Properties

Label 464.6.a.k.1.1
Level $464$
Weight $6$
Character 464.1
Self dual yes
Analytic conductor $74.418$
Analytic rank $1$
Dimension $7$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [464,6,Mod(1,464)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(464, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("464.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 464 = 2^{4} \cdot 29 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 464.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(74.4180923932\)
Analytic rank: \(1\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - 3x^{6} - 184x^{5} + 584x^{4} + 10145x^{3} - 34491x^{2} - 149754x + 524902 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 29)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.90786\) of defining polynomial
Character \(\chi\) \(=\) 464.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-29.3989 q^{3} +64.0801 q^{5} +138.793 q^{7} +621.298 q^{9} +O(q^{10})\) \(q-29.3989 q^{3} +64.0801 q^{5} +138.793 q^{7} +621.298 q^{9} -557.286 q^{11} -41.1854 q^{13} -1883.89 q^{15} -1643.99 q^{17} -258.134 q^{19} -4080.36 q^{21} +2828.17 q^{23} +981.257 q^{25} -11121.6 q^{27} +841.000 q^{29} +5980.62 q^{31} +16383.6 q^{33} +8893.86 q^{35} -3327.01 q^{37} +1210.81 q^{39} -3895.80 q^{41} +3589.20 q^{43} +39812.8 q^{45} +7502.91 q^{47} +2456.45 q^{49} +48331.6 q^{51} +9015.58 q^{53} -35710.9 q^{55} +7588.86 q^{57} -39101.0 q^{59} +3951.11 q^{61} +86231.7 q^{63} -2639.16 q^{65} -62985.3 q^{67} -83145.1 q^{69} -7121.60 q^{71} -13910.9 q^{73} -28847.9 q^{75} -77347.2 q^{77} +37581.7 q^{79} +175987. q^{81} +74905.7 q^{83} -105347. q^{85} -24724.5 q^{87} +102613. q^{89} -5716.23 q^{91} -175824. q^{93} -16541.2 q^{95} -25501.5 q^{97} -346241. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 26 q^{3} + 32 q^{5} - 184 q^{7} + 1005 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 26 q^{3} + 32 q^{5} - 184 q^{7} + 1005 q^{9} - 1106 q^{11} + 408 q^{13} + 614 q^{15} - 874 q^{17} - 4288 q^{19} - 4200 q^{21} + 4532 q^{23} + 5527 q^{25} - 5942 q^{27} + 5887 q^{29} - 7794 q^{31} + 34410 q^{33} - 7088 q^{35} + 5086 q^{37} - 33394 q^{39} + 19826 q^{41} - 19498 q^{43} + 7854 q^{45} - 14278 q^{47} + 38431 q^{49} - 23892 q^{51} - 58644 q^{53} + 25574 q^{55} - 88540 q^{57} - 12888 q^{59} + 102866 q^{61} + 88632 q^{63} - 149206 q^{65} - 102996 q^{67} - 107244 q^{69} + 51596 q^{71} - 17566 q^{73} - 39356 q^{75} - 94104 q^{77} - 212058 q^{79} - 128285 q^{81} + 122928 q^{83} - 109336 q^{85} - 21866 q^{87} - 66510 q^{89} - 194368 q^{91} - 474274 q^{93} + 131676 q^{95} - 118182 q^{97} - 300668 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 0
\(3\) −29.3989 −1.88594 −0.942972 0.332873i \(-0.891982\pi\)
−0.942972 + 0.332873i \(0.891982\pi\)
\(4\) 0 0
\(5\) 64.0801 1.14630 0.573150 0.819451i \(-0.305721\pi\)
0.573150 + 0.819451i \(0.305721\pi\)
\(6\) 0 0
\(7\) 138.793 1.07059 0.535293 0.844666i \(-0.320201\pi\)
0.535293 + 0.844666i \(0.320201\pi\)
\(8\) 0 0
\(9\) 621.298 2.55678
\(10\) 0 0
\(11\) −557.286 −1.38866 −0.694330 0.719656i \(-0.744299\pi\)
−0.694330 + 0.719656i \(0.744299\pi\)
\(12\) 0 0
\(13\) −41.1854 −0.0675903 −0.0337952 0.999429i \(-0.510759\pi\)
−0.0337952 + 0.999429i \(0.510759\pi\)
\(14\) 0 0
\(15\) −1883.89 −2.16186
\(16\) 0 0
\(17\) −1643.99 −1.37968 −0.689838 0.723964i \(-0.742318\pi\)
−0.689838 + 0.723964i \(0.742318\pi\)
\(18\) 0 0
\(19\) −258.134 −0.164044 −0.0820221 0.996631i \(-0.526138\pi\)
−0.0820221 + 0.996631i \(0.526138\pi\)
\(20\) 0 0
\(21\) −4080.36 −2.01907
\(22\) 0 0
\(23\) 2828.17 1.11477 0.557385 0.830254i \(-0.311805\pi\)
0.557385 + 0.830254i \(0.311805\pi\)
\(24\) 0 0
\(25\) 981.257 0.314002
\(26\) 0 0
\(27\) −11121.6 −2.93600
\(28\) 0 0
\(29\) 841.000 0.185695
\(30\) 0 0
\(31\) 5980.62 1.11774 0.558872 0.829254i \(-0.311234\pi\)
0.558872 + 0.829254i \(0.311234\pi\)
\(32\) 0 0
\(33\) 16383.6 2.61894
\(34\) 0 0
\(35\) 8893.86 1.22721
\(36\) 0 0
\(37\) −3327.01 −0.399531 −0.199765 0.979844i \(-0.564018\pi\)
−0.199765 + 0.979844i \(0.564018\pi\)
\(38\) 0 0
\(39\) 1210.81 0.127472
\(40\) 0 0
\(41\) −3895.80 −0.361940 −0.180970 0.983489i \(-0.557924\pi\)
−0.180970 + 0.983489i \(0.557924\pi\)
\(42\) 0 0
\(43\) 3589.20 0.296023 0.148012 0.988986i \(-0.452713\pi\)
0.148012 + 0.988986i \(0.452713\pi\)
\(44\) 0 0
\(45\) 39812.8 2.93084
\(46\) 0 0
