Properties

Label 42.3.g.a.19.2
Level $42$
Weight $3$
Character 42.19
Analytic conductor $1.144$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 42.g (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.14441711031\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 42.19
Dual form 42.3.g.a.31.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.24264 - 0.717439i) q^{5} -2.44949i q^{6} +(1.74264 + 6.77962i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-1.24264 - 0.717439i) q^{5} -2.44949i q^{6} +(1.74264 + 6.77962i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.75736 + 1.01461i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-3.00000 - 1.73205i) q^{12} +21.3280i q^{13} +(9.53553 + 2.65962i) q^{14} -2.48528 q^{15} +(-2.00000 + 3.46410i) q^{16} +(-7.75736 + 4.47871i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(-6.25736 - 3.61269i) q^{19} +2.86976i q^{20} +(8.48528 + 8.66025i) q^{21} -8.48528 q^{22} +(18.7279 - 32.4377i) q^{23} +(-4.24264 + 2.44949i) q^{24} +(-11.4706 - 19.8676i) q^{25} +(26.1213 + 15.0812i) q^{26} -5.19615i q^{27} +(10.0000 - 9.79796i) q^{28} -33.9411 q^{29} +(-1.75736 + 3.04384i) q^{30} +(38.2279 - 22.0709i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-9.00000 - 5.19615i) q^{33} +12.6677i q^{34} +(2.69848 - 9.67487i) q^{35} -6.00000 q^{36} +(13.9853 - 24.2232i) q^{37} +(-8.84924 + 5.10911i) q^{38} +(18.4706 + 31.9920i) q^{39} +(3.51472 + 2.02922i) q^{40} +54.8313i q^{41} +(16.6066 - 4.26858i) q^{42} -1.48528 q^{43} +(-6.00000 + 10.3923i) q^{44} +(-3.72792 + 2.15232i) q^{45} +(-26.4853 - 45.8739i) q^{46} +(-37.2426 - 21.5020i) q^{47} +6.92820i q^{48} +(-42.9264 + 23.6289i) q^{49} -32.4437 q^{50} +(-7.75736 + 13.4361i) q^{51} +(36.9411 - 21.3280i) q^{52} +(42.7279 + 74.0069i) q^{53} +(-6.36396 - 3.67423i) q^{54} +8.60927i q^{55} +(-4.92893 - 19.1757i) q^{56} -12.5147 q^{57} +(-24.0000 + 41.5692i) q^{58} +(-35.6985 + 20.6105i) q^{59} +(2.48528 + 4.30463i) q^{60} +(-1.02944 - 0.594346i) q^{61} -62.4259i q^{62} +(20.2279 + 5.64191i) q^{63} +8.00000 q^{64} +(15.3015 - 26.5030i) q^{65} +(-12.7279 + 7.34847i) q^{66} +(-2.19848 - 3.80789i) q^{67} +(15.5147 + 8.95743i) q^{68} -64.8754i q^{69} +(-9.94113 - 10.1461i) q^{70} +137.397 q^{71} +(-4.24264 + 7.34847i) q^{72} +(68.3528 - 39.4635i) q^{73} +(-19.7782 - 34.2568i) q^{74} +(-34.4117 - 19.8676i) q^{75} +14.4508i q^{76} +(30.0000 - 29.3939i) q^{77} +52.2426 q^{78} +(-49.1690 + 85.1633i) q^{79} +(4.97056 - 2.86976i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(67.1543 + 38.7716i) q^{82} -110.401i q^{83} +(6.51472 - 23.3572i) q^{84} +12.8528 q^{85} +(-1.05025 + 1.81909i) q^{86} +(-50.9117 + 29.3939i) q^{87} +(8.48528 + 14.6969i) q^{88} +(-18.0000 - 10.3923i) q^{89} +6.08767i q^{90} +(-144.595 + 37.1670i) q^{91} -74.9117 q^{92} +(38.2279 - 66.2127i) q^{93} +(-52.6690 + 30.4085i) q^{94} +(5.18377 + 8.97855i) q^{95} +(8.48528 + 4.89898i) q^{96} +10.9867i q^{97} +(-1.41421 + 69.2820i) q^{98} -18.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{3} - 4 q^{4} + 12 q^{5} - 10 q^{7} + 6 q^{9} + O(q^{10}) \) \( 4 q + 6 q^{3} - 4 q^{4} + 12 q^{5} - 10 q^{7} + 6 q^{9} - 24 q^{10} - 12 q^{11} - 12 q^{12} + 24 q^{14} + 24 q^{15} - 8 q^{16} - 48 q^{17} - 42 q^{19} + 24 q^{23} + 22 q^{25} + 96 q^{26} + 40 q^{28} - 24 q^{30} + 102 q^{31} - 36 q^{33} - 108 q^{35} - 24 q^{36} + 22 q^{37} + 24 q^{38} + 6 q^{39} + 48 q^{40} + 24 q^{42} + 28 q^{43} - 24 q^{44} + 36 q^{45} - 72 q^{46} - 132 q^{47} - 2 q^{49} - 192 q^{50} - 48 q^{51} + 12 q^{52} + 120 q^{53} - 48 q^{56} - 84 q^{57} - 96 q^{58} - 24 q^{59} - 24 q^{60} - 72 q^{61} + 30 q^{63} + 32 q^{64} + 180 q^{65} + 110 q^{67} + 96 q^{68} + 96 q^{70} + 312 q^{71} - 66 q^{73} - 48 q^{74} + 66 q^{75} + 120 q^{77} + 192 q^{78} - 10 q^{79} - 48 q^{80} - 18 q^{81} + 48 q^{82} + 60 q^{84} - 288 q^{85} - 24 q^{86} - 72 q^{89} - 222 q^{91} - 96 q^{92} + 102 q^{93} - 24 q^{94} - 132 q^{95} - 72 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.353553 0.612372i
\(3\) 1.50000 0.866025i 0.500000 0.288675i
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) −1.24264 0.717439i −0.248528 0.143488i 0.370562 0.928808i \(-0.379165\pi\)
−0.619090 + 0.785320i \(0.712498\pi\)
\(6\) 2.44949i 0.408248i
\(7\) 1.74264 + 6.77962i 0.248949 + 0.968517i
\(8\) −2.82843 −0.353553
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) −1.75736 + 1.01461i −0.175736 + 0.101461i
\(11\) −3.00000 5.19615i −0.272727 0.472377i 0.696832 0.717234i \(-0.254592\pi\)
−0.969559 + 0.244857i \(0.921259\pi\)
\(12\) −3.00000 1.73205i −0.250000 0.144338i
\(13\) 21.3280i 1.64061i 0.571924 + 0.820306i \(0.306197\pi\)
−0.571924 + 0.820306i \(0.693803\pi\)
\(14\) 9.53553 + 2.65962i 0.681110 + 0.189973i
\(15\) −2.48528 −0.165685
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) −7.75736 + 4.47871i −0.456315 + 0.263454i −0.710494 0.703704i \(-0.751528\pi\)
0.254178 + 0.967157i \(0.418195\pi\)
\(18\) −2.12132 3.67423i −0.117851 0.204124i
\(19\) −6.25736 3.61269i −0.329335 0.190141i 0.326211 0.945297i \(-0.394228\pi\)
−0.655546 + 0.755156i \(0.727561\pi\)
\(20\) 2.86976i 0.143488i
\(21\) 8.48528 + 8.66025i 0.404061 + 0.412393i
\(22\) −8.48528 −0.385695
\(23\) 18.7279 32.4377i 0.814257 1.41034i −0.0956024 0.995420i \(-0.530478\pi\)
0.909860 0.414916i \(-0.136189\pi\)
\(24\) −4.24264 + 2.44949i −0.176777 + 0.102062i
\(25\) −11.4706 19.8676i −0.458823 0.794704i
\(26\) 26.1213 + 15.0812i 1.00467 + 0.580044i
\(27\) 5.19615i 0.192450i
\(28\) 10.0000 9.79796i 0.357143 0.349927i
\(29\) −33.9411 −1.17038 −0.585192 0.810895i \(-0.698981\pi\)
−0.585192 + 0.810895i \(0.698981\pi\)
\(30\) −1.75736 + 3.04384i −0.0585786 + 0.101461i
\(31\) 38.2279 22.0709i 1.23316 0.711965i 0.265472 0.964119i \(-0.414472\pi\)
0.967687 + 0.252154i \(0.0811390\pi\)
