Properties

Label 4030.2.a.l.1.7
Level $4030$
Weight $2$
Character 4030.1
Self dual yes
Analytic conductor $32.180$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 14x^{6} - 6x^{5} + 54x^{4} + 46x^{3} - 32x^{2} - 43x - 11 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(-2.55848\) 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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +2.53701 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53701 q^{6} +1.50878 q^{7} -1.00000 q^{8} +3.43644 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +2.53701 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53701 q^{6} +1.50878 q^{7} -1.00000 q^{8} +3.43644 q^{9} -1.00000 q^{10} +0.351489 q^{11} +2.53701 q^{12} -1.00000 q^{13} -1.50878 q^{14} +2.53701 q^{15} +1.00000 q^{16} +2.31225 q^{17} -3.43644 q^{18} +1.18952 q^{19} +1.00000 q^{20} +3.82779 q^{21} -0.351489 q^{22} +5.37024 q^{23} -2.53701 q^{24} +1.00000 q^{25} +1.00000 q^{26} +1.10726 q^{27} +1.50878 q^{28} -0.355403 q^{29} -2.53701 q^{30} -1.00000 q^{31} -1.00000 q^{32} +0.891733 q^{33} -2.31225 q^{34} +1.50878 q^{35} +3.43644 q^{36} +7.91157 q^{37} -1.18952 q^{38} -2.53701 q^{39} -1.00000 q^{40} +9.73202 q^{41} -3.82779 q^{42} -4.51150 q^{43} +0.351489 q^{44} +3.43644 q^{45} -5.37024 q^{46} -9.03358 q^{47} +2.53701 q^{48} -4.72359 q^{49} -1.00000 q^{50} +5.86620 q^{51} -1.00000 q^{52} -4.72450 q^{53} -1.10726 q^{54} +0.351489 q^{55} -1.50878 q^{56} +3.01784 q^{57} +0.355403 q^{58} +4.09595 q^{59} +2.53701 q^{60} +3.70865 q^{61} +1.00000 q^{62} +5.18482 q^{63} +1.00000 q^{64} -1.00000 q^{65} -0.891733 q^{66} +11.6316 q^{67} +2.31225 q^{68} +13.6244 q^{69} -1.50878 q^{70} -5.16704 q^{71} -3.43644 q^{72} +7.39342 q^{73} -7.91157 q^{74} +2.53701 q^{75} +1.18952 q^{76} +0.530319 q^{77} +2.53701 q^{78} -2.26348 q^{79} +1.00000 q^{80} -7.50020 q^{81} -9.73202 q^{82} -5.61797 q^{83} +3.82779 q^{84} +2.31225 q^{85} +4.51150 q^{86} -0.901663 q^{87} -0.351489 q^{88} +11.4134 q^{89} -3.43644 q^{90} -1.50878 q^{91} +5.37024 q^{92} -2.53701 q^{93} +9.03358 q^{94} +1.18952 q^{95} -2.53701 q^{96} -14.5519 q^{97} +4.72359 q^{98} +1.20787 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} + q^{3} + 8 q^{4} + 8 q^{5} - q^{6} + 11 q^{7} - 8 q^{8} + 9 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} + q^{3} + 8 q^{4} + 8 q^{5} - q^{6} + 11 q^{7} - 8 q^{8} + 9 q^{9} - 8 q^{10} + q^{12} - 8 q^{13} - 11 q^{14} + q^{15} + 8 q^{16} + 7 q^{17} - 9 q^{18} - 2 q^{19} + 8 q^{20} + q^{21} + 8 q^{23} - q^{24} + 8 q^{25} + 8 q^{26} + 7 q^{27} + 11 q^{28} - q^{29} - q^{30} - 8 q^{31} - 8 q^{32} + 14 q^{33} - 7 q^{34} + 11 q^{35} + 9 q^{36} + q^{37} + 2 q^{38} - q^{39} - 8 q^{40} + 16 q^{41} - q^{42} + 3 q^{43} + 9 q^{45} - 8 q^{46} + 29 q^{47} + q^{48} + 11 q^{49} - 8 q^{50} + 11 q^{51} - 8 q^{52} + 22 q^{53} - 7 q^{54} - 11 q^{56} + 33 q^{57} + q^{58} - 8 q^{59} + q^{60} + 4 q^{61} + 8 q^{62} + 38 q^{63} + 8 q^{64} - 8 q^{65} - 14 q^{66} + 28 q^{67} + 7 q^{68} - 42 q^{69} - 11 q^{70} + 4 q^{71} - 9 q^{72} + 39 q^{73} - q^{74} + q^{75} - 2 q^{76} + 11 q^{77} + q^{78} - 16 q^{79} + 8 q^{80} + 32 q^{81} - 16 q^{82} + 25 q^{83} + q^{84} + 7 q^{85} - 3 q^{86} + 13 q^{87} + 21 q^{89} - 9 q^{90} - 11 q^{91} + 8 q^{92} - q^{93} - 29 q^{94} - 2 q^{95} - q^{96} + 28 q^{97} - 11 q^{98} + 23 q^{99}+O(q^{100}) \) 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
\(3\) 2.53701 1.46475 0.732373 0.680904i \(-0.238413\pi\)
0.732373 + 0.680904i \(0.238413\pi\)
\(4\) 1.00000 0.500000
\(5\) 1.00000 0.447214
\(6\) −2.53701 −1.03573
\(7\) 1.50878 0.570264 0.285132 0.958488i \(-0.407963\pi\)
0.285132 + 0.958488i \(0.407963\pi\)
\(8\) −1.00000 −0.353553
\(9\) 3.43644 1.14548
\(10\) −1.00000 −0.316228
\(11\) 0.351489 0.105978 0.0529890 0.998595i \(-0.483125\pi\)
0.0529890 + 0.998595i \(0.483125\pi\)
\(12\) 2.53701 0.732373
\(13\) −1.00000 −0.277350
\(14\) −1.50878 −0.403238
\(15\) 2.53701 0.655054
\(16\) 1.00000 0.250000
\(17\) 2.31225 0.560802 0.280401 0.959883i \(-0.409533\pi\)
0.280401 + 0.959883i \(0.409533\pi\)
\(18\) −3.43644 −0.809977
\(19\) 1.18952 0.272895 0.136448 0.990647i \(-0.456431\pi\)
0.136448 + 0.990647i \(0.456431\pi\)
\(20\) 1.00000 0.223607
\(21\) 3.82779 0.835292
\(22\) −0.351489 −0.0749377
\(23\) 5.37024 1.11977 0.559887 0.828569i \(-0.310845\pi\)
0.559887 + 0.828569i \(0.310845\pi\)
\(24\) −2.53701 −0.517866
\(25\) 1.00000 0.200000
\(26\) 1.00000 0.196116
\(27\) 1.10726 0.213091
\(28\) 1.50878 0.285132
\(29\) −0.355403 −0.0659968 −0.0329984 0.999455i \(-0.510506\pi\)
−0.0329984 + 0.999455i \(0.510506\pi\)
\(30\) −2.53701 −0.463193
\(31\) −1.00000 −0.179605
\(32\) −1.00000 −0.176777
\(33\) 0.891733 0.155231
\(34\) −2.31225 −0.396547
\(35\) 1.50878 0.255030
\(36\) 3.43644 0.572740
\(37\) 7.91157 1.30065 0.650327 0.759654i \(-0.274632\pi\)
0.650327 + 0.759654i \(0.274632\pi\)
\(38\) −1.18952 −0.192966
\(39\) −2.53701 −0.406247
\(40\) −1.00000 −0.158114
\(41\) 9.73202 1.51989 0.759943 0.649990i \(-0.225227\pi\)
0.759943 + 0.649990i \(0.225227\pi\)
\(42\) −3.82779 −0.590641
\(43\) −4.51150 −0.687998 −0.343999 0.938970i \(-0.611782\pi\)
−0.343999 + 0.938970i \(0.611782\pi\)
\(44\) 0.351489 0.0529890
\(45\) 3.43644 0.512274
\(46\) −5.37024 −0.791799