\(47\) 7502.91 0.495433 0.247717 0.968833i \(-0.420320\pi\)
0.247717 + 0.968833i \(0.420320\pi\)
\(48\) 0 0
\(49\) 2456.45 0.146156
\(50\) 0 0
\(51\) 48331.6 2.60199
\(52\) 0 0
\(53\) 9015.58 0.440863 0.220432 0.975402i \(-0.429253\pi\)
0.220432 + 0.975402i \(0.429253\pi\)
\(54\) 0 0
\(55\) −35710.9 −1.59182
\(56\) 0 0
\(57\) 7588.86 0.309378
\(58\) 0 0
\(59\) −39101.0 −1.46237 −0.731187 0.682177i \(-0.761033\pi\)
−0.731187 + 0.682177i \(0.761033\pi\)
\(60\) 0 0
\(61\) 3951.11 0.135955 0.0679773 0.997687i \(-0.478345\pi\)
0.0679773 + 0.997687i \(0.478345\pi\)
\(62\) 0 0
\(63\) 86231.7 2.73726
\(64\) 0 0
\(65\) −2639.16 −0.0774787
\(66\) 0 0
\(67\) −62985.3 −1.71416 −0.857082 0.515180i \(-0.827725\pi\)
−0.857082 + 0.515180i \(0.827725\pi\)
\(68\) 0 0
\(69\) −83145.1 −2.10239
\(70\) 0 0
\(71\) −7121.60 −0.167661 −0.0838304 0.996480i \(-0.526715\pi\)
−0.0838304 + 0.996480i \(0.526715\pi\)
\(72\) 0 0
\(73\) −13910.9 −0.305525 −0.152763 0.988263i \(-0.548817\pi\)
−0.152763 + 0.988263i \(0.548817\pi\)
\(74\) 0 0
\(75\) −28847.9 −0.592190
\(76\) 0 0
\(77\) −77347.2 −1.48668
\(78\) 0 0
\(79\) 37581.7 0.677499 0.338749 0.940877i \(-0.389996\pi\)
0.338749 + 0.940877i \(0.389996\pi\)
\(80\) 0 0
\(81\) 175987. 2.98035
\(82\) 0 0
\(83\) 74905.7 1.19349 0.596746 0.802430i \(-0.296460\pi\)
0.596746 + 0.802430i \(0.296460\pi\)
\(84\) 0 0
\(85\) −105347. −1.58152
\(86\) 0 0
\(87\) −24724.5 −0.350211
\(88\) 0 0
\(89\) 102613. 1.37318 0.686590 0.727045i \(-0.259107\pi\)
0.686590 + 0.727045i \(0.259107\pi\)
\(90\) 0 0
\(91\) −5716.23 −0.0723613
\(92\) 0 0
\(93\) −175824. −2.10800
\(94\) 0 0
\(95\) −16541.2 −0.188044
\(96\) 0 0
\(97\) −25501.5 −0.275193 −0.137596 0.990488i \(-0.543938\pi\)
−0.137596 + 0.990488i \(0.543938\pi\)
\(98\) 0 0
\(99\) −346241. −3.55050
\(100\) 0 0
\(101\) −29590.5 −0.288635 −0.144317 0.989531i \(-0.546099\pi\)
−0.144317 + 0.989531i \(0.546099\pi\)
\(102\) 0 0
\(103\) −170152. −1.58032 −0.790159 0.612902i \(-0.790002\pi\)
−0.790159 + 0.612902i \(0.790002\pi\)
\(104\) 0 0
\(105\) −261470. −2.31445
\(106\) 0 0
\(107\) 200423. 1.69234 0.846169 0.532915i \(-0.178903\pi\)
0.846169 + 0.532915i \(0.178903\pi\)
\(108\) 0 0
\(109\) −80642.9 −0.650130 −0.325065 0.945692i \(-0.605386\pi\)
−0.325065 + 0.945692i \(0.605386\pi\)
\(110\) 0 0
\(111\) 97810.6 0.753492
\(112\) 0 0
\(113\) 17299.3 0.127448 0.0637240 0.997968i \(-0.479702\pi\)
0.0637240 + 0.997968i \(0.479702\pi\)
\(114\) 0 0
\(115\) 181229. 1.27786
\(116\) 0 0
\(117\) −25588.4 −0.172814
\(118\) 0 0
\(119\) −228174. −1.47706
\(120\) 0 0
\(121\) 149516. 0.928378
\(122\) 0 0
\(123\) 114532. 0.682599
\(124\) 0 0
\(125\) −137371. −0.786359
\(126\) 0 0
\(127\) −191838. −1.05542 −0.527711 0.849424i \(-0.676949\pi\)
−0.527711 + 0.849424i \(0.676949\pi\)
\(128\) 0 0
\(129\) −105519. −0.558283
\(130\) 0 0
\(131\) −112493. −0.572726 −0.286363 0.958121i \(-0.592446\pi\)
−0.286363 + 0.958121i \(0.592446\pi\)
\(132\) 0 0
\(133\) −35827.1 −0.175623
\(134\) 0 0
\(135\) −712671. −3.36554
\(136\) 0 0
\(137\) −13514.2 −0.0615162 −0.0307581 0.999527i \(-0.509792\pi\)
−0.0307581 + 0.999527i \(0.509792\pi\)
\(138\) 0 0
\(139\) −315337. −1.38432 −0.692161 0.721743i \(-0.743341\pi\)
−0.692161 + 0.721743i \(0.743341\pi\)
\(140\) 0 0
\(141\) −220578. −0.934359
\(142\) 0 0
\(143\) 22952.0 0.0938600
\(144\) 0 0
\(145\) 53891.3 0.212862
\(146\) 0 0
\(147\) −72216.9 −0.275642
\(148\) 0 0
\(149\) −1500.22 −0.00553590 −0.00276795 0.999996i \(-0.500881\pi\)
−0.00276795 + 0.999996i \(0.500881\pi\)
\(150\) 0 0
\(151\) 141060. 0.503457 0.251729 0.967798i \(-0.419001\pi\)
0.251729 + 0.967798i \(0.419001\pi\)
\(152\) 0 0
\(153\) −1.02141e6 −3.52753
\(154\) 0 0
\(155\) 383239. 1.28127
\(156\) 0 0
\(157\) −335858. −1.08744 −0.543721 0.839266i \(-0.682985\pi\)
−0.543721 + 0.839266i \(0.682985\pi\)
\(158\) 0 0
\(159\) −265049. −0.831443
\(160\) 0 0
\(161\) 392529. 1.19346
\(162\) 0 0
\(163\) −208039. −0.613303 −0.306651 0.951822i \(-0.599209\pi\)
−0.306651 + 0.951822i \(0.599209\pi\)
\(164\) 0 0
\(165\) 1.04986e6 3.00208
\(166\) 0 0
\(167\) −235392. −0.653131 −0.326565 0.945175i \(-0.605891\pi\)
−0.326565 + 0.945175i \(0.605891\pi\)
\(168\) 0 0
\(169\) −369597. −0.995432
\(170\) 0 0
\(171\) −160378. −0.419425
\(172\) 0 0
\(173\) 126867. 0.322280 0.161140 0.986932i \(-0.448483\pi\)
0.161140 + 0.986932i \(0.448483\pi\)
\(174\) 0 0
\(175\) 136191. 0.336167
\(176\) 0 0
