Properties

Label 570.6.a.i.1.4
Level $570$
Weight $6$
Character 570.1
Self dual yes
Analytic conductor $91.419$
Analytic rank $1$
Dimension $4$
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] = [570,6,Mod(1,570)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(570, 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("570.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 570.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: \(91.4187772934\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\mathbb{Q}[x]/(x^{4} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2696x^{2} + 13833x + 894635 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2} \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(23.8661\) of defining polynomial
Character \(\chi\) \(=\) 570.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +241.678 q^{7} -64.0000 q^{8} +81.0000 q^{9} +O(q^{10})\) \(q-4.00000 q^{2} -9.00000 q^{3} +16.0000 q^{4} -25.0000 q^{5} +36.0000 q^{6} +241.678 q^{7} -64.0000 q^{8} +81.0000 q^{9} +100.000 q^{10} +48.9152 q^{11} -144.000 q^{12} -273.990 q^{13} -966.710 q^{14} +225.000 q^{15} +256.000 q^{16} +601.513 q^{17} -324.000 q^{18} -361.000 q^{19} -400.000 q^{20} -2175.10 q^{21} -195.661 q^{22} -4654.90 q^{23} +576.000 q^{24} +625.000 q^{25} +1095.96 q^{26} -729.000 q^{27} +3866.84 q^{28} +1701.83 q^{29} -900.000 q^{30} -4349.54 q^{31} -1024.00 q^{32} -440.237 q^{33} -2406.05 q^{34} -6041.94 q^{35} +1296.00 q^{36} -4042.97 q^{37} +1444.00 q^{38} +2465.91 q^{39} +1600.00 q^{40} -7242.68 q^{41} +8700.39 q^{42} +9462.67 q^{43} +782.643 q^{44} -2025.00 q^{45} +18619.6 q^{46} +3596.39 q^{47} -2304.00 q^{48} +41601.1 q^{49} -2500.00 q^{50} -5413.61 q^{51} -4383.85 q^{52} -12980.4 q^{53} +2916.00 q^{54} -1222.88 q^{55} -15467.4 q^{56} +3249.00 q^{57} -6807.33 q^{58} +2882.74 q^{59} +3600.00 q^{60} -17026.9 q^{61} +17398.2 q^{62} +19575.9 q^{63} +4096.00 q^{64} +6849.76 q^{65} +1760.95 q^{66} +18191.1 q^{67} +9624.20 q^{68} +41894.1 q^{69} +24167.8 q^{70} +2789.02 q^{71} -5184.00 q^{72} +47602.4 q^{73} +16171.9 q^{74} -5625.00 q^{75} -5776.00 q^{76} +11821.7 q^{77} -9863.65 q^{78} +58422.6 q^{79} -6400.00 q^{80} +6561.00 q^{81} +28970.7 q^{82} -50749.5 q^{83} -34801.6 q^{84} -15037.8 q^{85} -37850.7 q^{86} -15316.5 q^{87} -3130.57 q^{88} -55007.9 q^{89} +8100.00 q^{90} -66217.3 q^{91} -74478.4 q^{92} +39145.9 q^{93} -14385.6 q^{94} +9025.00 q^{95} +9216.00 q^{96} -85108.9 q^{97} -166404. q^{98} +3962.13 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} + 108 q^{7} - 256 q^{8} + 324 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 16 q^{2} - 36 q^{3} + 64 q^{4} - 100 q^{5} + 144 q^{6} + 108 q^{7} - 256 q^{8} + 324 q^{9} + 400 q^{10} - 460 q^{11} - 576 q^{12} + 296 q^{13} - 432 q^{14} + 900 q^{15} + 1024 q^{16} - 412 q^{17} - 1296 q^{18} - 1444 q^{19} - 1600 q^{20} - 972 q^{21} + 1840 q^{22} - 768 q^{23} + 2304 q^{24} + 2500 q^{25} - 1184 q^{26} - 2916 q^{27} + 1728 q^{28} - 1828 q^{29} - 3600 q^{30} + 3856 q^{31} - 4096 q^{32} + 4140 q^{33} + 1648 q^{34} - 2700 q^{35} + 5184 q^{36} + 11456 q^{37} + 5776 q^{38} - 2664 q^{39} + 6400 q^{40} - 12904 q^{41} + 3888 q^{42} + 15096 q^{43} - 7360 q^{44} - 8100 q^{45} + 3072 q^{46} + 17040 q^{47} - 9216 q^{48} + 33708 q^{49} - 10000 q^{50} + 3708 q^{51} + 4736 q^{52} + 16728 q^{53} + 11664 q^{54} + 11500 q^{55} - 6912 q^{56} + 12996 q^{57} + 7312 q^{58} - 19760 q^{59} + 14400 q^{60} + 47168 q^{61} - 15424 q^{62} + 8748 q^{63} + 16384 q^{64} - 7400 q^{65} - 16560 q^{66} + 104580 q^{67} - 6592 q^{68} + 6912 q^{69} + 10800 q^{70} - 36764 q^{71} - 20736 q^{72} + 74356 q^{73} - 45824 q^{74} - 22500 q^{75} - 23104 q^{76} + 75356 q^{77} + 10656 q^{78} + 80920 q^{79} - 25600 q^{80} + 26244 q^{81} + 51616 q^{82} + 19416 q^{83} - 15552 q^{84} + 10300 q^{85} - 60384 q^{86} + 16452 q^{87} + 29440 q^{88} - 4760 q^{89} + 32400 q^{90} + 32288 q^{91} - 12288 q^{92} - 34704 q^{93} - 68160 q^{94} + 36100 q^{95} + 36864 q^{96} + 139572 q^{97} - 134832 q^{98} - 37260 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.00000 −0.707107
\(3\) −9.00000 −0.577350
\(4\) 16.0000 0.500000
\(5\) −25.0000 −0.447214
\(6\) 36.0000 0.408248
\(7\) 241.678 1.86419 0.932097 0.362208i \(-0.117977\pi\)
0.932097 + 0.362208i \(0.117977\pi\)
\(8\) −64.0000 −0.353553
\(9\) 81.0000 0.333333
\(10\) 100.000 0.316228
\(11\) 48.9152 0.121888 0.0609441 0.998141i \(-0.480589\pi\)
0.0609441 + 0.998141i \(0.480589\pi\)
\(12\) −144.000 −0.288675
\(13\) −273.990 −0.449652 −0.224826 0.974399i \(-0.572181\pi\)
−0.224826 + 0.974399i \(0.572181\pi\)
\(14\) −966.710 −1.31818
\(15\) 225.000 0.258199
\(16\) 256.000 0.250000
\(17\) 601.513 0.504804 0.252402 0.967623i \(-0.418780\pi\)
0.252402 + 0.967623i \(0.418780\pi\)
\(18\) −324.000 −0.235702
\(19\) −361.000 −0.229416
\(20\) −400.000 −0.223607
\(21\) −2175.10 −1.07629
\(22\) −195.661 −0.0861880
\(23\) −4654.90 −1.83481 −0.917405 0.397955i \(-0.869720\pi\)
−0.917405 + 0.397955i \(0.869720\pi\)
\(24\) 576.000 0.204124
\(25\) 625.000 0.200000
\(26\) 1095.96 0.317952
\(27\) −729.000 −0.192450
\(28\) 3866.84 0.932097
\(29\) 1701.83 0.375770 0.187885 0.982191i \(-0.439837\pi\)
0.187885 + 0.982191i \(0.439837\pi\)
\(30\) −900.000 −0.182574
\(31\) −4349.54 −0.812904 −0.406452 0.913672i \(-0.633234\pi\)
−0.406452 + 0.913672i \(0.633234\pi\)
\(32\) −1024.00 −0.176777
\(33\) −440.237 −0.0703722
\(34\) −2406.05 −0.356950
\(35\) −6041.94 −0.833693
\(36\) 1296.00 0.166667
