Properties

Label 4025.2.a.u.1.8
Level $4025$
Weight $2$
Character 4025.1
Self dual yes
Analytic conductor $32.140$
Analytic rank $1$
Dimension $8$
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] = [4025,2,Mod(1,4025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4025, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4025.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: \(32.1397868136\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} - 10x^{6} + 9x^{5} + 28x^{4} - 22x^{3} - 16x^{2} + 7x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.8
Root \(-2.18675\) of defining polynomial
Character \(\chi\) \(=\) 4025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.18675 q^{2} -2.66680 q^{3} +2.78189 q^{4} -5.83163 q^{6} +1.00000 q^{7} +1.70979 q^{8} +4.11181 q^{9} +O(q^{10})\) \(q+2.18675 q^{2} -2.66680 q^{3} +2.78189 q^{4} -5.83163 q^{6} +1.00000 q^{7} +1.70979 q^{8} +4.11181 q^{9} -3.38662 q^{11} -7.41873 q^{12} +0.0686513 q^{13} +2.18675 q^{14} -1.82488 q^{16} +2.64995 q^{17} +8.99151 q^{18} +3.27497 q^{19} -2.66680 q^{21} -7.40569 q^{22} -1.00000 q^{23} -4.55967 q^{24} +0.150124 q^{26} -2.96497 q^{27} +2.78189 q^{28} -0.498885 q^{29} -0.846864 q^{31} -7.41015 q^{32} +9.03142 q^{33} +5.79479 q^{34} +11.4386 q^{36} -2.34362 q^{37} +7.16155 q^{38} -0.183079 q^{39} -2.68516 q^{41} -5.83163 q^{42} -9.07605 q^{43} -9.42118 q^{44} -2.18675 q^{46} -6.92879 q^{47} +4.86659 q^{48} +1.00000 q^{49} -7.06688 q^{51} +0.190980 q^{52} +0.0435836 q^{53} -6.48365 q^{54} +1.70979 q^{56} -8.73368 q^{57} -1.09094 q^{58} +4.71871 q^{59} +8.53139 q^{61} -1.85188 q^{62} +4.11181 q^{63} -12.5544 q^{64} +19.7495 q^{66} -8.46553 q^{67} +7.37186 q^{68} +2.66680 q^{69} -0.438487 q^{71} +7.03034 q^{72} -7.74306 q^{73} -5.12493 q^{74} +9.11059 q^{76} -3.38662 q^{77} -0.400349 q^{78} -9.44444 q^{79} -4.42846 q^{81} -5.87177 q^{82} -4.36410 q^{83} -7.41873 q^{84} -19.8471 q^{86} +1.33042 q^{87} -5.79041 q^{88} -6.14427 q^{89} +0.0686513 q^{91} -2.78189 q^{92} +2.25842 q^{93} -15.1515 q^{94} +19.7614 q^{96} -6.71968 q^{97} +2.18675 q^{98} -13.9251 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{2} - 4 q^{3} + 5 q^{4} - q^{6} + 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{2} - 4 q^{3} + 5 q^{4} - q^{6} + 8 q^{7} + 3 q^{11} - 9 q^{12} - 5 q^{13} - q^{14} - q^{16} - 5 q^{17} - 2 q^{18} - 2 q^{19} - 4 q^{21} - 21 q^{22} - 8 q^{23} - 6 q^{24} + 18 q^{26} - 7 q^{27} + 5 q^{28} - 9 q^{29} - 3 q^{31} - 6 q^{32} - 4 q^{33} - 10 q^{34} + 16 q^{36} - 6 q^{37} - 4 q^{38} - 2 q^{39} - 7 q^{41} - q^{42} - 8 q^{43} + 4 q^{44} + q^{46} - 22 q^{47} - 9 q^{48} + 8 q^{49} - 12 q^{51} - 11 q^{52} - 21 q^{53} - 15 q^{54} - 8 q^{57} - 16 q^{58} + 14 q^{59} + 8 q^{61} - 12 q^{62} - 40 q^{64} + 55 q^{66} - 21 q^{67} - 3 q^{68} + 4 q^{69} + 11 q^{71} + q^{72} - 26 q^{73} - 41 q^{74} + 21 q^{76} + 3 q^{77} - 17 q^{78} - 16 q^{79} - 20 q^{81} + q^{82} - 20 q^{83} - 9 q^{84} + 14 q^{86} + 29 q^{87} - 32 q^{88} + 15 q^{89} - 5 q^{91} - 5 q^{92} - 19 q^{93} + 21 q^{94} + 52 q^{96} - q^{97} - q^{98} + 15 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.18675 1.54627 0.773134 0.634243i \(-0.218688\pi\)
0.773134 + 0.634243i \(0.218688\pi\)
\(3\) −2.66680 −1.53968 −0.769838 0.638239i \(-0.779663\pi\)
−0.769838 + 0.638239i \(0.779663\pi\)
\(4\) 2.78189 1.39094
\(5\) 0 0
\(6\) −5.83163 −2.38075
\(7\) 1.00000 0.377964
\(8\) 1.70979 0.604503
\(9\) 4.11181 1.37060
\(10\) 0 0
\(11\) −3.38662 −1.02110 −0.510551 0.859847i \(-0.670559\pi\)
−0.510551 + 0.859847i \(0.670559\pi\)
\(12\) −7.41873 −2.14160
\(13\) 0.0686513 0.0190405 0.00952023 0.999955i \(-0.496970\pi\)
0.00952023 + 0.999955i \(0.496970\pi\)
\(14\) 2.18675 0.584434
\(15\) 0 0
\(16\) −1.82488 −0.456220
\(17\) 2.64995 0.642707 0.321354 0.946959i \(-0.395862\pi\)
0.321354 + 0.946959i \(0.395862\pi\)
\(18\) 8.99151 2.11932
\(19\) 3.27497 0.751329 0.375665 0.926756i \(-0.377414\pi\)
0.375665 + 0.926756i \(0.377414\pi\)
\(20\) 0 0
\(21\) −2.66680 −0.581943
\(22\) −7.40569 −1.57890
\(23\) −1.00000 −0.208514
\(24\) −4.55967 −0.930738
\(25\) 0 0
\(26\) 0.150124 0.0294416
\(27\) −2.96497 −0.570608
\(28\) 2.78189 0.525727
\(29\) −0.498885 −0.0926406 −0.0463203 0.998927i \(-0.514749\pi\)
−0.0463203 + 0.998927i \(0.514749\pi\)
\(30\) 0 0
\(31\) −0.846864 −0.152101 −0.0760507 0.997104i \(-0.524231\pi\)
−0.0760507 + 0.997104i \(0.524231\pi\)
\(32\) −7.41015 −1.30994
\(33\) 9.03142 1.57217
\(34\) 5.79479 0.993798
\(35\) 0 0
\(36\) 11.4386 1.90643
\(37\) −2.34362 −0.385289 −0.192645 0.981269i \(-0.561706\pi\)
−0.192645 + 0.981269i \(0.561706\pi\)
\(38\) 7.16155 1.16176
\(39\) −0.183079 −0.0293161
\(40\) 0 0
\(41\) −2.68516 −0.419351 −0.209675 0.977771i \(-0.567241\pi\)
−0.209675 + 0.977771i \(0.567241\pi\)
\(42\) −5.83163 −0.899839
\(43\) −9.07605 −1.38408 −0.692042 0.721857i \(-0.743289\pi\)
−0.692042 + 0.721857i \(0.743289\pi\)
