Properties

Label 966.4.a.l.1.5
Level $966$
Weight $4$
Character 966.1
Self dual yes
Analytic conductor $56.996$
Analytic rank $1$
Dimension $5$
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] = [966,4,Mod(1,966)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(966, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("966.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 966.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: \(56.9958450655\)
Analytic rank: \(1\)
Dimension: \(5\)
Coefficient field: \(\mathbb{Q}[x]/(x^{5} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{5} - 319x^{3} - 666x^{2} + 23460x + 101568 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-5.56964\) of defining polynomial
Character \(\chi\) \(=\) 966.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +10.3151 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +10.3151 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -20.6302 q^{10} -26.5800 q^{11} -12.0000 q^{12} +51.6261 q^{13} -14.0000 q^{14} -30.9454 q^{15} +16.0000 q^{16} -11.0220 q^{17} -18.0000 q^{18} -54.2997 q^{19} +41.2605 q^{20} -21.0000 q^{21} +53.1601 q^{22} -23.0000 q^{23} +24.0000 q^{24} -18.5983 q^{25} -103.252 q^{26} -27.0000 q^{27} +28.0000 q^{28} -310.900 q^{29} +61.8907 q^{30} +146.903 q^{31} -32.0000 q^{32} +79.7401 q^{33} +22.0441 q^{34} +72.2058 q^{35} +36.0000 q^{36} -230.486 q^{37} +108.599 q^{38} -154.878 q^{39} -82.5210 q^{40} +102.366 q^{41} +42.0000 q^{42} -224.105 q^{43} -106.320 q^{44} +92.8361 q^{45} +46.0000 q^{46} +197.357 q^{47} -48.0000 q^{48} +49.0000 q^{49} +37.1965 q^{50} +33.0661 q^{51} +206.504 q^{52} -577.290 q^{53} +54.0000 q^{54} -274.176 q^{55} -56.0000 q^{56} +162.899 q^{57} +621.800 q^{58} +360.111 q^{59} -123.781 q^{60} -24.5749 q^{61} -293.806 q^{62} +63.0000 q^{63} +64.0000 q^{64} +532.529 q^{65} -159.480 q^{66} +69.1973 q^{67} -44.0881 q^{68} +69.0000 q^{69} -144.412 q^{70} +213.781 q^{71} -72.0000 q^{72} -308.243 q^{73} +460.971 q^{74} +55.7948 q^{75} -217.199 q^{76} -186.060 q^{77} +309.757 q^{78} +1189.81 q^{79} +165.042 q^{80} +81.0000 q^{81} -204.731 q^{82} -134.809 q^{83} -84.0000 q^{84} -113.694 q^{85} +448.209 q^{86} +932.700 q^{87} +212.640 q^{88} +165.983 q^{89} -185.672 q^{90} +361.383 q^{91} -92.0000 q^{92} -440.710 q^{93} -394.714 q^{94} -560.108 q^{95} +96.0000 q^{96} +431.667 q^{97} -98.0000 q^{98} -239.220 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} - 15 q^{5} + 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 10 q^{2} - 15 q^{3} + 20 q^{4} - 15 q^{5} + 30 q^{6} + 35 q^{7} - 40 q^{8} + 45 q^{9} + 30 q^{10} - 19 q^{11} - 60 q^{12} - 19 q^{13} - 70 q^{14} + 45 q^{15} + 80 q^{16} - 42 q^{17} - 90 q^{18} - 25 q^{19} - 60 q^{20} - 105 q^{21} + 38 q^{22} - 115 q^{23} + 120 q^{24} + 206 q^{25} + 38 q^{26} - 135 q^{27} + 140 q^{28} - 292 q^{29} - 90 q^{30} - 60 q^{31} - 160 q^{32} + 57 q^{33} + 84 q^{34} - 105 q^{35} + 180 q^{36} + 264 q^{37} + 50 q^{38} + 57 q^{39} + 120 q^{40} + 223 q^{41} + 210 q^{42} + 661 q^{43} - 76 q^{44} - 135 q^{45} + 230 q^{46} - 279 q^{47} - 240 q^{48} + 245 q^{49} - 412 q^{50} + 126 q^{51} - 76 q^{52} - 324 q^{53} + 270 q^{54} + 1077 q^{55} - 280 q^{56} + 75 q^{57} + 584 q^{58} + 26 q^{59} + 180 q^{60} - 460 q^{61} + 120 q^{62} + 315 q^{63} + 320 q^{64} + 528 q^{65} - 114 q^{66} + 1541 q^{67} - 168 q^{68} + 345 q^{69} + 210 q^{70} - 319 q^{71} - 360 q^{72} + 1532 q^{73} - 528 q^{74} - 618 q^{75} - 100 q^{76} - 133 q^{77} - 114 q^{78} + 1242 q^{79} - 240 q^{80} + 405 q^{81} - 446 q^{82} - 1390 q^{83} - 420 q^{84} - 39 q^{85} - 1322 q^{86} + 876 q^{87} + 152 q^{88} - 1171 q^{89} + 270 q^{90} - 133 q^{91} - 460 q^{92} + 180 q^{93} + 558 q^{94} - 3435 q^{95} + 480 q^{96} - 1800 q^{97} - 490 q^{98} - 171 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 −0.707107
\(3\) −3.00000 −0.577350
\(4\) 4.00000 0.500000
\(5\) 10.3151 0.922612 0.461306 0.887241i \(-0.347381\pi\)
0.461306 + 0.887241i \(0.347381\pi\)
\(6\) 6.00000 0.408248
\(7\) 7.00000 0.377964
\(8\) −8.00000 −0.353553
\(9\) 9.00000 0.333333
\(10\) −20.6302 −0.652386
\(11\) −26.5800 −0.728562 −0.364281 0.931289i \(-0.618685\pi\)
−0.364281 + 0.931289i \(0.618685\pi\)
\(12\) −12.0000 −0.288675
\(13\) 51.6261 1.10142 0.550712 0.834696i \(-0.314356\pi\)
0.550712 + 0.834696i \(0.314356\pi\)
\(14\) −14.0000 −0.267261
\(15\) −30.9454 −0.532671
\(16\) 16.0000 0.250000
\(17\) −11.0220 −0.157249 −0.0786245 0.996904i \(-0.525053\pi\)
−0.0786245 + 0.996904i \(0.525053\pi\)
\(18\) −18.0000 −0.235702
\(19\) −54.2997 −0.655642 −0.327821 0.944740i \(-0.606314\pi\)
−0.327821 + 0.944740i \(0.606314\pi\)
\(20\) 41.2605 0.461306
\(21\) −21.0000 −0.218218
\(22\) 53.1601 0.515171
\(23\) −23.0000 −0.208514
\(24\) 24.0000 0.204124
\(25\) −18.5983 −0.148786
\(26\) −103.252 −0.778824
\(27\) −27.0000 −0.192450
\(28\) 28.0000 0.188982
\(29\) −310.900 −1.99078 −0.995392 0.0958941i \(-0.969429\pi\)
−0.995392 + 0.0958941i \(0.969429\pi\)
\(30\) 61.8907 0.376655
\(31\) 146.903 0.851116 0.425558 0.904931i \(-0.360078\pi\)
0.425558 + 0.904931i \(0.360078\pi\)
\(32\) −32.0000 −0.176777
\(33\) 79.7401 0.420635
\(34\) 22.0441 0.111192
\(35\) 72.2058 0.348715
\(36\) 36.0000 0.166667
\(37\) −230.486 −1.02410 −0.512049 0.858956i \(-0.671113\pi\)
−0.512049 + 0.858956i \(0.671113\pi\)
