Properties

Label 4030.2.a.c.1.2
Level $4030$
Weight $2$
Character 4030.1
Self dual yes
Analytic conductor $32.180$
Analytic rank $1$
Dimension $6$
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] = [4030,2,Mod(1,4030)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4030, 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("4030.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4030.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: \(32.1797120146\)
Analytic rank: \(1\)
Dimension: \(6\)
Coefficient field: 6.6.3081125.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} - 8x^{4} + 6x^{3} + 16x^{2} - 10x - 5 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.13283\) of defining polynomial
Character \(\chi\) \(=\) 4030.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.44295 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.44295 q^{6} -1.84953 q^{7} -1.00000 q^{8} -0.917908 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.44295 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.44295 q^{6} -1.84953 q^{7} -1.00000 q^{8} -0.917908 q^{9} +1.00000 q^{10} +2.03486 q^{11} -1.44295 q^{12} +1.00000 q^{13} +1.84953 q^{14} +1.44295 q^{15} +1.00000 q^{16} +4.02676 q^{17} +0.917908 q^{18} -3.37914 q^{19} -1.00000 q^{20} +2.66877 q^{21} -2.03486 q^{22} -4.58382 q^{23} +1.44295 q^{24} +1.00000 q^{25} -1.00000 q^{26} +5.65333 q^{27} -1.84953 q^{28} -5.94991 q^{29} -1.44295 q^{30} +1.00000 q^{31} -1.00000 q^{32} -2.93619 q^{33} -4.02676 q^{34} +1.84953 q^{35} -0.917908 q^{36} +5.74352 q^{37} +3.37914 q^{38} -1.44295 q^{39} +1.00000 q^{40} -3.43297 q^{41} -2.66877 q^{42} +3.71713 q^{43} +2.03486 q^{44} +0.917908 q^{45} +4.58382 q^{46} +10.4630 q^{47} -1.44295 q^{48} -3.57924 q^{49} -1.00000 q^{50} -5.81040 q^{51} +1.00000 q^{52} +5.37307 q^{53} -5.65333 q^{54} -2.03486 q^{55} +1.84953 q^{56} +4.87591 q^{57} +5.94991 q^{58} -4.54161 q^{59} +1.44295 q^{60} +1.05465 q^{61} -1.00000 q^{62} +1.69770 q^{63} +1.00000 q^{64} -1.00000 q^{65} +2.93619 q^{66} +7.49609 q^{67} +4.02676 q^{68} +6.61420 q^{69} -1.84953 q^{70} +4.90554 q^{71} +0.917908 q^{72} -9.06629 q^{73} -5.74352 q^{74} -1.44295 q^{75} -3.37914 q^{76} -3.76353 q^{77} +1.44295 q^{78} +11.0383 q^{79} -1.00000 q^{80} -5.40372 q^{81} +3.43297 q^{82} -3.39594 q^{83} +2.66877 q^{84} -4.02676 q^{85} -3.71713 q^{86} +8.58539 q^{87} -2.03486 q^{88} +9.80514 q^{89} -0.917908 q^{90} -1.84953 q^{91} -4.58382 q^{92} -1.44295 q^{93} -10.4630 q^{94} +3.37914 q^{95} +1.44295 q^{96} +6.54755 q^{97} +3.57924 q^{98} -1.86782 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} + 4 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} + 4 q^{7} - 6 q^{8} - q^{9} + 6 q^{10} - 6 q^{11} - q^{12} + 6 q^{13} - 4 q^{14} + q^{15} + 6 q^{16} - 4 q^{17} + q^{18} + 3 q^{19} - 6 q^{20} - q^{21} + 6 q^{22} - 7 q^{23} + q^{24} + 6 q^{25} - 6 q^{26} - q^{27} + 4 q^{28} - 14 q^{29} - q^{30} + 6 q^{31} - 6 q^{32} - 2 q^{33} + 4 q^{34} - 4 q^{35} - q^{36} + 14 q^{37} - 3 q^{38} - q^{39} + 6 q^{40} - 12 q^{41} + q^{42} + 3 q^{43} - 6 q^{44} + q^{45} + 7 q^{46} - 2 q^{47} - q^{48} - 6 q^{49} - 6 q^{50} - 7 q^{51} + 6 q^{52} - 4 q^{53} + q^{54} + 6 q^{55} - 4 q^{56} + 13 q^{57} + 14 q^{58} - 17 q^{59} + q^{60} - 5 q^{61} - 6 q^{62} - q^{63} + 6 q^{64} - 6 q^{65} + 2 q^{66} + 8 q^{67} - 4 q^{68} - 8 q^{69} + 4 q^{70} - 16 q^{71} + q^{72} + 11 q^{73} - 14 q^{74} - q^{75} + 3 q^{76} - 15 q^{77} + q^{78} - 2 q^{79} - 6 q^{80} - 26 q^{81} + 12 q^{82} + 4 q^{83} - q^{84} + 4 q^{85} - 3 q^{86} + 7 q^{87} + 6 q^{88} - 8 q^{89} - q^{90} + 4 q^{91} - 7 q^{92} - q^{93} + 2 q^{94} - 3 q^{95} + q^{96} + 5 q^{97} + 6 q^{98} + 15 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.44295 −0.833085 −0.416543 0.909116i \(-0.636758\pi\)
−0.416543 + 0.909116i \(0.636758\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.44295 0.589080
\(7\) −1.84953 −0.699056 −0.349528 0.936926i \(-0.613658\pi\)
−0.349528 + 0.936926i \(0.613658\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.917908 −0.305969
\(10\) 1.00000 0.316228
\(11\) 2.03486 0.613534 0.306767 0.951785i \(-0.400753\pi\)
0.306767 + 0.951785i \(0.400753\pi\)
\(12\) −1.44295 −0.416543
\(13\) 1.00000 0.277350
\(14\) 1.84953 0.494307
\(15\) 1.44295 0.372567
\(16\) 1.00000 0.250000
\(17\) 4.02676 0.976633 0.488317 0.872667i \(-0.337611\pi\)
0.488317 + 0.872667i \(0.337611\pi\)
\(18\) 0.917908 0.216353
\(19\) −3.37914 −0.775228 −0.387614 0.921822i \(-0.626701\pi\)
−0.387614 + 0.921822i \(0.626701\pi\)
\(20\) −1.00000 −0.223607
\(21\) 2.66877 0.582373
\(22\) −2.03486 −0.433834
\(23\) −4.58382 −0.955792 −0.477896 0.878417i \(-0.658600\pi\)
−0.477896 + 0.878417i \(0.658600\pi\)
\(24\) 1.44295 0.294540
\(25\) 1.00000 0.200000
\(26\) −1.00000 −0.196116
\(27\) 5.65333 1.08798
\(28\) −1.84953 −0.349528
\(29\) −5.94991 −1.10487 −0.552435 0.833556i \(-0.686301\pi\)
−0.552435 + 0.833556i \(0.686301\pi\)
\(30\) −1.44295 −0.263445
\(31\) 1.00000 0.179605
\(32\) −1.00000 −0.176777
\(33\) −2.93619 −0.511126
\(34\) −4.02676 −0.690584
\(35\) 1.84953 0.312627
\(36\) −0.917908 −0.152985
\(37\) 5.74352 0.944229 0.472114 0.881537i \(-0.343491\pi\)
0.472114 + 0.881537i \(0.343491\pi\)
\(38\) 3.37914 0.548169
\(39\) −1.44295 −0.231056
\(40\) 1.00000 0.158114
