Properties

Label 387.6.a.e.1.9
Level 387
Weight 6
Character 387.1
Self dual yes
Analytic conductor 62.069
Analytic rank 1
Dimension 10
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 387 = 3^{2} \cdot 43 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 387.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(62.0685382676\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
Defining polynomial: \(x^{10} - 2 x^{9} - 256 x^{8} + 266 x^{7} + 21986 x^{6} - 10450 x^{5} - 719484 x^{4} + 384582 x^{3} + 8437093 x^{2} - 5752252 x - 22734604\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{2} \)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(9.86547\) of defining polynomial
Character \(\chi\) \(=\) 387.1

$q$-expansion

\(f(q)\) \(=\) \(q+8.86547 q^{2} +46.5966 q^{4} +37.8251 q^{5} -124.747 q^{7} +129.406 q^{8} +O(q^{10})\) \(q+8.86547 q^{2} +46.5966 q^{4} +37.8251 q^{5} -124.747 q^{7} +129.406 q^{8} +335.337 q^{10} -590.079 q^{11} +434.774 q^{13} -1105.94 q^{14} -343.849 q^{16} -1925.58 q^{17} +654.129 q^{19} +1762.52 q^{20} -5231.33 q^{22} -2805.03 q^{23} -1694.26 q^{25} +3854.47 q^{26} -5812.80 q^{28} +1456.23 q^{29} +4419.85 q^{31} -7189.36 q^{32} -17071.2 q^{34} -4718.58 q^{35} +3753.09 q^{37} +5799.17 q^{38} +4894.78 q^{40} -1972.85 q^{41} +1849.00 q^{43} -27495.7 q^{44} -24867.9 q^{46} -2204.84 q^{47} -1245.12 q^{49} -15020.4 q^{50} +20259.0 q^{52} -24984.2 q^{53} -22319.8 q^{55} -16143.0 q^{56} +12910.1 q^{58} +42756.2 q^{59} -21022.8 q^{61} +39184.0 q^{62} -52733.9 q^{64} +16445.4 q^{65} -25272.1 q^{67} -89725.4 q^{68} -41832.4 q^{70} -48082.8 q^{71} +58801.2 q^{73} +33272.9 q^{74} +30480.2 q^{76} +73610.8 q^{77} +92704.7 q^{79} -13006.1 q^{80} -17490.3 q^{82} +1849.64 q^{83} -72835.2 q^{85} +16392.3 q^{86} -76359.5 q^{88} +70380.3 q^{89} -54236.8 q^{91} -130705. q^{92} -19546.9 q^{94} +24742.5 q^{95} -88842.1 q^{97} -11038.6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 8q^{2} + 202q^{4} - 138q^{5} + 60q^{7} - 294q^{8} + O(q^{10}) \) \( 10q - 8q^{2} + 202q^{4} - 138q^{5} + 60q^{7} - 294q^{8} - 17q^{10} - 745q^{11} + 1917q^{13} - 1936q^{14} + 5354q^{16} - 4017q^{17} - 2404q^{19} - 1311q^{20} - 5836q^{22} - 1733q^{23} + 7120q^{25} + 1484q^{26} - 15028q^{28} - 6996q^{29} - 4899q^{31} + 7554q^{32} - 27033q^{34} - 7084q^{35} + 1466q^{37} - 13905q^{38} - 93211q^{40} - 10297q^{41} + 18490q^{43} + 36140q^{44} + 17991q^{46} - 48592q^{47} + 29458q^{49} - 983q^{50} + 14232q^{52} - 127165q^{53} + 106672q^{55} + 7780q^{56} - 10305q^{58} - 99372q^{59} + 17408q^{61} - 28265q^{62} + 47202q^{64} - 54484q^{65} - 2021q^{67} - 192151q^{68} - 33194q^{70} - 11286q^{71} + 49892q^{73} + 125431q^{74} - 249803q^{76} - 98144q^{77} - 91524q^{79} - 12251q^{80} - 158909q^{82} + 105203q^{83} - 87212q^{85} - 14792q^{86} - 461824q^{88} + 62682q^{89} - 295304q^{91} - 183783q^{92} + 7259q^{94} + 305340q^{95} + 108383q^{97} - 354656q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.86547 1.56721 0.783604 0.621260i \(-0.213379\pi\)
0.783604 + 0.621260i \(0.213379\pi\)
\(3\) 0 0
\(4\) 46.5966 1.45614
\(5\) 37.8251 0.676636 0.338318 0.941032i \(-0.390142\pi\)
0.338318 + 0.941032i \(0.390142\pi\)
\(6\) 0 0
\(7\) −124.747 −0.962246 −0.481123 0.876653i \(-0.659771\pi\)
−0.481123 + 0.876653i \(0.659771\pi\)
\(8\) 129.406 0.714872
\(9\) 0 0
\(10\) 335.337 1.06043
\(11\) −590.079 −1.47038 −0.735188 0.677863i \(-0.762906\pi\)
−0.735188 + 0.677863i \(0.762906\pi\)
\(12\) 0 0
\(13\) 434.774 0.713518 0.356759 0.934196i \(-0.383882\pi\)
0.356759 + 0.934196i \(0.383882\pi\)
\(14\) −1105.94 −1.50804
\(15\) 0 0
\(16\) −343.849 −0.335790
\(17\) −1925.58 −1.61599 −0.807995 0.589189i \(-0.799447\pi\)
−0.807995 + 0.589189i \(0.799447\pi\)
\(18\) 0 0
\(19\) 654.129 0.415700 0.207850 0.978161i \(-0.433353\pi\)
0.207850 + 0.978161i \(0.433353\pi\)
\(20\) 1762.52 0.985279
\(21\) 0 0
\(22\) −5231.33 −2.30439
\(23\) −2805.03 −1.10565 −0.552825 0.833297i \(-0.686450\pi\)
−0.552825 + 0.833297i \(0.686450\pi\)
\(24\) 0 0
\(25\) −1694.26 −0.542163
\(26\) 3854.47 1.11823
\(27\) 0 0
\(28\) −5812.80 −1.40117
\(29\) 1456.23 0.321540 0.160770 0.986992i \(-0.448602\pi\)
0.160770 + 0.986992i \(0.448602\pi\)
\(30\) 0 0
\(31\) 4419.85 0.826044 0.413022 0.910721i \(-0.364473\pi\)
0.413022 + 0.910721i \(0.364473\pi\)
\(32\) −7189.36 −1.24112
\(33\) 0 0
\(34\) −17071.2 −2.53259
\(35\) −4718.58 −0.651090
\(36\) 0 0
\(37\) 3753.09 0.450697 0.225348 0.974278i \(-0.427648\pi\)
0.225348 + 0.974278i \(0.427648\pi\)
\(38\) 5799.17 0.651488
\(39\) 0 0
\(40\) 4894.78 0.483708
\(41\) −1972.85 −0.183288 −0.0916442 0.995792i \(-0.529212\pi\)
−0.0916442 + 0.995792i \(0.529212\pi\)
\(42\) 0 0
\(43\) 1849.00 0.152499
\(44\) −27495.7 −2.14108
\(45\) 0 0
