Properties

Label 210.3.o.b.61.8
Level 210
Weight 3
Character 210.61
Analytic conductor 5.722
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.o (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{8}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 61.8
Root \(-0.141814 + 0.245629i\) of \(x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + 4836403 x^{8} - 6808704 x^{7} + 64376800 x^{6} - 91953512 x^{5} + 595763862 x^{4} - 630430976 x^{3} + 1087013404 x^{2} + 294123256 x + 101626561\)
Character \(\chi\) \(=\) 210.61
Dual form 210.3.o.b.31.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(4.24494 + 5.56601i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.707107 - 1.22474i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(1.93649 + 1.11803i) q^{5} +2.44949i q^{6} +(4.24494 + 5.56601i) q^{7} -2.82843 q^{8} +(1.50000 - 2.59808i) q^{9} +(2.73861 - 1.58114i) q^{10} +(5.42967 + 9.40447i) q^{11} +(3.00000 + 1.73205i) q^{12} -0.772061i q^{13} +(9.81857 - 1.26320i) q^{14} -3.87298 q^{15} +(-2.00000 + 3.46410i) q^{16} +(16.7760 - 9.68565i) q^{17} +(-2.12132 - 3.67423i) q^{18} +(22.5766 + 13.0346i) q^{19} -4.47214i q^{20} +(-11.1877 - 4.67280i) q^{21} +15.3574 q^{22} +(6.84734 - 11.8599i) q^{23} +(4.24264 - 2.44949i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-0.945577 - 0.545929i) q^{26} +5.19615i q^{27} +(5.39568 - 12.9185i) q^{28} -6.99131 q^{29} +(-2.73861 + 4.74342i) q^{30} +(22.7559 - 13.1381i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-16.2890 - 9.40447i) q^{33} -27.3952i q^{34} +(1.99729 + 15.5245i) q^{35} -6.00000 q^{36} +(-32.3004 + 55.9459i) q^{37} +(31.9281 - 18.4337i) q^{38} +(0.668624 + 1.15809i) q^{39} +(-5.47723 - 3.16228i) q^{40} +5.54839i q^{41} +(-13.6339 + 10.3979i) q^{42} -68.9320 q^{43} +(10.8593 - 18.8089i) q^{44} +(5.80948 - 3.35410i) q^{45} +(-9.68361 - 16.7725i) q^{46} +(-19.5817 - 11.3055i) q^{47} -6.92820i q^{48} +(-12.9610 + 47.2548i) q^{49} +7.07107 q^{50} +(-16.7760 + 29.0570i) q^{51} +(-1.33725 + 0.772061i) q^{52} +(-37.2820 - 64.5742i) q^{53} +(6.36396 + 3.67423i) q^{54} +24.2822i q^{55} +(-12.0065 - 15.7431i) q^{56} -45.1532 q^{57} +(-4.94360 + 8.56257i) q^{58} +(96.6595 - 55.8064i) q^{59} +(3.87298 + 6.70820i) q^{60} +(-46.9572 - 27.1108i) q^{61} -37.1603i q^{62} +(20.8283 - 2.67965i) q^{63} +8.00000 q^{64} +(0.863190 - 1.49509i) q^{65} +(-23.0362 + 13.2999i) q^{66} +(22.1273 + 38.3255i) q^{67} +(-33.5521 - 19.3713i) q^{68} +23.7199i q^{69} +(20.4259 + 8.53132i) q^{70} +31.9550 q^{71} +(-4.24264 + 7.34847i) q^{72} +(-92.6322 + 53.4812i) q^{73} +(45.6797 + 79.1195i) q^{74} +(-7.50000 - 4.33013i) q^{75} -52.1384i q^{76} +(-29.2968 + 70.1430i) q^{77} +1.89115 q^{78} +(-14.8408 + 25.7050i) q^{79} +(-7.74597 + 4.47214i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(6.79536 + 3.92330i) q^{82} -15.8151i q^{83} +(3.09419 + 24.0505i) q^{84} +43.3156 q^{85} +(-48.7423 + 84.4242i) q^{86} +(10.4870 - 6.05465i) q^{87} +(-15.3574 - 26.5999i) q^{88} +(-31.8358 - 18.3804i) q^{89} -9.48683i q^{90} +(4.29730 - 3.27735i) q^{91} -27.3894 q^{92} +(-22.7559 + 39.4144i) q^{93} +(-27.6926 + 15.9884i) q^{94} +(29.1463 + 50.4828i) q^{95} +(-8.48528 - 4.89898i) q^{96} -134.212i q^{97} +(48.7102 + 49.2881i) q^{98} +32.5780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} + O(q^{10}) \) \( 16q - 24q^{3} - 16q^{4} + 4q^{7} + 24q^{9} - 4q^{11} + 48q^{12} + 8q^{14} - 32q^{16} + 12q^{17} - 72q^{19} - 24q^{21} - 48q^{22} - 12q^{23} + 40q^{25} + 32q^{28} + 72q^{29} + 120q^{31} + 12q^{33} - 20q^{35} - 96q^{36} + 44q^{37} - 72q^{38} + 36q^{39} - 24q^{42} - 56q^{43} - 8q^{44} + 8q^{46} - 24q^{47} - 40q^{49} - 12q^{51} - 72q^{52} + 32q^{53} + 16q^{56} + 144q^{57} - 88q^{58} + 132q^{59} + 96q^{61} + 60q^{63} + 128q^{64} + 20q^{65} + 72q^{66} - 164q^{67} - 24q^{68} - 136q^{71} - 348q^{73} - 112q^{74} - 120q^{75} + 96q^{77} + 280q^{79} - 72q^{81} + 264q^{82} - 24q^{84} + 120q^{85} - 88q^{86} - 108q^{87} + 48q^{88} - 300q^{89} - 272q^{91} + 48q^{92} - 120q^{93} + 200q^{95} + 384q^{98} - 24q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 1.22474i 0.353553 0.612372i
\(3\) −1.50000 + 0.866025i −0.500000 + 0.288675i
\(4\) −1.00000 1.73205i −0.250000 0.433013i
\(5\) 1.93649 + 1.11803i 0.387298 + 0.223607i
\(6\) 2.44949i 0.408248i
\(7\) 4.24494 + 5.56601i 0.606420 + 0.795145i
\(8\) −2.82843 −0.353553
\(9\) 1.50000 2.59808i 0.166667 0.288675i
\(10\) 2.73861 1.58114i 0.273861 0.158114i
\(11\) 5.42967 + 9.40447i 0.493607 + 0.854952i 0.999973 0.00736658i \(-0.00234488\pi\)
−0.506366 + 0.862319i \(0.669012\pi\)
\(12\) 3.00000 + 1.73205i 0.250000 + 0.144338i
\(13\) 0.772061i 0.0593893i −0.999559 0.0296946i \(-0.990547\pi\)
0.999559 0.0296946i \(-0.00945349\pi\)
\(14\) 9.81857 1.26320i 0.701326 0.0902284i
\(15\) −3.87298 −0.258199
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 16.7760 9.68565i 0.986826 0.569744i 0.0825021 0.996591i \(-0.473709\pi\)
0.904324 + 0.426847i \(0.140376\pi\)
\(18\) −2.12132 3.67423i −0.117851 0.204124i
\(19\) 22.5766 + 13.0346i 1.18824 + 0.686032i 0.957907 0.287079i \(-0.0926844\pi\)
0.230335 + 0.973111i \(0.426018\pi\)
\(20\) 4.47214i 0.223607i
\(21\) −11.1877 4.67280i −0.532748 0.222514i
\(22\) 15.3574 0.698065
\(23\) 6.84734 11.8599i 0.297711 0.515650i −0.677901 0.735153i \(-0.737110\pi\)
0.975612 + 0.219503i \(0.0704436\pi\)
\(24\) 4.24264 2.44949i 0.176777 0.102062i
\(25\) 2.50000 + 4.33013i 0.100000 + 0.173205i
\(26\) −0.945577 0.545929i −0.0363684 0.0209973i
\(27\) 5.19615i 0.192450i
\(28\) 5.39568 12.9185i 0.192703 0.461374i
\(29\) −6.99131 −0.241080 −0.120540 0.992708i \(-0.538463\pi\)
−0.120540 + 0.992708i \(0.538463\pi\)
\(30\) −2.73861 + 4.74342i −0.0912871 + 0.158114i
\(31\) 22.7559 13.1381i 0.734062 0.423811i −0.0858441 0.996309i \(-0.527359\pi\)
