Properties

Label 108.6.h.a.35.16
Level 108
Weight 6
Character 108.35
Analytic conductor 17.321
Analytic rank 0
Dimension 56
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 36)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 35.16
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.16

$q$-expansion

\(f(q)\) \(=\) \(q+(1.64008 + 5.41389i) q^{2} +(-26.6203 + 17.7584i) q^{4} +(-38.3603 + 22.1474i) q^{5} +(102.940 + 59.4323i) q^{7} +(-139.801 - 114.994i) q^{8} +O(q^{10})\) \(q+(1.64008 + 5.41389i) q^{2} +(-26.6203 + 17.7584i) q^{4} +(-38.3603 + 22.1474i) q^{5} +(102.940 + 59.4323i) q^{7} +(-139.801 - 114.994i) q^{8} +(-182.817 - 171.355i) q^{10} +(-349.253 + 604.924i) q^{11} +(-271.774 - 470.726i) q^{13} +(-152.931 + 654.777i) q^{14} +(393.281 - 945.466i) q^{16} -1884.06i q^{17} -961.023i q^{19} +(627.863 - 1270.79i) q^{20} +(-3847.79 - 898.695i) q^{22} +(-566.279 - 980.824i) q^{23} +(-581.490 + 1007.17i) q^{25} +(2102.73 - 2243.38i) q^{26} +(-3795.71 + 245.936i) q^{28} +(-173.063 - 99.9180i) q^{29} +(-225.699 + 130.308i) q^{31} +(5763.66 + 578.543i) q^{32} +(10200.1 - 3089.99i) q^{34} -5265.07 q^{35} -11136.8 q^{37} +(5202.87 - 1576.15i) q^{38} +(7909.63 + 1314.99i) q^{40} +(8446.51 - 4876.59i) q^{41} +(-5303.93 - 3062.23i) q^{43} +(-1445.24 - 22305.4i) q^{44} +(4381.33 - 4674.39i) q^{46} +(-589.363 + 1020.81i) q^{47} +(-1339.11 - 2319.40i) q^{49} +(-6406.39 - 1496.28i) q^{50} +(15594.0 + 7704.61i) q^{52} +34070.7i q^{53} -30940.1i q^{55} +(-7556.71 - 20146.2i) q^{56} +(257.108 - 1100.82i) q^{58} +(5319.11 + 9212.96i) q^{59} +(-5470.51 + 9475.20i) q^{61} +(-1075.63 - 1008.20i) q^{62} +(6320.66 + 32152.6i) q^{64} +(20850.7 + 12038.1i) q^{65} +(-49766.8 + 28732.9i) q^{67} +(33457.8 + 50154.1i) q^{68} +(-8635.12 - 28504.5i) q^{70} -70902.1 q^{71} -18551.8 q^{73} +(-18265.1 - 60293.2i) q^{74} +(17066.2 + 25582.7i) q^{76} +(-71904.1 + 41513.8i) q^{77} +(-12856.7 - 7422.81i) q^{79} +(5853.17 + 44978.5i) q^{80} +(40254.2 + 37730.4i) q^{82} +(1200.62 - 2079.54i) q^{83} +(41726.9 + 72273.0i) q^{85} +(7879.69 - 33737.2i) q^{86} +(118389. - 44406.9i) q^{88} +28779.3i q^{89} -64608.5i q^{91} +(32492.3 + 16053.6i) q^{92} +(-6493.13 - 1516.54i) q^{94} +(21284.1 + 36865.2i) q^{95} +(-78738.0 + 136378. i) q^{97} +(10360.7 - 11053.8i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.64008 + 5.41389i 0.289927 + 0.957049i
\(3\) 0 0
\(4\) −26.6203 + 17.7584i −0.831884 + 0.554949i
\(5\) −38.3603 + 22.1474i −0.686211 + 0.396184i −0.802191 0.597068i \(-0.796332\pi\)
0.115980 + 0.993252i \(0.462999\pi\)
\(6\) 0 0
\(7\) 102.940 + 59.4323i 0.794032 + 0.458435i 0.841380 0.540444i \(-0.181744\pi\)
−0.0473481 + 0.998878i \(0.515077\pi\)
\(8\) −139.801 114.994i −0.772299 0.635259i
\(9\) 0 0
\(10\) −182.817 171.355i −0.578118 0.541873i
\(11\) −349.253 + 604.924i −0.870279 + 1.50737i −0.00857110 + 0.999963i \(0.502728\pi\)
−0.861708 + 0.507404i \(0.830605\pi\)
\(12\) 0 0
\(13\) −271.774 470.726i −0.446014 0.772520i 0.552108 0.833773i \(-0.313824\pi\)
−0.998122 + 0.0612530i \(0.980490\pi\)
\(14\) −152.931 + 654.777i −0.208533 + 0.892840i
\(15\) 0 0
\(16\) 393.281 945.466i 0.384064 0.923307i
\(17\) 1884.06i 1.58114i −0.612369 0.790572i \(-0.709783\pi\)
0.612369 0.790572i \(-0.290217\pi\)
\(18\) 0 0
\(19\) 961.023i 0.610731i −0.952235 0.305366i \(-0.901221\pi\)
0.952235 0.305366i \(-0.0987786\pi\)
\(20\) 627.863 1270.79i 0.350986 0.710391i
\(21\) 0 0
\(22\) −3847.79 898.695i −1.69494 0.395873i
\(23\) −566.279 980.824i −0.223208 0.386608i 0.732572 0.680690i \(-0.238320\pi\)
−0.955780 + 0.294081i \(0.904986\pi\)
\(24\) 0 0
\(25\) −581.490 + 1007.17i −0.186077 + 0.322294i
\(26\) 2102.73 2243.38i 0.610027 0.650832i
\(27\) 0 0
\(28\) −3795.71 + 245.936i −0.914951 + 0.0592825i
\(29\) −173.063 99.9180i −0.0382128 0.0220622i 0.480772 0.876846i \(-0.340357\pi\)
−0.518985 + 0.854784i \(0.673690\pi\)
\(30\) 0 0
\(31\) −225.699 + 130.308i −0.0421819 + 0.0243537i −0.520943 0.853592i \(-0.674419\pi\)
0.478761 + 0.877945i \(0.341086\pi\)
\(32\) 5763.66 + 578.543i 0.995000 + 0.0998759i
\(33\) 0 0
\(34\) 10200.1 3089.99i 1.51323 0.458417i
\(35\) −5265.07 −0.726498
\(36\) 0 0
\(37\) −11136.8 −1.33738 −0.668690 0.743541i \(-0.733145\pi\)
−0.668690 + 0.743541i \(0.733145\pi\)
\(38\) 5202.87 1576.15i 0.584499 0.177068i
\(39\) 0 0
\(40\) 7909.63 + 1314.99i 0.781639 + 0.129949i
\(41\) 8446.51 4876.59i 0.784725 0.453061i −0.0533772 0.998574i \(-0.516999\pi\)
0.838102 + 0.545513i \(0.183665\pi\)
\(42\) 0 0
\(43\) −5303.93 3062.23i −0.437448 0.252561i 0.265066 0.964230i \(-0.414606\pi\)
−0.702515 + 0.711669i \(0.747939\pi\)
\(44\) −1445.24 22305.4i −0.112540 1.73692i
\(45\) 0 0
\(46\) 4381.33 4674.39i 0.305289 0.325710i
\(47\) −589.363 + 1020.81i −0.0389169 + 0.0674061i −0.884828 0.465918i \(-0.845724\pi\)
0.845911 + 0.533324i \(0.179057\pi\)
\(48\) 0 0
\(49\) −1339.11 2319.40i −0.0796755 0.138002i
