Properties

Label 1045.6.a.a.1.10
Level $1045$
Weight $6$
Character 1045.1
Self dual yes
Analytic conductor $167.601$
Analytic rank $1$
Dimension $35$
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] = [1045,6,Mod(1,1045)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1045.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1045 = 5 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 1045.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: \(167.601091705\)
Analytic rank: \(1\)
Dimension: \(35\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 1045.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-6.12909 q^{2} -3.52111 q^{3} +5.56569 q^{4} -25.0000 q^{5} +21.5812 q^{6} +66.3590 q^{7} +162.018 q^{8} -230.602 q^{9} +O(q^{10})\) \(q-6.12909 q^{2} -3.52111 q^{3} +5.56569 q^{4} -25.0000 q^{5} +21.5812 q^{6} +66.3590 q^{7} +162.018 q^{8} -230.602 q^{9} +153.227 q^{10} +121.000 q^{11} -19.5974 q^{12} -258.929 q^{13} -406.720 q^{14} +88.0279 q^{15} -1171.13 q^{16} -79.1073 q^{17} +1413.38 q^{18} +361.000 q^{19} -139.142 q^{20} -233.658 q^{21} -741.619 q^{22} -300.025 q^{23} -570.485 q^{24} +625.000 q^{25} +1587.00 q^{26} +1667.61 q^{27} +369.333 q^{28} +4039.24 q^{29} -539.530 q^{30} +1467.71 q^{31} +1993.34 q^{32} -426.055 q^{33} +484.855 q^{34} -1658.97 q^{35} -1283.46 q^{36} -4621.83 q^{37} -2212.60 q^{38} +911.718 q^{39} -4050.45 q^{40} -10855.9 q^{41} +1432.11 q^{42} -11329.9 q^{43} +673.448 q^{44} +5765.04 q^{45} +1838.88 q^{46} +13598.3 q^{47} +4123.67 q^{48} -12403.5 q^{49} -3830.68 q^{50} +278.546 q^{51} -1441.12 q^{52} +3881.38 q^{53} -10220.9 q^{54} -3025.00 q^{55} +10751.4 q^{56} -1271.12 q^{57} -24756.8 q^{58} -7937.40 q^{59} +489.935 q^{60} -803.334 q^{61} -8995.71 q^{62} -15302.5 q^{63} +25258.6 q^{64} +6473.22 q^{65} +2611.33 q^{66} -35178.6 q^{67} -440.286 q^{68} +1056.42 q^{69} +10168.0 q^{70} +35845.4 q^{71} -37361.7 q^{72} +34264.9 q^{73} +28327.6 q^{74} -2200.70 q^{75} +2009.21 q^{76} +8029.44 q^{77} -5588.00 q^{78} +81499.1 q^{79} +29278.1 q^{80} +50164.4 q^{81} +66536.5 q^{82} +15608.2 q^{83} -1300.46 q^{84} +1977.68 q^{85} +69442.0 q^{86} -14222.6 q^{87} +19604.2 q^{88} -80771.0 q^{89} -35334.4 q^{90} -17182.3 q^{91} -1669.84 q^{92} -5167.97 q^{93} -83345.4 q^{94} -9025.00 q^{95} -7018.79 q^{96} -23793.8 q^{97} +76022.0 q^{98} -27902.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.12909 −1.08348 −0.541740 0.840546i \(-0.682234\pi\)
−0.541740 + 0.840546i \(0.682234\pi\)
\(3\) −3.52111 −0.225880 −0.112940 0.993602i \(-0.536027\pi\)
−0.112940 + 0.993602i \(0.536027\pi\)
\(4\) 5.56569 0.173928
\(5\) −25.0000 −0.447214
\(6\) 21.5812 0.244736
\(7\) 66.3590 0.511864 0.255932 0.966695i \(-0.417618\pi\)
0.255932 + 0.966695i \(0.417618\pi\)
\(8\) 162.018 0.895032
\(9\) −230.602 −0.948978
\(10\) 153.227 0.484547
\(11\) 121.000 0.301511
\(12\) −19.5974 −0.0392867
\(13\) −258.929 −0.424935 −0.212467 0.977168i \(-0.568150\pi\)
−0.212467 + 0.977168i \(0.568150\pi\)
\(14\) −406.720 −0.554594
\(15\) 88.0279 0.101016
\(16\) −1171.13 −1.14368
\(17\) −79.1073 −0.0663887 −0.0331943 0.999449i \(-0.510568\pi\)
−0.0331943 + 0.999449i \(0.510568\pi\)
\(18\) 1413.38 1.02820
\(19\) 361.000 0.229416
\(20\) −139.142 −0.0777828
\(21\) −233.658 −0.115620
\(22\) −741.619 −0.326681
\(23\) −300.025 −0.118260 −0.0591299 0.998250i \(-0.518833\pi\)
−0.0591299 + 0.998250i \(0.518833\pi\)
\(24\) −570.485 −0.202170
\(25\) 625.000 0.200000
\(26\) 1587.00 0.460408
\(27\) 1667.61 0.440234
\(28\) 369.333 0.0890273
\(29\) 4039.24 0.891876 0.445938 0.895064i \(-0.352870\pi\)
0.445938 + 0.895064i \(0.352870\pi\)
\(30\) −539.530 −0.109449
\(31\) 1467.71 0.274306 0.137153 0.990550i \(-0.456205\pi\)
0.137153 + 0.990550i \(0.456205\pi\)
\(32\) 1993.34 0.344118
\(33\) −426.055 −0.0681053
\(34\) 484.855 0.0719308
\(35\) −1658.97 −0.228913
\(36\) −1283.46 −0.165054
\(37\) −4621.83 −0.555022 −0.277511 0.960722i \(-0.589509\pi\)
−0.277511 + 0.960722i \(0.589509\pi\)
\(38\) −2212.60 −0.248567
\(39\) 911.718 0.0959840
\(40\) −4050.45 −0.400271
\(41\) −10855.9 −1.00857 −0.504283 0.863538i \(-0.668243\pi\)
−0.504283 + 0.863538i \(0.668243\pi\)
\(42\) 1432.11 0.125272
\(43\) −11329.9 −0.934449 −0.467225 0.884139i \(-0.654746\pi\)
−0.467225 + 0.884139i \(0.654746\pi\)
\(44\) 673.448 0.0524412
\(45\) 5765.04 0.424396
\(46\) 1838.88 0.128132
\(47\) 13598.3 0.897928 0.448964 0.893550i \(-0.351793\pi\)
0.448964 + 0.893550i \(0.351793\pi\)
\(48\) 4123.67 0.258333
\(49\) −12403.5 −0.737995
\(50\) −3830.68 −0.216696
\(51\) 278.546 0.0149959
\(52\) −1441.12 −0.0739079
\(53\) 3881.38 0.189800 0.0949002 0.995487i \(-0.469747\pi\)
0.0949002 + 0.995487i \(0.469747\pi\)
\(54\) −10220.9 −0.476985
\(55\) −3025.00 −0.134840
\(56\) 10751.4 0.458135
\(57\) −1271.12 −0.0518203
\(58\) −24756.8 −0.966329
\(59\) −7937.40 −0.296858 −0.148429 0.988923i \(-0.547422\pi\)
−0.148429 + 0.988923i \(0.547422\pi\)
\(60\) 489.935 0.0175696
\(61\) −803.334 −0.0276421 −0.0138211 0.999904i \(-0.504400\pi\)
−0.0138211 + 0.999904i \(0.504400\pi\)
\(62\) −8995.71 −0.297205
\(63\) −15302.5 −0.485748
\(64\) 25258.6 0.770832
\(65\) 6473.22 0.190037
\(66\) 2611.33 0.0737907
\(67\) −35178.6 −0.957395 −0.478697 0.877980i \(-0.658891\pi\)
−0.478697 + 0.877980i \(0.658891\pi\)
