Properties

Label 731.2.j.a.135.8
Level 731
Weight 2
Character 731.135
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(64\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 135.8
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.8

$q$-expansion

\(f(q)\) \(=\) \(q-2.11821 q^{2} +(2.72590 + 1.57380i) q^{3} +2.48683 q^{4} +(0.994359 + 0.574094i) q^{5} +(-5.77403 - 3.33364i) q^{6} +(0.0492215 - 0.0284181i) q^{7} -1.03120 q^{8} +(3.45368 + 5.98195i) q^{9} +O(q^{10})\) \(q-2.11821 q^{2} +(2.72590 + 1.57380i) q^{3} +2.48683 q^{4} +(0.994359 + 0.574094i) q^{5} +(-5.77403 - 3.33364i) q^{6} +(0.0492215 - 0.0284181i) q^{7} -1.03120 q^{8} +(3.45368 + 5.98195i) q^{9} +(-2.10626 - 1.21605i) q^{10} +4.00839i q^{11} +(6.77884 + 3.91376i) q^{12} +(-1.18757 - 2.05692i) q^{13} +(-0.104262 + 0.0601955i) q^{14} +(1.80701 + 3.12984i) q^{15} -2.78935 q^{16} +(-3.10460 - 2.71320i) q^{17} +(-7.31563 - 12.6710i) q^{18} +(-3.77965 + 6.54654i) q^{19} +(2.47280 + 1.42767i) q^{20} +0.178897 q^{21} -8.49061i q^{22} +(5.11688 + 2.95423i) q^{23} +(-2.81095 - 1.62291i) q^{24} +(-1.84083 - 3.18842i) q^{25} +(2.51552 + 4.35700i) q^{26} +12.2988i q^{27} +(0.122405 - 0.0706708i) q^{28} +(-0.411323 + 0.237477i) q^{29} +(-3.82764 - 6.62967i) q^{30} +(8.46082 + 4.88485i) q^{31} +7.97084 q^{32} +(-6.30839 + 10.9264i) q^{33} +(6.57620 + 5.74714i) q^{34} +0.0652585 q^{35} +(8.58870 + 14.8761i) q^{36} +(-4.98246 - 2.87663i) q^{37} +(8.00610 - 13.8670i) q^{38} -7.47595i q^{39} +(-1.02539 - 0.592007i) q^{40} -5.15188i q^{41} -0.378942 q^{42} +(2.73431 - 5.96016i) q^{43} +9.96816i q^{44} +7.93094i q^{45} +(-10.8386 - 6.25769i) q^{46} +2.14463 q^{47} +(-7.60347 - 4.38987i) q^{48} +(-3.49838 + 6.05938i) q^{49} +(3.89928 + 6.75375i) q^{50} +(-4.19279 - 12.2819i) q^{51} +(-2.95327 - 5.11521i) q^{52} +(6.19828 - 10.7357i) q^{53} -26.0515i q^{54} +(-2.30119 + 3.98577i) q^{55} +(-0.0507574 + 0.0293048i) q^{56} +(-20.6059 + 11.8968i) q^{57} +(0.871270 - 0.503028i) q^{58} +4.91933 q^{59} +(4.49373 + 7.78337i) q^{60} +(-4.22781 + 2.44092i) q^{61} +(-17.9218 - 10.3472i) q^{62} +(0.339991 + 0.196294i) q^{63} -11.3052 q^{64} -2.72709i q^{65} +(13.3625 - 23.1445i) q^{66} +(-5.98273 + 10.3624i) q^{67} +(-7.72060 - 6.74726i) q^{68} +(9.29872 + 16.1059i) q^{69} -0.138231 q^{70} +(7.45598 - 4.30471i) q^{71} +(-3.56145 - 6.16860i) q^{72} +(13.2876 - 7.67163i) q^{73} +(10.5539 + 6.09331i) q^{74} -11.5884i q^{75} +(-9.39933 + 16.2801i) q^{76} +(0.113911 + 0.197299i) q^{77} +15.8357i q^{78} +(-6.06687 + 3.50271i) q^{79} +(-2.77361 - 1.60135i) q^{80} +(-8.99477 + 15.5794i) q^{81} +10.9128i q^{82} +(-2.29334 + 3.97218i) q^{83} +0.444886 q^{84} +(-1.52945 - 4.48023i) q^{85} +(-5.79185 + 12.6249i) q^{86} -1.49497 q^{87} -4.13346i q^{88} +(3.42427 - 5.93101i) q^{89} -16.7994i q^{90} +(-0.116908 - 0.0674966i) q^{91} +(12.7248 + 7.34666i) q^{92} +(15.3755 + 26.6312i) q^{93} -4.54279 q^{94} +(-7.51665 + 4.33974i) q^{95} +(21.7277 + 12.5445i) q^{96} -2.70862i q^{97} +(7.41032 - 12.8351i) q^{98} +(-23.9780 + 13.8437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + O(q^{10}) \) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + 4q^{13} - 12q^{15} + 76q^{16} + 2q^{17} - 16q^{18} - 2q^{19} - 20q^{21} + 60q^{25} - 2q^{26} - 28q^{30} - 48q^{32} + 22q^{33} - 18q^{34} - 112q^{35} + 36q^{36} - 40q^{38} + 36q^{42} + 10q^{43} + 36q^{47} + 52q^{49} + 16q^{50} + 10q^{51} + 10q^{52} + 24q^{55} - 12q^{59} - 78q^{60} + 36q^{64} + 14q^{66} + 10q^{67} - q^{68} - 64q^{70} - 68q^{72} - 22q^{76} - 28q^{77} - 20q^{81} - 6q^{83} + 32q^{84} + 6q^{85} - 58q^{86} + 32q^{87} + 36q^{89} + 6q^{93} + 132q^{94} - 48q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.11821 −1.49780 −0.748901 0.662681i \(-0.769418\pi\)
−0.748901 + 0.662681i \(0.769418\pi\)
\(3\) 2.72590 + 1.57380i 1.57380 + 0.908633i 0.995697 + 0.0926673i \(0.0295393\pi\)
0.578101 + 0.815965i \(0.303794\pi\)
\(4\) 2.48683 1.24341
\(5\) 0.994359 + 0.574094i 0.444691 + 0.256742i 0.705585 0.708625i \(-0.250684\pi\)
−0.260894 + 0.965367i \(0.584017\pi\)
\(6\) −5.77403 3.33364i −2.35724 1.36095i
\(7\) 0.0492215 0.0284181i 0.0186040 0.0107410i −0.490669 0.871346i \(-0.663248\pi\)
0.509273 + 0.860605i \(0.329914\pi\)
\(8\) −1.03120 −0.364585
\(9\) 3.45368 + 5.98195i 1.15123 + 1.99398i
\(10\) −2.10626 1.21605i −0.666059 0.384550i
\(11\) 4.00839i 1.20857i 0.796767 + 0.604287i \(0.206542\pi\)
−0.796767 + 0.604287i \(0.793458\pi\)
\(12\) 6.77884 + 3.91376i 1.95688 + 1.12981i
\(13\) −1.18757 2.05692i −0.329371 0.570488i 0.653016 0.757344i \(-0.273503\pi\)
−0.982387 + 0.186856i \(0.940170\pi\)
\(14\) −0.104262 + 0.0601955i −0.0278651 + 0.0160879i
\(15\) 1.80701 + 3.12984i 0.466569 + 0.808121i
\(16\) −2.78935 −0.697336
\(17\) −3.10460 2.71320i −0.752976 0.658048i
\(18\) −7.31563 12.6710i −1.72431 2.98659i
\(19\) −3.77965 + 6.54654i −0.867110 + 1.50188i −0.00217416 + 0.999998i \(0.500692\pi\)
−0.864936 + 0.501882i \(0.832641\pi\)
\(20\) 2.47280 + 1.42767i 0.552935 + 0.319237i
\(21\) 0.178897 0.0390386
\(22\) 8.49061i 1.81020i
\(23\) 5.11688 + 2.95423i 1.06694 + 0.616000i 0.927345 0.374209i \(-0.122086\pi\)
0.139598 + 0.990208i \(0.455419\pi\)
\(24\) −2.81095 1.62291i −0.573784 0.331274i
\(25\) −1.84083 3.18842i −0.368167 0.637683i
\(26\) 2.51552 + 4.35700i 0.493333 + 0.854478i
\(27\) 12.2988i 2.36690i
\(28\) 0.122405 0.0706708i 0.0231324 0.0133555i
\(29\) −0.411323 + 0.237477i −0.0763808 + 0.0440985i −0.537704 0.843134i \(-0.680708\pi\)
0.461323 + 0.887232i \(0.347375\pi\)
\(30\) −3.82764 6.62967i −0.698829 1.21041i
\(31\) 8.46082 + 4.88485i 1.51961 + 0.877346i 0.999733 + 0.0231031i \(0.00735458\pi\)
