Properties

Label 108.6.b.b.107.10
Level 108
Weight 6
Character 108.107
Analytic conductor 17.321
Analytic rank 0
Dimension 16
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.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.3214525398\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 30 x^{14} + 619 x^{12} + 5604 x^{10} + 40971 x^{8} - 4866 x^{6} + 568069 x^{4} - 7909632 x^{2} + 20340100\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{30}\cdot 3^{32}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 107.10
Root \(-1.73205 + 1.98106i\) of defining polynomial
Character \(\chi\) \(=\) 108.107
Dual form 108.6.b.b.107.9

$q$-expansion

\(f(q)\) \(=\) \(q+(1.79734 + 5.36373i) q^{2} +(-25.5392 + 19.2809i) q^{4} -44.9719i q^{5} -28.5094i q^{7} +(-149.320 - 102.331i) q^{8} +O(q^{10})\) \(q+(1.79734 + 5.36373i) q^{2} +(-25.5392 + 19.2809i) q^{4} -44.9719i q^{5} -28.5094i q^{7} +(-149.320 - 102.331i) q^{8} +(241.217 - 80.8297i) q^{10} +411.905 q^{11} +684.385 q^{13} +(152.917 - 51.2411i) q^{14} +(280.497 - 984.834i) q^{16} +1516.97i q^{17} -2045.09i q^{19} +(867.098 + 1148.55i) q^{20} +(740.332 + 2209.34i) q^{22} +3070.67 q^{23} +1102.53 q^{25} +(1230.07 + 3670.85i) q^{26} +(549.686 + 728.107i) q^{28} +643.596i q^{29} +731.030i q^{31} +(5786.53 - 265.570i) q^{32} +(-8136.61 + 2726.51i) q^{34} -1282.12 q^{35} -5461.90 q^{37} +(10969.3 - 3675.71i) q^{38} +(-4602.02 + 6715.20i) q^{40} +6382.62i q^{41} -17907.2i q^{43} +(-10519.7 + 7941.88i) q^{44} +(5519.03 + 16470.2i) q^{46} +19287.6 q^{47} +15994.2 q^{49} +(1981.61 + 5913.65i) q^{50} +(-17478.6 + 13195.5i) q^{52} +11400.4i q^{53} -18524.2i q^{55} +(-2917.39 + 4257.02i) q^{56} +(-3452.07 + 1156.76i) q^{58} -424.395 q^{59} -6907.86 q^{61} +(-3921.05 + 1313.91i) q^{62} +(11824.8 + 30560.0i) q^{64} -30778.1i q^{65} -58593.9i q^{67} +(-29248.5 - 38742.1i) q^{68} +(-2304.41 - 6876.97i) q^{70} -49133.0 q^{71} +70200.7 q^{73} +(-9816.87 - 29296.1i) q^{74} +(39431.1 + 52229.8i) q^{76} -11743.2i q^{77} -95223.5i q^{79} +(-44289.9 - 12614.5i) q^{80} +(-34234.6 + 11471.7i) q^{82} -55856.8 q^{83} +68221.1 q^{85} +(96049.4 - 32185.3i) q^{86} +(-61505.5 - 42150.6i) q^{88} -93780.9i q^{89} -19511.4i q^{91} +(-78422.3 + 59205.1i) q^{92} +(34666.3 + 103453. i) q^{94} -91971.6 q^{95} -182666. q^{97} +(28747.0 + 85788.6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 94q^{4} + O(q^{10}) \) \( 16q + 94q^{4} + 1454q^{10} + 896q^{13} + 178q^{16} + 30q^{22} + 9888q^{25} + 11454q^{28} - 6172q^{34} - 71008q^{37} - 16618q^{40} + 35304q^{46} - 49376q^{49} + 14876q^{52} - 10492q^{58} + 77888q^{61} + 89206q^{64} + 229398q^{70} - 38032q^{73} + 48960q^{76} - 224488q^{82} - 371264q^{85} + 249102q^{88} + 68772q^{94} - 976q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(55\)
\(\chi(n)\) \(-1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.79734 + 5.36373i 0.317727 + 0.948182i
\(3\) 0 0
\(4\) −25.5392 + 19.2809i −0.798099 + 0.602527i
\(5\) 44.9719i 0.804482i −0.915534 0.402241i \(-0.868231\pi\)
0.915534 0.402241i \(-0.131769\pi\)
\(6\) 0 0
\(7\) 28.5094i 0.219909i −0.993937 0.109955i \(-0.964929\pi\)
0.993937 0.109955i \(-0.0350706\pi\)
\(8\) −149.320 102.331i −0.824883 0.565303i
\(9\) 0 0
\(10\) 241.217 80.8297i 0.762796 0.255606i
\(11\) 411.905 1.02640 0.513198 0.858270i \(-0.328461\pi\)
0.513198 + 0.858270i \(0.328461\pi\)
\(12\) 0 0
\(13\) 684.385 1.12316 0.561580 0.827422i \(-0.310194\pi\)
0.561580 + 0.827422i \(0.310194\pi\)
\(14\) 152.917 51.2411i 0.208514 0.0698712i
\(15\) 0 0
\(16\) 280.497 984.834i 0.273923 0.961752i
\(17\) 1516.97i 1.27308i 0.771245 + 0.636538i \(0.219634\pi\)
−0.771245 + 0.636538i \(0.780366\pi\)
\(18\) 0 0
\(19\) 2045.09i 1.29966i −0.760082 0.649828i \(-0.774841\pi\)
0.760082 0.649828i \(-0.225159\pi\)
\(20\) 867.098 + 1148.55i 0.484722 + 0.642056i
\(21\) 0 0
\(22\) 740.332 + 2209.34i 0.326114 + 0.973211i
\(23\) 3070.67 1.21036 0.605178 0.796090i \(-0.293102\pi\)
0.605178 + 0.796090i \(0.293102\pi\)
\(24\) 0 0
\(25\) 1102.53 0.352808
\(26\) 1230.07 + 3670.85i 0.356859 + 1.06496i
\(27\) 0 0
\(28\) 549.686 + 728.107i 0.132501 + 0.175509i
\(29\) 643.596i 0.142108i 0.997472 + 0.0710539i \(0.0226362\pi\)
−0.997472 + 0.0710539i \(0.977364\pi\)
\(30\) 0 0
\(31\) 731.030i 0.136625i 0.997664 + 0.0683126i \(0.0217615\pi\)
−0.997664 + 0.0683126i \(0.978238\pi\)
\(32\) 5786.53 265.570i 0.998949 0.0458464i
\(33\) 0 0
\(34\) −8136.61 + 2726.51i −1.20711 + 0.404491i
\(35\) −1282.12 −0.176913
\(36\) 0 0
\(37\) −5461.90 −0.655902 −0.327951 0.944695i \(-0.606358\pi\)
