485678 0.485678i
\(579\) 376.936i 0.651011i
\(580\) −133.172 + 125.438i −0.229607 + 0.216272i
\(581\) 986.372 1.69771
\(582\) 354.216 + 354.216i 0.608619 + 0.608619i
\(583\) −111.630 + 111.630i −0.191475 + 0.191475i
\(584\) 254.045i 0.435008i
\(585\) 16.3183 + 0.488038i 0.0278945 + 0.000834253i
\(586\) −315.383 −0.538196
\(587\) 348.585 + 348.585i 0.593842 + 0.593842i 0.938667 0.344825i \(-0.112062\pi\)
−0.344825 + 0.938667i \(0.612062\pi\)
\(588\) 17.8307 17.8307i 0.0303243 0.0303243i
\(589\) 418.344i 0.710261i
\(590\) 1.75997 58.8474i 0.00298301 0.0997414i
\(591\) −17.6265 −0.0298248
\(592\) 88.5353 + 88.5353i 0.149553 + 0.149553i
\(593\) 483.268 483.268i 0.814954 0.814954i −0.170418 0.985372i \(-0.554512\pi\)
0.985372 + 0.170418i \(0.0545118\pi\)
\(594\) 305.244i 0.513879i
\(595\) −65.3566 69.3864i −0.109843 0.116616i
\(596\) −196.773 −0.330156
\(597\) 222.720 + 222.720i 0.373066 + 0.373066i
\(598\) −5.44044 + 5.44044i −0.00909772 + 0.00909772i
\(599\) 879.264i 1.46789i 0.679211 + 0.733943i \(0.262322\pi\)
−0.679211 + 0.733943i \(0.737678\pi\)
\(600\) 174.641 + 10.4555i 0.291068 + 0.0174258i
\(601\) −462.938 −0.770279 −0.385139 0.922858i \(-0.625847\pi\)
−0.385139 + 0.922858i \(0.625847\pi\)
\(602\) 146.784 + 146.784i 0.243827 + 0.243827i
\(603\) −62.9799 + 62.9799i −0.104444 + 0.104444i
\(604\) 148.694i 0.246181i
\(605\) 244.087 229.911i 0.403450 0.380018i
\(606\) −115.967 −0.191365
\(607\) 523.602 + 523.602i 0.862606 + 0.862606i 0.991640 0.129034i \(-0.0411877\pi\)
−0.129034 + 0.991640i \(0.541188\pi\)
\(608\) 50.7918 50.7918i 0.0835391 0.0835391i
\(609\) 299.927i 0.492491i
\(610\) −114.015 3.40988i −0.186909 0.00558997i
\(611\) 86.2692 0.141194
\(612\) −11.7113 11.7113i −0.0191362 0.0191362i
\(613\) −625.075 + 625.075i −1.01970 + 1.01970i −0.0198960 + 0.999802i \(0.506334\pi\)
−0.999802 + 0.0198960i \(0.993666\pi\)
\(614\) 315.694i 0.514159i
\(615\) 6.21744 207.890i 0.0101097 0.338032i
\(616\) −137.638 −0.223439
\(617\) −267.604 267.604i −0.433719 0.433719i 0.456173 0.889891i \(-0.349220\pi\)
−0.889891 + 0.456173i \(0.849220\pi\)
\(618\) 222.440 222.440i 0.359934 0.359934i
\(619\) 1088.11i 1.75785i 0.476960 + 0.878925i \(0.341739\pi\)
−0.476960 + 0.878925i \(0.658261\pi\)
\(620\) −225.894 239.822i −0.364345 0.386810i
\(621\) 140.946 0.226967
\(622\) −543.283 543.283i −0.873445 0.873445i
\(623\) 617.538 617.538i 0.991233 0.991233i
\(624\) 11.2271i 0.0179921i
\(625\) −620.536 74.5682i −0.992857 0.119309i
\(626\) 61.4285 0.0981286
\(627\) 163.154 + 163.154i 0.260214 + 0.260214i
