Properties

Label 6026.2.a.f.1.7
Level $6026$
Weight $2$
Character 6026.1
Self dual yes
Analytic conductor $48.118$
Analytic rank $1$
Dimension $20$
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] = [6026,2,Mod(1,6026)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6026.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6026 = 2 \cdot 23 \cdot 131 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6026.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: \(48.1178522580\)
Analytic rank: \(1\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} - 5 x^{19} - 17 x^{18} + 115 x^{17} + 78 x^{16} - 1083 x^{15} + 248 x^{14} + 5359 x^{13} - 3723 x^{12} - 14776 x^{11} + 14837 x^{10} + 21886 x^{9} - 28084 x^{8} - 14682 x^{7} + \cdots - 18 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(1.51806\) of defining polynomial
Character \(\chi\) \(=\) 6026.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.51806 q^{3} +1.00000 q^{4} -3.34509 q^{5} -1.51806 q^{6} +1.42565 q^{7} +1.00000 q^{8} -0.695496 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -1.51806 q^{3} +1.00000 q^{4} -3.34509 q^{5} -1.51806 q^{6} +1.42565 q^{7} +1.00000 q^{8} -0.695496 q^{9} -3.34509 q^{10} -0.242144 q^{11} -1.51806 q^{12} -0.284609 q^{13} +1.42565 q^{14} +5.07805 q^{15} +1.00000 q^{16} -0.0256674 q^{17} -0.695496 q^{18} -1.01981 q^{19} -3.34509 q^{20} -2.16422 q^{21} -0.242144 q^{22} +1.00000 q^{23} -1.51806 q^{24} +6.18963 q^{25} -0.284609 q^{26} +5.60998 q^{27} +1.42565 q^{28} +5.53979 q^{29} +5.07805 q^{30} +4.70532 q^{31} +1.00000 q^{32} +0.367589 q^{33} -0.0256674 q^{34} -4.76893 q^{35} -0.695496 q^{36} -9.28988 q^{37} -1.01981 q^{38} +0.432053 q^{39} -3.34509 q^{40} +2.00968 q^{41} -2.16422 q^{42} -1.53875 q^{43} -0.242144 q^{44} +2.32650 q^{45} +1.00000 q^{46} +4.25361 q^{47} -1.51806 q^{48} -4.96752 q^{49} +6.18963 q^{50} +0.0389646 q^{51} -0.284609 q^{52} +11.3478 q^{53} +5.60998 q^{54} +0.809994 q^{55} +1.42565 q^{56} +1.54814 q^{57} +5.53979 q^{58} -7.14634 q^{59} +5.07805 q^{60} +11.8713 q^{61} +4.70532 q^{62} -0.991535 q^{63} +1.00000 q^{64} +0.952042 q^{65} +0.367589 q^{66} +0.0480368 q^{67} -0.0256674 q^{68} -1.51806 q^{69} -4.76893 q^{70} -11.2135 q^{71} -0.695496 q^{72} -9.28856 q^{73} -9.28988 q^{74} -9.39623 q^{75} -1.01981 q^{76} -0.345213 q^{77} +0.432053 q^{78} -11.3638 q^{79} -3.34509 q^{80} -6.42980 q^{81} +2.00968 q^{82} -3.54124 q^{83} -2.16422 q^{84} +0.0858597 q^{85} -1.53875 q^{86} -8.40974 q^{87} -0.242144 q^{88} +5.04371 q^{89} +2.32650 q^{90} -0.405753 q^{91} +1.00000 q^{92} -7.14296 q^{93} +4.25361 q^{94} +3.41137 q^{95} -1.51806 q^{96} -8.28272 q^{97} -4.96752 q^{98} +0.168410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 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
\(3\) −1.51806 −0.876452 −0.438226 0.898865i \(-0.644393\pi\)
−0.438226 + 0.898865i \(0.644393\pi\)
\(4\) 1.00000 0.500000
\(5\) −3.34509 −1.49597 −0.747985 0.663716i \(-0.768979\pi\)
−0.747985 + 0.663716i \(0.768979\pi\)
\(6\) −1.51806 −0.619745
\(7\) 1.42565 0.538846 0.269423 0.963022i \(-0.413167\pi\)
0.269423 + 0.963022i \(0.413167\pi\)
\(8\) 1.00000 0.353553
\(9\) −0.695496 −0.231832
\(10\) −3.34509 −1.05781
\(11\) −0.242144 −0.0730092 −0.0365046 0.999333i \(-0.511622\pi\)
−0.0365046 + 0.999333i \(0.511622\pi\)
\(12\) −1.51806 −0.438226
\(13\) −0.284609 −0.0789362 −0.0394681 0.999221i \(-0.512566\pi\)
−0.0394681 + 0.999221i \(0.512566\pi\)
\(14\) 1.42565 0.381021
\(15\) 5.07805 1.31115
\(16\) 1.00000 0.250000
\(17\) −0.0256674 −0.00622525 −0.00311263 0.999995i \(-0.500991\pi\)
−0.00311263 + 0.999995i \(0.500991\pi\)
\(18\) −0.695496 −0.163930
\(19\) −1.01981 −0.233961 −0.116981 0.993134i \(-0.537322\pi\)
−0.116981 + 0.993134i \(0.537322\pi\)
\(20\) −3.34509 −0.747985
\(21\) −2.16422 −0.472272
\(22\) −0.242144 −0.0516253
\(23\) 1.00000 0.208514
\(24\) −1.51806 −0.309873
\(25\) 6.18963 1.23793
\(26\) −0.284609 −0.0558163
\(27\) 5.60998 1.07964
\(28\) 1.42565 0.269423
\(29\) 5.53979 1.02871 0.514357 0.857576i \(-0.328031\pi\)
0.514357 + 0.857576i \(0.328031\pi\)
\(30\) 5.07805 0.927120
\(31\) 4.70532 0.845101 0.422551 0.906339i \(-0.361135\pi\)
0.422551 + 0.906339i \(0.361135\pi\)
\(32\) 1.00000 0.176777
\(33\) 0.367589 0.0639890
\(34\) −0.0256674 −0.00440192
\(35\) −4.76893 −0.806097
\(36\) −0.695496 −0.115916
\(37\) −9.28988 −1.52725 −0.763624 0.645662i \(-0.776582\pi\)
−0.763624 + 0.645662i \(0.776582\pi\)
\(38\) −1.01981 −0.165436
\(39\) 0.432053 0.0691838
\(40\) −3.34509 −0.528905
\(41\) 2.00968 0.313859 0.156929 0.987610i \(-0.449841\pi\)
0.156929 + 0.987610i \(0.449841\pi\)
\(42\) −2.16422 −0.333947
\(43\) −1.53875 −0.234657 −0.117328 0.993093i \(-0.537433\pi\)
−0.117328 + 0.993093i \(0.537433\pi\)
\(44\) −0.242144 −0.0365046
\(45\) 2.32650 0.346814
\(46\) 1.00000 0.147442
\(47\) 4.25361 0.620453 0.310226 0.950663i \(-0.399595\pi\)
0.310226 + 0.950663i \(0.399595\pi\)
\(48\) −1.51806 −0.219113
\(49\) −4.96752 −0.709645
\(50\) 6.18963 0.875346
\(51\) 0.0389646 0.00545614
\(52\) −0.284609 −0.0394681
\(53\) 11.3478 1.55874 0.779370 0.626564i \(-0.215539\pi\)
0.779370 + 0.626564i \(0.215539\pi\)
\(54\) 5.60998 0.763422
\(55\) 0.809994 0.109220
\(56\) 1.42565 0.190511
\(57\) 1.54814 0.205056