\(38\) 108.599 0.463609
\(39\) −154.878 −0.635907
\(40\) −82.5210 −0.326193
\(41\) 102.366 0.389923 0.194961 0.980811i \(-0.437542\pi\)
0.194961 + 0.980811i \(0.437542\pi\)
\(42\) 42.0000 0.154303
\(43\) −224.105 −0.794783 −0.397391 0.917649i \(-0.630084\pi\)
−0.397391 + 0.917649i \(0.630084\pi\)
\(44\) −106.320 −0.364281
\(45\) 92.8361 0.307537
\(46\) 46.0000 0.147442
\(47\) 197.357 0.612500 0.306250 0.951951i \(-0.400926\pi\)
0.306250 + 0.951951i \(0.400926\pi\)
\(48\) −48.0000 −0.144338
\(49\) 49.0000 0.142857
\(50\) 37.1965 0.105208
\(51\) 33.0661 0.0907878
\(52\) 206.504 0.550712
\(53\) −577.290 −1.49617 −0.748084 0.663604i \(-0.769026\pi\)
−0.748084 + 0.663604i \(0.769026\pi\)
\(54\) 54.0000 0.136083
\(55\) −274.176 −0.672180
\(56\) −56.0000 −0.133631
\(57\) 162.899 0.378535
\(58\) 621.800 1.40770
\(59\) 360.111 0.794618 0.397309 0.917685i \(-0.369944\pi\)
0.397309 + 0.917685i \(0.369944\pi\)
\(60\) −123.781 −0.266335
\(61\) −24.5749 −0.0515819 −0.0257910 0.999667i \(-0.508210\pi\)
−0.0257910 + 0.999667i \(0.508210\pi\)
\(62\) −293.806 −0.601830
\(63\) 63.0000 0.125988
\(64\) 64.0000 0.125000
\(65\) 532.529 1.01619
\(66\) −159.480 −0.297434
\(67\) 69.1973 0.126176 0.0630880 0.998008i \(-0.479905\pi\)
0.0630880 + 0.998008i \(0.479905\pi\)
\(68\) −44.0881 −0.0786245
\(69\) 69.0000 0.120386
\(70\) −144.412 −0.246579
\(71\) 213.781 0.357341 0.178670 0.983909i \(-0.442820\pi\)
0.178670 + 0.983909i \(0.442820\pi\)
\(72\) −72.0000 −0.117851
\(73\) −308.243 −0.494207 −0.247103 0.968989i \(-0.579479\pi\)
−0.247103 + 0.968989i \(0.579479\pi\)
\(74\) 460.971 0.724146
\(75\) 55.7948 0.0859017
\(76\) −217.199 −0.327821
\(77\) −186.060 −0.275371
\(78\) 309.757 0.449654
\(79\) 1189.81 1.69449 0.847244 0.531203i \(-0.178260\pi\)
0.847244 + 0.531203i \(0.178260\pi\)
\(80\) 165.042 0.230653
\(81\) 81.0000 0.111111
\(82\) −204.731 −0.275717
\(83\) −134.809 −0.178279 −0.0891395 0.996019i \(-0.528412\pi\)
−0.0891395 + 0.996019i \(0.528412\pi\)
\(84\) −84.0000 −0.109109
\(85\) −113.694 −0.145080
\(86\) 448.209 0.561996
\(87\) 932.700 1.14938
\(88\) 212.640 0.257586
\(89\) 165.983 0.197687 0.0988436 0.995103i \(-0.468486\pi\)
0.0988436 + 0.995103i \(0.468486\pi\)
\(90\) −185.672 −0.217462
\(91\) 361.383 0.416299
\(92\) −92.0000 −0.104257
\(93\) −440.710 −0.491392
\(94\) −394.714 −0.433103
\(95\) −560.108 −0.604903
\(96\) 96.0000 0.102062
\(97\) 431.667 0.451847 0.225923 0.974145i \(-0.427460\pi\)
0.225923 + 0.974145i \(0.427460\pi\)
\(98\) −98.0000 −0.101015
\(99\) −239.220 −0.242854
\(100\) −74.3931 −0.0743931
\(101\) −1678.66 −1.65379 −0.826894 0.562358i \(-0.809894\pi\)
−0.826894 + 0.562358i \(0.809894\pi\)
\(102\) −66.1322 −0.0641967
\(103\) 425.480 0.407027 0.203513 0.979072i \(-0.434764\pi\)
0.203513 + 0.979072i \(0.434764\pi\)
\(104\) −413.009 −0.389412
\(105\) −216.618 −0.201331
\(106\) 1154.58 1.05795
\(107\) 318.046 0.287352 0.143676 0.989625i \(-0.454108\pi\)
0.143676 + 0.989625i \(0.454108\pi\)
\(108\) −108.000 −0.0962250
\(109\) −572.896 −0.503427 −0.251713 0.967802i \(-0.580994\pi\)
−0.251713 + 0.967802i \(0.580994\pi\)
\(110\) 548.353 0.475303
\(111\) 691.457 0.591263
\(112\) 112.000 0.0944911
\(113\) −1079.47 −0.898652 −0.449326 0.893368i \(-0.648336\pi\)
−0.449326 + 0.893368i \(0.648336\pi\)
\(114\) −325.798 −0.267665
\(115\) −237.248 −0.192378
\(116\) −1243.60 −0.995392
\(117\) 464.635 0.367141
\(118\) −720.222 −0.561880
\(119\) −77.1542 −0.0594346
\(120\) 247.563 0.188327
\(121\) −624.502 −0.469197
\(122\) 49.1498 0.0364739
\(123\) −307.097 −0.225122
\(124\) 587.613 0.425558
\(125\) −1481.23 −1.05988
\(126\) −126.000 −0.0890871
\(127\) −919.985 −0.642799 −0.321399 0.946944i \(-0.604153\pi\)
−0.321399 + 0.946944i \(0.604153\pi\)
\(128\) −128.000 −0.0883883
\(129\) 672.314 0.458868
\(130\) −1065.06 −0.718553
\(131\) 2582.58 1.72245 0.861225 0.508223i \(-0.169698\pi\)
0.861225 + 0.508223i \(0.169698\pi\)
\(132\) 318.960 0.210318
\(133\) −380.098 −0.247809
\(134\) −138.395 −0.0892199
\(135\) −278.508 −0.177557
\(136\) 88.1762 0.0555959
\(137\) −789.026 −0.492052 −0.246026 0.969263i \(-0.579125\pi\)
−0.246026 + 0.969263i \(0.579125\pi\)
\(138\) −138.000 −0.0851257
\(139\) −1504.62 −0.918133 −0.459067 0.888402i \(-0.651816\pi\)
−0.459067 + 0.888402i \(0.651816\pi\)
\(140\) 288.823 0.174357
\(141\) −592.071 −0.353627
\(142\) −427.563 −0.252678
\(143\) −1372.22 −0.802455
\(144\) 144.000 0.0833333
\(145\) −3206.97 −1.83672
\(146\) 616.486 0.349457
\(147\) −147.000 −0.0824786
\(148\) −921.943 −0.512049
\(149\) −2635.88 −1.44926 −0.724630 0.689138i \(-0.757989\pi\)
−0.724630 + 0.689138i \(0.757989\pi\)
\(150\) −111.590 −0.0607417
\(151\) 116.042 0.0625388 0.0312694 0.999511i \(-0.490045\pi\)
0.0312694 + 0.999511i \(0.490045\pi\)
\(152\) 434.397 0.231804
\(153\) −99.1982 −0.0524164
\(154\) 372.120 0.194716
\(155\) 1515.32 0.785250
\(156\) −619.513 −0.317953
\(157\) 805.667 0.409549 0.204775 0.978809i \(-0.434354\pi\)
0.204775 + 0.978809i \(0.434354\pi\)
\(158\) −2379.63 −1.19818
\(159\) 1731.87 0.863813
\(160\) −330.084 −0.163096
\(161\) −161.000 −0.0788110
\(162\) −162.000 −0.0785674
\(163\) −2814.39 −1.35239 −0.676196 0.736722i \(-0.736373\pi\)
−0.676196 + 0.736722i \(0.736373\pi\)
\(164\) 409.463 0.194961
\(165\) 822.529 0.388084
\(166\) 269.617 0.126062