\(47\) −9.03358 −1.31768 −0.658842 0.752282i \(-0.728953\pi\)
−0.658842 + 0.752282i \(0.728953\pi\)
\(48\) 2.53701 0.366186
\(49\) −4.72359 −0.674799
\(50\) −1.00000 −0.141421
\(51\) 5.86620 0.821432
\(52\) −1.00000 −0.138675
\(53\) −4.72450 −0.648960 −0.324480 0.945893i \(-0.605189\pi\)
−0.324480 + 0.945893i \(0.605189\pi\)
\(54\) −1.10726 −0.150678
\(55\) 0.351489 0.0473948
\(56\) −1.50878 −0.201619
\(57\) 3.01784 0.399722
\(58\) 0.355403 0.0466668
\(59\) 4.09595 0.533247 0.266624 0.963801i \(-0.414092\pi\)
0.266624 + 0.963801i \(0.414092\pi\)
\(60\) 2.53701 0.327527
\(61\) 3.70865 0.474844 0.237422 0.971407i \(-0.423698\pi\)
0.237422 + 0.971407i \(0.423698\pi\)
\(62\) 1.00000 0.127000
\(63\) 5.18482 0.653226
\(64\) 1.00000 0.125000
\(65\) −1.00000 −0.124035
\(66\) −0.891733 −0.109765
\(67\) 11.6316 1.42103 0.710514 0.703683i \(-0.248462\pi\)
0.710514 + 0.703683i \(0.248462\pi\)
\(68\) 2.31225 0.280401
\(69\) 13.6244 1.64018
\(70\) −1.50878 −0.180333
\(71\) −5.16704 −0.613215 −0.306607 0.951836i \(-0.599194\pi\)
−0.306607 + 0.951836i \(0.599194\pi\)
\(72\) −3.43644 −0.404988
\(73\) 7.39342 0.865334 0.432667 0.901554i \(-0.357573\pi\)
0.432667 + 0.901554i \(0.357573\pi\)
\(74\) −7.91157 −0.919701
\(75\) 2.53701 0.292949
\(76\) 1.18952 0.136448
\(77\) 0.530319 0.0604354
\(78\) 2.53701 0.287260
\(79\) −2.26348 −0.254661 −0.127331 0.991860i \(-0.540641\pi\)
−0.127331 + 0.991860i \(0.540641\pi\)
\(80\) 1.00000 0.111803
\(81\) −7.50020 −0.833355
\(82\) −9.73202 −1.07472
\(83\) −5.61797 −0.616653 −0.308326 0.951281i \(-0.599769\pi\)
−0.308326 + 0.951281i \(0.599769\pi\)
\(84\) 3.82779 0.417646
\(85\) 2.31225 0.250798
\(86\) 4.51150 0.486488
\(87\) −0.901663 −0.0966685
\(88\) −0.351489 −0.0374689
\(89\) 11.4134 1.20982 0.604911 0.796293i \(-0.293209\pi\)
0.604911 + 0.796293i \(0.293209\pi\)
\(90\) −3.43644 −0.362233
\(91\) −1.50878 −0.158163
\(92\) 5.37024 0.559887
\(93\) −2.53701 −0.263076
\(94\) 9.03358 0.931743
\(95\) 1.18952 0.122043
\(96\) −2.53701 −0.258933
\(97\) −14.5519 −1.47752 −0.738759 0.673969i \(-0.764588\pi\)
−0.738759 + 0.673969i \(0.764588\pi\)
\(98\) 4.72359 0.477155
\(99\) 1.20787 0.121396
\(100\) 1.00000 0.100000
\(101\) −10.3158 −1.02646 −0.513231 0.858251i \(-0.671552\pi\)
−0.513231 + 0.858251i \(0.671552\pi\)
\(102\) −5.86620 −0.580840
\(103\) −1.85938 −0.183210 −0.0916049 0.995795i \(-0.529200\pi\)
−0.0916049 + 0.995795i \(0.529200\pi\)
\(104\) 1.00000 0.0980581
\(105\) 3.82779 0.373554
\(106\) 4.72450 0.458884
\(107\) 18.0261 1.74265 0.871324 0.490708i \(-0.163262\pi\)
0.871324 + 0.490708i \(0.163262\pi\)
\(108\) 1.10726 0.106546
\(109\) 19.1988 1.83891 0.919456 0.393192i \(-0.128629\pi\)
0.919456 + 0.393192i \(0.128629\pi\)
\(110\) −0.351489 −0.0335132
\(111\) 20.0718 1.90513
\(112\) 1.50878 0.142566
\(113\) 16.7578 1.57644 0.788220 0.615394i \(-0.211003\pi\)
0.788220 + 0.615394i \(0.211003\pi\)
\(114\) −3.01784 −0.282646
\(115\) 5.37024 0.500778
\(116\) −0.355403 −0.0329984
\(117\) −3.43644 −0.317699
\(118\) −4.09595 −0.377063
\(119\) 3.48866 0.319805
\(120\) −2.53701 −0.231597
\(121\) −10.8765 −0.988769
\(122\) −3.70865 −0.335766
\(123\) 24.6903 2.22625
\(124\) −1.00000 −0.0898027
\(125\) 1.00000 0.0894427
\(126\) −5.18482 −0.461901
\(127\) −13.6448 −1.21078 −0.605388 0.795930i \(-0.706982\pi\)
−0.605388 + 0.795930i \(0.706982\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −11.4457 −1.00774
\(130\) 1.00000 0.0877058
\(131\) −8.03303 −0.701849 −0.350924 0.936404i \(-0.614133\pi\)
−0.350924 + 0.936404i \(0.614133\pi\)
\(132\) 0.891733 0.0776154
\(133\) 1.79473 0.155622
\(134\) −11.6316 −1.00482
\(135\) 1.10726 0.0952974
\(136\) −2.31225 −0.198273
\(137\) −17.7285 −1.51465 −0.757323 0.653040i \(-0.773493\pi\)
−0.757323 + 0.653040i \(0.773493\pi\)
\(138\) −13.6244 −1.15978
\(139\) −0.0867283 −0.00735620 −0.00367810 0.999993i \(-0.501171\pi\)
−0.00367810 + 0.999993i \(0.501171\pi\)
\(140\) 1.50878 0.127515
\(141\) −22.9183 −1.93007
\(142\) 5.16704 0.433608
\(143\) −0.351489 −0.0293930
\(144\) 3.43644 0.286370
\(145\) −0.355403 −0.0295146
\(146\) −7.39342 −0.611884
\(147\) −11.9838 −0.988408
\(148\) 7.91157 0.650327
\(149\) 2.85650 0.234014 0.117007 0.993131i \(-0.462670\pi\)
0.117007 + 0.993131i \(0.462670\pi\)
\(150\) −2.53701 −0.207146
\(151\) 10.5015 0.854600 0.427300 0.904110i \(-0.359465\pi\)
0.427300 + 0.904110i \(0.359465\pi\)
\(152\) −1.18952 −0.0964831
\(153\) 7.94589 0.642387
\(154\) −0.530319 −0.0427343
\(155\) −1.00000 −0.0803219
\(156\) −2.53701 −0.203124
\(157\) 0.674228 0.0538092 0.0269046 0.999638i \(-0.491435\pi\)
0.0269046 + 0.999638i \(0.491435\pi\)
\(158\) 2.26348 0.180073
\(159\) −11.9861 −0.950562
\(160\) −1.00000 −0.0790569
\(161\) 8.10250 0.638567
\(162\) 7.50020 0.589271
\(163\) 11.8583 0.928815 0.464407 0.885622i \(-0.346267\pi\)
0.464407 + 0.885622i \(0.346267\pi\)
\(164\) 9.73202 0.759943
\(165\) 0.891733 0.0694213
\(166\) 5.61797 0.436039
\(167\) 22.2641 1.72285 0.861426 0.507884i \(-0.169572\pi\)
0.861426 + 0.507884i \(0.169572\pi\)
\(168\) −3.82779 −0.295320
\(169\) 1.00000 0.0769231
\(170\) −2.31225 −0.177341
\(171\) 4.08773 0.312596
\(172\) −4.51150 −0.343999
\(173\) 11.2452 0.854960 0.427480 0.904025i \(-0.359402\pi\)
0.427480 + 0.904025i \(0.359402\pi\)
\(174\) 0.901663 0.0683549
