Properties

Label 285.6.a.a.1.1
Level $285$
Weight $6$
Character 285.1
Self dual yes
Analytic conductor $45.709$
Analytic rank $1$
Dimension $1$
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] = [285,6,Mod(1,285)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(285, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("285.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 285.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: \(45.7093886467\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 285.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} +9.00000 q^{3} -28.0000 q^{4} +25.0000 q^{5} +18.0000 q^{6} +22.0000 q^{7} -120.000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q+2.00000 q^{2} +9.00000 q^{3} -28.0000 q^{4} +25.0000 q^{5} +18.0000 q^{6} +22.0000 q^{7} -120.000 q^{8} +81.0000 q^{9} +50.0000 q^{10} -568.000 q^{11} -252.000 q^{12} +1046.00 q^{13} +44.0000 q^{14} +225.000 q^{15} +656.000 q^{16} -428.000 q^{17} +162.000 q^{18} -361.000 q^{19} -700.000 q^{20} +198.000 q^{21} -1136.00 q^{22} -4244.00 q^{23} -1080.00 q^{24} +625.000 q^{25} +2092.00 q^{26} +729.000 q^{27} -616.000 q^{28} -5110.00 q^{29} +450.000 q^{30} -378.000 q^{31} +5152.00 q^{32} -5112.00 q^{33} -856.000 q^{34} +550.000 q^{35} -2268.00 q^{36} +8622.00 q^{37} -722.000 q^{38} +9414.00 q^{39} -3000.00 q^{40} -5448.00 q^{41} +396.000 q^{42} -18724.0 q^{43} +15904.0 q^{44} +2025.00 q^{45} -8488.00 q^{46} -13428.0 q^{47} +5904.00 q^{48} -16323.0 q^{49} +1250.00 q^{50} -3852.00 q^{51} -29288.0 q^{52} -16774.0 q^{53} +1458.00 q^{54} -14200.0 q^{55} -2640.00 q^{56} -3249.00 q^{57} -10220.0 q^{58} +11030.0 q^{59} -6300.00 q^{60} +10682.0 q^{61} -756.000 q^{62} +1782.00 q^{63} -10688.0 q^{64} +26150.0 q^{65} -10224.0 q^{66} -54268.0 q^{67} +11984.0 q^{68} -38196.0 q^{69} +1100.00 q^{70} -3528.00 q^{71} -9720.00 q^{72} +75886.0 q^{73} +17244.0 q^{74} +5625.00 q^{75} +10108.0 q^{76} -12496.0 q^{77} +18828.0 q^{78} -89450.0 q^{79} +16400.0 q^{80} +6561.00 q^{81} -10896.0 q^{82} -57294.0 q^{83} -5544.00 q^{84} -10700.0 q^{85} -37448.0 q^{86} -45990.0 q^{87} +68160.0 q^{88} +18540.0 q^{89} +4050.00 q^{90} +23012.0 q^{91} +118832. q^{92} -3402.00 q^{93} -26856.0 q^{94} -9025.00 q^{95} +46368.0 q^{96} -52798.0 q^{97} -32646.0 q^{98} -46008.0 q^{99} +O(q^{100})\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 0.353553 0.176777 0.984251i \(-0.443433\pi\)
0.176777 + 0.984251i \(0.443433\pi\)
\(3\) 9.00000 0.577350
\(4\) −28.0000 −0.875000
\(5\) 25.0000 0.447214
\(6\) 18.0000 0.204124
\(7\) 22.0000 0.169698 0.0848492 0.996394i \(-0.472959\pi\)
0.0848492 + 0.996394i \(0.472959\pi\)
\(8\) −120.000 −0.662913
\(9\) 81.0000 0.333333
\(10\) 50.0000 0.158114
\(11\) −568.000 −1.41536 −0.707680 0.706534i \(-0.750258\pi\)
−0.707680 + 0.706534i \(0.750258\pi\)
\(12\) −252.000 −0.505181
\(13\) 1046.00 1.71662 0.858308 0.513134i \(-0.171516\pi\)
0.858308 + 0.513134i \(0.171516\pi\)
\(14\) 44.0000 0.0599974
\(15\) 225.000 0.258199
\(16\) 656.000 0.640625
\(17\) −428.000 −0.359188 −0.179594 0.983741i \(-0.557478\pi\)
−0.179594 + 0.983741i \(0.557478\pi\)
\(18\) 162.000 0.117851
\(19\) −361.000 −0.229416
\(20\) −700.000 −0.391312
\(21\) 198.000 0.0979754
\(22\) −1136.00 −0.500405
\(23\) −4244.00 −1.67285 −0.836423 0.548085i \(-0.815357\pi\)
−0.836423 + 0.548085i \(0.815357\pi\)
\(24\) −1080.00 −0.382733
\(25\) 625.000 0.200000
\(26\) 2092.00 0.606916
\(27\) 729.000 0.192450
\(28\) −616.000 −0.148486
\(29\) −5110.00 −1.12830 −0.564152 0.825671i \(-0.690797\pi\)
−0.564152 + 0.825671i \(0.690797\pi\)
\(30\) 450.000 0.0912871
\(31\) −378.000 −0.0706460 −0.0353230 0.999376i \(-0.511246\pi\)
−0.0353230 + 0.999376i \(0.511246\pi\)
\(32\) 5152.00 0.889408
\(33\) −5112.00 −0.817158
\(34\) −856.000 −0.126992
\(35\) 550.000 0.0758914
\(36\) −2268.00 −0.291667
\(37\) 8622.00 1.03539 0.517695 0.855565i \(-0.326790\pi\)
0.517695 + 0.855565i \(0.326790\pi\)
\(38\) −722.000 −0.0811107
\(39\) 9414.00 0.991089
\(40\) −3000.00 −0.296464
\(41\) −5448.00 −0.506148 −0.253074 0.967447i \(-0.581442\pi\)
−0.253074 + 0.967447i \(0.581442\pi\)
\(42\) 396.000 0.0346395
\(43\) −18724.0 −1.54429 −0.772143 0.635449i \(-0.780815\pi\)
−0.772143 + 0.635449i \(0.780815\pi\)
\(44\) 15904.0 1.23844
\(45\) 2025.00 0.149071
\(46\) −8488.00 −0.591440
\(47\) −13428.0 −0.886680 −0.443340 0.896354i \(-0.646206\pi\)
−0.443340 + 0.896354i \(0.646206\pi\)
\(48\) 5904.00 0.369865
\(49\) −16323.0 −0.971202
\(50\) 1250.00 0.0707107
\(51\) −3852.00 −0.207377
\(52\) −29288.0 −1.50204
\(53\) −16774.0 −0.820251 −0.410126 0.912029i \(-0.634515\pi\)
−0.410126 + 0.912029i \(0.634515\pi\)
\(54\) 1458.00 0.0680414
\(55\) −14200.0 −0.632968
\(56\) −2640.00 −0.112495
\(57\) −3249.00 −0.132453
\(58\) −10220.0 −0.398916
\(59\) 11030.0 0.412520 0.206260 0.978497i \(-0.433871\pi\)
0.206260 + 0.978497i \(0.433871\pi\)
\(60\) −6300.00 −0.225924
\(61\) 10682.0 0.367560 0.183780 0.982967i \(-0.441167\pi\)
0.183780 + 0.982967i \(0.441167\pi\)
\(62\) −756.000 −0.0249771
\(63\) 1782.00 0.0565661
\(64\) −10688.0 −0.326172
\(65\) 26150.0 0.767694
\(66\) −10224.0 −0.288909
\(67\) −54268.0 −1.47692 −0.738460 0.674298i \(-0.764447\pi\)
−0.738460 + 0.674298i \(0.764447\pi\)
\(68\) 11984.0 0.314289
\(69\) −38196.0 −0.965818
\(70\) 1100.00 0.0268317
