Properties

Label 108.6.h.a.71.19
Level 108
Weight 6
Character 108.71
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 71.19
Character \(\chi\) \(=\) 108.71
Dual form 108.6.h.a.35.19

$q$-expansion

\(f(q)\) \(=\) \(q+(2.01287 - 5.28662i) q^{2} +(-23.8967 - 21.2825i) q^{4} +(78.5398 + 45.3450i) q^{5} +(-69.6792 + 40.2293i) q^{7} +(-160.614 + 83.4942i) q^{8} +O(q^{10})\) \(q+(2.01287 - 5.28662i) q^{2} +(-23.8967 - 21.2825i) q^{4} +(78.5398 + 45.3450i) q^{5} +(-69.6792 + 40.2293i) q^{7} +(-160.614 + 83.4942i) q^{8} +(397.812 - 323.937i) q^{10} +(275.903 + 477.878i) q^{11} +(-307.186 + 532.062i) q^{13} +(72.4223 + 449.344i) q^{14} +(118.109 + 1017.17i) q^{16} +482.387i q^{17} +453.989i q^{19} +(-911.790 - 2755.12i) q^{20} +(3081.72 - 496.691i) q^{22} +(310.876 - 538.452i) q^{23} +(2549.83 + 4416.44i) q^{25} +(2194.49 + 2694.95i) q^{26} +(2521.29 + 521.599i) q^{28} +(7777.18 - 4490.16i) q^{29} +(-650.730 - 375.699i) q^{31} +(5615.11 + 1423.02i) q^{32} +(2550.20 + 970.980i) q^{34} -7296.79 q^{35} -4221.49 q^{37} +(2400.07 + 913.819i) q^{38} +(-16400.6 - 725.399i) q^{40} +(-11012.8 - 6358.24i) q^{41} +(13956.9 - 8058.04i) q^{43} +(3577.26 - 17291.6i) q^{44} +(-2220.84 - 2727.31i) q^{46} +(9570.02 + 16575.8i) q^{47} +(-5166.71 + 8949.00i) q^{49} +(28480.5 - 4590.30i) q^{50} +(18664.4 - 6176.86i) q^{52} +8422.39i q^{53} +50043.2i q^{55} +(7832.51 - 12279.2i) q^{56} +(-8083.35 - 50153.1i) q^{58} +(-2693.87 + 4665.91i) q^{59} +(-5910.89 - 10238.0i) q^{61} +(-3296.01 + 2683.93i) q^{62} +(18825.4 - 26820.6i) q^{64} +(-48252.7 + 27858.7i) q^{65} +(27131.6 + 15664.5i) q^{67} +(10266.4 - 11527.5i) q^{68} +(-14687.4 + 38575.3i) q^{70} -68895.9 q^{71} -23822.3 q^{73} +(-8497.30 + 22317.4i) q^{74} +(9662.03 - 10848.9i) q^{76} +(-38449.4 - 22198.8i) q^{77} +(-19337.5 + 11164.5i) q^{79} +(-36847.1 + 85243.6i) q^{80} +(-55780.9 + 45422.2i) q^{82} +(39320.2 + 68104.6i) q^{83} +(-21873.8 + 37886.6i) q^{85} +(-14506.4 - 90004.8i) q^{86} +(-84213.8 - 53717.4i) q^{88} -87925.1i q^{89} -49431.5i q^{91} +(-18888.5 + 6251.04i) q^{92} +(106893. - 17228.3i) q^{94} +(-20586.1 + 35656.2i) q^{95} +(-39159.6 - 67826.3i) q^{97} +(36910.1 + 45327.5i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.01287 5.28662i 0.355828 0.934552i
\(3\) 0 0
\(4\) −23.8967 21.2825i −0.746773 0.665079i
\(5\) 78.5398 + 45.3450i 1.40496 + 0.811155i 0.994897 0.100901i \(-0.0321724\pi\)
0.410066 + 0.912056i \(0.365506\pi\)
\(6\) 0 0
\(7\) −69.6792 + 40.2293i −0.537475 + 0.310311i −0.744055 0.668118i \(-0.767100\pi\)
0.206580 + 0.978430i \(0.433767\pi\)
\(8\) −160.614 + 83.4942i −0.887273 + 0.461245i
\(9\) 0 0
\(10\) 397.812 323.937i 1.25799 1.02438i
\(11\) 275.903 + 477.878i 0.687503 + 1.19079i 0.972643 + 0.232304i \(0.0746265\pi\)
−0.285140 + 0.958486i \(0.592040\pi\)
\(12\) 0 0
\(13\) −307.186 + 532.062i −0.504131 + 0.873180i 0.495858 + 0.868404i \(0.334854\pi\)
−0.999989 + 0.00477646i \(0.998480\pi\)
\(14\) 72.4223 + 449.344i 0.0987534 + 0.612715i
\(15\) 0 0
\(16\) 118.109 + 1017.17i 0.115341 + 0.993326i
\(17\) 482.387i 0.404830i 0.979300 + 0.202415i \(0.0648791\pi\)
−0.979300 + 0.202415i \(0.935121\pi\)
\(18\) 0 0
\(19\) 453.989i 0.288510i 0.989541 + 0.144255i \(0.0460786\pi\)
−0.989541 + 0.144255i \(0.953921\pi\)
\(20\) −911.790 2755.12i −0.509706 1.54016i
\(21\) 0 0
\(22\) 3081.72 496.691i 1.35749 0.218791i
\(23\) 310.876 538.452i 0.122537 0.212240i −0.798231 0.602352i \(-0.794230\pi\)
0.920767 + 0.390112i \(0.127564\pi\)
\(24\) 0 0
\(25\) 2549.83 + 4416.44i 0.815946 + 1.41326i
\(26\) 2194.49 + 2694.95i 0.636648 + 0.781838i
\(27\) 0 0
\(28\) 2521.29 + 521.599i 0.607753 + 0.125731i
\(29\) 7777.18 4490.16i 1.71723 0.991440i 0.793332 0.608789i \(-0.208344\pi\)
0.923893 0.382652i \(-0.124989\pi\)
\(30\) 0 0
\(31\) −650.730 375.699i −0.121618 0.0702159i 0.437957 0.898996i \(-0.355702\pi\)
−0.559575 + 0.828780i \(0.689035\pi\)
\(32\) 5615.11 + 1423.02i 0.969356 + 0.245661i
\(33\) 0 0
\(34\) 2550.20 + 970.980i 0.378335 + 0.144050i
\(35\) −7296.79 −1.00684
\(36\) 0 0
\(37\) −4221.49 −0.506946 −0.253473 0.967342i \(-0.581573\pi\)
−0.253473 + 0.967342i \(0.581573\pi\)
\(38\) 2400.07 + 913.819i 0.269628 + 0.102660i
\(39\) 0 0
\(40\) −16400.6 725.399i −1.62073 0.0716848i
\(41\) −11012.8 6358.24i −1.02315 0.590714i −0.108133 0.994136i \(-0.534487\pi\)
−0.915014 + 0.403422i \(0.867821\pi\)
\(42\) 0 0
\(43\) 13956.9 8058.04i 1.15112 0.664597i 0.201957 0.979394i \(-0.435270\pi\)
0.949159 + 0.314797i \(0.101937\pi\)
\(44\) 3577.26 17291.6i 0.278560 1.34649i
\(45\) 0 0
\(46\) −2220.84 2727.31i −0.154747 0.190038i
\(47\) 9570.02 + 16575.8i 0.631929 + 1.09453i 0.987157 + 0.159753i \(0.0510697\pi\)
−0.355228 + 0.934780i \(0.615597\pi\)
\(48\) 0 0
\(49\) −5166.71 + 8949.00i −0.307414 + 0.532457i
\(50\) 28480.5 4590.30i 1.61110 0.259667i
\(51\) 0 0
\(52\) 18664.4 6176.86i 0.957205 0.316781i