\(44\) −9.42118 −1.42030
\(45\) 0 0
\(46\) −2.18675 −0.322419
\(47\) −6.92879 −1.01067 −0.505334 0.862924i \(-0.668631\pi\)
−0.505334 + 0.862924i \(0.668631\pi\)
\(48\) 4.86659 0.702431
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −7.06688 −0.989561
\(52\) 0.190980 0.0264842
\(53\) 0.0435836 0.00598667 0.00299334 0.999996i \(-0.499047\pi\)
0.00299334 + 0.999996i \(0.499047\pi\)
\(54\) −6.48365 −0.882312
\(55\) 0 0
\(56\) 1.70979 0.228481
\(57\) −8.73368 −1.15680
\(58\) −1.09094 −0.143247
\(59\) 4.71871 0.614324 0.307162 0.951657i \(-0.400621\pi\)
0.307162 + 0.951657i \(0.400621\pi\)
\(60\) 0 0
\(61\) 8.53139 1.09233 0.546166 0.837677i \(-0.316087\pi\)
0.546166 + 0.837677i \(0.316087\pi\)
\(62\) −1.85188 −0.235189
\(63\) 4.11181 0.518039
\(64\) −12.5544 −1.56930
\(65\) 0 0
\(66\) 19.7495 2.43099
\(67\) −8.46553 −1.03423 −0.517114 0.855916i \(-0.672994\pi\)
−0.517114 + 0.855916i \(0.672994\pi\)
\(68\) 7.37186 0.893970
\(69\) 2.66680 0.321045
\(70\) 0 0
\(71\) −0.438487 −0.0520388 −0.0260194 0.999661i \(-0.508283\pi\)
−0.0260194 + 0.999661i \(0.508283\pi\)
\(72\) 7.03034 0.828533
\(73\) −7.74306 −0.906256 −0.453128 0.891445i \(-0.649692\pi\)
−0.453128 + 0.891445i \(0.649692\pi\)
\(74\) −5.12493 −0.595761
\(75\) 0 0
\(76\) 9.11059 1.04506
\(77\) −3.38662 −0.385941
\(78\) −0.400349 −0.0453306
\(79\) −9.44444 −1.06258 −0.531291 0.847189i \(-0.678293\pi\)
−0.531291 + 0.847189i \(0.678293\pi\)
\(80\) 0 0
\(81\) −4.42846 −0.492051
\(82\) −5.87177 −0.648429
\(83\) −4.36410 −0.479022 −0.239511 0.970894i \(-0.576987\pi\)
−0.239511 + 0.970894i \(0.576987\pi\)
\(84\) −7.41873 −0.809449
\(85\) 0 0
\(86\) −19.8471 −2.14016
\(87\) 1.33042 0.142636
\(88\) −5.79041 −0.617259
\(89\) −6.14427 −0.651292 −0.325646 0.945492i \(-0.605582\pi\)
−0.325646 + 0.945492i \(0.605582\pi\)
\(90\) 0 0
\(91\) 0.0686513 0.00719662
\(92\) −2.78189 −0.290032
\(93\) 2.25842 0.234187
\(94\) −15.1515 −1.56276
\(95\) 0 0
\(96\) 19.7614 2.01689
\(97\) −6.71968 −0.682280 −0.341140 0.940012i \(-0.610813\pi\)
−0.341140 + 0.940012i \(0.610813\pi\)
\(98\) 2.18675 0.220895
\(99\) −13.9251 −1.39953
\(100\) 0 0
\(101\) 12.6748 1.26119 0.630594 0.776113i \(-0.282811\pi\)
0.630594 + 0.776113i \(0.282811\pi\)
\(102\) −15.4535 −1.53013
\(103\) −1.67902 −0.165439 −0.0827196 0.996573i \(-0.526361\pi\)
−0.0827196 + 0.996573i \(0.526361\pi\)
\(104\) 0.117380 0.0115100
\(105\) 0 0
\(106\) 0.0953066 0.00925700
\(107\) −1.83599 −0.177492 −0.0887459 0.996054i \(-0.528286\pi\)
−0.0887459 + 0.996054i \(0.528286\pi\)
\(108\) −8.24820 −0.793683
\(109\) 15.3677 1.47195 0.735977 0.677006i \(-0.236723\pi\)
0.735977 + 0.677006i \(0.236723\pi\)
\(110\) 0 0
\(111\) 6.24997 0.593221
\(112\) −1.82488 −0.172435
\(113\) −12.0189 −1.13065 −0.565323 0.824870i \(-0.691248\pi\)
−0.565323 + 0.824870i \(0.691248\pi\)
\(114\) −19.0984 −1.78873
\(115\) 0 0
\(116\) −1.38784 −0.128858
\(117\) 0.282281 0.0260969
\(118\) 10.3187 0.949909
\(119\) 2.64995 0.242921
\(120\) 0 0
\(121\) 0.469162 0.0426511
\(122\) 18.6560 1.68904
\(123\) 7.16076 0.645664
\(124\) −2.35588 −0.211564
\(125\) 0 0
\(126\) 8.99151 0.801027
\(127\) −11.4855 −1.01917 −0.509587 0.860419i \(-0.670202\pi\)
−0.509587 + 0.860419i \(0.670202\pi\)
\(128\) −12.6331 −1.11662
\(129\) 24.2040 2.13104
\(130\) 0 0
\(131\) −4.79086 −0.418579 −0.209290 0.977854i \(-0.567115\pi\)
−0.209290 + 0.977854i \(0.567115\pi\)
\(132\) 25.1244 2.18680
\(133\) 3.27497 0.283976
\(134\) −18.5120 −1.59919
\(135\) 0 0
\(136\) 4.53086 0.388518
\(137\) −14.5227 −1.24076 −0.620378 0.784303i \(-0.713021\pi\)
−0.620378 + 0.784303i \(0.713021\pi\)
\(138\) 5.83163 0.496421
\(139\) −15.7239 −1.33369 −0.666844 0.745198i \(-0.732355\pi\)
−0.666844 + 0.745198i \(0.732355\pi\)
\(140\) 0 0
\(141\) 18.4777 1.55610
\(142\) −0.958862 −0.0804659
\(143\) −0.232496 −0.0194423
\(144\) −7.50356 −0.625297
\(145\) 0 0
\(146\) −16.9321 −1.40131
\(147\) −2.66680 −0.219954
\(148\) −6.51970 −0.535916
\(149\) −3.25848 −0.266945 −0.133472 0.991053i \(-0.542613\pi\)
−0.133472 + 0.991053i \(0.542613\pi\)
\(150\) 0 0
\(151\) 3.41686 0.278060 0.139030 0.990288i \(-0.455602\pi\)
0.139030 + 0.990288i \(0.455602\pi\)
\(152\) 5.59952 0.454181
\(153\) 10.8961 0.880896
\(154\) −7.40569 −0.596767
\(155\) 0 0
\(156\) −0.509306 −0.0407771
\(157\) −14.7913 −1.18047 −0.590236 0.807231i \(-0.700965\pi\)
−0.590236 + 0.807231i \(0.700965\pi\)
\(158\) −20.6527 −1.64304
\(159\) −0.116229 −0.00921754
\(160\) 0 0
\(161\) −1.00000 −0.0788110
\(162\) −9.68395 −0.760843
\(163\) −23.5301 −1.84302 −0.921512 0.388351i \(-0.873045\pi\)
−0.921512 + 0.388351i \(0.873045\pi\)
\(164\) −7.46980 −0.583293
\(165\) 0 0
\(166\) −9.54321 −0.740697
\(167\) 20.8784 1.61562 0.807810 0.589442i \(-0.200653\pi\)
0.807810 + 0.589442i \(0.200653\pi\)
\(168\) −4.55967 −0.351786
\(169\) −12.9953 −0.999637
\(170\) 0 0
\(171\) 13.4660 1.02977
\(172\) −25.2485 −1.92518
