Properties

Label 495.6.a.p.1.4
Level $495$
Weight $6$
Character 495.1
Self dual yes
Analytic conductor $79.390$
Analytic rank $0$
Dimension $10$
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] = [495,6,Mod(1,495)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(495, 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("495.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 495 = 3^{2} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 495.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: \(79.3899908074\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 3 x^{9} - 246 x^{8} + 640 x^{7} + 20433 x^{6} - 44595 x^{5} - 667026 x^{4} + 1173648 x^{3} + 7949136 x^{2} - 8226800 x - 30445728 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{6} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-3.29463\) of defining polynomial
Character \(\chi\) \(=\) 495.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.29463 q^{2} -21.1454 q^{4} +25.0000 q^{5} -180.725 q^{7} +175.095 q^{8} +O(q^{10})\) \(q-3.29463 q^{2} -21.1454 q^{4} +25.0000 q^{5} -180.725 q^{7} +175.095 q^{8} -82.3658 q^{10} -121.000 q^{11} -945.350 q^{13} +595.423 q^{14} +99.7806 q^{16} +844.526 q^{17} -2418.74 q^{19} -528.635 q^{20} +398.651 q^{22} -1493.94 q^{23} +625.000 q^{25} +3114.58 q^{26} +3821.51 q^{28} +3410.10 q^{29} -7071.07 q^{31} -5931.77 q^{32} -2782.40 q^{34} -4518.13 q^{35} -270.574 q^{37} +7968.85 q^{38} +4377.36 q^{40} -5475.08 q^{41} -14747.4 q^{43} +2558.59 q^{44} +4921.97 q^{46} -6997.75 q^{47} +15854.6 q^{49} -2059.15 q^{50} +19989.8 q^{52} +11572.5 q^{53} -3025.00 q^{55} -31644.0 q^{56} -11235.0 q^{58} -25557.7 q^{59} +30403.1 q^{61} +23296.6 q^{62} +16350.0 q^{64} -23633.7 q^{65} -29343.2 q^{67} -17857.8 q^{68} +14885.6 q^{70} -82066.9 q^{71} +26184.8 q^{73} +891.443 q^{74} +51145.1 q^{76} +21867.7 q^{77} -61005.4 q^{79} +2494.51 q^{80} +18038.4 q^{82} +109129. q^{83} +21113.2 q^{85} +48587.2 q^{86} -21186.4 q^{88} -63238.7 q^{89} +170848. q^{91} +31589.9 q^{92} +23055.0 q^{94} -60468.4 q^{95} +14447.4 q^{97} -52235.1 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 3 q^{2} + 181 q^{4} + 250 q^{5} + 116 q^{7} + 129 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 3 q^{2} + 181 q^{4} + 250 q^{5} + 116 q^{7} + 129 q^{8} + 75 q^{10} - 1210 q^{11} + 932 q^{13} - 1332 q^{14} + 2701 q^{16} + 96 q^{17} + 1664 q^{19} + 4525 q^{20} - 363 q^{22} + 6288 q^{23} + 6250 q^{25} + 13380 q^{26} + 13868 q^{28} + 11208 q^{29} + 9032 q^{31} + 9801 q^{32} + 14610 q^{34} + 2900 q^{35} + 21572 q^{37} + 15870 q^{38} + 3225 q^{40} + 10800 q^{41} + 21128 q^{43} - 21901 q^{44} + 83982 q^{46} - 17400 q^{47} + 71610 q^{49} + 1875 q^{50} + 40640 q^{52} + 5004 q^{53} - 30250 q^{55} - 54012 q^{56} - 9786 q^{58} - 25272 q^{59} + 52004 q^{61} + 34740 q^{62} + 56953 q^{64} + 23300 q^{65} + 4160 q^{67} - 87978 q^{68} - 33300 q^{70} - 65232 q^{71} + 44252 q^{73} - 49842 q^{74} + 233246 q^{76} - 14036 q^{77} + 112604 q^{79} + 67525 q^{80} + 167910 q^{82} + 70032 q^{83} + 2400 q^{85} - 72978 q^{86} - 15609 q^{88} - 46848 q^{89} + 130672 q^{91} + 121302 q^{92} + 252294 q^{94} + 41600 q^{95} + 129932 q^{97} - 316137 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.29463 −0.582414 −0.291207 0.956660i \(-0.594057\pi\)
−0.291207 + 0.956660i \(0.594057\pi\)
\(3\) 0 0
\(4\) −21.1454 −0.660794
\(5\) 25.0000 0.447214
\(6\) 0 0
\(7\) −180.725 −1.39403 −0.697017 0.717054i \(-0.745490\pi\)
−0.697017 + 0.717054i \(0.745490\pi\)
\(8\) 175.095 0.967270
\(9\) 0 0
\(10\) −82.3658 −0.260464
\(11\) −121.000 −0.301511
\(12\) 0 0
\(13\) −945.350 −1.55144 −0.775718 0.631079i \(-0.782612\pi\)
−0.775718 + 0.631079i \(0.782612\pi\)
\(14\) 595.423 0.811906
\(15\) 0 0
\(16\) 99.7806 0.0974420
\(17\) 844.526 0.708746 0.354373 0.935104i \(-0.384694\pi\)
0.354373 + 0.935104i \(0.384694\pi\)
\(18\) 0 0
\(19\) −2418.74 −1.53711 −0.768554 0.639785i \(-0.779024\pi\)
−0.768554 + 0.639785i \(0.779024\pi\)
\(20\) −528.635 −0.295516
\(21\) 0 0
\(22\) 398.651 0.175604
\(23\) −1493.94 −0.588860 −0.294430 0.955673i \(-0.595130\pi\)
−0.294430 + 0.955673i \(0.595130\pi\)
\(24\) 0 0
\(25\) 625.000 0.200000
\(26\) 3114.58 0.903579
\(27\) 0 0
\(28\) 3821.51 0.921169
\(29\) 3410.10 0.752961 0.376480 0.926425i \(-0.377134\pi\)
0.376480 + 0.926425i \(0.377134\pi\)
\(30\) 0 0
\(31\) −7071.07 −1.32154 −0.660771 0.750587i \(-0.729771\pi\)
−0.660771 + 0.750587i \(0.729771\pi\)
\(32\) −5931.77 −1.02402
\(33\) 0 0
\(34\) −2782.40 −0.412784
\(35\) −4518.13 −0.623431
\(36\) 0 0
\(37\) −270.574 −0.0324925 −0.0162462 0.999868i \(-0.505172\pi\)
−0.0162462 + 0.999868i \(0.505172\pi\)
\(38\) 7968.85 0.895234
\(39\) 0 0
\(40\) 4377.36 0.432576
\(41\) −5475.08 −0.508664 −0.254332 0.967117i \(-0.581856\pi\)
