Properties

Label 210.3.k.a.167.3
Level 210
Weight 3
Character 210.167
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 167.3
Character \(\chi\) \(=\) 210.167
Dual form 210.3.k.a.83.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 + 1.00000i) q^{2} +(-2.35150 - 1.86291i) q^{3} -2.00000i q^{4} +(-1.91622 + 4.61824i) q^{5} +(4.21441 - 0.488596i) q^{6} +(6.26242 - 3.12763i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.05914 + 8.76127i) q^{9} +O(q^{10})\) \(q+(-1.00000 + 1.00000i) q^{2} +(-2.35150 - 1.86291i) 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} +(-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} +(-20.5526 - 4.31167i) 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} +(-6.25527 - 12.5248i) 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} +(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} +(24.8643 - 16.2409i) 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} +(40.2973 + 48.4265i) 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} +(-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} +(0.367220 + 0.735279i) 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} +(-8.62335 + 41.1052i) 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} +(9.73729 + 68.6089i) q^{98} +(-1.02867 + 0.241767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

Character values

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

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

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
\(7\) 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 \(0.998301\pi\)
\(12\) −3.72582 + 4.70301i −0.310485 + 0.391917i
\(13\) −9.72258 9.72258i −0.747890 0.747890i 0.226192 0.974083i \(-0.427372\pi\)
−0.974083 + 0.226192i \(0.927372\pi\)
\(14\) −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 \(-0.445729\pi\)
−0.985500 + 0.169673i \(0.945729\pi\)
\(18\) −10.8204 6.70213i −0.601134 0.372341i
\(19\) −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
\(21\) −20.5526 4.31167i −0.978695 0.205318i
\(22\) −0.117411 0.117411i −0.00533688 0.00533688i
\(23\) 2.25150 + 2.25150i 0.0978912 + 0.0978912i 0.754356 0.656465i \(-0.227949\pi\)
−0.656465 + 0.754356i \(0.727949\pi\)
\(24\) −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
\(28\) −6.25527 12.5248i −0.223402 0.447316i
\(29\) −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
\(35\) 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 0.775409 0.631460i \(-0.217544\pi\)
−0.631460 + 0.775409i \(0.717544\pi\)
\(38\) 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 \(-0.447373\pi\)
0.164580 + 0.986364i \(0.447373\pi\)
\(42\) 24.8643 16.2409i 0.592007 0.386689i
\(43\) 36.8754 36.8754i 0.857568 0.857568i −0.133483 0.991051i \(-0.542616\pi\)
0.991051 + 0.133483i \(0.0426162\pi\)
\(44\) 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 \(-0.397878\pi\)
−0.948975 + 0.315351i \(0.897878\pi\)
\(48\) 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 −0.990404 0.138204i \(-0.955867\pi\)
−0.138204 0.990404i \(-0.544133\pi\)
\(54\) 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
\(63\) 40.2973 + 48.4265i 0.639639 + 0.768675i
\(64\) 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 0.401218 0.915982i \(-0.368587\pi\)
−0.915982 + 0.401218i \(0.868587\pi\)
\(68\) −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 \(0.815835\pi\)
\(72\) −13.4043 + 21.6408i −0.186170 + 0.300567i
