Properties

Label 280.6.a.g.1.2
Level $280$
Weight $6$
Character 280.1
Self dual yes
Analytic conductor $44.907$
Analytic rank $1$
Dimension $4$
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] = [280,6,Mod(1,280)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(280, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("280.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.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: \(44.9074695476\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - 2x^{3} - 232x^{2} + 60x + 5808 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{5} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-13.3078\) of defining polynomial
Character \(\chi\) \(=\) 280.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-15.6617 q^{3} +25.0000 q^{5} +49.0000 q^{7} +2.28996 q^{9} +O(q^{10})\) \(q-15.6617 q^{3} +25.0000 q^{5} +49.0000 q^{7} +2.28996 q^{9} -541.846 q^{11} +762.537 q^{13} -391.543 q^{15} +734.092 q^{17} +1106.05 q^{19} -767.425 q^{21} -4521.40 q^{23} +625.000 q^{25} +3769.94 q^{27} -4034.79 q^{29} +9248.86 q^{31} +8486.24 q^{33} +1225.00 q^{35} +11490.0 q^{37} -11942.7 q^{39} -11025.2 q^{41} -8340.65 q^{43} +57.2489 q^{45} -1060.61 q^{47} +2401.00 q^{49} -11497.2 q^{51} +5213.92 q^{53} -13546.1 q^{55} -17322.7 q^{57} -50307.0 q^{59} -12131.6 q^{61} +112.208 q^{63} +19063.4 q^{65} -66799.4 q^{67} +70812.9 q^{69} -60509.7 q^{71} -66790.8 q^{73} -9788.58 q^{75} -26550.4 q^{77} +61795.8 q^{79} -59600.2 q^{81} -123891. q^{83} +18352.3 q^{85} +63191.8 q^{87} +25976.4 q^{89} +37364.3 q^{91} -144853. q^{93} +27651.3 q^{95} -68019.8 q^{97} -1240.80 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 13 q^{3} + 100 q^{5} + 196 q^{7} - 193 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 13 q^{3} + 100 q^{5} + 196 q^{7} - 193 q^{9} - 595 q^{11} - 969 q^{13} - 325 q^{15} - 1315 q^{17} - 1090 q^{19} - 637 q^{21} - 1534 q^{23} + 2500 q^{25} + 173 q^{27} + 4099 q^{29} - 4820 q^{31} + 4149 q^{33} + 4900 q^{35} + 7692 q^{37} - 6371 q^{39} - 9722 q^{41} - 20610 q^{43} - 4825 q^{45} - 1661 q^{47} + 9604 q^{49} - 73361 q^{51} - 28898 q^{53} - 14875 q^{55} - 21246 q^{57} - 101872 q^{59} - 24742 q^{61} - 9457 q^{63} - 24225 q^{65} - 82060 q^{67} + 16914 q^{69} - 102784 q^{71} - 80652 q^{73} - 8125 q^{75} - 29155 q^{77} - 117801 q^{79} - 141052 q^{81} - 155440 q^{83} - 32875 q^{85} - 82519 q^{87} + 56426 q^{89} - 47481 q^{91} - 17332 q^{93} - 27250 q^{95} - 261031 q^{97} - 61686 q^{99}+O(q^{100}) \) 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
\(3\) −15.6617 −1.00470 −0.502350 0.864664i \(-0.667531\pi\)
−0.502350 + 0.864664i \(0.667531\pi\)
\(4\) 0 0
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) 49.0000 0.377964
\(8\) 0 0
\(9\) 2.28996 0.00942368
\(10\) 0 0
\(11\) −541.846 −1.35019 −0.675093 0.737732i \(-0.735897\pi\)
−0.675093 + 0.737732i \(0.735897\pi\)
\(12\) 0 0
\(13\) 762.537 1.25142 0.625709 0.780056i \(-0.284810\pi\)
0.625709 + 0.780056i \(0.284810\pi\)
\(14\) 0 0
\(15\) −391.543 −0.449316
\(16\) 0 0
\(17\) 734.092 0.616067 0.308034 0.951375i \(-0.400329\pi\)
0.308034 + 0.951375i \(0.400329\pi\)
\(18\) 0 0
\(19\) 1106.05 0.702897 0.351448 0.936207i \(-0.385689\pi\)
0.351448 + 0.936207i \(0.385689\pi\)
\(20\) 0 0
\(21\) −767.425 −0.379741
\(22\) 0 0
\(23\) −4521.40 −1.78219 −0.891093 0.453821i \(-0.850061\pi\)
−0.891093 + 0.453821i \(0.850061\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 0 0
\(27\) 3769.94 0.995233
\(28\) 0 0
\(29\) −4034.79 −0.890893 −0.445447 0.895308i \(-0.646955\pi\)
−0.445447 + 0.895308i \(0.646955\pi\)
\(30\) 0 0
\(31\) 9248.86 1.72856 0.864279 0.503013i \(-0.167775\pi\)
0.864279 + 0.503013i \(0.167775\pi\)
\(32\) 0 0
\(33\) 8486.24 1.35653
\(34\) 0 0
\(35\) 1225.00 0.169031
\(36\) 0 0
\(37\) 11490.0 1.37980 0.689900 0.723904i \(-0.257654\pi\)
0.689900 + 0.723904i \(0.257654\pi\)
\(38\) 0 0
\(39\) −11942.7 −1.25730
\(40\) 0 0
\(41\) −11025.2 −1.02430 −0.512148 0.858897i \(-0.671150\pi\)
−0.512148 + 0.858897i \(0.671150\pi\)
\(42\) 0 0
\(43\) −8340.65 −0.687905 −0.343953 0.938987i \(-0.611766\pi\)
−0.343953 + 0.938987i \(0.611766\pi\)
\(44\) 0 0
\(45\) 57.2489 0.00421440
\(46\) 0 0
\(47\) −1060.61 −0.0700342 −0.0350171 0.999387i \(-0.511149\pi\)
−0.0350171 + 0.999387i \(0.511149\pi\)
\(48\) 0 0
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) −11497.2 −0.618963
