Properties

Label 403.2.l.c.25.9
Level 403
Weight 2
Character 403.25
Analytic conductor 3.218
Analytic rank 0
Dimension 68
CM No

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Newspace parameters

Level: \( N \) = \( 403 = 13 \cdot 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 403.l (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(3.21797120146\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(34\) over \(\Q(\zeta_{6})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 25.9
Character \(\chi\) = 403.25
Dual form 403.2.l.c.129.26

$q$-expansion

\(f(q)\) \(=\) \(q-1.84455i q^{2} +(-1.26208 - 2.18598i) q^{3} -1.40238 q^{4} +(3.26306 + 1.88393i) q^{5} +(-4.03216 + 2.32797i) q^{6} +(1.26392 - 0.729726i) q^{7} -1.10234i q^{8} +(-1.68567 + 2.91967i) q^{9} +O(q^{10})\) \(q-1.84455i q^{2} +(-1.26208 - 2.18598i) q^{3} -1.40238 q^{4} +(3.26306 + 1.88393i) q^{5} +(-4.03216 + 2.32797i) q^{6} +(1.26392 - 0.729726i) q^{7} -1.10234i q^{8} +(-1.68567 + 2.91967i) q^{9} +(3.47501 - 6.01889i) q^{10} +(-5.25125 - 3.03181i) q^{11} +(1.76991 + 3.06558i) q^{12} +(-3.59287 - 0.302144i) q^{13} +(-1.34602 - 2.33137i) q^{14} -9.51064i q^{15} -4.83809 q^{16} +(-0.00325426 - 0.00563654i) q^{17} +(5.38549 + 3.10931i) q^{18} +(3.85044 - 2.22305i) q^{19} +(-4.57605 - 2.64198i) q^{20} +(-3.19033 - 1.84194i) q^{21} +(-5.59234 + 9.68621i) q^{22} +4.95595 q^{23} +(-2.40970 + 1.39124i) q^{24} +(4.59837 + 7.96461i) q^{25} +(-0.557320 + 6.62724i) q^{26} +0.937324 q^{27} +(-1.77250 + 1.02335i) q^{28} +0.860193 q^{29} -17.5429 q^{30} +(-0.183683 - 5.56473i) q^{31} +6.71944i q^{32} +15.3055i q^{33} +(-0.0103969 + 0.00600266i) q^{34} +5.49901 q^{35} +(2.36395 - 4.09449i) q^{36} +(5.71667 - 3.30052i) q^{37} +(-4.10054 - 7.10235i) q^{38} +(3.87399 + 8.23527i) q^{39} +(2.07673 - 3.59700i) q^{40} +(-0.392528 - 0.226626i) q^{41} +(-3.39756 + 5.88474i) q^{42} +(2.15806 + 3.73786i) q^{43} +(7.36425 + 4.25175i) q^{44} +(-11.0009 + 6.35137i) q^{45} -9.14152i q^{46} +8.08647i q^{47} +(6.10604 + 10.5760i) q^{48} +(-2.43500 + 4.21754i) q^{49} +(14.6912 - 8.48194i) q^{50} +(-0.00821425 + 0.0142275i) q^{51} +(5.03857 + 0.423720i) q^{52} +(-0.367881 + 0.637188i) q^{53} -1.72895i q^{54} +(-11.4234 - 19.7859i) q^{55} +(-0.804407 - 1.39327i) q^{56} +(-9.71910 - 5.61133i) q^{57} -1.58667i q^{58} +(7.33401 - 4.23429i) q^{59} +13.3375i q^{60} +9.39041 q^{61} +(-10.2645 + 0.338814i) q^{62} +4.92031i q^{63} +2.71819 q^{64} +(-11.1545 - 7.75462i) q^{65} +28.2318 q^{66} +(12.5249 + 7.23126i) q^{67} +(0.00456371 + 0.00790458i) q^{68} +(-6.25479 - 10.8336i) q^{69} -10.1432i q^{70} +(-11.6748 - 6.74046i) q^{71} +(3.21847 + 1.85818i) q^{72} +(4.05332 + 2.34019i) q^{73} +(-6.08799 - 10.5447i) q^{74} +(11.6070 - 20.1039i) q^{75} +(-5.39979 + 3.11757i) q^{76} -8.84957 q^{77} +(15.1904 - 7.14579i) q^{78} +(2.85074 + 4.93762i) q^{79} +(-15.7870 - 9.11461i) q^{80} +(3.87404 + 6.71003i) q^{81} +(-0.418025 + 0.724040i) q^{82} +(2.45139 + 1.41531i) q^{83} +(4.47406 + 2.58310i) q^{84} -0.0245232i q^{85} +(6.89469 - 3.98065i) q^{86} +(-1.08563 - 1.88037i) q^{87} +(-3.34209 + 5.78867i) q^{88} -8.26914i q^{89} +(11.7154 + 20.2917i) q^{90} +(-4.76159 + 2.23993i) q^{91} -6.95013 q^{92} +(-11.9326 + 7.42464i) q^{93} +14.9159 q^{94} +16.7523 q^{95} +(14.6886 - 8.48044i) q^{96} -5.36866i q^{97} +(7.77948 + 4.49149i) q^{98} +(17.7038 - 10.2213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68q - 6q^{3} - 76q^{4} - 40q^{9} + O(q^{10}) \) \( 68q - 6q^{3} - 76q^{4} - 40q^{9} + 8q^{10} - 10q^{12} - 3q^{13} + 10q^{14} + 84q^{16} + 6q^{17} + 4q^{22} - 44q^{23} + 30q^{25} - 3q^{26} - 12q^{27} + 48q^{29} - 4q^{30} - 48q^{35} + 40q^{36} + 60q^{38} - 14q^{39} + 20q^{40} - 10q^{42} - 12q^{43} + 32q^{48} + 58q^{49} + 20q^{51} - 27q^{52} + 8q^{53} - 36q^{55} - 50q^{56} - 12q^{61} - 74q^{62} - 15q^{65} + 164q^{66} + 4q^{68} - 34q^{69} - 4q^{74} + 20q^{75} - 200q^{77} - 58q^{78} - 80q^{79} - 82q^{81} - 66q^{82} + 52q^{87} + 16q^{88} - 14q^{90} - 70q^{91} + 108q^{92} - 4q^{94} + 76q^{95} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).

\(n\) \(249\) \(313\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.84455i 1.30430i −0.758091 0.652148i \(-0.773868\pi\)
0.758091 0.652148i \(-0.226132\pi\)
\(3\) −1.26208 2.18598i −0.728660 1.26208i −0.957450 0.288600i \(-0.906810\pi\)
0.228790 0.973476i \(-0.426523\pi\)
\(4\) −1.40238 −0.701190
\(5\) 3.26306 + 1.88393i 1.45928 + 0.842518i 0.998976 0.0452409i \(-0.0144055\pi\)
0.460308 + 0.887759i \(0.347739\pi\)
\(6\) −4.03216 + 2.32797i −1.64612 + 0.950389i
\(7\) 1.26392 0.729726i 0.477718 0.275811i −0.241747 0.970339i \(-0.577720\pi\)
0.719465 + 0.694529i \(0.244387\pi\)
\(8\) 1.10234i 0.389736i
\(9\) −1.68567 + 2.91967i −0.561890 + 0.973223i
\(10\) 3.47501 6.01889i 1.09889 1.90334i
\(11\) −5.25125 3.03181i −1.58331 0.914125i −0.994372 0.105948i \(-0.966212\pi\)
−0.588939 0.808177i \(-0.700454\pi\)
\(12\) 1.76991 + 3.06558i 0.510929 + 0.884955i
\(13\) −3.59287 0.302144i −0.996483 0.0837995i
\(14\) −1.34602 2.33137i −0.359739 0.623086i
\(15\) 9.51064i 2.45564i
\(16\) −4.83809 −1.20952
\(17\) −0.00325426 0.00563654i −0.000789274 0.00136706i 0.865630 0.500683i \(-0.166918\pi\)
−0.866420 + 0.499316i \(0.833585\pi\)
\(18\) 5.38549 + 3.10931i 1.26937 + 0.732872i
\(19\) 3.85044 2.22305i 0.883352 0.510004i 0.0115898 0.999933i \(-0.496311\pi\)
0.871762 + 0.489929i \(0.162977\pi\)
\(20\) −4.57605 2.64198i −1.02324 0.590766i
\(21\) −3.19033 1.84194i −0.696188 0.401944i
\(22\) −5.59234 + 9.68621i −1.19229 + 2.06511i
\(23\) 4.95595 1.03339 0.516694 0.856170i \(-0.327163\pi\)
0.516694 + 0.856170i \(0.327163\pi\)
\(24\) −2.40970 + 1.39124i −0.491877 + 0.283985i
\(25\) 4.59837 + 7.96461i 0.919674 + 1.59292i
