Properties

Label 3525.2.a.bh.1.4
Level $3525$
Weight $2$
Character 3525.1
Self dual yes
Analytic conductor $28.147$
Analytic rank $0$
Dimension $13$
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] = [3525,2,Mod(1,3525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3525, 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("3525.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3525 = 3 \cdot 5^{2} \cdot 47 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3525.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: \(28.1472667125\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{13} - 3 x^{12} - 17 x^{11} + 51 x^{10} + 106 x^{9} - 316 x^{8} - 288 x^{7} + 852 x^{6} + 309 x^{5} - 923 x^{4} - 107 x^{3} + 293 x^{2} + 12 x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{29}]\)
Coefficient ring index: \( 2^{3} \)
Twist minimal: no (minimal twist has level 705)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(1.67335\) of defining polynomial
Character \(\chi\) \(=\) 3525.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.67335 q^{2} -1.00000 q^{3} +0.800100 q^{4} +1.67335 q^{6} +2.75180 q^{7} +2.00785 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.67335 q^{2} -1.00000 q^{3} +0.800100 q^{4} +1.67335 q^{6} +2.75180 q^{7} +2.00785 q^{8} +1.00000 q^{9} -3.09151 q^{11} -0.800100 q^{12} -4.10277 q^{13} -4.60473 q^{14} -4.96004 q^{16} -4.07070 q^{17} -1.67335 q^{18} +5.75557 q^{19} -2.75180 q^{21} +5.17318 q^{22} -6.80592 q^{23} -2.00785 q^{24} +6.86536 q^{26} -1.00000 q^{27} +2.20171 q^{28} +1.81214 q^{29} +3.24850 q^{31} +4.28418 q^{32} +3.09151 q^{33} +6.81170 q^{34} +0.800100 q^{36} +5.48507 q^{37} -9.63109 q^{38} +4.10277 q^{39} +1.31661 q^{41} +4.60473 q^{42} -8.65847 q^{43} -2.47352 q^{44} +11.3887 q^{46} -1.00000 q^{47} +4.96004 q^{48} +0.572406 q^{49} +4.07070 q^{51} -3.28262 q^{52} +5.58252 q^{53} +1.67335 q^{54} +5.52521 q^{56} -5.75557 q^{57} -3.03234 q^{58} +0.623977 q^{59} +6.04084 q^{61} -5.43588 q^{62} +2.75180 q^{63} +2.75115 q^{64} -5.17318 q^{66} +4.05619 q^{67} -3.25696 q^{68} +6.80592 q^{69} +15.1185 q^{71} +2.00785 q^{72} -3.81119 q^{73} -9.17845 q^{74} +4.60503 q^{76} -8.50722 q^{77} -6.86536 q^{78} -5.60887 q^{79} +1.00000 q^{81} -2.20315 q^{82} -4.45627 q^{83} -2.20171 q^{84} +14.4886 q^{86} -1.81214 q^{87} -6.20730 q^{88} -2.86645 q^{89} -11.2900 q^{91} -5.44542 q^{92} -3.24850 q^{93} +1.67335 q^{94} -4.28418 q^{96} -6.01711 q^{97} -0.957836 q^{98} -3.09151 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 13 q - 3 q^{2} - 13 q^{3} + 17 q^{4} + 3 q^{6} + 4 q^{7} - 15 q^{8} + 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 13 q - 3 q^{2} - 13 q^{3} + 17 q^{4} + 3 q^{6} + 4 q^{7} - 15 q^{8} + 13 q^{9} + 16 q^{11} - 17 q^{12} + 8 q^{13} - 4 q^{14} + 29 q^{16} - 12 q^{17} - 3 q^{18} + 28 q^{19} - 4 q^{21} - 6 q^{23} + 15 q^{24} + 4 q^{26} - 13 q^{27} + 20 q^{28} + 12 q^{29} + 26 q^{31} - 53 q^{32} - 16 q^{33} + 8 q^{34} + 17 q^{36} + 4 q^{37} - 2 q^{38} - 8 q^{39} + 24 q^{41} + 4 q^{42} + 6 q^{43} + 4 q^{44} + 16 q^{46} - 13 q^{47} - 29 q^{48} + 21 q^{49} + 12 q^{51} + 32 q^{52} - 6 q^{53} + 3 q^{54} - 28 q^{57} + 4 q^{58} + 34 q^{59} + 24 q^{61} - 30 q^{62} + 4 q^{63} + 13 q^{64} + 24 q^{67} - 44 q^{68} + 6 q^{69} + 20 q^{71} - 15 q^{72} + 6 q^{73} + 20 q^{74} + 66 q^{76} + 2 q^{77} - 4 q^{78} + 6 q^{79} + 13 q^{81} - 20 q^{82} - 14 q^{83} - 20 q^{84} + 48 q^{86} - 12 q^{87} + 22 q^{88} + 36 q^{89} + 4 q^{91} - 4 q^{92} - 26 q^{93} + 3 q^{94} + 53 q^{96} + 32 q^{97} + 39 q^{98} + 16 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.67335 −1.18324 −0.591619 0.806218i \(-0.701511\pi\)
−0.591619 + 0.806218i \(0.701511\pi\)
\(3\) −1.00000 −0.577350
\(4\) 0.800100 0.400050
\(5\) 0 0
\(6\) 1.67335 0.683142
\(7\) 2.75180 1.04008 0.520041 0.854141i \(-0.325916\pi\)
0.520041 + 0.854141i \(0.325916\pi\)
\(8\) 2.00785 0.709883
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.09151 −0.932126 −0.466063 0.884752i \(-0.654328\pi\)
−0.466063 + 0.884752i \(0.654328\pi\)
\(12\) −0.800100 −0.230969
\(13\) −4.10277 −1.13790 −0.568951 0.822371i \(-0.692651\pi\)
−0.568951 + 0.822371i \(0.692651\pi\)
\(14\) −4.60473 −1.23066
\(15\) 0 0
\(16\) −4.96004 −1.24001
\(17\) −4.07070 −0.987290 −0.493645 0.869664i \(-0.664336\pi\)
−0.493645 + 0.869664i \(0.664336\pi\)
\(18\) −1.67335 −0.394412
\(19\) 5.75557 1.32042 0.660210 0.751081i \(-0.270467\pi\)
0.660210 + 0.751081i \(0.270467\pi\)
\(20\) 0 0
\(21\) −2.75180 −0.600492
\(22\) 5.17318 1.10293
\(23\) −6.80592 −1.41913 −0.709567 0.704638i \(-0.751109\pi\)
−0.709567 + 0.704638i \(0.751109\pi\)
\(24\) −2.00785 −0.409851
\(25\) 0 0
\(26\) 6.86536 1.34641
\(27\) −1.00000 −0.192450
\(28\) 2.20171 0.416085
\(29\) 1.81214 0.336506 0.168253 0.985744i \(-0.446187\pi\)
0.168253 + 0.985744i \(0.446187\pi\)
\(30\) 0 0
\(31\) 3.24850 0.583448 0.291724 0.956503i \(-0.405771\pi\)
0.291724 + 0.956503i \(0.405771\pi\)