\(53\) 8422.39i 0.411856i 0.978567 + 0.205928i \(0.0660213\pi\)
−0.978567 + 0.205928i \(0.933979\pi\)
\(54\) 0 0
\(55\) 50043.2i 2.23069i
\(56\) 7832.51 12279.2i 0.333757 0.523238i
\(57\) 0 0
\(58\) −8083.35 50153.1i −0.315516 1.95762i
\(59\) −2693.87 + 4665.91i −0.100750 + 0.174505i −0.911994 0.410204i \(-0.865458\pi\)
0.811244 + 0.584708i \(0.198791\pi\)
\(60\) 0 0
\(61\) −5910.89 10238.0i −0.203390 0.352281i 0.746229 0.665689i \(-0.231862\pi\)
−0.949618 + 0.313408i \(0.898529\pi\)
\(62\) −3296.01 + 2683.93i −0.108895 + 0.0886731i
\(63\) 0 0
\(64\) 18825.4 26820.6i 0.574507 0.818500i
\(65\) −48252.7 + 27858.7i −1.41657 + 0.817857i
\(66\) 0 0
\(67\) 27131.6 + 15664.5i 0.738395 + 0.426313i 0.821486 0.570229i \(-0.193146\pi\)
−0.0830902 + 0.996542i \(0.526479\pi\)
\(68\) 10266.4 11527.5i 0.269244 0.302317i
\(69\) 0 0
\(70\) −14687.4 + 38575.3i −0.358262 + 0.940946i
\(71\) −68895.9 −1.62199 −0.810994 0.585054i \(-0.801073\pi\)
−0.810994 + 0.585054i \(0.801073\pi\)
\(72\) 0 0
\(73\) −23822.3 −0.523210 −0.261605 0.965175i \(-0.584252\pi\)
−0.261605 + 0.965175i \(0.584252\pi\)
\(74\) −8497.30 + 22317.4i −0.180385 + 0.473767i
\(75\) 0 0
\(76\) 9662.03 10848.9i 0.191882 0.215452i
\(77\) −38449.4 22198.8i −0.739031 0.426680i
\(78\) 0 0
\(79\) −19337.5 + 11164.5i −0.348604 + 0.201267i −0.664070 0.747670i \(-0.731172\pi\)
0.315466 + 0.948937i \(0.397839\pi\)
\(80\) −36847.1 + 85243.6i −0.643692 + 1.48914i
\(81\) 0 0
\(82\) −55780.9 + 45422.2i −0.916117 + 0.745991i
\(83\) 39320.2 + 68104.6i 0.626499 + 1.08513i 0.988249 + 0.152853i \(0.0488461\pi\)
−0.361750 + 0.932275i \(0.617821\pi\)
\(84\) 0 0
\(85\) −21873.8 + 37886.6i −0.328380 + 0.568772i
\(86\) −14506.4 90004.8i −0.211501 1.31226i
\(87\) 0 0
\(88\) −84213.8 53717.4i −1.15925 0.739449i
\(89\) 87925.1i 1.17662i −0.808634 0.588312i \(-0.799793\pi\)
0.808634 0.588312i \(-0.200207\pi\)
\(90\) 0 0
\(91\) 49431.5i 0.625750i
\(92\) −18888.5 + 6251.04i −0.232664 + 0.0769986i
\(93\) 0 0
\(94\) 106893. 17228.3i 1.24775 0.201105i
\(95\) −20586.1 + 35656.2i −0.234027 + 0.405346i
\(96\) 0 0
\(97\) −39159.6 67826.3i −0.422580 0.731929i 0.573611 0.819128i \(-0.305542\pi\)
−0.996191 + 0.0871983i \(0.972209\pi\)
\(98\) 36910.1 + 45327.5i 0.388222 + 0.476757i
\(99\) 0 0
\(100\) 33060.2 159805.i 0.330602 1.59805i
\(101\) 22486.3 12982.5i 0.219339 0.126635i −0.386305 0.922371i \(-0.626249\pi\)
0.605644 + 0.795736i \(0.292916\pi\)
\(102\) 0 0
\(103\) −21490.3 12407.4i −0.199595 0.115236i 0.396872 0.917874i \(-0.370096\pi\)
−0.596466 + 0.802638i \(0.703429\pi\)
\(104\) 4914.16 111105.i 0.0445519 1.00728i
\(105\) 0 0
\(106\) 44526.0 + 16953.1i 0.384901 + 0.146550i
\(107\) 105956. 0.894680 0.447340 0.894364i \(-0.352371\pi\)
0.447340 + 0.894364i \(0.352371\pi\)
\(108\) 0 0
\(109\) −24092.4 −0.194229 −0.0971146 0.995273i \(-0.530961\pi\)
−0.0971146 + 0.995273i \(0.530961\pi\)
\(110\) 264560. + 100730.i 2.08469 + 0.793740i
\(111\) 0 0
\(112\) −49149.6 66123.9i −0.370233 0.498096i
\(113\) −7844.35 4528.94i −0.0577911 0.0333657i 0.470826 0.882226i \(-0.343956\pi\)
−0.528617 + 0.848860i \(0.677289\pi\)
\(114\) 0 0
\(115\) 48832.2 28193.3i 0.344320 0.198793i
\(116\) −281411. 58217.8i −1.94176 0.401709i
\(117\) 0 0
\(118\) 19244.5 + 23633.3i 0.127234 + 0.156250i
\(119\) −19406.1 33612.3i −0.125623 0.217586i
\(120\) 0 0
\(121\) −71719.4 + 124222.i −0.445321 + 0.771318i
\(122\) −66022.1 + 10641.0i −0.401596 + 0.0647267i
\(123\) 0 0
\(124\) 7554.50 + 22827.1i 0.0441216 + 0.133321i
\(125\) 179082.i 1.02513i
\(126\) 0 0
\(127\) 195212.i 1.07398i 0.843587 + 0.536992i \(0.180439\pi\)
−0.843587 + 0.536992i \(0.819561\pi\)
\(128\) −103897. 153509.i −0.560505 0.828151i
\(129\) 0 0
\(130\) 50152.2 + 311169.i 0.260275 + 1.61487i
\(131\) 126871. 219747.i 0.645929 1.11878i −0.338157 0.941090i \(-0.609803\pi\)
0.984086 0.177693i \(-0.0568632\pi\)
\(132\) 0 0
\(133\) −18263.7 31633.6i −0.0895280 0.155067i
\(134\) 137424. 111904.i 0.661153 0.538375i
\(135\) 0 0
\(136\) −40276.5 77477.9i −0.186726 0.359195i
\(137\) 108349. 62555.1i 0.493199 0.284748i −0.232702 0.972548i \(-0.574757\pi\)
0.725900 + 0.687800i \(0.241423\pi\)
\(138\) 0 0
\(139\) −155476. 89764.4i −0.682539 0.394064i 0.118272 0.992981i \(-0.462265\pi\)
−0.800811 + 0.598917i \(0.795598\pi\)
\(140\) 174369. + 155294.i 0.751883 + 0.669629i
\(141\) 0 0
\(142\) −138678. + 364227.i −0.577149 + 1.51583i
\(143\) −339014. −1.38637
\(144\) 0 0
\(145\) 814424. 3.21685
\(146\) −47951.1 + 125939.i −0.186173 + 0.488967i
\(147\) 0 0
\(148\) 100880. + 89844.0i 0.378574 + 0.337159i
\(149\) 395679. + 228445.i 1.46008 + 0.842978i 0.999014 0.0443874i \(-0.0141336\pi\)
0.461067 + 0.887366i \(0.347467\pi\)
\(150\) 0 0
\(151\) 189659. 109500.i 0.676909 0.390814i −0.121780 0.992557i \(-0.538860\pi\)
0.798690 + 0.601743i \(0.205527\pi\)
\(152\) −37905.4 72916.8i −0.133074 0.255987i
\(153\) 0 0
\(154\) −194750. + 158584.i −0.661722 + 0.538838i