\(26\) −0.557320 + 6.62724i −0.109299 + 1.29971i
\(27\) 0.937324 0.180388
\(28\) −1.77250 + 1.02335i −0.334971 + 0.193396i
\(29\) 0.860193 0.159734 0.0798670 0.996806i \(-0.474550\pi\)
0.0798670 + 0.996806i \(0.474550\pi\)
\(30\) −17.5429 −3.20288
\(31\) −0.183683 5.56473i −0.0329905 0.999456i
\(32\) 6.71944i 1.18784i
\(33\) 15.3055i 2.66434i
\(34\) −0.0103969 + 0.00600266i −0.00178306 + 0.00102945i
\(35\) 5.49901 0.929502
\(36\) 2.36395 4.09449i 0.393992 0.682414i
\(37\) 5.71667 3.30052i 0.939815 0.542602i 0.0499126 0.998754i \(-0.484106\pi\)
0.889902 + 0.456151i \(0.150772\pi\)
\(38\) −4.10054 7.10235i −0.665196 1.15215i
\(39\) 3.87399 + 8.23527i 0.620336 + 1.31870i
\(40\) 2.07673 3.59700i 0.328360 0.568736i
\(41\) −0.392528 0.226626i −0.0613026 0.0353931i 0.469035 0.883179i \(-0.344602\pi\)
−0.530338 + 0.847786i \(0.677935\pi\)
\(42\) −3.39756 + 5.88474i −0.524255 + 0.908036i
\(43\) 2.15806 + 3.73786i 0.329100 + 0.570019i 0.982334 0.187138i \(-0.0599212\pi\)
−0.653233 + 0.757157i \(0.726588\pi\)
\(44\) 7.36425 + 4.25175i 1.11020 + 0.640976i
\(45\) −11.0009 + 6.35137i −1.63992 + 0.946806i
\(46\) 9.14152i 1.34784i
\(47\) 8.08647i 1.17953i 0.807574 + 0.589766i \(0.200780\pi\)
−0.807574 + 0.589766i \(0.799220\pi\)
\(48\) 6.10604 + 10.5760i 0.881330 + 1.52651i
\(49\) −2.43500 + 4.21754i −0.347857 + 0.602506i
\(50\) 14.6912 8.48194i 2.07764 1.19953i
\(51\) −0.00821425 + 0.0142275i −0.00115022 + 0.00199225i
\(52\) 5.03857 + 0.423720i 0.698724 + 0.0587594i
\(53\) −0.367881 + 0.637188i −0.0505323 + 0.0875245i −0.890185 0.455599i \(-0.849425\pi\)
0.839653 + 0.543123i \(0.182758\pi\)
\(54\) 1.72895i 0.235280i
\(55\) −11.4234 19.7859i −1.54033 2.66794i
\(56\) −0.804407 1.39327i −0.107493 0.186184i
\(57\) −9.71910 5.61133i −1.28733 0.743238i
\(58\) 1.58667i 0.208340i
\(59\) 7.33401 4.23429i 0.954807 0.551258i 0.0602361 0.998184i \(-0.480815\pi\)
0.894571 + 0.446926i \(0.147481\pi\)
\(60\) 13.3375i 1.72187i
\(61\) 9.39041 1.20232 0.601159 0.799129i \(-0.294706\pi\)
0.601159 + 0.799129i \(0.294706\pi\)
\(62\) −10.2645 + 0.338814i −1.30359 + 0.0430294i
\(63\) 4.92031i 0.619901i
\(64\) 2.71819 0.339773
\(65\) −11.1545 7.75462i −1.38355 0.961842i
\(66\) 28.2318 3.47510
\(67\) 12.5249 + 7.23126i 1.53016 + 0.883440i 0.999354 + 0.0359478i \(0.0114450\pi\)
0.530809 + 0.847492i \(0.321888\pi\)
\(68\) 0.00456371 + 0.00790458i 0.000553431 + 0.000958571i
\(69\) −6.25479 10.8336i −0.752988 1.30421i
\(70\) 10.1432i 1.21235i
\(71\) −11.6748 6.74046i −1.38555 0.799945i −0.392736 0.919651i \(-0.628471\pi\)
−0.992809 + 0.119706i \(0.961805\pi\)
\(72\) 3.21847 + 1.85818i 0.379300 + 0.218989i
\(73\) 4.05332 + 2.34019i 0.474406 + 0.273898i 0.718082 0.695958i \(-0.245020\pi\)
−0.243676 + 0.969857i \(0.578354\pi\)
\(74\) −6.08799 10.5447i −0.707715 1.22580i
\(75\) 11.6070 20.1039i 1.34026 2.32140i
\(76\) −5.39979 + 3.11757i −0.619398 + 0.357610i
\(77\) −8.84957 −1.00850
\(78\) 15.1904 7.14579i 1.71997 0.809102i
\(79\) 2.85074 + 4.93762i 0.320733 + 0.555526i 0.980639 0.195822i \(-0.0627375\pi\)
−0.659907 + 0.751348i \(0.729404\pi\)
\(80\) −15.7870 9.11461i −1.76504 1.01904i
\(81\) 3.87404 + 6.71003i 0.430449 + 0.745559i
\(82\) −0.418025 + 0.724040i −0.0461631 + 0.0799568i
\(83\) 2.45139 + 1.41531i 0.269075 + 0.155350i 0.628467 0.777836i \(-0.283683\pi\)
−0.359392 + 0.933187i \(0.617016\pi\)
\(84\) 4.47406 + 2.58310i 0.488160 + 0.281839i
\(85\) 0.0245232i 0.00265991i
\(86\) 6.89469 3.98065i 0.743473 0.429245i
\(87\) −1.08563 1.88037i −0.116392 0.201596i
\(88\) −3.34209 + 5.78867i −0.356268 + 0.617074i
\(89\) 8.26914i 0.876528i −0.898846 0.438264i \(-0.855594\pi\)
0.898846 0.438264i \(-0.144406\pi\)
\(90\) 11.7154 + 20.2917i 1.23492 + 2.13894i
\(91\) −4.76159 + 2.23993i −0.499151 + 0.234808i
\(92\) −6.95013 −0.724601
\(93\) −11.9326 + 7.42464i −1.23735 + 0.769900i
\(94\) 14.9159 1.53846
\(95\) 16.7523 1.71875
\(96\) 14.6886 8.48044i 1.49914 0.865531i
\(97\) 5.36866i 0.545105i −0.962141 0.272553i \(-0.912132\pi\)
0.962141 0.272553i \(-0.0878678\pi\)
\(98\) 7.77948 + 4.49149i 0.785847 + 0.453709i
\(99\) 17.7038 10.2213i 1.77929 1.02728i
\(100\) −6.44867 11.1694i −0.644867 1.11694i
\(101\) 9.17334 0.912782 0.456391 0.889779i \(-0.349142\pi\)
0.456391 + 0.889779i \(0.349142\pi\)
\(102\) 0.0262434 + 0.0151516i 0.00259848 + 0.00150023i
\(103\) −2.26560 + 3.92413i −0.223236 + 0.386656i −0.955789 0.294054i \(-0.904995\pi\)
0.732553 + 0.680710i \(0.238329\pi\)
\(104\) −0.333065 + 3.96057i −0.0326597 + 0.388366i
\(105\) −6.94017 12.0207i −0.677291 1.17310i
\(106\) 1.17533 + 0.678576i 0.114158 + 0.0659091i
\(107\) −4.24679 7.35566i −0.410553 0.711099i 0.584397 0.811468i \(-0.301331\pi\)
−0.994950 + 0.100369i \(0.967998\pi\)
\(108\) −1.31449 −0.126486
\(109\) 7.23969i 0.693436i −0.937969 0.346718i \(-0.887296\pi\)
0.937969 0.346718i \(-0.112704\pi\)
\(110\) −36.4963 + 21.0711i −3.47978 + 2.00905i
\(111\) −14.4297 8.33102i −1.36961 0.790745i
\(112\) −6.11497 + 3.53048i −0.577811 + 0.333599i
\(113\) −8.67717 + 15.0293i −0.816280 + 1.41384i 0.0921256 + 0.995747i \(0.470634\pi\)
−0.908405 + 0.418091i \(0.862699\pi\)
\(114\) −10.3504 + 17.9274i −0.969403 + 1.67906i
\(115\) 16.1716 + 9.33666i 1.50801 + 0.870648i
\(116\) −1.20632 −0.112004
\(117\) 6.93855 9.98067i 0.641470 0.922713i
\(118\) −7.81038 13.5280i −0.719004 1.24535i
\(119\) −0.00822627 0.00474944i −0.000754101 0.000435380i
\(120\) −10.4840 −0.957051
\(121\) 12.8837 + 22.3153i 1.17125 + 2.02866i
\(122\) 17.3211i 1.56818i
\(123\) 1.14408i 0.103158i
\(124\) 0.257594 + 7.80388i 0.0231326 + 0.700809i
\(125\) 15.8127i 1.41433i
\(126\) 9.07579 0.808535
\(127\) 1.25273 + 2.16980i 0.111162 + 0.192539i 0.916239 0.400632i \(-0.131209\pi\)
