Properties

Label 130.6.a.f.1.1
Level $130$
Weight $6$
Character 130.1
Self dual yes
Analytic conductor $20.850$
Analytic rank $1$
Dimension $3$
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] = [130,6,Mod(1,130)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(130, 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("130.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 130 = 2 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 130.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: \(20.8498965757\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.1458804.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 361x - 1139 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(20.8905\) of defining polynomial
Character \(\chi\) \(=\) 130.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.00000 q^{2} -27.8905 q^{3} +16.0000 q^{4} +25.0000 q^{5} +111.562 q^{6} -240.426 q^{7} -64.0000 q^{8} +534.880 q^{9} -100.000 q^{10} +544.151 q^{11} -446.248 q^{12} +169.000 q^{13} +961.702 q^{14} -697.262 q^{15} +256.000 q^{16} +1629.30 q^{17} -2139.52 q^{18} -805.920 q^{19} +400.000 q^{20} +6705.59 q^{21} -2176.61 q^{22} +373.152 q^{23} +1784.99 q^{24} +625.000 q^{25} -676.000 q^{26} -8140.67 q^{27} -3846.81 q^{28} +1503.62 q^{29} +2789.05 q^{30} -2200.08 q^{31} -1024.00 q^{32} -15176.7 q^{33} -6517.20 q^{34} -6010.64 q^{35} +8558.08 q^{36} -13109.1 q^{37} +3223.68 q^{38} -4713.49 q^{39} -1600.00 q^{40} -17099.9 q^{41} -26822.4 q^{42} -8935.58 q^{43} +8706.42 q^{44} +13372.0 q^{45} -1492.61 q^{46} +15749.7 q^{47} -7139.97 q^{48} +40997.5 q^{49} -2500.00 q^{50} -45442.0 q^{51} +2704.00 q^{52} +40379.7 q^{53} +32562.7 q^{54} +13603.8 q^{55} +15387.2 q^{56} +22477.5 q^{57} -6014.46 q^{58} -47562.1 q^{59} -11156.2 q^{60} -30280.0 q^{61} +8800.31 q^{62} -128599. q^{63} +4096.00 q^{64} +4225.00 q^{65} +60706.6 q^{66} +38769.4 q^{67} +26068.8 q^{68} -10407.4 q^{69} +24042.6 q^{70} -10519.7 q^{71} -34232.3 q^{72} +1582.12 q^{73} +52436.5 q^{74} -17431.6 q^{75} -12894.7 q^{76} -130828. q^{77} +18854.0 q^{78} -6191.23 q^{79} +6400.00 q^{80} +97071.7 q^{81} +68399.8 q^{82} +37849.2 q^{83} +107289. q^{84} +40732.5 q^{85} +35742.3 q^{86} -41936.6 q^{87} -34825.7 q^{88} +49151.0 q^{89} -53488.0 q^{90} -40631.9 q^{91} +5970.43 q^{92} +61361.3 q^{93} -62999.0 q^{94} -20148.0 q^{95} +28559.9 q^{96} -15654.2 q^{97} -163990. q^{98} +291056. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 12 q^{2} - 22 q^{3} + 48 q^{4} + 75 q^{5} + 88 q^{6} - 234 q^{7} - 192 q^{8} + 155 q^{9} - 300 q^{10} + 48 q^{11} - 352 q^{12} + 507 q^{13} + 936 q^{14} - 550 q^{15} + 768 q^{16} + 1506 q^{17} - 620 q^{18}+ \cdots + 350340 q^{99}+O(q^{100}) \) 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
\(3\) −27.8905 −1.78918 −0.894588 0.446892i \(-0.852531\pi\)
−0.894588 + 0.446892i \(0.852531\pi\)
\(4\) 16.0000 0.500000
\(5\) 25.0000 0.447214
\(6\) 111.562 1.26514
\(7\) −240.426 −1.85454 −0.927269 0.374397i \(-0.877850\pi\)
−0.927269 + 0.374397i \(0.877850\pi\)
\(8\) −64.0000 −0.353553
\(9\) 534.880 2.20115
\(10\) −100.000 −0.316228
\(11\) 544.151 1.35593 0.677966 0.735093i \(-0.262862\pi\)
0.677966 + 0.735093i \(0.262862\pi\)
\(12\) −446.248 −0.894588
\(13\) 169.000 0.277350
\(14\) 961.702 1.31136
\(15\) −697.262 −0.800144
\(16\) 256.000 0.250000
\(17\) 1629.30 1.36735 0.683673 0.729788i \(-0.260381\pi\)
0.683673 + 0.729788i \(0.260381\pi\)
\(18\) −2139.52 −1.55645
\(19\) −805.920 −0.512162 −0.256081 0.966655i \(-0.582431\pi\)
−0.256081 + 0.966655i \(0.582431\pi\)
\(20\) 400.000 0.223607
\(21\) 6705.59 3.31809
\(22\) −2176.61 −0.958789
\(23\) 373.152 0.147084 0.0735421 0.997292i \(-0.476570\pi\)
0.0735421 + 0.997292i \(0.476570\pi\)
\(24\) 1784.99 0.632569
\(25\) 625.000 0.200000
\(26\) −676.000 −0.196116
\(27\) −8140.67 −2.14907
\(28\) −3846.81 −0.927269
\(29\) 1503.62 0.332003 0.166001 0.986126i \(-0.446914\pi\)
0.166001 + 0.986126i \(0.446914\pi\)
\(30\) 2789.05 0.565787
\(31\) −2200.08 −0.411182 −0.205591 0.978638i \(-0.565912\pi\)
−0.205591 + 0.978638i \(0.565912\pi\)
\(32\) −1024.00 −0.176777
\(33\) −15176.7 −2.42600
\(34\) −6517.20 −0.966860
\(35\) −6010.64 −0.829374
\(36\) 8558.08 1.10058
\(37\) −13109.1 −1.57423 −0.787117 0.616804i \(-0.788427\pi\)
−0.787117 + 0.616804i \(0.788427\pi\)
\(38\) 3223.68 0.362154
\(39\) −4713.49 −0.496228
\(40\) −1600.00 −0.158114
\(41\) −17099.9 −1.58867 −0.794337 0.607477i \(-0.792182\pi\)
−0.794337 + 0.607477i \(0.792182\pi\)
\(42\) −26822.4 −2.34625
\(43\) −8935.58 −0.736973 −0.368487 0.929633i \(-0.620124\pi\)
−0.368487 + 0.929633i \(0.620124\pi\)
\(44\) 8706.42 0.677966
\(45\) 13372.0 0.984385
\(46\) −1492.61 −0.104004
\(47\) 15749.7 1.03999 0.519995 0.854170i \(-0.325934\pi\)
0.519995 + 0.854170i \(0.325934\pi\)
\(48\) −7139.97 −0.447294
\(49\) 40997.5 2.43931
\(50\) −2500.00 −0.141421
\(51\) −45442.0 −2.44642
\(52\) 2704.00 0.138675
\(53\) 40379.7 1.97457 0.987286 0.158951i \(-0.0508112\pi\)
0.987286 + 0.158951i \(0.0508112\pi\)
\(54\) 32562.7 1.51962
\(55\) 13603.8 0.606391
\(56\) 15387.2 0.655678
\(57\) 22477.5 0.916349
\(58\) −6014.46 −0.234761
\(59\) −47562.1 −1.77881 −0.889407 0.457116i \(-0.848882\pi\)
−0.889407 + 0.457116i \(0.848882\pi\)
\(60\) −11156.2 −0.400072
\(61\) −30280.0 −1.04191 −0.520956 0.853584i \(-0.674424\pi\)
−0.520956 + 0.853584i \(0.674424\pi\)
