Properties

Label 108.6.h.a.35.18
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 35.18
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.18

$q$-expansion

\(f(q)\) \(=\) \(q+(1.90579 - 5.32616i) q^{2} +(-24.7359 - 20.3011i) q^{4} +(51.8636 - 29.9435i) q^{5} +(-33.8827 - 19.5622i) q^{7} +(-155.268 + 93.0578i) q^{8} +O(q^{10})\) \(q+(1.90579 - 5.32616i) q^{2} +(-24.7359 - 20.3011i) q^{4} +(51.8636 - 29.9435i) q^{5} +(-33.8827 - 19.5622i) q^{7} +(-155.268 + 93.0578i) q^{8} +(-60.6425 - 333.300i) q^{10} +(108.537 - 187.992i) q^{11} +(-532.156 - 921.721i) q^{13} +(-168.765 + 143.183i) q^{14} +(199.731 + 1004.33i) q^{16} -315.283i q^{17} +1889.72i q^{19} +(-1890.78 - 312.209i) q^{20} +(-794.425 - 936.359i) q^{22} +(-1200.19 - 2078.79i) q^{23} +(230.725 - 399.628i) q^{25} +(-5923.41 + 1077.74i) q^{26} +(440.986 + 1171.75i) q^{28} +(-5185.33 - 2993.75i) q^{29} +(-6949.56 + 4012.33i) q^{31} +(5729.88 + 850.247i) q^{32} +(-1679.25 - 600.864i) q^{34} -2343.04 q^{35} +5243.91 q^{37} +(10065.0 + 3601.42i) q^{38} +(-5266.31 + 9475.59i) q^{40} +(7589.92 - 4382.04i) q^{41} +(8780.43 + 5069.38i) q^{43} +(-6501.20 + 2446.73i) q^{44} +(-13359.2 + 2430.66i) q^{46} +(-7272.14 + 12595.7i) q^{47} +(-7638.14 - 13229.6i) q^{49} +(-1688.77 - 1990.49i) q^{50} +(-5548.58 + 33603.0i) q^{52} -19631.3i q^{53} -12999.9i q^{55} +(7081.33 - 115.661i) q^{56} +(-25827.4 + 21912.4i) q^{58} +(-909.551 - 1575.39i) q^{59} +(24421.5 - 42299.3i) q^{61} +(8125.89 + 44661.1i) q^{62} +(15448.5 - 28897.8i) q^{64} +(-55199.1 - 31869.2i) q^{65} +(37065.9 - 21400.0i) q^{67} +(-6400.60 + 7798.82i) q^{68} +(-4465.35 + 12479.4i) q^{70} +29409.1 q^{71} +38022.9 q^{73} +(9993.79 - 27929.9i) q^{74} +(38363.5 - 46744.1i) q^{76} +(-7355.06 + 4246.45i) q^{77} +(-12858.2 - 7423.70i) q^{79} +(40432.0 + 46107.7i) q^{80} +(-8874.65 - 48776.4i) q^{82} +(60168.3 - 104215. i) q^{83} +(-9440.69 - 16351.7i) q^{85} +(43734.0 - 37104.8i) q^{86} +(641.721 + 39289.4i) q^{88} +35496.5i q^{89} +41640.5i q^{91} +(-12513.9 + 75785.8i) q^{92} +(53227.6 + 62737.3i) q^{94} +(56584.9 + 98008.0i) q^{95} +(1491.62 - 2583.55i) q^{97} +(-85019.9 + 15469.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.90579 5.32616i 0.336899 0.941541i
\(3\) 0 0
\(4\) −24.7359 20.3011i −0.772997 0.634409i
\(5\) 51.8636 29.9435i 0.927765 0.535645i 0.0416611 0.999132i \(-0.486735\pi\)
0.886104 + 0.463486i \(0.153402\pi\)
\(6\) 0 0
\(7\) −33.8827 19.5622i −0.261356 0.150894i 0.363597 0.931556i \(-0.381549\pi\)
−0.624953 + 0.780662i \(0.714882\pi\)
\(8\) −155.268 + 93.0578i −0.857744 + 0.514076i
\(9\) 0 0
\(10\) −60.6425 333.300i −0.191768 1.05399i
\(11\) 108.537 187.992i 0.270456 0.468443i −0.698523 0.715588i \(-0.746159\pi\)
0.968979 + 0.247144i \(0.0794922\pi\)
\(12\) 0 0
\(13\) −532.156 921.721i −0.873334 1.51266i −0.858527 0.512769i \(-0.828620\pi\)
−0.0148071 0.999890i \(-0.504713\pi\)
\(14\) −168.765 + 143.183i −0.230124 + 0.195241i
\(15\) 0 0
\(16\) 199.731 + 1004.33i 0.195050 + 0.980793i
\(17\) 315.283i 0.264593i −0.991210 0.132297i \(-0.957765\pi\)
0.991210 0.132297i \(-0.0422351\pi\)
\(18\) 0 0
\(19\) 1889.72i 1.20092i 0.799655 + 0.600460i \(0.205016\pi\)
−0.799655 + 0.600460i \(0.794984\pi\)
\(20\) −1890.78 312.209i −1.05698 0.174530i
\(21\) 0 0
\(22\) −794.425 936.359i −0.349942 0.412464i
\(23\) −1200.19 2078.79i −0.473074 0.819389i 0.526451 0.850206i \(-0.323522\pi\)
−0.999525 + 0.0308168i \(0.990189\pi\)
\(24\) 0 0
\(25\) 230.725 399.628i 0.0738321 0.127881i
\(26\) −5923.41 + 1077.74i −1.71846 + 0.312665i
\(27\) 0 0
\(28\) 440.986 + 1171.75i 0.106299 + 0.282448i
\(29\) −5185.33 2993.75i −1.14494 0.661030i −0.197289 0.980345i \(-0.563214\pi\)
−0.947648 + 0.319315i \(0.896547\pi\)
\(30\) 0 0
\(31\) −6949.56 + 4012.33i −1.29883 + 0.749881i −0.980202 0.197999i \(-0.936556\pi\)
−0.318629 + 0.947879i \(0.603222\pi\)
\(32\) 5729.88 + 850.247i 0.989169 + 0.146781i
\(33\) 0 0
\(34\) −1679.25 600.864i −0.249125 0.0891413i
\(35\) −2343.04 −0.323303
\(36\) 0 0
\(37\) 5243.91 0.629725 0.314862 0.949137i \(-0.398042\pi\)
0.314862 + 0.949137i \(0.398042\pi\)
\(38\) 10065.0 + 3601.42i 1.13072 + 0.404590i
\(39\) 0 0
\(40\) −5266.31 + 9475.59i −0.520423 + 0.936389i
\(41\) 7589.92 4382.04i 0.705144 0.407115i −0.104117 0.994565i \(-0.533202\pi\)
0.809260 + 0.587450i \(0.199868\pi\)
\(42\) 0 0
\(43\) 8780.43 + 5069.38i 0.724176 + 0.418103i 0.816288 0.577645i \(-0.196028\pi\)
−0.0921115 + 0.995749i \(0.529362\pi\)
\(44\) −6501.20 + 2446.73i −0.506247 + 0.190526i
\(45\) 0 0
\(46\) −13359.2 + 2430.66i −0.930866 + 0.169367i
\(47\) −7272.14 + 12595.7i −0.480195 + 0.831721i −0.999742 0.0227202i \(-0.992767\pi\)
0.519547 + 0.854442i \(0.326101\pi\)
\(48\) 0 0
\(49\) −7638.14 13229.6i −0.454462 0.787151i
\(50\) −1688.77 1990.49i −0.0955311 0.112599i
\(51\) 0 0
\(52\) −5548.58 + 33603.0i −0.284560 + 1.72333i