\(175\) 1.50878 0.114053
\(176\) 0.351489 0.0264945
\(177\) 10.3915 0.781072
\(178\) −11.4134 −0.855474
\(179\) 14.5315 1.08613 0.543067 0.839689i \(-0.317263\pi\)
0.543067 + 0.839689i \(0.317263\pi\)
\(180\) 3.43644 0.256137
\(181\) −7.28922 −0.541804 −0.270902 0.962607i \(-0.587322\pi\)
−0.270902 + 0.962607i \(0.587322\pi\)
\(182\) 1.50878 0.111838
\(183\) 9.40890 0.695526
\(184\) −5.37024 −0.395900
\(185\) 7.91157 0.581670
\(186\) 2.53701 0.186023
\(187\) 0.812729 0.0594326
\(188\) −9.03358 −0.658842
\(189\) 1.67060 0.121518
\(190\) −1.18952 −0.0862971
\(191\) −3.20157 −0.231658 −0.115829 0.993269i \(-0.536952\pi\)
−0.115829 + 0.993269i \(0.536952\pi\)
\(192\) 2.53701 0.183093
\(193\) −17.2768 −1.24361 −0.621806 0.783172i \(-0.713601\pi\)
−0.621806 + 0.783172i \(0.713601\pi\)
\(194\) 14.5519 1.04476
\(195\) −2.53701 −0.181679
\(196\) −4.72359 −0.337399
\(197\) −11.8553 −0.844654 −0.422327 0.906443i \(-0.638787\pi\)
−0.422327 + 0.906443i \(0.638787\pi\)
\(198\) −1.20787 −0.0858397
\(199\) −0.350989 −0.0248809 −0.0124405 0.999923i \(-0.503960\pi\)
−0.0124405 + 0.999923i \(0.503960\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 29.5096 2.08145
\(202\) 10.3158 0.725818
\(203\) −0.536225 −0.0376356
\(204\) 5.86620 0.410716
\(205\) 9.73202 0.679714
\(206\) 1.85938 0.129549
\(207\) 18.4545 1.28268
\(208\) −1.00000 −0.0693375
\(209\) 0.418104 0.0289209
\(210\) −3.82779 −0.264143
\(211\) −22.3354 −1.53763 −0.768815 0.639471i \(-0.779153\pi\)
−0.768815 + 0.639471i \(0.779153\pi\)
\(212\) −4.72450 −0.324480
\(213\) −13.1089 −0.898204
\(214\) −18.0261 −1.23224
\(215\) −4.51150 −0.307682
\(216\) −1.10726 −0.0753392
\(217\) −1.50878 −0.102422
\(218\) −19.1988 −1.30031
\(219\) 18.7572 1.26749
\(220\) 0.351489 0.0236974
\(221\) −2.31225 −0.155538
\(222\) −20.0718 −1.34713
\(223\) −15.4957 −1.03767 −0.518834 0.854875i \(-0.673634\pi\)
−0.518834 + 0.854875i \(0.673634\pi\)
\(224\) −1.50878 −0.100809
\(225\) 3.43644 0.229096
\(226\) −16.7578 −1.11471
\(227\) −22.2125 −1.47430 −0.737148 0.675731i \(-0.763828\pi\)
−0.737148 + 0.675731i \(0.763828\pi\)
\(228\) 3.01784 0.199861
\(229\) 22.6989 1.49998 0.749991 0.661448i \(-0.230058\pi\)
0.749991 + 0.661448i \(0.230058\pi\)
\(230\) −5.37024 −0.354103
\(231\) 1.34543 0.0885226
\(232\) 0.355403 0.0233334
\(233\) 8.56342 0.561008 0.280504 0.959853i \(-0.409498\pi\)
0.280504 + 0.959853i \(0.409498\pi\)
\(234\) 3.43644 0.224647
\(235\) −9.03358 −0.589286
\(236\) 4.09595 0.266624
\(237\) −5.74247 −0.373014
\(238\) −3.48866 −0.226136
\(239\) −7.34936 −0.475391 −0.237695 0.971340i \(-0.576392\pi\)
−0.237695 + 0.971340i \(0.576392\pi\)
\(240\) 2.53701 0.163764
\(241\) −12.2953 −0.792010 −0.396005 0.918248i \(-0.629604\pi\)
−0.396005 + 0.918248i \(0.629604\pi\)
\(242\) 10.8765 0.699165
\(243\) −22.3499 −1.43375
\(244\) 3.70865 0.237422
\(245\) −4.72359 −0.301779
\(246\) −24.6903 −1.57419
\(247\) −1.18952 −0.0756876
\(248\) 1.00000 0.0635001
\(249\) −14.2529 −0.903239
\(250\) −1.00000 −0.0632456
\(251\) −0.765427 −0.0483133 −0.0241567 0.999708i \(-0.507690\pi\)
−0.0241567 + 0.999708i \(0.507690\pi\)
\(252\) 5.18482 0.326613
\(253\) 1.88758 0.118671
\(254\) 13.6448 0.856148
\(255\) 5.86620 0.367356
\(256\) 1.00000 0.0625000
\(257\) 19.2398 1.20015 0.600073 0.799945i \(-0.295138\pi\)
0.600073 + 0.799945i \(0.295138\pi\)
\(258\) 11.4457 0.712581
\(259\) 11.9368 0.741717
\(260\) −1.00000 −0.0620174
\(261\) −1.22132 −0.0755980
\(262\) 8.03303 0.496282
\(263\) 17.2134 1.06142 0.530712 0.847553i \(-0.321925\pi\)
0.530712 + 0.847553i \(0.321925\pi\)
\(264\) −0.891733 −0.0548824
\(265\) −4.72450 −0.290224
\(266\) −1.79473 −0.110042
\(267\) 28.9561 1.77208
\(268\) 11.6316 0.710514
\(269\) −17.4818 −1.06589 −0.532943 0.846151i \(-0.678914\pi\)
−0.532943 + 0.846151i \(0.678914\pi\)
\(270\) −1.10726 −0.0673854
\(271\) −17.3745 −1.05543 −0.527714 0.849422i \(-0.676951\pi\)
−0.527714 + 0.849422i \(0.676951\pi\)
\(272\) 2.31225 0.140200
\(273\) −3.82779 −0.231668
\(274\) 17.7285 1.07102
\(275\) 0.351489 0.0211956
\(276\) 13.6244 0.820092
\(277\) −14.3045 −0.859474 −0.429737 0.902954i \(-0.641394\pi\)
−0.429737 + 0.902954i \(0.641394\pi\)
\(278\) 0.0867283 0.00520162
\(279\) −3.43644 −0.205734
\(280\) −1.50878 −0.0901667
\(281\) 20.7352 1.23696 0.618478 0.785802i \(-0.287749\pi\)
0.618478 + 0.785802i \(0.287749\pi\)
\(282\) 22.9183 1.36477
\(283\) −9.54516 −0.567401 −0.283700 0.958913i \(-0.591562\pi\)
−0.283700 + 0.958913i \(0.591562\pi\)
\(284\) −5.16704 −0.306607
\(285\) 3.01784 0.178761
\(286\) 0.351489 0.0207840
\(287\) 14.6835 0.866737
\(288\) −3.43644 −0.202494
\(289\) −11.6535 −0.685501
\(290\) 0.355403 0.0208700
\(291\) −36.9183 −2.16419
\(292\) 7.39342 0.432667
\(293\) 23.9946 1.40178 0.700890 0.713270i \(-0.252787\pi\)
0.700890 + 0.713270i \(0.252787\pi\)
\(294\) 11.9838 0.698910
\(295\) 4.09595 0.238475
\(296\) −7.91157 −0.459851
\(297\) 0.389188 0.0225830
\(298\) −2.85650 −0.165473
\(299\) −5.37024 −0.310569
\(300\) 2.53701 0.146475
\(301\) −6.80686 −0.392341
\(302\) −10.5015 −0.604293
\(303\) −26.1714 −1.50351
\(304\) 1.18952 0.0682238
\(305\) 3.70865 0.212357
\(306\) −7.94589 −0.454236
\(307\) 9.07352 0.517853 0.258926 0.965897i \(-0.416631\pi\)
0.258926 + 0.965897i \(0.416631\pi\)
