Properties

Label 731.2.j.a.135.5
Level 731
Weight 2
Character 731.135
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 135.5
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.5

$q$-expansion

\(f(q)\) \(=\) \(q-2.51145 q^{2} +(-1.76122 - 1.01684i) q^{3} +4.30737 q^{4} +(1.18626 + 0.684888i) q^{5} +(4.42321 + 2.55374i) q^{6} +(3.84346 - 2.21902i) q^{7} -5.79485 q^{8} +(0.567928 + 0.983681i) q^{9} +O(q^{10})\) \(q-2.51145 q^{2} +(-1.76122 - 1.01684i) q^{3} +4.30737 q^{4} +(1.18626 + 0.684888i) q^{5} +(4.42321 + 2.55374i) q^{6} +(3.84346 - 2.21902i) q^{7} -5.79485 q^{8} +(0.567928 + 0.983681i) q^{9} +(-2.97923 - 1.72006i) q^{10} -5.71903i q^{11} +(-7.58623 - 4.37991i) q^{12} +(-0.967741 - 1.67618i) q^{13} +(-9.65264 + 5.57296i) q^{14} +(-1.39284 - 2.41247i) q^{15} +5.93872 q^{16} +(2.78875 + 3.03692i) q^{17} +(-1.42632 - 2.47046i) q^{18} +(3.28388 - 5.68786i) q^{19} +(5.10967 + 2.95007i) q^{20} -9.02556 q^{21} +14.3631i q^{22} +(3.56220 + 2.05664i) q^{23} +(10.2060 + 5.89244i) q^{24} +(-1.56186 - 2.70522i) q^{25} +(2.43043 + 4.20963i) q^{26} +3.79107i q^{27} +(16.5552 - 9.55815i) q^{28} +(-1.60279 + 0.925373i) q^{29} +(3.49805 + 6.05880i) q^{30} +(7.10692 + 4.10318i) q^{31} -3.32510 q^{32} +(-5.81534 + 10.0725i) q^{33} +(-7.00381 - 7.62706i) q^{34} +6.07912 q^{35} +(2.44628 + 4.23708i) q^{36} +(-0.467527 - 0.269927i) q^{37} +(-8.24731 + 14.2848i) q^{38} +3.93615i q^{39} +(-6.87420 - 3.96882i) q^{40} +3.51693i q^{41} +22.6672 q^{42} +(4.98908 - 4.25548i) q^{43} -24.6340i q^{44} +1.55587i q^{45} +(-8.94629 - 5.16514i) q^{46} -10.7488 q^{47} +(-10.4594 - 6.03873i) q^{48} +(6.34810 - 10.9952i) q^{49} +(3.92253 + 6.79401i) q^{50} +(-1.82355 - 8.18439i) q^{51} +(-4.16842 - 7.21992i) q^{52} +(-2.08650 + 3.61392i) q^{53} -9.52108i q^{54} +(3.91689 - 6.78426i) q^{55} +(-22.2723 + 12.8589i) q^{56} +(-11.5673 + 6.67837i) q^{57} +(4.02533 - 2.32403i) q^{58} -6.09785 q^{59} +(-5.99949 - 10.3914i) q^{60} +(-1.58893 + 0.917368i) q^{61} +(-17.8487 - 10.3049i) q^{62} +(4.36561 + 2.52049i) q^{63} -3.52664 q^{64} -2.65118i q^{65} +(14.6049 - 25.2965i) q^{66} +(-7.10904 + 12.3132i) q^{67} +(12.0122 + 13.0811i) q^{68} +(-4.18255 - 7.24438i) q^{69} -15.2674 q^{70} +(4.83502 - 2.79150i) q^{71} +(-3.29106 - 5.70028i) q^{72} +(5.46456 - 3.15496i) q^{73} +(1.17417 + 0.677908i) q^{74} +6.35264i q^{75} +(14.1449 - 24.4997i) q^{76} +(-12.6906 - 21.9808i) q^{77} -9.88544i q^{78} +(11.6828 - 6.74508i) q^{79} +(7.04487 + 4.06736i) q^{80} +(5.55870 - 9.62795i) q^{81} -8.83259i q^{82} +(-4.69845 + 8.13795i) q^{83} -38.8765 q^{84} +(1.22824 + 5.51255i) q^{85} +(-12.5298 + 10.6874i) q^{86} +3.76383 q^{87} +33.1409i q^{88} +(8.13518 - 14.0905i) q^{89} -3.90748i q^{90} +(-7.43894 - 4.29487i) q^{91} +(15.3437 + 8.85871i) q^{92} +(-8.34456 - 14.4532i) q^{93} +26.9951 q^{94} +(7.79108 - 4.49818i) q^{95} +(5.85622 + 3.38109i) q^{96} +18.8175i q^{97} +(-15.9429 + 27.6140i) q^{98} +(5.62570 - 3.24800i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + O(q^{10}) \) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + 4q^{13} - 12q^{15} + 76q^{16} + 2q^{17} - 16q^{18} - 2q^{19} - 20q^{21} + 60q^{25} - 2q^{26} - 28q^{30} - 48q^{32} + 22q^{33} - 18q^{34} - 112q^{35} + 36q^{36} - 40q^{38} + 36q^{42} + 10q^{43} + 36q^{47} + 52q^{49} + 16q^{50} + 10q^{51} + 10q^{52} + 24q^{55} - 12q^{59} - 78q^{60} + 36q^{64} + 14q^{66} + 10q^{67} - q^{68} - 64q^{70} - 68q^{72} - 22q^{76} - 28q^{77} - 20q^{81} - 6q^{83} + 32q^{84} + 6q^{85} - 58q^{86} + 32q^{87} + 36q^{89} + 6q^{93} + 132q^{94} - 48q^{98} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.51145 −1.77586 −0.887931 0.459976i \(-0.847858\pi\)
−0.887931 + 0.459976i \(0.847858\pi\)
\(3\) −1.76122 1.01684i −1.01684 0.587073i −0.103653 0.994614i \(-0.533053\pi\)
−0.913187 + 0.407540i \(0.866387\pi\)
\(4\) 4.30737 2.15369
\(5\) 1.18626 + 0.684888i 0.530512 + 0.306291i 0.741225 0.671257i \(-0.234245\pi\)
−0.210713 + 0.977548i \(0.567579\pi\)
\(6\) 4.42321 + 2.55374i 1.80577 + 1.04256i
\(7\) 3.84346 2.21902i 1.45269 0.838711i 0.454056 0.890973i \(-0.349976\pi\)
0.998633 + 0.0522621i \(0.0166431\pi\)
\(8\) −5.79485 −2.04879
\(9\) 0.567928 + 0.983681i 0.189309 + 0.327894i
\(10\) −2.97923 1.72006i −0.942116 0.543931i
\(11\) 5.71903i 1.72435i −0.506608 0.862176i \(-0.669101\pi\)
0.506608 0.862176i \(-0.330899\pi\)
\(12\) −7.58623 4.37991i −2.18996 1.26437i
\(13\) −0.967741 1.67618i −0.268403 0.464888i 0.700047 0.714097i \(-0.253163\pi\)
−0.968450 + 0.249210i \(0.919829\pi\)
\(14\) −9.65264 + 5.57296i −2.57978 + 1.48944i
\(15\) −1.39284 2.41247i −0.359630 0.622898i
\(16\) 5.93872 1.48468
\(17\) 2.78875 + 3.03692i 0.676372 + 0.736560i
\(18\) −1.42632 2.47046i −0.336187 0.582294i
\(19\) 3.28388 5.68786i 0.753375 1.30488i −0.192803 0.981237i \(-0.561758\pi\)
0.946178 0.323646i \(-0.104909\pi\)
\(20\) 5.10967 + 2.95007i 1.14256 + 0.659655i
\(21\) −9.02556 −1.96954
\(22\) 14.3631i 3.06221i
\(23\) 3.56220 + 2.05664i 0.742771 + 0.428839i 0.823076 0.567932i \(-0.192256\pi\)
−0.0803052 + 0.996770i \(0.525590\pi\)
\(24\) 10.2060 + 5.89244i 2.08329 + 1.20279i
\(25\) −1.56186 2.70522i −0.312372 0.541043i
\(26\) 2.43043 + 4.20963i 0.476647 + 0.825577i
\(27\) 3.79107i 0.729592i
\(28\) 16.5552 9.55815i 3.12864 1.80632i
\(29\) −1.60279 + 0.925373i −0.297631 + 0.171837i −0.641378 0.767225i \(-0.721637\pi\)
0.343747 + 0.939062i \(0.388304\pi\)
\(30\) 3.49805 + 6.05880i 0.638654 + 1.10618i
\(31\) 7.10692 + 4.10318i 1.27644 + 0.736953i 0.976192 0.216908i \(-0.0695971\pi\)
0.300248 + 0.953861i \(0.402930\pi\)