\(155\) −34072.1 59014.6i −0.113912 0.197301i
\(156\) 0 0
\(157\) 113832. 197163.i 0.368566 0.638375i −0.620776 0.783988i \(-0.713182\pi\)
0.989342 + 0.145614i \(0.0465156\pi\)
\(158\) 20098.8 + 124703.i 0.0640511 + 0.397405i
\(159\) 0 0
\(160\) 376483. + 366381.i 1.16264 + 1.13144i
\(161\) 50025.3i 0.152098i
\(162\) 0 0
\(163\) 460735.i 1.35826i −0.734020 0.679128i \(-0.762358\pi\)
0.734020 0.679128i \(-0.237642\pi\)
\(164\) 127851. + 386321.i 0.371187 + 1.12160i
\(165\) 0 0
\(166\) 439189. 70785.6i 1.23703 0.199377i
\(167\) 286572. 496357.i 0.795137 1.37722i −0.127614 0.991824i \(-0.540732\pi\)
0.922752 0.385395i \(-0.125935\pi\)
\(168\) 0 0
\(169\) −3080.17 5335.01i −0.00829579 0.0143687i
\(170\) 156263. + 191899.i 0.414699 + 0.509273i
\(171\) 0 0
\(172\) −505021. 104478.i −1.30163 0.269279i
\(173\) 283930. 163927.i 0.721268 0.416424i −0.0939514 0.995577i \(-0.529950\pi\)
0.815219 + 0.579153i \(0.196617\pi\)
\(174\) 0 0
\(175\) −355340. 205156.i −0.877101 0.506394i
\(176\) −453495. + 337081.i −1.10355 + 0.820261i
\(177\) 0 0
\(178\) −464827. 176981.i −1.09962 0.418676i
\(179\) 123110. 0.287185 0.143592 0.989637i \(-0.454135\pi\)
0.143592 + 0.989637i \(0.454135\pi\)
\(180\) 0 0
\(181\) −311888. −0.707622 −0.353811 0.935317i \(-0.615114\pi\)
−0.353811 + 0.935317i \(0.615114\pi\)
\(182\) −261326. 99499.0i −0.584795 0.222659i
\(183\) 0 0
\(184\) −4973.19 + 112439.i −0.0108290 + 0.244835i
\(185\) −331555. 191423.i −0.712240 0.411212i
\(186\) 0 0
\(187\) −230522. + 133092.i −0.482068 + 0.278322i
\(188\) 124082. 599781.i 0.256043 1.23765i
\(189\) 0 0
\(190\) 147064. + 180602.i 0.295544 + 0.362943i
\(191\) 97915.9 + 169595.i 0.194209 + 0.336380i 0.946641 0.322290i \(-0.104453\pi\)
−0.752432 + 0.658670i \(0.771119\pi\)
\(192\) 0 0
\(193\) −296774. + 514028.i −0.573499 + 0.993330i 0.422704 + 0.906268i \(0.361081\pi\)
−0.996203 + 0.0870619i \(0.972252\pi\)
\(194\) −437395. + 70496.5i −0.834391 + 0.134482i
\(195\) 0 0
\(196\) 313925. 103891.i 0.583694 0.193170i
\(197\) 100175.i 0.183905i 0.995763 + 0.0919523i \(0.0293107\pi\)
−0.995763 + 0.0919523i \(0.970689\pi\)
\(198\) 0 0
\(199\) 402805.i 0.721045i 0.932751 + 0.360522i \(0.117402\pi\)
−0.932751 + 0.360522i \(0.882598\pi\)
\(200\) −778285. 496444.i −1.37583 0.877597i
\(201\) 0 0
\(202\) −23371.6 145009.i −0.0403004 0.250044i
\(203\) −361272. + 625741.i −0.615310 + 1.06575i
\(204\) 0 0
\(205\) −576628. 998750.i −0.958322 1.65986i
\(206\) −108850. + 88636.5i −0.178715 + 0.145527i
\(207\) 0 0
\(208\) −577477. 249618.i −0.925499 0.400053i
\(209\) −216951. + 125257.i −0.343555 + 0.198352i
\(210\) 0 0
\(211\) −538419. 310856.i −0.832557 0.480677i 0.0221701 0.999754i \(-0.492942\pi\)
−0.854728 + 0.519077i \(0.826276\pi\)
\(212\) 179250. 201268.i 0.273917 0.307563i
\(213\) 0 0
\(214\) 213276. 560152.i 0.318352 0.836125i
\(215\) 1.46157e6 2.15637
\(216\) 0 0
\(217\) 60456.4 0.0871552
\(218\) −48494.9 + 127368.i −0.0691122 + 0.181517i
\(219\) 0 0
\(220\) 1.06505e6 1.19587e6i 1.48358 1.66582i
\(221\) −256660. 148183.i −0.353490 0.204088i
\(222\) 0 0
\(223\) 1.11763e6 645261.i 1.50499 0.868907i 0.505008 0.863115i \(-0.331490\pi\)
0.999983 0.00579252i \(-0.00184383\pi\)
\(224\) −448503. + 126737.i −0.597236 + 0.168765i
\(225\) 0 0
\(226\) −39732.4 + 32354.0i −0.0517456 + 0.0421363i
\(227\) −435023. 753483.i −0.560335 0.970529i −0.997467 0.0711316i \(-0.977339\pi\)
0.437132 0.899398i \(1.64401\pi\)
\(228\) 0 0
\(229\) 55144.9 95513.7i 0.0694891 0.120359i −0.829187 0.558971i \(-0.811196\pi\)
0.898677 + 0.438612i \(0.144530\pi\)
\(230\) −50754.6 314907.i −0.0632639 0.392521i
\(231\) 0 0
\(232\) −874219. + 1.37053e6i −1.06635 + 1.67174i
\(233\) 352716.i 0.425633i −0.977092 0.212817i \(-0.931736\pi\)
0.977092 0.212817i \(-0.0682637\pi\)
\(234\) 0 0
\(235\) 1.73581e6i 2.05037i
\(236\) 163677. 54167.9i 0.191297 0.0633085i
\(237\) 0 0
\(238\) −216758. + 34935.6i −0.248046 + 0.0399784i
\(239\) −345720. + 598804.i −0.391498 + 0.678094i −0.992647 0.121043i \(-0.961376\pi\)
0.601150 + 0.799137i \(0.294710\pi\)
\(240\) 0 0
\(241\) −37478.3 64914.3i −0.0415659 0.0719942i 0.844494 0.535565i \(-0.179901\pi\)
−0.886060 + 0.463571i \(0.846568\pi\)
\(242\) 512351. + 629195.i 0.562379 + 0.690632i
\(243\) 0 0
\(244\) −76638.6 + 370453.i −0.0824087 + 0.398344i
\(245\) −811584. + 468568.i −0.863810 + 0.498721i
\(246\) 0 0
\(247\) −241550. 139459.i −0.251921 0.145447i
\(248\) 135885. + 6010.18i 0.140295 + 0.00620524i
\(249\) 0 0
\(250\) 946739. + 360468.i 0.958033 + 0.364768i
\(251\) −1.33103e6 −1.33353 −0.666767 0.745266i \(-0.732322\pi\)
−0.666767 + 0.745266i \(0.732322\pi\)
\(252\) 0 0
\(253\) 343086. 0.336978
\(254\) 1.03201e6 + 392936.i 1.00369 + 0.382153i
\(255\) 0 0
\(256\) −1.02068e6 + 240273.i −0.973393 + 0.229142i
\(257\) 185992. + 107383.i 0.175656 + 0.101415i 0.585250 0.810853i \(-0.300996\pi\)
