Properties

Label 8018.2.a.k.1.1
Level $8018$
Weight $2$
Character 8018.1
Self dual yes
Analytic conductor $64.024$
Analytic rank $0$
Dimension $49$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8018,2,Mod(1,8018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8018, 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("8018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8018.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: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(49\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 8018.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.18331 q^{3} +1.00000 q^{4} +4.19262 q^{5} -3.18331 q^{6} -3.25533 q^{7} +1.00000 q^{8} +7.13346 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.18331 q^{3} +1.00000 q^{4} +4.19262 q^{5} -3.18331 q^{6} -3.25533 q^{7} +1.00000 q^{8} +7.13346 q^{9} +4.19262 q^{10} +2.73492 q^{11} -3.18331 q^{12} -0.0802502 q^{13} -3.25533 q^{14} -13.3464 q^{15} +1.00000 q^{16} +6.27732 q^{17} +7.13346 q^{18} +1.00000 q^{19} +4.19262 q^{20} +10.3627 q^{21} +2.73492 q^{22} +7.19971 q^{23} -3.18331 q^{24} +12.5781 q^{25} -0.0802502 q^{26} -13.1581 q^{27} -3.25533 q^{28} +5.00770 q^{29} -13.3464 q^{30} +8.11016 q^{31} +1.00000 q^{32} -8.70610 q^{33} +6.27732 q^{34} -13.6484 q^{35} +7.13346 q^{36} -2.14709 q^{37} +1.00000 q^{38} +0.255461 q^{39} +4.19262 q^{40} -8.32464 q^{41} +10.3627 q^{42} -1.83568 q^{43} +2.73492 q^{44} +29.9079 q^{45} +7.19971 q^{46} -5.19115 q^{47} -3.18331 q^{48} +3.59720 q^{49} +12.5781 q^{50} -19.9827 q^{51} -0.0802502 q^{52} +4.03344 q^{53} -13.1581 q^{54} +11.4665 q^{55} -3.25533 q^{56} -3.18331 q^{57} +5.00770 q^{58} +2.23813 q^{59} -13.3464 q^{60} -8.13553 q^{61} +8.11016 q^{62} -23.2218 q^{63} +1.00000 q^{64} -0.336459 q^{65} -8.70610 q^{66} +9.56026 q^{67} +6.27732 q^{68} -22.9189 q^{69} -13.6484 q^{70} -11.2757 q^{71} +7.13346 q^{72} +14.6029 q^{73} -2.14709 q^{74} -40.0399 q^{75} +1.00000 q^{76} -8.90308 q^{77} +0.255461 q^{78} -16.1807 q^{79} +4.19262 q^{80} +20.4858 q^{81} -8.32464 q^{82} +0.187647 q^{83} +10.3627 q^{84} +26.3184 q^{85} -1.83568 q^{86} -15.9410 q^{87} +2.73492 q^{88} -6.14015 q^{89} +29.9079 q^{90} +0.261241 q^{91} +7.19971 q^{92} -25.8172 q^{93} -5.19115 q^{94} +4.19262 q^{95} -3.18331 q^{96} +16.8692 q^{97} +3.59720 q^{98} +19.5094 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.18331 −1.83788 −0.918942 0.394392i \(-0.870955\pi\)
−0.918942 + 0.394392i \(0.870955\pi\)
\(4\) 1.00000 0.500000
\(5\) 4.19262 1.87500 0.937499 0.347988i \(-0.113135\pi\)
0.937499 + 0.347988i \(0.113135\pi\)
\(6\) −3.18331 −1.29958
\(7\) −3.25533 −1.23040 −0.615200 0.788371i \(-0.710925\pi\)
−0.615200 + 0.788371i \(0.710925\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.13346 2.37782
\(10\) 4.19262 1.32582
\(11\) 2.73492 0.824610 0.412305 0.911046i \(-0.364724\pi\)
0.412305 + 0.911046i \(0.364724\pi\)
\(12\) −3.18331 −0.918942
\(13\) −0.0802502 −0.0222574 −0.0111287 0.999938i \(-0.503542\pi\)
−0.0111287 + 0.999938i \(0.503542\pi\)
\(14\) −3.25533 −0.870025
\(15\) −13.3464 −3.44603
\(16\) 1.00000 0.250000
\(17\) 6.27732 1.52247 0.761237 0.648473i \(-0.224592\pi\)
0.761237 + 0.648473i \(0.224592\pi\)
\(18\) 7.13346 1.68137
\(19\) 1.00000 0.229416
\(20\) 4.19262 0.937499
\(21\) 10.3627 2.26133
\(22\) 2.73492 0.583087
\(23\) 7.19971 1.50124 0.750621 0.660733i \(-0.229754\pi\)
0.750621 + 0.660733i \(0.229754\pi\)
\(24\) −3.18331 −0.649790
\(25\) 12.5781 2.51562
\(26\) −0.0802502 −0.0157384
\(27\) −13.1581 −2.53227
\(28\) −3.25533 −0.615200
\(29\) 5.00770 0.929906 0.464953 0.885335i \(-0.346071\pi\)
0.464953 + 0.885335i \(0.346071\pi\)
\(30\) −13.3464 −2.43671
\(31\) 8.11016 1.45663 0.728314 0.685243i \(-0.240304\pi\)
0.728314 + 0.685243i \(0.240304\pi\)
\(32\) 1.00000 0.176777
\(33\) −8.70610 −1.51554
\(34\) 6.27732 1.07655
\(35\) −13.6484 −2.30700
\(36\) 7.13346 1.18891
\(37\) −2.14709 −0.352979 −0.176490 0.984302i \(-0.556474\pi\)
−0.176490 + 0.984302i \(0.556474\pi\)
\(38\) 1.00000 0.162221
\(39\) 0.255461 0.0409065
\(40\) 4.19262 0.662912
\(41\) −8.32464 −1.30009 −0.650045 0.759896i \(-0.725250\pi\)
−0.650045 + 0.759896i \(0.725250\pi\)
\(42\) 10.3627 1.59901
\(43\) −1.83568 −0.279938 −0.139969 0.990156i \(-0.544700\pi\)
−0.139969 + 0.990156i \(0.544700\pi\)
\(44\) 2.73492 0.412305
\(45\) 29.9079 4.45841
\(46\) 7.19971 1.06154
\(47\) −5.19115 −0.757207 −0.378603 0.925559i \(-0.623596\pi\)
−0.378603 + 0.925559i \(0.623596\pi\)
\(48\) −3.18331 −0.459471
\(49\) 3.59720 0.513886
\(50\) 12.5781 1.77881
\(51\) −19.9827 −2.79813
\(52\) −0.0802502 −0.0111287
\(53\) 4.03344 0.554035 0.277018 0.960865i \(-0.410654\pi\)
0.277018 + 0.960865i \(0.410654\pi\)
\(54\) −13.1581 −1.79059
\(55\) 11.4665 1.54614
\(56\) −3.25533 −0.435012
\(57\) −3.18331 −0.421640
\(58\) 5.00770 0.657543
\(59\) 2.23813 0.291379 0.145690 0.989330i \(-0.453460\pi\)
0.145690 + 0.989330i \(0.453460\pi\)
\(60\) −13.3464 −1.72301
\(61\) −8.13553 −1.04165 −0.520824 0.853664i \(-0.674375\pi\)
−0.520824 + 0.853664i \(0.674375\pi\)
\(62\) 8.11016 1.02999
\(63\) −23.2218 −2.92567
