Properties

Label 325.6.a.j.1.8
Level $325$
Weight $6$
Character 325.1
Self dual yes
Analytic conductor $52.125$
Analytic rank $0$
Dimension $11$
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] = [325,6,Mod(1,325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(325, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("325.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 325.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: \(52.1247414392\)
Analytic rank: \(0\)
Dimension: \(11\)
Coefficient field: \(\mathbb{Q}[x]/(x^{11} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{11} - 5 x^{10} - 257 x^{9} + 1165 x^{8} + 22234 x^{7} - 90282 x^{6} - 751180 x^{5} + 2564400 x^{4} + \cdots + 44115200 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{6}\cdot 5^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-3.78432\) of defining polynomial
Character \(\chi\) \(=\) 325.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+3.78432 q^{2} -8.20788 q^{3} -17.6789 q^{4} -31.0612 q^{6} -88.9969 q^{7} -188.001 q^{8} -175.631 q^{9} -156.575 q^{11} +145.107 q^{12} -169.000 q^{13} -336.793 q^{14} -145.729 q^{16} -447.890 q^{17} -664.642 q^{18} -269.669 q^{19} +730.476 q^{21} -592.531 q^{22} -1371.05 q^{23} +1543.09 q^{24} -639.550 q^{26} +3436.07 q^{27} +1573.37 q^{28} -3698.11 q^{29} +797.974 q^{31} +5464.54 q^{32} +1285.15 q^{33} -1694.96 q^{34} +3104.97 q^{36} +4394.83 q^{37} -1020.51 q^{38} +1387.13 q^{39} +14320.9 q^{41} +2764.35 q^{42} -11337.1 q^{43} +2768.09 q^{44} -5188.50 q^{46} +9974.03 q^{47} +1196.13 q^{48} -8886.54 q^{49} +3676.23 q^{51} +2987.74 q^{52} -11587.1 q^{53} +13003.2 q^{54} +16731.5 q^{56} +2213.41 q^{57} -13994.8 q^{58} +7133.45 q^{59} +16629.8 q^{61} +3019.79 q^{62} +15630.6 q^{63} +25342.9 q^{64} +4863.42 q^{66} -4211.88 q^{67} +7918.22 q^{68} +11253.4 q^{69} +12871.4 q^{71} +33018.7 q^{72} +13097.1 q^{73} +16631.4 q^{74} +4767.46 q^{76} +13934.7 q^{77} +5249.35 q^{78} +74729.2 q^{79} +14475.4 q^{81} +54194.7 q^{82} -8547.83 q^{83} -12914.0 q^{84} -42903.0 q^{86} +30353.6 q^{87} +29436.3 q^{88} +59586.0 q^{89} +15040.5 q^{91} +24238.8 q^{92} -6549.68 q^{93} +37744.9 q^{94} -44852.3 q^{96} +17376.2 q^{97} -33629.5 q^{98} +27499.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q - 5 q^{2} - 11 q^{3} + 187 q^{4} + 351 q^{6} - 208 q^{7} - 165 q^{8} + 1372 q^{9} + 1276 q^{11} - 1533 q^{12} - 1859 q^{13} + 578 q^{14} + 5707 q^{16} - 2218 q^{17} + 6776 q^{18} + 3520 q^{19} + 1706 q^{21}+ \cdots + 426698 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.78432 0.668979 0.334490 0.942399i \(-0.391436\pi\)
0.334490 + 0.942399i \(0.391436\pi\)
\(3\) −8.20788 −0.526536 −0.263268 0.964723i \(-0.584800\pi\)
−0.263268 + 0.964723i \(0.584800\pi\)
\(4\) −17.6789 −0.552467
\(5\) 0 0
\(6\) −31.0612 −0.352241
\(7\) −88.9969 −0.686483 −0.343242 0.939247i \(-0.611525\pi\)
−0.343242 + 0.939247i \(0.611525\pi\)
\(8\) −188.001 −1.03857
\(9\) −175.631 −0.722760
\(10\) 0 0
\(11\) −156.575 −0.390159 −0.195080 0.980787i \(-0.562497\pi\)
−0.195080 + 0.980787i \(0.562497\pi\)
\(12\) 145.107 0.290893
\(13\) −169.000 −0.277350
\(14\) −336.793 −0.459243
\(15\) 0 0
\(16\) −145.729 −0.142314
\(17\) −447.890 −0.375880 −0.187940 0.982181i \(-0.560181\pi\)
−0.187940 + 0.982181i \(0.560181\pi\)
\(18\) −664.642 −0.483512
\(19\) −269.669 −0.171375 −0.0856875 0.996322i \(-0.527309\pi\)
−0.0856875 + 0.996322i \(0.527309\pi\)
\(20\) 0 0
\(21\) 730.476 0.361458
\(22\) −592.531 −0.261008
\(23\) −1371.05 −0.540424 −0.270212 0.962801i \(-0.587094\pi\)
−0.270212 + 0.962801i \(0.587094\pi\)
\(24\) 1543.09 0.546843
\(25\) 0 0
\(26\) −639.550 −0.185541
\(27\) 3436.07 0.907095
\(28\) 1573.37 0.379259
\(29\) −3698.11 −0.816554 −0.408277 0.912858i \(-0.633870\pi\)
−0.408277 + 0.912858i \(0.633870\pi\)
\(30\) 0 0
\(31\) 797.974 0.149137 0.0745684 0.997216i \(-0.476242\pi\)
0.0745684 + 0.997216i \(0.476242\pi\)
\(32\) 5464.54 0.943363
\(33\) 1285.15 0.205433
\(34\) −1694.96 −0.251456
\(35\) 0 0
\(36\) 3104.97 0.399301
\(37\) 4394.83 0.527761 0.263881 0.964555i \(-0.414997\pi\)
0.263881 + 0.964555i \(0.414997\pi\)
\(38\) −1020.51 −0.114646
\(39\) 1387.13 0.146035
\(40\) 0 0
\(41\) 14320.9 1.33048 0.665242 0.746628i \(-0.268328\pi\)
0.665242 + 0.746628i \(0.268328\pi\)
\(42\) 2764.35 0.241808
\(43\) −11337.1 −0.935037 −0.467519 0.883983i \(-0.654852\pi\)
−0.467519 + 0.883983i \(0.654852\pi\)
\(44\) 2768.09 0.215550
\(45\) 0 0
\(46\) −5188.50 −0.361532
\(47\) 9974.03 0.658607 0.329303 0.944224i \(-0.393186\pi\)
0.329303 + 0.944224i \(0.393186\pi\)
\(48\) 1196.13 0.0749331
\(49\) −8886.54 −0.528741
\(50\) 0 0
\(51\) 3676.23 0.197914
\(52\) 2987.74 0.153227
\(53\) −11587.1 −0.566611 −0.283305 0.959030i \(-0.591431\pi\)
−0.283305 + 0.959030i \(0.591431\pi\)
\(54\) 13003.2 0.606827
\(55\) 0 0
\(56\) 16731.5 0.712960
\(57\) 2213.41 0.0902350
\(58\) −13994.8 −0.546258
\(59\) 7133.45 0.266790 0.133395 0.991063i \(-0.457412\pi\)