−0.254332 + 0.967117i \(0.581856\pi\)
\(42\) 0 0
\(43\) −14747.4 −1.21631 −0.608154 0.793819i \(-0.708090\pi\)
−0.608154 + 0.793819i \(0.708090\pi\)
\(44\) 2558.59 0.199237
\(45\) 0 0
\(46\) 4921.97 0.342961
\(47\) −6997.75 −0.462077 −0.231038 0.972945i \(-0.574212\pi\)
−0.231038 + 0.972945i \(0.574212\pi\)
\(48\) 0 0
\(49\) 15854.6 0.943333
\(50\) −2059.15 −0.116483
\(51\) 0 0
\(52\) 19989.8 1.02518
\(53\) 11572.5 0.565900 0.282950 0.959135i \(-0.408687\pi\)
0.282950 + 0.959135i \(0.408687\pi\)
\(54\) 0 0
\(55\) −3025.00 −0.134840
\(56\) −31644.0 −1.34841
\(57\) 0 0
\(58\) −11235.0 −0.438535
\(59\) −25557.7 −0.955855 −0.477928 0.878399i \(-0.658612\pi\)
−0.477928 + 0.878399i \(0.658612\pi\)
\(60\) 0 0
\(61\) 30403.1 1.04615 0.523075 0.852287i \(-0.324785\pi\)
0.523075 + 0.852287i \(0.324785\pi\)
\(62\) 23296.6 0.769685
\(63\) 0 0
\(64\) 16350.0 0.498963
\(65\) −23633.7 −0.693824
\(66\) 0 0
\(67\) −29343.2 −0.798583 −0.399291 0.916824i \(-0.630744\pi\)
−0.399291 + 0.916824i \(0.630744\pi\)
\(68\) −17857.8 −0.468335
\(69\) 0 0
\(70\) 14885.6 0.363095
\(71\) −82066.9 −1.93207 −0.966033 0.258418i \(-0.916799\pi\)
−0.966033 + 0.258418i \(0.916799\pi\)
\(72\) 0 0
\(73\) 26184.8 0.575097 0.287549 0.957766i \(-0.407160\pi\)
0.287549 + 0.957766i \(0.407160\pi\)
\(74\) 891.443 0.0189241
\(75\) 0 0
\(76\) 51145.1 1.01571
\(77\) 21867.7 0.420317
\(78\) 0 0
\(79\) −61005.4 −1.09977 −0.549883 0.835242i \(-0.685328\pi\)
−0.549883 + 0.835242i \(0.685328\pi\)
\(80\) 2494.51 0.0435774
\(81\) 0 0
\(82\) 18038.4 0.296253
\(83\) 109129. 1.73879 0.869394 0.494120i \(-0.164510\pi\)
0.869394 + 0.494120i \(0.164510\pi\)
\(84\) 0 0
\(85\) 21113.2 0.316961
\(86\) 48587.2 0.708395
\(87\) 0 0
\(88\) −21186.4 −0.291643
\(89\) −63238.7 −0.846268 −0.423134 0.906067i \(-0.639070\pi\)
−0.423134 + 0.906067i \(0.639070\pi\)
\(90\) 0 0
\(91\) 170848. 2.16276
\(92\) 31589.9 0.389115
\(93\) 0 0
\(94\) 23055.0 0.269120
\(95\) −60468.4 −0.687416
\(96\) 0 0
\(97\) 14447.4 0.155905 0.0779525 0.996957i \(-0.475162\pi\)
0.0779525 + 0.996957i \(0.475162\pi\)
\(98\) −52235.1 −0.549410
\(99\) 0 0
\(100\) −13215.9 −0.132159
\(101\) 200117. 1.95201 0.976004 0.217752i \(-0.0698725\pi\)
0.976004 + 0.217752i \(0.0698725\pi\)
\(102\) 0 0
\(103\) 91402.9 0.848920 0.424460 0.905447i \(-0.360464\pi\)
0.424460 + 0.905447i \(0.360464\pi\)
\(104\) −165526. −1.50066
\(105\) 0 0
\(106\) −38127.3 −0.329588
\(107\) −103550. −0.874358 −0.437179 0.899375i \(-0.644022\pi\)
−0.437179 + 0.899375i \(0.644022\pi\)
\(108\) 0 0
\(109\) −70943.0 −0.571931 −0.285965 0.958240i \(-0.592314\pi\)
−0.285965 + 0.958240i \(0.592314\pi\)
\(110\) 9966.26 0.0785327
\(111\) 0 0
\(112\) −18032.9 −0.135838
\(113\) −26564.6 −0.195707 −0.0978537 0.995201i \(-0.531198\pi\)
−0.0978537 + 0.995201i \(0.531198\pi\)
\(114\) 0 0
\(115\) −37348.4 −0.263346
\(116\) −72107.9 −0.497552
\(117\) 0 0
\(118\) 84203.3 0.556704
\(119\) −152627. −0.988017
\(120\) 0 0
\(121\) 14641.0 0.0909091
\(122\) −100167. −0.609292
\(123\) 0 0
\(124\) 149521. 0.873267
\(125\) 15625.0 0.0894427
\(126\) 0 0
\(127\) −56632.1 −0.311568 −0.155784 0.987791i \(-0.549790\pi\)
−0.155784 + 0.987791i \(0.549790\pi\)
\(128\) 135949. 0.733419
\(129\) 0 0
\(130\) 77864.5 0.404093
\(131\) 267308. 1.36092 0.680462 0.732783i \(-0.261779\pi\)
0.680462 + 0.732783i \(0.261779\pi\)
\(132\) 0 0
\(133\) 437127. 2.14278
\(134\) 96674.9 0.465106
\(135\) 0 0
\(136\) 147872. 0.685549
\(137\) −31486.0 −0.143323 −0.0716615 0.997429i \(-0.522830\pi\)
−0.0716615 + 0.997429i \(0.522830\pi\)
\(138\) 0 0
\(139\) 204257. 0.896686 0.448343 0.893862i \(-0.352014\pi\)
0.448343 + 0.893862i \(0.352014\pi\)
\(140\) 95537.7 0.411959
\(141\) 0 0
\(142\) 270380. 1.12526
\(143\) 114387. 0.467776
\(144\) 0 0
\(145\) 85252.5 0.336734
\(146\) −86269.2 −0.334945
\(147\) 0 0
\(148\) 5721.40 0.0214708
\(149\) 73706.2 0.271981 0.135990 0.990710i \(-0.456578\pi\)
0.135990 + 0.990710i \(0.456578\pi\)
\(150\) 0 0
\(151\) 394152. 1.40677 0.703383 0.710811i \(-0.251672\pi\)
0.703383 + 0.710811i \(0.251672\pi\)
\(152\) −423508. −1.48680
\(153\) 0 0
\(154\) −72046.2 −0.244799
\(155\) −176777. −0.591012
\(156\) 0 0
\(157\) −103881. −0.336345 −0.168173 0.985758i \(-0.553787\pi\)
−0.168173 + 0.985758i \(0.553787\pi\)
\(158\) 200990. 0.640519
\(159\) 0 0
\(160\) −148294. −0.457956
\(161\) 269992. 0.820892
\(162\) 0 0
\(163\) −128673. −0.379330 −0.189665 0.981849i \(-0.560740\pi\)
−0.189665 + 0.981849i \(0.560740\pi\)
\(164\) 115773. 0.336122
\(165\) 0 0
\(166\) −359541. −1.01269
\(167\) 172447. 0.478481 0.239240 0.970960i \(-0.423102\pi\)
0.239240 + 0.970960i \(0.423102\pi\)
\(168\) 0 0
\(169\) 522393. 1.40696
\(170\) −69560.1 −0.184603
\(171\) 0 0
\(172\) 311839. 0.803729
