Properties

Label 731.2.j.a.135.7
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 135.7
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.7

$q$-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} +(-0.797403 - 4.04526i) 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} +(1.68907 + 8.56873i) 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} +(-1.98300 - 10.0599i) 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 \(-0.970461\pi\)
−0.578101 0.815965i \(-0.696206\pi\)
\(4\) 2.48683 1.24341
\(5\) −0.994359 0.574094i −0.444691 0.256742i 0.260894 0.965367i \(-0.415983\pi\)
−0.705585 + 0.708625i \(0.749316\pi\)
\(6\) 5.77403 + 3.33364i 2.35724 + 1.36095i
\(7\) −0.0492215 + 0.0284181i −0.0186040 + 0.0107410i −0.509273 0.860605i \(-0.670086\pi\)
0.490669 + 0.871346i \(0.336752\pi\)
\(8\) −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 \(-0.793458\pi\)
0.796767 0.604287i \(-0.206542\pi\)
\(12\) −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
\(17\) −0.797403 4.04526i −0.193399 0.981120i
\(18\) −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 −0.139598 0.990208i \(-0.544581\pi\)
−0.927345 + 0.374209i \(0.877914\pi\)
\(24\) 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 −0.461323 0.887232i \(-0.652625\pi\)
0.537704 + 0.843134i \(0.319292\pi\)
\(30\) −3.82764 6.62967i −0.698829 1.21041i
\(31\) −8.46082 4.88485i −1.51961 0.877346i −0.999733 0.0231031i \(-0.992645\pi\)
−0.519874 0.854243i \(-0.674021\pi\)
\(32\) 7.97084 1.40906
\(33\) −6.30839 + 10.9264i −1.09815 + 1.90205i
\(34\) 1.68907 + 8.56873i 0.289673 + 1.46952i
\(35\) 0.0652585 0.0110307
\(36\) 8.58870 + 14.8761i 1.43145 + 2.47935i
\(37\) 4.98246 + 2.87663i 0.819112 + 0.472914i 0.850110 0.526605i \(-0.176535\pi\)
−0.0309983 + 0.999519i \(0.509869\pi\)
\(38\) 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 \(0.131787\pi\)
−0.915510 + 0.402294i \(0.868213\pi\)
\(42\) −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 −0.204297 0.978909i \(-0.565491\pi\)
0.745612 + 0.666381i \(0.232157\pi\)
\(62\) 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 \(0.905764\pi\)
\(68\) −1.98300 10.0599i −0.240474 1.21994i
\(69\) 9.29872 + 16.1059i 1.11943 + 1.93892i
\(70\) −0.138231 −0.0165218
\(71\) −7.45598 + 4.30471i −0.884862 + 0.510875i −0.872258 0.489045i \(-0.837345\pi\)
−0.0126035 + 0.999921i \(0.504012\pi\)
\(72\) −3.56145 6.16860i −0.419720 0.726977i
\(73\) −13.2876 + 7.67163i −1.55520 + 0.897896i −0.557497 + 0.830179i \(0.688238\pi\)
−0.997705 + 0.0677165i \(0.978429\pi\)
\(74\) −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 −0.118248 0.992984i \(-0.537728\pi\)
0.800825 + 0.598898i \(0.204395\pi\)
\(80\) 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 \(0.0439098\pi\)
−0.990500 + 0.137509i \(0.956090\pi\)
\(98\) 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 \(-0.842064\pi\)
0.879412 0.476062i \(-0.157936\pi\)
\(108\) 30.5850i 2.94304i
\(109\) 13.0422 + 7.52995i 1.24922 + 0.721238i 0.970954 0.239266i \(-0.0769068\pi\)
0.278267 + 0.960504i \(0.410240\pi\)
\(110\) 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 \(-0.848769\pi\)
0.889244 0.457434i \(-0.151231\pi\)
\(114\) −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
\(119\) 0.154208 + 0.176453i 0.0141362 + 0.0161755i
\(120\) −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 \(0.166828\pi\)
−0.865772 + 0.500439i \(0.833172\pi\)
\(132\) −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
\(136\) 0.822284 + 4.17149i 0.0705103 + 0.357702i
\(137\) 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 0.753319 0.657655i \(-0.228451\pi\)
−0.192886 + 0.981221i \(0.561785\pi\)
\(140\) 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
\(153\) 21.4446 18.7411i 1.73369 1.51513i
\(154\) −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 −0.602820 0.797877i \(-0.705956\pi\)
0.389572 + 0.920996i \(0.372623\pi\)
\(164\) 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 −0.220311 0.975430i \(-0.570707\pi\)
−0.954902 + 0.296920i \(0.904041\pi\)
\(168\) −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 \(0.0553182\pi\)
−0.984937 + 0.172914i \(0.944682\pi\)
\(174\) 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 0.00507041 0.999987i \(-0.498386\pi\)
0.868549 + 0.495602i \(0.165053\pi\)
\(182\) −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
\(187\) −16.2150 + 3.19630i −1.18576 + 0.233736i