−0.327951 + 0.944695i \(0.606358\pi\)
\(38\) 10969.3 3675.71i 1.23231 0.412936i
\(39\) 0 0
\(40\) −4602.02 + 6715.20i −0.454777 + 0.663604i
\(41\) 6382.62i 0.592979i 0.955036 + 0.296490i \(0.0958160\pi\)
−0.955036 + 0.296490i \(0.904184\pi\)
\(42\) 0 0
\(43\) 17907.2i 1.47692i −0.674297 0.738460i \(-0.735553\pi\)
0.674297 0.738460i \(-0.264447\pi\)
\(44\) −10519.7 + 7941.88i −0.819165 + 0.618431i
\(45\) 0 0
\(46\) 5519.03 + 16470.2i 0.384564 + 1.14764i
\(47\) 19287.6 1.27360 0.636801 0.771029i \(-0.280257\pi\)
0.636801 + 0.771029i \(0.280257\pi\)
\(48\) 0 0
\(49\) 15994.2 0.951640
\(50\) 1981.61 + 5913.65i 0.112097 + 0.334526i
\(51\) 0 0
\(52\) −17478.6 + 13195.5i −0.896393 + 0.676734i
\(53\) 11400.4i 0.557483i 0.960366 + 0.278741i \(0.0899172\pi\)
−0.960366 + 0.278741i \(0.910083\pi\)
\(54\) 0 0
\(55\) 18524.2i 0.825718i
\(56\) −2917.39 + 4257.02i −0.124315 + 0.181399i
\(57\) 0 0
\(58\) −3452.07 + 1156.76i −0.134744 + 0.0451516i
\(59\) −424.395 −0.0158723 −0.00793616 0.999969i \(-0.502526\pi\)
−0.00793616 + 0.999969i \(0.502526\pi\)
\(60\) 0 0
\(61\) −6907.86 −0.237695 −0.118847 0.992913i \(-0.537920\pi\)
−0.118847 + 0.992913i \(0.537920\pi\)
\(62\) −3921.05 + 1313.91i −0.129546 + 0.0434096i
\(63\) 0 0
\(64\) 11824.8 + 30560.0i 0.360864 + 0.932618i
\(65\) 30778.1i 0.903563i
\(66\) 0 0
\(67\) 58593.9i 1.59465i −0.603549 0.797326i \(-0.706247\pi\)
0.603549 0.797326i \(-0.293753\pi\)
\(68\) −29248.5 38742.1i −0.767063 1.01604i
\(69\) 0 0
\(70\) −2304.41 6876.97i −0.0562101 0.167746i
\(71\) −49133.0 −1.15672 −0.578359 0.815782i \(-0.696307\pi\)
−0.578359 + 0.815782i \(0.696307\pi\)
\(72\) 0 0
\(73\) 70200.7 1.54182 0.770911 0.636943i \(-0.219801\pi\)
0.770911 + 0.636943i \(0.219801\pi\)
\(74\) −9816.87 29296.1i −0.208398 0.621915i
\(75\) 0 0
\(76\) 39431.1 + 52229.8i 0.783077 + 1.03725i
\(77\) 11743.2i 0.225714i
\(78\) 0 0
\(79\) 95223.5i 1.71663i −0.513124 0.858315i \(-0.671512\pi\)
0.513124 0.858315i \(-0.328488\pi\)
\(80\) −44289.9 12614.5i −0.773712 0.220366i
\(81\) 0 0
\(82\) −34234.6 + 11471.7i −0.562252 + 0.188406i
\(83\) −55856.8 −0.889981 −0.444990 0.895535i \(-0.646793\pi\)
−0.444990 + 0.895535i \(0.646793\pi\)
\(84\) 0 0
\(85\) 68221.1 1.02417
\(86\) 96049.4 32185.3i 1.40039 0.469258i
\(87\) 0 0
\(88\) −61505.5 42150.6i −0.846657 0.580225i
\(89\) 93780.9i 1.25499i −0.778622 0.627493i \(-0.784081\pi\)
0.778622 0.627493i \(-0.215919\pi\)
\(90\) 0 0
\(91\) 19511.4i 0.246993i
\(92\) −78422.3 + 59205.1i −0.965984 + 0.729273i
\(93\) 0 0
\(94\) 34666.3 + 103453.i 0.404658 + 1.20761i
\(95\) −91971.6 −1.04555
\(96\) 0 0
\(97\) −182666. −1.97119 −0.985594 0.169129i \(-0.945905\pi\)
−0.985594 + 0.169129i \(0.945905\pi\)
\(98\) 28747.0 + 85788.6i 0.302362 + 0.902328i
\(99\) 0 0
\(100\) −28157.6 + 21257.6i −0.281576 + 0.212576i
\(101\) 13318.9i 0.129916i 0.997888 + 0.0649582i \(0.0206914\pi\)
−0.997888 + 0.0649582i \(0.979309\pi\)
\(102\) 0 0
\(103\) 173353.i 1.61005i 0.593242 + 0.805024i \(0.297848\pi\)
−0.593242 + 0.805024i \(0.702152\pi\)
\(104\) −102192. 70033.7i −0.926476 0.634927i
\(105\) 0 0
\(106\) −61148.8 + 20490.4i −0.528595 + 0.177128i
\(107\) 167439. 1.41383 0.706916 0.707298i \(-0.250086\pi\)
0.706916 + 0.707298i \(0.250086\pi\)
\(108\) 0 0
\(109\) 23854.1 0.192308 0.0961539 0.995366i \(-0.469346\pi\)
0.0961539 + 0.995366i \(0.469346\pi\)
\(110\) 99358.5 33294.2i 0.782931 0.262353i
\(111\) 0 0
\(112\) −28077.1 7996.80i −0.211498 0.0602381i
\(113\) 257760.i 1.89897i 0.313807 + 0.949487i \(0.398395\pi\)
−0.313807 + 0.949487i \(0.601605\pi\)
\(114\) 0 0
\(115\) 138094.i 0.973711i
\(116\) −12409.1 16436.9i −0.0856238 0.113416i
\(117\) 0 0
\(118\) −762.781 2276.34i −0.00504307 0.0150498i
\(119\) 43247.9 0.279961
\(120\) 0 0
\(121\) 8614.52 0.0534894
\(122\) −12415.8 37051.9i −0.0755221 0.225378i
\(123\) 0 0
\(124\) −14094.9 18669.9i −0.0823204 0.109040i
\(125\) 190120.i 1.08831i
\(126\) 0 0
\(127\) 172491.i 0.948978i 0.880261 + 0.474489i \(0.157367\pi\)
−0.880261 + 0.474489i \(0.842633\pi\)
\(128\) −142663. + 118352.i −0.769636 + 0.638483i
\(129\) 0 0
\(130\) 165085. 55318.6i 0.856742 0.287087i
\(131\) 50777.3 0.258518 0.129259 0.991611i \(-0.458740\pi\)
0.129259 + 0.991611i \(0.458740\pi\)
\(132\) 0 0
\(133\) −58304.3 −0.285806
\(134\) 314282. 105313.i 1.51202 0.506664i
\(135\) 0 0
\(136\) 155233. 226514.i 0.719675 1.05014i
\(137\) 57768.8i 0.262961i −0.991319 0.131481i \(-0.958027\pi\)
0.991319 0.131481i \(-0.0419731\pi\)
\(138\) 0 0
\(139\) 84989.7i 0.373103i 0.982445 + 0.186552i \(0.0597312\pi\)