\(628\) −204.912 + 204.912i −0.326293 + 0.326293i
\(629\) 90.0605i 0.143180i
\(630\) 98.1648 92.4636i 0.155817 0.146768i
\(631\) 742.234 1.17628 0.588141 0.808759i \(-0.299860\pi\)
0.588141 + 0.808759i \(0.299860\pi\)
\(632\) 39.4944 + 39.4944i 0.0624911 + 0.0624911i
\(633\) 16.7861 16.7861i 0.0265184 0.0265184i
\(634\) 741.822i 1.17007i
\(635\) −279.970 8.37319i −0.440898 0.0131861i
\(636\) −106.371 −0.167250
\(637\) 4.08762 + 4.08762i 0.00641699 + 0.00641699i
\(638\) 134.359 134.359i 0.210594 0.210594i
\(639\) 303.779i 0.475397i
\(640\) −1.69106 + 56.5433i −0.00264229 + 0.0883488i
\(641\) 799.585 1.24740 0.623702 0.781663i \(-0.285628\pi\)
0.623702 + 0.781663i \(0.285628\pi\)
\(642\) 171.518 + 171.518i 0.267162 + 0.267162i
\(643\) −647.571 + 647.571i −1.00711 + 1.00711i −0.00713404 + 0.999975i \(0.502271\pi\)
−0.999975 + 0.00713404i \(0.997729\pi\)
\(644\) 63.5546i 0.0986872i
\(645\) 187.904 + 199.490i 0.291324 + 0.309287i
\(646\) −51.6667 −0.0799794
\(647\) −710.350 710.350i −1.09791 1.09791i −0.994654 0.103259i \(-0.967073\pi\)
−0.103259 0.994654i \(-0.532927\pi\)
\(648\) −93.6228 + 93.6228i −0.144480 + 0.144480i
\(649\) 61.1474i 0.0942179i
\(650\) −2.39688 + 40.0357i −0.00368750 + 0.0615934i
\(651\) 540.120 0.829678
\(652\) 139.384 + 139.384i 0.213780 + 0.213780i
\(653\) 816.226 816.226i 1.24996 1.24996i 0.294228 0.955735i \(-0.404938\pi\)
0.955735 0.294228i \(-0.0950624\pi\)
\(654\) 673.300i 1.02951i
\(655\) 552.250 520.177i 0.843130 0.794163i
\(656\) 67.2480 0.102512
\(657\) 182.801 + 182.801i 0.278237 + 0.278237i
\(658\) 503.894 503.894i 0.765796 0.765796i
\(659\) 1221.53i 1.85361i 0.375542 + 0.926805i \(0.377457\pi\)
−0.375542 + 0.926805i \(0.622543\pi\)
\(660\) −181.629 5.43206i −0.275195 0.00823039i
\(661\) 269.209 0.407275 0.203638 0.979046i \(-0.434724\pi\)
0.203638 + 0.979046i \(0.434724\pi\)
\(662\) −334.223 334.223i −0.504869 0.504869i
\(663\) −5.71025 + 5.71025i −0.00861274 + 0.00861274i
\(664\) 421.049i 0.634110i
\(665\) 12.5760 420.496i 0.0189112 0.632325i
\(666\) 127.414 0.191312
\(667\) −62.0403 62.0403i −0.0930139 0.0930139i
\(668\) 269.335 269.335i 0.403195 0.403195i
\(669\) 809.348i 1.20979i
\(670\) −150.030 159.280i −0.223925 0.237732i
\(671\) 118.471 0.176558
\(672\) −65.5768 65.5768i −0.0975846 0.0975846i
\(673\) −19.4524 + 19.4524i −0.0289041 + 0.0289041i −0.721411 0.692507i \(-0.756506\pi\)
0.692507 + 0.721411i \(0.256506\pi\)
\(674\) 560.661i 0.831841i
\(675\) 549.655 487.559i 0.814304 0.722309i
\(676\) −335.426 −0.496193
