Properties

Label 8015.2.a.h.1.11
Level $8015$
Weight $2$
Character 8015.1
Self dual yes
Analytic conductor $64.000$
Analytic rank $1$
Dimension $38$
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] = [8015,2,Mod(1,8015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("8015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8015.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: \(64.0000972201\)
Analytic rank: \(1\)
Dimension: \(38\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.11
Character \(\chi\) \(=\) 8015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.66719 q^{2} +2.43876 q^{3} +0.779527 q^{4} +1.00000 q^{5} -4.06588 q^{6} +1.00000 q^{7} +2.03476 q^{8} +2.94756 q^{9} +O(q^{10})\) \(q-1.66719 q^{2} +2.43876 q^{3} +0.779527 q^{4} +1.00000 q^{5} -4.06588 q^{6} +1.00000 q^{7} +2.03476 q^{8} +2.94756 q^{9} -1.66719 q^{10} +3.17175 q^{11} +1.90108 q^{12} -2.08978 q^{13} -1.66719 q^{14} +2.43876 q^{15} -4.95139 q^{16} -2.91545 q^{17} -4.91414 q^{18} -5.66999 q^{19} +0.779527 q^{20} +2.43876 q^{21} -5.28792 q^{22} -1.71652 q^{23} +4.96230 q^{24} +1.00000 q^{25} +3.48406 q^{26} -0.127896 q^{27} +0.779527 q^{28} -5.05955 q^{29} -4.06588 q^{30} -3.30922 q^{31} +4.18539 q^{32} +7.73515 q^{33} +4.86061 q^{34} +1.00000 q^{35} +2.29770 q^{36} -3.21787 q^{37} +9.45296 q^{38} -5.09647 q^{39} +2.03476 q^{40} +3.49213 q^{41} -4.06588 q^{42} +2.26663 q^{43} +2.47247 q^{44} +2.94756 q^{45} +2.86177 q^{46} -1.59980 q^{47} -12.0753 q^{48} +1.00000 q^{49} -1.66719 q^{50} -7.11009 q^{51} -1.62904 q^{52} -0.825739 q^{53} +0.213227 q^{54} +3.17175 q^{55} +2.03476 q^{56} -13.8278 q^{57} +8.43523 q^{58} -11.8583 q^{59} +1.90108 q^{60} +8.83426 q^{61} +5.51711 q^{62} +2.94756 q^{63} +2.92493 q^{64} -2.08978 q^{65} -12.8960 q^{66} +0.605036 q^{67} -2.27267 q^{68} -4.18619 q^{69} -1.66719 q^{70} -6.38393 q^{71} +5.99758 q^{72} -8.89810 q^{73} +5.36480 q^{74} +2.43876 q^{75} -4.41991 q^{76} +3.17175 q^{77} +8.49678 q^{78} +8.19199 q^{79} -4.95139 q^{80} -9.15458 q^{81} -5.82205 q^{82} -4.56508 q^{83} +1.90108 q^{84} -2.91545 q^{85} -3.77890 q^{86} -12.3390 q^{87} +6.45377 q^{88} -6.31868 q^{89} -4.91414 q^{90} -2.08978 q^{91} -1.33808 q^{92} -8.07040 q^{93} +2.66717 q^{94} -5.66999 q^{95} +10.2072 q^{96} +9.41996 q^{97} -1.66719 q^{98} +9.34893 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.66719 −1.17888 −0.589441 0.807811i \(-0.700652\pi\)
−0.589441 + 0.807811i \(0.700652\pi\)
\(3\) 2.43876 1.40802 0.704010 0.710190i \(-0.251391\pi\)
0.704010 + 0.710190i \(0.251391\pi\)
\(4\) 0.779527 0.389763
\(5\) 1.00000 0.447214
\(6\) −4.06588 −1.65989
\(7\) 1.00000 0.377964
\(8\) 2.03476 0.719397
\(9\) 2.94756 0.982519
\(10\) −1.66719 −0.527212
\(11\) 3.17175 0.956320 0.478160 0.878273i \(-0.341304\pi\)
0.478160 + 0.878273i \(0.341304\pi\)
\(12\) 1.90108 0.548794
\(13\) −2.08978 −0.579600 −0.289800 0.957087i \(-0.593589\pi\)
−0.289800 + 0.957087i \(0.593589\pi\)
\(14\) −1.66719 −0.445576
\(15\) 2.43876 0.629685
\(16\) −4.95139 −1.23785
\(17\) −2.91545 −0.707100 −0.353550 0.935416i \(-0.615026\pi\)
−0.353550 + 0.935416i \(0.615026\pi\)
\(18\) −4.91414 −1.15827
\(19\) −5.66999 −1.30079 −0.650393 0.759598i \(-0.725396\pi\)
−0.650393 + 0.759598i \(0.725396\pi\)
\(20\) 0.779527 0.174307
\(21\) 2.43876 0.532181
\(22\) −5.28792 −1.12739
\(23\) −1.71652 −0.357920 −0.178960 0.983856i \(-0.557273\pi\)
−0.178960 + 0.983856i \(0.557273\pi\)
\(24\) 4.96230 1.01293
\(25\) 1.00000 0.200000
\(26\) 3.48406 0.683280
\(27\) −0.127896 −0.0246136
\(28\) 0.779527 0.147317
\(29\) −5.05955 −0.939534 −0.469767 0.882790i \(-0.655662\pi\)
−0.469767 + 0.882790i \(0.655662\pi\)
\(30\) −4.06588 −0.742325
\(31\) −3.30922 −0.594354 −0.297177 0.954822i \(-0.596045\pi\)
−0.297177 + 0.954822i \(0.596045\pi\)
\(32\) 4.18539 0.739880
\(33\) 7.73515 1.34652
\(34\) 4.86061 0.833588
\(35\) 1.00000 0.169031
\(36\) 2.29770 0.382950
\(37\) −3.21787 −0.529015 −0.264507 0.964384i \(-0.585209\pi\)
−0.264507 + 0.964384i \(0.585209\pi\)
\(38\) 9.45296 1.53347
\(39\) −5.09647 −0.816088
\(40\) 2.03476 0.321724
\(41\) 3.49213 0.545380 0.272690 0.962102i \(-0.412087\pi\)
0.272690 + 0.962102i \(0.412087\pi\)
\(42\) −4.06588 −0.627379
\(43\) 2.26663 0.345658 0.172829 0.984952i \(-0.444709\pi\)
0.172829 + 0.984952i \(0.444709\pi\)
\(44\) 2.47247 0.372738
\(45\) 2.94756 0.439396
\(46\) 2.86177 0.421945
\(47\) −1.59980 −0.233355 −0.116677 0.993170i \(-0.537224\pi\)
−0.116677 + 0.993170i \(0.537224\pi\)
\(48\) −12.0753 −1.74291
\(49\) 1.00000 0.142857
\(50\) −1.66719 −0.235776
\(51\) −7.11009 −0.995611
\(52\) −1.62904 −0.225907
\(53\) −0.825739 −0.113424 −0.0567120 0.998391i \(-0.518062\pi\)
−0.0567120 + 0.998391i \(0.518062\pi\)
\(54\) 0.213227 0.0290165
\(55\) 3.17175 0.427679
\(56\) 2.03476 0.271907
\(57\) −13.8278 −1.83153
\(58\) 8.43523 1.10760
\(59\) −11.8583 −1.54382 −0.771911 0.635730i \(-0.780699\pi\)
−0.771911 + 0.635730i \(0.780699\pi\)
\(60\) 1.90108 0.245428
\(61\) 8.83426 1.13111 0.565556 0.824710i \(-0.308662\pi\)
0.565556 + 0.824710i \(0.308662\pi\)
\(62\) 5.51711 0.700673
\(63\) 2.94756 0.371357
\(64\) 2.92493 0.365617
\(65\) −2.08978 −0.259205