\(52\) 0 0
\(53\) 5213.92 0.254961 0.127481 0.991841i \(-0.459311\pi\)
0.127481 + 0.991841i \(0.459311\pi\)
\(54\) 0 0
\(55\) −13546.1 −0.603822
\(56\) 0 0
\(57\) −17322.7 −0.706201
\(58\) 0 0
\(59\) −50307.0 −1.88147 −0.940737 0.339136i \(-0.889865\pi\)
−0.940737 + 0.339136i \(0.889865\pi\)
\(60\) 0 0
\(61\) −12131.6 −0.417441 −0.208721 0.977975i \(-0.566930\pi\)
−0.208721 + 0.977975i \(0.566930\pi\)
\(62\) 0 0
\(63\) 112.208 0.00356182
\(64\) 0 0
\(65\) 19063.4 0.559652
\(66\) 0 0
\(67\) −66799.4 −1.81796 −0.908982 0.416835i \(-0.863139\pi\)
−0.908982 + 0.416835i \(0.863139\pi\)
\(68\) 0 0
\(69\) 70812.9 1.79056
\(70\) 0 0
\(71\) −60509.7 −1.42455 −0.712277 0.701899i \(-0.752336\pi\)
−0.712277 + 0.701899i \(0.752336\pi\)
\(72\) 0 0
\(73\) −66790.8 −1.46693 −0.733465 0.679727i \(-0.762098\pi\)
−0.733465 + 0.679727i \(0.762098\pi\)
\(74\) 0 0
\(75\) −9788.58 −0.200940
\(76\) 0 0
\(77\) −26550.4 −0.510323
\(78\) 0 0
\(79\) 61795.8 1.11402 0.557008 0.830507i \(-0.311949\pi\)
0.557008 + 0.830507i \(0.311949\pi\)
\(80\) 0 0
\(81\) −59600.2 −1.00933
\(82\) 0 0
\(83\) −123891. −1.97399 −0.986995 0.160753i \(-0.948608\pi\)
−0.986995 + 0.160753i \(0.948608\pi\)
\(84\) 0 0
\(85\) 18352.3 0.275514
\(86\) 0 0
\(87\) 63191.8 0.895081
\(88\) 0 0
\(89\) 25976.4 0.347620 0.173810 0.984779i \(-0.444392\pi\)
0.173810 + 0.984779i \(0.444392\pi\)
\(90\) 0 0
\(91\) 37364.3 0.472992
\(92\) 0 0
\(93\) −144853. −1.73668
\(94\) 0 0
\(95\) 27651.3 0.314345
\(96\) 0 0
\(97\) −68019.8 −0.734017 −0.367008 0.930218i \(-0.619618\pi\)
−0.367008 + 0.930218i \(0.619618\pi\)
\(98\) 0 0
\(99\) −1240.80 −0.0127237
\(100\) 0 0
\(101\) −27324.6 −0.266533 −0.133266 0.991080i \(-0.542547\pi\)
−0.133266 + 0.991080i \(0.542547\pi\)
\(102\) 0 0
\(103\) −14070.9 −0.130686 −0.0653429 0.997863i \(-0.520814\pi\)
−0.0653429 + 0.997863i \(0.520814\pi\)
\(104\) 0 0
\(105\) −19185.6 −0.169825
\(106\) 0 0
\(107\) −186019. −1.57072 −0.785358 0.619042i \(-0.787521\pi\)
−0.785358 + 0.619042i \(0.787521\pi\)
\(108\) 0 0
\(109\) 57760.5 0.465655 0.232828 0.972518i \(-0.425202\pi\)
0.232828 + 0.972518i \(0.425202\pi\)
\(110\) 0 0
\(111\) −179954. −1.38629
\(112\) 0 0
\(113\) 232262. 1.71113 0.855563 0.517698i \(-0.173211\pi\)
0.855563 + 0.517698i \(0.173211\pi\)
\(114\) 0 0
\(115\) −113035. −0.797018
\(116\) 0 0
\(117\) 1746.18 0.0117930
\(118\) 0 0
\(119\) 35970.5 0.232852
\(120\) 0 0
\(121\) 132546. 0.823005
\(122\) 0 0
\(123\) 172673. 1.02911
\(124\) 0 0
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) 155827. 0.857302 0.428651 0.903470i \(-0.358989\pi\)
0.428651 + 0.903470i \(0.358989\pi\)
\(128\) 0 0
\(129\) 130629. 0.691139
\(130\) 0 0
\(131\) 276458. 1.40751 0.703755 0.710443i \(-0.251505\pi\)
0.703755 + 0.710443i \(0.251505\pi\)
\(132\) 0 0
\(133\) 54196.5 0.265670
\(134\) 0 0
\(135\) 94248.4 0.445082
\(136\) 0 0
\(137\) −206689. −0.940840 −0.470420 0.882443i \(-0.655898\pi\)
−0.470420 + 0.882443i \(0.655898\pi\)
\(138\) 0 0
\(139\) −121060. −0.531451 −0.265725 0.964049i \(-0.585611\pi\)
−0.265725 + 0.964049i \(0.585611\pi\)
\(140\) 0 0
\(141\) 16611.0 0.0703634
\(142\) 0 0
\(143\) −413178. −1.68965
\(144\) 0 0
\(145\) −100870. −0.398420
\(146\) 0 0
\(147\) −37603.8 −0.143529
\(148\) 0 0
\(149\) 213540. 0.787976 0.393988 0.919116i \(-0.371095\pi\)
0.393988 + 0.919116i \(0.371095\pi\)
\(150\) 0 0
\(151\) −306833. −1.09512 −0.547558 0.836768i \(-0.684442\pi\)
−0.547558 + 0.836768i \(0.684442\pi\)
\(152\) 0 0
\(153\) 1681.04 0.00580562
\(154\) 0 0
\(155\) 231221. 0.773034
\(156\) 0 0
\(157\) −113475. −0.367410 −0.183705 0.982981i \(-0.558809\pi\)
−0.183705 + 0.982981i \(0.558809\pi\)
\(158\) 0 0
\(159\) −81659.0 −0.256160
\(160\) 0 0
\(161\) −221548. −0.673603
\(162\) 0 0
\(163\) −519473. −1.53142 −0.765709 0.643187i \(-0.777612\pi\)
−0.765709 + 0.643187i \(0.777612\pi\)
\(164\) 0 0
\(165\) 212156. 0.606660
\(166\) 0 0
\(167\) 57730.3 0.160182 0.0800908 0.996788i \(-0.474479\pi\)
0.0800908 + 0.996788i \(0.474479\pi\)
\(168\) 0 0
\(169\) 210170. 0.566049
\(170\) 0 0
\(171\) 2532.81 0.00662388
\(172\) 0 0
\(173\) 298815. 0.759080 0.379540 0.925175i \(-0.376082\pi\)
0.379540 + 0.925175i \(0.376082\pi\)
\(174\) 0 0
\(175\) 30625.0 0.0755929
\(176\) 0 0
\(177\) 787895. 1.89032
\(178\) 0 0
\(179\) 112965. 0.263519 0.131760 0.991282i \(-0.457937\pi\)