\(173\) −10.5021 −0.798463 −0.399231 0.916850i \(-0.630723\pi\)
−0.399231 + 0.916850i \(0.630723\pi\)
\(174\) 2.90931 0.220554
\(175\) 0 0
\(176\) 6.18017 0.465848
\(177\) −12.5838 −0.945860
\(178\) −13.4360 −1.00707
\(179\) 22.0735 1.64985 0.824927 0.565239i \(-0.191216\pi\)
0.824927 + 0.565239i \(0.191216\pi\)
\(180\) 0 0
\(181\) 4.41151 0.327905 0.163952 0.986468i \(-0.447576\pi\)
0.163952 + 0.986468i \(0.447576\pi\)
\(182\) 0.150124 0.0111279
\(183\) −22.7515 −1.68184
\(184\) −1.70979 −0.126048
\(185\) 0 0
\(186\) 4.93860 0.362115
\(187\) −8.97436 −0.656270
\(188\) −19.2751 −1.40578
\(189\) −2.96497 −0.215670
\(190\) 0 0
\(191\) −5.98892 −0.433343 −0.216672 0.976245i \(-0.569520\pi\)
−0.216672 + 0.976245i \(0.569520\pi\)
\(192\) 33.4800 2.41621
\(193\) 12.5614 0.904186 0.452093 0.891971i \(-0.350677\pi\)
0.452093 + 0.891971i \(0.350677\pi\)
\(194\) −14.6943 −1.05499
\(195\) 0 0
\(196\) 2.78189 0.198706
\(197\) 2.61220 0.186112 0.0930558 0.995661i \(-0.470337\pi\)
0.0930558 + 0.995661i \(0.470337\pi\)
\(198\) −30.4508 −2.16404
\(199\) 9.74423 0.690750 0.345375 0.938465i \(-0.387752\pi\)
0.345375 + 0.938465i \(0.387752\pi\)
\(200\) 0 0
\(201\) 22.5758 1.59238
\(202\) 27.7166 1.95013
\(203\) −0.498885 −0.0350148
\(204\) −19.6593 −1.37642
\(205\) 0 0
\(206\) −3.67161 −0.255813
\(207\) −4.11181 −0.285790
\(208\) −0.125281 −0.00868664
\(209\) −11.0911 −0.767185
\(210\) 0 0
\(211\) −2.69331 −0.185415 −0.0927077 0.995693i \(-0.529552\pi\)
−0.0927077 + 0.995693i \(0.529552\pi\)
\(212\) 0.121245 0.00832712
\(213\) 1.16936 0.0801229
\(214\) −4.01485 −0.274450
\(215\) 0 0
\(216\) −5.06947 −0.344934
\(217\) −0.846864 −0.0574889
\(218\) 33.6053 2.27604
\(219\) 20.6492 1.39534
\(220\) 0 0
\(221\) 0.181923 0.0122374
\(222\) 13.6671 0.917278
\(223\) −5.41743 −0.362778 −0.181389 0.983411i \(-0.558059\pi\)
−0.181389 + 0.983411i \(0.558059\pi\)
\(224\) −7.41015 −0.495111
\(225\) 0 0
\(226\) −26.2824 −1.74828
\(227\) −5.86988 −0.389598 −0.194799 0.980843i \(-0.562405\pi\)
−0.194799 + 0.980843i \(0.562405\pi\)
\(228\) −24.2961 −1.60905
\(229\) 25.0481 1.65522 0.827612 0.561301i \(-0.189699\pi\)
0.827612 + 0.561301i \(0.189699\pi\)
\(230\) 0 0
\(231\) 9.03142 0.594224
\(232\) −0.852989 −0.0560015
\(233\) 12.5329 0.821057 0.410528 0.911848i \(-0.365344\pi\)
0.410528 + 0.911848i \(0.365344\pi\)
\(234\) 0.617279 0.0403528
\(235\) 0 0
\(236\) 13.1269 0.854489
\(237\) 25.1864 1.63603
\(238\) 5.79479 0.375620
\(239\) −14.2246 −0.920111 −0.460056 0.887890i \(-0.652171\pi\)
−0.460056 + 0.887890i \(0.652171\pi\)
\(240\) 0 0
\(241\) −2.95273 −0.190202 −0.0951011 0.995468i \(-0.530317\pi\)
−0.0951011 + 0.995468i \(0.530317\pi\)
\(242\) 1.02594 0.0659500
\(243\) 20.7047 1.32821
\(244\) 23.7334 1.51937
\(245\) 0 0
\(246\) 15.6588 0.998370
\(247\) 0.224831 0.0143057
\(248\) −1.44796 −0.0919457
\(249\) 11.6382 0.737539
\(250\) 0 0
\(251\) −26.3474 −1.66303 −0.831517 0.555499i \(-0.812527\pi\)
−0.831517 + 0.555499i \(0.812527\pi\)
\(252\) 11.4386 0.720563
\(253\) 3.38662 0.212915
\(254\) −25.1160 −1.57592
\(255\) 0 0
\(256\) −2.51659 −0.157287
\(257\) −7.76198 −0.484179 −0.242089 0.970254i \(-0.577833\pi\)
−0.242089 + 0.970254i \(0.577833\pi\)
\(258\) 52.9281 3.29516
\(259\) −2.34362 −0.145626
\(260\) 0 0
\(261\) −2.05132 −0.126973
\(262\) −10.4764 −0.647235
\(263\) 10.1109 0.623462 0.311731 0.950170i \(-0.399091\pi\)
0.311731 + 0.950170i \(0.399091\pi\)
\(264\) 15.4418 0.950380
\(265\) 0 0
\(266\) 7.16155 0.439103
\(267\) 16.3855 1.00278
\(268\) −23.5501 −1.43855
\(269\) 15.1067 0.921074 0.460537 0.887641i \(-0.347657\pi\)
0.460537 + 0.887641i \(0.347657\pi\)
\(270\) 0 0
\(271\) −3.27056 −0.198672 −0.0993362 0.995054i \(-0.531672\pi\)
−0.0993362 + 0.995054i \(0.531672\pi\)
\(272\) −4.83584 −0.293216
\(273\) −0.183079 −0.0110805
\(274\) −31.7575 −1.91854
\(275\) 0 0
\(276\) 7.41873 0.446555
\(277\) 9.29013 0.558190 0.279095 0.960264i \(-0.409966\pi\)
0.279095 + 0.960264i \(0.409966\pi\)
\(278\) −34.3844 −2.06224
\(279\) −3.48214 −0.208470
\(280\) 0 0
\(281\) −25.4571 −1.51864 −0.759321 0.650716i \(-0.774469\pi\)
−0.759321 + 0.650716i \(0.774469\pi\)
\(282\) 40.4061 2.40615
\(283\) 2.89396 0.172028 0.0860140 0.996294i \(-0.472587\pi\)
0.0860140 + 0.996294i \(0.472587\pi\)
\(284\) −1.21982 −0.0723830
\(285\) 0 0
\(286\) −0.508411 −0.0300629
\(287\) −2.68516 −0.158500
\(288\) −30.4691 −1.79541
\(289\) −9.97776 −0.586927
\(290\) 0 0
\(291\) 17.9200 1.05049
\(292\) −21.5403 −1.26055
\(293\) 22.0396 1.28757 0.643785 0.765207i \(-0.277363\pi\)
0.643785 + 0.765207i \(0.277363\pi\)
\(294\) −5.83163 −0.340107
\(295\) 0 0
\(296\) −4.00711 −0.232909
\(297\) 10.0412 0.582649
\(298\) −7.12548 −0.412768
\(299\) −0.0686513 −0.00397021
\(300\) 0 0
\(301\) −9.07605 −0.523135
\(302\) 7.47183 0.429956
\(303\) −33.8011 −1.94182
\(304\) −5.97643 −0.342772
\(305\) 0 0
\(306\) 23.8270 1.36210