\(46\) −24867.9 −1.73279
\(47\) −2204.84 −0.145590 −0.0727950 0.997347i \(-0.523192\pi\)
−0.0727950 + 0.997347i \(0.523192\pi\)
\(48\) 0 0
\(49\) −1245.12 −0.0740834
\(50\) −15020.4 −0.849683
\(51\) 0 0
\(52\) 20259.0 1.03898
\(53\) −24984.2 −1.22173 −0.610865 0.791735i \(-0.709178\pi\)
−0.610865 + 0.791735i \(0.709178\pi\)
\(54\) 0 0
\(55\) −22319.8 −0.994910
\(56\) −16143.0 −0.687882
\(57\) 0 0
\(58\) 12910.1 0.503920
\(59\) 42756.2 1.59907 0.799537 0.600616i \(-0.205078\pi\)
0.799537 + 0.600616i \(0.205078\pi\)
\(60\) 0 0
\(61\) −21022.8 −0.723379 −0.361689 0.932299i \(-0.617800\pi\)
−0.361689 + 0.932299i \(0.617800\pi\)
\(62\) 39184.0 1.29458
\(63\) 0 0
\(64\) −52733.9 −1.60931
\(65\) 16445.4 0.482792
\(66\) 0 0
\(67\) −25272.1 −0.687788 −0.343894 0.939008i \(-0.611746\pi\)
−0.343894 + 0.939008i \(0.611746\pi\)
\(68\) −89725.4 −2.35311
\(69\) 0 0
\(70\) −41832.4 −1.02039
\(71\) −48082.8 −1.13199 −0.565997 0.824407i \(-0.691509\pi\)
−0.565997 + 0.824407i \(0.691509\pi\)
\(72\) 0 0
\(73\) 58801.2 1.29145 0.645727 0.763568i \(-0.276554\pi\)
0.645727 + 0.763568i \(0.276554\pi\)
\(74\) 33272.9 0.706336
\(75\) 0 0
\(76\) 30480.2 0.605318
\(77\) 73610.8 1.41486
\(78\) 0 0
\(79\) 92704.7 1.67122 0.835611 0.549322i \(-0.185114\pi\)
0.835611 + 0.549322i \(0.185114\pi\)
\(80\) −13006.1 −0.227208
\(81\) 0 0
\(82\) −17490.3 −0.287251
\(83\) 1849.64 0.0294708 0.0147354 0.999891i \(-0.495309\pi\)
0.0147354 + 0.999891i \(0.495309\pi\)
\(84\) 0 0
\(85\) −72835.2 −1.09344
\(86\) 16392.3 0.238997
\(87\) 0 0
\(88\) −76359.5 −1.05113
\(89\) 70380.3 0.941838 0.470919 0.882176i \(-0.343922\pi\)
0.470919 + 0.882176i \(0.343922\pi\)
\(90\) 0 0
\(91\) −54236.8 −0.686579
\(92\) −130705. −1.60999
\(93\) 0 0
\(94\) −19546.9 −0.228170
\(95\) 24742.5 0.281277
\(96\) 0 0
\(97\) −88842.1 −0.958714 −0.479357 0.877620i \(-0.659130\pi\)
−0.479357 + 0.877620i \(0.659130\pi\)
\(98\) −11038.6 −0.116104
\(99\) 0 0
\(100\) −78946.8 −0.789468
\(101\) −179221. −1.74818 −0.874090 0.485763i \(-0.838542\pi\)
−0.874090 + 0.485763i \(0.838542\pi\)
\(102\) 0 0
\(103\) 123443. 1.14650 0.573248 0.819382i \(-0.305683\pi\)
0.573248 + 0.819382i \(0.305683\pi\)
\(104\) 56262.1 0.510074
\(105\) 0 0
\(106\) −221496. −1.91471
\(107\) −98991.7 −0.835871 −0.417936 0.908477i \(-0.637246\pi\)
−0.417936 + 0.908477i \(0.637246\pi\)
\(108\) 0 0
\(109\) 46356.0 0.373715 0.186857 0.982387i \(-0.440170\pi\)
0.186857 + 0.982387i \(0.440170\pi\)
\(110\) −197876. −1.55923
\(111\) 0 0
\(112\) 42894.2 0.323113
\(113\) −185076. −1.36350 −0.681750 0.731586i \(-0.738781\pi\)
−0.681750 + 0.731586i \(0.738781\pi\)
\(114\) 0 0
\(115\) −106101. −0.748123
\(116\) 67855.3 0.468208
\(117\) 0 0
\(118\) 379054. 2.50608
\(119\) 240211. 1.55498
\(120\) 0 0
\(121\) 187142. 1.16201
\(122\) −186377. −1.13369
\(123\) 0 0
\(124\) 205950. 1.20284
\(125\) −182289. −1.04348
\(126\) 0 0
\(127\) −237332. −1.30571 −0.652856 0.757482i \(-0.726429\pi\)
−0.652856 + 0.757482i \(0.726429\pi\)
\(128\) −237451. −1.28100
\(129\) 0 0
\(130\) 145796. 0.756636
\(131\) 283496. 1.44334 0.721671 0.692236i \(-0.243374\pi\)
0.721671 + 0.692236i \(0.243374\pi\)
\(132\) 0 0
\(133\) −81600.9 −0.400005
\(134\) −224049. −1.07791
\(135\) 0 0
\(136\) −249181. −1.15523
\(137\) −330992. −1.50666 −0.753331 0.657642i \(-0.771554\pi\)
−0.753331 + 0.657642i \(0.771554\pi\)
\(138\) 0 0
\(139\) 105975. 0.465230 0.232615 0.972569i \(-0.425272\pi\)
0.232615 + 0.972569i \(0.425272\pi\)
\(140\) −219870. −0.948081
\(141\) 0 0
\(142\) −426277. −1.77407
\(143\) −256551. −1.04914
\(144\) 0 0
\(145\) 55082.0 0.217565
\(146\) 521300. 2.02398
\(147\) 0 0
\(148\) 174881. 0.656279
\(149\) 196700. 0.725836 0.362918 0.931821i \(-0.381780\pi\)
0.362918 + 0.931821i \(0.381780\pi\)
\(150\) 0 0
\(151\) −412513. −1.47230 −0.736148 0.676820i \(-0.763357\pi\)
−0.736148 + 0.676820i \(0.763357\pi\)
\(152\) 84648.0 0.297172
\(153\) 0 0
\(154\) 652594. 2.21739
\(155\) 167181. 0.558931
\(156\) 0 0
\(157\) 410971. 1.33064 0.665322 0.746557i \(-0.268294\pi\)
0.665322 + 0.746557i \(0.268294\pi\)
\(158\) 821871. 2.61915
\(159\) 0 0
\(160\) −271938. −0.839790
\(161\) 349920. 1.06391
\(162\) 0 0
\(163\) −82488.7 −0.243179 −0.121589 0.992580i \(-0.538799\pi\)
−0.121589 + 0.992580i \(0.538799\pi\)
\(164\) −91928.2 −0.266894
\(165\) 0 0
\(166\) 16397.9 0.0461868
\(167\) 380336. 1.05530 0.527650 0.849462i \(-0.323073\pi\)
0.527650 + 0.849462i \(0.323073\pi\)
\(168\) 0 0
\(169\) −182265. −0.490892
\(170\) −645718. −1.71365
\(171\) 0 0
\(172\) 86157.1 0.222060
\(173\) −91482.2 −0.232392 −0.116196 0.993226i \(-0.537070\pi\)
−0.116196 + 0.993226i \(0.537070\pi\)
\(174\) 0 0
\(175\) 211354. 0.521694
\(176\) 202898. 0.493738
\(177\) 0 0
\(178\) 623955. 1.47606
