Properties

Label 325.6.a.j.1.3
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 1.3
Root \(6.07859\) 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)
 
\(f(q)\) \(=\) \(q-6.07859 q^{2} -25.6203 q^{3} +4.94922 q^{4} +155.735 q^{6} -137.301 q^{7} +164.431 q^{8} +413.398 q^{9} +169.031 q^{11} -126.800 q^{12} -169.000 q^{13} +834.595 q^{14} -1157.88 q^{16} +487.128 q^{17} -2512.87 q^{18} +2385.49 q^{19} +3517.68 q^{21} -1027.47 q^{22} -4144.47 q^{23} -4212.75 q^{24} +1027.28 q^{26} -4365.63 q^{27} -679.532 q^{28} -4570.45 q^{29} -2957.68 q^{31} +1776.50 q^{32} -4330.61 q^{33} -2961.05 q^{34} +2046.00 q^{36} -5733.02 q^{37} -14500.4 q^{38} +4329.82 q^{39} -1705.07 q^{41} -21382.5 q^{42} -10922.2 q^{43} +836.570 q^{44} +25192.5 q^{46} +7912.12 q^{47} +29665.2 q^{48} +2044.52 q^{49} -12480.4 q^{51} -836.418 q^{52} -26431.1 q^{53} +26536.9 q^{54} -22576.4 q^{56} -61116.8 q^{57} +27781.9 q^{58} +11248.5 q^{59} -40298.6 q^{61} +17978.5 q^{62} -56759.8 q^{63} +26253.6 q^{64} +26324.0 q^{66} +64887.2 q^{67} +2410.91 q^{68} +106182. q^{69} -47076.1 q^{71} +67975.2 q^{72} -42771.8 q^{73} +34848.7 q^{74} +11806.3 q^{76} -23208.1 q^{77} -26319.2 q^{78} +90057.0 q^{79} +11392.9 q^{81} +10364.4 q^{82} +16427.0 q^{83} +17409.8 q^{84} +66391.5 q^{86} +117096. q^{87} +27793.8 q^{88} -35632.7 q^{89} +23203.8 q^{91} -20511.9 q^{92} +75776.6 q^{93} -48094.5 q^{94} -45514.4 q^{96} +121030. q^{97} -12427.8 q^{98} +69876.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 11 q - 5 q^{2} - 11 q^{3} + 187 q^{4} + 351 q^{6} - 208 q^{7} - 165 q^{8} + 1372 q^{9} + 1276 q^{11} - 1533 q^{12} - 1859 q^{13} + 578 q^{14} + 5707 q^{16} - 2218 q^{17} + 6776 q^{18} + 3520 q^{19} + 1706 q^{21}+ \cdots + 426698 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.07859 −1.07455 −0.537276 0.843406i \(-0.680547\pi\)
−0.537276 + 0.843406i \(0.680547\pi\)
\(3\) −25.6203 −1.64354 −0.821770 0.569819i \(-0.807013\pi\)
−0.821770 + 0.569819i \(0.807013\pi\)
\(4\) 4.94922 0.154663
\(5\) 0 0
\(6\) 155.735 1.76607
\(7\) −137.301 −1.05908 −0.529539 0.848286i \(-0.677635\pi\)
−0.529539 + 0.848286i \(0.677635\pi\)
\(8\) 164.431 0.908359
\(9\) 413.398 1.70122
\(10\) 0 0
\(11\) 169.031 0.421196 0.210598 0.977573i \(-0.432459\pi\)
0.210598 + 0.977573i \(0.432459\pi\)
\(12\) −126.800 −0.254195
\(13\) −169.000 −0.277350
\(14\) 834.595 1.13804
\(15\) 0 0
\(16\) −1157.88 −1.13074
\(17\) 487.128 0.408810 0.204405 0.978886i \(-0.434474\pi\)
0.204405 + 0.978886i \(0.434474\pi\)
\(18\) −2512.87 −1.82806
\(19\) 2385.49 1.51598 0.757990 0.652267i \(-0.226182\pi\)
0.757990 + 0.652267i \(0.226182\pi\)
\(20\) 0 0
\(21\) 3517.68 1.74064
\(22\) −1027.47 −0.452597
\(23\) −4144.47 −1.63361 −0.816807 0.576911i \(-0.804258\pi\)
−0.816807 + 0.576911i \(0.804258\pi\)
\(24\) −4212.75 −1.49292
\(25\) 0 0
\(26\) 1027.28 0.298027
\(27\) −4365.63 −1.15249
\(28\) −679.532 −0.163800
\(29\) −4570.45 −1.00917 −0.504585 0.863362i \(-0.668354\pi\)
−0.504585 + 0.863362i \(0.668354\pi\)
\(30\) 0 0
\(31\) −2957.68 −0.552774 −0.276387 0.961046i \(-0.589137\pi\)
−0.276387 + 0.961046i \(0.589137\pi\)
\(32\) 1776.50 0.306683
\(33\) −4330.61 −0.692252
\(34\) −2961.05 −0.439287
\(35\) 0 0
\(36\) 2046.00 0.263117
\(37\) −5733.02 −0.688461 −0.344230 0.938885i \(-0.611860\pi\)
−0.344230 + 0.938885i \(0.611860\pi\)
\(38\) −14500.4 −1.62900
\(39\) 4329.82 0.455836
\(40\) 0 0
\(41\) −1705.07 −0.158410 −0.0792051 0.996858i \(-0.525238\pi\)
−0.0792051 + 0.996858i \(0.525238\pi\)
\(42\) −21382.5 −1.87041
\(43\) −10922.2 −0.900821 −0.450410 0.892822i \(-0.648722\pi\)
−0.450410 + 0.892822i \(0.648722\pi\)
\(44\) 836.570 0.0651434
\(45\) 0 0
\(46\) 25192.5 1.75540
\(47\) 7912.12 0.522454 0.261227 0.965277i \(-0.415873\pi\)
0.261227 + 0.965277i \(0.415873\pi\)
\(48\) 29665.2 1.85842
\(49\) 2044.52 0.121647
\(50\) 0 0
\(51\) −12480.4 −0.671895
\(52\) −836.418 −0.0428958
\(53\) −26431.1 −1.29249 −0.646244 0.763131i \(-0.723661\pi\)
−0.646244 + 0.763131i \(0.723661\pi\)
\(54\) 26536.9 1.23841
\(55\) 0 0
\(56\) −22576.4 −0.962023
\(57\) −61116.8 −2.49157
\(58\) 27781.9 1.08441
\(59\) 11248.5 0.420692 0.210346 0.977627i \(-0.432541\pi\)
0.210346 + 0.977627i \(0.432541\pi\)
\(60\) 0 0
\(61\) −40298.6 −1.38665 −0.693323 0.720627i \(-0.743854\pi\)
−0.693323 + 0.720627i \(0.743854\pi\)
\(62\) 17978.5 0.593984
\(63\) −56759.8 −1.80173
\(64\) 26253.6 0.801195
\(65\) 0 0
\(66\) 26324.0 0.743861
\(67\) 64887.2 1.76592 0.882962 0.469444i \(-0.155546\pi\)
0.882962 + 0.469444i \(0.155546\pi\)
\(68\) 2410.91 0.0632278
\(69\) 106182. 2.68491
\(70\) 0 0
\(71\) −47076.1 −1.10829 −0.554147 0.832419i \(-0.686955\pi\)
−0.554147 + 0.832419i \(0.686955\pi\)
\(72\) 67975.2 1.54532
\(73\) −42771.8 −0.939400 −0.469700 0.882826i \(-0.655638\pi\)
−0.469700 + 0.882826i \(0.655638\pi\)
\(74\) 34848.7 0.739787
\(75\) 0 0
