Properties

Label 108.6.h.a.71.13
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 71.13
Character \(\chi\) \(=\) 108.71
Dual form 108.6.h.a.35.13

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.253656 - 5.65116i) q^{2} +(-31.8713 + 2.86690i) q^{4} +(-84.3255 - 48.6853i) q^{5} +(-87.9661 + 50.7872i) q^{7} +(24.2857 + 179.383i) q^{8} +O(q^{10})\) \(q+(-0.253656 - 5.65116i) q^{2} +(-31.8713 + 2.86690i) q^{4} +(-84.3255 - 48.6853i) q^{5} +(-87.9661 + 50.7872i) q^{7} +(24.2857 + 179.383i) q^{8} +(-253.739 + 488.886i) q^{10} +(73.2291 + 126.837i) q^{11} +(402.832 - 697.726i) q^{13} +(309.320 + 484.228i) q^{14} +(1007.56 - 182.744i) q^{16} -1238.37i q^{17} +2616.12i q^{19} +(2827.14 + 1309.91i) q^{20} +(698.199 - 446.002i) q^{22} +(-84.5912 + 146.516i) q^{23} +(3178.02 + 5504.50i) q^{25} +(-4045.15 - 2099.49i) q^{26} +(2657.99 - 1870.85i) q^{28} +(-1952.82 + 1127.46i) q^{29} +(1787.03 + 1031.74i) q^{31} +(-1288.29 - 5647.54i) q^{32} +(-6998.21 + 314.119i) q^{34} +9890.37 q^{35} +445.632 q^{37} +(14784.1 - 663.594i) q^{38} +(6685.41 - 16308.9i) q^{40} +(1720.61 + 993.393i) q^{41} +(3464.26 - 2000.09i) q^{43} +(-2697.54 - 3832.51i) q^{44} +(849.444 + 440.874i) q^{46} +(3539.24 + 6130.14i) q^{47} +(-3244.81 + 5620.18i) q^{49} +(30300.7 - 19355.8i) q^{50} +(-10838.5 + 23392.3i) q^{52} -6234.98i q^{53} -14260.7i q^{55} +(-11246.7 - 14546.2i) q^{56} +(6866.81 + 10749.7i) q^{58} +(-16724.9 + 28968.4i) q^{59} +(14717.5 + 25491.5i) q^{61} +(5377.25 - 10360.5i) q^{62} +(-31588.4 + 8712.87i) q^{64} +(-67938.0 + 39224.1i) q^{65} +(23308.8 + 13457.4i) q^{67} +(3550.28 + 39468.4i) q^{68} +(-2508.75 - 55892.1i) q^{70} -36309.5 q^{71} -38203.0 q^{73} +(-113.037 - 2518.34i) q^{74} +(-7500.15 - 83379.1i) q^{76} +(-12883.4 - 7438.21i) q^{77} +(54553.0 - 31496.2i) q^{79} +(-93860.1 - 33643.5i) q^{80} +(5177.38 - 9975.41i) q^{82} +(39957.8 + 69208.9i) q^{83} +(-60290.3 + 104426. i) q^{85} +(-12181.6 - 19069.8i) q^{86} +(-20973.9 + 16216.4i) q^{88} +96604.3i q^{89} +81835.0i q^{91} +(2275.98 - 4912.18i) q^{92} +(33744.7 - 21555.8i) q^{94} +(127367. - 220605. i) q^{95} +(-8318.60 - 14408.2i) q^{97} +(32583.6 + 16911.4i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56q + 3q^{2} - q^{4} + 6q^{5} + O(q^{10}) \) \( 56q + 3q^{2} - q^{4} + 6q^{5} - 68q^{10} - 2q^{13} + 1518q^{14} - q^{16} + 1242q^{20} + 63q^{22} + 12498q^{25} - 2052q^{28} + 11946q^{29} + 7233q^{32} + 6361q^{34} - 8q^{37} + 14877q^{38} - 1526q^{40} + 43536q^{41} - 26880q^{46} + 38414q^{49} - 38631q^{50} + 24988q^{52} - 21186q^{56} - 3314q^{58} - 2q^{61} - 106342q^{64} - 35970q^{65} - 31413q^{68} + 10524q^{70} + 53620q^{73} + 20406q^{74} + 26193q^{76} - 26178q^{77} - 151286q^{82} + 6248q^{85} - 279237q^{86} - 122541q^{88} - 435804q^{92} + 63480q^{94} - 58148q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.253656 5.65116i −0.0448405 0.998994i
\(3\) 0 0
\(4\) −31.8713 + 2.86690i −0.995979 + 0.0895907i
\(5\) −84.3255 48.6853i −1.50846 0.870910i −0.999951 0.00985262i \(-0.996864\pi\)
−0.508508 0.861057i \(-0.669803\pi\)
\(6\) 0 0
\(7\) −87.9661 + 50.7872i −0.678532 + 0.391750i −0.799302 0.600930i \(-0.794797\pi\)
0.120770 + 0.992681i \(0.461464\pi\)
\(8\) 24.2857 + 179.383i 0.134161 + 0.990960i
\(9\) 0 0
\(10\) −253.739 + 488.886i −0.802394 + 1.54599i
\(11\) 73.2291 + 126.837i 0.182474 + 0.316055i 0.942723 0.333578i \(-0.108256\pi\)
−0.760248 + 0.649633i \(0.774923\pi\)
\(12\) 0 0
\(13\) 402.832 697.726i 0.661098 1.14506i −0.319229 0.947678i \(-0.603424\pi\)
0.980327 0.197378i \(-0.0632427\pi\)
\(14\) 309.320 + 484.228i 0.421782 + 0.660283i
\(15\) 0 0
\(16\) 1007.56 182.744i 0.983947 0.178461i
\(17\) 1238.37i 1.03927i −0.854389 0.519633i \(-0.826069\pi\)
0.854389 0.519633i \(-0.173931\pi\)
\(18\) 0 0
\(19\) 2616.12i 1.66254i 0.555866 + 0.831272i \(0.312387\pi\)
−0.555866 + 0.831272i \(0.687613\pi\)
\(20\) 2827.14 + 1309.91i 1.58042 + 0.732263i
\(21\) 0 0
\(22\) 698.199 446.002i 0.307555 0.196463i
\(23\) −84.5912 + 146.516i −0.0333431 + 0.0577519i −0.882215 0.470846i \(-0.843949\pi\)
0.848872 + 0.528598i \(0.177282\pi\)
\(24\) 0 0
\(25\) 3178.02 + 5504.50i 1.01697 + 1.76144i
\(26\) −4045.15 2099.49i −1.17355 0.609088i
\(27\) 0 0
\(28\) 2657.99 1870.85i 0.640706 0.450965i
\(29\) −1952.82 + 1127.46i −0.431189 + 0.248947i −0.699853 0.714287i \(-0.746751\pi\)
0.268664 + 0.963234i \(0.413418\pi\)
\(30\) 0 0
\(31\) 1787.03 + 1031.74i 0.333985 + 0.192826i 0.657609 0.753359i \(-0.271568\pi\)
−0.323624 + 0.946186i \(0.604901\pi\)
\(32\) −1288.29 5647.54i −0.222402 0.974955i
\(33\) 0 0
\(34\) −6998.21 + 314.119i −1.03822 + 0.0466012i
\(35\) 9890.37 1.36472
\(36\) 0 0
\(37\) 445.632 0.0535146 0.0267573 0.999642i \(-0.491482\pi\)
0.0267573 + 0.999642i \(0.491482\pi\)
\(38\) 14784.1 663.594i 1.66087 0.0745492i
\(39\) 0 0
\(40\) 6685.41 16308.9i 0.660660 1.61166i
\(41\) 1720.61 + 993.393i 0.159853 + 0.0922914i 0.577793 0.816184i \(-0.303914\pi\)
−0.417939 + 0.908475i \(0.637248\pi\)