\(58\) 5.53979 0.727411
\(59\) −7.14634 −0.930374 −0.465187 0.885212i \(-0.654013\pi\)
−0.465187 + 0.885212i \(0.654013\pi\)
\(60\) 5.07805 0.655573
\(61\) 11.8713 1.51996 0.759980 0.649947i \(-0.225209\pi\)
0.759980 + 0.649947i \(0.225209\pi\)
\(62\) 4.70532 0.597577
\(63\) −0.991535 −0.124922
\(64\) 1.00000 0.125000
\(65\) 0.952042 0.118086
\(66\) 0.367589 0.0452471
\(67\) 0.0480368 0.00586863 0.00293432 0.999996i \(-0.499066\pi\)
0.00293432 + 0.999996i \(0.499066\pi\)
\(68\) −0.0256674 −0.00311263
\(69\) −1.51806 −0.182753
\(70\) −4.76893 −0.569997
\(71\) −11.2135 −1.33080 −0.665400 0.746487i \(-0.731739\pi\)
−0.665400 + 0.746487i \(0.731739\pi\)
\(72\) −0.695496 −0.0819650
\(73\) −9.28856 −1.08714 −0.543572 0.839363i \(-0.682928\pi\)
−0.543572 + 0.839363i \(0.682928\pi\)
\(74\) −9.28988 −1.07993
\(75\) −9.39623 −1.08498
\(76\) −1.01981 −0.116981
\(77\) −0.345213 −0.0393407
\(78\) 0.432053 0.0489203
\(79\) −11.3638 −1.27852 −0.639262 0.768989i \(-0.720760\pi\)
−0.639262 + 0.768989i \(0.720760\pi\)
\(80\) −3.34509 −0.373993
\(81\) −6.42980 −0.714422
\(82\) 2.00968 0.221932
\(83\) −3.54124 −0.388702 −0.194351 0.980932i \(-0.562260\pi\)
−0.194351 + 0.980932i \(0.562260\pi\)
\(84\) −2.16422 −0.236136
\(85\) 0.0858597 0.00931280
\(86\) −1.53875 −0.165927
\(87\) −8.40974 −0.901618
\(88\) −0.242144 −0.0258126
\(89\) 5.04371 0.534632 0.267316 0.963609i \(-0.413863\pi\)
0.267316 + 0.963609i \(0.413863\pi\)
\(90\) 2.32650 0.245234
\(91\) −0.405753 −0.0425344
\(92\) 1.00000 0.104257
\(93\) −7.14296 −0.740691
\(94\) 4.25361 0.438726
\(95\) 3.41137 0.349999
\(96\) −1.51806 −0.154936
\(97\) −8.28272 −0.840983 −0.420491 0.907297i \(-0.638142\pi\)
−0.420491 + 0.907297i \(0.638142\pi\)
\(98\) −4.96752 −0.501795
\(99\) 0.168410 0.0169259
\(100\) 6.18963 0.618963
\(101\) −2.54819 −0.253554 −0.126777 0.991931i \(-0.540463\pi\)
−0.126777 + 0.991931i \(0.540463\pi\)
\(102\) 0.0389646 0.00385807
\(103\) 12.5761 1.23916 0.619581 0.784933i \(-0.287303\pi\)
0.619581 + 0.784933i \(0.287303\pi\)
\(104\) −0.284609 −0.0279082
\(105\) 7.23952 0.706505
\(106\) 11.3478 1.10220
\(107\) −0.240696 −0.0232690 −0.0116345 0.999932i \(-0.503703\pi\)
−0.0116345 + 0.999932i \(0.503703\pi\)
\(108\) 5.60998 0.539821
\(109\) 8.40992 0.805524 0.402762 0.915305i \(-0.368050\pi\)
0.402762 + 0.915305i \(0.368050\pi\)
\(110\) 0.809994 0.0772299
\(111\) 14.1026 1.33856
\(112\) 1.42565 0.134711
\(113\) −4.52840 −0.425996 −0.212998 0.977053i \(-0.568323\pi\)
−0.212998 + 0.977053i \(0.568323\pi\)
\(114\) 1.54814 0.144996
\(115\) −3.34509 −0.311931
\(116\) 5.53979 0.514357
\(117\) 0.197944 0.0182999
\(118\) −7.14634 −0.657874
\(119\) −0.0365927 −0.00335445
\(120\) 5.07805 0.463560
\(121\) −10.9414 −0.994670
\(122\) 11.8713 1.07477
\(123\) −3.05081 −0.275082
\(124\) 4.70532 0.422551
\(125\) −3.97943 −0.355931
\(126\) −0.991535 −0.0883329
\(127\) 3.57380 0.317124 0.158562 0.987349i \(-0.449314\pi\)
0.158562 + 0.987349i \(0.449314\pi\)
\(128\) 1.00000 0.0883883
\(129\) 2.33591 0.205665
\(130\) 0.952042 0.0834996
\(131\) −1.00000 −0.0873704
\(132\) 0.367589 0.0319945
\(133\) −1.45390 −0.126069
\(134\) 0.0480368 0.00414975
\(135\) −18.7659 −1.61511
\(136\) −0.0256674 −0.00220096
\(137\) −14.4973 −1.23859 −0.619293 0.785160i \(-0.712581\pi\)
−0.619293 + 0.785160i \(0.712581\pi\)
\(138\) −1.51806 −0.129226
\(139\) 3.57168 0.302946 0.151473 0.988461i \(-0.451598\pi\)
0.151473 + 0.988461i \(0.451598\pi\)
\(140\) −4.76893 −0.403048
\(141\) −6.45723 −0.543797
\(142\) −11.2135 −0.941018
\(143\) 0.0689163 0.00576307
\(144\) −0.695496 −0.0579580
\(145\) −18.5311 −1.53893
\(146\) −9.28856 −0.768726
\(147\) 7.54099 0.621970
\(148\) −9.28988 −0.763624
\(149\) 3.68598 0.301967 0.150984 0.988536i \(-0.451756\pi\)
0.150984 + 0.988536i \(0.451756\pi\)
\(150\) −9.39623 −0.767199
\(151\) −17.0736 −1.38943 −0.694716 0.719284i \(-0.744470\pi\)
−0.694716 + 0.719284i \(0.744470\pi\)
\(152\) −1.01981 −0.0827178
\(153\) 0.0178516 0.00144321
\(154\) −0.345213 −0.0278181
\(155\) −15.7397 −1.26425
\(156\) 0.432053 0.0345919
\(157\) 1.73823 0.138726 0.0693631 0.997591i \(-0.477903\pi\)
0.0693631 + 0.997591i \(0.477903\pi\)
\(158\) −11.3638 −0.904053
\(159\) −17.2266 −1.36616
\(160\) −3.34509 −0.264453
\(161\) 1.42565 0.112357
\(162\) −6.42980 −0.505173
\(163\) 1.72531 0.135137 0.0675685 0.997715i \(-0.478476\pi\)
0.0675685 + 0.997715i \(0.478476\pi\)
\(164\) 2.00968 0.156929
\(165\) −1.22962 −0.0957257
\(166\) −3.54124 −0.274854
\(167\) −23.3349 −1.80571 −0.902853 0.429950i \(-0.858531\pi\)
−0.902853 + 0.429950i \(0.858531\pi\)
\(168\) −2.16422 −0.166973
\(169\) −12.9190 −0.993769
\(170\) 0.0858597 0.00658514
\(171\) 0.709276 0.0542397
\(172\) −1.53875 −0.117328
\(173\) −2.53110 −0.192436 −0.0962178 0.995360i \(-0.530675\pi\)
−0.0962178 + 0.995360i \(0.530675\pi\)
\(174\) −8.40974 −0.637540
\(175\) 8.82426 0.667051
\(176\) −0.242144 −0.0182523
\(177\) 10.8486 0.815428
\(178\) 5.04371 0.378042
\(179\) −13.9783 −1.04479 −0.522394 0.852704i \(-0.674961\pi\)
−0.522394 + 0.852704i \(0.674961\pi\)
\(180\) 2.32650 0.173407
\(181\) 0.262286 0.0194956 0.00974778 0.999952i \(-0.496897\pi\)
0.00974778 + 0.999952i \(0.496897\pi\)
\(182\) −0.405753 −0.0300764
\(183\) −18.0213 −1.33217
\(184\) 1.00000 0.0737210