\(76\) 11806.3 0.234466
\(77\) −23208.1 −0.446079
\(78\) −26319.2 −0.489820
\(79\) 90057.0 1.62349 0.811745 0.584012i \(-0.198518\pi\)
0.811745 + 0.584012i \(0.198518\pi\)
\(80\) 0 0
\(81\) 11392.9 0.192941
\(82\) 10364.4 0.170220
\(83\) 16427.0 0.261735 0.130868 0.991400i \(-0.458224\pi\)
0.130868 + 0.991400i \(0.458224\pi\)
\(84\) 17409.8 0.269212
\(85\) 0 0
\(86\) 66391.5 0.967979
\(87\) 117096. 1.65861
\(88\) 27793.8 0.382597
\(89\) −35632.7 −0.476841 −0.238421 0.971162i \(-0.576630\pi\)
−0.238421 + 0.971162i \(0.576630\pi\)
\(90\) 0 0
\(91\) 23203.8 0.293735
\(92\) −20511.9 −0.252660
\(93\) 75776.6 0.908506
\(94\) −48094.5 −0.561405
\(95\) 0 0
\(96\) −45514.4 −0.504046
\(97\) 121030. 1.30606 0.653029 0.757333i \(-0.273498\pi\)
0.653029 + 0.757333i \(0.273498\pi\)
\(98\) −12427.8 −0.130716
\(99\) 69876.9 0.716549
\(100\) 0 0
\(101\) −33043.6 −0.322318 −0.161159 0.986928i \(-0.551523\pi\)
−0.161159 + 0.986928i \(0.551523\pi\)
\(102\) 75862.9 0.721987
\(103\) 198815. 1.84653 0.923265 0.384164i \(-0.125510\pi\)
0.923265 + 0.384164i \(0.125510\pi\)
\(104\) −27788.8 −0.251933
\(105\) 0 0
\(106\) 160664. 1.38885
\(107\) −183355. −1.54822 −0.774112 0.633049i \(-0.781803\pi\)
−0.774112 + 0.633049i \(0.781803\pi\)
\(108\) −21606.5 −0.178248
\(109\) −178328. −1.43765 −0.718827 0.695189i \(-0.755321\pi\)
−0.718827 + 0.695189i \(0.755321\pi\)
\(110\) 0 0
\(111\) 146881. 1.13151
\(112\) 158978. 1.19754
\(113\) 22426.7 0.165223 0.0826114 0.996582i \(-0.473674\pi\)
0.0826114 + 0.996582i \(0.473674\pi\)
\(114\) 371504. 2.67733
\(115\) 0 0
\(116\) −22620.2 −0.156081
\(117\) −69864.2 −0.471835
\(118\) −68374.9 −0.452056
\(119\) −66883.1 −0.432961
\(120\) 0 0
\(121\) −132480. −0.822594
\(122\) 244959. 1.49002
\(123\) 43684.4 0.260354
\(124\) −14638.2 −0.0854937
\(125\) 0 0
\(126\) 345020. 1.93605
\(127\) −90854.6 −0.499847 −0.249924 0.968266i \(-0.580406\pi\)
−0.249924 + 0.968266i \(0.580406\pi\)
\(128\) −216433. −1.16761
\(129\) 279829. 1.48054
\(130\) 0 0
\(131\) −78399.9 −0.399151 −0.199575 0.979882i \(-0.563956\pi\)
−0.199575 + 0.979882i \(0.563956\pi\)
\(132\) −21433.1 −0.107066
\(133\) −327530. −1.60554
\(134\) −394423. −1.89758
\(135\) 0 0
\(136\) 80098.8 0.371346
\(137\) 111261. 0.506456 0.253228 0.967407i \(-0.418508\pi\)
0.253228 + 0.967407i \(0.418508\pi\)
\(138\) −645439. −2.88508
\(139\) −226363. −0.993728 −0.496864 0.867828i \(-0.665515\pi\)
−0.496864 + 0.867828i \(0.665515\pi\)
\(140\) 0 0
\(141\) −202711. −0.858675
\(142\) 286156. 1.19092
\(143\) −28566.2 −0.116819
\(144\) −478665. −1.92365
\(145\) 0 0
\(146\) 259992. 1.00943
\(147\) −52381.1 −0.199931
\(148\) −28374.0 −0.106479
\(149\) 443036. 1.63483 0.817416 0.576047i \(-0.195406\pi\)
0.817416 + 0.576047i \(0.195406\pi\)
\(150\) 0 0
\(151\) −1334.00 −0.00476118 −0.00238059 0.999997i \(-0.500758\pi\)
−0.00238059 + 0.999997i \(0.500758\pi\)
\(152\) 392247. 1.37705
\(153\) 201378. 0.695477
\(154\) 141072. 0.479336
\(155\) 0 0
\(156\) 21429.2 0.0705010
\(157\) −66009.4 −0.213726 −0.106863 0.994274i \(-0.534081\pi\)
−0.106863 + 0.994274i \(0.534081\pi\)
\(158\) −547419. −1.74453
\(159\) 677173. 2.12425
\(160\) 0 0
\(161\) 569039. 1.73012
\(162\) −69253.0 −0.207325
\(163\) −57419.5 −0.169274 −0.0846371 0.996412i \(-0.526973\pi\)
−0.0846371 + 0.996412i \(0.526973\pi\)
\(164\) −8438.78 −0.0245002
\(165\) 0 0
\(166\) −99852.7 −0.281248
\(167\) −298875. −0.829275 −0.414637 0.909987i \(-0.636092\pi\)
−0.414637 + 0.909987i \(0.636092\pi\)
\(168\) 578414. 1.58112
\(169\) 28561.0 0.0769231
\(170\) 0 0
\(171\) 986155. 2.57902
\(172\) −54056.3 −0.139324
\(173\) −16389.5 −0.0416342 −0.0208171 0.999783i \(-0.506627\pi\)
−0.0208171 + 0.999783i \(0.506627\pi\)
\(174\) −711779. −1.78226
\(175\) 0 0
\(176\) −195717. −0.476264
\(177\) −288189. −0.691424
\(178\) 216596. 0.512391
\(179\) 420541. 0.981015 0.490507 0.871437i \(-0.336811\pi\)
0.490507 + 0.871437i \(0.336811\pi\)
\(180\) 0 0
\(181\) −598369. −1.35760 −0.678801 0.734322i \(-0.737500\pi\)
−0.678801 + 0.734322i \(0.737500\pi\)
\(182\) −141047. −0.315634
\(183\) 1.03246e6 2.27901
\(184\) −681477. −1.48391
\(185\) 0 0
\(186\) −460615. −0.976237
\(187\) 82339.7 0.172189
\(188\) 39158.8 0.0808044
\(189\) 599405. 1.22058
\(190\) 0 0
\(191\) 207706. 0.411971 0.205985 0.978555i \(-0.433960\pi\)
0.205985 + 0.978555i \(0.433960\pi\)
\(192\) −672623. −1.31680
\(193\) −545285. −1.05373 −0.526867 0.849948i \(-0.676633\pi\)
−0.526867 + 0.849948i \(0.676633\pi\)
\(194\) −735690. −1.40343
\(195\) 0 0
\(196\) 10118.8 0.0188143
\(197\) 559003. 1.02624 0.513119 0.858317i \(-0.328490\pi\)
0.513119 + 0.858317i \(0.328490\pi\)
\(198\) −424753. −0.769969
\(199\) −800588. −1.43310 −0.716549 0.697536i \(-0.754280\pi\)
−0.716549 + 0.697536i \(0.754280\pi\)
\(200\) 0 0
\(201\) −1.66243e6 −2.90237
\(202\) 200858. 0.346347