0.519874 + 0.854243i \(0.325979\pi\)
\(32\) 7.97084 1.40906
\(33\) −6.30839 + 10.9264i −1.09815 + 1.90205i
\(34\) 6.57620 + 5.74714i 1.12781 + 0.985626i
\(35\) 0.0652585 0.0110307
\(36\) 8.58870 + 14.8761i 1.43145 + 2.47935i
\(37\) −4.98246 2.87663i −0.819112 0.472914i 0.0309983 0.999519i \(-0.490131\pi\)
−0.850110 + 0.526605i \(0.823465\pi\)
\(38\) 8.00610 13.8670i 1.29876 2.24952i
\(39\) 7.47595i 1.19711i
\(40\) −1.02539 0.592007i −0.162128 0.0936045i
\(41\) 5.15188i 0.804589i −0.915510 0.402294i \(-0.868213\pi\)
0.915510 0.402294i \(-0.131787\pi\)
\(42\) −0.378942 −0.0584721
\(43\) 2.73431 5.96016i 0.416978 0.908917i
\(44\) 9.96816i 1.50276i
\(45\) 7.93094i 1.18227i
\(46\) −10.8386 6.25769i −1.59807 0.922646i
\(47\) 2.14463 0.312827 0.156414 0.987692i \(-0.450007\pi\)
0.156414 + 0.987692i \(0.450007\pi\)
\(48\) −7.60347 4.38987i −1.09747 0.633623i
\(49\) −3.49838 + 6.05938i −0.499769 + 0.865626i
\(50\) 3.89928 + 6.75375i 0.551441 + 0.955124i
\(51\) −4.19279 12.2819i −0.587108 1.71981i
\(52\) −2.95327 5.11521i −0.409545 0.709352i
\(53\) 6.19828 10.7357i 0.851399 1.47467i −0.0285472 0.999592i \(-0.509088\pi\)
0.879946 0.475074i \(-0.157579\pi\)
\(54\) 26.0515i 3.54515i
\(55\) −2.30119 + 3.98577i −0.310292 + 0.537442i
\(56\) −0.0507574 + 0.0293048i −0.00678274 + 0.00391602i
\(57\) −20.6059 + 11.8968i −2.72931 + 1.57577i
\(58\) 0.871270 0.503028i 0.114403 0.0660508i
\(59\) 4.91933 0.640442 0.320221 0.947343i \(-0.396243\pi\)
0.320221 + 0.947343i \(0.396243\pi\)
\(60\) 4.49373 + 7.78337i 0.580138 + 1.00483i
\(61\) −4.22781 + 2.44092i −0.541315 + 0.312528i −0.745612 0.666381i \(-0.767843\pi\)
0.204297 + 0.978909i \(0.434509\pi\)
\(62\) −17.9218 10.3472i −2.27607 1.31409i
\(63\) 0.339991 + 0.196294i 0.0428348 + 0.0247307i
\(64\) −11.3052 −1.41315
\(65\) 2.72709i 0.338254i
\(66\) 13.3625 23.1445i 1.64481 2.84890i
\(67\) −5.98273 + 10.3624i −0.730907 + 1.26597i 0.225590 + 0.974222i \(0.427569\pi\)
−0.956496 + 0.291745i \(0.905764\pi\)
\(68\) −7.72060 6.74726i −0.936260 0.818226i
\(69\) 9.29872 + 16.1059i 1.11943 + 1.93892i
\(70\) −0.138231 −0.0165218
\(71\) 7.45598 4.30471i 0.884862 0.510875i 0.0126035 0.999921i \(-0.495988\pi\)
0.872258 + 0.489045i \(0.162655\pi\)
\(72\) −3.56145 6.16860i −0.419720 0.726977i
\(73\) 13.2876 7.67163i 1.55520 0.897896i 0.557497 0.830179i \(-0.311762\pi\)
0.997705 0.0677165i \(-0.0215714\pi\)
\(74\) 10.5539 + 6.09331i 1.22687 + 0.708332i
\(75\) 11.5884i 1.33811i
\(76\) −9.39933 + 16.2801i −1.07818 + 1.86746i
\(77\) 0.113911 + 0.197299i 0.0129813 + 0.0224843i
\(78\) 15.8357i 1.79303i
\(79\) −6.06687 + 3.50271i −0.682577 + 0.394086i −0.800825 0.598898i \(-0.795605\pi\)
0.118248 + 0.992984i \(0.462272\pi\)
\(80\) −2.77361 1.60135i −0.310099 0.179036i
\(81\) −8.99477 + 15.5794i −0.999419 + 1.73104i
\(82\) 10.9128i 1.20512i
\(83\) −2.29334 + 3.97218i −0.251727 + 0.436004i −0.964001 0.265897i \(-0.914332\pi\)
0.712274 + 0.701901i \(0.247665\pi\)
\(84\) 0.444886 0.0485411
\(85\) −1.52945 4.48023i −0.165893 0.485949i
\(86\) −5.79185 + 12.6249i −0.624551 + 1.36138i
\(87\) −1.49497 −0.160277
\(88\) 4.13346i 0.440628i
\(89\) 3.42427 5.93101i 0.362972 0.628686i −0.625476 0.780243i \(-0.715095\pi\)
0.988449 + 0.151557i \(0.0484287\pi\)
\(90\) 16.7994i 1.77081i
\(91\) −0.116908 0.0674966i −0.0122552 0.00707556i
\(92\) 12.7248 + 7.34666i 1.32665 + 0.765942i
\(93\) 15.3755 + 26.6312i 1.59437 + 2.76153i
\(94\) −4.54279 −0.468553
\(95\) −7.51665 + 4.33974i −0.771192 + 0.445248i
\(96\) 21.7277 + 12.5445i 2.21757 + 1.28032i
\(97\) 2.70862i 0.275019i −0.990500 0.137509i \(-0.956090\pi\)
0.990500 0.137509i \(-0.0439098\pi\)
\(98\) 7.41032 12.8351i 0.748556 1.29654i
\(99\) −23.9780 + 13.8437i −2.40988 + 1.39134i
\(100\) −4.57783 7.92904i −0.457783 0.792904i
\(101\) 6.82234 + 11.8166i 0.678848 + 1.17580i 0.975328 + 0.220760i \(0.0708538\pi\)
−0.296480 + 0.955039i \(0.595813\pi\)
\(102\) 8.88122 + 26.0157i 0.879372 + 2.57594i
\(103\) −0.405998 0.703210i −0.0400042 0.0692893i 0.845330 0.534244i \(-0.179404\pi\)
−0.885334 + 0.464955i \(0.846070\pi\)
\(104\) 1.22462 + 2.12111i 0.120084 + 0.207991i
\(105\) 0.177888 + 0.102704i 0.0173601 + 0.0100229i
\(106\) −13.1293 + 22.7406i −1.27523 + 2.20876i
\(107\) 9.84886i 0.952125i 0.879412 + 0.476062i \(0.157936\pi\)
−0.879412 + 0.476062i \(0.842064\pi\)
\(108\) 30.5850i 2.94304i
\(109\) −13.0422 7.52995i −1.24922 0.721238i −0.278267 0.960504i \(-0.589760\pi\)
−0.970954 + 0.239266i \(0.923093\pi\)
\(110\) 4.87441 8.44272i 0.464756 0.804982i
\(111\) −9.05446 15.6828i −0.859411 1.48854i
\(112\) −0.137296 + 0.0792678i −0.0129732 + 0.00749010i
\(113\) 9.72518i 0.914868i 0.889244 + 0.457434i \(0.151231\pi\)
−0.889244 + 0.457434i \(0.848769\pi\)
\(114\) 43.6476 25.2000i 4.08797 2.36019i
\(115\) 3.39201 + 5.87513i 0.316306 + 0.547859i
\(116\) −1.02289 + 0.590565i −0.0949729 + 0.0548326i
\(117\) 8.20294 14.2079i 0.758362 1.31352i
\(118\) −10.4202 −0.959256
\(119\) −0.229917 0.0453213i −0.0210765 0.00415459i
\(120\) −1.86340 3.22750i −0.170104 0.294629i
\(121\) −5.06715 −0.460650
\(122\) 8.95539 5.17040i 0.810783 0.468106i
\(123\) 8.10802 14.0435i 0.731076 1.26626i
\(124\) 21.0406 + 12.1478i 1.88950 + 1.09090i
\(125\) 9.96818i 0.891581i
\(126\) −0.720173 0.415792i −0.0641581 0.0370417i
\(127\) −6.90186 −0.612441 −0.306221 0.951961i \(-0.599065\pi\)
−0.306221 + 0.951961i \(0.599065\pi\)
\(128\) 8.00523 0.707569
\(129\) 16.8335 11.9436i 1.48211 1.05157i
\(130\) 5.77657i 0.506638i
\(131\) 11.4556i 1.00088i −0.865772 0.500439i \(-0.833172\pi\)
0.865772 0.500439i \(-0.166828\pi\)
\(132\) −15.6879 + 27.1722i −1.36545 + 2.36504i
