Properties

Label 983.6.a.b.1.16
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 1.16
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)
 
\(f(q)\) \(=\) \(q-9.86337 q^{2} -14.1514 q^{3} +65.2861 q^{4} +8.97631 q^{5} +139.581 q^{6} -99.2905 q^{7} -328.313 q^{8} -42.7375 q^{9} +O(q^{10})\) \(q-9.86337 q^{2} -14.1514 q^{3} +65.2861 q^{4} +8.97631 q^{5} +139.581 q^{6} -99.2905 q^{7} -328.313 q^{8} -42.7375 q^{9} -88.5367 q^{10} +111.541 q^{11} -923.891 q^{12} -531.103 q^{13} +979.339 q^{14} -127.027 q^{15} +1149.12 q^{16} +1571.26 q^{17} +421.536 q^{18} -264.968 q^{19} +586.028 q^{20} +1405.10 q^{21} -1100.18 q^{22} -3900.63 q^{23} +4646.10 q^{24} -3044.43 q^{25} +5238.47 q^{26} +4043.59 q^{27} -6482.29 q^{28} -66.6159 q^{29} +1252.92 q^{30} -9708.03 q^{31} -828.191 q^{32} -1578.47 q^{33} -15498.0 q^{34} -891.262 q^{35} -2790.17 q^{36} -8340.98 q^{37} +2613.48 q^{38} +7515.86 q^{39} -2947.04 q^{40} +886.529 q^{41} -13859.0 q^{42} -8108.75 q^{43} +7282.11 q^{44} -383.625 q^{45} +38473.3 q^{46} +14909.8 q^{47} -16261.7 q^{48} -6948.39 q^{49} +30028.3 q^{50} -22235.6 q^{51} -34673.7 q^{52} +9636.89 q^{53} -39883.4 q^{54} +1001.23 q^{55} +32598.4 q^{56} +3749.67 q^{57} +657.057 q^{58} +15352.7 q^{59} -8293.13 q^{60} +23017.1 q^{61} +95753.9 q^{62} +4243.43 q^{63} -28603.2 q^{64} -4767.35 q^{65} +15569.0 q^{66} +48328.1 q^{67} +102582. q^{68} +55199.4 q^{69} +8790.85 q^{70} -82166.5 q^{71} +14031.3 q^{72} -33236.7 q^{73} +82270.2 q^{74} +43082.9 q^{75} -17298.7 q^{76} -11075.0 q^{77} -74131.8 q^{78} -21080.5 q^{79} +10314.9 q^{80} -46837.3 q^{81} -8744.17 q^{82} -73614.2 q^{83} +91733.6 q^{84} +14104.1 q^{85} +79979.7 q^{86} +942.709 q^{87} -36620.6 q^{88} +74582.2 q^{89} +3783.84 q^{90} +52733.5 q^{91} -254657. q^{92} +137382. q^{93} -147061. q^{94} -2378.44 q^{95} +11720.1 q^{96} +3359.59 q^{97} +68534.6 q^{98} -4767.01 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.86337 −1.74361 −0.871807 0.489849i \(-0.837052\pi\)
−0.871807 + 0.489849i \(0.837052\pi\)
\(3\) −14.1514 −0.907814 −0.453907 0.891049i \(-0.649970\pi\)
−0.453907 + 0.891049i \(0.649970\pi\)
\(4\) 65.2861 2.04019
\(5\) 8.97631 0.160573 0.0802865 0.996772i \(-0.474416\pi\)
0.0802865 + 0.996772i \(0.474416\pi\)
\(6\) 139.581 1.58288
\(7\) −99.2905 −0.765883 −0.382942 0.923772i \(-0.625089\pi\)
−0.382942 + 0.923772i \(0.625089\pi\)
\(8\) −328.313 −1.81369
\(9\) −42.7375 −0.175875
\(10\) −88.5367 −0.279977
\(11\) 111.541 0.277942 0.138971 0.990296i \(-0.455620\pi\)
0.138971 + 0.990296i \(0.455620\pi\)
\(12\) −923.891 −1.85211
\(13\) −531.103 −0.871607 −0.435804 0.900042i \(-0.643536\pi\)
−0.435804 + 0.900042i \(0.643536\pi\)
\(14\) 979.339 1.33541
\(15\) −127.027 −0.145770
\(16\) 1149.12 1.12219
\(17\) 1571.26 1.31864 0.659320 0.751862i \(-0.270844\pi\)
0.659320 + 0.751862i \(0.270844\pi\)
\(18\) 421.536 0.306657
\(19\) −264.968 −0.168387 −0.0841937 0.996449i \(-0.526831\pi\)
−0.0841937 + 0.996449i \(0.526831\pi\)
\(20\) 586.028 0.327600
\(21\) 1405.10 0.695279
\(22\) −1100.18 −0.484624
\(23\) −3900.63 −1.53750 −0.768750 0.639550i \(-0.779121\pi\)
−0.768750 + 0.639550i \(0.779121\pi\)
\(24\) 4646.10 1.64650
\(25\) −3044.43 −0.974216
\(26\) 5238.47 1.51975
\(27\) 4043.59 1.06747
\(28\) −6482.29 −1.56255
\(29\) −66.6159 −0.0147090 −0.00735449 0.999973i \(-0.502341\pi\)
−0.00735449 + 0.999973i \(0.502341\pi\)
\(30\) 1252.92 0.254167
\(31\) −9708.03 −1.81437 −0.907187 0.420727i \(-0.861775\pi\)
−0.907187 + 0.420727i \(0.861775\pi\)
\(32\) −828.191 −0.142974
\(33\) −1578.47 −0.252320
\(34\) −15498.0 −2.29920
\(35\) −891.262 −0.122980
\(36\) −2790.17 −0.358818
\(37\) −8340.98 −1.00164 −0.500821 0.865551i \(-0.666969\pi\)
−0.500821 + 0.865551i \(0.666969\pi\)
\(38\) 2613.48 0.293603
\(39\) 7515.86 0.791257
\(40\) −2947.04 −0.291230
\(41\) 886.529 0.0823632 0.0411816 0.999152i \(-0.486888\pi\)
0.0411816 + 0.999152i \(0.486888\pi\)
\(42\) −13859.0 −1.21230
\(43\) −8108.75 −0.668780 −0.334390 0.942435i \(-0.608530\pi\)
−0.334390 + 0.942435i \(0.608530\pi\)
\(44\) 7282.11 0.567055
\(45\) −383.625 −0.0282407
\(46\) 38473.3 2.68081
\(47\) 14909.8 0.984523 0.492262 0.870447i \(-0.336170\pi\)
0.492262 + 0.870447i \(0.336170\pi\)
\(48\) −16261.7 −1.01874
\(49\) −6948.39 −0.413422
\(50\) 30028.3 1.69866
\(51\) −22235.6 −1.19708
\(52\) −34673.7 −1.77825
\(53\) 9636.89 0.471246 0.235623 0.971845i \(-0.424287\pi\)
0.235623 + 0.971845i \(0.424287\pi\)
\(54\) −39883.4 −1.86126
\(55\) 1001.23 0.0446300
\(56\) 32598.4 1.38908
\(57\) 3749.67 0.152864
\(58\) 657.057 0.0256468
\(59\) 15352.7 0.574190 0.287095 0.957902i \(-0.407310\pi\)
0.287095 + 0.957902i \(0.407310\pi\)
\(60\) −8293.13 −0.297400
\(61\) 23017.1 0.792002 0.396001 0.918250i \(-0.370398\pi\)
0.396001 + 0.918250i \(0.370398\pi\)
\(62\) 95753.9 3.16357
\(63\) 4243.43 0.134699
\(64\) −28603.2 −0.872899
\(65\) −4767.35 −0.139957
\(66\) 15569.0 0.439948
\(67\) 48328.1 1.31526 0.657631 0.753340i \(-0.271559\pi\)
0.657631 + 0.753340i \(0.271559\pi\)
\(68\) 102582. 2.69028
\(69\) 55199.4 1.39576
\(70\) 8790.85 0.214430
\(71\) −82166.5 −1.93441 −0.967206 0.253995i \(-0.918255\pi\)
−0.967206 + 0.253995i \(0.918255\pi\)
\(72\) 14031.3 0.318982
