Properties

Label 210.3.k.b.83.6
Level 210
Weight 3
Character 210.83
Analytic conductor 5.722
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 83.6
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.6

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.86291 + 2.35150i) q^{3} +2.00000i q^{4} +(1.91622 + 4.61824i) q^{5} +(-4.21441 + 0.488596i) q^{6} +(6.26242 + 3.12763i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.05914 - 8.76127i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(-1.86291 + 2.35150i) q^{3} +2.00000i q^{4} +(1.91622 + 4.61824i) q^{5} +(-4.21441 + 0.488596i) q^{6} +(6.26242 + 3.12763i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.05914 - 8.76127i) q^{9} +(-2.70202 + 6.53446i) q^{10} +0.117411i q^{11} +(-4.70301 - 3.72582i) q^{12} +(-9.72258 + 9.72258i) q^{13} +(3.13479 + 9.39005i) q^{14} +(-14.4295 - 4.09735i) q^{15} -4.00000 q^{16} +(13.8691 - 13.8691i) q^{17} +(6.70213 - 10.8204i) q^{18} -29.7218 q^{19} +(-9.23647 + 3.83244i) q^{20} +(-19.0210 + 8.89961i) q^{21} +(-0.117411 + 0.117411i) q^{22} +(-2.25150 + 2.25150i) q^{23} +(-0.977191 - 8.42883i) q^{24} +(-17.6562 + 17.6991i) q^{25} -19.4452 q^{26} +(24.4382 + 11.4794i) q^{27} +(-6.25527 + 12.5248i) q^{28} +46.0711 q^{29} +(-10.3322 - 18.5269i) q^{30} -1.50946i q^{31} +(-4.00000 - 4.00000i) q^{32} +(-0.276093 - 0.218727i) q^{33} +27.7381 q^{34} +(-2.44398 + 34.9146i) q^{35} +(17.5225 - 4.11829i) q^{36} +(5.32611 - 5.32611i) q^{37} +(-29.7218 - 29.7218i) q^{38} +(-4.75041 - 40.9749i) q^{39} +(-13.0689 - 5.40403i) q^{40} -13.4956 q^{41} +(-27.9206 - 10.1213i) q^{42} +(36.8754 + 36.8754i) q^{43} -0.234823 q^{44} +(36.5159 - 26.2981i) q^{45} -4.50300 q^{46} +(29.7803 - 29.7803i) q^{47} +(7.45163 - 9.40602i) q^{48} +(29.4358 + 39.1731i) q^{49} +(-35.3553 + 0.0428987i) q^{50} +(6.77637 + 58.4500i) q^{51} +(-19.4452 - 19.4452i) q^{52} +(59.8162 - 59.8162i) q^{53} +(12.9588 + 35.9175i) q^{54} +(-0.542233 + 0.224986i) q^{55} +(-18.7801 + 6.26957i) q^{56} +(55.3690 - 69.8910i) q^{57} +(46.0711 + 46.0711i) q^{58} +84.9209i q^{59} +(8.19471 - 28.8591i) q^{60} -34.8141i q^{61} +(1.50946 - 1.50946i) q^{62} +(14.5068 - 61.3070i) q^{63} -8.00000i q^{64} +(-63.5317 - 26.2706i) q^{65} +(-0.0573667 - 0.494820i) q^{66} +(-34.4892 + 34.4892i) q^{67} +(27.7381 + 27.7381i) q^{68} +(-1.10007 - 9.48874i) q^{69} +(-37.3585 + 32.4706i) q^{70} +77.6498i q^{71} +(21.6408 + 13.4043i) q^{72} +(41.3259 - 41.3259i) q^{73} +10.6522 q^{74} +(-8.72762 - 74.4905i) q^{75} -59.4436i q^{76} +(-0.367220 + 0.735279i) q^{77} +(36.2245 - 45.7254i) q^{78} +0.865694i q^{79} +(-7.66488 - 18.4729i) q^{80} +(-72.5199 + 36.0814i) q^{81} +(-13.4956 - 13.4956i) q^{82} +(99.0630 + 99.0630i) q^{83} +(-17.7992 - 38.0419i) q^{84} +(90.6268 + 37.4745i) q^{85} +73.7509i q^{86} +(-85.8262 + 108.336i) q^{87} +(-0.234823 - 0.234823i) q^{88} -129.599i q^{89} +(62.8140 + 10.2177i) q^{90} +(-91.2955 + 30.4782i) q^{91} +(-4.50300 - 4.50300i) q^{92} +(3.54949 + 2.81198i) q^{93} +59.5607 q^{94} +(-56.9535 - 137.262i) q^{95} +(16.8577 - 1.95438i) q^{96} +(-15.7928 - 15.7928i) q^{97} +(-9.73729 + 68.6089i) q^{98} +(1.02867 - 0.241767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) −1.86291 + 2.35150i −0.620970 + 0.783835i
\(4\) 2.00000i 0.500000i
\(5\) 1.91622 + 4.61824i 0.383244 + 0.923647i
\(6\) −4.21441 + 0.488596i −0.702402 + 0.0814326i
\(7\) 6.26242 + 3.12763i 0.894631 + 0.446805i
\(8\) −2.00000 + 2.00000i −0.250000 + 0.250000i
\(9\) −2.05914 8.76127i −0.228794 0.973475i
\(10\) −2.70202 + 6.53446i −0.270202 + 0.653446i
\(11\) 0.117411i 0.0106738i 0.999986 + 0.00533688i \(0.00169879\pi\)
−0.999986 + 0.00533688i \(0.998301\pi\)
\(12\) −4.70301 3.72582i −0.391917 0.310485i
\(13\) −9.72258 + 9.72258i −0.747890 + 0.747890i −0.974083 0.226192i \(-0.927372\pi\)
0.226192 + 0.974083i \(0.427372\pi\)
\(14\) 3.13479 + 9.39005i 0.223913 + 0.670718i
\(15\) −14.4295 4.09735i −0.961969 0.273157i
\(16\) −4.00000 −0.250000
\(17\) 13.8691 13.8691i 0.815828 0.815828i −0.169673 0.985500i \(-0.554271\pi\)
0.985500 + 0.169673i \(0.0542710\pi\)
\(18\) 6.70213 10.8204i 0.372341 0.601134i
\(19\) −29.7218 −1.56431 −0.782153 0.623086i \(-0.785879\pi\)
−0.782153 + 0.623086i \(0.785879\pi\)
\(20\) −9.23647 + 3.83244i −0.461824 + 0.191622i
\(21\) −19.0210 + 8.89961i −0.905760 + 0.423791i
\(22\) −0.117411 + 0.117411i −0.00533688 + 0.00533688i
\(23\) −2.25150 + 2.25150i −0.0978912 + 0.0978912i −0.754356 0.656465i \(-0.772051\pi\)
0.656465 + 0.754356i \(0.272051\pi\)
\(24\) −0.977191 8.42883i −0.0407163 0.351201i
\(25\) −17.6562 + 17.6991i −0.706248 + 0.707964i
\(26\) −19.4452 −0.747890
\(27\) 24.4382 + 11.4794i 0.905117 + 0.425162i
\(28\) −6.25527 + 12.5248i −0.223402 + 0.447316i
\(29\) 46.0711 1.58866 0.794329 0.607488i \(-0.207823\pi\)
0.794329 + 0.607488i \(0.207823\pi\)
\(30\) −10.3322 18.5269i −0.344406 0.617563i
\(31\) 1.50946i 0.0486921i −0.999704 0.0243461i \(-0.992250\pi\)
0.999704 0.0243461i \(-0.00775036\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) −0.276093 0.218727i −0.00836646 0.00662808i
\(34\) 27.7381 0.815828
\(35\) −2.44398 + 34.9146i −0.0698280 + 0.997559i
\(36\) 17.5225 4.11829i 0.486737 0.114397i
\(37\) 5.32611 5.32611i 0.143949 0.143949i −0.631460 0.775409i \(-0.717544\pi\)
0.775409 + 0.631460i \(0.217544\pi\)
\(38\) −29.7218 29.7218i −0.782153 0.782153i
\(39\) −4.75041 40.9749i −0.121805 1.05064i
\(40\) −13.0689 5.40403i −0.326723 0.135101i
\(41\) −13.4956 −0.329160 −0.164580 0.986364i \(-0.552627\pi\)
−0.164580 + 0.986364i \(0.552627\pi\)
\(42\) −27.9206 10.1213i −0.664776 0.240984i
\(43\) 36.8754 + 36.8754i 0.857568 + 0.857568i 0.991051 0.133483i \(-0.0426162\pi\)
−0.133483 + 0.991051i \(0.542616\pi\)
\(44\) −0.234823 −0.00533688
