Properties

Label 108.5.f.a.91.11
Level 108
Weight 5
Character 108.91
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 91.11
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.0678484 - 3.99942i) q^{2} +(-15.9908 + 0.542709i) q^{4} +(-16.6139 + 28.7760i) q^{5} +(39.9759 - 23.0801i) q^{7} +(3.25547 + 63.9171i) q^{8} +O(q^{10})\) \(q+(-0.0678484 - 3.99942i) q^{2} +(-15.9908 + 0.542709i) q^{4} +(-16.6139 + 28.7760i) q^{5} +(39.9759 - 23.0801i) q^{7} +(3.25547 + 63.9171i) q^{8} +(116.215 + 64.4935i) q^{10} +(63.6109 - 36.7258i) q^{11} +(151.520 - 262.440i) q^{13} +(-95.0195 - 158.315i) q^{14} +(255.411 - 17.3567i) q^{16} +182.019 q^{17} +314.215i q^{19} +(250.052 - 469.168i) q^{20} +(-151.198 - 251.915i) q^{22} +(290.919 + 167.962i) q^{23} +(-239.540 - 414.896i) q^{25} +(-1059.89 - 588.185i) q^{26} +(-626.721 + 390.765i) q^{28} +(-357.370 - 618.983i) q^{29} +(985.186 + 568.798i) q^{31} +(-86.7460 - 1020.32i) q^{32} +(-12.3497 - 727.971i) q^{34} +1533.80i q^{35} +1008.45 q^{37} +(1256.68 - 21.3190i) q^{38} +(-1893.37 - 968.231i) q^{40} +(557.553 - 965.709i) q^{41} +(2182.06 - 1259.82i) q^{43} +(-997.257 + 621.796i) q^{44} +(652.014 - 1174.90i) q^{46} +(-980.476 + 566.078i) q^{47} +(-135.117 + 234.029i) q^{49} +(-1643.09 + 986.173i) q^{50} +(-2280.49 + 4278.85i) q^{52} +1057.77 q^{53} +2440.63i q^{55} +(1605.36 + 2480.01i) q^{56} +(-2451.33 + 1471.27i) q^{58} +(-878.476 - 507.188i) q^{59} +(-430.304 - 745.308i) q^{61} +(2208.02 - 3978.77i) q^{62} +(-4074.80 + 416.161i) q^{64} +(5034.65 + 8720.27i) q^{65} +(559.041 + 322.762i) q^{67} +(-2910.63 + 98.7833i) q^{68} +(6134.31 - 104.066i) q^{70} +9567.89i q^{71} +1899.10 q^{73} +(-68.4216 - 4033.22i) q^{74} +(-170.527 - 5024.55i) q^{76} +(1695.27 - 2936.29i) q^{77} +(-6768.11 + 3907.57i) q^{79} +(-3743.90 + 7638.08i) q^{80} +(-3900.11 - 2164.37i) q^{82} +(7052.56 - 4071.80i) q^{83} +(-3024.04 + 5237.78i) q^{85} +(-5186.58 - 8641.52i) q^{86} +(2554.49 + 3946.27i) q^{88} -7653.39 q^{89} -13988.4i q^{91} +(-4743.18 - 2527.96i) q^{92} +(2330.51 + 3882.93i) q^{94} +(-9041.87 - 5220.33i) q^{95} +(-6366.75 - 11027.5i) q^{97} +(945.149 + 524.510i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0678484 3.99942i −0.0169621 0.999856i
\(3\) 0 0
\(4\) −15.9908 + 0.542709i −0.999425 + 0.0339193i
\(5\) −16.6139 + 28.7760i −0.664554 + 1.15104i 0.314852 + 0.949141i \(0.398045\pi\)
−0.979406 + 0.201901i \(0.935288\pi\)
\(6\) 0 0
\(7\) 39.9759 23.0801i 0.815835 0.471023i −0.0331429 0.999451i \(-0.510552\pi\)
0.848978 + 0.528428i \(0.177218\pi\)
\(8\) 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 \(-0.568505\pi\)
0.739268 + 0.673412i \(0.235172\pi\)
\(12\) 0 0
\(13\) 151.520 262.440i 0.896566 1.55290i 0.0647110 0.997904i \(-0.479387\pi\)
0.831855 0.554993i \(-0.187279\pi\)
\(14\) −95.0195 158.315i −0.484793 0.807728i
\(15\) 0 0
\(16\) 255.411 17.3567i 0.997699 0.0677996i
\(17\) 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 \(0.856677\pi\)
\(20\) 250.052 469.168i 0.625129 1.17292i
\(21\) 0 0
\(22\) −151.198 251.915i −0.312392 0.520486i
\(23\) 290.919 + 167.962i 0.549941 + 0.317509i 0.749098 0.662459i \(-0.230487\pi\)
−0.199157 + 0.979968i \(0.563820\pi\)
\(24\) 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 0.571480 0.820616i \(-0.306370\pi\)
−0.996414 + 0.0846079i \(0.973036\pi\)
\(30\) 0 0
\(31\) 985.186 + 568.798i 1.02517 + 0.591881i 0.915597 0.402098i \(-0.131719\pi\)
0.109571 + 0.993979i \(0.465052\pi\)
\(32\) −86.7460 1020.32i −0.0847129 0.996405i
\(33\) 0 0
\(34\) −12.3497 727.971i −0.0106831 0.629733i
\(35\) 1533.80i 1.25208i
\(36\) 0 0
