Properties

Label 983.6.a.b.1.4
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 1.4
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)
 
\(f(q)\) \(=\) \(q-11.0108 q^{2} -2.28470 q^{3} +89.2387 q^{4} +53.2861 q^{5} +25.1565 q^{6} -155.822 q^{7} -630.246 q^{8} -237.780 q^{9} +O(q^{10})\) \(q-11.0108 q^{2} -2.28470 q^{3} +89.2387 q^{4} +53.2861 q^{5} +25.1565 q^{6} -155.822 q^{7} -630.246 q^{8} -237.780 q^{9} -586.724 q^{10} +217.525 q^{11} -203.883 q^{12} +243.228 q^{13} +1715.74 q^{14} -121.743 q^{15} +4083.90 q^{16} +2084.02 q^{17} +2618.16 q^{18} +1306.56 q^{19} +4755.18 q^{20} +356.007 q^{21} -2395.13 q^{22} +3740.51 q^{23} +1439.92 q^{24} -285.596 q^{25} -2678.15 q^{26} +1098.44 q^{27} -13905.4 q^{28} +7864.58 q^{29} +1340.49 q^{30} +983.718 q^{31} -24799.4 q^{32} -496.979 q^{33} -22946.8 q^{34} -8303.16 q^{35} -21219.2 q^{36} +14182.4 q^{37} -14386.3 q^{38} -555.703 q^{39} -33583.3 q^{40} -167.212 q^{41} -3919.94 q^{42} -5446.52 q^{43} +19411.6 q^{44} -12670.4 q^{45} -41186.2 q^{46} +6004.24 q^{47} -9330.49 q^{48} +7473.61 q^{49} +3144.65 q^{50} -4761.36 q^{51} +21705.4 q^{52} -8231.84 q^{53} -12094.7 q^{54} +11591.1 q^{55} +98206.4 q^{56} -2985.10 q^{57} -86595.6 q^{58} +42969.0 q^{59} -10864.1 q^{60} -16381.0 q^{61} -10831.6 q^{62} +37051.5 q^{63} +142377. q^{64} +12960.7 q^{65} +5472.16 q^{66} -48469.1 q^{67} +185975. q^{68} -8545.94 q^{69} +91424.8 q^{70} -57809.5 q^{71} +149860. q^{72} +67650.1 q^{73} -156160. q^{74} +652.500 q^{75} +116596. q^{76} -33895.3 q^{77} +6118.76 q^{78} -71461.7 q^{79} +217615. q^{80} +55271.0 q^{81} +1841.15 q^{82} -53097.9 q^{83} +31769.6 q^{84} +111049. q^{85} +59970.8 q^{86} -17968.2 q^{87} -137094. q^{88} -36484.4 q^{89} +139511. q^{90} -37900.4 q^{91} +333798. q^{92} -2247.50 q^{93} -66111.8 q^{94} +69621.5 q^{95} +56659.0 q^{96} +76922.5 q^{97} -82290.7 q^{98} -51723.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 218 q + 35 q^{2} + 70 q^{3} + 3685 q^{4} + 253 q^{5} + 529 q^{6} + 1567 q^{7} + 1695 q^{8} + 19812 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.0108 −1.94646 −0.973230 0.229832i \(-0.926182\pi\)
−0.973230 + 0.229832i \(0.926182\pi\)
\(3\) −2.28470 −0.146563 −0.0732817 0.997311i \(-0.523347\pi\)
−0.0732817 + 0.997311i \(0.523347\pi\)
\(4\) 89.2387 2.78871
\(5\) 53.2861 0.953210 0.476605 0.879118i \(-0.341867\pi\)
0.476605 + 0.879118i \(0.341867\pi\)
\(6\) 25.1565 0.285280
\(7\) −155.822 −1.20195 −0.600973 0.799270i \(-0.705220\pi\)
−0.600973 + 0.799270i \(0.705220\pi\)
\(8\) −630.246 −3.48165
\(9\) −237.780 −0.978519
\(10\) −586.724 −1.85539
\(11\) 217.525 0.542035 0.271018 0.962574i \(-0.412640\pi\)
0.271018 + 0.962574i \(0.412640\pi\)
\(12\) −203.883 −0.408723
\(13\) 243.228 0.399168 0.199584 0.979881i \(-0.436041\pi\)
0.199584 + 0.979881i \(0.436041\pi\)
\(14\) 1715.74 2.33954
\(15\) −121.743 −0.139706
\(16\) 4083.90 3.98819
\(17\) 2084.02 1.74896 0.874479 0.485063i \(-0.161203\pi\)
0.874479 + 0.485063i \(0.161203\pi\)
\(18\) 2618.16 1.90465
\(19\) 1306.56 0.830321 0.415160 0.909748i \(-0.363726\pi\)
0.415160 + 0.909748i \(0.363726\pi\)
\(20\) 4755.18 2.65823
\(21\) 356.007 0.176161
\(22\) −2395.13 −1.05505
\(23\) 3740.51 1.47439 0.737194 0.675681i \(-0.236151\pi\)
0.737194 + 0.675681i \(0.236151\pi\)
\(24\) 1439.92 0.510283
\(25\) −285.596 −0.0913906
\(26\) −2678.15 −0.776965
\(27\) 1098.44 0.289979
\(28\) −13905.4 −3.35187
\(29\) 7864.58 1.73652 0.868261 0.496107i \(-0.165238\pi\)
0.868261 + 0.496107i \(0.165238\pi\)
\(30\) 1340.49 0.271932
\(31\) 983.718 0.183851 0.0919256 0.995766i \(-0.470698\pi\)
0.0919256 + 0.995766i \(0.470698\pi\)
\(32\) −24799.4 −4.28120
\(33\) −496.979 −0.0794426
\(34\) −22946.8 −3.40428
\(35\) −8303.16 −1.14571
\(36\) −21219.2 −2.72880
\(37\) 14182.4 1.70312 0.851561 0.524256i \(-0.175656\pi\)
0.851561 + 0.524256i \(0.175656\pi\)
\(38\) −14386.3 −1.61619
\(39\) −555.703 −0.0585034
\(40\) −33583.3 −3.31874
\(41\) −167.212 −0.0155349 −0.00776745 0.999970i \(-0.502472\pi\)
−0.00776745 + 0.999970i \(0.502472\pi\)
\(42\) −3919.94 −0.342891
\(43\) −5446.52 −0.449209 −0.224604 0.974450i \(-0.572109\pi\)
−0.224604 + 0.974450i \(0.572109\pi\)
\(44\) 19411.6 1.51158
\(45\) −12670.4 −0.932734
\(46\) −41186.2 −2.86984
\(47\) 6004.24 0.396473 0.198236 0.980154i \(-0.436479\pi\)
0.198236 + 0.980154i \(0.436479\pi\)
\(48\) −9330.49 −0.584523
\(49\) 7473.61 0.444672
\(50\) 3144.65 0.177888
\(51\) −4761.36 −0.256333
\(52\) 21705.4 1.11316
\(53\) −8231.84 −0.402538 −0.201269 0.979536i \(-0.564507\pi\)
−0.201269 + 0.979536i \(0.564507\pi\)
\(54\) −12094.7 −0.564432
\(55\) 11591.1 0.516674
\(56\) 98206.4 4.18475
\(57\) −2985.10 −0.121695
\(58\) −86595.6 −3.38007
\(59\) 42969.0 1.60704 0.803518 0.595281i \(-0.202959\pi\)
0.803518 + 0.595281i \(0.202959\pi\)
\(60\) −10864.1 −0.389599
\(61\) −16381.0 −0.563658 −0.281829 0.959465i \(-0.590941\pi\)
−0.281829 + 0.959465i \(0.590941\pi\)
\(62\) −10831.6 −0.357859
\(63\) 37051.5 1.17613
\(64\) 142377. 4.34500
\(65\) 12960.7 0.380491
\(66\) 5472.16 0.154632
\(67\) −48469.1 −1.31910 −0.659550 0.751661i \(-0.729253\pi\)
−0.659550 + 0.751661i \(0.729253\pi\)
\(68\) 185975. 4.87733
\(69\) −8545.94 −0.216091
\(70\) 91424.8 2.23007