\(45\) 36.5159 26.2981i 0.811464 0.584403i
\(46\) −4.50300 −0.0978912
\(47\) 29.7803 29.7803i 0.633624 0.633624i −0.315351 0.948975i \(-0.602122\pi\)
0.948975 + 0.315351i \(0.102122\pi\)
\(48\) 7.45163 9.40602i 0.155242 0.195959i
\(49\) 29.4358 + 39.1731i 0.600731 + 0.799451i
\(50\) −35.3553 + 0.0428987i −0.707106 + 0.000857974i
\(51\) 6.77637 + 58.4500i 0.132870 + 1.14608i
\(52\) −19.4452 19.4452i −0.373945 0.373945i
\(53\) 59.8162 59.8162i 1.12861 1.12861i 0.138204 0.990404i \(-0.455867\pi\)
0.990404 0.138204i \(-0.0441329\pi\)
\(54\) 12.9588 + 35.9175i 0.239978 + 0.665140i
\(55\) −0.542233 + 0.224986i −0.00985879 + 0.00409065i
\(56\) −18.7801 + 6.26957i −0.335359 + 0.111957i
\(57\) 55.3690 69.8910i 0.971387 1.22616i
\(58\) 46.0711 + 46.0711i 0.794329 + 0.794329i
\(59\) 84.9209i 1.43934i 0.694317 + 0.719669i \(0.255706\pi\)
−0.694317 + 0.719669i \(0.744294\pi\)
\(60\) 8.19471 28.8591i 0.136578 0.480985i
\(61\) 34.8141i 0.570723i −0.958420 0.285361i \(-0.907886\pi\)
0.958420 0.285361i \(-0.0921137\pi\)
\(62\) 1.50946 1.50946i 0.0243461 0.0243461i
\(63\) 14.5068 61.3070i 0.230267 0.973127i
\(64\) 8.00000i 0.125000i
\(65\) −63.5317 26.2706i −0.977411 0.404163i
\(66\) −0.0573667 0.494820i −0.000869192 0.00749727i
\(67\) −34.4892 + 34.4892i −0.514764 + 0.514764i −0.915982 0.401218i \(-0.868587\pi\)
0.401218 + 0.915982i \(0.368587\pi\)
\(68\) 27.7381 + 27.7381i 0.407914 + 0.407914i
\(69\) −1.10007 9.48874i −0.0159431 0.137518i
\(70\) −37.3585 + 32.4706i −0.533694 + 0.463866i
\(71\) 77.6498i 1.09366i 0.837244 + 0.546829i \(0.184165\pi\)
−0.837244 + 0.546829i \(0.815835\pi\)
\(72\) 21.6408 + 13.4043i 0.300567 + 0.186170i
\(73\) 41.3259 41.3259i 0.566108 0.566108i −0.364928 0.931036i \(-0.618906\pi\)
0.931036 + 0.364928i \(0.118906\pi\)
\(74\) 10.6522 0.143949
\(75\) −8.72762 74.4905i −0.116368 0.993206i
\(76\) 59.4436i 0.782153i
\(77\) −0.367220 + 0.735279i −0.00476909 + 0.00954908i
\(78\) 36.2245 45.7254i 0.464417 0.586223i
\(79\) 0.865694i 0.0109582i 0.999985 + 0.00547908i \(0.00174405\pi\)
−0.999985 + 0.00547908i \(0.998256\pi\)
\(80\) −7.66488 18.4729i −0.0958110 0.230912i
\(81\) −72.5199 + 36.0814i −0.895307 + 0.445450i
\(82\) −13.4956 13.4956i −0.164580 0.164580i
\(83\) 99.0630 + 99.0630i 1.19353 + 1.19353i 0.976069 + 0.217461i \(0.0697776\pi\)
0.217461 + 0.976069i \(0.430222\pi\)
\(84\) −17.7992 38.0419i −0.211896 0.452880i
\(85\) 90.6268 + 37.4745i 1.06620 + 0.440876i
\(86\) 73.7509i 0.857568i
\(87\) −85.8262 + 108.336i −0.986508 + 1.24525i
\(88\) −0.234823 0.234823i −0.00266844 0.00266844i
\(89\) 129.599i 1.45616i −0.685490 0.728082i \(-0.740412\pi\)
0.685490 0.728082i \(-0.259588\pi\)
\(90\) 62.8140 + 10.2177i 0.697933 + 0.113530i
\(91\) −91.2955 + 30.4782i −1.00325 + 0.334925i
\(92\) −4.50300 4.50300i −0.0489456 0.0489456i
\(93\) 3.54949 + 2.81198i 0.0381666 + 0.0302363i
\(94\) 59.5607 0.633624
\(95\) −56.9535 137.262i −0.599511 1.44487i
\(96\) 16.8577 1.95438i 0.175601 0.0203581i
\(97\) −15.7928 15.7928i −0.162812 0.162812i 0.620999 0.783811i \(-0.286727\pi\)
−0.783811 + 0.620999i \(0.786727\pi\)
\(98\) −9.73729 + 68.6089i −0.0993602 + 0.700091i
\(99\) 1.02867 0.241767i 0.0103906 0.00244209i
\(100\) −35.3982 35.3124i −0.353982 0.353124i
\(101\) −14.4525 −0.143094 −0.0715470 0.997437i \(-0.522794\pi\)
−0.0715470 + 0.997437i \(0.522794\pi\)
\(102\) −51.6736 + 65.2264i −0.506604 + 0.639474i
\(103\) −31.3694 + 31.3694i −0.304557 + 0.304557i −0.842794 0.538237i \(-0.819091\pi\)
0.538237 + 0.842794i \(0.319091\pi\)
\(104\) 38.8903i 0.373945i
\(105\) −77.5488 70.7897i −0.738560 0.674187i
\(106\) 119.632 1.12861
\(107\) −105.856 105.856i −0.989310 0.989310i 0.0106339 0.999943i \(-0.496615\pi\)
−0.999943 + 0.0106339i \(0.996615\pi\)
\(108\) −22.9587 + 48.8763i −0.212581 + 0.452559i
\(109\) 95.4740i 0.875908i 0.898997 + 0.437954i \(0.144297\pi\)
−0.898997 + 0.437954i \(0.855703\pi\)
\(110\) −0.767219 0.317247i −0.00697472 0.00288407i
\(111\) 2.60231 + 22.4464i 0.0234443 + 0.202220i
\(112\) −25.0497 12.5105i −0.223658 0.111701i
\(113\) 60.1261 60.1261i 0.532089 0.532089i −0.389104 0.921194i \(-0.627215\pi\)
0.921194 + 0.389104i \(0.127215\pi\)
\(114\) 125.260 14.5219i 1.09877 0.127386i
\(115\) −14.7123 6.08359i −0.127933 0.0529007i
\(116\) 92.1422i 0.794329i
\(117\) 105.202 + 65.1620i 0.899165 + 0.556940i
\(118\) −84.9209 + 84.9209i −0.719669 + 0.719669i
\(119\) 130.231 43.4766i 1.09438 0.365350i
\(120\) 37.0538 20.6644i 0.308782 0.172203i
\(121\) 120.986 0.999886
\(122\) 34.8141 34.8141i 0.285361 0.285361i
\(123\) 25.1410 31.7349i 0.204398 0.258007i
\(124\) 3.01891 0.0243461
\(125\) −115.572 47.6252i −0.924575 0.381001i
\(126\) 75.8139 46.8002i 0.601697 0.371430i
\(127\) 171.860 171.860i 1.35323 1.35323i 0.471207 0.882022i \(-0.343818\pi\)
0.882022 0.471207i \(-0.156182\pi\)
\(128\) 8.00000 8.00000i 0.0625000 0.0625000i
\(129\) −155.408 + 18.0172i −1.20472 + 0.139668i
\(130\) −37.2612 89.8023i −0.286624 0.690787i
\(131\) −145.791 −1.11291 −0.556453 0.830879i \(-0.687838\pi\)
−0.556453 + 0.830879i \(0.687838\pi\)
\(132\) 0.437453 0.552187i 0.00331404 0.00418323i
\(133\) −186.131 92.9590i −1.39948 0.698940i
\(134\) −68.9784 −0.514764
\(135\) −6.18554 + 134.858i −0.0458188 + 0.998950i
\(136\) 55.4763i 0.407914i
\(137\) 37.8019 + 37.8019i 0.275926 + 0.275926i 0.831480 0.555554i \(-0.187494\pi\)
−0.555554 + 0.831480i \(0.687494\pi\)
\(138\) 8.38867 10.5888i 0.0607875 0.0767305i
\(139\) −65.4496 −0.470861 −0.235430 0.971891i \(-0.575650\pi\)
−0.235430 + 0.971891i \(0.575650\pi\)
\(140\) −69.8291 4.88796i −0.498780 0.0349140i
\(141\) 14.5505 + 125.507i 0.103195 + 0.890118i
\(142\) −77.6498 + 77.6498i −0.546829 + 0.546829i
\(143\) −1.14154 1.14154i −0.00798280 0.00798280i
\(144\) 8.23657 + 35.0451i 0.0571984 + 0.243369i
