Properties

Label 4033.2.a.c.1.5
Level $4033$
Weight $2$
Character 4033.1
Self dual yes
Analytic conductor $32.204$
Analytic rank $1$
Dimension $77$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4033,2,Mod(1,4033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4033, 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("4033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4033 = 37 \cdot 109 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4033.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: \(32.2036671352\)
Analytic rank: \(1\)
Dimension: \(77\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 4033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.57358 q^{2} -2.79713 q^{3} +4.62329 q^{4} +0.767586 q^{5} +7.19864 q^{6} -3.79460 q^{7} -6.75123 q^{8} +4.82396 q^{9} +O(q^{10})\) \(q-2.57358 q^{2} -2.79713 q^{3} +4.62329 q^{4} +0.767586 q^{5} +7.19864 q^{6} -3.79460 q^{7} -6.75123 q^{8} +4.82396 q^{9} -1.97544 q^{10} -3.35791 q^{11} -12.9320 q^{12} -5.51722 q^{13} +9.76569 q^{14} -2.14704 q^{15} +8.12822 q^{16} +1.14705 q^{17} -12.4148 q^{18} -0.276498 q^{19} +3.54877 q^{20} +10.6140 q^{21} +8.64182 q^{22} -5.90396 q^{23} +18.8841 q^{24} -4.41081 q^{25} +14.1990 q^{26} -5.10186 q^{27} -17.5435 q^{28} +4.65044 q^{29} +5.52557 q^{30} +8.20608 q^{31} -7.41613 q^{32} +9.39251 q^{33} -2.95203 q^{34} -2.91268 q^{35} +22.3026 q^{36} +1.00000 q^{37} +0.711589 q^{38} +15.4324 q^{39} -5.18215 q^{40} +3.88860 q^{41} -27.3160 q^{42} -0.0399814 q^{43} -15.5246 q^{44} +3.70280 q^{45} +15.1943 q^{46} +5.73139 q^{47} -22.7357 q^{48} +7.39901 q^{49} +11.3516 q^{50} -3.20846 q^{51} -25.5077 q^{52} +0.502954 q^{53} +13.1300 q^{54} -2.57748 q^{55} +25.6182 q^{56} +0.773402 q^{57} -11.9683 q^{58} -8.19480 q^{59} -9.92639 q^{60} +8.28663 q^{61} -21.1190 q^{62} -18.3050 q^{63} +2.82952 q^{64} -4.23494 q^{65} -24.1723 q^{66} -1.33314 q^{67} +5.30316 q^{68} +16.5142 q^{69} +7.49601 q^{70} -11.6076 q^{71} -32.5677 q^{72} +4.79490 q^{73} -2.57358 q^{74} +12.3376 q^{75} -1.27833 q^{76} +12.7419 q^{77} -39.7164 q^{78} -1.36951 q^{79} +6.23911 q^{80} -0.201290 q^{81} -10.0076 q^{82} +8.55030 q^{83} +49.0716 q^{84} +0.880462 q^{85} +0.102895 q^{86} -13.0079 q^{87} +22.6700 q^{88} -9.22223 q^{89} -9.52944 q^{90} +20.9356 q^{91} -27.2957 q^{92} -22.9535 q^{93} -14.7502 q^{94} -0.212236 q^{95} +20.7439 q^{96} +9.14002 q^{97} -19.0419 q^{98} -16.1984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 77 q - 9 q^{2} - 27 q^{3} + 73 q^{4} - 16 q^{5} - 2 q^{6} - 23 q^{7} - 24 q^{8} + 66 q^{9} - 11 q^{10} - 33 q^{11} - 52 q^{12} - 10 q^{13} - 18 q^{14} - 33 q^{15} + 53 q^{16} - 44 q^{17} - 27 q^{18} - 9 q^{19} - 45 q^{20} - 7 q^{21} - 3 q^{22} - 74 q^{23} + 21 q^{24} + 59 q^{25} - 47 q^{26} - 99 q^{27} - 49 q^{28} - 9 q^{29} - 39 q^{30} - 27 q^{31} - 47 q^{32} - 28 q^{33} - 23 q^{34} - 48 q^{35} + 77 q^{36} + 77 q^{37} - 66 q^{38} - 11 q^{39} - 2 q^{40} - 37 q^{41} - 24 q^{42} - 44 q^{43} - 54 q^{44} - 36 q^{45} - 41 q^{46} - 150 q^{47} - 135 q^{48} + 64 q^{49} + 4 q^{50} + 3 q^{51} - 57 q^{52} - 72 q^{53} + 21 q^{54} - 65 q^{55} - 92 q^{56} - 13 q^{57} - 12 q^{58} - 70 q^{59} - 22 q^{60} + 15 q^{61} - 86 q^{62} - 108 q^{63} + 10 q^{64} - 53 q^{65} - 55 q^{66} - 48 q^{67} - 70 q^{68} - 2 q^{69} + 11 q^{70} - 127 q^{71} - 12 q^{72} - 33 q^{73} - 9 q^{74} - 115 q^{75} - 24 q^{76} - 40 q^{77} + 81 q^{78} - 7 q^{79} - 62 q^{80} + 53 q^{81} - 68 q^{82} - 164 q^{83} + 7 q^{84} - 9 q^{85} - 50 q^{86} - 75 q^{87} - 82 q^{88} - 26 q^{89} + 23 q^{90} + 16 q^{91} - 117 q^{92} + 19 q^{93} + 23 q^{94} - 92 q^{95} - 35 q^{96} - 19 q^{97} - 10 q^{98} - 19 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.57358 −1.81979 −0.909896 0.414836i \(-0.863839\pi\)
−0.909896 + 0.414836i \(0.863839\pi\)
\(3\) −2.79713 −1.61493 −0.807463 0.589918i \(-0.799160\pi\)
−0.807463 + 0.589918i \(0.799160\pi\)
\(4\) 4.62329 2.31164
\(5\) 0.767586 0.343275 0.171637 0.985160i \(-0.445094\pi\)
0.171637 + 0.985160i \(0.445094\pi\)
\(6\) 7.19864 2.93883
\(7\) −3.79460 −1.43422 −0.717112 0.696958i \(-0.754537\pi\)
−0.717112 + 0.696958i \(0.754537\pi\)
\(8\) −6.75123 −2.38692
\(9\) 4.82396 1.60799
\(10\) −1.97544 −0.624689
\(11\) −3.35791 −1.01245 −0.506223 0.862402i \(-0.668959\pi\)
−0.506223 + 0.862402i \(0.668959\pi\)
\(12\) −12.9320 −3.73314
\(13\) −5.51722 −1.53020 −0.765100 0.643911i \(-0.777311\pi\)
−0.765100 + 0.643911i \(0.777311\pi\)
\(14\) 9.76569 2.60999
\(15\) −2.14704 −0.554364
\(16\) 8.12822 2.03206
\(17\) 1.14705 0.278201 0.139101 0.990278i \(-0.455579\pi\)
0.139101 + 0.990278i \(0.455579\pi\)
\(18\) −12.4148 −2.92620
\(19\) −0.276498 −0.0634330 −0.0317165 0.999497i \(-0.510097\pi\)
−0.0317165 + 0.999497i \(0.510097\pi\)
\(20\) 3.54877 0.793529
\(21\) 10.6140 2.31617
\(22\) 8.64182 1.84244
\(23\) −5.90396 −1.23106 −0.615530 0.788113i \(-0.711058\pi\)
−0.615530 + 0.788113i \(0.711058\pi\)
\(24\) 18.8841 3.85470
\(25\) −4.41081 −0.882162
\(26\) 14.1990 2.78465
\(27\) −5.10186 −0.981854
\(28\) −17.5435 −3.31542
\(29\) 4.65044 0.863565 0.431782 0.901978i \(-0.357885\pi\)
0.431782 + 0.901978i \(0.357885\pi\)
\(30\) 5.52557 1.00883
\(31\) 8.20608 1.47385 0.736927 0.675972i \(-0.236276\pi\)
0.736927 + 0.675972i \(0.236276\pi\)