−0.805077 + 0.593170i \(0.797876\pi\)
\(128\) 8.42503i 0.744674i
\(129\) 5.44726 9.43493i 0.479604 0.830699i
\(130\) −14.3038 + 20.5751i −1.25453 + 1.80456i
\(131\) −5.70997 9.88996i −0.498882 0.864090i 0.501117 0.865380i \(-0.332923\pi\)
−0.999999 + 0.00129000i \(0.999589\pi\)
\(132\) 21.4641i 1.86821i
\(133\) 3.24444 5.61954i 0.281329 0.487276i
\(134\) 13.3385 23.1029i 1.15227 1.99579i
\(135\) 3.05854 + 1.76585i 0.263238 + 0.151980i
\(136\) −0.00621339 + 0.00358731i −0.000532794 + 0.000307609i
\(137\) −4.30508 2.48554i −0.367808 0.212354i 0.304693 0.952451i \(-0.401446\pi\)
−0.672500 + 0.740097i \(0.734780\pi\)
\(138\) −19.9832 + 11.5373i −1.70108 + 0.982120i
\(139\) 7.37172 0.625261 0.312631 0.949875i \(-0.398790\pi\)
0.312631 + 0.949875i \(0.398790\pi\)
\(140\) −7.71170 −0.651758
\(141\) 17.6769 10.2057i 1.48866 0.859478i
\(142\) −12.4331 + 21.5348i −1.04337 + 1.80716i
\(143\) 17.9510 + 12.4795i 1.50114 + 1.04359i
\(144\) 8.15543 14.1256i 0.679619 1.17713i
\(145\) 2.80686 + 1.62054i 0.233097 + 0.134579i
\(146\) 4.31660 7.47658i 0.357245 0.618766i
\(147\) 12.2926 1.01388
\(148\) −8.01695 + 4.62859i −0.658989 + 0.380468i
\(149\) −4.37357 + 2.52508i −0.358297 + 0.206863i −0.668333 0.743862i \(-0.732992\pi\)
0.310037 + 0.950725i \(0.399659\pi\)
\(150\) −37.0827 21.4097i −3.02779 1.74810i
\(151\) 18.9378i 1.54113i 0.637359 + 0.770567i \(0.280027\pi\)
−0.637359 + 0.770567i \(0.719973\pi\)
\(152\) −2.45056 4.24450i −0.198767 0.344274i
\(153\) 0.0219425 0.00177394
\(154\) 16.3235i 1.31539i
\(155\) 9.88419 18.5041i 0.793917 1.48629i
\(156\) −5.43281 11.5490i −0.434973 0.924658i
\(157\) −11.0000 −0.877893 −0.438946 0.898513i \(-0.644648\pi\)
−0.438946 + 0.898513i \(0.644648\pi\)
\(158\) 9.10771 5.25834i 0.724571 0.418331i
\(159\) 1.85717 0.147283
\(160\) −12.6589 + 21.9259i −1.00078 + 1.73340i
\(161\) 6.26394 3.61649i 0.493668 0.285019i
\(162\) 12.3770 7.14588i 0.972430 0.561433i
\(163\) 11.1946i 0.876829i 0.898773 + 0.438414i \(0.144460\pi\)
−0.898773 + 0.438414i \(0.855540\pi\)
\(164\) 0.550474 + 0.317816i 0.0429848 + 0.0248173i
\(165\) −28.8345 + 49.9427i −2.24476 + 3.88804i
\(166\) 2.61061 4.52172i 0.202623 0.350953i
\(167\) −6.43455 + 3.71499i −0.497920 + 0.287474i −0.727854 0.685732i \(-0.759482\pi\)
0.229934 + 0.973206i \(0.426149\pi\)
\(168\) −2.03045 + 3.51684i −0.156652 + 0.271330i
\(169\) 12.8174 + 2.17112i 0.985955 + 0.167010i
\(170\) −0.0452343 −0.00346931
\(171\) 14.9894i 1.14626i
\(172\) −3.02642 5.24190i −0.230762 0.399691i
\(173\) 6.28007 10.8774i 0.477465 0.826993i −0.522202 0.852822i \(-0.674889\pi\)
0.999666 + 0.0258288i \(0.00822248\pi\)
\(174\) −3.46844 + 2.00250i −0.262941 + 0.151809i
\(175\) 11.6240 + 6.71110i 0.878690 + 0.507312i
\(176\) 25.4060 + 14.6682i 1.91505 + 1.10565i
\(177\) −18.5122 10.6880i −1.39146 0.803359i
\(178\) −15.2529 −1.14325
\(179\) −9.51037 16.4725i −0.710839 1.23121i −0.964543 0.263927i \(-0.914982\pi\)
0.253704 0.967282i \(-0.418351\pi\)
\(180\) 15.4274 8.90703i 1.14989 0.663891i
\(181\) −5.39144 + 9.33826i −0.400743 + 0.694107i −0.993816 0.111042i \(-0.964581\pi\)
0.593073 + 0.805149i \(0.297915\pi\)
\(182\) 4.13166 + 8.78302i 0.306259 + 0.651041i
\(183\) −11.8514 20.5272i −0.876081 1.51742i
\(184\) 5.46315i 0.402749i
\(185\) 24.8718 1.82861
\(186\) 13.6952 + 22.0103i 1.00418 + 1.61387i
\(187\) 0.0394652i 0.00288598i
\(188\) 11.3403i 0.827077i
\(189\) 1.18471 0.683990i 0.0861747 0.0497530i
\(190\) 30.9005i 2.24176i
\(191\) 10.6337 18.4181i 0.769428 1.33269i −0.168445 0.985711i \(-0.553875\pi\)
0.937873 0.346977i \(-0.112792\pi\)
\(192\) −3.43056 5.94190i −0.247579 0.428820i
\(193\) 22.0760 12.7456i 1.58907 0.917448i 0.595606 0.803277i \(-0.296912\pi\)
0.993461 0.114172i \(-0.0364215\pi\)
\(194\) −9.90279 −0.710979
\(195\) −2.87358 + 34.1705i −0.205781 + 2.44700i
\(196\) 3.41480 5.91460i 0.243914 0.422471i
\(197\) 15.7130 + 9.07192i 1.11951 + 0.646347i 0.941275 0.337641i \(-0.109629\pi\)
0.178232 + 0.983989i \(0.442962\pi\)
\(198\) −18.8537 32.6555i −1.33987 2.32073i
\(199\) −2.26858 + 3.92929i −0.160815 + 0.278540i −0.935161 0.354222i \(-0.884746\pi\)
0.774346 + 0.632762i \(0.218079\pi\)
\(200\) 8.77972 5.06897i 0.620820 0.358430i
\(201\) 36.5056i 2.57491i
\(202\) 16.9207i 1.19054i
\(203\) 1.08722 0.627706i 0.0763078 0.0440563i
\(204\) 0.0115195 0.0199524i 0.000806526 0.00139694i
\(205\) −0.853895 1.47899i −0.0596386 0.103297i
\(206\) 7.23827 + 4.17902i 0.504314 + 0.291166i
\(207\) −8.35411 + 14.4697i −0.580651 + 1.00572i
\(208\) 17.3826 + 1.46180i 1.20527 + 0.101357i
\(209\) −26.9595 −1.86483
\(210\) −22.1729 + 12.8015i −1.53007 + 0.883388i
\(211\) −3.08388 5.34144i −0.212303 0.367720i 0.740132 0.672462i \(-0.234763\pi\)
−0.952435 + 0.304742i \(0.901430\pi\)
\(212\) 0.515909 0.893580i 0.0354328 0.0613713i
\(213\) 34.0279i 2.33155i
\(214\) −13.5679 + 7.83344i −0.927484 + 0.535483i
\(215\) 16.2625i 1.10909i
\(216\) 1.03325i 0.0703038i
\(217\) −4.29289 6.89936i −0.291421 0.468359i
\(218\) −13.3540 −0.904447
\(219\) 11.8140i 0.798315i
\(220\) 16.0200 + 27.7474i 1.08007 + 1.87073i
\(221\) 0.00998909 + 0.0212346i 0.000671939 + 0.00142840i
\(222\) −15.3670 + 26.6164i −1.03137 + 1.78638i
\(223\) −14.5274 + 8.38740i −0.972826 + 0.561662i −0.900097 0.435690i \(-0.856504\pi\)
−0.0727296 + 0.997352i \(0.523171\pi\)
\(224\) 4.90335 + 8.49285i 0.327619 + 0.567453i
\(225\) −31.0054 −2.06702
\(226\) 27.7224 + 16.0055i 1.84406 + 1.06467i
\(227\) −23.1535 13.3677i −1.53675 0.887243i −0.999026 0.0441224i \(-0.985951\pi\)
−0.537724 0.843121i \(-0.680716\pi\)
\(228\) 13.6299 + 7.86921i 0.902661 + 0.521151i
\(229\) −11.5032 + 6.64135i −0.760150 + 0.438873i −0.829350 0.558730i \(-0.811289\pi\)
0.0691997 + 0.997603i \(0.477955\pi\)
