Properties

Label 108.5.f.a.91.4
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 91.4
Character \(\chi\) \(=\) 108.91
Dual form 108.5.f.a.19.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.61656 + 1.70894i) q^{2} +(10.1591 - 12.3610i) q^{4} +(2.83091 - 4.90328i) q^{5} +(-45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +O(q^{10})\) \(q+(-3.61656 + 1.70894i) q^{2} +(10.1591 - 12.3610i) q^{4} +(2.83091 - 4.90328i) q^{5} +(-45.1595 + 26.0728i) q^{7} +(-15.6169 + 62.0654i) q^{8} +(-1.85878 + 22.5709i) q^{10} +(92.3736 - 53.3319i) q^{11} +(61.0686 - 105.774i) q^{13} +(118.765 - 171.469i) q^{14} +(-49.5864 - 251.152i) q^{16} +122.675 q^{17} +593.624i q^{19} +(-31.8498 - 84.8055i) q^{20} +(-242.934 + 350.739i) q^{22} +(473.649 + 273.461i) q^{23} +(296.472 + 513.504i) q^{25} +(-40.0976 + 486.900i) q^{26} +(-136.493 + 823.090i) q^{28} +(367.933 + 637.279i) q^{29} +(-507.427 - 292.963i) q^{31} +(608.535 + 823.566i) q^{32} +(-443.662 + 209.644i) q^{34} +295.239i q^{35} +2289.29 q^{37} +(-1014.47 - 2146.88i) q^{38} +(260.114 + 252.275i) q^{40} +(-1434.13 + 2483.99i) q^{41} +(1943.81 - 1122.26i) q^{43} +(279.197 - 1683.63i) q^{44} +(-2180.31 - 179.555i) q^{46} +(-913.531 + 527.427i) q^{47} +(159.084 - 275.542i) q^{49} +(-1949.76 - 1350.47i) q^{50} +(-687.066 - 1829.43i) q^{52} +4752.60 q^{53} -603.911i q^{55} +(-912.971 - 3210.02i) q^{56} +(-2419.72 - 1675.99i) q^{58} +(-1864.25 - 1076.32i) q^{59} +(33.1660 + 57.4451i) q^{61} +(2335.80 + 192.360i) q^{62} +(-3608.23 - 1938.53i) q^{64} +(-345.759 - 598.872i) q^{65} +(-3554.82 - 2052.38i) q^{67} +(1246.26 - 1516.38i) q^{68} +(-504.545 - 1067.75i) q^{70} -5031.65i q^{71} +2705.16 q^{73} +(-8279.36 + 3912.25i) q^{74} +(7337.76 + 6030.67i) q^{76} +(-2781.03 + 4816.88i) q^{77} +(1196.02 - 690.524i) q^{79} +(-1371.84 - 467.852i) q^{80} +(941.652 - 11434.4i) q^{82} +(2605.31 - 1504.18i) q^{83} +(347.282 - 601.509i) q^{85} +(-5112.05 + 7380.57i) q^{86} +(1867.48 + 6566.08i) q^{88} -3186.35 q^{89} +6368.92i q^{91} +(8192.07 - 3076.64i) q^{92} +(2402.50 - 3468.64i) q^{94} +(2910.71 + 1680.50i) q^{95} +(2407.03 + 4169.10i) q^{97} +(-104.455 + 1268.38i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + O(q^{10}) \) \( 44q + q^{2} - q^{4} + 2q^{5} - 122q^{8} + 28q^{10} - 2q^{13} - 252q^{14} - q^{16} + 56q^{17} + 140q^{20} - 33q^{22} - 1752q^{25} - 1096q^{26} - 516q^{28} - 526q^{29} + 121q^{32} + 385q^{34} - 8q^{37} - 1395q^{38} - 2276q^{40} + 2762q^{41} - 6714q^{44} + 3576q^{46} + 3428q^{49} - 6375q^{50} + 1438q^{52} + 10088q^{53} + 7506q^{56} - 4064q^{58} - 2q^{61} + 18324q^{62} + 9026q^{64} + 2014q^{65} + 11405q^{68} + 3666q^{70} - 3416q^{73} - 14620q^{74} + 1581q^{76} + 3942q^{77} - 45520q^{80} - 8486q^{82} - 1252q^{85} - 22113q^{86} + 1995q^{88} - 13048q^{89} + 30294q^{92} + 7524q^{94} + 5638q^{97} + 92938q^{98} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.61656 + 1.70894i −0.904141 + 0.427234i
\(3\) 0 0
\(4\) 10.1591 12.3610i 0.634942 0.772560i
\(5\) 2.83091 4.90328i 0.113236 0.196131i −0.803837 0.594850i \(-0.797212\pi\)
0.917073 + 0.398718i \(0.130545\pi\)
\(6\) 0 0
\(7\) −45.1595 + 26.0728i −0.921621 + 0.532098i −0.884152 0.467199i \(-0.845263\pi\)
−0.0374695 + 0.999298i \(0.511930\pi\)
\(8\) −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 \(-0.521376\pi\)
0.830522 + 0.556986i \(0.188042\pi\)
\(12\) 0 0
\(13\) 61.0686 105.774i 0.361352 0.625881i −0.626831 0.779155i \(-0.715648\pi\)
0.988184 + 0.153274i \(0.0489818\pi\)
\(14\) 118.765 171.469i 0.605945 0.874840i
\(15\) 0 0
\(16\) −49.5864 251.152i −0.193697 0.981061i
\(17\) 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 \(0.692750\pi\)
\(20\) −31.8498 84.8055i −0.0796244 0.212014i