\(308\) 0.530319 0.0302177
\(309\) −4.71726 −0.268356
\(310\) 1.00000 0.0567962
\(311\) −16.5210 −0.936822 −0.468411 0.883511i \(-0.655173\pi\)
−0.468411 + 0.883511i \(0.655173\pi\)
\(312\) 2.53701 0.143630
\(313\) −20.1373 −1.13823 −0.569113 0.822260i \(-0.692713\pi\)
−0.569113 + 0.822260i \(0.692713\pi\)
\(314\) −0.674228 −0.0380489
\(315\) 5.18482 0.292132
\(316\) −2.26348 −0.127331
\(317\) −28.2431 −1.58629 −0.793145 0.609033i \(-0.791558\pi\)
−0.793145 + 0.609033i \(0.791558\pi\)
\(318\) 11.9861 0.672149
\(319\) −0.124920 −0.00699420
\(320\) 1.00000 0.0559017
\(321\) 45.7325 2.55254
\(322\) −8.10250 −0.451535
\(323\) 2.75047 0.153040
\(324\) −7.50020 −0.416678
\(325\) −1.00000 −0.0554700
\(326\) −11.8583 −0.656771
\(327\) 48.7077 2.69354
\(328\) −9.73202 −0.537361
\(329\) −13.6297 −0.751428
\(330\) −0.891733 −0.0490883
\(331\) 10.0590 0.552894 0.276447 0.961029i \(-0.410843\pi\)
0.276447 + 0.961029i \(0.410843\pi\)
\(332\) −5.61797 −0.308326
\(333\) 27.1876 1.48987
\(334\) −22.2641 −1.21824
\(335\) 11.6316 0.635503
\(336\) 3.82779 0.208823
\(337\) −9.40521 −0.512335 −0.256167 0.966632i \(-0.582460\pi\)
−0.256167 + 0.966632i \(0.582460\pi\)
\(338\) −1.00000 −0.0543928
\(339\) 42.5147 2.30908
\(340\) 2.31225 0.125399
\(341\) −0.351489 −0.0190342
\(342\) −4.08773 −0.221039
\(343\) −17.6883 −0.955078
\(344\) 4.51150 0.243244
\(345\) 13.6244 0.733512
\(346\) −11.2452 −0.604548
\(347\) 4.86051 0.260926 0.130463 0.991453i \(-0.458354\pi\)
0.130463 + 0.991453i \(0.458354\pi\)
\(348\) −0.901663 −0.0483342
\(349\) 14.6340 0.783338 0.391669 0.920106i \(-0.371898\pi\)
0.391669 + 0.920106i \(0.371898\pi\)
\(350\) −1.50878 −0.0806476
\(351\) −1.10726 −0.0591009
\(352\) −0.351489 −0.0187344
\(353\) −5.66589 −0.301565 −0.150783 0.988567i \(-0.548179\pi\)
−0.150783 + 0.988567i \(0.548179\pi\)
\(354\) −10.3915 −0.552301
\(355\) −5.16704 −0.274238
\(356\) 11.4134 0.604911
\(357\) 8.85079 0.468433
\(358\) −14.5315 −0.768013
\(359\) 24.3350 1.28435 0.642177 0.766556i \(-0.278031\pi\)
0.642177 + 0.766556i \(0.278031\pi\)
\(360\) −3.43644 −0.181116
\(361\) −17.5850 −0.925528
\(362\) 7.28922 0.383113
\(363\) −27.5937 −1.44829
\(364\) −1.50878 −0.0790814
\(365\) 7.39342 0.386989
\(366\) −9.40890 −0.491811
\(367\) −6.57967 −0.343456 −0.171728 0.985144i \(-0.554935\pi\)
−0.171728 + 0.985144i \(0.554935\pi\)
\(368\) 5.37024 0.279943
\(369\) 33.4435 1.74100
\(370\) −7.91157 −0.411303
\(371\) −7.12822 −0.370079
\(372\) −2.53701 −0.131538
\(373\) −21.4808 −1.11223 −0.556117 0.831104i \(-0.687709\pi\)
−0.556117 + 0.831104i \(0.687709\pi\)
\(374\) −0.812729 −0.0420252
\(375\) 2.53701 0.131011
\(376\) 9.03358 0.465871
\(377\) 0.355403 0.0183042
\(378\) −1.67060 −0.0859265
\(379\) −18.4095 −0.945633 −0.472817 0.881161i \(-0.656763\pi\)
−0.472817 + 0.881161i \(0.656763\pi\)
\(380\) 1.18952 0.0610213
\(381\) −34.6169 −1.77348
\(382\) 3.20157 0.163807
\(383\) 12.8708 0.657666 0.328833 0.944388i \(-0.393345\pi\)
0.328833 + 0.944388i \(0.393345\pi\)
\(384\) −2.53701 −0.129466
\(385\) 0.530319 0.0270276
\(386\) 17.2768 0.879366
\(387\) −15.5035 −0.788088
\(388\) −14.5519 −0.738759
\(389\) −6.12432 −0.310515 −0.155258 0.987874i \(-0.549621\pi\)
−0.155258 + 0.987874i \(0.549621\pi\)
\(390\) 2.53701 0.128467
\(391\) 12.4173 0.627971
\(392\) 4.72359 0.238577
\(393\) −20.3799 −1.02803
\(394\) 11.8553 0.597261
\(395\) −2.26348 −0.113888
\(396\) 1.20787 0.0606978
\(397\) 4.08647 0.205094 0.102547 0.994728i \(-0.467301\pi\)
0.102547 + 0.994728i \(0.467301\pi\)
\(398\) 0.350989 0.0175935
\(399\) 4.55325 0.227947
\(400\) 1.00000 0.0500000
\(401\) 19.6278 0.980167 0.490083 0.871676i \(-0.336966\pi\)
0.490083 + 0.871676i \(0.336966\pi\)
\(402\) −29.5096 −1.47180
\(403\) 1.00000 0.0498135
\(404\) −10.3158 −0.513231
\(405\) −7.50020 −0.372688
\(406\) 0.536225 0.0266124
\(407\) 2.78083 0.137841
\(408\) −5.86620 −0.290420
\(409\) 21.7862 1.07726 0.538629 0.842543i \(-0.318942\pi\)
0.538629 + 0.842543i \(0.318942\pi\)
\(410\) −9.73202 −0.480630
\(411\) −44.9774 −2.21857
\(412\) −1.85938 −0.0916049
\(413\) 6.17988 0.304092
\(414\) −18.4545 −0.906990
\(415\) −5.61797 −0.275775
\(416\) 1.00000 0.0490290
\(417\) −0.220031 −0.0107750
\(418\) −0.418104 −0.0204502
\(419\) −14.3735 −0.702189 −0.351095 0.936340i \(-0.614190\pi\)
−0.351095 + 0.936340i \(0.614190\pi\)
\(420\) 3.82779 0.186777
\(421\) −28.7493 −1.40115 −0.700577 0.713577i \(-0.747074\pi\)
−0.700577 + 0.713577i \(0.747074\pi\)
\(422\) 22.3354 1.08727
\(423\) −31.0434 −1.50938
\(424\) 4.72450 0.229442
\(425\) 2.31225 0.112160
\(426\) 13.1089 0.635126
\(427\) 5.59553 0.270787
\(428\) 18.0261 0.871324
\(429\) −0.891733 −0.0430533
\(430\) 4.51150 0.217564
\(431\) −27.6116 −1.33000 −0.665002 0.746842i \(-0.731569\pi\)
−0.665002 + 0.746842i \(0.731569\pi\)
\(432\) 1.10726 0.0532729
\(433\) −6.84402 −0.328902 −0.164451 0.986385i \(-0.552585\pi\)
−0.164451 + 0.986385i \(0.552585\pi\)
\(434\) 1.50878 0.0724236
\(435\) −0.901663 −0.0432315
\(436\) 19.1988 0.919456
\(437\) 6.38803 0.305581
\(438\) −18.7572 −0.896254
\(439\) −10.0002 −0.477284 −0.238642 0.971108i \(-0.576702\pi\)
−0.238642 + 0.971108i \(0.576702\pi\)
\(440\) −0.351489 −0.0167566
\(441\) −16.2323 −0.772968
\(442\) 2.31225 0.109982
\(443\) 2.61430 0.124209 0.0621045 0.998070i \(-0.480219\pi\)