\(37\) −4042.97 −0.485508 −0.242754 0.970088i \(-0.578051\pi\)
−0.242754 + 0.970088i \(0.578051\pi\)
\(38\) 1444.00 0.162221
\(39\) 2465.91 0.259607
\(40\) 1600.00 0.158114
\(41\) −7242.68 −0.672883 −0.336442 0.941704i \(-0.609223\pi\)
−0.336442 + 0.941704i \(0.609223\pi\)
\(42\) 8700.39 0.761054
\(43\) 9462.67 0.780445 0.390223 0.920720i \(-0.372398\pi\)
0.390223 + 0.920720i \(0.372398\pi\)
\(44\) 782.643 0.0609441
\(45\) −2025.00 −0.149071
\(46\) 18619.6 1.29741
\(47\) 3596.39 0.237477 0.118739 0.992926i \(-0.462115\pi\)
0.118739 + 0.992926i \(0.462115\pi\)
\(48\) −2304.00 −0.144338
\(49\) 41601.1 2.47522
\(50\) −2500.00 −0.141421
\(51\) −5413.61 −0.291449
\(52\) −4383.85 −0.224826
\(53\) −12980.4 −0.634743 −0.317371 0.948301i \(-0.602800\pi\)
−0.317371 + 0.948301i \(0.602800\pi\)
\(54\) 2916.00 0.136083
\(55\) −1222.88 −0.0545101
\(56\) −15467.4 −0.659092
\(57\) 3249.00 0.132453
\(58\) −6807.33 −0.265710
\(59\) 2882.74 0.107814 0.0539071 0.998546i \(-0.482833\pi\)
0.0539071 + 0.998546i \(0.482833\pi\)
\(60\) 3600.00 0.129099
\(61\) −17026.9 −0.585883 −0.292942 0.956130i \(-0.594634\pi\)
−0.292942 + 0.956130i \(0.594634\pi\)
\(62\) 17398.2 0.574810
\(63\) 19575.9 0.621398
\(64\) 4096.00 0.125000
\(65\) 6849.76 0.201091
\(66\) 1760.95 0.0497607
\(67\) 18191.1 0.495075 0.247538 0.968878i \(-0.420379\pi\)
0.247538 + 0.968878i \(0.420379\pi\)
\(68\) 9624.20 0.252402
\(69\) 41894.1 1.05933
\(70\) 24167.8 0.589510
\(71\) 2789.02 0.0656608 0.0328304 0.999461i \(-0.489548\pi\)
0.0328304 + 0.999461i \(0.489548\pi\)
\(72\) −5184.00 −0.117851
\(73\) 47602.4 1.04549 0.522747 0.852488i \(-0.324907\pi\)
0.522747 + 0.852488i \(0.324907\pi\)
\(74\) 16171.9 0.343306
\(75\) −5625.00 −0.115470
\(76\) −5776.00 −0.114708
\(77\) 11821.7 0.227223
\(78\) −9863.65 −0.183570
\(79\) 58422.6 1.05320 0.526602 0.850112i \(-0.323466\pi\)
0.526602 + 0.850112i \(0.323466\pi\)
\(80\) −6400.00 −0.111803
\(81\) 6561.00 0.111111
\(82\) 28970.7 0.475800
\(83\) −50749.5 −0.808605 −0.404302 0.914625i \(-0.632486\pi\)
−0.404302 + 0.914625i \(0.632486\pi\)
\(84\) −34801.6 −0.538147
\(85\) −15037.8 −0.225755
\(86\) −37850.7 −0.551858
\(87\) −15316.5 −0.216951
\(88\) −3130.57 −0.0430940
\(89\) −55007.9 −0.736123 −0.368061 0.929802i \(-0.619978\pi\)
−0.368061 + 0.929802i \(0.619978\pi\)
\(90\) 8100.00 0.105409
\(91\) −66217.3 −0.838239
\(92\) −74478.4 −0.917405
\(93\) 39145.9 0.469330
\(94\) −14385.6 −0.167922
\(95\) 9025.00 0.102598
\(96\) 9216.00 0.102062
\(97\) −85108.9 −0.918429 −0.459215 0.888325i \(-0.651869\pi\)
−0.459215 + 0.888325i \(0.651869\pi\)
\(98\) −166404. −1.75025
\(99\) 3962.13 0.0406294
\(100\) 10000.0 0.100000
\(101\) −112004. −1.09253 −0.546263 0.837614i \(-0.683950\pi\)
−0.546263 + 0.837614i \(0.683950\pi\)
\(102\) 21654.5 0.206085
\(103\) 121864. 1.13183 0.565915 0.824463i \(-0.308523\pi\)
0.565915 + 0.824463i \(0.308523\pi\)
\(104\) 17535.4 0.158976
\(105\) 54377.5 0.481333
\(106\) 51921.5 0.448831
\(107\) −151510. −1.27933 −0.639664 0.768655i \(-0.720926\pi\)
−0.639664 + 0.768655i \(0.720926\pi\)
\(108\) −11664.0 −0.0962250
\(109\) 26225.9 0.211429 0.105714 0.994397i \(-0.466287\pi\)
0.105714 + 0.994397i \(0.466287\pi\)
\(110\) 4891.52 0.0385445
\(111\) 36386.7 0.280308
\(112\) 61869.5 0.466049
\(113\) −157470. −1.16012 −0.580058 0.814575i \(-0.696970\pi\)
−0.580058 + 0.814575i \(0.696970\pi\)
\(114\) −12996.0 −0.0936586
\(115\) 116373. 0.820552
\(116\) 27229.3 0.187885
\(117\) −22193.2 −0.149884
\(118\) −11531.0 −0.0762362
\(119\) 145372. 0.941052
\(120\) −14400.0 −0.0912871
\(121\) −158658. −0.985143
\(122\) 68107.6 0.414282
\(123\) 65184.1 0.388489
\(124\) −69592.7 −0.406452
\(125\) −15625.0 −0.0894427
\(126\) −78303.5 −0.439395
\(127\) 170009. 0.935325 0.467663 0.883907i \(-0.345096\pi\)
0.467663 + 0.883907i \(0.345096\pi\)
\(128\) −16384.0 −0.0883883
\(129\) −85164.0 −0.450590
\(130\) −27399.0 −0.142193
\(131\) 254959. 1.29805 0.649026 0.760766i \(-0.275176\pi\)
0.649026 + 0.760766i \(0.275176\pi\)
\(132\) −7043.79 −0.0351861
\(133\) −87245.6 −0.427676
\(134\) −72764.3 −0.350071
\(135\) 18225.0 0.0860663
\(136\) −38496.8 −0.178475
\(137\) 301598. 1.37286 0.686431 0.727195i \(-0.259176\pi\)
0.686431 + 0.727195i \(0.259176\pi\)
\(138\) −167577. −0.749058
\(139\) −90083.8 −0.395466 −0.197733 0.980256i \(-0.563358\pi\)
−0.197733 + 0.980256i \(0.563358\pi\)
\(140\) −96671.0 −0.416847
\(141\) −32367.5 −0.137108
\(142\) −11156.1 −0.0464292
\(143\) −13402.3 −0.0548073
\(144\) 20736.0 0.0833333
\(145\) −42545.8 −0.168049
\(146\) −190410. −0.739277
\(147\) −374410. −1.42907
\(148\) −64687.5 −0.242754
\(149\) −37471.4 −0.138272 −0.0691361 0.997607i \(-0.522024\pi\)
−0.0691361 + 0.997607i \(0.522024\pi\)
\(150\) 22500.0 0.0816497
\(151\) −343904. −1.22743 −0.613713 0.789529i \(-0.710325\pi\)
−0.613713 + 0.789529i \(0.710325\pi\)
\(152\) 23104.0 0.0811107
\(153\) 48722.5 0.168268
\(154\) −47286.8 −0.160671
\(155\) 108739. 0.363542
\(156\) 39454.6 0.129803
\(157\) 211593. 0.685096 0.342548 0.939500i \(-0.388710\pi\)
0.342548 + 0.939500i \(0.388710\pi\)
\(158\) −233690. −0.744728
\(159\) 116823. 0.366469
\(160\) 25600.0 0.0790569
\(161\) −1.12499e6 −3.42044
\(162\) −26244.0 −0.0785674
\(163\) −460898. −1.35874 −0.679369 0.733797i \(-0.737746\pi\)
−0.679369 + 0.733797i \(0.737746\pi\)
\(164\) −115883. −0.336442
\(165\) 11005.9 0.0314714
\(166\) 202998. 0.571770
\(167\) 298005. 0.826860 0.413430 0.910536i \(-0.364331\pi\)
0.413430 + 0.910536i \(0.364331\pi\)