\(179\) 607572. 1.41731 0.708656 0.705554i \(-0.249302\pi\)
0.708656 + 0.705554i \(0.249302\pi\)
\(180\) 0 0
\(181\) 351519. 0.797540 0.398770 0.917051i \(-0.369437\pi\)
0.398770 + 0.917051i \(0.369437\pi\)
\(182\) −480835. −1.07601
\(183\) 0 0
\(184\) −362987. −0.790398
\(185\) 141961. 0.304958
\(186\) 0 0
\(187\) 1.13624e6 2.37611
\(188\) −102738. −0.212000
\(189\) 0 0
\(190\) 219354. 0.440820
\(191\) 123308. 0.244573 0.122286 0.992495i \(-0.460977\pi\)
0.122286 + 0.992495i \(0.460977\pi\)
\(192\) 0 0
\(193\) −163481. −0.315917 −0.157959 0.987446i \(-0.550491\pi\)
−0.157959 + 0.987446i \(0.550491\pi\)
\(194\) −787627. −1.50251
\(195\) 0 0
\(196\) −58018.3 −0.107876
\(197\) −581124. −1.06685 −0.533425 0.845848i \(-0.679095\pi\)
−0.533425 + 0.845848i \(0.679095\pi\)
\(198\) 0 0
\(199\) 351526. 0.629253 0.314627 0.949216i \(-0.398121\pi\)
0.314627 + 0.949216i \(0.398121\pi\)
\(200\) −219247. −0.387577
\(201\) 0 0
\(202\) −1.58888e6 −2.73976
\(203\) −181660. −0.309400
\(204\) 0 0
\(205\) −74623.4 −0.124020
\(206\) 1.09438e6 1.79680
\(207\) 0 0
\(208\) −149497. −0.239592
\(209\) −385988. −0.611235
\(210\) 0 0
\(211\) 327480. 0.506383 0.253192 0.967416i \(-0.418520\pi\)
0.253192 + 0.967416i \(0.418520\pi\)
\(212\) −1.16418e6 −1.77901
\(213\) 0 0
\(214\) −877608. −1.30998
\(215\) 69938.6 0.103186
\(216\) 0 0
\(217\) −551364. −0.794857
\(218\) 410968. 0.585689
\(219\) 0 0
\(220\) −1.04003e6 −1.44873
\(221\) −837191. −1.15304
\(222\) 0 0
\(223\) 619602. 0.834355 0.417177 0.908825i \(-0.363019\pi\)
0.417177 + 0.908825i \(0.363019\pi\)
\(224\) 896853. 1.19427
\(225\) 0 0
\(226\) −1.64079e6 −2.13689
\(227\) 757446. 0.975635 0.487817 0.872946i \(-0.337793\pi\)
0.487817 + 0.872946i \(0.337793\pi\)
\(228\) 0 0
\(229\) 1.21739e6 1.53405 0.767025 0.641617i \(-0.221736\pi\)
0.767025 + 0.641617i \(0.221736\pi\)
\(230\) −940632. −1.17247
\(231\) 0 0
\(232\) 188444. 0.229860
\(233\) −379715. −0.458213 −0.229107 0.973401i \(-0.573580\pi\)
−0.229107 + 0.973401i \(0.573580\pi\)
\(234\) 0 0
\(235\) −83398.2 −0.0985115
\(236\) 1.99229e6 2.32848
\(237\) 0 0
\(238\) 2.12958e6 2.43698
\(239\) −281756. −0.319064 −0.159532 0.987193i \(-0.550999\pi\)
−0.159532 + 0.987193i \(0.550999\pi\)
\(240\) 0 0
\(241\) −1.12524e6 −1.24796 −0.623981 0.781439i \(-0.714486\pi\)
−0.623981 + 0.781439i \(0.714486\pi\)
\(242\) 1.65911e6 1.82111
\(243\) 0 0
\(244\) −979590. −1.05334
\(245\) −47096.8 −0.0501275
\(246\) 0 0
\(247\) 284398. 0.296609
\(248\) 571953. 0.590515
\(249\) 0 0
\(250\) −1.61608e6 −1.63536
\(251\) 675567. 0.676837 0.338419 0.940996i \(-0.390108\pi\)
0.338419 + 0.940996i \(0.390108\pi\)
\(252\) 0 0
\(253\) 1.65519e6 1.62572
\(254\) −2.10406e6 −2.04632
\(255\) 0 0
\(256\) −417633. −0.398286
\(257\) −1.85623e6 −1.75306 −0.876532 0.481343i \(-0.840149\pi\)
−0.876532 + 0.481343i \(0.840149\pi\)
\(258\) 0 0
\(259\) −468188. −0.433681
\(260\) 766298. 0.703014
\(261\) 0 0
\(262\) 2.51333e6 2.26202
\(263\) 1.54160e6 1.37430 0.687149 0.726516i \(-0.258862\pi\)
0.687149 + 0.726516i \(0.258862\pi\)
\(264\) 0 0
\(265\) −945029. −0.826667
\(266\) −723430. −0.626892
\(267\) 0 0
\(268\) −1.17759e6 −1.00152
\(269\) −1.16775e6 −0.983945 −0.491973 0.870611i \(-0.663724\pi\)
−0.491973 + 0.870611i \(0.663724\pi\)
\(270\) 0 0
\(271\) −1.20256e6 −0.994684 −0.497342 0.867555i \(-0.665691\pi\)
−0.497342 + 0.867555i \(0.665691\pi\)
\(272\) 662109. 0.542634
\(273\) 0 0
\(274\) −2.93440e6 −2.36125
\(275\) 999748. 0.797184
\(276\) 0 0
\(277\) −504463. −0.395030 −0.197515 0.980300i \(-0.563287\pi\)
−0.197515 + 0.980300i \(0.563287\pi\)
\(278\) 939521. 0.729112
\(279\) 0 0
\(280\) −610610. −0.465446
\(281\) −1.52712e6 −1.15374 −0.576870 0.816836i \(-0.695726\pi\)
−0.576870 + 0.816836i \(0.695726\pi\)
\(282\) 0 0
\(283\) 1.81916e6 1.35022 0.675110 0.737717i \(-0.264096\pi\)
0.675110 + 0.737717i \(0.264096\pi\)
\(284\) −2.24049e6 −1.64834
\(285\) 0 0
\(286\) −2.27444e6 −1.64422
\(287\) 246108. 0.176369
\(288\) 0 0
\(289\) 2.28799e6 1.61143
\(290\) 488328. 0.340970
\(291\) 0 0
\(292\) 2.73993e6 1.88054
\(293\) 2.35975e6 1.60582 0.802911 0.596099i \(-0.203283\pi\)
0.802911 + 0.596099i \(0.203283\pi\)
\(294\) 0 0
\(295\) 1.61726e6 1.08199
\(296\) 485671. 0.322190
\(297\) 0 0
\(298\) 1.74384e6 1.13754
\(299\) −1.21955e6 −0.788901
\(300\) 0 0
\(301\) −230658. −0.146741
\(302\) −3.65712e6 −2.30740
\(303\) 0 0
\(304\) −224922. −0.139588
\(305\) −795189. −0.489464
\(306\) 0 0
\(307\) −2.59790e6 −1.57317 −0.786587 0.617480i \(-0.788154\pi\)
−0.786587 + 0.617480i \(0.788154\pi\)
\(308\) 3.43001e6 2.06024
\(309\) 0 0
\(310\) 1.48214e6 0.875962
\(311\) 2.21471e6 1.29842 0.649212 0.760607i \(-0.275099\pi\)
0.649212 + 0.760607i \(0.275099\pi\)
\(312\) 0 0