\(167\) −1809.34 −0.838390 −0.419195 0.907896i \(-0.637688\pi\)
−0.419195 + 0.907896i \(0.637688\pi\)
\(168\) 168.000 0.0771517
\(169\) 468.253 0.213133
\(170\) 227.387 0.102587
\(171\) −488.697 −0.218547
\(172\) −896.419 −0.397391
\(173\) −3254.97 −1.43047 −0.715233 0.698886i \(-0.753680\pi\)
−0.715233 + 0.698886i \(0.753680\pi\)
\(174\) −1865.40 −0.812734
\(175\) −130.188 −0.0562359
\(176\) −425.281 −0.182140
\(177\) −1080.33 −0.458773
\(178\) −331.966 −0.139786
\(179\) −3954.36 −1.65119 −0.825593 0.564266i \(-0.809159\pi\)
−0.825593 + 0.564266i \(0.809159\pi\)
\(180\) 371.344 0.153769
\(181\) −2310.90 −0.948995 −0.474498 0.880257i \(-0.657370\pi\)
−0.474498 + 0.880257i \(0.657370\pi\)
\(182\) −722.765 −0.294368
\(183\) 73.7248 0.0297808
\(184\) 184.000 0.0737210
\(185\) −2377.49 −0.944845
\(186\) 881.419 0.347467
\(187\) 292.966 0.114566
\(188\) 789.428 0.306250
\(189\) −189.000 −0.0727393
\(190\) 1120.22 0.427731
\(191\) −2662.01 −1.00846 −0.504232 0.863569i \(-0.668224\pi\)
−0.504232 + 0.863569i \(0.668224\pi\)
\(192\) −192.000 −0.0721688
\(193\) 2792.16 1.04137 0.520685 0.853749i \(-0.325677\pi\)
0.520685 + 0.853749i \(0.325677\pi\)
\(194\) −863.333 −0.319504
\(195\) −1597.59 −0.586696
\(196\) 196.000 0.0714286
\(197\) 917.766 0.331919 0.165960 0.986133i \(-0.446928\pi\)
0.165960 + 0.986133i \(0.446928\pi\)
\(198\) 478.441 0.171724
\(199\) 4426.36 1.57677 0.788383 0.615184i \(-0.210918\pi\)
0.788383 + 0.615184i \(0.210918\pi\)
\(200\) 148.786 0.0526039
\(201\) −207.592 −0.0728478
\(202\) 3357.31 1.16940
\(203\) −2176.30 −0.752445
\(204\) 132.264 0.0453939
\(205\) 1055.91 0.359748
\(206\) −850.960 −0.287812
\(207\) −207.000 −0.0695048
\(208\) 826.017 0.275356
\(209\) 1443.29 0.477676
\(210\) 433.235 0.142362
\(211\) 3054.43 0.996566 0.498283 0.867014i \(-0.333964\pi\)
0.498283 + 0.867014i \(0.333964\pi\)
\(212\) −2309.16 −0.748084
\(213\) −641.344 −0.206311
\(214\) −636.091 −0.203188
\(215\) −2311.67 −0.733276
\(216\) 216.000 0.0680414
\(217\) 1028.32 0.321692
\(218\) 1145.79 0.355976
\(219\) 924.729 0.285330
\(220\) −1096.71 −0.336090
\(221\) −569.024 −0.173198
\(222\) −1382.91 −0.418086
\(223\) 273.354 0.0820858 0.0410429 0.999157i \(-0.486932\pi\)
0.0410429 + 0.999157i \(0.486932\pi\)
\(224\) −224.000 −0.0668153
\(225\) −167.384 −0.0495954
\(226\) 2158.93 0.635443
\(227\) −2755.54 −0.805690 −0.402845 0.915268i \(-0.631979\pi\)
−0.402845 + 0.915268i \(0.631979\pi\)
\(228\) 651.596 0.189268
\(229\) 5096.83 1.47078 0.735388 0.677646i \(-0.237000\pi\)
0.735388 + 0.677646i \(0.237000\pi\)
\(230\) 474.496 0.136032
\(231\) 558.181 0.158985
\(232\) 2487.20 0.703848
\(233\) −1776.82 −0.499585 −0.249793 0.968299i \(-0.580362\pi\)
−0.249793 + 0.968299i \(0.580362\pi\)
\(234\) −929.270 −0.259608
\(235\) 2035.76 0.565100
\(236\) 1440.44 0.397309
\(237\) −3569.44 −0.978314
\(238\) 154.308 0.0420266
\(239\) −3910.70 −1.05842 −0.529209 0.848491i \(-0.677511\pi\)
−0.529209 + 0.848491i \(0.677511\pi\)
\(240\) −495.126 −0.133168
\(241\) −3272.18 −0.874604 −0.437302 0.899315i \(-0.644066\pi\)
−0.437302 + 0.899315i \(0.644066\pi\)
\(242\) 1249.00 0.331773
\(243\) −243.000 −0.0641500
\(244\) −98.2997 −0.0257910
\(245\) 505.441 0.131802
\(246\) 614.194 0.159185
\(247\) −2803.28 −0.722139
\(248\) −1175.23 −0.300915
\(249\) 404.426 0.102929
\(250\) 2962.47 0.749452
\(251\) −3253.33 −0.818121 −0.409060 0.912507i \(-0.634143\pi\)
−0.409060 + 0.912507i \(0.634143\pi\)
\(252\) 252.000 0.0629941
\(253\) 611.341 0.151916
\(254\) 1839.97 0.454527
\(255\) 341.081 0.0837620
\(256\) 256.000 0.0625000
\(257\) −1620.58 −0.393343 −0.196672 0.980469i \(-0.563013\pi\)
−0.196672 + 0.980469i \(0.563013\pi\)
\(258\) −1344.63 −0.324469
\(259\) −1613.40 −0.387073
\(260\) 2130.12 0.508093
\(261\) −2798.10 −0.663594
\(262\) −5165.16 −1.21796
\(263\) −2398.45 −0.562338 −0.281169 0.959658i \(-0.590722\pi\)
−0.281169 + 0.959658i \(0.590722\pi\)
\(264\) −637.921 −0.148717
\(265\) −5954.82 −1.38038
\(266\) 760.195 0.175228
\(267\) −497.949 −0.114135
\(268\) 276.789 0.0630880
\(269\) 4740.44 1.07446 0.537230 0.843436i \(-0.319471\pi\)
0.537230 + 0.843436i \(0.319471\pi\)
\(270\) 557.017 0.125552
\(271\) −1727.50 −0.387225 −0.193612 0.981078i \(-0.562020\pi\)
−0.193612 + 0.981078i \(0.562020\pi\)
\(272\) −176.352 −0.0393123
\(273\) −1084.15 −0.240350
\(274\) 1578.05 0.347933
\(275\) 494.343 0.108400
\(276\) 276.000 0.0601929
\(277\) 4704.28 1.02041 0.510203 0.860054i \(-0.329570\pi\)
0.510203 + 0.860054i \(0.329570\pi\)
\(278\) 3009.25 0.649218
\(279\) 1322.13 0.283705
\(280\) −577.647 −0.123289
\(281\) −5942.74 −1.26162 −0.630808 0.775939i \(-0.717276\pi\)
−0.630808 + 0.775939i \(0.717276\pi\)
\(282\) 1184.14 0.250052
\(283\) 4459.36 0.936684 0.468342 0.883547i \(-0.344851\pi\)
0.468342 + 0.883547i \(0.344851\pi\)
\(284\) 855.126 0.178670
\(285\) 1680.32 0.349241
\(286\) 2744.45 0.567421
\(287\) 716.560 0.147377
\(288\) −288.000 −0.0589256
\(289\) −4791.51 −0.975273
\(290\) 6413.95 1.29876
\(291\) −1295.00 −0.260874
\(292\) −1232.97 −0.247103
\(293\) 4888.30 0.974668 0.487334 0.873216i \(-0.337969\pi\)
0.487334 + 0.873216i \(0.337969\pi\)
\(294\) 294.000 0.0583212
\(295\) 3714.59 0.733124
\(296\) 1843.89 0.362073
\(297\) 717.661 0.140212
\(298\) 5271.76 1.02478
\(299\) −1187.40 −0.229663
\(300\) 223.179 0.0429509
\(301\) −1568.73 −0.300400
