Properties

Label 175.6.a.a.1.1
Level $175$
Weight $6$
Character 175.1
Self dual yes
Analytic conductor $28.067$
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] = [175,6,Mod(1,175)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(175, 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("175.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 175 = 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 175.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: \(28.0671684673\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 35)
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 175.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+8.00000 q^{2} -1.00000 q^{3} +32.0000 q^{4} -8.00000 q^{6} -49.0000 q^{7} -242.000 q^{9} +O(q^{10})\) \(q+8.00000 q^{2} -1.00000 q^{3} +32.0000 q^{4} -8.00000 q^{6} -49.0000 q^{7} -242.000 q^{9} -453.000 q^{11} -32.0000 q^{12} +969.000 q^{13} -392.000 q^{14} -1024.00 q^{16} -1637.00 q^{17} -1936.00 q^{18} -1550.00 q^{19} +49.0000 q^{21} -3624.00 q^{22} +1654.00 q^{23} +7752.00 q^{26} +485.000 q^{27} -1568.00 q^{28} -4985.00 q^{29} +1192.00 q^{31} -8192.00 q^{32} +453.000 q^{33} -13096.0 q^{34} -7744.00 q^{36} +11018.0 q^{37} -12400.0 q^{38} -969.000 q^{39} -1728.00 q^{41} +392.000 q^{42} +10814.0 q^{43} -14496.0 q^{44} +13232.0 q^{46} -26237.0 q^{47} +1024.00 q^{48} +2401.00 q^{49} +1637.00 q^{51} +31008.0 q^{52} -25936.0 q^{53} +3880.00 q^{54} +1550.00 q^{57} -39880.0 q^{58} -4580.00 q^{59} -12488.0 q^{61} +9536.00 q^{62} +11858.0 q^{63} -32768.0 q^{64} +3624.00 q^{66} +15848.0 q^{67} -52384.0 q^{68} -1654.00 q^{69} +51792.0 q^{71} -4846.00 q^{73} +88144.0 q^{74} -49600.0 q^{76} +22197.0 q^{77} -7752.00 q^{78} +62765.0 q^{79} +58321.0 q^{81} -13824.0 q^{82} +23644.0 q^{83} +1568.00 q^{84} +86512.0 q^{86} +4985.00 q^{87} -147300. q^{89} -47481.0 q^{91} +52928.0 q^{92} -1192.00 q^{93} -209896. q^{94} +8192.00 q^{96} +8343.00 q^{97} +19208.0 q^{98} +109626. q^{99} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.00000 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) −1.00000 −0.0641500 −0.0320750 0.999485i \(-0.510212\pi\)
−0.0320750 + 0.999485i \(0.510212\pi\)
\(4\) 32.0000 1.00000
\(5\) 0 0
\(6\) −8.00000 −0.0907218
\(7\) −49.0000 −0.377964
\(8\) 0 0
\(9\) −242.000 −0.995885
\(10\) 0 0
\(11\) −453.000 −1.12880 −0.564399 0.825502i \(-0.690892\pi\)
−0.564399 + 0.825502i \(0.690892\pi\)
\(12\) −32.0000 −0.0641500
\(13\) 969.000 1.59025 0.795125 0.606446i \(-0.207405\pi\)
0.795125 + 0.606446i \(0.207405\pi\)
\(14\) −392.000 −0.534522
\(15\) 0 0
\(16\) −1024.00 −1.00000
\(17\) −1637.00 −1.37381 −0.686905 0.726748i \(-0.741031\pi\)
−0.686905 + 0.726748i \(0.741031\pi\)
\(18\) −1936.00 −1.40839
\(19\) −1550.00 −0.985026 −0.492513 0.870305i \(-0.663922\pi\)
−0.492513 + 0.870305i \(0.663922\pi\)
\(20\) 0 0
\(21\) 49.0000 0.0242464
\(22\) −3624.00 −1.59636
\(23\) 1654.00 0.651952 0.325976 0.945378i \(-0.394307\pi\)
0.325976 + 0.945378i \(0.394307\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 7752.00 2.24895
\(27\) 485.000 0.128036
\(28\) −1568.00 −0.377964
\(29\) −4985.00 −1.10070 −0.550352 0.834933i \(-0.685506\pi\)
−0.550352 + 0.834933i \(0.685506\pi\)
\(30\) 0 0
\(31\) 1192.00 0.222778 0.111389 0.993777i \(-0.464470\pi\)
0.111389 + 0.993777i \(0.464470\pi\)
\(32\) −8192.00 −1.41421
\(33\) 453.000 0.0724125
\(34\) −13096.0 −1.94286
\(35\) 0 0
\(36\) −7744.00 −0.995885
\(37\) 11018.0 1.32312 0.661559 0.749893i \(-0.269895\pi\)
0.661559 + 0.749893i \(0.269895\pi\)
\(38\) −12400.0 −1.39304
\(39\) −969.000 −0.102015
\(40\) 0 0
\(41\) −1728.00 −0.160540 −0.0802702 0.996773i \(-0.525578\pi\)
−0.0802702 + 0.996773i \(0.525578\pi\)
\(42\) 392.000 0.0342896
\(43\) 10814.0 0.891898 0.445949 0.895058i \(-0.352866\pi\)
0.445949 + 0.895058i \(0.352866\pi\)
\(44\) −14496.0 −1.12880
\(45\) 0 0
\(46\) 13232.0 0.922000
\(47\) −26237.0 −1.73249 −0.866243 0.499624i \(-0.833472\pi\)
−0.866243 + 0.499624i \(0.833472\pi\)
\(48\) 1024.00 0.0641500
\(49\) 2401.00 0.142857
\(50\) 0 0
\(51\) 1637.00 0.0881299
\(52\) 31008.0 1.59025
\(53\) −25936.0 −1.26827 −0.634137 0.773220i \(-0.718645\pi\)
−0.634137 + 0.773220i \(0.718645\pi\)
\(54\) 3880.00 0.181070
\(55\) 0 0
\(56\) 0 0
\(57\) 1550.00 0.0631894
\(58\) −39880.0 −1.55663
\(59\) −4580.00 −0.171291 −0.0856457 0.996326i \(-0.527295\pi\)
−0.0856457 + 0.996326i \(0.527295\pi\)
\(60\) 0 0
\(61\) −12488.0 −0.429703 −0.214851 0.976647i \(-0.568927\pi\)
−0.214851 + 0.976647i \(0.568927\pi\)
\(62\) 9536.00 0.315055
\(63\) 11858.0 0.376409
\(64\) −32768.0 −1.00000
\(65\) 0 0
\(66\) 3624.00 0.102407
\(67\) 15848.0 0.431308 0.215654 0.976470i \(-0.430812\pi\)
0.215654 + 0.976470i \(0.430812\pi\)
\(68\) −52384.0 −1.37381
\(69\) −1654.00 −0.0418228
\(70\) 0 0
\(71\) 51792.0 1.21932 0.609659 0.792664i \(-0.291306\pi\)
