Properties

Label 108.6.h.a.35.19
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 35.19
Character \(\chi\) \(=\) 108.35
Dual form 108.6.h.a.71.19

$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 0.410066 0.912056i \(-0.365506\pi\)
0.994897 + 0.100901i \(0.0321724\pi\)
\(6\) 0 0
\(7\) −69.6792 40.2293i −0.537475 0.310311i 0.206580 0.978430i \(-0.433767\pi\)
−0.744055 + 0.668118i \(0.767100\pi\)
\(8\) −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 −0.285140 0.958486i \(-0.592040\pi\)
0.972643 0.232304i \(-0.0746265\pi\)
\(12\) 0 0
\(13\) −307.186 532.062i −0.504131 0.873180i −0.999989 0.00477646i \(-0.998480\pi\)
0.495858 0.868404i \(-0.334854\pi\)
\(14\) 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 \(-0.935121\pi\)
0.979300 0.202415i \(-0.0648791\pi\)
\(18\) 0 0
\(19\) 453.989i 0.288510i −0.989541 0.144255i \(-0.953921\pi\)
0.989541 0.144255i \(-0.0460786\pi\)
\(20\) −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 0.920767 0.390112i \(-0.127564\pi\)
−0.798231 + 0.602352i \(0.794230\pi\)
\(24\) 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 0.923893 + 0.382652i \(0.124989\pi\)
0.793332 + 0.608789i \(0.208344\pi\)
\(30\) 0 0
\(31\) −650.730 + 375.699i −0.121618 + 0.0702159i −0.559575 0.828780i \(-0.689035\pi\)
0.437957 + 0.898996i \(0.355702\pi\)
\(32\) 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 −0.915014 0.403422i \(-0.867821\pi\)
−0.108133 + 0.994136i \(0.534487\pi\)
\(42\) 0 0
\(43\) 13956.9 + 8058.04i 1.15112 + 0.664597i 0.949159 0.314797i \(-0.101937\pi\)
0.201957 + 0.979394i \(0.435270\pi\)
\(44\) 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 −0.355228 0.934780i \(-0.615597\pi\)
0.987157 0.159753i \(-0.0510697\pi\)
\(48\) 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 \(-0.933979\pi\)
0.978567 0.205928i \(-0.0660213\pi\)
\(54\) 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 0.811244 0.584708i \(-0.198791\pi\)
−0.911994 + 0.410204i \(0.865458\pi\)
\(60\) 0 0
\(61\) −5910.89 + 10238.0i −0.203390 + 0.352281i −0.949618 0.313408i \(-0.898529\pi\)
0.746229 + 0.665689i \(0.231862\pi\)
\(62\) −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 −0.0830902 0.996542i \(-0.526479\pi\)
0.821486 + 0.570229i \(0.193146\pi\)
\(68\) 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 0.315466 0.948937i \(-0.397839\pi\)
−0.664070 + 0.747670i \(0.731172\pi\)
\(80\) −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 −0.361750 0.932275i \(-0.617821\pi\)
0.988249 0.152853i \(-0.0488461\pi\)
\(84\) 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 \(0.200207\pi\)
−0.808634 + 0.588312i \(0.799793\pi\)
\(90\) 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 −0.996191 0.0871983i \(-0.972209\pi\)
0.573611 + 0.819128i \(0.305542\pi\)
\(98\) 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 0.605644 0.795736i \(-0.292916\pi\)
−0.386305 + 0.922371i \(0.626249\pi\)
\(102\) 0 0
\(103\) −21490.3 + 12407.4i −0.199595 + 0.115236i −0.596466 0.802638i \(-0.703429\pi\)
0.396872 + 0.917874i \(0.370096\pi\)
\(104\) 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 −0.528617 0.848860i \(-0.677289\pi\)
0.470826 + 0.882226i \(0.343956\pi\)
\(114\) 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 \(-0.819561\pi\)
0.843587 0.536992i \(-0.180439\pi\)
\(128\) −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 0.984086 + 0.177693i \(0.0568632\pi\)
−0.338157 + 0.941090i \(0.609803\pi\)
\(132\) 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 0.725900 0.687800i \(-0.241423\pi\)
−0.232702 + 0.972548i \(0.574757\pi\)
\(138\) 0 0
\(139\) −155476. + 89764.4i −0.682539 + 0.394064i −0.800811 0.598917i \(-0.795598\pi\)
0.118272 + 0.992981i \(0.462265\pi\)
\(140\) 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 0.461067 0.887366i \(-0.347467\pi\)
0.999014 + 0.0443874i \(0.0141336\pi\)