\(21\) 0 0
\(22\) −242.934 + 350.739i −0.501930 + 0.724667i
\(23\) 473.649 + 273.461i 0.895366 + 0.516940i 0.875694 0.482867i \(-0.160404\pi\)
0.0196720 + 0.999806i \(0.493738\pi\)
\(24\) 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 0.997496 0.0707290i \(-0.0225326\pi\)
−0.560001 + 0.828492i \(0.689199\pi\)
\(30\) 0 0
\(31\) −507.427 292.963i −0.528020 0.304853i 0.212190 0.977228i \(-0.431941\pi\)
−0.740210 + 0.672376i \(0.765274\pi\)
\(32\) 608.535 + 823.566i 0.594272 + 0.804264i
\(33\) 0 0
\(34\) −443.662 + 209.644i −0.383791 + 0.181353i
\(35\) 295.239i 0.241012i
\(36\) 0 0
\(37\) 2289.29 1.67223 0.836117 0.548551i \(-0.184820\pi\)
0.836117 + 0.548551i \(0.184820\pi\)
\(38\) −1014.47 2146.88i −0.702539 1.48676i
\(39\) 0 0
\(40\) 260.114 + 252.275i 0.162571 + 0.157672i
\(41\) −1434.13 + 2483.99i −0.853142 + 1.47769i 0.0252152 + 0.999682i \(0.491973\pi\)
−0.878358 + 0.478004i \(0.841360\pi\)
\(42\) 0 0
\(43\) 1943.81 1122.26i 1.05128 0.606955i 0.128270 0.991739i \(-0.459057\pi\)
0.923007 + 0.384784i \(0.125724\pi\)
\(44\) 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 \(-0.743409\pi\)
0.278764 + 0.960360i \(0.410075\pi\)
\(48\) 0 0
\(49\) 159.084 275.542i 0.0662574 0.114761i
\(50\) −1949.76 1350.47i −0.779902 0.540188i
\(51\) 0 0
\(52\) −687.066 1829.43i −0.254092 0.676564i
\(53\) 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
\(56\) −912.971 3210.02i −0.291126 1.02360i
\(57\) 0 0
\(58\) −2419.72 1675.99i −0.719299 0.498212i
\(59\) −1864.25 1076.32i −0.535549 0.309200i 0.207724 0.978188i \(-0.433394\pi\)
−0.743273 + 0.668988i \(0.766728\pi\)
\(60\) 0 0
\(61\) 33.1660 + 57.4451i 0.00891319 + 0.0154381i 0.870448 0.492261i \(-0.163829\pi\)
−0.861534 + 0.507699i \(0.830496\pi\)
\(62\) 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 \(-0.484482\pi\)
−0.840630 + 0.541610i \(0.817815\pi\)
\(68\) 1246.26 1516.38i 0.269521 0.327937i
\(69\) 0 0
\(70\) −504.545 1067.75i −0.102968 0.217908i
\(71\) 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 \(0.418314\pi\)
\(74\) −8279.36 + 3912.25i −1.51194 + 0.714435i
\(75\) 0 0
\(76\) 7337.76 + 6030.67i 1.27039 + 1.04409i
\(77\) −2781.03 + 4816.88i −0.469055 + 0.812427i
\(78\) 0 0
\(79\) 1196.02 690.524i 0.191639 0.110643i −0.401110 0.916030i \(-0.631376\pi\)
0.592750 + 0.805387i \(0.298042\pi\)
\(80\) −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 \(-0.596601\pi\)
0.677028 + 0.735957i \(0.263268\pi\)
\(84\) 0 0
\(85\) 347.282 601.509i 0.0480667 0.0832539i
\(86\) −5112.05 + 7380.57i −0.691191 + 0.997914i
\(87\) 0 0
\(88\) 1867.48 + 6566.08i 0.241152 + 0.847893i
\(89\) −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
\(92\) 8192.07 3076.64i 0.967872 0.363497i
\(93\) 0 0
\(94\) 2402.50 3468.64i 0.271899 0.392558i
\(95\) 2910.71 + 1680.50i 0.322516 + 0.186205i
\(96\) 0 0
\(97\) 2407.03 + 4169.10i 0.255822 + 0.443097i 0.965118 0.261814i \(-0.0843206\pi\)
−0.709296 + 0.704910i \(0.750987\pi\)
\(98\) −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 0.641066 0.767486i \(-0.278493\pi\)
−0.985195 + 0.171436i \(0.945159\pi\)
\(102\) 0 0
\(103\) 1858.85 + 1073.21i 0.175214 + 0.101160i 0.585042 0.811003i \(-0.301078\pi\)
−0.409828 + 0.912163i \(0.634411\pi\)
\(104\) 5611.20 + 5442.10i 0.518787 + 0.503153i
\(105\) 0 0
\(106\) −17188.1 + 8121.90i −1.52973 + 0.722846i
\(107\) 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 \(0.803699\pi\)
\(110\) 1032.05 + 2184.08i 0.0852930 + 0.180503i
\(111\) 0 0
\(112\) 8787.53 + 10049.0i 0.700536 + 0.801102i
\(113\) 6817.20 11807.7i 0.533887 0.924719i −0.465329 0.885138i \(-0.654064\pi\)
0.999216 0.0395818i \(-0.0126026\pi\)
\(114\) 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
