Properties

Label 6031.2.a.e.1.5
Level $6031$
Weight $2$
Character 6031.1
Self dual yes
Analytic conductor $48.158$
Analytic rank $0$
Dimension $134$
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] = [6031,2,Mod(1,6031)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6031, 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("6031.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6031 = 37 \cdot 163 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6031.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: \(48.1577774590\)
Analytic rank: \(0\)
Dimension: \(134\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 6031.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.62103 q^{2} -1.46003 q^{3} +4.86979 q^{4} +3.30025 q^{5} +3.82679 q^{6} -2.17387 q^{7} -7.52179 q^{8} -0.868300 q^{9} +O(q^{10})\) \(q-2.62103 q^{2} -1.46003 q^{3} +4.86979 q^{4} +3.30025 q^{5} +3.82679 q^{6} -2.17387 q^{7} -7.52179 q^{8} -0.868300 q^{9} -8.65005 q^{10} +5.62863 q^{11} -7.11006 q^{12} +0.817330 q^{13} +5.69779 q^{14} -4.81848 q^{15} +9.97526 q^{16} -3.22739 q^{17} +2.27584 q^{18} +1.28467 q^{19} +16.0715 q^{20} +3.17393 q^{21} -14.7528 q^{22} -0.920221 q^{23} +10.9821 q^{24} +5.89165 q^{25} -2.14224 q^{26} +5.64785 q^{27} -10.5863 q^{28} +0.512809 q^{29} +12.6294 q^{30} +7.33288 q^{31} -11.1018 q^{32} -8.21799 q^{33} +8.45907 q^{34} -7.17433 q^{35} -4.22844 q^{36} +1.00000 q^{37} -3.36715 q^{38} -1.19333 q^{39} -24.8238 q^{40} +4.14353 q^{41} -8.31896 q^{42} +3.69945 q^{43} +27.4102 q^{44} -2.86561 q^{45} +2.41192 q^{46} +2.26760 q^{47} -14.5642 q^{48} -2.27427 q^{49} -15.4422 q^{50} +4.71210 q^{51} +3.98022 q^{52} -2.68882 q^{53} -14.8032 q^{54} +18.5759 q^{55} +16.3514 q^{56} -1.87566 q^{57} -1.34409 q^{58} -8.75742 q^{59} -23.4650 q^{60} +3.88375 q^{61} -19.2197 q^{62} +1.88757 q^{63} +9.14772 q^{64} +2.69739 q^{65} +21.5396 q^{66} -15.1747 q^{67} -15.7167 q^{68} +1.34355 q^{69} +18.8041 q^{70} +3.51248 q^{71} +6.53117 q^{72} +2.24653 q^{73} -2.62103 q^{74} -8.60202 q^{75} +6.25605 q^{76} -12.2359 q^{77} +3.12775 q^{78} +1.34886 q^{79} +32.9208 q^{80} -5.64116 q^{81} -10.8603 q^{82} +4.42760 q^{83} +15.4564 q^{84} -10.6512 q^{85} -9.69637 q^{86} -0.748718 q^{87} -42.3374 q^{88} -6.63108 q^{89} +7.51083 q^{90} -1.77677 q^{91} -4.48128 q^{92} -10.7063 q^{93} -5.94345 q^{94} +4.23972 q^{95} +16.2091 q^{96} +16.1174 q^{97} +5.96093 q^{98} -4.88733 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 134 q + 9 q^{2} + 7 q^{3} + 149 q^{4} + 22 q^{5} + 20 q^{6} + 11 q^{7} + 27 q^{8} + 181 q^{9} + 15 q^{10} + 20 q^{11} + 28 q^{12} + 11 q^{13} + 17 q^{14} - 13 q^{15} + 143 q^{16} + 76 q^{17} + 23 q^{18} + 15 q^{19} + 67 q^{20} + 63 q^{21} + 2 q^{22} + 22 q^{23} + 33 q^{24} + 160 q^{25} + 65 q^{26} + 31 q^{27} + 10 q^{28} + 73 q^{29} + 20 q^{30} + 10 q^{31} + 53 q^{32} + 72 q^{33} - 7 q^{34} + 52 q^{35} + 201 q^{36} + 134 q^{37} + 70 q^{38} + 6 q^{39} + 11 q^{40} + 182 q^{41} - 15 q^{42} + 12 q^{43} + 33 q^{44} + 29 q^{45} + 24 q^{46} + 80 q^{47} + 21 q^{48} + 229 q^{49} + 37 q^{50} + 57 q^{51} - 15 q^{52} + 75 q^{53} + 95 q^{54} - 9 q^{55} + 39 q^{56} + 19 q^{57} - 21 q^{58} + 91 q^{59} + 62 q^{60} + 58 q^{61} + 108 q^{62} + 9 q^{63} + 167 q^{64} + 76 q^{65} + 105 q^{66} - 17 q^{67} + 109 q^{68} + 48 q^{69} - 55 q^{70} + 56 q^{71} + 48 q^{72} + 54 q^{73} + 9 q^{74} + 28 q^{75} + 82 q^{76} + 156 q^{77} + 16 q^{78} - 2 q^{79} + 98 q^{80} + 270 q^{81} - 42 q^{82} + 130 q^{83} + 229 q^{84} + 22 q^{85} + 72 q^{86} + 22 q^{87} + 61 q^{88} + 157 q^{89} + 176 q^{90} + 31 q^{91} - 18 q^{92} + 36 q^{93} + 83 q^{94} + 98 q^{95} + 111 q^{96} + 35 q^{97} + 53 q^{98} + 55 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.62103 −1.85335 −0.926673 0.375868i \(-0.877345\pi\)
−0.926673 + 0.375868i \(0.877345\pi\)
\(3\) −1.46003 −0.842951 −0.421476 0.906840i \(-0.638488\pi\)
−0.421476 + 0.906840i \(0.638488\pi\)
\(4\) 4.86979 2.43489
\(5\) 3.30025 1.47592 0.737958 0.674846i \(-0.235790\pi\)
0.737958 + 0.674846i \(0.235790\pi\)
\(6\) 3.82679 1.56228
\(7\) −2.17387 −0.821647 −0.410824 0.911715i \(-0.634759\pi\)
−0.410824 + 0.911715i \(0.634759\pi\)
\(8\) −7.52179 −2.65936
\(9\) −0.868300 −0.289433
\(10\) −8.65005 −2.73539
\(11\) 5.62863 1.69709 0.848547 0.529119i \(-0.177478\pi\)
0.848547 + 0.529119i \(0.177478\pi\)
\(12\) −7.11006 −2.05250
\(13\) 0.817330 0.226686 0.113343 0.993556i \(-0.463844\pi\)
0.113343 + 0.993556i \(0.463844\pi\)
\(14\) 5.69779 1.52280
\(15\) −4.81848 −1.24413
\(16\) 9.97526 2.49381
\(17\) −3.22739 −0.782757 −0.391378 0.920230i \(-0.628002\pi\)
−0.391378 + 0.920230i \(0.628002\pi\)
\(18\) 2.27584 0.536420
\(19\) 1.28467 0.294723 0.147361 0.989083i \(-0.452922\pi\)
0.147361 + 0.989083i \(0.452922\pi\)
\(20\) 16.0715 3.59370
\(21\) 3.17393 0.692609
\(22\) −14.7528 −3.14530
\(23\) −0.920221 −0.191879 −0.0959396 0.995387i \(-0.530586\pi\)
−0.0959396 + 0.995387i \(0.530586\pi\)
\(24\) 10.9821 2.24171
\(25\) 5.89165 1.17833
\(26\) −2.14224 −0.420129
\(27\) 5.64785 1.08693
\(28\) −10.5863 −2.00062
\(29\) 0.512809 0.0952262 0.0476131 0.998866i \(-0.484839\pi\)
0.0476131 + 0.998866i \(0.484839\pi\)
\(30\) 12.6294 2.30580
\(31\) 7.33288 1.31702 0.658512 0.752570i \(-0.271186\pi\)
0.658512 + 0.752570i \(0.271186\pi\)