\(313\) −2.43630e6 −1.40563 −0.702813 0.711374i \(-0.748073\pi\)
−0.702813 + 0.711374i \(0.748073\pi\)
\(314\) 3.64345e6 2.08540
\(315\) 0 0
\(316\) 4.31972e6 2.43354
\(317\) 2.59108e6 1.44821 0.724106 0.689689i \(-0.242253\pi\)
0.724106 + 0.689689i \(0.242253\pi\)
\(318\) 0 0
\(319\) −859290. −0.472784
\(320\) −1.99467e6 −1.08892
\(321\) 0 0
\(322\) 3.10220e6 1.66737
\(323\) −1.25958e6 −0.671767
\(324\) 0 0
\(325\) −736620. −0.386843
\(326\) −731301. −0.381112
\(327\) 0 0
\(328\) −255298. −0.131028
\(329\) 275047. 0.140093
\(330\) 0 0
\(331\) −2.49362e6 −1.25101 −0.625503 0.780221i \(-0.715106\pi\)
−0.625503 + 0.780221i \(0.715106\pi\)
\(332\) 86186.7 0.0429136
\(333\) 0 0
\(334\) 3.37186e6 1.65388
\(335\) −955921. −0.465383
\(336\) 0 0
\(337\) −159199. −0.0763600 −0.0381800 0.999271i \(-0.512156\pi\)
−0.0381800 + 0.999271i \(0.512156\pi\)
\(338\) −1.61586e6 −0.769331
\(339\) 0 0
\(340\) −3.39387e6 −1.59220
\(341\) −2.60806e6 −1.21460
\(342\) 0 0
\(343\) 2.25195e6 1.03353
\(344\) 239271. 0.109017
\(345\) 0 0
\(346\) −811033. −0.364207
\(347\) −4.35264e6 −1.94057 −0.970285 0.241966i \(-0.922208\pi\)
−0.970285 + 0.241966i \(0.922208\pi\)
\(348\) 0 0
\(349\) −502730. −0.220938 −0.110469 0.993880i \(-0.535235\pi\)
−0.110469 + 0.993880i \(0.535235\pi\)
\(350\) 1.87376e6 0.817604
\(351\) 0 0
\(352\) 4.24229e6 1.82492
\(353\) 990932. 0.423260 0.211630 0.977350i \(-0.432123\pi\)
0.211630 + 0.977350i \(0.432123\pi\)
\(354\) 0 0
\(355\) −1.81874e6 −0.765948
\(356\) 3.27948e6 1.37145
\(357\) 0 0
\(358\) 5.38641e6 2.22122
\(359\) 1.78805e6 0.732223 0.366112 0.930571i \(-0.380689\pi\)
0.366112 + 0.930571i \(0.380689\pi\)
\(360\) 0 0
\(361\) −2.04821e6 −0.827194
\(362\) 3.11638e6 1.24991
\(363\) 0 0
\(364\) −2.52725e6 −0.999758
\(365\) 2.22416e6 0.873844
\(366\) 0 0
\(367\) −68021.3 −0.0263621 −0.0131810 0.999913i \(-0.504196\pi\)
−0.0131810 + 0.999913i \(0.504196\pi\)
\(368\) 964507. 0.371267
\(369\) 0 0
\(370\) 1.25855e6 0.477933
\(371\) 3.11671e6 1.17560
\(372\) 0 0
\(373\) −949477. −0.353356 −0.176678 0.984269i \(-0.556535\pi\)
−0.176678 + 0.984269i \(0.556535\pi\)
\(374\) 1.00733e7 3.72387
\(375\) 0 0
\(376\) −285318. −0.104078
\(377\) 633130. 0.229424
\(378\) 0 0
\(379\) 2.53069e6 0.904982 0.452491 0.891769i \(-0.350535\pi\)
0.452491 + 0.891769i \(0.350535\pi\)
\(380\) 1.15292e6 0.409580
\(381\) 0 0
\(382\) 1.09318e6 0.383297
\(383\) −500631. −0.174390 −0.0871948 0.996191i \(-0.527790\pi\)
−0.0871948 + 0.996191i \(0.527790\pi\)
\(384\) 0 0
\(385\) 2.78434e6 0.957348
\(386\) −1.44933e6 −0.495108
\(387\) 0 0
\(388\) −4.13974e6 −1.39603
\(389\) 4.08546e6 1.36889 0.684443 0.729066i \(-0.260045\pi\)
0.684443 + 0.729066i \(0.260045\pi\)
\(390\) 0 0
\(391\) 5.40130e6 1.78672
\(392\) −161125. −0.0529601
\(393\) 0 0
\(394\) −5.15194e6 −1.67198
\(395\) 3.50657e6 1.13081
\(396\) 0 0
\(397\) 953651. 0.303678 0.151839 0.988405i \(-0.451480\pi\)
0.151839 + 0.988405i \(0.451480\pi\)
\(398\) 3.11645e6 0.986171
\(399\) 0 0
\(400\) 582570. 0.182053
\(401\) −4.81115e6 −1.49413 −0.747064 0.664752i \(-0.768537\pi\)
−0.747064 + 0.664752i \(0.768537\pi\)
\(402\) 0 0
\(403\) 1.92163e6 0.589397
\(404\) −8.35110e6 −2.54560
\(405\) 0 0
\(406\) −1.61051e6 −0.484894
\(407\) −2.21462e6 −0.662694
\(408\) 0 0
\(409\) −1.42551e6 −0.421370 −0.210685 0.977554i \(-0.567569\pi\)
−0.210685 + 0.977554i \(0.567569\pi\)
\(410\) −661572. −0.194365
\(411\) 0 0
\(412\) 5.75201e6 1.66946
\(413\) −5.33372e6 −1.53870
\(414\) 0 0
\(415\) 69962.7 0.0199410
\(416\) −3.12575e6 −0.885565
\(417\) 0 0
\(418\) −3.42197e6 −0.957933
\(419\) −2.91631e6 −0.811520 −0.405760 0.913980i \(-0.632993\pi\)
−0.405760 + 0.913980i \(0.632993\pi\)
\(420\) 0 0
\(421\) 6.91223e6 1.90070 0.950349 0.311186i \(-0.100726\pi\)
0.950349 + 0.311186i \(0.100726\pi\)
\(422\) 2.90327e6 0.793608
\(423\) 0 0
\(424\) −3.23309e6 −0.873380
\(425\) 3.26243e6 0.876131
\(426\) 0 0
\(427\) 2.62254e6 0.696068
\(428\) −4.61268e6 −1.21715
\(429\) 0 0
\(430\) 620039. 0.161714
\(431\) −2.58575e6 −0.670493 −0.335246 0.942131i \(-0.608820\pi\)
−0.335246 + 0.942131i \(0.608820\pi\)
\(432\) 0 0
\(433\) −3.71200e6 −0.951455 −0.475727 0.879593i \(-0.657815\pi\)
−0.475727 + 0.879593i \(0.657815\pi\)
\(434\) −4.88810e6 −1.24571
\(435\) 0 0
\(436\) 2.16003e6 0.544182
\(437\) −1.83485e6 −0.459619
\(438\) 0 0
\(439\) −415772. −0.102966 −0.0514830 0.998674i \(-0.516395\pi\)
−0.0514830 + 0.998674i \(0.516395\pi\)
\(440\) −2.88831e6 −0.711233
\(441\) 0 0
\(442\) −7.42209e6 −1.80705
\(443\) 602736. 0.145921 0.0729605 0.997335i \(-0.476755\pi\)
0.0729605 + 0.997335i \(0.476755\pi\)
\(444\) 0 0
\(445\) 2.66214e6 0.637282
\(446\) 5.49307e6 1.30761
\(447\) 0 0
\(448\) 6.57841e6 1.54855