0.609659 + 0.792664i \(0.291306\pi\)
\(72\) 0 0
\(73\) −4846.00 −0.106433 −0.0532165 0.998583i \(-0.516947\pi\)
−0.0532165 + 0.998583i \(0.516947\pi\)
\(74\) 88144.0 1.87117
\(75\) 0 0
\(76\) −49600.0 −0.985026
\(77\) 22197.0 0.426646
\(78\) −7752.00 −0.144270
\(79\) 62765.0 1.13149 0.565744 0.824581i \(-0.308589\pi\)
0.565744 + 0.824581i \(0.308589\pi\)
\(80\) 0 0
\(81\) 58321.0 0.987671
\(82\) −13824.0 −0.227038
\(83\) 23644.0 0.376726 0.188363 0.982099i \(-0.439682\pi\)
0.188363 + 0.982099i \(0.439682\pi\)
\(84\) 1568.00 0.0242464
\(85\) 0 0
\(86\) 86512.0 1.26133
\(87\) 4985.00 0.0706101
\(88\) 0 0
\(89\) −147300. −1.97119 −0.985593 0.169133i \(-0.945903\pi\)
−0.985593 + 0.169133i \(0.945903\pi\)
\(90\) 0 0
\(91\) −47481.0 −0.601058
\(92\) 52928.0 0.651952
\(93\) −1192.00 −0.0142912
\(94\) −209896. −2.45010
\(95\) 0 0
\(96\) 8192.00 0.0907218
\(97\) 8343.00 0.0900312 0.0450156 0.998986i \(-0.485666\pi\)
0.0450156 + 0.998986i \(0.485666\pi\)
\(98\) 19208.0 0.202031
\(99\) 109626. 1.12415
\(100\) 0 0
\(101\) −11878.0 −0.115862 −0.0579308 0.998321i \(-0.518450\pi\)
−0.0579308 + 0.998321i \(0.518450\pi\)
\(102\) 13096.0 0.124634
\(103\) 132439. 1.23005 0.615025 0.788508i \(-0.289146\pi\)
0.615025 + 0.788508i \(0.289146\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −207488. −1.79361
\(107\) −136842. −1.15547 −0.577737 0.816223i \(-0.696064\pi\)
−0.577737 + 0.816223i \(0.696064\pi\)
\(108\) 15520.0 0.128036
\(109\) 109485. 0.882650 0.441325 0.897347i \(-0.354509\pi\)
0.441325 + 0.897347i \(0.354509\pi\)
\(110\) 0 0
\(111\) −11018.0 −0.0848780
\(112\) 50176.0 0.377964
\(113\) 200934. 1.48033 0.740163 0.672428i \(-0.234748\pi\)
0.740163 + 0.672428i \(0.234748\pi\)
\(114\) 12400.0 0.0893634
\(115\) 0 0
\(116\) −159520. −1.10070
\(117\) −234498. −1.58371
\(118\) −36640.0 −0.242243
\(119\) 80213.0 0.519251
\(120\) 0 0
\(121\) 44158.0 0.274186
\(122\) −99904.0 −0.607692
\(123\) 1728.00 0.0102987
\(124\) 38144.0 0.222778
\(125\) 0 0
\(126\) 94864.0 0.532323
\(127\) −330692. −1.81934 −0.909671 0.415329i \(-0.863666\pi\)
−0.909671 + 0.415329i \(0.863666\pi\)
\(128\) 0 0
\(129\) −10814.0 −0.0572153
\(130\) 0 0
\(131\) 43982.0 0.223922 0.111961 0.993713i \(-0.464287\pi\)
0.111961 + 0.993713i \(0.464287\pi\)
\(132\) 14496.0 0.0724125
\(133\) 75950.0 0.372305
\(134\) 126784. 0.609962
\(135\) 0 0
\(136\) 0 0
\(137\) 99748.0 0.454049 0.227025 0.973889i \(-0.427100\pi\)
0.227025 + 0.973889i \(0.427100\pi\)
\(138\) −13232.0 −0.0591463
\(139\) 258930. 1.13670 0.568349 0.822787i \(-0.307582\pi\)
0.568349 + 0.822787i \(0.307582\pi\)
\(140\) 0 0
\(141\) 26237.0 0.111139
\(142\) 414336. 1.72438
\(143\) −438957. −1.79507
\(144\) 247808. 0.995885
\(145\) 0 0
\(146\) −38768.0 −0.150519
\(147\) −2401.00 −0.00916429
\(148\) 352576. 1.32312
\(149\) −498430. −1.83924 −0.919620 0.392809i \(-0.871503\pi\)
−0.919620 + 0.392809i \(0.871503\pi\)
\(150\) 0 0
\(151\) −245803. −0.877293 −0.438647 0.898660i \(-0.644542\pi\)
−0.438647 + 0.898660i \(0.644542\pi\)
\(152\) 0 0
\(153\) 396154. 1.36816
\(154\) 177576. 0.603368
\(155\) 0 0
\(156\) −31008.0 −0.102015
\(157\) 85478.0 0.276761 0.138381 0.990379i \(-0.455810\pi\)
0.138381 + 0.990379i \(0.455810\pi\)
\(158\) 502120. 1.60017
\(159\) 25936.0 0.0813599
\(160\) 0 0
\(161\) −81046.0 −0.246415
\(162\) 466568. 1.39678
\(163\) −193026. −0.569045 −0.284523 0.958669i \(-0.591835\pi\)
−0.284523 + 0.958669i \(0.591835\pi\)
\(164\) −55296.0 −0.160540
\(165\) 0 0
\(166\) 189152. 0.532771
\(167\) 157783. 0.437793 0.218897 0.975748i \(-0.429754\pi\)
0.218897 + 0.975748i \(0.429754\pi\)
\(168\) 0 0
\(169\) 567668. 1.52889
\(170\) 0 0
\(171\) 375100. 0.980972
\(172\) 346048. 0.891898
\(173\) 265659. 0.674853 0.337427 0.941352i \(-0.390444\pi\)
0.337427 + 0.941352i \(0.390444\pi\)
\(174\) 39880.0 0.0998578
\(175\) 0 0
\(176\) 463872. 1.12880
\(177\) 4580.00 0.0109883
\(178\) −1.17840e6 −2.78768
\(179\) 183660. 0.428432 0.214216 0.976786i \(-0.431280\pi\)
0.214216 + 0.976786i \(0.431280\pi\)
\(180\) 0 0
\(181\) −635048. −1.44082 −0.720411 0.693548i \(-0.756047\pi\)
−0.720411 + 0.693548i \(0.756047\pi\)
\(182\) −379848. −0.850024
\(183\) 12488.0 0.0275655
\(184\) 0 0
\(185\) 0 0
\(186\) −9536.00 −0.0202108
\(187\) 741561. 1.55075
\(188\) −839584. −1.73249
\(189\) −23765.0 −0.0483931
\(190\) 0 0
\(191\) −226613. −0.449471 −0.224735 0.974420i \(-0.572152\pi\)
−0.224735 + 0.974420i \(0.572152\pi\)
\(192\) 32768.0 0.0641500
\(193\) −46476.0 −0.0898122 −0.0449061 0.998991i \(-0.514299\pi\)
−0.0449061 + 0.998991i \(0.514299\pi\)
\(194\) 66744.0 0.127323
\(195\) 0 0
\(196\) 76832.0 0.142857
\(197\) −204972. −0.376295 −0.188148 0.982141i \(-0.560248\pi\)
−0.188148 + 0.982141i \(0.560248\pi\)
\(198\) 877008. 1.58979
\(199\) −953020. −1.70596 −0.852981 0.521942i \(-0.825208\pi\)