\(50\) −6406.39 1496.28i −0.362400 0.0846426i
\(51\) 0 0
\(52\) 15594.0 + 7704.61i 0.799741 + 0.395132i
\(53\) 34070.7i 1.66606i 0.553227 + 0.833031i \(0.313396\pi\)
−0.553227 + 0.833031i \(0.686604\pi\)
\(54\) 0 0
\(55\) 30940.1i 1.37916i
\(56\) −7556.71 20146.2i −0.322005 0.858465i
\(57\) 0 0
\(58\) 257.108 1100.82i 0.0100357 0.0429680i
\(59\) 5319.11 + 9212.96i 0.198934 + 0.344564i 0.948183 0.317725i \(-0.102919\pi\)
−0.749249 + 0.662288i \(0.769585\pi\)
\(60\) 0 0
\(61\) −5470.51 + 9475.20i −0.188236 + 0.326035i −0.944662 0.328045i \(-0.893610\pi\)
0.756426 + 0.654079i \(0.226944\pi\)
\(62\) −1075.63 1008.20i −0.0355374 0.0333093i
\(63\) 0 0
\(64\) 6320.66 + 32152.6i 0.192891 + 0.981220i
\(65\) 20850.7 + 12038.1i 0.612120 + 0.353408i
\(66\) 0 0
\(67\) −49766.8 + 28732.9i −1.35442 + 0.781974i −0.988865 0.148816i \(-0.952454\pi\)
−0.365554 + 0.930790i \(0.619121\pi\)
\(68\) 33457.8 + 50154.1i 0.877454 + 1.31533i
\(69\) 0 0
\(70\) −8635.12 28504.5i −0.210631 0.695294i
\(71\) −70902.1 −1.66922 −0.834610 0.550842i \(-0.814307\pi\)
−0.834610 + 0.550842i \(0.814307\pi\)
\(72\) 0 0
\(73\) −18551.8 −0.407454 −0.203727 0.979028i \(-0.565305\pi\)
−0.203727 + 0.979028i \(0.565305\pi\)
\(74\) −18265.1 60293.2i −0.387743 1.27994i
\(75\) 0 0
\(76\) 17066.2 + 25582.7i 0.338924 + 0.508058i
\(77\) −71904.1 + 41513.8i −1.38206 + 0.797932i
\(78\) 0 0
\(79\) −12856.7 7422.81i −0.231772 0.133814i 0.379617 0.925144i \(-0.376056\pi\)
−0.611389 + 0.791330i \(0.709389\pi\)
\(80\) 5853.17 + 44978.5i 0.102251 + 0.785743i
\(81\) 0 0
\(82\) 40254.2 + 37730.4i 0.661115 + 0.619665i
\(83\) 1200.62 2079.54i 0.0191298 0.0331338i −0.856302 0.516475i \(-0.827244\pi\)
0.875432 + 0.483342i \(0.160577\pi\)
\(84\) 0 0
\(85\) 41726.9 + 72273.0i 0.626424 + 1.08500i
\(86\) 7879.69 33737.2i 0.114885 0.491884i
\(87\) 0 0
\(88\) 118389. 44406.9i 1.62968 0.611286i
\(89\) 28779.3i 0.385129i 0.981284 + 0.192564i \(0.0616804\pi\)
−0.981284 + 0.192564i \(0.938320\pi\)
\(90\) 0 0
\(91\) 64608.5i 0.817874i
\(92\) 32492.3 + 16053.6i 0.400232 + 0.197744i
\(93\) 0 0
\(94\) −6493.13 1516.54i −0.0757940 0.0177025i
\(95\) 21284.1 + 36865.2i 0.241962 + 0.419090i
\(96\) 0 0
\(97\) −78738.0 + 136378.i −0.849680 + 1.47169i 0.0318145 + 0.999494i \(0.489871\pi\)
−0.881494 + 0.472195i \(0.843462\pi\)
\(98\) 10360.7 11053.8i 0.108975 0.116264i
\(99\) 0 0
\(100\) −2406.25 37137.5i −0.0240625 0.371375i
\(101\) 48022.2 + 27725.6i 0.468424 + 0.270444i 0.715580 0.698531i \(-0.246163\pi\)
−0.247156 + 0.968976i \(0.579496\pi\)
\(102\) 0 0
\(103\) 99722.3 57574.7i 0.926188 0.534735i 0.0405841 0.999176i \(-0.487078\pi\)
0.885604 + 0.464441i \(0.153745\pi\)
\(104\) −16136.5 + 97060.3i −0.146294 + 0.879951i
\(105\) 0 0
\(106\) −184455. + 55878.5i −1.59450 + 0.483037i
\(107\) −162431. −1.37155 −0.685773 0.727815i \(-0.740536\pi\)
−0.685773 + 0.727815i \(0.740536\pi\)
\(108\) 0 0
\(109\) 174442. 1.40632 0.703160 0.711032i \(-0.251772\pi\)
0.703160 + 0.711032i \(0.251772\pi\)
\(110\) 167506. 50744.1i 1.31993 0.399857i
\(111\) 0 0
\(112\) 96675.5 73952.4i 0.728234 0.557067i
\(113\) 79120.9 45680.5i 0.582901 0.336538i −0.179384 0.983779i \(-0.557411\pi\)
0.762286 + 0.647241i \(0.224077\pi\)
\(114\) 0 0
\(115\) 43445.3 + 25083.2i 0.306336 + 0.176863i
\(116\) 6381.37 413.469i 0.0440321 0.00285297i
\(117\) 0 0
\(118\) −41154.2 + 43907.0i −0.272088 + 0.290288i
\(119\) 111974. 193944.i 0.724851 1.25548i
\(120\) 0 0
\(121\) −163430. 283069.i −1.01477 1.75764i
\(122\) −60269.7 14076.7i −0.366606 0.0856249i
\(123\) 0 0
\(124\) 3694.14 7476.88i 0.0215754 0.0436683i
\(125\) 189935.i 1.08725i
\(126\) 0 0
\(127\) 188373.i 1.03636i 0.855273 + 0.518178i \(0.173389\pi\)
−0.855273 + 0.518178i \(0.826611\pi\)
\(128\) −163704. + 86952.1i −0.883151 + 0.469089i
\(129\) 0 0
\(130\) −30976.4 + 132627.i −0.160758 + 0.688291i
\(131\) 123193. + 213376.i 0.627201 + 1.08634i 0.988111 + 0.153743i \(0.0491328\pi\)
−0.360910 + 0.932601i \(0.617534\pi\)
\(132\) 0 0
\(133\) 57115.8 98927.5i 0.279980 0.484940i
\(134\) −237178. 222308.i −1.14107 1.06953i
\(135\) 0 0
\(136\) −216656. + 263393.i −1.00444 + 1.22112i
\(137\) −88854.7 51300.3i −0.404463 0.233517i 0.283945 0.958841i \(-0.408357\pi\)
−0.688408 + 0.725324i \(0.741690\pi\)
\(138\) 0 0
\(139\) −194249. + 112150.i −0.852750 + 0.492335i −0.861578 0.507626i \(-0.830523\pi\)
0.00882796 + 0.999961i \(0.497190\pi\)
\(140\) 140158. 93499.0i 0.604362 0.403169i
\(141\) 0 0
\(142\) −116285. 383856.i −0.483952 1.59752i
\(143\) 379671. 1.55263
\(144\) 0 0
\(145\) 8851.68 0.0349627
\(146\) −30426.3 100437.i −0.118132 0.389953i
\(147\) 0 0
\(148\) 296464. 197771.i 1.11255 0.742177i
\(149\) 27795.8 16047.9i 0.102568 0.0592179i −0.447838 0.894115i \(-0.647806\pi\)
0.550407 + 0.834897i \(0.314473\pi\)
\(150\) 0 0
\(151\) 65816.4 + 37999.1i 0.234905 + 0.135622i 0.612833 0.790213i \(-0.290030\pi\)
−0.377928 + 0.925835i \(0.623363\pi\)