\(73\) −33236.7 −0.729979 −0.364990 0.931012i \(-0.618927\pi\)
−0.364990 + 0.931012i \(0.618927\pi\)
\(74\) 82270.2 1.74648
\(75\) 43082.9 0.884407
\(76\) −17298.7 −0.343543
\(77\) −11075.0 −0.212871
\(78\) −74131.8 −1.37965
\(79\) −21080.5 −0.380025 −0.190013 0.981782i \(-0.560853\pi\)
−0.190013 + 0.981782i \(0.560853\pi\)
\(80\) 10314.9 0.180193
\(81\) −46837.3 −0.793194
\(82\) −8744.17 −0.143610
\(83\) −73614.2 −1.17291 −0.586457 0.809980i \(-0.699478\pi\)
−0.586457 + 0.809980i \(0.699478\pi\)
\(84\) 91733.6 1.41850
\(85\) 14104.1 0.211738
\(86\) 79979.7 1.16609
\(87\) 942.709 0.0133530
\(88\) −36620.6 −0.504102
\(89\) 74582.2 0.998068 0.499034 0.866583i \(-0.333688\pi\)
0.499034 + 0.866583i \(0.333688\pi\)
\(90\) 3783.84 0.0492409
\(91\) 52733.5 0.667549
\(92\) −254657. −3.13679
\(93\) 137382. 1.64711
\(94\) −147061. −1.71663
\(95\) −2378.44 −0.0270385
\(96\) 11720.1 0.129793
\(97\) 3359.59 0.0362541 0.0181271 0.999836i \(-0.494230\pi\)
0.0181271 + 0.999836i \(0.494230\pi\)
\(98\) 68534.6 0.720849
\(99\) −4767.01 −0.0488830
\(100\) −198759. −1.98759
\(101\) −148108. −1.44469 −0.722345 0.691533i \(-0.756936\pi\)
−0.722345 + 0.691533i \(0.756936\pi\)
\(102\) 219318. 2.08725
\(103\) −14922.1 −0.138592 −0.0692958 0.997596i \(-0.522075\pi\)
−0.0692958 + 0.997596i \(0.522075\pi\)
\(104\) 174368. 1.58083
\(105\) 12612.6 0.111643
\(106\) −95052.2 −0.821670
\(107\) −50031.3 −0.422457 −0.211229 0.977437i \(-0.567746\pi\)
−0.211229 + 0.977437i \(0.567746\pi\)
\(108\) 263990. 2.17785
\(109\) 20239.2 0.163165 0.0815827 0.996667i \(-0.474003\pi\)
0.0815827 + 0.996667i \(0.474003\pi\)
\(110\) −9875.51 −0.0778176
\(111\) 118037. 0.909305
\(112\) −114097. −0.859467
\(113\) −59127.0 −0.435602 −0.217801 0.975993i \(-0.569888\pi\)
−0.217801 + 0.975993i \(0.569888\pi\)
\(114\) −36984.4 −0.266537
\(115\) −35013.2 −0.246881
\(116\) −4349.09 −0.0300092
\(117\) 22698.0 0.153294
\(118\) −151430. −1.00117
\(119\) −156012. −1.00993
\(120\) 41704.8 0.264383
\(121\) −148610. −0.922748
\(122\) −227026. −1.38095
\(123\) −12545.6 −0.0747704
\(124\) −633800. −3.70167
\(125\) −55378.7 −0.317006
\(126\) −41854.5 −0.234864
\(127\) 34082.9 0.187511 0.0937556 0.995595i \(-0.470113\pi\)
0.0937556 + 0.995595i \(0.470113\pi\)
\(128\) 308626. 1.66497
\(129\) 114750. 0.607127
\(130\) 47022.1 0.244030
\(131\) −227377. −1.15763 −0.578814 0.815460i \(-0.696484\pi\)
−0.578814 + 0.815460i \(0.696484\pi\)
\(132\) −103052. −0.514781
\(133\) 26308.8 0.128965
\(134\) −476678. −2.29331
\(135\) 36296.5 0.171408
\(136\) −515867. −2.39161
\(137\) −392429. −1.78632 −0.893162 0.449736i \(-0.851518\pi\)
−0.893162 + 0.449736i \(0.851518\pi\)
\(138\) −544452. −2.43367
\(139\) −4264.18 −0.0187197 −0.00935985 0.999956i \(-0.502979\pi\)
−0.00935985 + 0.999956i \(0.502979\pi\)
\(140\) −58187.1 −0.250903
\(141\) −210994. −0.893764
\(142\) 810439. 3.37287
\(143\) −59240.1 −0.242256
\(144\) −49110.6 −0.197365
\(145\) −597.965 −0.00236187
\(146\) 327826. 1.27280
\(147\) 98329.6 0.375311
\(148\) −544550. −2.04354
\(149\) −329553. −1.21607 −0.608036 0.793909i \(-0.708043\pi\)
−0.608036 + 0.793909i \(0.708043\pi\)
\(150\) −424943. −1.54206
\(151\) −215741. −0.770000 −0.385000 0.922917i \(-0.625799\pi\)
−0.385000 + 0.922917i \(0.625799\pi\)
\(152\) 86992.6 0.305403
\(153\) −67151.9 −0.231915
\(154\) 109237. 0.371166
\(155\) −87142.3 −0.291340
\(156\) 490682. 1.61432
\(157\) 253368. 0.820357 0.410179 0.912005i \(-0.365466\pi\)
0.410179 + 0.912005i \(0.365466\pi\)
\(158\) 207924. 0.662617
\(159\) −136376. −0.427803
\(160\) −7434.10 −0.0229577
\(161\) 387295. 1.17755
\(162\) 461974. 1.38302
\(163\) −46194.6 −0.136183 −0.0680914 0.997679i \(-0.521691\pi\)
−0.0680914 + 0.997679i \(0.521691\pi\)
\(164\) 57878.0 0.168037
\(165\) −14168.8 −0.0405158
\(166\) 726084. 2.04511
\(167\) −129478. −0.359256 −0.179628 0.983735i \(-0.557489\pi\)
−0.179628 + 0.983735i \(0.557489\pi\)
\(168\) −461314. −1.26102
\(169\) −89222.1 −0.240301
\(170\) −139114. −0.369190
\(171\) 11324.1 0.0296151
\(172\) −529389. −1.36444
\(173\) −81131.0 −0.206097 −0.103048 0.994676i \(-0.532860\pi\)
−0.103048 + 0.994676i \(0.532860\pi\)
\(174\) −9298.29 −0.0232825
\(175\) 302283. 0.746136
\(176\) 128175. 0.311904
\(177\) −217263. −0.521258
\(178\) −735632. −1.74025
\(179\) −303006. −0.706836 −0.353418 0.935466i \(-0.614981\pi\)
−0.353418 + 0.935466i \(0.614981\pi\)
\(180\) −25045.4 −0.0576165
\(181\) −109800. −0.249119 −0.124560 0.992212i \(-0.539752\pi\)
−0.124560 + 0.992212i \(0.539752\pi\)
\(182\) −520131. −1.16395
\(183\) −325725. −0.718990
\(184\) 1.28063e6 2.78855
\(185\) −74871.2 −0.160837
\(186\) −1.35505e6 −2.87193
\(187\) 175261. 0.366506
\(188\) 973400. 2.00862
\(189\) −401490. −0.817561
\(190\) 23459.4 0.0471447
\(191\) −432893. −0.858612 −0.429306 0.903159i \(-0.641242\pi\)
−0.429306 + 0.903159i \(0.641242\pi\)
\(192\) 404775. 0.792430
\(193\) −595297. −1.15038 −0.575189 0.818021i \(-0.695071\pi\)
−0.575189 + 0.818021i \(0.695071\pi\)
\(194\) −33136.9 −0.0632132
\(195\) 67464.7 0.127055
\(196\) −453634. −0.843461
\(197\) 944989. 1.73485 0.867423 0.497571i \(-0.165775\pi\)
0.867423 + 0.497571i \(0.165775\pi\)
\(198\) 47018.8 0.0852331
\(199\) −96047.7 −0.171931 −0.0859655 0.996298i \(-0.527397\pi\)