\(42\) 0 0
\(43\) 3464.26 2000.09i 0.285719 0.164960i −0.350291 0.936641i \(-0.613917\pi\)
0.636010 + 0.771681i \(0.280584\pi\)
\(44\) −2697.54 3832.51i −0.210056 0.298436i
\(45\) 0 0
\(46\) 849.444 + 440.874i 0.0591889 + 0.0307199i
\(47\) 3539.24 + 6130.14i 0.233703 + 0.404786i 0.958895 0.283761i \(-0.0915822\pi\)
−0.725192 + 0.688547i \(0.758249\pi\)
\(48\) 0 0
\(49\) −3244.81 + 5620.18i −0.193063 + 0.334395i
\(50\) 30300.7 19355.8i 1.71407 1.09493i
\(51\) 0 0
\(52\) −10838.5 + 23392.3i −0.555853 + 1.19968i
\(53\) 6234.98i 0.304891i −0.988312 0.152446i \(-0.951285\pi\)
0.988312 0.152446i \(-0.0487149\pi\)
\(54\) 0 0
\(55\) 14260.7i 0.635675i
\(56\) −11246.7 14546.2i −0.479241 0.619840i
\(57\) 0 0
\(58\) 6866.81 + 10749.7i 0.268031 + 0.419592i
\(59\) −16724.9 + 28968.4i −0.625509 + 1.08341i 0.362933 + 0.931815i \(0.381775\pi\)
−0.988442 + 0.151598i \(0.951558\pi\)
\(60\) 0 0
\(61\) 14717.5 + 25491.5i 0.506420 + 0.877145i 0.999972 + 0.00742891i \(0.00236472\pi\)
−0.493553 + 0.869716i \(0.664302\pi\)
\(62\) 5377.25 10360.5i 0.177656 0.342296i
\(63\) 0 0
\(64\) −31588.4 + 8712.87i −0.964002 + 0.265896i
\(65\) −67938.0 + 39224.1i −1.99448 + 1.15151i
\(66\) 0 0
\(67\) 23308.8 + 13457.4i 0.634357 + 0.366246i 0.782437 0.622729i \(-0.213976\pi\)
−0.148081 + 0.988975i \(0.547310\pi\)
\(68\) 3550.28 + 39468.4i 0.0931086 + 1.03509i
\(69\) 0 0
\(70\) −2508.75 55892.1i −0.0611945 1.36334i
\(71\) −36309.5 −0.854819 −0.427409 0.904058i \(-0.640574\pi\)
−0.427409 + 0.904058i \(0.640574\pi\)
\(72\) 0 0
\(73\) −38203.0 −0.839056 −0.419528 0.907742i \(-0.637804\pi\)
−0.419528 + 0.907742i \(0.637804\pi\)
\(74\) −113.037 2518.34i −0.00239962 0.0534608i
\(75\) 0 0
\(76\) −7500.15 83379.1i −0.148948 1.65586i
\(77\) −12883.4 7438.21i −0.247629 0.142969i
\(78\) 0 0
\(79\) 54553.0 31496.2i 0.983448 0.567794i 0.0801384 0.996784i \(-0.474464\pi\)
0.903309 + 0.428990i \(0.141130\pi\)
\(80\) −93860.1 33643.5i −1.63967 0.587728i
\(81\) 0 0
\(82\) 5177.38 9975.41i 0.0850307 0.163831i
\(83\) 39957.8 + 69208.9i 0.636658 + 1.10272i 0.986161 + 0.165789i \(0.0530170\pi\)
−0.349503 + 0.936935i \(0.613650\pi\)
\(84\) 0 0
\(85\) −60290.3 + 104426.i −0.905107 + 1.56769i
\(86\) −12181.6 19069.8i −0.177606 0.278035i
\(87\) 0 0
\(88\) −20973.9 + 16216.4i −0.288717 + 0.223227i
\(89\) 96604.3i 1.29277i 0.763011 + 0.646385i \(0.223720\pi\)
−0.763011 + 0.646385i \(0.776280\pi\)
\(90\) 0 0
\(91\) 81835.0i 1.03594i
\(92\) 2275.98 4912.18i 0.0280349 0.0605069i
\(93\) 0 0
\(94\) 33744.7 21555.8i 0.393900 0.251619i
\(95\) 127367. 220605.i 1.44793 2.50788i
\(96\) 0 0
\(97\) −8318.60 14408.2i −0.0897678 0.155482i 0.817645 0.575723i \(-0.195279\pi\)
−0.907413 + 0.420240i \(0.861946\pi\)
\(98\) 32583.6 + 16911.4i 0.342716 + 0.177875i
\(99\) 0 0
\(100\) −117069. 166324.i −1.17069 1.66324i
\(101\) −25178.9 + 14537.1i −0.245603 + 0.141799i −0.617749 0.786375i \(-0.711955\pi\)
0.372146 + 0.928174i \(0.378622\pi\)
\(102\) 0 0
\(103\) −132194. 76322.2i −1.22777 0.708855i −0.261210 0.965282i \(-0.584121\pi\)
−0.966564 + 0.256427i \(0.917455\pi\)
\(104\) 134943. + 55316.5i 1.22340 + 0.501500i
\(105\) 0 0
\(106\) −35234.9 + 1581.54i −0.304585 + 0.0136715i
\(107\) −160032. −1.35129 −0.675645 0.737227i \(-0.736135\pi\)
−0.675645 + 0.737227i \(0.736135\pi\)
\(108\) 0 0
\(109\) 136775. 1.10265 0.551327 0.834289i \(-0.314122\pi\)
0.551327 + 0.834289i \(0.314122\pi\)
\(110\) −80589.7 + 3617.32i −0.635035 + 0.0285039i
\(111\) 0 0
\(112\) −79350.2 + 67246.5i −0.597727 + 0.506553i
\(113\) −29144.4 16826.5i −0.214713 0.123965i 0.388787 0.921328i \(-0.372894\pi\)
−0.603500 + 0.797363i \(0.706228\pi\)
\(114\) 0 0
\(115\) 14266.4 8236.70i 0.100593 0.0580776i
\(116\) 59006.6 41532.2i 0.407151 0.286576i
\(117\) 0 0
\(118\) 167947. + 87167.2i 1.11037 + 0.576299i
\(119\) 62893.2 + 108934.i 0.407133 + 0.705175i
\(120\) 0 0
\(121\) 69800.5 120898.i 0.433406 0.750682i
\(122\) 140324. 89637.3i 0.853555 0.545242i
\(123\) 0 0
\(124\) −59912.8 27759.7i −0.349917 0.162129i
\(125\) 314609.i 1.80093i
\(126\) 0 0
\(127\) 7342.22i 0.0403941i 0.999796 + 0.0201971i \(0.00642936\pi\)
−0.999796 + 0.0201971i \(0.993571\pi\)
\(128\) 57250.4 + 176301.i 0.308855 + 0.951109i
\(129\) 0 0
\(130\) 238894. + 373980.i 1.23979 + 1.94084i
\(131\) −104864. + 181630.i −0.533886 + 0.924718i 0.465330 + 0.885137i \(0.345936\pi\)
−0.999216 + 0.0395811i \(0.987398\pi\)
\(132\) 0 0
\(133\) −132865. 230130.i −0.651302 1.12809i
\(134\) 70137.3 135136.i 0.337433 0.650141i
\(135\) 0 0
\(136\) 222142. 30074.6i 1.02987 0.139429i
\(137\) 221740. 128022.i 1.00935 0.582749i 0.0983495 0.995152i \(-0.468644\pi\)
0.911002 + 0.412403i \(0.135310\pi\)
\(138\) 0 0
\(139\) 31429.4 + 18145.7i 0.137974 + 0.0796595i 0.567398 0.823444i \(-0.307950\pi\)
−0.429424 + 0.903103i \(0.641283\pi\)
\(140\) −315219. + 28354.7i −1.35923 + 0.122266i
\(141\) 0 0
\(142\) 9210.11 + 205191.i 0.0383305 + 0.853959i
\(143\) 117996. 0.482534
\(144\) 0 0
\(145\) 219563. 0.867241