\(32\) −7.41613 −1.31100
\(33\) 9.39251 1.63503
\(34\) −2.95203 −0.506269
\(35\) −2.91268 −0.492333
\(36\) 22.3026 3.71709
\(37\) 1.00000 0.164399
\(38\) 0.711589 0.115435
\(39\) 15.4324 2.47116
\(40\) −5.18215 −0.819370
\(41\) 3.88860 0.607297 0.303648 0.952784i \(-0.401795\pi\)
0.303648 + 0.952784i \(0.401795\pi\)
\(42\) −27.3160 −4.21494
\(43\) −0.0399814 −0.00609710 −0.00304855 0.999995i \(-0.500970\pi\)
−0.00304855 + 0.999995i \(0.500970\pi\)
\(44\) −15.5246 −2.34042
\(45\) 3.70280 0.551981
\(46\) 15.1943 2.24027
\(47\) 5.73139 0.836009 0.418005 0.908445i \(-0.362730\pi\)
0.418005 + 0.908445i \(0.362730\pi\)
\(48\) −22.7357 −3.28162
\(49\) 7.39901 1.05700
\(50\) 11.3516 1.60535
\(51\) −3.20846 −0.449275
\(52\) −25.5077 −3.53728
\(53\) 0.502954 0.0690860 0.0345430 0.999403i \(-0.489002\pi\)
0.0345430 + 0.999403i \(0.489002\pi\)
\(54\) 13.1300 1.78677
\(55\) −2.57748 −0.347548
\(56\) 25.6182 3.42338
\(57\) 0.773402 0.102440
\(58\) −11.9683 −1.57151
\(59\) −8.19480 −1.06687 −0.533436 0.845840i \(-0.679100\pi\)
−0.533436 + 0.845840i \(0.679100\pi\)
\(60\) −9.92639 −1.28149
\(61\) 8.28663 1.06099 0.530497 0.847687i \(-0.322005\pi\)
0.530497 + 0.847687i \(0.322005\pi\)
\(62\) −21.1190 −2.68211
\(63\) −18.3050 −2.30621
\(64\) 2.82952 0.353690
\(65\) −4.23494 −0.525279
\(66\) −24.1723 −2.97541
\(67\) −1.33314 −0.162868 −0.0814342 0.996679i \(-0.525950\pi\)
−0.0814342 + 0.996679i \(0.525950\pi\)
\(68\) 5.30316 0.643103
\(69\) 16.5142 1.98807
\(70\) 7.49601 0.895945
\(71\) −11.6076 −1.37757 −0.688787 0.724964i \(-0.741856\pi\)
−0.688787 + 0.724964i \(0.741856\pi\)
\(72\) −32.5677 −3.83814
\(73\) 4.79490 0.561201 0.280601 0.959825i \(-0.409466\pi\)
0.280601 + 0.959825i \(0.409466\pi\)
\(74\) −2.57358 −0.299172
\(75\) 12.3376 1.42463
\(76\) −1.27833 −0.146635
\(77\) 12.7419 1.45208
\(78\) −39.7164 −4.49700
\(79\) −1.36951 −0.154082 −0.0770410 0.997028i \(-0.524547\pi\)
−0.0770410 + 0.997028i \(0.524547\pi\)
\(80\) 6.23911 0.697554
\(81\) −0.201290 −0.0223656
\(82\) −10.0076 −1.10515
\(83\) 8.55030 0.938518 0.469259 0.883061i \(-0.344521\pi\)
0.469259 + 0.883061i \(0.344521\pi\)
\(84\) 49.0716 5.35416
\(85\) 0.880462 0.0954995
\(86\) 0.102895 0.0110955
\(87\) −13.0079 −1.39459
\(88\) 22.6700 2.41663
\(89\) −9.22223 −0.977554 −0.488777 0.872409i \(-0.662557\pi\)
−0.488777 + 0.872409i \(0.662557\pi\)
\(90\) −9.52944 −1.00449
\(91\) 20.9356 2.19465
\(92\) −27.2957 −2.84577
\(93\) −22.9535 −2.38017
\(94\) −14.7502 −1.52136
\(95\) −0.212236 −0.0217750
\(96\) 20.7439 2.11717
\(97\) 9.14002 0.928028 0.464014 0.885828i \(-0.346409\pi\)
0.464014 + 0.885828i \(0.346409\pi\)
\(98\) −19.0419 −1.92352
\(99\) −16.1984 −1.62800
\(100\) −20.3925 −2.03925
\(101\) 13.2634 1.31975 0.659877 0.751374i \(-0.270608\pi\)
0.659877 + 0.751374i \(0.270608\pi\)
\(102\) 8.25722 0.817587
\(103\) 12.2364 1.20569 0.602843 0.797860i \(-0.294034\pi\)
0.602843 + 0.797860i \(0.294034\pi\)
\(104\) 37.2480 3.65247
\(105\) 8.14717 0.795082
\(106\) −1.29439 −0.125722
\(107\) 2.66166 0.257313 0.128656 0.991689i \(-0.458934\pi\)
0.128656 + 0.991689i \(0.458934\pi\)
\(108\) −23.5874 −2.26970
\(109\) 1.00000 0.0957826
\(110\) 6.63334 0.632464
\(111\) −2.79713 −0.265492
\(112\) −30.8434 −2.91442
\(113\) 1.33424 0.125515 0.0627574 0.998029i \(-0.480011\pi\)
0.0627574 + 0.998029i \(0.480011\pi\)
\(114\) −1.99041 −0.186419
\(115\) −4.53179 −0.422592
\(116\) 21.5003 1.99625
\(117\) −26.6148 −2.46054
\(118\) 21.0899 1.94149
\(119\) −4.35261 −0.399003
\(120\) 14.4952 1.32322
\(121\) 0.275534 0.0250486
\(122\) −21.3263 −1.93079
\(123\) −10.8769 −0.980739
\(124\) 37.9391 3.40703
\(125\) −7.22361 −0.646099
\(126\) 47.1093 4.19683
\(127\) 6.44128 0.571571 0.285786 0.958294i \(-0.407745\pi\)
0.285786 + 0.958294i \(0.407745\pi\)
\(128\) 7.55027 0.667356
\(129\) 0.111833 0.00984637
\(130\) 10.8989 0.955899
\(131\) −14.3757 −1.25601 −0.628004 0.778210i \(-0.716128\pi\)
−0.628004 + 0.778210i \(0.716128\pi\)
\(132\) 43.4243 3.77960
\(133\) 1.04920 0.0909772
\(134\) 3.43092 0.296387
\(135\) −3.91612 −0.337046
\(136\) −7.74402 −0.664045
\(137\) −6.62586 −0.566086 −0.283043 0.959107i \(-0.591344\pi\)
−0.283043 + 0.959107i \(0.591344\pi\)
\(138\) −42.5004 −3.61788
\(139\) −12.7350 −1.08017 −0.540085 0.841611i \(-0.681608\pi\)
−0.540085 + 0.841611i \(0.681608\pi\)
\(140\) −13.4662 −1.13810
\(141\) −16.0315 −1.35009
\(142\) 29.8731 2.50690
\(143\) 18.5263 1.54925
\(144\) 39.2102 3.26752
\(145\) 3.56961 0.296440
\(146\) −12.3400 −1.02127
\(147\) −20.6960 −1.70698
\(148\) 4.62329 0.380032
\(149\) 19.1438 1.56832 0.784161 0.620558i \(-0.213094\pi\)
0.784161 + 0.620558i \(0.213094\pi\)
\(150\) −31.7518 −2.59253
\(151\) 10.8135 0.879986 0.439993 0.898001i \(-0.354981\pi\)
0.439993 + 0.898001i \(0.354981\pi\)
\(152\) 1.86670 0.151410
\(153\) 5.53334 0.447344
\(154\) −32.7923 −2.64248
\(155\) 6.29887 0.505937
\(156\) 71.3484 5.71245
\(157\) 5.47855 0.437236 0.218618 0.975811i \(-0.429845\pi\)
0.218618 + 0.975811i \(0.429845\pi\)
\(158\) 3.52454 0.280397
\(159\) −1.40683 −0.111569
\(160\) −5.69252 −0.450033
\(161\) 22.4032 1.76562
\(162\) 0.518036 0.0407008
\(163\) 2.88406 0.225897 0.112949 0.993601i \(-0.463970\pi\)
0.112949 + 0.993601i \(0.463970\pi\)
\(164\) 17.9781 1.40385
\(165\) 7.20956 0.561264