\(449\) −1.84907e6 −0.432849 −0.216424 0.976299i \(-0.569440\pi\)
−0.216424 + 0.976299i \(0.569440\pi\)
\(450\) 0 0
\(451\) 1.16414e6 0.269503
\(452\) −8.62393e6 −1.98545
\(453\) 0 0
\(454\) 6.71512e6 1.52902
\(455\) −2.05151e6 −0.464564
\(456\) 0 0
\(457\) −7.35472e6 −1.64731 −0.823655 0.567091i \(-0.808069\pi\)
−0.823655 + 0.567091i \(0.808069\pi\)
\(458\) 1.07927e7 2.40418
\(459\) 0 0
\(460\) −4.94392e6 −1.08937
\(461\) 3.51032e6 0.769298 0.384649 0.923063i \(-0.374322\pi\)
0.384649 + 0.923063i \(0.374322\pi\)
\(462\) 0 0
\(463\) −6.86607e6 −1.48852 −0.744262 0.667888i \(-0.767199\pi\)
−0.744262 + 0.667888i \(0.767199\pi\)
\(464\) −500723. −0.107970
\(465\) 0 0
\(466\) −3.36635e6 −0.718116
\(467\) −5.66490e6 −1.20199 −0.600993 0.799254i \(-0.705228\pi\)
−0.600993 + 0.799254i \(0.705228\pi\)
\(468\) 0 0
\(469\) 3.15263e6 0.661821
\(470\) −739364. −0.154388
\(471\) 0 0
\(472\) 5.53289e6 1.14313
\(473\) −1.09106e6 −0.224230
\(474\) 0 0
\(475\) −1.10827e6 −0.225377
\(476\) 1.11930e7 2.26427
\(477\) 0 0
\(478\) −2.49790e6 −0.500041
\(479\) −4.55961e6 −0.908006 −0.454003 0.891000i \(-0.650004\pi\)
−0.454003 + 0.891000i \(0.650004\pi\)
\(480\) 0 0
\(481\) 1.63174e6 0.321580
\(482\) −9.97576e6 −1.95582
\(483\) 0 0
\(484\) 8.72019e6 1.69205
\(485\) −3.36046e6 −0.648701
\(486\) 0 0
\(487\) −9.17550e6 −1.75310 −0.876552 0.481308i \(-0.840162\pi\)
−0.876552 + 0.481308i \(0.840162\pi\)
\(488\) −2.72047e6 −0.517123
\(489\) 0 0
\(490\) −417535. −0.0785603
\(491\) −3.41449e6 −0.639179 −0.319589 0.947556i \(-0.603545\pi\)
−0.319589 + 0.947556i \(0.603545\pi\)
\(492\) 0 0
\(493\) −2.80408e6 −0.519605
\(494\) 2.52132e6 0.464848
\(495\) 0 0
\(496\) −1.51976e6 −0.277377
\(497\) 5.99820e6 1.08926
\(498\) 0 0
\(499\) −1.99364e6 −0.358423 −0.179211 0.983811i \(-0.557355\pi\)
−0.179211 + 0.983811i \(0.557355\pi\)
\(500\) −8.49405e6 −1.51946
\(501\) 0 0
\(502\) 5.98922e6 1.06074
\(503\) −9.15685e6 −1.61371 −0.806856 0.590748i \(-0.798833\pi\)
−0.806856 + 0.590748i \(0.798833\pi\)
\(504\) 0 0
\(505\) −6.77907e6 −1.18288
\(506\) 1.46740e7 2.54785
\(507\) 0 0
\(508\) −1.10589e7 −1.90130
\(509\) −6.56697e6 −1.12349 −0.561746 0.827309i \(-0.689870\pi\)
−0.561746 + 0.827309i \(0.689870\pi\)
\(510\) 0 0
\(511\) −7.33529e6 −1.24270
\(512\) 3.89593e6 0.656805
\(513\) 0 0
\(514\) −1.64563e7 −2.74742
\(515\) 4.66924e6 0.775761
\(516\) 0 0
\(517\) 1.30103e6 0.214072
\(518\) −4.15070e6 −0.679669
\(519\) 0 0
\(520\) 2.12812e6 0.345134
\(521\) −6.45805e6 −1.04234 −0.521168 0.853454i \(-0.674503\pi\)
−0.521168 + 0.853454i \(0.674503\pi\)
\(522\) 0 0
\(523\) 184405. 0.0294794 0.0147397 0.999891i \(-0.495308\pi\)
0.0147397 + 0.999891i \(0.495308\pi\)
\(524\) 1.32100e7 2.10171
\(525\) 0 0
\(526\) 1.36670e7 2.15381
\(527\) −8.51076e6 −1.33488
\(528\) 0 0
\(529\) 1.43185e6 0.222463
\(530\) −8.37813e6 −1.29556
\(531\) 0 0
\(532\) −3.80232e6 −0.582465
\(533\) −857745. −0.130780
\(534\) 0 0
\(535\) −3.74437e6 −0.565581
\(536\) −3.27035e6 −0.491680
\(537\) 0 0
\(538\) −1.03527e7 −1.54205
\(539\) 734719. 0.108931
\(540\) 0 0
\(541\) −7.10369e6 −1.04350 −0.521748 0.853100i \(-0.674720\pi\)
−0.521748 + 0.853100i \(0.674720\pi\)
\(542\) −1.06613e7 −1.55888
\(543\) 0 0
\(544\) 1.38437e7 2.00565
\(545\) 1.75342e6 0.252869
\(546\) 0 0
\(547\) −9.75210e6 −1.39357 −0.696787 0.717279i \(-0.745388\pi\)
−0.696787 + 0.717279i \(0.745388\pi\)
\(548\) −1.54231e7 −2.19392
\(549\) 0 0
\(550\) 8.86324e6 1.24935
\(551\) 952562. 0.133664
\(552\) 0 0
\(553\) −1.15647e7 −1.60813
\(554\) −4.47230e6 −0.619094
\(555\) 0 0
\(556\) 4.93809e6 0.677441
\(557\) 2.28586e6 0.312185 0.156092 0.987742i \(-0.450110\pi\)
0.156092 + 0.987742i \(0.450110\pi\)
\(558\) 0 0
\(559\) 803896. 0.108810
\(560\) 1.62248e6 0.218630
\(561\) 0 0
\(562\) −1.35386e7 −1.80815
\(563\) −2.31099e6 −0.307275 −0.153638 0.988127i \(-0.549099\pi\)
−0.153638 + 0.988127i \(0.549099\pi\)
\(564\) 0 0
\(565\) −7.00054e6 −0.922593
\(566\) 1.61277e7 2.11608
\(567\) 0 0
\(568\) −6.22218e6 −0.809230
\(569\) −1.17226e7 −1.51790 −0.758949 0.651151i \(-0.774287\pi\)
−0.758949 + 0.651151i \(0.774287\pi\)
\(570\) 0 0
\(571\) −5.10057e6 −0.654679 −0.327340 0.944907i \(-0.606152\pi\)
−0.327340 + 0.944907i \(0.606152\pi\)
\(572\) −1.19544e7 −1.52770
\(573\) 0 0
\(574\) 2.18186e6 0.276406
\(575\) 4.75245e6 0.599443
\(576\) 0 0
\(577\) 599429. 0.0749546 0.0374773 0.999297i \(-0.488068\pi\)
0.0374773 + 0.999297i \(0.488068\pi\)
\(578\) 2.02841e7 2.52544
\(579\) 0 0
\(580\) 2.56663e6 0.316806
\(581\) −230737. −0.0283581
\(582\) 0 0
\(583\) 1.47426e7 1.79640
\(584\) 7.60920e6 0.923224
\(585\) 0 0
\(586\) 2.09203e7 2.51666
\(587\) −4.32755e6 −0.518379 −0.259189 0.965826i \(-0.583455\pi\)
−0.259189 + 0.965826i \(0.583455\pi\)
\(588\) 0 0
\(589\) 2.89115e6 0.343386