0.0621045 + 0.998070i \(0.480219\pi\)
\(444\) 20.0718 0.952564
\(445\) 11.4134 0.541049
\(446\) 15.4957 0.733742
\(447\) 7.24699 0.342771
\(448\) 1.50878 0.0712830
\(449\) 25.5365 1.20514 0.602571 0.798065i \(-0.294143\pi\)
0.602571 + 0.798065i \(0.294143\pi\)
\(450\) −3.43644 −0.161995
\(451\) 3.42070 0.161074
\(452\) 16.7578 0.788220
\(453\) 26.6424 1.25177
\(454\) 22.2125 1.04249
\(455\) −1.50878 −0.0707326
\(456\) −3.01784 −0.141323
\(457\) 5.50007 0.257282 0.128641 0.991691i \(-0.458938\pi\)
0.128641 + 0.991691i \(0.458938\pi\)
\(458\) −22.6989 −1.06065
\(459\) 2.56025 0.119502
\(460\) 5.37024 0.250389
\(461\) −39.9050 −1.85856 −0.929279 0.369378i \(-0.879571\pi\)
−0.929279 + 0.369378i \(0.879571\pi\)
\(462\) −1.34543 −0.0625949
\(463\) −20.9421 −0.973264 −0.486632 0.873607i \(-0.661775\pi\)
−0.486632 + 0.873607i \(0.661775\pi\)
\(464\) −0.355403 −0.0164992
\(465\) −2.53701 −0.117651
\(466\) −8.56342 −0.396693
\(467\) 24.9874 1.15628 0.578138 0.815939i \(-0.303779\pi\)
0.578138 + 0.815939i \(0.303779\pi\)
\(468\) −3.43644 −0.158850
\(469\) 17.5495 0.810362
\(470\) 9.03358 0.416688
\(471\) 1.71053 0.0788169
\(472\) −4.09595 −0.188531
\(473\) −1.58574 −0.0729126
\(474\) 5.74247 0.263761
\(475\) 1.18952 0.0545791
\(476\) 3.48866 0.159903
\(477\) −16.2355 −0.743371
\(478\) 7.34936 0.336152
\(479\) 2.03234 0.0928598 0.0464299 0.998922i \(-0.485216\pi\)
0.0464299 + 0.998922i \(0.485216\pi\)
\(480\) −2.53701 −0.115798
\(481\) −7.91157 −0.360736
\(482\) 12.2953 0.560036
\(483\) 20.5562 0.935338
\(484\) −10.8765 −0.494384
\(485\) −14.5519 −0.660766
\(486\) 22.3499 1.01381
\(487\) 39.5360 1.79155 0.895773 0.444512i \(-0.146623\pi\)
0.895773 + 0.444512i \(0.146623\pi\)
\(488\) −3.70865 −0.167883
\(489\) 30.0847 1.36048
\(490\) 4.72359 0.213390
\(491\) 33.9971 1.53427 0.767134 0.641487i \(-0.221682\pi\)
0.767134 + 0.641487i \(0.221682\pi\)
\(492\) 24.6903 1.11312
\(493\) −0.821780 −0.0370111
\(494\) 1.18952 0.0535192
\(495\) 1.20787 0.0542898
\(496\) −1.00000 −0.0449013
\(497\) −7.79591 −0.349695
\(498\) 14.2529 0.638687
\(499\) −20.1001 −0.899805 −0.449903 0.893078i \(-0.648541\pi\)
−0.449903 + 0.893078i \(0.648541\pi\)
\(500\) 1.00000 0.0447214
\(501\) 56.4845 2.52354
\(502\) 0.765427 0.0341627
\(503\) 3.03600 0.135369 0.0676844 0.997707i \(-0.478439\pi\)
0.0676844 + 0.997707i \(0.478439\pi\)
\(504\) −5.18482 −0.230950
\(505\) −10.3158 −0.459048
\(506\) −1.88758 −0.0839133
\(507\) 2.53701 0.112673
\(508\) −13.6448 −0.605388
\(509\) −14.7664 −0.654511 −0.327255 0.944936i \(-0.606124\pi\)
−0.327255 + 0.944936i \(0.606124\pi\)
\(510\) −5.86620 −0.259760
\(511\) 11.1550 0.493469
\(512\) −1.00000 −0.0441942
\(513\) 1.31711 0.0581517
\(514\) −19.2398 −0.848632
\(515\) −1.85938 −0.0819339
\(516\) −11.4457 −0.503871
\(517\) −3.17520 −0.139645
\(518\) −11.9368 −0.524473
\(519\) 28.5293 1.25230
\(520\) 1.00000 0.0438529
\(521\) −26.8402 −1.17589 −0.587945 0.808901i \(-0.700063\pi\)
−0.587945 + 0.808901i \(0.700063\pi\)
\(522\) 1.22132 0.0534558
\(523\) 1.49464 0.0653559 0.0326780 0.999466i \(-0.489596\pi\)
0.0326780 + 0.999466i \(0.489596\pi\)
\(524\) −8.03303 −0.350924
\(525\) 3.82779 0.167058
\(526\) −17.2134 −0.750539
\(527\) −2.31225 −0.100723
\(528\) 0.891733 0.0388077
\(529\) 5.83952 0.253892
\(530\) 4.72450 0.205219
\(531\) 14.0755 0.610824
\(532\) 1.79473 0.0778112
\(533\) −9.73202 −0.421541
\(534\) −28.9561 −1.25305
\(535\) 18.0261 0.779336
\(536\) −11.6316 −0.502410
\(537\) 36.8666 1.59091
\(538\) 17.4818 0.753696
\(539\) −1.66029 −0.0715138
\(540\) 1.10726 0.0476487
\(541\) 26.0272 1.11900 0.559499 0.828831i \(-0.310993\pi\)
0.559499 + 0.828831i \(0.310993\pi\)
\(542\) 17.3745 0.746300
\(543\) −18.4929 −0.793605
\(544\) −2.31225 −0.0991367
\(545\) 19.1988 0.822387
\(546\) 3.82779 0.163814
\(547\) 33.5020 1.43244 0.716222 0.697873i \(-0.245870\pi\)
0.716222 + 0.697873i \(0.245870\pi\)
\(548\) −17.7285 −0.757323
\(549\) 12.7446 0.543925
\(550\) −0.351489 −0.0149875
\(551\) −0.422761 −0.0180102
\(552\) −13.6244 −0.579892
\(553\) −3.41508 −0.145224
\(554\) 14.3045 0.607740
\(555\) 20.0718 0.851999
\(556\) −0.0867283 −0.00367810
\(557\) 20.5074 0.868928 0.434464 0.900689i \(-0.356938\pi\)
0.434464 + 0.900689i \(0.356938\pi\)
\(558\) 3.43644 0.145476
\(559\) 4.51150 0.190816
\(560\) 1.50878 0.0637575
\(561\) 2.06190 0.0870537
\(562\) −20.7352 −0.874660
\(563\) −24.3668 −1.02694 −0.513468 0.858109i \(-0.671640\pi\)
−0.513468 + 0.858109i \(0.671640\pi\)
\(564\) −22.9183 −0.965035
\(565\) 16.7578 0.705005
\(566\) 9.54516 0.401213
\(567\) −11.3161 −0.475233
\(568\) 5.16704 0.216804
\(569\) 24.2023 1.01461 0.507306 0.861766i \(-0.330642\pi\)
0.507306 + 0.861766i \(0.330642\pi\)
\(570\) −3.01784 −0.126403
\(571\) −30.3985 −1.27214 −0.636068 0.771633i \(-0.719440\pi\)
−0.636068 + 0.771633i \(0.719440\pi\)
\(572\) −0.351489 −0.0146965
\(573\) −8.12243 −0.339319
\(574\) −14.6835 −0.612875
\(575\) 5.37024 0.223955
\(576\) 3.43644 0.143185
\(577\) 12.8633 0.535507 0.267753 0.963487i \(-0.413719\pi\)
0.267753 + 0.963487i \(0.413719\pi\)
\(578\) 11.6535 0.484723
\(579\) −43.8315 −1.82157
\(580\) −0.355403 −0.0147573
\(581\) −8.47627 −0.351655
\(582\) 36.9183 1.53031
\(583\) −1.66061 −0.0687755
\(584\) −7.39342 −0.305942