\(122\) −218.117 151.076i −0.0146545 0.0101502i
\(123\) 0 0
\(124\) −8776.30 + 3296.05i −0.570779 + 0.214363i
\(125\) 6895.78 0.441330
\(126\) 0 0
\(127\) 15689.6i 0.972754i 0.873749 + 0.486377i \(0.161682\pi\)
−0.873749 + 0.486377i \(0.838318\pi\)
\(128\) 16362.2 + 844.606i 0.998670 + 0.0515506i
\(129\) 0 0
\(130\) 2273.89 + 1574.98i 0.134550 + 0.0931941i
\(131\) 7250.25 + 4185.93i 0.422484 + 0.243921i 0.696140 0.717907i \(-0.254899\pi\)
−0.273656 + 0.961828i \(0.588233\pi\)
\(132\) 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 −0.921347 0.388741i \(-0.872910\pi\)
0.124014 0.992280i \(-0.460423\pi\)
\(138\) 0 0
\(139\) −20651.8 11923.3i −1.06888 0.617118i −0.141005 0.990009i \(-0.545033\pi\)
−0.927875 + 0.372891i \(0.878367\pi\)
\(140\) 3649.44 + 2999.36i 0.186196 + 0.153028i
\(141\) 0 0
\(142\) 8598.76 + 18197.3i 0.426441 + 0.902464i
\(143\) 13027.6i 0.637078i
\(144\) 0 0
\(145\) 4166.34 0.198161
\(146\) −9783.40 + 4622.95i −0.458970 + 0.216877i
\(147\) 0 0
\(148\) 23257.0 28297.8i 1.06177 1.29190i
\(149\) 2636.98 4567.39i 0.118778 0.205729i −0.800506 0.599325i \(-0.795436\pi\)
0.919284 + 0.393596i \(0.128769\pi\)
\(150\) 0 0
\(151\) 28946.1 16712.0i 1.26951 0.732951i 0.294614 0.955616i \(-0.404809\pi\)
0.974895 + 0.222665i \(0.0714756\pi\)
\(152\) −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 −0.985330 0.170658i \(-0.945411\pi\)
0.640459 + 0.767992i \(0.278744\pi\)
\(158\) −3145.43 + 4541.25i −0.125999 + 0.181912i
\(159\) 0 0
\(160\) 5760.88 652.373i 0.225034 0.0254833i
\(161\) −28519.6 −1.10025
\(162\) 0 0
\(163\) 30843.8i 1.16089i 0.814298 + 0.580447i \(0.197122\pi\)
−0.814298 + 0.580447i \(0.802878\pi\)
\(164\) 16135.0 + 42962.3i 0.599904 + 1.59735i
\(165\) 0 0
\(166\) −6851.74 + 9892.27i −0.248648 + 0.358988i
\(167\) −13682.1 7899.35i −0.490591 0.283243i 0.234229 0.972181i \(-0.424743\pi\)
−0.724819 + 0.688939i \(0.758077\pi\)
\(168\) 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 0.928255 + 0.371944i \(0.121309\pi\)
−0.142015 + 0.989865i \(0.545358\pi\)
\(174\) 0 0
\(175\) −26777.0 15459.7i −0.874352 0.504807i
\(176\) −17974.9 20555.3i −0.580284 0.663586i
\(177\) 0 0
\(178\) 11523.7 5445.28i 0.363706 0.171862i
\(179\) 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 \(0.472388\pi\)
\(182\) −10884.1 23033.6i −0.328586 0.695375i
\(183\) 0 0
\(184\) −24369.4 + 25126.6i −0.719795 + 0.742160i
\(185\) 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 \(-0.519820\pi\)
0.833234 + 0.552920i \(0.186487\pi\)
\(192\) 0 0
\(193\) −393.717 + 681.937i −0.0105699 + 0.0183075i −0.871262 0.490818i \(-0.836698\pi\)
0.860692 + 0.509126i \(0.170031\pi\)
\(194\) −15829.9 10964.3i −0.420605 0.291326i
\(195\) 0 0
\(196\) −1789.81 4765.68i −0.0465903 0.124055i
\(197\) −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 \(-0.0484485\pi\)
\(200\) −36500.8 + 10381.3i −0.912520 + 0.259533i
\(201\) 0 0
\(202\) 23086.7 + 15990.7i 0.565794 + 0.391889i
\(203\) −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 \(-0.441771\pi\)
−0.760620 + 0.649198i \(0.775105\pi\)
\(212\) 48282.1 58746.7i 1.07427 1.30711i
\(213\) 0 0
\(214\) −23663.2 50077.6i −0.516708 1.09349i
\(215\) 12708.1i 0.274917i
\(216\) 0 0
\(217\) 30553.5 0.648846
\(218\) 70106.6 33127.5i 1.47518 0.697069i
\(219\) 0 0
\(220\) −7464.92 6135.18i −0.154234 0.126760i
\(221\) 7491.58 12975.8i 0.153387 0.265674i
\(222\) 0 0
\(223\) 45854.8 26474.3i 0.922093 0.532371i 0.0377910 0.999286i \(-0.487968\pi\)
0.884302 + 0.466915i \(0.154635\pi\)
\(224\) −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 \(-0.785663\pi\)
0.149203 + 0.988807i \(0.452329\pi\)
\(228\) 0 0
\(229\) 28619.2 49569.9i 0.545741 0.945251i −0.452819 0.891603i \(-0.649582\pi\)