−0.409594 + 0.912268i \(0.634330\pi\)
\(258\) 0 0
\(259\) 294150. 169828.i 0.272471 0.157311i
\(260\) 1.74598e6 + 361206.i 1.60180 + 0.331377i
\(261\) 0 0
\(262\) −906347. 1.11304e6i −0.815720 1.00175i
\(263\) −327806. 567776.i −0.292232 0.506160i 0.682106 0.731254i \(-0.261064\pi\)
−0.974337 + 0.225094i \(0.927731\pi\)
\(264\) 0 0
\(265\) −381913. + 661492.i −0.334079 + 0.578642i
\(266\) −203997. + 32878.9i −0.176775 + 0.0284914i
\(267\) 0 0
\(268\) −314979. 951759.i −0.267882 0.809450i
\(269\) 424539.i 0.357715i −0.983875 0.178857i \(-0.942760\pi\)
0.983875 0.178857i \(-0.0572401\pi\)
\(270\) 0 0
\(271\) 276579.i 0.228769i −0.993437 0.114384i \(-0.963510\pi\)
0.993437 0.114384i \(-0.0364895\pi\)
\(272\) −490667. + 56974.2i −0.402129 + 0.0466934i
\(273\) 0 0
\(274\) −112614. 698713.i −0.0906183 0.562241i
\(275\) −1.40701e6 + 2.43702e6i −1.12193 + 1.94324i
\(276\) 0 0
\(277\) 758444. + 1.31366e6i 0.593915 + 1.02869i 0.993699 + 0.112081i \(0.0357517\pi\)
−0.399784 + 0.916609i \(0.630915\pi\)
\(278\) −787503. + 641262.i −0.611140 + 0.497649i
\(279\) 0 0
\(280\) 1.17196e6 609239.i 0.893344 0.464401i
\(281\) −831581. + 480113.i −0.628259 + 0.362725i −0.780077 0.625683i \(-0.784820\pi\)
0.151819 + 0.988408i \(0.451487\pi\)
\(282\) 0 0
\(283\) 780527. + 450638.i 0.579325 + 0.334473i 0.760865 0.648910i \(-0.224775\pi\)
−0.181540 + 0.983384i \(0.558108\pi\)
\(284\) 1.64639e6 + 1.46628e6i 1.21126 + 1.07875i
\(285\) 0 0
\(286\) −682390. + 1.79224e6i −0.493307 + 1.29563i
\(287\) 1.02315e6 0.733221
\(288\) 0 0
\(289\) 1.18716e6 0.836112
\(290\) 1.63933e6 4.30555e6i 1.14464 3.00631i
\(291\) 0 0
\(292\) 569275. + 506998.i 0.390719 + 0.347976i
\(293\) 1.02663e6 + 592723.i 0.698623 + 0.403350i 0.806835 0.590778i \(-0.201179\pi\)
−0.108211 + 0.994128i \(0.534512\pi\)
\(294\) 0 0
\(295\) −423151. + 244307.i −0.283101 + 0.163448i
\(296\) 678029. 352470.i 0.449800 0.233826i
\(297\) 0 0
\(298\) 2.00415e6 1.63197e6i 1.30734 1.06457i
\(299\) 190993. + 330810.i 0.123549 + 0.213994i
\(300\) 0 0
\(301\) −648339. + 1.12296e6i −0.412464 + 0.714408i
\(302\) −197125. 1.22306e6i −0.124373 0.771669i
\(303\) 0 0
\(304\) −461782. + 53620.1i −0.286585 + 0.0332770i
\(305\) 1.07212e6i 0.659922i
\(306\) 0 0
\(307\) 740939.i 0.448680i 0.974511 + 0.224340i \(0.0720226\pi\)
−0.974511 + 0.224340i \(0.927977\pi\)
\(308\) 446370. + 1.34878e6i 0.268113 + 0.810147i
\(309\) 0 0
\(310\) −380571. + 61337.9i −0.224921 + 0.0362514i
\(311\) 1.37781e6 2.38644e6i 0.807771 1.39910i −0.106633 0.994298i \(-0.534007\pi\)
0.914404 0.404802i \(-0.132660\pi\)
\(312\) 0 0
\(313\) −1.36134e6 2.35791e6i −0.785427 1.36040i −0.928744 0.370722i \(-0.879110\pi\)
0.143317 0.989677i \(-0.454223\pi\)
\(314\) −813196. 998648.i −0.465448 0.571595i
\(315\) 0 0
\(316\) 699713. + 144755.i 0.394187 + 0.0815486i
\(317\) 731344. 422242.i 0.408765 0.236001i −0.281494 0.959563i \(-0.590830\pi\)
0.690259 + 0.723562i \(0.257497\pi\)
\(318\) 0 0
\(319\) 4.29149e6 + 2.47770e6i 2.36119 + 1.36324i
\(320\) 2.69472e6 1.25285e6i 1.47109 0.683947i
\(321\) 0 0
\(322\) 264465. + 100694.i 0.142144 + 0.0541208i
\(323\) −218998. −0.116798
\(324\) 0 0
\(325\) −3.13309e6 −1.64537
\(326\) −2.43573e6 927397.i −1.26936 0.483305i
\(327\) 0 0
\(328\) 2.29968e6 + 101715.i 1.18027 + 0.0522036i
\(329\) −1.33366e6 769990.i −0.679291 0.392189i
\(330\) 0 0
\(331\) −1.52485e6 + 880372.i −0.764992 + 0.441668i −0.831085 0.556145i \(-0.812280\pi\)
0.0660935 + 0.997813i \(0.478946\pi\)
\(332\) 509812. 2.46431e6i 0.253843 1.22702i
\(333\) 0 0
\(334\) −2.04722e6 2.51410e6i −1.00415 1.23315i
\(335\) 1.42061e6 + 2.46057e6i 0.691612 + 1.19791i
\(336\) 0 0
\(337\) −1.23174e6 + 2.13344e6i −0.590806 + 1.02331i 0.403318 + 0.915060i \(0.367857\pi\)
−0.994124 + 0.108246i \(0.965477\pi\)
\(338\) −34404.1 + 5545.03i −0.0163802 + 0.00264005i
\(339\) 0 0
\(340\) 1.32903e6 439836.i 0.623504 0.206345i
\(341\) 414626.i 0.193095i
\(342\) 0 0
\(343\) 2.18368e6i 1.00220i
\(344\) −1.56887e6 + 2.45955e6i −0.714812 + 1.12063i
\(345\) 0 0
\(346\) −295108. 1.83100e6i −0.132523 0.822237i
\(347\) −473354. + 819874.i −0.211039 + 0.365530i −0.952040 0.305974i \(-0.901018\pi\)
0.741001 + 0.671504i \(0.234351\pi\)
\(348\) 0 0
\(349\) 1.96690e6 + 3.40677e6i 0.864408 + 1.49720i 0.867633 + 0.497204i \(0.165640\pi\)
−0.00322519 + 0.999995i \(0.501027\pi\)
\(350\) −1.79983e6 + 1.46560e6i −0.785349 + 0.639507i
\(351\) 0 0
\(352\) 869195. + 3.07595e6i 0.373904 + 1.32319i
\(353\) 3.34675e6 1.93225e6i 1.42951 0.825327i 0.432426 0.901669i \(-0.357658\pi\)
0.997082 + 0.0763423i \(0.0243242\pi\)
\(354\) 0 0
\(355\) −5.41107e6 3.12408e6i −2.27883 1.31568i
\(356\) −1.87127e6 + 2.10112e6i −0.782548 + 0.878672i
\(357\) 0 0
\(358\) 247804. 650837.i 0.102188 0.268389i
\(359\) −1.23588e6 −0.506106 −0.253053 0.967452i \(-0.581435\pi\)
−0.253053 + 0.967452i \(0.581435\pi\)
\(360\) 0 0
\(361\) 2.26999e6 0.916762
