Properties

Label 2013.4.a.h.1.2
Level $2013$
Weight $4$
Character 2013.1
Self dual yes
Analytic conductor $118.771$
Analytic rank $0$
Dimension $39$
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] = [2013,4,Mod(1,2013)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2013, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2013.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2013 = 3 \cdot 11 \cdot 61 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2013.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: \(118.770844842\)
Analytic rank: \(0\)
Dimension: \(39\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 2013.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-5.19520 q^{2} +3.00000 q^{3} +18.9901 q^{4} +20.2319 q^{5} -15.5856 q^{6} -14.1923 q^{7} -57.0959 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-5.19520 q^{2} +3.00000 q^{3} +18.9901 q^{4} +20.2319 q^{5} -15.5856 q^{6} -14.1923 q^{7} -57.0959 q^{8} +9.00000 q^{9} -105.109 q^{10} -11.0000 q^{11} +56.9703 q^{12} +3.52655 q^{13} +73.7320 q^{14} +60.6957 q^{15} +144.704 q^{16} -78.5007 q^{17} -46.7568 q^{18} -11.9618 q^{19} +384.206 q^{20} -42.5770 q^{21} +57.1472 q^{22} +96.6536 q^{23} -171.288 q^{24} +284.330 q^{25} -18.3211 q^{26} +27.0000 q^{27} -269.514 q^{28} -57.3192 q^{29} -315.326 q^{30} -41.0071 q^{31} -294.997 q^{32} -33.0000 q^{33} +407.827 q^{34} -287.138 q^{35} +170.911 q^{36} +171.676 q^{37} +62.1441 q^{38} +10.5796 q^{39} -1155.16 q^{40} +25.8180 q^{41} +221.196 q^{42} +16.8900 q^{43} -208.891 q^{44} +182.087 q^{45} -502.135 q^{46} -230.926 q^{47} +434.111 q^{48} -141.578 q^{49} -1477.15 q^{50} -235.502 q^{51} +66.9695 q^{52} -264.082 q^{53} -140.270 q^{54} -222.551 q^{55} +810.323 q^{56} -35.8855 q^{57} +297.785 q^{58} +90.9484 q^{59} +1152.62 q^{60} +61.0000 q^{61} +213.040 q^{62} -127.731 q^{63} +374.941 q^{64} +71.3487 q^{65} +171.442 q^{66} -498.257 q^{67} -1490.74 q^{68} +289.961 q^{69} +1491.74 q^{70} +655.048 q^{71} -513.863 q^{72} +698.166 q^{73} -891.890 q^{74} +852.989 q^{75} -227.157 q^{76} +156.116 q^{77} -54.9634 q^{78} +937.199 q^{79} +2927.63 q^{80} +81.0000 q^{81} -134.130 q^{82} +1309.79 q^{83} -808.542 q^{84} -1588.22 q^{85} -87.7467 q^{86} -171.958 q^{87} +628.054 q^{88} +447.699 q^{89} -945.979 q^{90} -50.0499 q^{91} +1835.46 q^{92} -123.021 q^{93} +1199.71 q^{94} -242.011 q^{95} -884.991 q^{96} +883.212 q^{97} +735.525 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 39 q + 8 q^{2} + 117 q^{3} + 154 q^{4} + 65 q^{5} + 24 q^{6} + 35 q^{7} + 75 q^{8} + 351 q^{9} - 21 q^{10} - 429 q^{11} + 462 q^{12} - 27 q^{13} + 164 q^{14} + 195 q^{15} + 686 q^{16} + 170 q^{17} + 72 q^{18} + 139 q^{19} + 1056 q^{20} + 105 q^{21} - 88 q^{22} + 291 q^{23} + 225 q^{24} + 1236 q^{25} + 583 q^{26} + 1053 q^{27} + 976 q^{28} + 374 q^{29} - 63 q^{30} + 232 q^{31} + 933 q^{32} - 1287 q^{33} + 332 q^{34} + 626 q^{35} + 1386 q^{36} + 232 q^{37} + 989 q^{38} - 81 q^{39} - 263 q^{40} + 1014 q^{41} + 492 q^{42} + 515 q^{43} - 1694 q^{44} + 585 q^{45} - 371 q^{46} + 2005 q^{47} + 2058 q^{48} + 2064 q^{49} + 4582 q^{50} + 510 q^{51} + 216 q^{52} + 1485 q^{53} + 216 q^{54} - 715 q^{55} + 2307 q^{56} + 417 q^{57} + 573 q^{58} + 2749 q^{59} + 3168 q^{60} + 2379 q^{61} + 1837 q^{62} + 315 q^{63} + 7295 q^{64} + 3630 q^{65} - 264 q^{66} + 3575 q^{67} + 2630 q^{68} + 873 q^{69} + 4218 q^{70} + 4723 q^{71} + 675 q^{72} + 859 q^{73} + 4232 q^{74} + 3708 q^{75} + 2466 q^{76} - 385 q^{77} + 1749 q^{78} - 1887 q^{79} + 8933 q^{80} + 3159 q^{81} + 6806 q^{82} + 5609 q^{83} + 2928 q^{84} - 565 q^{85} + 5185 q^{86} + 1122 q^{87} - 825 q^{88} + 6725 q^{89} - 189 q^{90} + 2808 q^{91} + 3257 q^{92} + 696 q^{93} + 3184 q^{94} + 3216 q^{95} + 2799 q^{96} + 3512 q^{97} + 4464 q^{98} - 3861 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −5.19520 −1.83678 −0.918390 0.395675i \(-0.870511\pi\)
−0.918390 + 0.395675i \(0.870511\pi\)
\(3\) 3.00000 0.577350
\(4\) 18.9901 2.37376
\(5\) 20.2319 1.80960 0.904798 0.425841i \(-0.140022\pi\)
0.904798 + 0.425841i \(0.140022\pi\)
\(6\) −15.5856 −1.06047
\(7\) −14.1923 −0.766314 −0.383157 0.923683i \(-0.625163\pi\)
−0.383157 + 0.923683i \(0.625163\pi\)
\(8\) −57.0959 −2.52330
\(9\) 9.00000 0.333333
\(10\) −105.109 −3.32383
\(11\) −11.0000 −0.301511
\(12\) 56.9703 1.37049
\(13\) 3.52655 0.0752375 0.0376188 0.999292i \(-0.488023\pi\)
0.0376188 + 0.999292i \(0.488023\pi\)
\(14\) 73.7320 1.40755
\(15\) 60.6957 1.04477
\(16\) 144.704 2.26099
\(17\) −78.5007 −1.11995 −0.559977 0.828508i \(-0.689190\pi\)
−0.559977 + 0.828508i \(0.689190\pi\)
\(18\) −46.7568 −0.612260
\(19\) −11.9618 −0.144433 −0.0722166 0.997389i \(-0.523007\pi\)
−0.0722166 + 0.997389i \(0.523007\pi\)
\(20\) 384.206 4.29555
\(21\) −42.5770 −0.442432
\(22\) 57.1472 0.553810
\(23\) 96.6536 0.876246 0.438123 0.898915i \(-0.355643\pi\)
0.438123 + 0.898915i \(0.355643\pi\)
\(24\) −171.288 −1.45683
\(25\) 284.330 2.27464
\(26\) −18.3211 −0.138195
\(27\) 27.0000 0.192450
\(28\) −269.514 −1.81905
\(29\) −57.3192 −0.367031 −0.183516 0.983017i \(-0.558748\pi\)
−0.183516 + 0.983017i \(0.558748\pi\)
\(30\) −315.326 −1.91902
\(31\) −41.0071 −0.237583 −0.118792 0.992919i \(-0.537902\pi\)
−0.118792 + 0.992919i \(0.537902\pi\)
\(32\) −294.997 −1.62964