\(71\) −57809.5 −1.36099 −0.680493 0.732755i \(-0.738234\pi\)
−0.680493 + 0.732755i \(0.738234\pi\)
\(72\) 149860. 3.40686
\(73\) 67650.1 1.48580 0.742902 0.669400i \(-0.233449\pi\)
0.742902 + 0.669400i \(0.233449\pi\)
\(74\) −156160. −3.31506
\(75\) 652.500 0.0133945
\(76\) 116596. 2.31552
\(77\) −33895.3 −0.651497
\(78\) 6118.76 0.113875
\(79\) −71461.7 −1.28827 −0.644133 0.764913i \(-0.722782\pi\)
−0.644133 + 0.764913i \(0.722782\pi\)
\(80\) 217615. 3.80158
\(81\) 55271.0 0.936019
\(82\) 1841.15 0.0302381
\(83\) −53097.9 −0.846024 −0.423012 0.906124i \(-0.639027\pi\)
−0.423012 + 0.906124i \(0.639027\pi\)
\(84\) 31769.6 0.491262
\(85\) 111049. 1.66712
\(86\) 59970.8 0.874367
\(87\) −17968.2 −0.254511
\(88\) −137094. −1.88718
\(89\) −36484.4 −0.488239 −0.244119 0.969745i \(-0.578499\pi\)
−0.244119 + 0.969745i \(0.578499\pi\)
\(90\) 139511. 1.81553
\(91\) −37900.4 −0.479778
\(92\) 333798. 4.11164
\(93\) −2247.50 −0.0269459
\(94\) −66111.8 −0.771719
\(95\) 69621.5 0.791470
\(96\) 56659.0 0.627467
\(97\) 76922.5 0.830088 0.415044 0.909801i \(-0.363766\pi\)
0.415044 + 0.909801i \(0.363766\pi\)
\(98\) −82290.7 −0.865537
\(99\) −51723.1 −0.530392
\(100\) −25486.2 −0.254862
\(101\) −71112.7 −0.693655 −0.346828 0.937929i \(-0.612741\pi\)
−0.346828 + 0.937929i \(0.612741\pi\)
\(102\) 52426.5 0.498943
\(103\) −14390.0 −0.133650 −0.0668249 0.997765i \(-0.521287\pi\)
−0.0668249 + 0.997765i \(0.521287\pi\)
\(104\) −153294. −1.38976
\(105\) 18970.2 0.167919
\(106\) 90639.5 0.783525
\(107\) 189423. 1.59946 0.799729 0.600362i \(-0.204977\pi\)
0.799729 + 0.600362i \(0.204977\pi\)
\(108\) 98023.1 0.808666
\(109\) −10822.1 −0.0872457 −0.0436228 0.999048i \(-0.513890\pi\)
−0.0436228 + 0.999048i \(0.513890\pi\)
\(110\) −127627. −1.00568
\(111\) −32402.5 −0.249615
\(112\) −636364. −4.79358
\(113\) −37219.4 −0.274204 −0.137102 0.990557i \(-0.543779\pi\)
−0.137102 + 0.990557i \(0.543779\pi\)
\(114\) 32868.5 0.236874
\(115\) 199317. 1.40540
\(116\) 701825. 4.84266
\(117\) −57834.8 −0.390593
\(118\) −473125. −3.12803
\(119\) −324737. −2.10215
\(120\) 76727.8 0.486407
\(121\) −113734. −0.706198
\(122\) 180369. 1.09714
\(123\) 382.029 0.00227685
\(124\) 87785.7 0.512707
\(125\) −181737. −1.04032
\(126\) −407968. −2.28928
\(127\) −113235. −0.622973 −0.311487 0.950251i \(-0.600827\pi\)
−0.311487 + 0.950251i \(0.600827\pi\)
\(128\) −774110. −4.17617
\(129\) 12443.7 0.0658376
\(130\) −142708. −0.740610
\(131\) −256211. −1.30443 −0.652213 0.758036i \(-0.726159\pi\)
−0.652213 + 0.758036i \(0.726159\pi\)
\(132\) −44349.8 −0.221542
\(133\) −203591. −0.998000
\(134\) 533685. 2.56758
\(135\) 58531.4 0.276411
\(136\) −1.31345e6 −6.08926
\(137\) 272936. 1.24240 0.621198 0.783653i \(-0.286646\pi\)
0.621198 + 0.783653i \(0.286646\pi\)
\(138\) 94098.1 0.420613
\(139\) 182273. 0.800174 0.400087 0.916477i \(-0.368980\pi\)
0.400087 + 0.916477i \(0.368980\pi\)
\(140\) −740963. −3.19504
\(141\) −13717.9 −0.0581085
\(142\) 636532. 2.64911
\(143\) 52908.2 0.216363
\(144\) −971071. −3.90252
\(145\) 419072. 1.65527
\(146\) −744885. −2.89206
\(147\) −17074.9 −0.0651727
\(148\) 1.26562e6 4.74951
\(149\) −98402.4 −0.363112 −0.181556 0.983381i \(-0.558113\pi\)
−0.181556 + 0.983381i \(0.558113\pi\)
\(150\) −7184.58 −0.0260719
\(151\) 345272. 1.23231 0.616153 0.787627i \(-0.288690\pi\)
0.616153 + 0.787627i \(0.288690\pi\)
\(152\) −823455. −2.89089
\(153\) −495538. −1.71139
\(154\) 373215. 1.26811
\(155\) 52418.5 0.175249
\(156\) −49590.2 −0.163149
\(157\) 81303.7 0.263246 0.131623 0.991300i \(-0.457981\pi\)
0.131623 + 0.991300i \(0.457981\pi\)
\(158\) 786854. 2.50756
\(159\) 18807.3 0.0589974
\(160\) −1.32146e6 −4.08088
\(161\) −582856. −1.77213
\(162\) −608580. −1.82192
\(163\) −164978. −0.486360 −0.243180 0.969981i \(-0.578191\pi\)
−0.243180 + 0.969981i \(0.578191\pi\)
\(164\) −14921.8 −0.0433223
\(165\) −26482.1 −0.0757255
\(166\) 584653. 1.64675
\(167\) −74335.4 −0.206255 −0.103128 0.994668i \(-0.532885\pi\)
−0.103128 + 0.994668i \(0.532885\pi\)
\(168\) −224372. −0.613332
\(169\) −312133. −0.840665
\(170\) −1.22275e6 −3.24499
\(171\) −310674. −0.812485
\(172\) −486041. −1.25271
\(173\) 618915. 1.57223 0.786115 0.618080i \(-0.212089\pi\)
0.786115 + 0.618080i \(0.212089\pi\)
\(174\) 197845. 0.495395
\(175\) 44502.2 0.109847
\(176\) 888352. 2.16174
\(177\) −98171.3 −0.235533
\(178\) 401724. 0.950337
\(179\) 752051. 1.75434 0.877172 0.480176i \(-0.159427\pi\)
0.877172 + 0.480176i \(0.159427\pi\)
\(180\) −1.13069e6 −2.60112
\(181\) 416131. 0.944134 0.472067 0.881563i \(-0.343508\pi\)
0.472067 + 0.881563i \(0.343508\pi\)
\(182\) 417315. 0.933869
\(183\) 37425.6 0.0826117
\(184\) −2.35744e6 −5.13330
\(185\) 755725. 1.62343
\(186\) 24746.9 0.0524491
\(187\) 453326. 0.947997
\(188\) 535811. 1.10565
\(189\) −171161. −0.348538
\(190\) −766591. −1.54056
\(191\) −301813. −0.598625 −0.299312 0.954155i \(-0.596757\pi\)
−0.299312 + 0.954155i \(0.596757\pi\)
\(192\) −325288. −0.636818
\(193\) 870837. 1.68284 0.841421 0.540379i \(-0.181719\pi\)
0.841421 + 0.540379i \(0.181719\pi\)
\(194\) −846982. −1.61573
\(195\) −29611.2 −0.0557661
\(196\) 666935. 1.24006
\(197\) −646022. −1.18599 −0.592996 0.805205i \(-0.702055\pi\)
−0.592996 + 0.805205i \(0.702055\pi\)
\(198\) 569515. 1.03239