−0.982445 + 0.186552i \(0.940269\pi\)
\(140\) 32744.4 24720.5i 0.141194 0.106595i
\(141\) 0 0
\(142\) −88308.6 263536.i −0.367521 1.09678i
\(143\) 281901. 1.15281
\(144\) 0 0
\(145\) 28943.7 0.114323
\(146\) 126174. + 376538.i 0.489879 + 1.46193i
\(147\) 0 0
\(148\) 139492. 105310.i 0.523475 0.395199i
\(149\) 492003.i 1.81552i 0.419487 + 0.907761i \(0.362210\pi\)
−0.419487 + 0.907761i \(0.637790\pi\)
\(150\) 0 0
\(151\) 368120.i 1.31385i 0.753954 + 0.656927i \(0.228144\pi\)
−0.753954 + 0.656927i \(0.771856\pi\)
\(152\) −209276. + 305372.i −0.734699 + 1.07206i
\(153\) 0 0
\(154\) 62987.2 21106.4i 0.214018 0.0717155i
\(155\) 32875.8 0.109913
\(156\) 0 0
\(157\) 82795.9 0.268077 0.134039 0.990976i \(-0.457205\pi\)
0.134039 + 0.990976i \(0.457205\pi\)
\(158\) 510753. 171149.i 1.62768 0.545420i
\(159\) 0 0
\(160\) −11943.2 260231.i −0.0368826 0.803636i
\(161\) 87543.0i 0.266169i
\(162\) 0 0
\(163\) 191541.i 0.564668i 0.959316 + 0.282334i \(0.0911086\pi\)
−0.959316 + 0.282334i \(0.908891\pi\)
\(164\) −123062. 163007.i −0.357286 0.473256i
\(165\) 0 0
\(166\) −100394. 299601.i −0.282771 0.843864i
\(167\) −318616. −0.884048 −0.442024 0.897003i \(-0.645739\pi\)
−0.442024 + 0.897003i \(0.645739\pi\)
\(168\) 0 0
\(169\) 97089.3 0.261490
\(170\) 122616. + 365919.i 0.325406 + 0.971098i
\(171\) 0 0
\(172\) 345267. + 457335.i 0.889884 + 1.17873i
\(173\) 87741.7i 0.222890i −0.993771 0.111445i \(-0.964452\pi\)
0.993771 0.111445i \(-0.0355479\pi\)
\(174\) 0 0
\(175\) 31432.4i 0.0775858i
\(176\) 115538. 405658.i 0.281153 0.987138i
\(177\) 0 0
\(178\) 503015. 168556.i 1.18996 0.398744i
\(179\) −197646. −0.461057 −0.230528 0.973066i \(-0.574045\pi\)
−0.230528 + 0.973066i \(0.574045\pi\)
\(180\) 0 0
\(181\) −638617. −1.44892 −0.724459 0.689318i \(-0.757910\pi\)
−0.724459 + 0.689318i \(0.757910\pi\)
\(182\) 104654. 35068.6i 0.234195 0.0784766i
\(183\) 0 0
\(184\) −458512. 314224.i −0.998403 0.684219i
\(185\) 245632.i 0.527662i
\(186\) 0 0
\(187\) 624847.i 1.30668i
\(188\) −492589. + 371881.i −1.01646 + 0.767379i
\(189\) 0 0
\(190\) −165304. 493311.i −0.332200 0.991371i
\(191\) 280543. 0.556438 0.278219 0.960518i \(-0.410256\pi\)
0.278219 + 0.960518i \(0.410256\pi\)
\(192\) 0 0
\(193\) −366016. −0.707305 −0.353652 0.935377i \(-0.615060\pi\)
−0.353652 + 0.935377i \(0.615060\pi\)
\(194\) −328312. 979770.i −0.626300 1.86905i
\(195\) 0 0
\(196\) −408479. + 308382.i −0.759502 + 0.573389i
\(197\) 876478.i 1.60907i −0.593904 0.804536i \(-0.702414\pi\)
0.593904 0.804536i \(-0.297586\pi\)
\(198\) 0 0
\(199\) 146658.i 0.262527i 0.991348 + 0.131263i \(0.0419034\pi\)
−0.991348 + 0.131263i \(0.958097\pi\)
\(200\) −164629. 112822.i −0.291025 0.199444i
\(201\) 0 0
\(202\) −71438.8 + 23938.5i −0.123184 + 0.0412780i
\(203\) 18348.5 0.0312508
\(204\) 0 0
\(205\) 287039. 0.477041
\(206\) −929820. + 311574.i −1.52662 + 0.511556i
\(207\) 0 0
\(208\) 191968. 674005.i 0.307659 1.08020i
\(209\) 842382.i 1.33396i
\(210\) 0 0
\(211\) 616213.i 0.952850i 0.879215 + 0.476425i \(0.158068\pi\)
−0.879215 + 0.476425i \(0.841932\pi\)
\(212\) −219810. 291157.i −0.335898 0.444926i
\(213\) 0 0
\(214\) 300945. + 898099.i 0.449213 + 1.34057i
\(215\) −805322. −1.18816
\(216\) 0 0
\(217\) 20841.3 0.0300452
\(218\) 42873.9 + 127947.i 0.0611014 + 0.182343i
\(219\) 0 0
\(220\) 357162. + 473091.i 0.497517 + 0.659004i
\(221\) 1.03819e6i 1.42987i
\(222\) 0 0
\(223\) 541567.i 0.729273i −0.931150 0.364636i \(-0.881193\pi\)
0.931150 0.364636i \(-0.118807\pi\)
\(224\) −7571.26 164971.i −0.0100820 0.219678i
\(225\) 0 0
\(226\) −1.38255e6 + 463281.i −1.80057 + 0.603356i
\(227\) 164616. 0.212035 0.106017 0.994364i \(-0.466190\pi\)
0.106017 + 0.994364i \(0.466190\pi\)
\(228\) 0 0
\(229\) −624301. −0.786693 −0.393346 0.919390i \(-0.628683\pi\)
−0.393346 + 0.919390i \(0.628683\pi\)
\(230\) 740698. 248201.i 0.923255 0.309375i
\(231\) 0 0
\(232\) 65859.7 96101.6i 0.0803341 0.117222i
\(233\) 400393.i 0.483166i 0.970380 + 0.241583i \(0.0776666\pi\)
−0.970380 + 0.241583i \(0.922333\pi\)
\(234\) 0 0
\(235\) 867400.i 1.02459i
\(236\) 10838.7 8182.70i 0.0126677 0.00956350i
\(237\) 0 0
\(238\) 77731.2 + 231970.i 0.0889514 + 0.265454i
\(239\) −1.04899e6 −1.18789 −0.593945 0.804505i \(-0.702430\pi\)
−0.593945 + 0.804505i \(0.702430\pi\)
\(240\) 0 0
\(241\) 937726. 1.04000 0.520000 0.854166i \(-0.325932\pi\)
0.520000 + 0.854166i \(0.325932\pi\)
\(242\) 15483.2 + 46206.0i 0.0169951 + 0.0507177i
\(243\) 0 0
\(244\) 176421. 133190.i 0.189704 0.143217i
\(245\) 719291.i 0.765578i
\(246\) 0 0
\(247\) 1.39963e6i 1.45972i