0.131760 + 0.991282i \(0.457937\pi\)
\(180\) 0 0
\(181\) −163008. −0.369840 −0.184920 0.982754i \(-0.559203\pi\)
−0.184920 + 0.982754i \(0.559203\pi\)
\(182\) 0 0
\(183\) 190003. 0.419403
\(184\) 0 0
\(185\) 287250. 0.617066
\(186\) 0 0
\(187\) −397765. −0.831806
\(188\) 0 0
\(189\) 184727. 0.376163
\(190\) 0 0
\(191\) 414125. 0.821387 0.410693 0.911773i \(-0.365287\pi\)
0.410693 + 0.911773i \(0.365287\pi\)
\(192\) 0 0
\(193\) −782850. −1.51281 −0.756407 0.654102i \(-0.773047\pi\)
−0.756407 + 0.654102i \(0.773047\pi\)
\(194\) 0 0
\(195\) −298566. −0.562282
\(196\) 0 0
\(197\) −435399. −0.799322 −0.399661 0.916663i \(-0.630872\pi\)
−0.399661 + 0.916663i \(0.630872\pi\)
\(198\) 0 0
\(199\) 1.02204e6 1.82950 0.914752 0.404016i \(-0.132386\pi\)
0.914752 + 0.404016i \(0.132386\pi\)
\(200\) 0 0
\(201\) 1.04619e6 1.82651
\(202\) 0 0
\(203\) −197705. −0.336726
\(204\) 0 0
\(205\) −275629. −0.458079
\(206\) 0 0
\(207\) −10353.8 −0.0167948
\(208\) 0 0
\(209\) −599309. −0.949042
\(210\) 0 0
\(211\) −628212. −0.971404 −0.485702 0.874124i \(-0.661436\pi\)
−0.485702 + 0.874124i \(0.661436\pi\)
\(212\) 0 0
\(213\) 947686. 1.43125
\(214\) 0 0
\(215\) −208516. −0.307641
\(216\) 0 0
\(217\) 453194. 0.653333
\(218\) 0 0
\(219\) 1.04606e6 1.47383
\(220\) 0 0
\(221\) 559773. 0.770958
\(222\) 0 0
\(223\) −371528. −0.500299 −0.250149 0.968207i \(-0.580480\pi\)
−0.250149 + 0.968207i \(0.580480\pi\)
\(224\) 0 0
\(225\) 1431.22 0.00188474
\(226\) 0 0
\(227\) −1.32477e6 −1.70638 −0.853189 0.521602i \(-0.825335\pi\)
−0.853189 + 0.521602i \(0.825335\pi\)
\(228\) 0 0
\(229\) 1.08203e6 1.36349 0.681746 0.731589i \(-0.261221\pi\)
0.681746 + 0.731589i \(0.261221\pi\)
\(230\) 0 0
\(231\) 415826. 0.512722
\(232\) 0 0
\(233\) 1.12343e6 1.35568 0.677839 0.735210i \(-0.262916\pi\)
0.677839 + 0.735210i \(0.262916\pi\)
\(234\) 0 0
\(235\) −26515.2 −0.0313202
\(236\) 0 0
\(237\) −967830. −1.11925
\(238\) 0 0
\(239\) −438692. −0.496781 −0.248391 0.968660i \(-0.579902\pi\)
−0.248391 + 0.968660i \(0.579902\pi\)
\(240\) 0 0
\(241\) −1.55676e6 −1.72655 −0.863276 0.504731i \(-0.831592\pi\)
−0.863276 + 0.504731i \(0.831592\pi\)
\(242\) 0 0
\(243\) 17348.1 0.0188467
\(244\) 0 0
\(245\) 60025.0 0.0638877
\(246\) 0 0
\(247\) 843406. 0.879618
\(248\) 0 0
\(249\) 1.94035e6 1.98327
\(250\) 0 0
\(251\) 110717. 0.110926 0.0554628 0.998461i \(-0.482337\pi\)
0.0554628 + 0.998461i \(0.482337\pi\)
\(252\) 0 0
\(253\) 2.44990e6 2.40628
\(254\) 0 0
\(255\) −287429. −0.276809
\(256\) 0 0
\(257\) 1.48151e6 1.39918 0.699589 0.714545i \(-0.253366\pi\)
0.699589 + 0.714545i \(0.253366\pi\)
\(258\) 0 0
\(259\) 563011. 0.521516
\(260\) 0 0
\(261\) −9239.48 −0.00839550
\(262\) 0 0
\(263\) 456663. 0.407105 0.203553 0.979064i \(-0.434751\pi\)
0.203553 + 0.979064i \(0.434751\pi\)
\(264\) 0 0
\(265\) 130348. 0.114022
\(266\) 0 0
\(267\) −406836. −0.349254
\(268\) 0 0
\(269\) 642686. 0.541524 0.270762 0.962646i \(-0.412724\pi\)
0.270762 + 0.962646i \(0.412724\pi\)
\(270\) 0 0
\(271\) 1.17995e6 0.975975 0.487988 0.872851i \(-0.337731\pi\)
0.487988 + 0.872851i \(0.337731\pi\)
\(272\) 0 0
\(273\) −585190. −0.475215
\(274\) 0 0
\(275\) −338654. −0.270037
\(276\) 0 0
\(277\) −998004. −0.781507 −0.390753 0.920495i \(-0.627785\pi\)
−0.390753 + 0.920495i \(0.627785\pi\)
\(278\) 0 0
\(279\) 21179.5 0.0162894
\(280\) 0 0
\(281\) −577449. −0.436262 −0.218131 0.975919i \(-0.569996\pi\)
−0.218131 + 0.975919i \(0.569996\pi\)
\(282\) 0 0
\(283\) −67362.3 −0.0499978 −0.0249989 0.999687i \(-0.507958\pi\)
−0.0249989 + 0.999687i \(0.507958\pi\)
\(284\) 0 0
\(285\) −433067. −0.315823
\(286\) 0 0
\(287\) −540233. −0.387147
\(288\) 0 0
\(289\) −880966. −0.620461
\(290\) 0 0
\(291\) 1.06531e6 0.737467
\(292\) 0 0
\(293\) −1.10005e6 −0.748591 −0.374295 0.927310i \(-0.622115\pi\)
−0.374295 + 0.927310i \(0.622115\pi\)
\(294\) 0 0
\(295\) −1.25767e6 −0.841421
\(296\) 0 0
\(297\) −2.04272e6 −1.34375
\(298\) 0 0
\(299\) −3.44773e6 −2.23026
\(300\) 0 0
\(301\) −408692. −0.260004
\(302\) 0 0
\(303\) 427951. 0.267786
\(304\) 0 0
\(305\) −303291. −0.186685
\(306\) 0 0
\(307\) −49804.6 −0.0301595 −0.0150797 0.999886i \(-0.504800\pi\)
−0.0150797 + 0.999886i \(0.504800\pi\)
\(308\) 0 0
\(309\) 220374. 0.131300
\(310\) 0 0
\(311\) −443921. −0.260258 −0.130129 0.991497i \(-0.541539\pi\)
−0.130129 + 0.991497i \(0.541539\pi\)
\(312\) 0 0
