Properties

Label 108.5.f.a.19.5
Level 108
Weight 5
Character 108.19
Analytic conductor 11.164
Analytic rank 0
Dimension 44
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 19.5
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.42968 + 2.05847i) q^{2} +(7.52540 - 14.1198i) q^{4} +(-16.6139 - 28.7760i) q^{5} +(-39.9759 - 23.0801i) q^{7} +(3.25547 + 63.9171i) q^{8} +O(q^{10})\) \(q+(-3.42968 + 2.05847i) q^{2} +(7.52540 - 14.1198i) q^{4} +(-16.6139 - 28.7760i) q^{5} +(-39.9759 - 23.0801i) q^{7} +(3.25547 + 63.9171i) q^{8} +(116.215 + 64.4935i) q^{10} +(-63.6109 - 36.7258i) q^{11} +(151.520 + 262.440i) q^{13} +(184.614 - 3.13190i) q^{14} +(-142.737 - 212.514i) q^{16} +182.019 q^{17} +314.215i q^{19} +(-531.337 + 18.0330i) q^{20} +(293.764 - 4.98356i) q^{22} +(-290.919 + 167.962i) q^{23} +(-239.540 + 414.896i) q^{25} +(-1059.89 - 588.185i) q^{26} +(-626.721 + 390.765i) q^{28} +(-357.370 + 618.983i) q^{29} +(-985.186 + 568.798i) q^{31} +(926.995 + 435.035i) q^{32} +(-624.267 + 374.681i) q^{34} +1533.80i q^{35} +1008.45 q^{37} +(-646.803 - 1077.66i) q^{38} +(1785.20 - 1155.59i) q^{40} +(557.553 + 965.709i) q^{41} +(-2182.06 - 1259.82i) q^{43} +(-997.257 + 621.796i) q^{44} +(652.014 - 1174.90i) q^{46} +(980.476 + 566.078i) q^{47} +(-135.117 - 234.029i) q^{49} +(-32.5048 - 1916.05i) q^{50} +(4845.84 - 164.462i) q^{52} +1057.77 q^{53} +2440.63i q^{55} +(1345.07 - 2630.28i) q^{56} +(-48.4939 - 2858.55i) q^{58} +(878.476 - 507.188i) q^{59} +(-430.304 + 745.308i) q^{61} +(2208.02 - 3978.77i) q^{62} +(-4074.80 + 416.161i) q^{64} +(5034.65 - 8720.27i) q^{65} +(-559.041 + 322.762i) q^{67} +(1369.76 - 2570.07i) q^{68} +(-3157.28 - 5260.44i) q^{70} +9567.89i q^{71} +1899.10 q^{73} +(-3458.66 + 2075.86i) q^{74} +(4436.65 + 2364.59i) q^{76} +(1695.27 + 2936.29i) q^{77} +(6768.11 + 3907.57i) q^{79} +(-3743.90 + 7638.08i) q^{80} +(-3900.11 - 2164.37i) q^{82} +(-7052.56 - 4071.80i) q^{83} +(-3024.04 - 5237.78i) q^{85} +(10077.1 - 170.953i) q^{86} +(2140.32 - 4185.39i) q^{88} -7653.39 q^{89} -13988.4i q^{91} +(182.309 + 5371.70i) q^{92} +(-4527.97 + 76.8149i) q^{94} +(9041.87 - 5220.33i) q^{95} +(-6366.75 + 11027.5i) q^{97} +(945.149 + 524.510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.42968 + 2.05847i −0.857420 + 0.514618i
\(3\) 0 0
\(4\) 7.52540 14.1198i 0.470337 0.882487i
\(5\) −16.6139 28.7760i −0.664554 1.15104i −0.979406 0.201901i \(-0.935288\pi\)
0.314852 0.949141i \(-0.398045\pi\)
\(6\) 0 0
\(7\) −39.9759 23.0801i −0.815835 0.471023i 0.0331429 0.999451i \(-0.489448\pi\)
−0.848978 + 0.528428i \(0.822782\pi\)
\(8\) 3.25547 + 63.9171i 0.0508667 + 0.998705i
\(9\) 0 0
\(10\) 116.215 + 64.4935i 1.16215 + 0.644935i
\(11\) −63.6109 36.7258i −0.525710 0.303519i 0.213558 0.976930i \(-0.431495\pi\)
−0.739268 + 0.673412i \(0.764828\pi\)
\(12\) 0 0
\(13\) 151.520 + 262.440i 0.896566 + 1.55290i 0.831855 + 0.554993i \(0.187279\pi\)
0.0647110 + 0.997904i \(0.479387\pi\)
\(14\) 184.614 3.13190i 0.941910 0.0159791i
\(15\) 0 0
\(16\) −142.737 212.514i −0.557566 0.830133i
\(17\) 182.019 0.629823 0.314912 0.949121i \(-0.398025\pi\)
0.314912 + 0.949121i \(0.398025\pi\)
\(18\) 0 0
\(19\) 314.215i 0.870402i 0.900333 + 0.435201i \(0.143323\pi\)
−0.900333 + 0.435201i \(0.856677\pi\)
\(20\) −531.337 + 18.0330i −1.32834 + 0.0450824i
\(21\) 0 0
\(22\) 293.764 4.98356i 0.606950 0.0102966i
\(23\) −290.919 + 167.962i −0.549941 + 0.317509i −0.749098 0.662459i \(-0.769513\pi\)
0.199157 + 0.979968i \(0.436180\pi\)
\(24\) 0 0
\(25\) −239.540 + 414.896i −0.383265 + 0.663834i
\(26\) −1059.89 588.185i −1.56788 0.870096i
\(27\) 0 0
\(28\) −626.721 + 390.765i −0.799389 + 0.498424i
\(29\) −357.370 + 618.983i −0.424935 + 0.736008i −0.996414 0.0846079i \(-0.973036\pi\)
0.571480 + 0.820616i \(0.306370\pi\)
\(30\) 0 0
\(31\) −985.186 + 568.798i −1.02517 + 0.591881i −0.915597 0.402098i \(-0.868281\pi\)
−0.109571 + 0.993979i \(0.534948\pi\)
\(32\) 926.995 + 435.035i 0.905269 + 0.424839i
\(33\) 0 0
\(34\) −624.267 + 374.681i −0.540023 + 0.324118i
\(35\) 1533.80i 1.25208i
\(36\) 0 0
\(37\) 1008.45 0.736632 0.368316 0.929701i \(-0.379934\pi\)
0.368316 + 0.929701i \(0.379934\pi\)
\(38\) −646.803 1077.66i −0.447924 0.746300i
\(39\) 0 0
\(40\) 1785.20 1155.59i 1.11575 0.722244i
\(41\) 557.553 + 965.709i 0.331679 + 0.574485i 0.982841 0.184454i \(-0.0590516\pi\)
−0.651162 + 0.758939i \(0.725718\pi\)
\(42\) 0 0
\(43\) −2182.06 1259.82i −1.18013 0.681349i −0.224087 0.974569i \(-0.571940\pi\)
−0.956045 + 0.293220i \(0.905273\pi\)
\(44\) −997.257 + 621.796i −0.515112 + 0.321176i
\(45\) 0 0
\(46\) 652.014 1174.90i 0.308135 0.555248i
\(47\) 980.476 + 566.078i 0.443855 + 0.256260i 0.705232 0.708977i \(-0.250843\pi\)
−0.261376 + 0.965237i \(0.584176\pi\)
\(48\) 0 0
\(49\) −135.117 234.029i −0.0562752 0.0974714i
