Properties

Label 6041.2.a.c.1.4
Level $6041$
Weight $2$
Character 6041.1
Self dual yes
Analytic conductor $48.238$
Analytic rank $1$
Dimension $83$
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] = [6041,2,Mod(1,6041)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6041, 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("6041.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6041 = 7 \cdot 863 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6041.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: \(48.2376278611\)
Analytic rank: \(1\)
Dimension: \(83\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Character \(\chi\) \(=\) 6041.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.50484 q^{2} +1.86042 q^{3} +4.27422 q^{4} +2.20949 q^{5} -4.66004 q^{6} +1.00000 q^{7} -5.69655 q^{8} +0.461144 q^{9} +O(q^{10})\) \(q-2.50484 q^{2} +1.86042 q^{3} +4.27422 q^{4} +2.20949 q^{5} -4.66004 q^{6} +1.00000 q^{7} -5.69655 q^{8} +0.461144 q^{9} -5.53442 q^{10} +3.98616 q^{11} +7.95182 q^{12} -3.32354 q^{13} -2.50484 q^{14} +4.11057 q^{15} +5.72051 q^{16} -3.47214 q^{17} -1.15509 q^{18} -1.58300 q^{19} +9.44384 q^{20} +1.86042 q^{21} -9.98469 q^{22} -1.29720 q^{23} -10.5979 q^{24} -0.118152 q^{25} +8.32493 q^{26} -4.72333 q^{27} +4.27422 q^{28} -6.45859 q^{29} -10.2963 q^{30} -1.02891 q^{31} -2.93584 q^{32} +7.41591 q^{33} +8.69715 q^{34} +2.20949 q^{35} +1.97103 q^{36} -3.48735 q^{37} +3.96515 q^{38} -6.18316 q^{39} -12.5865 q^{40} +2.91634 q^{41} -4.66004 q^{42} +0.547380 q^{43} +17.0377 q^{44} +1.01889 q^{45} +3.24929 q^{46} -11.2193 q^{47} +10.6425 q^{48} +1.00000 q^{49} +0.295953 q^{50} -6.45962 q^{51} -14.2055 q^{52} -6.72493 q^{53} +11.8312 q^{54} +8.80738 q^{55} -5.69655 q^{56} -2.94503 q^{57} +16.1777 q^{58} -11.2668 q^{59} +17.5695 q^{60} -1.50408 q^{61} +2.57725 q^{62} +0.461144 q^{63} -4.08720 q^{64} -7.34332 q^{65} -18.5757 q^{66} +1.77027 q^{67} -14.8407 q^{68} -2.41334 q^{69} -5.53442 q^{70} -9.11314 q^{71} -2.62693 q^{72} -0.379090 q^{73} +8.73525 q^{74} -0.219812 q^{75} -6.76607 q^{76} +3.98616 q^{77} +15.4878 q^{78} +9.57473 q^{79} +12.6394 q^{80} -10.1708 q^{81} -7.30497 q^{82} +15.8931 q^{83} +7.95182 q^{84} -7.67165 q^{85} -1.37110 q^{86} -12.0157 q^{87} -22.7074 q^{88} -4.04735 q^{89} -2.55217 q^{90} -3.32354 q^{91} -5.54453 q^{92} -1.91420 q^{93} +28.1025 q^{94} -3.49762 q^{95} -5.46189 q^{96} +0.0214864 q^{97} -2.50484 q^{98} +1.83820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.50484 −1.77119 −0.885594 0.464460i \(-0.846249\pi\)
−0.885594 + 0.464460i \(0.846249\pi\)
\(3\) 1.86042 1.07411 0.537056 0.843547i \(-0.319537\pi\)
0.537056 + 0.843547i \(0.319537\pi\)
\(4\) 4.27422 2.13711
\(5\) 2.20949 0.988114 0.494057 0.869429i \(-0.335513\pi\)
0.494057 + 0.869429i \(0.335513\pi\)
\(6\) −4.66004 −1.90245
\(7\) 1.00000 0.377964
\(8\) −5.69655 −2.01403
\(9\) 0.461144 0.153715
\(10\) −5.53442 −1.75014
\(11\) 3.98616 1.20187 0.600936 0.799297i \(-0.294795\pi\)
0.600936 + 0.799297i \(0.294795\pi\)
\(12\) 7.95182 2.29549
\(13\) −3.32354 −0.921783 −0.460892 0.887456i \(-0.652470\pi\)
−0.460892 + 0.887456i \(0.652470\pi\)
\(14\) −2.50484 −0.669446
\(15\) 4.11057 1.06134
\(16\) 5.72051 1.43013
\(17\) −3.47214 −0.842117 −0.421059 0.907033i \(-0.638341\pi\)
−0.421059 + 0.907033i \(0.638341\pi\)
\(18\) −1.15509 −0.272258
\(19\) −1.58300 −0.363164 −0.181582 0.983376i \(-0.558122\pi\)
−0.181582 + 0.983376i \(0.558122\pi\)
\(20\) 9.44384 2.11171
\(21\) 1.86042 0.405976
\(22\) −9.98469 −2.12874
\(23\) −1.29720 −0.270486 −0.135243 0.990812i \(-0.543181\pi\)
−0.135243 + 0.990812i \(0.543181\pi\)
\(24\) −10.5979 −2.16330
\(25\) −0.118152 −0.0236305
\(26\) 8.32493 1.63265
\(27\) −4.72333 −0.909004
\(28\) 4.27422 0.807751
\(29\) −6.45859 −1.19933 −0.599665 0.800251i \(-0.704700\pi\)
−0.599665 + 0.800251i \(0.704700\pi\)
\(30\) −10.2963 −1.87984
\(31\) −1.02891 −0.184798 −0.0923988 0.995722i \(-0.529453\pi\)
−0.0923988 + 0.995722i \(0.529453\pi\)
\(32\) −2.93584 −0.518989
\(33\) 7.41591 1.29094
\(34\) 8.69715 1.49155
\(35\) 2.20949 0.373472
\(36\) 1.97103 0.328505
\(37\) −3.48735 −0.573317 −0.286658 0.958033i \(-0.592544\pi\)
−0.286658 + 0.958033i \(0.592544\pi\)
\(38\) 3.96515 0.643232
\(39\) −6.18316 −0.990098
\(40\) −12.5865 −1.99010
\(41\) 2.91634 0.455456 0.227728 0.973725i \(-0.426870\pi\)
0.227728 + 0.973725i \(0.426870\pi\)
\(42\) −4.66004 −0.719060
\(43\) 0.547380 0.0834747 0.0417373 0.999129i \(-0.486711\pi\)
0.0417373 + 0.999129i \(0.486711\pi\)
\(44\) 17.0377 2.56853
\(45\) 1.01889 0.151888
\(46\) 3.24929 0.479081
\(47\) −11.2193 −1.63650 −0.818251 0.574861i \(-0.805056\pi\)
−0.818251 + 0.574861i \(0.805056\pi\)
\(48\) 10.6425 1.53611
\(49\) 1.00000 0.142857
\(50\) 0.295953 0.0418540
\(51\) −6.45962 −0.904527
\(52\) −14.2055 −1.96995
\(53\) −6.72493 −0.923741 −0.461870 0.886947i \(-0.652821\pi\)
−0.461870 + 0.886947i \(0.652821\pi\)
\(54\) 11.8312 1.61002
\(55\) 8.80738 1.18759
\(56\) −5.69655 −0.761234
\(57\) −2.94503 −0.390079
\(58\) 16.1777 2.12424
\(59\) −11.2668 −1.46682 −0.733409 0.679788i \(-0.762072\pi\)
−0.733409 + 0.679788i \(0.762072\pi\)
\(60\) 17.5695 2.26821