\(307\) −11.8220 −0.674715 −0.337357 0.941377i \(-0.609533\pi\)
−0.337357 + 0.941377i \(0.609533\pi\)
\(308\) −9.42118 −0.536821
\(309\) 4.47762 0.254723
\(310\) 0 0
\(311\) −13.8962 −0.787981 −0.393990 0.919115i \(-0.628906\pi\)
−0.393990 + 0.919115i \(0.628906\pi\)
\(312\) −0.313027 −0.0177217
\(313\) −5.82462 −0.329227 −0.164614 0.986358i \(-0.552638\pi\)
−0.164614 + 0.986358i \(0.552638\pi\)
\(314\) −32.3449 −1.82533
\(315\) 0 0
\(316\) −26.2734 −1.47799
\(317\) 27.7561 1.55894 0.779468 0.626442i \(-0.215490\pi\)
0.779468 + 0.626442i \(0.215490\pi\)
\(318\) −0.254164 −0.0142528
\(319\) 1.68953 0.0945956
\(320\) 0 0
\(321\) 4.89621 0.273280
\(322\) −2.18675 −0.121863
\(323\) 8.67851 0.482885
\(324\) −12.3195 −0.684415
\(325\) 0 0
\(326\) −51.4546 −2.84981
\(327\) −40.9824 −2.26633
\(328\) −4.59106 −0.253499
\(329\) −6.92879 −0.381996
\(330\) 0 0
\(331\) −9.41366 −0.517421 −0.258711 0.965955i \(-0.583298\pi\)
−0.258711 + 0.965955i \(0.583298\pi\)
\(332\) −12.1404 −0.666293
\(333\) −9.63653 −0.528079
\(334\) 45.6559 2.49818
\(335\) 0 0
\(336\) 4.86659 0.265494
\(337\) 9.80625 0.534181 0.267090 0.963672i \(-0.413938\pi\)
0.267090 + 0.963672i \(0.413938\pi\)
\(338\) −28.4175 −1.54571
\(339\) 32.0520 1.74083
\(340\) 0 0
\(341\) 2.86800 0.155311
\(342\) 29.4469 1.59231
\(343\) 1.00000 0.0539949
\(344\) −15.5182 −0.836683
\(345\) 0 0
\(346\) −22.9656 −1.23464
\(347\) 12.9279 0.694008 0.347004 0.937864i \(-0.387199\pi\)
0.347004 + 0.937864i \(0.387199\pi\)
\(348\) 3.70109 0.198399
\(349\) −19.7938 −1.05954 −0.529769 0.848142i \(-0.677722\pi\)
−0.529769 + 0.848142i \(0.677722\pi\)
\(350\) 0 0
\(351\) −0.203549 −0.0108646
\(352\) 25.0953 1.33758
\(353\) 21.5440 1.14667 0.573335 0.819321i \(-0.305650\pi\)
0.573335 + 0.819321i \(0.305650\pi\)
\(354\) −27.5178 −1.46255
\(355\) 0 0
\(356\) −17.0927 −0.905910
\(357\) −7.06688 −0.374019
\(358\) 48.2694 2.55112
\(359\) 29.8229 1.57399 0.786996 0.616958i \(-0.211635\pi\)
0.786996 + 0.616958i \(0.211635\pi\)
\(360\) 0 0
\(361\) −8.27458 −0.435504
\(362\) 9.64688 0.507029
\(363\) −1.25116 −0.0656689
\(364\) 0.190980 0.0100101
\(365\) 0 0
\(366\) −49.7519 −2.60057
\(367\) −12.5327 −0.654203 −0.327102 0.944989i \(-0.606072\pi\)
−0.327102 + 0.944989i \(0.606072\pi\)
\(368\) 1.82488 0.0951285
\(369\) −11.0408 −0.574763
\(370\) 0 0
\(371\) 0.0435836 0.00226275
\(372\) 6.28266 0.325741
\(373\) −24.4351 −1.26520 −0.632600 0.774479i \(-0.718012\pi\)
−0.632600 + 0.774479i \(0.718012\pi\)
\(374\) −19.6247 −1.01477
\(375\) 0 0
\(376\) −11.8468 −0.610951
\(377\) −0.0342491 −0.00176392
\(378\) −6.48365 −0.333483
\(379\) 28.0657 1.44164 0.720820 0.693122i \(-0.243765\pi\)
0.720820 + 0.693122i \(0.243765\pi\)
\(380\) 0 0
\(381\) 30.6295 1.56920
\(382\) −13.0963 −0.670065
\(383\) 13.8519 0.707799 0.353900 0.935283i \(-0.384855\pi\)
0.353900 + 0.935283i \(0.384855\pi\)
\(384\) 33.6898 1.71923
\(385\) 0 0
\(386\) 27.4686 1.39811
\(387\) −37.3190 −1.89703
\(388\) −18.6934 −0.949013
\(389\) −0.469165 −0.0237876 −0.0118938 0.999929i \(-0.503786\pi\)
−0.0118938 + 0.999929i \(0.503786\pi\)
\(390\) 0 0
\(391\) −2.64995 −0.134014
\(392\) 1.70979 0.0863575
\(393\) 12.7762 0.644476
\(394\) 5.71224 0.287778
\(395\) 0 0
\(396\) −38.7381 −1.94666
\(397\) −11.8028 −0.592364 −0.296182 0.955132i \(-0.595713\pi\)
−0.296182 + 0.955132i \(0.595713\pi\)
\(398\) 21.3082 1.06808
\(399\) −8.73368 −0.437231
\(400\) 0 0
\(401\) −3.06276 −0.152947 −0.0764735 0.997072i \(-0.524366\pi\)
−0.0764735 + 0.997072i \(0.524366\pi\)
\(402\) 49.3678 2.46224
\(403\) −0.0581384 −0.00289608
\(404\) 35.2598 1.75424
\(405\) 0 0
\(406\) −1.09094 −0.0541423
\(407\) 7.93695 0.393420
\(408\) −12.0829 −0.598193
\(409\) 34.8685 1.72414 0.862068 0.506792i \(-0.169169\pi\)
0.862068 + 0.506792i \(0.169169\pi\)
\(410\) 0 0
\(411\) 38.7290 1.91036
\(412\) −4.67085 −0.230116
\(413\) 4.71871 0.232193
\(414\) −8.99151 −0.441908
\(415\) 0 0
\(416\) −0.508717 −0.0249419
\(417\) 41.9326 2.05345
\(418\) −24.2534 −1.18627
\(419\) 14.2917 0.698193 0.349096 0.937087i \(-0.386489\pi\)
0.349096 + 0.937087i \(0.386489\pi\)
\(420\) 0 0
\(421\) 20.5522 1.00165 0.500827 0.865548i \(-0.333029\pi\)
0.500827 + 0.865548i \(0.333029\pi\)
\(422\) −5.88961 −0.286702
\(423\) −28.4898 −1.38522
\(424\) 0.0745190 0.00361896
\(425\) 0 0
\(426\) 2.55709 0.123891
\(427\) 8.53139 0.412863
\(428\) −5.10751 −0.246881
\(429\) 0.620019 0.0299348
\(430\) 0 0
\(431\) −18.3898 −0.885806 −0.442903 0.896569i \(-0.646051\pi\)
−0.442903 + 0.896569i \(0.646051\pi\)
\(432\) 5.41071 0.260323
\(433\) 15.1621 0.728645 0.364323 0.931273i \(-0.381301\pi\)
0.364323 + 0.931273i \(0.381301\pi\)
\(434\) −1.85188 −0.0888932
\(435\) 0 0
\(436\) 42.7511 2.04741
\(437\) −3.27497 −0.156663
\(438\) 45.1546 2.15757
\(439\) −37.5351 −1.79145 −0.895727 0.444604i \(-0.853344\pi\)
−0.895727 + 0.444604i \(0.853344\pi\)
\(440\) 0 0
\(441\) 4.11181 0.195800