\(71\) −3528.00 −0.0830582 −0.0415291 0.999137i \(-0.513223\pi\)
−0.0415291 + 0.999137i \(0.513223\pi\)
\(72\) −9720.00 −0.220971
\(73\) 75886.0 1.66669 0.833344 0.552754i \(-0.186423\pi\)
0.833344 + 0.552754i \(0.186423\pi\)
\(74\) 17244.0 0.366065
\(75\) 5625.00 0.115470
\(76\) 10108.0 0.200739
\(77\) −12496.0 −0.240184
\(78\) 18828.0 0.350403
\(79\) −89450.0 −1.61255 −0.806274 0.591542i \(-0.798519\pi\)
−0.806274 + 0.591542i \(0.798519\pi\)
\(80\) 16400.0 0.286496
\(81\) 6561.00 0.111111
\(82\) −10896.0 −0.178950
\(83\) −57294.0 −0.912880 −0.456440 0.889754i \(-0.650876\pi\)
−0.456440 + 0.889754i \(0.650876\pi\)
\(84\) −5544.00 −0.0857285
\(85\) −10700.0 −0.160634
\(86\) −37448.0 −0.545987
\(87\) −45990.0 −0.651426
\(88\) 68160.0 0.938259
\(89\) 18540.0 0.248105 0.124052 0.992276i \(-0.460411\pi\)
0.124052 + 0.992276i \(0.460411\pi\)
\(90\) 4050.00 0.0527046
\(91\) 23012.0 0.291307
\(92\) 118832. 1.46374
\(93\) −3402.00 −0.0407875
\(94\) −26856.0 −0.313489
\(95\) −9025.00 −0.102598
\(96\) 46368.0 0.513500
\(97\) −52798.0 −0.569755 −0.284877 0.958564i \(-0.591953\pi\)
−0.284877 + 0.958564i \(0.591953\pi\)
\(98\) −32646.0 −0.343372
\(99\) −46008.0 −0.471786
\(100\) −17500.0 −0.175000
\(101\) −9398.00 −0.0916710 −0.0458355 0.998949i \(-0.514595\pi\)
−0.0458355 + 0.998949i \(0.514595\pi\)
\(102\) −7704.00 −0.0733189
\(103\) 35776.0 0.332276 0.166138 0.986103i \(-0.446870\pi\)
0.166138 + 0.986103i \(0.446870\pi\)
\(104\) −125520. −1.13797
\(105\) 4950.00 0.0438159
\(106\) −33548.0 −0.290003
\(107\) −188808. −1.59427 −0.797133 0.603803i \(-0.793651\pi\)
−0.797133 + 0.603803i \(0.793651\pi\)
\(108\) −20412.0 −0.168394
\(109\) 144880. 1.16800 0.583999 0.811754i \(-0.301487\pi\)
0.583999 + 0.811754i \(0.301487\pi\)
\(110\) −28400.0 −0.223788
\(111\) 77598.0 0.597782
\(112\) 14432.0 0.108713
\(113\) −46034.0 −0.339143 −0.169571 0.985518i \(-0.554238\pi\)
−0.169571 + 0.985518i \(0.554238\pi\)
\(114\) −6498.00 −0.0468293
\(115\) −106100. −0.748119
\(116\) 143080. 0.987265
\(117\) 84726.0 0.572206
\(118\) 22060.0 0.145848
\(119\) −9416.00 −0.0609536
\(120\) −27000.0 −0.171163
\(121\) 161573. 1.00324
\(122\) 21364.0 0.129952
\(123\) −49032.0 −0.292225
\(124\) 10584.0 0.0618152
\(125\) 15625.0 0.0894427
\(126\) 3564.00 0.0199991
\(127\) −271688. −1.49472 −0.747362 0.664417i \(-0.768680\pi\)
−0.747362 + 0.664417i \(0.768680\pi\)
\(128\) −186240. −1.00473
\(129\) −168516. −0.891593
\(130\) 52300.0 0.271421
\(131\) 344792. 1.75541 0.877706 0.479200i \(-0.159073\pi\)
0.877706 + 0.479200i \(0.159073\pi\)
\(132\) 143136. 0.715013
\(133\) −7942.00 −0.0389315
\(134\) −108536. −0.522170
\(135\) 18225.0 0.0860663
\(136\) 51360.0 0.238110
\(137\) −7488.00 −0.0340851 −0.0170425 0.999855i \(-0.505425\pi\)
−0.0170425 + 0.999855i \(0.505425\pi\)
\(138\) −76392.0 −0.341468
\(139\) −83860.0 −0.368144 −0.184072 0.982913i \(-0.558928\pi\)
−0.184072 + 0.982913i \(0.558928\pi\)
\(140\) −15400.0 −0.0664050
\(141\) −120852. −0.511925
\(142\) −7056.00 −0.0293655
\(143\) −594128. −2.42963
\(144\) 53136.0 0.213542
\(145\) −127750. −0.504593
\(146\) 151772. 0.589263
\(147\) −146907. −0.560724
\(148\) −241416. −0.905966
\(149\) −104310. −0.384911 −0.192455 0.981306i \(-0.561645\pi\)
−0.192455 + 0.981306i \(0.561645\pi\)
\(150\) 11250.0 0.0408248
\(151\) 300762. 1.07345 0.536723 0.843758i \(-0.319662\pi\)
0.536723 + 0.843758i \(0.319662\pi\)
\(152\) 43320.0 0.152083
\(153\) −34668.0 −0.119729
\(154\) −24992.0 −0.0849179
\(155\) −9450.00 −0.0315939
\(156\) −263592. −0.867203
\(157\) −14568.0 −0.0471684 −0.0235842 0.999722i \(-0.507508\pi\)
−0.0235842 + 0.999722i \(0.507508\pi\)
\(158\) −178900. −0.570122
\(159\) −150966. −0.473572
\(160\) 128800. 0.397755
\(161\) −93368.0 −0.283879
\(162\) 13122.0 0.0392837
\(163\) 353376. 1.04176 0.520880 0.853630i \(-0.325604\pi\)
0.520880 + 0.853630i \(0.325604\pi\)
\(164\) 152544. 0.442879
\(165\) −127800. −0.365444
\(166\) −114588. −0.322752
\(167\) −143848. −0.399128 −0.199564 0.979885i \(-0.563953\pi\)
−0.199564 + 0.979885i \(0.563953\pi\)
\(168\) −23760.0 −0.0649491
\(169\) 722823. 1.94677
\(170\) −21400.0 −0.0567926
\(171\) −29241.0 −0.0764719
\(172\) 524272. 1.35125
\(173\) 546306. 1.38778 0.693890 0.720081i \(-0.255895\pi\)
0.693890 + 0.720081i \(0.255895\pi\)
\(174\) −91980.0 −0.230314
\(175\) 13750.0 0.0339397
\(176\) −372608. −0.906714
\(177\) 99270.0 0.238169
\(178\) 37080.0 0.0877182
\(179\) 395130. 0.921738 0.460869 0.887468i \(-0.347538\pi\)
0.460869 + 0.887468i \(0.347538\pi\)
\(180\) −56700.0 −0.130437
\(181\) 393952. 0.893813 0.446907 0.894581i \(-0.352526\pi\)
0.446907 + 0.894581i \(0.352526\pi\)
\(182\) 46024.0 0.102993
\(183\) 96138.0 0.212211
\(184\) 509280. 1.10895
\(185\) 215550. 0.463040
\(186\) −6804.00 −0.0144206
\(187\) 243104. 0.508380
\(188\) 375984. 0.775845
\(189\) 16038.0 0.0326585
\(190\) −18050.0 −0.0362738
\(191\) 265632. 0.526862 0.263431 0.964678i \(-0.415146\pi\)
0.263431 + 0.964678i \(0.415146\pi\)
\(192\) −96192.0 −0.188315
\(193\) −125714. −0.242935 −0.121468 0.992595i \(-0.538760\pi\)
−0.121468 + 0.992595i \(0.538760\pi\)
\(194\) −105596. −0.201439
\(195\) 235350. 0.443228
\(196\) 457044. 0.849802
\(197\) −60598.0 −0.111248 −0.0556241 0.998452i \(-0.517715\pi\)
−0.0556241 + 0.998452i \(0.517715\pi\)