\(173\) 729257. 1.85253 0.926265 0.376872i \(-0.123000\pi\)
0.926265 + 0.376872i \(0.123000\pi\)
\(174\) 0 0
\(175\) −112953. −0.278807
\(176\) −12073.5 −0.0293799
\(177\) 0 0
\(178\) 208348. 0.492879
\(179\) 569405. 1.32828 0.664138 0.747610i \(-0.268799\pi\)
0.664138 + 0.747610i \(0.268799\pi\)
\(180\) 0 0
\(181\) −57038.7 −0.129412 −0.0647058 0.997904i \(-0.520611\pi\)
−0.0647058 + 0.997904i \(0.520611\pi\)
\(182\) −562883. −1.25962
\(183\) 0 0
\(184\) −261580. −0.569587
\(185\) −6764.36 −0.0145311
\(186\) 0 0
\(187\) −102188. −0.213695
\(188\) 147970. 0.305337
\(189\) 0 0
\(190\) 199221. 0.400361
\(191\) 8693.32 0.0172426 0.00862129 0.999963i \(-0.497256\pi\)
0.00862129 + 0.999963i \(0.497256\pi\)
\(192\) 0 0
\(193\) −373496. −0.721760 −0.360880 0.932612i \(-0.617524\pi\)
−0.360880 + 0.932612i \(0.617524\pi\)
\(194\) −47598.8 −0.0908013
\(195\) 0 0
\(196\) −335252. −0.623348
\(197\) 197958. 0.363418 0.181709 0.983352i \(-0.441837\pi\)
0.181709 + 0.983352i \(0.441837\pi\)
\(198\) 0 0
\(199\) −220261. −0.394281 −0.197140 0.980375i \(-0.563166\pi\)
−0.197140 + 0.980375i \(0.563166\pi\)
\(200\) 109434. 0.193454
\(201\) 0 0
\(202\) −659314. −1.13688
\(203\) −616291. −1.04965
\(204\) 0 0
\(205\) −136877. −0.227481
\(206\) −301139. −0.494423
\(207\) 0 0
\(208\) −94327.5 −0.151175
\(209\) 292667. 0.463456
\(210\) 0 0
\(211\) 917849. 1.41927 0.709635 0.704569i \(-0.248860\pi\)
0.709635 + 0.704569i \(0.248860\pi\)
\(212\) −244706. −0.373943
\(213\) 0 0
\(214\) 341158. 0.509238
\(215\) −368684. −0.543950
\(216\) 0 0
\(217\) 1.27792e6 1.84228
\(218\) 233731. 0.333101
\(219\) 0 0
\(220\) 63964.8 0.0891014
\(221\) −798372. −1.09958
\(222\) 0 0
\(223\) 1.19384e6 1.60763 0.803813 0.594882i \(-0.202801\pi\)
0.803813 + 0.594882i \(0.202801\pi\)
\(224\) 1.07202e6 1.42752
\(225\) 0 0
\(226\) 87520.6 0.113983
\(227\) −397814. −0.512407 −0.256204 0.966623i \(-0.582472\pi\)
−0.256204 + 0.966623i \(0.582472\pi\)
\(228\) 0 0
\(229\) −543516. −0.684895 −0.342447 0.939537i \(-0.611256\pi\)
−0.342447 + 0.939537i \(0.611256\pi\)
\(230\) 123049. 0.153377
\(231\) 0 0
\(232\) 597090. 0.728316
\(233\) −1.07137e6 −1.29285 −0.646426 0.762977i \(-0.723737\pi\)
−0.646426 + 0.762977i \(0.723737\pi\)
\(234\) 0 0
\(235\) −174944. −0.206647
\(236\) 540428. 0.631623
\(237\) 0 0
\(238\) 502850. 0.575435
\(239\) 127756. 0.144673 0.0723365 0.997380i \(-0.476954\pi\)
0.0723365 + 0.997380i \(0.476954\pi\)
\(240\) 0 0
\(241\) 209989. 0.232892 0.116446 0.993197i \(-0.462850\pi\)
0.116446 + 0.993197i \(0.462850\pi\)
\(242\) −48236.7 −0.0529467
\(243\) 0 0
\(244\) −642886. −0.691289
\(245\) 396365. 0.421871
\(246\) 0 0
\(247\) 2.28655e6 2.38473
\(248\) −1.23811e6 −1.27829
\(249\) 0 0
\(250\) −51478.6 −0.0520927
\(251\) 109061. 0.109266 0.0546329 0.998507i \(-0.482601\pi\)
0.0546329 + 0.998507i \(0.482601\pi\)
\(252\) 0 0
\(253\) 180766. 0.177548
\(254\) 186582. 0.181462
\(255\) 0 0
\(256\) −971103. −0.926116
\(257\) 1.90416e6 1.79834 0.899168 0.437603i \(-0.144173\pi\)
0.899168 + 0.437603i \(0.144173\pi\)
\(258\) 0 0
\(259\) 48899.6 0.0452956
\(260\) 499745. 0.458474
\(261\) 0 0
\(262\) −880683. −0.792622
\(263\) 1.97795e6 1.76330 0.881651 0.471903i \(-0.156433\pi\)
0.881651 + 0.471903i \(0.156433\pi\)
\(264\) 0 0
\(265\) 289314. 0.253078
\(266\) −1.44017e6 −1.24799
\(267\) 0 0
\(268\) 620473. 0.527699
\(269\) −1.41432e6 −1.19170 −0.595849 0.803096i \(-0.703184\pi\)
−0.595849 + 0.803096i \(0.703184\pi\)
\(270\) 0 0
\(271\) −1.62919e6 −1.34756 −0.673780 0.738932i \(-0.735331\pi\)
−0.673780 + 0.738932i \(0.735331\pi\)
\(272\) 84267.3 0.0690616
\(273\) 0 0
\(274\) 103735. 0.0834734
\(275\) −75625.0 −0.0603023
\(276\) 0 0
\(277\) 320454. 0.250938 0.125469 0.992098i \(-0.459956\pi\)
0.125469 + 0.992098i \(0.459956\pi\)
\(278\) −672953. −0.522243
\(279\) 0 0
\(280\) −791100. −0.603026
\(281\) −2.38129e6 −1.79906 −0.899530 0.436858i \(-0.856091\pi\)
−0.899530 + 0.436858i \(0.856091\pi\)
\(282\) 0 0
\(283\) −493913. −0.366593 −0.183297 0.983058i \(-0.558677\pi\)
−0.183297 + 0.983058i \(0.558677\pi\)
\(284\) 1.73534e6 1.27670
\(285\) 0 0
\(286\) −376864. −0.272439
\(287\) 989485. 0.709095
\(288\) 0 0
\(289\) −706633. −0.497679
\(290\) −280876. −0.196119
\(291\) 0 0
\(292\) −553687. −0.380021
\(293\) 2.24861e6 1.53019 0.765094 0.643919i \(-0.222693\pi\)
0.765094 + 0.643919i \(0.222693\pi\)
\(294\) 0 0
\(295\) −638943. −0.427472
\(296\) −47376.1 −0.0314290
\(297\) 0 0
\(298\) −242835. −0.158405
\(299\) 1.41229e6 0.913579
\(300\) 0 0
\(301\) 2.66522e6 1.69558
\(302\) −1.29859e6 −0.819320
\(303\) 0 0
\(304\) −241343. −0.149779
\(305\) 760078. 0.467852
\(306\) 0 0
\(307\) −1.86642e6 −1.13022 −0.565111 0.825015i \(-0.691167\pi\)
−0.565111 + 0.825015i \(0.691167\pi\)