\(248\) 74806.9 109157.i 0.0772347 0.112700i
\(249\) 0 0
\(250\) 1.01975e6 341710.i 1.03192 0.345786i
\(251\) 998062. 0.999938 0.499969 0.866043i \(-0.333345\pi\)
0.499969 + 0.866043i \(0.333345\pi\)
\(252\) 0 0
\(253\) 1.26482e6 1.24231
\(254\) −925193. + 310024.i −0.899804 + 0.301516i
\(255\) 0 0
\(256\) −891219. 552485.i −0.849933 0.526891i
\(257\) 428916.i 0.405079i 0.979274 + 0.202539i \(0.0649194\pi\)
−0.979274 + 0.202539i \(0.935081\pi\)
\(258\) 0 0
\(259\) 155716.i 0.144239i
\(260\) 593428. + 786047.i 0.544421 + 0.721132i
\(261\) 0 0
\(262\) 91264.0 + 272356.i 0.0821384 + 0.245122i
\(263\) −769512. −0.686003 −0.343001 0.939335i \(-0.611444\pi\)
−0.343001 + 0.939335i \(0.611444\pi\)
\(264\) 0 0
\(265\) 512699. 0.448485
\(266\) −104793. 312728.i −0.0908084 0.270996i
\(267\) 0 0
\(268\) 1.12974e6 + 1.49644e6i 0.960820 + 1.27269i
\(269\) 1.64167e6i 1.38326i −0.722251 0.691631i \(-0.756892\pi\)
0.722251 0.691631i \(-0.243108\pi\)
\(270\) 0 0
\(271\) 1.16025e6i 0.959680i −0.877356 0.479840i \(-0.840695\pi\)
0.877356 0.479840i \(-0.159305\pi\)
\(272\) 1.49396e6 + 425505.i 1.22438 + 0.348725i
\(273\) 0 0
\(274\) 309856. 103830.i 0.249335 0.0835500i
\(275\) 454135. 0.362121
\(276\) 0 0
\(277\) 422037. 0.330484 0.165242 0.986253i \(-0.447159\pi\)
0.165242 + 0.986253i \(0.447159\pi\)
\(278\) −455862. + 152755.i −0.353770 + 0.118545i
\(279\) 0 0
\(280\) 191447. + 131201.i 0.145933 + 0.100010i
\(281\) 545437.i 0.412077i 0.978544 + 0.206039i \(0.0660573\pi\)
−0.978544 + 0.206039i \(0.933943\pi\)
\(282\) 0 0
\(283\) 2.52288e6i 1.87253i −0.351289 0.936267i \(-0.614256\pi\)
0.351289 0.936267i \(-0.385744\pi\)
\(284\) 1.25482e6 947327.i 0.923175 0.696954i
\(285\) 0 0
\(286\) 506672. + 1.51204e6i 0.366279 + 1.09307i
\(287\) 181965. 0.130402
\(288\) 0 0
\(289\) −881340. −0.620725
\(290\) 52021.7 + 155246.i 0.0363236 + 0.108399i
\(291\) 0 0
\(292\) −1.79287e6 + 1.35353e6i −1.23053 + 0.928990i
\(293\) 1.91422e6i 1.30263i 0.758806 + 0.651317i \(0.225783\pi\)
−0.758806 + 0.651317i \(0.774217\pi\)
\(294\) 0 0
\(295\) 19085.9i 0.0127690i
\(296\) 815569. + 558921.i 0.541043 + 0.370784i
\(297\) 0 0
\(298\) −2.63897e6 + 884295.i −1.72145 + 0.576841i
\(299\) 2.10152e6 1.35942
\(300\) 0 0
\(301\) −510525. −0.324788
\(302\) −1.97449e6 + 661636.i −1.24577 + 0.417447i
\(303\) 0 0
\(304\) −2.01407e6 573641.i −1.24995 0.356005i
\(305\) 310660.i 0.191221i
\(306\) 0 0
\(307\) 759821.i 0.460114i 0.973177 + 0.230057i \(0.0738913\pi\)
−0.973177 + 0.230057i \(0.926109\pi\)
\(308\) 226418. + 299911.i 0.135999 + 0.180142i
\(309\) 0 0
\(310\) 59089.0 + 176337.i 0.0349223 + 0.104217i
\(311\) 1.14702e6 0.672464 0.336232 0.941779i \(-0.390847\pi\)
0.336232 + 0.941779i \(0.390847\pi\)
\(312\) 0 0
\(313\) 358045. 0.206575 0.103287 0.994652i \(-0.467064\pi\)
0.103287 + 0.994652i \(0.467064\pi\)
\(314\) 148812. + 444095.i 0.0851754 + 0.254186i
\(315\) 0 0
\(316\) 1.83599e6 + 2.43193e6i 1.03432 + 1.37004i
\(317\) 2.80135e6i 1.56574i 0.622186 + 0.782870i \(0.286245\pi\)
−0.622186 + 0.782870i \(0.713755\pi\)
\(318\) 0 0
\(319\) 265100.i 0.145859i
\(320\) 1.37434e6 531784.i 0.750275 0.290309i
\(321\) 0 0
\(322\) 469557. 157344.i 0.252376 0.0845691i
\(323\) 3.10234e6 1.65456
\(324\) 0 0
\(325\) 754551. 0.396260
\(326\) −1.02737e6 + 344264.i −0.535408 + 0.179410i
\(327\) 0 0
\(328\) 653139. 953051.i 0.335213 0.489138i
\(329\) 549878.i 0.280077i
\(330\) 0 0
\(331\) 465048.i 0.233307i −0.993173 0.116654i \(-0.962783\pi\)
0.993173 0.116654i \(-0.0372167\pi\)
\(332\) 1.42653e6 1.07697e6i 0.710292 0.536237i
\(333\) 0 0
\(334\) −572660. 1.70897e6i −0.280886 0.838239i
\(335\) −2.63508e6 −1.28287
\(336\) 0 0
\(337\) −1.16600e6 −0.559274 −0.279637 0.960106i \(-0.590214\pi\)
−0.279637 + 0.960106i \(0.590214\pi\)
\(338\) 174502. + 520761.i 0.0830825 + 0.247940i
\(339\) 0 0
\(340\) −1.74231e6 + 1.31536e6i −0.817387 + 0.617089i
\(341\) 301115.i 0.140232i
\(342\) 0 0
\(343\) 935144.i 0.429184i
\(344\) −1.83246e6 + 2.67390e6i −0.834908 + 1.21829i
\(345\) 0 0
\(346\) 470623. 157702.i 0.211341 0.0708183i
\(347\) −1.11960e6 −0.499160 −0.249580 0.968354i \(-0.580293\pi\)
−0.249580 + 0.968354i \(0.580293\pi\)
\(348\) 0 0
\(349\) −514671. −0.226186 −0.113093 0.993584i \(-0.536076\pi\)
−0.113093 + 0.993584i \(0.536076\pi\)
\(350\) 168595. 56494.6i 0.0735654 0.0246511i
\(351\) 0 0
\(352\) 2.38350e6 109390.i 1.02532 0.0470565i
\(353\) 2.78955e6i 1.19151i −0.803167 0.595754i \(-0.796853\pi\)
0.803167 0.595754i \(-0.203147\pi\)
\(354\) 0 0
\(355\) 2.20961e6i 0.930559i
