Properties

Label 210.3.k.b.83.11
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 83.11
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.11

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{2} +(1.86291 - 2.35150i) q^{3} +2.00000i q^{4} +(-1.91622 - 4.61824i) q^{5} +(4.21441 - 0.488596i) q^{6} +(-3.12763 - 6.26242i) q^{7} +(-2.00000 + 2.00000i) q^{8} +(-2.05914 - 8.76127i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{2} +(1.86291 - 2.35150i) 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} +(4.70301 + 3.72582i) q^{12} +(9.72258 - 9.72258i) q^{13} +(3.13479 - 9.39005i) q^{14} +(-14.4295 - 4.09735i) q^{15} -4.00000 q^{16} +(-13.8691 + 13.8691i) q^{17} +(6.70213 - 10.8204i) q^{18} +29.7218 q^{19} +(9.23647 - 3.83244i) q^{20} +(-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} +(-24.4382 - 11.4794i) q^{27} +(12.5248 - 6.25527i) q^{28} +46.0711 q^{29} +(-10.3322 - 18.5269i) q^{30} +1.50946i q^{31} +(-4.00000 - 4.00000i) q^{32} +(0.276093 + 0.218727i) q^{33} -27.7381 q^{34} +(-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} +(-16.2409 - 24.8643i) q^{42} +(36.8754 + 36.8754i) q^{43} -0.234823 q^{44} +(-36.5159 + 26.2981i) q^{45} -4.50300 q^{46} +(-29.7803 + 29.7803i) q^{47} +(-7.45163 + 9.40602i) q^{48} +(-29.4358 + 39.1731i) q^{49} +(-35.3553 + 0.0428987i) q^{50} +(6.77637 + 58.4500i) q^{51} +(19.4452 + 19.4452i) q^{52} +(59.8162 - 59.8162i) q^{53} +(-12.9588 - 35.9175i) q^{54} +(0.542233 - 0.224986i) q^{55} +(18.7801 + 6.26957i) q^{56} +(55.3690 - 69.8910i) q^{57} +(46.0711 + 46.0711i) q^{58} -84.9209i q^{59} +(8.19471 - 28.8591i) q^{60} +34.8141i q^{61} +(-1.50946 + 1.50946i) q^{62} +(-48.4265 + 40.2973i) 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} +(21.6408 + 13.4043i) q^{72} +(-41.3259 + 41.3259i) q^{73} +10.6522 q^{74} +(8.72762 + 74.4905i) q^{75} +59.4436i q^{76} +(0.735279 - 0.367220i) q^{77} +(36.2245 - 45.7254i) q^{78} +0.865694i q^{79} +(7.66488 + 18.4729i) q^{80} +(-72.5199 + 36.0814i) q^{81} +(13.4956 + 13.4956i) q^{82} +(-99.0630 - 99.0630i) q^{83} +(8.62335 - 41.1052i) q^{84} +(90.6268 + 37.4745i) q^{85} +73.7509i q^{86} +(85.8262 - 108.336i) q^{87} +(-0.234823 - 0.234823i) q^{88} +129.599i q^{89} +(-62.8140 - 10.2177i) q^{90} +(-91.2955 - 30.4782i) q^{91} +(-4.50300 - 4.50300i) q^{92} +(3.54949 + 2.81198i) q^{93} -59.5607 q^{94} +(-56.9535 - 137.262i) q^{95} +(-16.8577 + 1.95438i) q^{96} +(15.7928 + 15.7928i) q^{97} +(-68.6089 + 9.73729i) q^{98} +(1.02867 - 0.241767i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.00000i 0.500000 + 0.500000i
\(3\) 1.86291 2.35150i 0.620970 0.783835i
\(4\) 2.00000i 0.500000i
\(5\) −1.91622 4.61824i −0.383244 0.923647i
\(6\) 4.21441 0.488596i 0.702402 0.0814326i
\(7\) −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 \(0.00169879\pi\)
−0.999986 + 0.00533688i \(0.998301\pi\)
\(12\) 4.70301 + 3.72582i 0.391917 + 0.310485i
\(13\) 9.72258 9.72258i 0.747890 0.747890i −0.226192 0.974083i \(-0.572628\pi\)
0.974083 + 0.226192i \(0.0726277\pi\)
\(14\) 3.13479 9.39005i 0.223913 0.670718i
\(15\) −14.4295 4.09735i −0.961969 0.273157i
\(16\) −4.00000 −0.250000
\(17\) −13.8691 + 13.8691i −0.815828 + 0.815828i −0.985500 0.169673i \(-0.945729\pi\)
0.169673 + 0.985500i \(0.445729\pi\)
\(18\) 6.70213 10.8204i 0.372341 0.601134i
\(19\) 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
\(21\) −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 \(-0.772051\pi\)
0.656465 + 0.754356i \(0.272051\pi\)
\(24\) 0.977191 + 8.42883i 0.0407163 + 0.351201i
\(25\) −17.6562 + 17.6991i −0.706248 + 0.707964i
\(26\) 19.4452 0.747890
\(27\) −24.4382 11.4794i −0.905117 0.425162i
\(28\) 12.5248 6.25527i 0.447316 0.223402i
\(29\) 46.0711 1.58866 0.794329 0.607488i \(-0.207823\pi\)
0.794329 + 0.607488i \(0.207823\pi\)
\(30\) −10.3322 18.5269i −0.344406 0.617563i
\(31\) 1.50946i 0.0486921i 0.999704 + 0.0243461i \(0.00775036\pi\)
−0.999704 + 0.0243461i \(0.992250\pi\)
\(32\) −4.00000 4.00000i −0.125000 0.125000i
\(33\) 0.276093 + 0.218727i 0.00836646 + 0.00662808i
\(34\) −27.7381 −0.815828
\(35\) −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 \(-0.447373\pi\)
0.164580 + 0.986364i \(0.447373\pi\)
\(42\) −16.2409 24.8643i −0.386689 0.592007i
\(43\) 36.8754 + 36.8754i 0.857568 + 0.857568i 0.991051 0.133483i \(-0.0426162\pi\)
−0.133483 + 0.991051i \(0.542616\pi\)
\(44\) −0.234823 −0.00533688
\(45\) −36.5159 + 26.2981i −0.811464 + 0.584403i
\(46\) −4.50300 −0.0978912
\(47\) −29.7803 + 29.7803i −0.633624 + 0.633624i −0.948975 0.315351i \(-0.897878\pi\)