\(145\) 88.2823 + 212.767i 0.608844 + 1.46736i
\(146\) 82.6518 0.566108
\(147\) −146.952 3.75748i −0.999673 0.0255611i
\(148\) 10.6522 + 10.6522i 0.0719745 + 0.0719745i
\(149\) 109.296 0.733529 0.366765 0.930314i \(-0.380465\pi\)
0.366765 + 0.930314i \(0.380465\pi\)
\(150\) 65.7628 83.2181i 0.438419 0.554787i
\(151\) −223.334 −1.47903 −0.739516 0.673139i \(-0.764946\pi\)
−0.739516 + 0.673139i \(0.764946\pi\)
\(152\) 59.4436 59.4436i 0.391077 0.391077i
\(153\) −150.069 92.9524i −0.980844 0.607532i
\(154\) −1.10250 + 0.368060i −0.00715908 + 0.00239000i
\(155\) 6.97102 2.89245i 0.0449743 0.0186610i
\(156\) 81.9499 9.50082i 0.525320 0.0609027i
\(157\) −1.67144 1.67144i −0.0106461 0.0106461i 0.701764 0.712410i \(-0.252396\pi\)
−0.712410 + 0.701764i \(0.752396\pi\)
\(158\) −0.865694 + 0.865694i −0.00547908 + 0.00547908i
\(159\) 29.2259 + 252.090i 0.183811 + 1.58547i
\(160\) 10.8081 26.1378i 0.0675504 0.163361i
\(161\) −21.1417 + 7.05797i −0.131315 + 0.0438383i
\(162\) −108.601 36.4384i −0.670378 0.224929i
\(163\) −34.1872 34.1872i −0.209737 0.209737i 0.594419 0.804156i \(-0.297382\pi\)
−0.804156 + 0.594419i \(0.797382\pi\)
\(164\) 26.9911i 0.164580i
\(165\) 0.481076 1.69419i 0.00291561 0.0102678i
\(166\) 198.126i 1.19353i
\(167\) −122.479 + 122.479i −0.733409 + 0.733409i −0.971293 0.237884i \(-0.923546\pi\)
0.237884 + 0.971293i \(0.423546\pi\)
\(168\) 20.2427 55.8411i 0.120492 0.332388i
\(169\) 20.0570i 0.118680i
\(170\) 53.1524 + 128.101i 0.312661 + 0.753537i
\(171\) 61.2015 + 260.401i 0.357903 + 1.52281i
\(172\) −73.7509 + 73.7509i −0.428784 + 0.428784i
\(173\) −11.1204 11.1204i −0.0642800 0.0642800i 0.674236 0.738516i \(-0.264473\pi\)
−0.738516 + 0.674236i \(0.764473\pi\)
\(174\) −194.163 + 22.5101i −1.11588 + 0.129369i
\(175\) −165.927 + 55.6171i −0.948154 + 0.317812i
\(176\) 0.469645i 0.00266844i
\(177\) −199.692 158.200i −1.12820 0.893785i
\(178\) 129.599 129.599i 0.728082 0.728082i
\(179\) −167.194 −0.934042 −0.467021 0.884246i \(-0.654673\pi\)
−0.467021 + 0.884246i \(0.654673\pi\)
\(180\) 52.5963 + 73.0317i 0.292201 + 0.405732i
\(181\) 271.099i 1.49778i −0.662692 0.748892i \(-0.730586\pi\)
0.662692 0.748892i \(-0.269414\pi\)
\(182\) −121.774 60.8173i −0.669086 0.334161i
\(183\) 81.8655 + 64.8555i 0.447352 + 0.354402i
\(184\) 9.00599i 0.0489456i
\(185\) 34.8032 + 14.3912i 0.188126 + 0.0777905i
\(186\) 0.737513 + 6.36147i 0.00396513 + 0.0342015i
\(187\) 1.62839 + 1.62839i 0.00870795 + 0.00870795i
\(188\) 59.5607 + 59.5607i 0.316812 + 0.316812i
\(189\) 117.139 + 148.322i 0.619782 + 0.784774i
\(190\) 80.3089 194.216i 0.422678 1.02219i
\(191\) 274.726i 1.43835i −0.694827 0.719177i \(-0.744519\pi\)
0.694827 0.719177i \(-0.255481\pi\)
\(192\) 18.8120 + 14.9033i 0.0979793 + 0.0776212i
\(193\) −202.411 202.411i −1.04876 1.04876i −0.998749 0.0500128i \(-0.984074\pi\)
−0.0500128 0.998749i \(-0.515926\pi\)
\(194\) 31.5856i 0.162812i
\(195\) 180.129 100.455i 0.923739 0.515156i
\(196\) −78.3462 + 58.8716i −0.399726 + 0.300365i
\(197\) 182.638 + 182.638i 0.927095 + 0.927095i 0.997517 0.0704222i \(-0.0224347\pi\)
−0.0704222 + 0.997517i \(0.522435\pi\)
\(198\) 1.27044 + 0.786906i 0.00641636 + 0.00397427i
\(199\) 246.453 1.23846 0.619228 0.785211i \(-0.287446\pi\)
0.619228 + 0.785211i \(0.287446\pi\)
\(200\) −0.0857974 70.7106i −0.000428987 0.353553i
\(201\) −16.8513 145.352i −0.0838372 0.723143i
\(202\) −14.4525 14.4525i −0.0715470 0.0715470i
\(203\) 288.517 + 144.093i 1.42126 + 0.709820i
\(204\) −116.900 + 13.5527i −0.573039 + 0.0664350i
\(205\) −25.8605 62.3257i −0.126149 0.304028i
\(206\) −62.7388 −0.304557
\(207\) 24.3622 + 15.0898i 0.117692 + 0.0728978i
\(208\) 38.8903 38.8903i 0.186973 0.186973i
\(209\) 3.48968i 0.0166970i
\(210\) −6.75917 148.339i −0.0321865 0.706374i
\(211\) 165.881 0.786165 0.393083 0.919503i \(-0.371409\pi\)
0.393083 + 0.919503i \(0.371409\pi\)
\(212\) 119.632 + 119.632i 0.564304 + 0.564304i
\(213\) −182.594 144.654i −0.857248 0.679129i
\(214\) 211.712i 0.989310i
\(215\) −99.6380 + 240.961i −0.463433 + 1.12075i
\(216\) −71.8351 + 25.9176i −0.332570 + 0.119989i
\(217\) 4.72102 9.45285i 0.0217559 0.0435615i
\(218\) −95.4740 + 95.4740i −0.437954 + 0.437954i
\(219\) 20.1917 + 174.164i 0.0921994 + 0.795271i
\(220\) −0.449972 1.08447i −0.00204533 0.00492939i
\(221\) 269.686i 1.22030i
\(222\) −19.8441 + 25.0487i −0.0893879 + 0.112832i
\(223\) 44.8950 44.8950i 0.201323 0.201323i −0.599244 0.800567i \(-0.704532\pi\)
0.800567 + 0.599244i \(0.204532\pi\)
\(224\) −12.5391 37.5602i −0.0559783 0.167680i
\(225\) 191.423 + 118.246i 0.850771 + 0.525537i
\(226\) 120.252 0.532089
\(227\) 211.845 211.845i 0.933238 0.933238i −0.0646692 0.997907i \(-0.520599\pi\)
0.997907 + 0.0646692i \(0.0205992\pi\)
\(228\) 139.782 + 110.738i 0.613079 + 0.485693i
\(229\) −10.2429 −0.0447287 −0.0223644 0.999750i \(-0.507119\pi\)
−0.0223644 + 0.999750i \(0.507119\pi\)
\(230\) −8.62873 20.7959i −0.0375162 0.0904170i
\(231\) −1.04492 2.23328i −0.00452344 0.00966787i
\(232\) −92.1422 + 92.1422i −0.397165 + 0.397165i
\(233\) −135.649 + 135.649i −0.582186 + 0.582186i −0.935504 0.353317i \(-0.885054\pi\)
0.353317 + 0.935504i \(0.385054\pi\)
\(234\) 40.0404 + 170.364i 0.171113 + 0.728053i
\(235\) 194.598 + 80.4669i 0.828077 + 0.342413i
\(236\) −169.842 −0.719669
\(237\) −2.03568 1.61271i −0.00858938 0.00680468i
\(238\) 173.708 + 86.7548i 0.729865 + 0.364516i
\(239\) −25.1069 −0.105050 −0.0525250 0.998620i \(-0.516727\pi\)
−0.0525250 + 0.998620i \(0.516727\pi\)
\(240\) 57.7182 + 16.3894i 0.240492 + 0.0682892i
\(241\) 278.949i 1.15747i −0.815517 0.578733i \(-0.803548\pi\)
0.815517 0.578733i \(-0.196452\pi\)
\(242\) 120.986 + 120.986i 0.499943 + 0.499943i
\(243\) 50.2522 237.747i 0.206799 0.978383i
\(244\) 69.6282 0.285361