0.133395 + 0.991063i \(0.457412\pi\)
\(60\) 0 0
\(61\) 16629.8 0.572220 0.286110 0.958197i \(-0.407638\pi\)
0.286110 + 0.958197i \(0.407638\pi\)
\(62\) 3019.79 0.0997694
\(63\) 15630.6 0.496163
\(64\) 25342.9 0.773404
\(65\) 0 0
\(66\) 4863.42 0.137430
\(67\) −4211.88 −0.114628 −0.0573138 0.998356i \(-0.518254\pi\)
−0.0573138 + 0.998356i \(0.518254\pi\)
\(68\) 7918.22 0.207661
\(69\) 11253.4 0.284552
\(70\) 0 0
\(71\) 12871.4 0.303026 0.151513 0.988455i \(-0.451585\pi\)
0.151513 + 0.988455i \(0.451585\pi\)
\(72\) 33018.7 0.750636
\(73\) 13097.1 0.287653 0.143826 0.989603i \(-0.454059\pi\)
0.143826 + 0.989603i \(0.454059\pi\)
\(74\) 16631.4 0.353061
\(75\) 0 0
\(76\) 4767.46 0.0946790
\(77\) 13934.7 0.267838
\(78\) 5249.35 0.0976942
\(79\) 74729.2 1.34717 0.673586 0.739109i \(-0.264753\pi\)
0.673586 + 0.739109i \(0.264753\pi\)
\(80\) 0 0
\(81\) 14475.4 0.245143
\(82\) 54194.7 0.890066
\(83\) −8547.83 −0.136195 −0.0680974 0.997679i \(-0.521693\pi\)
−0.0680974 + 0.997679i \(0.521693\pi\)
\(84\) −12914.0 −0.199694
\(85\) 0 0
\(86\) −42903.0 −0.625521
\(87\) 30353.6 0.429945
\(88\) 29436.3 0.405207
\(89\) 59586.0 0.797387 0.398694 0.917084i \(-0.369464\pi\)
0.398694 + 0.917084i \(0.369464\pi\)
\(90\) 0 0
\(91\) 15040.5 0.190396
\(92\) 24238.8 0.298566
\(93\) −6549.68 −0.0785258
\(94\) 37744.9 0.440594
\(95\) 0 0
\(96\) −44852.3 −0.496714
\(97\) 17376.2 0.187510 0.0937552 0.995595i \(-0.470113\pi\)
0.0937552 + 0.995595i \(0.470113\pi\)
\(98\) −33629.5 −0.353716
\(99\) 27499.5 0.281992
\(100\) 0 0
\(101\) 68669.7 0.669825 0.334913 0.942249i \(-0.391293\pi\)
0.334913 + 0.942249i \(0.391293\pi\)
\(102\) 13912.0 0.132400
\(103\) −191203. −1.77584 −0.887918 0.460002i \(-0.847849\pi\)
−0.887918 + 0.460002i \(0.847849\pi\)
\(104\) 31772.2 0.288047
\(105\) 0 0
\(106\) −43849.2 −0.379051
\(107\) 46117.6 0.389410 0.194705 0.980862i \(-0.437625\pi\)
0.194705 + 0.980862i \(0.437625\pi\)
\(108\) −60746.1 −0.501140
\(109\) 187271. 1.50975 0.754873 0.655871i \(-0.227698\pi\)
0.754873 + 0.655871i \(0.227698\pi\)
\(110\) 0 0
\(111\) −36072.2 −0.277885
\(112\) 12969.4 0.0976959
\(113\) −189262. −1.39434 −0.697169 0.716907i \(-0.745557\pi\)
−0.697169 + 0.716907i \(0.745557\pi\)
\(114\) 8376.25 0.0603653
\(115\) 0 0
\(116\) 65378.7 0.451119
\(117\) 29681.6 0.200458
\(118\) 26995.2 0.178477
\(119\) 39860.9 0.258035
\(120\) 0 0
\(121\) −136535. −0.847776
\(122\) 62932.5 0.382803
\(123\) −117544. −0.700547
\(124\) −14107.3 −0.0823931
\(125\) 0 0
\(126\) 59151.2 0.331923
\(127\) −183029. −1.00695 −0.503477 0.864009i \(-0.667946\pi\)
−0.503477 + 0.864009i \(0.667946\pi\)
\(128\) −78959.8 −0.425972
\(129\) 93053.1 0.492331
\(130\) 0 0
\(131\) 221035. 1.12534 0.562668 0.826683i \(-0.309775\pi\)
0.562668 + 0.826683i \(0.309775\pi\)
\(132\) −22720.1 −0.113495
\(133\) 23999.7 0.117646
\(134\) −15939.1 −0.0766835
\(135\) 0 0
\(136\) 84203.7 0.390377
\(137\) −353821. −1.61058 −0.805290 0.592881i \(-0.797991\pi\)
−0.805290 + 0.592881i \(0.797991\pi\)
\(138\) 42586.6 0.190360
\(139\) 282625. 1.24072 0.620359 0.784318i \(-0.286987\pi\)
0.620359 + 0.784318i \(0.286987\pi\)
\(140\) 0 0
\(141\) −81865.7 −0.346780
\(142\) 48709.4 0.202718
\(143\) 26461.2 0.108211
\(144\) 25594.5 0.102859
\(145\) 0 0
\(146\) 49563.7 0.192434
\(147\) 72939.7 0.278401
\(148\) −77695.9 −0.291571
\(149\) −77579.6 −0.286274 −0.143137 0.989703i \(-0.545719\pi\)
−0.143137 + 0.989703i \(0.545719\pi\)
\(150\) 0 0
\(151\) −209693. −0.748412 −0.374206 0.927346i \(-0.622085\pi\)
−0.374206 + 0.927346i \(0.622085\pi\)
\(152\) 50698.0 0.177985
\(153\) 78663.3 0.271671
\(154\) 52733.5 0.179178
\(155\) 0 0
\(156\) −24523.0 −0.0806793
\(157\) −127745. −0.413612 −0.206806 0.978382i \(-0.566307\pi\)
−0.206806 + 0.978382i \(0.566307\pi\)
\(158\) 282799. 0.901230
\(159\) 95105.4 0.298341
\(160\) 0 0
\(161\) 122019. 0.370992
\(162\) 54779.6 0.163995
\(163\) −33444.3 −0.0985947 −0.0492973 0.998784i \(-0.515698\pi\)
−0.0492973 + 0.998784i \(0.515698\pi\)
\(164\) −253178. −0.735048
\(165\) 0 0
\(166\) −32347.7 −0.0911115
\(167\) 317479. 0.880893 0.440447 0.897779i \(-0.354820\pi\)
0.440447 + 0.897779i \(0.354820\pi\)
\(168\) −137330. −0.375399
\(169\) 28561.0 0.0769231
\(170\) 0 0
\(171\) 47362.2 0.123863
\(172\) 200427. 0.516577
\(173\) −84505.1 −0.214668 −0.107334 0.994223i \(-0.534231\pi\)
−0.107334 + 0.994223i \(0.534231\pi\)
\(174\) 114868. 0.287624
\(175\) 0 0
\(176\) 22817.6 0.0555249
\(177\) −58550.5 −0.140474
\(178\) 225492. 0.533435
\(179\) −734183. −1.71266 −0.856331 0.516428i \(-0.827261\pi\)
−0.856331 + 0.516428i \(0.827261\pi\)
\(180\) 0 0
\(181\) 363356. 0.824396 0.412198 0.911094i \(-0.364761\pi\)
0.412198 + 0.911094i \(0.364761\pi\)
\(182\) 56918.0 0.127371
\(183\) −136496. −0.301294
\(184\) 257759. 0.561267
\(185\) 0 0
\(186\) −24786.1 −0.0525321
\(187\) 70128.6 0.146653
\(188\) −176330. −0.363858
\(189\) −305800. −0.622705
\(190\) 0 0
\(191\) 54142.3 0.107387 0.0536937 0.998557i \(-0.482901\pi\)