\(50\) −32.5048 1916.05i −0.0130019 0.766419i
\(51\) 0 0
\(52\) 4845.84 164.462i 1.79210 0.0608218i
\(53\) 1057.77 0.376566 0.188283 0.982115i \(-0.439708\pi\)
0.188283 + 0.982115i \(0.439708\pi\)
\(54\) 0 0
\(55\) 2440.63i 0.806818i
\(56\) 1345.07 2630.28i 0.428914 0.838739i
\(57\) 0 0
\(58\) −48.4939 2858.55i −0.0144156 0.849747i
\(59\) 878.476 507.188i 0.252363 0.145702i −0.368483 0.929635i \(-0.620123\pi\)
0.620846 + 0.783933i \(0.286789\pi\)
\(60\) 0 0
\(61\) −430.304 + 745.308i −0.115642 + 0.200298i −0.918036 0.396497i \(-0.870226\pi\)
0.802394 + 0.596794i \(0.203559\pi\)
\(62\) 2208.02 3978.77i 0.574407 1.03506i
\(63\) 0 0
\(64\) −4074.80 + 416.161i −0.994825 + 0.101602i
\(65\) 5034.65 8720.27i 1.19163 2.06397i
\(66\) 0 0
\(67\) −559.041 + 322.762i −0.124536 + 0.0719008i −0.560974 0.827834i \(-0.689573\pi\)
0.436438 + 0.899734i \(0.356240\pi\)
\(68\) 1369.76 2570.07i 0.296229 0.555811i
\(69\) 0 0
\(70\) −3157.28 5260.44i −0.644343 1.07356i
\(71\) 9567.89i 1.89801i 0.315254 + 0.949007i \(0.397910\pi\)
−0.315254 + 0.949007i \(0.602090\pi\)
\(72\) 0 0
\(73\) 1899.10 0.356372 0.178186 0.983997i \(-0.442977\pi\)
0.178186 + 0.983997i \(0.442977\pi\)
\(74\) −3458.66 + 2075.86i −0.631603 + 0.379084i
\(75\) 0 0
\(76\) 4436.65 + 2364.59i 0.768119 + 0.409383i
\(77\) 1695.27 + 2936.29i 0.285928 + 0.495242i
\(78\) 0 0
\(79\) 6768.11 + 3907.57i 1.08446 + 0.626113i 0.932096 0.362212i \(-0.117978\pi\)
0.152363 + 0.988325i \(0.451312\pi\)
\(80\) −3743.90 + 7638.08i −0.584985 + 1.19345i
\(81\) 0 0
\(82\) −3900.11 2164.37i −0.580028 0.321887i
\(83\) −7052.56 4071.80i −1.02374 0.591058i −0.108556 0.994090i \(-0.534623\pi\)
−0.915186 + 0.403032i \(0.867956\pi\)
\(84\) 0 0
\(85\) −3024.04 5237.78i −0.418552 0.724953i
\(86\) 10077.1 170.953i 1.36250 0.0231142i
\(87\) 0 0
\(88\) 2140.32 4185.39i 0.276385 0.540468i
\(89\) −7653.39 −0.966215 −0.483107 0.875561i \(-0.660492\pi\)
−0.483107 + 0.875561i \(0.660492\pi\)
\(90\) 0 0
\(91\) 13988.4i 1.68921i
\(92\) 182.309 + 5371.70i 0.0215394 + 0.634652i
\(93\) 0 0
\(94\) −4527.97 + 76.8149i −0.512446 + 0.00869340i
\(95\) 9041.87 5220.33i 1.00187 0.578430i
\(96\) 0 0
\(97\) −6366.75 + 11027.5i −0.676666 + 1.17202i 0.299313 + 0.954155i \(0.403243\pi\)
−0.975979 + 0.217865i \(0.930091\pi\)
\(98\) 945.149 + 524.510i 0.0984120 + 0.0546137i
\(99\) 0 0
\(100\) 4055.61 + 6504.52i 0.405561 + 0.650452i
\(101\) −6873.20 + 11904.7i −0.673777 + 1.16702i 0.303048 + 0.952975i \(0.401996\pi\)
−0.976825 + 0.214040i \(0.931338\pi\)
\(102\) 0 0
\(103\) −11251.5 + 6496.03i −1.06056 + 0.612313i −0.925587 0.378536i \(-0.876428\pi\)
−0.134971 + 0.990850i \(0.543094\pi\)
\(104\) −16281.1 + 10539.1i −1.50528 + 0.974396i
\(105\) 0 0
\(106\) −3627.82 + 2177.40i −0.322875 + 0.193787i
\(107\) 14891.8i 1.30071i −0.759631 0.650354i \(-0.774621\pi\)
0.759631 0.650354i \(-0.225379\pi\)
\(108\) 0 0
\(109\) 7539.02 0.634544 0.317272 0.948335i \(-0.397233\pi\)
0.317272 + 0.948335i \(0.397233\pi\)
\(110\) −5023.96 8370.56i −0.415203 0.691782i
\(111\) 0 0
\(112\) 801.189 + 11789.8i 0.0638703 + 0.939878i
\(113\) −496.140 859.339i −0.0388550 0.0672988i 0.845944 0.533272i \(-0.179038\pi\)
−0.884799 + 0.465973i \(0.845704\pi\)
\(114\) 0 0
\(115\) 9666.57 + 5581.00i 0.730932 + 0.422004i
\(116\) 6050.56 + 9704.08i 0.449655 + 0.721171i
\(117\) 0 0
\(118\) −1968.86 + 3547.81i −0.141400 + 0.254798i
\(119\) −7276.38 4201.02i −0.513832 0.296661i
\(120\) 0 0
\(121\) −4622.94 8007.16i −0.315753 0.546900i
\(122\) −58.3908 3441.94i −0.00392306 0.231251i
\(123\) 0 0
\(124\) 617.383 + 18191.1i 0.0401524 + 1.18308i
\(125\) −4848.57 −0.310308
\(126\) 0 0
\(127\) 7123.52i 0.441659i −0.975312 0.220829i \(-0.929124\pi\)
0.975312 0.220829i \(-0.0708764\pi\)
\(128\) 13118.6 9815.16i 0.800697 0.599070i
\(129\) 0 0
\(130\) 683.185 + 40271.4i 0.0404252 + 2.38292i
\(131\) −6027.16 + 3479.78i −0.351212 + 0.202773i −0.665219 0.746648i \(-0.731662\pi\)
0.314007 + 0.949421i \(0.398329\pi\)
\(132\) 0 0
\(133\) 7252.12 12561.0i 0.409979 0.710105i
\(134\) 1252.93 2257.74i 0.0697780 0.125737i
\(135\) 0 0
\(136\) 592.557 + 11634.1i 0.0320371 + 0.629008i
\(137\) −4244.42 + 7351.56i −0.226140 + 0.391686i −0.956661 0.291204i \(-0.905944\pi\)
0.730521 + 0.682891i \(0.239277\pi\)
\(138\) 0 0
\(139\) 18483.9 10671.7i 0.956673 0.552335i 0.0615252 0.998106i \(-0.480404\pi\)
0.895147 + 0.445770i \(0.147070\pi\)
\(140\) 21656.9 + 11542.4i 1.10494 + 0.588900i
\(141\) 0 0
\(142\) −19695.2 32814.8i −0.976752 1.62740i
\(143\) 22258.7i 1.08850i
\(144\) 0 0
\(145\) 23749.2 1.12957
\(146\) −6513.32 + 3909.25i −0.305560 + 0.183395i
\(147\) 0 0
\(148\) 7588.98 14239.1i 0.346466 0.650068i
\(149\) −6366.78 11027.6i −0.286779 0.496716i 0.686260 0.727356i \(-0.259251\pi\)
−0.973039 + 0.230640i \(0.925918\pi\)