\(32\) 4.28418 0.757342
\(33\) 3.09151 0.538163
\(34\) 6.81170 1.16820
\(35\) 0 0
\(36\) 0.800100 0.133350
\(37\) 5.48507 0.901741 0.450870 0.892589i \(-0.351114\pi\)
0.450870 + 0.892589i \(0.351114\pi\)
\(38\) −9.63109 −1.56237
\(39\) 4.10277 0.656968
\(40\) 0 0
\(41\) 1.31661 0.205620 0.102810 0.994701i \(-0.467217\pi\)
0.102810 + 0.994701i \(0.467217\pi\)
\(42\) 4.60473 0.710524
\(43\) −8.65847 −1.32040 −0.660202 0.751088i \(-0.729529\pi\)
−0.660202 + 0.751088i \(0.729529\pi\)
\(44\) −2.47352 −0.372897
\(45\) 0 0
\(46\) 11.3887 1.67917
\(47\) −1.00000 −0.145865
\(48\) 4.96004 0.715920
\(49\) 0.572406 0.0817723
\(50\) 0 0
\(51\) 4.07070 0.570012
\(52\) −3.28262 −0.455218
\(53\) 5.58252 0.766819 0.383409 0.923579i \(-0.374750\pi\)
0.383409 + 0.923579i \(0.374750\pi\)
\(54\) 1.67335 0.227714
\(55\) 0 0
\(56\) 5.52521 0.738337
\(57\) −5.75557 −0.762344
\(58\) −3.03234 −0.398166
\(59\) 0.623977 0.0812349 0.0406175 0.999175i \(-0.487067\pi\)
0.0406175 + 0.999175i \(0.487067\pi\)
\(60\) 0 0
\(61\) 6.04084 0.773451 0.386725 0.922195i \(-0.373606\pi\)
0.386725 + 0.922195i \(0.373606\pi\)
\(62\) −5.43588 −0.690357
\(63\) 2.75180 0.346694
\(64\) 2.75115 0.343894
\(65\) 0 0
\(66\) −5.17318 −0.636774
\(67\) 4.05619 0.495542 0.247771 0.968819i \(-0.420302\pi\)
0.247771 + 0.968819i \(0.420302\pi\)
\(68\) −3.25696 −0.394965
\(69\) 6.80592 0.819337
\(70\) 0 0
\(71\) 15.1185 1.79423 0.897117 0.441794i \(-0.145658\pi\)
0.897117 + 0.441794i \(0.145658\pi\)
\(72\) 2.00785 0.236628
\(73\) −3.81119 −0.446067 −0.223033 0.974811i \(-0.571596\pi\)
−0.223033 + 0.974811i \(0.571596\pi\)
\(74\) −9.17845 −1.06697
\(75\) 0 0
\(76\) 4.60503 0.528233
\(77\) −8.50722 −0.969488
\(78\) −6.86536 −0.777349
\(79\) −5.60887 −0.631047 −0.315523 0.948918i \(-0.602180\pi\)
−0.315523 + 0.948918i \(0.602180\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −2.20315 −0.243297
\(83\) −4.45627 −0.489139 −0.244570 0.969632i \(-0.578647\pi\)
−0.244570 + 0.969632i \(0.578647\pi\)
\(84\) −2.20171 −0.240227
\(85\) 0 0
\(86\) 14.4886 1.56235
\(87\) −1.81214 −0.194282
\(88\) −6.20730 −0.661700
\(89\) −2.86645 −0.303844 −0.151922 0.988393i \(-0.548546\pi\)
−0.151922 + 0.988393i \(0.548546\pi\)
\(90\) 0 0
\(91\) −11.2900 −1.18351
\(92\) −5.44542 −0.567724
\(93\) −3.24850 −0.336854
\(94\) 1.67335 0.172593
\(95\) 0 0
\(96\) −4.28418 −0.437252
\(97\) −6.01711 −0.610945 −0.305473 0.952201i \(-0.598814\pi\)
−0.305473 + 0.952201i \(0.598814\pi\)
\(98\) −0.957836 −0.0967561
\(99\) −3.09151 −0.310709
\(100\) 0 0
\(101\) 9.07572 0.903068 0.451534 0.892254i \(-0.350877\pi\)
0.451534 + 0.892254i \(0.350877\pi\)
\(102\) −6.81170 −0.674459
\(103\) 8.36703 0.824428 0.412214 0.911087i \(-0.364756\pi\)
0.412214 + 0.911087i \(0.364756\pi\)
\(104\) −8.23775 −0.807778
\(105\) 0 0
\(106\) −9.34151 −0.907328
\(107\) −9.99601 −0.966350 −0.483175 0.875524i \(-0.660517\pi\)
−0.483175 + 0.875524i \(0.660517\pi\)
\(108\) −0.800100 −0.0769896
\(109\) 8.75321 0.838406 0.419203 0.907893i \(-0.362310\pi\)
0.419203 + 0.907893i \(0.362310\pi\)
\(110\) 0 0
\(111\) −5.48507 −0.520620
\(112\) −13.6490 −1.28971
\(113\) −14.6778 −1.38078 −0.690388 0.723439i \(-0.742560\pi\)
−0.690388 + 0.723439i \(0.742560\pi\)
\(114\) 9.63109 0.902034
\(115\) 0 0
\(116\) 1.44989 0.134619
\(117\) −4.10277 −0.379301
\(118\) −1.04413 −0.0961202
\(119\) −11.2018 −1.02686
\(120\) 0 0
\(121\) −1.44256 −0.131142
\(122\) −10.1084 −0.915176
\(123\) −1.31661 −0.118715
\(124\) 2.59912 0.233408
\(125\) 0 0
\(126\) −4.60473 −0.410222
\(127\) 20.1493 1.78796 0.893979 0.448109i \(-0.147902\pi\)
0.893979 + 0.448109i \(0.147902\pi\)
\(128\) −13.1720 −1.16425
\(129\) 8.65847 0.762336
\(130\) 0 0
\(131\) −18.7317 −1.63660 −0.818299 0.574793i \(-0.805083\pi\)
−0.818299 + 0.574793i \(0.805083\pi\)
\(132\) 2.47352 0.215292
\(133\) 15.8382 1.37335
\(134\) −6.78742 −0.586344
\(135\) 0 0
\(136\) −8.17337 −0.700860
\(137\) −13.3070 −1.13689 −0.568447 0.822720i \(-0.692455\pi\)
−0.568447 + 0.822720i \(0.692455\pi\)
\(138\) −11.3887 −0.969470
\(139\) −2.40184 −0.203721 −0.101861 0.994799i \(-0.532480\pi\)
−0.101861 + 0.994799i \(0.532480\pi\)
\(140\) 0 0
\(141\) 1.00000 0.0842152
\(142\) −25.2985 −2.12300
\(143\) 12.6837 1.06067
\(144\) −4.96004 −0.413337
\(145\) 0 0
\(146\) 6.37746 0.527803
\(147\) −0.572406 −0.0472113
\(148\) 4.38861 0.360741
\(149\) −2.94723 −0.241447 −0.120723 0.992686i \(-0.538521\pi\)
−0.120723 + 0.992686i \(0.538521\pi\)
\(150\) 0 0
\(151\) 20.3477 1.65587 0.827935 0.560824i \(-0.189516\pi\)
0.827935 + 0.560824i \(0.189516\pi\)
\(152\) 11.5563 0.937343
\(153\) −4.07070 −0.329097
\(154\) 14.2356 1.14713
\(155\) 0 0
\(156\) 3.28262 0.262820
\(157\) 16.7571 1.33736 0.668681 0.743549i \(-0.266859\pi\)
0.668681 + 0.743549i \(0.266859\pi\)
\(158\) 9.38560 0.746678
\(159\) −5.58252 −0.442723
\(160\) 0 0
\(161\) −18.7285 −1.47602
\(162\) −1.67335 −0.131471
\(163\) −14.5503 −1.13967 −0.569835 0.821759i \(-0.692993\pi\)