\(585\) −3.43644 −0.142079
\(586\) −23.9946 −0.991208
\(587\) −31.6787 −1.30752 −0.653760 0.756702i \(-0.726809\pi\)
−0.653760 + 0.756702i \(0.726809\pi\)
\(588\) −11.9838 −0.494204
\(589\) −1.18952 −0.0490135
\(590\) −4.09595 −0.168628
\(591\) −30.0770 −1.23720
\(592\) 7.91157 0.325163
\(593\) 11.2562 0.462238 0.231119 0.972925i \(-0.425761\pi\)
0.231119 + 0.972925i \(0.425761\pi\)
\(594\) −0.389188 −0.0159686
\(595\) 3.48866 0.143021
\(596\) 2.85650 0.117007
\(597\) −0.890464 −0.0364442
\(598\) 5.37024 0.219606
\(599\) −40.6496 −1.66090 −0.830449 0.557095i \(-0.811916\pi\)
−0.830449 + 0.557095i \(0.811916\pi\)
\(600\) −2.53701 −0.103573
\(601\) −9.73998 −0.397302 −0.198651 0.980070i \(-0.563656\pi\)
−0.198651 + 0.980070i \(0.563656\pi\)
\(602\) 6.80686 0.277427
\(603\) 39.9714 1.62776
\(604\) 10.5015 0.427300
\(605\) −10.8765 −0.442191
\(606\) 26.1714 1.06314
\(607\) 15.4422 0.626780 0.313390 0.949625i \(-0.398535\pi\)
0.313390 + 0.949625i \(0.398535\pi\)
\(608\) −1.18952 −0.0482415
\(609\) −1.36041 −0.0551266
\(610\) −3.70865 −0.150159
\(611\) 9.03358 0.365460
\(612\) 7.94589 0.321194
\(613\) 8.72746 0.352499 0.176249 0.984346i \(-0.443604\pi\)
0.176249 + 0.984346i \(0.443604\pi\)
\(614\) −9.07352 −0.366177
\(615\) 24.6903 0.995608
\(616\) −0.530319 −0.0213672
\(617\) 33.0295 1.32972 0.664859 0.746969i \(-0.268491\pi\)
0.664859 + 0.746969i \(0.268491\pi\)
\(618\) 4.71726 0.189756
\(619\) −6.35715 −0.255516 −0.127758 0.991805i \(-0.540778\pi\)
−0.127758 + 0.991805i \(0.540778\pi\)
\(620\) −1.00000 −0.0401610
\(621\) 5.94623 0.238614
\(622\) 16.5210 0.662433
\(623\) 17.2203 0.689919
\(624\) −2.53701 −0.101562
\(625\) 1.00000 0.0400000
\(626\) 20.1373 0.804847
\(627\) 1.06074 0.0423618
\(628\) 0.674228 0.0269046
\(629\) 18.2935 0.729409
\(630\) −5.18482 −0.206568
\(631\) 19.7621 0.786718 0.393359 0.919385i \(-0.371313\pi\)
0.393359 + 0.919385i \(0.371313\pi\)
\(632\) 2.26348 0.0900363
\(633\) −56.6652 −2.25224
\(634\) 28.2431 1.12168
\(635\) −13.6448 −0.541476
\(636\) −11.9861 −0.475281
\(637\) 4.72359 0.187155
\(638\) 0.124920 0.00494565
\(639\) −17.7562 −0.702425
\(640\) −1.00000 −0.0395285
\(641\) 12.0771 0.477019 0.238509 0.971140i \(-0.423341\pi\)
0.238509 + 0.971140i \(0.423341\pi\)
\(642\) −45.7325 −1.80492
\(643\) 25.2053 0.993999 0.497000 0.867751i \(-0.334435\pi\)
0.497000 + 0.867751i \(0.334435\pi\)
\(644\) 8.10250 0.319283
\(645\) −11.4457 −0.450676
\(646\) −2.75047 −0.108216
\(647\) 39.1661 1.53978 0.769890 0.638177i \(-0.220311\pi\)
0.769890 + 0.638177i \(0.220311\pi\)
\(648\) 7.50020 0.294636
\(649\) 1.43968 0.0565124
\(650\) 1.00000 0.0392232
\(651\) −3.82779 −0.150023
\(652\) 11.8583 0.464407
\(653\) −14.7230 −0.576157 −0.288078 0.957607i \(-0.593016\pi\)
−0.288078 + 0.957607i \(0.593016\pi\)
\(654\) −48.7077 −1.90462
\(655\) −8.03303 −0.313876
\(656\) 9.73202 0.379971
\(657\) 25.4070 0.991223
\(658\) 13.6297 0.531340
\(659\) 39.2072 1.52729 0.763647 0.645633i \(-0.223407\pi\)
0.763647 + 0.645633i \(0.223407\pi\)
\(660\) 0.891733 0.0347107
\(661\) −14.4903 −0.563609 −0.281805 0.959472i \(-0.590933\pi\)
−0.281805 + 0.959472i \(0.590933\pi\)
\(662\) −10.0590 −0.390955
\(663\) −5.86620 −0.227824
\(664\) 5.61797 0.218020
\(665\) 1.79473 0.0695965
\(666\) −27.1876 −1.05350
\(667\) −1.90860 −0.0739014
\(668\) 22.2641 0.861426
\(669\) −39.3128 −1.51992
\(670\) −11.6316 −0.449369
\(671\) 1.30355 0.0503230
\(672\) −3.82779 −0.147660
\(673\) 17.0240 0.656226 0.328113 0.944639i \(-0.393587\pi\)
0.328113 + 0.944639i \(0.393587\pi\)
\(674\) 9.40521 0.362275
\(675\) 1.10726 0.0426183
\(676\) 1.00000 0.0384615
\(677\) 33.7663 1.29774 0.648872 0.760898i \(-0.275241\pi\)
0.648872 + 0.760898i \(0.275241\pi\)
\(678\) −42.5147 −1.63277
\(679\) −21.9555 −0.842576
\(680\) −2.31225 −0.0886706
\(681\) −56.3535 −2.15947
\(682\) 0.351489 0.0134592
\(683\) 30.4675 1.16581 0.582904 0.812541i \(-0.301916\pi\)
0.582904 + 0.812541i \(0.301916\pi\)
\(684\) 4.08773 0.156298
\(685\) −17.7285 −0.677371
\(686\) 17.6883 0.675342
\(687\) 57.5873 2.19709
\(688\) −4.51150 −0.171999
\(689\) 4.72450 0.179989
\(690\) −13.6244 −0.518671
\(691\) 9.26119 0.352312 0.176156 0.984362i \(-0.443634\pi\)
0.176156 + 0.984362i \(0.443634\pi\)
\(692\) 11.2452 0.427480
\(693\) 1.82241 0.0692276
\(694\) −4.86051 −0.184503
\(695\) −0.0867283 −0.00328979
\(696\) 0.901663 0.0341775
\(697\) 22.5028 0.852355
\(698\) −14.6340 −0.553904
\(699\) 21.7255 0.821734
\(700\) 1.50878 0.0570264
\(701\) −24.3820 −0.920895 −0.460447 0.887687i \(-0.652311\pi\)
−0.460447 + 0.887687i \(0.652311\pi\)
\(702\) 1.10726 0.0417907
\(703\) 9.41100 0.354942
\(704\) 0.351489 0.0132472
\(705\) −22.9183 −0.863154
\(706\) 5.66589 0.213239
\(707\) −15.5643 −0.585355
\(708\) 10.3915 0.390536
\(709\) −24.5762 −0.922979 −0.461490 0.887146i \(-0.652685\pi\)
−0.461490 + 0.887146i \(0.652685\pi\)
\(710\) 5.16704 0.193916
\(711\) −7.77830 −0.291709
\(712\) −11.4134 −0.427737
\(713\) −5.37024 −0.201117
\(714\) −8.85079 −0.331232
\(715\) −0.351489 −0.0131449
\(716\) 14.5315 0.543067
\(717\) −18.6454 −0.696326
\(718\) −24.3350 −0.908176
\(719\) −46.8558 −1.74742 −0.873712 0.486443i \(-0.838294\pi\)
−0.873712 + 0.486443i \(0.838294\pi\)
\(720\) 3.43644 0.128069
\(721\) −2.80539 −0.104478