\(68\) −440.286 −0.0115468
\(69\) 1056.42 0.0267125
\(70\) 10168.0 0.248022
\(71\) 35845.4 0.843892 0.421946 0.906621i \(-0.361347\pi\)
0.421946 + 0.906621i \(0.361347\pi\)
\(72\) −37361.7 −0.849366
\(73\) 34264.9 0.752562 0.376281 0.926506i \(-0.377203\pi\)
0.376281 + 0.926506i \(0.377203\pi\)
\(74\) 28327.6 0.601355
\(75\) −2200.70 −0.0451759
\(76\) 2009.21 0.0399017
\(77\) 8029.44 0.154333
\(78\) −5588.00 −0.103997
\(79\) 81499.1 1.46921 0.734607 0.678493i \(-0.237367\pi\)
0.734607 + 0.678493i \(0.237367\pi\)
\(80\) 29278.1 0.511468
\(81\) 50164.4 0.849538
\(82\) 66536.5 1.09276
\(83\) 15608.2 0.248690 0.124345 0.992239i \(-0.460317\pi\)
0.124345 + 0.992239i \(0.460317\pi\)
\(84\) −1300.46 −0.0201095
\(85\) 1977.68 0.0296899
\(86\) 69442.0 1.01246
\(87\) −14222.6 −0.201457
\(88\) 19604.2 0.269862
\(89\) −80771.0 −1.08089 −0.540444 0.841380i \(-0.681744\pi\)
−0.540444 + 0.841380i \(0.681744\pi\)
\(90\) −35334.4 −0.459824
\(91\) −17182.3 −0.217509
\(92\) −1669.84 −0.0205687
\(93\) −5167.97 −0.0619602
\(94\) −83345.4 −0.972886
\(95\) −9025.00 −0.102598
\(96\) −7018.79 −0.0777292
\(97\) −23793.8 −0.256764 −0.128382 0.991725i \(-0.540978\pi\)
−0.128382 + 0.991725i \(0.540978\pi\)
\(98\) 76022.0 0.799603
\(99\) −27902.8 −0.286128
\(100\) 3478.55 0.0347855
\(101\) 1699.50 0.0165775 0.00828873 0.999966i \(-0.497362\pi\)
0.00828873 + 0.999966i \(0.497362\pi\)
\(102\) −1707.23 −0.0162477
\(103\) −38712.2 −0.359546 −0.179773 0.983708i \(-0.557536\pi\)
−0.179773 + 0.983708i \(0.557536\pi\)
\(104\) −41951.2 −0.380330
\(105\) 5841.44 0.0517067
\(106\) −23789.3 −0.205645
\(107\) 113177. 0.955648 0.477824 0.878456i \(-0.341426\pi\)
0.477824 + 0.878456i \(0.341426\pi\)
\(108\) 9281.37 0.0765690
\(109\) 172897. 1.39386 0.696932 0.717137i \(-0.254548\pi\)
0.696932 + 0.717137i \(0.254548\pi\)
\(110\) 18540.5 0.146096
\(111\) 16274.0 0.125368
\(112\) −77714.7 −0.585407
\(113\) 200084. 1.47407 0.737033 0.675857i \(-0.236226\pi\)
0.737033 + 0.675857i \(0.236226\pi\)
\(114\) 7790.82 0.0561463
\(115\) 7500.61 0.0528874
\(116\) 22481.1 0.155122
\(117\) 59709.4 0.403254
\(118\) 48649.0 0.321639
\(119\) −5249.48 −0.0339820
\(120\) 14262.1 0.0904130
\(121\) 14641.0 0.0909091
\(122\) 4923.70 0.0299497
\(123\) 38224.7 0.227814
\(124\) 8168.80 0.0477094
\(125\) −15625.0 −0.0894427
\(126\) 93790.3 0.526298
\(127\) −89177.5 −0.490621 −0.245311 0.969445i \(-0.578890\pi\)
−0.245311 + 0.969445i \(0.578890\pi\)
\(128\) −218599. −1.17930
\(129\) 39893.9 0.211073
\(130\) −39674.9 −0.205901
\(131\) 361081. 1.83834 0.919171 0.393859i \(-0.128860\pi\)
0.919171 + 0.393859i \(0.128860\pi\)
\(132\) −2371.29 −0.0118454
\(133\) 23955.6 0.117430
\(134\) 215612. 1.03732
\(135\) −41690.2 −0.196879
\(136\) −12816.8 −0.0594200
\(137\) −389149. −1.77139 −0.885697 0.464265i \(-0.846319\pi\)
−0.885697 + 0.464265i \(0.846319\pi\)
\(138\) −6474.89 −0.0289424
\(139\) 243135. 1.06736 0.533678 0.845688i \(-0.320809\pi\)
0.533678 + 0.845688i \(0.320809\pi\)
\(140\) −9233.33 −0.0398142
\(141\) −47881.3 −0.202824
\(142\) −219699. −0.914340
\(143\) −31330.4 −0.128123
\(144\) 270063. 1.08532
\(145\) −100981. −0.398859
\(146\) −210012. −0.815385
\(147\) 43674.1 0.166698
\(148\) −25723.7 −0.0965336
\(149\) 144484. 0.533158 0.266579 0.963813i \(-0.414107\pi\)
0.266579 + 0.963813i \(0.414107\pi\)
\(150\) 13488.3 0.0489472
\(151\) 271861. 0.970297 0.485149 0.874432i \(-0.338765\pi\)
0.485149 + 0.874432i \(0.338765\pi\)
\(152\) 58488.6 0.205335
\(153\) 18242.3 0.0630014
\(154\) −49213.1 −0.167216
\(155\) −36692.7 −0.122673
\(156\) 5074.34 0.0166943
\(157\) 72078.9 0.233377 0.116689 0.993169i \(-0.462772\pi\)
0.116689 + 0.993169i \(0.462772\pi\)
\(158\) −499515. −1.59186
\(159\) −13666.8 −0.0428720
\(160\) −49833.6 −0.153894
\(161\) −19909.3 −0.0605329
\(162\) −307462. −0.920457
\(163\) 271978. 0.801798 0.400899 0.916122i \(-0.368698\pi\)
0.400899 + 0.916122i \(0.368698\pi\)
\(164\) −60420.3 −0.175418
\(165\) 10651.4 0.0304576
\(166\) −95664.2 −0.269451
\(167\) −63921.7 −0.177361 −0.0886803 0.996060i \(-0.528265\pi\)
−0.0886803 + 0.996060i \(0.528265\pi\)
\(168\) −37856.8 −0.103483
\(169\) −304249. −0.819431
\(170\) −12121.4 −0.0321684
\(171\) −83247.2 −0.217711
\(172\) −63058.8 −0.162527
\(173\) −332899. −0.845662 −0.422831 0.906209i \(-0.638964\pi\)
−0.422831 + 0.906209i \(0.638964\pi\)
\(174\) 87171.6 0.218274
\(175\) 41474.4 0.102373
\(176\) −141706. −0.344832
\(177\) 27948.5 0.0670541
\(178\) 495052. 1.17112
\(179\) 123748. 0.288673 0.144337 0.989529i \(-0.453895\pi\)
0.144337 + 0.989529i \(0.453895\pi\)
\(180\) 32086.4 0.0738142
\(181\) −530556. −1.20375 −0.601873 0.798592i \(-0.705579\pi\)
−0.601873 + 0.798592i \(0.705579\pi\)
\(182\) 105312. 0.235666
\(183\) 2828.63 0.00624379
\(184\) −48609.4 −0.105846
\(185\) 115546. 0.248213
\(186\) 31674.9 0.0671326
\(187\) −9571.98 −0.0200169
\(188\) 75684.1 0.156174
\(189\) 110661. 0.225340
\(190\) 55315.0 0.111163
\(191\) −8344.74 −0.0165512 −0.00827560 0.999966i \(-0.502634\pi\)
−0.00827560 + 0.999966i \(0.502634\pi\)
\(192\) −88938.5 −0.174115
\(193\) 354967. 0.685953 0.342976 0.939344i \(-0.388565\pi\)
0.342976 + 0.939344i \(0.388565\pi\)
\(194\) 145834. 0.278199
\(195\) −22793.0 −0.0429254
\(196\) −69033.9 −0.128358
\(197\) 415434. 0.762670 0.381335 0.924437i \(-0.375464\pi\)
