Properties

Label 983.6.a.b.1.11
Level $983$
Weight $6$
Character 983.1
Self dual yes
Analytic conductor $157.657$
Analytic rank $0$
Dimension $218$
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] = [983,6,Mod(1,983)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(983, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("983.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 983 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 983.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: \(157.657294876\)
Analytic rank: \(0\)
Dimension: \(218\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 983.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-10.4420 q^{2} +0.0889574 q^{3} +77.0361 q^{4} -100.525 q^{5} -0.928896 q^{6} +31.6163 q^{7} -470.268 q^{8} -242.992 q^{9} +O(q^{10})\) \(q-10.4420 q^{2} +0.0889574 q^{3} +77.0361 q^{4} -100.525 q^{5} -0.928896 q^{6} +31.6163 q^{7} -470.268 q^{8} -242.992 q^{9} +1049.69 q^{10} -159.766 q^{11} +6.85293 q^{12} -98.8165 q^{13} -330.139 q^{14} -8.94244 q^{15} +2445.40 q^{16} +2018.30 q^{17} +2537.33 q^{18} +697.965 q^{19} -7744.05 q^{20} +2.81251 q^{21} +1668.29 q^{22} -85.8780 q^{23} -41.8338 q^{24} +6980.27 q^{25} +1031.84 q^{26} -43.2326 q^{27} +2435.60 q^{28} -2639.98 q^{29} +93.3772 q^{30} +5111.75 q^{31} -10486.4 q^{32} -14.2124 q^{33} -21075.1 q^{34} -3178.23 q^{35} -18719.2 q^{36} -6797.95 q^{37} -7288.18 q^{38} -8.79045 q^{39} +47273.7 q^{40} +11125.9 q^{41} -29.3683 q^{42} +4402.13 q^{43} -12307.8 q^{44} +24426.8 q^{45} +896.741 q^{46} -23451.8 q^{47} +217.536 q^{48} -15807.4 q^{49} -72888.2 q^{50} +179.542 q^{51} -7612.43 q^{52} -26681.2 q^{53} +451.436 q^{54} +16060.5 q^{55} -14868.2 q^{56} +62.0892 q^{57} +27566.7 q^{58} -12245.4 q^{59} -688.890 q^{60} +24761.1 q^{61} -53377.1 q^{62} -7682.52 q^{63} +31246.2 q^{64} +9933.52 q^{65} +148.406 q^{66} +13373.6 q^{67} +155482. q^{68} -7.63948 q^{69} +33187.2 q^{70} -60264.0 q^{71} +114271. q^{72} -44967.0 q^{73} +70984.4 q^{74} +620.947 q^{75} +53768.5 q^{76} -5051.23 q^{77} +91.7902 q^{78} -681.501 q^{79} -245824. q^{80} +59043.2 q^{81} -116177. q^{82} +25226.1 q^{83} +216.664 q^{84} -202889. q^{85} -45967.2 q^{86} -234.845 q^{87} +75133.1 q^{88} -1264.98 q^{89} -255065. q^{90} -3124.22 q^{91} -6615.70 q^{92} +454.728 q^{93} +244885. q^{94} -70163.0 q^{95} -932.840 q^{96} +116731. q^{97} +165061. q^{98} +38822.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9} + 2133 q^{10} + 1752 q^{11} + 3512 q^{12} + 5990 q^{13} + 2319 q^{14} + 4639 q^{15} + 66105 q^{16} + 10656 q^{17} + 11911 q^{18} + 11511 q^{19} + 10012 q^{20} + 12225 q^{21} + 19401 q^{22} + 9767 q^{23} + 21725 q^{24} + 185207 q^{25} + 7708 q^{26} + 23764 q^{27} + 77808 q^{28} + 25772 q^{29} + 15736 q^{30} + 35900 q^{31} + 60155 q^{32} + 70026 q^{33} + 17236 q^{34} + 28782 q^{35} + 382874 q^{36} + 126082 q^{37} + 62164 q^{38} + 54264 q^{39} + 102846 q^{40} + 70480 q^{41} + 102244 q^{42} + 137413 q^{43} + 116278 q^{44} + 93481 q^{45} + 126122 q^{46} + 63218 q^{47} + 124701 q^{48} + 732031 q^{49} + 131089 q^{50} + 109902 q^{51} + 229519 q^{52} + 102608 q^{53} + 149130 q^{54} + 167596 q^{55} + 87868 q^{56} + 408318 q^{57} + 304579 q^{58} + 67460 q^{59} + 150523 q^{60} + 195132 q^{61} + 132294 q^{62} + 374425 q^{63} + 1296639 q^{64} + 347092 q^{65} + 147397 q^{66} + 381238 q^{67} + 296321 q^{68} + 139362 q^{69} + 325675 q^{70} + 147818 q^{71} + 646059 q^{72} + 961992 q^{73} + 167410 q^{74} + 167324 q^{75} + 504875 q^{76} + 284328 q^{77} + 284295 q^{78} + 285792 q^{79} + 444932 q^{80} + 1980282 q^{81} + 336676 q^{82} + 276734 q^{83} + 378474 q^{84} + 1021245 q^{85} + 156051 q^{86} + 500457 q^{87} + 1068101 q^{88} + 398983 q^{89} + 463961 q^{90} + 273517 q^{91} + 577884 q^{92} + 967833 q^{93} + 224775 q^{94} + 482817 q^{95} + 780445 q^{96} + 1636277 q^{97} + 495958 q^{98} + 627643 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.4420 −1.84591 −0.922954 0.384910i \(-0.874232\pi\)
−0.922954 + 0.384910i \(0.874232\pi\)
\(3\) 0.0889574 0.00570662 0.00285331 0.999996i \(-0.499092\pi\)
0.00285331 + 0.999996i \(0.499092\pi\)
\(4\) 77.0361 2.40738
\(5\) −100.525 −1.79825 −0.899123 0.437696i \(-0.855794\pi\)
−0.899123 + 0.437696i \(0.855794\pi\)
\(6\) −0.928896 −0.0105339
\(7\) 31.6163 0.243875 0.121937 0.992538i \(-0.461089\pi\)
0.121937 + 0.992538i \(0.461089\pi\)
\(8\) −470.268 −2.59789
\(9\) −242.992 −0.999967
\(10\) 1049.69 3.31940
\(11\) −159.766 −0.398111 −0.199055 0.979988i \(-0.563787\pi\)
−0.199055 + 0.979988i \(0.563787\pi\)
\(12\) 6.85293 0.0137380
\(13\) −98.8165 −0.162170 −0.0810851 0.996707i \(-0.525839\pi\)
−0.0810851 + 0.996707i \(0.525839\pi\)
\(14\) −330.139 −0.450170
\(15\) −8.94244 −0.0102619
\(16\) 2445.40 2.38809
\(17\) 2018.30 1.69380 0.846901 0.531751i \(-0.178466\pi\)
0.846901 + 0.531751i \(0.178466\pi\)
\(18\) 2537.33 1.84585
\(19\) 697.965 0.443557 0.221779 0.975097i \(-0.428814\pi\)
0.221779 + 0.975097i \(0.428814\pi\)
\(20\) −7744.05 −4.32905
\(21\) 2.81251 0.00139170
\(22\) 1668.29 0.734876
\(23\) −85.8780 −0.0338503 −0.0169251 0.999857i \(-0.505388\pi\)
−0.0169251 + 0.999857i \(0.505388\pi\)
\(24\) −41.8338 −0.0148252
\(25\) 6980.27 2.23369
\(26\) 1031.84 0.299351
\(27\) −43.2326 −0.0114131
\(28\) 2435.60 0.587098
\(29\) −2639.98 −0.582915 −0.291457 0.956584i \(-0.594140\pi\)
−0.291457 + 0.956584i \(0.594140\pi\)
\(30\) 93.3772 0.0189425
\(31\) 5111.75 0.955356 0.477678 0.878535i \(-0.341479\pi\)
0.477678 + 0.878535i \(0.341479\pi\)