\(41\) −3.43297 −0.536140 −0.268070 0.963399i \(-0.586386\pi\)
−0.268070 + 0.963399i \(0.586386\pi\)
\(42\) −2.66877 −0.411800
\(43\) 3.71713 0.566858 0.283429 0.958993i \(-0.408528\pi\)
0.283429 + 0.958993i \(0.408528\pi\)
\(44\) 2.03486 0.306767
\(45\) 0.917908 0.136834
\(46\) 4.58382 0.675847
\(47\) 10.4630 1.52618 0.763090 0.646292i \(-0.223681\pi\)
0.763090 + 0.646292i \(0.223681\pi\)
\(48\) −1.44295 −0.208271
\(49\) −3.57924 −0.511320
\(50\) −1.00000 −0.141421
\(51\) −5.81040 −0.813618
\(52\) 1.00000 0.138675
\(53\) 5.37307 0.738047 0.369024 0.929420i \(-0.379692\pi\)
0.369024 + 0.929420i \(0.379692\pi\)
\(54\) −5.65333 −0.769321
\(55\) −2.03486 −0.274381
\(56\) 1.84953 0.247154
\(57\) 4.87591 0.645831
\(58\) 5.94991 0.781261
\(59\) −4.54161 −0.591268 −0.295634 0.955301i \(-0.595531\pi\)
−0.295634 + 0.955301i \(0.595531\pi\)
\(60\) 1.44295 0.186283
\(61\) 1.05465 0.135034 0.0675170 0.997718i \(-0.478492\pi\)
0.0675170 + 0.997718i \(0.478492\pi\)
\(62\) −1.00000 −0.127000
\(63\) 1.69770 0.213890
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) 2.93619 0.361421
\(67\) 7.49609 0.915794 0.457897 0.889005i \(-0.348603\pi\)
0.457897 + 0.889005i \(0.348603\pi\)
\(68\) 4.02676 0.488317
\(69\) 6.61420 0.796256
\(70\) −1.84953 −0.221061
\(71\) 4.90554 0.582180 0.291090 0.956696i \(-0.405982\pi\)
0.291090 + 0.956696i \(0.405982\pi\)
\(72\) 0.917908 0.108176
\(73\) −9.06629 −1.06113 −0.530564 0.847645i \(-0.678020\pi\)
−0.530564 + 0.847645i \(0.678020\pi\)
\(74\) −5.74352 −0.667671
\(75\) −1.44295 −0.166617
\(76\) −3.37914 −0.387614
\(77\) −3.76353 −0.428895
\(78\) 1.44295 0.163381
\(79\) 11.0383 1.24191 0.620953 0.783848i \(-0.286746\pi\)
0.620953 + 0.783848i \(0.286746\pi\)
\(80\) −1.00000 −0.111803
\(81\) −5.40372 −0.600413
\(82\) 3.43297 0.379108
\(83\) −3.39594 −0.372753 −0.186377 0.982478i \(-0.559674\pi\)
−0.186377 + 0.982478i \(0.559674\pi\)
\(84\) 2.66877 0.291187
\(85\) −4.02676 −0.436764
\(86\) −3.71713 −0.400829
\(87\) 8.58539 0.920451
\(88\) −2.03486 −0.216917
\(89\) 9.80514 1.03934 0.519672 0.854366i \(-0.326054\pi\)
0.519672 + 0.854366i \(0.326054\pi\)
\(90\) −0.917908 −0.0967560
\(91\) −1.84953 −0.193883
\(92\) −4.58382 −0.477896
\(93\) −1.44295 −0.149626
\(94\) −10.4630 −1.07917
\(95\) 3.37914 0.346692
\(96\) 1.44295 0.147270
\(97\) 6.54755 0.664803 0.332401 0.943138i \(-0.392141\pi\)
0.332401 + 0.943138i \(0.392141\pi\)
\(98\) 3.57924 0.361558
\(99\) −1.86782 −0.187722
\(100\) 1.00000 0.100000
\(101\) −8.77067 −0.872715 −0.436357 0.899773i \(-0.643732\pi\)
−0.436357 + 0.899773i \(0.643732\pi\)
\(102\) 5.81040 0.575315
\(103\) 8.52722 0.840212 0.420106 0.907475i \(-0.361993\pi\)
0.420106 + 0.907475i \(0.361993\pi\)
\(104\) −1.00000 −0.0980581
\(105\) −2.66877 −0.260445
\(106\) −5.37307 −0.521878
\(107\) 7.04378 0.680948 0.340474 0.940254i \(-0.389412\pi\)
0.340474 + 0.940254i \(0.389412\pi\)
\(108\) 5.65333 0.543992
\(109\) −16.2833 −1.55965 −0.779827 0.625995i \(-0.784693\pi\)
−0.779827 + 0.625995i \(0.784693\pi\)
\(110\) 2.03486 0.194016
\(111\) −8.28759 −0.786623
\(112\) −1.84953 −0.174764
\(113\) −1.74246 −0.163917 −0.0819584 0.996636i \(-0.526117\pi\)
−0.0819584 + 0.996636i \(0.526117\pi\)
\(114\) −4.87591 −0.456671
\(115\) 4.58382 0.427443
\(116\) −5.94991 −0.552435
\(117\) −0.917908 −0.0848606
\(118\) 4.54161 0.418089
\(119\) −7.44761 −0.682721
\(120\) −1.44295 −0.131722
\(121\) −6.85934 −0.623576
\(122\) −1.05465 −0.0954834
\(123\) 4.95359 0.446650
\(124\) 1.00000 0.0898027
\(125\) −1.00000 −0.0894427
\(126\) −1.69770 −0.151243
\(127\) −10.2278 −0.907574 −0.453787 0.891110i \(-0.649927\pi\)
−0.453787 + 0.891110i \(0.649927\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −5.36362 −0.472241
\(130\) 1.00000 0.0877058
\(131\) −11.6099 −1.01436 −0.507179 0.861841i \(-0.669312\pi\)
−0.507179 + 0.861841i \(0.669312\pi\)
\(132\) −2.93619 −0.255563
\(133\) 6.24982 0.541928
\(134\) −7.49609 −0.647564
\(135\) −5.65333 −0.486561
\(136\) −4.02676 −0.345292
\(137\) 0.710019 0.0606611 0.0303305 0.999540i \(-0.490344\pi\)
0.0303305 + 0.999540i \(0.490344\pi\)
\(138\) −6.61420 −0.563038
\(139\) 10.5855 0.897849 0.448924 0.893570i \(-0.351807\pi\)
0.448924 + 0.893570i \(0.351807\pi\)
\(140\) 1.84953 0.156314
\(141\) −15.0975 −1.27144
\(142\) −4.90554 −0.411664
\(143\) 2.03486 0.170164
\(144\) −0.917908 −0.0764923
\(145\) 5.94991 0.494113
\(146\) 9.06629 0.750331
\(147\) 5.16465 0.425973
\(148\) 5.74352 0.472114
\(149\) −3.46476 −0.283844 −0.141922 0.989878i \(-0.545328\pi\)
−0.141922 + 0.989878i \(0.545328\pi\)
\(150\) 1.44295 0.117816
\(151\) −8.55602 −0.696279 −0.348140 0.937443i \(-0.613186\pi\)
−0.348140 + 0.937443i \(0.613186\pi\)
\(152\) 3.37914 0.274084
\(153\) −3.69620 −0.298820
\(154\) 3.76353 0.303274
\(155\) −1.00000 −0.0803219
\(156\) −1.44295 −0.115528
\(157\) −2.04229 −0.162992 −0.0814962 0.996674i \(-0.525970\pi\)
−0.0814962 + 0.996674i \(0.525970\pi\)
\(158\) −11.0383 −0.878161
\(159\) −7.75304 −0.614856
\(160\) 1.00000 0.0790569
\(161\) 8.47790 0.668152
\(162\) 5.40372 0.424556
\(163\) 0.325069 0.0254614 0.0127307 0.999919i \(-0.495948\pi\)
0.0127307 + 0.999919i \(0.495948\pi\)
\(164\) −3.43297 −0.268070
\(165\) 2.93619 0.228582
\(166\) 3.39594 0.263576
\(167\) −10.3504 −0.800940 −0.400470 0.916310i \(-0.631153\pi\)
−0.400470 + 0.916310i \(0.631153\pi\)