\(37\) 1008.45 0.736632 0.368316 0.929701i \(-0.379934\pi\)
0.368316 + 0.929701i \(0.379934\pi\)
\(38\) 1256.68 21.3190i 0.870277 0.0147638i
\(39\) 0 0
\(40\) −1893.37 968.231i −1.18336 0.605144i
\(41\) 557.553 965.709i 0.331679 0.574485i −0.651162 0.758939i \(-0.725718\pi\)
0.982841 + 0.184454i \(0.0590516\pi\)
\(42\) 0 0
\(43\) 2182.06 1259.82i 1.18013 0.681349i 0.224087 0.974569i \(-0.428060\pi\)
0.956045 + 0.293220i \(0.0947268\pi\)
\(44\) −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 \(-0.749157\pi\)
0.261376 + 0.965237i \(0.415824\pi\)
\(48\) 0 0
\(49\) −135.117 + 234.029i −0.0562752 + 0.0974714i
\(50\) −1643.09 + 986.173i −0.657237 + 0.394469i
\(51\) 0 0
\(52\) −2280.49 + 4278.85i −0.843377 + 1.58241i
\(53\) 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
\(56\) 1605.36 + 2480.01i 0.511912 + 0.790820i
\(57\) 0 0
\(58\) −2451.33 + 1471.27i −0.728695 + 0.437358i
\(59\) −878.476 507.188i −0.252363 0.145702i 0.368483 0.929635i \(-0.379877\pi\)
−0.620846 + 0.783933i \(0.713211\pi\)
\(60\) 0 0
\(61\) −430.304 745.308i −0.115642 0.200298i 0.802394 0.596794i \(-0.203559\pi\)
−0.918036 + 0.396497i \(0.870226\pi\)
\(62\) 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 \(-0.310427\pi\)
−0.436438 + 0.899734i \(0.643760\pi\)
\(68\) −2910.63 + 98.7833i −0.629461 + 0.0213632i
\(69\) 0 0
\(70\) 6134.31 104.066i 1.25190 0.0212379i
\(71\) 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 \(0.442977\pi\)
\(74\) −68.4216 4033.22i −0.0124948 0.736526i
\(75\) 0 0
\(76\) −170.527 5024.55i −0.0295234 0.869902i
\(77\) 1695.27 2936.29i 0.285928 0.495242i
\(78\) 0 0
\(79\) −6768.11 + 3907.57i −1.08446 + 0.626113i −0.932096 0.362212i \(-0.882022\pi\)
−0.152363 + 0.988325i \(0.548688\pi\)
\(80\) −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 \(-0.465377\pi\)
0.915186 + 0.403032i \(0.132044\pi\)
\(84\) 0 0
\(85\) −3024.04 + 5237.78i −0.418552 + 0.724953i
\(86\) −5186.58 8641.52i −0.701269 1.16840i
\(87\) 0 0
\(88\) 2554.49 + 3946.27i 0.329867 + 0.509590i
\(89\) −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
\(92\) −4743.18 2527.96i −0.560395 0.298673i
\(93\) 0 0
\(94\) 2330.51 + 3882.93i 0.263752 + 0.439445i
\(95\) −9041.87 5220.33i −1.00187 0.578430i
\(96\) 0 0
\(97\) −6366.75 11027.5i −0.676666 1.17202i −0.975979 0.217865i \(-0.930091\pi\)
0.299313 0.954155i \(-0.403243\pi\)
\(98\) 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 −0.976825 0.214040i \(-0.931338\pi\)
0.303048 0.952975i \(-0.401996\pi\)
\(102\) 0 0
\(103\) 11251.5 + 6496.03i 1.06056 + 0.612313i 0.925587 0.378536i \(-0.123572\pi\)
0.134971 + 0.990850i \(0.456906\pi\)
\(104\) 17267.7 + 8830.34i 1.59649 + 0.816414i
\(105\) 0 0
\(106\) −71.7682 4230.49i −0.00638734 0.376512i
\(107\) 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 \(0.397233\pi\)
\(110\) 9761.10 165.592i 0.806702 0.0136853i
\(111\) 0 0
\(112\) 9809.70 6588.76i 0.782023 0.525252i
\(113\) −496.140 + 859.339i −0.0388550 + 0.0672988i −0.884799 0.465973i \(-0.845704\pi\)
0.845944 + 0.533272i \(0.179038\pi\)
\(114\) 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
\(122\) −2951.61 + 1771.54i −0.198307 + 0.119023i
\(123\) 0 0
\(124\) −16062.6 8560.86i −1.04465 0.556767i
\(125\) −4848.57 −0.310308
\(126\) 0 0
\(127\) 7123.52i 0.441659i −0.975312 0.220829i \(-0.929124\pi\)
0.975312 0.220829i \(-0.0708764\pi\)
\(128\) 1940.87 + 16268.6i 0.118461 + 0.992959i
\(129\) 0 0
\(130\) 34534.5 20727.4i 2.04346 1.22647i
\(131\) 6027.16 + 3479.78i 0.351212 + 0.202773i 0.665219 0.746648i \(-0.268338\pi\)
−0.314007 + 0.949421i \(0.601671\pi\)
\(132\) 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 0.730521 0.682891i \(-0.239277\pi\)