\(313\) 2.26926e6 1.30925 0.654627 0.755952i \(-0.272826\pi\)
0.654627 + 0.755952i \(0.272826\pi\)
\(314\) 0 0
\(315\) 2805.20 0.00159289
\(316\) 0 0
\(317\) −3.21532e6 −1.79712 −0.898558 0.438855i \(-0.855384\pi\)
−0.898558 + 0.438855i \(0.855384\pi\)
\(318\) 0 0
\(319\) 2.18623e6 1.20287
\(320\) 0 0
\(321\) 2.91338e6 1.57810
\(322\) 0 0
\(323\) 811944. 0.433032
\(324\) 0 0
\(325\) 476586. 0.250284
\(326\) 0 0
\(327\) −904629. −0.467844
\(328\) 0 0
\(329\) −51969.8 −0.0264704
\(330\) 0 0
\(331\) 1.64911e6 0.827330 0.413665 0.910429i \(-0.364249\pi\)
0.413665 + 0.910429i \(0.364249\pi\)
\(332\) 0 0
\(333\) 26311.6 0.0130028
\(334\) 0 0
\(335\) −1.66998e6 −0.813018
\(336\) 0 0
\(337\) −940021. −0.450882 −0.225441 0.974257i \(-0.572382\pi\)
−0.225441 + 0.974257i \(0.572382\pi\)
\(338\) 0 0
\(339\) −3.63763e6 −1.71917
\(340\) 0 0
\(341\) −5.01145e6 −2.33388
\(342\) 0 0
\(343\) 117649. 0.0539949
\(344\) 0 0
\(345\) 1.77032e6 0.800764
\(346\) 0 0
\(347\) 840254. 0.374617 0.187308 0.982301i \(-0.440024\pi\)
0.187308 + 0.982301i \(0.440024\pi\)
\(348\) 0 0
\(349\) −3.17991e6 −1.39750 −0.698748 0.715367i \(-0.746259\pi\)
−0.698748 + 0.715367i \(0.746259\pi\)
\(350\) 0 0
\(351\) 2.87472e6 1.24545
\(352\) 0 0
\(353\) 2.44355e6 1.04372 0.521861 0.853030i \(-0.325238\pi\)
0.521861 + 0.853030i \(0.325238\pi\)
\(354\) 0 0
\(355\) −1.51274e6 −0.637080
\(356\) 0 0
\(357\) −563361. −0.233946
\(358\) 0 0
\(359\) 2.33016e6 0.954224 0.477112 0.878842i \(-0.341684\pi\)
0.477112 + 0.878842i \(0.341684\pi\)
\(360\) 0 0
\(361\) −1.25275e6 −0.505936
\(362\) 0 0
\(363\) −2.07590e6 −0.826874
\(364\) 0 0
\(365\) −1.66977e6 −0.656031
\(366\) 0 0
\(367\) 1.32215e6 0.512408 0.256204 0.966623i \(-0.417528\pi\)
0.256204 + 0.966623i \(0.417528\pi\)
\(368\) 0 0
\(369\) −25247.1 −0.00965264
\(370\) 0 0
\(371\) 255482. 0.0963663
\(372\) 0 0
\(373\) −4.12859e6 −1.53649 −0.768246 0.640155i \(-0.778870\pi\)
−0.768246 + 0.640155i \(0.778870\pi\)
\(374\) 0 0
\(375\) −244715. −0.0898632
\(376\) 0 0
\(377\) −3.07668e6 −1.11488
\(378\) 0 0
\(379\) −1.98173e6 −0.708673 −0.354336 0.935118i \(-0.615293\pi\)
−0.354336 + 0.935118i \(0.615293\pi\)
\(380\) 0 0
\(381\) −2.44052e6 −0.861332
\(382\) 0 0
\(383\) 3.08393e6 1.07426 0.537128 0.843501i \(-0.319509\pi\)
0.537128 + 0.843501i \(0.319509\pi\)
\(384\) 0 0
\(385\) −663761. −0.228223
\(386\) 0 0
\(387\) −19099.7 −0.00648260
\(388\) 0 0
\(389\) −573834. −0.192270 −0.0961351 0.995368i \(-0.530648\pi\)
−0.0961351 + 0.995368i \(0.530648\pi\)
\(390\) 0 0
\(391\) −3.31912e6 −1.09795
\(392\) 0 0
\(393\) −4.32982e6 −1.41413
\(394\) 0 0
\(395\) 1.54490e6 0.498203
\(396\) 0 0
\(397\) −1.35793e6 −0.432414 −0.216207 0.976348i \(-0.569369\pi\)
−0.216207 + 0.976348i \(0.569369\pi\)
\(398\) 0 0
\(399\) −848812. −0.266919
\(400\) 0 0
\(401\) −3.00515e6 −0.933264 −0.466632 0.884451i \(-0.654533\pi\)
−0.466632 + 0.884451i \(0.654533\pi\)
\(402\) 0 0
\(403\) 7.05260e6 2.16315
\(404\) 0 0
\(405\) −1.49001e6 −0.451388
\(406\) 0 0
\(407\) −6.22582e6 −1.86299
\(408\) 0 0
\(409\) 71979.4 0.0212765 0.0106382 0.999943i \(-0.496614\pi\)
0.0106382 + 0.999943i \(0.496614\pi\)
\(410\) 0 0
\(411\) 3.23711e6 0.945262
\(412\) 0 0
\(413\) −2.46504e6 −0.711130
\(414\) 0 0
\(415\) −3.09728e6 −0.882795
\(416\) 0 0
\(417\) 1.89601e6 0.533949
\(418\) 0 0
\(419\) 5.86991e6 1.63341 0.816707 0.577052i \(-0.195797\pi\)
0.816707 + 0.577052i \(0.195797\pi\)
\(420\) 0 0
\(421\) 2.17367e6 0.597706 0.298853 0.954299i \(-0.403396\pi\)
0.298853 + 0.954299i \(0.403396\pi\)
\(422\) 0 0
\(423\) −2428.74 −0.000659980 0
\(424\) 0 0
\(425\) 458808. 0.123213
\(426\) 0 0
\(427\) −594451. −0.157778
\(428\) 0 0
\(429\) 6.47108e6 1.69759
\(430\) 0 0
\(431\) 1.95004e6 0.505649 0.252825 0.967512i \(-0.418640\pi\)
0.252825 + 0.967512i \(0.418640\pi\)
\(432\) 0 0
\(433\) 773400. 0.198237 0.0991185 0.995076i \(-0.468398\pi\)
0.0991185 + 0.995076i \(0.468398\pi\)
\(434\) 0 0
\(435\) 1.57979e6 0.400292
\(436\) 0 0
\(437\) −5.00090e6 −1.25269
\(438\) 0 0
\(439\) 3.22946e6 0.799777 0.399888 0.916564i \(-0.369049\pi\)
0.399888 + 0.916564i \(0.369049\pi\)
\(440\) 0 0
\(441\) 5498.18 0.00134624
\(442\) 0 0
\(443\) 636374. 0.154065 0.0770323 0.997029i \(-0.475456\pi\)
0.0770323 + 0.997029i \(0.475456\pi\)
\(444\) 0 0
\(445\) 649411. 0.155460
\(446\) 0 0
\(447\) −3.34440e6 −0.791680
\(448\) 0 0