\(150\) 0 0
\(151\) 189659. + 109500.i 0.676909 + 0.390814i 0.798690 0.601743i \(-0.205527\pi\)
−0.121780 + 0.992557i \(0.538860\pi\)
\(152\) −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 0.989342 0.145614i \(-0.0465156\pi\)
−0.620776 + 0.783988i \(0.713182\pi\)
\(158\) 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 \(0.237642\pi\)
−0.734020 + 0.679128i \(0.762358\pi\)
\(164\) 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 0.922752 + 0.385395i \(0.125935\pi\)
−0.127614 + 0.991824i \(0.540732\pi\)
\(168\) 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 0.815219 0.579153i \(-0.196617\pi\)
−0.0939514 + 0.995577i \(0.529950\pi\)
\(174\) 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 −0.752432 0.658670i \(-0.771119\pi\)
0.946641 + 0.322290i \(0.104453\pi\)
\(192\) 0 0
\(193\) −296774. 514028.i −0.573499 0.993330i −0.996203 0.0870619i \(-0.972252\pi\)
0.422704 0.906268i \(-0.361081\pi\)
\(194\) −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 \(-0.970689\pi\)
0.995763 0.0919523i \(-0.0293107\pi\)
\(198\) 0 0
\(199\) 402805.i 0.721045i −0.932751 0.360522i \(-0.882598\pi\)
0.932751 0.360522i \(-0.117402\pi\)
\(200\) −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 −0.854728 0.519077i \(-0.826276\pi\)
0.0221701 + 0.999754i \(0.492942\pi\)
\(212\) 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 0.999983 + 0.00579252i \(0.00184383\pi\)
0.505008 + 0.863115i \(0.331490\pi\)
\(224\) −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 0.437132 + 0.899398i \(0.355994\pi\)
−0.997467 + 0.0711316i \(0.977339\pi\)
\(228\) 0 0
\(229\) 55144.9 + 95513.7i 0.0694891 + 0.120359i 0.898677 0.438612i \(-0.144530\pi\)
−0.829187 + 0.558971i \(0.811196\pi\)
\(230\) −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 \(0.0682637\pi\)
−0.977092 + 0.212817i \(0.931736\pi\)
\(234\) 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 0.601150 0.799137i \(-0.294710\pi\)
−0.992647 + 0.121043i \(0.961376\pi\)
\(240\) 0 0
\(241\) −37478.3 + 64914.3i −0.0415659 + 0.0719942i −0.886060 0.463571i \(-0.846568\pi\)
0.844494 + 0.535565i \(0.179901\pi\)
\(242\) 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 −0.409594 0.912268i \(-0.634330\pi\)
0.585250 + 0.810853i \(0.300996\pi\)
\(258\) 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 −0.974337 0.225094i \(-0.927731\pi\)
0.682106 + 0.731254i \(0.261064\pi\)
\(264\) 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 \(0.0572401\pi\)
−0.983875 + 0.178857i \(0.942760\pi\)
\(270\) 0 0
\(271\) 276579.i 0.228769i 0.993437 + 0.114384i \(0.0364895\pi\)
−0.993437 + 0.114384i \(0.963510\pi\)
\(272\) −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 −0.399784 0.916609i \(-0.630915\pi\)
0.993699 0.112081i \(-0.0357517\pi\)
\(278\) −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 0.151819 0.988408i \(-0.451487\pi\)
−0.780077 + 0.625683i \(0.784820\pi\)
\(282\) 0 0
\(283\) 780527. 450638.i 0.579325 0.334473i −0.181540 0.983384i \(-0.558108\pi\)
0.760865 + 0.648910i \(0.224775\pi\)
\(284\) 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 −0.108211 0.994128i \(-0.534512\pi\)
0.806835 + 0.590778i \(0.201179\pi\)
\(294\) 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 \(-0.927977\pi\)
0.974511 0.224340i \(-0.0720226\pi\)
\(308\) 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 0.914404 + 0.404802i \(0.132660\pi\)
−0.106633 + 0.994298i \(0.534007\pi\)
\(312\) 0 0
\(313\) −1.36134e6 + 2.35791e6i −0.785427 + 1.36040i 0.143317 + 0.989677i \(0.454223\pi\)
−0.928744 + 0.370722i \(0.879110\pi\)
\(314\) −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 0.690259 0.723562i \(-0.257497\pi\)
−0.281494 + 0.959563i \(0.590830\pi\)
\(318\) 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 0.0660935 0.997813i \(-0.478946\pi\)