0.998560 0.0536486i \(-0.0170851\pi\)
\(230\) −7052.66 + 10182.4i −0.133321 + 0.192483i
\(231\) 0 0
\(232\) −45298.9 + 12883.6i −0.841612 + 0.239366i
\(233\) 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
\(236\) −32243.4 + 12109.4i −0.578918 + 0.217420i
\(237\) 0 0
\(238\) 14569.5 21034.9i 0.257212 0.371353i
\(239\) 45342.6 + 26178.6i 0.793799 + 0.458300i 0.841298 0.540571i \(-0.181792\pi\)
−0.0474993 + 0.998871i \(0.515125\pi\)
\(240\) 0 0
\(241\) 6755.56 + 11701.0i 0.116313 + 0.201460i 0.918304 0.395877i \(-0.129559\pi\)
−0.801991 + 0.597336i \(0.796226\pi\)
\(242\) 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
\(248\) 26107.3 26918.5i 0.424482 0.437671i
\(249\) 0 0
\(250\) −24939.0 + 11784.4i −0.399024 + 0.188551i
\(251\) 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
\(254\) −26812.4 56742.3i −0.415594 0.879507i
\(255\) 0 0
\(256\) −60618.4 + 24907.4i −0.924963 + 0.380057i
\(257\) −36956.5 + 64010.6i −0.559532 + 0.969138i 0.438003 + 0.898973i \(0.355686\pi\)
−0.997535 + 0.0701645i \(0.977648\pi\)
\(258\) 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 \(-0.649705\pi\)
0.545415 + 0.838166i \(0.316372\pi\)
\(264\) 0 0
\(265\) 13454.2 23303.3i 0.191587 0.331838i
\(266\) 101788. + 70502.0i 1.43858 + 0.996410i
\(267\) 0 0
\(268\) −61483.1 + 23090.8i −0.856024 + 0.321491i
\(269\) 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 \(-0.0272094\pi\)
\(272\) −6083.01 30810.0i −0.0822206 0.416442i
\(273\) 0 0
\(274\) 98418.7 + 68168.3i 1.31092 + 0.907990i
\(275\) 54772.4 + 31622.8i 0.724263 + 0.418153i
\(276\) 0 0
\(277\) 46052.4 + 79765.0i 0.600195 + 1.03957i 0.992791 + 0.119857i \(0.0382436\pi\)
−0.392596 + 0.919711i \(0.628423\pi\)
\(278\) 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 0.927942 0.372723i \(-0.121576\pi\)
−0.786759 + 0.617260i \(0.788243\pi\)
\(282\) 0 0
\(283\) 21648.6 + 12498.8i 0.270307 + 0.156062i 0.629027 0.777383i \(-0.283453\pi\)
−0.358720 + 0.933445i \(0.616787\pi\)
\(284\) −62196.0 51116.9i −0.771126 0.633764i
\(285\) 0 0
\(286\) 22263.4 + 47115.2i 0.272182 + 0.576009i
\(287\) 149568.i 1.81582i
\(288\) 0 0
\(289\) −68471.9 −0.819816
\(290\) −15067.8 + 7120.01i −0.179166 + 0.0846612i
\(291\) 0 0
\(292\) 27482.0 33438.4i 0.322316 0.392175i
\(293\) −11748.6 + 20349.1i −0.136852 + 0.237034i −0.926303 0.376779i \(-0.877032\pi\)
0.789452 + 0.613813i \(0.210365\pi\)
\(294\) 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
\(302\) −76125.6 + 109907.i −0.834673 + 1.20507i
\(303\) 0 0
\(304\) 149090. 29435.7i 1.61325 0.318513i
\(305\) 375.559 0.00403719
\(306\) 0 0
\(307\) 32060.0i 0.340163i −0.985430 0.170082i \(-0.945597\pi\)
0.985430 0.170082i \(-0.0544031\pi\)
\(308\) 31288.6 + 83311.2i 0.329826 + 0.878217i
\(309\) 0 0
\(310\) 7555.63 10908.5i 0.0786226 0.113512i
\(311\) −61441.4 35473.2i −0.635244 0.366758i 0.147536 0.989057i \(-0.452866\pi\)
−0.782780 + 0.622298i \(0.786199\pi\)
\(312\) 0 0
\(313\) −59259.6 102641.i −0.604882 1.04769i −0.992070 0.125685i \(-0.959887\pi\)
0.387189 0.922001i \(-0.373446\pi\)
\(314\) 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 −0.977727 0.209882i \(-0.932692\pi\)
0.307100 0.951677i \(-0.400641\pi\)
\(318\) 0 0
\(319\) 67974.6 + 39245.2i 0.667983 + 0.385660i
\(320\) −19719.7 + 12204.3i −0.192576 + 0.119183i
\(321\) 0 0
\(322\) 103143. 48738.2i 0.994782 0.470065i
\(323\) 72822.8i 0.698011i
\(324\) 0 0
\(325\) 72420.4 0.685637
\(326\) −52710.0 111548.i −0.495973 1.04961i
\(327\) 0 0
\(328\) −131773. 127802.i −1.22484 1.18793i
\(329\) 27503.0 47636.7i 0.254091 0.440098i
\(330\) 0 0
\(331\) −133143. + 76870.2i −1.21524 + 0.701620i −0.963896 0.266278i \(-0.914206\pi\)
−0.251345 + 0.967898i \(0.580873\pi\)