\(168\) 139206. 0.380527
\(169\) −296222. −0.797813
\(170\) 60151.3 0.159633
\(171\) −29241.0 −0.0764719
\(172\) 151403. 0.390223
\(173\) −422602. −1.07354 −0.536768 0.843730i \(-0.680355\pi\)
−0.536768 + 0.843730i \(0.680355\pi\)
\(174\) 61266.0 0.153407
\(175\) 151048. 0.372839
\(176\) 12522.3 0.0304721
\(177\) −25944.7 −0.0622466
\(178\) 220032. 0.520517
\(179\) −43456.8 −0.101374 −0.0506869 0.998715i \(-0.516141\pi\)
−0.0506869 + 0.998715i \(0.516141\pi\)
\(180\) −32400.0 −0.0745356
\(181\) −192237. −0.436155 −0.218077 0.975931i \(-0.569979\pi\)
−0.218077 + 0.975931i \(0.569979\pi\)
\(182\) 264869. 0.592725
\(183\) 153242. 0.338260
\(184\) 297914. 0.648703
\(185\) 101074. 0.217126
\(186\) −156584. −0.331867
\(187\) 29423.1 0.0615296
\(188\) 57542.2 0.118739
\(189\) −176183. −0.358764
\(190\) −36100.0 −0.0725476
\(191\) 51099.9 0.101353 0.0506766 0.998715i \(-0.483862\pi\)
0.0506766 + 0.998715i \(0.483862\pi\)
\(192\) −36864.0 −0.0721688
\(193\) −515621. −0.996409 −0.498205 0.867060i \(-0.666007\pi\)
−0.498205 + 0.867060i \(0.666007\pi\)
\(194\) 340436. 0.649427
\(195\) −61647.8 −0.116100
\(196\) 665617. 1.23761
\(197\) −559885. −1.02786 −0.513929 0.857833i \(-0.671810\pi\)
−0.513929 + 0.857833i \(0.671810\pi\)
\(198\) −15848.5 −0.0287293
\(199\) −905154. −1.62028 −0.810140 0.586237i \(-0.800609\pi\)
−0.810140 + 0.586237i \(0.800609\pi\)
\(200\) −40000.0 −0.0707107
\(201\) −163720. −0.285832
\(202\) 448018. 0.772532
\(203\) 411295. 0.700508
\(204\) −86617.8 −0.145724
\(205\) 181067. 0.300922
\(206\) −487455. −0.800325
\(207\) −377047. −0.611603
\(208\) −70141.5 −0.112413
\(209\) −17658.4 −0.0279631
\(210\) −217510. −0.340354
\(211\) −722060. −1.11652 −0.558261 0.829666i \(-0.688531\pi\)
−0.558261 + 0.829666i \(0.688531\pi\)
\(212\) −207686. −0.317371
\(213\) −25101.2 −0.0379093
\(214\) 606040. 0.904621
\(215\) −236567. −0.349026
\(216\) 46656.0 0.0680414
\(217\) −1.05119e6 −1.51541
\(218\) −104904. −0.149503
\(219\) −428422. −0.603617
\(220\) −19566.1 −0.0272550
\(221\) −164809. −0.226986
\(222\) −145547. −0.198208
\(223\) −408801. −0.550490 −0.275245 0.961374i \(-0.588759\pi\)
−0.275245 + 0.961374i \(0.588759\pi\)
\(224\) −247478. −0.329546
\(225\) 50625.0 0.0666667
\(226\) 629880. 0.820326
\(227\) −612099. −0.788419 −0.394210 0.919021i \(-0.628982\pi\)
−0.394210 + 0.919021i \(0.628982\pi\)
\(228\) 51984.0 0.0662266
\(229\) 274614. 0.346046 0.173023 0.984918i \(-0.444647\pi\)
0.173023 + 0.984918i \(0.444647\pi\)
\(230\) −465490. −0.580218
\(231\) −106395. −0.131188
\(232\) −108917. −0.132855
\(233\) 327043. 0.394653 0.197326 0.980338i \(-0.436774\pi\)
0.197326 + 0.980338i \(0.436774\pi\)
\(234\) 88772.9 0.105984
\(235\) −89909.8 −0.106203
\(236\) 46123.9 0.0539071
\(237\) −525803. −0.608068
\(238\) −581489. −0.665424
\(239\) −539189. −0.610585 −0.305293 0.952259i \(-0.598754\pi\)
−0.305293 + 0.952259i \(0.598754\pi\)
\(240\) 57600.0 0.0645497
\(241\) −102491. −0.113669 −0.0568346 0.998384i \(-0.518101\pi\)
−0.0568346 + 0.998384i \(0.518101\pi\)
\(242\) 634633. 0.696601
\(243\) −59049.0 −0.0641500
\(244\) −272431. −0.292942
\(245\) −1.04003e6 −1.10695
\(246\) −260736. −0.274703
\(247\) 98910.5 0.103157
\(248\) 278371. 0.287405
\(249\) 456745. 0.466848
\(250\) 62500.0 0.0632456
\(251\) −931446. −0.933197 −0.466599 0.884469i \(-0.654521\pi\)
−0.466599 + 0.884469i \(0.654521\pi\)
\(252\) 313214. 0.310699
\(253\) −227695. −0.223642
\(254\) −680036. −0.661375
\(255\) 135340. 0.130340
\(256\) 65536.0 0.0625000
\(257\) −29506.6 −0.0278668 −0.0139334 0.999903i \(-0.504435\pi\)
−0.0139334 + 0.999903i \(0.504435\pi\)
\(258\) 340656. 0.318616
\(259\) −977095. −0.905081
\(260\) 109596. 0.100545
\(261\) 137849. 0.125257
\(262\) −1.01984e6 −0.917862
\(263\) 1.26941e6 1.13165 0.565826 0.824525i \(-0.308558\pi\)
0.565826 + 0.824525i \(0.308558\pi\)
\(264\) 28175.1 0.0248803
\(265\) 324509. 0.283865
\(266\) 348982. 0.302412
\(267\) 495071. 0.425001
\(268\) 291057. 0.247538
\(269\) −1.96862e6 −1.65875 −0.829375 0.558692i \(-0.811303\pi\)
−0.829375 + 0.558692i \(0.811303\pi\)
\(270\) −72900.0 −0.0608581
\(271\) 548933. 0.454042 0.227021 0.973890i \(-0.427101\pi\)
0.227021 + 0.973890i \(0.427101\pi\)
\(272\) 153987. 0.126201
\(273\) 595956. 0.483958
\(274\) −1.20639e6 −0.970760
\(275\) 30572.0 0.0243777
\(276\) 670306. 0.529664
\(277\) 1.85299e6 1.45102 0.725512 0.688210i \(-0.241603\pi\)
0.725512 + 0.688210i \(0.241603\pi\)
\(278\) 360335. 0.279637
\(279\) −352313. −0.270968
\(280\) 386684. 0.294755
\(281\) −2.25804e6 −1.70595 −0.852975 0.521952i \(-0.825204\pi\)
−0.852975 + 0.521952i \(0.825204\pi\)
\(282\) 129470. 0.0969497
\(283\) 1.90922e6 1.41706 0.708532 0.705679i \(-0.249358\pi\)
0.708532 + 0.705679i \(0.249358\pi\)
\(284\) 44624.3 0.0328304
\(285\) −81225.0 −0.0592349
\(286\) 53609.1 0.0387546
\(287\) −1.75039e6 −1.25439
\(288\) −82944.0 −0.0589256
\(289\) −1.05804e6 −0.745173
\(290\) 170183. 0.118829
\(291\) 765980. 0.530255
\(292\) 761639. 0.522747
\(293\) 2.33353e6 1.58798 0.793989 0.607932i \(-0.208001\pi\)
0.793989 + 0.607932i \(0.208001\pi\)
\(294\) 1.49764e6 1.01051
\(295\) −72068.6 −0.0482160
\(296\) 258750. 0.171653
\(297\) −35659.2 −0.0234574
\(298\) 149886. 0.0977732
\(299\) 1.27540e6 0.825026
\(300\) −90000.0 −0.0577350
\(301\) 2.28692e6 1.45490
\(302\) 1.37562e6 0.867921
\(303\) 1.00804e6 0.630770
\(304\) −92416.0 −0.0573539
\(305\) 425673. 0.262015
\(306\) −194890. −0.118983