\(449\) 2.01084e6 0.470718 0.235359 0.971908i \(-0.424373\pi\)
0.235359 + 0.971908i \(0.424373\pi\)
\(450\) 0 0
\(451\) 5.97393e6 1.38299
\(452\) 0 0
\(453\) 4.80554e6 1.10026
\(454\) 0 0
\(455\) 934108. 0.211528
\(456\) 0 0
\(457\) −5.48087e6 −1.22761 −0.613804 0.789459i \(-0.710361\pi\)
−0.613804 + 0.789459i \(0.710361\pi\)
\(458\) 0 0
\(459\) 2.76748e6 0.613130
\(460\) 0 0
\(461\) 1.41469e6 0.310034 0.155017 0.987912i \(-0.450457\pi\)
0.155017 + 0.987912i \(0.450457\pi\)
\(462\) 0 0
\(463\) −2.34587e6 −0.508571 −0.254285 0.967129i \(-0.581840\pi\)
−0.254285 + 0.967129i \(0.581840\pi\)
\(464\) 0 0
\(465\) −3.62133e6 −0.776668
\(466\) 0 0
\(467\) −3.55705e6 −0.754741 −0.377370 0.926062i \(-0.623172\pi\)
−0.377370 + 0.926062i \(0.623172\pi\)
\(468\) 0 0
\(469\) −3.27317e6 −0.687126
\(470\) 0 0
\(471\) 1.77722e6 0.369137
\(472\) 0 0
\(473\) 4.51934e6 0.928801
\(474\) 0 0
\(475\) 691282. 0.140579
\(476\) 0 0
\(477\) 11939.6 0.00240267
\(478\) 0 0
\(479\) 2.54517e6 0.506848 0.253424 0.967355i \(-0.418443\pi\)
0.253424 + 0.967355i \(0.418443\pi\)
\(480\) 0 0
\(481\) 8.76157e6 1.72671
\(482\) 0 0
\(483\) 3.46983e6 0.676769
\(484\) 0 0
\(485\) −1.70049e6 −0.328262
\(486\) 0 0
\(487\) 1.84424e6 0.352366 0.176183 0.984357i \(-0.443625\pi\)
0.176183 + 0.984357i \(0.443625\pi\)
\(488\) 0 0
\(489\) 8.13585e6 1.53862
\(490\) 0 0
\(491\) −8.66566e6 −1.62218 −0.811088 0.584924i \(-0.801124\pi\)
−0.811088 + 0.584924i \(0.801124\pi\)
\(492\) 0 0
\(493\) −2.96191e6 −0.548850
\(494\) 0 0
\(495\) −31020.1 −0.00569023
\(496\) 0 0
\(497\) −2.96497e6 −0.538431
\(498\) 0 0
\(499\) −195522. −0.0351516 −0.0175758 0.999846i \(-0.505595\pi\)
−0.0175758 + 0.999846i \(0.505595\pi\)
\(500\) 0 0
\(501\) −904156. −0.160935
\(502\) 0 0
\(503\) 1.02277e7 1.80242 0.901210 0.433382i \(-0.142680\pi\)
0.901210 + 0.433382i \(0.142680\pi\)
\(504\) 0 0
\(505\) −683115. −0.119197
\(506\) 0 0
\(507\) −3.29163e6 −0.568710
\(508\) 0 0
\(509\) 437697. 0.0748823 0.0374412 0.999299i \(-0.488079\pi\)
0.0374412 + 0.999299i \(0.488079\pi\)
\(510\) 0 0
\(511\) −3.27275e6 −0.554448
\(512\) 0 0
\(513\) 4.16975e6 0.699546
\(514\) 0 0
\(515\) −351772. −0.0584444
\(516\) 0 0
\(517\) 574686. 0.0945593
\(518\) 0 0
\(519\) −4.67996e6 −0.762648
\(520\) 0 0
\(521\) −8.08466e6 −1.30487 −0.652435 0.757845i \(-0.726253\pi\)
−0.652435 + 0.757845i \(0.726253\pi\)
\(522\) 0 0
\(523\) 4.31342e6 0.689553 0.344777 0.938685i \(-0.387955\pi\)
0.344777 + 0.938685i \(0.387955\pi\)
\(524\) 0 0
\(525\) −479641. −0.0759482
\(526\) 0 0
\(527\) 6.78951e6 1.06491
\(528\) 0 0
\(529\) 1.40067e7 2.17619
\(530\) 0 0
\(531\) −115201. −0.0177304
\(532\) 0 0
\(533\) −8.40709e6 −1.28182
\(534\) 0 0
\(535\) −4.65047e6 −0.702446
\(536\) 0 0
\(537\) −1.76923e6 −0.264758
\(538\) 0 0
\(539\) −1.30097e6 −0.192884
\(540\) 0 0
\(541\) 1.05370e7 1.54783 0.773913 0.633292i \(-0.218297\pi\)
0.773913 + 0.633292i \(0.218297\pi\)
\(542\) 0 0
\(543\) 2.55299e6 0.371578
\(544\) 0 0
\(545\) 1.44401e6 0.208247
\(546\) 0 0
\(547\) 1.45511e6 0.207935 0.103968 0.994581i \(-0.466846\pi\)
0.103968 + 0.994581i \(0.466846\pi\)
\(548\) 0 0
\(549\) −27780.9 −0.00393383
\(550\) 0 0
\(551\) −4.46268e6 −0.626206
\(552\) 0 0
\(553\) 3.02800e6 0.421058
\(554\) 0 0
\(555\) −4.49884e6 −0.619966
\(556\) 0 0
\(557\) 4.83282e6 0.660028 0.330014 0.943976i \(-0.392946\pi\)
0.330014 + 0.943976i \(0.392946\pi\)
\(558\) 0 0
\(559\) −6.36006e6 −0.860858
\(560\) 0 0
\(561\) 6.22968e6 0.835716
\(562\) 0 0
\(563\) −1.28765e7 −1.71209 −0.856047 0.516898i \(-0.827086\pi\)
−0.856047 + 0.516898i \(0.827086\pi\)
\(564\) 0 0
\(565\) 5.80655e6 0.765239
\(566\) 0 0
\(567\) −2.92041e6 −0.381493
\(568\) 0 0
\(569\) −3.36290e6 −0.435445 −0.217722 0.976011i \(-0.569863\pi\)
−0.217722 + 0.976011i \(0.569863\pi\)
\(570\) 0 0
\(571\) 1.12235e7 1.44058 0.720288 0.693675i \(-0.244010\pi\)
0.720288 + 0.693675i \(0.244010\pi\)
\(572\) 0 0
\(573\) −6.48591e6 −0.825248
\(574\) 0 0
\(575\) −2.82587e6 −0.356437
\(576\) 0 0
\(577\) 4.07434e6 0.509468 0.254734 0.967011i \(-0.418012\pi\)
0.254734 + 0.967011i \(0.418012\pi\)
\(578\) 0 0
\(579\) 1.22608e7 1.51992
\(580\) 0 0
\(581\) −6.07066e6 −0.746098
\(582\) 0 0
\(583\) −2.82514e6 −0.344245
\(584\) 0 0
\(585\) 43654.4 0.00527398
\(586\) 0 0
\(587\) −4.50426e6 −0.539546 −0.269773 0.962924i \(-0.586949\pi\)
−0.269773 + 0.962924i \(0.586949\pi\)