−0.569835 + 0.821759i \(0.692993\pi\)
\(164\) 1.05342 0.0822583
\(165\) 0 0
\(166\) 7.45690 0.578768
\(167\) 7.15918 0.553994 0.276997 0.960871i \(-0.410661\pi\)
0.276997 + 0.960871i \(0.410661\pi\)
\(168\) −5.52521 −0.426279
\(169\) 3.83269 0.294822
\(170\) 0 0
\(171\) 5.75557 0.440140
\(172\) −6.92764 −0.528227
\(173\) 10.8401 0.824161 0.412081 0.911147i \(-0.364802\pi\)
0.412081 + 0.911147i \(0.364802\pi\)
\(174\) 3.03234 0.229881
\(175\) 0 0
\(176\) 15.3340 1.15584
\(177\) −0.623977 −0.0469010
\(178\) 4.79658 0.359519
\(179\) 10.0976 0.754731 0.377366 0.926064i \(-0.376830\pi\)
0.377366 + 0.926064i \(0.376830\pi\)
\(180\) 0 0
\(181\) −4.18508 −0.311075 −0.155537 0.987830i \(-0.549711\pi\)
−0.155537 + 0.987830i \(0.549711\pi\)
\(182\) 18.8921 1.40038
\(183\) −6.04084 −0.446552
\(184\) −13.6653 −1.00742
\(185\) 0 0
\(186\) 5.43588 0.398578
\(187\) 12.5846 0.920278
\(188\) −0.800100 −0.0583533
\(189\) −2.75180 −0.200164
\(190\) 0 0
\(191\) −19.2288 −1.39135 −0.695673 0.718358i \(-0.744894\pi\)
−0.695673 + 0.718358i \(0.744894\pi\)
\(192\) −2.75115 −0.198548
\(193\) 25.7747 1.85530 0.927652 0.373445i \(-0.121823\pi\)
0.927652 + 0.373445i \(0.121823\pi\)
\(194\) 10.0687 0.722893
\(195\) 0 0
\(196\) 0.457982 0.0327130
\(197\) 21.7824 1.55193 0.775966 0.630775i \(-0.217263\pi\)
0.775966 + 0.630775i \(0.217263\pi\)
\(198\) 5.17318 0.367642
\(199\) 17.3880 1.23260 0.616301 0.787511i \(-0.288630\pi\)
0.616301 + 0.787511i \(0.288630\pi\)
\(200\) 0 0
\(201\) −4.05619 −0.286101
\(202\) −15.1869 −1.06854
\(203\) 4.98665 0.349994
\(204\) 3.25696 0.228033
\(205\) 0 0
\(206\) −14.0010 −0.975494
\(207\) −6.80592 −0.473044
\(208\) 20.3499 1.41101
\(209\) −17.7934 −1.23080
\(210\) 0 0
\(211\) 17.2661 1.18864 0.594322 0.804227i \(-0.297420\pi\)
0.594322 + 0.804227i \(0.297420\pi\)
\(212\) 4.46657 0.306766
\(213\) −15.1185 −1.03590
\(214\) 16.7268 1.14342
\(215\) 0 0
\(216\) −2.00785 −0.136617
\(217\) 8.93923 0.606834
\(218\) −14.6472 −0.992033
\(219\) 3.81119 0.257537
\(220\) 0 0
\(221\) 16.7011 1.12344
\(222\) 9.17845 0.616017
\(223\) 7.59823 0.508815 0.254407 0.967097i \(-0.418120\pi\)
0.254407 + 0.967097i \(0.418120\pi\)
\(224\) 11.7892 0.787699
\(225\) 0 0
\(226\) 24.5612 1.63379
\(227\) −13.0082 −0.863387 −0.431694 0.902020i \(-0.642084\pi\)
−0.431694 + 0.902020i \(0.642084\pi\)
\(228\) −4.60503 −0.304976
\(229\) −4.17490 −0.275885 −0.137942 0.990440i \(-0.544049\pi\)
−0.137942 + 0.990440i \(0.544049\pi\)
\(230\) 0 0
\(231\) 8.50722 0.559734
\(232\) 3.63851 0.238880
\(233\) 26.2804 1.72169 0.860844 0.508870i \(-0.169936\pi\)
0.860844 + 0.508870i \(0.169936\pi\)
\(234\) 6.86536 0.448803
\(235\) 0 0
\(236\) 0.499244 0.0324980
\(237\) 5.60887 0.364335
\(238\) 18.7444 1.21502
\(239\) −1.61063 −0.104183 −0.0520915 0.998642i \(-0.516589\pi\)
−0.0520915 + 0.998642i \(0.516589\pi\)
\(240\) 0 0
\(241\) −4.95494 −0.319176 −0.159588 0.987184i \(-0.551017\pi\)
−0.159588 + 0.987184i \(0.551017\pi\)
\(242\) 2.41391 0.155172
\(243\) −1.00000 −0.0641500
\(244\) 4.83328 0.309419
\(245\) 0 0
\(246\) 2.20315 0.140468
\(247\) −23.6138 −1.50251
\(248\) 6.52251 0.414180
\(249\) 4.45627 0.282405
\(250\) 0 0
\(251\) −10.3337 −0.652260 −0.326130 0.945325i \(-0.605745\pi\)
−0.326130 + 0.945325i \(0.605745\pi\)
\(252\) 2.20171 0.138695
\(253\) 21.0406 1.32281
\(254\) −33.7168 −2.11558
\(255\) 0 0
\(256\) 16.5390 1.03369
\(257\) 17.4871 1.09082 0.545408 0.838171i \(-0.316375\pi\)
0.545408 + 0.838171i \(0.316375\pi\)
\(258\) −14.4886 −0.902024
\(259\) 15.0938 0.937885
\(260\) 0 0
\(261\) 1.81214 0.112169
\(262\) 31.3447 1.93648
\(263\) −12.2487 −0.755290 −0.377645 0.925951i \(-0.623266\pi\)
−0.377645 + 0.925951i \(0.623266\pi\)
\(264\) 6.20730 0.382033
\(265\) 0 0
\(266\) −26.5028 −1.62499
\(267\) 2.86645 0.175424
\(268\) 3.24535 0.198242
\(269\) −4.24499 −0.258822 −0.129411 0.991591i \(-0.541309\pi\)
−0.129411 + 0.991591i \(0.541309\pi\)
\(270\) 0 0
\(271\) 14.5778 0.885541 0.442770 0.896635i \(-0.353996\pi\)
0.442770 + 0.896635i \(0.353996\pi\)
\(272\) 20.1908 1.22425
\(273\) 11.2900 0.683301
\(274\) 22.2673 1.34521
\(275\) 0 0
\(276\) 5.44542 0.327776
\(277\) −27.7778 −1.66900 −0.834502 0.551005i \(-0.814244\pi\)
−0.834502 + 0.551005i \(0.814244\pi\)
\(278\) 4.01912 0.241051
\(279\) 3.24850 0.194483
\(280\) 0 0
\(281\) 13.0720 0.779807 0.389904 0.920856i \(-0.372508\pi\)
0.389904 + 0.920856i \(0.372508\pi\)
\(282\) −1.67335 −0.0996465
\(283\) 15.1027 0.897763 0.448881 0.893591i \(-0.351823\pi\)
0.448881 + 0.893591i \(0.351823\pi\)
\(284\) 12.0963 0.717783
\(285\) 0 0
\(286\) −21.2243 −1.25502
\(287\) 3.62305 0.213862
\(288\) 4.28418 0.252447
\(289\) −0.429409 −0.0252593
\(290\) 0 0
\(291\) 6.01711 0.352729
\(292\) −3.04934 −0.178449
\(293\) 11.9208 0.696423 0.348212 0.937416i \(-0.386789\pi\)
0.348212 + 0.937416i \(0.386789\pi\)
\(294\) 0.957836 0.0558621
\(295\) 0 0
\(296\) 11.0132 0.640131
\(297\) 3.09151 0.179388
\(298\) 4.93175 0.285688
