Properties

Label 1035.4.a.k.1.1
Level $1035$
Weight $4$
Character 1035.1
Self dual yes
Analytic conductor $61.067$
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] = [1035,4,Mod(1,1035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1035, 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("1035.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1035 = 3^{2} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1035.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: \(61.0669768559\)
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: \( x^{5} - x^{4} - 27x^{3} + 7x^{2} + 168x + 92 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 115)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(4.60878\) of defining polynomial
Character \(\chi\) \(=\) 1035.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.60878 q^{2} +23.4584 q^{4} +5.00000 q^{5} +11.4426 q^{7} -86.7031 q^{8} +O(q^{10})\) \(q-5.60878 q^{2} +23.4584 q^{4} +5.00000 q^{5} +11.4426 q^{7} -86.7031 q^{8} -28.0439 q^{10} -37.7245 q^{11} -8.69346 q^{13} -64.1788 q^{14} +298.631 q^{16} +105.687 q^{17} -128.279 q^{19} +117.292 q^{20} +211.588 q^{22} +23.0000 q^{23} +25.0000 q^{25} +48.7597 q^{26} +268.425 q^{28} +133.383 q^{29} +106.008 q^{31} -981.333 q^{32} -592.773 q^{34} +57.2128 q^{35} -248.835 q^{37} +719.491 q^{38} -433.515 q^{40} -134.233 q^{41} +108.684 q^{43} -884.957 q^{44} -129.002 q^{46} +76.2000 q^{47} -212.068 q^{49} -140.220 q^{50} -203.935 q^{52} -476.207 q^{53} -188.622 q^{55} -992.105 q^{56} -748.118 q^{58} -608.000 q^{59} -366.273 q^{61} -594.575 q^{62} +3115.03 q^{64} -43.4673 q^{65} +136.041 q^{67} +2479.24 q^{68} -320.894 q^{70} +152.874 q^{71} +1228.16 q^{73} +1395.66 q^{74} -3009.23 q^{76} -431.664 q^{77} -364.637 q^{79} +1493.16 q^{80} +752.882 q^{82} +762.744 q^{83} +528.433 q^{85} -609.583 q^{86} +3270.83 q^{88} -271.222 q^{89} -99.4754 q^{91} +539.544 q^{92} -427.389 q^{94} -641.396 q^{95} +574.510 q^{97} +1189.44 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 6 q^{2} + 22 q^{4} + 25 q^{5} - 3 q^{7} - 138 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 6 q^{2} + 22 q^{4} + 25 q^{5} - 3 q^{7} - 138 q^{8} - 30 q^{10} - 23 q^{11} + 132 q^{13} - 93 q^{14} + 282 q^{16} - 23 q^{17} - 161 q^{19} + 110 q^{20} + 193 q^{22} + 115 q^{23} + 125 q^{25} + 257 q^{26} + 17 q^{28} - 401 q^{29} + 32 q^{31} - 670 q^{32} - 663 q^{34} - 15 q^{35} - 38 q^{37} + 875 q^{38} - 690 q^{40} + 12 q^{41} - 566 q^{43} - 47 q^{44} - 138 q^{46} - 919 q^{47} - 738 q^{49} - 150 q^{50} - 305 q^{52} - 1156 q^{53} - 115 q^{55} - 343 q^{56} - 1042 q^{58} - 1324 q^{59} - 1673 q^{61} - 565 q^{62} + 2466 q^{64} + 660 q^{65} + 558 q^{67} + 2267 q^{68} - 465 q^{70} + 108 q^{71} + 1173 q^{73} - 1458 q^{74} - 3477 q^{76} - 2608 q^{77} + 656 q^{79} + 1410 q^{80} + 3505 q^{82} + 82 q^{83} - 115 q^{85} - 112 q^{86} + 2397 q^{88} - 570 q^{89} - 1589 q^{91} + 506 q^{92} - 948 q^{94} - 805 q^{95} + 633 q^{97} + 2555 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.60878 −1.98300 −0.991502 0.130090i \(-0.958473\pi\)
−0.991502 + 0.130090i \(0.958473\pi\)
\(3\) 0 0
\(4\) 23.4584 2.93231
\(5\) 5.00000 0.447214
\(6\) 0 0
\(7\) 11.4426 0.617840 0.308920 0.951088i \(-0.400032\pi\)
0.308920 + 0.951088i \(0.400032\pi\)
\(8\) −86.7031 −3.83177
\(9\) 0 0
\(10\) −28.0439 −0.886826
\(11\) −37.7245 −1.03403 −0.517016 0.855976i \(-0.672957\pi\)
−0.517016 + 0.855976i \(0.672957\pi\)
\(12\) 0 0
\(13\) −8.69346 −0.185472 −0.0927358 0.995691i \(-0.529561\pi\)
−0.0927358 + 0.995691i \(0.529561\pi\)
\(14\) −64.1788 −1.22518
\(15\) 0 0
\(16\) 298.631 4.66611
\(17\) 105.687 1.50781 0.753905 0.656983i \(-0.228168\pi\)
0.753905 + 0.656983i \(0.228168\pi\)
\(18\) 0 0
\(19\) −128.279 −1.54891 −0.774455 0.632629i \(-0.781976\pi\)
−0.774455 + 0.632629i \(0.781976\pi\)
\(20\) 117.292 1.31137
\(21\) 0 0
\(22\) 211.588 2.05049
\(23\) 23.0000 0.208514
\(24\) 0 0
\(25\) 25.0000 0.200000
\(26\) 48.7597 0.367791
\(27\) 0 0
\(28\) 268.425 1.81170
\(29\) 133.383 0.854092 0.427046 0.904230i \(-0.359554\pi\)
0.427046 + 0.904230i \(0.359554\pi\)
\(30\) 0 0
\(31\) 106.008 0.614179 0.307090 0.951681i \(-0.400645\pi\)
0.307090 + 0.951681i \(0.400645\pi\)
\(32\) −981.333 −5.42115
\(33\) 0 0
\(34\) −592.773 −2.98999
\(35\) 57.2128 0.276306
\(36\) 0 0
\(37\) −248.835 −1.10563 −0.552814 0.833305i \(-0.686446\pi\)
−0.552814 + 0.833305i \(0.686446\pi\)
\(38\) 719.491 3.07150
\(39\) 0 0
\(40\) −433.515 −1.71362
\(41\) −134.233 −0.511308 −0.255654 0.966768i \(-0.582291\pi\)
−0.255654 + 0.966768i \(0.582291\pi\)
\(42\) 0 0
\(43\) 108.684 0.385444 0.192722 0.981253i \(-0.438268\pi\)