\(146\) 9690.43 + 215892.i 0.0376236 + 0.838212i
\(147\) 0 0
\(148\) −14202.9 + 1277.58i −0.0532994 + 0.00479441i
\(149\) 411222. + 237419.i 1.51744 + 0.876092i 0.999790 + 0.0204977i \(0.00652507\pi\)
0.517646 + 0.855595i \(0.326808\pi\)
\(150\) 0 0
\(151\) 103973. 60029.0i 0.371090 0.214249i −0.302844 0.953040i \(-0.597936\pi\)
0.673935 + 0.738791i \(0.264603\pi\)
\(152\) −469287. + 63534.2i −1.64751 + 0.223048i
\(153\) 0 0
\(154\) −38766.6 + 74692.7i −0.131721 + 0.253791i
\(155\) −100461. 174004.i −0.335869 0.581742i
\(156\) 0 0
\(157\) −111283. + 192748.i −0.360312 + 0.624079i −0.988012 0.154376i \(-0.950663\pi\)
0.627700 + 0.778456i \(0.283997\pi\)
\(158\) −191828. 300299.i −0.611321 0.956998i
\(159\) 0 0
\(160\) −166317. + 538953.i −0.513613 + 1.66437i
\(161\) 17184.6i 0.0522486i
\(162\) 0 0
\(163\) 489772.i 1.44386i 0.691967 + 0.721929i \(0.256745\pi\)
−0.691967 + 0.721929i \(0.743255\pi\)
\(164\) −57686.0 26727.9i −0.167479 0.0775989i
\(165\) 0 0
\(166\) 380975. 243363.i 1.07307 0.685464i
\(167\) −43035.4 + 74539.6i −0.119408 + 0.206822i −0.919533 0.393012i \(-0.871433\pi\)
0.800125 + 0.599833i \(0.204766\pi\)
\(168\) 0 0
\(169\) −138901. 240584.i −0.374102 0.647963i
\(170\) 605421. + 314222.i 1.60670 + 0.833901i
\(171\) 0 0
\(172\) −104676. + 73677.2i −0.269791 + 0.189894i
\(173\) 170126. 98222.4i 0.432171 0.249514i −0.268100 0.963391i \(-0.586396\pi\)
0.700271 + 0.713877i \(0.253062\pi\)
\(174\) 0 0
\(175\) −559116. 322806.i −1.38009 0.796795i
\(176\) 96961.4 + 114413.i 0.235949 + 0.278417i
\(177\) 0 0
\(178\) 545927. 24504.2i 1.29147 0.0579684i
\(179\) 348859. 0.813799 0.406900 0.913473i \(-0.366610\pi\)
0.406900 + 0.913473i \(0.366610\pi\)
\(180\) 0 0
\(181\) −35362.9 −0.0802326 −0.0401163 0.999195i \(-0.512773\pi\)
−0.0401163 + 0.999195i \(0.512773\pi\)
\(182\) 462463. 20757.9i 1.03490 0.0464521i
\(183\) 0 0
\(184\) −28336.8 11616.0i −0.0617031 0.0252936i
\(185\) −37578.1 21695.7i −0.0807246 0.0466064i
\(186\) 0 0
\(187\) 157070. 90684.5i 0.328465 0.189640i
\(188\) −130375. 185229.i −0.269029 0.382221i
\(189\) 0 0
\(190\) −1.27898e6 663811.i −2.57028 1.33401i
\(191\) −434850. 753182.i −0.862494 1.49388i −0.869514 0.493908i \(-0.835568\pi\)
0.00701997 0.999975i \(1.50223\pi\)
\(192\) 0 0
\(193\) 426577. 738854.i 0.824336 1.42779i −0.0780890 0.996946i \(-0.524882\pi\)
0.902425 0.430846i \(-0.141785\pi\)
\(194\) −79313.2 + 50664.5i −0.151301 + 0.0966495i
\(195\) 0 0
\(196\) 87303.9 188425.i 0.162328 0.350347i
\(197\) 259841.i 0.477026i −0.971139 0.238513i \(-0.923340\pi\)
0.971139 0.238513i \(-0.0766600\pi\)
\(198\) 0 0
\(199\) 264379.i 0.473255i 0.971600 + 0.236627i \(0.0760420\pi\)
−0.971600 + 0.236627i \(0.923958\pi\)
\(200\) −910232. + 703763.i −1.60908 + 1.24409i
\(201\) 0 0
\(202\) 88538.2 + 138603.i 0.152669 + 0.238998i
\(203\) 114521. 198357.i 0.195050 0.337837i
\(204\) 0 0
\(205\) −96727.3 167537.i −0.160755 0.278436i
\(206\) −397777. + 766409.i −0.653089 + 1.25832i
\(207\) 0 0
\(208\) 278373. 776617.i 0.446138 1.24465i
\(209\) −331819. + 191576.i −0.525455 + 0.303372i
\(210\) 0 0
\(211\) −889657. 513644.i −1.37568 0.794247i −0.384041 0.923316i \(-0.625468\pi\)
−0.991636 + 0.129069i \(0.958801\pi\)
\(212\) 17875.1 + 198717.i 0.0273154 + 0.303665i
\(213\) 0 0
\(214\) 40593.2 + 904369.i 0.0605924 + 1.34993i
\(215\) −389500. −0.574661
\(216\) 0 0
\(217\) −209597. −0.302159
\(218\) −34693.7 772936.i −0.0494435 1.10155i
\(219\) 0 0
\(220\) 40884.1 + 454508.i 0.0569506 + 0.633119i
\(221\) −864041. 498854.i −1.19002 0.687057i
\(222\) 0 0
\(223\) 524934. 303071.i 0.706875 0.408115i −0.103028 0.994678i \(-0.532853\pi\)
0.809903 + 0.586564i \(0.199520\pi\)
\(224\) 400149. + 431364.i 0.532846 + 0.574412i
\(225\) 0 0
\(226\) −87696.8 + 168968.i −0.114212 + 0.220056i
\(227\) 85552.8 + 148182.i 0.110197 + 0.190867i 0.915850 0.401522i \(-0.131519\pi\)
−0.805653 + 0.592388i \(0.798185\pi\)
\(228\) 0 0
\(229\) −689040. + 1.19345e6i −0.868271 + 1.50389i −0.00450932 + 0.999990i \(0.501435\pi\)
−0.863762 + 0.503900i \(0.831898\pi\)
\(230\) −50165.7 78532.4i −0.0625298 0.0978879i
\(231\) 0 0
\(232\) −249673. 322921.i −0.304545 0.393892i
\(233\) 1.36894e6i 1.65194i 0.563711 + 0.825972i \(0.309373\pi\)
−0.563711 + 0.825972i \(0.690627\pi\)
\(234\) 0 0
\(235\) 689236.i 0.814138i
\(236\) 449995. 971209.i 0.525930 1.13510i
\(237\) 0 0
\(238\) 599652. 383052.i 0.686210 0.438344i
\(239\) −155455. + 269255.i −0.176039 + 0.304908i −0.940520 0.339737i \(-0.889662\pi\)
0.764481 + 0.644646i \(0.222995\pi\)
\(240\) 0 0
\(241\) 196168. + 339774.i 0.217564 + 0.376832i 0.954063 0.299607i \(-0.0968557\pi\)
−0.736499 + 0.676439i \(0.763522\pi\)
\(242\) −700920. 363788.i −0.769361 0.399309i
\(243\) 0 0
\(244\) −542149. 770255.i −0.582967 0.828247i
\(245\) 547241. 315950.i 0.582456 0.336281i
\(246\) 0 0
\(247\) 1.82533e6 + 1.05386e6i 1.90371 + 1.09910i
\(248\) −141677. + 345619.i −0.146275 + 0.356835i
\(249\) 0 0