\(166\) −22.0048 −1.70791
\(167\) −21.6857 −1.67809 −0.839046 0.544061i \(-0.816886\pi\)
−0.839046 + 0.544061i \(0.816886\pi\)
\(168\) −71.6576 −5.52851
\(169\) 17.4397 1.34151
\(170\) −2.26594 −0.173789
\(171\) −1.33382 −0.101999
\(172\) −0.184845 −0.0140943
\(173\) −5.33883 −0.405903 −0.202952 0.979189i \(-0.565053\pi\)
−0.202952 + 0.979189i \(0.565053\pi\)
\(174\) 33.4768 2.53787
\(175\) 16.7373 1.26522
\(176\) −27.2938 −2.05735
\(177\) 22.9220 1.72292
\(178\) 23.7341 1.77895
\(179\) 7.27425 0.543703 0.271852 0.962339i \(-0.412364\pi\)
0.271852 + 0.962339i \(0.412364\pi\)
\(180\) 17.1191 1.27598
\(181\) 20.8989 1.55340 0.776700 0.629871i \(-0.216892\pi\)
0.776700 + 0.629871i \(0.216892\pi\)
\(182\) −53.8794 −3.99381
\(183\) −23.1788 −1.71343
\(184\) 39.8590 2.93844
\(185\) 0.767586 0.0564340
\(186\) 59.0725 4.33141
\(187\) −3.85170 −0.281664
\(188\) 26.4979 1.93256
\(189\) 19.3595 1.40820
\(190\) 0.546206 0.0396259
\(191\) 15.0179 1.08665 0.543327 0.839521i \(-0.317164\pi\)
0.543327 + 0.839521i \(0.317164\pi\)
\(192\) −7.91455 −0.571184
\(193\) 25.7071 1.85043 0.925217 0.379438i \(-0.123883\pi\)
0.925217 + 0.379438i \(0.123883\pi\)
\(194\) −23.5225 −1.68882
\(195\) 11.8457 0.848287
\(196\) 34.2077 2.44341
\(197\) 23.5858 1.68042 0.840210 0.542262i \(-0.182432\pi\)
0.840210 + 0.542262i \(0.182432\pi\)
\(198\) 41.6878 2.96262
\(199\) −7.33314 −0.519833 −0.259916 0.965631i \(-0.583695\pi\)
−0.259916 + 0.965631i \(0.583695\pi\)
\(200\) 29.7784 2.10565
\(201\) 3.72896 0.263020
\(202\) −34.1343 −2.40168
\(203\) −17.6466 −1.23855
\(204\) −14.8336 −1.03856
\(205\) 2.98483 0.208470
\(206\) −31.4912 −2.19410
\(207\) −28.4805 −1.97953
\(208\) −44.8452 −3.10945
\(209\) 0.928455 0.0642226
\(210\) −20.9673 −1.44688
\(211\) −5.23824 −0.360615 −0.180308 0.983610i \(-0.557709\pi\)
−0.180308 + 0.983610i \(0.557709\pi\)
\(212\) 2.32530 0.159702
\(213\) 32.4681 2.22468
\(214\) −6.84999 −0.468256
\(215\) −0.0306891 −0.00209298
\(216\) 34.4438 2.34361
\(217\) −31.1388 −2.11384
\(218\) −2.57358 −0.174305
\(219\) −13.4120 −0.906298
\(220\) −11.9164 −0.803406
\(221\) −6.32854 −0.425704
\(222\) 7.19864 0.483141
\(223\) 7.11102 0.476189 0.238095 0.971242i \(-0.423477\pi\)
0.238095 + 0.971242i \(0.423477\pi\)
\(224\) 28.1413 1.88027
\(225\) −21.2776 −1.41851
\(226\) −3.43377 −0.228411
\(227\) 5.16276 0.342665 0.171332 0.985213i \(-0.445193\pi\)
0.171332 + 0.985213i \(0.445193\pi\)
\(228\) 3.57566 0.236804
\(229\) 16.8898 1.11611 0.558054 0.829805i \(-0.311548\pi\)
0.558054 + 0.829805i \(0.311548\pi\)
\(230\) 11.6629 0.769030
\(231\) −35.6409 −2.34500
\(232\) −31.3962 −2.06126
\(233\) −16.2147 −1.06226 −0.531130 0.847291i \(-0.678232\pi\)
−0.531130 + 0.847291i \(0.678232\pi\)
\(234\) 68.4953 4.47768
\(235\) 4.39933 0.286981
\(236\) −37.8869 −2.46623
\(237\) 3.83071 0.248831
\(238\) 11.2018 0.726103
\(239\) −23.4314 −1.51565 −0.757825 0.652458i \(-0.773738\pi\)
−0.757825 + 0.652458i \(0.773738\pi\)
\(240\) −17.4516 −1.12650
\(241\) 18.4882 1.19093 0.595466 0.803380i \(-0.296967\pi\)
0.595466 + 0.803380i \(0.296967\pi\)
\(242\) −0.709108 −0.0455832
\(243\) 15.8686 1.01797
\(244\) 38.3115 2.45264
\(245\) 5.67937 0.362842
\(246\) 27.9926 1.78474
\(247\) 1.52550 0.0970652
\(248\) −55.4011 −3.51797
\(249\) −23.9163 −1.51564
\(250\) 18.5905 1.17577
\(251\) 22.9496 1.44857 0.724284 0.689502i \(-0.242171\pi\)
0.724284 + 0.689502i \(0.242171\pi\)
\(252\) −84.6293 −5.33115
\(253\) 19.8249 1.24638
\(254\) −16.5771 −1.04014
\(255\) −2.46277 −0.154225
\(256\) −25.0902 −1.56814
\(257\) −25.2387 −1.57434 −0.787172 0.616734i \(-0.788456\pi\)
−0.787172 + 0.616734i \(0.788456\pi\)
\(258\) −0.287811 −0.0179183
\(259\) −3.79460 −0.235785
\(260\) −19.5793 −1.21426
\(261\) 22.4335 1.38860
\(262\) 36.9968 2.28567
\(263\) −14.0847 −0.868502 −0.434251 0.900792i \(-0.642987\pi\)
−0.434251 + 0.900792i \(0.642987\pi\)
\(264\) −63.4110 −3.90268
\(265\) 0.386060 0.0237155
\(266\) −2.70020 −0.165560
\(267\) 25.7958 1.57868
\(268\) −6.16347 −0.376494
\(269\) −20.5744 −1.25444 −0.627221 0.778841i \(-0.715808\pi\)
−0.627221 + 0.778841i \(0.715808\pi\)
\(270\) 10.0784 0.613353
\(271\) −5.67560 −0.344768 −0.172384 0.985030i \(-0.555147\pi\)
−0.172384 + 0.985030i \(0.555147\pi\)
\(272\) 9.32351 0.565321
\(273\) −58.5598 −3.54420
\(274\) 17.0522 1.03016
\(275\) 14.8111 0.893142
\(276\) 76.3497 4.59571
\(277\) −11.9693 −0.719165 −0.359583 0.933113i \(-0.617081\pi\)
−0.359583 + 0.933113i \(0.617081\pi\)
\(278\) 32.7745 1.96568
\(279\) 39.5858 2.36994
\(280\) 19.6642 1.17516
\(281\) −0.290839 −0.0173500 −0.00867500 0.999962i \(-0.502761\pi\)
−0.00867500 + 0.999962i \(0.502761\pi\)
\(282\) 41.2582 2.45689
\(283\) 22.7986 1.35523 0.677617 0.735415i \(-0.263013\pi\)
0.677617 + 0.735415i \(0.263013\pi\)
\(284\) −53.6655 −3.18446
\(285\) 0.593653 0.0351650
\(286\) −47.6788 −2.81931
\(287\) −14.7557 −0.871000
\(288\) −35.7751 −2.10807
\(289\) −15.6843 −0.922604
\(290\) −9.18666 −0.539459
\(291\) −25.5659 −1.49870
\(292\) 22.1682 1.29730
\(293\) −19.2419 −1.12412 −0.562062 0.827095i \(-0.689992\pi\)
−0.562062 + 0.827095i \(0.689992\pi\)
\(294\) 53.2627 3.10635
\(295\) −6.29022 −0.366231
\(296\) −6.75123 −0.392407
\(297\) 17.1316 0.994075
\(298\) −49.2680 −2.85402