\(61\) −1.50408 −0.192578 −0.0962889 0.995353i \(-0.530697\pi\)
−0.0962889 + 0.995353i \(0.530697\pi\)
\(62\) 2.57725 0.327311
\(63\) 0.461144 0.0580987
\(64\) −4.08720 −0.510899
\(65\) −7.34332 −0.910827
\(66\) −18.5757 −2.28651
\(67\) 1.77027 0.216273 0.108136 0.994136i \(-0.465512\pi\)
0.108136 + 0.994136i \(0.465512\pi\)
\(68\) −14.8407 −1.79970
\(69\) −2.41334 −0.290532
\(70\) −5.53442 −0.661489
\(71\) −9.11314 −1.08153 −0.540765 0.841173i \(-0.681865\pi\)
−0.540765 + 0.841173i \(0.681865\pi\)
\(72\) −2.62693 −0.309587
\(73\) −0.379090 −0.0443691 −0.0221846 0.999754i \(-0.507062\pi\)
−0.0221846 + 0.999754i \(0.507062\pi\)
\(74\) 8.73525 1.01545
\(75\) −0.219812 −0.0253817
\(76\) −6.76607 −0.776122
\(77\) 3.98616 0.454265
\(78\) 15.4878 1.75365
\(79\) 9.57473 1.07724 0.538621 0.842548i \(-0.318946\pi\)
0.538621 + 0.842548i \(0.318946\pi\)
\(80\) 12.6394 1.41313
\(81\) −10.1708 −1.13009
\(82\) −7.30497 −0.806699
\(83\) 15.8931 1.74449 0.872247 0.489066i \(-0.162662\pi\)
0.872247 + 0.489066i \(0.162662\pi\)
\(84\) 7.95182 0.867615
\(85\) −7.67165 −0.832108
\(86\) −1.37110 −0.147849
\(87\) −12.0157 −1.28821
\(88\) −22.7074 −2.42061
\(89\) −4.04735 −0.429018 −0.214509 0.976722i \(-0.568815\pi\)
−0.214509 + 0.976722i \(0.568815\pi\)
\(90\) −2.55217 −0.269022
\(91\) −3.32354 −0.348401
\(92\) −5.54453 −0.578057
\(93\) −1.91420 −0.198493
\(94\) 28.1025 2.89855
\(95\) −3.49762 −0.358848
\(96\) −5.46189 −0.557452
\(97\) 0.0214864 0.00218162 0.00109081 0.999999i \(-0.499653\pi\)
0.00109081 + 0.999999i \(0.499653\pi\)
\(98\) −2.50484 −0.253027
\(99\) 1.83820 0.184746
\(100\) −0.505009 −0.0505009
\(101\) −13.6927 −1.36248 −0.681239 0.732062i \(-0.738558\pi\)
−0.681239 + 0.732062i \(0.738558\pi\)
\(102\) 16.1803 1.60209
\(103\) 2.69409 0.265457 0.132728 0.991152i \(-0.457626\pi\)
0.132728 + 0.991152i \(0.457626\pi\)
\(104\) 18.9327 1.85650
\(105\) 4.11057 0.401150
\(106\) 16.8449 1.63612
\(107\) 14.7213 1.42317 0.711583 0.702602i \(-0.247979\pi\)
0.711583 + 0.702602i \(0.247979\pi\)
\(108\) −20.1885 −1.94264
\(109\) −8.12394 −0.778132 −0.389066 0.921210i \(-0.627202\pi\)
−0.389066 + 0.921210i \(0.627202\pi\)
\(110\) −22.0611 −2.10344
\(111\) −6.48792 −0.615806
\(112\) 5.72051 0.540537
\(113\) 16.6924 1.57028 0.785142 0.619316i \(-0.212590\pi\)
0.785142 + 0.619316i \(0.212590\pi\)
\(114\) 7.37683 0.690903
\(115\) −2.86616 −0.267271
\(116\) −27.6054 −2.56310
\(117\) −1.53263 −0.141692
\(118\) 28.2216 2.59801
\(119\) −3.47214 −0.318290
\(120\) −23.4161 −2.13758
\(121\) 4.88947 0.444498
\(122\) 3.76748 0.341091
\(123\) 5.42561 0.489211
\(124\) −4.39778 −0.394933
\(125\) −11.3085 −1.01146
\(126\) −1.15509 −0.102904
\(127\) −2.62536 −0.232963 −0.116482 0.993193i \(-0.537162\pi\)
−0.116482 + 0.993193i \(0.537162\pi\)
\(128\) 16.1095 1.42389
\(129\) 1.01835 0.0896611
\(130\) 18.3938 1.61325
\(131\) −12.5517 −1.09665 −0.548326 0.836265i \(-0.684735\pi\)
−0.548326 + 0.836265i \(0.684735\pi\)
\(132\) 31.6972 2.75889
\(133\) −1.58300 −0.137263
\(134\) −4.43424 −0.383060
\(135\) −10.4361 −0.898200
\(136\) 19.7792 1.69605
\(137\) 9.83236 0.840035 0.420017 0.907516i \(-0.362024\pi\)
0.420017 + 0.907516i \(0.362024\pi\)
\(138\) 6.04502 0.514586
\(139\) 0.266687 0.0226201 0.0113100 0.999936i \(-0.496400\pi\)
0.0113100 + 0.999936i \(0.496400\pi\)
\(140\) 9.44384 0.798151
\(141\) −20.8725 −1.75779
\(142\) 22.8270 1.91560
\(143\) −13.2482 −1.10787
\(144\) 2.63798 0.219832
\(145\) −14.2702 −1.18508
\(146\) 0.949559 0.0785861
\(147\) 1.86042 0.153444
\(148\) −14.9057 −1.22524
\(149\) −10.6944 −0.876120 −0.438060 0.898946i \(-0.644334\pi\)
−0.438060 + 0.898946i \(0.644334\pi\)
\(150\) 0.550595 0.0449559
\(151\) −21.2585 −1.72999 −0.864995 0.501780i \(-0.832679\pi\)
−0.864995 + 0.501780i \(0.832679\pi\)
\(152\) 9.01762 0.731425
\(153\) −1.60116 −0.129446
\(154\) −9.98469 −0.804589
\(155\) −2.27337 −0.182601
\(156\) −26.4282 −2.11595
\(157\) −19.0276 −1.51857 −0.759283 0.650760i \(-0.774450\pi\)
−0.759283 + 0.650760i \(0.774450\pi\)
\(158\) −23.9832 −1.90800
\(159\) −12.5112 −0.992200
\(160\) −6.48672 −0.512820
\(161\) −1.29720 −0.102234
\(162\) 25.4762 2.00160
\(163\) −14.4253 −1.12988 −0.564939 0.825132i \(-0.691100\pi\)
−0.564939 + 0.825132i \(0.691100\pi\)
\(164\) 12.4651 0.973360
\(165\) 16.3854 1.27560
\(166\) −39.8096 −3.08983
\(167\) 11.6529 0.901729 0.450865 0.892592i \(-0.351116\pi\)
0.450865 + 0.892592i \(0.351116\pi\)
\(168\) −10.5979 −0.817650
\(169\) −1.95410 −0.150315
\(170\) 19.2163 1.47382
\(171\) −0.729990 −0.0558237
\(172\) 2.33962 0.178395
\(173\) 12.0786 0.918320 0.459160 0.888354i \(-0.348150\pi\)
0.459160 + 0.888354i \(0.348150\pi\)
\(174\) 30.0973 2.28167
\(175\) −0.118152 −0.00893148
\(176\) 22.8029 1.71883
\(177\) −20.9610 −1.57553
\(178\) 10.1379 0.759871
\(179\) 19.0548 1.42422 0.712109 0.702068i \(-0.247740\pi\)
0.712109 + 0.702068i \(0.247740\pi\)
\(180\) 4.35498 0.324601
\(181\) 2.71672 0.201932 0.100966 0.994890i \(-0.467807\pi\)
0.100966 + 0.994890i \(0.467807\pi\)
\(182\) 8.32493 0.617085
\(183\) −2.79821 −0.206850
\(184\) 7.38959 0.544768
\(185\) −7.70526 −0.566502
\(186\) 4.79476 0.351569