\(66\) −12.8960 −1.58738
\(67\) 0.605036 0.0739169 0.0369585 0.999317i \(-0.488233\pi\)
0.0369585 + 0.999317i \(0.488233\pi\)
\(68\) −2.27267 −0.275602
\(69\) −4.18619 −0.503958
\(70\) −1.66719 −0.199267
\(71\) −6.38393 −0.757633 −0.378816 0.925472i \(-0.623669\pi\)
−0.378816 + 0.925472i \(0.623669\pi\)
\(72\) 5.99758 0.706821
\(73\) −8.89810 −1.04144 −0.520722 0.853726i \(-0.674337\pi\)
−0.520722 + 0.853726i \(0.674337\pi\)
\(74\) 5.36480 0.623646
\(75\) 2.43876 0.281604
\(76\) −4.41991 −0.506998
\(77\) 3.17175 0.361455
\(78\) 8.49678 0.962071
\(79\) 8.19199 0.921671 0.460835 0.887486i \(-0.347550\pi\)
0.460835 + 0.887486i \(0.347550\pi\)
\(80\) −4.95139 −0.553582
\(81\) −9.15458 −1.01718
\(82\) −5.82205 −0.642938
\(83\) −4.56508 −0.501083 −0.250541 0.968106i \(-0.580609\pi\)
−0.250541 + 0.968106i \(0.580609\pi\)
\(84\) 1.90108 0.207425
\(85\) −2.91545 −0.316225
\(86\) −3.77890 −0.407490
\(87\) −12.3390 −1.32288
\(88\) 6.45377 0.687974
\(89\) −6.31868 −0.669779 −0.334889 0.942257i \(-0.608699\pi\)
−0.334889 + 0.942257i \(0.608699\pi\)
\(90\) −4.91414 −0.517996
\(91\) −2.08978 −0.219068
\(92\) −1.33808 −0.139504
\(93\) −8.07040 −0.836862
\(94\) 2.66717 0.275098
\(95\) −5.66999 −0.581729
\(96\) 10.2072 1.04177
\(97\) 9.41996 0.956452 0.478226 0.878237i \(-0.341280\pi\)
0.478226 + 0.878237i \(0.341280\pi\)
\(98\) −1.66719 −0.168412
\(99\) 9.34893 0.939602
\(100\) 0.779527 0.0779527
\(101\) −16.3968 −1.63155 −0.815773 0.578373i \(-0.803688\pi\)
−0.815773 + 0.578373i \(0.803688\pi\)
\(102\) 11.8539 1.17371
\(103\) −17.8785 −1.76163 −0.880813 0.473464i \(-0.843003\pi\)
−0.880813 + 0.473464i \(0.843003\pi\)
\(104\) −4.25220 −0.416962
\(105\) 2.43876 0.237999
\(106\) 1.37667 0.133714
\(107\) −1.83151 −0.177059 −0.0885295 0.996074i \(-0.528217\pi\)
−0.0885295 + 0.996074i \(0.528217\pi\)
\(108\) −0.0996983 −0.00959347
\(109\) −15.5569 −1.49008 −0.745042 0.667018i \(-0.767570\pi\)
−0.745042 + 0.667018i \(0.767570\pi\)
\(110\) −5.28792 −0.504183
\(111\) −7.84762 −0.744863
\(112\) −4.95139 −0.467863
\(113\) −6.33363 −0.595818 −0.297909 0.954594i \(-0.596289\pi\)
−0.297909 + 0.954594i \(0.596289\pi\)
\(114\) 23.0535 2.15916
\(115\) −1.71652 −0.160067
\(116\) −3.94405 −0.366196
\(117\) −6.15974 −0.569468
\(118\) 19.7701 1.81998
\(119\) −2.91545 −0.267259
\(120\) 4.96230 0.452994
\(121\) −0.939978 −0.0854525
\(122\) −14.7284 −1.33345
\(123\) 8.51648 0.767905
\(124\) −2.57963 −0.231657
\(125\) 1.00000 0.0894427
\(126\) −4.91414 −0.437786
\(127\) −10.4074 −0.923510 −0.461755 0.887008i \(-0.652780\pi\)
−0.461755 + 0.887008i \(0.652780\pi\)
\(128\) −13.2472 −1.17090
\(129\) 5.52777 0.486693
\(130\) 3.48406 0.305572
\(131\) 3.86535 0.337717 0.168859 0.985640i \(-0.445992\pi\)
0.168859 + 0.985640i \(0.445992\pi\)
\(132\) 6.02976 0.524823
\(133\) −5.66999 −0.491651
\(134\) −1.00871 −0.0871394
\(135\) −0.127896 −0.0110075
\(136\) −5.93225 −0.508686
\(137\) −1.29536 −0.110670 −0.0553349 0.998468i \(-0.517623\pi\)
−0.0553349 + 0.998468i \(0.517623\pi\)
\(138\) 6.97918 0.594107
\(139\) −6.80695 −0.577358 −0.288679 0.957426i \(-0.593216\pi\)
−0.288679 + 0.957426i \(0.593216\pi\)
\(140\) 0.779527 0.0658820
\(141\) −3.90153 −0.328568
\(142\) 10.6432 0.893160
\(143\) −6.62826 −0.554283
\(144\) −14.5945 −1.21621
\(145\) −5.05955 −0.420173
\(146\) 14.8348 1.22774
\(147\) 2.43876 0.201146
\(148\) −2.50842 −0.206190
\(149\) −1.79556 −0.147098 −0.0735488 0.997292i \(-0.523432\pi\)
−0.0735488 + 0.997292i \(0.523432\pi\)
\(150\) −4.06588 −0.331978
\(151\) 20.7823 1.69124 0.845619 0.533787i \(-0.179232\pi\)
0.845619 + 0.533787i \(0.179232\pi\)
\(152\) −11.5371 −0.935781
\(153\) −8.59345 −0.694740
\(154\) −5.28792 −0.426113
\(155\) −3.30922 −0.265803
\(156\) −3.97283 −0.318081
\(157\) −4.31404 −0.344298 −0.172149 0.985071i \(-0.555071\pi\)
−0.172149 + 0.985071i \(0.555071\pi\)
\(158\) −13.6576 −1.08654
\(159\) −2.01378 −0.159703
\(160\) 4.18539 0.330884
\(161\) −1.71652 −0.135281
\(162\) 15.2624 1.19913
\(163\) 24.7220 1.93637 0.968187 0.250227i \(-0.0805054\pi\)
0.968187 + 0.250227i \(0.0805054\pi\)
\(164\) 2.72221 0.212569
\(165\) 7.73515 0.602181
\(166\) 7.61086 0.590718
\(167\) −5.97506 −0.462364 −0.231182 0.972911i \(-0.574259\pi\)
−0.231182 + 0.972911i \(0.574259\pi\)
\(168\) 4.96230 0.382850
\(169\) −8.63283 −0.664064
\(170\) 4.86061 0.372792
\(171\) −16.7126 −1.27805
\(172\) 1.76690 0.134725
\(173\) 16.8489 1.28100 0.640500 0.767958i \(-0.278727\pi\)
0.640500 + 0.767958i \(0.278727\pi\)
\(174\) 20.5715 1.55952
\(175\) 1.00000 0.0755929
\(176\) −15.7046 −1.18378
\(177\) −28.9196 −2.17373
\(178\) 10.5345 0.789590
\(179\) 1.22054 0.0912276 0.0456138 0.998959i \(-0.485476\pi\)
0.0456138 + 0.998959i \(0.485476\pi\)
\(180\) 2.29770 0.171260
\(181\) 19.3567 1.43877 0.719387 0.694610i \(-0.244423\pi\)
0.719387 + 0.694610i \(0.244423\pi\)
\(182\) 3.48406 0.258255
\(183\) 21.5447 1.59263
\(184\) −3.49272 −0.257487
\(185\) −3.21787 −0.236583
\(186\) 13.4549 0.986561
\(187\) −9.24709 −0.676214
\(188\) −1.24709 −0.0909530
\(189\) −0.127896 −0.00930306
\(190\) 9.45296 0.685790
\(191\) 10.9970 0.795713 0.397857 0.917448i \(-0.369754\pi\)