−0.852981 + 0.521942i \(0.825208\pi\)
\(200\) 0 0
\(201\) −15848.0 −0.0276684
\(202\) −95024.0 −0.163853
\(203\) 244265. 0.416027
\(204\) 52384.0 0.0881299
\(205\) 0 0
\(206\) 1.05951e6 1.73955
\(207\) −400268. −0.649270
\(208\) −992256. −1.59025
\(209\) 702150. 1.11190
\(210\) 0 0
\(211\) −223523. −0.345634 −0.172817 0.984954i \(-0.555287\pi\)
−0.172817 + 0.984954i \(0.555287\pi\)
\(212\) −829952. −1.26827
\(213\) −51792.0 −0.0782193
\(214\) −1.09474e6 −1.63409
\(215\) 0 0
\(216\) 0 0
\(217\) −58408.0 −0.0842021
\(218\) 875880. 1.24826
\(219\) 4846.00 0.00682768
\(220\) 0 0
\(221\) −1.58625e6 −2.18470
\(222\) −88144.0 −0.120036
\(223\) −1.01480e6 −1.36653 −0.683264 0.730171i \(-0.739440\pi\)
−0.683264 + 0.730171i \(0.739440\pi\)
\(224\) 401408. 0.534522
\(225\) 0 0
\(226\) 1.60747e6 2.09350
\(227\) −999797. −1.28780 −0.643898 0.765111i \(-0.722684\pi\)
−0.643898 + 0.765111i \(0.722684\pi\)
\(228\) 49600.0 0.0631894
\(229\) −851120. −1.07251 −0.536256 0.844055i \(-0.680162\pi\)
−0.536256 + 0.844055i \(0.680162\pi\)
\(230\) 0 0
\(231\) −22197.0 −0.0273693
\(232\) 0 0
\(233\) −1.09270e6 −1.31859 −0.659295 0.751885i \(-0.729145\pi\)
−0.659295 + 0.751885i \(0.729145\pi\)
\(234\) −1.87598e6 −2.23970
\(235\) 0 0
\(236\) −146560. −0.171291
\(237\) −62765.0 −0.0725850
\(238\) 641704. 0.734332
\(239\) 765905. 0.867322 0.433661 0.901076i \(-0.357222\pi\)
0.433661 + 0.901076i \(0.357222\pi\)
\(240\) 0 0
\(241\) −1.21094e6 −1.34301 −0.671505 0.741000i \(-0.734352\pi\)
−0.671505 + 0.741000i \(0.734352\pi\)
\(242\) 353264. 0.387758
\(243\) −176176. −0.191395
\(244\) −399616. −0.429703
\(245\) 0 0
\(246\) 13824.0 0.0145645
\(247\) −1.50195e6 −1.56644
\(248\) 0 0
\(249\) −23644.0 −0.0241670
\(250\) 0 0
\(251\) 278262. 0.278785 0.139393 0.990237i \(-0.455485\pi\)
0.139393 + 0.990237i \(0.455485\pi\)
\(252\) 379456. 0.376409
\(253\) −749262. −0.735923
\(254\) −2.64554e6 −2.57294
\(255\) 0 0
\(256\) 1.04858e6 1.00000
\(257\) 352998. 0.333380 0.166690 0.986009i \(-0.446692\pi\)
0.166690 + 0.986009i \(0.446692\pi\)
\(258\) −86512.0 −0.0809146
\(259\) −539882. −0.500091
\(260\) 0 0
\(261\) 1.20637e6 1.09617
\(262\) 351856. 0.316674
\(263\) 1.55809e6 1.38901 0.694503 0.719490i \(-0.255624\pi\)
0.694503 + 0.719490i \(0.255624\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 607600. 0.526519
\(267\) 147300. 0.126452
\(268\) 507136. 0.431308
\(269\) −1.21963e6 −1.02766 −0.513828 0.857893i \(-0.671773\pi\)
−0.513828 + 0.857893i \(0.671773\pi\)
\(270\) 0 0
\(271\) 405792. 0.335645 0.167823 0.985817i \(-0.446326\pi\)
0.167823 + 0.985817i \(0.446326\pi\)
\(272\) 1.67629e6 1.37381
\(273\) 47481.0 0.0385579
\(274\) 797984. 0.642122
\(275\) 0 0
\(276\) −52928.0 −0.0418228
\(277\) −652442. −0.510908 −0.255454 0.966821i \(-0.582225\pi\)
−0.255454 + 0.966821i \(0.582225\pi\)
\(278\) 2.07144e6 1.60753
\(279\) −288464. −0.221861
\(280\) 0 0
\(281\) 118827. 0.0897737 0.0448869 0.998992i \(-0.485707\pi\)
0.0448869 + 0.998992i \(0.485707\pi\)
\(282\) 209896. 0.157174
\(283\) −1.48801e6 −1.10443 −0.552217 0.833700i \(-0.686218\pi\)
−0.552217 + 0.833700i \(0.686218\pi\)
\(284\) 1.65734e6 1.21932
\(285\) 0 0
\(286\) −3.51166e6 −2.53862
\(287\) 84672.0 0.0606785
\(288\) 1.98246e6 1.40839
\(289\) 1.25991e6 0.887351
\(290\) 0 0
\(291\) −8343.00 −0.00577550
\(292\) −155072. −0.106433
\(293\) −1.89580e6 −1.29010 −0.645050 0.764140i \(-0.723164\pi\)
−0.645050 + 0.764140i \(0.723164\pi\)
\(294\) −19208.0 −0.0129603
\(295\) 0 0
\(296\) 0 0
\(297\) −219705. −0.144527
\(298\) −3.98744e6 −2.60108
\(299\) 1.60273e6 1.03677
\(300\) 0 0
\(301\) −529886. −0.337106
\(302\) −1.96642e6 −1.24068
\(303\) 11878.0 0.00743253
\(304\) 1.58720e6 0.985026
\(305\) 0 0
\(306\) 3.16923e6 1.93486
\(307\) 821853. 0.497678 0.248839 0.968545i \(-0.419951\pi\)
0.248839 + 0.968545i \(0.419951\pi\)
\(308\) 710304. 0.426646
\(309\) −132439. −0.0789078
\(310\) 0 0
\(311\) −2.09600e6 −1.22882 −0.614412 0.788985i \(-0.710607\pi\)
−0.614412 + 0.788985i \(0.710607\pi\)
\(312\) 0 0
\(313\) −394571. −0.227648 −0.113824 0.993501i \(-0.536310\pi\)
−0.113824 + 0.993501i \(0.536310\pi\)
\(314\) 683824. 0.391399
\(315\) 0 0
\(316\) 2.00848e6 1.13149
\(317\) −321422. −0.179650 −0.0898250 0.995958i \(-0.528631\pi\)
−0.0898250 + 0.995958i \(0.528631\pi\)
\(318\) 207488. 0.115060
\(319\) 2.25820e6 1.24247
\(320\) 0 0
\(321\) 136842. 0.0741237
\(322\) −648368. −0.348483
\(323\) 2.53735e6 1.35324
\(324\) 1.86627e6 0.987671
\(325\) 0 0
\(326\) −1.54421e6 −0.804752
\(327\) −109485. −0.0566220
\(328\) 0 0
\(329\) 1.28561e6 0.654818
\(330\) 0 0
\(331\) −2.23259e6 −1.12005 −0.560027 0.828475i \(-0.689209\pi\)
−0.560027 + 0.828475i \(0.689209\pi\)
\(332\) 756608. 0.376726
\(333\) −2.66636e6 −1.31767
\(334\) 1.26226e6 0.619133
\(335\) 0 0