\(198\) −92016.0 −0.166802
\(199\) −307980. −0.551302 −0.275651 0.961258i \(-0.588893\pi\)
−0.275651 + 0.961258i \(0.588893\pi\)
\(200\) −75000.0 −0.132583
\(201\) −488412. −0.852700
\(202\) −18796.0 −0.0324106
\(203\) −112420. −0.191471
\(204\) 107856. 0.181455
\(205\) −136200. −0.226356
\(206\) 71552.0 0.117477
\(207\) −343764. −0.557615
\(208\) 686176. 1.09971
\(209\) 205048. 0.324706
\(210\) 9900.00 0.0154913
\(211\) 744072. 1.15056 0.575279 0.817957i \(-0.304893\pi\)
0.575279 + 0.817957i \(0.304893\pi\)
\(212\) 469672. 0.717720
\(213\) −31752.0 −0.0479537
\(214\) −377616. −0.563658
\(215\) −468100. −0.690625
\(216\) −87480.0 −0.127578
\(217\) −8316.00 −0.0119885
\(218\) 289760. 0.412950
\(219\) 682974. 0.962263
\(220\) 397600. 0.553847
\(221\) −447688. −0.616588
\(222\) 155196. 0.211348
\(223\) 777036. 1.04635 0.523177 0.852224i \(-0.324747\pi\)
0.523177 + 0.852224i \(0.324747\pi\)
\(224\) 113344. 0.150931
\(225\) 50625.0 0.0666667
\(226\) −92068.0 −0.119905
\(227\) −378228. −0.487180 −0.243590 0.969878i \(-0.578325\pi\)
−0.243590 + 0.969878i \(0.578325\pi\)
\(228\) 90972.0 0.115897
\(229\) −883610. −1.11345 −0.556727 0.830696i \(-0.687943\pi\)
−0.556727 + 0.830696i \(0.687943\pi\)
\(230\) −212200. −0.264500
\(231\) −112464. −0.138670
\(232\) 613200. 0.747967
\(233\) 497796. 0.600705 0.300353 0.953828i \(-0.402896\pi\)
0.300353 + 0.953828i \(0.402896\pi\)
\(234\) 169452. 0.202305
\(235\) −335700. −0.396535
\(236\) −308840. −0.360955
\(237\) −805050. −0.931005
\(238\) −18832.0 −0.0215503
\(239\) −363600. −0.411746 −0.205873 0.978579i \(-0.566003\pi\)
−0.205873 + 0.978579i \(0.566003\pi\)
\(240\) 147600. 0.165409
\(241\) −713758. −0.791605 −0.395802 0.918336i \(-0.629533\pi\)
−0.395802 + 0.918336i \(0.629533\pi\)
\(242\) 323146. 0.354699
\(243\) 59049.0 0.0641500
\(244\) −299096. −0.321615
\(245\) −408075. −0.434335
\(246\) −98064.0 −0.103317
\(247\) −377606. −0.393819
\(248\) 45360.0 0.0468321
\(249\) −515646. −0.527052
\(250\) 31250.0 0.0316228
\(251\) 1.47105e6 1.47382 0.736909 0.675992i \(-0.236285\pi\)
0.736909 + 0.675992i \(0.236285\pi\)
\(252\) −49896.0 −0.0494953
\(253\) 2.41059e6 2.36768
\(254\) −543376. −0.528465
\(255\) −96300.0 −0.0927419
\(256\) −30464.0 −0.0290527
\(257\) 224402. 0.211931 0.105965 0.994370i \(-0.466207\pi\)
0.105965 + 0.994370i \(0.466207\pi\)
\(258\) −337032. −0.315226
\(259\) 189684. 0.175704
\(260\) −732200. −0.671732
\(261\) −413910. −0.376101
\(262\) 689584. 0.620632
\(263\) 1.31252e6 1.17008 0.585040 0.811005i \(-0.301079\pi\)
0.585040 + 0.811005i \(0.301079\pi\)
\(264\) 613440. 0.541704
\(265\) −419350. −0.366828
\(266\) −15884.0 −0.0137644
\(267\) 166860. 0.143243
\(268\) 1.51950e6 1.29230
\(269\) 7610.00 0.00641215 0.00320608 0.999995i \(-0.498979\pi\)
0.00320608 + 0.999995i \(0.498979\pi\)
\(270\) 36450.0 0.0304290
\(271\) −803508. −0.664610 −0.332305 0.943172i \(-0.607826\pi\)
−0.332305 + 0.943172i \(0.607826\pi\)
\(272\) −280768. −0.230105
\(273\) 207108. 0.168186
\(274\) −14976.0 −0.0120509
\(275\) −355000. −0.283072
\(276\) 1.06949e6 0.845090
\(277\) 1.82459e6 1.42878 0.714392 0.699746i \(-0.246704\pi\)
0.714392 + 0.699746i \(0.246704\pi\)
\(278\) −167720. −0.130159
\(279\) −30618.0 −0.0235487
\(280\) −66000.0 −0.0503094
\(281\) 1.57635e6 1.19093 0.595467 0.803380i \(-0.296967\pi\)
0.595467 + 0.803380i \(0.296967\pi\)
\(282\) −241704. −0.180993
\(283\) −1.34808e6 −1.00058 −0.500289 0.865859i \(-0.666773\pi\)
−0.500289 + 0.865859i \(0.666773\pi\)
\(284\) 98784.0 0.0726760
\(285\) −81225.0 −0.0592349
\(286\) −1.18826e6 −0.859003
\(287\) −119856. −0.0858925
\(288\) 417312. 0.296469
\(289\) −1.23667e6 −0.870984
\(290\) −255500. −0.178400
\(291\) −475182. −0.328948
\(292\) −2.12481e6 −1.45835
\(293\) −1.70539e6 −1.16053 −0.580264 0.814428i \(-0.697051\pi\)
−0.580264 + 0.814428i \(0.697051\pi\)
\(294\) −293814. −0.198246
\(295\) 275750. 0.184485
\(296\) −1.03464e6 −0.686373
\(297\) −414072. −0.272386
\(298\) −208620. −0.136087
\(299\) −4.43922e6 −2.87163
\(300\) −157500. −0.101036
\(301\) −411928. −0.262063
\(302\) 601524. 0.379521
\(303\) −84582.0 −0.0529263
\(304\) −236816. −0.146969
\(305\) 267050. 0.164378
\(306\) −69336.0 −0.0423307
\(307\) 2.38381e6 1.44353 0.721765 0.692138i \(-0.243331\pi\)
0.721765 + 0.692138i \(0.243331\pi\)
\(308\) 349888. 0.210161
\(309\) 321984. 0.191840
\(310\) −18900.0 −0.0111701
\(311\) −244008. −0.143055 −0.0715275 0.997439i \(-0.522787\pi\)
−0.0715275 + 0.997439i \(0.522787\pi\)
\(312\) −1.12968e6 −0.657005
\(313\) 1.25525e6 0.724216 0.362108 0.932136i \(-0.382057\pi\)
0.362108 + 0.932136i \(0.382057\pi\)
\(314\) −29136.0 −0.0166765
\(315\) 44550.0 0.0252971
\(316\) 2.50460e6 1.41098
\(317\) −2.89042e6 −1.61552 −0.807760 0.589511i \(-0.799320\pi\)
−0.807760 + 0.589511i \(0.799320\pi\)
\(318\) −301932. −0.167433
\(319\) 2.90248e6 1.59695
\(320\) −267200. −0.145868
\(321\) −1.69927e6 −0.920450
\(322\) −186736. −0.100366
\(323\) 154508. 0.0824033
\(324\) −183708. −0.0972222
\(325\) 653750. 0.343323
\(326\) 706752. 0.368318
\(327\) 1.30392e6 0.674344
\(328\) 653760. 0.335532
\(329\) −295416. −0.150468
\(330\) −255600. −0.129204
\(331\) −474148. −0.237872 −0.118936 0.992902i \(-0.537948\pi\)
−0.118936 + 0.992902i \(0.537948\pi\)
\(332\) 1.60423e6 0.798770