0.397857 + 0.917448i \(0.369754\pi\)
\(192\) 7.13322 0.514796
\(193\) −7.19974 −0.518249 −0.259124 0.965844i \(-0.583434\pi\)
−0.259124 + 0.965844i \(0.583434\pi\)
\(194\) −15.7049 −1.12754
\(195\) −5.09647 −0.364966
\(196\) 0.779527 0.0556805
\(197\) −0.491967 −0.0350512 −0.0175256 0.999846i \(-0.505579\pi\)
−0.0175256 + 0.999846i \(0.505579\pi\)
\(198\) −15.5864 −1.10768
\(199\) 1.47755 0.104740 0.0523702 0.998628i \(-0.483322\pi\)
0.0523702 + 0.998628i \(0.483322\pi\)
\(200\) 2.03476 0.143879
\(201\) 1.47554 0.104076
\(202\) 27.3366 1.92340
\(203\) −5.05955 −0.355111
\(204\) −5.54250 −0.388053
\(205\) 3.49213 0.243901
\(206\) 29.8070 2.07675
\(207\) −5.05955 −0.351663
\(208\) 10.3473 0.717456
\(209\) −17.9838 −1.24397
\(210\) −4.06588 −0.280572
\(211\) −5.31971 −0.366224 −0.183112 0.983092i \(-0.558617\pi\)
−0.183112 + 0.983092i \(0.558617\pi\)
\(212\) −0.643686 −0.0442085
\(213\) −15.5689 −1.06676
\(214\) 3.05348 0.208732
\(215\) 2.26663 0.154583
\(216\) −0.260238 −0.0177069
\(217\) −3.30922 −0.224645
\(218\) 25.9364 1.75663
\(219\) −21.7003 −1.46637
\(220\) 2.47247 0.166694
\(221\) 6.09264 0.409835
\(222\) 13.0835 0.878106
\(223\) 15.9044 1.06504 0.532519 0.846418i \(-0.321245\pi\)
0.532519 + 0.846418i \(0.321245\pi\)
\(224\) 4.18539 0.279648
\(225\) 2.94756 0.196504
\(226\) 10.5594 0.702399
\(227\) −6.38175 −0.423571 −0.211786 0.977316i \(-0.567928\pi\)
−0.211786 + 0.977316i \(0.567928\pi\)
\(228\) −10.7791 −0.713864
\(229\) −1.00000 −0.0660819
\(230\) 2.86177 0.188700
\(231\) 7.73515 0.508936
\(232\) −10.2950 −0.675898
\(233\) 20.3234 1.33143 0.665714 0.746207i \(-0.268127\pi\)
0.665714 + 0.746207i \(0.268127\pi\)
\(234\) 10.2695 0.671335
\(235\) −1.59980 −0.104359
\(236\) −9.24388 −0.601725
\(237\) 19.9783 1.29773
\(238\) 4.86061 0.315067
\(239\) 4.74198 0.306733 0.153366 0.988169i \(-0.450988\pi\)
0.153366 + 0.988169i \(0.450988\pi\)
\(240\) −12.0753 −0.779455
\(241\) 4.51309 0.290714 0.145357 0.989379i \(-0.453567\pi\)
0.145357 + 0.989379i \(0.453567\pi\)
\(242\) 1.56712 0.100738
\(243\) −21.9421 −1.40759
\(244\) 6.88654 0.440866
\(245\) 1.00000 0.0638877
\(246\) −14.1986 −0.905270
\(247\) 11.8490 0.753935
\(248\) −6.73348 −0.427576
\(249\) −11.1331 −0.705534
\(250\) −1.66719 −0.105442
\(251\) 7.19621 0.454221 0.227110 0.973869i \(-0.427072\pi\)
0.227110 + 0.973869i \(0.427072\pi\)
\(252\) 2.29770 0.144741
\(253\) −5.44439 −0.342286
\(254\) 17.3512 1.08871
\(255\) −7.11009 −0.445251
\(256\) 16.2358 1.01474
\(257\) 15.4803 0.965632 0.482816 0.875722i \(-0.339614\pi\)
0.482816 + 0.875722i \(0.339614\pi\)
\(258\) −9.21585 −0.573754
\(259\) −3.21787 −0.199949
\(260\) −1.62904 −0.101029
\(261\) −14.9133 −0.923110
\(262\) −6.44428 −0.398129
\(263\) −0.0244229 −0.00150598 −0.000752992 1.00000i \(-0.500240\pi\)
−0.000752992 1.00000i \(0.500240\pi\)
\(264\) 15.7392 0.968680
\(265\) −0.825739 −0.0507248
\(266\) 9.45296 0.579598
\(267\) −15.4098 −0.943062
\(268\) 0.471642 0.0288101
\(269\) 9.70154 0.591513 0.295757 0.955263i \(-0.404428\pi\)
0.295757 + 0.955263i \(0.404428\pi\)
\(270\) 0.213227 0.0129766
\(271\) 27.2886 1.65767 0.828833 0.559496i \(-0.189005\pi\)
0.828833 + 0.559496i \(0.189005\pi\)
\(272\) 14.4355 0.875283
\(273\) −5.09647 −0.308452
\(274\) 2.15961 0.130467
\(275\) 3.17175 0.191264
\(276\) −3.26325 −0.196424
\(277\) −24.3353 −1.46217 −0.731083 0.682289i \(-0.760985\pi\)
−0.731083 + 0.682289i \(0.760985\pi\)
\(278\) 11.3485 0.680637
\(279\) −9.75412 −0.583964
\(280\) 2.03476 0.121600
\(281\) −10.6345 −0.634401 −0.317200 0.948359i \(-0.602743\pi\)
−0.317200 + 0.948359i \(0.602743\pi\)
\(282\) 6.50459 0.387343
\(283\) 0.0230340 0.00136923 0.000684613 1.00000i \(-0.499782\pi\)
0.000684613 1.00000i \(0.499782\pi\)
\(284\) −4.97644 −0.295297
\(285\) −13.8278 −0.819086
\(286\) 11.0506 0.653434
\(287\) 3.49213 0.206134
\(288\) 12.3367 0.726946
\(289\) −8.50015 −0.500009
\(290\) 8.43523 0.495334
\(291\) 22.9730 1.34670
\(292\) −6.93631 −0.405917
\(293\) −2.21751 −0.129548 −0.0647740 0.997900i \(-0.520633\pi\)
−0.0647740 + 0.997900i \(0.520633\pi\)
\(294\) −4.06588 −0.237127
\(295\) −11.8583 −0.690418
\(296\) −6.54760 −0.380572
\(297\) −0.405654 −0.0235385
\(298\) 2.99353 0.173411
\(299\) 3.58715 0.207450
\(300\) 1.90108 0.109759
\(301\) 2.26663 0.130646
\(302\) −34.6480 −1.99377
\(303\) −39.9879 −2.29725
\(304\) 28.0743 1.61017
\(305\) 8.83426 0.505848
\(306\) 14.3269 0.819016
\(307\) −17.2889 −0.986728 −0.493364 0.869823i \(-0.664233\pi\)
−0.493364 + 0.869823i \(0.664233\pi\)
\(308\) 2.47247 0.140882
\(309\) −43.6015 −2.48040
\(310\) 5.51711 0.313351
\(311\) 14.1869 0.804468 0.402234 0.915537i \(-0.368234\pi\)
0.402234 + 0.915537i \(0.368234\pi\)
\(312\) −10.3701 −0.587091
\(313\) 29.0571 1.64241 0.821203 0.570636i \(-0.193303\pi\)
0.821203 + 0.570636i \(0.193303\pi\)
\(314\) 7.19232 0.405886
\(315\) 2.94756 0.166076
\(316\) 6.38587 0.359233
\(317\) 0.640357 0.0359660 0.0179830 0.999838i \(-0.494276\pi\)
0.0179830 + 0.999838i \(0.494276\pi\)
\(318\) 3.35736 0.188271
\(319\) −16.0476 −0.898495
\(320\) 2.92493 0.163509
\(321\) −4.46662 −0.249303
\(322\) 2.86177 0.159480