\(33\) −33.0000 −0.174078
\(34\) 407.827 2.05711
\(35\) −287.138 −1.38672
\(36\) 170.911 0.791255
\(37\) 171.676 0.762793 0.381396 0.924412i \(-0.375443\pi\)
0.381396 + 0.924412i \(0.375443\pi\)
\(38\) 62.1441 0.265292
\(39\) 10.5796 0.0434384
\(40\) −1155.16 −4.56616
\(41\) 25.8180 0.0983439 0.0491720 0.998790i \(-0.484342\pi\)
0.0491720 + 0.998790i \(0.484342\pi\)
\(42\) 221.196 0.812650
\(43\) 16.8900 0.0598998 0.0299499 0.999551i \(-0.490465\pi\)
0.0299499 + 0.999551i \(0.490465\pi\)
\(44\) −208.891 −0.715717
\(45\) 182.087 0.603199
\(46\) −502.135 −1.60947
\(47\) −230.926 −0.716681 −0.358340 0.933591i \(-0.616657\pi\)
−0.358340 + 0.933591i \(0.616657\pi\)
\(48\) 434.111 1.30538
\(49\) −141.578 −0.412763
\(50\) −1477.15 −4.17801
\(51\) −235.502 −0.646606
\(52\) 66.9695 0.178596
\(53\) −264.082 −0.684424 −0.342212 0.939623i \(-0.611176\pi\)
−0.342212 + 0.939623i \(0.611176\pi\)
\(54\) −140.270 −0.353489
\(55\) −222.551 −0.545614
\(56\) 810.323 1.93364
\(57\) −35.8855 −0.0833886
\(58\) 297.785 0.674156
\(59\) 90.9484 0.200686 0.100343 0.994953i \(-0.468006\pi\)
0.100343 + 0.994953i \(0.468006\pi\)
\(60\) 1152.62 2.48004
\(61\) 61.0000 0.128037
\(62\) 213.040 0.436389
\(63\) −127.731 −0.255438
\(64\) 374.941 0.732307
\(65\) 71.3487 0.136150
\(66\) 171.442 0.319743
\(67\) −498.257 −0.908534 −0.454267 0.890866i \(-0.650099\pi\)
−0.454267 + 0.890866i \(0.650099\pi\)
\(68\) −1490.74 −2.65851
\(69\) 289.961 0.505901
\(70\) 1491.74 2.54710
\(71\) 655.048 1.09493 0.547464 0.836829i \(-0.315593\pi\)
0.547464 + 0.836829i \(0.315593\pi\)
\(72\) −513.863 −0.841101
\(73\) 698.166 1.11937 0.559686 0.828705i \(-0.310922\pi\)
0.559686 + 0.828705i \(0.310922\pi\)
\(74\) −891.890 −1.40108
\(75\) 852.989 1.31326
\(76\) −227.157 −0.342851
\(77\) 156.116 0.231052
\(78\) −54.9634 −0.0797868
\(79\) 937.199 1.33472 0.667362 0.744734i \(-0.267424\pi\)
0.667362 + 0.744734i \(0.267424\pi\)
\(80\) 2927.63 4.09148
\(81\) 81.0000 0.111111
\(82\) −134.130 −0.180636
\(83\) 1309.79 1.73215 0.866074 0.499916i \(-0.166636\pi\)
0.866074 + 0.499916i \(0.166636\pi\)
\(84\) −808.542 −1.05023
\(85\) −1588.22 −2.02667
\(86\) −87.7467 −0.110023
\(87\) −171.958 −0.211906
\(88\) 628.054 0.760805
\(89\) 447.699 0.533213 0.266607 0.963805i \(-0.414098\pi\)
0.266607 + 0.963805i \(0.414098\pi\)
\(90\) −945.979 −1.10794
\(91\) −50.0499 −0.0576556
\(92\) 1835.46 2.08000
\(93\) −123.021 −0.137169
\(94\) 1199.71 1.31639
\(95\) −242.011 −0.261366
\(96\) −884.991 −0.940876
\(97\) 883.212 0.924501 0.462250 0.886749i \(-0.347042\pi\)
0.462250 + 0.886749i \(0.347042\pi\)
\(98\) 735.525 0.758155
\(99\) −99.0000 −0.100504
\(100\) 5399.45 5.39945
\(101\) −278.939 −0.274806 −0.137403 0.990515i \(-0.543876\pi\)
−0.137403 + 0.990515i \(0.543876\pi\)
\(102\) 1223.48 1.18767
\(103\) −416.553 −0.398488 −0.199244 0.979950i \(-0.563849\pi\)
−0.199244 + 0.979950i \(0.563849\pi\)
\(104\) −201.351 −0.189847
\(105\) −861.413 −0.800622
\(106\) 1371.96 1.25714
\(107\) 1693.07 1.52967 0.764836 0.644225i \(-0.222820\pi\)
0.764836 + 0.644225i \(0.222820\pi\)
\(108\) 512.733 0.456831
\(109\) −1172.28 −1.03013 −0.515063 0.857152i \(-0.672232\pi\)
−0.515063 + 0.857152i \(0.672232\pi\)
\(110\) 1156.20 1.00217
\(111\) 515.027 0.440399
\(112\) −2053.68 −1.73263
\(113\) 1950.16 1.62350 0.811750 0.584005i \(-0.198515\pi\)
0.811750 + 0.584005i \(0.198515\pi\)
\(114\) 186.432 0.153167
\(115\) 1955.49 1.58565
\(116\) −1088.50 −0.871246
\(117\) 31.7389 0.0250792
\(118\) −472.495 −0.368616
\(119\) 1114.11 0.858237
\(120\) −3465.47 −2.63627
\(121\) 121.000 0.0909091
\(122\) −316.907 −0.235176
\(123\) 77.4541 0.0567789
\(124\) −778.729 −0.563967
\(125\) 3223.54 2.30658
\(126\) 663.588 0.469184
\(127\) 793.341 0.554312 0.277156 0.960825i \(-0.410608\pi\)
0.277156 + 0.960825i \(0.410608\pi\)
\(128\) 412.083 0.284557
\(129\) 50.6699 0.0345832
\(130\) −370.671 −0.250077
\(131\) 824.555 0.549937 0.274968 0.961453i \(-0.411333\pi\)
0.274968 + 0.961453i \(0.411333\pi\)
\(132\) −626.674 −0.413219
\(133\) 169.766 0.110681
\(134\) 2588.54 1.66878
\(135\) 546.261 0.348257
\(136\) 4482.07 2.82599
\(137\) 1877.41 1.17079 0.585393 0.810750i \(-0.300940\pi\)
0.585393 + 0.810750i \(0.300940\pi\)
\(138\) −1506.40 −0.929229
\(139\) 1417.53 0.864986 0.432493 0.901637i \(-0.357634\pi\)
0.432493 + 0.901637i \(0.357634\pi\)
\(140\) −5452.78 −3.29174
\(141\) −692.778 −0.413776
\(142\) −3403.10 −2.01114
\(143\) −38.7920 −0.0226850
\(144\) 1302.33 0.753664
\(145\) −1159.68 −0.664178
\(146\) −3627.11 −2.05604
\(147\) −424.733 −0.238309
\(148\) 3260.14 1.81069
\(149\) −2221.54 −1.22145 −0.610723 0.791844i \(-0.709121\pi\)
−0.610723 + 0.791844i \(0.709121\pi\)
\(150\) −4431.45 −2.41218
\(151\) −1774.71 −0.956452 −0.478226 0.878237i \(-0.658720\pi\)
−0.478226 + 0.878237i \(0.658720\pi\)
\(152\) 682.971 0.364449
\(153\) −706.507 −0.373318
\(154\) −811.052 −0.424393
\(155\) −829.651 −0.429930
\(156\) 200.909 0.103113
\(157\) −1212.79 −0.616503 −0.308252 0.951305i \(-0.599744\pi\)
−0.308252 + 0.951305i \(0.599744\pi\)
\(158\) −4868.94 −2.45159
\(159\) −792.247 −0.395153
\(160\) −5968.35 −2.94900
\(161\) −1371.74 −0.671480
\(162\) −420.811 −0.204087
\(163\) −201.341 −0.0967500 −0.0483750 0.998829i \(-0.515404\pi\)
−0.0483750 + 0.998829i \(0.515404\pi\)