0.0536937 + 0.998557i \(0.482901\pi\)
\(192\) −208011. −0.407225
\(193\) 208911. 0.403709 0.201855 0.979416i \(-0.435303\pi\)
0.201855 + 0.979416i \(0.435303\pi\)
\(194\) 65757.1 0.125441
\(195\) 0 0
\(196\) 157105. 0.292112
\(197\) −581675. −1.06786 −0.533931 0.845528i \(-0.679286\pi\)
−0.533931 + 0.845528i \(0.679286\pi\)
\(198\) 104067. 0.188646
\(199\) −624788. −1.11841 −0.559204 0.829030i \(-0.688893\pi\)
−0.559204 + 0.829030i \(0.688893\pi\)
\(200\) 0 0
\(201\) 34570.6 0.0603555
\(202\) 259868. 0.448099
\(203\) 329121. 0.560551
\(204\) −64991.8 −0.109341
\(205\) 0 0
\(206\) −723575. −1.18800
\(207\) 240799. 0.390597
\(208\) 24628.2 0.0394707
\(209\) 42223.6 0.0668635
\(210\) 0 0
\(211\) 628250. 0.971464 0.485732 0.874108i \(-0.338553\pi\)
0.485732 + 0.874108i \(0.338553\pi\)
\(212\) 204847. 0.313034
\(213\) −105647. −0.159554
\(214\) 174524. 0.260507
\(215\) 0 0
\(216\) −645984. −0.942079
\(217\) −71017.3 −0.102380
\(218\) 708693. 1.00999
\(219\) −107500. −0.151459
\(220\) 0 0
\(221\) 75693.4 0.104250
\(222\) −136509. −0.185899
\(223\) 1.09757e6 1.47798 0.738992 0.673715i \(-0.235302\pi\)
0.738992 + 0.673715i \(0.235302\pi\)
\(224\) −486328. −0.647603
\(225\) 0 0
\(226\) −716229. −0.932783
\(227\) −161937. −0.208584 −0.104292 0.994547i \(-0.533258\pi\)
−0.104292 + 0.994547i \(0.533258\pi\)
\(228\) −39130.8 −0.0498518
\(229\) −645210. −0.813040 −0.406520 0.913642i \(-0.633258\pi\)
−0.406520 + 0.913642i \(0.633258\pi\)
\(230\) 0 0
\(231\) −114375. −0.141026
\(232\) 695248. 0.848047
\(233\) 839907. 1.01354 0.506770 0.862081i \(-0.330839\pi\)
0.506770 + 0.862081i \(0.330839\pi\)
\(234\) 112325. 0.134102
\(235\) 0 0
\(236\) −126112. −0.147393
\(237\) −613369. −0.709334
\(238\) 150846. 0.172620
\(239\) −532168. −0.602635 −0.301317 0.953524i \(-0.597426\pi\)
−0.301317 + 0.953524i \(0.597426\pi\)
\(240\) 0 0
\(241\) −11282.2 −0.0125127 −0.00625633 0.999980i \(-0.501991\pi\)
−0.00625633 + 0.999980i \(0.501991\pi\)
\(242\) −516692. −0.567144
\(243\) −953778. −1.03617
\(244\) −293998. −0.316133
\(245\) 0 0
\(246\) −444824. −0.468652
\(247\) 45574.1 0.0475308
\(248\) −150020. −0.154889
\(249\) 70159.5 0.0717114
\(250\) 0 0
\(251\) −592652. −0.593766 −0.296883 0.954914i \(-0.595947\pi\)
−0.296883 + 0.954914i \(0.595947\pi\)
\(252\) −276332. −0.274114
\(253\) 214673. 0.210851
\(254\) −692639. −0.673632
\(255\) 0 0
\(256\) −1.10978e6 −1.05837
\(257\) 161530. 0.152552 0.0762762 0.997087i \(-0.475697\pi\)
0.0762762 + 0.997087i \(0.475697\pi\)
\(258\) 352143. 0.329359
\(259\) −391126. −0.362299
\(260\) 0 0
\(261\) 649502. 0.590173
\(262\) 836466. 0.752826
\(263\) 377791. 0.336793 0.168396 0.985719i \(-0.446141\pi\)
0.168396 + 0.985719i \(0.446141\pi\)
\(264\) −241610. −0.213356
\(265\) 0 0
\(266\) 90822.6 0.0787027
\(267\) −489075. −0.419853
\(268\) 74461.6 0.0633280
\(269\) −689.090 −0.000580624 0 −0.000290312 1.00000i \(-0.500092\pi\)
−0.000290312 1.00000i \(0.500092\pi\)
\(270\) 0 0
\(271\) 625466. 0.517345 0.258673 0.965965i \(-0.416715\pi\)
0.258673 + 0.965965i \(0.416715\pi\)
\(272\) 65270.6 0.0534928
\(273\) −123450. −0.100250
\(274\) −1.33897e6 −1.07744
\(275\) 0 0
\(276\) −198949. −0.157206
\(277\) −744000. −0.582604 −0.291302 0.956631i \(-0.594088\pi\)
−0.291302 + 0.956631i \(0.594088\pi\)
\(278\) 1.06954e6 0.830015
\(279\) −140149. −0.107790
\(280\) 0 0
\(281\) 1.43786e6 1.08631 0.543153 0.839634i \(-0.317230\pi\)
0.543153 + 0.839634i \(0.317230\pi\)
\(282\) −309806. −0.231989
\(283\) 1.24662e6 0.925267 0.462634 0.886550i \(-0.346905\pi\)
0.462634 + 0.886550i \(0.346905\pi\)
\(284\) −227553. −0.167412
\(285\) 0 0
\(286\) 100138. 0.0723907
\(287\) −1.27451e6 −0.913355
\(288\) −959742. −0.681825
\(289\) −1.21925e6 −0.858714
\(290\) 0 0
\(291\) −142622. −0.0987309
\(292\) −231543. −0.158919
\(293\) −1.74658e6 −1.18855 −0.594276 0.804261i \(-0.702561\pi\)
−0.594276 + 0.804261i \(0.702561\pi\)
\(294\) 276027. 0.186244
\(295\) 0 0
\(296\) −826231. −0.548116
\(297\) −538004. −0.353911
\(298\) −293586. −0.191511
\(299\) 231708. 0.149887
\(300\) 0 0
\(301\) 1.00896e6 0.641888
\(302\) −793543. −0.500672
\(303\) −563632. −0.352687
\(304\) 39298.6 0.0243890
\(305\) 0 0
\(306\) 297687. 0.181742
\(307\) 239330. 0.144928 0.0724638 0.997371i \(-0.476914\pi\)
0.0724638 + 0.997371i \(0.476914\pi\)
\(308\) −246351. −0.147972
\(309\) 1.56937e6 0.935041
\(310\) 0 0
\(311\) 1.10338e6 0.646883 0.323441 0.946248i \(-0.395160\pi\)
0.323441 + 0.946248i \(0.395160\pi\)
\(312\) −260782. −0.151667
\(313\) 934831. 0.539352 0.269676 0.962951i \(-0.413083\pi\)
0.269676 + 0.962951i \(0.413083\pi\)
\(314\) −483426. −0.276698
\(315\) 0 0
\(316\) −1.32113e6 −0.744268
\(317\) −2.65437e6 −1.48359 −0.741794 0.670628i \(-0.766025\pi\)
−0.741794 + 0.670628i \(0.766025\pi\)
\(318\) 359909. 0.199584
\(319\) 579033. 0.318586
\(320\) 0 0
\(321\) −378528. −0.205038
\(322\) 461761. 0.248186
\(323\) 120782. 0.0644164
\(324\) −255910. −0.135433
\(325\) 0 0