0.381335 + 0.924437i \(0.375464\pi\)
\(198\) 171019. 0.310014
\(199\) −634264. −1.13537 −0.567685 0.823246i \(-0.692161\pi\)
−0.567685 + 0.823246i \(0.692161\pi\)
\(200\) 101261. 0.179006
\(201\) 123868. 0.216256
\(202\) −10416.4 −0.0179613
\(203\) 268040. 0.456519
\(204\) 1550.30 0.00260819
\(205\) 271396. 0.451044
\(206\) 237270. 0.389561
\(207\) 69186.2 0.112226
\(208\) 303238. 0.485988
\(209\) 43681.0 0.0691714
\(210\) −35802.7 −0.0560231
\(211\) 557857. 0.862614 0.431307 0.902205i \(-0.358053\pi\)
0.431307 + 0.902205i \(0.358053\pi\)
\(212\) 21602.6 0.0330115
\(213\) −126216. −0.190618
\(214\) −693670. −1.03542
\(215\) 283248. 0.417898
\(216\) 270182. 0.394024
\(217\) 97395.6 0.140407
\(218\) −1.05970e6 −1.51022
\(219\) −120651. −0.169988
\(220\) −16836.2 −0.0234524
\(221\) 20483.2 0.0282109
\(222\) −99744.8 −0.135834
\(223\) −258512. −0.348112 −0.174056 0.984736i \(-0.555687\pi\)
−0.174056 + 0.984736i \(0.555687\pi\)
\(224\) 132276. 0.176142
\(225\) −144126. −0.189796
\(226\) −1.22633e6 −1.59712
\(227\) −934603. −1.20382 −0.601911 0.798563i \(-0.705594\pi\)
−0.601911 + 0.798563i \(0.705594\pi\)
\(228\) −7074.67 −0.00901299
\(229\) 642630. 0.809789 0.404895 0.914363i \(-0.367308\pi\)
0.404895 + 0.914363i \(0.367308\pi\)
\(230\) −45971.9 −0.0573024
\(231\) −28272.6 −0.0348606
\(232\) 654430. 0.798258
\(233\) 1.30470e6 1.57442 0.787212 0.616682i \(-0.211524\pi\)
0.787212 + 0.616682i \(0.211524\pi\)
\(234\) −365964. −0.436917
\(235\) −339959. −0.401565
\(236\) −44177.1 −0.0516318
\(237\) −286968. −0.331865
\(238\) 32174.5 0.0368188
\(239\) 95610.5 0.108271 0.0541353 0.998534i \(-0.482760\pi\)
0.0541353 + 0.998534i \(0.482760\pi\)
\(240\) −103092. −0.115530
\(241\) −757816. −0.840468 −0.420234 0.907416i \(-0.638052\pi\)
−0.420234 + 0.907416i \(0.638052\pi\)
\(242\) −89735.9 −0.0984981
\(243\) −581863. −0.632128
\(244\) −4471.10 −0.00480773
\(245\) 310087. 0.330041
\(246\) −234282. −0.246832
\(247\) −93473.3 −0.0974867
\(248\) 237795. 0.245513
\(249\) −54958.4 −0.0561740
\(250\) 95767.0 0.0969093
\(251\) −156846. −0.157140 −0.0785702 0.996909i \(-0.525035\pi\)
−0.0785702 + 0.996909i \(0.525035\pi\)
\(252\) −85168.9 −0.0844850
\(253\) −36303.0 −0.0356567
\(254\) 546577. 0.531578
\(255\) −6963.64 −0.00670635
\(256\) 531538. 0.506914
\(257\) 31470.6 0.0297216 0.0148608 0.999890i \(-0.495269\pi\)
0.0148608 + 0.999890i \(0.495269\pi\)
\(258\) −244513. −0.228693
\(259\) −306700. −0.284096
\(260\) 36027.9 0.0330526
\(261\) −931455. −0.846371
\(262\) −2.21310e6 −1.99181
\(263\) 1.25606e6 1.11975 0.559877 0.828576i \(-0.310848\pi\)
0.559877 + 0.828576i \(0.310848\pi\)
\(264\) −69028.6 −0.0609564
\(265\) −97034.6 −0.0848813
\(266\) −146826. −0.127233
\(267\) 284404. 0.244150
\(268\) −195793. −0.166517
\(269\) −2.21915e6 −1.86985 −0.934925 0.354846i \(-0.884533\pi\)
−0.934925 + 0.354846i \(0.884533\pi\)
\(270\) 255522. 0.213314
\(271\) −720989. −0.596355 −0.298178 0.954510i \(-0.596379\pi\)
−0.298178 + 0.954510i \(0.596379\pi\)
\(272\) 92644.5 0.0759272
\(273\) 60500.7 0.0491308
\(274\) 2.38513e6 1.91927
\(275\) 75625.0 0.0603023
\(276\) 5879.71 0.00464604
\(277\) −1.50482e6 −1.17838 −0.589192 0.807993i \(-0.700554\pi\)
−0.589192 + 0.807993i \(0.700554\pi\)
\(278\) −1.49019e6 −1.15646
\(279\) −338456. −0.260311
\(280\) −268784. −0.204884
\(281\) −260752. −0.196998 −0.0984989 0.995137i \(-0.531404\pi\)
−0.0984989 + 0.995137i \(0.531404\pi\)
\(282\) 293469. 0.219755
\(283\) 2.19492e6 1.62912 0.814558 0.580082i \(-0.196980\pi\)
0.814558 + 0.580082i \(0.196980\pi\)
\(284\) 199504. 0.146776
\(285\) 31778.1 0.0231748
\(286\) 192027. 0.138818
\(287\) −720383. −0.516249
\(288\) −459669. −0.326560
\(289\) −1.41360e6 −0.995593
\(290\) 618921. 0.432155
\(291\) 83780.7 0.0579978
\(292\) 190708. 0.130891
\(293\) −1.44787e6 −0.985279 −0.492639 0.870234i \(-0.663968\pi\)
−0.492639 + 0.870234i \(0.663968\pi\)
\(294\) −267682. −0.180614
\(295\) 198435. 0.132759
\(296\) −748821. −0.496762
\(297\) 201780. 0.132736
\(298\) −885558. −0.577665
\(299\) 77685.0 0.0502527
\(300\) −12248.4 −0.00785734
\(301\) −751842. −0.478311
\(302\) −1.66626e6 −1.05130
\(303\) −5984.13 −0.00374451
\(304\) −422776. −0.262377
\(305\) 20083.3 0.0123619
\(306\) −111808. −0.0682608
\(307\) 1.00421e6 0.608105 0.304053 0.952655i \(-0.401660\pi\)
0.304053 + 0.952655i \(0.401660\pi\)
\(308\) 44689.3 0.0268427
\(309\) 136310. 0.0812141
\(310\) 224893. 0.132914
\(311\) 1.34266e6 0.787165 0.393582 0.919289i \(-0.371236\pi\)
0.393582 + 0.919289i \(0.371236\pi\)
\(312\) 147715. 0.0859088
\(313\) 126408. 0.0729311 0.0364655 0.999335i \(-0.488390\pi\)
0.0364655 + 0.999335i \(0.488390\pi\)
\(314\) −441778. −0.252860
\(315\) 382562. 0.217233
\(316\) 453598. 0.255537
\(317\) −64785.4 −0.0362101 −0.0181050 0.999836i \(-0.505763\pi\)
−0.0181050 + 0.999836i \(0.505763\pi\)
\(318\) 83765.0 0.0464509
\(319\) 488748. 0.268911
\(320\) −631466. −0.344727
\(321\) −398508. −0.215861
\(322\) 122026. 0.0655862
\(323\) −28557.7 −0.0152306
\(324\) 279199. 0.147758
\(325\) −161831. −0.0849869
\(326\) −1.66698e6 −0.868732
\(327\) −608789. −0.314845
\(328\) −1.75885e6 −0.902699
\(329\) 902372. 0.459617
\(330\) −65283.2 −0.0330002
\(331\) 631201. 0.316663 0.158332 0.987386i \(-0.449388\pi\)