\(32\) −3.32510 −0.587800
\(33\) −5.81534 + 10.0725i −1.01232 + 1.75339i
\(34\) −7.00381 7.62706i −1.20114 1.30803i
\(35\) 6.07912 1.02756
\(36\) 2.44628 + 4.23708i 0.407713 + 0.706180i
\(37\) −0.467527 0.269927i −0.0768610 0.0443757i 0.461077 0.887360i \(-0.347463\pi\)
−0.537938 + 0.842984i \(0.680797\pi\)
\(38\) −8.24731 + 14.2848i −1.33789 + 2.31729i
\(39\) 3.93615i 0.630289i
\(40\) −6.87420 3.96882i −1.08691 0.627526i
\(41\) 3.51693i 0.549253i 0.961551 + 0.274626i \(0.0885541\pi\)
−0.961551 + 0.274626i \(0.911446\pi\)
\(42\) 22.6672 3.49763
\(43\) 4.98908 4.25548i 0.760827 0.648955i
\(44\) 24.6340i 3.71372i
\(45\) 1.55587i 0.231935i
\(46\) −8.94629 5.16514i −1.31906 0.761559i
\(47\) −10.7488 −1.56788 −0.783939 0.620838i \(-0.786793\pi\)
−0.783939 + 0.620838i \(0.786793\pi\)
\(48\) −10.4594 6.03873i −1.50968 0.871616i
\(49\) 6.34810 10.9952i 0.906872 1.57075i
\(50\) 3.92253 + 6.79401i 0.554729 + 0.960819i
\(51\) −1.82355 8.18439i −0.255348 1.14604i
\(52\) −4.16842 7.21992i −0.578056 1.00122i
\(53\) −2.08650 + 3.61392i −0.286603 + 0.496411i −0.972997 0.230819i \(-0.925859\pi\)
0.686394 + 0.727230i \(0.259193\pi\)
\(54\) 9.52108i 1.29566i
\(55\) 3.91689 6.78426i 0.528154 0.914789i
\(56\) −22.2723 + 12.8589i −2.97626 + 1.71834i
\(57\) −11.5673 + 6.67837i −1.53212 + 0.884572i
\(58\) 4.02533 2.32403i 0.528552 0.305160i
\(59\) −6.09785 −0.793872 −0.396936 0.917846i \(-0.629927\pi\)
−0.396936 + 0.917846i \(0.629927\pi\)
\(60\) −5.99949 10.3914i −0.774531 1.34153i
\(61\) −1.58893 + 0.917368i −0.203441 + 0.117457i −0.598260 0.801302i \(-0.704141\pi\)
0.394818 + 0.918759i \(0.370808\pi\)
\(62\) −17.8487 10.3049i −2.26678 1.30873i
\(63\) 4.36561 + 2.52049i 0.550016 + 0.317552i
\(64\) −3.52664 −0.440830
\(65\) 2.65118i 0.328838i
\(66\) 14.6049 25.2965i 1.79774 3.11378i
\(67\) −7.10904 + 12.3132i −0.868508 + 1.50430i −0.00498622 + 0.999988i \(0.501587\pi\)
−0.863522 + 0.504312i \(0.831746\pi\)
\(68\) 12.0122 + 13.0811i 1.45669 + 1.58632i
\(69\) −4.18255 7.24438i −0.503519 0.872121i
\(70\) −15.2674 −1.82480
\(71\) 4.83502 2.79150i 0.573811 0.331290i −0.184859 0.982765i \(-0.559183\pi\)
0.758670 + 0.651475i \(0.225849\pi\)
\(72\) −3.29106 5.70028i −0.387855 0.671785i
\(73\) 5.46456 3.15496i 0.639578 0.369261i −0.144874 0.989450i \(-0.546278\pi\)
0.784452 + 0.620190i \(0.212944\pi\)
\(74\) 1.17417 + 0.677908i 0.136495 + 0.0788052i
\(75\) 6.35264i 0.733540i
\(76\) 14.1449 24.4997i 1.62253 2.81031i
\(77\) −12.6906 21.9808i −1.44623 2.50495i
\(78\) 9.88544i 1.11931i
\(79\) 11.6828 6.74508i 1.31442 0.758880i 0.331595 0.943422i \(-0.392413\pi\)
0.982825 + 0.184541i \(0.0590800\pi\)
\(80\) 7.04487 + 4.06736i 0.787641 + 0.454744i
\(81\) 5.55870 9.62795i 0.617633 1.06977i
\(82\) 8.83259i 0.975397i
\(83\) −4.69845 + 8.13795i −0.515722 + 0.893257i 0.484112 + 0.875006i \(0.339143\pi\)
−0.999833 + 0.0182503i \(0.994190\pi\)
\(84\) −38.8765 −4.24177
\(85\) 1.22824 + 5.51255i 0.133221 + 0.597920i
\(86\) −12.5298 + 10.6874i −1.35112 + 1.15245i
\(87\) 3.76383 0.403525
\(88\) 33.1409i 3.53284i
\(89\) 8.13518 14.0905i 0.862327 1.49359i −0.00734982 0.999973i \(-0.502340\pi\)
0.869677 0.493621i \(-0.164327\pi\)
\(90\) 3.90748i 0.411885i
\(91\) −7.43894 4.29487i −0.779813 0.450225i
\(92\) 15.3437 + 8.85871i 1.59970 + 0.923585i
\(93\) −8.34456 14.4532i −0.865291 1.49873i
\(94\) 26.9951 2.78434
\(95\) 7.79108 4.49818i 0.799348 0.461504i
\(96\) 5.85622 + 3.38109i 0.597698 + 0.345081i
\(97\) 18.8175i 1.91063i 0.295585 + 0.955316i \(0.404485\pi\)
−0.295585 + 0.955316i \(0.595515\pi\)
\(98\) −15.9429 + 27.6140i −1.61048 + 2.78943i
\(99\) 5.62570 3.24800i 0.565404 0.326436i
\(100\) −6.72751 11.6524i −0.672751 1.16524i
\(101\) −0.223258 0.386694i −0.0222150 0.0384775i 0.854704 0.519115i \(-0.173739\pi\)
−0.876919 + 0.480638i \(0.840405\pi\)
\(102\) 4.57974 + 20.5547i 0.453462 + 2.03522i
\(103\) −1.22446 2.12083i −0.120650 0.208971i 0.799374 0.600833i \(-0.205164\pi\)
−0.920024 + 0.391862i \(0.871831\pi\)
\(104\) 5.60792 + 9.71319i 0.549901 + 0.952457i
\(105\) −10.7067 6.18149i −1.04486 0.603252i
\(106\) 5.24014 9.07619i 0.508967 0.881557i
\(107\) 4.76103i 0.460266i −0.973159 0.230133i \(-0.926084\pi\)
0.973159 0.230133i \(-0.0739161\pi\)
\(108\) 16.3296i 1.57131i
\(109\) −9.19461 5.30851i −0.880684 0.508463i −0.00980034 0.999952i \(-0.503120\pi\)
−0.870884 + 0.491489i \(0.836453\pi\)
\(110\) −9.83708 + 17.0383i −0.937928 + 1.62454i
\(111\) 0.548945 + 0.950801i 0.0521036 + 0.0902460i
\(112\) 22.8252 13.1781i 2.15678 1.24522i
\(113\) 10.9962i 1.03443i −0.855854 0.517217i \(-0.826968\pi\)
0.855854 0.517217i \(-0.173032\pi\)
\(114\) 29.0506 16.7724i 2.72084 1.57088i
\(115\) 2.81713 + 4.87942i 0.262699 + 0.455008i
\(116\) −6.90383 + 3.98593i −0.641004 + 0.370084i
\(117\) 1.09921 1.90390i 0.101622 0.176015i
\(118\) 15.3144 1.40981
\(119\) 17.4574 + 5.48395i 1.60032 + 0.502713i
\(120\) 8.07132 + 13.9799i 0.736807 + 1.27619i
\(121\) −21.7073 −1.97339
\(122\) 3.99051 2.30392i 0.361284 0.208587i
\(123\) 3.57616 6.19409i 0.322451 0.558502i
\(124\) 30.6122 + 17.6739i 2.74905 + 1.58717i
\(125\) 11.1277i 0.995289i
\(126\) −10.9640 6.33008i −0.976752 0.563928i
\(127\) −4.14740 −0.368022 −0.184011 0.982924i \(-0.558908\pi\)
−0.184011 + 0.982924i \(0.558908\pi\)
\(128\) 15.5072 1.37065
\(129\) −13.1140 + 2.42174i −1.15462 + 0.213222i
\(130\) 6.65829i 0.583971i
\(131\) 5.10448i 0.445981i 0.974821 + 0.222990i \(0.0715819\pi\)
−0.974821 + 0.222990i \(0.928418\pi\)
\(132\) −25.0489 + 43.3859i −2.18022 + 3.77626i
\(133\) 29.1480i 2.52745i
\(134\) 17.8540 30.9240i 1.54235 2.67143i