\(332\) 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 −0.811090 0.584922i \(-0.801125\pi\)
0.912102 + 0.409964i \(0.134459\pi\)
\(338\) −44863.5 31074.1i −0.392699 0.271997i
\(339\) 0 0
\(340\) −3907.17 10403.5i −0.0337990 0.0899958i
\(341\) −62497.2 −0.537467
\(342\) 0 0
\(343\) 108611.i 0.923175i
\(344\) 39297.3 + 138170.i 0.332082 + 1.16760i
\(345\) 0 0
\(346\) −154755. 107189.i −1.29268 0.895358i
\(347\) 6260.87 + 3614.72i 0.0519967 + 0.0300203i 0.525773 0.850625i \(-0.323776\pi\)
−0.473776 + 0.880645i \(0.657109\pi\)
\(348\) 0 0
\(349\) −55282.6 95752.3i −0.453877 0.786137i 0.544746 0.838601i \(-0.316626\pi\)
−0.998623 + 0.0524636i \(0.983293\pi\)
\(350\) 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 0.715557 0.698554i \(-0.246173\pi\)
−0.962744 + 0.270414i \(0.912840\pi\)
\(354\) 0 0
\(355\) −24671.6 14244.1i −0.195767 0.113026i
\(356\) −32370.4 + 39386.4i −0.255416 + 0.310775i
\(357\) 0 0
\(358\) 4350.43 + 9206.66i 0.0339442 + 0.0718350i
\(359\) 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
\(362\) −20529.7 + 9700.91i −0.156663 + 0.0740279i
\(363\) 0 0
\(364\) 78725.9 + 64702.3i 0.594176 + 0.488334i
\(365\) 7658.07 13264.2i 0.0574823 0.0995622i
\(366\) 0 0
\(367\) 161018. 92963.9i 1.19548 0.690212i 0.235937 0.971768i \(-0.424184\pi\)
0.959545 + 0.281556i \(0.0908507\pi\)
\(368\) 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 −0.671639 0.740878i \(-0.734409\pi\)
0.977439 + 0.211217i \(0.0677428\pi\)
\(374\) −29801.9 + 43026.9i −0.213060 + 0.307607i
\(375\) 0 0
\(376\) −18468.5 64935.4i −0.130634 0.459310i
\(377\) 89876.5 0.632359
\(378\) 0 0
\(379\) 146982.i 1.02326i −0.859206 0.511630i \(-0.829042\pi\)
0.859206 0.511630i \(-0.170958\pi\)
\(380\) 50342.6 18906.8i 0.348633 0.130934i
\(381\) 0 0
\(382\) −73971.9 + 106798.i −0.506921 + 0.731872i
\(383\) −161253. 93099.7i −1.09929 0.634674i −0.163254 0.986584i \(-0.552199\pi\)
−0.936034 + 0.351910i \(0.885532\pi\)
\(384\) 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 −0.884840 0.465894i \(-0.845733\pi\)
0.0389437 0.999241i \(-0.487601\pi\)
\(390\) 0 0
\(391\) 58104.8 + 33546.8i 0.380066 + 0.219431i
\(392\) 14617.2 + 14176.7i 0.0951245 + 0.0922579i
\(393\) 0 0
\(394\) 89784.4 42425.9i 0.578374 0.273299i
\(395\) 7819.24i 0.0501153i
\(396\) 0 0
\(397\) −260735. −1.65432 −0.827159 0.561968i \(-0.810044\pi\)
−0.827159 + 0.561968i \(0.810044\pi\)
\(398\) 20521.7 + 43429.5i 0.129553 + 0.274169i
\(399\) 0 0
\(400\) 114267. 99922.3i 0.714166 0.624514i
\(401\) 26507.0 45911.4i 0.164843 0.285517i −0.771756 0.635918i \(-0.780621\pi\)
0.936600 + 0.350401i \(0.113955\pi\)
\(402\) 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 −0.997731 0.0673220i \(-0.978555\pi\)
0.557168 + 0.830400i \(0.311888\pi\)
\(410\) −53400.1 36986.8i −0.317668 0.220028i
\(411\) 0 0
\(412\) 32150.1 12074.4i 0.189403 0.0711328i
\(413\) 112251. 0.658099
\(414\) 0 0
\(415\) 17032.8i 0.0988983i
\(416\) 124274. 14073.0i 0.718115 0.0813206i
\(417\) 0 0
\(418\) −208207. 144212.i −1.19163 0.825368i
\(419\) 201431. + 116296.i 1.14736 + 0.662426i 0.948242 0.317550i \(-0.102860\pi\)
0.199115 + 0.979976i \(0.436193\pi\)
\(420\) 0 0
\(421\) 34900.8 + 60449.9i 0.196911 + 0.341060i 0.947525 0.319680i \(-0.103576\pi\)
−0.750614 + 0.660741i \(0.770242\pi\)
\(422\) 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
\(428\) 171159. + 140670.i 0.934354 + 0.767916i
\(429\) 0 0
\(430\) 21717.3 + 45959.5i 0.117454 + 0.248564i
\(431\) 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 \(0.211988\pi\)
\(434\) −110499. + 52214.0i −0.586649 + 0.277209i
\(435\) 0 0
\(436\) −196932. + 239615.i −1.03596 + 1.26050i
\(437\) −162333. + 281169.i −0.850050 + 1.47233i
\(438\) 0 0
