Properties

Label 230.4.a.f.1.2
Level $230$
Weight $4$
Character 230.1
Self dual yes
Analytic conductor $13.570$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [230,4,Mod(1,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("230.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 230.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: \(13.5704393013\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{73}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 18 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-3.77200\) of defining polynomial
Character \(\chi\) \(=\) 230.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.00000 q^{2} +2.77200 q^{3} +4.00000 q^{4} +5.00000 q^{5} -5.54400 q^{6} -4.22800 q^{7} -8.00000 q^{8} -19.3160 q^{9} +O(q^{10})\) \(q-2.00000 q^{2} +2.77200 q^{3} +4.00000 q^{4} +5.00000 q^{5} -5.54400 q^{6} -4.22800 q^{7} -8.00000 q^{8} -19.3160 q^{9} -10.0000 q^{10} -33.7200 q^{11} +11.0880 q^{12} -42.9480 q^{13} +8.45600 q^{14} +13.8600 q^{15} +16.0000 q^{16} +7.49202 q^{17} +38.6320 q^{18} -25.7200 q^{19} +20.0000 q^{20} -11.7200 q^{21} +67.4400 q^{22} -23.0000 q^{23} -22.1760 q^{24} +25.0000 q^{25} +85.8960 q^{26} -128.388 q^{27} -16.9120 q^{28} -47.4560 q^{29} -27.7200 q^{30} +65.0720 q^{31} -32.0000 q^{32} -93.4720 q^{33} -14.9840 q^{34} -21.1400 q^{35} -77.2640 q^{36} -215.596 q^{37} +51.4400 q^{38} -119.052 q^{39} -40.0000 q^{40} +150.128 q^{41} +23.4400 q^{42} -83.0160 q^{43} -134.880 q^{44} -96.5800 q^{45} +46.0000 q^{46} -278.140 q^{47} +44.3520 q^{48} -325.124 q^{49} -50.0000 q^{50} +20.7679 q^{51} -171.792 q^{52} -182.404 q^{53} +256.776 q^{54} -168.600 q^{55} +33.8240 q^{56} -71.2959 q^{57} +94.9120 q^{58} -270.060 q^{59} +55.4400 q^{60} -137.264 q^{61} -130.144 q^{62} +81.6680 q^{63} +64.0000 q^{64} -214.740 q^{65} +186.944 q^{66} -440.652 q^{67} +29.9681 q^{68} -63.7560 q^{69} +42.2800 q^{70} +1071.29 q^{71} +154.528 q^{72} -269.756 q^{73} +431.192 q^{74} +69.3000 q^{75} -102.880 q^{76} +142.568 q^{77} +238.104 q^{78} +195.232 q^{79} +80.0000 q^{80} +165.640 q^{81} -300.256 q^{82} +136.676 q^{83} -46.8801 q^{84} +37.4601 q^{85} +166.032 q^{86} -131.548 q^{87} +269.760 q^{88} +629.896 q^{89} +193.160 q^{90} +181.584 q^{91} -92.0000 q^{92} +180.380 q^{93} +556.280 q^{94} -128.600 q^{95} -88.7041 q^{96} -419.392 q^{97} +650.248 q^{98} +651.336 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{2} - 3 q^{3} + 8 q^{4} + 10 q^{5} + 6 q^{6} - 17 q^{7} - 16 q^{8} - 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{2} - 3 q^{3} + 8 q^{4} + 10 q^{5} + 6 q^{6} - 17 q^{7} - 16 q^{8} - 13 q^{9} - 20 q^{10} + 18 q^{11} - 12 q^{12} - 9 q^{13} + 34 q^{14} - 15 q^{15} + 32 q^{16} - 79 q^{17} + 26 q^{18} + 34 q^{19} + 40 q^{20} + 62 q^{21} - 36 q^{22} - 46 q^{23} + 24 q^{24} + 50 q^{25} + 18 q^{26} - 9 q^{27} - 68 q^{28} - 112 q^{29} + 30 q^{30} - 92 q^{31} - 64 q^{32} - 392 q^{33} + 158 q^{34} - 85 q^{35} - 52 q^{36} - 491 q^{37} - 68 q^{38} - 315 q^{39} - 80 q^{40} - 332 q^{41} - 124 q^{42} - 354 q^{43} + 72 q^{44} - 65 q^{45} + 92 q^{46} - 599 q^{47} - 48 q^{48} - 505 q^{49} - 100 q^{50} + 520 q^{51} - 36 q^{52} - 305 q^{53} + 18 q^{54} + 90 q^{55} + 136 q^{56} - 416 q^{57} + 224 q^{58} + 357 q^{59} - 60 q^{60} - 172 q^{61} + 184 q^{62} + q^{63} + 128 q^{64} - 45 q^{65} + 784 q^{66} - 531 q^{67} - 316 q^{68} + 69 q^{69} + 170 q^{70} + 1254 q^{71} + 104 q^{72} - 343 q^{73} + 982 q^{74} - 75 q^{75} + 136 q^{76} - 518 q^{77} + 630 q^{78} - 88 q^{79} + 160 q^{80} - 694 q^{81} + 664 q^{82} + 1273 q^{83} + 248 q^{84} - 395 q^{85} + 708 q^{86} + 241 q^{87} - 144 q^{88} + 1106 q^{89} + 130 q^{90} - 252 q^{91} - 184 q^{92} + 1087 q^{93} + 1198 q^{94} + 170 q^{95} + 96 q^{96} - 2240 q^{97} + 1010 q^{98} + 978 q^{99}+O(q^{100}) \) 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
\(3\) 2.77200 0.533472 0.266736 0.963770i \(-0.414055\pi\)
0.266736 + 0.963770i \(0.414055\pi\)
\(4\) 4.00000 0.500000
\(5\) 5.00000 0.447214
\(6\) −5.54400 −0.377222
\(7\) −4.22800 −0.228290 −0.114145 0.993464i \(-0.536413\pi\)
−0.114145 + 0.993464i \(0.536413\pi\)
\(8\) −8.00000 −0.353553
\(9\) −19.3160 −0.715408
\(10\) −10.0000 −0.316228
\(11\) −33.7200 −0.924270 −0.462135 0.886810i \(-0.652916\pi\)
−0.462135 + 0.886810i \(0.652916\pi\)
\(12\) 11.0880 0.266736
\(13\) −42.9480 −0.916280 −0.458140 0.888880i \(-0.651484\pi\)
−0.458140 + 0.888880i \(0.651484\pi\)
\(14\) 8.45600 0.161426
\(15\) 13.8600 0.238576
\(16\) 16.0000 0.250000
\(17\) 7.49202 0.106887 0.0534436 0.998571i \(-0.482980\pi\)
0.0534436 + 0.998571i \(0.482980\pi\)
\(18\) 38.6320 0.505870
\(19\) −25.7200 −0.310557 −0.155278 0.987871i \(-0.549627\pi\)
−0.155278 + 0.987871i \(0.549627\pi\)
\(20\) 20.0000 0.223607
\(21\) −11.7200 −0.121787
\(22\) 67.4400 0.653557
\(23\) −23.0000 −0.208514
\(24\) −22.1760 −0.188611
\(25\) 25.0000 0.200000
\(26\) 85.8960 0.647908
\(27\) −128.388 −0.915122
\(28\) −16.9120 −0.114145
\(29\) −47.4560 −0.303874 −0.151937 0.988390i \(-0.548551\pi\)
−0.151937 + 0.988390i \(0.548551\pi\)
\(30\) −27.7200 −0.168699
\(31\) 65.0720 0.377009 0.188505 0.982072i \(-0.439636\pi\)
0.188505 + 0.982072i \(0.439636\pi\)
\(32\) −32.0000 −0.176777
\(33\) −93.4720 −0.493072
\(34\) −14.9840 −0.0755806
\(35\) −21.1400 −0.102095
\(36\) −77.2640 −0.357704
\(37\) −215.596 −0.957940 −0.478970 0.877831i \(-0.658990\pi\)
−0.478970 + 0.877831i \(0.658990\pi\)
