Properties

Label 108.5.f.a.19.19
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 19.19
Character \(\chi\) \(=\) 108.19
Dual form 108.5.f.a.91.19

$q$-expansion

\(f(q)\) \(=\) \(q+(3.28826 + 2.27757i) q^{2} +(5.62536 + 14.9785i) q^{4} +(2.83091 + 4.90328i) q^{5} +(45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +O(q^{10})\) \(q+(3.28826 + 2.27757i) q^{2} +(5.62536 + 14.9785i) q^{4} +(2.83091 + 4.90328i) q^{5} +(45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +(-1.85878 + 22.5709i) q^{10} +(-92.3736 - 53.3319i) q^{11} +(61.0686 + 105.774i) q^{13} +(89.1136 + 188.588i) q^{14} +(-192.711 + 168.519i) q^{16} +122.675 q^{17} +593.624i q^{19} +(-57.5188 + 69.9855i) q^{20} +(-182.282 - 385.757i) q^{22} +(-473.649 + 273.461i) q^{23} +(296.472 - 513.504i) q^{25} +(-40.0976 + 486.900i) q^{26} +(-136.493 + 823.090i) q^{28} +(367.933 - 637.279i) q^{29} +(507.427 - 292.963i) q^{31} +(-1017.50 + 115.223i) q^{32} +(403.388 + 279.401i) q^{34} +295.239i q^{35} +2289.29 q^{37} +(-1352.02 + 1951.99i) q^{38} +(-348.534 + 99.1276i) q^{40} +(-1434.13 - 2483.99i) q^{41} +(-1943.81 - 1122.26i) q^{43} +(279.197 - 1683.63i) q^{44} +(-2180.31 - 179.555i) q^{46} +(913.531 + 527.427i) q^{47} +(159.084 + 275.542i) q^{49} +(2144.42 - 1013.30i) q^{50} +(-1240.80 + 1509.73i) q^{52} +4752.60 q^{53} -603.911i q^{55} +(-2323.47 + 2395.66i) q^{56} +(2661.31 - 1257.55i) q^{58} +(1864.25 - 1076.32i) q^{59} +(33.1660 - 57.4451i) q^{61} +(2335.80 + 192.360i) q^{62} +(-3608.23 - 1938.53i) q^{64} +(-345.759 + 598.872i) q^{65} +(3554.82 - 2052.38i) q^{67} +(690.091 + 1837.49i) q^{68} +(-672.427 + 970.824i) q^{70} -5031.65i q^{71} +2705.16 q^{73} +(7527.78 + 5214.01i) q^{74} +(-8891.60 + 3339.35i) q^{76} +(-2781.03 - 4816.88i) q^{77} +(-1196.02 - 690.524i) q^{79} +(-1371.84 - 467.852i) q^{80} +(941.652 - 11434.4i) q^{82} +(-2605.31 - 1504.18i) q^{83} +(347.282 + 601.509i) q^{85} +(-3835.74 - 8117.45i) q^{86} +(4752.65 - 4900.33i) q^{88} -3186.35 q^{89} +6368.92i q^{91} +(-6760.48 - 5556.22i) q^{92} +(1802.68 + 3814.95i) q^{94} +(-2910.71 + 1680.50i) q^{95} +(2407.03 - 4169.10i) q^{97} +(-104.455 + 1268.38i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.28826 + 2.27757i 0.822066 + 0.569392i
\(3\) 0 0
\(4\) 5.62536 + 14.9785i 0.351585 + 0.936156i
\(5\) 2.83091 + 4.90328i 0.113236 + 0.196131i 0.917073 0.398718i \(-0.130545\pi\)
−0.803837 + 0.594850i \(0.797212\pi\)
\(6\) 0 0
\(7\) 45.1595 + 26.0728i 0.921621 + 0.532098i 0.884152 0.467199i \(-0.154737\pi\)
0.0374695 + 0.999298i \(0.488070\pi\)
\(8\) −15.6169 + 62.0654i −0.244014 + 0.969772i
\(9\) 0 0
\(10\) −1.85878 + 22.5709i −0.0185878 + 0.225709i
\(11\) −92.3736 53.3319i −0.763418 0.440760i 0.0671034 0.997746i \(-0.478624\pi\)
−0.830522 + 0.556986i \(0.811958\pi\)
\(12\) 0 0
\(13\) 61.0686 + 105.774i 0.361352 + 0.625881i 0.988184 0.153274i \(-0.0489818\pi\)
−0.626831 + 0.779155i \(0.715648\pi\)
\(14\) 89.1136 + 188.588i 0.454661 + 0.962184i
\(15\) 0 0
\(16\) −192.711 + 168.519i −0.752776 + 0.658277i
\(17\) 122.675 0.424481 0.212240 0.977217i \(-0.431924\pi\)
0.212240 + 0.977217i \(0.431924\pi\)
\(18\) 0 0
\(19\) 593.624i 1.64439i 0.569207 + 0.822194i \(0.307250\pi\)
−0.569207 + 0.822194i \(0.692750\pi\)
\(20\) −57.5188 + 69.9855i −0.143797 + 0.174964i
\(21\) 0 0
\(22\) −182.282 385.757i −0.376615 0.797018i
\(23\) −473.649 + 273.461i −0.895366 + 0.516940i −0.875694 0.482867i \(-0.839596\pi\)
−0.0196720 + 0.999806i \(0.506262\pi\)
\(24\) 0 0
\(25\) 296.472 513.504i 0.474355 0.821607i
\(26\) −40.0976 + 486.900i −0.0593160 + 0.720266i
\(27\) 0 0
\(28\) −136.493 + 823.090i −0.174099 + 1.04986i
\(29\) 367.933 637.279i 0.437495 0.757763i −0.560001 0.828492i \(-0.689199\pi\)
0.997496 + 0.0707290i \(0.0225326\pi\)
\(30\) 0 0
\(31\) 507.427 292.963i 0.528020 0.304853i −0.212190 0.977228i \(-0.568059\pi\)
0.740210 + 0.672376i \(0.234726\pi\)
\(32\) −1017.50 + 115.223i −0.993649 + 0.112523i
\(33\) 0 0
\(34\) 403.388 + 279.401i 0.348951 + 0.241696i
\(35\) 295.239i 0.241012i
\(36\) 0 0
\(37\) 2289.29 1.67223 0.836117 0.548551i \(-0.184820\pi\)
0.836117 + 0.548551i \(0.184820\pi\)
\(38\) −1352.02 + 1951.99i −0.936302 + 1.35180i
\(39\) 0 0
\(40\) −348.534 + 99.1276i −0.217834 + 0.0619548i
\(41\) −1434.13 2483.99i −0.853142 1.47769i −0.878358 0.478004i \(-0.841360\pi\)
0.0252152 0.999682i \(-0.491973\pi\)
\(42\) 0 0
\(43\) −1943.81 1122.26i −1.05128 0.606955i −0.128270 0.991739i \(-0.540943\pi\)
−0.923007 + 0.384784i \(0.874276\pi\)
\(44\) 279.197 1683.63i 0.144213 0.869643i
\(45\) 0 0
\(46\) −2180.31 179.555i −1.03039 0.0848557i
\(47\) 913.531 + 527.427i 0.413550 + 0.238763i 0.692314 0.721597i \(-0.256591\pi\)
−0.278764 + 0.960360i \(0.589925\pi\)
\(48\) 0 0
\(49\) 159.084 + 275.542i 0.0662574 + 0.114761i