\(302\) −232.084 −0.0442216
\(303\) 5035.97 0.954815
\(304\) −868.794 −0.163910
\(305\) −253.493 −0.0475901
\(306\) 198.396 0.0370640
\(307\) −6956.41 −1.29324 −0.646618 0.762814i \(-0.723817\pi\)
−0.646618 + 0.762814i \(0.723817\pi\)
\(308\) −744.241 −0.137685
\(309\) −1276.44 −0.234997
\(310\) −3030.65 −0.555256
\(311\) −444.468 −0.0810400 −0.0405200 0.999179i \(-0.512901\pi\)
−0.0405200 + 0.999179i \(0.512901\pi\)
\(312\) 1239.03 0.224827
\(313\) 8317.74 1.50207 0.751033 0.660265i \(-0.229556\pi\)
0.751033 + 0.660265i \(0.229556\pi\)
\(314\) −1611.33 −0.289595
\(315\) 649.853 0.116238
\(316\) 4759.26 0.847244
\(317\) −2514.32 −0.445484 −0.222742 0.974877i \(-0.571501\pi\)
−0.222742 + 0.974877i \(0.571501\pi\)
\(318\) −3463.74 −0.610808
\(319\) 8263.74 1.45041
\(320\) 660.168 0.115327
\(321\) −954.137 −0.165903
\(322\) 322.000 0.0557278
\(323\) 598.492 0.103099
\(324\) 324.000 0.0555556
\(325\) −960.156 −0.163877
\(326\) 5628.77 0.956285
\(327\) 1718.69 0.290653
\(328\) −818.926 −0.137859
\(329\) 1381.50 0.231503
\(330\) −1645.06 −0.274416
\(331\) −4260.51 −0.707489 −0.353745 0.935342i \(-0.615092\pi\)
−0.353745 + 0.935342i \(0.615092\pi\)
\(332\) −539.234 −0.0891395
\(333\) −2074.37 −0.341366
\(334\) 3618.68 0.592831
\(335\) 713.778 0.116412
\(336\) −336.000 −0.0545545
\(337\) 8554.60 1.38278 0.691392 0.722479i \(-0.256998\pi\)
0.691392 + 0.722479i \(0.256998\pi\)
\(338\) −936.507 −0.150708
\(339\) 3238.40 0.518837
\(340\) −454.774 −0.0725400
\(341\) −3904.69 −0.620091
\(342\) 977.394 0.154536
\(343\) 343.000 0.0539949
\(344\) 1792.84 0.280998
\(345\) 711.743 0.111069
\(346\) 6509.94 1.01149
\(347\) −816.289 −0.126284 −0.0631422 0.998005i \(-0.520112\pi\)
−0.0631422 + 0.998005i \(0.520112\pi\)
\(348\) 3730.80 0.574690
\(349\) −10412.7 −1.59708 −0.798538 0.601945i \(-0.794393\pi\)
−0.798538 + 0.601945i \(0.794393\pi\)
\(350\) 260.376 0.0397648
\(351\) −1393.90 −0.211969
\(352\) 850.561 0.128793
\(353\) −1557.29 −0.234805 −0.117402 0.993084i \(-0.537457\pi\)
−0.117402 + 0.993084i \(0.537457\pi\)
\(354\) 2160.67 0.324401
\(355\) 2205.18 0.329687
\(356\) 663.932 0.0988436
\(357\) 231.463 0.0343146
\(358\) 7908.71 1.16757
\(359\) 1154.91 0.169788 0.0848938 0.996390i \(-0.472945\pi\)
0.0848938 + 0.996390i \(0.472945\pi\)
\(360\) −742.689 −0.108731
\(361\) −3910.55 −0.570134
\(362\) 4621.81 0.671041
\(363\) 1873.51 0.270891
\(364\) 1445.53 0.208149
\(365\) −3179.56 −0.455961
\(366\) −147.450 −0.0210582
\(367\) 6373.30 0.906495 0.453248 0.891385i \(-0.350265\pi\)
0.453248 + 0.891385i \(0.350265\pi\)
\(368\) −368.000 −0.0521286
\(369\) 921.291 0.129974
\(370\) 4754.98 0.668107
\(371\) −4041.03 −0.565498
\(372\) −1762.84 −0.245696
\(373\) 8965.73 1.24458 0.622289 0.782787i \(-0.286203\pi\)
0.622289 + 0.782787i \(0.286203\pi\)
\(374\) −585.932 −0.0810102
\(375\) 4443.70 0.611925
\(376\) −1578.86 −0.216551
\(377\) −16050.6 −2.19269
\(378\) 378.000 0.0514344
\(379\) −5837.30 −0.791139 −0.395570 0.918436i \(-0.629453\pi\)
−0.395570 + 0.918436i \(0.629453\pi\)
\(380\) −2240.43 −0.302452
\(381\) 2759.95 0.371120
\(382\) 5324.02 0.713091
\(383\) 11044.4 1.47348 0.736741 0.676175i \(-0.236364\pi\)
0.736741 + 0.676175i \(0.236364\pi\)
\(384\) 384.000 0.0510310
\(385\) −1919.23 −0.254060
\(386\) −5584.32 −0.736359
\(387\) −2016.94 −0.264928
\(388\) 1726.67 0.225923
\(389\) 3495.53 0.455605 0.227803 0.973707i \(-0.426846\pi\)
0.227803 + 0.973707i \(0.426846\pi\)
\(390\) 3195.18 0.414857
\(391\) 253.507 0.0327887
\(392\) −392.000 −0.0505076
\(393\) −7747.74 −0.994457
\(394\) −1835.53 −0.234703
\(395\) 12273.1 1.56336
\(396\) −956.881 −0.121427
\(397\) 603.402 0.0762818 0.0381409 0.999272i \(-0.487856\pi\)
0.0381409 + 0.999272i \(0.487856\pi\)
\(398\) −8852.73 −1.11494
\(399\) 1140.29 0.143073
\(400\) −297.572 −0.0371965
\(401\) 7929.97 0.987541 0.493771 0.869592i \(-0.335618\pi\)
0.493771 + 0.869592i \(0.335618\pi\)
\(402\) 415.184 0.0515111
\(403\) 7584.04 0.937439
\(404\) −6714.63 −0.826894
\(405\) 835.525 0.102512
\(406\) 4352.60 0.532059
\(407\) 6126.32 0.746119
\(408\) −264.529 −0.0320983
\(409\) −11257.3 −1.36098 −0.680488 0.732760i \(-0.738232\pi\)
−0.680488 + 0.732760i \(0.738232\pi\)
\(410\) −2111.83 −0.254380
\(411\) 2367.08 0.284086
\(412\) 1701.92 0.203513
\(413\) 2520.78 0.300337
\(414\) 414.000 0.0491473
\(415\) −1390.57 −0.164482
\(416\) −1652.03 −0.194706
\(417\) 4513.87 0.530084
\(418\) −2886.57 −0.337768
\(419\) −5241.74 −0.611159 −0.305579 0.952167i \(-0.598850\pi\)
−0.305579 + 0.952167i \(0.598850\pi\)
\(420\) −866.470 −0.100665
\(421\) 8393.67 0.971693 0.485846 0.874044i \(-0.338511\pi\)
0.485846 + 0.874044i \(0.338511\pi\)
\(422\) −6108.85 −0.704679
\(423\) 1776.21 0.204167
\(424\) 4618.32 0.528975
\(425\) 204.991 0.0233965
\(426\) 1282.69 0.145884
\(427\) −172.024 −0.0194961
\(428\) 1272.18 0.143676
\(429\) 4116.67 0.463298
\(430\) 4623.33 0.518505
\(431\) −14267.2 −1.59450 −0.797249 0.603651i \(-0.793712\pi\)
−0.797249 + 0.603651i \(0.793712\pi\)
\(432\) −432.000 −0.0481125
\(433\) −5685.40 −0.630999 −0.315500 0.948926i \(-0.602172\pi\)
−0.315500 + 0.948926i \(0.602172\pi\)
\(434\) −2056.64 −0.227470
\(435\) 9620.92 1.06043
\(436\) −2291.58 −0.251713
\(437\) 1248.89 0.136711
\(438\) −1849.46 −0.201759
\(439\) 5253.99 0.571206 0.285603 0.958348i \(-0.407806\pi\)