−0.956661 + 0.291204i \(0.905944\pi\)
\(138\) 0 0
\(139\) −18483.9 10671.7i −0.956673 0.552335i −0.0615252 0.998106i \(-0.519596\pi\)
−0.895147 + 0.445770i \(0.852930\pi\)
\(140\) −832.406 24526.7i −0.0424697 1.25136i
\(141\) 0 0
\(142\) 38266.1 649.166i 1.89774 0.0321943i
\(143\) 22258.7i 1.08850i
\(144\) 0 0
\(145\) 23749.2 1.12957
\(146\) −128.851 7595.32i −0.00604481 0.356320i
\(147\) 0 0
\(148\) −16125.9 + 547.294i −0.736208 + 0.0249860i
\(149\) −6366.78 + 11027.6i −0.286779 + 0.496716i −0.973039 0.230640i \(-0.925918\pi\)
0.686260 + 0.727356i \(0.259251\pi\)
\(150\) 0 0
\(151\) −3061.84 + 1767.75i −0.134285 + 0.0775296i −0.565638 0.824654i \(-0.691370\pi\)
0.431352 + 0.902184i \(0.358037\pi\)
\(152\) −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 0.389027 + 0.921227i \(0.372811\pi\)
−0.992319 + 0.123706i \(0.960522\pi\)
\(158\) 16087.2 + 26803.4i 0.644417 + 1.07368i
\(159\) 0 0
\(160\) 30801.9 + 14455.2i 1.20320 + 0.564657i
\(161\) 15506.3 0.598216
\(162\) 0 0
\(163\) 5903.96i 0.222213i 0.993809 + 0.111106i \(0.0354394\pi\)
−0.993809 + 0.111106i \(0.964561\pi\)
\(164\) −8391.61 + 15745.0i −0.312002 + 0.585405i
\(165\) 0 0
\(166\) −16763.4 27929.9i −0.608338 1.01357i
\(167\) 17810.7 + 10283.0i 0.638628 + 0.368712i 0.784086 0.620652i \(-0.213132\pi\)
−0.145458 + 0.989364i \(0.546465\pi\)
\(168\) 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 0.912539 0.408989i \(-0.134119\pi\)
−0.810465 + 0.585787i \(0.800785\pi\)
\(174\) 0 0
\(175\) −19151.7 11057.2i −0.625361 0.361053i
\(176\) 15609.5 10484.2i 0.503922 0.338463i
\(177\) 0 0
\(178\) 519.270 + 30609.1i 0.0163890 + 0.966076i
\(179\) 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 \(0.627475\pi\)
\(182\) −55945.4 + 949.087i −1.68897 + 0.0286526i
\(183\) 0 0
\(184\) −9788.59 + 19141.5i −0.289124 + 0.565380i
\(185\) −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 \(-0.486807\pi\)
0.885999 + 0.463687i \(0.153474\pi\)
\(192\) 0 0
\(193\) −13915.2 + 24101.8i −0.373572 + 0.647045i −0.990112 0.140278i \(-0.955200\pi\)
0.616541 + 0.787323i \(0.288534\pi\)
\(194\) −43671.8 + 26211.5i −1.16037 + 0.696449i
\(195\) 0 0
\(196\) 2033.61 3815.64i 0.0529366 0.0993242i
\(197\) 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 \(0.978087\pi\)
\(200\) 25739.2 16661.4i 0.643479 0.416535i
\(201\) 0 0
\(202\) −47145.7 + 28296.5i −1.15542 + 0.693475i
\(203\) −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 \(-0.0499520\pi\)
0.358509 + 0.933526i \(0.383285\pi\)
\(212\) −16914.6 + 574.063i −0.376349 + 0.0127729i
\(213\) 0 0
\(214\) −59558.7 + 1010.38i −1.30052 + 0.0220627i
\(215\) 83721.5i 1.81117i
\(216\) 0 0
\(217\) 52511.7 1.11516
\(218\) −511.510 30151.8i −0.0107632 0.634453i
\(219\) 0 0
\(220\) −1324.55 39027.5i −0.0273667 0.806354i
\(221\) 27579.4 47769.0i 0.564678 0.978051i
\(222\) 0 0
\(223\) −21934.5 + 12663.9i −0.441080 + 0.254658i −0.704056 0.710145i \(-0.748629\pi\)
0.262976 + 0.964802i \(0.415296\pi\)
\(224\) −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 −0.650792 + 0.759256i \(0.725563\pi\)
−0.982931 + 0.183975i \(0.941104\pi\)
\(228\) 0 0
\(229\) 42946.4 74385.3i 0.818947 1.41846i −0.0875119 0.996163i \(-0.527892\pi\)
0.906459 0.422294i \(-0.138775\pi\)
\(230\) 22976.6 + 38282.1i 0.434341 + 0.723669i
\(231\) 0 0
\(232\) 38400.2 24857.2i 0.713440 0.461823i
\(233\) 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
\(236\) 14322.8 + 7633.59i 0.257160 + 0.137058i
\(237\) 0 0
\(238\) −17295.3 28816.3i −0.305334 0.508726i
\(239\) 91748.4 + 52971.0i 1.60621 + 0.927347i 0.990207 + 0.139605i \(0.0445832\pi\)
