Properties

Label 210.3.k.a.83.14
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 83.14
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.14

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(2.35150 - 1.86291i) q^{3} +2.00000i q^{4} +(1.91622 + 4.61824i) q^{5} +(-4.21441 - 0.488596i) q^{6} +(-3.12763 - 6.26242i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.05914 - 8.76127i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(2.35150 - 1.86291i) q^{3} +2.00000i q^{4} +(1.91622 + 4.61824i) q^{5} +(-4.21441 - 0.488596i) q^{6} +(-3.12763 - 6.26242i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.05914 - 8.76127i) q^{9} +(2.70202 - 6.53446i) q^{10} -0.117411i q^{11} +(3.72582 + 4.70301i) q^{12} +(9.72258 - 9.72258i) q^{13} +(-3.13479 + 9.39005i) q^{14} +(13.1093 + 7.29006i) q^{15} -4.00000 q^{16} +(13.8691 - 13.8691i) q^{17} +(-10.8204 + 6.70213i) 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} +(-11.4794 - 24.4382i) q^{27} +(12.5248 - 6.25527i) q^{28} -46.0711 q^{29} +(-5.81929 - 20.3994i) q^{30} +1.50946i q^{31} +(4.00000 + 4.00000i) q^{32} +(-0.218727 - 0.276093i) q^{33} -27.7381 q^{34} +(22.9281 - 26.4443i) 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} +(10.1213 + 27.9206i) q^{42} +(36.8754 + 36.8754i) q^{43} +0.234823 q^{44} +(44.4074 - 7.27891i) q^{45} -4.50300 q^{46} +(29.7803 - 29.7803i) q^{47} +(-9.40602 + 7.45163i) 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} +(69.8910 - 55.3690i) q^{57} +(46.0711 + 46.0711i) q^{58} +84.9209i q^{59} +(-14.5801 + 26.2187i) q^{60} +34.8141i q^{61} +(1.50946 - 1.50946i) q^{62} +(-61.3070 + 14.5068i) 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} +(-49.3724 + 3.51622i) q^{70} -77.6498i q^{71} +(-13.4043 - 21.6408i) q^{72} +(-41.3259 + 41.3259i) q^{73} -10.6522 q^{74} +(-8.54683 + 74.5114i) q^{75} +59.4436i q^{76} +(-0.735279 + 0.367220i) q^{77} +(-45.7254 + 36.2245i) 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} +(-108.336 + 85.8262i) q^{87} +(-0.234823 - 0.234823i) q^{88} -129.599i q^{89} +(-51.6863 - 37.1285i) q^{90} +(-91.2955 - 30.4782i) q^{91} +(4.50300 + 4.50300i) q^{92} +(2.81198 + 3.54949i) q^{93} -59.5607 q^{94} +(56.9535 + 137.262i) q^{95} +(16.8577 + 1.95438i) q^{96} +(15.7928 + 15.7928i) q^{97} +(68.6089 - 9.73729i) q^{98} +(-1.02867 - 0.241767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

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
\(3\) 2.35150 1.86291i 0.783835 0.620970i
\(4\) 2.00000i 0.500000i
\(5\) 1.91622 + 4.61824i 0.383244 + 0.923647i
\(6\) −4.21441 0.488596i −0.702402 0.0814326i
\(7\) −3.12763 6.26242i −0.446805 0.894631i
\(8\) 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 \(-0.998301\pi\)
0.999986 0.00533688i \(-0.00169879\pi\)
\(12\) 3.72582 + 4.70301i 0.310485 + 0.391917i
\(13\) 9.72258 9.72258i 0.747890 0.747890i −0.226192 0.974083i \(-0.572628\pi\)
0.974083 + 0.226192i \(0.0726277\pi\)
\(14\) −3.13479 + 9.39005i −0.223913 + 0.670718i
\(15\) 13.1093 + 7.29006i 0.873957 + 0.486004i
\(16\) −4.00000 −0.250000
\(17\) 13.8691 13.8691i 0.815828 0.815828i −0.169673 0.985500i \(-0.554271\pi\)
0.985500 + 0.169673i \(0.0542710\pi\)
\(18\) −10.8204 + 6.70213i −0.601134 + 0.372341i
\(19\) 29.7218 1.56431 0.782153 0.623086i \(-0.214121\pi\)
0.782153 + 0.623086i \(0.214121\pi\)
\(20\) −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 −0.656465 0.754356i \(-0.727949\pi\)
0.754356 + 0.656465i \(0.227949\pi\)
\(24\) 0.977191 8.42883i 0.0407163 0.351201i
\(25\) −17.6562 + 17.6991i −0.706248 + 0.707964i
\(26\) −19.4452 −0.747890
\(27\) −11.4794 24.4382i −0.425162 0.905117i
\(28\) 12.5248 6.25527i 0.447316 0.223402i
\(29\) −46.0711 −1.58866 −0.794329 0.607488i \(-0.792177\pi\)
−0.794329 + 0.607488i \(0.792177\pi\)
\(30\) −5.81929 20.3994i −0.193976 0.679980i
\(31\) 1.50946i 0.0486921i 0.999704 + 0.0243461i \(0.00775036\pi\)
−0.999704 + 0.0243461i \(0.992250\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −0.218727 0.276093i −0.00662808 0.00836646i
