Properties

Label 3549.2.a.be.1.9
Level $3549$
Weight $2$
Character 3549.1
Self dual yes
Analytic conductor $28.339$
Analytic rank $0$
Dimension $9$
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] = [3549,2,Mod(1,3549)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3549, 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("3549.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3549.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: \(28.3389076774\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - x^{8} - 11x^{7} + 8x^{6} + 37x^{5} - 18x^{4} - 41x^{3} + 12x^{2} + 6x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(-2.31147\) of defining polynomial
Character \(\chi\) \(=\) 3549.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.31147 q^{2} -1.00000 q^{3} +3.34288 q^{4} +1.46052 q^{5} -2.31147 q^{6} +1.00000 q^{7} +3.10401 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+2.31147 q^{2} -1.00000 q^{3} +3.34288 q^{4} +1.46052 q^{5} -2.31147 q^{6} +1.00000 q^{7} +3.10401 q^{8} +1.00000 q^{9} +3.37595 q^{10} +0.0565977 q^{11} -3.34288 q^{12} +2.31147 q^{14} -1.46052 q^{15} +0.489065 q^{16} +5.75421 q^{17} +2.31147 q^{18} -0.807619 q^{19} +4.88235 q^{20} -1.00000 q^{21} +0.130824 q^{22} +6.01403 q^{23} -3.10401 q^{24} -2.86687 q^{25} -1.00000 q^{27} +3.34288 q^{28} +3.22124 q^{29} -3.37595 q^{30} +5.59058 q^{31} -5.07756 q^{32} -0.0565977 q^{33} +13.3007 q^{34} +1.46052 q^{35} +3.34288 q^{36} +0.780896 q^{37} -1.86679 q^{38} +4.53348 q^{40} -5.30154 q^{41} -2.31147 q^{42} +2.38217 q^{43} +0.189199 q^{44} +1.46052 q^{45} +13.9012 q^{46} -3.32663 q^{47} -0.489065 q^{48} +1.00000 q^{49} -6.62667 q^{50} -5.75421 q^{51} -9.52747 q^{53} -2.31147 q^{54} +0.0826623 q^{55} +3.10401 q^{56} +0.807619 q^{57} +7.44578 q^{58} +10.3267 q^{59} -4.88235 q^{60} +8.88239 q^{61} +12.9224 q^{62} +1.00000 q^{63} -12.7147 q^{64} -0.130824 q^{66} +7.80744 q^{67} +19.2356 q^{68} -6.01403 q^{69} +3.37595 q^{70} -11.4706 q^{71} +3.10401 q^{72} +13.1445 q^{73} +1.80501 q^{74} +2.86687 q^{75} -2.69977 q^{76} +0.0565977 q^{77} +10.8565 q^{79} +0.714292 q^{80} +1.00000 q^{81} -12.2543 q^{82} -7.70243 q^{83} -3.34288 q^{84} +8.40417 q^{85} +5.50631 q^{86} -3.22124 q^{87} +0.175680 q^{88} +8.12369 q^{89} +3.37595 q^{90} +20.1042 q^{92} -5.59058 q^{93} -7.68939 q^{94} -1.17955 q^{95} +5.07756 q^{96} +3.93035 q^{97} +2.31147 q^{98} +0.0565977 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - q^{2} - 9 q^{3} + 5 q^{4} + 9 q^{5} + q^{6} + 9 q^{7} - 6 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 9 q - q^{2} - 9 q^{3} + 5 q^{4} + 9 q^{5} + q^{6} + 9 q^{7} - 6 q^{8} + 9 q^{9} + q^{10} - q^{11} - 5 q^{12} - q^{14} - 9 q^{15} + 5 q^{16} + 11 q^{17} - q^{18} + 7 q^{19} + 23 q^{20} - 9 q^{21} - 3 q^{22} + 22 q^{23} + 6 q^{24} - 8 q^{25} - 9 q^{27} + 5 q^{28} + 11 q^{29} - q^{30} + 7 q^{31} - 18 q^{32} + q^{33} - 6 q^{34} + 9 q^{35} + 5 q^{36} - q^{37} - 6 q^{38} - 14 q^{40} + 16 q^{41} + q^{42} + 32 q^{43} + 18 q^{44} + 9 q^{45} - 9 q^{46} - 12 q^{47} - 5 q^{48} + 9 q^{49} + 10 q^{50} - 11 q^{51} + 13 q^{53} + q^{54} + 9 q^{55} - 6 q^{56} - 7 q^{57} + 4 q^{58} + 29 q^{59} - 23 q^{60} - 12 q^{61} + 30 q^{62} + 9 q^{63} + 6 q^{64} + 3 q^{66} - 20 q^{67} + 34 q^{68} - 22 q^{69} + q^{70} - 2 q^{71} - 6 q^{72} + q^{73} + 43 q^{74} + 8 q^{75} + 13 q^{76} - q^{77} + 3 q^{79} - 39 q^{80} + 9 q^{81} - 19 q^{82} + 24 q^{83} - 5 q^{84} + 15 q^{85} - 28 q^{86} - 11 q^{87} - 19 q^{88} + 11 q^{89} + q^{90} + 73 q^{92} - 7 q^{93} + 15 q^{94} + 39 q^{95} + 18 q^{96} + 20 q^{97} - q^{98} - q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.31147 1.63445 0.817227 0.576316i \(-0.195510\pi\)
0.817227 + 0.576316i \(0.195510\pi\)
\(3\) −1.00000 −0.577350
\(4\) 3.34288 1.67144
\(5\) 1.46052 0.653166 0.326583 0.945168i \(-0.394103\pi\)
0.326583 + 0.945168i \(0.394103\pi\)
\(6\) −2.31147 −0.943652
\(7\) 1.00000 0.377964
\(8\) 3.10401 1.09743
\(9\) 1.00000 0.333333
\(10\) 3.37595 1.06757
\(11\) 0.0565977 0.0170648 0.00853242 0.999964i \(-0.497284\pi\)
0.00853242 + 0.999964i \(0.497284\pi\)
\(12\) −3.34288 −0.965005
\(13\) 0 0
\(14\) 2.31147 0.617765
\(15\) −1.46052 −0.377106
\(16\) 0.489065 0.122266
\(17\) 5.75421 1.39560 0.697801 0.716292i \(-0.254162\pi\)
0.697801 + 0.716292i \(0.254162\pi\)
\(18\) 2.31147 0.544818
\(19\) −0.807619 −0.185281 −0.0926403 0.995700i \(-0.529531\pi\)
−0.0926403 + 0.995700i \(0.529531\pi\)
\(20\) 4.88235 1.09173
\(21\) −1.00000 −0.218218
\(22\) 0.130824 0.0278917
\(23\) 6.01403 1.25401 0.627006 0.779014i \(-0.284280\pi\)
0.627006 + 0.779014i \(0.284280\pi\)
\(24\) −3.10401 −0.633604
\(25\) −2.86687 −0.573374
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 3.34288 0.631744
\(29\) 3.22124 0.598168 0.299084 0.954227i \(-0.403319\pi\)
0.299084 + 0.954227i \(0.403319\pi\)
\(30\) −3.37595 −0.616362
\(31\) 5.59058 1.00410 0.502049 0.864839i \(-0.332580\pi\)
0.502049 + 0.864839i \(0.332580\pi\)
\(32\) −5.07756 −0.897595
\(33\) −0.0565977 −0.00985239
\(34\) 13.3007 2.28105
\(35\) 1.46052 0.246874
\(36\) 3.34288 0.557146
\(37\) 0.780896 0.128378 0.0641892 0.997938i \(-0.479554\pi\)
0.0641892 + 0.997938i \(0.479554\pi\)