\(152\) −110512. + 134352.i −0.387973 + 0.471667i
\(153\) 0 0
\(154\) −342679. 321194.i −1.16436 1.09136i
\(155\) 5771.93 9997.28i 0.0192971 0.0334236i
\(156\) 0 0
\(157\) −255695. 442876.i −0.827890 1.43395i −0.899690 0.436529i \(-0.856208\pi\)
0.0717997 0.997419i \(-0.477126\pi\)
\(158\) 19100.3 81778.6i 0.0608692 0.260614i
\(159\) 0 0
\(160\) −233909. + 105457.i −0.722349 + 0.325667i
\(161\) 134621.i 0.409306i
\(162\) 0 0
\(163\) 206451.i 0.608623i −0.952573 0.304311i \(-0.901574\pi\)
0.952573 0.304311i \(-0.0984263\pi\)
\(164\) −138248. + 279813.i −0.401375 + 0.812377i
\(165\) 0 0
\(166\) 13227.5 + 3089.43i 0.0372569 + 0.00870178i
\(167\) −160986. 278836.i −0.446681 0.773674i 0.551487 0.834184i \(-0.314061\pi\)
−0.998168 + 0.0605096i \(0.980727\pi\)
\(168\) 0 0
\(169\) 37924.7 65687.4i 0.102142 0.176915i
\(170\) −322843. + 344438.i −0.856779 + 0.914089i
\(171\) 0 0
\(172\) 195572. 12671.7i 0.504065 0.0326599i
\(173\) −474593. 274007.i −1.20561 0.696058i −0.243812 0.969823i \(-0.578398\pi\)
−0.961797 + 0.273764i \(0.911731\pi\)
\(174\) 0 0
\(175\) −119717. + 69118.5i −0.295502 + 0.170608i
\(176\) 434581. + 568112.i 1.05752 + 1.38246i
\(177\) 0 0
\(178\) −155808. + 47200.3i −0.368587 + 0.111659i
\(179\) 169767. 0.396024 0.198012 0.980200i \(-0.436551\pi\)
0.198012 + 0.980200i \(0.436551\pi\)
\(180\) 0 0
\(181\) 652433. 1.48027 0.740133 0.672461i \(-0.234763\pi\)
0.740133 + 0.672461i \(0.234763\pi\)
\(182\) 349783. 105963.i 0.782745 0.237124i
\(183\) 0 0
\(184\) −33622.7 + 202239.i −0.0732129 + 0.440373i
\(185\) 427210. 246650.i 0.917724 0.529848i
\(186\) 0 0
\(187\) 1.13971e6 + 658012.i 2.38337 + 1.37604i
\(188\) −2438.83 37640.3i −0.00503254 0.0776710i
\(189\) 0 0
\(190\) −164676. + 175692.i −0.330938 + 0.353075i
\(191\) −130899. + 226724.i −0.259629 + 0.449690i −0.966143 0.258009i \(-0.916934\pi\)
0.706514 + 0.707699i \(0.250267\pi\)
\(192\) 0 0
\(193\) 456035. + 789876.i 0.881262 + 1.52639i 0.849939 + 0.526882i \(0.176639\pi\)
0.0313238 + 0.999509i \(0.490028\pi\)
\(194\) −867473. 202608.i −1.65482 0.386502i
\(195\) 0 0
\(196\) 76836.1 + 37962.8i 0.142865 + 0.0705859i
\(197\) 141457.i 0.259693i 0.991534 + 0.129846i \(0.0414484\pi\)
−0.991534 + 0.129846i \(0.958552\pi\)
\(198\) 0 0
\(199\) 568072.i 1.01688i −0.861097 0.508441i \(-0.830222\pi\)
0.861097 0.508441i \(-0.169778\pi\)
\(200\) 197111. 73935.4i 0.348447 0.130701i
\(201\) 0 0
\(202\) −71343.4 + 305459.i −0.123020 + 0.526713i
\(203\) −11876.7 20571.1i −0.0202281 0.0350362i
\(204\) 0 0
\(205\) −216007. + 374136.i −0.358991 + 0.621791i
\(206\) 475255. + 445458.i 0.780294 + 0.731373i
\(207\) 0 0
\(208\) −551939. + 71825.2i −0.884571 + 0.115111i
\(209\) 581346. + 335640.i 0.920596 + 0.531506i
\(210\) 0 0
\(211\) −395205. + 228172.i −0.611106 + 0.352822i −0.773398 0.633920i \(-0.781445\pi\)
0.162292 + 0.986743i \(0.448111\pi\)
\(212\) −605039. 906972.i −0.924579 1.38597i
\(213\) 0 0
\(214\) −266400. 879385.i −0.397649 1.31264i
\(215\) 271281. 0.400242
\(216\) 0 0
\(217\) −30977.9 −0.0446584
\(218\) 286098. + 944408.i 0.407730 + 1.34592i
\(219\) 0 0
\(220\) 549446. + 823636.i 0.765364 + 1.14730i
\(221\) −886874. + 512037.i −1.22147 + 0.705213i
\(222\) 0 0
\(223\) −105529. 60927.0i −0.142105 0.0820441i 0.427262 0.904128i \(-0.359478\pi\)
−0.569367 + 0.822084i \(0.692812\pi\)
\(224\) 558925. + 402102.i 0.744275 + 0.535447i
\(225\) 0 0
\(226\) 377073. + 353432.i 0.491082 + 0.460293i
\(227\) 63879.8 110643.i 0.0822809 0.142515i −0.821948 0.569562i \(-0.807113\pi\)
0.904229 + 0.427047i \(0.140446\pi\)
\(228\) 0 0
\(229\) −194394. 336700.i −0.244959 0.424282i 0.717161 0.696908i \(-0.245441\pi\)
−0.962120 + 0.272626i \(0.912108\pi\)
\(230\) −64543.7 + 276346.i −0.0804516 + 0.344456i
\(231\) 0 0
\(232\) 12704.4 + 33869.9i 0.0154965 + 0.0413137i
\(233\) 147353.i 0.177815i 0.996040 + 0.0889077i \(0.0283376\pi\)
−0.996040 + 0.0889077i \(0.971662\pi\)
\(234\) 0 0
\(235\) 52211.3i 0.0616730i
\(236\) −305203. 150793.i −0.356705 0.176239i
\(237\) 0 0
\(238\) 1.23364e6 + 288130.i 1.41171 + 0.329720i
\(239\) −186495. 323018.i −0.211189 0.365790i 0.740898 0.671618i \(-0.234400\pi\)
−0.952087 + 0.305827i \(0.901067\pi\)
\(240\) 0 0
\(241\) −292951. + 507405.i −0.324902 + 0.562746i −0.981492 0.191501i \(-0.938665\pi\)
0.656591 + 0.754247i \(0.271998\pi\)
\(242\) 1.26447e6 1.34905e6i 1.38793 1.48077i
\(243\) 0 0
\(244\) −22637.4 349380.i −0.0243418 0.375684i
\(245\) 102737. + 59315.3i 0.109348 + 0.0631323i
\(246\) 0 0
\(247\) −452379. + 261181.i −0.471802 + 0.272395i
\(248\) 46537.6 + 7736.98i 0.0480480 + 0.00798808i
\(249\) 0 0
\(250\) 1.02829e6 311507.i 1.04055 0.315223i
\(251\) −713349. −0.714691 −0.357345 0.933972i \(-0.616318\pi\)
−0.357345 + 0.933972i \(0.616318\pi\)
\(252\) 0 0
\(253\) 791098. 0.777015
\(254\) −1.01983e6 + 308946.i −0.991843 + 0.300468i
\(255\) 0 0
\(256\) −739236. 743668.i −0.704990 0.709217i