\(62\) 8800.31 0.290749
\(63\) −128599. −4.08212
\(64\) 4096.00 0.125000
\(65\) 4225.00 0.124035
\(66\) 60706.6 1.71544
\(67\) 38769.4 1.05512 0.527561 0.849517i \(-0.323107\pi\)
0.527561 + 0.849517i \(0.323107\pi\)
\(68\) 26068.8 0.683673
\(69\) −10407.4 −0.263160
\(70\) 24042.6 0.586456
\(71\) −10519.7 −0.247660 −0.123830 0.992303i \(-0.539518\pi\)
−0.123830 + 0.992303i \(0.539518\pi\)
\(72\) −34232.3 −0.778225
\(73\) 1582.12 0.0347483 0.0173742 0.999849i \(-0.494469\pi\)
0.0173742 + 0.999849i \(0.494469\pi\)
\(74\) 52436.5 1.11315
\(75\) −17431.6 −0.357835
\(76\) −12894.7 −0.256081
\(77\) −130828. −2.51463
\(78\) 18854.0 0.350886
\(79\) −6191.23 −0.111612 −0.0558058 0.998442i \(-0.517773\pi\)
−0.0558058 + 0.998442i \(0.517773\pi\)
\(80\) 6400.00 0.111803
\(81\) 97071.7 1.64392
\(82\) 68399.8 1.12336
\(83\) 37849.2 0.603062 0.301531 0.953456i \(-0.402502\pi\)
0.301531 + 0.953456i \(0.402502\pi\)
\(84\) 107289. 1.65905
\(85\) 40732.5 0.611496
\(86\) 35742.3 0.521119
\(87\) −41936.6 −0.594011
\(88\) −34825.7 −0.479394
\(89\) 49151.0 0.657744 0.328872 0.944374i \(-0.393331\pi\)
0.328872 + 0.944374i \(0.393331\pi\)
\(90\) −53488.0 −0.696065
\(91\) −40631.9 −0.514356
\(92\) 5970.43 0.0735421
\(93\) 61361.3 0.735677
\(94\) −62999.0 −0.735383
\(95\) −20148.0 −0.229046
\(96\) 28559.9 0.316285
\(97\) −15654.2 −0.168928 −0.0844641 0.996427i \(-0.526918\pi\)
−0.0844641 + 0.996427i \(0.526918\pi\)
\(98\) −163990. −1.72485
\(99\) 291056. 2.98461
\(100\) 10000.0 0.100000
\(101\) −138108. −1.34714 −0.673572 0.739122i \(-0.735241\pi\)
−0.673572 + 0.739122i \(0.735241\pi\)
\(102\) 181768. 1.72988
\(103\) −47642.1 −0.442484 −0.221242 0.975219i \(-0.571011\pi\)
−0.221242 + 0.975219i \(0.571011\pi\)
\(104\) −10816.0 −0.0980581
\(105\) 167640. 1.48390
\(106\) −161519. −1.39623
\(107\) −186527. −1.57500 −0.787501 0.616313i \(-0.788626\pi\)
−0.787501 + 0.616313i \(0.788626\pi\)
\(108\) −130251. −1.07454
\(109\) 14407.1 0.116147 0.0580736 0.998312i \(-0.481504\pi\)
0.0580736 + 0.998312i \(0.481504\pi\)
\(110\) −54415.1 −0.428783
\(111\) 365620. 2.81658
\(112\) −61548.9 −0.463634
\(113\) −50802.0 −0.374270 −0.187135 0.982334i \(-0.559920\pi\)
−0.187135 + 0.982334i \(0.559920\pi\)
\(114\) −89910.0 −0.647957
\(115\) 9328.80 0.0657781
\(116\) 24057.8 0.166001
\(117\) 90394.7 0.610490
\(118\) 190248. 1.25781
\(119\) −391725. −2.53580
\(120\) 44624.8 0.282894
\(121\) 135050. 0.838552
\(122\) 121120. 0.736742
\(123\) 476926. 2.84242
\(124\) −35201.3 −0.205591
\(125\) 15625.0 0.0894427
\(126\) 514395. 2.88649
\(127\) −182278. −1.00282 −0.501411 0.865209i \(-0.667186\pi\)
−0.501411 + 0.865209i \(0.667186\pi\)
\(128\) −16384.0 −0.0883883
\(129\) 249218. 1.31858
\(130\) −16900.0 −0.0877058
\(131\) 199714. 1.01679 0.508394 0.861124i \(-0.330239\pi\)
0.508394 + 0.861124i \(0.330239\pi\)
\(132\) −242826. −1.21300
\(133\) 193764. 0.949824
\(134\) −155078. −0.746083
\(135\) −203517. −0.961094
\(136\) −104275. −0.483430
\(137\) −345418. −1.57233 −0.786165 0.618017i \(-0.787936\pi\)
−0.786165 + 0.618017i \(0.787936\pi\)
\(138\) 41629.6 0.186082
\(139\) 183088. 0.803754 0.401877 0.915694i \(-0.368358\pi\)
0.401877 + 0.915694i \(0.368358\pi\)
\(140\) −96170.2 −0.414687
\(141\) −439268. −1.86072
\(142\) 42078.7 0.175122
\(143\) 91961.6 0.376068
\(144\) 136929. 0.550288
\(145\) 37590.4 0.148476
\(146\) −6328.50 −0.0245708
\(147\) −1.14344e6 −4.36435
\(148\) −209746. −0.787117
\(149\) −187082. −0.690344 −0.345172 0.938540i \(-0.612179\pi\)
−0.345172 + 0.938540i \(0.612179\pi\)
\(150\) 69726.2 0.253028
\(151\) −10616.3 −0.0378907 −0.0189454 0.999821i \(-0.506031\pi\)
−0.0189454 + 0.999821i \(0.506031\pi\)
\(152\) 51578.9 0.181077
\(153\) 871480. 3.00974
\(154\) 523312. 1.77811
\(155\) −55002.0 −0.183886
\(156\) −75415.9 −0.248114
\(157\) −335884. −1.08753 −0.543764 0.839238i \(-0.683001\pi\)
−0.543764 + 0.839238i \(0.683001\pi\)
\(158\) 24764.9 0.0789213
\(159\) −1.12621e6 −3.53286
\(160\) −25600.0 −0.0790569
\(161\) −89715.3 −0.272773
\(162\) −388287. −1.16242
\(163\) 201881. 0.595150 0.297575 0.954698i \(-0.403822\pi\)
0.297575 + 0.954698i \(0.403822\pi\)
\(164\) −273599. −0.794337
\(165\) −379416. −1.08494
\(166\) −151397. −0.426429
\(167\) −446050. −1.23764 −0.618818 0.785535i \(-0.712388\pi\)
−0.618818 + 0.785535i \(0.712388\pi\)
\(168\) −429158. −1.17312
\(169\) 28561.0 0.0769231
\(170\) −162930. −0.432393
\(171\) −431070. −1.12735
\(172\) −142969. −0.368487
\(173\) 57408.8 0.145835 0.0729177 0.997338i \(-0.476769\pi\)
0.0729177 + 0.997338i \(0.476769\pi\)
\(174\) 167746. 0.420030
\(175\) −150266. −0.370907
\(176\) 139303. 0.338983
\(177\) 1.32653e6 3.18261
\(178\) −196604. −0.465095
\(179\) 87439.4 0.203974 0.101987 0.994786i \(-0.467480\pi\)
0.101987 + 0.994786i \(0.467480\pi\)
\(180\) 213952. 0.492192
\(181\) 21341.6 0.0484206 0.0242103 0.999707i \(-0.492293\pi\)
0.0242103 + 0.999707i \(0.492293\pi\)
\(182\) 162528. 0.363705
\(183\) 844523. 1.86416
\(184\) −23881.7 −0.0520021
\(185\) −327728. −0.704019
\(186\) −245445. −0.520202
\(187\) 886586. 1.85403
\(188\) 251996. 0.519995
\(189\) 1.95723e6 3.98553
\(190\) 80592.0 0.161960
\(191\) 307517. 0.609938 0.304969 0.952362i \(-0.401354\pi\)
0.304969 + 0.952362i \(0.401354\pi\)
\(192\) −114239. −0.223647
\(193\) 182409. 0.352496 0.176248 0.984346i \(-0.443604\pi\)