\(38\) −1.86679 −0.302833
\(39\) 0 0
\(40\) 4.53348 0.716807
\(41\) −5.30154 −0.827961 −0.413980 0.910286i \(-0.635862\pi\)
−0.413980 + 0.910286i \(0.635862\pi\)
\(42\) −2.31147 −0.356667
\(43\) 2.38217 0.363278 0.181639 0.983365i \(-0.441860\pi\)
0.181639 + 0.983365i \(0.441860\pi\)
\(44\) 0.189199 0.0285228
\(45\) 1.46052 0.217722
\(46\) 13.9012 2.04963
\(47\) −3.32663 −0.485239 −0.242620 0.970122i \(-0.578007\pi\)
−0.242620 + 0.970122i \(0.578007\pi\)
\(48\) −0.489065 −0.0705905
\(49\) 1.00000 0.142857
\(50\) −6.62667 −0.937153
\(51\) −5.75421 −0.805751
\(52\) 0 0
\(53\) −9.52747 −1.30870 −0.654350 0.756192i \(-0.727058\pi\)
−0.654350 + 0.756192i \(0.727058\pi\)
\(54\) −2.31147 −0.314551
\(55\) 0.0826623 0.0111462
\(56\) 3.10401 0.414791
\(57\) 0.807619 0.106972
\(58\) 7.44578 0.977678
\(59\) 10.3267 1.34443 0.672214 0.740357i \(-0.265344\pi\)
0.672214 + 0.740357i \(0.265344\pi\)
\(60\) −4.88235 −0.630309
\(61\) 8.88239 1.13727 0.568637 0.822589i \(-0.307471\pi\)
0.568637 + 0.822589i \(0.307471\pi\)
\(62\) 12.9224 1.64115
\(63\) 1.00000 0.125988
\(64\) −12.7147 −1.58934
\(65\) 0 0
\(66\) −0.130824 −0.0161033
\(67\) 7.80744 0.953830 0.476915 0.878949i \(-0.341755\pi\)
0.476915 + 0.878949i \(0.341755\pi\)
\(68\) 19.2356 2.33266
\(69\) −6.01403 −0.724005
\(70\) 3.37595 0.403504
\(71\) −11.4706 −1.36131 −0.680657 0.732602i \(-0.738306\pi\)
−0.680657 + 0.732602i \(0.738306\pi\)
\(72\) 3.10401 0.365811
\(73\) 13.1445 1.53845 0.769223 0.638980i \(-0.220643\pi\)
0.769223 + 0.638980i \(0.220643\pi\)
\(74\) 1.80501 0.209829
\(75\) 2.86687 0.331037
\(76\) −2.69977 −0.309685
\(77\) 0.0565977 0.00644991
\(78\) 0 0
\(79\) 10.8565 1.22145 0.610726 0.791842i \(-0.290878\pi\)
0.610726 + 0.791842i \(0.290878\pi\)
\(80\) 0.714292 0.0798602
\(81\) 1.00000 0.111111
\(82\) −12.2543 −1.35326
\(83\) −7.70243 −0.845452 −0.422726 0.906258i \(-0.638927\pi\)
−0.422726 + 0.906258i \(0.638927\pi\)
\(84\) −3.34288 −0.364738
\(85\) 8.40417 0.911560
\(86\) 5.50631 0.593760
\(87\) −3.22124 −0.345353
\(88\) 0.175680 0.0187275
\(89\) 8.12369 0.861109 0.430555 0.902564i \(-0.358318\pi\)
0.430555 + 0.902564i \(0.358318\pi\)
\(90\) 3.37595 0.355857
\(91\) 0 0
\(92\) 20.1042 2.09600
\(93\) −5.59058 −0.579716
\(94\) −7.68939 −0.793101
\(95\) −1.17955 −0.121019
\(96\) 5.07756 0.518227
\(97\) 3.93035 0.399066 0.199533 0.979891i \(-0.436057\pi\)
0.199533 + 0.979891i \(0.436057\pi\)
\(98\) 2.31147 0.233493
\(99\) 0.0565977 0.00568828
\(100\) −9.58358 −0.958358
\(101\) 6.75818 0.672464 0.336232 0.941779i \(-0.390847\pi\)
0.336232 + 0.941779i \(0.390847\pi\)
\(102\) −13.3007 −1.31696
\(103\) −12.4083 −1.22262 −0.611312 0.791390i \(-0.709358\pi\)
−0.611312 + 0.791390i \(0.709358\pi\)
\(104\) 0 0
\(105\) −1.46052 −0.142533
\(106\) −22.0224 −2.13901
\(107\) 18.1781 1.75734 0.878672 0.477425i \(-0.158430\pi\)
0.878672 + 0.477425i \(0.158430\pi\)
\(108\) −3.34288 −0.321668
\(109\) −9.12019 −0.873556 −0.436778 0.899569i \(-0.643880\pi\)
−0.436778 + 0.899569i \(0.643880\pi\)
\(110\) 0.191071 0.0182179
\(111\) −0.780896 −0.0741193
\(112\) 0.489065 0.0462123
\(113\) −14.7050 −1.38333 −0.691664 0.722220i \(-0.743122\pi\)
−0.691664 + 0.722220i \(0.743122\pi\)
\(114\) 1.86679 0.174840
\(115\) 8.78364 0.819079
\(116\) 10.7682 0.999801
\(117\) 0 0
\(118\) 23.8699 2.19740
\(119\) 5.75421 0.527488
\(120\) −4.53348 −0.413849
\(121\) −10.9968 −0.999709
\(122\) 20.5313 1.85882
\(123\) 5.30154 0.478023
\(124\) 18.6886 1.67829
\(125\) −11.4898 −1.02767
\(126\) 2.31147 0.205922
\(127\) −10.5900 −0.939714 −0.469857 0.882743i \(-0.655694\pi\)
−0.469857 + 0.882743i \(0.655694\pi\)
\(128\) −19.2346 −1.70011
\(129\) −2.38217 −0.209738
\(130\) 0 0
\(131\) −9.31173 −0.813570 −0.406785 0.913524i \(-0.633350\pi\)
−0.406785 + 0.913524i \(0.633350\pi\)
\(132\) −0.189199 −0.0164677
\(133\) −0.807619 −0.0700295
\(134\) 18.0466 1.55899
\(135\) −1.46052 −0.125702
\(136\) 17.8611 1.53158
\(137\) 4.10255 0.350505 0.175252 0.984524i \(-0.443926\pi\)
0.175252 + 0.984524i \(0.443926\pi\)
\(138\) −13.9012 −1.18335
\(139\) 16.2754 1.38046 0.690231 0.723589i \(-0.257509\pi\)
0.690231 + 0.723589i \(0.257509\pi\)
\(140\) 4.88235 0.412634
\(141\) 3.32663 0.280153
\(142\) −26.5140 −2.22500
\(143\) 0 0
\(144\) 0.489065 0.0407554
\(145\) 4.70469 0.390704
\(146\) 30.3830 2.51452
\(147\) −1.00000 −0.0824786
\(148\) 2.61044 0.214577
\(149\) −2.11348 −0.173143 −0.0865717 0.996246i \(-0.527591\pi\)
−0.0865717 + 0.996246i \(0.527591\pi\)
\(150\) 6.62667 0.541065
\(151\) −17.2235 −1.40163 −0.700814 0.713344i \(-0.747180\pi\)
−0.700814 + 0.713344i \(0.747180\pi\)
\(152\) −2.50686 −0.203333
\(153\) 5.75421 0.465201
\(154\) 0.130824 0.0105421
\(155\) 8.16518 0.655843
\(156\) 0 0
\(157\) −20.5730 −1.64190 −0.820951 0.570998i \(-0.806556\pi\)
−0.820951 + 0.570998i \(0.806556\pi\)
\(158\) 25.0944 1.99641
\(159\) 9.52747 0.755578
\(160\) −7.41591 −0.586279
\(161\) 6.01403 0.473972
\(162\) 2.31147 0.181606
\(163\) −8.77011 −0.686928 −0.343464 0.939166i \(-0.611600\pi\)
−0.343464 + 0.939166i \(0.611600\pi\)
\(164\) −17.7224 −1.38389
\(165\) −0.0826623 −0.00643525
\(166\) −17.8039 −1.38185