\(168\) −2.66877 −0.205900
\(169\) 1.00000 0.0769231
\(170\) 4.02676 0.308839
\(171\) 3.10174 0.237196
\(172\) 3.71713 0.283429
\(173\) −16.0351 −1.21913 −0.609563 0.792738i \(-0.708655\pi\)
−0.609563 + 0.792738i \(0.708655\pi\)
\(174\) −8.58539 −0.650857
\(175\) −1.84953 −0.139811
\(176\) 2.03486 0.153383
\(177\) 6.55330 0.492576
\(178\) −9.80514 −0.734927
\(179\) −1.57100 −0.117422 −0.0587111 0.998275i \(-0.518699\pi\)
−0.0587111 + 0.998275i \(0.518699\pi\)
\(180\) 0.917908 0.0684168
\(181\) 0.634377 0.0471529 0.0235764 0.999722i \(-0.492495\pi\)
0.0235764 + 0.999722i \(0.492495\pi\)
\(182\) 1.84953 0.137096
\(183\) −1.52180 −0.112495
\(184\) 4.58382 0.337923
\(185\) −5.74352 −0.422272
\(186\) 1.44295 0.105802
\(187\) 8.19390 0.599197
\(188\) 10.4630 0.763090
\(189\) −10.4560 −0.760562
\(190\) −3.37914 −0.245149
\(191\) −17.6588 −1.27774 −0.638872 0.769313i \(-0.720599\pi\)
−0.638872 + 0.769313i \(0.720599\pi\)
\(192\) −1.44295 −0.104136
\(193\) 6.30028 0.453504 0.226752 0.973952i \(-0.427189\pi\)
0.226752 + 0.973952i \(0.427189\pi\)
\(194\) −6.54755 −0.470086
\(195\) 1.44295 0.103331
\(196\) −3.57924 −0.255660
\(197\) 17.0669 1.21596 0.607982 0.793951i \(-0.291979\pi\)
0.607982 + 0.793951i \(0.291979\pi\)
\(198\) 1.86782 0.132740
\(199\) −9.09507 −0.644732 −0.322366 0.946615i \(-0.604478\pi\)
−0.322366 + 0.946615i \(0.604478\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −10.8165 −0.762934
\(202\) 8.77067 0.617102
\(203\) 11.0045 0.772366
\(204\) −5.81040 −0.406809
\(205\) 3.43297 0.239769
\(206\) −8.52722 −0.594119
\(207\) 4.20752 0.292443
\(208\) 1.00000 0.0693375
\(209\) −6.87608 −0.475628
\(210\) 2.66877 0.184163
\(211\) −6.77778 −0.466601 −0.233301 0.972405i \(-0.574953\pi\)
−0.233301 + 0.972405i \(0.574953\pi\)
\(212\) 5.37307 0.369024
\(213\) −7.07842 −0.485006
\(214\) −7.04378 −0.481503
\(215\) −3.71713 −0.253506
\(216\) −5.65333 −0.384660
\(217\) −1.84953 −0.125554
\(218\) 16.2833 1.10284
\(219\) 13.0822 0.884011
\(220\) −2.03486 −0.137190
\(221\) 4.02676 0.270869
\(222\) 8.28759 0.556226
\(223\) −9.58886 −0.642117 −0.321059 0.947059i \(-0.604039\pi\)
−0.321059 + 0.947059i \(0.604039\pi\)
\(224\) 1.84953 0.123577
\(225\) −0.917908 −0.0611939
\(226\) 1.74246 0.115907
\(227\) −8.92629 −0.592459 −0.296229 0.955117i \(-0.595729\pi\)
−0.296229 + 0.955117i \(0.595729\pi\)
\(228\) 4.87591 0.322915
\(229\) 15.4671 1.02210 0.511048 0.859552i \(-0.329257\pi\)
0.511048 + 0.859552i \(0.329257\pi\)
\(230\) −4.58382 −0.302248
\(231\) 5.43058 0.357306
\(232\) 5.94991 0.390631
\(233\) −3.49932 −0.229248 −0.114624 0.993409i \(-0.536566\pi\)
−0.114624 + 0.993409i \(0.536566\pi\)
\(234\) 0.917908 0.0600055
\(235\) −10.4630 −0.682529
\(236\) −4.54161 −0.295634
\(237\) −15.9277 −1.03461
\(238\) 7.44761 0.482757
\(239\) 28.4119 1.83781 0.918907 0.394474i \(-0.129073\pi\)
0.918907 + 0.394474i \(0.129073\pi\)
\(240\) 1.44295 0.0931417
\(241\) −9.81549 −0.632271 −0.316136 0.948714i \(-0.602385\pi\)
−0.316136 + 0.948714i \(0.602385\pi\)
\(242\) 6.85934 0.440935
\(243\) −9.16271 −0.587788
\(244\) 1.05465 0.0675170
\(245\) 3.57924 0.228669
\(246\) −4.95359 −0.315829
\(247\) −3.37914 −0.215010
\(248\) −1.00000 −0.0635001
\(249\) 4.90016 0.310535
\(250\) 1.00000 0.0632456
\(251\) 22.5522 1.42348 0.711741 0.702442i \(-0.247907\pi\)
0.711741 + 0.702442i \(0.247907\pi\)
\(252\) 1.69770 0.106945
\(253\) −9.32743 −0.586410
\(254\) 10.2278 0.641752
\(255\) 5.81040 0.363861
\(256\) 1.00000 0.0625000
\(257\) −19.3964 −1.20991 −0.604957 0.796258i \(-0.706810\pi\)
−0.604957 + 0.796258i \(0.706810\pi\)
\(258\) 5.36362 0.333925
\(259\) −10.6228 −0.660069
\(260\) −1.00000 −0.0620174
\(261\) 5.46147 0.338056
\(262\) 11.6099 0.717259
\(263\) −19.4265 −1.19789 −0.598944 0.800791i \(-0.704413\pi\)
−0.598944 + 0.800791i \(0.704413\pi\)
\(264\) 2.93619 0.180710
\(265\) −5.37307 −0.330065
\(266\) −6.24982 −0.383201
\(267\) −14.1483 −0.865861
\(268\) 7.49609 0.457897
\(269\) −17.4915 −1.06647 −0.533237 0.845966i \(-0.679024\pi\)
−0.533237 + 0.845966i \(0.679024\pi\)
\(270\) 5.65333 0.344051
\(271\) 23.9044 1.45209 0.726045 0.687647i \(-0.241356\pi\)
0.726045 + 0.687647i \(0.241356\pi\)
\(272\) 4.02676 0.244158
\(273\) 2.66877 0.161521
\(274\) −0.710019 −0.0428938
\(275\) 2.03486 0.122707
\(276\) 6.61420 0.398128
\(277\) −9.54560 −0.573539 −0.286770 0.958000i \(-0.592581\pi\)
−0.286770 + 0.958000i \(0.592581\pi\)
\(278\) −10.5855 −0.634875
\(279\) −0.917908 −0.0549537
\(280\) −1.84953 −0.110530
\(281\) −19.3263 −1.15291 −0.576455 0.817129i \(-0.695564\pi\)
−0.576455 + 0.817129i \(0.695564\pi\)
\(282\) 15.0975 0.899043
\(283\) −10.1976 −0.606187 −0.303093 0.952961i \(-0.598019\pi\)
−0.303093 + 0.952961i \(0.598019\pi\)
\(284\) 4.90554 0.291090
\(285\) −4.87591 −0.288824
\(286\) −2.03486 −0.120324
\(287\) 6.34938 0.374792
\(288\) 0.917908 0.0540882
\(289\) −0.785193 −0.0461878
\(290\) −5.94991 −0.349391
\(291\) −9.44775 −0.553837
\(292\) −9.06629 −0.530564
\(293\) −25.4078 −1.48434 −0.742170 0.670212i \(-0.766203\pi\)
−0.742170 + 0.670212i \(0.766203\pi\)
\(294\) −5.16465 −0.301209
\(295\) 4.54161 0.264423
\(296\) −5.74352 −0.333835
\(297\) 11.5037 0.667515
\(298\) 3.46476 0.200708
\(299\) −4.58382 −0.265089
\(300\) −1.44295 −0.0833085
\(301\) −6.87495 −0.396265