\(53\) 19631.3i 0.959974i −0.877276 0.479987i \(-0.840641\pi\)
0.877276 0.479987i \(-0.159359\pi\)
\(54\) 0 0
\(55\) 12999.9i 0.579474i
\(56\) 7081.33 115.661i 0.301748 0.00492851i
\(57\) 0 0
\(58\) −25827.4 + 21912.4i −1.00812 + 0.855304i
\(59\) −909.551 1575.39i −0.0340171 0.0589193i 0.848516 0.529170i \(-0.177497\pi\)
−0.882533 + 0.470251i \(0.844163\pi\)
\(60\) 0 0
\(61\) 24421.5 42299.3i 0.840327 1.45549i −0.0492921 0.998784i \(-0.515697\pi\)
0.889619 0.456704i \(-0.150970\pi\)
\(62\) 8125.89 + 44661.1i 0.268467 + 1.47554i
\(63\) 0 0
\(64\) 15448.5 28897.8i 0.471451 0.881892i
\(65\) −55199.1 31869.2i −1.62050 0.935595i
\(66\) 0 0
\(67\) 37065.9 21400.0i 1.00876 0.582407i 0.0979310 0.995193i \(-0.468778\pi\)
0.910828 + 0.412786i \(0.135444\pi\)
\(68\) −6400.60 + 7798.82i −0.167860 + 0.204530i
\(69\) 0 0
\(70\) −4465.35 + 12479.4i −0.108921 + 0.304403i
\(71\) 29409.1 0.692365 0.346183 0.938167i \(-0.387478\pi\)
0.346183 + 0.938167i \(0.387478\pi\)
\(72\) 0 0
\(73\) 38022.9 0.835099 0.417550 0.908654i \(-0.362889\pi\)
0.417550 + 0.908654i \(0.362889\pi\)
\(74\) 9993.79 27929.9i 0.212154 0.592911i
\(75\) 0 0
\(76\) 38363.5 46744.1i 0.761875 0.928309i
\(77\) −7355.06 + 4246.45i −0.141371 + 0.0816205i
\(78\) 0 0
\(79\) −12858.2 7423.70i −0.231800 0.133830i 0.379602 0.925150i \(-0.376061\pi\)
−0.611402 + 0.791320i \(0.709394\pi\)
\(80\) 40432.0 + 46107.7i 0.706318 + 0.805468i
\(81\) 0 0
\(82\) −8874.65 48776.4i −0.145753 0.801078i
\(83\) 60168.3 104215.i 0.958677 1.66048i 0.232959 0.972487i \(-0.425159\pi\)
0.725719 0.687991i \(-0.241507\pi\)
\(84\) 0 0
\(85\) −9440.69 16351.7i −0.141728 0.245480i
\(86\) 43734.0 37104.8i 0.637636 0.540983i
\(87\) 0 0
\(88\) 641.721 + 39289.4i 0.00883364 + 0.540840i
\(89\) 35496.5i 0.475019i 0.971385 + 0.237509i \(0.0763311\pi\)
−0.971385 + 0.237509i \(0.923669\pi\)
\(90\) 0 0
\(91\) 41640.5i 0.527124i
\(92\) −12513.9 + 75785.8i −0.154142 + 0.933508i
\(93\) 0 0
\(94\) 53227.6 + 62737.3i 0.621322 + 0.732329i
\(95\) 56584.9 + 98008.0i 0.643268 + 1.11417i
\(96\) 0 0
\(97\) 1491.62 2583.55i 0.0160964 0.0278797i −0.857865 0.513875i \(-0.828209\pi\)
0.873961 + 0.485995i \(0.161543\pi\)
\(98\) −85019.9 + 15469.0i −0.894243 + 0.162704i
\(99\) 0 0
\(100\) −13820.1 + 5201.19i −0.138201 + 0.0520119i
\(101\) −45537.2 26290.9i −0.444184 0.256450i 0.261187 0.965288i \(-0.415886\pi\)
−0.705371 + 0.708838i \(0.749220\pi\)
\(102\) 0 0
\(103\) 10418.1 6014.90i 0.0967600 0.0558644i −0.450839 0.892605i \(-0.648875\pi\)
0.547599 + 0.836741i \(0.315542\pi\)
\(104\) 168400. + 93592.8i 1.52672 + 0.848514i
\(105\) 0 0
\(106\) −104559. 37413.2i −0.903855 0.323415i
\(107\) −89559.8 −0.756229 −0.378115 0.925759i \(-0.623428\pi\)
−0.378115 + 0.925759i \(0.623428\pi\)
\(108\) 0 0
\(109\) −29876.1 −0.240856 −0.120428 0.992722i \(-0.538427\pi\)
−0.120428 + 0.992722i \(0.538427\pi\)
\(110\) −69239.6 24775.1i −0.545598 0.195225i
\(111\) 0 0
\(112\) 12879.5 37936.7i 0.0970184 0.285769i
\(113\) 214387. 123776.i 1.57943 0.911886i 0.584496 0.811397i \(-0.301292\pi\)
0.994938 0.100490i \(-0.0320409\pi\)
\(114\) 0 0
\(115\) −124492. 71875.6i −0.877804 0.506800i
\(116\) 67487.5 + 179321.i 0.465670 + 1.23733i
\(117\) 0 0
\(118\) −10124.2 + 1842.05i −0.0669352 + 0.0121786i
\(119\) −6167.64 + 10682.7i −0.0399256 + 0.0691531i
\(120\) 0 0
\(121\) 56964.9 + 98666.1i 0.353707 + 0.612639i
\(122\) −178751. 210687.i −1.08730 1.28155i
\(123\) 0 0
\(124\) 253358. + 41835.0i 1.47972 + 0.244335i
\(125\) 159512.i 0.913100i
\(126\) 0 0
\(127\) 265961.i 1.46322i 0.681724 + 0.731610i \(0.261231\pi\)
−0.681724 + 0.731610i \(0.738769\pi\)
\(128\) −124473. 137354.i −0.671506 0.740999i
\(129\) 0 0
\(130\) −274938. + 233263.i −1.42685 + 1.21056i
\(131\) −37162.9 64368.0i −0.189204 0.327712i 0.755781 0.654825i \(-0.227258\pi\)
−0.944985 + 0.327113i \(0.893924\pi\)
\(132\) 0 0
\(133\) 36967.1 64029.0i 0.181212 0.313868i
\(134\) −43339.9 238203.i −0.208510 1.14600i
\(135\) 0 0
\(136\) 29339.6 + 48953.5i 0.136021 + 0.226953i
\(137\) −20104.8 11607.5i −0.0915163 0.0528370i 0.453543 0.891234i \(-0.350160\pi\)
−0.545060 + 0.838397i \(0.683493\pi\)
\(138\) 0 0
\(139\) 287391. 165925.i 1.26164 0.728410i 0.288251 0.957555i \(-0.406926\pi\)
0.973392 + 0.229145i \(0.0735930\pi\)
\(140\) 57957.3 + 47566.3i 0.249912 + 0.205106i
\(141\) 0 0
\(142\) 56047.5 156637.i 0.233257 0.651890i
\(143\) −231035. −0.944794
\(144\) 0 0
\(145\) −358574. −1.41631
\(146\) 72463.7 202516.i 0.281345 0.786280i
\(147\) 0 0
\(148\) −129713. 106457.i −0.486776 0.399503i
\(149\) −287800. + 166162.i −1.06200 + 0.613147i −0.925985 0.377559i \(-0.876763\pi\)
−0.136017 + 0.990707i \(0.543430\pi\)
\(150\) 0 0
\(151\) −300515. 173503.i −1.07257 0.619247i −0.143685 0.989623i \(-0.545895\pi\)
−0.928882 + 0.370377i \(0.879229\pi\)
\(152\) −175853. 293414.i −0.617365 1.03008i
\(153\) 0 0
\(154\) 8600.04 + 47267.1i 0.0292212 + 0.160604i