\(32\) 2.82843 + 4.89898i 0.0883883 + 0.153093i
\(33\) −9.00000 5.19615i −0.272727 0.157459i
\(34\) 12.6677i 0.372580i
\(35\) 2.69848 9.67487i 0.0770996 0.276425i
\(36\) −6.00000 −0.166667
\(37\) 13.9853 24.2232i 0.377981 0.654682i −0.612788 0.790248i \(-0.709952\pi\)
0.990768 + 0.135566i \(0.0432853\pi\)
\(38\) −8.84924 + 5.10911i −0.232875 + 0.134450i
\(39\) 18.4706 + 31.9920i 0.473604 + 0.820306i
\(40\) 3.51472 + 2.02922i 0.0878680 + 0.0507306i
\(41\) 54.8313i 1.33735i 0.743556 + 0.668674i \(0.233138\pi\)
−0.743556 + 0.668674i \(0.766862\pi\)
\(42\) 16.6066 4.26858i 0.395395 0.101633i
\(43\) −1.48528 −0.0345414 −0.0172707 0.999851i \(-0.505498\pi\)
−0.0172707 + 0.999851i \(0.505498\pi\)
\(44\) −6.00000 + 10.3923i −0.136364 + 0.236189i
\(45\) −3.72792 + 2.15232i −0.0828427 + 0.0478293i
\(46\) −26.4853 45.8739i −0.575767 0.997258i
\(47\) −37.2426 21.5020i −0.792397 0.457490i 0.0484090 0.998828i \(-0.484585\pi\)
−0.840806 + 0.541337i \(0.817918\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −42.9264 + 23.6289i −0.876049 + 0.482222i
\(50\) −32.4437 −0.648873
\(51\) −7.75736 + 13.4361i −0.152105 + 0.263454i
\(52\) 36.9411 21.3280i 0.710406 0.410153i
\(53\) 42.7279 + 74.0069i 0.806187 + 1.39636i 0.915487 + 0.402348i \(0.131806\pi\)
−0.109299 + 0.994009i \(0.534861\pi\)
\(54\) −6.36396 3.67423i −0.117851 0.0680414i
\(55\) 8.60927i 0.156532i
\(56\) −4.92893 19.1757i −0.0880166 0.342422i
\(57\) −12.5147 −0.219556
\(58\) −24.0000 + 41.5692i −0.413793 + 0.716711i
\(59\) −35.6985 + 20.6105i −0.605059 + 0.349331i −0.771029 0.636800i \(-0.780258\pi\)
0.165970 + 0.986131i \(0.446924\pi\)
\(60\) 2.48528 + 4.30463i 0.0414214 + 0.0717439i
\(61\) −1.02944 0.594346i −0.0168760 0.00974337i 0.491538 0.870856i \(-0.336435\pi\)
−0.508414 + 0.861113i \(0.669768\pi\)
\(62\) 62.4259i 1.00687i
\(63\) 20.2279 + 5.64191i 0.321078 + 0.0895542i
\(64\) 8.00000 0.125000
\(65\) 15.3015 26.5030i 0.235408 0.407738i
\(66\) −12.7279 + 7.34847i −0.192847 + 0.111340i
\(67\) −2.19848 3.80789i −0.0328132 0.0568341i 0.849152 0.528148i \(-0.177113\pi\)
−0.881966 + 0.471314i \(0.843780\pi\)
\(68\) 15.5147 + 8.95743i 0.228158 + 0.131727i
\(69\) 64.8754i 0.940224i
\(70\) −9.94113 10.1461i −0.142016 0.144945i
\(71\) 137.397 1.93517 0.967584 0.252548i \(-0.0812687\pi\)
0.967584 + 0.252548i \(0.0812687\pi\)
\(72\) −4.24264 + 7.34847i −0.0589256 + 0.102062i
\(73\) 68.3528 39.4635i 0.936340 0.540596i 0.0475288 0.998870i \(-0.484865\pi\)
0.888811 + 0.458274i \(0.151532\pi\)
\(74\) −19.7782 34.2568i −0.267273 0.462930i
\(75\) −34.4117 19.8676i −0.458823 0.264901i
\(76\) 14.4508i 0.190141i
\(77\) 30.0000 29.3939i 0.389610 0.381739i
\(78\) 52.2426 0.669777
\(79\) −49.1690 + 85.1633i −0.622393 + 1.07802i 0.366646 + 0.930361i \(0.380506\pi\)
−0.989039 + 0.147656i \(0.952827\pi\)
\(80\) 4.97056 2.86976i 0.0621320 0.0358719i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 67.1543 + 38.7716i 0.818955 + 0.472824i
\(83\) 110.401i 1.33013i −0.746784 0.665067i \(-0.768403\pi\)
0.746784 0.665067i \(-0.231597\pi\)
\(84\) 6.51472 23.3572i 0.0775562 0.278062i
\(85\) 12.8528 0.151210
\(86\) −1.05025 + 1.81909i −0.0122122 + 0.0211522i
\(87\) −50.9117 + 29.3939i −0.585192 + 0.337861i
\(88\) 8.48528 + 14.6969i 0.0964237 + 0.167011i
\(89\) −18.0000 10.3923i −0.202247 0.116767i 0.395456 0.918485i \(-0.370587\pi\)
−0.597703 + 0.801717i \(0.703920\pi\)
\(90\) 6.08767i 0.0676408i
\(91\) −144.595 + 37.1670i −1.58896 + 0.408428i
\(92\) −74.9117 −0.814257
\(93\) 38.2279 66.2127i 0.411053 0.711965i
\(94\) −52.6690 + 30.4085i −0.560309 + 0.323495i
\(95\) 5.18377 + 8.97855i 0.0545660 + 0.0945110i
\(96\) 8.48528 + 4.89898i 0.0883883 + 0.0510310i
\(97\) 10.9867i 0.113264i 0.998395 + 0.0566322i \(0.0180362\pi\)
−0.998395 + 0.0566322i \(0.981964\pi\)
\(98\) −1.41421 + 69.2820i −0.0144308 + 0.706960i
\(99\) −18.0000 −0.181818
\(100\) −22.9411 + 39.7352i −0.229411 + 0.397352i
\(101\) −92.8234 + 53.5916i −0.919043 + 0.530610i −0.883330 0.468752i \(-0.844704\pi\)
−0.0357136 + 0.999362i \(0.511370\pi\)
\(102\) 10.9706 + 19.0016i 0.107555 + 0.186290i
\(103\) 91.1102 + 52.6025i 0.884565 + 0.510704i 0.872161 0.489219i \(-0.162718\pi\)
0.0124040 + 0.999923i \(0.496052\pi\)
\(104\) 60.3246i 0.580044i
\(105\) −4.33095 16.8493i −0.0412472 0.160469i
\(106\) 120.853 1.14012
\(107\) −59.2721 + 102.662i −0.553945 + 0.959460i 0.444040 + 0.896007i \(0.353545\pi\)
−0.997985 + 0.0634534i \(0.979789\pi\)
\(108\) −9.00000 + 5.19615i −0.0833333 + 0.0481125i
\(109\) −55.5294 96.1798i −0.509444 0.882384i −0.999940 0.0109400i \(-0.996518\pi\)
0.490496 0.871444i \(-0.336816\pi\)
\(110\) 10.5442 + 6.08767i 0.0958560 + 0.0553425i
\(111\) 48.4464i 0.436454i
\(112\) −26.9706 7.52255i −0.240809 0.0671656i
\(113\) 101.397 0.897318 0.448659 0.893703i \(-0.351902\pi\)
0.448659 + 0.893703i \(0.351902\pi\)
\(114\) −8.84924 + 15.3273i −0.0776249 + 0.134450i
\(115\) −46.5442 + 26.8723i −0.404732 + 0.233672i
\(116\) 33.9411 + 58.7878i 0.292596 + 0.506791i
\(117\) 55.4117 + 31.9920i 0.473604 + 0.273435i
\(118\) 58.2954i 0.494029i
\(119\) −43.8823 44.7871i −0.368758 0.376362i
\(120\) 7.02944 0.0585786
\(121\) 42.5000 73.6122i 0.351240 0.608365i
\(122\) −1.45584 + 0.840532i −0.0119331 + 0.00688961i
\(123\) 47.4853 + 82.2469i 0.386059 + 0.668674i
\(124\) −76.4558 44.1418i −0.616579 0.355982i
\(125\) 68.7897i 0.550317i
\(126\) 21.2132 20.7846i 0.168359 0.164957i
\(127\) 82.5736 0.650186 0.325093 0.945682i \(-0.394604\pi\)
0.325093 + 0.945682i \(0.394604\pi\)
\(128\) 5.65685 9.79796i 0.0441942 0.0765466i
\(129\) −2.22792 + 1.28629i −0.0172707 + 0.00997125i
\(130\) −21.6396 37.4809i −0.166459 0.288315i
\(131\) −52.4558 30.2854i −0.400426 0.231186i 0.286242 0.958157i \(-0.407594\pi\)
−0.686668 + 0.726971i \(0.740927\pi\)
\(132\) 20.7846i 0.157459i