\(133\) 0.429641i 0.0372546i
\(134\) 12.6727 21.9497i 1.09475 1.89617i
\(135\) −7.06066 + 12.2294i −0.607685 + 1.05254i
\(136\) 3.20147 + 2.79786i 0.274524 + 0.239915i
\(137\) 3.00746 0.256945 0.128472 0.991713i \(-0.458993\pi\)
0.128472 + 0.991713i \(0.458993\pi\)
\(138\) −19.6967 34.1156i −1.67669 2.90412i
\(139\) −6.60741 3.81479i −0.560433 0.323566i 0.192886 0.981221i \(-0.438215\pi\)
−0.753319 + 0.657655i \(0.771549\pi\)
\(140\) 0.162287 0.0137157
\(141\) 5.84606 + 3.37522i 0.492327 + 0.284245i
\(142\) −15.7934 + 9.11830i −1.32535 + 0.765190i
\(143\) 8.24494 4.76022i 0.689476 0.398069i
\(144\) −9.63351 16.6857i −0.802792 1.39048i
\(145\) −0.545337 −0.0452878
\(146\) −28.1461 + 16.2501i −2.32938 + 1.34487i
\(147\) −19.0725 + 11.0115i −1.57307 + 0.908213i
\(148\) −12.3905 7.15367i −1.01849 0.588028i
\(149\) 1.47640 2.55719i 0.120951 0.209493i −0.799192 0.601076i \(-0.794739\pi\)
0.920143 + 0.391582i \(0.128072\pi\)
\(150\) 24.5467i 2.00423i
\(151\) 10.4433 0.849866 0.424933 0.905225i \(-0.360298\pi\)
0.424933 + 0.905225i \(0.360298\pi\)
\(152\) 3.89758 6.75081i 0.316136 0.547563i
\(153\) 5.50795 27.9421i 0.445291 2.25898i
\(154\) −0.241287 0.417921i −0.0194434 0.0336770i
\(155\) 5.60873 + 9.71460i 0.450504 + 0.780295i
\(156\) 18.5914i 1.48850i
\(157\) 6.76380 + 11.7153i 0.539810 + 0.934979i 0.998914 + 0.0465960i \(0.0148373\pi\)
−0.459104 + 0.888383i \(0.651829\pi\)
\(158\) 12.8509 7.41949i 1.02237 0.590263i
\(159\) 33.7917 19.5097i 2.67986 1.54722i
\(160\) 7.92587 + 4.57601i 0.626595 + 0.361765i
\(161\) 0.335814 0.0264658
\(162\) 19.0528 33.0005i 1.49693 2.59276i
\(163\) 2.72257 1.57188i 0.213248 0.123119i −0.389572 0.920996i \(-0.627377\pi\)
0.602820 + 0.797877i \(0.294044\pi\)
\(164\) 12.8118i 1.00044i
\(165\) −12.5456 + 7.24321i −0.976674 + 0.563883i
\(166\) 4.85779 8.41393i 0.377037 0.653048i
\(167\) 15.1871 + 8.76828i 1.17521 + 0.678510i 0.954902 0.296920i \(-0.0959593\pi\)
0.220311 + 0.975430i \(0.429293\pi\)
\(168\) −0.184479 −0.0142329
\(169\) 3.67938 6.37287i 0.283029 0.490221i
\(170\) 3.23971 + 9.49008i 0.248474 + 0.727856i
\(171\) −52.2148 −3.99296
\(172\) 6.79975 14.8219i 0.518476 1.13016i
\(173\) 4.54865i 0.345828i −0.984937 0.172914i \(-0.944682\pi\)
0.984937 0.172914i \(-0.0553182\pi\)
\(174\) 3.16666 0.240064
\(175\) −0.181217 0.104626i −0.0136987 0.00790897i
\(176\) 11.1808i 0.842782i
\(177\) 13.4096 + 7.74203i 1.00793 + 0.581927i
\(178\) −7.25334 + 12.5631i −0.543661 + 0.941648i
\(179\) −7.95492 13.7783i −0.594579 1.02984i −0.993606 0.112902i \(-0.963986\pi\)
0.399027 0.916939i \(-0.369348\pi\)
\(180\) 19.7229i 1.47006i
\(181\) −11.7534 + 6.78580i −0.873620 + 0.504385i −0.868549 0.495602i \(-0.834947\pi\)
−0.00507041 + 0.999987i \(0.501614\pi\)
\(182\) 0.247635 + 0.142972i 0.0183559 + 0.0105978i
\(183\) −15.3661 −1.13589
\(184\) −5.27654 3.04641i −0.388992 0.224584i
\(185\) −3.30290 5.72080i −0.242834 0.420601i
\(186\) −32.5687 56.4106i −2.38805 4.13623i
\(187\) 10.8756 12.4444i 0.795300 0.910027i
\(188\) 5.33334 0.388973
\(189\) 0.349508 + 0.605365i 0.0254229 + 0.0440338i
\(190\) 15.9219 9.19250i 1.15509 0.666894i
\(191\) −0.0689499 + 0.119425i −0.00498904 + 0.00864127i −0.868509 0.495673i \(-0.834921\pi\)
0.863520 + 0.504314i \(0.168255\pi\)
\(192\) −30.8169 17.7922i −2.22402 1.28404i
\(193\) 27.1636i 1.95528i −0.210293 0.977639i \(-0.567442\pi\)
0.210293 0.977639i \(-0.432558\pi\)
\(194\) 5.73744i 0.411924i
\(195\) 4.29189 7.43378i 0.307349 0.532344i
\(196\) −8.69988 + 15.0686i −0.621420 + 1.07633i
\(197\) 6.60556 3.81372i 0.470627 0.271717i −0.245875 0.969302i \(-0.579075\pi\)
0.716502 + 0.697585i \(0.245742\pi\)
\(198\) 50.7904 29.3239i 3.60952 2.08396i
\(199\) 15.0154i 1.06441i −0.846615 0.532206i \(-0.821363\pi\)
0.846615 0.532206i \(-0.178637\pi\)
\(200\) 1.89827 + 3.28790i 0.134228 + 0.232490i
\(201\) −32.6166 + 18.8312i −2.30060 + 1.32825i
\(202\) −14.4512 25.0302i −1.01678 1.76112i
\(203\) −0.0134973 + 0.0233780i −0.000947324 + 0.00164081i
\(204\) −10.4267 30.5430i −0.730018 2.13844i
\(205\) 2.95766 5.12282i 0.206572 0.357793i
\(206\) 0.859991 + 1.48955i 0.0599184 + 0.103782i
\(207\) 40.8119i 2.83662i
\(208\) 3.31253 + 5.73747i 0.229683 + 0.397822i
\(209\) −26.2411 15.1503i −1.81513 1.04797i
\(210\) −0.376805 0.217548i −0.0260020 0.0150123i
\(211\) 2.48410i 0.171012i −0.996338 0.0855061i \(-0.972749\pi\)
0.996338 0.0855061i \(-0.0272507\pi\)
\(212\) 15.4140 26.6979i 1.05864 1.83362i
\(213\) 27.0990 1.85679
\(214\) 20.8620i 1.42610i
\(215\) 6.14058 4.35680i 0.418784 0.297131i
\(216\) 12.6826i 0.862938i
\(217\) 0.555272 0.0376943
\(218\) 27.6263 + 15.9500i 1.87109 + 1.08027i
\(219\) 48.2944 3.26343
\(220\) −5.72266 + 9.91193i −0.385821 + 0.668262i
\(221\) −1.89393 + 9.60802i −0.127400 + 0.646306i
\(222\) 19.1793 + 33.2195i 1.28723 + 2.22954i
\(223\) 14.4299 0.966299 0.483149 0.875538i \(-0.339493\pi\)
0.483149 + 0.875538i \(0.339493\pi\)
\(224\) 0.392337 0.226516i 0.0262141 0.0151347i
\(225\) 12.7153 22.0235i 0.847686 1.46824i
\(226\) 20.6000i 1.37029i
\(227\) 0.931409 + 0.537749i 0.0618198 + 0.0356917i 0.530591 0.847628i \(-0.321970\pi\)
−0.468772 + 0.883319i \(0.655303\pi\)
\(228\) −51.2432 + 29.5853i −3.39366 + 1.95933i
\(229\) −0.458393 0.793959i −0.0302914 0.0524663i 0.850482 0.526004i \(-0.176310\pi\)
−0.880774 + 0.473537i \(0.842977\pi\)
\(230\) −7.18500 12.4448i −0.473765 0.820585i
\(231\) 0.717089i 0.0471810i
\(232\) 0.424158 0.244887i 0.0278473 0.0160776i
\(233\) 8.09639 4.67446i 0.530412 0.306234i −0.210772 0.977535i \(-0.567598\pi\)
0.741184 + 0.671302i \(0.234264\pi\)
\(234\) −17.3756 + 30.0954i −1.13588 + 1.96740i