\(323\) 16.5306 0.919786
\(324\) −7.13624 −0.396458
\(325\) −2.08978 −0.115920
\(326\) −41.2163 −2.28276
\(327\) −37.9396 −2.09807
\(328\) 7.10566 0.392345
\(329\) −1.59980 −0.0881997
\(330\) −12.8960 −0.709900
\(331\) −9.08622 −0.499424 −0.249712 0.968320i \(-0.580336\pi\)
−0.249712 + 0.968320i \(0.580336\pi\)
\(332\) −3.55860 −0.195304
\(333\) −9.48486 −0.519767
\(334\) 9.96156 0.545072
\(335\) 0.605036 0.0330567
\(336\) −12.0753 −0.658760
\(337\) −15.6644 −0.853295 −0.426648 0.904418i \(-0.640306\pi\)
−0.426648 + 0.904418i \(0.640306\pi\)
\(338\) 14.3926 0.782853
\(339\) −15.4462 −0.838923
\(340\) −2.27267 −0.123253
\(341\) −10.4960 −0.568392
\(342\) 27.8631 1.50667
\(343\) 1.00000 0.0539949
\(344\) 4.61205 0.248665
\(345\) −4.18619 −0.225377
\(346\) −28.0904 −1.51015
\(347\) −7.07806 −0.379970 −0.189985 0.981787i \(-0.560844\pi\)
−0.189985 + 0.981787i \(0.560844\pi\)
\(348\) −9.61860 −0.515611
\(349\) 13.0009 0.695924 0.347962 0.937509i \(-0.386874\pi\)
0.347962 + 0.937509i \(0.386874\pi\)
\(350\) −1.66719 −0.0891151
\(351\) 0.267274 0.0142660
\(352\) 13.2750 0.707562
\(353\) −7.87559 −0.419176 −0.209588 0.977790i \(-0.567212\pi\)
−0.209588 + 0.977790i \(0.567212\pi\)
\(354\) 48.2145 2.56257
\(355\) −6.38393 −0.338824
\(356\) −4.92558 −0.261055
\(357\) −7.11009 −0.376306
\(358\) −2.03488 −0.107547
\(359\) 15.9735 0.843050 0.421525 0.906817i \(-0.361495\pi\)
0.421525 + 0.906817i \(0.361495\pi\)
\(360\) 5.99758 0.316100
\(361\) 13.1488 0.692042
\(362\) −32.2714 −1.69615
\(363\) −2.29238 −0.120319
\(364\) −1.62904 −0.0853847
\(365\) −8.89810 −0.465748
\(366\) −35.9191 −1.87752
\(367\) −34.3708 −1.79414 −0.897071 0.441886i \(-0.854309\pi\)
−0.897071 + 0.441886i \(0.854309\pi\)
\(368\) 8.49918 0.443050
\(369\) 10.2933 0.535846
\(370\) 5.36480 0.278903
\(371\) −0.825739 −0.0428702
\(372\) −6.29109 −0.326178
\(373\) −9.23275 −0.478053 −0.239027 0.971013i \(-0.576828\pi\)
−0.239027 + 0.971013i \(0.576828\pi\)
\(374\) 15.4167 0.797177
\(375\) 2.43876 0.125937
\(376\) −3.25521 −0.167875
\(377\) 10.5733 0.544554
\(378\) 0.213227 0.0109672
\(379\) −24.0056 −1.23308 −0.616542 0.787322i \(-0.711467\pi\)
−0.616542 + 0.787322i \(0.711467\pi\)
\(380\) −4.41991 −0.226737
\(381\) −25.3812 −1.30032
\(382\) −18.3341 −0.938052
\(383\) 2.91243 0.148818 0.0744091 0.997228i \(-0.476293\pi\)
0.0744091 + 0.997228i \(0.476293\pi\)
\(384\) −32.3068 −1.64865
\(385\) 3.17175 0.161648
\(386\) 12.0033 0.610954
\(387\) 6.68102 0.339615
\(388\) 7.34311 0.372790
\(389\) −10.2907 −0.521760 −0.260880 0.965371i \(-0.584013\pi\)
−0.260880 + 0.965371i \(0.584013\pi\)
\(390\) 8.49678 0.430251
\(391\) 5.00444 0.253085
\(392\) 2.03476 0.102771
\(393\) 9.42666 0.475512
\(394\) 0.820203 0.0413212
\(395\) 8.19199 0.412184
\(396\) 7.28774 0.366223
\(397\) 14.3226 0.718829 0.359415 0.933178i \(-0.382976\pi\)
0.359415 + 0.933178i \(0.382976\pi\)
\(398\) −2.46335 −0.123477
\(399\) −13.8278 −0.692254
\(400\) −4.95139 −0.247570
\(401\) −0.831367 −0.0415165 −0.0207582 0.999785i \(-0.506608\pi\)
−0.0207582 + 0.999785i \(0.506608\pi\)
\(402\) −2.46001 −0.122694
\(403\) 6.91553 0.344487
\(404\) −12.7818 −0.635916
\(405\) −9.15458 −0.454895
\(406\) 8.43523 0.418634
\(407\) −10.2063 −0.505907
\(408\) −14.4673 −0.716240
\(409\) 7.99114 0.395137 0.197568 0.980289i \(-0.436696\pi\)
0.197568 + 0.980289i \(0.436696\pi\)
\(410\) −5.82205 −0.287531
\(411\) −3.15907 −0.155825
\(412\) −13.9368 −0.686617
\(413\) −11.8583 −0.583510
\(414\) 8.43524 0.414569
\(415\) −4.56508 −0.224091
\(416\) −8.74653 −0.428834
\(417\) −16.6005 −0.812931
\(418\) 29.9825 1.46649
\(419\) 25.6358 1.25239 0.626196 0.779666i \(-0.284611\pi\)
0.626196 + 0.779666i \(0.284611\pi\)
\(420\) 1.90108 0.0927632
\(421\) 3.89261 0.189714 0.0948571 0.995491i \(-0.469761\pi\)
0.0948571 + 0.995491i \(0.469761\pi\)
\(422\) 8.86898 0.431735
\(423\) −4.71550 −0.229275
\(424\) −1.68018 −0.0815969
\(425\) −2.91545 −0.141420
\(426\) 25.9563 1.25759
\(427\) 8.83426 0.427520
\(428\) −1.42771 −0.0690111
\(429\) −16.1647 −0.780441
\(430\) −3.77890 −0.182235
\(431\) −9.23599 −0.444882 −0.222441 0.974946i \(-0.571402\pi\)
−0.222441 + 0.974946i \(0.571402\pi\)
\(432\) 0.633263 0.0304679
\(433\) 9.36806 0.450200 0.225100 0.974336i \(-0.427729\pi\)
0.225100 + 0.974336i \(0.427729\pi\)
\(434\) 5.51711 0.264830
\(435\) −12.3390 −0.591611
\(436\) −12.1270 −0.580780
\(437\) 9.73267 0.465577
\(438\) 36.1786 1.72868
\(439\) 15.8432 0.756156 0.378078 0.925774i \(-0.376585\pi\)
0.378078 + 0.925774i \(0.376585\pi\)
\(440\) 6.45377 0.307671
\(441\) 2.94756 0.140360
\(442\) −10.1576 −0.483147
\(443\) −19.6877 −0.935390 −0.467695 0.883890i \(-0.654916\pi\)
−0.467695 + 0.883890i \(0.654916\pi\)
\(444\) −6.11743 −0.290320
\(445\) −6.31868 −0.299534
\(446\) −26.5157 −1.25555
\(447\) −4.37893 −0.207116
\(448\) 2.92493 0.138190
\(449\) −15.1563 −0.715271 −0.357635 0.933861i \(-0.616417\pi\)
−0.357635 + 0.933861i \(0.616417\pi\)
\(450\) −4.91414 −0.231655
\(451\) 11.0762 0.521557
\(452\) −4.93723 −0.232228
\(453\) 50.6830 2.38130
\(454\) 10.6396 0.499341
\(455\) −2.08978 −0.0979702
\(456\) −28.1362 −1.31760
\(457\) −10.9152 −0.510593 −0.255297 0.966863i \(-0.582173\pi\)