\(64\) 1.00000 0.125000
\(65\) −0.336459 −0.0417326
\(66\) −8.70610 −1.07165
\(67\) 9.56026 1.16797 0.583986 0.811764i \(-0.301492\pi\)
0.583986 + 0.811764i \(0.301492\pi\)
\(68\) 6.27732 0.761237
\(69\) −22.9189 −2.75911
\(70\) −13.6484 −1.63129
\(71\) −11.2757 −1.33817 −0.669087 0.743184i \(-0.733315\pi\)
−0.669087 + 0.743184i \(0.733315\pi\)
\(72\) 7.13346 0.840686
\(73\) 14.6029 1.70914 0.854569 0.519339i \(-0.173822\pi\)
0.854569 + 0.519339i \(0.173822\pi\)
\(74\) −2.14709 −0.249594
\(75\) −40.0399 −4.62341
\(76\) 1.00000 0.114708
\(77\) −8.90308 −1.01460
\(78\) 0.255461 0.0289253
\(79\) −16.1807 −1.82047 −0.910236 0.414089i \(-0.864100\pi\)
−0.910236 + 0.414089i \(0.864100\pi\)
\(80\) 4.19262 0.468749
\(81\) 20.4858 2.27621
\(82\) −8.32464 −0.919302
\(83\) 0.187647 0.0205969 0.0102985 0.999947i \(-0.496722\pi\)
0.0102985 + 0.999947i \(0.496722\pi\)
\(84\) 10.3627 1.13067
\(85\) 26.3184 2.85464
\(86\) −1.83568 −0.197946
\(87\) −15.9410 −1.70906
\(88\) 2.73492 0.291544
\(89\) −6.14015 −0.650855 −0.325428 0.945567i \(-0.605508\pi\)
−0.325428 + 0.945567i \(0.605508\pi\)
\(90\) 29.9079 3.15257
\(91\) 0.261241 0.0273855
\(92\) 7.19971 0.750621
\(93\) −25.8172 −2.67711
\(94\) −5.19115 −0.535426
\(95\) 4.19262 0.430154
\(96\) −3.18331 −0.324895
\(97\) 16.8692 1.71280 0.856401 0.516310i \(-0.172695\pi\)
0.856401 + 0.516310i \(0.172695\pi\)
\(98\) 3.59720 0.363372
\(99\) 19.5094 1.96077
\(100\) 12.5781 1.25781
\(101\) −8.91662 −0.887237 −0.443618 0.896216i \(-0.646305\pi\)
−0.443618 + 0.896216i \(0.646305\pi\)
\(102\) −19.9827 −1.97858
\(103\) −1.91103 −0.188300 −0.0941498 0.995558i \(-0.530013\pi\)
−0.0941498 + 0.995558i \(0.530013\pi\)
\(104\) −0.0802502 −0.00786918
\(105\) 43.4470 4.24000
\(106\) 4.03344 0.391762
\(107\) 5.08997 0.492066 0.246033 0.969261i \(-0.420873\pi\)
0.246033 + 0.969261i \(0.420873\pi\)
\(108\) −13.1581 −1.26614
\(109\) 3.01265 0.288559 0.144280 0.989537i \(-0.453913\pi\)
0.144280 + 0.989537i \(0.453913\pi\)
\(110\) 11.4665 1.09329
\(111\) 6.83485 0.648735
\(112\) −3.25533 −0.307600
\(113\) 15.5786 1.46551 0.732757 0.680490i \(-0.238233\pi\)
0.732757 + 0.680490i \(0.238233\pi\)
\(114\) −3.18331 −0.298144
\(115\) 30.1857 2.81483
\(116\) 5.00770 0.464953
\(117\) −0.572461 −0.0529241
\(118\) 2.23813 0.206036
\(119\) −20.4348 −1.87325
\(120\) −13.3464 −1.21836
\(121\) −3.52021 −0.320019
\(122\) −8.13553 −0.736557
\(123\) 26.4999 2.38942
\(124\) 8.11016 0.728314
\(125\) 31.7720 2.84178
\(126\) −23.2218 −2.06876
\(127\) 4.94018 0.438370 0.219185 0.975683i \(-0.429660\pi\)
0.219185 + 0.975683i \(0.429660\pi\)
\(128\) 1.00000 0.0883883
\(129\) 5.84353 0.514495
\(130\) −0.336459 −0.0295094
\(131\) −2.50142 −0.218550 −0.109275 0.994012i \(-0.534853\pi\)
−0.109275 + 0.994012i \(0.534853\pi\)
\(132\) −8.70610 −0.757769
\(133\) −3.25533 −0.282273
\(134\) 9.56026 0.825881
\(135\) −55.1668 −4.74801
\(136\) 6.27732 0.538276
\(137\) −7.48159 −0.639196 −0.319598 0.947553i \(-0.603548\pi\)
−0.319598 + 0.947553i \(0.603548\pi\)
\(138\) −22.9189 −1.95099
\(139\) −8.29124 −0.703254 −0.351627 0.936140i \(-0.614371\pi\)
−0.351627 + 0.936140i \(0.614371\pi\)
\(140\) −13.6484 −1.15350
\(141\) 16.5250 1.39166
\(142\) −11.2757 −0.946232
\(143\) −0.219478 −0.0183537
\(144\) 7.13346 0.594455
\(145\) 20.9954 1.74357
\(146\) 14.6029 1.20854
\(147\) −11.4510 −0.944464
\(148\) −2.14709 −0.176490
\(149\) 18.1912 1.49028 0.745141 0.666907i \(-0.232382\pi\)
0.745141 + 0.666907i \(0.232382\pi\)
\(150\) −40.0399 −3.26925
\(151\) −9.58416 −0.779948 −0.389974 0.920826i \(-0.627516\pi\)
−0.389974 + 0.920826i \(0.627516\pi\)
\(152\) 1.00000 0.0811107
\(153\) 44.7790 3.62017
\(154\) −8.90308 −0.717431
\(155\) 34.0029 2.73118
\(156\) 0.255461 0.0204533
\(157\) −10.6000 −0.845973 −0.422986 0.906136i \(-0.639018\pi\)
−0.422986 + 0.906136i \(0.639018\pi\)
\(158\) −16.1807 −1.28727
\(159\) −12.8397 −1.01825
\(160\) 4.19262 0.331456
\(161\) −23.4375 −1.84713
\(162\) 20.4858 1.60952
\(163\) −10.7524 −0.842191 −0.421095 0.907016i \(-0.638354\pi\)
−0.421095 + 0.907016i \(0.638354\pi\)
\(164\) −8.32464 −0.650045
\(165\) −36.5014 −2.84163
\(166\) 0.187647 0.0145642
\(167\) −12.8734 −0.996175 −0.498087 0.867127i \(-0.665964\pi\)
−0.498087 + 0.867127i \(0.665964\pi\)
\(168\) 10.3627 0.799503
\(169\) −12.9936 −0.999505
\(170\) 26.3184 2.01853
\(171\) 7.13346 0.545509
\(172\) −1.83568 −0.139969
\(173\) −16.6802 −1.26817 −0.634086 0.773263i \(-0.718623\pi\)
−0.634086 + 0.773263i \(0.718623\pi\)
\(174\) −15.9410 −1.20849
\(175\) −40.9459 −3.09522
\(176\) 2.73492 0.206152
\(177\) −7.12465 −0.535522
\(178\) −6.14015 −0.460224
\(179\) 5.86458 0.438339 0.219170 0.975687i \(-0.429665\pi\)
0.219170 + 0.975687i \(0.429665\pi\)
\(180\) 29.9079 2.22920
\(181\) −16.1501 −1.20043 −0.600215 0.799839i \(-0.704918\pi\)
−0.600215 + 0.799839i \(0.704918\pi\)
\(182\) 0.261241 0.0193645
\(183\) 25.8979 1.91443
\(184\) 7.19971 0.530769
\(185\) −9.00193 −0.661835
\(186\) −25.8172 −1.89301
\(187\) 17.1680 1.25545
\(188\) −5.19115 −0.378603
\(189\) 42.8339 3.11571
\(190\) 4.19262 0.304165