\(245\) −124.505 + 211.006i −0.508184 + 0.861248i
\(246\) 56.8759 6.59387i 0.231203 0.0268044i
\(247\) 288.973 288.973i 1.16993 1.16993i
\(248\) 3.01891 + 3.01891i 0.0121730 + 0.0121730i
\(249\) −417.492 + 48.4017i −1.67668 + 0.194385i
\(250\) −67.9466 163.197i −0.271787 0.652788i
\(251\) 211.250 0.841633 0.420817 0.907146i \(-0.361744\pi\)
0.420817 + 0.907146i \(0.361744\pi\)
\(252\) 122.614 + 29.0137i 0.486564 + 0.115134i
\(253\) −0.264351 0.264351i −0.00104487 0.00104487i
\(254\) 343.720 1.35323
\(255\) −256.951 + 143.298i −1.00765 + 0.561953i
\(256\) 16.0000 0.0625000
\(257\) 330.432 330.432i 1.28573 1.28573i 0.348371 0.937357i \(-0.386735\pi\)
0.937357 0.348371i \(-0.113265\pi\)
\(258\) −173.425 137.391i −0.672192 0.532524i
\(259\) 50.0125 16.6962i 0.193098 0.0644642i
\(260\) 52.5411 127.063i 0.202081 0.488706i
\(261\) −94.8670 403.641i −0.363475 1.54652i
\(262\) −145.791 145.791i −0.556453 0.556453i
\(263\) −74.3401 + 74.3401i −0.282662 + 0.282662i −0.834170 0.551508i \(-0.814053\pi\)
0.551508 + 0.834170i \(0.314053\pi\)
\(264\) 0.989640 0.114733i 0.00374864 0.000434596i
\(265\) 390.866 + 161.624i 1.47497 + 0.609903i
\(266\) −93.1716 279.089i −0.350269 1.04921i
\(267\) 304.751 + 241.430i 1.14139 + 0.904233i
\(268\) −68.9784 68.9784i −0.257382 0.257382i
\(269\) 250.571i 0.931490i −0.884919 0.465745i \(-0.845786\pi\)
0.884919 0.465745i \(-0.154214\pi\)
\(270\) −141.044 + 128.673i −0.522384 + 0.476565i
\(271\) 207.488i 0.765638i −0.923823 0.382819i \(-0.874953\pi\)
0.923823 0.382819i \(-0.125047\pi\)
\(272\) −55.4763 + 55.4763i −0.203957 + 0.203957i
\(273\) 98.4056 271.460i 0.360460 0.994359i
\(274\) 75.6039i 0.275926i
\(275\) −2.07808 2.07304i −0.00755664 0.00753833i
\(276\) 18.9775 2.20014i 0.0687590 0.00797154i
\(277\) −64.7233 + 64.7233i −0.233658 + 0.233658i −0.814218 0.580560i \(-0.802834\pi\)
0.580560 + 0.814218i \(0.302834\pi\)
\(278\) −65.4496 65.4496i −0.235430 0.235430i
\(279\) −13.2248 + 3.10819i −0.0474006 + 0.0111405i
\(280\) −64.9412 74.7171i −0.231933 0.266847i
\(281\) 353.277i 1.25721i −0.777723 0.628607i \(-0.783626\pi\)
0.777723 0.628607i \(-0.216374\pi\)
\(282\) −110.956 + 140.057i −0.393461 + 0.496656i
\(283\) 181.090 181.090i 0.639894 0.639894i −0.310635 0.950529i \(-0.600542\pi\)
0.950529 + 0.310635i \(0.100542\pi\)
\(284\) −155.300 −0.546829
\(285\) 428.872 + 121.781i 1.50481 + 0.427301i
\(286\) 2.28308i 0.00798280i
\(287\) −84.5149 42.2092i −0.294477 0.147070i
\(288\) −26.8085 + 43.2817i −0.0930852 + 0.150284i
\(289\) 95.7024i 0.331150i
\(290\) −124.485 + 301.049i −0.429258 + 1.03810i
\(291\) 66.5574 7.71630i 0.228720 0.0265165i
\(292\) 82.6518 + 82.6518i 0.283054 + 0.283054i
\(293\) 72.3843 + 72.3843i 0.247045 + 0.247045i 0.819757 0.572712i \(-0.194108\pi\)
−0.572712 + 0.819757i \(0.694108\pi\)
\(294\) −143.194 150.709i −0.487056 0.512617i
\(295\) −392.185 + 162.727i −1.32944 + 0.551617i
\(296\) 21.3044i 0.0719745i
\(297\) −1.34781 + 2.86932i −0.00453808 + 0.00966101i
\(298\) 109.296 + 109.296i 0.366765 + 0.366765i
\(299\) 43.7807i 0.146424i
\(300\) 148.981 17.4552i 0.496603 0.0581841i
\(301\) 115.597 + 346.262i 0.384042 + 1.15037i
\(302\) −223.334 223.334i −0.739516 0.739516i
\(303\) 26.9237 33.9851i 0.0888571 0.112162i
\(304\) 118.887 0.391077
\(305\) 160.780 66.7115i 0.527147 0.218726i
\(306\) −57.1168 243.022i −0.186656 0.794188i
\(307\) 228.716 + 228.716i 0.745005 + 0.745005i 0.973536 0.228532i \(-0.0733925\pi\)
−0.228532 + 0.973536i \(0.573392\pi\)
\(308\) −1.47056 0.734439i −0.00477454 0.00238454i
\(309\) −15.3269 132.204i −0.0496018 0.427843i
\(310\) 9.86347 + 4.07857i 0.0318177 + 0.0131567i
\(311\) −269.223 −0.865670 −0.432835 0.901473i \(-0.642487\pi\)
−0.432835 + 0.901473i \(0.642487\pi\)
\(312\) 91.4507 + 72.4491i 0.293111 + 0.232209i
\(313\) −421.023 + 421.023i −1.34512 + 1.34512i −0.454244 + 0.890877i \(0.650091\pi\)
−0.890877 + 0.454244i \(0.849909\pi\)
\(314\) 3.34288i 0.0106461i
\(315\) 310.929 50.4817i 0.987075 0.160259i
\(316\) −1.73139 −0.00547908
\(317\) 74.8122 + 74.8122i 0.236001 + 0.236001i 0.815192 0.579191i \(-0.196632\pi\)
−0.579191 + 0.815192i \(0.696632\pi\)
\(318\) −222.864 + 281.316i −0.700831 + 0.884642i
\(319\) 5.40927i 0.0169570i
\(320\) 36.9459 15.3298i 0.115456 0.0479055i
\(321\) 446.121 51.7208i 1.38979 0.161124i
\(322\) −28.1997 14.0837i −0.0875766 0.0437383i
\(323\) −412.214 + 412.214i −1.27620 + 1.27620i
\(324\) −72.1629 145.040i −0.222725 0.447653i
\(325\) −0.417086 343.745i −0.00128334 1.05768i
\(326\) 68.3743i 0.209737i
\(327\) −224.507 177.859i −0.686567 0.543912i
\(328\) 26.9911 26.9911i 0.0822900 0.0822900i
\(329\) 279.639 93.3550i 0.849966 0.283754i
\(330\) 2.17527 1.21312i 0.00659172 0.00367611i
\(331\) −506.910 −1.53145 −0.765725 0.643168i \(-0.777620\pi\)
−0.765725 + 0.643168i \(0.777620\pi\)
\(332\) −198.126 + 198.126i −0.596765 + 0.596765i
\(333\) −57.6307 35.6963i −0.173065 0.107196i
\(334\) −244.959 −0.733409
\(335\) −225.368 93.1904i −0.672741 0.278180i
\(336\) 76.0838 35.5984i 0.226440 0.105948i
\(337\) −187.948 + 187.948i −0.557709 + 0.557709i −0.928655 0.370945i \(-0.879034\pi\)
0.370945 + 0.928655i \(0.379034\pi\)
\(338\) 20.0570 20.0570i 0.0593402 0.0593402i
\(339\) 29.3773 + 253.396i 0.0866588 + 0.747481i
\(340\) −74.9489 + 181.254i −0.220438 + 0.533099i
\(341\) 0.177227 0.000519728
\(342\) −199.200 + 321.603i −0.582455 + 0.940358i
\(343\) 61.8203 + 337.383i 0.180234 + 0.983624i
\(344\) −147.502 −0.428784
\(345\) 41.7133 23.2629i 0.120908 0.0674287i
\(346\) 22.2409i 0.0642800i
\(347\) 152.796 + 152.796i 0.440334 + 0.440334i 0.892124 0.451790i \(-0.149214\pi\)
−0.451790 + 0.892124i \(0.649214\pi\)
\(348\) −216.673 171.652i −0.622623 0.493254i
\(349\) −368.362 −1.05548 −0.527740 0.849406i \(-0.676960\pi\)