\(38\) 51.4400 0.219597
\(39\) −119.052 −0.488810
\(40\) −40.0000 −0.158114
\(41\) 150.128 0.571856 0.285928 0.958251i \(-0.407698\pi\)
0.285928 + 0.958251i \(0.407698\pi\)
\(42\) 23.4400 0.0861161
\(43\) −83.0160 −0.294414 −0.147207 0.989106i \(-0.547028\pi\)
−0.147207 + 0.989106i \(0.547028\pi\)
\(44\) −134.880 −0.462135
\(45\) −96.5800 −0.319940
\(46\) 46.0000 0.147442
\(47\) −278.140 −0.863210 −0.431605 0.902063i \(-0.642053\pi\)
−0.431605 + 0.902063i \(0.642053\pi\)
\(48\) 44.3520 0.133368
\(49\) −325.124 −0.947883
\(50\) −50.0000 −0.141421
\(51\) 20.7679 0.0570213
\(52\) −171.792 −0.458140
\(53\) −182.404 −0.472738 −0.236369 0.971663i \(-0.575957\pi\)
−0.236369 + 0.971663i \(0.575957\pi\)
\(54\) 256.776 0.647089
\(55\) −168.600 −0.413346
\(56\) 33.8240 0.0807129
\(57\) −71.2959 −0.165673
\(58\) 94.9120 0.214872
\(59\) −270.060 −0.595913 −0.297956 0.954580i \(-0.596305\pi\)
−0.297956 + 0.954580i \(0.596305\pi\)
\(60\) 55.4400 0.119288
\(61\) −137.264 −0.288112 −0.144056 0.989570i \(-0.546015\pi\)
−0.144056 + 0.989570i \(0.546015\pi\)
\(62\) −130.144 −0.266586
\(63\) 81.6680 0.163321
\(64\) 64.0000 0.125000
\(65\) −214.740 −0.409773
\(66\) 186.944 0.348655
\(67\) −440.652 −0.803496 −0.401748 0.915750i \(-0.631597\pi\)
−0.401748 + 0.915750i \(0.631597\pi\)
\(68\) 29.9681 0.0534436
\(69\) −63.7560 −0.111237
\(70\) 42.2800 0.0721918
\(71\) 1071.29 1.79068 0.895342 0.445380i \(-0.146931\pi\)
0.895342 + 0.445380i \(0.146931\pi\)
\(72\) 154.528 0.252935
\(73\) −269.756 −0.432501 −0.216250 0.976338i \(-0.569383\pi\)
−0.216250 + 0.976338i \(0.569383\pi\)
\(74\) 431.192 0.677366
\(75\) 69.3000 0.106694
\(76\) −102.880 −0.155278
\(77\) 142.568 0.211002
\(78\) 238.104 0.345641
\(79\) 195.232 0.278042 0.139021 0.990289i \(-0.455604\pi\)
0.139021 + 0.990289i \(0.455604\pi\)
\(80\) 80.0000 0.111803
\(81\) 165.640 0.227216
\(82\) −300.256 −0.404363
\(83\) 136.676 0.180748 0.0903742 0.995908i \(-0.471194\pi\)
0.0903742 + 0.995908i \(0.471194\pi\)
\(84\) −46.8801 −0.0608933
\(85\) 37.4601 0.0478014
\(86\) 166.032 0.208182
\(87\) −131.548 −0.162108
\(88\) 269.760 0.326779
\(89\) 629.896 0.750212 0.375106 0.926982i \(-0.377606\pi\)
0.375106 + 0.926982i \(0.377606\pi\)
\(90\) 193.160 0.226232
\(91\) 181.584 0.209178
\(92\) −92.0000 −0.104257
\(93\) 180.380 0.201124
\(94\) 556.280 0.610382
\(95\) −128.600 −0.138885
\(96\) −88.7041 −0.0943054
\(97\) −419.392 −0.438998 −0.219499 0.975613i \(-0.570442\pi\)
−0.219499 + 0.975613i \(0.570442\pi\)
\(98\) 650.248 0.670255
\(99\) 651.336 0.661230
\(100\) 100.000 0.100000
\(101\) 928.164 0.914414 0.457207 0.889360i \(-0.348850\pi\)
0.457207 + 0.889360i \(0.348850\pi\)
\(102\) −41.5358 −0.0403202
\(103\) 1381.78 1.32185 0.660925 0.750452i \(-0.270164\pi\)
0.660925 + 0.750452i \(0.270164\pi\)
\(104\) 343.584 0.323954
\(105\) −58.6001 −0.0544646
\(106\) 364.808 0.334276
\(107\) −763.820 −0.690106 −0.345053 0.938583i \(-0.612139\pi\)
−0.345053 + 0.938583i \(0.612139\pi\)
\(108\) −513.552 −0.457561
\(109\) −156.736 −0.137730 −0.0688651 0.997626i \(-0.521938\pi\)
−0.0688651 + 0.997626i \(0.521938\pi\)
\(110\) 337.200 0.292280
\(111\) −597.632 −0.511034
\(112\) −67.6480 −0.0570726
\(113\) 1036.12 0.862569 0.431285 0.902216i \(-0.358060\pi\)
0.431285 + 0.902216i \(0.358060\pi\)
\(114\) 142.592 0.117149
\(115\) −115.000 −0.0932505
\(116\) −189.824 −0.151937
\(117\) 829.584 0.655514
\(118\) 540.120 0.421374
\(119\) −31.6762 −0.0244013
\(120\) −110.880 −0.0843493
\(121\) −193.960 −0.145725
\(122\) 274.528 0.203726
\(123\) 416.155 0.305069
\(124\) 260.288 0.188505
\(125\) 125.000 0.0894427
\(126\) −163.336 −0.115485
\(127\) −1228.31 −0.858226 −0.429113 0.903251i \(-0.641174\pi\)
−0.429113 + 0.903251i \(0.641174\pi\)
\(128\) −128.000 −0.0883883
\(129\) −230.120 −0.157062
\(130\) 429.480 0.289753
\(131\) 1735.85 1.15773 0.578863 0.815425i \(-0.303497\pi\)
0.578863 + 0.815425i \(0.303497\pi\)
\(132\) −373.888 −0.246536
\(133\) 108.744 0.0708971
\(134\) 881.304 0.568157
\(135\) −641.940 −0.409255
\(136\) −59.9362 −0.0377903
\(137\) −1307.40 −0.815319 −0.407660 0.913134i \(-0.633655\pi\)
−0.407660 + 0.913134i \(0.633655\pi\)
\(138\) 127.512 0.0786562
\(139\) 1073.82 0.655256 0.327628 0.944807i \(-0.393751\pi\)
0.327628 + 0.944807i \(0.393751\pi\)
\(140\) −84.5600 −0.0510473
\(141\) −771.005 −0.460499
\(142\) −2142.58 −1.26620
\(143\) 1448.21 0.846890
\(144\) −309.056 −0.178852
\(145\) −237.280 −0.135897
\(146\) 539.512 0.305824
\(147\) −901.244 −0.505669
\(148\) −862.384 −0.478970
\(149\) 2309.08 1.26958 0.634789 0.772685i \(-0.281087\pi\)
0.634789 + 0.772685i \(0.281087\pi\)
\(150\) −138.600 −0.0754443
\(151\) −87.6037 −0.0472125 −0.0236063 0.999721i \(-0.507515\pi\)
−0.0236063 + 0.999721i \(0.507515\pi\)
\(152\) 205.760 0.109798
\(153\) −144.716 −0.0764679
\(154\) −285.136 −0.149201
\(155\) 325.360 0.168604
\(156\) −476.208 −0.244405
\(157\) −1862.30 −0.946673 −0.473337 0.880882i \(-0.656951\pi\)
−0.473337 + 0.880882i \(0.656951\pi\)
\(158\) −390.464 −0.196605
\(159\) −505.624 −0.252193
\(160\) −160.000 −0.0790569
\(161\) 97.2440 0.0476018
\(162\) −331.280 −0.160666
\(163\) 76.7391 0.0368753 0.0184377 0.999830i \(-0.494131\pi\)
0.0184377 + 0.999830i \(0.494131\pi\)
\(164\) 600.513 0.285928
\(165\) −467.360 −0.220509
\(166\) −273.352 −0.127808
\(167\) −2324.96 −1.07731 −0.538655 0.842526i \(-0.681068\pi\)