0.176248 + 0.984346i \(0.443604\pi\)
\(194\) 62616.9 0.119450
\(195\) −117837. −0.221920
\(196\) 655959. 1.21965
\(197\) −152508. −0.279980 −0.139990 0.990153i \(-0.544707\pi\)
−0.139990 + 0.990153i \(0.544707\pi\)
\(198\) −1.16422e6 −2.11044
\(199\) −586606. −1.05006 −0.525029 0.851084i \(-0.675946\pi\)
−0.525029 + 0.851084i \(0.675946\pi\)
\(200\) −40000.0 −0.0707107
\(201\) −1.08130e6 −1.88780
\(202\) 552430. 0.952574
\(203\) −361508. −0.615711
\(204\) −727072. −1.22321
\(205\) −427498. −0.710477
\(206\) 190568. 0.312884
\(207\) 199592. 0.323755
\(208\) 43264.0 0.0693375
\(209\) −438542. −0.694458
\(210\) −670559. −1.04927
\(211\) −207041. −0.320147 −0.160073 0.987105i \(-0.551173\pi\)
−0.160073 + 0.987105i \(0.551173\pi\)
\(212\) 646075. 0.987286
\(213\) 293399. 0.443108
\(214\) 746106. 1.11369
\(215\) −223390. −0.329585
\(216\) 521003. 0.759812
\(217\) 528955. 0.762552
\(218\) −57628.2 −0.0821285
\(219\) −44126.3 −0.0621708
\(220\) 217661. 0.303196
\(221\) 275352. 0.379234
\(222\) −1.46248e6 −1.99162
\(223\) −1.04889e6 −1.41243 −0.706214 0.707998i \(-0.749599\pi\)
−0.706214 + 0.707998i \(0.749599\pi\)
\(224\) 246196. 0.327839
\(225\) 334300. 0.440230
\(226\) 203208. 0.264649
\(227\) −100709. −0.129719 −0.0648593 0.997894i \(-0.520660\pi\)
−0.0648593 + 0.997894i \(0.520660\pi\)
\(228\) 359640. 0.458174
\(229\) 487174. 0.613896 0.306948 0.951726i \(-0.400692\pi\)
0.306948 + 0.951726i \(0.400692\pi\)
\(230\) −37315.2 −0.0465121
\(231\) 3.64886e6 4.49911
\(232\) −96231.4 −0.117381
\(233\) −832844. −1.00502 −0.502509 0.864572i \(-0.667590\pi\)
−0.502509 + 0.864572i \(0.667590\pi\)
\(234\) −361579. −0.431681
\(235\) 393744. 0.465097
\(236\) −760993. −0.889407
\(237\) 172677. 0.199693
\(238\) 1.56690e6 1.79308
\(239\) 1.34919e6 1.52785 0.763923 0.645308i \(-0.223271\pi\)
0.763923 + 0.645308i \(0.223271\pi\)
\(240\) −178499. −0.200036
\(241\) −1.66283e6 −1.84419 −0.922096 0.386962i \(-0.873524\pi\)
−0.922096 + 0.386962i \(0.873524\pi\)
\(242\) −540199. −0.592946
\(243\) −729193. −0.792185
\(244\) −484479. −0.520956
\(245\) 1.02494e6 1.09089
\(246\) −1.90770e6 −2.00989
\(247\) −136200. −0.142048
\(248\) 140805. 0.145375
\(249\) −1.05563e6 −1.07898
\(250\) −62500.0 −0.0632456
\(251\) −291273. −0.291820 −0.145910 0.989298i \(-0.546611\pi\)
−0.145910 + 0.989298i \(0.546611\pi\)
\(252\) −2.05758e6 −2.04106
\(253\) 203051. 0.199436
\(254\) 729110. 0.709102
\(255\) −1.13605e6 −1.09407
\(256\) 65536.0 0.0625000
\(257\) −548204. −0.517737 −0.258868 0.965913i \(-0.583350\pi\)
−0.258868 + 0.965913i \(0.583350\pi\)
\(258\) −996872. −0.932374
\(259\) 3.15177e6 2.91947
\(260\) 67600.0 0.0620174
\(261\) 804253. 0.730788
\(262\) −798857. −0.718978
\(263\) 818412. 0.729596 0.364798 0.931087i \(-0.381138\pi\)
0.364798 + 0.931087i \(0.381138\pi\)
\(264\) 971306. 0.857721
\(265\) 1.00949e6 0.883056
\(266\) −775055. −0.671627
\(267\) −1.37085e6 −1.17682
\(268\) 620311. 0.527561
\(269\) −939455. −0.791581 −0.395790 0.918341i \(-0.629529\pi\)
−0.395790 + 0.918341i \(0.629529\pi\)
\(270\) 814067. 0.679596
\(271\) −1.52416e6 −1.26069 −0.630345 0.776315i \(-0.717087\pi\)
−0.630345 + 0.776315i \(0.717087\pi\)
\(272\) 417101. 0.341837
\(273\) 1.13324e6 0.920274
\(274\) 1.38167e6 1.11180
\(275\) 340095. 0.271186
\(276\) −166518. −0.131580
\(277\) −439704. −0.344319 −0.172159 0.985069i \(-0.555074\pi\)
−0.172159 + 0.985069i \(0.555074\pi\)
\(278\) −732352. −0.568340
\(279\) −1.17678e6 −0.905074
\(280\) 384681. 0.293228
\(281\) −592033. −0.447280 −0.223640 0.974672i \(-0.571794\pi\)
−0.223640 + 0.974672i \(0.571794\pi\)
\(282\) 1.75707e6 1.31573
\(283\) −777226. −0.576875 −0.288437 0.957499i \(-0.593136\pi\)
−0.288437 + 0.957499i \(0.593136\pi\)
\(284\) −168315. −0.123830
\(285\) 561938. 0.409804
\(286\) −367846. −0.265920
\(287\) 4.11126e6 2.94626
\(288\) −547717. −0.389112
\(289\) 1.23476e6 0.869637
\(290\) −150362. −0.104988
\(291\) 436604. 0.302242
\(292\) 25314.0 0.0173742
\(293\) 609025. 0.414444 0.207222 0.978294i \(-0.433558\pi\)
0.207222 + 0.978294i \(0.433558\pi\)
\(294\) 4.57376e6 3.08606
\(295\) −1.18905e6 −0.795510
\(296\) 838984. 0.556576
\(297\) −4.42976e6 −2.91400
\(298\) 748326. 0.488147
\(299\) 63062.7 0.0407938
\(300\) −278905. −0.178918
\(301\) 2.14834e6 1.36674
\(302\) 42465.4 0.0267928
\(303\) 3.85189e6 2.41028
\(304\) −206315. −0.128041
\(305\) −756999. −0.465957
\(306\) −3.48592e6 −2.12821
\(307\) −2.66761e6 −1.61538 −0.807692 0.589604i \(-0.799284\pi\)
−0.807692 + 0.589604i \(0.799284\pi\)
\(308\) −2.09325e6 −1.25731
\(309\) 1.32876e6 0.791682
\(310\) 220008. 0.130027
\(311\) −1.62320e6 −0.951634 −0.475817 0.879544i \(-0.657847\pi\)
−0.475817 + 0.879544i \(0.657847\pi\)
\(312\) 301664. 0.175443
\(313\) 592115. 0.341622 0.170811 0.985304i \(-0.445361\pi\)
0.170811 + 0.985304i \(0.445361\pi\)
\(314\) 1.34354e6 0.768998
\(315\) −3.21497e6 −1.82558
\(316\) −99059.7 −0.0558058
\(317\) −2.61036e6 −1.45899 −0.729494 0.683987i \(-0.760244\pi\)
−0.729494 + 0.683987i \(0.760244\pi\)
\(318\) 4.50484e6 2.49811
\(319\) 818194. 0.450173
\(320\) 102400. 0.0559017
\(321\) 5.20232e6 2.81796
\(322\) 358861. 0.192880
\(323\) −1.31308e6 −0.700304
\(324\) 1.55315e6 0.821959
\(325\) 105625. 0.0554700
\(326\) −807524. −0.420834
\(327\) −401820. −0.207808
\(328\) 1.09440e6 0.561681
\(329\) −3.78664e6 −1.92870