\(442\) 0.397820 0.0189224
\(443\) −25.7620 −1.22399 −0.611995 0.790861i \(-0.709633\pi\)
−0.611995 + 0.790861i \(0.709633\pi\)
\(444\) 17.3867 0.825137
\(445\) 0 0
\(446\) −11.8466 −0.560952
\(447\) 8.68969 0.411008
\(448\) −12.5544 −0.593139
\(449\) 35.3393 1.66777 0.833883 0.551942i \(-0.186113\pi\)
0.833883 + 0.551942i \(0.186113\pi\)
\(450\) 0 0
\(451\) 9.09359 0.428200
\(452\) −33.4353 −1.57266
\(453\) −9.11208 −0.428123
\(454\) −12.8360 −0.602422
\(455\) 0 0
\(456\) −14.9328 −0.699291
\(457\) −8.30606 −0.388541 −0.194271 0.980948i \(-0.562234\pi\)
−0.194271 + 0.980948i \(0.562234\pi\)
\(458\) 54.7739 2.55942
\(459\) −7.85701 −0.366734
\(460\) 0 0
\(461\) 20.6213 0.960431 0.480216 0.877150i \(-0.340558\pi\)
0.480216 + 0.877150i \(0.340558\pi\)
\(462\) 19.7495 0.918829
\(463\) −13.7920 −0.640968 −0.320484 0.947254i \(-0.603845\pi\)
−0.320484 + 0.947254i \(0.603845\pi\)
\(464\) 0.910405 0.0422645
\(465\) 0 0
\(466\) 27.4063 1.26957
\(467\) 16.7233 0.773860 0.386930 0.922109i \(-0.373535\pi\)
0.386930 + 0.922109i \(0.373535\pi\)
\(468\) 0.785274 0.0362993
\(469\) −8.46553 −0.390902
\(470\) 0 0
\(471\) 39.4453 1.81754
\(472\) 8.06801 0.371360
\(473\) 30.7371 1.41329
\(474\) 55.0765 2.52975
\(475\) 0 0
\(476\) 7.37186 0.337889
\(477\) 0.179208 0.00820535
\(478\) −31.1056 −1.42274
\(479\) 36.9462 1.68812 0.844058 0.536252i \(-0.180160\pi\)
0.844058 + 0.536252i \(0.180160\pi\)
\(480\) 0 0
\(481\) −0.160893 −0.00733609
\(482\) −6.45690 −0.294104
\(483\) 2.66680 0.121343
\(484\) 1.30516 0.0593252
\(485\) 0 0
\(486\) 45.2761 2.05376
\(487\) −1.03549 −0.0469224 −0.0234612 0.999725i \(-0.507469\pi\)
−0.0234612 + 0.999725i \(0.507469\pi\)
\(488\) 14.5869 0.660318
\(489\) 62.7501 2.83766
\(490\) 0 0
\(491\) 3.49792 0.157859 0.0789294 0.996880i \(-0.474850\pi\)
0.0789294 + 0.996880i \(0.474850\pi\)
\(492\) 19.9204 0.898083
\(493\) −1.32202 −0.0595408
\(494\) 0.491650 0.0221204
\(495\) 0 0
\(496\) 1.54543 0.0693917
\(497\) −0.438487 −0.0196688
\(498\) 25.4498 1.14043
\(499\) 12.9687 0.580559 0.290279 0.956942i \(-0.406252\pi\)
0.290279 + 0.956942i \(0.406252\pi\)
\(500\) 0 0
\(501\) −55.6785 −2.48753
\(502\) −57.6153 −2.57150
\(503\) −6.09468 −0.271748 −0.135874 0.990726i \(-0.543384\pi\)
−0.135874 + 0.990726i \(0.543384\pi\)
\(504\) 7.03034 0.313156
\(505\) 0 0
\(506\) 7.40569 0.329223
\(507\) 34.6558 1.53912
\(508\) −31.9514 −1.41761
\(509\) 28.0398 1.24284 0.621420 0.783478i \(-0.286556\pi\)
0.621420 + 0.783478i \(0.286556\pi\)
\(510\) 0 0
\(511\) −7.74306 −0.342533
\(512\) 19.7630 0.873408
\(513\) −9.71017 −0.428715
\(514\) −16.9735 −0.748670
\(515\) 0 0
\(516\) 67.3327 2.96416
\(517\) 23.4651 1.03200
\(518\) −5.12493 −0.225176
\(519\) 28.0071 1.22937
\(520\) 0 0
\(521\) −12.7913 −0.560396 −0.280198 0.959942i \(-0.590400\pi\)
−0.280198 + 0.959942i \(0.590400\pi\)
\(522\) −4.48573 −0.196335
\(523\) −26.9318 −1.17765 −0.588823 0.808262i \(-0.700409\pi\)
−0.588823 + 0.808262i \(0.700409\pi\)
\(524\) −13.3276 −0.582220
\(525\) 0 0
\(526\) 22.1099 0.964039
\(527\) −2.24415 −0.0977567
\(528\) −16.4813 −0.717255
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 19.4024 0.841994
\(532\) 9.11059 0.394994
\(533\) −0.184340 −0.00798463
\(534\) 35.8311 1.55056
\(535\) 0 0
\(536\) −14.4743 −0.625194
\(537\) −58.8657 −2.54024
\(538\) 33.0347 1.42423
\(539\) −3.38662 −0.145872
\(540\) 0 0
\(541\) 37.0305 1.59207 0.796033 0.605253i \(-0.206928\pi\)
0.796033 + 0.605253i \(0.206928\pi\)
\(542\) −7.15191 −0.307201
\(543\) −11.7646 −0.504867
\(544\) −19.6365 −0.841909
\(545\) 0 0
\(546\) −0.400349 −0.0171334
\(547\) 14.7399 0.630232 0.315116 0.949053i \(-0.397957\pi\)
0.315116 + 0.949053i \(0.397957\pi\)
\(548\) −40.4004 −1.72582
\(549\) 35.0794 1.49715
\(550\) 0 0
\(551\) −1.63383 −0.0696036
\(552\) 4.55967 0.194072
\(553\) −9.44444 −0.401619
\(554\) 20.3152 0.863111
\(555\) 0 0
\(556\) −43.7422 −1.85508
\(557\) −27.7047 −1.17388 −0.586942 0.809629i \(-0.699668\pi\)
−0.586942 + 0.809629i \(0.699668\pi\)
\(558\) −7.61459 −0.322351
\(559\) −0.623083 −0.0263536
\(560\) 0 0
\(561\) 23.9328 1.01044
\(562\) −55.6684 −2.34823
\(563\) 14.9839 0.631498 0.315749 0.948843i \(-0.397744\pi\)
0.315749 + 0.948843i \(0.397744\pi\)
\(564\) 51.4028 2.16445
\(565\) 0 0
\(566\) 6.32837 0.266001
\(567\) −4.42846 −0.185978
\(568\) −0.749721 −0.0314576
\(569\) −25.2881 −1.06013 −0.530067 0.847956i \(-0.677833\pi\)
−0.530067 + 0.847956i \(0.677833\pi\)
\(570\) 0 0
\(571\) 18.7514 0.784721 0.392360 0.919812i \(-0.371659\pi\)
0.392360 + 0.919812i \(0.371659\pi\)
\(572\) −0.646777 −0.0270431
\(573\) 15.9712 0.667208
\(574\) −5.87177 −0.245083
\(575\) 0 0
\(576\) −51.6213 −2.15089
\(577\) −16.3012 −0.678626 −0.339313 0.940673i \(-0.610195\pi\)
−0.339313 + 0.940673i \(0.610195\pi\)
\(578\) −21.8189 −0.907546
\(579\) −33.4986 −1.39215
\(580\) 0 0
\(581\) −4.36410 −0.181053