\(187\) −13.8405 −1.01212
\(188\) −47.9537 −3.49738
\(189\) −4.72333 −0.343571
\(190\) 8.76096 0.635587
\(191\) −8.21262 −0.594245 −0.297122 0.954839i \(-0.596027\pi\)
−0.297122 + 0.954839i \(0.596027\pi\)
\(192\) −7.60388 −0.548763
\(193\) −13.1291 −0.945051 −0.472525 0.881317i \(-0.656658\pi\)
−0.472525 + 0.881317i \(0.656658\pi\)
\(194\) −0.0538200 −0.00386405
\(195\) −13.6616 −0.978330
\(196\) 4.27422 0.305301
\(197\) −5.93017 −0.422507 −0.211253 0.977431i \(-0.567755\pi\)
−0.211253 + 0.977431i \(0.567755\pi\)
\(198\) −4.60438 −0.327219
\(199\) −6.45110 −0.457307 −0.228653 0.973508i \(-0.573432\pi\)
−0.228653 + 0.973508i \(0.573432\pi\)
\(200\) 0.673061 0.0475926
\(201\) 3.29343 0.232301
\(202\) 34.2981 2.41320
\(203\) −6.45859 −0.453304
\(204\) −27.6098 −1.93307
\(205\) 6.44363 0.450043
\(206\) −6.74826 −0.470174
\(207\) −0.598198 −0.0415777
\(208\) −19.0123 −1.31827
\(209\) −6.31008 −0.436477
\(210\) −10.2963 −0.710513
\(211\) 6.56557 0.451992 0.225996 0.974128i \(-0.427436\pi\)
0.225996 + 0.974128i \(0.427436\pi\)
\(212\) −28.7438 −1.97413
\(213\) −16.9542 −1.16168
\(214\) −36.8746 −2.52070
\(215\) 1.20943 0.0824825
\(216\) 26.9067 1.83077
\(217\) −1.02891 −0.0698469
\(218\) 20.3492 1.37822
\(219\) −0.705264 −0.0476574
\(220\) 37.6447 2.53800
\(221\) 11.5398 0.776249
\(222\) 16.2512 1.09071
\(223\) 0.244783 0.0163919 0.00819594 0.999966i \(-0.497391\pi\)
0.00819594 + 0.999966i \(0.497391\pi\)
\(224\) −2.93584 −0.196159
\(225\) −0.0544853 −0.00363235
\(226\) −41.8117 −2.78127
\(227\) 8.30758 0.551393 0.275697 0.961245i \(-0.411091\pi\)
0.275697 + 0.961245i \(0.411091\pi\)
\(228\) −12.5877 −0.833641
\(229\) −2.40294 −0.158791 −0.0793953 0.996843i \(-0.525299\pi\)
−0.0793953 + 0.996843i \(0.525299\pi\)
\(230\) 7.17927 0.473387
\(231\) 7.41591 0.487931
\(232\) 36.7917 2.41549
\(233\) 14.2580 0.934075 0.467038 0.884237i \(-0.345321\pi\)
0.467038 + 0.884237i \(0.345321\pi\)
\(234\) 3.83899 0.250963
\(235\) −24.7889 −1.61705
\(236\) −48.1569 −3.13475
\(237\) 17.8130 1.15708
\(238\) 8.69715 0.563752
\(239\) 10.5027 0.679362 0.339681 0.940541i \(-0.389681\pi\)
0.339681 + 0.940541i \(0.389681\pi\)
\(240\) 23.5145 1.51786
\(241\) −27.8277 −1.79254 −0.896270 0.443508i \(-0.853734\pi\)
−0.896270 + 0.443508i \(0.853734\pi\)
\(242\) −12.2473 −0.787289
\(243\) −4.75190 −0.304834
\(244\) −6.42877 −0.411560
\(245\) 2.20949 0.141159
\(246\) −13.5903 −0.866485
\(247\) 5.26115 0.334759
\(248\) 5.86124 0.372189
\(249\) 29.5677 1.87378
\(250\) 28.3260 1.79149
\(251\) 22.1457 1.39783 0.698913 0.715207i \(-0.253667\pi\)
0.698913 + 0.715207i \(0.253667\pi\)
\(252\) 1.97103 0.124163
\(253\) −5.17086 −0.325089
\(254\) 6.57612 0.412622
\(255\) −14.2725 −0.893776
\(256\) −32.1772 −2.01107
\(257\) 19.7499 1.23197 0.615984 0.787759i \(-0.288759\pi\)
0.615984 + 0.787759i \(0.288759\pi\)
\(258\) −2.55081 −0.158807
\(259\) −3.48735 −0.216693
\(260\) −31.3870 −1.94654
\(261\) −2.97834 −0.184355
\(262\) 31.4401 1.94238
\(263\) −8.38937 −0.517311 −0.258656 0.965970i \(-0.583279\pi\)
−0.258656 + 0.965970i \(0.583279\pi\)
\(264\) −42.2451 −2.60001
\(265\) −14.8587 −0.912761
\(266\) 3.96515 0.243119
\(267\) −7.52974 −0.460813
\(268\) 7.56651 0.462198
\(269\) −3.43841 −0.209644 −0.104822 0.994491i \(-0.533427\pi\)
−0.104822 + 0.994491i \(0.533427\pi\)
\(270\) 26.1409 1.59088
\(271\) 21.0323 1.27762 0.638811 0.769364i \(-0.279427\pi\)
0.638811 + 0.769364i \(0.279427\pi\)
\(272\) −19.8624 −1.20433
\(273\) −6.18316 −0.374222
\(274\) −24.6285 −1.48786
\(275\) −0.470974 −0.0284008
\(276\) −10.3151 −0.620898
\(277\) −3.40316 −0.204476 −0.102238 0.994760i \(-0.532600\pi\)
−0.102238 + 0.994760i \(0.532600\pi\)
\(278\) −0.668008 −0.0400644
\(279\) −0.474476 −0.0284061
\(280\) −12.5865 −0.752186
\(281\) −0.106490 −0.00635268 −0.00317634 0.999995i \(-0.501011\pi\)
−0.00317634 + 0.999995i \(0.501011\pi\)
\(282\) 52.2824 3.11337
\(283\) 30.1565 1.79262 0.896309 0.443430i \(-0.146238\pi\)
0.896309 + 0.443430i \(0.146238\pi\)
\(284\) −38.9516 −2.31135
\(285\) −6.50702 −0.385442
\(286\) 33.1845 1.96224
\(287\) 2.91634 0.172146
\(288\) −1.35385 −0.0797763
\(289\) −4.94426 −0.290839
\(290\) 35.7445 2.09899
\(291\) 0.0399737 0.00234330
\(292\) −1.62031 −0.0948216
\(293\) 18.9673 1.10808 0.554041 0.832490i \(-0.313085\pi\)
0.554041 + 0.832490i \(0.313085\pi\)
\(294\) −4.66004 −0.271779
\(295\) −24.8940 −1.44938
\(296\) 19.8659 1.15468
\(297\) −18.8279 −1.09251
\(298\) 26.7878 1.55177
\(299\) 4.31131 0.249329
\(300\) −0.939526 −0.0542436
\(301\) 0.547380 0.0315505
\(302\) 53.2491 3.06414
\(303\) −25.4742 −1.46345
\(304\) −9.05554 −0.519371
\(305\) −3.32325 −0.190289
\(306\) 4.01064 0.229273
\(307\) 22.8872 1.30624 0.653121 0.757254i \(-0.273459\pi\)
0.653121 + 0.757254i \(0.273459\pi\)
\(308\) 17.0377 0.970814
\(309\) 5.01213 0.285130
\(310\) 5.69442 0.323421
\(311\) 22.8738 1.29705 0.648526 0.761192i \(-0.275386\pi\)
0.648526 + 0.761192i \(0.275386\pi\)
\(312\) 35.2227 1.99409
\(313\) −4.55585 −0.257512 −0.128756 0.991676i \(-0.541098\pi\)
−0.128756 + 0.991676i \(0.541098\pi\)
\(314\) 47.6610 2.68967
\(315\) 1.01889 0.0574082
\(316\) 40.9245 2.30218