\(257\) −487256. + 281317.i −0.460176 + 0.265683i −0.712118 0.702059i \(-0.752264\pi\)
0.251942 + 0.967742i \(0.418931\pi\)
\(258\) 0 0
\(259\) −1.14642e6 661883.i −1.06192 0.613101i
\(260\) −768828. + 49814.8i −0.705336 + 0.0457009i
\(261\) 0 0
\(262\) −953148. + 1.01690e6i −0.857841 + 0.915222i
\(263\) −833666. + 1.44395e6i −0.743195 + 1.28725i 0.207838 + 0.978163i \(0.433357\pi\)
−0.951033 + 0.309088i \(0.899976\pi\)
\(264\) 0 0
\(265\) −754575. 1.30696e6i −0.660067 1.14327i
\(266\) 629256. + 146970.i 0.545285 + 0.127357i
\(267\) 0 0
\(268\) 814559. 1.64866e6i 0.692765 1.40215i
\(269\) 909140.i 0.766038i 0.923740 + 0.383019i \(0.125116\pi\)
−0.923740 + 0.383019i \(0.874884\pi\)
\(270\) 0 0
\(271\) 1.38725e6i 1.14744i −0.819050 0.573722i \(-0.805499\pi\)
0.819050 0.573722i \(-0.194501\pi\)
\(272\) −1.78131e6 740964.i −1.45988 0.607260i
\(273\) 0 0
\(274\) 132005. 565185.i 0.106222 0.454794i
\(275\) −406174. 703514.i −0.323877 0.560972i
\(276\) 0 0
\(277\) −540237. + 935718.i −0.423044 + 0.732733i −0.996235 0.0866882i \(-0.972372\pi\)
0.573192 + 0.819421i \(0.305705\pi\)
\(278\) −925748. 867707.i −0.718424 0.673382i
\(279\) 0 0
\(280\) 736063. + 605453.i 0.561073 + 0.461514i
\(281\) 340589. + 196639.i 0.257315 + 0.148561i 0.623109 0.782135i \(-0.285869\pi\)
−0.365794 + 0.930696i \(0.619203\pi\)
\(282\) 0 0
\(283\) −248928. + 143719.i −0.184760 + 0.106671i −0.589527 0.807749i \(-0.700686\pi\)
0.404767 + 0.914420i \(0.367353\pi\)
\(284\) 1.88744e6 1.25911e6i 1.38860 0.926331i
\(285\) 0 0
\(286\) 622689. + 2.05550e6i 0.450149 + 1.48594i
\(287\) 1.15931e6 0.830796
\(288\) 0 0
\(289\) −2.12981e6 −1.50002
\(290\) 14517.4 + 47922.0i 0.0101366 + 0.0334610i
\(291\) 0 0
\(292\) 493854. 329449.i 0.338954 0.226116i
\(293\) 1.55571e6 898188.i 1.05867 0.611221i 0.133603 0.991035i \(-0.457345\pi\)
0.925063 + 0.379814i \(0.124012\pi\)
\(294\) 0 0
\(295\) −408086. 235608.i −0.273021 0.157629i
\(296\) 1.55693e6 + 1.28066e6i 1.03286 + 0.849583i
\(297\) 0 0
\(298\) 132469. + 124164.i 0.0864118 + 0.0809941i
\(299\) −307799. + 533124.i −0.199108 + 0.344866i
\(300\) 0 0
\(301\) −363990. 630450.i −0.231565 0.401083i
\(302\) −97779.0 + 418644.i −0.0616919 + 0.264136i
\(303\) 0 0
\(304\) −908615. 377952.i −0.563892 0.234560i
\(305\) 484629.i 0.298304i
\(306\) 0 0
\(307\) 1.13601e6i 0.687918i 0.938985 + 0.343959i \(0.111768\pi\)
−0.938985 + 0.343959i \(0.888232\pi\)
\(308\) 1.17689e6 2.38201e6i 0.706902 1.43076i
\(309\) 0 0
\(310\) 63590.6 + 14852.3i 0.0375827 + 0.00877787i
\(311\) −176499. 305706.i −0.103477 0.179227i 0.809638 0.586929i \(-0.199663\pi\)
−0.913115 + 0.407703i \(0.866330\pi\)
\(312\) 0 0
\(313\) 68385.0 118446.i 0.0394548 0.0683377i −0.845624 0.533780i \(-0.820771\pi\)
0.885078 + 0.465442i \(0.154105\pi\)
\(314\) 1.97832e6 2.11065e6i 1.13233 1.20807i
\(315\) 0 0
\(316\) 474066. 30716.2i 0.267068 0.0173041i
\(317\) 609932. + 352144.i 0.340905 + 0.196822i 0.660672 0.750675i \(-0.270271\pi\)
−0.319767 + 0.947496i \(0.603605\pi\)
\(318\) 0 0
\(319\) 120886. 69793.3i 0.0665117 0.0384005i
\(320\) −954558. 1.09340e6i −0.521108 0.596903i
\(321\) 0 0
\(322\) 728822. 220789.i 0.391726 0.118669i
\(323\) −1.81062e6 −0.965654
\(324\) 0 0
\(325\) 632134. 0.331972
\(326\) 1.11770e6 338595.i 0.582482 0.176456i
\(327\) 0 0
\(328\) −1.74161e6 289547.i −0.893854 0.148605i
\(329\) −121338. + 70054.4i −0.0618025 + 0.0356817i
\(330\) 0 0
\(331\) 1.21122e6 + 699299.i 0.607650 + 0.350827i 0.772045 0.635567i \(-0.219234\pi\)
−0.164395 + 0.986395i \(0.552567\pi\)
\(332\) 4968.27 + 76679.0i 0.00247377 + 0.0381796i
\(333\) 0 0
\(334\) 1.24556e6 1.32887e6i 0.610939 0.651805i
\(335\) 1.27272e6 2.20441e6i 0.619611 1.07320i
\(336\) 0 0
\(337\) 565468. + 979419.i 0.271227 + 0.469779i 0.969176 0.246368i \(-0.0792372\pi\)
−0.697949 + 0.716147i \(0.745904\pi\)
\(338\) 417824. + 97587.4i 0.198930 + 0.0464624i
\(339\) 0 0
\(340\) −2.39423e6 1.18293e6i −1.12323 0.554960i
\(341\) 182041.i 0.0847781i
\(342\) 0 0
\(343\) 2.31610e6i 1.06297i
\(344\) 389357. + 1.03802e6i 0.177399 + 0.472946i
\(345\) 0 0
\(346\) 705071. 3.01878e6i 0.316623 1.35563i
\(347\) 669599. + 1.15978e6i 0.298532 + 0.517073i 0.975800 0.218663i \(-0.0701697\pi\)
−0.677268 + 0.735736i \(0.736836\pi\)
\(348\) 0 0
\(349\) −997138. + 1.72709e6i −0.438220 + 0.759019i −0.997552 0.0699247i \(-0.977724\pi\)
0.559333 + 0.828943i \(0.311057\pi\)
\(350\) −570544. 534773.i −0.248954 0.233346i
\(351\) 0 0
\(352\) −2.36295e6 + 3.28452e6i −1.01648 + 1.41291i
\(353\) −1.57369e6 908571.i −0.672175 0.388081i 0.124725 0.992191i \(-0.460195\pi\)
−0.796900 + 0.604111i \(0.793528\pi\)
\(354\) 0 0
\(355\) 2.71983e6 1.57029e6i 1.14544 0.661318i
\(356\) −511074. 766115.i −0.213727 0.320383i
\(357\) 0 0
\(358\) 278431. + 919101.i 0.114818 + 0.379014i
\(359\) −1.16638e6 −0.477644 −0.238822 0.971063i \(-0.576761\pi\)
−0.238822 + 0.971063i \(0.576761\pi\)