0.315351 + 0.948975i \(0.397878\pi\)
\(48\) −7.45163 + 9.40602i −0.155242 + 0.195959i
\(49\) −29.4358 + 39.1731i −0.600731 + 0.799451i
\(50\) −35.3553 + 0.0428987i −0.707106 + 0.000857974i
\(51\) 6.77637 + 58.4500i 0.132870 + 1.14608i
\(52\) 19.4452 + 19.4452i 0.373945 + 0.373945i
\(53\) 59.8162 59.8162i 1.12861 1.12861i 0.138204 0.990404i \(-0.455867\pi\)
0.990404 0.138204i \(-0.0441329\pi\)
\(54\) −12.9588 35.9175i −0.239978 0.665140i
\(55\) 0.542233 0.224986i 0.00985879 0.00409065i
\(56\) 18.7801 + 6.26957i 0.335359 + 0.111957i
\(57\) 55.3690 69.8910i 0.971387 1.22616i
\(58\) 46.0711 + 46.0711i 0.794329 + 0.794329i
\(59\) 84.9209i 1.43934i −0.694317 0.719669i \(-0.744294\pi\)
0.694317 0.719669i \(-0.255706\pi\)
\(60\) 8.19471 28.8591i 0.136578 0.480985i
\(61\) 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
\(63\) −48.4265 + 40.2973i −0.768675 + 0.639639i
\(64\) 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 \(0.184165\pi\)
−0.837244 + 0.546829i \(0.815835\pi\)
\(72\) 21.6408 + 13.4043i 0.300567 + 0.186170i
\(73\) −41.3259 + 41.3259i −0.566108 + 0.566108i −0.931036 0.364928i \(-0.881094\pi\)
0.364928 + 0.931036i \(0.381094\pi\)
\(74\) 10.6522 0.143949
\(75\) 8.72762 + 74.4905i 0.116368 + 0.993206i
\(76\) 59.4436i 0.782153i
\(77\) 0.735279 0.367220i 0.00954908 0.00476909i
\(78\) 36.2245 45.7254i 0.464417 0.586223i
\(79\) 0.865694i 0.0109582i 0.999985 + 0.00547908i \(0.00174405\pi\)
−0.999985 + 0.00547908i \(0.998256\pi\)
\(80\) 7.66488 + 18.4729i 0.0958110 + 0.230912i
\(81\) −72.5199 + 36.0814i −0.895307 + 0.445450i
\(82\) 13.4956 + 13.4956i 0.164580 + 0.164580i
\(83\) −99.0630 99.0630i −1.19353 1.19353i −0.976069 0.217461i \(-0.930222\pi\)
−0.217461 0.976069i \(-0.569778\pi\)
\(84\) 8.62335 41.1052i 0.102659 0.489348i
\(85\) 90.6268 + 37.4745i 1.06620 + 0.440876i
\(86\) 73.7509i 0.857568i
\(87\) 85.8262 108.336i 0.986508 1.24525i
\(88\) −0.234823 0.234823i −0.00266844 0.00266844i
\(89\) 129.599i 1.45616i 0.685490 + 0.728082i \(0.259588\pi\)
−0.685490 + 0.728082i \(0.740412\pi\)
\(90\) −62.8140 10.2177i −0.697933 0.113530i
\(91\) −91.2955 30.4782i −1.00325 0.334925i
\(92\) −4.50300 4.50300i −0.0489456 0.0489456i
\(93\) 3.54949 + 2.81198i 0.0381666 + 0.0302363i
\(94\) −59.5607 −0.633624
\(95\) −56.9535 137.262i −0.599511 1.44487i
\(96\) −16.8577 + 1.95438i −0.175601 + 0.0203581i
\(97\) 15.7928 + 15.7928i 0.162812 + 0.162812i 0.783811 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 \(-0.477206\pi\)
0.0715470 + 0.997437i \(0.477206\pi\)
\(102\) −51.6736 + 65.2264i −0.506604 + 0.639474i
\(103\) 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
\(105\) 19.4710 + 103.179i 0.185438 + 0.982656i
\(106\) 119.632 1.12861
\(107\) −105.856 105.856i −0.989310 0.989310i 0.0106339 0.999943i \(-0.496615\pi\)
−0.999943 + 0.0106339i \(0.996615\pi\)
\(108\) 22.9587 48.8763i 0.212581 0.452559i
\(109\) 95.4740i 0.875908i 0.898997 + 0.437954i \(0.144297\pi\)
−0.898997 + 0.437954i \(0.855703\pi\)
\(110\) 0.767219 + 0.317247i 0.00697472 + 0.00288407i
\(111\) −2.60231 22.4464i −0.0234443 0.202220i
\(112\) 12.5105 + 25.0497i 0.111701 + 0.223658i
\(113\) 60.1261 60.1261i 0.532089 0.532089i −0.389104 0.921194i \(-0.627215\pi\)
0.921194 + 0.389104i \(0.127215\pi\)
\(114\) 125.260 14.5219i 1.09877 0.127386i
\(115\) 14.7123 + 6.08359i 0.127933 + 0.0529007i
\(116\) 92.1422i 0.794329i
\(117\) −105.202 65.1620i −0.899165 0.556940i
\(118\) 84.9209 84.9209i 0.719669 0.719669i
\(119\) 130.231 + 43.4766i 1.09438 + 0.365350i
\(120\) 37.0538 20.6644i 0.308782 0.172203i
\(121\) 120.986 0.999886
\(122\) −34.8141 + 34.8141i −0.285361 + 0.285361i
\(123\) 25.1410 31.7349i 0.204398 0.258007i
\(124\) −3.01891 −0.0243461
\(125\) 115.572 + 47.6252i 0.924575 + 0.381001i
\(126\) −88.7238 8.12926i −0.704157 0.0645179i
\(127\) 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 \(-0.312162\pi\)
0.556453 + 0.830879i \(0.312162\pi\)
\(132\) −0.437453 + 0.552187i −0.00331404 + 0.00418323i
\(133\) −92.9590 186.131i −0.698940 1.39948i
\(134\) −68.9784 −0.514764
\(135\) −6.18554 + 134.858i −0.0458188 + 0.998950i
\(136\) 55.4763i 0.407914i
\(137\) 37.8019 + 37.8019i 0.275926 + 0.275926i 0.831480 0.555554i \(-0.187494\pi\)
−0.555554 + 0.831480i \(0.687494\pi\)
\(138\) −8.38867 + 10.5888i −0.0607875 + 0.0767305i
\(139\) 65.4496 0.470861 0.235430 0.971891i \(-0.424350\pi\)
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
\(147\) 37.2795 + 142.194i 0.253602 + 0.967309i
\(148\) 10.6522 + 10.6522i 0.0719745 + 0.0719745i