\(308\) −462402. −0.277743
\(309\) 0 0
\(310\) 582415. 0.344214
\(311\) −1.35283e6 −0.793128 −0.396564 0.918007i \(-0.629797\pi\)
−0.396564 + 0.918007i \(0.629797\pi\)
\(312\) 0 0
\(313\) 528408. 0.304866 0.152433 0.988314i \(-0.451289\pi\)
0.152433 + 0.988314i \(0.451289\pi\)
\(314\) 342248. 0.195892
\(315\) 0 0
\(316\) 1.28998e6 0.726718
\(317\) −1.64065e6 −0.916996 −0.458498 0.888695i \(-0.651612\pi\)
−0.458498 + 0.888695i \(0.651612\pi\)
\(318\) 0 0
\(319\) −412622. −0.227026
\(320\) 408750. 0.223143
\(321\) 0 0
\(322\) −889524. −0.478099
\(323\) −2.04269e6 −1.08942
\(324\) 0 0
\(325\) −590844. −0.310287
\(326\) 423929. 0.220927
\(327\) 0 0
\(328\) −958657. −0.492015
\(329\) 1.26467e6 0.644151
\(330\) 0 0
\(331\) −2.07626e6 −1.04163 −0.520814 0.853670i \(-0.674371\pi\)
−0.520814 + 0.853670i \(0.674371\pi\)
\(332\) −2.30758e6 −1.14898
\(333\) 0 0
\(334\) −568150. −0.278674
\(335\) −733579. −0.357137
\(336\) 0 0
\(337\) −2.66930e6 −1.28033 −0.640165 0.768237i \(-0.721134\pi\)
−0.640165 + 0.768237i \(0.721134\pi\)
\(338\) −1.72109e6 −0.819431
\(339\) 0 0
\(340\) −446446. −0.209446
\(341\) 855600. 0.398460
\(342\) 0 0
\(343\) 172124. 0.0789960
\(344\) −2.58219e6 −1.17650
\(345\) 0 0
\(346\) −2.40263e6 −1.07894
\(347\) −1.83737e6 −0.819169 −0.409585 0.912272i \(-0.634326\pi\)
−0.409585 + 0.912272i \(0.634326\pi\)
\(348\) 0 0
\(349\) −3.67575e6 −1.61541 −0.807705 0.589587i \(-0.799291\pi\)
−0.807705 + 0.589587i \(0.799291\pi\)
\(350\) 372139. 0.162381
\(351\) 0 0
\(352\) 717744. 0.308754
\(353\) 3.11656e6 1.33118 0.665592 0.746316i \(-0.268179\pi\)
0.665592 + 0.746316i \(0.268179\pi\)
\(354\) 0 0
\(355\) −2.05167e6 −0.864046
\(356\) 1.33721e6 0.559209
\(357\) 0 0
\(358\) −1.87598e6 −0.773607
\(359\) −1.30402e6 −0.534008 −0.267004 0.963695i \(-0.586034\pi\)
−0.267004 + 0.963695i \(0.586034\pi\)
\(360\) 0 0
\(361\) 3.37419e6 1.36270
\(362\) 187922. 0.0753712
\(363\) 0 0
\(364\) −3.61266e6 −1.42914
\(365\) 654619. 0.257191
\(366\) 0 0
\(367\) −3.47448e6 −1.34656 −0.673279 0.739388i \(-0.735115\pi\)
−0.673279 + 0.739388i \(0.735115\pi\)
\(368\) −149066. −0.0573797
\(369\) 0 0
\(370\) 22286.1 0.00846310
\(371\) −2.09145e6 −0.788884
\(372\) 0 0
\(373\) −2.49852e6 −0.929846 −0.464923 0.885351i \(-0.653918\pi\)
−0.464923 + 0.885351i \(0.653918\pi\)
\(374\) 336671. 0.124459
\(375\) 0 0
\(376\) −1.22527e6 −0.446953
\(377\) −3.22374e6 −1.16817
\(378\) 0 0
\(379\) −1.45997e6 −0.522091 −0.261045 0.965327i \(-0.584067\pi\)
−0.261045 + 0.965327i \(0.584067\pi\)
\(380\) 1.27863e6 0.454240
\(381\) 0 0
\(382\) −28641.3 −0.0100423
\(383\) −286578. −0.0998267 −0.0499133 0.998754i \(-0.515895\pi\)
−0.0499133 + 0.998754i \(0.515895\pi\)
\(384\) 0 0
\(385\) 546694. 0.187972
\(386\) 1.23053e6 0.420363
\(387\) 0 0
\(388\) −305496. −0.103021
\(389\) −3.29651e6 −1.10454 −0.552269 0.833666i \(-0.686238\pi\)
−0.552269 + 0.833666i \(0.686238\pi\)
\(390\) 0 0
\(391\) −1.26167e6 −0.417353
\(392\) 2.77605e6 0.912457
\(393\) 0 0
\(394\) −652197. −0.211660
\(395\) −1.52513e6 −0.491830
\(396\) 0 0
\(397\) 1.23453e6 0.393119 0.196559 0.980492i \(-0.437023\pi\)
0.196559 + 0.980492i \(0.437023\pi\)
\(398\) 725680. 0.229635
\(399\) 0 0
\(400\) 62362.9 0.0194884
\(401\) −1.22869e6 −0.381575 −0.190788 0.981631i \(-0.561104\pi\)
−0.190788 + 0.981631i \(0.561104\pi\)
\(402\) 0 0
\(403\) 6.68464e6 2.05029
\(404\) −4.23156e6 −1.28987
\(405\) 0 0
\(406\) 2.03045e6 0.611333
\(407\) 32739.5 0.00979684
\(408\) 0 0
\(409\) 1.55858e6 0.460703 0.230351 0.973107i \(-0.426012\pi\)
0.230351 + 0.973107i \(0.426012\pi\)
\(410\) 450960. 0.132488
\(411\) 0 0
\(412\) −1.93275e6 −0.560961
\(413\) 4.61893e6 1.33250
\(414\) 0 0
\(415\) 2.72823e6 0.777609
\(416\) 5.60759e6 1.58870
\(417\) 0 0
\(418\) −964230. −0.269923
\(419\) 2.29946e6 0.639868 0.319934 0.947440i \(-0.396339\pi\)
0.319934 + 0.947440i \(0.396339\pi\)
\(420\) 0 0
\(421\) 145656. 0.0400520 0.0200260 0.999799i \(-0.493625\pi\)
0.0200260 + 0.999799i \(0.493625\pi\)
\(422\) −3.02398e6 −0.826603
\(423\) 0 0
\(424\) 2.02629e6 0.547378
\(425\) 527829. 0.141749
\(426\) 0 0
\(427\) −5.49461e6 −1.45837
\(428\) 2.18960e6 0.577770
\(429\) 0 0
\(430\) 1.21468e6 0.316804
\(431\) −2069.36 −0.000536589 0 −0.000268295 1.00000i \(-0.500085\pi\)
−0.000268295 1.00000i \(0.500085\pi\)
\(432\) 0 0
\(433\) 3.66773e6 0.940108 0.470054 0.882638i \(-0.344235\pi\)
0.470054 + 0.882638i \(0.344235\pi\)
\(434\) −4.21028e6 −1.07297
\(435\) 0 0
\(436\) 1.50012e6 0.377928
\(437\) 3.61344e6 0.905142
\(438\) 0 0
\(439\) −7.46332e6 −1.84829 −0.924147 0.382038i \(-0.875222\pi\)
−0.924147 + 0.382038i \(0.875222\pi\)
\(440\) −529661. −0.130427
\(441\) 0 0
\(442\) 2.63034e6 0.640408
\(443\) 6.66093e6 1.61260 0.806298 0.591509i \(-0.201468\pi\)
0.806298 + 0.591509i \(0.201468\pi\)