\(150\) 0 0
\(151\) 3061.84 + 1767.75i 0.134285 + 0.0775296i 0.565638 0.824654i \(-0.308630\pi\)
−0.431352 + 0.902184i \(0.641963\pi\)
\(152\) −20083.7 + 1022.92i −0.869276 + 0.0442745i
\(153\) 0 0
\(154\) −11858.5 6580.88i −0.500021 0.277487i
\(155\) 32735.5 + 18899.8i 1.36256 + 0.786674i
\(156\) 0 0
\(157\) −14870.6 25756.6i −0.603292 1.04493i −0.992319 0.123706i \(-0.960522\pi\)
0.389027 0.921227i \(-0.372811\pi\)
\(158\) −31256.1 + 530.244i −1.25205 + 0.0212404i
\(159\) 0 0
\(160\) −2882.37 33902.9i −0.112593 1.32433i
\(161\) 15506.3 0.598216
\(162\) 0 0
\(163\) 5903.96i 0.222213i 0.993809 + 0.111106i \(0.0354394\pi\)
−0.993809 + 0.111106i \(0.964561\pi\)
\(164\) 17831.4 605.177i 0.662976 0.0225006i
\(165\) 0 0
\(166\) 32569.7 552.529i 1.18195 0.0200511i
\(167\) −17810.7 + 10283.0i −0.638628 + 0.368712i −0.784086 0.620652i \(-0.786868\pi\)
0.145458 + 0.989364i \(0.453535\pi\)
\(168\) 0 0
\(169\) −31635.9 + 54795.0i −1.10766 + 1.91852i
\(170\) 21153.3 + 11739.0i 0.731948 + 0.406195i
\(171\) 0 0
\(172\) −34209.2 + 21329.7i −1.15634 + 0.720987i
\(173\) 3054.99 5291.39i 0.102074 0.176798i −0.810465 0.585787i \(-0.800785\pi\)
0.912539 + 0.408989i \(0.134119\pi\)
\(174\) 0 0
\(175\) 19151.7 11057.2i 0.625361 0.361053i
\(176\) 1274.87 + 18760.3i 0.0411569 + 0.605641i
\(177\) 0 0
\(178\) 26248.7 15754.3i 0.828451 0.497231i
\(179\) 11534.8i 0.360001i −0.983667 0.180001i \(-0.942390\pi\)
0.983667 0.180001i \(-0.0576099\pi\)
\(180\) 0 0
\(181\) −25544.2 −0.779713 −0.389857 0.920876i \(-0.627475\pi\)
−0.389857 + 0.920876i \(0.627475\pi\)
\(182\) 28794.6 + 47975.6i 0.869298 + 1.44836i
\(183\) 0 0
\(184\) −11682.7 18047.9i −0.345072 0.533079i
\(185\) −16754.2 29019.2i −0.489532 0.847894i
\(186\) 0 0
\(187\) −11578.4 6684.78i −0.331104 0.191163i
\(188\) 15371.4 9584.15i 0.434908 0.271168i
\(189\) 0 0
\(190\) −20264.8 + 36516.5i −0.561353 + 1.01154i
\(191\) −33833.7 19533.9i −0.927433 0.535454i −0.0414344 0.999141i \(-0.513193\pi\)
−0.885999 + 0.463687i \(0.846526\pi\)
\(192\) 0 0
\(193\) −13915.2 24101.8i −0.373572 0.647045i 0.616541 0.787323i \(-0.288534\pi\)
−0.990112 + 0.140278i \(0.955200\pi\)
\(194\) −863.947 50926.7i −0.0229553 1.35314i
\(195\) 0 0
\(196\) −4321.25 + 146.658i −0.112486 + 0.00381763i
\(197\) 21103.0 0.543765 0.271883 0.962330i \(-0.412354\pi\)
0.271883 + 0.962330i \(0.412354\pi\)
\(198\) 0 0
\(199\) 5447.97i 0.137572i 0.997631 + 0.0687858i \(0.0219125\pi\)
−0.997631 + 0.0687858i \(0.978087\pi\)
\(200\) −27298.8 13960.1i −0.682470 0.349001i
\(201\) 0 0
\(202\) −932.670 54977.7i −0.0228573 1.34736i
\(203\) 28572.4 16496.3i 0.693353 0.400308i
\(204\) 0 0
\(205\) 18526.2 32088.3i 0.440837 0.763553i
\(206\) 25217.0 45440.1i 0.594236 1.07079i
\(207\) 0 0
\(208\) 34144.7 69659.8i 0.789217 1.61011i
\(209\) 11539.8 19987.5i 0.264183 0.457579i
\(210\) 0 0
\(211\) −59935.1 + 34603.5i −1.34622 + 0.777241i −0.987712 0.156286i \(-0.950048\pi\)
−0.358509 + 0.933526i \(0.616715\pi\)
\(212\) 7960.17 14935.5i 0.177113 0.332314i
\(213\) 0 0
\(214\) 30654.4 + 51074.1i 0.669367 + 1.11525i
\(215\) 83721.5i 1.81117i
\(216\) 0 0
\(217\) 52511.7 1.11516
\(218\) −25856.4 + 15518.9i −0.544071 + 0.326548i
\(219\) 0 0
\(220\) 34461.1 + 18366.7i 0.712007 + 0.379477i
\(221\) 27579.4 + 47769.0i 0.564678 + 0.978051i
\(222\) 0 0
\(223\) 21934.5 + 12663.9i 0.441080 + 0.254658i 0.704056 0.710145i \(-0.251371\pi\)
−0.262976 + 0.964802i \(0.584704\pi\)
\(224\) −27016.8 38786.1i −0.538441 0.773001i
\(225\) 0 0
\(226\) 3470.52 + 1925.97i 0.0679482 + 0.0377079i
\(227\) 84184.1 + 48603.7i 1.63372 + 0.943230i 0.982931 + 0.183975i \(0.0588964\pi\)
0.650792 + 0.759256i \(0.274437\pi\)
\(228\) 0 0
\(229\) 42946.4 + 74385.3i 0.818947 + 1.41846i 0.906459 + 0.422294i \(0.138775\pi\)
−0.0875119 + 0.996163i \(0.527892\pi\)
\(230\) −44641.6 + 757.323i −0.843886 + 0.0143161i
\(231\) 0 0
\(232\) −40727.0 20827.0i −0.756671 0.386946i
\(233\) 12774.0 0.235297 0.117649 0.993055i \(-0.462464\pi\)
0.117649 + 0.993055i \(0.462464\pi\)
\(234\) 0 0
\(235\) 37619.0i 0.681194i
\(236\) −550.511 16220.7i −0.00988421 0.291236i
\(237\) 0 0
\(238\) 33603.3 570.064i 0.593237 0.0100640i
\(239\) −91748.4 + 52971.0i −1.60621 + 0.927347i −0.616005 + 0.787742i \(0.711250\pi\)
−0.990207 + 0.139605i \(0.955417\pi\)
\(240\) 0 0
\(241\) 5089.73 8815.67i 0.0876316 0.151782i −0.818878 0.573968i \(-0.805404\pi\)
0.906510 + 0.422185i \(0.138737\pi\)
\(242\) 32337.7 + 17945.8i 0.552177 + 0.306431i
\(243\) 0 0
\(244\) 7285.38 + 11684.5i 0.122369 + 0.196260i
\(245\) −4489.62 + 7776.25i −0.0747958 + 0.129550i
\(246\) 0 0
\(247\) −82462.6 + 47609.8i −1.35165 + 0.780373i
\(248\) −39563.2 61118.6i −0.643262 0.993734i
\(249\) 0 0
\(250\) 16629.0 9980.63i 0.266064 0.159690i