\(177\) 1.14953e6 2.75795
\(178\) 0 0
\(179\) 582710. 1.35932 0.679658 0.733529i \(-0.262128\pi\)
0.679658 + 0.733529i \(0.262128\pi\)
\(180\) 0 0
\(181\) 469745. 1.06578 0.532888 0.846186i \(-0.321107\pi\)
0.532888 + 0.846186i \(0.321107\pi\)
\(182\) 0 0
\(183\) −116158. −0.256403
\(184\) 0 0
\(185\) −213195. −0.457982
\(186\) 0 0
\(187\) 916172. 1.91590
\(188\) 0 0
\(189\) −1.54359e6 −3.14325
\(190\) 0 0
\(191\) −808559. −1.60372 −0.801860 0.597512i \(-0.796156\pi\)
−0.801860 + 0.597512i \(0.796156\pi\)
\(192\) 0 0
\(193\) 397971. 0.769057 0.384528 0.923113i \(-0.374364\pi\)
0.384528 + 0.923113i \(0.374364\pi\)
\(194\) 0 0
\(195\) 77588.6 0.146121
\(196\) 0 0
\(197\) −821639. −1.50840 −0.754198 0.656647i \(-0.771974\pi\)
−0.754198 + 0.656647i \(0.771974\pi\)
\(198\) 0 0
\(199\) −304702. −0.545435 −0.272718 0.962094i \(-0.587922\pi\)
−0.272718 + 0.962094i \(0.587922\pi\)
\(200\) 0 0
\(201\) 1.85170e6 3.23282
\(202\) 0 0
\(203\) 116725. 0.198803
\(204\) 0 0
\(205\) −249643. −0.414892
\(206\) 0 0
\(207\) 1.75714e6 2.85023
\(208\) 0 0
\(209\) 143854. 0.227802
\(210\) 0 0
\(211\) −657135. −1.01613 −0.508064 0.861319i \(-0.669639\pi\)
−0.508064 + 0.861319i \(0.669639\pi\)
\(212\) 0 0
\(213\) 209367. 0.316199
\(214\) 0 0
\(215\) 229996. 0.339331
\(216\) 0 0
\(217\) 830067. 1.19664
\(218\) 0 0
\(219\) 408965. 0.576204
\(220\) 0 0
\(221\) 67708.4 0.0932528
\(222\) 0 0
\(223\) 899606. 1.21141 0.605703 0.795690i \(-0.292892\pi\)
0.605703 + 0.795690i \(0.292892\pi\)
\(224\) 0 0
\(225\) 609653. 0.802835
\(226\) 0 0
\(227\) −660017. −0.850139 −0.425070 0.905161i \(-0.639750\pi\)
−0.425070 + 0.905161i \(0.639750\pi\)
\(228\) 0 0
\(229\) −622380. −0.784273 −0.392136 0.919907i \(-0.628264\pi\)
−0.392136 + 0.919907i \(0.628264\pi\)
\(230\) 0 0
\(231\) 2.27393e6 2.80380
\(232\) 0 0
\(233\) 24182.1 0.0291813 0.0145906 0.999894i \(-0.495355\pi\)
0.0145906 + 0.999894i \(0.495355\pi\)
\(234\) 0 0
\(235\) 480787. 0.567915
\(236\) 0 0
\(237\) −1.10486e6 −1.27772
\(238\) 0 0
\(239\) −201571. −0.228262 −0.114131 0.993466i \(-0.536408\pi\)
−0.114131 + 0.993466i \(0.536408\pi\)
\(240\) 0 0
\(241\) −1.01961e6 −1.13081 −0.565407 0.824812i \(-0.691281\pi\)
−0.565407 + 0.824812i \(0.691281\pi\)
\(242\) 0 0
\(243\) −2.47129e6 −2.68478
\(244\) 0 0
\(245\) 157409. 0.167539
\(246\) 0 0
\(247\) 10631.3 0.0110878
\(248\) 0 0
\(249\) −2.20215e6 −2.25086
\(250\) 0 0
\(251\) −1.41854e6 −1.42121 −0.710604 0.703593i \(-0.751578\pi\)
−0.710604 + 0.703593i \(0.751578\pi\)
\(252\) 0 0
\(253\) −1.57610e6 −1.54804
\(254\) 0 0
\(255\) 3.09709e6 2.98266
\(256\) 0 0
\(257\) −54526.1 −0.0514958 −0.0257479 0.999668i \(-0.508197\pi\)
−0.0257479 + 0.999668i \(0.508197\pi\)
\(258\) 0 0
\(259\) −461765. −0.427732
\(260\) 0 0
\(261\) 522512. 0.474783
\(262\) 0 0
\(263\) −2.15754e6 −1.92340 −0.961702 0.274098i \(-0.911621\pi\)
−0.961702 + 0.274098i \(0.911621\pi\)
\(264\) 0 0
\(265\) 577719. 0.505361
\(266\) 0 0
\(267\) −3.01672e6 −2.58974
\(268\) 0 0
\(269\) −128043. −0.107888 −0.0539442 0.998544i \(-0.517179\pi\)
−0.0539442 + 0.998544i \(0.517179\pi\)
\(270\) 0 0
\(271\) −691071. −0.571610 −0.285805 0.958288i \(-0.592261\pi\)
−0.285805 + 0.958288i \(0.592261\pi\)
\(272\) 0 0
\(273\) 168051. 0.136469
\(274\) 0 0
\(275\) −546840. −0.436042
\(276\) 0 0
\(277\) 589147. 0.461343 0.230672 0.973032i \(-0.425908\pi\)
0.230672 + 0.973032i \(0.425908\pi\)
\(278\) 0 0
\(279\) 3.71575e6 2.85783
\(280\) 0 0
\(281\) −1.20853e6 −0.913044 −0.456522 0.889712i \(-0.650905\pi\)
−0.456522 + 0.889712i \(0.650905\pi\)
\(282\) 0 0
\(283\) −1.88980e6 −1.40265 −0.701325 0.712842i \(-0.747408\pi\)
−0.701325 + 0.712842i \(0.747408\pi\)
\(284\) 0 0
\(285\) 486295. 0.354640
\(286\) 0 0
\(287\) −540709. −0.387489
\(288\) 0 0
\(289\) 1.28285e6 0.903506
\(290\) 0 0
\(291\) 749718. 0.518998
\(292\) 0 0
\(293\) −2.43906e6 −1.65979 −0.829895 0.557920i \(-0.811600\pi\)
−0.829895 + 0.557920i \(0.811600\pi\)
\(294\) 0 0
\(295\) −2.50560e6 −1.67632
\(296\) 0 0
\(297\) 6.19789e6 4.07711
\(298\) 0 0
\(299\) −116479. −0.0753477
\(300\) 0 0
\(301\) 498154. 0.316919
\(302\) 0 0
\(303\) 869929. 0.544349
\(304\) 0 0
\(305\) 253187. 0.155845
\(306\) 0 0
\(307\) 842448. 0.510149 0.255074 0.966921i \(-0.417900\pi\)
0.255074 + 0.966921i \(0.417900\pi\)
\(308\) 0 0
\(309\) 5.00229e6 2.98039
\(310\) 0 0
\(311\) 1.78495e6 1.04647 0.523233 0.852190i \(-0.324726\pi\)