\(317\) 3.52818 0.198162 0.0990811 0.995079i \(-0.468410\pi\)
0.0990811 + 0.995079i \(0.468410\pi\)
\(318\) 31.3385 1.75737
\(319\) −25.7450 −1.44144
\(320\) −9.03062 −0.504827
\(321\) 27.3878 1.52864
\(322\) 3.24929 0.181076
\(323\) 5.49638 0.305827
\(324\) −43.4721 −2.41512
\(325\) 0.392684 0.0217822
\(326\) 36.1331 2.00123
\(327\) −15.1139 −0.835800
\(328\) −16.6131 −0.917305
\(329\) −11.2193 −0.618540
\(330\) −41.0428 −2.25933
\(331\) −33.0532 −1.81677 −0.908385 0.418134i \(-0.862684\pi\)
−0.908385 + 0.418134i \(0.862684\pi\)
\(332\) 67.9305 3.72817
\(333\) −1.60817 −0.0881273
\(334\) −29.1887 −1.59713
\(335\) 3.91139 0.213702
\(336\) 10.6425 0.580597
\(337\) −20.2071 −1.10075 −0.550376 0.834917i \(-0.685516\pi\)
−0.550376 + 0.834917i \(0.685516\pi\)
\(338\) 4.89471 0.266237
\(339\) 31.0547 1.68666
\(340\) −32.7903 −1.77831
\(341\) −4.10140 −0.222103
\(342\) 1.82851 0.0988744
\(343\) 1.00000 0.0539949
\(344\) −3.11818 −0.168121
\(345\) −5.33225 −0.287078
\(346\) −30.2550 −1.62652
\(347\) 5.40419 0.290112 0.145056 0.989423i \(-0.453664\pi\)
0.145056 + 0.989423i \(0.453664\pi\)
\(348\) −51.3576 −2.75305
\(349\) −6.96367 −0.372757 −0.186378 0.982478i \(-0.559675\pi\)
−0.186378 + 0.982478i \(0.559675\pi\)
\(350\) 0.295953 0.0158193
\(351\) 15.6981 0.837905
\(352\) −11.7027 −0.623758
\(353\) −2.61675 −0.139275 −0.0696377 0.997572i \(-0.522184\pi\)
−0.0696377 + 0.997572i \(0.522184\pi\)
\(354\) 52.5039 2.79055
\(355\) −20.1354 −1.06868
\(356\) −17.2992 −0.916858
\(357\) −6.45962 −0.341879
\(358\) −47.7291 −2.52256
\(359\) 15.2528 0.805014 0.402507 0.915417i \(-0.368139\pi\)
0.402507 + 0.915417i \(0.368139\pi\)
\(360\) −5.80418 −0.305907
\(361\) −16.4941 −0.868112
\(362\) −6.80493 −0.357659
\(363\) 9.09645 0.477440
\(364\) −14.2055 −0.744572
\(365\) −0.837595 −0.0438417
\(366\) 7.00907 0.366370
\(367\) 0.396559 0.0207002 0.0103501 0.999946i \(-0.496705\pi\)
0.0103501 + 0.999946i \(0.496705\pi\)
\(368\) −7.42066 −0.386829
\(369\) 1.34486 0.0700104
\(370\) 19.3004 1.00338
\(371\) −6.72493 −0.349141
\(372\) −8.18170 −0.424202
\(373\) 7.04128 0.364583 0.182292 0.983244i \(-0.441648\pi\)
0.182292 + 0.983244i \(0.441648\pi\)
\(374\) 34.6682 1.79265
\(375\) −21.0385 −1.08642
\(376\) 63.9113 3.29597
\(377\) 21.4654 1.10552
\(378\) 11.8312 0.608530
\(379\) 31.8265 1.63482 0.817408 0.576059i \(-0.195410\pi\)
0.817408 + 0.576059i \(0.195410\pi\)
\(380\) −14.9496 −0.766897
\(381\) −4.88427 −0.250229
\(382\) 20.5713 1.05252
\(383\) 12.2753 0.627240 0.313620 0.949549i \(-0.398458\pi\)
0.313620 + 0.949549i \(0.398458\pi\)
\(384\) 29.9703 1.52941
\(385\) 8.80738 0.448866
\(386\) 32.8862 1.67386
\(387\) 0.252421 0.0128313
\(388\) 0.0918377 0.00466235
\(389\) 18.8537 0.955922 0.477961 0.878381i \(-0.341376\pi\)
0.477961 + 0.878381i \(0.341376\pi\)
\(390\) 34.2202 1.73281
\(391\) 4.50407 0.227781
\(392\) −5.69655 −0.287719
\(393\) −23.3515 −1.17793
\(394\) 14.8541 0.748339
\(395\) 21.1553 1.06444
\(396\) 7.85685 0.394822
\(397\) −4.55642 −0.228680 −0.114340 0.993442i \(-0.536475\pi\)
−0.114340 + 0.993442i \(0.536475\pi\)
\(398\) 16.1590 0.809976
\(399\) −2.94503 −0.147436
\(400\) −0.675891 −0.0337946
\(401\) 22.0508 1.10116 0.550582 0.834781i \(-0.314406\pi\)
0.550582 + 0.834781i \(0.314406\pi\)
\(402\) −8.24952 −0.411449
\(403\) 3.41962 0.170343
\(404\) −58.5257 −2.91176
\(405\) −22.4722 −1.11665
\(406\) 16.1777 0.802887
\(407\) −13.9011 −0.689054
\(408\) 36.7975 1.82175
\(409\) 28.8258 1.42535 0.712673 0.701497i \(-0.247484\pi\)
0.712673 + 0.701497i \(0.247484\pi\)
\(410\) −16.1403 −0.797111
\(411\) 18.2923 0.902291
\(412\) 11.5151 0.567310
\(413\) −11.2668 −0.554405
\(414\) 1.49839 0.0736419
\(415\) 35.1156 1.72376
\(416\) 9.75739 0.478395
\(417\) 0.496148 0.0242965
\(418\) 15.8057 0.773083
\(419\) 0.893769 0.0436635 0.0218317 0.999762i \(-0.493050\pi\)
0.0218317 + 0.999762i \(0.493050\pi\)
\(420\) 17.5695 0.857302
\(421\) 5.18115 0.252514 0.126257 0.991998i \(-0.459704\pi\)
0.126257 + 0.991998i \(0.459704\pi\)
\(422\) −16.4457 −0.800563
\(423\) −5.17372 −0.251555
\(424\) 38.3089 1.86045
\(425\) 0.410241 0.0198996
\(426\) 42.4676 2.05756
\(427\) −1.50408 −0.0727875
\(428\) 62.9222 3.04146
\(429\) −24.6471 −1.18997
\(430\) −3.02943 −0.146092
\(431\) 17.5355 0.844657 0.422329 0.906443i \(-0.361213\pi\)
0.422329 + 0.906443i \(0.361213\pi\)
\(432\) −27.0198 −1.29999
\(433\) 12.3477 0.593391 0.296696 0.954972i \(-0.404115\pi\)
0.296696 + 0.954972i \(0.404115\pi\)
\(434\) 2.57725 0.123712
\(435\) −26.5485 −1.27290
\(436\) −34.7235 −1.66295
\(437\) 2.05347 0.0982307
\(438\) 1.76657 0.0844102
\(439\) 13.7986 0.658572 0.329286 0.944230i \(-0.393192\pi\)
0.329286 + 0.944230i \(0.393192\pi\)
\(440\) −50.1717 −2.39184
\(441\) 0.461144 0.0219593
\(442\) −28.9053 −1.37488
\(443\) −20.8176 −0.989073 −0.494536 0.869157i \(-0.664662\pi\)
−0.494536 + 0.869157i \(0.664662\pi\)
\(444\) −27.7308 −1.31604
\(445\) −8.94257 −0.423918
\(446\) −0.613142 −0.0290331
\(447\) −19.8960 −0.941050
\(448\) −4.08720 −0.193102
\(449\) −3.58796 −0.169326 −0.0846631 0.996410i \(-0.526981\pi\)
−0.0846631 + 0.996410i \(0.526981\pi\)
\(450\) 0.136477 0.00643358