\(444\) 0 0
\(445\) −1.58097e6 −0.378463
\(446\) −3.93327e6 −0.936304
\(447\) 0 0
\(448\) −2.95486e6 −0.695571
\(449\) −1.48930e6 −0.348631 −0.174316 0.984690i \(-0.555771\pi\)
−0.174316 + 0.984690i \(0.555771\pi\)
\(450\) 0 0
\(451\) 662485. 0.153368
\(452\) 561719. 0.129322
\(453\) 0 0
\(454\) 1.31065e6 0.298433
\(455\) 4.27121e6 0.967214
\(456\) 0 0
\(457\) 7.53066e6 1.68672 0.843359 0.537351i \(-0.180575\pi\)
0.843359 + 0.537351i \(0.180575\pi\)
\(458\) 1.79069e6 0.398892
\(459\) 0 0
\(460\) 789746. 0.174018
\(461\) −7.53965e6 −1.65234 −0.826169 0.563422i \(-0.809484\pi\)
−0.826169 + 0.563422i \(0.809484\pi\)
\(462\) 0 0
\(463\) −4.38293e6 −0.950193 −0.475096 0.879934i \(-0.657587\pi\)
−0.475096 + 0.879934i \(0.657587\pi\)
\(464\) 340262. 0.0733700
\(465\) 0 0
\(466\) 3.52976e6 0.752975
\(467\) 5.28954e6 1.12234 0.561172 0.827699i \(-0.310351\pi\)
0.561172 + 0.827699i \(0.310351\pi\)
\(468\) 0 0
\(469\) 5.30305e6 1.11325
\(470\) 576376. 0.120354
\(471\) 0 0
\(472\) −4.47502e6 −0.924570
\(473\) 1.78443e6 0.366731
\(474\) 0 0
\(475\) −1.51171e6 −0.307422
\(476\) 3.22736e6 0.652875
\(477\) 0 0
\(478\) −420910. −0.0842596
\(479\) −5.14928e6 −1.02543 −0.512717 0.858558i \(-0.671361\pi\)
−0.512717 + 0.858558i \(0.671361\pi\)
\(480\) 0 0
\(481\) 255787. 0.0504100
\(482\) −691838. −0.135640
\(483\) 0 0
\(484\) −309590. −0.0600722
\(485\) 361185. 0.0697228
\(486\) 0 0
\(487\) 1.47941e6 0.282661 0.141331 0.989962i \(-0.454862\pi\)
0.141331 + 0.989962i \(0.454862\pi\)
\(488\) 5.32342e6 1.01191
\(489\) 0 0
\(490\) −1.30588e6 −0.245704
\(491\) 324127. 0.0606753 0.0303376 0.999540i \(-0.490342\pi\)
0.0303376 + 0.999540i \(0.490342\pi\)
\(492\) 0 0
\(493\) 2.87992e6 0.533658
\(494\) −7.53335e6 −1.38890
\(495\) 0 0
\(496\) −705556. −0.128774
\(497\) 1.48316e7 2.69337
\(498\) 0 0
\(499\) −8.12721e6 −1.46113 −0.730567 0.682841i \(-0.760744\pi\)
−0.730567 + 0.682841i \(0.760744\pi\)
\(500\) −330397. −0.0591032
\(501\) 0 0
\(502\) −359315. −0.0636379
\(503\) 4.32339e6 0.761911 0.380956 0.924593i \(-0.375595\pi\)
0.380956 + 0.924593i \(0.375595\pi\)
\(504\) 0 0
\(505\) 5.00294e6 0.872965
\(506\) −595558. −0.103407
\(507\) 0 0
\(508\) 1.19751e6 0.205882
\(509\) 8.17724e6 1.39898 0.699491 0.714641i \(-0.253410\pi\)
0.699491 + 0.714641i \(0.253410\pi\)
\(510\) 0 0
\(511\) −4.73225e6 −0.801706
\(512\) −1.15095e6 −0.194035
\(513\) 0 0
\(514\) −6.27351e6 −1.04738
\(515\) 2.28507e6 0.379649
\(516\) 0 0
\(517\) 846728. 0.139321
\(518\) −161106. −0.0263808
\(519\) 0 0
\(520\) −4.13814e6 −0.671115
\(521\) −7.40849e6 −1.19574 −0.597868 0.801595i \(-0.703985\pi\)
−0.597868 + 0.801595i \(0.703985\pi\)
\(522\) 0 0
\(523\) 6.52332e6 1.04283 0.521416 0.853303i \(-0.325404\pi\)
0.521416 + 0.853303i \(0.325404\pi\)
\(524\) −5.65234e6 −0.899291
\(525\) 0 0
\(526\) −6.51663e6 −1.02697
\(527\) −5.97171e6 −0.936638
\(528\) 0 0
\(529\) −4.20450e6 −0.653244
\(530\) −953182. −0.147396
\(531\) 0 0
\(532\) −9.24321e6 −1.41594
\(533\) 5.17587e6 0.789160
\(534\) 0 0
\(535\) −2.58874e6 −0.391025
\(536\) −5.13783e6 −0.772445
\(537\) 0 0
\(538\) 4.65966e6 0.694062
\(539\) −1.91841e6 −0.284426
\(540\) 0 0
\(541\) 1.91809e6 0.281758 0.140879 0.990027i \(-0.455007\pi\)
0.140879 + 0.990027i \(0.455007\pi\)
\(542\) 5.36758e6 0.784839
\(543\) 0 0
\(544\) −5.00953e6 −0.725771
\(545\) −1.77358e6 −0.255775
\(546\) 0 0
\(547\) 7.18882e6 1.02728 0.513640 0.858006i \(-0.328297\pi\)
0.513640 + 0.858006i \(0.328297\pi\)
\(548\) 665784. 0.0947069
\(549\) 0 0
\(550\) 249157. 0.0351209
\(551\) −8.24813e6 −1.15738
\(552\) 0 0
\(553\) 1.10252e7 1.53311
\(554\) −1.05578e6 −0.146150
\(555\) 0 0
\(556\) −4.31910e6 −0.592525
\(557\) 5.90963e6 0.807091 0.403546 0.914960i \(-0.367778\pi\)
0.403546 + 0.914960i \(0.367778\pi\)
\(558\) 0 0
\(559\) 1.39414e7 1.88703
\(560\) −450822. −0.0607484
\(561\) 0 0
\(562\) 7.84546e6 1.04780
\(563\) 1.11686e6 0.148501 0.0742504 0.997240i \(-0.476344\pi\)
0.0742504 + 0.997240i \(0.476344\pi\)
\(564\) 0 0
\(565\) −664115. −0.0875230
\(566\) 1.62726e6 0.213509
\(567\) 0 0
\(568\) −1.43695e7 −1.86883
\(569\) 2.10146e6 0.272107 0.136054 0.990701i \(-0.456558\pi\)
0.136054 + 0.990701i \(0.456558\pi\)
\(570\) 0 0
\(571\) 1.14330e7 1.46747 0.733736 0.679435i \(-0.237775\pi\)
0.733736 + 0.679435i \(0.237775\pi\)
\(572\) −2.41877e6 −0.309103
\(573\) 0 0
\(574\) −3.25999e6 −0.412987
\(575\) −933710. −0.117772
\(576\) 0 0
\(577\) 9.77121e6 1.22182 0.610912 0.791698i \(-0.290803\pi\)
0.610912 + 0.791698i \(0.290803\pi\)
\(578\) 2.32809e6 0.289855
\(579\) 0 0
\(580\) −1.80270e6 −0.222512
\(581\) −1.97224e7 −2.42393
\(582\) 0 0
\(583\) −1.40028e6 −0.170625
\(584\) 4.58481e6 0.556274
\(585\) 0 0
\(586\) −7.40833e6 −0.891203