\(167\) 16.9542 1.31195 0.655976 0.754782i \(-0.272257\pi\)
0.655976 + 0.754782i \(0.272257\pi\)
\(168\) −3.10401 −0.239480
\(169\) 0 0
\(170\) 19.4260 1.48990
\(171\) −0.807619 −0.0617602
\(172\) 7.96330 0.607196
\(173\) 1.91338 0.145472 0.0727360 0.997351i \(-0.476827\pi\)
0.0727360 + 0.997351i \(0.476827\pi\)
\(174\) −7.44578 −0.564463
\(175\) −2.86687 −0.216715
\(176\) 0.0276800 0.00208646
\(177\) −10.3267 −0.776206
\(178\) 18.7776 1.40744
\(179\) −26.1240 −1.95260 −0.976300 0.216421i \(-0.930562\pi\)
−0.976300 + 0.216421i \(0.930562\pi\)
\(180\) 4.88235 0.363909
\(181\) −1.98010 −0.147180 −0.0735899 0.997289i \(-0.523446\pi\)
−0.0735899 + 0.997289i \(0.523446\pi\)
\(182\) 0 0
\(183\) −8.88239 −0.656605
\(184\) 18.6676 1.37620
\(185\) 1.14052 0.0838525
\(186\) −12.9224 −0.947520
\(187\) 0.325675 0.0238157
\(188\) −11.1205 −0.811047
\(189\) −1.00000 −0.0727393
\(190\) −2.72649 −0.197800
\(191\) −20.6851 −1.49672 −0.748359 0.663294i \(-0.769158\pi\)
−0.748359 + 0.663294i \(0.769158\pi\)
\(192\) 12.7147 0.917608
\(193\) 2.88929 0.207976 0.103988 0.994579i \(-0.466840\pi\)
0.103988 + 0.994579i \(0.466840\pi\)
\(194\) 9.08487 0.652256
\(195\) 0 0
\(196\) 3.34288 0.238777
\(197\) 3.01713 0.214962 0.107481 0.994207i \(-0.465722\pi\)
0.107481 + 0.994207i \(0.465722\pi\)
\(198\) 0.130824 0.00929723
\(199\) 24.5542 1.74060 0.870301 0.492520i \(-0.163924\pi\)
0.870301 + 0.492520i \(0.163924\pi\)
\(200\) −8.89879 −0.629240
\(201\) −7.80744 −0.550694
\(202\) 15.6213 1.09911
\(203\) 3.22124 0.226086
\(204\) −19.2356 −1.34676
\(205\) −7.74302 −0.540796
\(206\) −28.6813 −1.99832
\(207\) 6.01403 0.418004
\(208\) 0 0
\(209\) −0.0457094 −0.00316179
\(210\) −3.37595 −0.232963
\(211\) 15.2596 1.05052 0.525259 0.850943i \(-0.323969\pi\)
0.525259 + 0.850943i \(0.323969\pi\)
\(212\) −31.8492 −2.18741
\(213\) 11.4706 0.785955
\(214\) 42.0181 2.87230
\(215\) 3.47922 0.237281
\(216\) −3.10401 −0.211201
\(217\) 5.59058 0.379514
\(218\) −21.0810 −1.42779
\(219\) −13.1445 −0.888222
\(220\) 0.276330 0.0186302
\(221\) 0 0
\(222\) −1.80501 −0.121145
\(223\) −3.41178 −0.228470 −0.114235 0.993454i \(-0.536442\pi\)
−0.114235 + 0.993454i \(0.536442\pi\)
\(224\) −5.07756 −0.339259
\(225\) −2.86687 −0.191125
\(226\) −33.9900 −2.26098
\(227\) −1.36962 −0.0909046 −0.0454523 0.998967i \(-0.514473\pi\)
−0.0454523 + 0.998967i \(0.514473\pi\)
\(228\) 2.69977 0.178797
\(229\) −17.3194 −1.14450 −0.572249 0.820080i \(-0.693929\pi\)
−0.572249 + 0.820080i \(0.693929\pi\)
\(230\) 20.3031 1.33875
\(231\) −0.0565977 −0.00372386
\(232\) 9.99875 0.656450
\(233\) 5.77054 0.378041 0.189020 0.981973i \(-0.439469\pi\)
0.189020 + 0.981973i \(0.439469\pi\)
\(234\) 0 0
\(235\) −4.85863 −0.316942
\(236\) 34.5210 2.24713
\(237\) −10.8565 −0.705206
\(238\) 13.3007 0.862154
\(239\) −2.80755 −0.181605 −0.0908027 0.995869i \(-0.528943\pi\)
−0.0908027 + 0.995869i \(0.528943\pi\)
\(240\) −0.714292 −0.0461073
\(241\) −7.55528 −0.486678 −0.243339 0.969941i \(-0.578243\pi\)
−0.243339 + 0.969941i \(0.578243\pi\)
\(242\) −25.4187 −1.63398
\(243\) −1.00000 −0.0641500
\(244\) 29.6927 1.90088
\(245\) 1.46052 0.0933095
\(246\) 12.2543 0.781307
\(247\) 0 0
\(248\) 17.3532 1.10193
\(249\) 7.70243 0.488122
\(250\) −26.5582 −1.67969
\(251\) 26.2186 1.65491 0.827453 0.561535i \(-0.189789\pi\)
0.827453 + 0.561535i \(0.189789\pi\)
\(252\) 3.34288 0.210581
\(253\) 0.340380 0.0213995
\(254\) −24.4785 −1.53592
\(255\) −8.40417 −0.526290
\(256\) −19.0306 −1.18941
\(257\) −3.58179 −0.223426 −0.111713 0.993741i \(-0.535634\pi\)
−0.111713 + 0.993741i \(0.535634\pi\)
\(258\) −5.50631 −0.342808
\(259\) 0.780896 0.0485225
\(260\) 0 0
\(261\) 3.22124 0.199389
\(262\) −21.5237 −1.32974
\(263\) 26.7600 1.65009 0.825046 0.565066i \(-0.191149\pi\)
0.825046 + 0.565066i \(0.191149\pi\)
\(264\) −0.175680 −0.0108123
\(265\) −13.9151 −0.854798
\(266\) −1.86679 −0.114460
\(267\) −8.12369 −0.497162
\(268\) 26.0993 1.59427
\(269\) 14.7193 0.897454 0.448727 0.893669i \(-0.351878\pi\)
0.448727 + 0.893669i \(0.351878\pi\)
\(270\) −3.37595 −0.205454
\(271\) 13.1874 0.801075 0.400537 0.916280i \(-0.368824\pi\)
0.400537 + 0.916280i \(0.368824\pi\)
\(272\) 2.81419 0.170635
\(273\) 0 0
\(274\) 9.48291 0.572884
\(275\) −0.162258 −0.00978454
\(276\) −20.1042 −1.21013
\(277\) 21.5726 1.29617 0.648087 0.761566i \(-0.275569\pi\)
0.648087 + 0.761566i \(0.275569\pi\)
\(278\) 37.6200 2.25630
\(279\) 5.59058 0.334699
\(280\) 4.53348 0.270927
\(281\) −0.186485 −0.0111248 −0.00556238 0.999985i \(-0.501771\pi\)
−0.00556238 + 0.999985i \(0.501771\pi\)
\(282\) 7.68939 0.457897
\(283\) −14.0208 −0.833452 −0.416726 0.909032i \(-0.636823\pi\)
−0.416726 + 0.909032i \(0.636823\pi\)
\(284\) −38.3449 −2.27535
\(285\) 1.17955 0.0698704
\(286\) 0 0
\(287\) −5.30154 −0.312940
\(288\) −5.07756 −0.299198
\(289\) 16.1110 0.947705
\(290\) 10.8747 0.638587
\(291\) −3.93035 −0.230401
\(292\) 43.9404 2.57142
\(293\) −15.8832 −0.927907 −0.463953 0.885860i \(-0.653570\pi\)
−0.463953 + 0.885860i \(0.653570\pi\)
\(294\) −2.31147 −0.134807
\(295\) 15.0825 0.878135
\(296\) 2.42391 0.140887
\(297\) −0.0565977 −0.00328413
\(298\) −4.88525 −0.282995
\(299\) 0 0
\(300\) 9.58358 0.553309