\(203\) 627527. 1.06879
\(204\) −61768.0 −0.103917
\(205\) 0 0
\(206\) −1.20851e6 −1.98419
\(207\) −1.71331e6 −2.77914
\(208\) 195682. 0.313612
\(209\) 403221. 0.638524
\(210\) 0 0
\(211\) −971904. −1.50285 −0.751427 0.659816i \(-0.770634\pi\)
−0.751427 + 0.659816i \(0.770634\pi\)
\(212\) −130814. −0.199900
\(213\) 1.20610e6 1.82153
\(214\) 1.11454e6 1.66365
\(215\) 0 0
\(216\) −717843. −1.04688
\(217\) 406092. 0.585431
\(218\) 1.08398e6 1.54483
\(219\) 1.09582e6 1.54394
\(220\) 0 0
\(221\) −82324.7 −0.113383
\(222\) −892831. −1.21587
\(223\) 401286. 0.540371 0.270186 0.962808i \(-0.412915\pi\)
0.270186 + 0.962808i \(0.412915\pi\)
\(224\) −243915. −0.324802
\(225\) 0 0
\(226\) −136323. −0.177541
\(227\) 1.30062e6 1.67527 0.837637 0.546227i \(-0.183936\pi\)
0.837637 + 0.546227i \(0.183936\pi\)
\(228\) −302481. −0.385354
\(229\) −864830. −1.08979 −0.544894 0.838505i \(-0.683430\pi\)
−0.544894 + 0.838505i \(0.683430\pi\)
\(230\) 0 0
\(231\) 594596. 0.733149
\(232\) −751521. −0.916688
\(233\) −1.19230e6 −1.43878 −0.719390 0.694606i \(-0.755579\pi\)
−0.719390 + 0.694606i \(0.755579\pi\)
\(234\) 424676. 0.507011
\(235\) 0 0
\(236\) 55671.3 0.0650655
\(237\) −2.30728e6 −2.66827
\(238\) 406555. 0.465240
\(239\) −1.23057e6 −1.39352 −0.696759 0.717305i \(-0.745375\pi\)
−0.696759 + 0.717305i \(0.745375\pi\)
\(240\) 0 0
\(241\) 1.64306e6 1.82226 0.911129 0.412122i \(-0.135212\pi\)
0.911129 + 0.412122i \(0.135212\pi\)
\(242\) 805289. 0.883921
\(243\) 768958. 0.835385
\(244\) −199447. −0.214463
\(245\) 0 0
\(246\) −265539. −0.279764
\(247\) −403148. −0.420457
\(248\) −486333. −0.502117
\(249\) −420863. −0.430172
\(250\) 0 0
\(251\) −447259. −0.448100 −0.224050 0.974578i \(-0.571928\pi\)
−0.224050 + 0.974578i \(0.571928\pi\)
\(252\) −280917. −0.278661
\(253\) −700543. −0.688071
\(254\) 552267. 0.537112
\(255\) 0 0
\(256\) 475490. 0.453463
\(257\) −465085. −0.439237 −0.219619 0.975586i \(-0.570481\pi\)
−0.219619 + 0.975586i \(0.570481\pi\)
\(258\) −1.70097e6 −1.59091
\(259\) 787148. 0.729134
\(260\) 0 0
\(261\) −1.88941e6 −1.71682
\(262\) 476560. 0.428909
\(263\) 1.88192e6 1.67769 0.838846 0.544369i \(-0.183231\pi\)
0.838846 + 0.544369i \(0.183231\pi\)
\(264\) −712085. −0.628813
\(265\) 0 0
\(266\) 1.99092e6 1.72524
\(267\) 912919. 0.783707
\(268\) 321141. 0.273123
\(269\) 39508.5 0.0332897 0.0166448 0.999861i \(-0.494702\pi\)
0.0166448 + 0.999861i \(0.494702\pi\)
\(270\) 0 0
\(271\) 2.01156e6 1.66383 0.831916 0.554902i \(-0.187244\pi\)
0.831916 + 0.554902i \(0.187244\pi\)
\(272\) −564036. −0.462258
\(273\) −594488. −0.482766
\(274\) −676310. −0.544214
\(275\) 0 0
\(276\) 525520. 0.415256
\(277\) 750989. 0.588077 0.294039 0.955794i \(-0.405001\pi\)
0.294039 + 0.955794i \(0.405001\pi\)
\(278\) 1.37596e6 1.06781
\(279\) −1.22270e6 −0.940392
\(280\) 0 0
\(281\) −116949. −0.0883550 −0.0441775 0.999024i \(-0.514067\pi\)
−0.0441775 + 0.999024i \(0.514067\pi\)
\(282\) 1.23219e6 0.922691
\(283\) −1.08953e6 −0.808671 −0.404335 0.914611i \(-0.632497\pi\)
−0.404335 + 0.914611i \(0.632497\pi\)
\(284\) −232990. −0.171412
\(285\) 0 0
\(286\) 173642. 0.125528
\(287\) 234108. 0.167769
\(288\) 734400. 0.521737
\(289\) −1.18256e6 −0.832875
\(290\) 0 0
\(291\) −3.10081e6 −2.14656
\(292\) −211687. −0.145290
\(293\) 2.35419e6 1.60204 0.801020 0.598638i \(-0.204291\pi\)
0.801020 + 0.598638i \(0.204291\pi\)
\(294\) 318403. 0.214837
\(295\) 0 0
\(296\) −942683. −0.625369
\(297\) −737926. −0.485424
\(298\) −2.69303e6 −1.75671
\(299\) 700415. 0.453083
\(300\) 0 0
\(301\) 1.49963e6 0.954040
\(302\) 8108.85 0.00511613
\(303\) 846585. 0.529742
\(304\) −2.76211e6 −1.71418
\(305\) 0 0
\(306\) −1.22409e6 −0.747327
\(307\) 1.40614e6 0.851495 0.425748 0.904842i \(-0.360011\pi\)
0.425748 + 0.904842i \(0.360011\pi\)
\(308\) −114862. −0.0689920
\(309\) −5.09369e6 −3.03485
\(310\) 0 0
\(311\) 1.46661e6 0.859832 0.429916 0.902869i \(-0.358543\pi\)
0.429916 + 0.902869i \(0.358543\pi\)
\(312\) 711955. 0.414063
\(313\) −310576. −0.179187 −0.0895935 0.995978i \(-0.528557\pi\)
−0.0895935 + 0.995978i \(0.528557\pi\)
\(314\) 401244. 0.229659
\(315\) 0 0
\(316\) 445712. 0.251094
\(317\) −2.21756e6 −1.23944 −0.619721 0.784822i \(-0.712754\pi\)
−0.619721 + 0.784822i \(0.712754\pi\)
\(318\) −4.11625e6 −2.28262
\(319\) −772546. −0.425058
\(320\) 0 0
\(321\) 4.69761e6 2.54457
\(322\) −3.45895e6 −1.85911
\(323\) 1.16204e6 0.619747
\(324\) 56386.2 0.0298408
\(325\) 0 0
\(326\) 349030. 0.181894
\(327\) 4.56882e6 2.36284
\(328\) −280366. −0.143893
\(329\) −1.08634e6 −0.553320
\(330\) 0 0
\(331\) 439684. 0.220582 0.110291 0.993899i \(-0.464822\pi\)
0.110291 + 0.993899i \(0.464822\pi\)
\(332\) 81300.7 0.0404808
\(333\) −2.37002e6 −1.17123
\(334\) 1.81674e6 0.891099
\(335\) 0 0
\(336\) −4.07306e6 −1.96821
\(337\) −65125.6 −0.0312376 −0.0156188 0.999878i \(-0.504972\pi\)