\(32\) −10486.4 −1.81030
\(33\) −14.2124 −0.00227187
\(34\) −21075.1 −3.12660
\(35\) −3178.23 −0.438546
\(36\) −18719.2 −2.40730
\(37\) −6797.95 −0.816345 −0.408172 0.912905i \(-0.633834\pi\)
−0.408172 + 0.912905i \(0.633834\pi\)
\(38\) −7288.18 −0.818766
\(39\) −8.79045 −0.000925443 0
\(40\) 47273.7 4.67164
\(41\) 11125.9 1.03365 0.516826 0.856091i \(-0.327114\pi\)
0.516826 + 0.856091i \(0.327114\pi\)
\(42\) −29.3683 −0.00256895
\(43\) 4402.13 0.363071 0.181536 0.983384i \(-0.441893\pi\)
0.181536 + 0.983384i \(0.441893\pi\)
\(44\) −12307.8 −0.958403
\(45\) 24426.8 1.79819
\(46\) 896.741 0.0624845
\(47\) −23451.8 −1.54858 −0.774288 0.632834i \(-0.781892\pi\)
−0.774288 + 0.632834i \(0.781892\pi\)
\(48\) 217.536 0.0136279
\(49\) −15807.4 −0.940525
\(50\) −72888.2 −4.12318
\(51\) 179.542 0.00966588
\(52\) −7612.43 −0.390405
\(53\) −26681.2 −1.30471 −0.652357 0.757912i \(-0.726220\pi\)
−0.652357 + 0.757912i \(0.726220\pi\)
\(54\) 451.436 0.0210674
\(55\) 16060.5 0.715901
\(56\) −14868.2 −0.633559
\(57\) 62.0892 0.00253121
\(58\) 27566.7 1.07601
\(59\) −12245.4 −0.457978 −0.228989 0.973429i \(-0.573542\pi\)
−0.228989 + 0.973429i \(0.573542\pi\)
\(60\) −688.890 −0.0247043
\(61\) 24761.1 0.852010 0.426005 0.904721i \(-0.359921\pi\)
0.426005 + 0.904721i \(0.359921\pi\)
\(62\) −53377.1 −1.76350
\(63\) −7682.52 −0.243867
\(64\) 31246.2 0.953559
\(65\) 9933.52 0.291622
\(66\) 148.406 0.00419366
\(67\) 13373.6 0.363967 0.181983 0.983302i \(-0.441748\pi\)
0.181983 + 0.983302i \(0.441748\pi\)
\(68\) 155482. 4.07762
\(69\) −7.63948 −0.000193171 0
\(70\) 33187.2 0.809517
\(71\) −60264.0 −1.41877 −0.709385 0.704822i \(-0.751027\pi\)
−0.709385 + 0.704822i \(0.751027\pi\)
\(72\) 114271. 2.59780
\(73\) −44967.0 −0.987612 −0.493806 0.869572i \(-0.664395\pi\)
−0.493806 + 0.869572i \(0.664395\pi\)
\(74\) 70984.4 1.50690
\(75\) 620.947 0.0127468
\(76\) 53768.5 1.06781
\(77\) −5051.23 −0.0970891
\(78\) 91.7902 0.00170828
\(79\) −681.501 −0.0122857 −0.00614284 0.999981i \(-0.501955\pi\)
−0.00614284 + 0.999981i \(0.501955\pi\)
\(80\) −245824. −4.29436
\(81\) 59043.2 0.999902
\(82\) −116177. −1.90803
\(83\) 25226.1 0.401934 0.200967 0.979598i \(-0.435592\pi\)
0.200967 + 0.979598i \(0.435592\pi\)
\(84\) 216.664 0.00335034
\(85\) −202889. −3.04587
\(86\) −45967.2 −0.670196
\(87\) −234.845 −0.00332647
\(88\) 75133.1 1.03425
\(89\) −1264.98 −0.0169281 −0.00846406 0.999964i \(-0.502694\pi\)
−0.00846406 + 0.999964i \(0.502694\pi\)
\(90\) −255065. −3.31929
\(91\) −3124.22 −0.0395492
\(92\) −6615.70 −0.0814904
\(93\) 454.728 0.00545185
\(94\) 244885. 2.85853
\(95\) −70163.0 −0.797625
\(96\) −932.840 −0.0103307
\(97\) 116731. 1.25967 0.629833 0.776731i \(-0.283123\pi\)
0.629833 + 0.776731i \(0.283123\pi\)
\(98\) 165061. 1.73612
\(99\) 38822.0 0.398098
\(100\) 537733. 5.37733
\(101\) 73619.7 0.718110 0.359055 0.933316i \(-0.383099\pi\)
0.359055 + 0.933316i \(0.383099\pi\)
\(102\) −1874.79 −0.0178423
\(103\) 104162. 0.967421 0.483711 0.875228i \(-0.339289\pi\)
0.483711 + 0.875228i \(0.339289\pi\)
\(104\) 46470.2 0.421300
\(105\) −282.727 −0.00250262
\(106\) 278606. 2.40838
\(107\) −168312. −1.42120 −0.710600 0.703596i \(-0.751577\pi\)
−0.710600 + 0.703596i \(0.751577\pi\)
\(108\) −3330.47 −0.0274755
\(109\) 134927. 1.08776 0.543880 0.839163i \(-0.316955\pi\)
0.543880 + 0.839163i \(0.316955\pi\)
\(110\) −167705. −1.32149
\(111\) −604.728 −0.00465857
\(112\) 77314.6 0.582394
\(113\) −144432. −1.06406 −0.532032 0.846724i \(-0.678571\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(114\) −648.337 −0.00467239
\(115\) 8632.88 0.0608711
\(116\) −203373. −1.40330
\(117\) 24011.6 0.162165
\(118\) 127867. 0.845385
\(119\) 63811.1 0.413075
\(120\) 4205.34 0.0266593
\(121\) −135526. −0.841508
\(122\) −258556. −1.57273
\(123\) 989.728 0.00589865
\(124\) 393789. 2.29990
\(125\) −387551. −2.21847
\(126\) 80221.2 0.450155
\(127\) −254256. −1.39882 −0.699411 0.714720i \(-0.746554\pi\)
−0.699411 + 0.714720i \(0.746554\pi\)
\(128\) 9289.65 0.0501158
\(129\) 391.602 0.00207191
\(130\) −103726. −0.538307
\(131\) −265140. −1.34989 −0.674943 0.737870i \(-0.735832\pi\)
−0.674943 + 0.737870i \(0.735832\pi\)
\(132\) −1094.87 −0.00546924
\(133\) 22067.1 0.108172
\(134\) −139648. −0.671849
\(135\) 4345.95 0.0205235
\(136\) −949140. −4.40031
\(137\) 401274. 1.82658 0.913291 0.407307i \(-0.133532\pi\)
0.913291 + 0.407307i \(0.133532\pi\)
\(138\) 79.7717 0.000356575 0
\(139\) −419606. −1.84206 −0.921031 0.389489i \(-0.872651\pi\)
−0.921031 + 0.389489i \(0.872651\pi\)
\(140\) −244839. −1.05575
\(141\) −2086.21 −0.00883713
\(142\) 629278. 2.61892
\(143\) 15787.6 0.0645617
\(144\) −594213. −2.38801
\(145\) 265384. 1.04822
\(146\) 469547. 1.82304
\(147\) −1406.19 −0.00536722
\(148\) −523687. −1.96525
\(149\) −62487.5 −0.230583 −0.115292 0.993332i \(-0.536780\pi\)
−0.115292 + 0.993332i \(0.536780\pi\)
\(150\) −6483.95 −0.0235294
\(151\) −31897.9 −0.113847 −0.0569233 0.998379i \(-0.518129\pi\)
−0.0569233 + 0.998379i \(0.518129\pi\)
\(152\) −328231. −1.15231
\(153\) −490430. −1.69375
\(154\) 52745.1 0.179218
\(155\) −513859. −1.71797
\(156\) −677.182 −0.00222789
\(157\) −187586. −0.607366 −0.303683 0.952773i \(-0.598216\pi\)
−0.303683 + 0.952773i \(0.598216\pi\)
\(158\) 7116.26 0.0226782
\(159\) −2373.49 −0.00744551
\(160\) 1.05414e6 3.25536
\(161\) −2715.15 −0.00825522
\(162\) −616531. −1.84573
\(163\) 180119. 0.530995 0.265497 0.964112i \(-0.414464\pi\)
0.265497 + 0.964112i \(0.414464\pi\)
\(164\) 857092. 2.48839