\(250\) −1.77791e6 + 79802.4i −1.79912 + 0.0807544i
\(251\) 241581. 0.242035 0.121017 0.992650i \(-0.461384\pi\)
0.121017 + 0.992650i \(0.461384\pi\)
\(252\) 0 0
\(253\) −24778.1 −0.0243370
\(254\) 41492.1 1862.40i 0.0403535 0.00181129i
\(255\) 0 0
\(256\) 981785. 368252.i 0.936303 0.351192i
\(257\) 231851. + 133859.i 0.218966 + 0.126420i 0.605471 0.795867i \(-0.292985\pi\)
−0.386506 + 0.922287i \(0.626318\pi\)
\(258\) 0 0
\(259\) −39200.5 + 22632.4i −0.0363113 + 0.0209644i
\(260\) 2.05282e6 1.44489e6i 1.88329 1.32557i
\(261\) 0 0
\(262\) 1.05302e6 + 546533.i 0.947728 + 0.491885i
\(263\) 829311. + 1.43641e6i 0.739313 + 1.28053i 0.952805 + 0.303582i \(0.0981827\pi\)
−0.213493 + 0.976945i \(0.568484\pi\)
\(264\) 0 0
\(265\) −303552. + 525767.i −0.265533 + 0.459916i
\(266\) −1.26680e6 + 809218.i −1.09775 + 0.701231i
\(267\) 0 0
\(268\) −781464. 362080.i −0.664618 0.307941i
\(269\) 1.42634e6i 1.20183i 0.799312 + 0.600916i \(0.205197\pi\)
−0.799312 + 0.600916i \(0.794803\pi\)
\(270\) 0 0
\(271\) 1.91215e6i 1.58161i 0.612068 + 0.790805i \(0.290338\pi\)
−0.612068 + 0.790805i \(0.709662\pi\)
\(272\) −226304. 1.24773e6i −0.185468 1.02258i
\(273\) 0 0
\(274\) −779716. 1.22061e6i −0.627423 0.982205i
\(275\) −465447. + 806179.i −0.371141 + 0.642835i
\(276\) 0 0
\(277\) 169154. + 292983.i 0.132459 + 0.229426i 0.924624 0.380881i \(-0.124379\pi\)
−0.792165 + 0.610307i \(0.791046\pi\)
\(278\) 94572.4 182215.i 0.0733926 0.141408i
\(279\) 0 0
\(280\) 240195. + 1.77416e6i 0.183091 + 1.35238i
\(281\) −817291. + 471863.i −0.617463 + 0.356492i −0.775881 0.630880i \(-0.782694\pi\)
0.158418 + 0.987372i \(0.449361\pi\)
\(282\) 0 0
\(283\) −1.92014e6 1.10859e6i −1.42517 0.822821i −0.428434 0.903573i \(-0.640935\pi\)
−0.996734 + 0.0807515i \(0.974268\pi\)
\(284\) 1.15723e6 104096.i 0.851381 0.0765838i
\(285\) 0 0
\(286\) −29930.4 666816.i −0.0216370 0.482049i
\(287\) −201807. −0.144621
\(288\) 0 0
\(289\) −113695. −0.0800752
\(290\) −55693.5 1.24079e6i −0.0388875 0.866369i
\(291\) 0 0
\(292\) 1.21758e6 109524.i 0.835682 0.0751716i
\(293\) −1.18621e6 684857.i −0.807219 0.466048i 0.0387699 0.999248i \(-0.487656\pi\)
−0.845989 + 0.533200i \(0.820989\pi\)
\(294\) 0 0
\(295\) 2.82067e6 1.62851e6i 1.88711 1.08952i
\(296\) 10822.5 + 79938.8i 0.00717956 + 0.0530308i
\(297\) 0 0
\(298\) 1.23739e6 2.38410e6i 0.807169 1.55519i
\(299\) 68152.1 + 118043.i 0.0440861 + 0.0763593i
\(300\) 0 0
\(301\) −203158. + 351880.i −0.129246 + 0.223861i
\(302\) −365607. 572343.i −0.230673 0.361110i
\(303\) 0 0
\(304\) 478079. + 2.63590e6i 0.296699 + 1.63586i
\(305\) 2.86611e6i 1.76418i
\(306\) 0 0
\(307\) 809224.i 0.490030i 0.969519 + 0.245015i \(0.0787929\pi\)
−0.969519 + 0.245015i \(0.921207\pi\)
\(308\) 431934. + 200130.i 0.259442 + 0.120209i
\(309\) 0 0
\(310\) −957843. + 611860.i −0.566096 + 0.361616i
\(311\) 35523.7 61528.8i 0.0208265 0.0360726i −0.855424 0.517928i \(-0.826704\pi\)
0.876251 + 0.481855i \(0.160037\pi\)
\(312\) 0 0
\(313\) 893740. + 1.54800e6i 0.515644 + 0.893122i 0.999835 + 0.0181599i \(0.00578080\pi\)
−0.484191 + 0.874963i \(0.660886\pi\)
\(314\) 1.11748e6 + 579986.i 0.639608 + 0.331966i
\(315\) 0 0
\(316\) −1.64838e6 + 1.16022e6i −0.928624 + 0.653618i
\(317\) 287153. 165788.i 0.160496 0.0926627i −0.417601 0.908631i \(-0.637129\pi\)
0.578097 + 0.815968i \(0.303796\pi\)
\(318\) 0 0
\(319\) −286007. 165126.i −0.157362 0.0908529i
\(320\) 3.08790e6 + 803175.i 1.68573 + 0.438466i
\(321\) 0 0
\(322\) −97113.0 + 4358.98i −0.0521961 + 0.00234285i
\(323\) 3.23971e6 1.72783
\(324\) 0 0
\(325\) 5.12084e6 2.68926
\(326\) 2.76778e6 124234.i 1.44241 0.0647433i
\(327\) 0 0
\(328\) −136412. + 332773.i −0.0700110 + 0.170790i
\(329\) −622666. 359496.i −0.317150 0.183107i
\(330\) 0 0
\(331\) −2.05838e6 + 1.18840e6i −1.03265 + 0.596203i −0.917744 0.397173i \(-0.869991\pi\)
−0.114910 + 0.993376i \(0.536658\pi\)
\(332\) −1.47192e6 2.09122e6i −0.732891 1.04125i
\(333\) 0 0
\(334\) 432152. + 224293.i 0.211968 + 0.110014i
\(335\) −1.31035e6 2.26960e6i −0.637934 1.10493i
\(336\) 0 0
\(337\) −62983.9 + 109091.i −0.0302103 + 0.0523257i −0.880735 0.473609i \(-0.842951\pi\)
0.850525 + 0.525935i \(0.176284\pi\)
\(338\) −1.32435e6 + 845980.i −0.630536 + 0.402780i
\(339\) 0 0
\(340\) 1.62215e6 3.50104e6i 0.761017 1.64248i
\(341\) 302214.i 0.140743i
\(342\) 0 0
\(343\) 2.36634e6i 1.08603i
\(344\) 442914. + 572855.i 0.201801 + 0.261005i
\(345\) 0 0
\(346\) −598224. 936496.i −0.268642 0.420548i
\(347\) −577346. + 999992.i −0.257402 + 0.445834i −0.965545 0.260235i \(-0.916200\pi\)
0.708143 + 0.706069i \(0.249533\pi\)
\(348\) 0 0
\(349\) −1.82275e6 3.15709e6i −0.801056 1.38747i −0.918922 0.394440i \(-0.870938\pi\)
0.117865 0.993030i \(-0.462395\pi\)
\(350\) −1.68241e6 + 3.24154e6i −0.734110 + 1.41443i
\(351\) 0 0
\(352\) 621974. 576967.i 0.267557 0.248196i
\(353\) −990369. + 571790.i −0.423020 + 0.244230i −0.696368 0.717685i \(-0.745202\pi\)
0.273349 + 0.961915i \(0.411869\pi\)
\(354\) 0 0