−0.831085 + 0.556145i \(0.812280\pi\)
\(332\) 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 −0.994124 0.108246i \(-0.965477\pi\)
0.403318 0.915060i \(-0.367857\pi\)
\(338\) −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 0.741001 0.671504i \(-0.234351\pi\)
−0.952040 + 0.305974i \(0.901018\pi\)
\(348\) 0 0
\(349\) 1.96690e6 3.40677e6i 0.864408 1.49720i −0.00322519 0.999995i \(-0.501027\pi\)
0.867633 0.497204i \(-0.165640\pi\)
\(350\) −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 0.997082 0.0763423i \(-0.0243242\pi\)
0.432426 + 0.901669i \(0.357658\pi\)
\(354\) 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 0.582050 0.813153i \(-0.302251\pi\)
−0.413186 + 0.910647i \(0.635584\pi\)
\(368\) 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 0.882052 + 0.471151i \(0.156161\pi\)
−0.0329973 + 0.999455i \(0.510505\pi\)
\(374\) 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 \(0.216752\pi\)
−0.776977 + 0.629529i \(0.783248\pi\)
\(380\) 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 0.951226 0.308494i \(-0.0998250\pi\)
−0.742777 + 0.669539i \(0.766492\pi\)
\(384\) 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 0.280698 0.959796i \(-0.409434\pi\)
−0.690859 + 0.722990i \(0.742767\pi\)
\(390\) 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 −0.395561 0.918440i \(-0.629450\pi\)
0.597612 + 0.801785i \(0.296116\pi\)
\(402\) 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 0.988078 0.153955i \(-0.0492011\pi\)
−0.627368 + 0.778723i \(0.715868\pi\)
\(410\) −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 0.684158 + 0.729334i \(0.260170\pi\)
0.289543 + 0.957165i \(0.406497\pi\)
\(420\) 0 0
\(421\) 575740. 997211.i 0.158315 0.274209i −0.775946 0.630799i \(-0.782727\pi\)
0.934261 + 0.356590i \(0.116061\pi\)
\(422\) −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 0.298213 0.954499i \(-0.403609\pi\)
−0.677514 + 0.735510i \(0.736943\pi\)
\(440\) −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 −0.125605 0.992080i \(-0.540087\pi\)
0.921969 0.387263i \(-0.126579\pi\)
\(444\) 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 \(-0.963620\pi\)
0.993476 0.114042i \(-0.0363798\pi\)
\(450\) 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 −0.477072 0.878864i \(-0.658302\pi\)
0.999655 0.0262754i \(-0.00836468\pi\)
\(458\) −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 0.234680 0.972073i \(-0.424596\pi\)
−0.724500 + 0.689275i \(0.757929\pi\)
\(462\) 0 0
\(463\) 2.00581e6 1.15806e6i 0.434849 0.251060i −0.266561 0.963818i \(-0.585887\pi\)
0.701410 + 0.712758i \(0.252554\pi\)
\(464\) 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 0.354332 + 0.935120i \(0.384708\pi\)
−0.987003 + 0.160699i \(0.948625\pi\)
\(480\) 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 \(0.238513\pi\)
−0.732159 + 0.681134i \(0.761487\pi\)
\(488\) 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 −0.936827 0.349793i \(-0.886252\pi\)
0.165483 0.986213i \(1.55292\pi\)
\(492\) 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 −0.982998 0.183614i \(-0.941220\pi\)
−0.332485 + 0.943109i \(0.607887\pi\)
\(500\) 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 −0.483253 0.875481i \(-0.660545\pi\)
0.516562 + 0.856250i \(0.327212\pi\)
\(510\) 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 \(0.148976\pi\)
−0.892462 + 0.451122i \(0.851024\pi\)
\(522\) 0 0
\(523\) 193807.i 0.0309825i 0.999880 + 0.0154912i \(0.00493121\pi\)
−0.999880 + 0.0154912i \(0.995069\pi\)
\(524\) −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 0.346284 0.938130i \(-0.387443\pi\)
−0.639302 + 0.768955i \(0.720777\pi\)
\(548\) −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 \(-0.690580\pi\)
0.563589 0.826056i \(-0.309420\pi\)
\(558\) 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 0.650907 0.759157i \(-0.274389\pi\)