\(326\) −126564. −0.0659578
\(327\) −1.53710e6 −0.794935
\(328\) −2.69234e6 −1.38180
\(329\) −887659. −0.452123
\(330\) 0 0
\(331\) 648335. 0.325259 0.162630 0.986687i \(-0.448002\pi\)
0.162630 + 0.986687i \(0.448002\pi\)
\(332\) 151117. 0.0752431
\(333\) −771867. −0.381445
\(334\) 1.20144e6 0.589299
\(335\) 0 0
\(336\) −106452. −0.0514404
\(337\) 761016. 0.365022 0.182511 0.983204i \(-0.441577\pi\)
0.182511 + 0.983204i \(0.441577\pi\)
\(338\) 108084. 0.0514599
\(339\) 1.55344e6 0.734169
\(340\) 0 0
\(341\) −124943. −0.0581871
\(342\) 179234. 0.0828617
\(343\) 2.28665e6 1.04945
\(344\) 2.13138e6 0.971100
\(345\) 0 0
\(346\) −319794. −0.143609
\(347\) 1.06891e6 0.476561 0.238281 0.971196i \(-0.423416\pi\)
0.238281 + 0.971196i \(0.423416\pi\)
\(348\) −536620. −0.237530
\(349\) 1.57765e6 0.693342 0.346671 0.937987i \(-0.387312\pi\)
0.346671 + 0.937987i \(0.387312\pi\)
\(350\) 0 0
\(351\) −580696. −0.251583
\(352\) −855613. −0.368062
\(353\) −109374. −0.0467173 −0.0233587 0.999727i \(-0.507436\pi\)
−0.0233587 + 0.999727i \(0.507436\pi\)
\(354\) −221574. −0.0939745
\(355\) 0 0
\(356\) −1.05342e6 −0.440530
\(357\) −327173. −0.135865
\(358\) −2.77838e6 −1.14573
\(359\) 3.75166e6 1.53634 0.768169 0.640247i \(-0.221168\pi\)
0.768169 + 0.640247i \(0.221168\pi\)
\(360\) 0 0
\(361\) −2.40338e6 −0.970631
\(362\) 1.37506e6 0.551504
\(363\) 1.12066e6 0.446384
\(364\) −265900. −0.105188
\(365\) 0 0
\(366\) −516543. −0.201560
\(367\) 2.12587e6 0.823895 0.411947 0.911208i \(-0.364849\pi\)
0.411947 + 0.911208i \(0.364849\pi\)
\(368\) 199802. 0.0769096
\(369\) −2.51518e6 −0.961621
\(370\) 0 0
\(371\) 1.03122e6 0.388969
\(372\) 115791. 0.0433829
\(373\) 725713. 0.270080 0.135040 0.990840i \(-0.456884\pi\)
0.135040 + 0.990840i \(0.456884\pi\)
\(374\) 265389. 0.0981078
\(375\) 0 0
\(376\) −1.87513e6 −0.684008
\(377\) 624981. 0.226471
\(378\) −1.15724e6 −0.416577
\(379\) 1.40410e6 0.502111 0.251056 0.967973i \(-0.419222\pi\)
0.251056 + 0.967973i \(0.419222\pi\)
\(380\) 0 0
\(381\) 1.50228e6 0.530197
\(382\) 204892. 0.0718400
\(383\) 2.82085e6 0.982615 0.491307 0.870986i \(-0.336519\pi\)
0.491307 + 0.870986i \(0.336519\pi\)
\(384\) 648093. 0.224290
\(385\) 0 0
\(386\) 790587. 0.270073
\(387\) 1.99113e6 0.675808
\(388\) −307193. −0.103593
\(389\) −1.71293e6 −0.573940 −0.286970 0.957940i \(-0.592648\pi\)
−0.286970 + 0.957940i \(0.592648\pi\)
\(390\) 0 0
\(391\) 614081. 0.203135
\(392\) 1.67068e6 0.549133
\(393\) −1.81423e6 −0.592530
\(394\) −2.20124e6 −0.714377
\(395\) 0 0
\(396\) −486161. −0.155791
\(397\) 3.80080e6 1.21032 0.605158 0.796106i \(-0.293110\pi\)
0.605158 + 0.796106i \(0.293110\pi\)
\(398\) −2.36440e6 −0.748191
\(399\) −196987. −0.0619448
\(400\) 0 0
\(401\) 1.09440e6 0.339871 0.169936 0.985455i \(-0.445644\pi\)
0.169936 + 0.985455i \(0.445644\pi\)
\(402\) 130826. 0.0403766
\(403\) −134858. −0.0413631
\(404\) −1.21401e6 −0.370056
\(405\) 0 0
\(406\) 1.24550e6 0.374997
\(407\) −688122. −0.205911
\(408\) −691134. −0.205547
\(409\) 6.63162e6 1.96025 0.980125 0.198380i \(-0.0635679\pi\)
0.980125 + 0.198380i \(0.0635679\pi\)
\(410\) 0 0
\(411\) 2.90412e6 0.848028
\(412\) 3.38027e6 0.981090
\(413\) −634855. −0.183147
\(414\) 911260. 0.261301
\(415\) 0 0
\(416\) −923508. −0.261642
\(417\) −2.31975e6 −0.653283
\(418\) 159787. 0.0447303
\(419\) −1.50034e6 −0.417499 −0.208749 0.977969i \(-0.566939\pi\)
−0.208749 + 0.977969i \(0.566939\pi\)
\(420\) 0 0
\(421\) −1.91392e6 −0.526282 −0.263141 0.964757i \(-0.584758\pi\)
−0.263141 + 0.964757i \(0.584758\pi\)
\(422\) 2.37750e6 0.649889
\(423\) −1.75175e6 −0.476015
\(424\) 2.17838e6 0.588464
\(425\) 0 0
\(426\) −399801. −0.106738
\(427\) −1.48000e6 −0.392820
\(428\) −815311. −0.215136
\(429\) −217191. −0.0569768
\(430\) 0 0
\(431\) 6.04255e6 1.56685 0.783424 0.621488i \(-0.213471\pi\)
0.783424 + 0.621488i \(0.213471\pi\)
\(432\) −500735. −0.129092
\(433\) 1.81284e6 0.464666 0.232333 0.972636i \(-0.425364\pi\)
0.232333 + 0.972636i \(0.425364\pi\)
\(434\) −268752. −0.0684900
\(435\) 0 0
\(436\) −3.31075e6 −0.834085
\(437\) 369731. 0.0926151
\(438\) −406813. −0.101323
\(439\) 3.45414e6 0.855418 0.427709 0.903916i \(-0.359321\pi\)
0.427709 + 0.903916i \(0.359321\pi\)
\(440\) 0 0
\(441\) 1.56075e6 0.382153
\(442\) 286448. 0.0697413
\(443\) 1.64299e6 0.397764 0.198882 0.980023i \(-0.436269\pi\)
0.198882 + 0.980023i \(0.436269\pi\)
\(444\) 637718. 0.153522
\(445\) 0 0
\(446\) 4.15355e6 0.988740
\(447\) 636764. 0.150733
\(448\) −2.25544e6 −0.530929
\(449\) 3.90173e6 0.913359 0.456680 0.889631i \(-0.349039\pi\)
0.456680 + 0.889631i \(0.349039\pi\)
\(450\) 0 0
\(451\) −2.24230e6 −0.519101
\(452\) 3.34596e6 0.770325
\(453\) 1.72113e6 0.394066
\(454\) −612821. −0.139539
\(455\) 0 0
\(456\) −416123. −0.0937152
\(457\) 6.09815e6 1.36586 0.682932 0.730482i \(-0.260704\pi\)
0.682932 + 0.730482i \(0.260704\pi\)
\(458\) −2.44168e6 −0.543907
\(459\) −1.53898e6 −0.340959
\(460\) 0 0