−0.255297 + 0.966863i \(0.582173\pi\)
\(458\) 1.66719 0.0779027
\(459\) 0.372874 0.0174043
\(460\) −1.33808 −0.0623881
\(461\) 7.32827 0.341311 0.170656 0.985331i \(-0.445411\pi\)
0.170656 + 0.985331i \(0.445411\pi\)
\(462\) −12.8960 −0.599975
\(463\) −36.9367 −1.71660 −0.858298 0.513152i \(-0.828478\pi\)
−0.858298 + 0.513152i \(0.828478\pi\)
\(464\) 25.0518 1.16300
\(465\) −8.07040 −0.374256
\(466\) −33.8829 −1.56960
\(467\) 30.0042 1.38843 0.694214 0.719769i \(-0.255752\pi\)
0.694214 + 0.719769i \(0.255752\pi\)
\(468\) −4.80168 −0.221958
\(469\) 0.605036 0.0279380
\(470\) 2.66717 0.123027
\(471\) −10.5209 −0.484778
\(472\) −24.1289 −1.11062
\(473\) 7.18919 0.330559
\(474\) −33.3077 −1.52987
\(475\) −5.66999 −0.260157
\(476\) −2.27267 −0.104168
\(477\) −2.43391 −0.111441
\(478\) −7.90578 −0.361602
\(479\) 12.9333 0.590939 0.295470 0.955352i \(-0.404524\pi\)
0.295470 + 0.955352i \(0.404524\pi\)
\(480\) 10.2072 0.465891
\(481\) 6.72463 0.306617
\(482\) −7.52419 −0.342717
\(483\) −4.18619 −0.190478
\(484\) −0.732738 −0.0333063
\(485\) 9.41996 0.427738
\(486\) 36.5818 1.65938
\(487\) 15.4342 0.699392 0.349696 0.936863i \(-0.386285\pi\)
0.349696 + 0.936863i \(0.386285\pi\)
\(488\) 17.9756 0.813718
\(489\) 60.2910 2.72645
\(490\) −1.66719 −0.0753160
\(491\) −11.1986 −0.505386 −0.252693 0.967546i \(-0.581316\pi\)
−0.252693 + 0.967546i \(0.581316\pi\)
\(492\) 6.63882 0.299301
\(493\) 14.7509 0.664345
\(494\) −19.7546 −0.888800
\(495\) 9.34893 0.420203
\(496\) 16.3853 0.735720
\(497\) −6.38393 −0.286358
\(498\) 18.5611 0.831742
\(499\) −14.6729 −0.656850 −0.328425 0.944530i \(-0.606518\pi\)
−0.328425 + 0.944530i \(0.606518\pi\)
\(500\) 0.779527 0.0348615
\(501\) −14.5717 −0.651017
\(502\) −11.9975 −0.535473
\(503\) −6.84700 −0.305293 −0.152646 0.988281i \(-0.548780\pi\)
−0.152646 + 0.988281i \(0.548780\pi\)
\(504\) 5.99758 0.267153
\(505\) −16.3968 −0.729649
\(506\) 9.07684 0.403515
\(507\) −21.0534 −0.935015
\(508\) −8.11287 −0.359950
\(509\) −17.9549 −0.795837 −0.397919 0.917421i \(-0.630267\pi\)
−0.397919 + 0.917421i \(0.630267\pi\)
\(510\) 11.8539 0.524898
\(511\) −8.89810 −0.393629
\(512\) −0.573701 −0.0253542
\(513\) 0.725169 0.0320170
\(514\) −25.8085 −1.13837
\(515\) −17.8785 −0.787823
\(516\) 4.30904 0.189695
\(517\) −5.07417 −0.223162
\(518\) 5.36480 0.235716
\(519\) 41.0905 1.80367
\(520\) −4.25220 −0.186471
\(521\) −7.52954 −0.329875 −0.164938 0.986304i \(-0.552742\pi\)
−0.164938 + 0.986304i \(0.552742\pi\)
\(522\) 24.8633 1.08824
\(523\) −13.7576 −0.601578 −0.300789 0.953691i \(-0.597250\pi\)
−0.300789 + 0.953691i \(0.597250\pi\)
\(524\) 3.01314 0.131630
\(525\) 2.43876 0.106436
\(526\) 0.0407177 0.00177538
\(527\) 9.64787 0.420268
\(528\) −38.2998 −1.66678
\(529\) −20.0535 −0.871893
\(530\) 1.37667 0.0597985
\(531\) −34.9531 −1.51683
\(532\) −4.41991 −0.191627
\(533\) −7.29778 −0.316102
\(534\) 25.6910 1.11176
\(535\) −1.83151 −0.0791832
\(536\) 1.23110 0.0531756
\(537\) 2.97661 0.128450
\(538\) −16.1743 −0.697325
\(539\) 3.17175 0.136617
\(540\) −0.0996983 −0.00429033
\(541\) 20.5871 0.885108 0.442554 0.896742i \(-0.354073\pi\)
0.442554 + 0.896742i \(0.354073\pi\)
\(542\) −45.4954 −1.95419
\(543\) 47.2064 2.02582
\(544\) −12.2023 −0.523169
\(545\) −15.5569 −0.666386
\(546\) 8.49678 0.363629
\(547\) 19.3715 0.828266 0.414133 0.910216i \(-0.364085\pi\)
0.414133 + 0.910216i \(0.364085\pi\)
\(548\) −1.00977 −0.0431350
\(549\) 26.0395 1.11134
\(550\) −5.28792 −0.225478
\(551\) 28.6876 1.22213
\(552\) −8.51791 −0.362546
\(553\) 8.19199 0.348359
\(554\) 40.5716 1.72372
\(555\) −7.84762 −0.333113
\(556\) −5.30620 −0.225033
\(557\) 43.3532 1.83694 0.918468 0.395496i \(-0.129427\pi\)
0.918468 + 0.395496i \(0.129427\pi\)
\(558\) 16.2620 0.688425
\(559\) −4.73675 −0.200343
\(560\) −4.95139 −0.209234
\(561\) −22.5514 −0.952123
\(562\) 17.7297 0.747884
\(563\) 28.1107 1.18472 0.592362 0.805672i \(-0.298195\pi\)
0.592362 + 0.805672i \(0.298195\pi\)
\(564\) −3.04134 −0.128064
\(565\) −6.33363 −0.266458
\(566\) −0.0384020 −0.00161416
\(567\) −9.15458 −0.384456
\(568\) −12.9898 −0.545039
\(569\) −3.05925 −0.128250 −0.0641252 0.997942i \(-0.520426\pi\)
−0.0641252 + 0.997942i \(0.520426\pi\)
\(570\) 23.0535 0.965605
\(571\) −17.0220 −0.712349 −0.356174 0.934419i \(-0.615919\pi\)
−0.356174 + 0.934419i \(0.615919\pi\)
\(572\) −5.16690 −0.216039
\(573\) 26.8190 1.12038
\(574\) −5.82205 −0.243008
\(575\) −1.71652 −0.0715840
\(576\) 8.62141 0.359226
\(577\) −24.5318 −1.02127 −0.510636 0.859797i \(-0.670590\pi\)
−0.510636 + 0.859797i \(0.670590\pi\)
\(578\) 14.1714 0.589452
\(579\) −17.5585 −0.729704
\(580\) −3.94405 −0.163768
\(581\) −4.56508 −0.189392
\(582\) −38.3004 −1.58760
\(583\) −2.61904 −0.108470
\(584\) −18.1055 −0.749212
\(585\) −6.15974 −0.254674
\(586\) 3.69701 0.152722
\(587\) 1.78129 0.0735218 0.0367609 0.999324i \(-0.488296\pi\)
0.0367609 + 0.999324i \(0.488296\pi\)
\(588\) 1.90108 0.0783992
\(589\) 18.7633 0.773127
\(590\) 19.7701 0.813922
\(591\) −1.19979 −0.0493528
\(592\) 15.9329 0.654840
\(593\) 37.9104 1.55680 0.778398 0.627771i \(-0.216033\pi\)