\(199\) −130234. −0.233126 −0.116563 0.993183i \(-0.537188\pi\)
−0.116563 + 0.993183i \(0.537188\pi\)
\(200\) 179996. 0.318190
\(201\) 110737. 0.193332
\(202\) 783011. 1.35017
\(203\) −1.22548e6 −2.08721
\(204\) −424897. −0.714839
\(205\) −8910.08 −0.0148080
\(206\) 158446. 0.260144
\(207\) −889420. −1.44272
\(208\) 993321. 1.59196
\(209\) 284210. 0.450063
\(210\) −208878. −0.326847
\(211\) 422732. 0.653670 0.326835 0.945081i \(-0.394018\pi\)
0.326835 + 0.945081i \(0.394018\pi\)
\(212\) −734598. −1.12256
\(213\) 132077. 0.199471
\(214\) −2.08570e6 −3.11328
\(215\) −290224. −0.428190
\(216\) −692286. −1.00960
\(217\) −153285. −0.220979
\(218\) 119160. 0.169820
\(219\) −154560. −0.217765
\(220\) 1.03437e6 1.44085
\(221\) 506892. 0.698128
\(222\) 356779. 0.485867
\(223\) −443348. −0.597011 −0.298506 0.954408i \(-0.596488\pi\)
−0.298506 + 0.954408i \(0.596488\pi\)
\(224\) 3.86429e6 5.14577
\(225\) 67909.0 0.0894275
\(226\) 409817. 0.533727
\(227\) 839246. 1.08100 0.540498 0.841345i \(-0.318236\pi\)
0.540498 + 0.841345i \(0.318236\pi\)
\(228\) −266386. −0.339371
\(229\) −546725. −0.688938 −0.344469 0.938798i \(-0.611941\pi\)
−0.344469 + 0.938798i \(0.611941\pi\)
\(230\) −2.19465e6 −2.73556
\(231\) 77440.5 0.0954856
\(232\) −4.95662e6 −6.04597
\(233\) −357259. −0.431116 −0.215558 0.976491i \(-0.569157\pi\)
−0.215558 + 0.976491i \(0.569157\pi\)
\(234\) 636810. 0.760275
\(235\) 319942. 0.377922
\(236\) 3.83450e6 4.48155
\(237\) 163268. 0.188813
\(238\) 3.57563e6 4.09176
\(239\) −677830. −0.767585 −0.383792 0.923419i \(-0.625382\pi\)
−0.383792 + 0.923419i \(0.625382\pi\)
\(240\) −497185. −0.557173
\(241\) 958280. 1.06280 0.531398 0.847122i \(-0.321667\pi\)
0.531398 + 0.847122i \(0.321667\pi\)
\(242\) 1.25231e6 1.37459
\(243\) −393198. −0.427165
\(244\) −1.46182e6 −1.57188
\(245\) 398239. 0.423866
\(246\) −4206.47 −0.00443179
\(247\) 317793. 0.331437
\(248\) −619985. −0.640106
\(249\) 121313. 0.123996
\(250\) 2.00108e6 2.02495
\(251\) −1.33663e6 −1.33914 −0.669570 0.742749i \(-0.733522\pi\)
−0.669570 + 0.742749i \(0.733522\pi\)
\(252\) 3.30642e6 3.27987
\(253\) 813655. 0.799170
\(254\) 1.24681e6 1.21259
\(255\) −253714. −0.244340
\(256\) 3.96755e6 3.78375
\(257\) 910408. 0.859812 0.429906 0.902874i \(-0.358547\pi\)
0.429906 + 0.902874i \(0.358547\pi\)
\(258\) −137015. −0.128150
\(259\) −2.20994e6 −2.04706
\(260\) 1.15659e6 1.06108
\(261\) −1.87004e6 −1.69922
\(262\) 2.82110e6 2.53901
\(263\) 1.77275e6 1.58037 0.790183 0.612871i \(-0.209985\pi\)
0.790183 + 0.612871i \(0.209985\pi\)
\(264\) 313219. 0.276591
\(265\) −438642. −0.383703
\(266\) 2.24171e6 1.94257
\(267\) 83355.8 0.0715579
\(268\) −4.32531e6 −3.67858
\(269\) −353105. −0.297525 −0.148762 0.988873i \(-0.547529\pi\)
−0.148762 + 0.988873i \(0.547529\pi\)
\(270\) −644480. −0.538022
\(271\) 1.26264e6 1.04437 0.522187 0.852831i \(-0.325116\pi\)
0.522187 + 0.852831i \(0.325116\pi\)
\(272\) 8.51093e6 6.97517
\(273\) 86591.0 0.0703179
\(274\) −3.00526e6 −2.41828
\(275\) −62124.2 −0.0495369
\(276\) −762629. −0.602616
\(277\) −691468. −0.541468 −0.270734 0.962654i \(-0.587266\pi\)
−0.270734 + 0.962654i \(0.587266\pi\)
\(278\) −2.00698e6 −1.55751
\(279\) −233909. −0.179902
\(280\) 5.23303e6 3.98895
\(281\) −1.47133e6 −1.11159 −0.555793 0.831321i \(-0.687585\pi\)
−0.555793 + 0.831321i \(0.687585\pi\)
\(282\) 151045. 0.113106
\(283\) 70113.3 0.0520396 0.0260198 0.999661i \(-0.491717\pi\)
0.0260198 + 0.999661i \(0.491717\pi\)
\(284\) −5.15885e6 −3.79539
\(285\) −159064. −0.116001
\(286\) −582564. −0.421142
\(287\) 26055.4 0.0186721
\(288\) 5.89679e6 4.18924
\(289\) 2.92328e6 2.05885
\(290\) −4.61434e6 −3.22192
\(291\) −175745. −0.121661
\(292\) 6.03701e6 4.14347
\(293\) 862952. 0.587242 0.293621 0.955922i \(-0.405140\pi\)
0.293621 + 0.955922i \(0.405140\pi\)
\(294\) 188009. 0.126856
\(295\) 2.28965e6 1.53184
\(296\) −8.93841e6 −5.92968
\(297\) 238938. 0.157179
\(298\) 1.08349e6 0.706782
\(299\) 909798. 0.588528
\(300\) 58228.2 0.0373534
\(301\) 848690. 0.539924
\(302\) −3.80173e6 −2.39863
\(303\) 162471. 0.101665
\(304\) 5.33587e6 3.31147
\(305\) −872879. −0.537285
\(306\) 5.45630e6 3.33115
\(307\) −2.91488e6 −1.76512 −0.882562 0.470196i \(-0.844183\pi\)
−0.882562 + 0.470196i \(0.844183\pi\)
\(308\) −3.02477e6 −1.81683
\(309\) 32876.9 0.0195882
\(310\) −577172. −0.341115
\(311\) −678022. −0.397505 −0.198752 0.980050i \(-0.563689\pi\)
−0.198752 + 0.980050i \(0.563689\pi\)
\(312\) 350230. 0.203689
\(313\) 1.89750e6 1.09476 0.547382 0.836883i \(-0.315625\pi\)
0.547382 + 0.836883i \(0.315625\pi\)
\(314\) −895223. −0.512397
\(315\) 1.97433e6 1.12110
\(316\) −6.37715e6 −3.59260
\(317\) −1.86471e6 −1.04223 −0.521114 0.853487i \(-0.674483\pi\)
−0.521114 + 0.853487i \(0.674483\pi\)
\(318\) −207084. −0.114836
\(319\) 1.71074e6 0.941257
\(320\) 7.58670e6 4.14170
\(321\) −432774. −0.234422
\(322\) 6.41773e6 3.44939
\(323\) 2.72290e6 1.45220
\(324\) 4.93231e6 2.61028
\(325\) −69464.9 −0.0364802
\(326\) 1.81655e6 0.946681
\(327\) 24725.2 0.0127870
\(328\) 105385. 0.0540871
\(329\) −935595. −0.476539
\(330\) 291590. 0.147397
\(331\) −1.43989e6 −0.722371 −0.361185 0.932494i \(-0.617628\pi\)
−0.361185 + 0.932494i \(0.617628\pi\)
\(332\) −4.73839e6 −2.35931