\(135\) −2.59646 + 4.49720i −0.223468 + 0.387057i
\(136\) −16.1604 17.5985i −1.38574 1.50906i
\(137\) −8.15290 −0.696549 −0.348275 0.937393i \(-0.613232\pi\)
−0.348275 + 0.937393i \(0.613232\pi\)
\(138\) 10.5042 + 18.1939i 0.894181 + 1.54877i
\(139\) −11.7337 6.77447i −0.995242 0.574603i −0.0884048 0.996085i \(-0.528177\pi\)
−0.906837 + 0.421482i \(0.861510\pi\)
\(140\) 26.1850 2.21304
\(141\) 18.9310 + 10.9298i 1.59428 + 0.920459i
\(142\) −12.1429 + 7.01071i −1.01901 + 0.588325i
\(143\) −9.58611 + 5.53454i −0.801630 + 0.462822i
\(144\) 3.37277 + 5.84181i 0.281064 + 0.486817i
\(145\) −2.53511 −0.210529
\(146\) −13.7240 + 7.92353i −1.13580 + 0.655756i
\(147\) −22.3608 + 12.9100i −1.84429 + 1.06480i
\(148\) −2.01381 1.16268i −0.165535 0.0955714i
\(149\) 0.586861 1.01647i 0.0480775 0.0832727i −0.840985 0.541058i \(-0.818024\pi\)
0.889063 + 0.457785i \(0.151357\pi\)
\(150\) 15.9543i 1.30267i
\(151\) 4.37075 0.355687 0.177843 0.984059i \(-0.443088\pi\)
0.177843 + 0.984059i \(0.443088\pi\)
\(152\) −19.0296 + 32.9603i −1.54351 + 2.67343i
\(153\) −1.40354 + 4.46799i −0.113470 + 0.361216i
\(154\) 31.8719 + 55.2038i 2.56831 + 4.44845i
\(155\) 5.62044 + 9.73488i 0.451444 + 0.781924i
\(156\) 16.9545i 1.35744i
\(157\) 4.38370 + 7.59279i 0.349857 + 0.605971i 0.986224 0.165416i \(-0.0528967\pi\)
−0.636367 + 0.771387i \(0.719563\pi\)
\(158\) −29.3408 + 16.9399i −2.33423 + 1.34767i
\(159\) 7.34957 4.24328i 0.582859 0.336514i
\(160\) −3.94443 2.27732i −0.311835 0.180038i
\(161\) 18.2549 1.43869
\(162\) −13.9604 + 24.1801i −1.09683 + 1.89977i
\(163\) 3.58760 2.07130i 0.281003 0.162237i −0.352875 0.935671i \(-0.614796\pi\)
0.633877 + 0.773434i \(0.281462\pi\)
\(164\) 15.1487i 1.18292i
\(165\) −13.7970 + 7.96571i −1.07410 + 0.620130i
\(166\) 11.7999 20.4381i 0.915851 1.58630i
\(167\) 2.80154 + 1.61747i 0.216790 + 0.125164i 0.604463 0.796633i \(-0.293388\pi\)
−0.387673 + 0.921797i \(0.626721\pi\)
\(168\) 52.3018 4.03517
\(169\) 4.62696 8.01412i 0.355920 0.616471i
\(170\) −3.08466 13.8445i −0.236583 1.06182i
\(171\) 7.46004 0.570484
\(172\) 21.4898 18.3300i 1.63858 1.39765i
\(173\) 7.13873i 0.542748i 0.962474 + 0.271374i \(0.0874780\pi\)
−0.962474 + 0.271374i \(0.912522\pi\)
\(174\) −9.45266 −0.716604
\(175\) −12.0059 6.93159i −0.907558 0.523979i
\(176\) 33.9637i 2.56011i
\(177\) 10.7396 + 6.20054i 0.807241 + 0.466061i
\(178\) −20.4311 + 35.3877i −1.53137 + 2.65242i
\(179\) 2.57082 + 4.45279i 0.192152 + 0.332817i 0.945963 0.324274i \(-0.105120\pi\)
−0.753811 + 0.657091i \(0.771787\pi\)
\(180\) 6.70171i 0.499516i
\(181\) −11.0474 + 6.37822i −0.821147 + 0.474089i −0.850812 0.525470i \(-0.823889\pi\)
0.0296649 + 0.999560i \(0.490556\pi\)
\(182\) 18.6825 + 10.7864i 1.38484 + 0.799538i
\(183\) 3.73127 0.275823
\(184\) −20.6424 11.9179i −1.52178 0.878600i
\(185\) −0.369739 0.640407i −0.0271838 0.0470837i
\(186\) 20.9569 + 36.2985i 1.53664 + 2.66153i
\(187\) 17.3682 15.9490i 1.27009 1.16630i
\(188\) −46.2992 −3.37672
\(189\) 8.41247 + 14.5708i 0.611917 + 1.05987i
\(190\) −19.5669 + 11.2970i −1.41953 + 0.819567i
\(191\) 2.78150 4.81770i 0.201262 0.348597i −0.747673 0.664067i \(-0.768829\pi\)
0.948935 + 0.315470i \(0.102162\pi\)
\(192\) 6.21118 + 3.58603i 0.448254 + 0.258799i
\(193\) 0.578350i 0.0416306i 0.999783 + 0.0208153i \(0.00662619\pi\)
−0.999783 + 0.0208153i \(0.993374\pi\)
\(194\) 47.2593i 3.39302i
\(195\) −2.69582 + 4.66930i −0.193052 + 0.334376i
\(196\) 27.3437 47.3606i 1.95312 3.38290i
\(197\) 5.49896 3.17483i 0.391785 0.226197i −0.291148 0.956678i \(-0.594037\pi\)
0.682933 + 0.730481i \(0.260704\pi\)
\(198\) −14.1287 + 8.15718i −1.00408 + 0.579706i
\(199\) 10.0023i 0.709042i 0.935048 + 0.354521i \(0.115356\pi\)
−0.935048 + 0.354521i \(0.884644\pi\)
\(200\) 9.05074 + 15.6763i 0.639984 + 1.10848i
\(201\) 25.0412 14.4575i 1.76627 1.01975i
\(202\) 0.560701 + 0.971163i 0.0394508 + 0.0683308i
\(203\) −4.10684 + 7.11326i −0.288244 + 0.499253i
\(204\) −7.85470 35.2532i −0.549939 2.46822i
\(205\) −2.40870 + 4.17200i −0.168231 + 0.291385i
\(206\) 3.07517 + 5.32635i 0.214257 + 0.371104i
\(207\) 4.67209i 0.324733i
\(208\) −5.74715 9.95435i −0.398493 0.690210i
\(209\) −32.5290 18.7806i −2.25008 1.29908i
\(210\) 26.8892 + 15.5245i 1.85553 + 1.07129i
\(211\) 13.1262i 0.903642i −0.892109 0.451821i \(-0.850775\pi\)
0.892109 0.451821i \(-0.149225\pi\)
\(212\) −8.98734 + 15.5665i −0.617253 + 1.06911i
\(213\) −11.3540 −0.777966
\(214\) 11.9571i 0.817369i
\(215\) 8.83287 1.63115i 0.602397 0.111244i
\(216\) 21.9687i 1.49478i
\(217\) 36.4202 2.47236
\(218\) 23.0918 + 13.3321i 1.56397 + 0.902961i
\(219\) −12.8324 −0.867132
\(220\) 16.8715 29.2223i 1.13748 1.97017i
\(221\) 2.39162 7.61339i 0.160878 0.512132i
\(222\) −1.37865 2.38789i −0.0925288 0.160265i
\(223\) −13.2886 −0.889872 −0.444936 0.895562i \(-0.646774\pi\)
−0.444936 + 0.895562i \(0.646774\pi\)
\(224\) −12.7799 + 7.37846i −0.853890 + 0.492994i
\(225\) 1.77405 3.07274i 0.118270 0.204849i
\(226\) 27.6163i 1.83701i
\(227\) −3.39154 1.95811i −0.225105 0.129964i 0.383207 0.923662i \(-0.374820\pi\)
−0.608312 + 0.793698i \(0.708153\pi\)
\(228\) −49.8246 + 28.7662i −3.29971 + 1.90509i
\(229\) 2.79328 + 4.83811i 0.184585 + 0.319711i 0.943437 0.331553i \(-0.107572\pi\)
−0.758851 + 0.651264i \(0.774239\pi\)
\(230\) −7.07508 12.2544i −0.466517 0.808031i
\(231\) 51.6174i 3.39618i
\(232\) 9.28795 5.36240i 0.609784 0.352059i
\(233\) 9.70656 5.60409i 0.635898 0.367136i −0.147135 0.989116i \(-0.547005\pi\)
0.783033 + 0.621981i \(0.213672\pi\)
\(234\) −2.76062 + 4.78154i −0.180467 + 0.312579i