0.819906 + 0.572497i \(0.194025\pi\)
\(32\) 2.82843 + 4.89898i 0.0883883 + 0.153093i
\(33\) −16.2890 9.40447i −0.493607 0.284984i
\(34\) 27.3952i 0.805740i
\(35\) 1.99729 + 15.5245i 0.0570655 + 0.443558i
\(36\) −6.00000 −0.166667
\(37\) −32.3004 + 55.9459i −0.872984 + 1.51205i −0.0140890 + 0.999901i \(0.504485\pi\)
−0.858895 + 0.512152i \(0.828849\pi\)
\(38\) 31.9281 18.4337i 0.840214 0.485098i
\(39\) 0.668624 + 1.15809i 0.0171442 + 0.0296946i
\(40\) −5.47723 3.16228i −0.136931 0.0790569i
\(41\) 5.54839i 0.135327i 0.997708 + 0.0676633i \(0.0215544\pi\)
−0.997708 + 0.0676633i \(0.978446\pi\)
\(42\) −13.6339 + 10.3979i −0.324617 + 0.247570i
\(43\) −68.9320 −1.60307 −0.801535 0.597948i \(-0.795983\pi\)
−0.801535 + 0.597948i \(0.795983\pi\)
\(44\) 10.8593 18.8089i 0.246803 0.427476i
\(45\) 5.80948 3.35410i 0.129099 0.0745356i
\(46\) −9.68361 16.7725i −0.210513 0.364620i
\(47\) −19.5817 11.3055i −0.416631 0.240542i 0.277004 0.960869i \(-0.410658\pi\)
−0.693635 + 0.720327i \(0.743992\pi\)
\(48\) 6.92820i 0.144338i
\(49\) −12.9610 + 47.2548i −0.264511 + 0.964383i
\(50\) 7.07107 0.141421
\(51\) −16.7760 + 29.0570i −0.328942 + 0.569744i
\(52\) −1.33725 + 0.772061i −0.0257163 + 0.0148473i
\(53\) −37.2820 64.5742i −0.703433 1.21838i −0.967254 0.253810i \(-0.918316\pi\)
0.263821 0.964572i \(-0.415017\pi\)
\(54\) 6.36396 + 3.67423i 0.117851 + 0.0680414i
\(55\) 24.2822i 0.441495i
\(56\) −12.0065 15.7431i −0.214402 0.281126i
\(57\) −45.1532 −0.792161
\(58\) −4.94360 + 8.56257i −0.0852345 + 0.147631i
\(59\) 96.6595 55.8064i 1.63830 0.945871i 0.656878 0.753997i \(-0.271877\pi\)
0.981420 0.191874i \(-0.0614566\pi\)
\(60\) 3.87298 + 6.70820i 0.0645497 + 0.111803i
\(61\) −46.9572 27.1108i −0.769790 0.444439i 0.0630096 0.998013i \(-0.479930\pi\)
−0.832800 + 0.553574i \(0.813263\pi\)
\(62\) 37.1603i 0.599359i
\(63\) 20.8283 2.67965i 0.330608 0.0425341i
\(64\) 8.00000 0.125000
\(65\) 0.863190 1.49509i 0.0132798 0.0230014i
\(66\) −23.0362 + 13.2999i −0.349033 + 0.201514i
\(67\) 22.1273 + 38.3255i 0.330258 + 0.572023i 0.982562 0.185934i \(-0.0595310\pi\)
−0.652305 + 0.757957i \(0.726198\pi\)
\(68\) −33.5521 19.3713i −0.493413 0.284872i
\(69\) 23.7199i 0.343767i
\(70\) 20.4259 + 8.53132i 0.291798 + 0.121876i
\(71\) 31.9550 0.450071 0.225035 0.974351i \(-0.427750\pi\)
0.225035 + 0.974351i \(0.427750\pi\)
\(72\) −4.24264 + 7.34847i −0.0589256 + 0.102062i
\(73\) −92.6322 + 53.4812i −1.26893 + 0.732619i −0.974786 0.223141i \(-0.928369\pi\)
−0.294147 + 0.955760i \(0.595036\pi\)
\(74\) 45.6797 + 79.1195i 0.617293 + 1.06918i
\(75\) −7.50000 4.33013i −0.100000 0.0577350i
\(76\) 52.1384i 0.686032i
\(77\) −29.2968 + 70.1430i −0.380478 + 0.910949i
\(78\) 1.89115 0.0242456
\(79\) −14.8408 + 25.7050i −0.187858 + 0.325380i −0.944536 0.328408i \(-0.893488\pi\)
0.756678 + 0.653788i \(0.226821\pi\)
\(80\) −7.74597 + 4.47214i −0.0968246 + 0.0559017i
\(81\) −4.50000 7.79423i −0.0555556 0.0962250i
\(82\) 6.79536 + 3.92330i 0.0828702 + 0.0478451i
\(83\) 15.8151i 0.190543i −0.995451 0.0952717i \(-0.969628\pi\)
0.995451 0.0952717i \(-0.0303720\pi\)
\(84\) 3.09419 + 24.0505i 0.0368356 + 0.286315i
\(85\) 43.3156 0.509595
\(86\) −48.7423 + 84.4242i −0.566771 + 0.981676i
\(87\) 10.4870 6.05465i 0.120540 0.0695937i
\(88\) −15.3574 26.5999i −0.174516 0.302271i
\(89\) −31.8358 18.3804i −0.357706 0.206521i 0.310368 0.950616i \(-0.399548\pi\)
−0.668074 + 0.744095i \(0.732881\pi\)
\(90\) 9.48683i 0.105409i
\(91\) 4.29730 3.27735i 0.0472231 0.0360148i
\(92\) −27.3894 −0.297711
\(93\) −22.7559 + 39.4144i −0.244687 + 0.423811i
\(94\) −27.6926 + 15.9884i −0.294603 + 0.170089i
\(95\) 29.1463 + 50.4828i 0.306803 + 0.531398i
\(96\) −8.48528 4.89898i −0.0883883 0.0510310i
\(97\) 134.212i 1.38363i −0.722077 0.691813i \(-0.756812\pi\)
0.722077 0.691813i \(-0.243188\pi\)
\(98\) 48.7102 + 49.2881i 0.497043 + 0.502940i
\(99\) 32.5780 0.329071
\(100\) 5.00000 8.66025i 0.0500000 0.0866025i
\(101\) 132.760 76.6490i 1.31445 0.758901i 0.331624 0.943412i \(-0.392404\pi\)
0.982830 + 0.184511i \(0.0590702\pi\)
\(102\) 23.7249 + 41.0927i 0.232597 + 0.402870i
\(103\) −54.8504 31.6679i −0.532529 0.307456i 0.209517 0.977805i \(-0.432811\pi\)
−0.742046 + 0.670349i \(0.766144\pi\)
\(104\) 2.18372i 0.0209973i
\(105\) −16.4406 21.5571i −0.156577 0.205306i
\(106\) −105.449 −0.994805
\(107\) 21.9277 37.9800i 0.204932 0.354953i −0.745179 0.666865i \(-0.767636\pi\)
0.950111 + 0.311912i \(0.100969\pi\)
\(108\) 9.00000 5.19615i 0.0833333 0.0481125i
\(109\) −2.64166 4.57549i −0.0242354 0.0419770i 0.853653 0.520842i \(-0.174382\pi\)
−0.877889 + 0.478865i \(0.841048\pi\)
\(110\) 29.7396 + 17.1701i 0.270360 + 0.156092i
\(111\) 111.892i 1.00804i
\(112\) −27.7711 + 3.57286i −0.247956 + 0.0319006i
\(113\) −106.725 −0.944469 −0.472234 0.881473i \(-0.656552\pi\)
−0.472234 + 0.881473i \(0.656552\pi\)
\(114\) −31.9281 + 55.3011i −0.280071 + 0.485098i
\(115\) 26.5196 15.3111i 0.230606 0.133140i
\(116\) 6.99131 + 12.1093i 0.0602699 + 0.104391i
\(117\) −2.00587 1.15809i −0.0171442 0.00989821i
\(118\) 157.844i 1.33766i
\(119\) 125.124 + 52.2607i 1.05146 + 0.439166i
\(120\) 10.9545 0.0912871
\(121\) 1.53727 2.66262i 0.0127047 0.0220051i
\(122\) −66.4075 + 38.3404i −0.544324 + 0.314266i
\(123\) −4.80504 8.32258i −0.0390654 0.0676633i
\(124\) −45.5119 26.2763i −0.367031 0.211906i
\(125\) 11.1803i 0.0894427i
\(126\) 11.4460 27.4042i 0.0908410 0.217494i
\(127\) 203.641 1.60348 0.801738 0.597676i \(-0.203909\pi\)
0.801738 + 0.597676i \(0.203909\pi\)
\(128\) 5.65685 9.79796i 0.0441942 0.0765466i
\(129\) 103.398 59.6969i 0.801535 0.462767i
\(130\) −1.22073 2.11437i −0.00939027 0.0162644i
\(131\) −67.2791 38.8436i −0.513581 0.296516i 0.220724 0.975336i \(-0.429158\pi\)
−0.734304 + 0.678820i \(0.762491\pi\)