\(230\) 17.2220 29.8293i 1.13558 1.96689i
\(231\) 11.1688 + 19.3450i 0.734855 + 1.27281i
\(232\) 0.948227i 0.0622541i
\(233\) 4.74614 0.310930 0.155465 0.987841i \(-0.450312\pi\)
0.155465 + 0.987841i \(0.450312\pi\)
\(234\) −18.4099 12.7985i −1.20349 0.836667i
\(235\) −15.2343 + 26.3866i −0.993778 + 1.72127i
\(236\) −10.2851 + 5.93809i −0.669501 + 0.386537i
\(237\) 7.19569 12.4633i 0.467410 0.809579i
\(238\) −0.00876060 + 0.0151738i −0.000567865 + 0.000983571i
\(239\) −17.6328 10.1803i −1.14057 0.658508i −0.193998 0.981002i \(-0.562146\pi\)
−0.946572 + 0.322494i \(0.895479\pi\)
\(240\) 46.0133i 2.97015i
\(241\) −14.8743 + 8.58771i −0.958141 + 0.553183i −0.895600 0.444860i \(-0.853254\pi\)
−0.0625404 + 0.998042i \(0.519920\pi\)
\(242\) 41.1618 23.7648i 2.64598 1.52766i
\(243\) 11.1846 19.3724i 0.717496 1.24274i
\(244\) −13.1689 −0.843054
\(245\) −15.8911 + 9.17473i −1.01524 + 0.586152i
\(246\) 2.11032 0.134549
\(247\) −14.5058 + 6.82376i −0.922983 + 0.434185i
\(248\) −6.13424 + 0.202482i −0.389524 + 0.0128576i
\(249\) 7.14491i 0.452790i
\(250\) 29.1674 1.84471
\(251\) 6.35149 + 11.0011i 0.400903 + 0.694384i 0.993835 0.110868i \(-0.0353632\pi\)
−0.592932 + 0.805252i \(0.702030\pi\)
\(252\) 6.90015i 0.434669i
\(253\) −26.0249 15.0255i −1.63617 0.944645i
\(254\) 4.00231 2.31074i 0.251127 0.144989i
\(255\) −0.0536071 + 0.0309501i −0.00335701 + 0.00193817i
\(256\) 20.9768 1.31105
\(257\) −8.05542 + 13.9524i −0.502483 + 0.870326i 0.497513 + 0.867457i \(0.334247\pi\)
−0.999996 + 0.00286970i \(0.999087\pi\)
\(258\) −17.4032 10.0478i −1.08348 0.625547i
\(259\) 4.81696 8.34321i 0.299311 0.518422i
\(260\) 15.6429 + 10.8749i 0.970131 + 0.674434i
\(261\) −1.45000 + 2.51148i −0.0897529 + 0.155457i
\(262\) −18.2426 + 10.5324i −1.12703 + 0.650691i
\(263\) −4.79915 −0.295928 −0.147964 0.988993i \(-0.547272\pi\)
−0.147964 + 0.988993i \(0.547272\pi\)
\(264\) 16.8719 1.03839
\(265\) −2.40083 + 1.38612i −0.147482 + 0.0851488i
\(266\) −10.3655 5.98455i −0.635552 0.366936i
\(267\) −18.0762 + 10.4363i −1.10624 + 0.638690i
\(268\) −17.5647 10.1410i −1.07293 0.619459i
\(269\) −6.82814 + 11.8267i −0.416319 + 0.721086i −0.995566 0.0940666i \(-0.970013\pi\)
0.579247 + 0.815152i \(0.303347\pi\)
\(270\) 3.25721 5.64165i 0.198227 0.343340i
\(271\) 1.75331i 0.106506i 0.998581 + 0.0532529i \(0.0169590\pi\)
−0.998581 + 0.0532529i \(0.983041\pi\)
\(272\) 0.0157444 + 0.0272701i 0.000954645 + 0.00165349i
\(273\) 10.9059 + 7.58179i 0.660056 + 0.458871i
\(274\) −4.58471 + 7.94095i −0.276972 + 0.479730i
\(275\) 55.7655i 3.36279i
\(276\) 8.77159 + 15.1928i 0.527988 + 0.914502i
\(277\) −3.01250 −0.181004 −0.0905019 0.995896i \(-0.528847\pi\)
−0.0905019 + 0.995896i \(0.528847\pi\)
\(278\) 13.5975i 0.815526i
\(279\) 16.5568 + 8.84402i 0.991230 + 0.529477i
\(280\) 6.06178i 0.362261i
\(281\) 1.71530i 0.102326i −0.998690 0.0511632i \(-0.983707\pi\)
0.998690 0.0511632i \(-0.0162929\pi\)
\(282\) −18.8250 32.6059i −1.12101 1.94165i
\(283\) 7.35168 0.437012 0.218506 0.975836i \(-0.429882\pi\)
0.218506 + 0.975836i \(0.429882\pi\)
\(284\) 16.3725 + 9.45269i 0.971531 + 0.560914i
\(285\) −21.1427 36.6202i −1.25238 2.16919i
\(286\) 23.0192 33.1116i 1.36115 1.95793i
\(287\) −0.661501 −0.0390472
\(288\) −19.6185 11.3268i −1.15603 0.667436i
\(289\) 8.49998 14.7224i 0.499999 0.866023i
\(290\) 2.98918 5.17741i 0.175531 0.304028i
\(291\) −11.7358 + 6.77566i −0.687964 + 0.397196i
\(292\) −5.68430 3.28183i −0.332649 0.192055i
\(293\) −8.14501 + 4.70252i −0.475837 + 0.274724i −0.718680 0.695341i \(-0.755253\pi\)
0.242843 + 0.970066i \(0.421920\pi\)
\(294\) 22.6744i 1.32240i
\(295\) 31.9084 1.85778
\(296\) −3.63830 6.30172i −0.211472 0.366280i
\(297\) −4.92212 2.84179i −0.285611 0.164897i
\(298\) 4.65765 + 8.06729i 0.269811 + 0.467326i
\(299\) −17.8061 1.49741i −1.02975 0.0865974i
\(300\) −16.2774 + 28.1933i −0.939777 + 1.62774i
\(301\) 5.45523 + 3.14958i 0.314434 + 0.181539i
\(302\) 34.9317 2.01010
\(303\) −11.5775 20.0527i −0.665107 1.15200i
\(304\) −18.6288 + 10.7553i −1.06843 + 0.616861i
\(305\) 30.6415 + 17.6909i 1.75452 + 1.01298i
\(306\) 0.0404740i 0.00231375i
\(307\) 17.8619 10.3126i 1.01943 0.588570i 0.105494 0.994420i \(-0.466358\pi\)
0.913940 + 0.405849i \(0.133024\pi\)
\(308\) 12.4105 0.707152
\(309\) 11.4374 0.650652
\(310\) −34.1318 18.2319i −1.93856 1.03550i
\(311\) −21.0994 −1.19644 −0.598220 0.801332i \(-0.704125\pi\)
−0.598220 + 0.801332i \(0.704125\pi\)
\(312\) 9.07807 4.27046i 0.513945 0.241767i
\(313\) 2.46526 + 4.26996i 0.139345 + 0.241352i 0.927249 0.374446i \(-0.122167\pi\)
−0.787904 + 0.615798i \(0.788834\pi\)
\(314\) 20.2900i 1.14503i
\(315\) −9.26952 + 16.0553i −0.522278 + 0.904612i
\(316\) −3.99782 6.92442i −0.224895 0.389529i
\(317\) −2.97665 + 1.71857i −0.167185 + 0.0965245i −0.581258 0.813719i \(-0.697439\pi\)
0.414073 + 0.910244i \(0.364106\pi\)
\(318\) 3.42566i 0.192101i
\(319\) −4.51709 2.60794i −0.252908 0.146017i
\(320\) 8.86961 + 5.12087i 0.495826 + 0.286265i
\(321\) −10.7196 + 18.5668i −0.598307 + 1.03630i
\(322\) −6.67081 11.5542i −0.371750 0.643889i
\(323\) −0.0250607 0.0144688i −0.00139441 0.000805065i
\(324\) −5.43288 9.41002i −0.301827 0.522779i
\(325\) −14.1149 30.0052i −0.782953 1.66439i
\(326\) 20.6490 1.14364
\(327\) −15.8258 + 9.13703i −0.875169 + 0.505279i
\(328\) −0.249820 + 0.432700i −0.0137940 + 0.0238919i
\(329\) 5.90091 + 10.2207i 0.325328 + 0.563484i
\(330\) 92.1221 + 53.1867i 5.07115 + 2.92783i
\(331\) 24.4806 + 14.1339i 1.34558 + 0.776869i 0.987619 0.156870i \(-0.0501402\pi\)
0.357957 + 0.933738i \(0.383474\pi\)
\(332\) −3.43778 1.98480i −0.188673 0.108930i
\(333\) 22.2544i 1.21953i
\(334\) 6.85249 + 11.8689i 0.374952 + 0.649436i
\(335\) 27.2464 + 47.1921i 1.48863 + 2.57838i