\(590\) 1.43377e7 1.69571
\(591\) 0 0
\(592\) −1.29050e6 −0.151340
\(593\) 1.59099e7 1.85794 0.928968 0.370160i \(-0.120697\pi\)
0.928968 + 0.370160i \(0.120697\pi\)
\(594\) 0 0
\(595\) 9.08599e6 1.05216
\(596\) 9.16555e6 1.05692
\(597\) 0 0
\(598\) −1.08119e7 −1.23637
\(599\) −73202.1 −0.00833598 −0.00416799 0.999991i \(-0.501327\pi\)
−0.00416799 + 0.999991i \(0.501327\pi\)
\(600\) 0 0
\(601\) −3.77328e6 −0.426121 −0.213060 0.977039i \(-0.568343\pi\)
−0.213060 + 0.977039i \(0.568343\pi\)
\(602\) −2.04489e6 −0.229974
\(603\) 0 0
\(604\) −1.92217e7 −2.14387
\(605\) 7.07868e6 0.786256
\(606\) 0 0
\(607\) 3.39314e6 0.373792 0.186896 0.982380i \(-0.440157\pi\)
0.186896 + 0.982380i \(0.440157\pi\)
\(608\) −4.70277e6 −0.515935
\(609\) 0 0
\(610\) −7.04973e6 −0.767093
\(611\) −958605. −0.103881
\(612\) 0 0
\(613\) 5.93491e6 0.637915 0.318957 0.947769i \(-0.396667\pi\)
0.318957 + 0.947769i \(0.396667\pi\)
\(614\) −2.30316e7 −2.46549
\(615\) 0 0
\(616\) 9.52564e6 1.01145
\(617\) 1.07871e7 1.14076 0.570379 0.821382i \(-0.306796\pi\)
0.570379 + 0.821382i \(0.306796\pi\)
\(618\) 0 0
\(619\) 9.97743e6 1.04663 0.523313 0.852140i \(-0.324696\pi\)
0.523313 + 0.852140i \(0.324696\pi\)
\(620\) 7.79008e6 0.813884
\(621\) 0 0
\(622\) 1.96345e7 2.03490
\(623\) −8.77976e6 −0.906280
\(624\) 0 0
\(625\) −1.60054e6 −0.163895
\(626\) −2.15990e7 −2.20291
\(627\) 0 0
\(628\) 1.91498e7 1.93761
\(629\) −7.22687e6 −0.728322
\(630\) 0 0
\(631\) −3.42994e6 −0.342936 −0.171468 0.985190i \(-0.554851\pi\)
−0.171468 + 0.985190i \(0.554851\pi\)
\(632\) 1.19965e7 1.19471
\(633\) 0 0
\(634\) 2.29711e7 2.26965
\(635\) −8.97711e6 −0.883492
\(636\) 0 0
\(637\) −541345. −0.0528598
\(638\) −7.61801e6 −0.740952
\(639\) 0 0
\(640\) −8.98163e6 −0.866772
\(641\) 1.41725e7 1.36239 0.681193 0.732104i \(-0.261462\pi\)
0.681193 + 0.732104i \(0.261462\pi\)
\(642\) 0 0
\(643\) 4.26802e6 0.407098 0.203549 0.979065i \(-0.434752\pi\)
0.203549 + 0.979065i \(0.434752\pi\)
\(644\) 1.63051e7 1.54920
\(645\) 0 0
\(646\) −1.11667e7 −1.05280
\(647\) −1.26038e7 −1.18370 −0.591849 0.806049i \(-0.701602\pi\)
−0.591849 + 0.806049i \(0.701602\pi\)
\(648\) 0 0
\(649\) −2.52295e7 −2.35124
\(650\) −6.53048e6 −0.606264
\(651\) 0 0
\(652\) −3.84369e6 −0.354103
\(653\) −1.67724e7 −1.53926 −0.769631 0.638489i \(-0.779560\pi\)
−0.769631 + 0.638489i \(0.779560\pi\)
\(654\) 0 0
\(655\) 1.07233e7 0.976618
\(656\) 678364. 0.0615465
\(657\) 0 0
\(658\) 2.43842e6 0.219556
\(659\) 1.72113e7 1.54383 0.771915 0.635725i \(-0.219299\pi\)
0.771915 + 0.635725i \(0.219299\pi\)
\(660\) 0 0
\(661\) 5.67723e6 0.505397 0.252699 0.967545i \(-0.418682\pi\)
0.252699 + 0.967545i \(0.418682\pi\)
\(662\) −2.21071e7 −1.96059
\(663\) 0 0
\(664\) 239353. 0.0210678
\(665\) −3.08656e6 −0.270658
\(666\) 0 0
\(667\) −4.08476e6 −0.355510
\(668\) 1.77223e7 1.53667
\(669\) 0 0
\(670\) −8.47469e6 −0.729352
\(671\) 1.24051e7 1.06364
\(672\) 0 0
\(673\) 4.92989e6 0.419565 0.209783 0.977748i \(-0.432724\pi\)
0.209783 + 0.977748i \(0.432724\pi\)
\(674\) −1.41137e6 −0.119672
\(675\) 0 0
\(676\) −8.49292e6 −0.714809
\(677\) 1.25498e7 1.05236 0.526180 0.850373i \(-0.323624\pi\)
0.526180 + 0.850373i \(0.323624\pi\)
\(678\) 0 0
\(679\) 1.10828e7 0.922519
\(680\) −9.42528e6 −0.781668
\(681\) 0 0
\(682\) −2.31217e7 −1.90352
\(683\) 7.08503e6 0.581152 0.290576 0.956852i \(-0.406153\pi\)
0.290576 + 0.956852i \(0.406153\pi\)
\(684\) 0 0
\(685\) −1.25198e7 −1.01946
\(686\) 1.99646e7 1.61976
\(687\) 0 0
\(688\) −635777. −0.0512075
\(689\) −1.08625e7 −0.871726
\(690\) 0 0
\(691\) −9.40053e6 −0.748958 −0.374479 0.927235i \(-0.622178\pi\)
−0.374479 + 0.927235i \(0.622178\pi\)
\(692\) −4.26276e6 −0.338396
\(693\) 0 0
\(694\) −3.85882e7 −3.04128
\(695\) 4.00853e6 0.314791
\(696\) 0 0
\(697\) 3.79888e6 0.296192
\(698\) −4.45694e6 −0.346256
\(699\) 0 0
\(700\) 9.84839e6 0.759662
\(701\) −2.14131e7 −1.64583 −0.822914 0.568167i \(-0.807653\pi\)
−0.822914 + 0.568167i \(0.807653\pi\)
\(702\) 0 0
\(703\) 2.45501e6 0.187355
\(704\) 3.11172e7 2.36629
\(705\) 0 0
\(706\) 8.78508e6 0.663337
\(707\) 2.23574e7 1.68218
\(708\) 0 0
\(709\) 1.70494e7 1.27377 0.636887 0.770957i \(-0.280222\pi\)
0.636887 + 0.770957i \(0.280222\pi\)
\(710\) −1.61240e7 −1.20040
\(711\) 0 0
\(712\) 9.10761e6 0.673293
\(713\) −1.23978e7 −0.913316
\(714\) 0 0
\(715\) −9.70406e6 −0.709886
\(716\) 2.83108e7 2.06381
\(717\) 0 0
\(718\) 1.58519e7 1.14755
\(719\) 1.59376e7 1.14974 0.574872 0.818243i \(-0.305052\pi\)
0.574872 + 0.818243i \(0.305052\pi\)
\(720\) 0 0
\(721\) −1.53991e7 −1.10321
\(722\) −1.81584e7 −1.29639
\(723\) 0 0
\(724\) 1.63796e7 1.16133
\(725\) −2.46723e6 −0.174327
\(726\) 0 0
\(727\) 8.26202e6 0.579763 0.289881 0.957063i \(-0.406384\pi\)