\(50\) 2144.42 1013.30i 0.857768 0.405321i
\(51\) 0 0
\(52\) −1240.80 + 1509.73i −0.458876 + 0.558333i
\(53\) 4752.60 1.69192 0.845960 0.533246i \(-0.179028\pi\)
0.845960 + 0.533246i \(0.179028\pi\)
\(54\) 0 0
\(55\) 603.911i 0.199640i
\(56\) −2323.47 + 2395.66i −0.740902 + 0.763923i
\(57\) 0 0
\(58\) 2661.31 1257.55i 0.791114 0.373825i
\(59\) 1864.25 1076.32i 0.535549 0.309200i −0.207724 0.978188i \(-0.566606\pi\)
0.743273 + 0.668988i \(0.233272\pi\)
\(60\) 0 0
\(61\) 33.1660 57.4451i 0.00891319 0.0154381i −0.861534 0.507699i \(-0.830496\pi\)
0.870448 + 0.492261i \(0.163829\pi\)
\(62\) 2335.80 + 192.360i 0.607648 + 0.0500416i
\(63\) 0 0
\(64\) −3608.23 1938.53i −0.880915 0.473275i
\(65\) −345.759 + 598.872i −0.0818365 + 0.141745i
\(66\) 0 0
\(67\) 3554.82 2052.38i 0.791897 0.457202i −0.0487331 0.998812i \(-0.515518\pi\)
0.840630 + 0.541610i \(0.182185\pi\)
\(68\) 690.091 + 1837.49i 0.149241 + 0.397380i
\(69\) 0 0
\(70\) −672.427 + 970.824i −0.137230 + 0.198127i
\(71\) 5031.65i 0.998145i −0.866560 0.499072i \(-0.833674\pi\)
0.866560 0.499072i \(-0.166326\pi\)
\(72\) 0 0
\(73\) 2705.16 0.507631 0.253815 0.967253i \(-0.418314\pi\)
0.253815 + 0.967253i \(0.418314\pi\)
\(74\) 7527.78 + 5214.01i 1.37469 + 0.952157i
\(75\) 0 0
\(76\) −8891.60 + 3339.35i −1.53940 + 0.578143i
\(77\) −2781.03 4816.88i −0.469055 0.812427i
\(78\) 0 0
\(79\) −1196.02 690.524i −0.191639 0.110643i 0.401110 0.916030i \(-0.368624\pi\)
−0.592750 + 0.805387i \(0.701958\pi\)
\(80\) −1371.84 467.852i −0.214350 0.0731019i
\(81\) 0 0
\(82\) 941.652 11434.4i 0.140043 1.70053i
\(83\) −2605.31 1504.18i −0.378184 0.218345i 0.298844 0.954302i \(-0.403399\pi\)
−0.677028 + 0.735957i \(0.736732\pi\)
\(84\) 0 0
\(85\) 347.282 + 601.509i 0.0480667 + 0.0832539i
\(86\) −3835.74 8117.45i −0.518624 1.09755i
\(87\) 0 0
\(88\) 4752.65 4900.33i 0.613721 0.632790i
\(89\) −3186.35 −0.402267 −0.201133 0.979564i \(-0.564462\pi\)
−0.201133 + 0.979564i \(0.564462\pi\)
\(90\) 0 0
\(91\) 6368.92i 0.769100i
\(92\) −6760.48 5556.22i −0.798734 0.656454i
\(93\) 0 0
\(94\) 1802.68 + 3814.95i 0.204015 + 0.431751i
\(95\) −2910.71 + 1680.50i −0.322516 + 0.186205i
\(96\) 0 0
\(97\) 2407.03 4169.10i 0.255822 0.443097i −0.709296 0.704910i \(-0.750987\pi\)
0.965118 + 0.261814i \(0.0843206\pi\)
\(98\) −104.455 + 1268.38i −0.0108762 + 0.132068i
\(99\) 0 0
\(100\) 9359.28 + 1552.05i 0.935928 + 0.155205i
\(101\) −3510.47 + 6080.30i −0.344130 + 0.596050i −0.985195 0.171436i \(-0.945159\pi\)
0.641066 + 0.767486i \(0.278493\pi\)
\(102\) 0 0
\(103\) −1858.85 + 1073.21i −0.175214 + 0.101160i −0.585042 0.811003i \(-0.698922\pi\)
0.409828 + 0.912163i \(0.365589\pi\)
\(104\) −7518.59 + 2138.39i −0.695136 + 0.197706i
\(105\) 0 0
\(106\) 15627.8 + 10824.4i 1.39087 + 0.963366i
\(107\) 13846.7i 1.20943i 0.796443 + 0.604713i \(0.206712\pi\)
−0.796443 + 0.604713i \(0.793288\pi\)
\(108\) 0 0
\(109\) −19384.9 −1.63159 −0.815793 0.578344i \(-0.803699\pi\)
−0.815793 + 0.578344i \(0.803699\pi\)
\(110\) 1375.45 1985.82i 0.113674 0.164117i
\(111\) 0 0
\(112\) −13096.5 + 2585.71i −1.04404 + 0.206132i
\(113\) 6817.20 + 11807.7i 0.533887 + 0.924719i 0.999216 + 0.0395818i \(0.0126026\pi\)
−0.465329 + 0.885138i \(0.654064\pi\)
\(114\) 0 0
\(115\) −2681.71 1548.29i −0.202776 0.117073i
\(116\) 11615.2 + 1926.16i 0.863201 + 0.143145i
\(117\) 0 0
\(118\) 8581.54 + 706.715i 0.616313 + 0.0507551i
\(119\) 5539.93 + 3198.48i 0.391211 + 0.225866i
\(120\) 0 0
\(121\) −1631.91 2826.55i −0.111462 0.193057i
\(122\) 239.894 113.357i 0.0161176 0.00761603i
\(123\) 0 0
\(124\) 7242.61 + 5952.47i 0.471034 + 0.387128i
\(125\) 6895.78 0.441330
\(126\) 0 0
\(127\) 15689.6i 0.972754i 0.873749 + 0.486377i \(0.161682\pi\)
−0.873749 + 0.486377i \(0.838318\pi\)
\(128\) −7449.66 14592.4i −0.454691 0.890649i
\(129\) 0 0
\(130\) −2500.92 + 1181.76i −0.147983 + 0.0699266i
\(131\) −7250.25 + 4185.93i −0.422484 + 0.243921i −0.696140 0.717907i \(-0.745101\pi\)
0.273656 + 0.961828i \(0.411767\pi\)
\(132\) 0 0
\(133\) −15477.5 + 26807.7i −0.874977 + 1.51550i
\(134\) 16363.6 + 1347.59i 0.911319 + 0.0750497i
\(135\) 0 0
\(136\) −1915.80 + 7613.87i −0.103579 + 0.411650i
\(137\) −14965.1 + 25920.4i −0.797333 + 1.38102i 0.124014 + 0.992280i \(0.460423\pi\)
−0.921347 + 0.388741i \(0.872910\pi\)
\(138\) 0 0
\(139\) 20651.8 11923.3i 1.06888 0.617118i 0.141005 0.990009i \(-0.454967\pi\)
0.927875 + 0.372891i \(0.121633\pi\)
\(140\) −4422.24 + 1660.83i −0.225624 + 0.0847361i
\(141\) 0 0
\(142\) 11459.9 16545.4i 0.568336 0.820541i
\(143\) 13027.6i 0.637078i
\(144\) 0 0
\(145\) 4166.34 0.198161
\(146\) 8895.30 + 6161.20i 0.417306 + 0.289041i
\(147\) 0 0
\(148\) 12878.1 + 34290.1i 0.587933 + 1.56547i
\(149\) 2636.98 + 4567.39i 0.118778 + 0.205729i 0.919284 0.393596i \(-0.128769\pi\)
−0.800506 + 0.599325i \(0.795436\pi\)