\(336\) −50176.0 −0.0242464
\(337\) 3.65656e6 1.75387 0.876936 0.480608i \(-0.159584\pi\)
0.876936 + 0.480608i \(0.159584\pi\)
\(338\) 4.54134e6 2.16218
\(339\) −200934. −0.0949629
\(340\) 0 0
\(341\) −539976. −0.251471
\(342\) 3.00080e6 1.38730
\(343\) −117649. −0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 2.12527e6 0.954386
\(347\) 1.88962e6 0.842462 0.421231 0.906953i \(-0.361598\pi\)
0.421231 + 0.906953i \(0.361598\pi\)
\(348\) 159520. 0.0706101
\(349\) −2.69329e6 −1.18364 −0.591820 0.806070i \(-0.701590\pi\)
−0.591820 + 0.806070i \(0.701590\pi\)
\(350\) 0 0
\(351\) 469965. 0.203609
\(352\) 3.71098e6 1.59636
\(353\) 1.57468e6 0.672598 0.336299 0.941755i \(-0.390825\pi\)
0.336299 + 0.941755i \(0.390825\pi\)
\(354\) 36640.0 0.0155399
\(355\) 0 0
\(356\) −4.71360e6 −1.97119
\(357\) −80213.0 −0.0333100
\(358\) 1.46928e6 0.605894
\(359\) 4.05576e6 1.66087 0.830436 0.557114i \(-0.188091\pi\)
0.830436 + 0.557114i \(0.188091\pi\)
\(360\) 0 0
\(361\) −73599.0 −0.0297238
\(362\) −5.08038e6 −2.03763
\(363\) −44158.0 −0.0175891
\(364\) −1.51939e6 −0.601058
\(365\) 0 0
\(366\) 99904.0 0.0389834
\(367\) 4.90628e6 1.90146 0.950731 0.310018i \(-0.100335\pi\)
0.950731 + 0.310018i \(0.100335\pi\)
\(368\) −1.69370e6 −0.651952
\(369\) 418176. 0.159880
\(370\) 0 0
\(371\) 1.27086e6 0.479363
\(372\) −38144.0 −0.0142912
\(373\) 3.45336e6 1.28520 0.642599 0.766202i \(-0.277856\pi\)
0.642599 + 0.766202i \(0.277856\pi\)
\(374\) 5.93249e6 2.19310
\(375\) 0 0
\(376\) 0 0
\(377\) −4.83046e6 −1.75039
\(378\) −190120. −0.0684382
\(379\) −4.23466e6 −1.51433 −0.757165 0.653224i \(-0.773416\pi\)
−0.757165 + 0.653224i \(0.773416\pi\)
\(380\) 0 0
\(381\) 330692. 0.116711
\(382\) −1.81290e6 −0.635648
\(383\) 1.86460e6 0.649516 0.324758 0.945797i \(-0.394717\pi\)
0.324758 + 0.945797i \(0.394717\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −371808. −0.127014
\(387\) −2.61699e6 −0.888228
\(388\) 266976. 0.0900312
\(389\) −4.81502e6 −1.61333 −0.806666 0.591008i \(-0.798730\pi\)
−0.806666 + 0.591008i \(0.798730\pi\)
\(390\) 0 0
\(391\) −2.70760e6 −0.895658
\(392\) 0 0
\(393\) −43982.0 −0.0143646
\(394\) −1.63978e6 −0.532162
\(395\) 0 0
\(396\) 3.50803e6 1.12415
\(397\) −1.21376e6 −0.386505 −0.193253 0.981149i \(-0.561904\pi\)
−0.193253 + 0.981149i \(0.561904\pi\)
\(398\) −7.62416e6 −2.41259
\(399\) −75950.0 −0.0238834
\(400\) 0 0
\(401\) 5.90442e6 1.83365 0.916824 0.399291i \(-0.130744\pi\)
0.916824 + 0.399291i \(0.130744\pi\)
\(402\) −126784. −0.0391291
\(403\) 1.15505e6 0.354272
\(404\) −380096. −0.115862
\(405\) 0 0
\(406\) 1.95412e6 0.588351
\(407\) −4.99115e6 −1.49353
\(408\) 0 0
\(409\) 4.84289e6 1.43152 0.715758 0.698348i \(-0.246081\pi\)
0.715758 + 0.698348i \(0.246081\pi\)
\(410\) 0 0
\(411\) −99748.0 −0.0291273
\(412\) 4.23805e6 1.23005
\(413\) 224420. 0.0647420
\(414\) −3.20214e6 −0.918206
\(415\) 0 0
\(416\) −7.93805e6 −2.24895
\(417\) −258930. −0.0729193
\(418\) 5.61720e6 1.57246
\(419\) 270360. 0.0752328 0.0376164 0.999292i \(-0.488023\pi\)
0.0376164 + 0.999292i \(0.488023\pi\)
\(420\) 0 0
\(421\) 3.13648e6 0.862456 0.431228 0.902243i \(-0.358080\pi\)
0.431228 + 0.902243i \(0.358080\pi\)
\(422\) −1.78818e6 −0.488800
\(423\) 6.34935e6 1.72536
\(424\) 0 0
\(425\) 0 0
\(426\) −414336. −0.110619
\(427\) 611912. 0.162412
\(428\) −4.37894e6 −1.15547
\(429\) 438957. 0.115154
\(430\) 0 0
\(431\) −1.87703e6 −0.486719 −0.243360 0.969936i \(-0.578250\pi\)
−0.243360 + 0.969936i \(0.578250\pi\)
\(432\) −496640. −0.128036
\(433\) −3.20357e6 −0.821134 −0.410567 0.911830i \(-0.634669\pi\)
−0.410567 + 0.911830i \(0.634669\pi\)
\(434\) −467264. −0.119080
\(435\) 0 0
\(436\) 3.50352e6 0.882650
\(437\) −2.56370e6 −0.642190
\(438\) 38768.0 0.00965580
\(439\) −6.27209e6 −1.55328 −0.776642 0.629942i \(-0.783079\pi\)
−0.776642 + 0.629942i \(0.783079\pi\)
\(440\) 0 0
\(441\) −581042. −0.142269
\(442\) −1.26900e7 −3.08963
\(443\) −724986. −0.175517 −0.0877587 0.996142i \(-0.527970\pi\)
−0.0877587 + 0.996142i \(0.527970\pi\)
\(444\) −352576. −0.0848780
\(445\) 0 0
\(446\) −8.11841e6 −1.93256
\(447\) 498430. 0.117987
\(448\) 1.60563e6 0.377964
\(449\) −875985. −0.205060 −0.102530 0.994730i \(-0.532694\pi\)
−0.102530 + 0.994730i \(0.532694\pi\)
\(450\) 0 0
\(451\) 782784. 0.181218
\(452\) 6.42989e6 1.48033
\(453\) 245803. 0.0562784
\(454\) −7.99838e6 −1.82122
\(455\) 0 0
\(456\) 0 0
\(457\) 832668. 0.186501 0.0932505 0.995643i \(-0.470274\pi\)
0.0932505 + 0.995643i \(0.470274\pi\)
\(458\) −6.80896e6 −1.51676
\(459\) −793945. −0.175897
\(460\) 0 0
\(461\) 5.92115e6 1.29764 0.648820 0.760942i \(-0.275263\pi\)
0.648820 + 0.760942i \(0.275263\pi\)
\(462\) −177576. −0.0387061
\(463\) −682776. −0.148022 −0.0740109 0.997257i \(-0.523580\pi\)
−0.0740109 + 0.997257i \(0.523580\pi\)
\(464\) 5.10464e6 1.10070