\(155\) −240286. + 416188.i −0.803340 + 1.39143i
\(156\) 0 0
\(157\) 72572.9 + 125700.i 0.234977 + 0.406992i 0.959266 0.282504i \(-0.0911651\pi\)
−0.724289 + 0.689497i \(0.757832\pi\)
\(158\) −64044.9 + 54336.9i −0.204099 + 0.173162i
\(159\) 0 0
\(160\) 322632. 127476.i 0.996339 0.393665i
\(161\) 93913.2i 0.285537i
\(162\) 0 0
\(163\) 240037.i 0.707635i 0.935314 + 0.353818i \(0.115117\pi\)
−0.935314 + 0.353818i \(0.884883\pi\)
\(164\) −276704. 45689.8i −0.803352 0.132651i
\(165\) 0 0
\(166\) −440395. 519077.i −1.24043 1.46205i
\(167\) −144730. 250679.i −0.401575 0.695548i 0.592341 0.805687i \(-0.298204\pi\)
−0.993916 + 0.110139i \(0.964870\pi\)
\(168\) 0 0
\(169\) −380733. + 659449.i −1.02542 + 1.77609i
\(170\) −105084. + 19119.6i −0.278878 + 0.0507406i
\(171\) 0 0
\(172\) −114278. 303648.i −0.294538 0.782617i
\(173\) 490809. + 283369.i 1.24680 + 0.719841i 0.970470 0.241221i \(-0.0775479\pi\)
0.276332 + 0.961062i \(0.410881\pi\)
\(174\) 0 0
\(175\) −15635.2 + 9026.99i −0.0385930 + 0.0222817i
\(176\) 210485. + 71459.5i 0.512199 + 0.173891i
\(177\) 0 0
\(178\) 189060. + 67649.0i 0.447250 + 0.160034i
\(179\) 440866. 1.02843 0.514214 0.857662i \(-0.328084\pi\)
0.514214 + 0.857662i \(0.328084\pi\)
\(180\) 0 0
\(181\) 103852. 0.235623 0.117812 0.993036i \(-0.462412\pi\)
0.117812 + 0.993036i \(0.462412\pi\)
\(182\) 221784. + 79358.2i 0.496309 + 0.177588i
\(183\) 0 0
\(184\) 379798. + 211083.i 0.827005 + 0.459630i
\(185\) 271968. 157021.i 0.584237 0.337309i
\(186\) 0 0
\(187\) −59270.7 34220.0i −0.123947 0.0715608i
\(188\) 435590. 163934.i 0.898841 0.338279i
\(189\) 0 0
\(190\) 629845. 114598.i 1.26576 0.230299i
\(191\) 215522. 373294.i 0.427472 0.740403i −0.569176 0.822216i \(-0.692738\pi\)
0.996648 + 0.0818131i \(0.0260711\pi\)
\(192\) 0 0
\(193\) 20745.9 + 35932.9i 0.0400903 + 0.0694384i 0.885374 0.464879i \(-0.153902\pi\)
−0.845284 + 0.534317i \(0.820569\pi\)
\(194\) −10917.7 12868.3i −0.0208270 0.0245480i
\(195\) 0 0
\(196\) −79639.9 + 482310.i −0.148078 + 0.896781i
\(197\) 353610.i 0.649170i 0.945856 + 0.324585i \(0.105225\pi\)
−0.945856 + 0.324585i \(0.894775\pi\)
\(198\) 0 0
\(199\) 167614.i 0.300038i −0.988683 0.150019i \(-0.952066\pi\)
0.988683 0.150019i \(-0.0479336\pi\)
\(200\) 1364.15 + 83520.3i 0.00241150 + 0.147644i
\(201\) 0 0
\(202\) −226814. + 192434.i −0.391104 + 0.331820i
\(203\) 117129. + 202873.i 0.199491 + 0.345529i
\(204\) 0 0
\(205\) 262427. 454537.i 0.436138 0.755414i
\(206\) −12181.6 66951.7i −0.0200002 0.109924i
\(207\) 0 0
\(208\) 819426. 718558.i 1.31326 1.15160i
\(209\) 355253. + 205105.i 0.562563 + 0.324796i
\(210\) 0 0
\(211\) 60893.8 35157.0i 0.0941601 0.0543633i −0.452181 0.891926i \(-0.649354\pi\)
0.546341 + 0.837563i \(0.316020\pi\)
\(212\) −398537. + 485598.i −0.609016 + 0.742058i
\(213\) 0 0
\(214\) −170682. + 477010.i −0.254773 + 0.712021i
\(215\) 607180. 0.895821
\(216\) 0 0
\(217\) 313960. 0.452611
\(218\) −56937.7 + 159125.i −0.0811444 + 0.226776i
\(219\) 0 0
\(220\) −263913. + 321565.i −0.367624 + 0.447932i
\(221\) −290603. + 167780.i −0.400239 + 0.231078i
\(222\) 0 0
\(223\) −439612. 253810.i −0.591980 0.341780i 0.173900 0.984763i \(-0.444363\pi\)
−0.765880 + 0.642983i \(0.777696\pi\)
\(224\) −177511. 140898.i −0.236377 0.187622i
\(225\) 0 0
\(226\) −250675. 1.37775e6i −0.326468 1.79432i
\(227\) 54791.0 94900.8i 0.0705739 0.122238i −0.828579 0.559872i \(-0.810850\pi\)
0.899153 + 0.437634i \(0.144184\pi\)
\(228\) 0 0
\(229\) 180234. + 312174.i 0.227116 + 0.393376i 0.956952 0.290246i \(-0.0937370\pi\)
−0.729836 + 0.683622i \(0.760404\pi\)
\(230\) −620077. + 526085.i −0.772905 + 0.655747i
\(231\) 0 0
\(232\) 1.08371e6 17700.4i 1.32188 0.0215906i
\(233\) 938716.i 1.13278i −0.824138 0.566389i \(-0.808340\pi\)
0.824138 0.566389i \(-0.191660\pi\)
\(234\) 0 0
\(235\) 871012.i 1.02886i
\(236\) −9483.52 + 57433.5i −0.0110838 + 0.0671252i
\(237\) 0 0
\(238\) 45143.3 + 53208.7i 0.0516596 + 0.0608892i
\(239\) 163017. + 282354.i 0.184603 + 0.319742i 0.943443 0.331536i \(-0.107567\pi\)
−0.758840 + 0.651278i \(0.774233\pi\)
\(240\) 0 0
\(241\) 37903.3 65650.4i 0.0420373 0.0728107i −0.844241 0.535963i \(-0.819949\pi\)
0.886279 + 0.463153i \(0.153282\pi\)
\(242\) 634074. 115367.i 0.695988 0.126632i
\(243\) 0 0
\(244\) −1.46281e6 + 550529.i −1.57295 + 0.591978i
\(245\) −792284. 457425.i −0.843268 0.486861i
\(246\) 0 0
\(247\) 1.74180e6 1.00563e6i 1.81658 1.04880i
\(248\) 705668. 1.26970e6i 0.728569 1.31090i
\(249\) 0 0
\(250\) 849586. + 303996.i 0.859720 + 0.307623i
\(251\) −971568. −0.973394 −0.486697 0.873571i \(-0.661798\pi\)
−0.486697 + 0.873571i \(0.661798\pi\)
\(252\) 0 0
\(253\) −521060. −0.511783
\(254\) 1.41655e6 + 506867.i 1.37768 + 0.492958i
\(255\) 0 0
\(256\) −968791. + 401193.i −0.923911 + 0.382608i
\(257\) −1.19547e6 + 690206.i −1.12903 + 0.651848i −0.943692 0.330826i \(-0.892673\pi\)