0.778398 + 0.627771i \(0.216033\pi\)
\(594\) 0.676304 0.0277491
\(595\) −2.91545 −0.119522
\(596\) −1.39968 −0.0573333
\(597\) 3.60338 0.147477
\(598\) −5.98047 −0.244559
\(599\) −36.6172 −1.49614 −0.748070 0.663620i \(-0.769019\pi\)
−0.748070 + 0.663620i \(0.769019\pi\)
\(600\) 4.96230 0.202585
\(601\) 17.5314 0.715122 0.357561 0.933890i \(-0.383608\pi\)
0.357561 + 0.933890i \(0.383608\pi\)
\(602\) −3.77890 −0.154017
\(603\) 1.78338 0.0726248
\(604\) 16.2003 0.659182
\(605\) −0.939978 −0.0382155
\(606\) 66.6676 2.70818
\(607\) −43.3240 −1.75847 −0.879234 0.476391i \(-0.841945\pi\)
−0.879234 + 0.476391i \(0.841945\pi\)
\(608\) −23.7311 −0.962425
\(609\) −12.3390 −0.500003
\(610\) −14.7284 −0.596336
\(611\) 3.34322 0.135252
\(612\) −6.69883 −0.270784
\(613\) −22.1347 −0.894013 −0.447007 0.894531i \(-0.647510\pi\)
−0.447007 + 0.894531i \(0.647510\pi\)
\(614\) 28.8238 1.16324
\(615\) 8.51648 0.343418
\(616\) 6.45377 0.260030
\(617\) 0.114211 0.00459797 0.00229898 0.999997i \(-0.499268\pi\)
0.00229898 + 0.999997i \(0.499268\pi\)
\(618\) 72.6921 2.92410
\(619\) −18.3523 −0.737641 −0.368820 0.929501i \(-0.620238\pi\)
−0.368820 + 0.929501i \(0.620238\pi\)
\(620\) −2.57963 −0.103600
\(621\) 0.219536 0.00880969
\(622\) −23.6524 −0.948373
\(623\) −6.31868 −0.253153
\(624\) 25.2346 1.01019
\(625\) 1.00000 0.0400000
\(626\) −48.4438 −1.93620
\(627\) −43.8582 −1.75153
\(628\) −3.36291 −0.134195
\(629\) 9.38154 0.374066
\(630\) −4.91414 −0.195784
\(631\) −17.0517 −0.678817 −0.339408 0.940639i \(-0.610227\pi\)
−0.339408 + 0.940639i \(0.610227\pi\)
\(632\) 16.6687 0.663047
\(633\) −12.9735 −0.515651
\(634\) −1.06760 −0.0423997
\(635\) −10.4074 −0.413006
\(636\) −1.56980 −0.0622465
\(637\) −2.08978 −0.0828000
\(638\) 26.7545 1.05922
\(639\) −18.8170 −0.744389
\(640\) −13.2472 −0.523642
\(641\) −0.496602 −0.0196146 −0.00980731 0.999952i \(-0.503122\pi\)
−0.00980731 + 0.999952i \(0.503122\pi\)
\(642\) 7.44671 0.293898
\(643\) 10.4999 0.414075 0.207038 0.978333i \(-0.433618\pi\)
0.207038 + 0.978333i \(0.433618\pi\)
\(644\) −1.33808 −0.0527276
\(645\) 5.52777 0.217656
\(646\) −27.5596 −1.08432
\(647\) −13.3030 −0.522996 −0.261498 0.965204i \(-0.584217\pi\)
−0.261498 + 0.965204i \(0.584217\pi\)
\(648\) −18.6274 −0.731753
\(649\) −37.6117 −1.47639
\(650\) 3.48406 0.136656
\(651\) −8.07040 −0.316304
\(652\) 19.2714 0.754728
\(653\) −7.51134 −0.293942 −0.146971 0.989141i \(-0.546952\pi\)
−0.146971 + 0.989141i \(0.546952\pi\)
\(654\) 63.2526 2.47337
\(655\) 3.86535 0.151032
\(656\) −17.2909 −0.675097
\(657\) −26.2277 −1.02324
\(658\) 2.66717 0.103977
\(659\) −16.9594 −0.660646 −0.330323 0.943868i \(-0.607158\pi\)
−0.330323 + 0.943868i \(0.607158\pi\)
\(660\) 6.02976 0.234708
\(661\) −27.2567 −1.06016 −0.530082 0.847946i \(-0.677839\pi\)
−0.530082 + 0.847946i \(0.677839\pi\)
\(662\) 15.1485 0.588762
\(663\) 14.8585 0.577056
\(664\) −9.28886 −0.360478
\(665\) −5.66999 −0.219873
\(666\) 15.8131 0.612744
\(667\) 8.68483 0.336278
\(668\) −4.65772 −0.180212
\(669\) 38.7871 1.49959
\(670\) −1.00871 −0.0389699
\(671\) 28.0201 1.08170
\(672\) 10.2072 0.393750
\(673\) 33.9613 1.30911 0.654556 0.756013i \(-0.272855\pi\)
0.654556 + 0.756013i \(0.272855\pi\)
\(674\) 26.1156 1.00593
\(675\) −0.127896 −0.00492272
\(676\) −6.72952 −0.258828
\(677\) 38.2594 1.47043 0.735214 0.677835i \(-0.237082\pi\)
0.735214 + 0.677835i \(0.237082\pi\)
\(678\) 25.7518 0.988991
\(679\) 9.41996 0.361505
\(680\) −5.93225 −0.227491
\(681\) −15.5636 −0.596397
\(682\) 17.4989 0.670068
\(683\) 24.4927 0.937188 0.468594 0.883414i \(-0.344761\pi\)
0.468594 + 0.883414i \(0.344761\pi\)
\(684\) −13.0279 −0.498136
\(685\) −1.29536 −0.0494930
\(686\) −1.66719 −0.0636537
\(687\) −2.43876 −0.0930445
\(688\) −11.2230 −0.427872
\(689\) 1.72561 0.0657405
\(690\) 6.97918 0.265693
\(691\) −2.43951 −0.0928033 −0.0464016 0.998923i \(-0.514775\pi\)
−0.0464016 + 0.998923i \(0.514775\pi\)
\(692\) 13.1342 0.499287
\(693\) 9.34893 0.355136
\(694\) 11.8005 0.447940
\(695\) −6.80695 −0.258202
\(696\) −25.1070 −0.951678
\(697\) −10.1811 −0.385638
\(698\) −21.6750 −0.820412
\(699\) 49.5638 1.87468
\(700\) 0.779527 0.0294633
\(701\) −13.7058 −0.517660 −0.258830 0.965923i \(-0.583337\pi\)
−0.258830 + 0.965923i \(0.583337\pi\)
\(702\) −0.445597 −0.0168180
\(703\) 18.2453 0.688134
\(704\) 9.27717 0.349647
\(705\) −3.90153 −0.146940
\(706\) 13.1301 0.494159
\(707\) −16.3968 −0.616666
\(708\) −22.5436 −0.847241
\(709\) 14.6988 0.552027 0.276013 0.961154i \(-0.410987\pi\)
0.276013 + 0.961154i \(0.410987\pi\)
\(710\) 10.6432 0.399433
\(711\) 24.1464 0.905559
\(712\) −12.8570 −0.481837
\(713\) 5.68036 0.212731
\(714\) 11.8539 0.443620
\(715\) −6.62826 −0.247883
\(716\) 0.951445 0.0355572
\(717\) 11.5646 0.431886
\(718\) −26.6309 −0.993856
\(719\) 27.2236 1.01527 0.507635 0.861572i \(-0.330520\pi\)
0.507635 + 0.861572i \(0.330520\pi\)
\(720\) −14.5945 −0.543905
\(721\) −17.8785 −0.665832
\(722\) −21.9216 −0.815836
\(723\) 11.0064 0.409331
\(724\) 15.0891 0.560781
\(725\) −5.05955 −0.187907
\(726\) 3.82184 0.141842
\(727\) −41.7627 −1.54889 −0.774447 0.632639i \(-0.781972\pi\)
−0.774447 + 0.632639i \(0.781972\pi\)