0.523233 + 0.852190i \(0.324726\pi\)
\(312\) 0 0
\(313\) 1.79477e6 1.03550 0.517749 0.855533i \(-0.326770\pi\)
0.517749 + 0.855533i \(0.326770\pi\)
\(314\) 0 0
\(315\) 5.52574e6 3.13772
\(316\) 0 0
\(317\) −1.00473e6 −0.561564 −0.280782 0.959772i \(-0.590594\pi\)
−0.280782 + 0.959772i \(0.590594\pi\)
\(318\) 0 0
\(319\) −468677. −0.257868
\(320\) 0 0
\(321\) −5.89221e6 −3.19165
\(322\) 0 0
\(323\) 424369. 0.226328
\(324\) 0 0
\(325\) −40413.4 −0.0212235
\(326\) 0 0
\(327\) 2.37082e6 1.22611
\(328\) 0 0
\(329\) 1.04135e6 0.530404
\(330\) 0 0
\(331\) −3.52272e6 −1.76729 −0.883646 0.468155i \(-0.844919\pi\)
−0.883646 + 0.468155i \(0.844919\pi\)
\(332\) 0 0
\(333\) −2.06707e6 −1.02151
\(334\) 0 0
\(335\) −4.03610e6 −1.96494
\(336\) 0 0
\(337\) 2.94676e6 1.41342 0.706708 0.707506i \(-0.250180\pi\)
0.706708 + 0.707506i \(0.250180\pi\)
\(338\) 0 0
\(339\) −508582. −0.240360
\(340\) 0 0
\(341\) −3.33291e6 −1.55217
\(342\) 0 0
\(343\) −1.99175e6 −0.914114
\(344\) 0 0
\(345\) −5.32795e6 −2.40997
\(346\) 0 0
\(347\) 2.31985e6 1.03428 0.517138 0.855902i \(-0.326997\pi\)
0.517138 + 0.855902i \(0.326997\pi\)
\(348\) 0 0
\(349\) 1.13664e6 0.499526 0.249763 0.968307i \(-0.419647\pi\)
0.249763 + 0.968307i \(0.419647\pi\)
\(350\) 0 0
\(351\) 458046. 0.198445
\(352\) 0 0
\(353\) −942783. −0.402694 −0.201347 0.979520i \(-0.564532\pi\)
−0.201347 + 0.979520i \(0.564532\pi\)
\(354\) 0 0
\(355\) −456352. −0.192189
\(356\) 0 0
\(357\) 6.70808e6 2.78566
\(358\) 0 0
\(359\) 2.78926e6 1.14223 0.571113 0.820871i \(-0.306512\pi\)
0.571113 + 0.820871i \(0.306512\pi\)
\(360\) 0 0
\(361\) −2.40947e6 −0.973090
\(362\) 0 0
\(363\) −4.39562e6 −1.75087
\(364\) 0 0
\(365\) −891410. −0.350224
\(366\) 0 0
\(367\) 4.20179e6 1.62843 0.814215 0.580564i \(-0.197168\pi\)
0.814215 + 0.580564i \(0.197168\pi\)
\(368\) 0 0
\(369\) −2.42045e6 −0.925403
\(370\) 0 0
\(371\) 1.25130e6 0.471982
\(372\) 0 0
\(373\) 4.83152e6 1.79809 0.899045 0.437856i \(-0.144262\pi\)
0.899045 + 0.437856i \(0.144262\pi\)
\(374\) 0 0
\(375\) 4.03857e6 1.48303
\(376\) 0 0
\(377\) −34636.9 −0.0125512
\(378\) 0 0
\(379\) −2.03959e6 −0.729366 −0.364683 0.931132i \(-0.618823\pi\)
−0.364683 + 0.931132i \(0.618823\pi\)
\(380\) 0 0
\(381\) 5.63984e6 1.99046
\(382\) 0 0
\(383\) −923917. −0.321837 −0.160919 0.986968i \(-0.551446\pi\)
−0.160919 + 0.986968i \(0.551446\pi\)
\(384\) 0 0
\(385\) −4.95642e6 −1.70418
\(386\) 0 0
\(387\) 2.22996e6 0.756867
\(388\) 0 0
\(389\) −3.39429e6 −1.13730 −0.568650 0.822580i \(-0.692534\pi\)
−0.568650 + 0.822580i \(0.692534\pi\)
\(390\) 0 0
\(391\) −4.64948e6 −1.53802
\(392\) 0 0
\(393\) 3.30717e6 1.08013
\(394\) 0 0
\(395\) 2.40824e6 0.776616
\(396\) 0 0
\(397\) −1.00161e6 −0.318949 −0.159475 0.987202i \(-0.550980\pi\)
−0.159475 + 0.987202i \(0.550980\pi\)
\(398\) 0 0
\(399\) 1.05328e6 0.331216
\(400\) 0 0
\(401\) 5.53448e6 1.71876 0.859381 0.511337i \(-0.170849\pi\)
0.859381 + 0.511337i \(0.170849\pi\)
\(402\) 0 0
\(403\) −246314. −0.0755486
\(404\) 0 0
\(405\) 1.12773e7 3.41638
\(406\) 0 0
\(407\) 1.85410e6 0.554812
\(408\) 0 0
\(409\) 1.93289e6 0.571345 0.285672 0.958327i \(-0.407783\pi\)
0.285672 + 0.958327i \(0.407783\pi\)
\(410\) 0 0
\(411\) 397304. 0.116016
\(412\) 0 0
\(413\) −5.42694e6 −1.56560
\(414\) 0 0
\(415\) 4.79997e6 1.36810
\(416\) 0 0
\(417\) 9.27057e6 2.61075
\(418\) 0 0
\(419\) −1.80082e6 −0.501112 −0.250556 0.968102i \(-0.580613\pi\)
−0.250556 + 0.968102i \(0.580613\pi\)
\(420\) 0 0
\(421\) −1.32654e6 −0.364766 −0.182383 0.983228i \(-0.558381\pi\)
−0.182383 + 0.983228i \(0.558381\pi\)
\(422\) 0 0
\(423\) 4.66154e6 1.26671
\(424\) 0 0
\(425\) −1.61318e6 −0.433221
\(426\) 0 0
\(427\) 548385. 0.145551
\(428\) 0 0
\(429\) −674765. −0.177015
\(430\) 0 0
\(431\) −584408. −0.151539 −0.0757693 0.997125i \(-0.524141\pi\)
−0.0757693 + 0.997125i \(0.524141\pi\)
\(432\) 0 0
\(433\) −707379. −0.181315 −0.0906573 0.995882i \(-0.528897\pi\)
−0.0906573 + 0.995882i \(0.528897\pi\)
\(434\) 0 0
\(435\) −1.58435e6 −0.401447
\(436\) 0 0
\(437\) −730045. −0.182872
\(438\) 0 0
\(439\) −5.06180e6 −1.25356 −0.626778 0.779198i \(-0.715627\pi\)
−0.626778 + 0.779198i \(0.715627\pi\)
\(440\) 0 0
\(441\) 1.52619e6 0.373689
\(442\) 0 0
\(443\) 3.33111e6 0.806453 0.403227 0.915100i \(-0.367889\pi\)
0.403227 + 0.915100i \(0.367889\pi\)
\(444\) 0 0
\(445\) 6.57545e6 1.57408
\(446\) 0 0
\(447\) 44104.8 0.0104404
\(448\) 0 0