\(307\) 878028. 0.531695 0.265847 0.964015i \(-0.414348\pi\)
0.265847 + 0.964015i \(0.414348\pi\)
\(308\) 189147. 0.113612
\(309\) −1.09677e6 −0.653463
\(310\) −434954. −0.257063
\(311\) −469932. −0.275508 −0.137754 0.990466i \(-0.543988\pi\)
−0.137754 + 0.990466i \(0.543988\pi\)
\(312\) −157818. −0.0917849
\(313\) 1.34014e6 0.773194 0.386597 0.922249i \(-0.373650\pi\)
0.386597 + 0.922249i \(0.373650\pi\)
\(314\) −846371. −0.484436
\(315\) −489397. −0.277898
\(316\) 934761. 0.526602
\(317\) −2.61609e6 −1.46219 −0.731096 0.682274i \(-0.760991\pi\)
−0.731096 + 0.682274i \(0.760991\pi\)
\(318\) −467294. −0.259133
\(319\) 83245.5 0.0458020
\(320\) −102400. −0.0559017
\(321\) 1.36359e6 0.738620
\(322\) 4.49994e6 2.41862
\(323\) −217146. −0.115810
\(324\) 104976. 0.0555556
\(325\) −171244. −0.0899305
\(326\) 1.84359e6 0.960772
\(327\) −236033. −0.122068
\(328\) 463531. 0.237900
\(329\) 869167. 0.442704
\(330\) −44023.7 −0.0222537
\(331\) −2.14809e6 −1.07766 −0.538831 0.842414i \(-0.681134\pi\)
−0.538831 + 0.842414i \(0.681134\pi\)
\(332\) −811991. −0.404302
\(333\) −327480. −0.161836
\(334\) −1.19202e6 −0.584678
\(335\) −454777. −0.221404
\(336\) −556825. −0.269073
\(337\) 3.34596e6 1.60489 0.802447 0.596723i \(-0.203531\pi\)
0.802447 + 0.596723i \(0.203531\pi\)
\(338\) 1.18489e6 0.564139
\(339\) 1.41723e6 0.669794
\(340\) −240605. −0.112878
\(341\) −212759. −0.0990835
\(342\) 116964. 0.0540738
\(343\) 5.99217e6 2.75010
\(344\) −605611. −0.275929
\(345\) −1.04735e6 −0.473746
\(346\) 1.69041e6 0.759104
\(347\) −495113. −0.220740 −0.110370 0.993891i \(-0.535204\pi\)
−0.110370 + 0.993891i \(0.535204\pi\)
\(348\) −245064. −0.108475
\(349\) 388990. 0.170952 0.0854762 0.996340i \(-0.472759\pi\)
0.0854762 + 0.996340i \(0.472759\pi\)
\(350\) −604194. −0.263637
\(351\) 199739. 0.0865356
\(352\) −50089.1 −0.0215470
\(353\) −1.91329e6 −0.817227 −0.408614 0.912707i \(-0.633988\pi\)
−0.408614 + 0.912707i \(0.633988\pi\)
\(354\) 103779. 0.0440150
\(355\) −69725.5 −0.0293644
\(356\) −880127. −0.368061
\(357\) −1.30835e6 −0.543317
\(358\) 173827. 0.0716820
\(359\) −1.12700e6 −0.461515 −0.230758 0.973011i \(-0.574120\pi\)
−0.230758 + 0.973011i \(0.574120\pi\)
\(360\) 129600. 0.0527046
\(361\) 130321. 0.0526316
\(362\) 768948. 0.308408
\(363\) 1.42792e6 0.568773
\(364\) −1.05948e6 −0.419120
\(365\) −1.19006e6 −0.467560
\(366\) −612969. −0.239186
\(367\) 4.69344e6 1.81897 0.909486 0.415735i \(-0.136475\pi\)
0.909486 + 0.415735i \(0.136475\pi\)
\(368\) −1.19166e6 −0.458702
\(369\) −586657. −0.224294
\(370\) −404297. −0.153531
\(371\) −3.13707e6 −1.18328
\(372\) 626334. 0.234665
\(373\) −325600. −0.121175 −0.0605874 0.998163i \(-0.519297\pi\)
−0.0605874 + 0.998163i \(0.519297\pi\)
\(374\) −117692. −0.0435080
\(375\) 140625. 0.0516398
\(376\) −230169. −0.0839609
\(377\) −466286. −0.168966
\(378\) 704732. 0.253685
\(379\) −4.29635e6 −1.53639 −0.768195 0.640216i \(-0.778845\pi\)
−0.768195 + 0.640216i \(0.778845\pi\)
\(380\) 144400. 0.0512989
\(381\) −1.53008e6 −0.540010
\(382\) −204400. −0.0716675
\(383\) −778069. −0.271032 −0.135516 0.990775i \(-0.543269\pi\)
−0.135516 + 0.990775i \(0.543269\pi\)
\(384\) 147456. 0.0510310
\(385\) −295543. −0.101617
\(386\) 2.06249e6 0.704568
\(387\) 766476. 0.260148
\(388\) −1.36174e6 −0.459215
\(389\) 1.40575e6 0.471015 0.235508 0.971873i \(-0.424325\pi\)
0.235508 + 0.971873i \(0.424325\pi\)
\(390\) 246591. 0.0820949
\(391\) −2.79998e6 −0.926219
\(392\) −2.66247e6 −0.875123
\(393\) −2.29463e6 −0.749431
\(394\) 2.23954e6 0.726805
\(395\) −1.46056e6 −0.471008
\(396\) 63394.1 0.0203147
\(397\) 4.27508e6 1.36134 0.680672 0.732589i \(-0.261688\pi\)
0.680672 + 0.732589i \(0.261688\pi\)
\(398\) 3.62062e6 1.14571
\(399\) 785210. 0.246919
\(400\) 160000. 0.0500000
\(401\) 5.58537e6 1.73457 0.867283 0.497816i \(-0.165865\pi\)
0.867283 + 0.497816i \(0.165865\pi\)
\(402\) 654878. 0.202114
\(403\) 1.19173e6 0.365524
\(404\) −1.79207e6 −0.546263
\(405\) −164025. −0.0496904
\(406\) −1.64518e6 −0.495334
\(407\) −197763. −0.0591777
\(408\) 346471. 0.103043
\(409\) −5.31519e6 −1.57112 −0.785562 0.618783i \(-0.787626\pi\)
−0.785562 + 0.618783i \(0.787626\pi\)
\(410\) −724268. −0.212784
\(411\) −2.71438e6 −0.792622
\(412\) 1.94982e6 0.565915
\(413\) 696695. 0.200987
\(414\) 1.50819e6 0.432469
\(415\) 1.26874e6 0.361619
\(416\) 280566. 0.0794880
\(417\) 810754. 0.228323
\(418\) 70633.5 0.0197729
\(419\) −6.55749e6 −1.82475 −0.912373 0.409361i \(-0.865752\pi\)
−0.912373 + 0.409361i \(0.865752\pi\)
\(420\) 870039. 0.240667
\(421\) 1.95134e6 0.536570 0.268285 0.963340i \(-0.413543\pi\)
0.268285 + 0.963340i \(0.413543\pi\)
\(422\) 2.88824e6 0.789500
\(423\) 291308. 0.0791591
\(424\) 830744. 0.224415
\(425\) 375945. 0.100961
\(426\) 100405. 0.0268059
\(427\) −4.11502e6 −1.09220
\(428\) −2.42416e6 −0.639664
\(429\) 120621. 0.0316430
\(430\) 946267. 0.246799
\(431\) 1.28413e6 0.332979 0.166490 0.986043i \(-0.446757\pi\)
0.166490 + 0.986043i \(0.446757\pi\)
\(432\) −186624. −0.0481125
\(433\) 3.19273e6 0.818356 0.409178 0.912455i \(-0.365815\pi\)
0.409178 + 0.912455i \(0.365815\pi\)
\(434\) 4.20475e6 1.07156
\(435\) 382913. 0.0970234
\(436\) 419614. 0.105714
\(437\) 1.68042e6 0.420934
\(438\) 1.71369e6 0.426822
\(439\) −6.27887e6 −1.55496 −0.777482 0.628905i \(-0.783503\pi\)
−0.777482 + 0.628905i \(0.783503\pi\)
\(440\) 78264.3 0.0192722
\(441\) 3.36969e6 0.825074
\(442\) 659235. 0.160503
\(443\) −1.54141e6 −0.373172 −0.186586 0.982439i \(-0.559742\pi\)