\(251\) 21848.1i 0.346790i −0.984852 0.173395i \(-0.944526\pi\)
0.984852 0.173395i \(-0.0554738\pi\)
\(252\) 0 0
\(253\) 24674.2 0.385479
\(254\) 14663.5 + 24431.4i 0.227285 + 0.378687i
\(255\) 0 0
\(256\) −24788.4 + 60667.1i −0.378241 + 0.925707i
\(257\) 27780.7 + 48117.6i 0.420608 + 0.728514i 0.995999 0.0893643i \(-0.0284835\pi\)
−0.575391 + 0.817878i \(0.695150\pi\)
\(258\) 0 0
\(259\) −40313.7 23275.1i −0.600971 0.346971i
\(260\) −85240.6 136712.i −1.26096 2.02236i
\(261\) 0 0
\(262\) 13508.2 24341.3i 0.196786 0.354601i
\(263\) −21792.0 12581.6i −0.315055 0.181897i 0.334131 0.942527i \(-0.391557\pi\)
−0.649186 + 0.760629i \(0.724890\pi\)
\(264\) 0 0
\(265\) −17573.7 30438.5i −0.250248 0.433443i
\(266\) 984.089 + 58008.6i 0.0139082 + 0.819841i
\(267\) 0 0
\(268\) 350.332 + 10322.5i 0.00487765 + 0.143719i
\(269\) −54154.0 −0.748386 −0.374193 0.927351i \(-0.622080\pi\)
−0.374193 + 0.927351i \(0.622080\pi\)
\(270\) 0 0
\(271\) 94942.5i 1.29277i 0.763011 + 0.646386i \(0.223720\pi\)
−0.763011 + 0.646386i \(0.776280\pi\)
\(272\) −25980.8 38681.6i −0.351168 0.522837i
\(273\) 0 0
\(274\) −575.954 33950.5i −0.00767162 0.452215i
\(275\) 30474.7 17594.6i 0.402972 0.232656i
\(276\) 0 0
\(277\) −54019.7 + 93564.9i −0.704033 + 1.21942i 0.263006 + 0.964794i \(0.415286\pi\)
−0.967039 + 0.254627i \(0.918047\pi\)
\(278\) −41426.4 + 74648.9i −0.536029 + 0.965904i
\(279\) 0 0
\(280\) −98036.0 + 4993.24i −1.25046 + 0.0636893i
\(281\) −34463.0 + 59691.7i −0.436456 + 0.755964i −0.997413 0.0718805i \(-0.977100\pi\)
0.560957 + 0.827845i \(0.310433\pi\)
\(282\) 0 0
\(283\) 39154.2 22605.7i 0.488884 0.282257i −0.235228 0.971940i \(-0.575584\pi\)
0.724111 + 0.689683i \(0.242250\pi\)
\(284\) 135097. + 72002.2i 1.67497 + 0.892707i
\(285\) 0 0
\(286\) 45818.9 + 76340.2i 0.560160 + 0.933299i
\(287\) 51473.5i 0.624914i
\(288\) 0 0
\(289\) −50390.1 −0.603323
\(290\) −81452.0 + 48887.0i −0.968514 + 0.581296i
\(291\) 0 0
\(292\) 14291.5 26814.9i 0.167615 0.314493i
\(293\) −35853.6 62100.3i −0.417636 0.723366i 0.578065 0.815990i \(-0.303808\pi\)
−0.995701 + 0.0926242i \(0.970474\pi\)
\(294\) 0 0
\(295\) −29189.7 16852.7i −0.335418 0.193654i
\(296\) 3282.98 + 64457.2i 0.0374701 + 0.735679i
\(297\) 0 0
\(298\) 44536.0 + 24715.3i 0.501509 + 0.278313i
\(299\) −88159.9 50899.1i −0.986117 0.569335i
\(300\) 0 0
\(301\) 58153.4 + 100725.i 0.641862 + 1.11174i
\(302\) −14140.0 + 239.878i −0.155037 + 0.00263013i
\(303\) 0 0
\(304\) 66775.2 44850.1i 0.722550 0.485306i
\(305\) 28596.0 0.307401
\(306\) 0 0
\(307\) 95866.9i 1.01717i −0.861013 0.508583i \(-0.830170\pi\)
0.861013 0.508583i \(-0.169830\pi\)
\(308\) 54217.4 1840.08i 0.571528 0.0193970i
\(309\) 0 0
\(310\) −151177. + 2564.65i −1.57312 + 0.0266873i
\(311\) 20844.0 12034.3i 0.215506 0.124423i −0.388362 0.921507i \(-0.626959\pi\)
0.603868 + 0.797085i \(0.293626\pi\)
\(312\) 0 0
\(313\) 49654.5 86004.2i 0.506839 0.877871i −0.493130 0.869956i \(-0.664147\pi\)
0.999969 0.00791525i \(-0.00251953\pi\)
\(314\) 104020. + 57726.1i 1.05502 + 0.585481i
\(315\) 0 0
\(316\) 106107. 66158.2i 1.06260 0.662536i
\(317\) 29720.5 51477.4i 0.295759 0.512269i −0.679402 0.733766i \(-0.737761\pi\)
0.975161 + 0.221497i \(0.0710942\pi\)
\(318\) 0 0
\(319\) 45465.2 26249.4i 0.446785 0.257951i
\(320\) 79673.7 + 110343.i 0.778063 + 1.07757i
\(321\) 0 0
\(322\) −53181.8 + 31919.4i −0.512922 + 0.307852i
\(323\) 57193.1i 0.548200i
\(324\) 0 0
\(325\) −145180. −1.37449
\(326\) −12153.1 20248.7i −0.114354 0.190529i
\(327\) 0 0
\(328\) −59910.3 + 38781.0i −0.556870 + 0.360472i
\(329\) −26130.3 45259.0i −0.241408 0.418132i
\(330\) 0 0
\(331\) 79852.0 + 46102.6i 0.728836 + 0.420794i 0.817996 0.575223i \(-0.195085\pi\)
−0.0891599 + 0.996017i \(0.528418\pi\)
\(332\) −110566. + 68938.8i −1.00310 + 0.625442i
\(333\) 0 0
\(334\) 39917.7 71930.3i 0.357827 0.644791i
\(335\) 18575.7 + 10724.7i 0.165522 + 0.0955639i
\(336\) 0 0
\(337\) −22954.2 39757.8i −0.202117 0.350076i 0.747094 0.664719i \(-0.231449\pi\)
−0.949210 + 0.314643i \(0.898115\pi\)
\(338\) −4292.89 253051.i −0.0375765 2.21500i
\(339\) 0 0
\(340\) −96713.5 + 3282.34i −0.836622 + 0.0283940i
\(341\) 83558.1 0.718588
\(342\) 0 0
\(343\) 123305.i 1.04807i
\(344\) 73420.1 143573.i 0.620438 1.21326i
\(345\) 0 0
\(346\) 414.552 + 24436.4i 0.00346279 + 0.204120i
\(347\) 131615. 75987.9i 1.09306 0.631081i 0.158674 0.987331i \(-0.449278\pi\)
0.934391 + 0.356250i \(0.115945\pi\)
\(348\) 0 0
\(349\) 93645.6 162199.i 0.768841 1.33167i −0.169350 0.985556i \(-0.554167\pi\)
0.938192 0.346116i \(-0.112500\pi\)
\(350\) −42923.2 + 77346.0i −0.350393 + 0.631396i
\(351\) 0 0
\(352\) −42990.0 61717.6i −0.346962 0.498108i
\(353\) 22707.8 39331.1i 0.182232 0.315636i −0.760408 0.649446i \(-0.775001\pi\)
0.942640 + 0.333810i \(0.108334\pi\)
\(354\) 0 0