\(362\) −627788. + 1.64883e6i −0.251792 + 0.661310i
\(363\) 0 0
\(364\) −1.05203e6 + 1.18125e6i −0.416173 + 0.467293i
\(365\) −1.87100e6 1.08022e6i −0.735091 0.424405i
\(366\) 0 0
\(367\) 435715. 251560.i 0.168864 0.0974937i −0.413186 0.910647i \(-0.635584\pi\)
0.582050 + 0.813153i \(0.302251\pi\)
\(368\) 584413. + 252616.i 0.224957 + 0.0972392i
\(369\) 0 0
\(370\) −1.67936e6 + 1.36750e6i −0.637734 + 0.519305i
\(371\) −338827. 586865.i −0.127804 0.221362i
\(372\) 0 0
\(373\) 2.28143e6 3.95156e6i 0.849055 1.47061i −0.0329973 0.999455i \(-0.510505\pi\)
0.882052 0.471151i \(-0.156161\pi\)
\(374\) 239597. + 1.48658e6i 0.0885732 + 0.549552i
\(375\) 0 0
\(376\) −2.92105e6 1.86325e6i −1.06554 0.679675i
\(377\) 5.51726e6i 1.99926i
\(378\) 0 0
\(379\) 3.52082e6i 1.25906i −0.776977 0.629529i \(-0.783248\pi\)
0.776977 0.629529i \(-0.216752\pi\)
\(380\) 1.25079e6 413943.i 0.444352 0.147055i
\(381\) 0 0
\(382\) 1.09368e6 176272.i 0.383470 0.0618051i
\(383\) 598408. 1.03647e6i 0.208449 0.361045i −0.742777 0.669539i \(-0.766492\pi\)
0.951226 + 0.308494i \(0.0998250\pi\)
\(384\) 0 0
\(385\) −2.01320e6 3.48697e6i −0.692207 1.19894i
\(386\) 2.12011e6 + 2.60360e6i 0.724251 + 0.889419i
\(387\) 0 0
\(388\) −507729. + 2.45424e6i −0.171219 + 0.827634i
\(389\) −1.22413e6 + 706752.i −0.410160 + 0.236806i −0.690859 0.722990i \(-0.742767\pi\)
0.280698 + 0.959796i \(0.409434\pi\)
\(390\) 0 0
\(391\) 259742. + 149962.i 0.0859213 + 0.0496067i
\(392\) 82653.6 1.86872e6i 0.0271673 0.614227i
\(393\) 0 0
\(394\) 529586. + 201638.i 0.171868 + 0.0654383i
\(395\) −2.02502e6 −0.653035
\(396\) 0 0
\(397\) 1.97577e6 0.629160 0.314580 0.949231i \(-0.398136\pi\)
0.314580 + 0.949231i \(0.398136\pi\)
\(398\) 2.12948e6 + 810792.i 0.673854 + 0.256568i
\(399\) 0 0
\(400\) −4.19109e6 + 3.11522e6i −1.30972 + 0.973507i
\(401\) 650613. + 375632.i 0.202052 + 0.116654i 0.597612 0.801785i \(-0.296116\pi\)
−0.395561 + 0.918440i \(0.629450\pi\)
\(402\) 0 0
\(403\) 399790. 230819.i 0.122622 0.0707960i
\(404\) −813650. 168327.i −0.248019 0.0513097i
\(405\) 0 0
\(406\) 2.58087e6 + 3.16944e6i 0.777052 + 0.954262i
\(407\) −1.16472e6 2.01736e6i −0.348527 0.603666i
\(408\) 0 0
\(409\) 1.22030e6 2.11362e6i 0.360710 0.624768i −0.627368 0.778723i \(-0.715868\pi\)
0.988078 + 0.153955i \(0.0492011\pi\)
\(410\) −6.44069e6 + 1.03807e6i −1.89222 + 0.304976i
\(411\) 0 0
\(412\) 249487. + 753864.i 0.0724109 + 0.218801i
\(413\) 433490.i 0.125056i
\(414\) 0 0
\(415\) 7.13189e6i 2.03275i
\(416\) −2.48202e6 + 2.55045e6i −0.703189 + 0.722577i
\(417\) 0 0
\(418\) 225492. + 1.39906e6i 0.0631234 + 0.391649i
\(419\) 3.49913e6 6.06068e6i 0.973701 1.68650i 0.289543 0.957165i \(-0.406497\pi\)
0.684158 0.729334i \(-0.260170\pi\)
\(420\) 0 0
\(421\) 575740. + 997211.i 0.158315 + 0.274209i 0.934261 0.356590i \(-0.116061\pi\)
−0.775946 + 0.630799i \(0.782727\pi\)
\(422\) −2.72714e6 + 2.22071e6i −0.745465 + 0.607030i
\(423\) 0 0
\(424\) −703220. 1.35275e6i −0.189966 0.365429i
\(425\) −2.13043e6 + 1.23001e6i −0.572131 + 0.330320i
\(426\) 0 0
\(427\) 823733. + 475582.i 0.218633 + 0.126228i
\(428\) −2.53201e6 2.25502e6i −0.668123 0.595033i
\(429\) 0 0
\(430\) 2.94194e6 7.72675e6i 0.767295 2.01524i
\(431\) −61287.6 −0.0158920 −0.00794601 0.999968i \(-0.502529\pi\)
−0.00794601 + 0.999968i \(0.502529\pi\)
\(432\) 0 0
\(433\) −6.42481e6 −1.64680 −0.823399 0.567462i \(-0.807925\pi\)
−0.823399 + 0.567462i \(0.807925\pi\)
\(434\) 121691. 319610.i 0.0310122 0.0814510i
\(435\) 0 0
\(436\) 575731. + 512748.i 0.145045 + 0.129178i
\(437\) 244451. + 141134.i 0.0612335 + 0.0353532i
\(438\) 0 0
\(439\) −1.53160e6 + 884268.i −0.379301 + 0.218989i −0.677514 0.735510i \(-0.736943\pi\)
0.298213 + 0.954499i \(0.403609\pi\)
\(440\) −4.17832e6 8.03762e6i −1.02889 1.97923i
\(441\) 0 0
\(442\) −1.30001e6 + 1.05859e6i −0.316512 + 0.257735i
\(443\) 3.28943e6 + 5.69747e6i 0.796364 + 1.37934i 0.921969 + 0.387263i \(0.126579\pi\)
−0.125605 + 0.992080i \(0.540087\pi\)
\(444\) 0 0
\(445\) 3.98696e6 6.90562e6i 0.954425 1.65311i
\(446\) −1.16162e6 7.20729e6i −0.276521 1.71567i
\(447\) 0 0
\(448\) −232767. + 2.62617e6i −0.0547931 + 0.618199i
\(449\) 974339.i 0.228084i 0.993476 + 0.114042i \(0.0363798\pi\)
−0.993476 + 0.114042i \(0.963620\pi\)
\(450\) 0 0
\(451\) 7.01703e6i 1.62447i
\(452\) 91067.2 + 275174.i 0.0209660 + 0.0633522i
\(453\) 0 0
\(454\) −4.85902e6 + 783145.i −1.10639 + 0.178321i
\(455\) 2.24147e6 3.88234e6i 0.507580 0.879155i
\(456\) 0 0
\(457\) 2.33316e6 + 4.04116e6i 0.522583 + 0.905140i 0.999655 + 0.0262754i \(0.00836468\pi\)
−0.477072 + 0.878864i \(0.658302\pi\)
\(458\) −393946. 483787.i −0.0877552 0.107768i
\(459\) 0 0
\(460\) −1.76696e6 365545.i −0.389342 0.0805463i
\(461\) −2.23506e6 + 1.29041e6i −0.489820 + 0.282798i −0.724500 0.689275i \(-0.757929\pi\)
0.234680 + 0.972073i \(0.424596\pi\)
\(462\) 0 0