0.192722 + 0.981253i \(0.438268\pi\)
\(44\) −884.957 −3.03210
\(45\) 0 0
\(46\) −129.002 −0.413485
\(47\) 76.2000 0.236488 0.118244 0.992985i \(-0.462274\pi\)
0.118244 + 0.992985i \(0.462274\pi\)
\(48\) 0 0
\(49\) −212.068 −0.618274
\(50\) −140.220 −0.396601
\(51\) 0 0
\(52\) −203.935 −0.543859
\(53\) −476.207 −1.23419 −0.617095 0.786889i \(-0.711691\pi\)
−0.617095 + 0.786889i \(0.711691\pi\)
\(54\) 0 0
\(55\) −188.622 −0.462433
\(56\) −992.105 −2.36742
\(57\) 0 0
\(58\) −748.118 −1.69367
\(59\) −608.000 −1.34161 −0.670804 0.741635i \(-0.734051\pi\)
−0.670804 + 0.741635i \(0.734051\pi\)
\(60\) 0 0
\(61\) −366.273 −0.768794 −0.384397 0.923168i \(-0.625591\pi\)
−0.384397 + 0.923168i \(0.625591\pi\)
\(62\) −594.575 −1.21792
\(63\) 0 0
\(64\) 3115.03 6.08405
\(65\) −43.4673 −0.0829454
\(66\) 0 0
\(67\) 136.041 0.248060 0.124030 0.992278i \(-0.460418\pi\)
0.124030 + 0.992278i \(0.460418\pi\)
\(68\) 2479.24 4.42136
\(69\) 0 0
\(70\) −320.894 −0.547917
\(71\) 152.874 0.255533 0.127766 0.991804i \(-0.459219\pi\)
0.127766 + 0.991804i \(0.459219\pi\)
\(72\) 0 0
\(73\) 1228.16 1.96911 0.984556 0.175070i \(-0.0560151\pi\)
0.984556 + 0.175070i \(0.0560151\pi\)
\(74\) 1395.66 2.19246
\(75\) 0 0
\(76\) −3009.23 −4.54188
\(77\) −431.664 −0.638867
\(78\) 0 0
\(79\) −364.637 −0.519302 −0.259651 0.965702i \(-0.583608\pi\)
−0.259651 + 0.965702i \(0.583608\pi\)
\(80\) 1493.16 2.08675
\(81\) 0 0
\(82\) 752.882 1.01393
\(83\) 762.744 1.00870 0.504350 0.863499i \(-0.331732\pi\)
0.504350 + 0.863499i \(0.331732\pi\)
\(84\) 0 0
\(85\) 528.433 0.674313
\(86\) −609.583 −0.764338
\(87\) 0 0
\(88\) 3270.83 3.96217
\(89\) −271.222 −0.323028 −0.161514 0.986870i \(-0.551638\pi\)
−0.161514 + 0.986870i \(0.551638\pi\)
\(90\) 0 0
\(91\) −99.4754 −0.114592
\(92\) 539.544 0.611428
\(93\) 0 0
\(94\) −427.389 −0.468956
\(95\) −641.396 −0.692694
\(96\) 0 0
\(97\) 574.510 0.601367 0.300684 0.953724i \(-0.402785\pi\)
0.300684 + 0.953724i \(0.402785\pi\)
\(98\) 1189.44 1.22604
\(99\) 0 0
\(100\) 586.461 0.586461
\(101\) −1372.25 −1.35192 −0.675958 0.736940i \(-0.736270\pi\)
−0.675958 + 0.736940i \(0.736270\pi\)
\(102\) 0 0
\(103\) −242.428 −0.231914 −0.115957 0.993254i \(-0.536993\pi\)
−0.115957 + 0.993254i \(0.536993\pi\)
\(104\) 753.749 0.710685
\(105\) 0 0
\(106\) 2670.94 2.44740
\(107\) −650.896 −0.588079 −0.294039 0.955793i \(-0.595000\pi\)
−0.294039 + 0.955793i \(0.595000\pi\)
\(108\) 0 0
\(109\) −1230.43 −1.08123 −0.540613 0.841271i \(-0.681808\pi\)
−0.540613 + 0.841271i \(0.681808\pi\)
\(110\) 1057.94 0.917007
\(111\) 0 0
\(112\) 3417.10 2.88291
\(113\) −238.959 −0.198932 −0.0994662 0.995041i \(-0.531714\pi\)
−0.0994662 + 0.995041i \(0.531714\pi\)
\(114\) 0 0
\(115\) 115.000 0.0932505
\(116\) 3128.97 2.50446
\(117\) 0 0
\(118\) 3410.14 2.66041
\(119\) 1209.33 0.931586
\(120\) 0 0
\(121\) 92.1354 0.0692227
\(122\) 2054.34 1.52452
\(123\) 0 0
\(124\) 2486.78 1.80096
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) 2608.48 1.82256 0.911280 0.411788i \(-0.135096\pi\)
0.911280 + 0.411788i \(0.135096\pi\)
\(128\) −9620.89 −6.64355
\(129\) 0 0
\(130\) 243.799 0.164481
\(131\) 936.409 0.624538 0.312269 0.949994i \(-0.398911\pi\)
0.312269 + 0.949994i \(0.398911\pi\)
\(132\) 0 0
\(133\) −1467.84 −0.956979
\(134\) −763.023 −0.491904
\(135\) 0 0
\(136\) −9163.36 −5.77758
\(137\) −415.511 −0.259121 −0.129560 0.991572i \(-0.541357\pi\)
−0.129560 + 0.991572i \(0.541357\pi\)
\(138\) 0 0
\(139\) −949.629 −0.579471 −0.289736 0.957107i \(-0.593567\pi\)
−0.289736 + 0.957107i \(0.593567\pi\)
\(140\) 1342.12 0.810215
\(141\) 0 0
\(142\) −857.439 −0.506723
\(143\) 327.956 0.191784
\(144\) 0 0
\(145\) 666.917 0.381962
\(146\) −6888.48 −3.90476
\(147\) 0 0
\(148\) −5837.28 −3.24204
\(149\) −2209.84 −1.21502 −0.607508 0.794314i \(-0.707831\pi\)
−0.607508 + 0.794314i \(0.707831\pi\)
\(150\) 0 0
\(151\) −1384.25 −0.746018 −0.373009 0.927828i \(-0.621674\pi\)
−0.373009 + 0.927828i \(0.621674\pi\)
\(152\) 11122.2 5.93507
\(153\) 0 0
\(154\) 2421.11 1.26688
\(155\) 530.039 0.274669
\(156\) 0 0
\(157\) 561.399 0.285379 0.142690 0.989767i \(-0.454425\pi\)
0.142690 + 0.989767i \(0.454425\pi\)
\(158\) 2045.17 1.02978
\(159\) 0 0
\(160\) −4906.66 −2.42441
\(161\) 263.179 0.128829
\(162\) 0 0
\(163\) 2134.47 1.02567 0.512836 0.858487i \(-0.328595\pi\)
0.512836 + 0.858487i \(0.328595\pi\)
\(164\) −3148.89 −1.49931
\(165\) 0 0
\(166\) −4278.07 −2.00026
\(167\) 1315.64 0.609623 0.304812 0.952413i \(-0.401406\pi\)
0.304812 + 0.952413i \(0.401406\pi\)
\(168\) 0 0
\(169\) −2121.42 −0.965600
\(170\) −2963.87 −1.33717
\(171\) 0 0
\(172\) 2549.55 1.13024