\(149\) 109.296 0.733529 0.366765 0.930314i \(-0.380465\pi\)
0.366765 + 0.930314i \(0.380465\pi\)
\(150\) −65.7628 + 83.2181i −0.438419 + 0.554787i
\(151\) −223.334 −1.47903 −0.739516 0.673139i \(-0.764946\pi\)
−0.739516 + 0.673139i \(0.764946\pi\)
\(152\) −59.4436 + 59.4436i −0.391077 + 0.391077i
\(153\) 150.069 + 92.9524i 0.980844 + 0.607532i
\(154\) 1.10250 + 0.368060i 0.00715908 + 0.00239000i
\(155\) 6.97102 2.89245i 0.0449743 0.0186610i
\(156\) 81.9499 9.50082i 0.525320 0.0609027i
\(157\) 1.67144 + 1.67144i 0.0106461 + 0.0106461i 0.712410 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
\(162\) −108.601 36.4384i −0.670378 0.224929i
\(163\) −34.1872 34.1872i −0.209737 0.209737i 0.594419 0.804156i \(-0.297382\pi\)
−0.804156 + 0.594419i \(0.797382\pi\)
\(164\) 26.9911i 0.164580i
\(165\) 0.481076 1.69419i 0.00291561 0.0102678i
\(166\) 198.126i 1.19353i
\(167\) 122.479 122.479i 0.733409 0.733409i −0.237884 0.971293i \(-0.576454\pi\)
0.971293 + 0.237884i \(0.0764539\pi\)
\(168\) 49.7286 32.4819i 0.296003 0.193344i
\(169\) 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 0.738516 0.674236i \(-0.235527\pi\)
−0.674236 + 0.738516i \(0.735527\pi\)
\(174\) 194.163 22.5101i 1.11588 0.129369i
\(175\) 166.061 + 55.2143i 0.948922 + 0.315510i
\(176\) 0.469645i 0.00266844i
\(177\) −199.692 158.200i −1.12820 0.893785i
\(178\) −129.599 + 129.599i −0.728082 + 0.728082i
\(179\) −167.194 −0.934042 −0.467021 0.884246i \(-0.654673\pi\)
−0.467021 + 0.884246i \(0.654673\pi\)
\(180\) −52.5963 73.0317i −0.292201 0.405732i
\(181\) 271.099i 1.49778i 0.662692 + 0.748892i \(0.269414\pi\)
−0.662692 + 0.748892i \(0.730586\pi\)
\(182\) −60.8173 121.774i −0.334161 0.669086i
\(183\) 81.8655 + 64.8555i 0.447352 + 0.354402i
\(184\) 9.00599i 0.0489456i
\(185\) −34.8032 14.3912i −0.188126 0.0777905i
\(186\) 0.737513 + 6.36147i 0.00396513 + 0.0342015i
\(187\) −1.62839 1.62839i −0.00870795 0.00870795i
\(188\) −59.5607 59.5607i −0.316812 0.316812i
\(189\) 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 \(-0.255481\pi\)
\(192\) −18.8120 14.9033i −0.0979793 0.0776212i
\(193\) −202.411 202.411i −1.04876 1.04876i −0.998749 0.0500128i \(-0.984074\pi\)
−0.0500128 0.998749i \(-0.515926\pi\)
\(194\) 31.5856i 0.162812i
\(195\) −180.129 + 100.455i −0.923739 + 0.515156i
\(196\) −78.3462 58.8716i −0.399726 0.300365i
\(197\) 182.638 + 182.638i 0.927095 + 0.927095i 0.997517 0.0704222i \(-0.0224347\pi\)
−0.0704222 + 0.997517i \(0.522435\pi\)
\(198\) 1.27044 + 0.786906i 0.00641636 + 0.00397427i
\(199\) −246.453 −1.23846 −0.619228 0.785211i \(-0.712554\pi\)
−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
\(207\) 24.3622 + 15.0898i 0.117692 + 0.0728978i
\(208\) −38.8903 + 38.8903i −0.186973 + 0.186973i
\(209\) 3.48968i 0.0166970i
\(210\) −83.7079 + 122.650i −0.398609 + 0.584047i
\(211\) 165.881 0.786165 0.393083 0.919503i \(-0.371409\pi\)
0.393083 + 0.919503i \(0.371409\pi\)
\(212\) 119.632 + 119.632i 0.564304 + 0.564304i
\(213\) 182.594 + 144.654i 0.857248 + 0.679129i
\(214\) 211.712i 0.989310i
\(215\) 99.6380 240.961i 0.463433 1.12075i
\(216\) 71.8351 25.9176i 0.332570 0.119989i
\(217\) 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
\(222\) 19.8441 25.0487i 0.0893879 0.112832i
\(223\) −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
\(225\) 191.423 + 118.246i 0.850771 + 0.525537i
\(226\) 120.252 0.532089
\(227\) −211.845 + 211.845i −0.933238 + 0.933238i −0.997907 0.0646692i \(-0.979401\pi\)
0.0646692 + 0.997907i \(0.479401\pi\)
\(228\) 139.782 + 110.738i 0.613079 + 0.485693i
\(229\) 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
\(231\) 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 \(-0.885054\pi\)
0.353317 + 0.935504i \(0.385054\pi\)
\(234\) −40.0404 170.364i −0.171113 0.728053i
\(235\) 194.598 + 80.4669i 0.828077 + 0.342413i
\(236\) 169.842 0.719669
\(237\) 2.03568 + 1.61271i 0.00858938 + 0.00680468i
\(238\) 86.7548 + 173.708i 0.364516 + 0.729865i
\(239\) −25.1069 −0.105050 −0.0525250 0.998620i \(-0.516727\pi\)
−0.0525250 + 0.998620i \(0.516727\pi\)
\(240\) 57.7182 + 16.3894i 0.240492 + 0.0682892i
\(241\) 278.949i 1.15747i 0.815517 + 0.578733i \(0.196452\pi\)
−0.815517 + 0.578733i \(0.803548\pi\)
\(242\) 120.986 + 120.986i 0.499943 + 0.499943i
\(243\) −50.2522 + 237.747i −0.206799 + 0.978383i
\(244\) −69.6282 −0.285361
\(245\) 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 \(-0.638256\pi\)
−0.420817 + 0.907146i \(0.638256\pi\)
\(252\) −80.5946 96.8531i −0.319820 0.384338i