\(150\) 0 0
\(151\) −28946.1 16712.0i −1.26951 0.732951i −0.294614 0.955616i \(-0.595191\pi\)
−0.974895 + 0.222665i \(0.928524\pi\)
\(152\) −36843.5 9270.55i −1.59468 0.401253i
\(153\) 0 0
\(154\) 1826.02 22173.2i 0.0769954 0.934945i
\(155\) 2872.96 + 1658.71i 0.119582 + 0.0690408i
\(156\) 0 0
\(157\) −8500.73 14723.7i −0.344871 0.597334i 0.640459 0.767992i \(-0.278744\pi\)
−0.985330 + 0.170658i \(0.945411\pi\)
\(158\) −2360.12 4994.65i −0.0945410 0.200074i
\(159\) 0 0
\(160\) −3445.41 4662.88i −0.134586 0.182144i
\(161\) −28519.6 −1.10025
\(162\) 0 0
\(163\) 30843.8i 1.16089i 0.814298 + 0.580447i \(0.197122\pi\)
−0.814298 + 0.580447i \(0.802878\pi\)
\(164\) 29138.9 35454.5i 1.08339 1.31821i
\(165\) 0 0
\(166\) −5141.09 10879.9i −0.186569 0.394829i
\(167\) 13682.1 7899.35i 0.490591 0.283243i −0.234229 0.972181i \(-0.575257\pi\)
0.724819 + 0.688939i \(0.241923\pi\)
\(168\) 0 0
\(169\) 6821.76 11815.6i 0.238849 0.413698i
\(170\) −228.025 + 2768.88i −0.00789015 + 0.0958090i
\(171\) 0 0
\(172\) 5875.12 35428.5i 0.198591 1.19756i
\(173\) 23531.4 40757.6i 0.786241 1.36181i −0.142015 0.989865i \(-0.545358\pi\)
0.928255 0.371944i \(-0.121309\pi\)
\(174\) 0 0
\(175\) 26777.0 15459.7i 0.874352 0.504807i
\(176\) 26788.8 5289.07i 0.864825 0.170747i
\(177\) 0 0
\(178\) −10477.6 7257.14i −0.330690 0.229047i
\(179\) 2545.69i 0.0794511i −0.999211 0.0397256i \(-0.987352\pi\)
0.999211 0.0397256i \(-0.0126484\pi\)
\(180\) 0 0
\(181\) 5676.58 0.173272 0.0866362 0.996240i \(-0.472388\pi\)
0.0866362 + 0.996240i \(0.472388\pi\)
\(182\) −14505.6 + 20942.7i −0.437920 + 0.632251i
\(183\) 0 0
\(184\) −9575.56 33667.8i −0.282832 0.994441i
\(185\) 6480.77 + 11225.0i 0.189358 + 0.327977i
\(186\) 0 0
\(187\) −11331.9 6542.49i −0.324056 0.187094i
\(188\) −2761.12 + 16650.3i −0.0781214 + 0.471092i
\(189\) 0 0
\(190\) −13398.6 1103.41i −0.371153 0.0305655i
\(191\) −28127.2 16239.2i −0.771009 0.445142i 0.0622257 0.998062i \(-0.480180\pi\)
−0.833234 + 0.552920i \(0.813513\pi\)
\(192\) 0 0
\(193\) −393.717 681.937i −0.0105699 0.0183075i 0.860692 0.509126i \(-0.170031\pi\)
−0.871262 + 0.490818i \(0.836698\pi\)
\(194\) 17410.3 8226.92i 0.462598 0.218592i
\(195\) 0 0
\(196\) −3232.29 + 3932.86i −0.0841393 + 0.102376i
\(197\) −24825.9 −0.639694 −0.319847 0.947469i \(-0.603632\pi\)
−0.319847 + 0.947469i \(0.603632\pi\)
\(198\) 0 0
\(199\) 12008.5i 0.303237i −0.988439 0.151619i \(-0.951551\pi\)
0.988439 0.151619i \(-0.0484485\pi\)
\(200\) 27240.9 + 26420.0i 0.681022 + 0.660499i
\(201\) 0 0
\(202\) −25391.6 + 11998.3i −0.622283 + 0.294048i
\(203\) 33231.3 19186.1i 0.806409 0.465580i
\(204\) 0 0
\(205\) 8119.80 14063.9i 0.193213 0.334656i
\(206\) −8556.69 704.668i −0.201638 0.0166054i
\(207\) 0 0
\(208\) −29593.5 10092.5i −0.684020 0.233278i
\(209\) 31659.1 54835.2i 0.724780 1.25536i
\(210\) 0 0
\(211\) 25764.7 14875.2i 0.578708 0.334117i −0.181912 0.983315i \(-0.558229\pi\)
0.760620 + 0.649198i \(0.224895\pi\)
\(212\) 26735.1 + 71186.9i 0.594854 + 1.58390i
\(213\) 0 0
\(214\) −31536.9 + 45531.7i −0.688638 + 0.994228i
\(215\) 12708.1i 0.274917i
\(216\) 0 0
\(217\) 30553.5 0.648846
\(218\) −63742.6 44150.4i −1.34127 0.929012i
\(219\) 0 0
\(220\) 9045.68 3397.22i 0.186894 0.0701905i
\(221\) 7491.58 + 12975.8i 0.153387 + 0.265674i
\(222\) 0 0
\(223\) −45854.8 26474.3i −0.922093 0.532371i −0.0377910 0.999286i \(-0.512032\pi\)
−0.884302 + 0.466915i \(0.845365\pi\)
\(224\) −48953.8 21325.6i −0.975642 0.425016i
\(225\) 0 0
\(226\) −4476.18 + 54353.6i −0.0876376 + 1.06417i
\(227\) 32593.5 + 18817.9i 0.632528 + 0.365190i 0.781730 0.623616i \(-0.214337\pi\)
−0.149203 + 0.988807i \(0.547671\pi\)
\(228\) 0 0
\(229\) 28619.2 + 49569.9i 0.545741 + 0.945251i 0.998560 + 0.0536486i \(0.0170851\pi\)
−0.452819 + 0.891603i \(0.649582\pi\)
\(230\) −5291.85 11199.0i −0.100035 0.211701i
\(231\) 0 0
\(232\) 33807.0 + 32788.2i 0.628102 + 0.609174i
\(233\) 36468.7 0.671751 0.335876 0.941906i \(-0.390968\pi\)
0.335876 + 0.941906i \(0.390968\pi\)
\(234\) 0 0
\(235\) 5972.39i 0.108147i
\(236\) 26608.8 + 21868.9i 0.477750 + 0.392648i
\(237\) 0 0
\(238\) 10932.0 + 23135.0i 0.192995 + 0.408429i
\(239\) −45342.6 + 26178.6i −0.793799 + 0.458300i −0.841298 0.540571i \(-0.818208\pi\)
0.0474993 + 0.998871i \(0.484875\pi\)
\(240\) 0 0
\(241\) 6755.56 11701.0i 0.116313 0.201460i −0.801991 0.597336i \(-0.796226\pi\)
0.918304 + 0.395877i \(0.129559\pi\)
\(242\) 1071.51 13011.2i 0.0182964 0.222171i
\(243\) 0 0
\(244\) 1047.01 + 173.627i 0.0175862 + 0.00291633i
\(245\) −900.705 + 1560.07i −0.0150055 + 0.0259903i
\(246\) 0 0
\(247\) −62789.9 + 36251.8i −1.02919 + 0.594204i
\(248\) 10258.5 + 36068.9i 0.166793 + 0.586447i
\(249\) 0 0
\(250\) 22675.1 + 15705.6i 0.362802 + 0.251290i