\(360\) 0 0
\(361\) 1.55253e6 0.627008
\(362\) 1.07004e6 + 3.53220e6i 0.429169 + 1.41669i
\(363\) 0 0
\(364\) 1.14734e6 + 1.71990e6i 0.453878 + 0.680377i
\(365\) 711652. 410873.i 0.279599 0.161427i
\(366\) 0 0
\(367\) −1.42589e6 823237.i −0.552612 0.319051i 0.197563 0.980290i \(-0.436697\pi\)
−0.750175 + 0.661240i \(0.770031\pi\)
\(368\) −1.15004e6 + 149658.i −0.442684 + 0.0576076i
\(369\) 0 0
\(370\) 2.03599e6 + 1.90834e6i 0.773164 + 0.724689i
\(371\) −2.02490e6 + 3.50723e6i −0.763780 + 1.32291i
\(372\) 0 0
\(373\) 973750. + 1.68658e6i 0.362389 + 0.627677i 0.988354 0.152175i \(-0.0486278\pi\)
−0.625964 + 0.779852i \(0.715294\pi\)
\(374\) −1.69319e6 + 7.24945e6i −0.625932 + 2.67995i
\(375\) 0 0
\(376\) 199780. 74936.5i 0.0728758 0.0273353i
\(377\) 108620.i 0.0393602i
\(378\) 0 0
\(379\) 4.71999e6i 1.68789i 0.536432 + 0.843943i \(0.319772\pi\)
−0.536432 + 0.843943i \(0.680228\pi\)
\(380\) −1.22126e6 603391.i −0.433858 0.214358i
\(381\) 0 0
\(382\) −1.44214e6 336828.i −0.505649 0.118100i
\(383\) −252323. 437037.i −0.0878943 0.152237i 0.818727 0.574184i \(-0.194680\pi\)
−0.906621 + 0.421946i \(0.861347\pi\)
\(384\) 0 0
\(385\) 1.83884e6 3.18497e6i 0.632256 1.09510i
\(386\) −3.52837e6 + 3.76438e6i −1.20533 + 1.28595i
\(387\) 0 0
\(388\) −325824. 5.02869e6i −0.109876 1.69580i
\(389\) −1.60551e6 926943.i −0.537947 0.310584i 0.206299 0.978489i \(-0.433858\pi\)
−0.744247 + 0.667905i \(0.767191\pi\)
\(390\) 0 0
\(391\) −1.84793e6 + 1.06690e6i −0.611284 + 0.352925i
\(392\) −79509.1 + 478244.i −0.0261337 + 0.157193i
\(393\) 0 0
\(394\) −765834. + 232001.i −0.248539 + 0.0752920i
\(395\) 657583. 0.212059
\(396\) 0 0
\(397\) −2.32765e6 −0.741209 −0.370605 0.928791i \(-0.620850\pi\)
−0.370605 + 0.928791i \(0.620850\pi\)
\(398\) 3.07548e6 931682.i 0.973207 0.294822i
\(399\) 0 0
\(400\) 723556. + 945879.i 0.226111 + 0.295587i
\(401\) −3.17463e6 + 1.83287e6i −0.985897 + 0.569208i −0.904045 0.427436i \(-0.859417\pi\)
−0.0818519 + 0.996645i \(0.526083\pi\)
\(402\) 0 0
\(403\) 122678. + 70828.3i 0.0376275 + 0.0217242i
\(404\) −1.77073e6 + 114731.i −0.539757 + 0.0349725i
\(405\) 0 0
\(406\) 91890.7 98037.2i 0.0276666 0.0295173i
\(407\) 3.88955e6 6.73690e6i 1.16389 2.01592i
\(408\) 0 0
\(409\) 699640. + 1.21181e6i 0.206807 + 0.358201i 0.950707 0.310090i \(-0.100359\pi\)
−0.743900 + 0.668291i \(0.767026\pi\)
\(410\) −2.37980e6 555828.i −0.699165 0.163298i
\(411\) 0 0
\(412\) −1.63221e6 + 3.30356e6i −0.473731 + 0.958825i
\(413\) 1.26451e6i 0.364793i
\(414\) 0 0
\(415\) 106362.i 0.0303157i
\(416\) −1.29407e6 2.87033e6i −0.366628 0.813203i
\(417\) 0 0
\(418\) −863667. + 3.69782e6i −0.241772 + 1.03515i
\(419\) 1.83298e6 + 3.17481e6i 0.510061 + 0.883452i 0.999932 + 0.0116570i \(0.00371063\pi\)
−0.489871 + 0.871795i \(0.662956\pi\)
\(420\) 0 0
\(421\) 2.68932e6 4.65804e6i 0.739498 1.28085i −0.213224 0.977003i \(-0.568396\pi\)
0.952722 0.303845i \(-0.0982704\pi\)
\(422\) −1.88346e6 1.76538e6i −0.514844 0.482566i
\(423\) 0 0
\(424\) 3.91793e6 4.76312e6i 1.05838 1.28670i
\(425\) 1.89756e6 + 1.09556e6i 0.509594 + 0.294214i
\(426\) 0 0
\(427\) −1.12627e6 + 650249.i −0.298931 + 0.172588i
\(428\) 4.32397e6 2.88452e6i 1.14097 0.761138i
\(429\) 0 0
\(430\) 444921. + 1.46868e6i 0.116041 + 0.383051i
\(431\) 7.43683e6 1.92839 0.964194 0.265198i \(-0.0854372\pi\)
0.964194 + 0.265198i \(0.0854372\pi\)
\(432\) 0 0
\(433\) 4.75454e6 1.21868 0.609339 0.792910i \(-0.291435\pi\)
0.609339 + 0.792910i \(0.291435\pi\)
\(434\) −50806.1 167711.i −0.0129477 0.0427402i
\(435\) 0 0
\(436\) −4.64369e6 + 3.09780e6i −1.16990 + 0.780436i
\(437\) −942594. + 544207.i −0.236114 + 0.136320i
\(438\) 0 0
\(439\) 1.50776e6 + 870508.i 0.373398 + 0.215582i 0.674942 0.737871i \(-0.264169\pi\)
−0.301544 + 0.953452i \(0.597502\pi\)
\(440\) −3.55794e6 + 4.32546e6i −0.876126 + 1.06513i
\(441\) 0 0
\(442\) −4.22665e6 3.96165e6i −1.02906 0.964541i
\(443\) 412027. 713652.i 0.0997509 0.172774i −0.811831 0.583893i \(-0.801529\pi\)
0.911582 + 0.411119i \(0.134862\pi\)
\(444\) 0 0
\(445\) −637386. 1.10399e6i −0.152582 0.264279i
\(446\) 156777. 671245.i 0.0373202 0.159788i
\(447\) 0 0
\(448\) −1.26026e6 + 3.68543e6i −0.296663 + 0.867548i
\(449\) 3.08674e6i 0.722577i −0.932454 0.361289i \(-0.882337\pi\)
0.932454 0.361289i \(-0.117663\pi\)
\(450\) 0 0
\(451\) 6.81266e6i 1.57716i
\(452\) −1.29501e6 + 2.62109e6i −0.298145 + 0.603441i
\(453\) 0 0
\(454\) 703776. + 164375.i 0.160249 + 0.0374279i
\(455\) 1.43091e6 + 2.47840e6i 0.324028 + 0.561234i
\(456\) 0 0
\(457\) 1.12118e6 1.94195e6i 0.251123 0.434958i −0.712712 0.701456i \(-0.752534\pi\)
0.963835 + 0.266499i \(0.0858668\pi\)
\(458\) 1.50404e6 1.60464e6i 0.335038 0.357449i
\(459\) 0 0
\(460\) −1.60196e6 + 103796.i −0.352986 + 0.0228711i
\(461\) 3.91078e6 + 2.25789e6i 0.857059 + 0.494823i 0.863026 0.505159i \(-0.168566\pi\)
−0.00596751 + 0.999982i \(0.501900\pi\)
\(462\) 0 0