−0.0859655 + 0.996298i \(0.527397\pi\)
\(200\) 999526. 1.76693
\(201\) −683910. −1.19401
\(202\) 1.46084e6 2.51898
\(203\) 6614.33 0.0112654
\(204\) −1.45168e6 −2.44227
\(205\) 7957.75 0.0132253
\(206\) 147182. 0.241650
\(207\) 166703. 0.270407
\(208\) −610303. −0.978109
\(209\) −29554.9 −0.0468020
\(210\) −124403. −0.194663
\(211\) −547771. −0.847018 −0.423509 0.905892i \(-0.639202\pi\)
−0.423509 + 0.905892i \(0.639202\pi\)
\(212\) 629155. 0.961431
\(213\) 1.16277e6 1.75608
\(214\) 493478. 0.736602
\(215\) −72786.7 −0.107388
\(216\) −1.32757e6 −1.93607
\(217\) 963916. 1.38960
\(218\) −199627. −0.284497
\(219\) 470346. 0.662685
\(220\) 65366.5 0.0910538
\(221\) −834503. −1.14934
\(222\) −1.16424e6 −1.58548
\(223\) −831358. −1.11950 −0.559752 0.828660i \(-0.689104\pi\)
−0.559752 + 0.828660i \(0.689104\pi\)
\(224\) 82231.5 0.109501
\(225\) 130111. 0.171340
\(226\) 583192. 0.759522
\(227\) −1.06213e6 −1.36808 −0.684041 0.729444i \(-0.739779\pi\)
−0.684041 + 0.729444i \(0.739779\pi\)
\(228\) 244802. 0.311873
\(229\) 336960. 0.424609 0.212304 0.977204i \(-0.431903\pi\)
0.212304 + 0.977204i \(0.431903\pi\)
\(230\) 345349. 0.430465
\(231\) 156727. 0.193248
\(232\) 21870.9 0.0266776
\(233\) −1.05063e6 −1.26782 −0.633912 0.773405i \(-0.718552\pi\)
−0.633912 + 0.773405i \(0.718552\pi\)
\(234\) −223879. −0.267285
\(235\) 133835. 0.158088
\(236\) 1.00232e6 1.17146
\(237\) 298318. 0.344992
\(238\) 1.53880e6 1.76092
\(239\) −713976. −0.808517 −0.404258 0.914645i \(-0.632470\pi\)
−0.404258 + 0.914645i \(0.632470\pi\)
\(240\) −145970. −0.163582
\(241\) −1.39830e6 −1.55081 −0.775406 0.631463i \(-0.782455\pi\)
−0.775406 + 0.631463i \(0.782455\pi\)
\(242\) 1.46579e6 1.60892
\(243\) −319779. −0.347403
\(244\) 1.50270e6 1.61583
\(245\) −62370.9 −0.0663845
\(246\) 123742. 0.130371
\(247\) 140726. 0.146768
\(248\) 3.18728e6 3.29072
\(249\) 1.04174e6 1.06479
\(250\) 546220. 0.552736
\(251\) 1.10081e6 1.10288 0.551439 0.834215i \(-0.314079\pi\)
0.551439 + 0.834215i \(0.314079\pi\)
\(252\) 277037. 0.274813
\(253\) −435082. −0.427336
\(254\) −336172. −0.326947
\(255\) −199593. −0.192219
\(256\) −2.12879e6 −2.03017
\(257\) 1.59543e6 1.50676 0.753380 0.657585i \(-0.228422\pi\)
0.753380 + 0.657585i \(0.228422\pi\)
\(258\) −1.13183e6 −1.05860
\(259\) 828180. 0.767142
\(260\) −311242. −0.285538
\(261\) 2847.00 0.00258694
\(262\) 2.24271e6 2.01846
\(263\) −1.49855e6 −1.33592 −0.667962 0.744195i \(-0.732833\pi\)
−0.667962 + 0.744195i \(0.732833\pi\)
\(264\) 518233. 0.457631
\(265\) 86503.7 0.0756693
\(266\) −259494. −0.224866
\(267\) −1.05544e6 −0.906059
\(268\) 3.15515e6 2.68339
\(269\) 455961. 0.384191 0.192096 0.981376i \(-0.438472\pi\)
0.192096 + 0.981376i \(0.438472\pi\)
\(270\) −358006. −0.298869
\(271\) 871573. 0.720909 0.360454 0.932777i \(-0.382622\pi\)
0.360454 + 0.932777i \(0.382622\pi\)
\(272\) 1.80557e6 1.47977
\(273\) −746254. −0.606010
\(274\) 3.87068e6 3.11466
\(275\) −339580. −0.270776
\(276\) 3.60375e6 2.84762
\(277\) 505821. 0.396094 0.198047 0.980193i \(-0.436540\pi\)
0.198047 + 0.980193i \(0.436540\pi\)
\(278\) 42059.2 0.0326399
\(279\) 414897. 0.319102
\(280\) 292613. 0.223048
\(281\) 917159. 0.692913 0.346457 0.938066i \(-0.387385\pi\)
0.346457 + 0.938066i \(0.387385\pi\)
\(282\) 2.08111e6 1.55838
\(283\) 97454.2 0.0723326 0.0361663 0.999346i \(-0.488485\pi\)
0.0361663 + 0.999346i \(0.488485\pi\)
\(284\) −5.36433e6 −3.94657
\(285\) 33658.2 0.0245459
\(286\) 584307. 0.422402
\(287\) −88023.9 −0.0630806
\(288\) 35394.8 0.0251454
\(289\) 1.04901e6 0.738814
\(290\) 5897.95 0.00411819
\(291\) −47543.0 −0.0329120
\(292\) −2.16989e6 −1.48930
\(293\) 1.03378e6 0.703493 0.351746 0.936095i \(-0.385588\pi\)
0.351746 + 0.936095i \(0.385588\pi\)
\(294\) −969861. −0.654397
\(295\) 137811. 0.0921995
\(296\) 2.73846e6 1.81667
\(297\) 451028. 0.296696
\(298\) 3.25050e6 2.12036
\(299\) 2.07164e6 1.34010
\(300\) 2.81272e6 1.80436
\(301\) 805122. 0.512207
\(302\) 2.12794e6 1.34258
\(303\) 2.09593e6 1.31151
\(304\) −304481. −0.188963
\(305\) 206609. 0.127174
\(306\) 662344. 0.404371
\(307\) 718916. 0.435344 0.217672 0.976022i \(-0.430154\pi\)
0.217672 + 0.976022i \(0.430154\pi\)
\(308\) −723045. −0.434298
\(309\) 211169. 0.125815
\(310\) 859517. 0.507984
\(311\) −878326. −0.514938 −0.257469 0.966287i \(-0.582888\pi\)
−0.257469 + 0.966287i \(0.582888\pi\)
\(312\) −2.46756e6 −1.43510
\(313\) 1.26268e6 0.728502 0.364251 0.931301i \(-0.381325\pi\)
0.364251 + 0.931301i \(0.381325\pi\)
\(314\) −2.49907e6 −1.43039
\(315\) 38090.3 0.0216291
\(316\) −1.37626e6 −0.775324
\(317\) 2.19292e6 1.22567 0.612837 0.790209i \(-0.290028\pi\)
0.612837 + 0.790209i \(0.290028\pi\)
\(318\) 1.34512e6 0.745924
\(319\) −7430.43 −0.00408825
\(320\) −256751. −0.140164
\(321\) 708014. 0.383512
\(322\) −3.82004e6 −2.05319
\(323\) −416335. −0.222043
\(324\) −3.05783e6 −1.61827
\(325\) 1.61691e6 0.849134
\(326\) 455635. 0.237450
\(327\) −286414. −0.148124
\(328\) −291059. −0.149382
\(329\) −1.48040e6 −0.754030
\(330\) 139752. 0.0706439
\(331\) −2.67827e6 −1.34365 −0.671823 0.740711i \(-0.734489\pi\)
−0.671823 + 0.740711i \(0.734489\pi\)
\(332\) −4.80599e6 −2.39297
\(333\) 356473. 0.176163
\(334\) 1.27709e6 0.626404
\(335\) 433807. 0.211196