\(449\) 37802.9 0.00884930 0.00442465 0.999990i \(-0.498592\pi\)
0.00442465 + 0.999990i \(0.498592\pi\)
\(450\) 0 0
\(451\) 2.17107e6 0.502612
\(452\) 0 0
\(453\) −4.14702e6 −0.949491
\(454\) 0 0
\(455\) −366297. −0.0829477
\(456\) 0 0
\(457\) −7.55109e6 −1.69129 −0.845647 0.533743i \(-0.820785\pi\)
−0.845647 + 0.533743i \(0.820785\pi\)
\(458\) 0 0
\(459\) 1.82838e7 4.05073
\(460\) 0 0
\(461\) 1.97564e6 0.432967 0.216484 0.976286i \(-0.430541\pi\)
0.216484 + 0.976286i \(0.430541\pi\)
\(462\) 0 0
\(463\) 8.35199e6 1.81066 0.905331 0.424707i \(-0.139623\pi\)
0.905331 + 0.424707i \(0.139623\pi\)
\(464\) 0 0
\(465\) −1.12668e7 −2.41640
\(466\) 0 0
\(467\) 856159. 0.181661 0.0908306 0.995866i \(-0.471048\pi\)
0.0908306 + 0.995866i \(0.471048\pi\)
\(468\) 0 0
\(469\) −8.74191e6 −1.83516
\(470\) 0 0
\(471\) 9.87387e6 2.05086
\(472\) 0 0
\(473\) −2.00021e6 −0.411076
\(474\) 0 0
\(475\) −253296. −0.0515102
\(476\) 0 0
\(477\) 5.60136e6 1.12719
\(478\) 0 0
\(479\) −3.97374e6 −0.791336 −0.395668 0.918394i \(-0.629487\pi\)
−0.395668 + 0.918394i \(0.629487\pi\)
\(480\) 0 0
\(481\) 137024. 0.0270044
\(482\) 0 0
\(483\) −1.15399e7 −2.25080
\(484\) 0 0
\(485\) −1.63414e6 −0.315453
\(486\) 0 0
\(487\) −2.73024e6 −0.521649 −0.260824 0.965386i \(-0.583994\pi\)
−0.260824 + 0.965386i \(0.583994\pi\)
\(488\) 0 0
\(489\) 6.11611e6 1.15665
\(490\) 0 0
\(491\) −2.52027e6 −0.471785 −0.235892 0.971779i \(-0.575801\pi\)
−0.235892 + 0.971779i \(0.575801\pi\)
\(492\) 0 0
\(493\) −1.38260e6 −0.256199
\(494\) 0 0
\(495\) −2.21871e7 −4.06994
\(496\) 0 0
\(497\) −988426. −0.179495
\(498\) 0 0
\(499\) −8.63079e6 −1.55167 −0.775834 0.630937i \(-0.782671\pi\)
−0.775834 + 0.630937i \(0.782671\pi\)
\(500\) 0 0
\(501\) 6.92027e6 1.23177
\(502\) 0 0
\(503\) 8.02315e6 1.41392 0.706960 0.707254i \(-0.250066\pi\)
0.706960 + 0.707254i \(0.250066\pi\)
\(504\) 0 0
\(505\) −1.89616e6 −0.330862
\(506\) 0 0
\(507\) 1.08658e7 1.87733
\(508\) 0 0
\(509\) 5.81312e6 0.994523 0.497261 0.867601i \(-0.334339\pi\)
0.497261 + 0.867601i \(0.334339\pi\)
\(510\) 0 0
\(511\) −1.93073e6 −0.327092
\(512\) 0 0
\(513\) 2.87085e6 0.481634
\(514\) 0 0
\(515\) −1.09034e7 −1.81152
\(516\) 0 0
\(517\) −4.18126e6 −0.687988
\(518\) 0 0
\(519\) −3.72975e6 −0.607801
\(520\) 0 0
\(521\) 381523. 0.0615781 0.0307891 0.999526i \(-0.490198\pi\)
0.0307891 + 0.999526i \(0.490198\pi\)
\(522\) 0 0
\(523\) −1.85496e6 −0.296538 −0.148269 0.988947i \(-0.547370\pi\)
−0.148269 + 0.988947i \(0.547370\pi\)
\(524\) 0 0
\(525\) −4.00388e6 −0.633991
\(526\) 0 0
\(527\) −9.83209e6 −1.54212
\(528\) 0 0
\(529\) 1.56219e6 0.242713
\(530\) 0 0
\(531\) −2.42934e7 −3.73897
\(532\) 0 0
\(533\) 160450. 0.0244637
\(534\) 0 0
\(535\) 1.28431e7 1.93993
\(536\) 0 0
\(537\) −1.71311e7 −2.56359
\(538\) 0 0
\(539\) −1.36894e6 −0.202961
\(540\) 0 0
\(541\) −4.92237e6 −0.723071 −0.361535 0.932358i \(-0.617747\pi\)
−0.361535 + 0.932358i \(0.617747\pi\)
\(542\) 0 0
\(543\) −1.38100e7 −2.00999
\(544\) 0 0
\(545\) −5.16760e6 −0.745243
\(546\) 0 0
\(547\) 1.35722e6 0.193947 0.0969735 0.995287i \(-0.469084\pi\)
0.0969735 + 0.995287i \(0.469084\pi\)
\(548\) 0 0
\(549\) 2.45481e6 0.347607
\(550\) 0 0
\(551\) −217090. −0.0304622
\(552\) 0 0
\(553\) 5.21607e6 0.725321
\(554\) 0 0
\(555\) 6.26771e6 0.863727
\(556\) 0 0
\(557\) −629428. −0.0859623 −0.0429811 0.999076i \(-0.513686\pi\)
−0.0429811 + 0.999076i \(0.513686\pi\)
\(558\) 0 0
\(559\) −147822. −0.0200083
\(560\) 0 0
\(561\) −2.69345e7 −3.61328
\(562\) 0 0
\(563\) 706922. 0.0939941 0.0469971 0.998895i \(-0.485035\pi\)
0.0469971 + 0.998895i \(0.485035\pi\)
\(564\) 0 0
\(565\) 1.10854e6 0.146094
\(566\) 0 0
\(567\) 2.44257e7 3.19073
\(568\) 0 0
\(569\) 1.26921e7 1.64343 0.821716 0.569898i \(-0.193017\pi\)
0.821716 + 0.569898i \(0.193017\pi\)
\(570\) 0 0
\(571\) 8.06713e6 1.03545 0.517725 0.855547i \(-0.326779\pi\)
0.517725 + 0.855547i \(0.326779\pi\)
\(572\) 0 0
\(573\) 2.37708e7 3.02452
\(574\) 0 0
\(575\) 2.77516e6 0.350040
\(576\) 0 0
\(577\) 5.23139e6 0.654150 0.327075 0.944998i \(-0.393937\pi\)
0.327075 + 0.944998i \(0.393937\pi\)
\(578\) 0 0
\(579\) −1.16999e7 −1.45040
\(580\) 0 0
\(581\) 1.03964e7 1.27774
\(582\) 0 0
\(583\) −5.02425e6 −0.612209
\(584\) 0 0
\(585\) −1.63971e6 −0.198096
\(586\) 0 0
\(587\) 1.22738e7 1.47022 0.735111 0.677947i \(-0.237130\pi\)
0.735111 + 0.677947i \(0.237130\pi\)
\(588\) 0 0
\(589\) −1.54380e6 −0.183359