\(133\) 13.5883 48.7181i 0.102168 0.366302i
\(134\) −6.21825 −0.0464049
\(135\) −3.72792 + 6.45695i −0.0276142 + 0.0478293i
\(136\) 21.9411 12.6677i 0.161332 0.0931450i
\(137\) −33.5147 58.0492i −0.244633 0.423717i 0.717395 0.696666i \(-0.245334\pi\)
−0.962028 + 0.272949i \(0.912001\pi\)
\(138\) −79.4558 45.8739i −0.575767 0.332419i
\(139\) 91.5525i 0.658651i −0.944216 0.329326i \(-0.893179\pi\)
0.944216 0.329326i \(-0.106821\pi\)
\(140\) −19.4558 + 5.00095i −0.138970 + 0.0357211i
\(141\) −74.4853 −0.528264
\(142\) 97.1543 168.276i 0.684185 1.18504i
\(143\) 110.823 63.9839i 0.774989 0.447440i
\(144\) 6.00000 + 10.3923i 0.0416667 + 0.0721688i
\(145\) 42.1766 + 24.3507i 0.290873 + 0.167936i
\(146\) 111.620i 0.764518i
\(147\) −43.9264 + 72.6187i −0.298819 + 0.494005i
\(148\) −55.9411 −0.377981
\(149\) −40.5442 + 70.2245i −0.272108 + 0.471306i −0.969402 0.245480i \(-0.921054\pi\)
0.697293 + 0.716786i \(0.254388\pi\)
\(150\) −48.6655 + 28.0970i −0.324437 + 0.187314i
\(151\) 25.6030 + 44.3457i 0.169556 + 0.293680i 0.938264 0.345920i \(-0.112433\pi\)
−0.768708 + 0.639600i \(0.779100\pi\)
\(152\) 17.6985 + 10.2182i 0.116437 + 0.0672252i
\(153\) 26.8723i 0.175636i
\(154\) −14.7868 57.5270i −0.0960182 0.373552i
\(155\) −63.3381 −0.408633
\(156\) 36.9411 63.9839i 0.236802 0.410153i
\(157\) 162.000 93.5307i 1.03185 0.595737i 0.114334 0.993442i \(-0.463527\pi\)
0.917513 + 0.397705i \(0.130193\pi\)
\(158\) 69.5355 + 120.439i 0.440098 + 0.762273i
\(159\) 128.184 + 74.0069i 0.806187 + 0.465452i
\(160\) 8.11689i 0.0507306i
\(161\) 252.551 + 70.4409i 1.56864 + 0.437521i
\(162\) −12.7279 −0.0785674
\(163\) −41.9706 + 72.6951i −0.257488 + 0.445982i −0.965568 0.260149i \(-0.916228\pi\)
0.708080 + 0.706132i \(0.249561\pi\)
\(164\) 94.9706 54.8313i 0.579089 0.334337i
\(165\) 7.45584 + 12.9139i 0.0451869 + 0.0782661i
\(166\) −135.213 78.0654i −0.814537 0.470273i
\(167\) 127.620i 0.764190i 0.924123 + 0.382095i \(0.124797\pi\)
−0.924123 + 0.382095i \(0.875203\pi\)
\(168\) −24.0000 24.4949i −0.142857 0.145803i
\(169\) −285.882 −1.69161
\(170\) 9.08831 15.7414i 0.0534607 0.0925966i
\(171\) −18.7721 + 10.8381i −0.109778 + 0.0633805i
\(172\) 1.48528 + 2.57258i 0.00863536 + 0.0149569i
\(173\) −123.816 71.4853i −0.715701 0.413210i 0.0974675 0.995239i \(-0.468926\pi\)
−0.813168 + 0.582029i \(0.802259\pi\)
\(174\) 83.1384i 0.477807i
\(175\) 114.706 112.388i 0.655461 0.642218i
\(176\) 24.0000 0.136364
\(177\) −35.6985 + 61.8316i −0.201686 + 0.349331i
\(178\) −25.4558 + 14.6969i −0.143010 + 0.0825671i
\(179\) −84.6396 146.600i −0.472847 0.818995i 0.526670 0.850070i \(-0.323440\pi\)
−0.999517 + 0.0310748i \(0.990107\pi\)
\(180\) 7.45584 + 4.30463i 0.0414214 + 0.0239146i
\(181\) 209.969i 1.16005i 0.814600 + 0.580024i \(0.196957\pi\)
−0.814600 + 0.580024i \(0.803043\pi\)
\(182\) −56.7244 + 203.374i −0.311672 + 1.11744i
\(183\) −2.05887 −0.0112507
\(184\) −52.9706 + 91.7477i −0.287883 + 0.498629i
\(185\) −34.7574 + 20.0672i −0.187878 + 0.108471i
\(186\) −54.0624 93.6389i −0.290658 0.503435i
\(187\) 46.5442 + 26.8723i 0.248899 + 0.143702i
\(188\) 86.0082i 0.457490i
\(189\) 35.2279 9.05503i 0.186391 0.0479102i
\(190\) 14.6619 0.0771679
\(191\) −33.3015 + 57.6799i −0.174353 + 0.301989i −0.939937 0.341347i \(-0.889117\pi\)
0.765584 + 0.643336i \(0.222450\pi\)
\(192\) 12.0000 6.92820i 0.0625000 0.0360844i
\(193\) 4.89697 + 8.48180i 0.0253729 + 0.0439472i 0.878433 0.477865i \(-0.158589\pi\)
−0.853060 + 0.521813i \(0.825256\pi\)
\(194\) 13.4558 + 7.76874i 0.0693600 + 0.0400450i
\(195\) 53.0060i 0.271826i
\(196\) 83.8528 + 50.7218i 0.427820 + 0.258785i
\(197\) −267.161 −1.35615 −0.678075 0.734993i \(-0.737185\pi\)
−0.678075 + 0.734993i \(0.737185\pi\)
\(198\) −12.7279 + 22.0454i −0.0642824 + 0.111340i
\(199\) −113.397 + 65.4698i −0.569834 + 0.328994i −0.757083 0.653319i \(-0.773376\pi\)
0.187249 + 0.982312i \(0.440043\pi\)
\(200\) 32.4437 + 56.1941i 0.162218 + 0.280970i
\(201\) −6.59545 3.80789i −0.0328132 0.0189447i
\(202\) 151.580i 0.750396i
\(203\) −59.1472 230.108i −0.291365 1.13354i
\(204\) 31.0294 0.152105
\(205\) 39.3381 68.1356i 0.191893 0.332369i
\(206\) 128.849 74.3911i 0.625482 0.361122i
\(207\) −56.1838 97.3131i −0.271419 0.470112i
\(208\) −73.8823 42.6559i −0.355203 0.205077i
\(209\) 43.3523i 0.207427i
\(210\) −23.6985 6.60991i −0.112850 0.0314758i
\(211\) −23.0883 −0.109423 −0.0547116 0.998502i \(-0.517424\pi\)
−0.0547116 + 0.998502i \(0.517424\pi\)
\(212\) 85.4558 148.014i 0.403094 0.698179i
\(213\) 206.095 118.989i 0.967584 0.558635i
\(214\) 83.8234 + 145.186i 0.391698 + 0.678441i
\(215\) 1.84567 + 1.06560i 0.00858452 + 0.00495627i
\(216\) 14.6969i 0.0680414i
\(217\) 216.250 + 220.709i 0.996543 + 1.01709i
\(218\) −157.061 −0.720463
\(219\) 68.3528 118.391i 0.312113 0.540596i
\(220\) 14.9117 8.60927i 0.0677804 0.0391330i
\(221\) −95.5219 165.449i −0.432226 0.748637i
\(222\) −59.3345 34.2568i −0.267273 0.154310i
\(223\) 228.631i 1.02525i −0.858613 0.512625i \(-0.828673\pi\)
0.858613 0.512625i \(-0.171327\pi\)
\(224\) −28.2843 + 27.7128i −0.126269 + 0.123718i
\(225\) −68.8234 −0.305882
\(226\) 71.6985 124.185i 0.317250 0.549493i
\(227\) 56.8234 32.8070i 0.250323 0.144524i −0.369589 0.929195i \(-0.620502\pi\)
0.619912 + 0.784671i \(0.287168\pi\)
\(228\) 12.5147 + 21.6761i 0.0548891 + 0.0950707i
\(229\) 80.9558 + 46.7399i 0.353519 + 0.204104i 0.666234 0.745743i \(-0.267905\pi\)
−0.312715 + 0.949847i \(0.601239\pi\)
\(230\) 76.0063i 0.330462i
\(231\) 19.5442 70.0716i 0.0846067 0.303340i
\(232\) 96.0000 0.413793
\(233\) 118.757 205.694i 0.509688 0.882806i −0.490249 0.871583i \(-0.663094\pi\)
0.999937 0.0112234i \(-0.00357259\pi\)
\(234\) 78.3640 45.2435i 0.334889 0.193348i
\(235\) 30.8528 + 53.4386i 0.131289 + 0.227398i
\(236\) 71.3970 + 41.2211i 0.302530 + 0.174666i