\(73\) 41.3259 + 41.3259i 0.566108 + 0.566108i 0.931036 0.364928i \(-0.118906\pi\)
−0.364928 + 0.931036i \(0.618906\pi\)
\(74\) −10.6522 −0.143949
\(75\) 8.54683 + 74.5114i 0.113958 + 0.993486i
\(76\) 59.4436i 0.782153i
\(77\) 0.367220 + 0.735279i 0.00476909 + 0.00954908i
\(78\) −45.7254 36.2245i −0.586223 0.464417i
\(79\) 0.865694i 0.0109582i −0.999985 0.00547908i \(-0.998256\pi\)
0.999985 0.00547908i \(-0.00174405\pi\)
\(80\) 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 −0.217461 + 0.976069i \(0.569778\pi\)
−0.976069 + 0.217461i \(0.930222\pi\)
\(84\) −8.62335 + 41.1052i −0.102659 + 0.489348i
\(85\) 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 \(-0.786727\pi\)
0.620999 + 0.783811i \(0.286727\pi\)
\(98\) 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 \(-0.477206\pi\)
0.0715470 + 0.997437i \(0.477206\pi\)
\(102\) −65.2264 51.6736i −0.639474 0.506604i
\(103\) −31.3694 31.3694i −0.304557 0.304557i 0.538237 0.842794i \(-0.319091\pi\)
−0.842794 + 0.538237i \(0.819091\pi\)
\(104\) 38.8903i 0.373945i
\(105\) 59.2956 86.6547i 0.564720 0.825282i
\(106\) 119.632 1.12861
\(107\) 105.856 105.856i 0.989310 0.989310i −0.0106339 0.999943i \(-0.503385\pi\)
0.999943 + 0.0106339i \(0.00338493\pi\)
\(108\) −48.8763 22.9587i −0.452559 0.212581i
\(109\) 95.4740i 0.875908i −0.898997 0.437954i \(-0.855703\pi\)
0.898997 0.437954i \(-0.144297\pi\)
\(110\) 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 \(-0.372785\pi\)
−0.921194 + 0.389104i \(0.872785\pi\)
\(114\) −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
\(126\) −88.7238 8.12926i −0.704157 0.0645179i
\(127\) 171.860 + 171.860i 1.35323 + 1.35323i 0.882022 + 0.471207i \(0.156182\pi\)
0.471207 + 0.882022i \(0.343818\pi\)
\(128\) −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 \(-0.312162\pi\)
0.556453 + 0.830879i \(0.312162\pi\)
\(132\) −0.552187 0.437453i −0.00418323 0.00331404i
\(133\) −186.131 + 92.9590i −1.39948 + 0.698940i
\(134\) 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 −0.831480 0.555554i \(-0.812506\pi\)
0.555554 + 0.831480i \(0.312506\pi\)
\(138\) 10.5888 + 8.38867i 0.0767305 + 0.0607875i
\(139\) −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
\(147\) −142.194 + 37.2795i −0.967309 + 0.253602i
\(148\) 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 \(-0.752396\pi\)
0.701764 + 0.712410i \(0.252396\pi\)
\(158\) 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 −0.804156 0.594419i \(-0.797382\pi\)
0.594419 + 0.804156i \(0.297382\pi\)
\(164\) 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 \(-0.0764539\pi\)
−0.237884 + 0.971293i \(0.576454\pi\)
\(168\) −32.4819 49.7286i −0.193344 0.296003i
\(169\) 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 \(-0.735527\pi\)
0.738516 + 0.674236i \(0.235527\pi\)
\(174\) −194.163 + 22.5101i −1.11588 + 0.129369i
\(175\) −165.927 55.6171i −0.948154 0.317812i
\(176\) 0.469645i 0.00266844i
\(177\) 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 \(0.730586\pi\)
\(182\) 121.774 60.8173i 0.669086 0.334161i
\(183\) 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
\(189\) −4.54500 188.945i −0.0240476 0.999711i
\(190\) 80.3089 + 194.216i 0.422678 + 1.02219i
\(191\) 274.726i 1.43835i −0.694827 0.719177i \(-0.744519\pi\)
0.694827 0.719177i \(-0.255481\pi\)
\(192\) 14.9033 18.8120i 0.0776212 0.0979793i
\(193\) −202.411 + 202.411i −1.04876 + 1.04876i −0.0500128 + 0.998749i \(0.515926\pi\)
−0.998749 + 0.0500128i \(0.984074\pi\)