\(185\) 31.0755 2.28472
\(186\) −7.14296 −0.523747
\(187\) 0.00621520 0.000454501 0
\(188\) 4.25361 0.310226
\(189\) 7.99788 0.581760
\(190\) 3.41137 0.247487
\(191\) −0.485117 −0.0351019 −0.0175509 0.999846i \(-0.505587\pi\)
−0.0175509 + 0.999846i \(0.505587\pi\)
\(192\) −1.51806 −0.109556
\(193\) −10.6447 −0.766223 −0.383111 0.923702i \(-0.625147\pi\)
−0.383111 + 0.923702i \(0.625147\pi\)
\(194\) −8.28272 −0.594665
\(195\) −1.44526 −0.103497
\(196\) −4.96752 −0.354823
\(197\) 23.5902 1.68073 0.840366 0.542019i \(-0.182340\pi\)
0.840366 + 0.542019i \(0.182340\pi\)
\(198\) 0.168410 0.0119684
\(199\) 3.73124 0.264501 0.132250 0.991216i \(-0.457780\pi\)
0.132250 + 0.991216i \(0.457780\pi\)
\(200\) 6.18963 0.437673
\(201\) −0.0729227 −0.00514357
\(202\) −2.54819 −0.179290
\(203\) 7.89782 0.554318
\(204\) 0.0389646 0.00272807
\(205\) −6.72255 −0.469523
\(206\) 12.5761 0.876220
\(207\) −0.695496 −0.0483403
\(208\) −0.284609 −0.0197341
\(209\) 0.246942 0.0170813
\(210\) 7.23952 0.499575
\(211\) −10.4901 −0.722170 −0.361085 0.932533i \(-0.617594\pi\)
−0.361085 + 0.932533i \(0.617594\pi\)
\(212\) 11.3478 0.779370
\(213\) 17.0228 1.16638
\(214\) −0.240696 −0.0164537
\(215\) 5.14725 0.351039
\(216\) 5.60998 0.381711
\(217\) 6.70815 0.455379
\(218\) 8.40992 0.569592
\(219\) 14.1006 0.952829
\(220\) 0.809994 0.0546098
\(221\) 0.00730516 0.000491398 0
\(222\) 14.1026 0.946504
\(223\) −11.4435 −0.766313 −0.383156 0.923684i \(-0.625163\pi\)
−0.383156 + 0.923684i \(0.625163\pi\)
\(224\) 1.42565 0.0952553
\(225\) −4.30486 −0.286991
\(226\) −4.52840 −0.301225
\(227\) −11.2876 −0.749186 −0.374593 0.927189i \(-0.622218\pi\)
−0.374593 + 0.927189i \(0.622218\pi\)
\(228\) 1.54814 0.102528
\(229\) −2.10543 −0.139131 −0.0695655 0.997577i \(-0.522161\pi\)
−0.0695655 + 0.997577i \(0.522161\pi\)
\(230\) −3.34509 −0.220569
\(231\) 0.524054 0.0344802
\(232\) 5.53979 0.363705
\(233\) −20.9416 −1.37193 −0.685966 0.727634i \(-0.740620\pi\)
−0.685966 + 0.727634i \(0.740620\pi\)
\(234\) 0.197944 0.0129400
\(235\) −14.2287 −0.928179
\(236\) −7.14634 −0.465187
\(237\) 17.2509 1.12056
\(238\) −0.0365927 −0.00237196
\(239\) 1.88750 0.122093 0.0610463 0.998135i \(-0.480556\pi\)
0.0610463 + 0.998135i \(0.480556\pi\)
\(240\) 5.07805 0.327787
\(241\) 10.5965 0.682578 0.341289 0.939958i \(-0.389136\pi\)
0.341289 + 0.939958i \(0.389136\pi\)
\(242\) −10.9414 −0.703338
\(243\) −7.06913 −0.453485
\(244\) 11.8713 0.759980
\(245\) 16.6168 1.06161
\(246\) −3.05081 −0.194512
\(247\) 0.290248 0.0184680
\(248\) 4.70532 0.298788
\(249\) 5.37582 0.340678
\(250\) −3.97943 −0.251682
\(251\) −4.15487 −0.262253 −0.131126 0.991366i \(-0.541859\pi\)
−0.131126 + 0.991366i \(0.541859\pi\)
\(252\) −0.991535 −0.0624608
\(253\) −0.242144 −0.0152235
\(254\) 3.57380 0.224240
\(255\) −0.130340 −0.00816222
\(256\) 1.00000 0.0625000
\(257\) 15.4462 0.963506 0.481753 0.876307i \(-0.340000\pi\)
0.481753 + 0.876307i \(0.340000\pi\)
\(258\) 2.33591 0.145427
\(259\) −13.2441 −0.822951
\(260\) 0.952042 0.0590431
\(261\) −3.85290 −0.238489
\(262\) −1.00000 −0.0617802
\(263\) −14.0059 −0.863640 −0.431820 0.901960i \(-0.642129\pi\)
−0.431820 + 0.901960i \(0.642129\pi\)
\(264\) 0.367589 0.0226235
\(265\) −37.9594 −2.33183
\(266\) −1.45390 −0.0891443
\(267\) −7.65664 −0.468579
\(268\) 0.0480368 0.00293432
\(269\) 15.9454 0.972207 0.486104 0.873901i \(-0.338418\pi\)
0.486104 + 0.873901i \(0.338418\pi\)
\(270\) −18.7659 −1.14206
\(271\) −29.9498 −1.81932 −0.909661 0.415353i \(-0.863658\pi\)
−0.909661 + 0.415353i \(0.863658\pi\)
\(272\) −0.0256674 −0.00155631
\(273\) 0.615957 0.0372794
\(274\) −14.4973 −0.875813
\(275\) −1.49878 −0.0903800
\(276\) −1.51806 −0.0913764
\(277\) −11.4541 −0.688208 −0.344104 0.938931i \(-0.611817\pi\)
−0.344104 + 0.938931i \(0.611817\pi\)
\(278\) 3.57168 0.214215
\(279\) −3.27253 −0.195921
\(280\) −4.76893 −0.284998
\(281\) 13.5857 0.810452 0.405226 0.914216i \(-0.367193\pi\)
0.405226 + 0.914216i \(0.367193\pi\)
\(282\) −6.45723 −0.384523
\(283\) 23.4573 1.39439 0.697197 0.716879i \(-0.254430\pi\)
0.697197 + 0.716879i \(0.254430\pi\)
\(284\) −11.2135 −0.665400
\(285\) −5.17866 −0.306758
\(286\) 0.0689163 0.00407510
\(287\) 2.86510 0.169121
\(288\) −0.695496 −0.0409825
\(289\) −16.9993 −0.999961
\(290\) −18.5311 −1.08818
\(291\) 12.5737 0.737081
\(292\) −9.28856 −0.543572
\(293\) −20.7920 −1.21468 −0.607341 0.794441i \(-0.707764\pi\)
−0.607341 + 0.794441i \(0.707764\pi\)
\(294\) 7.54099 0.439799
\(295\) 23.9051 1.39181
\(296\) −9.28988 −0.539964
\(297\) −1.35842 −0.0788237
\(298\) 3.68598 0.213523
\(299\) −0.284609 −0.0164593
\(300\) −9.39623 −0.542492
\(301\) −2.19372 −0.126444
\(302\) −17.0736 −0.982477
\(303\) 3.86830 0.222228
\(304\) −1.01981 −0.0584904
\(305\) −39.7105 −2.27381
\(306\) 0.0178516 0.00102051
\(307\) −14.5758 −0.831886 −0.415943 0.909391i \(-0.636548\pi\)
−0.415943 + 0.909391i \(0.636548\pi\)
\(308\) −0.345213 −0.0196703
\(309\) −19.0913 −1.08607
\(310\) −15.7397 −0.893957
\(311\) 21.0112 1.19144 0.595718 0.803194i \(-0.296868\pi\)
0.595718 + 0.803194i \(0.296868\pi\)
\(312\) 0.432053 0.0244602
\(313\) 5.22613 0.295398 0.147699 0.989032i \(-0.452813\pi\)
0.147699 + 0.989032i \(0.452813\pi\)
\(314\) 1.73823 0.0980942
\(315\) 3.31677 0.186879