\(333\) 698382. 0.345130
\(334\) −287696. −0.141113
\(335\) −1.35670e6 −0.660498
\(336\) 129888. 0.0627655
\(337\) −545618. −0.261706 −0.130853 0.991402i \(-0.541772\pi\)
−0.130853 + 0.991402i \(0.541772\pi\)
\(338\) 1.44565e6 0.688288
\(339\) −414306. −0.195804
\(340\) 299600. 0.140554
\(341\) 214704. 0.0999895
\(342\) −58482.0 −0.0270369
\(343\) −728860. −0.334510
\(344\) 2.24688e6 1.02373
\(345\) −954900. −0.431927
\(346\) 1.09261e6 0.490654
\(347\) 3.77690e6 1.68388 0.841942 0.539568i \(-0.181413\pi\)
0.841942 + 0.539568i \(0.181413\pi\)
\(348\) 1.28772e6 0.569998
\(349\) 1.44579e6 0.635392 0.317696 0.948193i \(-0.397091\pi\)
0.317696 + 0.948193i \(0.397091\pi\)
\(350\) 27500.0 0.0119995
\(351\) 762534. 0.330363
\(352\) −2.92634e6 −1.25883
\(353\) −2.90370e6 −1.24027 −0.620134 0.784496i \(-0.712922\pi\)
−0.620134 + 0.784496i \(0.712922\pi\)
\(354\) 198540. 0.0842054
\(355\) −88200.0 −0.0371448
\(356\) −519120. −0.217091
\(357\) −84744.0 −0.0351916
\(358\) 790260. 0.325884
\(359\) −3.21580e6 −1.31690 −0.658450 0.752624i \(-0.728788\pi\)
−0.658450 + 0.752624i \(0.728788\pi\)
\(360\) −243000. −0.0988212
\(361\) 130321. 0.0526316
\(362\) 787904. 0.316011
\(363\) 1.45416e6 0.579222
\(364\) −644336. −0.254894
\(365\) 1.89715e6 0.745366
\(366\) 192276. 0.0750278
\(367\) 4.01084e6 1.55443 0.777214 0.629237i \(-0.216632\pi\)
0.777214 + 0.629237i \(0.216632\pi\)
\(368\) −2.78406e6 −1.07167
\(369\) −441288. −0.168716
\(370\) 431100. 0.163709
\(371\) −369028. −0.139195
\(372\) 95256.0 0.0356891
\(373\) −567974. −0.211376 −0.105688 0.994399i \(-0.533705\pi\)
−0.105688 + 0.994399i \(0.533705\pi\)
\(374\) 486208. 0.179739
\(375\) 140625. 0.0516398
\(376\) 1.61136e6 0.587791
\(377\) −5.34506e6 −1.93686
\(378\) 32076.0 0.0115465
\(379\) −2.99588e6 −1.07134 −0.535669 0.844428i \(-0.679940\pi\)
−0.535669 + 0.844428i \(0.679940\pi\)
\(380\) 252700. 0.0897731
\(381\) −2.44519e6 −0.862980
\(382\) 531264. 0.186274
\(383\) −1.91746e6 −0.667929 −0.333964 0.942586i \(-0.608387\pi\)
−0.333964 + 0.942586i \(0.608387\pi\)
\(384\) −1.67616e6 −0.580079
\(385\) −312400. −0.107414
\(386\) −251428. −0.0858905
\(387\) −1.51664e6 −0.514762
\(388\) 1.47834e6 0.498536
\(389\) −5.28843e6 −1.77196 −0.885978 0.463728i \(-0.846512\pi\)
−0.885978 + 0.463728i \(0.846512\pi\)
\(390\) 470700. 0.156705
\(391\) 1.81643e6 0.600865
\(392\) 1.95876e6 0.643822
\(393\) 3.10313e6 1.01349
\(394\) −121196. −0.0393322
\(395\) −2.23625e6 −0.721153
\(396\) 1.28822e6 0.412813
\(397\) −4.33759e6 −1.38125 −0.690625 0.723213i \(-0.742664\pi\)
−0.690625 + 0.723213i \(0.742664\pi\)
\(398\) −615960. −0.194915
\(399\) −71478.0 −0.0224771
\(400\) 410000. 0.128125
\(401\) −3.85559e6 −1.19737 −0.598687 0.800983i \(-0.704311\pi\)
−0.598687 + 0.800983i \(0.704311\pi\)
\(402\) −976824. −0.301475
\(403\) −395388. −0.121272
\(404\) 263144. 0.0802121
\(405\) 164025. 0.0496904
\(406\) −224840. −0.0676953
\(407\) −4.89730e6 −1.46545
\(408\) 462240. 0.137473
\(409\) −4.11143e6 −1.21530 −0.607652 0.794204i \(-0.707888\pi\)
−0.607652 + 0.794204i \(0.707888\pi\)
\(410\) −272400. −0.0800290
\(411\) −67392.0 −0.0196790
\(412\) −1.00173e6 −0.290741
\(413\) 242660. 0.0700040
\(414\) −687528. −0.197147
\(415\) −1.43235e6 −0.408253
\(416\) 5.38899e6 1.52677
\(417\) −754740. −0.212548
\(418\) 410096. 0.114801
\(419\) −2.92810e6 −0.814800 −0.407400 0.913250i \(-0.633564\pi\)
−0.407400 + 0.913250i \(0.633564\pi\)
\(420\) −138600. −0.0383389
\(421\) −4.62213e6 −1.27097 −0.635487 0.772111i \(-0.719201\pi\)
−0.635487 + 0.772111i \(0.719201\pi\)
\(422\) 1.48814e6 0.406784
\(423\) −1.08767e6 −0.295560
\(424\) 2.01288e6 0.543755
\(425\) −267500. −0.0718375
\(426\) −63504.0 −0.0169542
\(427\) 235004. 0.0623743
\(428\) 5.28662e6 1.39498
\(429\) −5.34715e6 −1.40275
\(430\) −936200. −0.244173
\(431\) −5.47753e6 −1.42034 −0.710169 0.704032i \(-0.751381\pi\)
−0.710169 + 0.704032i \(0.751381\pi\)
\(432\) 478224. 0.123288
\(433\) 3.64693e6 0.934775 0.467388 0.884052i \(-0.345195\pi\)
0.467388 + 0.884052i \(0.345195\pi\)
\(434\) −16632.0 −0.00423858
\(435\) −1.14975e6 −0.291327
\(436\) −4.05664e6 −1.02200
\(437\) 1.53208e6 0.383777
\(438\) 1.36595e6 0.340211
\(439\) −5.10181e6 −1.26346 −0.631732 0.775187i \(-0.717656\pi\)
−0.631732 + 0.775187i \(0.717656\pi\)
\(440\) 1.70400e6 0.419602
\(441\) −1.32216e6 −0.323734
\(442\) −895376. −0.217997
\(443\) 1.67445e6 0.405380 0.202690 0.979243i \(-0.435032\pi\)
0.202690 + 0.979243i \(0.435032\pi\)
\(444\) −2.17274e6 −0.523060
\(445\) 463500. 0.110956
\(446\) 1.55407e6 0.369942
\(447\) −938790. −0.222228
\(448\) −235136. −0.0553508
\(449\) 6.65748e6 1.55845 0.779227 0.626742i \(-0.215612\pi\)
0.779227 + 0.626742i \(0.215612\pi\)
\(450\) 101250. 0.0235702
\(451\) 3.09446e6 0.716381
\(452\) 1.28895e6 0.296750
\(453\) 2.70686e6 0.619755
\(454\) −756456. −0.172244
\(455\) 575300. 0.130276
\(456\) 389880. 0.0878049
\(457\) −2.54308e6 −0.569599 −0.284799 0.958587i \(-0.591927\pi\)
−0.284799 + 0.958587i \(0.591927\pi\)
\(458\) −1.76722e6 −0.393665
\(459\) −312012. −0.0691257
\(460\) 2.97080e6 0.654604
\(461\) −4.28906e6 −0.939961 −0.469980 0.882677i \(-0.655739\pi\)
−0.469980 + 0.882677i \(0.655739\pi\)
\(462\) −224928. −0.0490274
\(463\) 7.10925e6 1.54124 0.770621 0.637293i \(-0.219946\pi\)
