Properties

Label 4034.2.a.c.1.16
Level $4034$
Weight $2$
Character 4034.1
Self dual yes
Analytic conductor $32.212$
Analytic rank $0$
Dimension $49$
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] = [4034,2,Mod(1,4034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4034.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: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(49\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.16
Character \(\chi\) \(=\) 4034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.09618 q^{3} +1.00000 q^{4} -0.358556 q^{5} +1.09618 q^{6} -2.93033 q^{7} -1.00000 q^{8} -1.79840 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.09618 q^{3} +1.00000 q^{4} -0.358556 q^{5} +1.09618 q^{6} -2.93033 q^{7} -1.00000 q^{8} -1.79840 q^{9} +0.358556 q^{10} -2.70254 q^{11} -1.09618 q^{12} +0.734401 q^{13} +2.93033 q^{14} +0.393040 q^{15} +1.00000 q^{16} +0.422719 q^{17} +1.79840 q^{18} +8.46145 q^{19} -0.358556 q^{20} +3.21216 q^{21} +2.70254 q^{22} -8.04082 q^{23} +1.09618 q^{24} -4.87144 q^{25} -0.734401 q^{26} +5.25989 q^{27} -2.93033 q^{28} -6.64530 q^{29} -0.393040 q^{30} +3.26346 q^{31} -1.00000 q^{32} +2.96246 q^{33} -0.422719 q^{34} +1.05069 q^{35} -1.79840 q^{36} -3.52408 q^{37} -8.46145 q^{38} -0.805034 q^{39} +0.358556 q^{40} -4.23707 q^{41} -3.21216 q^{42} -0.269063 q^{43} -2.70254 q^{44} +0.644825 q^{45} +8.04082 q^{46} -13.2554 q^{47} -1.09618 q^{48} +1.58684 q^{49} +4.87144 q^{50} -0.463375 q^{51} +0.734401 q^{52} +2.29767 q^{53} -5.25989 q^{54} +0.969011 q^{55} +2.93033 q^{56} -9.27525 q^{57} +6.64530 q^{58} -12.3501 q^{59} +0.393040 q^{60} +5.42653 q^{61} -3.26346 q^{62} +5.26990 q^{63} +1.00000 q^{64} -0.263324 q^{65} -2.96246 q^{66} -2.25327 q^{67} +0.422719 q^{68} +8.81417 q^{69} -1.05069 q^{70} -6.19112 q^{71} +1.79840 q^{72} -14.6030 q^{73} +3.52408 q^{74} +5.33996 q^{75} +8.46145 q^{76} +7.91934 q^{77} +0.805034 q^{78} +7.19226 q^{79} -0.358556 q^{80} -0.370583 q^{81} +4.23707 q^{82} -2.45871 q^{83} +3.21216 q^{84} -0.151568 q^{85} +0.269063 q^{86} +7.28443 q^{87} +2.70254 q^{88} +5.76865 q^{89} -0.644825 q^{90} -2.15204 q^{91} -8.04082 q^{92} -3.57733 q^{93} +13.2554 q^{94} -3.03390 q^{95} +1.09618 q^{96} -7.90103 q^{97} -1.58684 q^{98} +4.86024 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 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
\(3\) −1.09618 −0.632878 −0.316439 0.948613i \(-0.602487\pi\)
−0.316439 + 0.948613i \(0.602487\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.358556 −0.160351 −0.0801755 0.996781i \(-0.525548\pi\)
−0.0801755 + 0.996781i \(0.525548\pi\)
\(6\) 1.09618 0.447512
\(7\) −2.93033 −1.10756 −0.553781 0.832663i \(-0.686815\pi\)
−0.553781 + 0.832663i \(0.686815\pi\)
\(8\) −1.00000 −0.353553
\(9\) −1.79840 −0.599465
\(10\) 0.358556 0.113385
\(11\) −2.70254 −0.814847 −0.407423 0.913239i \(-0.633573\pi\)
−0.407423 + 0.913239i \(0.633573\pi\)
\(12\) −1.09618 −0.316439
\(13\) 0.734401 0.203686 0.101843 0.994800i \(-0.467526\pi\)
0.101843 + 0.994800i \(0.467526\pi\)
\(14\) 2.93033 0.783164
\(15\) 0.393040 0.101483
\(16\) 1.00000 0.250000
\(17\) 0.422719 0.102524 0.0512622 0.998685i \(-0.483676\pi\)
0.0512622 + 0.998685i \(0.483676\pi\)
\(18\) 1.79840 0.423886
\(19\) 8.46145 1.94119 0.970595 0.240717i \(-0.0773826\pi\)
0.970595 + 0.240717i \(0.0773826\pi\)
\(20\) −0.358556 −0.0801755
\(21\) 3.21216 0.700951
\(22\) 2.70254 0.576184
\(23\) −8.04082 −1.67663 −0.838314 0.545188i \(-0.816458\pi\)
−0.838314 + 0.545188i \(0.816458\pi\)
\(24\) 1.09618 0.223756
\(25\) −4.87144 −0.974288
\(26\) −0.734401 −0.144028
\(27\) 5.25989 1.01227
\(28\) −2.93033 −0.553781
\(29\) −6.64530 −1.23400 −0.617001 0.786962i \(-0.711653\pi\)
−0.617001 + 0.786962i \(0.711653\pi\)
\(30\) −0.393040 −0.0717590
\(31\) 3.26346 0.586134 0.293067 0.956092i \(-0.405324\pi\)
0.293067 + 0.956092i \(0.405324\pi\)
\(32\) −1.00000 −0.176777
\(33\) 2.96246 0.515699
\(34\) −0.422719 −0.0724957
\(35\) 1.05069 0.177598
\(36\) −1.79840 −0.299733
\(37\) −3.52408 −0.579356 −0.289678 0.957124i \(-0.593548\pi\)
−0.289678 + 0.957124i \(0.593548\pi\)
\(38\) −8.46145 −1.37263
\(39\) −0.805034 −0.128909
\(40\) 0.358556 0.0566926
\(41\) −4.23707 −0.661719 −0.330860 0.943680i \(-0.607339\pi\)
−0.330860 + 0.943680i \(0.607339\pi\)
\(42\) −3.21216 −0.495647
\(43\) −0.269063 −0.0410316 −0.0205158 0.999790i \(-0.506531\pi\)
−0.0205158 + 0.999790i \(0.506531\pi\)
\(44\) −2.70254 −0.407423
\(45\) 0.644825 0.0961248
\(46\) 8.04082 1.18555
\(47\) −13.2554 −1.93350 −0.966751 0.255721i \(-0.917687\pi\)
−0.966751 + 0.255721i \(0.917687\pi\)
\(48\) −1.09618 −0.158220
\(49\) 1.58684 0.226691
\(50\) 4.87144 0.688925
\(51\) −0.463375 −0.0648855
\(52\) 0.734401 0.101843
\(53\) 2.29767 0.315610 0.157805 0.987470i \(-0.449558\pi\)
0.157805 + 0.987470i \(0.449558\pi\)
\(54\) −5.25989 −0.715781
\(55\) 0.969011 0.130661
\(56\) 2.93033 0.391582
\(57\) −9.27525 −1.22854
\(58\) 6.64530 0.872571
\(59\) −12.3501 −1.60784 −0.803921 0.594736i \(-0.797256\pi\)
−0.803921 + 0.594736i \(0.797256\pi\)
\(60\) 0.393040 0.0507413
\(61\) 5.42653 0.694796 0.347398 0.937718i \(-0.387065\pi\)
0.347398 + 0.937718i \(0.387065\pi\)