\(439\) −62468.0 + 36065.9i −0.324137 + 0.187140i −0.653235 0.757155i \(-0.726589\pi\)
0.329098 + 0.944296i \(0.393255\pi\)
\(440\) 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 \(-0.828353\pi\)
0.0156440 + 0.999878i \(0.495020\pi\)
\(444\) 0 0
\(445\) −9020.28 + 15623.6i −0.0455512 + 0.0788970i
\(446\) −120594. + 174109.i −0.606255 + 0.875288i
\(447\) 0 0
\(448\) 213489. 6533.50i 1.06370 0.0325529i
\(449\) −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
\(452\) −76698.5 204223.i −0.375414 0.999603i
\(453\) 0 0
\(454\) 85718.0 123756.i 0.415873 0.600421i
\(455\) 31228.6 + 18029.8i 0.150844 + 0.0870901i
\(456\) 0 0
\(457\) 2962.66 + 5131.48i 0.0141857 + 0.0245703i 0.873031 0.487665i \(-0.162151\pi\)
−0.858845 + 0.512235i \(0.828818\pi\)
\(458\) −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 0.975690 0.219156i \(-0.0703304\pi\)
−0.677640 + 0.735394i \(0.736997\pi\)
\(462\) 0 0
\(463\) 204011. + 117786.i 0.951682 + 0.549454i 0.893603 0.448858i \(-0.148169\pi\)
0.0580790 + 0.998312i \(0.481502\pi\)
\(464\) 141809. 124007.i 0.658671 0.575985i
\(465\) 0 0
\(466\) −131891. + 62322.7i −0.607358 + 0.286995i
\(467\) 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
\(470\) −10206.4 21599.5i −0.0462039 0.0977798i
\(471\) 0 0
\(472\) 95916.2 98896.5i 0.430534 0.443912i
\(473\) 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 0.522126 0.852869i \(-0.325139\pi\)
0.999669 0.0257398i \(-0.00819415\pi\)
\(480\) 0 0
\(481\) 139803. 242147.i 0.604266 1.04662i
\(482\) −44428.1 30772.5i −0.191233 0.132455i
\(483\) 0 0
\(484\) 18360.2 + 48887.1i 0.0783766 + 0.208691i
\(485\) 27256.3 0.115873
\(486\) 0 0
\(487\) 195207.i 0.823071i −0.911394 0.411536i \(-0.864993\pi\)
0.911394 0.411536i \(-0.135007\pi\)
\(488\) −4083.30 + 1161.35i −0.0171464 + 0.00487665i
\(489\) 0 0
\(490\) 5923.51 + 4102.83i 0.0246710 + 0.0170880i
\(491\) 65937.1 + 38068.8i 0.273506 + 0.157909i 0.630480 0.776206i \(-0.282858\pi\)
−0.356974 + 0.934114i \(0.616191\pi\)
\(492\) 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 \(-0.342648\pi\)
−0.525124 + 0.851026i \(0.675981\pi\)
\(500\) 70054.7 85238.4i 0.280219 0.340953i
\(501\) 0 0
\(502\) −190220. 402557.i −0.754830 1.59742i
\(503\) 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
\(506\) −210979. + 99693.9i −0.824020 + 0.389375i
\(507\) 0 0
\(508\) 193938. + 159391.i 0.751511 + 0.617643i
\(509\) 101505. 175811.i 0.391787 0.678595i −0.600899 0.799325i \(-0.705190\pi\)
0.992685 + 0.120731i \(0.0385238\pi\)
\(510\) 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
\(518\) 271888. 392541.i 1.01328 1.46294i
\(519\) 0 0
\(520\) 42568.9 12107.2i 0.157429 0.0447750i
\(521\) 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 \(-0.0552109\pi\)
\(524\) 125398. 47094.8i 0.456697 0.171518i
\(525\) 0 0
\(526\) −16781.0 + 24227.8i −0.0606523 + 0.0875674i
\(527\) −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
\(536\) 182897. 188580.i 0.636615 0.656396i
\(537\) 0 0
\(538\) −139617. + 65973.1i −0.482361 + 0.227930i
\(539\) 33937.0i 0.116814i
\(540\) 0 0
\(541\) 166561. 0.569087 0.284544 0.958663i \(-0.408158\pi\)
0.284544 + 0.958663i \(0.408158\pi\)
\(542\) 21430.6 + 45352.8i 0.0729517 + 0.154385i
\(543\) 0 0
\(544\) 74651.9 + 101031.i 0.252257 + 0.341395i
\(545\) −54876.8 + 95049.4i −0.184755 + 0.320005i
\(546\) 0 0
\(547\) 256245. 147943.i 0.856410 0.494448i −0.00639865 0.999980i \(-0.502037\pi\)
0.862808 + 0.505531i \(0.168703\pi\)
\(548\) −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
\(554\) −302865. 209775.i −0.986800 0.683492i
\(555\) 0 0
\(556\) −357187. + 134146.i −1.15544 + 0.433939i
\(557\) 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