\(235\) 2.13254 + 1.23122i 0.139111 + 0.0803160i
\(236\) 12.2335 0.796334
\(237\) −22.0502 −1.43232
\(238\) 0.487013 + 0.0960001i 0.0315684 + 0.00622276i
\(239\) 4.26439 7.38613i 0.275840 0.477769i −0.694507 0.719486i \(-0.744377\pi\)
0.970347 + 0.241717i \(0.0777106\pi\)
\(240\) −5.04039 8.73021i −0.325356 0.563533i
\(241\) 7.98068 4.60765i 0.514081 0.296805i −0.220429 0.975403i \(-0.570746\pi\)
0.734510 + 0.678598i \(0.237412\pi\)
\(242\) 10.7333 0.689963
\(243\) −17.0845 + 9.86372i −1.09597 + 0.632758i
\(244\) −10.5138 + 6.07016i −0.673078 + 0.388602i
\(245\) −6.95730 + 4.01680i −0.444486 + 0.256624i
\(246\) −17.1745 + 29.7471i −1.09501 + 1.89661i
\(247\) 17.9543 1.14241
\(248\) −8.72482 5.03728i −0.554027 0.319867i
\(249\) −12.5028 + 7.21851i −0.792335 + 0.457455i
\(250\) 21.1147i 1.33541i
\(251\) −2.78849 4.82980i −0.176008 0.304854i 0.764502 0.644622i \(-0.222985\pi\)
−0.940510 + 0.339767i \(0.889652\pi\)
\(252\) 0.845498 + 0.488149i 0.0532614 + 0.0307505i
\(253\) −11.8417 + 20.5104i −0.744481 + 1.28948i
\(254\) 14.6196 0.917316
\(255\) 2.88184 14.6197i 0.180468 0.915521i
\(256\) 5.65369 0.353356
\(257\) −8.19852 −0.511410 −0.255705 0.966755i \(-0.582308\pi\)
−0.255705 + 0.966755i \(0.582308\pi\)
\(258\) −35.6570 + 25.2990i −2.21991 + 1.57505i
\(259\) −0.326992 −0.0203183
\(260\) 6.78181i 0.420590i
\(261\) −2.84116 1.64034i −0.175863 0.101535i
\(262\) 24.2654i 1.49912i
\(263\) −12.1600 + 21.0617i −0.749815 + 1.29872i 0.198096 + 0.980183i \(0.436524\pi\)
−0.947911 + 0.318535i \(0.896809\pi\)
\(264\) 6.50523 11.2674i 0.400369 0.693460i
\(265\) 12.3266 7.11678i 0.757219 0.437180i
\(266\) 0.910071i 0.0558000i
\(267\) 18.6684 10.7782i 1.14249 0.659616i
\(268\) −14.8780 + 25.7695i −0.908819 + 1.57412i
\(269\) 25.9319i 1.58109i −0.612402 0.790547i \(-0.709797\pi\)
0.612402 0.790547i \(-0.290203\pi\)
\(270\) 14.9560 25.9045i 0.910192 1.57650i
\(271\) 4.79161 + 8.29931i 0.291069 + 0.504147i 0.974063 0.226278i \(-0.0726556\pi\)
−0.682994 + 0.730424i \(0.739322\pi\)
\(272\) 8.65980 + 7.56806i 0.525078 + 0.458881i
\(273\) −0.212452 0.367978i −0.0128582 0.0222710i
\(274\) −6.37045 −0.384853
\(275\) 12.7804 7.37877i 0.770687 0.444956i
\(276\) 23.1243 + 40.0525i 1.39192 + 2.41088i
\(277\) −5.31892 3.07088i −0.319583 0.184511i 0.331624 0.943412i \(-0.392404\pi\)
−0.651207 + 0.758900i \(0.725737\pi\)
\(278\) 13.9959 + 8.08054i 0.839419 + 0.484639i
\(279\) 67.4829i 4.04010i
\(280\) −0.0672948 −0.00402163
\(281\) 4.98060 8.62666i 0.297118 0.514623i −0.678357 0.734732i \(-0.737308\pi\)
0.975475 + 0.220109i \(0.0706413\pi\)
\(282\) −12.3832 7.14944i −0.737408 0.425743i
\(283\) −5.21302 + 3.00974i −0.309882 + 0.178910i −0.646874 0.762597i \(-0.723924\pi\)
0.336992 + 0.941508i \(0.390591\pi\)
\(284\) 18.5417 10.7051i 1.10025 0.635229i
\(285\) −27.3195 −1.61827
\(286\) −17.4645 + 10.0832i −1.03270 + 0.596230i
\(287\) −0.146407 0.253584i −0.00864210 0.0149686i
\(288\) 27.5287 + 47.6811i 1.62215 + 2.80964i
\(289\) 2.27707 + 16.8468i 0.133945 + 0.990989i
\(290\) 1.15514 0.0678322
\(291\) 4.26283 7.38343i 0.249891 0.432824i
\(292\) 33.0441 19.0780i 1.93376 1.11646i
\(293\) 16.7758 0.980051 0.490025 0.871708i \(-0.336987\pi\)
0.490025 + 0.871708i \(0.336987\pi\)
\(294\) 40.3996 23.3247i 2.35615 1.36032i
\(295\) 4.89158 + 2.82415i 0.284799 + 0.164429i
\(296\) 5.13793 + 2.96639i 0.298636 + 0.172418i
\(297\) −49.2983 −2.86058
\(298\) −3.12732 + 5.41668i −0.181161 + 0.313780i
\(299\) 14.0334i 0.811570i
\(300\) 28.8183i 1.66383i
\(301\) −0.0347895 0.371072i −0.00200523 0.0213882i
\(302\) −22.1212 −1.27293
\(303\) 42.9479i 2.46729i
\(304\) 10.5427 18.2606i 0.604668 1.04732i
\(305\) −5.60528 −0.320957
\(306\) −11.6670 + 59.1873i −0.666958 + 3.38351i
\(307\) 6.14165 10.6376i 0.350522 0.607122i −0.635819 0.771838i \(-0.719337\pi\)
0.986341 + 0.164716i \(0.0526708\pi\)
\(308\) 0.283276 + 0.490648i 0.0161411 + 0.0279573i
\(309\) 2.55584i 0.145397i
\(310\) −11.8805 20.5776i −0.674766 1.16873i
\(311\) 13.3603 + 7.71357i 0.757593 + 0.437397i 0.828431 0.560091i \(-0.189234\pi\)
−0.0708379 + 0.997488i \(0.522567\pi\)
\(312\) 7.70922i 0.436449i
\(313\) −6.90015 3.98380i −0.390019 0.225178i 0.292149 0.956373i \(-0.405630\pi\)
−0.682169 + 0.731195i \(0.738963\pi\)
\(314\) −14.3272 24.8154i −0.808529 1.40041i
\(315\) 0.225382 + 0.390373i 0.0126988 + 0.0219950i
\(316\) −15.0873 + 8.71064i −0.848725 + 0.490012i
\(317\) 0.454346i 0.0255186i −0.999919 0.0127593i \(-0.995938\pi\)
0.999919 0.0127593i \(-0.00406152\pi\)
\(318\) −71.5781 + 41.3256i −4.01390 + 2.31743i
\(319\) −0.951901 1.64874i −0.0532962 0.0923118i
\(320\) −11.2415 6.49026i −0.628417 0.362817i
\(321\) −15.5001 + 26.8470i −0.865132 + 1.49845i
\(322\) −0.711325 −0.0396406
\(323\) 29.4964 10.0694i 1.64122 0.560278i
\(324\) −22.3684 + 38.7433i −1.24269 + 2.15240i
\(325\) −4.37222 + 7.57290i −0.242527 + 0.420069i
\(326\) −5.76698 + 3.32957i −0.319404 + 0.184408i
\(327\) −23.7012 41.0517i −1.31068 2.27017i
\(328\) 5.31264i 0.293341i
\(329\) 0.105562 0.0609464i 0.00581983 0.00336008i
\(330\) 26.5743 15.3427i 1.46287 0.844586i
\(331\) −14.1582 24.5228i −0.778207 1.34789i −0.932974 0.359943i \(-0.882796\pi\)
0.154768 0.987951i \(-0.450537\pi\)
\(332\) −5.70314 + 9.87814i −0.313001 + 0.542133i
\(333\) 39.7398i 2.17773i
\(334\) −32.1695 18.5731i −1.76024 1.01627i
\(335\) −11.8980 + 6.86929i −0.650055 + 0.375309i
\(336\) −0.499006 −0.0272230
\(337\) 15.3528 8.86392i 0.836318 0.482849i −0.0196929 0.999806i \(-0.506269\pi\)
0.856011 + 0.516958i \(0.172936\pi\)
\(338\) −7.79371 + 13.4991i −0.423922 + 0.734254i
\(339\) −15.3055 + 26.5098i −0.831279 + 1.43982i