\(62\) −3.26346 −0.414459
\(63\) 5.26990 0.663945
\(64\) 1.00000 0.125000
\(65\) −0.263324 −0.0326613
\(66\) −2.96246 −0.364654
\(67\) −2.25327 −0.275281 −0.137640 0.990482i \(-0.543952\pi\)
−0.137640 + 0.990482i \(0.543952\pi\)
\(68\) 0.422719 0.0512622
\(69\) 8.81417 1.06110
\(70\) −1.05069 −0.125581
\(71\) −6.19112 −0.734751 −0.367375 0.930073i \(-0.619744\pi\)
−0.367375 + 0.930073i \(0.619744\pi\)
\(72\) 1.79840 0.211943
\(73\) −14.6030 −1.70916 −0.854579 0.519322i \(-0.826185\pi\)
−0.854579 + 0.519322i \(0.826185\pi\)
\(74\) 3.52408 0.409666
\(75\) 5.33996 0.616605
\(76\) 8.46145 0.970595
\(77\) 7.91934 0.902493
\(78\) 0.805034 0.0911521
\(79\) 7.19226 0.809192 0.404596 0.914496i \(-0.367412\pi\)
0.404596 + 0.914496i \(0.367412\pi\)
\(80\) −0.358556 −0.0400877
\(81\) −0.370583 −0.0411759
\(82\) 4.23707 0.467906
\(83\) −2.45871 −0.269879 −0.134939 0.990854i \(-0.543084\pi\)
−0.134939 + 0.990854i \(0.543084\pi\)
\(84\) 3.21216 0.350476
\(85\) −0.151568 −0.0164399
\(86\) 0.269063 0.0290138
\(87\) 7.28443 0.780973
\(88\) 2.70254 0.288092
\(89\) 5.76865 0.611476 0.305738 0.952116i \(-0.401097\pi\)
0.305738 + 0.952116i \(0.401097\pi\)
\(90\) −0.644825 −0.0679705
\(91\) −2.15204 −0.225595
\(92\) −8.04082 −0.838314
\(93\) −3.57733 −0.370951
\(94\) 13.2554 1.36719
\(95\) −3.03390 −0.311272
\(96\) 1.09618 0.111878
\(97\) −7.90103 −0.802228 −0.401114 0.916028i \(-0.631377\pi\)
−0.401114 + 0.916028i \(0.631377\pi\)
\(98\) −1.58684 −0.160295
\(99\) 4.86024 0.488472
\(100\) −4.87144 −0.487144
\(101\) 4.10390 0.408353 0.204177 0.978934i \(-0.434548\pi\)
0.204177 + 0.978934i \(0.434548\pi\)
\(102\) 0.463375 0.0458809
\(103\) 6.15301 0.606274 0.303137 0.952947i \(-0.401966\pi\)
0.303137 + 0.952947i \(0.401966\pi\)
\(104\) −0.734401 −0.0720140
\(105\) −1.15174 −0.112398
\(106\) −2.29767 −0.223170
\(107\) 18.7240 1.81011 0.905057 0.425290i \(-0.139828\pi\)
0.905057 + 0.425290i \(0.139828\pi\)
\(108\) 5.25989 0.506133
\(109\) 14.3555 1.37501 0.687505 0.726180i \(-0.258706\pi\)
0.687505 + 0.726180i \(0.258706\pi\)
\(110\) −0.969011 −0.0923916
\(111\) 3.86302 0.366662
\(112\) −2.93033 −0.276890
\(113\) 9.25940 0.871051 0.435525 0.900176i \(-0.356563\pi\)
0.435525 + 0.900176i \(0.356563\pi\)
\(114\) 9.27525 0.868707
\(115\) 2.88308 0.268849
\(116\) −6.64530 −0.617001
\(117\) −1.32074 −0.122103
\(118\) 12.3501 1.13692
\(119\) −1.23871 −0.113552
\(120\) −0.393040 −0.0358795
\(121\) −3.69627 −0.336025
\(122\) −5.42653 −0.491295
\(123\) 4.64458 0.418788
\(124\) 3.26346 0.293067
\(125\) 3.53946 0.316579
\(126\) −5.26990 −0.469480
\(127\) −4.51743 −0.400857 −0.200428 0.979708i \(-0.564233\pi\)
−0.200428 + 0.979708i \(0.564233\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0.294940 0.0259680
\(130\) 0.263324 0.0230950
\(131\) 11.9861 1.04723 0.523616 0.851954i \(-0.324583\pi\)
0.523616 + 0.851954i \(0.324583\pi\)
\(132\) 2.96246 0.257849
\(133\) −24.7949 −2.14999
\(134\) 2.25327 0.194653
\(135\) −1.88596 −0.162318
\(136\) −0.422719 −0.0362479
\(137\) 1.25766 0.107449 0.0537246 0.998556i \(-0.482891\pi\)
0.0537246 + 0.998556i \(0.482891\pi\)
\(138\) −8.81417 −0.750312
\(139\) 8.62203 0.731311 0.365655 0.930750i \(-0.380845\pi\)
0.365655 + 0.930750i \(0.380845\pi\)
\(140\) 1.05069 0.0887992
\(141\) 14.5303 1.22367
\(142\) 6.19112 0.519547
\(143\) −1.98475 −0.165973
\(144\) −1.79840 −0.149866
\(145\) 2.38271 0.197873
\(146\) 14.6030 1.20856
\(147\) −1.73946 −0.143468
\(148\) −3.52408 −0.289678
\(149\) 20.3125 1.66407 0.832033 0.554727i \(-0.187177\pi\)
0.832033 + 0.554727i \(0.187177\pi\)
\(150\) −5.33996 −0.436006
\(151\) 7.78097 0.633206 0.316603 0.948558i \(-0.397458\pi\)
0.316603 + 0.948558i \(0.397458\pi\)
\(152\) −8.46145 −0.686315
\(153\) −0.760216 −0.0614598
\(154\) −7.91934 −0.638159
\(155\) −1.17013 −0.0939871
\(156\) −0.805034 −0.0644543
\(157\) −7.94526 −0.634101 −0.317051 0.948409i \(-0.602692\pi\)
−0.317051 + 0.948409i \(0.602692\pi\)
\(158\) −7.19226 −0.572185
\(159\) −2.51866 −0.199742
\(160\) 0.358556 0.0283463
\(161\) 23.5623 1.85697
\(162\) 0.370583 0.0291157
\(163\) 5.48851 0.429893 0.214947 0.976626i \(-0.431042\pi\)
0.214947 + 0.976626i \(0.431042\pi\)
\(164\) −4.23707 −0.330860
\(165\) −1.06221 −0.0826928
\(166\) 2.45871 0.190833
\(167\) 6.87509 0.532010 0.266005 0.963972i \(-0.414296\pi\)
0.266005 + 0.963972i \(0.414296\pi\)
\(168\) −3.21216 −0.247824
\(169\) −12.4607 −0.958512
\(170\) 0.151568 0.0116248
\(171\) −15.2170 −1.16368
\(172\) −0.269063 −0.0205158
\(173\) −1.08625 −0.0825858 −0.0412929 0.999147i \(-0.513148\pi\)
−0.0412929 + 0.999147i \(0.513148\pi\)
\(174\) −7.28443 −0.552231
\(175\) 14.2749 1.07908
\(176\) −2.70254 −0.203712
\(177\) 13.5379 1.01757
\(178\) −5.76865 −0.432379
\(179\) −4.58642 −0.342805 −0.171402 0.985201i \(-0.554830\pi\)
−0.171402 + 0.985201i \(0.554830\pi\)
\(180\) 0.644825 0.0480624
\(181\) −16.6934 −1.24081 −0.620405 0.784281i \(-0.713032\pi\)
−0.620405 + 0.784281i \(0.713032\pi\)
\(182\) 2.15204 0.159520
\(183\) −5.94844 −0.439721
\(184\) 8.04082 0.592777
\(185\) 1.26358 0.0929002
\(186\) 3.57733 0.262302
\(187\) −1.14242 −0.0835417
\(188\) −13.2554 −0.966751
\(189\) −15.4132 −1.12115