\(463\) 2.00581e6 + 1.15806e6i 0.434849 + 0.251060i 0.701410 0.712758i \(-0.252554\pi\)
−0.266561 + 0.963818i \(0.585887\pi\)
\(464\) 5.48579e6 + 7.38036e6i 1.18289 + 1.59141i
\(465\) 0 0
\(466\) −1.86468e6 709970.i −0.397776 0.151452i
\(467\) 26296.7 0.00557969 0.00278984 0.999996i \(-0.499112\pi\)
0.00278984 + 0.999996i \(0.499112\pi\)
\(468\) 0 0
\(469\) −2.52068e6 −0.529159
\(470\) 9.17656e6 + 3.49395e6i 1.91618 + 0.729578i
\(471\) 0 0
\(472\) 43094.7 974331.i 0.00890367 0.201304i
\(473\) 7.70152e6 + 4.44648e6i 1.58279 + 0.913825i
\(474\) 0 0
\(475\) −2.00501e6 + 1.15760e6i −0.407740 + 0.235409i
\(476\) −251613. + 1.21624e6i −0.0508997 + 0.246037i
\(477\) 0 0
\(478\) 2.46976e6 + 3.03300e6i 0.494408 + 0.607159i
\(479\) −3.17700e6 5.50272e6i −0.632671 1.09582i −0.987003 0.160699i \(-0.948625\pi\)
0.354332 0.935120i \(1.61529\pi\)
\(480\) 0 0
\(481\) 1.29678e6 2.24610e6i 0.255567 0.442655i
\(482\) −418616. + 67469.7i −0.0820726 + 0.0132279i
\(483\) 0 0
\(484\) 4.35761e6 1.44212e6i 0.845541 0.279827i
\(485\) 7.10276e6i 1.37111i
\(486\) 0 0
\(487\) 7.12992e6i 1.36227i −0.732159 0.681134i \(-0.761487\pi\)
0.732159 0.681134i \(-0.238513\pi\)
\(488\) 1.80418e6 + 1.15083e6i 0.342950 + 0.218757i
\(489\) 0 0
\(490\) 843534. + 5.23370e6i 0.158713 + 0.984734i
\(491\) −4.12052e6 + 7.13694e6i −0.771343 + 1.33601i 0.165483 + 0.986213i \(0.447082\pi\)
−0.936827 + 0.349793i \(0.886252\pi\)
\(492\) 0 0
\(493\) 2.16599e6 + 3.75161e6i 0.401365 + 0.695185i
\(494\) −1.22348e6 + 996273.i −0.225568 + 0.183680i
\(495\) 0 0
\(496\) 305291. 706273.i 0.0557199 0.128905i
\(497\) 4.80061e6 2.77164e6i 0.871778 0.503321i
\(498\) 0 0
\(499\) −7.31706e6 4.22451e6i −1.31548 0.759495i −0.332485 0.943109i \(-0.607887\pi\)
−0.982998 + 0.183614i \(0.941220\pi\)
\(500\) 3.81132e6 4.27948e6i 0.681789 0.765536i
\(501\) 0 0
\(502\) −2.67919e6 + 7.03666e6i −0.474508 + 1.24626i
\(503\) 6.32200e6 1.11413 0.557063 0.830470i \(-0.311928\pi\)
0.557063 + 0.830470i \(0.311928\pi\)
\(504\) 0 0
\(505\) 2.35476e6 0.410883
\(506\) 690586. 1.81377e6i 0.119906 0.314923i
\(507\) 0 0
\(508\) 4.15461e6 4.66494e6i 0.714284 0.802023i
\(509\) 194691. + 112405.i 0.0333082 + 0.0192305i 0.516562 0.856250i \(-0.327212\pi\)
−0.483253 + 0.875481i \(0.660545\pi\)
\(510\) 0 0
\(511\) 1.65992e6 958354.i 0.281212 0.162358i
\(512\) −784254. + 5.87957e6i −0.132215 + 0.991221i
\(513\) 0 0
\(514\) 942070. 767124.i 0.157281 0.128073i
\(515\) −1.12523e6 1.94895e6i −0.186949 0.323805i
\(516\) 0 0
\(517\) −5.28079e6 + 9.14660e6i −0.868906 + 1.50499i
\(518\) −305730. 1.89690e6i −0.0500627 0.310614i
\(519\) 0 0
\(520\) 5.42399e6 8.50330e6i 0.879652 1.37905i
\(521\) 5.59008e6i 0.902243i −0.892462 0.451122i \(-0.851024\pi\)
0.892462 0.451122i \(-0.148976\pi\)
\(522\) 0 0
\(523\) 193807.i 0.0309825i −0.999880 0.0154912i \(-0.995069\pi\)
0.999880 0.0154912i \(-0.00493121\pi\)
\(524\) −7.70859e6 + 2.55111e6i −1.22644 + 0.405883i
\(525\) 0 0
\(526\) −3.66145e6 + 590128.i −0.577017 + 0.0929997i
\(527\) 181232. 313903.i 0.0284255 0.0492345i
\(528\) 0 0
\(529\) 3.02488e6 + 5.23925e6i 0.469969 + 0.814011i
\(530\) 2.72832e6 + 3.35052e6i 0.421896 + 0.518111i
\(531\) 0 0
\(532\) −236800. + 1.14464e6i −0.0362747 + 0.175343i
\(533\) 6.76596e6 3.90633e6i 1.03160 0.595594i
\(534\) 0 0
\(535\) 8.32179e6 + 4.80459e6i 1.25699 + 0.725725i
\(536\) −5.66560e6 250590.i −0.851793 0.0376748i
\(537\) 0 0
\(538\) −2.24438e6 854540.i −0.334303 0.127285i
\(539\) −5.70204e6 −0.845392
\(540\) 0 0
\(541\) 3.08637e6 0.453373 0.226686 0.973968i \(-0.427211\pi\)
0.226686 + 0.973968i \(0.427211\pi\)
\(542\) −1.46217e6 556717.i −0.213796 0.0814022i
\(543\) 0 0
\(544\) −686447. + 2.70865e6i −0.0994511 + 0.392425i
\(545\) −1.89222e6 1.09247e6i −0.272885 0.157550i
\(546\) 0 0
\(547\) −2.05052e6 + 1.18387e6i −0.293018 + 0.169174i −0.639302 0.768955i \(-0.720777\pi\)
0.346284 + 0.938130i \(0.387443\pi\)
\(548\) −3.92051e6 811068.i −0.557688 0.115373i
\(549\) 0 0
\(550\) 1.00515e7 + 1.23437e7i 1.41685 + 1.73996i
\(551\) 2.03848e6 + 3.53075e6i 0.286041 + 0.495437i
\(552\) 0 0
\(553\) 898281. 1.55587e6i 0.124911 0.216352i
\(554\) 8.47149e6 1.36538e6i 1.17270 0.189007i
\(555\) 0 0
\(556\) 1.80497e6 + 5.45401e6i 0.247618 + 0.748219i
\(557\) 1.20970e7i 1.65211i 0.563589 + 0.826056i \(0.309420\pi\)
−0.563589 + 0.826056i \(0.690580\pi\)
\(558\) 0 0
\(559\) 9.90128e6i 1.34018i
\(560\) −861815. 7.42204e6i −0.116130 1.00012i
\(561\) 0 0
\(562\) 864318. + 5.36266e6i 0.115434 + 0.716208i
\(563\) −2.49691e6 + 4.32478e6i −0.331996 + 0.575033i −0.982903 0.184124i \(-0.941055\pi\)
0.650907 + 0.759157i \(0.274389\pi\)
\(564\) 0 0
\(565\) −410729. 711403.i −0.0541295 0.0937551i
\(566\) 3.95345e6 3.21928e6i 0.518722 0.422394i
\(567\) 0 0
\(568\) 1.10656e7 5.75241e6i 1.43915 0.748134i
\(569\) −5.38818e6 + 3.11087e6i −0.697688 + 0.402810i −0.806486 0.591253i \(-0.798633\pi\)
0.108798 + 0.994064i \(0.465300\pi\)
