Properties

Label 108.5.f.a.19.11
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 19.11
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.11

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 −0.979406 0.201901i \(-0.935288\pi\)
0.314852 0.949141i \(-0.398045\pi\)
\(6\) 0 0
\(7\) 39.9759 + 23.0801i 0.815835 + 0.471023i 0.848978 0.528428i \(-0.177218\pi\)
−0.0331429 + 0.999451i \(0.510552\pi\)
\(8\) 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 0.739268 0.673412i \(-0.235172\pi\)
−0.213558 + 0.976930i \(0.568505\pi\)
\(12\) 0 0
\(13\) 151.520 + 262.440i 0.896566 + 1.55290i 0.831855 + 0.554993i \(0.187279\pi\)
0.0647110 + 0.997904i \(0.479387\pi\)
\(14\) −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 \(-0.856677\pi\)
0.900333 0.435201i \(-0.143323\pi\)
\(20\) 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 −0.199157 0.979968i \(-0.563820\pi\)
0.749098 + 0.662459i \(0.230487\pi\)
\(24\) 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 0.109571 0.993979i \(-0.465052\pi\)
0.915597 + 0.402098i \(0.131719\pi\)
\(32\) −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 0.982841 0.184454i \(-0.0590516\pi\)
−0.651162 + 0.758939i \(0.725718\pi\)
\(42\) 0 0
\(43\) 2182.06 + 1259.82i 1.18013 + 0.681349i 0.956045 0.293220i \(-0.0947268\pi\)
0.224087 + 0.974569i \(0.428060\pi\)
\(44\) −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 0.261376 0.965237i \(-0.415824\pi\)
−0.705232 + 0.708977i \(0.749157\pi\)
\(48\) 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 −0.620846 0.783933i \(-0.713211\pi\)
0.368483 + 0.929635i \(0.379877\pi\)
\(60\) 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 −0.436438 0.899734i \(-0.643760\pi\)
0.560974 + 0.827834i \(0.310427\pi\)
\(68\) −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 \(-0.602090\pi\)
0.315254 0.949007i \(-0.397910\pi\)
\(72\) 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 −0.152363 0.988325i \(-0.548688\pi\)
−0.932096 + 0.362212i \(0.882022\pi\)
\(80\) −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 0.915186 0.403032i \(-0.132044\pi\)
0.108556 + 0.994090i \(0.465377\pi\)
\(84\) 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 0.299313 + 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 0.134971 0.990850i \(-0.456906\pi\)
0.925587 + 0.378536i \(0.123572\pi\)
\(104\) 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 \(0.225379\pi\)
−0.759631 + 0.650354i \(0.774621\pi\)
\(108\) 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 0.845944 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
\(122\) −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 \(0.0708764\pi\)
−0.975312 + 0.220829i \(0.929124\pi\)
\(128\) 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 −0.314007 0.949421i \(-0.601671\pi\)
0.665219 + 0.746648i \(0.268338\pi\)
\(132\) 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 −0.895147 0.445770i \(-0.852930\pi\)
−0.0615252 + 0.998106i \(0.519596\pi\)
\(140\) −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 0.686260 0.727356i \(-0.259251\pi\)
−0.973039 + 0.230640i \(0.925918\pi\)
\(150\) 0 0
\(151\) −3061.84 1767.75i −0.134285 0.0775296i 0.431352 0.902184i \(-0.358037\pi\)
−0.565638 + 0.824654i \(0.691370\pi\)
\(152\) −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 \(-0.372811\pi\)
\(158\) 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 \(-0.964561\pi\)
0.993809 0.111106i \(-0.0354394\pi\)
\(164\) −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 −0.145458 0.989364i \(-0.546465\pi\)
0.784086 + 0.620652i \(0.213132\pi\)
\(168\) 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
\(176\) 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 \(0.0576099\pi\)
−0.983667 + 0.180001i \(0.942390\pi\)
\(180\) 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 0.885999 0.463687i \(-0.153474\pi\)
0.0414344 + 0.999141i \(0.486807\pi\)
\(192\) 0 0
\(193\) −13915.2 24101.8i −0.373572 0.647045i 0.616541 0.787323i \(-0.288534\pi\)
−0.990112 + 0.140278i \(0.955200\pi\)
\(194\) −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 \(-0.978087\pi\)