\(301\) 2.38217 0.137306
\(302\) −39.8115 −2.29090
\(303\) −6.75818 −0.388247
\(304\) −0.394979 −0.0226536
\(305\) 12.9729 0.742829
\(306\) 13.3007 0.760349
\(307\) 12.3994 0.707669 0.353834 0.935308i \(-0.384878\pi\)
0.353834 + 0.935308i \(0.384878\pi\)
\(308\) 0.189199 0.0107806
\(309\) 12.4083 0.705882
\(310\) 18.8735 1.07195
\(311\) 7.17624 0.406927 0.203463 0.979083i \(-0.434780\pi\)
0.203463 + 0.979083i \(0.434780\pi\)
\(312\) 0 0
\(313\) −21.8602 −1.23561 −0.617806 0.786330i \(-0.711978\pi\)
−0.617806 + 0.786330i \(0.711978\pi\)
\(314\) −47.5537 −2.68361
\(315\) 1.46052 0.0822912
\(316\) 36.2919 2.04158
\(317\) −26.2740 −1.47570 −0.737848 0.674967i \(-0.764158\pi\)
−0.737848 + 0.674967i \(0.764158\pi\)
\(318\) 22.0224 1.23496
\(319\) 0.182315 0.0102077
\(320\) −18.5702 −1.03811
\(321\) −18.1781 −1.01460
\(322\) 13.9012 0.774686
\(323\) −4.64722 −0.258578
\(324\) 3.34288 0.185715
\(325\) 0 0
\(326\) −20.2718 −1.12275
\(327\) 9.12019 0.504348
\(328\) −16.4560 −0.908632
\(329\) −3.32663 −0.183403
\(330\) −0.191071 −0.0105181
\(331\) −27.3837 −1.50515 −0.752573 0.658509i \(-0.771188\pi\)
−0.752573 + 0.658509i \(0.771188\pi\)
\(332\) −25.7483 −1.41312
\(333\) 0.780896 0.0427928
\(334\) 39.1889 2.14432
\(335\) 11.4030 0.623010
\(336\) −0.489065 −0.0266807
\(337\) −20.0655 −1.09304 −0.546520 0.837446i \(-0.684048\pi\)
−0.546520 + 0.837446i \(0.684048\pi\)
\(338\) 0 0
\(339\) 14.7050 0.798664
\(340\) 28.0941 1.52362
\(341\) 0.316414 0.0171348
\(342\) −1.86679 −0.100944
\(343\) 1.00000 0.0539949
\(344\) 7.39428 0.398673
\(345\) −8.78364 −0.472895
\(346\) 4.42272 0.237767
\(347\) 17.6754 0.948865 0.474432 0.880292i \(-0.342653\pi\)
0.474432 + 0.880292i \(0.342653\pi\)
\(348\) −10.7682 −0.577236
\(349\) −11.8130 −0.632336 −0.316168 0.948703i \(-0.602396\pi\)
−0.316168 + 0.948703i \(0.602396\pi\)
\(350\) −6.62667 −0.354210
\(351\) 0 0
\(352\) −0.287378 −0.0153173
\(353\) −28.9315 −1.53987 −0.769935 0.638122i \(-0.779712\pi\)
−0.769935 + 0.638122i \(0.779712\pi\)
\(354\) −23.8699 −1.26867
\(355\) −16.7531 −0.889164
\(356\) 27.1565 1.43929
\(357\) −5.75421 −0.304545
\(358\) −60.3848 −3.19143
\(359\) 1.69739 0.0895850 0.0447925 0.998996i \(-0.485737\pi\)
0.0447925 + 0.998996i \(0.485737\pi\)
\(360\) 4.53348 0.238936
\(361\) −18.3478 −0.965671
\(362\) −4.57694 −0.240559
\(363\) 10.9968 0.577182
\(364\) 0 0
\(365\) 19.1978 1.00486
\(366\) −20.5313 −1.07319
\(367\) −30.9753 −1.61690 −0.808448 0.588567i \(-0.799692\pi\)
−0.808448 + 0.588567i \(0.799692\pi\)
\(368\) 2.94126 0.153324
\(369\) −5.30154 −0.275987
\(370\) 2.63627 0.137053
\(371\) −9.52747 −0.494642
\(372\) −18.6886 −0.968960
\(373\) −10.6807 −0.553026 −0.276513 0.961010i \(-0.589179\pi\)
−0.276513 + 0.961010i \(0.589179\pi\)
\(374\) 0.752787 0.0389257
\(375\) 11.4898 0.593328
\(376\) −10.3259 −0.532518
\(377\) 0 0
\(378\) −2.31147 −0.118889
\(379\) −28.1251 −1.44469 −0.722344 0.691534i \(-0.756935\pi\)
−0.722344 + 0.691534i \(0.756935\pi\)
\(380\) −3.94308 −0.202276
\(381\) 10.5900 0.542544
\(382\) −47.8128 −2.44632
\(383\) 12.2466 0.625772 0.312886 0.949791i \(-0.398704\pi\)
0.312886 + 0.949791i \(0.398704\pi\)
\(384\) 19.2346 0.981561
\(385\) 0.0826623 0.00421286
\(386\) 6.67849 0.339926
\(387\) 2.38217 0.121093
\(388\) 13.1387 0.667015
\(389\) −13.6432 −0.691738 −0.345869 0.938283i \(-0.612416\pi\)
−0.345869 + 0.938283i \(0.612416\pi\)
\(390\) 0 0
\(391\) 34.6060 1.75010
\(392\) 3.10401 0.156776
\(393\) 9.31173 0.469715
\(394\) 6.97399 0.351345
\(395\) 15.8562 0.797811
\(396\) 0.189199 0.00950761
\(397\) 12.4375 0.624219 0.312109 0.950046i \(-0.398964\pi\)
0.312109 + 0.950046i \(0.398964\pi\)
\(398\) 56.7562 2.84493
\(399\) 0.807619 0.0404315
\(400\) −1.40209 −0.0701043
\(401\) −25.0321 −1.25004 −0.625021 0.780608i \(-0.714910\pi\)
−0.625021 + 0.780608i \(0.714910\pi\)
\(402\) −18.0466 −0.900084
\(403\) 0 0
\(404\) 22.5918 1.12398
\(405\) 1.46052 0.0725740
\(406\) 7.44578 0.369528
\(407\) 0.0441969 0.00219076
\(408\) −17.8611 −0.884258
\(409\) −35.3470 −1.74780 −0.873899 0.486108i \(-0.838416\pi\)
−0.873899 + 0.486108i \(0.838416\pi\)
\(410\) −17.8977 −0.883906
\(411\) −4.10255 −0.202364
\(412\) −41.4793 −2.04354
\(413\) 10.3267 0.508146
\(414\) 13.9012 0.683208
\(415\) −11.2496 −0.552221
\(416\) 0 0
\(417\) −16.2754 −0.797010
\(418\) −0.105656 −0.00516779
\(419\) 26.0985 1.27499 0.637496 0.770453i \(-0.279970\pi\)
0.637496 + 0.770453i \(0.279970\pi\)
\(420\) −4.88235 −0.238234
\(421\) 0.465309 0.0226778 0.0113389 0.999936i \(-0.496391\pi\)
0.0113389 + 0.999936i \(0.496391\pi\)
\(422\) 35.2722 1.71702
\(423\) −3.32663 −0.161746
\(424\) −29.5734 −1.43621
\(425\) −16.4966 −0.800201
\(426\) 26.5140 1.28461
\(427\) 8.88239 0.429849
\(428\) 60.7672 2.93729
\(429\) 0 0
\(430\) 8.04209 0.387824
\(431\) −26.8469 −1.29317 −0.646584 0.762843i \(-0.723803\pi\)
−0.646584 + 0.762843i \(0.723803\pi\)
\(432\) −0.489065 −0.0235302
\(433\) 28.8450 1.38620 0.693101 0.720840i \(-0.256244\pi\)
0.693101 + 0.720840i \(0.256244\pi\)
\(434\) 12.9224 0.620297
\(435\) −4.70469 −0.225573
\(436\) −30.4877 −1.46009
\(437\) −4.85705 −0.232344
\(438\) −30.3830 −1.45176