\(463\) 7.40455e6 4.27502e6i 1.60526 0.926799i 0.614853 0.788642i \(-0.289216\pi\)
0.990410 0.138157i \(-0.0441178\pi\)
\(464\) −162531. + 124329.i −0.0350463 + 0.0268089i
\(465\) 0 0
\(466\) −797752. + 241670.i −0.170178 + 0.0515535i
\(467\) −7.67458e6 −1.62841 −0.814203 0.580581i \(-0.802826\pi\)
−0.814203 + 0.580581i \(0.802826\pi\)
\(468\) 0 0
\(469\) −6.83065e6 −1.43394
\(470\) 282666. 85630.5i 0.0590241 0.0178807i
\(471\) 0 0
\(472\) 315821. 1.89965e6i 0.0652508 0.392481i
\(473\) 3.70483e6 2.13898e6i 0.761404 0.439597i
\(474\) 0 0
\(475\) 967913. + 558825.i 0.196835 + 0.113643i
\(476\) 463357. + 7.15133e6i 0.0937342 + 1.44667i
\(477\) 0 0
\(478\) 1.44292e6 1.53943e6i 0.288850 0.308171i
\(479\) 2.80988e6 4.86685e6i 0.559562 0.969191i −0.437970 0.898989i \(-0.644303\pi\)
0.997533 0.0702012i \(-0.0223641\pi\)
\(480\) 0 0
\(481\) 3.02668e6 + 5.24236e6i 0.596491 + 1.03315i
\(482\) −3.22750e6 753818.i −0.632773 0.147791i
\(483\) 0 0
\(484\) 9.37740e6 + 4.63313e6i 1.81957 + 0.899004i
\(485\) 6.97536e6i 1.34652i
\(486\) 0 0
\(487\) 4.64134e6i 0.886790i −0.896326 0.443395i \(-0.853774\pi\)
0.896326 0.443395i \(-0.146226\pi\)
\(488\) 1.85438e6 695566.i 0.352491 0.132217i
\(489\) 0 0
\(490\) −152630. + 653488.i −0.0287176 + 0.122955i
\(491\) −32004.7 55433.7i −0.00599115 0.0103770i 0.863014 0.505180i \(-0.168574\pi\)
−0.869005 + 0.494803i \(0.835240\pi\)
\(492\) 0 0
\(493\) −188251. + 326060.i −0.0348835 + 0.0604200i
\(494\) −2.15594e6 2.02077e6i −0.397483 0.372563i
\(495\) 0 0
\(496\) 34438.1 + 264639.i 0.00628543 + 0.0483002i
\(497\) −7.29865e6 4.21388e6i −1.32541 0.765228i
\(498\) 0 0
\(499\) −3.98798e6 + 2.30246e6i −0.716972 + 0.413944i −0.813637 0.581373i \(-0.802516\pi\)
0.0966654 + 0.995317i \(0.469182\pi\)
\(500\) 3.37293e6 + 5.05612e6i 0.603368 + 0.904466i
\(501\) 0 0
\(502\) −1.16995e6 3.86199e6i −0.207208 0.683994i
\(503\) −4.30022e6 −0.757829 −0.378914 0.925432i \(-0.623703\pi\)
−0.378914 + 0.925432i \(0.623703\pi\)
\(504\) 0 0
\(505\) −2.45620e6 −0.428583
\(506\) 1.29746e6 + 4.28292e6i 0.225278 + 0.743641i
\(507\) 0 0
\(508\) −3.34519e6 5.01454e6i −0.575124 0.862128i
\(509\) 6.05140e6 3.49378e6i 1.03529 0.597724i 0.116793 0.993156i \(-0.462739\pi\)
0.918495 + 0.395433i \(0.129405\pi\)
\(510\) 0 0
\(511\) −1.90971e6 1.10257e6i −0.323531 0.186791i
\(512\) 2.81373e6 5.22181e6i 0.474359 0.880331i
\(513\) 0 0
\(514\) −2.32216e6 2.17657e6i −0.387689 0.363382i
\(515\) −2.55025e6 + 4.41717e6i −0.423707 + 0.733882i
\(516\) 0 0
\(517\) −411674. 713040.i −0.0677372 0.117324i
\(518\) 1.70315e6 7.29210e6i 0.278888 1.19407i
\(519\) 0 0
\(520\) −1.53063e6 4.08065e6i −0.248234 0.661791i
\(521\) 6.03385e6i 0.973868i 0.873439 + 0.486934i \(0.161885\pi\)
−0.873439 + 0.486934i \(0.838115\pi\)
\(522\) 0 0
\(523\) 1.21106e6i 0.193603i −0.995304 0.0968013i \(-0.969139\pi\)
0.995304 0.0968013i \(-0.0308612\pi\)
\(524\) −7.06863e6 3.49243e6i −1.12462 0.555648i
\(525\) 0 0
\(526\) −9.18467e6 2.14518e6i −1.44743 0.338065i
\(527\) 245507. + 425230.i 0.0385067 + 0.0666956i
\(528\) 0 0
\(529\) 2.57683e6 4.46320e6i 0.400356 0.693437i
\(530\) 5.83819e6 6.22870e6i 0.902793 0.963181i
\(531\) 0 0
\(532\) 236350. + 3.64776e6i 0.0362057 + 0.558789i
\(533\) −4.59108e6 2.65066e6i −0.699997 0.404144i
\(534\) 0 0
\(535\) 6.23092e6 3.59743e6i 0.941170 0.543385i
\(536\) 1.02616e7 + 1.70601e6i 1.54277 + 0.256489i
\(537\) 0 0
\(538\) −4.92198e6 + 1.49106e6i −0.733136 + 0.222095i
\(539\) 1.87075e6 0.277360
\(540\) 0 0
\(541\) −4.95265e6 −0.727519 −0.363760 0.931493i \(-0.618507\pi\)
−0.363760 + 0.931493i \(0.618507\pi\)
\(542\) 7.51041e6 2.27519e6i 1.09816 0.332675i
\(543\) 0 0
\(544\) 1.09001e6 1.08590e7i 0.157918 1.57324i
\(545\) −6.69165e6 + 3.86342e6i −0.965032 + 0.557161i
\(546\) 0 0
\(547\) −381241. 220109.i −0.0544792 0.0314536i 0.472513 0.881324i \(-0.343347\pi\)
−0.526992 + 0.849870i \(0.676680\pi\)
\(548\) 3.27635e6 212285.i 0.466056 0.0301972i
\(549\) 0 0
\(550\) 3.14259e6 3.35280e6i 0.442977 0.472607i
\(551\) −96023.5 + 166318.i −0.0134741 + 0.0233378i
\(552\) 0 0
\(553\) −882310. 1.52821e6i −0.122690 0.212505i
\(554\) −5.95190e6 1.39013e6i −0.823913 0.192434i
\(555\) 0 0
\(556\) 3.17937e6 6.43500e6i 0.436168 0.882799i
\(557\) 2.77476e6i 0.378955i −0.981885 0.189477i \(-0.939321\pi\)
0.981885 0.189477i \(-0.0606794\pi\)
\(558\) 0 0
\(559\) 3.32893e6i 0.450583i
\(560\) −2.07065e6 + 4.97795e6i −0.279021 + 0.670780i
\(561\) 0 0
\(562\) −505991. + 2.16641e6i −0.0675774 + 0.289335i
\(563\) −1.99125e6 3.44895e6i −0.264762 0.458581i 0.702740 0.711447i \(-0.251960\pi\)
−0.967501 + 0.252867i \(0.918627\pi\)
\(564\) 0 0
\(565\) −2.02340e6 + 3.50464e6i −0.266662 + 0.461872i
\(566\) −1.18634e6 1.11196e6i −0.155656 0.145897i
\(567\) 0 0
\(568\) 9.91219e6 + 8.15334e6i 1.28914 + 1.06039i
\(569\) 6.64391e6 + 3.83587e6i 0.860287 + 0.496687i 0.864108 0.503306i \(-0.167883\pi\)