\(237\) 170.327i 0.718678i
\(238\) −85.8823 + 22.0753i −0.360850 + 0.0927533i
\(239\) 366.853 1.53495 0.767475 0.641079i \(-0.221513\pi\)
0.767475 + 0.641079i \(0.221513\pi\)
\(240\) 4.97056 8.60927i 0.0207107 0.0358719i
\(241\) −364.617 + 210.512i −1.51293 + 0.873493i −0.513049 + 0.858359i \(0.671484\pi\)
−0.999885 + 0.0151343i \(0.995182\pi\)
\(242\) −60.1041 104.103i −0.248364 0.430179i
\(243\) −13.5000 7.79423i −0.0555556 0.0320750i
\(244\) 2.37738i 0.00974337i
\(245\) 70.2944 + 1.43488i 0.286916 + 0.00585664i
\(246\) 134.309 0.545970
\(247\) 77.0513 133.457i 0.311949 0.540311i
\(248\) −108.125 + 62.4259i −0.435987 + 0.251717i
\(249\) −95.6102 165.602i −0.383977 0.665067i
\(250\) 84.2498 + 48.6416i 0.336999 + 0.194567i
\(251\) 146.621i 0.584148i 0.956396 + 0.292074i \(0.0943454\pi\)
−0.956396 + 0.292074i \(0.905655\pi\)
\(252\) −10.4558 40.6777i −0.0414914 0.161419i
\(253\) −224.735 −0.888281
\(254\) 58.3883 101.132i 0.229875 0.398156i
\(255\) 19.2792 11.1309i 0.0756048 0.0436504i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 21.7279 + 12.5446i 0.0845444 + 0.0488118i 0.541676 0.840587i \(-0.317790\pi\)
−0.457132 + 0.889399i \(0.651123\pi\)
\(258\) 3.63818i 0.0141015i
\(259\) 188.595 + 52.6025i 0.728168 + 0.203098i
\(260\) −61.2061 −0.235408
\(261\) −50.9117 + 88.1816i −0.195064 + 0.337861i
\(262\) −74.1838 + 42.8300i −0.283144 + 0.163473i
\(263\) 45.3381 + 78.5279i 0.172388 + 0.298585i 0.939254 0.343222i \(-0.111518\pi\)
−0.766866 + 0.641807i \(0.778185\pi\)
\(264\) 25.4558 + 14.6969i 0.0964237 + 0.0556702i
\(265\) 122.619i 0.462712i
\(266\) −50.0589 51.0911i −0.188191 0.192072i
\(267\) −36.0000 −0.134831
\(268\) −4.39697 + 7.61577i −0.0164066 + 0.0284171i
\(269\) −59.2355 + 34.1996i −0.220206 + 0.127136i −0.606046 0.795430i \(-0.707245\pi\)
0.385839 + 0.922566i \(0.373912\pi\)
\(270\) 5.27208 + 9.13151i 0.0195262 + 0.0338204i
\(271\) −106.971 61.7595i −0.394725 0.227895i 0.289480 0.957184i \(-0.406518\pi\)
−0.684206 + 0.729289i \(0.739851\pi\)
\(272\) 35.8297i 0.131727i
\(273\) −184.706 + 180.974i −0.676577 + 0.662908i
\(274\) −94.7939 −0.345963
\(275\) −68.8234 + 119.206i −0.250267 + 0.433475i
\(276\) −112.368 + 64.8754i −0.407129 + 0.235056i
\(277\) 136.441 + 236.323i 0.492567 + 0.853151i 0.999963 0.00856145i \(-0.00272523\pi\)
−0.507396 + 0.861713i \(0.669392\pi\)
\(278\) −112.128 64.7374i −0.403340 0.232868i
\(279\) 132.425i 0.474643i
\(280\) −7.63247 + 27.3647i −0.0272588 + 0.0977309i
\(281\) 133.103 0.473675 0.236837 0.971549i \(-0.423889\pi\)
0.236837 + 0.971549i \(0.423889\pi\)
\(282\) −52.6690 + 91.2255i −0.186770 + 0.323495i
\(283\) −111.507 + 64.3787i −0.394018 + 0.227486i −0.683900 0.729576i \(-0.739717\pi\)
0.289882 + 0.957063i \(0.406384\pi\)
\(284\) −137.397 237.979i −0.483792 0.837953i
\(285\) 15.5513 + 8.97855i 0.0545660 + 0.0315037i
\(286\) 180.974i 0.632776i
\(287\) −371.735 + 95.5512i −1.29524 + 0.332931i
\(288\) 16.9706 0.0589256
\(289\) −104.382 + 180.795i −0.361184 + 0.625589i
\(290\) 59.6468 34.4371i 0.205678 0.118749i
\(291\) 9.51472 + 16.4800i 0.0326966 + 0.0566322i
\(292\) −136.706 78.9270i −0.468170 0.270298i
\(293\) 308.984i 1.05455i 0.849694 + 0.527276i \(0.176787\pi\)
−0.849694 + 0.527276i \(0.823213\pi\)
\(294\) 57.8787 + 105.148i 0.196866 + 0.357646i
\(295\) 59.1472 0.200499
\(296\) −39.5563 + 68.5136i −0.133636 + 0.231465i
\(297\) −27.0000 + 15.5885i −0.0909091 + 0.0524864i
\(298\) 57.3381 + 99.3125i 0.192410 + 0.333263i
\(299\) 691.831 + 399.429i 2.31381 + 1.33588i
\(300\) 79.4704i 0.264901i
\(301\) −2.58831 10.0696i −0.00859904 0.0334539i
\(302\) 72.4163 0.239789
\(303\) −92.8234 + 160.775i −0.306348 + 0.530610i
\(304\) 25.0294 14.4508i 0.0823337 0.0475354i
\(305\) 0.852814 + 1.47712i 0.00279611 + 0.00484301i
\(306\) 32.9117 + 19.0016i 0.107555 + 0.0620966i
\(307\) 606.090i 1.97423i −0.160003 0.987117i \(-0.551150\pi\)
0.160003 0.987117i \(-0.448850\pi\)
\(308\) −80.9117 22.5676i −0.262700 0.0732716i
\(309\) 182.220 0.589710
\(310\) −44.7868 + 77.5730i −0.144474 + 0.250236i
\(311\) −176.044 + 101.639i −0.566057 + 0.326813i −0.755573 0.655064i \(-0.772641\pi\)
0.189516 + 0.981878i \(0.439308\pi\)
\(312\) −52.2426 90.4869i −0.167444 0.290022i
\(313\) −351.294 202.820i −1.12234 0.647986i −0.180346 0.983603i \(-0.557722\pi\)
−0.941999 + 0.335617i \(0.891055\pi\)
\(314\) 264.545i 0.842500i
\(315\) −21.0883 21.5232i −0.0669470 0.0683275i
\(316\) 196.676 0.622393
\(317\) 13.0294 22.5676i 0.0411023 0.0711913i −0.844742 0.535173i \(-0.820246\pi\)
0.885845 + 0.463982i \(0.153580\pi\)
\(318\) 181.279 104.662i 0.570060 0.329125i
\(319\) 101.823 + 176.363i 0.319196 + 0.552863i
\(320\) −9.94113 5.73951i −0.0310660 0.0179360i
\(321\) 205.325i 0.639640i
\(322\) 264.853 259.502i 0.822524 0.805906i
\(323\) 64.7208 0.200374
\(324\) −9.00000 + 15.5885i −0.0277778 + 0.0481125i
\(325\) 423.735 244.644i 1.30380 0.752750i
\(326\) 59.3553 + 102.806i 0.182072 + 0.315357i
\(327\) −166.588 96.1798i −0.509444 0.294128i
\(328\) 155.086i 0.472824i
\(329\) 80.8751 289.961i 0.245821 0.881341i
\(330\) 21.0883 0.0639040
\(331\) 54.3162 94.0785i 0.164097 0.284225i −0.772237 0.635335i \(-0.780862\pi\)
0.936334 + 0.351110i \(0.114196\pi\)
\(332\) −191.220 + 110.401i −0.575965 + 0.332533i
\(333\) −41.9558 72.6697i −0.125994 0.218227i
\(334\) 156.302 + 90.2407i 0.467969 + 0.270182i
\(335\) 6.30911i 0.0188332i
\(336\) −46.9706 + 12.0734i −0.139793 + 0.0359326i
\(337\) 441.735 1.31079 0.655393 0.755288i \(-0.272503\pi\)
0.655393 + 0.755288i \(0.272503\pi\)
\(338\) −202.149 + 350.133i −0.598075 + 1.03590i
\(339\) 152.095 87.8124i 0.448659 0.259033i
\(340\) −12.8528 22.2617i −0.0378024 0.0654757i
\(341\) −229.368 132.425i −0.672632 0.388344i
\(342\) 30.6547i 0.0896336i
\(343\) −235.000 249.848i −0.685131 0.728420i
\(344\) 4.20101 0.0122122