\(588\) 0 0
\(589\) 1.02297e7 1.21500
\(590\) 0 0
\(591\) 6.81910e6 0.803079
\(592\) 0 0
\(593\) −2.53126e6 −0.295597 −0.147798 0.989018i \(-0.547219\pi\)
−0.147798 + 0.989018i \(0.547219\pi\)
\(594\) 0 0
\(595\) 899263. 0.104134
\(596\) 0 0
\(597\) −1.60069e7 −1.83810
\(598\) 0 0
\(599\) 3.46047e6 0.394065 0.197033 0.980397i \(-0.436869\pi\)
0.197033 + 0.980397i \(0.436869\pi\)
\(600\) 0 0
\(601\) −1.07573e7 −1.21483 −0.607416 0.794384i \(-0.707794\pi\)
−0.607416 + 0.794384i \(0.707794\pi\)
\(602\) 0 0
\(603\) −152968. −0.0171319
\(604\) 0 0
\(605\) 3.31364e6 0.368059
\(606\) 0 0
\(607\) 2.74702e6 0.302614 0.151307 0.988487i \(-0.451652\pi\)
0.151307 + 0.988487i \(0.451652\pi\)
\(608\) 0 0
\(609\) 3.09640e6 0.338309
\(610\) 0 0
\(611\) −808753. −0.0876421
\(612\) 0 0
\(613\) 3.93872e6 0.423354 0.211677 0.977340i \(-0.432107\pi\)
0.211677 + 0.977340i \(0.432107\pi\)
\(614\) 0 0
\(615\) 4.31683e6 0.460232
\(616\) 0 0
\(617\) 6.90587e6 0.730307 0.365153 0.930947i \(-0.381017\pi\)
0.365153 + 0.930947i \(0.381017\pi\)
\(618\) 0 0
\(619\) 5.92686e6 0.621725 0.310863 0.950455i \(-0.399382\pi\)
0.310863 + 0.950455i \(0.399382\pi\)
\(620\) 0 0
\(621\) −1.70454e7 −1.77369
\(622\) 0 0
\(623\) 1.27285e6 0.131388
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) 0 0
\(627\) 9.38623e6 0.953503
\(628\) 0 0
\(629\) 8.43473e6 0.850050
\(630\) 0 0
\(631\) −6.64774e6 −0.664662 −0.332331 0.943163i \(-0.607835\pi\)
−0.332331 + 0.943163i \(0.607835\pi\)
\(632\) 0 0
\(633\) 9.83889e6 0.975971
\(634\) 0 0
\(635\) 3.89568e6 0.383397
\(636\) 0 0
\(637\) 1.83085e6 0.178774
\(638\) 0 0
\(639\) −138564. −0.0134245
\(640\) 0 0
\(641\) 1.08946e7 1.04729 0.523645 0.851936i \(-0.324572\pi\)
0.523645 + 0.851936i \(0.324572\pi\)
\(642\) 0 0
\(643\) 2.48078e6 0.236625 0.118313 0.992976i \(-0.462252\pi\)
0.118313 + 0.992976i \(0.462252\pi\)
\(644\) 0 0
\(645\) 3.26573e6 0.309087
\(646\) 0 0
\(647\) −1.46723e7 −1.37796 −0.688981 0.724779i \(-0.741942\pi\)
−0.688981 + 0.724779i \(0.741942\pi\)
\(648\) 0 0
\(649\) 2.72586e7 2.54034
\(650\) 0 0
\(651\) −7.09780e6 −0.656404
\(652\) 0 0
\(653\) −1.88045e7 −1.72576 −0.862878 0.505413i \(-0.831340\pi\)
−0.862878 + 0.505413i \(0.831340\pi\)
\(654\) 0 0
\(655\) 6.91146e6 0.629458
\(656\) 0 0
\(657\) −152948. −0.0138239
\(658\) 0 0
\(659\) −1.22517e6 −0.109896 −0.0549482 0.998489i \(-0.517499\pi\)
−0.0549482 + 0.998489i \(0.517499\pi\)
\(660\) 0 0
\(661\) −1.39727e7 −1.24388 −0.621940 0.783065i \(-0.713655\pi\)
−0.621940 + 0.783065i \(0.713655\pi\)
\(662\) 0 0
\(663\) −8.76701e6 −0.774582
\(664\) 0 0
\(665\) 1.35491e6 0.118811
\(666\) 0 0
\(667\) 1.82429e7 1.58774
\(668\) 0 0
\(669\) 5.81877e6 0.502651
\(670\) 0 0
\(671\) 6.57348e6 0.563623
\(672\) 0 0
\(673\) −4.48808e6 −0.381964 −0.190982 0.981594i \(-0.561167\pi\)
−0.190982 + 0.981594i \(0.561167\pi\)
\(674\) 0 0
\(675\) 2.35621e6 0.199047
\(676\) 0 0
\(677\) −1.67787e6 −0.140697 −0.0703486 0.997522i \(-0.522411\pi\)
−0.0703486 + 0.997522i \(0.522411\pi\)
\(678\) 0 0
\(679\) −3.33297e6 −0.277432
\(680\) 0 0
\(681\) 2.07482e7 1.71440
\(682\) 0 0
\(683\) 1.68480e7 1.38197 0.690983 0.722871i \(-0.257178\pi\)
0.690983 + 0.722871i \(0.257178\pi\)
\(684\) 0 0
\(685\) −5.16722e6 −0.420756
\(686\) 0 0
\(687\) −1.69465e7 −1.36990
\(688\) 0 0
\(689\) 3.97581e6 0.319063
\(690\) 0 0
\(691\) −7.49162e6 −0.596871 −0.298435 0.954430i \(-0.596465\pi\)
−0.298435 + 0.954430i \(0.596465\pi\)
\(692\) 0 0
\(693\) −60799.3 −0.00480912
\(694\) 0 0
\(695\) −3.02650e6 −0.237672
\(696\) 0 0
\(697\) −8.09348e6 −0.631035
\(698\) 0 0
\(699\) −1.75949e7 −1.36205
\(700\) 0 0
\(701\) 1.73756e7 1.33550 0.667750 0.744386i \(-0.267258\pi\)
0.667750 + 0.744386i \(0.267258\pi\)
\(702\) 0 0
\(703\) 1.27086e7 0.969857
\(704\) 0 0
\(705\) 415274. 0.0314675
\(706\) 0 0
\(707\) −1.33891e6 −0.100740
\(708\) 0 0
\(709\) −7.80073e6 −0.582800 −0.291400 0.956601i \(-0.594121\pi\)
−0.291400 + 0.956601i \(0.594121\pi\)
\(710\) 0 0
\(711\) 141510. 0.0104981
\(712\) 0 0
\(713\) −4.18178e7 −3.08061
\(714\) 0 0
\(715\) −1.03294e7 −0.755634
\(716\) 0 0
\(717\) 6.87068e6 0.499116
\(718\) 0 0
\(719\) 3.74606e6 0.270242 0.135121 0.990829i \(-0.456858\pi\)
0.135121 + 0.990829i \(0.456858\pi\)
\(720\) 0 0
\(721\) −689473. −0.0493946
\(722\) 0 0
\(723\) 2.43816e7 1.73467
\(724\) 0 0
\(725\) −2.52174e6 −0.178179