\(587\) −1.31926e7 −1.58028 −0.790140 0.612927i \(-0.789992\pi\)
−0.790140 + 0.612927i \(0.789992\pi\)
\(588\) 0 0
\(589\) 1.71031e7 2.03135
\(590\) 2.10508e6 0.248965
\(591\) 0 0
\(592\) −26998.1 −0.00316613
\(593\) −5.13585e6 −0.599757 −0.299879 0.953977i \(-0.596946\pi\)
−0.299879 + 0.953977i \(0.596946\pi\)
\(594\) 0 0
\(595\) −3.81568e6 −0.441855
\(596\) −1.55855e6 −0.179723
\(597\) 0 0
\(598\) −4.65298e6 −0.532082
\(599\) 4.57610e6 0.521109 0.260554 0.965459i \(-0.416095\pi\)
0.260554 + 0.965459i \(0.416095\pi\)
\(600\) 0 0
\(601\) 1.10948e7 1.25295 0.626477 0.779440i \(-0.284496\pi\)
0.626477 + 0.779440i \(0.284496\pi\)
\(602\) −8.78093e6 −0.987527
\(603\) 0 0
\(604\) −8.33451e6 −0.929582
\(605\) 366025. 0.0406558
\(606\) 0 0
\(607\) 1.73172e7 1.90768 0.953838 0.300320i \(-0.0970935\pi\)
0.953838 + 0.300320i \(0.0970935\pi\)
\(608\) 1.43474e7 1.57403
\(609\) 0 0
\(610\) −2.50418e6 −0.272484
\(611\) 6.61532e6 0.716883
\(612\) 0 0
\(613\) 1.17134e7 1.25902 0.629509 0.776993i \(-0.283256\pi\)
0.629509 + 0.776993i \(0.283256\pi\)
\(614\) 6.14917e6 0.658258
\(615\) 0 0
\(616\) 3.82892e6 0.406560
\(617\) 4.37822e6 0.463003 0.231502 0.972834i \(-0.425636\pi\)
0.231502 + 0.972834i \(0.425636\pi\)
\(618\) 0 0
\(619\) 2.72030e6 0.285358 0.142679 0.989769i \(-0.454428\pi\)
0.142679 + 0.989769i \(0.454428\pi\)
\(620\) 3.73802e6 0.390537
\(621\) 0 0
\(622\) 4.45709e6 0.461929
\(623\) 1.14288e7 1.17973
\(624\) 0 0
\(625\) 390625. 0.0400000
\(626\) −1.74091e6 −0.177558
\(627\) 0 0
\(628\) 2.19660e6 0.222255
\(629\) −228507. −0.0230289
\(630\) 0 0
\(631\) 1.12758e7 1.12739 0.563696 0.825982i \(-0.309379\pi\)
0.563696 + 0.825982i \(0.309379\pi\)
\(632\) −1.06817e7 −1.06377
\(633\) 0 0
\(634\) 5.40533e6 0.534071
\(635\) −1.41580e6 −0.139338
\(636\) 0 0
\(637\) −1.49881e7 −1.46352
\(638\) 1.35944e6 0.132223
\(639\) 0 0
\(640\) 3.39873e6 0.327995
\(641\) 9.52986e6 0.916097 0.458049 0.888927i \(-0.348549\pi\)
0.458049 + 0.888927i \(0.348549\pi\)
\(642\) 0 0
\(643\) 74782.1 0.00713297 0.00356648 0.999994i \(-0.498865\pi\)
0.00356648 + 0.999994i \(0.498865\pi\)
\(644\) −5.70908e6 −0.542440
\(645\) 0 0
\(646\) 6.72990e6 0.634494
\(647\) −1.16024e7 −1.08965 −0.544827 0.838549i \(-0.683405\pi\)
−0.544827 + 0.838549i \(0.683405\pi\)
\(648\) 0 0
\(649\) 3.09248e6 0.288201
\(650\) 1.94661e6 0.180716
\(651\) 0 0
\(652\) 2.72084e6 0.250659
\(653\) −1.51711e7 −1.39231 −0.696154 0.717892i \(-0.745107\pi\)
−0.696154 + 0.717892i \(0.745107\pi\)
\(654\) 0 0
\(655\) 6.68271e6 0.608624
\(656\) −546307. −0.0495652
\(657\) 0 0
\(658\) −4.16662e6 −0.375163
\(659\) 1.44146e7 1.29298 0.646488 0.762924i \(-0.276237\pi\)
0.646488 + 0.762924i \(0.276237\pi\)
\(660\) 0 0
\(661\) −8.51827e6 −0.758312 −0.379156 0.925333i \(-0.623786\pi\)
−0.379156 + 0.925333i \(0.623786\pi\)
\(662\) 6.84053e6 0.606659
\(663\) 0 0
\(664\) 1.91080e7 1.68188
\(665\) 1.09282e7 0.958281
\(666\) 0 0
\(667\) −5.09447e6 −0.443389
\(668\) −3.64646e6 −0.316177
\(669\) 0 0
\(670\) 2.41687e6 0.208002
\(671\) −3.67878e6 −0.315426
\(672\) 0 0
\(673\) 9.99938e6 0.851012 0.425506 0.904956i \(-0.360096\pi\)
0.425506 + 0.904956i \(0.360096\pi\)
\(674\) 8.79435e6 0.745683
\(675\) 0 0
\(676\) −1.10462e7 −0.929708
\(677\) −3.47845e6 −0.291685 −0.145842 0.989308i \(-0.546589\pi\)
−0.145842 + 0.989308i \(0.546589\pi\)
\(678\) 0 0
\(679\) −2.61101e6 −0.217337
\(680\) 3.69680e6 0.306587
\(681\) 0 0
\(682\) −2.81889e6 −0.232069
\(683\) 156171. 0.0128099 0.00640497 0.999979i \(-0.497961\pi\)
0.00640497 + 0.999979i \(0.497961\pi\)
\(684\) 0 0
\(685\) −787150. −0.0640960
\(686\) −567084. −0.0460084
\(687\) 0 0
\(688\) −1.47150e6 −0.118519
\(689\) −1.09401e7 −0.877957
\(690\) 0 0
\(691\) −5.30184e6 −0.422407 −0.211204 0.977442i \(-0.567738\pi\)
−0.211204 + 0.977442i \(0.567738\pi\)
\(692\) −1.54204e7 −1.22414
\(693\) 0 0
\(694\) 6.05347e6 0.477096
\(695\) 5.10643e6 0.401010
\(696\) 0 0
\(697\) −4.62385e6 −0.360514
\(698\) 1.21103e7 0.940838
\(699\) 0 0
\(700\) 2.38844e6 0.184234
\(701\) −2.17241e7 −1.66973 −0.834865 0.550455i \(-0.814454\pi\)
−0.834865 + 0.550455i \(0.814454\pi\)
\(702\) 0 0
\(703\) 654448. 0.0499444
\(704\) −1.97835e6 −0.150443
\(705\) 0 0
\(706\) −1.02679e7 −0.775301
\(707\) −3.61663e7 −2.72117
\(708\) 0 0
\(709\) −138290. −0.0103318 −0.00516589 0.999987i \(-0.501644\pi\)
−0.00516589 + 0.999987i \(0.501644\pi\)
\(710\) 6.75950e6 0.503233
\(711\) 0 0
\(712\) −1.10728e7 −0.818570
\(713\) 1.05637e7 0.778204
\(714\) 0 0
\(715\) 2.85968e6 0.209196
\(716\) −1.20403e7 −0.877717
\(717\) 0 0
\(718\) 4.29626e6 0.311014
\(719\) −2.45634e7 −1.77201 −0.886007 0.463672i \(-0.846532\pi\)
−0.886007 + 0.463672i \(0.846532\pi\)
\(720\) 0 0
\(721\) −1.65188e7 −1.18342
\(722\) −1.11167e7 −0.793657
\(723\) 0 0
\(724\) 1.20611e6 0.0855144