\(164\) 490.288 0.233445
\(165\) −667.653 −0.315010
\(166\) −6804.63 −3.18158
\(167\) 1879.88 0.871077 0.435538 0.900170i \(-0.356558\pi\)
0.435538 + 0.900170i \(0.356558\pi\)
\(168\) 2430.97 1.11639
\(169\) −2184.56 −0.994339
\(170\) 8251.12 3.72254
\(171\) −107.656 −0.0481444
\(172\) 320.742 0.142188
\(173\) −755.825 −0.332164 −0.166082 0.986112i \(-0.553112\pi\)
−0.166082 + 0.986112i \(0.553112\pi\)
\(174\) 893.354 0.389224
\(175\) −4035.30 −1.74309
\(176\) −1591.74 −0.681715
\(177\) 272.845 0.115866
\(178\) −2325.88 −0.979396
\(179\) 2500.82 1.04424 0.522122 0.852871i \(-0.325140\pi\)
0.522122 + 0.852871i \(0.325140\pi\)
\(180\) 3457.85 1.43185
\(181\) 283.622 0.116472 0.0582362 0.998303i \(-0.481452\pi\)
0.0582362 + 0.998303i \(0.481452\pi\)
\(182\) 260.019 0.105901
\(183\) 183.000 0.0739221
\(184\) −5518.52 −2.21104
\(185\) 3473.33 1.38035
\(186\) 639.120 0.251949
\(187\) 863.508 0.337679
\(188\) −4385.31 −1.70123
\(189\) −383.193 −0.147477
\(190\) 1257.29 0.480072
\(191\) 1071.87 0.406061 0.203030 0.979172i \(-0.434921\pi\)
0.203030 + 0.979172i \(0.434921\pi\)
\(192\) 1124.82 0.422798
\(193\) −3395.00 −1.26620 −0.633101 0.774069i \(-0.718218\pi\)
−0.633101 + 0.774069i \(0.718218\pi\)
\(194\) −4588.46 −1.69811
\(195\) 214.046 0.0786060
\(196\) −2688.58 −0.979802
\(197\) 3436.28 1.24277 0.621383 0.783507i \(-0.286571\pi\)
0.621383 + 0.783507i \(0.286571\pi\)
\(198\) 514.325 0.184603
\(199\) −3160.28 −1.12576 −0.562881 0.826538i \(-0.690307\pi\)
−0.562881 + 0.826538i \(0.690307\pi\)
\(200\) −16234.0 −5.73960
\(201\) −1494.77 −0.524542
\(202\) 1449.14 0.504759
\(203\) 813.493 0.281261
\(204\) −4472.21 −1.53489
\(205\) 522.348 0.177963
\(206\) 2164.08 0.731935
\(207\) 869.882 0.292082
\(208\) 510.304 0.170112
\(209\) 131.580 0.0435483
\(210\) 4475.22 1.47057
\(211\) 5289.73 1.72588 0.862938 0.505309i \(-0.168622\pi\)
0.862938 + 0.505309i \(0.168622\pi\)
\(212\) −5014.95 −1.62466
\(213\) 1965.14 0.632157
\(214\) −8795.82 −2.80967
\(215\) 341.716 0.108395
\(216\) −1541.59 −0.485610
\(217\) 581.986 0.182064
\(218\) 6090.21 1.89212
\(219\) 2094.50 0.646270
\(220\) −4226.27 −1.29516
\(221\) −276.836 −0.0842626
\(222\) −2675.67 −0.808916
\(223\) 1423.29 0.427401 0.213700 0.976899i \(-0.431448\pi\)
0.213700 + 0.976899i \(0.431448\pi\)
\(224\) 4186.70 1.24882
\(225\) 2558.97 0.758213
\(226\) −10131.5 −2.98202
\(227\) −4068.61 −1.18962 −0.594808 0.803868i \(-0.702772\pi\)
−0.594808 + 0.803868i \(0.702772\pi\)
\(228\) −681.470 −0.197945
\(229\) 639.092 0.184421 0.0922104 0.995740i \(-0.470607\pi\)
0.0922104 + 0.995740i \(0.470607\pi\)
\(230\) −10159.1 −2.91249
\(231\) 468.347 0.133398
\(232\) 3272.69 0.926131
\(233\) 3664.11 1.03023 0.515116 0.857120i \(-0.327749\pi\)
0.515116 + 0.857120i \(0.327749\pi\)
\(234\) −164.890 −0.0460650
\(235\) −4672.07 −1.29690
\(236\) 1727.12 0.476381
\(237\) 2811.60 0.770603
\(238\) −5788.02 −1.57639
\(239\) 3999.89 1.08256 0.541279 0.840843i \(-0.317940\pi\)
0.541279 + 0.840843i \(0.317940\pi\)
\(240\) 8782.88 2.36222
\(241\) 1352.84 0.361593 0.180796 0.983521i \(-0.442132\pi\)
0.180796 + 0.983521i \(0.442132\pi\)
\(242\) −628.619 −0.166980
\(243\) 243.000 0.0641500
\(244\) 1158.40 0.303929
\(245\) −2864.39 −0.746934
\(246\) −402.390 −0.104290
\(247\) −42.1839 −0.0108668
\(248\) 2341.33 0.599495
\(249\) 3929.37 1.00006
\(250\) −16747.0 −4.23668
\(251\) 4334.84 1.09009 0.545045 0.838407i \(-0.316513\pi\)
0.545045 + 0.838407i \(0.316513\pi\)
\(252\) −2425.63 −0.606350
\(253\) −1063.19 −0.264198
\(254\) −4121.57 −1.01815
\(255\) −4764.66 −1.17010
\(256\) −5140.38 −1.25498
\(257\) −6384.84 −1.54971 −0.774855 0.632139i \(-0.782177\pi\)
−0.774855 + 0.632139i \(0.782177\pi\)
\(258\) −263.240 −0.0635218
\(259\) −2436.48 −0.584539
\(260\) 1354.92 0.323187
\(261\) −515.873 −0.122344
\(262\) −4283.73 −1.01011
\(263\) −231.068 −0.0541760 −0.0270880 0.999633i \(-0.508623\pi\)
−0.0270880 + 0.999633i \(0.508623\pi\)
\(264\) 1884.16 0.439251
\(265\) −5342.89 −1.23853
\(266\) −881.970 −0.203297
\(267\) 1343.10 0.307851
\(268\) −9461.95 −2.15664
\(269\) 2380.36 0.539529 0.269764 0.962926i \(-0.413054\pi\)
0.269764 + 0.962926i \(0.413054\pi\)
\(270\) −2837.94 −0.639672
\(271\) 5017.08 1.12460 0.562299 0.826934i \(-0.309917\pi\)
0.562299 + 0.826934i \(0.309917\pi\)
\(272\) −11359.3 −2.53221
\(273\) −150.150 −0.0332875
\(274\) −9753.51 −2.15048
\(275\) −3127.63 −0.685829
\(276\) 5506.39 1.20089
\(277\) 5746.75 1.24653 0.623265 0.782011i \(-0.285806\pi\)
0.623265 + 0.782011i \(0.285806\pi\)
\(278\) −7364.34 −1.58879
\(279\) −369.064 −0.0791945
\(280\) 16394.4 3.49911
\(281\) 1962.23 0.416571 0.208286 0.978068i \(-0.433212\pi\)
0.208286 + 0.978068i \(0.433212\pi\)
\(282\) 3599.12 0.760016
\(283\) 1538.47 0.323154 0.161577 0.986860i \(-0.448342\pi\)
0.161577 + 0.986860i \(0.448342\pi\)
\(284\) 12439.4 2.59910
\(285\) −726.032 −0.150900
\(286\) 201.532 0.0416673
\(287\) −366.418 −0.0753623
\(288\) −2654.97 −0.543215
\(289\) 1249.37 0.254298
\(290\) 6024.75 1.21995
\(291\) 2649.64 0.533761
\(292\) 13258.3 2.65713
\(293\) 1389.98 0.277144 0.138572 0.990352i \(-0.455749\pi\)
0.138572 + 0.990352i \(0.455749\pi\)
\(294\) 2206.57 0.437721
\(295\) 1840.06 0.363161
\(296\) −9801.98 −1.92476
\(297\) −297.000 −0.0580259
\(298\) 11541.3 2.24353