\(330\) 1.51767e6 0.767169
\(331\) 818785. 0.410771 0.205386 0.978681i \(-0.434155\pi\)
0.205386 + 0.978681i \(0.434155\pi\)
\(332\) 605588. 0.301531
\(333\) −7.01180e6 −3.46513
\(334\) 1.78420e6 0.875140
\(335\) 969236. 0.471864
\(336\) 1.71663e6 0.829523
\(337\) 3.28910e6 1.57762 0.788809 0.614638i \(-0.210698\pi\)
0.788809 + 0.614638i \(0.210698\pi\)
\(338\) −114244. −0.0543928
\(339\) 1.41689e6 0.669634
\(340\) 651720. 0.305748
\(341\) −1.19718e6 −0.557535
\(342\) 1.72428e6 0.797155
\(343\) −5.81600e6 −2.66925
\(344\) 571877. 0.260559
\(345\) −260185. −0.117689
\(346\) −229635. −0.103121
\(347\) 139108. 0.0620195 0.0310098 0.999519i \(-0.490128\pi\)
0.0310098 + 0.999519i \(0.490128\pi\)
\(348\) −670985. −0.297006
\(349\) 1.41781e6 0.623097 0.311549 0.950230i \(-0.399152\pi\)
0.311549 + 0.950230i \(0.399152\pi\)
\(350\) 601064. 0.262271
\(351\) −1.37577e6 −0.596045
\(352\) −557211. −0.239697
\(353\) 2.45675e6 1.04936 0.524679 0.851300i \(-0.324185\pi\)
0.524679 + 0.851300i \(0.324185\pi\)
\(354\) −5.30612e6 −2.25045
\(355\) −262992. −0.110757
\(356\) 786416. 0.328872
\(357\) 1.09254e7 4.53698
\(358\) −349758. −0.144231
\(359\) −2.88601e6 −1.18185 −0.590924 0.806727i \(-0.701237\pi\)
−0.590924 + 0.806727i \(0.701237\pi\)
\(360\) −855808. −0.348033
\(361\) −1.82659e6 −0.737690
\(362\) −85366.4 −0.0342386
\(363\) −3.76660e6 −1.50032
\(364\) −650111. −0.257178
\(365\) 39553.1 0.0155399
\(366\) −3.37809e6 −1.31816
\(367\) −2.83587e6 −1.09906 −0.549530 0.835474i \(-0.685193\pi\)
−0.549530 + 0.835474i \(0.685193\pi\)
\(368\) 95526.9 0.0367711
\(369\) −9.14641e6 −3.49691
\(370\) 1.31091e6 0.497816
\(371\) −9.70831e6 −3.66192
\(372\) 981781. 0.367838
\(373\) 5.02691e6 1.87081 0.935403 0.353583i \(-0.115037\pi\)
0.935403 + 0.353583i \(0.115037\pi\)
\(374\) −3.54634e6 −1.31100
\(375\) −435789. −0.160029
\(376\) −1.00798e6 −0.367692
\(377\) 254111. 0.0920810
\(378\) −7.82891e6 −2.81820
\(379\) 2.14892e6 0.768462 0.384231 0.923237i \(-0.374467\pi\)
0.384231 + 0.923237i \(0.374467\pi\)
\(380\) −322368. −0.114523
\(381\) 5.08381e6 1.79423
\(382\) −1.23007e6 −0.431291
\(383\) 832971. 0.290157 0.145078 0.989420i \(-0.453657\pi\)
0.145078 + 0.989420i \(0.453657\pi\)
\(384\) 456958. 0.158142
\(385\) −3.27070e6 −1.12458
\(386\) −729637. −0.249252
\(387\) −4.77946e6 −1.62219
\(388\) −250468. −0.0844641
\(389\) −725243. −0.243002 −0.121501 0.992591i \(-0.538771\pi\)
−0.121501 + 0.992591i \(0.538771\pi\)
\(390\) 471349. 0.156921
\(391\) 607976. 0.201115
\(392\) −2.62384e6 −0.862426
\(393\) −5.57013e6 −1.81921
\(394\) 610032. 0.197976
\(395\) −154781. −0.0499142
\(396\) 4.65689e6 1.49231
\(397\) 2.42654e6 0.772701 0.386351 0.922352i \(-0.373735\pi\)
0.386351 + 0.922352i \(0.373735\pi\)
\(398\) 2.34642e6 0.742504
\(399\) −5.40417e6 −1.69940
\(400\) 160000. 0.0500000
\(401\) −2.14376e6 −0.665758 −0.332879 0.942970i \(-0.608020\pi\)
−0.332879 + 0.942970i \(0.608020\pi\)
\(402\) 4.32519e6 1.33487
\(403\) −371813. −0.114041
\(404\) −2.20972e6 −0.673572
\(405\) 2.42679e6 0.735182
\(406\) 1.44603e6 0.435374
\(407\) −7.13335e6 −2.13455
\(408\) 2.90829e6 0.864942
\(409\) −3.66144e6 −1.08229 −0.541145 0.840929i \(-0.682009\pi\)
−0.541145 + 0.840929i \(0.682009\pi\)
\(410\) 1.70999e6 0.502383
\(411\) 9.63388e6 2.81317
\(412\) −762273. −0.221242
\(413\) 1.14351e7 3.29888
\(414\) −798366. −0.228929
\(415\) 946231. 0.269698
\(416\) −173056. −0.0490290
\(417\) −5.10642e6 −1.43806
\(418\) 1.75417e6 0.491056
\(419\) 3.03786e6 0.845341 0.422671 0.906283i \(-0.361093\pi\)
0.422671 + 0.906283i \(0.361093\pi\)
\(420\) 2.68224e6 0.741948
\(421\) −1.88663e6 −0.518777 −0.259389 0.965773i \(-0.583521\pi\)
−0.259389 + 0.965773i \(0.583521\pi\)
\(422\) 828162. 0.226378
\(423\) 8.42422e6 2.28917
\(424\) −2.58430e6 −0.698117
\(425\) 1.01831e6 0.273469
\(426\) −1.17360e6 −0.313325
\(427\) 7.28008e6 1.93226
\(428\) −2.98442e6 −0.787501
\(429\) −2.56485e6 −0.672852
\(430\) 893558. 0.233051
\(431\) 717193. 0.185970 0.0929850 0.995668i \(-0.470359\pi\)
0.0929850 + 0.995668i \(0.470359\pi\)
\(432\) −2.08401e6 −0.537268
\(433\) 2.64569e6 0.678140 0.339070 0.940761i \(-0.389888\pi\)
0.339070 + 0.940761i \(0.389888\pi\)
\(434\) −2.11582e6 −0.539206
\(435\) −1.04841e6 −0.265650
\(436\) 230513. 0.0580736
\(437\) −300731. −0.0753310
\(438\) 176505. 0.0439614
\(439\) 4.47973e6 1.10941 0.554704 0.832048i \(-0.312832\pi\)
0.554704 + 0.832048i \(0.312832\pi\)
\(440\) −870642. −0.214392
\(441\) 2.19287e7 5.36929
\(442\) −1.10141e6 −0.268159
\(443\) 4.30731e6 1.04279 0.521395 0.853315i \(-0.325412\pi\)
0.521395 + 0.853315i \(0.325412\pi\)
\(444\) 5.84992e6 1.40829
\(445\) 1.22877e6 0.294152
\(446\) 4.19555e6 0.998738
\(447\) 5.21780e6 1.23515
\(448\) −984783. −0.231817
\(449\) −25272.9 −0.00591615 −0.00295808 0.999996i \(-0.500942\pi\)
−0.00295808 + 0.999996i \(0.500942\pi\)
\(450\) −1.33720e6 −0.311290
\(451\) −9.30495e6 −2.15413
\(452\) −812832. −0.187135
\(453\) 296095. 0.0677932
\(454\) 402835. 0.0917250
\(455\) −1.01580e6 −0.230027
\(456\) −1.43856e6 −0.323978
\(457\) 1.14360e6 0.256143 0.128072 0.991765i \(-0.459121\pi\)
0.128072 + 0.991765i \(0.459121\pi\)
\(458\) −1.94869e6 −0.434090
\(459\) −1.32636e7 −2.93853
\(460\) 149261. 0.0328890
\(461\) −8.34911e6 −1.82973 −0.914867 0.403755i \(-0.867705\pi\)
−0.914867 + 0.403755i \(0.867705\pi\)