\(190\) 3.03390 0.220102
\(191\) −12.8395 −0.929037 −0.464518 0.885563i \(-0.653773\pi\)
−0.464518 + 0.885563i \(0.653773\pi\)
\(192\) −1.09618 −0.0791098
\(193\) 9.93167 0.714897 0.357448 0.933933i \(-0.383647\pi\)
0.357448 + 0.933933i \(0.383647\pi\)
\(194\) 7.90103 0.567261
\(195\) 0.288649 0.0206706
\(196\) 1.58684 0.113346
\(197\) 4.63936 0.330541 0.165270 0.986248i \(-0.447150\pi\)
0.165270 + 0.986248i \(0.447150\pi\)
\(198\) −4.86024 −0.345402
\(199\) −11.9552 −0.847483 −0.423741 0.905783i \(-0.639283\pi\)
−0.423741 + 0.905783i \(0.639283\pi\)
\(200\) 4.87144 0.344463
\(201\) 2.46998 0.174219
\(202\) −4.10390 −0.288749
\(203\) 19.4729 1.36673
\(204\) −0.463375 −0.0324427
\(205\) 1.51923 0.106107
\(206\) −6.15301 −0.428701
\(207\) 14.4606 1.00508
\(208\) 0.734401 0.0509216
\(209\) −22.8674 −1.58177
\(210\) 1.15174 0.0794775
\(211\) 21.8957 1.50736 0.753681 0.657241i \(-0.228276\pi\)
0.753681 + 0.657241i \(0.228276\pi\)
\(212\) 2.29767 0.157805
\(213\) 6.78656 0.465008
\(214\) −18.7240 −1.27994
\(215\) 0.0964739 0.00657946
\(216\) −5.25989 −0.357890
\(217\) −9.56301 −0.649179
\(218\) −14.3555 −0.972278
\(219\) 16.0075 1.08169
\(220\) 0.969011 0.0653307
\(221\) 0.310445 0.0208828
\(222\) −3.86302 −0.259269
\(223\) 14.9834 1.00336 0.501681 0.865053i \(-0.332715\pi\)
0.501681 + 0.865053i \(0.332715\pi\)
\(224\) 2.93033 0.195791
\(225\) 8.76078 0.584052
\(226\) −9.25940 −0.615926
\(227\) −4.60248 −0.305477 −0.152739 0.988267i \(-0.548809\pi\)
−0.152739 + 0.988267i \(0.548809\pi\)
\(228\) −9.27525 −0.614268
\(229\) −13.7986 −0.911838 −0.455919 0.890021i \(-0.650689\pi\)
−0.455919 + 0.890021i \(0.650689\pi\)
\(230\) −2.88308 −0.190105
\(231\) −8.68100 −0.571168
\(232\) 6.64530 0.436286
\(233\) −16.4695 −1.07895 −0.539477 0.842000i \(-0.681378\pi\)
−0.539477 + 0.842000i \(0.681378\pi\)
\(234\) 1.32074 0.0863398
\(235\) 4.75280 0.310039
\(236\) −12.3501 −0.803921
\(237\) −7.88398 −0.512120
\(238\) 1.23871 0.0802934
\(239\) −11.9731 −0.774474 −0.387237 0.921980i \(-0.626570\pi\)
−0.387237 + 0.921980i \(0.626570\pi\)
\(240\) 0.393040 0.0253706
\(241\) −9.79923 −0.631224 −0.315612 0.948888i \(-0.602210\pi\)
−0.315612 + 0.948888i \(0.602210\pi\)
\(242\) 3.69627 0.237605
\(243\) −15.3734 −0.986207
\(244\) 5.42653 0.347398
\(245\) −0.568971 −0.0363502
\(246\) −4.64458 −0.296128
\(247\) 6.21410 0.395394
\(248\) −3.26346 −0.207230
\(249\) 2.69518 0.170800
\(250\) −3.53946 −0.223855
\(251\) 7.68150 0.484852 0.242426 0.970170i \(-0.422057\pi\)
0.242426 + 0.970170i \(0.422057\pi\)
\(252\) 5.26990 0.331972
\(253\) 21.7307 1.36619
\(254\) 4.51743 0.283449
\(255\) 0.166146 0.0104044
\(256\) 1.00000 0.0625000
\(257\) −24.4175 −1.52312 −0.761560 0.648094i \(-0.775566\pi\)
−0.761560 + 0.648094i \(0.775566\pi\)
\(258\) −0.294940 −0.0183622
\(259\) 10.3267 0.641672
\(260\) −0.263324 −0.0163306
\(261\) 11.9509 0.739741
\(262\) −11.9861 −0.740505
\(263\) 24.5723 1.51519 0.757597 0.652723i \(-0.226373\pi\)
0.757597 + 0.652723i \(0.226373\pi\)
\(264\) −2.96246 −0.182327
\(265\) −0.823843 −0.0506083
\(266\) 24.7949 1.52027
\(267\) −6.32346 −0.386990
\(268\) −2.25327 −0.137640
\(269\) 26.3214 1.60485 0.802423 0.596756i \(-0.203544\pi\)
0.802423 + 0.596756i \(0.203544\pi\)
\(270\) 1.88596 0.114776
\(271\) 14.7005 0.892994 0.446497 0.894785i \(-0.352671\pi\)
0.446497 + 0.894785i \(0.352671\pi\)
\(272\) 0.422719 0.0256311
\(273\) 2.35902 0.142774
\(274\) −1.25766 −0.0759780
\(275\) 13.1653 0.793895
\(276\) 8.81417 0.530550
\(277\) 31.7443 1.90733 0.953665 0.300872i \(-0.0972777\pi\)
0.953665 + 0.300872i \(0.0972777\pi\)
\(278\) −8.62203 −0.517115
\(279\) −5.86899 −0.351367
\(280\) −1.05069 −0.0627905
\(281\) −21.4480 −1.27948 −0.639740 0.768591i \(-0.720958\pi\)
−0.639740 + 0.768591i \(0.720958\pi\)
\(282\) −14.5303 −0.865266
\(283\) 25.4345 1.51193 0.755963 0.654614i \(-0.227169\pi\)
0.755963 + 0.654614i \(0.227169\pi\)
\(284\) −6.19112 −0.367375
\(285\) 3.32569 0.196997
\(286\) 1.98475 0.117361
\(287\) 12.4160 0.732894
\(288\) 1.79840 0.105972
\(289\) −16.8213 −0.989489
\(290\) −2.38271 −0.139918
\(291\) 8.66093 0.507713
\(292\) −14.6030 −0.854579
\(293\) −31.1876 −1.82200 −0.910998 0.412411i \(-0.864687\pi\)
−0.910998 + 0.412411i \(0.864687\pi\)
\(294\) 1.73946 0.101447
\(295\) 4.42818 0.257819
\(296\) 3.52408 0.204833
\(297\) −14.2151 −0.824842
\(298\) −20.3125 −1.17667
\(299\) −5.90519 −0.341506
\(300\) 5.33996 0.308303
\(301\) 0.788442 0.0454451
\(302\) −7.78097 −0.447744
\(303\) −4.49860 −0.258438
\(304\) 8.46145 0.485298
\(305\) −1.94571 −0.111411
\(306\) 0.760216 0.0434587
\(307\) 15.3678 0.877085 0.438542 0.898711i \(-0.355495\pi\)
0.438542 + 0.898711i \(0.355495\pi\)
\(308\) 7.91934 0.451246
\(309\) −6.74479 −0.383698
\(310\) 1.17013 0.0664589
\(311\) 31.9496 1.81169 0.905847 0.423605i \(-0.139235\pi\)
0.905847 + 0.423605i \(0.139235\pi\)
\(312\) 0.805034 0.0455761
\(313\) −29.7455 −1.68132 −0.840658 0.541566i \(-0.817832\pi\)
−0.840658 + 0.541566i \(0.817832\pi\)
\(314\) 7.94526 0.448377
\(315\) −1.88955 −0.106464
\(316\) 7.19226 0.404596
\(317\) 16.4561 0.924269 0.462134 0.886810i \(-0.347084\pi\)
0.462134 + 0.886810i \(0.347084\pi\)
\(318\) 2.51866 0.141239