\(132\) 37.6179i 0.284984i
\(133\) 23.2854 + 180.993i 0.175078 + 1.36085i
\(134\) 62.5853 0.467055
\(135\) −5.80948 + 10.0623i −0.0430331 + 0.0745356i
\(136\) −47.4498 + 27.3952i −0.348896 + 0.201435i
\(137\) −114.504 198.326i −0.835794 1.44764i −0.893382 0.449297i \(-0.851674\pi\)
0.0575883 0.998340i \(-0.481659\pi\)
\(138\) 29.0508 + 16.7725i 0.210513 + 0.121540i
\(139\) 61.7421i 0.444188i 0.975025 + 0.222094i \(0.0712892\pi\)
−0.975025 + 0.222094i \(0.928711\pi\)
\(140\) 24.8920 18.9839i 0.177800 0.135600i
\(141\) 39.1633 0.277754
\(142\) 22.5956 39.1368i 0.159124 0.275611i
\(143\) 7.26082 4.19204i 0.0507750 0.0293149i
\(144\) 6.00000 + 10.3923i 0.0416667 + 0.0721688i
\(145\) −13.5386 7.81652i −0.0933697 0.0539070i
\(146\) 151.268i 1.03608i
\(147\) −21.4823 82.1067i −0.146138 0.558549i
\(148\) 129.202 0.872984
\(149\) 14.6523 25.3785i 0.0983373 0.170325i −0.812659 0.582739i \(-0.801981\pi\)
0.910997 + 0.412414i \(0.135314\pi\)
\(150\) −10.6066 + 6.12372i −0.0707107 + 0.0408248i
\(151\) −81.8479 141.765i −0.542039 0.938839i −0.998787 0.0492431i \(-0.984319\pi\)
0.456748 0.889596i \(-0.349014\pi\)
\(152\) −63.8563 36.8674i −0.420107 0.242549i
\(153\) 58.1139i 0.379830i
\(154\) 65.1914 + 85.4797i 0.423320 + 0.555063i
\(155\) 58.7556 0.379068
\(156\) 1.33725 2.31618i 0.00857210 0.0148473i
\(157\) 180.741 104.351i 1.15122 0.664657i 0.202035 0.979378i \(-0.435245\pi\)
0.949184 + 0.314722i \(0.101911\pi\)
\(158\) 20.9880 + 36.3524i 0.132836 + 0.230078i
\(159\) 111.846 + 64.5742i 0.703433 + 0.406127i
\(160\) 12.6491i 0.0790569i
\(161\) 95.0792 12.2323i 0.590554 0.0759771i
\(162\) −12.7279 −0.0785674
\(163\) −69.5841 + 120.523i −0.426896 + 0.739406i −0.996595 0.0824475i \(-0.973726\pi\)
0.569699 + 0.821853i \(0.307060\pi\)
\(164\) 9.61009 5.54839i 0.0585981 0.0338316i
\(165\) −21.0290 36.4234i −0.127449 0.220748i
\(166\) −19.3695 11.1830i −0.116683 0.0673672i
\(167\) 54.4023i 0.325762i −0.986646 0.162881i \(-0.947921\pi\)
0.986646 0.162881i \(-0.0520787\pi\)
\(168\) 31.6436 + 13.2167i 0.188355 + 0.0786707i
\(169\) 168.404 0.996473
\(170\) 30.6287 53.0505i 0.180169 0.312062i
\(171\) 67.7298 39.1038i 0.396081 0.228677i
\(172\) 68.9320 + 119.394i 0.400768 + 0.694150i
\(173\) 54.3723 + 31.3918i 0.314291 + 0.181456i 0.648845 0.760921i \(-0.275252\pi\)
−0.334554 + 0.942376i \(0.608586\pi\)
\(174\) 17.1251i 0.0984203i
\(175\) −13.4892 + 32.2961i −0.0770812 + 0.184549i
\(176\) −43.4374 −0.246803
\(177\) −96.6595 + 167.419i −0.546099 + 0.945871i
\(178\) −45.0226 + 25.9938i −0.252936 + 0.146033i
\(179\) 70.3978 + 121.933i 0.393284 + 0.681187i 0.992880 0.119115i \(-0.0380057\pi\)
−0.599597 + 0.800302i \(0.704672\pi\)
\(180\) −11.6190 6.70820i −0.0645497 0.0372678i
\(181\) 222.987i 1.23197i 0.787757 + 0.615986i \(0.211242\pi\)
−0.787757 + 0.615986i \(0.788758\pi\)
\(182\) −0.975265 7.58053i −0.00535860 0.0416513i
\(183\) 93.9144 0.513193
\(184\) −19.3672 + 33.5450i −0.105257 + 0.182310i
\(185\) −125.099 + 72.2259i −0.676210 + 0.390410i
\(186\) 32.1817 + 55.7404i 0.173020 + 0.299680i
\(187\) 182.177 + 105.180i 0.974208 + 0.562459i
\(188\) 45.2219i 0.240542i
\(189\) −28.9219 + 22.0573i −0.153026 + 0.116705i
\(190\) 82.4381 0.433885
\(191\) −66.5069 + 115.193i −0.348204 + 0.603106i −0.985930 0.167156i \(-0.946542\pi\)
0.637727 + 0.770263i \(0.279875\pi\)
\(192\) −12.0000 + 6.92820i −0.0625000 + 0.0360844i
\(193\) −142.611 247.010i −0.738919 1.27984i −0.952983 0.303025i \(-0.902003\pi\)
0.214064 0.976820i \(-0.431330\pi\)
\(194\) −164.375 94.9020i −0.847295 0.489186i
\(195\) 2.99018i 0.0153342i
\(196\) 94.8087 24.8056i 0.483718 0.126559i
\(197\) −307.784 −1.56236 −0.781178 0.624309i \(-0.785381\pi\)
−0.781178 + 0.624309i \(0.785381\pi\)
\(198\) 23.0362 39.8998i 0.116344 0.201514i
\(199\) −8.39167 + 4.84493i −0.0421692 + 0.0243464i −0.520936 0.853595i \(-0.674417\pi\)
0.478767 + 0.877942i \(0.341084\pi\)
\(200\) −7.07107 12.2474i −0.0353553 0.0612372i
\(201\) −66.3818 38.3255i −0.330258 0.190674i
\(202\) 216.796i 1.07325i
\(203\) −29.6777 38.9137i −0.146195 0.191693i
\(204\) 67.1042 0.328942
\(205\) −6.20329 + 10.7444i −0.0302599 + 0.0524117i
\(206\) −77.5702 + 44.7852i −0.376555 + 0.217404i
\(207\) −20.5420 35.5798i −0.0992369 0.171883i
\(208\) 2.67450 + 1.54412i 0.0128582 + 0.00742366i
\(209\) 283.095i 1.35452i
\(210\) −38.0272 + 4.89234i −0.181082 + 0.0232969i
\(211\) 175.954 0.833903 0.416952 0.908929i \(-0.363098\pi\)
0.416952 + 0.908929i \(0.363098\pi\)
\(212\) −74.5639 + 129.148i −0.351717 + 0.609191i
\(213\) −47.9326 + 27.6739i −0.225035 + 0.129924i
\(214\) −31.0105 53.7118i −0.144909 0.250990i
\(215\) −133.486 77.0684i −0.620867 0.358457i
\(216\) 14.6969i 0.0680414i
\(217\) 169.725 + 70.8893i 0.782141 + 0.326679i
\(218\) −7.47174 −0.0342740
\(219\) 92.6322 160.444i 0.422978 0.732619i
\(220\) 42.0581 24.2822i 0.191173 0.110374i
\(221\) −7.47791 12.9521i −0.0338367 0.0586069i
\(222\) −137.039 79.1195i −0.617293 0.356394i
\(223\) 50.0854i 0.224598i −0.993674 0.112299i \(-0.964178\pi\)
0.993674 0.112299i \(-0.0358215\pi\)
\(224\) −15.2613 + 36.5389i −0.0681308 + 0.163120i
\(225\) 15.0000 0.0666667
\(226\) −75.4659 + 130.711i −0.333920 + 0.578366i
\(227\) 264.301 152.594i 1.16432 0.672221i 0.211985 0.977273i \(-0.432007\pi\)
0.952336 + 0.305052i \(0.0986740\pi\)
\(228\) 45.1532 + 78.2076i 0.198040 + 0.343016i
\(229\) −353.428 204.052i −1.54335 0.891055i −0.998624 0.0524421i \(-0.983299\pi\)
−0.544728 0.838613i \(-0.683367\pi\)
\(230\) 43.3064i 0.188289i
\(231\) −16.8004 130.586i −0.0727292 0.565309i
\(232\) 19.7744 0.0852345
\(233\) −108.404 + 187.762i −0.465255 + 0.805846i −0.999213 0.0396654i \(-0.987371\pi\)
0.533958 + 0.845511i \(0.320704\pi\)
\(234\) −2.83673 + 1.63779i −0.0121228 + 0.00699909i
\(235\) −25.2798 43.7859i −0.107574 0.186323i