\(461\) 8.52589e6 1.86848 0.934238 0.356651i \(-0.116081\pi\)
0.934238 + 0.356651i \(0.116081\pi\)
\(462\) −432830. −0.0943436
\(463\) 2.70655e6 0.586765 0.293382 0.955995i \(-0.405219\pi\)
0.293382 + 0.955995i \(0.405219\pi\)
\(464\) 538922. 0.116207
\(465\) 0 0
\(466\) 3.17847e6 0.678038
\(467\) 350172. 0.0743001 0.0371501 0.999310i \(-0.488172\pi\)
0.0371501 + 0.999310i \(0.488172\pi\)
\(468\) −524739. −0.110746
\(469\) 374845. 0.0786900
\(470\) 0 0
\(471\) 1.04851e6 0.217782
\(472\) −1.34110e6 −0.277080
\(473\) 1.77510e6 0.364813
\(474\) −2.32118e6 −0.474529
\(475\) 0 0
\(476\) −704698. −0.142556
\(477\) 2.03505e6 0.409524
\(478\) −2.01389e6 −0.403150
\(479\) 8.49125e6 1.69096 0.845479 0.534009i \(-0.179315\pi\)
0.845479 + 0.534009i \(0.179315\pi\)
\(480\) 0 0
\(481\) −742726. −0.146375
\(482\) −42695.3 −0.00837071
\(483\) −1.00152e6 −0.195341
\(484\) 2.41380e6 0.468368
\(485\) 0 0
\(486\) −3.60940e6 −0.693177
\(487\) −3034.65 −0.000579811 0 −0.000289905 1.00000i \(-0.500092\pi\)
−0.000289905 1.00000i \(0.500092\pi\)
\(488\) −3.12642e6 −0.594289
\(489\) 274507. 0.0519136
\(490\) 0 0
\(491\) −3.43114e6 −0.642295 −0.321147 0.947029i \(-0.604068\pi\)
−0.321147 + 0.947029i \(0.604068\pi\)
\(492\) 2.07805e6 0.387029
\(493\) 1.65635e6 0.306926
\(494\) 172467. 0.0317971
\(495\) 0 0
\(496\) −116288. −0.0212242
\(497\) −1.14551e6 −0.208022
\(498\) 265506. 0.0479735
\(499\) −1.11566e6 −0.200577 −0.100289 0.994958i \(-0.531977\pi\)
−0.100289 + 0.994958i \(0.531977\pi\)
\(500\) 0 0
\(501\) −2.60583e6 −0.463822
\(502\) −2.24278e6 −0.397217
\(503\) −4.99165e6 −0.879679 −0.439840 0.898076i \(-0.644965\pi\)
−0.439840 + 0.898076i \(0.644965\pi\)
\(504\) −2.93857e6 −0.515299
\(505\) 0 0
\(506\) 812391. 0.141055
\(507\) −234425. −0.0405027
\(508\) 3.23575e6 0.556309
\(509\) −398811. −0.0682296 −0.0341148 0.999418i \(-0.510861\pi\)
−0.0341148 + 0.999418i \(0.510861\pi\)
\(510\) 0 0
\(511\) −1.16560e6 −0.197469
\(512\) −1.67305e6 −0.282056
\(513\) −926602. −0.155453
\(514\) 611279. 0.102054
\(515\) 0 0
\(516\) −1.64508e6 −0.271996
\(517\) −1.56169e6 −0.256962
\(518\) −1.48015e6 −0.242371
\(519\) 693607. 0.113030
\(520\) 0 0
\(521\) 9.33110e6 1.50605 0.753023 0.657994i \(-0.228595\pi\)
0.753023 + 0.657994i \(0.228595\pi\)
\(522\) 2.45792e6 0.394813
\(523\) 4.93297e6 0.788596 0.394298 0.918983i \(-0.370988\pi\)
0.394298 + 0.918983i \(0.370988\pi\)
\(524\) −3.90766e6 −0.621711
\(525\) 0 0
\(526\) 1.42968e6 0.225307
\(527\) −357405. −0.0560575
\(528\) −187284. −0.0292359
\(529\) −4.55656e6 −0.707942
\(530\) 0 0
\(531\) −1.25285e6 −0.192825
\(532\) −424290. −0.0649955
\(533\) −2.42023e6 −0.369010
\(534\) −1.85081e6 −0.280873
\(535\) 0 0
\(536\) 791838. 0.119049
\(537\) 6.02608e6 0.901777
\(538\) −2607.73 −0.000388425 0
\(539\) 1.39141e6 0.206293
\(540\) 0 0
\(541\) 2.72340e6 0.400054 0.200027 0.979790i \(-0.435897\pi\)
0.200027 + 0.979790i \(0.435897\pi\)
\(542\) 2.36696e6 0.346093
\(543\) −2.98238e6 −0.434074
\(544\) −2.44751e6 −0.354591
\(545\) 0 0
\(546\) −467176. −0.0670654
\(547\) −1.28669e7 −1.83867 −0.919337 0.393472i \(-0.871274\pi\)
−0.919337 + 0.393472i \(0.871274\pi\)
\(548\) 6.25518e6 0.889792
\(549\) −2.92071e6 −0.413578
\(550\) 0 0
\(551\) 997266. 0.139937
\(552\) −2.11566e6 −0.295527
\(553\) −6.65067e6 −0.924811
\(554\) −2.81553e6 −0.389750
\(555\) 0 0
\(556\) −4.99651e6 −0.685456
\(557\) −1.03791e7 −1.41750 −0.708751 0.705459i \(-0.750741\pi\)
−0.708751 + 0.705459i \(0.750741\pi\)
\(558\) −530368. −0.0721094
\(559\) 1.91596e6 0.259333
\(560\) 0 0
\(561\) −575607. −0.0772180
\(562\) 5.44133e6 0.726716
\(563\) 3.37237e6 0.448399 0.224199 0.974543i \(-0.428023\pi\)
0.224199 + 0.974543i \(0.428023\pi\)
\(564\) 1.44730e6 0.191584
\(565\) 0 0
\(566\) 4.71760e6 0.618984
\(567\) −1.28827e6 −0.168286
\(568\) −2.41983e6 −0.314713
\(569\) −9.65718e6 −1.25046 −0.625230 0.780441i \(-0.714995\pi\)
−0.625230 + 0.780441i \(0.714995\pi\)
\(570\) 0 0
\(571\) −3.19460e6 −0.410040 −0.205020 0.978758i \(-0.565726\pi\)
−0.205020 + 0.978758i \(0.565726\pi\)
\(572\) −467807. −0.0597828
\(573\) −444394. −0.0565433
\(574\) −4.82316e6 −0.611016
\(575\) 0 0
\(576\) −4.45099e6 −0.558986
\(577\) −1.01384e7 −1.26774 −0.633872 0.773438i \(-0.718535\pi\)
−0.633872 + 0.773438i \(0.718535\pi\)
\(578\) −4.61403e6 −0.574462
\(579\) −1.71472e6 −0.212567
\(580\) 0 0
\(581\) 760731. 0.0934955
\(582\) −539726. −0.0660489
\(583\) 1.81425e6 0.221068
\(584\) −2.46227e6 −0.298747
\(585\) 0 0
\(586\) −6.60960e6 −0.795117
\(587\) −777799. −0.0931691 −0.0465846 0.998914i \(-0.514834\pi\)
−0.0465846 + 0.998914i \(0.514834\pi\)
\(588\) −1.28950e6 −0.153807
\(589\) −215189. −0.0255583
\(590\) 0 0
\(591\) 4.77432e6 0.562267
\(592\) −640454. −0.0751076
\(593\) 8.28738e6 0.967789 0.483894 0.875126i \(-0.339222\pi\)
0.483894 + 0.875126i \(0.339222\pi\)
\(594\) −2.03598e6 −0.236759
\(595\) 0 0
\(596\) 1.37153e6 0.158157
\(597\) 5.12818e6 0.588881
\(598\) 876856. 0.100271