\(590\) 0 0
\(591\) 2.41553e7 2.84475
\(592\) 0 0
\(593\) −1.56297e7 −1.82521 −0.912607 0.408838i \(-0.865934\pi\)
−0.912607 + 0.408838i \(0.865934\pi\)
\(594\) 0 0
\(595\) −1.46214e7 −1.69316
\(596\) 0 0
\(597\) 8.95793e6 1.02866
\(598\) 0 0
\(599\) 909739. 0.103598 0.0517988 0.998658i \(-0.483505\pi\)
0.0517988 + 0.998658i \(0.483505\pi\)
\(600\) 0 0
\(601\) −1.28807e7 −1.45463 −0.727315 0.686303i \(-0.759232\pi\)
−0.727315 + 0.686303i \(0.759232\pi\)
\(602\) 0 0
\(603\) −3.91327e7 −4.38274
\(604\) 0 0
\(605\) 9.58101e6 1.06420
\(606\) 0 0
\(607\) −1.39560e7 −1.53741 −0.768706 0.639602i \(-0.779099\pi\)
−0.768706 + 0.639602i \(0.779099\pi\)
\(608\) 0 0
\(609\) −3.43159e6 −0.374931
\(610\) 0 0
\(611\) −309010. −0.0334865
\(612\) 0 0
\(613\) −4.77628e6 −0.513380 −0.256690 0.966494i \(-0.582632\pi\)
−0.256690 + 0.966494i \(0.582632\pi\)
\(614\) 0 0
\(615\) 7.33925e6 0.782463
\(616\) 0 0
\(617\) −5.08319e6 −0.537556 −0.268778 0.963202i \(-0.586620\pi\)
−0.268778 + 0.963202i \(0.586620\pi\)
\(618\) 0 0
\(619\) −2.45717e6 −0.257755 −0.128878 0.991660i \(-0.541137\pi\)
−0.128878 + 0.991660i \(0.541137\pi\)
\(620\) 0 0
\(621\) −3.14537e7 −3.27297
\(622\) 0 0
\(623\) 1.42420e7 1.47011
\(624\) 0 0
\(625\) −1.18692e7 −1.21540
\(626\) 0 0
\(627\) −4.22916e6 −0.429621
\(628\) 0 0
\(629\) 5.46958e6 0.551223
\(630\) 0 0
\(631\) 1.11683e7 1.11664 0.558322 0.829624i \(-0.311445\pi\)
0.558322 + 0.829624i \(0.311445\pi\)
\(632\) 0 0
\(633\) 1.93191e7 1.91636
\(634\) 0 0
\(635\) −1.22930e7 −1.20983
\(636\) 0 0
\(637\) −101170. −0.00987874
\(638\) 0 0
\(639\) −4.42463e6 −0.428672
\(640\) 0 0
\(641\) −9.24222e6 −0.888446 −0.444223 0.895916i \(-0.646520\pi\)
−0.444223 + 0.895916i \(0.646520\pi\)
\(642\) 0 0
\(643\) −1.65662e6 −0.158014 −0.0790069 0.996874i \(-0.525175\pi\)
−0.0790069 + 0.996874i \(0.525175\pi\)
\(644\) 0 0
\(645\) −6.76164e6 −0.639960
\(646\) 0 0
\(647\) 1.26223e6 0.118544 0.0592720 0.998242i \(-0.481122\pi\)
0.0592720 + 0.998242i \(0.481122\pi\)
\(648\) 0 0
\(649\) 2.17904e7 2.03074
\(650\) 0 0
\(651\) −2.44031e7 −2.25680
\(652\) 0 0
\(653\) 1.64066e7 1.50569 0.752843 0.658200i \(-0.228682\pi\)
0.752843 + 0.658200i \(0.228682\pi\)
\(654\) 0 0
\(655\) −7.20855e6 −0.656515
\(656\) 0 0
\(657\) −8.64280e6 −0.781162
\(658\) 0 0
\(659\) 2.46135e6 0.220780 0.110390 0.993888i \(-0.464790\pi\)
0.110390 + 0.993888i \(0.464790\pi\)
\(660\) 0 0
\(661\) −1.29962e7 −1.15694 −0.578471 0.815703i \(-0.696350\pi\)
−0.578471 + 0.815703i \(0.696350\pi\)
\(662\) 0 0
\(663\) −1.99055e6 −0.175869
\(664\) 0 0
\(665\) −2.29580e6 −0.201317
\(666\) 0 0
\(667\) 2.37849e6 0.207008
\(668\) 0 0
\(669\) −2.64475e7 −2.28464
\(670\) 0 0
\(671\) −2.20189e6 −0.188795
\(672\) 0 0
\(673\) −1.00711e7 −0.857119 −0.428559 0.903514i \(-0.640979\pi\)
−0.428559 + 0.903514i \(0.640979\pi\)
\(674\) 0 0
\(675\) −1.09131e7 −0.921912
\(676\) 0 0
\(677\) 9.82242e6 0.823658 0.411829 0.911261i \(-0.364890\pi\)
0.411829 + 0.911261i \(0.364890\pi\)
\(678\) 0 0
\(679\) −3.53943e6 −0.294618
\(680\) 0 0
\(681\) 1.94038e7 1.60331
\(682\) 0 0
\(683\) 1.66547e7 1.36611 0.683053 0.730369i \(-0.260652\pi\)
0.683053 + 0.730369i \(0.260652\pi\)
\(684\) 0 0
\(685\) −865992. −0.0705160
\(686\) 0 0
\(687\) 1.82973e7 1.47909
\(688\) 0 0
\(689\) −371310. −0.0297981
\(690\) 0 0
\(691\) −6.35915e6 −0.506645 −0.253323 0.967382i \(-0.581523\pi\)
−0.253323 + 0.967382i \(0.581523\pi\)
\(692\) 0 0
\(693\) −4.80557e7 −3.80112
\(694\) 0 0
\(695\) −2.02068e7 −1.58685
\(696\) 0 0
\(697\) 6.40466e6 0.499360
\(698\) 0 0
\(699\) −710929. −0.0550342
\(700\) 0 0
\(701\) −167796. −0.0128969 −0.00644846 0.999979i \(-0.502053\pi\)
−0.00644846 + 0.999979i \(0.502053\pi\)
\(702\) 0 0
\(703\) 858814. 0.0655406
\(704\) 0 0
\(705\) −1.41346e7 −1.07105
\(706\) 0 0
\(707\) −4.10695e6 −0.309009
\(708\) 0 0
\(709\) −2.01558e7 −1.50586 −0.752932 0.658099i \(-0.771361\pi\)
−0.752932 + 0.658099i \(0.771361\pi\)
\(710\) 0 0
\(711\) 2.33494e7 1.73222
\(712\) 0 0
\(713\) 1.69142e7 1.24603
\(714\) 0 0
\(715\) 1.47077e6 0.107592
\(716\) 0 0
\(717\) 5.92597e6 0.430488
\(718\) 0 0
\(719\) 1.06393e7 0.767523 0.383761 0.923432i \(-0.374628\pi\)
0.383761 + 0.923432i \(0.374628\pi\)
\(720\) 0 0
\(721\) −2.36159e7 −1.69187
\(722\) 0 0
\(723\) 2.99754e7 2.13265
\(724\) 0 0
\(725\) 825237. 0.0583087
\(726\) 0 0
\(727\) −1.07639e7 −0.755323 −0.377661 0.925944i \(-0.623272\pi\)