\(191\) 7.32475 0.530000 0.265000 0.964248i \(-0.414628\pi\)
0.265000 + 0.964248i \(0.414628\pi\)
\(192\) −3.18331 −0.229736
\(193\) −12.4506 −0.896211 −0.448105 0.893981i \(-0.647901\pi\)
−0.448105 + 0.893981i \(0.647901\pi\)
\(194\) 16.8692 1.21113
\(195\) 1.07105 0.0766996
\(196\) 3.59720 0.256943
\(197\) −8.70333 −0.620086 −0.310043 0.950722i \(-0.600344\pi\)
−0.310043 + 0.950722i \(0.600344\pi\)
\(198\) 19.5094 1.38648
\(199\) 3.37370 0.239155 0.119577 0.992825i \(-0.461846\pi\)
0.119577 + 0.992825i \(0.461846\pi\)
\(200\) 12.5781 0.889405
\(201\) −30.4333 −2.14660
\(202\) −8.91662 −0.627371
\(203\) −16.3017 −1.14416
\(204\) −19.9827 −1.39907
\(205\) −34.9021 −2.43767
\(206\) −1.91103 −0.133148
\(207\) 51.3588 3.56968
\(208\) −0.0802502 −0.00556435
\(209\) 2.73492 0.189178
\(210\) 43.4470 2.99813
\(211\) 1.00000 0.0688428
\(212\) 4.03344 0.277018
\(213\) 35.8939 2.45941
\(214\) 5.08997 0.347944
\(215\) −7.69631 −0.524884
\(216\) −13.1581 −0.895294
\(217\) −26.4013 −1.79224
\(218\) 3.01265 0.204042
\(219\) −46.4855 −3.14120
\(220\) 11.4665 0.773071
\(221\) −0.503756 −0.0338863
\(222\) 6.83485 0.458725
\(223\) −16.6419 −1.11442 −0.557211 0.830371i \(-0.688129\pi\)
−0.557211 + 0.830371i \(0.688129\pi\)
\(224\) −3.25533 −0.217506
\(225\) 89.7252 5.98168
\(226\) 15.5786 1.03628
\(227\) 16.9296 1.12366 0.561829 0.827253i \(-0.310098\pi\)
0.561829 + 0.827253i \(0.310098\pi\)
\(228\) −3.18331 −0.210820
\(229\) 12.0050 0.793315 0.396657 0.917967i \(-0.370170\pi\)
0.396657 + 0.917967i \(0.370170\pi\)
\(230\) 30.1857 1.99038
\(231\) 28.3413 1.86472
\(232\) 5.00770 0.328771
\(233\) 26.4162 1.73059 0.865293 0.501267i \(-0.167132\pi\)
0.865293 + 0.501267i \(0.167132\pi\)
\(234\) −0.572461 −0.0374230
\(235\) −21.7645 −1.41976
\(236\) 2.23813 0.145690
\(237\) 51.5082 3.34582
\(238\) −20.4348 −1.32459
\(239\) −8.87463 −0.574052 −0.287026 0.957923i \(-0.592667\pi\)
−0.287026 + 0.957923i \(0.592667\pi\)
\(240\) −13.3464 −0.861507
\(241\) −25.8003 −1.66195 −0.830973 0.556313i \(-0.812215\pi\)
−0.830973 + 0.556313i \(0.812215\pi\)
\(242\) −3.52021 −0.226288
\(243\) −25.7386 −1.65113
\(244\) −8.13553 −0.520824
\(245\) 15.0817 0.963536
\(246\) 26.4999 1.68957
\(247\) −0.0802502 −0.00510620
\(248\) 8.11016 0.514996
\(249\) −0.597338 −0.0378548
\(250\) 31.7720 2.00944
\(251\) 15.2550 0.962886 0.481443 0.876477i \(-0.340113\pi\)
0.481443 + 0.876477i \(0.340113\pi\)
\(252\) −23.2218 −1.46284
\(253\) 19.6906 1.23794
\(254\) 4.94018 0.309974
\(255\) −83.7798 −5.24649
\(256\) 1.00000 0.0625000
\(257\) 9.48851 0.591877 0.295939 0.955207i \(-0.404368\pi\)
0.295939 + 0.955207i \(0.404368\pi\)
\(258\) 5.84353 0.363803
\(259\) 6.98949 0.434306
\(260\) −0.336459 −0.0208663
\(261\) 35.7222 2.21115
\(262\) −2.50142 −0.154538
\(263\) −7.79152 −0.480446 −0.240223 0.970718i \(-0.577221\pi\)
−0.240223 + 0.970718i \(0.577221\pi\)
\(264\) −8.70610 −0.535823
\(265\) 16.9107 1.03882
\(266\) −3.25533 −0.199597
\(267\) 19.5460 1.19620
\(268\) 9.56026 0.583986
\(269\) 9.31142 0.567727 0.283864 0.958865i \(-0.408384\pi\)
0.283864 + 0.958865i \(0.408384\pi\)
\(270\) −55.1668 −3.35735
\(271\) −7.02734 −0.426881 −0.213440 0.976956i \(-0.568467\pi\)
−0.213440 + 0.976956i \(0.568467\pi\)
\(272\) 6.27732 0.380619
\(273\) −0.831611 −0.0503314
\(274\) −7.48159 −0.451980
\(275\) 34.4001 2.07440
\(276\) −22.9189 −1.37956
\(277\) 16.6198 0.998587 0.499294 0.866433i \(-0.333593\pi\)
0.499294 + 0.866433i \(0.333593\pi\)
\(278\) −8.29124 −0.497275
\(279\) 57.8535 3.46360
\(280\) −13.6484 −0.815647
\(281\) 23.5129 1.40266 0.701332 0.712835i \(-0.252589\pi\)
0.701332 + 0.712835i \(0.252589\pi\)
\(282\) 16.5250 0.984051
\(283\) −3.62052 −0.215217 −0.107609 0.994193i \(-0.534319\pi\)
−0.107609 + 0.994193i \(0.534319\pi\)
\(284\) −11.2757 −0.669087
\(285\) −13.3464 −0.790573
\(286\) −0.219478 −0.0129780
\(287\) 27.0995 1.59963
\(288\) 7.13346 0.420343
\(289\) 22.4048 1.31793
\(290\) 20.9954 1.23289
\(291\) −53.6997 −3.14793
\(292\) 14.6029 0.854569
\(293\) −21.8893 −1.27879 −0.639395 0.768879i \(-0.720815\pi\)
−0.639395 + 0.768879i \(0.720815\pi\)
\(294\) −11.4510 −0.667837
\(295\) 9.38363 0.546336
\(296\) −2.14709 −0.124797
\(297\) −35.9863 −2.08814
\(298\) 18.1912 1.05379
\(299\) −0.577778 −0.0334137
\(300\) −40.0399 −2.31171
\(301\) 5.97575 0.344437
\(302\) −9.58416 −0.551506
\(303\) 28.3843 1.63064
\(304\) 1.00000 0.0573539
\(305\) −34.1092 −1.95309
\(306\) 44.7790 2.55985
\(307\) −3.48408 −0.198847 −0.0994236 0.995045i \(-0.531700\pi\)
−0.0994236 + 0.995045i \(0.531700\pi\)
\(308\) −8.90308 −0.507300
\(309\) 6.08340 0.346073
\(310\) 34.0029 1.93123
\(311\) −29.3947 −1.66682 −0.833410 0.552655i \(-0.813615\pi\)
−0.833410 + 0.552655i \(0.813615\pi\)
\(312\) 0.255461 0.0144626
\(313\) 24.7919 1.40132 0.700659 0.713496i \(-0.252889\pi\)
0.700659 + 0.713496i \(0.252889\pi\)
\(314\) −10.6000 −0.598193
\(315\) −97.3602 −5.48563
\(316\) −16.1807 −0.910236
\(317\) −17.0015 −0.954898 −0.477449 0.878660i \(-0.658438\pi\)
−0.477449 + 0.878660i \(0.658438\pi\)
\(318\) −12.8397 −0.720014
\(319\) 13.6957 0.766809
\(320\) 4.19262 0.234375