−0.527740 + 0.849406i \(0.676960\pi\)
\(350\) −221.544 110.310i −0.632983 0.315171i
\(351\) −349.211 + 125.993i −0.994903 + 0.358954i
\(352\) 0.469645 0.469645i 0.00133422 0.00133422i
\(353\) 244.718 + 244.718i 0.693251 + 0.693251i 0.962946 0.269695i \(-0.0869228\pi\)
−0.269695 + 0.962946i \(0.586923\pi\)
\(354\) −41.4920 357.892i −0.117209 1.01099i
\(355\) −358.605 + 148.794i −1.01015 + 0.419138i
\(356\) 259.197 0.728082
\(357\) −140.374 + 387.232i −0.393204 + 1.08468i
\(358\) −167.194 167.194i −0.467021 0.467021i
\(359\) −599.498 −1.66991 −0.834956 0.550317i \(-0.814507\pi\)
−0.834956 + 0.550317i \(0.814507\pi\)
\(360\) −20.4355 + 125.628i −0.0567652 + 0.348967i
\(361\) 522.387 1.44705
\(362\) 271.099 271.099i 0.748892 0.748892i
\(363\) −225.386 + 284.500i −0.620899 + 0.783745i
\(364\) −60.9564 182.591i −0.167463 0.501624i
\(365\) 270.042 + 111.663i 0.739842 + 0.305927i
\(366\) 17.0100 + 146.721i 0.0464755 + 0.400877i
\(367\) 38.8678 + 38.8678i 0.105907 + 0.105907i 0.758075 0.652168i \(-0.226140\pi\)
−0.652168 + 0.758075i \(0.726140\pi\)
\(368\) 9.00599 9.00599i 0.0244728 0.0244728i
\(369\) 27.7893 + 118.238i 0.0753097 + 0.320429i
\(370\) 20.4120 + 49.1945i 0.0551676 + 0.132958i
\(371\) 561.677 187.511i 1.51396 0.505421i
\(372\) −5.62396 + 7.09898i −0.0151182 + 0.0190833i
\(373\) 228.366 + 228.366i 0.612241 + 0.612241i 0.943529 0.331289i \(-0.107483\pi\)
−0.331289 + 0.943529i \(0.607483\pi\)
\(374\) 3.25677i 0.00870795i
\(375\) 327.290 183.046i 0.872775 0.488123i
\(376\) 119.121i 0.316812i
\(377\) −447.930 + 447.930i −1.18814 + 1.18814i
\(378\) −31.1834 + 265.461i −0.0824959 + 0.702278i
\(379\) 217.075i 0.572757i −0.958117 0.286378i \(-0.907549\pi\)
0.958117 0.286378i \(-0.0924515\pi\)
\(380\) 274.525 113.907i 0.722434 0.299755i
\(381\) 83.9701 + 724.290i 0.220394 + 1.90102i
\(382\) 274.726 274.726i 0.719177 0.719177i
\(383\) −301.020 301.020i −0.785953 0.785953i 0.194875 0.980828i \(-0.437570\pi\)
−0.980828 + 0.194875i \(0.937570\pi\)
\(384\) 3.90876 + 33.7153i 0.0101791 + 0.0878003i
\(385\) −4.09937 0.286951i −0.0106477 0.000745327i
\(386\) 404.822i 1.04876i
\(387\) 247.144 399.008i 0.638615 1.03103i
\(388\) 31.5856 31.5856i 0.0814062 0.0814062i
\(389\) −369.112 −0.948875 −0.474438 0.880289i \(-0.657349\pi\)
−0.474438 + 0.880289i \(0.657349\pi\)
\(390\) 280.585 + 79.6737i 0.719448 + 0.204291i
\(391\) 62.4524i 0.159725i
\(392\) −137.218 19.4746i −0.350046 0.0496801i
\(393\) 271.595 342.828i 0.691081 0.872335i
\(394\) 365.275i 0.927095i
\(395\) −3.99798 + 1.65886i −0.0101215 + 0.00419965i
\(396\) 0.483534 + 2.05735i 0.00122104 + 0.00519532i
\(397\) 13.0242 + 13.0242i 0.0328066 + 0.0328066i 0.723320 0.690513i \(-0.242615\pi\)
−0.690513 + 0.723320i \(0.742615\pi\)
\(398\) 246.453 + 246.453i 0.619228 + 0.619228i
\(399\) 565.338 264.513i 1.41689 0.662939i
\(400\) 70.6248 70.7964i 0.176562 0.176991i
\(401\) 17.1182i 0.0426889i −0.999772 0.0213444i \(-0.993205\pi\)
0.999772 0.0213444i \(-0.00679466\pi\)
\(402\) 128.500 162.203i 0.319653 0.403490i
\(403\) 14.6758 + 14.6758i 0.0364164 + 0.0364164i
\(404\) 28.9050i 0.0715470i
\(405\) −305.597 265.774i −0.754559 0.656232i
\(406\) 144.423 + 432.610i 0.355722 + 1.06554i
\(407\) 0.625346 + 0.625346i 0.00153648 + 0.00153648i
\(408\) −130.453 103.347i −0.319737 0.253302i
\(409\) −186.052 −0.454895 −0.227447 0.973790i \(-0.573038\pi\)
−0.227447 + 0.973790i \(0.573038\pi\)
\(410\) 36.4652 88.1861i 0.0889396 0.215088i
\(411\) −159.313 + 18.4699i −0.387623 + 0.0449388i
\(412\) −62.7388 62.7388i −0.152279 0.152279i
\(413\) −265.602 + 531.811i −0.643103 + 1.28768i
\(414\) 9.27232 + 39.4520i 0.0223969 + 0.0952947i
\(415\) −267.670 + 647.323i −0.644988 + 1.55981i
\(416\) 77.7806 0.186973
\(417\) 121.927 153.905i 0.292390 0.369077i
\(418\) 3.48968 3.48968i 0.00834852 0.00834852i
\(419\) 606.909i 1.44847i −0.689553 0.724235i \(-0.742193\pi\)
0.689553 0.724235i \(-0.257807\pi\)
\(420\) 141.579 155.098i 0.337094 0.369280i
\(421\) −642.340 −1.52575 −0.762874 0.646547i \(-0.776212\pi\)
−0.762874 + 0.646547i \(0.776212\pi\)
\(422\) 165.881 + 165.881i 0.393083 + 0.393083i
\(423\) −322.236 199.592i −0.761786 0.471848i
\(424\) 239.265i 0.564304i
\(425\) 0.594965 + 490.345i 0.00139992 + 1.15375i
\(426\) −37.9393 327.248i −0.0890595 0.768188i
\(427\) 108.886 218.021i 0.255002 0.510587i
\(428\) 211.712 211.712i 0.494655 0.494655i
\(429\) 4.81092 0.557752i 0.0112143 0.00130012i
\(430\) −340.599 + 141.323i −0.792090 + 0.328658i
\(431\) 455.692i 1.05729i −0.848843 0.528645i \(-0.822700\pi\)
0.848843 0.528645i \(-0.177300\pi\)
\(432\) −97.7527 45.9175i −0.226279 0.106290i
\(433\) −201.636 + 201.636i −0.465672 + 0.465672i −0.900509 0.434837i \(-0.856806\pi\)
0.434837 + 0.900509i \(0.356806\pi\)
\(434\) 14.1739 4.73182i 0.0326587 0.0109028i
\(435\) −664.785 188.770i −1.52824 0.433953i
\(436\) −190.948 −0.437954
\(437\) 66.9186 66.9186i 0.153132 0.153132i
\(438\) −153.973 + 194.356i −0.351536 + 0.443735i
\(439\) −94.0452 −0.214226 −0.107113 0.994247i \(-0.534161\pi\)
−0.107113 + 0.994247i \(0.534161\pi\)
\(440\) 0.634495 1.53444i 0.00144203 0.00348736i
\(441\) 282.594 338.558i 0.640802 0.767706i
\(442\) −269.686 + 269.686i −0.610150 + 0.610150i
\(443\) −125.233 + 125.233i −0.282693 + 0.282693i −0.834182 0.551489i \(-0.814060\pi\)
0.551489 + 0.834182i \(0.314060\pi\)
\(444\) −44.8929 + 5.20463i −0.101110 + 0.0117221i
\(445\) 598.517 248.339i 1.34498 0.558066i
\(446\) 89.7899 0.201323
\(447\) −203.608 + 257.010i −0.455499 + 0.574966i
\(448\) 25.0211 50.0994i 0.0558506 0.111829i
\(449\) 324.260 0.722184 0.361092 0.932530i \(-0.382404\pi\)
0.361092 + 0.932530i \(0.382404\pi\)
\(450\) 73.1775 + 309.669i 0.162617 + 0.688154i
\(451\) 1.58453i 0.00351337i
\(452\) 120.252 + 120.252i 0.266045 + 0.266045i