−0.538655 + 0.842526i \(0.681068\pi\)
\(168\) 93.7601 0.0430581
\(169\) −352.468 −0.160431
\(170\) −74.9202 −0.0338007
\(171\) 496.808 0.222175
\(172\) −332.064 −0.147207
\(173\) −2425.51 −1.06594 −0.532972 0.846133i \(-0.678925\pi\)
−0.532972 + 0.846133i \(0.678925\pi\)
\(174\) 263.096 0.114628
\(175\) −105.700 −0.0456581
\(176\) −539.520 −0.231067
\(177\) −748.607 −0.317903
\(178\) −1259.79 −0.530480
\(179\) 1911.86 0.798320 0.399160 0.916881i \(-0.369302\pi\)
0.399160 + 0.916881i \(0.369302\pi\)
\(180\) −386.320 −0.159970
\(181\) −3990.39 −1.63869 −0.819345 0.573300i \(-0.805663\pi\)
−0.819345 + 0.573300i \(0.805663\pi\)
\(182\) −363.168 −0.147911
\(183\) −380.496 −0.153700
\(184\) 184.000 0.0737210
\(185\) −1077.98 −0.428404
\(186\) −360.760 −0.142216
\(187\) −252.631 −0.0987926
\(188\) −1112.56 −0.431605
\(189\) 542.824 0.208914
\(190\) 257.200 0.0982066
\(191\) 3212.75 1.21710 0.608550 0.793516i \(-0.291752\pi\)
0.608550 + 0.793516i \(0.291752\pi\)
\(192\) 177.408 0.0666840
\(193\) −2131.32 −0.794899 −0.397450 0.917624i \(-0.630105\pi\)
−0.397450 + 0.917624i \(0.630105\pi\)
\(194\) 838.783 0.310418
\(195\) −595.260 −0.218602
\(196\) −1300.50 −0.473942
\(197\) 3389.48 1.22584 0.612920 0.790145i \(-0.289995\pi\)
0.612920 + 0.790145i \(0.289995\pi\)
\(198\) −1302.67 −0.467560
\(199\) −689.032 −0.245448 −0.122724 0.992441i \(-0.539163\pi\)
−0.122724 + 0.992441i \(0.539163\pi\)
\(200\) −200.000 −0.0707107
\(201\) −1221.49 −0.428643
\(202\) −1856.33 −0.646588
\(203\) 200.644 0.0693716
\(204\) 83.0716 0.0285107
\(205\) 750.641 0.255742
\(206\) −2763.55 −0.934689
\(207\) 444.268 0.149173
\(208\) −687.168 −0.229070
\(209\) 867.280 0.287038
\(210\) 117.200 0.0385123
\(211\) 135.653 0.0442593 0.0221296 0.999755i \(-0.492955\pi\)
0.0221296 + 0.999755i \(0.492955\pi\)
\(212\) −729.616 −0.236369
\(213\) 2969.61 0.955279
\(214\) 1527.64 0.487978
\(215\) −415.080 −0.131666
\(216\) 1027.10 0.323544
\(217\) −275.124 −0.0860676
\(218\) 313.472 0.0973899
\(219\) −747.764 −0.230727
\(220\) −674.400 −0.206673
\(221\) −321.767 −0.0979385
\(222\) 1195.26 0.361356
\(223\) 205.321 0.0616560 0.0308280 0.999525i \(-0.490186\pi\)
0.0308280 + 0.999525i \(0.490186\pi\)
\(224\) 135.296 0.0403564
\(225\) −482.900 −0.143082
\(226\) −2072.25 −0.609929
\(227\) 1800.57 0.526467 0.263233 0.964732i \(-0.415211\pi\)
0.263233 + 0.964732i \(0.415211\pi\)
\(228\) −285.184 −0.0828366
\(229\) −1265.24 −0.365106 −0.182553 0.983196i \(-0.558436\pi\)
−0.182553 + 0.983196i \(0.558436\pi\)
\(230\) 230.000 0.0659380
\(231\) 395.199 0.112564
\(232\) 379.648 0.107436
\(233\) 1252.76 0.352235 0.176118 0.984369i \(-0.443646\pi\)
0.176118 + 0.984369i \(0.443646\pi\)
\(234\) −1659.17 −0.463518
\(235\) −1390.70 −0.386039
\(236\) −1080.24 −0.297956
\(237\) 541.184 0.148328
\(238\) 63.3525 0.0172543
\(239\) 4345.22 1.17602 0.588010 0.808854i \(-0.299912\pi\)
0.588010 + 0.808854i \(0.299912\pi\)
\(240\) 221.760 0.0596440
\(241\) 427.153 0.114171 0.0570857 0.998369i \(-0.481819\pi\)
0.0570857 + 0.998369i \(0.481819\pi\)
\(242\) 387.921 0.103043
\(243\) 3925.63 1.03634
\(244\) −549.056 −0.144056
\(245\) −1625.62 −0.423906
\(246\) −832.311 −0.215716
\(247\) 1104.62 0.284557
\(248\) −520.576 −0.133293
\(249\) 378.866 0.0964242
\(250\) −250.000 −0.0632456
\(251\) 3079.51 0.774411 0.387205 0.921993i \(-0.373440\pi\)
0.387205 + 0.921993i \(0.373440\pi\)
\(252\) 326.672 0.0816604
\(253\) 775.560 0.192724
\(254\) 2456.62 0.606857
\(255\) 103.839 0.0255007
\(256\) 256.000 0.0625000
\(257\) −5829.41 −1.41490 −0.707448 0.706765i \(-0.750154\pi\)
−0.707448 + 0.706765i \(0.750154\pi\)
\(258\) 460.241 0.111059
\(259\) 911.539 0.218688
\(260\) −858.960 −0.204886
\(261\) 916.660 0.217394
\(262\) −3471.71 −0.818636
\(263\) 3528.99 0.827402 0.413701 0.910413i \(-0.364236\pi\)
0.413701 + 0.910413i \(0.364236\pi\)
\(264\) 747.776 0.174327
\(265\) −912.020 −0.211415
\(266\) −217.488 −0.0501318
\(267\) 1746.07 0.400217
\(268\) −1762.61 −0.401748
\(269\) −4112.06 −0.932032 −0.466016 0.884776i \(-0.654311\pi\)
−0.466016 + 0.884776i \(0.654311\pi\)
\(270\) 1283.88 0.289387
\(271\) 1119.28 0.250890 0.125445 0.992101i \(-0.459964\pi\)
0.125445 + 0.992101i \(0.459964\pi\)
\(272\) 119.872 0.0267218
\(273\) 503.352 0.111591
\(274\) 2614.80 0.576518
\(275\) −843.000 −0.184854
\(276\) −255.024 −0.0556183
\(277\) −2919.79 −0.633333 −0.316666 0.948537i \(-0.602564\pi\)
−0.316666 + 0.948537i \(0.602564\pi\)
\(278\) −2147.65 −0.463336
\(279\) −1256.93 −0.269715
\(280\) 169.120 0.0360959
\(281\) 2925.91 0.621156 0.310578 0.950548i \(-0.399477\pi\)
0.310578 + 0.950548i \(0.399477\pi\)
\(282\) 1542.01 0.325622
\(283\) 7023.11 1.47520 0.737598 0.675240i \(-0.235960\pi\)
0.737598 + 0.675240i \(0.235960\pi\)
\(284\) 4285.15 0.895342
\(285\) −356.480 −0.0740914
\(286\) −2896.42 −0.598841
\(287\) −634.741 −0.130549
\(288\) 618.112 0.126467
\(289\) −4856.87 −0.988575
\(290\) 474.560 0.0960935
\(291\) −1162.55 −0.234193
\(292\) −1079.02 −0.216250
\(293\) 634.237 0.126459 0.0632296 0.997999i \(-0.479860\pi\)
0.0632296 + 0.997999i \(0.479860\pi\)
\(294\) 1802.49 0.357562
\(295\) −1350.30 −0.266500
\(296\) 1724.77 0.338683
\(297\) 4329.25 0.845820
\(298\) −4618.16 −0.897728
\(299\) 987.804 0.191058
\(300\) 277.200 0.0533472
\(301\) 350.991 0.0672120
\(302\) 175.207 0.0333843
\(303\) 2572.87 0.487814