\(299\) 27.9231 1.61484
\(300\) 0 0
\(301\) −23.8264 −1.37333
\(302\) −34.0488 −1.95929
\(303\) −9.07572 −0.521386
\(304\) −28.5479 −1.63733
\(305\) 0 0
\(306\) 6.81170 0.389399
\(307\) 25.3094 1.44448 0.722242 0.691641i \(-0.243112\pi\)
0.722242 + 0.691641i \(0.243112\pi\)
\(308\) −6.80662 −0.387843
\(309\) −8.36703 −0.475984
\(310\) 0 0
\(311\) 22.2759 1.26315 0.631575 0.775315i \(-0.282409\pi\)
0.631575 + 0.775315i \(0.282409\pi\)
\(312\) 8.23775 0.466371
\(313\) 8.85418 0.500468 0.250234 0.968185i \(-0.419492\pi\)
0.250234 + 0.968185i \(0.419492\pi\)
\(314\) −28.0405 −1.58242
\(315\) 0 0
\(316\) −4.48765 −0.252450
\(317\) 25.6447 1.44035 0.720174 0.693793i \(-0.244062\pi\)
0.720174 + 0.693793i \(0.244062\pi\)
\(318\) 9.34151 0.523846
\(319\) −5.60225 −0.313666
\(320\) 0 0
\(321\) 9.99601 0.557923
\(322\) 31.3394 1.74648
\(323\) −23.4292 −1.30364
\(324\) 0.800100 0.0444500
\(325\) 0 0
\(326\) 24.3478 1.34850
\(327\) −8.75321 −0.484054
\(328\) 2.64356 0.145966
\(329\) −2.75180 −0.151712
\(330\) 0 0
\(331\) 29.7383 1.63456 0.817282 0.576237i \(-0.195480\pi\)
0.817282 + 0.576237i \(0.195480\pi\)
\(332\) −3.56546 −0.195680
\(333\) 5.48507 0.300580
\(334\) −11.9798 −0.655506
\(335\) 0 0
\(336\) 13.6490 0.744616
\(337\) 16.4731 0.897344 0.448672 0.893696i \(-0.351897\pi\)
0.448672 + 0.893696i \(0.351897\pi\)
\(338\) −6.41343 −0.348844
\(339\) 14.6778 0.797191
\(340\) 0 0
\(341\) −10.0428 −0.543847
\(342\) −9.63109 −0.520790
\(343\) −17.6875 −0.955033
\(344\) −17.3849 −0.937333
\(345\) 0 0
\(346\) −18.1394 −0.975178
\(347\) 10.8365 0.581734 0.290867 0.956763i \(-0.406056\pi\)
0.290867 + 0.956763i \(0.406056\pi\)
\(348\) −1.44989 −0.0777224
\(349\) 5.80101 0.310521 0.155260 0.987874i \(-0.450378\pi\)
0.155260 + 0.987874i \(0.450378\pi\)
\(350\) 0 0
\(351\) 4.10277 0.218989
\(352\) −13.2446 −0.705938
\(353\) −14.9999 −0.798364 −0.399182 0.916872i \(-0.630706\pi\)
−0.399182 + 0.916872i \(0.630706\pi\)
\(354\) 1.04413 0.0554950
\(355\) 0 0
\(356\) −2.29345 −0.121553
\(357\) 11.2018 0.592860
\(358\) −16.8968 −0.893026
\(359\) −10.7284 −0.566223 −0.283112 0.959087i \(-0.591367\pi\)
−0.283112 + 0.959087i \(0.591367\pi\)
\(360\) 0 0
\(361\) 14.1266 0.743506
\(362\) 7.00311 0.368075
\(363\) 1.44256 0.0757148
\(364\) −9.03312 −0.473464
\(365\) 0 0
\(366\) 10.1084 0.528377
\(367\) 28.5989 1.49285 0.746425 0.665470i \(-0.231769\pi\)
0.746425 + 0.665470i \(0.231769\pi\)
\(368\) 33.7577 1.75974
\(369\) 1.31661 0.0685400
\(370\) 0 0
\(371\) 15.3620 0.797555
\(372\) −2.59912 −0.134758
\(373\) 6.36548 0.329592 0.164796 0.986328i \(-0.447303\pi\)
0.164796 + 0.986328i \(0.447303\pi\)
\(374\) −21.0585 −1.08891
\(375\) 0 0
\(376\) −2.00785 −0.103547
\(377\) −7.43478 −0.382911
\(378\) 4.60473 0.236841
\(379\) −30.3510 −1.55903 −0.779513 0.626386i \(-0.784534\pi\)
−0.779513 + 0.626386i \(0.784534\pi\)
\(380\) 0 0
\(381\) −20.1493 −1.03228
\(382\) 32.1765 1.64629
\(383\) −30.9748 −1.58274 −0.791370 0.611338i \(-0.790632\pi\)
−0.791370 + 0.611338i \(0.790632\pi\)
\(384\) 13.1720 0.672181
\(385\) 0 0
\(386\) −43.1301 −2.19527
\(387\) −8.65847 −0.440135
\(388\) −4.81429 −0.244409
\(389\) 26.6200 1.34969 0.674843 0.737962i \(-0.264211\pi\)
0.674843 + 0.737962i \(0.264211\pi\)
\(390\) 0 0
\(391\) 27.7049 1.40110
\(392\) 1.14931 0.0580488
\(393\) 18.7317 0.944890
\(394\) −36.4496 −1.83630
\(395\) 0 0
\(396\) −2.47352 −0.124299
\(397\) −31.2708 −1.56944 −0.784719 0.619851i \(-0.787193\pi\)
−0.784719 + 0.619851i \(0.787193\pi\)
\(398\) −29.0962 −1.45846
\(399\) −15.8382 −0.792901
\(400\) 0 0
\(401\) 11.1993 0.559266 0.279633 0.960107i \(-0.409787\pi\)
0.279633 + 0.960107i \(0.409787\pi\)
\(402\) 6.78742 0.338526
\(403\) −13.3278 −0.663907
\(404\) 7.26148 0.361272
\(405\) 0 0
\(406\) −8.34440 −0.414126
\(407\) −16.9572 −0.840536
\(408\) 8.17337 0.404642
\(409\) −25.7028 −1.27092 −0.635462 0.772132i \(-0.719190\pi\)
−0.635462 + 0.772132i \(0.719190\pi\)
\(410\) 0 0
\(411\) 13.3070 0.656386
\(412\) 6.69446 0.329812
\(413\) 1.71706 0.0844911
\(414\) 11.3887 0.559724
\(415\) 0 0
\(416\) −17.5770 −0.861782
\(417\) 2.40184 0.117619
\(418\) 29.7746 1.45632
\(419\) 26.7057 1.30466 0.652329 0.757936i \(-0.273792\pi\)
0.652329 + 0.757936i \(0.273792\pi\)
\(420\) 0 0
\(421\) 15.7159 0.765947 0.382973 0.923759i \(-0.374900\pi\)
0.382973 + 0.923759i \(0.374900\pi\)
\(422\) −28.8921 −1.40645
\(423\) −1.00000 −0.0486217
\(424\) 11.2089 0.544352
\(425\) 0 0
\(426\) 25.2985 1.22572
\(427\) 16.6232 0.804453
\(428\) −7.99780 −0.386588
\(429\) −12.6837 −0.612377
\(430\) 0 0
\(431\) −29.9696 −1.44358 −0.721792 0.692110i \(-0.756681\pi\)
−0.721792 + 0.692110i \(0.756681\pi\)
\(432\) 4.96004 0.238640
\(433\) 16.0442 0.771033 0.385517 0.922701i \(-0.374023\pi\)
0.385517 + 0.922701i \(0.374023\pi\)
\(434\) −14.9585 −0.718029
\(435\) 0 0
\(436\) 7.00344 0.335404
\(437\) −39.1720 −1.87385
\(438\) −6.37746 −0.304727
\(439\) −5.53502 −0.264172 −0.132086 0.991238i \(-0.542168\pi\)