\(453\) 416.050 525.170i 0.918434 1.15932i
\(454\) 423.690 0.933238
\(455\) −315.698 363.221i −0.693841 0.798289i
\(456\) 29.0439 + 250.520i 0.0636928 + 0.549386i
\(457\) −411.756 + 411.756i −0.900999 + 0.900999i −0.995523 0.0945240i \(-0.969867\pi\)
0.0945240 + 0.995523i \(0.469867\pi\)
\(458\) −10.2429 10.2429i −0.0223644 0.0223644i
\(459\) 498.143 179.727i 1.08528 0.391561i
\(460\) 12.1672 29.4246i 0.0264504 0.0639666i
\(461\) −484.084 −1.05007 −0.525037 0.851080i \(-0.675948\pi\)
−0.525037 + 0.851080i \(0.675948\pi\)
\(462\) 1.18836 3.27819i 0.00257221 0.00709565i
\(463\) 239.772 + 239.772i 0.517866 + 0.517866i 0.916925 0.399059i \(-0.130663\pi\)
−0.399059 + 0.916925i \(0.630663\pi\)
\(464\) −184.284 −0.397165
\(465\) −6.18477 + 21.7808i −0.0133006 + 0.0468403i
\(466\) −271.299 −0.582186
\(467\) 302.621 302.621i 0.648011 0.648011i −0.304501 0.952512i \(-0.598490\pi\)
0.952512 + 0.304501i \(0.0984897\pi\)
\(468\) −130.324 + 210.405i −0.278470 + 0.449583i
\(469\) −323.855 + 108.116i −0.690523 + 0.230525i
\(470\) 114.131 + 275.065i 0.242832 + 0.585245i
\(471\) 7.04413 0.816658i 0.0149557 0.00173388i
\(472\) −169.842 169.842i −0.359835 0.359835i
\(473\) −4.32959 + 4.32959i −0.00915348 + 0.00915348i
\(474\) −0.422974 3.64839i −0.000892351 0.00769703i
\(475\) 524.775 526.050i 1.10479 1.10747i
\(476\) 86.9532 + 260.463i 0.182675 + 0.547191i
\(477\) −647.236 400.896i −1.35689 0.840453i
\(478\) −25.1069 25.1069i −0.0525250 0.0525250i
\(479\) 444.701i 0.928395i −0.885732 0.464198i \(-0.846343\pi\)
0.885732 0.464198i \(-0.153657\pi\)
\(480\) 41.3288 + 74.1076i 0.0861016 + 0.154391i
\(481\) 103.567i 0.215316i
\(482\) 278.949 278.949i 0.578733 0.578733i
\(483\) 22.7882 62.8631i 0.0471805 0.130151i
\(484\) 241.972i 0.499943i
\(485\) 42.6724 103.197i 0.0879844 0.212778i
\(486\) 287.999 187.495i 0.592591 0.385792i
\(487\) −4.30834 + 4.30834i −0.00884670 + 0.00884670i −0.711516 0.702670i \(-0.751991\pi\)
0.702670 + 0.711516i \(0.251991\pi\)
\(488\) 69.6282 + 69.6282i 0.142681 + 0.142681i
\(489\) 144.079 16.7037i 0.294640 0.0341589i
\(490\) −335.511 + 86.5006i −0.684716 + 0.176532i
\(491\) 85.1811i 0.173485i 0.996231 + 0.0867425i \(0.0276457\pi\)
−0.996231 + 0.0867425i \(0.972354\pi\)
\(492\) 63.4697 + 50.2820i 0.129004 + 0.102199i
\(493\) 638.963 638.963i 1.29607 1.29607i
\(494\) 577.945 1.16993
\(495\) 3.08770 + 4.28738i 0.00623778 + 0.00866137i
\(496\) 6.03782i 0.0121730i
\(497\) −242.860 + 486.275i −0.488652 + 0.978421i
\(498\) −465.894 369.091i −0.935530 0.741146i
\(499\) 352.315i 0.706043i −0.935615 0.353021i \(-0.885154\pi\)
0.935615 0.353021i \(-0.114846\pi\)
\(500\) 95.2503 231.144i 0.190501 0.462287i
\(501\) −59.8429 516.178i −0.119447 1.03030i
\(502\) 211.250 + 211.250i 0.420817 + 0.420817i
\(503\) 109.956 + 109.956i 0.218600 + 0.218600i 0.807908 0.589308i \(-0.200600\pi\)
−0.589308 + 0.807908i \(0.700600\pi\)
\(504\) 93.6004 + 151.628i 0.185715 + 0.300849i
\(505\) −27.6942 66.7451i −0.0548399 0.132168i
\(506\) 0.528703i 0.00104487i
\(507\) 47.1641 + 37.3643i 0.0930257 + 0.0736969i
\(508\) 343.720 + 343.720i 0.676615 + 0.676615i
\(509\) 930.732i 1.82855i 0.405094 + 0.914275i \(0.367239\pi\)
−0.405094 + 0.914275i \(0.632761\pi\)
\(510\) −400.249 113.653i −0.784802 0.222849i
\(511\) 388.053 129.548i 0.759398 0.253518i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −726.347 341.188i −1.41588 0.665083i
\(514\) 660.864 1.28573
\(515\) −204.982 84.7606i −0.398023 0.164584i
\(516\) −36.0343 310.817i −0.0698340 0.602358i
\(517\) 3.49655 + 3.49655i 0.00676315 + 0.00676315i
\(518\) 66.7087 + 33.3162i 0.128781 + 0.0643171i
\(519\) 46.8662 5.43340i 0.0903009 0.0104690i
\(520\) 179.605 74.5224i 0.345393 0.143312i
\(521\) 22.2801 0.0427641 0.0213821 0.999771i \(-0.493193\pi\)
0.0213821 + 0.999771i \(0.493193\pi\)
\(522\) 308.774 498.508i 0.591522 0.954997i
\(523\) −110.356 + 110.356i −0.211006 + 0.211006i −0.804695 0.593689i \(-0.797671\pi\)
0.593689 + 0.804695i \(0.297671\pi\)
\(524\) 291.582i 0.556453i
\(525\) 178.323 493.787i 0.339663 0.940547i
\(526\) −148.680 −0.282662
\(527\) −20.9348 20.9348i −0.0397244 0.0397244i
\(528\) 1.10437 + 0.874907i 0.00209162 + 0.00165702i
\(529\) 518.862i 0.980835i
\(530\) 229.242 + 552.491i 0.432532 + 1.04244i
\(531\) 744.016 174.864i 1.40116 0.329311i
\(532\) 185.918 372.261i 0.349470 0.699739i
\(533\) 131.212 131.212i 0.246176 0.246176i
\(534\) 63.3213 + 546.182i 0.118579 + 1.02281i
\(535\) 286.025 691.712i 0.534626 1.29292i
\(536\) 137.957i 0.257382i
\(537\) 311.466 393.156i 0.580012 0.732134i
\(538\) 250.571 250.571i 0.465745 0.465745i
\(539\) −4.59937 + 3.45610i −0.00853315 + 0.00641206i
\(540\) −269.716 12.3711i −0.499475 0.0229094i
\(541\) 693.609 1.28209 0.641044 0.767504i \(-0.278502\pi\)
0.641044 + 0.767504i \(0.278502\pi\)
\(542\) 207.488 207.488i 0.382819 0.382819i
\(543\) 637.490 + 505.032i 1.17401 + 0.930078i
\(544\) −110.953 −0.203957
\(545\) −440.921 + 182.949i −0.809030 + 0.335686i
\(546\) 369.865 173.054i 0.677409 0.316949i
\(547\) −529.859 + 529.859i −0.968664 + 0.968664i −0.999524 0.0308595i \(-0.990176\pi\)
0.0308595 + 0.999524i \(0.490176\pi\)
\(548\) −75.6039 + 75.6039i −0.137963 + 0.137963i
\(549\) −305.016 + 71.6872i −0.555585 + 0.130578i
\(550\) −0.00503679 4.15112i −9.15781e−6 0.00754748i
\(551\) −1369.32 −2.48515
\(552\) 21.1776 + 16.7773i 0.0383653 + 0.0303937i
\(553\) −2.70757 + 5.42134i −0.00489616 + 0.00980351i
\(554\) −129.447 −0.233658
\(555\) −98.6763 + 55.0304i −0.177795 + 0.0991538i
\(556\) 130.899i 0.235430i
\(557\) −242.020 242.020i −0.434506 0.434506i 0.455652 0.890158i \(-0.349406\pi\)
−0.890158 + 0.455652i \(0.849406\pi\)
\(558\) −16.3329 10.1166i −0.0292705 0.0181301i
\(559\) −717.048 −1.28273