\(355\) 275326. 158960.i 2.18469 1.26133i
\(356\) −57594.8 + 108064.i −0.454447 + 0.852671i
\(357\) 0 0
\(358\) 23744.0 + 39560.6i 0.185263 + 0.308672i
\(359\) 71504.2i 0.554808i 0.960753 + 0.277404i \(0.0894740\pi\)
−0.960753 + 0.277404i \(0.910526\pi\)
\(360\) 0 0
\(361\) 31589.8 0.242400
\(362\) 87608.4 52582.0i 0.668542 0.401254i
\(363\) 0 0
\(364\) −197513. 105268.i −1.49071 0.794499i
\(365\) −31551.4 54648.7i −0.236828 0.410199i
\(366\) 0 0
\(367\) 57406.0 + 33143.4i 0.426211 + 0.246073i 0.697731 0.716360i \(-0.254193\pi\)
−0.271520 + 0.962433i \(0.587526\pi\)
\(368\) 77219.2 + 37850.0i 0.570203 + 0.279492i
\(369\) 0 0
\(370\) 117197. + 65038.4i 0.856076 + 0.475080i
\(371\) −42285.5 24413.5i −0.307216 0.177371i
\(372\) 0 0
\(373\) −71784.3 124334.i −0.515955 0.893660i −0.999828 0.0185223i \(-0.994104\pi\)
0.483873 0.875138i \(-0.339229\pi\)
\(374\) 53470.6 907.103i 0.382271 0.00648505i
\(375\) 0 0
\(376\) −32990.2 + 64512.1i −0.233351 + 0.456316i
\(377\) −216594. −1.52393
\(378\) 0 0
\(379\) 183178.i 1.27525i −0.770348 0.637624i \(-0.779917\pi\)
0.770348 0.637624i \(-0.220083\pi\)
\(380\) −5666.23 166954.i −0.0392398 1.15619i
\(381\) 0 0
\(382\) 156249. 2650.69i 1.07075 0.0181648i
\(383\) 15175.9 8761.79i 0.103456 0.0597303i −0.447379 0.894344i \(-0.647643\pi\)
0.550835 + 0.834614i \(0.314309\pi\)
\(384\) 0 0
\(385\) 56329.9 97566.3i 0.380030 0.658231i
\(386\) 97337.4 + 54017.4i 0.653288 + 0.362543i
\(387\) 0 0
\(388\) 107794. + 172884.i 0.716031 + 1.14839i
\(389\) 38430.8 66564.0i 0.253968 0.439886i −0.710646 0.703549i \(-0.751597\pi\)
0.964615 + 0.263663i \(0.0849307\pi\)
\(390\) 0 0
\(391\) −52952.8 + 30572.3i −0.346366 + 0.199974i
\(392\) 14518.6 9398.15i 0.0944827 0.0611604i
\(393\) 0 0
\(394\) −72376.5 + 43439.9i −0.466235 + 0.279831i
\(395\) 259679.i 1.66434i
\(396\) 0 0
\(397\) −73295.7 −0.465047 −0.232524 0.972591i \(-0.574698\pi\)
−0.232524 + 0.972591i \(0.574698\pi\)
\(398\) −11214.5 18684.8i −0.0707968 0.117957i
\(399\) 0 0
\(400\) 122362. 8315.25i 0.764765 0.0519703i
\(401\) 142274. + 246426.i 0.884784 + 1.53249i 0.845961 + 0.533244i \(0.179027\pi\)
0.0388226 + 0.999246i \(0.487639\pi\)
\(402\) 0 0
\(403\) −298550. 172368.i −1.83826 1.06132i
\(404\) 116369. + 186636.i 0.712973 + 1.14349i
\(405\) 0 0
\(406\) −64037.0 + 115392.i −0.388489 + 0.700044i
\(407\) −64148.4 37036.1i −0.387255 0.223582i
\(408\) 0 0
\(409\) 56577.0 + 97994.2i 0.338215 + 0.585806i 0.984097 0.177632i \(-0.0568435\pi\)
−0.645882 + 0.763437i \(0.723510\pi\)
\(410\) 2513.94 + 148188.i 0.0149550 + 0.881548i
\(411\) 0 0
\(412\) 7050.91 + 207753.i 0.0415385 + 1.22392i
\(413\) −46823.9 −0.274516
\(414\) 0 0
\(415\) 270593.i 1.57116i
\(416\) 26287.4 + 309197.i 0.151901 + 1.78669i
\(417\) 0 0
\(418\) 1565.91 + 92305.1i 0.00896220 + 0.528291i
\(419\) 237314. 137013.i 1.35175 0.780431i 0.363252 0.931691i \(-0.381666\pi\)
0.988494 + 0.151260i \(0.0483331\pi\)
\(420\) 0 0
\(421\) −6241.89 + 10811.3i −0.0352170 + 0.0609976i −0.883097 0.469191i \(-0.844546\pi\)
0.847880 + 0.530189i \(0.177879\pi\)
\(422\) 134328. 242054.i 0.754294 1.35921i
\(423\) 0 0
\(424\) 3443.55 + 67609.9i 0.0191547 + 0.376078i
\(425\) −43600.9 + 75518.9i −0.241389 + 0.418098i
\(426\) 0 0
\(427\) 34403.6 19862.9i 0.188690 0.108940i
\(428\) −210269. 112067.i −1.14786 0.611772i
\(429\) 0 0
\(430\) −172338. 287138.i −0.932062 1.55294i
\(431\) 119855.i 0.645211i 0.946533 + 0.322606i \(0.104559\pi\)
−0.946533 + 0.322606i \(0.895441\pi\)
\(432\) 0 0
\(433\) −282465. −1.50657 −0.753284 0.657696i \(-0.771531\pi\)
−0.753284 + 0.657696i \(0.771531\pi\)
\(434\) −180098. + 108094.i −0.956158 + 0.573880i
\(435\) 0 0
\(436\) 56734.1 106449.i 0.298450 0.559977i
\(437\) −52776.3 91411.2i −0.276360 0.478670i
\(438\) 0 0
\(439\) 148459. + 85712.8i 0.770331 + 0.444751i 0.832993 0.553284i \(-0.186626\pi\)
−0.0626618 + 0.998035i \(0.519959\pi\)
\(440\) −155998. + 7945.39i −0.805774 + 0.0410402i
\(441\) 0 0
\(442\) −192920. 107061.i −0.987488 0.548007i
\(443\) −71888.2 41504.7i −0.366311 0.211490i 0.305535 0.952181i \(-0.401165\pi\)
−0.671846 + 0.740691i \(0.734498\pi\)
\(444\) 0 0
\(445\) 127152. + 220234.i 0.642102 + 1.11215i
\(446\) −101296. + 1718.45i −0.509242 + 0.00863905i
\(447\) 0 0
\(448\) 172499. + 77410.5i 0.859470 + 0.385695i
\(449\) −252767. −1.25380 −0.626898 0.779101i \(-0.715676\pi\)
−0.626898 + 0.779101i \(0.715676\pi\)
\(450\) 0 0
\(451\) 81906.2i 0.402683i
\(452\) −15867.3 + 538.519i −0.0776653 + 0.00263587i
\(453\) 0 0
\(454\) −388774. + 6595.37i −1.88619 + 0.0319983i
\(455\) −402530. + 232401.i −1.94435 + 1.12257i
\(456\) 0 0
\(457\) 9489.80 16436.8i 0.0454386 0.0787019i −0.842412 0.538835i \(-0.818865\pi\)
0.887850 + 0.460133i \(0.152198\pi\)
\(458\) −300412. 166714.i −1.43214 0.794769i
\(459\) 0 0