\(316\) −11.3638 −0.639262
\(317\) −15.7787 −0.886222 −0.443111 0.896467i \(-0.646125\pi\)
−0.443111 + 0.896467i \(0.646125\pi\)
\(318\) −17.2266 −0.966021
\(319\) −1.34143 −0.0751056
\(320\) −3.34509 −0.186996
\(321\) 0.365391 0.0203941
\(322\) 1.42565 0.0794484
\(323\) 0.0261760 0.00145647
\(324\) −6.42980 −0.357211
\(325\) −1.76162 −0.0977173
\(326\) 1.72531 0.0955562
\(327\) −12.7668 −0.706003
\(328\) 2.00968 0.110966
\(329\) 6.06416 0.334328
\(330\) −1.22962 −0.0676883
\(331\) 15.0855 0.829173 0.414586 0.910010i \(-0.363926\pi\)
0.414586 + 0.910010i \(0.363926\pi\)
\(332\) −3.54124 −0.194351
\(333\) 6.46107 0.354065
\(334\) −23.3349 −1.27683
\(335\) −0.160688 −0.00877930
\(336\) −2.16422 −0.118068
\(337\) −25.5476 −1.39167 −0.695833 0.718203i \(-0.744965\pi\)
−0.695833 + 0.718203i \(0.744965\pi\)
\(338\) −12.9190 −0.702701
\(339\) 6.87438 0.373365
\(340\) 0.0858597 0.00465640
\(341\) −1.13937 −0.0617001
\(342\) 0.709276 0.0383533
\(343\) −17.0615 −0.921235
\(344\) −1.53875 −0.0829637
\(345\) 5.07805 0.273393
\(346\) −2.53110 −0.136073
\(347\) 0.898187 0.0482172 0.0241086 0.999709i \(-0.492325\pi\)
0.0241086 + 0.999709i \(0.492325\pi\)
\(348\) −8.40974 −0.450809
\(349\) −11.0097 −0.589337 −0.294669 0.955599i \(-0.595209\pi\)
−0.294669 + 0.955599i \(0.595209\pi\)
\(350\) 8.82426 0.471677
\(351\) −1.59665 −0.0852228
\(352\) −0.242144 −0.0129063
\(353\) 9.77410 0.520223 0.260111 0.965579i \(-0.416241\pi\)
0.260111 + 0.965579i \(0.416241\pi\)
\(354\) 10.8486 0.576595
\(355\) 37.5102 1.99084
\(356\) 5.04371 0.267316
\(357\) 0.0555500 0.00294002
\(358\) −13.9783 −0.738776
\(359\) −5.52789 −0.291751 −0.145875 0.989303i \(-0.546600\pi\)
−0.145875 + 0.989303i \(0.546600\pi\)
\(360\) 2.32650 0.122617
\(361\) −17.9600 −0.945262
\(362\) 0.262286 0.0137854
\(363\) 16.6096 0.871780
\(364\) −0.405753 −0.0212672
\(365\) 31.0711 1.62633
\(366\) −18.0213 −0.941988
\(367\) −20.1212 −1.05032 −0.525160 0.851004i \(-0.675994\pi\)
−0.525160 + 0.851004i \(0.675994\pi\)
\(368\) 1.00000 0.0521286
\(369\) −1.39772 −0.0727624
\(370\) 31.0755 1.61554
\(371\) 16.1780 0.839920
\(372\) −7.14296 −0.370345
\(373\) 8.89645 0.460640 0.230320 0.973115i \(-0.426023\pi\)
0.230320 + 0.973115i \(0.426023\pi\)
\(374\) 0.00621520 0.000321381 0
\(375\) 6.04102 0.311957
\(376\) 4.25361 0.219363
\(377\) −1.57667 −0.0812028
\(378\) 7.99788 0.411367
\(379\) −24.6742 −1.26743 −0.633714 0.773567i \(-0.718470\pi\)
−0.633714 + 0.773567i \(0.718470\pi\)
\(380\) 3.41137 0.175000
\(381\) −5.42525 −0.277944
\(382\) −0.485117 −0.0248208
\(383\) −1.03057 −0.0526598 −0.0263299 0.999653i \(-0.508382\pi\)
−0.0263299 + 0.999653i \(0.508382\pi\)
\(384\) −1.51806 −0.0774681
\(385\) 1.15477 0.0588525
\(386\) −10.6447 −0.541801
\(387\) 1.07019 0.0544009
\(388\) −8.28272 −0.420491
\(389\) −10.7550 −0.545298 −0.272649 0.962114i \(-0.587900\pi\)
−0.272649 + 0.962114i \(0.587900\pi\)
\(390\) −1.44526 −0.0731834
\(391\) −0.0256674 −0.00129806
\(392\) −4.96752 −0.250898
\(393\) 1.51806 0.0765760
\(394\) 23.5902 1.18846
\(395\) 38.0128 1.91263
\(396\) 0.168410 0.00846293
\(397\) −8.17805 −0.410445 −0.205222 0.978715i \(-0.565792\pi\)
−0.205222 + 0.978715i \(0.565792\pi\)
\(398\) 3.73124 0.187030
\(399\) 2.20711 0.110493
\(400\) 6.18963 0.309482
\(401\) −28.2132 −1.40890 −0.704451 0.709752i \(-0.748807\pi\)
−0.704451 + 0.709752i \(0.748807\pi\)
\(402\) −0.0729227 −0.00363706
\(403\) −1.33918 −0.0667091
\(404\) −2.54819 −0.126777
\(405\) 21.5083 1.06875
\(406\) 7.89782 0.391962
\(407\) 2.24949 0.111503
\(408\) 0.0389646 0.00192904
\(409\) 15.0756 0.745441 0.372721 0.927944i \(-0.378425\pi\)
0.372721 + 0.927944i \(0.378425\pi\)
\(410\) −6.72255 −0.332003
\(411\) 22.0077 1.08556
\(412\) 12.5761 0.619581
\(413\) −10.1882 −0.501328
\(414\) −0.695496 −0.0341818
\(415\) 11.8458 0.581486
\(416\) −0.284609 −0.0139541
\(417\) −5.42202 −0.265517
\(418\) 0.246942 0.0120783
\(419\) −15.9757 −0.780463 −0.390232 0.920717i \(-0.627605\pi\)
−0.390232 + 0.920717i \(0.627605\pi\)
\(420\) 7.23952 0.353253
\(421\) 20.6924 1.00849 0.504243 0.863562i \(-0.331772\pi\)
0.504243 + 0.863562i \(0.331772\pi\)
\(422\) −10.4901 −0.510652
\(423\) −2.95837 −0.143841
\(424\) 11.3478 0.551098
\(425\) −0.158872 −0.00770641
\(426\) 17.0228 0.824757
\(427\) 16.9243 0.819024
\(428\) −0.240696 −0.0116345
\(429\) −0.104619 −0.00505105
\(430\) 5.14725 0.248222
\(431\) 33.2990 1.60395 0.801977 0.597355i \(-0.203781\pi\)
0.801977 + 0.597355i \(0.203781\pi\)
\(432\) 5.60998 0.269910
\(433\) 3.63773 0.174818 0.0874091 0.996173i \(-0.472141\pi\)
0.0874091 + 0.996173i \(0.472141\pi\)
\(434\) 6.70815 0.322002
\(435\) 28.1313 1.34879
\(436\) 8.40992 0.402762
\(437\) −1.01981 −0.0487843
\(438\) 14.1006 0.673752
\(439\) −30.7511 −1.46767 −0.733835 0.679328i \(-0.762271\pi\)
−0.733835 + 0.679328i \(0.762271\pi\)
\(440\) 0.809994 0.0386149
\(441\) 3.45489 0.164518
\(442\) 0.00730516 0.000347471 0
\(443\) 15.9167 0.756226 0.378113 0.925759i \(-0.376573\pi\)
0.378113 + 0.925759i \(0.376573\pi\)
\(444\) 14.1026 0.669280
\(445\) −16.8717 −0.799793
\(446\) −11.4435 −0.541865
\(447\) −5.59554 −0.264660
\(448\) 1.42565 0.0673557
\(449\) 1.59335 0.0751949 0.0375975 0.999293i \(-0.488030\pi\)
0.0375975 + 0.999293i \(0.488030\pi\)