−0.186586 + 0.982439i \(0.559742\pi\)
\(444\) 582187. 0.140154
\(445\) 1.37520e6 0.329204
\(446\) 1.63520e6 0.389255
\(447\) 337243. 0.0798315
\(448\) 989911. 0.233024
\(449\) 6.96040e6 1.62937 0.814683 0.579907i \(-0.196911\pi\)
0.814683 + 0.579907i \(0.196911\pi\)
\(450\) −202500. −0.0471405
\(451\) −354277. −0.0820166
\(452\) −2.51952e6 −0.580058
\(453\) 3.09514e6 0.708655
\(454\) 2.44840e6 0.557497
\(455\) 1.65543e6 0.374872
\(456\) −207936. −0.0468293
\(457\) −529337. −0.118561 −0.0592805 0.998241i \(-0.518881\pi\)
−0.0592805 + 0.998241i \(0.518881\pi\)
\(458\) −1.09845e6 −0.244691
\(459\) −438503. −0.0971495
\(460\) 1.86196e6 0.410276
\(461\) −7.40968e6 −1.62385 −0.811927 0.583759i \(-0.801581\pi\)
−0.811927 + 0.583759i \(0.801581\pi\)
\(462\) 425581. 0.0927636
\(463\) −2.51847e6 −0.545989 −0.272995 0.962016i \(-0.588014\pi\)
−0.272995 + 0.962016i \(0.588014\pi\)
\(464\) 435669. 0.0939425
\(465\) −978647. −0.209891
\(466\) −1.30817e6 −0.279061
\(467\) −6.81787e6 −1.44663 −0.723313 0.690520i \(-0.757382\pi\)
−0.723313 + 0.690520i \(0.757382\pi\)
\(468\) −355091. −0.0749421
\(469\) 4.39637e6 0.922917
\(470\) 359639. 0.0750969
\(471\) −1.90433e6 −0.395541
\(472\) −184496. −0.0381181
\(473\) 462868. 0.0951272
\(474\) 2.10321e6 0.429969
\(475\) −225625. −0.0458831
\(476\) 2.32595e6 0.470526
\(477\) −1.05141e6 −0.211581
\(478\) 2.15676e6 0.431749
\(479\) 9.82434e6 1.95643 0.978215 0.207593i \(-0.0665628\pi\)
0.978215 + 0.207593i \(0.0665628\pi\)
\(480\) −230400. −0.0456435
\(481\) 1.10773e6 0.218310
\(482\) 409964. 0.0803763
\(483\) 1.01249e7 1.97479
\(484\) −2.53853e6 −0.492572
\(485\) 2.12772e6 0.410734
\(486\) 236196. 0.0453609
\(487\) −7.71482e6 −1.47402 −0.737010 0.675882i \(-0.763763\pi\)
−0.737010 + 0.675882i \(0.763763\pi\)
\(488\) 1.08972e6 0.207141
\(489\) 4.14808e6 0.784467
\(490\) 4.16011e6 0.782734
\(491\) 3.43591e6 0.643189 0.321595 0.946877i \(-0.395781\pi\)
0.321595 + 0.946877i \(0.395781\pi\)
\(492\) 1.04295e6 0.194245
\(493\) 1.02367e6 0.189690
\(494\) −395642. −0.0729432
\(495\) −99053.2 −0.0181700
\(496\) −1.11348e6 −0.203226
\(497\) 674044. 0.122404
\(498\) −1.82698e6 −0.330111
\(499\) −485954. −0.0873663 −0.0436832 0.999045i \(-0.513909\pi\)
−0.0436832 + 0.999045i \(0.513909\pi\)
\(500\) −250000. −0.0447214
\(501\) −2.68204e6 −0.477388
\(502\) 3.72579e6 0.659870
\(503\) −4.76630e6 −0.839966 −0.419983 0.907532i \(-0.637964\pi\)
−0.419983 + 0.907532i \(0.637964\pi\)
\(504\) −1.25286e6 −0.219697
\(505\) 2.80011e6 0.488592
\(506\) 910782. 0.158139
\(507\) 2.66600e6 0.460617
\(508\) 2.72014e6 0.467663
\(509\) −9.08039e6 −1.55350 −0.776748 0.629812i \(-0.783132\pi\)
−0.776748 + 0.629812i \(0.783132\pi\)
\(510\) −541361. −0.0921641
\(511\) 1.15044e7 1.94901
\(512\) −262144. −0.0441942
\(513\) 263169. 0.0441511
\(514\) 118027. 0.0197048
\(515\) −3.04659e6 −0.506170
\(516\) −1.36262e6 −0.225295
\(517\) 175918. 0.0289457
\(518\) 3.90838e6 0.639989
\(519\) 3.80342e6 0.619806
\(520\) −438385. −0.0710963
\(521\) 4.07561e6 0.657807 0.328904 0.944363i \(-0.393321\pi\)
0.328904 + 0.944363i \(0.393321\pi\)
\(522\) −551394. −0.0885698
\(523\) −7.54955e6 −1.20689 −0.603444 0.797405i \(-0.706205\pi\)
−0.603444 + 0.797405i \(0.706205\pi\)
\(524\) 4.07935e6 0.649026
\(525\) −1.35944e6 −0.215259
\(526\) −5.07764e6 −0.800198
\(527\) −2.61630e6 −0.410357
\(528\) −112701. −0.0175931
\(529\) 1.52318e7 2.36653
\(530\) −1.29804e6 −0.200723
\(531\) 233502. 0.0359381
\(532\) −1.39593e6 −0.213838
\(533\) 1.98442e6 0.302563
\(534\) −1.98029e6 −0.300521
\(535\) 3.78775e6 0.572133
\(536\) −1.16423e6 −0.175036
\(537\) 391111. 0.0585281
\(538\) 7.87448e6 1.17291
\(539\) 2.03492e6 0.301701
\(540\) 291600. 0.0430331
\(541\) −6.84906e6 −1.00609 −0.503046 0.864260i \(-0.667787\pi\)
−0.503046 + 0.864260i \(0.667787\pi\)
\(542\) −2.19573e6 −0.321056
\(543\) 1.73013e6 0.251814
\(544\) −615949. −0.0892375
\(545\) −655647. −0.0945537
\(546\) −2.38382e6 −0.342210
\(547\) −4.68823e6 −0.669948 −0.334974 0.942227i \(-0.608727\pi\)
−0.334974 + 0.942227i \(0.608727\pi\)
\(548\) 4.82557e6 0.686431
\(549\) −1.37918e6 −0.195294
\(550\) −122288. −0.0172376
\(551\) −614362. −0.0862075
\(552\) −2.68122e6 −0.374529
\(553\) 1.41194e7 1.96338
\(554\) −7.41197e6 −1.02603
\(555\) −909668. −0.125358
\(556\) −1.44134e6 −0.197733
\(557\) −3.10332e6 −0.423827 −0.211913 0.977288i \(-0.567969\pi\)
−0.211913 + 0.977288i \(0.567969\pi\)
\(558\) 1.40925e6 0.191603
\(559\) −2.59268e6 −0.350929
\(560\) −1.54674e6 −0.208423
\(561\) −264808. −0.0355242
\(562\) 9.03217e6 1.20629
\(563\) 3.39399e6 0.451274 0.225637 0.974211i \(-0.427554\pi\)
0.225637 + 0.974211i \(0.427554\pi\)
\(564\) −517880. −0.0685538
\(565\) 3.93675e6 0.518820
\(566\) −7.63687e6 −1.00202
\(567\) 1.58565e6 0.207133
\(568\) −178497. −0.0232146
\(569\) 5.18383e6 0.671228 0.335614 0.942000i \(-0.391056\pi\)
0.335614 + 0.942000i \(0.391056\pi\)
\(570\) 324900. 0.0418854
\(571\) −2.15935e6 −0.277161 −0.138581 0.990351i \(-0.544254\pi\)
−0.138581 + 0.990351i \(0.544254\pi\)
\(572\) −214437. −0.0274037
\(573\) −459900. −0.0585162
\(574\) 7.00157e6 0.886984
\(575\) −2.90931e6 −0.366962
\(576\) 331776. 0.0416667
\(577\) 1.52795e6 0.191060 0.0955299 0.995427i \(-0.469545\pi\)
0.0955299 + 0.995427i \(0.469545\pi\)
\(578\) 4.23216e6 0.526917
\(579\) 4.64059e6 0.575277
\(580\) −680733. −0.0840247
\(581\) −1.22650e7 −1.50740
\(582\) −3.06392e6 −0.374947
\(583\) −634937. −0.0773677
\(584\) −3.04656e6 −0.369638
\(585\) 554830. 0.0670302