\(340\) −3.80349 11.1416i −0.206273 0.604235i
\(341\) −19.5804 + 33.9142i −1.06034 + 1.83656i
\(342\) 110.602 5.98067
\(343\) 0.795522i 0.0429542i
\(344\) −2.81963 + 6.14614i −0.152024 + 0.331378i
\(345\) 21.3533i 1.14963i
\(346\) 9.63501i 0.517982i
\(347\) −22.0711 12.7428i −1.18484 0.684068i −0.227711 0.973729i \(-0.573124\pi\)
−0.957129 + 0.289661i \(0.906458\pi\)
\(348\) −3.71772 −0.199291
\(349\) −10.3655 + 17.9536i −0.554853 + 0.961034i 0.443062 + 0.896491i \(0.353892\pi\)
−0.997915 + 0.0645431i \(0.979441\pi\)
\(350\) 0.383857 + 0.221620i 0.0205180 + 0.0118461i
\(351\) 25.2977 14.6056i 1.35029 0.779590i
\(352\) 31.9502i 1.70295i
\(353\) 15.3584 + 26.6015i 0.817443 + 1.41585i 0.907560 + 0.419922i \(0.137942\pi\)
−0.0901172 + 0.995931i \(0.528724\pi\)
\(354\) −28.4044 16.3993i −1.50967 0.871611i
\(355\) 9.88523 0.524653
\(356\) 8.51557 14.7494i 0.451324 0.781717i
\(357\) −0.555404 0.485384i −0.0293951 0.0256892i
\(358\) 16.8502 + 29.1854i 0.890562 + 1.54250i
\(359\) 11.4659 + 19.8595i 0.605146 + 1.04814i 0.992028 + 0.126015i \(0.0402188\pi\)
−0.386882 + 0.922129i \(0.626448\pi\)
\(360\) 8.17841i 0.431040i
\(361\) −19.0715 33.0327i −1.00376 1.73857i
\(362\) 24.8961 14.3738i 1.30851 0.755469i
\(363\) −13.8125 7.97467i −0.724970 0.418562i
\(364\) −0.290729 0.167852i −0.0152383 0.00879785i
\(365\) 17.6169 0.922112
\(366\) 32.5486 1.70135
\(367\) −19.8950 11.4864i −1.03851 0.599586i −0.119101 0.992882i \(-0.538001\pi\)
−0.919412 + 0.393296i \(0.871335\pi\)
\(368\) −14.2727 8.24037i −0.744018 0.429559i
\(369\) 30.8183 17.7930i 1.60434 0.926264i
\(370\) 6.99626 + 12.1179i 0.363718 + 0.629978i
\(371\) 0.704572i 0.0365796i
\(372\) 38.2363 + 66.2273i 1.98246 + 3.43372i
\(373\) −15.1177 26.1845i −0.782762 1.35578i −0.930327 0.366732i \(-0.880477\pi\)
0.147564 0.989052i \(-0.452857\pi\)
\(374\) −23.0368 + 26.3600i −1.19120 + 1.36304i
\(375\) 15.6879 27.1722i 0.810120 1.40317i
\(376\) −2.21155 −0.114052
\(377\) 0.976946 + 0.564040i 0.0503153 + 0.0290495i
\(378\) −0.740332 1.28229i −0.0380786 0.0659540i
\(379\) 16.0953i 0.826758i 0.910559 + 0.413379i \(0.135652\pi\)
−0.910559 + 0.413379i \(0.864348\pi\)
\(380\) −18.6926 + 10.7922i −0.958911 + 0.553627i
\(381\) −18.8138 10.8621i −0.963859 0.556484i
\(382\) 0.146051 0.252967i 0.00747260 0.0129429i
\(383\) −25.6141 −1.30882 −0.654410 0.756140i \(-0.727083\pi\)
−0.654410 + 0.756140i \(0.727083\pi\)
\(384\) 21.8214 + 12.5986i 1.11357 + 0.642920i
\(385\) 0.261581i 0.0133314i
\(386\) 57.5382i 2.92862i
\(387\) 45.0968 4.22800i 2.29240 0.214922i
\(388\) 6.73588i 0.341962i
\(389\) 8.42828 0.427331 0.213665 0.976907i \(-0.431460\pi\)
0.213665 + 0.976907i \(0.431460\pi\)
\(390\) −9.09115 + 15.7463i −0.460348 + 0.797346i
\(391\) −7.87043 23.0548i −0.398025 1.16593i
\(392\) 3.60755 6.24845i 0.182209 0.315594i
\(393\) 18.0288 31.2267i 0.909431 1.57518i
\(394\) −13.9920 + 8.07828i −0.704906 + 0.406978i
\(395\) −8.04354 −0.404714
\(396\) −59.6290 + 34.4268i −2.99647 + 1.73001i
\(397\) 29.2524 + 16.8889i 1.46813 + 0.847627i 0.999363 0.0356927i \(-0.0113637\pi\)
0.468771 + 0.883320i \(0.344697\pi\)
\(398\) 31.8058i 1.59428i
\(399\) −0.676168 + 1.17116i −0.0338507 + 0.0586312i
\(400\) 5.13472 + 8.89360i 0.256736 + 0.444680i
\(401\) 1.33628 0.771502i 0.0667307 0.0385270i −0.466263 0.884646i \(-0.654400\pi\)
0.532994 + 0.846119i \(0.321067\pi\)
\(402\) 69.0889 39.8885i 3.44584 1.98946i
\(403\) 23.2043i 1.15589i
\(404\) 16.9660 + 29.3859i 0.844089 + 1.46200i
\(405\) −17.8881 + 10.3277i −0.888865 + 0.513187i
\(406\) 0.0285901 0.0495196i 0.00141891 0.00245762i
\(407\) 11.5306 19.9716i 0.571552 0.989957i
\(408\) 4.32362 + 12.6652i 0.214051 + 0.627019i
\(409\) −19.5522 −0.966795 −0.483397 0.875401i \(-0.660597\pi\)
−0.483397 + 0.875401i \(0.660597\pi\)
\(410\) −6.26496 + 10.8512i −0.309404 + 0.535904i
\(411\) 8.19804 + 4.73314i 0.404379 + 0.233468i
\(412\) −1.00965 1.74876i −0.0497418 0.0861553i
\(413\) 0.242137 0.139798i 0.0119148 0.00687900i
\(414\) 86.4482i 4.24870i
\(415\) −4.56081 + 2.63319i −0.223881 + 0.129258i
\(416\) −9.46588 16.3954i −0.464103 0.803850i
\(417\) −12.0074 20.7975i −0.588006 1.01846i
\(418\) 55.5841 + 32.0915i 2.71871 + 1.56965i
\(419\) 4.62079i 0.225741i 0.993610 + 0.112870i \(0.0360045\pi\)
−0.993610 + 0.112870i \(0.963996\pi\)
\(420\) 0.442377 + 0.255406i 0.0215858 + 0.0124626i
\(421\) 1.87387 + 3.24564i 0.0913270 + 0.158183i 0.908070 0.418819i \(-0.137556\pi\)
−0.816743 + 0.577002i \(0.804222\pi\)
\(422\) 5.26184i 0.256143i
\(423\) 7.40688 + 12.8291i 0.360135 + 0.623772i
\(424\) −6.39168 + 11.0707i −0.310408 + 0.537642i
\(425\) −2.93577 + 14.8933i −0.142406 + 0.722432i
\(426\) −57.4014 −2.78111
\(427\) −0.138733 + 0.240292i −0.00671374 + 0.0116285i
\(428\) 24.4924i 1.18388i
\(429\) 29.9665 1.44680
\(430\) −13.0071 + 9.22862i −0.627256 + 0.445044i
\(431\) 22.4150i 1.07969i 0.841764 + 0.539845i \(0.181517\pi\)
−0.841764 + 0.539845i \(0.818483\pi\)
\(432\) 34.3056i 1.65053i
\(433\) 0.0678302 0.117485i 0.00325971 0.00564599i −0.864391 0.502820i \(-0.832296\pi\)
0.867651 + 0.497174i \(0.165629\pi\)
\(434\) −1.17619 −0.0564587
\(435\) −1.48653 0.858250i −0.0712738 0.0411500i
\(436\) −32.4338 18.7257i −1.55330 0.896797i
\(437\) −38.6800 + 22.3319i −1.85031 + 1.06828i
\(438\) −102.298 −4.88797
\(439\) 3.34371 1.93049i 0.159587 0.0921373i −0.418080 0.908410i \(-0.637297\pi\)
0.577666 + 0.816273i \(0.303963\pi\)
\(440\) 2.37299 4.11014i 0.113128 0.195943i
\(441\) −48.3292 −2.30139
\(442\) 4.01176 20.3518i 0.190820 0.968038i
\(443\) −10.6980 18.5294i −0.508276 0.880360i −0.999954 0.00958284i \(-0.996950\pi\)
0.491678 0.870777i \(-0.336384\pi\)