\(356\) 1.80818e6 + 2.39508e6i 0.756163 + 1.00160i
\(357\) 0 0
\(358\) −355236. 1.06012e6i −0.146490 0.437166i
\(359\) −1.28814e6 −0.527504 −0.263752 0.964590i \(-0.584960\pi\)
−0.263752 + 0.964590i \(0.584960\pi\)
\(360\) 0 0
\(361\) −1.70629e6 −0.689103
\(362\) −1.14781e6 3.42537e6i −0.460361 1.37384i
\(363\) 0 0
\(364\) 376197. + 498305.i 0.148820 + 0.197125i
\(365\) 3.15706e6i 1.24037i
\(366\) 0 0
\(367\) 1.88011e6i 0.728648i −0.931272 0.364324i \(-0.881300\pi\)
0.931272 0.364324i \(-0.118700\pi\)
\(368\) 861313. 3.02410e6i 0.331544 1.16406i
\(369\) 0 0
\(370\) −1.31750e6 + 441484.i −0.500320 + 0.167653i
\(371\) 325020. 0.122596
\(372\) 0 0
\(373\) 4.22175e6 1.57116 0.785580 0.618761i \(-0.212365\pi\)
0.785580 + 0.618761i \(0.212365\pi\)
\(374\) −3.35151e6 + 1.12306e6i −1.23897 + 0.415169i
\(375\) 0 0
\(376\) −2.88002e6 1.97372e6i −1.05057 0.719971i
\(377\) 440467.i 0.159610i
\(378\) 0 0
\(379\) 770147.i 0.275407i 0.990473 + 0.137704i \(0.0439722\pi\)
−0.990473 + 0.137704i \(0.956028\pi\)
\(380\) 2.34888e6 1.77329e6i 0.834452 0.629972i
\(381\) 0 0
\(382\) 504231. + 1.50476e6i 0.176796 + 0.527604i
\(383\) −2.69430e6 −0.938532 −0.469266 0.883057i \(-0.655482\pi\)
−0.469266 + 0.883057i \(0.655482\pi\)
\(384\) 0 0
\(385\) −528113. −0.181583
\(386\) −657854. 1.96321e6i −0.224730 0.670654i
\(387\) 0 0
\(388\) 4.66513e6 3.52195e6i 1.57320 1.18769i
\(389\) 220210.i 0.0737843i 0.999319 + 0.0368922i \(0.0117458\pi\)
−0.999319 + 0.0368922i \(0.988254\pi\)
\(390\) 0 0
\(391\) 4.65811e6i 1.54088i
\(392\) −2.38825e6 1.63670e6i −0.784992 0.537965i
\(393\) 0 0
\(394\) 4.70119e6 1.57533e6i 1.52569 0.511246i
\(395\) −4.28239e6 −1.38100
\(396\) 0 0
\(397\) −2.28702e6 −0.728271 −0.364135 0.931346i \(-0.618635\pi\)
−0.364135 + 0.931346i \(0.618635\pi\)
\(398\) −786635. + 263594.i −0.248923 + 0.0834120i
\(399\) 0 0
\(400\) 309255. 1.08580e6i 0.0966421 0.339314i
\(401\) 640352.i 0.198865i −0.995044 0.0994324i \(-0.968297\pi\)
0.995044 0.0994324i \(-0.0317027\pi\)
\(402\) 0 0
\(403\) 500306.i 0.153452i
\(404\) −256799. 340153.i −0.0782781 0.103686i
\(405\) 0 0
\(406\) 32978.5 + 98416.6i 0.00992925 + 0.0296315i
\(407\) −2.24978e6 −0.673216
\(408\) 0 0
\(409\) 2.58655e6 0.764562 0.382281 0.924046i \(-0.375139\pi\)
0.382281 + 0.924046i \(0.375139\pi\)
\(410\) 515906. + 1.53960e6i 0.151569 + 0.452322i
\(411\) 0 0
\(412\) −3.34240e6 4.42730e6i −0.970097 1.28498i
\(413\) 12099.3i 0.00349047i
\(414\) 0 0
\(415\) 2.51199e6i 0.715974i
\(416\) 3.96021e6 181752.i 1.12198 0.0514928i
\(417\) 0 0
\(418\) 4.51831e6 1.51404e6i 1.26484 0.423836i
\(419\) 5.31201e6 1.47817 0.739084 0.673614i \(-0.235259\pi\)
0.739084 + 0.673614i \(0.235259\pi\)
\(420\) 0 0
\(421\) −5.16990e6 −1.42160 −0.710799 0.703395i \(-0.751666\pi\)
−0.710799 + 0.703395i \(0.751666\pi\)
\(422\) −3.30520e6 + 1.10754e6i −0.903476 + 0.302747i
\(423\) 0 0
\(424\) 1.16662e6 1.70231e6i 0.315147 0.459858i
\(425\) 1.67250e6i 0.449152i
\(426\) 0 0
\(427\) 196939.i 0.0522712i
\(428\) −4.27626e6 + 3.22837e6i −1.12838 + 0.851872i
\(429\) 0 0
\(430\) −1.44744e6 4.31953e6i −0.377510 1.12659i
\(431\) −2.70546e6 −0.701534 −0.350767 0.936463i \(-0.614079\pi\)
−0.350767 + 0.936463i \(0.614079\pi\)
\(432\) 0 0
\(433\) 6.62153e6 1.69722 0.848611 0.529018i \(-0.177439\pi\)
0.848611 + 0.529018i \(0.177439\pi\)
\(434\) 37458.8 + 111787.i 0.00954617 + 0.0284883i
\(435\) 0 0
\(436\) −609213. + 459927.i −0.153481 + 0.115871i
\(437\) 6.27979e6i 1.57305i
\(438\) 0 0
\(439\) 4.18212e6i 1.03570i 0.855470 + 0.517852i \(0.173268\pi\)
−0.855470 + 0.517852i \(0.826732\pi\)
\(440\) −1.89559e6 + 2.76602e6i −0.466781 + 0.681121i
\(441\) 0 0
\(442\) −5.56857e6 + 1.86598e6i −1.35578 + 0.454309i
\(443\) 5.45464e6 1.32056 0.660278 0.751021i \(-0.270438\pi\)
0.660278 + 0.751021i \(0.270438\pi\)
\(444\) 0 0
\(445\) −4.21751e6 −1.00961
\(446\) 2.90482e6 973379.i 0.691484 0.231710i
\(447\) 0 0
\(448\) 871249. 337118.i 0.205091 0.0793573i
\(449\) 6.49269e6i 1.51988i 0.649994 + 0.759939i \(0.274771\pi\)
−0.649994 + 0.759939i \(0.725229\pi\)
\(450\) 0 0
\(451\) 2.62903e6i 0.608631i
\(452\) −4.96983e6 6.58296e6i −1.14418 1.51557i
\(453\) 0 0
\(454\) 295870. + 882955.i 0.0673693 + 0.201048i
\(455\) −877466. −0.198702
\(456\) 0 0
\(457\) −5.42147e6 −1.21430 −0.607151 0.794586i \(-0.707688\pi\)
−0.607151 + 0.794586i \(0.707688\pi\)
\(458\) −1.12208e6 3.34858e6i −0.249954 0.745928i
\(459\) 0 0
\(460\) 2.66257e6 + 3.52680e6i 0.586687 + 0.777117i
\(461\) 585086.i 0.128223i 0.997943 + 0.0641117i \(0.0204214\pi\)
−0.997943 + 0.0641117i \(0.979579\pi\)