0.158332 + 0.987386i \(0.449388\pi\)
\(332\) 86870.5 0.0432541
\(333\) 1.06580e6 0.526704
\(334\) 391782. 0.192167
\(335\) 879464. 0.428160
\(336\) 273642. 0.132232
\(337\) 2.94849e6 1.41425 0.707123 0.707091i \(-0.249993\pi\)
0.707123 + 0.707091i \(0.249993\pi\)
\(338\) 1.86477e6 0.887836
\(339\) −704520. −0.332961
\(340\) 11007.2 0.00516390
\(341\) 177593. 0.0827064
\(342\) 510229. 0.235885
\(343\) −1.93838e6 −0.889617
\(344\) −1.83565e6 −0.836362
\(345\) −26410.5 −0.0119462
\(346\) 2.04036e6 0.916257
\(347\) −4.29871e6 −1.91653 −0.958263 0.285888i \(-0.907711\pi\)
−0.958263 + 0.285888i \(0.907711\pi\)
\(348\) −79158.6 −0.0350389
\(349\) −3.85898e6 −1.69594 −0.847968 0.530048i \(-0.822174\pi\)
−0.847968 + 0.530048i \(0.822174\pi\)
\(350\) −254200. −0.110919
\(351\) −431791. −0.187071
\(352\) 241195. 0.103755
\(353\) −560930. −0.239592 −0.119796 0.992799i \(-0.538224\pi\)
−0.119796 + 0.992799i \(0.538224\pi\)
\(354\) −171299. −0.0726517
\(355\) −896134. −0.377400
\(356\) −449546. −0.187996
\(357\) 18484.0 0.00767584
\(358\) −758464. −0.312772
\(359\) −3.63173e6 −1.48723 −0.743614 0.668609i \(-0.766890\pi\)
−0.743614 + 0.668609i \(0.766890\pi\)
\(360\) 934042. 0.379848
\(361\) 130321. 0.0526316
\(362\) 3.25182e6 1.30423
\(363\) −51552.6 −0.0205345
\(364\) −95631.0 −0.0378308
\(365\) −856622. −0.336556
\(366\) −17336.9 −0.00676502
\(367\) 1.28554e6 0.498218 0.249109 0.968475i \(-0.419862\pi\)
0.249109 + 0.968475i \(0.419862\pi\)
\(368\) 351366. 0.135251
\(369\) 2.50338e6 0.957107
\(370\) −708190. −0.268934
\(371\) 257565. 0.0971520
\(372\) −28763.3 −0.0107766
\(373\) −4.39605e6 −1.63603 −0.818013 0.575199i \(-0.804925\pi\)
−0.818013 + 0.575199i \(0.804925\pi\)
\(374\) 58667.5 0.0216879
\(375\) 55017.4 0.0202033
\(376\) 2.20318e6 0.803674
\(377\) −1.04587e6 −0.378989
\(378\) −678249. −0.244151
\(379\) −4.80435e6 −1.71805 −0.859026 0.511932i \(-0.828930\pi\)
−0.859026 + 0.511932i \(0.828930\pi\)
\(380\) −50230.3 −0.0178446
\(381\) 314004. 0.110821
\(382\) 51145.6 0.0179329
\(383\) −2.15034e6 −0.749047 −0.374524 0.927217i \(-0.622194\pi\)
−0.374524 + 0.927217i \(0.622194\pi\)
\(384\) 769713. 0.266380
\(385\) −200736. −0.0690197
\(386\) −2.17562e6 −0.743216
\(387\) 2.61270e6 0.886772
\(388\) −132429. −0.0446584
\(389\) −4.17313e6 −1.39826 −0.699131 0.714994i \(-0.746429\pi\)
−0.699131 + 0.714994i \(0.746429\pi\)
\(390\) 139700. 0.0465088
\(391\) 23734.1 0.00785111
\(392\) −2.00959e6 −0.660530
\(393\) −1.27141e6 −0.415244
\(394\) −2.54623e6 −0.826338
\(395\) −2.03748e6 −0.657052
\(396\) −155298. −0.0497655
\(397\) 865597. 0.275638 0.137819 0.990457i \(-0.455991\pi\)
0.137819 + 0.990457i \(0.455991\pi\)
\(398\) 3.88746e6 1.23015
\(399\) −84350.4 −0.0265250
\(400\) −731953. −0.228735
\(401\) −2.70235e6 −0.839230 −0.419615 0.907702i \(-0.637835\pi\)
−0.419615 + 0.907702i \(0.637835\pi\)
\(402\) −759196. −0.234309
\(403\) −380032. −0.116562
\(404\) 9458.88 0.00288328
\(405\) −1.25411e6 −0.379925
\(406\) −1.64284e6 −0.494629
\(407\) −559242. −0.167345
\(408\) 45129.5 0.0134218
\(409\) −4.70657e6 −1.39122 −0.695610 0.718419i \(-0.744866\pi\)
−0.695610 + 0.718419i \(0.744866\pi\)
\(410\) −1.66341e6 −0.488697
\(411\) 1.37024e6 0.400122
\(412\) −215460. −0.0625350
\(413\) −526718. −0.151951
\(414\) −424048. −0.121595
\(415\) −390206. −0.111218
\(416\) −516134. −0.146228
\(417\) −856104. −0.241094
\(418\) −267725. −0.0749458
\(419\) −2.18241e6 −0.607296 −0.303648 0.952784i \(-0.598205\pi\)
−0.303648 + 0.952784i \(0.598205\pi\)
\(420\) 32511.6 0.00899322
\(421\) −6.78164e6 −1.86479 −0.932393 0.361445i \(-0.882284\pi\)
−0.932393 + 0.361445i \(0.882284\pi\)
\(422\) −3.41915e6 −0.934625
\(423\) −3.13580e6 −0.852114
\(424\) 628855. 0.169877
\(425\) −49442.0 −0.0132777
\(426\) 773586. 0.206531
\(427\) −53308.4 −0.0141490
\(428\) 629906. 0.166214
\(429\) 110318. 0.0289403
\(430\) −1.73605e6 −0.452784
\(431\) −2.80849e6 −0.728249 −0.364125 0.931350i \(-0.618632\pi\)
−0.364125 + 0.931350i \(0.618632\pi\)
\(432\) −1.95298e6 −0.503486
\(433\) −1.55510e6 −0.398601 −0.199301 0.979938i \(-0.563867\pi\)
−0.199301 + 0.979938i \(0.563867\pi\)
\(434\) −596946. −0.152129
\(435\) 355565. 0.0900941
\(436\) 962289. 0.242432
\(437\) −108309. −0.0271307
\(438\) 739478. 0.184179
\(439\) 4.09040e6 1.01299 0.506494 0.862243i \(-0.330941\pi\)
0.506494 + 0.862243i \(0.330941\pi\)
\(440\) −490105. −0.120686
\(441\) 2.86027e6 0.700341
\(442\) −125543. −0.0305659
\(443\) 4.01440e6 0.971876 0.485938 0.873993i \(-0.338478\pi\)
0.485938 + 0.873993i \(0.338478\pi\)
\(444\) 90576.0 0.0218050
\(445\) 2.01928e6 0.483388
\(446\) 1.58444e6 0.377172
\(447\) −508746. −0.120429
\(448\) 1.67614e6 0.394561
\(449\) −2.58697e6 −0.605586 −0.302793 0.953056i \(-0.597919\pi\)
−0.302793 + 0.953056i \(0.597919\pi\)
\(450\) 883361. 0.205640
\(451\) −1.31356e6 −0.304094
\(452\) 1.11361e6 0.256381
\(453\) −957254. −0.219170
\(454\) 5.72826e6 1.30432
\(455\) 429556. 0.0972729
\(456\) −205945. −0.0463809
\(457\) 3.30693e6 0.740687 0.370344 0.928895i \(-0.379240\pi\)
0.370344 + 0.928895i \(0.379240\pi\)
\(458\) −3.93873e6 −0.877390
\(459\) −131920. −0.0292266
\(460\) 41746.1 0.00919858
\(461\) −4.93804e6 −1.08219 −0.541093 0.840963i \(-0.681989\pi\)
−0.541093 + 0.840963i \(0.681989\pi\)