\(235\) −12.7509 7.36174i −0.831778 0.480227i
\(236\) −26.2657 −1.70975
\(237\) −27.4347 −1.78207
\(238\) −43.8434 13.7727i −2.84195 0.892749i
\(239\) −13.4872 + 23.3605i −0.872413 + 1.51106i −0.0129202 + 0.999917i \(0.504113\pi\)
−0.859493 + 0.511148i \(0.829221\pi\)
\(240\) −8.27171 14.3270i −0.533936 0.924805i
\(241\) −5.97009 + 3.44683i −0.384567 + 0.222030i −0.679804 0.733394i \(-0.737935\pi\)
0.295236 + 0.955424i \(0.404602\pi\)
\(242\) 54.5168 3.50447
\(243\) −9.73068 + 5.61801i −0.624223 + 0.360396i
\(244\) −6.84411 + 3.95145i −0.438149 + 0.252965i
\(245\) 15.0610 8.69547i 0.962212 0.555533i
\(246\) −8.98134 + 15.5561i −0.572629 + 0.991823i
\(247\) −12.7118 −0.808832
\(248\) −41.1835 23.7773i −2.61516 1.50986i
\(249\) 16.5500 9.55515i 1.04881 0.605533i
\(250\) 27.9466i 1.76750i
\(251\) −12.1298 21.0095i −0.765629 1.32611i −0.939913 0.341413i \(-0.889094\pi\)
0.174284 0.984695i \(-0.444239\pi\)
\(252\) 18.8043 + 10.8567i 1.18456 + 0.683907i
\(253\) 11.7620 20.3723i 0.739469 1.28080i
\(254\) 10.4160 0.653556
\(255\) 3.44219 10.9577i 0.215558 0.686200i
\(256\) −31.8922 −1.99326
\(257\) 1.53014 0.0954475 0.0477237 0.998861i \(-0.484803\pi\)
0.0477237 + 0.998861i \(0.484803\pi\)
\(258\) 32.9351 6.08208i 2.05045 0.378654i
\(259\) −2.39589 −0.148874
\(260\) 11.4196i 0.708214i
\(261\) −1.82054 1.05109i −0.112689 0.0650609i
\(262\) 12.8196i 0.792001i
\(263\) 6.75217 11.6951i 0.416357 0.721151i −0.579213 0.815176i \(-0.696640\pi\)
0.995570 + 0.0940254i \(0.0299735\pi\)
\(264\) 33.6990 58.3684i 2.07403 3.59233i
\(265\) −4.95026 + 2.85804i −0.304092 + 0.175568i
\(266\) 73.2038i 4.48841i
\(267\) −28.6557 + 16.5444i −1.75370 + 1.01250i
\(268\) −30.6213 + 53.0377i −1.87049 + 3.23979i
\(269\) 9.71634i 0.592416i −0.955124 0.296208i \(-0.904278\pi\)
0.955124 0.296208i \(-0.0957221\pi\)
\(270\) 6.52087 11.2945i 0.396848 0.687360i
\(271\) 14.0264 + 24.2944i 0.852042 + 1.47578i 0.879363 + 0.476153i \(0.157969\pi\)
−0.0273211 + 0.999627i \(0.508698\pi\)
\(272\) 16.5616 + 18.0354i 1.00420 + 1.09356i
\(273\) 8.73440 + 15.1284i 0.528630 + 0.915614i
\(274\) 20.4756 1.23698
\(275\) −15.4712 + 8.93231i −0.932950 + 0.538639i
\(276\) −18.0158 31.2043i −1.08442 1.87828i
\(277\) 19.5223 + 11.2712i 1.17298 + 0.677222i 0.954381 0.298593i \(-0.0965172\pi\)
0.218601 + 0.975814i \(0.429851\pi\)
\(278\) 29.4687 + 17.0137i 1.76741 + 1.02042i
\(279\) 9.32125i 0.558049i
\(280\) −35.2276 −2.10525
\(281\) −7.71795 + 13.3679i −0.460414 + 0.797461i −0.998981 0.0451218i \(-0.985632\pi\)
0.538567 + 0.842582i \(0.318966\pi\)
\(282\) −47.5444 27.4497i −2.83123 1.63461i
\(283\) 25.7997 14.8955i 1.53364 0.885445i 0.534446 0.845203i \(-0.320520\pi\)
0.999190 0.0402423i \(-0.0128130\pi\)
\(284\) 20.8262 12.0240i 1.23581 0.713495i
\(285\) −18.2957 −1.08375
\(286\) 24.0750 13.8997i 1.42359 0.821907i
\(287\) 7.80414 + 13.5172i 0.460664 + 0.797894i
\(288\) −1.88842 3.27083i −0.111276 0.192736i
\(289\) −1.44572 + 16.9384i −0.0850421 + 0.996377i
\(290\) 6.36679 0.373871
\(291\) 19.1344 33.1418i 1.12168 1.94281i
\(292\) 23.5379 13.5896i 1.37745 0.795272i
\(293\) −14.1121 −0.824440 −0.412220 0.911084i \(-0.635247\pi\)
−0.412220 + 0.911084i \(0.635247\pi\)
\(294\) 56.1580 32.4228i 3.27520 1.89094i
\(295\) −7.23363 4.17634i −0.421158 0.243156i
\(296\) 2.70925 + 1.56419i 0.157472 + 0.0909165i
\(297\) 21.6813 1.25807
\(298\) −1.47387 + 2.55282i −0.0853791 + 0.147881i
\(299\) 7.96117i 0.460407i
\(300\) 27.3632i 1.57982i
\(301\) 9.73229 27.4266i 0.560960 1.58084i
\(302\) −10.9769 −0.631650
\(303\) 0.908071i 0.0521673i
\(304\) 19.5021 33.7786i 1.11852 1.93734i
\(305\) −2.51318 −0.143904
\(306\) 3.52493 11.2211i 0.201507 0.641470i
\(307\) 8.07909 13.9934i 0.461098 0.798646i −0.537918 0.842997i \(-0.680789\pi\)
0.999016 + 0.0443517i \(0.0141222\pi\)
\(308\) −54.6634 94.6797i −3.11473 5.39488i
\(309\) 4.98032i 0.283320i
\(310\) −14.1154 24.4487i −0.801703 1.38859i
\(311\) 15.8950 + 9.17695i 0.901320 + 0.520377i 0.877628 0.479342i \(-0.159125\pi\)
0.0236918 + 0.999719i \(0.492458\pi\)
\(312\) 22.8094i 1.29133i
\(313\) −2.33614 1.34877i −0.132046 0.0762370i 0.432522 0.901624i \(-0.357624\pi\)
−0.564568 + 0.825387i \(0.690957\pi\)
\(314\) −11.0094 19.0689i −0.621298 1.07612i
\(315\) 3.45250 + 5.97991i 0.194527 + 0.336930i
\(316\) 50.3223 29.0536i 2.83085 1.63439i
\(317\) 14.9707i 0.840835i −0.907331 0.420418i \(-0.861884\pi\)
0.907331 0.420418i \(-0.138116\pi\)
\(318\) −18.4581 + 10.6568i −1.03508 + 0.597602i
\(319\) 5.29224 + 9.16642i 0.296308 + 0.513221i
\(320\) −4.18351 2.41535i −0.233865 0.135022i
\(321\) −4.84121 + 8.38521i −0.270210 + 0.468017i
\(322\) −45.8462 −2.55491
\(323\) 26.4315 5.88914i 1.47069 0.327681i
\(324\) 23.9434 41.4712i 1.33019 2.30395i
\(325\) −3.02295 + 5.23590i −0.167683 + 0.290435i
\(326\) −9.01007 + 5.20197i −0.499022 + 0.288110i
\(327\) 10.7958 + 18.6989i 0.597010 + 1.03405i
\(328\) 20.3801i 1.12530i
\(329\) −41.3127 + 23.8519i −2.27764 + 1.31500i
\(330\) 34.6505 20.0055i 1.90745 1.10126i
\(331\) 2.62803 + 4.55188i 0.144449 + 0.250194i 0.929167 0.369659i \(-0.120526\pi\)
−0.784718 + 0.619853i \(0.787192\pi\)
\(332\) −20.2380 + 35.0532i −1.11070 + 1.92380i
\(333\) 0.613196i 0.0336030i
\(334\) −7.03593 4.06219i −0.384989 0.222273i
\(335\) −16.8663 + 9.73779i −0.921507 + 0.532032i
\(336\) −53.6003 −2.92414
\(337\) −19.8729 + 11.4736i −1.08255 + 0.625008i −0.931582 0.363531i \(-0.881571\pi\)
−0.150964 + 0.988539i \(0.548238\pi\)
\(338\) −11.6204 + 20.1271i −0.632064 + 1.09477i
\(339\) −11.1814 + 19.3667i −0.607288 + 1.05185i