\(188\) 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 \(0.432558\pi\)
−0.210293 + 0.977639i \(0.567442\pi\)
\(194\) 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 −0.716502 0.697585i \(-0.754258\pi\)
0.245875 + 0.969302i \(0.420925\pi\)
\(198\) −50.7904 + 29.3239i −3.60952 + 2.08396i
\(199\) 15.0154i 1.06441i 0.846615 + 0.532206i \(0.178637\pi\)
−0.846615 + 0.532206i \(0.821363\pi\)
\(200\) 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 \(0.0272507\pi\)
−0.996338 + 0.0855061i \(0.972749\pi\)
\(212\) 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
\(221\) −7.37383 + 6.44421i −0.496017 + 0.433484i
\(222\) 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 0.468772 0.883319i \(-0.344697\pi\)
−0.530591 + 0.847628i \(0.678030\pi\)
\(228\) 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 −0.741184 0.671302i \(-0.765736\pi\)
0.210772 + 0.977535i \(0.432402\pi\)
\(234\) −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
\(238\) −0.326645 0.373766i −0.0211733 0.0242276i
\(239\) 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 −0.734510 0.678598i \(-0.762588\pi\)
0.220429 + 0.975403i \(0.429254\pi\)
\(242\) 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
\(255\) 11.2201 9.80559i 0.702631 0.614050i
\(256\) 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 \(0.290203\pi\)
−0.612402 + 0.790547i \(0.709797\pi\)
\(270\) 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 \(0.739322\pi\)
\(272\) 2.22423 + 11.2836i 0.134864 + 0.684171i
\(273\) −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 0.651207 0.758900i \(-0.274263\pi\)
−0.331624 + 0.943412i \(0.607596\pi\)
\(278\) −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 −0.336992 0.941508i \(-0.609409\pi\)
0.646874 + 0.762597i \(0.276076\pi\)
\(284\) −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
\(289\) −15.7283 + 6.45141i −0.925194 + 0.379494i
\(290\) 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
\(306\) −45.4242 + 39.6976i −2.59673 + 2.26936i
\(307\) 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 0.0708379 0.997488i \(-0.477433\pi\)
−0.828431 + 0.560091i \(0.810766\pi\)
\(312\) 7.70922i 0.436449i
\(313\) 6.90015 + 3.98380i 0.390019 + 0.225178i 0.682169 0.731195i \(-0.261037\pi\)
−0.292149 + 0.956373i \(0.594370\pi\)
\(314\) −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 \(0.00406152\pi\)
−0.999919 + 0.0127593i \(0.995938\pi\)
\(318\) 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 −0.856011 0.516958i \(-0.827064\pi\)
0.0196929 + 0.999806i \(0.493731\pi\)
\(338\) −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 0.957129 0.289661i \(-0.0935424\pi\)
0.227711 + 0.973729i \(0.426876\pi\)
\(348\) −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
\(357\) −0.142653 0.723686i −0.00755000 0.0383015i
\(358\) 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 0.919412 0.393296i \(-0.128665\pi\)
0.119101 + 0.992882i \(0.461999\pi\)
\(368\) 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 \(-0.452857\pi\)
\(374\) 34.3468 6.77044i 1.77603 0.350091i
\(375\) 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 \(-0.864348\pi\)
0.910559 0.413379i \(-0.135652\pi\)
\(380\) 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 −0.468771 0.883320i \(-0.655303\pi\)
−0.999363 + 0.0356927i \(0.988636\pi\)
\(398\) 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 −0.532994 0.846119i \(-0.678933\pi\)
0.466263 + 0.884646i \(0.345600\pi\)
\(402\) −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 \(-0.963996\pi\)
0.993610 0.112870i \(-0.0360045\pi\)
\(420\) −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
\(425\) −11.4301 + 9.98911i −0.554441 + 0.484543i
\(426\) −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 \(-0.818483\pi\)
0.841764 0.539845i \(-0.181517\pi\)
\(432\) 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 −0.577666 0.816273i \(-0.696037\pi\)
0.418080 + 0.908410i \(0.362703\pi\)
\(440\) 2.37299 4.11014i 0.113128 0.195943i
\(441\) −48.3292 −2.30139
\(442\) 15.6193 13.6502i 0.742936 0.649274i
\(443\) −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 \(-0.931804\pi\)
−0.672694 0.739921i \(-0.734863\pi\)
\(450\) −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
\(459\) −49.7518 + 9.80709i −2.32222 + 0.457756i
\(460\) 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
\(476\) 0.383488 + 0.438809i 0.0175772 + 0.0201128i
\(477\) 85.6275 3.92061
