Properties

Label 108.6.h.a.35.9
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 35.9
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.9

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.65969 + 4.31354i) q^{2} +(-5.21330 - 31.5725i) q^{4} +(51.8636 - 29.9435i) q^{5} +(33.8827 + 19.5622i) q^{7} +(155.268 + 93.0578i) q^{8} +O(q^{10})\) \(q+(-3.65969 + 4.31354i) q^{2} +(-5.21330 - 31.5725i) q^{4} +(51.8636 - 29.9435i) q^{5} +(33.8827 + 19.5622i) q^{7} +(155.268 + 93.0578i) q^{8} +(-60.6425 + 333.300i) q^{10} +(-108.537 + 187.992i) q^{11} +(-532.156 - 921.721i) q^{13} +(-208.383 + 74.5629i) q^{14} +(-969.643 + 329.194i) q^{16} -315.283i q^{17} -1889.72i q^{19} +(-1215.77 - 1481.36i) q^{20} +(-413.698 - 1156.17i) q^{22} +(1200.19 + 2078.79i) q^{23} +(230.725 - 399.628i) q^{25} +(5923.41 + 1077.74i) q^{26} +(440.986 - 1171.75i) q^{28} +(-5185.33 - 2993.75i) q^{29} +(6949.56 - 4012.33i) q^{31} +(2128.60 - 5387.34i) q^{32} +(1359.99 + 1153.84i) q^{34} +2343.04 q^{35} +5243.91 q^{37} +(8151.40 + 6915.81i) q^{38} +(10839.3 + 177.040i) q^{40} +(7589.92 - 4382.04i) q^{41} +(-8780.43 - 5069.38i) q^{43} +(6501.20 + 2446.73i) q^{44} +(-13359.2 - 2430.66i) q^{46} +(7272.14 - 12595.7i) q^{47} +(-7638.14 - 13229.6i) q^{49} +(879.429 + 2457.76i) q^{50} +(-26326.7 + 21606.7i) q^{52} -19631.3i q^{53} +12999.9i q^{55} +(3440.50 + 6190.44i) q^{56} +(31890.4 - 11410.9i) q^{58} +(909.551 + 1575.39i) q^{59} +(24421.5 - 42299.3i) q^{61} +(-8125.89 + 44661.1i) q^{62} +(15448.5 + 28897.8i) q^{64} +(-55199.1 - 31869.2i) q^{65} +(-37065.9 + 21400.0i) q^{67} +(-9954.28 + 1643.67i) q^{68} +(-8574.81 + 10106.8i) q^{70} -29409.1 q^{71} +38022.9 q^{73} +(-19191.1 + 22619.8i) q^{74} +(-59663.3 + 9851.70i) q^{76} +(-7355.06 + 4246.45i) q^{77} +(12858.2 + 7423.70i) q^{79} +(-40432.0 + 46107.7i) q^{80} +(-8874.65 + 48776.4i) q^{82} +(-60168.3 + 104215. i) q^{83} +(-9440.69 - 16351.7i) q^{85} +(54000.6 - 19322.4i) q^{86} +(-34346.5 + 19089.0i) q^{88} +35496.5i q^{89} -41640.5i q^{91} +(59375.5 - 48730.2i) q^{92} +(27718.3 + 77465.1i) q^{94} +(-56584.9 - 98008.0i) q^{95} +(1491.62 - 2583.55i) q^{97} +(85019.9 + 15469.0i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.65969 + 4.31354i −0.646948 + 0.762534i
\(3\) 0 0
\(4\) −5.21330 31.5725i −0.162916 0.986640i
\(5\) 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 0.624953 0.780662i \(-0.285118\pi\)
−0.363597 + 0.931556i \(0.618451\pi\)
\(8\) 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 −0.968979 0.247144i \(-0.920508\pi\)
0.698523 + 0.715588i \(0.253841\pi\)
\(12\) 0 0
\(13\) −532.156 921.721i −0.873334 1.51266i −0.858527 0.512769i \(-0.828620\pi\)
−0.0148071 0.999890i \(-0.504713\pi\)
\(14\) −208.383 + 74.5629i −0.284146 + 0.101672i
\(15\) 0 0
\(16\) −969.643 + 329.194i −0.946917 + 0.321478i
\(17\) 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 \(-0.794984\pi\)
0.799655 0.600460i \(-0.205016\pi\)
\(20\) −1215.77 1481.36i −0.679637 0.828105i
\(21\) 0 0
\(22\) −413.698 1156.17i −0.182233 0.509291i
\(23\) 1200.19 + 2078.79i 0.473074 + 0.819389i 0.999525 0.0308168i \(-0.00981084\pi\)
−0.526451 + 0.850206i \(0.676478\pi\)
\(24\) 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 0.318629 0.947879i \(-0.396778\pi\)