0.616005 + 0.787742i \(0.288750\pi\)
\(240\) 0 0
\(241\) 5089.73 + 8815.67i 0.0876316 + 0.151782i 0.906510 0.422185i \(-0.138737\pi\)
−0.818878 + 0.573968i \(0.805404\pi\)
\(242\) 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
\(248\) −33148.7 + 64822.0i −0.538968 + 1.05395i
\(249\) 0 0
\(250\) 328.967 + 19391.5i 0.00526347 + 0.310264i
\(251\) 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
\(254\) −28490.0 + 483.319i −0.441595 + 0.00749146i
\(255\) 0 0
\(256\) 64933.5 8866.17i 0.990806 0.135287i
\(257\) 27780.7 48117.6i 0.420608 0.728514i −0.575391 0.817878i \(-0.695150\pi\)
0.995999 + 0.0893643i \(0.0284835\pi\)
\(258\) 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 \(-0.608443\pi\)
0.649186 + 0.760629i \(0.275110\pi\)
\(264\) 0 0
\(265\) −17573.7 + 30438.5i −0.250248 + 0.433443i
\(266\) 49744.9 29856.6i 0.703049 0.421965i
\(267\) 0 0
\(268\) −9114.67 4857.83i −0.126903 0.0676352i
\(269\) −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 \(0.776280\pi\)
\(272\) 46489.6 3159.25i 0.628374 0.0427017i
\(273\) 0 0
\(274\) −29114.0 + 17474.0i −0.387794 + 0.232751i
\(275\) −30474.7 17594.6i −0.402972 0.232656i
\(276\) 0 0
\(277\) −54019.7 93564.9i −0.704033 1.21942i −0.967039 0.254627i \(-0.918047\pi\)
0.263006 0.964794i \(-0.415286\pi\)
\(278\) −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 0.560957 0.827845i \(-0.310433\pi\)
−0.997413 + 0.0718805i \(0.977100\pi\)
\(282\) 0 0
\(283\) −39154.2 22605.7i −0.488884 0.282257i 0.235228 0.971940i \(-0.424416\pi\)
−0.724111 + 0.689683i \(0.757750\pi\)
\(284\) −5192.58 152998.i −0.0643793 1.89692i
\(285\) 0 0
\(286\) −89022.0 + 1510.22i −1.08834 + 0.0184632i
\(287\) 51473.5i 0.624914i
\(288\) 0 0
\(289\) −50390.1 −0.603323
\(290\) −1611.34 94983.0i −0.0191598 1.12941i
\(291\) 0 0
\(292\) −30368.2 + 1030.66i −0.356167 + 0.0120879i
\(293\) −35853.6 + 62100.3i −0.417636 + 0.723366i −0.995701 0.0926242i \(-0.970474\pi\)
0.578065 + 0.815990i \(0.303808\pi\)
\(294\) 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
\(302\) 7277.73 + 12125.6i 0.0797962 + 0.132951i
\(303\) 0 0
\(304\) 5453.74 + 80254.0i 0.0590129 + 0.868400i
\(305\) 28596.0 0.307401
\(306\) 0 0
\(307\) 95866.9i 1.01717i −0.861013 0.508583i \(-0.830170\pi\)
0.861013 0.508583i \(-0.169830\pi\)
\(308\) −25515.2 + 47873.7i −0.268966 + 0.504656i
\(309\) 0 0
\(310\) 77809.5 + 129641.i 0.809673 + 1.34902i
\(311\) −20844.0 12034.3i −0.215506 0.124423i 0.388362 0.921507i \(-0.373041\pi\)
−0.603868 + 0.797085i \(0.706374\pi\)
\(312\) 0 0
\(313\) 49654.5 + 86004.2i 0.506839 + 0.877871i 0.999969 + 0.00791525i \(0.00251953\pi\)
−0.493130 + 0.869956i \(0.664147\pi\)
\(314\) 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 0.975161 0.221497i \(-0.0710942\pi\)
−0.679402 + 0.733766i \(0.737761\pi\)
\(318\) 0 0
\(319\) −45465.2 26249.4i −0.446785 0.257951i
\(320\) 55722.7 124171.i 0.544167 1.21261i
\(321\) 0 0
\(322\) −1052.08 62016.5i −0.0101470 0.598129i
\(323\) 57193.1i 0.548200i
\(324\) 0 0
\(325\) −145180. −1.37449
\(326\) 23612.5 400.574i 0.222181 0.00376919i
\(327\) 0 0
\(328\) 63540.5 + 32493.3i 0.590613 + 0.302028i
\(329\) −26130.3 + 45259.0i −0.241408 + 0.418132i
\(330\) 0 0
\(331\) −79852.0 + 46102.6i −0.728836 + 0.420794i −0.817996 0.575223i \(-0.804915\pi\)
0.0891599 + 0.996017i \(0.471582\pi\)
\(332\) −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 −0.949210 0.314643i \(-0.898115\pi\)
0.747094 + 0.664719i \(0.231449\pi\)
\(338\) −217002. + 130243.i −1.89946 + 1.14004i
\(339\) 0 0
\(340\) 45514.1 85397.5i 0.393721 0.738733i
\(341\) 83558.1 0.718588
\(342\) 0 0
\(343\) 123305.i 1.04807i