\(340\) 5.29049 + 23.7446i 0.286917 + 1.28773i
\(341\) 23.4662 40.6447i 1.27077 2.20103i
\(342\) −18.7355 −1.01310
\(343\) 25.2800i 1.36499i
\(344\) −28.9110 + 24.6599i −1.55877 + 1.32957i
\(345\) 11.4583i 0.616894i
\(346\) 17.9286i 0.963846i
\(347\) −12.0411 6.95194i −0.646401 0.373200i 0.140675 0.990056i \(-0.455073\pi\)
−0.787076 + 0.616856i \(0.788406\pi\)
\(348\) 16.2122 0.869066
\(349\) −14.8500 + 25.7210i −0.794905 + 1.37682i 0.127995 + 0.991775i \(0.459146\pi\)
−0.922900 + 0.385041i \(0.874187\pi\)
\(350\) 30.1521 + 17.4083i 1.61170 + 0.930514i
\(351\) 6.35451 3.66878i 0.339178 0.195825i
\(352\) 19.0163i 1.01357i
\(353\) 2.32936 + 4.03456i 0.123979 + 0.214738i 0.921333 0.388773i \(-0.127101\pi\)
−0.797354 + 0.603511i \(0.793768\pi\)
\(354\) −26.9721 15.5723i −1.43355 0.827660i
\(355\) 7.64745 0.405885
\(356\) 35.0413 60.6932i 1.85718 3.21673i
\(357\) −25.1700 27.4099i −1.33214 1.45068i
\(358\) −6.45649 11.1830i −0.341236 0.591038i
\(359\) 1.62902 + 2.82155i 0.0859766 + 0.148916i 0.905807 0.423691i \(-0.139266\pi\)
−0.819830 + 0.572606i \(0.805932\pi\)
\(360\) 9.01603i 0.475186i
\(361\) −12.0678 20.9020i −0.635147 1.10011i
\(362\) 27.7450 16.0186i 1.45824 0.841918i
\(363\) 38.2313 + 22.0729i 2.00662 + 1.15853i
\(364\) −32.0423 18.4996i −1.67947 0.969644i
\(365\) 8.64318 0.452405
\(366\) −9.37088 −0.489824
\(367\) 20.2158 + 11.6716i 1.05526 + 0.609253i 0.924117 0.382111i \(-0.124803\pi\)
0.131141 + 0.991364i \(0.458136\pi\)
\(368\) 21.1549 + 12.2138i 1.10278 + 0.636689i
\(369\) −3.45954 + 1.99737i −0.180096 + 0.103979i
\(370\) 0.928581 + 1.60835i 0.0482746 + 0.0836141i
\(371\) 18.5199i 0.961508i
\(372\) −35.9431 62.2554i −1.86357 3.22779i
\(373\) −1.92466 3.33361i −0.0996550 0.172608i 0.811887 0.583815i \(-0.198441\pi\)
−0.911542 + 0.411207i \(0.865107\pi\)
\(374\) −43.6194 + 40.0550i −2.25550 + 2.07119i
\(375\) −11.3151 + 19.5983i −0.584307 + 1.01205i
\(376\) 62.2879 3.21225
\(377\) 3.10218 + 1.79104i 0.159770 + 0.0922434i
\(378\) −21.1275 36.5939i −1.08668 1.88219i
\(379\) 0.0120364i 0.000618270i −1.00000 0.000309135i \(-0.999902\pi\)
1.00000 0.000309135i \(-9.84007e-5\pi\)
\(380\) 33.5591 19.3754i 1.72155 0.993935i
\(381\) 7.30447 + 4.21724i 0.374220 + 0.216056i
\(382\) −6.98560 + 12.0994i −0.357414 + 0.619060i
\(383\) 34.3781 1.75664 0.878320 0.478073i \(-0.158665\pi\)
0.878320 + 0.478073i \(0.158665\pi\)
\(384\) −27.3115 15.7683i −1.39373 0.804673i
\(385\) 34.7667i 1.77187i
\(386\) 1.45250i 0.0739302i
\(387\) 7.01947 + 2.49085i 0.356820 + 0.126617i
\(388\) 81.0542i 4.11490i
\(389\) 22.0169 1.11630 0.558150 0.829740i \(-0.311512\pi\)
0.558150 + 0.829740i \(0.311512\pi\)
\(390\) 6.77042 11.7267i 0.342833 0.593805i
\(391\) 3.68826 + 16.5536i 0.186524 + 0.837150i
\(392\) −36.7863 + 63.7158i −1.85799 + 3.21813i
\(393\) 5.19044 8.99011i 0.261823 0.453491i
\(394\) −13.8104 + 7.97341i −0.695756 + 0.401695i
\(395\) 18.4785 0.929753
\(396\) 24.2320 13.9903i 1.21770 0.703042i
\(397\) −17.7075 10.2234i −0.888715 0.513100i −0.0151930 0.999885i \(-0.504836\pi\)
−0.873522 + 0.486785i \(0.838170\pi\)
\(398\) 25.1202i 1.25916i
\(399\) −29.6389 + 51.3361i −1.48380 + 2.57002i
\(400\) −9.27544 16.0655i −0.463772 0.803277i
\(401\) 1.42805 0.824485i 0.0713134 0.0411728i −0.463919 0.885877i \(-0.653557\pi\)
0.535233 + 0.844705i \(0.320224\pi\)
\(402\) −62.8896 + 36.3093i −3.13665 + 1.81094i
\(403\) 15.8833i 0.791202i
\(404\) −0.961656 1.66564i −0.0478442 0.0828686i
\(405\) 13.1881 7.61417i 0.655323 0.378351i
\(406\) 10.3141 17.8646i 0.511881 0.886605i
\(407\) −1.54372 + 2.67380i −0.0765194 + 0.132535i
\(408\) 10.5672 + 47.4273i 0.523153 + 2.34800i
\(409\) −30.2220 −1.49438 −0.747191 0.664609i \(-0.768598\pi\)
−0.747191 + 0.664609i \(0.768598\pi\)
\(410\) 6.04933 10.4778i 0.298755 0.517459i
\(411\) 14.3590 + 8.29020i 0.708280 + 0.408925i
\(412\) −5.27421 9.13519i −0.259841 0.450059i
\(413\) −23.4368 + 13.5312i −1.15325 + 0.665829i
\(414\) 11.7337i 0.576681i
\(415\) −11.1472 + 6.43582i −0.547193 + 0.315922i
\(416\) 3.21783 + 5.57345i 0.157767 + 0.273261i
\(417\) 13.7771 + 23.8627i 0.674668 + 1.16856i
\(418\) 81.6950 + 47.1666i 3.99583 + 2.30699i
\(419\) 4.37648i 0.213805i 0.994270 + 0.106902i \(0.0340933\pi\)
−0.994270 + 0.106902i \(0.965907\pi\)
\(420\) −46.1176 26.6260i −2.25031 1.29922i
\(421\) 4.11951 + 7.13520i 0.200773 + 0.347749i 0.948778 0.315945i \(-0.102321\pi\)
−0.748005 + 0.663693i \(0.768988\pi\)
\(422\) 32.9657i 1.60474i
\(423\) −6.10457 10.5734i −0.296814 0.514097i
\(424\) 12.0910 20.9422i 0.587189 1.01704i
\(425\) 3.85988 12.2874i 0.187232 0.596027i
\(426\) 28.5151 1.38156
\(427\) −4.07132 + 7.05173i −0.197025 + 0.341257i
\(428\) 20.5075i 0.991269i
\(429\) 22.5110 1.08684
\(430\) −22.1833 + 4.09655i −1.06977 + 0.197553i
\(431\) 15.6456i 0.753621i 0.926290 + 0.376810i \(0.122979\pi\)
−0.926290 + 0.376810i \(0.877021\pi\)
\(432\) 22.5141i 1.08321i
\(433\) −14.9478 + 25.8904i −0.718347 + 1.24421i 0.243307 + 0.969949i \(0.421768\pi\)
−0.961654 + 0.274265i \(0.911566\pi\)
\(434\) −91.4674 −4.39058
\(435\) 4.46488 + 2.57780i 0.214074 + 0.123596i
\(436\) −39.6046 22.8658i −1.89672 1.09507i
\(437\) 23.3957 13.5075i 1.11917 0.646153i
\(438\) 32.2279 1.53991
\(439\) −8.11746 + 4.68662i −0.387425 + 0.223680i −0.681044 0.732242i \(-0.738474\pi\)
0.293619 + 0.955923i \(0.405140\pi\)
\(440\) −22.6978 + 39.3138i −1.08208 + 1.87421i
\(441\) 14.4211 0.686718
\(442\) −6.00642 + 19.1206i −0.285696 + 0.909476i
\(443\) 0.638830 + 1.10649i 0.0303517 + 0.0525707i 0.880802 0.473484i \(-0.157004\pi\)
−0.850451 + 0.526055i \(0.823671\pi\)