\(462\) −1.45954e7 −3.18135
\(463\) −3.41596e6 −0.740561 −0.370280 0.928920i \(-0.620738\pi\)
−0.370280 + 0.928920i \(0.620738\pi\)
\(464\) 384925. 0.0830007
\(465\) 1.53403e6 0.329005
\(466\) 3.33138e6 0.710655
\(467\) 5.67105e6 1.20329 0.601646 0.798763i \(-0.294512\pi\)
0.601646 + 0.798763i \(0.294512\pi\)
\(468\) 1.44632e6 0.305245
\(469\) −9.32116e6 −1.95676
\(470\) −1.57497e6 −0.328873
\(471\) 9.36797e6 1.94578
\(472\) 3.04397e6 0.628906
\(473\) −4.86231e6 −0.999286
\(474\) −690706. −0.141204
\(475\) −503700. −0.102432
\(476\) −6.26760e6 −1.26790
\(477\) 2.15983e7 4.34633
\(478\) −5.39677e6 −1.08035
\(479\) −6.16340e6 −1.22739 −0.613694 0.789544i \(-0.710317\pi\)
−0.613694 + 0.789544i \(0.710317\pi\)
\(480\) 713997. 0.141447
\(481\) −2.21544e6 −0.436614
\(482\) 6.65133e6 1.30404
\(483\) 2.50220e6 0.488039
\(484\) 2.16080e6 0.419276
\(485\) −391356. −0.0755470
\(486\) 2.91677e6 0.560160
\(487\) −7.32701e6 −1.39992 −0.699962 0.714180i \(-0.746800\pi\)
−0.699962 + 0.714180i \(0.746800\pi\)
\(488\) 1.93792e6 0.368371
\(489\) −5.63056e6 −1.06483
\(490\) −4.09975e6 −0.771377
\(491\) 8.89739e6 1.66555 0.832777 0.553608i \(-0.186750\pi\)
0.832777 + 0.553608i \(0.186750\pi\)
\(492\) 7.63081e6 1.42121
\(493\) 2.44984e6 0.453963
\(494\) 544802. 0.100443
\(495\) 7.27639e6 1.33476
\(496\) −563220. −0.102795
\(497\) 2.52920e6 0.459295
\(498\) 4.22254e6 0.762957
\(499\) 3.02237e6 0.543371 0.271686 0.962386i \(-0.412419\pi\)
0.271686 + 0.962386i \(0.412419\pi\)
\(500\) 250000. 0.0447214
\(501\) 1.24406e7 2.21435
\(502\) 1.16509e6 0.206348
\(503\) −7.48799e6 −1.31961 −0.659805 0.751437i \(-0.729361\pi\)
−0.659805 + 0.751437i \(0.729361\pi\)
\(504\) 8.23032e6 1.44325
\(505\) −3.45269e6 −0.602461
\(506\) −812205. −0.141023
\(507\) −796581. −0.137629
\(508\) −2.91644e6 −0.501411
\(509\) 4.87997e6 0.834878 0.417439 0.908705i \(-0.362928\pi\)
0.417439 + 0.908705i \(0.362928\pi\)
\(510\) 4.54420e6 0.773627
\(511\) −380383. −0.0644420
\(512\) −262144. −0.0441942
\(513\) 6.56073e6 1.10067
\(514\) 2.19281e6 0.366095
\(515\) −1.19105e6 −0.197885
\(516\) 3.98749e6 0.659288
\(517\) 8.57024e6 1.41015
\(518\) −1.26071e7 −2.06438
\(519\) −1.60116e6 −0.260925
\(520\) −270400. −0.0438529
\(521\) −3.79679e6 −0.612805 −0.306403 0.951902i \(-0.599125\pi\)
−0.306403 + 0.951902i \(0.599125\pi\)
\(522\) −3.21701e6 −0.516745
\(523\) −5.66643e6 −0.905848 −0.452924 0.891549i \(-0.649619\pi\)
−0.452924 + 0.891549i \(0.649619\pi\)
\(524\) 3.19543e6 0.508394
\(525\) 4.19099e6 0.663619
\(526\) −3.27365e6 −0.515902
\(527\) −3.58459e6 −0.562228
\(528\) −3.88522e6 −0.606500
\(529\) −6.29710e6 −0.978366
\(530\) −4.03797e6 −0.624415
\(531\) −2.54400e7 −3.91544
\(532\) 3.10022e6 0.474912
\(533\) −2.88989e6 −0.440619
\(534\) 5.48338e6 0.832138
\(535\) −4.66316e6 −0.704362
\(536\) −2.48124e6 −0.373042
\(537\) −2.43873e6 −0.364945
\(538\) 3.75782e6 0.559732
\(539\) 2.23088e7 3.30754
\(540\) −3.25627e6 −0.480547
\(541\) 1.15648e7 1.69881 0.849403 0.527745i \(-0.176962\pi\)
0.849403 + 0.527745i \(0.176962\pi\)
\(542\) 6.09665e6 0.891442
\(543\) −595228. −0.0866330
\(544\) −1.66840e6 −0.241715
\(545\) 360176. 0.0519426
\(546\) −4.53298e6 −0.650732
\(547\) −1.28104e7 −1.83060 −0.915299 0.402776i \(-0.868045\pi\)
−0.915299 + 0.402776i \(0.868045\pi\)
\(548\) −5.52669e6 −0.786165
\(549\) −1.61961e7 −2.29340
\(550\) −1.36038e6 −0.191758
\(551\) −1.21179e6 −0.170039
\(552\) 666073. 0.0930410
\(553\) 1.48853e6 0.206988
\(554\) 1.75881e6 0.243470
\(555\) 9.14050e6 1.25961
\(556\) 2.92941e6 0.401877
\(557\) 3.51737e6 0.480374 0.240187 0.970727i \(-0.422791\pi\)
0.240187 + 0.970727i \(0.422791\pi\)
\(558\) 4.70711e6 0.639984
\(559\) −1.51011e6 −0.204400
\(560\) −1.53872e6 −0.207344
\(561\) −2.47273e7 −3.31719
\(562\) 2.36813e6 0.316275
\(563\) 9.45258e6 1.25684 0.628419 0.777875i \(-0.283702\pi\)
0.628419 + 0.777875i \(0.283702\pi\)
\(564\) −7.02829e6 −0.930362
\(565\) −1.27005e6 −0.167378
\(566\) 3.10891e6 0.407912
\(567\) −2.33385e7 −3.04871
\(568\) 673259. 0.0875611
\(569\) 1.11315e7 1.44136 0.720679 0.693269i \(-0.243830\pi\)
0.720679 + 0.693269i \(0.243830\pi\)
\(570\) −2.24775e6 −0.289775
\(571\) 4.92935e6 0.632702 0.316351 0.948642i \(-0.397542\pi\)
0.316351 + 0.948642i \(0.397542\pi\)
\(572\) 1.47139e6 0.188034
\(573\) −8.57680e6 −1.09129
\(574\) −1.64450e7 −2.08332
\(575\) 233220. 0.0294169
\(576\) 2.19087e6 0.275144
\(577\) 1.09437e7 1.36843 0.684217 0.729279i \(-0.260144\pi\)
0.684217 + 0.729279i \(0.260144\pi\)
\(578\) −4.93904e6 −0.614926
\(579\) −5.08749e6 −0.630677
\(580\) 601446. 0.0742381
\(581\) −9.09993e6 −1.11840
\(582\) −1.74642e6 −0.213718
\(583\) 2.19727e7 2.67739
\(584\) −101256. −0.0122854
\(585\) 2.25987e6 0.273019
\(586\) −2.43610e6 −0.293056
\(587\) 7.96444e6 0.954025 0.477013 0.878896i \(-0.341720\pi\)
0.477013 + 0.878896i \(0.341720\pi\)
\(588\) −1.82950e7 −2.18218
\(589\) 1.77309e6 0.210592
\(590\) 4.75621e6 0.562510
\(591\) 4.25352e6 0.500934
\(592\) −3.35593e6 −0.393558
\(593\) −1.19793e7 −1.39892 −0.699460 0.714671i \(-0.746576\pi\)
−0.699460 + 0.714671i \(0.746576\pi\)
\(594\) 1.77190e7 2.06051
\(595\) −9.79313e6 −1.13404
\(596\) −2.99330e6 −0.345172
\(597\) 1.63607e7 1.87874
\(598\) −252251. −0.0288456
\(599\) 7.45663e6 0.849132 0.424566 0.905397i \(-0.360427\pi\)
0.424566 + 0.905397i \(0.360427\pi\)