\(304\) −411.520 −0.0776392
\(305\) −686.320 −0.128848
\(306\) 289.432 0.0540710
\(307\) 5365.54 0.997485 0.498742 0.866750i \(-0.333795\pi\)
0.498742 + 0.866750i \(0.333795\pi\)
\(308\) 570.273 0.105501
\(309\) 3830.29 0.705170
\(310\) −650.720 −0.119221
\(311\) −9570.36 −1.74497 −0.872484 0.488642i \(-0.837492\pi\)
−0.872484 + 0.488642i \(0.837492\pi\)
\(312\) 952.416 0.172820
\(313\) −8376.76 −1.51272 −0.756361 0.654154i \(-0.773025\pi\)
−0.756361 + 0.654154i \(0.773025\pi\)
\(314\) 3724.60 0.669399
\(315\) 408.340 0.0730392
\(316\) 780.928 0.139021
\(317\) −5672.79 −1.00510 −0.502549 0.864549i \(-0.667604\pi\)
−0.502549 + 0.864549i \(0.667604\pi\)
\(318\) 1011.25 0.178327
\(319\) 1600.22 0.280862
\(320\) 320.000 0.0559017
\(321\) −2117.31 −0.368152
\(322\) −194.488 −0.0336596
\(323\) −192.695 −0.0331945
\(324\) 662.561 0.113608
\(325\) −1073.70 −0.183256
\(326\) −153.478 −0.0260748
\(327\) −434.472 −0.0734752
\(328\) −1201.03 −0.202181
\(329\) 1175.98 0.197063
\(330\) 934.720 0.155923
\(331\) 5436.79 0.902819 0.451410 0.892317i \(-0.350921\pi\)
0.451410 + 0.892317i \(0.350921\pi\)
\(332\) 546.703 0.0903742
\(333\) 4164.45 0.685317
\(334\) 4649.92 0.761774
\(335\) −2203.26 −0.359334
\(336\) −187.520 −0.0304466
\(337\) 6693.79 1.08200 0.541000 0.841022i \(-0.318046\pi\)
0.541000 + 0.841022i \(0.318046\pi\)
\(338\) 704.936 0.113442
\(339\) 2872.14 0.460157
\(340\) 149.840 0.0239007
\(341\) −2194.23 −0.348458
\(342\) −993.616 −0.157101
\(343\) 2824.83 0.444683
\(344\) 664.128 0.104091
\(345\) −318.780 −0.0497465
\(346\) 4851.03 0.753736
\(347\) 2556.53 0.395509 0.197755 0.980252i \(-0.436635\pi\)
0.197755 + 0.980252i \(0.436635\pi\)
\(348\) −526.192 −0.0810542
\(349\) −10566.7 −1.62069 −0.810344 0.585954i \(-0.800720\pi\)
−0.810344 + 0.585954i \(0.800720\pi\)
\(350\) 211.400 0.0322851
\(351\) 5514.01 0.838508
\(352\) 1079.04 0.163389
\(353\) 4561.90 0.687834 0.343917 0.939000i \(-0.388246\pi\)
0.343917 + 0.939000i \(0.388246\pi\)
\(354\) 1497.21 0.224791
\(355\) 5356.44 0.800818
\(356\) 2519.58 0.375106
\(357\) −87.8066 −0.0130174
\(358\) −3823.72 −0.564497
\(359\) −12107.3 −1.77995 −0.889974 0.456012i \(-0.849278\pi\)
−0.889974 + 0.456012i \(0.849278\pi\)
\(360\) 772.640 0.113116
\(361\) −6197.48 −0.903555
\(362\) 7980.77 1.15873
\(363\) −537.658 −0.0777404
\(364\) 726.337 0.104589
\(365\) −1348.78 −0.193420
\(366\) 760.992 0.108682
\(367\) −2215.89 −0.315174 −0.157587 0.987505i \(-0.550371\pi\)
−0.157587 + 0.987505i \(0.550371\pi\)
\(368\) −368.000 −0.0521286
\(369\) −2899.88 −0.409110
\(370\) 2155.96 0.302927
\(371\) 771.204 0.107922
\(372\) 721.519 0.100562
\(373\) −3872.34 −0.537539 −0.268770 0.963205i \(-0.586617\pi\)
−0.268770 + 0.963205i \(0.586617\pi\)
\(374\) 505.262 0.0698569
\(375\) 346.500 0.0477152
\(376\) 2225.12 0.305191
\(377\) 2038.14 0.278434
\(378\) −1085.65 −0.147724
\(379\) −819.918 −0.111125 −0.0555625 0.998455i \(-0.517695\pi\)
−0.0555625 + 0.998455i \(0.517695\pi\)
\(380\) −514.400 −0.0694426
\(381\) −3404.87 −0.457840
\(382\) −6425.49 −0.860620
\(383\) 6281.54 0.838046 0.419023 0.907976i \(-0.362373\pi\)
0.419023 + 0.907976i \(0.362373\pi\)
\(384\) −354.816 −0.0471527
\(385\) 712.841 0.0943629
\(386\) 4262.63 0.562079
\(387\) 1603.54 0.210626
\(388\) −1677.57 −0.219499
\(389\) −13939.3 −1.81684 −0.908419 0.418060i \(-0.862710\pi\)
−0.908419 + 0.418060i \(0.862710\pi\)
\(390\) 1190.52 0.154575
\(391\) −172.316 −0.0222875
\(392\) 2600.99 0.335127
\(393\) 4811.79 0.617615
\(394\) −6778.96 −0.866799
\(395\) 976.161 0.124344
\(396\) 2605.34 0.330615
\(397\) −2540.96 −0.321227 −0.160613 0.987017i \(-0.551347\pi\)
−0.160613 + 0.987017i \(0.551347\pi\)
\(398\) 1378.06 0.173558
\(399\) 301.439 0.0378216
\(400\) 400.000 0.0500000
\(401\) 4996.13 0.622181 0.311091 0.950380i \(-0.399306\pi\)
0.311091 + 0.950380i \(0.399306\pi\)
\(402\) 2442.98 0.303096
\(403\) −2794.72 −0.345446
\(404\) 3712.66 0.457207
\(405\) 828.201 0.101614
\(406\) −401.288 −0.0490531
\(407\) 7269.90 0.885395
\(408\) −166.143 −0.0201601
\(409\) −1768.34 −0.213787 −0.106894 0.994270i \(-0.534090\pi\)
−0.106894 + 0.994270i \(0.534090\pi\)
\(410\) −1501.28 −0.180837
\(411\) −3624.11 −0.434950
\(412\) 5527.11 0.660925
\(413\) 1141.81 0.136041
\(414\) −888.536 −0.105481
\(415\) 683.379 0.0808331
\(416\) 1374.34 0.161977
\(417\) 2976.64 0.349561
\(418\) −1734.56 −0.202967
\(419\) 45.6353 0.00532083 0.00266042 0.999996i \(-0.499153\pi\)
0.00266042 + 0.999996i \(0.499153\pi\)
\(420\) −234.400 −0.0272323
\(421\) −817.214 −0.0946047 −0.0473023 0.998881i \(-0.515062\pi\)
−0.0473023 + 0.998881i \(0.515062\pi\)
\(422\) −271.305 −0.0312960
\(423\) 5372.55 0.617547
\(424\) 1459.23 0.167138
\(425\) 187.301 0.0213774
\(426\) −5939.23 −0.675485
\(427\) 580.352 0.0657733
\(428\) −3055.28 −0.345053
\(429\) 4014.44 0.451792
\(430\) 830.160 0.0931020
\(431\) 2475.30 0.276639 0.138319 0.990388i \(-0.455830\pi\)
0.138319 + 0.990388i \(0.455830\pi\)
\(432\) −2054.21 −0.228780
\(433\) −59.6371 −0.00661888 −0.00330944 0.999995i \(-0.501053\pi\)
−0.00330944 + 0.999995i \(0.501053\pi\)
\(434\) 550.249 0.0608590
\(435\) −657.741 −0.0724971
\(436\) −626.944 −0.0688651
\(437\) 591.560 0.0647555
\(438\) 1495.53 0.163149
\(439\) −7258.27 −0.789108 −0.394554 0.918873i \(-0.629101\pi\)
−0.394554 + 0.918873i \(0.629101\pi\)
\(440\) 1348.80 0.146140
\(441\) 6280.10 0.678123