−0.0156188 + 0.999878i \(0.504972\pi\)
\(338\) −173611. −0.0826579
\(339\) −574579. −0.271550
\(340\) 0 0
\(341\) −499939. −0.232826
\(342\) −5.99443e6 −2.77129
\(343\) 2.02690e6 0.930245
\(344\) −1.79594e6 −0.818269
\(345\) 0 0
\(346\) 99625.0 0.0447382
\(347\) 3.63163e6 1.61912 0.809558 0.587039i \(-0.199707\pi\)
0.809558 + 0.587039i \(0.199707\pi\)
\(348\) 579534. 0.256526
\(349\) 755061. 0.331832 0.165916 0.986140i \(-0.446942\pi\)
0.165916 + 0.986140i \(0.446942\pi\)
\(350\) 0 0
\(351\) 737791. 0.319643
\(352\) 300283. 0.129174
\(353\) 3.06050e6 1.30724 0.653620 0.756823i \(-0.273249\pi\)
0.653620 + 0.756823i \(0.273249\pi\)
\(354\) 1.75178e6 0.742972
\(355\) 0 0
\(356\) −176354. −0.0737497
\(357\) 1.71356e6 0.711590
\(358\) −2.55629e6 −1.05415
\(359\) 3.68034e6 1.50713 0.753567 0.657371i \(-0.228332\pi\)
0.753567 + 0.657371i \(0.228332\pi\)
\(360\) 0 0
\(361\) 3.21446e6 1.29819
\(362\) 3.63724e6 1.45882
\(363\) 3.39416e6 1.35197
\(364\) 114841. 0.0454300
\(365\) 0 0
\(366\) −6.27591e6 −2.44891
\(367\) 2.22414e6 0.861978 0.430989 0.902357i \(-0.358165\pi\)
0.430989 + 0.902357i \(0.358165\pi\)
\(368\) 4.79880e6 1.84720
\(369\) −704873. −0.269491
\(370\) 0 0
\(371\) 3.62902e6 1.36885
\(372\) 375035. 0.140512
\(373\) −3.73922e6 −1.39158 −0.695791 0.718244i \(-0.744946\pi\)
−0.695791 + 0.718244i \(0.744946\pi\)
\(374\) −500509. −0.185026
\(375\) 0 0
\(376\) 1.30099e6 0.474576
\(377\) 772406. 0.279893
\(378\) −3.64353e6 −1.31158
\(379\) 656559. 0.234788 0.117394 0.993085i \(-0.462546\pi\)
0.117394 + 0.993085i \(0.462546\pi\)
\(380\) 0 0
\(381\) 2.32772e6 0.821519
\(382\) −1.26256e6 −0.442684
\(383\) −3.33584e6 −1.16200 −0.581002 0.813902i \(-0.697339\pi\)
−0.581002 + 0.813902i \(0.697339\pi\)
\(384\) 5.54506e6 1.91901
\(385\) 0 0
\(386\) 3.31456e6 1.13229
\(387\) −4.51521e6 −1.53250
\(388\) 599003. 0.201999
\(389\) 4.44083e6 1.48796 0.743978 0.668204i \(-0.232937\pi\)
0.743978 + 0.668204i \(0.232937\pi\)
\(390\) 0 0
\(391\) −2.01889e6 −0.667837
\(392\) 336181. 0.110499
\(393\) 2.00863e6 0.656021
\(394\) −3.39795e6 −1.10275
\(395\) 0 0
\(396\) 345836. 0.110824
\(397\) −2.72643e6 −0.868196 −0.434098 0.900866i \(-0.642933\pi\)
−0.434098 + 0.900866i \(0.642933\pi\)
\(398\) 4.86644e6 1.53994
\(399\) 8.39139e6 2.63877
\(400\) 0 0
\(401\) 5.27026e6 1.63671 0.818353 0.574715i \(-0.194887\pi\)
0.818353 + 0.574715i \(0.194887\pi\)
\(402\) 1.01052e7 3.11875
\(403\) 499848. 0.153312
\(404\) −163540. −0.0498506
\(405\) 0 0
\(406\) −3.81447e6 −1.14847
\(407\) −969056. −0.289977
\(408\) −2.05215e6 −0.610322
\(409\) 4.58065e6 1.35400 0.677000 0.735983i \(-0.263280\pi\)
0.677000 + 0.735983i \(0.263280\pi\)
\(410\) 0 0
\(411\) −2.85054e6 −0.832381
\(412\) 983979. 0.285590
\(413\) −1.54443e6 −0.445546
\(414\) 1.04145e7 2.98634
\(415\) 0 0
\(416\) −300228. −0.0850586
\(417\) 5.79947e6 1.63323
\(418\) −2.45101e6 −0.686128
\(419\) 3.94543e6 1.09789 0.548945 0.835858i \(-0.315030\pi\)
0.548945 + 0.835858i \(0.315030\pi\)
\(420\) 0 0
\(421\) 4.17743e6 1.14869 0.574347 0.818612i \(-0.305256\pi\)
0.574347 + 0.818612i \(0.305256\pi\)
\(422\) 5.90780e6 1.61490
\(423\) 3.27085e6 0.888812
\(424\) −4.34609e6 −1.17404
\(425\) 0 0
\(426\) −7.33140e6 −1.95732
\(427\) 5.53304e6 1.46857
\(428\) −907465. −0.239453
\(429\) 731873. 0.191996
\(430\) 0 0
\(431\) −7.66563e6 −1.98772 −0.993859 0.110652i \(-0.964706\pi\)
−0.993859 + 0.110652i \(0.964706\pi\)
\(432\) 5.05488e6 1.30317
\(433\) 5.49209e6 1.40773 0.703863 0.710336i \(-0.251457\pi\)
0.703863 + 0.710336i \(0.251457\pi\)
\(434\) −2.46847e6 −0.629076
\(435\) 0 0
\(436\) −882586. −0.222352
\(437\) −9.88658e6 −2.47652
\(438\) −6.66107e6 −1.65905
\(439\) −2.56331e6 −0.634805 −0.317403 0.948291i \(-0.602811\pi\)
−0.317403 + 0.948291i \(0.602811\pi\)
\(440\) 0 0
\(441\) 845199. 0.206949
\(442\) 500418. 0.121836
\(443\) −1.41896e6 −0.343526 −0.171763 0.985138i \(-0.554946\pi\)
−0.171763 + 0.985138i \(0.554946\pi\)
\(444\) 726948. 0.175003
\(445\) 0 0
\(446\) −2.43925e6 −0.580657
\(447\) −1.13507e7 −2.68691
\(448\) −3.60464e6 −0.848528
\(449\) 3.56619e6 0.834813 0.417406 0.908720i \(-0.362939\pi\)
0.417406 + 0.908720i \(0.362939\pi\)
\(450\) 0 0
\(451\) −288210. −0.0667217
\(452\) 110995. 0.0255539
\(453\) 34177.5 0.00782519
\(454\) −7.90593e6 −1.80017
\(455\) 0 0
\(456\) −1.00495e7 −2.26324
\(457\) −3.71538e6 −0.832172 −0.416086 0.909325i \(-0.636598\pi\)
−0.416086 + 0.909325i \(0.636598\pi\)
\(458\) 5.25694e6 1.17103
\(459\) −2.12662e6 −0.471149
\(460\) 0 0
\(461\) 3.74184e6 0.820035 0.410018 0.912078i \(-0.365523\pi\)
0.410018 + 0.912078i \(0.365523\pi\)
\(462\) −3.61431e6 −0.787807
\(463\) −3.53774e6 −0.766962 −0.383481 0.923549i \(-0.625275\pi\)
−0.383481 + 0.923549i \(0.625275\pi\)
\(464\) 5.29203e6 1.14111
\(465\) 0 0
\(466\) 7.24748e6 1.54605
\(467\) −1.97789e6 −0.419671 −0.209836 0.977737i \(-0.567293\pi\)