\(570\) 0 0
\(571\) 8.67863e6 + 5.01061e6i 1.11394 + 0.643132i 0.939846 0.341597i \(-0.110968\pi\)
0.174091 + 0.984730i \(0.444301\pi\)
\(572\) 8.10134e6 + 7.21508e6i 1.03530 + 0.922042i
\(573\) 0 0
\(574\) 2.05946e6 5.40901e6i 0.260900 0.685233i
\(575\) 3.17072e6 0.399934
\(576\) 0 0
\(577\) −6.84784e6 −0.856276 −0.428138 0.903713i \(-0.640830\pi\)
−0.428138 + 0.903713i \(0.640830\pi\)
\(578\) 2.38959e6 6.27607e6i 0.297512 0.781390i
\(579\) 0 0
\(580\) −1.94621e7 1.73330e7i −2.40226 2.13946i
\(581\) −5.47960e6 3.16365e6i −0.673455 0.388819i
\(582\) 0 0
\(583\) −4.02487e6 + 2.32376e6i −0.490434 + 0.283152i
\(584\) 3.82618e6 1.98902e6i 0.464230 0.241328i
\(585\) 0 0
\(586\) 5.19996e6 4.23431e6i 0.625541 0.509376i
\(587\) 636726. + 1.10284e6i 0.0762706 + 0.132105i 0.901638 0.432491i \(-0.142365\pi\)
−0.825368 + 0.564596i \(0.809032\pi\)
\(588\) 0 0
\(589\) 170563. 295424.i 0.0202580 0.0350879i
\(590\) 439810. + 2.72880e6i 0.0520157 + 0.322731i
\(591\) 0 0
\(592\) −498596. 4.29396e6i −0.0584715 0.503563i
\(593\) 1.18555e6i 0.138447i 0.997601 + 0.0692233i \(0.0220521\pi\)
−0.997601 + 0.0692233i \(0.977948\pi\)
\(594\) 0 0
\(595\) 3.51987e6i 0.407600i
\(596\) −4.59354e6 1.38801e7i −0.529703 1.60058i
\(597\) 0 0
\(598\) 2.13331e6 343833.i 0.243950 0.0393183i
\(599\) 124447. 215548.i 0.0141715 0.0245458i −0.858853 0.512223i \(-0.828822\pi\)
0.873024 + 0.487677i \(0.162156\pi\)
\(600\) 0 0
\(601\) −2.20084e6 3.81197e6i −0.248544 0.430491i 0.714578 0.699556i \(-0.246619\pi\)
−0.963122 + 0.269065i \(0.913285\pi\)
\(602\) 4.63163e6 + 5.68788e6i 0.520885 + 0.639675i
\(603\) 0 0
\(604\) −6.86265e6 1.41973e6i −0.765420 0.158349i
\(605\) −1.12656e7 + 6.50422e6i −1.25132 + 0.722449i
\(606\) 0 0
\(607\) 5.35875e6 + 3.09387e6i 0.590325 + 0.340824i 0.765226 0.643762i \(-0.222627\pi\)
−0.174901 + 0.984586i \(0.555960\pi\)
\(608\) −646036. + 2.54920e6i −0.0708758 + 0.279669i
\(609\) 0 0
\(610\) −5.66788e6 2.15803e6i −0.616731 0.234819i
\(611\) −1.17591e7 −1.27430
\(612\) 0 0
\(613\) −1.13948e7 −1.22478 −0.612389 0.790557i \(-0.709791\pi\)
−0.612389 + 0.790557i \(0.709791\pi\)
\(614\) 3.91707e6 + 1.49141e6i 0.419314 + 0.159653i
\(615\) 0 0
\(616\) 8.02896e6 + 355121.i 0.852526 + 0.0377073i
\(617\) −1.05792e7 6.10788e6i −1.11876 0.645918i −0.177678 0.984089i \(-0.556859\pi\)
−0.941085 + 0.338170i \(0.890192\pi\)
\(618\) 0 0
\(619\) −1.02681e7 + 5.92826e6i −1.07711 + 0.621872i −0.930116 0.367265i \(-0.880294\pi\)
−0.146997 + 0.989137i \(0.546961\pi\)
\(620\) −441767. + 2.13540e6i −0.0461545 + 0.223100i
\(621\) 0 0
\(622\) −9.84284e6 1.20875e7i −1.02010 1.25274i
\(623\) 3.53717e6 + 6.12655e6i 0.365120 + 0.632406i
\(624\) 0 0
\(625\) −152246. + 263699.i −0.0155900 + 0.0270027i
\(626\) −1.52056e7 + 2.45073e6i −1.55084 + 0.249954i
\(627\) 0 0
\(628\) −6.91633e6 + 2.28892e6i −0.699804 + 0.231596i
\(629\) 2.03639e6i 0.205227i
\(630\) 0 0
\(631\) 2.84995e6i 0.284947i 0.989799 + 0.142474i \(0.0455056\pi\)
−0.989799 + 0.142474i \(0.954494\pi\)
\(632\) 2.17369e6 3.40774e6i 0.216474 0.339371i
\(633\) 0 0
\(634\) −760135. 4.71626e6i −0.0751048 0.465987i
\(635\) −8.85189e6 + 1.53319e7i −0.871168 + 1.50891i
\(636\) 0 0
\(637\) −3.17428e6 5.49802e6i −0.309954 0.536856i
\(638\) 2.17368e7 1.77002e7i 2.11419 1.72158i
\(639\) 0 0
\(640\) −1.19920e6 1.67678e7i −0.115729 1.61818i
\(641\) −174871. + 100962.i −0.0168102 + 0.00970538i −0.508382 0.861132i \(-0.669756\pi\)
0.491571 + 0.870837i \(0.336423\pi\)
\(642\) 0 0
\(643\) 3.06513e6 + 1.76965e6i 0.292362 + 0.168795i 0.639007 0.769201i \(-0.279346\pi\)
−0.346644 + 0.937997i \(0.612679\pi\)
\(644\) 1.06466e6 1.19544e6i 0.101157 0.113583i
\(645\) 0 0
\(646\) −440814. + 1.15776e6i −0.0415599 + 0.109154i
\(647\) 1.88702e7 1.77221 0.886106 0.463482i \(-0.153400\pi\)
0.886106 + 0.463482i \(0.153400\pi\)
\(648\) 0 0
\(649\) −2.97298e6 −0.277064
\(650\) −6.30649e6 + 1.65635e7i −0.585470 + 1.53769i
\(651\) 0 0
\(652\) −9.80559e6 + 1.10101e7i −0.903347 + 1.01431i
\(653\) −7.69628e6 4.44345e6i −0.706314 0.407790i 0.103381 0.994642i \(-0.467034\pi\)
−0.809695 + 0.586851i \(0.800367\pi\)
\(654\) 0 0
\(655\) 1.99289e7 1.15059e7i 1.81501 1.04790i
\(656\) 5.16668e6 1.19528e7i 0.468761 1.08445i
\(657\) 0 0
\(658\) −6.75513e6 + 5.50068e6i −0.608232 + 0.495281i
\(659\) −3.43642e6 5.95205e6i −0.308242 0.533892i 0.669736 0.742600i \(-0.266407\pi\)
−0.977978 + 0.208708i \(0.933074\pi\)
\(660\) 0 0
\(661\) −219686. + 380507.i −0.0195568 + 0.0338734i −0.875638 0.482968i \(-0.839559\pi\)
0.856081 + 0.516841i \(0.172892\pi\)
\(662\) 1.58488e6 + 9.83337e6i 0.140556 + 0.872082i
\(663\) 0 0
\(664\) −1.20017e7 7.65551e6i −1.05639 0.673835i
\(665\) 3.31266e6i 0.290484i
\(666\) 0 0
\(667\) 5.58352e6i 0.485952i
\(668\) −1.74119e7 + 5.76234e6i −1.50975 + 0.499641i
\(669\) 0 0
\(670\) 1.58676e7 2.55743e6i 1.36560 0.220098i
\(671\) 3.26167e6 5.64937e6i 0.279662 0.484388i