\(336\) 1.61463e6 0.780235
\(337\) −597512. −0.286597 −0.143299 0.989680i \(-0.545771\pi\)
−0.143299 + 0.989680i \(0.545771\pi\)
\(338\) 880031. 0.418992
\(339\) 836731. 0.395445
\(340\) 920805. 0.431986
\(341\) −1.08285e6 −0.504291
\(342\) −111694. −0.0516373
\(343\) 2.35869e6 1.08252
\(344\) 2.66221e6 1.21296
\(345\) 495487. 0.224122
\(346\) 800225. 0.359354
\(347\) 3.47608e6 1.54976 0.774882 0.632106i \(-0.217809\pi\)
0.774882 + 0.632106i \(0.217809\pi\)
\(348\) 61545.8 0.0272427
\(349\) −2.84825e6 −1.25174 −0.625871 0.779926i \(-0.715256\pi\)
−0.625871 + 0.779926i \(0.715256\pi\)
\(350\) −2.98153e6 −1.30097
\(351\) −2.14756e6 −0.930419
\(352\) −92377.7 −0.0397384
\(353\) −2.74391e6 −1.17201 −0.586007 0.810306i \(-0.699301\pi\)
−0.586007 + 0.810306i \(0.699301\pi\)
\(354\) 2.14294e6 0.908872
\(355\) −737551. −0.310614
\(356\) 4.86918e6 2.03625
\(357\) 2.20778e6 0.916824
\(358\) 2.98866e6 1.23245
\(359\) −2.96720e6 −1.21510 −0.607549 0.794282i \(-0.707847\pi\)
−0.607549 + 0.794282i \(0.707847\pi\)
\(360\) 125949. 0.0512200
\(361\) −2.40589e6 −0.971646
\(362\) 1.08300e6 0.434368
\(363\) 2.10303e6 0.837683
\(364\) 3.44277e6 1.36193
\(365\) −298343. −0.117215
\(366\) 3.21274e6 1.25364
\(367\) 1.23117e6 0.477150 0.238575 0.971124i \(-0.423320\pi\)
0.238575 + 0.971124i \(0.423320\pi\)
\(368\) −4.48230e6 −1.72537
\(369\) −37888.0 −0.0144856
\(370\) 738483. 0.280437
\(371\) −956852. −0.360919
\(372\) 8.96916e6 3.36043
\(373\) 583045. 0.216985 0.108493 0.994097i \(-0.465398\pi\)
0.108493 + 0.994097i \(0.465398\pi\)
\(374\) −1.72866e6 −0.639045
\(375\) 783686. 0.287782
\(376\) −4.89508e6 −1.78562
\(377\) 35379.9 0.0128205
\(378\) 3.96005e6 1.42551
\(379\) −4.59556e6 −1.64339 −0.821695 0.569928i \(-0.806971\pi\)
−0.821695 + 0.569928i \(0.806971\pi\)
\(380\) −155279. −0.0551637
\(381\) −482321. −0.170225
\(382\) 4.26978e6 1.49709
\(383\) 150837. 0.0525424 0.0262712 0.999655i \(-0.491637\pi\)
0.0262712 + 0.999655i \(0.491637\pi\)
\(384\) −4.36749e6 −1.51149
\(385\) −99412.7 −0.0341814
\(386\) 5.87164e6 2.00581
\(387\) 346548. 0.117621
\(388\) 219335. 0.0739653
\(389\) 3.83980e6 1.28657 0.643286 0.765626i \(-0.277570\pi\)
0.643286 + 0.765626i \(0.277570\pi\)
\(390\) −665430. −0.221534
\(391\) −6.12891e6 −2.02741
\(392\) 2.28125e6 0.749821
\(393\) 3.21771e6 1.05091
\(394\) −9.32078e6 −3.02490
\(395\) −189225. −0.0610218
\(396\) −311219. −0.0997306
\(397\) −3.29694e6 −1.04987 −0.524934 0.851143i \(-0.675910\pi\)
−0.524934 + 0.851143i \(0.675910\pi\)
\(398\) 947354. 0.299781
\(399\) −372307. −0.117076
\(400\) −3.49842e6 −1.09326
\(401\) −806095. −0.250337 −0.125169 0.992135i \(-0.539947\pi\)
−0.125169 + 0.992135i \(0.539947\pi\)
\(402\) 6.74566e6 2.08190
\(403\) 5.15597e6 1.58142
\(404\) −9.66939e6 −2.94744
\(405\) −420426. −0.127366
\(406\) −65239.6 −0.0196425
\(407\) −930365. −0.278399
\(408\) 7.30024e6 2.17114
\(409\) 1.88559e6 0.557363 0.278682 0.960384i \(-0.410103\pi\)
0.278682 + 0.960384i \(0.410103\pi\)
\(410\) −78490.3 −0.0230598
\(411\) 5.55343e6 1.62165
\(412\) −974207. −0.282754
\(413\) −1.52438e6 −0.439763
\(414\) −1.64426e6 −0.471486
\(415\) −660783. −0.188338
\(416\) 439855. 0.124617
\(417\) 60344.2 0.0169940
\(418\) 291511. 0.0816046
\(419\) 1.71269e6 0.476590 0.238295 0.971193i \(-0.423412\pi\)
0.238295 + 0.971193i \(0.423412\pi\)
\(420\) 823429. 0.227773
\(421\) 5.62613e6 1.54705 0.773526 0.633765i \(-0.218491\pi\)
0.773526 + 0.633765i \(0.218491\pi\)
\(422\) 5.40287e6 1.47687
\(423\) −637206. −0.173153
\(424\) −3.16392e6 −0.854695
\(425\) −4.78359e6 −1.28464
\(426\) −1.14689e7 −3.06193
\(427\) −2.28538e6 −0.606581
\(428\) −3.26635e6 −0.861893
\(429\) 838331. 0.219924
\(430\) 717922. 0.187243
\(431\) −2.32510e6 −0.602905 −0.301452 0.953481i \(-0.597471\pi\)
−0.301452 + 0.953481i \(0.597471\pi\)
\(432\) 4.64658e6 1.19791
\(433\) −3.55174e6 −0.910377 −0.455189 0.890395i \(-0.650428\pi\)
−0.455189 + 0.890395i \(0.650428\pi\)
\(434\) −9.50746e6 −2.42293
\(435\) 8462.04 0.00214413
\(436\) 1.32134e6 0.332889
\(437\) 1.03354e6 0.258896
\(438\) −4.63920e6 −1.15547
\(439\) 5.81929e6 1.44115 0.720574 0.693378i \(-0.243878\pi\)
0.720574 + 0.693378i \(0.243878\pi\)
\(440\) −328717. −0.0809452
\(441\) 296957. 0.0727105
\(442\) 8.23102e6 2.00400
\(443\) −5.26135e6 −1.27376 −0.636880 0.770963i \(-0.719775\pi\)
−0.636880 + 0.770963i \(0.719775\pi\)
\(444\) 7.70616e6 1.85516
\(445\) 669472. 0.160263
\(446\) 8.20000e6 1.95198
\(447\) 4.66364e6 1.10397
\(448\) 2.84002e6 0.668539
\(449\) 4.43910e6 1.03915 0.519576 0.854424i \(-0.326090\pi\)
0.519576 + 0.854424i \(0.326090\pi\)
\(450\) −1.28334e6 −0.298751
\(451\) 98884.7 0.0228922
\(452\) −3.86017e6 −0.888711
\(453\) 3.05304e6 0.699016
\(454\) 1.04762e7 2.38541
\(455\) 473352. 0.107190
\(456\) −1.23107e6 −0.277249
\(457\) −540340. −0.121025 −0.0605127 0.998167i \(-0.519274\pi\)
−0.0605127 + 0.998167i \(0.519274\pi\)
\(458\) −3.32356e6 −0.740354
\(459\) 6.35354e6 1.40762
\(460\) −2.28588e6 −0.503684
\(461\) 1.56355e6 0.342657 0.171329 0.985214i \(-0.445194\pi\)
0.171329 + 0.985214i \(0.445194\pi\)
\(462\) −1.54586e6 −0.336949
\(463\) 5.64955e6 1.22479 0.612395 0.790552i \(-0.290206\pi\)
0.612395 + 0.790552i \(0.290206\pi\)