\(321\) −16.2030 −0.904361
\(322\) −23.4375 −1.30612
\(323\) 6.27732 0.349280
\(324\) 20.4858 1.13810
\(325\) −1.00939 −0.0559911
\(326\) −10.7524 −0.595519
\(327\) −9.59019 −0.530339
\(328\) −8.32464 −0.459651
\(329\) 16.8989 0.931668
\(330\) −36.5014 −2.00934
\(331\) 18.4660 1.01499 0.507493 0.861656i \(-0.330572\pi\)
0.507493 + 0.861656i \(0.330572\pi\)
\(332\) 0.187647 0.0102985
\(333\) −15.3162 −0.839321
\(334\) −12.8734 −0.704402
\(335\) 40.0826 2.18995
\(336\) 10.3627 0.565334
\(337\) −10.9336 −0.595589 −0.297795 0.954630i \(-0.596251\pi\)
−0.297795 + 0.954630i \(0.596251\pi\)
\(338\) −12.9936 −0.706756
\(339\) −49.5916 −2.69345
\(340\) 26.3184 1.42732
\(341\) 22.1807 1.20115
\(342\) 7.13346 0.385733
\(343\) 11.0772 0.598115
\(344\) −1.83568 −0.0989732
\(345\) −96.0903 −5.17333
\(346\) −16.6802 −0.896732
\(347\) 29.0472 1.55933 0.779667 0.626195i \(-0.215388\pi\)
0.779667 + 0.626195i \(0.215388\pi\)
\(348\) −15.9410 −0.854530
\(349\) 4.58892 0.245640 0.122820 0.992429i \(-0.460806\pi\)
0.122820 + 0.992429i \(0.460806\pi\)
\(350\) −40.9459 −2.18865
\(351\) 1.05594 0.0563618
\(352\) 2.73492 0.145772
\(353\) 26.3882 1.40450 0.702250 0.711930i \(-0.252179\pi\)
0.702250 + 0.711930i \(0.252179\pi\)
\(354\) −7.12465 −0.378671
\(355\) −47.2746 −2.50907
\(356\) −6.14015 −0.325428
\(357\) 65.0503 3.44282
\(358\) 5.86458 0.309953
\(359\) 15.7431 0.830887 0.415444 0.909619i \(-0.363626\pi\)
0.415444 + 0.909619i \(0.363626\pi\)
\(360\) 29.9079 1.57628
\(361\) 1.00000 0.0526316
\(362\) −16.1501 −0.848833
\(363\) 11.2059 0.588158
\(364\) 0.261241 0.0136928
\(365\) 61.2243 3.20463
\(366\) 25.8979 1.35371
\(367\) 23.7044 1.23736 0.618679 0.785644i \(-0.287668\pi\)
0.618679 + 0.785644i \(0.287668\pi\)
\(368\) 7.19971 0.375311
\(369\) −59.3834 −3.09138
\(370\) −9.00193 −0.467988
\(371\) −13.1302 −0.681686
\(372\) −25.8172 −1.33856
\(373\) −25.4986 −1.32027 −0.660133 0.751148i \(-0.729500\pi\)
−0.660133 + 0.751148i \(0.729500\pi\)
\(374\) 17.1680 0.887735
\(375\) −101.140 −5.22286
\(376\) −5.19115 −0.267713
\(377\) −0.401868 −0.0206973
\(378\) 42.8339 2.20314
\(379\) −8.82584 −0.453353 −0.226676 0.973970i \(-0.572786\pi\)
−0.226676 + 0.973970i \(0.572786\pi\)
\(380\) 4.19262 0.215077
\(381\) −15.7261 −0.805674
\(382\) 7.32475 0.374767
\(383\) −3.69767 −0.188942 −0.0944709 0.995528i \(-0.530116\pi\)
−0.0944709 + 0.995528i \(0.530116\pi\)
\(384\) −3.18331 −0.162448
\(385\) −37.3273 −1.90237
\(386\) −12.4506 −0.633717
\(387\) −13.0947 −0.665643
\(388\) 16.8692 0.856401
\(389\) 25.2395 1.27969 0.639847 0.768502i \(-0.278998\pi\)
0.639847 + 0.768502i \(0.278998\pi\)
\(390\) 1.07105 0.0542348
\(391\) 45.1949 2.28560
\(392\) 3.59720 0.181686
\(393\) 7.96278 0.401669
\(394\) −8.70333 −0.438467
\(395\) −67.8396 −3.41338
\(396\) 19.5094 0.980386
\(397\) 29.1297 1.46198 0.730990 0.682388i \(-0.239059\pi\)
0.730990 + 0.682388i \(0.239059\pi\)
\(398\) 3.37370 0.169108
\(399\) 10.3627 0.518786
\(400\) 12.5781 0.628904
\(401\) −14.9761 −0.747872 −0.373936 0.927455i \(-0.621992\pi\)
−0.373936 + 0.927455i \(0.621992\pi\)
\(402\) −30.4333 −1.51787
\(403\) −0.650842 −0.0324207
\(404\) −8.91662 −0.443618
\(405\) 85.8894 4.26788
\(406\) −16.3017 −0.809041
\(407\) −5.87212 −0.291070
\(408\) −19.9827 −0.989289
\(409\) −37.1151 −1.83522 −0.917611 0.397480i \(-0.869885\pi\)
−0.917611 + 0.397480i \(0.869885\pi\)
\(410\) −34.9021 −1.72369
\(411\) 23.8162 1.17477
\(412\) −1.91103 −0.0941498
\(413\) −7.28586 −0.358513
\(414\) 51.3588 2.52415
\(415\) 0.786733 0.0386192
\(416\) −0.0802502 −0.00393459
\(417\) 26.3936 1.29250
\(418\) 2.73492 0.133769
\(419\) −7.10982 −0.347337 −0.173669 0.984804i \(-0.555562\pi\)
−0.173669 + 0.984804i \(0.555562\pi\)
\(420\) 43.4470 2.12000
\(421\) −10.7837 −0.525568 −0.262784 0.964855i \(-0.584641\pi\)
−0.262784 + 0.964855i \(0.584641\pi\)
\(422\) 1.00000 0.0486792
\(423\) −37.0308 −1.80050
\(424\) 4.03344 0.195881
\(425\) 78.9567 3.82996
\(426\) 35.8939 1.73907
\(427\) 26.4839 1.28164
\(428\) 5.08997 0.246033
\(429\) 0.698666 0.0337319
\(430\) −7.69631 −0.371149
\(431\) −25.6930 −1.23759 −0.618795 0.785553i \(-0.712379\pi\)
−0.618795 + 0.785553i \(0.712379\pi\)
\(432\) −13.1581 −0.633068
\(433\) 10.2487 0.492519 0.246260 0.969204i \(-0.420798\pi\)
0.246260 + 0.969204i \(0.420798\pi\)
\(434\) −26.4013 −1.26730
\(435\) −66.8348 −3.20448
\(436\) 3.01265 0.144280
\(437\) 7.19971 0.344409
\(438\) −46.4855 −2.22116
\(439\) 13.7272 0.655165 0.327582 0.944823i \(-0.393766\pi\)
0.327582 + 0.944823i \(0.393766\pi\)
\(440\) 11.4665 0.546644
\(441\) 25.6605 1.22193
\(442\) −0.503756 −0.0239612
\(443\) 38.6960 1.83850 0.919252 0.393670i \(-0.128795\pi\)
0.919252 + 0.393670i \(0.128795\pi\)
\(444\) 6.83485 0.324368
\(445\) −25.7434 −1.22035
\(446\) −16.6419 −0.788015
\(447\) −57.9083 −2.73897
\(448\) −3.25533 −0.153800
\(449\) 32.7741 1.54671 0.773353 0.633975i \(-0.218578\pi\)
0.773353 + 0.633975i \(0.218578\pi\)
\(450\) 89.7252 4.22969
\(451\) −22.7672 −1.07207
\(452\) 15.5786 0.732757
\(453\) 30.5093 1.43345
\(454\) 16.9296 0.794546
\(455\) 1.09529 0.0513478
\(456\) −3.18331 −0.149072