\(728\) −4.25220 −0.157597
\(729\) −26.0479 −0.964738
\(730\) 14.8348 0.549062
\(731\) −6.60824 −0.244415
\(732\) 16.7946 0.620748
\(733\) 36.3783 1.34366 0.671832 0.740704i \(-0.265508\pi\)
0.671832 + 0.740704i \(0.265508\pi\)
\(734\) 57.3027 2.11508
\(735\) 2.43876 0.0899551
\(736\) −7.18432 −0.264818
\(737\) 1.91903 0.0706882
\(738\) −17.1608 −0.631699
\(739\) −38.1788 −1.40443 −0.702215 0.711965i \(-0.747805\pi\)
−0.702215 + 0.711965i \(0.747805\pi\)
\(740\) −2.50842 −0.0922112
\(741\) 28.8969 1.06155
\(742\) 1.37667 0.0505390
\(743\) 21.0449 0.772061 0.386030 0.922486i \(-0.373846\pi\)
0.386030 + 0.922486i \(0.373846\pi\)
\(744\) −16.4214 −0.602036
\(745\) −1.79556 −0.0657841
\(746\) 15.3928 0.563569
\(747\) −13.4558 −0.492323
\(748\) −7.20835 −0.263563
\(749\) −1.83151 −0.0669220
\(750\) −4.06588 −0.148465
\(751\) 18.1076 0.660757 0.330379 0.943848i \(-0.392824\pi\)
0.330379 + 0.943848i \(0.392824\pi\)
\(752\) 7.92123 0.288857
\(753\) 17.5498 0.639552
\(754\) −17.6278 −0.641965
\(755\) 20.7823 0.756344
\(756\) −0.0996983 −0.00362599
\(757\) 31.5581 1.14700 0.573499 0.819207i \(-0.305586\pi\)
0.573499 + 0.819207i \(0.305586\pi\)
\(758\) 40.0219 1.45366
\(759\) −13.2776 −0.481945
\(760\) −11.5371 −0.418494
\(761\) −42.5852 −1.54371 −0.771856 0.635797i \(-0.780671\pi\)
−0.771856 + 0.635797i \(0.780671\pi\)
\(762\) 42.3154 1.53292
\(763\) −15.5569 −0.563199
\(764\) 8.57244 0.310140
\(765\) −8.59345 −0.310697
\(766\) −4.85557 −0.175439
\(767\) 24.7812 0.894799
\(768\) 39.5951 1.42877
\(769\) 10.8966 0.392940 0.196470 0.980510i \(-0.437052\pi\)
0.196470 + 0.980510i \(0.437052\pi\)
\(770\) −5.28792 −0.190563
\(771\) 37.7526 1.35963
\(772\) −5.61239 −0.201994
\(773\) −5.52820 −0.198835 −0.0994177 0.995046i \(-0.531698\pi\)
−0.0994177 + 0.995046i \(0.531698\pi\)
\(774\) −11.1385 −0.400366
\(775\) −3.30922 −0.118871
\(776\) 19.1674 0.688069
\(777\) −7.84762 −0.281532
\(778\) 17.1566 0.615094
\(779\) −19.8004 −0.709422
\(780\) −3.97283 −0.142250
\(781\) −20.2482 −0.724539
\(782\) −8.34336 −0.298358
\(783\) 0.647096 0.0231253
\(784\) −4.95139 −0.176835
\(785\) −4.31404 −0.153975
\(786\) −15.7160 −0.560573
\(787\) 26.1952 0.933757 0.466879 0.884321i \(-0.345378\pi\)
0.466879 + 0.884321i \(0.345378\pi\)
\(788\) −0.383502 −0.0136617
\(789\) −0.0595617 −0.00212045
\(790\) −13.6576 −0.485916
\(791\) −6.33363 −0.225198
\(792\) 19.0228 0.675947
\(793\) −18.4616 −0.655592
\(794\) −23.8785 −0.847415
\(795\) −2.01378 −0.0714214
\(796\) 1.15179 0.0408240
\(797\) 6.07751 0.215276 0.107638 0.994190i \(-0.465671\pi\)
0.107638 + 0.994190i \(0.465671\pi\)
\(798\) 23.0535 0.816085
\(799\) 4.66413 0.165005
\(800\) 4.18539 0.147976
\(801\) −18.6247 −0.658071
\(802\) 1.38605 0.0489430
\(803\) −28.2226 −0.995953
\(804\) 1.15022 0.0405652
\(805\) −1.71652 −0.0604995
\(806\) −11.5295 −0.406110
\(807\) 23.6597 0.832862
\(808\) −33.3636 −1.17373
\(809\) −14.5431 −0.511309 −0.255655 0.966768i \(-0.582291\pi\)
−0.255655 + 0.966768i \(0.582291\pi\)
\(810\) 15.2624 0.536267
\(811\) 27.5081 0.965941 0.482970 0.875637i \(-0.339558\pi\)
0.482970 + 0.875637i \(0.339558\pi\)
\(812\) −3.94405 −0.138409
\(813\) 66.5505 2.33403
\(814\) 17.0158 0.596405
\(815\) 24.7220 0.865973
\(816\) 35.2048 1.23242
\(817\) −12.8518 −0.449626
\(818\) −13.3228 −0.465820
\(819\) −6.15974 −0.215239
\(820\) 2.72221 0.0950637
\(821\) 46.7674 1.63219 0.816097 0.577914i \(-0.196133\pi\)
0.816097 + 0.577914i \(0.196133\pi\)
\(822\) 5.26677 0.183700
\(823\) −21.9743 −0.765975 −0.382988 0.923753i \(-0.625105\pi\)
−0.382988 + 0.923753i \(0.625105\pi\)
\(824\) −36.3786 −1.26731
\(825\) 7.73515 0.269303
\(826\) 19.7701 0.687890
\(827\) −33.5813 −1.16774 −0.583868 0.811848i \(-0.698462\pi\)
−0.583868 + 0.811848i \(0.698462\pi\)
\(828\) −3.94406 −0.137065
\(829\) −4.04046 −0.140331 −0.0701655 0.997535i \(-0.522353\pi\)
−0.0701655 + 0.997535i \(0.522353\pi\)
\(830\) 7.61086 0.264177
\(831\) −59.3479 −2.05876
\(832\) −6.11246 −0.211911
\(833\) −2.91545 −0.101014
\(834\) 27.6762 0.958350
\(835\) −5.97506 −0.206775
\(836\) −14.0189 −0.484853
\(837\) 0.423236 0.0146292
\(838\) −42.7398 −1.47642
\(839\) 55.8314 1.92751 0.963756 0.266784i \(-0.0859609\pi\)
0.963756 + 0.266784i \(0.0859609\pi\)
\(840\) 4.96230 0.171216
\(841\) −3.40098 −0.117275
\(842\) −6.48972 −0.223651
\(843\) −25.9350 −0.893249
\(844\) −4.14686 −0.142741
\(845\) −8.63283 −0.296979
\(846\) 7.86163 0.270289
\(847\) −0.939978 −0.0322980
\(848\) 4.08856 0.140402
\(849\) 0.0561743 0.00192790
\(850\) 4.86061 0.166718
\(851\) 5.52355 0.189345
\(852\) −12.1364 −0.415785
\(853\) 51.9975 1.78036 0.890181 0.455608i \(-0.150578\pi\)
0.890181 + 0.455608i \(0.150578\pi\)
\(854\) −14.7284 −0.503996
\(855\) −16.7126 −0.571560
\(856\) −3.72669 −0.127376
\(857\) 10.8023 0.369000 0.184500 0.982832i \(-0.440933\pi\)
0.184500 + 0.982832i \(0.440933\pi\)
\(858\) 26.9497 0.920048
\(859\) −3.50191 −0.119484 −0.0597418 0.998214i \(-0.519028\pi\)
−0.0597418 + 0.998214i \(0.519028\pi\)
\(860\) 1.76690 0.0602507
\(861\) 8.51648 0.290241
\(862\) 15.3982 0.524463
\(863\) −32.4769 −1.10553 −0.552764 0.833338i \(-0.686427\pi\)