\(586\) −9.33413e6 −1.12287
\(587\) −8.44316e6 −1.01137 −0.505684 0.862719i \(-0.668760\pi\)
−0.505684 + 0.862719i \(0.668760\pi\)
\(588\) −5.99055e6 −0.714535
\(589\) 1.57018e6 0.186493
\(590\) 288274. 0.0340939
\(591\) 5.03896e6 0.593434
\(592\) −1.03500e6 −0.121377
\(593\) 4.70109e6 0.548987 0.274494 0.961589i \(-0.411490\pi\)
0.274494 + 0.961589i \(0.411490\pi\)
\(594\) 142637. 0.0165869
\(595\) −3.63430e6 −0.420851
\(596\) −599543. −0.0691361
\(597\) 8.14639e6 0.935469
\(598\) −5.10159e6 −0.583382
\(599\) −3.34478e6 −0.380891 −0.190445 0.981698i \(-0.560993\pi\)
−0.190445 + 0.981698i \(0.560993\pi\)
\(600\) 360000. 0.0408248
\(601\) −2.61862e6 −0.295723 −0.147862 0.989008i \(-0.547239\pi\)
−0.147862 + 0.989008i \(0.547239\pi\)
\(602\) −9.14766e6 −1.02877
\(603\) 1.47348e6 0.165025
\(604\) −5.50247e6 −0.613713
\(605\) 3.96646e6 0.440569
\(606\) −4.03216e6 −0.446022
\(607\) −7.66986e6 −0.844920 −0.422460 0.906382i \(-0.638833\pi\)
−0.422460 + 0.906382i \(0.638833\pi\)
\(608\) 369664. 0.0405554
\(609\) −3.70166e6 −0.404439
\(610\) −1.70269e6 −0.185273
\(611\) −985376. −0.106782
\(612\) 779560. 0.0841339
\(613\) −6.36378e6 −0.684012 −0.342006 0.939698i \(-0.611106\pi\)
−0.342006 + 0.939698i \(0.611106\pi\)
\(614\) −3.51211e6 −0.375965
\(615\) −1.62960e6 −0.173738
\(616\) −756589. −0.0803356
\(617\) −3.24409e6 −0.343068 −0.171534 0.985178i \(-0.554872\pi\)
−0.171534 + 0.985178i \(0.554872\pi\)
\(618\) 4.38709e6 0.462068
\(619\) −5.90973e6 −0.619928 −0.309964 0.950748i \(-0.600317\pi\)
−0.309964 + 0.950748i \(0.600317\pi\)
\(620\) 1.73982e6 0.181771
\(621\) 3.39342e6 0.353109
\(622\) 1.87973e6 0.194813
\(623\) −1.32942e7 −1.37228
\(624\) 631274. 0.0649017
\(625\) 390625. 0.0400000
\(626\) −5.36055e6 −0.546731
\(627\) 158925. 0.0161445
\(628\) 3.38548e6 0.342548
\(629\) −2.43190e6 −0.245086
\(630\) 1.95759e6 0.196503
\(631\) −9.48728e6 −0.948568 −0.474284 0.880372i \(-0.657293\pi\)
−0.474284 + 0.880372i \(0.657293\pi\)
\(632\) −3.73904e6 −0.372364
\(633\) 6.49854e6 0.644624
\(634\) 1.04644e7 1.03393
\(635\) −4.25023e6 −0.418290
\(636\) 1.86917e6 0.183234
\(637\) −1.13983e7 −1.11299
\(638\) −332982. −0.0323869
\(639\) 225911. 0.0218869
\(640\) 409600. 0.0395285
\(641\) −1.30834e7 −1.25770 −0.628849 0.777528i \(-0.716473\pi\)
−0.628849 + 0.777528i \(0.716473\pi\)
\(642\) −5.45436e6 −0.522283
\(643\) −1.53137e6 −0.146067 −0.0730337 0.997329i \(-0.523268\pi\)
−0.0730337 + 0.997329i \(0.523268\pi\)
\(644\) −1.79998e7 −1.71022
\(645\) 2.12910e6 0.201510
\(646\) 868584. 0.0818900
\(647\) −1.02797e7 −0.965428 −0.482714 0.875778i \(-0.660349\pi\)
−0.482714 + 0.875778i \(0.660349\pi\)
\(648\) −419904. −0.0392837
\(649\) 141010. 0.0131413
\(650\) 684976. 0.0635904
\(651\) 9.46068e6 0.874923
\(652\) −7.37436e6 −0.679369
\(653\) 8.17907e6 0.750621 0.375311 0.926899i \(-0.377536\pi\)
0.375311 + 0.926899i \(0.377536\pi\)
\(654\) 944132. 0.0863154
\(655\) −6.37398e6 −0.580507
\(656\) −1.85413e6 −0.168221
\(657\) 3.85580e6 0.348498
\(658\) −3.47667e6 −0.313039
\(659\) 9.70084e6 0.870153 0.435076 0.900394i \(-0.356721\pi\)
0.435076 + 0.900394i \(0.356721\pi\)
\(660\) 176095. 0.0157357
\(661\) 4.46335e6 0.397336 0.198668 0.980067i \(-0.436339\pi\)
0.198668 + 0.980067i \(0.436339\pi\)
\(662\) 8.59236e6 0.762022
\(663\) 1.48328e6 0.131050
\(664\) 3.24797e6 0.285885
\(665\) 2.18114e6 0.191262
\(666\) 1.30992e6 0.114435
\(667\) −7.92187e6 −0.689466
\(668\) 4.76808e6 0.413430
\(669\) 3.67921e6 0.317826
\(670\) 1.81911e6 0.156557
\(671\) −832874. −0.0714123
\(672\) 2.22730e6 0.190264
\(673\) 3.74229e6 0.318493 0.159246 0.987239i \(-0.449094\pi\)
0.159246 + 0.987239i \(0.449094\pi\)
\(674\) −1.33839e7 −1.13483
\(675\) −455625. −0.0384900
\(676\) −4.73956e6 −0.398906
\(677\) 4.60520e6 0.386168 0.193084 0.981182i \(-0.438151\pi\)
0.193084 + 0.981182i \(0.438151\pi\)
\(678\) −5.66892e6 −0.473616
\(679\) −2.05689e7 −1.71213
\(680\) 962420. 0.0798165
\(681\) 5.50889e6 0.455194
\(682\) 851034. 0.0700626
\(683\) −1.04539e7 −0.857484 −0.428742 0.903427i \(-0.641043\pi\)
−0.428742 + 0.903427i \(0.641043\pi\)
\(684\) −467856. −0.0382360
\(685\) −7.53995e6 −0.613963
\(686\) −2.39687e7 −1.94462
\(687\) −2.47152e6 −0.199789
\(688\) 2.42244e6 0.195111
\(689\) 3.55650e6 0.285413
\(690\) 4.18941e6 0.334989
\(691\) 1.22485e7 0.975863 0.487931 0.872882i \(-0.337752\pi\)
0.487931 + 0.872882i \(0.337752\pi\)
\(692\) −6.76163e6 −0.536768
\(693\) 957558. 0.0757412
\(694\) 1.98045e6 0.156087
\(695\) 2.25209e6 0.176858
\(696\) 980256. 0.0767037
\(697\) −4.35656e6 −0.339674
\(698\) −1.55596e6 −0.120882
\(699\) −2.94339e6 −0.227853
\(700\) 2.41678e6 0.186419
\(701\) 1.70224e7 1.30835 0.654177 0.756342i \(-0.273015\pi\)
0.654177 + 0.756342i \(0.273015\pi\)
\(702\) −798956. −0.0611899
\(703\) 1.45951e6 0.111383
\(704\) 200357. 0.0152360
\(705\) 809188. 0.0613164
\(706\) 7.65314e6 0.577867
\(707\) −2.70690e7 −2.03668
\(708\) −415115. −0.0311233
\(709\) −1.32934e7 −0.993160 −0.496580 0.867991i \(-0.665411\pi\)
−0.496580 + 0.867991i \(0.665411\pi\)
\(710\) 278902. 0.0207638
\(711\) 4.73223e6 0.351068
\(712\) 3.52051e6 0.260259
\(713\) 2.02467e7 1.49152
\(714\) 5.23340e6 0.384183
\(715\) 335057. 0.0245106
\(716\) −695309. −0.0506869
\(717\) 4.85270e6 0.352522
\(718\) 4.50798e6 0.326341
\(719\) 1.73058e7 1.24845 0.624224 0.781246i \(-0.285415\pi\)
0.624224 + 0.781246i \(0.285415\pi\)
\(720\) −518400. −0.0372678
\(721\) 2.94517e7 2.10995
\(722\) −521284. −0.0372161