\(336\) 15.4351 + 8.91147i 0.842055 + 0.486161i
\(337\) 31.7427 1.72914 0.864568 0.502515i \(-0.167592\pi\)
0.864568 + 0.502515i \(0.167592\pi\)
\(338\) 4.00476 23.6424i 0.217830 1.28598i
\(339\) 43.8050 2.37916
\(340\) 0.0343908i 0.00186510i
\(341\) −15.9066 + 29.7787i −0.861393 + 1.61261i
\(342\) 27.6487 1.49507
\(343\) 17.3237i 0.935392i
\(344\) 4.12040 2.37891i 0.222157 0.128262i
\(345\) 47.1343i 2.53762i
\(346\) −20.0640 11.5839i −1.07864 0.622756i
\(347\) 6.05701 + 10.4911i 0.325157 + 0.563189i 0.981544 0.191235i \(-0.0612494\pi\)
−0.656387 + 0.754425i \(0.727916\pi\)
\(348\) 1.52247 + 2.63699i 0.0816127 + 0.141357i
\(349\) 12.2402i 0.655203i −0.944816 0.327601i \(-0.893760\pi\)
0.944816 0.327601i \(-0.106240\pi\)
\(350\) 12.3790 21.4410i 0.661685 1.14607i
\(351\) −3.36768 0.283206i −0.179754 0.0151164i
\(352\) 20.3721 35.2854i 1.08583 1.88072i
\(353\) −5.99723 + 3.46251i −0.319201 + 0.184291i −0.651036 0.759047i \(-0.725665\pi\)
0.331836 + 0.943337i \(0.392332\pi\)
\(354\) −19.7146 + 34.1467i −1.04782 + 1.81488i
\(355\) −25.3971 43.9890i −1.34794 2.33469i
\(356\) 11.5965i 0.614613i
\(357\) 0.0239766i 0.00126898i
\(358\) −30.3843 + 17.5424i −1.60586 + 0.927145i
\(359\) −8.59293 4.96113i −0.453517 0.261838i 0.255797 0.966730i \(-0.417662\pi\)
−0.709314 + 0.704892i \(0.750995\pi\)
\(360\) 7.00137 + 12.1267i 0.369005 + 0.639135i
\(361\) 0.383936 0.664997i 0.0202072 0.0349998i
\(362\) 17.2249 + 9.94481i 0.905322 + 0.522688i
\(363\) 32.5205 56.3272i 1.70688 2.95641i
\(364\) 6.67757 3.14123i 0.350000 0.164645i
\(365\) 8.81749 + 15.2723i 0.461529 + 0.799391i
\(366\) −37.8636 + 21.8606i −1.97916 + 1.14267i
\(367\) −0.846646 + 1.46643i −0.0441946 + 0.0765472i −0.887277 0.461238i \(-0.847405\pi\)
0.843082 + 0.537785i \(0.180739\pi\)
\(368\) −23.9773 −1.24991
\(369\) 1.32335 0.764035i 0.0688907 0.0397741i
\(370\) 45.8773i 2.38505i
\(371\) 1.07381i 0.0557494i
\(372\) 16.7340 10.4122i 0.867618 0.539846i
\(373\) 19.0784 0.987842 0.493921 0.869507i \(-0.335563\pi\)
0.493921 + 0.869507i \(0.335563\pi\)
\(374\) 0.0727957 0.00376418
\(375\) 34.5663 19.9568i 1.78499 1.03057i
\(376\) 8.91405 0.459707
\(377\) −3.09056 0.259902i −0.159172 0.0133856i
\(378\) −1.26166 2.18525i −0.0648927 0.112397i
\(379\) −21.7888 + 12.5798i −1.11922 + 0.646180i −0.941201 0.337848i \(-0.890301\pi\)
−0.178016 + 0.984028i \(0.556968\pi\)
\(380\) −23.4931 −1.20517
\(381\) 3.16209 5.47690i 0.161999 0.280590i
\(382\) −33.9732 19.6145i −1.73822 1.00356i
\(383\) 21.4469 + 12.3824i 1.09589 + 0.632711i 0.935138 0.354285i \(-0.115276\pi\)
0.160749 + 0.986995i \(0.448609\pi\)
\(384\) 18.4169 10.6330i 0.939836 0.542614i
\(385\) −28.8767 16.6719i −1.47169 0.849681i
\(386\) −23.5100 40.7204i −1.19663 2.07262i
\(387\) −14.5511 −0.739673
\(388\) 7.52891i 0.382222i
\(389\) −2.23451 3.87028i −0.113294 0.196231i 0.803802 0.594896i \(-0.202807\pi\)
−0.917097 + 0.398665i \(0.869474\pi\)
\(390\) 63.0293 + 5.30047i 3.19161 + 0.268400i
\(391\) −0.0161280 0.0279344i −0.000815626 0.00141271i
\(392\) 4.64917 + 2.68420i 0.234819 + 0.135573i
\(393\) −14.4128 + 24.9638i −0.727031 + 1.25925i
\(394\) 16.7336 28.9835i 0.843029 1.46017i
\(395\) 21.4823i 1.08089i
\(396\) −24.8274 + 14.3341i −1.24762 + 0.720316i
\(397\) −9.03983 + 5.21915i −0.453696 + 0.261941i −0.709390 0.704816i \(-0.751029\pi\)
0.255694 + 0.966758i \(0.417696\pi\)
\(398\) 7.24779 + 4.18451i 0.363299 + 0.209751i
\(399\) −16.3789 −0.819972
\(400\) −22.2473 38.5335i −1.11237 1.92667i
\(401\) 28.5696i 1.42670i 0.700809 + 0.713349i \(0.252822\pi\)
−0.700809 + 0.713349i \(0.747178\pi\)
\(402\) −67.3366 −3.35844
\(403\) −1.02140 + 20.0489i −0.0508794 + 0.998705i
\(404\) −12.8645 −0.640034
\(405\) 29.1936i 1.45064i
\(406\) −1.15784 2.00543i −0.0574625 0.0995280i
\(407\) −40.0262 −1.98403
\(408\) 0.0156836 + 0.00905490i 0.000776452 + 0.000448284i
\(409\) 11.1062 6.41219i 0.549168 0.317063i −0.199618 0.979874i \(-0.563970\pi\)
0.748787 + 0.662811i \(0.230637\pi\)
\(410\) −2.72808 + 1.57506i −0.134730 + 0.0777865i
\(411\) 12.5477i 0.618935i
\(412\) 3.17723 5.50312i 0.156531 0.271119i
\(413\) 6.17975 10.7036i 0.304086 0.526692i
\(414\) 26.6902 + 15.4096i 1.31175 + 0.757341i
\(415\) 5.33268 + 9.23647i 0.261771 + 0.453401i
\(416\) 2.03023 24.1421i 0.0995404 1.18366i
\(417\) −9.30367 16.1144i −0.455603 0.789127i
\(418\) 49.7283i 2.43229i
\(419\) −21.1787 −1.03465 −0.517323 0.855790i \(-0.673071\pi\)
−0.517323 + 0.855790i \(0.673071\pi\)
\(420\) 9.73275 + 16.8576i 0.474910 + 0.822568i
\(421\) −7.98149 4.60812i −0.388994 0.224586i 0.292730 0.956195i \(-0.405436\pi\)
−0.681724 + 0.731609i \(0.738770\pi\)
\(422\) −9.85258 + 5.68839i −0.479616 + 0.276906i
\(423\) −23.6098 13.6311i −1.14795 0.662768i
\(424\) 0.702399 + 0.405530i 0.0341115 + 0.0196943i
\(425\) 0.0299286 0.0518378i 0.00145175 0.00251450i
\(426\) 62.7663 3.04104
\(427\) 11.8688 6.85243i 0.574369 0.331612i
\(428\) 5.95562 + 10.3154i 0.287876 + 0.498616i
\(429\) 4.62446 54.9906i 0.223271 2.65497i
\(430\) 29.9970 1.44659
\(431\) 19.0373 10.9912i 0.916994 0.529427i 0.0343193 0.999411i \(-0.489074\pi\)
0.882675 + 0.469984i \(0.155740\pi\)
\(432\) −4.53486 −0.218184
\(433\) 8.05251 0.386979 0.193490 0.981102i \(-0.438019\pi\)
0.193490 + 0.981102i \(0.438019\pi\)
\(434\) −12.7262 + 7.91848i −0.610879 + 0.380099i
\(435\) 8.18099i 0.392248i
\(436\) 10.1528i 0.486231i
\(437\) 19.0826 11.0173i 0.912845 0.527031i
\(438\) −21.7915 −1.04124
\(439\) −13.3603 + 23.1407i −0.637651 + 1.10444i 0.348296 + 0.937384i \(0.386760\pi\)
−0.985947 + 0.167059i \(0.946573\pi\)
\(440\) −21.8109 + 12.5925i −1.03979 + 0.600324i
\(441\) −8.20921 14.2188i −0.390915 0.677085i
\(442\) 0.0391684 0.0184254i 0.00186305 0.000876408i