\(236\) −193.319 111.613i −0.819149 0.472936i
\(237\) 51.4100i 0.216920i
\(238\) 152.482 116.291i 0.640680 0.488617i
\(239\) −389.739 −1.63071 −0.815354 0.578963i \(-0.803457\pi\)
−0.815354 + 0.578963i \(0.803457\pi\)
\(240\) 7.74597 13.4164i 0.0322749 0.0559017i
\(241\) 60.0686 34.6806i 0.249247 0.143903i −0.370172 0.928963i \(-0.620701\pi\)
0.619419 + 0.785060i \(0.287368\pi\)
\(242\) −2.17402 3.76552i −0.00898356 0.0155600i
\(243\) 13.5000 + 7.79423i 0.0555556 + 0.0320750i
\(244\) 108.443i 0.444439i
\(245\) −77.9313 + 77.0176i −0.318087 + 0.314357i
\(246\) −13.5907 −0.0552468
\(247\) 10.0635 17.4305i 0.0407429 0.0705688i
\(248\) −64.3635 + 37.1603i −0.259530 + 0.149840i
\(249\) 13.6963 + 23.7226i 0.0550051 + 0.0952717i
\(250\) 13.6931 + 7.90569i 0.0547723 + 0.0316228i
\(251\) 256.631i 1.02244i 0.859451 + 0.511218i \(0.170805\pi\)
−0.859451 + 0.511218i \(0.829195\pi\)
\(252\) −25.4696 33.3961i −0.101070 0.132524i
\(253\) 148.715 0.587808
\(254\) 143.996 249.409i 0.566914 0.981924i
\(255\) −64.9733 + 37.5124i −0.254797 + 0.147107i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) −173.998 100.458i −0.677034 0.390886i 0.121703 0.992567i \(-0.461165\pi\)
−0.798737 + 0.601681i \(0.794498\pi\)
\(258\) 168.848i 0.654451i
\(259\) −448.509 + 57.7025i −1.73170 + 0.222789i
\(260\) −3.45276 −0.0132798
\(261\) −10.4870 + 18.1640i −0.0401799 + 0.0695937i
\(262\) −95.1470 + 54.9331i −0.363156 + 0.209668i
\(263\) −251.495 435.602i −0.956256 1.65628i −0.731469 0.681875i \(-0.761165\pi\)
−0.224787 0.974408i \(-0.572169\pi\)
\(264\) 46.0723 + 26.5999i 0.174516 + 0.100757i
\(265\) 166.730i 0.629170i
\(266\) 238.135 + 99.4625i 0.895245 + 0.373919i
\(267\) 63.6716 0.238470
\(268\) 44.2545 76.6511i 0.165129 0.286012i
\(269\) −121.754 + 70.2945i −0.452616 + 0.261318i −0.708934 0.705275i \(-0.750824\pi\)
0.256318 + 0.966592i \(0.417490\pi\)
\(270\) 8.21584 + 14.2302i 0.0304290 + 0.0527046i
\(271\) 103.808 + 59.9334i 0.383054 + 0.221157i 0.679146 0.734003i \(-0.262350\pi\)
−0.296092 + 0.955159i \(0.595684\pi\)
\(272\) 77.4852i 0.284872i
\(273\) −3.60768 + 8.63759i −0.0132150 + 0.0316395i
\(274\) −323.866 −1.18199
\(275\) −27.1484 + 47.0224i −0.0987214 + 0.170990i
\(276\) 41.0841 23.7199i 0.148855 0.0859416i
\(277\) 53.5034 + 92.6706i 0.193153 + 0.334551i 0.946293 0.323309i \(-0.104795\pi\)
−0.753140 + 0.657860i \(0.771462\pi\)
\(278\) 75.6183 + 43.6583i 0.272008 + 0.157044i
\(279\) 78.8289i 0.282541i
\(280\) −5.64919 43.9100i −0.0201757 0.156821i
\(281\) −85.5187 −0.304337 −0.152169 0.988355i \(-0.548626\pi\)
−0.152169 + 0.988355i \(0.548626\pi\)
\(282\) 27.6926 47.9651i 0.0982008 0.170089i
\(283\) −339.501 + 196.011i −1.19965 + 0.692619i −0.960477 0.278358i \(-0.910210\pi\)
−0.239173 + 0.970977i \(0.576876\pi\)
\(284\) −31.9550 55.3477i −0.112518 0.194886i
\(285\) −87.4388 50.4828i −0.306803 0.177133i
\(286\) 11.8569i 0.0414576i
\(287\) −30.8824 + 23.5526i −0.107604 + 0.0820646i
\(288\) 16.9706 0.0589256
\(289\) 43.1238 74.6926i 0.149217 0.258452i
\(290\) −19.1465 + 11.0542i −0.0660224 + 0.0381180i
\(291\) 116.231 + 201.318i 0.399419 + 0.691813i
\(292\) 185.264 + 106.962i 0.634467 + 0.366310i
\(293\) 500.595i 1.70851i 0.519850 + 0.854257i \(0.325988\pi\)
−0.519850 + 0.854257i \(0.674012\pi\)
\(294\) −115.750 31.7479i −0.393708 0.107986i
\(295\) 249.574 0.846013
\(296\) 91.3593 158.239i 0.308646 0.534591i
\(297\) −48.8671 + 28.2134i −0.164536 + 0.0949947i
\(298\) −20.7214 35.8906i −0.0695350 0.120438i
\(299\) −9.15660 5.28656i −0.0306241 0.0176808i
\(300\) 17.3205i 0.0577350i
\(301\) −292.612 383.677i −0.972133 1.27467i
\(302\) −231.501 −0.766559
\(303\) −132.760 + 229.947i −0.438151 + 0.758901i
\(304\) −90.3064 + 52.1384i −0.297061 + 0.171508i
\(305\) −60.6215 104.999i −0.198759 0.344261i
\(306\) −71.1747 41.0927i −0.232597 0.134290i
\(307\) 398.171i 1.29698i 0.761225 + 0.648488i \(0.224598\pi\)
−0.761225 + 0.648488i \(0.775402\pi\)
\(308\) 150.788 19.3995i 0.489572 0.0629853i
\(309\) 109.701 0.355019
\(310\) 41.5465 71.9606i 0.134021 0.232131i
\(311\) 322.107 185.968i 1.03571 0.597969i 0.117097 0.993120i \(-0.462641\pi\)
0.918616 + 0.395151i \(0.129308\pi\)
\(312\) −1.89115 3.27558i −0.00606139 0.0104986i
\(313\) 365.884 + 211.243i 1.16896 + 0.674899i 0.953435 0.301600i \(-0.0975207\pi\)
0.215524 + 0.976499i \(0.430854\pi\)
\(314\) 295.149i 0.939966i
\(315\) 43.3298 + 18.0977i 0.137555 + 0.0574529i
\(316\) 59.3632 0.187858
\(317\) −108.091 + 187.219i −0.340981 + 0.590597i −0.984615 0.174737i \(-0.944093\pi\)
0.643634 + 0.765333i \(0.277426\pi\)
\(318\) 158.174 91.3218i 0.497402 0.287175i
\(319\) −37.9605 65.7496i −0.118999 0.206112i
\(320\) 15.4919 + 8.94427i 0.0484123 + 0.0279508i
\(321\) 75.9599i 0.236635i
\(322\) 52.2497 125.097i 0.162266 0.388501i
\(323\) 504.995 1.56345
\(324\) −9.00000 + 15.5885i −0.0277778 + 0.0481125i
\(325\) 3.34312 1.93015i 0.0102865 0.00593893i
\(326\) 98.4067 + 170.445i 0.301861 + 0.522839i
\(327\) 7.92498 + 4.57549i 0.0242354 + 0.0139923i
\(328\) 15.6932i 0.0478451i
\(329\) −20.1965 156.983i −0.0613874 0.477151i
\(330\) −59.4791 −0.180240
\(331\) −105.730 + 183.130i −0.319426 + 0.553262i −0.980368 0.197175i \(-0.936823\pi\)
0.660942 + 0.750437i \(0.270157\pi\)
\(332\) −27.3926 + 15.8151i −0.0825077 + 0.0476358i
\(333\) 96.9012 + 167.838i 0.290995 + 0.504018i
\(334\) −66.6289 38.4682i −0.199488 0.115174i
\(335\) 98.9561i 0.295391i
\(336\) 38.5625 29.4098i 0.114769 0.0875291i
\(337\) 260.379 0.772639 0.386319 0.922365i \(-0.373746\pi\)
0.386319 + 0.922365i \(0.373746\pi\)
\(338\) 119.080 206.252i 0.352306 0.610213i
\(339\) 160.087 92.4265i 0.472234 0.272645i
\(340\) −43.3156 75.0247i −0.127399 0.220661i
\(341\) 247.115 + 142.672i 0.724676 + 0.418392i
\(342\) 110.602i 0.323399i