\(460\) 151547. 94490.7i 0.716197 0.446554i
\(461\) −97075.9 + 168140.i −0.456783 + 0.791171i −0.998789 0.0492038i \(-0.984332\pi\)
0.542006 + 0.840375i \(0.317665\pi\)
\(462\) 0 0
\(463\) 86227.9 49783.7i 0.402240 0.232234i −0.285210 0.958465i \(-0.592063\pi\)
0.687450 + 0.726232i \(0.258730\pi\)
\(464\) 182552. 12405.5i 0.847914 0.0576208i
\(465\) 0 0
\(466\) −43810.9 + 26295.0i −0.201748 + 0.121088i
\(467\) 126990.i 0.582287i 0.956679 + 0.291144i \(0.0940358\pi\)
−0.956679 + 0.291144i \(0.905964\pi\)
\(468\) 0 0
\(469\) 29797.6 0.135468
\(470\) 77437.5 + 129021.i 0.350555 + 0.584069i
\(471\) 0 0
\(472\) 35277.9 + 54498.5i 0.158350 + 0.244625i
\(473\) 92535.3 + 160276.i 0.413605 + 0.716384i
\(474\) 0 0
\(475\) −130367. 75267.2i −0.577802 0.333594i
\(476\) −114075. + 71126.6i −0.503474 + 0.313919i
\(477\) 0 0
\(478\) 205628. 370535.i 0.899969 1.62171i
\(479\) 48437.8 + 27965.6i 0.211112 + 0.121886i 0.601828 0.798626i \(-0.294439\pi\)
−0.390716 + 0.920511i \(0.627773\pi\)
\(480\) 0 0
\(481\) 152800. + 264657.i 0.660439 + 1.14391i
\(482\) 690.660 + 40712.0i 0.00297283 + 0.175238i
\(483\) 0 0
\(484\) −147849. + 5017.82i −0.631142 + 0.0214202i
\(485\) 423105. 1.79872
\(486\) 0 0
\(487\) 274913.i 1.15914i 0.814921 + 0.579572i \(0.196780\pi\)
−0.814921 + 0.579572i \(0.803220\pi\)
\(488\) −49038.8 25077.5i −0.205921 0.105304i
\(489\) 0 0
\(490\) −609.226 35911.8i −0.00253739 0.149570i
\(491\) −28037.6 + 16187.5i −0.116299 + 0.0671455i −0.557021 0.830498i \(-0.688056\pi\)
0.440722 + 0.897644i \(0.354723\pi\)
\(492\) 0 0
\(493\) −65048.1 + 112667.i −0.267634 + 0.463555i
\(494\) 184817. 333033.i 0.757334 1.36469i
\(495\) 0 0
\(496\) 261500. + 128178.i 1.06294 + 0.521013i
\(497\) 220828. 382485.i 0.894008 1.54847i
\(498\) 0 0
\(499\) −251446. + 145172.i −1.00982 + 0.583019i −0.911139 0.412100i \(-0.864796\pi\)
−0.0986806 + 0.995119i \(0.531462\pi\)
\(500\) −36487.4 + 68460.7i −0.145950 + 0.273843i
\(501\) 0 0
\(502\) 44973.7 + 74932.1i 0.178464 + 0.297345i
\(503\) 9486.90i 0.0374963i −0.999824 0.0187481i \(-0.994032\pi\)
0.999824 0.0187481i \(-0.00596807\pi\)
\(504\) 0 0
\(505\) 456761. 1.79104
\(506\) −84624.4 + 50791.0i −0.330518 + 0.198375i
\(507\) 0 0
\(508\) −100583. 53607.3i −0.389758 0.207729i
\(509\) −146376. 253530.i −0.564980 0.978575i −0.997052 0.0767350i \(-0.975550\pi\)
0.432071 0.901839i \(-0.357783\pi\)
\(510\) 0 0
\(511\) −75918.5 43831.5i −0.290741 0.167859i
\(512\) −39865.2 259095.i −0.152074 0.988369i
\(513\) 0 0
\(514\) −194328. 107842.i −0.735544 0.408190i
\(515\) 373860. + 215848.i 1.40960 + 0.813831i
\(516\) 0 0
\(517\) −41579.3 72017.4i −0.155559 0.269437i
\(518\) 186174. 3158.36i 0.693841 0.0117707i
\(519\) 0 0
\(520\) 573765. + 293412.i 2.12191 + 1.08510i
\(521\) 344253. 1.26824 0.634120 0.773234i \(-0.281362\pi\)
0.634120 + 0.773234i \(0.281362\pi\)
\(522\) 0 0
\(523\) 79326.1i 0.290010i 0.989431 + 0.145005i \(0.0463198\pi\)
−0.989431 + 0.145005i \(0.953680\pi\)
\(524\) 3777.01 + 111289.i 0.0137558 + 0.405312i
\(525\) 0 0
\(526\) 100639. 1707.29i 0.363742 0.00617071i
\(527\) −179323. + 103532.i −0.645675 + 0.372780i
\(528\) 0 0
\(529\) −83497.9 + 144623.i −0.298376 + 0.516803i
\(530\) 122929. + 68219.5i 0.437625 + 0.242860i
\(531\) 0 0
\(532\) −122784. 196925.i −0.433830 0.695790i
\(533\) −168960. + 292648.i −0.594744 + 1.03013i
\(534\) 0 0
\(535\) −428527. + 247410.i −1.49717 + 0.864391i
\(536\) −22450.0 34681.6i −0.0781424 0.120717i
\(537\) 0 0
\(538\) 185731. 111474.i 0.641681 0.385133i
\(539\) 19849.0i 0.0683223i
\(540\) 0 0
\(541\) 167330. 0.571715 0.285857 0.958272i \(-0.407722\pi\)
0.285857 + 0.958272i \(0.407722\pi\)
\(542\) −195436. 325622.i −0.665283 1.10845i
\(543\) 0 0
\(544\) 168731. + 79184.7i 0.570159 + 0.267574i
\(545\) −125252. 216943.i −0.421689 0.730387i
\(546\) 0 0
\(547\) 246877. + 142535.i 0.825100 + 0.476372i 0.852172 0.523262i \(-0.175285\pi\)
−0.0270722 + 0.999633i \(0.508618\pi\)
\(548\) 71861.5 + 115254.i 0.239296 + 0.383790i
\(549\) 0 0
\(550\) −68300.6 + 123075.i −0.225787 + 0.406860i
\(551\) −194494. 112291.i −0.640623 0.369864i
\(552\) 0 0
\(553\) −180374. 312417.i −0.589827 1.02161i
\(554\) −7330.30 432096.i −0.0238837 1.40786i
\(555\) 0 0
\(556\) −11583.2 341297.i −0.0374696 1.10403i
\(557\) −51271.9 −0.165260 −0.0826302 0.996580i \(-0.526332\pi\)
−0.0826302 + 0.996580i \(0.526332\pi\)
\(558\) 0 0
\(559\) 763547.i 2.44350i
\(560\) 325954. 218930.i 1.03939 0.698117i
\(561\) 0 0
\(562\) −4676.52 275665.i −0.0148064 0.872787i
\(563\) −2488.80 + 1436.91i −0.00785187 + 0.00453328i −0.503921 0.863750i \(-0.668110\pi\)
0.496069 + 0.868283i \(0.334776\pi\)
\(564\) 0 0
\(565\) −16485.6 + 28553.9i −0.0516425 + 0.0894474i
\(566\) −87753.2 + 158128.i −0.273924 + 0.493601i
\(567\) 0 0