\(600\) 1.11562e6 0.126514
\(601\) −1.04196e7 −1.17670 −0.588351 0.808606i \(-0.700223\pi\)
−0.588351 + 0.808606i \(0.700223\pi\)
\(602\) −8.59337e6 −0.966434
\(603\) 2.07370e7 2.32248
\(604\) −169862. −0.0189454
\(605\) 3.37624e6 0.375012
\(606\) −1.54075e7 −1.70432
\(607\) 571939. 0.0630054 0.0315027 0.999504i \(-0.489971\pi\)
0.0315027 + 0.999504i \(0.489971\pi\)
\(608\) 825262. 0.0905384
\(609\) 1.00826e7 1.10162
\(610\) 3.02800e6 0.329481
\(611\) 2.66171e6 0.288441
\(612\) 1.39437e7 1.50487
\(613\) −1.61323e7 −1.73398 −0.866991 0.498323i \(-0.833949\pi\)
−0.866991 + 0.498323i \(0.833949\pi\)
\(614\) 1.06704e7 1.14225
\(615\) 1.19231e7 1.27117
\(616\) 8.37299e6 0.889055
\(617\) −6.39133e6 −0.675894 −0.337947 0.941165i \(-0.609732\pi\)
−0.337947 + 0.941165i \(0.609732\pi\)
\(618\) −5.31505e6 −0.559804
\(619\) 1.27062e7 1.33287 0.666435 0.745563i \(-0.267819\pi\)
0.666435 + 0.745563i \(0.267819\pi\)
\(620\) −880031. −0.0919431
\(621\) −3.03771e6 −0.316095
\(622\) 6.49278e6 0.672907
\(623\) −1.18172e7 −1.21981
\(624\) −1.20665e6 −0.124057
\(625\) 390625. 0.0400000
\(626\) −2.36846e6 −0.241563
\(627\) 1.22312e7 1.24251
\(628\) −5.37414e6 −0.543764
\(629\) −2.13587e7 −2.15252
\(630\) 1.28599e7 1.29088
\(631\) −694354. −0.0694237 −0.0347118 0.999397i \(-0.511051\pi\)
−0.0347118 + 0.999397i \(0.511051\pi\)
\(632\) 396239. 0.0394607
\(633\) 5.77447e6 0.572799
\(634\) 1.04414e7 1.03166
\(635\) −4.55694e6 −0.448476
\(636\) −1.80193e7 −1.76643
\(637\) 6.92857e6 0.676542
\(638\) −3.27278e6 −0.318321
\(639\) −5.62676e6 −0.545138
\(640\) −409600. −0.0395285
\(641\) −8.71863e6 −0.838114 −0.419057 0.907960i \(-0.637639\pi\)
−0.419057 + 0.907960i \(0.637639\pi\)
\(642\) −2.08093e7 −1.99260
\(643\) 5.98737e6 0.571096 0.285548 0.958364i \(-0.407824\pi\)
0.285548 + 0.958364i \(0.407824\pi\)
\(644\) −1.43544e6 −0.136387
\(645\) 6.23045e6 0.589685
\(646\) 5.25234e6 0.495189
\(647\) −1.09581e7 −1.02914 −0.514571 0.857448i \(-0.672049\pi\)
−0.514571 + 0.857448i \(0.672049\pi\)
\(648\) −6.21259e6 −0.581212
\(649\) −2.58810e7 −2.41195
\(650\) −422500. −0.0392232
\(651\) −1.47528e7 −1.36434
\(652\) 3.23009e6 0.297575
\(653\) 6.47503e6 0.594236 0.297118 0.954841i \(-0.403975\pi\)
0.297118 + 0.954841i \(0.403975\pi\)
\(654\) 1.60728e6 0.146942
\(655\) 4.99285e6 0.454722
\(656\) −4.37758e6 −0.397169
\(657\) 846247. 0.0764863
\(658\) 1.51466e7 1.36380
\(659\) 501723. 0.0450039 0.0225020 0.999747i \(-0.492837\pi\)
0.0225020 + 0.999747i \(0.492837\pi\)
\(660\) −6.07066e6 −0.542471
\(661\) 4.00659e6 0.356674 0.178337 0.983969i \(-0.442928\pi\)
0.178337 + 0.983969i \(0.442928\pi\)
\(662\) −3.27514e6 −0.290459
\(663\) −7.67969e6 −0.678516
\(664\) −2.42235e6 −0.213215
\(665\) 4.84409e6 0.424774
\(666\) 2.80472e7 2.45021
\(667\) 561077. 0.0488324
\(668\) −7.13681e6 −0.618818
\(669\) 2.92540e7 2.52708
\(670\) −3.87694e6 −0.333659
\(671\) −1.64769e7 −1.41276
\(672\) −6.86652e6 −0.586562
\(673\) 8.17473e6 0.695722 0.347861 0.937546i \(-0.386908\pi\)
0.347861 + 0.937546i \(0.386908\pi\)
\(674\) −1.31564e7 −1.11554
\(675\) −5.08792e6 −0.429814
\(676\) 456976. 0.0384615
\(677\) 1.00935e6 0.0846392 0.0423196 0.999104i \(-0.486525\pi\)
0.0423196 + 0.999104i \(0.486525\pi\)
\(678\) −5.66757e6 −0.473503
\(679\) 3.76368e6 0.313284
\(680\) −2.60688e6 −0.216196
\(681\) 2.80882e6 0.232090
\(682\) 4.78870e6 0.394237
\(683\) 1.99189e7 1.63386 0.816928 0.576739i \(-0.195675\pi\)
0.816928 + 0.576739i \(0.195675\pi\)
\(684\) −6.89712e6 −0.563674
\(685\) −8.63545e6 −0.703167
\(686\) 2.32640e7 1.88745
\(687\) −1.35875e7 −1.09837
\(688\) −2.28751e6 −0.184243
\(689\) 6.82417e6 0.547648
\(690\) 1.04074e6 0.0832184
\(691\) −677407. −0.0539703 −0.0269851 0.999636i \(-0.508591\pi\)
−0.0269851 + 0.999636i \(0.508591\pi\)
\(692\) 918541. 0.0729177
\(693\) −6.99772e7 −5.53508
\(694\) −556432. −0.0438544
\(695\) 4.57720e6 0.359450
\(696\) 2.68394e6 0.210015
\(697\) −2.78609e7 −2.17227
\(698\) −5.67126e6 −0.440596
\(699\) 2.32284e7 1.79815
\(700\) −2.40426e6 −0.185454
\(701\) 1.04542e7 0.803518 0.401759 0.915745i \(-0.368399\pi\)
0.401759 + 0.915745i \(0.368399\pi\)
\(702\) 5.50310e6 0.421468
\(703\) 1.05649e7 0.806263
\(704\) 2.22884e6 0.169492
\(705\) −1.09817e7 −0.832141
\(706\) −9.82700e6 −0.742009
\(707\) 3.32046e7 2.49833
\(708\) 2.12245e7 1.59131
\(709\) −2.25125e7 −1.68193 −0.840964 0.541091i \(-0.818011\pi\)
−0.840964 + 0.541091i \(0.818011\pi\)
\(710\) 1.05197e6 0.0783170
\(711\) −3.31157e6 −0.245674
\(712\) −3.14566e6 −0.232548
\(713\) −820964. −0.0604784
\(714\) −4.37017e7 −3.20813
\(715\) 2.29904e6 0.168183
\(716\) 1.39903e6 0.101987
\(717\) −3.76297e7 −2.73358
\(718\) 1.15440e7 0.835693
\(719\) −2.77678e6 −0.200317 −0.100159 0.994971i \(-0.531935\pi\)
−0.100159 + 0.994971i \(0.531935\pi\)
\(720\) 3.42323e6 0.246096
\(721\) 1.14544e7 0.820603
\(722\) 7.30637e6 0.521625
\(723\) 4.63772e7 3.29958
\(724\) 341466. 0.0242103
\(725\) 939759. 0.0664006
\(726\) 1.50664e7 1.06089
\(727\) 2.76872e6 0.194287 0.0971434 0.995270i \(-0.469029\pi\)
0.0971434 + 0.995270i \(0.469029\pi\)
\(728\) 2.60044e6 0.181852
\(729\) −3.25086e6 −0.226558
\(730\) −158212. −0.0109884
\(731\) −1.45587e7 −1.00770
\(732\) 1.35124e7 0.932081
\(733\) −1.80998e7 −1.24427 −0.622133 0.782911i \(-0.713734\pi\)
−0.622133 + 0.782911i \(0.713734\pi\)
\(734\) 1.13435e7 0.777152