\(462\) 173285. 0.0377708
\(463\) 4.05661e6 0.879450 0.439725 0.898132i \(-0.355076\pi\)
0.439725 + 0.898132i \(0.355076\pi\)
\(464\) −4.73045e6 −1.02002
\(465\) 129199. 0.0277094
\(466\) −7.99663e6 −1.70586
\(467\) −433114. −0.0918988 −0.0459494 0.998944i \(-0.514631\pi\)
−0.0459494 + 0.998944i \(0.514631\pi\)
\(468\) 332324. 0.0701370
\(469\) −2.33441e6 −0.490056
\(470\) 2.08363e6 0.435088
\(471\) −253798. −0.0527152
\(472\) −1.28600e6 −0.265697
\(473\) −1.37092e6 −0.281747
\(474\) 1.75885e6 0.359569
\(475\) 225625. 0.0458831
\(476\) −29216.9 −0.00591041
\(477\) −895054. −0.180116
\(478\) −586005. −0.117309
\(479\) −848551. −0.168982 −0.0844908 0.996424i \(-0.526926\pi\)
−0.0844908 + 0.996424i \(0.526926\pi\)
\(480\) 175470. 0.0347616
\(481\) 1.19673e6 0.235848
\(482\) 4.64472e6 0.910630
\(483\) 70103.0 0.0136732
\(484\) 81487.2 0.0158116
\(485\) 594845. 0.114828
\(486\) 3.56629e6 0.684898
\(487\) 166891. 0.0318868 0.0159434 0.999873i \(-0.494925\pi\)
0.0159434 + 0.999873i \(0.494925\pi\)
\(488\) −130155. −0.0247406
\(489\) −957666. −0.181110
\(490\) −1.90055e6 −0.357593
\(491\) 7.95201e6 1.48858 0.744292 0.667854i \(-0.232787\pi\)
0.744292 + 0.667854i \(0.232787\pi\)
\(492\) 212747. 0.0396232
\(493\) −319533. −0.0592105
\(494\) 572906. 0.105625
\(495\) 697570. 0.127960
\(496\) −1.71887e6 −0.313718
\(497\) 2.37866e6 0.431958
\(498\) 336845. 0.0608634
\(499\) −2.46610e6 −0.443363 −0.221681 0.975119i \(-0.571154\pi\)
−0.221681 + 0.975119i \(0.571154\pi\)
\(500\) −86963.8 −0.0155566
\(501\) 225076. 0.0400622
\(502\) 961320. 0.170258
\(503\) −7.62765e6 −1.34422 −0.672110 0.740451i \(-0.734612\pi\)
−0.672110 + 0.740451i \(0.734612\pi\)
\(504\) −2.47928e6 −0.434760
\(505\) −42487.5 −0.00741366
\(506\) 222504. 0.0386333
\(507\) 1.07130e6 0.185093
\(508\) −496334. −0.0853326
\(509\) −1.57613e6 −0.269648 −0.134824 0.990870i \(-0.543047\pi\)
−0.134824 + 0.990870i \(0.543047\pi\)
\(510\) 42680.8 0.00726619
\(511\) 2.27378e6 0.385209
\(512\) 3.73734e6 0.630068
\(513\) 602006. 0.100997
\(514\) −192886. −0.0322027
\(515\) 967804. 0.160794
\(516\) 222037. 0.0367114
\(517\) 1.64540e6 0.270735
\(518\) 1.87979e6 0.307812
\(519\) 1.17217e6 0.191018
\(520\) 1.04878e6 0.170089
\(521\) 2.02209e6 0.326366 0.163183 0.986596i \(-0.447824\pi\)
0.163183 + 0.986596i \(0.447824\pi\)
\(522\) 5.70897e6 0.917025
\(523\) 7.30394e6 1.16762 0.583812 0.811889i \(-0.301560\pi\)
0.583812 + 0.811889i \(0.301560\pi\)
\(524\) 2.00966e6 0.319738
\(525\) −146036. −0.0231239
\(526\) −7.69852e6 −1.21323
\(527\) −116106. −0.0182108
\(528\) 498964. 0.0778904
\(529\) −6.34633e6 −0.986015
\(530\) 594733. 0.0919671
\(531\) 1.83038e6 0.281712
\(532\) 133329. 0.0204243
\(533\) 2.81089e6 0.428575
\(534\) −1.74314e6 −0.264532
\(535\) −2.82942e6 −0.427379
\(536\) −5.69956e6 −0.856899
\(537\) −435732. −0.0652054
\(538\) 1.36014e7 2.02594
\(539\) −1.50082e6 −0.222514
\(540\) −232034. −0.0342427
\(541\) −2.47936e6 −0.364205 −0.182103 0.983280i \(-0.558290\pi\)
−0.182103 + 0.983280i \(0.558290\pi\)
\(542\) 4.41900e6 0.646139
\(543\) 1.86815e6 0.271902
\(544\) −157688. −0.0228455
\(545\) −4.32242e6 −0.623355
\(546\) −370814. −0.0532322
\(547\) 9.79661e6 1.39993 0.699967 0.714175i \(-0.253198\pi\)
0.699967 + 0.714175i \(0.253198\pi\)
\(548\) −2.16588e6 −0.308094
\(549\) 185250. 0.0262318
\(550\) −463512. −0.0653363
\(551\) 1.45816e6 0.204610
\(552\) 171159. 0.0239085
\(553\) 5.40819e6 0.752038
\(554\) 9.22320e6 1.27675
\(555\) −406850. −0.0560663
\(556\) 1.35321e6 0.185643
\(557\) −1.03889e7 −1.41884 −0.709420 0.704786i \(-0.751043\pi\)
−0.709420 + 0.704786i \(0.751043\pi\)
\(558\) 2.07443e6 0.282041
\(559\) 2.93364e6 0.397080
\(560\) 1.94287e6 0.261802
\(561\) 33704.0 0.00452142
\(562\) 1.59817e6 0.213443
\(563\) 7.00356e6 0.931210 0.465605 0.884993i \(-0.345837\pi\)
0.465605 + 0.884993i \(0.345837\pi\)
\(564\) −266492. −0.0352766
\(565\) −5.00211e6 −0.659222
\(566\) −1.34528e7 −1.76511
\(567\) 3.32886e6 0.434848
\(568\) 5.80760e6 0.755311
\(569\) −1.60867e6 −0.208299 −0.104149 0.994562i \(-0.533212\pi\)
−0.104149 + 0.994562i \(0.533212\pi\)
\(570\) −194770. −0.0251094
\(571\) 7.74529e6 0.994140 0.497070 0.867711i \(-0.334409\pi\)
0.497070 + 0.867711i \(0.334409\pi\)
\(572\) −174375. −0.0222841
\(573\) 29382.8 0.00373858
\(574\) 4.41529e6 0.559345
\(575\) −187515. −0.0236520
\(576\) −5.82468e6 −0.731503
\(577\) −7.94489e6 −0.993455 −0.496728 0.867906i \(-0.665465\pi\)
−0.496728 + 0.867906i \(0.665465\pi\)
\(578\) 8.66407e6 1.07870
\(579\) −1.24988e6 −0.154943
\(580\) −562028. −0.0693726
\(581\) 1.03575e6 0.127296
\(582\) −513499. −0.0628394
\(583\) 469647. 0.0572269
\(584\) 5.55153e6 0.673567
\(585\) −1.49274e6 −0.180341
\(586\) 8.87409e6 1.06753
\(587\) −9.21609e6 −1.10396 −0.551978 0.833859i \(-0.686127\pi\)
−0.551978 + 0.833859i \(0.686127\pi\)
\(588\) 243076. 0.0289934
\(589\) 529843. 0.0629301
\(590\) −1.21623e6 −0.143841
\(591\) −1.46279e6 −0.172272
\(592\) 5.41275e6 0.634766
\(593\) −4.22598e6 −0.493504 −0.246752 0.969079i \(-0.579363\pi\)
−0.246752 + 0.969079i \(0.579363\pi\)
\(594\) −1.23673e6 −0.143816
\(595\) 131237. 0.0151972
\(596\) 804155. 0.0927308
\(597\) 2.23332e6 0.256457
\(598\) −476138. −0.0544477
\(599\) 4.30342e6 0.490057 0.245028 0.969516i \(-0.421203\pi\)