\(478\) −9.03288 + 15.6454i −0.413154 + 0.715604i
\(479\) −1.34371 0.775789i −0.0613955 0.0354467i 0.468988 0.883205i \(-0.344619\pi\)
−0.530384 + 0.847758i \(0.677952\pi\)
\(480\) 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 −0.361487 0.932377i \(-0.617731\pi\)
0.626719 + 0.779246i \(0.284398\pi\)
\(488\) −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
\(493\) −1.28865 1.47454i −0.0580378 0.0664101i
\(494\) −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 −0.0406256 0.999174i \(-0.512935\pi\)
0.844998 + 0.534770i \(0.179602\pi\)
\(500\) 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 −0.331761 0.943363i \(-0.607643\pi\)
0.651096 + 0.758995i \(0.274309\pi\)
\(504\) 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 \(-0.408640\pi\)
\(510\) −23.7666 + 20.7703i −1.05240 + 0.919726i
\(511\) 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 0.766199 0.642603i \(-0.222145\pi\)
−0.173411 + 0.984850i \(0.555479\pi\)
\(522\) −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 −0.793900 0.608048i \(-0.791953\pi\)
0.129635 + 0.991562i \(0.458619\pi\)
\(542\) −10.1496 17.5797i −0.435965 0.755113i
\(543\) −42.7179 −1.83320
\(544\) −6.35596 32.2441i −0.272510 1.38246i
\(545\) −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 −0.262023 0.965062i \(-0.584390\pi\)
−0.966779 + 0.255612i \(0.917723\pi\)
\(548\) 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 0.897501 0.441013i \(-0.145381\pi\)
0.0668218 + 0.997765i \(0.478714\pi\)
\(572\) −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 \(0.951290\pi\)
\(578\) 33.3159 13.6655i 1.38576 0.568408i
\(579\) 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
\(595\) −0.0520373 0.263988i −0.00213332 0.0108224i
\(596\) 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 \(-0.950391\pi\)
0.987880 0.155222i \(-0.0496094\pi\)
\(602\) −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 0.337419 0.941355i \(-0.390446\pi\)
−0.646528 + 0.762891i \(0.723779\pi\)
\(608\) −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
\(612\) 53.3290 46.6058i 2.15570 1.88393i
\(613\) 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 0.00176704 0.999998i \(-0.499438\pi\)
0.866908 + 0.498469i \(0.166104\pi\)
\(618\) 5.41381i 0.217775i
\(619\) 11.3737 6.56662i 0.457148 0.263935i −0.253696 0.967284i \(-0.581646\pi\)
0.710844 + 0.703349i \(0.248313\pi\)
\(620\) 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 \(-0.858675\pi\)
0.903047 0.429542i \(-0.141325\pi\)
\(642\) 32.8325 56.8676i 1.29580 2.24439i
\(643\) 33.0057i 1.30162i 0.759242 + 0.650808i \(0.225570\pi\)
−0.759242 + 0.650808i \(0.774430\pi\)
\(644\) 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 \(0.323091\pi\)
−0.527602 + 0.849492i \(0.676909\pi\)
\(654\) 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
\(663\) 30.2422 5.96134i 1.17451 0.231519i
\(664\) 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 −0.310374 0.950614i \(-0.600454\pi\)
0.668069 + 0.744099i \(0.267121\pi\)
\(674\) 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 \(-0.891044\pi\)
0.941987 0.335650i \(-0.108956\pi\)
\(678\) 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 0.933232 0.359275i \(-0.116976\pi\)
0.155475 + 0.987840i \(0.450309\pi\)
\(684\) −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 0.381142 0.924517i \(-0.375531\pi\)
−0.610084 + 0.792337i \(0.708864\pi\)
\(692\) 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
\(697\) 20.8407 4.10812i 0.789398 0.155606i
\(698\) 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 \(-0.907150\pi\)
0.957757 0.287578i \(-0.0928500\pi\)
\(710\) −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
\(714\) 0.302170 + 1.53292i 0.0113084 + 0.0573681i
\(715\) 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 0.0340098 0.999421i \(-0.489172\pi\)
−0.848520 + 0.529164i \(0.822506\pi\)
\(720\) 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
\(731\) −26.2908 6.30835i −0.972399 0.233323i
\(732\) −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 −0.331986 0.943284i \(-0.607719\pi\)
−0.982901 + 0.184134i \(0.941052\pi\)
\(744\) −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
\(748\) −40.3238 + 7.94864i −1.47439 + 0.290631i
\(749\) 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 0.585315 0.810806i \(-0.300971\pi\)
−0.409521 + 0.912301i \(0.634304\pi\)
\(752\) −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