\(582\) 39.1867 1.62434
\(583\) −0.147601 −0.00611301
\(584\) −13.2390 −0.547834
\(585\) 0 0
\(586\) 48.1952 1.99093
\(587\) 8.75631 0.361412 0.180706 0.983537i \(-0.442162\pi\)
0.180706 + 0.983537i \(0.442162\pi\)
\(588\) −7.41873 −0.305943
\(589\) −2.77345 −0.114278
\(590\) 0 0
\(591\) −6.96621 −0.286552
\(592\) 4.27684 0.175777
\(593\) −16.0251 −0.658071 −0.329036 0.944317i \(-0.606724\pi\)
−0.329036 + 0.944317i \(0.606724\pi\)
\(594\) 21.9576 0.900932
\(595\) 0 0
\(596\) −9.06471 −0.371305
\(597\) −25.9859 −1.06353
\(598\) −0.150124 −0.00613901
\(599\) 0.892426 0.0364635 0.0182318 0.999834i \(-0.494196\pi\)
0.0182318 + 0.999834i \(0.494196\pi\)
\(600\) 0 0
\(601\) −37.7711 −1.54072 −0.770358 0.637611i \(-0.779923\pi\)
−0.770358 + 0.637611i \(0.779923\pi\)
\(602\) −19.8471 −0.808906
\(603\) −34.8086 −1.41752
\(604\) 9.50532 0.386766
\(605\) 0 0
\(606\) −73.9146 −3.00257
\(607\) −26.4468 −1.07344 −0.536722 0.843759i \(-0.680338\pi\)
−0.536722 + 0.843759i \(0.680338\pi\)
\(608\) −24.2680 −0.984197
\(609\) 1.33042 0.0539115
\(610\) 0 0
\(611\) −0.475671 −0.0192436
\(612\) 30.3117 1.22528
\(613\) 32.7728 1.32368 0.661841 0.749644i \(-0.269775\pi\)
0.661841 + 0.749644i \(0.269775\pi\)
\(614\) −25.8517 −1.04329
\(615\) 0 0
\(616\) −5.79041 −0.233302
\(617\) 29.5205 1.18845 0.594226 0.804298i \(-0.297459\pi\)
0.594226 + 0.804298i \(0.297459\pi\)
\(618\) 9.79144 0.393869
\(619\) 45.4373 1.82628 0.913139 0.407649i \(-0.133651\pi\)
0.913139 + 0.407649i \(0.133651\pi\)
\(620\) 0 0
\(621\) 2.96497 0.118980
\(622\) −30.3875 −1.21843
\(623\) −6.14427 −0.246165
\(624\) 0.334098 0.0133746
\(625\) 0 0
\(626\) −12.7370 −0.509073
\(627\) 29.5776 1.18122
\(628\) −41.1476 −1.64197
\(629\) −6.21049 −0.247628
\(630\) 0 0
\(631\) 6.03836 0.240383 0.120192 0.992751i \(-0.461649\pi\)
0.120192 + 0.992751i \(0.461649\pi\)
\(632\) −16.1480 −0.642334
\(633\) 7.18252 0.285480
\(634\) 60.6956 2.41053
\(635\) 0 0
\(636\) −0.323335 −0.0128211
\(637\) 0.0686513 0.00272007
\(638\) 3.69459 0.146270
\(639\) −1.80297 −0.0713245
\(640\) 0 0
\(641\) 26.1481 1.03279 0.516394 0.856351i \(-0.327274\pi\)
0.516394 + 0.856351i \(0.327274\pi\)
\(642\) 10.7068 0.422564
\(643\) 23.3377 0.920350 0.460175 0.887828i \(-0.347787\pi\)
0.460175 + 0.887828i \(0.347787\pi\)
\(644\) −2.78189 −0.109622
\(645\) 0 0
\(646\) 18.9777 0.746669
\(647\) 28.5192 1.12121 0.560603 0.828085i \(-0.310569\pi\)
0.560603 + 0.828085i \(0.310569\pi\)
\(648\) −7.57175 −0.297446
\(649\) −15.9805 −0.627288
\(650\) 0 0
\(651\) 2.25842 0.0885143
\(652\) −65.4582 −2.56354
\(653\) 22.4429 0.878258 0.439129 0.898424i \(-0.355287\pi\)
0.439129 + 0.898424i \(0.355287\pi\)
\(654\) −89.6184 −3.50436
\(655\) 0 0
\(656\) 4.90009 0.191316
\(657\) −31.8380 −1.24212
\(658\) −15.1515 −0.590669
\(659\) −31.9129 −1.24315 −0.621576 0.783354i \(-0.713507\pi\)
−0.621576 + 0.783354i \(0.713507\pi\)
\(660\) 0 0
\(661\) 44.5132 1.73136 0.865681 0.500596i \(-0.166886\pi\)
0.865681 + 0.500596i \(0.166886\pi\)
\(662\) −20.5853 −0.800072
\(663\) −0.485151 −0.0188417
\(664\) −7.46171 −0.289570
\(665\) 0 0
\(666\) −21.0727 −0.816551
\(667\) 0.498885 0.0193169
\(668\) 58.0814 2.24724
\(669\) 14.4472 0.558561
\(670\) 0 0
\(671\) −28.8925 −1.11538
\(672\) 19.7614 0.762311
\(673\) 31.5630 1.21667 0.608333 0.793682i \(-0.291839\pi\)
0.608333 + 0.793682i \(0.291839\pi\)
\(674\) 21.4438 0.825986
\(675\) 0 0
\(676\) −36.1514 −1.39044
\(677\) 27.7525 1.06662 0.533308 0.845921i \(-0.320949\pi\)
0.533308 + 0.845921i \(0.320949\pi\)
\(678\) 70.0899 2.69179
\(679\) −6.71968 −0.257878
\(680\) 0 0
\(681\) 15.6538 0.599854
\(682\) 6.27161 0.240153
\(683\) −35.4743 −1.35739 −0.678694 0.734421i \(-0.737454\pi\)
−0.678694 + 0.734421i \(0.737454\pi\)
\(684\) 37.4610 1.43236
\(685\) 0 0
\(686\) 2.18675 0.0834906
\(687\) −66.7981 −2.54851
\(688\) 16.5627 0.631447
\(689\) 0.00299208 0.000113989 0
\(690\) 0 0
\(691\) −41.1938 −1.56709 −0.783543 0.621338i \(-0.786590\pi\)
−0.783543 + 0.621338i \(0.786590\pi\)
\(692\) −29.2158 −1.11062
\(693\) −13.9251 −0.528971
\(694\) 28.2702 1.07312
\(695\) 0 0
\(696\) 2.27475 0.0862241
\(697\) −7.11553 −0.269520
\(698\) −43.2842 −1.63833
\(699\) −33.4227 −1.26416
\(700\) 0 0
\(701\) 8.69638 0.328458 0.164229 0.986422i \(-0.447486\pi\)
0.164229 + 0.986422i \(0.447486\pi\)
\(702\) −0.445111 −0.0167996
\(703\) −7.67530 −0.289479
\(704\) 42.5169 1.60242
\(705\) 0 0
\(706\) 47.1113 1.77306
\(707\) 12.6748 0.476684
\(708\) −35.0068 −1.31564
\(709\) −43.8845 −1.64812 −0.824059 0.566503i \(-0.808296\pi\)
−0.824059 + 0.566503i \(0.808296\pi\)
\(710\) 0 0
\(711\) −38.8337 −1.45638
\(712\) −10.5054 −0.393708
\(713\) 0.846864 0.0317153
\(714\) −15.4535 −0.578333
\(715\) 0 0
\(716\) 61.4061 2.29485
\(717\) 37.9341 1.41667
\(718\) 65.2153 2.43381
\(719\) −18.6846 −0.696819 −0.348410 0.937342i \(-0.613278\pi\)
−0.348410 + 0.937342i \(0.613278\pi\)
\(720\) 0 0