\(450\) −4.30486 −0.202933
\(451\) −0.486631 −0.0229146
\(452\) −4.52840 −0.212998
\(453\) 25.9188 1.21777
\(454\) −11.2876 −0.529754
\(455\) 1.35728 0.0636302
\(456\) 1.54814 0.0724982
\(457\) −20.2064 −0.945215 −0.472607 0.881273i \(-0.656687\pi\)
−0.472607 + 0.881273i \(0.656687\pi\)
\(458\) −2.10543 −0.0983805
\(459\) −0.143994 −0.00672104
\(460\) −3.34509 −0.155966
\(461\) −35.4263 −1.64997 −0.824983 0.565157i \(-0.808816\pi\)
−0.824983 + 0.565157i \(0.808816\pi\)
\(462\) 0.524054 0.0243812
\(463\) −12.8218 −0.595880 −0.297940 0.954585i \(-0.596300\pi\)
−0.297940 + 0.954585i \(0.596300\pi\)
\(464\) 5.53979 0.257178
\(465\) 23.8939 1.10805
\(466\) −20.9416 −0.970102
\(467\) 0.0775715 0.00358958 0.00179479 0.999998i \(-0.499429\pi\)
0.00179479 + 0.999998i \(0.499429\pi\)
\(468\) 0.197944 0.00914997
\(469\) 0.0684838 0.00316229
\(470\) −14.2287 −0.656321
\(471\) −2.63874 −0.121587
\(472\) −7.14634 −0.328937
\(473\) 0.372598 0.0171321
\(474\) 17.2509 0.792359
\(475\) −6.31228 −0.289627
\(476\) −0.0365927 −0.00167723
\(477\) −7.89234 −0.361366
\(478\) 1.88750 0.0863325
\(479\) 34.8965 1.59446 0.797230 0.603676i \(-0.206298\pi\)
0.797230 + 0.603676i \(0.206298\pi\)
\(480\) 5.07805 0.231780
\(481\) 2.64398 0.120555
\(482\) 10.5965 0.482656
\(483\) −2.16422 −0.0984756
\(484\) −10.9414 −0.497335
\(485\) 27.7064 1.25808
\(486\) −7.06913 −0.320662
\(487\) 10.5321 0.477257 0.238629 0.971111i \(-0.423302\pi\)
0.238629 + 0.971111i \(0.423302\pi\)
\(488\) 11.8713 0.537387
\(489\) −2.61913 −0.118441
\(490\) 16.6168 0.750670
\(491\) −5.87798 −0.265269 −0.132635 0.991165i \(-0.542344\pi\)
−0.132635 + 0.991165i \(0.542344\pi\)
\(492\) −3.05081 −0.137541
\(493\) −0.142192 −0.00640401
\(494\) 0.290248 0.0130589
\(495\) −0.563347 −0.0253206
\(496\) 4.70532 0.211275
\(497\) −15.9866 −0.717096
\(498\) 5.37582 0.240896
\(499\) −36.7786 −1.64644 −0.823219 0.567724i \(-0.807824\pi\)
−0.823219 + 0.567724i \(0.807824\pi\)
\(500\) −3.97943 −0.177966
\(501\) 35.4237 1.58261
\(502\) −4.15487 −0.185441
\(503\) 8.00730 0.357028 0.178514 0.983937i \(-0.442871\pi\)
0.178514 + 0.983937i \(0.442871\pi\)
\(504\) −0.991535 −0.0441665
\(505\) 8.52392 0.379309
\(506\) −0.242144 −0.0107646
\(507\) 19.6118 0.870991
\(508\) 3.57380 0.158562
\(509\) 17.3759 0.770173 0.385086 0.922881i \(-0.374172\pi\)
0.385086 + 0.922881i \(0.374172\pi\)
\(510\) −0.130340 −0.00577156
\(511\) −13.2422 −0.585802
\(512\) 1.00000 0.0441942
\(513\) −5.72114 −0.252594
\(514\) 15.4462 0.681302
\(515\) −42.0683 −1.85375
\(516\) 2.33591 0.102833
\(517\) −1.02999 −0.0452987
\(518\) −13.2441 −0.581914
\(519\) 3.84235 0.168661
\(520\) 0.952042 0.0417498
\(521\) 1.68675 0.0738978 0.0369489 0.999317i \(-0.488236\pi\)
0.0369489 + 0.999317i \(0.488236\pi\)
\(522\) −3.85290 −0.168637
\(523\) 40.9102 1.78888 0.894438 0.447191i \(-0.147576\pi\)
0.894438 + 0.447191i \(0.147576\pi\)
\(524\) −1.00000 −0.0436852
\(525\) −13.3958 −0.584639
\(526\) −14.0059 −0.610686
\(527\) −0.120773 −0.00526097
\(528\) 0.367589 0.0159973
\(529\) 1.00000 0.0434783
\(530\) −37.9594 −1.64885
\(531\) 4.97025 0.215690
\(532\) −1.45390 −0.0630345
\(533\) −0.571971 −0.0247748
\(534\) −7.65664 −0.331335
\(535\) 0.805151 0.0348097
\(536\) 0.0480368 0.00207487
\(537\) 21.2199 0.915706
\(538\) 15.9454 0.687454
\(539\) 1.20285 0.0518106
\(540\) −18.7659 −0.807556
\(541\) −0.421542 −0.0181235 −0.00906175 0.999959i \(-0.502884\pi\)
−0.00906175 + 0.999959i \(0.502884\pi\)
\(542\) −29.9498 −1.28645
\(543\) −0.398166 −0.0170869
\(544\) −0.0256674 −0.00110048
\(545\) −28.1319 −1.20504
\(546\) 0.615957 0.0263605
\(547\) −12.8562 −0.549693 −0.274847 0.961488i \(-0.588627\pi\)
−0.274847 + 0.961488i \(0.588627\pi\)
\(548\) −14.4973 −0.619293
\(549\) −8.25641 −0.352375
\(550\) −1.49878 −0.0639083
\(551\) −5.64956 −0.240679
\(552\) −1.51806 −0.0646129
\(553\) −16.2008 −0.688927
\(554\) −11.4541 −0.486637
\(555\) −47.1745 −2.00244
\(556\) 3.57168 0.151473
\(557\) 15.5151 0.657397 0.328699 0.944435i \(-0.393390\pi\)
0.328699 + 0.944435i \(0.393390\pi\)
\(558\) −3.27253 −0.138537
\(559\) 0.437941 0.0185229
\(560\) −4.76893 −0.201524
\(561\) −0.00943505 −0.000398348 0
\(562\) 13.5857 0.573076
\(563\) 43.3884 1.82860 0.914301 0.405036i \(-0.132741\pi\)
0.914301 + 0.405036i \(0.132741\pi\)
\(564\) −6.45723 −0.271898
\(565\) 15.1479 0.637278
\(566\) 23.4573 0.985986
\(567\) −9.16665 −0.384963
\(568\) −11.2135 −0.470509
\(569\) 18.6647 0.782465 0.391232 0.920292i \(-0.372049\pi\)
0.391232 + 0.920292i \(0.372049\pi\)
\(570\) −5.17866 −0.216910
\(571\) 1.17536 0.0491871 0.0245936 0.999698i \(-0.492171\pi\)
0.0245936 + 0.999698i \(0.492171\pi\)
\(572\) 0.0689163 0.00288153
\(573\) 0.736437 0.0307651
\(574\) 2.86510 0.119587
\(575\) 6.18963 0.258126
\(576\) −0.695496 −0.0289790
\(577\) −14.7055 −0.612197 −0.306098 0.952000i \(-0.599024\pi\)
−0.306098 + 0.952000i \(0.599024\pi\)
\(578\) −16.9993 −0.707079
\(579\) 16.1593 0.671557
\(580\) −18.5311 −0.769463
\(581\) −5.04858 −0.209450
\(582\) 12.5737 0.521195
\(583\) −2.74780 −0.113802
\(584\) −9.28856 −0.384363
\(585\) −0.662141 −0.0273762
\(586\) −20.7920 −0.858910
\(587\) 33.4349 1.38001 0.690004 0.723806i \(-0.257609\pi\)
0.690004 + 0.723806i \(0.257609\pi\)
\(588\) 7.54099 0.310985