\(439\) −19.1983 −0.916286 −0.458143 0.888879i \(-0.651485\pi\)
−0.458143 + 0.888879i \(0.651485\pi\)
\(440\) 0.256585 0.0122322
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) 23.9117 1.13608 0.568040 0.823001i \(-0.307702\pi\)
0.568040 + 0.823001i \(0.307702\pi\)
\(444\) −2.61044 −0.123886
\(445\) 11.8648 0.562448
\(446\) −7.88621 −0.373423
\(447\) 2.11348 0.0999644
\(448\) −12.7147 −0.600715
\(449\) −31.8784 −1.50444 −0.752218 0.658914i \(-0.771016\pi\)
−0.752218 + 0.658914i \(0.771016\pi\)
\(450\) −6.62667 −0.312384
\(451\) −0.300055 −0.0141290
\(452\) −49.1569 −2.31215
\(453\) 17.2235 0.809231
\(454\) −3.16582 −0.148579
\(455\) 0 0
\(456\) 2.50686 0.117394
\(457\) −31.4570 −1.47149 −0.735747 0.677256i \(-0.763169\pi\)
−0.735747 + 0.677256i \(0.763169\pi\)
\(458\) −40.0332 −1.87063
\(459\) −5.75421 −0.268584
\(460\) 29.3626 1.36904
\(461\) −25.1219 −1.17004 −0.585021 0.811018i \(-0.698914\pi\)
−0.585021 + 0.811018i \(0.698914\pi\)
\(462\) −0.130824 −0.00608647
\(463\) −20.4492 −0.950354 −0.475177 0.879890i \(-0.657616\pi\)
−0.475177 + 0.879890i \(0.657616\pi\)
\(464\) 1.57539 0.0731359
\(465\) −8.16518 −0.378651
\(466\) 13.3384 0.617890
\(467\) 22.0746 1.02149 0.510745 0.859732i \(-0.329370\pi\)
0.510745 + 0.859732i \(0.329370\pi\)
\(468\) 0 0
\(469\) 7.80744 0.360514
\(470\) −11.2305 −0.518027
\(471\) 20.5730 0.947953
\(472\) 32.0543 1.47542
\(473\) 0.134825 0.00619928
\(474\) −25.0944 −1.15263
\(475\) 2.31534 0.106235
\(476\) 19.2356 0.881663
\(477\) −9.52747 −0.436233
\(478\) −6.48956 −0.296825
\(479\) −12.1574 −0.555486 −0.277743 0.960655i \(-0.589586\pi\)
−0.277743 + 0.960655i \(0.589586\pi\)
\(480\) 7.41591 0.338488
\(481\) 0 0
\(482\) −17.4638 −0.795453
\(483\) −6.01403 −0.273648
\(484\) −36.7609 −1.67095
\(485\) 5.74037 0.260657
\(486\) −2.31147 −0.104850
\(487\) −18.6677 −0.845914 −0.422957 0.906150i \(-0.639008\pi\)
−0.422957 + 0.906150i \(0.639008\pi\)
\(488\) 27.5710 1.24808
\(489\) 8.77011 0.396598
\(490\) 3.37595 0.152510
\(491\) 18.8532 0.850833 0.425416 0.904998i \(-0.360128\pi\)
0.425416 + 0.904998i \(0.360128\pi\)
\(492\) 17.7224 0.798986
\(493\) 18.5357 0.834805
\(494\) 0 0
\(495\) 0.0826623 0.00371539
\(496\) 2.73416 0.122767
\(497\) −11.4706 −0.514528
\(498\) 17.8039 0.797813
\(499\) −23.7688 −1.06404 −0.532018 0.846733i \(-0.678566\pi\)
−0.532018 + 0.846733i \(0.678566\pi\)
\(500\) −38.4088 −1.71769
\(501\) −16.9542 −0.757456
\(502\) 60.6035 2.70487
\(503\) 8.31234 0.370629 0.185314 0.982679i \(-0.440670\pi\)
0.185314 + 0.982679i \(0.440670\pi\)
\(504\) 3.10401 0.138264
\(505\) 9.87049 0.439231
\(506\) 0.786778 0.0349765
\(507\) 0 0
\(508\) −35.4012 −1.57067
\(509\) 8.75231 0.387939 0.193970 0.981008i \(-0.437864\pi\)
0.193970 + 0.981008i \(0.437864\pi\)
\(510\) −19.4260 −0.860196
\(511\) 13.1445 0.581478
\(512\) −5.51939 −0.243925
\(513\) 0.807619 0.0356573
\(514\) −8.27918 −0.365179
\(515\) −18.1226 −0.798577
\(516\) −7.96330 −0.350565
\(517\) −0.188280 −0.00828053
\(518\) 1.80501 0.0793078
\(519\) −1.91338 −0.0839882
\(520\) 0 0
\(521\) −32.1915 −1.41033 −0.705167 0.709041i \(-0.749128\pi\)
−0.705167 + 0.709041i \(0.749128\pi\)
\(522\) 7.44578 0.325893
\(523\) −13.3302 −0.582891 −0.291446 0.956587i \(-0.594136\pi\)
−0.291446 + 0.956587i \(0.594136\pi\)
\(524\) −31.1280 −1.35983
\(525\) 2.86687 0.125120
\(526\) 61.8548 2.69700
\(527\) 32.1694 1.40132
\(528\) −0.0276800 −0.00120462
\(529\) 13.1686 0.572548
\(530\) −32.1643 −1.39713
\(531\) 10.3267 0.448143
\(532\) −2.69977 −0.117050
\(533\) 0 0
\(534\) −18.7776 −0.812588
\(535\) 26.5496 1.14784
\(536\) 24.2344 1.04677
\(537\) 26.1240 1.12733
\(538\) 34.0232 1.46685
\(539\) 0.0565977 0.00243784
\(540\) −4.88235 −0.210103
\(541\) −22.2023 −0.954553 −0.477277 0.878753i \(-0.658376\pi\)
−0.477277 + 0.878753i \(0.658376\pi\)
\(542\) 30.4821 1.30932
\(543\) 1.98010 0.0849743
\(544\) −29.2174 −1.25269
\(545\) −13.3203 −0.570577
\(546\) 0 0
\(547\) 36.3118 1.55258 0.776289 0.630377i \(-0.217100\pi\)
0.776289 + 0.630377i \(0.217100\pi\)
\(548\) 13.7143 0.585847
\(549\) 8.88239 0.379091
\(550\) −0.375054 −0.0159924
\(551\) −2.60153 −0.110829
\(552\) −18.6676 −0.794547
\(553\) 10.8565 0.461666
\(554\) 49.8644 2.11854
\(555\) −1.14052 −0.0484123
\(556\) 54.4066 2.30736
\(557\) 42.7664 1.81207 0.906036 0.423200i \(-0.139093\pi\)
0.906036 + 0.423200i \(0.139093\pi\)
\(558\) 12.9224 0.547051
\(559\) 0 0
\(560\) 0.714292 0.0301843
\(561\) −0.325675 −0.0137500
\(562\) −0.431054 −0.0181829
\(563\) −13.8742 −0.584728 −0.292364 0.956307i \(-0.594442\pi\)
−0.292364 + 0.956307i \(0.594442\pi\)
\(564\) 11.1205 0.468258
\(565\) −21.4770 −0.903543
\(566\) −32.4087 −1.36224
\(567\) 1.00000 0.0419961
\(568\) −35.6050 −1.49395
\(569\) 7.44608 0.312156 0.156078 0.987745i \(-0.450115\pi\)
0.156078 + 0.987745i \(0.450115\pi\)
\(570\) 2.72649 0.114200
\(571\) 24.7091 1.03404 0.517021 0.855973i \(-0.327041\pi\)
0.517021 + 0.855973i \(0.327041\pi\)
\(572\) 0 0
\(573\) 20.6851 0.864131
\(574\) −12.2543 −0.511486
\(575\) −17.2414 −0.719018
\(576\) −12.7147 −0.529781
\(577\) −26.2593 −1.09319 −0.546595 0.837397i \(-0.684076\pi\)
−0.546595 + 0.837397i \(0.684076\pi\)
\(578\) 37.2400 1.54898