−0.132086 + 0.991238i \(0.542168\pi\)
\(440\) 0 0
\(441\) 0.572406 0.0272574
\(442\) −27.9468 −1.32929
\(443\) −8.49669 −0.403690 −0.201845 0.979417i \(-0.564694\pi\)
−0.201845 + 0.979417i \(0.564694\pi\)
\(444\) −4.38861 −0.208274
\(445\) 0 0
\(446\) −12.7145 −0.602049
\(447\) 2.94723 0.139399
\(448\) 7.57063 0.357679
\(449\) 6.82306 0.322000 0.161000 0.986954i \(-0.448528\pi\)
0.161000 + 0.986954i \(0.448528\pi\)
\(450\) 0 0
\(451\) −4.07032 −0.191664
\(452\) −11.7437 −0.552379
\(453\) −20.3477 −0.956017
\(454\) 21.7673 1.02159
\(455\) 0 0
\(456\) −11.5563 −0.541175
\(457\) −40.7763 −1.90743 −0.953717 0.300706i \(-0.902778\pi\)
−0.953717 + 0.300706i \(0.902778\pi\)
\(458\) 6.98606 0.326437
\(459\) 4.07070 0.190004
\(460\) 0 0
\(461\) −22.8707 −1.06519 −0.532597 0.846369i \(-0.678784\pi\)
−0.532597 + 0.846369i \(0.678784\pi\)
\(462\) −14.2356 −0.662298
\(463\) −25.9393 −1.20550 −0.602752 0.797929i \(-0.705929\pi\)
−0.602752 + 0.797929i \(0.705929\pi\)
\(464\) −8.98828 −0.417271
\(465\) 0 0
\(466\) −43.9763 −2.03716
\(467\) −20.3302 −0.940768 −0.470384 0.882462i \(-0.655885\pi\)
−0.470384 + 0.882462i \(0.655885\pi\)
\(468\) −3.28262 −0.151739
\(469\) 11.1618 0.515405
\(470\) 0 0
\(471\) −16.7571 −0.772127
\(472\) 1.25286 0.0576673
\(473\) 26.7677 1.23078
\(474\) −9.38560 −0.431095
\(475\) 0 0
\(476\) −8.96252 −0.410796
\(477\) 5.58252 0.255606
\(478\) 2.69515 0.123273
\(479\) 15.5445 0.710247 0.355123 0.934819i \(-0.384439\pi\)
0.355123 + 0.934819i \(0.384439\pi\)
\(480\) 0 0
\(481\) −22.5040 −1.02609
\(482\) 8.29135 0.377661
\(483\) 18.7285 0.852178
\(484\) −1.15419 −0.0524633
\(485\) 0 0
\(486\) 1.67335 0.0759047
\(487\) 42.3974 1.92121 0.960605 0.277919i \(-0.0896446\pi\)
0.960605 + 0.277919i \(0.0896446\pi\)
\(488\) 12.1291 0.549060
\(489\) 14.5503 0.657988
\(490\) 0 0
\(491\) 27.8996 1.25909 0.629546 0.776963i \(-0.283241\pi\)
0.629546 + 0.776963i \(0.283241\pi\)
\(492\) −1.05342 −0.0474918
\(493\) −7.37667 −0.332229
\(494\) 39.5141 1.77782
\(495\) 0 0
\(496\) −16.1127 −0.723481
\(497\) 41.6030 1.86615
\(498\) −7.45690 −0.334152
\(499\) 4.67712 0.209377 0.104688 0.994505i \(-0.466616\pi\)
0.104688 + 0.994505i \(0.466616\pi\)
\(500\) 0 0
\(501\) −7.15918 −0.319849
\(502\) 17.2920 0.771778
\(503\) 34.3219 1.53034 0.765168 0.643830i \(-0.222656\pi\)
0.765168 + 0.643830i \(0.222656\pi\)
\(504\) 5.52521 0.246112
\(505\) 0 0
\(506\) −35.2083 −1.56520
\(507\) −3.83269 −0.170216
\(508\) 16.1214 0.715272
\(509\) 31.2751 1.38625 0.693123 0.720819i \(-0.256234\pi\)
0.693123 + 0.720819i \(0.256234\pi\)
\(510\) 0 0
\(511\) −10.4876 −0.463946
\(512\) −1.33162 −0.0588499
\(513\) −5.75557 −0.254115
\(514\) −29.2620 −1.29069
\(515\) 0 0
\(516\) 6.92764 0.304972
\(517\) 3.09151 0.135964
\(518\) −25.2573 −1.10974
\(519\) −10.8401 −0.475830
\(520\) 0 0
\(521\) 25.4663 1.11570 0.557849 0.829942i \(-0.311627\pi\)
0.557849 + 0.829942i \(0.311627\pi\)
\(522\) −3.03234 −0.132722
\(523\) 20.9218 0.914848 0.457424 0.889249i \(-0.348772\pi\)
0.457424 + 0.889249i \(0.348772\pi\)
\(524\) −14.9872 −0.654721
\(525\) 0 0
\(526\) 20.4964 0.893687
\(527\) −13.2237 −0.576032
\(528\) −15.3340 −0.667327
\(529\) 23.3206 1.01394
\(530\) 0 0
\(531\) 0.623977 0.0270783
\(532\) 12.6721 0.549406
\(533\) −5.40175 −0.233976
\(534\) −4.79658 −0.207568
\(535\) 0 0
\(536\) 8.14423 0.351777
\(537\) −10.0976 −0.435744
\(538\) 7.10335 0.306247
\(539\) −1.76960 −0.0762221
\(540\) 0 0
\(541\) −0.461908 −0.0198590 −0.00992948 0.999951i \(-0.503161\pi\)
−0.00992948 + 0.999951i \(0.503161\pi\)
\(542\) −24.3938 −1.04780
\(543\) 4.18508 0.179599
\(544\) −17.4396 −0.747716
\(545\) 0 0
\(546\) −18.8921 −0.808508
\(547\) 23.3606 0.998827 0.499413 0.866364i \(-0.333549\pi\)
0.499413 + 0.866364i \(0.333549\pi\)
\(548\) −10.6469 −0.454814
\(549\) 6.04084 0.257817
\(550\) 0 0
\(551\) 10.4299 0.444329
\(552\) 13.6653 0.581634
\(553\) −15.4345 −0.656341
\(554\) 46.4819 1.97483
\(555\) 0 0
\(556\) −1.92171 −0.0814987
\(557\) 22.3707 0.947877 0.473939 0.880558i \(-0.342832\pi\)
0.473939 + 0.880558i \(0.342832\pi\)
\(558\) −5.43588 −0.230119
\(559\) 35.5237 1.50249
\(560\) 0 0
\(561\) −12.5846 −0.531323
\(562\) −21.8740 −0.922697
\(563\) −47.1758 −1.98822 −0.994112 0.108362i \(-0.965439\pi\)
−0.994112 + 0.108362i \(0.965439\pi\)
\(564\) 0.800100 0.0336903
\(565\) 0 0
\(566\) −25.2721 −1.06227
\(567\) 2.75180 0.115565
\(568\) 30.3557 1.27370
\(569\) 14.1917 0.594945 0.297473 0.954730i \(-0.403856\pi\)
0.297473 + 0.954730i \(0.403856\pi\)
\(570\) 0 0
\(571\) −10.4724 −0.438256 −0.219128 0.975696i \(-0.570321\pi\)
−0.219128 + 0.975696i \(0.570321\pi\)
\(572\) 10.1483 0.424320
\(573\) 19.2288 0.803294
\(574\) −6.06263 −0.253049
\(575\) 0 0
\(576\) 2.75115 0.114631
\(577\) 15.7927 0.657458 0.328729 0.944424i \(-0.393380\pi\)
0.328729 + 0.944424i \(0.393380\pi\)
\(578\) 0.718551 0.0298878
\(579\) −25.7747 −1.07116
\(580\) 0 0
\(581\) −12.2628 −0.508746