\(735\) −2.85860e7 −1.95180
\(736\) −382108. −0.0260011
\(737\) 2.10964e7 1.43067
\(738\) 3.65857e7 2.47269
\(739\) −3.57016e6 −0.240479 −0.120239 0.992745i \(-0.538366\pi\)
−0.120239 + 0.992745i \(0.538366\pi\)
\(740\) −5.24365e6 −0.352009
\(741\) 3.79870e6 0.254149
\(742\) 3.88332e7 2.58937
\(743\) −1.73285e7 −1.15157 −0.575783 0.817603i \(-0.695303\pi\)
−0.575783 + 0.817603i \(0.695303\pi\)
\(744\) −3.92712e6 −0.260101
\(745\) −4.67704e6 −0.308731
\(746\) −2.01076e7 −1.32286
\(747\) 2.02448e7 1.32743
\(748\) 1.41854e7 0.927015
\(749\) 4.48457e7 2.92090
\(750\) 1.74316e6 0.113157
\(751\) 3.04634e6 0.197096 0.0985480 0.995132i \(-0.468580\pi\)
0.0985480 + 0.995132i \(0.468580\pi\)
\(752\) 4.03193e6 0.259997
\(753\) 8.12374e6 0.522118
\(754\) −1.01644e6 −0.0651111
\(755\) −265409. −0.0169452
\(756\) 3.13156e7 1.99277
\(757\) −8.98398e6 −0.569808 −0.284904 0.958556i \(-0.591962\pi\)
−0.284904 + 0.958556i \(0.591962\pi\)
\(758\) −8.59568e6 −0.543384
\(759\) −5.66320e6 −0.356827
\(760\) 1.28947e6 0.0809800
\(761\) 1.31757e7 0.824731 0.412366 0.911018i \(-0.364703\pi\)
0.412366 + 0.911018i \(0.364703\pi\)
\(762\) −2.03352e7 −1.26871
\(763\) −3.46382e6 −0.215399
\(764\) 4.92027e6 0.304969
\(765\) 2.17870e7 1.34600
\(766\) −3.33188e6 −0.205172
\(767\) −8.03799e6 −0.493354
\(768\) −1.82783e6 −0.111824
\(769\) 3.53661e6 0.215661 0.107830 0.994169i \(-0.465610\pi\)
0.107830 + 0.994169i \(0.465610\pi\)
\(770\) 1.30828e7 0.795195
\(771\) 1.52897e7 0.926322
\(772\) 2.91855e6 0.176248
\(773\) −3.14397e7 −1.89247 −0.946235 0.323479i \(-0.895147\pi\)
−0.946235 + 0.323479i \(0.895147\pi\)
\(774\) 1.91179e7 1.14706
\(775\) −1.37505e6 −0.0822364
\(776\) 1.00187e6 0.0597251
\(777\) −8.79044e7 −5.22346
\(778\) 2.90097e6 0.171828
\(779\) 1.37812e7 0.813659
\(780\) −1.88540e6 −0.110960
\(781\) −5.72429e6 −0.335810
\(782\) −2.43191e6 −0.142210
\(783\) −1.22404e7 −0.713498
\(784\) 1.04953e7 0.609827
\(785\) −8.39710e6 −0.486357
\(786\) 2.22805e7 1.28638
\(787\) 1.27213e7 0.732139 0.366069 0.930588i \(-0.380703\pi\)
0.366069 + 0.930588i \(0.380703\pi\)
\(788\) −2.44013e6 −0.139990
\(789\) −2.28259e7 −1.30538
\(790\) 619123. 0.0352947
\(791\) 1.22141e7 0.694097
\(792\) −1.86276e7 −1.05522
\(793\) −5.11731e6 −0.288974
\(794\) −9.70617e6 −0.546382
\(795\) −2.81552e7 −1.57994
\(796\) −9.38569e6 −0.525029
\(797\) 1.84237e7 1.02738 0.513689 0.857977i \(-0.328279\pi\)
0.513689 + 0.857977i \(0.328279\pi\)
\(798\) 2.16167e7 1.20166
\(799\) 2.56610e7 1.42203
\(800\) −640000. −0.0353553
\(801\) 2.62899e7 1.44780
\(802\) 8.57506e6 0.470762
\(803\) 860915. 0.0471164
\(804\) −1.73008e7 −0.943899
\(805\) −2.24288e6 −0.121988
\(806\) 1.48725e6 0.0806394
\(807\) 2.62019e7 1.41628
\(808\) 8.83888e6 0.476287
\(809\) 2.10360e7 1.13004 0.565018 0.825079i \(-0.308869\pi\)
0.565018 + 0.825079i \(0.308869\pi\)
\(810\) −9.70717e6 −0.519852
\(811\) 3.53571e7 1.88767 0.943833 0.330424i \(-0.107192\pi\)
0.943833 + 0.330424i \(0.107192\pi\)
\(812\) −5.78412e6 −0.307856
\(813\) 4.25097e7 2.25560
\(814\) 2.85334e7 1.50936
\(815\) 5.04702e6 0.266159
\(816\) −1.16331e7 −0.611606
\(817\) 7.20136e6 0.377450
\(818\) 1.46458e7 0.765295
\(819\) −2.17332e7 −1.13218
\(820\) −6.83998e6 −0.355238
\(821\) 1.72038e7 0.890770 0.445385 0.895339i \(-0.353067\pi\)
0.445385 + 0.895339i \(0.353067\pi\)
\(822\) −3.85355e7 −1.98921
\(823\) −947098. −0.0487411 −0.0243705 0.999703i \(-0.507758\pi\)
−0.0243705 + 0.999703i \(0.507758\pi\)
\(824\) 3.04909e6 0.156442
\(825\) −9.48541e6 −0.485200
\(826\) −4.57405e7 −2.33266
\(827\) −3.05385e7 −1.55269 −0.776345 0.630308i \(-0.782928\pi\)
−0.776345 + 0.630308i \(0.782928\pi\)
\(828\) 3.19346e6 0.161877
\(829\) −1.57415e7 −0.795538 −0.397769 0.917486i \(-0.630215\pi\)
−0.397769 + 0.917486i \(0.630215\pi\)
\(830\) −3.78492e6 −0.190705
\(831\) 1.22636e7 0.616047
\(832\) 692224. 0.0346688
\(833\) 6.67971e7 3.33538
\(834\) 2.04257e7 1.01686
\(835\) −1.11513e7 −0.553487
\(836\) −7.01668e6 −0.347229
\(837\) 1.79101e7 0.883659
\(838\) −1.21514e7 −0.597746
\(839\) 2.07700e7 1.01867 0.509333 0.860570i \(-0.329892\pi\)
0.509333 + 0.860570i \(0.329892\pi\)
\(840\) −1.07289e7 −0.524637
\(841\) −1.82503e7 −0.889774
\(842\) 7.54651e6 0.366831
\(843\) 1.65121e7 0.800263
\(844\) −3.31265e6 −0.160073
\(845\) 714025. 0.0344010
\(846\) −3.36969e7 −1.61869
\(847\) −3.24694e7 −1.55513
\(848\) 1.03372e7 0.493643
\(849\) 2.16772e7 1.03213
\(850\) −4.07325e6 −0.193372
\(851\) −4.89169e6 −0.231545
\(852\) 4.69438e6 0.221554
\(853\) −1.91838e7 −0.902740 −0.451370 0.892337i \(-0.649064\pi\)
−0.451370 + 0.892337i \(0.649064\pi\)
\(854\) −2.91203e7 −1.36632
\(855\) −1.07768e7 −0.504165
\(856\) 1.19377e7 0.556847
\(857\) 2.64211e7 1.22885 0.614425 0.788975i \(-0.289388\pi\)
0.614425 + 0.788975i \(0.289388\pi\)
\(858\) 1.02594e7 0.475778
\(859\) −3.30576e7 −1.52858 −0.764289 0.644873i \(-0.776910\pi\)
−0.764289 + 0.644873i \(0.776910\pi\)
\(860\) −3.57423e6 −0.164792
\(861\) −1.14665e8 −5.27137
\(862\) −2.86877e6 −0.131501
\(863\) 1.19324e7 0.545380 0.272690 0.962102i \(-0.412087\pi\)
0.272690 + 0.962102i \(0.412087\pi\)
\(864\) 8.33605e6 0.379906
\(865\) 1.43522e6 0.0652196
\(866\) −1.05828e7 −0.479518
\(867\) −3.44381e7 −1.55593
\(868\) 8.46328e6 0.381276
\(869\) −3.36897e6 −0.151338
\(870\) 4.19366e6 0.187843
\(871\) 6.55203e6 0.292638