\(444\) −22.5169 39.0004i −1.06860 1.85087i
\(445\) 6.80991 3.93170i 0.322821 0.186381i
\(446\) −30.5656 −1.44733
\(447\) 8.04901 4.64710i 0.380705 0.219800i
\(448\) −0.556461 + 0.321273i −0.0262903 + 0.0151787i
\(449\) 34.9593 + 20.1838i 1.64983 + 0.952531i 0.977137 + 0.212610i \(0.0681964\pi\)
0.672694 + 0.739921i \(0.265137\pi\)
\(450\) −26.9337 + 46.6506i −1.26967 + 2.19913i
\(451\) 20.6507 0.972405
\(452\) 24.1848i 1.13756i
\(453\) 28.4674 + 16.4357i 1.33752 + 0.772216i
\(454\) −1.97292 1.13907i −0.0925939 0.0534591i
\(455\) −0.0774987 0.134232i −0.00363320 0.00629288i
\(456\) 21.2488 12.2680i 0.995068 0.574503i
\(457\) 31.5352 1.47515 0.737577 0.675263i \(-0.235970\pi\)
0.737577 + 0.675263i \(0.235970\pi\)
\(458\) 0.970973 + 1.68177i 0.0453706 + 0.0785842i
\(459\) 33.3691 38.1828i 1.55754 1.78222i
\(460\) 8.43534 + 14.6104i 0.393300 + 0.681215i
\(461\) 0.708553 1.22725i 0.0330006 0.0571587i −0.849053 0.528307i \(-0.822827\pi\)
0.882054 + 0.471148i \(0.156160\pi\)
\(462\) 1.51895i 0.0706678i
\(463\) −6.91126 + 11.9707i −0.321193 + 0.556323i −0.980735 0.195345i \(-0.937417\pi\)
0.659541 + 0.751669i \(0.270751\pi\)
\(464\) 1.14732 0.662407i 0.0532631 0.0307515i
\(465\) 35.3080i 1.63737i
\(466\) −17.1499 + 9.90149i −0.794453 + 0.458678i
\(467\) −7.70949 + 13.3532i −0.356753 + 0.617914i −0.987416 0.158143i \(-0.949449\pi\)
0.630664 + 0.776056i \(0.282783\pi\)
\(468\) 20.3993 35.3326i 0.942957 1.63325i
\(469\) 0.680070i 0.0314027i
\(470\) −4.51717 2.60799i −0.208361 0.120298i
\(471\) 42.5794i 1.96196i
\(472\) −5.07283 −0.233496
\(473\) 23.8906 + 10.9602i 1.09849 + 0.503949i
\(474\) 46.7071 2.14533
\(475\) 27.8308 1.27696
\(476\) −0.571764 0.112706i −0.0262068 0.00516588i
\(477\) 85.6275 3.92061
\(478\) −9.03288 + 15.6454i −0.413154 + 0.715604i
\(479\) 1.34371 + 0.775789i 0.0613955 + 0.0354467i 0.530384 0.847758i \(-0.322048\pi\)
−0.468988 + 0.883205i \(0.655381\pi\)
\(480\) 14.4034 + 24.9474i 0.657423 + 1.13869i
\(481\) 13.6647i 0.623058i
\(482\) −16.9048 + 9.75998i −0.769992 + 0.444555i
\(483\) 0.915395 + 0.528503i 0.0416519 + 0.0240477i
\(484\) −12.6011 −0.572779
\(485\) 1.55500 2.69334i 0.0706090 0.122298i
\(486\) 36.1885 20.8935i 1.64155 0.947747i
\(487\) −5.85315 + 3.37932i −0.265231 + 0.153131i −0.626719 0.779246i \(-0.715602\pi\)
0.361487 + 0.932377i \(0.382269\pi\)
\(488\) 4.35973 2.51709i 0.197356 0.113943i
\(489\) 9.89526 0.447479
\(490\) 14.7370 8.50844i 0.665752 0.384372i
\(491\) −6.86965 11.8986i −0.310023 0.536976i 0.668344 0.743852i \(-0.267003\pi\)
−0.978367 + 0.206877i \(0.933670\pi\)
\(492\) 20.1632 34.9238i 0.909029 1.57449i
\(493\) 1.92132 + 0.378730i 0.0865318 + 0.0170572i
\(494\) −38.0310 −1.71110
\(495\) −31.7903 −1.42887
\(496\) −23.6001 13.6255i −1.05968 0.611805i
\(497\) 0.244663 0.423769i 0.0109746 0.0190086i
\(498\) 26.4837 15.2904i 1.18676 0.685177i
\(499\) −17.9683 + 10.3740i −0.804372 + 0.464404i −0.844998 0.534770i \(-0.820398\pi\)
0.0406256 + 0.999174i \(0.487065\pi\)
\(500\) 24.7891i 1.10860i
\(501\) 27.5990 + 47.8029i 1.23303 + 2.13568i
\(502\) 5.90661 + 10.2305i 0.263625 + 0.456612i
\(503\) −7.16194 + 4.13495i −0.319335 + 0.184368i −0.651096 0.758995i \(-0.725691\pi\)
0.331761 + 0.943363i \(0.392357\pi\)
\(504\) −0.350600 0.202419i −0.0156169 0.00901645i
\(505\) 15.6666i 0.697156i
\(506\) 25.0832 43.4454i 1.11509 1.93138i
\(507\) 20.0592 11.5812i 0.890861 0.514339i
\(508\) −17.1637 −0.761518
\(509\) −15.5457 26.9260i −0.689052 1.19347i −0.972145 0.234381i \(-0.924694\pi\)
0.283092 0.959093i \(-0.408640\pi\)
\(510\) −6.10434 + 30.9676i −0.270305 + 1.37127i
\(511\) 0.436025 0.755218i 0.0192886 0.0334089i
\(512\) −27.9862 −1.23683
\(513\) −80.5145 46.4851i −3.55480 2.05237i
\(514\) 17.3662 0.765991
\(515\) 0.932324i 0.0410831i
\(516\) 41.8621 29.7015i 1.84288 1.30754i
\(517\) 8.59652i 0.378075i
\(518\) 0.692640 0.0304328
\(519\) 7.15866 12.3992i 0.314230 0.544263i
\(520\) 2.81219i 0.123323i
\(521\) −13.5307 7.81193i −0.592789 0.342247i 0.173411 0.984850i \(-0.444521\pi\)
−0.766199 + 0.642603i \(0.777855\pi\)
\(522\) 6.01817 + 3.47459i 0.263408 + 0.152079i
\(523\) −6.61887 11.4642i −0.289423 0.501296i 0.684249 0.729248i \(-0.260130\pi\)
−0.973672 + 0.227953i \(0.926797\pi\)
\(524\) 28.4880i 1.24451i
\(525\) −0.329320 0.570399i −0.0143727 0.0248942i
\(526\) 25.7574 44.6131i 1.12308 1.94522i
\(527\) −13.0138 38.1214i −0.566892 1.66060i
\(528\) 17.5963 30.4776i 0.765780 1.32637i
\(529\) 5.95495 + 10.3143i 0.258911 + 0.448447i
\(530\) −26.1104 + 15.0749i −1.13416 + 0.654810i
\(531\) 16.9898 + 29.4272i 0.737294 + 1.27703i
\(532\) 1.06844i 0.0463229i
\(533\) −10.5970 + 6.11820i −0.459008 + 0.265008i
\(534\) −39.5437 + 22.8306i −1.71122 + 0.987975i
\(535\) −5.65416 + 9.79330i −0.244451 + 0.423401i
\(536\) 6.16941 10.6857i 0.266478 0.461553i
\(537\) 50.0778i 2.16101i
\(538\) 54.9292i 2.36817i
\(539\) −24.2883 14.0229i −1.04617 0.604008i
\(540\) −17.5586 + 30.4124i −0.755603 + 1.30874i
\(541\) 15.4504 8.92030i 0.664265 0.383514i −0.129635 0.991562i \(-0.541381\pi\)
0.793900 + 0.608048i \(0.208047\pi\)
\(542\) −10.1496 17.5797i −0.435965 0.755113i
\(543\) −42.7179 −1.83320
\(544\) −24.7462 21.6265i −1.06099 0.927228i
\(545\) −8.64579 14.9749i −0.370345 0.641456i
\(546\) 0.450019 + 0.779455i 0.0192590 + 0.0333576i
\(547\) 28.7393 + 16.5926i 1.22880 + 0.709450i 0.966779 0.255612i \(-0.0822769\pi\)
0.262023 + 0.965062i \(0.415610\pi\)
\(548\) 7.47904 0.319489
\(549\) −29.2030 16.8603i −1.24635 0.719582i
\(550\) −27.0716 + 15.6298i −1.15434 + 0.666457i
\(551\) 3.59032i 0.152953i
\(552\) −9.58887 16.6084i −0.408129 0.706901i