\(442\) 643.535 0.0692530
\(443\) −9721.43 −1.04262 −0.521308 0.853369i \(-0.674556\pi\)
−0.521308 + 0.853369i \(0.674556\pi\)
\(444\) −2390.53 −0.255517
\(445\) 3149.48 0.335505
\(446\) −410.641 −0.0435974
\(447\) 6400.78 0.677285
\(448\) −270.592 −0.0285363
\(449\) −10662.3 −1.12068 −0.560340 0.828263i \(-0.689329\pi\)
−0.560340 + 0.828263i \(0.689329\pi\)
\(450\) 965.800 0.101174
\(451\) −5062.32 −0.528549
\(452\) 4144.50 0.431285
\(453\) −242.838 −0.0251866
\(454\) −3601.14 −0.372268
\(455\) 907.921 0.0935472
\(456\) 570.368 0.0585744
\(457\) 4135.30 0.423284 0.211642 0.977347i \(-0.432119\pi\)
0.211642 + 0.977347i \(0.432119\pi\)
\(458\) 2530.48 0.258169
\(459\) −961.886 −0.0978148
\(460\) −460.000 −0.0466252
\(461\) −12080.6 −1.22050 −0.610249 0.792210i \(-0.708931\pi\)
−0.610249 + 0.792210i \(0.708931\pi\)
\(462\) −790.399 −0.0795945
\(463\) −2114.39 −0.212234 −0.106117 0.994354i \(-0.533842\pi\)
−0.106117 + 0.994354i \(0.533842\pi\)
\(464\) −759.296 −0.0759686
\(465\) 901.899 0.0899453
\(466\) −2505.51 −0.249068
\(467\) −14182.0 −1.40527 −0.702637 0.711548i \(-0.747994\pi\)
−0.702637 + 0.711548i \(0.747994\pi\)
\(468\) 3318.34 0.327757
\(469\) 1863.08 0.183430
\(470\) 2781.40 0.272971
\(471\) −5162.30 −0.505024
\(472\) 2160.48 0.210687
\(473\) 2799.30 0.272118
\(474\) −1082.37 −0.104884
\(475\) −643.000 −0.0621113
\(476\) −126.705 −0.0122007
\(477\) 3523.32 0.338200
\(478\) −8690.43 −0.831571
\(479\) −7546.93 −0.719891 −0.359946 0.932973i \(-0.617205\pi\)
−0.359946 + 0.932973i \(0.617205\pi\)
\(480\) −443.520 −0.0421747
\(481\) 9259.42 0.877741
\(482\) −854.306 −0.0807314
\(483\) 269.560 0.0253943
\(484\) −775.841 −0.0728626
\(485\) −2096.96 −0.196326
\(486\) −7851.26 −0.732800
\(487\) −17109.7 −1.59202 −0.796010 0.605284i \(-0.793060\pi\)
−0.796010 + 0.605284i \(0.793060\pi\)
\(488\) 1098.11 0.101863
\(489\) 212.721 0.0196719
\(490\) 3251.24 0.299747
\(491\) 9833.66 0.903843 0.451922 0.892058i \(-0.350739\pi\)
0.451922 + 0.892058i \(0.350739\pi\)
\(492\) 1664.62 0.152534
\(493\) −355.541 −0.0324803
\(494\) −2209.25 −0.201212
\(495\) 3256.68 0.295711
\(496\) 1041.15 0.0942523
\(497\) −4529.40 −0.408796
\(498\) −757.731 −0.0681822
\(499\) −1705.54 −0.153007 −0.0765036 0.997069i \(-0.524376\pi\)
−0.0765036 + 0.997069i \(0.524376\pi\)
\(500\) 500.000 0.0447214
\(501\) −6444.80 −0.574715
\(502\) −6159.03 −0.547591
\(503\) −8705.79 −0.771713 −0.385857 0.922559i \(-0.626094\pi\)
−0.385857 + 0.922559i \(0.626094\pi\)
\(504\) −653.344 −0.0577426
\(505\) 4640.82 0.408938
\(506\) −1551.12 −0.136276
\(507\) −977.042 −0.0855857
\(508\) −4913.23 −0.429113
\(509\) −14926.4 −1.29980 −0.649902 0.760018i \(-0.725190\pi\)
−0.649902 + 0.760018i \(0.725190\pi\)
\(510\) −207.679 −0.0180317
\(511\) 1140.53 0.0987358
\(512\) −512.000 −0.0441942
\(513\) 3302.14 0.284197
\(514\) 11658.8 1.00048
\(515\) 6908.88 0.591149
\(516\) −920.482 −0.0785309
\(517\) 9378.89 0.797839
\(518\) −1823.08 −0.154636
\(519\) −6723.53 −0.568651
\(520\) 1717.92 0.144877
\(521\) 17922.0 1.50706 0.753529 0.657415i \(-0.228350\pi\)
0.753529 + 0.657415i \(0.228350\pi\)
\(522\) −1833.32 −0.153721
\(523\) −21926.5 −1.83323 −0.916615 0.399771i \(-0.869090\pi\)
−0.916615 + 0.399771i \(0.869090\pi\)
\(524\) 6943.41 0.578863
\(525\) −293.000 −0.0243573
\(526\) −7057.98 −0.585062
\(527\) 487.521 0.0402974
\(528\) −1495.55 −0.123268
\(529\) 529.000 0.0434783
\(530\) 1824.04 0.149493
\(531\) 5216.48 0.426320
\(532\) 434.977 0.0354486
\(533\) −6447.71 −0.523980
\(534\) −3492.15 −0.282996
\(535\) −3819.10 −0.308625
\(536\) 3525.22 0.284079
\(537\) 5299.68 0.425881
\(538\) 8224.12 0.659046
\(539\) 10963.2 0.876100
\(540\) −2567.76 −0.204627
\(541\) −17623.6 −1.40055 −0.700275 0.713873i \(-0.746939\pi\)
−0.700275 + 0.713873i \(0.746939\pi\)
\(542\) −2238.55 −0.177406
\(543\) −11061.4 −0.874196
\(544\) −239.745 −0.0188952
\(545\) −783.680 −0.0615948
\(546\) −1006.70 −0.0789064
\(547\) −9204.79 −0.719504 −0.359752 0.933048i \(-0.617139\pi\)
−0.359752 + 0.933048i \(0.617139\pi\)
\(548\) −5229.60 −0.407660
\(549\) 2651.39 0.206118
\(550\) 1686.00 0.130711
\(551\) 1220.57 0.0943702
\(552\) 510.048 0.0393281
\(553\) −825.441 −0.0634744
\(554\) 5839.58 0.447834
\(555\) −2988.16 −0.228541
\(556\) 4295.30 0.327628
\(557\) 3584.33 0.272663 0.136331 0.990663i \(-0.456469\pi\)
0.136331 + 0.990663i \(0.456469\pi\)
\(558\) 2513.86 0.190717
\(559\) 3565.37 0.269766
\(560\) −338.240 −0.0255236
\(561\) −700.294 −0.0527031
\(562\) −5851.81 −0.439224
\(563\) −9052.50 −0.677651 −0.338826 0.940849i \(-0.610030\pi\)
−0.338826 + 0.940849i \(0.610030\pi\)
\(564\) −3084.02 −0.230249
\(565\) 5180.62 0.385753
\(566\) −14046.2 −1.04312
\(567\) −700.327 −0.0518712
\(568\) −8570.31 −0.633102
\(569\) −13714.1 −1.01042 −0.505208 0.862998i \(-0.668584\pi\)
−0.505208 + 0.862998i \(0.668584\pi\)
\(570\) 712.959 0.0523905
\(571\) 1903.12 0.139480 0.0697398 0.997565i \(-0.477783\pi\)
0.0697398 + 0.997565i \(0.477783\pi\)
\(572\) 5792.83 0.423445
\(573\) 8905.74 0.649289
\(574\) 1269.48 0.0923122
\(575\) −575.000 −0.0417029
\(576\) −1236.22 −0.0894260
\(577\) 14582.1 1.05210 0.526050 0.850454i \(-0.323672\pi\)
0.526050 + 0.850454i \(0.323672\pi\)
\(578\) 9713.74 0.699028
\(579\) −5908.02 −0.424057
\(580\) −949.120 −0.0679484
\(581\) −577.865 −0.0412631
\(582\) 2325.11 0.165599
\(583\) 6150.67 0.436938
\(584\) 2158.05 0.152912