0.980202 + 0.197999i \(0.0634442\pi\)
\(32\) 2128.60 5387.34i 0.367468 0.930036i
\(33\) 0 0
\(34\) 1359.99 + 1153.84i 0.201761 + 0.171178i
\(35\) 2343.04 0.323303
\(36\) 0 0
\(37\) 5243.91 0.629725 0.314862 0.949137i \(-0.398042\pi\)
0.314862 + 0.949137i \(0.398042\pi\)
\(38\) 8151.40 + 6915.81i 0.915743 + 0.776934i
\(39\) 0 0
\(40\) 10839.3 + 177.040i 1.07115 + 0.0174953i
\(41\) 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 0.0921115 0.995749i \(-0.470638\pi\)
−0.816288 + 0.577645i \(0.803972\pi\)
\(44\) 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 −0.519547 0.854442i \(-0.673899\pi\)
0.999742 + 0.0227202i \(0.00723270\pi\)
\(48\) 0 0
\(49\) −7638.14 13229.6i −0.454462 0.787151i
\(50\) 879.429 + 2457.76i 0.0497480 + 0.139032i
\(51\) 0 0
\(52\) −26326.7 + 21606.7i −1.35017 + 1.10810i
\(53\) 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
\(56\) 3440.50 + 6190.44i 0.146606 + 0.263786i
\(57\) 0 0
\(58\) 31890.4 11410.9i 1.24477 0.445401i
\(59\) 909.551 + 1575.39i 0.0340171 + 0.0589193i 0.882533 0.470251i \(-0.155837\pi\)
−0.848516 + 0.529170i \(0.822503\pi\)
\(60\) 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 −0.910828 0.412786i \(-0.864556\pi\)
−0.0979310 + 0.995193i \(0.531222\pi\)
\(68\) −9954.28 + 1643.67i −0.261058 + 0.0431064i
\(69\) 0 0
\(70\) −8574.81 + 10106.8i −0.209160 + 0.246530i
\(71\) −29409.1 −0.692365 −0.346183 0.938167i \(-0.612522\pi\)
−0.346183 + 0.938167i \(0.612522\pi\)
\(72\) 0 0
\(73\) 38022.9 0.835099 0.417550 0.908654i \(-0.362889\pi\)
0.417550 + 0.908654i \(0.362889\pi\)
\(74\) −19191.1 + 22619.8i −0.407399 + 0.480186i
\(75\) 0 0
\(76\) −59663.3 + 9851.70i −1.18488 + 0.195649i
\(77\) −7355.06 + 4246.45i −0.141371 + 0.0816205i
\(78\) 0 0
\(79\) 12858.2 + 7423.70i 0.231800 + 0.133830i 0.611402 0.791320i \(-0.290606\pi\)
−0.379602 + 0.925150i \(0.623939\pi\)
\(80\) −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 \(0.574841\pi\)
−0.725719 + 0.687991i \(0.758493\pi\)
\(84\) 0 0
\(85\) −9440.69 16351.7i −0.141728 0.245480i
\(86\) 54000.6 19322.4i 0.787323 0.281718i
\(87\) 0 0
\(88\) −34346.5 + 19089.0i −0.472798 + 0.262770i
\(89\) 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
\(92\) 59375.5 48730.2i 0.731371 0.600245i
\(93\) 0 0
\(94\) 27718.3 + 77465.1i 0.323555 + 0.904245i
\(95\) −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 −0.547599 0.836741i \(-0.684458\pi\)
0.450839 + 0.892605i \(0.351125\pi\)
\(104\) 3146.35 192635.i 0.0285248 1.74644i
\(105\) 0 0
\(106\) 84680.5 + 71844.5i 0.732013 + 0.621054i
\(107\) 89559.8 0.756229 0.378115 0.925759i \(-0.376572\pi\)
0.378115 + 0.925759i \(0.376572\pi\)
\(108\) 0 0
\(109\) −29876.1 −0.240856 −0.120428 0.992722i \(-0.538427\pi\)
−0.120428 + 0.992722i \(0.538427\pi\)
\(110\) −56075.7 47575.7i −0.441869 0.374890i
\(111\) 0 0
\(112\) −39293.9 7814.37i −0.295992 0.0588639i
\(113\) 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
\(122\) 93084.6 + 260146.i 0.566211 + 1.58240i
\(123\) 0 0
\(124\) −162909. 198497.i −0.951462 1.15931i
\(125\) 159512.i 0.913100i
\(126\) 0 0
\(127\) 265961.i 1.46322i −0.681724 0.731610i \(-0.738769\pi\)
0.681724 0.731610i \(-0.261231\pi\)
\(128\) −181189. 39119.4i −0.977477 0.211041i
\(129\) 0 0