0.285603 + 0.958348i \(0.407806\pi\)
\(440\) 2193.41 0.237652
\(441\) 441.000 0.0476190
\(442\) 1138.05 0.122469
\(443\) 11033.4 1.18333 0.591664 0.806184i \(-0.298471\pi\)
0.591664 + 0.806184i \(0.298471\pi\)
\(444\) 2765.83 0.295632
\(445\) 1712.14 0.182389
\(446\) −546.708 −0.0580435
\(447\) 7907.64 0.836731
\(448\) 448.000 0.0472456
\(449\) −14836.1 −1.55937 −0.779685 0.626171i \(-0.784621\pi\)
−0.779685 + 0.626171i \(0.784621\pi\)
\(450\) 334.769 0.0350692
\(451\) −2720.88 −0.284083
\(452\) −4317.87 −0.449326
\(453\) −348.126 −0.0361068
\(454\) 5511.08 0.569709
\(455\) 3727.71 0.384083
\(456\) −1303.19 −0.133832
\(457\) −9660.95 −0.988884 −0.494442 0.869211i \(-0.664628\pi\)
−0.494442 + 0.869211i \(0.664628\pi\)
\(458\) −10193.7 −1.04000
\(459\) 297.595 0.0302626
\(460\) −948.991 −0.0961890
\(461\) 11397.9 1.15153 0.575765 0.817615i \(-0.304704\pi\)
0.575765 + 0.817615i \(0.304704\pi\)
\(462\) −1116.36 −0.112420
\(463\) −85.1822 −0.00855022 −0.00427511 0.999991i \(-0.501361\pi\)
−0.00427511 + 0.999991i \(0.501361\pi\)
\(464\) −4974.40 −0.497696
\(465\) −4545.97 −0.453364
\(466\) 3553.64 0.353260
\(467\) 5205.23 0.515780 0.257890 0.966174i \(-0.416973\pi\)
0.257890 + 0.966174i \(0.416973\pi\)
\(468\) 1858.54 0.183571
\(469\) 484.381 0.0476901
\(470\) −4071.52 −0.399586
\(471\) −2417.00 −0.236453
\(472\) −2880.89 −0.280940
\(473\) 5956.71 0.579048
\(474\) 7138.89 0.691772
\(475\) 1009.88 0.0975505
\(476\) −308.617 −0.0297173
\(477\) −5195.61 −0.498723
\(478\) 7821.40 0.748415
\(479\) −2379.83 −0.227009 −0.113504 0.993537i \(-0.536208\pi\)
−0.113504 + 0.993537i \(0.536208\pi\)
\(480\) 990.252 0.0941637
\(481\) −11899.1 −1.12796
\(482\) 6544.36 0.618439
\(483\) 483.000 0.0455016
\(484\) −2498.01 −0.234599
\(485\) 4452.69 0.416879
\(486\) 486.000 0.0453609
\(487\) −17.3278 −0.00161231 −0.000806157 1.00000i \(-0.500257\pi\)
−0.000806157 1.00000i \(0.500257\pi\)
\(488\) 196.599 0.0182370
\(489\) 8443.16 0.780804
\(490\) −1010.88 −0.0931979
\(491\) 5073.91 0.466359 0.233179 0.972434i \(-0.425087\pi\)
0.233179 + 0.972434i \(0.425087\pi\)
\(492\) −1228.39 −0.112561
\(493\) 3426.75 0.313049
\(494\) 5606.56 0.510629
\(495\) −2467.59 −0.224060
\(496\) 2350.45 0.212779
\(497\) 1496.47 0.135062
\(498\) −808.851 −0.0727821
\(499\) 2523.93 0.226426 0.113213 0.993571i \(-0.463886\pi\)
0.113213 + 0.993571i \(0.463886\pi\)
\(500\) −5924.93 −0.529942
\(501\) 5428.03 0.484045
\(502\) 6506.66 0.578499
\(503\) −17881.7 −1.58510 −0.792548 0.609809i \(-0.791246\pi\)
−0.792548 + 0.609809i \(0.791246\pi\)
\(504\) −504.000 −0.0445435
\(505\) −17315.5 −1.52581
\(506\) −1222.68 −0.107421
\(507\) −1404.76 −0.123052
\(508\) −3679.94 −0.321399
\(509\) −14906.1 −1.29804 −0.649019 0.760772i \(-0.724821\pi\)
−0.649019 + 0.760772i \(0.724821\pi\)
\(510\) −682.161 −0.0592286
\(511\) −2157.70 −0.186793
\(512\) −512.000 −0.0441942
\(513\) 1466.09 0.126178
\(514\) 3241.17 0.278136
\(515\) 4388.88 0.375528
\(516\) 2689.26 0.229434
\(517\) −5245.76 −0.446244
\(518\) 3226.80 0.273702
\(519\) 9764.91 0.825880
\(520\) −4260.24 −0.359276
\(521\) 13724.6 1.15410 0.577049 0.816710i \(-0.304204\pi\)
0.577049 + 0.816710i \(0.304204\pi\)
\(522\) 5596.20 0.469232
\(523\) −261.061 −0.0218268 −0.0109134 0.999940i \(-0.503474\pi\)
−0.0109134 + 0.999940i \(0.503474\pi\)
\(524\) 10330.3 0.861225
\(525\) 390.564 0.0324678
\(526\) 4796.91 0.397633
\(527\) −1619.17 −0.133837
\(528\) 1275.84 0.105159
\(529\) 529.000 0.0434783
\(530\) 11909.6 0.976078
\(531\) 3241.00 0.264873
\(532\) −1520.39 −0.123905
\(533\) 5284.74 0.429470
\(534\) 995.898 0.0807055
\(535\) 3280.68 0.265114
\(536\) −553.578 −0.0446100
\(537\) 11863.1 0.953313
\(538\) −9480.88 −0.759758
\(539\) −1302.42 −0.104080
\(540\) −1114.03 −0.0887784
\(541\) 8406.10 0.668034 0.334017 0.942567i \(-0.391596\pi\)
0.334017 + 0.942567i \(0.391596\pi\)
\(542\) 3454.99 0.273809
\(543\) 6932.71 0.547903
\(544\) 352.705 0.0277980
\(545\) −5909.49 −0.464468
\(546\) 2168.30 0.169953
\(547\) 12280.1 0.959888 0.479944 0.877299i \(-0.340657\pi\)
0.479944 + 0.877299i \(0.340657\pi\)
\(548\) −3156.11 −0.246026
\(549\) −221.174 −0.0171940
\(550\) −988.685 −0.0766503
\(551\) 16881.8 1.30524
\(552\) −552.000 −0.0425628
\(553\) 8328.70 0.640457
\(554\) −9408.55 −0.721536
\(555\) 7132.46 0.545507
\(556\) −6018.50 −0.459067
\(557\) 6430.03 0.489137 0.244569 0.969632i \(-0.421354\pi\)
0.244569 + 0.969632i \(0.421354\pi\)
\(558\) −2644.26 −0.200610
\(559\) −11569.7 −0.875392
\(560\) 1155.29 0.0871787
\(561\) −878.898 −0.0661445
\(562\) 11885.5 0.892097
\(563\) −6302.21 −0.471770 −0.235885 0.971781i \(-0.575799\pi\)
−0.235885 + 0.971781i \(0.575799\pi\)
\(564\) −2368.28 −0.176813
\(565\) −11134.8 −0.829108
\(566\) −8918.73 −0.662336
\(567\) 567.000 0.0419961
\(568\) −1710.25 −0.126339
\(569\) 2751.75 0.202740 0.101370 0.994849i \(-0.467677\pi\)
0.101370 + 0.994849i \(0.467677\pi\)
\(570\) −3360.65 −0.246951
\(571\) 15093.6 1.10621 0.553105 0.833112i \(-0.313443\pi\)
0.553105 + 0.833112i \(0.313443\pi\)
\(572\) −5488.89 −0.401228
\(573\) 7986.04 0.582236
\(574\) −1433.12 −0.104211
\(575\) 427.760 0.0310241
\(576\) 576.000 0.0416667
\(577\) 20704.9 1.49386 0.746928 0.664904i \(-0.231528\pi\)
0.746928 + 0.664904i \(0.231528\pi\)
\(578\) 9583.03 0.689622
\(579\) −8376.49 −0.601235