\(34\) −27.7381 −0.815828
\(35\) 22.9281 26.4443i 0.655089 0.755552i
\(36\) 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 \(0.552627\pi\)
\(42\) 10.1213 + 27.9206i 0.240984 + 0.664776i
\(43\) 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
\(45\) 44.4074 7.27891i 0.986831 0.161754i
\(46\) −4.50300 −0.0978912
\(47\) 29.7803 29.7803i 0.633624 0.633624i −0.315351 0.948975i \(-0.602122\pi\)
0.948975 + 0.315351i \(0.102122\pi\)
\(48\) −9.40602 + 7.45163i −0.195959 + 0.155242i
\(49\) −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 \(0.544133\pi\)
−0.990404 + 0.138204i \(0.955867\pi\)
\(54\) −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
\(57\) 69.8910 55.3690i 1.22616 0.971387i
\(58\) 46.0711 + 46.0711i 0.794329 + 0.794329i
\(59\) 84.9209i 1.43934i 0.694317 + 0.719669i \(0.255706\pi\)
−0.694317 + 0.719669i \(0.744294\pi\)
\(60\) −14.5801 + 26.2187i −0.243002 + 0.436978i
\(61\) 34.8141i 0.570723i 0.958420 + 0.285361i \(0.0921137\pi\)
−0.958420 + 0.285361i \(0.907886\pi\)
\(62\) 1.50946 1.50946i 0.0243461 0.0243461i
\(63\) −61.3070 + 14.5068i −0.973127 + 0.230267i
\(64\) 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
\(70\) −49.3724 + 3.51622i −0.705320 + 0.0502317i
\(71\) 77.6498i 1.09366i −0.837244 0.546829i \(-0.815835\pi\)
0.837244 0.546829i \(-0.184165\pi\)
\(72\) −13.4043 21.6408i −0.186170 0.300567i
\(73\) −41.3259 + 41.3259i −0.566108 + 0.566108i −0.931036 0.364928i \(-0.881094\pi\)
0.364928 + 0.931036i \(0.381094\pi\)
\(74\) −10.6522 −0.143949
\(75\) −8.54683 + 74.5114i −0.113958 + 0.993486i
\(76\) 59.4436i 0.782153i
\(77\) −0.735279 + 0.367220i −0.00954908 + 0.00476909i
\(78\) −45.7254 + 36.2245i −0.586223 + 0.464417i
\(79\) 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
\(87\) −108.336 + 85.8262i −1.24525 + 0.986508i
\(88\) −0.234823 0.234823i −0.00266844 0.00266844i
\(89\) 129.599i 1.45616i −0.685490 0.728082i \(-0.740412\pi\)
0.685490 0.728082i \(-0.259588\pi\)
\(90\) −51.6863 37.1285i −0.574292 0.412539i
\(91\) −91.2955 30.4782i −1.00325 0.334925i
\(92\) 4.50300 + 4.50300i 0.0489456 + 0.0489456i
\(93\) 2.81198 + 3.54949i 0.0302363 + 0.0381666i
\(94\) −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 0.783811 0.620999i \(-0.213273\pi\)
−0.620999 + 0.783811i \(0.713273\pi\)
\(98\) 68.6089 9.73729i 0.700091 0.0993602i
\(99\) −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 \(0.522794\pi\)
\(102\) −65.2264 + 51.6736i −0.639474 + 0.506604i
\(103\) 31.3694 31.3694i 0.304557 0.304557i −0.538237 0.842794i \(-0.680909\pi\)
0.842794 + 0.538237i \(0.180909\pi\)
\(104\) 38.8903i 0.373945i
\(105\) 4.65218 104.897i 0.0443065 0.999018i
\(106\) 119.632 1.12861
\(107\) 105.856 + 105.856i 0.989310 + 0.989310i 0.999943 0.0106339i \(-0.00338493\pi\)
−0.0106339 + 0.999943i \(0.503385\pi\)
\(108\) 48.8763 22.9587i 0.452559 0.212581i
\(109\) 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
\(112\) 12.5105 + 25.0497i 0.111701 + 0.223658i
\(113\) −60.1261 + 60.1261i −0.532089 + 0.532089i −0.921194 0.389104i \(-0.872785\pi\)
0.389104 + 0.921194i \(0.372785\pi\)
\(114\) −125.260 14.5219i −1.09877 0.127386i
\(115\) 14.7123 + 6.08359i 0.127933 + 0.0529007i
\(116\) 92.1422i 0.794329i
\(117\) −65.1620 105.202i −0.556940 0.899165i
\(118\) 84.9209 84.9209i 0.719669 0.719669i
\(119\) −130.231 43.4766i −1.09438 0.365350i
\(120\) 40.7988 11.6386i 0.339990 0.0969882i
\(121\) 120.986 0.999886
\(122\) 34.8141 34.8141i 0.285361 0.285361i
\(123\) −31.7349 + 25.1410i −0.258007 + 0.204398i
\(124\) −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 \(0.687838\pi\)
\(132\) 0.552187 0.437453i 0.00418323 0.00331404i
\(133\) −92.9590 186.131i −0.698940 1.39948i
\(134\) 68.9784 0.514764
\(135\) 90.8642 99.8433i 0.673068 0.739580i
\(136\) 55.4763i 0.407914i
\(137\) −37.8019 37.8019i −0.275926 0.275926i 0.555554 0.831480i \(-0.312506\pi\)
−0.831480 + 0.555554i \(0.812506\pi\)