\(251\) 111309.i 1.76678i 0.468635 + 0.883392i \(0.344746\pi\)
−0.468635 + 0.883392i \(0.655254\pi\)
\(252\) 0 0
\(253\) 58336.8 0.911385
\(254\) −35734.0 + 51591.4i −0.553879 + 0.799668i
\(255\) 0 0
\(256\) 8738.74 64950.8i 0.133343 0.991070i
\(257\) −36956.5 64010.6i −0.559532 0.969138i −0.997535 0.0701645i \(-0.977648\pi\)
0.438003 0.898973i \(-0.355686\pi\)
\(258\) 0 0
\(259\) 103383. + 59688.2i 1.54117 + 0.889793i
\(260\) −10915.2 1810.08i −0.161468 0.0267763i
\(261\) 0 0
\(262\) −33374.5 2748.48i −0.486197 0.0400397i
\(263\) −6380.84 3683.98i −0.0922500 0.0532606i 0.453165 0.891426i \(-0.350295\pi\)
−0.545415 + 0.838166i \(0.683628\pi\)
\(264\) 0 0
\(265\) 13454.2 + 23303.3i 0.191587 + 0.331838i
\(266\) −111950. + 52900.0i −1.58220 + 0.747639i
\(267\) 0 0
\(268\) 50738.7 + 41700.5i 0.706431 + 0.580593i
\(269\) 38604.8 0.533502 0.266751 0.963765i \(-0.414050\pi\)
0.266751 + 0.963765i \(0.414050\pi\)
\(270\) 0 0
\(271\) 12540.3i 0.170753i −0.996349 0.0853767i \(-0.972791\pi\)
0.996349 0.0853767i \(-0.0272094\pi\)
\(272\) −23640.8 + 20673.1i −0.319539 + 0.279426i
\(273\) 0 0
\(274\) −108245. + 51148.9i −1.44180 + 0.681295i
\(275\) −54772.4 + 31622.8i −0.724263 + 0.418153i
\(276\) 0 0
\(277\) 46052.4 79765.0i 0.600195 1.03957i −0.392596 0.919711i \(-0.628423\pi\)
0.992791 0.119857i \(-0.0382436\pi\)
\(278\) 95064.9 + 7828.87i 1.23007 + 0.101300i
\(279\) 0 0
\(280\) −18324.1 4610.71i −0.233726 0.0588101i
\(281\) 11148.0 19308.8i 0.141183 0.244537i −0.786759 0.617260i \(-0.788243\pi\)
0.927942 + 0.372723i \(0.121576\pi\)
\(282\) 0 0
\(283\) −21648.6 + 12498.8i −0.270307 + 0.156062i −0.629027 0.777383i \(-0.716547\pi\)
0.358720 + 0.933445i \(0.383213\pi\)
\(284\) 75366.5 28304.8i 0.934419 0.350933i
\(285\) 0 0
\(286\) 29671.3 42838.2i 0.362747 0.523720i
\(287\) 149568.i 1.81582i
\(288\) 0 0
\(289\) −68471.9 −0.819816
\(290\) 13700.0 + 9489.12i 0.162902 + 0.112831i
\(291\) 0 0
\(292\) 15217.5 + 40519.3i 0.178475 + 0.475222i
\(293\) −11748.6 20349.1i −0.136852 0.237034i 0.789452 0.613813i \(-0.210365\pi\)
−0.926303 + 0.376779i \(0.877032\pi\)
\(294\) 0 0
\(295\) 10555.0 + 6093.95i 0.121287 + 0.0700253i
\(296\) −35751.5 + 142086.i −0.408048 + 1.62169i
\(297\) 0 0
\(298\) −1731.44 + 21024.7i −0.0194974 + 0.236754i
\(299\) −57850.1 33399.7i −0.647085 0.373595i
\(300\) 0 0
\(301\) −58521.0 101361.i −0.645920 1.11877i
\(302\) −57119.6 120880.i −0.626283 1.32538i
\(303\) 0 0
\(304\) −100037. 114398.i −1.08246 1.23786i
\(305\) 375.559 0.00403719
\(306\) 0 0
\(307\) 32060.0i 0.340163i −0.985430 0.170082i \(-0.945597\pi\)
0.985430 0.170082i \(-0.0544031\pi\)
\(308\) 56505.3 68752.3i 0.595646 0.724746i
\(309\) 0 0
\(310\) 5669.24 + 11997.6i 0.0589931 + 0.124845i
\(311\) 61441.4 35473.2i 0.635244 0.366758i −0.147536 0.989057i \(-0.547134\pi\)
0.782780 + 0.622298i \(0.213801\pi\)
\(312\) 0 0
\(313\) −59259.6 + 102641.i −0.604882 + 1.04769i 0.387189 + 0.922001i \(0.373446\pi\)
−0.992070 + 0.125685i \(0.959887\pi\)
\(314\) 5581.58 67776.4i 0.0566106 0.687415i
\(315\) 0 0
\(316\) 3614.95 21799.1i 0.0362016 0.218305i
\(317\) −67390.6 + 116724.i −0.670626 + 1.16156i 0.307100 + 0.951677i \(0.400641\pi\)
−0.977727 + 0.209882i \(0.932692\pi\)
\(318\) 0 0
\(319\) −67974.6 + 39245.2i −0.667983 + 0.385660i
\(320\) −709.388 23180.0i −0.00692762 0.226367i
\(321\) 0 0
\(322\) −93780.0 64955.4i −0.904479 0.626474i
\(323\) 72822.8i 0.698011i
\(324\) 0 0
\(325\) 72420.4 0.685637
\(326\) −70248.8 + 101422.i −0.661003 + 0.954331i
\(327\) 0 0
\(328\) 176567. 50217.8i 1.64120 0.466778i
\(329\) 27503.0 + 47636.7i 0.254091 + 0.440098i
\(330\) 0 0
\(331\) 133143. + 76870.2i 1.21524 + 0.701620i 0.963896 0.266278i \(-0.0857939\pi\)
0.251345 + 0.967898i \(0.419127\pi\)
\(332\) 7874.49 47485.2i 0.0714408 0.430806i
\(333\) 0 0
\(334\) 62981.6 + 5186.72i 0.564574 + 0.0464943i
\(335\) 20126.8 + 11620.2i 0.179343 + 0.103544i
\(336\) 0 0
\(337\) 11471.8 + 19869.8i 0.101012 + 0.174958i 0.912102 0.409964i \(-0.134459\pi\)
−0.811090 + 0.584922i \(0.801125\pi\)
\(338\) 49342.7 23315.9i 0.431906 0.204089i
\(339\) 0 0
\(340\) −7056.12 + 8585.46i −0.0610391 + 0.0742687i
\(341\) −62497.2 −0.537467
\(342\) 0 0
\(343\) 108611.i 0.923175i
\(344\) 100010. 103117.i 0.845134 0.871393i
\(345\) 0 0
\(346\) 170206. 80427.3i 1.42174 0.671817i
\(347\) −6260.87 + 3614.72i −0.0519967 + 0.0300203i −0.525773 0.850625i \(-0.676224\pi\)
0.473776 + 0.880645i \(0.342891\pi\)
\(348\) 0 0
\(349\) −55282.6 + 95752.3i −0.453877 + 0.786137i −0.998623 0.0524636i \(-0.983293\pi\)
0.544746 + 0.838601i \(0.316626\pi\)
\(350\) 123260. + 10150.9i 1.00621 + 0.0828641i
\(351\) 0 0
\(352\) 100135. + 43621.5i 0.808165 + 0.352059i
\(353\) −30801.7 + 53350.1i −0.247187 + 0.428140i −0.962744 0.270414i \(-0.912840\pi\)
0.715557 + 0.698554i \(0.246173\pi\)