\(355\) 3.06181e6 + 1.76774e6i 1.28946 + 0.744470i
\(356\) −276955. 3.07891e6i −0.115820 1.28757i
\(357\) 0 0
\(358\) −88490.1 1.97146e6i −0.0364911 0.812981i
\(359\) −111222. −0.0455466 −0.0227733 0.999741i \(-0.507250\pi\)
−0.0227733 + 0.999741i \(0.507250\pi\)
\(360\) 0 0
\(361\) −4.36797e6 −1.76405
\(362\) 8970.00 + 199841.i 0.00359767 + 0.0801519i
\(363\) 0 0
\(364\) −234613. 2.60819e6i −0.0928108 1.03178i
\(365\) 3.22149e6 + 1.85993e6i 1.26568 + 0.730742i
\(366\) 0 0
\(367\) −3.77385e6 + 2.17883e6i −1.46258 + 0.844421i −0.999130 0.0417025i \(-0.986722\pi\)
−0.463450 + 0.886123i \(0.653388\pi\)
\(368\) −58455.9 + 163083.i −0.0225014 + 0.0627752i
\(369\) 0 0
\(370\) −113074. + 217863.i −0.0429398 + 0.0827333i
\(371\) 316657. + 548466.i 0.119441 + 0.206878i
\(372\) 0 0
\(373\) −1.34963e6 + 2.33763e6i −0.502277 + 0.869970i 0.497719 + 0.867338i \(0.334171\pi\)
−0.999997 + 0.00263144i \(0.999162\pi\)
\(374\) −552315. 864626.i −0.204177 0.319631i
\(375\) 0 0
\(376\) −1.01369e6 + 783753.i −0.369773 + 0.285897i
\(377\) 1.81671e6i 0.658313i
\(378\) 0 0
\(379\) 2.05325e6i 0.734249i 0.930172 + 0.367125i \(0.119658\pi\)
−0.930172 + 0.367125i \(0.880342\pi\)
\(380\) −3.42689e6 + 7.39613e6i −1.21742 + 2.62752i
\(381\) 0 0
\(382\) −4.14606e6 + 2.64846e6i −1.45371 + 0.928613i
\(383\) 2.72270e6 4.71586e6i 0.948426 1.64272i 0.199685 0.979860i \(-0.436008\pi\)
0.748741 0.662862i \(-0.230658\pi\)
\(384\) 0 0
\(385\) 724263. + 1.25446e6i 0.249026 + 0.431326i
\(386\) −4.28359e6 2.22324e6i −1.46332 0.759484i
\(387\) 0 0
\(388\) 306432. + 435361.i 0.103337 + 0.146815i
\(389\) −2.51571e6 + 1.45244e6i −0.842919 + 0.486660i −0.858255 0.513223i \(-0.828451\pi\)
0.0153362 + 0.999882i \(0.495118\pi\)
\(390\) 0 0
\(391\) 181441. + 104755.i 0.0600196 + 0.0346523i
\(392\) −1.08697e6 445574.i −0.357274 0.146455i
\(393\) 0 0
\(394\) −1.46841e6 + 65910.3i −0.476547 + 0.0213901i
\(395\) −6.13361e6 −1.97799
\(396\) 0 0
\(397\) −1.59810e6 −0.508896 −0.254448 0.967086i \(-0.581894\pi\)
−0.254448 + 0.967086i \(0.581894\pi\)
\(398\) 1.49405e6 67061.4i 0.472779 0.0212210i
\(399\) 0 0
\(400\) 4.20797e6 + 4.96536e6i 1.31499 + 1.55167i
\(401\) 1.48732e6 + 858705.i 0.461895 + 0.266675i 0.712841 0.701326i \(-0.247408\pi\)
−0.250945 + 0.968001i \(0.580741\pi\)
\(402\) 0 0
\(403\) 1.43974e6 831237.i 0.441594 0.254954i
\(404\) 760810. 535501.i 0.231912 0.163233i
\(405\) 0 0
\(406\) −1.15000e6 596864.i −0.346243 0.179705i
\(407\) 32633.2 + 56522.4i 0.00976504 + 0.0169135i
\(408\) 0 0
\(409\) 2.74998e6 4.76310e6i 0.812870 1.40793i −0.0979768 0.995189i \(-0.531237\pi\)
0.910847 0.412744i \(-0.135430\pi\)
\(410\) −922242. + 589119.i −0.270947 + 0.173079i
\(411\) 0 0
\(412\) 4.43200e6 + 2.05350e6i 1.28634 + 0.596008i
\(413\) 3.39765e6i 0.980174i
\(414\) 0 0
\(415\) 7.78143e6i 2.21789i
\(416\) −4.45940e6 1.37614e6i −1.26341 0.389878i
\(417\) 0 0
\(418\) 1.16679e6 + 1.82657e6i 0.326628 + 0.511323i
\(419\) −3.22137e6 + 5.57958e6i −0.896408 + 1.55262i −0.0643564 + 0.997927i \(0.520499\pi\)
−0.832052 + 0.554698i \(0.812834\pi\)
\(420\) 0 0
\(421\) −1.68713e6 2.92220e6i −0.463921 0.803535i 0.535231 0.844706i \(-0.320225\pi\)
−0.999152 + 0.0411706i \(0.986891\pi\)
\(422\) −2.67702e6 + 5.15789e6i −0.731762 + 1.40991i
\(423\) 0 0
\(424\) 1.11845e6 151421.i 0.302135 0.0409044i
\(425\) 6.81659e6 3.93556e6i 1.83060 1.05690i
\(426\) 0 0
\(427\) −2.58929e6 1.49493e6i −0.687244 0.396780i
\(428\) 5.10044e6 458797.i 1.34586 0.121063i
\(429\) 0 0
\(430\) 98799.1 + 2.20113e6i 0.0257681 + 0.574083i
\(431\) −1.69209e6 −0.438763 −0.219382 0.975639i \(-0.570404\pi\)
−0.219382 + 0.975639i \(0.570404\pi\)
\(432\) 0 0
\(433\) −3.34335e6 −0.856964 −0.428482 0.903550i \(-0.640951\pi\)
−0.428482 + 0.903550i \(0.640951\pi\)
\(434\) 53165.5 + 1.18447e6i 0.0135490 + 0.301855i
\(435\) 0 0
\(436\) −4.35919e6 + 392120.i −1.09822 + 0.0987876i
\(437\) −383304. 221300.i −0.0960150 0.0554343i
\(438\) 0 0
\(439\) 4.12524e6 2.38171e6i 1.02162 0.589831i 0.107045 0.994254i \(-0.465861\pi\)
0.914572 + 0.404424i \(0.132528\pi\)
\(440\) 2.55813e6 346332.i 0.629928 0.0852826i
\(441\) 0 0
\(442\) −2.59994e6 + 5.00937e6i −0.633005 + 1.21963i
\(443\) 2.19145e6 + 3.79571e6i 0.530546 + 0.918932i 0.999365 + 0.0356380i \(0.0113463\pi\)
−0.468819 + 0.883294i \(0.655320\pi\)
\(444\) 0 0
\(445\) 4.70321e6 8.14620e6i 1.12589 1.95009i
\(446\) −1.84586e6 2.88961e6i −0.439401 0.687864i
\(447\) 0 0
\(448\) 2.33621e6 2.37073e6i 0.549941 0.558067i
\(449\) 2.64215e6i 0.618502i −0.950981 0.309251i \(-0.899922\pi\)
0.950981 0.309251i \(-0.100078\pi\)
\(450\) 0 0
\(451\) 290981.i 0.0673633i
\(452\) 977110. + 452729.i 0.224956 + 0.104230i
\(453\) 0 0
\(454\) 815699. 521060.i 0.185733 0.118645i
\(455\) 3.98416e6 6.90077e6i 0.902212 1.56268i
\(456\) 0 0
\(457\) 1.74172e6 + 3.01674e6i 0.390110 + 0.675690i 0.992464 0.122539i \(-0.0391037\pi\)
−0.602354 + 0.798229i \(0.705770\pi\)
\(458\) 6.91917e6 + 3.59115e6i 1.54131 + 0.799963i
\(459\) 0 0