\(872\) −922051. −0.0410643
\(873\) −8.37313e6 −0.371837
\(874\) 1.20292e6 0.0532671
\(875\) −3.75665e6 −0.165875
\(876\) −706020. −0.0310854
\(877\) 3.88434e6 0.170537 0.0852684 0.996358i \(-0.472825\pi\)
0.0852684 + 0.996358i \(0.472825\pi\)
\(878\) −1.79189e7 −0.784469
\(879\) −1.69860e7 −0.741513
\(880\) 3.48257e6 0.151598
\(881\) −8.93397e6 −0.387797 −0.193899 0.981022i \(-0.562113\pi\)
−0.193899 + 0.981022i \(0.562113\pi\)
\(882\) −8.77148e7 −3.79666
\(883\) −4.32552e6 −0.186697 −0.0933484 0.995634i \(-0.529757\pi\)
−0.0933484 + 0.995634i \(0.529757\pi\)
\(884\) 4.40563e6 0.189617
\(885\) 3.31632e7 1.42331
\(886\) −1.72292e7 −0.737364
\(887\) 3.55552e7 1.51738 0.758689 0.651453i \(-0.225840\pi\)
0.758689 + 0.651453i \(0.225840\pi\)
\(888\) −2.33997e7 −0.995812
\(889\) 4.38242e7 1.85977
\(890\) −4.91510e6 −0.207997
\(891\) 5.28217e7 2.22904
\(892\) −1.67822e7 −0.706214
\(893\) −1.26930e7 −0.532643
\(894\) −2.08712e7 −0.873380
\(895\) 2.18599e6 0.0912199
\(896\) 3.93913e6 0.163919
\(897\) −1.75885e6 −0.0729874
\(898\) 101092. 0.00418335
\(899\) −3.30807e6 −0.136514
\(900\) 5.34880e6 0.220115
\(901\) 6.57906e7 2.69993
\(902\) 3.72198e7 1.52320
\(903\) −5.99184e7 −2.44535
\(904\) 3.25133e6 0.132324
\(905\) 533540. 0.0216544
\(906\) −1.18438e6 −0.0479370
\(907\) 2.44157e7 0.985486 0.492743 0.870175i \(-0.335994\pi\)
0.492743 + 0.870175i \(0.335994\pi\)
\(908\) −1.61134e6 −0.0648593
\(909\) −7.38709e7 −2.96527
\(910\) 4.06319e6 0.162654
\(911\) 3.00267e7 1.19870 0.599352 0.800486i \(-0.295425\pi\)
0.599352 + 0.800486i \(0.295425\pi\)
\(912\) 5.75424e6 0.229087
\(913\) 2.05957e7 0.817711
\(914\) −4.57439e6 −0.181120
\(915\) 2.11131e7 0.833679
\(916\) 7.79478e6 0.306948
\(917\) −4.80164e7 −1.88567
\(918\) 5.30544e7 2.07785
\(919\) −1.30118e7 −0.508216 −0.254108 0.967176i \(-0.581782\pi\)
−0.254108 + 0.967176i \(0.581782\pi\)
\(920\) −597043. −0.0232561
\(921\) 7.44009e7 2.89021
\(922\) 3.33964e7 1.29382
\(923\) −1.77782e6 −0.0686886
\(924\) 5.83817e7 2.24956
\(925\) −8.19320e6 −0.314847
\(926\) 1.36639e7 0.523656
\(927\) −2.54828e7 −0.973975
\(928\) −1.53970e6 −0.0586904
\(929\) −5.16678e7 −1.96418 −0.982089 0.188419i \(-0.939664\pi\)
−0.982089 + 0.188419i \(0.939664\pi\)
\(930\) −6.13613e6 −0.232641
\(931\) −3.30407e7 −1.24932
\(932\) −1.33255e7 −0.502509
\(933\) 4.52717e7 1.70264
\(934\) −2.26842e7 −0.850857
\(935\) 2.21646e7 0.829147
\(936\) −5.78526e6 −0.215841
\(937\) −4.04703e6 −0.150587 −0.0752936 0.997161i \(-0.523989\pi\)
−0.0752936 + 0.997161i \(0.523989\pi\)
\(938\) 3.72846e7 1.38364
\(939\) −1.65144e7 −0.611221
\(940\) 6.29990e6 0.232549
\(941\) −4.43008e7 −1.63094 −0.815470 0.578799i \(-0.803521\pi\)
−0.815470 + 0.578799i \(0.803521\pi\)
\(942\) −3.74719e7 −1.37587
\(943\) −6.38088e6 −0.233669
\(944\) −1.21759e7 −0.444704
\(945\) 4.89307e7 1.78239
\(946\) 1.94492e7 0.706602
\(947\) −3.60463e7 −1.30613 −0.653064 0.757303i \(-0.726517\pi\)
−0.653064 + 0.757303i \(0.726517\pi\)
\(948\) 2.76283e6 0.0998464
\(949\) 267379. 0.00963745
\(950\) 2.01480e6 0.0724307
\(951\) 7.28042e7 2.61039
\(952\) 2.50704e7 0.896539
\(953\) −1.31248e7 −0.468123 −0.234061 0.972222i \(-0.575202\pi\)
−0.234061 + 0.972222i \(0.575202\pi\)
\(954\) −8.63931e7 −3.07332
\(955\) 7.68792e6 0.272773
\(956\) 2.15871e7 0.763923
\(957\) −2.28198e7 −0.805439
\(958\) 2.46536e7 0.867894
\(959\) 8.30473e7 2.91594
\(960\) −2.85599e6 −0.100018
\(961\) −2.37888e7 −0.830929
\(962\) 8.86176e6 0.308733
\(963\) −9.97693e7 −3.46682
\(964\) −2.66053e7 −0.922096
\(965\) 4.56023e6 0.157641
\(966\) −1.00088e7 −0.345096
\(967\) 2.48150e7 0.853390 0.426695 0.904396i \(-0.359678\pi\)
0.426695 + 0.904396i \(0.359678\pi\)
\(968\) −8.64318e6 −0.296473
\(969\) 3.66226e7 1.25297
\(970\) 1.56542e6 0.0534198
\(971\) −3.54227e6 −0.120569 −0.0602843 0.998181i \(-0.519201\pi\)
−0.0602843 + 0.998181i \(0.519201\pi\)
\(972\) −1.16671e7 −0.396093
\(973\) −4.40191e7 −1.49059
\(974\) 2.93080e7 0.989896
\(975\) −2.94593e6 −0.0992456
\(976\) −7.75167e6 −0.260478
\(977\) 9.16916e6 0.307322 0.153661 0.988124i \(-0.450894\pi\)
0.153661 + 0.988124i \(0.450894\pi\)
\(978\) 2.25222e7 0.752947
\(979\) 2.67456e7 0.891857
\(980\) 1.63990e7 0.545446
\(981\) 7.70604e6 0.255658
\(982\) −3.55895e7 −1.17772
\(983\) −3.05912e7 −1.00975 −0.504874 0.863193i \(-0.668461\pi\)
−0.504874 + 0.863193i \(0.668461\pi\)
\(984\) −3.05233e7 −1.00495
\(985\) −3.81270e6 −0.125211
\(986\) −9.79936e6 −0.321000
\(987\) 1.05611e8 3.45078
\(988\) −2.17921e6 −0.0710242
\(989\) −3.33433e6 −0.108397
\(990\) −2.91056e7 −0.943817
\(991\) 3.47852e7 1.12515 0.562575 0.826746i \(-0.309811\pi\)
0.562575 + 0.826746i \(0.309811\pi\)
\(992\) 2.25288e6 0.0726874
\(993\) −2.28363e7 −0.734942
\(994\) −1.01168e7 −0.324771
\(995\) −1.46651e7 −0.469600
\(996\) −1.68902e7 −0.539492
\(997\) −4.21812e7 −1.34394 −0.671972 0.740577i \(-0.734552\pi\)
−0.671972 + 0.740577i \(0.734552\pi\)
\(998\) −1.20895e7 −0.384222
\(999\) 1.06717e8 3.38314
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 130.6.a.f.1.1 3
4.3 odd 2 1040.6.a.l.1.3 3
5.2 odd 4 650.6.b.j.599.3 6
5.3 odd 4 650.6.b.j.599.4 6
5.4 even 2 650.6.a.j.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
130.6.a.f.1.1 3 1.1 even 1 trivial
650.6.a.j.1.3 3 5.4 even 2
650.6.b.j.599.3 6 5.2 odd 4
650.6.b.j.599.4 6 5.3 odd 4
1040.6.a.l.1.3 3 4.3 odd 2