\(354\) 0 0
\(355\) 24671.6 14244.1i 0.195767 0.113026i
\(356\) −17924.4 47726.8i −0.141431 0.376584i
\(357\) 0 0
\(358\) 5797.99 8370.91i 0.0452388 0.0653141i
\(359\) 84462.7i 0.655354i −0.944790 0.327677i \(-0.893734\pi\)
0.944790 0.327677i \(-0.106266\pi\)
\(360\) 0 0
\(361\) −222069. −1.70401
\(362\) 18666.1 + 12928.8i 0.142441 + 0.0986600i
\(363\) 0 0
\(364\) −95396.8 + 35827.5i −0.719998 + 0.270404i
\(365\) 7658.07 + 13264.2i 0.0574823 + 0.0995622i
\(366\) 0 0
\(367\) −161018. 92963.9i −1.19548 0.690212i −0.235937 0.971768i \(-0.575816\pi\)
−0.959545 + 0.281556i \(0.909149\pi\)
\(368\) 45193.7 132518.i 0.333720 0.978538i
\(369\) 0 0
\(370\) −4255.27 + 51671.2i −0.0310831 + 0.377438i
\(371\) 214625. + 123914.i 1.55931 + 0.900268i
\(372\) 0 0
\(373\) 42545.6 + 73691.2i 0.305800 + 0.529661i 0.977439 0.211217i \(-0.0677428\pi\)
−0.671639 + 0.740878i \(0.734409\pi\)
\(374\) −22361.4 47322.7i −0.159866 0.338319i
\(375\) 0 0
\(376\) −47001.5 + 48461.9i −0.332457 + 0.342787i
\(377\) 89876.5 0.632359
\(378\) 0 0
\(379\) 146982.i 1.02326i −0.859206 0.511630i \(-0.829042\pi\)
0.859206 0.511630i \(-0.170958\pi\)
\(380\) −41545.1 34144.6i −0.287708 0.236458i
\(381\) 0 0
\(382\) −55503.6 117460.i −0.380360 0.804942i
\(383\) 161253. 93099.7i 1.09929 0.634674i 0.163254 0.986584i \(-0.447801\pi\)
0.936034 + 0.351910i \(0.114468\pi\)
\(384\) 0 0
\(385\) 15745.7 27272.3i 0.106228 0.183993i
\(386\) 258.515 3139.11i 0.00173504 0.0210684i
\(387\) 0 0
\(388\) 75987.2 + 12601.0i 0.504751 + 0.0837030i
\(389\) −128002. + 221706.i −0.845897 + 1.46514i 0.0389437 + 0.999241i \(0.487601\pi\)
−0.884840 + 0.465894i \(0.845733\pi\)
\(390\) 0 0
\(391\) −58104.8 + 33546.8i −0.380066 + 0.219431i
\(392\) −19586.0 + 5570.52i −0.127460 + 0.0362513i
\(393\) 0 0
\(394\) −81634.1 56542.7i −0.525871 0.364237i
\(395\) 7819.24i 0.0501153i
\(396\) 0 0
\(397\) −260735. −1.65432 −0.827159 0.561968i \(-0.810044\pi\)
−0.827159 + 0.561968i \(0.810044\pi\)
\(398\) 27350.2 39487.1i 0.172661 0.249281i
\(399\) 0 0
\(400\) 29401.9 + 148919.i 0.183762 + 0.930743i
\(401\) 26507.0 + 45911.4i 0.164843 + 0.285517i 0.936600 0.350401i \(-0.113955\pi\)
−0.771756 + 0.635918i \(0.780621\pi\)
\(402\) 0 0
\(403\) 61975.7 + 35781.7i 0.381603 + 0.220318i
\(404\) −110821. 18377.6i −0.678986 0.112597i
\(405\) 0 0
\(406\) 152971. + 12597.6i 0.928019 + 0.0764251i
\(407\) −211470. 122092.i −1.27661 0.737053i
\(408\) 0 0
\(409\) −73697.8 127648.i −0.440563 0.763078i 0.557168 0.830400i \(-0.311888\pi\)
−0.997731 + 0.0673220i \(0.978555\pi\)
\(410\) 58731.5 27752.4i 0.349385 0.165095i
\(411\) 0 0
\(412\) −26531.7 21805.6i −0.156304 0.128462i
\(413\) 112251. 0.658099
\(414\) 0 0
\(415\) 17032.8i 0.0988983i
\(416\) −74324.7 100588.i −0.429483 0.581246i
\(417\) 0 0
\(418\) 228995. 108207.i 1.31061 0.619302i
\(419\) −201431. + 116296.i −1.14736 + 0.662426i −0.948242 0.317550i \(-0.897140\pi\)
−0.199115 + 0.979976i \(0.563807\pi\)
\(420\) 0 0
\(421\) 34900.8 60449.9i 0.196911 0.341060i −0.750614 0.660741i \(-0.770242\pi\)
0.947525 + 0.319680i \(0.103576\pi\)
\(422\) 118600. + 9767.08i 0.665980 + 0.0548454i
\(423\) 0 0
\(424\) −74220.8 + 294972.i −0.412852 + 1.64078i
\(425\) 36369.7 62994.1i 0.201355 0.348756i
\(426\) 0 0
\(427\) 2995.51 1729.46i 0.0164292 0.00948539i
\(428\) −207403. + 77892.8i −1.13221 + 0.425216i
\(429\) 0 0
\(430\) 28943.5 41787.5i 0.156536 0.226000i
\(431\) 147873.i 0.796037i 0.917377 + 0.398019i \(0.130302\pi\)
−0.917377 + 0.398019i \(0.869698\pi\)
\(432\) 0 0
\(433\) 294850. 1.57262 0.786312 0.617830i \(-0.211988\pi\)
0.786312 + 0.617830i \(0.211988\pi\)
\(434\) 100468. + 69587.7i 0.533395 + 0.369448i
\(435\) 0 0
\(436\) −109047. 290356.i −0.573641 1.52742i
\(437\) −162333. 281169.i −0.850050 1.47233i
\(438\) 0 0
\(439\) 62468.0 + 36065.9i 0.324137 + 0.187140i 0.653235 0.757155i \(-0.273411\pi\)
−0.329098 + 0.944296i \(0.606745\pi\)
\(440\) 37482.0 + 9431.20i 0.193605 + 0.0487149i
\(441\) 0 0
\(442\) −4918.98 + 59730.5i −0.0251785 + 0.305739i
\(443\) 165331. + 95453.7i 0.842453 + 0.486391i 0.858097 0.513487i \(-0.171647\pi\)
−0.0156440 + 0.999878i \(0.504980\pi\)
\(444\) 0 0
\(445\) −9020.28 15623.6i −0.0455512 0.0788970i
\(446\) −90485.7 191492.i −0.454894 0.962677i
\(447\) 0 0
\(448\) −112402. 181620.i −0.560041 0.904914i
\(449\) −192859. −0.956639 −0.478319 0.878186i \(-0.658754\pi\)
−0.478319 + 0.878186i \(0.658754\pi\)
\(450\) 0 0
\(451\) 305940.i 1.50412i
\(452\) −138513. + 168534.i −0.677975 + 0.824919i
\(453\) 0 0
\(454\) 64317.1 + 136112.i 0.312043 + 0.660367i
\(455\) −31228.6 + 18029.8i −0.150844 + 0.0870901i
\(456\) 0 0
\(457\) 2962.66 5131.48i 0.0141857 0.0245703i −0.858845 0.512235i \(-0.828818\pi\)
0.873031 + 0.487665i \(0.162151\pi\)
\(458\) −18791.4 + 228181.i −0.0895834 + 1.08780i