\(443\) −1.35680 + 2.35005i −0.0644637 + 0.111654i −0.896456 0.443133i \(-0.853867\pi\)
0.831992 + 0.554787i \(0.187200\pi\)
\(444\) 20.2360 + 11.6833i 0.960358 + 0.554463i
\(445\) 15.5785 26.9827i 0.738490 1.27910i
\(446\) 15.4710 + 26.7966i 0.732573 + 1.26885i
\(447\) 11.0396 + 6.37369i 0.522153 + 0.301465i
\(448\) 3.43558 1.98353i 0.162316 0.0937131i
\(449\) 12.9562i 0.611441i −0.952121 0.305720i \(-0.901103\pi\)
0.952121 0.305720i \(-0.0988973\pi\)
\(450\) 57.1911i 2.69601i
\(451\) 1.37418 + 2.38014i 0.0647074 + 0.112077i
\(452\) 12.1687 21.0768i 0.572368 0.991370i
\(453\) 41.3976 23.9009i 1.94503 1.12296i
\(454\) −24.6574 + 42.7078i −1.15723 + 2.00438i
\(455\) −19.7572 1.66149i −0.926233 0.0778918i
\(456\) −6.18560 + 10.7138i −0.289667 + 0.501718i
\(457\) 24.0216i 1.12368i −0.827245 0.561841i \(-0.810093\pi\)
0.827245 0.561841i \(-0.189907\pi\)
\(458\) 12.2503 + 21.2182i 0.572420 + 0.991461i
\(459\) −0.00305030 0.00528327i −0.000142376 0.000246602i
\(460\) −22.6787 13.0935i −1.05740 0.610490i
\(461\) 3.09838i 0.144306i 0.997394 + 0.0721529i \(0.0229870\pi\)
−0.997394 + 0.0721529i \(0.977013\pi\)
\(462\) 35.6828 20.6015i 1.66012 0.958469i
\(463\) 34.5600i 1.60614i 0.595885 + 0.803070i \(0.296802\pi\)
−0.595885 + 0.803070i \(0.703198\pi\)
\(464\) −4.16169 −0.193202
\(465\) −52.9242 + 1.74695i −2.45430 + 0.0810127i
\(466\) 8.75452i 0.405545i
\(467\) −0.115305 −0.00533569 −0.00266784 0.999996i \(-0.500849\pi\)
−0.00266784 + 0.999996i \(0.500849\pi\)
\(468\) −9.73050 + 13.9967i −0.449792 + 0.646998i
\(469\) 21.1074 0.974648
\(470\) 48.6716 + 28.1005i 2.24505 + 1.29618i
\(471\) 13.8828 + 24.0457i 0.639685 + 1.10797i
\(472\) −4.66764 8.08458i −0.214845 0.372123i
\(473\) 26.1713i 1.20336i
\(474\) −22.9892 13.2728i −1.05593 0.609642i
\(475\) 35.4115 + 20.4448i 1.62479 + 0.938074i
\(476\) 0.0115364 + 0.00666052i 0.000528768 + 0.000305285i
\(477\) −1.24025 2.14818i −0.0567872 0.0983584i
\(478\) −18.7781 + 32.5246i −0.858890 + 1.48764i
\(479\) −32.1898 + 18.5848i −1.47079 + 0.849161i −0.999462 0.0327969i \(-0.989559\pi\)
−0.471328 + 0.881958i \(0.656225\pi\)
\(480\) 63.9062 2.91690
\(481\) −21.5365 + 10.1311i −0.981979 + 0.461938i
\(482\) 15.8405 + 27.4365i 0.721515 + 1.24970i
\(483\) −15.8111 9.12857i −0.719432 0.415364i
\(484\) −18.0679 31.2945i −0.821269 1.42248i
\(485\) 10.1142 17.5183i 0.459261 0.795463i
\(486\) −35.7334 20.6307i −1.62090 0.935827i
\(487\) −31.3966 18.1268i −1.42272 0.821405i −0.426186 0.904636i \(-0.640143\pi\)
−0.996530 + 0.0832302i \(0.973476\pi\)
\(488\) 10.3514i 0.468587i
\(489\) 24.4712 14.1284i 1.10662 0.638910i
\(490\) 16.9233 + 29.3120i 0.764516 + 1.32418i
\(491\) −0.258148 + 0.447125i −0.0116500 + 0.0201785i −0.871792 0.489877i \(-0.837042\pi\)
0.860142 + 0.510055i \(0.170375\pi\)
\(492\) 1.60443i 0.0723335i
\(493\) −0.00279929 0.00484852i −0.000126074 0.000218366i
\(494\) 12.5868 + 26.7568i 0.566306 + 1.20384i
\(495\) 77.0245 3.46200
\(496\) 0.888677 + 26.9227i 0.0399028 + 1.20886i
\(497\) −19.6748 −0.882533
\(498\) −13.1792 −0.590573
\(499\) 19.7131 11.3814i 0.882479 0.509499i 0.0110038 0.999939i \(-0.496497\pi\)
0.871475 + 0.490440i \(0.163164\pi\)
\(500\) 22.1754i 0.991716i
\(501\) 16.2418 + 9.37719i 0.725629 + 0.418942i
\(502\) 20.2921 11.7157i 0.905683 0.522896i
\(503\) 21.0765 + 36.5055i 0.939754 + 1.62770i 0.765930 + 0.642924i \(0.222279\pi\)
0.173824 + 0.984777i \(0.444388\pi\)
\(504\) 5.42387 0.241598
\(505\) 29.9332 + 17.2819i 1.33201 + 0.769035i
\(506\) −27.7154 + 48.0044i −1.23210 + 2.13406i
\(507\) −11.4305 30.7587i −0.507647 1.36604i
\(508\) −1.75681 3.04289i −0.0779459 0.135006i
\(509\) −10.0638 5.81032i −0.446069 0.257538i 0.260100 0.965582i \(-0.416245\pi\)
−0.706169 + 0.708044i \(0.749578\pi\)
\(510\) 0.0570891 + 0.0988813i 0.00252795 + 0.00437854i
\(511\) 6.83079 0.302176
\(512\) 21.8428i 0.965324i
\(513\) 3.60911 2.08372i 0.159346 0.0919986i
\(514\) 25.7359 + 14.8587i 1.13516 + 0.655387i
\(515\) −14.7856 + 8.53645i −0.651530 + 0.376161i
\(516\) −7.63913 + 13.2314i −0.336294 + 0.582478i
\(517\) 24.5166 42.4640i 1.07824 1.86757i
\(518\) −15.3895 8.88514i −0.676176 0.390390i
\(519\) −31.7037 −1.39164
\(520\) −8.54824 + 12.2961i −0.374865 + 0.539219i
\(521\) 2.68024 + 4.64232i 0.117424 + 0.203384i 0.918746 0.394849i \(-0.129203\pi\)
−0.801322 + 0.598233i \(0.795870\pi\)
\(522\) 4.63256 + 2.67461i 0.202762 + 0.117064i
\(523\) −44.3905 −1.94106 −0.970530 0.240980i \(-0.922531\pi\)
−0.970530 + 0.240980i \(0.922531\pi\)
\(524\) 8.00755 + 13.8695i 0.349812 + 0.605891i
\(525\) 33.8797i 1.47863i
\(526\) 8.85229i 0.385978i
\(527\) −0.0307681 + 0.0191444i −0.00134028 + 0.000833945i
\(528\) 74.0494i 3.22258i
\(529\) 1.56147 0.0678898
\(530\) 2.55678 + 4.42847i 0.111059 + 0.192360i
\(531\) 28.5505i 1.23899i
\(532\) −4.54994 + 7.88073i −0.197265 + 0.341673i
\(533\) 1.34183 + 0.932839i 0.0581211 + 0.0404057i
\(534\) 19.2503 + 33.3425i 0.833042 + 1.44287i
\(535\) 32.0026i 1.38359i
\(536\) 7.97132 13.8067i 0.344309 0.596360i
\(537\) −24.0056 + 41.5790i −1.03592 + 1.79427i
\(538\) 21.8150 + 12.5949i 0.940510 + 0.543003i
\(539\) 25.5736 14.7649i 1.10153 0.635970i
\(540\) −4.28924 2.47640i −0.184580 0.106567i
\(541\) 28.7875 16.6205i 1.23767 0.714570i 0.269053 0.963125i \(-0.413289\pi\)
0.968618 + 0.248556i \(0.0799559\pi\)
\(542\) 3.23407 0.138915
\(543\) 27.2176 1.16802
\(544\) 0.0378744 0.0218668i 0.00162385 0.000937531i
\(545\) 13.6390 23.6235i 0.584233 1.01192i
\(546\) 13.9850 20.1166i 0.598504 0.860910i
\(547\) 10.3666 17.9555i 0.443245 0.767722i −0.554683 0.832061i \(-0.687161\pi\)
0.997928 + 0.0643392i \(0.0204940\pi\)
\(548\) 6.03736 + 3.48567i 0.257903 + 0.148900i
\(549\) −15.8291 + 27.4169i −0.675571 + 1.17012i
\(550\) −102.863 −4.38607