\(165\) 1428.70 0.00408537
\(166\) −263412. −0.741933
\(167\) −490978. −1.36229 −0.681146 0.732147i \(-0.738518\pi\)
−0.681146 + 0.732147i \(0.738518\pi\)
\(168\) −1322.63 −0.00361548
\(169\) −361528. −0.973701
\(170\) 2.11858e6 5.62240
\(171\) −169600. −0.443543
\(172\) 339123. 0.874049
\(173\) 194845. 0.494965 0.247482 0.968892i \(-0.420397\pi\)
0.247482 + 0.968892i \(0.420397\pi\)
\(174\) 2452.26 0.00614036
\(175\) 220691. 0.544740
\(176\) −390693. −0.950723
\(177\) −1089.32 −0.00261350
\(178\) 13209.0 0.0312477
\(179\) −52037.2 −0.121390 −0.0606948 0.998156i \(-0.519332\pi\)
−0.0606948 + 0.998156i \(0.519332\pi\)
\(180\) 1.88174e6 4.32891
\(181\) −237165. −0.538088 −0.269044 0.963128i \(-0.586708\pi\)
−0.269044 + 0.963128i \(0.586708\pi\)
\(182\) 32623.2 0.0730042
\(183\) 2202.68 0.00486210
\(184\) 40385.7 0.0879392
\(185\) 683364. 1.46799
\(186\) −4748.28 −0.0100636
\(187\) −322456. −0.674321
\(188\) −1.80664e6 −3.72800
\(189\) −1366.86 −0.00278335
\(190\) 732644. 1.47234
\(191\) −583998. −1.15832 −0.579159 0.815214i \(-0.696619\pi\)
−0.579159 + 0.815214i \(0.696619\pi\)
\(192\) 2779.58 0.00544160
\(193\) 924290. 1.78614 0.893069 0.449920i \(-0.148548\pi\)
0.893069 + 0.449920i \(0.148548\pi\)
\(194\) −1.21890e6 −2.32523
\(195\) 883.660 0.00166417
\(196\) −1.21774e6 −2.26420
\(197\) −951391. −1.74660 −0.873300 0.487184i \(-0.838024\pi\)
−0.873300 + 0.487184i \(0.838024\pi\)
\(198\) −405381. −0.734852
\(199\) 646034. 1.15644 0.578219 0.815881i \(-0.303748\pi\)
0.578219 + 0.815881i \(0.303748\pi\)
\(200\) −3.28260e6 −5.80287
\(201\) 1189.68 0.00207702
\(202\) −768740. −1.32556
\(203\) −83466.4 −0.142158
\(204\) 13831.2 0.0232694
\(205\) −1.11843e6 −1.85876
\(206\) −1.08766e6 −1.78577
\(207\) 20867.7 0.0338492
\(208\) −241646. −0.387276
\(209\) −111511. −0.176585
\(210\) 2952.25 0.00461960
\(211\) 247955. 0.383413 0.191706 0.981452i \(-0.438598\pi\)
0.191706 + 0.981452i \(0.438598\pi\)
\(212\) −2.05541e6 −3.14094
\(213\) −5360.92 −0.00809638
\(214\) 1.75752e6 2.62341
\(215\) −442524. −0.652891
\(216\) 20330.9 0.0296498
\(217\) 161615. 0.232987
\(218\) −1.40891e6 −2.00790
\(219\) −4000.14 −0.00563593
\(220\) 1.23724e6 1.72344
\(221\) −199441. −0.274684
\(222\) 6314.59 0.00859929
\(223\) −1.12586e6 −1.51608 −0.758039 0.652210i \(-0.773842\pi\)
−0.758039 + 0.652210i \(0.773842\pi\)
\(224\) −331541. −0.441486
\(225\) −1.69615e6 −2.23361
\(226\) 1.50816e6 1.96416
\(227\) 139771. 0.180033 0.0900165 0.995940i \(-0.471308\pi\)
0.0900165 + 0.995940i \(0.471308\pi\)
\(228\) 4783.10 0.00609358
\(229\) 7027.20 0.00885510 0.00442755 0.999990i \(-0.498591\pi\)
0.00442755 + 0.999990i \(0.498591\pi\)
\(230\) −90144.8 −0.112362
\(231\) −449.344 −0.000554051 0
\(232\) 1.24150e6 1.51435
\(233\) −221897. −0.267770 −0.133885 0.990997i \(-0.542745\pi\)
−0.133885 + 0.990997i \(0.542745\pi\)
\(234\) −250730. −0.299341
\(235\) 2.35750e6 2.78472
\(236\) −943340. −1.10252
\(237\) −60.6246 −7.01096e−5 0
\(238\) −666318. −0.762499
\(239\) 1.59854e6 1.81021 0.905105 0.425188i \(-0.139792\pi\)
0.905105 + 0.425188i \(0.139792\pi\)
\(240\) −21867.8 −0.0245063
\(241\) −401743. −0.445559 −0.222780 0.974869i \(-0.571513\pi\)
−0.222780 + 0.974869i \(0.571513\pi\)
\(242\) 1.41516e6 1.55335
\(243\) 15757.8 0.0171191
\(244\) 1.90750e6 2.05111
\(245\) 1.58904e6 1.69130
\(246\) −10334.8 −0.0108884
\(247\) −68970.5 −0.0719318
\(248\) −2.40389e6 −2.48191
\(249\) 2244.05 0.00229368
\(250\) 4.04682e6 4.09510
\(251\) −719741. −0.721094 −0.360547 0.932741i \(-0.617410\pi\)
−0.360547 + 0.932741i \(0.617410\pi\)
\(252\) −591831. −0.587079
\(253\) 13720.4 0.0134762
\(254\) 2.65495e6 2.58210
\(255\) −18048.5 −0.0173816
\(256\) −1.09688e6 −1.04607
\(257\) −432916. −0.408856 −0.204428 0.978882i \(-0.565533\pi\)
−0.204428 + 0.978882i \(0.565533\pi\)
\(258\) −4089.12 −0.00382455
\(259\) −214926. −0.199086
\(260\) 765239. 0.702043
\(261\) 641493. 0.582896
\(262\) 2.76860e6 2.49176
\(263\) −1.38264e6 −1.23259 −0.616296 0.787514i \(-0.711368\pi\)
−0.616296 + 0.787514i \(0.711368\pi\)
\(264\) 6683.64 0.00590205
\(265\) 2.68213e6 2.34620
\(266\) −230426. −0.199676
\(267\) −112.529 −9.66023e−5 0
\(268\) 1.03025e6 0.876205
\(269\) 2.00653e6 1.69069 0.845347 0.534217i \(-0.179394\pi\)
0.845347 + 0.534217i \(0.179394\pi\)
\(270\) −45380.6 −0.0378844
\(271\) 418116. 0.345839 0.172919 0.984936i \(-0.444680\pi\)
0.172919 + 0.984936i \(0.444680\pi\)
\(272\) 4.93554e6 4.04494
\(273\) −277.922 −0.000225692 0
\(274\) −4.19011e6 −3.37170
\(275\) −1.11521e6 −0.889255
\(276\) −588.515 −0.000465034 0
\(277\) −3749.78 −0.00293634 −0.00146817 0.999999i \(-0.500467\pi\)
−0.00146817 + 0.999999i \(0.500467\pi\)
\(278\) 4.38153e6 3.40028
\(279\) −1.24211e6 −0.955325
\(280\) 1.49462e6 1.13929
\(281\) 557740. 0.421372 0.210686 0.977554i \(-0.432430\pi\)
0.210686 + 0.977554i \(0.432430\pi\)
\(282\) 21784.3 0.0163125
\(283\) 483364. 0.358763 0.179382 0.983780i \(-0.442590\pi\)
0.179382 + 0.983780i \(0.442590\pi\)
\(284\) −4.64250e6 −3.41551
\(285\) −6241.51 −0.00455174
\(286\) −164854. −0.119175
\(287\) 351759. 0.252081
\(288\) 2.54811e6 1.81024
\(289\) 2.65366e6 1.86896
\(290\) −2.77114e6 −1.93493
\(291\) 10384.0 0.00718843
\(292\) −3.46408e6 −2.37755
\(293\) −156481. −0.106486 −0.0532429 0.998582i \(-0.516956\pi\)
−0.0532429 + 0.998582i \(0.516956\pi\)
\(294\) 14683.4 0.00990739
\(295\) 1.23097e6 0.823556
\(296\) 3.19686e6 2.12077
\(297\) 6907.12 0.00454366
\(298\) 652496. 0.425635
\(299\) 8486.16 0.00548950
\(300\) 47835.3 0.0306864