\(582\) −10.0687 −0.417363
\(583\) −17.2584 −0.714771
\(584\) −7.65232 −0.316655
\(585\) 0 0
\(586\) −19.9477 −0.824034
\(587\) 43.0436 1.77660 0.888300 0.459264i \(-0.151887\pi\)
0.888300 + 0.459264i \(0.151887\pi\)
\(588\) −0.457982 −0.0188869
\(589\) 18.6970 0.770396
\(590\) 0 0
\(591\) −21.7824 −0.896008
\(592\) −27.2062 −1.11817
\(593\) 15.8784 0.652049 0.326025 0.945361i \(-0.394291\pi\)
0.326025 + 0.945361i \(0.394291\pi\)
\(594\) −5.17318 −0.212258
\(595\) 0 0
\(596\) −2.35808 −0.0965907
\(597\) −17.3880 −0.711643
\(598\) −46.7251 −1.91073
\(599\) 42.2747 1.72730 0.863649 0.504094i \(-0.168173\pi\)
0.863649 + 0.504094i \(0.168173\pi\)
\(600\) 0 0
\(601\) −46.9712 −1.91600 −0.957998 0.286776i \(-0.907416\pi\)
−0.957998 + 0.286776i \(0.907416\pi\)
\(602\) 39.8699 1.62497
\(603\) 4.05619 0.165181
\(604\) 16.2802 0.662431
\(605\) 0 0
\(606\) 15.1869 0.616924
\(607\) −37.6395 −1.52774 −0.763870 0.645371i \(-0.776703\pi\)
−0.763870 + 0.645371i \(0.776703\pi\)
\(608\) 24.6579 1.00001
\(609\) −4.98665 −0.202069
\(610\) 0 0
\(611\) 4.10277 0.165980
\(612\) −3.25696 −0.131655
\(613\) 30.7507 1.24201 0.621005 0.783807i \(-0.286725\pi\)
0.621005 + 0.783807i \(0.286725\pi\)
\(614\) −42.3515 −1.70917
\(615\) 0 0
\(616\) −17.0812 −0.688223
\(617\) −17.0417 −0.686073 −0.343037 0.939322i \(-0.611455\pi\)
−0.343037 + 0.939322i \(0.611455\pi\)
\(618\) 14.0010 0.563202
\(619\) 42.9648 1.72690 0.863450 0.504435i \(-0.168299\pi\)
0.863450 + 0.504435i \(0.168299\pi\)
\(620\) 0 0
\(621\) 6.80592 0.273112
\(622\) −37.2753 −1.49461
\(623\) −7.88791 −0.316022
\(624\) −20.3499 −0.814647
\(625\) 0 0
\(626\) −14.8161 −0.592172
\(627\) 17.7934 0.710601
\(628\) 13.4074 0.535012
\(629\) −22.3281 −0.890279
\(630\) 0 0
\(631\) 14.7446 0.586972 0.293486 0.955963i \(-0.405185\pi\)
0.293486 + 0.955963i \(0.405185\pi\)
\(632\) −11.2618 −0.447970
\(633\) −17.2661 −0.686264
\(634\) −42.9125 −1.70427
\(635\) 0 0
\(636\) −4.46657 −0.177111
\(637\) −2.34845 −0.0930490
\(638\) 9.37452 0.371141
\(639\) 15.1185 0.598078
\(640\) 0 0
\(641\) 0.488794 0.0193062 0.00965311 0.999953i \(-0.496927\pi\)
0.00965311 + 0.999953i \(0.496927\pi\)
\(642\) −16.7268 −0.660155
\(643\) 37.6682 1.48549 0.742744 0.669576i \(-0.233524\pi\)
0.742744 + 0.669576i \(0.233524\pi\)
\(644\) −14.9847 −0.590480
\(645\) 0 0
\(646\) 39.2053 1.54251
\(647\) 15.9964 0.628884 0.314442 0.949277i \(-0.398183\pi\)
0.314442 + 0.949277i \(0.398183\pi\)
\(648\) 2.00785 0.0788759
\(649\) −1.92903 −0.0757212
\(650\) 0 0
\(651\) −8.93923 −0.350356
\(652\) −11.6417 −0.455924
\(653\) −1.45400 −0.0568993 −0.0284496 0.999595i \(-0.509057\pi\)
−0.0284496 + 0.999595i \(0.509057\pi\)
\(654\) 14.6472 0.572750
\(655\) 0 0
\(656\) −6.53044 −0.254971
\(657\) −3.81119 −0.148689
\(658\) 4.60473 0.179511
\(659\) 44.3803 1.72881 0.864406 0.502795i \(-0.167695\pi\)
0.864406 + 0.502795i \(0.167695\pi\)
\(660\) 0 0
\(661\) −22.2944 −0.867152 −0.433576 0.901117i \(-0.642748\pi\)
−0.433576 + 0.901117i \(0.642748\pi\)
\(662\) −49.7626 −1.93408
\(663\) −16.7011 −0.648618
\(664\) −8.94754 −0.347232
\(665\) 0 0
\(666\) −9.17845 −0.355658
\(667\) −12.3333 −0.477547
\(668\) 5.72806 0.221625
\(669\) −7.59823 −0.293764
\(670\) 0 0
\(671\) −18.6753 −0.720953
\(672\) −11.7892 −0.454778
\(673\) −32.3309 −1.24626 −0.623132 0.782117i \(-0.714140\pi\)
−0.623132 + 0.782117i \(0.714140\pi\)
\(674\) −27.5652 −1.06177
\(675\) 0 0
\(676\) 3.06653 0.117944
\(677\) −18.7864 −0.722021 −0.361011 0.932562i \(-0.617568\pi\)
−0.361011 + 0.932562i \(0.617568\pi\)
\(678\) −24.5612 −0.943266
\(679\) −16.5579 −0.635434
\(680\) 0 0
\(681\) 13.0082 0.498477
\(682\) 16.8051 0.643500
\(683\) −29.3802 −1.12420 −0.562102 0.827068i \(-0.690007\pi\)
−0.562102 + 0.827068i \(0.690007\pi\)
\(684\) 4.60503 0.176078
\(685\) 0 0
\(686\) 29.5973 1.13003
\(687\) 4.17490 0.159282
\(688\) 42.9463 1.63731
\(689\) −22.9038 −0.872565
\(690\) 0 0
\(691\) −11.2695 −0.428710 −0.214355 0.976756i \(-0.568765\pi\)
−0.214355 + 0.976756i \(0.568765\pi\)
\(692\) 8.67320 0.329705
\(693\) −8.50722 −0.323163
\(694\) −18.1333 −0.688330
\(695\) 0 0
\(696\) −3.63851 −0.137917
\(697\) −5.35953 −0.203007
\(698\) −9.70711 −0.367420
\(699\) −26.2804 −0.994017
\(700\) 0 0
\(701\) −21.0991 −0.796901 −0.398451 0.917190i \(-0.630452\pi\)
−0.398451 + 0.917190i \(0.630452\pi\)
\(702\) −6.86536 −0.259116
\(703\) 31.5697 1.19068
\(704\) −8.50523 −0.320553
\(705\) 0 0
\(706\) 25.1001 0.944653
\(707\) 24.9746 0.939265
\(708\) −0.499244 −0.0187627
\(709\) −24.0964 −0.904961 −0.452481 0.891774i \(-0.649461\pi\)
−0.452481 + 0.891774i \(0.649461\pi\)
\(710\) 0 0
\(711\) −5.60887 −0.210349
\(712\) −5.75542 −0.215693
\(713\) −22.1090 −0.827990
\(714\) −18.7444 −0.701493
\(715\) 0 0
\(716\) 8.07910 0.301930
\(717\) 1.61063 0.0601501
\(718\) 17.9524 0.669976
\(719\) −17.5539 −0.654649 −0.327325 0.944912i \(-0.606147\pi\)
−0.327325 + 0.944912i \(0.606147\pi\)
\(720\) 0 0
\(721\) 23.0244 0.857474