−0.185342 + 0.982674i \(0.559339\pi\)
\(258\) 0 0
\(259\) −177678. 102582.i −0.164583 0.0950218i
\(260\) 718420. + 1.90892e6i 0.659091 + 1.75127i
\(261\) 0 0
\(262\) −413659. + 75263.4i −0.372297 + 0.0677377i
\(263\) 240670. 416853.i 0.214552 0.371615i −0.738582 0.674164i \(-0.764504\pi\)
0.953134 + 0.302549i \(0.0978374\pi\)
\(264\) 0 0
\(265\) −587830. 1.01815e6i −0.514206 0.890631i
\(266\) −270577. 318919.i −0.234470 0.276360i
\(267\) 0 0
\(268\) −1.35130e6 223129.i −1.14925 0.189767i
\(269\) 1.12150e6i 0.944969i −0.881339 0.472484i \(-0.843357\pi\)
0.881339 0.472484i \(-0.156643\pi\)
\(270\) 0 0
\(271\) 873330.i 0.722362i −0.932496 0.361181i \(-0.882374\pi\)
0.932496 0.361181i \(-0.117626\pi\)
\(272\) 316649. 62972.0i 0.259511 0.0516090i
\(273\) 0 0
\(274\) −100139. + 84959.9i −0.0805800 + 0.0683656i
\(275\) −50084.5 86748.9i −0.0399367 0.0691723i
\(276\) 0 0
\(277\) 900195. 1.55918e6i 0.704915 1.22095i −0.261807 0.965120i \(-0.584318\pi\)
0.966722 0.255829i \(-0.0823483\pi\)
\(278\) −336037. 1.84691e6i −0.260781 1.43329i
\(279\) 0 0
\(280\) 363800. 218038.i 0.277311 0.166203i
\(281\) 236453. + 136516.i 0.178640 + 0.103138i 0.586654 0.809838i \(-0.300445\pi\)
−0.408014 + 0.912976i \(0.633778\pi\)
\(282\) 0 0
\(283\) −644438. + 372067.i −0.478316 + 0.276156i −0.719715 0.694270i \(-0.755727\pi\)
0.241398 + 0.970426i \(0.422394\pi\)
\(284\) −727460. 597036.i −0.535196 0.439243i
\(285\) 0 0
\(286\) −440304. + 1.23053e6i −0.318301 + 0.889562i
\(287\) −342889. −0.245725
\(288\) 0 0
\(289\) 1.32045e6 0.929990
\(290\) −683367. + 1.90982e6i −0.477154 + 1.33351i
\(291\) 0 0
\(292\) −940531. 771906.i −0.645530 0.529795i
\(293\) 330601. 190873.i 0.224976 0.129890i −0.383276 0.923634i \(-0.625204\pi\)
0.608252 + 0.793744i \(0.291871\pi\)
\(294\) 0 0
\(295\) −94345.2 54470.2i −0.0631197 0.0364422i
\(296\) −814213. + 487986.i −0.540143 + 0.323727i
\(297\) 0 0
\(298\) 336515. + 1.84954e6i 0.219515 + 1.20649i
\(299\) −1.27737e6 + 2.21248e6i −0.826304 + 1.43120i
\(300\) 0 0
\(301\) −198336. 343529.i −0.126179 0.218548i
\(302\) −1.49682e6 + 1.26993e6i −0.944393 + 0.801241i
\(303\) 0 0
\(304\) −1.89791e6 + 377437.i −1.17785 + 0.234240i
\(305\) 2.92506e6i 1.80047i
\(306\) 0 0
\(307\) 3.21986e6i 1.94980i 0.222640 + 0.974901i \(0.428533\pi\)
−0.222640 + 0.974901i \(0.571467\pi\)
\(308\) 268142. + 44276.0i 0.161060 + 0.0265945i
\(309\) 0 0
\(310\) 1.75875e6 + 2.07297e6i 1.03944 + 1.22515i
\(311\) −775835. 1.34378e6i −0.454850 0.787823i 0.543830 0.839196i \(-0.316974\pi\)
−0.998680 + 0.0513724i \(0.983640\pi\)
\(312\) 0 0
\(313\) 263995. 457253.i 0.152312 0.263813i −0.779765 0.626073i \(-0.784661\pi\)
0.932077 + 0.362260i \(0.117995\pi\)
\(314\) 807807. 146977.i 0.462364 0.0841250i
\(315\) 0 0
\(316\) 167351. + 444668.i 0.0942779 + 0.250506i
\(317\) −764737. 441521.i −0.427429 0.246776i 0.270822 0.962630i \(-0.412705\pi\)
−0.698251 + 0.715853i \(0.746038\pi\)
\(318\) 0 0
\(319\) −1.12560e6 + 649867.i −0.619310 + 0.357559i
\(320\) −64086.6 1.96133e6i −0.0349858 1.07072i
\(321\) 0 0
\(322\) 500197. + 178979.i 0.268844 + 0.0961972i
\(323\) 595799. 0.317756
\(324\) 0 0
\(325\) −491127. −0.257920
\(326\) 1.27848e6 + 457461.i 0.666267 + 0.238402i
\(327\) 0 0
\(328\) −770691. + 1.38669e6i −0.395545 + 0.711698i
\(329\) 492799. 284518.i 0.251004 0.144917i
\(330\) 0 0
\(331\) 128289. + 74067.9i 0.0643607 + 0.0371587i 0.531835 0.846848i \(-0.321503\pi\)
−0.467474 + 0.884007i \(0.654836\pi\)
\(332\) −3.60399e6 + 1.35636e6i −1.79448 + 0.675352i
\(333\) 0 0
\(334\) −1.61098e6 + 293111.i −0.790177 + 0.143769i
\(335\) 1.28158e6 2.21976e6i 0.623928 1.08067i
\(336\) 0 0
\(337\) 191733. + 332092.i 0.0919651 + 0.159288i 0.908338 0.418237i \(-0.137352\pi\)
−0.816373 + 0.577525i \(0.804019\pi\)
\(338\) 2.78673e6 + 3.28462e6i 1.32679 + 1.56384i
\(339\) 0 0
\(340\) −98434.3 + 596132.i −0.0461795 + 0.279669i
\(341\) 1.74195e6i 0.811239i
\(342\) 0 0
\(343\) 1.25524e6i 0.576091i
\(344\) −1.83507e6 + 29972.5i −0.836095 + 0.0136561i
\(345\) 0 0
\(346\) 2.44465e6 2.07409e6i 1.09781 0.931400i
\(347\) 602848. + 1.04416e6i 0.268772 + 0.465527i 0.968545 0.248839i \(-0.0800489\pi\)
−0.699773 + 0.714365i \(0.746716\pi\)
\(348\) 0 0
\(349\) −145755. + 252456.i −0.0640562 + 0.110949i −0.896275 0.443499i \(-0.853737\pi\)
0.832219 + 0.554447i \(0.187070\pi\)
\(350\) 18281.7 + 100479.i 0.00797714 + 0.0438435i
\(351\) 0 0
\(352\) 781744. 984887.i 0.336285 0.423672i
\(353\) 162770. + 93975.5i 0.0695246 + 0.0401400i 0.534359 0.845257i \(-0.320553\pi\)
−0.464835 + 0.885397i \(0.653886\pi\)
\(354\) 0 0
\(355\) 1.52526e6 880610.i 0.642352 0.370862i
\(356\) 720618. 878039.i 0.301356 0.367188i
\(357\) 0 0
\(358\) 840199. 2.34812e6i 0.346477 0.968307i
\(359\) 1.70884e6 0.699786 0.349893 0.936790i \(-0.386218\pi\)
0.349893 + 0.936790i \(0.386218\pi\)
\(360\) 0 0
\(361\) −1.09496e6 −0.442211