\(302\) 8.55602 0.492344
\(303\) 12.6556 0.727046
\(304\) −3.37914 −0.193807
\(305\) −1.05465 −0.0603890
\(306\) 3.69620 0.211297
\(307\) −31.0455 −1.77186 −0.885929 0.463821i \(-0.846478\pi\)
−0.885929 + 0.463821i \(0.846478\pi\)
\(308\) −3.76353 −0.214447
\(309\) −12.3043 −0.699968
\(310\) 1.00000 0.0567962
\(311\) −11.0997 −0.629408 −0.314704 0.949190i \(-0.601905\pi\)
−0.314704 + 0.949190i \(0.601905\pi\)
\(312\) 1.44295 0.0816907
\(313\) 28.4814 1.60986 0.804932 0.593367i \(-0.202202\pi\)
0.804932 + 0.593367i \(0.202202\pi\)
\(314\) 2.04229 0.115253
\(315\) −1.69770 −0.0956544
\(316\) 11.0383 0.620953
\(317\) 13.5242 0.759597 0.379798 0.925069i \(-0.375993\pi\)
0.379798 + 0.925069i \(0.375993\pi\)
\(318\) 7.75304 0.434769
\(319\) −12.1072 −0.677875
\(320\) −1.00000 −0.0559017
\(321\) −10.1638 −0.567288
\(322\) −8.47790 −0.472455
\(323\) −13.6070 −0.757113
\(324\) −5.40372 −0.300207
\(325\) 1.00000 0.0554700
\(326\) −0.325069 −0.0180039
\(327\) 23.4959 1.29932
\(328\) 3.43297 0.189554
\(329\) −19.3516 −1.06689
\(330\) −2.93619 −0.161632
\(331\) 21.5750 1.18587 0.592936 0.805250i \(-0.297969\pi\)
0.592936 + 0.805250i \(0.297969\pi\)
\(332\) −3.39594 −0.186377
\(333\) −5.27202 −0.288905
\(334\) 10.3504 0.566350
\(335\) −7.49609 −0.409555
\(336\) 2.66877 0.145593
\(337\) −10.5216 −0.573148 −0.286574 0.958058i \(-0.592516\pi\)
−0.286574 + 0.958058i \(0.592516\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 2.51427 0.136557
\(340\) −4.02676 −0.218382
\(341\) 2.03486 0.110194
\(342\) −3.10174 −0.167723
\(343\) 19.5666 1.05650
\(344\) −3.71713 −0.200414
\(345\) −6.61420 −0.356096
\(346\) 16.0351 0.862052
\(347\) −31.3970 −1.68548 −0.842741 0.538320i \(-0.819059\pi\)
−0.842741 + 0.538320i \(0.819059\pi\)
\(348\) 8.58539 0.460225
\(349\) −12.0383 −0.644394 −0.322197 0.946673i \(-0.604421\pi\)
−0.322197 + 0.946673i \(0.604421\pi\)
\(350\) 1.84953 0.0988615
\(351\) 5.65333 0.301752
\(352\) −2.03486 −0.108458
\(353\) −13.7981 −0.734397 −0.367199 0.930143i \(-0.619683\pi\)
−0.367199 + 0.930143i \(0.619683\pi\)
\(354\) −6.55330 −0.348304
\(355\) −4.90554 −0.260359
\(356\) 9.80514 0.519672
\(357\) 10.7465 0.568765
\(358\) 1.57100 0.0830300
\(359\) −21.0996 −1.11359 −0.556796 0.830649i \(-0.687969\pi\)
−0.556796 + 0.830649i \(0.687969\pi\)
\(360\) −0.917908 −0.0483780
\(361\) −7.58141 −0.399022
\(362\) −0.634377 −0.0333421
\(363\) 9.89765 0.519492
\(364\) −1.84953 −0.0969417
\(365\) 9.06629 0.474551
\(366\) 1.52180 0.0795458
\(367\) 26.5184 1.38425 0.692124 0.721778i \(-0.256675\pi\)
0.692124 + 0.721778i \(0.256675\pi\)
\(368\) −4.58382 −0.238948
\(369\) 3.15115 0.164042
\(370\) 5.74352 0.298591
\(371\) −9.93764 −0.515937
\(372\) −1.44295 −0.0748132
\(373\) −4.72751 −0.244781 −0.122391 0.992482i \(-0.539056\pi\)
−0.122391 + 0.992482i \(0.539056\pi\)
\(374\) −8.19390 −0.423697
\(375\) 1.44295 0.0745134
\(376\) −10.4630 −0.539586
\(377\) −5.94991 −0.306436
\(378\) 10.4560 0.537798
\(379\) −21.7669 −1.11809 −0.559046 0.829137i \(-0.688833\pi\)
−0.559046 + 0.829137i \(0.688833\pi\)
\(380\) 3.37914 0.173346
\(381\) 14.7582 0.756086
\(382\) 17.6588 0.903502
\(383\) 11.2822 0.576491 0.288246 0.957557i \(-0.406928\pi\)
0.288246 + 0.957557i \(0.406928\pi\)
\(384\) 1.44295 0.0736350
\(385\) 3.76353 0.191807
\(386\) −6.30028 −0.320676
\(387\) −3.41199 −0.173441
\(388\) 6.54755 0.332401
\(389\) −14.1684 −0.718367 −0.359183 0.933267i \(-0.616945\pi\)
−0.359183 + 0.933267i \(0.616945\pi\)
\(390\) −1.44295 −0.0730664
\(391\) −18.4579 −0.933458
\(392\) 3.57924 0.180779
\(393\) 16.7524 0.845046
\(394\) −17.0669 −0.859817
\(395\) −11.0383 −0.555398
\(396\) −1.86782 −0.0938612
\(397\) 12.1144 0.608006 0.304003 0.952671i \(-0.401677\pi\)
0.304003 + 0.952671i \(0.401677\pi\)
\(398\) 9.09507 0.455895
\(399\) −9.01815 −0.451472
\(400\) 1.00000 0.0500000
\(401\) −31.4824 −1.57216 −0.786079 0.618126i \(-0.787892\pi\)
−0.786079 + 0.618126i \(0.787892\pi\)
\(402\) 10.8165 0.539476
\(403\) 1.00000 0.0498135
\(404\) −8.77067 −0.436357
\(405\) 5.40372 0.268513
\(406\) −11.0045 −0.546145
\(407\) 11.6873 0.579316
\(408\) 5.81040 0.287658
\(409\) −27.9065 −1.37989 −0.689944 0.723863i \(-0.742365\pi\)
−0.689944 + 0.723863i \(0.742365\pi\)
\(410\) −3.43297 −0.169542
\(411\) −1.02452 −0.0505358
\(412\) 8.52722 0.420106
\(413\) 8.39984 0.413329
\(414\) −4.20752 −0.206788
\(415\) 3.39594 0.166700
\(416\) −1.00000 −0.0490290
\(417\) −15.2743 −0.747984
\(418\) 6.87608 0.336320
\(419\) 6.49496 0.317300 0.158650 0.987335i \(-0.449286\pi\)
0.158650 + 0.987335i \(0.449286\pi\)
\(420\) −2.66877 −0.130223
\(421\) −15.8856 −0.774218 −0.387109 0.922034i \(-0.626526\pi\)
−0.387109 + 0.922034i \(0.626526\pi\)
\(422\) 6.77778 0.329937
\(423\) −9.60404 −0.466964
\(424\) −5.37307 −0.260939
\(425\) 4.02676 0.195327
\(426\) 7.07842 0.342951
\(427\) −1.95060 −0.0943963
\(428\) 7.04378 0.340474
\(429\) −2.93619 −0.141761
\(430\) 3.71713 0.179256
\(431\) −24.8265 −1.19585 −0.597924 0.801553i \(-0.704008\pi\)
−0.597924 + 0.801553i \(0.704008\pi\)
\(432\) 5.65333 0.271996
\(433\) 16.9214 0.813190 0.406595 0.913609i \(-0.366716\pi\)
0.406595 + 0.913609i \(0.366716\pi\)
\(434\) 1.84953 0.0887802
\(435\) −8.58539 −0.411638
\(436\) −16.2833 −0.779827
\(437\) 15.4894 0.740956
\(438\) −13.0822 −0.625090