\(459\) 0 0
\(460\) 8105.41 48877.7i 0.0383053 0.230991i
\(461\) 63341.9 109711.i 0.298050 0.516238i −0.677640 0.735394i \(-0.736997\pi\)
0.975690 + 0.219156i \(0.0703304\pi\)
\(462\) 0 0
\(463\) −204011. + 117786.i −0.951682 + 0.549454i −0.893603 0.448858i \(-0.851831\pi\)
−0.0580790 + 0.998312i \(0.518498\pi\)
\(464\) 36488.9 + 184814.i 0.169483 + 0.858418i
\(465\) 0 0
\(466\) 119919. + 83060.0i 0.552224 + 0.382490i
\(467\) 97776.2i 0.448332i 0.974551 + 0.224166i \(0.0719658\pi\)
−0.974551 + 0.224166i \(0.928034\pi\)
\(468\) 0 0
\(469\) 214045. 0.973105
\(470\) −13602.5 + 19638.8i −0.0615778 + 0.0889036i
\(471\) 0 0
\(472\) 37688.8 + 132514.i 0.169172 + 0.594810i
\(473\) 119705. + 207334.i 0.535043 + 0.926721i
\(474\) 0 0
\(475\) 304829. + 175993.i 1.35104 + 0.780024i
\(476\) −16744.3 + 100972.i −0.0739015 + 0.445645i
\(477\) 0 0
\(478\) −208722. 17188.8i −0.913508 0.0752300i
\(479\) −349162. 201589.i −1.52179 0.878608i −0.999669 0.0257398i \(-0.991806\pi\)
−0.522126 0.852869i \(1.32514\pi\)
\(480\) 0 0
\(481\) 139803. + 242147.i 0.604266 + 1.04662i
\(482\) 48863.8 23089.6i 0.210326 0.0993855i
\(483\) 0 0
\(484\) 33157.4 40344.0i 0.141543 0.172222i
\(485\) 27256.3 0.115873
\(486\) 0 0
\(487\) 195207.i 0.823071i −0.911394 0.411536i \(-0.864993\pi\)
0.911394 0.411536i \(-0.135007\pi\)
\(488\) 3047.41 + 2955.57i 0.0127965 + 0.0124109i
\(489\) 0 0
\(490\) −6514.92 + 3078.49i −0.0271342 + 0.0128217i
\(491\) −65937.1 + 38068.8i −0.273506 + 0.157909i −0.630480 0.776206i \(-0.717142\pi\)
0.356974 + 0.934114i \(0.383809\pi\)
\(492\) 0 0
\(493\) 45136.2 78178.1i 0.185708 0.321656i
\(494\) −289036. 23802.9i −1.18440 0.0975386i
\(495\) 0 0
\(496\) −48416.8 + 141968.i −0.196803 + 0.577069i
\(497\) 131189. 227226.i 0.531111 0.919912i
\(498\) 0 0
\(499\) 12618.3 7285.17i 0.0506757 0.0292576i −0.474448 0.880283i \(-0.657352\pi\)
0.525124 + 0.851026i \(0.324019\pi\)
\(500\) 38791.2 + 103288.i 0.155165 + 0.413153i
\(501\) 0 0
\(502\) −253514. + 366014.i −1.00599 + 1.45241i
\(503\) 280154.i 1.10729i −0.832753 0.553645i \(-0.813236\pi\)
0.832753 0.553645i \(-0.186764\pi\)
\(504\) 0 0
\(505\) −39751.2 −0.155872
\(506\) 191827. + 132866.i 0.749219 + 0.518935i
\(507\) 0 0
\(508\) −235006. + 88259.4i −0.910650 + 0.342006i
\(509\) 101505. + 175811.i 0.391787 + 0.678595i 0.992685 0.120731i \(-0.0385238\pi\)
−0.600899 + 0.799325i \(0.705190\pi\)
\(510\) 0 0
\(511\) 122164. + 70531.3i 0.467843 + 0.270110i
\(512\) 176665. 193672.i 0.673924 0.738801i
\(513\) 0 0
\(514\) 24265.7 294655.i 0.0918472 1.11529i
\(515\) −10524.5 6076.30i −0.0396813 0.0229100i
\(516\) 0 0
\(517\) −56257.4 97440.7i −0.210474 0.364552i
\(518\) 204007. + 431732.i 0.760300 + 1.60900i
\(519\) 0 0
\(520\) −31769.6 30812.2i −0.117491 0.113950i
\(521\) 30822.1 0.113550 0.0567749 0.998387i \(-0.481918\pi\)
0.0567749 + 0.998387i \(0.481918\pi\)
\(522\) 0 0
\(523\) 94412.3i 0.345164i −0.984995 0.172582i \(-0.944789\pi\)
0.984995 0.172582i \(-0.0552109\pi\)
\(524\) −103484. 85050.4i −0.376887 0.309752i
\(525\) 0 0
\(526\) −12591.4 26646.7i −0.0455095 0.0963101i
\(527\) 62248.6 35939.3i 0.224134 0.129404i
\(528\) 0 0
\(529\) 9641.45 16699.5i 0.0344533 0.0596749i
\(530\) −8834.03 + 107270.i −0.0314490 + 0.381881i
\(531\) 0 0
\(532\) −488606. 81025.8i −1.72638 0.286286i
\(533\) 175161. 303387.i 0.616570 1.06793i
\(534\) 0 0
\(535\) −67894.3 + 39198.8i −0.237206 + 0.136951i
\(536\) 71866.5 + 252683.i 0.250148 + 0.879523i
\(537\) 0 0
\(538\) 126943. + 87925.0i 0.438574 + 0.303772i
\(539\) 33937.0i 0.116814i
\(540\) 0 0
\(541\) 166561. 0.569087 0.284544 0.958663i \(-0.408158\pi\)
0.284544 + 0.958663i \(0.408158\pi\)
\(542\) 28561.4 41235.8i 0.0972257 0.140371i
\(543\) 0 0
\(544\) −124821. + 14135.0i −0.421785 + 0.0477637i
\(545\) −54876.8 95049.4i −0.184755 0.320005i
\(546\) 0 0
\(547\) −256245. 147943.i −0.856410 0.494448i 0.00639865 0.999980i \(-0.497963\pi\)
−0.862808 + 0.505531i \(0.831297\pi\)
\(548\) −472433. 78343.7i −1.57318 0.260881i
\(549\) 0 0
\(550\) −252129. 20763.6i −0.833485 0.0686399i
\(551\) 378304. + 218414.i 1.24606 + 0.719411i
\(552\) 0 0
\(553\) −36007.8 62367.3i −0.117746 0.203942i
\(554\) 333103. 157401.i 1.08532 0.512847i
\(555\) 0 0
\(556\) 294768. + 242260.i 0.953521 + 0.783669i
\(557\) 30600.2 0.0986312 0.0493156 0.998783i \(-0.484296\pi\)
0.0493156 + 0.998783i \(0.484296\pi\)
\(558\) 0 0
\(559\) 274139.i 0.877298i
\(560\) −49753.4 56895.7i −0.158652 0.181428i
\(561\) 0 0
\(562\) 80634.7 38102.3i 0.255299 0.120637i
\(563\) 210267. 121398.i 0.663369 0.382996i −0.130191 0.991489i \(-0.541559\pi\)
0.793559 + 0.608493i \(0.208226\pi\)
\(564\) 0 0
\(565\) −38597.8 + 66853.3i −0.120911 + 0.209424i
\(566\) −99653.3 8206.73i −0.311070 0.0256175i
\(567\) 0 0