\(138\) −10.5888 + 8.38867i −0.0767305 + 0.0607875i
\(139\) 65.4496 0.470861 0.235430 0.971891i \(-0.424350\pi\)
0.235430 + 0.971891i \(0.424350\pi\)
\(140\) 52.8886 + 45.8562i 0.377776 + 0.327544i
\(141\) 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
\(147\) 3.75748 + 146.952i 0.0255611 + 0.999673i
\(148\) 10.6522 + 10.6522i 0.0719745 + 0.0719745i
\(149\) −109.296 −0.733529 −0.366765 0.930314i \(-0.619535\pi\)
−0.366765 + 0.930314i \(0.619535\pi\)
\(150\) 83.0582 65.9646i 0.553722 0.439764i
\(151\) −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
\(153\) −92.9524 150.069i −0.607532 0.980844i
\(154\) 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 0.712410 0.701764i \(-0.247604\pi\)
−0.701764 + 0.712410i \(0.747604\pi\)
\(158\) 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
\(162\) 36.4384 + 108.601i 0.224929 + 0.670378i
\(163\) −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
\(165\) 0.855936 1.53919i 0.00518749 0.00932840i
\(166\) 198.126i 1.19353i
\(167\) −122.479 + 122.479i −0.733409 + 0.733409i −0.971293 0.237884i \(-0.923546\pi\)
0.237884 + 0.971293i \(0.423546\pi\)
\(168\) −55.8411 + 20.2427i −0.332388 + 0.120492i
\(169\) 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
\(175\) 166.061 + 55.2143i 0.948922 + 0.315510i
\(176\) 0.469645i 0.00266844i
\(177\) 158.200 + 199.692i 0.893785 + 1.12820i
\(178\) −129.599 + 129.599i −0.728082 + 0.728082i
\(179\) 167.194 0.934042 0.467021 0.884246i \(-0.345327\pi\)
0.467021 + 0.884246i \(0.345327\pi\)
\(180\) 14.5578 + 88.8148i 0.0808768 + 0.493416i
\(181\) 271.099i 1.49778i 0.662692 + 0.748892i \(0.269414\pi\)
−0.662692 + 0.748892i \(0.730586\pi\)
\(182\) 60.8173 + 121.774i 0.334161 + 0.669086i
\(183\) 64.8555 + 81.8655i 0.354402 + 0.447352i
\(184\) 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 \(0.255481\pi\)
−0.694827 + 0.719177i \(0.744519\pi\)
\(192\) −14.9033 18.8120i −0.0776212 0.0979793i
\(193\) −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
\(195\) 198.335 56.5785i 1.01710 0.290146i
\(196\) −78.3462 58.8716i −0.399726 0.300365i
\(197\) −182.638 182.638i −0.927095 0.927095i 0.0704222 0.997517i \(-0.477565\pi\)
−0.997517 + 0.0704222i \(0.977565\pi\)
\(198\) 0.786906 + 1.27044i 0.00397427 + 0.00641636i
\(199\) −246.453 −1.23846 −0.619228 0.785211i \(-0.712554\pi\)
−0.619228 + 0.785211i \(0.712554\pi\)
\(200\) 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
\(203\) 144.093 + 288.517i 0.709820 + 1.42126i
\(204\) 116.900 + 13.5527i 0.573039 + 0.0664350i
\(205\) −25.8605 62.3257i −0.126149 0.304028i
\(206\) −62.7388 −0.304557
\(207\) −15.0898 24.3622i −0.0728978 0.117692i
\(208\) −38.8903 + 38.8903i −0.186973 + 0.186973i
\(209\) 3.48968i 0.0166970i
\(210\) −109.549 + 100.245i −0.521662 + 0.477356i
\(211\) 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
\(213\) −144.654 182.594i −0.679129 0.857248i
\(214\) 211.712i 0.989310i
\(215\) −99.6380 + 240.961i −0.463433 + 1.12075i
\(216\) −71.8351 25.9176i −0.332570 0.119989i
\(217\) 9.45285 4.72102i 0.0435615 0.0217559i
\(218\) 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
\(222\) −25.0487 + 19.8441i −0.112832 + 0.0893879i
\(223\) −44.8950 + 44.8950i −0.201323 + 0.201323i −0.800567 0.599244i \(-0.795468\pi\)
0.599244 + 0.800567i \(0.295468\pi\)
\(224\) 12.5391 37.5602i 0.0559783 0.167680i
\(225\) 118.710 + 191.136i 0.527600 + 0.849493i
\(226\) 120.252 0.532089
\(227\) 211.845 211.845i 0.933238 0.933238i −0.0646692 0.997907i \(-0.520599\pi\)
0.997907 + 0.0646692i \(0.0205992\pi\)
\(228\) 110.738 + 139.782i 0.485693 + 0.613079i
\(229\) 10.2429 0.0447287 0.0223644 0.999750i \(-0.492881\pi\)
0.0223644 + 0.999750i \(0.492881\pi\)
\(230\) −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 −0.353317 0.935504i \(-0.614946\pi\)
0.935504 + 0.353317i \(0.114946\pi\)
\(234\) −40.0404 + 170.364i −0.171113 + 0.728053i
\(235\) 194.598 + 80.4669i 0.828077 + 0.342413i
\(236\) −169.842 −0.719669