\(345\) −46.5442 + 80.6168i −0.134911 + 0.233672i
\(346\) −175.103 + 101.096i −0.506077 + 0.292184i
\(347\) −17.0955 29.6102i −0.0492664 0.0853320i 0.840341 0.542059i \(-0.182355\pi\)
−0.889607 + 0.456727i \(0.849022\pi\)
\(348\) 101.823 + 58.7878i 0.292596 + 0.168930i
\(349\) 221.787i 0.635493i −0.948176 0.317746i \(-0.897074\pi\)
0.948176 0.317746i \(-0.102926\pi\)
\(350\) −56.5376 219.956i −0.161536 0.628444i
\(351\) 110.823 0.315736
\(352\) 16.9706 29.3939i 0.0482118 0.0835053i
\(353\) 387.448 223.693i 1.09759 0.633692i 0.162000 0.986791i \(-0.448206\pi\)
0.935586 + 0.353099i \(0.114872\pi\)
\(354\) 50.4853 + 87.4431i 0.142614 + 0.247014i
\(355\) −170.735 98.5739i −0.480944 0.277673i
\(356\) 41.5692i 0.116767i
\(357\) −104.610 29.1776i −0.293026 0.0817299i
\(358\) −239.397 −0.668707
\(359\) −145.882 + 252.675i −0.406357 + 0.703831i −0.994478 0.104941i \(-0.966534\pi\)
0.588121 + 0.808773i \(0.299868\pi\)
\(360\) 10.5442 6.08767i 0.0292893 0.0169102i
\(361\) −154.397 267.423i −0.427692 0.740785i
\(362\) 257.158 + 148.470i 0.710381 + 0.410139i
\(363\) 147.224i 0.405577i
\(364\) 208.971 + 213.280i 0.574095 + 0.585933i
\(365\) −113.251 −0.310276
\(366\) −1.45584 + 2.52160i −0.00397772 + 0.00688961i
\(367\) −363.169 + 209.676i −0.989561 + 0.571324i −0.905143 0.425107i \(-0.860237\pi\)
−0.0844183 + 0.996430i \(0.526903\pi\)
\(368\) 74.9117 + 129.751i 0.203564 + 0.352584i
\(369\) 142.456 + 82.2469i 0.386059 + 0.222891i
\(370\) 56.7585i 0.153401i
\(371\) −427.279 + 418.646i −1.15170 + 1.12843i
\(372\) −152.912 −0.411053
\(373\) −15.6909 + 27.1775i −0.0420668 + 0.0728618i −0.886292 0.463127i \(-0.846728\pi\)
0.844225 + 0.535988i \(0.180061\pi\)
\(374\) 65.8234 38.0031i 0.175998 0.101613i
\(375\) 59.5736 + 103.184i 0.158863 + 0.275159i
\(376\) 105.338 + 60.8170i 0.280155 + 0.161747i
\(377\) 723.895i 1.92015i
\(378\) 13.8198 49.5481i 0.0365603 0.131080i
\(379\) 206.779 0.545590 0.272795 0.962072i \(-0.412052\pi\)
0.272795 + 0.962072i \(0.412052\pi\)
\(380\) 10.3675 17.9571i 0.0272830 0.0472555i
\(381\) 123.860 71.5108i 0.325093 0.187692i
\(382\) 47.0955 + 81.5717i 0.123287 + 0.213539i
\(383\) −431.772 249.283i −1.12734 0.650871i −0.184076 0.982912i \(-0.558929\pi\)
−0.943265 + 0.332041i \(0.892263\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −58.3675 + 15.0029i −0.151604 + 0.0389685i
\(386\) 13.8507 0.0358827
\(387\) −2.22792 + 3.85887i −0.00575690 + 0.00997125i
\(388\) 19.0294 10.9867i 0.0490449 0.0283161i
\(389\) 324.213 + 561.554i 0.833453 + 1.44358i 0.895284 + 0.445496i \(0.146973\pi\)
−0.0618308 + 0.998087i \(0.519694\pi\)
\(390\) −64.9188 37.4809i −0.166459 0.0961049i
\(391\) 335.508i 0.858077i
\(392\) 121.414 66.8325i 0.309730 0.170491i
\(393\) −104.912 −0.266951
\(394\) −188.912 + 327.205i −0.479471 + 0.830469i
\(395\) 122.199 70.5516i 0.309364 0.178612i
\(396\) 18.0000 + 31.1769i 0.0454545 + 0.0787296i
\(397\) 65.6026 + 37.8757i 0.165246 + 0.0954047i 0.580342 0.814373i \(-0.302919\pi\)
−0.415096 + 0.909777i \(0.636252\pi\)
\(398\) 185.176i 0.465268i
\(399\) −21.8087 84.8450i −0.0546583 0.212644i
\(400\) 91.7645 0.229411
\(401\) 282.125 488.655i 0.703553 1.21859i −0.263658 0.964616i \(-0.584929\pi\)
0.967211 0.253974i \(-0.0817377\pi\)
\(402\) −9.32738 + 5.38517i −0.0232024 + 0.0133959i
\(403\) 470.727 + 815.324i 1.16806 + 2.02314i
\(404\) 185.647 + 107.183i 0.459522 + 0.265305i
\(405\) 12.9139i 0.0318862i
\(406\) −323.647 90.2706i −0.797159 0.222341i
\(407\) −167.823 −0.412342
\(408\) 21.9411 38.0031i 0.0537773 0.0931450i
\(409\) −309.559 + 178.724i −0.756868 + 0.436978i −0.828170 0.560477i \(-0.810618\pi\)
0.0713023 + 0.997455i \(0.477284\pi\)
\(410\) −55.6325 96.3583i −0.135689 0.235020i
\(411\) −100.544 58.0492i −0.244633 0.141239i
\(412\) 210.410i 0.510704i
\(413\) −201.941 206.105i −0.488962 0.499044i
\(414\) −158.912 −0.383845
\(415\) −79.2061 + 137.189i −0.190858 + 0.330576i
\(416\) −104.485 + 60.3246i −0.251167 + 0.145011i
\(417\) −79.2868 137.329i −0.190136 0.329326i
\(418\) 53.0955 + 30.6547i 0.127023 + 0.0733365i
\(419\) 502.175i 1.19851i 0.800559 + 0.599254i \(0.204536\pi\)
−0.800559 + 0.599254i \(0.795464\pi\)
\(420\) −24.8528 + 24.3507i −0.0591734 + 0.0579778i
\(421\) 33.7939 0.0802706 0.0401353 0.999194i \(-0.487221\pi\)
0.0401353 + 0.999194i \(0.487221\pi\)
\(422\) −16.3259 + 28.2773i −0.0386870 + 0.0670078i
\(423\) −111.728 + 64.5061i −0.264132 + 0.152497i
\(424\) −120.853 209.323i −0.285030 0.493687i
\(425\) 177.963 + 102.747i 0.418735 + 0.241757i
\(426\) 336.552i 0.790029i
\(427\) 2.23550 8.01492i 0.00523536 0.0187703i
\(428\) 237.088 0.553945
\(429\) 110.823 191.952i 0.258330 0.447440i
\(430\) 2.61017 1.50698i 0.00607017 0.00350461i
\(431\) −251.860 436.234i −0.584362 1.01214i −0.994955 0.100326i \(-0.968012\pi\)
0.410593 0.911819i \(-0.365322\pi\)
\(432\) 18.0000 + 10.3923i 0.0416667 + 0.0240563i
\(433\) 837.548i 1.93429i 0.254224 + 0.967145i \(0.418180\pi\)
−0.254224 + 0.967145i \(0.581820\pi\)
\(434\) 423.224 108.786i 0.975170 0.250659i
\(435\) 84.3532 0.193916
\(436\) −111.059 + 192.360i −0.254722 + 0.441192i
\(437\) −234.375 + 135.316i −0.536326 + 0.309648i
\(438\) −96.6655 167.430i −0.220697 0.382259i
\(439\) −164.558 95.0079i −0.374848 0.216419i 0.300726 0.953711i \(-0.402771\pi\)
−0.675575 + 0.737292i \(0.736104\pi\)
\(440\) 24.3507i 0.0553425i
\(441\) −3.00000 + 146.969i −0.00680272 + 0.333264i
\(442\) −270.177 −0.611259
\(443\) 84.7279 146.753i 0.191259 0.331271i −0.754408 0.656405i \(-0.772076\pi\)
0.945668 + 0.325134i \(0.105409\pi\)
\(444\) −83.9117 + 48.4464i −0.188990 + 0.109114i
\(445\) 14.9117 + 25.8278i 0.0335094 + 0.0580400i
\(446\) −280.014 161.666i −0.627835 0.362481i
\(447\) 140.449i 0.314204i
\(448\) 13.9411 + 54.2369i 0.0311186 + 0.121065i