\(451\) 11.6250 0.547401
\(452\) 71.3468 3.35587
\(453\) −39.5496 −1.85820
\(454\) −20.8091 −0.976621
\(455\) −7.34332 −0.344260
\(456\) 16.7765 0.785632
\(457\) −9.89547 −0.462891 −0.231445 0.972848i \(-0.574345\pi\)
−0.231445 + 0.972848i \(0.574345\pi\)
\(458\) 6.01897 0.281248
\(459\) 16.4000 0.765488
\(460\) −12.2506 −0.571187
\(461\) 24.8767 1.15862 0.579311 0.815107i \(-0.303322\pi\)
0.579311 + 0.815107i \(0.303322\pi\)
\(462\) −18.5757 −0.864218
\(463\) −14.6485 −0.680773 −0.340387 0.940286i \(-0.610558\pi\)
−0.340387 + 0.940286i \(0.610558\pi\)
\(464\) −36.9464 −1.71519
\(465\) −4.22940 −0.196134
\(466\) −35.7141 −1.65442
\(467\) 23.9023 1.10607 0.553033 0.833160i \(-0.313470\pi\)
0.553033 + 0.833160i \(0.313470\pi\)
\(468\) −6.55080 −0.302811
\(469\) 1.77027 0.0817434
\(470\) 62.0923 2.86410
\(471\) −35.3992 −1.63111
\(472\) 64.1821 2.95422
\(473\) 2.18194 0.100326
\(474\) −44.6186 −2.04940
\(475\) 0.187035 0.00858174
\(476\) −14.8407 −0.680221
\(477\) −3.10117 −0.141993
\(478\) −26.3075 −1.20328
\(479\) −0.163964 −0.00749172 −0.00374586 0.999993i \(-0.501192\pi\)
−0.00374586 + 0.999993i \(0.501192\pi\)
\(480\) −12.0680 −0.550826
\(481\) 11.5903 0.528474
\(482\) 69.7040 3.17493
\(483\) −2.41334 −0.109811
\(484\) 20.8987 0.949940
\(485\) 0.0474740 0.00215569
\(486\) 11.9027 0.539919
\(487\) 25.3053 1.14669 0.573347 0.819313i \(-0.305645\pi\)
0.573347 + 0.819313i \(0.305645\pi\)
\(488\) 8.56807 0.387858
\(489\) −26.8371 −1.21362
\(490\) −5.53442 −0.250020
\(491\) −5.94539 −0.268312 −0.134156 0.990960i \(-0.542832\pi\)
−0.134156 + 0.990960i \(0.542832\pi\)
\(492\) 23.1902 1.04550
\(493\) 22.4251 1.00998
\(494\) −13.1783 −0.592921
\(495\) 4.06148 0.182550
\(496\) −5.88588 −0.264284
\(497\) −9.11314 −0.408780
\(498\) −74.0624 −3.31882
\(499\) −33.6053 −1.50438 −0.752190 0.658947i \(-0.771002\pi\)
−0.752190 + 0.658947i \(0.771002\pi\)
\(500\) −48.3350 −2.16161
\(501\) 21.6793 0.968558
\(502\) −55.4715 −2.47581
\(503\) −0.879890 −0.0392323 −0.0196162 0.999808i \(-0.506244\pi\)
−0.0196162 + 0.999808i \(0.506244\pi\)
\(504\) −2.62693 −0.117013
\(505\) −30.2539 −1.34628
\(506\) 12.9522 0.575794
\(507\) −3.63544 −0.161455
\(508\) −11.2214 −0.497868
\(509\) −35.6092 −1.57835 −0.789176 0.614167i \(-0.789492\pi\)
−0.789176 + 0.614167i \(0.789492\pi\)
\(510\) 35.7502 1.58305
\(511\) −0.379090 −0.0167699
\(512\) 48.3798 2.13810
\(513\) 7.47701 0.330118
\(514\) −49.4704 −2.18205
\(515\) 5.95257 0.262301
\(516\) 4.35267 0.191616
\(517\) −44.7219 −1.96687
\(518\) 8.73525 0.383805
\(519\) 22.4712 0.986378
\(520\) 41.8316 1.83444
\(521\) −10.6697 −0.467447 −0.233724 0.972303i \(-0.575091\pi\)
−0.233724 + 0.972303i \(0.575091\pi\)
\(522\) 7.46027 0.326527
\(523\) 19.0981 0.835103 0.417552 0.908653i \(-0.362888\pi\)
0.417552 + 0.908653i \(0.362888\pi\)
\(524\) −53.6489 −2.34366
\(525\) −0.219812 −0.00959340
\(526\) 21.0140 0.916255
\(527\) 3.57252 0.155621
\(528\) 42.4228 1.84621
\(529\) −21.3173 −0.926837
\(530\) 37.2186 1.61667
\(531\) −5.19564 −0.225472
\(532\) −6.76607 −0.293346
\(533\) −9.69258 −0.419832
\(534\) 18.8608 0.816186
\(535\) 32.5267 1.40625
\(536\) −10.0844 −0.435581
\(537\) 35.4497 1.52977
\(538\) 8.61267 0.371318
\(539\) 3.98616 0.171696
\(540\) −44.6063 −1.91955
\(541\) −11.1307 −0.478544 −0.239272 0.970953i \(-0.576909\pi\)
−0.239272 + 0.970953i \(0.576909\pi\)
\(542\) −52.6825 −2.26291
\(543\) 5.05422 0.216897
\(544\) 10.1937 0.437049
\(545\) −17.9498 −0.768883
\(546\) 15.4878 0.662817
\(547\) −12.1905 −0.521228 −0.260614 0.965443i \(-0.583925\pi\)
−0.260614 + 0.965443i \(0.583925\pi\)
\(548\) 42.0256 1.79525
\(549\) −0.693598 −0.0296021
\(550\) 1.17971 0.0503032
\(551\) 10.2239 0.435554
\(552\) 13.7477 0.585141
\(553\) 9.57473 0.407159
\(554\) 8.52436 0.362165
\(555\) −14.3350 −0.608486
\(556\) 1.13988 0.0483416
\(557\) −32.4232 −1.37381 −0.686907 0.726745i \(-0.741032\pi\)
−0.686907 + 0.726745i \(0.741032\pi\)
\(558\) 1.18849 0.0503126
\(559\) −1.81924 −0.0769456
\(560\) 12.6394 0.534112
\(561\) −25.7491 −1.08713
\(562\) 0.266741 0.0112518
\(563\) 28.6414 1.20709 0.603546 0.797328i \(-0.293754\pi\)
0.603546 + 0.797328i \(0.293754\pi\)
\(564\) −89.2138 −3.75658
\(565\) 36.8816 1.55162
\(566\) −75.5372 −3.17507
\(567\) −10.1708 −0.427133
\(568\) 51.9135 2.17824
\(569\) 23.7488 0.995602 0.497801 0.867291i \(-0.334141\pi\)
0.497801 + 0.867291i \(0.334141\pi\)
\(570\) 16.2990 0.682691
\(571\) 25.8537 1.08195 0.540973 0.841040i \(-0.318056\pi\)
0.540973 + 0.841040i \(0.318056\pi\)
\(572\) −56.6255 −2.36763
\(573\) −15.2789 −0.638285
\(574\) −7.30497 −0.304904
\(575\) 0.153268 0.00639170
\(576\) −1.88479 −0.0785328
\(577\) −18.3638 −0.764493 −0.382247 0.924060i \(-0.624850\pi\)
−0.382247 + 0.924060i \(0.624850\pi\)
\(578\) 12.3846 0.515131
\(579\) −24.4255 −1.01509
\(580\) −60.9939 −2.53263
\(581\) 15.8931 0.659357
\(582\) −0.100128 −0.00415042
\(583\) −26.8067 −1.11022
\(584\) 2.15950 0.0893609
\(585\) −3.38633 −0.140008
\(586\) −47.5100 −1.96262
\(587\) −26.4890 −1.09332 −0.546660 0.837355i \(-0.684101\pi\)
−0.546660 + 0.837355i \(0.684101\pi\)
\(588\) 7.95182 0.327928
\(589\) 1.62876 0.0671119