−0.00382141 + 0.999993i \(0.501216\pi\)
\(570\) 0 0
\(571\) −4.95051e6 + 2.85818e6i −0.635418 + 0.366859i −0.782847 0.622214i \(-0.786234\pi\)
0.147429 + 0.989073i \(0.452900\pi\)
\(572\) −1.01070e7 + 6.74234e6i −1.29161 + 0.861629i
\(573\) 0 0
\(574\) 1.90135e6 + 6.27636e6i 0.240870 + 0.795112i
\(575\) 1.31714e6 0.166136
\(576\) 0 0
\(577\) −9.39744e6 −1.17509 −0.587544 0.809192i \(-0.699905\pi\)
−0.587544 + 0.809192i \(0.699905\pi\)
\(578\) −3.49305e6 1.15305e7i −0.434896 1.43559i
\(579\) 0 0
\(580\) −235634. + 157191.i −0.0290850 + 0.0194025i
\(581\) 247183. 142711.i 0.0303794 0.0175395i
\(582\) 0 0
\(583\) −2.06102e7 1.18993e7i −2.51137 1.44994i
\(584\) 2.59356e6 + 2.13335e6i 0.314676 + 0.258839i
\(585\) 0 0
\(586\) 7.41416e6 + 6.94932e6i 0.891904 + 0.835985i
\(587\) −7.92251e6 + 1.37222e7i −0.949002 + 1.64372i −0.201471 + 0.979495i \(0.564572\pi\)
−0.747532 + 0.664226i \(0.768761\pi\)
\(588\) 0 0
\(589\) 125229. + 216902.i 0.0148736 + 0.0257618i
\(590\) 606265. 2.59574e6i 0.0717022 0.306995i
\(591\) 0 0
\(592\) −4.37988e6 + 1.05294e7i −0.513639 + 1.23481i
\(593\) 945465.i 0.110410i 0.998475 + 0.0552050i \(0.0175812\pi\)
−0.998475 + 0.0552050i \(0.982419\pi\)
\(594\) 0 0
\(595\) 9.91969e6i 1.14870i
\(596\) −454948. + 920809.i −0.0524622 + 0.106183i
\(597\) 0 0
\(598\) −3.39109e6 792026.i −0.387780 0.0905705i
\(599\) −3.63749e6 6.30031e6i −0.414223 0.717455i 0.581123 0.813815i \(-0.302613\pi\)
−0.995347 + 0.0963599i \(0.969280\pi\)
\(600\) 0 0
\(601\) −2.93990e6 + 5.09206e6i −0.332007 + 0.575053i −0.982905 0.184112i \(-0.941059\pi\)
0.650898 + 0.759165i \(0.274392\pi\)
\(602\) 2.81621e6 3.00459e6i 0.316719 0.337904i
\(603\) 0 0
\(604\) −2.42686e6 + 157244.i −0.270677 + 0.0175380i
\(605\) 1.25385e7 + 7.23908e6i 1.39269 + 0.804072i
\(606\) 0 0
\(607\) 3.03686e6 1.75333e6i 0.334544 0.193149i −0.323313 0.946292i \(-0.604797\pi\)
0.657857 + 0.753143i \(0.271463\pi\)
\(608\) 555994. 5.53901e6i 0.0609973 0.607677i
\(609\) 0 0
\(610\) 2.62373e6 794828.i 0.285492 0.0864866i
\(611\) 640694. 0.0694300
\(612\) 0 0
\(613\) 1.60744e7 1.72776 0.863880 0.503697i \(-0.168027\pi\)
0.863880 + 0.503697i \(0.168027\pi\)
\(614\) −6.15023e6 + 1.86314e6i −0.658371 + 0.199446i
\(615\) 0 0
\(616\) 1.48261e7 + 2.46487e6i 1.57426 + 0.261724i
\(617\) −5.66445e6 + 3.27037e6i −0.599024 + 0.345847i −0.768658 0.639660i \(-0.779075\pi\)
0.169633 + 0.985507i \(0.445742\pi\)
\(618\) 0 0
\(619\) 9.47481e6 + 5.47028e6i 0.993903 + 0.573830i 0.906439 0.422338i \(-0.138790\pi\)
0.0874641 + 0.996168i \(0.472124\pi\)
\(620\) 23884.7 + 368631.i 0.00249541 + 0.0385135i
\(621\) 0 0
\(622\) 1.36558e6 1.45693e6i 0.141528 0.150995i
\(623\) −1.71042e6 + 2.96254e6i −0.176556 + 0.305805i
\(624\) 0 0
\(625\) 2.38940e6 + 4.13856e6i 0.244674 + 0.423788i
\(626\) 753411. + 175968.i 0.0768415 + 0.0179472i
\(627\) 0 0
\(628\) 1.46714e7 + 7.24878e6i 1.48448 + 0.733443i
\(629\) 2.09823e7i 2.11459i
\(630\) 0 0
\(631\) 1.64472e7i 1.64444i −0.569168 0.822221i \(-0.692735\pi\)
0.569168 0.822221i \(-0.307265\pi\)
\(632\) 943798. + 2.51616e6i 0.0939910 + 0.250580i
\(633\) 0 0
\(634\) −906135. + 3.87965e6i −0.0895302 + 0.383327i
\(635\) −4.17196e6 7.22604e6i −0.410587 0.711158i
\(636\) 0 0
\(637\) −727867. + 1.26070e6i −0.0710728 + 0.123102i
\(638\) 576115. + 539994.i 0.0560347 + 0.0525216i
\(639\) 0 0
\(640\) 4.35399e6 6.96113e6i 0.420182 0.671784i
\(641\) 6.01469e6 + 3.47258e6i 0.578187 + 0.333816i 0.760413 0.649440i \(-0.224997\pi\)
−0.182226 + 0.983257i \(0.558330\pi\)
\(642\) 0 0
\(643\) 1.22490e7 7.07195e6i 1.16835 0.674546i 0.215057 0.976601i \(-0.431006\pi\)
0.953290 + 0.302055i \(0.0976728\pi\)
\(644\) 2.39065e6 + 3.58365e6i 0.227144 + 0.340495i
\(645\) 0 0
\(646\) −2.96956e6 9.80250e6i −0.279969 0.924178i
\(647\) 1.06848e7 1.00347 0.501736 0.865021i \(-0.332695\pi\)
0.501736 + 0.865021i \(0.332695\pi\)
\(648\) 0 0
\(649\) −7.43086e6 −0.692512
\(650\) 1.03675e6 + 3.42230e6i 0.0962476 + 0.317713i
\(651\) 0 0
\(652\) 3.66623e6 + 5.49579e6i 0.337755 + 0.506304i
\(653\) −7.15281e6 + 4.12968e6i −0.656438 + 0.378995i −0.790919 0.611921i \(-0.790397\pi\)
0.134480 + 0.990916i \(0.457064\pi\)
\(654\) 0 0
\(655\) −9.45143e6 5.45678e6i −0.860784 0.496974i
\(656\) −1.28880e6 9.90376e6i −0.116930 0.898546i
\(657\) 0 0
\(658\) −578270. 542014.i −0.0520674 0.0488030i
\(659\) −1.13554e6 + 1.96681e6i −0.101856 + 0.176420i −0.912450 0.409189i \(-0.865812\pi\)
0.810593 + 0.585610i \(0.199145\pi\)
\(660\) 0 0
\(661\) 6.82941e6 + 1.18289e7i 0.607967 + 1.05303i 0.991575 + 0.129533i \(0.0413480\pi\)
−0.383608 + 0.923496i \(0.625319\pi\)
\(662\) −1.79943e6 + 7.70432e6i −0.159584 + 0.683265i
\(663\) 0 0
\(664\) −406983. + 152657.i −0.0358225 + 0.0134368i
\(665\) 5.05986e6i 0.443695i
\(666\) 0 0
\(667\) 226326.i 0.0196979i
\(668\) 9.23718e6 + 4.56385e6i 0.800936 + 0.395722i
\(669\) 0 0
\(670\) 1.40218e7 + 3.27494e6i 1.20674 + 0.281849i