\(449\) 18.1035 0.0403195 0.0201598 0.999797i \(-0.493583\pi\)
0.0201598 + 0.999797i \(0.493583\pi\)
\(450\) −48.6655 + 84.2911i −0.108146 + 0.187314i
\(451\) 284.912 164.494i 0.631733 0.364731i
\(452\) −101.397 175.625i −0.224330 0.388550i
\(453\) 76.8091 + 44.3457i 0.169556 + 0.0978935i
\(454\) 92.7922i 0.204388i
\(455\) 206.345 + 57.5532i 0.453506 + 0.126491i
\(456\) 35.3970 0.0776249
\(457\) 164.412 284.769i 0.359763 0.623128i −0.628158 0.778086i \(-0.716191\pi\)
0.987921 + 0.154958i \(0.0495242\pi\)
\(458\) 114.489 66.1002i 0.249976 0.144324i
\(459\) 23.2721 + 40.3084i 0.0507017 + 0.0878179i
\(460\) 93.0883 + 53.7446i 0.202366 + 0.116836i
\(461\) 794.331i 1.72306i −0.507706 0.861530i \(-0.669506\pi\)
0.507706 0.861530i \(-0.330494\pi\)
\(462\) −72.0000 73.4847i −0.155844 0.159058i
\(463\) −403.396 −0.871266 −0.435633 0.900124i \(-0.643475\pi\)
−0.435633 + 0.900124i \(0.643475\pi\)
\(464\) 67.8823 117.576i 0.146298 0.253395i
\(465\) −95.0071 + 54.8524i −0.204316 + 0.117962i
\(466\) −167.948 290.895i −0.360404 0.624238i
\(467\) −2.44870 1.41376i −0.00524347 0.00302732i 0.497376 0.867535i \(-0.334297\pi\)
−0.502619 + 0.864508i \(0.667630\pi\)
\(468\) 127.968i 0.273435i
\(469\) 21.9848 21.5407i 0.0468760 0.0459289i
\(470\) 87.2649 0.185670
\(471\) 162.000 280.592i 0.343949 0.595737i
\(472\) 100.971 58.2954i 0.213921 0.123507i
\(473\) 4.45584 + 7.71775i 0.00942039 + 0.0163166i
\(474\) 208.607 + 120.439i 0.440098 + 0.254091i
\(475\) 165.758i 0.348965i
\(476\) −33.6913 + 120.793i −0.0707801 + 0.253768i
\(477\) 256.368 0.537458
\(478\) 259.404 449.301i 0.542686 0.939960i
\(479\) 328.669 189.757i 0.686157 0.396153i −0.116014 0.993248i \(-0.537012\pi\)
0.802171 + 0.597095i \(0.203678\pi\)
\(480\) −7.02944 12.1753i −0.0146447 0.0253653i
\(481\) 516.632 + 298.278i 1.07408 + 0.620120i
\(482\) 595.418i 1.23531i
\(483\) 439.831 113.055i 0.910622 0.234067i
\(484\) −170.000 −0.351240
\(485\) 7.88225 13.6525i 0.0162521 0.0281494i
\(486\) −19.0919 + 11.0227i −0.0392837 + 0.0226805i
\(487\) −287.757 498.410i −0.590877 1.02343i −0.994115 0.108333i \(-0.965449\pi\)
0.403238 0.915095i \(-0.367885\pi\)
\(488\) 2.91169 + 1.68106i 0.00596657 + 0.00344480i
\(489\) 145.390i 0.297322i
\(490\) 51.4630 85.0781i 0.105027 0.173629i
\(491\) 238.441 0.485623 0.242811 0.970074i \(-0.421930\pi\)
0.242811 + 0.970074i \(0.421930\pi\)
\(492\) 94.9706 164.494i 0.193030 0.334337i
\(493\) 263.294 152.013i 0.534064 0.308342i
\(494\) −108.967 188.736i −0.220581 0.382057i
\(495\) 22.3675 + 12.9139i 0.0451869 + 0.0260887i
\(496\) 176.567i 0.355982i
\(497\) 239.434 + 931.499i 0.481758 + 1.87424i
\(498\) −270.426 −0.543025
\(499\) 143.287 248.180i 0.287148 0.497355i −0.685980 0.727620i \(-0.740626\pi\)
0.973128 + 0.230266i \(0.0739595\pi\)
\(500\) 119.147 68.7897i 0.238294 0.137579i
\(501\) 110.522 + 191.429i 0.220603 + 0.382095i
\(502\) 179.574 + 103.677i 0.357716 + 0.206528i
\(503\) 25.4374i 0.0505714i 0.999680 + 0.0252857i \(0.00804954\pi\)
−0.999680 + 0.0252857i \(0.991950\pi\)
\(504\) −57.2132 15.9577i −0.113518 0.0316622i
\(505\) 153.795 0.304544
\(506\) −158.912 + 275.243i −0.314055 + 0.543959i
\(507\) −428.823 + 247.581i −0.845805 + 0.488326i
\(508\) −82.5736 143.022i −0.162546 0.281539i
\(509\) −697.889 402.926i −1.37110 0.791603i −0.380031 0.924974i \(-0.624087\pi\)
−0.991066 + 0.133370i \(0.957420\pi\)
\(510\) 31.4828i 0.0617310i
\(511\) 386.662 + 394.635i 0.756677 + 0.772280i
\(512\) −22.6274 −0.0441942
\(513\) −18.7721 + 32.5142i −0.0365927 + 0.0633805i
\(514\) 30.7279 17.7408i 0.0597819 0.0345151i
\(515\) −75.4781 130.732i −0.146559 0.253848i
\(516\) 4.45584 + 2.57258i 0.00863536 + 0.00498563i
\(517\) 258.025i 0.499080i
\(518\) 197.782 193.786i 0.381818 0.374104i
\(519\) −247.632 −0.477134
\(520\) −43.2792 + 74.9618i −0.0832293 + 0.144157i
\(521\) −661.706 + 382.036i −1.27007 + 0.733274i −0.975001 0.222202i \(-0.928676\pi\)
−0.295068 + 0.955476i \(0.595342\pi\)
\(522\) 72.0000 + 124.708i 0.137931 + 0.238904i
\(523\) −153.096 88.3900i −0.292726 0.169006i 0.346444 0.938071i \(-0.387389\pi\)
−0.639171 + 0.769065i \(0.720722\pi\)
\(524\) 121.142i 0.231186i
\(525\) 74.7275 267.920i 0.142338 0.510324i
\(526\) 128.235 0.243794
\(527\) −197.698 + 342.424i −0.375139 + 0.649761i
\(528\) 36.0000 20.7846i 0.0681818 0.0393648i
\(529\) −436.970 756.854i −0.826030 1.43073i
\(530\) −150.177 86.7045i −0.283352 0.163593i
\(531\) 123.663i 0.232887i
\(532\) −97.9706 + 25.1825i −0.184155 + 0.0473355i
\(533\) −1169.44 −2.19407
\(534\) −25.4558 + 44.0908i −0.0476701 + 0.0825671i
\(535\) 147.308 85.0482i 0.275342 0.158969i
\(536\) 6.21825 + 10.7703i 0.0116012 + 0.0200939i
\(537\) −253.919 146.600i −0.472847 0.272998i
\(538\) 96.7312i 0.179798i
\(539\) 251.558 + 152.166i 0.466713 + 0.282311i
\(540\) 14.9117 0.0276142
\(541\) −8.58831 + 14.8754i −0.0158749 + 0.0274961i −0.873854 0.486189i \(-0.838387\pi\)
0.857979 + 0.513685i \(0.171720\pi\)
\(542\) −151.279 + 87.3411i −0.279113 + 0.161146i
\(543\) 181.838 + 314.953i 0.334877 + 0.580024i
\(544\) −43.8823 25.3354i −0.0806659 0.0465725i
\(545\) 159.356i 0.292396i
\(546\) 91.0402 + 354.185i 0.166740 + 0.648691i
\(547\) 212.676 0.388805 0.194402 0.980922i \(-0.437723\pi\)
0.194402 + 0.980922i \(0.437723\pi\)
\(548\) −67.0294 + 116.098i −0.122316 + 0.211858i
\(549\) −3.08831 + 1.78304i −0.00562534 + 0.00324779i
\(550\) 97.3310 + 168.582i 0.176965 + 0.306513i
\(551\) 212.382 + 122.619i 0.385448 + 0.222538i
\(552\) 183.495i 0.332419i
\(553\) −663.058 184.938i −1.19902 0.334427i
\(554\) 385.914 0.696595
\(555\) −34.7574 + 60.2015i −0.0626259 + 0.108471i
\(556\) −158.574 + 91.5525i −0.285204 + 0.164663i
\(557\) 440.823 + 763.528i 0.791424 + 1.37079i 0.925085 + 0.379760i \(0.123993\pi\)
−0.133661 + 0.991027i \(0.542673\pi\)
\(558\) −162.187 93.6389i −0.290658 0.167812i