\(677\) 173.259 + 173.259i 0.255922 + 0.255922i 0.823393 0.567471i \(-0.192078\pi\)
−0.567471 + 0.823393i \(0.692078\pi\)
\(678\) 240.174 240.174i 0.354239 0.354239i
\(679\) 948.601i 1.39706i
\(680\) 29.6187 27.8986i 0.0435570 0.0410273i
\(681\) −1032.88 −1.51671
\(682\) 241.959 + 241.959i 0.354779 + 0.354779i
\(683\) 155.847 155.847i 0.228181 0.228181i −0.583752 0.811932i \(-0.698416\pi\)
0.811932 + 0.583752i \(0.198416\pi\)
\(684\) 73.0958i 0.106865i
\(685\) −813.028 24.3156i −1.18690 0.0354972i
\(686\) 506.911 0.738937
\(687\) −772.928 772.928i −1.12508 1.12508i
\(688\) −62.6570 + 62.6570i −0.0910713 + 0.0910713i
\(689\) 24.3851i 0.0353920i
\(690\) −2.50825 + 83.8673i −0.00363515 + 0.121547i
\(691\) −834.701 −1.20796 −0.603981 0.796999i \(-0.706420\pi\)
−0.603981 + 0.796999i \(0.706420\pi\)
\(692\) −109.961 109.961i −0.158904 0.158904i
\(693\) −99.0395 + 99.0395i −0.142914 + 0.142914i
\(694\) 867.929i 1.25062i
\(695\) 30.4207 + 32.2964i 0.0437708 + 0.0464697i
\(696\) 128.029 0.183949
\(697\) −34.2032 34.2032i −0.0490720 0.0490720i
\(698\) 221.072 221.072i 0.316721 0.316721i
\(699\) 498.117i 0.712613i
\(700\) 219.847 + 247.847i 0.314066 + 0.354066i
\(701\) −1081.67 −1.54304 −0.771520 0.636205i \(-0.780503\pi\)
−0.771520 + 0.636205i \(0.780503\pi\)
\(702\) −33.3396 33.3396i −0.0474923 0.0474923i
\(703\) 281.054 281.054i 0.399792 0.399792i
\(704\) 58.7532i 0.0834563i
\(705\) 684.830 645.057i 0.971390 0.914974i
\(706\) −20.8305 −0.0295049
\(707\) −155.282 155.282i −0.219635 0.219635i
\(708\) −29.1333 + 29.1333i −0.0411487 + 0.0411487i
\(709\) 736.698i 1.03907i 0.854450 + 0.519533i \(0.173894\pi\)
−0.854450 + 0.519533i \(0.826106\pi\)
\(710\) 745.966 + 22.3099i 1.05066 + 0.0314224i
\(711\) 56.8374 0.0799401
\(712\) 263.606 + 263.606i 0.370234 + 0.370234i
\(713\) 111.725 111.725i 0.156697 0.156697i
\(714\) 66.7065i 0.0934265i
\(715\) 1.24528 41.6378i 0.00174165 0.0582346i
\(716\) −303.563 −0.423970
\(717\) 181.028 + 181.028i 0.252480 + 0.252480i
\(718\) −92.8731 + 92.8731i −0.129350 + 0.129350i
\(719\) 158.393i 0.220297i −0.993915 0.110148i \(-0.964867\pi\)
0.993915 0.110148i \(-0.0351326\pi\)
\(720\) 39.4696 + 41.9033i 0.0548189 + 0.0581990i
\(721\) 595.699 0.826213
\(722\) 199.762 + 199.762i 0.276679 + 0.276679i
\(723\) 20.0599 20.0599i 0.0277454 0.0277454i
\(724\) 27.3919i 0.0378341i
\(725\) −456.550 27.3329i −0.629724 0.0377006i
\(726\) −234.660 −0.323223
\(727\) −470.451 470.451i −0.647112 0.647112i 0.305182 0.952294i \(-0.401283\pi\)
−0.952294 + 0.305182i \(0.901283\pi\)