\(560\) 74149.8 14639.8i 0.236447 0.0466832i
\(561\) 0 0
\(562\) −73314.9 50780.5i −0.232124 0.160777i
\(563\) −210267. 121398.i −0.663369 0.382996i 0.130191 0.991489i \(-0.458441\pi\)
−0.793559 + 0.608493i \(0.791774\pi\)
\(564\) 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 0.998884 0.0472242i \(-0.0150375\pi\)
−0.540339 + 0.841447i \(0.681704\pi\)
\(570\) 0 0
\(571\) −228446. 131893.i −0.700665 0.404529i 0.106930 0.994267i \(-0.465898\pi\)
−0.807595 + 0.589737i \(0.799231\pi\)
\(572\) −161034. 132349.i −0.492181 0.404508i
\(573\) 0 0
\(574\) 255601. + 540921.i 0.775781 + 1.64176i
\(575\) 324294.i 0.980852i
\(576\) 0 0
\(577\) 350367. 1.05238 0.526188 0.850368i \(-0.323621\pi\)
0.526188 + 0.850368i \(0.323621\pi\)
\(578\) 247633. 117014.i 0.741229 0.350253i
\(579\) 0 0
\(580\) 42326.2 51499.9i 0.125821 0.153091i
\(581\) −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 \(-0.669849\pi\)
0.491318 + 0.870980i \(0.336515\pi\)
\(588\) 0 0
\(589\) 173910. 301221.i 0.501296 0.868270i
\(590\) 27758.8 40077.0i 0.0797437 0.115131i
\(591\) 0 0
\(592\) −113517. 574959.i −0.323906 1.64056i
\(593\) −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
\(596\) −29668.0 78996.0i −0.0835209 0.222389i
\(597\) 0 0
\(598\) −152140. + 219654.i −0.425444 + 0.614239i
\(599\) −122771. 70881.9i −0.342170 0.197552i 0.319061 0.947734i \(-0.396633\pi\)
−0.661231 + 0.750182i \(0.729966\pi\)
\(600\) 0 0
\(601\) 265380. + 459652.i 0.734715 + 1.27256i 0.954848 + 0.297094i \(0.0960176\pi\)
−0.220133 + 0.975470i \(0.570649\pi\)
\(602\) 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 \(-0.350907\pi\)
−0.547027 + 0.837115i \(0.684241\pi\)
\(608\) −488889. + 361241.i −1.32252 + 0.977214i
\(609\) 0 0
\(610\) −1358.23 + 641.807i −0.00365019 + 0.00172482i
\(611\) 128837.i 0.345110i
\(612\) 0 0
\(613\) −498556. −1.32676 −0.663382 0.748281i \(-0.730879\pi\)
−0.663382 + 0.748281i \(0.730879\pi\)
\(614\) 54788.5 + 115947.i 0.145329 + 0.307555i
\(615\) 0 0
\(616\) −255531. 247830.i −0.673413 0.653120i
\(617\) −45030.4 + 77995.0i −0.118287 + 0.204879i −0.919089 0.394050i \(-0.871074\pi\)
0.800802 + 0.598929i \(0.204407\pi\)
\(618\) 0 0
\(619\) 149379. 86244.1i 0.389860 0.225086i −0.292240 0.956345i \(-0.594400\pi\)
0.682099 + 0.731259i \(0.261067\pi\)
\(620\) −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
\(626\) 389723. + 269936.i 0.994505 + 0.688830i
\(627\) 0 0
\(628\) 95639.3 + 254656.i 0.242503 + 0.645706i
\(629\) 280838. 0.709831
\(630\) 0 0
\(631\) 210621.i 0.528985i 0.964388 + 0.264492i \(0.0852044\pi\)
−0.964388 + 0.264492i \(0.914796\pi\)
\(632\) 24179.5 + 85015.4i 0.0605359 + 0.212845i
\(633\) 0 0
\(634\) 443196. + 306973.i 1.10260 + 0.763699i
\(635\) 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 −0.997024 0.0770943i \(-0.975436\pi\)
0.431746 0.901995i \(-0.357898\pi\)
\(642\) 0 0
\(643\) −361978. 208988.i −0.875509 0.505476i −0.00633423 0.999980i \(-0.502016\pi\)
−0.869175 + 0.494504i \(0.835350\pi\)
\(644\) −289733. + 352530.i −0.698596 + 0.850010i
\(645\) 0 0
\(646\) −124450. 263368.i −0.298214 0.631101i
\(647\) 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
\(650\) −261913. + 123762.i −0.619913 + 0.292928i
\(651\) 0 0
\(652\) 381258. + 313344.i 0.896859 + 0.737100i
\(653\) 164273. 284529.i 0.385247 0.667267i −0.606557 0.795040i \(-0.707450\pi\)
0.991803 + 0.127773i \(0.0407830\pi\)
\(654\) 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 \(-0.604946\pi\)
0.657502 + 0.753453i \(0.271613\pi\)
\(660\) 0 0
\(661\) 152616. 264339.i 0.349300 0.605005i −0.636826 0.771008i \(-0.719753\pi\)
0.986125 + 0.166003i \(0.0530862\pi\)
\(662\) 350154. 505539.i 0.798994 1.15356i
\(663\) 0 0