\(194\) 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 −0.997517 0.0704222i \(-0.977565\pi\)
0.0704222 + 0.997517i \(0.477565\pi\)
\(198\) 0.786906 1.27044i 0.00397427 0.00641636i
\(199\) 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
\(207\) −15.0898 + 24.3622i −0.0728978 + 0.117692i
\(208\) 38.8903 + 38.8903i 0.186973 + 0.186973i
\(209\) 3.48968i 0.0166970i
\(210\) 27.3590 + 145.950i 0.130281 + 0.695001i
\(211\) 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
\(217\) 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
\(222\) 25.0487 + 19.8441i 0.112832 + 0.0893879i
\(223\) 44.8950 + 44.8950i 0.201323 + 0.201323i 0.800567 0.599244i \(-0.204532\pi\)
−0.599244 + 0.800567i \(0.704532\pi\)
\(224\) 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 \(-0.479401\pi\)
−0.997907 + 0.0646692i \(0.979401\pi\)
\(228\) 110.738 139.782i 0.485693 0.613079i
\(229\) −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
\(231\) 0.506239 2.41311i 0.00219151 0.0104464i
\(232\) −92.1422 92.1422i −0.397165 0.397165i
\(233\) 135.649 + 135.649i 0.582186 + 0.582186i 0.935504 0.353317i \(-0.114946\pi\)
−0.353317 + 0.935504i \(0.614946\pi\)
\(234\) 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
\(238\) 173.708 86.7548i 0.729865 0.364516i
\(239\) 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
\(245\) 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 \(-0.638256\pi\)
−0.420817 + 0.907146i \(0.638256\pi\)
\(252\) 96.8531 80.5946i 0.384338 0.319820i
\(253\) −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 −0.937357 0.348371i \(-0.886735\pi\)
−0.348371 0.937357i \(-0.613265\pi\)
\(258\) 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 0.834170 0.551508i \(-0.185947\pi\)
−0.551508 + 0.834170i \(0.685947\pi\)
\(264\) 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
\(273\) 157.904 + 241.745i 0.578402 + 0.885512i
\(274\) 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 0.580560 0.814218i \(-0.302834\pi\)
−0.814218 + 0.580560i \(0.802834\pi\)
\(278\) 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 \(-0.216374\pi\)
\(282\) −140.057 110.956i −0.496656 0.393461i
\(283\) 181.090 + 181.090i 0.639894 + 0.639894i 0.950529 0.310635i \(-0.100542\pi\)
−0.310635 + 0.950529i \(0.600542\pi\)
\(284\) 155.300 0.546829
\(285\) −389.634 + 216.674i −1.36714 + 0.760259i
\(286\) 2.28308i 0.00798280i
\(287\) 84.5149 42.2092i 0.294477 0.147070i
\(288\) 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 \(-0.805892\pi\)
0.572712 + 0.819757i \(0.305892\pi\)
\(294\) 104.915 179.474i 0.356853 0.610455i
\(295\) −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 \(-0.573392\pi\)
0.973536 + 0.228532i \(0.0733925\pi\)
\(308\) 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 \(-0.357513\pi\)
0.432835 + 0.901473i \(0.357513\pi\)
\(312\) −72.4491 + 91.4507i −0.232209 + 0.293111i
\(313\) −421.023 421.023i −1.34512 1.34512i −0.890877 0.454244i \(-0.849909\pi\)
−0.454244 0.890877i \(-0.650091\pi\)
\(314\) 3.34288i 0.0106461i
\(315\) −300.864 + 93.3065i −0.955123 + 0.296211i
\(316\) −1.73139 −0.00547908
\(317\) −74.8122 + 74.8122i −0.236001 + 0.236001i −0.815192 0.579191i \(-0.803368\pi\)
0.579191 + 0.815192i \(0.303368\pi\)
\(318\) −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
\(322\) −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
\(327\) −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
\(336\) 82.2104 + 17.2467i 0.244674 + 0.0513294i