\(32\) −11.1018 −1.96255
\(33\) −8.21799 −1.43057
\(34\) 8.45907 1.45072
\(35\) −7.17433 −1.21268
\(36\) −4.22844 −0.704739
\(37\) 1.00000 0.164399
\(38\) −3.36715 −0.546223
\(39\) −1.19333 −0.191086
\(40\) −24.8238 −3.92499
\(41\) 4.14353 0.647111 0.323556 0.946209i \(-0.395122\pi\)
0.323556 + 0.946209i \(0.395122\pi\)
\(42\) −8.31896 −1.28364
\(43\) 3.69945 0.564161 0.282081 0.959391i \(-0.408975\pi\)
0.282081 + 0.959391i \(0.408975\pi\)
\(44\) 27.4102 4.13225
\(45\) −2.86561 −0.427179
\(46\) 2.41192 0.355619
\(47\) 2.26760 0.330764 0.165382 0.986230i \(-0.447114\pi\)
0.165382 + 0.986230i \(0.447114\pi\)
\(48\) −14.5642 −2.10216
\(49\) −2.27427 −0.324896
\(50\) −15.4422 −2.18386
\(51\) 4.71210 0.659826
\(52\) 3.98022 0.551957
\(53\) −2.68882 −0.369338 −0.184669 0.982801i \(-0.559121\pi\)
−0.184669 + 0.982801i \(0.559121\pi\)
\(54\) −14.8032 −2.01446
\(55\) 18.5759 2.50477
\(56\) 16.3514 2.18505
\(57\) −1.87566 −0.248437
\(58\) −1.34409 −0.176487
\(59\) −8.75742 −1.14012 −0.570060 0.821603i \(-0.693080\pi\)
−0.570060 + 0.821603i \(0.693080\pi\)
\(60\) −23.4650 −3.02931
\(61\) 3.88375 0.497263 0.248632 0.968598i \(-0.420019\pi\)
0.248632 + 0.968598i \(0.420019\pi\)
\(62\) −19.2197 −2.44090
\(63\) 1.88757 0.237812
\(64\) 9.14772 1.14347
\(65\) 2.69739 0.334570
\(66\) 21.5396 2.65134
\(67\) −15.1747 −1.85388 −0.926941 0.375206i \(-0.877572\pi\)
−0.926941 + 0.375206i \(0.877572\pi\)
\(68\) −15.7167 −1.90593
\(69\) 1.34355 0.161745
\(70\) 18.8041 2.24752
\(71\) 3.51248 0.416854 0.208427 0.978038i \(-0.433166\pi\)
0.208427 + 0.978038i \(0.433166\pi\)
\(72\) 6.53117 0.769706
\(73\) 2.24653 0.262936 0.131468 0.991320i \(-0.458031\pi\)
0.131468 + 0.991320i \(0.458031\pi\)
\(74\) −2.62103 −0.304688
\(75\) −8.60202 −0.993275
\(76\) 6.25605 0.717619
\(77\) −12.2359 −1.39441
\(78\) 3.12775 0.354148
\(79\) 1.34886 0.151758 0.0758792 0.997117i \(-0.475824\pi\)
0.0758792 + 0.997117i \(0.475824\pi\)
\(80\) 32.9208 3.68066
\(81\) −5.64116 −0.626795
\(82\) −10.8603 −1.19932
\(83\) 4.42760 0.485992 0.242996 0.970027i \(-0.421870\pi\)
0.242996 + 0.970027i \(0.421870\pi\)
\(84\) 15.4564 1.68643
\(85\) −10.6512 −1.15528
\(86\) −9.69637 −1.04559
\(87\) −0.748718 −0.0802710
\(88\) −42.3374 −4.51318
\(89\) −6.63108 −0.702893 −0.351446 0.936208i \(-0.614310\pi\)
−0.351446 + 0.936208i \(0.614310\pi\)
\(90\) 7.51083 0.791711
\(91\) −1.77677 −0.186256
\(92\) −4.48128 −0.467206
\(93\) −10.7063 −1.11019
\(94\) −5.94345 −0.613020
\(95\) 4.23972 0.434986
\(96\) 16.2091 1.65433
\(97\) 16.1174 1.63647 0.818235 0.574884i \(-0.194953\pi\)
0.818235 + 0.574884i \(0.194953\pi\)
\(98\) 5.96093 0.602145
\(99\) −4.88733 −0.491196
\(100\) 28.6911 2.86911
\(101\) 15.1330 1.50579 0.752894 0.658142i \(-0.228657\pi\)
0.752894 + 0.658142i \(0.228657\pi\)
\(102\) −12.3505 −1.22289
\(103\) −4.93266 −0.486030 −0.243015 0.970023i \(-0.578136\pi\)
−0.243015 + 0.970023i \(0.578136\pi\)
\(104\) −6.14778 −0.602840
\(105\) 10.4748 1.02223
\(106\) 7.04747 0.684511
\(107\) −9.51550 −0.919898 −0.459949 0.887945i \(-0.652132\pi\)
−0.459949 + 0.887945i \(0.652132\pi\)
\(108\) 27.5038 2.64656
\(109\) 12.7355 1.21984 0.609921 0.792462i \(-0.291201\pi\)
0.609921 + 0.792462i \(0.291201\pi\)
\(110\) −48.6879 −4.64221
\(111\) −1.46003 −0.138580
\(112\) −21.6850 −2.04904
\(113\) 0.226430 0.0213007 0.0106504 0.999943i \(-0.496610\pi\)
0.0106504 + 0.999943i \(0.496610\pi\)
\(114\) 4.91615 0.460440
\(115\) −3.03696 −0.283198
\(116\) 2.49727 0.231866
\(117\) −0.709687 −0.0656106
\(118\) 22.9534 2.11304
\(119\) 7.01594 0.643150
\(120\) 36.2436 3.30857
\(121\) 20.6814 1.88013
\(122\) −10.1794 −0.921601
\(123\) −6.04970 −0.545483
\(124\) 35.7096 3.20681
\(125\) 2.94268 0.263201
\(126\) −4.94738 −0.440748
\(127\) 11.8938 1.05540 0.527702 0.849429i \(-0.323054\pi\)
0.527702 + 0.849429i \(0.323054\pi\)
\(128\) −1.77275 −0.156691
\(129\) −5.40133 −0.475560
\(130\) −7.06994 −0.620075
\(131\) −4.73913 −0.414060 −0.207030 0.978335i \(-0.566380\pi\)
−0.207030 + 0.978335i \(0.566380\pi\)
\(132\) −40.0199 −3.48328
\(133\) −2.79270 −0.242158
\(134\) 39.7733 3.43589
\(135\) 18.6393 1.60422
\(136\) 24.2757 2.08163
\(137\) 19.0911 1.63107 0.815533 0.578711i \(-0.196444\pi\)
0.815533 + 0.578711i \(0.196444\pi\)
\(138\) −3.52149 −0.299769
\(139\) 3.97473 0.337133 0.168566 0.985690i \(-0.446086\pi\)
0.168566 + 0.985690i \(0.446086\pi\)
\(140\) −34.9375 −2.95275
\(141\) −3.31078 −0.278818
\(142\) −9.20630 −0.772576
\(143\) 4.60044 0.384708
\(144\) −8.66151 −0.721793
\(145\) 1.69240 0.140546
\(146\) −5.88822 −0.487312
\(147\) 3.32051 0.273871
\(148\) 4.86979 0.400294
\(149\) 10.3780 0.850202 0.425101 0.905146i \(-0.360239\pi\)
0.425101 + 0.905146i \(0.360239\pi\)
\(150\) 22.5461 1.84088
\(151\) 4.47409 0.364097 0.182048 0.983290i \(-0.441727\pi\)
0.182048 + 0.983290i \(0.441727\pi\)
\(152\) −9.66300 −0.783773
\(153\) 2.80234 0.226556
\(154\) 32.0707 2.58433
\(155\) 24.2003 1.94382
\(156\) −5.81126 −0.465273
\(157\) −6.71841 −0.536187 −0.268094 0.963393i \(-0.586394\pi\)
−0.268094 + 0.963393i \(0.586394\pi\)
\(158\) −3.53539 −0.281261
\(159\) 3.92577 0.311334
\(160\) −36.6389 −2.89656
\(161\) 2.00044 0.157657
\(162\) 14.7856 1.16167
\(163\) −1.00000 −0.0783260
\(164\) 20.1781 1.57565
\(165\) −27.1214 −2.11140