\(299\) 32.5734 1.88377
\(300\) 57.0404 3.29323
\(301\) 0.151713 0.00874461
\(302\) −27.8292 −1.60139
\(303\) −37.0994 −2.13130
\(304\) −2.24744 −0.128899
\(305\) 6.36070 0.364213
\(306\) −14.2405 −0.814073
\(307\) −32.1616 −1.83556 −0.917781 0.397087i \(-0.870021\pi\)
−0.917781 + 0.397087i \(0.870021\pi\)
\(308\) 58.9096 3.35668
\(309\) −34.2268 −1.94709
\(310\) −16.2106 −0.920701
\(311\) −15.6063 −0.884953 −0.442477 0.896780i \(-0.645900\pi\)
−0.442477 + 0.896780i \(0.645900\pi\)
\(312\) −104.188 −5.89846
\(313\) 23.1099 1.30625 0.653125 0.757250i \(-0.273458\pi\)
0.653125 + 0.757250i \(0.273458\pi\)
\(314\) −14.0995 −0.795679
\(315\) −14.0507 −0.791665
\(316\) −6.33164 −0.356183
\(317\) −14.6109 −0.820628 −0.410314 0.911944i \(-0.634581\pi\)
−0.410314 + 0.911944i \(0.634581\pi\)
\(318\) 3.62058 0.203032
\(319\) −15.6157 −0.874313
\(320\) 2.17190 0.121413
\(321\) −7.44503 −0.415541
\(322\) −57.6562 −3.21306
\(323\) −0.317158 −0.0176472
\(324\) −0.930624 −0.0517013
\(325\) 24.3354 1.34989
\(326\) −7.42236 −0.411086
\(327\) −2.79713 −0.154682
\(328\) −26.2528 −1.44957
\(329\) −21.7483 −1.19903
\(330\) −18.5544 −1.02138
\(331\) −18.8464 −1.03589 −0.517946 0.855413i \(-0.673303\pi\)
−0.517946 + 0.855413i \(0.673303\pi\)
\(332\) 39.5305 2.16952
\(333\) 4.82396 0.264351
\(334\) 55.8098 3.05378
\(335\) −1.02330 −0.0559086
\(336\) 86.2731 4.70658
\(337\) 6.09462 0.331995 0.165998 0.986126i \(-0.446916\pi\)
0.165998 + 0.986126i \(0.446916\pi\)
\(338\) −44.8823 −2.44128
\(339\) −3.73205 −0.202697
\(340\) 4.07063 0.220761
\(341\) −27.5552 −1.49220
\(342\) 3.43268 0.185618
\(343\) −1.51407 −0.0817520
\(344\) 0.269923 0.0145533
\(345\) 12.6760 0.682455
\(346\) 13.7399 0.738660
\(347\) 4.15108 0.222842 0.111421 0.993773i \(-0.464460\pi\)
0.111421 + 0.993773i \(0.464460\pi\)
\(348\) −60.1393 −3.22380
\(349\) 1.11621 0.0597494 0.0298747 0.999554i \(-0.490489\pi\)
0.0298747 + 0.999554i \(0.490489\pi\)
\(350\) −43.0746 −2.30244
\(351\) 28.1481 1.50243
\(352\) 24.9027 1.32732
\(353\) −24.3085 −1.29381 −0.646905 0.762570i \(-0.723937\pi\)
−0.646905 + 0.762570i \(0.723937\pi\)
\(354\) −58.9914 −3.13536
\(355\) −8.90986 −0.472886
\(356\) −42.6370 −2.25976
\(357\) 12.1748 0.644361
\(358\) −18.7208 −0.989427
\(359\) 21.0044 1.10857 0.554285 0.832327i \(-0.312992\pi\)
0.554285 + 0.832327i \(0.312992\pi\)
\(360\) −24.9985 −1.31754
\(361\) −18.9235 −0.995976
\(362\) −53.7848 −2.82687
\(363\) −0.770707 −0.0404516
\(364\) 96.7915 5.07325
\(365\) 3.68050 0.192646
\(366\) 59.6524 3.11808
\(367\) 7.53376 0.393259 0.196629 0.980478i \(-0.437000\pi\)
0.196629 + 0.980478i \(0.437000\pi\)
\(368\) −47.9887 −2.50158
\(369\) 18.7584 0.976525
\(370\) −1.97544 −0.102698
\(371\) −1.90851 −0.0990849
\(372\) −106.121 −5.50210
\(373\) 3.67283 0.190172 0.0950861 0.995469i \(-0.469687\pi\)
0.0950861 + 0.995469i \(0.469687\pi\)
\(374\) 9.91263 0.512570
\(375\) 20.2054 1.04340
\(376\) −38.6939 −1.99549
\(377\) −25.6575 −1.32143
\(378\) −49.8232 −2.56263
\(379\) −7.97831 −0.409818 −0.204909 0.978781i \(-0.565690\pi\)
−0.204909 + 0.978781i \(0.565690\pi\)
\(380\) −0.981229 −0.0503360
\(381\) −18.0171 −0.923046
\(382\) −38.6496 −1.97749
\(383\) 15.5308 0.793589 0.396795 0.917907i \(-0.370123\pi\)
0.396795 + 0.917907i \(0.370123\pi\)
\(384\) −21.1191 −1.07773
\(385\) 9.78052 0.498461
\(386\) −66.1590 −3.36741
\(387\) −0.192868 −0.00980406
\(388\) 42.2569 2.14527
\(389\) 23.1812 1.17533 0.587667 0.809103i \(-0.300047\pi\)
0.587667 + 0.809103i \(0.300047\pi\)
\(390\) −30.4858 −1.54371
\(391\) −6.77215 −0.342483
\(392\) −49.9524 −2.52298
\(393\) 40.2107 2.02836
\(394\) −60.6999 −3.05801
\(395\) −1.05122 −0.0528925
\(396\) −74.8899 −3.76336
\(397\) 32.1465 1.61339 0.806694 0.590969i \(-0.201255\pi\)
0.806694 + 0.590969i \(0.201255\pi\)
\(398\) 18.8724 0.945987
\(399\) −2.93475 −0.146921
\(400\) −35.8521 −1.79260
\(401\) −24.8193 −1.23942 −0.619709 0.784832i \(-0.712749\pi\)
−0.619709 + 0.784832i \(0.712749\pi\)
\(402\) −9.59676 −0.478643
\(403\) −45.2747 −2.25529
\(404\) 61.3203 3.05080
\(405\) −0.154508 −0.00767755
\(406\) 45.4148 2.25390
\(407\) −3.35791 −0.166445
\(408\) 21.6611 1.07238
\(409\) 21.2342 1.04996 0.524981 0.851114i \(-0.324072\pi\)
0.524981 + 0.851114i \(0.324072\pi\)
\(410\) −7.68169 −0.379372
\(411\) 18.5334 0.914187
\(412\) 56.5723 2.78712
\(413\) 31.0960 1.53013
\(414\) 73.2966 3.60233
\(415\) 6.56309 0.322170
\(416\) 40.9164 2.00609
\(417\) 35.6215 1.74439
\(418\) −2.38945 −0.116872
\(419\) −18.0652 −0.882541 −0.441271 0.897374i \(-0.645472\pi\)
−0.441271 + 0.897374i \(0.645472\pi\)
\(420\) 37.6667 1.83795
\(421\) 2.97743 0.145111 0.0725556 0.997364i \(-0.476885\pi\)
0.0725556 + 0.997364i \(0.476885\pi\)
\(422\) 13.4810 0.656245
\(423\) 27.6480 1.34429
\(424\) −3.39556 −0.164903
\(425\) −5.05944 −0.245419
\(426\) −83.5591 −4.04845
\(427\) −31.4445 −1.52170
\(428\) 12.3056 0.594815
\(429\) −51.8205 −2.50192
\(430\) 0.0789808 0.00380879
\(431\) 10.9728 0.528542 0.264271 0.964448i \(-0.414869\pi\)
0.264271 + 0.964448i \(0.414869\pi\)
\(432\) −41.4691 −1.99518
\(433\) 5.18439 0.249146 0.124573 0.992210i \(-0.460244\pi\)
0.124573 + 0.992210i \(0.460244\pi\)
\(434\) 80.1380 3.84675
\(435\) −9.98468 −0.478729
\(436\) 4.62329 0.221415