\(672\) 0 0
\(673\) −4.79543e6 8.30592e6i −0.408122 0.706887i 0.586558 0.809908i \(-0.300483\pi\)
−0.994679 + 0.103020i \(0.967149\pi\)
\(674\) 8.79935e6 + 1.08061e7i 0.746107 + 0.916259i
\(675\) 0 0
\(676\) −39936.4 + 193043.i −0.00336126 + 0.0162475i
\(677\) 4.71537e6 2.72242e6i 0.395407 0.228288i −0.289093 0.957301i \(-0.593354\pi\)
0.684500 + 0.729013i \(0.260020\pi\)
\(678\) 0 0
\(679\) 5.45721e6 + 3.15072e6i 0.454252 + 0.262262i
\(680\) 349923. 7.91143e6i 0.0290202 0.656119i
\(681\) 0 0
\(682\) −2.19197e6 834586.i −0.180457 0.0687084i
\(683\) −1.41906e7 −1.16399 −0.581995 0.813193i \(-0.697728\pi\)
−0.581995 + 0.813193i \(0.697728\pi\)
\(684\) 0 0
\(685\) 1.13462e7 0.923901
\(686\) −1.15443e7 4.39545e6i −0.936606 0.356610i
\(687\) 0 0
\(688\) 9.84480e6 + 1.32448e7i 0.792932 + 1.06678i
\(689\) −4.48123e6 2.58724e6i −0.359625 0.207629i
\(690\) 0 0
\(691\) −1.74007e7 + 1.00463e7i −1.38634 + 0.800406i −0.992901 0.118943i \(-0.962049\pi\)
−0.393443 + 0.919349i \(0.628716\pi\)
\(692\) −1.02738e7 2.12542e6i −0.815578 0.168725i
\(693\) 0 0
\(694\) 3.38156e6 + 4.15274e6i 0.266513 + 0.327293i
\(695\) −8.14072e6 1.41001e7i −0.639295 1.10729i
\(696\) 0 0
\(697\) 3.06713e6 5.31243e6i 0.239139 0.414201i
\(698\) 2.19694e7 3.54089e6i 1.70679 0.275089i
\(699\) 0 0
\(700\) 4.12525e6 + 1.24651e7i 0.318203 + 0.961503i
\(701\) 1.36721e7i 1.05085i −0.850841 0.525423i \(-0.823907\pi\)
0.850841 0.525423i \(-0.176093\pi\)
\(702\) 0 0
\(703\) 1.91651e6i 0.146259i
\(704\) 1.80110e7 + 1.59637e6i 1.36964 + 0.121396i
\(705\) 0 0
\(706\) −3.47850e6 2.15824e7i −0.262652 1.62962i
\(707\) −1.04455e6 + 1.80922e6i −0.0785927 + 0.136126i
\(708\) 0 0
\(709\) −1.00757e6 1.74517e6i −0.0752767 0.130383i 0.825930 0.563773i \(-0.190651\pi\)
−0.901207 + 0.433390i \(0.857317\pi\)
\(710\) −2.74076e7 + 2.23179e7i −2.04045 + 1.66153i
\(711\) 0 0
\(712\) 7.34124e6 + 1.41220e7i 0.542712 + 1.04399i
\(713\) −404592. + 233591.i −0.0298053 + 0.0172081i
\(714\) 0 0
\(715\) −2.66261e7 1.53726e7i −1.94779 1.12456i
\(716\) −2.94193e6 2.62009e6i −0.214462 0.191000i
\(717\) 0 0
\(718\) −2.48767e6 + 6.53365e6i −0.180087 + 0.472982i
\(719\) 1.07956e7 0.778796 0.389398 0.921070i \(-0.372683\pi\)
0.389398 + 0.921070i \(0.372683\pi\)
\(720\) 0 0
\(721\) 1.99657e6 0.143036
\(722\) 4.56919e6 1.20006e7i 0.326209 0.856761i
\(723\) 0 0
\(724\) 7.45310e6 + 6.63775e6i 0.528433 + 0.470625i
\(725\) 3.96610e7 + 2.28983e7i 2.80233 + 1.61792i
\(726\) 0 0
\(727\) 2.00659e7 1.15851e7i 1.40807 0.812947i 0.412864 0.910793i \(-0.364528\pi\)
0.995202 + 0.0978454i \(0.0311951\pi\)
\(728\) 4.12725e6 + 7.93938e6i 0.288624 + 0.555211i
\(729\) 0 0
\(730\) −9.47678e6 + 7.71691e6i −0.658194 + 0.535965i
\(731\) 3.88709e6 + 6.73265e6i 0.269049 + 0.466007i
\(732\) 0 0
\(733\) −3.96332e6 + 6.86468e6i −0.272458 + 0.471911i −0.969491 0.245128i \(-0.921170\pi\)
0.697033 + 0.717039i \(0.254503\pi\)
\(734\) −452868. 2.80982e6i −0.0310264 0.192503i
\(735\) 0 0
\(736\) 2.51183e6 2.58109e6i 0.170921 0.175634i
\(737\) 1.72875e7i 1.17237i
\(738\) 0 0
\(739\) 2.45640e7i 1.65458i 0.561776 + 0.827289i \(0.310118\pi\)
−0.561776 + 0.827289i \(0.689882\pi\)
\(740\) 3.84912e6 + 1.16307e7i 0.258394 + 0.780778i
\(741\) 0 0
\(742\) −3.78455e6 + 609968.i −0.252350 + 0.0406722i
\(743\) −2.79240e6 + 4.83658e6i −0.185569 + 0.321415i −0.943768 0.330608i \(-0.892746\pi\)
0.758199 + 0.652023i \(0.226080\pi\)
\(744\) 0 0
\(745\) 2.07177e7 + 3.58841e7i 1.36757 + 2.36871i
\(746\) −1.62982e7 2.00150e7i −1.07224 1.31677i
\(747\) 0 0
\(748\) 8.34126e6 + 1.72562e6i 0.545102 + 0.112770i
\(749\) −7.38296e6 + 4.26255e6i −0.480868 + 0.277629i
\(750\) 0 0
\(751\) −1.13834e7 6.57223e6i −0.736501 0.425219i 0.0842946 0.996441i \(-0.473136\pi\)
−0.820796 + 0.571222i \(0.806470\pi\)
\(752\) −1.57300e7 + 1.16920e7i −1.01434 + 0.753955i
\(753\) 0 0
\(754\) 2.91677e7 + 1.11055e7i 1.86841 + 0.711393i
\(755\) 1.98610e7 1.26804
\(756\) 0 0
\(757\) 1.33312e7 0.845528 0.422764 0.906240i \(-0.361060\pi\)
0.422764 + 0.906240i \(0.361060\pi\)
\(758\) −1.86132e7 7.08694e6i −1.17666 0.448008i
\(759\) 0 0
\(760\) 329323. 7.44569e6i 0.0206818 0.467596i
\(761\) −9.74299e6 5.62512e6i −0.609861 0.352103i 0.163050 0.986618i \(-0.447867\pi\)
−0.772911 + 0.634515i \(0.781200\pi\)
\(762\) 0 0
\(763\) 1.67874e6 969222.i 0.104393 0.0602715i
\(764\) 1.26954e6 6.13667e6i 0.0786891 0.380364i
\(765\) 0 0
\(766\) −4.27493e6 5.24984e6i −0.263243 0.323276i
\(767\) −1.65504e6 2.86661e6i −0.101583 0.175946i
\(768\) 0 0
\(769\) −1.05229e7 + 1.82262e7i −0.641680 + 1.11142i 0.343378 + 0.939197i \(0.388429\pi\)
−0.985058 + 0.172225i \(0.944904\pi\)
\(770\) −2.24866e7 + 3.62424e6i −1.36678 + 0.220288i
\(771\) 0 0
\(772\) 1.80317e7 5.96749e6i 1.08892 0.360370i
\(773\) 5.93037e6i 0.356971i −0.983943 0.178486i \(-0.942880\pi\)
0.983943 0.178486i \(-0.0571198\pi\)
\(774\) 0 0
\(775\) 3.83188e6i 0.229170i
\(776\)