\(725\) 2.13131e6 0.150592
\(726\) 0 0
\(727\) 1.75381e7 1.23068 0.615342 0.788260i \(-0.289018\pi\)
0.615342 + 0.788260i \(0.289018\pi\)
\(728\) 2.99146e7 2.09197
\(729\) 0 0
\(730\) −2.15673e6 −0.149792
\(731\) −1.24545e7 −0.862054
\(732\) 0 0
\(733\) −1.22300e7 −0.840750 −0.420375 0.907350i \(-0.638101\pi\)
−0.420375 + 0.907350i \(0.638101\pi\)
\(734\) 1.14471e7 0.784255
\(735\) 0 0
\(736\) 8.86168e6 0.603006
\(737\) 3.55052e6 0.240782
\(738\) 0 0
\(739\) 1.41581e7 0.953664 0.476832 0.878995i \(-0.341785\pi\)
0.476832 + 0.878995i \(0.341785\pi\)
\(740\) 143035. 0.00960204
\(741\) 0 0
\(742\) 6.89056e6 0.459457
\(743\) −1.13314e7 −0.753029 −0.376515 0.926411i \(-0.622878\pi\)
−0.376515 + 0.926411i \(0.622878\pi\)
\(744\) 0 0
\(745\) 1.84265e6 0.121634
\(746\) 8.23171e6 0.541556
\(747\) 0 0
\(748\) 2.16080e6 0.141208
\(749\) 1.87140e7 1.21889
\(750\) 0 0
\(751\) 2.62110e7 1.69584 0.847919 0.530125i \(-0.177855\pi\)
0.847919 + 0.530125i \(0.177855\pi\)
\(752\) −698240. −0.0450257
\(753\) 0 0
\(754\) 1.06210e7 0.680359
\(755\) 9.85381e6 0.629125
\(756\) 0 0
\(757\) −83559.5 −0.00529976 −0.00264988 0.999996i \(-0.500843\pi\)
−0.00264988 + 0.999996i \(0.500843\pi\)
\(758\) 4.81007e6 0.304073
\(759\) 0 0
\(760\) −1.05877e7 −0.664917
\(761\) −2.52607e7 −1.58119 −0.790596 0.612339i \(-0.790229\pi\)
−0.790596 + 0.612339i \(0.790229\pi\)
\(762\) 0 0
\(763\) 1.28212e7 0.797291
\(764\) −183824. −0.0113938
\(765\) 0 0
\(766\) 944171. 0.0581405
\(767\) 2.41610e7 1.48295
\(768\) 0 0
\(769\) 4.97858e6 0.303592 0.151796 0.988412i \(-0.451494\pi\)
0.151796 + 0.988412i \(0.451494\pi\)
\(770\) −1.80115e6 −0.109477
\(771\) 0 0
\(772\) 7.89773e6 0.476935
\(773\) −500595. −0.0301327 −0.0150664 0.999886i \(-0.504796\pi\)
−0.0150664 + 0.999886i \(0.504796\pi\)
\(774\) 0 0
\(775\) −4.41942e6 −0.264308
\(776\) 2.52966e6 0.150802
\(777\) 0 0
\(778\) 1.08608e7 0.643298
\(779\) 1.32428e7 0.781872
\(780\) 0 0
\(781\) 9.93009e6 0.582540
\(782\) 4.15673e6 0.243072
\(783\) 0 0
\(784\) 1.58198e6 0.0919202
\(785\) −2.59701e6 −0.150418
\(786\) 0 0
\(787\) −1.50797e7 −0.867873 −0.433936 0.900944i \(-0.642876\pi\)
−0.433936 + 0.900944i \(0.642876\pi\)
\(788\) −4.18589e6 −0.240144
\(789\) 0 0
\(790\) 5.02476e6 0.286449
\(791\) 4.80089e6 0.272823
\(792\) 0 0
\(793\) −2.87416e7 −1.62303
\(794\) −4.06731e6 −0.228958
\(795\) 0 0
\(796\) 4.65752e6 0.260538
\(797\) −1.57167e6 −0.0876426 −0.0438213 0.999039i \(-0.513953\pi\)
−0.0438213 + 0.999039i \(0.513953\pi\)
\(798\) 0 0
\(799\) −5.90979e6 −0.327495
\(800\) −3.70735e6 −0.204804
\(801\) 0 0
\(802\) 4.04807e6 0.222235
\(803\) −3.16836e6 −0.173398
\(804\) 0 0
\(805\) 6.74979e6 0.367114
\(806\) −2.20234e7 −1.19412
\(807\) 0 0
\(808\) 3.50395e7 1.88812
\(809\) −5.11766e6 −0.274916 −0.137458 0.990508i \(-0.543893\pi\)
−0.137458 + 0.990508i \(0.543893\pi\)
\(810\) 0 0
\(811\) 1.33210e7 0.711189 0.355594 0.934640i \(-0.384278\pi\)
0.355594 + 0.934640i \(0.384278\pi\)
\(812\) 1.30317e7 0.693604
\(813\) 0 0
\(814\) −107865. −0.00570582
\(815\) −3.21682e6 −0.169642
\(816\) 0 0
\(817\) 3.56700e7 1.86960
\(818\) −5.13495e6 −0.268320
\(819\) 0 0
\(820\) 2.89432e6 0.150318
\(821\) 1.78379e7 0.923603 0.461802 0.886983i \(-0.347203\pi\)
0.461802 + 0.886983i \(0.347203\pi\)
\(822\) 0 0
\(823\) −3.28197e7 −1.68902 −0.844510 0.535540i \(-0.820108\pi\)
−0.844510 + 0.535540i \(0.820108\pi\)
\(824\) 1.60041e7 0.821135
\(825\) 0 0
\(826\) −1.52177e7 −0.776064
\(827\) −3.90869e7 −1.98732 −0.993658 0.112440i \(-0.964133\pi\)
−0.993658 + 0.112440i \(0.964133\pi\)
\(828\) 0 0
\(829\) −3.52155e7 −1.77970 −0.889851 0.456252i \(-0.849192\pi\)
−0.889851 + 0.456252i \(0.849192\pi\)
\(830\) −8.98853e6 −0.452891
\(831\) 0 0
\(832\) −1.54565e7 −0.774109
\(833\) 1.33896e7 0.668584
\(834\) 0 0
\(835\) 4.31118e6 0.213983
\(836\) −6.18856e6 −0.306249
\(837\) 0 0
\(838\) −7.57587e6 −0.372668
\(839\) −1.90083e7 −0.932265 −0.466132 0.884715i \(-0.654353\pi\)
−0.466132 + 0.884715i \(0.654353\pi\)
\(840\) 0 0
\(841\) −8.88236e6 −0.433050
\(842\) −479884. −0.0233269
\(843\) 0 0
\(844\) −1.94083e7 −0.937845
\(845\) 1.30598e7 0.629210
\(846\) 0 0
\(847\) −2.64600e6 −0.126730
\(848\) 1.15472e6 0.0551424
\(849\) 0 0
\(850\) −1.73900e6 −0.0825568
\(851\) 404221. 0.0191335
\(852\) 0 0
\(853\) −3.07361e7 −1.44636 −0.723179 0.690660i \(-0.757320\pi\)
−0.723179 + 0.690660i \(0.757320\pi\)
\(854\) 1.81027e7 0.849374
\(855\) 0 0
\(856\) −1.81310e7 −0.845740
\(857\) 1.34454e7 0.625349 0.312675 0.949860i \(-0.398775\pi\)
0.312675 + 0.949860i \(0.398775\pi\)
\(858\) 0 0
\(859\) 4.39306e6 0.203135 0.101567 0.994829i \(-0.467614\pi\)
0.101567 + 0.994829i \(0.467614\pi\)
\(860\) 7.79598e6 0.359438
\(861\) 0 0
\(862\) 6817.77 0.000312517 0