\(579\) −2.88929 −0.120075
\(580\) 15.7272 0.653037
\(581\) −7.70243 −0.319551
\(582\) −9.08487 −0.376580
\(583\) −0.539233 −0.0223328
\(584\) 40.8006 1.68834
\(585\) 0 0
\(586\) −36.7135 −1.51662
\(587\) −36.7338 −1.51617 −0.758084 0.652157i \(-0.773864\pi\)
−0.758084 + 0.652157i \(0.773864\pi\)
\(588\) −3.34288 −0.137858
\(589\) −4.51506 −0.186040
\(590\) 34.8626 1.43527
\(591\) −3.01713 −0.124108
\(592\) 0.381909 0.0156964
\(593\) 8.94989 0.367528 0.183764 0.982970i \(-0.441172\pi\)
0.183764 + 0.982970i \(0.441172\pi\)
\(594\) −0.130824 −0.00536776
\(595\) 8.40417 0.344537
\(596\) −7.06511 −0.289398
\(597\) −24.5542 −1.00494
\(598\) 0 0
\(599\) −32.4529 −1.32599 −0.662995 0.748624i \(-0.730715\pi\)
−0.662995 + 0.748624i \(0.730715\pi\)
\(600\) 8.89879 0.363292
\(601\) −30.4411 −1.24172 −0.620859 0.783922i \(-0.713216\pi\)
−0.620859 + 0.783922i \(0.713216\pi\)
\(602\) 5.50631 0.224420
\(603\) 7.80744 0.317943
\(604\) −57.5760 −2.34273
\(605\) −16.0611 −0.652976
\(606\) −15.6213 −0.634572
\(607\) −18.0074 −0.730899 −0.365449 0.930831i \(-0.619085\pi\)
−0.365449 + 0.930831i \(0.619085\pi\)
\(608\) 4.10074 0.166307
\(609\) −3.22124 −0.130531
\(610\) 29.9865 1.21412
\(611\) 0 0
\(612\) 19.2356 0.777554
\(613\) 43.6064 1.76125 0.880623 0.473817i \(-0.157124\pi\)
0.880623 + 0.473817i \(0.157124\pi\)
\(614\) 28.6607 1.15665
\(615\) 7.74302 0.312229
\(616\) 0.175680 0.00707834
\(617\) 11.4509 0.460997 0.230499 0.973073i \(-0.425964\pi\)
0.230499 + 0.973073i \(0.425964\pi\)
\(618\) 28.6813 1.15373
\(619\) 33.0974 1.33030 0.665148 0.746712i \(-0.268369\pi\)
0.665148 + 0.746712i \(0.268369\pi\)
\(620\) 27.2952 1.09620
\(621\) −6.01403 −0.241335
\(622\) 16.5876 0.665103
\(623\) 8.12369 0.325469
\(624\) 0 0
\(625\) −2.44672 −0.0978689
\(626\) −50.5292 −2.01955
\(627\) 0.0457094 0.00182546
\(628\) −68.7729 −2.74434
\(629\) 4.49344 0.179165
\(630\) 3.37595 0.134501
\(631\) 5.34538 0.212796 0.106398 0.994324i \(-0.466068\pi\)
0.106398 + 0.994324i \(0.466068\pi\)
\(632\) 33.6987 1.34046
\(633\) −15.2596 −0.606517
\(634\) −60.7315 −2.41196
\(635\) −15.4670 −0.613789
\(636\) 31.8492 1.26290
\(637\) 0 0
\(638\) 0.421414 0.0166839
\(639\) −11.4706 −0.453771
\(640\) −28.0926 −1.11046
\(641\) −18.3832 −0.726091 −0.363046 0.931771i \(-0.618263\pi\)
−0.363046 + 0.931771i \(0.618263\pi\)
\(642\) −42.0181 −1.65832
\(643\) 3.77097 0.148712 0.0743562 0.997232i \(-0.476310\pi\)
0.0743562 + 0.997232i \(0.476310\pi\)
\(644\) 20.1042 0.792215
\(645\) −3.47922 −0.136994
\(646\) −10.7419 −0.422634
\(647\) −1.95293 −0.0767775 −0.0383888 0.999263i \(-0.512223\pi\)
−0.0383888 + 0.999263i \(0.512223\pi\)
\(648\) 3.10401 0.121937
\(649\) 0.584470 0.0229425
\(650\) 0 0
\(651\) −5.59058 −0.219112
\(652\) −29.3174 −1.14816
\(653\) 21.9347 0.858372 0.429186 0.903216i \(-0.358801\pi\)
0.429186 + 0.903216i \(0.358801\pi\)
\(654\) 21.0810 0.824333
\(655\) −13.6000 −0.531396
\(656\) −2.59280 −0.101232
\(657\) 13.1445 0.512815
\(658\) −7.68939 −0.299764
\(659\) 34.8515 1.35762 0.678812 0.734312i \(-0.262495\pi\)
0.678812 + 0.734312i \(0.262495\pi\)
\(660\) −0.276330 −0.0107561
\(661\) 30.3342 1.17986 0.589931 0.807454i \(-0.299155\pi\)
0.589931 + 0.807454i \(0.299155\pi\)
\(662\) −63.2966 −2.46009
\(663\) 0 0
\(664\) −23.9084 −0.927827
\(665\) −1.17955 −0.0457409
\(666\) 1.80501 0.0699429
\(667\) 19.3726 0.750111
\(668\) 56.6756 2.19285
\(669\) 3.41178 0.131907
\(670\) 26.3575 1.01828
\(671\) 0.502723 0.0194074
\(672\) 5.07756 0.195871
\(673\) 42.8800 1.65290 0.826451 0.563009i \(-0.190356\pi\)
0.826451 + 0.563009i \(0.190356\pi\)
\(674\) −46.3808 −1.78652
\(675\) 2.86687 0.110346
\(676\) 0 0
\(677\) −14.2890 −0.549171 −0.274586 0.961563i \(-0.588541\pi\)
−0.274586 + 0.961563i \(0.588541\pi\)
\(678\) 33.9900 1.30538
\(679\) 3.93035 0.150833
\(680\) 26.0866 1.00038
\(681\) 1.36962 0.0524838
\(682\) 0.731381 0.0280060
\(683\) −24.5455 −0.939209 −0.469604 0.882877i \(-0.655603\pi\)
−0.469604 + 0.882877i \(0.655603\pi\)
\(684\) −2.69977 −0.103228
\(685\) 5.99188 0.228938
\(686\) 2.31147 0.0882522
\(687\) 17.3194 0.660776
\(688\) 1.16504 0.0444166
\(689\) 0 0
\(690\) −20.3031 −0.772926
\(691\) −27.7763 −1.05666 −0.528331 0.849039i \(-0.677182\pi\)
−0.528331 + 0.849039i \(0.677182\pi\)
\(692\) 6.39620 0.243147
\(693\) 0.0565977 0.00214997
\(694\) 40.8561 1.55087
\(695\) 23.7706 0.901671
\(696\) −9.99875 −0.379002
\(697\) −30.5062 −1.15550
\(698\) −27.3054 −1.03352
\(699\) −5.77054 −0.218262
\(700\) −9.58358 −0.362225
\(701\) 37.2216 1.40584 0.702921 0.711268i \(-0.251879\pi\)
0.702921 + 0.711268i \(0.251879\pi\)
\(702\) 0 0
\(703\) −0.630667 −0.0237860
\(704\) −0.719625 −0.0271219
\(705\) 4.85863 0.182986
\(706\) −66.8743 −2.51685
\(707\) 6.75818 0.254168
\(708\) −34.5210 −1.29738
\(709\) 40.3434 1.51513 0.757564 0.652760i \(-0.226389\pi\)
0.757564 + 0.652760i \(0.226389\pi\)
\(710\) −38.7243 −1.45330
\(711\) 10.8565 0.407151
\(712\) 25.2160 0.945010
\(713\) 33.6220 1.25915
\(714\) −13.3007 −0.497765
\(715\) 0 0
\(716\) −87.3293 −3.26365
\(717\) 2.80755 0.104850
\(718\) 3.92347 0.146423
\(719\) −5.37519 −0.200461 −0.100230 0.994964i \(-0.531958\pi\)
−0.100230 + 0.994964i \(0.531958\pi\)