\(130\) 339481. 121472.i 1.76180 0.630403i
\(131\) 37162.9 + 64368.0i 0.189204 + 0.327712i 0.944985 0.327113i \(-0.106076\pi\)
−0.755781 + 0.654825i \(0.772742\pi\)
\(132\) 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 −0.973392 0.229145i \(-0.926407\pi\)
−0.288251 + 0.957555i \(0.593074\pi\)
\(140\) −12215.0 73975.6i −0.0526712 0.318984i
\(141\) 0 0
\(142\) 107628. 126857.i 0.447924 0.527952i
\(143\) 231035. 0.944794
\(144\) 0 0
\(145\) −358574. −1.41631
\(146\) −139152. + 164013.i −0.540266 + 0.636791i
\(147\) 0 0
\(148\) −27338.1 165563.i −0.102592 0.621312i
\(149\) −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 0.928882 0.370377i \(-0.120771\pi\)
0.143685 + 0.989623i \(0.454105\pi\)
\(152\) 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 \(0.757832\pi\)
\(158\) −79079.6 + 28296.0i −0.252012 + 0.0901743i
\(159\) 0 0
\(160\) −50918.7 343145.i −0.157245 1.05969i
\(161\) 93913.2i 0.285537i
\(162\) 0 0
\(163\) 240037.i 0.707635i −0.935314 0.353818i \(-0.884883\pi\)
0.935314 0.353818i \(-0.115117\pi\)
\(164\) −177920. 216788.i −0.516555 0.629397i
\(165\) 0 0
\(166\) −229336. 640932.i −0.645956 1.80527i
\(167\) 144730. + 250679.i 0.401575 + 0.695548i 0.993916 0.110139i \(-0.0351296\pi\)
−0.592341 + 0.805687i \(0.701796\pi\)
\(168\) 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
\(176\) 43356.5 218015.i 0.105505 0.530523i
\(177\) 0 0
\(178\) −153116. 129906.i −0.362218 0.307313i
\(179\) −440866. −1.02843 −0.514214 0.857662i \(-0.671916\pi\)
−0.514214 + 0.857662i \(0.671916\pi\)
\(180\) 0 0
\(181\) 103852. 0.235623 0.117812 0.993036i \(-0.462412\pi\)
0.117812 + 0.993036i \(0.462412\pi\)
\(182\) 179618. + 152392.i 0.401950 + 0.341022i
\(183\) 0 0
\(184\) −7096.05 + 434456.i −0.0154516 + 0.946023i
\(185\) 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 −0.996648 0.0818131i \(-0.973929\pi\)
0.569176 + 0.822216i \(0.307262\pi\)
\(192\) 0 0
\(193\) 20745.9 + 35932.9i 0.0400903 + 0.0694384i 0.885374 0.464879i \(-0.153902\pi\)
−0.845284 + 0.534317i \(0.820569\pi\)
\(194\) 5685.42 + 15889.2i 0.0108457 + 0.0303107i
\(195\) 0 0
\(196\) −377873. + 310125.i −0.702596 + 0.576630i
\(197\) 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 \(0.0479336\pi\)
−0.988683 + 0.150019i \(0.952066\pi\)
\(200\) 73012.8 40578.8i 0.129070 0.0717338i
\(201\) 0 0
\(202\) 280059. 100210.i 0.482916 0.172796i
\(203\) −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 −0.546341 0.837563i \(-0.683980\pi\)
0.452181 + 0.891926i \(0.350646\pi\)
\(212\) −619809. + 102344.i −0.947149 + 0.156395i
\(213\) 0 0
\(214\) −327761. + 386320.i −0.489241 + 0.576651i
\(215\) −607180. −0.895821
\(216\) 0 0
\(217\) 313960. 0.452611
\(218\) 109337. 128872.i 0.155822 0.183661i
\(219\) 0 0
\(220\) 410440. 67772.5i 0.571732 0.0944054i
\(221\) −290603. + 167780.i −0.400239 + 0.231078i
\(222\) 0 0
\(223\) 439612. + 253810.i 0.591980 + 0.341780i 0.765880 0.642983i \(-0.222304\pi\)
−0.173900 + 0.984763i \(0.555637\pi\)
\(224\) 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 −0.899153 0.437634i \(-0.855816\pi\)
0.828579 + 0.559872i \(0.189150\pi\)
\(228\) 0 0
\(229\) 180234. + 312174.i 0.227116 + 0.393376i 0.956952 0.290246i \(-0.0937370\pi\)
−0.729836 + 0.683622i \(0.760404\pi\)