\(722\) 17.5850 0.654447
\(723\) −31.1933 −1.16009
\(724\) −7.28922 −0.270902
\(725\) −0.355403 −0.0131994
\(726\) 27.5937 1.02410
\(727\) 13.5076 0.500970 0.250485 0.968121i \(-0.419410\pi\)
0.250485 + 0.968121i \(0.419410\pi\)
\(728\) 1.50878 0.0559190
\(729\) −34.2014 −1.26672
\(730\) −7.39342 −0.273643
\(731\) −10.4317 −0.385831
\(732\) 9.40890 0.347763
\(733\) 21.3998 0.790419 0.395210 0.918591i \(-0.370672\pi\)
0.395210 + 0.918591i \(0.370672\pi\)
\(734\) 6.57967 0.242860
\(735\) −11.9838 −0.442030
\(736\) −5.37024 −0.197950
\(737\) 4.08839 0.150598
\(738\) −33.4435 −1.23107
\(739\) −43.2269 −1.59013 −0.795064 0.606526i \(-0.792563\pi\)
−0.795064 + 0.606526i \(0.792563\pi\)
\(740\) 7.91157 0.290835
\(741\) −3.01784 −0.110863
\(742\) 7.12822 0.261685
\(743\) −15.8489 −0.581439 −0.290720 0.956808i \(-0.593895\pi\)
−0.290720 + 0.956808i \(0.593895\pi\)
\(744\) 2.53701 0.0930114
\(745\) 2.85650 0.104654
\(746\) 21.4808 0.786468
\(747\) −19.3058 −0.706363
\(748\) 0.812729 0.0297163
\(749\) 27.1974 0.993770
\(750\) −2.53701 −0.0926387
\(751\) −32.2809 −1.17795 −0.588974 0.808152i \(-0.700468\pi\)
−0.588974 + 0.808152i \(0.700468\pi\)
\(752\) −9.03358 −0.329421
\(753\) −1.94190 −0.0707667
\(754\) −0.355403 −0.0129430
\(755\) 10.5015 0.382189
\(756\) 1.67060 0.0607592
\(757\) −2.77202 −0.100751 −0.0503754 0.998730i \(-0.516042\pi\)
−0.0503754 + 0.998730i \(0.516042\pi\)
\(758\) 18.4095 0.668664
\(759\) 4.78882 0.173823
\(760\) −1.18952 −0.0431485
\(761\) −1.32550 −0.0480492 −0.0240246 0.999711i \(-0.507648\pi\)
−0.0240246 + 0.999711i \(0.507648\pi\)
\(762\) 34.6169 1.25404
\(763\) 28.9667 1.04867
\(764\) −3.20157 −0.115829
\(765\) 7.94589 0.287284
\(766\) −12.8708 −0.465040
\(767\) −4.09595 −0.147896
\(768\) 2.53701 0.0915466
\(769\) −22.9980 −0.829330 −0.414665 0.909974i \(-0.636101\pi\)
−0.414665 + 0.909974i \(0.636101\pi\)
\(770\) −0.530319 −0.0191114
\(771\) 48.8117 1.75791
\(772\) −17.2768 −0.621806
\(773\) 5.85021 0.210417 0.105209 0.994450i \(-0.466449\pi\)
0.105209 + 0.994450i \(0.466449\pi\)
\(774\) 15.5035 0.557262
\(775\) −1.00000 −0.0359211
\(776\) 14.5519 0.522382
\(777\) 30.2838 1.08643
\(778\) 6.12432 0.219567
\(779\) 11.5765 0.414770
\(780\) −2.53701 −0.0908397
\(781\) −1.81616 −0.0649872
\(782\) −12.4173 −0.444043
\(783\) −0.393522 −0.0140633
\(784\) −4.72359 −0.168700
\(785\) 0.674228 0.0240642
\(786\) 20.3799 0.726927
\(787\) 26.6262 0.949122 0.474561 0.880223i \(-0.342607\pi\)
0.474561 + 0.880223i \(0.342607\pi\)
\(788\) −11.8553 −0.422327
\(789\) 43.6706 1.55471
\(790\) 2.26348 0.0805309
\(791\) 25.2838 0.898988
\(792\) −1.20787 −0.0429198
\(793\) −3.70865 −0.131698
\(794\) −4.08647 −0.145023
\(795\) −11.9861 −0.425104
\(796\) −0.350989 −0.0124405
\(797\) −27.6444 −0.979216 −0.489608 0.871943i \(-0.662860\pi\)
−0.489608 + 0.871943i \(0.662860\pi\)
\(798\) −4.55325 −0.161183
\(799\) −20.8879 −0.738959
\(800\) −1.00000 −0.0353553
\(801\) 39.2216 1.38583
\(802\) −19.6278 −0.693083
\(803\) 2.59871 0.0917063
\(804\) 29.5096 1.04072
\(805\) 8.10250 0.285576
\(806\) −1.00000 −0.0352235
\(807\) −44.3517 −1.56125
\(808\) 10.3158 0.362909
\(809\) 1.02448 0.0360189 0.0180095 0.999838i \(-0.494267\pi\)
0.0180095 + 0.999838i \(0.494267\pi\)
\(810\) 7.50020 0.263530
\(811\) −49.8840 −1.75166 −0.875832 0.482616i \(-0.839687\pi\)
−0.875832 + 0.482616i \(0.839687\pi\)
\(812\) −0.536225 −0.0188178
\(813\) −44.0794 −1.54593
\(814\) −2.78083 −0.0974680
\(815\) 11.8583 0.415379
\(816\) 5.86620 0.205358
\(817\) −5.36654 −0.187751
\(818\) −21.7862 −0.761737
\(819\) −5.18482 −0.181172
\(820\) 9.73202 0.339857
\(821\) 15.4504 0.539223 0.269612 0.962969i \(-0.413105\pi\)
0.269612 + 0.962969i \(0.413105\pi\)
\(822\) 44.9774 1.56877
\(823\) 8.02554 0.279753 0.139876 0.990169i \(-0.455330\pi\)
0.139876 + 0.990169i \(0.455330\pi\)
\(824\) 1.85938 0.0647744
\(825\) 0.891733 0.0310461
\(826\) −6.17988 −0.215025
\(827\) 28.4999 0.991040 0.495520 0.868596i \(-0.334977\pi\)
0.495520 + 0.868596i \(0.334977\pi\)
\(828\) 18.4545 0.641339
\(829\) −53.5090 −1.85845 −0.929223 0.369520i \(-0.879522\pi\)
−0.929223 + 0.369520i \(0.879522\pi\)
\(830\) 5.61797 0.195003
\(831\) −36.2907 −1.25891
\(832\) −1.00000 −0.0346688
\(833\) −10.9221 −0.378428
\(834\) 0.220031 0.00761905
\(835\) 22.2641 0.770483
\(836\) 0.418104 0.0144604
\(837\) −1.10726 −0.0382723
\(838\) 14.3735 0.496523
\(839\) 7.20463 0.248731 0.124366 0.992236i \(-0.460310\pi\)
0.124366 + 0.992236i \(0.460310\pi\)
\(840\) −3.82779 −0.132071
\(841\) −28.8737 −0.995644
\(842\) 28.7493 0.990765
\(843\) 52.6054 1.81183
\(844\) −22.3354 −0.768815
\(845\) 1.00000 0.0344010
\(846\) 31.0434 1.06729
\(847\) −16.4102 −0.563859
\(848\) −4.72450 −0.162240
\(849\) −24.2162 −0.831098
\(850\) −2.31225 −0.0793094
\(851\) 42.4871 1.45644
\(852\) −13.1089 −0.449102
\(853\) −50.2269 −1.71974 −0.859868 0.510517i \(-0.829454\pi\)
−0.859868 + 0.510517i \(0.829454\pi\)
\(854\) −5.59553 −0.191475
\(855\) 4.08773 0.139797
\(856\) −18.0261 −0.616119
\(857\) −43.4960 −1.48579 −0.742897 0.669406i \(-0.766549\pi\)
−0.742897 + 0.669406i \(0.766549\pi\)
\(858\) 0.891733 0.0304433
\(859\) −49.4152 −1.68603 −0.843013 0.537893i \(-0.819221\pi\)
−0.843013 + 0.537893i \(0.819221\pi\)
\(860\) −4.51150 −0.153841