\(720\) 0.714292 0.0266201
\(721\) −12.4083 −0.462108
\(722\) −42.4102 −1.57834
\(723\) 7.55528 0.280984
\(724\) −6.61924 −0.246002
\(725\) −9.23486 −0.342974
\(726\) 25.4187 0.943377
\(727\) −9.42472 −0.349544 −0.174772 0.984609i \(-0.555919\pi\)
−0.174772 + 0.984609i \(0.555919\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 44.3752 1.64240
\(731\) 13.7075 0.506991
\(732\) −29.6927 −1.09747
\(733\) −33.3006 −1.22999 −0.614994 0.788532i \(-0.710841\pi\)
−0.614994 + 0.788532i \(0.710841\pi\)
\(734\) −71.5983 −2.64274
\(735\) −1.46052 −0.0538723
\(736\) −30.5366 −1.12560
\(737\) 0.441883 0.0162770
\(738\) −12.2543 −0.451088
\(739\) −34.6898 −1.27608 −0.638042 0.770001i \(-0.720256\pi\)
−0.638042 + 0.770001i \(0.720256\pi\)
\(740\) 3.81261 0.140154
\(741\) 0 0
\(742\) −22.0224 −0.808469
\(743\) 29.0170 1.06453 0.532264 0.846578i \(-0.321341\pi\)
0.532264 + 0.846578i \(0.321341\pi\)
\(744\) −17.3532 −0.636200
\(745\) −3.08679 −0.113091
\(746\) −24.6881 −0.903895
\(747\) −7.70243 −0.281817
\(748\) 1.08869 0.0398065
\(749\) 18.1781 0.664214
\(750\) 26.5582 0.969767
\(751\) −22.3606 −0.815949 −0.407974 0.912993i \(-0.633765\pi\)
−0.407974 + 0.912993i \(0.633765\pi\)
\(752\) −1.62694 −0.0593284
\(753\) −26.2186 −0.955460
\(754\) 0 0
\(755\) −25.1553 −0.915497
\(756\) −3.34288 −0.121579
\(757\) −41.1339 −1.49504 −0.747519 0.664240i \(-0.768755\pi\)
−0.747519 + 0.664240i \(0.768755\pi\)
\(758\) −65.0102 −2.36128
\(759\) −0.340380 −0.0123550
\(760\) −3.66133 −0.132810
\(761\) 34.0410 1.23398 0.616992 0.786969i \(-0.288351\pi\)
0.616992 + 0.786969i \(0.288351\pi\)
\(762\) 24.4785 0.886763
\(763\) −9.12019 −0.330173
\(764\) −69.1476 −2.50167
\(765\) 8.40417 0.303853
\(766\) 28.3076 1.02280
\(767\) 0 0
\(768\) 19.0306 0.686707
\(769\) 50.1326 1.80783 0.903914 0.427714i \(-0.140681\pi\)
0.903914 + 0.427714i \(0.140681\pi\)
\(770\) 0.191071 0.00688573
\(771\) 3.58179 0.128995
\(772\) 9.65853 0.347618
\(773\) 10.6809 0.384167 0.192083 0.981379i \(-0.438476\pi\)
0.192083 + 0.981379i \(0.438476\pi\)
\(774\) 5.50631 0.197920
\(775\) −16.0275 −0.575724
\(776\) 12.1998 0.437949
\(777\) −0.780896 −0.0280145
\(778\) −31.5358 −1.13061
\(779\) 4.28162 0.153405
\(780\) 0 0
\(781\) −0.649211 −0.0232306
\(782\) 79.9907 2.86046
\(783\) −3.22124 −0.115118
\(784\) 0.489065 0.0174666
\(785\) −30.0473 −1.07244
\(786\) 21.5237 0.767727
\(787\) 8.44505 0.301033 0.150517 0.988607i \(-0.451906\pi\)
0.150517 + 0.988607i \(0.451906\pi\)
\(788\) 10.0859 0.359295
\(789\) −26.7600 −0.952681
\(790\) 36.6510 1.30399
\(791\) −14.7050 −0.522849
\(792\) 0.175680 0.00624251
\(793\) 0 0
\(794\) 28.7488 1.02026
\(795\) 13.9151 0.493518
\(796\) 82.0817 2.90931
\(797\) −8.37296 −0.296586 −0.148293 0.988944i \(-0.547378\pi\)
−0.148293 + 0.988944i \(0.547378\pi\)
\(798\) 1.86679 0.0660835
\(799\) −19.1421 −0.677201
\(800\) 14.5567 0.514657
\(801\) 8.12369 0.287036
\(802\) −57.8608 −2.04314
\(803\) 0.743948 0.0262534
\(804\) −26.0993 −0.920451
\(805\) 8.78364 0.309583
\(806\) 0 0
\(807\) −14.7193 −0.518145
\(808\) 20.9775 0.737985
\(809\) −4.04870 −0.142345 −0.0711723 0.997464i \(-0.522674\pi\)
−0.0711723 + 0.997464i \(0.522674\pi\)
\(810\) 3.37595 0.118619
\(811\) 40.7122 1.42960 0.714800 0.699329i \(-0.246518\pi\)
0.714800 + 0.699329i \(0.246518\pi\)
\(812\) 10.7682 0.377889
\(813\) −13.1874 −0.462501
\(814\) 0.102160 0.00358069
\(815\) −12.8090 −0.448678
\(816\) −2.81419 −0.0985162
\(817\) −1.92389 −0.0673083
\(818\) −81.7035 −2.85669
\(819\) 0 0
\(820\) −25.8840 −0.903907
\(821\) 15.5618 0.543110 0.271555 0.962423i \(-0.412462\pi\)
0.271555 + 0.962423i \(0.412462\pi\)
\(822\) −9.48291 −0.330755
\(823\) −4.81985 −0.168009 −0.0840046 0.996465i \(-0.526771\pi\)
−0.0840046 + 0.996465i \(0.526771\pi\)
\(824\) −38.5154 −1.34175
\(825\) 0.162258 0.00564910
\(826\) 23.8699 0.830541
\(827\) 3.38418 0.117680 0.0588398 0.998267i \(-0.481260\pi\)
0.0588398 + 0.998267i \(0.481260\pi\)
\(828\) 20.1042 0.698668
\(829\) −14.4519 −0.501937 −0.250968 0.967995i \(-0.580749\pi\)
−0.250968 + 0.967995i \(0.580749\pi\)
\(830\) −26.0031 −0.902579
\(831\) −21.5726 −0.748347
\(832\) 0 0
\(833\) 5.75421 0.199372
\(834\) −37.6200 −1.30268
\(835\) 24.7620 0.856923
\(836\) −0.152801 −0.00528473
\(837\) −5.59058 −0.193239
\(838\) 60.3257 2.08392
\(839\) 29.5887 1.02152 0.510758 0.859725i \(-0.329365\pi\)
0.510758 + 0.859725i \(0.329365\pi\)
\(840\) −4.53348 −0.156420
\(841\) −18.6236 −0.642194
\(842\) 1.07555 0.0370657
\(843\) 0.186485 0.00642289
\(844\) 51.0111 1.75587
\(845\) 0 0
\(846\) −7.68939 −0.264367
\(847\) −10.9968 −0.377854
\(848\) −4.65956 −0.160010
\(849\) 14.0208 0.481194
\(850\) −38.1313 −1.30789
\(851\) 4.69633 0.160988
\(852\) 38.3449 1.31367
\(853\) 30.7580 1.05313 0.526567 0.850134i \(-0.323479\pi\)
0.526567 + 0.850134i \(0.323479\pi\)
\(854\) 20.5313 0.702568
\(855\) −1.17955 −0.0403397
\(856\) 56.4251 1.92857
\(857\) −15.7106 −0.536663 −0.268331 0.963327i \(-0.586472\pi\)
−0.268331 + 0.963327i \(0.586472\pi\)
\(858\) 0 0
\(859\) −23.2361 −0.792807 −0.396403 0.918076i \(-0.629742\pi\)
−0.396403 + 0.918076i \(0.629742\pi\)
\(860\) 11.6306 0.396600