\(333\) −3.37230e6 −1.66654
\(334\) 818496. 0.401467
\(335\) −2.58273e6 −1.25738
\(336\) 1.45390e6 0.702564
\(337\) 1.61221e6 0.773298 0.386649 0.922227i \(-0.373632\pi\)
0.386649 + 0.922227i \(0.373632\pi\)
\(338\) 3.43685e6 1.63632
\(339\) 85035.1 0.0401883
\(340\) 9.90988e6 4.64912
\(341\) 213983. 0.0996538
\(342\) 3.42079e6 1.58147
\(343\) 1.45435e6 0.667474
\(344\) 3.43265e6 1.56399
\(345\) −455380. −0.205980
\(346\) −6.81478e6 −3.06028
\(347\) 163830. 0.0730414 0.0365207 0.999333i \(-0.488373\pi\)
0.0365207 + 0.999333i \(0.488373\pi\)
\(348\) −1.60346e6 −0.709756
\(349\) 2.27839e6 1.00130 0.500651 0.865649i \(-0.333094\pi\)
0.500651 + 0.865649i \(0.333094\pi\)
\(350\) −490007. −0.213812
\(351\) 267171. 0.115750
\(352\) −5.39448e6 −2.32056
\(353\) −2.44490e6 −1.04430 −0.522148 0.852855i \(-0.674869\pi\)
−0.522148 + 0.852855i \(0.674869\pi\)
\(354\) 1.08095e6 0.458455
\(355\) −3.08044e6 −1.29731
\(356\) −3.25582e6 −1.36156
\(357\) 741926. 0.308099
\(358\) −8.28072e6 −3.41476
\(359\) 630896. 0.258358 0.129179 0.991621i \(-0.458766\pi\)
0.129179 + 0.991621i \(0.458766\pi\)
\(360\) 7.98545e6 3.24746
\(361\) −768997. −0.310568
\(362\) −4.58195e6 −1.83772
\(363\) 259848. 0.103503
\(364\) −3.38218e6 −1.33796
\(365\) 3.60481e6 1.41628
\(366\) −412088. −0.160800
\(367\) 4.50319e6 1.74524 0.872619 0.488401i \(-0.162420\pi\)
0.872619 + 0.488401i \(0.162420\pi\)
\(368\) 1.52759e7 5.88013
\(369\) 39759.7 0.0152012
\(370\) −8.32117e6 −3.15995
\(371\) 1.28270e6 0.483829
\(372\) −200564. −0.0751442
\(373\) −2.91475e6 −1.08475 −0.542374 0.840137i \(-0.682474\pi\)
−0.542374 + 0.840137i \(0.682474\pi\)
\(374\) −4.99151e6 −1.84524
\(375\) 415215. 0.152474
\(376\) −3.78415e6 −1.38038
\(377\) 1.91289e6 0.693164
\(378\) 1.88463e6 0.678416
\(379\) 3.35371e6 1.19930 0.599650 0.800263i \(-0.295307\pi\)
0.599650 + 0.800263i \(0.295307\pi\)
\(380\) 6.21293e6 2.20718
\(381\) 258707. 0.0913052
\(382\) 3.32322e6 1.16520
\(383\) −4.08288e6 −1.42223 −0.711115 0.703076i \(-0.751810\pi\)
−0.711115 + 0.703076i \(0.751810\pi\)
\(384\) 1.76861e6 0.612074
\(385\) −1.80615e6 −0.621013
\(386\) −9.58865e6 −3.27559
\(387\) 1.29508e6 0.439559
\(388\) 6.86446e6 2.31487
\(389\) −3.04530e6 −1.02037 −0.510183 0.860066i \(-0.670422\pi\)
−0.510183 + 0.860066i \(0.670422\pi\)
\(390\) 326045. 0.108546
\(391\) 7.79530e6 2.57864
\(392\) −4.71021e6 −1.54819
\(393\) 585364. 0.191181
\(394\) 7.11325e6 2.30849
\(395\) −3.80791e6 −1.22799
\(396\) −4.61571e6 −1.47911
\(397\) 555960. 0.177038 0.0885192 0.996074i \(-0.471787\pi\)
0.0885192 + 0.996074i \(0.471787\pi\)
\(398\) 1.43398e6 0.453770
\(399\) 465145. 0.146270
\(400\) −1.16635e6 −0.364483
\(401\) −1.46495e6 −0.454947 −0.227474 0.973784i \(-0.573047\pi\)
−0.227474 + 0.973784i \(0.573047\pi\)
\(402\) −1.21931e6 −0.376313
\(403\) 239268. 0.0733875
\(404\) −6.34600e6 −1.93440
\(405\) 2.94517e6 0.892223
\(406\) 1.34935e7 4.06266
\(407\) 3.08503e6 0.923152
\(408\) 3.00083e6 0.892463
\(409\) 732963. 0.216658 0.108329 0.994115i \(-0.465450\pi\)
0.108329 + 0.994115i \(0.465450\pi\)
\(410\) 98107.5 0.0288232
\(411\) −623578. −0.182090
\(412\) −1.28415e6 −0.372710
\(413\) −6.69553e6 −1.93157
\(414\) 9.79326e6 2.80819
\(415\) −2.82938e6 −0.806438
\(416\) −6.03190e6 −1.70892
\(417\) −416438. −0.117276
\(418\) −3.12939e6 −0.876030
\(419\) 3.71422e6 1.03355 0.516776 0.856121i \(-0.327132\pi\)
0.516776 + 0.856121i \(0.327132\pi\)
\(420\) 1.69288e6 0.468276
\(421\) 3.39542e6 0.933659 0.466829 0.884347i \(-0.345396\pi\)
0.466829 + 0.884347i \(0.345396\pi\)
\(422\) −4.65463e6 −1.27234
\(423\) −1.42769e6 −0.387956
\(424\) 5.18808e6 1.40150
\(425\) −595187. −0.159838
\(426\) −1.45428e6 −0.388262
\(427\) 2.55253e6 0.677486
\(428\) 1.69038e7 4.46042
\(429\) −120879. −0.0317109
\(430\) 3.19561e6 0.833456
\(431\) 313706. 0.0813448 0.0406724 0.999173i \(-0.487050\pi\)
0.0406724 + 0.999173i \(0.487050\pi\)
\(432\) 4.48591e6 1.15649
\(433\) −5.15537e6 −1.32142 −0.660709 0.750642i \(-0.729744\pi\)
−0.660709 + 0.750642i \(0.729744\pi\)
\(434\) 1.68780e6 0.430127
\(435\) −957454. −0.242602
\(436\) −965747. −0.243303
\(437\) 4.88721e6 1.22421
\(438\) 1.70184e6 0.423870
\(439\) −2.05460e6 −0.508821 −0.254411 0.967096i \(-0.581882\pi\)
−0.254411 + 0.967096i \(0.581882\pi\)
\(440\) −7.30522e6 −1.79888
\(441\) −1.77707e6 −0.435120
\(442\) −5.58131e6 −1.35888
\(443\) 399939. 0.0968244 0.0484122 0.998827i \(-0.484584\pi\)
0.0484122 + 0.998827i \(0.484584\pi\)
\(444\) −2.89156e6 −0.696105
\(445\) −1.94411e6 −0.465394
\(446\) 4.88164e6 1.16206
\(447\) 224820. 0.0532189
\(448\) −2.21855e7 −5.22245
\(449\) −5.93650e6 −1.38968 −0.694840 0.719165i \(-0.744525\pi\)
−0.694840 + 0.719165i \(0.744525\pi\)
\(450\) −747735. −0.174067
\(451\) −36372.8 −0.00842046
\(452\) −3.32141e6 −0.764674
\(453\) −788841. −0.180611
\(454\) −9.24080e6 −2.10412
\(455\) −2.01956e6 −0.457329
\(456\) 1.88135e6 0.423698
\(457\) 7.70943e6 1.72676 0.863380 0.504555i \(-0.168343\pi\)
0.863380 + 0.504555i \(0.168343\pi\)
\(458\) 6.01990e6 1.34099
\(459\) 2.28917e6 0.507160
\(460\) 1.77868e7 3.91925
\(461\) 7.30818e6 1.60161 0.800805 0.598925i \(-0.204405\pi\)
0.800805 + 0.598925i \(0.204405\pi\)
\(462\) −852685. −0.185859
\(463\) 1.87526e6 0.406545 0.203273 0.979122i \(-0.434842\pi\)