\(721\) −1.67902 −0.0625301
\(722\) −18.0945 −0.673406
\(723\) 7.87434 0.292850
\(724\) 12.2723 0.456097
\(725\) 0 0
\(726\) −2.73598 −0.101542
\(727\) −31.5659 −1.17071 −0.585357 0.810776i \(-0.699046\pi\)
−0.585357 + 0.810776i \(0.699046\pi\)
\(728\) 0.117380 0.00435037
\(729\) −41.9299 −1.55296
\(730\) 0 0
\(731\) −24.0511 −0.889561
\(732\) −63.2921 −2.33934
\(733\) 29.9205 1.10514 0.552569 0.833467i \(-0.313648\pi\)
0.552569 + 0.833467i \(0.313648\pi\)
\(734\) −27.4060 −1.01157
\(735\) 0 0
\(736\) 7.41015 0.273142
\(737\) 28.6695 1.05605
\(738\) −24.1436 −0.888738
\(739\) 12.1667 0.447560 0.223780 0.974640i \(-0.428160\pi\)
0.223780 + 0.974640i \(0.428160\pi\)
\(740\) 0 0
\(741\) −0.599579 −0.0220261
\(742\) 0.0953066 0.00349882
\(743\) −36.1379 −1.32577 −0.662886 0.748720i \(-0.730669\pi\)
−0.662886 + 0.748720i \(0.730669\pi\)
\(744\) 3.86142 0.141567
\(745\) 0 0
\(746\) −53.4335 −1.95634
\(747\) −17.9443 −0.656549
\(748\) −24.9657 −0.912835
\(749\) −1.83599 −0.0670856
\(750\) 0 0
\(751\) 27.5432 1.00507 0.502533 0.864558i \(-0.332401\pi\)
0.502533 + 0.864558i \(0.332401\pi\)
\(752\) 12.6442 0.461087
\(753\) 70.2632 2.56053
\(754\) −0.0748943 −0.00272749
\(755\) 0 0
\(756\) −8.24820 −0.299984
\(757\) −19.1764 −0.696977 −0.348489 0.937313i \(-0.613305\pi\)
−0.348489 + 0.937313i \(0.613305\pi\)
\(758\) 61.3728 2.22916
\(759\) −9.03142 −0.327820
\(760\) 0 0
\(761\) −4.83852 −0.175396 −0.0876981 0.996147i \(-0.527951\pi\)
−0.0876981 + 0.996147i \(0.527951\pi\)
\(762\) 66.9792 2.42640
\(763\) 15.3677 0.556347
\(764\) −16.6605 −0.602756
\(765\) 0 0
\(766\) 30.2907 1.09445
\(767\) 0.323946 0.0116970
\(768\) 6.71122 0.242170
\(769\) −40.2108 −1.45004 −0.725019 0.688728i \(-0.758169\pi\)
−0.725019 + 0.688728i \(0.758169\pi\)
\(770\) 0 0
\(771\) 20.6996 0.745479
\(772\) 34.9443 1.25767
\(773\) 15.1467 0.544790 0.272395 0.962186i \(-0.412184\pi\)
0.272395 + 0.962186i \(0.412184\pi\)
\(774\) −81.6073 −2.93332
\(775\) 0 0
\(776\) −11.4893 −0.412440
\(777\) 6.24997 0.224216
\(778\) −1.02595 −0.0367820
\(779\) −8.79380 −0.315071
\(780\) 0 0
\(781\) 1.48499 0.0531370
\(782\) −5.79479 −0.207221
\(783\) 1.47918 0.0528614
\(784\) −1.82488 −0.0651743
\(785\) 0 0
\(786\) 27.9385 0.996533
\(787\) −43.3536 −1.54539 −0.772695 0.634778i \(-0.781092\pi\)
−0.772695 + 0.634778i \(0.781092\pi\)
\(788\) 7.26685 0.258871
\(789\) −26.9636 −0.959930
\(790\) 0 0
\(791\) −12.0189 −0.427344
\(792\) −23.8090 −0.846017
\(793\) 0.585692 0.0207985
\(794\) −25.8097 −0.915953
\(795\) 0 0
\(796\) 27.1073 0.960794
\(797\) −31.6543 −1.12125 −0.560626 0.828069i \(-0.689440\pi\)
−0.560626 + 0.828069i \(0.689440\pi\)
\(798\) −19.0984 −0.676076
\(799\) −18.3609 −0.649564
\(800\) 0 0
\(801\) −25.2641 −0.892662
\(802\) −6.69750 −0.236497
\(803\) 26.2228 0.925381
\(804\) 62.8034 2.21491
\(805\) 0 0
\(806\) −0.127134 −0.00447811
\(807\) −40.2866 −1.41816
\(808\) 21.6712 0.762392
\(809\) 9.67754 0.340244 0.170122 0.985423i \(-0.445584\pi\)
0.170122 + 0.985423i \(0.445584\pi\)
\(810\) 0 0
\(811\) −3.68358 −0.129348 −0.0646740 0.997906i \(-0.520601\pi\)
−0.0646740 + 0.997906i \(0.520601\pi\)
\(812\) −1.38784 −0.0487037
\(813\) 8.72192 0.305891
\(814\) 17.3562 0.608333
\(815\) 0 0
\(816\) 12.8962 0.451458
\(817\) −29.7238 −1.03990
\(818\) 76.2488 2.66598
\(819\) 0.282281 0.00986370
\(820\) 0 0
\(821\) 20.0592 0.700072 0.350036 0.936736i \(-0.386169\pi\)
0.350036 + 0.936736i \(0.386169\pi\)
\(822\) 84.6908 2.95393
\(823\) −41.2668 −1.43847 −0.719236 0.694766i \(-0.755508\pi\)
−0.719236 + 0.694766i \(0.755508\pi\)
\(824\) −2.87078 −0.100008
\(825\) 0 0
\(826\) 10.3187 0.359032
\(827\) 6.03898 0.209996 0.104998 0.994472i \(-0.466516\pi\)
0.104998 + 0.994472i \(0.466516\pi\)
\(828\) −11.4386 −0.397518
\(829\) −15.7649 −0.547536 −0.273768 0.961796i \(-0.588270\pi\)
−0.273768 + 0.961796i \(0.588270\pi\)
\(830\) 0 0
\(831\) −24.7749 −0.859431
\(832\) −0.861876 −0.0298802
\(833\) 2.64995 0.0918154
\(834\) 91.6961 3.17518
\(835\) 0 0
\(836\) −30.8541 −1.06711
\(837\) 2.51092 0.0867902
\(838\) 31.2523 1.07959
\(839\) −40.0524 −1.38276 −0.691381 0.722490i \(-0.742997\pi\)
−0.691381 + 0.722490i \(0.742997\pi\)
\(840\) 0 0
\(841\) −28.7511 −0.991418
\(842\) 44.9426 1.54882
\(843\) 67.8889 2.33822
\(844\) −7.49249 −0.257902
\(845\) 0 0
\(846\) −62.3002 −2.14193
\(847\) 0.469162 0.0161206
\(848\) −0.0795350 −0.00273124
\(849\) −7.71760 −0.264867
\(850\) 0 0
\(851\) 2.34362 0.0803384
\(852\) 3.25301 0.111446
\(853\) 39.8281 1.36369 0.681844 0.731498i \(-0.261178\pi\)
0.681844 + 0.731498i \(0.261178\pi\)
\(854\) 18.6560 0.638397
\(855\) 0 0
\(856\) −3.13916 −0.107294
\(857\) 15.6310 0.533945 0.266972 0.963704i \(-0.413977\pi\)
0.266972 + 0.963704i \(0.413977\pi\)
\(858\) 1.35583 0.0462872
\(859\) 9.42293 0.321506 0.160753 0.986995i \(-0.448608\pi\)
0.160753 + 0.986995i \(0.448608\pi\)
\(860\) 0 0
\(861\) 7.16076 0.244038