\(462\) 0 0
\(463\) 2.73814e6i 0.593613i 0.954938 + 0.296806i \(0.0959216\pi\)
−0.954938 + 0.296806i \(0.904078\pi\)
\(464\) 633835. + 180527.i 0.136673 + 0.0389266i
\(465\) 0 0
\(466\) −2.14760e6 + 719641.i −0.458129 + 0.153515i
\(467\) 3.07143e6 0.651701 0.325850 0.945421i \(-0.394349\pi\)
0.325850 + 0.945421i \(0.394349\pi\)
\(468\) 0 0
\(469\) −1.67048e6 −0.350679
\(470\) 4.65250e6 1.55901e6i 0.971498 0.325540i
\(471\) 0 0
\(472\) 63370.6 + 43428.7i 0.0130928 + 0.00897267i
\(473\) 7.37607e6i 1.51591i
\(474\) 0 0
\(475\) 2.25476e6i 0.458529i
\(476\) −1.10452e6 + 833858.i −0.223437 + 0.168684i
\(477\) 0 0
\(478\) −1.88539e6 5.62649e6i −0.377425 1.12634i
\(479\) −6.67442e6 −1.32915 −0.664576 0.747221i \(-0.731388\pi\)
−0.664576 + 0.747221i \(0.731388\pi\)
\(480\) 0 0
\(481\) −3.73804e6 −0.736684
\(482\) 1.68541e6 + 5.02971e6i 0.330437 + 0.986110i
\(483\) 0 0
\(484\) −220008. + 166095.i −0.0426898 + 0.0322288i
\(485\) 8.21484e6i 1.58579i
\(486\) 0 0
\(487\) 9.75720e6i 1.86425i 0.362143 + 0.932123i \(0.382045\pi\)
−0.362143 + 0.932123i \(0.617955\pi\)
\(488\) 1.03148e6 + 706888.i 0.196070 + 0.134370i
\(489\) 0 0
\(490\) 3.85808e6 1.29281e6i 0.725907 0.243245i
\(491\) 9.36580e6 1.75324 0.876619 0.481185i \(-0.159793\pi\)
0.876619 + 0.481185i \(0.159793\pi\)
\(492\) 0 0
\(493\) −976315. −0.180914
\(494\) 7.50722e6 2.51560e6i 1.38408 0.463793i
\(495\) 0 0
\(496\) 719943. + 205052.i 0.131400 + 0.0374248i
\(497\) 1.40075e6i 0.254373i
\(498\) 0 0
\(499\) 3930.38i 0.000706615i −1.00000 0.000353307i \(-0.999888\pi\)
1.00000 0.000353307i \(-0.000112461\pi\)
\(500\) 3.66568e6 + 4.85550e6i 0.655736 + 0.868579i
\(501\) 0 0
\(502\) 1.79385e6 + 5.35333e6i 0.317708 + 0.948123i
\(503\) −8.81634e6 −1.55371 −0.776853 0.629683i \(-0.783185\pi\)
−0.776853 + 0.629683i \(0.783185\pi\)
\(504\) 0 0
\(505\) 598975. 0.104515
\(506\) 2.27331e6 + 6.78417e6i 0.394715 + 1.17793i
\(507\) 0 0
\(508\) −3.32577e6 4.40527e6i −0.571785 0.757378i
\(509\) 1.95674e6i 0.334764i −0.985892 0.167382i \(-0.946469\pi\)
0.985892 0.167382i \(-0.0535313\pi\)
\(510\) 0 0
\(511\) 2.00138e6i 0.339061i
\(512\) 1.36156e6 5.77326e6i 0.229542 0.973299i
\(513\) 0 0
\(514\) −2.30059e6 + 770907.i −0.384089 + 0.128705i
\(515\) 7.79603e6 1.29526
\(516\) 0 0
\(517\) 7.94465e6 1.30722
\(518\) −835216. + 279873.i −0.136765 + 0.0458287i
\(519\) 0 0
\(520\) −3.14955e6 + 4.59578e6i −0.510787 + 0.745334i
\(521\) 3.57120e6i 0.576394i 0.957571 + 0.288197i \(0.0930558\pi\)
−0.957571 + 0.288197i \(0.906944\pi\)
\(522\) 0 0
\(523\) 7.38907e6i 1.18123i −0.806953 0.590616i \(-0.798885\pi\)
0.806953 0.590616i \(-0.201115\pi\)
\(524\) −1.29681e6 + 979030.i −0.206323 + 0.155764i
\(525\) 0 0
\(526\) −1.38307e6 4.12745e6i −0.217962 0.650456i
\(527\) −1.10895e6 −0.173934
\(528\) 0 0
\(529\) 2.99266e6 0.464963
\(530\) 921494. + 2.74998e6i 0.142496 + 0.425246i
\(531\) 0 0
\(532\) 1.48904e6 1.12416e6i 0.228101 0.172206i
\(533\) 4.36817e6i 0.666011i
\(534\) 0 0
\(535\) 7.53007e6i 1.13740i
\(536\) −5.99597e6 + 8.74923e6i −0.901462 + 1.31540i
\(537\) 0 0
\(538\) 8.80546e6 2.95063e6i 1.31158 0.439500i
\(539\) 6.58809e6 0.976760
\(540\) 0 0
\(541\) 2.71204e6 0.398385 0.199192 0.979960i \(-0.436168\pi\)
0.199192 + 0.979960i \(0.436168\pi\)
\(542\) 6.22324e6 2.08535e6i 0.909952 0.304917i
\(543\) 0 0
\(544\) 402862. + 8.77799e6i 0.0583659 + 1.27174i
\(545\) 1.07276e6i 0.154708i
\(546\) 0 0
\(547\) 6.90947e6i 0.987362i −0.869643 0.493681i \(-0.835651\pi\)
0.869643 0.493681i \(-0.164349\pi\)
\(548\) 1.11383e6 + 1.47537e6i 0.158441 + 0.209869i
\(549\) 0 0
\(550\) 816235. + 2.43586e6i 0.115056 + 0.343357i
\(551\) 1.31621e6 0.184691
\(552\) 0 0
\(553\) −2.71477e6 −0.377503
\(554\) 758542. + 2.26369e6i 0.105004 + 0.313359i
\(555\) 0 0
\(556\) −1.63867e6 2.17057e6i −0.224805 0.297773i
\(557\) 2.31133e6i 0.315664i −0.987466 0.157832i \(-0.949550\pi\)
0.987466 0.157832i \(-0.0504504\pi\)
\(558\) 0 0
\(559\) 1.22554e7i 1.65882i
\(560\) −359632. + 1.26268e6i −0.0484605 + 0.170146i
\(561\) 0 0
\(562\) −2.92558e6 + 980335.i −0.390724 + 0.130928i
\(563\) 579007. 0.0769862 0.0384931 0.999259i \(-0.487744\pi\)
0.0384931 + 0.999259i \(0.487744\pi\)
\(564\) 0 0
\(565\) 1.15920e7 1.52769
\(566\) 1.35320e7 4.53446e6i 1.77550 0.594955i
\(567\) 0 0
\(568\) 7.33653e6 + 5.02782e6i 0.954157 + 0.653897i
\(569\) 4.15072e6i 0.537456i 0.963216 + 0.268728i \(0.0866033\pi\)
−0.963216 + 0.268728i \(0.913397\pi\)
\(570\) 0 0
\(571\) 4.30846e6i 0.553009i 0.961013 + 0.276504i \(0.0891760\pi\)
−0.961013 + 0.276504i \(0.910824\pi\)