\(343\) −318.039 + 128.452i −0.927228 + 0.374496i
\(344\) 194.969 0.566771
\(345\) −26.5196 + 45.9334i −0.0768685 + 0.133140i
\(346\) 76.8940 44.3948i 0.222237 0.128309i
\(347\) 255.968 + 443.350i 0.737661 + 1.27767i 0.953546 + 0.301247i \(0.0974030\pi\)
−0.215885 + 0.976419i \(0.569264\pi\)
\(348\) −20.9739 12.1093i −0.0602699 0.0347968i
\(349\) 527.872i 1.51253i −0.654266 0.756264i \(-0.727022\pi\)
0.654266 0.756264i \(-0.272978\pi\)
\(350\) 30.0162 + 39.3577i 0.0857607 + 0.112450i
\(351\) 4.01174 0.0114295
\(352\) −30.7149 + 53.1997i −0.0872582 + 0.151136i
\(353\) 118.226 68.2579i 0.334918 0.193365i −0.323104 0.946363i \(-0.604726\pi\)
0.658023 + 0.752998i \(0.271393\pi\)
\(354\) 136.697 + 236.767i 0.386150 + 0.668832i
\(355\) 61.8807 + 35.7268i 0.174312 + 0.100639i
\(356\) 73.5216i 0.206521i
\(357\) −232.945 + 29.9693i −0.652506 + 0.0839475i
\(358\) 199.115 0.556187
\(359\) 278.525 482.419i 0.775835 1.34379i −0.158490 0.987361i \(-0.550662\pi\)
0.934324 0.356424i \(-0.116004\pi\)
\(360\) −16.4317 + 9.48683i −0.0456435 + 0.0263523i
\(361\) 159.302 + 275.919i 0.441279 + 0.764318i
\(362\) 273.102 + 157.676i 0.754426 + 0.435568i
\(363\) 5.32525i 0.0146701i
\(364\) −9.97383 4.16579i −0.0274006 0.0114445i
\(365\) −239.175 −0.655274
\(366\) 66.4075 115.021i 0.181441 0.314266i
\(367\) 102.210 59.0110i 0.278502 0.160793i −0.354243 0.935153i \(-0.615262\pi\)
0.632745 + 0.774360i \(0.281928\pi\)
\(368\) 27.3894 + 47.4398i 0.0744276 + 0.128912i
\(369\) 14.4151 + 8.32258i 0.0390654 + 0.0225544i
\(370\) 204.286i 0.552124i
\(371\) 201.162 481.625i 0.542215 1.29818i
\(372\) 91.0237 0.244687
\(373\) 159.186 275.718i 0.426772 0.739191i −0.569812 0.821775i \(-0.692984\pi\)
0.996584 + 0.0825840i \(0.0263173\pi\)
\(374\) 257.637 148.747i 0.688869 0.397719i
\(375\) −9.68246 16.7705i −0.0258199 0.0447214i
\(376\) 55.3853 + 31.9767i 0.147301 + 0.0850444i
\(377\) 5.39771i 0.0143175i
\(378\) 6.56377 + 51.0188i 0.0173645 + 0.134970i
\(379\) −579.699 −1.52955 −0.764774 0.644299i \(-0.777149\pi\)
−0.764774 + 0.644299i \(0.777149\pi\)
\(380\) 58.2925 100.966i 0.153401 0.265699i
\(381\) −305.462 + 176.359i −0.801738 + 0.462883i
\(382\) 94.0549 + 162.908i 0.246217 + 0.426461i
\(383\) 526.581 + 304.022i 1.37488 + 0.793790i 0.991538 0.129815i \(-0.0414383\pi\)
0.383346 + 0.923605i \(0.374772\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −135.155 + 103.077i −0.351053 + 0.267731i
\(386\) −403.366 −1.04499
\(387\) −103.398 + 179.091i −0.267178 + 0.462767i
\(388\) −232.462 + 134.212i −0.599128 + 0.345907i
\(389\) −57.5081 99.6069i −0.147836 0.256059i 0.782592 0.622535i \(-0.213897\pi\)
−0.930427 + 0.366476i \(0.880564\pi\)
\(390\) 3.66220 + 2.11437i 0.00939027 + 0.00542147i
\(391\) 265.284i 0.678476i
\(392\) 36.6593 133.657i 0.0935187 0.340961i
\(393\) 134.558 0.342387
\(394\) −217.636 + 376.957i −0.552376 + 0.956744i
\(395\) −57.4781 + 33.1850i −0.145514 + 0.0840127i
\(396\) −32.5780 56.4268i −0.0822678 0.142492i
\(397\) −139.249 80.3952i −0.350752 0.202507i 0.314264 0.949336i \(-0.398242\pi\)
−0.665016 + 0.746829i \(0.731575\pi\)
\(398\) 13.7035i 0.0344310i
\(399\) −191.672 251.323i −0.480382 0.629883i
\(400\) −20.0000 −0.0500000
\(401\) 29.4028 50.9272i 0.0733238 0.127000i −0.827032 0.562154i \(-0.809973\pi\)
0.900356 + 0.435154i \(0.143306\pi\)
\(402\) −93.8780 + 54.2005i −0.233527 + 0.134827i
\(403\) −10.1434 17.5690i −0.0251698 0.0435954i
\(404\) −265.520 153.298i −0.657227 0.379450i
\(405\) 20.1246i 0.0496904i
\(406\) −68.6447 + 8.83141i −0.169076 + 0.0217522i
\(407\) −701.523 −1.72364
\(408\) 47.4498 82.1855i 0.116299 0.201435i
\(409\) 182.052 105.108i 0.445114 0.256987i −0.260650 0.965433i \(-0.583937\pi\)
0.705765 + 0.708446i \(0.250604\pi\)
\(410\) 8.77277 + 15.1949i 0.0213970 + 0.0370607i
\(411\) 343.511 + 198.326i 0.835794 + 0.482546i
\(412\) 126.672i 0.307456i
\(413\) 720.933 + 301.114i 1.74560 + 0.729089i
\(414\) −58.1016 −0.140342
\(415\) 17.6818 30.6258i 0.0426068 0.0737971i
\(416\) 3.78231 2.18372i 0.00909209 0.00524932i
\(417\) −53.4702 92.6132i −0.128226 0.222094i
\(418\) 346.719 + 200.178i 0.829471 + 0.478895i
\(419\) 690.319i 1.64754i 0.566924 + 0.823770i \(0.308133\pi\)
−0.566924 + 0.823770i \(0.691867\pi\)
\(420\) −20.8974 + 50.0330i −0.0497557 + 0.119126i
\(421\) 407.084 0.966945 0.483472 0.875360i \(-0.339375\pi\)
0.483472 + 0.875360i \(0.339375\pi\)
\(422\) 124.418 215.498i 0.294829 0.510659i
\(423\) −58.7450 + 33.9164i −0.138877 + 0.0801807i
\(424\) 105.449 + 182.644i 0.248701 + 0.430763i
\(425\) 83.8802 + 48.4283i 0.197365 + 0.113949i
\(426\) 78.2735i 0.183741i
\(427\) −48.4315 376.448i −0.113423 0.881611i
\(428\) −87.7110 −0.204932
\(429\) −7.26082 + 12.5761i −0.0169250 + 0.0293149i
\(430\) −188.778 + 108.991i −0.439019 + 0.253468i
\(431\) 28.0096 + 48.5141i 0.0649875 + 0.112562i 0.896688 0.442662i \(-0.145966\pi\)
−0.831701 + 0.555224i \(0.812633\pi\)
\(432\) −18.0000 10.3923i −0.0416667 0.0240563i
\(433\) 71.4593i 0.165033i −0.996590 0.0825165i \(-0.973704\pi\)
0.996590 0.0825165i \(-0.0262957\pi\)
\(434\) 206.835 157.743i 0.476578 0.363463i
\(435\) 27.0772 0.0622465
\(436\) −5.28332 + 9.15098i −0.0121177 + 0.0209885i
\(437\) 309.179 178.505i 0.707504 0.408478i
\(438\) −131.002 226.902i −0.299091 0.518040i
\(439\) −691.975 399.512i −1.57625 0.910050i −0.995376 0.0960592i \(-0.969376\pi\)
−0.580878 0.813991i \(-0.697290\pi\)
\(440\) 68.6806i 0.156092i
\(441\) 103.330 + 104.556i 0.234308 + 0.237088i
\(442\) −21.1507 −0.0478523
\(443\) 406.200 703.559i 0.916930 1.58817i 0.112879 0.993609i \(-0.463993\pi\)
0.804051 0.594561i \(-0.202674\pi\)
\(444\) −193.802 + 111.892i −0.436492 + 0.252009i
\(445\) −41.0998 71.1870i −0.0923592 0.159971i
\(446\) −61.3419 35.4157i −0.137538 0.0794075i
\(447\) 50.7569i 0.113550i