\(237\) 1.61271 + 2.03568i 0.00680468 + 0.00858938i
\(238\) 86.7548 + 173.708i 0.364516 + 0.729865i
\(239\) 25.1069 0.105050 0.0525250 0.998620i \(-0.483273\pi\)
0.0525250 + 0.998620i \(0.483273\pi\)
\(240\) −52.4374 29.1602i −0.218489 0.121501i
\(241\) 278.949i 1.15747i 0.815517 + 0.578733i \(0.196452\pi\)
−0.815517 + 0.578733i \(0.803548\pi\)
\(242\) −120.986 120.986i −0.499943 0.499943i
\(243\) −237.747 + 50.2522i −0.978383 + 0.206799i
\(244\) −69.6282 −0.285361
\(245\) −237.316 60.8773i −0.968637 0.248479i
\(246\) 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 \(0.361744\pi\)
\(252\) −29.0137 122.614i −0.115134 0.486564i
\(253\) −0.264351 0.264351i −0.00104487 0.00104487i
\(254\) −343.720 −1.35323
\(255\) 282.921 80.7082i 1.10949 0.316503i
\(256\) 16.0000 0.0625000
\(257\) 330.432 330.432i 1.28573 1.28573i 0.348371 0.937357i \(-0.386735\pi\)
0.937357 0.348371i \(-0.113265\pi\)
\(258\) −137.391 173.425i −0.532524 0.672192i
\(259\) −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 −0.551508 0.834170i \(-0.685947\pi\)
0.834170 + 0.551508i \(0.185947\pi\)
\(264\) −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
\(267\) −241.430 304.751i −0.904233 1.14139i
\(268\) −68.9784 68.9784i −0.257382 0.257382i
\(269\) 250.571i 0.931490i −0.884919 0.465745i \(-0.845786\pi\)
0.884919 0.465745i \(-0.154214\pi\)
\(270\) −190.708 + 8.97908i −0.706324 + 0.0332559i
\(271\) 207.488i 0.765638i 0.923823 + 0.382819i \(0.125047\pi\)
−0.923823 + 0.382819i \(0.874953\pi\)
\(272\) −55.4763 + 55.4763i −0.203957 + 0.203957i
\(273\) −271.460 + 98.4056i −0.994359 + 0.360460i
\(274\) 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
\(280\) −7.03243 98.7448i −0.0251158 0.352660i
\(281\) 353.277i 1.25721i 0.777723 + 0.628607i \(0.216374\pi\)
−0.777723 + 0.628607i \(0.783626\pi\)
\(282\) −140.057 + 110.956i −0.496656 + 0.393461i
\(283\) −181.090 + 181.090i −0.639894 + 0.639894i −0.950529 0.310635i \(-0.899458\pi\)
0.310635 + 0.950529i \(0.399458\pi\)
\(284\) 155.300 0.546829
\(285\) 389.634 + 216.674i 1.36714 + 0.760259i
\(286\) 2.28308i 0.00798280i
\(287\) 42.2092 + 84.5149i 0.147070 + 0.294477i
\(288\) 43.2817 26.8085i 0.150284 0.0930852i
\(289\) 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
\(297\) −2.86932 + 1.34781i −0.00966101 + 0.00453808i
\(298\) 109.296 + 109.296i 0.366765 + 0.366765i
\(299\) 43.7807i 0.146424i
\(300\) −149.023 17.0937i −0.496743 0.0569789i
\(301\) 115.597 346.262i 0.384042 1.15037i
\(302\) 223.334 + 223.334i 0.739516 + 0.739516i
\(303\) −33.9851 + 26.9237i −0.112162 + 0.0888571i
\(304\) −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 0.228532 0.973536i \(-0.426608\pi\)
−0.973536 + 0.228532i \(0.926608\pi\)
\(308\) −0.734439 1.47056i −0.00238454 0.00477454i
\(309\) 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 \(0.642487\pi\)
\(312\) −72.4491 91.4507i −0.232209 0.293111i
\(313\) 421.023 421.023i 1.34512 1.34512i 0.454244 0.890877i \(-0.349909\pi\)
0.890877 0.454244i \(-0.150091\pi\)
\(314\) 3.34288i 0.0106461i
\(315\) −184.474 255.332i −0.585631 0.810578i
\(316\) −1.73139 −0.00547908
\(317\) −74.8122 74.8122i −0.236001 0.236001i 0.579191 0.815192i \(-0.303368\pi\)
−0.815192 + 0.579191i \(0.803368\pi\)
\(318\) 281.316 222.864i 0.884642 0.700831i
\(319\) 5.40927i 0.0169570i
\(320\) 36.9459 15.3298i 0.115456 0.0479055i
\(321\) 446.121 + 51.7208i 1.38979 + 0.161124i
\(322\) 14.0837 + 28.1997i 0.0437383 + 0.0875766i
\(323\) 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
\(327\) 177.859 + 224.507i 0.543912 + 0.686567i
\(328\) −26.9911 + 26.9911i −0.0822900 + 0.0822900i
\(329\) −279.639 93.3550i −0.849966 0.283754i
\(330\) −2.39512 + 0.683251i −0.00725795 + 0.00207046i
\(331\) −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
\(333\) −35.6963 57.6307i −0.107196 0.173065i
\(334\) 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
\(342\) −321.603 + 199.200i −0.940358 + 0.582455i
\(343\) 337.383 + 61.8203i 0.983624 + 0.180234i