0.997631 0.0687858i \(-0.0219125\pi\)
\(200\) 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 0.358509 0.933526i \(-0.383285\pi\)
0.987712 + 0.156286i \(0.0499520\pi\)
\(212\) −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 0.262976 0.964802i \(-0.415296\pi\)
−0.704056 + 0.710145i \(0.748629\pi\)
\(224\) −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 \(-0.941104\pi\)
−0.650792 0.759256i \(1.27444\pi\)
\(228\) 0 0
\(229\) 42946.4 + 74385.3i 0.818947 + 1.41846i 0.906459 + 0.422294i \(0.138775\pi\)
−0.0875119 + 0.996163i \(0.527892\pi\)
\(230\) 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 0.616005 0.787742i \(-0.288750\pi\)
0.990207 0.139605i \(-0.0445832\pi\)
\(240\) 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
\(248\) −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 \(0.0554738\pi\)
−0.984852 + 0.173395i \(0.944526\pi\)
\(252\) 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 0.995999 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 0.649186 0.760629i \(-0.275110\pi\)
−0.334131 + 0.942527i \(0.608443\pi\)
\(264\) 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 \(-0.776280\pi\)
0.763011 0.646386i \(-0.223720\pi\)
\(272\) 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 0.263006 + 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 −0.724111 0.689683i \(-0.757750\pi\)
0.235228 + 0.971940i \(0.424416\pi\)
\(284\) −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 0.578065 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
\(302\) 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 \(0.169830\pi\)
−0.861013 + 0.508583i \(0.830170\pi\)
\(308\) −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 −0.603868 0.797085i \(-0.706374\pi\)
0.388362 + 0.921507i \(0.373041\pi\)
\(312\) 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
\(320\) 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 0.0891599 0.996017i \(-0.471582\pi\)
−0.817996 + 0.575223i \(0.804915\pi\)
\(332\) −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 \(0.898115\pi\)
\(338\) −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 −0.934391 0.356250i \(-0.884055\pi\)
−0.158674 + 0.987331i \(0.550722\pi\)
\(348\) 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
\(356\) 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 \(-0.910526\pi\)
0.960753 0.277404i \(-0.0894740\pi\)
\(360\) 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 0.271520 0.962433i \(-0.412474\pi\)
−0.697731 + 0.716360i \(0.745807\pi\)
\(368\) 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 \(-0.339229\pi\)
\(374\) −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 \(0.220083\pi\)
−0.770348 + 0.637624i \(0.779917\pi\)
\(380\) 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 −0.550835 0.834614i \(-0.685691\pi\)
0.447379 + 0.894344i \(0.352357\pi\)
\(384\) 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
\(392\) −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 0.845961 + 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 \(0.723510\pi\)
\(410\) 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 −0.988494 0.151260i \(-0.951667\pi\)
−0.363252 + 0.931691i \(0.618334\pi\)
\(420\) 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
\(428\) 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 \(-0.895441\pi\)
0.946533 0.322606i \(-0.104559\pi\)
\(432\) 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 0.0626618 0.998035i \(-0.480041\pi\)
−0.832993 + 0.553284i \(0.813374\pi\)
\(440\) −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 0.671846 0.740691i \(-0.265502\pi\)
−0.305535 + 0.952181i \(0.598835\pi\)
\(444\) 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 −0.842412 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 −0.687450 0.726232i \(-0.741270\pi\)
0.285210 + 0.958465i \(0.407937\pi\)
\(464\) −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 \(-0.905964\pi\)
0.956679 0.291144i \(-0.0940358\pi\)
\(468\) 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 0.390716 0.920511i \(-0.372227\pi\)
−0.601828 + 0.798626i \(0.705561\pi\)