−0.209836 + 0.977737i \(0.567293\pi\)
\(468\) −345773. −0.0729754
\(469\) −8.90907e6 −1.87025
\(470\) 0 0
\(471\) 1.69118e6 0.351267
\(472\) 1.84960e6 0.382139
\(473\) −1.84619e6 −0.379422
\(474\) 1.40250e7 2.86720
\(475\) 0 0
\(476\) −331019. −0.0669632
\(477\) −1.09266e7 −2.19881
\(478\) 7.48014e6 1.49741
\(479\) −2.88196e6 −0.573918 −0.286959 0.957943i \(-0.592644\pi\)
−0.286959 + 0.957943i \(0.592644\pi\)
\(480\) 0 0
\(481\) 968880. 0.190945
\(482\) −9.98746e6 −1.95811
\(483\) −1.45789e7 −2.84353
\(484\) −655671. −0.127225
\(485\) 0 0
\(486\) −4.67418e6 −0.897665
\(487\) −2.88578e6 −0.551366 −0.275683 0.961249i \(-0.588904\pi\)
−0.275683 + 0.961249i \(0.588904\pi\)
\(488\) −6.62632e6 −1.25957
\(489\) 1.47110e6 0.278209
\(490\) 0 0
\(491\) 5.27189e6 0.986876 0.493438 0.869781i \(-0.335740\pi\)
0.493438 + 0.869781i \(0.335740\pi\)
\(492\) 216204. 0.0402671
\(493\) −2.22640e6 −0.412558
\(494\) 2.45057e6 0.451803
\(495\) 0 0
\(496\) 3.42464e6 0.625045
\(497\) 6.46359e6 1.17377
\(498\) 2.55825e6 0.462243
\(499\) −308093. −0.0553898 −0.0276949 0.999616i \(-0.508817\pi\)
−0.0276949 + 0.999616i \(0.508817\pi\)
\(500\) 0 0
\(501\) 7.65725e6 1.36295
\(502\) 2.71870e6 0.481507
\(503\) 4.27447e6 0.753291 0.376645 0.926358i \(-0.377078\pi\)
0.376645 + 0.926358i \(0.377078\pi\)
\(504\) −9.33305e6 −1.63662
\(505\) 0 0
\(506\) 4.25831e6 0.739368
\(507\) −731740. −0.126426
\(508\) −449659. −0.0773080
\(509\) −405253. −0.0693317 −0.0346658 0.999399i \(-0.511037\pi\)
−0.0346658 + 0.999399i \(0.511037\pi\)
\(510\) 0 0
\(511\) 5.87260e6 0.994898
\(512\) 4.03553e6 0.680340
\(513\) −1.04142e7 −1.74715
\(514\) 2.82706e6 0.471984
\(515\) 0 0
\(516\) 1.38494e6 0.228984
\(517\) 1.33739e6 0.220056
\(518\) −4.78475e6 −0.783492
\(519\) 419903. 0.0684275
\(520\) 0 0
\(521\) −7.00100e6 −1.12997 −0.564983 0.825102i \(-0.691117\pi\)
−0.564983 + 0.825102i \(0.691117\pi\)
\(522\) 1.14850e7 1.84482
\(523\) −7.78764e6 −1.24495 −0.622475 0.782640i \(-0.713873\pi\)
−0.622475 + 0.782640i \(0.713873\pi\)
\(524\) −388018. −0.0617339
\(525\) 0 0
\(526\) −1.14394e7 −1.80277
\(527\) −1.44077e6 −0.225979
\(528\) 5.01433e6 0.782759
\(529\) 1.07403e7 1.66869
\(530\) 0 0
\(531\) 4.65010e6 0.715692
\(532\) −1.62102e6 −0.248318
\(533\) 288157. 0.0439351
\(534\) −5.54926e6 −0.842135
\(535\) 0 0
\(536\) 1.06694e7 1.60409
\(537\) −1.07744e7 −1.61234
\(538\) −240156. −0.0357715
\(539\) 345586. 0.0512371
\(540\) 0 0
\(541\) 3.36678e6 0.494562 0.247281 0.968944i \(-0.420463\pi\)
0.247281 + 0.968944i \(0.420463\pi\)
\(542\) −1.22274e7 −1.78787
\(543\) 1.53304e7 2.23128
\(544\) 865383. 0.125375
\(545\) 0 0
\(546\) 3.61365e6 0.518757
\(547\) 1.32125e7 1.88806 0.944030 0.329860i \(-0.107001\pi\)
0.944030 + 0.329860i \(0.107001\pi\)
\(548\) 550656. 0.0783301
\(549\) −1.66594e7 −2.35900
\(550\) 0 0
\(551\) −1.09028e7 −1.52988
\(552\) 1.74596e7 2.43886
\(553\) −1.23649e7 −1.71940
\(554\) −4.56495e6 −0.631920
\(555\) 0 0
\(556\) −1.12032e6 −0.153693
\(557\) 7.47598e6 1.02101 0.510505 0.859875i \(-0.329459\pi\)
0.510505 + 0.859875i \(0.329459\pi\)
\(558\) 7.43228e6 1.01050
\(559\) 1.84585e6 0.249843
\(560\) 0 0
\(561\) −2.10956e6 −0.282999
\(562\) 710886. 0.0949421
\(563\) 1.32316e7 1.75931 0.879653 0.475617i \(-0.157775\pi\)
0.879653 + 0.475617i \(0.157775\pi\)
\(564\) −1.00326e6 −0.132805
\(565\) 0 0
\(566\) 6.62278e6 0.868959
\(567\) −1.56426e6 −0.204339
\(568\) −7.74075e6 −1.00673
\(569\) −9.80441e6 −1.26952 −0.634762 0.772708i \(-0.718902\pi\)
−0.634762 + 0.772708i \(0.718902\pi\)
\(570\) 0 0
\(571\) 2.98442e6 0.383063 0.191532 0.981486i \(-0.438655\pi\)
0.191532 + 0.981486i \(0.438655\pi\)
\(572\) −141380. −0.0180675
\(573\) −5.32149e6 −0.677091
\(574\) −1.42305e6 −0.180276
\(575\) 0 0
\(576\) 1.08532e7 1.36301
\(577\) −1.47218e7 −1.84086 −0.920429 0.390911i \(-0.872160\pi\)
−0.920429 + 0.390911i \(0.872160\pi\)
\(578\) 7.18831e6 0.894968
\(579\) 1.39704e7 1.73185
\(580\) 0 0
\(581\) −2.25544e6 −0.277198
\(582\) 1.88486e7 2.30659
\(583\) −4.46768e6 −0.544390
\(584\) −7.03299e6 −0.853312
\(585\) 0 0
\(586\) −1.43102e7 −1.72148
\(587\) −9.66987e6 −1.15831 −0.579156 0.815217i \(-0.696618\pi\)
−0.579156 + 0.815217i \(0.696618\pi\)
\(588\) −259245. −0.0309220
\(589\) −7.05552e6 −0.837993
\(590\) 0 0
\(591\) −1.43218e7 −1.68666
\(592\) 6.63815e6 0.778472
\(593\) −1.52788e7 −1.78424 −0.892121 0.451797i \(-0.850783\pi\)
−0.892121 + 0.451797i \(0.850783\pi\)
\(594\) 4.48554e6 0.521614
\(595\) 0 0
\(596\) 2.19268e6 0.252848
\(597\) 2.05113e7 2.35536
\(598\) −4.25754e6 −0.486861
\(599\) 7.95473e6 0.905854 0.452927 0.891548i \(-0.350380\pi\)
0.452927 + 0.891548i \(0.350380\pi\)
\(600\) 0 0
\(601\) 5.48231e6 0.619123 0.309562 0.950879i \(-0.399818\pi\)
0.309562 + 0.950879i \(0.399818\pi\)
\(602\) −9.11560e6 −1.02517
\(603\) 2.68242e7 3.00423