\(560\) 9.77592 139.658i 0.0174570 0.249390i
\(561\) −6.86269 + 0.795623i −0.0122330 + 0.00141822i
\(562\) 353.277 353.277i 0.628607 0.628607i
\(563\) 19.8889 + 19.8889i 0.0353266 + 0.0353266i 0.724549 0.689223i \(-0.242048\pi\)
−0.689223 + 0.724549i \(0.742048\pi\)
\(564\) −251.013 + 29.1011i −0.445059 + 0.0515976i
\(565\) 392.891 + 162.462i 0.695383 + 0.287543i
\(566\) 362.180 0.639894
\(567\) −566.999 0.858397i −0.999999 0.00151393i
\(568\) −155.300 155.300i −0.273415 0.273415i
\(569\) −147.022 −0.258387 −0.129194 0.991619i \(-0.541239\pi\)
−0.129194 + 0.991619i \(0.541239\pi\)
\(570\) 307.091 + 550.653i 0.538757 + 0.966058i
\(571\) 831.318 1.45590 0.727949 0.685631i \(-0.240474\pi\)
0.727949 + 0.685631i \(0.240474\pi\)
\(572\) 2.28308 2.28308i 0.00399140 0.00399140i
\(573\) 646.018 + 511.789i 1.12743 + 0.893174i
\(574\) −42.3057 126.724i −0.0737033 0.220774i
\(575\) −0.0965863 79.6024i −0.000167976 0.138439i
\(576\) −70.0902 + 16.4731i −0.121684 + 0.0285992i
\(577\) 331.614 + 331.614i 0.574721 + 0.574721i 0.933444 0.358723i \(-0.116788\pi\)
−0.358723 + 0.933444i \(0.616788\pi\)
\(578\) 95.7024 95.7024i 0.165575 0.165575i
\(579\) 853.043 98.8971i 1.47330 0.170807i
\(580\) −425.534 + 176.565i −0.733680 + 0.304422i
\(581\) 310.541 + 930.207i 0.534495 + 1.60104i
\(582\) 74.2737 + 58.8411i 0.127618 + 0.101102i
\(583\) 7.02310 + 7.02310i 0.0120465 + 0.0120465i
\(584\) 165.304i 0.283054i
\(585\) −99.3427 + 610.714i −0.169816 + 1.04396i
\(586\) 144.769i 0.247045i
\(587\) 216.371 216.371i 0.368605 0.368605i −0.498363 0.866968i \(-0.666065\pi\)
0.866968 + 0.498363i \(0.166065\pi\)
\(588\) 7.51496 293.904i 0.0127805 0.499837i
\(589\) 44.8638i 0.0761694i
\(590\) −554.912 229.458i −0.940529 0.388912i
\(591\) −769.711 + 89.2360i −1.30239 + 0.150992i
\(592\) −21.3044 + 21.3044i −0.0359872 + 0.0359872i
\(593\) −332.499 332.499i −0.560706 0.560706i 0.368802 0.929508i \(-0.379768\pi\)
−0.929508 + 0.368802i \(0.879768\pi\)
\(594\) −4.21713 + 1.52151i −0.00709954 + 0.00256147i
\(595\) 450.337 + 518.128i 0.756869 + 0.870804i
\(596\) 218.592i 0.366765i
\(597\) −459.119 + 579.534i −0.769043 + 0.970744i
\(598\) 43.7807 43.7807i 0.0732119 0.0732119i
\(599\) 735.946 1.22862 0.614312 0.789063i \(-0.289433\pi\)
0.614312 + 0.789063i \(0.289433\pi\)
\(600\) 166.436 + 131.526i 0.277394 + 0.219209i
\(601\) 851.749i 1.41722i −0.705600 0.708610i \(-0.749323\pi\)
0.705600 0.708610i \(-0.250677\pi\)
\(602\) −230.666 + 461.859i −0.383166 + 0.767207i
\(603\) 373.188 + 231.151i 0.618885 + 0.383335i
\(604\) 446.668i 0.739516i
\(605\) 231.836 + 558.743i 0.383200 + 0.923542i
\(606\) 60.9088 7.06143i 0.100510 0.0116525i
\(607\) 468.483 + 468.483i 0.771801 + 0.771801i 0.978421 0.206621i \(-0.0662466\pi\)
−0.206621 + 0.978421i \(0.566247\pi\)
\(608\) 118.887 + 118.887i 0.195538 + 0.195538i
\(609\) −876.316 + 410.015i −1.43894 + 0.673259i
\(610\) 227.491 + 94.0683i 0.372936 + 0.154210i
\(611\) 579.083i 0.947763i
\(612\) 185.905 300.138i 0.303766 0.490422i
\(613\) −653.475 653.475i −1.06603 1.06603i −0.997660 0.0683679i \(-0.978221\pi\)
−0.0683679 0.997660i \(-0.521779\pi\)
\(614\) 457.433i 0.745005i
\(615\) 194.735 + 55.2961i 0.316642 + 0.0899123i
\(616\) −0.736119 2.20500i −0.00119500 0.00357954i
\(617\) 238.684 + 238.684i 0.386845 + 0.386845i 0.873561 0.486715i \(-0.161805\pi\)
−0.486715 + 0.873561i \(0.661805\pi\)
\(618\) 116.877 147.531i 0.189121 0.238723i
\(619\) −400.073 −0.646322 −0.323161 0.946344i \(-0.604746\pi\)
−0.323161 + 0.946344i \(0.604746\pi\)
\(620\) 5.78490 + 13.9420i 0.00933048 + 0.0224872i
\(621\) −80.8683 + 29.1767i −0.130223 + 0.0469834i
\(622\) −269.223 269.223i −0.432835 0.432835i
\(623\) 405.337 811.600i 0.650621 1.30273i
\(624\) 19.0016 + 163.900i 0.0304513 + 0.262660i
\(625\) −1.51670 624.998i −0.00242671 0.999997i
\(626\) −842.046 −1.34512
\(627\) 8.20600 + 6.50095i 0.0130877 + 0.0103683i
\(628\) 3.34288 3.34288i 0.00532305 0.00532305i
\(629\) 147.736i 0.234875i
\(630\) 361.410 + 260.447i 0.573667 + 0.413408i
\(631\) −343.679 −0.544658 −0.272329 0.962204i \(-0.587794\pi\)
−0.272329 + 0.962204i \(0.587794\pi\)
\(632\) −1.73139 1.73139i −0.00273954 0.00273954i
\(633\) −309.021 + 390.069i −0.488185 + 0.616223i
\(634\) 149.624i 0.236001i
\(635\) 1123.01 + 464.369i 1.76852 + 0.731290i
\(636\) −504.180 + 58.4519i −0.792736 + 0.0919055i
\(637\) −667.056 94.6716i −1.04718 0.148621i
\(638\) −5.40927 + 5.40927i −0.00847848 + 0.00847848i
\(639\) 680.311 159.892i 1.06465 0.250222i
\(640\) 52.2756 + 21.6161i 0.0816807 + 0.0337752i
\(641\) 976.273i 1.52305i 0.648137 + 0.761524i \(0.275548\pi\)
−0.648137 + 0.761524i \(0.724452\pi\)
\(642\) 497.842 + 394.401i 0.775455 + 0.614331i
\(643\) −155.167 + 155.167i −0.241317 + 0.241317i −0.817395 0.576078i \(-0.804583\pi\)
0.576078 + 0.817395i \(0.304583\pi\)
\(644\) −14.1159 42.2834i −0.0219192 0.0656574i
\(645\) −381.004 683.187i −0.590704 1.05920i
\(646\) −824.428 −1.27620
\(647\) 122.968 122.968i 0.190059 0.190059i −0.605663 0.795722i \(-0.707092\pi\)
0.795722 + 0.605663i \(0.207092\pi\)
\(648\) 72.8768 217.203i 0.112464 0.335189i
\(649\) −9.97068 −0.0153631
\(650\) 343.328 344.162i 0.528196 0.529480i
\(651\) 13.4336 + 28.7113i 0.0206353 + 0.0441034i
\(652\) 68.3743 68.3743i 0.104869 0.104869i
\(653\) 621.793 621.793i 0.952209 0.952209i −0.0466996 0.998909i \(-0.514870\pi\)
0.998909 + 0.0466996i \(0.0148703\pi\)
\(654\) −46.6482 402.367i −0.0713275 0.615240i
\(655\) −279.367 673.296i −0.426515 1.02793i
\(656\) 53.9822 0.0822900
\(657\) −447.164 276.972i −0.680614 0.421570i
\(658\) 372.994 + 186.284i 0.566860 + 0.283106i
\(659\) −307.522 −0.466650 −0.233325 0.972399i \(-0.574961\pi\)
−0.233325 + 0.972399i \(0.574961\pi\)
\(660\) 3.38838 + 0.962152i 0.00513392 + 0.00145781i