\(448\) 33.9595 + 44.5281i 0.0758024 + 0.0993931i
\(449\) 434.785 0.968340 0.484170 0.874974i \(-0.339122\pi\)
0.484170 + 0.874974i \(0.339122\pi\)
\(450\) 10.6066 18.3712i 0.0235702 0.0408248i
\(451\) −52.1797 + 30.1259i −0.115698 + 0.0667981i
\(452\) 106.725 + 184.853i 0.236117 + 0.408967i
\(453\) 245.544 + 141.765i 0.542039 + 0.312946i
\(454\) 431.601i 0.950663i
\(455\) 11.9859 1.54203i 0.0263426 0.00338908i
\(456\) 127.713 0.280071
\(457\) 372.524 645.231i 0.815151 1.41188i −0.0940682 0.995566i \(-0.529987\pi\)
0.909219 0.416317i \(-0.136680\pi\)
\(458\) −499.822 + 288.572i −1.09131 + 0.630071i
\(459\) 50.3281 + 87.1709i 0.109647 + 0.189915i
\(460\) −53.0393 30.6223i −0.115303 0.0665701i
\(461\) 516.757i 1.12095i −0.828172 0.560474i \(-0.810619\pi\)
0.828172 0.560474i \(-0.189381\pi\)
\(462\) −171.815 71.7622i −0.371893 0.155329i
\(463\) −538.823 −1.16376 −0.581882 0.813273i \(-0.697684\pi\)
−0.581882 + 0.813273i \(0.697684\pi\)
\(464\) 13.9826 24.2186i 0.0301350 0.0521953i
\(465\) −88.1334 + 50.8838i −0.189534 + 0.109428i
\(466\) 153.307 + 265.536i 0.328985 + 0.569819i
\(467\) 549.839 + 317.450i 1.17739 + 0.679764i 0.955408 0.295288i \(-0.0954157\pi\)
0.221977 + 0.975052i \(0.428749\pi\)
\(468\) 4.63236i 0.00989821i
\(469\) −119.392 + 285.850i −0.254566 + 0.609489i
\(470\) −71.5021 −0.152132
\(471\) −180.741 + 313.053i −0.383740 + 0.664657i
\(472\) −273.394 + 157.844i −0.579226 + 0.334416i
\(473\) −374.279 648.269i −0.791286 1.37055i
\(474\) −62.9641 36.3524i −0.132836 0.0766928i
\(475\) 130.346i 0.274413i
\(476\) −34.6055 268.981i −0.0727007 0.565087i
\(477\) −223.692 −0.468955
\(478\) −275.587 + 477.331i −0.576542 + 0.998600i
\(479\) −427.580 + 246.863i −0.892650 + 0.515372i −0.874809 0.484469i \(-0.839013\pi\)
−0.0178420 + 0.999841i \(0.505680\pi\)
\(480\) −10.9545 18.9737i −0.0228218 0.0395285i
\(481\) 43.1937 + 24.9379i 0.0897997 + 0.0518459i
\(482\) 98.0915i 0.203509i
\(483\) −132.025 + 100.689i −0.273344 + 0.208467i
\(484\) −6.14906 −0.0127047
\(485\) 150.053 259.900i 0.309388 0.535876i
\(486\) 19.0919 11.0227i 0.0392837 0.0226805i
\(487\) 165.873 + 287.301i 0.340603 + 0.589941i 0.984545 0.175133i \(-0.0560356\pi\)
−0.643942 + 0.765074i \(0.722702\pi\)
\(488\) 132.815 + 76.6808i 0.272162 + 0.157133i
\(489\) 241.046i 0.492937i
\(490\) 39.2211 + 149.906i 0.0800430 + 0.305930i
\(491\) −744.294 −1.51587 −0.757937 0.652328i \(-0.773793\pi\)
−0.757937 + 0.652328i \(0.773793\pi\)
\(492\) −9.61009 + 16.6452i −0.0195327 + 0.0338316i
\(493\) −117.287 + 67.7154i −0.237904 + 0.137354i
\(494\) −14.2319 24.6505i −0.0288096 0.0498997i
\(495\) 63.0871 + 36.4234i 0.127449 + 0.0735826i
\(496\) 105.105i 0.211906i
\(497\) 135.647 + 177.862i 0.272932 + 0.357872i
\(498\) 38.7389 0.0777890
\(499\) 252.414 437.194i 0.505840 0.876141i −0.494137 0.869384i \(-0.664516\pi\)
0.999977 0.00675693i \(-0.00215081\pi\)
\(500\) 19.3649 11.1803i 0.0387298 0.0223607i
\(501\) 47.1138 + 81.6034i 0.0940394 + 0.162881i
\(502\) 314.308 + 181.466i 0.626111 + 0.361486i
\(503\) 402.412i 0.800024i −0.916510 0.400012i \(-0.869006\pi\)
0.916510 0.400012i \(-0.130994\pi\)
\(504\) −58.9114 + 7.57919i −0.116888 + 0.0150381i
\(505\) 342.785 0.678781
\(506\) 105.158 182.138i 0.207821 0.359957i
\(507\) −252.606 + 145.842i −0.498236 + 0.287657i
\(508\) −203.641 352.717i −0.400869 0.694325i
\(509\) 409.218 + 236.262i 0.803965 + 0.464169i 0.844856 0.534994i \(-0.179686\pi\)
−0.0408910 + 0.999164i \(0.513020\pi\)
\(510\) 106.101i 0.208041i
\(511\) −690.895 288.568i −1.35204 0.564712i
\(512\) −22.6274 −0.0441942
\(513\) −67.7298 + 117.311i −0.132027 + 0.228677i
\(514\) −246.070 + 142.069i −0.478735 + 0.276398i
\(515\) −70.8116 122.649i −0.137498 0.238154i
\(516\) −206.796 119.394i −0.400768 0.231383i
\(517\) 245.540i 0.474933i
\(518\) −246.473 + 590.111i −0.475817 + 1.13921i
\(519\) −108.745 −0.209527
\(520\) −2.44147 + 4.22875i −0.00469513 + 0.00813221i
\(521\) 48.2368 27.8496i 0.0925851 0.0534540i −0.452993 0.891514i \(-0.649644\pi\)
0.545578 + 0.838060i \(0.316310\pi\)
\(522\) 14.8308 + 25.6877i 0.0284115 + 0.0492102i
\(523\) 459.405 + 265.238i 0.878403 + 0.507146i 0.870132 0.492819i \(-0.164034\pi\)
0.00827171 + 0.999966i \(0.497367\pi\)
\(524\) 155.374i 0.296516i
\(525\) −7.73548 60.1262i −0.0147342 0.114526i
\(526\) −711.336 −1.35235
\(527\) 254.503 440.812i 0.482928 0.836456i
\(528\) 65.1561 37.6179i 0.123402 0.0712460i
\(529\) 170.728 + 295.709i 0.322737 + 0.558997i
\(530\) −204.202 117.896i −0.385286 0.222445i
\(531\) 334.838i 0.630581i
\(532\) 290.203 221.324i 0.545495 0.416023i
\(533\) 4.28369 0.00803694
\(534\) 45.0226 77.9815i 0.0843120 0.146033i
\(535\) 84.9258 49.0319i 0.158740 0.0916485i
\(536\) −62.5853 108.401i −0.116764 0.202241i
\(537\) −211.193 121.933i −0.393284 0.227062i
\(538\) 198.823i 0.369559i
\(539\) −514.780 + 134.686i −0.955065 + 0.249882i
\(540\) 23.2379 0.0430331
\(541\) −222.070 + 384.636i −0.410480 + 0.710972i −0.994942 0.100449i \(-0.967972\pi\)
0.584462 + 0.811421i \(0.301306\pi\)
\(542\) 146.806 84.7586i 0.270860 0.156381i
\(543\) −193.112 334.480i −0.355640 0.615986i
\(544\) 94.8996 + 54.7903i 0.174448 + 0.100718i
\(545\) 11.8139i 0.0216768i
\(546\) 8.02783 + 10.5262i 0.0147030 + 0.0192787i
\(547\) −308.345 −0.563702 −0.281851 0.959458i \(-0.590948\pi\)
−0.281851 + 0.959458i \(0.590948\pi\)
\(548\) −229.008 + 396.653i −0.417897 + 0.723819i
\(549\) −140.872 + 81.3323i −0.256597 + 0.148146i
\(550\) 38.3936 + 66.4997i 0.0698065 + 0.120908i
\(551\) −157.840 91.1289i −0.286461 0.165388i
\(552\) 67.0900i 0.121540i
\(553\) −206.073 + 26.5121i −0.372645 + 0.0479422i
\(554\) 151.330 0.273160
\(555\) 125.099 216.678i 0.225403 0.390410i
\(556\) 106.940 61.7421i 0.192339 0.111047i
\(557\) −223.840 387.702i −0.401867 0.696054i 0.592084 0.805876i \(-0.298305\pi\)