−0.552764 + 0.833338i \(0.686427\pi\)
\(864\) −0.535295 −0.0182111
\(865\) 16.8489 0.572881
\(866\) −15.6184 −0.530733
\(867\) −20.7298 −0.704022
\(868\) −2.57963 −0.0875582
\(869\) 25.9830 0.881412
\(870\) 20.5715 0.697440
\(871\) −1.26439 −0.0428422
\(872\) −31.6547 −1.07196
\(873\) 27.7659 0.939732
\(874\) −16.2262 −0.548860
\(875\) 1.00000 0.0338062
\(876\) −16.9160 −0.571539
\(877\) −56.7011 −1.91466 −0.957331 0.288994i \(-0.906679\pi\)
−0.957331 + 0.288994i \(0.906679\pi\)
\(878\) −26.4137 −0.891419
\(879\) −5.40797 −0.182406
\(880\) −15.7046 −0.529402
\(881\) 12.9094 0.434929 0.217464 0.976068i \(-0.430221\pi\)
0.217464 + 0.976068i \(0.430221\pi\)
\(882\) −4.91414 −0.165468
\(883\) −16.0655 −0.540647 −0.270324 0.962770i \(-0.587131\pi\)
−0.270324 + 0.962770i \(0.587131\pi\)
\(884\) 4.74937 0.159739
\(885\) −28.9196 −0.972123
\(886\) 32.8231 1.10272
\(887\) 25.2387 0.847434 0.423717 0.905795i \(-0.360725\pi\)
0.423717 + 0.905795i \(0.360725\pi\)
\(888\) −15.9680 −0.535852
\(889\) −10.4074 −0.349054
\(890\) 10.5345 0.353116
\(891\) −29.0361 −0.972745
\(892\) 12.3979 0.415113
\(893\) 9.07084 0.303544
\(894\) 7.30052 0.244166
\(895\) 1.22054 0.0407982
\(896\) −13.2472 −0.442558
\(897\) 8.74821 0.292094
\(898\) 25.2685 0.843220
\(899\) 16.7432 0.558416
\(900\) 2.29770 0.0765900
\(901\) 2.40740 0.0802022
\(902\) −18.4661 −0.614855
\(903\) 5.52777 0.183953
\(904\) −12.8874 −0.428630
\(905\) 19.3567 0.643439
\(906\) −84.4983 −2.80727
\(907\) 39.3096 1.30525 0.652626 0.757680i \(-0.273667\pi\)
0.652626 + 0.757680i \(0.273667\pi\)
\(908\) −4.97474 −0.165093
\(909\) −48.3306 −1.60302
\(910\) 3.48406 0.115495
\(911\) −39.4741 −1.30783 −0.653917 0.756566i \(-0.726876\pi\)
−0.653917 + 0.756566i \(0.726876\pi\)
\(912\) 68.4666 2.26716
\(913\) −14.4793 −0.479195
\(914\) 18.1978 0.601929
\(915\) 21.5447 0.712245
\(916\) −0.779527 −0.0257563
\(917\) 3.86535 0.127645
\(918\) −0.621653 −0.0205176
\(919\) −30.7682 −1.01495 −0.507475 0.861666i \(-0.669421\pi\)
−0.507475 + 0.861666i \(0.669421\pi\)
\(920\) −3.49272 −0.115152
\(921\) −42.1634 −1.38933
\(922\) −12.2176 −0.402366
\(923\) 13.3410 0.439124
\(924\) 6.02976 0.198364
\(925\) −3.21787 −0.105803
\(926\) 61.5806 2.02366
\(927\) −52.6980 −1.73083
\(928\) −21.1762 −0.695142
\(929\) 20.9931 0.688760 0.344380 0.938830i \(-0.388089\pi\)
0.344380 + 0.938830i \(0.388089\pi\)
\(930\) 13.4549 0.441204
\(931\) −5.66999 −0.185826
\(932\) 15.8426 0.518942
\(933\) 34.5986 1.13271
\(934\) −50.0227 −1.63679
\(935\) −9.24709 −0.302412
\(936\) −12.5336 −0.409673
\(937\) −1.56738 −0.0512040 −0.0256020 0.999672i \(-0.508150\pi\)
−0.0256020 + 0.999672i \(0.508150\pi\)
\(938\) −1.00871 −0.0329356
\(939\) 70.8634 2.31254
\(940\) −1.24709 −0.0406754
\(941\) −30.0695 −0.980237 −0.490118 0.871656i \(-0.663046\pi\)
−0.490118 + 0.871656i \(0.663046\pi\)
\(942\) 17.5404 0.571496
\(943\) −5.99433 −0.195202
\(944\) 58.7152 1.91102
\(945\) −0.127896 −0.00416046
\(946\) −11.9858 −0.389691
\(947\) −46.5781 −1.51358 −0.756792 0.653656i \(-0.773234\pi\)
−0.756792 + 0.653656i \(0.773234\pi\)
\(948\) 15.5736 0.505808
\(949\) 18.5950 0.603621
\(950\) 9.45296 0.306695
\(951\) 1.56168 0.0506409
\(952\) −5.93225 −0.192265
\(953\) 34.8143 1.12775 0.563873 0.825862i \(-0.309311\pi\)
0.563873 + 0.825862i \(0.309311\pi\)
\(954\) 4.05780 0.131376
\(955\) 10.9970 0.355854
\(956\) 3.69650 0.119553
\(957\) −39.1364 −1.26510
\(958\) −21.5623 −0.696648
\(959\) −1.29536 −0.0418293
\(960\) 7.13322 0.230224
\(961\) −20.0490 −0.646744
\(962\) −11.2112 −0.361465
\(963\) −5.39849 −0.173964
\(964\) 3.51807 0.113310
\(965\) −7.19974 −0.231768
\(966\) 6.97918 0.224552
\(967\) 29.6580 0.953738 0.476869 0.878974i \(-0.341772\pi\)
0.476869 + 0.878974i \(0.341772\pi\)
\(968\) −1.91263 −0.0614743
\(969\) 40.3141 1.29508
\(970\) −15.7049 −0.504253
\(971\) −45.2029 −1.45063 −0.725316 0.688416i \(-0.758306\pi\)
−0.725316 + 0.688416i \(0.758306\pi\)
\(972\) −17.1045 −0.548627
\(973\) −6.80695 −0.218221
\(974\) −25.7318 −0.824501
\(975\) −5.09647 −0.163218
\(976\) −43.7419 −1.40014
\(977\) 2.94679 0.0942763 0.0471382 0.998888i \(-0.484990\pi\)
0.0471382 + 0.998888i \(0.484990\pi\)
\(978\) −100.517 −3.21417
\(979\) −20.0413 −0.640523
\(980\) 0.779527 0.0249011
\(981\) −45.8549 −1.46404
\(982\) 18.6702 0.595791
\(983\) −33.1113 −1.05609 −0.528044 0.849217i \(-0.677074\pi\)
−0.528044 + 0.849217i \(0.677074\pi\)
\(984\) 17.3290 0.552429
\(985\) −0.491967 −0.0156754
\(986\) −24.5925 −0.783185
\(987\) −3.90153 −0.124187
\(988\) 9.23662 0.293856
\(989\) −3.89072 −0.123718
\(990\) −15.5864 −0.495370
\(991\) −36.6569 −1.16444 −0.582222 0.813030i \(-0.697816\pi\)
−0.582222 + 0.813030i \(0.697816\pi\)
\(992\) −13.8504 −0.439750
\(993\) −22.1591 −0.703198
\(994\) 10.6432 0.337583
\(995\) 1.47755 0.0468413
\(996\) −8.67858 −0.274991
\(997\) −44.6807 −1.41505 −0.707525 0.706688i \(-0.750188\pi\)
−0.707525 + 0.706688i \(0.750188\pi\)
\(998\) 24.4625 0.774348
\(999\) 0.411553 0.0130209
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 8015.2.a.h.1.11 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8015.2.a.h.1.11 38 1.1 even 1 trivial