\(344\) 87627.4 + 135370.i 0.740497 + 1.14395i
\(345\) 0 0
\(346\) 20955.3 12577.2i 0.175041 0.105059i
\(347\) −131615. 75987.9i −1.09306 0.631081i −0.158674 0.987331i \(-0.550722\pi\)
−0.934391 + 0.356250i \(0.884055\pi\)
\(348\) 0 0
\(349\) 93645.6 + 162199.i 0.768841 + 1.33167i 0.938192 + 0.346116i \(0.112500\pi\)
−0.169350 + 0.985556i \(0.554167\pi\)
\(350\) −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 0.942640 0.333810i \(-0.108334\pi\)
−0.760408 + 0.649446i \(0.775001\pi\)
\(354\) 0 0
\(355\) −275326. 158960.i −2.18469 1.26133i
\(356\) 122384. 4153.56i 0.965659 0.0327733i
\(357\) 0 0
\(358\) −46132.5 + 782.617i −0.359949 + 0.00610637i
\(359\) 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
\(362\) 1733.13 + 102162.i 0.0132256 + 0.779601i
\(363\) 0 0
\(364\) 7591.61 + 223685.i 0.0572969 + 1.68824i
\(365\) −31551.4 + 54648.7i −0.236828 + 0.410199i
\(366\) 0 0
\(367\) −57406.0 + 33143.4i −0.426211 + 0.246073i −0.697731 0.716360i \(-0.745807\pi\)
0.271520 + 0.962433i \(0.412474\pi\)
\(368\) 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 0.483873 + 0.875138i \(0.339229\pi\)
−0.999828 + 0.0185223i \(0.994104\pi\)
\(374\) −27520.9 45853.3i −0.196752 0.327814i
\(375\) 0 0
\(376\) −39374.0 60826.4i −0.278506 0.430245i
\(377\) −216594. −1.52393
\(378\) 0 0
\(379\) 183178.i 1.27525i −0.770348 0.637624i \(-0.779917\pi\)
0.770348 0.637624i \(-0.220083\pi\)
\(380\) 147420. + 78570.1i 1.02091 + 0.544114i
\(381\) 0 0
\(382\) −80419.9 133990.i −0.551108 0.918218i
\(383\) −15175.9 8761.79i −0.103456 0.0597303i 0.447379 0.894344i \(-0.352357\pi\)
−0.550835 + 0.834614i \(0.685691\pi\)
\(384\) 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 0.964615 0.263663i \(-0.0849307\pi\)
−0.710646 + 0.703549i \(0.751597\pi\)
\(390\) 0 0
\(391\) 52952.8 + 30572.3i 0.346366 + 0.199974i
\(392\) −15398.3 7874.40i −0.100208 0.0512443i
\(393\) 0 0
\(394\) −1431.80 84399.8i −0.00922340 0.543687i
\(395\) 259679.i 1.66434i
\(396\) 0 0
\(397\) −73295.7 −0.465047 −0.232524 0.972591i \(-0.574698\pi\)
−0.232524 + 0.972591i \(0.574698\pi\)
\(398\) 21788.8 369.636i 0.137552 0.00233350i
\(399\) 0 0
\(400\) −68382.4 101811.i −0.427390 0.636321i
\(401\) 142274. 246426.i 0.884784 1.53249i 0.0388226 0.999246i \(-0.487639\pi\)
0.845961 0.533244i \(-0.179027\pi\)
\(402\) 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 −0.645882 0.763437i \(-0.723510\pi\)
0.984097 + 0.177632i \(0.0568435\pi\)
\(410\) 127078. 76271.3i 0.755965 0.453725i
\(411\) 0 0
\(412\) −183445. 97770.4i −1.08072 0.575988i
\(413\) −46823.9 −0.274516
\(414\) 0 0
\(415\) 270593.i 1.57116i
\(416\) −280916. 131833.i −1.62327 0.761793i
\(417\) 0 0
\(418\) 79155.6 47508.7i 0.453032 0.271907i
\(419\) −237314. 137013.i −1.35175 0.780431i −0.363252 0.931691i \(-0.618334\pi\)
−0.988494 + 0.151260i \(0.951667\pi\)
\(420\) 0 0
\(421\) −6241.89 10811.3i −0.0352170 0.0609976i 0.847880 0.530189i \(-0.177879\pi\)
−0.883097 + 0.469191i \(0.844546\pi\)
\(422\) 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
\(428\) 8081.91 + 238132.i 0.0441191 + 1.29996i
\(429\) 0 0
\(430\) 334838. 5680.37i 1.81091 0.0307213i
\(431\) 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 \(0.771531\pi\)
\(434\) −3562.83 210016.i −0.0189154 1.11500i
\(435\) 0 0
\(436\) −120555. + 4091.49i −0.634179 + 0.0215233i
\(437\) −52776.3 + 91411.2i −0.276360 + 0.478670i
\(438\) 0 0
\(439\) −148459. + 85712.8i −0.770331 + 0.444751i −0.832993 0.553284i \(-0.813374\pi\)
0.0626618 + 0.998035i \(0.480041\pi\)
\(440\) −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 \(-0.598835\pi\)
0.671846 + 0.740691i \(0.265502\pi\)