\(465\) 0 0
\(466\) −8.74157e6 −1.86477
\(467\) 5.41667e6 1.14932 0.574659 0.818393i \(-0.305135\pi\)
0.574659 + 0.818393i \(0.305135\pi\)
\(468\) −7.50394e6 −1.58371
\(469\) −776552. −0.163019
\(470\) 0 0
\(471\) −85478.0 −0.0177542
\(472\) 0 0
\(473\) −4.89874e6 −1.00677
\(474\) −502120. −0.102651
\(475\) 0 0
\(476\) 2.56682e6 0.519251
\(477\) 6.27651e6 1.26306
\(478\) 6.12724e6 1.22658
\(479\) 1.98599e6 0.395493 0.197746 0.980253i \(-0.436638\pi\)
0.197746 + 0.980253i \(0.436638\pi\)
\(480\) 0 0
\(481\) 1.06764e7 2.10409
\(482\) −9.68750e6 −1.89930
\(483\) 81046.0 0.0158075
\(484\) 1.41306e6 0.274186
\(485\) 0 0
\(486\) −1.40941e6 −0.270674
\(487\) 1.06974e6 0.204388 0.102194 0.994764i \(-0.467414\pi\)
0.102194 + 0.994764i \(0.467414\pi\)
\(488\) 0 0
\(489\) 193026. 0.0365043
\(490\) 0 0
\(491\) 4.59246e6 0.859689 0.429844 0.902903i \(-0.358568\pi\)
0.429844 + 0.902903i \(0.358568\pi\)
\(492\) 55296.0 0.0102987
\(493\) 8.16045e6 1.51216
\(494\) −1.20156e7 −2.21528
\(495\) 0 0
\(496\) −1.22061e6 −0.222778
\(497\) −2.53781e6 −0.460859
\(498\) −189152. −0.0341773
\(499\) 1.96066e6 0.352492 0.176246 0.984346i \(-0.443605\pi\)
0.176246 + 0.984346i \(0.443605\pi\)
\(500\) 0 0
\(501\) −157783. −0.0280844
\(502\) 2.22610e6 0.394262
\(503\) −3.51483e6 −0.619419 −0.309709 0.950831i \(-0.600232\pi\)
−0.309709 + 0.950831i \(0.600232\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −5.99410e6 −1.04075
\(507\) −567668. −0.0980787
\(508\) −1.05821e7 −1.81934
\(509\) −1.45211e6 −0.248431 −0.124215 0.992255i \(-0.539641\pi\)
−0.124215 + 0.992255i \(0.539641\pi\)
\(510\) 0 0
\(511\) 237454. 0.0402279
\(512\) 8.38861e6 1.41421
\(513\) −751750. −0.126119
\(514\) 2.82398e6 0.471470
\(515\) 0 0
\(516\) −346048. −0.0572153
\(517\) 1.18854e7 1.95563
\(518\) −4.31906e6 −0.707236
\(519\) −265659. −0.0432918
\(520\) 0 0
\(521\) −4.24240e6 −0.684726 −0.342363 0.939568i \(-0.611227\pi\)
−0.342363 + 0.939568i \(0.611227\pi\)
\(522\) 9.65096e6 1.55022
\(523\) 7.56012e6 1.20858 0.604289 0.796765i \(-0.293457\pi\)
0.604289 + 0.796765i \(0.293457\pi\)
\(524\) 1.40742e6 0.223922
\(525\) 0 0
\(526\) 1.24648e7 1.96435
\(527\) −1.95130e6 −0.306054
\(528\) −463872. −0.0724125
\(529\) −3.70063e6 −0.574958
\(530\) 0 0
\(531\) 1.10836e6 0.170586
\(532\) 2.43040e6 0.372305
\(533\) −1.67443e6 −0.255299
\(534\) 1.17840e6 0.178830
\(535\) 0 0
\(536\) 0 0
\(537\) −183660. −0.0274839
\(538\) −9.75704e6 −1.45332
\(539\) −1.08765e6 −0.161257
\(540\) 0 0
\(541\) 1.24065e6 0.182245 0.0911224 0.995840i \(-0.470955\pi\)
0.0911224 + 0.995840i \(0.470955\pi\)
\(542\) 3.24634e6 0.474674
\(543\) 635048. 0.0924287
\(544\) 1.34103e7 1.94286
\(545\) 0 0
\(546\) 379848. 0.0545291
\(547\) 1.85057e6 0.264446 0.132223 0.991220i \(-0.457789\pi\)
0.132223 + 0.991220i \(0.457789\pi\)
\(548\) 3.19194e6 0.454049
\(549\) 3.02210e6 0.427935
\(550\) 0 0
\(551\) 7.72675e6 1.08422
\(552\) 0 0
\(553\) −3.07548e6 −0.427662
\(554\) −5.21954e6 −0.722533
\(555\) 0 0
\(556\) 8.28576e6 1.13670
\(557\) −7.77555e6 −1.06192 −0.530962 0.847396i \(-0.678169\pi\)
−0.530962 + 0.847396i \(0.678169\pi\)
\(558\) −2.30771e6 −0.313759
\(559\) 1.04788e7 1.41834
\(560\) 0 0
\(561\) −741561. −0.0994809
\(562\) 950616. 0.126959
\(563\) −8.37716e6 −1.11385 −0.556924 0.830564i \(-0.688018\pi\)
−0.556924 + 0.830564i \(0.688018\pi\)
\(564\) 839584. 0.111139
\(565\) 0 0
\(566\) −1.19041e7 −1.56191
\(567\) −2.85773e6 −0.373305
\(568\) 0 0
\(569\) −6.15591e6 −0.797098 −0.398549 0.917147i \(-0.630486\pi\)
−0.398549 + 0.917147i \(0.630486\pi\)
\(570\) 0 0
\(571\) 7.21513e6 0.926092 0.463046 0.886334i \(-0.346757\pi\)
0.463046 + 0.886334i \(0.346757\pi\)
\(572\) −1.40466e7 −1.79507
\(573\) 226613. 0.0288336
\(574\) 677376. 0.0858124
\(575\) 0 0
\(576\) 7.92986e6 0.995885
\(577\) −1.36699e7 −1.70933 −0.854666 0.519177i \(-0.826238\pi\)
−0.854666 + 0.519177i \(0.826238\pi\)
\(578\) 1.00793e7 1.25490
\(579\) 46476.0 0.00576146
\(580\) 0 0
\(581\) −1.15856e6 −0.142389
\(582\) −66744.0 −0.00816779
\(583\) 1.17490e7 1.43163
\(584\) 0 0
\(585\) 0 0
\(586\) −1.51664e7 −1.82448
\(587\) 1.00686e7 1.20608 0.603040 0.797711i \(-0.293956\pi\)
0.603040 + 0.797711i \(0.293956\pi\)
\(588\) −76832.0 −0.00916429
\(589\) −1.84760e6 −0.219442
\(590\) 0 0
\(591\) 204972. 0.0241394
\(592\) −1.12824e7 −1.32312
\(593\) −9.80615e6 −1.14515 −0.572574 0.819853i \(-0.694055\pi\)
−0.572574 + 0.819853i \(0.694055\pi\)
\(594\) −1.75764e6 −0.204392
\(595\) 0 0
\(596\) −1.59498e7 −1.83924
\(597\) 953020. 0.109438
\(598\) 1.28218e7 1.46621
\(599\) 8.26257e6 0.940911 0.470455 0.882424i \(-0.344090\pi\)
0.470455 + 0.882424i \(0.344090\pi\)
\(600\) 0 0
\(601\) −3.59492e6 −0.405978 −0.202989 0.979181i \(-0.565066\pi\)
−0.202989 + 0.979181i \(0.565066\pi\)
\(602\) −4.23909e6 −0.476740
\(603\) −3.83522e6 −0.429533