0.245028 + 0.969516i \(0.421203\pi\)
\(600\) −356553. −0.0404339
\(601\) −2.40661e6 −0.271782 −0.135891 0.990724i \(-0.543390\pi\)
−0.135891 + 0.990724i \(0.543390\pi\)
\(602\) 4.60810e6 0.518240
\(603\) 8.11224e6 0.908547
\(604\) 1.51309e6 0.168762
\(605\) −366025. −0.0406558
\(606\) 36677.3 0.00405710
\(607\) 9.89092e6 1.08960 0.544798 0.838568i \(-0.316606\pi\)
0.544798 + 0.838568i \(0.316606\pi\)
\(608\) 719597. 0.0789461
\(609\) −943798. −0.103118
\(610\) −123093. −0.0133939
\(611\) −3.52100e6 −0.381560
\(612\) 101531. 0.0109577
\(613\) 8.57915e6 0.922132 0.461066 0.887366i \(-0.347467\pi\)
0.461066 + 0.887366i \(0.347467\pi\)
\(614\) −6.15489e6 −0.658870
\(615\) −955618. −0.101882
\(616\) 1.30091e6 0.138133
\(617\) 5.76038e6 0.609170 0.304585 0.952485i \(-0.401482\pi\)
0.304585 + 0.952485i \(0.401482\pi\)
\(618\) −835455. −0.0879938
\(619\) −5.46621e6 −0.573402 −0.286701 0.958020i \(-0.592559\pi\)
−0.286701 + 0.958020i \(0.592559\pi\)
\(620\) −204220. −0.0213363
\(621\) −500323. −0.0520620
\(622\) −8.22929e6 −0.852877
\(623\) −5.35988e6 −0.553268
\(624\) −1.06774e6 −0.109775
\(625\) 390625. 0.0400000
\(626\) −774764. −0.0790193
\(627\) −153806. −0.0156244
\(628\) 401168. 0.0405908
\(629\) 365621. 0.0368472
\(630\) −2.34476e6 −0.235368
\(631\) 1.16461e7 1.16441 0.582207 0.813041i \(-0.302189\pi\)
0.582207 + 0.813041i \(0.302189\pi\)
\(632\) 1.32043e7 1.31499
\(633\) −1.96428e6 −0.194847
\(634\) 397076. 0.0392329
\(635\) 2.22944e6 0.219412
\(636\) −76065.1 −0.00745663
\(637\) 3.21162e6 0.313600
\(638\) −2.99558e6 −0.291359
\(639\) −8.26600e6 −0.800836
\(640\) 5.46498e6 0.527398
\(641\) −1.79189e7 −1.72252 −0.861262 0.508161i \(-0.830326\pi\)
−0.861262 + 0.508161i \(0.830326\pi\)
\(642\) 2.44249e6 0.233881
\(643\) 6.34522e6 0.605228 0.302614 0.953113i \(-0.402141\pi\)
0.302614 + 0.953113i \(0.402141\pi\)
\(644\) −110809. −0.0105284
\(645\) −997349. −0.0943947
\(646\) 175033. 0.0165021
\(647\) 1.44082e7 1.35316 0.676581 0.736368i \(-0.263461\pi\)
0.676581 + 0.736368i \(0.263461\pi\)
\(648\) 8.12754e6 0.760364
\(649\) −960426. −0.0895060
\(650\) 991873. 0.0920816
\(651\) −342941. −0.0317152
\(652\) 1.51375e6 0.139455
\(653\) 1.71783e7 1.57652 0.788258 0.615345i \(-0.210983\pi\)
0.788258 + 0.615345i \(0.210983\pi\)
\(654\) 3.73132e6 0.341129
\(655\) −9.02702e6 −0.822131
\(656\) 1.27136e7 1.15347
\(657\) −7.90154e6 −0.714165
\(658\) −5.53072e6 −0.497985
\(659\) −2.55642e6 −0.229308 −0.114654 0.993406i \(-0.536576\pi\)
−0.114654 + 0.993406i \(0.536576\pi\)
\(660\) 59282.2 0.00529742
\(661\) 3.95119e6 0.351742 0.175871 0.984413i \(-0.443726\pi\)
0.175871 + 0.984413i \(0.443726\pi\)
\(662\) −3.86869e6 −0.343098
\(663\) −72123.5 −0.00637226
\(664\) 2.52882e6 0.222586
\(665\) −598890. −0.0525161
\(666\) −6.53240e6 −0.570673
\(667\) −1.21187e6 −0.105473
\(668\) −355768. −0.0308479
\(669\) 910251. 0.0786314
\(670\) −5.39031e6 −0.463902
\(671\) −97203.4 −0.00833442
\(672\) −465760. −0.0397868
\(673\) 7.32719e6 0.623591 0.311796 0.950149i \(-0.399070\pi\)
0.311796 + 0.950149i \(0.399070\pi\)
\(674\) −1.80715e7 −1.53231
\(675\) 1.04225e6 0.0880469
\(676\) −1.69335e6 −0.142522
\(677\) 5.81850e6 0.487910 0.243955 0.969787i \(-0.421555\pi\)
0.243955 + 0.969787i \(0.421555\pi\)
\(678\) 4.31806e6 0.360757
\(679\) −1.57893e6 −0.131428
\(680\) 320420. 0.0265734
\(681\) 3.29084e6 0.271919
\(682\) −1.08848e6 −0.0896107
\(683\) 2.77439e6 0.227571 0.113785 0.993505i \(-0.463702\pi\)
0.113785 + 0.993505i \(0.463702\pi\)
\(684\) −463328. −0.0378659
\(685\) 9.72873e6 0.792191
\(686\) 1.18805e7 0.963882
\(687\) −2.26277e6 −0.182915
\(688\) 1.32688e7 1.06871
\(689\) −1.00500e6 −0.0806527
\(690\) 161872. 0.0129434
\(691\) 6.99799e6 0.557543 0.278771 0.960357i \(-0.410073\pi\)
0.278771 + 0.960357i \(0.410073\pi\)
\(692\) −1.85281e6 −0.147084
\(693\) −1.85160e6 −0.146459
\(694\) 2.63472e7 2.07652
\(695\) −6.07836e6 −0.477336
\(696\) −2.30432e6 −0.180310
\(697\) 858777. 0.0669574
\(698\) 2.36520e7 1.83751
\(699\) −4.59401e6 −0.355630
\(700\) 230833. 0.0178055
\(701\) 2.57702e6 0.198072 0.0990360 0.995084i \(-0.468424\pi\)
0.0990360 + 0.995084i \(0.468424\pi\)
\(702\) 2.64649e6 0.202687
\(703\) −1.66848e6 −0.127331
\(704\) 3.05629e6 0.232415
\(705\) 1.19703e6 0.0907054
\(706\) 3.43799e6 0.259593
\(707\) 112777. 0.00848540
\(708\) 155553. 0.0116626
\(709\) −6.24043e6 −0.466229 −0.233114 0.972449i \(-0.574892\pi\)
−0.233114 + 0.972449i \(0.574892\pi\)
\(710\) 5.49248e6 0.408905
\(711\) −1.87938e7 −1.39425
\(712\) −1.30864e7 −0.967429
\(713\) −440349. −0.0324394
\(714\) −113290. −0.00831661
\(715\) 783260. 0.0572982
\(716\) 688744. 0.0502083
\(717\) −336656. −0.0244561
\(718\) 2.22592e7 1.61138
\(719\) −1.91821e7 −1.38380 −0.691900 0.721994i \(-0.743226\pi\)
−0.691900 + 0.721994i \(0.743226\pi\)
\(720\) −6.75159e6 −0.485372
\(721\) −2.56890e6 −0.184039
\(722\) −798749. −0.0570252
\(723\) 2.66836e6 0.189845
\(724\) −2.95291e6 −0.209365
\(725\) 2.52452e6 0.178375
\(726\) 315971. 0.0222487
\(727\) −8.02243e6 −0.562950 −0.281475 0.959568i \(-0.590824\pi\)
−0.281475 + 0.959568i \(0.590824\pi\)
\(728\) −2.78384e6 −0.194677
\(729\) −1.01411e7 −0.706754
\(730\) 5.25031e6 0.364651
\(731\) 896279. 0.0620369
\(732\) 15743.3 0.00108597
\(733\) 7.56459e6 0.520027 0.260013 0.965605i \(-0.416273\pi\)