\(862\) −40.2140 −1.36969
\(863\) −9.46081 −0.322050 −0.161025 0.986950i \(-0.551480\pi\)
−0.161025 + 0.986950i \(0.551480\pi\)
\(864\) 21.9708 0.747463
\(865\) 0 0
\(866\) 33.1558 1.12668
\(867\) 26.6087 0.903678
\(868\) −2.35588 −0.0799638
\(869\) 31.9847 1.08501
\(870\) 0 0
\(871\) −0.581170 −0.0196922
\(872\) 26.2755 0.889801
\(873\) −27.6300 −0.935135
\(874\) −7.16155 −0.242243
\(875\) 0 0
\(876\) 57.4436 1.94084
\(877\) −41.0285 −1.38544 −0.692718 0.721209i \(-0.743587\pi\)
−0.692718 + 0.721209i \(0.743587\pi\)
\(878\) −82.0801 −2.77007
\(879\) −58.7752 −1.98244
\(880\) 0 0
\(881\) 43.1627 1.45419 0.727093 0.686538i \(-0.240871\pi\)
0.727093 + 0.686538i \(0.240871\pi\)
\(882\) 8.99151 0.302760
\(883\) 11.3463 0.381835 0.190917 0.981606i \(-0.438854\pi\)
0.190917 + 0.981606i \(0.438854\pi\)
\(884\) 0.506088 0.0170216
\(885\) 0 0
\(886\) −56.3352 −1.89262
\(887\) 20.7827 0.697813 0.348907 0.937157i \(-0.386553\pi\)
0.348907 + 0.937157i \(0.386553\pi\)
\(888\) 10.6861 0.358604
\(889\) −11.4855 −0.385212
\(890\) 0 0
\(891\) 14.9975 0.502435
\(892\) −15.0707 −0.504604
\(893\) −22.6916 −0.759344
\(894\) 19.0022 0.635529
\(895\) 0 0
\(896\) −12.6331 −0.422041
\(897\) 0.183079 0.00611284
\(898\) 77.2783 2.57881
\(899\) 0.422488 0.0140908
\(900\) 0 0
\(901\) 0.115495 0.00384768
\(902\) 19.8854 0.662112
\(903\) 24.2040 0.805458
\(904\) −20.5499 −0.683478
\(905\) 0 0
\(906\) −19.9259 −0.661992
\(907\) 20.4570 0.679264 0.339632 0.940558i \(-0.389697\pi\)
0.339632 + 0.940558i \(0.389697\pi\)
\(908\) −16.3293 −0.541908
\(909\) 52.1163 1.72859
\(910\) 0 0
\(911\) 34.8765 1.15551 0.577755 0.816210i \(-0.303929\pi\)
0.577755 + 0.816210i \(0.303929\pi\)
\(912\) 15.9379 0.527757
\(913\) 14.7795 0.489131
\(914\) −18.1633 −0.600789
\(915\) 0 0
\(916\) 69.6809 2.30232
\(917\) −4.79086 −0.158208
\(918\) −17.1813 −0.567069
\(919\) −45.0649 −1.48655 −0.743277 0.668984i \(-0.766730\pi\)
−0.743277 + 0.668984i \(0.766730\pi\)
\(920\) 0 0
\(921\) 31.5268 1.03884
\(922\) 45.0938 1.48508
\(923\) −0.0301027 −0.000990843 0
\(924\) 25.1244 0.826531
\(925\) 0 0
\(926\) −30.1596 −0.991107
\(927\) −6.90382 −0.226751
\(928\) 3.69681 0.121354
\(929\) 30.5061 1.00087 0.500436 0.865774i \(-0.333173\pi\)
0.500436 + 0.865774i \(0.333173\pi\)
\(930\) 0 0
\(931\) 3.27497 0.107333
\(932\) 34.8651 1.14204
\(933\) 37.0583 1.21324
\(934\) 36.5696 1.19659
\(935\) 0 0
\(936\) 0.482642 0.0157756
\(937\) −5.72001 −0.186865 −0.0934323 0.995626i \(-0.529784\pi\)
−0.0934323 + 0.995626i \(0.529784\pi\)
\(938\) −18.5120 −0.604439
\(939\) 15.5331 0.506903
\(940\) 0 0
\(941\) −32.6577 −1.06461 −0.532305 0.846553i \(-0.678674\pi\)
−0.532305 + 0.846553i \(0.678674\pi\)
\(942\) 86.2572 2.81041
\(943\) 2.68516 0.0874407
\(944\) −8.61108 −0.280267
\(945\) 0 0
\(946\) 67.2144 2.18533
\(947\) 9.01828 0.293055 0.146527 0.989207i \(-0.453190\pi\)
0.146527 + 0.989207i \(0.453190\pi\)
\(948\) 70.0657 2.27563
\(949\) −0.531571 −0.0172555
\(950\) 0 0
\(951\) −74.0198 −2.40026
\(952\) 4.53086 0.146846
\(953\) 14.4232 0.467212 0.233606 0.972331i \(-0.424947\pi\)
0.233606 + 0.972331i \(0.424947\pi\)
\(954\) 0.391883 0.0126877
\(955\) 0 0
\(956\) −39.5712 −1.27982
\(957\) −4.50564 −0.145647
\(958\) 80.7922 2.61028
\(959\) −14.5227 −0.468962
\(960\) 0 0
\(961\) −30.2828 −0.976865
\(962\) −0.351833 −0.0113436
\(963\) −7.54923 −0.243271
\(964\) −8.21417 −0.264561
\(965\) 0 0
\(966\) 5.83163 0.187629
\(967\) 22.8714 0.735493 0.367747 0.929926i \(-0.380129\pi\)
0.367747 + 0.929926i \(0.380129\pi\)
\(968\) 0.802169 0.0257827
\(969\) −23.1438 −0.743487
\(970\) 0 0
\(971\) −6.18825 −0.198590 −0.0992952 0.995058i \(-0.531659\pi\)
−0.0992952 + 0.995058i \(0.531659\pi\)
\(972\) 57.5981 1.84746
\(973\) −15.7239 −0.504086
\(974\) −2.26435 −0.0725545
\(975\) 0 0
\(976\) −15.5688 −0.498344
\(977\) −1.03108 −0.0329871 −0.0164936 0.999864i \(-0.505250\pi\)
−0.0164936 + 0.999864i \(0.505250\pi\)
\(978\) 137.219 4.38778
\(979\) 20.8083 0.665036
\(980\) 0 0
\(981\) 63.1889 2.01747
\(982\) 7.64908 0.244092
\(983\) −57.5700 −1.83620 −0.918098 0.396352i \(-0.870276\pi\)
−0.918098 + 0.396352i \(0.870276\pi\)
\(984\) 12.2434 0.390306
\(985\) 0 0
\(986\) −2.89093 −0.0920660
\(987\) 18.4777 0.588151
\(988\) 0.625454 0.0198984
\(989\) 9.07605 0.288602
\(990\) 0 0
\(991\) 17.2309 0.547359 0.273680 0.961821i \(-0.411759\pi\)
0.273680 + 0.961821i \(0.411759\pi\)
\(992\) 6.27539 0.199244
\(993\) 25.1043 0.796661
\(994\) −0.958862 −0.0304133
\(995\) 0 0
\(996\) 32.3761 1.02588
\(997\) 4.57213 0.144801 0.0724004 0.997376i \(-0.476934\pi\)
0.0724004 + 0.997376i \(0.476934\pi\)
\(998\) 28.3593 0.897699
\(999\) 6.94877 0.219849
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 4025.2.a.u.1.8 8
5.4 even 2 4025.2.a.v.1.1 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4025.2.a.u.1.8 8 1.1 even 1 trivial
4025.2.a.v.1.1 yes 8 5.4 even 2