0.203273 + 0.979122i \(0.434842\pi\)
\(464\) 3.21182e7 6.92558
\(465\) −119760. −0.0256851
\(466\) 3.93373e6 0.839150
\(467\) 4.74025e6 1.00579 0.502897 0.864346i \(-0.332268\pi\)
0.502897 + 0.864346i \(0.332268\pi\)
\(468\) −5.16110e6 −1.08925
\(469\) 7.55256e6 1.58549
\(470\) −3.52284e6 −0.735610
\(471\) −185755. −0.0385822
\(472\) −2.70811e7 −5.59514
\(473\) −1.18476e6 −0.243487
\(474\) −1.79772e6 −0.367517
\(475\) −373148. −0.0758835
\(476\) −2.89791e7 −5.86229
\(477\) 1.95737e6 0.393891
\(478\) 7.46348e6 1.49407
\(479\) 5.85191e6 1.16536 0.582679 0.812703i \(-0.302005\pi\)
0.582679 + 0.812703i \(0.302005\pi\)
\(480\) 3.01914e6 0.598108
\(481\) 3.44956e6 0.679832
\(482\) −1.05515e7 −2.06869
\(483\) 1.33165e6 0.259730
\(484\) −1.01495e7 −1.96938
\(485\) 4.09890e6 0.791248
\(486\) 4.32944e6 0.831459
\(487\) 8.68893e6 1.66014 0.830068 0.557662i \(-0.188301\pi\)
0.830068 + 0.557662i \(0.188301\pi\)
\(488\) 1.03241e7 1.96246
\(489\) 376926. 0.0712827
\(490\) −4.38495e6 −0.825038
\(491\) −82009.0 −0.0153517 −0.00767587 0.999971i \(-0.502443\pi\)
−0.00767587 + 0.999971i \(0.502443\pi\)
\(492\) 34091.8 0.00634947
\(493\) 1.63899e7 3.03711
\(494\) −3.49916e6 −0.645130
\(495\) −2.75612e6 −0.505575
\(496\) 4.01741e6 0.733233
\(497\) 9.00802e6 1.63583
\(498\) −1.33576e6 −0.241354
\(499\) 497257. 0.0893983 0.0446992 0.999000i \(-0.485767\pi\)
0.0446992 + 0.999000i \(0.485767\pi\)
\(500\) −1.62180e7 −2.90116
\(501\) 169834. 0.0302295
\(502\) 1.47174e7 2.60658
\(503\) 1.37133e6 0.241669 0.120835 0.992673i \(-0.461443\pi\)
0.120835 + 0.992673i \(0.461443\pi\)
\(504\) −2.33515e7 −4.09486
\(505\) −3.78931e6 −0.661199
\(506\) −8.95903e6 −1.55555
\(507\) 713130. 0.123211
\(508\) −1.01049e7 −1.73729
\(509\) −3.31526e6 −0.567182 −0.283591 0.958945i \(-0.591526\pi\)
−0.283591 + 0.958945i \(0.591526\pi\)
\(510\) 2.79360e6 0.475597
\(511\) −1.05414e7 −1.78585
\(512\) −1.89145e7 −3.18875
\(513\) 1.43518e6 0.240775
\(514\) −1.00244e7 −1.67359
\(515\) −766788. −0.127396
\(516\) 1.11046e6 0.183602
\(517\) 1.30607e6 0.214902
\(518\) 2.43333e7 3.98452
\(519\) −1.41403e6 −0.230431
\(520\) −8.16841e6 −1.32474
\(521\) −1.47501e6 −0.238069 −0.119034 0.992890i \(-0.537980\pi\)
−0.119034 + 0.992890i \(0.537980\pi\)
\(522\) 2.05907e7 3.30747
\(523\) −9.15225e6 −1.46310 −0.731549 0.681788i \(-0.761203\pi\)
−0.731549 + 0.681788i \(0.761203\pi\)
\(524\) −2.28639e7 −3.63766
\(525\) −101674. −0.0160995
\(526\) −1.95195e7 −3.07612
\(527\) 2.05009e6 0.321548
\(528\) −2.02962e6 −0.316832
\(529\) 7.55510e6 1.17382
\(530\) 4.82982e6 0.746864
\(531\) −1.02172e7 −1.57251
\(532\) −1.81682e7 −2.78313
\(533\) −40670.7 −0.00620103
\(534\) −917818. −0.139285
\(535\) 1.00936e7 1.52462
\(536\) 3.05474e7 4.59264
\(537\) −1.71821e6 −0.257123
\(538\) 3.88798e6 0.579120
\(539\) 1.62570e6 0.241028
\(540\) 5.22327e6 0.770829
\(541\) −7.71693e6 −1.13358 −0.566789 0.823863i \(-0.691815\pi\)
−0.566789 + 0.823863i \(0.691815\pi\)
\(542\) −1.39027e7 −2.03283
\(543\) −950734. −0.138376
\(544\) −5.16823e7 −7.48764
\(545\) −576665. −0.0831635
\(546\) −953440. −0.136871
\(547\) −8.83614e6 −1.26268 −0.631341 0.775505i \(-0.717495\pi\)
−0.631341 + 0.775505i \(0.717495\pi\)
\(548\) 2.43565e7 3.46468
\(549\) 3.89508e6 0.551550
\(550\) 684040. 0.0964217
\(551\) 1.02756e7 1.44187
\(552\) 5.38605e6 0.752355
\(553\) 1.11353e7 1.54843
\(554\) 7.61365e6 1.05395
\(555\) −1.72660e6 −0.237936
\(556\) 1.62658e7 2.23145
\(557\) 8.19942e6 1.11981 0.559906 0.828556i \(-0.310837\pi\)
0.559906 + 0.828556i \(0.310837\pi\)
\(558\) 2.57553e6 0.350172
\(559\) −1.32475e6 −0.179310
\(560\) −3.39093e7 −4.56929
\(561\) −1.03571e6 −0.138942
\(562\) 1.62005e7 2.16366
\(563\) −1.07596e7 −1.43062 −0.715312 0.698806i \(-0.753715\pi\)
−0.715312 + 0.698806i \(0.753715\pi\)
\(564\) −1.22417e6 −0.162048
\(565\) −1.98328e6 −0.261374
\(566\) −772006. −0.101293
\(567\) −8.61245e6 −1.12504
\(568\) 3.64342e7 4.73848
\(569\) 6.88906e6 0.892029 0.446015 0.895026i \(-0.352843\pi\)
0.446015 + 0.895026i \(0.352843\pi\)
\(570\) 1.75143e6 0.225791
\(571\) −1.07655e7 −1.38179 −0.690895 0.722955i \(-0.742783\pi\)
−0.690895 + 0.722955i \(0.742783\pi\)
\(572\) 4.72146e6 0.603374
\(573\) 689552. 0.0877365
\(574\) −286892. −0.0363445
\(575\) −1.06827e6 −0.134745
\(576\) −3.38544e7 −4.25166
\(577\) 1.25111e7 1.56443 0.782217 0.623006i \(-0.214089\pi\)
0.782217 + 0.623006i \(0.214089\pi\)
\(578\) −3.21878e7 −4.00748
\(579\) −1.98960e6 −0.246643
\(580\) 3.73975e7 4.61607
\(581\) 8.27385e6 1.01687
\(582\) 1.93510e6 0.236807
\(583\) −1.79063e6 −0.218190
\(584\) −4.26362e7 −5.17305
\(585\) −3.08179e6 −0.372318
\(586\) −9.50183e6 −1.14304
\(587\) 1.05563e7 1.26449 0.632247 0.774767i \(-0.282133\pi\)
0.632247 + 0.774767i \(0.282133\pi\)
\(588\) −1.52374e6 −0.181748
\(589\) 1.28529e6 0.152655
\(590\) −2.52110e7 −2.98167
\(591\) 1.47597e6 0.173823
\(592\) 5.79196e7 6.79237
\(593\) 2.54089e6 0.296721 0.148361 0.988933i \(-0.452600\pi\)
0.148361 + 0.988933i \(0.452600\pi\)
\(594\) −2.63091e6 −0.305942
\(595\) −1.73039e7 −2.00379
\(596\) −8.78130e6 −1.01261
\(597\) 297544. 0.0341677
\(598\) −1.00176e7 −1.14555
\(599\) −1.48177e7 −1.68739 −0.843694 0.536824i \(-0.819624\pi\)