\(726\) 0 0
\(727\) −7.41411e6 −0.520263 −0.260131 0.965573i \(-0.583766\pi\)
−0.260131 + 0.965573i \(0.583766\pi\)
\(728\) 0 0
\(729\) 1.42112e7 0.990400
\(730\) 0 0
\(731\) −6.12280e6 −0.423796
\(732\) 0 0
\(733\) −3.73393e6 −0.256688 −0.128344 0.991730i \(-0.540966\pi\)
−0.128344 + 0.991730i \(0.540966\pi\)
\(734\) 0 0
\(735\) −940096. −0.0641880
\(736\) 0 0
\(737\) 3.61950e7 2.45459
\(738\) 0 0
\(739\) −2.73088e7 −1.83946 −0.919732 0.392548i \(-0.871594\pi\)
−0.919732 + 0.392548i \(0.871594\pi\)
\(740\) 0 0
\(741\) −1.32092e7 −0.883753
\(742\) 0 0
\(743\) 2.93553e6 0.195081 0.0975404 0.995232i \(-0.468902\pi\)
0.0975404 + 0.995232i \(0.468902\pi\)
\(744\) 0 0
\(745\) 5.33849e6 0.352394
\(746\) 0 0
\(747\) −283705. −0.0186023
\(748\) 0 0
\(749\) −9.11493e6 −0.593675
\(750\) 0 0
\(751\) 1.23130e7 0.796640 0.398320 0.917246i \(-0.369593\pi\)
0.398320 + 0.917246i \(0.369593\pi\)
\(752\) 0 0
\(753\) −1.73403e6 −0.111447
\(754\) 0 0
\(755\) −7.67083e6 −0.489751
\(756\) 0 0
\(757\) −1.45128e7 −0.920473 −0.460236 0.887796i \(-0.652235\pi\)
−0.460236 + 0.887796i \(0.652235\pi\)
\(758\) 0 0
\(759\) −3.83697e7 −2.41760
\(760\) 0 0
\(761\) −4.54961e6 −0.284782 −0.142391 0.989811i \(-0.545479\pi\)
−0.142391 + 0.989811i \(0.545479\pi\)
\(762\) 0 0
\(763\) 2.83026e6 0.176001
\(764\) 0 0
\(765\) 42025.9 0.00259635
\(766\) 0 0
\(767\) −3.83610e7 −2.35451
\(768\) 0 0
\(769\) 1.17832e6 0.0718532 0.0359266 0.999354i \(-0.488562\pi\)
0.0359266 + 0.999354i \(0.488562\pi\)
\(770\) 0 0
\(771\) −2.32031e7 −1.40576
\(772\) 0 0
\(773\) −1.52351e7 −0.917055 −0.458528 0.888680i \(-0.651623\pi\)
−0.458528 + 0.888680i \(0.651623\pi\)
\(774\) 0 0
\(775\) 5.78054e6 0.345711
\(776\) 0 0
\(777\) −8.81773e6 −0.523967
\(778\) 0 0
\(779\) −1.21944e7 −0.719974
\(780\) 0 0
\(781\) 3.27869e7 1.92341
\(782\) 0 0
\(783\) −1.52109e7 −0.886646
\(784\) 0 0
\(785\) −2.83688e6 −0.164311
\(786\) 0 0
\(787\) −1.26864e7 −0.730131 −0.365066 0.930982i \(-0.618953\pi\)
−0.365066 + 0.930982i \(0.618953\pi\)
\(788\) 0 0
\(789\) −7.15214e6 −0.409019
\(790\) 0 0
\(791\) 1.13808e7 0.646745
\(792\) 0 0
\(793\) −9.25083e6 −0.522394
\(794\) 0 0
\(795\) −2.04147e6 −0.114558
\(796\) 0 0
\(797\) −1.22399e7 −0.682546 −0.341273 0.939964i \(-0.610858\pi\)
−0.341273 + 0.939964i \(0.610858\pi\)
\(798\) 0 0
\(799\) −778584. −0.0431458
\(800\) 0 0
\(801\) 59484.9 0.00327586
\(802\) 0 0
\(803\) 3.61903e7 1.98063
\(804\) 0 0
\(805\) −5.53871e6 −0.301244
\(806\) 0 0
\(807\) −1.00656e7 −0.544070
\(808\) 0 0
\(809\) 1.87712e7 1.00837 0.504186 0.863595i \(-0.331793\pi\)
0.504186 + 0.863595i \(0.331793\pi\)
\(810\) 0 0
\(811\) −3.49853e6 −0.186781 −0.0933906 0.995630i \(-0.529771\pi\)
−0.0933906 + 0.995630i \(0.529771\pi\)
\(812\) 0 0
\(813\) −1.84800e7 −0.980563
\(814\) 0 0
\(815\) −1.29868e7 −0.684871
\(816\) 0 0
\(817\) −9.22519e6 −0.483526
\(818\) 0 0
\(819\) 85562.6 0.00445733
\(820\) 0 0
\(821\) −2.45084e7 −1.26899 −0.634494 0.772928i \(-0.718791\pi\)
−0.634494 + 0.772928i \(0.718791\pi\)
\(822\) 0 0
\(823\) 2.94753e7 1.51691 0.758453 0.651728i \(-0.225956\pi\)
0.758453 + 0.651728i \(0.225956\pi\)
\(824\) 0 0
\(825\) 5.30390e6 0.271307
\(826\) 0 0
\(827\) 1.52430e7 0.775008 0.387504 0.921868i \(-0.373337\pi\)
0.387504 + 0.921868i \(0.373337\pi\)
\(828\) 0 0
\(829\) 1.20806e7 0.610523 0.305262 0.952268i \(-0.401256\pi\)
0.305262 + 0.952268i \(0.401256\pi\)
\(830\) 0 0
\(831\) 1.56305e7 0.785180
\(832\) 0 0
\(833\) 1.76255e6 0.0880096
\(834\) 0 0
\(835\) 1.44326e6 0.0716354
\(836\) 0 0
\(837\) 3.48676e7 1.72032
\(838\) 0 0
\(839\) −5.25581e6 −0.257771 −0.128886 0.991659i \(-0.541140\pi\)
−0.128886 + 0.991659i \(0.541140\pi\)
\(840\) 0 0
\(841\) −4.23164e6 −0.206309
\(842\) 0 0
\(843\) 9.04385e6 0.438313
\(844\) 0 0
\(845\) 5.25425e6 0.253145
\(846\) 0 0
\(847\) 6.49474e6 0.311067
\(848\) 0 0
\(849\) 1.05501e6 0.0502329
\(850\) 0 0
\(851\) −5.19509e7 −2.45906
\(852\) 0 0
\(853\) −1.01496e7 −0.477615 −0.238808 0.971067i \(-0.576757\pi\)
−0.238808 + 0.971067i \(0.576757\pi\)
\(854\) 0 0
\(855\) 63320.2 0.00296229
\(856\) 0 0
\(857\) −2.47951e7 −1.15323 −0.576613 0.817018i \(-0.695626\pi\)
−0.576613 + 0.817018i \(0.695626\pi\)
\(858\) 0 0
\(859\) −3.93873e7 −1.82127 −0.910634 0.413214i \(-0.864406\pi\)
−0.910634 + 0.413214i \(0.864406\pi\)
\(860\) 0 0
\(861\) 8.46098e6 0.388967
\(862\) 0 0