\(589\) −4.79856 −0.197721
\(590\) 23.9051 0.984159
\(591\) −35.8113 −1.47308
\(592\) −9.28988 −0.381812
\(593\) 8.92318 0.366431 0.183216 0.983073i \(-0.441349\pi\)
0.183216 + 0.983073i \(0.441349\pi\)
\(594\) −1.35842 −0.0557368
\(595\) 0.122406 0.00501816
\(596\) 3.68598 0.150984
\(597\) −5.66425 −0.231822
\(598\) −0.284609 −0.0116385
\(599\) −13.5307 −0.552847 −0.276424 0.961036i \(-0.589149\pi\)
−0.276424 + 0.961036i \(0.589149\pi\)
\(600\) −9.39623 −0.383600
\(601\) 41.4625 1.69129 0.845644 0.533747i \(-0.179216\pi\)
0.845644 + 0.533747i \(0.179216\pi\)
\(602\) −2.19372 −0.0894092
\(603\) −0.0334094 −0.00136054
\(604\) −17.0736 −0.694716
\(605\) 36.5999 1.48800
\(606\) 3.86830 0.157139
\(607\) 11.9826 0.486361 0.243180 0.969981i \(-0.421809\pi\)
0.243180 + 0.969981i \(0.421809\pi\)
\(608\) −1.01981 −0.0413589
\(609\) −11.9894 −0.485833
\(610\) −39.7105 −1.60783
\(611\) −1.21061 −0.0489762
\(612\) 0.0178516 0.000721606 0
\(613\) 32.5549 1.31488 0.657439 0.753508i \(-0.271640\pi\)
0.657439 + 0.753508i \(0.271640\pi\)
\(614\) −14.5758 −0.588232
\(615\) 10.2052 0.411514
\(616\) −0.345213 −0.0139090
\(617\) −12.9067 −0.519604 −0.259802 0.965662i \(-0.583657\pi\)
−0.259802 + 0.965662i \(0.583657\pi\)
\(618\) −19.0913 −0.767965
\(619\) 19.5392 0.785345 0.392673 0.919678i \(-0.371551\pi\)
0.392673 + 0.919678i \(0.371551\pi\)
\(620\) −15.7397 −0.632123
\(621\) 5.60998 0.225121
\(622\) 21.0112 0.842472
\(623\) 7.19057 0.288084
\(624\) 0.432053 0.0172960
\(625\) −17.6366 −0.705464
\(626\) 5.22613 0.208878
\(627\) −0.374873 −0.0149710
\(628\) 1.73823 0.0693631
\(629\) 0.238447 0.00950750
\(630\) 3.31677 0.132143
\(631\) −22.0761 −0.878834 −0.439417 0.898283i \(-0.644815\pi\)
−0.439417 + 0.898283i \(0.644815\pi\)
\(632\) −11.3638 −0.452026
\(633\) 15.9246 0.632948
\(634\) −15.7787 −0.626654
\(635\) −11.9547 −0.474408
\(636\) −17.2266 −0.683080
\(637\) 1.41380 0.0560167
\(638\) −1.34143 −0.0531077
\(639\) 7.79895 0.308522
\(640\) −3.34509 −0.132226
\(641\) −25.7924 −1.01874 −0.509370 0.860548i \(-0.670122\pi\)
−0.509370 + 0.860548i \(0.670122\pi\)
\(642\) 0.365391 0.0144208
\(643\) −5.32432 −0.209971 −0.104985 0.994474i \(-0.533480\pi\)
−0.104985 + 0.994474i \(0.533480\pi\)
\(644\) 1.42565 0.0561785
\(645\) −7.81383 −0.307669
\(646\) 0.0261760 0.00102988
\(647\) 20.7785 0.816886 0.408443 0.912784i \(-0.366072\pi\)
0.408443 + 0.912784i \(0.366072\pi\)
\(648\) −6.42980 −0.252586
\(649\) 1.73044 0.0679258
\(650\) −1.76162 −0.0690965
\(651\) −10.1834 −0.399118
\(652\) 1.72531 0.0675685
\(653\) −2.71806 −0.106366 −0.0531829 0.998585i \(-0.516937\pi\)
−0.0531829 + 0.998585i \(0.516937\pi\)
\(654\) −12.7668 −0.499220
\(655\) 3.34509 0.130704
\(656\) 2.00968 0.0784647
\(657\) 6.46015 0.252035
\(658\) 6.06416 0.236406
\(659\) 8.40079 0.327248 0.163624 0.986523i \(-0.447682\pi\)
0.163624 + 0.986523i \(0.447682\pi\)
\(660\) −1.22962 −0.0478628
\(661\) −31.2897 −1.21703 −0.608514 0.793543i \(-0.708234\pi\)
−0.608514 + 0.793543i \(0.708234\pi\)
\(662\) 15.0855 0.586314
\(663\) −0.0110897 −0.000430687 0
\(664\) −3.54124 −0.137427
\(665\) 4.86343 0.188596
\(666\) 6.46107 0.250362
\(667\) 5.53979 0.214502
\(668\) −23.3349 −0.902853
\(669\) 17.3719 0.671636
\(670\) −0.160688 −0.00620790
\(671\) −2.87456 −0.110971
\(672\) −2.16422 −0.0834867
\(673\) −9.16447 −0.353264 −0.176632 0.984277i \(-0.556520\pi\)
−0.176632 + 0.984277i \(0.556520\pi\)
\(674\) −25.5476 −0.984057
\(675\) 34.7237 1.33652
\(676\) −12.9190 −0.496885
\(677\) −42.6490 −1.63913 −0.819567 0.572984i \(-0.805786\pi\)
−0.819567 + 0.572984i \(0.805786\pi\)
\(678\) 6.87438 0.264009
\(679\) −11.8083 −0.453160
\(680\) 0.0858597 0.00329257
\(681\) 17.1353 0.656625
\(682\) −1.13937 −0.0436286
\(683\) 48.6322 1.86086 0.930430 0.366469i \(-0.119434\pi\)
0.930430 + 0.366469i \(0.119434\pi\)
\(684\) 0.709276 0.0271199
\(685\) 48.4947 1.85289
\(686\) −17.0615 −0.651411
\(687\) 3.19617 0.121942
\(688\) −1.53875 −0.0586642
\(689\) −3.22968 −0.123041
\(690\) 5.07805 0.193318
\(691\) 11.8745 0.451727 0.225864 0.974159i \(-0.427480\pi\)
0.225864 + 0.974159i \(0.427480\pi\)
\(692\) −2.53110 −0.0962178
\(693\) 0.240094 0.00912042
\(694\) 0.898187 0.0340947
\(695\) −11.9476 −0.453198
\(696\) −8.40974 −0.318770
\(697\) −0.0515831 −0.00195385
\(698\) −11.0097 −0.416724
\(699\) 31.7906 1.20243
\(700\) 8.82426 0.333526
\(701\) 13.6797 0.516674 0.258337 0.966055i \(-0.416825\pi\)
0.258337 + 0.966055i \(0.416825\pi\)
\(702\) −1.59665 −0.0602616
\(703\) 9.47395 0.357317
\(704\) −0.242144 −0.00912615
\(705\) 21.6000 0.813504
\(706\) 9.77410 0.367853
\(707\) −3.63283 −0.136627
\(708\) 10.8486 0.407714
\(709\) −34.5404 −1.29719 −0.648596 0.761133i \(-0.724644\pi\)
−0.648596 + 0.761133i \(0.724644\pi\)
\(710\) 37.5102 1.40773
\(711\) 7.90345 0.296403
\(712\) 5.04371 0.189021
\(713\) 4.70532 0.176216
\(714\) 0.0555500 0.00207890
\(715\) −0.230531 −0.00862138
\(716\) −13.9783 −0.522394
\(717\) −2.86534 −0.107008
\(718\) −5.52789 −0.206299
\(719\) −28.5673 −1.06538 −0.532690 0.846311i \(-0.678819\pi\)
−0.532690 + 0.846311i \(0.678819\pi\)
\(720\) 2.32650 0.0867034
\(721\) 17.9292 0.667717
\(722\) −17.9600 −0.668401
\(723\) −16.0861 −0.598247
\(724\) 0.262286 0.00974778
\(725\) 34.2893 1.27347