\(301\) 139179. 0.0885438
\(302\) 333079. 0.210150
\(303\) 6549.02 0.00409798
\(304\) 1.70680e6 1.05925
\(305\) −2.48911e6 −1.53212
\(306\) 5.12109e6 3.12650
\(307\) 2.92997e6 1.77426 0.887130 0.461520i \(-0.152696\pi\)
0.887130 + 0.461520i \(0.152696\pi\)
\(308\) −389127. −0.233730
\(309\) 9265.97 0.00552071
\(310\) 5.36573e6 3.17121
\(311\) 2.78448e6 1.63246 0.816231 0.577725i \(-0.196060\pi\)
0.816231 + 0.577725i \(0.196060\pi\)
\(312\) 4133.87 0.00240420
\(313\) 1.58517e6 0.914568 0.457284 0.889321i \(-0.348822\pi\)
0.457284 + 0.889321i \(0.348822\pi\)
\(314\) 1.95877e6 1.12114
\(315\) 772286. 0.438532
\(316\) −52500.2 −0.0295762
\(317\) −1.04444e6 −0.583759 −0.291879 0.956455i \(-0.594281\pi\)
−0.291879 + 0.956455i \(0.594281\pi\)
\(318\) 24784.1 0.0137437
\(319\) 421780. 0.232065
\(320\) −3.14103e6 −1.71473
\(321\) −14972.6 −0.00811025
\(322\) 28351.7 0.0152384
\(323\) 1.40870e6 0.751298
\(324\) 4.54846e6 2.40714
\(325\) −689766. −0.362237
\(326\) −1.88081e6 −0.980168
\(327\) 12002.8 0.00620743
\(328\) −5.23214e6 −2.68531
\(329\) −741462. −0.377658
\(330\) −14918.6 −0.00754123
\(331\) −365932. −0.183582 −0.0917912 0.995778i \(-0.529259\pi\)
−0.0917912 + 0.995778i \(0.529259\pi\)
\(332\) 1.94332e6 0.967606
\(333\) 1.65185e6 0.816318
\(334\) 5.12680e6 2.51467
\(335\) −1.34438e6 −0.654501
\(336\) 6877.71 0.00332350
\(337\) −1.92618e6 −0.923892 −0.461946 0.886908i \(-0.652849\pi\)
−0.461946 + 0.886908i \(0.652849\pi\)
\(338\) 3.77509e6 1.79736
\(339\) −12848.3 −0.00607221
\(340\) −1.56298e7 −7.33256
\(341\) −816686. −0.380338
\(342\) 1.77097e6 0.818740
\(343\) −1.03115e6 −0.473245
\(344\) −2.07018e6 −0.943218
\(345\) 767.959 0.000347368 0
\(346\) −2.03458e6 −0.913660
\(347\) −175556. −0.0782696 −0.0391348 0.999234i \(-0.512460\pi\)
−0.0391348 + 0.999234i \(0.512460\pi\)
\(348\) −18091.6 −0.00800807
\(349\) 2.21755e6 0.974562 0.487281 0.873245i \(-0.337989\pi\)
0.487281 + 0.873245i \(0.337989\pi\)
\(350\) −2.30446e6 −1.00554
\(351\) 4272.09 0.00185086
\(352\) 1.67537e6 0.720700
\(353\) 4.28620e6 1.83078 0.915388 0.402573i \(-0.131884\pi\)
0.915388 + 0.402573i \(0.131884\pi\)
\(354\) 11374.7 0.00482429
\(355\) 6.05803e6 2.55130
\(356\) −97449.0 −0.0407523
\(357\) 5676.47 0.00235726
\(358\) 543374. 0.224074
\(359\) −4.30538e6 −1.76310 −0.881548 0.472095i \(-0.843498\pi\)
−0.881548 + 0.472095i \(0.843498\pi\)
\(360\) −1.14871e7 −4.67149
\(361\) −1.98894e6 −0.803257
\(362\) 2.47648e6 0.993262
\(363\) −12056.0 −0.00480216
\(364\) −240677. −0.0952098
\(365\) 4.52030e6 1.77597
\(366\) −23000.5 −0.00897499
\(367\) −40326.4 −0.0156287 −0.00781437 0.999969i \(-0.502487\pi\)
−0.00781437 + 0.999969i \(0.502487\pi\)
\(368\) −210006. −0.0808374
\(369\) −2.70350e6 −1.03362
\(370\) −7.13571e6 −2.70977
\(371\) −843562. −0.318187
\(372\) 35030.4 0.0131247
\(373\) 996746. 0.370947 0.185474 0.982649i \(-0.440618\pi\)
0.185474 + 0.982649i \(0.440618\pi\)
\(374\) 3.36710e6 1.24473
\(375\) −34475.5 −0.0126600
\(376\) 1.10287e7 4.02303
\(377\) 260873. 0.0945314
\(378\) 14272.8 0.00513782
\(379\) −71793.7 −0.0256737 −0.0128368 0.999918i \(-0.504086\pi\)
−0.0128368 + 0.999918i \(0.504086\pi\)
\(380\) −5.40508e6 −1.92018
\(381\) −22618.0 −0.00798255
\(382\) 6.09813e6 2.13815
\(383\) 2.07445e6 0.722614 0.361307 0.932447i \(-0.382331\pi\)
0.361307 + 0.932447i \(0.382331\pi\)
\(384\) 826.383 0.000285992 0
\(385\) 507775. 0.174590
\(386\) −9.65146e6 −3.29705
\(387\) −1.06968e6 −0.363059
\(388\) 8.99246e6 3.03249
\(389\) −3.92235e6 −1.31423 −0.657117 0.753789i \(-0.728224\pi\)
−0.657117 + 0.753789i \(0.728224\pi\)
\(390\) −9227.21 −0.00307191
\(391\) −173327. −0.0573356
\(392\) 7.43372e6 2.44338
\(393\) −23586.2 −0.00770328
\(394\) 9.93445e6 3.22406
\(395\) 68507.9 0.0220927
\(396\) 2.99069e6 0.958371
\(397\) −3.37991e6 −1.07629 −0.538144 0.842853i \(-0.680874\pi\)
−0.538144 + 0.842853i \(0.680874\pi\)
\(398\) −6.74591e6 −2.13468
\(399\) 1963.03 0.000617299 0
\(400\) 1.70696e7 5.33424
\(401\) −783083. −0.243191 −0.121595 0.992580i \(-0.538801\pi\)
−0.121595 + 0.992580i \(0.538801\pi\)
\(402\) −12422.7 −0.00383399
\(403\) −505125. −0.154930
\(404\) 5.67137e6 1.72876
\(405\) −5.93532e6 −1.79807
\(406\) 871559. 0.262411
\(407\) 1.08608e6 0.324996
\(408\) −84433.0 −0.0251109
\(409\) −260533. −0.0770113 −0.0385056 0.999258i \(-0.512260\pi\)
−0.0385056 + 0.999258i \(0.512260\pi\)
\(410\) 1.16787e7 3.43110
\(411\) 35696.3 0.0104236
\(412\) 8.02422e6 2.32895
\(413\) −387156. −0.111689
\(414\) −217901. −0.0624825
\(415\) −2.53585e6 −0.722776
\(416\) 1.03623e6 0.293576
\(417\) −37327.0 −0.0105119
\(418\) 1.16441e6 0.325960
\(419\) 1.92332e6 0.535202 0.267601 0.963530i \(-0.413769\pi\)
0.267601 + 0.963530i \(0.413769\pi\)
\(420\) −21780.2 −0.00602474
\(421\) −1.94410e6 −0.534580 −0.267290 0.963616i \(-0.586128\pi\)
−0.267290 + 0.963616i \(0.586128\pi\)
\(422\) −2.58915e6 −0.707744
\(423\) 5.69861e6 1.54853
\(424\) 1.25473e7 3.38950
\(425\) 1.40883e7 3.78342
\(426\) 55978.9 0.0149452
\(427\) 782855. 0.207784
\(428\) −1.29661e7 −3.42136
\(429\) 1404.42 0.000368429 0
\(430\) 4.62085e6 1.20518
\(431\) −2.11453e6 −0.548303 −0.274152 0.961686i \(-0.588397\pi\)
−0.274152 + 0.961686i \(0.588397\pi\)
\(432\) −105721. −0.0272553
\(433\) 4.91778e6 1.26052 0.630260 0.776384i \(-0.282948\pi\)
0.630260 + 0.776384i \(0.282948\pi\)
\(434\) −1.68759e6 −0.430073
\(435\) 23607.8 0.00598181
\(436\) 1.03943e7 2.61865
\(437\) −59939.8 −0.0150145
\(438\) 41769.6 0.0104034
\(439\) 1.10707e6 0.274167 0.137084 0.990559i \(-0.456227\pi\)