\(861\) 5.30154 0.180676
\(862\) −62.0556 −2.11362
\(863\) 29.7433 1.01247 0.506236 0.862395i \(-0.331036\pi\)
0.506236 + 0.862395i \(0.331036\pi\)
\(864\) 5.07756 0.172742
\(865\) 2.79454 0.0950174
\(866\) 66.6743 2.26568
\(867\) −16.1110 −0.547158
\(868\) 18.6886 0.634333
\(869\) 0.614453 0.0208439
\(870\) −10.8747 −0.368688
\(871\) 0 0
\(872\) −28.3092 −0.958670
\(873\) 3.93035 0.133022
\(874\) −11.2269 −0.379756
\(875\) −11.4898 −0.388425
\(876\) −43.9404 −1.48461
\(877\) −12.7398 −0.430193 −0.215097 0.976593i \(-0.569007\pi\)
−0.215097 + 0.976593i \(0.569007\pi\)
\(878\) −44.3763 −1.49763
\(879\) 15.8832 0.535727
\(880\) 0.0404273 0.00136280
\(881\) 10.9904 0.370277 0.185139 0.982712i \(-0.440727\pi\)
0.185139 + 0.982712i \(0.440727\pi\)
\(882\) 2.31147 0.0778311
\(883\) 8.60222 0.289488 0.144744 0.989469i \(-0.453764\pi\)
0.144744 + 0.989469i \(0.453764\pi\)
\(884\) 0 0
\(885\) −15.0825 −0.506991
\(886\) 55.2711 1.85687
\(887\) 21.0197 0.705773 0.352886 0.935666i \(-0.385200\pi\)
0.352886 + 0.935666i \(0.385200\pi\)
\(888\) −2.42391 −0.0813410
\(889\) −10.5900 −0.355178
\(890\) 27.4252 0.919295
\(891\) 0.0565977 0.00189609
\(892\) −11.4052 −0.381873
\(893\) 2.68665 0.0899054
\(894\) 4.88525 0.163387
\(895\) −38.1548 −1.27537
\(896\) −19.2346 −0.642582
\(897\) 0 0
\(898\) −73.6859 −2.45893
\(899\) 18.0086 0.600620
\(900\) −9.58358 −0.319453
\(901\) −54.8231 −1.82642
\(902\) −0.693566 −0.0230932
\(903\) −2.38217 −0.0792737
\(904\) −45.6444 −1.51811
\(905\) −2.89199 −0.0961329
\(906\) 39.8115 1.32265
\(907\) 4.64057 0.154087 0.0770437 0.997028i \(-0.475452\pi\)
0.0770437 + 0.997028i \(0.475452\pi\)
\(908\) −4.57845 −0.151941
\(909\) 6.75818 0.224155
\(910\) 0 0
\(911\) 32.2392 1.06813 0.534067 0.845442i \(-0.320663\pi\)
0.534067 + 0.845442i \(0.320663\pi\)
\(912\) 0.394979 0.0130790
\(913\) −0.435940 −0.0144275
\(914\) −72.7117 −2.40509
\(915\) −12.9729 −0.428872
\(916\) −57.8965 −1.91296
\(917\) −9.31173 −0.307500
\(918\) −13.3007 −0.438988
\(919\) 21.0489 0.694339 0.347169 0.937802i \(-0.387143\pi\)
0.347169 + 0.937802i \(0.387143\pi\)
\(920\) 27.2645 0.898885
\(921\) −12.3994 −0.408573
\(922\) −58.0683 −1.91238
\(923\) 0 0
\(924\) −0.189199 −0.00622419
\(925\) −2.23873 −0.0736088
\(926\) −47.2676 −1.55331
\(927\) −12.4083 −0.407541
\(928\) −16.3560 −0.536913
\(929\) −36.3949 −1.19408 −0.597038 0.802213i \(-0.703656\pi\)
−0.597038 + 0.802213i \(0.703656\pi\)
\(930\) −18.8735 −0.618888
\(931\) −0.807619 −0.0264687
\(932\) 19.2902 0.631871
\(933\) −7.17624 −0.234939
\(934\) 51.0246 1.66958
\(935\) 0.475657 0.0155556
\(936\) 0 0
\(937\) 23.6753 0.773438 0.386719 0.922198i \(-0.373608\pi\)
0.386719 + 0.922198i \(0.373608\pi\)
\(938\) 18.0466 0.589243
\(939\) 21.8602 0.713381
\(940\) −16.2418 −0.529748
\(941\) −15.2440 −0.496940 −0.248470 0.968640i \(-0.579928\pi\)
−0.248470 + 0.968640i \(0.579928\pi\)
\(942\) 47.5537 1.54938
\(943\) −31.8836 −1.03827
\(944\) 5.05045 0.164378
\(945\) −1.46052 −0.0475109
\(946\) 0.311644 0.0101324
\(947\) −5.38308 −0.174926 −0.0874632 0.996168i \(-0.527876\pi\)
−0.0874632 + 0.996168i \(0.527876\pi\)
\(948\) −36.2919 −1.17871
\(949\) 0 0
\(950\) 5.35183 0.173636
\(951\) 26.2740 0.851994
\(952\) 17.8611 0.578883
\(953\) 20.2342 0.655451 0.327725 0.944773i \(-0.393718\pi\)
0.327725 + 0.944773i \(0.393718\pi\)
\(954\) −22.0224 −0.713003
\(955\) −30.2110 −0.977606
\(956\) −9.38529 −0.303542
\(957\) −0.182315 −0.00589339
\(958\) −28.1014 −0.907916
\(959\) 4.10255 0.132478
\(960\) 18.5702 0.599351
\(961\) 0.254620 0.00821356
\(962\) 0 0
\(963\) 18.1781 0.585782
\(964\) −25.2564 −0.813453
\(965\) 4.21988 0.135843
\(966\) −13.9012 −0.447265
\(967\) −19.0150 −0.611482 −0.305741 0.952115i \(-0.598904\pi\)
−0.305741 + 0.952115i \(0.598904\pi\)
\(968\) −34.1342 −1.09711
\(969\) 4.64722 0.149290
\(970\) 13.2687 0.426031
\(971\) −25.4007 −0.815148 −0.407574 0.913172i \(-0.633625\pi\)
−0.407574 + 0.913172i \(0.633625\pi\)
\(972\) −3.34288 −0.107223
\(973\) 16.2754 0.521765
\(974\) −43.1497 −1.38261
\(975\) 0 0
\(976\) 4.34407 0.139050
\(977\) 18.9933 0.607650 0.303825 0.952728i \(-0.401736\pi\)
0.303825 + 0.952728i \(0.401736\pi\)
\(978\) 20.2718 0.648221
\(979\) 0.459782 0.0146947
\(980\) 4.88235 0.155961
\(981\) −9.12019 −0.291185
\(982\) 43.5785 1.39065
\(983\) 40.4777 1.29104 0.645519 0.763744i \(-0.276641\pi\)
0.645519 + 0.763744i \(0.276641\pi\)
\(984\) 16.4560 0.524599
\(985\) 4.40659 0.140406
\(986\) 42.8446 1.36445
\(987\) 3.32663 0.105888
\(988\) 0 0
\(989\) 14.3265 0.455555
\(990\) 0.191071 0.00607264
\(991\) 54.2021 1.72179 0.860893 0.508786i \(-0.169906\pi\)
0.860893 + 0.508786i \(0.169906\pi\)
\(992\) −28.3865 −0.901274
\(993\) 27.3837 0.868997
\(994\) −26.5140 −0.840972
\(995\) 35.8620 1.13690
\(996\) 25.7483 0.815865
\(997\) −36.0609 −1.14206 −0.571029 0.820930i \(-0.693456\pi\)
−0.571029 + 0.820930i \(0.693456\pi\)
\(998\) −54.9407 −1.73912
\(999\) −0.780896 −0.0247064
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 3549.2.a.be.1.9 9
13.12 even 2 3549.2.a.bf.1.1 yes 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3549.2.a.be.1.9 9 1.1 even 1 trivial
3549.2.a.bf.1.1 yes 9 13.12 even 2