\(253\) −0.264351 0.264351i −0.00104487 0.00104487i
\(254\) 343.720 1.35323
\(255\) 256.951 143.298i 1.00765 0.561953i
\(256\) 16.0000 0.0625000
\(257\) −330.432 + 330.432i −1.28573 + 1.28573i −0.348371 + 0.937357i \(0.613265\pi\)
−0.937357 + 0.348371i \(0.886735\pi\)
\(258\) 173.425 + 137.391i 0.672192 + 0.532524i
\(259\) −50.0125 16.6962i −0.193098 0.0644642i
\(260\) 52.5411 127.063i 0.202081 0.488706i
\(261\) −94.8670 403.641i −0.363475 1.54652i
\(262\) 145.791 + 145.791i 0.556453 + 0.556453i
\(263\) −74.3401 + 74.3401i −0.282662 + 0.282662i −0.834170 0.551508i \(-0.814053\pi\)
0.551508 + 0.834170i \(0.314053\pi\)
\(264\) −0.989640 + 0.114733i −0.00374864 + 0.000434596i
\(265\) −390.866 161.624i −1.47497 0.609903i
\(266\) 93.1716 279.089i 0.350269 1.04921i
\(267\) 304.751 + 241.430i 1.14139 + 0.904233i
\(268\) −68.9784 68.9784i −0.257382 0.257382i
\(269\) 250.571i 0.931490i 0.884919 + 0.465745i \(0.154214\pi\)
−0.884919 + 0.465745i \(0.845786\pi\)
\(270\) −141.044 + 128.673i −0.522384 + 0.476565i
\(271\) 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
\(273\) −241.745 + 157.904i −0.885512 + 0.578402i
\(274\) 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 \(-0.783626\pi\)
0.777723 0.628607i \(-0.216374\pi\)
\(282\) −110.956 + 140.057i −0.393461 + 0.496656i
\(283\) −181.090 + 181.090i −0.639894 + 0.639894i −0.950529 0.310635i \(-0.899458\pi\)
0.310635 + 0.950529i \(0.399458\pi\)
\(284\) −155.300 −0.546829
\(285\) −428.872 121.781i −1.50481 0.427301i
\(286\) 2.28308i 0.00798280i
\(287\) −42.2092 84.5149i −0.147070 0.294477i
\(288\) −26.8085 + 43.2817i −0.0930852 + 0.150284i
\(289\) 95.7024i 0.331150i
\(290\) 124.485 301.049i 0.429258 1.03810i
\(291\) 66.5574 7.71630i 0.228720 0.0265165i
\(292\) −82.6518 82.6518i −0.283054 0.283054i
\(293\) −72.3843 72.3843i −0.247045 0.247045i 0.572712 0.819757i \(-0.305892\pi\)
−0.819757 + 0.572712i \(0.805892\pi\)
\(294\) −104.915 + 179.474i −0.356853 + 0.610455i
\(295\) −392.185 + 162.727i −1.32944 + 0.551617i
\(296\) 21.3044i 0.0719745i
\(297\) 1.34781 2.86932i 0.00453808 0.00966101i
\(298\) 109.296 + 109.296i 0.366765 + 0.366765i
\(299\) 43.7807i 0.146424i
\(300\) −148.981 + 17.4552i −0.496603 + 0.0581841i
\(301\) 115.597 346.262i 0.384042 1.15037i
\(302\) −223.334 223.334i −0.739516 0.739516i
\(303\) 26.9237 33.9851i 0.0888571 0.112162i
\(304\) −118.887 −0.391077
\(305\) 160.780 66.7115i 0.527147 0.218726i
\(306\) 57.1168 + 243.022i 0.186656 + 0.794188i
\(307\) −228.716 228.716i −0.745005 0.745005i 0.228532 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 \(-0.357513\pi\)
0.432835 + 0.901473i \(0.357513\pi\)
\(312\) 91.4507 + 72.4491i 0.293111 + 0.232209i
\(313\) 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
\(315\) 278.898 + 146.427i 0.885391 + 0.464847i
\(316\) −1.73139 −0.00547908
\(317\) 74.8122 + 74.8122i 0.236001 + 0.236001i 0.815192 0.579191i \(-0.196632\pi\)
−0.579191 + 0.815192i \(0.696632\pi\)
\(318\) 222.864 281.316i 0.700831 0.884642i
\(319\) 5.40927i 0.0169570i
\(320\) −36.9459 + 15.3298i −0.115456 + 0.0479055i
\(321\) −446.121 + 51.7208i −1.38979 + 0.161124i
\(322\) 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
\(327\) 224.507 + 177.859i 0.686567 + 0.543912i
\(328\) −26.9911 + 26.9911i −0.0822900 + 0.0822900i
\(329\) 279.639 + 93.3550i 0.849966 + 0.283754i
\(330\) 2.17527 1.21312i 0.00659172 0.00367611i
\(331\) −506.910 −1.53145 −0.765725 0.643168i \(-0.777620\pi\)
−0.765725 + 0.643168i \(0.777620\pi\)
\(332\) 198.126 198.126i 0.596765 0.596765i
\(333\) −57.6307 35.6963i −0.173065 0.107196i
\(334\) 244.959 0.733409
\(335\) 225.368 + 93.1904i 0.672741 + 0.278180i
\(336\) 82.2104 + 17.2467i 0.244674 + 0.0513294i
\(337\) −187.948 + 187.948i −0.557709 + 0.557709i −0.928655 0.370945i \(-0.879034\pi\)
0.370945 + 0.928655i \(0.379034\pi\)
\(338\) 20.0570 20.0570i 0.0593402 0.0593402i
\(339\) −29.3773 253.396i −0.0866588 0.747481i
\(340\) −74.9489 + 181.254i −0.220438 + 0.533099i
\(341\) −0.177227 −0.000519728
\(342\) 199.200 321.603i 0.582455 0.940358i
\(343\) 337.383 + 61.8203i 0.983624 + 0.180234i
\(344\) −147.502 −0.428784
\(345\) 41.7133 23.2629i 0.120908 0.0674287i
\(346\) 22.2409i 0.0642800i
\(347\) 152.796 + 152.796i 0.440334 + 0.440334i 0.892124 0.451790i \(-0.149214\pi\)
−0.451790 + 0.892124i \(0.649214\pi\)
\(348\) 216.673 + 171.652i 0.622623 + 0.493254i
\(349\) 368.362 1.05548 0.527740 0.849406i \(-0.323040\pi\)
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 0.269695 0.962946i \(-0.413077\pi\)
−0.962946 + 0.269695i \(0.913077\pi\)