\(604\) −7.86570e6 −0.877293
\(605\) 0 0
\(606\) 95024.0 0.0105112
\(607\) 1.32969e7 1.46480 0.732401 0.680873i \(-0.238400\pi\)
0.732401 + 0.680873i \(0.238400\pi\)
\(608\) 1.26976e7 1.39304
\(609\) −244265. −0.0266881
\(610\) 0 0
\(611\) −2.54237e7 −2.75508
\(612\) 1.26769e7 1.36816
\(613\) −2.50327e6 −0.269064 −0.134532 0.990909i \(-0.542953\pi\)
−0.134532 + 0.990909i \(0.542953\pi\)
\(614\) 6.57482e6 0.703823
\(615\) 0 0
\(616\) 0 0
\(617\) −1.88254e6 −0.199082 −0.0995409 0.995033i \(-0.531737\pi\)
−0.0995409 + 0.995033i \(0.531737\pi\)
\(618\) −1.05951e6 −0.111592
\(619\) 8.21487e6 0.861736 0.430868 0.902415i \(-0.358208\pi\)
0.430868 + 0.902415i \(0.358208\pi\)
\(620\) 0 0
\(621\) 802190. 0.0834734
\(622\) −1.67680e7 −1.73782
\(623\) 7.21770e6 0.745038
\(624\) 992256. 0.102015
\(625\) 0 0
\(626\) −3.15657e6 −0.321943
\(627\) −702150. −0.0713282
\(628\) 2.73530e6 0.276761
\(629\) −1.80365e7 −1.81771
\(630\) 0 0
\(631\) 1.61155e7 1.61128 0.805638 0.592408i \(-0.201823\pi\)
0.805638 + 0.592408i \(0.201823\pi\)
\(632\) 0 0
\(633\) 223523. 0.0221724
\(634\) −2.57138e6 −0.254064
\(635\) 0 0
\(636\) 829952. 0.0813599
\(637\) 2.32657e6 0.227179
\(638\) 1.80656e7 1.75712
\(639\) −1.25337e7 −1.21430
\(640\) 0 0
\(641\) −8.50544e6 −0.817620 −0.408810 0.912619i \(-0.634056\pi\)
−0.408810 + 0.912619i \(0.634056\pi\)
\(642\) 1.09474e6 0.104827
\(643\) 1.32191e7 1.26088 0.630440 0.776238i \(-0.282874\pi\)
0.630440 + 0.776238i \(0.282874\pi\)
\(644\) −2.59347e6 −0.246415
\(645\) 0 0
\(646\) 2.02988e7 1.91377
\(647\) −1.89115e6 −0.177609 −0.0888047 0.996049i \(-0.528305\pi\)
−0.0888047 + 0.996049i \(0.528305\pi\)
\(648\) 0 0
\(649\) 2.07474e6 0.193353
\(650\) 0 0
\(651\) 58408.0 0.00540157
\(652\) −6.17683e6 −0.569045
\(653\) −4.90587e6 −0.450228 −0.225114 0.974332i \(-0.572275\pi\)
−0.225114 + 0.974332i \(0.572275\pi\)
\(654\) −875880. −0.0800756
\(655\) 0 0
\(656\) 1.76947e6 0.160540
\(657\) 1.17273e6 0.105995
\(658\) 1.02849e7 0.926052
\(659\) 1.36367e7 1.22319 0.611597 0.791169i \(-0.290527\pi\)
0.611597 + 0.791169i \(0.290527\pi\)
\(660\) 0 0
\(661\) −2.22345e6 −0.197935 −0.0989677 0.995091i \(-0.531554\pi\)
−0.0989677 + 0.995091i \(0.531554\pi\)
\(662\) −1.78607e7 −1.58399
\(663\) 1.58625e6 0.140149
\(664\) 0 0
\(665\) 0 0
\(666\) −2.13308e7 −1.86347
\(667\) −8.24519e6 −0.717606
\(668\) 5.04906e6 0.437793
\(669\) 1.01480e6 0.0876629
\(670\) 0 0
\(671\) 5.65706e6 0.485048
\(672\) −401408. −0.0342896
\(673\) −4.88484e6 −0.415731 −0.207865 0.978157i \(-0.566652\pi\)
−0.207865 + 0.978157i \(0.566652\pi\)
\(674\) 2.92525e7 2.48035
\(675\) 0 0
\(676\) 1.81654e7 1.52889
\(677\) 1.98785e7 1.66691 0.833453 0.552590i \(-0.186360\pi\)
0.833453 + 0.552590i \(0.186360\pi\)
\(678\) −1.60747e6 −0.134298
\(679\) −408807. −0.0340286
\(680\) 0 0
\(681\) 999797. 0.0826122
\(682\) −4.31981e6 −0.355634
\(683\) −4.27870e6 −0.350962 −0.175481 0.984483i \(-0.556148\pi\)
−0.175481 + 0.984483i \(0.556148\pi\)
\(684\) 1.20032e7 0.980972
\(685\) 0 0
\(686\) −941192. −0.0763604
\(687\) 851120. 0.0688017
\(688\) −1.10735e7 −0.891898
\(689\) −2.51320e7 −2.01687
\(690\) 0 0
\(691\) 9.48925e6 0.756026 0.378013 0.925800i \(-0.376607\pi\)
0.378013 + 0.925800i \(0.376607\pi\)
\(692\) 8.50109e6 0.674853
\(693\) −5.37167e6 −0.424890
\(694\) 1.51169e7 1.19142
\(695\) 0 0
\(696\) 0 0
\(697\) 2.82874e6 0.220552
\(698\) −2.15463e7 −1.67392
\(699\) 1.09270e6 0.0845875
\(700\) 0 0
\(701\) −5.86385e6 −0.450700 −0.225350 0.974278i \(-0.572353\pi\)
−0.225350 + 0.974278i \(0.572353\pi\)
\(702\) 3.75972e6 0.287947
\(703\) −1.70779e7 −1.30331
\(704\) 1.48439e7 1.12880
\(705\) 0 0
\(706\) 1.25974e7 0.951197
\(707\) 582022. 0.0437916
\(708\) 146560. 0.0109883
\(709\) −2.66670e6 −0.199232 −0.0996161 0.995026i \(-0.531761\pi\)
−0.0996161 + 0.995026i \(0.531761\pi\)
\(710\) 0 0
\(711\) −1.51891e7 −1.12683
\(712\) 0 0
\(713\) 1.97157e6 0.145241
\(714\) −641704. −0.0471074
\(715\) 0 0
\(716\) 5.87712e6 0.428432
\(717\) −765905. −0.0556387
\(718\) 3.24461e7 2.34883
\(719\) −4.46629e6 −0.322199 −0.161100 0.986938i \(-0.551504\pi\)
−0.161100 + 0.986938i \(0.551504\pi\)
\(720\) 0 0
\(721\) −6.48951e6 −0.464915
\(722\) −588792. −0.0420358
\(723\) 1.21094e6 0.0861541
\(724\) −2.03215e7 −1.44082
\(725\) 0 0
\(726\) −353264. −0.0248747
\(727\) 7.47757e6 0.524716 0.262358 0.964971i \(-0.415500\pi\)
0.262358 + 0.964971i \(0.415500\pi\)
\(728\) 0 0
\(729\) −1.39958e7 −0.975393
\(730\) 0 0
\(731\) −1.77025e7 −1.22530
\(732\) 399616. 0.0275655
\(733\) 4.39751e6 0.302306 0.151153 0.988510i \(-0.451701\pi\)
0.151153 + 0.988510i \(0.451701\pi\)
\(734\) 3.92503e7 2.68907
\(735\) 0 0
\(736\) −1.35496e7 −0.922000
\(737\) −7.17914e6 −0.486860
\(738\) 3.34541e6 0.226104
\(739\) 2.84036e7 1.91321 0.956603 0.291395i \(-0.0941195\pi\)