\(460\) −431075. + 303415.i −0.0949856 + 0.0668563i
\(461\) −2.93883e6 + 1.69673e6i −0.644054 + 0.371845i −0.786174 0.618005i \(-0.787941\pi\)
0.142121 + 0.989849i \(0.454608\pi\)
\(462\) 0 0
\(463\) −167674. 96806.8i −0.0363508 0.0209871i 0.481714 0.876328i \(-0.340014\pi\)
−0.518065 + 0.855341i \(0.673348\pi\)
\(464\) −1.76155e6 + 1.49285e6i −0.379840 + 0.321901i
\(465\) 0 0
\(466\) 7.73612e6 347240.i 1.65028 0.0740739i
\(467\) −3.24407e6 −0.688332 −0.344166 0.938909i \(-0.611838\pi\)
−0.344166 + 0.938909i \(0.611838\pi\)
\(468\) 0 0
\(469\) −2.73385e6 −0.573908
\(470\) −3.89498e6 + 174829.i −0.813319 + 0.0365063i
\(471\) 0 0
\(472\) −5.60261e6 2.29664e6i −1.15754 0.474503i
\(473\) 507369. + 292930.i 0.104273 + 0.0602020i
\(474\) 0 0
\(475\) −1.44004e7 + 8.31408e6i −2.92847 + 1.69075i
\(476\) −2.31679e6 3.29157e6i −0.468673 0.665864i
\(477\) 0 0
\(478\) 1.56104e6 + 810201.i 0.312495 + 0.162190i
\(479\) −4.10699e6 7.11352e6i −0.817871 1.41659i −0.907248 0.420596i \(-0.861821\pi\)
0.0893767 0.995998i \(1.52849\pi\)
\(480\) 0 0
\(481\) 179515. 310929.i 0.0353784 0.0612772i
\(482\) 1.87036e6 1.19477e6i 0.366697 0.234242i
\(483\) 0 0
\(484\) −1.87803e6 + 4.05329e6i −0.364409 + 0.786492i
\(485\) 1.61997e6i 0.312719i
\(486\) 0 0
\(487\) 1.63906e6i 0.313165i −0.987665 0.156583i \(-0.949952\pi\)
0.987665 0.156583i \(-0.0500477\pi\)
\(488\) −4.21532e6 + 3.25915e6i −0.801273 + 0.619520i
\(489\) 0 0
\(490\) −1.92429e6 3.01240e6i −0.362060 0.566791i
\(491\) 2.03219e6 3.51985e6i 0.380417 0.658902i −0.610705 0.791858i \(-0.709114\pi\)
0.991122 + 0.132957i \(0.0424471\pi\)
\(492\) 0 0
\(493\) 1.39621e6 + 2.41831e6i 0.258722 + 0.448120i
\(494\) 5.49251e6 1.05826e7i 1.01264 1.95107i
\(495\) 0 0
\(496\) 1.98908e6 + 712974.i 0.363036 + 0.130128i
\(497\) 3.19400e6 1.84406e6i 0.580022 0.334876i
\(498\) 0 0
\(499\) 2.92199e6 + 1.68701e6i 0.525325 + 0.303296i 0.739111 0.673584i \(-0.235246\pi\)
−0.213786 + 0.976881i \(0.568579\pi\)
\(500\) 901954. + 1.00270e7i 0.161346 + 1.79369i
\(501\) 0 0
\(502\) −61278.3 1.36521e6i −0.0108529 0.241791i
\(503\) 7.37612e6 1.29989 0.649947 0.759979i \(-0.274791\pi\)
0.649947 + 0.759979i \(0.274791\pi\)
\(504\) 0 0
\(505\) 2.83097e6 0.493977
\(506\) 6285.12 + 140025.i 0.00109128 + 0.0243125i
\(507\) 0 0
\(508\) −21049.4 234006.i −0.00361894 0.0402317i
\(509\) 5.72270e6 + 3.30400e6i 0.979054 + 0.565257i 0.901984 0.431769i \(-0.142110\pi\)
0.0770693 + 0.997026i \(0.475444\pi\)
\(510\) 0 0
\(511\) 3.36057e6 1.94023e6i 0.569326 0.328700i
\(512\) −2.33009e6 5.45482e6i −0.392823 0.919614i
\(513\) 0 0
\(514\) 697650. 1.34418e6i 0.116474 0.224414i
\(515\) 7.43154e6 + 1.28718e7i 1.23470 + 2.13856i
\(516\) 0 0
\(517\) −518350. + 897809.i −0.0852898 + 0.147726i
\(518\) 137843. + 215788.i 0.0225715 + 0.0353348i
\(519\) 0 0
\(520\) −8.68604e6 1.12343e7i −1.40868 1.82196i
\(521\) 1.91733e6i 0.309459i −0.987957 0.154730i \(-0.950549\pi\)
0.987957 0.154730i \(-0.0494506\pi\)
\(522\) 0 0
\(523\) 5.16891e6i 0.826313i 0.910660 + 0.413157i \(0.135574\pi\)
−0.910660 + 0.413157i \(0.864426\pi\)
\(524\) 2.82144e6 6.08943e6i 0.448893 0.968831i
\(525\) 0 0
\(526\) 7.90702e6 5.05093e6i 1.24609 0.795988i
\(527\) 1.27767e6 2.21300e6i 0.200398 0.347100i
\(528\) 0 0
\(529\) 3.20386e6 + 5.54925e6i 0.497776 + 0.862174i
\(530\) 3.04819e6 + 1.58206e6i 0.471360 + 0.244643i
\(531\) 0 0
\(532\) 4.89435e6 + 6.95362e6i 0.749750 + 1.06520i
\(533\) 1.38623e6 800342.i 0.211358 0.122027i
\(534\) 0 0
\(535\) 1.34948e7 + 7.79123e6i 2.03837 + 1.17685i
\(536\) −1.84795e6 + 4.50803e6i −0.277829 + 0.677758i
\(537\) 0 0
\(538\) 8.06051e6 361801.i 1.20062 0.0538907i
\(539\) −950459. −0.140916
\(540\) 0 0
\(541\) 3.10786e6 0.456528 0.228264 0.973599i \(-0.426695\pi\)
0.228264 + 0.973599i \(0.426695\pi\)
\(542\) 1.08059e7 485029.i 1.58002 0.0709201i
\(543\) 0 0
\(544\) −6.99373e6 + 1.59538e6i −1.01324 + 0.231135i
\(545\) −1.15336e7 6.65892e6i −1.66331 0.960313i
\(546\) 0 0
\(547\) −3.78249e6 + 2.18382e6i −0.540517 + 0.312068i −0.745288 0.666742i \(-0.767688\pi\)
0.204772 + 0.978810i \(0.434355\pi\)
\(548\) −6.70011e6 + 4.71592e6i −0.953083 + 0.670834i
\(549\) 0 0
\(550\) 4.67391e6 + 2.42583e6i 0.658831 + 0.341943i
\(551\) −2.94957e6 5.10881e6i −0.413885 0.716870i
\(552\) 0 0
\(553\) −3.19921e6 + 5.54120e6i −0.444867 + 0.770532i
\(554\) 1.61279e6 1.03023e6i 0.223256 0.142614i
\(555\) 0 0
\(556\) −1.05372e6 488224.i −0.144556 0.0669780i
\(557\) 4.46009e6i 0.609124i 0.952493 + 0.304562i \(0.0985100\pi\)
−0.952493 + 0.304562i \(0.901490\pi\)
\(558\) 0 0
\(559\) 3.22281e6i 0.436219i
\(560\) 9.96516e6 1.80741e6i 1.34281 0.243549i
\(561\) 0 0
\(562\) 2.87389e6 + 4.49896e6i 0.383821 + 0.600857i
\(563\) −5.22200e6 + 9.04476e6i −0.694330 + 1.20261i 0.276077 + 0.961136i \(0.410966\pi\)
−0.970406 + 0.241478i \(0.922368\pi\)
\(564\) 0 0
\(565\) 1.63841e6 + 2.83781e6i 0.215924 + 0.373992i
\(566\) −5.77778e6 + 1.11322e7i −0.758089 + 1.46063i
\(567\) 0 0
\(568\) −881801. 6.51330e6i −0.114683 0.847091i