\(726\) 16.6096 0.616442
\(727\) −34.1512 −1.26660 −0.633299 0.773907i \(-0.718300\pi\)
−0.633299 + 0.773907i \(0.718300\pi\)
\(728\) −0.405753 −0.0150382
\(729\) 30.0208 1.11188
\(730\) 31.0711 1.14999
\(731\) 0.0394956 0.00146080
\(732\) −18.0213 −0.666086
\(733\) −28.0442 −1.03584 −0.517918 0.855430i \(-0.673293\pi\)
−0.517918 + 0.855430i \(0.673293\pi\)
\(734\) −20.1212 −0.742688
\(735\) −25.2253 −0.930449
\(736\) 1.00000 0.0368605
\(737\) −0.0116318 −0.000428464 0
\(738\) −1.39772 −0.0514508
\(739\) 10.2899 0.378519 0.189260 0.981927i \(-0.439391\pi\)
0.189260 + 0.981927i \(0.439391\pi\)
\(740\) 31.0755 1.14236
\(741\) −0.440613 −0.0161863
\(742\) 16.1780 0.593913
\(743\) −21.7983 −0.799704 −0.399852 0.916580i \(-0.630938\pi\)
−0.399852 + 0.916580i \(0.630938\pi\)
\(744\) −7.14296 −0.261874
\(745\) −12.3299 −0.451734
\(746\) 8.89645 0.325722
\(747\) 2.46292 0.0901135
\(748\) 0.00621520 0.000227250 0
\(749\) −0.343149 −0.0125384
\(750\) 6.04102 0.220587
\(751\) 30.2844 1.10509 0.552547 0.833482i \(-0.313656\pi\)
0.552547 + 0.833482i \(0.313656\pi\)
\(752\) 4.25361 0.155113
\(753\) 6.30734 0.229852
\(754\) −1.57667 −0.0574190
\(755\) 57.1128 2.07855
\(756\) 7.99788 0.290880
\(757\) 35.9962 1.30830 0.654152 0.756363i \(-0.273026\pi\)
0.654152 + 0.756363i \(0.273026\pi\)
\(758\) −24.6742 −0.896207
\(759\) 0.367589 0.0133426
\(760\) 3.41137 0.123743
\(761\) 34.1259 1.23706 0.618532 0.785760i \(-0.287728\pi\)
0.618532 + 0.785760i \(0.287728\pi\)
\(762\) −5.42525 −0.196536
\(763\) 11.9896 0.434053
\(764\) −0.485117 −0.0175509
\(765\) −0.0597151 −0.00215900
\(766\) −1.03057 −0.0372361
\(767\) 2.03391 0.0734402
\(768\) −1.51806 −0.0547782
\(769\) −19.9982 −0.721154 −0.360577 0.932729i \(-0.617420\pi\)
−0.360577 + 0.932729i \(0.617420\pi\)
\(770\) 1.15477 0.0416150
\(771\) −23.4482 −0.844467
\(772\) −10.6447 −0.383111
\(773\) −20.7467 −0.746207 −0.373104 0.927790i \(-0.621706\pi\)
−0.373104 + 0.927790i \(0.621706\pi\)
\(774\) 1.07019 0.0384673
\(775\) 29.1242 1.04617
\(776\) −8.28272 −0.297332
\(777\) 20.1054 0.721277
\(778\) −10.7550 −0.385584
\(779\) −2.04950 −0.0734308
\(780\) −1.44526 −0.0517485
\(781\) 2.71529 0.0971606
\(782\) −0.0256674 −0.000917864 0
\(783\) 31.0781 1.11064
\(784\) −4.96752 −0.177411
\(785\) −5.81455 −0.207530
\(786\) 1.51806 0.0541474
\(787\) −4.87434 −0.173751 −0.0868757 0.996219i \(-0.527688\pi\)
−0.0868757 + 0.996219i \(0.527688\pi\)
\(788\) 23.5902 0.840366
\(789\) 21.2618 0.756939
\(790\) 38.0128 1.35244
\(791\) −6.45592 −0.229546
\(792\) 0.168410 0.00598419
\(793\) −3.37866 −0.119980
\(794\) −8.17805 −0.290228
\(795\) 57.6246 2.04373
\(796\) 3.73124 0.132250
\(797\) −3.49650 −0.123852 −0.0619261 0.998081i \(-0.519724\pi\)
−0.0619261 + 0.998081i \(0.519724\pi\)
\(798\) 2.20711 0.0781307
\(799\) −0.109179 −0.00386248
\(800\) 6.18963 0.218837
\(801\) −3.50788 −0.123945
\(802\) −28.2132 −0.996244
\(803\) 2.24917 0.0793714
\(804\) −0.0729227 −0.00257179
\(805\) −4.76893 −0.168083
\(806\) −1.33918 −0.0471704
\(807\) −24.2060 −0.852093
\(808\) −2.54819 −0.0896449
\(809\) 54.0935 1.90183 0.950914 0.309456i \(-0.100147\pi\)
0.950914 + 0.309456i \(0.100147\pi\)
\(810\) 21.5083 0.755723
\(811\) −51.5933 −1.81169 −0.905844 0.423612i \(-0.860762\pi\)
−0.905844 + 0.423612i \(0.860762\pi\)
\(812\) 7.89782 0.277159
\(813\) 45.4656 1.59455
\(814\) 2.24949 0.0788446
\(815\) −5.77133 −0.202161
\(816\) 0.0389646 0.00136403
\(817\) 1.56924 0.0549006
\(818\) 15.0756 0.527107
\(819\) 0.282199 0.00986084
\(820\) −6.72255 −0.234762
\(821\) 3.60087 0.125671 0.0628356 0.998024i \(-0.479986\pi\)
0.0628356 + 0.998024i \(0.479986\pi\)
\(822\) 22.0077 0.767608
\(823\) 37.5669 1.30950 0.654750 0.755845i \(-0.272774\pi\)
0.654750 + 0.755845i \(0.272774\pi\)
\(824\) 12.5761 0.438110
\(825\) 2.27524 0.0792137
\(826\) −10.1882 −0.354492
\(827\) 9.55413 0.332230 0.166115 0.986106i \(-0.446878\pi\)
0.166115 + 0.986106i \(0.446878\pi\)
\(828\) −0.695496 −0.0241701
\(829\) −5.87724 −0.204125 −0.102063 0.994778i \(-0.532544\pi\)
−0.102063 + 0.994778i \(0.532544\pi\)
\(830\) 11.8458 0.411173
\(831\) 17.3880 0.603182
\(832\) −0.284609 −0.00986703
\(833\) 0.127503 0.00441772
\(834\) −5.42202 −0.187749
\(835\) 78.0572 2.70128
\(836\) 0.246942 0.00854067
\(837\) 26.3968 0.912406
\(838\) −15.9757 −0.551871
\(839\) 14.2876 0.493263 0.246631 0.969109i \(-0.420676\pi\)
0.246631 + 0.969109i \(0.420676\pi\)
\(840\) 7.23952 0.249787
\(841\) 1.68932 0.0582524
\(842\) 20.6924 0.713107
\(843\) −20.6238 −0.710323
\(844\) −10.4901 −0.361085
\(845\) 43.2152 1.48665
\(846\) −2.95837 −0.101711
\(847\) −15.5986 −0.535973
\(848\) 11.3478 0.389685
\(849\) −35.6096 −1.22212
\(850\) −0.158872 −0.00544925
\(851\) −9.28988 −0.318453
\(852\) 17.0228 0.583191
\(853\) −9.43993 −0.323217 −0.161609 0.986855i \(-0.551668\pi\)
−0.161609 + 0.986855i \(0.551668\pi\)
\(854\) 16.9243 0.579137
\(855\) −2.37259 −0.0811410
\(856\) −0.240696 −0.00822683
\(857\) −35.2303 −1.20344 −0.601722 0.798706i \(-0.705519\pi\)
−0.601722 + 0.798706i \(0.705519\pi\)
\(858\) −0.104619 −0.00357163
\(859\) 17.7354 0.605123 0.302561 0.953130i \(-0.402158\pi\)
0.302561 + 0.953130i \(0.402158\pi\)
\(860\) 5.14725 0.175520
\(861\) −4.34939 −0.148227
\(862\) 33.2990 1.13417