\(722\) −23.6388 −0.879744
\(723\) 4.95494 0.184276
\(724\) −3.34848 −0.124445
\(725\) 0 0
\(726\) −2.41391 −0.0895886
\(727\) 39.1878 1.45340 0.726698 0.686958i \(-0.241054\pi\)
0.726698 + 0.686958i \(0.241054\pi\)
\(728\) −22.6686 −0.840156
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 35.2460 1.30362
\(732\) −4.83328 −0.178643
\(733\) 5.50231 0.203232 0.101616 0.994824i \(-0.467599\pi\)
0.101616 + 0.994824i \(0.467599\pi\)
\(734\) −47.8559 −1.76639
\(735\) 0 0
\(736\) −29.1578 −1.07477
\(737\) −12.5397 −0.461907
\(738\) −2.20315 −0.0810991
\(739\) 2.23210 0.0821090 0.0410545 0.999157i \(-0.486928\pi\)
0.0410545 + 0.999157i \(0.486928\pi\)
\(740\) 0 0
\(741\) 23.6138 0.867473
\(742\) −25.7060 −0.943696
\(743\) 48.9867 1.79715 0.898573 0.438823i \(-0.144605\pi\)
0.898573 + 0.438823i \(0.144605\pi\)
\(744\) −6.52251 −0.239127
\(745\) 0 0
\(746\) −10.6517 −0.389985
\(747\) −4.45627 −0.163046
\(748\) 10.0689 0.368157
\(749\) −27.5070 −1.00508
\(750\) 0 0
\(751\) 39.2338 1.43166 0.715831 0.698274i \(-0.246048\pi\)
0.715831 + 0.698274i \(0.246048\pi\)
\(752\) 4.96004 0.180874
\(753\) 10.3337 0.376582
\(754\) 12.4410 0.453074
\(755\) 0 0
\(756\) −2.20171 −0.0800756
\(757\) 31.3025 1.13771 0.568854 0.822439i \(-0.307387\pi\)
0.568854 + 0.822439i \(0.307387\pi\)
\(758\) 50.7879 1.84470
\(759\) −21.0406 −0.763725
\(760\) 0 0
\(761\) −11.6565 −0.422548 −0.211274 0.977427i \(-0.567761\pi\)
−0.211274 + 0.977427i \(0.567761\pi\)
\(762\) 33.7168 1.22143
\(763\) 24.0871 0.872012
\(764\) −15.3849 −0.556608
\(765\) 0 0
\(766\) 51.8317 1.87276
\(767\) −2.56003 −0.0924375
\(768\) −16.5390 −0.596801
\(769\) −40.4684 −1.45933 −0.729664 0.683806i \(-0.760324\pi\)
−0.729664 + 0.683806i \(0.760324\pi\)
\(770\) 0 0
\(771\) −17.4871 −0.629782
\(772\) 20.6223 0.742214
\(773\) −28.4120 −1.02191 −0.510955 0.859608i \(-0.670708\pi\)
−0.510955 + 0.859608i \(0.670708\pi\)
\(774\) 14.4886 0.520784
\(775\) 0 0
\(776\) −12.0815 −0.433700
\(777\) −15.0938 −0.541488
\(778\) −44.5445 −1.59700
\(779\) 7.57785 0.271505
\(780\) 0 0
\(781\) −46.7389 −1.67245
\(782\) −46.3599 −1.65783
\(783\) −1.81214 −0.0647606
\(784\) −2.83916 −0.101399
\(785\) 0 0
\(786\) −31.3447 −1.11803
\(787\) −37.2934 −1.32937 −0.664683 0.747126i \(-0.731433\pi\)
−0.664683 + 0.747126i \(0.731433\pi\)
\(788\) 17.4281 0.620850
\(789\) 12.2487 0.436067
\(790\) 0 0
\(791\) −40.3905 −1.43612
\(792\) −6.20730 −0.220567
\(793\) −24.7842 −0.880112
\(794\) 52.3271 1.85702
\(795\) 0 0
\(796\) 13.9121 0.493102
\(797\) 36.9191 1.30774 0.653870 0.756607i \(-0.273144\pi\)
0.653870 + 0.756607i \(0.273144\pi\)
\(798\) 26.5028 0.938190
\(799\) 4.07070 0.144011
\(800\) 0 0
\(801\) −2.86645 −0.101281
\(802\) −18.7403 −0.661744
\(803\) 11.7824 0.415790
\(804\) −3.24535 −0.114455
\(805\) 0 0
\(806\) 22.3021 0.785559
\(807\) 4.24499 0.149431
\(808\) 18.2227 0.641073
\(809\) −47.8896 −1.68371 −0.841854 0.539706i \(-0.818535\pi\)
−0.841854 + 0.539706i \(0.818535\pi\)
\(810\) 0 0
\(811\) 42.9542 1.50833 0.754163 0.656687i \(-0.228043\pi\)
0.754163 + 0.656687i \(0.228043\pi\)
\(812\) 3.98981 0.140015
\(813\) −14.5778 −0.511267
\(814\) 28.3753 0.994553
\(815\) 0 0
\(816\) −20.1908 −0.706820
\(817\) −49.8344 −1.74349
\(818\) 43.0098 1.50380
\(819\) −11.2900 −0.394504
\(820\) 0 0
\(821\) 3.99177 0.139314 0.0696569 0.997571i \(-0.477810\pi\)
0.0696569 + 0.997571i \(0.477810\pi\)
\(822\) −22.2673 −0.776660
\(823\) −5.89579 −0.205514 −0.102757 0.994706i \(-0.532766\pi\)
−0.102757 + 0.994706i \(0.532766\pi\)
\(824\) 16.7998 0.585248
\(825\) 0 0
\(826\) −2.87324 −0.0999730
\(827\) 16.7716 0.583204 0.291602 0.956540i \(-0.405812\pi\)
0.291602 + 0.956540i \(0.405812\pi\)
\(828\) −5.44542 −0.189241
\(829\) −42.2432 −1.46717 −0.733583 0.679599i \(-0.762154\pi\)
−0.733583 + 0.679599i \(0.762154\pi\)
\(830\) 0 0
\(831\) 27.7778 0.963600
\(832\) −11.2873 −0.391318
\(833\) −2.33009 −0.0807330
\(834\) −4.01912 −0.139171
\(835\) 0 0
\(836\) −14.2365 −0.492380
\(837\) −3.24850 −0.112285
\(838\) −44.6880 −1.54372
\(839\) −1.08010 −0.0372891 −0.0186445 0.999826i \(-0.505935\pi\)
−0.0186445 + 0.999826i \(0.505935\pi\)
\(840\) 0 0
\(841\) −25.7162 −0.886764
\(842\) −26.2982 −0.906297
\(843\) −13.0720 −0.450222
\(844\) 13.8146 0.475517
\(845\) 0 0
\(846\) 1.67335 0.0575310
\(847\) −3.96964 −0.136398
\(848\) −27.6895 −0.950863
\(849\) −15.1027 −0.518323
\(850\) 0 0
\(851\) −37.3310 −1.27969
\(852\) −12.0963 −0.414412
\(853\) −11.3175 −0.387503 −0.193751 0.981051i \(-0.562065\pi\)
−0.193751 + 0.981051i \(0.562065\pi\)
\(854\) −27.8164 −0.951859
\(855\) 0 0
\(856\) −20.0705 −0.685996
\(857\) −52.2813 −1.78589 −0.892947 0.450162i \(-0.851366\pi\)
−0.892947 + 0.450162i \(0.851366\pi\)
\(858\) 21.2243 0.724587
\(859\) −20.2984 −0.692574 −0.346287 0.938129i \(-0.612558\pi\)
−0.346287 + 0.938129i \(0.612558\pi\)
\(860\) 0 0
\(861\) −3.62305 −0.123473
\(862\) 50.1496 1.70810
\(863\) −37.2057 −1.26650 −0.633249 0.773948i \(-0.718279\pi\)