\(166\) −11.6049 −0.900712
\(167\) 11.1665 0.864089 0.432044 0.901852i \(-0.357792\pi\)
0.432044 + 0.901852i \(0.357792\pi\)
\(168\) −23.8737 −1.84189
\(169\) −12.3320 −0.948613
\(170\) 27.9171 2.14114
\(171\) −1.11548 −0.0853026
\(172\) 18.0156 1.37367
\(173\) 3.28535 0.249781 0.124890 0.992171i \(-0.460142\pi\)
0.124890 + 0.992171i \(0.460142\pi\)
\(174\) 1.96241 0.148770
\(175\) −12.8077 −0.968172
\(176\) 56.1470 4.23224
\(177\) 12.7861 0.961065
\(178\) 17.3802 1.30270
\(179\) −18.7965 −1.40492 −0.702460 0.711723i \(-0.747915\pi\)
−0.702460 + 0.711723i \(0.747915\pi\)
\(180\) −13.9549 −1.04014
\(181\) −1.04912 −0.0779803 −0.0389901 0.999240i \(-0.512414\pi\)
−0.0389901 + 0.999240i \(0.512414\pi\)
\(182\) 4.65697 0.345197
\(183\) −5.67041 −0.419169
\(184\) 6.92171 0.510275
\(185\) 3.30025 0.242639
\(186\) 28.0614 2.05756
\(187\) −18.1658 −1.32841
\(188\) 11.0427 0.805375
\(189\) −12.2777 −0.893072
\(190\) −11.1124 −0.806180
\(191\) 10.2687 0.743015 0.371508 0.928430i \(-0.378841\pi\)
0.371508 + 0.928430i \(0.378841\pi\)
\(192\) −13.3560 −0.963886
\(193\) −14.7945 −1.06493 −0.532466 0.846451i \(-0.678735\pi\)
−0.532466 + 0.846451i \(0.678735\pi\)
\(194\) −42.2441 −3.03295
\(195\) −3.93829 −0.282026
\(196\) −11.0752 −0.791087
\(197\) −16.7798 −1.19551 −0.597757 0.801677i \(-0.703941\pi\)
−0.597757 + 0.801677i \(0.703941\pi\)
\(198\) 12.8098 0.910356
\(199\) −13.3054 −0.943197 −0.471599 0.881813i \(-0.656323\pi\)
−0.471599 + 0.881813i \(0.656323\pi\)
\(200\) −44.3158 −3.13360
\(201\) 22.1556 1.56273
\(202\) −39.6640 −2.79075
\(203\) −1.11478 −0.0782423
\(204\) 22.9469 1.60661
\(205\) 13.6747 0.955082
\(206\) 12.9286 0.900782
\(207\) 0.799027 0.0555362
\(208\) 8.15307 0.565314
\(209\) 7.23091 0.500172
\(210\) −27.4547 −1.89455
\(211\) −6.73316 −0.463530 −0.231765 0.972772i \(-0.574450\pi\)
−0.231765 + 0.972772i \(0.574450\pi\)
\(212\) −13.0940 −0.899298
\(213\) −5.12834 −0.351388
\(214\) 24.9404 1.70489
\(215\) 12.2091 0.832655
\(216\) −42.4820 −2.89053
\(217\) −15.9408 −1.08213
\(218\) −33.3802 −2.26079
\(219\) −3.28001 −0.221643
\(220\) 90.4606 6.09885
\(221\) −2.63784 −0.177440
\(222\) 3.82679 0.256837
\(223\) −2.34828 −0.157252 −0.0786262 0.996904i \(-0.525053\pi\)
−0.0786262 + 0.996904i \(0.525053\pi\)
\(224\) 24.1340 1.61252
\(225\) −5.11572 −0.341048
\(226\) −0.593479 −0.0394776
\(227\) −9.36369 −0.621490 −0.310745 0.950493i \(-0.600579\pi\)
−0.310745 + 0.950493i \(0.600579\pi\)
\(228\) −9.13406 −0.604918
\(229\) 0.134441 0.00888411 0.00444205 0.999990i \(-0.498586\pi\)
0.00444205 + 0.999990i \(0.498586\pi\)
\(230\) 7.95995 0.524864
\(231\) 17.8649 1.17542
\(232\) −3.85724 −0.253240
\(233\) 2.75353 0.180390 0.0901948 0.995924i \(-0.471251\pi\)
0.0901948 + 0.995924i \(0.471251\pi\)
\(234\) 1.86011 0.121599
\(235\) 7.48366 0.488180
\(236\) −42.6468 −2.77607
\(237\) −1.96938 −0.127925
\(238\) −18.3890 −1.19198
\(239\) 9.70374 0.627683 0.313841 0.949475i \(-0.398384\pi\)
0.313841 + 0.949475i \(0.398384\pi\)
\(240\) −48.0656 −3.10262
\(241\) 11.3094 0.728502 0.364251 0.931301i \(-0.381325\pi\)
0.364251 + 0.931301i \(0.381325\pi\)
\(242\) −54.2066 −3.48453
\(243\) −8.70727 −0.558572
\(244\) 18.9130 1.21078
\(245\) −7.50566 −0.479519
\(246\) 15.8564 1.01097
\(247\) 1.05000 0.0668097
\(248\) −55.1564 −3.50244
\(249\) −6.46445 −0.409668
\(250\) −7.71284 −0.487803
\(251\) 15.9191 1.00480 0.502402 0.864634i \(-0.332450\pi\)
0.502402 + 0.864634i \(0.332450\pi\)
\(252\) 9.19209 0.579047
\(253\) −5.17958 −0.325637
\(254\) −31.1740 −1.95603
\(255\) 15.5511 0.973848
\(256\) −13.6490 −0.853063
\(257\) −7.49795 −0.467709 −0.233855 0.972272i \(-0.575134\pi\)
−0.233855 + 0.972272i \(0.575134\pi\)
\(258\) 14.1570 0.881378
\(259\) −2.17387 −0.135078
\(260\) 13.1357 0.814643
\(261\) −0.445272 −0.0275616
\(262\) 12.4214 0.767396
\(263\) 7.35883 0.453765 0.226882 0.973922i \(-0.427147\pi\)
0.226882 + 0.973922i \(0.427147\pi\)
\(264\) 61.8140 3.80439
\(265\) −8.87377 −0.545112
\(266\) 7.31976 0.448803
\(267\) 9.68160 0.592504
\(268\) −73.8975 −4.51401
\(269\) 28.8341 1.75804 0.879022 0.476781i \(-0.158196\pi\)
0.879022 + 0.476781i \(0.158196\pi\)
\(270\) −48.8542 −2.97317
\(271\) 5.62339 0.341596 0.170798 0.985306i \(-0.445365\pi\)
0.170798 + 0.985306i \(0.445365\pi\)
\(272\) −32.1940 −1.95205
\(273\) 2.59415 0.157005
\(274\) −50.0384 −3.02293
\(275\) 33.1619 1.99974
\(276\) 6.54282 0.393832
\(277\) 3.23546 0.194400 0.0971999 0.995265i \(-0.469011\pi\)
0.0971999 + 0.995265i \(0.469011\pi\)
\(278\) −10.4179 −0.624823
\(279\) −6.36714 −0.381191
\(280\) 53.9638 3.22496
\(281\) 14.3038 0.853291 0.426645 0.904419i \(-0.359695\pi\)
0.426645 + 0.904419i \(0.359695\pi\)
\(282\) 8.67764 0.516746
\(283\) −4.23118 −0.251517 −0.125759 0.992061i \(-0.540136\pi\)
−0.125759 + 0.992061i \(0.540136\pi\)
\(284\) 17.1050 1.01500
\(285\) −6.19014 −0.366672
\(286\) −12.0579 −0.712998
\(287\) −9.00752 −0.531697
\(288\) 9.63973 0.568026
\(289\) −6.58397 −0.387292
\(290\) −4.43582 −0.260480
\(291\) −23.5319 −1.37946
\(292\) 10.9401 0.640222
\(293\) −17.0595 −0.996626 −0.498313 0.866997i \(-0.666047\pi\)
−0.498313 + 0.866997i \(0.666047\pi\)
\(294\) −8.70316 −0.507579
\(295\) −28.9017 −1.68272
\(296\) −7.52179 −0.437195
\(297\) 31.7896 1.84462