\(661\) 621.533i 0.940292i 0.882589 + 0.470146i \(0.155799\pi\)
−0.882589 + 0.470146i \(0.844201\pi\)
\(662\) −506.910 506.910i −0.765725 0.765725i
\(663\) −634.168 502.401i −0.956513 0.757769i
\(664\) −396.252 −0.596765
\(665\) 72.6395 1037.72i 0.109232 1.56049i
\(666\) −21.9345 93.3270i −0.0329346 0.140131i
\(667\) −103.729 + 103.729i −0.155516 + 0.155516i
\(668\) −244.959 244.959i −0.366705 0.366705i
\(669\) 21.9355 + 189.206i 0.0327885 + 0.282819i
\(670\) −132.178 318.559i −0.197280 0.475461i
\(671\) 4.08757 0.00609176
\(672\) 111.682 + 40.4854i 0.166194 + 0.0602461i
\(673\) −571.899 571.899i −0.849776 0.849776i 0.140329 0.990105i \(-0.455184\pi\)
−0.990105 + 0.140329i \(0.955184\pi\)
\(674\) −375.896 −0.557709
\(675\) −634.660 + 229.852i −0.940237 + 0.340521i
\(676\) 40.1139 0.0593402
\(677\) 679.334 679.334i 1.00345 1.00345i 0.00345318 0.999994i \(-0.498901\pi\)
0.999994 0.00345318i \(-0.00109918\pi\)
\(678\) −224.019 + 282.773i −0.330411 + 0.417070i
\(679\) −49.5071 148.295i −0.0729118 0.218403i
\(680\) −256.203 + 106.305i −0.376769 + 0.156331i
\(681\) 103.506 + 892.802i 0.151992 + 1.31102i
\(682\) 0.177227 + 0.177227i 0.000259864 + 0.000259864i
\(683\) 807.265 807.265i 1.18194 1.18194i 0.202700 0.979241i \(-0.435028\pi\)
0.979241 0.202700i \(-0.0649715\pi\)
\(684\) −520.802 + 122.403i −0.761407 + 0.178952i
\(685\) −102.141 + 247.015i −0.149112 + 0.360606i
\(686\) −275.563 + 399.203i −0.401695 + 0.581929i
\(687\) 19.0815 24.0862i 0.0277752 0.0350599i
\(688\) −147.502 147.502i −0.214392 0.214392i
\(689\) 1163.14i 1.68815i
\(690\) 64.9762 + 18.4504i 0.0941684 + 0.0267397i
\(691\) 287.198i 0.415626i 0.978169 + 0.207813i \(0.0666346\pi\)
−0.978169 + 0.207813i \(0.933365\pi\)
\(692\) 22.2409 22.2409i 0.0321400 0.0321400i
\(693\) 7.19814 + 1.70327i 0.0103869 + 0.00245782i
\(694\) 305.592i 0.440334i
\(695\) −125.416 302.262i −0.180454 0.434909i
\(696\) −45.0203 388.325i −0.0646843 0.557938i
\(697\) −187.171 + 187.171i −0.268538 + 0.268538i
\(698\) −368.362 368.362i −0.527740 0.527740i
\(699\) −66.2777 571.682i −0.0948179 0.817858i
\(700\) −111.234 331.854i −0.158906 0.474077i
\(701\) 791.451i 1.12903i −0.825422 0.564516i \(-0.809063\pi\)
0.825422 0.564516i \(-0.190937\pi\)
\(702\) −475.204 223.218i −0.676929 0.317974i
\(703\) −158.302 + 158.302i −0.225180 + 0.225180i
\(704\) 0.939291 0.00133422
\(705\) −551.737 + 307.696i −0.782606 + 0.436448i
\(706\) 489.435i 0.693251i
\(707\) −90.5076 45.2021i −0.128016 0.0639351i
\(708\) 316.400 399.384i 0.446893 0.564102i
\(709\) 56.1623i 0.0792133i 0.999215 + 0.0396067i \(0.0126105\pi\)
−0.999215 + 0.0396067i \(0.987390\pi\)
\(710\) −507.399 209.811i −0.714646 0.295508i
\(711\) 7.58459 1.78259i 0.0106675 0.00250716i
\(712\) 259.197 + 259.197i 0.364041 + 0.364041i
\(713\) 3.39854 + 3.39854i 0.00476653 + 0.00476653i
\(714\) −527.606 + 246.859i −0.738944 + 0.345741i
\(715\) 3.08446 7.45935i 0.00431393 0.0104327i
\(716\) 334.387i 0.467021i
\(717\) 46.7719 59.0391i 0.0652328 0.0823418i
\(718\) −599.498 599.498i −0.834956 0.834956i
\(719\) 364.303i 0.506680i 0.967377 + 0.253340i \(0.0815291\pi\)
−0.967377 + 0.253340i \(0.918471\pi\)
\(720\) −146.063 + 105.193i −0.202866 + 0.146101i
\(721\) −294.560 + 98.3364i −0.408544 + 0.136389i
\(722\) 522.387 + 522.387i 0.723527 + 0.723527i
\(723\) 655.950 + 519.657i 0.907261 + 0.718751i
\(724\) 542.198 0.748892
\(725\) −813.441 + 815.417i −1.12199 + 1.12471i
\(726\) −509.886 + 59.1133i −0.702322 + 0.0814233i
\(727\) 188.513 + 188.513i 0.259303 + 0.259303i 0.824771 0.565468i \(-0.191304\pi\)
−0.565468 + 0.824771i \(0.691304\pi\)
\(728\) 121.635 243.547i 0.167081 0.334543i
\(729\) 465.448 + 561.070i 0.638475 + 0.769643i
\(730\) 158.379 + 381.706i 0.216958 + 0.522884i
\(731\) 1022.86 1.39926
\(732\) −129.711 + 163.731i −0.177201 + 0.223676i
\(733\) −1.46070 + 1.46070i −0.00199277 + 0.00199277i −0.708102 0.706110i \(-0.750449\pi\)
0.706110 + 0.708102i \(0.250449\pi\)
\(734\) 77.7356i 0.105907i
\(735\) −264.239 685.859i −0.359509 0.933142i
\(736\) 18.0120 0.0244728
\(737\) −4.04942 4.04942i −0.00549447 0.00549447i
\(738\) −90.4490 + 146.028i −0.122560 + 0.197869i
\(739\) 757.965i 1.02566i −0.858489 0.512832i \(-0.828596\pi\)
0.858489 0.512832i \(-0.171404\pi\)
\(740\) −28.7825 + 69.6065i −0.0388952 + 0.0940628i
\(741\) 141.191 + 1217.85i 0.190541 + 1.64352i
\(742\) 749.188 + 374.166i 1.00969 + 0.504267i
\(743\) −781.133 + 781.133i −1.05132 + 1.05132i −0.0527138 + 0.998610i \(0.516787\pi\)
−0.998610 + 0.0527138i \(0.983213\pi\)
\(744\) −12.7229 + 1.47503i −0.0171007 + 0.00198256i
\(745\) 209.435 + 504.754i 0.281121 + 0.677522i
\(746\) 456.732i 0.612241i
\(747\) 663.933 1071.90i 0.888800 1.43494i
\(748\) −3.25677 + 3.25677i −0.00435398 + 0.00435398i
\(749\) −331.836 993.995i −0.443039 1.32710i
\(750\) 510.337 + 144.244i 0.680449 + 0.192326i
\(751\) −483.342 −0.643598 −0.321799 0.946808i \(-0.604287\pi\)
−0.321799 + 0.946808i \(0.604287\pi\)
\(752\) −119.121 + 119.121i −0.158406 + 0.158406i
\(753\) −393.539 + 496.755i −0.522629 + 0.659701i
\(754\) −895.859 −1.18814
\(755\) −427.957 1031.41i −0.566830 1.36610i
\(756\) −296.645 + 234.278i −0.392387 + 0.309891i
\(757\) 669.202 669.202i 0.884018 0.884018i −0.109922 0.993940i \(-0.535060\pi\)
0.993940 + 0.109922i \(0.0350601\pi\)
\(758\) 217.075 217.075i 0.286378 0.286378i
\(759\) 1.11409 0.129161i 0.00146783 0.000170173i
\(760\) 388.432 + 160.618i 0.511094 + 0.211339i
\(761\) −318.737 −0.418840 −0.209420 0.977826i \(-0.567158\pi\)
−0.209420 + 0.977826i \(0.567158\pi\)
\(762\) −640.320 + 808.260i −0.840314 + 1.06071i
\(763\) −298.608 + 597.898i −0.391360 + 0.783615i
\(764\) 549.451 0.719177
\(765\) 141.710 871.172i 0.185242 1.13879i
\(766\) 602.040i 0.785953i
\(767\) −825.650 825.650i −1.07647