\(444\) 2.36451 + 4.09545i 0.112215 + 0.194362i
\(445\) 19.3009 11.1434i 0.914949 0.528246i
\(446\) 33.3737 1.58029
\(447\) −2.06718 + 1.19349i −0.0977743 + 0.0564500i
\(448\) −13.5545 + 7.82568i −0.640389 + 0.369729i
\(449\) 18.8811 + 10.9010i 0.891057 + 0.514452i 0.874288 0.485408i \(-0.161329\pi\)
0.0167686 + 0.999859i \(0.494662\pi\)
\(450\) −4.45543 + 7.71703i −0.210031 + 0.363784i
\(451\) 20.1134 0.947105
\(452\) 47.3647i 2.22785i
\(453\) −7.69785 4.44436i −0.361676 0.208814i
\(454\) 8.51768 + 4.91769i 0.399755 + 0.230798i
\(455\) −5.88301 10.1897i −0.275800 0.477699i
\(456\) 67.0307 38.7002i 3.13900 1.81230i
\(457\) −27.1570 −1.27035 −0.635175 0.772368i \(-0.719072\pi\)
−0.635175 + 0.772368i \(0.719072\pi\)
\(458\) −7.01519 12.1507i −0.327798 0.567763i
\(459\) −11.5132 + 10.5724i −0.537389 + 0.493476i
\(460\) 12.1344 + 21.0175i 0.565771 + 0.979945i
\(461\) −0.901498 + 1.56144i −0.0419869 + 0.0727235i −0.886255 0.463197i \(-0.846702\pi\)
0.844268 + 0.535921i \(0.180035\pi\)
\(462\) 129.635i 6.03115i
\(463\) −14.8320 + 25.6897i −0.689301 + 1.19390i 0.282764 + 0.959190i \(0.408749\pi\)
−0.972064 + 0.234714i \(0.924585\pi\)
\(464\) −9.51855 + 5.49553i −0.441887 + 0.255124i
\(465\) 22.8603i 1.06012i
\(466\) −24.3775 + 14.0744i −1.12927 + 0.651983i
\(467\) −10.2978 + 17.8363i −0.476524 + 0.825363i −0.999638 0.0268992i \(-0.991437\pi\)
0.523114 + 0.852262i \(0.324770\pi\)
\(468\) 4.73473 8.20079i 0.218863 0.379082i
\(469\) 63.1004i 2.91371i
\(470\) 32.0233 + 18.4886i 1.47712 + 0.852817i
\(471\) 17.8301i 0.821567i
\(472\) 35.3361 1.62648
\(473\) −24.3372 28.5327i −1.11903 1.31193i
\(474\) 68.9008 3.16472
\(475\) −20.5158 −0.941332
\(476\) 75.1957 + 23.6214i 3.44659 + 1.08269i
\(477\) −4.73993 −0.217027
\(478\) 33.8724 58.6687i 1.54929 2.68344i
\(479\) 19.3025 + 11.1443i 0.881952 + 0.509195i 0.871302 0.490748i \(-0.163276\pi\)
0.0106505 + 0.999943i \(0.496610\pi\)
\(480\) 4.63134 + 8.02171i 0.211391 + 0.366139i
\(481\) 1.04488i 0.0476423i
\(482\) 14.9936 8.65654i 0.682939 0.394295i
\(483\) −32.1509 18.5623i −1.46291 0.844614i
\(484\) −93.5015 −4.25007
\(485\) −12.8879 + 22.3225i −0.585210 + 1.01361i
\(486\) 24.4381 14.1093i 1.10853 0.640013i
\(487\) −19.8836 + 11.4798i −0.901010 + 0.520198i −0.877528 0.479526i \(-0.840809\pi\)
−0.0234821 + 0.999724i \(0.507475\pi\)
\(488\) 9.20760 5.31601i 0.416808 0.240644i
\(489\) −8.42473 −0.380980
\(490\) −37.8249 + 21.8382i −1.70876 + 0.986551i
\(491\) −3.40750 5.90197i −0.153778 0.266352i 0.778835 0.627229i \(-0.215811\pi\)
−0.932614 + 0.360877i \(0.882478\pi\)
\(492\) 15.4039 26.6803i 0.694459 1.20284i
\(493\) −7.28007 2.28691i −0.327878 0.102997i
\(494\) 31.9250 1.43637
\(495\) 8.89806 0.399938
\(496\) 42.2060 + 24.3677i 1.89511 + 1.09414i
\(497\) 12.3888 21.4580i 0.555713 0.962523i
\(498\) −41.5645 + 23.9973i −1.86255 + 1.07534i
\(499\) 5.83929 3.37132i 0.261403 0.150921i −0.363572 0.931566i \(-0.618443\pi\)
0.624974 + 0.780645i \(0.285109\pi\)
\(500\) 47.9310i 2.14354i
\(501\) −3.28942 5.69744i −0.146960 0.254543i
\(502\) 30.4635 + 52.7643i 1.35965 + 2.35499i
\(503\) 13.2162 7.63037i 0.589281 0.340221i −0.175532 0.984474i \(-0.556165\pi\)
0.764813 + 0.644252i \(0.222831\pi\)
\(504\) −25.2981 14.6059i −1.12687 0.650597i
\(505\) 0.611627i 0.0272170i
\(506\) −29.5396 + 51.1641i −1.31320 + 2.27452i
\(507\) −16.2982 + 9.40975i −0.723827 + 0.417902i
\(508\) −17.8644 −0.792604
\(509\) −5.14392 8.90953i −0.228000 0.394908i 0.729215 0.684285i \(-0.239885\pi\)
−0.957215 + 0.289376i \(0.906552\pi\)
\(510\) −8.64488 + 27.5198i −0.382802 + 1.21860i
\(511\) 14.0019 24.2519i 0.619406 1.07284i
\(512\) 49.0812 2.16910
\(513\) 21.5631 + 12.4494i 0.952033 + 0.549656i
\(514\) −3.84287 −0.169502
\(515\) 3.35447i 0.147816i
\(516\) −56.4869 + 10.4313i −2.48670 + 0.459214i
\(517\) 61.4729i 2.70358i
\(518\) 6.01716 0.264379
\(519\) 7.25895 12.5729i 0.318633 0.551888i
\(520\) 15.3632i 0.673719i
\(521\) 18.6103 + 10.7447i 0.815334 + 0.470733i 0.848805 0.528707i \(-0.177323\pi\)
−0.0334709 + 0.999440i \(0.510656\pi\)
\(522\) 4.57220 + 2.63976i 0.200120 + 0.115539i
\(523\) 14.3812 + 24.9090i 0.628846 + 1.08919i 0.987784 + 0.155832i \(0.0498058\pi\)
−0.358937 + 0.933362i \(0.616861\pi\)
\(524\) 21.9869i 0.960503i
\(525\) 14.0966 + 24.4161i 0.615228 + 1.06561i
\(526\) −16.9577 + 29.3716i −0.739392 + 1.28066i
\(527\) 7.35842 + 33.0259i 0.320538 + 1.43863i
\(528\) −34.5357 + 59.8176i −1.50297 + 2.60323i
\(529\) −3.04048 5.26626i −0.132195 0.228968i
\(530\) 12.4323 7.17781i 0.540026 0.311784i
\(531\) −3.46314 5.99833i −0.150287 0.260306i
\(532\) 125.551i 5.44335i
\(533\) 5.89500 3.40348i 0.255341 0.147421i
\(534\) 71.9672 41.5503i 3.11433 1.79806i
\(535\) 3.26077 5.64782i 0.140975 0.244176i
\(536\) 41.1958 71.3533i 1.77939 3.08199i
\(537\) 10.4565i 0.451230i
\(538\) 24.4021i 1.05205i
\(539\) −62.8821 36.3050i −2.70852 1.56377i
\(540\) −11.1839 + 19.3711i −0.481279 + 0.833600i
\(541\) −4.91450 + 2.83739i −0.211291 + 0.121989i −0.601911 0.798563i \(-0.705594\pi\)
0.390620 + 0.920552i \(0.372261\pi\)
\(542\) −35.2265 61.0141i −1.51311 2.62078i
\(543\) 25.9425 1.11330
\(544\) −9.27287 10.0980i −0.397571 0.432950i
\(545\) −7.27147 12.5946i −0.311476 0.539491i
\(546\) −21.9360 37.9943i −0.938774 1.62600i
\(547\) −23.2117 13.4013i −0.992460 0.572997i −0.0864512 0.996256i \(-0.527553\pi\)
−0.906009 + 0.423259i \(0.860886\pi\)
\(548\) −35.1176 −1.50015
\(549\) −1.80479 1.04200i −0.0770267 0.0444714i
\(550\) 38.8552 22.4330i 1.65679 0.956548i
\(551\) 12.1553i 0.517832i
\(552\) 24.2372 + 41.9801i 1.03161 + 1.78679i