\(568\) 312291. + 78578.6i 0.967973 + 0.243561i
\(569\) 148459. 257138.i 0.458545 0.794223i −0.540339 0.841447i \(-0.681704\pi\)
0.998884 + 0.0472242i \(0.0150375\pi\)
\(570\) 0 0
\(571\) 228446. 131893.i 0.700665 0.404529i −0.106930 0.994267i \(-0.534102\pi\)
0.807595 + 0.589737i \(0.200769\pi\)
\(572\) 195134. 73285.1i 0.596405 0.223987i
\(573\) 0 0
\(574\) 340650. 491818.i 1.03392 1.49273i
\(575\) 324294.i 0.980852i
\(576\) 0 0
\(577\) 350367. 1.05238 0.526188 0.850368i \(-0.323621\pi\)
0.526188 + 0.850368i \(0.323621\pi\)
\(578\) −225154. 155949.i −0.673943 0.466797i
\(579\) 0 0
\(580\) 23437.2 + 62405.5i 0.0696705 + 0.185510i
\(581\) −78436.3 135856.i −0.232362 0.402463i
\(582\) 0 0
\(583\) −439015. 253466.i −1.29164 0.745730i
\(584\) −42246.2 + 167897.i −0.123869 + 0.492286i
\(585\) 0 0
\(586\) 7714.12 93671.5i 0.0224642 0.272780i
\(587\) 5965.76 + 3444.33i 0.0173137 + 0.00999606i 0.508632 0.860984i \(-0.330151\pi\)
−0.491318 + 0.870980i \(0.663485\pi\)
\(588\) 0 0
\(589\) 173910. + 301221.i 0.501296 + 0.868270i
\(590\) 20828.3 + 44078.3i 0.0598344 + 0.126625i
\(591\) 0 0
\(592\) −441170. + 385788.i −1.25882 + 1.10079i
\(593\) −544416. −1.54818 −0.774090 0.633076i \(-0.781792\pi\)
−0.774090 + 0.633076i \(0.781792\pi\)
\(594\) 0 0
\(595\) 36218.4i 0.102305i
\(596\) −53578.6 + 65191.2i −0.150834 + 0.183526i
\(597\) 0 0
\(598\) −114156. 241585.i −0.319225 0.675565i
\(599\) 122771. 70881.9i 0.342170 0.197552i −0.319061 0.947734i \(-0.603367\pi\)
0.661231 + 0.750182i \(0.270034\pi\)
\(600\) 0 0
\(601\) 265380. 459652.i 0.734715 1.27256i −0.220133 0.975470i \(-0.570649\pi\)
0.954848 0.297094i \(-0.0960176\pi\)
\(602\) 38424.9 466588.i 0.106028 1.28748i
\(603\) 0 0
\(604\) 87488.8 527580.i 0.239816 1.44615i
\(605\) 9239.58 16003.4i 0.0252430 0.0437222i
\(606\) 0 0
\(607\) 35215.7 20331.8i 0.0955782 0.0551821i −0.451449 0.892297i \(-0.649093\pi\)
0.547027 + 0.837115i \(0.315759\pi\)
\(608\) −68399.3 604011.i −0.185031 1.63395i
\(609\) 0 0
\(610\) 1234.94 + 855.362i 0.00331883 + 0.00229874i
\(611\) 128837.i 0.345110i
\(612\) 0 0
\(613\) −498556. −1.32676 −0.663382 0.748281i \(-0.730879\pi\)
−0.663382 + 0.748281i \(0.730879\pi\)
\(614\) 73018.9 105422.i 0.193686 0.279636i
\(615\) 0 0
\(616\) 342393. 97381.0i 0.902325 0.256633i
\(617\) −45030.4 77995.0i −0.118287 0.204879i 0.800802 0.598929i \(-0.204407\pi\)
−0.919089 + 0.394050i \(0.871074\pi\)
\(618\) 0 0
\(619\) −149379. 86244.1i −0.389860 0.225086i 0.292240 0.956345i \(-0.405600\pi\)
−0.682099 + 0.731259i \(0.738933\pi\)
\(620\) −8683.45 + 52363.5i −0.0225896 + 0.136221i
\(621\) 0 0
\(622\) 282828. + 23291.7i 0.731042 + 0.0602034i
\(623\) −143894. 83077.2i −0.370738 0.214045i
\(624\) 0 0
\(625\) −165774. 287128.i −0.424380 0.735049i
\(626\) −428633. + 202542.i −1.09380 + 0.516852i
\(627\) 0 0
\(628\) 172719. 210154.i 0.437946 0.532867i
\(629\) 280838. 0.709831
\(630\) 0 0
\(631\) 210621.i 0.528985i 0.964388 + 0.264492i \(0.0852044\pi\)
−0.964388 + 0.264492i \(0.914796\pi\)
\(632\) 61535.7 63447.8i 0.154061 0.158848i
\(633\) 0 0
\(634\) −487445. + 230332.i −1.21268 + 0.573029i
\(635\) −76930.2 + 44415.7i −0.190787 + 0.110151i
\(636\) 0 0
\(637\) −19430.1 + 33653.9i −0.0478846 + 0.0829385i
\(638\) −312902. 25768.4i −0.768718 0.0633061i
\(639\) 0 0
\(640\) 50461.3 77837.5i 0.123196 0.190033i
\(641\) −232262. + 402289.i −0.565278 + 0.979089i 0.431746 + 0.901995i \(0.357898\pi\)
−0.997024 + 0.0770943i \(0.975436\pi\)
\(642\) 0 0
\(643\) 361978. 208988.i 0.875509 0.505476i 0.00633423 0.999980i \(-0.497984\pi\)
0.869175 + 0.494504i \(0.164650\pi\)
\(644\) −160433. 427181.i −0.386832 1.03001i
\(645\) 0 0
\(646\) −165859. + 239461.i −0.397442 + 0.573811i
\(647\) 825841.i 1.97282i −0.164299 0.986411i \(-0.552536\pi\)
0.164299 0.986411i \(-0.447464\pi\)
\(648\) 0 0
\(649\) −229610. −0.545131
\(650\) 238138. + 164943.i 0.563639 + 0.390397i
\(651\) 0 0
\(652\) −461993. + 173507.i −1.08678 + 0.408153i
\(653\) 164273. + 284529.i 0.385247 + 0.667267i 0.991803 0.127773i \(-0.0407830\pi\)
−0.606557 + 0.795040i \(0.707450\pi\)
\(654\) 0 0
\(655\) −41049.6 23700.0i −0.0956811 0.0552415i
\(656\) 694972. + 237013.i 1.61495 + 0.550762i
\(657\) 0 0
\(658\) −18058.5 + 219282.i −0.0417090 + 0.506467i
\(659\) −144939. 83680.3i −0.333744 0.192687i 0.323758 0.946140i \(-0.395054\pi\)
−0.657502 + 0.753453i \(0.728387\pi\)
\(660\) 0 0
\(661\) 152616. + 264339.i 0.349300 + 0.605005i 0.986125 0.166003i \(-0.0530862\pi\)
−0.636826 + 0.771008i \(0.719753\pi\)
\(662\) 262732. + 556012.i 0.599512 + 1.26873i
\(663\) 0 0
\(664\) 134044. 138209.i 0.304027 0.313473i
\(665\) −175261. −0.396317
\(666\) 0 0
\(667\) 402461.i 0.904633i
\(668\) 195287. + 160500.i 0.437644 + 0.359685i
\(669\) 0 0
\(670\) 39716.3 + 84050.4i 0.0884748 + 0.187236i