\(437\) 1.63243 0.0780899
\(438\) 34.5168 1.64927
\(439\) −21.7006 −1.03571 −0.517855 0.855468i \(-0.673269\pi\)
−0.517855 + 0.855468i \(0.673269\pi\)
\(440\) 17.4012 0.829568
\(441\) 35.6925 1.69964
\(442\) 16.2870 0.774693
\(443\) 10.0546 0.477708 0.238854 0.971055i \(-0.423228\pi\)
0.238854 + 0.971055i \(0.423228\pi\)
\(444\) −12.9320 −0.613724
\(445\) −7.07885 −0.335570
\(446\) −18.3008 −0.866566
\(447\) −53.5478 −2.53272
\(448\) −10.7369 −0.507271
\(449\) −27.5531 −1.30031 −0.650157 0.759800i \(-0.725297\pi\)
−0.650157 + 0.759800i \(0.725297\pi\)
\(450\) 54.7594 2.58139
\(451\) −13.0575 −0.614856
\(452\) 6.16858 0.290146
\(453\) −30.2467 −1.42111
\(454\) −13.2868 −0.623578
\(455\) 16.0699 0.753369
\(456\) −5.22142 −0.244515
\(457\) −6.43745 −0.301131 −0.150566 0.988600i \(-0.548109\pi\)
−0.150566 + 0.988600i \(0.548109\pi\)
\(458\) −43.4671 −2.03108
\(459\) −5.85211 −0.273153
\(460\) −20.9518 −0.976883
\(461\) 22.8235 1.06300 0.531498 0.847060i \(-0.321629\pi\)
0.531498 + 0.847060i \(0.321629\pi\)
\(462\) 91.7244 4.26741
\(463\) −5.67923 −0.263936 −0.131968 0.991254i \(-0.542130\pi\)
−0.131968 + 0.991254i \(0.542130\pi\)
\(464\) 37.7998 1.75481
\(465\) −17.6188 −0.817051
\(466\) 41.7297 1.93309
\(467\) −26.7411 −1.23743 −0.618716 0.785615i \(-0.712347\pi\)
−0.618716 + 0.785615i \(0.712347\pi\)
\(468\) −123.048 −5.68790
\(469\) 5.05872 0.233590
\(470\) −11.3220 −0.522246
\(471\) −15.3242 −0.706104
\(472\) 55.3250 2.54654
\(473\) 0.134254 0.00617299
\(474\) −9.85861 −0.452821
\(475\) 1.21958 0.0559582
\(476\) −20.1234 −0.922354
\(477\) 2.42623 0.111089
\(478\) 60.3024 2.75817
\(479\) −34.5141 −1.57699 −0.788494 0.615043i \(-0.789139\pi\)
−0.788494 + 0.615043i \(0.789139\pi\)
\(480\) 15.9227 0.726770
\(481\) −5.51722 −0.251563
\(482\) −47.5809 −2.16725
\(483\) −62.6647 −2.85134
\(484\) 1.27387 0.0579034
\(485\) 7.01575 0.318569
\(486\) −40.8391 −1.85250
\(487\) −12.9759 −0.587993 −0.293997 0.955806i \(-0.594985\pi\)
−0.293997 + 0.955806i \(0.594985\pi\)
\(488\) −55.9449 −2.53251
\(489\) −8.06711 −0.364807
\(490\) −14.6163 −0.660297
\(491\) −10.4326 −0.470814 −0.235407 0.971897i \(-0.575642\pi\)
−0.235407 + 0.971897i \(0.575642\pi\)
\(492\) −50.2872 −2.26712
\(493\) 5.33430 0.240245
\(494\) −3.92599 −0.176639
\(495\) −12.4337 −0.558852
\(496\) 66.7008 2.99495
\(497\) 44.0464 1.97575
\(498\) 61.5505 2.75814
\(499\) 11.8480 0.530391 0.265195 0.964195i \(-0.414564\pi\)
0.265195 + 0.964195i \(0.414564\pi\)
\(500\) −33.3968 −1.49355
\(501\) 60.6579 2.70999
\(502\) −59.0626 −2.63609
\(503\) 7.03071 0.313484 0.156742 0.987640i \(-0.449901\pi\)
0.156742 + 0.987640i \(0.449901\pi\)
\(504\) 123.581 5.50475
\(505\) 10.1808 0.453038
\(506\) −51.0210 −2.26816
\(507\) −48.7811 −2.16645
\(508\) 29.7799 1.32127
\(509\) 14.6601 0.649795 0.324898 0.945749i \(-0.394670\pi\)
0.324898 + 0.945749i \(0.394670\pi\)
\(510\) 6.33813 0.280657
\(511\) −18.1948 −0.804888
\(512\) 49.4711 2.18633
\(513\) 1.41065 0.0622819
\(514\) 64.9536 2.86498
\(515\) 9.39248 0.413882
\(516\) 0.517037 0.0227613
\(517\) −19.2455 −0.846415
\(518\) 9.76569 0.429080
\(519\) 14.9334 0.655504
\(520\) 28.5910 1.25380
\(521\) 10.8376 0.474803 0.237402 0.971412i \(-0.423704\pi\)
0.237402 + 0.971412i \(0.423704\pi\)
\(522\) −57.7344 −2.52696
\(523\) −42.1034 −1.84105 −0.920526 0.390682i \(-0.872239\pi\)
−0.920526 + 0.390682i \(0.872239\pi\)
\(524\) −66.4628 −2.90344
\(525\) −46.8164 −2.04324
\(526\) 36.2481 1.58049
\(527\) 9.41281 0.410028
\(528\) 76.3445 3.32247
\(529\) 11.8567 0.515509
\(530\) −0.993555 −0.0431573
\(531\) −39.5314 −1.71552
\(532\) 4.85076 0.210307
\(533\) −21.4542 −0.929286
\(534\) −66.3874 −2.87287
\(535\) 2.04306 0.0883290
\(536\) 9.00031 0.388754
\(537\) −20.3471 −0.878040
\(538\) 52.9497 2.28283
\(539\) −24.8452 −1.07016
\(540\) −18.1053 −0.779130
\(541\) −40.1221 −1.72498 −0.862492 0.506070i \(-0.831098\pi\)
−0.862492 + 0.506070i \(0.831098\pi\)
\(542\) 14.6066 0.627406
\(543\) −58.4569 −2.50863
\(544\) −8.50670 −0.364722
\(545\) 0.767586 0.0328798
\(546\) 150.708 6.44971
\(547\) 15.6923 0.670956 0.335478 0.942048i \(-0.391102\pi\)
0.335478 + 0.942048i \(0.391102\pi\)
\(548\) −30.6333 −1.30859
\(549\) 39.9744 1.70606
\(550\) −38.1175 −1.62533
\(551\) −1.28584 −0.0547785
\(552\) −111.491 −4.74537
\(553\) 5.19675 0.220988
\(554\) 30.8039 1.30873
\(555\) −2.14704 −0.0911368
\(556\) −58.8776 −2.49697
\(557\) 6.60905 0.280035 0.140017 0.990149i \(-0.455284\pi\)
0.140017 + 0.990149i \(0.455284\pi\)
\(558\) −101.877 −4.31280
\(559\) 0.220586 0.00932979
\(560\) −23.6749 −1.00045
\(561\) 10.7737 0.454867
\(562\) 0.748496 0.0315734
\(563\) 31.5226 1.32852 0.664259 0.747503i \(-0.268747\pi\)
0.664259 + 0.747503i \(0.268747\pi\)
\(564\) −74.1181 −3.12094
\(565\) 1.02414 0.0430861
\(566\) −58.6738 −2.46624
\(567\) 0.763817 0.0320773
\(568\) 78.3658 3.28816
\(569\) −24.2340 −1.01594 −0.507970 0.861375i \(-0.669604\pi\)
−0.507970 + 0.861375i \(0.669604\pi\)
\(570\) −1.52781 −0.0639929
\(571\) −34.7542 −1.45442 −0.727210 0.686415i \(-0.759183\pi\)
−0.727210 + 0.686415i \(0.759183\pi\)
\(572\) 85.6524 3.58131
\(573\) −42.0070 −1.75487
\(574\) 37.9748 1.58504
\(575\) 26.0412 1.08599
\(576\) 13.6495 0.568729
\(577\) 33.3451 1.38817 0.694087 0.719891i \(-0.255808\pi\)