\(553\) 29.9349 51.8488i 1.27296 2.20484i
\(554\) −49.0293 28.3071i −2.08305 1.20265i
\(555\) 1.50386i 0.0638354i
\(556\) −50.5416 29.1802i −2.14344 1.23752i
\(557\) −4.61019 −0.195340 −0.0976699 0.995219i \(-0.531139\pi\)
−0.0976699 + 0.995219i \(0.531139\pi\)
\(558\) 23.4098i 0.991018i
\(559\) −11.9611 4.24437i −0.505899 0.179518i
\(560\) 36.1022 1.52560
\(561\) −46.8068 + 10.4289i −1.97618 + 0.440309i
\(562\) 19.3832 33.5727i 0.817632 1.41618i
\(563\) 22.1779 0.934688 0.467344 0.884076i \(-0.345211\pi\)
0.467344 + 0.884076i \(0.345211\pi\)
\(564\) 81.5431 + 47.0789i 3.43358 + 1.98238i
\(565\) 7.53115 13.0443i 0.316838 0.548779i
\(566\) −64.7947 + 37.4093i −2.72353 + 1.57243i
\(567\) 49.3395i 2.07206i
\(568\) −28.0182 + 16.1763i −1.17562 + 0.678744i
\(569\) −20.3358 + 35.2226i −0.852519 + 1.47661i 0.0264086 + 0.999651i \(0.491593\pi\)
−0.878928 + 0.476955i \(0.841740\pi\)
\(570\) 45.9488 1.92458
\(571\) 39.4525 + 22.7779i 1.65103 + 0.953225i 0.976648 + 0.214846i \(0.0689249\pi\)
0.674386 + 0.738379i \(0.264408\pi\)
\(572\) −41.2909 + 23.8393i −1.72646 + 0.996773i
\(573\) −9.79767 + 5.65669i −0.409303 + 0.236311i
\(574\) −19.5997 33.9477i −0.818076 1.41695i
\(575\) 12.8487i 0.535828i
\(576\) −2.00288 3.46909i −0.0834532 0.144545i
\(577\) −8.81635 15.2704i −0.367030 0.635714i 0.622070 0.782962i \(-0.286292\pi\)
−0.989100 + 0.147248i \(0.952959\pi\)
\(578\) 3.63084 42.5400i 0.151023 1.76943i
\(579\) 0.588090 1.01860i 0.0244402 0.0423316i
\(580\) −10.9196 −0.453414
\(581\) 41.7038i 1.73017i
\(582\) −48.0552 + 83.2340i −1.99195 + 3.45016i
\(583\) 20.6681 + 11.9328i 0.855987 + 0.494204i
\(584\) −31.6663 + 18.2825i −1.31036 + 0.756537i
\(585\) 2.60791 1.50568i 0.107824 0.0622521i
\(586\) 35.4419 1.46409
\(587\) −15.6017 27.0230i −0.643953 1.11536i −0.984542 0.175147i \(-0.943960\pi\)
0.340590 0.940212i \(-0.389373\pi\)
\(588\) −96.3163 + 55.6083i −3.97202 + 2.29325i
\(589\) 46.6766 26.9487i 1.92328 1.11040i
\(590\) 18.1669 + 10.4887i 0.747919 + 0.431811i
\(591\) −12.9132 −0.531177
\(592\) −2.77651 1.60302i −0.114114 0.0658838i
\(593\) −11.3200 19.6068i −0.464855 0.805153i 0.534340 0.845270i \(-0.320560\pi\)
−0.999195 + 0.0401168i \(0.987227\pi\)
\(594\) −54.4514 −2.23417
\(595\) 16.9532 + 18.4618i 0.695012 + 0.756859i
\(596\) 2.52783 4.37833i 0.103544 0.179343i
\(597\) 10.1707 17.6162i 0.416259 0.720982i
\(598\) 19.9941i 0.817619i
\(599\) 0.0513591 0.0889565i 0.00209848 0.00363467i −0.864974 0.501816i \(-0.832665\pi\)
0.867073 + 0.498182i \(0.165999\pi\)
\(600\) 36.8126i 1.50287i
\(601\) 16.2904i 0.664500i −0.943191 0.332250i \(-0.892192\pi\)
0.943191 0.332250i \(-0.107808\pi\)
\(602\) −24.4422 + 68.8805i −0.996188 + 2.80736i
\(603\) −16.1497 −0.657667
\(604\) 18.8265 0.766038
\(605\) −25.7505 14.8671i −1.04691 0.604432i
\(606\) 2.28057i 0.0926420i
\(607\) 31.4586 + 18.1626i 1.27686 + 0.737198i 0.976271 0.216554i \(-0.0694819\pi\)
0.300594 + 0.953752i \(0.402815\pi\)
\(608\) −10.9192 + 18.9127i −0.442833 + 0.767010i
\(609\) 14.4661 8.35201i 0.586196 0.338440i
\(610\) 6.31171 0.255554
\(611\) 10.4021 + 18.0169i 0.420823 + 0.728887i
\(612\) −6.04559 + 19.2453i −0.244378 + 0.777946i
\(613\) 28.5802 1.15434 0.577171 0.816623i \(-0.304156\pi\)
0.577171 + 0.816623i \(0.304156\pi\)
\(614\) −20.2902 + 35.1437i −0.818847 + 1.41828i
\(615\) 8.48451 4.89853i 0.342128 0.197528i
\(616\) 73.5404 + 127.376i 2.96303 + 5.13211i
\(617\) 6.79067 3.92060i 0.273382 0.157837i −0.357042 0.934089i \(-0.616215\pi\)
0.630424 + 0.776251i \(0.282881\pi\)
\(618\) 12.5078i 0.503138i
\(619\) 31.9910 18.4700i 1.28583 0.742372i 0.307919 0.951413i \(-0.400367\pi\)
0.977907 + 0.209041i \(0.0670341\pi\)
\(620\) 24.2093 + 41.9318i 0.972270 + 1.68402i
\(621\) −7.79687 + 13.5046i −0.312877 + 0.541920i
\(622\) −39.9194 23.0474i −1.60062 0.924119i
\(623\) 72.2085i 2.89297i
\(624\) 23.3757i 0.935778i
\(625\) −0.188091 + 0.325782i −0.00752362 + 0.0130313i
\(626\) 5.86710 + 3.38737i 0.234496 + 0.135386i
\(627\) 38.1938 + 66.1536i 1.52531 + 2.64192i
\(628\) 18.8822 + 32.7050i 0.753483 + 1.30507i
\(629\) −0.484072 2.17260i −0.0193012 0.0866272i
\(630\) −8.67078 15.0182i −0.345452 0.598341i
\(631\) −3.32085 5.75188i −0.132201 0.228979i 0.792324 0.610101i \(-0.208871\pi\)
−0.924525 + 0.381122i \(0.875538\pi\)
\(632\) −67.7002 + 39.0867i −2.69297 + 1.55479i
\(633\) −13.3472 + 23.1180i −0.530504 + 0.918859i
\(634\) 37.5980i 1.49321i
\(635\) −4.91989 2.84050i −0.195240 0.112722i
\(636\) 31.6573 18.2774i 1.25530 0.724745i
\(637\) −24.5733 −0.973629
\(638\) −13.2912 23.0210i −0.526203 0.911410i
\(639\) 5.49189 + 3.17074i 0.217256 + 0.125433i
\(640\) 18.3955 + 10.6207i 0.727147 + 0.419819i
\(641\) 25.1134i 0.991919i −0.868346 0.495960i \(-0.834816\pi\)
0.868346 0.495960i \(-0.165184\pi\)
\(642\) 12.1584 21.0590i 0.479855 0.831134i
\(643\) 3.42114i 0.134916i 0.997722 + 0.0674582i \(0.0214889\pi\)
−0.997722 + 0.0674582i \(0.978511\pi\)
\(644\) 78.6306 3.09848
\(645\) −17.2152 6.10880i −0.677849 0.240534i
\(646\) −66.3813 + 14.7903i −2.61174 + 0.581916i
\(647\) −13.7238 −0.539537 −0.269769 0.962925i \(-0.586947\pi\)
−0.269769 + 0.962925i \(0.586947\pi\)
\(648\) −32.2118 + 55.7925i −1.26540 + 2.19174i
\(649\) 34.8738i 1.36892i
\(650\) 7.59198 13.1497i 0.297782 0.515773i
\(651\) −64.1439 37.0335i −2.51400 1.45146i
\(652\) 15.4531 8.92187i 0.605192 0.349408i
\(653\) 20.9825i 0.821110i −0.911836 0.410555i \(-0.865335\pi\)
0.911836 0.410555i \(-0.134665\pi\)
\(654\) −27.1131 46.9613i −1.06021 1.83633i
\(655\) −3.49600 + 6.05525i −0.136600 + 0.236598i