\(354\) −41.4920 357.892i −0.117209 1.01099i
\(355\) 358.605 148.794i 1.01015 0.419138i
\(356\) −259.197 −0.728082
\(357\) 344.844 225.247i 0.965951 0.630943i
\(358\) −167.194 167.194i −0.467021 0.467021i
\(359\) −599.498 −1.66991 −0.834956 0.550317i \(-0.814507\pi\)
−0.834956 + 0.550317i \(0.814507\pi\)
\(360\) 20.4355 125.628i 0.0567652 0.348967i
\(361\) 522.387 1.44705
\(362\) −271.099 + 271.099i −0.748892 + 0.748892i
\(363\) 225.386 284.500i 0.620899 0.783745i
\(364\) 60.9564 182.591i 0.167463 0.501624i
\(365\) 270.042 + 111.663i 0.739842 + 0.305927i
\(366\) 17.0100 + 146.721i 0.0464755 + 0.400877i
\(367\) −38.8678 38.8678i −0.105907 0.105907i 0.652168 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
\(372\) −5.62396 + 7.09898i −0.0151182 + 0.0190833i
\(373\) 228.366 + 228.366i 0.612241 + 0.612241i 0.943529 0.331289i \(-0.107483\pi\)
−0.331289 + 0.943529i \(0.607483\pi\)
\(374\) 3.25677i 0.00870795i
\(375\) 327.290 183.046i 0.872775 0.488123i
\(376\) 119.121i 0.316812i
\(377\) 447.930 447.930i 1.18814 1.18814i
\(378\) −184.400 + 193.490i −0.487832 + 0.511879i
\(379\) 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 0.980828 0.194875i \(-0.0624303\pi\)
−0.194875 + 0.980828i \(0.562430\pi\)
\(384\) −3.90876 33.7153i −0.0101791 0.0878003i
\(385\) −3.10486 2.69202i −0.00806458 0.00699226i
\(386\) 404.822i 1.04876i
\(387\) 247.144 399.008i 0.638615 1.03103i
\(388\) −31.5856 + 31.5856i −0.0814062 + 0.0814062i
\(389\) −369.112 −0.948875 −0.474438 0.880289i \(-0.657349\pi\)
−0.474438 + 0.880289i \(0.657349\pi\)
\(390\) −280.585 79.6737i −0.719448 0.204291i
\(391\) 62.4524i 0.159725i
\(392\) −19.4746 137.218i −0.0496801 0.350046i
\(393\) 271.595 342.828i 0.691081 0.872335i
\(394\) 365.275i 0.927095i
\(395\) 3.99798 1.65886i 0.0101215 0.00419965i
\(396\) 0.483534 + 2.05735i 0.00122104 + 0.00519532i
\(397\) −13.0242 13.0242i −0.0328066 0.0328066i 0.690513 0.723320i \(-0.257385\pi\)
−0.723320 + 0.690513i \(0.757385\pi\)
\(398\) −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 \(-0.00679466\pi\)
\(402\) −128.500 + 162.203i −0.319653 + 0.403490i
\(403\) 14.6758 + 14.6758i 0.0364164 + 0.0364164i
\(404\) 28.9050i 0.0715470i
\(405\) 305.597 + 265.774i 0.754559 + 0.656232i
\(406\) 144.423 432.610i 0.355722 1.06554i
\(407\) 0.625346 + 0.625346i 0.00153648 + 0.00153648i
\(408\) −130.453 103.347i −0.319737 0.253302i
\(409\) 186.052 0.454895 0.227447 0.973790i \(-0.426962\pi\)
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
\(417\) 121.927 153.905i 0.292390 0.369077i
\(418\) −3.48968 + 3.48968i −0.00834852 + 0.00834852i
\(419\) 606.909i 1.44847i 0.689553 + 0.724235i \(0.257807\pi\)
−0.689553 + 0.724235i \(0.742193\pi\)
\(420\) −206.358 + 38.9419i −0.491328 + 0.0927189i
\(421\) −642.340 −1.52575 −0.762874 0.646547i \(-0.776212\pi\)
−0.762874 + 0.646547i \(0.776212\pi\)
\(422\) 165.881 + 165.881i 0.393083 + 0.393083i
\(423\) 322.236 + 199.592i 0.761786 + 0.471848i
\(424\) 239.265i 0.564304i
\(425\) −0.594965 490.345i −0.00139992 1.15375i
\(426\) 37.9393 + 327.248i 0.0890595 + 0.768188i
\(427\) 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 \(-0.822700\pi\)
0.848843 0.528645i \(-0.177300\pi\)
\(432\) 97.7527 + 45.9175i 0.226279 + 0.106290i
\(433\) 201.636 201.636i 0.465672 0.465672i −0.434837 0.900509i \(-0.643194\pi\)
0.900509 + 0.434837i \(0.143194\pi\)
\(434\) 14.1739 + 4.73182i 0.0326587 + 0.0109028i
\(435\) −664.785 188.770i −1.52824 0.433953i
\(436\) −190.948 −0.437954
\(437\) −66.9186 + 66.9186i −0.153132 + 0.153132i
\(438\) −153.973 + 194.356i −0.351536 + 0.443735i
\(439\) 94.0452 0.214226 0.107113 0.994247i \(-0.465839\pi\)
0.107113 + 0.994247i \(0.465839\pi\)
\(440\) −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 \(-0.814060\pi\)
0.551489 + 0.834182i \(0.314060\pi\)
\(444\) 44.8929 5.20463i 0.101110 0.0117221i
\(445\) 598.517 248.339i 1.34498 0.558066i
\(446\) −89.7899 −0.201323
\(447\) 203.608 257.010i 0.455499 0.574966i
\(448\) −50.0994 + 25.0211i −0.111829 + 0.0558506i
\(449\) 324.260 0.722184 0.361092 0.932530i \(-0.382404\pi\)
0.361092 + 0.932530i \(0.382404\pi\)
\(450\) 73.1775 + 309.669i 0.162617 + 0.688154i
\(451\) 1.58453i 0.00351337i
\(452\) 120.252 + 120.252i 0.266045 + 0.266045i
\(453\) −416.050 + 525.170i −0.918434 + 1.15932i
\(454\) −423.690 −0.933238
\(455\) 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 \(-0.324052\pi\)
0.525037 + 0.851080i \(0.324052\pi\)
\(462\) 2.91935 1.90687i 0.00631894 0.00412742i