0.137084 + 0.990559i \(0.456227\pi\)
\(440\) −7.55275e6 −1.85983
\(441\) 3.84107e6 0.940495
\(442\) 2.08257e6 0.507041
\(443\) 244752. 0.0592538 0.0296269 0.999561i \(-0.490568\pi\)
0.0296269 + 0.999561i \(0.490568\pi\)
\(444\) −46585.8 −0.0112149
\(445\) 127162. 0.0304409
\(446\) 1.17562e7 2.79854
\(447\) −5558.72 −0.00131585
\(448\) 987892. 0.232549
\(449\) 6.29578e6 1.47378 0.736891 0.676011i \(-0.236293\pi\)
0.736891 + 0.676011i \(0.236293\pi\)
\(450\) 1.77113e7 4.12305
\(451\) −1.77754e6 −0.411508
\(452\) −1.11265e7 −2.56160
\(453\) −2837.56 −0.000649679 0
\(454\) −1.45949e6 −0.332324
\(455\) 314062. 0.0711191
\(456\) −29198.5 −0.00657581
\(457\) −3.86683e6 −0.866094 −0.433047 0.901371i \(-0.642562\pi\)
−0.433047 + 0.901371i \(0.642562\pi\)
\(458\) −73378.3 −0.0163457
\(459\) −87256.1 −0.0193314
\(460\) 665043. 0.146540
\(461\) −643858. −0.141103 −0.0705517 0.997508i \(-0.522476\pi\)
−0.0705517 + 0.997508i \(0.522476\pi\)
\(462\) 4692.07 0.00102273
\(463\) 2.77132e6 0.600806 0.300403 0.953812i \(-0.402879\pi\)
0.300403 + 0.953812i \(0.402879\pi\)
\(464\) −6.45580e6 −1.39205
\(465\) −45711.5 −0.00980377
\(466\) 2.31706e6 0.494280
\(467\) 1.91983e6 0.407353 0.203676 0.979038i \(-0.434711\pi\)
0.203676 + 0.979038i \(0.434711\pi\)
\(468\) 1.84976e6 0.390392
\(469\) 422825. 0.0887622
\(470\) −2.46171e7 −5.14034
\(471\) −16687.1 −0.00346600
\(472\) 5.75864e6 1.18977
\(473\) −703313. −0.144543
\(474\) 633.044 0.000129416 0
\(475\) 4.87199e6 0.990769
\(476\) 4.91576e6 0.994428
\(477\) 6.48332e6 1.30467
\(478\) −1.66920e7 −3.34148
\(479\) 3.58877e6 0.714673 0.357336 0.933976i \(-0.383685\pi\)
0.357336 + 0.933976i \(0.383685\pi\)
\(480\) 93773.7 0.0185771
\(481\) 671749. 0.132387
\(482\) 4.19501e6 0.822462
\(483\) −241.532 −4.71094e−5 0
\(484\) −1.04404e7 −2.02583
\(485\) −1.17343e7 −2.26519
\(486\) −164544. −0.0316003
\(487\) −1.13660e6 −0.217163 −0.108582 0.994088i \(-0.534631\pi\)
−0.108582 + 0.994088i \(0.534631\pi\)
\(488\) −1.16443e7 −2.21343
\(489\) 16022.9 0.00303018
\(490\) −1.65928e7 −3.12198
\(491\) 1.08305e6 0.202742 0.101371 0.994849i \(-0.467677\pi\)
0.101371 + 0.994849i \(0.467677\pi\)
\(492\) 76244.7 0.0142003
\(493\) −5.32825e6 −0.987342
\(494\) 720192. 0.132779
\(495\) −3.90258e6 −0.715878
\(496\) 1.25003e7 2.28147
\(497\) −1.90533e6 −0.346002
\(498\) −23432.4 −0.00423393
\(499\) 3.16842e6 0.569627 0.284814 0.958583i \(-0.408068\pi\)
0.284814 + 0.958583i \(0.408068\pi\)
\(500\) −2.98554e7 −5.34070
\(501\) −43676.1 −0.00777409
\(502\) 7.51556e6 1.33107
\(503\) −1.22467e6 −0.215824 −0.107912 0.994160i \(-0.534416\pi\)
−0.107912 + 0.994160i \(0.534416\pi\)
\(504\) 3.61284e6 0.633538
\(505\) −7.40062e6 −1.29134
\(506\) −143269. −0.0248758
\(507\) −32160.6 −0.00555654
\(508\) −1.95869e7 −3.36749
\(509\) −4.33780e6 −0.742122 −0.371061 0.928609i \(-0.621006\pi\)
−0.371061 + 0.928609i \(0.621006\pi\)
\(510\) 188463. 0.0320849
\(511\) −1.42169e6 −0.240854
\(512\) 1.11564e7 1.88083
\(513\) −30174.8 −0.00506234
\(514\) 4.52052e6 0.754711
\(515\) −1.04709e7 −1.73966
\(516\) 30167.5 0.00498786
\(517\) 3.74682e6 0.616505
\(518\) 2.24427e6 0.367494
\(519\) 17332.9 0.00282458
\(520\) −4.67142e6 −0.757601
\(521\) −8.15290e6 −1.31588 −0.657942 0.753068i \(-0.728573\pi\)
−0.657942 + 0.753068i \(0.728573\pi\)
\(522\) −6.69850e6 −1.07597
\(523\) 9.26451e6 1.48105 0.740523 0.672032i \(-0.234578\pi\)
0.740523 + 0.672032i \(0.234578\pi\)
\(524\) −2.04253e7 −3.24968
\(525\) 19632.1 0.00310862
\(526\) 1.44376e7 2.27525
\(527\) 1.03170e7 1.61818
\(528\) −34755.0 −0.00542541
\(529\) −6.42897e6 −0.998854
\(530\) −2.80069e7 −4.33087
\(531\) 2.97554e6 0.457963
\(532\) 1.69996e6 0.260412
\(533\) −1.09942e6 −0.167627
\(534\) 1175.03 0.000178319 0
\(535\) 1.69195e7 2.55567
\(536\) −6.28918e6 −0.945544
\(537\) −4629.09 −0.000692724 0
\(538\) −2.09523e7 −3.12087
\(539\) 2.52549e6 0.374433
\(540\) 334795. 0.0494077
\(541\) −7.81513e6 −1.14800 −0.574002 0.818854i \(-0.694610\pi\)
−0.574002 + 0.818854i \(0.694610\pi\)
\(542\) −4.36598e6 −0.638387
\(543\) −21097.6 −0.00307067
\(544\) −2.11646e7 −3.06629
\(545\) −1.35635e7 −1.95606
\(546\) 2902.07 0.000416607 0
\(547\) −2.68525e6 −0.383721 −0.191861 0.981422i \(-0.561452\pi\)
−0.191861 + 0.981422i \(0.561452\pi\)
\(548\) 3.09125e7 4.39727
\(549\) −6.01674e6 −0.851983
\(550\) 1.16451e7 1.64148
\(551\) −1.84261e6 −0.258556
\(552\) 3592.60 0.000501836 0
\(553\) −21546.6 −0.00299616
\(554\) 39155.3 0.00542022
\(555\) 60790.2 0.00837725
\(556\) −3.23248e7 −4.43454
\(557\) 2.78292e6 0.380070 0.190035 0.981777i \(-0.439140\pi\)
0.190035 + 0.981777i \(0.439140\pi\)
\(558\) 1.29702e7 1.76344
\(559\) −435003. −0.0588793
\(560\) −7.77205e6 −1.04729
\(561\) −28684.8 −0.00384809
\(562\) −5.82394e6 −0.777815
\(563\) −5.91196e6 −0.786069 −0.393034 0.919524i \(-0.628575\pi\)
−0.393034 + 0.919524i \(0.628575\pi\)
\(564\) −160714. −0.0212743
\(565\) 1.45190e7 1.91345
\(566\) −5.04730e6 −0.662244
\(567\) 1.86673e6 0.243851
\(568\) 2.83402e7 3.68580
\(569\) −448359. −0.0580557 −0.0290279 0.999579i \(-0.509241\pi\)
−0.0290279 + 0.999579i \(0.509241\pi\)
\(570\) 65174.1 0.00840210
\(571\) 621363. 0.0797545 0.0398772 0.999205i \(-0.487303\pi\)
0.0398772 + 0.999205i \(0.487303\pi\)
\(572\) 1.21621e6 0.155424
\(573\) −51950.9 −0.00661008
\(574\) −3.67308e6 −0.465319
\(575\) −599452. −0.0756109
\(576\) −7.59259e6 −0.953528
\(577\) 498167. 0.0622925 0.0311463 0.999515i \(-0.490084\pi\)
0.0311463 + 0.999515i \(0.490084\pi\)