\(444\) 0 0
\(445\) 127152. 220234.i 0.642102 1.11215i
\(446\) 52136.4 + 86866.0i 0.262103 + 0.436697i
\(447\) 0 0
\(448\) −153289. + 110683.i −0.763757 + 0.551476i
\(449\) −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
\(452\) 7467.29 14010.8i 0.0365499 0.0685780i
\(453\) 0 0
\(454\) 200099. + 333390.i 0.970806 + 1.61749i
\(455\) 402530. + 232401.i 1.94435 + 1.12257i
\(456\) 0 0
\(457\) 9489.80 + 16436.8i 0.0454386 + 0.0787019i 0.887850 0.460133i \(-0.152198\pi\)
−0.842412 + 0.538835i \(0.818865\pi\)
\(458\) −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 0.542006 0.840375i \(-0.317665\pi\)
−0.998789 + 0.0492038i \(0.984332\pi\)
\(462\) 0 0
\(463\) −86227.9 49783.7i −0.402240 0.232234i 0.285210 0.958465i \(-0.407937\pi\)
−0.687450 + 0.726232i \(0.741270\pi\)
\(464\) −102020. 151892.i −0.473858 0.705504i
\(465\) 0 0
\(466\) −866.698 51088.8i −0.00399113 0.235263i
\(467\) 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
\(470\) −150454. + 2552.38i −0.681096 + 0.0115545i
\(471\) 0 0
\(472\) 29558.2 57800.8i 0.132676 0.259448i
\(473\) 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 \(-0.705561\pi\)
0.390716 + 0.920511i \(0.372227\pi\)
\(480\) 0 0
\(481\) 152800. 264657.i 0.660439 1.14391i
\(482\) 34912.3 20954.1i 0.150274 0.0901935i
\(483\) 0 0
\(484\) 69578.9 130550.i 0.297021 0.557295i
\(485\) 423105. 1.79872
\(486\) 0 0
\(487\) 274913.i 1.15914i 0.814921 + 0.579572i \(0.196780\pi\)
−0.814921 + 0.579572i \(0.803220\pi\)
\(488\) 46237.1 29930.1i 0.194156 0.125681i
\(489\) 0 0
\(490\) −30795.9 + 18483.5i −0.128263 + 0.0769825i
\(491\) 28037.6 + 16187.5i 0.116299 + 0.0671455i 0.557021 0.830498i \(-0.311944\pi\)
−0.440722 + 0.897644i \(0.645277\pi\)
\(492\) 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 \(-0.135204\pi\)
0.0986806 + 0.995119i \(0.468538\pi\)
\(500\) 77532.4 2631.36i 0.310130 0.0105254i
\(501\) 0 0
\(502\) −87380.0 + 1482.36i −0.346740 + 0.00588229i
\(503\) 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
\(506\) −1674.10 98682.4i −0.00653854 0.385424i
\(507\) 0 0
\(508\) 3865.99 + 113911.i 0.0149808 + 0.441405i
\(509\) −146376. + 253530.i −0.564980 + 0.978575i 0.432071 + 0.901839i \(0.357783\pi\)
−0.997052 + 0.0767350i \(0.975550\pi\)
\(510\) 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
\(518\) −95822.3 159652.i −0.357114 0.594999i
\(519\) 0 0
\(520\) −540985. + 350189.i −2.00068 + 1.29508i
\(521\) 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 \(0.953680\pi\)
\(524\) −98267.5 52373.4i −0.357888 0.190743i
\(525\) 0 0
\(526\) −51797.9 86302.0i −0.187215 0.311924i
\(527\) 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
\(536\) −18810.1 + 36783.1i −0.0654729 + 0.128032i
\(537\) 0 0
\(538\) 3674.26 + 216585.i 0.0126942 + 0.748278i
\(539\) 19849.0i 0.0683223i
\(540\) 0 0
\(541\) 167330. 0.571715 0.285857 0.958272i \(-0.407722\pi\)
0.285857 + 0.958272i \(0.407722\pi\)
\(542\) 379715. 6441.69i 1.29259 0.0219281i
\(543\) 0 0
\(544\) −15789.4 185717.i −0.0533541 0.627559i
\(545\) −125252. + 216943.i −0.421689 + 0.730387i
\(546\) 0 0
\(547\) −246877. + 142535.i −0.825100 + 0.476372i −0.852172 0.523262i \(-0.824715\pi\)
0.0270722 + 0.999633i \(0.491382\pi\)
\(548\) 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
\(554\) −370541. + 222396.i −1.20730 + 0.724616i
\(555\) 0 0
\(556\) 301363. + 160617.i 0.974857 + 0.519568i
\(557\) −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
\(560\) 26621.7 + 391749.i 0.0848905 + 1.24920i
\(561\) 0 0
\(562\) −236394. + 141882.i −0.748452 + 0.449216i
\(563\) 2488.80 + 1436.91i 0.00785187 + 0.00453328i 0.503921 0.863750i \(-0.331890\pi\)