\(863\) −3.66198e7 −1.67374 −0.836872 0.547398i \(-0.815618\pi\)
−0.836872 + 0.547398i \(0.815618\pi\)
\(864\) 0 0
\(865\) 7.47038e6 0.339471
\(866\) 0 0
\(867\) 1.37975e7 0.623378
\(868\) 0 0
\(869\) −3.34838e7 −1.50413
\(870\) 0 0
\(871\) −5.09370e7 −2.27504
\(872\) 0 0
\(873\) −155762. −0.00691714
\(874\) 0 0
\(875\) 765625. 0.0338062
\(876\) 0 0
\(877\) 1.56298e7 0.686207 0.343104 0.939298i \(-0.388522\pi\)
0.343104 + 0.939298i \(0.388522\pi\)
\(878\) 0 0
\(879\) 1.72287e7 0.752110
\(880\) 0 0
\(881\) −1.32549e7 −0.575357 −0.287678 0.957727i \(-0.592883\pi\)
−0.287678 + 0.957727i \(0.592883\pi\)
\(882\) 0 0
\(883\) −4.30665e7 −1.85882 −0.929411 0.369045i \(-0.879685\pi\)
−0.929411 + 0.369045i \(0.879685\pi\)
\(884\) 0 0
\(885\) 1.96974e7 0.845376
\(886\) 0 0
\(887\) 3.62803e7 1.54832 0.774162 0.632987i \(-0.218171\pi\)
0.774162 + 0.632987i \(0.218171\pi\)
\(888\) 0 0
\(889\) 7.63553e6 0.324030
\(890\) 0 0
\(891\) 3.22941e7 1.36279
\(892\) 0 0
\(893\) −1.17309e6 −0.0492268
\(894\) 0 0
\(895\) 2.82413e6 0.117849
\(896\) 0 0
\(897\) 5.39975e7 2.24075
\(898\) 0 0
\(899\) −3.73172e7 −1.53996
\(900\) 0 0
\(901\) 3.82749e6 0.157073
\(902\) 0 0
\(903\) 6.40082e6 0.261226
\(904\) 0 0
\(905\) −4.07521e6 −0.165397
\(906\) 0 0
\(907\) 3.15142e7 1.27200 0.636002 0.771688i \(-0.280587\pi\)
0.636002 + 0.771688i \(0.280587\pi\)
\(908\) 0 0
\(909\) −62572.1 −0.00251172
\(910\) 0 0
\(911\) 3.94324e7 1.57419 0.787096 0.616830i \(-0.211584\pi\)
0.787096 + 0.616830i \(0.211584\pi\)
\(912\) 0 0
\(913\) 6.71298e7 2.66525
\(914\) 0 0
\(915\) 4.75007e6 0.187563
\(916\) 0 0
\(917\) 1.35465e7 0.531989
\(918\) 0 0
\(919\) 1.11238e7 0.434474 0.217237 0.976119i \(-0.430296\pi\)
0.217237 + 0.976119i \(0.430296\pi\)
\(920\) 0 0
\(921\) 780027. 0.0303013
\(922\) 0 0
\(923\) −4.61409e7 −1.78271
\(924\) 0 0
\(925\) 7.18126e6 0.275960
\(926\) 0 0
\(927\) −32221.7 −0.00123154
\(928\) 0 0
\(929\) −4.19210e7 −1.59365 −0.796823 0.604212i \(-0.793488\pi\)
−0.796823 + 0.604212i \(0.793488\pi\)
\(930\) 0 0
\(931\) 2.65563e6 0.100414
\(932\) 0 0
\(933\) 6.95257e6 0.261482
\(934\) 0 0
\(935\) −9.94411e6 −0.371995
\(936\) 0 0
\(937\) 3.80494e7 1.41579 0.707895 0.706318i \(-0.249645\pi\)
0.707895 + 0.706318i \(0.249645\pi\)
\(938\) 0 0
\(939\) −3.55406e7 −1.31541
\(940\) 0 0
\(941\) −2.85268e7 −1.05022 −0.525109 0.851035i \(-0.675976\pi\)
−0.525109 + 0.851035i \(0.675976\pi\)
\(942\) 0 0
\(943\) 4.98491e7 1.82548
\(944\) 0 0
\(945\) 4.61817e6 0.168225
\(946\) 0 0
\(947\) 2.47030e7 0.895108 0.447554 0.894257i \(-0.352295\pi\)
0.447554 + 0.894257i \(0.352295\pi\)
\(948\) 0 0
\(949\) −5.09305e7 −1.83574
\(950\) 0 0
\(951\) 5.03575e7 1.80556
\(952\) 0 0
\(953\) 2.30722e7 0.822918 0.411459 0.911428i \(-0.365019\pi\)
0.411459 + 0.911428i \(0.365019\pi\)
\(954\) 0 0
\(955\) 1.03531e7 0.367335
\(956\) 0 0
\(957\) −3.42402e7 −1.20853
\(958\) 0 0
\(959\) −1.01278e7 −0.355604
\(960\) 0 0
\(961\) 5.69122e7 1.98791
\(962\) 0 0
\(963\) −425975. −0.0148019
\(964\) 0 0
\(965\) −1.95713e7 −0.676551
\(966\) 0 0
\(967\) −2.88977e6 −0.0993797 −0.0496898 0.998765i \(-0.515823\pi\)
−0.0496898 + 0.998765i \(0.515823\pi\)
\(968\) 0 0
\(969\) −1.27165e7 −0.435067
\(970\) 0 0
\(971\) 1.27702e7 0.434660 0.217330 0.976098i \(-0.430265\pi\)
0.217330 + 0.976098i \(0.430265\pi\)
\(972\) 0 0
\(973\) −5.93193e6 −0.200870
\(974\) 0 0
\(975\) −7.46416e6 −0.251460
\(976\) 0 0
\(977\) 1.52358e7 0.510657 0.255329 0.966854i \(-0.417816\pi\)
0.255329 + 0.966854i \(0.417816\pi\)
\(978\) 0 0
\(979\) −1.40752e7 −0.469352
\(980\) 0 0
\(981\) 132269. 0.00438819
\(982\) 0 0
\(983\) 3.91000e7 1.29060 0.645301 0.763928i \(-0.276732\pi\)
0.645301 + 0.763928i \(0.276732\pi\)
\(984\) 0 0
\(985\) −1.08850e7 −0.357468
\(986\) 0 0
\(987\) 813937. 0.0265949
\(988\) 0 0
\(989\) 3.77114e7 1.22598
\(990\) 0 0
\(991\) −4.15949e7 −1.34541 −0.672706 0.739910i \(-0.734868\pi\)
−0.672706 + 0.739910i \(0.734868\pi\)
\(992\) 0 0
\(993\) −2.58279e7 −0.831219
\(994\) 0 0
\(995\) 2.55509e7 0.818179
\(996\) 0 0
\(997\) 1.76387e7 0.561989 0.280994 0.959709i \(-0.409336\pi\)
0.280994 + 0.959709i \(0.409336\pi\)
\(998\) 0 0
\(999\) 4.33166e7 1.37322
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 280.6.a.g.1.2 4
4.3 odd 2 560.6.a.x.1.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
280.6.a.g.1.2 4 1.1 even 1 trivial
560.6.a.x.1.3 4 4.3 odd 2