\(299\) 340.853 0.0659266
\(300\) 16198.4 3.11738
\(301\) −239.708 −0.0459021
\(302\) 9220.00 1.75679
\(303\) −836.816 −0.158659
\(304\) −1730.92 −0.326563
\(305\) 1234.15 0.231695
\(306\) 3670.44 0.685704
\(307\) −2534.31 −0.471142 −0.235571 0.971857i \(-0.575696\pi\)
−0.235571 + 0.971857i \(0.575696\pi\)
\(308\) 2964.65 0.548464
\(309\) −1249.66 −0.230067
\(310\) 4310.20 0.789687
\(311\) −7391.61 −1.34772 −0.673858 0.738861i \(-0.735364\pi\)
−0.673858 + 0.738861i \(0.735364\pi\)
\(312\) −604.054 −0.109608
\(313\) −1255.43 −0.226712 −0.113356 0.993554i \(-0.536160\pi\)
−0.113356 + 0.993554i \(0.536160\pi\)
\(314\) 6300.68 1.13238
\(315\) −2584.24 −0.462240
\(316\) 17797.5 3.16832
\(317\) 5649.49 1.00097 0.500484 0.865746i \(-0.333155\pi\)
0.500484 + 0.865746i \(0.333155\pi\)
\(318\) 4115.88 0.725809
\(319\) 630.511 0.110664
\(320\) 7585.77 1.32518
\(321\) 5079.20 0.883157
\(322\) 7126.46 1.23336
\(323\) 939.013 0.161759
\(324\) 1538.20 0.263752
\(325\) 1002.70 0.171138
\(326\) 1046.01 0.177709
\(327\) −3516.83 −0.594744
\(328\) −1474.10 −0.248152
\(329\) 3277.38 0.549203
\(330\) 3468.59 0.578605
\(331\) −861.414 −0.143044 −0.0715220 0.997439i \(-0.522786\pi\)
−0.0715220 + 0.997439i \(0.522786\pi\)
\(332\) 24873.1 4.11171
\(333\) 1545.08 0.254264
\(334\) −9766.38 −1.59998
\(335\) −10080.7 −1.64408
\(336\) −6161.04 −1.00033
\(337\) 6399.02 1.03435 0.517177 0.855879i \(-0.326983\pi\)
0.517177 + 0.855879i \(0.326983\pi\)
\(338\) 11349.2 1.82638
\(339\) 5850.48 0.937329
\(340\) −30160.5 −4.81083
\(341\) 451.078 0.0716341
\(342\) 559.297 0.0884308
\(343\) 6877.29 1.08262
\(344\) −964.346 −0.151146
\(345\) 5866.46 0.915476
\(346\) 3926.66 0.610112
\(347\) 3387.04 0.523994 0.261997 0.965069i \(-0.415619\pi\)
0.261997 + 0.965069i \(0.415619\pi\)
\(348\) −3265.49 −0.503014
\(349\) −5484.44 −0.841190 −0.420595 0.907249i \(-0.638179\pi\)
−0.420595 + 0.907249i \(0.638179\pi\)
\(350\) 20964.2 3.20167
\(351\) 95.2168 0.0144795
\(352\) 3244.97 0.491356
\(353\) 8776.63 1.32332 0.661661 0.749803i \(-0.269852\pi\)
0.661661 + 0.749803i \(0.269852\pi\)
\(354\) −1417.49 −0.212821
\(355\) 13252.9 1.98138
\(356\) 8501.85 1.26572
\(357\) 3342.33 0.495503
\(358\) −12992.2 −1.91805
\(359\) 704.904 0.103631 0.0518153 0.998657i \(-0.483499\pi\)
0.0518153 + 0.998657i \(0.483499\pi\)
\(360\) −10396.4 −1.52205
\(361\) −6715.91 −0.979139
\(362\) −1473.48 −0.213934
\(363\) 363.000 0.0524864
\(364\) −950.454 −0.136861
\(365\) 14125.2 2.02561
\(366\) −950.722 −0.135779
\(367\) 1966.99 0.279771 0.139885 0.990168i \(-0.455327\pi\)
0.139885 + 0.990168i \(0.455327\pi\)
\(368\) 13986.1 1.98119
\(369\) 232.362 0.0327813
\(370\) −18044.6 −2.53539
\(371\) 3747.94 0.524484
\(372\) −2336.19 −0.325607
\(373\) −12306.8 −1.70837 −0.854187 0.519965i \(-0.825945\pi\)
−0.854187 + 0.519965i \(0.825945\pi\)
\(374\) −4486.10 −0.620242
\(375\) 9670.63 1.33170
\(376\) 13184.9 1.80840
\(377\) −202.139 −0.0276145
\(378\) 1990.76 0.270883
\(379\) −8902.15 −1.20652 −0.603262 0.797543i \(-0.706133\pi\)
−0.603262 + 0.797543i \(0.706133\pi\)
\(380\) −4595.81 −0.620421
\(381\) 2380.02 0.320032
\(382\) −5568.56 −0.745844
\(383\) −7231.26 −0.964752 −0.482376 0.875964i \(-0.660226\pi\)
−0.482376 + 0.875964i \(0.660226\pi\)
\(384\) 1236.25 0.164289
\(385\) 3158.52 0.418111
\(386\) 17637.7 2.32574
\(387\) 152.010 0.0199666
\(388\) 16772.3 2.19455
\(389\) 12110.5 1.57847 0.789236 0.614090i \(-0.210477\pi\)
0.789236 + 0.614090i \(0.210477\pi\)
\(390\) −1112.01 −0.144382
\(391\) −7587.38 −0.981356
\(392\) 8083.50 1.04153
\(393\) 2473.67 0.317506
\(394\) −17852.2 −2.28269
\(395\) 18961.3 2.41531
\(396\) −1880.02 −0.238572
\(397\) 632.133 0.0799140 0.0399570 0.999201i \(-0.487278\pi\)
0.0399570 + 0.999201i \(0.487278\pi\)
\(398\) 16418.3 2.06778
\(399\) 509.299 0.0639018
\(400\) 41143.5 5.14294
\(401\) 3506.63 0.436690 0.218345 0.975872i \(-0.429934\pi\)
0.218345 + 0.975872i \(0.429934\pi\)
\(402\) 7765.63 0.963469
\(403\) −144.613 −0.0178752
\(404\) −5297.08 −0.652325
\(405\) 1638.78 0.201066
\(406\) −4226.26 −0.516615
\(407\) −1888.43 −0.229991
\(408\) 13446.2 1.63158
\(409\) −7392.68 −0.893752 −0.446876 0.894596i \(-0.647464\pi\)
−0.446876 + 0.894596i \(0.647464\pi\)
\(410\) −2713.70 −0.326879
\(411\) 5632.22 0.675954
\(412\) −7910.40 −0.945916
\(413\) −1290.77 −0.153789
\(414\) −4519.21 −0.536491
\(415\) 26499.6 3.13449
\(416\) −1040.32 −0.122610
\(417\) 4252.58 0.499400
\(418\) −683.585 −0.0799886
\(419\) −9993.07 −1.16514 −0.582569 0.812781i \(-0.697953\pi\)
−0.582569 + 0.812781i \(0.697953\pi\)
\(420\) −16358.3 −1.90049
\(421\) −2520.43 −0.291777 −0.145888 0.989301i \(-0.546604\pi\)
−0.145888 + 0.989301i \(0.546604\pi\)
\(422\) −27481.2 −3.17006
\(423\) −2078.33 −0.238894
\(424\) 15078.0 1.72701
\(425\) −22320.1 −2.54749
\(426\) −10209.3 −1.16113
\(427\) −865.732 −0.0981164
\(428\) 32151.5 3.63108
\(429\) −116.376 −0.0130972
\(430\) −1775.28 −0.199097
\(431\) 4735.27 0.529212 0.264606 0.964357i \(-0.414758\pi\)
0.264606 + 0.964357i \(0.414758\pi\)
\(432\) 3907.00 0.435128
\(433\) 2677.76 0.297194 0.148597 0.988898i \(-0.452524\pi\)
0.148597 + 0.988898i \(0.452524\pi\)
\(434\) −3023.53 −0.334411
\(435\) −3479.03 −0.383463
\(436\) −22261.7 −2.44528
\(437\) −1156.15 −0.126559