\(230\) −765642. + 273960.i −0.954346 + 0.341482i
\(231\) 0 0
\(232\) −526526. 947371.i −0.642244 1.15558i
\(233\) 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
\(236\) 44997.1 36929.7i 0.0525902 0.0431615i
\(237\) 0 0
\(238\) 23508.5 + 65699.6i 0.0269018 + 0.0751831i
\(239\) −163017. 282354.i −0.184603 0.319742i 0.758840 0.651278i \(-0.225767\pi\)
−0.943443 + 0.331536i \(0.892433\pi\)
\(240\) 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
\(248\) 1.45242e6 + 23722.7i 1.49956 + 0.0244926i
\(249\) 0 0
\(250\) −688062. 583765.i −0.696269 0.590728i
\(251\) 971568. 0.973394 0.486697 0.873571i \(-0.338202\pi\)
0.486697 + 0.873571i \(0.338202\pi\)
\(252\) 0 0
\(253\) −521060. −0.511783
\(254\) 1.14724e6 + 973337.i 1.11575 + 0.946627i
\(255\) 0 0
\(256\) 831839. 638401.i 0.793303 0.608826i
\(257\) −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 −0.953134 0.302549i \(-0.902163\pi\)
0.738582 + 0.674164i \(0.235496\pi\)
\(264\) 0 0
\(265\) −587830. 1.01815e6i −0.514206 0.890631i
\(266\) 140903. + 393786.i 0.122100 + 0.341237i
\(267\) 0 0
\(268\) 868887. + 1.05870e6i 0.738969 + 0.900399i
\(269\) 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 \(0.117626\pi\)
−0.932496 + 0.361181i \(0.882374\pi\)
\(272\) 103789. + 305712.i 0.0850610 + 0.250548i
\(273\) 0 0
\(274\) 123647. 44243.0i 0.0994963 0.0356015i
\(275\) 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 −0.241398 0.970426i \(-0.577606\pi\)
0.719715 + 0.694270i \(0.244273\pi\)
\(284\) 153318. + 928517.i 0.112797 + 0.683115i
\(285\) 0 0
\(286\) −845516. + 996578.i −0.611233 + 0.720437i
\(287\) 342889. 0.245725
\(288\) 0 0
\(289\) 1.32045e6 0.929990
\(290\) 1.31227e6 1.54672e6i 0.916280 1.07998i
\(291\) 0 0
\(292\) −198225. 1.20048e6i −0.136051 0.823942i
\(293\) 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
\(302\) −1.84820e6 + 661319.i −1.16609 + 0.417248i
\(303\) 0 0
\(304\) 622085. + 1.83236e6i 0.386070 + 1.13717i
\(305\) 2.92506e6i 1.80047i
\(306\) 0 0
\(307\) 3.21986e6i 1.94980i −0.222640 0.974901i \(-0.571467\pi\)
0.222640 0.974901i \(-0.428533\pi\)
\(308\) 172415. + 210080.i 0.103562 + 0.126185i
\(309\) 0 0
\(310\) 915871. + 2.55960e6i 0.541290 + 1.51276i
\(311\) 775835. + 1.34378e6i 0.454850 + 0.787823i 0.998680 0.0513724i \(-0.0163596\pi\)
−0.543830 + 0.839196i \(0.683026\pi\)
\(312\) 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
\(320\) 1.66652e6 + 1.03617e6i 0.909777 + 0.565658i
\(321\) 0 0
\(322\) −405099. 343693.i −0.217731 0.184727i
\(323\) −595799. −0.317756
\(324\) 0 0
\(325\) −491127. −0.257920
\(326\) 1.03541e6 + 878462.i 0.539596 + 0.457803i
\(327\) 0 0
\(328\) 1.58626e6 + 25908.6i 0.814121 + 0.0132972i
\(329\) 492799. 284518.i 0.251004 0.144917i
\(330\) 0 0
\(331\) −128289. 74067.9i −0.0643607 0.0371587i 0.467474 0.884007i \(-0.345164\pi\)
−0.531835 + 0.846848i \(0.678497\pi\)
\(332\) 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 \(0.804019\pi\)
\(338\) −1.45120e6 4.05569e6i −0.690930 1.93096i
\(339\) 0 0
\(340\) −467048. + 383312.i −0.219111 + 0.179827i
\(341\) 1.74195e6i 0.811239i
\(342\) 0 0
\(343\) 1.25524e6i 0.576091i
\(344\) −891577. 1.60420e6i −0.406221 0.730908i
\(345\) 0 0
\(346\) −3.01853e6 + 1.08008e6i −1.35552 + 0.485028i