0.770621 + 0.637293i \(0.219946\pi\)
\(464\) −3.35216e6 −0.722819
\(465\) −85050.0 −0.0182407
\(466\) 995592. 0.212381
\(467\) 7.77612e6 1.64995 0.824975 0.565169i \(-0.191189\pi\)
0.824975 + 0.565169i \(0.191189\pi\)
\(468\) −2.37233e6 −0.500680
\(469\) −1.19390e6 −0.250631
\(470\) −671400. −0.140196
\(471\) −131112. −0.0272327
\(472\) −1.32360e6 −0.273465
\(473\) 1.06352e7 2.18572
\(474\) −1.61010e6 −0.329160
\(475\) −225625. −0.0458831
\(476\) 263648. 0.0533344
\(477\) −1.35869e6 −0.273417
\(478\) −727200. −0.145574
\(479\) −6.24992e6 −1.24462 −0.622308 0.782772i \(-0.713805\pi\)
−0.622308 + 0.782772i \(0.713805\pi\)
\(480\) 1.15920e6 0.229644
\(481\) 9.01861e6 1.77737
\(482\) −1.42752e6 −0.279875
\(483\) −840312. −0.163898
\(484\) −4.52404e6 −0.877836
\(485\) −1.31995e6 −0.254802
\(486\) 118098. 0.0226805
\(487\) −9.15561e6 −1.74930 −0.874651 0.484753i \(-0.838909\pi\)
−0.874651 + 0.484753i \(0.838909\pi\)
\(488\) −1.28184e6 −0.243660
\(489\) 3.18038e6 0.601461
\(490\) −816150. −0.153561
\(491\) 8.06191e6 1.50916 0.754578 0.656210i \(-0.227841\pi\)
0.754578 + 0.656210i \(0.227841\pi\)
\(492\) 1.37290e6 0.255697
\(493\) 2.18708e6 0.405273
\(494\) −755212. −0.139236
\(495\) −1.15020e6 −0.210989
\(496\) −247968. −0.0452576
\(497\) −77616.0 −0.0140948
\(498\) −1.03129e6 −0.186341
\(499\) −490540. −0.0881908 −0.0440954 0.999027i \(-0.514041\pi\)
−0.0440954 + 0.999027i \(0.514041\pi\)
\(500\) −437500. −0.0782624
\(501\) −1.29463e6 −0.230437
\(502\) 2.94210e6 0.521073
\(503\) −7.04310e6 −1.24121 −0.620603 0.784125i \(-0.713112\pi\)
−0.620603 + 0.784125i \(0.713112\pi\)
\(504\) −213840. −0.0374984
\(505\) −234950. −0.0409965
\(506\) 4.82118e6 0.837100
\(507\) 6.50541e6 1.12397
\(508\) 7.60726e6 1.30788
\(509\) −3.22455e6 −0.551664 −0.275832 0.961206i \(-0.588953\pi\)
−0.275832 + 0.961206i \(0.588953\pi\)
\(510\) −192600. −0.0327892
\(511\) 1.66949e6 0.282834
\(512\) 5.89875e6 0.994455
\(513\) −263169. −0.0441511
\(514\) 448804. 0.0749288
\(515\) 894400. 0.148598
\(516\) 4.71845e6 0.780144
\(517\) 7.62710e6 1.25497
\(518\) 379368. 0.0621207
\(519\) 4.91675e6 0.801235
\(520\) −3.13800e6 −0.508914
\(521\) 6.75985e6 1.09105 0.545523 0.838096i \(-0.316331\pi\)
0.545523 + 0.838096i \(0.316331\pi\)
\(522\) −827820. −0.132972
\(523\) −6.02808e6 −0.963663 −0.481831 0.876264i \(-0.660028\pi\)
−0.481831 + 0.876264i \(0.660028\pi\)
\(524\) −9.65418e6 −1.53599
\(525\) 123750. 0.0195951
\(526\) 2.62503e6 0.413685
\(527\) 161784. 0.0253752
\(528\) −3.35347e6 −0.523492
\(529\) 1.15752e7 1.79841
\(530\) −838700. −0.129693
\(531\) 893430. 0.137507
\(532\) 222376. 0.0340650
\(533\) −5.69861e6 −0.868862
\(534\) 333720. 0.0506441
\(535\) −4.72020e6 −0.712978
\(536\) 6.51216e6 0.979069
\(537\) 3.55617e6 0.532166
\(538\) 15220.0 0.00226704
\(539\) 9.27146e6 1.37460
\(540\) −510300. −0.0753080
\(541\) 1.07697e7 1.58202 0.791010 0.611803i \(-0.209555\pi\)
0.791010 + 0.611803i \(0.209555\pi\)
\(542\) −1.60702e6 −0.234975
\(543\) 3.54557e6 0.516043
\(544\) −2.20506e6 −0.319464
\(545\) 3.62200e6 0.522345
\(546\) 414216. 0.0594628
\(547\) −7.71151e6 −1.10197 −0.550987 0.834514i \(-0.685748\pi\)
−0.550987 + 0.834514i \(0.685748\pi\)
\(548\) 209664. 0.0298245
\(549\) 865242. 0.122520
\(550\) −710000. −0.100081
\(551\) 1.84471e6 0.258851
\(552\) 4.58352e6 0.640253
\(553\) −1.96790e6 −0.273647
\(554\) 3.64918e6 0.505151
\(555\) 1.93995e6 0.267336
\(556\) 2.34808e6 0.322126
\(557\) 5.37078e6 0.733499 0.366750 0.930320i \(-0.380471\pi\)
0.366750 + 0.930320i \(0.380471\pi\)
\(558\) −61236.0 −0.00832571
\(559\) −1.95853e7 −2.65095
\(560\) 360800. 0.0486179
\(561\) 2.18794e6 0.293513
\(562\) 3.15270e6 0.421058
\(563\) 1.27062e7 1.68944 0.844722 0.535205i \(-0.179766\pi\)
0.844722 + 0.535205i \(0.179766\pi\)
\(564\) 3.38386e6 0.447934
\(565\) −1.15085e6 −0.151669
\(566\) −2.69617e6 −0.353758
\(567\) 144342. 0.0188554
\(568\) 423360. 0.0550604
\(569\) 1.06604e7 1.38037 0.690183 0.723635i \(-0.257530\pi\)
0.690183 + 0.723635i \(0.257530\pi\)
\(570\) −162450. −0.0209427
\(571\) −5.38271e6 −0.690893 −0.345446 0.938439i \(-0.612272\pi\)
−0.345446 + 0.938439i \(0.612272\pi\)
\(572\) 1.66356e7 2.12593
\(573\) 2.39069e6 0.304184
\(574\) −239712. −0.0303676
\(575\) −2.65250e6 −0.334569
\(576\) −865728. −0.108724
\(577\) −9.03488e6 −1.12975 −0.564876 0.825176i \(-0.691076\pi\)
−0.564876 + 0.825176i \(0.691076\pi\)
\(578\) −2.47335e6 −0.307939
\(579\) −1.13143e6 −0.140259
\(580\) 3.57700e6 0.441519
\(581\) −1.26047e6 −0.154914
\(582\) −950364. −0.116301
\(583\) 9.52763e6 1.16095
\(584\) −9.10632e6 −1.10487
\(585\) 2.11815e6 0.255898
\(586\) −3.41079e6 −0.410309
\(587\) −3.54030e6 −0.424077 −0.212038 0.977261i \(-0.568010\pi\)
−0.212038 + 0.977261i \(0.568010\pi\)
\(588\) 4.11340e6 0.490634
\(589\) 136458. 0.0162073
\(590\) 551500. 0.0652252
\(591\) −545382. −0.0642291
\(592\) 5.65603e6 0.663296
\(593\) 2.00350e6 0.233965 0.116983 0.993134i \(-0.462678\pi\)
0.116983 + 0.993134i \(0.462678\pi\)
\(594\) −828144. −0.0963030
\(595\) −235400. −0.0272593
\(596\) 2.92068e6 0.336797
\(597\) −2.77182e6 −0.318295
\(598\) −8.87845e6 −1.01528
\(599\) −3.50202e6 −0.398797 −0.199398 0.979919i \(-0.563899\pi\)
−0.199398 + 0.979919i \(0.563899\pi\)
\(600\) −675000. −0.0765466