\(590\) 62.3554 2.56713
\(591\) −11.0326 −0.453819
\(592\) −19.9494 −0.819915
\(593\) −13.4733 −0.553281 −0.276641 0.960973i \(-0.589221\pi\)
−0.276641 + 0.960973i \(0.589221\pi\)
\(594\) 47.1609 1.93504
\(595\) −7.67165 −0.314507
\(596\) −45.7102 −1.87236
\(597\) −12.0017 −0.491198
\(598\) −10.7991 −0.441609
\(599\) −17.0337 −0.695980 −0.347990 0.937498i \(-0.613136\pi\)
−0.347990 + 0.937498i \(0.613136\pi\)
\(600\) 1.25217 0.0511197
\(601\) −44.0185 −1.79555 −0.897777 0.440450i \(-0.854819\pi\)
−0.897777 + 0.440450i \(0.854819\pi\)
\(602\) −1.37110 −0.0558818
\(603\) 0.816349 0.0332443
\(604\) −90.8634 −3.69718
\(605\) 10.8032 0.439214
\(606\) 63.8086 2.59205
\(607\) −1.31107 −0.0532147 −0.0266073 0.999646i \(-0.508470\pi\)
−0.0266073 + 0.999646i \(0.508470\pi\)
\(608\) 4.64743 0.188478
\(609\) −12.0157 −0.486899
\(610\) 8.32421 0.337037
\(611\) 37.2877 1.50850
\(612\) −6.84369 −0.276640
\(613\) 38.4074 1.55126 0.775629 0.631189i \(-0.217433\pi\)
0.775629 + 0.631189i \(0.217433\pi\)
\(614\) −57.3288 −2.31360
\(615\) 11.9878 0.483396
\(616\) −22.7074 −0.914906
\(617\) 5.27196 0.212241 0.106121 0.994353i \(-0.466157\pi\)
0.106121 + 0.994353i \(0.466157\pi\)
\(618\) −12.5546 −0.505019
\(619\) −1.54284 −0.0620119 −0.0310059 0.999519i \(-0.509871\pi\)
−0.0310059 + 0.999519i \(0.509871\pi\)
\(620\) −9.71686 −0.390239
\(621\) 6.12712 0.245873
\(622\) −57.2951 −2.29732
\(623\) −4.04735 −0.162153
\(624\) −35.3708 −1.41596
\(625\) −24.3953 −0.975811
\(626\) 11.4117 0.456102
\(627\) −11.7394 −0.468825
\(628\) −81.3280 −3.24534
\(629\) 12.1086 0.482800
\(630\) −2.55217 −0.101681
\(631\) 9.47469 0.377182 0.188591 0.982056i \(-0.439608\pi\)
0.188591 + 0.982056i \(0.439608\pi\)
\(632\) −54.5430 −2.16960
\(633\) 12.2147 0.485490
\(634\) −8.83751 −0.350983
\(635\) −5.80072 −0.230194
\(636\) −53.4755 −2.12044
\(637\) −3.32354 −0.131683
\(638\) 64.4870 2.55307
\(639\) −4.20247 −0.166247
\(640\) 35.5937 1.40696
\(641\) −0.637557 −0.0251820 −0.0125910 0.999921i \(-0.504008\pi\)
−0.0125910 + 0.999921i \(0.504008\pi\)
\(642\) −68.6021 −2.70751
\(643\) 22.5675 0.889977 0.444989 0.895536i \(-0.353208\pi\)
0.444989 + 0.895536i \(0.353208\pi\)
\(644\) −5.54453 −0.218485
\(645\) 2.25004 0.0885954
\(646\) −13.7675 −0.541677
\(647\) 19.8306 0.779622 0.389811 0.920895i \(-0.372540\pi\)
0.389811 + 0.920895i \(0.372540\pi\)
\(648\) 57.9384 2.27603
\(649\) −44.9114 −1.76293
\(650\) −0.983609 −0.0385803
\(651\) −1.91420 −0.0750234
\(652\) −61.6570 −2.41467
\(653\) −22.6337 −0.885726 −0.442863 0.896589i \(-0.646037\pi\)
−0.442863 + 0.896589i \(0.646037\pi\)
\(654\) 37.8579 1.48036
\(655\) −27.7330 −1.08362
\(656\) 16.6830 0.651360
\(657\) −0.174815 −0.00682019
\(658\) 28.1025 1.09555
\(659\) −6.35338 −0.247492 −0.123746 0.992314i \(-0.539491\pi\)
−0.123746 + 0.992314i \(0.539491\pi\)
\(660\) 70.0347 2.72610
\(661\) −3.70713 −0.144190 −0.0720952 0.997398i \(-0.522969\pi\)
−0.0720952 + 0.997398i \(0.522969\pi\)
\(662\) 82.7931 3.21784
\(663\) 21.4688 0.833778
\(664\) −90.5358 −3.51347
\(665\) −3.49762 −0.135632
\(666\) 4.02821 0.156090
\(667\) 8.37811 0.324402
\(668\) 49.8071 1.92709
\(669\) 0.455398 0.0176067
\(670\) −9.79740 −0.378507
\(671\) −5.99550 −0.231454
\(672\) −5.46189 −0.210697
\(673\) −6.74909 −0.260158 −0.130079 0.991504i \(-0.541523\pi\)
−0.130079 + 0.991504i \(0.541523\pi\)
\(674\) 50.6156 1.94964
\(675\) 0.558072 0.0214802
\(676\) −8.35225 −0.321241
\(677\) −15.8817 −0.610385 −0.305192 0.952291i \(-0.598721\pi\)
−0.305192 + 0.952291i \(0.598721\pi\)
\(678\) −77.7870 −2.98739
\(679\) 0.0214864 0.000824573 0
\(680\) 43.7020 1.67589
\(681\) 15.4555 0.592258
\(682\) 10.2733 0.393387
\(683\) 19.4604 0.744632 0.372316 0.928106i \(-0.378564\pi\)
0.372316 + 0.928106i \(0.378564\pi\)
\(684\) −3.12014 −0.119301
\(685\) 21.7245 0.830050
\(686\) −2.50484 −0.0956352
\(687\) −4.47046 −0.170559
\(688\) 3.13129 0.119379
\(689\) 22.3506 0.851489
\(690\) 13.3564 0.508470
\(691\) −5.09501 −0.193823 −0.0969117 0.995293i \(-0.530896\pi\)
−0.0969117 + 0.995293i \(0.530896\pi\)
\(692\) 51.6266 1.96255
\(693\) 1.83820 0.0698273
\(694\) −13.5366 −0.513843
\(695\) 0.589242 0.0223512
\(696\) 68.4478 2.59451
\(697\) −10.1259 −0.383548
\(698\) 17.4429 0.660222
\(699\) 26.5259 1.00330
\(700\) −0.505009 −0.0190875
\(701\) −12.3684 −0.467150 −0.233575 0.972339i \(-0.575042\pi\)
−0.233575 + 0.972339i \(0.575042\pi\)
\(702\) −39.3213 −1.48409
\(703\) 5.52046 0.208208
\(704\) −16.2922 −0.614036
\(705\) −46.1177 −1.73689
\(706\) 6.55453 0.246683
\(707\) −13.6927 −0.514968
\(708\) −89.5919 −3.36707
\(709\) 29.7263 1.11640 0.558198 0.829708i \(-0.311493\pi\)
0.558198 + 0.829708i \(0.311493\pi\)
\(710\) 50.4359 1.89283
\(711\) 4.41534 0.165588
\(712\) 23.0559 0.864057
\(713\) 1.33471 0.0499851
\(714\) 16.1803 0.605533
\(715\) −29.2717 −1.09470
\(716\) 81.4442 3.04371
\(717\) 19.5393 0.729710
\(718\) −38.2059 −1.42583
\(719\) 4.04614 0.150896 0.0754478 0.997150i \(-0.475961\pi\)
0.0754478 + 0.997150i \(0.475961\pi\)
\(720\) 5.82859 0.217219
\(721\) 2.69409 0.100333
\(722\) 41.3151 1.53759
\(723\) −51.7711 −1.92539
\(724\) 11.6118 0.431550
\(725\) 0.763098 0.0283407