\(337\) −187.948 187.948i −0.557709 0.557709i 0.370945 0.928655i \(-0.379034\pi\)
−0.928655 + 0.370945i \(0.879034\pi\)
\(338\) −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
\(343\) 61.8203 337.383i 0.180234 0.983624i
\(344\) 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 −0.892124 0.451790i \(-0.850786\pi\)
0.451790 + 0.892124i \(0.350786\pi\)
\(348\) 171.652 216.673i 0.493254 0.622623i
\(349\) −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 \(-0.913077\pi\)
0.269695 + 0.962946i \(0.413077\pi\)
\(354\) 41.4920 + 357.892i 0.117209 + 1.01099i
\(355\) −358.605 148.794i −1.01015 0.419138i
\(356\) −259.197 −0.728082
\(357\) 225.247 + 344.844i 0.630943 + 0.965951i
\(358\) −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 \(-0.726140\pi\)
0.758075 + 0.652168i \(0.226140\pi\)
\(368\) −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 −0.331289 0.943529i \(-0.607483\pi\)
0.943529 + 0.331289i \(0.107483\pi\)
\(374\) 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
\(378\) 193.490 + 184.400i 0.511879 + 0.487832i
\(379\) 217.075i 0.572757i 0.958117 + 0.286378i \(0.0924515\pi\)
−0.958117 + 0.286378i \(0.907549\pi\)
\(380\) −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 \(-0.562430\pi\)
0.980828 + 0.194875i \(0.0624303\pi\)
\(384\) 3.90876 + 33.7153i 0.0101791 + 0.0878003i
\(385\) −4.09937 + 0.286951i −0.0106477 + 0.000745327i
\(386\) 404.822i 1.04876i
\(387\) 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
\(392\) 137.218 19.4746i 0.350046 0.0496801i
\(393\) −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 \(-0.742615\pi\)
0.723320 + 0.690513i \(0.242615\pi\)
\(398\) −246.453 + 246.453i −0.619228 + 0.619228i
\(399\) 610.861 + 128.151i 1.53098 + 0.321180i
\(400\) 70.6248 + 70.7964i 0.176562 + 0.176991i
\(401\) 17.1182i 0.0426889i −0.999772 0.0213444i \(-0.993205\pi\)
0.999772 0.0213444i \(-0.00679466\pi\)
\(402\) −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 \(-0.573038\pi\)
−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
\(417\) 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 \(-0.257807\pi\)
\(420\) −173.309 118.591i −0.412641 0.282360i
\(421\) −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
\(427\) 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 \(-0.177300\pi\)
\(432\) −45.9175 + 97.7527i −0.106290 + 0.226279i
\(433\) −201.636 201.636i −0.465672 0.465672i 0.434837 0.900509i \(-0.356806\pi\)
−0.900509 + 0.434837i \(0.856806\pi\)
\(434\) −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 \(-0.534161\pi\)
−0.107113 + 0.994247i \(0.534161\pi\)
\(440\) −0.634495 1.53444i −0.00144203 0.00348736i
\(441\) 403.819 + 177.232i 0.915689 + 0.401887i
\(442\) −269.686 269.686i −0.610150 0.610150i
\(443\) 125.233 + 125.233i 0.282693 + 0.282693i 0.834182 0.551489i \(-0.185940\pi\)
−0.551489 + 0.834182i \(0.685940\pi\)
\(444\) −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
\(448\) 25.0211 + 50.0994i 0.0558506 + 0.111829i
\(449\) −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
\(455\) 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 0.0945240 0.995523i \(-0.469867\pi\)
−0.995523 + 0.0945240i \(0.969867\pi\)
\(458\) 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 \(-0.324052\pi\)
0.525037 + 0.851080i \(0.324052\pi\)
\(462\) 1.90687 + 2.91935i 0.00412742 + 0.00631894i
\(463\) 239.772 239.772i 0.517866 0.517866i −0.399059 0.916925i \(-0.630663\pi\)
0.916925 + 0.399059i \(0.130663\pi\)