\(439\) 12.9144 0.616373 0.308186 0.951326i \(-0.400278\pi\)
0.308186 + 0.951326i \(0.400278\pi\)
\(440\) 2.03486 0.0970082
\(441\) 3.28542 0.156448
\(442\) −4.02676 −0.191534
\(443\) −37.8803 −1.79975 −0.899874 0.436149i \(-0.856342\pi\)
−0.899874 + 0.436149i \(0.856342\pi\)
\(444\) −8.28759 −0.393311
\(445\) −9.80514 −0.464808
\(446\) 9.58886 0.454046
\(447\) 4.99946 0.236466
\(448\) −1.84953 −0.0873820
\(449\) −5.72002 −0.269944 −0.134972 0.990849i \(-0.543095\pi\)
−0.134972 + 0.990849i \(0.543095\pi\)
\(450\) 0.917908 0.0432706
\(451\) −6.98562 −0.328940
\(452\) −1.74246 −0.0819584
\(453\) 12.3459 0.580060
\(454\) 8.92629 0.418932
\(455\) 1.84953 0.0867073
\(456\) −4.87591 −0.228336
\(457\) −28.4558 −1.33111 −0.665554 0.746350i \(-0.731805\pi\)
−0.665554 + 0.746350i \(0.731805\pi\)
\(458\) −15.4671 −0.722731
\(459\) 22.7646 1.06256
\(460\) 4.58382 0.213722
\(461\) −1.88939 −0.0879975 −0.0439987 0.999032i \(-0.514010\pi\)
−0.0439987 + 0.999032i \(0.514010\pi\)
\(462\) −5.43058 −0.252653
\(463\) 11.4219 0.530821 0.265411 0.964135i \(-0.414492\pi\)
0.265411 + 0.964135i \(0.414492\pi\)
\(464\) −5.94991 −0.276218
\(465\) 1.44295 0.0669150
\(466\) 3.49932 0.162103
\(467\) −26.9535 −1.24726 −0.623630 0.781719i \(-0.714343\pi\)
−0.623630 + 0.781719i \(0.714343\pi\)
\(468\) −0.917908 −0.0424303
\(469\) −13.8642 −0.640191
\(470\) 10.4630 0.482621
\(471\) 2.94691 0.135787
\(472\) 4.54161 0.209045
\(473\) 7.56385 0.347786
\(474\) 15.9277 0.731583
\(475\) −3.37914 −0.155046
\(476\) −7.44761 −0.341361
\(477\) −4.93198 −0.225820
\(478\) −28.4119 −1.29953
\(479\) −29.2802 −1.33785 −0.668924 0.743331i \(-0.733245\pi\)
−0.668924 + 0.743331i \(0.733245\pi\)
\(480\) −1.44295 −0.0658612
\(481\) 5.74352 0.261882
\(482\) 9.81549 0.447083
\(483\) −12.2331 −0.556628
\(484\) −6.85934 −0.311788
\(485\) −6.54755 −0.297309
\(486\) 9.16271 0.415629
\(487\) 10.9477 0.496088 0.248044 0.968749i \(-0.420212\pi\)
0.248044 + 0.968749i \(0.420212\pi\)
\(488\) −1.05465 −0.0477417
\(489\) −0.469057 −0.0212115
\(490\) −3.57924 −0.161694
\(491\) −5.83895 −0.263508 −0.131754 0.991282i \(-0.542061\pi\)
−0.131754 + 0.991282i \(0.542061\pi\)
\(492\) 4.95359 0.223325
\(493\) −23.9589 −1.07905
\(494\) 3.37914 0.152035
\(495\) 1.86782 0.0839520
\(496\) 1.00000 0.0449013
\(497\) −9.07293 −0.406977
\(498\) −4.90016 −0.219581
\(499\) 33.0226 1.47830 0.739148 0.673543i \(-0.235228\pi\)
0.739148 + 0.673543i \(0.235228\pi\)
\(500\) −1.00000 −0.0447214
\(501\) 14.9351 0.667251
\(502\) −22.5522 −1.00655
\(503\) −3.48253 −0.155278 −0.0776391 0.996982i \(-0.524738\pi\)
−0.0776391 + 0.996982i \(0.524738\pi\)
\(504\) −1.69770 −0.0756214
\(505\) 8.77067 0.390290
\(506\) 9.32743 0.414655
\(507\) −1.44295 −0.0640835
\(508\) −10.2278 −0.453787
\(509\) 4.00085 0.177334 0.0886672 0.996061i \(-0.471739\pi\)
0.0886672 + 0.996061i \(0.471739\pi\)
\(510\) −5.81040 −0.257289
\(511\) 16.7684 0.741789
\(512\) −1.00000 −0.0441942
\(513\) −19.1034 −0.843435
\(514\) 19.3964 0.855538
\(515\) −8.52722 −0.375754
\(516\) −5.36362 −0.236120
\(517\) 21.2907 0.936363
\(518\) 10.6228 0.466739
\(519\) 23.1378 1.01564
\(520\) 1.00000 0.0438529
\(521\) −4.08024 −0.178759 −0.0893793 0.995998i \(-0.528488\pi\)
−0.0893793 + 0.995998i \(0.528488\pi\)
\(522\) −5.46147 −0.239042
\(523\) −8.81282 −0.385358 −0.192679 0.981262i \(-0.561718\pi\)
−0.192679 + 0.981262i \(0.561718\pi\)
\(524\) −11.6099 −0.507179
\(525\) 2.66877 0.116475
\(526\) 19.4265 0.847034
\(527\) 4.02676 0.175408
\(528\) −2.93619 −0.127781
\(529\) −1.98863 −0.0864623
\(530\) 5.37307 0.233391
\(531\) 4.16878 0.180910
\(532\) 6.24982 0.270964
\(533\) −3.43297 −0.148698
\(534\) 14.1483 0.612256
\(535\) −7.04378 −0.304529
\(536\) −7.49609 −0.323782
\(537\) 2.26687 0.0978226
\(538\) 17.4915 0.754111
\(539\) −7.28326 −0.313712
\(540\) −5.65333 −0.243281
\(541\) 43.6811 1.87800 0.938998 0.343922i \(-0.111756\pi\)
0.938998 + 0.343922i \(0.111756\pi\)
\(542\) −23.9044 −1.02678
\(543\) −0.915371 −0.0392823
\(544\) −4.02676 −0.172646
\(545\) 16.2833 0.697499
\(546\) −2.66877 −0.114213
\(547\) 28.4757 1.21753 0.608766 0.793350i \(-0.291665\pi\)
0.608766 + 0.793350i \(0.291665\pi\)
\(548\) 0.710019 0.0303305
\(549\) −0.968070 −0.0413162
\(550\) −2.03486 −0.0867668
\(551\) 20.1056 0.856526
\(552\) −6.61420 −0.281519
\(553\) −20.4157 −0.868163
\(554\) 9.54560 0.405554
\(555\) 8.28759 0.351788
\(556\) 10.5855 0.448924
\(557\) 16.2543 0.688715 0.344357 0.938839i \(-0.388097\pi\)
0.344357 + 0.938839i \(0.388097\pi\)
\(558\) 0.917908 0.0388581
\(559\) 3.71713 0.157218
\(560\) 1.84953 0.0781569
\(561\) −11.8234 −0.499182
\(562\) 19.3263 0.815230
\(563\) −28.6742 −1.20847 −0.604236 0.796805i \(-0.706522\pi\)
−0.604236 + 0.796805i \(0.706522\pi\)
\(564\) −15.0975 −0.635719
\(565\) 1.74246 0.0733058
\(566\) 10.1976 0.428639
\(567\) 9.99434 0.419723
\(568\) −4.90554 −0.205832
\(569\) −18.2284 −0.764174 −0.382087 0.924126i \(-0.624795\pi\)
−0.382087 + 0.924126i \(0.624795\pi\)
\(570\) 4.87591 0.204230
\(571\) −8.54529 −0.357609 −0.178805 0.983885i \(-0.557223\pi\)
−0.178805 + 0.983885i \(0.557223\pi\)
\(572\) 2.03486 0.0850818
\(573\) 25.4807 1.06447
\(574\) −6.34938 −0.265018
\(575\) −4.58382 −0.191158
\(576\) −0.917908 −0.0382462
\(577\) −3.39145 −0.141188 −0.0705939 0.997505i \(-0.522489\pi\)