\(723\) 922418. 0.0656270
\(724\) −3.07579e6 −0.218077
\(725\) 1.06365e6 0.0751540
\(726\) −5.71170e6 −0.402183
\(727\) −1.60509e7 −1.12632 −0.563161 0.826347i \(-0.690415\pi\)
−0.563161 + 0.826347i \(0.690415\pi\)
\(728\) 4.23791e6 0.296362
\(729\) 531441. 0.0370370
\(730\) 4.76024e6 0.330615
\(731\) 5.69192e6 0.393972
\(732\) 2.45188e6 0.169130
\(733\) −1.83712e7 −1.26292 −0.631461 0.775408i \(-0.717544\pi\)
−0.631461 + 0.775408i \(0.717544\pi\)
\(734\) −1.87738e7 −1.28621
\(735\) 9.36024e6 0.639100
\(736\) 4.76662e6 0.324352
\(737\) 889819. 0.0603439
\(738\) 2.34663e6 0.158600
\(739\) −1.07251e7 −0.722420 −0.361210 0.932484i \(-0.617636\pi\)
−0.361210 + 0.932484i \(0.617636\pi\)
\(740\) 1.61719e6 0.108563
\(741\) −890195. −0.0595579
\(742\) 1.25483e7 0.836708
\(743\) 2.08108e7 1.38299 0.691493 0.722384i \(-0.256953\pi\)
0.691493 + 0.722384i \(0.256953\pi\)
\(744\) −2.50534e6 −0.165933
\(745\) 936786. 0.0618372
\(746\) 1.30240e6 0.0856836
\(747\) −4.11071e6 −0.269535
\(748\) 470770. 0.0307648
\(749\) −3.66166e7 −2.38492
\(750\) −562500. −0.0365148
\(751\) −1.73564e7 −1.12295 −0.561475 0.827494i \(-0.689766\pi\)
−0.561475 + 0.827494i \(0.689766\pi\)
\(752\) 920676. 0.0593693
\(753\) 8.38302e6 0.538782
\(754\) 1.86514e6 0.119477
\(755\) 8.59761e6 0.548922
\(756\) −2.81893e6 −0.179382
\(757\) −1.81699e7 −1.15243 −0.576214 0.817299i \(-0.695470\pi\)
−0.576214 + 0.817299i \(0.695470\pi\)
\(758\) 1.71854e7 1.08639
\(759\) 2.04926e6 0.129120
\(760\) −577600. −0.0362738
\(761\) −1.77814e7 −1.11303 −0.556513 0.830839i \(-0.687861\pi\)
−0.556513 + 0.830839i \(0.687861\pi\)
\(762\) 6.12032e6 0.381845
\(763\) 6.33821e6 0.394144
\(764\) 817599. 0.0506766
\(765\) −1.21806e6 −0.0752517
\(766\) 3.11228e6 0.191649
\(767\) −789844. −0.0484789
\(768\) −589824. −0.0360844
\(769\) −2.28095e7 −1.39091 −0.695457 0.718568i \(-0.744798\pi\)
−0.695457 + 0.718568i \(0.744798\pi\)
\(770\) 1.18217e6 0.0718544
\(771\) 265560. 0.0160889
\(772\) −8.24994e6 −0.498205
\(773\) −1.00065e7 −0.602326 −0.301163 0.953573i \(-0.597375\pi\)
−0.301163 + 0.953573i \(0.597375\pi\)
\(774\) −3.06591e6 −0.183953
\(775\) −2.71846e6 −0.162581
\(776\) 5.44697e6 0.324714
\(777\) 8.79385e6 0.522549
\(778\) −5.62301e6 −0.333058
\(779\) 2.61461e6 0.154370
\(780\) −986365. −0.0580499
\(781\) 136425. 0.00800328
\(782\) 1.11999e7 0.654935
\(783\) −1.24064e6 −0.0723170
\(784\) 1.06499e7 0.618806
\(785\) −5.28982e6 −0.306384
\(786\) 9.17853e6 0.529928
\(787\) 1.54717e7 0.890434 0.445217 0.895423i \(-0.353127\pi\)
0.445217 + 0.895423i \(0.353127\pi\)
\(788\) −8.95815e6 −0.513929
\(789\) −1.14247e7 −0.653359
\(790\) 5.84226e6 0.333053
\(791\) −3.80570e7 −2.16268
\(792\) −253576. −0.0143647
\(793\) 4.66521e6 0.263444
\(794\) −1.71003e7 −0.962615
\(795\) −2.92058e6 −0.163890
\(796\) −1.44825e7 −0.810140
\(797\) 1.03258e6 0.0575806 0.0287903 0.999585i \(-0.490834\pi\)
0.0287903 + 0.999585i \(0.490834\pi\)
\(798\) −3.14084e6 −0.174598
\(799\) 2.16327e6 0.119879
\(800\) −640000. −0.0353553
\(801\) −4.45564e6 −0.245374
\(802\) −2.23415e7 −1.22652
\(803\) 2.32848e6 0.127434
\(804\) −2.61951e6 −0.142916
\(805\) 2.81246e7 1.52967
\(806\) −4.76693e6 −0.258465
\(807\) 1.77176e7 0.957680
\(808\) 7.16828e6 0.386266
\(809\) 5.97165e6 0.320792 0.160396 0.987053i \(-0.448723\pi\)
0.160396 + 0.987053i \(0.448723\pi\)
\(810\) 656100. 0.0351364
\(811\) 1.63253e7 0.871586 0.435793 0.900047i \(-0.356468\pi\)
0.435793 + 0.900047i \(0.356468\pi\)
\(812\) 6.58072e6 0.350254
\(813\) −4.94040e6 −0.262141
\(814\) 791050. 0.0418449
\(815\) 1.15224e7 0.607646
\(816\) −1.38589e6 −0.0728621
\(817\) −3.41602e6 −0.179046
\(818\) 2.12607e7 1.11095
\(819\) −5.36360e6 −0.279413
\(820\) 2.89707e6 0.150461
\(821\) −1.91047e7 −0.989199 −0.494599 0.869121i \(-0.664685\pi\)
−0.494599 + 0.869121i \(0.664685\pi\)
\(822\) 1.08575e7 0.560469
\(823\) 1.42437e7 0.733031 0.366516 0.930412i \(-0.380551\pi\)
0.366516 + 0.930412i \(0.380551\pi\)
\(824\) −7.79928e6 −0.400163
\(825\) −275148. −0.0140744
\(826\) −2.78678e6 −0.142119
\(827\) −5.77314e6 −0.293527 −0.146764 0.989172i \(-0.546886\pi\)
−0.146764 + 0.989172i \(0.546886\pi\)
\(828\) −6.03275e6 −0.305802
\(829\) −2.71339e7 −1.37128 −0.685640 0.727941i \(-0.740478\pi\)
−0.685640 + 0.727941i \(0.740478\pi\)
\(830\) −5.07495e6 −0.255703
\(831\) −1.66769e7 −0.837749
\(832\) −1.12226e6 −0.0562065
\(833\) 2.50236e7 1.24950
\(834\) −3.24302e6 −0.161448
\(835\) −7.45012e6 −0.369783
\(836\) −282534. −0.0139815
\(837\) 3.17082e6 0.156443
\(838\) 2.62299e7 1.29029
\(839\) 2.28209e7 1.11925 0.559627 0.828745i \(-0.310944\pi\)
0.559627 + 0.828745i \(0.310944\pi\)
\(840\) −3.48016e6 −0.170177
\(841\) −1.76149e7 −0.858797
\(842\) −7.80534e6 −0.379413
\(843\) 2.03224e7 0.984931
\(844\) −1.15530e7 −0.558261
\(845\) 7.40556e6 0.356793
\(846\) −1.16523e6 −0.0559739
\(847\) −3.83442e7 −1.83650
\(848\) −3.32298e6 −0.158686
\(849\) −1.71830e7 −0.818142
\(850\) −1.50378e6 −0.0713900
\(851\) 1.88196e7 0.890814
\(852\) −401619. −0.0189546
\(853\) 3.22282e7 1.51657 0.758287 0.651921i \(-0.226037\pi\)
0.758287 + 0.651921i \(0.226037\pi\)
\(854\) 1.64601e7 0.772303
\(855\) 731025. 0.0341993
\(856\) 9.69664e6 0.452310
\(857\) 1.78756e7 0.831396 0.415698 0.909503i \(-0.363537\pi\)
0.415698 + 0.909503i \(0.363537\pi\)
\(858\) −482482. −0.0223750
\(859\) 1.66307e7 0.769005 0.384502 0.923124i \(-0.374373\pi\)
0.384502 + 0.923124i \(0.374373\pi\)
\(860\) −3.78507e6 −0.174513
\(861\) 1.57535e7 0.724220