\(604\) −6602.27 −0.000736378 0
\(605\) 0 0
\(606\) −5.14604e6 −0.569235
\(607\) −1.49346e6 −0.164521 −0.0822605 0.996611i \(-0.526214\pi\)
−0.0822605 + 0.996611i \(0.526214\pi\)
\(608\) 4.23782e6 0.464926
\(609\) −1.60774e7 −1.75660
\(610\) 0 0
\(611\) −1.33715e6 −0.144903
\(612\) 996663. 0.107565
\(613\) −9.31063e6 −1.00076 −0.500378 0.865807i \(-0.666805\pi\)
−0.500378 + 0.865807i \(0.666805\pi\)
\(614\) −8.54733e6 −0.914976
\(615\) 0 0
\(616\) −3.81611e6 −0.405200
\(617\) 245403. 0.0259517 0.0129759 0.999916i \(-0.495870\pi\)
0.0129759 + 0.999916i \(0.495870\pi\)
\(618\) 3.09625e7 3.26110
\(619\) 2.82756e6 0.296610 0.148305 0.988942i \(-0.452618\pi\)
0.148305 + 0.988942i \(0.452618\pi\)
\(620\) 0 0
\(621\) 1.80932e7 1.88272
\(622\) −8.91491e6 −0.923934
\(623\) 4.89240e6 0.505012
\(624\) −5.01342e6 −0.515433
\(625\) 0 0
\(626\) 1.88786e6 0.192546
\(627\) −1.03306e7 −1.04944
\(628\) −326695. −0.0330555
\(629\) −2.79272e6 −0.281449
\(630\) 0 0
\(631\) −1.53391e7 −1.53366 −0.766828 0.641853i \(-0.778166\pi\)
−0.766828 + 0.641853i \(0.778166\pi\)
\(632\) 1.48081e7 1.47471
\(633\) 2.49004e7 2.47000
\(634\) 1.34796e7 1.33185
\(635\) 0 0
\(636\) 3.35148e6 0.328544
\(637\) −345523. −0.0337388
\(638\) 4.69599e6 0.456747
\(639\) −1.94612e7 −1.88546
\(640\) 0 0
\(641\) 1.02617e7 0.986444 0.493222 0.869904i \(-0.335819\pi\)
0.493222 + 0.869904i \(0.335819\pi\)
\(642\) −2.85548e7 −2.73427
\(643\) 5.26807e6 0.502486 0.251243 0.967924i \(-0.419161\pi\)
0.251243 + 0.967924i \(0.419161\pi\)
\(644\) 2.81630e6 0.267586
\(645\) 0 0
\(646\) −7.06356e6 −0.665951
\(647\) −2.03948e7 −1.91540 −0.957698 0.287775i \(-0.907085\pi\)
−0.957698 + 0.287775i \(0.907085\pi\)
\(648\) 1.87335e6 0.175259
\(649\) 1.90134e6 0.177194
\(650\) 0 0
\(651\) −1.04042e7 −0.962179
\(652\) −284182. −0.0261805
\(653\) 8.69527e6 0.797994 0.398997 0.916952i \(-0.369358\pi\)
0.398997 + 0.916952i \(0.369358\pi\)
\(654\) −2.77720e7 −2.53900
\(655\) 0 0
\(656\) 1.97427e6 0.179121
\(657\) −1.76818e7 −1.59813
\(658\) 6.60342e6 0.594571
\(659\) 1.85493e7 1.66385 0.831926 0.554886i \(-0.187238\pi\)
0.831926 + 0.554886i \(0.187238\pi\)
\(660\) 0 0
\(661\) 1.00321e6 0.0893078 0.0446539 0.999003i \(-0.485782\pi\)
0.0446539 + 0.999003i \(0.485782\pi\)
\(662\) −2.67266e6 −0.237027
\(663\) 2.10918e6 0.186350
\(664\) 2.70109e6 0.237750
\(665\) 0 0
\(666\) 1.44063e7 1.25854
\(667\) 1.89421e7 1.64859
\(668\) −1.47920e6 −0.128258
\(669\) −1.02811e7 −0.888122
\(670\) 0 0
\(671\) −6.81171e6 −0.584049
\(672\) 6.24916e6 0.533824
\(673\) 653810. 0.0556434 0.0278217 0.999613i \(-0.491143\pi\)
0.0278217 + 0.999613i \(0.491143\pi\)
\(674\) 395872. 0.0335664
\(675\) 0 0
\(676\) 141355. 0.0118972
\(677\) −831237. −0.0697033 −0.0348516 0.999392i \(-0.511096\pi\)
−0.0348516 + 0.999392i \(0.511096\pi\)
\(678\) 3.49263e6 0.291795
\(679\) −1.66175e7 −1.38322
\(680\) 0 0
\(681\) −3.33222e7 −2.75338
\(682\) 3.03892e6 0.250184
\(683\) 4.86860e6 0.399349 0.199675 0.979862i \(-0.436012\pi\)
0.199675 + 0.979862i \(0.436012\pi\)
\(684\) 4.88070e6 0.398879
\(685\) 0 0
\(686\) −1.23207e7 −0.999597
\(687\) 2.21572e7 1.79111
\(688\) 1.26466e7 1.01860
\(689\) 4.46686e6 0.358471
\(690\) 0 0
\(691\) −7.17359e6 −0.571533 −0.285767 0.958299i \(-0.592248\pi\)
−0.285767 + 0.958299i \(0.592248\pi\)
\(692\) −81115.2 −0.00643928
\(693\) −9.59416e6 −0.758881
\(694\) −2.20752e7 −1.73983
\(695\) 0 0
\(696\) 1.92542e7 1.50661
\(697\) −830589. −0.0647596
\(698\) −4.58970e6 −0.356571
\(699\) 3.05470e7 2.36469
\(700\) 0 0
\(701\) −9.45026e6 −0.726355 −0.363177 0.931720i \(-0.618308\pi\)
−0.363177 + 0.931720i \(0.618308\pi\)
\(702\) −4.48473e6 −0.343474
\(703\) −1.36761e7 −1.04369
\(704\) 4.43766e6 0.337460
\(705\) 0 0
\(706\) −1.86035e7 −1.40470
\(707\) 4.53691e6 0.341359
\(708\) −1.42631e6 −0.106938
\(709\) −2.98225e6 −0.222807 −0.111404 0.993775i \(-0.535535\pi\)
−0.111404 + 0.993775i \(0.535535\pi\)
\(710\) 0 0
\(711\) 3.72293e7 2.76192
\(712\) −5.85910e6 −0.433143
\(713\) 1.22580e7 0.903019
\(714\) −1.04160e7 −0.764640
\(715\) 0 0
\(716\) 2.08135e6 0.151727
\(717\) 3.15276e7 2.29030
\(718\) −2.23713e7 −1.61949
\(719\) 1.65959e7 1.19723 0.598617 0.801036i \(-0.295717\pi\)
0.598617 + 0.801036i \(0.295717\pi\)
\(720\) 0 0
\(721\) −2.72975e7 −1.95562
\(722\) −1.95394e7 −1.39498
\(723\) −4.20955e7 −2.99495
\(724\) −2.96146e6 −0.209971
\(725\) 0 0
\(726\) −2.06317e7 −1.45276
\(727\) −47580.6 −0.00333882 −0.00166941 0.999999i \(-0.500531\pi\)
−0.00166941 + 0.999999i \(0.500531\pi\)
\(728\) 3.81542e6 0.266817
\(729\) −2.24694e7 −1.56593
\(730\) 0 0
\(731\) −5.32051e6 −0.368264
\(732\) 5.10988e6 0.352479
\(733\) −6.02222e6 −0.413996 −0.206998 0.978341i \(-0.566369\pi\)
−0.206998 + 0.978341i \(0.566369\pi\)
\(734\) −1.35196e7 −0.926241
\(735\) 0 0
\(736\) −7.36265e6 −0.501002
\(737\) 1.09679e7 0.743800