0.289881 + 0.957063i \(0.406384\pi\)
\(728\) −7.01855e6 −0.490816
\(729\) 0 0
\(730\) 1.97182e7 1.36950
\(731\) −3.56039e6 −0.246436
\(732\) 0 0
\(733\) 6.20168e6 0.426334 0.213167 0.977016i \(-0.431622\pi\)
0.213167 + 0.977016i \(0.431622\pi\)
\(734\) −603041. −0.0413149
\(735\) 0 0
\(736\) 2.01664e7 1.37225
\(737\) 1.49126e7 1.01131
\(738\) 0 0
\(739\) −1.19003e7 −0.801578 −0.400789 0.916170i \(-0.631264\pi\)
−0.400789 + 0.916170i \(0.631264\pi\)
\(740\) 6.61490e6 0.444062
\(741\) 0 0
\(742\) 2.76311e7 1.84242
\(743\) −7.41722e6 −0.492912 −0.246456 0.969154i \(-0.579266\pi\)
−0.246456 + 0.969154i \(0.579266\pi\)
\(744\) 0 0
\(745\) 7.44020e6 0.491127
\(746\) −8.41756e6 −0.553782
\(747\) 0 0
\(748\) 5.29451e7 3.45996
\(749\) 1.23489e7 0.804314
\(750\) 0 0
\(751\) 1.46691e7 0.949084 0.474542 0.880233i \(-0.342614\pi\)
0.474542 + 0.880233i \(0.342614\pi\)
\(752\) 758131. 0.0488877
\(753\) 0 0
\(754\) 5.61299e6 0.359556
\(755\) −1.56033e7 −0.996209
\(756\) 0 0
\(757\) 2.41775e6 0.153346 0.0766729 0.997056i \(-0.475570\pi\)
0.0766729 + 0.997056i \(0.475570\pi\)
\(758\) 2.24357e7 1.41830
\(759\) 0 0
\(760\) 3.20182e6 0.201077
\(761\) −2.32422e7 −1.45484 −0.727422 0.686191i \(-0.759282\pi\)
−0.727422 + 0.686191i \(0.759282\pi\)
\(762\) 0 0
\(763\) −5.78279e6 −0.359605
\(764\) 5.74574e6 0.356133
\(765\) 0 0
\(766\) −4.43833e6 −0.273305
\(767\) 1.85893e7 1.14097
\(768\) 0 0
\(769\) −2.55432e7 −1.55761 −0.778806 0.627265i \(-0.784174\pi\)
−0.778806 + 0.627265i \(0.784174\pi\)
\(770\) 2.46844e7 1.50036
\(771\) 0 0
\(772\) −7.61765e6 −0.460021
\(773\) −1.72159e7 −1.03629 −0.518146 0.855292i \(-0.673378\pi\)
−0.518146 + 0.855292i \(0.673378\pi\)
\(774\) 0 0
\(775\) −7.48838e6 −0.447851
\(776\) −1.14967e7 −0.685358
\(777\) 0 0
\(778\) 3.62196e7 2.14533
\(779\) −1.29050e6 −0.0761930
\(780\) 0 0
\(781\) 2.83727e7 1.66446
\(782\) 4.78851e7 2.80016
\(783\) 0 0
\(784\) 428134. 0.0248765
\(785\) 1.55450e7 0.900362
\(786\) 0 0
\(787\) −1.48812e7 −0.856449 −0.428225 0.903672i \(-0.640861\pi\)
−0.428225 + 0.903672i \(0.640861\pi\)
\(788\) −2.70784e7 −1.55349
\(789\) 0 0
\(790\) 3.10874e7 1.77221
\(791\) 2.30878e7 1.31202
\(792\) 0 0
\(793\) −9.14016e6 −0.516144
\(794\) 8.45456e6 0.475927
\(795\) 0 0
\(796\) 1.63799e7 0.916283
\(797\) −5.81135e6 −0.324064 −0.162032 0.986785i \(-0.551805\pi\)
−0.162032 + 0.986785i \(0.551805\pi\)
\(798\) 0 0
\(799\) 4.24559e6 0.235272
\(800\) 1.21807e7 0.672893
\(801\) 0 0
\(802\) −4.26531e7 −2.34161
\(803\) −3.46973e7 −1.89892
\(804\) 0 0
\(805\) 1.32358e7 0.719878
\(806\) 1.70362e7 0.923708
\(807\) 0 0
\(808\) −2.31922e7 −1.24972
\(809\) 2.41530e7 1.29748 0.648740 0.761010i \(-0.275296\pi\)
0.648740 + 0.761010i \(0.275296\pi\)
\(810\) 0 0
\(811\) 2.14467e7 1.14501 0.572505 0.819901i \(-0.305972\pi\)
0.572505 + 0.819901i \(0.305972\pi\)
\(812\) −8.46476e6 −0.450531
\(813\) 0 0
\(814\) −1.96336e7 −1.03858
\(815\) −3.12014e6 −0.164543
\(816\) 0 0
\(817\) 1.20949e6 0.0633936
\(818\) −1.26379e7 −0.660375
\(819\) 0 0
\(820\) −3.47720e6 −0.180590
\(821\) 1.06313e7 0.550465 0.275232 0.961378i \(-0.411245\pi\)
0.275232 + 0.961378i \(0.411245\pi\)
\(822\) 0 0
\(823\) −871518. −0.0448515 −0.0224257 0.999749i \(-0.507139\pi\)
−0.0224257 + 0.999749i \(0.507139\pi\)
\(824\) 1.59742e7 0.819597
\(825\) 0 0
\(826\) −4.72859e7 −2.41147
\(827\) 1.70354e7 0.866141 0.433071 0.901360i \(-0.357430\pi\)
0.433071 + 0.901360i \(0.357430\pi\)
\(828\) 0 0
\(829\) 5.65731e6 0.285906 0.142953 0.989729i \(-0.454340\pi\)
0.142953 + 0.989729i \(0.454340\pi\)
\(830\) 620252. 0.0312517
\(831\) 0 0
\(832\) −2.29273e7 −1.14827
\(833\) 2.39758e6 0.119718
\(834\) 0 0
\(835\) 1.43862e7 0.714054
\(836\) −1.79857e7 −0.890046
\(837\) 0 0
\(838\) −2.58545e7 −1.27182
\(839\) −3.42452e7 −1.67956 −0.839779 0.542929i \(-0.817315\pi\)
−0.839779 + 0.542929i \(0.817315\pi\)
\(840\) 0 0
\(841\) −1.83905e7 −0.896612
\(842\) 6.12802e7 2.97879
\(843\) 0 0
\(844\) 1.52595e7 0.737366
\(845\) −6.89419e6 −0.332155
\(846\) 0 0
\(847\) −2.33455e7 −1.11814
\(848\) 8.59078e6 0.410245
\(849\) 0 0
\(850\) 2.89230e7 1.37308
\(851\) −1.05275e7 −0.498313
\(852\) 0 0
\(853\) −2.21968e7 −1.04452 −0.522261 0.852785i \(-0.674911\pi\)
−0.522261 + 0.852785i \(0.674911\pi\)
\(854\) 2.32500e7 1.09088
\(855\) 0 0
\(856\) −1.28101e7 −0.597541
\(857\) −3.15803e7 −1.46881 −0.734403 0.678714i \(-0.762538\pi\)
−0.734403 + 0.678714i \(0.762538\pi\)
\(858\) 0 0
\(859\) −1.22037e6 −0.0564297 −0.0282148 0.999602i \(-0.508982\pi\)
−0.0282148 + 0.999602i \(0.508982\pi\)
\(860\) 3.25890e6 0.150254
\(861\) 0 0
\(862\) −2.29239e7 −1.05080
\(863\) 2.43543e7 1.11314 0.556570 0.830801i \(-0.312117\pi\)
0.556570 + 0.830801i \(0.312117\pi\)
\(864\) 0 0
\(865\) −3.46032e6 −0.157245