\(173\) −676.565 −0.297331 −0.148666 0.988888i \(-0.547498\pi\)
−0.148666 + 0.988888i \(0.547498\pi\)
\(174\) 0 0
\(175\) 286.064 0.123568
\(176\) −11265.7 −4.82491
\(177\) 0 0
\(178\) 1521.23 0.640566
\(179\) 3737.96 1.56083 0.780414 0.625263i \(-0.215008\pi\)
0.780414 + 0.625263i \(0.215008\pi\)
\(180\) 0 0
\(181\) −1873.40 −0.769330 −0.384665 0.923056i \(-0.625683\pi\)
−0.384665 + 0.923056i \(0.625683\pi\)
\(182\) 557.936 0.227236
\(183\) 0 0
\(184\) −1994.17 −0.798979
\(185\) −1244.18 −0.494452
\(186\) 0 0
\(187\) −3986.97 −1.55912
\(188\) 1787.53 0.693454
\(189\) 0 0
\(190\) 3597.45 1.37361
\(191\) 5158.92 1.95438 0.977190 0.212366i \(-0.0681169\pi\)
0.977190 + 0.212366i \(0.0681169\pi\)
\(192\) 0 0
\(193\) −4806.41 −1.79261 −0.896303 0.443442i \(-0.853757\pi\)
−0.896303 + 0.443442i \(0.853757\pi\)
\(194\) −3222.30 −1.19251
\(195\) 0 0
\(196\) −4974.78 −1.81297
\(197\) −3202.59 −1.15825 −0.579125 0.815239i \(-0.696606\pi\)
−0.579125 + 0.815239i \(0.696606\pi\)
\(198\) 0 0
\(199\) −2210.46 −0.787415 −0.393707 0.919236i \(-0.628808\pi\)
−0.393707 + 0.919236i \(0.628808\pi\)
\(200\) −2167.58 −0.766354
\(201\) 0 0
\(202\) 7696.62 2.68085
\(203\) 1526.25 0.527692
\(204\) 0 0
\(205\) −671.163 −0.228664
\(206\) 1359.73 0.459886
\(207\) 0 0
\(208\) −2596.14 −0.865431
\(209\) 4839.27 1.60162
\(210\) 0 0
\(211\) 153.164 0.0499726 0.0249863 0.999688i \(-0.492046\pi\)
0.0249863 + 0.999688i \(0.492046\pi\)
\(212\) −11171.1 −3.61902
\(213\) 0 0
\(214\) 3650.73 1.16616
\(215\) 543.419 0.172376
\(216\) 0 0
\(217\) 1213.00 0.379465
\(218\) 6901.21 2.14408
\(219\) 0 0
\(220\) −4424.79 −1.35600
\(221\) −918.782 −0.279656
\(222\) 0 0
\(223\) −3068.41 −0.921416 −0.460708 0.887552i \(-0.652405\pi\)
−0.460708 + 0.887552i \(0.652405\pi\)
\(224\) −11229.0 −3.34940
\(225\) 0 0
\(226\) 1340.27 0.394484
\(227\) −4540.20 −1.32750 −0.663752 0.747953i \(-0.731037\pi\)
−0.663752 + 0.747953i \(0.731037\pi\)
\(228\) 0 0
\(229\) 1476.25 0.425996 0.212998 0.977053i \(-0.431677\pi\)
0.212998 + 0.977053i \(0.431677\pi\)
\(230\) −645.010 −0.184916
\(231\) 0 0
\(232\) −11564.7 −3.27269
\(233\) 90.7306 0.0255106 0.0127553 0.999919i \(-0.495940\pi\)
0.0127553 + 0.999919i \(0.495940\pi\)
\(234\) 0 0
\(235\) 381.000 0.105760
\(236\) −14262.7 −3.93400
\(237\) 0 0
\(238\) −6782.85 −1.84734
\(239\) 1619.16 0.438221 0.219111 0.975700i \(-0.429684\pi\)
0.219111 + 0.975700i \(0.429684\pi\)
\(240\) 0 0
\(241\) −6447.48 −1.72331 −0.861657 0.507491i \(-0.830573\pi\)
−0.861657 + 0.507491i \(0.830573\pi\)
\(242\) −516.768 −0.137269
\(243\) 0 0
\(244\) −8592.19 −2.25434
\(245\) −1060.34 −0.276500
\(246\) 0 0
\(247\) 1115.19 0.287279
\(248\) −9191.20 −2.35339
\(249\) 0 0
\(250\) −701.098 −0.177365
\(251\) −3428.17 −0.862089 −0.431044 0.902331i \(-0.641855\pi\)
−0.431044 + 0.902331i \(0.641855\pi\)
\(252\) 0 0
\(253\) −867.663 −0.215611
\(254\) −14630.4 −3.61414
\(255\) 0 0
\(256\) 29041.2 7.09014
\(257\) −2261.08 −0.548803 −0.274402 0.961615i \(-0.588480\pi\)
−0.274402 + 0.961615i \(0.588480\pi\)
\(258\) 0 0
\(259\) −2847.31 −0.683101
\(260\) −1019.67 −0.243221
\(261\) 0 0
\(262\) −5252.11 −1.23846
\(263\) −5319.64 −1.24724 −0.623618 0.781729i \(-0.714338\pi\)
−0.623618 + 0.781729i \(0.714338\pi\)
\(264\) 0 0
\(265\) −2381.04 −0.551947
\(266\) 8232.81 1.89769
\(267\) 0 0
\(268\) 3191.31 0.727388
\(269\) 1992.51 0.451620 0.225810 0.974171i \(-0.427497\pi\)
0.225810 + 0.974171i \(0.427497\pi\)
\(270\) 0 0
\(271\) 3950.62 0.885546 0.442773 0.896634i \(-0.353995\pi\)
0.442773 + 0.896634i \(0.353995\pi\)
\(272\) 31561.3 7.03561
\(273\) 0 0
\(274\) 2330.51 0.513837
\(275\) −943.112 −0.206806
\(276\) 0 0
\(277\) −178.126 −0.0386375 −0.0193187 0.999813i \(-0.506150\pi\)
−0.0193187 + 0.999813i \(0.506150\pi\)
\(278\) 5326.27 1.14909
\(279\) 0 0
\(280\) −4960.53 −1.05874
\(281\) −3523.49 −0.748020 −0.374010 0.927425i \(-0.622017\pi\)
−0.374010 + 0.927425i \(0.622017\pi\)
\(282\) 0 0
\(283\) −699.284 −0.146884 −0.0734419 0.997300i \(-0.523398\pi\)
−0.0734419 + 0.997300i \(0.523398\pi\)
\(284\) 3586.19 0.749301
\(285\) 0 0
\(286\) −1839.43 −0.380308
\(287\) −1535.96 −0.315906
\(288\) 0 0
\(289\) 6256.67 1.27349
\(290\) −3740.59 −0.757431
\(291\) 0 0
\(292\) 28810.7 5.77404
\(293\) −8552.97 −1.70536 −0.852678 0.522436i \(-0.825023\pi\)
−0.852678 + 0.522436i \(0.825023\pi\)
\(294\) 0 0
\(295\) −3040.00 −0.599985
\(296\) 21574.8 4.23651
\(297\) 0 0
\(298\) 12394.5 2.40938
\(299\) −199.949 −0.0386735
\(300\) 0 0
\(301\) 1243.62 0.238143
\(302\) 7763.96 1.47936
\(303\) 0 0
\(304\) −38308.2 −7.22739
\(305\) −1831.36 −0.343815
\(306\) 0 0
\(307\) −5621.73 −1.04511 −0.522555 0.852606i \(-0.675021\pi\)