\(585\) 4147.92 0.293155
\(586\) −1268.47 −0.0894201
\(587\) −13023.5 −0.915734 −0.457867 0.889021i \(-0.651386\pi\)
−0.457867 + 0.889021i \(0.651386\pi\)
\(588\) −3604.98 −0.252835
\(589\) −1673.65 −0.117083
\(590\) 2700.60 0.188444
\(591\) 9395.64 0.653951
\(592\) −3449.54 −0.239485
\(593\) −17936.3 −1.24209 −0.621043 0.783776i \(-0.713291\pi\)
−0.621043 + 0.783776i \(0.713291\pi\)
\(594\) −8658.50 −0.598085
\(595\) −158.381 −0.0109126
\(596\) 9236.32 0.634789
\(597\) −1910.00 −0.130940
\(598\) −1975.61 −0.135098
\(599\) 18292.2 1.24774 0.623872 0.781526i \(-0.285559\pi\)
0.623872 + 0.781526i \(0.285559\pi\)
\(600\) −554.400 −0.0377222
\(601\) 205.155 0.0139242 0.00696211 0.999976i \(-0.497784\pi\)
0.00696211 + 0.999976i \(0.497784\pi\)
\(602\) −701.983 −0.0475260
\(603\) 8511.64 0.574827
\(604\) −350.415 −0.0236063
\(605\) −969.802 −0.0651703
\(606\) −5145.75 −0.344937
\(607\) 23244.3 1.55429 0.777147 0.629319i \(-0.216666\pi\)
0.777147 + 0.629319i \(0.216666\pi\)
\(608\) 823.041 0.0548992
\(609\) 556.185 0.0370078
\(610\) 1372.64 0.0911091
\(611\) 11945.6 0.790942
\(612\) −578.864 −0.0382339
\(613\) 15518.5 1.02249 0.511245 0.859435i \(-0.329184\pi\)
0.511245 + 0.859435i \(0.329184\pi\)
\(614\) −10731.1 −0.705328
\(615\) 2080.78 0.136431
\(616\) −1140.55 −0.0746005
\(617\) 26922.8 1.75668 0.878340 0.478036i \(-0.158651\pi\)
0.878340 + 0.478036i \(0.158651\pi\)
\(618\) −7660.57 −0.498630
\(619\) 31.7390 0.00206090 0.00103045 0.999999i \(-0.499672\pi\)
0.00103045 + 0.999999i \(0.499672\pi\)
\(620\) 1301.44 0.0843018
\(621\) 2952.93 0.190816
\(622\) 19140.7 1.23388
\(623\) −2663.20 −0.171266
\(624\) −1904.83 −0.122202
\(625\) 625.000 0.0400000
\(626\) 16753.5 1.06966
\(627\) 2404.10 0.153127
\(628\) −7449.20 −0.473337
\(629\) −1615.25 −0.102391
\(630\) −816.680 −0.0516465
\(631\) 16322.7 1.02979 0.514894 0.857254i \(-0.327831\pi\)
0.514894 + 0.857254i \(0.327831\pi\)
\(632\) −1561.86 −0.0983027
\(633\) 376.029 0.0236111
\(634\) 11345.6 0.710711
\(635\) −6141.54 −0.383810
\(636\) −2022.50 −0.126096
\(637\) 13963.4 0.868526
\(638\) −3200.43 −0.198599
\(639\) −20693.0 −1.28107
\(640\) −640.000 −0.0395285
\(641\) 13384.6 0.824744 0.412372 0.911016i \(-0.364700\pi\)
0.412372 + 0.911016i \(0.364700\pi\)
\(642\) 4234.62 0.260323
\(643\) 9985.79 0.612443 0.306222 0.951960i \(-0.400935\pi\)
0.306222 + 0.951960i \(0.400935\pi\)
\(644\) 388.976 0.0238009
\(645\) −1150.60 −0.0702402
\(646\) 385.390 0.0234721
\(647\) 1910.99 0.116119 0.0580593 0.998313i \(-0.481509\pi\)
0.0580593 + 0.998313i \(0.481509\pi\)
\(648\) −1325.12 −0.0803329
\(649\) 9106.43 0.550784
\(650\) 2147.40 0.129582
\(651\) −762.646 −0.0459147
\(652\) 306.957 0.0184377
\(653\) −18735.8 −1.12280 −0.561399 0.827545i \(-0.689737\pi\)
−0.561399 + 0.827545i \(0.689737\pi\)
\(654\) 868.945 0.0519548
\(655\) 8679.26 0.517751
\(656\) 2402.05 0.142964
\(657\) 5210.61 0.309414
\(658\) −2351.95 −0.139344
\(659\) 1222.24 0.0722486 0.0361243 0.999347i \(-0.488499\pi\)
0.0361243 + 0.999347i \(0.488499\pi\)
\(660\) −1869.44 −0.110254
\(661\) −14293.5 −0.841076 −0.420538 0.907275i \(-0.638159\pi\)
−0.420538 + 0.907275i \(0.638159\pi\)
\(662\) −10873.6 −0.638390
\(663\) −891.940 −0.0522475
\(664\) −1093.41 −0.0639042
\(665\) 543.721 0.0317062
\(666\) −8328.91 −0.484592
\(667\) 1091.49 0.0633622
\(668\) −9299.85 −0.538655
\(669\) 569.149 0.0328917
\(670\) 4406.52 0.254088
\(671\) 4628.55 0.266294
\(672\) 375.041 0.0215290
\(673\) 11462.0 0.656506 0.328253 0.944590i \(-0.393540\pi\)
0.328253 + 0.944590i \(0.393540\pi\)
\(674\) −13387.6 −0.765090
\(675\) −3209.70 −0.183024
\(676\) −1409.87 −0.0802157
\(677\) 12842.2 0.729046 0.364523 0.931194i \(-0.381232\pi\)
0.364523 + 0.931194i \(0.381232\pi\)
\(678\) −5744.28 −0.325380
\(679\) 1773.19 0.100219
\(680\) −299.681 −0.0169003
\(681\) 4991.18 0.280855
\(682\) 4388.46 0.246397
\(683\) 15416.5 0.863683 0.431841 0.901950i \(-0.357864\pi\)
0.431841 + 0.901950i \(0.357864\pi\)
\(684\) 1987.23 0.111087
\(685\) −6537.00 −0.364622
\(686\) −5649.65 −0.314438
\(687\) −3507.25 −0.194774
\(688\) −1328.26 −0.0736036
\(689\) 7833.89 0.433160
\(690\) 637.560 0.0351761
\(691\) 15247.1 0.839400 0.419700 0.907663i \(-0.362135\pi\)
0.419700 + 0.907663i \(0.362135\pi\)
\(692\) −9702.05 −0.532972
\(693\) −2753.85 −0.150952
\(694\) −5113.06 −0.279667
\(695\) 5369.12 0.293039
\(696\) 1052.38 0.0573140
\(697\) 1124.76 0.0611240
\(698\) 21133.3 1.14600
\(699\) 3472.64 0.187908
\(700\) −422.800 −0.0228290
\(701\) −8160.98 −0.439709 −0.219855 0.975533i \(-0.570558\pi\)
−0.219855 + 0.975533i \(0.570558\pi\)
\(702\) −11028.0 −0.592914
\(703\) 5545.13 0.297495
\(704\) −2158.08 −0.115534
\(705\) −3855.02 −0.205941
\(706\) −9123.80 −0.486372
\(707\) −3924.28 −0.208752
\(708\) −2994.43 −0.158951
\(709\) 14069.0 0.745235 0.372618 0.927985i \(-0.378460\pi\)
0.372618 + 0.927985i \(0.378460\pi\)
\(710\) −10712.9 −0.566264
\(711\) −3771.10 −0.198913
\(712\) −5039.17 −0.265240
\(713\) −1496.66 −0.0786119
\(714\) 175.613 0.00920471
\(715\) 7241.04 0.378741
\(716\) 7647.44 0.399160
\(717\) 12044.9 0.627374
\(718\) 24214.7 1.25861
\(719\) −19040.6 −0.987613 −0.493807 0.869572i \(-0.664395\pi\)
−0.493807 + 0.869572i \(0.664395\pi\)
\(720\) −1545.28 −0.0799850
\(721\) −5842.15 −0.301766
\(722\) 12395.0 0.638910
\(723\) 1184.07 0.0609073
\(724\) −15961.5 −0.819345