0.956603 + 0.291395i \(0.0941195\pi\)
\(740\) 0 0
\(741\) 1.50195e6 0.100487
\(742\) 1.01669e7 0.677921
\(743\) 1.96012e7 1.30260 0.651299 0.758821i \(-0.274224\pi\)
0.651299 + 0.758821i \(0.274224\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 2.76269e7 1.81755
\(747\) −5.72185e6 −0.375176
\(748\) 2.37300e7 1.55075
\(749\) 6.70526e6 0.436728
\(750\) 0 0
\(751\) −2.60344e6 −0.168441 −0.0842206 0.996447i \(-0.526840\pi\)
−0.0842206 + 0.996447i \(0.526840\pi\)
\(752\) 2.68667e7 1.73249
\(753\) −278262. −0.0178841
\(754\) −3.86437e7 −2.47543
\(755\) 0 0
\(756\) −760480. −0.0483931
\(757\) 2.98869e7 1.89558 0.947789 0.318899i \(-0.103313\pi\)
0.947789 + 0.318899i \(0.103313\pi\)
\(758\) −3.38773e7 −2.14159
\(759\) 749262. 0.0472095
\(760\) 0 0
\(761\) 1.21470e7 0.760338 0.380169 0.924917i \(-0.375866\pi\)
0.380169 + 0.924917i \(0.375866\pi\)
\(762\) 2.64554e6 0.165054
\(763\) −5.36476e6 −0.333610
\(764\) −7.25162e6 −0.449471
\(765\) 0 0
\(766\) 1.49168e7 0.918554
\(767\) −4.43802e6 −0.272396
\(768\) −1.04858e6 −0.0641500
\(769\) 4.53845e6 0.276753 0.138376 0.990380i \(-0.455812\pi\)
0.138376 + 0.990380i \(0.455812\pi\)
\(770\) 0 0
\(771\) −352998. −0.0213863
\(772\) −1.48723e6 −0.0898122
\(773\) −1.93330e7 −1.16372 −0.581861 0.813288i \(-0.697675\pi\)
−0.581861 + 0.813288i \(0.697675\pi\)
\(774\) −2.09359e7 −1.25614
\(775\) 0 0
\(776\) 0 0
\(777\) 539882. 0.0320809
\(778\) −3.85201e7 −2.28160
\(779\) 2.67840e6 0.158136
\(780\) 0 0
\(781\) −2.34618e7 −1.37636
\(782\) −2.16608e7 −1.26665
\(783\) −2.41772e6 −0.140930
\(784\) −2.45862e6 −0.142857
\(785\) 0 0
\(786\) −351856. −0.0203146
\(787\) −1.66392e7 −0.957627 −0.478814 0.877917i \(-0.658933\pi\)
−0.478814 + 0.877917i \(0.658933\pi\)
\(788\) −6.55910e6 −0.376295
\(789\) −1.55809e6 −0.0891048
\(790\) 0 0
\(791\) −9.84577e6 −0.559511
\(792\) 0 0
\(793\) −1.21009e7 −0.683335
\(794\) −9.71006e6 −0.546601
\(795\) 0 0
\(796\) −3.04966e7 −1.70596
\(797\) −1.80409e7 −1.00603 −0.503017 0.864276i \(-0.667777\pi\)
−0.503017 + 0.864276i \(0.667777\pi\)
\(798\) −607600. −0.0337762
\(799\) 4.29500e7 2.38010
\(800\) 0 0
\(801\) 3.56466e7 1.96307
\(802\) 4.72353e7 2.59317
\(803\) 2.19524e6 0.120141
\(804\) −507136. −0.0276684
\(805\) 0 0
\(806\) 9.24038e6 0.501017
\(807\) 1.21963e6 0.0659241
\(808\) 0 0
\(809\) 2.33891e7 1.25644 0.628220 0.778036i \(-0.283784\pi\)
0.628220 + 0.778036i \(0.283784\pi\)
\(810\) 0 0
\(811\) −2.29037e7 −1.22279 −0.611397 0.791324i \(-0.709392\pi\)
−0.611397 + 0.791324i \(0.709392\pi\)
\(812\) 7.81648e6 0.416027
\(813\) −405792. −0.0215316
\(814\) −3.99292e7 −2.11218
\(815\) 0 0
\(816\) −1.67629e6 −0.0881299
\(817\) −1.67617e7 −0.878543
\(818\) 3.87431e7 2.02447
\(819\) 1.14904e7 0.598585
\(820\) 0 0
\(821\) −1.80745e7 −0.935853 −0.467926 0.883767i \(-0.654999\pi\)
−0.467926 + 0.883767i \(0.654999\pi\)
\(822\) −797984. −0.0411922
\(823\) −1.17989e7 −0.607216 −0.303608 0.952797i \(-0.598191\pi\)
−0.303608 + 0.952797i \(0.598191\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 1.79536e6 0.0915591
\(827\) −2.57650e6 −0.130999 −0.0654993 0.997853i \(-0.520864\pi\)
−0.0654993 + 0.997853i \(0.520864\pi\)
\(828\) −1.28086e7 −0.649270
\(829\) −3.84340e7 −1.94236 −0.971178 0.238356i \(-0.923392\pi\)
−0.971178 + 0.238356i \(0.923392\pi\)
\(830\) 0 0
\(831\) 652442. 0.0327747
\(832\) −3.17522e7 −1.59025
\(833\) −3.93044e6 −0.196258
\(834\) −2.07144e6 −0.103123
\(835\) 0 0
\(836\) 2.24688e7 1.11190
\(837\) 578120. 0.0285236
\(838\) 2.16288e6 0.106395
\(839\) −1.24222e7 −0.609247 −0.304623 0.952473i \(-0.598531\pi\)
−0.304623 + 0.952473i \(0.598531\pi\)
\(840\) 0 0
\(841\) 4.33908e6 0.211547
\(842\) 2.50918e7 1.21970
\(843\) −118827. −0.00575899
\(844\) −7.15274e6 −0.345634
\(845\) 0 0
\(846\) 5.07948e7 2.44002
\(847\) −2.16374e6 −0.103633
\(848\) 2.65585e7 1.26827
\(849\) 1.48801e6 0.0708495
\(850\) 0 0
\(851\) 1.82238e7 0.862610
\(852\) −1.65734e6 −0.0782193
\(853\) −7.92067e6 −0.372726 −0.186363 0.982481i \(-0.559670\pi\)
−0.186363 + 0.982481i \(0.559670\pi\)
\(854\) 4.89530e6 0.229686
\(855\) 0 0
\(856\) 0 0
\(857\) −1.48983e7 −0.692924 −0.346462 0.938064i \(-0.612617\pi\)
−0.346462 + 0.938064i \(0.612617\pi\)
\(858\) 3.51166e6 0.162852
\(859\) −1.38740e7 −0.641534 −0.320767 0.947158i \(-0.603941\pi\)
−0.320767 + 0.947158i \(0.603941\pi\)
\(860\) 0 0
\(861\) −84672.0 −0.00389253
\(862\) −1.50163e7 −0.688325
\(863\) −1.25500e7 −0.573610 −0.286805 0.957989i \(-0.592593\pi\)
−0.286805 + 0.957989i \(0.592593\pi\)
\(864\) −3.97312e6 −0.181070
\(865\) 0 0
\(866\) −2.56285e7 −1.16126
\(867\) −1.25991e6 −0.0569236
\(868\) −1.86906e6 −0.0842021
\(869\) −2.84325e7 −1.27722
\(870\) 0 0
\(871\) 1.53567e7 0.685887
\(872\) 0 0
\(873\) −2.01901e6 −0.0896607
\(874\) −2.05096e7 −0.908194
\(875\) 0 0
\(876\) 155072. 0.00682768