\(438\) −10881.3 −1.18706
\(439\) −3687.05 −0.400851 −0.200425 0.979709i \(-0.564232\pi\)
−0.200425 + 0.979709i \(0.564232\pi\)
\(440\) 12706.7 1.37675
\(441\) −1274.20 −0.137588
\(442\) 1438.22 0.154772
\(443\) −12049.1 −1.29226 −0.646128 0.763229i \(-0.723613\pi\)
−0.646128 + 0.763229i \(0.723613\pi\)
\(444\) 9780.43 1.04540
\(445\) 9057.79 0.964900
\(446\) −7394.27 −0.785042
\(447\) −6664.61 −0.705202
\(448\) −5321.29 −0.561177
\(449\) −7912.30 −0.831635 −0.415818 0.909448i \(-0.636505\pi\)
−0.415818 + 0.909448i \(0.636505\pi\)
\(450\) −13294.4 −1.39267
\(451\) −283.998 −0.0296518
\(452\) 37033.8 3.85381
\(453\) −5324.14 −0.552208
\(454\) 21137.2 2.18506
\(455\) −1012.60 −0.104333
\(456\) 2048.91 0.210415
\(457\) −8701.19 −0.890644 −0.445322 0.895370i \(-0.646911\pi\)
−0.445322 + 0.895370i \(0.646911\pi\)
\(458\) −3320.21 −0.338741
\(459\) −2119.52 −0.215535
\(460\) 37134.9 3.76396
\(461\) −4328.61 −0.437318 −0.218659 0.975801i \(-0.570168\pi\)
−0.218659 + 0.975801i \(0.570168\pi\)
\(462\) −2433.16 −0.245023
\(463\) −6802.73 −0.682829 −0.341414 0.939913i \(-0.610906\pi\)
−0.341414 + 0.939913i \(0.610906\pi\)
\(464\) −8294.29 −0.829855
\(465\) −2488.95 −0.248220
\(466\) −19035.8 −1.89231
\(467\) 9079.59 0.899686 0.449843 0.893108i \(-0.351480\pi\)
0.449843 + 0.893108i \(0.351480\pi\)
\(468\) 602.726 0.0595321
\(469\) 7071.43 0.696222
\(470\) 24272.3 2.38213
\(471\) −3638.36 −0.355938
\(472\) −5192.78 −0.506392
\(473\) −185.789 −0.0180605
\(474\) −14606.8 −1.41543
\(475\) −3401.10 −0.328533
\(476\) 21157.1 2.03725
\(477\) −2376.74 −0.228141
\(478\) −20780.2 −1.98842
\(479\) −9756.02 −0.930614 −0.465307 0.885149i \(-0.654056\pi\)
−0.465307 + 0.885149i \(0.654056\pi\)
\(480\) −17905.1 −1.70260
\(481\) 605.423 0.0573906
\(482\) −7028.26 −0.664167
\(483\) −4115.22 −0.387679
\(484\) 2297.80 0.215797
\(485\) 17869.1 1.67297
\(486\) −1262.43 −0.117830
\(487\) 15102.4 1.40525 0.702624 0.711561i \(-0.252012\pi\)
0.702624 + 0.711561i \(0.252012\pi\)
\(488\) −3482.85 −0.323076
\(489\) −604.023 −0.0558586
\(490\) 14881.1 1.37195
\(491\) −6404.28 −0.588637 −0.294319 0.955707i \(-0.595093\pi\)
−0.294319 + 0.955707i \(0.595093\pi\)
\(492\) 1470.86 0.134780
\(493\) 4499.60 0.411058
\(494\) 219.154 0.0199599
\(495\) −2002.96 −0.181871
\(496\) −5933.87 −0.537174
\(497\) −9296.65 −0.839058
\(498\) −20413.9 −1.83688
\(499\) 3981.40 0.357178 0.178589 0.983924i \(-0.442847\pi\)
0.178589 + 0.983924i \(0.442847\pi\)
\(500\) 61215.4 5.47528
\(501\) 5639.65 0.502916
\(502\) −22520.4 −2.00226
\(503\) 10949.9 0.970641 0.485320 0.874336i \(-0.338703\pi\)
0.485320 + 0.874336i \(0.338703\pi\)
\(504\) 7292.91 0.644548
\(505\) −5643.46 −0.497288
\(506\) 5523.48 0.485274
\(507\) −6553.69 −0.574082
\(508\) 15065.6 1.31581
\(509\) 411.376 0.0358230 0.0179115 0.999840i \(-0.494298\pi\)
0.0179115 + 0.999840i \(0.494298\pi\)
\(510\) 24753.4 2.14921
\(511\) −9908.61 −0.857790
\(512\) 23408.7 2.02056
\(513\) −322.969 −0.0277962
\(514\) 33170.5 2.84648
\(515\) −8427.67 −0.721102
\(516\) 962.226 0.0820924
\(517\) 2540.18 0.216087
\(518\) 12658.0 1.07367
\(519\) −2267.48 −0.191775
\(520\) −4073.72 −0.343547
\(521\) 1527.57 0.128453 0.0642264 0.997935i \(-0.479542\pi\)
0.0642264 + 0.997935i \(0.479542\pi\)
\(522\) 2680.06 0.224719
\(523\) −10845.4 −0.906760 −0.453380 0.891317i \(-0.649782\pi\)
−0.453380 + 0.891317i \(0.649782\pi\)
\(524\) 15658.4 1.30542
\(525\) −12105.9 −1.00637
\(526\) 1200.45 0.0995094
\(527\) 3219.09 0.266083
\(528\) −4775.22 −0.393588
\(529\) −2825.09 −0.232193
\(530\) 27757.4 2.27491
\(531\) 818.536 0.0668954
\(532\) 3223.88 0.262731
\(533\) 91.0485 0.00739915
\(534\) −6977.65 −0.565454
\(535\) 34254.0 2.76809
\(536\) 28448.4 2.29251
\(537\) 7502.45 0.602895
\(538\) −12366.5 −0.990996
\(539\) 1557.35 0.124453
\(540\) 10373.6 0.826680
\(541\) −20350.6 −1.61727 −0.808634 0.588312i \(-0.799793\pi\)
−0.808634 + 0.588312i \(0.799793\pi\)
\(542\) −26064.8 −2.06564
\(543\) 850.867 0.0672453
\(544\) 23157.5 1.82513
\(545\) −23717.4 −1.86411
\(546\) 780.058 0.0611418
\(547\) 21276.7 1.66312 0.831559 0.555437i \(-0.187449\pi\)
0.831559 + 0.555437i \(0.187449\pi\)
\(548\) 35652.2 2.77917
\(549\) 549.000 0.0426790
\(550\) 16248.7 1.25972
\(551\) 685.642 0.0530115
\(552\) −16555.6 −1.27654
\(553\) −13301.0 −1.02282
\(554\) −29855.5 −2.28960
\(555\) 10420.0 0.796944
\(556\) 26919.0 2.05327
\(557\) 10163.9 0.773172 0.386586 0.922253i \(-0.373654\pi\)
0.386586 + 0.922253i \(0.373654\pi\)
\(558\) 1917.36 0.145463
\(559\) 59.5632 0.00450672
\(560\) −41549.9 −3.13536
\(561\) 2590.52 0.194959
\(562\) −10194.2 −0.765150
\(563\) −9195.42 −0.688349 −0.344175 0.938906i \(-0.611841\pi\)
−0.344175 + 0.938906i \(0.611841\pi\)
\(564\) −13155.9 −0.982207
\(565\) 39455.4 2.93788
\(566\) −7992.67 −0.593563
\(567\) −1149.58 −0.0851460
\(568\) −37400.5 −2.76283
\(569\) −10516.8 −0.774842 −0.387421 0.921903i \(-0.626634\pi\)
−0.387421 + 0.921903i \(0.626634\pi\)
\(570\) 3771.88 0.277170
\(571\) 21919.5 1.60648 0.803241 0.595654i \(-0.203107\pi\)
0.803241 + 0.595654i \(0.203107\pi\)
\(572\) −736.665 −0.0538488
\(573\) 3215.60 0.234439
\(574\) 1903.62 0.138424
\(575\) 27481.5 1.99314
\(576\) 3374.47 0.244102
\(577\) −3682.02 −0.265658 −0.132829 0.991139i \(-0.542406\pi\)
−0.132829 + 0.991139i \(0.542406\pi\)