\(725\) −1186.40 −0.0607749
\(726\) 1075.32 0.0549707
\(727\) −25001.6 −1.27546 −0.637728 0.770262i \(-0.720126\pi\)
−0.637728 + 0.770262i \(0.720126\pi\)
\(728\) −1452.67 −0.0739556
\(729\) 6409.57 0.325640
\(730\) 2697.56 0.136769
\(731\) −621.957 −0.0314691
\(732\) −1521.98 −0.0768500
\(733\) 7755.07 0.390778 0.195389 0.980726i \(-0.437403\pi\)
0.195389 + 0.980726i \(0.437403\pi\)
\(734\) 4431.79 0.222861
\(735\) −4506.22 −0.226142
\(736\) 736.000 0.0368605
\(737\) 14858.8 0.742647
\(738\) 5799.75 0.289284
\(739\) 1304.33 0.0649265 0.0324632 0.999473i \(-0.489665\pi\)
0.0324632 + 0.999473i \(0.489665\pi\)
\(740\) −4311.92 −0.214202
\(741\) 3062.02 0.151803
\(742\) −1542.41 −0.0763121
\(743\) 2431.00 0.120033 0.0600165 0.998197i \(-0.480885\pi\)
0.0600165 + 0.998197i \(0.480885\pi\)
\(744\) −1443.04 −0.0711080
\(745\) 11545.4 0.567773
\(746\) 7744.68 0.380098
\(747\) −2640.03 −0.129309
\(748\) −1010.52 −0.0493963
\(749\) 3229.43 0.157545
\(750\) −693.000 −0.0337397
\(751\) 1841.29 0.0894667 0.0447334 0.998999i \(-0.485756\pi\)
0.0447334 + 0.998999i \(0.485756\pi\)
\(752\) −4450.24 −0.215803
\(753\) 8536.42 0.413127
\(754\) −4076.28 −0.196883
\(755\) −438.019 −0.0211141
\(756\) 2171.30 0.104457
\(757\) 32667.3 1.56845 0.784223 0.620479i \(-0.213062\pi\)
0.784223 + 0.620479i \(0.213062\pi\)
\(758\) 1639.84 0.0785772
\(759\) 2149.85 0.102813
\(760\) 1028.80 0.0491033
\(761\) 20717.4 0.986864 0.493432 0.869784i \(-0.335742\pi\)
0.493432 + 0.869784i \(0.335742\pi\)
\(762\) 6809.74 0.323741
\(763\) 662.679 0.0314425
\(764\) 12851.0 0.608550
\(765\) −723.580 −0.0341975
\(766\) −12563.1 −0.592588
\(767\) 11598.5 0.546023
\(768\) 709.632 0.0333420
\(769\) 41399.2 1.94134 0.970671 0.240412i \(-0.0772826\pi\)
0.970671 + 0.240412i \(0.0772826\pi\)
\(770\) −1425.68 −0.0667247
\(771\) −16159.1 −0.754808
\(772\) −8525.27 −0.397450
\(773\) −29071.8 −1.35270 −0.676352 0.736578i \(-0.736440\pi\)
−0.676352 + 0.736578i \(0.736440\pi\)
\(774\) −3207.07 −0.148935
\(775\) 1626.80 0.0754018
\(776\) 3355.13 0.155209
\(777\) 2526.79 0.116664
\(778\) 27878.6 1.28470
\(779\) −3861.30 −0.177594
\(780\) −2381.04 −0.109301
\(781\) −36123.9 −1.65507
\(782\) 344.633 0.0157597
\(783\) 6092.78 0.278082
\(784\) −5201.98 −0.236971
\(785\) −9311.50 −0.423365
\(786\) −9623.57 −0.436719
\(787\) −13953.9 −0.632026 −0.316013 0.948755i \(-0.602344\pi\)
−0.316013 + 0.948755i \(0.602344\pi\)
\(788\) 13557.9 0.612920
\(789\) 9782.36 0.441396
\(790\) −1952.32 −0.0879246
\(791\) −4380.73 −0.196916
\(792\) −5210.69 −0.233780
\(793\) 5895.22 0.263992
\(794\) 5081.91 0.227141
\(795\) −2528.12 −0.112784
\(796\) −2756.13 −0.122724
\(797\) −10192.3 −0.452986 −0.226493 0.974013i \(-0.572726\pi\)
−0.226493 + 0.974013i \(0.572726\pi\)
\(798\) −602.878 −0.0267439
\(799\) −2083.83 −0.0922661
\(800\) −800.000 −0.0353553
\(801\) −12167.1 −0.536707
\(802\) −9992.26 −0.439949
\(803\) 9096.18 0.399747
\(804\) −4885.95 −0.214321
\(805\) 486.220 0.0212882
\(806\) 5589.43 0.244267
\(807\) −11398.6 −0.497213
\(808\) −7425.31 −0.323294
\(809\) −6977.15 −0.303218 −0.151609 0.988441i \(-0.548445\pi\)
−0.151609 + 0.988441i \(0.548445\pi\)
\(810\) −1656.40 −0.0718519
\(811\) −26658.1 −1.15424 −0.577122 0.816658i \(-0.695824\pi\)
−0.577122 + 0.816658i \(0.695824\pi\)
\(812\) 802.575 0.0346858
\(813\) 3102.64 0.133843
\(814\) −14539.8 −0.626069
\(815\) 383.696 0.0164911
\(816\) 332.286 0.0142553
\(817\) 2135.17 0.0914323
\(818\) 3536.69 0.151170
\(819\) −3507.48 −0.149647
\(820\) 3002.56 0.127871
\(821\) −15664.5 −0.665890 −0.332945 0.942946i \(-0.608042\pi\)
−0.332945 + 0.942946i \(0.608042\pi\)
\(822\) 7248.23 0.307556
\(823\) −10077.6 −0.426833 −0.213417 0.976961i \(-0.568459\pi\)
−0.213417 + 0.976961i \(0.568459\pi\)
\(824\) −11054.2 −0.467344
\(825\) −2336.80 −0.0986144
\(826\) −2283.63 −0.0961956
\(827\) −383.213 −0.0161132 −0.00805660 0.999968i \(-0.502565\pi\)
−0.00805660 + 0.999968i \(0.502565\pi\)
\(828\) 1777.07 0.0745864
\(829\) 36788.5 1.54128 0.770639 0.637272i \(-0.219937\pi\)
0.770639 + 0.637272i \(0.219937\pi\)
\(830\) −1366.76 −0.0571577
\(831\) −8093.66 −0.337865
\(832\) −2748.67 −0.114535
\(833\) −2435.84 −0.101317
\(834\) −5953.29 −0.247177
\(835\) −11624.8 −0.481788
\(836\) 3469.12 0.143519
\(837\) −8354.47 −0.345009
\(838\) −91.2706 −0.00376240
\(839\) −31031.6 −1.27691 −0.638457 0.769657i \(-0.720427\pi\)
−0.638457 + 0.769657i \(0.720427\pi\)
\(840\) 468.801 0.0192561
\(841\) −22136.9 −0.907660
\(842\) 1634.43 0.0668956
\(843\) 8110.61 0.331369
\(844\) 542.610 0.0221296
\(845\) −1762.34 −0.0717471
\(846\) −10745.1 −0.436672
\(847\) 820.064 0.0332677
\(848\) −2918.46 −0.118185
\(849\) 19468.1 0.786976
\(850\) −374.601 −0.0151161
\(851\) 4958.71 0.199744
\(852\) 11878.5 0.477640
\(853\) 16764.1 0.672909 0.336454 0.941700i \(-0.390772\pi\)
0.336454 + 0.941700i \(0.390772\pi\)
\(854\) −1160.70 −0.0465088
\(855\) 2484.04 0.0993595
\(856\) 6110.56 0.243989
\(857\) −10890.8 −0.434101 −0.217050 0.976160i \(-0.569644\pi\)
−0.217050 + 0.976160i \(0.569644\pi\)
\(858\) −8028.87 −0.319465
\(859\) 31687.9 1.25864 0.629322 0.777144i \(-0.283332\pi\)
0.629322 + 0.777144i \(0.283332\pi\)
\(860\) −1660.32 −0.0658330
\(861\) −1759.50 −0.0696443
\(862\) −4950.61 −0.195613
\(863\) −28981.6 −1.14316 −0.571580 0.820547i \(-0.693669\pi\)
−0.571580 + 0.820547i \(0.693669\pi\)
\(864\) 4108.42 0.161772