\(464\) 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 \(-0.401510\pi\)
−0.952512 + 0.304501i \(0.901510\pi\)
\(468\) −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
\(483\) −36.5664 55.9819i −0.0757069 0.115904i
\(484\) 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 0.702670 0.711516i \(-0.251991\pi\)
−0.711516 + 0.702670i \(0.751991\pi\)
\(488\) −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 \(0.972354\pi\)
\(492\) −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
\(497\) 242.860 + 486.275i 0.488652 + 0.978421i
\(498\) −369.091 + 465.894i −0.741146 + 0.935530i
\(499\) 352.315i 0.706043i 0.935615 + 0.353021i \(0.114846\pi\)
−0.935615 + 0.353021i \(0.885154\pi\)
\(500\) −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 \(-0.799400\pi\)
0.589308 + 0.807908i \(0.299400\pi\)
\(504\) −16.2585 + 177.448i −0.0322590 + 0.352079i
\(505\) −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
\(518\) −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 \(-0.506807\pi\)
−0.0213821 + 0.999771i \(0.506807\pi\)
\(522\) 498.508 + 308.774i 0.954997 + 0.591522i
\(523\) −110.356 110.356i −0.211006 0.211006i 0.593689 0.804695i \(-0.297671\pi\)
−0.804695 + 0.593689i \(0.797671\pi\)
\(524\) 291.582i 0.556453i
\(525\) 286.568 + 439.890i 0.545844 + 0.837887i
\(526\) −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
\(532\) 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
\(537\) −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
\(546\) −399.648 83.8411i −0.731957 0.153555i
\(547\) −529.859 529.859i −0.968664 0.968664i 0.0308595 0.999524i \(-0.490176\pi\)
−0.999524 + 0.0308595i \(0.990176\pi\)
\(548\) 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
\(553\) −2.70757 5.42134i −0.00489616 0.00980351i
\(554\) 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 −0.455652 0.890158i \(-0.650594\pi\)
0.890158 + 0.455652i \(0.150594\pi\)
\(558\) 10.1166 16.3329i 0.0181301 0.0292705i
\(559\) −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 \(-0.757952\pi\)
0.689223 + 0.724549i \(0.257952\pi\)
\(564\) 251.013 29.1011i 0.445059 0.0515976i
\(565\) 392.891 162.462i 0.695383 0.287543i
\(566\) −362.180 −0.639894
\(567\) −341.300 + 452.773i −0.601941 + 0.798541i
\(568\) −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 \(-0.616788\pi\)
0.933444 + 0.358723i \(0.116788\pi\)
\(578\) −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 \(-0.333935\pi\)
−0.866968 + 0.498363i \(0.833935\pi\)
\(588\) 74.5590 + 284.389i 0.126801 + 0.483654i
\(589\) 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 \(-0.620232\pi\)
0.929508 + 0.368802i \(0.120232\pi\)
\(594\) −4.21713 + 1.52151i −0.00709954 + 0.00256147i
\(595\) 450.337 518.128i 0.756869 0.870804i
\(596\) 218.592i 0.366765i
\(597\) −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 \(0.749323\pi\)
\(602\) 230.666 + 461.859i 0.383166 + 0.767207i
\(603\) 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 \(-0.566247\pi\)
0.978421 + 0.206621i \(0.0662466\pi\)
\(608\) −118.887 + 118.887i −0.195538 + 0.195538i
\(609\) 946.881 + 198.643i 1.55481 + 0.326180i
\(610\) 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 −0.0683679 + 0.997660i \(0.521779\pi\)
−0.997660 + 0.0683679i \(0.978221\pi\)
\(614\) 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 −0.873561 0.486715i \(-0.838195\pi\)
0.486715 + 0.873561i \(0.338195\pi\)
\(618\) −147.531 116.877i −0.238723 0.189121i