\(464\) −76549.8 −0.0165063
\(465\) 1.23319e6 0.264482
\(466\) 1.03627e7 2.21060
\(467\) 8.59103e6 1.82286 0.911430 0.411456i \(-0.134980\pi\)
0.911430 + 0.411456i \(0.134980\pi\)
\(468\) 1.48187e6 0.312748
\(469\) −4.79852e6 −1.00734
\(470\) −1.32006e6 −0.275644
\(471\) −3.58552e6 −0.744732
\(472\) −5.04051e6 −1.04140
\(473\) −904462. −0.185882
\(474\) −2.94242e6 −0.601533
\(475\) 806676. 0.164046
\(476\) −1.01854e7 −2.06044
\(477\) −411857. −0.0828801
\(478\) 7.04221e6 1.40974
\(479\) −3.22040e6 −0.641315 −0.320658 0.947195i \(-0.603904\pi\)
−0.320658 + 0.947195i \(0.603904\pi\)
\(480\) 105203. 0.0208413
\(481\) 4.42992e6 0.873039
\(482\) 1.37920e7 2.70402
\(483\) −5.48078e6 −1.06899
\(484\) −9.70214e6 −1.88258
\(485\) 30156.7 0.00582143
\(486\) 3.15409e6 0.605737
\(487\) 5.76818e6 1.10209 0.551044 0.834476i \(-0.314230\pi\)
0.551044 + 0.834476i \(0.314230\pi\)
\(488\) −7.55683e6 −1.43645
\(489\) 653719. 0.123629
\(490\) 615187. 0.115749
\(491\) −6.36396e6 −1.19131 −0.595654 0.803241i \(-0.703107\pi\)
−0.595654 + 0.803241i \(0.703107\pi\)
\(492\) −819056. −0.152546
\(493\) −104671. −0.0193959
\(494\) −1.38803e6 −0.255906
\(495\) −42790.1 −0.00784929
\(496\) −1.11557e7 −2.03607
\(497\) 8.15835e6 1.48153
\(498\) −1.02751e7 −1.85658
\(499\) 4.12358e6 0.741349 0.370675 0.928763i \(-0.379126\pi\)
0.370675 + 0.928763i \(0.379126\pi\)
\(500\) −3.61546e6 −0.646753
\(501\) 1.83229e6 0.326138
\(502\) −1.08577e7 −1.92299
\(503\) 4.25725e6 0.750256 0.375128 0.926973i \(-0.377599\pi\)
0.375128 + 0.926973i \(0.377599\pi\)
\(504\) −1.39318e6 −0.244303
\(505\) −1.32946e6 −0.231978
\(506\) 4.29137e6 0.745109
\(507\) 1.26262e6 0.218149
\(508\) 2.22514e6 0.382559
\(509\) 3.04625e6 0.521160 0.260580 0.965452i \(-0.416086\pi\)
0.260580 + 0.965452i \(0.416086\pi\)
\(510\) 1.96866e6 0.335155
\(511\) 3.30009e6 0.559079
\(512\) 1.11210e7 1.87486
\(513\) −1.07142e6 −0.179749
\(514\) −1.57363e7 −2.62721
\(515\) −133945. −0.0222541
\(516\) 7.49160e6 1.23866
\(517\) 1.66306e6 0.273641
\(518\) −8.16865e6 −1.33760
\(519\) 1.14812e6 0.187098
\(520\) 1.56518e6 0.253838
\(521\) −1.05140e7 −1.69696 −0.848480 0.529227i \(-0.822482\pi\)
−0.848480 + 0.529227i \(0.822482\pi\)
\(522\) −28081.0 −0.00451062
\(523\) 1.12338e7 1.79586 0.897932 0.440134i \(-0.145069\pi\)
0.897932 + 0.440134i \(0.145069\pi\)
\(524\) −1.48446e7 −2.36178
\(525\) −4.27773e6 −0.677353
\(526\) 1.47808e7 2.32934
\(527\) −1.52539e7 −2.39251
\(528\) −1.81385e6 −0.283151
\(529\) 8.77856e6 1.36390
\(530\) −853218. −0.131938
\(531\) −656138. −0.100985
\(532\) 1.71760e6 0.263114
\(533\) −470839. −0.0717884
\(534\) 1.04102e7 1.57982
\(535\) −449097. −0.0678352
\(536\) −1.58668e7 −2.38548
\(537\) 4.28796e6 0.641675
\(538\) −4.49732e6 −0.669881
\(539\) −775034. −0.114908
\(540\) 2.36966e6 0.349705
\(541\) 2.97668e6 0.437259 0.218629 0.975808i \(-0.429841\pi\)
0.218629 + 0.975808i \(0.429841\pi\)
\(542\) −8.59665e6 −1.25699
\(543\) 1.55383e6 0.226154
\(544\) −1.30131e6 −0.188531
\(545\) 181674. 0.0262000
\(546\) 7.36058e6 1.05665
\(547\) −5.53177e6 −0.790488 −0.395244 0.918576i \(-0.629340\pi\)
−0.395244 + 0.918576i \(0.629340\pi\)
\(548\) −2.56202e7 −3.64444
\(549\) −983694. −0.139293
\(550\) 3.34940e6 0.472129
\(551\) 17651.1 0.00247681
\(552\) −1.81227e7 −2.53149
\(553\) 2.09309e6 0.291055
\(554\) −4.98911e6 −0.690635
\(555\) 1.05953e6 0.146010
\(556\) −278392. −0.0381918
\(557\) −1.09629e7 −1.49723 −0.748613 0.663007i \(-0.769280\pi\)
−0.748613 + 0.663007i \(0.769280\pi\)
\(558\) −4.09229e6 −0.556392
\(559\) 4.30659e6 0.582913
\(560\) −1.02417e6 −0.138007
\(561\) −2.48019e6 −0.332719
\(562\) −9.04628e6 −1.20817
\(563\) −2.26278e6 −0.300865 −0.150433 0.988620i \(-0.548067\pi\)
−0.150433 + 0.988620i \(0.548067\pi\)
\(564\) −1.37750e7 −1.82345
\(565\) −530742. −0.0699459
\(566\) −961227. −0.126120
\(567\) 4.65050e6 0.607494
\(568\) 2.69764e7 3.50843
\(569\) −286044. −0.0370385 −0.0185192 0.999829i \(-0.505895\pi\)
−0.0185192 + 0.999829i \(0.505895\pi\)
\(570\) −331984. −0.0427986
\(571\) −5.52774e6 −0.709508 −0.354754 0.934960i \(-0.615435\pi\)
−0.354754 + 0.934960i \(0.615435\pi\)
\(572\) −3.86755e6 −0.494250
\(573\) 6.12604e6 0.779459
\(574\) 868213. 0.109988
\(575\) 1.18752e7 1.49786
\(576\) 1.22243e6 0.153521
\(577\) −334668. −0.0418480 −0.0209240 0.999781i \(-0.506661\pi\)
−0.0209240 + 0.999781i \(0.506661\pi\)
\(578\) −1.03468e7 −1.28821
\(579\) 8.42429e6 1.04433
\(580\) −39038.8 −0.00481866
\(581\) 7.30919e6 0.898316
\(582\) 468934. 0.0573858
\(583\) 1.07491e6 0.130979
\(584\) 1.09120e7 1.32396
\(585\) 203745. 0.0246148
\(586\) −1.01966e7 −1.22662
\(587\) 1.56616e7 1.87604 0.938020 0.346582i \(-0.112658\pi\)
0.938020 + 0.346582i \(0.112658\pi\)
\(588\) 6.41956e6 0.765705
\(589\) 2.57232e6 0.305518
\(590\) −1.35928e6 −0.160760
\(591\) −1.33729e7 −1.57492
\(592\) −9.58481e6 −1.12403
\(593\) 7.06151e6 0.824634 0.412317 0.911040i \(-0.364720\pi\)
0.412317 + 0.911040i \(0.364720\pi\)
\(594\) −4.44866e6 −0.517324
\(595\) −1.40041e6 −0.162167
\(596\) −2.15152e7 −2.48102
\(597\) 1.35921e6 0.156081
\(598\) −2.04333e7 −2.33661
\(599\) 4.87247e6 0.554858 0.277429 0.960746i \(-0.410518\pi\)
0.277429 + 0.960746i \(0.410518\pi\)
\(600\) −1.41447e7 −1.60404