\(457\) −17.0309 −0.796671 −0.398336 0.917240i \(-0.630412\pi\)
−0.398336 + 0.917240i \(0.630412\pi\)
\(458\) 12.0050 0.560958
\(459\) −82.5975 −3.85532
\(460\) 30.1857 1.40741
\(461\) 29.1873 1.35939 0.679694 0.733496i \(-0.262113\pi\)
0.679694 + 0.733496i \(0.262113\pi\)
\(462\) 28.3413 1.31856
\(463\) −26.4771 −1.23050 −0.615248 0.788333i \(-0.710944\pi\)
−0.615248 + 0.788333i \(0.710944\pi\)
\(464\) 5.00770 0.232476
\(465\) −108.242 −5.01958
\(466\) 26.4162 1.22371
\(467\) 10.0890 0.466863 0.233431 0.972373i \(-0.425005\pi\)
0.233431 + 0.972373i \(0.425005\pi\)
\(468\) −0.572461 −0.0264620
\(469\) −31.1219 −1.43707
\(470\) −21.7645 −1.00392
\(471\) 33.7431 1.55480
\(472\) 2.23813 0.103018
\(473\) −5.02044 −0.230840
\(474\) 51.5082 2.36585
\(475\) 12.5781 0.577122
\(476\) −20.4348 −0.936627
\(477\) 28.7724 1.31740
\(478\) −8.87463 −0.405916
\(479\) 28.8990 1.32043 0.660215 0.751077i \(-0.270465\pi\)
0.660215 + 0.751077i \(0.270465\pi\)
\(480\) −13.3464 −0.609178
\(481\) 0.172304 0.00785640
\(482\) −25.8003 −1.17517
\(483\) 74.6087 3.39481
\(484\) −3.52021 −0.160009
\(485\) 70.7260 3.21150
\(486\) −25.7386 −1.16752
\(487\) 16.4153 0.743847 0.371923 0.928263i \(-0.378698\pi\)
0.371923 + 0.928263i \(0.378698\pi\)
\(488\) −8.13553 −0.368278
\(489\) 34.2281 1.54785
\(490\) 15.0817 0.681323
\(491\) 39.1618 1.76735 0.883673 0.468105i \(-0.155063\pi\)
0.883673 + 0.468105i \(0.155063\pi\)
\(492\) 26.4999 1.19471
\(493\) 31.4349 1.41576
\(494\) −0.0802502 −0.00361063
\(495\) 81.7957 3.67644
\(496\) 8.11016 0.364157
\(497\) 36.7060 1.64649
\(498\) −0.597338 −0.0267674
\(499\) −30.6427 −1.37176 −0.685879 0.727716i \(-0.740582\pi\)
−0.685879 + 0.727716i \(0.740582\pi\)
\(500\) 31.7720 1.42089
\(501\) 40.9801 1.83085
\(502\) 15.2550 0.680863
\(503\) −18.0073 −0.802906 −0.401453 0.915880i \(-0.631495\pi\)
−0.401453 + 0.915880i \(0.631495\pi\)
\(504\) −23.2218 −1.03438
\(505\) −37.3840 −1.66357
\(506\) 19.6906 0.875355
\(507\) 41.3625 1.83697
\(508\) 4.94018 0.219185
\(509\) −31.9643 −1.41679 −0.708396 0.705815i \(-0.750581\pi\)
−0.708396 + 0.705815i \(0.750581\pi\)
\(510\) −83.7798 −3.70983
\(511\) −47.5372 −2.10292
\(512\) 1.00000 0.0441942
\(513\) −13.1581 −0.580943
\(514\) 9.48851 0.418520
\(515\) −8.01223 −0.353061
\(516\) 5.84353 0.257247
\(517\) −14.1974 −0.624400
\(518\) 6.98949 0.307101
\(519\) 53.0982 2.33075
\(520\) −0.336459 −0.0147547
\(521\) −9.32473 −0.408524 −0.204262 0.978916i \(-0.565479\pi\)
−0.204262 + 0.978916i \(0.565479\pi\)
\(522\) 35.7222 1.56352
\(523\) 4.33459 0.189539 0.0947693 0.995499i \(-0.469789\pi\)
0.0947693 + 0.995499i \(0.469789\pi\)
\(524\) −2.50142 −0.109275
\(525\) 130.343 5.68865
\(526\) −7.79152 −0.339726
\(527\) 50.9101 2.21768
\(528\) −8.70610 −0.378884
\(529\) 28.8358 1.25373
\(530\) 16.9107 0.734553
\(531\) 15.9656 0.692848
\(532\) −3.25533 −0.141137
\(533\) 0.668053 0.0289366
\(534\) 19.5460 0.845839
\(535\) 21.3403 0.922624
\(536\) 9.56026 0.412941
\(537\) −18.6688 −0.805617
\(538\) 9.31142 0.401444
\(539\) 9.83807 0.423756
\(540\) −55.1668 −2.37400
\(541\) −33.0984 −1.42301 −0.711505 0.702681i \(-0.751986\pi\)
−0.711505 + 0.702681i \(0.751986\pi\)
\(542\) −7.02734 −0.301850
\(543\) 51.4109 2.20625
\(544\) 6.27732 0.269138
\(545\) 12.6309 0.541048
\(546\) −0.831611 −0.0355897
\(547\) −31.3055 −1.33852 −0.669262 0.743026i \(-0.733390\pi\)
−0.669262 + 0.743026i \(0.733390\pi\)
\(548\) −7.48159 −0.319598
\(549\) −58.0345 −2.47685
\(550\) 34.4001 1.46682
\(551\) 5.00770 0.213335
\(552\) −22.9189 −0.975493
\(553\) 52.6736 2.23991
\(554\) 16.6198 0.706108
\(555\) 28.6559 1.21638
\(556\) −8.29124 −0.351627
\(557\) −7.90195 −0.334817 −0.167408 0.985888i \(-0.553540\pi\)
−0.167408 + 0.985888i \(0.553540\pi\)
\(558\) 57.8535 2.44913
\(559\) 0.147314 0.00623070
\(560\) −13.6484 −0.576750
\(561\) −54.6510 −2.30737
\(562\) 23.5129 0.991834
\(563\) 36.2460 1.52759 0.763794 0.645460i \(-0.223334\pi\)
0.763794 + 0.645460i \(0.223334\pi\)
\(564\) 16.5250 0.695829
\(565\) 65.3153 2.74784
\(566\) −3.62052 −0.152182
\(567\) −66.6883 −2.80064
\(568\) −11.2757 −0.473116
\(569\) −34.0957 −1.42937 −0.714683 0.699449i \(-0.753429\pi\)
−0.714683 + 0.699449i \(0.753429\pi\)
\(570\) −13.3464 −0.559020
\(571\) −0.862828 −0.0361082 −0.0180541 0.999837i \(-0.505747\pi\)
−0.0180541 + 0.999837i \(0.505747\pi\)
\(572\) −0.219478 −0.00917683
\(573\) −23.3169 −0.974079
\(574\) 27.0995 1.13111
\(575\) 90.5585 3.77655
\(576\) 7.13346 0.297227
\(577\) 13.7947 0.574282 0.287141 0.957888i \(-0.407295\pi\)
0.287141 + 0.957888i \(0.407295\pi\)
\(578\) 22.4048 0.931917
\(579\) 39.6340 1.64713
\(580\) 20.9954 0.871786
\(581\) −0.610853 −0.0253425
\(582\) −53.6997 −2.22593
\(583\) 11.0311 0.456863
\(584\) 14.6029 0.604271
\(585\) −2.40011 −0.0992325
\(586\) −21.8893 −0.904240
\(587\) −35.2971 −1.45687 −0.728434 0.685116i \(-0.759751\pi\)
−0.728434 + 0.685116i \(0.759751\pi\)
\(588\) −11.4510 −0.472232
\(589\) 8.11016 0.334173
\(590\) 9.38363 0.386318
\(591\) 27.7054 1.13965
\(592\) −2.14709 −0.0882448
\(593\) −42.7033 −1.75361 −0.876807 0.480842i \(-0.840331\pi\)