\(578\) −2.77096e7 −3.44994
\(579\) 82222.4 0.0101928
\(580\) 2.04441e7 2.52347
\(581\) 797557. 0.0980215
\(582\) −108431. −0.0132692
\(583\) 4.26276e6 0.519421
\(584\) 2.11465e7 2.56571
\(585\) −2.41377e6 −0.291612
\(586\) 1.63398e6 0.196563
\(587\) −6.21374e6 −0.744317 −0.372158 0.928169i \(-0.621382\pi\)
−0.372158 + 0.928169i \(0.621382\pi\)
\(588\) −108327. −0.0129209
\(589\) 3.56782e6 0.423755
\(590\) −1.28539e7 −1.52021
\(591\) −84633.2 −0.00996718
\(592\) −1.66237e7 −1.94950
\(593\) 9.00459e6 1.05154 0.525772 0.850626i \(-0.323777\pi\)
0.525772 + 0.850626i \(0.323777\pi\)
\(594\) −72124.4 −0.00838718
\(595\) −6.41461e6 −0.742811
\(596\) −4.81379e6 −0.555100
\(597\) 57469.5 0.00659935
\(598\) −88612.7 −0.0101331
\(599\) −1.01975e7 −1.16125 −0.580626 0.814170i \(-0.697192\pi\)
−0.580626 + 0.814170i \(0.697192\pi\)
\(600\) −292011. −0.0331148
\(601\) −4.69600e6 −0.530325 −0.265162 0.964204i \(-0.585426\pi\)
−0.265162 + 0.964204i \(0.585426\pi\)
\(602\) −1.45331e6 −0.163444
\(603\) −3.24968e6 −0.363955
\(604\) −2.45729e6 −0.274072
\(605\) 1.36237e7 1.51324
\(606\) −68385.1 −0.00756449
\(607\) −2.60515e6 −0.286986 −0.143493 0.989651i \(-0.545833\pi\)
−0.143493 + 0.989651i \(0.545833\pi\)
\(608\) −7.31912e6 −0.802971
\(609\) −7424.95 −0.000811242 0
\(610\) 2.59913e7 2.82816
\(611\) 2.31743e6 0.251133
\(612\) −3.77808e7 −4.07749
\(613\) −5.37292e6 −0.577510 −0.288755 0.957403i \(-0.593241\pi\)
−0.288755 + 0.957403i \(0.593241\pi\)
\(614\) −3.05948e7 −3.27512
\(615\) −99492.3 −0.0106072
\(616\) 2.37543e6 0.252227
\(617\) 1.49370e7 1.57961 0.789805 0.613358i \(-0.210182\pi\)
0.789805 + 0.613358i \(0.210182\pi\)
\(618\) −96755.5 −0.0101907
\(619\) 1.32292e6 0.138773 0.0693866 0.997590i \(-0.477896\pi\)
0.0693866 + 0.997590i \(0.477896\pi\)
\(620\) −3.95856e7 −4.13579
\(621\) 3712.73 0.000386335 0
\(622\) −2.90756e7 −3.01338
\(623\) −39994.0 −0.00412834
\(624\) −21496.2 −0.00221004
\(625\) 1.71452e7 1.75567
\(626\) −1.65524e7 −1.68821
\(627\) −9919.77 −0.00100770
\(628\) −1.44508e7 −1.46216
\(629\) −1.37203e7 −1.38273
\(630\) −8.06423e6 −0.809490
\(631\) 1.10949e7 1.10931 0.554653 0.832082i \(-0.312851\pi\)
0.554653 + 0.832082i \(0.312851\pi\)
\(632\) 320488. 0.0319168
\(633\) 22057.4 0.00218799
\(634\) 1.09060e7 1.07757
\(635\) 2.55591e7 2.51543
\(636\) −182844. −0.0179241
\(637\) 1.56203e6 0.152525
\(638\) −4.40424e6 −0.428370
\(639\) 1.46437e7 1.41872
\(640\) −933842. −0.0901205
\(641\) −5.36946e6 −0.516162 −0.258081 0.966123i \(-0.583090\pi\)
−0.258081 + 0.966123i \(0.583090\pi\)
\(642\) 156344. 0.0149708
\(643\) 1.43277e7 1.36663 0.683314 0.730124i \(-0.260538\pi\)
0.683314 + 0.730124i \(0.260538\pi\)
\(644\) −209164. −0.0198734
\(645\) −39365.8 −0.00372580
\(646\) −1.47097e7 −1.38683
\(647\) 1.91039e7 1.79417 0.897083 0.441863i \(-0.145682\pi\)
0.897083 + 0.441863i \(0.145682\pi\)
\(648\) −2.77661e7 −2.59763
\(649\) 1.95641e6 0.182326
\(650\) 7.20256e6 0.668657
\(651\) 14376.8 0.00132957
\(652\) 1.38756e7 1.27830
\(653\) −1.10569e7 −1.01473 −0.507367 0.861730i \(-0.669381\pi\)
−0.507367 + 0.861730i \(0.669381\pi\)
\(654\) −125333. −0.0114583
\(655\) 2.66532e7 2.42743
\(656\) 2.72072e7 2.46845
\(657\) 1.09266e7 0.987580
\(658\) 7.74237e6 0.697123
\(659\) −1.56580e7 −1.40451 −0.702253 0.711928i \(-0.747822\pi\)
−0.702253 + 0.711928i \(0.747822\pi\)
\(660\) 110062. 0.00983503
\(661\) −4.90242e6 −0.436422 −0.218211 0.975902i \(-0.570022\pi\)
−0.218211 + 0.975902i \(0.570022\pi\)
\(662\) 3.82108e6 0.338876
\(663\) −17741.7 −0.00156752
\(664\) −1.18630e7 −1.04418
\(665\) −2.21830e6 −0.194521
\(666\) −1.72486e7 −1.50685
\(667\) 226716. 0.0197318
\(668\) −3.78230e7 −3.27955
\(669\) −100153. −0.00865167
\(670\) 1.40381e7 1.20815
\(671\) −3.95599e6 −0.339195
\(672\) −29493.0 −0.00251939
\(673\) −3.58886e6 −0.305435 −0.152717 0.988270i \(-0.548802\pi\)
−0.152717 + 0.988270i \(0.548802\pi\)
\(674\) 2.01132e7 1.70542
\(675\) −301775. −0.0254932
\(676\) −2.78507e7 −2.34406
\(677\) 2.29248e6 0.192235 0.0961176 0.995370i \(-0.469358\pi\)
0.0961176 + 0.995370i \(0.469358\pi\)
\(678\) 134162. 0.0112087
\(679\) 3.69060e6 0.307201
\(680\) 9.54123e7 7.91283
\(681\) 12433.7 0.00102738
\(682\) 8.52786e6 0.702068
\(683\) 4.74085e6 0.388870 0.194435 0.980915i \(-0.437713\pi\)
0.194435 + 0.980915i \(0.437713\pi\)
\(684\) −1.30653e7 −1.06778
\(685\) −4.03380e7 −3.28464
\(686\) 1.07673e7 0.873567
\(687\) 625.121 5.05327e−5 0
\(688\) 1.07650e7 0.867045
\(689\) 2.63654e6 0.211586
\(690\) −8019.05 −0.000641210 0
\(691\) 1.78575e7 1.42274 0.711368 0.702819i \(-0.248076\pi\)
0.711368 + 0.702819i \(0.248076\pi\)
\(692\) 1.50101e7 1.19157
\(693\) 1.22741e6 0.0970860
\(694\) 1.83317e6 0.144478
\(695\) 4.21808e7 3.31248
\(696\) 110440. 0.00864180
\(697\) 2.24553e7 1.75080
\(698\) −2.31557e7 −1.79895
\(699\) −19739.4 −0.00152806
\(700\) 1.70011e7 1.31139
\(701\) 2.21731e7 1.70425 0.852123 0.523342i \(-0.175315\pi\)
0.852123 + 0.523342i \(0.175315\pi\)
\(702\) −44609.3 −0.00341651
\(703\) −4.74473e6 −0.362096
\(704\) −4.99210e6 −0.379622
\(705\) 209717. 0.0158913
\(706\) −4.47566e7 −3.37944
\(707\) 2.32759e6 0.175129
\(708\) −83917.1 −0.00629169
\(709\) −2.21990e7 −1.65851 −0.829256 0.558869i \(-0.811235\pi\)
−0.829256 + 0.558869i \(0.811235\pi\)
\(710\) −6.32582e7 −4.70946
\(711\) 165599. 0.0122853
\(712\) 594879. 0.0439773
\(713\) −438987. −0.0323391
\(714\) −59273.9 −0.00435129
\(715\) −1.58704e6 −0.116098
\(716\) −4.00874e6 −0.292230
\(717\) 142202. 0.0103302
\(718\) 4.49570e7 3.25451