0.260013 + 0.965605i \(0.416273\pi\)
\(734\) −7.87916e6 −0.539809
\(735\) −1.09185e6 −0.0745496
\(736\) −598052. −0.0406953
\(737\) −4.25660e6 −0.288665
\(738\) −1.53434e7 −1.03701
\(739\) −1.22451e6 −0.0824805 −0.0412402 0.999149i \(-0.513131\pi\)
−0.0412402 + 0.999149i \(0.513131\pi\)
\(740\) 643092. 0.0431712
\(741\) 329130. 0.0220203
\(742\) −1.57864e6 −0.105262
\(743\) −2.01415e7 −1.33850 −0.669251 0.743037i \(-0.733385\pi\)
−0.669251 + 0.743037i \(0.733385\pi\)
\(744\) −837305. −0.0554564
\(745\) −3.61211e6 −0.238435
\(746\) 2.69438e7 1.77260
\(747\) −3.59929e6 −0.236002
\(748\) −53274.6 −0.00348150
\(749\) 7.51030e6 0.489162
\(750\) −337206. −0.0218898
\(751\) 8.63154e6 0.558455 0.279228 0.960225i \(-0.409922\pi\)
0.279228 + 0.960225i \(0.409922\pi\)
\(752\) −1.59254e7 −1.02694
\(753\) 552271. 0.0354948
\(754\) 6.41026e6 0.410627
\(755\) −6.79653e6 −0.433930
\(756\) 615902. 0.0391929
\(757\) −1.86237e7 −1.18121 −0.590604 0.806961i \(-0.701111\pi\)
−0.590604 + 0.806961i \(0.701111\pi\)
\(758\) 2.94462e7 1.86147
\(759\) 127827. 0.00805412
\(760\) −1.46221e6 −0.0918284
\(761\) 6.00562e6 0.375921 0.187960 0.982177i \(-0.439812\pi\)
0.187960 + 0.982177i \(0.439812\pi\)
\(762\) −1.92456e6 −0.120073
\(763\) 1.14733e7 0.713469
\(764\) −46444.2 −0.00287871
\(765\) −456057. −0.0281751
\(766\) 1.31796e7 0.811577
\(767\) 2.05522e6 0.126145
\(768\) −1.87160e6 −0.114501
\(769\) 1.48691e7 0.906712 0.453356 0.891330i \(-0.350227\pi\)
0.453356 + 0.891330i \(0.350227\pi\)
\(770\) 1.23033e6 0.0747815
\(771\) −110811. −0.00671350
\(772\) 1.97563e6 0.119306
\(773\) −1.75443e7 −1.05606 −0.528028 0.849227i \(-0.677068\pi\)
−0.528028 + 0.849227i \(0.677068\pi\)
\(774\) −1.60135e7 −0.960799
\(775\) 917318. 0.0548612
\(776\) −3.85503e6 −0.229812
\(777\) 1.07993e6 0.0641714
\(778\) 2.55775e7 1.51499
\(779\) −3.91896e6 −0.231381
\(780\) −126858. −0.00746591
\(781\) 4.33729e6 0.254443
\(782\) −145468. −0.00850652
\(783\) 6.73586e6 0.392634
\(784\) 1.45260e7 0.844028
\(785\) −1.80197e6 −0.104370
\(786\) 7.79256e6 0.449908
\(787\) −5.55400e6 −0.319646 −0.159823 0.987146i \(-0.551092\pi\)
−0.159823 + 0.987146i \(0.551092\pi\)
\(788\) 2.31218e6 0.132649
\(789\) −4.42275e6 −0.252929
\(790\) 1.24879e7 0.711902
\(791\) 1.32774e7 0.754521
\(792\) −4.52076e6 −0.256094
\(793\) 208006. 0.0117461
\(794\) −5.30532e6 −0.298648
\(795\) 341670. 0.0191729
\(796\) −3.53011e6 −0.197472
\(797\) −3.60622e6 −0.201097 −0.100549 0.994932i \(-0.532060\pi\)
−0.100549 + 0.994932i \(0.532060\pi\)
\(798\) 516991. 0.0287393
\(799\) −1.07573e6 −0.0596122
\(800\) 1.24584e6 0.0688236
\(801\) 1.86259e7 1.02574
\(802\) 1.65629e7 0.909288
\(803\) 4.14605e6 0.226906
\(804\) 689409. 0.0376129
\(805\) 497733. 0.0270712
\(806\) 2.32925e6 0.126293
\(807\) 7.81389e6 0.422361
\(808\) 275350. 0.0148374
\(809\) −8.69499e6 −0.467087 −0.233543 0.972346i \(-0.575032\pi\)
−0.233543 + 0.972346i \(0.575032\pi\)
\(810\) 7.68655e6 0.411641
\(811\) 6.45171e6 0.344447 0.172224 0.985058i \(-0.444905\pi\)
0.172224 + 0.985058i \(0.444905\pi\)
\(812\) 1.49182e6 0.0794013
\(813\) 2.53868e6 0.134705
\(814\) 3.42764e6 0.181315
\(815\) −6.79946e6 −0.358575
\(816\) −326212. −0.0171504
\(817\) −4.09010e6 −0.214377
\(818\) 2.88469e7 1.50736
\(819\) 3.96226e6 0.206411
\(820\) 1.51051e6 0.0784491
\(821\) −9.35989e6 −0.484633 −0.242316 0.970197i \(-0.577907\pi\)
−0.242316 + 0.970197i \(0.577907\pi\)
\(822\) −8.39832e6 −0.433523
\(823\) −1.75646e7 −0.903940 −0.451970 0.892033i \(-0.649279\pi\)
−0.451970 + 0.892033i \(0.649279\pi\)
\(824\) −6.27207e6 −0.321805
\(825\) −266284. −0.0136211
\(826\) 3.22830e6 0.164636
\(827\) −1.21583e6 −0.0618169 −0.0309085 0.999522i \(-0.509840\pi\)
−0.0309085 + 0.999522i \(0.509840\pi\)
\(828\) 385068. 0.0195192
\(829\) 1.44716e7 0.731360 0.365680 0.930741i \(-0.380836\pi\)
0.365680 + 0.930741i \(0.380836\pi\)
\(830\) 2.39160e6 0.120502
\(831\) 5.29866e6 0.266173
\(832\) −6.54019e6 −0.327553
\(833\) 981206. 0.0489945
\(834\) 5.24714e6 0.261221
\(835\) 1.59804e6 0.0793181
\(836\) 243115. 0.0120308
\(837\) 2.44756e6 0.120759
\(838\) 1.33761e7 0.657993
\(839\) 483536. 0.0237151 0.0118575 0.999930i \(-0.496226\pi\)
0.0118575 + 0.999930i \(0.496226\pi\)
\(840\) 946419. 0.0462792
\(841\) −4.19572e6 −0.204558
\(842\) 4.15652e7 2.02046
\(843\) 918137. 0.0444978
\(844\) 3.10486e6 0.150032
\(845\) 7.60622e6 0.366461
\(846\) 1.92196e7 0.923248
\(847\) 971562. 0.0465331
\(848\) −4.54559e6 −0.217070
\(849\) −7.72855e6 −0.367984
\(850\) 303035. 0.0143862
\(851\) 1.38666e6 0.0656368
\(852\) −702476. −0.0331538
\(853\) −2.49242e7 −1.17287 −0.586433 0.809998i \(-0.699468\pi\)
−0.586433 + 0.809998i \(0.699468\pi\)
\(854\) 326732. 0.0153302
\(855\) 2.08118e6 0.0973631
\(856\) 1.83367e7 0.855336
\(857\) −2.26913e7 −1.05538 −0.527688 0.849438i \(-0.676941\pi\)
−0.527688 + 0.849438i \(0.676941\pi\)
\(858\) −676148. −0.0313562
\(859\) −4.02087e7 −1.85925 −0.929624 0.368510i \(-0.879868\pi\)
−0.929624 + 0.368510i \(0.879868\pi\)
\(860\) 1.57647e6 0.0726841
\(861\) 2.53655e6 0.116610
\(862\) 1.72135e7 0.789043
\(863\) −2.30864e6 −0.105518 −0.0527592 0.998607i \(-0.516802\pi\)
−0.0527592 + 0.998607i \(0.516802\pi\)
\(864\) 3.32411e6 0.151493
\(865\) 8.32246e6 0.378191
\(866\) 9.53134e6 0.431876