\(601\) −8.47016e6 −0.956545 −0.478272 0.878212i \(-0.658737\pi\)
−0.478272 + 0.878212i \(0.658737\pi\)
\(602\) −823856. −0.0926531
\(603\) −4.39571e6 −0.492306
\(604\) −8.42134e6 −0.939266
\(605\) 4.03932e6 0.448663
\(606\) −169164. −0.0187123
\(607\) −7.16889e6 −0.789733 −0.394866 0.918739i \(-0.629209\pi\)
−0.394866 + 0.918739i \(0.629209\pi\)
\(608\) −1.85987e6 −0.204044
\(609\) −1.01178e6 −0.110546
\(610\) 534100. 0.0581163
\(611\) −1.40457e7 −1.52209
\(612\) 970704. 0.104763
\(613\) −9.28124e6 −0.997597 −0.498798 0.866718i \(-0.666225\pi\)
−0.498798 + 0.866718i \(0.666225\pi\)
\(614\) 4.76762e6 0.510365
\(615\) −1.22580e6 −0.130687
\(616\) 1.49952e6 0.159221
\(617\) 7.01191e6 0.741521 0.370761 0.928728i \(-0.379097\pi\)
0.370761 + 0.928728i \(0.379097\pi\)
\(618\) 643968. 0.0678255
\(619\) 1.20603e7 1.26512 0.632562 0.774510i \(-0.282003\pi\)
0.632562 + 0.774510i \(0.282003\pi\)
\(620\) 264600. 0.0276446
\(621\) −3.09388e6 −0.321939
\(622\) −488016. −0.0505776
\(623\) 407880. 0.0421029
\(624\) 6.17558e6 0.634916
\(625\) 390625. 0.0400000
\(626\) 2.51049e6 0.256049
\(627\) 1.84543e6 0.187469
\(628\) 407904. 0.0412723
\(629\) −3.69022e6 −0.371899
\(630\) 89100.0 0.00894389
\(631\) 1.74396e7 1.74366 0.871830 0.489808i \(-0.162933\pi\)
0.871830 + 0.489808i \(0.162933\pi\)
\(632\) 1.07340e7 1.06898
\(633\) 6.69665e6 0.664275
\(634\) −5.78084e6 −0.571173
\(635\) −6.79220e6 −0.668461
\(636\) 4.22705e6 0.414376
\(637\) −1.70739e7 −1.66718
\(638\) 5.80496e6 0.564609
\(639\) −285768. −0.0276861
\(640\) −4.65600e6 −0.449328
\(641\) 3.69931e6 0.355612 0.177806 0.984066i \(-0.443100\pi\)
0.177806 + 0.984066i \(0.443100\pi\)
\(642\) −3.39854e6 −0.325428
\(643\) 1.52184e6 0.145158 0.0725789 0.997363i \(-0.476877\pi\)
0.0725789 + 0.997363i \(0.476877\pi\)
\(644\) 2.61430e6 0.248394
\(645\) −4.21290e6 −0.398733
\(646\) 309016. 0.0291340
\(647\) 1.65952e7 1.55856 0.779278 0.626678i \(-0.215586\pi\)
0.779278 + 0.626678i \(0.215586\pi\)
\(648\) −787320. −0.0736570
\(649\) −6.26504e6 −0.583865
\(650\) 1.30750e6 0.121383
\(651\) −74844.0 −0.00692157
\(652\) −9.89453e6 −0.911541
\(653\) 4.78897e6 0.439500 0.219750 0.975556i \(-0.429476\pi\)
0.219750 + 0.975556i \(0.429476\pi\)
\(654\) 2.60784e6 0.238417
\(655\) 8.61980e6 0.785044
\(656\) −3.57389e6 −0.324251
\(657\) 6.14677e6 0.555563
\(658\) −590832. −0.0531985
\(659\) −1.11973e7 −1.00438 −0.502191 0.864757i \(-0.667472\pi\)
−0.502191 + 0.864757i \(0.667472\pi\)
\(660\) 3.57840e6 0.319764
\(661\) −4.18841e6 −0.372860 −0.186430 0.982468i \(-0.559692\pi\)
−0.186430 + 0.982468i \(0.559692\pi\)
\(662\) −948296. −0.0841006
\(663\) −4.02919e6 −0.355987
\(664\) 6.87528e6 0.605160
\(665\) −198550. −0.0174107
\(666\) 1.39676e6 0.122022
\(667\) 2.16868e7 1.88748
\(668\) 4.02774e6 0.349237
\(669\) 6.99332e6 0.604113
\(670\) −2.71340e6 −0.233521
\(671\) −6.06738e6 −0.520229
\(672\) 1.02010e6 0.0871401
\(673\) −1.04587e7 −0.890099 −0.445049 0.895506i \(-0.646814\pi\)
−0.445049 + 0.895506i \(0.646814\pi\)
\(674\) −1.09124e6 −0.0925271
\(675\) 455625. 0.0384900
\(676\) −2.02390e7 −1.70343
\(677\) −9.63054e6 −0.807568 −0.403784 0.914854i \(-0.632305\pi\)
−0.403784 + 0.914854i \(0.632305\pi\)
\(678\) −828612. −0.0692272
\(679\) −1.16156e6 −0.0966865
\(680\) 1.28400e6 0.106486
\(681\) −3.40405e6 −0.281273
\(682\) 429408. 0.0353516
\(683\) 9.35044e6 0.766973 0.383487 0.923546i \(-0.374723\pi\)
0.383487 + 0.923546i \(0.374723\pi\)
\(684\) 818748. 0.0669129
\(685\) −187200. −0.0152433
\(686\) −1.45772e6 −0.118267
\(687\) −7.95249e6 −0.642852
\(688\) −1.22829e7 −0.989308
\(689\) −1.75456e7 −1.40806
\(690\) −1.90980e6 −0.152709
\(691\) 2.94225e6 0.234415 0.117207 0.993107i \(-0.462606\pi\)
0.117207 + 0.993107i \(0.462606\pi\)
\(692\) −1.52966e7 −1.21431
\(693\) −1.01218e6 −0.0800614
\(694\) 7.55380e6 0.595343
\(695\) −2.09650e6 −0.164639
\(696\) 5.51880e6 0.431839
\(697\) 2.33174e6 0.181802
\(698\) 2.89158e6 0.224645
\(699\) 4.48016e6 0.346817
\(700\) −385000. −0.0296972
\(701\) 2.08017e7 1.59883 0.799416 0.600777i \(-0.205142\pi\)
0.799416 + 0.600777i \(0.205142\pi\)
\(702\) 1.52507e6 0.116801
\(703\) −3.11254e6 −0.237535
\(704\) 6.07078e6 0.461650
\(705\) −3.02130e6 −0.228940
\(706\) −5.80741e6 −0.438501
\(707\) −206756. −0.0155564
\(708\) −2.77956e6 −0.208398
\(709\) 2.21691e6 0.165628 0.0828138 0.996565i \(-0.473609\pi\)
0.0828138 + 0.996565i \(0.473609\pi\)
\(710\) −176400. −0.0131327
\(711\) −7.24545e6 −0.537516
\(712\) −2.22480e6 −0.164472
\(713\) 1.60423e6 0.118180
\(714\) −169488. −0.0124421
\(715\) −1.48532e7 −1.08656
\(716\) −1.10636e7 −0.806521
\(717\) −3.27240e6 −0.237722
\(718\) −6.43160e6 −0.465595
\(719\) −2.32663e7 −1.67844 −0.839219 0.543793i \(-0.816988\pi\)
−0.839219 + 0.543793i \(0.816988\pi\)
\(720\) 1.32840e6 0.0954987
\(721\) 787072. 0.0563867
\(722\) 260642. 0.0186081
\(723\) −6.42382e6 −0.457033
\(724\) −1.10307e7 −0.782087
\(725\) −3.19375e6 −0.225661
\(726\) 2.90831e6 0.204786
\(727\) 1.39628e7 0.979798 0.489899 0.871779i \(-0.337034\pi\)
0.489899 + 0.871779i \(0.337034\pi\)
\(728\) −2.76144e6 −0.193111
\(729\) 531441. 0.0370370
\(730\) 3.79430e6 0.263527
\(731\) 8.01387e6 0.554688
\(732\) −2.69186e6 −0.185684
\(733\) −960884. −0.0660558 −0.0330279 0.999454i \(-0.510515\pi\)
−0.0330279 + 0.999454i \(0.510515\pi\)