\(728\) 15.0332 15.0332i 0.0206501 0.0206501i
\(729\) 789.176i 1.08255i
\(730\) −462.317 + 435.466i −0.633311 + 0.596529i
\(731\) 63.7364 0.0871907
\(732\) 56.4446 + 56.4446i 0.0771101 + 0.0771101i
\(733\) −83.7227 + 83.7227i −0.114219 + 0.114219i −0.761906 0.647687i \(-0.775736\pi\)
0.647687 + 0.761906i \(0.275736\pi\)
\(734\) 84.6586i 0.115339i
\(735\) 63.0129 + 1.88455i 0.0857318 + 0.00256402i
\(736\) −27.1293 −0.0368605
\(737\) 160.700 + 160.700i 0.218046 + 0.218046i
\(738\) 48.3892 48.3892i 0.0655680 0.0655680i
\(739\) 786.751i 1.06462i 0.846551 + 0.532308i \(0.178675\pi\)
−0.846551 + 0.532308i \(0.821325\pi\)
\(740\) −9.35743 + 312.880i −0.0126452 + 0.422810i
\(741\) −35.6402 −0.0480975
\(742\) −142.432 142.432i −0.191957 0.191957i
\(743\) 434.532 434.532i 0.584834 0.584834i −0.351394 0.936228i \(-0.614292\pi\)
0.936228 + 0.351394i \(0.114292\pi\)
\(744\) 230.559i 0.309892i
\(745\) −337.295 358.092i −0.452745 0.480661i
\(746\) −198.195 −0.265677
\(747\) 302.972 + 302.972i 0.405585 + 0.405585i
\(748\) −29.8827 + 29.8827i −0.0399501 + 0.0399501i
\(749\) 459.330i 0.613258i
\(750\) 280.330 + 335.737i 0.373774 + 0.447650i
\(751\) −36.0488 −0.0480010 −0.0240005 0.999712i \(-0.507640\pi\)
−0.0240005 + 0.999712i \(0.507640\pi\)
\(752\) 215.095 + 215.095i 0.286031 + 0.286031i
\(753\) 81.6769 81.6769i 0.108469 0.108469i
\(754\) 29.3501i 0.0389259i
\(755\) 270.596 254.880i 0.358405 0.337590i
\(756\) −389.469 −0.515171
\(757\) 991.601 + 991.601i 1.30991 + 1.30991i 0.921478 + 0.388431i \(0.126983\pi\)
0.388431 + 0.921478i \(0.373017\pi\)
\(758\) −267.871 + 267.871i −0.353392 + 0.353392i
\(759\) 87.1452i 0.114816i
\(760\) 179.496 + 5.36826i 0.236179 + 0.00706350i
\(761\) 1444.95 1.89875 0.949375 0.314145i \(-0.101718\pi\)
0.949375 + 0.314145i \(0.101718\pi\)
\(762\) 138.603 + 138.603i 0.181894 + 0.181894i
\(763\) −901.559 + 901.559i −1.18160 + 1.18160i
\(764\) 444.673i 0.582032i
\(765\) 1.23779 41.3873i 0.00161802 0.0541011i
\(766\) 387.862 0.506347
\(767\) −6.67869 6.67869i −0.00870755 0.00870755i
\(768\) 27.9926 27.9926i 0.0364486 0.0364486i
\(769\) 630.455i 0.819838i −0.912122 0.409919i \(-0.865557\pi\)
0.912122 0.409919i \(-0.134443\pi\)
\(770\) −235.930 250.477i −0.306403 0.325295i
\(771\) −1084.28 −1.40633
\(772\) 215.449 + 215.449i 0.279079 + 0.279079i
\(773\) −333.366 + 333.366i −0.431262 + 0.431262i −0.889058 0.457795i \(-0.848639\pi\)
0.457795 + 0.889058i \(0.348639\pi\)
\(774\) 90.1714i 0.116501i
\(775\) 49.2222 822.173i 0.0635125 1.06087i
\(776\) −404.926 −0.521812
\(777\)