\(319\) 17.9592 1.00552
\(320\) −0.358556 −0.0200439
\(321\) −20.5248 −1.14558
\(322\) −23.5623 −1.31307
\(323\) 3.57682 0.199019
\(324\) −0.370583 −0.0205879
\(325\) −3.57759 −0.198449
\(326\) −5.48851 −0.303980
\(327\) −15.7362 −0.870213
\(328\) 4.23707 0.233953
\(329\) 38.8428 2.14147
\(330\) 1.06221 0.0584726
\(331\) 8.39583 0.461476 0.230738 0.973016i \(-0.425886\pi\)
0.230738 + 0.973016i \(0.425886\pi\)
\(332\) −2.45871 −0.134939
\(333\) 6.33770 0.347304
\(334\) −6.87509 −0.376188
\(335\) 0.807922 0.0441415
\(336\) 3.21216 0.175238
\(337\) −1.46106 −0.0795890 −0.0397945 0.999208i \(-0.512670\pi\)
−0.0397945 + 0.999208i \(0.512670\pi\)
\(338\) 12.4607 0.677770
\(339\) −10.1499 −0.551269
\(340\) −0.151568 −0.00821994
\(341\) −8.81962 −0.477609
\(342\) 15.2170 0.822844
\(343\) 15.8623 0.856486
\(344\) 0.269063 0.0145069
\(345\) −3.16037 −0.170149
\(346\) 1.08625 0.0583970
\(347\) −1.47347 −0.0791002 −0.0395501 0.999218i \(-0.512592\pi\)
−0.0395501 + 0.999218i \(0.512592\pi\)
\(348\) 7.28443 0.390486
\(349\) 20.6350 1.10457 0.552284 0.833656i \(-0.313756\pi\)
0.552284 + 0.833656i \(0.313756\pi\)
\(350\) −14.2749 −0.763027
\(351\) 3.86287 0.206185
\(352\) 2.70254 0.144046
\(353\) 12.8922 0.686183 0.343092 0.939302i \(-0.388526\pi\)
0.343092 + 0.939302i \(0.388526\pi\)
\(354\) −13.5379 −0.719529
\(355\) 2.21986 0.117818
\(356\) 5.76865 0.305738
\(357\) 1.35784 0.0718646
\(358\) 4.58642 0.242400
\(359\) 24.5565 1.29604 0.648022 0.761621i \(-0.275596\pi\)
0.648022 + 0.761621i \(0.275596\pi\)
\(360\) −0.644825 −0.0339853
\(361\) 52.5962 2.76822
\(362\) 16.6934 0.877385
\(363\) 4.05177 0.212663
\(364\) −2.15204 −0.112798
\(365\) 5.23600 0.274065
\(366\) 5.94844 0.310930
\(367\) 30.9871 1.61751 0.808757 0.588143i \(-0.200141\pi\)
0.808757 + 0.588143i \(0.200141\pi\)
\(368\) −8.04082 −0.419157
\(369\) 7.61993 0.396678
\(370\) −1.26358 −0.0656904
\(371\) −6.73294 −0.349557
\(372\) −3.57733 −0.185476
\(373\) −8.80764 −0.456042 −0.228021 0.973656i \(-0.573226\pi\)
−0.228021 + 0.973656i \(0.573226\pi\)
\(374\) 1.14242 0.0590729
\(375\) −3.87987 −0.200356
\(376\) 13.2554 0.683596
\(377\) −4.88032 −0.251349
\(378\) 15.4132 0.792771
\(379\) −10.3435 −0.531312 −0.265656 0.964068i \(-0.585589\pi\)
−0.265656 + 0.964068i \(0.585589\pi\)
\(380\) −3.03390 −0.155636
\(381\) 4.95190 0.253694
\(382\) 12.8395 0.656928
\(383\) 12.6260 0.645156 0.322578 0.946543i \(-0.395451\pi\)
0.322578 + 0.946543i \(0.395451\pi\)
\(384\) 1.09618 0.0559390
\(385\) −2.83952 −0.144716
\(386\) −9.93167 −0.505509
\(387\) 0.483881 0.0245971
\(388\) −7.90103 −0.401114
\(389\) 1.18354 0.0600080 0.0300040 0.999550i \(-0.490448\pi\)
0.0300040 + 0.999550i \(0.490448\pi\)
\(390\) −0.288649 −0.0146163
\(391\) −3.39901 −0.171895
\(392\) −1.58684 −0.0801475
\(393\) −13.1389 −0.662770
\(394\) −4.63936 −0.233728
\(395\) −2.57882 −0.129755
\(396\) 4.86024 0.244236
\(397\) 14.4391 0.724679 0.362339 0.932046i \(-0.381978\pi\)
0.362339 + 0.932046i \(0.381978\pi\)
\(398\) 11.9552 0.599261
\(399\) 27.1796 1.36068
\(400\) −4.87144 −0.243572
\(401\) 7.71569 0.385303 0.192652 0.981267i \(-0.438291\pi\)
0.192652 + 0.981267i \(0.438291\pi\)
\(402\) −2.46998 −0.123191
\(403\) 2.39669 0.119387
\(404\) 4.10390 0.204177
\(405\) 0.132875 0.00660259
\(406\) −19.4729 −0.966426
\(407\) 9.52398 0.472086
\(408\) 0.463375 0.0229405
\(409\) 2.51025 0.124124 0.0620619 0.998072i \(-0.480232\pi\)
0.0620619 + 0.998072i \(0.480232\pi\)
\(410\) −1.51923 −0.0750292
\(411\) −1.37862 −0.0680022
\(412\) 6.15301 0.303137
\(413\) 36.1898 1.78078
\(414\) −14.4606 −0.710699
\(415\) 0.881585 0.0432753
\(416\) −0.734401 −0.0360070
\(417\) −9.45127 −0.462831
\(418\) 22.8674 1.11848
\(419\) 11.5020 0.561912 0.280956 0.959721i \(-0.409349\pi\)
0.280956 + 0.959721i \(0.409349\pi\)
\(420\) −1.15174 −0.0561991
\(421\) 23.1953 1.13047 0.565234 0.824931i \(-0.308786\pi\)
0.565234 + 0.824931i \(0.308786\pi\)
\(422\) −21.8957 −1.06587
\(423\) 23.8385 1.15907
\(424\) −2.29767 −0.111585
\(425\) −2.05925 −0.0998883
\(426\) −6.78656 −0.328810
\(427\) −15.9015 −0.769529
\(428\) 18.7240 0.905057
\(429\) 2.17564 0.105041
\(430\) −0.0964739 −0.00465238
\(431\) −8.18662 −0.394336 −0.197168 0.980370i \(-0.563174\pi\)
−0.197168 + 0.980370i \(0.563174\pi\)
\(432\) 5.25989 0.253067
\(433\) −14.8621 −0.714229 −0.357114 0.934061i \(-0.616239\pi\)
−0.357114 + 0.934061i \(0.616239\pi\)
\(434\) 9.56301 0.459039
\(435\) −2.61187 −0.125230
\(436\) 14.3555 0.687505
\(437\) −68.0371 −3.25465
\(438\) −16.0075 −0.764869
\(439\) 8.67971 0.414260 0.207130 0.978313i \(-0.433588\pi\)
0.207130 + 0.978313i \(0.433588\pi\)
\(440\) −0.969011 −0.0461958
\(441\) −2.85377 −0.135894
\(442\) −0.310445 −0.0147664
\(443\) −28.4688 −1.35259 −0.676296 0.736630i \(-0.736416\pi\)
−0.676296 + 0.736630i \(0.736416\pi\)
\(444\) 3.86302 0.183331
\(445\) −2.06838 −0.0980507
\(446\) −14.9834 −0.709484
\(447\) −22.2661 −1.05315
\(448\) −2.93033 −0.138445
\(449\) −12.7608 −0.602218 −0.301109 0.953590i \(-0.597357\pi\)
−0.301109 + 0.953590i \(0.597357\pi\)
\(450\) −8.76078 −0.412987
\(451\) 11.4509 0.539200
\(452\) 9.25940 0.435525
\(453\) −8.52932 −0.400742
\(454\) 4.60248 0.216005