−0.843694 + 0.536824i \(0.819624\pi\)
\(600\) −411236. −0.0466351
\(601\) −2.79389e6 −0.315517 −0.157759 0.987478i \(-0.550427\pi\)
−0.157759 + 0.987478i \(0.550427\pi\)
\(602\) −9.34479e6 −1.05094
\(603\) 1.15250e7 1.29076
\(604\) 3.08116e7 3.43654
\(605\) −6.06043e6 −0.673155
\(606\) −1.78894e6 −0.197886
\(607\) 2.70648e6 0.298149 0.149074 0.988826i \(-0.452371\pi\)
0.149074 + 0.988826i \(0.452371\pi\)
\(608\) −3.24019e7 −3.55477
\(609\) 2.79985e6 0.305908
\(610\) 9.61113e6 1.04580
\(611\) 1.46040e6 0.158259
\(612\) −4.42212e7 −4.77257
\(613\) 1.48550e7 1.59670 0.798348 0.602197i \(-0.205708\pi\)
0.798348 + 0.602197i \(0.205708\pi\)
\(614\) 3.20953e7 3.43574
\(615\) 20356.8 0.00217031
\(616\) 2.13624e7 2.26828
\(617\) −7.75787e6 −0.820407 −0.410204 0.911994i \(-0.634542\pi\)
−0.410204 + 0.911994i \(0.634542\pi\)
\(618\) −362002. −0.0381276
\(619\) −1.34491e7 −1.41080 −0.705400 0.708810i \(-0.749232\pi\)
−0.705400 + 0.708810i \(0.749232\pi\)
\(620\) 4.67775e6 0.488718
\(621\) 4.10872e6 0.427541
\(622\) 7.46559e6 0.773728
\(623\) 5.68508e6 0.586836
\(624\) −2.26944e6 −0.233323
\(625\) −8.79157e6 −0.900257
\(626\) −2.08930e7 −2.13091
\(627\) −649334. −0.0659628
\(628\) 7.25544e6 0.734116
\(629\) 2.95564e7 2.97869
\(630\) −2.17390e7 −2.18217
\(631\) −1.19256e7 −1.19236 −0.596179 0.802852i \(-0.703315\pi\)
−0.596179 + 0.802852i \(0.703315\pi\)
\(632\) 4.50385e7 4.48529
\(633\) −965815. −0.0958042
\(634\) 2.05320e7 2.02866
\(635\) −6.03382e6 −0.593825
\(636\) 1.67834e6 0.164527
\(637\) 1.81779e6 0.177499
\(638\) −1.88367e7 −1.83212
\(639\) 1.37460e7 1.33175
\(640\) −4.12493e7 −3.98076
\(641\) 5.46967e6 0.525795 0.262897 0.964824i \(-0.415322\pi\)
0.262897 + 0.964824i \(0.415322\pi\)
\(642\) 4.76520e6 0.456293
\(643\) 1.92397e6 0.183515 0.0917575 0.995781i \(-0.470752\pi\)
0.0917575 + 0.995781i \(0.470752\pi\)
\(644\) −5.20133e7 −4.94196
\(645\) 663074. 0.0627571
\(646\) −2.99814e7 −2.82664
\(647\) 1.29937e7 1.22031 0.610156 0.792282i \(-0.291107\pi\)
0.610156 + 0.792282i \(0.291107\pi\)
\(648\) −3.48343e7 −3.25889
\(649\) 9.34684e6 0.871070
\(650\) 764868. 0.0710073
\(651\) 350211. 0.0323875
\(652\) −1.47225e7 −1.35632
\(653\) −1.87036e7 −1.71650 −0.858249 0.513234i \(-0.828447\pi\)
−0.858249 + 0.513234i \(0.828447\pi\)
\(654\) −272245. −0.0248895
\(655\) −1.36525e7 −1.24339
\(656\) −682879. −0.0619561
\(657\) −1.60859e7 −1.45389
\(658\) 1.03017e7 0.927564
\(659\) 740764. 0.0664456 0.0332228 0.999448i \(-0.489423\pi\)
0.0332228 + 0.999448i \(0.489423\pi\)
\(660\) −2.36322e6 −0.211176
\(661\) −1.69004e7 −1.50450 −0.752252 0.658876i \(-0.771032\pi\)
−0.752252 + 0.658876i \(0.771032\pi\)
\(662\) 1.58544e7 1.40607
\(663\) −1.15810e6 −0.102320
\(664\) 3.34648e7 2.94556
\(665\) −1.08486e7 −0.951303
\(666\) 3.71318e7 3.24385
\(667\) 2.94176e7 2.56031
\(668\) −6.63359e6 −0.575185
\(669\) 1.01292e6 0.0875001
\(670\) 2.84380e7 2.44744
\(671\) −3.56328e6 −0.305523
\(672\) −8.82875e6 −0.754181
\(673\) 4.63004e6 0.394046 0.197023 0.980399i \(-0.436873\pi\)
0.197023 + 0.980399i \(0.436873\pi\)
\(674\) −1.77518e7 −1.50519
\(675\) −313709. −0.0265013
\(676\) −2.78543e7 −2.34437
\(677\) 4.66171e6 0.390907 0.195454 0.980713i \(-0.437382\pi\)
0.195454 + 0.980713i \(0.437382\pi\)
\(678\) −936309. −0.0782248
\(679\) −1.19862e7 −0.997720
\(680\) −6.99883e7 −5.80435
\(681\) −1.91742e6 −0.158435
\(682\) −2.35614e6 −0.193972
\(683\) 6.47801e6 0.531362 0.265681 0.964061i \(-0.414403\pi\)
0.265681 + 0.964061i \(0.414403\pi\)
\(684\) −2.77242e7 −2.26578
\(685\) 1.45437e7 1.18426
\(686\) −1.60136e7 −1.29921
\(687\) 1.24910e6 0.100973
\(688\) −2.22431e7 −1.79153
\(689\) −2.00221e6 −0.160680
\(690\) 5.01411e6 0.400933
\(691\) 8.03340e6 0.640036 0.320018 0.947411i \(-0.396311\pi\)
0.320018 + 0.947411i \(0.396311\pi\)
\(692\) 5.52312e7 4.38449
\(693\) 8.05962e6 0.637502
\(694\) −1.80390e6 −0.142172
\(695\) 9.71259e6 0.762734
\(696\) 1.13244e7 0.886118
\(697\) −348473. −0.0271699
\(698\) −2.50870e7 −1.94899
\(699\) 816230. 0.0631858
\(700\) 3.97132e6 0.306330
\(701\) −1.97958e6 −0.152152 −0.0760759 0.997102i \(-0.524239\pi\)
−0.0760759 + 0.997102i \(0.524239\pi\)
\(702\) −2.94178e6 −0.225303
\(703\) 1.85302e7 1.41414
\(704\) 3.09705e7 2.35514
\(705\) −730972. −0.0553896
\(706\) 2.69204e7 2.03268
\(707\) 1.10809e7 0.833735
\(708\) −8.76067e6 −0.656832
\(709\) 5.10052e6 0.381065 0.190532 0.981681i \(-0.438979\pi\)
0.190532 + 0.981681i \(0.438979\pi\)
\(710\) 3.39183e7 2.52515
\(711\) 1.69922e7 1.26059
\(712\) 2.29941e7 1.69988
\(713\) 3.67961e6 0.271068
\(714\) −8.16923e6 −0.599702
\(715\) 2.81927e6 0.206239
\(716\) 6.71120e7 4.89235
\(717\) 1.54864e6 0.112500
\(718\) −6.94670e6 −0.502883
\(719\) 1.89165e6 0.136464 0.0682319 0.997669i \(-0.478264\pi\)
0.0682319 + 0.997669i \(0.478264\pi\)
\(720\) −5.17446e7 −3.71992
\(721\) 2.24229e6 0.160640
\(722\) 8.46730e6 0.604508
\(723\) −2.18938e6 −0.155767
\(724\) 3.71350e7 2.63291
\(725\) −2.24609e6 −0.158702
\(726\) −2.86114e6 −0.201464
\(727\) −1.36241e7 −0.956030 −0.478015 0.878352i \(-0.658644\pi\)
−0.478015 + 0.878352i \(0.658644\pi\)
\(728\) 2.38866e7 1.67042
\(729\) −1.25325e7 −0.873412
\(730\) −3.96920e7 −2.75674
\(731\) −1.13507e7 −0.785647
\(732\) 3.33981e6 0.230380