\(619\) −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
\(627\) −6.50095 + 8.20600i −0.0103683 + 0.0130877i
\(628\) 3.34288 + 3.34288i 0.00532305 + 0.00532305i
\(629\) 147.736i 0.234875i
\(630\) 207.557 394.170i 0.329456 0.625667i
\(631\) −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
\(637\) −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 \(0.724452\pi\)
\(642\) 394.401 497.842i 0.614331 0.775455i
\(643\) −155.167 155.167i −0.241317 0.241317i 0.576078 0.817395i \(-0.304583\pi\)
−0.817395 + 0.576078i \(0.804583\pi\)
\(644\) 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 \(-0.292908\pi\)
−0.795722 + 0.605663i \(0.792908\pi\)
\(648\) −217.203 72.8768i −0.335189 0.112464i
\(649\) −9.97068 −0.0153631
\(650\) −343.328 344.162i −0.528196 0.529480i
\(651\) 6.50828 31.0232i 0.00999736 0.0476548i
\(652\) 68.3743 + 68.3743i 0.104869 + 0.104869i
\(653\) −621.793 621.793i −0.952209 0.952209i 0.0466996 0.998909i \(-0.485130\pi\)
−0.998909 + 0.0466996i \(0.985130\pi\)
\(654\) −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
\(658\) 372.994 186.284i 0.566860 0.283106i
\(659\) 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
\(665\) −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
\(672\) −99.4571 + 64.9637i −0.148002 + 0.0966722i
\(673\) −571.899 + 571.899i −0.849776 + 0.849776i −0.990105 0.140329i \(-0.955184\pi\)
0.140329 + 0.990105i \(0.455184\pi\)
\(674\) 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 −0.999994 0.00345318i \(-0.998901\pi\)
−0.00345318 0.999994i \(-0.501099\pi\)
\(678\) −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 −0.979241 0.202700i \(-0.935028\pi\)
−0.202700 0.979241i \(-0.564972\pi\)
\(684\) −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
\(693\) −5.68583 + 4.73136i −0.00820465 + 0.00682736i
\(694\) 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 \(-0.190937\pi\)
\(702\) 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
\(707\) 90.5076 45.2021i 0.128016 0.0639351i
\(708\) −399.384 316.400i −0.564102 0.446893i
\(709\) 56.1623i 0.0792133i −0.999215 0.0396067i \(-0.987390\pi\)
0.999215 0.0396067i \(-0.0126105\pi\)
\(710\) 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
\(714\) −570.091 119.598i −0.798447 0.167504i
\(715\) 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 \(-0.691304\pi\)
0.824771 + 0.565468i \(0.191304\pi\)
\(728\) −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
\(732\) −163.731 129.711i −0.223676 0.177201i
\(733\) −1.46070 1.46070i −0.00199277 0.00199277i 0.706110 0.708102i \(-0.250449\pi\)
−0.708102 + 0.706110i \(0.750449\pi\)
\(734\) 77.7356i 0.105907i
\(735\) 100.310 728.123i 0.136476 0.990643i
\(736\) 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 \(0.171404\pi\)
−0.858489 + 0.512832i \(0.828596\pi\)
\(740\) 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 0.998610 + 0.0527138i \(0.0167871\pi\)
0.0527138 + 0.998610i \(0.483213\pi\)
\(744\) 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
\(756\) −377.891 + 9.09000i −0.499855 + 0.0120238i
\(757\) 669.202 + 669.202i 0.884018 + 0.884018i 0.993940 0.109922i \(-0.0350601\pi\)
−0.109922 + 0.993940i \(0.535060\pi\)
\(758\) −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 \(-0.432842\pi\)
0.209420 + 0.977826i \(0.432842\pi\)
\(762\) 808.260 + 640.320i 1.06071 + 0.840314i
\(763\) −298.608 597.898i −0.391360 0.783615i
\(764\) −549.451 −0.719177
\(765\) 514.938 + 716.841i 0.673121 + 0.937048i
\(766\) 602.040i