\(719\) 1.65127e6 0.119123 0.0595617 0.998225i \(-0.481030\pi\)
0.0595617 + 0.998225i \(0.481030\pi\)
\(720\) 5.97332e7 4.29422
\(721\) 3.29322e6 0.235930
\(722\) 2.07686e7 1.48274
\(723\) −35738.0 −0.00254264
\(724\) −1.82702e7 −1.29538
\(725\) −1.84278e7 −1.30205
\(726\) 125889. 0.00886435
\(727\) 2.79297e6 0.195988 0.0979942 0.995187i \(-0.468757\pi\)
0.0979942 + 0.995187i \(0.468757\pi\)
\(728\) 1.46922e6 0.102744
\(729\) −1.43461e7 −0.999805
\(730\) −4.72012e7 −3.27828
\(731\) 8.88480e6 0.614970
\(732\) 169686. 0.0117049
\(733\) −1.07026e7 −0.735751 −0.367875 0.929875i \(-0.619915\pi\)
−0.367875 + 0.929875i \(0.619915\pi\)
\(734\) 421089. 0.0288492
\(735\) 141357. 0.00965158
\(736\) 900548. 0.0612791
\(737\) −2.13665e6 −0.144899
\(738\) 2.82300e7 1.90796
\(739\) 1.14888e7 0.773863 0.386932 0.922108i \(-0.373535\pi\)
0.386932 + 0.922108i \(0.373535\pi\)
\(740\) 5.26436e7 3.53400
\(741\) −6135.43 −0.000410487 0
\(742\) 8.80850e6 0.587344
\(743\) 1.74855e7 1.16200 0.580999 0.813904i \(-0.302662\pi\)
0.580999 + 0.813904i \(0.302662\pi\)
\(744\) −213844. −0.0141633
\(745\) 6.28155e6 0.414645
\(746\) −1.04081e7 −0.684735
\(747\) −6.12974e6 −0.401921
\(748\) −2.48407e7 −1.62334
\(749\) −5.32141e6 −0.346595
\(750\) 359995. 0.0233692
\(751\) −315794. −0.0204317 −0.0102158 0.999948i \(-0.503252\pi\)
−0.0102158 + 0.999948i \(0.503252\pi\)
\(752\) −5.73491e7 −3.69813
\(753\) −64026.3 −0.00411501
\(754\) −2.72405e6 −0.174496
\(755\) 3.20654e6 0.204724
\(756\) −105297. −0.00670058
\(757\) −9.36700e6 −0.594101 −0.297051 0.954862i \(-0.596003\pi\)
−0.297051 + 0.954862i \(0.596003\pi\)
\(758\) 749672. 0.0473913
\(759\) 1220.53 7.69033e−5 0
\(760\) 3.29954e7 2.07214
\(761\) 1.44409e7 0.903926 0.451963 0.892037i \(-0.350724\pi\)
0.451963 + 0.892037i \(0.350724\pi\)
\(762\) 236178. 0.0147350
\(763\) 4.26590e6 0.265277
\(764\) −4.49889e7 −2.78851
\(765\) 4.93005e7 3.04577
\(766\) −2.16615e7 −1.33388
\(767\) 1.21005e6 0.0742703
\(768\) −97575.8 −0.00596951
\(769\) 2.40377e7 1.46581 0.732903 0.680334i \(-0.238165\pi\)
0.732903 + 0.680334i \(0.238165\pi\)
\(770\) −5.30220e6 −0.322277
\(771\) −38511.0 −0.00233319
\(772\) 7.12036e7 4.29991
\(773\) 2.30732e7 1.38886 0.694430 0.719560i \(-0.255657\pi\)
0.694430 + 0.719560i \(0.255657\pi\)
\(774\) 1.11697e7 0.670174
\(775\) 3.56814e7 2.13397
\(776\) −5.48947e7 −3.27247
\(777\) −19119.3 −0.00113611
\(778\) 4.09573e7 2.42595
\(779\) 7.76547e6 0.458484
\(780\) 68073.7 0.00400629
\(781\) 9.62816e6 0.564827
\(782\) 1.80989e6 0.105836
\(783\) 114133. 0.00665284
\(784\) −3.86554e7 −2.24605
\(785\) 1.88570e7 1.09219
\(786\) 246287. 0.0142195
\(787\) 1.28552e7 0.739847 0.369923 0.929062i \(-0.379384\pi\)
0.369923 + 0.929062i \(0.379384\pi\)
\(788\) −7.32914e7 −4.20472
\(789\) −122996. −0.00703394
\(790\) −715362. −0.0407810
\(791\) −4.56642e6 −0.259498
\(792\) −1.82567e7 −1.03421
\(793\) −2.44680e6 −0.138171
\(794\) 3.52931e7 1.98673
\(795\) 238595. 0.0133889
\(796\) 4.97679e7 2.78398
\(797\) 3.15312e7 1.75831 0.879153 0.476540i \(-0.158109\pi\)
0.879153 + 0.476540i \(0.158109\pi\)
\(798\) −20498.1 −0.00113948
\(799\) −4.73328e7 −2.62298
\(800\) −7.31977e7 −4.04364
\(801\) 307380. 0.0169276
\(802\) 8.17698e6 0.448908
\(803\) 7.18422e6 0.393179
\(804\) 91648.3 0.00500017
\(805\) 272940. 0.0148449
\(806\) 5.27453e6 0.285987
\(807\) 178496. 0.00964815
\(808\) −3.46210e7 −1.86557
\(809\) 2.88320e7 1.54883 0.774416 0.632677i \(-0.218044\pi\)
0.774416 + 0.632677i \(0.218044\pi\)
\(810\) 6.19768e7 3.31907
\(811\) −1.99774e7 −1.06656 −0.533281 0.845938i \(-0.679041\pi\)
−0.533281 + 0.845938i \(0.679041\pi\)
\(812\) −6.42992e6 −0.342228
\(813\) 37194.5 0.00197357
\(814\) −1.13409e7 −0.599912
\(815\) −1.81064e7 −0.954859
\(816\) 439053. 0.0230829
\(817\) 3.07253e6 0.161043
\(818\) 2.72049e6 0.142156
\(819\) 759160. 0.0395479
\(820\) −8.61592e7 −4.47473
\(821\) −1.23656e7 −0.640259 −0.320130 0.947374i \(-0.603727\pi\)
−0.320130 + 0.947374i \(0.603727\pi\)
\(822\) −372741. −0.0192410
\(823\) 3.86496e6 0.198905 0.0994524 0.995042i \(-0.468291\pi\)
0.0994524 + 0.995042i \(0.468291\pi\)
\(824\) −4.89840e7 −2.51325
\(825\) −99206.5 −0.00507464
\(826\) 4.04270e6 0.206168
\(827\) 2.97722e7 1.51372 0.756862 0.653574i \(-0.226731\pi\)
0.756862 + 0.653574i \(0.226731\pi\)
\(828\) 1.60756e6 0.0814877
\(829\) −2.29386e7 −1.15926 −0.579630 0.814880i \(-0.696803\pi\)
−0.579630 + 0.814880i \(0.696803\pi\)
\(830\) 2.64795e7 1.33418
\(831\) −333.571 −1.67566e−5 0
\(832\) −3.08764e6 −0.154639
\(833\) −3.19040e7 −1.59306
\(834\) 389770. 0.0194041
\(835\) 4.93555e7 2.44974
\(836\) −8.59040e6 −0.425107
\(837\) −220994. −0.0109035
\(838\) −2.00834e7 −0.987933
\(839\) 2.32540e7 1.14049 0.570246 0.821474i \(-0.306848\pi\)
0.570246 + 0.821474i \(0.306848\pi\)
\(840\) 132958. 0.00650152
\(841\) −1.35417e7 −0.660210
\(842\) 2.03003e7 0.986786
\(843\) 49615.1 0.00240461
\(844\) 1.91015e7 0.923019
\(845\) 3.63426e7 1.75095
\(846\) −5.95051e7 −2.85844
\(847\) −4.28483e6 −0.205222
\(848\) −6.52462e7 −3.11577
\(849\) 42998.8 0.00204733
\(850\) −1.47110e8 −6.98385
\(851\) 583794. 0.0276335
\(852\) −412984. −0.0194910
\(853\) −2.88545e7 −1.35782 −0.678909 0.734222i \(-0.737547\pi\)
−0.678909 + 0.734222i \(0.737547\pi\)
\(854\) −8.17459e6 −0.383550
\(855\) 1.70490e7 0.797599
\(856\) 7.91517e7 3.69212
\(857\) 3.82033e7 1.77684 0.888420 0.459031i \(-0.151803\pi\)
0.888420 + 0.459031i \(0.151803\pi\)
\(858\) −14665.0 −0.000680086 0
\(859\) −2.75321e7 −1.27308 −0.636542 0.771242i \(-0.719636\pi\)