−0.993951 + 0.109822i \(0.964972\pi\)
\(558\) −96.5452 55.7404i −0.173020 0.0998932i
\(559\) 53.2197i 0.0952052i
\(560\) −57.7731 24.1302i −0.103166 0.0430897i
\(561\) −364.354 −0.649472
\(562\) −60.4709 + 104.739i −0.107599 + 0.186368i
\(563\) −733.087 + 423.248i −1.30211 + 0.751773i −0.980765 0.195190i \(-0.937468\pi\)
−0.321343 + 0.946963i \(0.604134\pi\)
\(564\) −39.1633 67.8328i −0.0694385 0.120271i
\(565\) −206.672 119.322i −0.365791 0.211190i
\(566\) 554.403i 0.979511i
\(567\) 24.2806 58.1331i 0.0428229 0.102527i
\(568\) −90.3825 −0.159124
\(569\) −175.038 + 303.174i −0.307623 + 0.532819i −0.977842 0.209345i \(-0.932867\pi\)
0.670219 + 0.742164i \(0.266200\pi\)
\(570\) −123.657 + 71.3935i −0.216942 + 0.125252i
\(571\) 382.891 + 663.186i 0.670562 + 1.16145i 0.977745 + 0.209797i \(0.0672803\pi\)
−0.307183 + 0.951650i \(0.599386\pi\)
\(572\) −14.5216 8.38408i −0.0253875 0.0146575i
\(573\) 230.387i 0.402071i
\(574\) 7.00871 + 54.4772i 0.0122103 + 0.0949081i
\(575\) 68.4734 0.119084
\(576\) 12.0000 20.7846i 0.0208333 0.0360844i
\(577\) −91.9471 + 53.0857i −0.159354 + 0.0920029i −0.577556 0.816351i \(-0.695994\pi\)
0.418203 + 0.908354i \(0.362660\pi\)
\(578\) −60.9862 105.631i −0.105512 0.182753i
\(579\) 427.834 + 247.010i 0.738919 + 0.426615i
\(580\) 31.2661i 0.0539070i
\(581\) 88.0271 67.1341i 0.151510 0.115549i
\(582\) 328.750 0.564863
\(583\) 404.858 701.234i 0.694439 1.20280i
\(584\) 262.003 151.268i 0.448636 0.259020i
\(585\) −2.58957 4.48527i −0.00442662 0.00766712i
\(586\) 613.101 + 353.974i 1.04625 + 0.604051i
\(587\) 802.707i 1.36747i 0.729729 + 0.683737i \(0.239646\pi\)
−0.729729 + 0.683737i \(0.760354\pi\)
\(588\) −120.731 + 119.315i −0.205324 + 0.202917i
\(589\) 685.002 1.16299
\(590\) 176.475 305.664i 0.299111 0.518075i
\(591\) 461.676 266.549i 0.781178 0.451013i
\(592\) −129.202 223.784i −0.218246 0.378013i
\(593\) −73.6360 42.5138i −0.124175 0.0716927i 0.436626 0.899643i \(-0.356173\pi\)
−0.560801 + 0.827951i \(0.689507\pi\)
\(594\) 79.7996i 0.134343i
\(595\) 183.872 + 241.095i 0.309028 + 0.405202i
\(596\) −58.6090 −0.0983373
\(597\) 8.39167 14.5348i 0.0140564 0.0243464i
\(598\) −12.9494 + 7.47633i −0.0216545 + 0.0125022i
\(599\) −185.040 320.498i −0.308914 0.535055i 0.669211 0.743072i \(-0.266632\pi\)
−0.978125 + 0.208017i \(0.933299\pi\)
\(600\) 21.2132 + 12.2474i 0.0353553 + 0.0204124i
\(601\) 462.547i 0.769628i 0.922994 + 0.384814i \(0.125734\pi\)
−0.922994 + 0.384814i \(0.874266\pi\)
\(602\) −676.814 + 87.0748i −1.12428 + 0.144643i
\(603\) 132.764 0.220172
\(604\) −163.696 + 283.529i −0.271020 + 0.469420i
\(605\) 5.95381 3.43743i 0.00984100 0.00568170i
\(606\) 187.751 + 325.194i 0.309820 + 0.536624i
\(607\) −598.134 345.333i −0.985394 0.568918i −0.0814998 0.996673i \(-0.525971\pi\)
−0.903894 + 0.427756i \(0.859304\pi\)
\(608\) 147.470i 0.242549i
\(609\) 78.2168 + 32.6690i 0.128435 + 0.0536436i
\(610\) −171.463 −0.281088
\(611\) −8.72851 + 15.1182i −0.0142856 + 0.0247434i
\(612\) −100.656 + 58.1139i −0.164471 + 0.0949574i
\(613\) 49.1726 + 85.1695i 0.0802163 + 0.138939i 0.903343 0.428919i \(-0.141106\pi\)
−0.823126 + 0.567858i \(0.807772\pi\)
\(614\) 487.658 + 281.550i 0.794232 + 0.458550i
\(615\) 21.4888i 0.0349412i
\(616\) 82.8639 198.394i 0.134519 0.322069i
\(617\) −794.667 −1.28795 −0.643976 0.765045i \(-0.722717\pi\)
−0.643976 + 0.765045i \(0.722717\pi\)
\(618\) 77.5702 134.356i 0.125518 0.217404i
\(619\) −114.032 + 65.8365i −0.184220 + 0.106359i −0.589274 0.807933i \(-0.700586\pi\)
0.405054 + 0.914293i \(0.367253\pi\)
\(620\) −58.7556 101.768i −0.0947670 0.164141i
\(621\) 61.6261 + 35.5798i 0.0992369 + 0.0572944i
\(622\) 525.998i 0.845656i
\(623\) −32.8353 255.222i −0.0527052 0.409666i
\(624\) −5.34899 −0.00857210
\(625\) −12.5000 + 21.6506i −0.0200000 + 0.0346410i
\(626\) 517.438 298.743i 0.826579 0.477225i
\(627\) −245.167 424.642i −0.391016 0.677260i
\(628\) −361.483 208.702i −0.575609 0.332328i
\(629\) 1251.40i 1.98951i
\(630\) 52.8038 40.2710i 0.0838156 0.0639222i
\(631\) −1086.67 −1.72213 −0.861067 0.508492i \(-0.830203\pi\)
−0.861067 + 0.508492i \(0.830203\pi\)
\(632\) 41.9761 72.7047i 0.0664179 0.115039i
\(633\) −263.930 + 152.380i −0.416952 + 0.240727i
\(634\) 152.864 + 264.768i 0.241110 + 0.417615i
\(635\) 394.350 + 227.678i 0.621023 + 0.358548i
\(636\) 258.297i 0.406127i
\(637\) 36.4835 + 10.0067i 0.0572740 + 0.0157091i
\(638\) −107.369 −0.168289
\(639\) 47.9326 83.0216i 0.0750118 0.129924i
\(640\) 21.9089 12.6491i 0.0342327 0.0197642i
\(641\) 310.496 + 537.795i 0.484393 + 0.838993i 0.999839 0.0179287i \(-0.00570718\pi\)
−0.515446 + 0.856922i \(0.672374\pi\)
\(642\) 93.0316 + 53.7118i 0.144909 + 0.0836632i
\(643\) 75.8433i 0.117952i 0.998259 + 0.0589761i \(0.0187836\pi\)
−0.998259 + 0.0589761i \(0.981216\pi\)
\(644\) −116.266 152.450i −0.180538 0.236723i
\(645\) 266.973 0.413911
\(646\) 357.085 618.490i 0.552763 0.957414i
\(647\) 136.611 78.8723i 0.211145 0.121905i −0.390698 0.920519i \(-0.627766\pi\)
0.601843 + 0.798614i \(0.294433\pi\)
\(648\) 12.7279 + 22.0454i 0.0196419 + 0.0340207i
\(649\) 1049.66 + 606.021i 1.61735 + 0.933777i
\(650\) 5.45929i 0.00839891i
\(651\) −315.979 + 40.6519i −0.485374 + 0.0624453i
\(652\) 278.336 0.426896
\(653\) 359.691 623.004i 0.550829 0.954064i −0.447386 0.894341i \(-0.647645\pi\)
0.998215 0.0597229i \(-0.0190217\pi\)
\(654\) 11.2076 6.47072i 0.0171370 0.00989407i
\(655\) −86.8569 150.441i −0.132606 0.229680i
\(656\) −19.2202 11.0968i −0.0292991 0.0169158i
\(657\) 320.887i 0.488413i
\(658\) −206.545 86.2681i −0.313898 0.131106i
\(659\) −10.5090 −0.0159469 −0.00797343 0.999968i \(-0.502538\pi\)
−0.00797343 + 0.999968i \(0.502538\pi\)
\(660\) −42.0581 + 72.8467i −0.0637244 + 0.110374i