\(569\) −2.55116e6 + 1.47291e6i −0.330337 + 0.190720i −0.655991 0.754769i \(-0.727749\pi\)
0.325654 + 0.945489i \(0.394416\pi\)
\(570\) 0 0
\(571\) −199833. 115373.i −0.0256493 0.0148086i 0.487121 0.873335i \(-0.338047\pi\)
−0.512770 + 0.858526i \(0.671381\pi\)
\(572\) −3.76069e6 + 338284.i −0.480594 + 0.0432306i
\(573\) 0 0
\(574\) 51189.5 + 1.14044e6i 0.00648487 + 0.144475i
\(575\) −1.07533e6 −0.135635
\(576\) 0 0
\(577\) 4.42964e6 0.553897 0.276949 0.960885i \(-0.410677\pi\)
0.276949 + 0.960885i \(0.410677\pi\)
\(578\) 28839.5 + 642511.i 0.00359061 + 0.0799947i
\(579\) 0 0
\(580\) −6.99777e6 + 629467.i −0.863754 + 0.0776967i
\(581\) −7.02986e6 4.05869e6i −0.863985 0.498822i
\(582\) 0 0
\(583\) 790822. 456582.i 0.0963624 0.0556349i
\(584\) −927787. 6.85297e6i −0.112568 0.831470i
\(585\) 0 0
\(586\) −3.56935e6 + 6.87717e6i −0.429383 + 0.827305i
\(587\) 509131. + 881841.i 0.0609866 + 0.105632i 0.894907 0.446253i \(-0.147242\pi\)
−0.833920 + 0.551885i \(0.813909\pi\)
\(588\) 0 0
\(589\) −2.69915e6 + 4.67507e6i −0.320582 + 0.555265i
\(590\) −9.91848e6 1.55270e7i −1.17305 1.83636i
\(591\) 0 0
\(592\) 449002. 81436.6i 0.0526555 0.00955026i
\(593\) 1.12943e6i 0.131893i 0.997823 + 0.0659466i \(0.0210067\pi\)
−0.997823 + 0.0659466i \(0.978993\pi\)
\(594\) 0 0
\(595\) 1.22479e7i 1.41831i
\(596\) −1.37868e7 6.38792e6i −1.58982 0.736621i
\(597\) 0 0
\(598\) 649793. 415081.i 0.0743057 0.0474657i
\(599\) −6.98600e6 + 1.21001e7i −0.795539 + 1.37791i 0.126958 + 0.991908i \(0.459479\pi\)
−0.922496 + 0.386006i \(0.873855\pi\)
\(600\) 0 0
\(601\) −7.90974e6 1.37001e7i −0.893256 1.54717i −0.835948 0.548809i \(-0.815081\pi\)
−0.0573087 0.998357i \(-0.518252\pi\)
\(602\) 2.04007e6 + 1.05882e6i 0.229432 + 0.119078i
\(603\) 0 0
\(604\) −3.14167e6 + 2.21128e6i −0.350403 + 0.246634i
\(605\) −1.17719e7 + 6.79652e6i −1.30755 + 0.754915i
\(606\) 0 0
\(607\) −4.40500e6 2.54323e6i −0.485259 0.280165i 0.237346 0.971425i \(-0.423722\pi\)
−0.722606 + 0.691261i \(0.757056\pi\)
\(608\) 1.47746e7 3.37032e6i 1.62091 0.369753i
\(609\) 0 0
\(610\) −1.61969e7 + 727007.i −1.76241 + 0.0791068i
\(611\) 5.70288e6 0.618004
\(612\) 0 0
\(613\) −2.62634e6 −0.282293 −0.141147 0.989989i \(-0.545079\pi\)
−0.141147 + 0.989989i \(0.545079\pi\)
\(614\) 4.57306e6 205264.i 0.489537 0.0219732i
\(615\) 0 0
\(616\) 1.02141e6 2.49169e6i 0.108454 0.264571i
\(617\) 8.21879e6 + 4.74512e6i 0.869150 + 0.501804i 0.867066 0.498194i \(-0.166003\pi\)
0.00208438 + 0.999998i \(0.499337\pi\)
\(618\) 0 0
\(619\) 2.66128e6 1.53649e6i 0.279167 0.161177i −0.353879 0.935291i \(-0.615138\pi\)
0.633046 + 0.774114i \(0.281804\pi\)
\(620\) 3.70069e6 + 5.25773e6i 0.386637 + 0.549312i
\(621\) 0 0
\(622\) −356720. 185143.i −0.0369702 0.0191881i
\(623\) −4.90627e6 8.49790e6i −0.506443 0.877186i
\(624\) 0 0
\(625\) −5.38553e6 + 9.32800e6i −0.551478 + 0.955188i
\(626\) 8.52132e6 5.44333e6i 0.869102 0.555174i
\(627\) 0 0
\(628\) 2.99414e6 6.46216e6i 0.302952 0.653850i
\(629\) 551856.i 0.0556159i
\(630\) 0 0
\(631\) 2.80779e6i 0.280731i 0.990100 + 0.140366i \(0.0448278\pi\)
−0.990100 + 0.140366i \(0.955172\pi\)
\(632\) 6.97474e6 + 9.02097e6i 0.694601 + 0.898381i
\(633\) 0 0
\(634\) −1.00973e6 1.58070e6i −0.0997662 0.156180i
\(635\) 357459. 619137.i 0.0351796 0.0609329i
\(636\) 0 0
\(637\) 2.61423e6 + 4.52798e6i 0.255267 + 0.442136i
\(638\) −860607. + 1.65816e6i −0.0837053 + 0.161277i
\(639\) 0 0
\(640\) 3.75561e6 1.76539e7i 0.362436 1.70369i
\(641\) −8.96448e6 + 5.17564e6i −0.861747 + 0.497530i −0.864597 0.502466i \(-0.832426\pi\)
0.00284982 + 0.999996i \(0.499093\pi\)
\(642\) 0 0
\(643\) −4.22376e6 2.43859e6i −0.402876 0.232601i 0.284848 0.958573i \(-0.408057\pi\)
−0.687724 + 0.725972i \(0.741390\pi\)
\(644\) 49266.6 + 547696.i 0.00468099 + 0.0520385i
\(645\) 0 0
\(646\) −821772. 1.83081e7i −0.0774765 1.72609i
\(647\) 9.58644e6 0.900319 0.450160 0.892948i \(-0.351367\pi\)
0.450160 + 0.892948i \(0.351367\pi\)
\(648\) 0 0
\(649\) −4.89900e6 −0.456557
\(650\) −1.29893e6 2.89387e7i −0.120588 2.68656i
\(651\) 0 0
\(652\) −1.40413e6 1.56097e7i −0.129356 1.43805i
\(653\) 3.50930e6 + 2.02609e6i 0.322060 + 0.185942i 0.652311 0.757952i \(-0.273800\pi\)
−0.330250 + 0.943893i \(0.607133\pi\)
\(654\) 0 0
\(655\) 1.76854e7 1.02107e7i 1.61069 0.929934i
\(656\) 1.91515e6 + 686474.i 0.173758 + 0.0622823i
\(657\) 0 0
\(658\) −1.87363e6 + 3.60997e6i −0.168702 + 0.325042i
\(659\) −3.07530e6 5.32657e6i −0.275850 0.477787i 0.694499 0.719494i \(-0.255626\pi\)
−0.970349 + 0.241707i \(0.922293\pi\)
\(660\) 0 0
\(661\) 1.19391e6 2.06791e6i 0.106284 0.184089i −0.807978 0.589212i \(-0.799438\pi\)
0.914262 + 0.405124i \(0.132771\pi\)
\(662\) 7.23798e6 + 1.13308e7i 0.641908 + 1.00488i
\(663\) 0 0
\(664\) −1.14445e7 + 8.84853e6i −1.00734 + 0.778844i
\(665\) 2.58744e7i 2.26890i
\(666\) 0 0
\(667\) 381493.i 0.0332026i
\(668\) 1.15790e6 2.49905e6i 0.100399 0.216688i
\(669\) 0 0
\(670\) −1.24935e7 + 7.98071e6i −1.07522 + 0.686838i