\(298\) −27.2011 −1.57572
\(299\) −0.752123 −0.0434964
\(300\) −41.8900 −2.41852
\(301\) −8.04215 −0.463542
\(302\) −11.7267 −0.674797
\(303\) −22.0947 −1.26931
\(304\) 12.8149 0.734984
\(305\) 12.8173 0.733919
\(306\) −7.34501 −0.419886
\(307\) −24.7356 −1.41173 −0.705867 0.708344i \(-0.749443\pi\)
−0.705867 + 0.708344i \(0.749443\pi\)
\(308\) −59.5864 −3.39525
\(309\) 7.20186 0.409699
\(310\) −63.4298 −3.60257
\(311\) −2.82690 −0.160299 −0.0801493 0.996783i \(-0.525540\pi\)
−0.0801493 + 0.996783i \(0.525540\pi\)
\(312\) 8.97598 0.508165
\(313\) −27.8602 −1.57475 −0.787375 0.616474i \(-0.788560\pi\)
−0.787375 + 0.616474i \(0.788560\pi\)
\(314\) 17.6091 0.993741
\(315\) 6.22947 0.350991
\(316\) 6.56865 0.369516
\(317\) 26.9396 1.51308 0.756538 0.653950i \(-0.226889\pi\)
0.756538 + 0.653950i \(0.226889\pi\)
\(318\) −10.2895 −0.577009
\(319\) 2.88641 0.161608
\(320\) 30.1898 1.68766
\(321\) 13.8930 0.775429
\(322\) −5.24322 −0.292193
\(323\) −4.14612 −0.230696
\(324\) −27.4712 −1.52618
\(325\) 4.81542 0.267112
\(326\) 2.62103 0.145165
\(327\) −18.5943 −1.02827
\(328\) −31.1668 −1.72090
\(329\) −4.92948 −0.271771
\(330\) 71.0860 3.91316
\(331\) 6.99012 0.384212 0.192106 0.981374i \(-0.438468\pi\)
0.192106 + 0.981374i \(0.438468\pi\)
\(332\) 21.5615 1.18334
\(333\) −0.868300 −0.0475825
\(334\) −29.2677 −1.60146
\(335\) −50.0803 −2.73618
\(336\) 31.6608 1.72724
\(337\) −14.7790 −0.805061 −0.402531 0.915407i \(-0.631869\pi\)
−0.402531 + 0.915407i \(0.631869\pi\)
\(338\) 32.3224 1.75811
\(339\) −0.330595 −0.0179555
\(340\) −51.8690 −2.81299
\(341\) 41.2741 2.23512
\(342\) 2.92369 0.158095
\(343\) 20.1611 1.08860
\(344\) −27.8265 −1.50031
\(345\) 4.43406 0.238722
\(346\) −8.61100 −0.462930
\(347\) −0.569225 −0.0305576 −0.0152788 0.999883i \(-0.504864\pi\)
−0.0152788 + 0.999883i \(0.504864\pi\)
\(348\) −3.64610 −0.195451
\(349\) 4.38665 0.234812 0.117406 0.993084i \(-0.462542\pi\)
0.117406 + 0.993084i \(0.462542\pi\)
\(350\) 33.5694 1.79436
\(351\) 4.61615 0.246392
\(352\) −62.4881 −3.33063
\(353\) 5.03369 0.267916 0.133958 0.990987i \(-0.457231\pi\)
0.133958 + 0.990987i \(0.457231\pi\)
\(354\) −33.5128 −1.78119
\(355\) 11.5921 0.615243
\(356\) −32.2919 −1.71147
\(357\) −10.2435 −0.542144
\(358\) 49.2663 2.60380
\(359\) 14.0137 0.739613 0.369806 0.929109i \(-0.379424\pi\)
0.369806 + 0.929109i \(0.379424\pi\)
\(360\) 21.5545 1.13602
\(361\) −17.3496 −0.913138
\(362\) 2.74977 0.144525
\(363\) −30.1956 −1.58486
\(364\) −8.65250 −0.453514
\(365\) 7.41411 0.388072
\(366\) 14.8623 0.776865
\(367\) −12.9983 −0.678507 −0.339253 0.940695i \(-0.610174\pi\)
−0.339253 + 0.940695i \(0.610174\pi\)
\(368\) −9.17944 −0.478511
\(369\) −3.59783 −0.187295
\(370\) −8.65005 −0.449695
\(371\) 5.84515 0.303465
\(372\) −52.1372 −2.70319
\(373\) 13.4590 0.696879 0.348440 0.937331i \(-0.386712\pi\)
0.348440 + 0.937331i \(0.386712\pi\)
\(374\) 47.6130 2.46201
\(375\) −4.29641 −0.221866
\(376\) −17.0564 −0.879619
\(377\) 0.419134 0.0215865
\(378\) 32.1802 1.65517
\(379\) −15.3522 −0.788588 −0.394294 0.918984i \(-0.629011\pi\)
−0.394294 + 0.918984i \(0.629011\pi\)
\(380\) 20.6465 1.05915
\(381\) −17.3654 −0.889655
\(382\) −26.9145 −1.37707
\(383\) 16.0048 0.817806 0.408903 0.912578i \(-0.365911\pi\)
0.408903 + 0.912578i \(0.365911\pi\)
\(384\) 2.58828 0.132083
\(385\) −40.3816 −2.05804
\(386\) 38.7768 1.97369
\(387\) −3.21223 −0.163287
\(388\) 78.4881 3.98463
\(389\) 8.76024 0.444162 0.222081 0.975028i \(-0.428715\pi\)
0.222081 + 0.975028i \(0.428715\pi\)
\(390\) 10.3224 0.522693
\(391\) 2.96991 0.150195
\(392\) 17.1066 0.864014
\(393\) 6.91930 0.349032
\(394\) 43.9804 2.21570
\(395\) 4.45157 0.223983
\(396\) −23.8003 −1.19601
\(397\) 29.4983 1.48048 0.740238 0.672344i \(-0.234713\pi\)
0.740238 + 0.672344i \(0.234713\pi\)
\(398\) 34.8739 1.74807
\(399\) 4.07744 0.204128
\(400\) 58.7708 2.93854
\(401\) −14.2018 −0.709206 −0.354603 0.935017i \(-0.615384\pi\)
−0.354603 + 0.935017i \(0.615384\pi\)
\(402\) −58.0703 −2.89629
\(403\) 5.99338 0.298552
\(404\) 73.6944 3.66643
\(405\) −18.6172 −0.925098
\(406\) 2.92187 0.145010
\(407\) 5.62863 0.279001
\(408\) −35.4434 −1.75471
\(409\) −16.9959 −0.840394 −0.420197 0.907433i \(-0.638039\pi\)
−0.420197 + 0.907433i \(0.638039\pi\)
\(410\) −35.8418 −1.77010
\(411\) −27.8737 −1.37491
\(412\) −24.0210 −1.18343
\(413\) 19.0375 0.936776
\(414\) −2.09427 −0.102928
\(415\) 14.6122 0.717284
\(416\) −9.07386 −0.444883
\(417\) −5.80325 −0.284186
\(418\) −18.9524 −0.926993
\(419\) −22.4549 −1.09699 −0.548496 0.836153i \(-0.684799\pi\)
−0.548496 + 0.836153i \(0.684799\pi\)
\(420\) 51.0099 2.48903
\(421\) 38.3914 1.87108 0.935542 0.353216i \(-0.114912\pi\)
0.935542 + 0.353216i \(0.114912\pi\)
\(422\) 17.6478 0.859082
\(423\) −1.96896 −0.0957340
\(424\) 20.2247 0.982200
\(425\) −19.0146 −0.922346
\(426\) 13.4415 0.651244
\(427\) −8.44278 −0.408575
\(428\) −46.3385 −2.23985
\(429\) −6.71680 −0.324290
\(430\) −32.0004 −1.54320
\(431\) −25.8940 −1.24727 −0.623636 0.781715i \(-0.714345\pi\)
−0.623636 + 0.781715i \(0.714345\pi\)
\(432\) 56.3388 2.71060
\(433\) −9.71837 −0.467035 −0.233518 0.972353i \(-0.575024\pi\)
−0.233518 + 0.972353i \(0.575024\pi\)
\(434\) 41.7812 2.00556
\(435\) −2.47096 −0.118473
\(436\) 62.0193 2.97019