−0.876807 + 0.480842i \(0.840331\pi\)
\(594\) −35.9863 −1.47654
\(595\) −85.6754 −3.51235
\(596\) 18.1912 0.745141
\(597\) −10.7395 −0.439539
\(598\) −0.577778 −0.0236271
\(599\) 15.8078 0.645889 0.322945 0.946418i \(-0.395327\pi\)
0.322945 + 0.946418i \(0.395327\pi\)
\(600\) −40.0399 −1.63462
\(601\) −0.884434 −0.0360768 −0.0180384 0.999837i \(-0.505742\pi\)
−0.0180384 + 0.999837i \(0.505742\pi\)
\(602\) 5.97575 0.243553
\(603\) 68.1977 2.77723
\(604\) −9.58416 −0.389974
\(605\) −14.7589 −0.600035
\(606\) 28.3843 1.15304
\(607\) −3.17519 −0.128877 −0.0644385 0.997922i \(-0.520526\pi\)
−0.0644385 + 0.997922i \(0.520526\pi\)
\(608\) 1.00000 0.0405554
\(609\) 51.8934 2.10283
\(610\) −34.1092 −1.38104
\(611\) 0.416591 0.0168535
\(612\) 44.7790 1.81008
\(613\) 38.1141 1.53941 0.769707 0.638398i \(-0.220402\pi\)
0.769707 + 0.638398i \(0.220402\pi\)
\(614\) −3.48408 −0.140606
\(615\) 111.104 4.48015
\(616\) −8.90308 −0.358715
\(617\) 14.9849 0.603271 0.301636 0.953423i \(-0.402467\pi\)
0.301636 + 0.953423i \(0.402467\pi\)
\(618\) 6.08340 0.244710
\(619\) −16.0629 −0.645622 −0.322811 0.946463i \(-0.604628\pi\)
−0.322811 + 0.946463i \(0.604628\pi\)
\(620\) 34.0029 1.36559
\(621\) −94.7343 −3.80156
\(622\) −29.3947 −1.17862
\(623\) 19.9883 0.800813
\(624\) 0.255461 0.0102266
\(625\) 70.3178 2.81271
\(626\) 24.7919 0.990882
\(627\) −8.70610 −0.347688
\(628\) −10.6000 −0.422986
\(629\) −13.4780 −0.537402
\(630\) −97.3602 −3.87892
\(631\) −18.2539 −0.726678 −0.363339 0.931657i \(-0.618363\pi\)
−0.363339 + 0.931657i \(0.618363\pi\)
\(632\) −16.1807 −0.643634
\(633\) −3.18331 −0.126525
\(634\) −17.0015 −0.675215
\(635\) 20.7123 0.821943
\(636\) −12.8397 −0.509127
\(637\) −0.288676 −0.0114378
\(638\) 13.6957 0.542216
\(639\) −80.4344 −3.18194
\(640\) 4.19262 0.165728
\(641\) 27.9599 1.10435 0.552175 0.833728i \(-0.313798\pi\)
0.552175 + 0.833728i \(0.313798\pi\)
\(642\) −16.2030 −0.639480
\(643\) 23.2147 0.915500 0.457750 0.889081i \(-0.348655\pi\)
0.457750 + 0.889081i \(0.348655\pi\)
\(644\) −23.4375 −0.923565
\(645\) 24.4997 0.964676
\(646\) 6.27732 0.246978
\(647\) −9.93842 −0.390720 −0.195360 0.980732i \(-0.562587\pi\)
−0.195360 + 0.980732i \(0.562587\pi\)
\(648\) 20.4858 0.804760
\(649\) 6.12110 0.240274
\(650\) −1.00939 −0.0395917
\(651\) 84.0435 3.29392
\(652\) −10.7524 −0.421095
\(653\) −27.2956 −1.06816 −0.534079 0.845434i \(-0.679342\pi\)
−0.534079 + 0.845434i \(0.679342\pi\)
\(654\) −9.59019 −0.375006
\(655\) −10.4875 −0.409780
\(656\) −8.32464 −0.325022
\(657\) 104.169 4.06402
\(658\) 16.8989 0.658789
\(659\) 38.0242 1.48121 0.740606 0.671940i \(-0.234539\pi\)
0.740606 + 0.671940i \(0.234539\pi\)
\(660\) −36.5014 −1.42081
\(661\) 23.3898 0.909757 0.454879 0.890553i \(-0.349683\pi\)
0.454879 + 0.890553i \(0.349683\pi\)
\(662\) 18.4660 0.717703
\(663\) 1.60361 0.0622791
\(664\) 0.187647 0.00728211
\(665\) −13.6484 −0.529262
\(666\) −15.3162 −0.593490
\(667\) 36.0539 1.39601
\(668\) −12.8734 −0.498087
\(669\) 52.9762 2.04818
\(670\) 40.0826 1.54853
\(671\) −22.2500 −0.858953
\(672\) 10.3627 0.399751
\(673\) 12.8414 0.495001 0.247500 0.968888i \(-0.420391\pi\)
0.247500 + 0.968888i \(0.420391\pi\)
\(674\) −10.9336 −0.421145
\(675\) −165.503 −6.37023
\(676\) −12.9936 −0.499752
\(677\) −17.2092 −0.661403 −0.330701 0.943735i \(-0.607285\pi\)
−0.330701 + 0.943735i \(0.607285\pi\)
\(678\) −49.5916 −1.90455
\(679\) −54.9147 −2.10743
\(680\) 26.3184 1.00927
\(681\) −53.8922 −2.06515
\(682\) 22.1807 0.849341
\(683\) −5.33621 −0.204185 −0.102092 0.994775i \(-0.532554\pi\)
−0.102092 + 0.994775i \(0.532554\pi\)
\(684\) 7.13346 0.272755
\(685\) −31.3675 −1.19849
\(686\) 11.0772 0.422931
\(687\) −38.2157 −1.45802
\(688\) −1.83568 −0.0699846
\(689\) −0.323684 −0.0123314
\(690\) −96.0903 −3.65809
\(691\) 2.06385 0.0785126 0.0392563 0.999229i \(-0.487501\pi\)
0.0392563 + 0.999229i \(0.487501\pi\)
\(692\) −16.6802 −0.634086
\(693\) −63.5098 −2.41254
\(694\) 29.0472 1.10262
\(695\) −34.7620 −1.31860
\(696\) −15.9410 −0.604244
\(697\) −52.2564 −1.97935
\(698\) 4.58892 0.173693
\(699\) −84.0911 −3.18062
\(700\) −40.9459 −1.54761
\(701\) 20.3479 0.768529 0.384265 0.923223i \(-0.374455\pi\)
0.384265 + 0.923223i \(0.374455\pi\)
\(702\) 1.05594 0.0398538
\(703\) −2.14709 −0.0809790
\(704\) 2.73492 0.103076
\(705\) 69.2832 2.60936
\(706\) 26.3882 0.993132
\(707\) 29.0266 1.09166
\(708\) −7.12465 −0.267761
\(709\) −47.3214 −1.77719 −0.888595 0.458692i \(-0.848318\pi\)
−0.888595 + 0.458692i \(0.848318\pi\)
\(710\) −47.2746 −1.77418
\(711\) −115.424 −4.32875
\(712\) −6.14015 −0.230112
\(713\) 58.3908 2.18675
\(714\) 65.0503 2.43444
\(715\) −0.920188 −0.0344131
\(716\) 5.86458 0.219170
\(717\) 28.2507 1.05504
\(718\) 15.7431 0.587526
\(719\) −18.1144 −0.675553 −0.337777 0.941226i \(-0.609675\pi\)
−0.337777 + 0.941226i \(0.609675\pi\)
\(720\) 29.9079 1.11460
\(721\) 6.22105 0.231684
\(722\) 1.00000 0.0372161
\(723\) 82.1304 3.05446
\(724\) −16.1501 −0.600215
\(725\) 62.9872 2.33929
\(726\) 11.2059 0.415890
\(727\) 29.2594 1.08517 0.542585 0.840001i \(-0.317446\pi\)
0.542585 + 0.840001i \(0.317446\pi\)