\(578\) −6490.71 −0.467090
\(579\) −10185.0 −0.731043
\(580\) −22022.4 −1.57660
\(581\) −18589.0 −1.32737
\(582\) −13765.4 −0.980402
\(583\) 2904.91 0.206362
\(584\) −39862.4 −2.82452
\(585\) 642.139 0.0453832
\(586\) −7221.21 −0.509053
\(587\) 21123.0 1.48525 0.742624 0.669709i \(-0.233581\pi\)
0.742624 + 0.669709i \(0.233581\pi\)
\(588\) −8065.73 −0.565689
\(589\) 490.520 0.0343150
\(590\) −9559.48 −0.667047
\(591\) 10308.9 0.717512
\(592\) 24842.1 1.72467
\(593\) 8474.91 0.586885 0.293442 0.955977i \(-0.405199\pi\)
0.293442 + 0.955977i \(0.405199\pi\)
\(594\) 1542.97 0.106581
\(595\) 22540.5 1.55306
\(596\) −42187.2 −2.89942
\(597\) −9480.85 −0.649958
\(598\) −1770.80 −0.121093
\(599\) 9210.29 0.628251 0.314125 0.949381i \(-0.398289\pi\)
0.314125 + 0.949381i \(0.398289\pi\)
\(600\) −48702.1 −3.31376
\(601\) −19870.6 −1.34865 −0.674324 0.738436i \(-0.735565\pi\)
−0.674324 + 0.738436i \(0.735565\pi\)
\(602\) 1245.33 0.0843121
\(603\) −4484.31 −0.302845
\(604\) −33702.0 −2.27039
\(605\) 2448.06 0.164509
\(606\) 4347.43 0.291423
\(607\) 22915.6 1.53232 0.766158 0.642652i \(-0.222166\pi\)
0.766158 + 0.642652i \(0.222166\pi\)
\(608\) 3528.71 0.235375
\(609\) 2440.48 0.162386
\(610\) −6411.64 −0.425573
\(611\) −814.371 −0.0539213
\(612\) −13416.6 −0.886169
\(613\) −17870.8 −1.17748 −0.588741 0.808322i \(-0.700376\pi\)
−0.588741 + 0.808322i \(0.700376\pi\)
\(614\) 13166.2 0.865384
\(615\) 1567.04 0.102747
\(616\) −8913.56 −0.583015
\(617\) 19689.7 1.28473 0.642365 0.766399i \(-0.277954\pi\)
0.642365 + 0.766399i \(0.277954\pi\)
\(618\) 6492.24 0.422583
\(619\) −3004.27 −0.195076 −0.0975378 0.995232i \(-0.531097\pi\)
−0.0975378 + 0.995232i \(0.531097\pi\)
\(620\) −15755.2 −1.02055
\(621\) 2609.65 0.168634
\(622\) 38400.9 2.47546
\(623\) −6353.89 −0.408609
\(624\) 1530.91 0.0982139
\(625\) 29677.2 1.89934
\(626\) 6522.20 0.416421
\(627\) 394.740 0.0251426
\(628\) −23031.0 −1.46343
\(629\) −13476.7 −0.854293
\(630\) 13425.6 0.849033
\(631\) 21673.9 1.36739 0.683697 0.729766i \(-0.260371\pi\)
0.683697 + 0.729766i \(0.260371\pi\)
\(632\) −53510.2 −3.36791
\(633\) 15869.2 0.996435
\(634\) −29350.2 −1.83856
\(635\) 16050.8 1.00308
\(636\) −15044.9 −0.937999
\(637\) −499.280 −0.0310553
\(638\) −3275.63 −0.203266
\(639\) 5895.43 0.364976
\(640\) 8337.21 0.514933
\(641\) −7667.71 −0.472475 −0.236237 0.971695i \(-0.575914\pi\)
−0.236237 + 0.971695i \(0.575914\pi\)
\(642\) −26387.5 −1.62217
\(643\) −27570.3 −1.69093 −0.845463 0.534035i \(-0.820675\pi\)
−0.845463 + 0.534035i \(0.820675\pi\)
\(644\) −26049.5 −1.59393
\(645\) 1025.15 0.0625816
\(646\) −4878.36 −0.297115
\(647\) 10873.6 0.660719 0.330360 0.943855i \(-0.392830\pi\)
0.330360 + 0.943855i \(0.392830\pi\)
\(648\) −4624.76 −0.280367
\(649\) −1000.43 −0.0605091
\(650\) −5209.24 −0.314343
\(651\) 1745.96 0.105114
\(652\) −3823.49 −0.229662
\(653\) −2866.96 −0.171811 −0.0859057 0.996303i \(-0.527378\pi\)
−0.0859057 + 0.996303i \(0.527378\pi\)
\(654\) 18270.6 1.09241
\(655\) 16682.3 0.995163
\(656\) 3735.96 0.222355
\(657\) 6283.50 0.373124
\(658\) −17026.6 −1.00876
\(659\) −5297.83 −0.313162 −0.156581 0.987665i \(-0.550047\pi\)
−0.156581 + 0.987665i \(0.550047\pi\)
\(660\) −12678.8 −0.747760
\(661\) 27215.1 1.60143 0.800716 0.599044i \(-0.204453\pi\)
0.800716 + 0.599044i \(0.204453\pi\)
\(662\) 4475.22 0.262741
\(663\) −830.509 −0.0486490
\(664\) −74783.7 −4.37074
\(665\) 3434.69 0.200288
\(666\) −8027.01 −0.467028
\(667\) −5540.10 −0.321610
\(668\) 35699.2 2.06773
\(669\) 4269.86 0.246760
\(670\) 52371.2 3.01981
\(671\) −671.000 −0.0386046
\(672\) 12560.1 0.721006
\(673\) 22581.3 1.29338 0.646691 0.762752i \(-0.276152\pi\)
0.646691 + 0.762752i \(0.276152\pi\)
\(674\) −33244.2 −1.89988
\(675\) 7676.90 0.437754
\(676\) −41485.1 −2.36033
\(677\) −5985.20 −0.339778 −0.169889 0.985463i \(-0.554341\pi\)
−0.169889 + 0.985463i \(0.554341\pi\)
\(678\) −30394.4 −1.72167
\(679\) −12534.8 −0.708458
\(680\) 90680.7 5.11389
\(681\) −12205.8 −0.686825
\(682\) −2343.44 −0.131576
\(683\) 9712.88 0.544148 0.272074 0.962276i \(-0.412290\pi\)
0.272074 + 0.962276i \(0.412290\pi\)
\(684\) −2044.41 −0.114284
\(685\) 37983.5 2.11865
\(686\) −35728.9 −1.98854
\(687\) 1917.28 0.106475
\(688\) 2444.04 0.135433
\(689\) −931.299 −0.0514944
\(690\) −30477.4 −1.68153
\(691\) 20436.0 1.12507 0.562533 0.826775i \(-0.309827\pi\)
0.562533 + 0.826775i \(0.309827\pi\)
\(692\) −14353.2 −0.788478
\(693\) 1405.04 0.0770174
\(694\) −17596.4 −0.962463
\(695\) 28679.3 1.56528
\(696\) 9818.06 0.534702
\(697\) −2026.74 −0.110141
\(698\) 28492.8 1.54508
\(699\) 10992.3 0.594805
\(700\) −76630.8 −4.13768
\(701\) −13067.5 −0.704069 −0.352035 0.935987i \(-0.614510\pi\)
−0.352035 + 0.935987i \(0.614510\pi\)
\(702\) −494.670 −0.0265956
\(703\) −2053.56 −0.110173
\(704\) −4124.35 −0.220799
\(705\) −14016.2 −0.748767
\(706\) −45596.4 −2.43065
\(707\) 3958.79 0.210588
\(708\) 5181.36 0.275039
\(709\) −26035.0 −1.37908 −0.689539 0.724249i \(-0.742187\pi\)
−0.689539 + 0.724249i \(0.742187\pi\)
\(710\) −68851.2 −3.63935
\(711\) 8434.79 0.444908
\(712\) −25561.7 −1.34546
\(713\) −3963.48 −0.208182
\(714\) −17364.1 −0.910131
\(715\) −784.836 −0.0410506
\(716\) 47490.8 2.47879
\(717\) 11999.7 0.625015
\(718\) −3662.12 −0.190347