\(861\) 37.2521 1.26955
\(862\) 27.6116 0.940455
\(863\) 8.21167 0.279529 0.139764 0.990185i \(-0.455366\pi\)
0.139764 + 0.990185i \(0.455366\pi\)
\(864\) −1.10726 −0.0376696
\(865\) 11.2452 0.382350
\(866\) 6.84402 0.232569
\(867\) −29.5651 −1.00409
\(868\) −1.50878 −0.0512112
\(869\) −0.795587 −0.0269885
\(870\) 0.901663 0.0305693
\(871\) −11.6316 −0.394122
\(872\) −19.1988 −0.650154
\(873\) −50.0066 −1.69247
\(874\) −6.38803 −0.216078
\(875\) 1.50878 0.0510060
\(876\) 18.7572 0.633747
\(877\) −35.5763 −1.20133 −0.600664 0.799502i \(-0.705097\pi\)
−0.600664 + 0.799502i \(0.705097\pi\)
\(878\) 10.0002 0.337490
\(879\) 60.8746 2.05325
\(880\) 0.351489 0.0118487
\(881\) −42.7984 −1.44191 −0.720957 0.692980i \(-0.756297\pi\)
−0.720957 + 0.692980i \(0.756297\pi\)
\(882\) 16.2323 0.546571
\(883\) −34.9828 −1.17726 −0.588632 0.808401i \(-0.700333\pi\)
−0.588632 + 0.808401i \(0.700333\pi\)
\(884\) −2.31225 −0.0777692
\(885\) 10.3915 0.349306
\(886\) −2.61430 −0.0878291
\(887\) 26.3669 0.885315 0.442657 0.896691i \(-0.354036\pi\)
0.442657 + 0.896691i \(0.354036\pi\)
\(888\) −20.0718 −0.673564
\(889\) −20.5869 −0.690463
\(890\) −11.4134 −0.382579
\(891\) −2.63624 −0.0883173
\(892\) −15.4957 −0.518834
\(893\) −10.7457 −0.359590
\(894\) −7.24699 −0.242376
\(895\) 14.5315 0.485734
\(896\) −1.50878 −0.0504047
\(897\) −13.6244 −0.454905
\(898\) −25.5365 −0.852164
\(899\) 0.355403 0.0118534
\(900\) 3.43644 0.114548
\(901\) −10.9242 −0.363938
\(902\) −3.42070 −0.113897
\(903\) −17.2691 −0.574679
\(904\) −16.7578 −0.557356
\(905\) −7.28922 −0.242302
\(906\) −26.6424 −0.885136
\(907\) 30.6581 1.01798 0.508992 0.860771i \(-0.330018\pi\)
0.508992 + 0.860771i \(0.330018\pi\)
\(908\) −22.2125 −0.737148
\(909\) −35.4497 −1.17579
\(910\) 1.50878 0.0500155
\(911\) −39.2573 −1.30065 −0.650327 0.759655i \(-0.725368\pi\)
−0.650327 + 0.759655i \(0.725368\pi\)
\(912\) 3.01784 0.0999306
\(913\) −1.97466 −0.0653516
\(914\) −5.50007 −0.181926
\(915\) 9.40890 0.311049
\(916\) 22.6989 0.749991
\(917\) −12.1201 −0.400239
\(918\) −2.56025 −0.0845007
\(919\) −35.4666 −1.16993 −0.584967 0.811057i \(-0.698893\pi\)
−0.584967 + 0.811057i \(0.698893\pi\)
\(920\) −5.37024 −0.177052
\(921\) 23.0196 0.758523
\(922\) 39.9050 1.31420
\(923\) 5.16704 0.170075
\(924\) 1.34543 0.0442613
\(925\) 7.91157 0.260131
\(926\) 20.9421 0.688201
\(927\) −6.38964 −0.209863
\(928\) 0.355403 0.0116667
\(929\) 42.8782 1.40679 0.703395 0.710800i \(-0.251667\pi\)
0.703395 + 0.710800i \(0.251667\pi\)
\(930\) 2.53701 0.0831920
\(931\) −5.61882 −0.184149
\(932\) 8.56342 0.280504
\(933\) −41.9141 −1.37221
\(934\) −24.9874 −0.817611
\(935\) 0.812729 0.0265791
\(936\) 3.43644 0.112324
\(937\) 24.9524 0.815160 0.407580 0.913170i \(-0.366373\pi\)
0.407580 + 0.913170i \(0.366373\pi\)
\(938\) −17.5495 −0.573012
\(939\) −51.0885 −1.66721
\(940\) −9.03358 −0.294643
\(941\) −28.2746 −0.921725 −0.460862 0.887472i \(-0.652460\pi\)
−0.460862 + 0.887472i \(0.652460\pi\)
\(942\) −1.71053 −0.0557319
\(943\) 52.2633 1.70193
\(944\) 4.09595 0.133312
\(945\) 1.67060 0.0543447
\(946\) 1.58574 0.0515570
\(947\) −42.8817 −1.39347 −0.696734 0.717329i \(-0.745364\pi\)
−0.696734 + 0.717329i \(0.745364\pi\)
\(948\) −5.74247 −0.186507
\(949\) −7.39342 −0.240000
\(950\) −1.18952 −0.0385932
\(951\) −71.6531 −2.32351
\(952\) −3.48866 −0.113068
\(953\) 25.5367 0.827215 0.413607 0.910455i \(-0.364269\pi\)
0.413607 + 0.910455i \(0.364269\pi\)
\(954\) 16.2355 0.525643
\(955\) −3.20157 −0.103600
\(956\) −7.34936 −0.237695
\(957\) −0.316925 −0.0102447
\(958\) −2.03234 −0.0656618
\(959\) −26.7483 −0.863749
\(960\) 2.53701 0.0818818
\(961\) 1.00000 0.0322581
\(962\) 7.91157 0.255079
\(963\) 61.9456 1.99617
\(964\) −12.2953 −0.396005
\(965\) −17.2768 −0.556160
\(966\) −20.5562 −0.661384
\(967\) −20.4243 −0.656800 −0.328400 0.944539i \(-0.606509\pi\)
−0.328400 + 0.944539i \(0.606509\pi\)
\(968\) 10.8765 0.349583
\(969\) 6.97798 0.224165
\(970\) 14.5519 0.467232
\(971\) −20.6215 −0.661776 −0.330888 0.943670i \(-0.607348\pi\)
−0.330888 + 0.943670i \(0.607348\pi\)
\(972\) −22.3499 −0.716873
\(973\) −0.130854 −0.00419498
\(974\) −39.5360 −1.26681
\(975\) −2.53701 −0.0812495
\(976\) 3.70865 0.118711
\(977\) −49.7860 −1.59279 −0.796397 0.604774i \(-0.793264\pi\)
−0.796397 + 0.604774i \(0.793264\pi\)
\(978\) −30.0847 −0.962003
\(979\) 4.01170 0.128215
\(980\) −4.72359 −0.150890
\(981\) 65.9756 2.10644
\(982\) −33.9971 −1.08489
\(983\) −18.4745 −0.589244 −0.294622 0.955614i \(-0.595194\pi\)
−0.294622 + 0.955614i \(0.595194\pi\)
\(984\) −24.6903 −0.787097
\(985\) −11.8553 −0.377741
\(986\) 0.821780 0.0261708
\(987\) −34.5786 −1.10065
\(988\) −1.18952 −0.0378438
\(989\) −24.2279 −0.770402
\(990\) −1.20787 −0.0383887
\(991\) 39.0056 1.23905 0.619527 0.784975i \(-0.287324\pi\)
0.619527 + 0.784975i \(0.287324\pi\)
\(992\) 1.00000 0.0317500
\(993\) 25.5199 0.809849
\(994\) 7.79591 0.247271
\(995\) −0.350989 −0.0111271
\(996\) −14.2529 −0.451620
\(997\) −26.3619 −0.834891 −0.417446 0.908702i \(-0.637075\pi\)
−0.417446 + 0.908702i \(0.637075\pi\)
\(998\) 20.1001 0.636258
\(999\) 8.76013 0.277158
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.l.1.7 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4030.2.a.l.1.7 8 1.1 even 1 trivial