\(601\) 1.08737e6 0.122798 0.0613990 0.998113i \(-0.480444\pi\)
0.0613990 + 0.998113i \(0.480444\pi\)
\(602\) −7.94122e6 −0.893092
\(603\) −2.06542e6 −0.231321
\(604\) −1.40849e7 −1.57095
\(605\) −1.33396e6 −0.148168
\(606\) −2.06730e7 −2.28677
\(607\) −1.18003e6 −0.129993 −0.0649966 0.997885i \(-0.520704\pi\)
−0.0649966 + 0.997885i \(0.520704\pi\)
\(608\) 219444. 0.0240749
\(609\) −93602.0 −0.0102269
\(610\) −2.03786e6 −0.221743
\(611\) −7.91862e6 −0.858117
\(612\) −4.38409e6 −0.473152
\(613\) −1.06660e7 −1.14643 −0.573217 0.819404i \(-0.694305\pi\)
−0.573217 + 0.819404i \(0.694305\pi\)
\(614\) −7.09094e6 −0.759072
\(615\) −112613. −0.0120061
\(616\) 3.63608e6 0.386083
\(617\) −1.26485e7 −1.33760 −0.668799 0.743443i \(-0.733191\pi\)
−0.668799 + 0.743443i \(0.733191\pi\)
\(618\) −2.08284e6 −0.219374
\(619\) 1.18606e7 1.24417 0.622083 0.782951i \(-0.286286\pi\)
0.622083 + 0.782951i \(0.286286\pi\)
\(620\) −5.68918e6 −0.594389
\(621\) −1.57725e7 −1.64124
\(622\) 8.66325e6 0.897853
\(623\) −7.40530e6 −0.764403
\(624\) 8.63665e6 0.887940
\(625\) 9.01674e6 0.923314
\(626\) −1.24542e7 −1.27023
\(627\) 418244. 0.0424875
\(628\) 1.65414e7 1.67369
\(629\) −1.31059e7 −1.32081
\(630\) −375699. −0.0377128
\(631\) 9.66478e6 0.966314 0.483157 0.875534i \(-0.339490\pi\)
0.483157 + 0.875534i \(0.339490\pi\)
\(632\) 6.92100e6 0.689249
\(633\) 7.75173e6 0.768934
\(634\) −2.16296e7 −2.13710
\(635\) 305938. 0.0301092
\(636\) −8.90344e6 −0.872800
\(637\) 3.69032e6 0.360342
\(638\) 73289.1 0.00712833
\(639\) 3.51159e6 0.340214
\(640\) 2.77032e6 0.267350
\(641\) −8.00413e6 −0.769430 −0.384715 0.923035i \(-0.625700\pi\)
−0.384715 + 0.923035i \(0.625700\pi\)
\(642\) −6.98341e6 −0.668697
\(643\) −5.13318e6 −0.489619 −0.244810 0.969571i \(-0.578725\pi\)
−0.244810 + 0.969571i \(0.578725\pi\)
\(644\) 2.52850e7 2.40242
\(645\) 1.03003e6 0.0974883
\(646\) 4.10646e6 0.387157
\(647\) 1.08589e7 1.01982 0.509910 0.860228i \(-0.329679\pi\)
0.509910 + 0.860228i \(0.329679\pi\)
\(648\) 1.53773e7 1.43861
\(649\) 1.71247e6 0.159592
\(650\) −1.59481e7 −1.48056
\(651\) −1.36408e7 −1.26150
\(652\) −3.01587e6 −0.277839
\(653\) −8.01399e6 −0.735472 −0.367736 0.929930i \(-0.619867\pi\)
−0.367736 + 0.929930i \(0.619867\pi\)
\(654\) 2.82501e6 0.258271
\(655\) −2.04101e6 −0.185884
\(656\) 1.01873e6 0.0924272
\(657\) 1.42045e6 0.128385
\(658\) 1.46017e7 1.31474
\(659\) −1.11015e7 −0.995792 −0.497896 0.867237i \(-0.665894\pi\)
−0.497896 + 0.867237i \(0.665894\pi\)
\(660\) −925028. −0.0826599
\(661\) −134707. −0.0119918 −0.00599592 0.999982i \(-0.501909\pi\)
−0.00599592 + 0.999982i \(0.501909\pi\)
\(662\) 2.64168e7 2.34280
\(663\) 1.18094e7 1.04338
\(664\) 2.41685e7 2.12731
\(665\) 236156. 0.0207083
\(666\) −3.51603e6 −0.307161
\(667\) 259844. 0.0226151
\(668\) −8.45311e6 −0.732951
\(669\) 1.17649e7 1.01630
\(670\) −4.27880e6 −0.368244
\(671\) 2.56736e6 0.220131
\(672\) −1.16369e6 −0.0994066
\(673\) 1.43311e7 1.21967 0.609834 0.792529i \(-0.291236\pi\)
0.609834 + 0.792529i \(0.291236\pi\)
\(674\) 5.89348e6 0.499715
\(675\) −1.23104e7 −1.03995
\(676\) −5.82497e6 −0.490260
\(677\) 9.12082e6 0.764825 0.382413 0.923992i \(-0.375093\pi\)
0.382413 + 0.923992i \(0.375093\pi\)
\(678\) −8.25299e6 −0.689504
\(679\) −333576. −0.0277664
\(680\) −4.63058e6 −0.384028
\(681\) 1.50306e7 1.24196
\(682\) 1.06805e7 0.879290
\(683\) 7.63895e6 0.626587 0.313294 0.949656i \(-0.398568\pi\)
0.313294 + 0.949656i \(0.398568\pi\)
\(684\) 739306. 0.0604204
\(685\) −3.52257e6 −0.286835
\(686\) −2.32646e7 −1.88749
\(687\) −4.76845e6 −0.385466
\(688\) −9.31795e6 −0.750498
\(689\) −5.11819e6 −0.410741
\(690\) −4.88717e6 −0.390782
\(691\) 2.36484e7 1.88411 0.942056 0.335455i \(-0.108890\pi\)
0.942056 + 0.335455i \(0.108890\pi\)
\(692\) −5.29673e6 −0.420477
\(693\) 473318. 0.0374387
\(694\) −3.42858e7 −2.70219
\(695\) −38276.6 −0.00300588
\(696\) −309504. −0.0242183
\(697\) 1.39297e6 0.108608
\(698\) 2.80934e7 2.18256
\(699\) 1.48679e7 1.15095
\(700\) 1.97349e7 1.52226
\(701\) −2.04164e7 −1.56922 −0.784609 0.619991i \(-0.787136\pi\)
−0.784609 + 0.619991i \(0.787136\pi\)
\(702\) 2.11822e7 1.62229
\(703\) 2.21009e6 0.168664
\(704\) −3.19044e6 −0.242616
\(705\) −1.89395e6 −0.143514
\(706\) 2.70642e7 2.04354
\(707\) 1.47057e7 1.10646
\(708\) −1.41843e7 −1.06347
\(709\) 1.44443e7 1.07915 0.539575 0.841938i \(-0.318585\pi\)
0.539575 + 0.841938i \(0.318585\pi\)
\(710\) 7.27474e6 0.541592
\(711\) 900927. 0.0668368
\(712\) −2.44863e7 −1.81019
\(713\) 3.78674e7 2.78960
\(714\) −2.17762e7 −1.59859
\(715\) −531757. −0.0388999
\(716\) −1.97821e7 −1.44208
\(717\) 1.01038e7 0.733982
\(718\) 2.92666e7 2.11866
\(719\) −2.54689e7 −1.83733 −0.918667 0.395032i \(-0.870733\pi\)
−0.918667 + 0.395032i \(0.870733\pi\)
\(720\) −440832. −0.0316914
\(721\) 1.48162e6 0.106145
\(722\) 2.37302e7 1.69418
\(723\) 1.97880e7 1.40785
\(724\) −7.16845e6 −0.508251
\(725\) 202807. 0.0143297
\(726\) −2.07430e7 −1.46060
\(727\) −3.13310e6 −0.219856 −0.109928 0.993940i \(-0.535062\pi\)
−0.109928 + 0.993940i \(0.535062\pi\)
\(728\) −1.73131e7 −1.21073
\(729\) 1.59068e7 1.10857
\(730\) 2.94266e6 0.204378
\(731\) −1.27410e7 −0.881880
\(732\) −2.12653e7 −1.46688
\(733\) 7.30024e6 0.501854 0.250927 0.968006i \(-0.419265\pi\)