\(455\) 0.771626 0.0361744
\(456\) 9.27525 0.434353
\(457\) −16.2696 −0.761058 −0.380529 0.924769i \(-0.624258\pi\)
−0.380529 + 0.924769i \(0.624258\pi\)
\(458\) 13.7986 0.644767
\(459\) 2.22346 0.103782
\(460\) 2.88308 0.134424
\(461\) −7.67436 −0.357431 −0.178715 0.983901i \(-0.557194\pi\)
−0.178715 + 0.983901i \(0.557194\pi\)
\(462\) 8.68100 0.403877
\(463\) −8.10682 −0.376756 −0.188378 0.982097i \(-0.560323\pi\)
−0.188378 + 0.982097i \(0.560323\pi\)
\(464\) −6.64530 −0.308500
\(465\) 1.28267 0.0594824
\(466\) 16.4695 0.762936
\(467\) −34.5921 −1.60073 −0.800367 0.599511i \(-0.795362\pi\)
−0.800367 + 0.599511i \(0.795362\pi\)
\(468\) −1.32074 −0.0610514
\(469\) 6.60282 0.304890
\(470\) −4.75280 −0.219231
\(471\) 8.70942 0.401309
\(472\) 12.3501 0.568458
\(473\) 0.727152 0.0334345
\(474\) 7.88398 0.362123
\(475\) −41.2194 −1.89128
\(476\) −1.23871 −0.0567760
\(477\) −4.13213 −0.189197
\(478\) 11.9731 0.547636
\(479\) 27.7791 1.26926 0.634630 0.772816i \(-0.281153\pi\)
0.634630 + 0.772816i \(0.281153\pi\)
\(480\) −0.393040 −0.0179398
\(481\) −2.58809 −0.118007
\(482\) 9.79923 0.446343
\(483\) −25.8284 −1.17523
\(484\) −3.69627 −0.168012
\(485\) 2.83296 0.128638
\(486\) 15.3734 0.697354
\(487\) −34.7919 −1.57657 −0.788287 0.615308i \(-0.789032\pi\)
−0.788287 + 0.615308i \(0.789032\pi\)
\(488\) −5.42653 −0.245648
\(489\) −6.01637 −0.272070
\(490\) 0.568971 0.0257035
\(491\) 3.24788 0.146575 0.0732874 0.997311i \(-0.476651\pi\)
0.0732874 + 0.997311i \(0.476651\pi\)
\(492\) 4.64458 0.209394
\(493\) −2.80910 −0.126515
\(494\) −6.21410 −0.279586
\(495\) −1.74267 −0.0783270
\(496\) 3.26346 0.146534
\(497\) 18.1420 0.813781
\(498\) −2.69518 −0.120774
\(499\) 1.21762 0.0545081 0.0272541 0.999629i \(-0.491324\pi\)
0.0272541 + 0.999629i \(0.491324\pi\)
\(500\) 3.53946 0.158289
\(501\) −7.53631 −0.336698
\(502\) −7.68150 −0.342842
\(503\) −27.0511 −1.20615 −0.603074 0.797685i \(-0.706058\pi\)
−0.603074 + 0.797685i \(0.706058\pi\)
\(504\) −5.26990 −0.234740
\(505\) −1.47148 −0.0654798
\(506\) −21.7307 −0.966046
\(507\) 13.6591 0.606621
\(508\) −4.51743 −0.200428
\(509\) 36.7216 1.62766 0.813828 0.581106i \(-0.197380\pi\)
0.813828 + 0.581106i \(0.197380\pi\)
\(510\) −0.166146 −0.00735705
\(511\) 42.7918 1.89300
\(512\) −1.00000 −0.0441942
\(513\) 44.5063 1.96500
\(514\) 24.4175 1.07701
\(515\) −2.20620 −0.0972166
\(516\) 0.294940 0.0129840
\(517\) 35.8233 1.57551
\(518\) −10.3267 −0.453731
\(519\) 1.19072 0.0522667
\(520\) 0.263324 0.0115475
\(521\) −38.4714 −1.68546 −0.842732 0.538334i \(-0.819054\pi\)
−0.842732 + 0.538334i \(0.819054\pi\)
\(522\) −11.9509 −0.523076
\(523\) 9.02479 0.394627 0.197313 0.980340i \(-0.436778\pi\)
0.197313 + 0.980340i \(0.436778\pi\)
\(524\) 11.9861 0.523616
\(525\) −15.6478 −0.682928
\(526\) −24.5723 −1.07140
\(527\) 1.37952 0.0600930
\(528\) 2.96246 0.128925
\(529\) 41.6549 1.81108
\(530\) 0.823843 0.0357855
\(531\) 22.2103 0.963845
\(532\) −24.7949 −1.07499
\(533\) −3.11171 −0.134783
\(534\) 6.32346 0.273643
\(535\) −6.71358 −0.290254
\(536\) 2.25327 0.0973264
\(537\) 5.02752 0.216954
\(538\) −26.3214 −1.13480
\(539\) −4.28850 −0.184719
\(540\) −1.88596 −0.0811589
\(541\) 0.258241 0.0111027 0.00555133 0.999985i \(-0.498233\pi\)
0.00555133 + 0.999985i \(0.498233\pi\)
\(542\) −14.7005 −0.631442
\(543\) 18.2989 0.785282
\(544\) −0.422719 −0.0181239
\(545\) −5.14725 −0.220484
\(546\) −2.35902 −0.100957
\(547\) −13.3586 −0.571173 −0.285587 0.958353i \(-0.592188\pi\)
−0.285587 + 0.958353i \(0.592188\pi\)
\(548\) 1.25766 0.0537246
\(549\) −9.75906 −0.416506
\(550\) −13.1653 −0.561369
\(551\) −56.2289 −2.39543
\(552\) −8.81417 −0.375156
\(553\) −21.0757 −0.896229
\(554\) −31.7443 −1.34869
\(555\) −1.38511 −0.0587945
\(556\) 8.62203 0.365655
\(557\) −37.8202 −1.60249 −0.801247 0.598334i \(-0.795830\pi\)
−0.801247 + 0.598334i \(0.795830\pi\)
\(558\) 5.86899 0.248454
\(559\) −0.197600 −0.00835758
\(560\) 1.05069 0.0443996
\(561\) 1.25229 0.0528717
\(562\) 21.4480 0.904729
\(563\) −0.802330 −0.0338142 −0.0169071 0.999857i \(-0.505382\pi\)
−0.0169071 + 0.999857i \(0.505382\pi\)
\(564\) 14.5303 0.611835
\(565\) −3.32001 −0.139674
\(566\) −25.4345 −1.06909
\(567\) 1.08593 0.0456048
\(568\) 6.19112 0.259774
\(569\) 7.01152 0.293938 0.146969 0.989141i \(-0.453048\pi\)
0.146969 + 0.989141i \(0.453048\pi\)
\(570\) −3.32569 −0.139298
\(571\) 19.1422 0.801078 0.400539 0.916280i \(-0.368823\pi\)
0.400539 + 0.916280i \(0.368823\pi\)
\(572\) −1.98475 −0.0829866
\(573\) 14.0744 0.587967
\(574\) −12.4160 −0.518235
\(575\) 39.1704 1.63352
\(576\) −1.79840 −0.0749332
\(577\) −30.6062 −1.27415 −0.637077 0.770800i \(-0.719857\pi\)
−0.637077 + 0.770800i \(0.719857\pi\)
\(578\) 16.8213 0.699674
\(579\) −10.8869 −0.452443
\(580\) 2.38271 0.0989367
\(581\) 7.20484 0.298907
\(582\) −8.66093 −0.359007
\(583\) −6.20955 −0.257173
\(584\) 14.6030 0.604278
\(585\) 0.473560 0.0195793
\(586\) 31.1876 1.28835
\(587\) 16.1249 0.665547 0.332773 0.943007i \(-0.392016\pi\)
0.332773 + 0.943007i \(0.392016\pi\)
\(588\) −1.73946 −0.0717340
\(589\) 27.6136 1.13780
\(590\) −4.42818 −0.182305
\(591\) −5.08556 −0.209192
\(592\) −3.52408 −0.144839