\(362\) 197920. 553132.i 0.0793814 0.221849i
\(363\) 0 0
\(364\) 845348. 1.03002e6i 0.334412 0.407466i
\(365\) 1.97201e6 1.13854e6i 0.774776 0.447317i
\(366\) 0 0
\(367\) −3.26612e6 1.88569e6i −1.26581 0.730813i −0.291614 0.956536i \(-0.594192\pi\)
−0.974191 + 0.225723i \(0.927526\pi\)
\(368\) 1.84808e6 1.62059e6i 0.711378 0.623810i
\(369\) 0 0
\(370\) −318004. 1.74779e6i −0.120761 0.663722i
\(371\) −384031. + 665162.i −0.144855 + 0.250895i
\(372\) 0 0
\(373\) 1.13464e6 + 1.96526e6i 0.422267 + 0.731388i 0.996161 0.0875420i \(-0.0279012\pi\)
−0.573894 + 0.818930i \(0.694568\pi\)
\(374\) −295218. + 250469.i −0.109135 + 0.0925923i
\(375\) 0 0
\(376\) −42996.2 2.63244e6i −0.0156841 0.960261i
\(377\) 6.37257e6i 2.30920i
\(378\) 0 0
\(379\) 4.07165e6i 1.45604i −0.685557 0.728019i \(-0.740441\pi\)
0.685557 0.728019i \(-0.259559\pi\)
\(380\) 589989. 3.57305e6i 0.209597 1.26935i
\(381\) 0 0
\(382\) −1.57749e6 1.85932e6i −0.553104 0.651923i
\(383\) −1.22056e6 2.11407e6i −0.425170 0.736415i 0.571267 0.820765i \(-0.306452\pi\)
−0.996436 + 0.0843491i \(0.973119\pi\)
\(384\) 0 0
\(385\) −254307. + 440473.i −0.0874393 + 0.151449i
\(386\) 230922. 42015.2i 0.0788854 0.0143529i
\(387\) 0 0
\(388\) −89345.5 + 33625.2i −0.0301296 + 0.0113393i
\(389\) −924047. 533499.i −0.309614 0.178756i 0.337140 0.941455i \(-0.390540\pi\)
−0.646754 + 0.762699i \(0.723874\pi\)
\(390\) 0 0
\(391\) −655407. + 378399.i −0.216805 + 0.125172i
\(392\) 2.41708e6 + 1.34336e6i 0.794468 + 0.441546i
\(393\) 0 0
\(394\) 1.88338e6 + 673906.i 0.611220 + 0.218705i
\(395\) −889166. −0.286741
\(396\) 0 0
\(397\) −2.64187e6 −0.841271 −0.420635 0.907230i \(-0.638193\pi\)
−0.420635 + 0.907230i \(0.638193\pi\)
\(398\) −892737. 319437.i −0.282498 0.101083i
\(399\) 0 0
\(400\) 447442. + 151907.i 0.139826 + 0.0474708i
\(401\) −2.41745e6 + 1.39571e6i −0.750751 + 0.433446i −0.825965 0.563721i \(-0.809369\pi\)
0.0752142 + 0.997167i \(0.476036\pi\)
\(402\) 0 0
\(403\) 7.39649e6 + 4.27037e6i 2.26863 + 1.30979i
\(404\) 592671. + 1.57479e6i 0.180659 + 0.480030i
\(405\) 0 0
\(406\) 1.30376e6 237213.i 0.392538 0.0714205i
\(407\) 569159. 985812.i 0.170313 0.294990i
\(408\) 0 0
\(409\) −502887. 871025.i −0.148649 0.257468i 0.782079 0.623179i \(-0.214159\pi\)
−0.930728 + 0.365711i \(0.880826\pi\)
\(410\) −1.92081e6 2.26398e6i −0.564318 0.665141i
\(411\) 0 0
\(412\) −379811. 62715.0i −0.110236 0.0182024i
\(413\) 71171.2i 0.0205319i
\(414\) 0 0
\(415\) 7.20660e6i 2.05404i
\(416\) −2.26550e6 5.73381e6i −0.641845 1.62446i
\(417\) 0 0
\(418\) 1.76946e6 1.50124e6i 0.495336 0.420253i
\(419\) 2.85052e6 + 4.93724e6i 0.793210 + 1.37388i 0.923969 + 0.382466i \(0.124925\pi\)
−0.130759 + 0.991414i \(0.541741\pi\)
\(420\) 0 0
\(421\) −2.95835e6 + 5.12400e6i −0.813474 + 1.40898i 0.0969446 + 0.995290i \(0.469093\pi\)
−0.910419 + 0.413688i \(0.864240\pi\)
\(422\) −71201.1 391332.i −0.0194628 0.106971i
\(423\) 0 0
\(424\) 1.82685e6 + 3.04812e6i 0.493500 + 0.823412i
\(425\) −125996. 72743.8i −0.0338364 0.0195355i
\(426\) 0 0
\(427\) −1.65493e6 + 955477.i −0.439249 + 0.253601i
\(428\) 2.21534e6 + 1.81816e6i 0.584563 + 0.479759i
\(429\) 0 0
\(430\) 1.15716e6 3.23394e6i 0.301802 0.843452i
\(431\) 516224. 0.133858 0.0669291 0.997758i \(-0.478680\pi\)
0.0669291 + 0.997758i \(0.478680\pi\)
\(432\) 0 0
\(433\) 6.50137e6 1.66642 0.833212 0.552954i \(-0.186499\pi\)
0.833212 + 0.552954i \(0.186499\pi\)
\(434\) 598342. 1.67220e6i 0.152484 0.426151i
\(435\) 0 0
\(436\) 739014. + 606518.i 0.186181 + 0.152801i
\(437\) 3.92833e6 2.26802e6i 0.984021 0.568125i
\(438\) 0 0
\(439\) 762498. + 440228.i 0.188833 + 0.109023i 0.591436 0.806352i \(-0.298561\pi\)
−0.402603 + 0.915375i \(0.631895\pi\)
\(440\) 1.20974e6 + 2.01848e6i 0.297894 + 0.497041i
\(441\) 0 0
\(442\) 339793. + 1.86755e6i 0.0827292 + 0.454692i
\(443\) −372571. + 645312.i −0.0901985 + 0.156228i −0.907595 0.419848i \(-0.862083\pi\)
0.817396 + 0.576076i \(0.195417\pi\)
\(444\) 0 0
\(445\) 1.06289e6 + 1.84098e6i 0.254442 + 0.440706i
\(446\) −2.18964e6 + 1.85773e6i −0.521238 + 0.442228i
\(447\) 0 0
\(448\) −1.08874e6 + 676931.i −0.256289 + 0.159349i
\(449\) 3.80614e6i 0.890983i 0.895286 + 0.445492i \(0.146971\pi\)
−0.895286 + 0.445492i \(0.853029\pi\)
\(450\) 0 0
\(451\) 1.90246e6i 0.440427i
\(452\) −7.81584e6 1.29056e6i −1.79941 0.297121i
\(453\) 0 0
\(454\) −401036. 472686.i −0.0913154 0.107630i
\(455\) 1.24686e6 + 2.15963e6i 0.282352 + 0.489047i
\(456\) 0 0
\(457\) −1.54711e6 + 2.67967e6i −0.346521 + 0.600192i −0.985629 0.168925i \(-0.945970\pi\)
0.639108 + 0.769117i \(0.279304\pi\)
\(458\) 2.00618e6 365015.i 0.446895 0.0813106i
\(459\) 0 0
\(460\) 1.62028e6 + 4.30524e6i 0.357021 + 0.948642i
\(461\) 6.16631e6 + 3.56012e6i 1.35137 + 0.780212i 0.988441 0.151606i \(-0.0484445\pi\)
0.362926 + 0.931818i \(0.381778\pi\)
\(462\) 0 0