\(344\) 147.502 0.428784
\(345\) 45.9292 13.1021i 0.133128 0.0379772i
\(346\) 22.2409i 0.0642800i
\(347\) −152.796 152.796i −0.440334 0.440334i 0.451790 0.892124i \(-0.350786\pi\)
−0.892124 + 0.451790i \(0.850786\pi\)
\(348\) −171.652 216.673i −0.493254 0.622623i
\(349\) 368.362 1.05548 0.527740 0.849406i \(-0.323040\pi\)
0.527740 + 0.849406i \(0.323040\pi\)
\(350\) −110.847 221.276i −0.316706 0.632216i
\(351\) −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
\(357\) −387.232 + 140.374i −1.08468 + 0.393204i
\(358\) −167.194 167.194i −0.467021 0.467021i
\(359\) 599.498 1.66991 0.834956 0.550317i \(-0.185493\pi\)
0.834956 + 0.550317i \(0.185493\pi\)
\(360\) 74.2570 103.373i 0.206269 0.287146i
\(361\) 522.387 1.44705
\(362\) 271.099 271.099i 0.748892 0.748892i
\(363\) 284.500 225.386i 0.783745 0.620899i
\(364\) 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 0.652168 0.758075i \(-0.273860\pi\)
−0.758075 + 0.652168i \(0.773860\pi\)
\(368\) −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
\(372\) −7.09898 + 5.62396i −0.0190833 + 0.0151182i
\(373\) 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
\(375\) −360.489 + 103.309i −0.961304 + 0.275491i
\(376\) 119.121i 0.316812i
\(377\) −447.930 + 447.930i −1.18814 + 1.18814i
\(378\) 265.461 31.1834i 0.702278 0.0824959i
\(379\) 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
\(385\) −3.10486 2.69202i −0.00806458 0.00699226i
\(386\) 404.822i 1.04876i
\(387\) 399.008 247.144i 1.03103 0.638615i
\(388\) −31.5856 + 31.5856i −0.0814062 + 0.0814062i
\(389\) 369.112 0.948875 0.474438 0.880289i \(-0.342651\pi\)
0.474438 + 0.880289i \(0.342651\pi\)
\(390\) −254.913 141.756i −0.653624 0.363478i
\(391\) 62.4524i 0.159725i
\(392\) 19.4746 + 137.218i 0.0496801 + 0.350046i
\(393\) −342.828 + 271.595i −0.872335 + 0.691081i
\(394\) 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 0.690513 0.723320i \(-0.257385\pi\)
−0.723320 + 0.690513i \(0.757385\pi\)
\(398\) 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 \(0.00679466\pi\)
−0.999772 + 0.0213444i \(0.993205\pi\)
\(402\) 162.203 128.500i 0.403490 0.319653i
\(403\) 14.6758 + 14.6758i 0.0364164 + 0.0364164i
\(404\) 28.9050i 0.0715470i
\(405\) 27.6687 404.054i 0.0683177 0.997664i
\(406\) 144.423 432.610i 0.355722 1.06554i
\(407\) −0.625346 0.625346i −0.00153648 0.00153648i
\(408\) −103.347 130.453i −0.253302 0.319737i
\(409\) 186.052 0.454895 0.227447 0.973790i \(-0.426962\pi\)
0.227447 + 0.973790i \(0.426962\pi\)
\(410\) −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
\(413\) 531.811 265.602i 1.28768 0.643103i
\(414\) −9.27232 + 39.4520i −0.0223969 + 0.0952947i
\(415\) −267.670 + 647.323i −0.644988 + 1.55981i
\(416\) 77.7806 0.186973
\(417\) 153.905 121.927i 0.369077 0.292390i
\(418\) −3.48968 + 3.48968i −0.00834852 + 0.00834852i
\(419\) 606.909i 1.44847i −0.689553 0.724235i \(-0.742193\pi\)
0.689553 0.724235i \(-0.257807\pi\)
\(420\) 209.794 + 9.30436i 0.499509 + 0.0221532i
\(421\) −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
\(423\) −199.592 322.236i −0.471848 0.761786i
\(424\) 239.265i 0.564304i
\(425\) 0.594965 + 490.345i 0.00139992 + 1.15375i
\(426\) −37.9393 + 327.248i −0.0890595 + 0.768188i
\(427\) 218.021 108.886i 0.510587 0.255002i
\(428\) −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 \(0.177300\pi\)
−0.848843 + 0.528645i \(0.822700\pi\)
\(432\) 45.9175 + 97.7527i 0.106290 + 0.226279i
\(433\) 201.636 201.636i 0.465672 0.465672i −0.434837 0.900509i \(-0.643194\pi\)
0.900509 + 0.434837i \(0.143194\pi\)
\(434\) −14.1739 4.73182i −0.0326587 0.0109028i
\(435\) −603.962 335.861i −1.38842 0.772094i
\(436\) −190.948 −0.437954
\(437\) 66.9186 66.9186i 0.153132 0.153132i
\(438\) 194.356 153.973i 0.443735 0.351536i
\(439\) 94.0452 0.214226 0.107113 0.994247i \(-0.465839\pi\)
0.107113 + 0.994247i \(0.465839\pi\)
\(440\) 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 −0.551489 0.834182i \(-0.685940\pi\)