\(568\) −611552. + 31148.0i −1.89556 + 0.0965458i
\(569\) −56876.7 + 98513.3i −0.175675 + 0.304278i −0.940395 0.340085i \(-0.889544\pi\)
0.764720 + 0.644363i \(0.222877\pi\)
\(570\) 0 0
\(571\) 27258.4 15737.7i 0.0836043 0.0482689i −0.457615 0.889150i \(-0.651296\pi\)
0.541219 + 0.840881i \(0.317963\pi\)
\(572\) −314288. 167505.i −0.960585 0.511961i
\(573\) 0 0
\(574\) 105957. + 176538.i 0.321592 + 0.535813i
\(575\) 160935.i 0.486760i
\(576\) 0 0
\(577\) −654654. −1.96635 −0.983174 0.182671i \(-0.941526\pi\)
−0.983174 + 0.182671i \(0.941526\pi\)
\(578\) 172822. 103727.i 0.517301 0.310480i
\(579\) 0 0
\(580\) 178722. 335333.i 0.531278 0.996829i
\(581\) 187955. + 325548.i 0.556803 + 0.964412i
\(582\) 0 0
\(583\) −67285.9 38847.5i −0.197964 0.114295i
\(584\) 6182.48 + 121385.i 0.0181275 + 0.355910i
\(585\) 0 0
\(586\) 250798. + 139180.i 0.730346 + 0.405306i
\(587\) 557280. + 321746.i 1.61732 + 0.933763i 0.987609 + 0.156937i \(0.0501620\pi\)
0.629716 + 0.776825i \(0.283171\pi\)
\(588\) 0 0
\(589\) −178725. 309561.i −0.515175 0.892309i
\(590\) 134802. 2286.86i 0.387251 0.00656954i
\(591\) 0 0
\(592\) −143943. 214310.i −0.410721 0.611503i
\(593\) 183090. 0.520661 0.260330 0.965520i \(-0.416169\pi\)
0.260330 + 0.965520i \(0.416169\pi\)
\(594\) 0 0
\(595\) 279180.i 0.788589i
\(596\) −203620. + 6910.62i −0.573228 + 0.0194547i
\(597\) 0 0
\(598\) 407134. 6906.84i 1.13851 0.0193142i
\(599\) 24104.3 13916.6i 0.0671800 0.0387864i −0.466034 0.884767i \(-0.654317\pi\)
0.533214 + 0.845981i \(0.320984\pi\)
\(600\) 0 0
\(601\) 135764. 235150.i 0.375868 0.651022i −0.614589 0.788848i \(-0.710678\pi\)
0.990457 + 0.137826i \(0.0440113\pi\)
\(602\) −406786. 225746.i −1.12247 0.622912i
\(603\) 0 0
\(604\) 48001.8 29929.5i 0.131578 0.0820399i
\(605\) −153610. + 266060.i −0.419670 + 0.726889i
\(606\) 0 0
\(607\) −86991.8 + 50224.8i −0.236103 + 0.136314i −0.613384 0.789785i \(-0.710192\pi\)
0.377281 + 0.926099i \(0.376859\pi\)
\(608\) −136695. + 291276.i −0.369781 + 0.787948i
\(609\) 0 0
\(610\) −98075.2 + 58864.1i −0.263572 + 0.158194i
\(611\) 343088.i 0.919015i
\(612\) 0 0
\(613\) 458408. 1.21992 0.609960 0.792432i \(-0.291185\pi\)
0.609960 + 0.792432i \(0.291185\pi\)
\(614\) 197339. + 328793.i 0.523451 + 0.872138i
\(615\) 0 0
\(616\) −182161. + 117916.i −0.480057 + 0.310750i
\(617\) −237317. 411046.i −0.623389 1.07974i −0.988850 0.148915i \(-0.952422\pi\)
0.365461 0.930827i \(-0.380911\pi\)
\(618\) 0 0
\(619\) 5714.30 + 3299.15i 0.0149136 + 0.00861036i 0.507438 0.861688i \(-0.330593\pi\)
−0.492525 + 0.870298i \(0.663926\pi\)
\(620\) 513209. 319989.i 1.33509 0.832438i
\(621\) 0 0
\(622\) −46715.9 + 84180.4i −0.120749 + 0.217586i
\(623\) 305951. + 176641.i 0.788272 + 0.455109i
\(624\) 0 0
\(625\) 230266. + 398833.i 0.589481 + 1.02101i
\(626\) 6737.96 + 397179.i 0.0171941 + 1.01353i
\(627\) 0 0
\(628\) −475584. + 16140.8i −1.20589 + 0.0409265i
\(629\) 183557. 0.463948
\(630\) 0 0
\(631\) 102946.i 0.258553i 0.991609 + 0.129277i \(0.0412655\pi\)
−0.991609 + 0.129277i \(0.958734\pi\)
\(632\) −227727. + 445319.i −0.570139 + 1.11490i
\(633\) 0 0
\(634\) 4032.97 + 237730.i 0.0100334 + 0.591432i
\(635\) −204987. + 118349.i −0.508368 + 0.293506i
\(636\) 0 0
\(637\) 40945.7 70919.9i 0.100909 0.174779i
\(638\) −101898. + 183616.i −0.250336 + 0.451096i
\(639\) 0 0
\(640\) −500392. 214434.i −1.22166 0.523521i
\(641\) 202403. 350572.i 0.492607 0.853221i −0.507356 0.861736i \(-0.669377\pi\)
0.999964 + 0.00851530i \(0.00271054\pi\)
\(642\) 0 0
\(643\) 426111. 246015.i 1.03063 0.595032i 0.113462 0.993542i \(-0.463806\pi\)
0.917164 + 0.398510i \(0.130473\pi\)
\(644\) 116691. 218946.i 0.281363 0.527917i
\(645\) 0 0
\(646\) −117730. 196154.i −0.282113 0.470037i
\(647\) 306912.i 0.733171i −0.930384 0.366586i \(-0.880527\pi\)
0.930384 0.366586i \(-0.119473\pi\)
\(648\) 0 0
\(649\) −74507.5 −0.176893
\(650\) 497922. 298849.i 1.17851 0.707335i
\(651\) 0 0
\(652\) 83362.7 + 44429.7i 0.196100 + 0.104515i
\(653\) 97661.8 + 169155.i 0.229033 + 0.396697i 0.957522 0.288361i \(-0.0931103\pi\)
−0.728489 + 0.685058i \(0.759777\pi\)
\(654\) 0 0
\(655\) 200269. + 115625.i 0.466799 + 0.269507i
\(656\) 125644. 256330.i 0.291966 0.595651i
\(657\) 0 0
\(658\) 182783. + 101435.i 0.422166 + 0.234281i
\(659\) −678872. 391947.i −1.56321 0.902519i −0.996929 0.0783055i \(-0.975049\pi\)
−0.566279 0.824213i \(1.30838\pi\)
\(660\) 0 0
\(661\) −371075. 642721.i −0.849295 1.47102i −0.881838 0.471552i \(-0.843694\pi\)
0.0325431 0.999470i \(-0.489639\pi\)
\(662\) −368768. + 6255.97i −0.841467 + 0.0142751i
\(663\) 0 0
\(664\) 237298. 464035.i 0.538218 1.05248i
\(665\) −481943. −1.08981
\(666\) 0 0
\(667\) 240099.i 0.539682i
\(668\) 11161.4 + 328867.i 0.0250129 + 0.737000i
\(669\) 0 0
\(670\) −85784.9 + 1455.30i −0.191100 + 0.00324193i