−0.522555 + 0.852606i \(0.675021\pi\)
\(308\) −10126.2 −1.87335
\(309\) 0 0
\(310\) −2972.87 −0.544671
\(311\) 6533.62 1.19128 0.595639 0.803252i \(-0.296899\pi\)
0.595639 + 0.803252i \(0.296899\pi\)
\(312\) 0 0
\(313\) −2713.24 −0.489973 −0.244987 0.969526i \(-0.578784\pi\)
−0.244987 + 0.969526i \(0.578784\pi\)
\(314\) −3148.77 −0.565908
\(315\) 0 0
\(316\) −8553.82 −1.52275
\(317\) 7544.32 1.33669 0.668346 0.743851i \(-0.267003\pi\)
0.668346 + 0.743851i \(0.267003\pi\)
\(318\) 0 0
\(319\) −5031.82 −0.883159
\(320\) 15575.2 2.72087
\(321\) 0 0
\(322\) −1476.11 −0.255468
\(323\) −13557.4 −2.33546
\(324\) 0 0
\(325\) −217.336 −0.0370943
\(326\) −11971.8 −2.03391
\(327\) 0 0
\(328\) 11638.4 1.95921
\(329\) 871.923 0.146111
\(330\) 0 0
\(331\) 5991.64 0.994956 0.497478 0.867477i \(-0.334260\pi\)
0.497478 + 0.867477i \(0.334260\pi\)
\(332\) 17892.8 2.95782
\(333\) 0 0
\(334\) −7379.13 −1.20889
\(335\) 680.204 0.110936
\(336\) 0 0
\(337\) 5665.46 0.915778 0.457889 0.889009i \(-0.348606\pi\)
0.457889 + 0.889009i \(0.348606\pi\)
\(338\) 11898.6 1.91479
\(339\) 0 0
\(340\) 12396.2 1.97729
\(341\) −3999.09 −0.635081
\(342\) 0 0
\(343\) −6351.40 −0.999834
\(344\) −9423.21 −1.47693
\(345\) 0 0
\(346\) 3794.71 0.589609
\(347\) −5593.30 −0.865315 −0.432657 0.901558i \(-0.642424\pi\)
−0.432657 + 0.901558i \(0.642424\pi\)
\(348\) 0 0
\(349\) 4304.61 0.660230 0.330115 0.943941i \(-0.392912\pi\)
0.330115 + 0.943941i \(0.392912\pi\)
\(350\) −1604.47 −0.245036
\(351\) 0 0
\(352\) 37020.3 5.60564
\(353\) −1056.64 −0.159318 −0.0796592 0.996822i \(-0.525383\pi\)
−0.0796592 + 0.996822i \(0.525383\pi\)
\(354\) 0 0
\(355\) 764.371 0.114278
\(356\) −6362.45 −0.947217
\(357\) 0 0
\(358\) −20965.4 −3.09513
\(359\) −5186.43 −0.762477 −0.381238 0.924477i \(-0.624502\pi\)
−0.381238 + 0.924477i \(0.624502\pi\)
\(360\) 0 0
\(361\) 9596.58 1.39912
\(362\) 10507.5 1.52558
\(363\) 0 0
\(364\) −2333.54 −0.336018
\(365\) 6140.80 0.880614
\(366\) 0 0
\(367\) 178.772 0.0254274 0.0127137 0.999919i \(-0.495953\pi\)
0.0127137 + 0.999919i \(0.495953\pi\)
\(368\) 6868.52 0.972952
\(369\) 0 0
\(370\) 6978.31 0.980500
\(371\) −5449.03 −0.762532
\(372\) 0 0
\(373\) 7463.86 1.03610 0.518049 0.855351i \(-0.326659\pi\)
0.518049 + 0.855351i \(0.326659\pi\)
\(374\) 22362.1 3.09175
\(375\) 0 0
\(376\) −6606.78 −0.906166
\(377\) −1159.56 −0.158410
\(378\) 0 0
\(379\) −6075.99 −0.823490 −0.411745 0.911299i \(-0.635081\pi\)
−0.411745 + 0.911299i \(0.635081\pi\)
\(380\) −15046.2 −2.03119
\(381\) 0 0
\(382\) −28935.3 −3.87554
\(383\) 580.709 0.0774747 0.0387374 0.999249i \(-0.487666\pi\)
0.0387374 + 0.999249i \(0.487666\pi\)
\(384\) 0 0
\(385\) −2158.32 −0.285710
\(386\) 26958.1 3.55475
\(387\) 0 0
\(388\) 13477.1 1.76339
\(389\) −11373.5 −1.48241 −0.741205 0.671278i \(-0.765745\pi\)
−0.741205 + 0.671278i \(0.765745\pi\)
\(390\) 0 0
\(391\) 2430.79 0.314400
\(392\) 18386.9 2.36908
\(393\) 0 0
\(394\) 17962.6 2.29681
\(395\) −1823.19 −0.232239
\(396\) 0 0
\(397\) 3701.46 0.467937 0.233969 0.972244i \(-0.424829\pi\)
0.233969 + 0.972244i \(0.424829\pi\)
\(398\) 12398.0 1.56145
\(399\) 0 0
\(400\) 7465.78 0.933222
\(401\) 7615.01 0.948317 0.474159 0.880439i \(-0.342752\pi\)
0.474159 + 0.880439i \(0.342752\pi\)
\(402\) 0 0
\(403\) −921.574 −0.113913
\(404\) −32190.7 −3.96423
\(405\) 0 0
\(406\) −8560.39 −1.04642
\(407\) 9387.17 1.14325
\(408\) 0 0
\(409\) −15423.6 −1.86466 −0.932330 0.361608i \(-0.882228\pi\)
−0.932330 + 0.361608i \(0.882228\pi\)
\(410\) 3764.41 0.453441
\(411\) 0 0
\(412\) −5686.98 −0.680042
\(413\) −6957.07 −0.828899
\(414\) 0 0
\(415\) 3813.72 0.451104
\(416\) 8531.17 1.00547
\(417\) 0 0
\(418\) −27142.4 −3.17603
\(419\) −4273.20 −0.498233 −0.249116 0.968474i \(-0.580140\pi\)
−0.249116 + 0.968474i \(0.580140\pi\)
\(420\) 0 0
\(421\) −6076.38 −0.703432 −0.351716 0.936107i \(-0.614402\pi\)
−0.351716 + 0.936107i \(0.614402\pi\)
\(422\) −859.061 −0.0990958
\(423\) 0 0
\(424\) 41288.6 4.72913
\(425\) 2642.17 0.301562
\(426\) 0 0
\(427\) −4191.10 −0.474991
\(428\) −15269.0 −1.72443
\(429\) 0 0
\(430\) −3047.92 −0.341822
\(431\) 3386.04 0.378422 0.189211 0.981936i \(-0.439407\pi\)
0.189211 + 0.981936i \(0.439407\pi\)
\(432\) 0 0
\(433\) 7924.63 0.879523 0.439762 0.898114i \(-0.355063\pi\)
0.439762 + 0.898114i \(0.355063\pi\)
\(434\) −6803.46 −0.752480
\(435\) 0 0
\(436\) −28863.9 −3.17049
\(437\) −2950.42 −0.322970
\(438\) 0 0
\(439\) 13530.9 1.47106 0.735530 0.677492i \(-0.236933\pi\)
0.735530 + 0.677492i \(0.236933\pi\)
\(440\) 16354.1 1.77194
\(441\) 0 0
\(442\) 5153.25 0.554559
\(443\) −996.052 −0.106826 −0.0534129 0.998573i \(-0.517010\pi\)