0.834182 + 0.551489i \(0.185940\pi\)
\(444\) 44.8929 + 5.20463i 0.101110 + 0.0117221i
\(445\) 598.517 248.339i 1.34498 0.558066i
\(446\) 89.7899 0.201323
\(447\) −257.010 + 203.608i −0.574966 + 0.455499i
\(448\) −50.0994 + 25.0211i −0.111829 + 0.0558506i
\(449\) −324.260 −0.722184 −0.361092 0.932530i \(-0.617596\pi\)
−0.361092 + 0.932530i \(0.617596\pi\)
\(450\) 72.4258 309.846i 0.160946 0.688547i
\(451\) 1.58453i 0.00351337i
\(452\) −120.252 120.252i −0.266045 0.266045i
\(453\) −525.170 + 416.050i −1.15932 + 0.918434i
\(454\) −423.690 −0.933238
\(455\) −34.1867 480.027i −0.0751356 1.05500i
\(456\) 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 \(0.675948\pi\)
\(462\) 3.27819 1.18836i 0.00709565 0.00257221i
\(463\) 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
\(465\) −11.0040 + 19.7880i −0.0236646 + 0.0425548i
\(466\) −271.299 −0.582186
\(467\) 302.621 302.621i 0.648011 0.648011i −0.304501 0.952512i \(-0.598490\pi\)
0.952512 + 0.304501i \(0.0984897\pi\)
\(468\) 210.405 130.324i 0.449583 0.278470i
\(469\) 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
\(477\) 400.896 + 647.236i 0.840453 + 1.35689i
\(478\) −25.1069 25.1069i −0.0525250 0.0525250i
\(479\) 444.701i 0.928395i −0.885732 0.464198i \(-0.846343\pi\)
0.885732 0.464198i \(-0.153657\pi\)
\(480\) 23.2772 + 81.5976i 0.0484941 + 0.169995i
\(481\) 103.567i 0.215316i
\(482\) 278.949 278.949i 0.578733 0.578733i
\(483\) −62.8631 + 22.7882i −0.130151 + 0.0471805i
\(484\) 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
\(490\) 176.439 + 298.193i 0.360079 + 0.608558i
\(491\) 85.1811i 0.173485i −0.996231 0.0867425i \(-0.972354\pi\)
0.996231 0.0867425i \(-0.0276457\pi\)
\(492\) −50.2820 63.4697i −0.102199 0.129004i
\(493\) −638.963 + 638.963i −1.29607 + 1.29607i
\(494\) −577.945 −1.16993
\(495\) −0.854627 5.21393i −0.00172652 0.0105332i
\(496\) 6.03782i 0.0121730i
\(497\) −486.275 + 242.860i −0.978421 + 0.488652i
\(498\) −369.091 465.894i −0.741146 0.935530i
\(499\) 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
\(507\) −37.3643 47.1641i −0.0736969 0.0930257i
\(508\) 343.720 + 343.720i 0.676615 + 0.676615i
\(509\) 930.732i 1.82855i 0.405094 + 0.914275i \(0.367239\pi\)
−0.405094 + 0.914275i \(0.632761\pi\)
\(510\) −363.629 202.213i −0.712998 0.396496i
\(511\) 388.053 + 129.548i 0.759398 + 0.253518i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −341.188 726.347i −0.665083 1.41588i
\(514\) −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
\(518\) 33.3162 + 66.7087i 0.0643171 + 0.128781i
\(519\) −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 \(0.493193\pi\)
\(522\) 498.508 308.774i 0.954997 0.591522i
\(523\) 110.356 110.356i 0.211006 0.211006i −0.593689 0.804695i \(-0.702329\pi\)
0.804695 + 0.593689i \(0.202329\pi\)
\(524\) 291.582i 0.556453i
\(525\) 493.353 179.521i 0.939720 0.341944i
\(526\) −148.680 −0.282662
\(527\) 20.9348 + 20.9348i 0.0397244 + 0.0397244i
\(528\) 0.874907 + 1.10437i 0.00165702 + 0.00209162i
\(529\) 518.862i 0.980835i
\(530\) 229.242 + 552.491i 0.432532 + 1.04244i
\(531\) 744.016 + 174.864i 1.40116 + 0.329311i
\(532\) 372.261 185.918i 0.699739 0.349470i
\(533\) −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
\(537\) 393.156 311.466i 0.732134 0.580012i
\(538\) −250.571 + 250.571i −0.465745 + 0.465745i
\(539\) 4.59937 + 3.45610i 0.00853315 + 0.00641206i
\(540\) 199.687 + 181.728i 0.369790 + 0.336534i
\(541\) 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
\(543\) 505.032 + 637.490i 0.930078 + 1.17401i
\(544\) 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
\(552\) −16.7773 21.1776i −0.0303937 0.0383653i
\(553\) 5.42134 2.70757i 0.00980351 0.00489616i
\(554\) 129.447 0.233658
\(555\) 108.650 30.9942i 0.195765 0.0558454i
\(556\) 130.899i 0.235430i
\(557\) 242.020 + 242.020i 0.434506 + 0.434506i 0.890158 0.455652i \(-0.150594\pi\)
−0.455652 + 0.890158i \(0.650594\pi\)
\(558\) −10.1166 16.3329i −0.0181301 0.0292705i