\(599\) 1.39700e7 1.59085 0.795423 0.606054i \(-0.207249\pi\)
0.795423 + 0.606054i \(0.207249\pi\)
\(600\) 0 0
\(601\) −1.27397e7 −1.43871 −0.719355 0.694643i \(-0.755562\pi\)
−0.719355 + 0.694643i \(0.755562\pi\)
\(602\) 3.81824e6 0.429409
\(603\) 739736. 0.0828483
\(604\) 3.70714e6 0.413473
\(605\) 0 0
\(606\) −2.13296e6 −0.235940
\(607\) 6.25976e6 0.689583 0.344791 0.938679i \(-0.387950\pi\)
0.344791 + 0.938679i \(0.387950\pi\)
\(608\) −1.47362e6 −0.161669
\(609\) −2.70138e6 −0.295150
\(610\) 0 0
\(611\) −1.68561e6 −0.182665
\(612\) −1.39068e6 −0.150089
\(613\) 1.17405e7 1.26193 0.630964 0.775812i \(-0.282660\pi\)
0.630964 + 0.775812i \(0.282660\pi\)
\(614\) 905700. 0.0969535
\(615\) 0 0
\(616\) −2.61974e6 −0.278168
\(617\) −1.57982e7 −1.67069 −0.835343 0.549729i \(-0.814731\pi\)
−0.835343 + 0.549729i \(0.814731\pi\)
\(618\) 5.93901e6 0.625523
\(619\) 3.16596e6 0.332108 0.166054 0.986117i \(-0.446897\pi\)
0.166054 + 0.986117i \(0.446897\pi\)
\(620\) 0 0
\(621\) −4.71103e6 −0.490216
\(622\) 4.17556e6 0.432751
\(623\) −5.30297e6 −0.547393
\(624\) −202145. −0.0207827
\(625\) 0 0
\(626\) 3.53770e6 0.360815
\(627\) −346566. −0.0352060
\(628\) 2.25839e6 0.228507
\(629\) −1.96840e6 −0.198375
\(630\) 0 0
\(631\) −1.95795e7 −1.95762 −0.978811 0.204764i \(-0.934357\pi\)
−0.978811 + 0.204764i \(0.934357\pi\)
\(632\) −1.40492e7 −1.39913
\(633\) −5.15660e6 −0.511510
\(634\) −1.00450e7 −0.992489
\(635\) 0 0
\(636\) −1.68136e6 −0.164823
\(637\) 1.50183e6 0.146646
\(638\) 2.19125e6 0.213127
\(639\) −2.26061e6 −0.219015
\(640\) 0 0
\(641\) −7.23060e6 −0.695072 −0.347536 0.937667i \(-0.612981\pi\)
−0.347536 + 0.937667i \(0.612981\pi\)
\(642\) −1.43247e6 −0.137166
\(643\) 1.17438e7 1.12016 0.560081 0.828438i \(-0.310770\pi\)
0.560081 + 0.828438i \(0.310770\pi\)
\(644\) −2.15718e6 −0.204961
\(645\) 0 0
\(646\) 457078. 0.0430932
\(647\) −9.24080e6 −0.867858 −0.433929 0.900947i \(-0.642873\pi\)
−0.433929 + 0.900947i \(0.642873\pi\)
\(648\) −2.72139e6 −0.254597
\(649\) −1.11692e6 −0.104091
\(650\) 0 0
\(651\) 582901. 0.0539067
\(652\) 591260. 0.0544703
\(653\) 1.11349e7 1.02188 0.510942 0.859615i \(-0.329297\pi\)
0.510942 + 0.859615i \(0.329297\pi\)
\(654\) −5.81686e6 −0.531795
\(655\) 0 0
\(656\) −2.08697e6 −0.189346
\(657\) −2.30026e6 −0.207904
\(658\) −3.35918e6 −0.302461
\(659\) 8.65776e6 0.776590 0.388295 0.921535i \(-0.373064\pi\)
0.388295 + 0.921535i \(0.373064\pi\)
\(660\) 0 0
\(661\) −1.23594e7 −1.10025 −0.550127 0.835081i \(-0.685421\pi\)
−0.550127 + 0.835081i \(0.685421\pi\)
\(662\) 2.45351e6 0.217592
\(663\) −621282. −0.0548915
\(664\) 1.60700e6 0.141448
\(665\) 0 0
\(666\) −2.92099e6 −0.255179
\(667\) 5.07030e6 0.441285
\(668\) −5.61268e6 −0.486664
\(669\) −9.00871e6 −0.778211
\(670\) 0 0
\(671\) −2.60382e6 −0.223257
\(672\) 3.99172e6 0.340986
\(673\) 6.11057e6 0.520048 0.260024 0.965602i \(-0.416269\pi\)
0.260024 + 0.965602i \(0.416269\pi\)
\(674\) 2.87993e6 0.244192
\(675\) 0 0
\(676\) −504928. −0.0424974
\(677\) −1.48518e7 −1.24540 −0.622698 0.782462i \(-0.713964\pi\)
−0.622698 + 0.782462i \(0.713964\pi\)
\(678\) 5.87872e6 0.491144
\(679\) −1.54643e6 −0.128723
\(680\) 0 0
\(681\) 1.32916e6 0.109827
\(682\) −472825. −0.0389260
\(683\) 6.13145e6 0.502934 0.251467 0.967866i \(-0.419087\pi\)
0.251467 + 0.967866i \(0.419087\pi\)
\(684\) −837313. −0.0684302
\(685\) 0 0
\(686\) 8.65340e6 0.702064
\(687\) 5.29580e6 0.428095
\(688\) 1.65214e6 0.133068
\(689\) 1.95822e6 0.157150
\(690\) 0 0
\(691\) 2.33358e7 1.85920 0.929602 0.368566i \(-0.120151\pi\)
0.929602 + 0.368566i \(0.120151\pi\)
\(692\) 1.49396e6 0.118597
\(693\) −2.44737e6 −0.193582
\(694\) 4.04511e6 0.318809
\(695\) 0 0
\(696\) −5.70651e6 −0.446527
\(697\) −6.41417e6 −0.500102
\(698\) 5.97033e6 0.463831
\(699\) −6.89385e6 −0.533665
\(700\) 0 0
\(701\) 2.53633e7 1.94944 0.974721 0.223426i \(-0.0717242\pi\)
0.974721 + 0.223426i \(0.0717242\pi\)
\(702\) −2.19754e6 −0.168304
\(703\) −1.18515e6 −0.0904450
\(704\) −3.96807e6 −0.301751
\(705\) 0 0
\(706\) −413907. −0.0312529
\(707\) −6.11139e6 −0.459824
\(708\) 1.03511e6 0.0776075
\(709\) −1.64964e7 −1.23246 −0.616232 0.787565i \(-0.711342\pi\)
−0.616232 + 0.787565i \(0.711342\pi\)
\(710\) 0 0
\(711\) −1.31248e7 −0.973682
\(712\) −1.12022e7 −0.828141
\(713\) −1.09407e6 −0.0805971
\(714\) −1.23813e6 −0.0908907
\(715\) 0 0
\(716\) 1.29796e7 0.946189
\(717\) 4.36797e6 0.317309
\(718\) 1.41975e7 1.02778
\(719\) −9.96268e6 −0.718710 −0.359355 0.933201i \(-0.617003\pi\)
−0.359355 + 0.933201i \(0.617003\pi\)
\(720\) 0 0
\(721\) 1.70165e7 1.21908
\(722\) −9.09514e6 −0.649332
\(723\) 92602.6 0.00658836
\(724\) −6.42375e6 −0.455452
\(725\) 0 0
\(726\) 4.24095e6 0.298622
\(727\) 2.53565e7 1.77932 0.889658 0.456627i \(-0.150943\pi\)
0.889658 + 0.456627i \(0.150943\pi\)
\(728\) −2.82762e6 −0.197739
\(729\) 4.31096e6 0.300438
\(730\) 0 0
\(731\) 5.07775e6 0.351462
\(732\) 2.41310e6 0.166455
\(733\) −1.70653e7 −1.17315 −0.586576 0.809894i \(-0.699524\pi\)