0.250927 + 0.968006i \(0.419265\pi\)
\(734\) −1.21435e7 −0.831965
\(735\) 882636. 0.0602648
\(736\) 3.23047e6 0.219822
\(737\) 5.39058e6 0.365567
\(738\) 373704. 0.0252573
\(739\) −2.06051e6 −0.138792 −0.0693958 0.997589i \(-0.522107\pi\)
−0.0693958 + 0.997589i \(0.522107\pi\)
\(740\) −4.88805e6 −0.328138
\(741\) −1.99146e6 −0.133238
\(742\) 9.43779e6 0.629304
\(743\) −8.21654e6 −0.546031 −0.273015 0.962010i \(-0.588021\pi\)
−0.273015 + 0.962010i \(0.588021\pi\)
\(744\) −4.51045e7 −2.98736
\(745\) −2.95817e6 −0.195269
\(746\) −5.75079e6 −0.378339
\(747\) 3.14609e6 0.206286
\(748\) 1.14421e7 0.747743
\(749\) 4.96764e6 0.323553
\(750\) −7.72979e6 −0.501781
\(751\) −2.81267e7 −1.81978 −0.909889 0.414852i \(-0.863833\pi\)
−0.909889 + 0.414852i \(0.863833\pi\)
\(752\) 1.71331e7 1.10482
\(753\) −1.55780e7 −1.00121
\(754\) −348965. −0.0223539
\(755\) −1.93656e6 −0.123641
\(756\) −2.62117e7 −1.66798
\(757\) 2.57239e6 0.163154 0.0815770 0.996667i \(-0.474004\pi\)
0.0815770 + 0.996667i \(0.474004\pi\)
\(758\) 4.53277e7 2.86544
\(759\) 6.15702e6 0.387941
\(760\) 780872. 0.0490395
\(761\) 1.65869e7 1.03825 0.519127 0.854697i \(-0.326257\pi\)
0.519127 + 0.854697i \(0.326257\pi\)
\(762\) 4.75731e6 0.296807
\(763\) −2.00956e6 −0.124966
\(764\) −2.82619e7 −1.75173
\(765\) −602776. −0.0372394
\(766\) −1.48776e6 −0.0916136
\(767\) −8.15389e6 −0.500468
\(768\) 3.01254e7 1.84302
\(769\) −2.57160e7 −1.56815 −0.784075 0.620666i \(-0.786862\pi\)
−0.784075 + 0.620666i \(0.786862\pi\)
\(770\) 980544. 0.0595992
\(771\) −2.25776e7 −1.36786
\(772\) −3.88646e7 −2.34699
\(773\) 5.61581e6 0.338036 0.169018 0.985613i \(-0.445940\pi\)
0.169018 + 0.985613i \(0.445940\pi\)
\(774\) −3.41813e6 −0.205086
\(775\) 2.95554e7 1.76759
\(776\) −1.10300e6 −0.0657538
\(777\) −1.17199e7 −0.696422
\(778\) −3.78734e7 −2.24329
\(779\) −234902. −0.0138689
\(780\) 4.40451e6 0.259216
\(781\) −9.16497e6 −0.537655
\(782\) 6.04517e7 3.53502
\(783\) −269367. −0.0157015
\(784\) −7.98455e6 −0.463939
\(785\) 2.27431e6 0.131727
\(786\) −3.17375e7 −1.83238
\(787\) 3.01795e7 1.73690 0.868451 0.495775i \(-0.165116\pi\)
0.868451 + 0.495775i \(0.165116\pi\)
\(788\) 6.16946e7 3.53942
\(789\) 2.12066e7 1.21277
\(790\) 1.86639e6 0.106399
\(791\) 5.87075e6 0.333620
\(792\) 1.56507e6 0.0886587
\(793\) −1.22245e7 −0.690314
\(794\) 3.25189e7 1.83056
\(795\) −1.22415e6 −0.0686936
\(796\) −6.27058e6 −0.350772
\(797\) −4.92765e6 −0.274785 −0.137393 0.990517i \(-0.543872\pi\)
−0.137393 + 0.990517i \(0.543872\pi\)
\(798\) 3.67220e6 0.204136
\(799\) 2.34272e7 1.29823
\(800\) 2.52137e6 0.139287
\(801\) −3.18746e6 −0.175535
\(802\) 7.95082e6 0.436492
\(803\) −3.70727e6 −0.202892
\(804\) −4.46499e7 −2.43601
\(805\) 3.47648e6 0.189082
\(806\) −5.08553e7 −2.75739
\(807\) −6.45250e6 −0.348774
\(808\) 4.86258e7 2.62022
\(809\) 2.11048e7 1.13373 0.566864 0.823811i \(-0.308156\pi\)
0.566864 + 0.823811i \(0.308156\pi\)
\(810\) 4.14682e6 0.222076
\(811\) −1.10101e7 −0.587814 −0.293907 0.955834i \(-0.594956\pi\)
−0.293907 + 0.955834i \(0.594956\pi\)
\(812\) 431824. 0.0229835
\(813\) −1.23340e7 −0.654451
\(814\) 9.17654e6 0.485420
\(815\) −414657. −0.0218673
\(816\) −2.55514e7 −1.34335
\(817\) 2.14856e6 0.112614
\(818\) −1.85983e7 −0.971827
\(819\) −2.25370e6 −0.117405
\(820\) 519531. 0.0269822
\(821\) 2.92979e7 1.51698 0.758488 0.651687i \(-0.225938\pi\)
0.758488 + 0.651687i \(0.225938\pi\)
\(822\) −5.47755e7 −2.82753
\(823\) −3.59573e7 −1.85050 −0.925248 0.379364i \(-0.876143\pi\)
−0.925248 + 0.379364i \(0.876143\pi\)
\(824\) 4.89913e6 0.251363
\(825\) 4.80553e6 0.245814
\(826\) 1.50355e7 0.766777
\(827\) −2.08172e7 −1.05842 −0.529211 0.848490i \(-0.677512\pi\)
−0.529211 + 0.848490i \(0.677512\pi\)
\(828\) 1.08834e7 0.551682
\(829\) 1.14738e6 0.0579857 0.0289929 0.999580i \(-0.490770\pi\)
0.0289929 + 0.999580i \(0.490770\pi\)
\(830\) 6.51755e6 0.328390
\(831\) −7.15809e6 −0.359579
\(832\) 1.51912e7 0.760825
\(833\) −1.09178e7 −0.545156
\(834\) −595197. −0.0296310
\(835\) −1.16223e6 −0.0576869
\(836\) −1.92953e6 −0.0954850
\(837\) −3.92553e7 −1.93680
\(838\) −1.68929e7 −0.830989
\(839\) −3.34395e7 −1.64004 −0.820021 0.572333i \(-0.806038\pi\)
−0.820021 + 0.572333i \(0.806038\pi\)
\(840\) −4.14089e6 −0.202486
\(841\) −2.05067e7 −0.999784
\(842\) −5.54927e7 −2.69746
\(843\) −1.29791e7 −0.629036
\(844\) −3.57618e7 −1.72808
\(845\) −800885. −0.0385859
\(846\) 6.28500e6 0.301911
\(847\) 1.47555e7 0.706718
\(848\) 1.10740e7 0.528827
\(849\) −1.37911e6 −0.0656645
\(850\) 4.71824e7 2.23992
\(851\) 3.25351e7 1.54003
\(852\) 7.59129e7 3.58275
\(853\) 2.30119e7 1.08288 0.541441 0.840739i \(-0.317879\pi\)
0.541441 + 0.840739i \(0.317879\pi\)
\(854\) 2.25416e7 1.05764
\(855\) 101648. 0.00475538
\(856\) 1.64260e7 0.766207
\(857\) 1.97851e7 0.920207 0.460103 0.887865i \(-0.347812\pi\)
0.460103 + 0.887865i \(0.347812\pi\)
\(858\) −8.26877e6 −0.383462
\(859\) 3.01949e7 1.39621 0.698104 0.715997i \(-0.254027\pi\)
0.698104 + 0.715997i \(0.254027\pi\)
\(860\) −4.75196e6 −0.219092
\(861\) 1.24566e6 0.0572654
\(862\) 2.29333e7 1.05123
\(863\) −3.53884e7 −1.61746 −0.808731 0.588178i \(-0.799845\pi\)
−0.808731 + 0.588178i \(0.799845\pi\)
\(864\) −3.34887e6 −0.152621