\(863\) 3.82863e7 1.74991 0.874956 0.484203i \(-0.160890\pi\)
0.874956 + 0.484203i \(0.160890\pi\)
\(864\) 0 0
\(865\) 1.82314e7 0.828477
\(866\) −1.20838e7 −0.547532
\(867\) 0 0
\(868\) −2.70221e7 −1.21736
\(869\) 7.38165e6 0.331592
\(870\) 0 0
\(871\) 2.77396e7 1.23895
\(872\) −1.24217e7 −0.553211
\(873\) 0 0
\(874\) −1.19049e7 −0.527168
\(875\) −2.82383e6 −0.124686
\(876\) 0 0
\(877\) −4.33306e7 −1.90237 −0.951186 0.308617i \(-0.900134\pi\)
−0.951186 + 0.308617i \(0.900134\pi\)
\(878\) 2.45889e7 1.07647
\(879\) 0 0
\(880\) −301836. −0.0131391
\(881\) −3.08399e7 −1.33867 −0.669335 0.742961i \(-0.733421\pi\)
−0.669335 + 0.742961i \(0.733421\pi\)
\(882\) 0 0
\(883\) 2.89082e7 1.24772 0.623862 0.781534i \(-0.285563\pi\)
0.623862 + 0.781534i \(0.285563\pi\)
\(884\) 1.68819e7 0.726592
\(885\) 0 0
\(886\) −2.19453e7 −0.939199
\(887\) 2.37686e7 1.01436 0.507182 0.861839i \(-0.330687\pi\)
0.507182 + 0.861839i \(0.330687\pi\)
\(888\) 0 0
\(889\) 1.02348e7 0.434337
\(890\) 5.20871e6 0.220422
\(891\) 0 0
\(892\) −2.52443e7 −1.06231
\(893\) 1.69257e7 0.710262
\(894\) 0 0
\(895\) 1.42351e7 0.594023
\(896\) −2.45695e7 −1.02241
\(897\) 0 0
\(898\) 4.90670e6 0.203048
\(899\) −2.41131e7 −0.995069
\(900\) 0 0
\(901\) 9.77332e6 0.401079
\(902\) −2.18264e6 −0.0893237
\(903\) 0 0
\(904\) −4.65132e6 −0.189302
\(905\) −1.42597e6 −0.0578746
\(906\) 0 0
\(907\) 9.36759e6 0.378102 0.189051 0.981967i \(-0.439459\pi\)
0.189051 + 0.981967i \(0.439459\pi\)
\(908\) 8.41193e6 0.338595
\(909\) 0 0
\(910\) −1.40721e7 −0.563319
\(911\) 2.58520e7 1.03205 0.516023 0.856575i \(-0.327412\pi\)
0.516023 + 0.856575i \(0.327412\pi\)
\(912\) 0 0
\(913\) −1.32047e7 −0.524264
\(914\) −2.48107e7 −0.982368
\(915\) 0 0
\(916\) 1.14929e7 0.452574
\(917\) −4.83093e7 −1.89718
\(918\) 0 0
\(919\) 4.61821e7 1.80378 0.901892 0.431961i \(-0.142178\pi\)
0.901892 + 0.431961i \(0.142178\pi\)
\(920\) −6.53950e6 −0.254727
\(921\) 0 0
\(922\) 2.48404e7 0.962345
\(923\) 7.75819e7 2.99748
\(924\) 0 0
\(925\) −169109. −0.00649849
\(926\) 1.44401e7 0.553406
\(927\) 0 0
\(928\) −2.02279e7 −0.771048
\(929\) 1.95110e6 0.0741721 0.0370860 0.999312i \(-0.488192\pi\)
0.0370860 + 0.999312i \(0.488192\pi\)
\(930\) 0 0
\(931\) −3.83481e7 −1.45000
\(932\) 2.26545e7 0.854308
\(933\) 0 0
\(934\) −1.74271e7 −0.653669
\(935\) −2.55469e6 −0.0955673
\(936\) 0 0
\(937\) −3.45128e7 −1.28420 −0.642098 0.766623i \(-0.721936\pi\)
−0.642098 + 0.766623i \(0.721936\pi\)
\(938\) −1.74716e7 −0.648374
\(939\) 0 0
\(940\) 3.69926e6 0.136551
\(941\) −4.64180e7 −1.70888 −0.854442 0.519547i \(-0.826101\pi\)
−0.854442 + 0.519547i \(0.826101\pi\)
\(942\) 0 0
\(943\) 8.17942e6 0.299532
\(944\) −2.55017e6 −0.0931404
\(945\) 0 0
\(946\) −5.87905e6 −0.213589
\(947\) −4.57523e7 −1.65782 −0.828911 0.559381i \(-0.811039\pi\)
−0.828911 + 0.559381i \(0.811039\pi\)
\(948\) 0 0
\(949\) −2.47538e7 −0.892227
\(950\) 4.98053e6 0.179047
\(951\) 0 0
\(952\) −2.67242e7 −0.955679
\(953\) 1.34380e7 0.479294 0.239647 0.970860i \(-0.422968\pi\)
0.239647 + 0.970860i \(0.422968\pi\)
\(954\) 0 0
\(955\) 217333. 0.00771112
\(956\) −2.70146e6 −0.0955990
\(957\) 0 0
\(958\) 1.69650e7 0.597228
\(959\) 5.69031e6 0.199797
\(960\) 0 0
\(961\) 2.13709e7 0.746474
\(962\) −842726. −0.0293595
\(963\) 0 0
\(964\) −4.44031e6 −0.153894
\(965\) −9.33741e6 −0.322781
\(966\) 0 0
\(967\) −3.71470e7 −1.27749 −0.638745 0.769418i \(-0.720546\pi\)
−0.638745 + 0.769418i \(0.720546\pi\)
\(968\) 2.56356e6 0.0879336
\(969\) 0 0
\(970\) −1.18997e6 −0.0406076
\(971\) 4.08269e7 1.38963 0.694813 0.719190i \(-0.255487\pi\)
0.694813 + 0.719190i \(0.255487\pi\)
\(972\) 0 0
\(973\) −3.69144e7 −1.25001
\(974\) −4.87411e6 −0.164626
\(975\) 0 0
\(976\) 3.03364e6 0.101939
\(977\) 1.52450e6 0.0510965 0.0255482 0.999674i \(-0.491867\pi\)
0.0255482 + 0.999674i \(0.491867\pi\)
\(978\) 0 0
\(979\) 7.65188e6 0.255159
\(980\) −8.38129e6 −0.278770
\(981\) 0 0
\(982\) −1.06788e6 −0.0353381
\(983\) 5.19287e7 1.71405 0.857026 0.515273i \(-0.172310\pi\)
0.857026 + 0.515273i \(0.172310\pi\)
\(984\) 0 0
\(985\) 4.94894e6 0.162526
\(986\) −9.48827e6 −0.310810
\(987\) 0 0
\(988\) −4.83500e7 −1.57581
\(989\) 2.20316e7 0.716236
\(990\) 0 0
\(991\) −4.75062e7 −1.53662 −0.768310 0.640078i \(-0.778902\pi\)
−0.768310 + 0.640078i \(0.778902\pi\)
\(992\) 4.19440e7 1.35329
\(993\) 0 0
\(994\) −4.88645e7 −1.56866
\(995\) −5.50654e6 −0.176328
\(996\) 0 0
\(997\) −1.39702e7 −0.445107 −0.222554 0.974920i \(-0.571439\pi\)
−0.222554 + 0.974920i \(0.571439\pi\)
\(998\) 2.67762e7 0.850986
\(999\) 0 0
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 495.6.a.p.1.4 yes 10
3.2 odd 2 495.6.a.o.1.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
495.6.a.o.1.7 10 3.2 odd 2
495.6.a.p.1.4 yes 10 1.1 even 1 trivial