\(593\) 46.1521 1.89524 0.947619 0.319403i \(-0.103482\pi\)
0.947619 + 0.319403i \(0.103482\pi\)
\(594\) 14.2151 0.583251
\(595\) 0.444145 0.0182082
\(596\) 20.3125 0.832033
\(597\) 13.1050 0.536353
\(598\) 5.90519 0.241481
\(599\) −21.7115 −0.887107 −0.443553 0.896248i \(-0.646282\pi\)
−0.443553 + 0.896248i \(0.646282\pi\)
\(600\) −5.33996 −0.218003
\(601\) −17.7558 −0.724273 −0.362136 0.932125i \(-0.617953\pi\)
−0.362136 + 0.932125i \(0.617953\pi\)
\(602\) −0.788442 −0.0321345
\(603\) 4.05227 0.165021
\(604\) 7.78097 0.316603
\(605\) 1.32532 0.0538819
\(606\) 4.49860 0.182743
\(607\) −25.2321 −1.02414 −0.512071 0.858943i \(-0.671121\pi\)
−0.512071 + 0.858943i \(0.671121\pi\)
\(608\) −8.46145 −0.343157
\(609\) −21.3458 −0.864975
\(610\) 1.94571 0.0787796
\(611\) −9.73480 −0.393828
\(612\) −0.760216 −0.0307299
\(613\) −11.4350 −0.461856 −0.230928 0.972971i \(-0.574176\pi\)
−0.230928 + 0.972971i \(0.574176\pi\)
\(614\) −15.3678 −0.620192
\(615\) −1.66534 −0.0671530
\(616\) −7.91934 −0.319079
\(617\) −2.43581 −0.0980618 −0.0490309 0.998797i \(-0.515613\pi\)
−0.0490309 + 0.998797i \(0.515613\pi\)
\(618\) 6.74479 0.271315
\(619\) −10.3162 −0.414643 −0.207322 0.978273i \(-0.566475\pi\)
−0.207322 + 0.978273i \(0.566475\pi\)
\(620\) −1.17013 −0.0469936
\(621\) −42.2939 −1.69719
\(622\) −31.9496 −1.28106
\(623\) −16.9041 −0.677247
\(624\) −0.805034 −0.0322271
\(625\) 23.0881 0.923524
\(626\) 29.7455 1.18887
\(627\) 25.0667 1.00107
\(628\) −7.94526 −0.317051
\(629\) −1.48970 −0.0593981
\(630\) 1.88955 0.0752815
\(631\) 5.94009 0.236471 0.118236 0.992986i \(-0.462276\pi\)
0.118236 + 0.992986i \(0.462276\pi\)
\(632\) −7.19226 −0.286093
\(633\) −24.0016 −0.953976
\(634\) −16.4561 −0.653557
\(635\) 1.61975 0.0642778
\(636\) −2.51866 −0.0998712
\(637\) 1.16538 0.0461740
\(638\) −17.9592 −0.711012
\(639\) 11.1341 0.440458
\(640\) 0.358556 0.0141732
\(641\) −13.0381 −0.514976 −0.257488 0.966282i \(-0.582895\pi\)
−0.257488 + 0.966282i \(0.582895\pi\)
\(642\) 20.5248 0.810049
\(643\) 36.9822 1.45844 0.729219 0.684281i \(-0.239884\pi\)
0.729219 + 0.684281i \(0.239884\pi\)
\(644\) 23.5623 0.928484
\(645\) −0.105752 −0.00416400
\(646\) −3.57682 −0.140728
\(647\) 33.1192 1.30205 0.651025 0.759056i \(-0.274339\pi\)
0.651025 + 0.759056i \(0.274339\pi\)
\(648\) 0.370583 0.0145579
\(649\) 33.3766 1.31014
\(650\) 3.57759 0.140325
\(651\) 10.4827 0.410851
\(652\) 5.48851 0.214947
\(653\) 42.6703 1.66982 0.834908 0.550389i \(-0.185521\pi\)
0.834908 + 0.550389i \(0.185521\pi\)
\(654\) 15.7362 0.615334
\(655\) −4.29769 −0.167925
\(656\) −4.23707 −0.165430
\(657\) 26.2621 1.02458
\(658\) −38.8428 −1.51425
\(659\) 6.23098 0.242725 0.121362 0.992608i \(-0.461274\pi\)
0.121362 + 0.992608i \(0.461274\pi\)
\(660\) −1.06221 −0.0413464
\(661\) 7.65082 0.297583 0.148791 0.988869i \(-0.452462\pi\)
0.148791 + 0.988869i \(0.452462\pi\)
\(662\) −8.39583 −0.326313
\(663\) −0.340303 −0.0132163
\(664\) 2.45871 0.0954165
\(665\) 8.89034 0.344752
\(666\) −6.33770 −0.245581
\(667\) 53.4337 2.06896
\(668\) 6.87509 0.266005
\(669\) −16.4244 −0.635005
\(670\) −0.807922 −0.0312127
\(671\) −14.6654 −0.566153
\(672\) −3.21216 −0.123912
\(673\) −27.1191 −1.04536 −0.522682 0.852528i \(-0.675068\pi\)
−0.522682 + 0.852528i \(0.675068\pi\)
\(674\) 1.46106 0.0562779
\(675\) −25.6232 −0.986239
\(676\) −12.4607 −0.479256
\(677\) −39.7777 −1.52878 −0.764390 0.644754i \(-0.776960\pi\)
−0.764390 + 0.644754i \(0.776960\pi\)
\(678\) 10.1499 0.389806
\(679\) 23.1526 0.888517
\(680\) 0.151568 0.00581238
\(681\) 5.04513 0.193330
\(682\) 8.81962 0.337721
\(683\) −13.7287 −0.525314 −0.262657 0.964889i \(-0.584599\pi\)
−0.262657 + 0.964889i \(0.584599\pi\)
\(684\) −15.2170 −0.581838
\(685\) −0.450941 −0.0172296
\(686\) −15.8623 −0.605627
\(687\) 15.1257 0.577082
\(688\) −0.269063 −0.0102579
\(689\) 1.68741 0.0642853
\(690\) 3.16037 0.120313
\(691\) −26.7142 −1.01626 −0.508128 0.861282i \(-0.669662\pi\)
−0.508128 + 0.861282i \(0.669662\pi\)
\(692\) −1.08625 −0.0412929
\(693\) −14.2421 −0.541013
\(694\) 1.47347 0.0559323
\(695\) −3.09148 −0.117266
\(696\) −7.28443 −0.276116
\(697\) −1.79109 −0.0678424
\(698\) −20.6350 −0.781048
\(699\) 18.0535 0.682846
\(700\) 14.2749 0.539541
\(701\) −40.8236 −1.54188 −0.770942 0.636905i \(-0.780214\pi\)
−0.770942 + 0.636905i \(0.780214\pi\)
\(702\) −3.86287 −0.145795
\(703\) −29.8189 −1.12464
\(704\) −2.70254 −0.101856
\(705\) −5.20991 −0.196217
\(706\) −12.8922 −0.485205
\(707\) −12.0258 −0.452276
\(708\) 13.5379 0.508784
\(709\) 29.0677 1.09166 0.545830 0.837896i \(-0.316215\pi\)
0.545830 + 0.837896i \(0.316215\pi\)
\(710\) −2.21986 −0.0833099
\(711\) −12.9345 −0.485083
\(712\) −5.76865 −0.216189
\(713\) −26.2409 −0.982729
\(714\) −1.35784 −0.0508159
\(715\) 0.711643 0.0266139
\(716\) −4.58642 −0.171402
\(717\) 13.1246 0.490147
\(718\) −24.5565 −0.916442
\(719\) −6.42812 −0.239728 −0.119864 0.992790i \(-0.538246\pi\)
−0.119864 + 0.992790i \(0.538246\pi\)
\(720\) 0.644825 0.0240312
\(721\) −18.0304 −0.671486
\(722\) −52.5962 −1.95743
\(723\) 10.7417 0.399488
\(724\) −16.6934 −0.620405
\(725\) 32.3722 1.20227
\(726\) −4.05177 −0.150375
\(727\) −29.4922 −1.09380 −0.546902 0.837197i \(-0.684193\pi\)