\(347\) −602848. 1.04416e6i −0.268772 0.465527i 0.699773 0.714365i \(-0.253284\pi\)
−0.968545 + 0.248839i \(0.919951\pi\)
\(348\) 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
\(356\) 1.12071e6 185054.i 0.468673 0.0773880i
\(357\) 0 0
\(358\) 1.61343e6 1.90169e6i 0.665340 0.784211i
\(359\) −1.70884e6 −0.699786 −0.349893 0.936790i \(-0.613782\pi\)
−0.349893 + 0.936790i \(0.613782\pi\)
\(360\) 0 0
\(361\) −1.09496e6 −0.442211
\(362\) −380066. + 447970.i −0.152436 + 0.179671i
\(363\) 0 0
\(364\) −1.31470e6 + 217085.i −0.520082 + 0.0858768i
\(365\) 1.97201e6 1.13854e6i 0.774776 0.447317i
\(366\) 0 0
\(367\) 3.26612e6 + 1.88569e6i 1.26581 + 0.730813i 0.974191 0.225723i \(-0.0724745\pi\)
0.291614 + 0.956536i \(0.405808\pi\)
\(368\) −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 \(0.694568\pi\)
\(374\) −364522. + 130432.i −0.134755 + 0.0482176i
\(375\) 0 0
\(376\) 2.30126e6 1.27899e6i 0.839453 0.466548i
\(377\) 6.37257e6i 2.30920i
\(378\) 0 0
\(379\) 4.07165e6i 1.45604i 0.685557 + 0.728019i \(0.259559\pi\)
−0.685557 + 0.728019i \(0.740441\pi\)
\(380\) −2.79936e6 + 2.29747e6i −0.994489 + 0.816190i
\(381\) 0 0
\(382\) −821478. 2.29580e6i −0.288030 0.804964i
\(383\) 1.22056e6 + 2.11407e6i 0.425170 + 0.736415i 0.996436 0.0843491i \(-0.0268811\pi\)
−0.571267 + 0.820765i \(0.693548\pi\)
\(384\) 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
\(392\) 45160.2 2.76493e6i 0.0148436 0.908803i
\(393\) 0 0
\(394\) −1.52531e6 1.29410e6i −0.495014 0.419980i
\(395\) 889166. 0.286741
\(396\) 0 0
\(397\) −2.64187e6 −0.841271 −0.420635 0.907230i \(-0.638193\pi\)
−0.420635 + 0.907230i \(0.638193\pi\)
\(398\) −723009. 613415.i −0.228789 0.194109i
\(399\) 0 0
\(400\) −92166.1 + 463450.i −0.0288019 + 0.144828i
\(401\) −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 \(0.880826\pi\)
\(410\) 1.00026e6 + 2.79546e6i 0.293870 + 0.821284i
\(411\) 0 0
\(412\) 244218. + 297568.i 0.0708818 + 0.0863661i
\(413\) 71171.2i 0.0205319i
\(414\) 0 0
\(415\) 7.20660e6i 2.05404i
\(416\) −6.09838e6 + 904928.i −1.72775 + 0.256378i
\(417\) 0 0
\(418\) −2.18485e6 + 781775.i −0.611618 + 0.218847i
\(419\) −2.85052e6 4.93724e6i −0.793210 1.37388i −0.923969 0.382466i \(-0.875075\pi\)
0.130759 0.991414i \(1.54174\pi\)
\(420\) 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
\(428\) −466902. 2.82762e6i −0.123202 0.746126i
\(429\) 0 0
\(430\) 2.22209e6 2.61910e6i 0.579550 0.683094i
\(431\) −516224. −0.133858 −0.0669291 0.997758i \(-0.521320\pi\)
−0.0669291 + 0.997758i \(0.521320\pi\)
\(432\) 0 0
\(433\) 6.50137e6 1.66642 0.833212 0.552954i \(-0.186499\pi\)
0.833212 + 0.552954i \(0.186499\pi\)
\(434\) −1.14900e6 + 1.35428e6i −0.292816 + 0.345131i
\(435\) 0 0
\(436\) 155753. + 943264.i 0.0392393 + 0.237639i
\(437\) 3.92833e6 2.26802e6i 0.984021 0.568125i
\(438\) 0 0
\(439\) −762498. 440228.i −0.188833 0.109023i 0.402603 0.915375i \(-0.368105\pi\)
−0.591436 + 0.806352i \(0.701439\pi\)
\(440\) −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 −0.817396 0.576076i \(-0.804583\pi\)
0.907595 + 0.419848i \(0.137917\pi\)
\(444\) 0 0
\(445\) 1.06289e6 + 1.84098e6i 0.254442 + 0.440706i
\(446\) −2.70366e6 + 967418.i −0.643599 + 0.230291i
\(447\) 0 0