\(877\) 2.86002e7 1.25565 0.627827 0.778353i \(-0.283944\pi\)
0.627827 + 0.778353i \(0.283944\pi\)
\(878\) −5.01767e7 −2.19668
\(879\) 1.89580e6 0.0827600
\(880\) 0 0
\(881\) 4.09608e7 1.77799 0.888993 0.457922i \(-0.151406\pi\)
0.888993 + 0.457922i \(0.151406\pi\)
\(882\) −4.64834e6 −0.201199
\(883\) −1.30504e7 −0.563279 −0.281639 0.959520i \(-0.590878\pi\)
−0.281639 + 0.959520i \(0.590878\pi\)
\(884\) −5.07601e7 −2.18470
\(885\) 0 0
\(886\) −5.79989e6 −0.248219
\(887\) −2.53595e7 −1.08226 −0.541129 0.840939i \(-0.682003\pi\)
−0.541129 + 0.840939i \(0.682003\pi\)
\(888\) 0 0
\(889\) 1.62039e7 0.687647
\(890\) 0 0
\(891\) −2.64194e7 −1.11488
\(892\) −3.24736e7 −1.36653
\(893\) 4.06674e7 1.70654
\(894\) 3.98744e6 0.166859
\(895\) 0 0
\(896\) 0 0
\(897\) −1.60273e6 −0.0665087
\(898\) −7.00788e6 −0.289999
\(899\) −5.94212e6 −0.245212
\(900\) 0 0
\(901\) 4.24572e7 1.74237
\(902\) 6.26227e6 0.256281
\(903\) 529886. 0.0216253
\(904\) 0 0
\(905\) 0 0
\(906\) 1.96642e6 0.0795897
\(907\) −1.98595e7 −0.801585 −0.400793 0.916169i \(-0.631265\pi\)
−0.400793 + 0.916169i \(0.631265\pi\)
\(908\) −3.19935e7 −1.28780
\(909\) 2.87448e6 0.115385
\(910\) 0 0
\(911\) −1.99344e7 −0.795808 −0.397904 0.917427i \(-0.630262\pi\)
−0.397904 + 0.917427i \(0.630262\pi\)
\(912\) −1.58720e6 −0.0631894
\(913\) −1.07107e7 −0.425248
\(914\) 6.66134e6 0.263752
\(915\) 0 0
\(916\) −2.72358e7 −1.07251
\(917\) −2.15512e6 −0.0846346
\(918\) −6.35156e6 −0.248756
\(919\) −1.10695e7 −0.432355 −0.216178 0.976354i \(-0.569359\pi\)
−0.216178 + 0.976354i \(0.569359\pi\)
\(920\) 0 0
\(921\) −821853. −0.0319260
\(922\) 4.73692e7 1.83514
\(923\) 5.01864e7 1.93902
\(924\) −710304. −0.0273693
\(925\) 0 0
\(926\) −5.46221e6 −0.209334
\(927\) −3.20502e7 −1.22499
\(928\) 4.08371e7 1.55663
\(929\) −3.25682e7 −1.23810 −0.619048 0.785353i \(-0.712481\pi\)
−0.619048 + 0.785353i \(0.712481\pi\)
\(930\) 0 0
\(931\) −3.72155e6 −0.140718
\(932\) −3.49663e7 −1.31859
\(933\) 2.09600e6 0.0788291
\(934\) 4.33334e7 1.62538
\(935\) 0 0
\(936\) 0 0
\(937\) −3.15690e7 −1.17466 −0.587329 0.809348i \(-0.699821\pi\)
−0.587329 + 0.809348i \(0.699821\pi\)
\(938\) −6.21242e6 −0.230544
\(939\) 394571. 0.0146036
\(940\) 0 0
\(941\) −3.67997e7 −1.35479 −0.677393 0.735622i \(-0.736890\pi\)
−0.677393 + 0.735622i \(0.736890\pi\)
\(942\) −683824. −0.0251083
\(943\) −2.85811e6 −0.104665
\(944\) 4.68992e6 0.171291
\(945\) 0 0
\(946\) −3.91899e7 −1.42379
\(947\) −1.88453e7 −0.682853 −0.341426 0.939909i \(-0.610910\pi\)
−0.341426 + 0.939909i \(0.610910\pi\)
\(948\) −2.00848e6 −0.0725850
\(949\) −4.69577e6 −0.169255
\(950\) 0 0
\(951\) 321422. 0.0115246
\(952\) 0 0
\(953\) 1.25120e7 0.446265 0.223133 0.974788i \(-0.428372\pi\)
0.223133 + 0.974788i \(0.428372\pi\)
\(954\) 5.02121e7 1.78623
\(955\) 0 0
\(956\) 2.45090e7 0.867322
\(957\) −2.25820e6 −0.0797046
\(958\) 1.58879e7 0.559311
\(959\) −4.88765e6 −0.171614
\(960\) 0 0
\(961\) −2.72083e7 −0.950370
\(962\) 8.54115e7 2.97563
\(963\) 3.31158e7 1.15072
\(964\) −3.87500e7 −1.34301
\(965\) 0 0
\(966\) 648368. 0.0223552
\(967\) 3.42344e7 1.17733 0.588663 0.808379i \(-0.299654\pi\)
0.588663 + 0.808379i \(0.299654\pi\)
\(968\) 0 0
\(969\) −2.53735e6 −0.0868102
\(970\) 0 0
\(971\) −2.62027e7 −0.891864 −0.445932 0.895067i \(-0.647128\pi\)
−0.445932 + 0.895067i \(0.647128\pi\)
\(972\) −5.63763e6 −0.191395
\(973\) −1.26876e7 −0.429632
\(974\) 8.55790e6 0.289048
\(975\) 0 0
\(976\) 1.27877e7 0.429703
\(977\) 8.01114e6 0.268508 0.134254 0.990947i \(-0.457136\pi\)
0.134254 + 0.990947i \(0.457136\pi\)
\(978\) 1.54421e6 0.0516248
\(979\) 6.67269e7 2.22507
\(980\) 0 0
\(981\) −2.64954e7 −0.879017
\(982\) 3.67397e7 1.21578
\(983\) 4.60126e7 1.51877 0.759387 0.650639i \(-0.225499\pi\)
0.759387 + 0.650639i \(0.225499\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 6.52836e7 2.13851
\(987\) −1.28561e6 −0.0420066
\(988\) −4.80624e7 −1.56644
\(989\) 1.78864e7 0.581475
\(990\) 0 0
\(991\) −3.75828e7 −1.21564 −0.607821 0.794074i \(-0.707956\pi\)
−0.607821 + 0.794074i \(0.707956\pi\)
\(992\) −9.76486e6 −0.315055
\(993\) 2.23259e6 0.0718514
\(994\) −2.03025e7 −0.651753
\(995\) 0 0
\(996\) −756608. −0.0241670
\(997\) −2.22066e7 −0.707529 −0.353765 0.935334i \(-0.615099\pi\)
−0.353765 + 0.935334i \(0.615099\pi\)
\(998\) 1.56852e7 0.498500
\(999\) 5.34373e6 0.169407
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 175.6.a.a.1.1 1
5.2 odd 4 175.6.b.b.99.2 2
5.3 odd 4 175.6.b.b.99.1 2
5.4 even 2 35.6.a.a.1.1 1
15.14 odd 2 315.6.a.a.1.1 1
20.19 odd 2 560.6.a.c.1.1 1
35.34 odd 2 245.6.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.6.a.a.1.1 1 5.4 even 2
175.6.a.a.1.1 1 1.1 even 1 trivial
175.6.b.b.99.1 2 5.3 odd 4
175.6.b.b.99.2 2 5.2 odd 4
245.6.a.a.1.1 1 35.34 odd 2
315.6.a.a.1.1 1 15.14 odd 2
560.6.a.c.1.1 1 20.19 odd 2