\(865\) −12127.6 −0.476705
\(866\) 119.274 0.00468025
\(867\) −13463.3 −0.527377
\(868\) −1100.50 −0.0430338
\(869\) −6583.23 −0.256986
\(870\) 1315.48 0.0512632
\(871\) 18925.1 0.736227
\(872\) 1253.89 0.0486950
\(873\) 8100.97 0.314062
\(874\) −1183.12 −0.0457891
\(875\) −528.500 −0.0204189
\(876\) −2991.06 −0.115364
\(877\) −27450.6 −1.05695 −0.528473 0.848950i \(-0.677235\pi\)
−0.528473 + 0.848950i \(0.677235\pi\)
\(878\) 14516.5 0.557984
\(879\) 1758.11 0.0674624
\(880\) −2697.60 −0.103337
\(881\) −34848.0 −1.33264 −0.666322 0.745664i \(-0.732132\pi\)
−0.666322 + 0.745664i \(0.732132\pi\)
\(882\) −12560.2 −0.479505
\(883\) −45419.0 −1.73100 −0.865499 0.500911i \(-0.832998\pi\)
−0.865499 + 0.500911i \(0.832998\pi\)
\(884\) −1287.07 −0.0489693
\(885\) −3743.04 −0.142170
\(886\) 19442.9 0.737241
\(887\) −44670.7 −1.69098 −0.845488 0.533994i \(-0.820691\pi\)
−0.845488 + 0.533994i \(0.820691\pi\)
\(888\) 4781.06 0.180678
\(889\) 5193.28 0.195925
\(890\) −6298.96 −0.237238
\(891\) −5585.39 −0.210009
\(892\) 821.282 0.0308280
\(893\) 7153.77 0.268076
\(894\) −12801.6 −0.478913
\(895\) 9559.30 0.357019
\(896\) 541.184 0.0201782
\(897\) 2738.20 0.101924
\(898\) 21324.6 0.792440
\(899\) −3088.06 −0.114563
\(900\) −1931.60 −0.0715408
\(901\) −1366.57 −0.0505296
\(902\) 10124.6 0.373740
\(903\) 972.949 0.0358557
\(904\) −8288.99 −0.304964
\(905\) −19951.9 −0.732845
\(906\) 485.675 0.0178096
\(907\) −9483.83 −0.347195 −0.173597 0.984817i \(-0.555539\pi\)
−0.173597 + 0.984817i \(0.555539\pi\)
\(908\) 7202.27 0.263233
\(909\) −17928.4 −0.654179
\(910\) −1815.84 −0.0661479
\(911\) −10553.9 −0.383827 −0.191913 0.981412i \(-0.561469\pi\)
−0.191913 + 0.981412i \(0.561469\pi\)
\(912\) −1140.74 −0.0414183
\(913\) −4608.71 −0.167060
\(914\) −8270.59 −0.299307
\(915\) −1902.48 −0.0687367
\(916\) −5060.96 −0.182553
\(917\) −7339.18 −0.264298
\(918\) 1923.77 0.0691655
\(919\) −1949.12 −0.0699624 −0.0349812 0.999388i \(-0.511137\pi\)
−0.0349812 + 0.999388i \(0.511137\pi\)
\(920\) 920.000 0.0329690
\(921\) 14873.3 0.532130
\(922\) 24161.2 0.863023
\(923\) −46009.7 −1.64077
\(924\) 1580.80 0.0562818
\(925\) −5389.90 −0.191588
\(926\) 4228.79 0.150072
\(927\) −26690.4 −0.945661
\(928\) 1518.59 0.0537179
\(929\) −7106.96 −0.250992 −0.125496 0.992094i \(-0.540052\pi\)
−0.125496 + 0.992094i \(0.540052\pi\)
\(930\) −1803.80 −0.0636009
\(931\) 8362.20 0.294372
\(932\) 5011.03 0.176118
\(933\) −26529.1 −0.930892
\(934\) 28363.9 0.993679
\(935\) −1263.16 −0.0441814
\(936\) −6636.67 −0.231759
\(937\) −44989.6 −1.56857 −0.784283 0.620403i \(-0.786969\pi\)
−0.784283 + 0.620403i \(0.786969\pi\)
\(938\) −3726.15 −0.129705
\(939\) −23220.4 −0.806995
\(940\) −5562.80 −0.193020
\(941\) −9932.51 −0.344092 −0.172046 0.985089i \(-0.555038\pi\)
−0.172046 + 0.985089i \(0.555038\pi\)
\(942\) 10324.6 0.357106
\(943\) −3452.95 −0.119240
\(944\) −4320.96 −0.148978
\(945\) 2714.12 0.0934290
\(946\) −5598.60 −0.192417
\(947\) −15455.2 −0.530334 −0.265167 0.964203i \(-0.585427\pi\)
−0.265167 + 0.964203i \(0.585427\pi\)
\(948\) 2164.74 0.0741638
\(949\) 11585.5 0.396292
\(950\) 1286.00 0.0439193
\(951\) −15725.0 −0.536191
\(952\) 253.410 0.00862717
\(953\) 46941.7 1.59558 0.797792 0.602932i \(-0.206001\pi\)
0.797792 + 0.602932i \(0.206001\pi\)
\(954\) −7046.63 −0.239144
\(955\) 16063.7 0.544304
\(956\) 17380.9 0.588010
\(957\) 4435.80 0.149832
\(958\) 15093.9 0.509040
\(959\) 5527.68 0.186130
\(960\) 887.041 0.0298220
\(961\) −25556.6 −0.857864
\(962\) −18518.8 −0.620656
\(963\) 14754.0 0.493707
\(964\) 1708.61 0.0570857
\(965\) −10656.6 −0.355490
\(966\) −539.121 −0.0179564
\(967\) 25323.3 0.842134 0.421067 0.907029i \(-0.361656\pi\)
0.421067 + 0.907029i \(0.361656\pi\)
\(968\) 1551.68 0.0515217
\(969\) −534.151 −0.0177083
\(970\) 4193.92 0.138823
\(971\) 28679.0 0.947840 0.473920 0.880568i \(-0.342839\pi\)
0.473920 + 0.880568i \(0.342839\pi\)
\(972\) 15702.5 0.518168
\(973\) −4540.13 −0.149589
\(974\) 34219.3 1.12573
\(975\) −2976.30 −0.0977619
\(976\) −2196.22 −0.0720281
\(977\) 7950.41 0.260344 0.130172 0.991491i \(-0.458447\pi\)
0.130172 + 0.991491i \(0.458447\pi\)
\(978\) −425.442 −0.0139102
\(979\) −21240.1 −0.693398
\(980\) −6502.48 −0.211953
\(981\) 3027.51 0.0985332
\(982\) −19667.3 −0.639114
\(983\) 6734.80 0.218522 0.109261 0.994013i \(-0.465152\pi\)
0.109261 + 0.994013i \(0.465152\pi\)
\(984\) −3329.24 −0.107858
\(985\) 16947.4 0.548212
\(986\) 711.083 0.0229670
\(987\) 3259.81 0.105127
\(988\) 4418.50 0.142278
\(989\) 1909.37 0.0613896
\(990\) −6513.36 −0.209099
\(991\) 46563.5 1.49257 0.746285 0.665626i \(-0.231835\pi\)
0.746285 + 0.665626i \(0.231835\pi\)
\(992\) −2082.31 −0.0666464
\(993\) 15070.8 0.481629
\(994\) 9058.81 0.289062
\(995\) −3445.16 −0.109768
\(996\) 1515.46 0.0482121
\(997\) 14783.7 0.469613 0.234806 0.972042i \(-0.424554\pi\)
0.234806 + 0.972042i \(0.424554\pi\)
\(998\) 3411.09 0.108192
\(999\) 27679.9 0.876631
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 230.4.a.f.1.2 2
3.2 odd 2 2070.4.a.s.1.2 2
4.3 odd 2 1840.4.a.i.1.1 2
5.2 odd 4 1150.4.b.k.599.1 4
5.3 odd 4 1150.4.b.k.599.4 4
5.4 even 2 1150.4.a.l.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.4.a.f.1.2 2 1.1 even 1 trivial
1150.4.a.l.1.1 2 5.4 even 2
1150.4.b.k.599.1 4 5.2 odd 4
1150.4.b.k.599.4 4 5.3 odd 4
1840.4.a.i.1.1 2 4.3 odd 2
2070.4.a.s.1.2 2 3.2 odd 2