\(580\) −12827.9 −0.918361
\(581\) −943.660 −0.0673831
\(582\) 2590.00 0.184466
\(583\) 15344.4 1.09005
\(584\) 2465.94 0.174729
\(585\) 4792.76 0.338729
\(586\) −9776.61 −0.689194
\(587\) −18630.0 −1.30995 −0.654976 0.755650i \(-0.727321\pi\)
−0.654976 + 0.755650i \(0.727321\pi\)
\(588\) −588.000 −0.0412393
\(589\) −7976.79 −0.558027
\(590\) −7429.17 −0.518397
\(591\) −2753.30 −0.191634
\(592\) −3687.77 −0.256024
\(593\) 9724.26 0.673402 0.336701 0.941612i \(-0.390689\pi\)
0.336701 + 0.941612i \(0.390689\pi\)
\(594\) −1435.32 −0.0991447
\(595\) −795.855 −0.0548351
\(596\) −10543.5 −0.724630
\(597\) −13279.1 −0.910347
\(598\) 2374.80 0.162396
\(599\) −11688.9 −0.797324 −0.398662 0.917098i \(-0.630525\pi\)
−0.398662 + 0.917098i \(0.630525\pi\)
\(600\) −446.359 −0.0303709
\(601\) −27475.5 −1.86481 −0.932405 0.361416i \(-0.882293\pi\)
−0.932405 + 0.361416i \(0.882293\pi\)
\(602\) 3137.47 0.212415
\(603\) 622.776 0.0420587
\(604\) 464.168 0.0312694
\(605\) −6441.81 −0.432887
\(606\) −10071.9 −0.675156
\(607\) 18175.7 1.21537 0.607685 0.794178i \(-0.292098\pi\)
0.607685 + 0.794178i \(0.292098\pi\)
\(608\) 1737.59 0.115902
\(609\) 6528.90 0.434424
\(610\) 506.987 0.0336513
\(611\) 10188.8 0.674621
\(612\) −396.793 −0.0262082
\(613\) 13946.9 0.918940 0.459470 0.888193i \(-0.348039\pi\)
0.459470 + 0.888193i \(0.348039\pi\)
\(614\) 13912.8 0.914455
\(615\) −3167.74 −0.207700
\(616\) 1488.48 0.0973582
\(617\) 12686.5 0.827780 0.413890 0.910327i \(-0.364170\pi\)
0.413890 + 0.910327i \(0.364170\pi\)
\(618\) 2552.88 0.166168
\(619\) −11200.5 −0.727282 −0.363641 0.931539i \(-0.618467\pi\)
−0.363641 + 0.931539i \(0.618467\pi\)
\(620\) 6061.30 0.392625
\(621\) 621.000 0.0401286
\(622\) 888.935 0.0573040
\(623\) 1161.88 0.0747188
\(624\) −2478.05 −0.158977
\(625\) −12954.3 −0.829076
\(626\) −16635.5 −1.06212
\(627\) −4329.86 −0.275786
\(628\) 3222.67 0.204775
\(629\) 2540.42 0.161038
\(630\) −1299.71 −0.0821929
\(631\) −17301.2 −1.09152 −0.545761 0.837941i \(-0.683759\pi\)
−0.545761 + 0.837941i \(0.683759\pi\)
\(632\) −9518.52 −0.599092
\(633\) −9163.28 −0.575368
\(634\) 5028.65 0.315005
\(635\) −9489.76 −0.593054
\(636\) 6927.48 0.431906
\(637\) 2529.68 0.157346
\(638\) −16527.5 −1.02559
\(639\) 1924.03 0.119114
\(640\) −1320.34 −0.0815482
\(641\) 23278.1 1.43437 0.717183 0.696885i \(-0.245431\pi\)
0.717183 + 0.696885i \(0.245431\pi\)
\(642\) 1908.27 0.117311
\(643\) −3495.34 −0.214374 −0.107187 0.994239i \(-0.534184\pi\)
−0.107187 + 0.994239i \(0.534184\pi\)
\(644\) −644.000 −0.0394055
\(645\) 6935.00 0.423357
\(646\) −1196.98 −0.0729021
\(647\) 28365.2 1.72357 0.861787 0.507271i \(-0.169346\pi\)
0.861787 + 0.507271i \(0.169346\pi\)
\(648\) −648.000 −0.0392837
\(649\) −9571.76 −0.578928
\(650\) 1920.31 0.115878
\(651\) −3084.97 −0.185729
\(652\) −11257.5 −0.676196
\(653\) 3225.35 0.193289 0.0966444 0.995319i \(-0.469189\pi\)
0.0966444 + 0.995319i \(0.469189\pi\)
\(654\) −3437.38 −0.205523
\(655\) 26639.6 1.58915
\(656\) 1637.85 0.0974807
\(657\) −2774.19 −0.164736
\(658\) −2763.00 −0.163697
\(659\) −1969.27 −0.116407 −0.0582033 0.998305i \(-0.518537\pi\)
−0.0582033 + 0.998305i \(0.518537\pi\)
\(660\) 3290.12 0.194042
\(661\) −17204.2 −1.01235 −0.506177 0.862430i \(-0.668942\pi\)
−0.506177 + 0.862430i \(0.668942\pi\)
\(662\) 8521.02 0.500270
\(663\) 1707.07 0.0999958
\(664\) 1078.47 0.0630311
\(665\) −3920.75 −0.228632
\(666\) 4148.74 0.241382
\(667\) 7150.70 0.415107
\(668\) −7237.37 −0.419195
\(669\) −820.062 −0.0473923
\(670\) −1427.56 −0.0823154
\(671\) 653.202 0.0375806
\(672\) 672.000 0.0385758
\(673\) −20587.6 −1.17919 −0.589595 0.807699i \(-0.700713\pi\)
−0.589595 + 0.807699i \(0.700713\pi\)
\(674\) −17109.2 −0.977777
\(675\) 502.153 0.0286339
\(676\) 1873.01 0.106567
\(677\) 14983.0 0.850584 0.425292 0.905056i \(-0.360171\pi\)
0.425292 + 0.905056i \(0.360171\pi\)
\(678\) −6476.80 −0.366873
\(679\) 3021.67 0.170782
\(680\) 909.548 0.0512935
\(681\) 8266.62 0.465165
\(682\) 7809.38 0.438470
\(683\) 10817.8 0.606050 0.303025 0.952983i \(-0.402003\pi\)
0.303025 + 0.952983i \(0.402003\pi\)
\(684\) −1954.79 −0.109274
\(685\) −8138.90 −0.453973
\(686\) −686.000 −0.0381802
\(687\) −15290.5 −0.849153
\(688\) −3585.68 −0.198696
\(689\) −29803.2 −1.64791
\(690\) −1423.49 −0.0785380
\(691\) −24646.1 −1.35685 −0.678425 0.734670i \(-0.737337\pi\)
−0.678425 + 0.734670i \(0.737337\pi\)
\(692\) −13019.9 −0.715233
\(693\) −1674.54 −0.0917902
\(694\) 1632.58 0.0892966
\(695\) −15520.4 −0.847081
\(696\) −7461.60 −0.406367
\(697\) −1128.28 −0.0613150
\(698\) 20825.4 1.12930
\(699\) 5330.46 0.288436
\(700\) −520.752 −0.0281179
\(701\) −29986.4 −1.61565 −0.807824 0.589423i \(-0.799355\pi\)
−0.807824 + 0.589423i \(0.799355\pi\)
\(702\) 2787.81 0.149885
\(703\) 12515.3 0.671441
\(704\) −1701.12 −0.0910702
\(705\) −6107.29 −0.326261
\(706\) 3114.58 0.166032
\(707\) −11750.6 −0.625073
\(708\) −4321.33 −0.229386
\(709\) −8413.34 −0.445655 −0.222828 0.974858i \(-0.571529\pi\)
−0.222828 + 0.974858i \(0.571529\pi\)
\(710\) −4410.36 −0.233124
\(711\) 10708.3 0.564830
\(712\) −1327.86 −0.0698930
\(713\) −3378.77 −0.177470
\(714\) −462.925 −0.0242641
\(715\) −14154.6 −0.740355
\(716\) −15817.4 −0.825593
\(717\) 11732.1 0.611078
\(718\) −2309.82 −0.120058
\(719\) 12474.8 0.647055 0.323528 0.946219i \(-0.395131\pi\)