\(437\) −1.18218 −0.0565512
\(438\) 8.59700 0.410781
\(439\) −15.5978 −0.744444 −0.372222 0.928144i \(-0.621404\pi\)
−0.372222 + 0.928144i \(0.621404\pi\)
\(440\) −139.724 −6.66108
\(441\) 1.97475 0.0940356
\(442\) 6.91385 0.328858
\(443\) 25.3305 1.20349 0.601743 0.798690i \(-0.294473\pi\)
0.601743 + 0.798690i \(0.294473\pi\)
\(444\) −7.11006 −0.337428
\(445\) −21.8842 −1.03741
\(446\) 6.15490 0.291443
\(447\) −15.1523 −0.716679
\(448\) −19.8860 −0.939525
\(449\) 24.3338 1.14838 0.574191 0.818721i \(-0.305317\pi\)
0.574191 + 0.818721i \(0.305317\pi\)
\(450\) 13.4084 0.632080
\(451\) 23.3224 1.09821
\(452\) 1.10267 0.0518650
\(453\) −6.53233 −0.306916
\(454\) 24.5425 1.15184
\(455\) −5.86379 −0.274899
\(456\) 14.1083 0.660682
\(457\) 31.9899 1.49642 0.748211 0.663460i \(-0.230913\pi\)
0.748211 + 0.663460i \(0.230913\pi\)
\(458\) −0.352373 −0.0164653
\(459\) −18.2278 −0.850801
\(460\) −14.7893 −0.689557
\(461\) 28.5225 1.32843 0.664213 0.747543i \(-0.268767\pi\)
0.664213 + 0.747543i \(0.268767\pi\)
\(462\) −46.8243 −2.17847
\(463\) −37.1043 −1.72438 −0.862191 0.506583i \(-0.830908\pi\)
−0.862191 + 0.506583i \(0.830908\pi\)
\(464\) 5.11540 0.237476
\(465\) −35.3333 −1.63854
\(466\) −7.21707 −0.334324
\(467\) −11.0594 −0.511767 −0.255883 0.966708i \(-0.582366\pi\)
−0.255883 + 0.966708i \(0.582366\pi\)
\(468\) −3.45602 −0.159755
\(469\) 32.9879 1.52324
\(470\) −19.6149 −0.904767
\(471\) 9.80911 0.451980
\(472\) 65.8715 3.03198
\(473\) 20.8228 0.957435
\(474\) 5.16180 0.237089
\(475\) 7.56881 0.347281
\(476\) 34.1661 1.56600
\(477\) 2.33470 0.106899
\(478\) −25.4338 −1.16331
\(479\) −32.2584 −1.47392 −0.736962 0.675934i \(-0.763740\pi\)
−0.736962 + 0.675934i \(0.763740\pi\)
\(480\) 53.4940 2.44166
\(481\) 0.817330 0.0372670
\(482\) −29.6422 −1.35017
\(483\) −2.92072 −0.132897
\(484\) 100.714 4.57792
\(485\) 53.1913 2.41529
\(486\) 22.8220 1.03523
\(487\) 16.5561 0.750227 0.375113 0.926979i \(-0.377604\pi\)
0.375113 + 0.926979i \(0.377604\pi\)
\(488\) −29.2128 −1.32240
\(489\) 1.46003 0.0660250
\(490\) 19.6726 0.888715
\(491\) 35.3475 1.59521 0.797604 0.603181i \(-0.206100\pi\)
0.797604 + 0.603181i \(0.206100\pi\)
\(492\) −29.4608 −1.32819
\(493\) −1.65503 −0.0745389
\(494\) −2.75207 −0.123821
\(495\) −16.1294 −0.724964
\(496\) 73.1474 3.28441
\(497\) −7.63569 −0.342507
\(498\) 16.9435 0.759257
\(499\) −4.02250 −0.180072 −0.0900358 0.995939i \(-0.528698\pi\)
−0.0900358 + 0.995939i \(0.528698\pi\)
\(500\) 14.3302 0.640867
\(501\) −16.3035 −0.728385
\(502\) −41.7244 −1.86225
\(503\) −7.32232 −0.326486 −0.163243 0.986586i \(-0.552195\pi\)
−0.163243 + 0.986586i \(0.552195\pi\)
\(504\) −14.1979 −0.632427
\(505\) 49.9426 2.22242
\(506\) 13.5758 0.603519
\(507\) 18.0051 0.799635
\(508\) 57.9203 2.56980
\(509\) 29.7770 1.31984 0.659922 0.751334i \(-0.270589\pi\)
0.659922 + 0.751334i \(0.270589\pi\)
\(510\) −40.7599 −1.80488
\(511\) −4.88367 −0.216041
\(512\) 39.3199 1.73771
\(513\) 7.25561 0.320343
\(514\) 19.6523 0.866827
\(515\) −16.2790 −0.717339
\(516\) −26.3033 −1.15794
\(517\) 12.7635 0.561338
\(518\) 5.69779 0.250346
\(519\) −4.79673 −0.210553
\(520\) −20.2892 −0.889742
\(521\) −35.8449 −1.57040 −0.785198 0.619245i \(-0.787439\pi\)
−0.785198 + 0.619245i \(0.787439\pi\)
\(522\) 1.16707 0.0510813
\(523\) −13.2570 −0.579686 −0.289843 0.957074i \(-0.593603\pi\)
−0.289843 + 0.957074i \(0.593603\pi\)
\(524\) −23.0786 −1.00819
\(525\) 18.6997 0.816122
\(526\) −19.2877 −0.840984
\(527\) −23.6661 −1.03091
\(528\) −81.9766 −3.56757
\(529\) −22.1532 −0.963182
\(530\) 23.2584 1.01028
\(531\) 7.60407 0.329988
\(532\) −13.5999 −0.589629
\(533\) 3.38663 0.146691
\(534\) −25.3757 −1.09812
\(535\) −31.4035 −1.35769
\(536\) 114.141 4.93013
\(537\) 27.4436 1.18428
\(538\) −75.5749 −3.25827
\(539\) −12.8010 −0.551379
\(540\) 90.7695 3.90610
\(541\) −28.3408 −1.21847 −0.609234 0.792990i \(-0.708523\pi\)
−0.609234 + 0.792990i \(0.708523\pi\)
\(542\) −14.7391 −0.633097
\(543\) 1.53175 0.0657336
\(544\) 35.8299 1.53620
\(545\) 42.0304 1.80039
\(546\) −6.79933 −0.290985
\(547\) 16.2003 0.692676 0.346338 0.938110i \(-0.387425\pi\)
0.346338 + 0.938110i \(0.387425\pi\)
\(548\) 92.9697 3.97147
\(549\) −3.37226 −0.143925
\(550\) −86.9183 −3.70621
\(551\) 0.658788 0.0280653
\(552\) −10.1059 −0.430137
\(553\) −2.93225 −0.124692
\(554\) −8.48023 −0.360290
\(555\) −4.81848 −0.204533
\(556\) 19.3561 0.820882
\(557\) 24.9327 1.05643 0.528216 0.849110i \(-0.322861\pi\)
0.528216 + 0.849110i \(0.322861\pi\)
\(558\) 16.6884 0.706478
\(559\) 3.02367 0.127888
\(560\) −71.5658 −3.02421
\(561\) 26.5226 1.11979
\(562\) −37.4906 −1.58144
\(563\) 22.3564 0.942210 0.471105 0.882077i \(-0.343855\pi\)
0.471105 + 0.882077i \(0.343855\pi\)
\(564\) −16.1228 −0.678892
\(565\) 0.747275 0.0314381
\(566\) 11.0900 0.466149
\(567\) 12.2632 0.515005
\(568\) −26.4201 −1.10856
\(569\) −6.63494 −0.278151 −0.139076 0.990282i \(-0.544413\pi\)
−0.139076 + 0.990282i \(0.544413\pi\)
\(570\) 16.2245 0.679571
\(571\) 34.1090 1.42742 0.713709 0.700442i \(-0.247014\pi\)
0.713709 + 0.700442i \(0.247014\pi\)
\(572\) 22.4032 0.936724
\(573\) −14.9926 −0.626326
\(574\) 23.6090 0.985419
\(575\) −5.42162 −0.226097
\(576\) −7.94296 −0.330957
\(577\) 16.5632 0.689535 0.344767 0.938688i \(-0.387958\pi\)