\(559\) 717.048 1.28273
\(560\) −91.7124 + 105.777i −0.163772 + 0.188888i
\(561\) −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
\(567\) 0.858397 + 566.999i 0.00151393 + 0.999999i
\(568\) −155.300 155.300i −0.273415 0.273415i
\(569\) 147.022 0.258387 0.129194 0.991619i \(-0.458761\pi\)
0.129194 + 0.991619i \(0.458761\pi\)
\(570\) −172.960 606.308i −0.303438 1.06370i
\(571\) 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
\(573\) 511.789 + 646.018i 0.893174 + 1.12743i
\(574\) 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 0.358723 0.933444i \(-0.383212\pi\)
−0.933444 + 0.358723i \(0.883212\pi\)
\(578\) −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
\(582\) −58.8411 74.2737i −0.101102 0.127618i
\(583\) 7.02310 + 7.02310i 0.0120465 + 0.0120465i
\(584\) 165.304i 0.283054i
\(585\) 360.985 502.524i 0.617068 0.859016i
\(586\) 144.769i 0.247045i
\(587\) 216.371 216.371i 0.368605 0.368605i −0.498363 0.866968i \(-0.666065\pi\)
0.866968 + 0.498363i \(0.166065\pi\)
\(588\) −293.904 + 7.51496i −0.499837 + 0.0127805i
\(589\) 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
\(595\) −48.7667 684.750i −0.0819608 1.15084i
\(596\) 218.592i 0.366765i
\(597\) −579.534 + 459.119i −0.970744 + 0.769043i
\(598\) −43.7807 + 43.7807i −0.0732119 + 0.0732119i
\(599\) −735.946 −1.22862 −0.614312 0.789063i \(-0.710567\pi\)
−0.614312 + 0.789063i \(0.710567\pi\)
\(600\) 131.929 + 166.116i 0.219882 + 0.276861i
\(601\) 851.749i 1.41722i 0.705600 + 0.708610i \(0.250677\pi\)
−0.705600 + 0.708610i \(0.749323\pi\)
\(602\) −461.859 + 230.666i −0.767207 + 0.383166i
\(603\) 231.151 + 373.188i 0.383335 + 0.618885i
\(604\) 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 0.206621 0.978421i \(-0.433753\pi\)
−0.978421 + 0.206621i \(0.933753\pi\)
\(608\) 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
\(612\) 300.138 185.905i 0.490422 0.303766i
\(613\) −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
\(615\) −176.918 98.3834i −0.287672 0.159973i
\(616\) −0.736119 + 2.20500i −0.00119500 + 0.00357954i
\(617\) −238.684 238.684i −0.386845 0.386845i 0.486715 0.873561i \(-0.338195\pi\)
−0.873561 + 0.486715i \(0.838195\pi\)
\(618\) −147.531 + 116.877i −0.238723 + 0.189121i
\(619\) 400.073 0.646322 0.323161 0.946344i \(-0.395254\pi\)
0.323161 + 0.946344i \(0.395254\pi\)
\(620\) −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
\(623\) −811.600 + 405.337i −1.30273 + 0.650621i
\(624\) −19.0016 + 163.900i −0.0304513 + 0.262660i
\(625\) −1.51670 624.998i −0.00242671 0.999997i
\(626\) −842.046 −1.34512
\(627\) −6.50095 8.20600i −0.0103683 0.0130877i
\(628\) −3.34288 + 3.34288i −0.00532305 + 0.00532305i
\(629\) 147.736i 0.234875i
\(630\) −70.8584 + 439.806i −0.112474 + 0.698104i
\(631\) −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
\(633\) 390.069 309.021i 0.616223 0.488185i
\(634\) 149.624i 0.236001i
\(635\) 1123.01 + 464.369i 1.76852 + 0.731290i
\(636\) −504.180 58.4519i −0.792736 0.0919055i
\(637\) 94.6716 + 667.056i 0.148621 + 1.04718i
\(638\) 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 \(-0.724452\pi\)
0.648137 0.761524i \(-0.275548\pi\)
\(642\) −394.401 497.842i −0.614331 0.775455i
\(643\) 155.167 155.167i 0.241317 0.241317i −0.576078 0.817395i \(-0.695417\pi\)
0.817395 + 0.576078i \(0.195417\pi\)
\(644\) 14.1159 42.2834i 0.0219192 0.0656574i
\(645\) 214.589 + 752.237i 0.332696 + 1.16626i
\(646\) −824.428 −1.27620
\(647\) 122.968 122.968i 0.190059 0.190059i −0.605663 0.795722i \(-0.707092\pi\)
0.795722 + 0.605663i \(0.207092\pi\)
\(648\) −217.203 + 72.8768i −0.335189 + 0.112464i
\(649\) 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 −0.998909 0.0466996i \(-0.985130\pi\)
0.0466996 + 0.998909i \(0.485130\pi\)
\(654\) 46.6482 402.367i 0.0713275 0.615240i
\(655\) −279.367 673.296i −0.426515 1.02793i
\(656\) 53.9822 0.0822900
\(657\) 276.972 + 447.164i 0.421570 + 0.680614i
\(658\) 186.284 + 372.994i 0.283106 + 0.566860i