\(463\) 239.772 + 239.772i 0.517866 + 0.517866i 0.916925 0.399059i \(-0.130663\pi\)
−0.399059 + 0.916925i \(0.630663\pi\)
\(464\) −184.284 −0.397165
\(465\) 6.18477 21.7808i 0.0133006 0.0468403i
\(466\) −271.299 −0.582186
\(467\) −302.621 + 302.621i −0.648011 + 0.648011i −0.952512 0.304501i \(-0.901510\pi\)
0.304501 + 0.952512i \(0.401510\pi\)
\(468\) 130.324 210.405i 0.278470 0.449583i
\(469\) 323.855 + 108.116i 0.690523 + 0.230525i
\(470\) 114.131 + 275.065i 0.242832 + 0.585245i
\(471\) 7.04413 0.816658i 0.0149557 0.00173388i
\(472\) 169.842 + 169.842i 0.359835 + 0.359835i
\(473\) −4.32959 + 4.32959i −0.00915348 + 0.00915348i
\(474\) 0.422974 + 3.64839i 0.000892351 + 0.00769703i
\(475\) −524.775 + 526.050i −1.10479 + 1.10747i
\(476\) −86.9532 + 260.463i −0.182675 + 0.547191i
\(477\) −647.236 400.896i −1.35689 0.840453i
\(478\) −25.1069 25.1069i −0.0525250 0.0525250i
\(479\) 444.701i 0.928395i 0.885732 + 0.464198i \(0.153657\pi\)
−0.885732 + 0.464198i \(0.846343\pi\)
\(480\) 41.3288 + 74.1076i 0.0861016 + 0.154391i
\(481\) 103.567i 0.215316i
\(482\) −278.949 + 278.949i −0.578733 + 0.578733i
\(483\) 55.9819 36.5664i 0.115904 0.0757069i
\(484\) 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 \(0.0276457\pi\)
−0.996231 + 0.0867425i \(0.972354\pi\)
\(492\) 63.4697 + 50.2820i 0.129004 + 0.102199i
\(493\) −638.963 + 638.963i −1.29607 + 1.29607i
\(494\) 577.945 1.16993
\(495\) −3.08770 4.28738i −0.00623778 0.00866137i
\(496\) 6.03782i 0.0121730i
\(497\) 486.275 242.860i 0.978421 0.488652i
\(498\) −465.894 369.091i −0.935530 0.741146i
\(499\) 352.315i 0.706043i −0.935615 0.353021i \(-0.885154\pi\)
0.935615 0.353021i \(-0.114846\pi\)
\(500\) −95.2503 + 231.144i −0.190501 + 0.462287i
\(501\) −59.8429 516.178i −0.119447 1.03030i
\(502\) −211.250 211.250i −0.420817 0.420817i
\(503\) −109.956 109.956i −0.218600 0.218600i 0.589308 0.807908i \(-0.299400\pi\)
−0.807908 + 0.589308i \(0.799400\pi\)
\(504\) 16.2585 177.448i 0.0322590 0.352079i
\(505\) −27.6942 66.7451i −0.0548399 0.132168i
\(506\) 0.528703i 0.00104487i
\(507\) −47.1641 37.3643i −0.0930257 0.0736969i
\(508\) 343.720 + 343.720i 0.676615 + 0.676615i
\(509\) 930.732i 1.82855i −0.405094 0.914275i \(-0.632761\pi\)
0.405094 0.914275i \(-0.367239\pi\)
\(510\) 400.249 + 113.653i 0.784802 + 0.222849i
\(511\) 388.053 + 129.548i 0.759398 + 0.253518i
\(512\) 16.0000 + 16.0000i 0.0312500 + 0.0312500i
\(513\) −726.347 341.188i −1.41588 0.665083i
\(514\) −660.864 −1.28573
\(515\) −204.982 84.7606i −0.398023 0.164584i
\(516\) 36.0343 + 310.817i 0.0698340 + 0.602358i
\(517\) −3.49655 3.49655i −0.00676315 0.00676315i
\(518\) −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 \(-0.506807\pi\)
−0.0213821 + 0.999771i \(0.506807\pi\)
\(522\) 308.774 498.508i 0.591522 0.954997i
\(523\) 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
\(525\) 439.194 287.635i 0.836560 0.547876i
\(526\) −148.680 −0.282662
\(527\) −20.9348 20.9348i −0.0397244 0.0397244i
\(528\) −1.10437 0.874907i −0.00209162 0.00165702i
\(529\) 518.862i 0.980835i
\(530\) −229.242 552.491i −0.432532 1.04244i
\(531\) −744.016 + 174.864i −1.40116 + 0.329311i
\(532\) 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
\(537\) −311.466 + 393.156i −0.580012 + 0.732134i
\(538\) −250.571 + 250.571i −0.465745 + 0.465745i
\(539\) −4.59937 3.45610i −0.00853315 0.00641206i
\(540\) −269.716 12.3711i −0.499475 0.0229094i
\(541\) 693.609 1.28209 0.641044 0.767504i \(-0.278502\pi\)
0.641044 + 0.767504i \(0.278502\pi\)
\(542\) −207.488 + 207.488i −0.382819 + 0.382819i
\(543\) 637.490 + 505.032i 1.17401 + 0.930078i
\(544\) 110.953 0.203957
\(545\) 440.921 182.949i 0.809030 0.335686i
\(546\) −399.648 83.8411i −0.731957 0.153555i
\(547\) −529.859 + 529.859i −0.968664 + 0.968664i −0.999524 0.0308595i \(-0.990176\pi\)
0.0308595 + 0.999524i \(0.490176\pi\)
\(548\) −75.6039 + 75.6039i −0.137963 + 0.137963i
\(549\) 305.016 71.6872i 0.555585 0.130578i
\(550\) −0.00503679 4.15112i −9.15781e−6 0.00754748i
\(551\) 1369.32 2.48515
\(552\) −21.1776 16.7773i −0.0383653 0.0303937i
\(553\) 5.42134 2.70757i 0.00980351 0.00489616i
\(554\) −129.447 −0.233658
\(555\) −98.6763 + 55.0304i −0.177795 + 0.0991538i
\(556\) 130.899i 0.235430i
\(557\) −242.020 242.020i −0.434506 0.434506i 0.455652 0.890158i \(-0.349406\pi\)
−0.890158 + 0.455652i \(0.849406\pi\)
\(558\) 16.3329 + 10.1166i 0.0292705 + 0.0181301i
\(559\) 717.048 1.28273
\(560\) 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 0.689223 0.724549i \(-0.257952\pi\)
−0.724549 + 0.689223i \(0.757952\pi\)