\(719\) −2941.21 −0.152557 −0.0762785 0.997087i \(-0.524304\pi\)
−0.0762785 + 0.997087i \(0.524304\pi\)
\(720\) 26348.6 1.36383
\(721\) 5911.87 0.305367
\(722\) 34890.5 1.79846
\(723\) 4058.51 0.208766
\(724\) 5386.02 0.276478
\(725\) −16297.5 −0.834863
\(726\) −1885.86 −0.0964060
\(727\) 2186.49 0.111544 0.0557719 0.998444i \(-0.482238\pi\)
0.0557719 + 0.998444i \(0.482238\pi\)
\(728\) 2857.64 0.145483
\(729\) 729.000 0.0370370
\(730\) −73383.4 −3.72060
\(731\) −1325.87 −0.0670851
\(732\) 3475.19 0.175474
\(733\) 12452.5 0.627479 0.313740 0.949509i \(-0.398418\pi\)
0.313740 + 0.949509i \(0.398418\pi\)
\(734\) −10218.9 −0.513878
\(735\) −8593.16 −0.431243
\(736\) −28512.5 −1.42797
\(737\) 5480.82 0.273933
\(738\) −1207.17 −0.0602121
\(739\) −1009.12 −0.0502313 −0.0251157 0.999685i \(-0.507995\pi\)
−0.0251157 + 0.999685i \(0.507995\pi\)
\(740\) 65958.9 3.27662
\(741\) −126.552 −0.00627395
\(742\) −19471.3 −0.963362
\(743\) −5922.18 −0.292414 −0.146207 0.989254i \(-0.546707\pi\)
−0.146207 + 0.989254i \(0.546707\pi\)
\(744\) 7024.00 0.346119
\(745\) −44945.9 −2.21032
\(746\) 63936.5 3.13791
\(747\) 11788.1 0.577383
\(748\) 16398.1 0.801570
\(749\) −24028.6 −1.17221
\(750\) −50240.9 −2.44605
\(751\) −28675.3 −1.39331 −0.696654 0.717407i \(-0.745329\pi\)
−0.696654 + 0.717407i \(0.745329\pi\)
\(752\) −33415.8 −1.62041
\(753\) 13004.5 0.629364
\(754\) 1050.15 0.0507218
\(755\) −35905.8 −1.73079
\(756\) −7276.88 −0.350076
\(757\) 17950.6 0.861856 0.430928 0.902386i \(-0.358186\pi\)
0.430928 + 0.902386i \(0.358186\pi\)
\(758\) 46248.5 2.21612
\(759\) −3189.57 −0.152535
\(760\) 13817.8 0.659506
\(761\) 30285.6 1.44264 0.721321 0.692600i \(-0.243535\pi\)
0.721321 + 0.692600i \(0.243535\pi\)
\(762\) −12364.7 −0.587829
\(763\) 16637.3 0.789400
\(764\) 20354.9 0.963892
\(765\) −14294.0 −0.675555
\(766\) 37567.9 1.77204
\(767\) 320.734 0.0150991
\(768\) −15421.1 −0.724561
\(769\) −34159.7 −1.60186 −0.800931 0.598757i \(-0.795662\pi\)
−0.800931 + 0.598757i \(0.795662\pi\)
\(770\) −16409.1 −0.767979
\(771\) −19154.5 −0.894725
\(772\) −64471.4 −3.00567
\(773\) 26424.3 1.22952 0.614759 0.788715i \(-0.289253\pi\)
0.614759 + 0.788715i \(0.289253\pi\)
\(774\) −789.720 −0.0366743
\(775\) −11659.5 −0.540416
\(776\) −50427.7 −2.33280
\(777\) −7309.44 −0.337484
\(778\) −62916.4 −2.89931
\(779\) −308.831 −0.0142041
\(780\) 4064.76 0.186592
\(781\) −7205.52 −0.330133
\(782\) 39417.9 1.80254
\(783\) −1547.62 −0.0706352
\(784\) −20486.8 −0.933254
\(785\) −24537.0 −1.11562
\(786\) −12851.2 −0.583189
\(787\) 25200.9 1.14144 0.570720 0.821145i \(-0.306664\pi\)
0.570720 + 0.821145i \(0.306664\pi\)
\(788\) 65255.4 2.95004
\(789\) −693.205 −0.0312785
\(790\) −98507.9 −4.43640
\(791\) −27677.3 −1.24411
\(792\) 5652.49 0.253602
\(793\) 215.119 0.00963318
\(794\) −3284.06 −0.146784
\(795\) −16028.7 −0.715067
\(796\) −60014.1 −2.67229
\(797\) −4756.15 −0.211382 −0.105691 0.994399i \(-0.533705\pi\)
−0.105691 + 0.994399i \(0.533705\pi\)
\(798\) −2645.91 −0.117374
\(799\) 18127.9 0.802650
\(800\) −83876.4 −3.70685
\(801\) 4029.29 0.177738
\(802\) −18217.6 −0.802103
\(803\) −7679.83 −0.337503
\(804\) −28385.9 −1.24514
\(805\) −27752.9 −1.21511
\(806\) 751.295 0.0328328
\(807\) 7141.09 0.311497
\(808\) 15926.2 0.693420
\(809\) −26343.8 −1.14487 −0.572435 0.819950i \(-0.694001\pi\)
−0.572435 + 0.819950i \(0.694001\pi\)
\(810\) −8513.81 −0.369315
\(811\) 27595.0 1.19481 0.597406 0.801939i \(-0.296198\pi\)
0.597406 + 0.801939i \(0.296198\pi\)
\(812\) 15448.3 0.667648
\(813\) 15051.3 0.649287
\(814\) 9810.79 0.422442
\(815\) −4073.51 −0.175078
\(816\) −34078.0 −1.46197
\(817\) −202.035 −0.00865153
\(818\) 38406.5 1.64163
\(819\) −450.449 −0.0192185
\(820\) 9919.45 0.422442
\(821\) −14264.7 −0.606386 −0.303193 0.952929i \(-0.598053\pi\)
−0.303193 + 0.952929i \(0.598053\pi\)
\(822\) −29260.5 −1.24158
\(823\) 8243.99 0.349171 0.174585 0.984642i \(-0.444141\pi\)
0.174585 + 0.984642i \(0.444141\pi\)
\(824\) 23783.5 1.00551
\(825\) −9382.88 −0.395964
\(826\) 6705.81 0.282476
\(827\) 38487.5 1.61831 0.809155 0.587596i \(-0.199925\pi\)
0.809155 + 0.587596i \(0.199925\pi\)
\(828\) 16519.2 0.693334
\(829\) −25969.6 −1.08801 −0.544007 0.839081i \(-0.683093\pi\)
−0.544007 + 0.839081i \(0.683093\pi\)
\(830\) −137671. −5.75737
\(831\) 17240.2 0.719684
\(832\) 1322.25 0.0550970
\(833\) 11114.0 0.462276
\(834\) −22093.0 −0.917289
\(835\) 38033.6 1.57630
\(836\) 2498.72 0.103373
\(837\) −1107.19 −0.0457230
\(838\) 51916.0 2.14010
\(839\) 18635.0 0.766806 0.383403 0.923581i \(-0.374752\pi\)
0.383403 + 0.923581i \(0.374752\pi\)
\(840\) 49183.1 2.02021
\(841\) −21103.5 −0.865288
\(842\) 13094.1 0.535930
\(843\) 5886.68 0.240508
\(844\) 100453. 4.09682
\(845\) −44197.9 −1.79935
\(846\) 10797.4 0.438795
\(847\) −1717.27 −0.0696649
\(848\) −38213.6 −1.54748
\(849\) 4615.41 0.186573
\(850\) 115957. 4.67918
\(851\) 16593.1 0.668394
\(852\) 37318.3 1.50059
\(853\) 35743.1 1.43472 0.717362 0.696701i \(-0.245350\pi\)
0.717362 + 0.696701i \(0.245350\pi\)
\(854\) 4497.65 0.180218
\(855\) −2178.09 −0.0871220
\(856\) −96667.1 −3.85983
\(857\) 11207.6 0.446727 0.223363 0.974735i \(-0.428296\pi\)
0.223363 + 0.974735i \(0.428296\pi\)
\(858\) 604.597 0.0240566
\(859\) 42173.7 1.67514 0.837572 0.546328i \(-0.183975\pi\)