\(863\) 56.5877 1.92627 0.963134 0.269023i \(-0.0867009\pi\)
0.963134 + 0.269023i \(0.0867009\pi\)
\(864\) 5.60998 0.190855
\(865\) 8.46674 0.287878
\(866\) 3.63773 0.123615
\(867\) 25.8060 0.876418
\(868\) 6.70815 0.227690
\(869\) 2.75167 0.0933440
\(870\) 28.1313 0.953742
\(871\) −0.0136717 −0.000463248 0
\(872\) 8.40992 0.284796
\(873\) 5.76060 0.194967
\(874\) −1.01981 −0.0344957
\(875\) −5.67329 −0.191792
\(876\) 14.1006 0.476414
\(877\) −28.1482 −0.950499 −0.475249 0.879851i \(-0.657642\pi\)
−0.475249 + 0.879851i \(0.657642\pi\)
\(878\) −30.7511 −1.03780
\(879\) 31.5635 1.06461
\(880\) 0.809994 0.0273049
\(881\) 54.8871 1.84919 0.924597 0.380946i \(-0.124401\pi\)
0.924597 + 0.380946i \(0.124401\pi\)
\(882\) 3.45489 0.116332
\(883\) 28.5953 0.962309 0.481155 0.876636i \(-0.340218\pi\)
0.481155 + 0.876636i \(0.340218\pi\)
\(884\) 0.00730516 0.000245699 0
\(885\) −36.2894 −1.21986
\(886\) 15.9167 0.534733
\(887\) 41.7374 1.40141 0.700703 0.713453i \(-0.252870\pi\)
0.700703 + 0.713453i \(0.252870\pi\)
\(888\) 14.1026 0.473252
\(889\) 5.09500 0.170881
\(890\) −16.8717 −0.565539
\(891\) 1.55694 0.0521594
\(892\) −11.4435 −0.383156
\(893\) −4.33789 −0.145162
\(894\) −5.59554 −0.187143
\(895\) 46.7587 1.56297
\(896\) 1.42565 0.0476277
\(897\) 0.432053 0.0144258
\(898\) 1.59335 0.0531708
\(899\) 26.0665 0.869367
\(900\) −4.30486 −0.143495
\(901\) −0.291268 −0.00970355
\(902\) −0.486631 −0.0162030
\(903\) 3.33019 0.110822
\(904\) −4.52840 −0.150612
\(905\) −0.877370 −0.0291648
\(906\) 25.9188 0.861094
\(907\) −11.6471 −0.386735 −0.193368 0.981126i \(-0.561941\pi\)
−0.193368 + 0.981126i \(0.561941\pi\)
\(908\) −11.2876 −0.374593
\(909\) 1.77225 0.0587820
\(910\) 1.35728 0.0449934
\(911\) −6.13556 −0.203280 −0.101640 0.994821i \(-0.532409\pi\)
−0.101640 + 0.994821i \(0.532409\pi\)
\(912\) 1.54814 0.0512640
\(913\) 0.857491 0.0283788
\(914\) −20.2064 −0.668368
\(915\) 60.2828 1.99289
\(916\) −2.10543 −0.0695655
\(917\) −1.42565 −0.0470792
\(918\) −0.143994 −0.00475250
\(919\) −12.3695 −0.408034 −0.204017 0.978967i \(-0.565400\pi\)
−0.204017 + 0.978967i \(0.565400\pi\)
\(920\) −3.34509 −0.110284
\(921\) 22.1270 0.729108
\(922\) −35.4263 −1.16670
\(923\) 3.19146 0.105048
\(924\) 0.524054 0.0172401
\(925\) −57.5010 −1.89062
\(926\) −12.8218 −0.421351
\(927\) −8.74664 −0.287277
\(928\) 5.53979 0.181853
\(929\) −9.44974 −0.310036 −0.155018 0.987912i \(-0.549544\pi\)
−0.155018 + 0.987912i \(0.549544\pi\)
\(930\) 23.8939 0.783510
\(931\) 5.06594 0.166030
\(932\) −20.9416 −0.685966
\(933\) −31.8962 −1.04424
\(934\) 0.0775715 0.00253822
\(935\) −0.0207904 −0.000679920 0
\(936\) 0.197944 0.00647000
\(937\) −11.3421 −0.370531 −0.185266 0.982688i \(-0.559315\pi\)
−0.185266 + 0.982688i \(0.559315\pi\)
\(938\) 0.0684838 0.00223607
\(939\) −7.93357 −0.258902
\(940\) −14.2287 −0.464089
\(941\) −21.6547 −0.705922 −0.352961 0.935638i \(-0.614825\pi\)
−0.352961 + 0.935638i \(0.614825\pi\)
\(942\) −2.63874 −0.0859749
\(943\) 2.00968 0.0654440
\(944\) −7.14634 −0.232593
\(945\) −26.7536 −0.870296
\(946\) 0.372598 0.0121142
\(947\) −41.1382 −1.33681 −0.668406 0.743796i \(-0.733023\pi\)
−0.668406 + 0.743796i \(0.733023\pi\)
\(948\) 17.2509 0.560282
\(949\) 2.64360 0.0858150
\(950\) −6.31228 −0.204797
\(951\) 23.9531 0.776731
\(952\) −0.0365927 −0.00118598
\(953\) −1.92653 −0.0624065 −0.0312033 0.999513i \(-0.509934\pi\)
−0.0312033 + 0.999513i \(0.509934\pi\)
\(954\) −7.89234 −0.255524
\(955\) 1.62276 0.0525113
\(956\) 1.88750 0.0610463
\(957\) 2.03637 0.0658264
\(958\) 34.8965 1.12745
\(959\) −20.6681 −0.667407
\(960\) 5.07805 0.163893
\(961\) −8.85993 −0.285804
\(962\) 2.64398 0.0852454
\(963\) 0.167403 0.00539449
\(964\) 10.5965 0.341289
\(965\) 35.6075 1.14625
\(966\) −2.16422 −0.0696328
\(967\) −41.1207 −1.32235 −0.661176 0.750231i \(-0.729942\pi\)
−0.661176 + 0.750231i \(0.729942\pi\)
\(968\) −10.9414 −0.351669
\(969\) −0.0397367 −0.00127653
\(970\) 27.7064 0.889600
\(971\) 51.0303 1.63764 0.818820 0.574050i \(-0.194628\pi\)
0.818820 + 0.574050i \(0.194628\pi\)
\(972\) −7.06913 −0.226742
\(973\) 5.09197 0.163241
\(974\) 10.5321 0.337472
\(975\) 2.67425 0.0856445
\(976\) 11.8713 0.379990
\(977\) −7.47761 −0.239230 −0.119615 0.992820i \(-0.538166\pi\)
−0.119615 + 0.992820i \(0.538166\pi\)
\(978\) −2.61913 −0.0837505
\(979\) −1.22130 −0.0390330
\(980\) 16.6168 0.530804
\(981\) −5.84906 −0.186746
\(982\) −5.87798 −0.187574
\(983\) 33.2459 1.06038 0.530191 0.847879i \(-0.322120\pi\)
0.530191 + 0.847879i \(0.322120\pi\)
\(984\) −3.05081 −0.0972562
\(985\) −78.9114 −2.51433
\(986\) −0.142192 −0.00452832
\(987\) −9.20576 −0.293023
\(988\) 0.290248 0.00923401
\(989\) −1.53875 −0.0489293
\(990\) −0.563347 −0.0179044
\(991\) −61.0702 −1.93996 −0.969979 0.243188i \(-0.921807\pi\)
−0.969979 + 0.243188i \(0.921807\pi\)
\(992\) 4.70532 0.149394
\(993\) −22.9007 −0.726730
\(994\) −15.9866 −0.507063
\(995\) −12.4813 −0.395685
\(996\) 5.37582 0.170339
\(997\) 41.4885 1.31395 0.656976 0.753911i \(-0.271835\pi\)
0.656976 + 0.753911i \(0.271835\pi\)
\(998\) −36.7786 −1.16421
\(999\) −52.1161 −1.64888
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 6026.2.a.f.1.7 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6026.2.a.f.1.7 20 1.1 even 1 trivial