\(564\) −251.013 + 29.1011i −0.445059 + 0.0515976i
\(565\) −392.891 162.462i −0.695383 0.287543i
\(566\) −362.180 −0.639894
\(567\) 452.773 + 341.300i 0.798541 + 0.601941i
\(568\) −155.300 155.300i −0.273415 0.273415i
\(569\) −147.022 −0.258387 −0.129194 0.991619i \(-0.541239\pi\)
−0.129194 + 0.991619i \(0.541239\pi\)
\(570\) −307.091 550.653i −0.538757 0.966058i
\(571\) 831.318 1.45590 0.727949 0.685631i \(-0.240474\pi\)
0.727949 + 0.685631i \(0.240474\pi\)
\(572\) −2.28308 + 2.28308i −0.00399140 + 0.00399140i
\(573\) −646.018 511.789i −1.12743 0.893174i
\(574\) 42.3057 126.724i 0.0737033 0.220774i
\(575\) −0.0965863 79.6024i −0.000167976 0.138439i
\(576\) −70.0902 + 16.4731i −0.121684 + 0.0285992i
\(577\) −331.614 331.614i −0.574721 0.574721i 0.358723 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
\(582\) 74.2737 + 58.8411i 0.127618 + 0.101102i
\(583\) 7.02310 + 7.02310i 0.0120465 + 0.0120465i
\(584\) 165.304i 0.283054i
\(585\) −99.3427 + 610.714i −0.169816 + 1.04396i
\(586\) 144.769i 0.247045i
\(587\) −216.371 + 216.371i −0.368605 + 0.368605i −0.866968 0.498363i \(-0.833935\pi\)
0.498363 + 0.866968i \(0.333935\pi\)
\(588\) −284.389 + 74.5590i −0.483654 + 0.126801i
\(589\) 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 0.929508 0.368802i \(-0.120232\pi\)
−0.368802 + 0.929508i \(0.620232\pi\)
\(594\) 4.21713 1.52151i 0.00709954 0.00256147i
\(595\) −48.7667 684.750i −0.0819608 1.15084i
\(596\) 218.592i 0.366765i
\(597\) −459.119 + 579.534i −0.769043 + 0.970744i
\(598\) −43.7807 + 43.7807i −0.0732119 + 0.0732119i
\(599\) 735.946 1.22862 0.614312 0.789063i \(-0.289433\pi\)
0.614312 + 0.789063i \(0.289433\pi\)
\(600\) −166.436 131.526i −0.277394 0.219209i
\(601\) 851.749i 1.41722i 0.705600 + 0.708610i \(0.250677\pi\)
−0.705600 + 0.708610i \(0.749323\pi\)
\(602\) 461.859 230.666i 0.767207 0.383166i
\(603\) 373.188 + 231.151i 0.618885 + 0.383335i
\(604\) 446.668i 0.739516i
\(605\) −231.836 558.743i −0.383200 0.923542i
\(606\) 60.9088 7.06143i 0.100510 0.0116525i
\(607\) −468.483 468.483i −0.771801 0.771801i 0.206621 0.978421i \(-0.433753\pi\)
−0.978421 + 0.206621i \(0.933753\pi\)
\(608\) −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
\(612\) −185.905 + 300.138i −0.303766 + 0.490422i
\(613\) −653.475 653.475i −1.06603 1.06603i −0.997660 0.0683679i \(-0.978221\pi\)
−0.0683679 0.997660i \(-0.521779\pi\)
\(614\) 457.433i 0.745005i
\(615\) −194.735 55.2961i −0.316642 0.0899123i
\(616\) −0.736119 + 2.20500i −0.00119500 + 0.00357954i
\(617\) 238.684 + 238.684i 0.386845 + 0.386845i 0.873561 0.486715i \(-0.161805\pi\)
−0.486715 + 0.873561i \(0.661805\pi\)
\(618\) 116.877 147.531i 0.189121 0.238723i
\(619\) 400.073 0.646322 0.323161 0.946344i \(-0.395254\pi\)
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
\(627\) 8.20600 + 6.50095i 0.0130877 + 0.0103683i
\(628\) −3.34288 + 3.34288i −0.00532305 + 0.00532305i
\(629\) 147.736i 0.234875i
\(630\) 132.471 + 425.325i 0.210272 + 0.675119i
\(631\) −343.679 −0.544658 −0.272329 0.962204i \(-0.587794\pi\)
−0.272329 + 0.962204i \(0.587794\pi\)
\(632\) −1.73139 1.73139i −0.00273954 0.00273954i
\(633\) 309.021 390.069i 0.488185 0.616223i
\(634\) 149.624i 0.236001i
\(635\) −1123.01 464.369i −1.76852 0.731290i
\(636\) 504.180 58.4519i 0.792736 0.0919055i
\(637\) 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 \(0.275548\pi\)
−0.648137 + 0.761524i \(0.724452\pi\)
\(642\) −497.842 394.401i −0.775455 0.614331i
\(643\) 155.167 155.167i 0.241317 0.241317i −0.576078 0.817395i \(-0.695417\pi\)
0.817395 + 0.576078i \(0.195417\pi\)
\(644\) −14.1159 + 42.2834i −0.0219192 + 0.0656574i
\(645\) −381.004 683.187i −0.590704 1.05920i
\(646\) −824.428 −1.27620
\(647\) −122.968 + 122.968i −0.190059 + 0.190059i −0.795722 0.605663i \(-0.792908\pi\)
0.605663 + 0.795722i \(0.292908\pi\)
\(648\) 72.8768 217.203i 0.112464 0.335189i
\(649\) 9.97068 0.0153631
\(650\) −343.328 + 344.162i −0.528196 + 0.529480i
\(651\) 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 \(-0.514870\pi\)
0.998909 + 0.0466996i \(0.0148703\pi\)
\(654\) 46.6482 + 402.367i 0.0713275 + 0.615240i
\(655\) −279.367 673.296i −0.426515 1.02793i
\(656\) −53.9822 −0.0822900
\(657\) 447.164 + 276.972i 0.680614 + 0.421570i
\(658\) 186.284 + 372.994i 0.283106 + 0.566860i
\(659\) −307.522 −0.466650 −0.233325 0.972399i \(-0.574961\pi\)
−0.233325 + 0.972399i \(0.574961\pi\)
\(660\) 3.38838 + 0.962152i 0.00513392 + 0.00145781i
\(661\) 621.533i 0.940292i −0.882589 0.470146i \(-0.844201\pi\)
0.882589 0.470146i \(-0.155799\pi\)