\(728\) 0.261241 0.00968224
\(729\) 20.4763 0.758380
\(730\) 61.2243 2.26601
\(731\) −11.5232 −0.426199
\(732\) 25.8979 0.957215
\(733\) −10.3405 −0.381936 −0.190968 0.981596i \(-0.561163\pi\)
−0.190968 + 0.981596i \(0.561163\pi\)
\(734\) 23.7044 0.874944
\(735\) −48.0098 −1.77087
\(736\) 7.19971 0.265385
\(737\) 26.1466 0.963121
\(738\) −59.3834 −2.18593
\(739\) −2.75158 −0.101219 −0.0506093 0.998719i \(-0.516116\pi\)
−0.0506093 + 0.998719i \(0.516116\pi\)
\(740\) −9.00193 −0.330918
\(741\) 0.255461 0.00938460
\(742\) −13.1302 −0.482025
\(743\) 15.0850 0.553414 0.276707 0.960954i \(-0.410757\pi\)
0.276707 + 0.960954i \(0.410757\pi\)
\(744\) −25.8172 −0.946503
\(745\) 76.2689 2.79428
\(746\) −25.4986 −0.933570
\(747\) 1.33857 0.0489758
\(748\) 17.1680 0.627724
\(749\) −16.5696 −0.605439
\(750\) −101.140 −3.69312
\(751\) 26.9716 0.984207 0.492103 0.870537i \(-0.336228\pi\)
0.492103 + 0.870537i \(0.336228\pi\)
\(752\) −5.19115 −0.189302
\(753\) −48.5613 −1.76967
\(754\) −0.401868 −0.0146352
\(755\) −40.1828 −1.46240
\(756\) 42.8339 1.55786
\(757\) −36.5567 −1.32867 −0.664337 0.747433i \(-0.731286\pi\)
−0.664337 + 0.747433i \(0.731286\pi\)
\(758\) −8.82584 −0.320569
\(759\) −62.6814 −2.27519
\(760\) 4.19262 0.152082
\(761\) −13.9314 −0.505011 −0.252506 0.967595i \(-0.581255\pi\)
−0.252506 + 0.967595i \(0.581255\pi\)
\(762\) −15.7261 −0.569697
\(763\) −9.80718 −0.355044
\(764\) 7.32475 0.265000
\(765\) 187.742 6.78781
\(766\) −3.69767 −0.133602
\(767\) −0.179610 −0.00648535
\(768\) −3.18331 −0.114868
\(769\) 3.73616 0.134729 0.0673647 0.997728i \(-0.478541\pi\)
0.0673647 + 0.997728i \(0.478541\pi\)
\(770\) −37.3273 −1.34518
\(771\) −30.2049 −1.08780
\(772\) −12.4506 −0.448105
\(773\) −42.3879 −1.52459 −0.762294 0.647231i \(-0.775927\pi\)
−0.762294 + 0.647231i \(0.775927\pi\)
\(774\) −13.0947 −0.470681
\(775\) 102.010 3.66432
\(776\) 16.8692 0.605567
\(777\) −22.2497 −0.798204
\(778\) 25.2395 0.904880
\(779\) −8.32464 −0.298261
\(780\) 1.07105 0.0383498
\(781\) −30.8380 −1.10347
\(782\) 45.1949 1.61617
\(783\) −65.8916 −2.35478
\(784\) 3.59720 0.128472
\(785\) −44.4418 −1.58620
\(786\) 7.96278 0.284023
\(787\) −7.55044 −0.269144 −0.134572 0.990904i \(-0.542966\pi\)
−0.134572 + 0.990904i \(0.542966\pi\)
\(788\) −8.70333 −0.310043
\(789\) 24.8028 0.883004
\(790\) −67.8396 −2.41363
\(791\) −50.7137 −1.80317
\(792\) 19.5094 0.693238
\(793\) 0.652878 0.0231844
\(794\) 29.1297 1.03378
\(795\) −53.8319 −1.90922
\(796\) 3.37370 0.119577
\(797\) −15.7873 −0.559216 −0.279608 0.960114i \(-0.590204\pi\)
−0.279608 + 0.960114i \(0.590204\pi\)
\(798\) 10.3627 0.366837
\(799\) −32.5865 −1.15283
\(800\) 12.5781 0.444702
\(801\) −43.8005 −1.54762
\(802\) −14.9761 −0.528825
\(803\) 39.9377 1.40937
\(804\) −30.4333 −1.07330
\(805\) −98.2644 −3.46336
\(806\) −0.650842 −0.0229249
\(807\) −29.6411 −1.04342
\(808\) −8.91662 −0.313685
\(809\) −28.7958 −1.01241 −0.506203 0.862414i \(-0.668951\pi\)
−0.506203 + 0.862414i \(0.668951\pi\)
\(810\) 85.8894 3.01785
\(811\) −46.9791 −1.64966 −0.824830 0.565380i \(-0.808729\pi\)
−0.824830 + 0.565380i \(0.808729\pi\)
\(812\) −16.3017 −0.572079
\(813\) 22.3702 0.784557
\(814\) −5.87212 −0.205818
\(815\) −45.0806 −1.57911
\(816\) −19.9827 −0.699533
\(817\) −1.83568 −0.0642223
\(818\) −37.1151 −1.29770
\(819\) 1.86355 0.0651178
\(820\) −34.9021 −1.21883
\(821\) 1.63843 0.0571815 0.0285908 0.999591i \(-0.490898\pi\)
0.0285908 + 0.999591i \(0.490898\pi\)
\(822\) 23.8162 0.830686
\(823\) 51.1330 1.78238 0.891192 0.453626i \(-0.149870\pi\)
0.891192 + 0.453626i \(0.149870\pi\)
\(824\) −1.91103 −0.0665739
\(825\) −109.506 −3.81251
\(826\) −7.28586 −0.253507
\(827\) 47.2225 1.64209 0.821044 0.570864i \(-0.193392\pi\)
0.821044 + 0.570864i \(0.193392\pi\)
\(828\) 51.3588 1.78484
\(829\) −12.7314 −0.442179 −0.221089 0.975254i \(-0.570961\pi\)
−0.221089 + 0.975254i \(0.570961\pi\)
\(830\) 0.786733 0.0273079
\(831\) −52.9060 −1.83529
\(832\) −0.0802502 −0.00278217
\(833\) 22.5808 0.782379
\(834\) 26.3936 0.913935
\(835\) −53.9734 −1.86783
\(836\) 2.73492 0.0945892
\(837\) −106.714 −3.68858
\(838\) −7.10982 −0.245605
\(839\) 16.8141 0.580489 0.290244 0.956953i \(-0.406263\pi\)
0.290244 + 0.956953i \(0.406263\pi\)
\(840\) 43.4470 1.49907
\(841\) −3.92297 −0.135275
\(842\) −10.7837 −0.371632
\(843\) −74.8490 −2.57794
\(844\) 1.00000 0.0344214
\(845\) −54.4771 −1.87407
\(846\) −37.0308 −1.27315
\(847\) 11.4595 0.393751
\(848\) 4.03344 0.138509
\(849\) 11.5252 0.395545
\(850\) 78.9567 2.70819
\(851\) −15.4584 −0.529908
\(852\) 35.8939 1.22970
\(853\) 16.3062 0.558314 0.279157 0.960246i \(-0.409945\pi\)
0.279157 + 0.960246i \(0.409945\pi\)
\(854\) 26.4839 0.906260
\(855\) 29.9079 1.02283
\(856\) 5.08997 0.173972
\(857\) 54.9625 1.87748 0.938741 0.344624i \(-0.111994\pi\)
0.938741 + 0.344624i \(0.111994\pi\)
\(858\) 0.698666 0.0238521
\(859\) −12.2688 −0.418605 −0.209302 0.977851i \(-0.567119\pi\)
−0.209302 + 0.977851i \(0.567119\pi\)
\(860\) −7.69631 −0.262442
\(861\) −86.2660 −2.93994
\(862\) −25.6930 −0.875108
\(863\) −0.184328 −0.00627460 −0.00313730 0.999995i \(-0.500999\pi\)