\(480\) 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 \(-0.803220\pi\)
0.814921 0.579572i \(-0.196780\pi\)
\(488\) 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 −0.440722 0.897644i \(-0.645277\pi\)
0.557021 + 0.830498i \(0.311944\pi\)
\(492\) 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 0.0986806 0.995119i \(-0.468538\pi\)
0.911139 + 0.412100i \(0.135204\pi\)
\(500\) 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 \(0.00596807\pi\)
−0.999824 + 0.0187481i \(0.994032\pi\)
\(504\) 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 −0.997052 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
\(518\) −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 \(-0.953680\pi\)
0.989431 0.145005i \(-0.0463198\pi\)
\(524\) −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 0.0270722 0.999633i \(-0.491382\pi\)
−0.852172 + 0.523262i \(0.824715\pi\)
\(548\) 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 −0.496069 0.868283i \(-0.665224\pi\)
0.503921 + 0.863750i \(0.331890\pi\)
\(564\) 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 −0.541219 0.840881i \(-0.682037\pi\)
0.457615 + 0.889150i \(0.348704\pi\)
\(572\) 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 −0.987609 0.156937i \(-0.949838\pi\)
−0.629716 0.776825i \(1.28317\pi\)
\(588\) 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 −0.533214 0.845981i \(-0.679016\pi\)
0.466034 + 0.884767i \(0.345683\pi\)
\(600\) 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 −0.377281 0.926099i \(-0.623141\pi\)
0.613384 + 0.789785i \(0.289808\pi\)
\(608\) 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 −0.988850 0.148915i \(-0.952422\pi\)
0.365461 0.930827i \(-0.380911\pi\)
\(618\) 0 0
\(619\) −5714.30 3299.15i −0.0149136 0.00861036i 0.492525 0.870298i \(-0.336074\pi\)
−0.507438 + 0.861688i \(0.669407\pi\)
\(620\) 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 \(-0.958734\pi\)
0.991609 0.129277i \(-0.0412655\pi\)
\(632\) −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 −0.507356 0.861736i \(-0.669377\pi\)
0.999964 + 0.00851530i \(0.00271054\pi\)
\(642\) 0 0
\(643\) −426111. + 246015.i −1.03063 + 0.595032i −0.917164 0.398510i \(-0.869527\pi\)
−0.113462 + 0.993542i \(0.536194\pi\)
\(644\) −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 \(0.119473\pi\)
−0.930384 + 0.366586i \(0.880527\pi\)
\(648\) 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 0.957522 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 \(0.0249510\pi\)
0.566279 + 0.824213i \(0.308382\pi\)
\(660\) 0 0
\(661\) −371075. 642721.i −0.849295 1.47102i −0.881838 0.471552i \(-0.843694\pi\)
0.0325431 0.999470i \(-0.489639\pi\)
\(662\) 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 −0.999297 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
\(680\) −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 \(0.303210\pi\)
−0.579597 + 0.814903i \(0.696790\pi\)
\(684\) 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 0.134742 0.990881i \(-0.456980\pi\)
−0.790757 + 0.612130i \(0.790313\pi\)
\(692\) −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 0.0162593 + 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
\(716\) 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 \(-0.865495\pi\)
0.912042 0.410097i \(-0.134505\pi\)
\(720\) 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 0.572724 0.819748i \(-0.305887\pi\)
−0.423561 + 0.905868i \(0.639220\pi\)
\(728\) 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 \(0.829400\pi\)
\(734\) 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 \(0.192921\pi\)
−0.821888 + 0.569650i \(0.807079\pi\)
\(740\) 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 −0.935904 0.352255i \(-0.885415\pi\)
−0.162890 + 0.986644i \(0.552082\pi\)
\(744\) 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 −0.563935 0.825819i \(-0.690713\pi\)
0.433213 + 0.901292i \(0.357380\pi\)
\(752\) −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 0.982931 + 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 \(-0.422041\pi\)
\(770\) 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.