\(463\) −4.12079e6 + 2.37914e6i −0.893363 + 0.515784i −0.875041 0.484049i \(-0.839166\pi\)
−0.0183222 + 0.999832i \(0.505832\pi\)
\(464\) 1.97105e6 5.80575e6i 0.425014 1.25188i
\(465\) 0 0
\(466\) −4.99975e6 1.78900e6i −1.06656 0.381632i
\(467\) −7.37952e6 −1.56580 −0.782900 0.622148i \(-0.786260\pi\)
−0.782900 + 0.622148i \(0.786260\pi\)
\(468\) 0 0
\(469\) −1.67452e6 −0.351528
\(470\) 4.63915e6 + 1.65997e6i 0.968710 + 0.346621i
\(471\) 0 0
\(472\) 287826. + 159967.i 0.0594670 + 0.0330503i
\(473\) 1.90600e6 1.10043e6i 0.391716 0.226157i
\(474\) 0 0
\(475\) 755186. + 436007.i 0.153575 + 0.0886665i
\(476\) 369432. 139036.i 0.0747338 0.0281260i
\(477\) 0 0
\(478\) 1.81454e6 330148.i 0.363243 0.0660904i
\(479\) −553793. + 959197.i −0.110283 + 0.191016i −0.915884 0.401442i \(-0.868509\pi\)
0.805601 + 0.592458i \(0.201842\pi\)
\(480\) 0 0
\(481\) −2.79058e6 4.83342e6i −0.549960 0.952559i
\(482\) −277429. 326995.i −0.0543919 0.0641097i
\(483\) 0 0
\(484\) 593950. 3.59705e6i 0.115249 0.697963i
\(485\) 178657.i 0.0344878i
\(486\) 0 0
\(487\) 763869.i 0.145948i −0.997334 0.0729738i \(-0.976751\pi\)
0.997334 0.0729738i \(-0.0232489\pi\)
\(488\) 144391. + 8.84036e6i 0.0274468 + 1.68043i
\(489\) 0 0
\(490\) −3.94625e6 + 3.34807e6i −0.742496 + 0.629948i
\(491\) −3.47276e6 6.01500e6i −0.650087 1.12598i −0.983101 0.183061i \(-0.941399\pi\)
0.333015 0.942922i \(1.60807\pi\)
\(492\) 0 0
\(493\) −943881. + 1.63485e6i −0.174904 + 0.302943i
\(494\) −2.03663e6 1.11936e7i −0.375486 2.06373i
\(495\) 0 0
\(496\) −5.41775e6 6.17828e6i −0.988815 1.12762i
\(497\) −996459. 575306.i −0.180954 0.104474i
\(498\) 0 0
\(499\) −5.34730e6 + 3.08727e6i −0.961354 + 0.555038i −0.896590 0.442862i \(-0.853963\pi\)
−0.0647647 + 0.997901i \(0.520630\pi\)
\(500\) 3.23827e6 3.94567e6i 0.579279 0.705824i
\(501\) 0 0
\(502\) −1.85161e6 + 5.17472e6i −0.327936 + 0.916490i
\(503\) 3.43627e6 0.605574 0.302787 0.953058i \(-0.402083\pi\)
0.302787 + 0.953058i \(0.402083\pi\)
\(504\) 0 0
\(505\) −3.14897e6 −0.549465
\(506\) −993031. + 2.77525e6i −0.172420 + 0.481865i
\(507\) 0 0
\(508\) 5.39931e6 6.57880e6i 0.928280 1.13106i
\(509\) −2.45696e6 + 1.41853e6i −0.420343 + 0.242685i −0.695224 0.718793i \(-0.744695\pi\)
0.274881 + 0.961478i \(0.411362\pi\)
\(510\) 0 0
\(511\) −1.28832e6 743811.i −0.218259 0.126012i
\(512\) 290506. + 5.92452e6i 0.0489756 + 0.998800i
\(513\) 0 0
\(514\) 1.39783e6 + 7.68266e6i 0.233370 + 1.28264i
\(515\) 360214. 623909.i 0.0598470 0.103658i
\(516\) 0 0
\(517\) 1.57859e6 + 2.73420e6i 0.259743 + 0.449888i
\(518\) −884987. + 750840.i −0.144915 + 0.122948i
\(519\) 0 0
\(520\) 1.15363e7 188425.i 1.87094 0.0305584i
\(521\) 1.84176e6i 0.297261i −0.988893 0.148631i \(-0.952513\pi\)
0.988893 0.148631i \(-0.0474866\pi\)
\(522\) 0 0
\(523\) 1.03954e7i 1.66183i 0.556398 + 0.830916i \(0.312183\pi\)
−0.556398 + 0.830916i \(0.687817\pi\)
\(524\) −387483. + 2.34665e6i −0.0616487 + 0.373353i
\(525\) 0 0
\(526\) −1.76156e6 2.07628e6i −0.277608 0.327207i
\(527\) 1.26502e6 + 2.19108e6i 0.198413 + 0.343662i
\(528\) 0 0
\(529\) 337272. 584172.i 0.0524012 0.0907615i
\(530\) −6.54312e6 + 1.19049e6i −1.01180 + 0.184093i
\(531\) 0 0
\(532\) −2.21427e6 + 833342.i −0.339197 + 0.127657i
\(533\) −8.07804e6 4.66386e6i −1.23165 0.711094i
\(534\) 0 0
\(535\) −4.64490e6 + 2.68173e6i −0.701603 + 0.405071i
\(536\) −3.76372e6 + 6.77201e6i −0.565856 + 1.01814i
\(537\) 0 0
\(538\) −5.97327e6 2.13734e6i −0.889726 0.318359i
\(539\) −3.31609e6 −0.491648
\(540\) 0 0
\(541\) 330411. 0.0485357 0.0242679 0.999705i \(-0.492275\pi\)
0.0242679 + 0.999705i \(0.492275\pi\)
\(542\) −4.65149e6 1.66438e6i −0.680133 0.243364i
\(543\) 0 0
\(544\) 268069. 1.80654e6i 0.0388373 0.261727i
\(545\) −1.54949e6 + 894596.i −0.223458 + 0.129014i
\(546\) 0 0
\(547\) 1.06834e7 + 6.16808e6i 1.52666 + 0.881417i 0.999499 + 0.0316507i \(0.0100764\pi\)
0.527160 + 0.849766i \(0.323257\pi\)
\(548\) 261666. + 695272.i 0.0372216 + 0.0989017i
\(549\) 0 0
\(550\) −557489. + 101433.i −0.0785832 + 0.0142979i
\(551\) 5.65737e6 9.79885e6i 0.793845 1.37498i
\(552\) 0 0
\(553\) 290448. + 503070.i 0.0403883 + 0.0699545i
\(554\) −6.58887e6 7.76606e6i −0.912088 1.07504i
\(555\) 0 0
\(556\) −1.04774e7 1.73004e6i −1.43736 0.237339i
\(557\) 5.94173e6i 0.811474i −0.913990 0.405737i \(-0.867015\pi\)
0.913990 0.405737i \(-0.132985\pi\)
\(558\) 0 0
\(559\) 1.07908e7i 1.46058i
\(560\) −467979. 2.35319e6i −0.0630603 0.317094i
\(561\) 0 0
\(562\) 1.17774e6 999214.i 0.157292 0.133450i
\(563\) 66573.9 + 115309.i 0.00885182 + 0.0153318i 0.870417 0.492315i \(-0.163849\pi\)
−0.861566 + 0.507646i \(0.830516\pi\)
\(564\) 0 0
\(565\) 7.41258e6 1.28390e7i 0.976896 1.69203i
\(566\) 753521. + 4.14146e6i 0.0988676 + 0.543391i
\(567\) 0 0
\(568\) −4.56629e6 + 2.73674e6i −0.593872 + 0.355929i
\(569\) −3.70587e6 2.13959e6i −0.479854 0.277044i 0.240501 0.970649i \(-0.422688\pi\)
−0.720356 + 0.693605i \(0.756021\pi\)