\(553\) −0.199081 + 0.344818i −0.00846576 + 0.0146631i
\(554\) 11.2666 + 6.50478i 0.478672 + 0.276362i
\(555\) 20.7924i 0.882589i
\(556\) −16.4315 9.48673i −0.696850 0.402327i
\(557\) −3.61081 −0.152995 −0.0764975 0.997070i \(-0.524374\pi\)
−0.0764975 + 0.997070i \(0.524374\pi\)
\(558\) 142.943i 6.05127i
\(559\) −15.5068 + 1.45382i −0.655866 + 0.0614900i
\(560\) −0.182029 −0.00769211
\(561\) 49.2307 16.8063i 2.07852 0.709563i
\(562\) −10.5500 + 18.2731i −0.445024 + 0.770804i
\(563\) 17.5394 0.739197 0.369599 0.929192i \(-0.379495\pi\)
0.369599 + 0.929192i \(0.379495\pi\)
\(564\) 14.5381 + 8.39359i 0.612166 + 0.353434i
\(565\) −5.58316 + 9.67032i −0.234885 + 0.406834i
\(566\) 11.0423 6.37527i 0.464142 0.267973i
\(567\) 1.02246i 0.0429391i
\(568\) −7.68863 + 4.43903i −0.322608 + 0.186258i
\(569\) −17.1054 + 29.6273i −0.717094 + 1.24204i 0.245053 + 0.969510i \(0.421195\pi\)
−0.962146 + 0.272533i \(0.912139\pi\)
\(570\) 57.8685 2.42385
\(571\) −23.0431 13.3039i −0.964322 0.556752i −0.0668218 0.997765i \(-0.521286\pi\)
−0.897501 + 0.441013i \(0.854619\pi\)
\(572\) 20.5037 11.8378i 0.857304 0.494965i
\(573\) −0.375901 + 0.217027i −0.0157035 + 0.00906641i
\(574\) 0.310120 + 0.537144i 0.0129442 + 0.0224200i
\(575\) 21.7530i 0.907162i
\(576\) −39.0447 67.6273i −1.62686 2.81781i
\(577\) −8.69908 15.0673i −0.362148 0.627258i 0.626166 0.779689i \(-0.284623\pi\)
−0.988314 + 0.152431i \(0.951290\pi\)
\(578\) −4.82332 35.6851i −0.200623 1.48431i
\(579\) 42.7500 74.0451i 1.77663 3.07721i
\(580\) −1.35616 −0.0563114
\(581\) 0.260689i 0.0108152i
\(582\) −9.02957 + 15.6397i −0.374288 + 0.648285i
\(583\) 43.0329 + 24.8451i 1.78224 + 1.02898i
\(584\) −13.7023 + 7.91100i −0.567004 + 0.327360i
\(585\) 16.3133 9.41851i 0.674473 0.389407i
\(586\) −35.5346 −1.46792
\(587\) −2.31505 4.00979i −0.0955525 0.165502i 0.814287 0.580463i \(-0.197128\pi\)
−0.909839 + 0.414961i \(0.863795\pi\)
\(588\) −47.4300 + 27.3837i −1.95598 + 1.12928i
\(589\) −63.9578 + 36.9260i −2.63533 + 1.52151i
\(590\) −10.3614 5.98216i −0.426572 0.246282i
\(591\) 24.0081 0.987562
\(592\) 13.8978 + 8.02390i 0.571196 + 0.329780i
\(593\) −21.6963 37.5790i −0.890959 1.54319i −0.838727 0.544552i \(-0.816700\pi\)
−0.0522319 0.998635i \(-0.516633\pi\)
\(594\) 104.424 4.28458
\(595\) −0.202601 0.177059i −0.00830585 0.00725873i
\(596\) 3.67154 6.35930i 0.150392 0.260487i
\(597\) 23.6312 40.9304i 0.967160 1.67517i
\(598\) 29.7256i 1.21557i
\(599\) −18.2542 + 31.6173i −0.745848 + 1.29185i 0.203950 + 0.978981i \(0.434622\pi\)
−0.949798 + 0.312865i \(0.898711\pi\)
\(600\) 11.9500i 0.487856i
\(601\) 7.61065i 0.310445i 0.987880 + 0.155222i \(0.0496094\pi\)
−0.987880 + 0.155222i \(0.950391\pi\)
\(602\) 0.0736915 + 0.786010i 0.00300344 + 0.0320354i
\(603\) −82.6497 −3.36576
\(604\) 25.9707 1.05673
\(605\) −5.03857 2.90902i −0.204847 0.118268i
\(606\) 90.9729i 3.69552i
\(607\) 7.61563 + 4.39688i 0.309109 + 0.178464i 0.646528 0.762891i \(-0.276221\pi\)
−0.337419 + 0.941355i \(0.609554\pi\)
\(608\) −30.1269 + 52.1814i −1.22181 + 2.11623i
\(609\) −0.0735845 + 0.0424840i −0.00298179 + 0.00172154i
\(610\) 11.8732 0.480731
\(611\) −2.54689 4.41135i −0.103036 0.178464i
\(612\) 13.6973 69.4871i 0.553681 2.80885i
\(613\) 11.5011 0.464527 0.232263 0.972653i \(-0.425387\pi\)
0.232263 + 0.972653i \(0.425387\pi\)
\(614\) −13.0093 + 22.5328i −0.525013 + 0.909350i
\(615\) 16.1246 9.30953i 0.650206 0.375396i
\(616\) −0.117465 0.203455i −0.00473280 0.00819744i
\(617\) −21.5774 + 12.4577i −0.868675 + 0.501530i −0.866908 0.498469i \(-0.833896\pi\)
−0.00176704 + 0.999998i \(0.500562\pi\)
\(618\) 5.41381i 0.217775i
\(619\) −11.3737 + 6.56662i −0.457148 + 0.263935i −0.710844 0.703349i \(-0.751687\pi\)
0.253696 + 0.967284i \(0.418354\pi\)
\(620\) 13.9479 + 24.1585i 0.560162 + 0.970230i
\(621\) −36.3335 + 62.9314i −1.45801 + 2.52535i
\(622\) −28.3000 16.3390i −1.13472 0.655134i
\(623\) 0.389245i 0.0155948i
\(624\) 20.8530i 0.834788i
\(625\) −3.48150 + 6.03013i −0.139260 + 0.241205i
\(626\) 14.6160 + 8.43854i 0.584172 + 0.337272i
\(627\) −47.6870 82.5962i −1.90443 3.29858i
\(628\) 16.8204 + 29.1338i 0.671207 + 1.16257i
\(629\) 7.66368 + 22.4492i 0.305571 + 0.895108i
\(630\) −0.477407 0.826893i −0.0190204 0.0329442i
\(631\) 19.7163 + 34.1497i 0.784894 + 1.35948i 0.929062 + 0.369923i \(0.120616\pi\)
−0.144169 + 0.989553i \(0.546051\pi\)
\(632\) 6.25618 3.61201i 0.248857 0.143678i
\(633\) 3.90947 6.77139i 0.155387 0.269139i
\(634\) 0.962401i 0.0382218i
\(635\) −6.86293 3.96232i −0.272347 0.157240i
\(636\) 84.0342 48.5172i 3.33217 1.92383i
\(637\) 16.6182 0.658439
\(638\) 2.01633 + 3.49238i 0.0798272 + 0.138265i
\(639\) 51.5011 + 29.7342i 2.03735 + 1.17627i
\(640\) 7.96007 + 4.59575i 0.314650 + 0.181663i
\(641\) 21.7503i 0.859084i 0.903047 + 0.429542i \(0.141325\pi\)
−0.903047 + 0.429542i \(0.858675\pi\)
\(642\) 32.8325 56.8676i 1.29580 2.24439i
\(643\) 33.0057i 1.30162i −0.759242 0.650808i \(-0.774430\pi\)
0.759242 0.650808i \(-0.225570\pi\)
\(644\) 0.835111 0.0329080
\(645\) 23.5953 2.21215i 0.929064 0.0871034i
\(646\) −62.4796 + 21.3292i −2.45823 + 0.839187i
\(647\) −43.0565 −1.69272 −0.846362 0.532607i \(-0.821212\pi\)
−0.846362 + 0.532607i \(0.821212\pi\)
\(648\) 9.27544 16.0655i 0.364374 0.631113i
\(649\) 19.7186i 0.774021i
\(650\) 9.26129 16.0410i 0.363258 0.629181i
\(651\) 1.51362 + 0.873886i 0.0593233 + 0.0342503i
\(652\) 6.77056 3.90898i 0.265156 0.153088i
\(653\) 43.4156i 1.69898i −0.527602 0.849492i \(-0.676909\pi\)
0.527602 0.849492i \(-0.323091\pi\)
\(654\) 50.2042 + 86.9563i 1.96314 + 3.40026i
\(655\) 6.57657 11.3910i 0.256968 0.445082i
\(656\) 14.3704i 0.561069i