0.694087 + 0.719891i \(0.255808\pi\)
\(578\) 40.3646 1.67895
\(579\) −71.9061 −2.98831
\(580\) 16.5033 0.685264
\(581\) −32.4450 −1.34605
\(582\) 65.7957 2.72732
\(583\) −1.68887 −0.0699459
\(584\) −32.3715 −1.33954
\(585\) −20.4292 −0.844642
\(586\) 49.5205 2.04567
\(587\) −12.4789 −0.515060 −0.257530 0.966270i \(-0.582909\pi\)
−0.257530 + 0.966270i \(0.582909\pi\)
\(588\) −95.6836 −3.94593
\(589\) −2.26896 −0.0934911
\(590\) 16.1883 0.666464
\(591\) −65.9727 −2.71375
\(592\) 8.12822 0.334068
\(593\) −8.27400 −0.339772 −0.169886 0.985464i \(-0.554340\pi\)
−0.169886 + 0.985464i \(0.554340\pi\)
\(594\) −44.0894 −1.80901
\(595\) −3.34100 −0.136968
\(596\) 88.5073 3.62540
\(597\) 20.5118 0.839491
\(598\) −83.8301 −3.42807
\(599\) 3.22235 0.131662 0.0658309 0.997831i \(-0.479030\pi\)
0.0658309 + 0.997831i \(0.479030\pi\)
\(600\) −83.2942 −3.40047
\(601\) −36.4396 −1.48640 −0.743200 0.669069i \(-0.766693\pi\)
−0.743200 + 0.669069i \(0.766693\pi\)
\(602\) −0.390446 −0.0159134
\(603\) −6.43099 −0.261890
\(604\) 49.9937 2.03422
\(605\) 0.211496 0.00859855
\(606\) 95.4781 3.87853
\(607\) 39.1463 1.58890 0.794449 0.607331i \(-0.207760\pi\)
0.794449 + 0.607331i \(0.207760\pi\)
\(608\) 2.05055 0.0831606
\(609\) 49.3598 2.00016
\(610\) −16.3697 −0.662791
\(611\) −31.6213 −1.27926
\(612\) 25.5822 1.03410
\(613\) 26.5512 1.07239 0.536196 0.844093i \(-0.319861\pi\)
0.536196 + 0.844093i \(0.319861\pi\)
\(614\) 82.7704 3.34034
\(615\) −8.34898 −0.336663
\(616\) −86.0236 −3.46599
\(617\) 23.5946 0.949883 0.474941 0.880017i \(-0.342469\pi\)
0.474941 + 0.880017i \(0.342469\pi\)
\(618\) 88.0852 3.54331
\(619\) 31.1957 1.25386 0.626930 0.779076i \(-0.284311\pi\)
0.626930 + 0.779076i \(0.284311\pi\)
\(620\) 29.1215 1.16955
\(621\) 30.1212 1.20872
\(622\) 40.1640 1.61043
\(623\) 34.9947 1.40203
\(624\) 125.438 5.02154
\(625\) 16.5093 0.660373
\(626\) −59.4751 −2.37710
\(627\) −2.59701 −0.103715
\(628\) 25.3289 1.01073
\(629\) 1.14705 0.0457360
\(630\) 36.1605 1.44067
\(631\) 20.2848 0.807523 0.403762 0.914864i \(-0.367703\pi\)
0.403762 + 0.914864i \(0.367703\pi\)
\(632\) 9.24588 0.367782
\(633\) 14.6521 0.582367
\(634\) 37.6022 1.49337
\(635\) 4.94424 0.196206
\(636\) −6.50418 −0.257908
\(637\) −40.8219 −1.61742
\(638\) 40.1883 1.59107
\(639\) −55.9948 −2.21512
\(640\) 5.79548 0.229087
\(641\) −17.5595 −0.693560 −0.346780 0.937946i \(-0.612725\pi\)
−0.346780 + 0.937946i \(0.612725\pi\)
\(642\) 19.1603 0.756198
\(643\) 8.88187 0.350267 0.175133 0.984545i \(-0.443964\pi\)
0.175133 + 0.984545i \(0.443964\pi\)
\(644\) 103.576 4.08148
\(645\) 0.0858416 0.00338001
\(646\) 0.816230 0.0321142
\(647\) 16.0580 0.631304 0.315652 0.948875i \(-0.397777\pi\)
0.315652 + 0.948875i \(0.397777\pi\)
\(648\) 1.35896 0.0533849
\(649\) 27.5174 1.08015
\(650\) −62.6290 −2.45651
\(651\) 87.0994 3.41369
\(652\) 13.3339 0.522194
\(653\) −43.0734 −1.68559 −0.842796 0.538234i \(-0.819092\pi\)
−0.842796 + 0.538234i \(0.819092\pi\)
\(654\) 7.19864 0.281489
\(655\) −11.0346 −0.431156
\(656\) 31.6074 1.23406
\(657\) 23.1304 0.902404
\(658\) 55.9710 2.18198
\(659\) 35.6114 1.38722 0.693611 0.720350i \(-0.256019\pi\)
0.693611 + 0.720350i \(0.256019\pi\)
\(660\) 33.3319 1.29744
\(661\) −19.1643 −0.745404 −0.372702 0.927951i \(-0.621569\pi\)
−0.372702 + 0.927951i \(0.621569\pi\)
\(662\) 48.5027 1.88511
\(663\) 17.7018 0.687480
\(664\) −57.7251 −2.24017
\(665\) 0.805352 0.0312302
\(666\) −12.4148 −0.481065
\(667\) −27.4560 −1.06310
\(668\) −100.259 −3.87915
\(669\) −19.8905 −0.769011
\(670\) 2.63353 0.101742
\(671\) −27.8257 −1.07420
\(672\) −78.7149 −3.03649
\(673\) 25.3342 0.976560 0.488280 0.872687i \(-0.337624\pi\)
0.488280 + 0.872687i \(0.337624\pi\)
\(674\) −15.6850 −0.604162
\(675\) 22.5033 0.866154
\(676\) 80.6287 3.10110
\(677\) 25.4550 0.978317 0.489158 0.872195i \(-0.337304\pi\)
0.489158 + 0.872195i \(0.337304\pi\)
\(678\) 9.60471 0.368867
\(679\) −34.6827 −1.33100
\(680\) −5.94420 −0.227950
\(681\) −14.4409 −0.553378
\(682\) 70.9155 2.71549
\(683\) −24.2521 −0.927980 −0.463990 0.885841i \(-0.653583\pi\)
−0.463990 + 0.885841i \(0.653583\pi\)
\(684\) −6.16662 −0.235786
\(685\) −5.08592 −0.194323
\(686\) 3.89657 0.148772
\(687\) −47.2430 −1.80243
\(688\) −0.324977 −0.0123896
\(689\) −2.77491 −0.105715
\(690\) −32.6227 −1.24193
\(691\) 34.0736 1.29622 0.648111 0.761546i \(-0.275559\pi\)
0.648111 + 0.761546i \(0.275559\pi\)
\(692\) −24.6829 −0.938304
\(693\) 61.4665 2.33492
\(694\) −10.6831 −0.405525
\(695\) −9.77521 −0.370795
\(696\) 87.8193 3.32878
\(697\) 4.46043 0.168951
\(698\) −2.87265 −0.108732
\(699\) 45.3546 1.71547
\(700\) 77.3813 2.92474
\(701\) 17.0263 0.643074 0.321537 0.946897i \(-0.395801\pi\)
0.321537 + 0.946897i \(0.395801\pi\)
\(702\) −72.4412 −2.73412
\(703\) −0.276498 −0.0104283
\(704\) −9.50127 −0.358093
\(705\) −12.3055 −0.463453
\(706\) 62.5597 2.35447
\(707\) −50.3292 −1.89282
\(708\) 105.975 3.98278
\(709\) −16.6910 −0.626844 −0.313422 0.949614i \(-0.601475\pi\)
−0.313422 + 0.949614i \(0.601475\pi\)
\(710\) 22.9302 0.860555
\(711\) −6.60647 −0.247762
\(712\) 62.2614 2.33334
\(713\) −48.4483 −1.81440
\(714\) −31.3329 −1.17260
\(715\) 14.2205 0.531817
\(716\) 33.6310 1.25685
\(717\) 65.5407 2.44766
\(718\) −54.0564 −2.01737