−0.0705939 + 0.997505i \(0.522489\pi\)
\(578\) 0.785193 0.0326597
\(579\) −9.09097 −0.377808
\(580\) 5.94991 0.247056
\(581\) 6.28089 0.260575
\(582\) 9.44775 0.391622
\(583\) 10.9334 0.452817
\(584\) 9.06629 0.375166
\(585\) 0.917908 0.0379508
\(586\) 25.4078 1.04959
\(587\) 12.6807 0.523389 0.261694 0.965151i \(-0.415719\pi\)
0.261694 + 0.965151i \(0.415719\pi\)
\(588\) 5.16465 0.212987
\(589\) −3.37914 −0.139235
\(590\) −4.54161 −0.186975
\(591\) −24.6266 −1.01300
\(592\) 5.74352 0.236057
\(593\) −3.53097 −0.145000 −0.0724998 0.997368i \(-0.523098\pi\)
−0.0724998 + 0.997368i \(0.523098\pi\)
\(594\) −11.5037 −0.472004
\(595\) 7.44761 0.305322
\(596\) −3.46476 −0.141922
\(597\) 13.1237 0.537117
\(598\) 4.58382 0.187446
\(599\) 7.12763 0.291227 0.145614 0.989342i \(-0.453484\pi\)
0.145614 + 0.989342i \(0.453484\pi\)
\(600\) 1.44295 0.0589080
\(601\) −2.28025 −0.0930132 −0.0465066 0.998918i \(-0.514809\pi\)
−0.0465066 + 0.998918i \(0.514809\pi\)
\(602\) 6.87495 0.280202
\(603\) −6.88072 −0.280205
\(604\) −8.55602 −0.348140
\(605\) 6.85934 0.278872
\(606\) −12.6556 −0.514099
\(607\) 26.3775 1.07063 0.535315 0.844652i \(-0.320193\pi\)
0.535315 + 0.844652i \(0.320193\pi\)
\(608\) 3.37914 0.137042
\(609\) −15.8789 −0.643447
\(610\) 1.05465 0.0427015
\(611\) 10.4630 0.423286
\(612\) −3.69620 −0.149410
\(613\) 12.0990 0.488674 0.244337 0.969690i \(-0.421430\pi\)
0.244337 + 0.969690i \(0.421430\pi\)
\(614\) 31.0455 1.25289
\(615\) −4.95359 −0.199748
\(616\) 3.76353 0.151637
\(617\) −2.81564 −0.113353 −0.0566767 0.998393i \(-0.518050\pi\)
−0.0566767 + 0.998393i \(0.518050\pi\)
\(618\) 12.3043 0.494952
\(619\) −3.30714 −0.132925 −0.0664627 0.997789i \(-0.521171\pi\)
−0.0664627 + 0.997789i \(0.521171\pi\)
\(620\) −1.00000 −0.0401610
\(621\) −25.9138 −1.03989
\(622\) 11.0997 0.445058
\(623\) −18.1349 −0.726559
\(624\) −1.44295 −0.0577641
\(625\) 1.00000 0.0400000
\(626\) −28.4814 −1.13835
\(627\) 9.92181 0.396239
\(628\) −2.04229 −0.0814962
\(629\) 23.1278 0.922165
\(630\) 1.69770 0.0676379
\(631\) 31.1347 1.23945 0.619727 0.784818i \(-0.287243\pi\)
0.619727 + 0.784818i \(0.287243\pi\)
\(632\) −11.0383 −0.439080
\(633\) 9.77997 0.388719
\(634\) −13.5242 −0.537116
\(635\) 10.2278 0.405879
\(636\) −7.75304 −0.307428
\(637\) −3.57924 −0.141815
\(638\) 12.1072 0.479330
\(639\) −4.50283 −0.178129
\(640\) 1.00000 0.0395285
\(641\) −18.3670 −0.725452 −0.362726 0.931896i \(-0.618154\pi\)
−0.362726 + 0.931896i \(0.618154\pi\)
\(642\) 10.1638 0.401133
\(643\) 32.8550 1.29568 0.647838 0.761778i \(-0.275674\pi\)
0.647838 + 0.761778i \(0.275674\pi\)
\(644\) 8.47790 0.334076
\(645\) 5.36362 0.211192
\(646\) 13.6070 0.535360
\(647\) −24.4053 −0.959470 −0.479735 0.877413i \(-0.659267\pi\)
−0.479735 + 0.877413i \(0.659267\pi\)
\(648\) 5.40372 0.212278
\(649\) −9.24155 −0.362763
\(650\) −1.00000 −0.0392232
\(651\) 2.66877 0.104597
\(652\) 0.325069 0.0127307
\(653\) −29.1601 −1.14112 −0.570562 0.821254i \(-0.693275\pi\)
−0.570562 + 0.821254i \(0.693275\pi\)
\(654\) −23.4959 −0.918761
\(655\) 11.6099 0.453634
\(656\) −3.43297 −0.134035
\(657\) 8.32202 0.324673
\(658\) 19.3516 0.754402
\(659\) 17.9074 0.697575 0.348788 0.937202i \(-0.386593\pi\)
0.348788 + 0.937202i \(0.386593\pi\)
\(660\) 2.93619 0.114291
\(661\) −19.2398 −0.748340 −0.374170 0.927360i \(-0.622072\pi\)
−0.374170 + 0.927360i \(0.622072\pi\)
\(662\) −21.5750 −0.838538
\(663\) −5.81040 −0.225657
\(664\) 3.39594 0.131788
\(665\) −6.24982 −0.242357
\(666\) 5.27202 0.204287
\(667\) 27.2733 1.05603
\(668\) −10.3504 −0.400470
\(669\) 13.8362 0.534938
\(670\) 7.49609 0.289599
\(671\) 2.14606 0.0828479
\(672\) −2.66877 −0.102950
\(673\) 3.54166 0.136521 0.0682605 0.997668i \(-0.478255\pi\)
0.0682605 + 0.997668i \(0.478255\pi\)
\(674\) 10.5216 0.405277
\(675\) 5.65333 0.217597
\(676\) 1.00000 0.0384615
\(677\) 19.9209 0.765623 0.382812 0.923826i \(-0.374956\pi\)
0.382812 + 0.923826i \(0.374956\pi\)
\(678\) −2.51427 −0.0965601
\(679\) −12.1099 −0.464734
\(680\) 4.02676 0.154419
\(681\) 12.8802 0.493569
\(682\) −2.03486 −0.0779189
\(683\) 11.5006 0.440059 0.220029 0.975493i \(-0.429385\pi\)
0.220029 + 0.975493i \(0.429385\pi\)
\(684\) 3.10174 0.118598
\(685\) −0.710019 −0.0271285
\(686\) −19.5666 −0.747057
\(687\) −22.3182 −0.851493
\(688\) 3.71713 0.141714
\(689\) 5.37307 0.204697
\(690\) 6.61420 0.251798
\(691\) 23.5873 0.897302 0.448651 0.893707i \(-0.351905\pi\)
0.448651 + 0.893707i \(0.351905\pi\)
\(692\) −16.0351 −0.609563
\(693\) 3.45458 0.131229
\(694\) 31.3970 1.19182
\(695\) −10.5855 −0.401530
\(696\) −8.58539 −0.325428
\(697\) −13.8237 −0.523612
\(698\) 12.0383 0.455655
\(699\) 5.04933 0.190983
\(700\) −1.84953 −0.0699056
\(701\) 19.3998 0.732720 0.366360 0.930473i \(-0.380604\pi\)
0.366360 + 0.930473i \(0.380604\pi\)
\(702\) −5.65333 −0.213371
\(703\) −19.4082 −0.731992
\(704\) 2.03486 0.0766917
\(705\) 15.0975 0.568605
\(706\) 13.7981 0.519297
\(707\) 16.2216 0.610077
\(708\) 6.55330 0.246288
\(709\) 9.25576 0.347607 0.173804 0.984780i \(-0.444394\pi\)
0.173804 + 0.984780i \(0.444394\pi\)
\(710\) 4.90554 0.184102
\(711\) −10.1322 −0.379985
\(712\) −9.80514 −0.367463
\(713\) −4.58382 −0.171665
\(714\) −10.7465 −0.402178
\(715\) −2.03486 −0.0760995
\(716\) −1.57100 −0.0587111
\(717\) −40.9969 −1.53106
\(718\) 21.0996 0.787428