−0.982903 + 0.184124i \(0.941055\pi\)
\(564\) 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 0.108798 0.994064i \(-0.465300\pi\)
−0.806486 + 0.591253i \(0.798633\pi\)
\(570\) 0 0
\(571\) 8.67863e6 5.01061e6i 1.11394 0.643132i 0.174091 0.984730i \(-0.444301\pi\)
0.939846 + 0.341597i \(0.110968\pi\)
\(572\) 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 −0.825368 0.564596i \(-0.809032\pi\)
0.901638 + 0.432491i \(0.142365\pi\)
\(588\) 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 \(-0.977948\pi\)
0.997601 0.0692233i \(-0.0220521\pi\)
\(594\) 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 0.873024 0.487677i \(-0.162156\pi\)
−0.858853 + 0.512223i \(0.828822\pi\)
\(600\) 0 0
\(601\) −2.20084e6 + 3.81197e6i −0.248544 + 0.430491i −0.963122 0.269065i \(-0.913285\pi\)
0.714578 + 0.699556i \(0.246619\pi\)
\(602\) 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 −0.174901 0.984586i \(-0.555960\pi\)
0.765226 + 0.643762i \(0.222627\pi\)
\(608\) −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 −0.941085 0.338170i \(-0.890192\pi\)
−0.177678 + 0.984089i \(0.556859\pi\)
\(618\) 0 0
\(619\) −1.02681e7 5.92826e6i −1.07711 0.621872i −0.146997 0.989137i \(-0.546961\pi\)
−0.930116 + 0.367265i \(0.880294\pi\)
\(620\) −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 \(-0.954494\pi\)
0.989799 0.142474i \(-0.0455056\pi\)
\(632\) 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 0.491571 0.870837i \(-0.336423\pi\)
−0.508382 + 0.861132i \(0.669756\pi\)
\(642\) 0 0
\(643\) 3.06513e6 1.76965e6i 0.292362 0.168795i −0.346644 0.937997i \(-0.612679\pi\)
0.639007 + 0.769201i \(0.279346\pi\)
\(644\) 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 −0.809695 0.586851i \(-0.800367\pi\)
0.103381 + 0.994642i \(0.467034\pi\)
\(654\) 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 −0.977978 0.208708i \(-0.933074\pi\)
0.669736 + 0.742600i \(0.266407\pi\)
\(660\) 0 0
\(661\) −219686. 380507.i −0.0195568 0.0338734i 0.856081 0.516841i \(-0.172892\pi\)
−0.875638 + 0.482968i \(0.839559\pi\)
\(662\) 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 −0.994679 0.103020i \(-0.967149\pi\)
0.586558 + 0.809908i \(0.300483\pi\)
\(674\) 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 0.684500 0.729013i \(-0.260020\pi\)
−0.289093 + 0.957301i \(0.593354\pi\)
\(678\) 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 −0.393443 0.919349i \(-0.628716\pi\)
−0.992901 + 0.118943i \(0.962049\pi\)
\(692\) −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 \(0.176093\pi\)
−0.850841 + 0.525423i \(0.823907\pi\)
\(702\) 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 −0.901207 0.433390i \(-0.857317\pi\)
0.825930 + 0.563773i \(0.190651\pi\)
\(710\) −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 0.995202 0.0978454i \(-0.0311951\pi\)
0.412864 + 0.910793i \(0.364528\pi\)
\(728\) 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 0.697033 0.717039i \(-0.254503\pi\)
−0.969491 + 0.245128i \(0.921170\pi\)
\(734\) −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 \(-0.689882\pi\)
0.561776 0.827289i \(-0.310118\pi\)
\(740\) 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 0.758199 0.652023i \(-0.226080\pi\)
−0.943768 + 0.330608i \(0.892746\pi\)
\(744\) 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 −0.820796 0.571222i \(-0.806470\pi\)
0.0842946 + 0.996441i \(0.473136\pi\)
\(752\) −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 −0.772911 0.634515i \(-0.781200\pi\)
0.163050 + 0.986618i \(0.447867\pi\)
\(762\) 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 −0.985058 0.172225i \(-0.944904\pi\)
0.343378 0.939197i \(-0.388429\pi\)
\(770\) −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 \(0.0571198\pi\)
−0.983943 + 0.178486i \(0.942880\pi\)
\(774\) 0 0
\(775\) 3.83188e6i 0.229170i