\(661\) 1040.86 600.938i 1.57467 0.909135i 0.579083 0.815268i \(-0.303411\pi\)
0.995585 0.0938667i \(-0.0299227\pi\)
\(662\) 149.525 + 258.985i 0.225868 + 0.391215i
\(663\) 22.4337 + 12.9521i 0.0338367 + 0.0195356i
\(664\) 44.7318i 0.0673672i
\(665\) −157.264 + 376.525i −0.236487 + 0.566203i
\(666\) 274.078 0.411529
\(667\) −47.8719 + 82.9166i −0.0717720 + 0.124313i
\(668\) −94.2275 + 54.4023i −0.141059 + 0.0814405i
\(669\) 43.3753 + 75.1282i 0.0648360 + 0.112299i
\(670\) 121.196 + 69.9725i 0.180890 + 0.104437i
\(671\) 588.810i 0.877512i
\(672\) −8.75169 68.0251i −0.0130234 0.101228i
\(673\) 1070.49 1.59062 0.795310 0.606203i \(-0.207308\pi\)
0.795310 + 0.606203i \(0.207308\pi\)
\(674\) 184.116 318.898i 0.273169 0.473143i
\(675\) −22.5000 + 12.9904i −0.0333333 + 0.0192450i
\(676\) −168.404 291.684i −0.249118 0.431485i
\(677\) −517.691 298.889i −0.764685 0.441491i 0.0662906 0.997800i \(-0.478884\pi\)
−0.830975 + 0.556309i \(0.812217\pi\)
\(678\) 261.422i 0.385578i
\(679\) 747.024 569.720i 1.10018 0.839058i
\(680\) −122.515 −0.180169
\(681\) −264.301 + 457.782i −0.388107 + 0.672221i
\(682\) 349.473 201.768i 0.512424 0.295848i
\(683\) −261.801 453.453i −0.383310 0.663913i 0.608223 0.793766i \(-0.291883\pi\)
−0.991533 + 0.129853i \(0.958549\pi\)
\(684\) −135.460 78.2076i −0.198040 0.114339i
\(685\) 512.076i 0.747557i
\(686\) −67.5667 + 480.346i −0.0984937 + 0.700214i
\(687\) 706.855 1.02890
\(688\) 137.864 238.788i 0.200384 0.347075i
\(689\) −49.8552 + 28.7839i −0.0723588 + 0.0417764i
\(690\) 37.5044 + 64.9596i 0.0543543 + 0.0941444i
\(691\) 170.271 + 98.3059i 0.246412 + 0.142266i 0.618120 0.786083i \(-0.287894\pi\)
−0.371708 + 0.928350i \(0.621228\pi\)
\(692\) 125.567i 0.181456i
\(693\) 138.292 + 181.330i 0.199555 + 0.261659i
\(694\) 723.988 1.04321
\(695\) −69.0298 + 119.563i −0.0993234 + 0.172033i
\(696\) −29.6616 + 17.1251i −0.0426173 + 0.0246051i
\(697\) 53.7398 + 93.0800i 0.0771015 + 0.133544i
\(698\) −646.509 373.262i −0.926231 0.534760i
\(699\) 375.524i 0.537231i
\(700\) 69.4278 8.93216i 0.0991825 0.0127602i
\(701\) 132.968 0.189683 0.0948414 0.995492i \(-0.469766\pi\)
0.0948414 + 0.995492i \(0.469766\pi\)
\(702\) 2.83673 4.91336i 0.00404093 0.00699909i
\(703\) −1458.47 + 842.046i −2.07463 + 1.19779i
\(704\) 43.4374 + 75.2358i 0.0617008 + 0.106869i
\(705\) 75.8394 + 43.7859i 0.107574 + 0.0621077i
\(706\) 193.062i 0.273460i
\(707\) 990.186 + 413.573i 1.40055 + 0.584969i
\(708\) 386.638 0.546099
\(709\) −151.618 + 262.609i −0.213847 + 0.370394i −0.952915 0.303237i \(-0.901933\pi\)
0.739068 + 0.673631i \(0.235266\pi\)
\(710\) 87.5125 50.5254i 0.123257 0.0711625i
\(711\) 44.5224 + 77.1150i 0.0626194 + 0.108460i
\(712\) 90.0453 + 51.9877i 0.126468 + 0.0730164i
\(713\) 359.846i 0.504692i
\(714\) −128.012 + 306.489i −0.179289 + 0.429257i
\(715\) 18.7474 0.0262201
\(716\) 140.796 243.865i 0.196642 0.340594i
\(717\) 584.608 337.524i 0.815354 0.470745i
\(718\) −393.893 682.243i −0.548598 0.950200i
\(719\) −118.785 68.5808i −0.165209 0.0953835i 0.415116 0.909769i \(-0.363741\pi\)
−0.580325 + 0.814385i \(0.697074\pi\)
\(720\) 26.8328i 0.0372678i
\(721\) −56.5726 439.727i −0.0784640 0.609884i
\(722\) 450.574 0.624063
\(723\) −60.0686 + 104.042i −0.0830824 + 0.143903i
\(724\) 386.225 222.987i 0.533460 0.307993i
\(725\) −17.4783 30.2733i −0.0241080 0.0417562i
\(726\) 6.52207 + 3.76552i 0.00898356 + 0.00518666i
\(727\) 741.058i 1.01934i 0.860371 + 0.509669i \(0.170232\pi\)
−0.860371 + 0.509669i \(0.829768\pi\)
\(728\) −12.1546 + 9.26974i −0.0166959 + 0.0127332i
\(729\) −27.0000 −0.0370370
\(730\) −169.122 + 292.929i −0.231675 + 0.401272i
\(731\) −1156.41 + 667.652i −1.58195 + 0.913340i
\(732\) −93.9144 162.665i −0.128298 0.222219i
\(733\) 124.538 + 71.9021i 0.169902 + 0.0980929i 0.582540 0.812802i \(-0.302059\pi\)
−0.412638 + 0.910895i \(0.635392\pi\)
\(734\) 166.908i 0.227396i
\(735\) 50.1978 183.017i 0.0682964 0.249003i
\(736\) 77.4688 0.105257
\(737\) −240.288 + 416.190i −0.326035 + 0.564709i
\(738\) 20.3861 11.7699i 0.0276234 0.0159484i
\(739\) 522.722 + 905.381i 0.707337 + 1.22514i 0.965842 + 0.259133i \(0.0834368\pi\)
−0.258505 + 0.966010i \(0.583230\pi\)
\(740\) 250.198 + 144.452i 0.338105 + 0.195205i
\(741\) 34.8610i 0.0470459i
\(742\) −447.626 586.932i −0.603269 0.791014i
\(743\) 660.175 0.888526 0.444263 0.895896i \(-0.353466\pi\)
0.444263 + 0.895896i \(0.353466\pi\)
\(744\) 64.3635 111.481i 0.0865101 0.149840i
\(745\) 56.7480 32.7634i 0.0761717 0.0439778i
\(746\) −225.123 389.925i −0.301774 0.522687i
\(747\) −41.0888 23.7226i −0.0550051 0.0317572i
\(748\) 420.720i 0.562459i
\(749\) 304.479 39.1724i 0.406514 0.0522996i
\(750\) −27.3861 −0.0365148
\(751\) −79.4795 + 137.663i −0.105832 + 0.183306i −0.914078 0.405539i \(-0.867084\pi\)
0.808246 + 0.588845i \(0.200417\pi\)
\(752\) 78.3266 45.2219i 0.104158 0.0601355i
\(753\) −222.249 384.947i −0.295152 0.511218i
\(754\) 6.61082 + 3.81676i 0.00876767 + 0.00506202i
\(755\) 366.035i 0.484815i
\(756\) 67.1263 + 28.0368i 0.0887914 + 0.0370857i
\(757\) −777.212 −1.02670 −0.513350 0.858179i \(-0.671596\pi\)
−0.513350 + 0.858179i \(0.671596\pi\)
\(758\) −409.909 + 709.983i −0.540777 + 0.936653i
\(759\) −223.073 + 128.791i −0.293904 + 0.169686i
\(760\) −82.4381 142.787i −0.108471 0.187878i
\(761\) −989.290 571.167i −1.29999 0.750548i −0.319585 0.947558i \(-0.603544\pi\)
−0.980401 + 0.197010i \(0.936877\pi\)
\(762\) 498.817i 0.654616i
\(763\) 14.2536 34.1262i 0.0186809 0.0447263i
\(764\) 266.028 0.348204
\(765\) 64.9733 112.537i 0.0849325 0.147107i
\(766\) 744.698 429.951i 0.972190 0.561294i
\(767\) −43.0859 74.6270i −0.0561746 0.0972973i
\(768\) 24.0000 + 13.8564i 0.0312500 + 0.0180422i
\(769\) 166.927i 0.217070i −0.994093 0.108535i \(-0.965384\pi\)
0.994093 0.108535i \(-0.0346159\pi\)
\(770\) 30.6733 + 238.417i