\(719\) 4.53546 0.169144 0.0845721 0.996417i \(-0.473048\pi\)
0.0845721 + 0.996417i \(0.473048\pi\)
\(720\) 0.917908 0.0342084
\(721\) −15.7713 −0.587355
\(722\) 7.58141 0.282151
\(723\) 14.1632 0.526736
\(724\) 0.634377 0.0235764
\(725\) −5.94991 −0.220974
\(726\) −9.89765 −0.367336
\(727\) 5.90250 0.218912 0.109456 0.993992i \(-0.465089\pi\)
0.109456 + 0.993992i \(0.465089\pi\)
\(728\) 1.84953 0.0685481
\(729\) 29.4325 1.09009
\(730\) −9.06629 −0.335558
\(731\) 14.9680 0.553612
\(732\) −1.52180 −0.0562474
\(733\) −0.947728 −0.0350051 −0.0175026 0.999847i \(-0.505572\pi\)
−0.0175026 + 0.999847i \(0.505572\pi\)
\(734\) −26.5184 −0.978812
\(735\) −5.16465 −0.190501
\(736\) 4.58382 0.168962
\(737\) 15.2535 0.561870
\(738\) −3.15115 −0.115995
\(739\) 49.2084 1.81016 0.905081 0.425240i \(-0.139810\pi\)
0.905081 + 0.425240i \(0.139810\pi\)
\(740\) −5.74352 −0.211136
\(741\) 4.87591 0.179121
\(742\) 9.93764 0.364822
\(743\) −13.5439 −0.496877 −0.248439 0.968648i \(-0.579917\pi\)
−0.248439 + 0.968648i \(0.579917\pi\)
\(744\) 1.44295 0.0529010
\(745\) 3.46476 0.126939
\(746\) 4.72751 0.173086
\(747\) 3.11716 0.114051
\(748\) 8.19390 0.299599
\(749\) −13.0277 −0.476021
\(750\) −1.44295 −0.0526889
\(751\) 28.2562 1.03108 0.515542 0.856864i \(-0.327591\pi\)
0.515542 + 0.856864i \(0.327591\pi\)
\(752\) 10.4630 0.381545
\(753\) −32.5416 −1.18588
\(754\) 5.94991 0.216683
\(755\) 8.55602 0.311386
\(756\) −10.4560 −0.380281
\(757\) 1.21705 0.0442344 0.0221172 0.999755i \(-0.492959\pi\)
0.0221172 + 0.999755i \(0.492959\pi\)
\(758\) 21.7669 0.790611
\(759\) 13.4590 0.488530
\(760\) −3.37914 −0.122574
\(761\) −38.3444 −1.38998 −0.694991 0.719018i \(-0.744592\pi\)
−0.694991 + 0.719018i \(0.744592\pi\)
\(762\) −14.7582 −0.534634
\(763\) 30.1164 1.09029
\(764\) −17.6588 −0.638872
\(765\) 3.69620 0.133636
\(766\) −11.2822 −0.407641
\(767\) −4.54161 −0.163988
\(768\) −1.44295 −0.0520678
\(769\) −26.1540 −0.943138 −0.471569 0.881829i \(-0.656312\pi\)
−0.471569 + 0.881829i \(0.656312\pi\)
\(770\) −3.76353 −0.135628
\(771\) 27.9879 1.00796
\(772\) 6.30028 0.226752
\(773\) 7.96569 0.286506 0.143253 0.989686i \(-0.454244\pi\)
0.143253 + 0.989686i \(0.454244\pi\)
\(774\) 3.41199 0.122641
\(775\) 1.00000 0.0359211
\(776\) −6.54755 −0.235043
\(777\) 15.3281 0.549894
\(778\) 14.1684 0.507962
\(779\) 11.6005 0.415630
\(780\) 1.44295 0.0516657
\(781\) 9.98209 0.357187
\(782\) 18.4579 0.660054
\(783\) −33.6368 −1.20208
\(784\) −3.57924 −0.127830
\(785\) 2.04229 0.0728925
\(786\) −16.7524 −0.597538
\(787\) 11.7439 0.418624 0.209312 0.977849i \(-0.432878\pi\)
0.209312 + 0.977849i \(0.432878\pi\)
\(788\) 17.0669 0.607982
\(789\) 28.0313 0.997942
\(790\) 11.0383 0.392725
\(791\) 3.22273 0.114587
\(792\) 1.86782 0.0663699
\(793\) 1.05465 0.0374517
\(794\) −12.1144 −0.429925
\(795\) 7.75304 0.274972
\(796\) −9.09507 −0.322366
\(797\) 17.3224 0.613592 0.306796 0.951775i \(-0.400743\pi\)
0.306796 + 0.951775i \(0.400743\pi\)
\(798\) 9.01815 0.319239
\(799\) 42.1319 1.49052
\(800\) −1.00000 −0.0353553
\(801\) −9.00022 −0.318007
\(802\) 31.4824 1.11168
\(803\) −18.4486 −0.651038
\(804\) −10.8165 −0.381467
\(805\) −8.47790 −0.298807
\(806\) −1.00000 −0.0352235
\(807\) 25.2392 0.888463
\(808\) 8.77067 0.308551
\(809\) −24.4215 −0.858613 −0.429306 0.903159i \(-0.641242\pi\)
−0.429306 + 0.903159i \(0.641242\pi\)
\(810\) −5.40372 −0.189867
\(811\) 43.2200 1.51766 0.758830 0.651288i \(-0.225771\pi\)
0.758830 + 0.651288i \(0.225771\pi\)
\(812\) 11.0045 0.386183
\(813\) −34.4928 −1.20971
\(814\) −11.6873 −0.409638
\(815\) −0.325069 −0.0113867
\(816\) −5.81040 −0.203405
\(817\) −12.5607 −0.439444
\(818\) 27.9065 0.975728
\(819\) 1.69770 0.0593223
\(820\) 3.43297 0.119884
\(821\) −10.6087 −0.370247 −0.185124 0.982715i \(-0.559269\pi\)
−0.185124 + 0.982715i \(0.559269\pi\)
\(822\) 1.02452 0.0357342
\(823\) −20.9897 −0.731654 −0.365827 0.930683i \(-0.619214\pi\)
−0.365827 + 0.930683i \(0.619214\pi\)
\(824\) −8.52722 −0.297060
\(825\) −2.93619 −0.102225
\(826\) −8.39984 −0.292268
\(827\) 17.0443 0.592687 0.296343 0.955081i \(-0.404233\pi\)
0.296343 + 0.955081i \(0.404233\pi\)
\(828\) 4.20752 0.146221
\(829\) −42.1519 −1.46400 −0.731999 0.681306i \(-0.761412\pi\)
−0.731999 + 0.681306i \(0.761412\pi\)
\(830\) −3.39594 −0.117875
\(831\) 13.7738 0.477807
\(832\) 1.00000 0.0346688
\(833\) −14.4128 −0.499372
\(834\) 15.2743 0.528905
\(835\) 10.3504 0.358191
\(836\) −6.87608 −0.237814
\(837\) 5.65333 0.195408
\(838\) −6.49496 −0.224365
\(839\) 6.21357 0.214516 0.107258 0.994231i \(-0.465793\pi\)
0.107258 + 0.994231i \(0.465793\pi\)
\(840\) 2.66877 0.0920813
\(841\) 6.40140 0.220738
\(842\) 15.8856 0.547455
\(843\) 27.8868 0.960472
\(844\) −6.77778 −0.233301
\(845\) −1.00000 −0.0344010
\(846\) 9.60404 0.330194
\(847\) 12.6865 0.435915
\(848\) 5.37307 0.184512
\(849\) 14.7146 0.505005
\(850\) −4.02676 −0.138117
\(851\) −26.3272 −0.902486
\(852\) −7.07842 −0.242503
\(853\) 14.9176 0.510770 0.255385 0.966839i \(-0.417798\pi\)
0.255385 + 0.966839i \(0.417798\pi\)
\(854\) 1.95060 0.0667483
\(855\) −3.10174 −0.106077
\(856\) −7.04378 −0.240751
\(857\) 42.2741 1.44406 0.722029 0.691863i \(-0.243210\pi\)
0.722029 + 0.691863i \(0.243210\pi\)
\(858\) 2.93619 0.100240
\(859\) −22.0777 −0.753283 −0.376642 0.926359i \(-0.622921\pi\)