\(733\) 2.84192e7 1.95367 0.976835 0.213993i \(-0.0686471\pi\)
0.976835 + 0.213993i \(0.0686471\pi\)
\(734\) −4.95839e7 −3.39704
\(735\) −909856. −0.0621233
\(736\) −9.27623e7 −6.31215
\(737\) −1.05432e7 −0.714999
\(738\) −437788. −0.0295885
\(739\) 1.55531e7 1.04762 0.523811 0.851834i \(-0.324510\pi\)
0.523811 + 0.851834i \(0.324510\pi\)
\(740\) 6.74399e7 4.52728
\(741\) −726060. −0.0485766
\(742\) −1.41237e7 −0.941754
\(743\) −1.26836e7 −0.842892 −0.421446 0.906853i \(-0.638477\pi\)
−0.421446 + 0.906853i \(0.638477\pi\)
\(744\) 1.41648e6 0.0938161
\(745\) −5.24348e6 −0.346122
\(746\) 3.20938e7 2.11142
\(747\) 1.26256e7 0.827850
\(748\) 4.04542e7 2.64369
\(749\) −2.95163e7 −1.92246
\(750\) −4.57186e6 −0.296784
\(751\) 2.60057e6 0.168255 0.0841277 0.996455i \(-0.473190\pi\)
0.0841277 + 0.996455i \(0.473190\pi\)
\(752\) 2.45208e7 1.58121
\(753\) 3.05379e6 0.196269
\(754\) −2.10625e7 −1.34922
\(755\) 1.83982e7 1.17465
\(756\) −1.52742e7 −0.971972
\(757\) 8.94406e6 0.567277 0.283639 0.958931i \(-0.408458\pi\)
0.283639 + 0.958931i \(0.408458\pi\)
\(758\) −3.69272e7 −2.33439
\(759\) −1.85896e6 −0.117129
\(760\) −4.38787e7 −2.75562
\(761\) −1.86914e6 −0.116998 −0.0584991 0.998287i \(-0.518631\pi\)
−0.0584991 + 0.998287i \(0.518631\pi\)
\(762\) −2.84858e6 −0.177722
\(763\) 1.68632e6 0.104865
\(764\) −2.69334e7 −1.66939
\(765\) −2.64053e7 −1.63131
\(766\) 4.49560e7 2.76832
\(767\) 1.04513e7 0.641477
\(768\) −9.06465e6 −0.554559
\(769\) −1.40225e6 −0.0855087 −0.0427544 0.999086i \(-0.513613\pi\)
−0.0427544 + 0.999086i \(0.513613\pi\)
\(770\) 1.98872e7 1.20878
\(771\) −2.08001e6 −0.126017
\(772\) 7.77123e7 4.69296
\(773\) 4.11509e6 0.247702 0.123851 0.992301i \(-0.460475\pi\)
0.123851 + 0.992301i \(0.460475\pi\)
\(774\) −1.42599e7 −0.855585
\(775\) −280946. −0.0168023
\(776\) −4.84801e7 −2.89008
\(777\) 5.04904e6 0.300024
\(778\) 3.35313e7 1.98610
\(779\) −218473. −0.0128989
\(780\) −2.64247e6 −0.155515
\(781\) −1.25750e7 −0.737702
\(782\) −8.58328e7 −5.01922
\(783\) 8.63875e6 0.503554
\(784\) 3.05215e7 1.77344
\(785\) 4.33236e6 0.250928
\(786\) −6.44536e6 −0.372127
\(787\) −3.13109e7 −1.80202 −0.901008 0.433802i \(-0.857172\pi\)
−0.901008 + 0.433802i \(0.857172\pi\)
\(788\) −5.76502e7 −3.30739
\(789\) −4.05019e6 −0.231624
\(790\) 4.19283e7 2.39023
\(791\) 5.79962e6 0.329578
\(792\) 3.25983e7 1.84664
\(793\) −3.98432e6 −0.224994
\(794\) −6.12159e6 −0.344598
\(795\) 1.00216e6 0.0562369
\(796\) −1.16219e7 −0.650120
\(797\) −3.69257e6 −0.205913 −0.102956 0.994686i \(-0.532830\pi\)
−0.102956 + 0.994686i \(0.532830\pi\)
\(798\) −5.12164e6 −0.284709
\(799\) 1.25130e7 0.693415
\(800\) 7.08259e6 0.391261
\(801\) 8.67526e6 0.477751
\(802\) 1.61303e7 0.885537
\(803\) 1.47156e7 0.805358
\(804\) 9.88204e6 0.539146
\(805\) −3.10581e7 −1.68921
\(806\) −2.63454e6 −0.142846
\(807\) 806738. 0.0436063
\(808\) 4.48185e7 2.41507
\(809\) −2.83800e7 −1.52455 −0.762275 0.647253i \(-0.775918\pi\)
−0.762275 + 0.647253i \(0.775918\pi\)
\(810\) −3.24288e7 −1.73668
\(811\) −1.03767e7 −0.553995 −0.276997 0.960871i \(-0.589339\pi\)
−0.276997 + 0.960871i \(0.589339\pi\)
\(812\) −1.09360e8 −5.82061
\(813\) −2.88475e6 −0.153067
\(814\) −3.39688e7 −1.79688
\(815\) −8.79105e6 −0.463604
\(816\) −1.94449e7 −1.02231
\(817\) −7.11622e6 −0.372987
\(818\) −8.07054e6 −0.421715
\(819\) 9.01196e6 0.469472
\(820\) −795124. −0.0412952
\(821\) 3.15619e7 1.63420 0.817100 0.576497i \(-0.195581\pi\)
0.817100 + 0.576497i \(0.195581\pi\)
\(822\) 6.86612e6 0.354431
\(823\) 5.81986e6 0.299511 0.149756 0.988723i \(-0.452151\pi\)
0.149756 + 0.988723i \(0.452151\pi\)
\(824\) 9.06926e6 0.465322
\(825\) 141935. 0.00726031
\(826\) 7.37235e7 3.75972
\(827\) −1.84354e7 −0.937322 −0.468661 0.883378i \(-0.655263\pi\)
−0.468661 + 0.883378i \(0.655263\pi\)
\(828\) −7.93706e7 −4.02332
\(829\) 1.93633e7 0.978571 0.489285 0.872124i \(-0.337258\pi\)
0.489285 + 0.872124i \(0.337258\pi\)
\(830\) 3.11539e7 1.56970
\(831\) 1.57980e6 0.0793594
\(832\) 3.46301e7 1.73438
\(833\) 1.55751e7 0.777713
\(834\) 4.58533e6 0.228274
\(835\) −3.96104e6 −0.196604
\(836\) 2.53625e7 1.25509
\(837\) 1.08055e6 0.0533129
\(838\) −4.08967e7 −2.01177
\(839\) −2.79155e7 −1.36911 −0.684557 0.728959i \(-0.740005\pi\)
−0.684557 + 0.728959i \(0.740005\pi\)
\(840\) −1.19559e7 −0.584634
\(841\) 4.13404e7 2.01551
\(842\) −3.73864e7 −1.81733
\(843\) 3.36154e6 0.162918
\(844\) 3.77240e7 1.82290
\(845\) −1.66323e7 −0.801330
\(846\) 1.57201e7 0.755142
\(847\) 1.77223e7 0.848811
\(848\) −3.36180e7 −1.60540
\(849\) −160188. −0.00762711
\(850\) 6.55351e6 0.311119
\(851\) 5.30495e7 2.51106
\(852\) 1.17864e7 0.556266
\(853\) 3.67026e7 1.72713 0.863563 0.504242i \(-0.168228\pi\)
0.863563 + 0.504242i \(0.168228\pi\)
\(854\) −2.81055e7 −1.31870
\(855\) −1.65546e7 −0.774468
\(856\) −1.19383e8 −5.56875
\(857\) 467751. 0.0217552 0.0108776 0.999941i \(-0.496537\pi\)
0.0108776 + 0.999941i \(0.496537\pi\)
\(858\) 1.33098e6 0.0617241
\(859\) −1.66567e7 −0.770206 −0.385103 0.922873i \(-0.625834\pi\)
−0.385103 + 0.922873i \(0.625834\pi\)
\(860\) −2.58992e7 −1.19410
\(861\) −59528.7 −0.00273665
\(862\) −3.45417e6 −0.158334
\(863\) −2.83692e7 −1.29664 −0.648321 0.761367i \(-0.724529\pi\)
−0.648321 + 0.761367i \(0.724529\pi\)