\(671\) 54744.0 31606.5i 0.121588 0.0701990i
\(672\) 0 0
\(673\) −211601. + 366503.i −0.467183 + 0.809185i −0.999297 0.0374878i \(-0.988064\pi\)
0.532114 + 0.846673i \(0.321398\pi\)
\(674\) 160566. + 89106.0i 0.353454 + 0.196149i
\(675\) 0 0
\(676\) 535621. + 859046.i 1.17210 + 1.87985i
\(677\) 154122. 266947.i 0.336269 0.582435i −0.647459 0.762100i \(-0.724168\pi\)
0.983728 + 0.179665i \(0.0575015\pi\)
\(678\) 0 0
\(679\) 509034. 293891.i 1.10410 0.637450i
\(680\) 324940. 210339.i 0.702724 0.454886i
\(681\) 0 0
\(682\) −286577. + 172002.i −0.616131 + 0.369798i
\(683\) 760287.i 1.62981i −0.579597 0.814903i \(-0.696790\pi\)
0.579597 0.814903i \(-0.303210\pi\)
\(684\) 0 0
\(685\) 282065. 0.601130
\(686\) −253819. 422896.i −0.539357 0.898639i
\(687\) 0 0
\(688\) 43732.4 + 643541.i 0.0923904 + 1.35956i
\(689\) 160273. + 277602.i 0.337616 + 0.584768i
\(690\) 0 0
\(691\) 313235. + 180846.i 0.656016 + 0.378751i 0.790757 0.612130i \(-0.209687\pi\)
−0.134742 + 0.990881i \(0.543020\pi\)
\(692\) −51723.4 82955.6i −0.108013 0.173234i
\(693\) 0 0
\(694\) −294978. + 531539.i −0.612450 + 1.10361i
\(695\) −614177. 354595.i −1.27152 0.734113i
\(696\) 0 0
\(697\) 101485. + 175777.i 0.208899 + 0.361824i
\(698\) 12707.4 + 749057.i 0.0260823 + 1.53746i
\(699\) 0 0
\(700\) −12001.7 353628.i −0.0244933 0.721690i
\(701\) −878492. −1.78773 −0.893864 0.448337i \(-0.852016\pi\)
−0.893864 + 0.448337i \(0.852016\pi\)
\(702\) 0 0
\(703\) 316870.i 0.641167i
\(704\) 274486. + 123178.i 0.553827 + 0.248535i
\(705\) 0 0
\(706\) 3081.37 + 181636.i 0.00618208 + 0.364412i
\(707\) 549525. 317268.i 1.09938 0.634728i
\(708\) 0 0
\(709\) −431190. + 746844.i −0.857781 + 1.48572i 0.0162593 + 0.999868i \(0.494824\pi\)
−0.874041 + 0.485853i \(0.838509\pi\)
\(710\) −617066. + 1.11193e6i −1.22409 + 2.20577i
\(711\) 0 0
\(712\) −24915.4 489183.i −0.0491482 0.964964i
\(713\) 191073. 330948.i 0.375855 0.651000i
\(714\) 0 0
\(715\) −640517. + 369803.i −1.25291 + 0.723366i
\(716\) −162869. 86803.9i −0.317696 0.169322i
\(717\) 0 0
\(718\) −147189. 245236.i −0.285514 0.475703i
\(719\) 424008.i 0.820193i 0.912042 + 0.410097i \(0.134505\pi\)
−0.912042 + 0.410097i \(0.865495\pi\)
\(720\) 0 0
\(721\) 599717. 1.15365
\(722\) −108343. + 65026.6i −0.207838 + 0.124743i
\(723\) 0 0
\(724\) −192230. + 360679.i −0.366728 + 0.688087i
\(725\) −171209. 296543.i −0.325725 0.564172i
\(726\) 0 0
\(727\) −78836.8 45516.5i −0.149163 0.0861191i 0.423561 0.905868i \(-0.360780\pi\)
−0.572724 + 0.819748i \(0.694113\pi\)
\(728\) 894096. 45538.7i 1.68702 0.0859247i
\(729\) 0 0
\(730\) 220704. + 122480.i 0.414157 + 0.229836i
\(731\) −397177. 229310.i −0.743275 0.429130i
\(732\) 0 0
\(733\) 6638.99 + 11499.1i 0.0123565 + 0.0214020i 0.872138 0.489261i \(-0.162733\pi\)
−0.859781 + 0.510663i \(0.829400\pi\)
\(734\) −265109. + 4497.44i −0.492076 + 0.00834783i
\(735\) 0 0
\(736\) −342750. + 29140.1i −0.632735 + 0.0537942i
\(737\) 47414.8 0.0872929
\(738\) 0 0
\(739\) 622195.i 1.13930i −0.821888 0.569650i \(-0.807079\pi\)
0.821888 0.569650i \(-0.192921\pi\)
\(740\) −535827. + 18185.3i −0.978501 + 0.0332092i
\(741\) 0 0
\(742\) 195280. 3312.84i 0.354691 0.00601717i
\(743\) 606588. 350214.i 1.09879 0.634389i 0.162890 0.986644i \(-0.447918\pi\)
0.935904 + 0.352255i \(0.114585\pi\)
\(744\) 0 0
\(745\) −211554. + 366422.i −0.381161 + 0.660189i
\(746\) 502135. + 278660.i 0.902283 + 0.500722i
\(747\) 0 0
\(748\) −181520. + 113179.i −0.324430 + 0.202284i
\(749\) −343705. + 595314.i −0.612663 + 1.06116i
\(750\) 0 0
\(751\) 73727.4 42566.6i 0.130722 0.0754725i −0.433213 0.901292i \(-0.642620\pi\)
0.563935 + 0.825819i \(0.309287\pi\)
\(752\) −19650.5 289165.i −0.0347486 0.511340i
\(753\) 0 0
\(754\) 742849. 445853.i 1.30665 0.784240i
\(755\) 117477.i 0.206091i
\(756\) 0 0
\(757\) 319528. 0.557592 0.278796 0.960350i \(-0.410065\pi\)
0.278796 + 0.960350i \(0.410065\pi\)
\(758\) 377066. + 628241.i 0.656265 + 1.09342i
\(759\) 0 0
\(760\) 363104. + 560936.i 0.628643 + 0.971150i
\(761\) 376888. + 652790.i 0.650794 + 1.12721i 0.982931 + 0.183977i \(0.0588971\pi\)
−0.332137 + 0.943231i \(0.607770\pi\)
\(762\) 0 0
\(763\) −301379. 174001.i −0.517684 0.298885i
\(764\) −530426. + 330724.i −0.908737 + 0.566604i
\(765\) 0 0
\(766\) −34012.4 + 61289.2i −0.0579669 + 0.104454i
\(767\) 266213. + 153698.i 0.452520 + 0.261263i
\(768\) 0 0
\(769\) −425156. 736392.i −0.718945 1.24525i −0.961418 0.275091i \(-0.911292\pi\)
0.242473 0.970158i \(-0.422041\pi\)
\(770\) 7643.78 + 450575.i 0.0128922 + 0.759950i
\(771\) 0 0
\(772\) −445029. + 15103.8i −0.746713 + 0.0253426i
\(773\) −13034.7 −0.0218143 −0.0109071 0.999941i \(-0.503472\pi\)
−0.0109071 + 0.999941i \(0.503472\pi\)
\(774\) 0 0
\(775\) 545000.i 0.907388i
\(776\) −725575. 371045.i −1.20492 0.616173i