\(448\) −41868.0 + 1.28134e6i −0.00985570 + 0.301627i
\(449\) 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
\(452\) −5.02558e6 6.12343e6i −1.15702 1.40977i
\(453\) 0 0
\(454\) −208840. 583651.i −0.0475527 0.132896i
\(455\) −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 0.0183222 0.999832i \(-0.494168\pi\)
0.875041 + 0.484049i \(0.160834\pi\)
\(464\) 6.01345e6 + 1.19589e6i 1.29667 + 0.257868i
\(465\) 0 0
\(466\) 4.04919e6 + 3.43541e6i 0.863781 + 0.732848i
\(467\) 7.37952e6 1.56580 0.782900 0.622148i \(-0.213740\pi\)
0.782900 + 0.622148i \(0.213740\pi\)
\(468\) 0 0
\(469\) −1.67452e6 −0.351528
\(470\) 3.75715e6 + 3.18764e6i 0.784538 + 0.665617i
\(471\) 0 0
\(472\) −5377.68 + 329249.i −0.00111107 + 0.0680251i
\(473\) 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 −0.805601 0.592458i \(-0.798158\pi\)
0.915884 + 0.401442i \(0.131491\pi\)
\(480\) 0 0
\(481\) −2.79058e6 4.83342e6i −0.549960 0.952559i
\(482\) 144472. + 403758.i 0.0283247 + 0.0791596i
\(483\) 0 0
\(484\) 2.81816e6 2.31290e6i 0.546829 0.448790i
\(485\) 178657.i 0.0344878i
\(486\) 0 0
\(487\) 763869.i 0.145948i 0.997334 + 0.0729738i \(0.0232489\pi\)
−0.997334 + 0.0729738i \(0.976751\pi\)
\(488\) 7.72817e6 4.29513e6i 1.46902 0.816445i
\(489\) 0 0
\(490\) 4.87264e6 1.74351e6i 0.916799 0.328046i
\(491\) 3.47276e6 + 6.01500e6i 0.650087 + 1.12598i 0.983101 + 0.183061i \(0.0586007\pi\)
−0.333015 + 0.942922i \(0.608066\pi\)
\(492\) 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 0.0647647 0.997901i \(-0.479370\pi\)
0.896590 + 0.442862i \(0.146037\pi\)
\(500\) 5.03619e6 831584.i 0.900901 0.148758i
\(501\) 0 0
\(502\) −3.55564e6 + 4.19090e6i −0.629736 + 0.742246i
\(503\) −3.43627e6 −0.605574 −0.302787 0.953058i \(-0.597917\pi\)
−0.302787 + 0.953058i \(0.597917\pi\)
\(504\) 0 0
\(505\) −3.14897e6 −0.549465
\(506\) 1.90692e6 2.24761e6i 0.331097 0.390252i
\(507\) 0 0
\(508\) −8.39706e6 + 1.38654e6i −1.44367 + 0.238381i
\(509\) −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
\(518\) −1.09274e6 + 391001.i −0.178934 + 0.0640256i
\(519\) 0 0
\(520\) −5.60499e6 1.00850e7i −0.909006 1.63556i
\(521\) 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 \(-0.687817\pi\)
0.556398 0.830916i \(-0.312183\pi\)
\(524\) 1.83852e6 1.50889e6i 0.292509 0.240066i
\(525\) 0 0
\(526\) −917335. 2.56370e6i −0.144565 0.404019i
\(527\) −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
\(536\) −7.74660e6 126527.i −1.16466 0.0190226i
\(537\) 0 0
\(538\) 4.83762e6 + 4.10433e6i 0.720570 + 0.611346i
\(539\) 3.31609e6 0.491648
\(540\) 0 0
\(541\) 330411. 0.0485357 0.0242679 0.999705i \(-0.492275\pi\)
0.0242679 + 0.999705i \(0.492275\pi\)
\(542\) −3.76715e6 3.19612e6i −0.550826 0.467331i
\(543\) 0 0
\(544\) −1.69854e6 671113.i −0.246081 0.0972296i
\(545\) −1.54949e6 + 894596.i −0.223458 + 0.129014i
\(546\) 0 0
\(547\) −1.06834e7 6.16808e6i −1.52666 0.881417i −0.999499 0.0316507i \(-0.989924\pi\)
−0.527160 0.849766i \(1.32326\pi\)
\(548\) −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
\(554\) 3.43117e6 + 9.58916e6i 0.474971 + 1.32741i
\(555\) 0 0
\(556\) 6.73693e6 + 8.20863e6i 0.924220 + 1.12612i
\(557\) 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
\(560\) −2.27191e6 + 771315.i −0.306141 + 0.103935i