\(719\) −22.3267 −0.832644 −0.416322 0.909217i \(-0.636681\pi\)
−0.416322 + 0.909217i \(0.636681\pi\)
\(720\) 30.0972 1.12166
\(721\) −46.4322 −1.72923
\(722\) 48.7012 1.81247
\(723\) −51.7141 −1.92327
\(724\) 96.6215 3.59091
\(725\) −20.5122 −0.761804
\(726\) 1.98347 0.0736135
\(727\) 31.8223 1.18022 0.590112 0.807321i \(-0.299084\pi\)
0.590112 + 0.807321i \(0.299084\pi\)
\(728\) −141.341 −5.23846
\(729\) −43.7828 −1.62158
\(730\) −9.47205 −0.350576
\(731\) −0.0458608 −0.00169622
\(732\) −107.162 −3.96083
\(733\) 9.69282 0.358012 0.179006 0.983848i \(-0.442712\pi\)
0.179006 + 0.983848i \(0.442712\pi\)
\(734\) −19.3887 −0.715649
\(735\) −15.8860 −0.585963
\(736\) 43.7845 1.61392
\(737\) 4.47654 0.164896
\(738\) −48.2762 −1.77707
\(739\) 44.9298 1.65277 0.826384 0.563107i \(-0.190394\pi\)
0.826384 + 0.563107i \(0.190394\pi\)
\(740\) 3.54877 0.130455
\(741\) −4.26703 −0.156753
\(742\) 4.91169 0.180314
\(743\) −17.8303 −0.654128 −0.327064 0.945002i \(-0.606059\pi\)
−0.327064 + 0.945002i \(0.606059\pi\)
\(744\) 154.964 5.68127
\(745\) 14.6945 0.538365
\(746\) −9.45232 −0.346074
\(747\) 41.2463 1.50912
\(748\) −17.8075 −0.651107
\(749\) −10.1000 −0.369044
\(750\) −52.0001 −1.89878
\(751\) 14.2598 0.520348 0.260174 0.965562i \(-0.416220\pi\)
0.260174 + 0.965562i \(0.416220\pi\)
\(752\) 46.5860 1.69882
\(753\) −64.1932 −2.33933
\(754\) 66.0314 2.40472
\(755\) 8.30025 0.302077
\(756\) 89.5047 3.25525
\(757\) −42.2575 −1.53587 −0.767937 0.640526i \(-0.778716\pi\)
−0.767937 + 0.640526i \(0.778716\pi\)
\(758\) 20.5328 0.745784
\(759\) −55.4530 −2.01282
\(760\) 1.43285 0.0519751
\(761\) −5.79752 −0.210160 −0.105080 0.994464i \(-0.533510\pi\)
−0.105080 + 0.994464i \(0.533510\pi\)
\(762\) 46.3684 1.67975
\(763\) −3.79460 −0.137374
\(764\) 69.4319 2.51196
\(765\) 4.24731 0.153562
\(766\) −39.9698 −1.44417
\(767\) 45.2125 1.63253
\(768\) 70.1808 2.53243
\(769\) −41.7493 −1.50552 −0.752759 0.658296i \(-0.771278\pi\)
−0.752759 + 0.658296i \(0.771278\pi\)
\(770\) −25.1709 −0.907096
\(771\) 70.5959 2.54245
\(772\) 118.851 4.27755
\(773\) 9.73903 0.350289 0.175144 0.984543i \(-0.443961\pi\)
0.175144 + 0.984543i \(0.443961\pi\)
\(774\) 0.496362 0.0178413
\(775\) −36.1955 −1.30018
\(776\) −61.7064 −2.21513
\(777\) 10.6140 0.380776
\(778\) −59.6585 −2.13886
\(779\) −1.07519 −0.0385227
\(780\) 54.7660 1.96094
\(781\) 38.9774 1.39472
\(782\) 17.4286 0.623247
\(783\) −23.7259 −0.847894
\(784\) 60.1408 2.14788
\(785\) 4.20526 0.150092
\(786\) −103.485 −3.69119
\(787\) −15.3198 −0.546091 −0.273045 0.962001i \(-0.588031\pi\)
−0.273045 + 0.962001i \(0.588031\pi\)
\(788\) 109.044 3.88453
\(789\) 39.3969 1.40257
\(790\) 2.70539 0.0962533
\(791\) −5.06291 −0.180016
\(792\) 109.359 3.88591
\(793\) −45.7191 −1.62353
\(794\) −82.7315 −2.93603
\(795\) −1.07986 −0.0382988
\(796\) −33.9032 −1.20167
\(797\) −40.0378 −1.41821 −0.709105 0.705103i \(-0.750901\pi\)
−0.709105 + 0.705103i \(0.750901\pi\)
\(798\) 7.55281 0.267367
\(799\) 6.57421 0.232579
\(800\) 32.7112 1.15651
\(801\) −44.4877 −1.57189
\(802\) 63.8744 2.25548
\(803\) −16.1008 −0.568186
\(804\) 17.2401 0.608010
\(805\) 17.1964 0.606092
\(806\) 116.518 4.10417
\(807\) 57.5493 2.02583
\(808\) −89.5440 −3.15015
\(809\) 30.5895 1.07547 0.537735 0.843114i \(-0.319280\pi\)
0.537735 + 0.843114i \(0.319280\pi\)
\(810\) 0.397637 0.0139715
\(811\) −46.7273 −1.64082 −0.820409 0.571776i \(-0.806254\pi\)
−0.820409 + 0.571776i \(0.806254\pi\)
\(812\) −81.5852 −2.86308
\(813\) 15.8754 0.556775
\(814\) 8.64182 0.302896
\(815\) 2.21377 0.0775449
\(816\) −26.0791 −0.912951
\(817\) 0.0110548 0.000386758 0
\(818\) −54.6477 −1.91071
\(819\) 100.993 3.52897
\(820\) 13.7997 0.481908
\(821\) 17.3017 0.603832 0.301916 0.953335i \(-0.402374\pi\)
0.301916 + 0.953335i \(0.402374\pi\)
\(822\) −47.6972 −1.66363
\(823\) −22.5515 −0.786097 −0.393049 0.919518i \(-0.628580\pi\)
−0.393049 + 0.919518i \(0.628580\pi\)
\(824\) −82.6106 −2.87788
\(825\) −41.4286 −1.44236
\(826\) −80.0279 −2.78453
\(827\) −30.5809 −1.06340 −0.531701 0.846932i \(-0.678447\pi\)
−0.531701 + 0.846932i \(0.678447\pi\)
\(828\) −131.673 −4.57597
\(829\) −4.08466 −0.141866 −0.0709331 0.997481i \(-0.522598\pi\)
−0.0709331 + 0.997481i \(0.522598\pi\)
\(830\) −16.8906 −0.586282
\(831\) 33.4797 1.16140
\(832\) −15.6111 −0.541217
\(833\) 8.48706 0.294059
\(834\) −91.6747 −3.17443
\(835\) −16.6457 −0.576047
\(836\) 4.29251 0.148460
\(837\) −41.8663 −1.44711
\(838\) 46.4921 1.60604
\(839\) −34.6580 −1.19653 −0.598263 0.801300i \(-0.704142\pi\)
−0.598263 + 0.801300i \(0.704142\pi\)
\(840\) −55.0034 −1.89780
\(841\) −7.37343 −0.254256
\(842\) −7.66265 −0.264072
\(843\) 0.813516 0.0280190
\(844\) −24.2179 −0.833615
\(845\) 13.3864 0.460508
\(846\) −71.1542 −2.44633
\(847\) −1.04554 −0.0359253
\(848\) 4.08812 0.140387
\(849\) −63.7706 −2.18860
\(850\) 13.0208 0.446611
\(851\) −5.90396 −0.202385
\(852\) 150.110 5.14267
\(853\) 6.82471 0.233674 0.116837 0.993151i \(-0.462725\pi\)
0.116837 + 0.993151i \(0.462725\pi\)
\(854\) 80.9247 2.76919
\(855\) −1.02382 −0.0350138
\(856\) −17.9695 −0.614185
\(857\) −21.9574 −0.750052 −0.375026 0.927014i \(-0.622366\pi\)
−0.375026 + 0.927014i \(0.622366\pi\)
\(858\) 133.364 4.55297
\(859\) 0.141623 0.00483210 0.00241605 0.999997i \(-0.499231\pi\)