−0.00313730 + 0.999995i \(0.500999\pi\)
\(864\) −13.1581 −0.447647
\(865\) −69.9337 −2.37782
\(866\) 10.2487 0.348264
\(867\) −71.3214 −2.42220
\(868\) −26.4013 −0.896118
\(869\) −44.2530 −1.50118
\(870\) −66.8348 −2.26591
\(871\) −0.767213 −0.0259960
\(872\) 3.01265 0.102021
\(873\) 120.335 4.07274
\(874\) 7.19971 0.243534
\(875\) −103.429 −3.49653
\(876\) −46.4855 −1.57060
\(877\) 22.8180 0.770510 0.385255 0.922810i \(-0.374113\pi\)
0.385255 + 0.922810i \(0.374113\pi\)
\(878\) 13.7272 0.463271
\(879\) 69.6805 2.35027
\(880\) 11.4665 0.386535
\(881\) 14.7740 0.497747 0.248874 0.968536i \(-0.419940\pi\)
0.248874 + 0.968536i \(0.419940\pi\)
\(882\) 25.6605 0.864034
\(883\) −54.6426 −1.83887 −0.919436 0.393240i \(-0.871354\pi\)
−0.919436 + 0.393240i \(0.871354\pi\)
\(884\) −0.503756 −0.0169432
\(885\) −29.8710 −1.00410
\(886\) 38.6960 1.30002
\(887\) −55.3480 −1.85841 −0.929203 0.369571i \(-0.879505\pi\)
−0.929203 + 0.369571i \(0.879505\pi\)
\(888\) 6.83485 0.229363
\(889\) −16.0819 −0.539371
\(890\) −25.7434 −0.862919
\(891\) 56.0272 1.87698
\(892\) −16.6419 −0.557211
\(893\) −5.19115 −0.173715
\(894\) −57.9083 −1.93674
\(895\) 24.5880 0.821885
\(896\) −3.25533 −0.108753
\(897\) 1.83924 0.0614106
\(898\) 32.7741 1.09369
\(899\) 40.6132 1.35453
\(900\) 89.7252 2.99084
\(901\) 25.3192 0.843505
\(902\) −22.7672 −0.758066
\(903\) −19.0227 −0.633035
\(904\) 15.5786 0.518138
\(905\) −67.7114 −2.25080
\(906\) 30.5093 1.01360
\(907\) 14.7928 0.491186 0.245593 0.969373i \(-0.421017\pi\)
0.245593 + 0.969373i \(0.421017\pi\)
\(908\) 16.9296 0.561829
\(909\) −63.6063 −2.10969
\(910\) 1.09529 0.0363084
\(911\) 24.9019 0.825037 0.412519 0.910949i \(-0.364649\pi\)
0.412519 + 0.910949i \(0.364649\pi\)
\(912\) −3.18331 −0.105410
\(913\) 0.513199 0.0169844
\(914\) −17.0309 −0.563332
\(915\) 108.580 3.58955
\(916\) 12.0050 0.396657
\(917\) 8.14294 0.268904
\(918\) −82.5975 −2.72612
\(919\) 24.2850 0.801089 0.400545 0.916277i \(-0.368821\pi\)
0.400545 + 0.916277i \(0.368821\pi\)
\(920\) 30.1857 0.995191
\(921\) 11.0909 0.365458
\(922\) 29.1873 0.961232
\(923\) 0.904873 0.0297843
\(924\) 28.3413 0.932359
\(925\) −27.0063 −0.887961
\(926\) −26.4771 −0.870092
\(927\) −13.6323 −0.447742
\(928\) 5.00770 0.164386
\(929\) −25.0883 −0.823120 −0.411560 0.911383i \(-0.635016\pi\)
−0.411560 + 0.911383i \(0.635016\pi\)
\(930\) −108.242 −3.54938
\(931\) 3.59720 0.117894
\(932\) 26.4162 0.865293
\(933\) 93.5724 3.06342
\(934\) 10.0890 0.330122
\(935\) 71.9789 2.35396
\(936\) −0.572461 −0.0187115
\(937\) −47.9762 −1.56731 −0.783656 0.621194i \(-0.786648\pi\)
−0.783656 + 0.621194i \(0.786648\pi\)
\(938\) −31.1219 −1.01616
\(939\) −78.9202 −2.57546
\(940\) −21.7645 −0.709881
\(941\) −25.8127 −0.841469 −0.420734 0.907184i \(-0.638228\pi\)
−0.420734 + 0.907184i \(0.638228\pi\)
\(942\) 33.7431 1.09941
\(943\) −59.9349 −1.95175
\(944\) 2.23813 0.0728449
\(945\) 179.587 5.84195
\(946\) −5.02044 −0.163229
\(947\) 8.58591 0.279005 0.139502 0.990222i \(-0.455450\pi\)
0.139502 + 0.990222i \(0.455450\pi\)
\(948\) 51.5082 1.67291
\(949\) −1.17188 −0.0380409
\(950\) 12.5781 0.408087
\(951\) 54.1209 1.75499
\(952\) −20.4348 −0.662295
\(953\) 39.9878 1.29533 0.647666 0.761924i \(-0.275745\pi\)
0.647666 + 0.761924i \(0.275745\pi\)
\(954\) 28.7724 0.931540
\(955\) 30.7099 0.993749
\(956\) −8.87463 −0.287026
\(957\) −43.5975 −1.40931
\(958\) 28.8990 0.933685
\(959\) 24.3551 0.786467
\(960\) −13.3464 −0.430754
\(961\) 34.7748 1.12177
\(962\) 0.172304 0.00555531
\(963\) 36.3091 1.17005
\(964\) −25.8003 −0.830973
\(965\) −52.2005 −1.68039
\(966\) 74.6087 2.40049
\(967\) 33.0845 1.06393 0.531963 0.846767i \(-0.321454\pi\)
0.531963 + 0.846767i \(0.321454\pi\)
\(968\) −3.52021 −0.113144
\(969\) −19.9827 −0.641936
\(970\) 70.7260 2.27087
\(971\) −8.12573 −0.260767 −0.130384 0.991464i \(-0.541621\pi\)
−0.130384 + 0.991464i \(0.541621\pi\)
\(972\) −25.7386 −0.825565
\(973\) 26.9908 0.865284
\(974\) 16.4153 0.525979
\(975\) 3.21321 0.102905
\(976\) −8.13553 −0.260412
\(977\) −11.2374 −0.359516 −0.179758 0.983711i \(-0.557531\pi\)
−0.179758 + 0.983711i \(0.557531\pi\)
\(978\) 34.2281 1.09449
\(979\) −16.7928 −0.536701
\(980\) 15.0817 0.481768
\(981\) 21.4906 0.686142
\(982\) 39.1618 1.24970
\(983\) 35.2013 1.12275 0.561373 0.827563i \(-0.310273\pi\)
0.561373 + 0.827563i \(0.310273\pi\)
\(984\) 26.4999 0.844786
\(985\) −36.4898 −1.16266
\(986\) 31.4349 1.00109
\(987\) −53.7945 −1.71230
\(988\) −0.0802502 −0.00255310
\(989\) −13.2164 −0.420256
\(990\) 81.7957 2.59964
\(991\) −32.5063 −1.03260 −0.516298 0.856409i \(-0.672690\pi\)
−0.516298 + 0.856409i \(0.672690\pi\)
\(992\) 8.11016 0.257498
\(993\) −58.7831 −1.86543
\(994\) 36.7060 1.16424
\(995\) 14.1446 0.448415
\(996\) −0.597338 −0.0189274
\(997\) −39.1174 −1.23886 −0.619430 0.785052i \(-0.712636\pi\)
−0.619430 + 0.785052i \(0.712636\pi\)
\(998\) −30.6427 −0.969979
\(999\) 28.2516 0.893840
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 8018.2.a.k.1.1 49
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8018.2.a.k.1.1 49 1.1 even 1 trivial