−0.636542 + 0.771242i \(0.719636\pi\)
\(860\) −3.40903e7 −1.57175
\(861\) 31291.6 0.00143853
\(862\) 2.20800e7 1.01212
\(863\) 3.05194e7 1.39492 0.697460 0.716624i \(-0.254313\pi\)
0.697460 + 0.716624i \(0.254313\pi\)
\(864\) 453353. 0.0206610
\(865\) −1.95868e7 −0.890068
\(866\) −5.13517e7 −2.32680
\(867\) 236063. 0.0106655
\(868\) 1.24502e7 0.560888
\(869\) 108881. 0.00489106
\(870\) −246514. −0.0110419
\(871\) −1.32153e6 −0.0590245
\(872\) −6.34519e7 −2.82588
\(873\) −2.83646e7 −1.25962
\(874\) 625894. 0.0277155
\(875\) −1.22530e7 −0.541029
\(876\) −308155. −0.0135678
\(877\) −8.70280e6 −0.382085 −0.191042 0.981582i \(-0.561187\pi\)
−0.191042 + 0.981582i \(0.561187\pi\)
\(878\) −1.15601e7 −0.506087
\(879\) −13920.1 −0.000607673 0
\(880\) 3.92744e7 1.70963
\(881\) 2.81193e7 1.22057 0.610287 0.792180i \(-0.291054\pi\)
0.610287 + 0.792180i \(0.291054\pi\)
\(882\) −4.01086e7 −1.73607
\(883\) 3.78696e7 1.63452 0.817258 0.576272i \(-0.195493\pi\)
0.817258 + 0.576272i \(0.195493\pi\)
\(884\) −1.53641e7 −0.661268
\(885\) 109504. 0.00469972
\(886\) −2.55570e6 −0.109377
\(887\) −4.01123e7 −1.71186 −0.855931 0.517090i \(-0.827015\pi\)
−0.855931 + 0.517090i \(0.827015\pi\)
\(888\) 284384. 0.0121024
\(889\) −8.03866e6 −0.341137
\(890\) −1.32783e6 −0.0561911
\(891\) −9.43313e6 −0.398072
\(892\) −8.67316e7 −3.64977
\(893\) −1.63686e7 −0.686882
\(894\) 58044.4 0.00242894
\(895\) 5.23104e6 0.218288
\(896\) 293705. 0.0122220
\(897\) 754.906 3.13265e−5 0
\(898\) −6.57407e7 −2.72047
\(899\) −1.34949e7 −0.556891
\(900\) −1.30665e8 −5.37715
\(901\) −5.38505e7 −2.20993
\(902\) 1.85611e7 0.759605
\(903\) 12381.0 0.000505286 0
\(904\) 6.79218e7 2.76432
\(905\) 2.38410e7 0.967615
\(906\) 29629.9 0.00119925
\(907\) −2.61559e7 −1.05573 −0.527863 0.849330i \(-0.677007\pi\)
−0.527863 + 0.849330i \(0.677007\pi\)
\(908\) 1.07674e7 0.433407
\(909\) −1.78890e7 −0.718086
\(910\) −3.27944e6 −0.131279
\(911\) 8.13328e6 0.324690 0.162345 0.986734i \(-0.448094\pi\)
0.162345 + 0.986734i \(0.448094\pi\)
\(912\) 151833. 0.00604475
\(913\) −4.03028e6 −0.160014
\(914\) 4.03776e7 1.59873
\(915\) −221424. −0.00874325
\(916\) 541348. 0.0213176
\(917\) −8.38276e6 −0.329203
\(918\) 911132. 0.0356841
\(919\) 1.94329e7 0.759010 0.379505 0.925190i \(-0.376094\pi\)
0.379505 + 0.925190i \(0.376094\pi\)
\(920\) −4.05977e6 −0.158136
\(921\) 260642. 0.0101250
\(922\) 6.72319e6 0.260464
\(923\) 5.95507e6 0.230082
\(924\) −34615.7 −0.00133381
\(925\) −4.74515e7 −1.82346
\(926\) −2.89382e7 −1.10903
\(927\) −2.53105e7 −0.967390
\(928\) 2.76838e7 1.05525
\(929\) 2.81125e6 0.106871 0.0534355 0.998571i \(-0.482983\pi\)
0.0534355 + 0.998571i \(0.482983\pi\)
\(930\) 477321. 0.0180969
\(931\) −1.10330e7 −0.417177
\(932\) −1.70941e7 −0.644624
\(933\) 247700. 0.00931584
\(934\) −2.00469e7 −0.751936
\(935\) 3.24149e7 1.21259
\(936\) −1.12919e7 −0.421286
\(937\) 3.29554e7 1.22625 0.613123 0.789988i \(-0.289913\pi\)
0.613123 + 0.789988i \(0.289913\pi\)
\(938\) −4.41515e6 −0.163847
\(939\) 141013. 0.00521909
\(940\) 1.81612e8 6.70387
\(941\) 1.20204e7 0.442531 0.221265 0.975214i \(-0.428981\pi\)
0.221265 + 0.975214i \(0.428981\pi\)
\(942\) 174247. 0.00639792
\(943\) −955466. −0.0349894
\(944\) −2.99450e7 −1.09369
\(945\) 137403. 0.00500515
\(946\) 7.34402e6 0.266812
\(947\) 3.05242e7 1.10604 0.553019 0.833169i \(-0.313476\pi\)
0.553019 + 0.833169i \(0.313476\pi\)
\(948\) −4670.28 −0.000168780 0
\(949\) 4.44348e6 0.160161
\(950\) −5.08735e7 −1.82887
\(951\) −92910.3 −0.00333129
\(952\) −3.00083e7 −1.07312
\(953\) −5.11762e7 −1.82531 −0.912654 0.408733i \(-0.865971\pi\)
−0.912654 + 0.408733i \(0.865971\pi\)
\(954\) −6.76990e7 −2.40831
\(955\) 5.87064e7 2.08294
\(956\) 1.23145e8 4.35786
\(957\) 37520.4 0.00132430
\(958\) −3.74741e7 −1.31922
\(959\) 1.26868e7 0.445457
\(960\) −279418. −0.00978533
\(961\) −2.49917e6 −0.0872946
\(962\) −7.01443e6 −0.244374
\(963\) 4.08985e7 1.42115
\(964\) −3.09487e7 −1.07263
\(965\) −9.29142e7 −3.21191
\(966\) 2522.09 8.69596e−5 0
\(967\) −4.38794e6 −0.150902 −0.0754509 0.997150i \(-0.524040\pi\)
−0.0754509 + 0.997150i \(0.524040\pi\)
\(968\) 6.37334e7 2.18614
\(969\) 125314. 0.00428737
\(970\) 1.22530e8 4.18133
\(971\) −1.15532e7 −0.393236 −0.196618 0.980480i \(-0.562996\pi\)
−0.196618 + 0.980480i \(0.562996\pi\)
\(972\) 1.21392e6 0.0412122
\(973\) −1.32664e7 −0.449232
\(974\) 1.18684e7 0.400863
\(975\) −61359.8 −0.00206715
\(976\) 6.05507e7 2.03467
\(977\) 2.24021e7 0.750850 0.375425 0.926853i \(-0.377497\pi\)
0.375425 + 0.926853i \(0.377497\pi\)
\(978\) −167312. −0.00559344
\(979\) 202101. 0.00673926
\(980\) 1.22413e8 4.07158
\(981\) −3.27862e7 −1.08772
\(982\) −1.13092e7 −0.374243
\(983\) 966289. 0.0318950
\(984\) −465437. −0.0153240
\(985\) 9.56385e7 3.14081
\(986\) 5.56378e7 1.82254
\(987\) −65958.5 −0.00215515
\(988\) −5.31321e6 −0.173167
\(989\) −378046. −0.0122901
\(990\) 4.07509e7 1.32144
\(991\) −3.76398e7 −1.21748 −0.608741 0.793369i \(-0.708325\pi\)
−0.608741 + 0.793369i \(0.708325\pi\)
\(992\) −5.36037e7 −1.72948
\(993\) −32552.4 −0.00104763
\(994\) 1.98955e7 0.638688
\(995\) −6.49425e7 −2.07956
\(996\) 172872. 0.00552176
\(997\) −2.78546e7 −0.887480 −0.443740 0.896156i \(-0.646349\pi\)
−0.443740 + 0.896156i \(0.646349\pi\)
\(998\) −3.30847e7 −1.05148
\(999\) 293893. 0.00931698
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 983.6.a.b.1.11 218
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
983.6.a.b.1.11 218 1.1 even 1 trivial