0.344767 + 0.938688i \(0.387958\pi\)
\(578\) 17.2568 0.717787
\(579\) 21.6005 0.897686
\(580\) 8.24162 0.342215
\(581\) −9.62505 −0.399314
\(582\) 61.6778 2.55663
\(583\) −15.1344 −0.626801
\(584\) −16.8979 −0.699241
\(585\) −2.34214 −0.0968358
\(586\) 44.7134 1.84709
\(587\) 32.4446 1.33913 0.669566 0.742752i \(-0.266480\pi\)
0.669566 + 0.742752i \(0.266480\pi\)
\(588\) 16.1702 0.666848
\(589\) 9.42031 0.388157
\(590\) 75.7521 3.11867
\(591\) 24.4991 1.00776
\(592\) 9.97526 0.409981
\(593\) 11.1792 0.459075 0.229538 0.973300i \(-0.426279\pi\)
0.229538 + 0.973300i \(0.426279\pi\)
\(594\) −83.3215 −3.41872
\(595\) 23.1543 0.949236
\(596\) 50.5389 2.07015
\(597\) 19.4264 0.795069
\(598\) 1.97134 0.0806140
\(599\) −20.7370 −0.847292 −0.423646 0.905828i \(-0.639250\pi\)
−0.423646 + 0.905828i \(0.639250\pi\)
\(600\) 64.7026 2.64147
\(601\) 1.16058 0.0473410 0.0236705 0.999720i \(-0.492465\pi\)
0.0236705 + 0.999720i \(0.492465\pi\)
\(602\) 21.0787 0.859103
\(603\) 13.1762 0.536575
\(604\) 21.7879 0.886537
\(605\) 68.2539 2.77492
\(606\) 57.9107 2.35246
\(607\) 14.8697 0.603540 0.301770 0.953381i \(-0.402422\pi\)
0.301770 + 0.953381i \(0.402422\pi\)
\(608\) −14.2622 −0.578407
\(609\) 1.62762 0.0659545
\(610\) −33.5946 −1.36021
\(611\) 1.85338 0.0749797
\(612\) 13.6468 0.551639
\(613\) 28.7128 1.15970 0.579849 0.814724i \(-0.303112\pi\)
0.579849 + 0.814724i \(0.303112\pi\)
\(614\) 64.8327 2.61643
\(615\) −19.9655 −0.805088
\(616\) 92.0361 3.70824
\(617\) 28.5590 1.14974 0.574870 0.818244i \(-0.305052\pi\)
0.574870 + 0.818244i \(0.305052\pi\)
\(618\) −18.8763 −0.759315
\(619\) −46.0483 −1.85084 −0.925419 0.378944i \(-0.876287\pi\)
−0.925419 + 0.378944i \(0.876287\pi\)
\(620\) 117.851 4.73299
\(621\) −5.19727 −0.208559
\(622\) 7.40938 0.297089
\(623\) 14.4151 0.577530
\(624\) −11.9038 −0.476532
\(625\) −19.7467 −0.789868
\(626\) 73.0223 2.91856
\(627\) −10.5574 −0.421621
\(628\) −32.7172 −1.30556
\(629\) −3.22739 −0.128684
\(630\) −16.3276 −0.650508
\(631\) 23.4598 0.933922 0.466961 0.884278i \(-0.345349\pi\)
0.466961 + 0.884278i \(0.345349\pi\)
\(632\) −10.1458 −0.403579
\(633\) 9.83065 0.390733
\(634\) −70.6093 −2.80425
\(635\) 39.2525 1.55769
\(636\) 19.1177 0.758064
\(637\) −1.85883 −0.0736495
\(638\) −7.56536 −0.299515
\(639\) −3.04988 −0.120652
\(640\) −5.85053 −0.231263
\(641\) −6.35476 −0.250998 −0.125499 0.992094i \(-0.540053\pi\)
−0.125499 + 0.992094i \(0.540053\pi\)
\(642\) −36.4138 −1.43714
\(643\) 34.3452 1.35444 0.677221 0.735780i \(-0.263184\pi\)
0.677221 + 0.735780i \(0.263184\pi\)
\(644\) 9.74174 0.383878
\(645\) −17.8257 −0.701888
\(646\) 10.8671 0.427560
\(647\) 36.8936 1.45044 0.725218 0.688519i \(-0.241739\pi\)
0.725218 + 0.688519i \(0.241739\pi\)
\(648\) 42.4316 1.66687
\(649\) −49.2923 −1.93489
\(650\) −12.6214 −0.495050
\(651\) 23.2741 0.912182
\(652\) −4.86979 −0.190716
\(653\) 41.4575 1.62236 0.811180 0.584797i \(-0.198826\pi\)
0.811180 + 0.584797i \(0.198826\pi\)
\(654\) 48.7362 1.90574
\(655\) −15.6403 −0.611118
\(656\) 41.3328 1.61377
\(657\) −1.95066 −0.0761025
\(658\) 12.9203 0.503686
\(659\) −26.0760 −1.01578 −0.507888 0.861423i \(-0.669574\pi\)
−0.507888 + 0.861423i \(0.669574\pi\)
\(660\) −132.076 −5.14103
\(661\) −27.3158 −1.06246 −0.531230 0.847227i \(-0.678270\pi\)
−0.531230 + 0.847227i \(0.678270\pi\)
\(662\) −18.3213 −0.712077
\(663\) 3.85134 0.149573
\(664\) −33.3035 −1.29243
\(665\) −9.21662 −0.357405
\(666\) 2.27584 0.0881869
\(667\) −0.471897 −0.0182719
\(668\) 54.3784 2.10396
\(669\) 3.42857 0.132556
\(670\) 131.262 5.07108
\(671\) 21.8602 0.843903
\(672\) −35.2365 −1.35928
\(673\) 26.1960 1.00978 0.504891 0.863183i \(-0.331533\pi\)
0.504891 + 0.863183i \(0.331533\pi\)
\(674\) 38.7361 1.49206
\(675\) 33.2752 1.28076
\(676\) −60.0541 −2.30977
\(677\) 4.55034 0.174884 0.0874419 0.996170i \(-0.472131\pi\)
0.0874419 + 0.996170i \(0.472131\pi\)
\(678\) 0.866500 0.0332777
\(679\) −35.0371 −1.34460
\(680\) 80.1160 3.07231
\(681\) 13.6713 0.523886
\(682\) −108.180 −4.14244
\(683\) 10.8077 0.413546 0.206773 0.978389i \(-0.433704\pi\)
0.206773 + 0.978389i \(0.433704\pi\)
\(684\) −5.43213 −0.207703
\(685\) 63.0055 2.40732
\(686\) −52.8428 −2.01755
\(687\) −0.196288 −0.00748887
\(688\) 36.9030 1.40691
\(689\) −2.19765 −0.0837238
\(690\) −11.6218 −0.442435
\(691\) −22.6618 −0.862095 −0.431047 0.902329i \(-0.641856\pi\)
−0.431047 + 0.902329i \(0.641856\pi\)
\(692\) 15.9990 0.608189
\(693\) 10.6245 0.403590
\(694\) 1.49195 0.0566338
\(695\) 13.1176 0.497580
\(696\) 5.63171 0.213469
\(697\) −13.3728 −0.506530
\(698\) −11.4975 −0.435188
\(699\) −4.02025 −0.152060
\(700\) −62.3708 −2.35740
\(701\) 8.49659 0.320912 0.160456 0.987043i \(-0.448704\pi\)
0.160456 + 0.987043i \(0.448704\pi\)
\(702\) −12.0991 −0.456650
\(703\) 1.28467 0.0484521
\(704\) 51.4891 1.94057
\(705\) −10.9264 −0.411512
\(706\) −13.1934 −0.496542
\(707\) −32.8972 −1.23723
\(708\) 62.2658 2.34009
\(709\) 44.4148 1.66803 0.834017 0.551738i \(-0.186035\pi\)
0.834017 + 0.551738i \(0.186035\pi\)
\(710\) −30.3831 −1.14026
\(711\) −1.17121 −0.0439239
\(712\) 49.8776 1.86924
\(713\) −6.74787 −0.252710
\(714\) 26.8485 1.00478
\(715\) 15.1826 0.567798
\(716\) −91.5352 −3.42083
\(717\) −14.1678 −0.529106
\(718\) −36.7302 −1.37076