\(867\) 4.97744e6 0.224884
\(868\) 542074. 0.0244207
\(869\) 9.86139e6 0.442984
\(870\) −2.17929e6 −0.0976151
\(871\) 9.10874e6 0.406830
\(872\) 2.80124e7 1.24755
\(873\) 5.48689e6 0.243664
\(874\) 663834. 0.0293955
\(875\) −1.03686e6 −0.0457825
\(876\) −671503. −0.0295657
\(877\) −1.65067e7 −0.724705 −0.362353 0.932041i \(-0.618026\pi\)
−0.362353 + 0.932041i \(0.618026\pi\)
\(878\) −2.50704e7 −1.09755
\(879\) 5.09810e6 0.222554
\(880\) 3.54265e6 0.154213
\(881\) −3.31242e7 −1.43782 −0.718912 0.695101i \(-0.755360\pi\)
−0.718912 + 0.695101i \(0.755360\pi\)
\(882\) −1.75308e7 −0.758806
\(883\) 4.43697e7 1.91507 0.957535 0.288317i \(-0.0930958\pi\)
0.957535 + 0.288317i \(0.0930958\pi\)
\(884\) 114003. 0.00490665
\(885\) −698713. −0.0299875
\(886\) −2.46046e7 −1.05301
\(887\) 1.25234e7 0.534456 0.267228 0.963633i \(-0.413892\pi\)
0.267228 + 0.963633i \(0.413892\pi\)
\(888\) 2.63668e6 0.112209
\(889\) −5.91773e6 −0.251131
\(890\) −1.23763e7 −0.523741
\(891\) 6.06989e6 0.256145
\(892\) −1.43880e6 −0.0605463
\(893\) 4.90900e6 0.205999
\(894\) 3.11815e6 0.130483
\(895\) −3.09371e6 −0.129099
\(896\) −1.45060e7 −0.603641
\(897\) −273538. −0.0113511
\(898\) 1.58558e7 0.656140
\(899\) 5.92842e6 0.244647
\(900\) −802160. −0.0330107
\(901\) −307046. −0.0126006
\(902\) 8.05091e6 0.329480
\(903\) 2.64732e6 0.108041
\(904\) 3.24173e7 1.31934
\(905\) 1.32639e7 0.538332
\(906\) 5.86709e6 0.237467
\(907\) −3.99966e7 −1.61437 −0.807187 0.590295i \(-0.799011\pi\)
−0.807187 + 0.590295i \(0.799011\pi\)
\(908\) −5.20170e6 −0.209378
\(909\) −391908. −0.0157316
\(910\) −2.63279e6 −0.105393
\(911\) 2.53678e6 0.101272 0.0506358 0.998717i \(-0.483875\pi\)
0.0506358 + 0.998717i \(0.483875\pi\)
\(912\) 1.48864e6 0.0592657
\(913\) 1.88860e6 0.0749829
\(914\) −2.02685e7 −0.802519
\(915\) −70715.8 −0.00279231
\(916\) 3.57667e6 0.140845
\(917\) 2.39610e7 0.940981
\(918\) 808548. 0.0316664
\(919\) 1.96621e7 0.767963 0.383981 0.923341i \(-0.374553\pi\)
0.383981 + 0.923341i \(0.374553\pi\)
\(920\) 1.21524e6 0.0473359
\(921\) −3.53594e6 −0.137359
\(922\) 3.02657e7 1.17253
\(923\) −9.28140e6 −0.358599
\(924\) −157356. −0.00606323
\(925\) −2.88865e6 −0.111004
\(926\) −2.48633e7 −0.952866
\(927\) 8.92709e6 0.341201
\(928\) 8.05159e6 0.306910
\(929\) 2.75281e6 0.104650 0.0523248 0.998630i \(-0.483337\pi\)
0.0523248 + 0.998630i \(0.483337\pi\)
\(930\) −791873. −0.0300226
\(931\) −4.47766e6 −0.169308
\(932\) 7.26156e6 0.273836
\(933\) −4.72766e6 −0.177804
\(934\) 2.65459e6 0.0995705
\(935\) 239300. 0.00895185
\(936\) 9.67401e6 0.360925
\(937\) 6.87582e6 0.255844 0.127922 0.991784i \(-0.459169\pi\)
0.127922 + 0.991784i \(0.459169\pi\)
\(938\) 1.43078e7 0.530966
\(939\) −445096. −0.0164736
\(940\) −1.89210e6 −0.0698433
\(941\) 2.30189e7 0.847444 0.423722 0.905792i \(-0.360723\pi\)
0.423722 + 0.905792i \(0.360723\pi\)
\(942\) 1.55555e6 0.0571158
\(943\) 3.25702e6 0.119273
\(944\) 9.29569e6 0.339509
\(945\) −2.76652e6 −0.100775
\(946\) 8.40249e6 0.305267
\(947\) −2.03916e7 −0.738883 −0.369441 0.929254i \(-0.620451\pi\)
−0.369441 + 0.929254i \(0.620451\pi\)
\(948\) −1.59717e6 −0.0577206
\(949\) −8.87217e6 −0.319790
\(950\) −1.38287e6 −0.0497134
\(951\) 228117. 0.00817912
\(952\) −850511. −0.0304150
\(953\) −7.84956e6 −0.279971 −0.139985 0.990154i \(-0.544706\pi\)
−0.139985 + 0.990154i \(0.544706\pi\)
\(954\) 5.48586e6 0.195152
\(955\) 208618. 0.00740192
\(956\) 532138. 0.0188313
\(957\) −1.72094e6 −0.0607414
\(958\) 5.20084e6 0.183088
\(959\) −2.58236e7 −0.906713
\(960\) 2.22346e6 0.0778667
\(961\) −2.64750e7 −0.924756
\(962\) −7.33484e6 −0.255536
\(963\) −2.60988e7 −0.906889
\(964\) −4.21777e6 −0.146181
\(965\) −8.87417e6 −0.306767
\(966\) −429667. −0.0148146
\(967\) 1.61301e7 0.554716 0.277358 0.960767i \(-0.410541\pi\)
0.277358 + 0.960767i \(0.410541\pi\)
\(968\) 2.37211e6 0.0813666
\(969\) 100555. 0.00344028
\(970\) −3.64586e6 −0.124414
\(971\) 3.77106e7 1.28356 0.641779 0.766890i \(-0.278197\pi\)
0.641779 + 0.766890i \(0.278197\pi\)
\(972\) −3.23847e6 −0.109945
\(973\) 1.61342e7 0.546342
\(974\) −1.02289e6 −0.0345487
\(975\) 569824. 0.0191968
\(976\) 940805. 0.0316137
\(977\) −2.52479e7 −0.846232 −0.423116 0.906076i \(-0.639064\pi\)
−0.423116 + 0.906076i \(0.639064\pi\)
\(978\) 5.86962e6 0.196229
\(979\) −9.77329e6 −0.325900
\(980\) 1.72585e6 0.0574033
\(981\) −3.98703e7 −1.32275
\(982\) −4.87386e7 −1.61285
\(983\) −460177. −0.0151894 −0.00759471 0.999971i \(-0.502417\pi\)
−0.00759471 + 0.999971i \(0.502417\pi\)
\(984\) 6.19310e6 0.203901
\(985\) −1.03859e7 −0.341077
\(986\) 1.95845e6 0.0641533
\(987\) −3.17736e6 −0.103818
\(988\) −520243. −0.0169556
\(989\) 3.39925e6 0.110508
\(990\) −4.27547e6 −0.138642
\(991\) 1.33944e7 0.433252 0.216626 0.976255i \(-0.430495\pi\)
0.216626 + 0.976255i \(0.430495\pi\)
\(992\) 2.92565e6 0.0943937
\(993\) −2.22253e6 −0.0715278
\(994\) −1.45790e7 −0.468018
\(995\) 1.58566e7 0.507753
\(996\) −305881. −0.00977022
\(997\) −5.74306e7 −1.82981 −0.914904 0.403672i \(-0.867734\pi\)
−0.914904 + 0.403672i \(0.867734\pi\)
\(998\) 1.51149e7 0.480374
\(999\) −7.70740e6 −0.244340
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 1045.6.a.a.1.10 35
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.6.a.a.1.10 35 1.1 even 1 trivial