\(551\) 3.31212 1.91226i 0.141101 0.0814649i
\(552\) −11.9423 + 6.89491i −0.508300 + 0.293467i
\(553\) 7.20622 + 4.16052i 0.306440 + 0.176923i
\(554\) 5.55672i 0.236083i
\(555\) −31.3901 54.3692i −1.33243 2.30784i
\(556\) −10.3380 −0.438427
\(557\) 5.82569i 0.246842i −0.992354 0.123421i \(-0.960613\pi\)
0.992354 0.123421i \(-0.0393866\pi\)
\(558\) 16.3133 30.5399i 0.690596 1.29286i
\(559\) −6.62424 14.0817i −0.280175 0.595592i
\(560\) −26.6047 −1.12425
\(561\) 0.0862701 0.0498081i 0.00364233 0.00210290i
\(562\) −3.16397 −0.133464
\(563\) 7.71984 13.3712i 0.325353 0.563527i −0.656231 0.754560i \(-0.727850\pi\)
0.981584 + 0.191033i \(0.0611837\pi\)
\(564\) −24.7897 + 14.3123i −1.04383 + 0.602658i
\(565\) −56.6283 + 32.6943i −2.38237 + 1.37546i
\(566\) 13.5606i 0.569994i
\(567\) 9.79298 + 5.65398i 0.411266 + 0.237445i
\(568\) −7.43028 + 12.8696i −0.311768 + 0.539998i
\(569\) −10.4787 + 18.1497i −0.439290 + 0.760873i −0.997635 0.0687359i \(-0.978103\pi\)
0.558345 + 0.829609i \(0.311437\pi\)
\(570\) −67.5479 + 38.9988i −2.82927 + 1.63348i
\(571\) −1.30982 + 2.26867i −0.0548142 + 0.0949410i −0.892130 0.451778i \(-0.850790\pi\)
0.837316 + 0.546719i \(0.184123\pi\)
\(572\) −25.1741 17.5010i −1.05258 0.731756i
\(573\) −53.6822 −2.24261
\(574\) 1.22017i 0.0509291i
\(575\) 22.7893 + 39.4722i 0.950380 + 1.64611i
\(576\) −4.58197 + 7.93620i −0.190915 + 0.330675i
\(577\) −29.7600 + 17.1819i −1.23892 + 0.715293i −0.968874 0.247554i \(-0.920373\pi\)
−0.270049 + 0.962846i \(0.587040\pi\)
\(578\) −27.1563 15.6787i −1.12955 0.652147i
\(579\) −55.7232 32.1718i −2.31578 1.33702i
\(580\) −3.93629 2.27262i −0.163446 0.0943653i
\(581\) 4.13115 0.171389
\(582\) 12.4981 + 21.6473i 0.518062 + 0.897309i
\(583\) 3.86367 2.23069i 0.160017 0.0923857i
\(584\) 2.57969 4.46815i 0.106748 0.184893i
\(585\) 41.4438 19.4958i 1.71349 0.806051i
\(586\) 8.67406 + 15.0239i 0.358322 + 0.620632i
\(587\) 12.1177i 0.500149i 0.968227 + 0.250075i \(0.0804552\pi\)
−0.968227 + 0.250075i \(0.919545\pi\)
\(588\) −17.2389 −0.710921
\(589\) −13.0780 21.0183i −0.538868 0.866046i
\(590\) 58.8568i 2.42310i
\(591\) 45.7978i 1.88387i
\(592\) −27.6578 + 15.9682i −1.13673 + 0.656290i
\(593\) 1.31568i 0.0540284i −0.999635 0.0270142i \(-0.991400\pi\)
0.999635 0.0270142i \(-0.00859993\pi\)
\(594\) −5.24183 + 9.07912i −0.215075 + 0.372521i
\(595\) −0.0178952 0.0309954i −0.000733632 0.00127069i
\(596\) 6.13341 3.54113i 0.251234 0.145050i
\(597\) 11.4525 0.468718
\(598\) −2.76205 + 32.8443i −0.112949 + 1.34310i
\(599\) 21.0549 36.4682i 0.860281 1.49005i −0.0113771 0.999935i \(-0.503622\pi\)
0.871658 0.490115i \(-0.163045\pi\)
\(600\) −22.1613 12.7949i −0.904733 0.522348i
\(601\) −14.0503 24.3358i −0.573124 0.992680i −0.996243 0.0866054i \(-0.972398\pi\)
0.423119 0.906074i \(-0.360935\pi\)
\(602\) 5.80957 10.0625i 0.236780 0.410116i
\(603\) −42.2258 + 24.3791i −1.71957 + 0.992792i
\(604\) 26.5580i 1.08063i
\(605\) 97.0882i 3.94719i
\(606\) −36.9884 + 21.3552i −1.50255 + 0.867497i
\(607\) −0.767548 + 1.32943i −0.0311538 + 0.0539600i −0.881182 0.472777i \(-0.843252\pi\)
0.850028 + 0.526737i \(0.176585\pi\)
\(608\) 14.9377 + 25.8728i 0.605803 + 1.04928i
\(609\) −2.74430 1.58442i −0.111205 0.0642041i
\(610\) 32.6317 56.5198i 1.32122 2.28842i
\(611\) 2.44327 29.0536i 0.0988443 1.17538i
\(612\) −0.0307717 −0.00124387
\(613\) −15.6784 + 9.05195i −0.633246 + 0.365605i −0.782008 0.623268i \(-0.785805\pi\)
0.148762 + 0.988873i \(0.452471\pi\)
\(614\) −19.0221 32.9473i −0.767671 1.32964i
\(615\) −2.15536 + 3.73320i −0.0869126 + 0.150537i
\(616\) 9.75524i 0.393050i
\(617\) −27.2494 + 15.7325i −1.09702 + 0.633365i −0.935437 0.353494i \(-0.884994\pi\)
−0.161584 + 0.986859i \(0.551660\pi\)
\(618\) 21.0970i 0.848644i
\(619\) 20.8783i 0.839168i 0.907716 + 0.419584i \(0.137824\pi\)
−0.907716 + 0.419584i \(0.862176\pi\)
\(620\) −13.8614 + 25.9498i −0.556687 + 1.04217i
\(621\) 4.64534 0.186411
\(622\) 38.9191i 1.56051i
\(623\) −6.03421 10.4516i −0.241756 0.418733i
\(624\) −18.7427 39.8430i −0.750310 1.59499i
\(625\) −6.79816 + 11.7748i −0.271926 + 0.470990i
\(626\) 7.87617 4.54731i 0.314795 0.181747i
\(627\) 34.0249 + 58.9329i 1.35883 + 2.35355i
\(628\) 15.4261 0.615570
\(629\) −0.0372071 0.0214815i −0.00148354 0.000856524i
\(630\) 29.6148 + 17.0981i 1.17988 + 0.681206i
\(631\) −20.7788 11.9967i −0.827192 0.477579i 0.0256984 0.999670i \(-0.491819\pi\)
−0.852890 + 0.522090i \(0.825152\pi\)
\(632\) 5.44294 3.14248i 0.216509 0.125001i
\(633\) −7.78419 + 13.4826i −0.309394 + 0.535886i
\(634\) 3.17000 + 5.49059i 0.125897 + 0.218059i
\(635\) 9.44025i 0.374625i
\(636\) −2.60446 −0.103274
\(637\) 10.0229 14.4174i 0.397123 0.571236i
\(638\) −4.81049 + 8.33202i −0.190449 + 0.329868i
\(639\) 39.3598 22.7244i 1.55705 0.898963i
\(640\) −15.8722 + 27.4914i −0.627402 + 1.08669i
\(641\) 4.68683 8.11783i 0.185119 0.320635i −0.758498 0.651676i \(-0.774066\pi\)
0.943617 + 0.331041i \(0.107400\pi\)
\(642\) 34.2475 + 19.7728i 1.35164 + 0.780370i
\(643\) 23.3392i 0.920408i −0.887813 0.460204i \(-0.847776\pi\)
0.887813 0.460204i \(-0.152224\pi\)
\(644\) −8.78443 + 5.07170i −0.346155 + 0.199853i
\(645\) 35.5495 20.5245i 1.39976 0.808151i
\(646\) −0.0266885 + 0.0462258i −0.00105004 + 0.00181873i
\(647\) −27.8988 −1.09682 −0.548408 0.836211i \(-0.684766\pi\)
−0.548408 + 0.836211i \(0.684766\pi\)
\(648\) 7.39675 4.27051i 0.290572 0.167762i
\(649\) −51.3503 −2.01568
\(650\) −55.3462 + 26.0357i −2.17086 + 1.02120i
\(651\) −9.66389 + 18.0917i −0.378758 + 0.709069i
\(652\) 15.6991i 0.614824i
\(653\) 1.27131 0.0497502 0.0248751 0.999691i \(-0.492081\pi\)
0.0248751 + 0.999691i \(0.492081\pi\)
\(654\) 16.8538 + 29.1916i 0.659034 + 1.14148i
\(655\) 43.0287i 1.68127i