\(719\) 39.5177 1.47376 0.736881 0.676023i \(-0.236298\pi\)
0.736881 + 0.676023i \(0.236298\pi\)
\(720\) −28.5852 −1.06531
\(721\) 10.7230 0.399345
\(722\) 45.4739 1.69236
\(723\) −16.5121 −0.614092
\(724\) −5.10898 −0.189874
\(725\) 3.02129 0.112208
\(726\) 79.1435 2.93729
\(727\) −29.8683 −1.10775 −0.553877 0.832599i \(-0.686852\pi\)
−0.553877 + 0.832599i \(0.686852\pi\)
\(728\) 13.3645 0.495322
\(729\) 29.6364 1.09764
\(730\) −19.4326 −0.719232
\(731\) −11.9396 −0.441601
\(732\) −27.6137 −1.02063
\(733\) 18.8344 0.695664 0.347832 0.937557i \(-0.386918\pi\)
0.347832 + 0.937557i \(0.386918\pi\)
\(734\) 34.0689 1.25751
\(735\) 10.9585 0.404211
\(736\) 10.2161 0.376572
\(737\) −85.4126 −3.14621
\(738\) 9.43001 0.347123
\(739\) −2.74405 −0.100942 −0.0504708 0.998726i \(-0.516072\pi\)
−0.0504708 + 0.998726i \(0.516072\pi\)
\(740\) 16.0715 0.590801
\(741\) −1.53303 −0.0563173
\(742\) −15.3203 −0.562426
\(743\) −0.698995 −0.0256436 −0.0128218 0.999918i \(-0.504081\pi\)
−0.0128218 + 0.999918i \(0.504081\pi\)
\(744\) 80.5303 2.95238
\(745\) 34.2501 1.25483
\(746\) −35.2764 −1.29156
\(747\) −3.84448 −0.140662
\(748\) −88.4634 −3.23454
\(749\) 20.6855 0.755832
\(750\) 11.2610 0.411194
\(751\) −14.3569 −0.523893 −0.261946 0.965082i \(-0.584364\pi\)
−0.261946 + 0.965082i \(0.584364\pi\)
\(752\) 22.6199 0.824864
\(753\) −23.2424 −0.847000
\(754\) −1.09856 −0.0400072
\(755\) 14.7656 0.537376
\(756\) −59.7899 −2.17454
\(757\) −29.6858 −1.07895 −0.539475 0.842001i \(-0.681377\pi\)
−0.539475 + 0.842001i \(0.681377\pi\)
\(758\) 40.2385 1.46153
\(759\) 7.56236 0.274496
\(760\) −31.8903 −1.15678
\(761\) 47.9582 1.73848 0.869242 0.494387i \(-0.164607\pi\)
0.869242 + 0.494387i \(0.164607\pi\)
\(762\) 45.5151 1.64884
\(763\) −27.6854 −1.00228
\(764\) 50.0063 1.80916
\(765\) 9.24842 0.334377
\(766\) −41.9490 −1.51568
\(767\) −7.15770 −0.258450
\(768\) 19.9280 0.719090
\(769\) 16.1027 0.580677 0.290338 0.956924i \(-0.406232\pi\)
0.290338 + 0.956924i \(0.406232\pi\)
\(770\) 105.841 3.81426
\(771\) 10.9473 0.394256
\(772\) −72.0461 −2.59300
\(773\) −14.2944 −0.514134 −0.257067 0.966394i \(-0.582756\pi\)
−0.257067 + 0.966394i \(0.582756\pi\)
\(774\) 8.41935 0.302627
\(775\) 43.2028 1.55189
\(776\) −121.231 −4.35196
\(777\) 3.17393 0.113864
\(778\) −22.9608 −0.823186
\(779\) 5.32306 0.190718
\(780\) −19.1786 −0.686705
\(781\) 19.7704 0.707442
\(782\) −7.78421 −0.278363
\(783\) 2.89627 0.103504
\(784\) −22.6864 −0.810230
\(785\) −22.1724 −0.791368
\(786\) −18.1357 −0.646878
\(787\) 35.3593 1.26042 0.630211 0.776424i \(-0.282968\pi\)
0.630211 + 0.776424i \(0.282968\pi\)
\(788\) −81.7142 −2.91095
\(789\) −10.7441 −0.382502
\(790\) −11.6677 −0.415118
\(791\) −0.492230 −0.0175017
\(792\) 36.7615 1.30626
\(793\) 3.17430 0.112723
\(794\) −77.3159 −2.74384
\(795\) 12.9560 0.459503
\(796\) −64.7946 −2.29658
\(797\) −38.1353 −1.35082 −0.675411 0.737441i \(-0.736034\pi\)
−0.675411 + 0.737441i \(0.736034\pi\)
\(798\) −10.6871 −0.378319
\(799\) −7.31843 −0.258908
\(800\) −65.4082 −2.31253
\(801\) 5.75776 0.203441
\(802\) 37.2234 1.31440
\(803\) 12.6449 0.446228
\(804\) 107.893 3.80509
\(805\) 6.60197 0.232689
\(806\) −15.7088 −0.553320
\(807\) −42.0987 −1.48195
\(808\) −113.827 −4.00442
\(809\) 15.1448 0.532464 0.266232 0.963909i \(-0.414221\pi\)
0.266232 + 0.963909i \(0.414221\pi\)
\(810\) 48.7963 1.71453
\(811\) 15.3824 0.540151 0.270075 0.962839i \(-0.412951\pi\)
0.270075 + 0.962839i \(0.412951\pi\)
\(812\) −5.42875 −0.190512
\(813\) −8.21034 −0.287949
\(814\) −14.7528 −0.517085
\(815\) −3.30025 −0.115603
\(816\) 47.0044 1.64548
\(817\) 4.75256 0.166271
\(818\) 44.5468 1.55754
\(819\) 1.54277 0.0539088
\(820\) 66.5929 2.32552
\(821\) 44.5002 1.55307 0.776535 0.630075i \(-0.216976\pi\)
0.776535 + 0.630075i \(0.216976\pi\)
\(822\) 73.0578 2.54818
\(823\) 27.5382 0.959921 0.479960 0.877290i \(-0.340651\pi\)
0.479960 + 0.877290i \(0.340651\pi\)
\(824\) 37.1025 1.29253
\(825\) −48.4175 −1.68568
\(826\) −49.8979 −1.73617
\(827\) −14.5409 −0.505638 −0.252819 0.967514i \(-0.581358\pi\)
−0.252819 + 0.967514i \(0.581358\pi\)
\(828\) 3.89109 0.135225
\(829\) 2.29849 0.0798297 0.0399149 0.999203i \(-0.487291\pi\)
0.0399149 + 0.999203i \(0.487291\pi\)
\(830\) −38.2990 −1.32938
\(831\) −4.72388 −0.163870
\(832\) 7.47670 0.259208
\(833\) 7.33995 0.254314
\(834\) 15.2105 0.526696
\(835\) 36.8522 1.27532
\(836\) 35.2130 1.21787
\(837\) 41.4150 1.43151
\(838\) 58.8548 2.03311
\(839\) 12.4061 0.428306 0.214153 0.976800i \(-0.431301\pi\)
0.214153 + 0.976800i \(0.431301\pi\)
\(840\) −78.7890 −2.71848
\(841\) −28.7370 −0.990932
\(842\) −100.625 −3.46777
\(843\) −20.8840 −0.719282
\(844\) −32.7891 −1.12865
\(845\) −40.6986 −1.40007
\(846\) 5.16070 0.177428
\(847\) −44.9588 −1.54480
\(848\) −26.8217 −0.921059
\(849\) 6.17766 0.212017
\(850\) 49.8379 1.70943
\(851\) −0.920221 −0.0315448
\(852\) −24.9739 −0.855593
\(853\) −28.3282 −0.969938 −0.484969 0.874531i \(-0.661169\pi\)
−0.484969 + 0.874531i \(0.661169\pi\)
\(854\) 22.1288 0.757231
\(855\) −3.68135 −0.125899
\(856\) 71.5736 2.44634
\(857\) 20.3224 0.694201 0.347101 0.937828i \(-0.387166\pi\)
0.347101 + 0.937828i \(0.387166\pi\)
\(858\) 17.6049 0.601022
\(859\) 43.2434 1.47545 0.737723 0.675103i \(-0.235901\pi\)