\(862\) −5.13653e6 −0.235452
\(863\) −6.66946e6 −0.304834 −0.152417 0.988316i \(-0.548706\pi\)
−0.152417 + 0.988316i \(0.548706\pi\)
\(864\) 746496. 0.0340207
\(865\) 1.05651e7 0.480100
\(866\) −1.27709e7 −0.578665
\(867\) 9.52236e6 0.430226
\(868\) −1.68190e7 −0.757706
\(869\) 2.85775e6 0.128373
\(870\) −1.53165e6 −0.0686059
\(871\) −4.98418e6 −0.222612
\(872\) −1.67846e6 −0.0747513
\(873\) −6.89382e6 −0.306143
\(874\) −6.72168e6 −0.297645
\(875\) −3.77621e6 −0.166739
\(876\) −6.85475e6 −0.301808
\(877\) −2.26346e7 −0.993744 −0.496872 0.867824i \(-0.665518\pi\)
−0.496872 + 0.867824i \(0.665518\pi\)
\(878\) 2.51155e7 1.09953
\(879\) −2.10018e7 −0.916820
\(880\) −313057. −0.0136275
\(881\) −1.51706e7 −0.658512 −0.329256 0.944241i \(-0.606798\pi\)
−0.329256 + 0.944241i \(0.606798\pi\)
\(882\) −1.34787e7 −0.583415
\(883\) 1.10451e7 0.476724 0.238362 0.971176i \(-0.423390\pi\)
0.238362 + 0.971176i \(0.423390\pi\)
\(884\) −2.63694e6 −0.113493
\(885\) 648617. 0.0278375
\(886\) 6.16565e6 0.263873
\(887\) 5.03118e6 0.214714 0.107357 0.994221i \(-0.465761\pi\)
0.107357 + 0.994221i \(0.465761\pi\)
\(888\) −2.32875e6 −0.0991038
\(889\) 4.10874e7 1.74363
\(890\) −5.50079e6 −0.232782
\(891\) 320932. 0.0135431
\(892\) −6.54081e6 −0.275245
\(893\) −1.29830e6 −0.0544810
\(894\) −1.34897e6 −0.0564494
\(895\) 1.08642e6 0.0453357
\(896\) −3.95965e6 −0.164773
\(897\) −1.14786e7 −0.476329
\(898\) −2.78416e7 −1.15214
\(899\) −7.40220e6 −0.305465
\(900\) 810000. 0.0333333
\(901\) −7.80786e6 −0.320420
\(902\) 1.41711e6 0.0579945
\(903\) −2.05822e7 −0.839988
\(904\) 1.00781e7 0.410163
\(905\) 4.80593e6 0.195054
\(906\) −1.23806e7 −0.501095
\(907\) −1.33481e7 −0.538768 −0.269384 0.963033i \(-0.586820\pi\)
−0.269384 + 0.963033i \(0.586820\pi\)
\(908\) −9.79359e6 −0.394210
\(909\) −9.07236e6 −0.364175
\(910\) −6.62173e6 −0.265075
\(911\) 1.03425e7 0.412884 0.206442 0.978459i \(-0.433812\pi\)
0.206442 + 0.978459i \(0.433812\pi\)
\(912\) 831744. 0.0331133
\(913\) −2.48242e6 −0.0985594
\(914\) 2.11735e6 0.0838353
\(915\) −3.83105e6 −0.151274
\(916\) 4.39382e6 0.173023
\(917\) 6.16179e7 2.41982
\(918\) 1.75401e6 0.0686951
\(919\) 3.74100e7 1.46116 0.730582 0.682825i \(-0.239249\pi\)
0.730582 + 0.682825i \(0.239249\pi\)
\(920\) −7.44784e6 −0.290109
\(921\) −7.90225e6 −0.306974
\(922\) 2.96387e7 1.14824
\(923\) −764165. −0.0295245
\(924\) −1.70233e6 −0.0655938
\(925\) −2.52686e6 −0.0971015
\(926\) 1.00739e7 0.386073
\(927\) 9.87096e6 0.377277
\(928\) −1.74268e6 −0.0664274
\(929\) 1.06945e7 0.406556 0.203278 0.979121i \(-0.434840\pi\)
0.203278 + 0.979121i \(0.434840\pi\)
\(930\) 3.91459e6 0.148415
\(931\) −1.50180e7 −0.567855
\(932\) 5.23269e6 0.197326
\(933\) 4.22939e6 0.159065
\(934\) 2.72715e7 1.02292
\(935\) −735577. −0.0275169
\(936\) 1.42037e6 0.0529920
\(937\) 3.74036e7 1.39176 0.695881 0.718157i \(-0.255014\pi\)
0.695881 + 0.718157i \(0.255014\pi\)
\(938\) −1.75855e7 −0.652601
\(939\) −1.20612e7 −0.446404
\(940\) −1.43856e6 −0.0531016
\(941\) 3.60949e7 1.32884 0.664419 0.747360i \(-0.268679\pi\)
0.664419 + 0.747360i \(0.268679\pi\)
\(942\) 7.61734e6 0.279689
\(943\) 3.37140e7 1.23461
\(944\) 737982. 0.0269536
\(945\) 4.40457e6 0.160444
\(946\) −1.85147e6 −0.0672651
\(947\) −2.01552e7 −0.730320 −0.365160 0.930945i \(-0.618986\pi\)
−0.365160 + 0.930945i \(0.618986\pi\)
\(948\) −8.41285e6 −0.304034
\(949\) −1.30426e7 −0.470109
\(950\) 902500. 0.0324443
\(951\) 2.35448e7 0.844197
\(952\) −9.30382e6 −0.332712
\(953\) 3.16559e7 1.12907 0.564537 0.825408i \(-0.309055\pi\)
0.564537 + 0.825408i \(0.309055\pi\)
\(954\) 4.20564e6 0.149610
\(955\) −1.27750e6 −0.0453265
\(956\) −8.62702e6 −0.305293
\(957\) −749209. −0.0264438
\(958\) −3.92973e7 −1.38341
\(959\) 7.28895e7 2.55928
\(960\) 921600. 0.0322749
\(961\) −9.71064e6 −0.339187
\(962\) −4.43094e6 −0.154368
\(963\) −1.22723e7 −0.426442
\(964\) −1.63986e6 −0.0568346
\(965\) 1.28905e7 0.445608
\(966\) −4.04995e7 −1.39639
\(967\) 7.36938e6 0.253434 0.126717 0.991939i \(-0.459556\pi\)
0.126717 + 0.991939i \(0.459556\pi\)
\(968\) 1.01541e7 0.348301
\(969\) 1.95431e6 0.0668629
\(970\) −8.51089e6 −0.290433
\(971\) −2.15114e7 −0.732183 −0.366092 0.930579i \(-0.619304\pi\)
−0.366092 + 0.930579i \(0.619304\pi\)
\(972\) −944784. −0.0320750
\(973\) −2.17712e7 −0.737226
\(974\) 3.08593e7 1.04229
\(975\) 1.54120e6 0.0519214
\(976\) −4.35889e6 −0.146471
\(977\) −8.15455e6 −0.273315 −0.136657 0.990618i \(-0.543636\pi\)
−0.136657 + 0.990618i \(0.543636\pi\)
\(978\) −1.65923e7 −0.554702
\(979\) −2.69072e6 −0.0897247
\(980\) −1.66404e7 −0.553476
\(981\) 2.12430e6 0.0704762
\(982\) −1.37437e7 −0.454803
\(983\) 4.52106e7 1.49230 0.746150 0.665778i \(-0.231900\pi\)
0.746150 + 0.665778i \(0.231900\pi\)
\(984\) −4.17178e6 −0.137352
\(985\) 1.39971e7 0.459672
\(986\) −4.09470e6 −0.134131
\(987\) −7.82250e6 −0.255595
\(988\) 1.58257e6 0.0515787
\(989\) −4.40478e7 −1.43197
\(990\) 396213. 0.0128482
\(991\) −1.96001e7 −0.633979 −0.316989 0.948429i \(-0.602672\pi\)
−0.316989 + 0.948429i \(0.602672\pi\)
\(992\) 4.45393e6 0.143702
\(993\) 1.93328e7 0.622189
\(994\) −2.69618e6 −0.0865530
\(995\) 2.26289e7 0.724611
\(996\) 7.30792e6 0.233424
\(997\) 5.61167e7 1.78794 0.893972 0.448122i \(-0.147907\pi\)
0.893972 + 0.448122i \(0.147907\pi\)
\(998\) 1.94382e6 0.0617773
\(999\) 2.94732e6 0.0934360
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 570.6.a.i.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
570.6.a.i.1.4 4 1.1 even 1 trivial