−0.546902 + 0.837197i \(0.684193\pi\)
\(728\) 2.15204 0.0797599
\(729\) 17.9638 0.665325
\(730\) −5.23600 −0.193793
\(731\) −0.113738 −0.00420675
\(732\) −5.94844 −0.219861
\(733\) 24.1213 0.890942 0.445471 0.895296i \(-0.353036\pi\)
0.445471 + 0.895296i \(0.353036\pi\)
\(734\) −30.9871 −1.14376
\(735\) 0.623692 0.0230052
\(736\) 8.04082 0.296389
\(737\) 6.08955 0.224311
\(738\) −7.61993 −0.280494
\(739\) 13.4016 0.492986 0.246493 0.969145i \(-0.420722\pi\)
0.246493 + 0.969145i \(0.420722\pi\)
\(740\) 1.26358 0.0464501
\(741\) −6.81176 −0.250236
\(742\) 6.73294 0.247174
\(743\) −20.4592 −0.750574 −0.375287 0.926909i \(-0.622456\pi\)
−0.375287 + 0.926909i \(0.622456\pi\)
\(744\) 3.57733 0.131151
\(745\) −7.28316 −0.266834
\(746\) 8.80764 0.322471
\(747\) 4.42174 0.161783
\(748\) −1.14242 −0.0417708
\(749\) −54.8674 −2.00481
\(750\) 3.87987 0.141673
\(751\) 36.2381 1.32235 0.661173 0.750233i \(-0.270059\pi\)
0.661173 + 0.750233i \(0.270059\pi\)
\(752\) −13.2554 −0.483375
\(753\) −8.42029 −0.306852
\(754\) 4.88032 0.177731
\(755\) −2.78991 −0.101535
\(756\) −15.4132 −0.560573
\(757\) −8.11863 −0.295076 −0.147538 0.989056i \(-0.547135\pi\)
−0.147538 + 0.989056i \(0.547135\pi\)
\(758\) 10.3435 0.375694
\(759\) −23.8206 −0.864635
\(760\) 3.03390 0.110051
\(761\) 11.1274 0.403367 0.201683 0.979451i \(-0.435359\pi\)
0.201683 + 0.979451i \(0.435359\pi\)
\(762\) −4.95190 −0.179388
\(763\) −42.0664 −1.52291
\(764\) −12.8395 −0.464518
\(765\) 0.272580 0.00985514
\(766\) −12.6260 −0.456194
\(767\) −9.06990 −0.327495
\(768\) −1.09618 −0.0395549
\(769\) −12.7554 −0.459972 −0.229986 0.973194i \(-0.573868\pi\)
−0.229986 + 0.973194i \(0.573868\pi\)
\(770\) 2.83952 0.102329
\(771\) 26.7659 0.963949
\(772\) 9.93167 0.357448
\(773\) −4.78832 −0.172224 −0.0861120 0.996285i \(-0.527444\pi\)
−0.0861120 + 0.996285i \(0.527444\pi\)
\(774\) −0.483881 −0.0173927
\(775\) −15.8977 −0.571063
\(776\) 7.90103 0.283630
\(777\) −11.3199 −0.406100
\(778\) −1.18354 −0.0424321
\(779\) −35.8518 −1.28452
\(780\) 0.288649 0.0103353
\(781\) 16.7318 0.598709
\(782\) 3.39901 0.121548
\(783\) −34.9536 −1.24914
\(784\) 1.58684 0.0566729
\(785\) 2.84882 0.101679
\(786\) 13.1389 0.468649
\(787\) 6.76875 0.241280 0.120640 0.992696i \(-0.461505\pi\)
0.120640 + 0.992696i \(0.461505\pi\)
\(788\) 4.63936 0.165270
\(789\) −26.9356 −0.958933
\(790\) 2.57882 0.0917504
\(791\) −27.1331 −0.964742
\(792\) −4.86024 −0.172701
\(793\) 3.98525 0.141520
\(794\) −14.4391 −0.512425
\(795\) 0.903078 0.0320289
\(796\) −11.9552 −0.423741
\(797\) 50.8398 1.80084 0.900418 0.435025i \(-0.143260\pi\)
0.900418 + 0.435025i \(0.143260\pi\)
\(798\) −27.1796 −0.962146
\(799\) −5.60332 −0.198231
\(800\) 4.87144 0.172231
\(801\) −10.3743 −0.366559
\(802\) −7.71569 −0.272451
\(803\) 39.4653 1.39270
\(804\) 2.46998 0.0871095
\(805\) −8.44839 −0.297766
\(806\) −2.39669 −0.0844197
\(807\) −28.8529 −1.01567
\(808\) −4.10390 −0.144375
\(809\) 14.5923 0.513039 0.256520 0.966539i \(-0.417424\pi\)
0.256520 + 0.966539i \(0.417424\pi\)
\(810\) −0.132875 −0.00466873
\(811\) −13.1291 −0.461026 −0.230513 0.973069i \(-0.574040\pi\)
−0.230513 + 0.973069i \(0.574040\pi\)
\(812\) 19.4729 0.683366
\(813\) −16.1144 −0.565156
\(814\) −9.52398 −0.333815
\(815\) −1.96793 −0.0689338
\(816\) −0.463375 −0.0162214
\(817\) −2.27666 −0.0796503
\(818\) −2.51025 −0.0877688
\(819\) 3.87022 0.135236
\(820\) 1.51923 0.0530537
\(821\) −8.57345 −0.299215 −0.149608 0.988745i \(-0.547801\pi\)
−0.149608 + 0.988745i \(0.547801\pi\)
\(822\) 1.37862 0.0480848
\(823\) 17.0908 0.595747 0.297874 0.954605i \(-0.403723\pi\)
0.297874 + 0.954605i \(0.403723\pi\)
\(824\) −6.15301 −0.214350
\(825\) −14.4315 −0.502439
\(826\) −36.1898 −1.25920
\(827\) 22.1162 0.769057 0.384528 0.923113i \(-0.374364\pi\)
0.384528 + 0.923113i \(0.374364\pi\)
\(828\) 14.4606 0.502540
\(829\) −37.9819 −1.31917 −0.659583 0.751632i \(-0.729267\pi\)
−0.659583 + 0.751632i \(0.729267\pi\)
\(830\) −0.881585 −0.0306003
\(831\) −34.7973 −1.20711
\(832\) 0.734401 0.0254608
\(833\) 0.670788 0.0232414
\(834\) 9.45127 0.327271
\(835\) −2.46510 −0.0853083
\(836\) −22.8674 −0.790887
\(837\) 17.1654 0.593324
\(838\) −11.5020 −0.397332
\(839\) −47.7541 −1.64866 −0.824328 0.566113i \(-0.808447\pi\)
−0.824328 + 0.566113i \(0.808447\pi\)
\(840\) 1.15174 0.0397388
\(841\) 15.1601 0.522761
\(842\) −23.1953 −0.799362
\(843\) 23.5108 0.809755
\(844\) 21.8957 0.753681
\(845\) 4.46784 0.153698
\(846\) −23.8385 −0.819584
\(847\) 10.8313 0.372168
\(848\) 2.29767 0.0789024
\(849\) −27.8808 −0.956865
\(850\) 2.05925 0.0706317
\(851\) 28.3365 0.971364
\(852\) 6.78656 0.232504
\(853\) −4.93563 −0.168993 −0.0844963 0.996424i \(-0.526928\pi\)
−0.0844963 + 0.996424i \(0.526928\pi\)
\(854\) 15.9015 0.544139
\(855\) 5.45616 0.186597
\(856\) −18.7240 −0.639972
\(857\) 26.6849 0.911539 0.455770 0.890098i \(-0.349364\pi\)
0.455770 + 0.890098i \(0.349364\pi\)
\(858\) −2.17564 −0.0742750
\(859\) −10.0307 −0.342245 −0.171122 0.985250i \(-0.554739\pi\)
−0.171122 + 0.985250i \(0.554739\pi\)
\(860\) 0.0964739 0.00328973
\(861\) −13.6102 −0.463833
\(862\) 8.18662 0.278837