0.737723 + 0.675103i \(0.235901\pi\)
\(860\) 59.4558 2.02743
\(861\) 13.1513 0.448195
\(862\) 67.8690 2.31163
\(863\) −3.35841 −0.114322 −0.0571608 0.998365i \(-0.518205\pi\)
−0.0571608 + 0.998365i \(0.518205\pi\)
\(864\) −62.7015 −2.13315
\(865\) 10.8425 0.368655
\(866\) 25.4721 0.865578
\(867\) 9.61282 0.326468
\(868\) −77.6281 −2.63487
\(869\) 7.59222 0.257548
\(870\) 6.47645 0.219572
\(871\) −12.4027 −0.420250
\(872\) −95.7940 −3.24399
\(873\) −13.9947 −0.473649
\(874\) 3.09852 0.104809
\(875\) −6.39701 −0.216258
\(876\) −15.9730 −0.539676
\(877\) −36.1661 −1.22124 −0.610621 0.791923i \(-0.709080\pi\)
−0.610621 + 0.791923i \(0.709080\pi\)
\(878\) 40.8823 1.37971
\(879\) 24.9074 0.840107
\(880\) 185.299 6.24643
\(881\) −46.3196 −1.56055 −0.780273 0.625439i \(-0.784920\pi\)
−0.780273 + 0.625439i \(0.784920\pi\)
\(882\) −5.17587 −0.174281
\(883\) −23.6623 −0.796301 −0.398150 0.917320i \(-0.630348\pi\)
−0.398150 + 0.917320i \(0.630348\pi\)
\(884\) −12.8457 −0.432048
\(885\) 42.1975 1.41845
\(886\) −66.3918 −2.23048
\(887\) 35.2104 1.18225 0.591125 0.806580i \(-0.298684\pi\)
0.591125 + 0.806580i \(0.298684\pi\)
\(888\) 10.9821 0.368534
\(889\) −25.8556 −0.867171
\(890\) 57.3591 1.92268
\(891\) −31.7520 −1.06373
\(892\) −11.4356 −0.382893
\(893\) 2.91311 0.0974836
\(894\) 39.7146 1.32825
\(895\) −62.0333 −2.07354
\(896\) 3.85375 0.128745
\(897\) 1.09813 0.0366654
\(898\) −63.7796 −2.12835
\(899\) 3.76037 0.125415
\(900\) −24.9125 −0.830416
\(901\) 8.67786 0.289101
\(902\) −61.1287 −2.03536
\(903\) 11.7418 0.390743
\(904\) −1.70316 −0.0566462
\(905\) −3.46235 −0.115092
\(906\) 17.1214 0.568821
\(907\) −25.4931 −0.846486 −0.423243 0.906016i \(-0.639108\pi\)
−0.423243 + 0.906016i \(0.639108\pi\)
\(908\) −45.5992 −1.51326
\(909\) −13.1400 −0.435825
\(910\) 15.3692 0.509483
\(911\) 32.9035 1.09014 0.545071 0.838390i \(-0.316503\pi\)
0.545071 + 0.838390i \(0.316503\pi\)
\(912\) −18.7102 −0.619556
\(913\) 24.9213 0.824775
\(914\) −83.8463 −2.77339
\(915\) −18.7138 −0.618658
\(916\) 0.654699 0.0216319
\(917\) 10.3023 0.340211
\(918\) 47.7756 1.57683
\(919\) −29.6909 −0.979414 −0.489707 0.871887i \(-0.662896\pi\)
−0.489707 + 0.871887i \(0.662896\pi\)
\(920\) 22.8434 0.753124
\(921\) 36.1148 1.19002
\(922\) −74.7583 −2.46203
\(923\) 2.87085 0.0944953
\(924\) 86.9981 2.86203
\(925\) 5.89165 0.193716
\(926\) 97.2514 3.19588
\(927\) 4.28303 0.140673
\(928\) −5.69312 −0.186886
\(929\) 20.8585 0.684346 0.342173 0.939637i \(-0.388837\pi\)
0.342173 + 0.939637i \(0.388837\pi\)
\(930\) 92.6097 3.03679
\(931\) −2.92168 −0.0957542
\(932\) 13.4091 0.439230
\(933\) 4.12737 0.135124
\(934\) 28.9869 0.948481
\(935\) −59.9516 −1.96063
\(936\) 5.33812 0.174482
\(937\) 28.8313 0.941877 0.470938 0.882166i \(-0.343915\pi\)
0.470938 + 0.882166i \(0.343915\pi\)
\(938\) −86.4621 −2.82309
\(939\) 40.6768 1.32744
\(940\) 36.4438 1.18867
\(941\) 49.6151 1.61741 0.808704 0.588216i \(-0.200170\pi\)
0.808704 + 0.588216i \(0.200170\pi\)
\(942\) −25.7099 −0.837675
\(943\) −3.81296 −0.124167
\(944\) −87.3575 −2.84325
\(945\) −40.5195 −1.31810
\(946\) −54.5772 −1.77446
\(947\) 43.9608 1.42853 0.714267 0.699873i \(-0.246760\pi\)
0.714267 + 0.699873i \(0.246760\pi\)
\(948\) −9.59046 −0.311484
\(949\) 1.83615 0.0596041
\(950\) −19.8381 −0.643632
\(951\) −39.3327 −1.27545
\(952\) −52.7724 −1.71036
\(953\) −37.0086 −1.19883 −0.599414 0.800439i \(-0.704600\pi\)
−0.599414 + 0.800439i \(0.704600\pi\)
\(954\) −6.11931 −0.198120
\(955\) 33.8892 1.09663
\(956\) 47.2552 1.52834
\(957\) −4.21426 −0.136228
\(958\) 84.5502 2.73169
\(959\) −41.5017 −1.34016
\(960\) −44.0781 −1.42261
\(961\) 22.7711 0.734553
\(962\) −2.14224 −0.0690687
\(963\) 8.26230 0.266249
\(964\) 55.0744 1.77383
\(965\) −48.8256 −1.57175
\(966\) 7.65528 0.246305
\(967\) −9.46540 −0.304387 −0.152193 0.988351i \(-0.548634\pi\)
−0.152193 + 0.988351i \(0.548634\pi\)
\(968\) −155.562 −4.99994
\(969\) 6.05347 0.194466
\(970\) −139.416 −4.47638
\(971\) −44.5417 −1.42941 −0.714705 0.699426i \(-0.753439\pi\)
−0.714705 + 0.699426i \(0.753439\pi\)
\(972\) −42.4026 −1.36006
\(973\) −8.64057 −0.277004
\(974\) −43.3939 −1.39043
\(975\) −7.03068 −0.225162
\(976\) 38.7414 1.24008
\(977\) 39.7834 1.27278 0.636392 0.771366i \(-0.280426\pi\)
0.636392 + 0.771366i \(0.280426\pi\)
\(978\) −3.82679 −0.122367
\(979\) −37.3239 −1.19288
\(980\) −36.5510 −1.16758
\(981\) −11.0582 −0.353063
\(982\) −92.6467 −2.95648
\(983\) −22.5075 −0.717878 −0.358939 0.933361i \(-0.616861\pi\)
−0.358939 + 0.933361i \(0.616861\pi\)
\(984\) 45.5046 1.45063
\(985\) −55.3777 −1.76448
\(986\) 4.33789 0.138146
\(987\) 7.19721 0.229090
\(988\) 5.11326 0.162674
\(989\) −3.40431 −0.108251
\(990\) 42.2757 1.34361
\(991\) −36.6954 −1.16567 −0.582834 0.812591i \(-0.698056\pi\)
−0.582834 + 0.812591i \(0.698056\pi\)
\(992\) −81.4085 −2.58472
\(993\) −10.2058 −0.323872
\(994\) 20.0133 0.634785
\(995\) −43.9113 −1.39208
\(996\) −31.4805 −0.997498
\(997\) −44.6114 −1.41286 −0.706429 0.707784i \(-0.749695\pi\)
−0.706429 + 0.707784i \(0.749695\pi\)
\(998\) 10.5431 0.333735
\(999\) 5.64785 0.178690
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 6031.2.a.e.1.5 134
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6031.2.a.e.1.5 134 1.1 even 1 trivial