−0.496069 + 0.868283i \(0.665224\pi\)
\(564\) 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 0.764720 0.644363i \(-0.222877\pi\)
−0.940395 + 0.340085i \(0.889544\pi\)
\(570\) 0 0
\(571\) −27258.4 15737.7i −0.0836043 0.0482689i 0.457615 0.889150i \(-0.348704\pi\)
−0.541219 + 0.840881i \(0.682037\pi\)
\(572\) 12080.0 + 355934.i 0.0369211 + 1.08787i
\(573\) 0 0
\(574\) −205864. + 3492.39i −0.624824 + 0.0105998i
\(575\) 160935.i 0.486760i
\(576\) 0 0
\(577\) −654654. −1.96635 −0.983174 0.182671i \(-0.941526\pi\)
−0.983174 + 0.182671i \(0.941526\pi\)
\(578\) 3418.89 + 201531.i 0.0102336 + 0.603236i
\(579\) 0 0
\(580\) −379768. + 12888.9i −1.12892 + 0.0383142i
\(581\) 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 −0.629716 + 0.776825i \(0.716829\pi\)
−0.987609 + 0.156937i \(0.949838\pi\)
\(588\) 0 0
\(589\) −178725. + 309561.i −0.515175 + 0.892309i
\(590\) −69381.6 115599.i −0.199315 0.332085i
\(591\) 0 0
\(592\) 257569. 17503.3i 0.734937 0.0499433i
\(593\) 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
\(596\) 95825.2 179795.i 0.269766 0.506158i
\(597\) 0 0
\(598\) −209549. 349135.i −0.585980 0.976318i
\(599\) −24104.3 13916.6i −0.0671800 0.0387864i 0.466034 0.884767i \(-0.345683\pi\)
−0.533214 + 0.845981i \(0.679016\pi\)
\(600\) 0 0
\(601\) 135764. + 235150.i 0.375868 + 0.651022i 0.990457 0.137826i \(-0.0440113\pi\)
−0.614589 + 0.788848i \(0.710678\pi\)
\(602\) −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 \(-0.289808\pi\)
−0.377281 + 0.926099i \(0.623141\pi\)
\(608\) 320600. 27256.9i 0.867274 0.0737343i
\(609\) 0 0
\(610\) −1940.19 114368.i −0.00521417 0.307357i
\(611\) 343088.i 0.919015i
\(612\) 0 0
\(613\) 458408. 1.21992 0.609960 0.792432i \(-0.291185\pi\)
0.609960 + 0.792432i \(0.291185\pi\)
\(614\) −383412. + 6504.41i −1.01702 + 0.0172533i
\(615\) 0 0
\(616\) 193198. + 98797.8i 0.509146 + 0.260367i
\(617\) −237317. + 411046.i −0.623389 + 1.07974i 0.365461 + 0.930827i \(0.380911\pi\)
−0.988850 + 0.148915i \(0.952422\pi\)
\(618\) 0 0
\(619\) −5714.30 + 3299.15i −0.0149136 + 0.00861036i −0.507438 0.861688i \(-0.669407\pi\)
0.492525 + 0.870298i \(0.336074\pi\)
\(620\) 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
\(626\) 340598. 204425.i 0.869148 0.521657i
\(627\) 0 0
\(628\) 223814. 419938.i 0.567502 1.06479i
\(629\) 183557. 0.463948
\(630\) 0 0
\(631\) 102946.i 0.258553i 0.991609 + 0.129277i \(0.0412655\pi\)
−0.991609 + 0.129277i \(0.958734\pi\)
\(632\) −271794. 419877.i −0.680465 1.05121i
\(633\) 0 0
\(634\) 203864. 122358.i 0.507179 0.304405i
\(635\) 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 0.999964 0.00851530i \(-0.00271054\pi\)
−0.507356 + 0.861736i \(0.669377\pi\)
\(642\) 0 0
\(643\) −426111. 246015.i −1.03063 0.595032i −0.113462 0.993542i \(-0.536194\pi\)
−0.917164 + 0.398510i \(0.869527\pi\)
\(644\) −247959. + 8415.43i −0.597871 + 0.0202911i
\(645\) 0 0
\(646\) 228740. 3880.46i 0.548121 0.00929861i
\(647\) 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
\(650\) 9850.24 + 580637.i 0.0233142 + 1.37429i
\(651\) 0 0
\(652\) −3204.13 94409.1i −0.00753729 0.222085i
\(653\) 97661.8 169155.i 0.229033 0.396697i −0.728489 0.685058i \(-0.759777\pi\)
0.957522 + 0.288361i \(0.0931103\pi\)
\(654\) 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 0.566279 0.824213i \(-0.308382\pi\)
0.996929 0.0783055i \(-0.0249510\pi\)
\(660\) 0 0
\(661\) −371075. + 642721.i −0.849295 + 1.47102i 0.0325431 + 0.999470i \(0.489639\pi\)
−0.881838 + 0.471552i \(0.843694\pi\)
\(662\) 189802. + 316234.i 0.433096 + 0.721594i
\(663\) 0 0
\(664\) 283217. + 437524.i 0.642367 + 0.992352i