\(572\) −7.19952e6 + 5.43530e6i −0.920054 + 0.694598i
\(573\) 0 0
\(574\) 327052. + 976010.i 0.0414322 + 0.123644i
\(575\) 3.38549e6 0.427024
\(576\) 0 0
\(577\) 1.61480e6 0.201921 0.100960 0.994890i \(-0.467809\pi\)
0.100960 + 0.994890i \(0.467809\pi\)
\(578\) −1.58407e6 4.72727e6i −0.197221 0.588560i
\(579\) 0 0
\(580\) −739199. + 558060.i −0.0912413 + 0.0688829i
\(581\) 1.59245e6i 0.195715i
\(582\) 0 0
\(583\) 4.69589e6i 0.572198i
\(584\) −1.04824e7 7.18370e6i −1.27182 0.871598i
\(585\) 0 0
\(586\) −1.02673e7 + 3.44050e6i −1.23513 + 0.413882i
\(587\) −9.37987e6 −1.12357 −0.561787 0.827282i \(-0.689886\pi\)
−0.561787 + 0.827282i \(0.689886\pi\)
\(588\) 0 0
\(589\) 1.49502e6 0.177566
\(590\) −102371. + 34303.7i −0.0121073 + 0.00405706i
\(591\) 0 0
\(592\) −1.53204e6 + 5.37906e6i −0.179667 + 0.630815i
\(593\) 4.50800e6i 0.526438i −0.964736 0.263219i \(-0.915216\pi\)
0.964736 0.263219i \(-0.0847842\pi\)
\(594\) 0 0
\(595\) 1.94494e6i 0.225224i
\(596\) −9.48623e6 1.25653e7i −1.09390 1.44897i
\(597\) 0 0
\(598\) 3.77714e6 + 1.12720e7i 0.431927 + 1.28898i
\(599\) −1.18281e7 −1.34694 −0.673469 0.739215i \(-0.735197\pi\)
−0.673469 + 0.739215i \(0.735197\pi\)
\(600\) 0 0
\(601\) 501339. 0.0566168 0.0283084 0.999599i \(-0.490988\pi\)
0.0283084 + 0.999599i \(0.490988\pi\)
\(602\) −917585. 2.73832e6i −0.103194 0.307958i
\(603\) 0 0
\(604\) −7.09767e6 9.40147e6i −0.791632 1.04858i
\(605\) 387412.i 0.0430313i
\(606\) 0 0
\(607\) 1.52223e7i 1.67691i −0.544972 0.838454i \(-0.683460\pi\)
0.544972 0.838454i \(-0.316540\pi\)
\(608\) −543115. 1.18340e7i −0.0595844 1.29829i
\(609\) 0 0
\(610\) −1.66630e6 + 558361.i −0.181312 + 0.0607562i
\(611\) 1.32001e7 1.43046
\(612\) 0 0
\(613\) −1.50361e7 −1.61616 −0.808080 0.589073i \(-0.799493\pi\)
−0.808080 + 0.589073i \(0.799493\pi\)
\(614\) −4.07547e6 + 1.36566e6i −0.436272 + 0.146191i
\(615\) 0 0
\(616\) −1.20169e6 + 1.75349e6i −0.127597 + 0.186188i
\(617\) 1.04780e7i 1.10807i −0.832495 0.554033i \(-0.813088\pi\)
0.832495 0.554033i \(-0.186912\pi\)
\(618\) 0 0
\(619\) 5.04678e6i 0.529404i 0.964330 + 0.264702i \(0.0852737\pi\)
−0.964330 + 0.264702i \(0.914726\pi\)
\(620\) −839621. + 633875.i −0.0877211 + 0.0662253i
\(621\) 0 0
\(622\) 2.06158e6 + 6.15229e6i 0.213660 + 0.637618i
\(623\) −2.67364e6 −0.275983
\(624\) 0 0
\(625\) −5.10467e6 −0.522718
\(626\) 643528. + 1.92046e6i 0.0656344 + 0.195870i
\(627\) 0 0
\(628\) −2.11454e6 + 1.59638e6i −0.213952 + 0.161524i
\(629\) 8.28553e6i 0.835014i
\(630\) 0 0
\(631\) 1.24449e7i 1.24428i −0.782907 0.622139i \(-0.786264\pi\)
0.782907 0.622139i \(-0.213736\pi\)
\(632\) −9.74431e6 + 1.42188e7i −0.970417 + 1.41602i
\(633\) 0 0
\(634\) −1.50257e7 + 5.03497e6i −1.48461 + 0.497478i
\(635\) 7.75724e6 0.763436
\(636\) 0 0
\(637\) 1.09462e7 1.06884
\(638\) −1.42193e6 + 476474.i −0.138301 + 0.0463434i
\(639\) 0 0
\(640\) 5.32250e6 + 6.41581e6i 0.513649 + 0.619158i
\(641\) 2.36665e6i 0.227504i 0.993509 + 0.113752i \(0.0362870\pi\)
−0.993509 + 0.113752i \(0.963713\pi\)
\(642\) 0 0
\(643\) 4.58591e6i 0.437419i −0.975790 0.218710i \(-0.929815\pi\)
0.975790 0.218710i \(-0.0701847\pi\)
\(644\) 1.68790e6 + 2.23577e6i 0.160374 + 0.212429i
\(645\) 0 0
\(646\) 5.57595e6 + 1.66401e7i 0.525699 + 1.56882i
\(647\) −1.96170e7 −1.84235 −0.921175 0.389149i \(-0.872769\pi\)
−0.921175 + 0.389149i \(0.872769\pi\)
\(648\) 0 0
\(649\) −174810. −0.0162913
\(650\) 1.35618e6 + 4.04721e6i 0.125903 + 0.375727i
\(651\) 0 0
\(652\) −3.69308e6 4.89180e6i −0.340227 0.450660i
\(653\) 1.11892e6i 0.102687i 0.998681 + 0.0513435i \(0.0163503\pi\)
−0.998681 + 0.0513435i \(0.983650\pi\)
\(654\) 0 0
\(655\) 2.28355e6i 0.207973i
\(656\) 6.28582e6 + 1.79030e6i 0.570299 + 0.162430i
\(657\) 0 0
\(658\) 2.94940e6 988317.i 0.265564 0.0889880i
\(659\) −1.42425e7 −1.27753 −0.638766 0.769401i \(-0.720555\pi\)
−0.638766 + 0.769401i \(0.720555\pi\)
\(660\) 0 0
\(661\) −1.50585e6 −0.134053 −0.0670267 0.997751i \(-0.521351\pi\)
−0.0670267 + 0.997751i \(0.521351\pi\)
\(662\) 2.49439e6 835849.i 0.221218 0.0741281i
\(663\) 0 0
\(664\) 8.34052e6 + 5.71587e6i 0.734130 + 0.503109i
\(665\) 2.62206e6i 0.229926i
\(666\) 0 0
\(667\) 1.97627e6i 0.172001i
\(668\) 8.13717e6 6.14318e6i 0.705558 0.532663i
\(669\) 0 0
\(670\) −4.73613e6 1.41339e7i −0.407603 1.21639i
\(671\) −2.84538e6 −0.243969
\(672\) 0 0
\(673\) 1.34440e7 1.14417 0.572084 0.820195i \(-0.306135\pi\)
0.572084 + 0.820195i \(0.306135\pi\)
\(674\) −2.09570e6 6.25412e6i −0.177697 0.530294i
\(675\) 0 0
\(676\) −2.47958e6 + 1.87197e6i −0.208695 + 0.157555i