\(864\) −2.72405e7 −1.24146
\(865\) 3.29796e7 1.49867
\(866\) 5.67650e7 2.57209
\(867\) −6.67881e6 −0.301753
\(868\) −1.36790e7 −0.616246
\(869\) −1.55447e7 −0.698286
\(870\) 1.05424e7 0.472216
\(871\) −1.17890e7 −0.526542
\(872\) 6.82057e6 0.303759
\(873\) −1.82906e7 −0.812257
\(874\) −5.38123e7 −2.38288
\(875\) 2.83187e7 1.25041
\(876\) −1.37927e7 −0.607282
\(877\) 1.84690e7 0.810856 0.405428 0.914127i \(-0.367122\pi\)
0.405428 + 0.914127i \(0.367122\pi\)
\(878\) 2.26229e7 0.990401
\(879\) −1.97158e6 −0.0860683
\(880\) 4.73368e7 2.06059
\(881\) −2.04875e7 −0.889303 −0.444651 0.895704i \(-0.646672\pi\)
−0.444651 + 0.895704i \(0.646672\pi\)
\(882\) 1.95671e7 0.846944
\(883\) −3.82446e6 −0.165070 −0.0825350 0.996588i \(-0.526302\pi\)
−0.0825350 + 0.996588i \(0.526302\pi\)
\(884\) 4.52344e7 1.94688
\(885\) −5.23116e6 −0.224512
\(886\) −4.40367e6 −0.188465
\(887\) −4.25938e7 −1.81776 −0.908881 0.417055i \(-0.863062\pi\)
−0.908881 + 0.417055i \(0.863062\pi\)
\(888\) 2.04216e7 0.869074
\(889\) 1.76445e7 0.748780
\(890\) 2.14063e7 0.905871
\(891\) 1.20228e7 0.507355
\(892\) −3.95638e7 −1.66489
\(893\) 7.84491e6 0.329200
\(894\) −2.47546e6 −0.103588
\(895\) 4.00738e7 1.67226
\(896\) 1.20624e8 5.01952
\(897\) −2.07861e6 −0.0862567
\(898\) 6.53659e7 2.70496
\(899\) 7.73653e6 0.319262
\(900\) 6.06011e6 0.249387
\(901\) −1.71553e7 −0.704022
\(902\) 400496. 0.0163901
\(903\) −1.93900e6 −0.0791332
\(904\) 2.34574e7 0.954682
\(905\) 2.21740e7 0.899958
\(906\) 8.68581e6 0.351552
\(907\) 4.91611e7 1.98428 0.992140 0.125131i \(-0.0399352\pi\)
0.992140 + 0.125131i \(0.0399352\pi\)
\(908\) 7.48932e7 3.01459
\(909\) 1.69092e7 0.678755
\(910\) 2.22371e7 0.890173
\(911\) 6.96714e6 0.278137 0.139068 0.990283i \(-0.455589\pi\)
0.139068 + 0.990283i \(0.455589\pi\)
\(912\) −1.21909e7 −0.485341
\(913\) −1.15501e7 −0.458575
\(914\) −8.48874e7 −3.36107
\(915\) 1.99427e6 0.0787463
\(916\) −4.87890e7 −1.92125
\(917\) 3.99234e7 1.56785
\(918\) −2.52056e7 −0.987168
\(919\) 1.03025e7 0.402398 0.201199 0.979550i \(-0.435516\pi\)
0.201199 + 0.979550i \(0.435516\pi\)
\(920\) −1.25619e8 −4.89312
\(921\) 6.65963e6 0.258703
\(922\) −8.04692e7 −3.11747
\(923\) −1.40609e7 −0.543262
\(924\) 6.91068e6 0.266282
\(925\) −4.05044e6 −0.155649
\(926\) −2.06482e7 −0.791324
\(927\) 3.42166e6 0.130779
\(928\) −1.95036e8 −7.43440
\(929\) 9.04403e6 0.343813 0.171907 0.985113i \(-0.445007\pi\)
0.171907 + 0.985113i \(0.445007\pi\)
\(930\) 1.31866e6 0.0499950
\(931\) 9.76472e6 0.369220
\(932\) −3.18814e7 −1.20226
\(933\) 1.54907e6 0.0582597
\(934\) −5.21941e7 −1.95774
\(935\) 2.41560e7 0.903640
\(936\) 3.64502e7 1.35991
\(937\) −7.60906e6 −0.283128 −0.141564 0.989929i \(-0.545213\pi\)
−0.141564 + 0.989929i \(0.545213\pi\)
\(938\) −8.31601e7 −3.08608
\(939\) −4.33521e6 −0.160452
\(940\) 2.85512e7 1.05391
\(941\) 3.49843e7 1.28795 0.643976 0.765046i \(-0.277284\pi\)
0.643976 + 0.765046i \(0.277284\pi\)
\(942\) 2.04531e6 0.0750988
\(943\) −625459. −0.0229044
\(944\) 1.75481e8 6.40916
\(945\) −9.12050e6 −0.332230
\(946\) 1.30452e7 0.473938
\(947\) −1.56286e7 −0.566298 −0.283149 0.959076i \(-0.591379\pi\)
−0.283149 + 0.959076i \(0.591379\pi\)
\(948\) 1.45699e7 0.526544
\(949\) 1.64544e7 0.593085
\(950\) 4.10868e6 0.147704
\(951\) 4.26030e6 0.152753
\(952\) 2.04664e8 7.31896
\(953\) −2.51790e7 −0.898062 −0.449031 0.893516i \(-0.648231\pi\)
−0.449031 + 0.893516i \(0.648231\pi\)
\(954\) −2.15523e7 −0.766694
\(955\) −1.60824e7 −0.570615
\(956\) −6.04887e7 −2.14057
\(957\) −3.90853e6 −0.137954
\(958\) −6.44345e7 −2.26832
\(959\) −4.25296e7 −1.49329
\(960\) −1.73333e7 −0.607021
\(961\) −2.76614e7 −0.966199
\(962\) −3.79826e7 −1.32327
\(963\) −4.50410e7 −1.56510
\(964\) 8.55157e7 2.96383
\(965\) 4.64035e7 1.60410
\(966\) −1.46626e7 −0.505554
\(967\) 2.41861e7 0.831765 0.415882 0.909418i \(-0.363473\pi\)
0.415882 + 0.909418i \(0.363473\pi\)
\(968\) 7.16803e7 2.45873
\(969\) −6.22100e6 −0.212839
\(970\) −4.51323e7 −1.54013
\(971\) −2.98587e7 −1.01630 −0.508152 0.861267i \(-0.669671\pi\)
−0.508152 + 0.861267i \(0.669671\pi\)
\(972\) −3.50885e7 −1.19124
\(973\) −2.84021e7 −0.961765
\(974\) −9.56725e7 −3.23139
\(975\) 158706. 0.00534666
\(976\) −6.68984e7 −2.24797
\(977\) 8.08644e6 0.271032 0.135516 0.990775i \(-0.456731\pi\)
0.135516 + 0.990775i \(0.456731\pi\)
\(978\) −4.15027e6 −0.138749
\(979\) −7.93627e6 −0.264643
\(980\) 3.55383e7 1.18204
\(981\) 2.57327e6 0.0853716
\(982\) 902988. 0.0298816
\(983\) 966289. 0.0318950
\(984\) −240773. −0.00792719
\(985\) −3.44240e7 −1.13050
\(986\) −1.80467e8 −5.91161
\(987\) 2.13755e6 0.0698432
\(988\) 2.83594e7 0.924282
\(989\) −2.03728e7 −0.662308
\(990\) 3.03472e7 0.984082
\(991\) −3.46275e7 −1.12005 −0.560025 0.828476i \(-0.689208\pi\)
−0.560025 + 0.828476i \(0.689208\pi\)
\(992\) −2.43956e7 −0.787104
\(993\) 3.28972e6 0.105873
\(994\) −9.91859e7 −3.18408
\(995\) −6.93963e6 −0.222218
\(996\) 1.08258e7 0.345789
\(997\) 5.61449e7 1.78884 0.894422 0.447225i \(-0.147588\pi\)
0.894422 + 0.447225i \(0.147588\pi\)
\(998\) −5.47522e6 −0.174010
\(999\) 1.55785e7 0.493869
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.1.4 218
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
983.6.a.b.1.4 218 1.1 even 1 trivial