\(664\) 52670.6 + 185190.i 0.119463 + 0.420032i
\(665\) −175261. −0.396317
\(666\) 0 0
\(667\) 402461.i 0.904633i
\(668\) −236641. + 88873.4i −0.530318 + 0.199168i
\(669\) 0 0
\(670\) 52931.6 76420.5i 0.117914 0.170240i
\(671\) 6127.32 + 3537.61i 0.0136090 + 0.00785715i
\(672\) 0 0
\(673\) −403032. 698073.i −0.889836 1.54124i −0.840069 0.542480i \(-0.817485\pi\)
−0.0497671 0.998761i \(-0.515848\pi\)
\(674\) −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 0.594136 0.804365i \(-0.297494\pi\)
−0.993668 + 0.112354i \(0.964161\pi\)
\(678\) 0 0
\(679\) −217400. 125516.i −0.471542 0.272245i
\(680\) 31909.5 + 30947.9i 0.0690084 + 0.0669288i
\(681\) 0 0
\(682\) 226025. 106804.i 0.485946 0.229624i
\(683\) 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
\(686\) 185609. + 392797.i 0.394412 + 0.834680i
\(687\) 0 0
\(688\) −378244. 432543.i −0.799089 0.913802i
\(689\) 290235. 502701.i 0.611379 1.05894i
\(690\) 0 0
\(691\) −304679. + 175906.i −0.638096 + 0.368405i −0.783881 0.620912i \(-0.786763\pi\)
0.145785 + 0.989316i \(0.453429\pi\)
\(692\) 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
\(698\) 363568. + 251820.i 0.746233 + 0.516868i
\(699\) 0 0
\(700\) −463127. + 173933.i −0.945156 + 0.354965i
\(701\) 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
\(704\) −436691. + 13364.3i −0.881107 + 0.0269650i
\(705\) 0 0
\(706\) 202568. + 140306.i 0.406408 + 0.281493i
\(707\) 317061. + 183055.i 0.634314 + 0.366222i
\(708\) 0 0
\(709\) −157448. 272708.i −0.313217 0.542508i 0.665840 0.746095i \(-0.268073\pi\)
−0.979057 + 0.203587i \(0.934740\pi\)
\(710\) 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
\(716\) −31467.2 25861.9i −0.0613807 0.0504469i
\(717\) 0 0
\(718\) 144341. + 305465.i 0.279990 + 0.592533i
\(719\) 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
\(722\) 803126. 379501.i 1.54067 0.728013i
\(723\) 0 0
\(724\) 57668.8 70167.9i 0.110018 0.133863i
\(725\) −218164. + 377870.i −0.415056 + 0.718897i
\(726\) 0 0
\(727\) 267542. 154465.i 0.506200 0.292255i −0.225070 0.974343i \(-0.572261\pi\)
0.731270 + 0.682088i \(0.238928\pi\)
\(728\) −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 0.0834259 + 0.996514i \(0.473414\pi\)
−0.904719 + 0.426008i \(0.859920\pi\)
\(734\) −423464. + 611380.i −0.786002 + 1.13480i
\(735\) 0 0
\(736\) 63018.1 + 556492.i 0.116335 + 1.02731i
\(737\) −437829. −0.806065
\(738\) 0 0
\(739\) 396910.i 0.726781i 0.931637 + 0.363390i \(0.118381\pi\)
−0.931637 + 0.363390i \(0.881619\pi\)
\(740\) −72913.3 194144.i −0.133151 0.354537i
\(741\) 0 0
\(742\) 564444. 814923.i 1.02521 1.48016i
\(743\) 831366. + 479989.i 1.50596 + 0.869469i 0.999976 + 0.00692819i \(0.00220533\pi\)
0.505988 + 0.862541i \(0.331128\pi\)
\(744\) 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 \(-0.532536\pi\)
−0.912523 + 0.409025i \(0.865869\pi\)
\(752\) 177763. + 203282.i 0.314344 + 0.359470i
\(753\) 0 0
\(754\) −325044. + 153593.i −0.571742 + 0.270165i
\(755\) 189241.i 0.331987i
\(756\) 0 0
\(757\) 326842. 0.570356 0.285178 0.958475i \(-0.407947\pi\)
0.285178 + 0.958475i \(0.407947\pi\)
\(758\) 251183. + 531570.i 0.437171 + 0.925171i
\(759\) 0 0
\(760\) −149757. + 154410.i −0.259274 + 0.267330i
\(761\) 164813. 285464.i 0.284591 0.492927i −0.687919 0.725788i \(-0.741475\pi\)
0.972510 + 0.232861i \(0.0748088\pi\)
\(762\) 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 −0.493107 0.869969i \(-0.664139\pi\)
0.999968 0.00794129i \(-0.00252782\pi\)
\(770\) −103552. 71723.7i −0.174653 0.120971i
\(771\) 0 0
\(772\) 4429.60 + 11794.6i 0.00743241 + 0.0197901i
\(773\) 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
\(776\) −296347. + 84285.0i −0.492127 + 0.139967i
\(777\) 0 0
\(778\) 841808. +