\(734\) 8.02168e6 0.549573
\(735\) −3.67268e6 −0.250763
\(736\) −2.18651e7 −1.48784
\(737\) 3.08242e7 2.09037
\(738\) −882576. −0.0596501
\(739\) 1.89541e7 1.27671 0.638355 0.769742i \(-0.279615\pi\)
0.638355 + 0.769742i \(0.279615\pi\)
\(740\) −6.03540e6 −0.405160
\(741\) −3.39845e6 −0.227371
\(742\) −738056. −0.0492130
\(743\) 1.79566e7 1.19331 0.596654 0.802499i \(-0.296497\pi\)
0.596654 + 0.802499i \(0.296497\pi\)
\(744\) 408240. 0.0270385
\(745\) −2.60775e6 −0.172137
\(746\) −1.13595e6 −0.0747328
\(747\) −4.64081e6 −0.304293
\(748\) −6.80691e6 −0.444832
\(749\) −4.15378e6 −0.270544
\(750\) 281250. 0.0182574
\(751\) 1.95505e7 1.26491 0.632453 0.774599i \(-0.282048\pi\)
0.632453 + 0.774599i \(0.282048\pi\)
\(752\) −8.80877e6 −0.568029
\(753\) 1.32395e7 0.850909
\(754\) −1.06901e7 −0.684785
\(755\) 7.51905e6 0.480060
\(756\) −449064. −0.0285762
\(757\) −7.93759e6 −0.503441 −0.251721 0.967800i \(-0.580996\pi\)
−0.251721 + 0.967800i \(0.580996\pi\)
\(758\) −5.99176e6 −0.378775
\(759\) 2.16953e7 1.36698
\(760\) 1.08300e6 0.0680134
\(761\) −2.61185e7 −1.63488 −0.817441 0.576012i \(-0.804608\pi\)
−0.817441 + 0.576012i \(0.804608\pi\)
\(762\) −4.89038e6 −0.305109
\(763\) 3.18736e6 0.198207
\(764\) −7.43770e6 −0.461004
\(765\) −866700. −0.0535445
\(766\) −3.83493e6 −0.236149
\(767\) 1.15374e7 0.708139
\(768\) −274176. −0.0167736
\(769\) −1.37101e6 −0.0836036 −0.0418018 0.999126i \(-0.513310\pi\)
−0.0418018 + 0.999126i \(0.513310\pi\)
\(770\) −624800. −0.0379764
\(771\) 2.01962e6 0.122358
\(772\) 3.51999e6 0.212568
\(773\) −2.49589e6 −0.150237 −0.0751186 0.997175i \(-0.523934\pi\)
−0.0751186 + 0.997175i \(0.523934\pi\)
\(774\) −3.03329e6 −0.181996
\(775\) −236250. −0.0141292
\(776\) 6.33576e6 0.377698
\(777\) 1.70716e6 0.101443
\(778\) −1.05769e7 −0.626481
\(779\) 1.96673e6 0.116118
\(780\) −6.58980e6 −0.387825
\(781\) 2.00390e6 0.117557
\(782\) 3.63286e6 0.212438
\(783\) −3.72519e6 −0.217142
\(784\) −1.07079e7 −0.622177
\(785\) −364200. −0.0210943
\(786\) 6.20626e6 0.358322
\(787\) −348188. −0.0200390 −0.0100195 0.999950i \(-0.503189\pi\)
−0.0100195 + 0.999950i \(0.503189\pi\)
\(788\) 1.69674e6 0.0973421
\(789\) 1.18126e7 0.675546
\(790\) −4.47250e6 −0.254966
\(791\) −1.01275e6 −0.0575520
\(792\) 5.52096e6 0.312753
\(793\) 1.11734e7 0.630959
\(794\) −8.67518e6 −0.488345
\(795\) −3.77415e6 −0.211788
\(796\) 8.62344e6 0.482390
\(797\) −2.66990e7 −1.48884 −0.744421 0.667710i \(-0.767275\pi\)
−0.744421 + 0.667710i \(0.767275\pi\)
\(798\) −142956. −0.00794685
\(799\) 5.74718e6 0.318484
\(800\) 3.22000e6 0.177882
\(801\) 1.50174e6 0.0827015
\(802\) −7.71118e6 −0.423336
\(803\) −4.31032e7 −2.35896
\(804\) 1.36755e7 0.746112
\(805\) −2.33420e6 −0.126955
\(806\) −790776. −0.0428762
\(807\) 68490.0 0.00370206
\(808\) 1.12776e6 0.0607699
\(809\) −910130. −0.0488914 −0.0244457 0.999701i \(-0.507782\pi\)
−0.0244457 + 0.999701i \(0.507782\pi\)
\(810\) 328050. 0.0175682
\(811\) 1.27022e7 0.678153 0.339077 0.940759i \(-0.389885\pi\)
0.339077 + 0.940759i \(0.389885\pi\)
\(812\) 3.14776e6 0.167537
\(813\) −7.23157e6 −0.383713
\(814\) −9.79459e6 −0.518114
\(815\) 8.83440e6 0.465890
\(816\) −2.52691e6 −0.132851
\(817\) 6.75936e6 0.354283
\(818\) −8.22286e6 −0.429675
\(819\) 1.86397e6 0.0971023
\(820\) 3.81360e6 0.198062
\(821\) −2.63397e7 −1.36381 −0.681904 0.731442i \(-0.738848\pi\)
−0.681904 + 0.731442i \(0.738848\pi\)
\(822\) −134784. −0.00695759
\(823\) 1.67862e7 0.863881 0.431941 0.901902i \(-0.357829\pi\)
0.431941 + 0.901902i \(0.357829\pi\)
\(824\) −4.29312e6 −0.220270
\(825\) −3.19500e6 −0.163432
\(826\) 485320. 0.0247502
\(827\) −1.69912e7 −0.863894 −0.431947 0.901899i \(-0.642173\pi\)
−0.431947 + 0.901899i \(0.642173\pi\)
\(828\) 9.62539e6 0.487913
\(829\) 9.15460e6 0.462651 0.231325 0.972876i \(-0.425694\pi\)
0.231325 + 0.972876i \(0.425694\pi\)
\(830\) −2.86470e6 −0.144339
\(831\) 1.64213e7 0.824908
\(832\) −1.11796e7 −0.559912
\(833\) 6.98624e6 0.348844
\(834\) −1.50948e6 −0.0751471
\(835\) −3.59620e6 −0.178496
\(836\) −5.74134e6 −0.284117
\(837\) −275562. −0.0135958
\(838\) −5.85620e6 −0.288075
\(839\) 1.87430e7 0.919253 0.459627 0.888112i \(-0.347983\pi\)
0.459627 + 0.888112i \(0.347983\pi\)
\(840\) −594000. −0.0290461
\(841\) 5.60095e6 0.273069
\(842\) −9.24426e6 −0.449357
\(843\) 1.41872e7 0.687586
\(844\) −2.08340e7 −1.00674
\(845\) 1.80706e7 0.870623
\(846\) −2.17534e6 −0.104496
\(847\) 3.55461e6 0.170248
\(848\) −1.10037e7 −0.525474
\(849\) −1.21328e7 −0.577684
\(850\) −535000. −0.0253984
\(851\) −3.65918e7 −1.73205
\(852\) 889056. 0.0419595
\(853\) −3.23933e7 −1.52434 −0.762171 0.647376i \(-0.775866\pi\)
−0.762171 + 0.647376i \(0.775866\pi\)
\(854\) 470008. 0.0220526
\(855\) −731025. −0.0341993
\(856\) 2.26570e7 1.05686
\(857\) 2.64966e7 1.23236 0.616181 0.787605i \(-0.288679\pi\)
0.616181 + 0.787605i \(0.288679\pi\)
\(858\) −1.06943e7 −0.495946
\(859\) −5.87286e6 −0.271561 −0.135780 0.990739i \(-0.543354\pi\)
−0.135780 + 0.990739i \(0.543354\pi\)
\(860\) 1.31068e7 0.604297
\(861\) −1.07870e6 −0.0495900
\(862\) −1.09551e7 −0.502165
\(863\) 8.09514e6 0.369996 0.184998 0.982739i \(-0.440772\pi\)
0.184998 + 0.982739i \(0.440772\pi\)
\(864\) 3.75581e6 0.171167
\(865\) 1.36576e7 0.620634
\(866\) 7.29385e6 0.330493
\(867\) −1.11301e7 −0.502863