\(570\) 0 0
\(571\) 525371. 303323.i 0.0674335 0.0389328i −0.465904 0.884835i \(-0.654271\pi\)
0.533338 + 0.845902i \(0.320938\pi\)
\(572\) 5.71485e6 + 4.69025e6i 0.730323 + 0.599386i
\(573\) 0 0
\(574\) −653476. + 1.82628e6i −0.0827846 + 0.231360i
\(575\) −1.10765e6 −0.139712
\(576\) 0 0
\(577\) −496600. −0.0620965 −0.0310483 0.999518i \(-0.509885\pi\)
−0.0310483 + 0.999518i \(0.509885\pi\)
\(578\) 2.51651e6 7.03294e6i 0.313313 0.875624i
\(579\) 0 0
\(580\) 8.86965e6 + 7.27944e6i 1.09480 + 0.898520i
\(581\) −4.07733e6 + 2.35405e6i −0.501113 + 0.289318i
\(582\) 0 0
\(583\) −3.69053e6 2.13073e6i −0.449694 0.259631i
\(584\) −5.90375e6 + 3.53833e6i −0.716302 + 0.429305i
\(585\) 0 0
\(586\) −386561. 2.12460e6i −0.0465023 0.255583i
\(587\) −7.37488e6 + 1.27737e7i −0.883405 + 1.53010i −0.0358744 + 0.999356i \(0.511422\pi\)
−0.847531 + 0.530746i \(0.821912\pi\)
\(588\) 0 0
\(589\) −7.58219e6 1.31327e7i −0.900547 1.55979i
\(590\) −469919. + 398689.i −0.0555768 + 0.0471524i
\(591\) 0 0
\(592\) 1.04737e6 + 5.26663e6i 0.122828 + 0.617630i
\(593\) 1.01532e7i 1.18568i −0.805322 0.592838i \(-0.798008\pi\)
0.805322 0.592838i \(-0.201992\pi\)
\(594\) 0 0
\(595\) 738722.i 0.0855438i
\(596\) 1.04923e7 + 1.73250e6i 1.20991 + 0.199783i
\(597\) 0 0
\(598\) 9.34959e6 + 1.10200e7i 1.06915 + 1.26017i
\(599\) −5.29325e6 9.16817e6i −0.602775 1.04404i −0.992399 0.123062i \(-0.960728\pi\)
0.389624 0.920974i \(1.62740\pi\)
\(600\) 0 0
\(601\) 6.67071e6 1.15540e7i 0.753331 1.30481i −0.192869 0.981224i \(-0.561779\pi\)
0.946200 0.323583i \(-0.104887\pi\)
\(602\) −2.20768e6 + 401677.i −0.248281 + 0.0451737i
\(603\) 0 0
\(604\) 3.91123e6 + 1.03925e7i 0.436235 + 1.15912i
\(605\) 5.90881e6 + 3.41146e6i 0.656314 + 0.378923i
\(606\) 0 0
\(607\) 6.57795e6 3.79778e6i 0.724635 0.418368i −0.0918216 0.995775i \(-0.529269\pi\)
0.816456 + 0.577408i \(0.195936\pi\)
\(608\) −1.60673e6 + 1.08279e7i −0.176273 + 1.18791i
\(609\) 0 0
\(610\) −1.55793e7 5.57456e6i −1.69521 0.606577i
\(611\) 1.54796e7 1.67748
\(612\) 0 0
\(613\) 1.15773e7 1.24438 0.622192 0.782865i \(-0.286242\pi\)
0.622192 + 0.782865i \(0.286242\pi\)
\(614\) 1.71495e7 + 6.13637e6i 1.83582 + 0.656887i
\(615\) 0 0
\(616\) 746844. 1.34378e6i 0.0793009 0.142685i
\(617\) 4.79775e6 2.76998e6i 0.507370 0.292930i −0.224382 0.974501i \(-0.572036\pi\)
0.731752 + 0.681571i \(0.238703\pi\)
\(618\) 0 0
\(619\) 399838. + 230847.i 0.0419428 + 0.0242157i 0.520825 0.853664i \(-0.325624\pi\)
−0.478882 + 0.877879i \(0.658958\pi\)
\(620\) 1.43928e7 5.41672e6i 1.50371 0.565923i
\(621\) 0 0
\(622\) −8.63579e6 + 1.57124e6i −0.895006 + 0.162842i
\(623\) 694390. 1.20272e6i 0.0716776 0.124149i
\(624\) 0 0
\(625\) 5.49736e6 + 9.52171e6i 0.562930 + 0.975023i
\(626\) −1.93228e6 2.27751e6i −0.197076 0.232287i
\(627\) 0 0
\(628\) 756689. 4.58262e6i 0.0765629 0.463676i
\(629\) 1.65332e6i 0.166621i
\(630\) 0 0
\(631\) 1.33405e7i 1.33383i −0.745136 0.666913i \(-0.767615\pi\)
0.745136 0.666913i \(-0.232385\pi\)
\(632\) 2.68731e6 43892.3i 0.267624 0.00437115i
\(633\) 0 0
\(634\) −3.80904e6 + 3.23166e6i −0.376350 + 0.319303i
\(635\) 7.96382e6 + 1.37937e7i 0.783767 + 1.35752i
\(636\) 0 0
\(637\) −8.12936e6 + 1.40805e7i −0.793794 + 1.37489i
\(638\) 1.31613e6 + 7.23365e6i 0.128011 + 0.703567i
\(639\) 0 0
\(640\) −1.05685e7 3.39655e6i −1.01991 0.327784i
\(641\) 2.31892e6 + 1.33883e6i 0.222915 + 0.128700i 0.607299 0.794473i \(-0.292253\pi\)
−0.384384 + 0.923173i \(0.625586\pi\)
\(642\) 0 0
\(643\) 1.46328e7 8.44826e6i 1.39573 0.805824i 0.401786 0.915734i \(-0.368390\pi\)
0.993942 + 0.109910i \(0.0350563\pi\)
\(644\) 1.90654e6 2.32303e6i 0.181147 0.220719i
\(645\) 0 0
\(646\) 1.13547e6 3.17332e6i 0.107052 0.299180i
\(647\) 7.65712e6 0.719126 0.359563 0.933121i \(-0.382926\pi\)
0.359563 + 0.933121i \(0.382926\pi\)
\(648\) 0 0
\(649\) −394880. −0.0368005
\(650\) −935986. + 2.61582e6i −0.0868932 + 0.242842i
\(651\) 0 0
\(652\) 4.87302e6 5.93754e6i 0.448930 0.547000i
\(653\) −957462. + 552791.i −0.0878696 + 0.0507315i −0.543291 0.839544i \(-0.682822\pi\)
0.455421 + 0.890276i \(0.349489\pi\)
\(654\) 0 0
\(655\) −3.85480e6 2.22557e6i −0.351074 0.202693i
\(656\) 5.91697e6 + 6.74757e6i 0.536834 + 0.612192i
\(657\) 0 0
\(658\) −576214. 3.16696e6i −0.0518823 0.285153i
\(659\) −7.66650e6 + 1.32788e7i −0.687675 + 1.19109i 0.284912 + 0.958554i \(0.408035\pi\)
−0.972588 + 0.232535i \(0.925298\pi\)
\(660\) 0 0
\(661\) 3.77496e6 + 6.53842e6i 0.336054 + 0.582062i 0.983687 0.179890i \(-0.0575743\pi\)
−0.647633 + 0.761952i \(0.724241\pi\)
\(662\) 638990. 542131.i 0.0566695 0.0480795i
\(663\) 0 0
\(664\) 355742. + 2.17803e7i 0.0313123 + 1.91710i
\(665\) 4.42770e6i 0.388261i
\(666\) 0 0
\(667\) 1.43723e7i 1.25087i
\(668\) −1.50904e6 + 9.13895e6i −0.130846 + 0.792420i
\(669\) 0 0
\(670\) −9.38039e6 1.10563e7i −0.807298 0.951532i
\(671\) −5.30128e6 9.18209e6i −0.454543 0.787291i