\(671\) −2.15550e6 + 3.73344e6i −0.184817 + 0.320113i
\(672\) 0 0
\(673\) 5.33582e6 + 9.24191e6i 0.454113 + 0.786546i 0.998637 0.0521992i \(-0.0166231\pi\)
−0.544524 + 0.838745i \(0.683290\pi\)
\(674\) 632469. + 328261.i 0.0536278 + 0.0278336i
\(675\) 0 0
\(676\) 5.11670e6 + 7.26951e6i 0.430649 + 0.611841i
\(677\) 1.20806e7 6.97471e6i 1.01301 0.584864i 0.100941 0.994892i \(-0.467815\pi\)
0.912073 + 0.410029i \(0.134481\pi\)
\(678\) 0 0
\(679\) 1.46351e6 + 844957.i 0.121821 + 0.0703332i
\(680\) −2.01964e7 8.27899e6i −1.67495 0.686602i
\(681\) 0 0
\(682\) 1.70786e6 76658.3i 0.140602 0.00631100i
\(683\) 1.34097e7 1.09994 0.549968 0.835186i \(-0.314640\pi\)
0.549968 + 0.835186i \(0.314640\pi\)
\(684\) 0 0
\(685\) −2.49311e7 −2.03009
\(686\) −1.33726e7 + 600237.i −1.08494 + 0.0486981i
\(687\) 0 0
\(688\) 3.12495e6 2.64829e6i 0.251694 0.213302i
\(689\) −4.35030e6 2.51165e6i −0.349118 0.201563i
\(690\) 0 0
\(691\) −1.05848e6 + 611111.i −0.0843307 + 0.0486883i −0.541572 0.840654i \(-0.682171\pi\)
0.457242 + 0.889342i \(0.348837\pi\)
\(692\) −5.14055e6 + 3.61821e6i −0.408079 + 0.287229i
\(693\) 0 0
\(694\) 5.79757e6 + 3.00902e6i 0.456927 + 0.237152i
\(695\) −1.76686e6 3.06030e6i −0.138753 0.240326i
\(696\) 0 0
\(697\) 1.23018e6 2.13074e6i 0.0959154 0.166130i
\(698\) −1.73789e7 + 1.11015e7i −1.35015 + 0.862465i
\(699\) 0 0
\(700\) 1.87452e7 + 8.68532e6i 1.44592 + 0.669948i
\(701\) 1.38380e7i 1.06360i −0.846870 0.531801i \(-0.821516\pi\)
0.846870 0.531801i \(-0.178484\pi\)
\(702\) 0 0
\(703\) 1.16583e6i 0.0889704i
\(704\) −3.41830e6 3.36853e6i −0.259943 0.256158i
\(705\) 0 0
\(706\) 3.48249e6 + 5.45170e6i 0.262953 + 0.411643i
\(707\) 1.47660e6 2.55754e6i 0.111100 0.192430i
\(708\) 0 0
\(709\) 1.12116e7 + 1.94191e7i 0.837632 + 1.45082i 0.891870 + 0.452292i \(0.149394\pi\)
−0.0542381 + 0.998528i \(0.517273\pi\)
\(710\) 9.21314e6 1.77512e7i 0.685901 1.32155i
\(711\) 0 0
\(712\) −1.73292e7 + 2.34610e6i −1.28108 + 0.173439i
\(713\) −302333. + 174552.i −0.0222722 + 0.0128588i
\(714\) 0 0
\(715\) −9.95008e6 5.74468e6i −0.727883 0.420243i
\(716\) −1.11186e7 + 1.00014e6i −0.810527 + 0.0729088i
\(717\) 0 0
\(718\) 28212.2 + 628536.i 0.00204233 + 0.0455008i
\(719\) −1.71887e7 −1.24000 −0.619999 0.784603i \(-0.712867\pi\)
−0.619999 + 0.784603i \(0.712867\pi\)
\(720\) 0 0
\(721\) 1.55048e7 1.11078
\(722\) 1.10796e6 + 2.46841e7i 0.0791009 + 1.76228i
\(723\) 0 0
\(724\) 1.12706e6 101382.i 0.0799100 0.00718810i
\(725\) −1.24122e7 7.16620e6i −0.877010 0.506342i
\(726\) 0 0
\(727\) −1.12449e7 + 6.49227e6i −0.789081 + 0.455576i −0.839639 0.543145i \(-0.817233\pi\)
0.0505582 + 0.998721i \(0.483900\pi\)
\(728\) −1.46798e7 + 1.98742e6i −1.02658 + 0.138983i
\(729\) 0 0
\(730\) 9.69361e6 1.86769e7i 0.673253 1.29718i
\(731\) −2.47685e6 4.29002e6i −0.171437 0.296938i
\(732\) 0 0
\(733\) 3.50187e6 6.06542e6i 0.240736 0.416967i −0.720188 0.693779i \(-0.755945\pi\)
0.960924 + 0.276812i \(0.0892780\pi\)
\(734\) 1.32702e7 + 2.07740e7i 0.909154 + 1.42324i
\(735\) 0 0
\(736\) 936434. + 288977.i 0.0637210 + 0.0196639i
\(737\) 3.94188e6i 0.267322i
\(738\) 0 0
\(739\) 2.74291e7i 1.84757i 0.382917 + 0.923783i \(0.374920\pi\)
−0.382917 + 0.923783i \(0.625080\pi\)
\(740\) 1.25986e6 + 583739.i 0.0845755 + 0.0391868i
\(741\) 0 0
\(742\) 3.01915e6 1.92860e6i 0.201315 0.128598i
\(743\) 3.05209e6 5.28638e6i 0.202827 0.351306i −0.746611 0.665260i \(-0.768320\pi\)
0.949438 + 0.313954i \(0.101654\pi\)
\(744\) 0 0
\(745\) −2.31176e7 4.00409e7i −1.52599 2.64310i
\(746\) 1.35527e7 + 7.03404e6i 0.891617 + 0.462762i
\(747\) 0 0
\(748\) −4.74605e6 + 3.34054e6i −0.310155 + 0.218304i
\(749\) 1.40774e7 8.12760e6i 0.916893 0.529368i
\(750\) 0 0
\(751\) 1.95951e7 + 1.13132e7i 1.26779 + 0.731958i 0.974569 0.224088i \(-0.0719402\pi\)
0.293219 + 0.956045i \(0.405274\pi\)
\(752\) 4.68625e6 + 5.52972e6i 0.302190 + 0.356581i
\(753\) 0 0
\(754\) 1.02665e7 460820.i 0.657651 0.0295191i
\(755\) −1.16901e7 −0.746366
\(756\) 0 0
\(757\) 2.79038e7 1.76980 0.884900 0.465781i \(-0.154226\pi\)
0.884900 + 0.465781i \(0.154226\pi\)
\(758\) 1.16032e7 520819.i 0.733511 0.0329241i
\(759\) 0 0
\(760\) 4.26660e7 + 1.74898e7i 2.67946 + 1.09838i
\(761\) −8.70509e6 5.02588e6i −0.544893 0.314594i 0.202166 0.979351i \(-0.435202\pi\)
−0.747060 + 0.664757i \(0.768535\pi\)
\(762\) 0 0
\(763\) −1.20315e7 + 6.94641e6i −0.748186 + 0.431966i
\(764\) 1.60185e7 + 2.27582e7i 0.992864 + 1.41060i
\(765\) 0 0
\(766\) −2.73407e7 1.41902e7i −1.68360 0.873812i
\(767\) 1.34747e7 + 2.33388e7i 0.827046 + 1.43249i
\(768\) 0 0
\(769\) 1.07441e7 1.86093e7i 0.655169 1.13479i −0.326682 0.945134i \(-0.605931\pi\)
0.981851 0.189652i \(-0.0607361\pi\)
\(770\) 6.90545e6 4.41113e6i 0.419725 0.268116i
\(771\) 0 0
\(772\) −1.14774e7 + 2.47712e7i −0.693105 + 1.49590i
\(773\) 3.11372e7i 1.87426i −0.348977 0.937131i \(-0.613471\pi\)
0.348977 0.937131i \(-0.386529\pi\)
\(774\) 0 0
\(775\) 1.31156e7i 0.784392i
\(776\) 2.38257e6