0.837572 + 0.546328i \(0.183975\pi\)
\(860\) 6489.22 0.257303
\(861\) −1099.25 −0.0435105
\(862\) −24600.7 −0.972046
\(863\) −27461.7 −1.08320 −0.541602 0.840635i \(-0.682182\pi\)
−0.541602 + 0.840635i \(0.682182\pi\)
\(864\) −7964.92 −0.313625
\(865\) −15291.8 −0.601082
\(866\) −13911.5 −0.545879
\(867\) 3748.10 0.146819
\(868\) 11052.0 0.432176
\(869\) −10309.2 −0.402434
\(870\) 18074.2 0.704338
\(871\) −1757.13 −0.0683558
\(872\) 66932.2 2.59932
\(873\) 7948.91 0.308167
\(874\) 6006.45 0.232461
\(875\) −45749.6 −1.76756
\(876\) 39774.8 1.53409
\(877\) −1472.63 −0.0567016 −0.0283508 0.999598i \(-0.509026\pi\)
−0.0283508 + 0.999598i \(0.509026\pi\)
\(878\) 19155.0 0.736275
\(879\) 4169.93 0.160009
\(880\) −32203.9 −1.23363
\(881\) 33279.2 1.27265 0.636326 0.771421i \(-0.280454\pi\)
0.636326 + 0.771421i \(0.280454\pi\)
\(882\) 6619.72 0.252718
\(883\) −5560.78 −0.211931 −0.105966 0.994370i \(-0.533793\pi\)
−0.105966 + 0.994370i \(0.533793\pi\)
\(884\) −5257.16 −0.200020
\(885\) 5520.18 0.209671
\(886\) 62597.4 2.37359
\(887\) −50200.0 −1.90028 −0.950142 0.311817i \(-0.899062\pi\)
−0.950142 + 0.311817i \(0.899062\pi\)
\(888\) −29405.9 −1.11126
\(889\) −11259.4 −0.424777
\(890\) −47057.1 −1.77231
\(891\) −891.000 −0.0335013
\(892\) 27028.4 1.01455
\(893\) 2762.30 0.103513
\(894\) 34624.0 1.29530
\(895\) 50596.3 1.88966
\(896\) −5848.41 −0.218060
\(897\) 1022.56 0.0380627
\(898\) 41106.0 1.52753
\(899\) 2350.49 0.0872005
\(900\) 48595.1 1.79982
\(901\) 20730.7 0.766524
\(902\) 1475.43 0.0544639
\(903\) −719.123 −0.0265016
\(904\) −111346. −4.09659
\(905\) 5738.22 0.210768
\(906\) 27660.0 1.01428
\(907\) −6586.91 −0.241141 −0.120570 0.992705i \(-0.538472\pi\)
−0.120570 + 0.992705i \(0.538472\pi\)
\(908\) −77263.3 −2.82387
\(909\) −2510.45 −0.0916021
\(910\) 5260.69 0.191637
\(911\) 23707.7 0.862208 0.431104 0.902302i \(-0.358124\pi\)
0.431104 + 0.902302i \(0.358124\pi\)
\(912\) −5192.76 −0.188541
\(913\) −14407.7 −0.522262
\(914\) 45204.4 1.63592
\(915\) 3702.44 0.133769
\(916\) 12136.4 0.437772
\(917\) −11702.4 −0.421424
\(918\) 11011.3 0.395891
\(919\) 20270.2 0.727586 0.363793 0.931480i \(-0.381482\pi\)
0.363793 + 0.931480i \(0.381482\pi\)
\(920\) −111650. −4.00108
\(921\) −7602.92 −0.272014
\(922\) 22488.0 0.803257
\(923\) 2310.06 0.0823796
\(924\) 8893.96 0.316656
\(925\) 48812.5 1.73508
\(926\) 35341.6 1.25421
\(927\) −3748.98 −0.132829
\(928\) 16909.0 0.598130
\(929\) −34261.8 −1.21000 −0.605001 0.796225i \(-0.706827\pi\)
−0.605001 + 0.796225i \(0.706827\pi\)
\(930\) 12930.6 0.455926
\(931\) 1693.53 0.0596167
\(932\) 69582.0 2.44553
\(933\) −22174.8 −0.778104
\(934\) −47170.3 −1.65253
\(935\) 17470.4 0.611063
\(936\) −1812.16 −0.0632824
\(937\) −17501.4 −0.610189 −0.305095 0.952322i \(-0.598688\pi\)
−0.305095 + 0.952322i \(0.598688\pi\)
\(938\) −36737.5 −1.27881
\(939\) −3766.28 −0.130892
\(940\) −88723.1 −3.07854
\(941\) 47973.9 1.66196 0.830980 0.556303i \(-0.187781\pi\)
0.830980 + 0.556303i \(0.187781\pi\)
\(942\) 18902.0 0.653781
\(943\) 2495.41 0.0861735
\(944\) 13160.6 0.453750
\(945\) −7752.72 −0.266874
\(946\) 965.214 0.0331732
\(947\) −25129.6 −0.862305 −0.431153 0.902279i \(-0.641893\pi\)
−0.431153 + 0.902279i \(0.641893\pi\)
\(948\) 53392.6 1.82923
\(949\) 2462.12 0.0842188
\(950\) 17669.4 0.603444
\(951\) 16948.5 0.577909
\(952\) −63611.0 −2.16559
\(953\) −37420.9 −1.27196 −0.635982 0.771704i \(-0.719405\pi\)
−0.635982 + 0.771704i \(0.719405\pi\)
\(954\) 12347.6 0.419046
\(955\) 21685.9 0.734806
\(956\) 75958.4 2.56974
\(957\) 1891.53 0.0638919
\(958\) 50684.5 1.70933
\(959\) −26644.8 −0.897190
\(960\) 22757.3 0.765093
\(961\) −28109.4 −0.943554
\(962\) −3145.29 −0.105414
\(963\) 15237.6 0.509891
\(964\) 25690.5 0.858337
\(965\) −68687.2 −2.29132
\(966\) 21379.4 0.712081
\(967\) −46220.4 −1.53707 −0.768536 0.639806i \(-0.779015\pi\)
−0.768536 + 0.639806i \(0.779015\pi\)
\(968\) −6908.60 −0.229391
\(969\) 2817.04 0.0933914
\(970\) −92833.3 −3.07288
\(971\) 24103.9 0.796632 0.398316 0.917248i \(-0.369595\pi\)
0.398316 + 0.917248i \(0.369595\pi\)
\(972\) 4614.60 0.152277
\(973\) −20118.0 −0.662851
\(974\) −78460.1 −2.58113
\(975\) 3008.11 0.0988066
\(976\) 8826.92 0.289490
\(977\) −12247.8 −0.401066 −0.200533 0.979687i \(-0.564267\pi\)
−0.200533 + 0.979687i \(0.564267\pi\)
\(978\) 3138.02 0.102600
\(979\) −4924.69 −0.160770
\(980\) −54395.0 −1.77305
\(981\) −10550.5 −0.343375
\(982\) 33271.5 1.08120
\(983\) 22411.3 0.727172 0.363586 0.931561i \(-0.381552\pi\)
0.363586 + 0.931561i \(0.381552\pi\)
\(984\) −4422.31 −0.143270
\(985\) 69522.5 2.24891
\(986\) −23376.3 −0.755024
\(987\) 9832.13 0.317082
\(988\) −801.078 −0.0257952
\(989\) 1632.47 0.0524870
\(990\) 10405.8 0.334058
\(991\) −11091.1 −0.355521 −0.177760 0.984074i \(-0.556885\pi\)
−0.177760 + 0.984074i \(0.556885\pi\)
\(992\) 12097.0 0.387177
\(993\) −2584.24 −0.0825865
\(994\) 48298.0 1.54117
\(995\) −63938.5 −2.03717
\(996\) 74619.3 2.37390
\(997\) −13750.9 −0.436805 −0.218402 0.975859i \(-0.570085\pi\)
−0.218402 + 0.975859i \(0.570085\pi\)
\(998\) −20684.2 −0.656058
\(999\) 4635.25 0.146800
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 2013.4.a.h.1.2 39
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2013.4.a.h.1.2 39 1.1 even 1 trivial