−0.0534129 + 0.998573i \(0.517010\pi\)
\(444\) 0 0
\(445\) −1356.11 −0.144463
\(446\) 17210.0 1.82717
\(447\) 0 0
\(448\) 35644.0 3.75897
\(449\) 5079.36 0.533875 0.266938 0.963714i \(-0.413988\pi\)
0.266938 + 0.963714i \(0.413988\pi\)
\(450\) 0 0
\(451\) 5063.85 0.528709
\(452\) −5605.60 −0.583331
\(453\) 0 0
\(454\) 25465.0 2.63245
\(455\) −497.377 −0.0512470
\(456\) 0 0
\(457\) −11190.9 −1.14549 −0.572747 0.819732i \(-0.694122\pi\)
−0.572747 + 0.819732i \(0.694122\pi\)
\(458\) −8279.94 −0.844752
\(459\) 0 0
\(460\) 2697.72 0.273439
\(461\) −2426.07 −0.245105 −0.122553 0.992462i \(-0.539108\pi\)
−0.122553 + 0.992462i \(0.539108\pi\)
\(462\) 0 0
\(463\) −16349.2 −1.64106 −0.820531 0.571602i \(-0.806322\pi\)
−0.820531 + 0.571602i \(0.806322\pi\)
\(464\) 39832.4 3.98529
\(465\) 0 0
\(466\) −508.889 −0.0505876
\(467\) 2880.80 0.285455 0.142728 0.989762i \(-0.454413\pi\)
0.142728 + 0.989762i \(0.454413\pi\)
\(468\) 0 0
\(469\) 1556.65 0.153261
\(470\) −2136.95 −0.209723
\(471\) 0 0
\(472\) 52715.4 5.14073
\(473\) −4100.03 −0.398562
\(474\) 0 0
\(475\) −3206.98 −0.309782
\(476\) 28368.9 2.73169
\(477\) 0 0
\(478\) −9081.53 −0.868994
\(479\) −7850.31 −0.748831 −0.374415 0.927261i \(-0.622157\pi\)
−0.374415 + 0.927261i \(0.622157\pi\)
\(480\) 0 0
\(481\) 2163.24 0.205063
\(482\) 36162.5 3.41734
\(483\) 0 0
\(484\) 2161.35 0.202982
\(485\) 2872.55 0.268940
\(486\) 0 0
\(487\) −11262.4 −1.04794 −0.523971 0.851736i \(-0.675550\pi\)
−0.523971 + 0.851736i \(0.675550\pi\)
\(488\) 31757.0 2.94584
\(489\) 0 0
\(490\) 5947.21 0.548301
\(491\) −15810.7 −1.45321 −0.726607 0.687054i \(-0.758904\pi\)
−0.726607 + 0.687054i \(0.758904\pi\)
\(492\) 0 0
\(493\) 14096.8 1.28781
\(494\) −6254.86 −0.569675
\(495\) 0 0
\(496\) 31657.2 2.86583
\(497\) 1749.27 0.157878
\(498\) 0 0
\(499\) −10470.4 −0.939322 −0.469661 0.882847i \(-0.655624\pi\)
−0.469661 + 0.882847i \(0.655624\pi\)
\(500\) 2932.31 0.262273
\(501\) 0 0
\(502\) 19227.9 1.70953
\(503\) 5425.35 0.480923 0.240462 0.970659i \(-0.422701\pi\)
0.240462 + 0.970659i \(0.422701\pi\)
\(504\) 0 0
\(505\) −6861.23 −0.604595
\(506\) 4866.53 0.427557
\(507\) 0 0
\(508\) 61190.9 5.34430
\(509\) −8098.38 −0.705215 −0.352608 0.935771i \(-0.614705\pi\)
−0.352608 + 0.935771i \(0.614705\pi\)
\(510\) 0 0
\(511\) 14053.3 1.21660
\(512\) −85918.7 −7.41622
\(513\) 0 0
\(514\) 12681.9 1.08828
\(515\) −1212.14 −0.103715
\(516\) 0 0
\(517\) −2874.60 −0.244536
\(518\) 15969.9 1.35459
\(519\) 0 0
\(520\) 3768.75 0.317828
\(521\) −14691.8 −1.23543 −0.617717 0.786400i \(-0.711942\pi\)
−0.617717 + 0.786400i \(0.711942\pi\)
\(522\) 0 0
\(523\) −19263.6 −1.61059 −0.805297 0.592872i \(-0.797994\pi\)
−0.805297 + 0.592872i \(0.797994\pi\)
\(524\) 21966.7 1.83134
\(525\) 0 0
\(526\) 29836.7 2.47327
\(527\) 11203.6 0.926066
\(528\) 0 0
\(529\) 529.000 0.0434783
\(530\) 13354.7 1.09451
\(531\) 0 0
\(532\) −34433.3 −2.80615
\(533\) 1166.95 0.0948331
\(534\) 0 0
\(535\) −3254.48 −0.262997
\(536\) −11795.2 −0.950510
\(537\) 0 0
\(538\) −11175.6 −0.895564
\(539\) 8000.15 0.639315
\(540\) 0 0
\(541\) −18737.4 −1.48906 −0.744531 0.667588i \(-0.767327\pi\)
−0.744531 + 0.667588i \(0.767327\pi\)
\(542\) −22158.2 −1.75604
\(543\) 0 0
\(544\) −103714. −8.17407
\(545\) −6152.14 −0.483539
\(546\) 0 0
\(547\) −14180.2 −1.10841 −0.554207 0.832379i \(-0.686978\pi\)
−0.554207 + 0.832379i \(0.686978\pi\)
\(548\) −9747.25 −0.759821
\(549\) 0 0
\(550\) 5289.71 0.410098
\(551\) −17110.3 −1.32291
\(552\) 0 0
\(553\) −4172.38 −0.320846
\(554\) 999.073 0.0766183
\(555\) 0 0
\(556\) −22276.8 −1.69919
\(557\) −15154.2 −1.15279 −0.576397 0.817170i \(-0.695542\pi\)
−0.576397 + 0.817170i \(0.695542\pi\)
\(558\) 0 0
\(559\) −944.837 −0.0714890
\(560\) 17085.5 1.28928
\(561\) 0 0
\(562\) 19762.5 1.48333
\(563\) −14444.7 −1.08130 −0.540651 0.841247i \(-0.681822\pi\)
−0.540651 + 0.841247i \(0.681822\pi\)
\(564\) 0 0
\(565\) −1194.79 −0.0889653
\(566\) 3922.13 0.291271
\(567\) 0 0
\(568\) −13254.7 −0.979144
\(569\) 8851.15 0.652125 0.326063 0.945348i \(-0.394278\pi\)
0.326063 + 0.945348i \(0.394278\pi\)
\(570\) 0 0
\(571\) −22318.9 −1.63576 −0.817879 0.575391i \(-0.804850\pi\)
−0.817879 + 0.575391i \(0.804850\pi\)
\(572\) 7693.34 0.562368
\(573\) 0 0
\(574\) 8614.89 0.626444
\(575\) 575.000 0.0417029
\(576\) 0 0
\(577\) −4530.99 −0.326911 −0.163455 0.986551i \(-0.552264\pi\)
−0.163455 + 0.986551i \(0.552264\pi\)
\(578\) −35092.3 −2.52534
\(579\) 0 0
\(580\) 15644.8 1.12003
\(581\) 8727.75 0.623215
\(582\) 0 0
\(583\) 17964.7 1.27619
\(584\) −106485. −7.54519
\(585\) 0 0
\(586\) 47971.7 3.38173