\(559\) 31.6780i 0.0566691i
\(560\) 28.1177 + 28.6976i 0.0502103 + 0.0512456i
\(561\) 93.0883 0.165933
\(562\) 94.1177 163.017i 0.167469 0.290065i
\(563\) 664.301 383.534i 1.17993 0.681233i 0.223932 0.974605i \(-0.428111\pi\)
0.955998 + 0.293372i \(0.0947774\pi\)
\(564\) 74.4853 + 129.012i 0.132066 + 0.228745i
\(565\) −126.000 72.7461i −0.223009 0.128754i
\(566\) 182.090i 0.321714i
\(567\) 45.0000 44.0908i 0.0793651 0.0777616i
\(568\) −388.617 −0.684185
\(569\) 14.6468 25.3689i 0.0257412 0.0445851i −0.852868 0.522127i \(-0.825139\pi\)
0.878609 + 0.477542i \(0.158472\pi\)
\(570\) 21.9929 12.6976i 0.0385840 0.0222765i
\(571\) −482.521 835.752i −0.845046 1.46366i −0.885581 0.464485i \(-0.846239\pi\)
0.0405347 0.999178i \(-0.487094\pi\)
\(572\) −221.647 127.968i −0.387494 0.223720i
\(573\) 115.360i 0.201326i
\(574\) −145.831 + 522.846i −0.254060 + 0.910881i
\(575\) −859.279 −1.49440
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) 227.883 131.568i 0.394944 0.228021i −0.289356 0.957222i \(-0.593441\pi\)
0.684300 + 0.729201i \(0.260108\pi\)
\(578\) 147.619 + 255.683i 0.255396 + 0.442359i
\(579\) 14.6909 + 8.48180i 0.0253729 + 0.0146491i
\(580\) 97.4027i 0.167936i
\(581\) 748.477 192.389i 1.28826 0.331135i
\(582\) 26.9117 0.0462400
\(583\) 256.368 444.042i 0.439738 0.761649i
\(584\) −193.331 + 111.620i −0.331046 + 0.191130i
\(585\) −45.9045 79.5090i −0.0784693 0.135913i
\(586\) 378.426 + 218.485i 0.645779 + 0.372841i
\(587\) 436.477i 0.743572i −0.928318 0.371786i \(-0.878746\pi\)
0.928318 0.371786i \(-0.121254\pi\)
\(588\) 169.706 + 3.46410i 0.288615 + 0.00589133i
\(589\) −318.941 −0.541496
\(590\) 41.8234 72.4402i 0.0708871 0.122780i
\(591\) −400.742 + 231.369i −0.678075 + 0.391487i
\(592\) 55.9411 + 96.8929i 0.0944951 + 0.163670i
\(593\) 603.603 + 348.490i 1.01788 + 0.587673i 0.913489 0.406863i \(-0.133377\pi\)
0.104391 + 0.994536i \(0.466711\pi\)
\(594\) 44.0908i 0.0742270i
\(595\) 22.3978 + 87.1372i 0.0376434 + 0.146449i
\(596\) 162.177 0.272108
\(597\) −113.397 + 196.409i −0.189945 + 0.328994i
\(598\) 978.396 564.877i 1.63611 0.944611i
\(599\) −199.206 345.035i −0.332564 0.576018i 0.650450 0.759549i \(-0.274581\pi\)
−0.983014 + 0.183531i \(0.941247\pi\)
\(600\) 97.3310 + 56.1941i 0.162218 + 0.0936568i
\(601\) 36.1691i 0.0601816i −0.999547 0.0300908i \(-0.990420\pi\)
0.999547 0.0300908i \(-0.00957964\pi\)
\(602\) −14.1630 3.95029i −0.0235265 0.00656194i
\(603\) −13.1909 −0.0218755
\(604\) 51.2061 88.6915i 0.0847782 0.146840i
\(605\) −105.624 + 60.9823i −0.174586 + 0.100797i
\(606\) 131.272 + 227.370i 0.216621 + 0.375198i
\(607\) 27.3457 + 15.7880i 0.0450505 + 0.0260099i 0.522356 0.852727i \(-0.325053\pi\)
−0.477306 + 0.878737i \(0.658387\pi\)
\(608\) 40.8729i 0.0672252i
\(609\) −288.000 293.939i −0.472906 0.482658i
\(610\) 2.41212 0.00395430
\(611\) 458.595 794.310i 0.750565 1.30002i
\(612\) 46.5442 26.8723i 0.0760525 0.0439090i
\(613\) 204.632 + 354.434i 0.333821 + 0.578195i 0.983258 0.182220i \(-0.0583285\pi\)
−0.649436 + 0.760416i \(0.724995\pi\)
\(614\) −742.305 428.570i −1.20897 0.697997i
\(615\) 136.271i 0.221579i
\(616\) −84.8528 + 83.1384i −0.137748 + 0.134965i
\(617\) 1227.38 1.98927 0.994636 0.103436i \(-0.0329837\pi\)
0.994636 + 0.103436i \(0.0329837\pi\)
\(618\) 128.849 223.173i 0.208494 0.361122i
\(619\) 412.022 237.881i 0.665625 0.384299i −0.128792 0.991672i \(-0.541110\pi\)
0.794417 + 0.607373i \(0.207777\pi\)
\(620\) 63.3381 + 109.705i 0.102158 + 0.176943i
\(621\) −168.551 97.3131i −0.271419 0.156704i
\(622\) 287.478i 0.462184i
\(623\) 39.0883 140.143i 0.0627421 0.224949i
\(624\) −147.765 −0.236802
\(625\) −237.412 + 411.209i −0.379859 + 0.657935i
\(626\) −496.805 + 286.830i −0.793618 + 0.458195i
\(627\) 37.5442 + 65.0284i 0.0598790 + 0.103714i
\(628\) −324.000 187.061i −0.515924 0.297869i
\(629\) 250.544i 0.398322i
\(630\) −41.2721 + 10.6086i −0.0655112 + 0.0168391i
\(631\) −54.9420 −0.0870713 −0.0435357 0.999052i \(-0.513862\pi\)
−0.0435357 + 0.999052i \(0.513862\pi\)
\(632\) 139.071 240.878i 0.220049 0.381136i
\(633\) −34.6325 + 19.9951i −0.0547116 + 0.0315878i
\(634\) −18.4264 31.9155i −0.0290637 0.0503399i
\(635\) −102.609 59.2415i −0.161589 0.0932937i
\(636\) 296.028i 0.465452i
\(637\) −503.956 915.533i −0.791139 1.43726i
\(638\) 288.000 0.451411
\(639\) 206.095 356.968i 0.322528 0.558635i
\(640\) −14.0589 + 8.11689i −0.0219670 + 0.0126826i
\(641\) 114.551 + 198.409i 0.178707 + 0.309530i 0.941438 0.337186i \(-0.109475\pi\)
−0.762731 + 0.646716i \(0.776142\pi\)
\(642\) 251.470 + 145.186i 0.391698 + 0.226147i
\(643\) 854.640i 1.32914i 0.747224 + 0.664572i \(0.231386\pi\)
−0.747224 + 0.664572i \(0.768614\pi\)
\(644\) −130.544 507.873i −0.202708 0.788622i
\(645\) 3.69134 0.00572301
\(646\) 45.7645 79.2664i 0.0708429 0.122703i
\(647\) 868.632 501.505i 1.34255 0.775124i 0.355372 0.934725i \(-0.384354\pi\)
0.987182 + 0.159601i \(0.0510207\pi\)
\(648\) 12.7279 + 22.0454i 0.0196419 + 0.0340207i
\(649\) 214.191 + 123.663i 0.330032 + 0.190544i
\(650\) 691.957i 1.06455i
\(651\) 515.514 + 143.786i 0.791881 + 0.220869i
\(652\) 167.882 0.257488
\(653\) −635.382 + 1100.51i −0.973020 + 1.68532i −0.286698 + 0.958021i \(0.592558\pi\)
−0.686321 + 0.727299i \(0.740776\pi\)
\(654\) −235.591 + 136.019i −0.360232 + 0.207980i
\(655\) 43.4558 + 75.2677i 0.0663448 + 0.114913i
\(656\) −189.941 109.663i −0.289544 0.167169i
\(657\) 236.781i 0.360397i
\(658\) −297.941 304.085i −0.452798 0.462135i
\(659\) −783.308 −1.18863 −0.594315 0.804232i \(-0.702577\pi\)
−0.594315 + 0.804232i \(0.702577\pi\)
\(660\) 14.9117 25.8278i 0.0225935 0.0391330i
\(661\) 72.5589 41.8919i 0.109771 0.0633765i −0.444109 0.895973i \(-0.646480\pi\)
0.553881 + 0.832596i \(0.313146\pi\)
\(662\) −76.8148 133.047i −0.116034 0.200977i
\(663\) −286.566 165.449i −0.432226 0.249546i