\(726\) −22.7851 −0.845636
\(727\) −29.6643 −1.10019 −0.550094 0.835102i \(-0.685408\pi\)
−0.550094 + 0.835102i \(0.685408\pi\)
\(728\) 18.9327 0.701692
\(729\) 21.6718 0.802661
\(730\) 2.09804 0.0776520
\(731\) −1.90058 −0.0702955
\(732\) −11.9602 −0.442061
\(733\) −21.8489 −0.807009 −0.403504 0.914978i \(-0.632208\pi\)
−0.403504 + 0.914978i \(0.632208\pi\)
\(734\) −0.993317 −0.0366640
\(735\) 4.11057 0.151621
\(736\) 3.80839 0.140379
\(737\) 7.05657 0.259932
\(738\) −3.36865 −0.124002
\(739\) −24.8060 −0.912502 −0.456251 0.889851i \(-0.650808\pi\)
−0.456251 + 0.889851i \(0.650808\pi\)
\(740\) −32.9340 −1.21068
\(741\) 9.78792 0.359568
\(742\) 16.8449 0.618395
\(743\) −4.12351 −0.151277 −0.0756384 0.997135i \(-0.524099\pi\)
−0.0756384 + 0.997135i \(0.524099\pi\)
\(744\) 10.9043 0.399772
\(745\) −23.6292 −0.865707
\(746\) −17.6373 −0.645746
\(747\) 7.32901 0.268154
\(748\) −59.1573 −2.16301
\(749\) 14.7213 0.537906
\(750\) 52.6981 1.92426
\(751\) −17.2718 −0.630256 −0.315128 0.949049i \(-0.602047\pi\)
−0.315128 + 0.949049i \(0.602047\pi\)
\(752\) −64.1800 −2.34040
\(753\) 41.2002 1.50142
\(754\) −53.7673 −1.95809
\(755\) −46.9704 −1.70943
\(756\) −20.1885 −0.734249
\(757\) −14.5235 −0.527867 −0.263934 0.964541i \(-0.585020\pi\)
−0.263934 + 0.964541i \(0.585020\pi\)
\(758\) −79.7202 −2.89557
\(759\) −9.61995 −0.349182
\(760\) 19.9243 0.722732
\(761\) −32.8399 −1.19044 −0.595222 0.803561i \(-0.702936\pi\)
−0.595222 + 0.803561i \(0.702936\pi\)
\(762\) 12.2343 0.443202
\(763\) −8.12394 −0.294106
\(764\) −35.1025 −1.26997
\(765\) −3.53774 −0.127907
\(766\) −30.7477 −1.11096
\(767\) 37.4458 1.35209
\(768\) −59.8629 −2.16012
\(769\) −5.26142 −0.189732 −0.0948658 0.995490i \(-0.530242\pi\)
−0.0948658 + 0.995490i \(0.530242\pi\)
\(770\) −22.0611 −0.795026
\(771\) 36.7431 1.32327
\(772\) −56.1165 −2.01968
\(773\) −42.9071 −1.54326 −0.771630 0.636072i \(-0.780558\pi\)
−0.771630 + 0.636072i \(0.780558\pi\)
\(774\) −0.632275 −0.0227266
\(775\) 0.121568 0.00436685
\(776\) −0.122398 −0.00439385
\(777\) −6.48792 −0.232753
\(778\) −47.2256 −1.69312
\(779\) −4.61656 −0.165405
\(780\) −58.3928 −2.09080
\(781\) −36.3264 −1.29986
\(782\) −11.2820 −0.403442
\(783\) 30.5060 1.09020
\(784\) 5.72051 0.204304
\(785\) −42.0413 −1.50052
\(786\) 58.4916 2.08633
\(787\) 21.4261 0.763757 0.381878 0.924213i \(-0.375277\pi\)
0.381878 + 0.924213i \(0.375277\pi\)
\(788\) −25.3468 −0.902943
\(789\) −15.6077 −0.555650
\(790\) −52.9906 −1.88532
\(791\) 16.6924 0.593512
\(792\) −10.4714 −0.372084
\(793\) 4.99887 0.177515
\(794\) 11.4131 0.405036
\(795\) −27.6433 −0.980407
\(796\) −27.5734 −0.977314
\(797\) −20.2470 −0.717187 −0.358594 0.933494i \(-0.616744\pi\)
−0.358594 + 0.933494i \(0.616744\pi\)
\(798\) 7.37683 0.261137
\(799\) 38.9549 1.37813
\(800\) 0.346877 0.0122639
\(801\) −1.86641 −0.0659464
\(802\) −55.2337 −1.95037
\(803\) −1.51111 −0.0533260
\(804\) 14.0768 0.496452
\(805\) −2.86616 −0.101019
\(806\) −8.56560 −0.301710
\(807\) −6.39687 −0.225181
\(808\) 78.0013 2.74408
\(809\) 32.6308 1.14724 0.573619 0.819122i \(-0.305539\pi\)
0.573619 + 0.819122i \(0.305539\pi\)
\(810\) 56.2893 1.97781
\(811\) 36.4847 1.28115 0.640576 0.767895i \(-0.278696\pi\)
0.640576 + 0.767895i \(0.278696\pi\)
\(812\) −27.6054 −0.968761
\(813\) 39.1288 1.37231
\(814\) 34.8201 1.22044
\(815\) −31.8726 −1.11645
\(816\) −36.9523 −1.29359
\(817\) −0.866501 −0.0303150
\(818\) −72.2041 −2.52456
\(819\) −1.53263 −0.0535545
\(820\) 27.5415 0.961791
\(821\) −25.7410 −0.898368 −0.449184 0.893439i \(-0.648285\pi\)
−0.449184 + 0.893439i \(0.648285\pi\)
\(822\) −45.8192 −1.59813
\(823\) −48.4857 −1.69010 −0.845052 0.534684i \(-0.820431\pi\)
−0.845052 + 0.534684i \(0.820431\pi\)
\(824\) −15.3470 −0.534639
\(825\) −0.876207 −0.0305056
\(826\) 28.2216 0.981956
\(827\) 2.41438 0.0839561 0.0419781 0.999119i \(-0.486634\pi\)
0.0419781 + 0.999119i \(0.486634\pi\)
\(828\) −2.55683 −0.0888560
\(829\) −22.0487 −0.765784 −0.382892 0.923793i \(-0.625072\pi\)
−0.382892 + 0.923793i \(0.625072\pi\)
\(830\) −87.9590 −3.05310
\(831\) −6.33128 −0.219630
\(832\) 13.5839 0.470939
\(833\) −3.47214 −0.120302
\(834\) −1.24277 −0.0430337
\(835\) 25.7470 0.891011
\(836\) −26.9706 −0.932799
\(837\) 4.85987 0.167982
\(838\) −2.23875 −0.0773362
\(839\) −25.5581 −0.882364 −0.441182 0.897418i \(-0.645441\pi\)
−0.441182 + 0.897418i \(0.645441\pi\)
\(840\) −23.4161 −0.807931
\(841\) 12.7134 0.438393
\(842\) −12.9779 −0.447250
\(843\) −0.198116 −0.00682348
\(844\) 28.0627 0.965957
\(845\) −4.31757 −0.148529
\(846\) 12.9593 0.445551
\(847\) 4.88947 0.168004
\(848\) −38.4700 −1.32107
\(849\) 56.1036 1.92547
\(850\) −1.02759 −0.0352460
\(851\) 4.52380 0.155074
\(852\) −72.4661 −2.48265
\(853\) 42.3468 1.44993 0.724964 0.688787i \(-0.241856\pi\)
0.724964 + 0.688787i \(0.241856\pi\)
\(854\) 3.76748 0.128920
\(855\) −1.61291 −0.0551602
\(856\) −83.8609 −2.86631
\(857\) 0.526136 0.0179725 0.00898623 0.999960i \(-0.497140\pi\)
0.00898623 + 0.999960i \(0.497140\pi\)
\(858\) 61.7369 2.10766
\(859\) −35.0044 −1.19433 −0.597167 0.802117i \(-0.703707\pi\)
−0.597167 + 0.802117i \(0.703707\pi\)
\(860\) 5.16937 0.176274