0.00241605 + 0.999997i \(0.499231\pi\)
\(860\) −0.141885 −0.00483823
\(861\) 41.2736 1.40660
\(862\) −28.2394 −0.961837
\(863\) −31.2078 −1.06232 −0.531162 0.847270i \(-0.678245\pi\)
−0.531162 + 0.847270i \(0.678245\pi\)
\(864\) 37.8361 1.28721
\(865\) −4.09801 −0.139336
\(866\) −13.3424 −0.453394
\(867\) 43.8710 1.48994
\(868\) −143.964 −4.88644
\(869\) 4.59869 0.156000
\(870\) 25.6963 0.871187
\(871\) 7.35520 0.249221
\(872\) −6.75123 −0.228626
\(873\) 44.0911 1.49226
\(874\) −4.20119 −0.142107
\(875\) 27.4107 0.926651
\(876\) −62.0075 −2.09504
\(877\) −44.2548 −1.49438 −0.747189 0.664612i \(-0.768597\pi\)
−0.747189 + 0.664612i \(0.768597\pi\)
\(878\) 55.8480 1.88478
\(879\) 53.8222 1.81538
\(880\) −20.9503 −0.706236
\(881\) 30.2757 1.02001 0.510007 0.860170i \(-0.329643\pi\)
0.510007 + 0.860170i \(0.329643\pi\)
\(882\) −91.8574 −3.09300
\(883\) −20.2487 −0.681424 −0.340712 0.940168i \(-0.610668\pi\)
−0.340712 + 0.940168i \(0.610668\pi\)
\(884\) −29.2587 −0.984076
\(885\) 17.5946 0.591435
\(886\) −25.8763 −0.869330
\(887\) −37.7946 −1.26902 −0.634509 0.772916i \(-0.718798\pi\)
−0.634509 + 0.772916i \(0.718798\pi\)
\(888\) 18.8841 0.633709
\(889\) −24.4421 −0.819762
\(890\) 18.2180 0.610667
\(891\) 0.675915 0.0226440
\(892\) 32.8763 1.10078
\(893\) −1.58472 −0.0530306
\(894\) 137.809 4.60903
\(895\) 5.58361 0.186640
\(896\) −28.6503 −0.957139
\(897\) −91.1122 −3.04215
\(898\) 70.9101 2.36630
\(899\) 38.1618 1.27277
\(900\) −98.3724 −3.27908
\(901\) 0.576915 0.0192198
\(902\) 33.6046 1.11891
\(903\) −0.424363 −0.0141219
\(904\) −9.00777 −0.299594
\(905\) 16.0417 0.533243
\(906\) 77.8421 2.58613
\(907\) −23.9684 −0.795859 −0.397929 0.917416i \(-0.630271\pi\)
−0.397929 + 0.917416i \(0.630271\pi\)
\(908\) 23.8689 0.792119
\(909\) 63.9819 2.12215
\(910\) −41.3571 −1.37097
\(911\) 22.9683 0.760974 0.380487 0.924786i \(-0.375756\pi\)
0.380487 + 0.924786i \(0.375756\pi\)
\(912\) 6.28639 0.208163
\(913\) −28.7111 −0.950199
\(914\) 16.5673 0.547996
\(915\) −17.7917 −0.588177
\(916\) 78.0863 2.58004
\(917\) 54.5499 1.80140
\(918\) 15.0608 0.497082
\(919\) −3.41070 −0.112509 −0.0562543 0.998416i \(-0.517916\pi\)
−0.0562543 + 0.998416i \(0.517916\pi\)
\(920\) 30.5952 1.00869
\(921\) 89.9604 2.96430
\(922\) −58.7380 −1.93443
\(923\) 64.0418 2.10796
\(924\) −164.778 −5.42080
\(925\) −4.41081 −0.145027
\(926\) 14.6159 0.480309
\(927\) 59.0278 1.93873
\(928\) −34.4883 −1.13213
\(929\) −19.4744 −0.638933 −0.319467 0.947598i \(-0.603504\pi\)
−0.319467 + 0.947598i \(0.603504\pi\)
\(930\) 45.3433 1.48686
\(931\) −2.04581 −0.0670488
\(932\) −74.9652 −2.45557
\(933\) 43.6530 1.42913
\(934\) 68.8203 2.25187
\(935\) −2.95651 −0.0966882
\(936\) 179.683 5.87312
\(937\) −2.62172 −0.0856478 −0.0428239 0.999083i \(-0.513635\pi\)
−0.0428239 + 0.999083i \(0.513635\pi\)
\(938\) −13.0190 −0.425085
\(939\) −64.6415 −2.10950
\(940\) 20.3394 0.663398
\(941\) 45.9973 1.49947 0.749735 0.661738i \(-0.230181\pi\)
0.749735 + 0.661738i \(0.230181\pi\)
\(942\) 39.4381 1.28496
\(943\) −22.9581 −0.747619
\(944\) −66.6092 −2.16794
\(945\) 14.8601 0.483399
\(946\) −0.345512 −0.0112336
\(947\) 19.8395 0.644697 0.322348 0.946621i \(-0.395528\pi\)
0.322348 + 0.946621i \(0.395528\pi\)
\(948\) 17.7105 0.575209
\(949\) −26.4545 −0.858750
\(950\) −3.13868 −0.101832
\(951\) 40.8686 1.32525
\(952\) 29.3855 0.952389
\(953\) 33.6483 1.08998 0.544988 0.838444i \(-0.316534\pi\)
0.544988 + 0.838444i \(0.316534\pi\)
\(954\) −6.24408 −0.202160
\(955\) 11.5275 0.373021
\(956\) −108.330 −3.50364
\(957\) 43.6793 1.41195
\(958\) 88.8245 2.86979
\(959\) 25.1425 0.811894
\(960\) −6.07510 −0.196073
\(961\) 36.3397 1.17225
\(962\) 14.1990 0.457793
\(963\) 12.8398 0.413755
\(964\) 85.4765 2.75301
\(965\) 19.7324 0.635208
\(966\) 161.272 5.18885
\(967\) −33.3040 −1.07098 −0.535492 0.844540i \(-0.679874\pi\)
−0.535492 + 0.844540i \(0.679874\pi\)
\(968\) −1.86020 −0.0597890
\(969\) 0.887134 0.0284988
\(970\) −18.0556 −0.579729
\(971\) 5.80116 0.186168 0.0930840 0.995658i \(-0.470327\pi\)
0.0930840 + 0.995658i \(0.470327\pi\)
\(972\) 73.3652 2.35319
\(973\) 48.3243 1.54921
\(974\) 33.3944 1.07003
\(975\) −68.0694 −2.17997
\(976\) 67.3556 2.15600
\(977\) 17.6175 0.563632 0.281816 0.959468i \(-0.409063\pi\)
0.281816 + 0.959468i \(0.409063\pi\)
\(978\) 20.7613 0.663874
\(979\) 30.9674 0.989722
\(980\) 26.2574 0.838761
\(981\) 4.82396 0.154017
\(982\) 26.8490 0.856785
\(983\) −47.7074 −1.52163 −0.760814 0.648970i \(-0.775200\pi\)
−0.760814 + 0.648970i \(0.775200\pi\)
\(984\) 73.4326 2.34095
\(985\) 18.1041 0.576846
\(986\) −13.7282 −0.437196
\(987\) 60.8330 1.93634
\(988\) 7.05283 0.224380
\(989\) 0.236048 0.00750590
\(990\) 31.9990 1.01699
\(991\) 15.9733 0.507409 0.253704 0.967282i \(-0.418351\pi\)
0.253704 + 0.967282i \(0.418351\pi\)
\(992\) −60.8573 −1.93222
\(993\) 52.7160 1.67289
\(994\) −113.357 −3.59545
\(995\) −5.62882 −0.178445
\(996\) −110.572 −3.50361
\(997\) 44.3315 1.40399 0.701997 0.712180i \(-0.252292\pi\)
0.701997 + 0.712180i \(0.252292\pi\)
\(998\) −30.4918 −0.965201
\(999\) −5.10186 −0.161416
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 4033.2.a.c.1.5 77
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.c.1.5 77 1.1 even 1 trivial