−0.377661 + 0.925944i \(0.623272\pi\)
\(728\) 0 0
\(729\) 2.98885e7 2.08298
\(730\) 0 0
\(731\) −5.90060e6 −0.408416
\(732\) 0 0
\(733\) 8.86456e6 0.609393 0.304696 0.952450i \(-0.401445\pi\)
0.304696 + 0.952450i \(0.401445\pi\)
\(734\) 0 0
\(735\) −4.62767e6 −0.315968
\(736\) 0 0
\(737\) 3.51008e7 2.38039
\(738\) 0 0
\(739\) −1.34276e7 −0.904457 −0.452229 0.891902i \(-0.649371\pi\)
−0.452229 + 0.891902i \(0.649371\pi\)
\(740\) 0 0
\(741\) −312550. −0.0209110
\(742\) 0 0
\(743\) 3.76228e6 0.250023 0.125011 0.992155i \(-0.460103\pi\)
0.125011 + 0.992155i \(0.460103\pi\)
\(744\) 0 0
\(745\) −96134.1 −0.00634580
\(746\) 0 0
\(747\) 4.65388e7 3.05150
\(748\) 0 0
\(749\) 2.78172e7 1.81179
\(750\) 0 0
\(751\) −1.97179e7 −1.27574 −0.637870 0.770144i \(-0.720184\pi\)
−0.637870 + 0.770144i \(0.720184\pi\)
\(752\) 0 0
\(753\) 4.17036e7 2.68032
\(754\) 0 0
\(755\) 9.03915e6 0.577112
\(756\) 0 0
\(757\) −1.91175e7 −1.21253 −0.606264 0.795264i \(-0.707332\pi\)
−0.606264 + 0.795264i \(0.707332\pi\)
\(758\) 0 0
\(759\) 4.63356e7 2.91951
\(760\) 0 0
\(761\) −4.51417e6 −0.282563 −0.141282 0.989969i \(-0.545122\pi\)
−0.141282 + 0.989969i \(0.545122\pi\)
\(762\) 0 0
\(763\) −1.11927e7 −0.696020
\(764\) 0 0
\(765\) −6.54519e7 −4.04361
\(766\) 0 0
\(767\) 1.61039e6 0.0988423
\(768\) 0 0
\(769\) 2.08251e7 1.26990 0.634952 0.772551i \(-0.281020\pi\)
0.634952 + 0.772551i \(0.281020\pi\)
\(770\) 0 0
\(771\) 1.60301e6 0.0971182
\(772\) 0 0
\(773\) −1.68649e7 −1.01516 −0.507581 0.861604i \(-0.669460\pi\)
−0.507581 + 0.861604i \(0.669460\pi\)
\(774\) 0 0
\(775\) 5.86853e6 0.350974
\(776\) 0 0
\(777\) 1.35754e7 0.806679
\(778\) 0 0
\(779\) 1.00564e6 0.0593742
\(780\) 0 0
\(781\) 3.96876e6 0.232824
\(782\) 0 0
\(783\) −9.35324e6 −0.545202
\(784\) 0 0
\(785\) −2.15218e7 −1.24654
\(786\) 0 0
\(787\) 532946. 0.0306723 0.0153361 0.999882i \(-0.495118\pi\)
0.0153361 + 0.999882i \(0.495118\pi\)
\(788\) 0 0
\(789\) 6.34295e7 3.62743
\(790\) 0 0
\(791\) 2.40102e6 0.136444
\(792\) 0 0
\(793\) −162728. −0.00918922
\(794\) 0 0
\(795\) −1.69843e7 −0.953083
\(796\) 0 0
\(797\) 2.74340e6 0.152983 0.0764916 0.997070i \(-0.475628\pi\)
0.0764916 + 0.997070i \(0.475628\pi\)
\(798\) 0 0
\(799\) −1.23347e7 −0.683537
\(800\) 0 0
\(801\) 6.37533e7 3.51092
\(802\) 0 0
\(803\) 7.75233e6 0.424271
\(804\) 0 0
\(805\) 2.51533e7 1.36806
\(806\) 0 0
\(807\) 3.76433e6 0.203471
\(808\) 0 0
\(809\) 3.60884e6 0.193864 0.0969318 0.995291i \(-0.469097\pi\)
0.0969318 + 0.995291i \(0.469097\pi\)
\(810\) 0 0
\(811\) 2.42636e7 1.29540 0.647698 0.761897i \(-0.275732\pi\)
0.647698 + 0.761897i \(0.275732\pi\)
\(812\) 0 0
\(813\) 2.03168e7 1.07802
\(814\) 0 0
\(815\) −1.33311e7 −0.703028
\(816\) 0 0
\(817\) −926492. −0.0485609
\(818\) 0 0
\(819\) −3.55149e6 −0.185012
\(820\) 0 0
\(821\) −2.65430e6 −0.137433 −0.0687167 0.997636i \(-0.521890\pi\)
−0.0687167 + 0.997636i \(0.521890\pi\)
\(822\) 0 0
\(823\) 1.45761e7 0.750137 0.375068 0.926997i \(-0.377619\pi\)
0.375068 + 0.926997i \(0.377619\pi\)
\(824\) 0 0
\(825\) 1.60765e7 0.822351
\(826\) 0 0
\(827\) 2.56966e7 1.30651 0.653254 0.757139i \(-0.273403\pi\)
0.653254 + 0.757139i \(0.273403\pi\)
\(828\) 0 0
\(829\) 5.04257e6 0.254839 0.127419 0.991849i \(-0.459331\pi\)
0.127419 + 0.991849i \(0.459331\pi\)
\(830\) 0 0
\(831\) −1.73203e7 −0.870067
\(832\) 0 0
\(833\) −4.03838e6 −0.201648
\(834\) 0 0
\(835\) −1.50839e7 −0.748684
\(836\) 0 0
\(837\) −6.65139e7 −3.28170
\(838\) 0 0
\(839\) 6.91282e6 0.339039 0.169520 0.985527i \(-0.445778\pi\)
0.169520 + 0.985527i \(0.445778\pi\)
\(840\) 0 0
\(841\) 707281. 0.0344828
\(842\) 0 0
\(843\) 3.55295e7 1.72195
\(844\) 0 0
\(845\) −2.36838e7 −1.14106
\(846\) 0 0
\(847\) 2.07518e7 0.993909
\(848\) 0 0
\(849\) 5.55581e7 2.64532
\(850\) 0 0
\(851\) −9.40934e6 −0.445385
\(852\) 0 0
\(853\) −2.16826e7 −1.02033 −0.510164 0.860077i \(-0.670415\pi\)
−0.510164 + 0.860077i \(0.670415\pi\)
\(854\) 0 0
\(855\) −1.02770e7 −0.480787
\(856\) 0 0
\(857\) −2.22637e7 −1.03549 −0.517745 0.855535i \(-0.673228\pi\)
−0.517745 + 0.855535i \(0.673228\pi\)
\(858\) 0 0
\(859\) 1.56538e7 0.723828 0.361914 0.932211i \(-0.382123\pi\)
0.361914 + 0.932211i \(0.382123\pi\)
\(860\) 0 0
\(861\) 1.58963e7 0.730781
\(862\) 0 0
\(863\) −3.14396e7 −1.43698 −0.718489 0.695538i \(-0.755166\pi\)
−0.718489 + 0.695538i \(0.755166\pi\)
\(864\) 0 0
\(865\) 8.12964e6 0.369429
\(866\) 0 0