\(659\) 307.522 0.466650 0.233325 0.972399i \(-0.425039\pi\)
0.233325 + 0.972399i \(0.425039\pi\)
\(660\) 3.07837 + 1.71187i 0.00466420 + 0.00259375i
\(661\) 621.533i 0.940292i −0.882589 0.470146i \(-0.844201\pi\)
0.882589 0.470146i \(-0.155799\pi\)
\(662\) 506.910 + 506.910i 0.765725 + 0.765725i
\(663\) −502.401 634.168i −0.757769 0.956513i
\(664\) 396.252 0.596765
\(665\) 681.465 785.973i 1.02476 1.18191i
\(666\) −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
\(672\) −40.4854 111.682i −0.0602461 0.166194i
\(673\) −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
\(675\) 635.216 + 228.311i 0.941061 + 0.338238i
\(676\) 40.1139 0.0593402
\(677\) 679.334 679.334i 1.00345 1.00345i 0.00345318 0.999994i \(-0.498901\pi\)
0.999994 0.00345318i \(-0.00109918\pi\)
\(678\) 282.773 224.019i 0.417070 0.330411i
\(679\) 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 \(0.564972\pi\)
−0.979241 + 0.202700i \(0.935028\pi\)
\(684\) 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
\(687\) 24.0862 19.0815i 0.0350599 0.0277752i
\(688\) −147.502 147.502i −0.214392 0.214392i
\(689\) 1163.14i 1.68815i
\(690\) −59.0314 32.8271i −0.0855527 0.0475755i
\(691\) 287.198i 0.415626i −0.978169 0.207813i \(-0.933365\pi\)
0.978169 0.207813i \(-0.0666346\pi\)
\(692\) 22.2409 22.2409i 0.0321400 0.0321400i
\(693\) 1.70327 + 7.19814i 0.00245782 + 0.0103869i
\(694\) 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
\(700\) −110.429 + 332.123i −0.157755 + 0.474461i
\(701\) 791.451i 1.12903i 0.825422 + 0.564516i \(0.190937\pi\)
−0.825422 + 0.564516i \(0.809063\pi\)
\(702\) 223.218 + 475.204i 0.317974 + 0.676929i
\(703\) 158.302 158.302i 0.225180 0.225180i
\(704\) −0.939291 −0.00133422
\(705\) 607.501 173.300i 0.861704 0.245816i
\(706\) 489.435i 0.693251i
\(707\) 45.2021 + 90.5076i 0.0639351 + 0.128016i
\(708\) −399.384 + 316.400i −0.564102 + 0.446893i
\(709\) 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
\(717\) 59.0391 46.7719i 0.0823418 0.0652328i
\(718\) −599.498 599.498i −0.834956 0.834956i
\(719\) 364.303i 0.506680i 0.967377 + 0.253340i \(0.0815291\pi\)
−0.967377 + 0.253340i \(0.918471\pi\)
\(720\) −177.630 + 29.1157i −0.246708 + 0.0404384i
\(721\) −294.560 98.3364i −0.408544 0.136389i
\(722\) −522.387 522.387i −0.723527 0.723527i
\(723\) 519.657 + 655.950i 0.718751 + 0.907261i
\(724\) −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 0.565468 0.824771i \(-0.308696\pi\)
−0.824771 + 0.565468i \(0.808696\pi\)
\(728\) −243.547 + 121.635i −0.334543 + 0.167081i
\(729\) −465.448 + 561.070i −0.638475 + 0.769643i
\(730\) 158.379 + 381.706i 0.216958 + 0.522884i
\(731\) 1022.86 1.39926
\(732\) −163.731 + 129.711i −0.223676 + 0.177201i
\(733\) 1.46070 1.46070i 0.00199277 0.00199277i −0.706110 0.708102i \(-0.749551\pi\)
0.708102 + 0.706110i \(0.249551\pi\)
\(734\) 77.7356i 0.105907i
\(735\) −671.459 + 298.945i −0.913549 + 0.406728i
\(736\) 18.0120 0.0244728
\(737\) 4.04942 + 4.04942i 0.00549447 + 0.00549447i
\(738\) 146.028 90.4490i 0.197869 0.122560i
\(739\) 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
\(742\) −374.166 749.188i −0.504267 1.00969i
\(743\) 781.133 781.133i 1.05132 1.05132i 0.0527138 0.998610i \(-0.483213\pi\)
0.998610 0.0527138i \(-0.0167871\pi\)
\(744\) 12.7229 + 1.47503i 0.0171007 + 0.00198256i
\(745\) −209.435 504.754i −0.281121 0.677522i
\(746\) 456.732i 0.612241i
\(747\) 1071.90 663.933i 1.43494 0.888800i
\(748\) 3.25677 3.25677i 0.00435398 0.00435398i
\(749\) 331.836 993.995i 0.443039 1.32710i
\(750\) 463.798 + 257.180i 0.618397 + 0.342907i
\(751\) −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
\(753\) 496.755 393.539i 0.659701 0.522629i
\(754\) 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 \(0.567158\pi\)
\(762\) −808.260 + 640.320i −1.06071 + 0.840314i
\(763\) 597.898 298.608i 0.783615 0.391360i
\(764\) −549.451 −0.719177
\(765\) 514.938 716.841i 0.673121 0.937048i
\(766\) 602.040i 0.785953i