\(738\) 4.28463e6 0.289583
\(739\) 8.15662e6 0.549413 0.274707 0.961528i \(-0.411419\pi\)
0.274707 + 0.961528i \(0.411419\pi\)
\(740\) 0 0
\(741\) 1.03287e7 0.691038
\(742\) −2.20593e7 −1.47090
\(743\) −473118. −0.0314411 −0.0157205 0.999876i \(-0.505004\pi\)
−0.0157205 + 0.999876i \(0.505004\pi\)
\(744\) 1.24600e7 0.825249
\(745\) 0 0
\(746\) 2.27292e7 1.49533
\(747\) 6.79087e6 0.445270
\(748\) 407517. 0.0266313
\(749\) 2.51748e7 1.63969
\(750\) 0 0
\(751\) 5.49506e6 0.355527 0.177764 0.984073i \(-0.443114\pi\)
0.177764 + 0.984073i \(0.443114\pi\)
\(752\) −9.16129e6 −0.590761
\(753\) 1.14589e7 0.736470
\(754\) −4.69514e6 −0.300760
\(755\) 0 0
\(756\) 2.96659e6 0.188778
\(757\) −6.82041e6 −0.432585 −0.216292 0.976329i \(-0.569396\pi\)
−0.216292 + 0.976329i \(0.569396\pi\)
\(758\) −3.99095e6 −0.252292
\(759\) 1.79481e7 1.13087
\(760\) 0 0
\(761\) 1.14435e7 0.716304 0.358152 0.933663i \(-0.383407\pi\)
0.358152 + 0.933663i \(0.383407\pi\)
\(762\) −1.41492e7 −0.882766
\(763\) 2.44846e7 1.52259
\(764\) 1.02798e6 0.0637167
\(765\) 0 0
\(766\) 2.02772e7 1.24863
\(767\) −1.90100e6 −0.116679
\(768\) −1.21822e7 −0.745284
\(769\) −5.05628e6 −0.308330 −0.154165 0.988045i \(-0.549269\pi\)
−0.154165 + 0.988045i \(0.549269\pi\)
\(770\) 0 0
\(771\) 1.19156e7 0.721904
\(772\) −2.69874e6 −0.162974
\(773\) −3.54919e6 −0.213639 −0.106820 0.994278i \(-0.534067\pi\)
−0.106820 + 0.994278i \(0.534067\pi\)
\(774\) 2.74461e7 1.64675
\(775\) 0 0
\(776\) 1.99010e7 1.18637
\(777\) −2.01669e7 −1.19836
\(778\) −2.69940e7 −1.59889
\(779\) −4.06743e6 −0.240147
\(780\) 0 0
\(781\) −7.95731e6 −0.466809
\(782\) 1.22720e7 0.717626
\(783\) 1.99529e7 1.16306
\(784\) −2.36731e6 −0.137551
\(785\) 0 0
\(786\) −1.22096e7 −0.704929
\(787\) −2.14355e7 −1.23367 −0.616833 0.787094i \(-0.711585\pi\)
−0.616833 + 0.787094i \(0.711585\pi\)
\(788\) 2.76663e6 0.158721
\(789\) −4.82153e7 −2.75735
\(790\) 0 0
\(791\) −3.07921e6 −0.174984
\(792\) 1.14899e7 0.650883
\(793\) 6.81047e6 0.384586
\(794\) 1.65728e7 0.932923
\(795\) 0 0
\(796\) −3.96228e6 −0.221648
\(797\) −1.94471e7 −1.08445 −0.542223 0.840235i \(-0.682417\pi\)
−0.542223 + 0.840235i \(0.682417\pi\)
\(798\) −5.10078e7 −2.83550
\(799\) 3.85422e6 0.213584
\(800\) 0 0
\(801\) −1.47305e7 −0.811214
\(802\) −3.20357e7 −1.75873
\(803\) −7.22975e6 −0.395671
\(804\) −8.22772e6 −0.448889
\(805\) 0 0
\(806\) −3.03837e6 −0.164742
\(807\) −1.01222e6 −0.0547129
\(808\) −5.43338e6 −0.292780
\(809\) 1.45681e7 0.782585 0.391292 0.920266i \(-0.372028\pi\)
0.391292 + 0.920266i \(0.372028\pi\)
\(810\) 0 0
\(811\) 1.86252e7 0.994371 0.497185 0.867644i \(-0.334367\pi\)
0.497185 + 0.867644i \(0.334367\pi\)
\(812\) 3.10577e6 0.165302
\(813\) −5.15366e7 −2.73457
\(814\) 5.89049e6 0.311595
\(815\) 0 0
\(816\) 1.44508e7 0.759740
\(817\) −2.60548e7 −1.36563
\(818\) −2.78439e7 −1.45494
\(819\) 9.59241e6 0.499710
\(820\) 0 0
\(821\) 1.61122e7 0.834252 0.417126 0.908849i \(-0.363037\pi\)
0.417126 + 0.908849i \(0.363037\pi\)
\(822\) 1.73272e7 0.894438
\(823\) 1.15862e7 0.596269 0.298134 0.954524i \(-0.403636\pi\)
0.298134 + 0.954524i \(0.403636\pi\)
\(824\) 3.26913e7 1.67731
\(825\) 0 0
\(826\) 9.38794e6 0.478762
\(827\) −8.40345e6 −0.427262 −0.213631 0.976914i \(-0.568529\pi\)
−0.213631 + 0.976914i \(0.568529\pi\)
\(828\) −8.47957e6 −0.429831
\(829\) −4.77193e6 −0.241161 −0.120581 0.992704i \(-0.538476\pi\)
−0.120581 + 0.992704i \(0.538476\pi\)
\(830\) 0 0
\(831\) −1.92405e7 −0.966528
\(832\) −4.43685e6 −0.222212
\(833\) 995943. 0.0497304
\(834\) −3.52526e7 −1.75499
\(835\) 0 0
\(836\) 1.99563e6 0.0987561
\(837\) 1.29121e7 0.637067
\(838\) −2.39826e7 −1.17974
\(839\) −2.32624e7 −1.14091 −0.570453 0.821330i \(-0.693232\pi\)
−0.570453 + 0.821330i \(0.693232\pi\)
\(840\) 0 0
\(841\) 377863. 0.0184223
\(842\) −2.53929e7 −1.23433
\(843\) 2.99627e6 0.145215
\(844\) −4.81016e6 −0.232436
\(845\) 0 0
\(846\) −1.98822e7 −0.955075
\(847\) 1.81896e7 0.871192
\(848\) 3.06041e7 1.46147
\(849\) 2.79140e7 1.32908
\(850\) 0 0
\(851\) 2.37603e7 1.12468
\(852\) 5.96927e6 0.281723
\(853\) 6.88858e6 0.324158 0.162079 0.986778i \(-0.448180\pi\)
0.162079 + 0.986778i \(0.448180\pi\)
\(854\) −3.36330e7 −1.57805
\(855\) 0 0
\(856\) −3.01492e7 −1.40634
\(857\) −782343. −0.0363869 −0.0181935 0.999834i \(-0.505791\pi\)
−0.0181935 + 0.999834i \(0.505791\pi\)
\(858\) −4.44876e6 −0.206310
\(859\) 1.23216e7 0.569751 0.284875 0.958565i \(-0.408048\pi\)
0.284875 + 0.958565i \(0.408048\pi\)
\(860\) 0 0
\(861\) −5.99790e6 −0.275735
\(862\) 4.65962e7 2.13591
\(863\) 7.42942e6 0.339569 0.169785 0.985481i \(-0.445693\pi\)
0.169785 + 0.985481i \(0.445693\pi\)
\(864\) −7.75554e6 −0.353450
\(865\) 0 0
\(866\) −3.33842e7 −1.51268
\(867\) 3.02976e7 1.36886
\(868\) 2.00984e6 0.0905445
\(869\) 1.52224e7 0.683807
\(870\) 0 0
\(871\) −1.09659e7 −0.489779