\(671\) −6127.32 + 3537.61i −0.0136090 + 0.00785715i
\(672\) 0 0
\(673\) −403032. + 698073.i −0.889836 + 1.54124i −0.0497671 + 0.998761i \(0.515848\pi\)
−0.840069 + 0.542480i \(0.817485\pi\)
\(674\) −7532.41 + 91465.0i −0.0165811 + 0.201342i
\(675\) 0 0
\(676\) 215355. + 35712.5i 0.471262 + 0.0781496i
\(677\) −183117. + 317169.i −0.399533 + 0.692011i −0.993668 0.112354i \(-0.964161\pi\)
0.594136 + 0.804365i \(0.297494\pi\)
\(678\) 0 0
\(679\) 217400. 125516.i 0.471542 0.272245i
\(680\) −42756.4 + 12160.5i −0.0924662 + 0.0262986i
\(681\) 0 0
\(682\) −205507. 142342.i −0.441833 0.306029i
\(683\) 398332.i 0.853894i 0.904277 + 0.426947i \(0.140411\pi\)
−0.904277 + 0.426947i \(0.859589\pi\)
\(684\) 0 0
\(685\) −169460. −0.361148
\(686\) 247368. 357140.i 0.525649 0.758911i
\(687\) 0 0
\(688\) 563715. 111298.i 1.19092 0.235130i
\(689\) 290235. + 502701.i 0.611379 + 1.05894i
\(690\) 0 0
\(691\) 304679. + 175906.i 0.638096 + 0.368405i 0.783881 0.620912i \(-0.213237\pi\)
−0.145785 + 0.989316i \(0.546571\pi\)
\(692\) 742860. + 123189.i 1.55130 + 0.257252i
\(693\) 0 0
\(694\) −28820.2 2373.42i −0.0598381 0.00492784i
\(695\) 116927. + 67507.8i 0.242072 + 0.139760i
\(696\) 0 0
\(697\) −175932. 304723.i −0.362143 0.627249i
\(698\) −399866. + 188949.i −0.820737 + 0.387823i
\(699\) 0 0
\(700\) 382194. + 314113.i 0.779987 + 0.641047i
\(701\) 620142. 1.26199 0.630994 0.775788i \(-0.282647\pi\)
0.630994 + 0.775788i \(0.282647\pi\)
\(702\) 0 0
\(703\) 1.35898e6i 2.74980i
\(704\) 229919. + 371503.i 0.463906 + 0.749579i
\(705\) 0 0
\(706\) −222793. + 105276.i −0.446984 + 0.211213i
\(707\) −317061. + 183055.i −0.634314 + 0.366222i
\(708\) 0 0
\(709\) −157448. + 272708.i −0.313217 + 0.542508i −0.979057 0.203587i \(-0.934740\pi\)
0.665840 + 0.746095i \(0.268073\pi\)
\(710\) 113569. + 9352.70i 0.225290 + 0.0185533i
\(711\) 0 0
\(712\) 49760.9 197762.i 0.0981585 0.390107i
\(713\) −160228. + 277523.i −0.315181 + 0.545909i
\(714\) 0 0
\(715\) 63878.0 36880.0i 0.124951 0.0721404i
\(716\) 38130.7 14320.4i 0.0743786 0.0279338i
\(717\) 0 0
\(718\) 192370. 277736.i 0.373154 0.538745i
\(719\) 361941.i 0.700132i 0.936725 + 0.350066i \(0.113841\pi\)
−0.936725 + 0.350066i \(0.886159\pi\)
\(720\) 0 0
\(721\) −111926. −0.215308
\(722\) −730221. 505777.i −1.40081 0.970252i
\(723\) 0 0
\(724\) 31932.8 + 85026.6i 0.0609200 + 0.162210i
\(725\) −218164. 377870.i −0.415056 0.718897i
\(726\) 0 0
\(727\) −267542. 154465.i −0.506200 0.292255i 0.225070 0.974343i \(-0.427739\pi\)
−0.731270 + 0.682088i \(0.761072\pi\)
\(728\) −395289. 99462.6i −0.745852 0.187671i
\(729\) 0 0
\(730\) −5028.29 + 61057.9i −0.00943572 + 0.114577i
\(731\) −238457. 137673.i −0.446247 0.257641i
\(732\) 0 0
\(733\) −441272. 764305.i −0.821293 1.42252i −0.904719 0.426008i \(-0.859920\pi\)
0.0834259 0.996514i \(-0.473414\pi\)
\(734\) −317739. 672420.i −0.589764 1.24810i
\(735\) 0 0
\(736\) 450427. 332821.i 0.831512 0.614406i
\(737\) −437829. −0.806065
\(738\) 0 0
\(739\) 396910.i 0.726781i 0.931637 + 0.363390i \(0.118381\pi\)
−0.931637 + 0.363390i \(0.881619\pi\)
\(740\) −131677. + 160217.i −0.240462 + 0.292580i
\(741\) 0 0
\(742\) 423522. + 896284.i 0.769250 + 1.62794i
\(743\) −831366. + 479989.i −1.50596 + 0.869469i −0.505988 + 0.862541i \(0.668872\pi\)
−0.999976 + 0.00692819i \(0.997795\pi\)
\(744\) 0 0
\(745\) −14930.1 + 25859.7i −0.0268999 + 0.0465920i
\(746\) −27935.5 + 339217.i −0.0501971 + 0.609536i
\(747\) 0 0
\(748\) 34250.5 206539.i 0.0612158 0.369147i
\(749\) −361023. + 625310.i −0.643534 + 1.11463i
\(750\) 0 0
\(751\) 572212. 330367.i 1.01456 0.585756i 0.102036 0.994781i \(-0.467464\pi\)
0.912523 + 0.409025i \(0.134131\pi\)
\(752\) −264929. + 52306.4i −0.468482 + 0.0924952i
\(753\) 0 0
\(754\) 295538. + 204700.i 0.519841 + 0.360060i
\(755\) 189241.i 0.331987i
\(756\) 0 0
\(757\) 326842. 0.570356 0.285178 0.958475i \(-0.407947\pi\)
0.285178 + 0.958475i \(0.407947\pi\)
\(758\) 334762. 483316.i 0.582636 0.841187i
\(759\) 0 0
\(760\) −58844.6 206898.i −0.101878 0.358203i
\(761\) 164813. + 285464.i 0.284591 + 0.492927i 0.972510 0.232861i \(-0.0748088\pi\)
−0.687919 + 0.725788i \(0.741475\pi\)
\(762\) 0 0
\(763\) −875410. 505418.i −1.50370 0.868164i
\(764\) 85013.7 512654.i 0.145647 0.878290i
\(765\) 0 0
\(766\) 742285. + 61129.3i 1.26507 + 0.104182i
\(767\) 227694. + 131459.i 0.387044 + 0.223460i
\(768\) 0 0
\(769\) 299738. + 519162.i 0.506862 + 0.877910i 0.999968 + 0.00794129i \(0.00252782\pi\)
−0.493107 + 0.869969i \(0.664139\pi\)
\(770\) 113890. 53816.7i 0.192091 0.0907686i
\(771\) 0 0
\(772\) 7999.60 9733.43i 0.0134225 0.0163317i
\(773\) 58555.0 0.0979952 0.0489976 0.998799i \(-0.484397\pi\)
0.0489976 + 0.998799i \(0.484397\pi\)
\(774\) 0 0
\(775\) 347422.i 0.578433i
\(776\) 221166. + 214501.i 0.367279 + 0.356211i