\(656\) 1.89909 + 1.09644i 0.0741469 + 0.0428087i
\(657\) −13.6651 + 7.88957i −0.533128 + 0.307802i
\(658\) 18.8526 10.8845i 0.734950 0.424324i
\(659\) 28.6250 1.11507 0.557536 0.830153i \(-0.311747\pi\)
0.557536 + 0.830153i \(0.311747\pi\)
\(660\) 40.4369 70.0387i 1.57400 2.72625i
\(661\) −12.8888 7.44134i −0.501316 0.289435i 0.227941 0.973675i \(-0.426801\pi\)
−0.729257 + 0.684240i \(0.760134\pi\)
\(662\) 26.0707 45.1558i 1.01327 1.75503i
\(663\) 0.0338115 0.0486356i 0.00131313 0.00188885i
\(664\) 1.56015 2.70226i 0.0605457 0.104868i
\(665\) 21.1736 12.2246i 0.821077 0.474049i
\(666\) 41.0494 1.59063
\(667\) 4.26308 0.165067
\(668\) 9.02368 5.20983i 0.349137 0.201574i
\(669\) 36.6694 + 21.1711i 1.41772 + 0.818520i
\(670\) 87.0484 50.2574i 3.36297 1.94161i
\(671\) −49.3114 28.4699i −1.90364 1.09907i
\(672\) 12.3768 21.4372i 0.477445 0.826960i
\(673\) −14.6108 + 25.3066i −0.563204 + 0.975499i 0.434010 + 0.900908i \(0.357098\pi\)
−0.997214 + 0.0745904i \(0.976235\pi\)
\(674\) 58.5512i 2.25531i
\(675\) 4.31016 + 7.46542i 0.165898 + 0.287344i
\(676\) −17.9749 3.04474i −0.691342 0.117105i
\(677\) −6.81146 + 11.7978i −0.261786 + 0.453426i −0.966717 0.255850i \(-0.917645\pi\)
0.704931 + 0.709276i \(0.250978\pi\)
\(678\) 80.8007i 3.10313i
\(679\) −3.91765 6.78558i −0.150346 0.260407i
\(680\) −0.0270329 −0.00103666
\(681\) 67.4840i 2.58599i
\(682\) 54.9284 + 29.3407i 2.10332 + 1.12351i
\(683\) 21.3781i 0.818009i 0.912532 + 0.409005i \(0.134124\pi\)
−0.912532 + 0.409005i \(0.865876\pi\)
\(684\) 21.0208i 0.803749i
\(685\) −9.36515 16.2209i −0.357824 0.619769i
\(686\) 31.9545 1.22003
\(687\) 29.0357 + 16.7638i 1.10778 + 0.639578i
\(688\) −10.4409 18.0841i −0.398054 0.689450i
\(689\) 1.51427 2.17818i 0.0576891 0.0829821i
\(690\) −86.9418 −3.30982
\(691\) −16.0239 9.25143i −0.609580 0.351941i 0.163221 0.986589i \(-0.447812\pi\)
−0.772801 + 0.634649i \(0.781145\pi\)
\(692\) −8.80705 + 15.2543i −0.334794 + 0.579880i
\(693\) 14.9175 25.8378i 0.566667 0.981497i
\(694\) 19.3513 11.1725i 0.734566 0.424102i
\(695\) 24.0544 + 13.8878i 0.912434 + 0.526794i
\(696\) −2.07280 + 1.19673i −0.0785694 + 0.0453621i
\(697\) 0.00295000i 0.000111739i
\(698\) −22.5777 −0.854579
\(699\) −5.98999 10.3750i −0.226562 0.392417i
\(700\) −16.3012 9.41152i −0.616129 0.355722i
\(701\) 5.30476 + 9.18811i 0.200358 + 0.347030i 0.948644 0.316346i \(-0.102456\pi\)
−0.748286 + 0.663376i \(0.769123\pi\)
\(702\) −0.522390 + 6.21188i −0.0197163 + 0.234452i
\(703\) 14.6745 25.4169i 0.553458 0.958618i
\(704\) −14.2739 8.24103i −0.537967 0.310595i
\(705\) 76.9075 2.89650
\(706\) 6.38678 + 11.0622i 0.240370 + 0.416332i
\(707\) 11.5944 6.69403i 0.436052 0.251755i
\(708\) 25.9611 + 14.9886i 0.975678 + 0.563308i
\(709\) 16.7061i 0.627412i −0.949520 0.313706i \(-0.898429\pi\)
0.949520 0.313706i \(-0.101571\pi\)
\(710\) −81.1401 + 46.8463i −3.04514 + 1.75811i
\(711\) −19.2216 −0.720867
\(712\) −9.11542 −0.341615
\(713\) −0.910327 27.5786i −0.0340920 1.03283i
\(714\) 0.0442262 0.00165512
\(715\) 35.0647 + 74.5398i 1.31134 + 2.78763i
\(716\) 13.3372 + 23.1006i 0.498433 + 0.863312i
\(717\) 51.3932i 1.91931i
\(718\) −9.15107 + 15.8501i −0.341515 + 0.591521i
\(719\) 8.42740 + 14.5967i 0.314289 + 0.544365i 0.979286 0.202481i \(-0.0649006\pi\)
−0.664997 + 0.746846i \(0.731567\pi\)
\(720\) 53.2233 30.7285i 1.98351 1.14518i
\(721\) 6.61307i 0.246283i
\(722\) −1.22662 0.708191i −0.0456502 0.0263561i
\(723\) 37.5451 + 21.6767i 1.39632 + 0.806164i
\(724\) 7.56086 13.0958i 0.280997 0.486701i
\(725\) 3.95549 + 6.85111i 0.146903 + 0.254444i
\(726\) −103.899 59.9859i −3.85604 2.22628i
\(727\) 22.0252 + 38.1487i 0.816868 + 1.41486i 0.907979 + 0.419016i \(0.137625\pi\)
−0.0911112 + 0.995841i \(0.529042\pi\)
\(728\) 2.46916 + 5.24890i 0.0915132 + 0.194537i
\(729\) −33.2193 −1.23034
\(730\) 28.1707 16.2643i 1.04264 0.601970i
\(731\) 0.0140457 0.0243279i 0.000519501 0.000899802i
\(732\) 16.6202 + 28.7870i 0.614300 + 1.06400i
\(733\) 32.8412 + 18.9609i 1.21302 + 0.700337i 0.963416 0.268011i \(-0.0863664\pi\)
0.249603 + 0.968348i \(0.419700\pi\)
\(734\) 2.70492 + 1.56168i 0.0998403 + 0.0576428i
\(735\) 40.1115 + 23.1584i 1.47954 + 0.854210i
\(736\) 33.3012i 1.22750i
\(737\) −43.8476 75.9463i −1.61515 2.79752i
\(738\) −1.40930 2.44099i −0.0518772 0.0898539i
\(739\) −16.4014 9.46937i −0.603336 0.348336i 0.167017 0.985954i \(-0.446587\pi\)
−0.770353 + 0.637618i \(0.779920\pi\)
\(740\) −34.8797 −1.28220
\(741\) 33.2240 + 23.0973i 1.22052 + 0.848501i
\(742\) 1.98070 0.0727138
\(743\) 24.3107i 0.891873i −0.895065 0.445937i \(-0.852871\pi\)
0.895065 0.445937i \(-0.147129\pi\)
\(744\) 8.18449 + 13.1538i 0.300058 + 0.482240i
\(745\) −19.0283 −0.697143
\(746\) 35.1911i 1.28844i
\(747\) −8.26446 + 4.77149i −0.302381 + 0.174580i
\(748\) 0.0553452i 0.00202362i
\(749\) −10.7352 6.19799i −0.392257 0.226470i
\(750\) −36.8115 63.7594i −1.34417 2.32816i
\(751\) −7.42825 12.8661i −0.271061 0.469491i 0.698073 0.716027i \(-0.254041\pi\)
−0.969134 + 0.246536i \(0.920708\pi\)
\(752\) 39.1231i 1.42667i
\(753\) 16.0321 27.7685i 0.584243 1.01194i
\(754\) −0.479403 + 5.70071i −0.0174588 + 0.207608i
\(755\) −35.6774 + 61.7951i −1.29843 + 2.24895i
\(756\) −1.66141 + 0.959215i −0.0604249 + 0.0348863i
\(757\) 3.02296 5.23593i 0.109871 0.190303i −0.805847 0.592124i \(-0.798289\pi\)
0.915718 + 0.401821i \(0.131623\pi\)
\(758\) 23.2041 + 40.1907i 0.842811 + 1.45979i
\(759\) 75.8533i 2.75330i
\(760\) 18.4667i 0.669859i
\(761\) 14.9727 8.64451i 0.542761 0.313363i −0.203436 0.979088i \(-0.565211\pi\)
0.746197 + 0.665725i \(0.231878\pi\)
\(762\) −10.1024 5.83265i −0.365973 0.211295i
\(763\) −5.28299 9.15041i −0.191257 0.331267i
\(764\) −14.9125 + 25.8292i −0.539516 + 0.934468i
\(765\)