\(866\) −3.29086e7 −1.49113
\(867\) 0 0
\(868\) −2.56917e7 −1.15743
\(869\) −5.47031e7 −2.45732
\(870\) 0 0
\(871\) −1.09877e7 −0.490749
\(872\) 5.99873e6 0.267158
\(873\) 0 0
\(874\) −1.62668e7 −0.720318
\(875\) 2.27401e7 1.00409
\(876\) 0 0
\(877\) 2.52016e6 0.110644 0.0553222 0.998469i \(-0.482381\pi\)
0.0553222 + 0.998469i \(0.482381\pi\)
\(878\) −3.68601e6 −0.161369
\(879\) 0 0
\(880\) 7.67465e6 0.334081
\(881\) −1.04311e6 −0.0452785 −0.0226393 0.999744i \(-0.507207\pi\)
−0.0226393 + 0.999744i \(0.507207\pi\)
\(882\) 0 0
\(883\) −3.57753e7 −1.54412 −0.772061 0.635548i \(-0.780774\pi\)
−0.772061 + 0.635548i \(0.780774\pi\)
\(884\) −3.90102e7 −1.67899
\(885\) 0 0
\(886\) 5.34354e6 0.228689
\(887\) 1.66616e7 0.711061 0.355531 0.934665i \(-0.384300\pi\)
0.355531 + 0.934665i \(0.384300\pi\)
\(888\) 0 0
\(889\) 2.96065e7 1.25642
\(890\) 2.36012e7 0.998754
\(891\) 0 0
\(892\) 2.88713e7 1.21494
\(893\) −1.44225e6 −0.0605218
\(894\) 0 0
\(895\) 2.29815e7 0.959004
\(896\) 2.96214e7 1.23264
\(897\) 0 0
\(898\) −1.63928e7 −0.678365
\(899\) 6.43631e6 0.265606
\(900\) 0 0
\(901\) 4.81090e7 1.97430
\(902\) 1.03206e7 0.422368
\(903\) 0 0
\(904\) −2.39499e7 −0.974727
\(905\) 1.32963e7 0.539645
\(906\) 0 0
\(907\) 3.59470e7 1.45092 0.725462 0.688262i \(-0.241626\pi\)
0.725462 + 0.688262i \(0.241626\pi\)
\(908\) 3.52944e7 1.42066
\(909\) 0 0
\(910\) −1.81876e7 −0.728069
\(911\) −7.56404e6 −0.301966 −0.150983 0.988536i \(-0.548244\pi\)
−0.150983 + 0.988536i \(0.548244\pi\)
\(912\) 0 0
\(913\) −1.09143e6 −0.0433331
\(914\) −6.52030e7 −2.58168
\(915\) 0 0
\(916\) 5.67260e7 2.23380
\(917\) −3.53654e7 −1.38885
\(918\) 0 0
\(919\) −2.22167e7 −0.867741 −0.433870 0.900975i \(-0.642852\pi\)
−0.433870 + 0.900975i \(0.642852\pi\)
\(920\) −1.37300e7 −0.534812
\(921\) 0 0
\(922\) 3.11207e7 1.20565
\(923\) −2.09051e7 −0.807698
\(924\) 0 0
\(925\) −6.35871e6 −0.244351
\(926\) −6.08709e7 −2.33283
\(927\) 0 0
\(928\) −1.04694e7 −0.399071
\(929\) −9.18809e6 −0.349290 −0.174645 0.984631i \(-0.555878\pi\)
−0.174645 + 0.984631i \(0.555878\pi\)
\(930\) 0 0
\(931\) −814470. −0.0307965
\(932\) −1.76934e7 −0.667224
\(933\) 0 0
\(934\) −5.02220e7 −1.88376
\(935\) 4.29785e7 1.60777
\(936\) 0 0
\(937\) 4.06654e7 1.51313 0.756565 0.653919i \(-0.226876\pi\)
0.756565 + 0.653919i \(0.226876\pi\)
\(938\) 2.79495e7 1.03721
\(939\) 0 0
\(940\) −3.88607e6 −0.143447
\(941\) 2.60105e7 0.957580 0.478790 0.877930i \(-0.341076\pi\)
0.478790 + 0.877930i \(0.341076\pi\)
\(942\) 0 0
\(943\) 5.53391e6 0.202653
\(944\) −1.47017e7 −0.536954
\(945\) 0 0
\(946\) −9.67273e6 −0.351416
\(947\) 2.03967e7 0.739067 0.369534 0.929217i \(-0.379517\pi\)
0.369534 + 0.929217i \(0.379517\pi\)
\(948\) 0 0
\(949\) 2.55652e7 0.921475
\(950\) −9.82530e6 −0.353213
\(951\) 0 0
\(952\) 3.10846e7 1.11161
\(953\) 4.87462e6 0.173864 0.0869318 0.996214i \(-0.472294\pi\)
0.0869318 + 0.996214i \(0.472294\pi\)
\(954\) 0 0
\(955\) 4.66414e6 0.165487
\(956\) −1.31289e7 −0.464603
\(957\) 0 0
\(958\) −4.04231e7 −1.42304
\(959\) 4.12903e7 1.44978
\(960\) 0 0
\(961\) −9.09409e6 −0.317651
\(962\) 1.44662e7 0.503984
\(963\) 0 0
\(964\) −5.24322e7 −1.81721
\(965\) −6.18368e6 −0.213761
\(966\) 0 0
\(967\) −1.26016e7 −0.433371 −0.216686 0.976241i \(-0.569525\pi\)
−0.216686 + 0.976241i \(0.569525\pi\)
\(968\) 2.42173e7 0.830686
\(969\) 0 0
\(970\) −2.97921e7 −1.01665
\(971\) 1.39978e6 0.0476443 0.0238221 0.999716i \(-0.492416\pi\)
0.0238221 + 0.999716i \(0.492416\pi\)
\(972\) 0 0
\(973\) −1.32201e7 −0.447665
\(974\) −8.13452e7 −2.74748
\(975\) 0 0
\(976\) 7.22867e6 0.242904
\(977\) −1.43010e6 −0.0479325 −0.0239662 0.999713i \(-0.507629\pi\)
−0.0239662 + 0.999713i \(0.507629\pi\)
\(978\) 0 0
\(979\) −4.15300e7 −1.38486
\(980\) −2.19455e6 −0.0729928
\(981\) 0 0
\(982\) −3.02711e7 −1.00173
\(983\) −4.26255e7 −1.40697 −0.703487 0.710708i \(-0.748375\pi\)
−0.703487 + 0.710708i \(0.748375\pi\)
\(984\) 0 0
\(985\) −2.19811e7 −0.721869
\(986\) −2.48595e7 −0.814329
\(987\) 0 0
\(988\) 1.32520e7 0.431905
\(989\) −5.18650e6 −0.168610
\(990\) 0 0
\(991\) 1.88273e7 0.608980 0.304490 0.952516i \(-0.401514\pi\)
0.304490 + 0.952516i \(0.401514\pi\)
\(992\) −3.17759e7 −1.02522
\(993\) 0 0
\(994\) 5.31769e7 1.70709
\(995\) 1.32965e7 0.425775
\(996\) 0 0
\(997\) 2.10574e7 0.670915 0.335458 0.942055i \(-0.391109\pi\)
0.335458 + 0.942055i \(0.391109\pi\)
\(998\) −1.76746e7 −0.561724
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 387.6.a.e.1.9 10
3.2 odd 2 43.6.a.b.1.2 10
12.11 even 2 688.6.a.h.1.6 10
15.14 odd 2 1075.6.a.b.1.9 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.6.a.b.1.2 10 3.2 odd 2
387.6.a.e.1.9 10 1.1 even 1 trivial
688.6.a.h.1.6 10 12.11 even 2
1075.6.a.b.1.9 10 15.14 odd 2