\(867\) −3.77144e7 −1.70396
\(868\) 0 0
\(869\) −2.09437e7 −0.940816
\(870\) 0 0
\(871\) 2.59407e6 0.115861
\(872\) 0 0
\(873\) −1.58440e7 −0.703608
\(874\) 0 0
\(875\) −1.90661e7 −0.841865
\(876\) 0 0
\(877\) 9.99092e6 0.438638 0.219319 0.975653i \(-0.429616\pi\)
0.219319 + 0.975653i \(0.429616\pi\)
\(878\) 0 0
\(879\) 7.17057e7 3.13027
\(880\) 0 0
\(881\) −2.37367e6 −0.103034 −0.0515169 0.998672i \(-0.516406\pi\)
−0.0515169 + 0.998672i \(0.516406\pi\)
\(882\) 0 0
\(883\) 686405. 0.0296264 0.0148132 0.999890i \(-0.495285\pi\)
0.0148132 + 0.999890i \(0.495285\pi\)
\(884\) 0 0
\(885\) 7.36619e7 3.16144
\(886\) 0 0
\(887\) −1.54019e7 −0.657302 −0.328651 0.944451i \(-0.606594\pi\)
−0.328651 + 0.944451i \(0.606594\pi\)
\(888\) 0 0
\(889\) −2.66258e7 −1.12992
\(890\) 0 0
\(891\) −9.80750e7 −4.13870
\(892\) 0 0
\(893\) −1.93675e6 −0.0812729
\(894\) 0 0
\(895\) 3.73401e7 1.55818
\(896\) 0 0
\(897\) 3.42436e6 0.142102
\(898\) 0 0
\(899\) 5.02970e6 0.207560
\(900\) 0 0
\(901\) −1.48215e7 −0.608248
\(902\) 0 0
\(903\) −1.46452e7 −0.597691
\(904\) 0 0
\(905\) 3.01013e7 1.22170
\(906\) 0 0
\(907\) 2.67004e7 1.07770 0.538852 0.842401i \(-0.318858\pi\)
0.538852 + 0.842401i \(0.318858\pi\)
\(908\) 0 0
\(909\) −1.83845e7 −0.737976
\(910\) 0 0
\(911\) −1.90851e7 −0.761902 −0.380951 0.924595i \(-0.624403\pi\)
−0.380951 + 0.924595i \(0.624403\pi\)
\(912\) 0 0
\(913\) −4.17439e7 −1.65736
\(914\) 0 0
\(915\) −7.44344e6 −0.293914
\(916\) 0 0
\(917\) −1.56132e7 −0.613153
\(918\) 0 0
\(919\) −3.04815e7 −1.19055 −0.595274 0.803523i \(-0.702957\pi\)
−0.595274 + 0.803523i \(0.702957\pi\)
\(920\) 0 0
\(921\) −2.47671e7 −0.962112
\(922\) 0 0
\(923\) 293306. 0.0113322
\(924\) 0 0
\(925\) −3.26465e6 −0.125453
\(926\) 0 0
\(927\) −1.05715e8 −4.04053
\(928\) 0 0
\(929\) −2.44730e7 −0.930352 −0.465176 0.885218i \(-0.654009\pi\)
−0.465176 + 0.885218i \(0.654009\pi\)
\(930\) 0 0
\(931\) −634092. −0.0239761
\(932\) 0 0
\(933\) −5.24757e7 −1.97358
\(934\) 0 0
\(935\) 5.87084e7 2.19620
\(936\) 0 0
\(937\) −3.03413e7 −1.12898 −0.564489 0.825441i \(-0.690927\pi\)
−0.564489 + 0.825441i \(0.690927\pi\)
\(938\) 0 0
\(939\) −5.27645e7 −1.95289
\(940\) 0 0
\(941\) 4.32048e7 1.59059 0.795294 0.606224i \(-0.207317\pi\)
0.795294 + 0.606224i \(0.207317\pi\)
\(942\) 0 0
\(943\) −1.10180e7 −0.403480
\(944\) 0 0
\(945\) −9.89136e7 −3.60310
\(946\) 0 0
\(947\) 2.50483e7 0.907620 0.453810 0.891099i \(-0.350065\pi\)
0.453810 + 0.891099i \(0.350065\pi\)
\(948\) 0 0
\(949\) 572925. 0.0206506
\(950\) 0 0
\(951\) 2.95379e7 1.05908
\(952\) 0 0
\(953\) 4.30580e7 1.53576 0.767878 0.640596i \(-0.221313\pi\)
0.767878 + 0.640596i \(0.221313\pi\)
\(954\) 0 0
\(955\) −5.18125e7 −1.83834
\(956\) 0 0
\(957\) 1.37786e7 0.486324
\(958\) 0 0
\(959\) −1.87568e6 −0.0658584
\(960\) 0 0
\(961\) 7.13868e6 0.249350
\(962\) 0 0
\(963\) 1.24522e8 4.32694
\(964\) 0 0
\(965\) 2.55020e7 0.881569
\(966\) 0 0
\(967\) 3.26447e7 1.12266 0.561328 0.827593i \(-0.310290\pi\)
0.561328 + 0.827593i \(0.310290\pi\)
\(968\) 0 0
\(969\) −1.24760e7 −0.426841
\(970\) 0 0
\(971\) 9.02885e6 0.307315 0.153658 0.988124i \(-0.450895\pi\)
0.153658 + 0.988124i \(0.450895\pi\)
\(972\) 0 0
\(973\) −4.37665e7 −1.48204
\(974\) 0 0
\(975\) 1.18811e6 0.0400263
\(976\) 0 0
\(977\) 8.87743e6 0.297544 0.148772 0.988872i \(-0.452468\pi\)
0.148772 + 0.988872i \(0.452468\pi\)
\(978\) 0 0
\(979\) −5.71848e7 −1.90688
\(980\) 0 0
\(981\) −5.01033e7 −1.66224
\(982\) 0 0
\(983\) 4.56481e7 1.50674 0.753371 0.657596i \(-0.228427\pi\)
0.753371 + 0.657596i \(0.228427\pi\)
\(984\) 0 0
\(985\) −5.26507e7 −1.72907
\(986\) 0 0
\(987\) −3.06146e7 −1.00031
\(988\) 0 0
\(989\) 1.01508e7 0.329998
\(990\) 0 0
\(991\) 7.74121e6 0.250395 0.125197 0.992132i \(-0.460044\pi\)
0.125197 + 0.992132i \(0.460044\pi\)
\(992\) 0 0
\(993\) 1.03564e8 3.33301
\(994\) 0 0
\(995\) −1.95253e7 −0.625232
\(996\) 0 0
\(997\) 5.64996e7 1.80014 0.900072 0.435740i \(-0.143513\pi\)
0.900072 + 0.435740i \(0.143513\pi\)
\(998\) 0 0
\(999\) 3.70016e7 1.17302
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 464.6.a.k.1.1 7
4.3 odd 2 29.6.a.b.1.3 7
12.11 even 2 261.6.a.e.1.5 7
20.19 odd 2 725.6.a.b.1.5 7
116.115 odd 2 841.6.a.b.1.5 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.6.a.b.1.3 7 4.3 odd 2
261.6.a.e.1.5 7 12.11 even 2
464.6.a.k.1.1 7 1.1 even 1 trivial
725.6.a.b.1.5 7 20.19 odd 2
841.6.a.b.1.5 7 116.115 odd 2