0.323528 + 0.946219i \(0.395131\pi\)
\(720\) 1485.38 0.0768844
\(721\) 2978.36 0.153842
\(722\) 7821.09 0.403145
\(723\) 9816.54 0.504953
\(724\) −9243.62 −0.474498
\(725\) 5782.21 0.296201
\(726\) −3747.01 −0.191549
\(727\) 2009.59 0.102519 0.0512597 0.998685i \(-0.483676\pi\)
0.0512597 + 0.998685i \(0.483676\pi\)
\(728\) −2891.06 −0.147184
\(729\) 729.000 0.0370370
\(730\) 6359.13 0.322413
\(731\) 2470.09 0.124979
\(732\) 294.899 0.0148904
\(733\) −30858.6 −1.55496 −0.777482 0.628905i \(-0.783504\pi\)
−0.777482 + 0.628905i \(0.783504\pi\)
\(734\) −12746.6 −0.640989
\(735\) −1516.32 −0.0760958
\(736\) 736.000 0.0368605
\(737\) −1839.27 −0.0919271
\(738\) −1842.58 −0.0919057
\(739\) 27765.2 1.38208 0.691042 0.722814i \(-0.257152\pi\)
0.691042 + 0.722814i \(0.257152\pi\)
\(740\) −9509.95 −0.472423
\(741\) 8409.84 0.416927
\(742\) 8082.06 0.399868
\(743\) 11628.5 0.574171 0.287085 0.957905i \(-0.407314\pi\)
0.287085 + 0.957905i \(0.407314\pi\)
\(744\) 3525.68 0.173733
\(745\) −27189.4 −1.33711
\(746\) −17931.5 −0.880050
\(747\) −1213.28 −0.0594263
\(748\) 1171.86 0.0572828
\(749\) 2226.32 0.108609
\(750\) −8887.40 −0.432696
\(751\) 25645.6 1.24610 0.623050 0.782182i \(-0.285893\pi\)
0.623050 + 0.782182i \(0.285893\pi\)
\(752\) 3157.71 0.153125
\(753\) 9759.98 0.472342
\(754\) 32101.1 1.55047
\(755\) 1196.99 0.0576991
\(756\) −756.000 −0.0363696
\(757\) 4553.97 0.218649 0.109324 0.994006i \(-0.465131\pi\)
0.109324 + 0.994006i \(0.465131\pi\)
\(758\) 11674.6 0.559420
\(759\) −1834.02 −0.0877086
\(760\) 4480.86 0.213866
\(761\) −874.513 −0.0416571 −0.0208286 0.999783i \(-0.506630\pi\)
−0.0208286 + 0.999783i \(0.506630\pi\)
\(762\) −5519.91 −0.262422
\(763\) −4010.27 −0.190277
\(764\) −10648.0 −0.504232
\(765\) −1023.24 −0.0483600
\(766\) −22088.8 −1.04191
\(767\) 18591.1 0.875210
\(768\) −768.000 −0.0360844
\(769\) 10434.0 0.489286 0.244643 0.969613i \(-0.421329\pi\)
0.244643 + 0.969613i \(0.421329\pi\)
\(770\) 3838.47 0.179648
\(771\) 4861.75 0.227097
\(772\) 11168.6 0.520685
\(773\) −7118.89 −0.331240 −0.165620 0.986190i \(-0.552963\pi\)
−0.165620 + 0.986190i \(0.552963\pi\)
\(774\) 4033.89 0.187332
\(775\) −2732.15 −0.126634
\(776\) −3453.33 −0.159752
\(777\) 4840.20 0.223476
\(778\) −6991.06 −0.322161
\(779\) −5558.42 −0.255650
\(780\) −6390.35 −0.293348
\(781\) −5682.32 −0.260345
\(782\) −507.013 −0.0231851
\(783\) 8394.30 0.383126
\(784\) 784.000 0.0357143
\(785\) 8310.55 0.377855
\(786\) 15495.5 0.703187
\(787\) −20000.3 −0.905890 −0.452945 0.891539i \(-0.649627\pi\)
−0.452945 + 0.891539i \(0.649627\pi\)
\(788\) 3671.06 0.165960
\(789\) 7195.36 0.324666
\(790\) −24546.2 −1.10546
\(791\) −7556.27 −0.339659
\(792\) 1913.76 0.0858619
\(793\) −1268.71 −0.0568135
\(794\) −1206.80 −0.0539394
\(795\) 17864.4 0.796964
\(796\) 17705.5 0.788383
\(797\) −22900.8 −1.01780 −0.508900 0.860826i \(-0.669948\pi\)
−0.508900 + 0.860826i \(0.669948\pi\)
\(798\) −2280.59 −0.101168
\(799\) −2175.27 −0.0963150
\(800\) 595.145 0.0263019
\(801\) 1493.85 0.0658958
\(802\) −15859.9 −0.698297
\(803\) 8193.11 0.360060
\(804\) −830.367 −0.0364239
\(805\) −1660.73 −0.0727121
\(806\) −15168.1 −0.662869
\(807\) −14221.3 −0.620340
\(808\) 13429.3 0.584702
\(809\) −14228.0 −0.618332 −0.309166 0.951008i \(-0.600050\pi\)
−0.309166 + 0.951008i \(0.600050\pi\)
\(810\) −1671.05 −0.0724873
\(811\) −6818.47 −0.295227 −0.147613 0.989045i \(-0.547159\pi\)
−0.147613 + 0.989045i \(0.547159\pi\)
\(812\) −8705.20 −0.376223
\(813\) 5182.49 0.223564
\(814\) −12252.6 −0.527586
\(815\) −29030.7 −1.24773
\(816\) 529.057 0.0226969
\(817\) 12168.8 0.521093
\(818\) 22514.6 0.962355
\(819\) 3252.44 0.138766
\(820\) 4223.66 0.179874
\(821\) −9205.60 −0.391325 −0.195662 0.980671i \(-0.562686\pi\)
−0.195662 + 0.980671i \(0.562686\pi\)
\(822\) −4734.16 −0.200879
\(823\) −8350.74 −0.353692 −0.176846 0.984239i \(-0.556589\pi\)
−0.176846 + 0.984239i \(0.556589\pi\)
\(824\) −3403.84 −0.143906
\(825\) −1483.03 −0.0625847
\(826\) −5041.55 −0.212371
\(827\) −45162.5 −1.89898 −0.949488 0.313802i \(-0.898397\pi\)
−0.949488 + 0.313802i \(0.898397\pi\)
\(828\) −828.000 −0.0347524
\(829\) 27508.8 1.15250 0.576248 0.817275i \(-0.304516\pi\)
0.576248 + 0.817275i \(0.304516\pi\)
\(830\) 2781.13 0.116307
\(831\) −14112.8 −0.589132
\(832\) 3304.07 0.137678
\(833\) −540.079 −0.0224642
\(834\) −9027.74 −0.374826
\(835\) −18663.6 −0.773509
\(836\) 5773.15 0.238838
\(837\) −3966.39 −0.163797
\(838\) 10483.5 0.432155
\(839\) 35911.5 1.47771 0.738857 0.673862i \(-0.235366\pi\)
0.738857 + 0.673862i \(0.235366\pi\)
\(840\) 1732.94 0.0711811
\(841\) 72269.9 2.96322
\(842\) −16787.3 −0.687090
\(843\) 17828.2 0.728394
\(844\) 12217.7 0.498283
\(845\) 4830.09 0.196639
\(846\) −3552.43 −0.144368
\(847\) −4371.51 −0.177340
\(848\) −9236.64 −0.374042
\(849\) −13378.1 −0.540795
\(850\) −409.981 −0.0165438
\(851\) 5301.17 0.213539
\(852\) −2565.38 −0.103155
\(853\) −928.378 −0.0372650 −0.0186325 0.999826i \(-0.505931\pi\)
−0.0186325 + 0.999826i \(0.505931\pi\)
\(854\) 344.049 0.0137858
\(855\) −5040.97 −0.201634
\(856\) −2544.36 −0.101594
\(857\) 28986.8 1.15539 0.577696 0.816252i \(-0.303952\pi\)
0.577696 + 0.816252i \(0.303952\pi\)
\(858\) −8233.34 −0.327601
\(859\) −42067.7 −1.67093 −0.835466 0.549542i \(-0.814802\pi\)
−0.835466 + 0.549542i \(0.814802\pi\)