\(657\) 91.7825 + 52.9907i 3.58078 + 2.06736i
\(658\) −0.223603 + 0.129097i −0.00871696 + 0.00503274i
\(659\) −8.04186 13.9289i −0.313266 0.542593i 0.665801 0.746129i \(-0.268090\pi\)
−0.979067 + 0.203536i \(0.934757\pi\)
\(660\) −31.1988 + 18.0126i −1.21441 + 0.701140i
\(661\) −12.5321 −0.487441 −0.243721 0.969846i \(-0.578368\pi\)
−0.243721 + 0.969846i \(0.578368\pi\)
\(662\) 29.9902 + 51.9445i 1.16560 + 2.01888i
\(663\) −20.2838 + 23.2098i −0.787756 + 0.901395i
\(664\) 2.36490 4.09613i 0.0917760 0.158961i
\(665\) −0.246654 + 0.427217i −0.00956483 + 0.0165668i
\(666\) 84.1773i 3.26181i
\(667\) −2.80625 −0.108659
\(668\) 37.7677 + 21.8052i 1.46128 + 0.843668i
\(669\) 39.3345 + 22.7098i 1.52076 + 0.878011i
\(670\) 25.2024 14.5506i 0.973654 0.562140i
\(671\) −9.78416 16.9467i −0.377714 0.654219i
\(672\) 1.42596 0.0550076
\(673\) −9.27941 + 5.35747i −0.357695 + 0.206515i −0.668069 0.744099i \(-0.732879\pi\)
0.310374 + 0.950614i \(0.399546\pi\)
\(674\) −32.5204 + 18.7757i −1.25264 + 0.723212i
\(675\) 39.2137 22.6400i 1.50933 0.871415i
\(676\) 9.14998 15.8482i 0.351922 0.609547i
\(677\) 17.4667i 0.671301i 0.941987 + 0.335650i \(0.108956\pi\)
−0.941987 + 0.335650i \(0.891044\pi\)
\(678\) 32.4202 56.1535i 1.24509 2.15656i
\(679\) −0.0769738 0.133323i −0.00295398 0.00511645i
\(680\) 1.57718 + 4.62002i 0.0604820 + 0.177170i
\(681\) 1.69262 + 2.93170i 0.0648612 + 0.112343i
\(682\) 41.4754 71.8375i 1.58818 2.75080i
\(683\) −28.4525 16.4271i −1.08871 0.628565i −0.155475 0.987840i \(-0.549691\pi\)
−0.933232 + 0.359275i \(0.883024\pi\)
\(684\) −129.849 −4.96490
\(685\) 2.99050 + 1.72656i 0.114261 + 0.0659686i
\(686\) 1.68509i 0.0643369i
\(687\) 2.88567i 0.110095i
\(688\) −7.62693 + 16.6250i −0.290774 + 0.633821i
\(689\) −29.4434 −1.12171
\(690\) 45.2309i 1.72191i
\(691\) 6.01819 + 3.47460i 0.228943 + 0.132180i 0.610084 0.792337i \(-0.291136\pi\)
−0.381142 + 0.924517i \(0.624469\pi\)
\(692\) 11.3117i 0.430007i
\(693\) −0.786821 + 1.36281i −0.0298889 + 0.0517690i
\(694\) 46.7514 + 26.9919i 1.77466 + 1.02460i
\(695\) −4.38009 7.58655i −0.166146 0.287774i
\(696\) 1.54161 0.0584347
\(697\) −13.9781 + 15.9945i −0.529458 + 0.605836i
\(698\) 21.9564 38.0296i 0.831061 1.43944i
\(699\) 29.4266 1.11302
\(700\) −0.450656 0.260186i −0.0170332 0.00983412i
\(701\) −4.95741 8.58649i −0.187239 0.324307i 0.757090 0.653311i \(-0.226621\pi\)
−0.944329 + 0.329003i \(0.893287\pi\)
\(702\) −53.5858 + 30.9378i −2.02247 + 1.16767i
\(703\) 37.6639 21.7453i 1.42052 0.820138i
\(704\) 45.3157i 1.70790i
\(705\) 3.87539 + 6.71237i 0.145955 + 0.252802i
\(706\) −32.5323 56.3476i −1.22437 2.12067i
\(707\) 0.671612 + 0.387755i 0.0252586 + 0.0145830i
\(708\) 33.3473 + 19.2531i 1.25327 + 0.723575i
\(709\) 15.3147i 0.575156i 0.957757 + 0.287578i \(0.0928500\pi\)
−0.957757 + 0.287578i \(0.907150\pi\)
\(710\) −20.9390 −0.785827
\(711\) −41.9061 24.1945i −1.57160 0.907364i
\(712\) −3.53112 + 6.11608i −0.132334 + 0.229210i
\(713\) 28.8620 + 49.9904i 1.08089 + 1.87215i
\(714\) 1.17646 + 1.02815i 0.0440280 + 0.0384774i
\(715\) 10.9312 0.408805
\(716\) −19.7825 34.2643i −0.739307 1.28052i
\(717\) 23.2486 13.4226i 0.868233 0.501275i
\(718\) −24.2872 42.0667i −0.906390 1.56991i
\(719\) 21.8404 + 12.6096i 0.814510 + 0.470257i 0.848520 0.529164i \(-0.177494\pi\)
−0.0340098 + 0.999421i \(0.510828\pi\)
\(720\) 22.1221i 0.824443i
\(721\) −0.0399677 0.0230754i −0.00148848 0.000859372i
\(722\) 40.3974 + 69.9704i 1.50344 + 2.60403i
\(723\) 29.0060 1.07875
\(724\) −29.2286 + 16.8751i −1.08627 + 0.627159i
\(725\) 1.51435 + 0.874313i 0.0562417 + 0.0324712i
\(726\) 29.2579 + 16.8921i 1.08586 + 0.626923i
\(727\) 8.59486 0.318766 0.159383 0.987217i \(-0.449050\pi\)
0.159383 + 0.987217i \(0.449050\pi\)
\(728\) 0.120555 + 0.0696027i 0.00446808 + 0.00257965i
\(729\) −8.12538 −0.300940
\(730\) −37.3164 −1.38114
\(731\) −24.6601 + 11.0852i −0.912085 + 0.410000i
\(732\) −38.2128 −1.41239
\(733\) −52.8235 −1.95108 −0.975540 0.219823i \(-0.929452\pi\)
−0.975540 + 0.219823i \(0.929452\pi\)
\(734\) 42.1419 + 24.3307i 1.55549 + 0.898061i
\(735\) −25.2865 −0.932708
\(736\) 40.7858 + 23.5477i 1.50338 + 0.867979i
\(737\) −41.5364 23.9811i −1.53001 0.883354i
\(738\) −65.2797 + 37.6893i −2.40298 + 1.38736i
\(739\) −33.2664 −1.22372 −0.611862 0.790964i \(-0.709579\pi\)
−0.611862 + 0.790964i \(0.709579\pi\)
\(740\) −8.21375 14.2266i −0.301944 0.522982i
\(741\) 48.9416 + 28.2564i 1.79791 + 1.03803i
\(742\) 1.49243i 0.0547890i
\(743\) 35.8412 + 20.6929i 1.31489 + 0.759150i 0.982901 0.184134i \(-0.0589480\pi\)
0.331986 + 0.943284i \(0.392281\pi\)
\(744\) −15.8553 27.4622i −0.581284 1.00681i
\(745\) 2.93614 1.69518i 0.107572 0.0621066i
\(746\) 32.0224 + 55.4644i 1.17242 + 2.03070i
\(747\) −31.6819 −1.15918
\(748\) 27.0456 30.9471i 0.988886 1.13154i
\(749\) 0.279885 + 0.484776i 0.0102268 + 0.0177133i
\(750\) −33.2303 + 57.5566i −1.21340 + 2.10167i
\(751\) −4.81752 2.78140i −0.175794 0.101495i 0.409521 0.912301i \(-0.365696\pi\)
−0.585315 + 0.810806i \(0.699029\pi\)
\(752\) −5.98213 −0.218146
\(753\) 17.5541i 0.639705i
\(754\) −2.06938 1.19476i −0.0753623 0.0435105i
\(755\) 10.3844 + 5.99545i 0.377928 + 0.218197i
\(756\) 0.869165 + 1.50544i 0.0316112 + 0.0547523i
\(757\) 2.48711 + 4.30781i 0.0903957 + 0.156570i 0.907678 0.419668i \(-0.137854\pi\)
−0.817282 + 0.576238i \(0.804520\pi\)
\(758\) 34.0932i 1.23832i
\(759\) −64.5585 + 37.2729i −2.34332 + 1.35292i
\(760\) 7.75120 4.47515i 0.281165 0.162331i
\(761\) 22.1736 + 38.4059i 0.803794 + 1.39221i 0.917102 + 0.398652i \(0.130522\pi\)
−0.113309 + 0.993560i \(0.536145\pi\)
\(762\) 39.8516 + 23.0083i 1.44367 +