−0.586576 + 0.809894i \(0.699524\pi\)
\(734\) 8.04497e6 0.551168
\(735\) 0 0
\(736\) −7.49218e6 −0.509816
\(737\) 659478. 0.0447230
\(738\) −9.51826e6 −0.643304
\(739\) −1.40560e7 −0.946781 −0.473391 0.880853i \(-0.656970\pi\)
−0.473391 + 0.880853i \(0.656970\pi\)
\(740\) 0 0
\(741\) −374067. −0.0250267
\(742\) 3.90245e6 0.260212
\(743\) 1.55718e7 1.03483 0.517413 0.855736i \(-0.326895\pi\)
0.517413 + 0.855736i \(0.326895\pi\)
\(744\) 1.23135e6 0.0815544
\(745\) 0 0
\(746\) 2.74633e6 0.180678
\(747\) 1.50126e6 0.0984362
\(748\) −1.23980e6 −0.0810209
\(749\) −4.10433e6 −0.267324
\(750\) 0 0
\(751\) −5.89761e6 −0.381572 −0.190786 0.981632i \(-0.561104\pi\)
−0.190786 + 0.981632i \(0.561104\pi\)
\(752\) −1.45351e6 −0.0937287
\(753\) 4.86441e6 0.312639
\(754\) 2.36513e6 0.151505
\(755\) 0 0
\(756\) 5.40622e6 0.344024
\(757\) 2.57205e6 0.163132 0.0815660 0.996668i \(-0.474008\pi\)
0.0815660 + 0.996668i \(0.474008\pi\)
\(758\) 5.31356e6 0.335902
\(759\) −1.76201e6 −0.111021
\(760\) 0 0
\(761\) −2.56012e7 −1.60250 −0.801252 0.598328i \(-0.795832\pi\)
−0.801252 + 0.598328i \(0.795832\pi\)
\(762\) 5.68509e6 0.354691
\(763\) −1.66665e7 −1.03642
\(764\) −957179. −0.0593280
\(765\) 0 0
\(766\) 1.06750e7 0.657349
\(767\) −1.20555e6 −0.0739942
\(768\) 9.10895e6 0.557270
\(769\) −1.15095e7 −0.701842 −0.350921 0.936405i \(-0.614131\pi\)
−0.350921 + 0.936405i \(0.614131\pi\)
\(770\) 0 0
\(771\) −1.32582e6 −0.0803243
\(772\) −3.69333e6 −0.223036
\(773\) 5.18479e6 0.312092 0.156046 0.987750i \(-0.450125\pi\)
0.156046 + 0.987750i \(0.450125\pi\)
\(774\) 7.53509e6 0.452101
\(775\) 0 0
\(776\) −3.26674e6 −0.194742
\(777\) 3.21032e6 0.190764
\(778\) −6.48229e6 −0.383954
\(779\) −3.86190e6 −0.228012
\(780\) 0 0
\(781\) −2.01534e6 −0.118228
\(782\) 2.32388e6 0.135893
\(783\) −1.27070e7 −0.740692
\(784\) 1.29503e6 0.0752469
\(785\) 0 0
\(786\) −6.86561e6 −0.396390
\(787\) 1.28463e7 0.739333 0.369667 0.929165i \(-0.379472\pi\)
0.369667 + 0.929165i \(0.379472\pi\)
\(788\) 1.02834e7 0.589958
\(789\) −3.10087e6 −0.177333
\(790\) 0 0
\(791\) 1.68438e7 0.957190
\(792\) −5.16992e6 −0.292867
\(793\) −2.81044e6 −0.158705
\(794\) 1.43834e7 0.809676
\(795\) 0 0
\(796\) 1.10456e7 0.617883
\(797\) 2.11768e7 1.18090 0.590452 0.807073i \(-0.298950\pi\)
0.590452 + 0.807073i \(0.298950\pi\)
\(798\) −745461. −0.0414398
\(799\) −4.46727e6 −0.247557
\(800\) 0 0
\(801\) −1.04651e7 −0.576320
\(802\) 4.14155e6 0.227367
\(803\) −2.05069e6 −0.112230
\(804\) −611172. −0.0333444
\(805\) 0 0
\(806\) −510344. −0.0276711
\(807\) 5655.97 0.000305719 0
\(808\) −1.29100e7 −0.695659
\(809\) 1.58537e6 0.0851648 0.0425824 0.999093i \(-0.486442\pi\)
0.0425824 + 0.999093i \(0.486442\pi\)
\(810\) 0 0
\(811\) −2.18155e7 −1.16470 −0.582350 0.812938i \(-0.697867\pi\)
−0.582350 + 0.812938i \(0.697867\pi\)
\(812\) −5.81850e6 −0.309686
\(813\) −5.13375e6 −0.272401
\(814\) −2.60407e6 −0.137750
\(815\) 0 0
\(816\) −535733. −0.0281659
\(817\) 3.05725e6 0.160242
\(818\) 2.50962e7 1.31137
\(819\) −2.64157e6 −0.137611
\(820\) 0 0
\(821\) 3.09541e7 1.60273 0.801365 0.598176i \(-0.204108\pi\)
0.801365 + 0.598176i \(0.204108\pi\)
\(822\) 1.09901e7 0.567313
\(823\) −2.68746e7 −1.38307 −0.691533 0.722345i \(-0.743064\pi\)
−0.691533 + 0.722345i \(0.743064\pi\)
\(824\) 3.59464e7 1.84433
\(825\) 0 0
\(826\) −2.40249e6 −0.122521
\(827\) −9.94152e6 −0.505462 −0.252731 0.967537i \(-0.581329\pi\)
−0.252731 + 0.967537i \(0.581329\pi\)
\(828\) −4.25707e6 −0.215792
\(829\) 7.20887e6 0.364318 0.182159 0.983269i \(-0.441691\pi\)
0.182159 + 0.983269i \(0.441691\pi\)
\(830\) 0 0
\(831\) 6.10666e6 0.306762
\(832\) −4.28295e6 −0.214504
\(833\) 3.98020e6 0.198743
\(834\) −8.77867e6 −0.437032
\(835\) 0 0
\(836\) −746468. −0.0369399
\(837\) 2.74190e6 0.135281
\(838\) −5.67777e6 −0.279298
\(839\) 1.96670e7 0.964569 0.482285 0.876015i \(-0.339807\pi\)
0.482285 + 0.876015i \(0.339807\pi\)
\(840\) 0 0
\(841\) −6.83513e6 −0.333240
\(842\) −7.24288e6 −0.352072
\(843\) −1.18018e7 −0.571979
\(844\) −1.11068e7 −0.536702
\(845\) 0 0
\(846\) −6.62917e6 −0.318444
\(847\) 1.21512e7 0.581984
\(848\) 1.68858e6 0.0806364
\(849\) −1.02321e7 −0.487186
\(850\) 0 0
\(851\) −6.02554e6 −0.285215
\(852\) 1.86772e6 0.0881482
\(853\) −2.60044e7 −1.22370 −0.611848 0.790975i \(-0.709574\pi\)
−0.611848 + 0.790975i \(0.709574\pi\)
\(854\) −5.60080e6 −0.262788
\(855\) 0 0
\(856\) −8.67015e6 −0.404429
\(857\) 2.74925e7 1.27868 0.639341 0.768923i \(-0.279207\pi\)
0.639341 + 0.768923i \(0.279207\pi\)
\(858\) −821919. −0.0381163
\(859\) 3.86634e7 1.78779 0.893896 0.448274i \(-0.147961\pi\)
0.893896 + 0.448274i \(0.147961\pi\)
\(860\) 0 0
\(861\) 1.04611e7 0.480914
\(862\) 2.28669e7 1.04819
\(863\) −8.41848e6 −0.384775 −0.192387 0.981319i \(-0.561623\pi\)
−0.192387 + 0.981319i \(0.561623\pi\)
\(864\) 1.87766e7 0.855720
\(865\) 0 0
\(866\) 6.86038e6 0.310852
\(867\) 1.00075e7 0.452144
\(868\) 1.25551e6 0.0565615
\(869\) −1.17008e7 −0.525611
\(870\) 0 0