\(561\) 0 0
\(562\) −1.45421e6 + 520343.i −0.194217 + 0.0694942i
\(563\) −66573.9 115309.i −0.00885182 0.0153318i 0.861566 0.507646i \(-0.169484\pi\)
−0.870417 + 0.492315i \(0.836151\pi\)
\(564\) 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 −0.533338 0.845902i \(-0.679062\pi\)
0.465904 + 0.884835i \(0.345729\pi\)
\(572\) −1.20445e6 7.29434e6i −0.153922 0.932171i
\(573\) 0 0
\(574\) −1.25487e6 + 1.47907e6i −0.158971 + 0.187374i
\(575\) 1.10765e6 0.139712
\(576\) 0 0
\(577\) −496600. −0.0620965 −0.0310483 0.999518i \(-0.509885\pi\)
−0.0310483 + 0.999518i \(0.509885\pi\)
\(578\) −4.83245e6 + 5.69583e6i −0.601656 + 0.709149i
\(579\) 0 0
\(580\) 1.86935e6 + 1.13211e7i 0.230739 + 1.39739i
\(581\) −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 \(-0.488578\pi\)
0.847531 0.530746i \(-0.178088\pi\)
\(588\) 0 0
\(589\) −7.58219e6 1.31327e7i −0.900547 1.55979i
\(590\) −580234. + 207618.i −0.0686236 + 0.0245547i
\(591\) 0 0
\(592\) −5.08472e6 + 1.72626e6i −0.596297 + 0.202443i
\(593\) 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
\(596\) 6.74652e6 + 8.22032e6i 0.777973 + 0.947923i
\(597\) 0 0
\(598\) 4.86881e6 + 1.36070e7i 0.556763 + 1.55600i
\(599\) 5.29325e6 + 9.16817e6i 0.602775 + 1.04404i 0.992399 + 0.123062i \(0.0392715\pi\)
−0.389624 + 0.920974i \(0.627395\pi\)
\(600\) 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 −0.816456 0.577408i \(-0.804064\pi\)
0.0918216 + 0.995775i \(0.470731\pi\)
\(608\) −1.01806e7 4.02247e6i −1.11690 0.441300i
\(609\) 0 0
\(610\) 1.26174e7 + 1.07048e7i 1.37292 + 1.16481i
\(611\) −1.54796e7 −1.67748
\(612\) 0 0
\(613\) 1.15773e7 1.24438 0.622192 0.782865i \(-0.286242\pi\)
0.622192 + 0.782865i \(0.286242\pi\)
\(614\) 1.38890e7 + 1.17837e7i 1.48679 + 1.26142i
\(615\) 0 0
\(616\) −1.53717e6 25106.9i −0.163219 0.00266589i
\(617\) 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 0.478882 0.877879i \(-0.341042\pi\)
−0.520825 + 0.853664i \(0.674376\pi\)
\(620\) −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
\(626\) 1.00624e6 + 2.81216e6i 0.102628 + 0.286816i
\(627\) 0 0
\(628\) 3.59032e6 2.94662e6i 0.363273 0.298143i
\(629\) 1.65332e6i 0.166621i
\(630\) 0 0
\(631\) 1.33405e7i 1.33383i 0.745136 + 0.666913i \(0.232385\pi\)
−0.745136 + 0.666913i \(0.767615\pi\)
\(632\) 1.30564e6 + 2.34922e6i 0.130026 + 0.233955i
\(633\) 0 0
\(634\) 4.70322e6 1.68289e6i 0.464700 0.166278i
\(635\) −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 −0.993942 0.109910i \(-0.964944\pi\)
−0.401786 + 0.915734i \(0.631610\pi\)
\(644\) 2.96507e6 489598.i 0.281722 0.0465184i
\(645\) 0 0
\(646\) 2.18044e6 2.57000e6i 0.205571 0.242299i
\(647\) −7.65712e6 −0.719126 −0.359563 0.933121i \(-0.617074\pi\)
−0.359563 + 0.933121i \(0.617074\pi\)
\(648\) 0 0
\(649\) −394880. −0.0368005
\(650\) 1.79737e6 2.11850e6i 0.166861 0.196673i
\(651\) 0 0
\(652\) −7.57857e6 + 1.25139e6i −0.698181 + 0.115285i
\(653\) −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 \(-0.591965\pi\)
0.972588 0.232535i \(-0.0747021\pi\)
\(660\) 0 0
\(661\) 3.77496e6 + 6.53842e6i 0.336054 + 0.582062i 0.983687 0.179890i \(-0.0575743\pi\)
−0.647633 + 0.761952i \(0.724241\pi\)
\(662\) 788995. 282316.i 0.0699728 0.0250375i
\(663\) 0 0