−0.376642 + 0.926359i \(0.622921\pi\)
\(860\) −3.71713 −0.126753
\(861\) −9.16180 −0.312233
\(862\) 24.8265 0.845592
\(863\) 27.1135 0.922953 0.461477 0.887152i \(-0.347320\pi\)
0.461477 + 0.887152i \(0.347320\pi\)
\(864\) −5.65333 −0.192330
\(865\) 16.0351 0.545210
\(866\) −16.9214 −0.575012
\(867\) 1.13299 0.0384784
\(868\) −1.84953 −0.0627771
\(869\) 22.4614 0.761952
\(870\) 8.58539 0.291072
\(871\) 7.49609 0.253995
\(872\) 16.2833 0.551421
\(873\) −6.01004 −0.203409
\(874\) −15.4894 −0.523935
\(875\) 1.84953 0.0625255
\(876\) 13.0822 0.442005
\(877\) −40.7572 −1.37627 −0.688137 0.725581i \(-0.741571\pi\)
−0.688137 + 0.725581i \(0.741571\pi\)
\(878\) −12.9144 −0.435842
\(879\) 36.6621 1.23658
\(880\) −2.03486 −0.0685952
\(881\) −49.7166 −1.67500 −0.837498 0.546441i \(-0.815982\pi\)
−0.837498 + 0.546441i \(0.815982\pi\)
\(882\) −3.28542 −0.110626
\(883\) −26.9476 −0.906860 −0.453430 0.891292i \(-0.649800\pi\)
−0.453430 + 0.891292i \(0.649800\pi\)
\(884\) 4.02676 0.135435
\(885\) −6.55330 −0.220287
\(886\) 37.8803 1.27261
\(887\) −7.33741 −0.246366 −0.123183 0.992384i \(-0.539310\pi\)
−0.123183 + 0.992384i \(0.539310\pi\)
\(888\) 8.28759 0.278113
\(889\) 18.9167 0.634445
\(890\) 9.80514 0.328669
\(891\) −10.9958 −0.368374
\(892\) −9.58886 −0.321059
\(893\) −35.3558 −1.18314
\(894\) −4.99946 −0.167207
\(895\) 1.57100 0.0525128
\(896\) 1.84953 0.0617884
\(897\) 6.61420 0.220842
\(898\) 5.72002 0.190880
\(899\) −5.94991 −0.198441
\(900\) −0.917908 −0.0305969
\(901\) 21.6361 0.720801
\(902\) 6.98562 0.232596
\(903\) 9.92017 0.330123
\(904\) 1.74246 0.0579533
\(905\) −0.634377 −0.0210874
\(906\) −12.3459 −0.410164
\(907\) 7.26600 0.241263 0.120632 0.992697i \(-0.461508\pi\)
0.120632 + 0.992697i \(0.461508\pi\)
\(908\) −8.92629 −0.296229
\(909\) 8.05067 0.267024
\(910\) −1.84953 −0.0613113
\(911\) 17.9114 0.593430 0.296715 0.954966i \(-0.404109\pi\)
0.296715 + 0.954966i \(0.404109\pi\)
\(912\) 4.87591 0.161458
\(913\) −6.91027 −0.228697
\(914\) 28.4558 0.941236
\(915\) 1.52180 0.0503092
\(916\) 15.4671 0.511048
\(917\) 21.4728 0.709093
\(918\) −22.7646 −0.751344
\(919\) 8.94938 0.295213 0.147606 0.989046i \(-0.452843\pi\)
0.147606 + 0.989046i \(0.452843\pi\)
\(920\) −4.58382 −0.151124
\(921\) 44.7969 1.47611
\(922\) 1.88939 0.0622236
\(923\) 4.90554 0.161468
\(924\) 5.43058 0.178653
\(925\) 5.74352 0.188846
\(926\) −11.4219 −0.375347
\(927\) −7.82720 −0.257079
\(928\) 5.94991 0.195315
\(929\) −5.22227 −0.171337 −0.0856686 0.996324i \(-0.527303\pi\)
−0.0856686 + 0.996324i \(0.527303\pi\)
\(930\) −1.44295 −0.0473161
\(931\) 12.0948 0.396390
\(932\) −3.49932 −0.114624
\(933\) 16.0163 0.524350
\(934\) 26.9535 0.881946
\(935\) −8.19390 −0.267969
\(936\) 0.917908 0.0300028
\(937\) −2.15383 −0.0703627 −0.0351813 0.999381i \(-0.511201\pi\)
−0.0351813 + 0.999381i \(0.511201\pi\)
\(938\) 13.8642 0.452684
\(939\) −41.0971 −1.34115
\(940\) −10.4630 −0.341264
\(941\) 1.98296 0.0646425 0.0323213 0.999478i \(-0.489710\pi\)
0.0323213 + 0.999478i \(0.489710\pi\)
\(942\) −2.94691 −0.0960156
\(943\) 15.7361 0.512438
\(944\) −4.54161 −0.147817
\(945\) 10.4560 0.340134
\(946\) −7.56385 −0.245922
\(947\) 55.9977 1.81968 0.909840 0.414960i \(-0.136204\pi\)
0.909840 + 0.414960i \(0.136204\pi\)
\(948\) −15.9277 −0.517307
\(949\) −9.06629 −0.294304
\(950\) 3.37914 0.109634
\(951\) −19.5147 −0.632809
\(952\) 7.44761 0.241378
\(953\) −48.7331 −1.57862 −0.789310 0.613994i \(-0.789562\pi\)
−0.789310 + 0.613994i \(0.789562\pi\)
\(954\) 4.93198 0.159679
\(955\) 17.6588 0.571425
\(956\) 28.4119 0.918907
\(957\) 17.4701 0.564728
\(958\) 29.2802 0.946001
\(959\) −1.31320 −0.0424055
\(960\) 1.44295 0.0465709
\(961\) 1.00000 0.0322581
\(962\) −5.74352 −0.185179
\(963\) −6.46554 −0.208349
\(964\) −9.81549 −0.316136
\(965\) −6.30028 −0.202813
\(966\) 12.2331 0.393595
\(967\) 11.8907 0.382378 0.191189 0.981553i \(-0.438766\pi\)
0.191189 + 0.981553i \(0.438766\pi\)
\(968\) 6.85934 0.220468
\(969\) 19.6341 0.630740
\(970\) 6.54755 0.210229
\(971\) 51.5315 1.65373 0.826863 0.562404i \(-0.190123\pi\)
0.826863 + 0.562404i \(0.190123\pi\)
\(972\) −9.16271 −0.293894
\(973\) −19.5782 −0.627647
\(974\) −10.9477 −0.350787
\(975\) −1.44295 −0.0462112
\(976\) 1.05465 0.0337585
\(977\) 22.1561 0.708835 0.354418 0.935087i \(-0.384679\pi\)
0.354418 + 0.935087i \(0.384679\pi\)
\(978\) 0.469057 0.0149988
\(979\) 19.9521 0.637672
\(980\) 3.57924 0.114335
\(981\) 14.9465 0.477206
\(982\) 5.83895 0.186328
\(983\) 35.9323 1.14606 0.573031 0.819534i \(-0.305768\pi\)
0.573031 + 0.819534i \(0.305768\pi\)
\(984\) −4.95359 −0.157915
\(985\) −17.0669 −0.543796
\(986\) 23.9589 0.763005
\(987\) 27.9233 0.888807
\(988\) −3.37914 −0.107505
\(989\) −17.0387 −0.541798
\(990\) −1.86782 −0.0593631
\(991\) 20.1323 0.639525 0.319762 0.947498i \(-0.396397\pi\)
0.319762 + 0.947498i \(0.396397\pi\)
\(992\) −1.00000 −0.0317500
\(993\) −31.1316 −0.987932
\(994\) 9.07293 0.287776
\(995\) 9.09507 0.288333
\(996\) 4.90016 0.155268
\(997\) 41.2043 1.30495 0.652477 0.757808i \(-0.273730\pi\)
0.652477 + 0.757808i \(0.273730\pi\)
\(998\) −33.0226 −1.04531
\(999\) 32.4700 1.02731
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 4030.2.a.c.1.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4030.2.a.c.1.2 6 1.1 even 1 trivial