\(672\) 0 0
\(673\) 1.45359e6 2.51769e6i 0.123710 0.214271i −0.797518 0.603295i \(-0.793854\pi\)
0.921228 + 0.389023i \(0.127188\pi\)
\(674\) 2.13418e6 388304.i 0.180959 0.0329248i
\(675\) 0 0
\(676\) 2.28053e7 8.58278e6i 1.91942 0.722372i
\(677\) −8.20582e6 4.73763e6i −0.688098 0.397274i 0.114801 0.993389i \(-0.463377\pi\)
−0.802899 + 0.596115i \(0.796710\pi\)
\(678\) 0 0
\(679\) −101080. + 58358.6i −0.00841377 + 0.00485769i
\(680\) 2.98750e6 + 1.66038e6i 0.247762 + 0.137700i
\(681\) 0 0
\(682\) 9.27788e6 + 3.31979e6i 0.763814 + 0.273306i
\(683\) −6.62953e6 −0.543789 −0.271895 0.962327i \(-0.587650\pi\)
−0.271895 + 0.962327i \(0.587650\pi\)
\(684\) 0 0
\(685\) −1.39028e6 −0.113208
\(686\) 6.68560e6 + 2.39222e6i 0.542413 + 0.194085i
\(687\) 0 0
\(688\) −3.33762e6 + 9.83098e6i −0.268822 + 0.791819i
\(689\) −1.80946e7 + 1.04469e7i −1.45211 + 0.838378i
\(690\) 0 0
\(691\) −6.59285e6 3.80638e6i −0.525264 0.303261i 0.213822 0.976873i \(-0.431409\pi\)
−0.739086 + 0.673611i \(0.764742\pi\)
\(692\) −6.38792e6 1.69733e7i −0.507101 1.34742i
\(693\) 0 0
\(694\) 6.71028e6 1.22091e6i 0.528861 0.0962240i
\(695\) 9.93677e6 1.72110e7i 0.780339 1.35159i
\(696\) 0 0
\(697\) −1.38159e6 2.39298e6i −0.107720 0.186576i
\(698\) 1.06684e6 + 1.25744e6i 0.0828821 + 0.0976900i
\(699\) 0 0
\(700\) 570009. + 94120.8i 0.0439680 + 0.00726007i
\(701\) 3.35628e6i 0.257966i 0.991647 + 0.128983i \(0.0411713\pi\)
−0.991647 + 0.128983i \(0.958829\pi\)
\(702\) 0 0
\(703\) 9.90954e6i 0.756249i
\(704\) −3.75582e6 6.04068e6i −0.285610 0.459361i
\(705\) 0 0
\(706\) 810734. 687842.i 0.0612163 0.0519370i
\(707\) 1.02862e6 + 1.78162e6i 0.0773936 + 0.134050i
\(708\) 0 0
\(709\) 3.57561e6 6.19313e6i 0.267137 0.462695i −0.700984 0.713177i \(-0.747256\pi\)
0.968121 + 0.250482i \(0.0805890\pi\)
\(710\) −1.78344e6 9.80204e6i −0.132774 0.729744i
\(711\) 0 0
\(712\) −3.30323e6 5.51149e6i −0.244196 0.407445i
\(713\) 1.66815e7 + 9.63109e6i 1.22889 + 0.709499i
\(714\) 0 0
\(715\) −1.19823e7 + 6.91798e6i −0.876547 + 0.506074i
\(716\) −1.09052e7 8.95006e6i −0.794972 0.652444i
\(717\) 0 0
\(718\) 3.25669e6 9.10155e6i 0.235758 0.658877i
\(719\) 1.05572e7 0.761603 0.380801 0.924657i \(-0.375648\pi\)
0.380801 + 0.924657i \(0.375648\pi\)
\(720\) 0 0
\(721\) −470659. −0.0337185
\(722\) −2.08676e6 + 5.83191e6i −0.148981 + 0.416359i
\(723\) 0 0
\(724\) −2.56887e6 2.10831e6i −0.182136 0.149482i
\(725\) −2.39278e6 + 1.38147e6i −0.169066 + 0.0976104i
\(726\) 0 0
\(727\) 457178. + 263952.i 0.0320811 + 0.0185220i 0.515955 0.856616i \(-0.327437\pi\)
−0.483874 + 0.875138i \(0.660771\pi\)
\(728\) −3.87498e6 6.46546e6i −0.270982 0.452138i
\(729\) 0 0
\(730\) −2.30580e6 1.26730e7i −0.160146 0.880184i
\(731\) 1.59829e6 2.76832e6i 0.110627 0.191612i
\(732\) 0 0
\(733\) −1.01725e7 1.76192e7i −0.699304 1.21123i −0.968708 0.248202i \(-0.920160\pi\)
0.269404 0.963027i \(-0.413173\pi\)
\(734\) −1.62681e7 + 1.38021e7i −1.11454 + 0.945596i
\(735\) 0 0
\(736\) −5.10945e6 1.29316e7i −0.347680 0.879953i
\(737\) 9.29078e6i 0.630062i
\(738\) 0 0
\(739\) 4.56621e6i 0.307570i −0.988104 0.153785i \(-0.950854\pi\)
0.988104 0.153785i \(-0.0491464\pi\)
\(740\) −9.91508e6 1.63719e6i −0.665605 0.109906i
\(741\) 0 0
\(742\) 2.81087e6 + 3.31307e6i 0.187427 + 0.220913i
\(743\) −8.52924e6 1.47731e7i −0.566811 0.981745i −0.996879 0.0789485i \(-0.974844\pi\)
0.430068 0.902797i \(1.64151\pi\)
\(744\) 0 0
\(745\) −9.95091e6 + 1.72355e7i −0.656859 + 1.13771i
\(746\) 1.26297e7 2.29791e6i 0.830893 0.151177i
\(747\) 0 0
\(748\) 771413. + 2.04972e6i 0.0504119 + 0.133949i
\(749\) 3.03453e6 + 1.75199e6i 0.197645 + 0.114111i
\(750\) 0 0
\(751\) 4.42935e6 2.55729e6i 0.286576 0.165455i −0.349821 0.936817i \(-0.613757\pi\)
0.636397 + 0.771362i \(0.280424\pi\)
\(752\) −1.41027e7 4.78788e6i −0.909409 0.308744i
\(753\) 0 0
\(754\) 3.39413e7 + 1.21448e7i 2.17421 + 0.777968i
\(755\) −2.07811e7 −1.32679
\(756\) 0 0
\(757\) 6.36558e6 0.403736 0.201868 0.979413i \(-0.435299\pi\)
0.201868 + 0.979413i \(0.435299\pi\)
\(758\) −2.16863e7 7.75972e6i −1.37092 0.490539i
\(759\) 0 0
\(760\) −1.79062e7 9.95187e6i −1.12453 0.624986i
\(761\) 9.28199e6 5.35896e6i 0.581005 0.335443i −0.180528 0.983570i \(-0.557781\pi\)
0.761533 + 0.648127i \(0.224447\pi\)
\(762\) 0 0
\(763\) 1.01228e6 + 584443.i 0.0629494 + 0.0363438i
\(764\) −1.29094e7 + 4.85845e6i −0.800153 + 0.301137i
\(765\) 0 0
\(766\) −1.35860e7 + 2.47192e6i −0.836605 + 0.152217i
\(767\) −968045. + 1.67670e6i −0.0594165 + 0.102912i
\(768\) 0 0
\(769\) 7.59857e6 + 1.31611e7i 0.463358 + 0.802559i 0.999126 0.0418063i \(-0.0133112\pi\)
−0.535768 + 0.844365i \(0.679978\pi\)
\(770\) 1.86137e6 + 2.19393e6i 0.113137 + 0.133351i
\(771\) 0 0
\(772\) 216309. 1.31000e6i 0.0130627 0.0791093i
\(773\) 2.52966e7i 1.52270i 0.648342 + 0.761349i \(0.275463\pi\)
−0.648342 + 0.761349i \(0.724537\pi\)
\(774\) 0 0