\(861\) 5.42561 0.184904
\(862\) −43.9237 −1.49605
\(863\) 1.00000 0.0340404
\(864\) 13.8669 0.471763
\(865\) 26.6876 0.907405
\(866\) −30.9289 −1.05101
\(867\) −9.19838 −0.312393
\(868\) −4.39778 −0.149271
\(869\) 38.1664 1.29471
\(870\) 66.4997 2.25455
\(871\) −5.88355 −0.199356
\(872\) 46.2784 1.56719
\(873\) 0.00990835 0.000335347 0
\(874\) −5.14361 −0.173985
\(875\) −11.3085 −0.382297
\(876\) −3.01445 −0.101849
\(877\) −23.0587 −0.778637 −0.389318 0.921103i \(-0.627289\pi\)
−0.389318 + 0.921103i \(0.627289\pi\)
\(878\) −34.5633 −1.16646
\(879\) 35.2870 1.19020
\(880\) 50.3827 1.69840
\(881\) −49.6781 −1.67370 −0.836848 0.547435i \(-0.815604\pi\)
−0.836848 + 0.547435i \(0.815604\pi\)
\(882\) −1.15509 −0.0388940
\(883\) 23.7020 0.797636 0.398818 0.917030i \(-0.369421\pi\)
0.398818 + 0.917030i \(0.369421\pi\)
\(884\) 49.3235 1.65893
\(885\) −46.3131 −1.55680
\(886\) 52.1447 1.75183
\(887\) −22.2971 −0.748663 −0.374331 0.927295i \(-0.622128\pi\)
−0.374331 + 0.927295i \(0.622128\pi\)
\(888\) 36.9587 1.24025
\(889\) −2.62536 −0.0880519
\(890\) 22.3997 0.750840
\(891\) −40.5424 −1.35822
\(892\) 1.04626 0.0350312
\(893\) 17.7601 0.594319
\(894\) 49.8364 1.66678
\(895\) 42.1013 1.40729
\(896\) 16.1095 0.538179
\(897\) 8.02082 0.267807
\(898\) 8.98725 0.299909
\(899\) 6.64531 0.221633
\(900\) −0.232882 −0.00776273
\(901\) 23.3499 0.777898
\(902\) −29.1188 −0.969550
\(903\) 1.01835 0.0338887
\(904\) −95.0888 −3.16261
\(905\) 6.00256 0.199532
\(906\) 99.0654 3.29123
\(907\) −14.7309 −0.489131 −0.244566 0.969633i \(-0.578645\pi\)
−0.244566 + 0.969633i \(0.578645\pi\)
\(908\) 35.5084 1.17839
\(909\) −6.31432 −0.209433
\(910\) 18.3938 0.609750
\(911\) −17.2748 −0.572340 −0.286170 0.958179i \(-0.592382\pi\)
−0.286170 + 0.958179i \(0.592382\pi\)
\(912\) −16.8471 −0.557862
\(913\) 63.3524 2.09666
\(914\) 24.7866 0.819866
\(915\) −6.18263 −0.204391
\(916\) −10.2707 −0.339353
\(917\) −12.5517 −0.414495
\(918\) −41.0794 −1.35582
\(919\) 36.2464 1.19566 0.597829 0.801624i \(-0.296030\pi\)
0.597829 + 0.801624i \(0.296030\pi\)
\(920\) 16.3272 0.538293
\(921\) 42.5797 1.40305
\(922\) −62.3120 −2.05214
\(923\) 30.2879 0.996937
\(924\) 31.6972 1.04276
\(925\) 0.412038 0.0135477
\(926\) 36.6921 1.20578
\(927\) 1.24236 0.0408046
\(928\) 18.9614 0.622439
\(929\) 11.8426 0.388543 0.194271 0.980948i \(-0.437766\pi\)
0.194271 + 0.980948i \(0.437766\pi\)
\(930\) 10.5940 0.347390
\(931\) −1.58300 −0.0518806
\(932\) 60.9420 1.99622
\(933\) 42.5547 1.39318
\(934\) −59.8714 −1.95905
\(935\) −30.5804 −1.00009
\(936\) 8.73071 0.285372
\(937\) 20.9163 0.683304 0.341652 0.939826i \(-0.389014\pi\)
0.341652 + 0.939826i \(0.389014\pi\)
\(938\) −4.43424 −0.144783
\(939\) −8.47576 −0.276596
\(940\) −105.953 −3.45581
\(941\) 10.1482 0.330820 0.165410 0.986225i \(-0.447105\pi\)
0.165410 + 0.986225i \(0.447105\pi\)
\(942\) 88.6693 2.88900
\(943\) −3.78309 −0.123194
\(944\) −64.4520 −2.09773
\(945\) −10.4361 −0.339488
\(946\) −5.46542 −0.177696
\(947\) −50.5995 −1.64426 −0.822132 0.569297i \(-0.807216\pi\)
−0.822132 + 0.569297i \(0.807216\pi\)
\(948\) 76.1366 2.47280
\(949\) 1.25992 0.0408987
\(950\) −0.468492 −0.0151999
\(951\) 6.56387 0.212848
\(952\) 19.7792 0.641048
\(953\) −39.5231 −1.28028 −0.640140 0.768258i \(-0.721124\pi\)
−0.640140 + 0.768258i \(0.721124\pi\)
\(954\) 7.76792 0.251496
\(955\) −18.1457 −0.587181
\(956\) 44.8907 1.45187
\(957\) −47.8963 −1.54827
\(958\) 0.410704 0.0132692
\(959\) 9.83236 0.317503
\(960\) −16.8007 −0.542240
\(961\) −29.9413 −0.965850
\(962\) −29.0319 −0.936027
\(963\) 6.78867 0.218762
\(964\) −118.942 −3.83086
\(965\) −29.0085 −0.933818
\(966\) 6.04502 0.194495
\(967\) −3.80816 −0.122462 −0.0612311 0.998124i \(-0.519503\pi\)
−0.0612311 + 0.998124i \(0.519503\pi\)
\(968\) −27.8531 −0.895233
\(969\) 10.2256 0.328492
\(970\) −0.118915 −0.00381813
\(971\) −40.0942 −1.28669 −0.643343 0.765578i \(-0.722453\pi\)
−0.643343 + 0.765578i \(0.722453\pi\)
\(972\) −20.3106 −0.651464
\(973\) 0.266687 0.00854959
\(974\) −63.3857 −2.03101
\(975\) 0.730555 0.0233965
\(976\) −8.60410 −0.275410
\(977\) −32.8753 −1.05177 −0.525887 0.850555i \(-0.676266\pi\)
−0.525887 + 0.850555i \(0.676266\pi\)
\(978\) 67.2226 2.14954
\(979\) −16.1334 −0.515625
\(980\) 9.44384 0.301673
\(981\) −3.74631 −0.119610
\(982\) 14.8922 0.475231
\(983\) 17.9314 0.571923 0.285962 0.958241i \(-0.407687\pi\)
0.285962 + 0.958241i \(0.407687\pi\)
\(984\) −30.9073 −0.985288
\(985\) −13.1026 −0.417485
\(986\) −56.1713 −1.78886
\(987\) −20.8725 −0.664380
\(988\) 22.4873 0.715416
\(989\) −0.710064 −0.0225787
\(990\) −10.1733 −0.323330
\(991\) 47.0682 1.49517 0.747586 0.664165i \(-0.231213\pi\)
0.747586 + 0.664165i \(0.231213\pi\)
\(992\) 3.02072 0.0959079
\(993\) −61.4928 −1.95141
\(994\) 22.8270 0.724027
\(995\) −14.2536 −0.451871
\(996\) 126.379 4.00447
\(997\) 17.2356 0.545856 0.272928 0.962034i \(-0.412008\pi\)
0.272928 + 0.962034i \(0.412008\pi\)
\(998\) 84.1758 2.66454
\(999\) 16.4719 0.521147
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 6041.2.a.c.1.4 83
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6041.2.a.c.1.4 83 1.1 even 1 trivial