\(865\) −728257. −0.0330936
\(866\) 3.50321e7 1.58735
\(867\) −1.48450e7 −0.670705
\(868\) 6.29303e7 2.83505
\(869\) −2.35135e6 −0.105625
\(870\) −83464.3 −0.00373854
\(871\) −2.56672e7 −1.14639
\(872\) −6.64482e6 −0.295932
\(873\) −143581. −0.00637618
\(874\) −1.01942e7 −0.451414
\(875\) 5.49858e6 0.242790
\(876\) 3.07071e7 1.35200
\(877\) −1.51182e7 −0.663745 −0.331872 0.943324i \(-0.607680\pi\)
−0.331872 + 0.943324i \(0.607680\pi\)
\(878\) −5.73978e7 −2.51281
\(879\) −1.46295e7 −0.638640
\(880\) 1.15054e6 0.0500834
\(881\) 2.69041e7 1.16783 0.583913 0.811816i \(-0.301521\pi\)
0.583913 + 0.811816i \(0.301521\pi\)
\(882\) −2.92900e6 −0.126779
\(883\) 2.44399e6 0.105487 0.0527434 0.998608i \(-0.483203\pi\)
0.0527434 + 0.998608i \(0.483203\pi\)
\(884\) −5.44815e7 −2.34487
\(885\) −1.95022e6 −0.0836999
\(886\) 5.18946e7 2.22095
\(887\) −1.21459e6 −0.0518347 −0.0259174 0.999664i \(-0.508251\pi\)
−0.0259174 + 0.999664i \(0.508251\pi\)
\(888\) −3.87530e7 −1.64920
\(889\) −3.38411e6 −0.143612
\(890\) −6.60325e6 −0.279436
\(891\) −5.22430e6 −0.220462
\(892\) −5.42762e7 −2.28400
\(893\) −3.95061e6 −0.165781
\(894\) −4.59992e7 −1.92489
\(895\) −2.71987e6 −0.113499
\(896\) −3.06436e7 −1.27518
\(897\) −2.93166e7 −1.21656
\(898\) −4.37845e7 −1.81188
\(899\) 646709. 0.0266876
\(900\) 8.49446e6 0.349566
\(901\) 1.51421e7 0.621404
\(902\) −975337. −0.0399152
\(903\) −1.13936e7 −0.464989
\(904\) 1.94122e7 0.790048
\(905\) −985602. −0.0400019
\(906\) −3.01133e7 −1.21882
\(907\) −1.06834e7 −0.431212 −0.215606 0.976480i \(-0.569173\pi\)
−0.215606 + 0.976480i \(0.569173\pi\)
\(908\) −6.93422e7 −2.79115
\(909\) 6.32976e6 0.254084
\(910\) −4.66885e6 −0.186899
\(911\) 1.24982e7 0.498944 0.249472 0.968382i \(-0.419743\pi\)
0.249472 + 0.968382i \(0.419743\pi\)
\(912\) 4.30883e6 0.171543
\(913\) −8.21103e6 −0.326002
\(914\) 5.32957e6 0.211022
\(915\) −2.92380e6 −0.115450
\(916\) 2.19988e7 0.866283
\(917\) 2.25764e7 0.886608
\(918\) −6.26674e7 −2.45434
\(919\) −1.94664e7 −0.760322 −0.380161 0.924920i \(-0.624131\pi\)
−0.380161 + 0.924920i \(0.624131\pi\)
\(920\) 1.14953e7 0.447766
\(921\) −1.01737e7 −0.395211
\(922\) −1.54219e7 −0.597462
\(923\) 4.36389e7 1.68605
\(924\) 1.02321e7 0.394262
\(925\) 2.53935e7 0.975817
\(926\) −5.57236e7 −2.13556
\(927\) 637734. 0.0243748
\(928\) 55170.7 0.00210300
\(929\) 2.43227e7 0.924638 0.462319 0.886714i \(-0.347017\pi\)
0.462319 + 0.886714i \(0.347017\pi\)
\(930\) −1.21634e7 −0.461155
\(931\) 1.84110e6 0.0696152
\(932\) −6.85914e7 −2.58661
\(933\) 1.24295e7 0.467467
\(934\) −8.47366e7 −3.17836
\(935\) 1.57320e6 0.0588510
\(936\) −7.45208e6 −0.278027
\(937\) 1.22842e7 0.457088 0.228544 0.973534i \(-0.426604\pi\)
0.228544 + 0.973534i \(0.426604\pi\)
\(938\) 4.73296e7 1.75641
\(939\) −1.78686e7 −0.661344
\(940\) 8.73754e6 0.322530
\(941\) −9.16247e6 −0.337317 −0.168659 0.985675i \(-0.553944\pi\)
−0.168659 + 0.985675i \(0.553944\pi\)
\(942\) 3.53653e7 1.29852
\(943\) −3.45802e6 −0.126633
\(944\) 1.76422e7 0.644350
\(945\) −3.60390e6 −0.131278
\(946\) 8.92105e6 0.324107
\(947\) 1.96327e7 0.711386 0.355693 0.934603i \(-0.384245\pi\)
0.355693 + 0.934603i \(0.384245\pi\)
\(948\) 1.94760e7 0.703850
\(949\) 1.76521e7 0.636255
\(950\) −7.95655e6 −0.286033
\(951\) −3.10330e7 −1.11268
\(952\) 5.12207e7 1.83169
\(953\) 2.96559e7 1.05774 0.528870 0.848703i \(-0.322616\pi\)
0.528870 + 0.848703i \(0.322616\pi\)
\(954\) 4.06230e6 0.144511
\(955\) −3.88578e6 −0.137870
\(956\) −4.66127e7 −1.64953
\(957\) 105151. 0.00371137
\(958\) 3.17640e7 1.11821
\(959\) 3.89645e7 1.36812
\(960\) 3.63339e6 0.127243
\(961\) 6.56167e7 2.29196
\(962\) −4.36940e7 −1.52224
\(963\) 2.13821e6 0.0742995
\(964\) −9.12899e7 −3.16395
\(965\) −5.34357e6 −0.184720
\(966\) 5.40589e7 1.86391
\(967\) 1.72509e7 0.593260 0.296630 0.954992i \(-0.404137\pi\)
0.296630 + 0.954992i \(0.404137\pi\)
\(968\) 4.87905e7 1.67358
\(969\) 5.89172e6 0.201573
\(970\) −297447. −0.0101503
\(971\) −120921. −0.00411578 −0.00205789 0.999998i \(-0.500655\pi\)
−0.00205789 + 0.999998i \(0.500655\pi\)
\(972\) −2.08771e7 −0.708769
\(973\) 423393. 0.0143371
\(974\) −5.68937e7 −1.92162
\(975\) −2.28815e7 −0.770855
\(976\) 2.64495e7 0.888776
\(977\) −9.07671e6 −0.304223 −0.152112 0.988363i \(-0.548607\pi\)
−0.152112 + 0.988363i \(0.548607\pi\)
\(978\) −6.44788e6 −0.215561
\(979\) 8.31900e6 0.277405
\(980\) −4.07195e6 −0.135437
\(981\) −864975. −0.0286966
\(982\) 6.27701e7 2.07718
\(983\) 966289. 0.0318950
\(984\) 4.11890e6 0.135611
\(985\) 8.48251e6 0.278570
\(986\) 1.03241e6 0.0338189
\(987\) 2.09497e7 0.684519
\(988\) 9.18742e6 0.299434
\(989\) 3.16292e7 1.02825
\(990\) 422055. 0.0136861
\(991\) 1.11150e7 0.359523 0.179761 0.983710i \(-0.442467\pi\)
0.179761 + 0.983710i \(0.442467\pi\)
\(992\) 8.04011e6 0.259408
\(993\) 3.79014e7 1.21978
\(994\) −8.04689e7 −2.58322
\(995\) −862153. −0.0276075
\(996\) 6.80115e7 2.17237
\(997\) −2.67032e7 −0.850794 −0.425397 0.905007i \(-0.639866\pi\)
−0.425397 + 0.905007i \(0.639866\pi\)
\(998\) −4.06724e7 −1.29263
\(999\) −3.37275e7 −1.06923
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.1.16 218
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
983.6.a.b.1.16 218 1.1 even 1 trivial