\(665\) −481943. −1.08981
\(666\) 0 0
\(667\) 240099.i 0.539682i
\(668\) −290388. 154768.i −0.650767 0.346838i
\(669\) 0 0
\(670\) 44152.8 + 73564.3i 0.0983577 + 0.163877i
\(671\) −54744.0 31606.5i −0.121588 0.0701990i
\(672\) 0 0
\(673\) −211601. 366503.i −0.467183 0.809185i 0.532114 0.846673i \(-0.321398\pi\)
−0.999297 + 0.0374878i \(0.988064\pi\)
\(674\) 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 0.983728 0.179665i \(-0.0575015\pi\)
−0.647459 + 0.762100i \(0.724168\pi\)
\(678\) 0 0
\(679\) −509034. 293891.i −1.10410 0.637450i
\(680\) −344629. 176236.i −0.745305 0.381134i
\(681\) 0 0
\(682\) −5669.28 334184.i −0.0121887 0.718484i
\(683\) 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
\(686\) 493148. 8366.02i 1.04792 0.0177775i
\(687\) 0 0
\(688\) 535457. 359644.i 1.13122 0.759794i
\(689\) 160273. 277602.i 0.337616 0.584768i
\(690\) 0 0
\(691\) −313235. + 180846.i −0.656016 + 0.378751i −0.790757 0.612130i \(-0.790313\pi\)
0.134742 + 0.990881i \(0.456980\pi\)
\(692\) −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
\(698\) 642349. 385534.i 1.31844 0.791319i
\(699\) 0 0
\(700\) 312252. + 166420.i 0.637248 + 0.339633i
\(701\) −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
\(704\) −243918. + 176123.i −0.492151 + 0.355361i
\(705\) 0 0
\(706\) 155761. 93486.7i 0.312499 0.187560i
\(707\) −549525. 317268.i −1.09938 0.634728i
\(708\) 0 0
\(709\) −431190. 746844.i −0.857781 1.48572i −0.874041 0.485853i \(-0.838509\pi\)
0.0162593 0.999868i \(-0.494824\pi\)
\(710\) −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
\(716\) 6260.03 + 184450.i 0.0122110 + 0.359794i
\(717\) 0 0
\(718\) 285976. 4851.44i 0.554728 0.00941070i
\(719\) 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
\(722\) −2143.31 126341.i −0.00411160 0.242365i
\(723\) 0 0
\(724\) 408472. 13863.1i 0.779265 0.0264473i
\(725\) −171209. + 296543.i −0.325725 + 0.564172i
\(726\) 0 0
\(727\) 78836.8 45516.5i 0.149163 0.0861191i −0.423561 0.905868i \(-0.639220\pi\)
0.572724 + 0.819748i \(0.305887\pi\)
\(728\) 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 −0.859781 0.510663i \(-0.829400\pi\)
0.872138 + 0.489261i \(0.162733\pi\)
\(734\) 136449. + 227342.i 0.253267 + 0.421976i
\(735\) 0 0
\(736\) 146139. 311400.i 0.269780 0.574862i
\(737\) 47414.8 0.0872929
\(738\) 0 0
\(739\) 622195.i 1.13930i −0.821888 0.569650i \(-0.807079\pi\)
0.821888 0.569650i \(-0.192921\pi\)
\(740\) 252165. 473132.i 0.460490 0.864011i
\(741\) 0 0
\(742\) −100509. 167461.i −0.182557 0.304163i
\(743\) −606588. 350214.i −1.09879 0.634389i −0.162890 0.986644i \(-0.552082\pi\)
−0.935904 + 0.352255i \(0.885415\pi\)
\(744\) 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 \(-0.357380\pi\)
−0.563935 + 0.825819i \(0.690713\pi\)
\(752\) −240599. + 161600.i −0.425459 + 0.285763i
\(753\) 0 0
\(754\) 14695.6 + 866252.i 0.0258490 + 1.52371i
\(755\) 117477.i 0.206091i
\(756\) 0 0
\(757\) 319528. 0.557592 0.278796 0.960350i \(-0.410065\pi\)
0.278796 + 0.960350i \(0.410065\pi\)
\(758\) −732606. + 12428.3i −1.27506 + 0.0216309i
\(759\) 0 0
\(760\) 304233. 594925.i 0.526719 1.03000i
\(761\) 376888. 652790.i 0.650794 1.12721i −0.332137 0.943231i \(-0.607770\pi\)
0.982931 0.183977i \(-0.0588971\pi\)
\(762\) 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 0.242473 + 0.970158i \(0.422041\pi\)
−0.961418 + 0.275091i \(0.911292\pi\)
\(770\) 386387. 231907.i 0.651690 0.391140i
\(771\) 0 0
\(772\) 209434. 392958.i 0.351409 0.659344i
\(773\) −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
\(776\) 684122. 442844.i 1.13608 0.735407i
\(777\) 0 0
\(778\) 263610.