\(587\) 5092.89 0.358103 0.179051 0.983840i \(-0.442697\pi\)
0.179051 + 0.983840i \(0.442697\pi\)
\(588\) 0 0
\(589\) −13598.6 −0.951309
\(590\) 17050.7 1.18977
\(591\) 0 0
\(592\) −74309.9 −5.15898
\(593\) −4193.92 −0.290427 −0.145214 0.989400i \(-0.546387\pi\)
−0.145214 + 0.989400i \(0.546387\pi\)
\(594\) 0 0
\(595\) 6046.63 0.416618
\(596\) −51839.5 −3.56280
\(597\) 0 0
\(598\) 1121.47 0.0766897
\(599\) −17663.0 −1.20483 −0.602414 0.798184i \(-0.705794\pi\)
−0.602414 + 0.798184i \(0.705794\pi\)
\(600\) 0 0
\(601\) −15817.7 −1.07357 −0.536785 0.843719i \(-0.680361\pi\)
−0.536785 + 0.843719i \(0.680361\pi\)
\(602\) −6975.19 −0.472239
\(603\) 0 0
\(604\) −32472.4 −2.18755
\(605\) 460.677 0.0309573
\(606\) 0 0
\(607\) −740.284 −0.0495011 −0.0247506 0.999694i \(-0.507879\pi\)
−0.0247506 + 0.999694i \(0.507879\pi\)
\(608\) 125885. 8.39687
\(609\) 0 0
\(610\) 10271.7 0.681786
\(611\) −662.441 −0.0438617
\(612\) 0 0
\(613\) −12412.1 −0.817815 −0.408908 0.912576i \(-0.634090\pi\)
−0.408908 + 0.912576i \(0.634090\pi\)
\(614\) 31531.0 2.07246
\(615\) 0 0
\(616\) 37426.6 2.44799
\(617\) 27047.9 1.76484 0.882422 0.470459i \(-0.155911\pi\)
0.882422 + 0.470459i \(0.155911\pi\)
\(618\) 0 0
\(619\) 193.644 0.0125738 0.00628691 0.999980i \(-0.497999\pi\)
0.00628691 + 0.999980i \(0.497999\pi\)
\(620\) 12433.9 0.805415
\(621\) 0 0
\(622\) −36645.6 −2.36231
\(623\) −3103.48 −0.199580
\(624\) 0 0
\(625\) 625.000 0.0400000
\(626\) 15218.0 0.971619
\(627\) 0 0
\(628\) 13169.6 0.836819
\(629\) −26298.5 −1.66708
\(630\) 0 0
\(631\) 11459.7 0.722982 0.361491 0.932376i \(-0.382268\pi\)
0.361491 + 0.932376i \(0.382268\pi\)
\(632\) 31615.2 1.98985
\(633\) 0 0
\(634\) −42314.4 −2.65066
\(635\) 13042.4 0.815073
\(636\) 0 0
\(637\) 1843.60 0.114672
\(638\) 28222.4 1.75131
\(639\) 0 0
\(640\) −48104.4 −2.97109
\(641\) −2261.29 −0.139338 −0.0696689 0.997570i \(-0.522194\pi\)
−0.0696689 + 0.997570i \(0.522194\pi\)
\(642\) 0 0
\(643\) 10224.8 0.627101 0.313551 0.949572i \(-0.398481\pi\)
0.313551 + 0.949572i \(0.398481\pi\)
\(644\) 6173.77 0.377765
\(645\) 0 0
\(646\) 76040.6 4.63123
\(647\) 16733.4 1.01678 0.508390 0.861127i \(-0.330241\pi\)
0.508390 + 0.861127i \(0.330241\pi\)
\(648\) 0 0
\(649\) 22936.5 1.38727
\(650\) 1218.99 0.0735582
\(651\) 0 0
\(652\) 50071.3 3.00758
\(653\) 9106.08 0.545710 0.272855 0.962055i \(-0.412032\pi\)
0.272855 + 0.962055i \(0.412032\pi\)
\(654\) 0 0
\(655\) 4682.04 0.279302
\(656\) −40086.0 −2.38582
\(657\) 0 0
\(658\) −4890.43 −0.289740
\(659\) 19951.5 1.17936 0.589680 0.807637i \(-0.299254\pi\)
0.589680 + 0.807637i \(0.299254\pi\)
\(660\) 0 0
\(661\) 16531.2 0.972750 0.486375 0.873750i \(-0.338319\pi\)
0.486375 + 0.873750i \(0.338319\pi\)
\(662\) −33605.8 −1.97300
\(663\) 0 0
\(664\) −66132.3 −3.86511
\(665\) −7339.22 −0.427974
\(666\) 0 0
\(667\) 3067.82 0.178091
\(668\) 30862.8 1.78760
\(669\) 0 0
\(670\) −3815.12 −0.219986
\(671\) 13817.4 0.794957
\(672\) 0 0
\(673\) −10268.9 −0.588169 −0.294084 0.955779i \(-0.595015\pi\)
−0.294084 + 0.955779i \(0.595015\pi\)
\(674\) −31776.3 −1.81599
\(675\) 0 0
\(676\) −49765.3 −2.83144
\(677\) −4729.79 −0.268509 −0.134254 0.990947i \(-0.542864\pi\)
−0.134254 + 0.990947i \(0.542864\pi\)
\(678\) 0 0
\(679\) 6573.86 0.371549
\(680\) −45816.8 −2.58381
\(681\) 0 0
\(682\) 22430.0 1.25937
\(683\) −11551.0 −0.647123 −0.323561 0.946207i \(-0.604880\pi\)
−0.323561 + 0.946207i \(0.604880\pi\)
\(684\) 0 0
\(685\) −2077.56 −0.115882
\(686\) 35623.6 1.98268
\(687\) 0 0
\(688\) 32456.3 1.79853
\(689\) 4139.89 0.228907
\(690\) 0 0
\(691\) 26575.2 1.46305 0.731526 0.681813i \(-0.238808\pi\)
0.731526 + 0.681813i \(0.238808\pi\)
\(692\) −15871.2 −0.871866
\(693\) 0 0
\(694\) 31371.6 1.71592
\(695\) −4748.15 −0.259147
\(696\) 0 0
\(697\) −14186.6 −0.770955
\(698\) −24143.6 −1.30924
\(699\) 0 0
\(700\) 6710.62 0.362339
\(701\) −5886.27 −0.317149 −0.158574 0.987347i \(-0.550690\pi\)
−0.158574 + 0.987347i \(0.550690\pi\)
\(702\) 0 0
\(703\) 31920.4 1.71252
\(704\) −117513. −6.29110
\(705\) 0 0
\(706\) 5926.48 0.315929
\(707\) −15702.0 −0.835268
\(708\) 0 0
\(709\) −2588.26 −0.137100 −0.0685501 0.997648i \(-0.521837\pi\)
−0.0685501 + 0.997648i \(0.521837\pi\)
\(710\) −4287.19 −0.226613
\(711\) 0 0
\(712\) 23515.8 1.23777
\(713\) 2438.18 0.128065
\(714\) 0 0
\(715\) 1639.78 0.0857682
\(716\) 87686.8 4.57683
\(717\) 0 0
\(718\) 29089.5 1.51199
\(719\) −1170.46 −0.0607106 −0.0303553 0.999539i \(-0.509664\pi\)
−0.0303553 + 0.999539i \(0.509664\pi\)
\(720\) 0 0
\(721\) −2774.00 −0.143286
\(722\) −53825.1 −2.77447
\(723\) 0 0
\(724\) −43947.0 −2.25591
\(725\) 3334.58 0.170818
\(726\) 0 0