\(671\) −3.82118e6 6.61848e6i −0.327636 0.567482i
\(672\) 0 0
\(673\) −5.08153e6 + 8.80146e6i −0.432471 + 0.749061i −0.997085 0.0762934i \(-0.975691\pi\)
0.564615 + 0.825355i \(0.309025\pi\)
\(674\) −4.37505e6 + 4.66770e6i −0.370966 + 0.395779i
\(675\) 0 0
\(676\) 156935. + 2.42210e6i 0.0132085 + 0.203857i
\(677\) −2.00175e7 1.15571e7i −1.67856 0.969120i −0.962578 0.271006i \(-0.912644\pi\)
−0.715987 0.698113i \(-0.754023\pi\)
\(678\) 0 0
\(679\) −1.62105e7 + 9.35916e6i −1.34935 + 0.779045i
\(680\) 2.47752e6 1.49022e7i 0.205469 1.23588i
\(681\) 0 0
\(682\) 985550. 298561.i 0.0811368 0.0245795i
\(683\) −5.18871e6 −0.425606 −0.212803 0.977095i \(-0.568259\pi\)
−0.212803 + 0.977095i \(0.568259\pi\)
\(684\) 0 0
\(685\) 4.54466e6 0.370062
\(686\) 1.25391e7 3.79858e6i 1.01732 0.308185i
\(687\) 0 0
\(688\) −4.98117e6 + 3.81037e6i −0.401199 + 0.306900i
\(689\) 1.60379e7 9.25951e6i 1.28707 0.743088i
\(690\) 0 0
\(691\) 1.57664e6 + 910275.i 0.125614 + 0.0725233i 0.561490 0.827483i \(-0.310228\pi\)
−0.435876 + 0.900007i \(0.643562\pi\)
\(692\) 1.74997e7 1.13386e6i 1.38920 0.0900108i
\(693\) 0 0
\(694\) −5.18072e6 + 5.52726e6i −0.408311 + 0.435623i
\(695\) 4.96764e6 8.60420e6i 0.390111 0.675691i
\(696\) 0 0
\(697\) −9.18777e6 1.59137e7i −0.716355 1.24076i
\(698\) −1.09857e7 2.56583e6i −0.853469 0.199337i
\(699\) 0 0
\(700\) 1.95947e6 3.96593e6i 0.151145 0.305914i
\(701\) 1.38877e7i 1.06742i 0.845667 + 0.533711i \(0.179203\pi\)
−0.845667 + 0.533711i \(0.820797\pi\)
\(702\) 0 0
\(703\) 1.07027e7i 0.816779i
\(704\) −2.16574e7 7.40588e6i −1.64693 0.563177i
\(705\) 0 0
\(706\) 2.33793e6 1.00099e7i 0.176530 0.755820i
\(707\) 3.29560e6 + 5.70814e6i 0.247962 + 0.429483i
\(708\) 0 0
\(709\) −2.24469e6 + 3.88792e6i −0.167703 + 0.290470i −0.937612 0.347684i \(-0.886968\pi\)
0.769909 + 0.638154i \(0.220302\pi\)
\(710\) 1.29621e7 + 1.21494e7i 0.965006 + 0.904504i
\(711\) 0 0
\(712\) 3.30946e6 4.02338e6i 0.244657 0.297434i
\(713\) 255617. + 147581.i 0.0188307 + 0.0108719i
\(714\) 0 0
\(715\) −1.45643e7 + 8.40871e6i −1.06543 + 0.615126i
\(716\) −4.51926e6 + 3.01479e6i −0.329446 + 0.219773i
\(717\) 0 0
\(718\) −1.91295e6 6.31466e6i −0.138482 0.457129i
\(719\) −603305. −0.0435226 −0.0217613 0.999763i \(-0.506927\pi\)
−0.0217613 + 0.999763i \(0.506927\pi\)
\(720\) 0 0
\(721\) 1.36872e7 0.980564
\(722\) 2.54627e6 + 8.40523e6i 0.181787 + 0.600077i
\(723\) 0 0
\(724\) −1.73680e7 + 1.15861e7i −1.23141 + 0.821472i
\(725\) 201269. 116203.i 0.0142210 0.00821052i
\(726\) 0 0
\(727\) 1.84417e7 + 1.06473e7i 1.29409 + 0.747144i 0.979377 0.202043i \(-0.0647579\pi\)
0.314714 + 0.949186i \(0.398091\pi\)
\(728\) −7.42961e6 + 9.03234e6i −0.519562 + 0.631643i
\(729\) 0 0
\(730\) 3.39158e6 + 3.17894e6i 0.235556 + 0.220788i
\(731\) −5.76941e6 + 9.99291e6i −0.399335 + 0.691669i
\(732\) 0 0
\(733\) −4.21399e6 7.29884e6i −0.289690 0.501758i 0.684046 0.729439i \(-0.260219\pi\)
−0.973736 + 0.227682i \(0.926885\pi\)
\(734\) 2.11834e6 9.06976e6i 0.145130 0.621378i
\(735\) 0 0
\(736\) −2.69639e6 5.98075e6i −0.183480 0.406968i
\(737\) 4.01402e7i 2.72214i
\(738\) 0 0
\(739\) 1.72623e7i 1.16275i −0.813635 0.581376i \(-0.802514\pi\)
0.813635 0.581376i \(-0.197486\pi\)
\(740\) −6.99237e6 + 1.41524e7i −0.469402 + 0.950063i
\(741\) 0 0
\(742\) −2.23087e7 5.21045e6i −1.48753 0.347428i
\(743\) 8.79333e6 + 1.52305e7i 0.584361 + 1.01214i 0.994955 + 0.100324i \(0.0319881\pi\)
−0.410594 + 0.911818i \(0.634679\pi\)
\(744\) 0 0
\(745\) −710838. + 1.23121e6i −0.0469224 + 0.0812719i
\(746\) −7.53395e6 + 8.03789e6i −0.495651 + 0.528805i
\(747\) 0 0
\(748\) −4.20247e7 + 2.72291e6i −2.74632 + 0.177942i
\(749\) −1.67206e7 9.65367e6i −1.08905 0.628764i
\(750\) 0 0
\(751\) 1.82336e7 1.05272e7i 1.17970 0.681101i 0.223756 0.974645i \(-0.428168\pi\)
0.955945 + 0.293544i \(0.0948349\pi\)
\(752\) 733353. + 958687.i 0.0472899 + 0.0618205i
\(753\) 0 0
\(754\) −588058. + 178146.i −0.0376697 + 0.0114116i
\(755\) −3.36632e6 −0.214926
\(756\) 0 0
\(757\) −7.12325e6 −0.451792 −0.225896 0.974151i \(-0.572531\pi\)
−0.225896 + 0.974151i \(0.572531\pi\)
\(758\) −2.55535e7 + 7.74114e6i −1.61539 + 0.489364i
\(759\) 0 0
\(760\) 1.26374e6 7.60134e6i 0.0793640 0.477371i
\(761\) 4.12690e6 2.38267e6i 0.258323 0.149143i −0.365247 0.930911i \(-0.619015\pi\)
0.623569 + 0.781768i \(0.285682\pi\)
\(762\) 0 0
\(763\) 1.79570e7 + 1.03675e7i 1.11666 + 0.644706i
\(764\) −541671. 8.36001e6i −0.0335739 0.518171i
\(765\) 0 0
\(766\) 1.95224e6 2.08282e6i 0.120216 0.128257i
\(767\) 2.89119e6 5.00768e6i 0.177455 0.307361i
\(768\) 0 0
\(769\) −1.98809e6 3.44347e6i −0.121233 0.209981i 0.799021 0.601303i \(-0.205351\pi\)
−0.920254 + 0.391321i \(0.872018\pi\)
\(770\) 2.02589e7 + 4.73169e6i 1.23137 + 0.287601i
\(771\) 0 0
\(772\) −2.61667e7 1.29283e7i −1.58018 0.780726i
\(773\) 2.42703e7i 1.46092i −0.682957 0.730459i \(-0.739306\pi\)
0.682957 0.730459i \(-0.260694\pi\)
\(774\) 0 0