\(863\) −49.9245 −1.69945 −0.849724 0.527228i \(-0.823231\pi\)
−0.849724 + 0.527228i \(0.823231\pi\)
\(864\) −5.25989 −0.178945
\(865\) 0.389480 0.0132427
\(866\) 14.8621 0.505036
\(867\) 18.4391 0.626226
\(868\) −9.56301 −0.324590
\(869\) −19.4374 −0.659367
\(870\) 2.61187 0.0885508
\(871\) −1.65480 −0.0560709
\(872\) −14.3555 −0.486139
\(873\) 14.2092 0.480908
\(874\) 68.0371 2.30139
\(875\) −10.3718 −0.350630
\(876\) 16.0075 0.540844
\(877\) −24.7868 −0.836990 −0.418495 0.908219i \(-0.637442\pi\)
−0.418495 + 0.908219i \(0.637442\pi\)
\(878\) −8.67971 −0.292926
\(879\) 34.1871 1.15310
\(880\) 0.969011 0.0326654
\(881\) −36.4293 −1.22734 −0.613668 0.789564i \(-0.710306\pi\)
−0.613668 + 0.789564i \(0.710306\pi\)
\(882\) 2.85377 0.0960914
\(883\) −28.6990 −0.965797 −0.482899 0.875676i \(-0.660416\pi\)
−0.482899 + 0.875676i \(0.660416\pi\)
\(884\) 0.310445 0.0104414
\(885\) −4.85407 −0.163168
\(886\) 28.4688 0.956428
\(887\) 34.3180 1.15229 0.576144 0.817348i \(-0.304557\pi\)
0.576144 + 0.817348i \(0.304557\pi\)
\(888\) −3.86302 −0.129634
\(889\) 13.2376 0.443974
\(890\) 2.06838 0.0693323
\(891\) 1.00152 0.0335520
\(892\) 14.9834 0.501681
\(893\) −112.160 −3.75330
\(894\) 22.2661 0.744690
\(895\) 1.64449 0.0549691
\(896\) 2.93033 0.0978955
\(897\) 6.47314 0.216132
\(898\) 12.7608 0.425833
\(899\) −21.6867 −0.723290
\(900\) 8.76078 0.292026
\(901\) 0.971270 0.0323577
\(902\) −11.4509 −0.381272
\(903\) −0.864272 −0.0287612
\(904\) −9.25940 −0.307963
\(905\) 5.98551 0.198965
\(906\) 8.52932 0.283368
\(907\) 11.6428 0.386593 0.193297 0.981140i \(-0.438082\pi\)
0.193297 + 0.981140i \(0.438082\pi\)
\(908\) −4.60248 −0.152739
\(909\) −7.38043 −0.244794
\(910\) −0.771626 −0.0255791
\(911\) 22.5346 0.746606 0.373303 0.927709i \(-0.378225\pi\)
0.373303 + 0.927709i \(0.378225\pi\)
\(912\) −9.27525 −0.307134
\(913\) 6.64477 0.219910
\(914\) 16.2696 0.538149
\(915\) 2.13285 0.0705097
\(916\) −13.7986 −0.455919
\(917\) −35.1233 −1.15987
\(918\) −2.22346 −0.0733850
\(919\) 31.4988 1.03905 0.519525 0.854455i \(-0.326109\pi\)
0.519525 + 0.854455i \(0.326109\pi\)
\(920\) −2.88308 −0.0950524
\(921\) −16.8458 −0.555088
\(922\) 7.67436 0.252742
\(923\) −4.54677 −0.149659
\(924\) −8.68100 −0.285584
\(925\) 17.1674 0.564459
\(926\) 8.10682 0.266407
\(927\) −11.0656 −0.363440
\(928\) 6.64530 0.218143
\(929\) −50.6852 −1.66293 −0.831464 0.555579i \(-0.812497\pi\)
−0.831464 + 0.555579i \(0.812497\pi\)
\(930\) −1.28267 −0.0420604
\(931\) 13.4270 0.440051
\(932\) −16.4695 −0.539477
\(933\) −35.0224 −1.14658
\(934\) 34.5921 1.13189
\(935\) 0.409619 0.0133960
\(936\) 1.32074 0.0431699
\(937\) 22.9403 0.749426 0.374713 0.927141i \(-0.377741\pi\)
0.374713 + 0.927141i \(0.377741\pi\)
\(938\) −6.60282 −0.215590
\(939\) 32.6064 1.06407
\(940\) 4.75280 0.155019
\(941\) 7.43703 0.242440 0.121220 0.992626i \(-0.461319\pi\)
0.121220 + 0.992626i \(0.461319\pi\)
\(942\) −8.70942 −0.283768
\(943\) 34.0695 1.10946
\(944\) −12.3501 −0.401960
\(945\) 5.52650 0.179777
\(946\) −0.727152 −0.0236418
\(947\) 10.4075 0.338199 0.169099 0.985599i \(-0.445914\pi\)
0.169099 + 0.985599i \(0.445914\pi\)
\(948\) −7.88398 −0.256060
\(949\) −10.7245 −0.348132
\(950\) 41.2194 1.33734
\(951\) −18.0388 −0.584949
\(952\) 1.23871 0.0401467
\(953\) −27.4734 −0.889952 −0.444976 0.895543i \(-0.646788\pi\)
−0.444976 + 0.895543i \(0.646788\pi\)
\(954\) 4.13213 0.133782
\(955\) 4.60369 0.148972
\(956\) −11.9731 −0.387237
\(957\) −19.6865 −0.636373
\(958\) −27.7791 −0.897502
\(959\) −3.68536 −0.119006
\(960\) 0.393040 0.0126853
\(961\) −20.3499 −0.656447
\(962\) 2.58809 0.0834434
\(963\) −33.6731 −1.08510
\(964\) −9.79923 −0.315612
\(965\) −3.56105 −0.114634
\(966\) 25.8284 0.831016
\(967\) 16.0041 0.514656 0.257328 0.966324i \(-0.417158\pi\)
0.257328 + 0.966324i \(0.417158\pi\)
\(968\) 3.69627 0.118803
\(969\) −3.92082 −0.125955
\(970\) −2.83296 −0.0909608
\(971\) −4.02698 −0.129232 −0.0646160 0.997910i \(-0.520582\pi\)
−0.0646160 + 0.997910i \(0.520582\pi\)
\(972\) −15.3734 −0.493104
\(973\) −25.2654 −0.809971
\(974\) 34.7919 1.11481
\(975\) 3.92167 0.125594
\(976\) 5.42653 0.173699
\(977\) 60.5704 1.93782 0.968910 0.247414i \(-0.0795809\pi\)
0.968910 + 0.247414i \(0.0795809\pi\)
\(978\) 6.01637 0.192382
\(979\) −15.5900 −0.498259
\(980\) −0.568971 −0.0181751
\(981\) −25.8169 −0.824270
\(982\) −3.24788 −0.103644
\(983\) −28.9909 −0.924667 −0.462334 0.886706i \(-0.652988\pi\)
−0.462334 + 0.886706i \(0.652988\pi\)
\(984\) −4.64458 −0.148064
\(985\) −1.66347 −0.0530025
\(986\) 2.80910 0.0894598
\(987\) −42.5785 −1.35529
\(988\) 6.21410 0.197697
\(989\) 2.16348 0.0687948
\(990\) 1.74267 0.0553856
\(991\) 54.5881 1.73405 0.867023 0.498267i \(-0.166030\pi\)
0.867023 + 0.498267i \(0.166030\pi\)
\(992\) −3.26346 −0.103615
\(993\) −9.20331 −0.292058
\(994\) −18.1420 −0.575430
\(995\) 4.28661 0.135895
\(996\) 2.69518 0.0854001
\(997\) −25.0683 −0.793920 −0.396960 0.917836i \(-0.629935\pi\)
−0.396960 + 0.917836i \(0.629935\pi\)
\(998\) −1.21762 −0.0385431
\(999\) −18.5363 −0.586462
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 4034.2.a.c.1.16 49
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.c.1.16 49 1.1 even 1 trivial