\(872\) −2.93226e7 −1.30591
\(873\) 5.00334e7 2.22190
\(874\) 6.00965e7 2.66116
\(875\) 0 0
\(876\) 5.42348e6 0.238791
\(877\) 7.95778e6 0.349376 0.174688 0.984624i \(-0.444108\pi\)
0.174688 + 0.984624i \(0.444108\pi\)
\(878\) 1.55813e7 0.682132
\(879\) −6.03151e7 −2.63302
\(880\) 0 0
\(881\) 3.11775e7 1.35333 0.676663 0.736293i \(-0.263426\pi\)
0.676663 + 0.736293i \(0.263426\pi\)
\(882\) −5.13761e6 −0.222377
\(883\) 2.20671e7 0.952452 0.476226 0.879323i \(-0.342004\pi\)
0.476226 + 0.879323i \(0.342004\pi\)
\(884\) −407443. −0.0175362
\(885\) 0 0
\(886\) 8.62524e6 0.369137
\(887\) 1.08566e6 0.0463323 0.0231662 0.999732i \(-0.492625\pi\)
0.0231662 + 0.999732i \(0.492625\pi\)
\(888\) 2.41518e7 1.02782
\(889\) 1.24744e7 0.529378
\(890\) 0 0
\(891\) 1.92576e6 0.0812657
\(892\) 1.98605e6 0.0835755
\(893\) 1.88743e7 0.792030
\(894\) 6.89962e7 2.88723
\(895\) 0 0
\(896\) 2.97164e7 1.23659
\(897\) −1.79448e7 −0.744660
\(898\) −2.16774e7 −0.897050
\(899\) 1.35179e7 0.557842
\(900\) 0 0
\(901\) −1.28754e7 −0.528381
\(902\) 1.75191e6 0.0716960
\(903\) −3.84208e7 −1.56800
\(904\) 3.68764e6 0.150082
\(905\) 0 0
\(906\) −207751. −0.00840857
\(907\) 3.82701e7 1.54469 0.772345 0.635203i \(-0.219084\pi\)
0.772345 + 0.635203i \(0.219084\pi\)
\(908\) 6.43706e6 0.259103
\(909\) −1.36601e7 −0.548334
\(910\) 0 0
\(911\) −4.01079e7 −1.60116 −0.800579 0.599227i \(-0.795475\pi\)
−0.800579 + 0.599227i \(0.795475\pi\)
\(912\) 7.07660e7 2.81733
\(913\) 2.77666e6 0.110242
\(914\) 2.25843e7 0.894212
\(915\) 0 0
\(916\) −4.28023e6 −0.168550
\(917\) 1.07644e7 0.422732
\(918\) 1.29269e7 0.506275
\(919\) 1.38759e6 0.0541967 0.0270984 0.999633i \(-0.491373\pi\)
0.0270984 + 0.999633i \(0.491373\pi\)
\(920\) 0 0
\(921\) −3.60256e7 −1.39947
\(922\) −2.27451e7 −0.881171
\(923\) 7.95587e6 0.307385
\(924\) 2.94279e6 0.113391
\(925\) 0 0
\(926\) 2.15045e7 0.824141
\(927\) 8.21897e7 3.14136
\(928\) −8.11940e6 −0.309495
\(929\) −7.82980e6 −0.297654 −0.148827 0.988863i \(-0.547550\pi\)
−0.148827 + 0.988863i \(0.547550\pi\)
\(930\) 0 0
\(931\) 4.87717e6 0.184414
\(932\) −5.90094e6 −0.222526
\(933\) −3.75749e7 −1.41317
\(934\) 1.20228e7 0.450959
\(935\) 0 0
\(936\) −1.14878e7 −0.428595
\(937\) 5.19939e7 1.93465 0.967327 0.253532i \(-0.0815925\pi\)
0.967327 + 0.253532i \(0.0815925\pi\)
\(938\) 5.41546e7 2.00968
\(939\) 7.95703e6 0.294501
\(940\) 0 0
\(941\) 2.54802e7 0.938055 0.469028 0.883184i \(-0.344605\pi\)
0.469028 + 0.883184i \(0.344605\pi\)
\(942\) −1.02800e7 −0.377455
\(943\) 7.06662e6 0.258781
\(944\) −1.30244e7 −0.475694
\(945\) 0 0
\(946\) 1.12222e7 0.407709
\(947\) 6.45145e6 0.233767 0.116883 0.993146i \(-0.462710\pi\)
0.116883 + 0.993146i \(0.462710\pi\)
\(948\) −1.14193e7 −0.412683
\(949\) 7.22843e6 0.260543
\(950\) 0 0
\(951\) 5.68143e7 2.03707
\(952\) −1.09976e7 −0.393284
\(953\) −2.82313e7 −1.00693 −0.503465 0.864016i \(-0.667942\pi\)
−0.503465 + 0.864016i \(0.667942\pi\)
\(954\) 6.64181e7 2.36274
\(955\) 0 0
\(956\) −6.09038e6 −0.215526
\(957\) 1.97928e7 0.698599
\(958\) 1.75183e7 0.616705
\(959\) −1.52762e7 −0.536377
\(960\) 0 0
\(961\) −1.98813e7 −0.694441
\(962\) −5.88942e6 −0.205180
\(963\) −7.57986e7 −2.63388
\(964\) 8.13185e6 0.281836
\(965\) 0 0
\(966\) 8.86193e7 3.05552
\(967\) 5.33839e7 1.83588 0.917939 0.396722i \(-0.129852\pi\)
0.917939 + 0.396722i \(0.129852\pi\)
\(968\) −2.17837e7 −0.747211
\(969\) −2.97717e7 −1.01858
\(970\) 0 0
\(971\) 3.29212e7 1.12054 0.560270 0.828310i \(-0.310697\pi\)
0.560270 + 0.828310i \(0.310697\pi\)
\(972\) 3.80574e6 0.129203
\(973\) 3.10798e7 1.05244
\(974\) 1.75414e7 0.592472
\(975\) 0 0
\(976\) 4.66610e7 1.56794
\(977\) 4.57380e7 1.53300 0.766498 0.642247i \(-0.221997\pi\)
0.766498 + 0.642247i \(0.221997\pi\)
\(978\) −8.94223e6 −0.298950
\(979\) −6.02302e6 −0.200843
\(980\) 0 0
\(981\) −7.37205e7 −2.44577
\(982\) −3.20457e7 −1.06045
\(983\) 5.78671e7 1.91006 0.955031 0.296505i \(-0.0958211\pi\)
0.955031 + 0.296505i \(0.0958211\pi\)
\(984\) 7.18305e6 0.236495
\(985\) 0 0
\(986\) 1.35333e7 0.443315
\(987\) 2.78323e7 0.909404
\(988\) −1.99527e6 −0.0650292
\(989\) 4.52667e7 1.47159
\(990\) 0 0
\(991\) −4.51653e7 −1.46090 −0.730451 0.682965i \(-0.760690\pi\)
−0.730451 + 0.682965i \(0.760690\pi\)
\(992\) −5.25432e6 −0.169526
\(993\) −1.12648e7 −0.362536
\(994\) −3.92895e7 −1.26128
\(995\) 0 0
\(996\) −2.08294e6 −0.0665318
\(997\) 1.89237e7 0.602933 0.301467 0.953477i \(-0.402524\pi\)
0.301467 + 0.953477i \(0.402524\pi\)
\(998\) 1.87277e6 0.0595193
\(999\) 2.50282e7 0.793445
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.1.3 11
5.2 odd 4 325.6.b.i.274.5 22
5.3 odd 4 325.6.b.i.274.18 22
5.4 even 2 325.6.a.k.1.9 yes 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
325.6.a.j.1.3 11 1.1 even 1 trivial
325.6.a.k.1.9 yes 11 5.4 even 2
325.6.b.i.274.5 22 5.2 odd 4
325.6.b.i.274.18 22 5.3 odd 4