\(664\) 312.262i 0.470273i
\(665\) −51.8377 + 50.7903i −0.0779514 + 0.0763764i
\(666\) −118.669 −0.178182
\(667\) −635.647 + 1100.97i −0.952994 + 1.65063i
\(668\) 221.044 127.620i 0.330904 0.191047i
\(669\) −198.000 342.946i −0.295964 0.512625i
\(670\) 7.72706 + 4.46122i 0.0115329 + 0.00665853i
\(671\) 7.13215i 0.0106291i
\(672\) −18.4264 + 66.0641i −0.0274202 + 0.0983097i
\(673\) 415.676 0.617647 0.308823 0.951119i \(-0.400065\pi\)
0.308823 + 0.951119i \(0.400065\pi\)
\(674\) 312.354 541.013i 0.463433 0.802690i
\(675\) −103.235 + 59.6028i −0.152941 + 0.0883004i
\(676\) 285.882 + 495.163i 0.422903 + 0.732489i
\(677\) 685.279 + 395.646i 1.01223 + 0.584411i 0.911844 0.410538i \(-0.134659\pi\)
0.100386 + 0.994949i \(0.467992\pi\)
\(678\) 248.371i 0.366329i
\(679\) −74.4853 + 19.1458i −0.109698 + 0.0281970i
\(680\) −36.3532 −0.0534607
\(681\) 56.8234 98.4210i 0.0834411 0.144524i
\(682\) −324.375 + 187.278i −0.475623 + 0.274601i
\(683\) 164.080 + 284.195i 0.240235 + 0.416099i 0.960781 0.277308i \(-0.0894423\pi\)
−0.720546 + 0.693407i \(0.756109\pi\)
\(684\) 37.5442 + 21.6761i 0.0548891 + 0.0316902i
\(685\) 96.1791i 0.140407i
\(686\) −472.170 + 111.146i −0.688295 + 0.162020i
\(687\) 161.912 0.235679
\(688\) 2.97056 5.14517i 0.00431768 0.00747844i
\(689\) −1578.42 + 911.300i −2.29088 + 1.32264i
\(690\) 65.8234 + 114.009i 0.0953962 + 0.165231i
\(691\) 875.182 + 505.287i 1.26654 + 0.731240i 0.974333 0.225113i \(-0.0722753\pi\)
0.292212 + 0.956353i \(0.405609\pi\)
\(692\) 285.941i 0.413210i
\(693\) −31.3675 122.033i −0.0452634 0.176094i
\(694\) −48.3532 −0.0696733
\(695\) −65.6833 + 113.767i −0.0945084 + 0.163693i
\(696\) 144.000 83.1384i 0.206897 0.119452i
\(697\) −245.574 425.346i −0.352329 0.610252i
\(698\) −271.632 156.827i −0.389158 0.224681i
\(699\) 411.388i 0.588537i
\(700\) −309.368 86.2879i −0.441954 0.123268i
\(701\) −0.103464 −0.000147594 −7.37972e−5 1.00000i \(-0.500023\pi\)
−7.37972e−5 1.00000i \(0.500023\pi\)
\(702\) 78.3640 135.730i 0.111630 0.193348i
\(703\) −175.022 + 101.049i −0.248964 + 0.143740i
\(704\) −24.0000 41.5692i −0.0340909 0.0590472i
\(705\) 92.5584 + 53.4386i 0.131289 + 0.0757995i
\(706\) 632.700i 0.896175i
\(707\) −525.088 535.916i −0.742699 0.758014i
\(708\) 142.794 0.201686
\(709\) −602.588 + 1043.71i −0.849912 + 1.47209i 0.0313734 + 0.999508i \(0.490012\pi\)
−0.881286 + 0.472584i \(0.843321\pi\)
\(710\) −241.456 + 139.405i −0.340079 + 0.196345i
\(711\) 147.507 + 255.490i 0.207464 + 0.359339i
\(712\) 50.9117 + 29.3939i 0.0715052 + 0.0412835i
\(713\) 1653.37i 2.31889i
\(714\) −109.706 + 107.489i −0.153649 + 0.150545i
\(715\) −183.618 −0.256809
\(716\) −169.279 + 293.200i −0.236423 + 0.409498i
\(717\) 550.279 317.704i 0.767475 0.443102i
\(718\) 206.309 + 357.337i 0.287338 + 0.497684i
\(719\) 850.925 + 491.282i 1.18348 + 0.683285i 0.956818 0.290688i \(-0.0938840\pi\)
0.226666 + 0.973973i \(0.427217\pi\)
\(720\) 17.2185i 0.0239146i
\(721\) −197.852 + 709.359i −0.274414 + 0.983855i
\(722\) −436.701 −0.604848
\(723\) −364.617 + 631.536i −0.504312 + 0.873493i
\(724\) 363.676 209.969i 0.502315 0.290012i
\(725\) 389.324 + 674.329i 0.536998 + 0.930108i
\(726\) −180.312 104.103i −0.248364 0.143393i
\(727\) 630.440i 0.867181i 0.901110 + 0.433590i \(0.142753\pi\)
−0.901110 + 0.433590i \(0.857247\pi\)
\(728\) 408.978 105.124i 0.561783 0.144401i
\(729\) −27.0000 −0.0370370
\(730\) −80.0803 + 138.703i −0.109699 + 0.190004i
\(731\) 11.5219 6.65215i 0.0157618 0.00910007i
\(732\) 2.05887 + 3.56608i 0.00281267 + 0.00487169i
\(733\) 258.486 + 149.237i 0.352641 + 0.203597i 0.665848 0.746088i \(-0.268070\pi\)
−0.313207 + 0.949685i \(0.601403\pi\)
\(734\) 593.053i 0.807974i
\(735\) 106.684 58.7244i 0.145149 0.0798971i
\(736\) 211.882 0.287883
\(737\) −13.1909 + 22.8473i −0.0178981 + 0.0310004i
\(738\) 201.463 116.315i 0.272985 0.157608i
\(739\) −172.684 299.097i −0.233672 0.404732i 0.725214 0.688524i \(-0.241741\pi\)
−0.958886 + 0.283792i \(0.908408\pi\)
\(740\) 69.5147 + 40.1343i 0.0939388 + 0.0542356i
\(741\) 266.914i 0.360207i
\(742\) 210.603 + 819.336i 0.283832 + 1.10423i
\(743\) 683.616 0.920076 0.460038 0.887899i \(-0.347836\pi\)
0.460038 + 0.887899i \(0.347836\pi\)
\(744\) −108.125 + 187.278i −0.145329 + 0.251717i
\(745\) 100.764 58.1759i 0.135253 0.0780885i
\(746\) 22.1903 + 38.4347i 0.0297457 + 0.0515211i
\(747\) −286.831 165.602i −0.383977 0.221689i
\(748\) 107.489i 0.143702i
\(749\) −799.301 222.939i −1.06716 0.297648i
\(750\) 168.500 0.224666
\(751\) 289.169 500.855i 0.385045 0.666918i −0.606730 0.794908i \(-0.707519\pi\)
0.991775 + 0.127990i \(0.0408525\pi\)
\(752\) 148.971 86.0082i 0.198099 0.114373i
\(753\) 126.978 + 219.932i 0.168629 + 0.292074i
\(754\) −886.587 511.871i −1.17584 0.678874i
\(755\) 73.4744i 0.0973171i
\(756\) −50.9117 51.9615i −0.0673435 0.0687322i
\(757\) 1204.82 1.59158 0.795788 0.605576i \(-0.207057\pi\)
0.795788 + 0.605576i \(0.207057\pi\)
\(758\) 146.215 253.251i 0.192895 0.334105i
\(759\) −337.103 + 194.626i −0.444140 + 0.256425i
\(760\) −14.6619 25.3952i −0.0192920 0.0334147i
\(761\) −202.669 117.011i −0.266319 0.153760i 0.360894 0.932607i \(-0.382471\pi\)
−0.627214 + 0.778847i \(0.715805\pi\)
\(762\) 202.263i 0.265437i
\(763\) 555.294 544.075i 0.727778 0.713074i
\(764\) 133.206 0.174353
\(765\) 19.2792 33.3926i 0.0252016 0.0436504i
\(766\) −610.617 + 352.540i −0.797151 + 0.460235i
\(767\) −439.581 761.376i −0.573117 0.992668i
\(768\) −24.0000 13.8564i −0.0312500 0.0180422i
\(769\) 1290.16i 1.67771i −0.544358 0.838853i \(-0.683226\pi\)
0.544358 0.838853i \(-0.316774\pi\)
\(770\) −22.8974 + 82.0940i −0.0297369 + 0.106616i
\(771\) 43.4558 0.0563630
\(772\) 9.79394 16.9636i 0.0126864 0.0219736i
\(773\) 345.646 199.559i 0.447149 0.258161i −0.259477 0.965749i \(-0.583550\pi\)
0.706625 +