\(860\) −9246.67 −0.366638
\(861\) −2149.68 −0.0850881
\(862\) 28534.5 1.12748
\(863\) −19844.8 −0.782764 −0.391382 0.920228i \(-0.628003\pi\)
−0.391382 + 0.920228i \(0.628003\pi\)
\(864\) 864.000 0.0340207
\(865\) −33575.4 −1.31977
\(866\) 11370.8 0.446184
\(867\) 14374.5 0.563074
\(868\) 4113.29 0.160846
\(869\) −31625.3 −1.23454
\(870\) −19241.8 −0.749838
\(871\) 3572.39 0.138973
\(872\) 4583.17 0.177988
\(873\) 3885.00 0.150616
\(874\) −2497.78 −0.0966691
\(875\) −10368.6 −0.400599
\(876\) 3698.91 0.142665
\(877\) −13668.2 −0.526273 −0.263136 0.964759i \(-0.584757\pi\)
−0.263136 + 0.964759i \(0.584757\pi\)
\(878\) −10508.0 −0.403904
\(879\) −14664.9 −0.562725
\(880\) −4386.82 −0.168045
\(881\) −11477.4 −0.438916 −0.219458 0.975622i \(-0.570429\pi\)
−0.219458 + 0.975622i \(0.570429\pi\)
\(882\) −882.000 −0.0336718
\(883\) 5768.82 0.219860 0.109930 0.993939i \(-0.464937\pi\)
0.109930 + 0.993939i \(0.464937\pi\)
\(884\) −2276.10 −0.0865989
\(885\) −11143.8 −0.423269
\(886\) −22066.9 −0.836740
\(887\) 23527.1 0.890602 0.445301 0.895381i \(-0.353097\pi\)
0.445301 + 0.895381i \(0.353097\pi\)
\(888\) −5531.66 −0.209043
\(889\) −6439.89 −0.242955
\(890\) −3424.27 −0.128968
\(891\) −2152.98 −0.0809513
\(892\) 1093.42 0.0410429
\(893\) −10716.4 −0.401580
\(894\) −15815.3 −0.591658
\(895\) −40789.7 −1.52341
\(896\) −896.000 −0.0334077
\(897\) 3562.20 0.132596
\(898\) 29672.1 1.10264
\(899\) −45672.2 −1.69439
\(900\) −669.538 −0.0247977
\(901\) 6362.91 0.235271
\(902\) 5441.77 0.200877
\(903\) 4706.20 0.173436
\(904\) 8635.73 0.317722
\(905\) −23837.3 −0.875555
\(906\) 696.252 0.0255314
\(907\) −11549.8 −0.422827 −0.211413 0.977397i \(-0.567807\pi\)
−0.211413 + 0.977397i \(0.567807\pi\)
\(908\) −11022.2 −0.402845
\(909\) −15107.9 −0.551263
\(910\) −7455.41 −0.271587
\(911\) −27036.2 −0.983261 −0.491630 0.870804i \(-0.663599\pi\)
−0.491630 + 0.870804i \(0.663599\pi\)
\(912\) 2606.38 0.0946338
\(913\) 3583.21 0.129887
\(914\) 19321.9 0.699247
\(915\) 760.480 0.0274762
\(916\) 20387.3 0.735388
\(917\) 18078.1 0.651025
\(918\) −595.189 −0.0213989
\(919\) −2635.88 −0.0946132 −0.0473066 0.998880i \(-0.515064\pi\)
−0.0473066 + 0.998880i \(0.515064\pi\)
\(920\) 1897.98 0.0680159
\(921\) 20869.2 0.746650
\(922\) −22795.9 −0.814255
\(923\) 11036.7 0.393583
\(924\) 2232.72 0.0794926
\(925\) 4286.64 0.152372
\(926\) 170.364 0.00604592
\(927\) 3829.32 0.135676
\(928\) 9948.80 0.351924
\(929\) −48008.9 −1.69550 −0.847751 0.530395i \(-0.822044\pi\)
−0.847751 + 0.530395i \(0.822044\pi\)
\(930\) 9091.94 0.320577
\(931\) −2660.68 −0.0936631
\(932\) −7107.28 −0.249793
\(933\) 1333.40 0.0467885
\(934\) −10410.5 −0.364712
\(935\) 3021.98 0.105700
\(936\) −3717.08 −0.129804
\(937\) −11442.4 −0.398940 −0.199470 0.979904i \(-0.563922\pi\)
−0.199470 + 0.979904i \(0.563922\pi\)
\(938\) −968.762 −0.0337220
\(939\) −24953.2 −0.867218
\(940\) 8143.05 0.282550
\(941\) 53365.5 1.84874 0.924371 0.381496i \(-0.124591\pi\)
0.924371 + 0.381496i \(0.124591\pi\)
\(942\) 4834.00 0.167198
\(943\) −2354.41 −0.0813045
\(944\) 5761.77 0.198654
\(945\) −1949.56 −0.0671102
\(946\) −11913.4 −0.409449
\(947\) 19151.9 0.657183 0.328592 0.944472i \(-0.393426\pi\)
0.328592 + 0.944472i \(0.393426\pi\)
\(948\) −14277.8 −0.489157
\(949\) −15913.4 −0.544331
\(950\) −2019.76 −0.0689786
\(951\) 7542.97 0.257200
\(952\) 617.234 0.0210133
\(953\) −5300.55 −0.180170 −0.0900849 0.995934i \(-0.528714\pi\)
−0.0900849 + 0.995934i \(0.528714\pi\)
\(954\) 10391.2 0.352650
\(955\) −27459.0 −0.930421
\(956\) −15642.8 −0.529209
\(957\) −24791.2 −0.837394
\(958\) 4759.66 0.160519
\(959\) −5523.18 −0.185978
\(960\) −1980.50 −0.0665838
\(961\) −8210.46 −0.275602
\(962\) 23798.2 0.797592
\(963\) 2862.41 0.0957839
\(964\) −13088.7 −0.437302
\(965\) 28801.5 0.960780
\(966\) −966.000 −0.0321745
\(967\) −23837.0 −0.792706 −0.396353 0.918098i \(-0.629724\pi\)
−0.396353 + 0.918098i \(0.629724\pi\)
\(968\) 4996.01 0.165886
\(969\) −1795.48 −0.0595243
\(970\) −8905.39 −0.294778
\(971\) 4331.23 0.143147 0.0715735 0.997435i \(-0.477198\pi\)
0.0715735 + 0.997435i \(0.477198\pi\)
\(972\) −972.000 −0.0320750
\(973\) −10532.4 −0.347022
\(974\) 34.6556 0.00114008
\(975\) 2880.47 0.0946142
\(976\) −393.199 −0.0128955
\(977\) 20300.1 0.664748 0.332374 0.943148i \(-0.392150\pi\)
0.332374 + 0.943148i \(0.392150\pi\)
\(978\) −16886.3 −0.552112
\(979\) −4411.84 −0.144027
\(980\) 2021.76 0.0659009
\(981\) −5156.06 −0.167809
\(982\) −10147.8 −0.329765
\(983\) 23851.1 0.773890 0.386945 0.922103i \(-0.373530\pi\)
0.386945 + 0.922103i \(0.373530\pi\)
\(984\) 2456.78 0.0795927
\(985\) 9466.87 0.306233
\(986\) −6853.50 −0.221359
\(987\) −4144.50 −0.133658
\(988\) −11213.1 −0.361070
\(989\) 5154.41 0.165724
\(990\) 4935.17 0.158434
\(991\) 12071.5 0.386948 0.193474 0.981105i \(-0.438025\pi\)
0.193474 + 0.981105i \(0.438025\pi\)
\(992\) −4700.90 −0.150457
\(993\) 12781.5 0.408469
\(994\) −2992.94 −0.0955033
\(995\) 45658.5 1.45474
\(996\) 1617.70 0.0514647
\(997\) −21936.7 −0.696832 −0.348416 0.937340i \(-0.613280\pi\)
−0.348416 + 0.937340i \(0.613280\pi\)
\(998\) −5047.87 −0.160108
\(999\) 6223.11 0.197088
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 966.4.a.l.1.5 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
966.4.a.l.1.5 5 1.1 even 1 trivial