\(677\) 1.49438e7i 1.25311i −0.779378 0.626554i \(-0.784465\pi\)
0.779378 0.626554i \(-0.215535\pi\)
\(678\) 0 0
\(679\) 5.20770e6i 0.433482i
\(680\) −1.01868e7 6.98112e6i −0.844819 0.578966i
\(681\) 0 0
\(682\) −1.61510e6 + 541205.i −0.132965 + 0.0445555i
\(683\) −3.84256e6 −0.315187 −0.157594 0.987504i \(-0.550374\pi\)
−0.157594 + 0.987504i \(0.550374\pi\)
\(684\) 0 0
\(685\) −2.59797e6 −0.211548
\(686\) 5.01586e6 1.68077e6i 0.406944 0.136363i
\(687\) 0 0
\(688\) −1.76356e7 5.02292e6i −1.42043 0.404562i
\(689\) 7.80228e6i 0.626143i
\(690\) 0 0
\(691\) 1.36756e7i 1.08956i 0.838578 + 0.544781i \(0.183387\pi\)
−0.838578 + 0.544781i \(0.816613\pi\)
\(692\) 1.69174e6 + 2.24085e6i 0.134297 + 0.177888i
\(693\) 0 0
\(694\) −2.01230e6 6.00523e6i −0.158597 0.473294i
\(695\) 3.82215e6 0.300155
\(696\) 0 0
\(697\) −9.68224e6 −0.754908
\(698\) −925038. 2.76056e6i −0.0718656 0.214466i
\(699\) 0 0
\(700\) 606043. + 802756.i 0.0467475 + 0.0619211i
\(701\) 1.32451e7i 1.01803i 0.860758 + 0.509015i \(0.169990\pi\)
−0.860758 + 0.509015i \(0.830010\pi\)
\(702\) 0 0
\(703\) 1.11701e7i 0.852447i
\(704\) 4.87069e6 + 1.25878e7i 0.370390 + 0.957236i
\(705\) 0 0
\(706\) 1.49624e7 5.01376e6i 1.12977 0.378575i
\(707\) 379713. 0.0285698
\(708\) 0 0
\(709\) −1.82356e7 −1.36240 −0.681200 0.732098i \(-0.738541\pi\)
−0.681200 + 0.732098i \(0.738541\pi\)
\(710\) −1.18517e7 + 3.97141e6i −0.882340 + 0.295664i
\(711\) 0 0
\(712\) −9.59668e6 + 1.40033e7i −0.709448 + 1.03522i
\(713\) 2.24475e6i 0.165365i
\(714\) 0 0
\(715\) 1.26776e7i 0.927414i
\(716\) 5.04770e6 3.81078e6i 0.367969 0.277799i
\(717\) 0 0
\(718\) −2.31522e6 6.90922e6i −0.167603 0.500170i
\(719\) 555013. 0.0400388 0.0200194 0.999800i \(-0.493627\pi\)
0.0200194 + 0.999800i \(0.493627\pi\)
\(720\) 0 0
\(721\) 4.94220e6 0.354064
\(722\) −3.06678e6 9.15206e6i −0.218947 0.653395i
\(723\) 0 0
\(724\) 1.63097e7 1.23131e7i 1.15638 0.873012i
\(725\) 709581.i 0.0501368i
\(726\) 0 0
\(727\) 1.12242e7i 0.787625i −0.919191 0.393813i \(-0.871156\pi\)
0.919191 0.393813i \(-0.128844\pi\)
\(728\) −1.99662e6 + 2.91344e6i −0.139626 + 0.203741i
\(729\) 0 0
\(730\) 1.69336e7 5.67431e6i 1.17610 0.394099i
\(731\) 2.71647e7 1.88023
\(732\) 0 0
\(733\) 7.30346e6 0.502075 0.251038 0.967977i \(-0.419228\pi\)
0.251038 + 0.967977i \(0.419228\pi\)
\(734\) 1.00844e7 3.37919e6i 0.690891 0.231511i
\(735\) 0 0
\(736\) 1.77685e7 815479.i 1.20908 0.0554904i
\(737\) 2.41351e7i 1.63674i
\(738\) 0 0
\(739\) 1.03409e7i 0.696543i 0.937394 + 0.348271i \(0.113231\pi\)
−0.937394 + 0.348271i \(0.886769\pi\)
\(740\) −4.73600e6 6.27324e6i −0.317930 0.421126i
\(741\) 0 0
\(742\) 584170. + 1.74332e6i 0.0389520 + 0.116243i
\(743\) −1.25176e7 −0.831858 −0.415929 0.909397i \(-0.636543\pi\)
−0.415929 + 0.909397i \(0.636543\pi\)
\(744\) 0 0
\(745\) 2.21263e7 1.46056
\(746\) 7.58791e6 + 2.26443e7i 0.499200 + 1.48975i
\(747\) 0 0
\(748\) −1.20476e7 1.59581e7i −0.787311 1.04286i
\(749\) 4.77360e6i 0.310915i
\(750\) 0 0
\(751\) 1.04022e7i 0.673015i 0.941681 + 0.336508i \(0.109246\pi\)
−0.941681 + 0.336508i \(0.890754\pi\)
\(752\) 5.41011e6 1.89951e7i 0.348868 1.22489i
\(753\) 0 0
\(754\) −2.36255e6 + 791668.i −0.151339 + 0.0507125i
\(755\) 1.65551e7 1.05697
\(756\) 0 0
\(757\) 1.77986e7 1.12888 0.564438 0.825475i \(-0.309093\pi\)
0.564438 + 0.825475i \(0.309093\pi\)
\(758\) −4.13086e6 + 1.38421e6i −0.261136 + 0.0875045i
\(759\) 0 0
\(760\) 1.37332e7 + 9.41153e6i 0.862456 + 0.591053i
\(761\) 2.42339e7i 1.51691i 0.651723 + 0.758457i \(0.274047\pi\)
−0.651723 + 0.758457i \(0.725953\pi\)
\(762\) 0 0
\(763\) 680067.i 0.0422902i
\(764\) −7.16484e6 + 5.40912e6i −0.444092 + 0.335269i
\(765\) 0 0
\(766\) −4.84257e6 1.44515e7i −0.298197 0.889900i
\(767\) −290449. −0.0178272
\(768\) 0 0
\(769\) −1.26552e7 −0.771708 −0.385854 0.922560i \(-0.626093\pi\)
−0.385854 + 0.922560i \(0.626093\pi\)
\(770\) −949198. 2.83265e6i −0.0576939 0.172174i
\(771\) 0 0
\(772\) 9.34774e6 7.05710e6i 0.564499 0.426170i
\(773\) 9.16670e6i 0.551778i 0.961190 + 0.275889i \(0.0889722\pi\)
−0.961190 + 0.275889i \(0.911028\pi\)
\(774\) 0 0
\(775\) 805979.i 0.0482025i
\(776\) 2.72756e7 + 1.86924e7i 1.62600 + 1.11432i
\(777\) 0 0
\(778\) −1.18115e6 + 395793.i −0.0699610 + 0.0234433i
\(779\) 1.30530e7 0.770668
\(780\) 0 0
\(781\) −2.02381e7 −1.18725
\(782\) −2.49848e7 + 8.37220e6i −1.46103 + 0.489579i
\(783\) 0 0
\(784\) 4.48633e6 1.57516e7i 0.260676 0.915241i
\(785\) 3.72349e6i 0.215663i
\(786\) 0 0
\(787\) 8.49494e6i 0.488904i 0.969661 + 0.244452i \(0.0786080\pi\)
−0.969661 + 0.244452i \(0.921392\pi\)
\(788\)