\(662\) −506.910 506.910i −0.765725 0.765725i
\(663\) 634.168 + 502.401i 0.956513 + 0.757769i
\(664\) 396.252 0.596765
\(665\) −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
\(672\) 64.9637 + 99.4571i 0.0966722 + 0.148002i
\(673\) −571.899 571.899i −0.849776 0.849776i 0.140329 0.990105i \(-0.455184\pi\)
−0.990105 + 0.140329i \(0.955184\pi\)
\(674\) −375.896 −0.557709
\(675\) 634.660 229.852i 0.940237 0.340521i
\(676\) 40.1139 0.0593402
\(677\) −679.334 + 679.334i −1.00345 + 1.00345i −0.00345318 + 0.999994i \(0.501099\pi\)
−0.999994 + 0.00345318i \(0.998901\pi\)
\(678\) 224.019 282.773i 0.330411 0.417070i
\(679\) 49.5071 148.295i 0.0729118 0.218403i
\(680\) −256.203 + 106.305i −0.376769 + 0.156331i
\(681\) 103.506 + 892.802i 0.151992 + 1.31102i
\(682\) −0.177227 0.177227i −0.000259864 0.000259864i
\(683\) 807.265 807.265i 1.18194 1.18194i 0.202700 0.979241i \(-0.435028\pi\)
0.979241 0.202700i \(-0.0649715\pi\)
\(684\) 520.802 122.403i 0.761407 0.178952i
\(685\) 102.141 247.015i 0.149112 0.360606i
\(686\) 275.563 + 399.203i 0.401695 + 0.581929i
\(687\) 19.0815 24.0862i 0.0277752 0.0350599i
\(688\) −147.502 147.502i −0.214392 0.214392i
\(689\) 1163.14i 1.68815i
\(690\) 64.9762 + 18.4504i 0.0941684 + 0.0267397i
\(691\) 287.198i 0.415626i −0.978169 0.207813i \(-0.933365\pi\)
0.978169 0.207813i \(-0.0666346\pi\)
\(692\) −22.2409 + 22.2409i −0.0321400 + 0.0321400i
\(693\) −4.73136 5.68583i −0.00682736 0.00820465i
\(694\) 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 \(-0.809063\pi\)
0.825422 0.564516i \(-0.190937\pi\)
\(702\) −475.204 223.218i −0.676929 0.317974i
\(703\) 158.302 158.302i 0.225180 0.225180i
\(704\) 0.939291 0.00133422
\(705\) 551.737 307.696i 0.782606 0.436448i
\(706\) 489.435i 0.693251i
\(707\) −45.2021 90.5076i −0.0639351 0.128016i
\(708\) 316.400 399.384i 0.446893 0.564102i
\(709\) 56.1623i 0.0792133i 0.999215 + 0.0396067i \(0.0126105\pi\)
−0.999215 + 0.0396067i \(0.987390\pi\)
\(710\) 507.399 + 209.811i 0.714646 + 0.295508i
\(711\) 7.58459 1.78259i 0.0106675 0.00250716i
\(712\) −259.197 259.197i −0.364041 0.364041i
\(713\) −3.39854 3.39854i −0.00476653 0.00476653i
\(714\) 570.091 + 119.598i 0.798447 + 0.167504i
\(715\) 3.08446 7.45935i 0.00431393 0.0104327i
\(716\) 334.387i 0.467021i
\(717\) −46.7719 + 59.0391i −0.0652328 + 0.0823418i
\(718\) −599.498 599.498i −0.834956 0.834956i
\(719\) 364.303i 0.506680i −0.967377 0.253340i \(-0.918471\pi\)
0.967377 0.253340i \(-0.0815291\pi\)
\(720\) 146.063 105.193i 0.202866 0.146101i
\(721\) −294.560 98.3364i −0.408544 0.136389i
\(722\) 522.387 + 522.387i 0.723527 + 0.723527i
\(723\) 655.950 + 519.657i 0.907261 + 0.718751i
\(724\) −542.198 −0.748892
\(725\) −813.441 + 815.417i −1.12199 + 1.12471i
\(726\) 509.886 59.1133i 0.702322 0.0814233i
\(727\) −188.513 188.513i −0.259303 0.259303i 0.565468 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
\(732\) −129.711 + 163.731i −0.177201 + 0.223676i
\(733\) 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
\(735\) 585.251 444.641i 0.796260 0.604954i
\(736\) 18.0120 0.0244728
\(737\) −4.04942 4.04942i −0.00549447 0.00549447i
\(738\) 90.4490 146.028i 0.122560 0.197869i
\(739\) 757.965i 1.02566i −0.858489 0.512832i \(-0.828596\pi\)
0.858489 0.512832i \(-0.171404\pi\)
\(740\) 28.7825 69.6065i 0.0388952 0.0940628i
\(741\) −141.191 1217.85i −0.190541 1.64352i
\(742\) −374.166 749.188i −0.504267 1.00969i
\(743\) −781.133 + 781.133i −1.05132 + 1.05132i −0.0527138 + 0.998610i \(0.516787\pi\)
−0.998610 + 0.0527138i \(0.983213\pi\)
\(744\) −12.7229 + 1.47503i −0.0171007 + 0.00198256i
\(745\) −209.435 504.754i −0.281121 0.677522i
\(746\) 456.732i 0.612241i
\(747\) −663.933 + 1071.90i −0.888800 + 1.43494i
\(748\) 3.25677 3.25677i 0.00435398 0.00435398i
\(749\) −331.836 + 993.995i −0.443039 + 1.32710i
\(750\) 510.337 + 144.244i 0.680449 + 0.192326i
\(751\) −483.342 −0.643598 −0.321799 0.946808i \(-0.604287\pi\)
−0.321799 + 0.946808i \(0.604287\pi\)
\(752\) 119.121 119.121i 0.158406 0.158406i
\(753\) −393.539 + 496.755i −0.522629 + 0.659701i
\(754\) 895.859 1.18814
\(755\) 427.957 + 1031.41i 0.566830 + 1.36610i
\(756\) −377.891 + 9.09000i −0.499855 + 0.0120238i
\(757\) 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 \(-0.432842\pi\)
0.209420 + 0.977826i \(0.432842\pi\)
\(762\) 640.320 808.260i 0.840314 1.06071i
\(763\) 597.898 298.608i 0.783615 0.391360i
\(764\) 549.451 0.719177
\(765\) 141.710 871.172i 0.185242 1.13879i
\(766\) 602.040i 0.785953i
\(767\) −825.650 825.650i −1.07647 1.07647i