\(727\) −3135.70 −0.159968 −0.0799838 0.996796i \(-0.525487\pi\)
−0.0799838 + 0.996796i \(0.525487\pi\)
\(728\) 8624.82 0.439089
\(729\) 0 0
\(730\) −34442.4 −1.74626
\(731\) 11486.4 0.581177
\(732\) 0 0
\(733\) −25792.4 −1.29968 −0.649839 0.760072i \(-0.725164\pi\)
−0.649839 + 0.760072i \(0.725164\pi\)
\(734\) −1002.70 −0.0504225
\(735\) 0 0
\(736\) −22570.7 −1.13039
\(737\) −5132.07 −0.256502
\(738\) 0 0
\(739\) −809.931 −0.0403164 −0.0201582 0.999797i \(-0.506417\pi\)
−0.0201582 + 0.999797i \(0.506417\pi\)
\(740\) −29186.4 −1.44988
\(741\) 0 0
\(742\) 30562.4 1.51210
\(743\) −1825.32 −0.0901270 −0.0450635 0.998984i \(-0.514349\pi\)
−0.0450635 + 0.998984i \(0.514349\pi\)
\(744\) 0 0
\(745\) −11049.2 −0.543371
\(746\) −41863.2 −2.05459
\(747\) 0 0
\(748\) −93528.2 −4.57183
\(749\) −7447.91 −0.363339
\(750\) 0 0
\(751\) 4310.27 0.209433 0.104716 0.994502i \(-0.466606\pi\)
0.104716 + 0.994502i \(0.466606\pi\)
\(752\) 22755.7 1.10348
\(753\) 0 0
\(754\) 6503.73 0.314127
\(755\) −6921.25 −0.333629
\(756\) 0 0
\(757\) 19302.2 0.926750 0.463375 0.886162i \(-0.346638\pi\)
0.463375 + 0.886162i \(0.346638\pi\)
\(758\) 34078.9 1.63298
\(759\) 0 0
\(760\) 55611.1 2.65424
\(761\) 30144.8 1.43594 0.717968 0.696076i \(-0.245073\pi\)
0.717968 + 0.696076i \(0.245073\pi\)
\(762\) 0 0
\(763\) −14079.3 −0.668025
\(764\) 121020. 5.73084
\(765\) 0 0
\(766\) −3257.07 −0.153633
\(767\) 5285.62 0.248830
\(768\) 0 0
\(769\) 37297.7 1.74901 0.874506 0.485015i \(-0.161186\pi\)
0.874506 + 0.485015i \(0.161186\pi\)
\(770\) 12105.6 0.566564
\(771\) 0 0
\(772\) −112751. −5.25647
\(773\) 13602.8 0.632933 0.316467 0.948604i \(-0.397503\pi\)
0.316467 + 0.948604i \(0.397503\pi\)
\(774\) 0 0
\(775\) 2650.19 0.122836
\(776\) −49811.8 −2.30430
\(777\) 0 0
\(778\) 63791.3 2.93963
\(779\) 17219.3 0.791970
\(780\) 0 0
\(781\) −5767.10 −0.264229
\(782\) −13633.8 −0.623457
\(783\) 0 0
\(784\) −63330.1 −2.88493
\(785\) 2807.00 0.127625
\(786\) 0 0
\(787\) 14129.9 0.639997 0.319998 0.947418i \(-0.396318\pi\)
0.319998 + 0.947418i \(0.396318\pi\)
\(788\) −75127.8 −3.39634
\(789\) 0 0
\(790\) 10225.9 0.460531
\(791\) −2734.30 −0.122908
\(792\) 0 0
\(793\) 3184.18 0.142589
\(794\) −20760.7 −0.927922
\(795\) 0 0
\(796\) −51854.0 −2.30894
\(797\) −16171.3 −0.718715 −0.359357 0.933200i \(-0.617004\pi\)
−0.359357 + 0.933200i \(0.617004\pi\)
\(798\) 0 0
\(799\) 8053.32 0.356578
\(800\) −24533.3 −1.08423
\(801\) 0 0
\(802\) −42710.9 −1.88052
\(803\) −46331.7 −2.03613
\(804\) 0 0
\(805\) 1315.89 0.0576139
\(806\) 5168.91 0.225890
\(807\) 0 0
\(808\) 118978. 5.18023
\(809\) 41744.9 1.81418 0.907090 0.420937i \(-0.138299\pi\)
0.907090 + 0.420937i \(0.138299\pi\)
\(810\) 0 0
\(811\) −12210.2 −0.528679 −0.264340 0.964430i \(-0.585154\pi\)
−0.264340 + 0.964430i \(0.585154\pi\)
\(812\) 35803.4 1.54736
\(813\) 0 0
\(814\) −52650.6 −2.26708
\(815\) 10672.3 0.458694
\(816\) 0 0
\(817\) −13941.9 −0.597019
\(818\) 86507.4 3.69763
\(819\) 0 0
\(820\) −15744.4 −0.670512
\(821\) 22326.2 0.949074 0.474537 0.880236i \(-0.342615\pi\)
0.474537 + 0.880236i \(0.342615\pi\)
\(822\) 0 0
\(823\) −29128.6 −1.23373 −0.616864 0.787069i \(-0.711597\pi\)
−0.616864 + 0.787069i \(0.711597\pi\)
\(824\) 21019.2 0.888641
\(825\) 0 0
\(826\) 39020.7 1.64371
\(827\) 13540.8 0.569357 0.284679 0.958623i \(-0.408113\pi\)
0.284679 + 0.958623i \(0.408113\pi\)
\(828\) 0 0
\(829\) 93.8298 0.00393105 0.00196553 0.999998i \(-0.499374\pi\)
0.00196553 + 0.999998i \(0.499374\pi\)
\(830\) −21390.3 −0.894542
\(831\) 0 0
\(832\) −27080.4 −1.12842
\(833\) −22412.7 −0.932239
\(834\) 0 0
\(835\) 6578.19 0.272632
\(836\) 113522. 4.69645
\(837\) 0 0
\(838\) 23967.4 0.987997
\(839\) 33750.6 1.38880 0.694398 0.719591i \(-0.255671\pi\)
0.694398 + 0.719591i \(0.255671\pi\)
\(840\) 0 0
\(841\) −6597.88 −0.270527
\(842\) 34081.1 1.39491
\(843\) 0 0
\(844\) 3592.98 0.146535
\(845\) −10607.1 −0.431830
\(846\) 0 0
\(847\) 1054.26 0.0427686
\(848\) −142210. −5.75887
\(849\) 0 0
\(850\) −14819.3 −0.597999
\(851\) −5723.21 −0.230539
\(852\) 0 0
\(853\) −2680.73 −0.107604 −0.0538022 0.998552i \(-0.517134\pi\)
−0.0538022 + 0.998552i \(0.517134\pi\)
\(854\) 23506.9 0.941910
\(855\) 0 0
\(856\) 56434.7 2.25338
\(857\) −29267.7 −1.16659 −0.583295 0.812261i \(-0.698237\pi\)
−0.583295 + 0.812261i \(0.698237\pi\)
\(858\) 0 0
\(859\) 34842.9 1.38396 0.691982 0.721914i \(-0.256738\pi\)
0.691982 + 0.721914i \(0.256738\pi\)
\(860\) 12747.8 0.505459
\(861\) 0 0
\(862\) −18991.6 −0.750412
\(863\) 4041.96 0.159432 0.0797161 0.996818i \(-0.474599\pi\)
0.0797161 + 0.996818i \(0.474599\pi\)
\(864\) 0 0
\(865\) −3382.83 −0.132971
\(866\) −44447.6 −1.74410