−0.633249 + 0.773948i \(0.718279\pi\)
\(864\) −4.28418 −0.145751
\(865\) 0 0
\(866\) −26.8475 −0.912315
\(867\) 0.429409 0.0145835
\(868\) 7.15227 0.242764
\(869\) 17.3399 0.588215
\(870\) 0 0
\(871\) −16.6416 −0.563879
\(872\) 17.5752 0.595170
\(873\) −6.01711 −0.203648
\(874\) 65.5485 2.21721
\(875\) 0 0
\(876\) 3.04934 0.103028
\(877\) 35.9906 1.21532 0.607659 0.794198i \(-0.292109\pi\)
0.607659 + 0.794198i \(0.292109\pi\)
\(878\) 9.26203 0.312578
\(879\) −11.9208 −0.402080
\(880\) 0 0
\(881\) 32.2664 1.08708 0.543541 0.839382i \(-0.317083\pi\)
0.543541 + 0.839382i \(0.317083\pi\)
\(882\) −0.957836 −0.0322520
\(883\) −18.6132 −0.626383 −0.313192 0.949690i \(-0.601398\pi\)
−0.313192 + 0.949690i \(0.601398\pi\)
\(884\) 13.3626 0.449432
\(885\) 0 0
\(886\) 14.2179 0.477661
\(887\) 25.5149 0.856705 0.428353 0.903612i \(-0.359094\pi\)
0.428353 + 0.903612i \(0.359094\pi\)
\(888\) −11.0132 −0.369580
\(889\) 55.4467 1.85962
\(890\) 0 0
\(891\) −3.09151 −0.103570
\(892\) 6.07934 0.203551
\(893\) −5.75557 −0.192603
\(894\) −4.93175 −0.164942
\(895\) 0 0
\(896\) −36.2467 −1.21092
\(897\) −27.9231 −0.932326
\(898\) −11.4174 −0.381002
\(899\) 5.88674 0.196334
\(900\) 0 0
\(901\) −22.7248 −0.757072
\(902\) 6.81106 0.226784
\(903\) 23.8264 0.792892
\(904\) −29.4710 −0.980190
\(905\) 0 0
\(906\) 34.0488 1.13119
\(907\) 47.4369 1.57512 0.787559 0.616240i \(-0.211345\pi\)
0.787559 + 0.616240i \(0.211345\pi\)
\(908\) −10.4079 −0.345398
\(909\) 9.07572 0.301023
\(910\) 0 0
\(911\) −32.9807 −1.09270 −0.546350 0.837557i \(-0.683983\pi\)
−0.546350 + 0.837557i \(0.683983\pi\)
\(912\) 28.5479 0.945314
\(913\) 13.7766 0.455939
\(914\) 68.2330 2.25695
\(915\) 0 0
\(916\) −3.34033 −0.110368
\(917\) −51.5460 −1.70220
\(918\) −6.81170 −0.224820
\(919\) 25.7949 0.850895 0.425447 0.904983i \(-0.360117\pi\)
0.425447 + 0.904983i \(0.360117\pi\)
\(920\) 0 0
\(921\) −25.3094 −0.833973
\(922\) 38.2707 1.26038
\(923\) −62.0276 −2.04166
\(924\) 6.80662 0.223922
\(925\) 0 0
\(926\) 43.4056 1.42640
\(927\) 8.36703 0.274809
\(928\) 7.76352 0.254850
\(929\) 33.8137 1.10939 0.554696 0.832053i \(-0.312835\pi\)
0.554696 + 0.832053i \(0.312835\pi\)
\(930\) 0 0
\(931\) 3.29453 0.107974
\(932\) 21.0270 0.688761
\(933\) −22.2759 −0.729280
\(934\) 34.0195 1.11315
\(935\) 0 0
\(936\) −8.23775 −0.269259
\(937\) −19.6956 −0.643427 −0.321714 0.946837i \(-0.604259\pi\)
−0.321714 + 0.946837i \(0.604259\pi\)
\(938\) −18.6776 −0.609846
\(939\) −8.85418 −0.288945
\(940\) 0 0
\(941\) 51.4267 1.67646 0.838231 0.545315i \(-0.183590\pi\)
0.838231 + 0.545315i \(0.183590\pi\)
\(942\) 28.0405 0.913609
\(943\) −8.96075 −0.291802
\(944\) −3.09495 −0.100732
\(945\) 0 0
\(946\) −44.7918 −1.45631
\(947\) −2.31054 −0.0750825 −0.0375413 0.999295i \(-0.511953\pi\)
−0.0375413 + 0.999295i \(0.511953\pi\)
\(948\) 4.48765 0.145752
\(949\) 15.6364 0.507580
\(950\) 0 0
\(951\) −25.6447 −0.831585
\(952\) −22.4915 −0.728953
\(953\) −18.2392 −0.590825 −0.295413 0.955370i \(-0.595457\pi\)
−0.295413 + 0.955370i \(0.595457\pi\)
\(954\) −9.34151 −0.302443
\(955\) 0 0
\(956\) −1.28866 −0.0416784
\(957\) 5.60225 0.181095
\(958\) −26.0114 −0.840390
\(959\) −36.6182 −1.18246
\(960\) 0 0
\(961\) −20.4472 −0.659589
\(962\) 37.6570 1.21411
\(963\) −9.99601 −0.322117
\(964\) −3.96445 −0.127686
\(965\) 0 0
\(966\) −31.3394 −1.00833
\(967\) −19.6701 −0.632548 −0.316274 0.948668i \(-0.602432\pi\)
−0.316274 + 0.948668i \(0.602432\pi\)
\(968\) −2.89645 −0.0930955
\(969\) 23.4292 0.752655
\(970\) 0 0
\(971\) 38.6396 1.24000 0.620002 0.784600i \(-0.287132\pi\)
0.620002 + 0.784600i \(0.287132\pi\)
\(972\) −0.800100 −0.0256632
\(973\) −6.60938 −0.211887
\(974\) −70.9457 −2.27325
\(975\) 0 0
\(976\) −29.9628 −0.959087
\(977\) −32.9862 −1.05532 −0.527662 0.849455i \(-0.676931\pi\)
−0.527662 + 0.849455i \(0.676931\pi\)
\(978\) −24.3478 −0.778556
\(979\) 8.86167 0.283220
\(980\) 0 0
\(981\) 8.75321 0.279469
\(982\) −46.6858 −1.48980
\(983\) −3.94238 −0.125742 −0.0628711 0.998022i \(-0.520026\pi\)
−0.0628711 + 0.998022i \(0.520026\pi\)
\(984\) −2.64356 −0.0842736
\(985\) 0 0
\(986\) 12.3438 0.393105
\(987\) 2.75180 0.0875908
\(988\) −18.8934 −0.601078
\(989\) 58.9289 1.87383
\(990\) 0 0
\(991\) 12.0682 0.383360 0.191680 0.981457i \(-0.438606\pi\)
0.191680 + 0.981457i \(0.438606\pi\)
\(992\) 13.9171 0.441870
\(993\) −29.7383 −0.943716
\(994\) −69.6164 −2.20810
\(995\) 0 0
\(996\) 3.56546 0.112976
\(997\) −2.87188 −0.0909535 −0.0454767 0.998965i \(-0.514481\pi\)
−0.0454767 + 0.998965i \(0.514481\pi\)
\(998\) −7.82646 −0.247742
\(999\) −5.48507 −0.173540
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 3525.2.a.bh.1.4 13
5.2 odd 4 705.2.c.c.424.7 26
5.3 odd 4 705.2.c.c.424.20 yes 26
5.4 even 2 3525.2.a.bi.1.10 13
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
705.2.c.c.424.7 26 5.2 odd 4
705.2.c.c.424.20 yes 26 5.3 odd 4
3525.2.a.bh.1.4 13 1.1 even 1 trivial
3525.2.a.bi.1.10 13 5.4 even 2