\(664\) −1.90402e7 + 1.05821e7i −1.67591 + 0.931432i
\(665\) 4.42770e6i 0.388261i
\(666\) 0 0
\(667\) 1.43723e7i 1.25087i
\(668\) 7.16005e6 5.87634e6i 0.620833 0.509526i
\(669\) 0 0
\(670\) −4.88485e6 1.36518e7i −0.420402 1.17491i
\(671\) 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
\(680\) 55817.6 3.41744e6i 0.00462913 0.283419i
\(681\) 0 0
\(682\) −7.51396e6 6.37499e6i −0.618597 0.524830i
\(683\) 6.62953e6 0.543789 0.271895 0.962327i \(-0.412350\pi\)
0.271895 + 0.962327i \(0.412350\pi\)
\(684\) 0 0
\(685\) −1.39028e6 −0.113208
\(686\) 5.41453e6 + 4.59379e6i 0.439289 + 0.372701i
\(687\) 0 0
\(688\) 1.01827e7 + 2.02503e6i 0.820146 + 0.163102i
\(689\) −1.80946e7 + 1.04469e7i −1.45211 + 0.838378i
\(690\) 0 0
\(691\) 6.59285e6 + 3.80638e6i 0.525264 + 0.303261i 0.739086 0.673611i \(-0.235258\pi\)
−0.213822 + 0.976873i \(0.568591\pi\)
\(692\) 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
\(698\) −555559. 1.55263e6i −0.0431610 0.120623i
\(699\) 0 0
\(700\) −366515. 446582.i −0.0282714 0.0344473i
\(701\) 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
\(704\) −7.10929e6 232297.i −0.540623 0.0176649i
\(705\) 0 0
\(706\) −1.00106e6 + 358195.i −0.0755869 + 0.0270463i
\(707\) −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
\(716\) 2.29837e6 + 1.39192e7i 0.167547 + 1.01469i
\(717\) 0 0
\(718\) 6.25383e6 7.37116e6i 0.452725 0.533611i
\(719\) −1.05572e7 −0.761603 −0.380801 0.924657i \(-0.624352\pi\)
−0.380801 + 0.924657i \(0.624352\pi\)
\(720\) 0 0
\(721\) −470659. −0.0337185
\(722\) 4.00721e6 4.72314e6i 0.286087 0.337200i
\(723\) 0 0
\(724\) −541412. 3.27887e6i −0.0383868 0.232475i
\(725\) −2.39278e6 + 1.38147e6i −0.169066 + 0.0976104i
\(726\) 0 0
\(727\) −457178. 263952.i −0.0320811 0.0185220i 0.483874 0.875138i \(-0.339229\pi\)
−0.515955 + 0.856616i \(0.672563\pi\)
\(728\) 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 \(-0.413173\pi\)
\(734\) −2.00870e7 + 7.18748e6i −1.37618 + 0.492421i
\(735\) 0 0
\(736\) 1.37539e7 2.04091e6i 0.935901 0.138877i
\(737\) 9.29078e6i 0.630062i
\(738\) 0 0
\(739\) 4.56621e6i 0.307570i 0.988104 + 0.153785i \(0.0491464\pi\)
−0.988104 + 0.153785i \(0.950854\pi\)
\(740\) −6.37539e6 7.76811e6i −0.427984 0.521478i
\(741\) 0 0
\(742\) 1.46377e6 + 4.09082e6i 0.0976028 + 0.272773i
\(743\) 8.52924e6 + 1.47731e7i 0.566811 + 0.981745i 0.996879 + 0.0789485i \(0.0251563\pi\)
−0.430068 + 0.902797i \(0.641510\pi\)
\(744\) 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 −0.636397 0.771362i \(-0.719576\pi\)
0.349821 + 0.936817i \(0.386243\pi\)
\(752\) −2.90495e6 + 1.46073e7i −0.187324 + 0.941943i
\(753\) 0 0
\(754\) −2.74884e7 2.33217e7i −1.76084 1.49393i
\(755\) 2.07811e7 1.32679
\(756\) 0 0
\(757\) 6.36558e6 0.403736 0.201868 0.979413i \(-0.435299\pi\)
0.201868 + 0.979413i \(0.435299\pi\)
\(758\) −1.75633e7 1.49010e7i −1.11028 0.941981i
\(759\) 0 0
\(760\) 334556. 2.04832e7i 0.0210104 1.28636i
\(761\) 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 \(0.679978\pi\)
\(770\) −969312. 2.70896e6i −0.0589165 0.164655i
\(771\) 0 0
\(772\) 1.02634e6 842329.i 0.0619794 0.0508673i
\(773\) 2.52966e7i 1.52270i 0.648342 + 0.761349i \(0.275463\pi\)
−0.648342 + 0.761349i \(0.724537\pi\)
\(774\) 0 0
\(775\) 3.70298e6i 0.221461i
\(776\)