\(868\) 232848. 0.0104899
\(869\) 5.08076e7 2.28233
\(870\) −2.29950e6 −0.103000
\(871\) −5.67643e7 −2.53530
\(872\) −1.73856e7 −0.774281
\(873\) −4.27664e6 −0.189918
\(874\) 3.06417e6 0.135686
\(875\) 343750. 0.0151783
\(876\) −1.91233e7 −0.841980
\(877\) 4.07559e7 1.78933 0.894667 0.446734i \(-0.147413\pi\)
0.894667 + 0.446734i \(0.147413\pi\)
\(878\) −1.02036e7 −0.446702
\(879\) −1.53485e7 −0.670031
\(880\) −9.31520e6 −0.405495
\(881\) −3.05794e7 −1.32736 −0.663681 0.748016i \(-0.731007\pi\)
−0.663681 + 0.748016i \(0.731007\pi\)
\(882\) −2.64433e6 −0.114457
\(883\) 3.95008e7 1.70492 0.852459 0.522794i \(-0.175110\pi\)
0.852459 + 0.522794i \(0.175110\pi\)
\(884\) 1.25353e7 0.539514
\(885\) 2.48175e6 0.106512
\(886\) 3.34889e6 0.143323
\(887\) 1.76361e7 0.752651 0.376326 0.926487i \(-0.377187\pi\)
0.376326 + 0.926487i \(0.377187\pi\)
\(888\) −9.31176e6 −0.396277
\(889\) −5.97714e6 −0.253652
\(890\) 927000. 0.0392288
\(891\) −3.72665e6 −0.157262
\(892\) −2.17570e7 −0.915560
\(893\) 4.84751e6 0.203418
\(894\) −1.87758e6 −0.0785696
\(895\) 9.87825e6 0.412214
\(896\) −4.09728e6 −0.170500
\(897\) −3.99530e7 −1.65794
\(898\) 1.33150e7 0.550997
\(899\) 1.93158e6 0.0797101
\(900\) −1.41750e6 −0.0583333
\(901\) 7.17927e6 0.294624
\(902\) 6.18893e6 0.253279
\(903\) −3.70735e6 −0.151302
\(904\) 5.52408e6 0.224822
\(905\) 9.84880e6 0.399726
\(906\) 5.41372e6 0.219116
\(907\) −2.03963e7 −0.823255 −0.411627 0.911352i \(-0.635039\pi\)
−0.411627 + 0.911352i \(0.635039\pi\)
\(908\) 1.05904e7 0.426282
\(909\) −761238. −0.0305570
\(910\) 1.15060e6 0.0460597
\(911\) −8.32427e6 −0.332315 −0.166158 0.986099i \(-0.553136\pi\)
−0.166158 + 0.986099i \(0.553136\pi\)
\(912\) −2.13134e6 −0.0848529
\(913\) 3.25430e7 1.29205
\(914\) −5.08616e6 −0.201384
\(915\) 2.40345e6 0.0949035
\(916\) 2.47411e7 0.974271
\(917\) 7.58542e6 0.297890
\(918\) −624024. −0.0244396
\(919\) −8.00884e6 −0.312810 −0.156405 0.987693i \(-0.549991\pi\)
−0.156405 + 0.987693i \(0.549991\pi\)
\(920\) 1.27320e7 0.495938
\(921\) 2.14543e7 0.833423
\(922\) −8.57812e6 −0.332326
\(923\) −3.69029e6 −0.142579
\(924\) 3.14899e6 0.121337
\(925\) 5.38875e6 0.207078
\(926\) 1.42185e7 0.544912
\(927\) 2.89786e6 0.110759
\(928\) −2.63267e7 −1.00352
\(929\) −2.33140e7 −0.886295 −0.443147 0.896449i \(-0.646138\pi\)
−0.443147 + 0.896449i \(0.646138\pi\)
\(930\) −170100. −0.00644907
\(931\) 5.89260e6 0.222809
\(932\) −1.39383e7 −0.525617
\(933\) −2.19607e6 −0.0825929
\(934\) 1.55522e7 0.583346
\(935\) 6.07760e6 0.227354
\(936\) −1.01671e7 −0.379322
\(937\) −3.61748e7 −1.34604 −0.673019 0.739625i \(-0.735003\pi\)
−0.673019 + 0.739625i \(0.735003\pi\)
\(938\) −2.38779e6 −0.0886114
\(939\) 1.12972e7 0.418126
\(940\) 9.39960e6 0.346968
\(941\) −2.83898e6 −0.104517 −0.0522586 0.998634i \(-0.516642\pi\)
−0.0522586 + 0.998634i \(0.516642\pi\)
\(942\) −262224. −0.00962820
\(943\) 2.31213e7 0.846707
\(944\) 7.23568e6 0.264271
\(945\) 400950. 0.0146053
\(946\) 2.12705e7 0.772768
\(947\) −3.75062e7 −1.35903 −0.679513 0.733664i \(-0.737809\pi\)
−0.679513 + 0.733664i \(0.737809\pi\)
\(948\) 2.25414e7 0.814629
\(949\) 7.93768e7 2.86107
\(950\) −451250. −0.0162221
\(951\) −2.60138e7 −0.932721
\(952\) 1.12992e6 0.0404069
\(953\) −2.16804e7 −0.773276 −0.386638 0.922232i \(-0.626364\pi\)
−0.386638 + 0.922232i \(0.626364\pi\)
\(954\) −2.71739e6 −0.0966676
\(955\) 6.64080e6 0.235620
\(956\) 1.01808e7 0.360278
\(957\) 2.61223e7 0.922002
\(958\) −1.24998e7 −0.440039
\(959\) −164736. −0.00578418
\(960\) −2.40480e6 −0.0842172
\(961\) −2.84863e7 −0.995009
\(962\) 1.80372e7 0.628394
\(963\) −1.52934e7 −0.531422
\(964\) 1.99852e7 0.692654
\(965\) −3.14285e6 −0.108644
\(966\) −1.68062e6 −0.0579466
\(967\) −3.65064e7 −1.25546 −0.627730 0.778432i \(-0.716016\pi\)
−0.627730 + 0.778432i \(0.716016\pi\)
\(968\) −1.93888e7 −0.665061
\(969\) 1.39057e6 0.0475756
\(970\) −2.63990e6 −0.0900862
\(971\) 7.22236e6 0.245828 0.122914 0.992417i \(-0.460776\pi\)
0.122914 + 0.992417i \(0.460776\pi\)
\(972\) −1.65337e6 −0.0561313
\(973\) −1.84492e6 −0.0624734
\(974\) −1.83112e7 −0.618472
\(975\) 5.88375e6 0.198218
\(976\) 7.00739e6 0.235468
\(977\) 2.85227e7 0.955993 0.477996 0.878362i \(-0.341363\pi\)
0.477996 + 0.878362i \(0.341363\pi\)
\(978\) 6.36077e6 0.212649
\(979\) −1.05307e7 −0.351157
\(980\) 1.14261e7 0.380043
\(981\) 1.17353e7 0.389333
\(982\) 1.61238e7 0.533567
\(983\) −3.14578e7 −1.03835 −0.519176 0.854667i \(-0.673761\pi\)
−0.519176 + 0.854667i \(0.673761\pi\)
\(984\) 5.88384e6 0.193719
\(985\) −1.51495e6 −0.0497517
\(986\) 4.37416e6 0.143286
\(987\) −2.65874e6 −0.0868728
\(988\) 1.05730e7 0.344591
\(989\) 7.94647e7 2.58335
\(990\) −2.30040e6 −0.0745960
\(991\) −1.24902e7 −0.404004 −0.202002 0.979385i \(-0.564745\pi\)
−0.202002 + 0.979385i \(0.564745\pi\)
\(992\) −1.94746e6 −0.0628331
\(993\) −4.26733e6 −0.137336
\(994\) −155232. −0.00498328
\(995\) −7.69950e6 −0.246550
\(996\) 1.44381e7 0.461170
\(997\) 4.99147e7 1.59034 0.795171 0.606385i \(-0.207381\pi\)
0.795171 + 0.606385i \(0.207381\pi\)
\(998\) −981080. −0.0311801
\(999\) 6.28544e6 0.199261
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 285.6.a.a.1.1 1
3.2 odd 2 855.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
285.6.a.a.1.1 1 1.1 even 1 trivial
855.6.a.a.1.1 1 3.2 odd 2