\(867\) 0 0
\(868\) 28455.1 1.11271
\(869\) 13755.7 0.536975
\(870\) 0 0
\(871\) −1182.66 −0.0460081
\(872\) 106682. 4.14301
\(873\) 0 0
\(874\) 16548.3 0.640451
\(875\) 1430.32 0.0552613
\(876\) 0 0
\(877\) 34918.5 1.34448 0.672242 0.740331i \(-0.265331\pi\)
0.672242 + 0.740331i \(0.265331\pi\)
\(878\) −75891.9 −2.91712
\(879\) 0 0
\(880\) −56328.5 −2.15777
\(881\) −2473.77 −0.0946008 −0.0473004 0.998881i \(-0.515062\pi\)
−0.0473004 + 0.998881i \(0.515062\pi\)
\(882\) 0 0
\(883\) 16956.8 0.646252 0.323126 0.946356i \(-0.395266\pi\)
0.323126 + 0.946356i \(0.395266\pi\)
\(884\) −21553.2 −0.820037
\(885\) 0 0
\(886\) 5586.64 0.211836
\(887\) −582.058 −0.0220334 −0.0110167 0.999939i \(-0.503507\pi\)
−0.0110167 + 0.999939i \(0.503507\pi\)
\(888\) 0 0
\(889\) 29847.7 1.12605
\(890\) 7606.13 0.286470
\(891\) 0 0
\(892\) −71980.1 −2.70188
\(893\) −9774.88 −0.366298
\(894\) 0 0
\(895\) 18689.8 0.698024
\(896\) −110088. −4.10465
\(897\) 0 0
\(898\) −28489.0 −1.05868
\(899\) 14139.7 0.524566
\(900\) 0 0
\(901\) −50328.7 −1.86092
\(902\) −28402.1 −1.04843
\(903\) 0 0
\(904\) 20718.5 0.762263
\(905\) −9367.00 −0.344055
\(906\) 0 0
\(907\) 26224.8 0.960065 0.480033 0.877251i \(-0.340625\pi\)
0.480033 + 0.877251i \(0.340625\pi\)
\(908\) −106506. −3.89265
\(909\) 0 0
\(910\) 2789.68 0.101623
\(911\) 12266.6 0.446117 0.223058 0.974805i \(-0.428396\pi\)
0.223058 + 0.974805i \(0.428396\pi\)
\(912\) 0 0
\(913\) −28774.1 −1.04303
\(914\) 62767.6 2.27152
\(915\) 0 0
\(916\) 34630.4 1.24915
\(917\) 10714.9 0.385864
\(918\) 0 0
\(919\) 12114.7 0.434850 0.217425 0.976077i \(-0.430234\pi\)
0.217425 + 0.976077i \(0.430234\pi\)
\(920\) −9970.85 −0.357314
\(921\) 0 0
\(922\) 13607.3 0.486045
\(923\) −1329.01 −0.0473941
\(924\) 0 0
\(925\) −6220.88 −0.221126
\(926\) 91699.1 3.25423
\(927\) 0 0
\(928\) −130893. −4.63016
\(929\) 2418.31 0.0854059 0.0427029 0.999088i \(-0.486403\pi\)
0.0427029 + 0.999088i \(0.486403\pi\)
\(930\) 0 0
\(931\) 27203.9 0.957650
\(932\) 2128.40 0.0748048
\(933\) 0 0
\(934\) −16157.8 −0.566059
\(935\) −19934.9 −0.697262
\(936\) 0 0
\(937\) 16448.7 0.573486 0.286743 0.958008i \(-0.407427\pi\)
0.286743 + 0.958008i \(0.407427\pi\)
\(938\) −8730.94 −0.303918
\(939\) 0 0
\(940\) 8937.67 0.310122
\(941\) 17373.2 0.601859 0.300929 0.953646i \(-0.402703\pi\)
0.300929 + 0.953646i \(0.402703\pi\)
\(942\) 0 0
\(943\) −3087.35 −0.106615
\(944\) −181568. −6.26009
\(945\) 0 0
\(946\) 22996.2 0.790350
\(947\) −18638.9 −0.639579 −0.319790 0.947489i \(-0.603612\pi\)
−0.319790 + 0.947489i \(0.603612\pi\)
\(948\) 0 0
\(949\) −10676.9 −0.365214
\(950\) 17987.3 0.614299
\(951\) 0 0
\(952\) −104852. −3.56962
\(953\) 31188.1 1.06011 0.530053 0.847965i \(-0.322172\pi\)
0.530053 + 0.847965i \(0.322172\pi\)
\(954\) 0 0
\(955\) 25794.6 0.874025
\(956\) 37983.0 1.28500
\(957\) 0 0
\(958\) 44030.7 1.48493
\(959\) −4754.51 −0.160095
\(960\) 0 0
\(961\) −18553.3 −0.622784
\(962\) −12133.1 −0.406640
\(963\) 0 0
\(964\) −151248. −5.05328
\(965\) −24032.1 −0.801678
\(966\) 0 0
\(967\) 43197.8 1.43655 0.718277 0.695757i \(-0.244931\pi\)
0.718277 + 0.695757i \(0.244931\pi\)
\(968\) −7988.42 −0.265246
\(969\) 0 0
\(970\) −16111.5 −0.533308
\(971\) −13497.0 −0.446074 −0.223037 0.974810i \(-0.571597\pi\)
−0.223037 + 0.974810i \(0.571597\pi\)
\(972\) 0 0
\(973\) −10866.2 −0.358021
\(974\) 63168.4 2.07808
\(975\) 0 0
\(976\) −109380. −3.58728
\(977\) 34955.4 1.14465 0.572325 0.820027i \(-0.306042\pi\)
0.572325 + 0.820027i \(0.306042\pi\)
\(978\) 0 0
\(979\) 10231.7 0.334021
\(980\) −24873.9 −0.810784
\(981\) 0 0
\(982\) 88678.9 2.88173
\(983\) 27521.6 0.892984 0.446492 0.894788i \(-0.352673\pi\)
0.446492 + 0.894788i \(0.352673\pi\)
\(984\) 0 0
\(985\) −16013.0 −0.517985
\(986\) −79066.1 −2.55373
\(987\) 0 0
\(988\) 26160.6 0.842389
\(989\) 2499.73 0.0803707
\(990\) 0 0
\(991\) 24567.9 0.787513 0.393756 0.919215i \(-0.371175\pi\)
0.393756 + 0.919215i \(0.371175\pi\)
\(992\) −104029. −3.32956
\(993\) 0 0
\(994\) −9811.29 −0.313074
\(995\) −11052.3 −0.352143
\(996\) 0 0
\(997\) 2293.84 0.0728652 0.0364326 0.999336i \(-0.488401\pi\)
0.0364326 + 0.999336i \(0.488401\pi\)
\(998\) 58726.5 1.86268
\(999\) 0 0
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 1035.4.a.k.1.1 5
3.2 odd 2 115.4.a.e.1.5 5
12.11 even 2 1840.4.a.n.1.3 5
15.2 even 4 575.4.b.i.24.10 10
15.8 even 4 575.4.b.i.24.1 10
15.14 odd 2 575.4.a.j.1.1 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.4.a.e.1.5 5 3.2 odd 2
575.4.a.j.1.1 5 15.14 odd 2
575.4.b.i.24.1 10 15.8 even 4
575.4.b.i.24.10 10 15.2 even 4
1035.4.a.k.1.1 5 1.1 even 1 trivial
1840.4.a.n.1.3 5 12.11 even 2