\(656\) 20.8861i 0.815465i
\(657\) 6.20695 + 3.58359i 0.242156 + 0.139809i
\(658\) 103.755 59.9028i 4.04478 2.33525i
\(659\) −7.21480 12.4964i −0.281049 0.486790i 0.690595 0.723242i \(-0.257349\pi\)
−0.971643 + 0.236452i \(0.924016\pi\)
\(660\) −59.4289 + 34.3113i −2.31327 + 1.33557i
\(661\) 37.9604 1.47649 0.738245 0.674533i \(-0.235655\pi\)
0.738245 + 0.674533i \(0.235655\pi\)
\(662\) −6.60016 11.4318i −0.256522 0.444310i
\(663\) −11.9538 + 10.9770i −0.464246 + 0.426310i
\(664\) 27.2268 47.1582i 1.05661 1.83009i
\(665\) 19.9631 34.5771i 0.774137 1.34084i
\(666\) 1.54001i 0.0596742i
\(667\) −7.61263 −0.294762
\(668\) 12.0673 + 6.96705i 0.466897 + 0.269563i
\(669\) 23.4042 + 13.5124i 0.904857 + 0.522420i
\(670\) 42.3590 24.4560i 1.63647 0.944816i
\(671\) 5.24646 + 9.08713i 0.202537 + 0.350805i
\(672\) 30.0108 1.15769
\(673\) −15.4260 + 8.90621i −0.594629 + 0.343309i −0.766926 0.641736i \(-0.778215\pi\)
0.172297 + 0.985045i \(0.444881\pi\)
\(674\) 49.9098 28.8154i 1.92245 1.10993i
\(675\) 10.2557 5.92112i 0.394741 0.227904i
\(676\) 19.9300 34.5198i 0.766539 1.32769i
\(677\) 16.4685i 0.632936i 0.948603 + 0.316468i \(0.102497\pi\)
−0.948603 + 0.316468i \(0.897503\pi\)
\(678\) 28.0814 48.6384i 1.07846 1.86795i
\(679\) 41.7565 + 72.3244i 1.60247 + 2.77556i
\(680\) −7.11747 31.9444i −0.272943 1.22501i
\(681\) 3.98217 + 6.89731i 0.152597 + 0.264306i
\(682\) −58.9342 + 102.077i −2.25671 + 3.90873i
\(683\) −9.20879 5.31670i −0.352365 0.203438i 0.313362 0.949634i \(-0.398545\pi\)
−0.665726 + 0.746196i \(0.731878\pi\)
\(684\) 32.1332 1.22864
\(685\) −9.67146 5.58382i −0.369528 0.213347i
\(686\) 63.4894i 2.42404i
\(687\) 11.3613i 0.433460i
\(688\) 29.6287 25.2721i 1.12959 0.963491i
\(689\) 8.07677 0.307700
\(690\) 28.7769i 1.09552i
\(691\) −8.97676 5.18273i −0.341492 0.197160i 0.319440 0.947607i \(-0.396505\pi\)
−0.660932 + 0.750446i \(0.729839\pi\)
\(692\) 30.7492i 1.16891i
\(693\) 14.4148 24.9671i 0.547571 0.948421i
\(694\) 30.2407 + 17.4594i 1.14792 + 0.662752i
\(695\) −9.27950 16.0726i −0.351992 0.609667i
\(696\) −21.8108 −0.826737
\(697\) −10.6806 + 9.80785i −0.404558 + 0.371499i
\(698\) 37.2951 64.5971i 1.41164 2.44503i
\(699\) −22.7938 −0.862142
\(700\) −51.7138 29.8569i −1.95460 1.12849i
\(701\) 10.6373 + 18.4243i 0.401765 + 0.695877i 0.993939 0.109933i \(-0.0350636\pi\)
−0.592174 + 0.805810i \(0.701730\pi\)
\(702\) −15.9590 + 9.21394i −0.602334 + 0.347758i
\(703\) −3.07061 + 1.77282i −0.115810 + 0.0668631i
\(704\) 20.1690i 0.760146i
\(705\) 14.9714 + 25.9313i 0.563857 + 0.976629i
\(706\) −5.85006 10.1326i −0.220170 0.381345i
\(707\) −1.71617 0.990828i −0.0645430 0.0372639i
\(708\) 46.2597 + 26.7080i 1.73854 + 1.00375i
\(709\) 45.3238i 1.70217i 0.525027 + 0.851086i \(0.324055\pi\)
−0.525027 + 0.851086i \(0.675945\pi\)
\(710\) −19.2062 −0.720795
\(711\) 13.2700 + 7.66144i 0.497664 + 0.287326i
\(712\) −47.1421 + 81.6526i −1.76673 + 3.06006i
\(713\) 16.8775 + 29.2327i 0.632068 + 1.09477i
\(714\) 63.2133 + 68.8384i 2.36570 + 2.57621i
\(715\) −15.1622 −0.567032
\(716\) 11.0735 + 19.1798i 0.413836 + 0.716785i
\(717\) 47.5078 27.4286i 1.77421 1.02434i
\(718\) −4.09121 7.08618i −0.152683 0.264454i
\(719\) 20.7953 + 12.0062i 0.775534 + 0.447755i 0.834845 0.550485i \(-0.185557\pi\)
−0.0593112 + 0.998240i \(0.518890\pi\)
\(720\) 9.23987i 0.344350i
\(721\) −9.41231 5.43420i −0.350533 0.202380i
\(722\) 30.3077 + 52.4944i 1.12793 + 1.95364i
\(723\) 14.0195 0.521391
\(724\) −47.5853 + 27.4734i −1.76849 + 1.02104i
\(725\) 5.00667 + 2.89060i 0.185943 + 0.107354i
\(726\) −96.0160 55.4349i −3.56349 2.05738i
\(727\) 25.2064 0.934853 0.467426 0.884032i \(-0.345181\pi\)
0.467426 + 0.884032i \(0.345181\pi\)
\(728\) 43.1075 + 24.8882i 1.59767 + 0.922416i
\(729\) −10.5017 −0.388953
\(730\) −21.7069 −0.803409
\(731\) 26.8368 + 3.28392i 0.992596 + 0.121460i
\(732\) 16.0720 0.594037
\(733\) 17.5659 0.648813 0.324406 0.945918i \(-0.394835\pi\)
0.324406 + 0.945918i \(0.394835\pi\)
\(734\) −50.7710 29.3126i −1.87399 1.08195i
\(735\) −35.3676 −1.30455
\(736\) −11.8447 6.83852i −0.436600 0.252071i
\(737\) 70.4197 + 40.6568i 2.59394 + 1.49761i
\(738\) 8.68845 5.01628i 0.319826 0.184652i
\(739\) 31.7737 1.16882 0.584408 0.811460i \(-0.301327\pi\)
0.584408 + 0.811460i \(0.301327\pi\)
\(740\) −1.59260 2.75847i −0.0585453 0.101403i
\(741\) 22.3883 + 12.9259i 0.822453 + 0.474844i
\(742\) 46.5119i 1.70751i
\(743\) 5.91820 + 3.41688i 0.217118 + 0.125353i 0.604615 0.796518i \(-0.293327\pi\)
−0.387497 + 0.921871i \(0.626660\pi\)
\(744\) 48.3555 + 83.7542i 1.77280 + 3.07058i
\(745\) 1.39234 0.803867i 0.0510114 0.0294514i
\(746\) 4.83368 + 8.37218i 0.176974 + 0.306527i
\(747\) −10.6735 −0.390524
\(748\) 74.8114 68.6982i 2.73538 2.51185i
\(749\) −10.5648 18.2988i −0.386030 0.668624i
\(750\) 28.4172 49.2200i 1.03765 1.79726i
\(751\) −24.3491 14.0579i −0.888510 0.512982i −0.0150554 0.999887i \(-0.504792\pi\)
−0.873455 + 0.486905i \(0.838126\pi\)
\(752\) −63.8343 −2.32780
\(753\) 49.3365i 1.79792i
\(754\) −7.79096 4.49811i −0.283730 0.163812i
\(755\) 5.18485 + 2.99347i 0.188696 + 0.108944i
\(756\) 36.2356 + 62.7620i 1.31788 + 2.28263i
\(757\) −20.6236 35.7212i −0.749579 1.29831i −0.948025 0.318197i \(-0.896923\pi\)
0.198446 0.980112i \(-0.436411\pi\)
\(758\) 0.0302289i 0.00109796i
\(759\) −41.4308 + 23.9201i −1.50384 + 0.868245i
\(760\) −45.1482 + 26.0663i −1.63770 + 0.945524i
\(761\) −26.9871 46.7431i −0.978282 1.69443i −0.668648 0.743579i \(-0.733127\pi\)
−0.309635 0.950856i \(-0.600207\pi\)
\(762\) −18.3448 10.5914i −0.664562 0.383685i
\(763\) −47.1188