\(871\) 711808. 0.0317920
\(872\) −3.52071e7 −1.56797
\(873\) −3.05179e6 −0.135525
\(874\) 1.39918e6 0.0619576
\(875\) 0 0
\(876\) 1.90048e6 0.0836763
\(877\) −1.24226e7 −0.545399 −0.272699 0.962099i \(-0.587916\pi\)
−0.272699 + 0.962099i \(0.587916\pi\)
\(878\) 1.30716e7 0.572257
\(879\) 1.43357e7 0.625815
\(880\) 0 0
\(881\) 7.24684e6 0.314564 0.157282 0.987554i \(-0.449727\pi\)
0.157282 + 0.987554i \(0.449727\pi\)
\(882\) 5.90637e6 0.255652
\(883\) −1.58232e7 −0.682958 −0.341479 0.939889i \(-0.610928\pi\)
−0.341479 + 0.939889i \(0.610928\pi\)
\(884\) −1.33818e6 −0.0575949
\(885\) 0 0
\(886\) 6.21760e6 0.266096
\(887\) 1.85905e7 0.793382 0.396691 0.917952i \(-0.370158\pi\)
0.396691 + 0.917952i \(0.370158\pi\)
\(888\) 6.78161e6 0.288603
\(889\) 1.62890e7 0.691257
\(890\) 0 0
\(891\) −2.26650e6 −0.0956446
\(892\) −1.94038e7 −0.816537
\(893\) −2.68969e6 −0.112869
\(894\) 2.40972e6 0.100838
\(895\) 0 0
\(896\) 7.02718e6 0.292423
\(897\) −1.90183e6 −0.0789206
\(898\) 1.47654e7 0.611018
\(899\) −2.95100e6 −0.121778
\(900\) 0 0
\(901\) 5.18974e6 0.212978
\(902\) −8.48556e6 −0.347267
\(903\) −8.28144e6 −0.337977
\(904\) 3.55815e7 1.44811
\(905\) 0 0
\(906\) 6.51331e6 0.263622
\(907\) 4.30877e7 1.73914 0.869571 0.493808i \(-0.164395\pi\)
0.869571 + 0.493808i \(0.164395\pi\)
\(908\) 2.86288e6 0.115236
\(909\) −1.20605e7 −0.484123
\(910\) 0 0
\(911\) 870987. 0.0347709 0.0173854 0.999849i \(-0.494466\pi\)
0.0173854 + 0.999849i \(0.494466\pi\)
\(912\) −322558. −0.0128417
\(913\) 1.33838e6 0.0531377
\(914\) 2.30773e7 0.913735
\(915\) 0 0
\(916\) 1.14066e7 0.449178
\(917\) −1.96714e7 −0.772524
\(918\) −5.82400e6 −0.228094
\(919\) −7.81477e6 −0.305230 −0.152615 0.988286i \(-0.548769\pi\)
−0.152615 + 0.988286i \(0.548769\pi\)
\(920\) 0 0
\(921\) −1.96439e6 −0.0763095
\(922\) 3.22647e7 1.24997
\(923\) −2.17526e6 −0.0840442
\(924\) 2.02202e6 0.0779123
\(925\) 0 0
\(926\) 1.02425e7 0.392533
\(927\) 3.35812e7 1.28350
\(928\) −2.02085e7 −0.770307
\(929\) 6.93323e6 0.263570 0.131785 0.991278i \(-0.457929\pi\)
0.131785 + 0.991278i \(0.457929\pi\)
\(930\) 0 0
\(931\) 2.39643e6 0.0906129
\(932\) −1.48487e7 −0.559948
\(933\) −9.05644e6 −0.340607
\(934\) 1.32516e6 0.0497052
\(935\) 0 0
\(936\) −5.58017e6 −0.208189
\(937\) −3.31684e7 −1.23417 −0.617085 0.786896i \(-0.711687\pi\)
−0.617085 + 0.786896i \(0.711687\pi\)
\(938\) 1.41853e6 0.0526420
\(939\) −7.67298e6 −0.283988
\(940\) 0 0
\(941\) −5.00778e6 −0.184362 −0.0921809 0.995742i \(-0.529384\pi\)
−0.0921809 + 0.995742i \(0.529384\pi\)
\(942\) 3.96790e6 0.145691
\(943\) −1.96347e7 −0.719025
\(944\) −1.03955e6 −0.0379678
\(945\) 0 0
\(946\) 6.71756e6 0.244053
\(947\) −7.37028e6 −0.267060 −0.133530 0.991045i \(-0.542631\pi\)
−0.133530 + 0.991045i \(0.542631\pi\)
\(948\) 1.08437e7 0.391883
\(949\) −2.21341e6 −0.0797805
\(950\) 0 0
\(951\) 2.17867e7 0.781162
\(952\) −7.49388e6 −0.267987
\(953\) 7.45227e6 0.265801 0.132900 0.991129i \(-0.457571\pi\)
0.132900 + 0.991129i \(0.457571\pi\)
\(954\) 7.70127e6 0.273963
\(955\) 0 0
\(956\) 9.40817e6 0.332936
\(957\) −4.75263e6 −0.167747
\(958\) 3.21336e7 1.13122
\(959\) 3.14890e7 1.10564
\(960\) 0 0
\(961\) −2.79924e7 −0.977758
\(962\) −2.81071e6 −0.0979216
\(963\) −8.09967e6 −0.281450
\(964\) 199457. 0.00691283
\(965\) 0 0
\(966\) −3.79007e6 −0.130679
\(967\) −4.78544e7 −1.64572 −0.822860 0.568244i \(-0.807623\pi\)
−0.822860 + 0.568244i \(0.807623\pi\)
\(968\) 2.56687e7 0.880473
\(969\) −991365. −0.0339175
\(970\) 0 0
\(971\) −2.54187e7 −0.865177 −0.432588 0.901592i \(-0.642400\pi\)
−0.432588 + 0.901592i \(0.642400\pi\)
\(972\) 1.68618e7 0.572450
\(973\) −2.51527e7 −0.851733
\(974\) −11484.1 −0.000387881 0
\(975\) 0 0
\(976\) −2.42345e6 −0.0814347
\(977\) 3.10699e7 1.04137 0.520683 0.853750i \(-0.325677\pi\)
0.520683 + 0.853750i \(0.325677\pi\)
\(978\) 1.03882e6 0.0347291
\(979\) −9.32970e6 −0.311108
\(980\) 0 0
\(981\) −3.28905e7 −1.09118
\(982\) −1.29845e7 −0.429682
\(983\) 1.28575e6 0.0424398 0.0212199 0.999775i \(-0.493245\pi\)
0.0212199 + 0.999775i \(0.493245\pi\)
\(984\) 2.20984e7 0.727566
\(985\) 0 0
\(986\) 6.26814e6 0.205327
\(987\) 7.28579e6 0.238059
\(988\) −805701. −0.0262592
\(989\) 1.55437e7 0.505317
\(990\) 0 0
\(991\) −4.43766e6 −0.143539 −0.0717695 0.997421i \(-0.522865\pi\)
−0.0717695 + 0.997421i \(0.522865\pi\)
\(992\) 4.36057e6 0.140690
\(993\) −5.32146e6 −0.171261
\(994\) −4.33499e6 −0.139162
\(995\) 0 0
\(996\) −1.24035e6 −0.0396182
\(997\) −2.72549e7 −0.868375 −0.434187 0.900823i \(-0.642964\pi\)
−0.434187 + 0.900823i \(0.642964\pi\)
\(998\) −4.22202e6 −0.134182
\(999\) 1.51009e7 0.478729
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 325.6.a.j.1.8 11
5.2 odd 4 325.6.b.i.274.15 22
5.3 odd 4 325.6.b.i.274.8 22
5.4 even 2 325.6.a.k.1.4 yes 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
325.6.a.j.1.8 11 1.1 even 1 trivial
325.6.a.k.1.4 yes 11 5.4 even 2
325.6.b.i.274.8 22 5.3 odd 4
325.6.b.i.274.15 22 5.2 odd 4