Properties

Label 4034.2.a.c.1.2
Level $4034$
Weight $2$
Character 4034.1
Self dual yes
Analytic conductor $32.212$
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] = [4034,2,Mod(1,4034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4034 = 2 \cdot 2017 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4034.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: \(32.2116521754\)
Analytic rank: \(0\)
Dimension: \(49\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 4034.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -3.09927 q^{3} +1.00000 q^{4} -2.61970 q^{5} +3.09927 q^{6} -2.12795 q^{7} -1.00000 q^{8} +6.60550 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -3.09927 q^{3} +1.00000 q^{4} -2.61970 q^{5} +3.09927 q^{6} -2.12795 q^{7} -1.00000 q^{8} +6.60550 q^{9} +2.61970 q^{10} +0.148791 q^{11} -3.09927 q^{12} +3.47687 q^{13} +2.12795 q^{14} +8.11917 q^{15} +1.00000 q^{16} -5.38312 q^{17} -6.60550 q^{18} +5.56518 q^{19} -2.61970 q^{20} +6.59510 q^{21} -0.148791 q^{22} +3.85549 q^{23} +3.09927 q^{24} +1.86283 q^{25} -3.47687 q^{26} -11.1744 q^{27} -2.12795 q^{28} -5.49729 q^{29} -8.11917 q^{30} +3.00511 q^{31} -1.00000 q^{32} -0.461146 q^{33} +5.38312 q^{34} +5.57459 q^{35} +6.60550 q^{36} +9.30172 q^{37} -5.56518 q^{38} -10.7758 q^{39} +2.61970 q^{40} +4.64584 q^{41} -6.59510 q^{42} -3.45167 q^{43} +0.148791 q^{44} -17.3044 q^{45} -3.85549 q^{46} -4.44000 q^{47} -3.09927 q^{48} -2.47184 q^{49} -1.86283 q^{50} +16.6838 q^{51} +3.47687 q^{52} -11.9870 q^{53} +11.1744 q^{54} -0.389789 q^{55} +2.12795 q^{56} -17.2480 q^{57} +5.49729 q^{58} +13.4011 q^{59} +8.11917 q^{60} -2.74011 q^{61} -3.00511 q^{62} -14.0562 q^{63} +1.00000 q^{64} -9.10837 q^{65} +0.461146 q^{66} -14.1888 q^{67} -5.38312 q^{68} -11.9492 q^{69} -5.57459 q^{70} -5.84157 q^{71} -6.60550 q^{72} +8.90902 q^{73} -9.30172 q^{74} -5.77343 q^{75} +5.56518 q^{76} -0.316621 q^{77} +10.7758 q^{78} -5.50715 q^{79} -2.61970 q^{80} +14.8162 q^{81} -4.64584 q^{82} -9.90711 q^{83} +6.59510 q^{84} +14.1022 q^{85} +3.45167 q^{86} +17.0376 q^{87} -0.148791 q^{88} +2.44980 q^{89} +17.3044 q^{90} -7.39861 q^{91} +3.85549 q^{92} -9.31367 q^{93} +4.44000 q^{94} -14.5791 q^{95} +3.09927 q^{96} -5.79639 q^{97} +2.47184 q^{98} +0.982843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 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
\(3\) −3.09927 −1.78937 −0.894684 0.446701i \(-0.852599\pi\)
−0.894684 + 0.446701i \(0.852599\pi\)
\(4\) 1.00000 0.500000
\(5\) −2.61970 −1.17157 −0.585783 0.810468i \(-0.699213\pi\)
−0.585783 + 0.810468i \(0.699213\pi\)
\(6\) 3.09927 1.26527
\(7\) −2.12795 −0.804289 −0.402144 0.915576i \(-0.631735\pi\)
−0.402144 + 0.915576i \(0.631735\pi\)
\(8\) −1.00000 −0.353553
\(9\) 6.60550 2.20183
\(10\) 2.61970 0.828422
\(11\) 0.148791 0.0448623 0.0224312 0.999748i \(-0.492859\pi\)
0.0224312 + 0.999748i \(0.492859\pi\)
\(12\) −3.09927 −0.894684
\(13\) 3.47687 0.964312 0.482156 0.876085i \(-0.339854\pi\)
0.482156 + 0.876085i \(0.339854\pi\)
\(14\) 2.12795 0.568718
\(15\) 8.11917 2.09636
\(16\) 1.00000 0.250000
\(17\) −5.38312 −1.30560 −0.652799 0.757531i \(-0.726405\pi\)
−0.652799 + 0.757531i \(0.726405\pi\)
\(18\) −6.60550 −1.55693
\(19\) 5.56518 1.27674 0.638370 0.769730i \(-0.279609\pi\)
0.638370 + 0.769730i \(0.279609\pi\)
\(20\) −2.61970 −0.585783
\(21\) 6.59510 1.43917
\(22\) −0.148791 −0.0317225
\(23\) 3.85549 0.803925 0.401963 0.915656i \(-0.368328\pi\)
0.401963 + 0.915656i \(0.368328\pi\)
\(24\) 3.09927 0.632637
\(25\) 1.86283 0.372566
\(26\) −3.47687 −0.681871
\(27\) −11.1744 −2.15052
\(28\) −2.12795 −0.402144
\(29\) −5.49729 −1.02082 −0.510411 0.859931i \(-0.670507\pi\)
−0.510411 + 0.859931i \(0.670507\pi\)
\(30\) −8.11917 −1.48235
\(31\) 3.00511 0.539734 0.269867 0.962898i \(-0.413020\pi\)
0.269867 + 0.962898i \(0.413020\pi\)
\(32\) −1.00000 −0.176777
\(33\) −0.461146 −0.0802752
\(34\) 5.38312 0.923197
\(35\) 5.57459 0.942277
\(36\) 6.60550 1.10092
\(37\) 9.30172 1.52919 0.764597 0.644509i \(-0.222938\pi\)
0.764597 + 0.644509i \(0.222938\pi\)
\(38\) −5.56518 −0.902791
\(39\) −10.7758 −1.72551
\(40\) 2.61970 0.414211
\(41\) 4.64584 0.725559 0.362779 0.931875i \(-0.381828\pi\)
0.362779 + 0.931875i \(0.381828\pi\)
\(42\) −6.59510 −1.01765
\(43\) −3.45167 −0.526374 −0.263187 0.964745i \(-0.584774\pi\)
−0.263187 + 0.964745i \(0.584774\pi\)
\(44\) 0.148791 0.0224312
\(45\) −17.3044 −2.57959
\(46\) −3.85549 −0.568461
\(47\) −4.44000 −0.647640 −0.323820 0.946119i \(-0.604967\pi\)
−0.323820 + 0.946119i \(0.604967\pi\)
\(48\) −3.09927 −0.447342
\(49\) −2.47184 −0.353120
\(50\) −1.86283 −0.263444
\(51\) 16.6838 2.33619
\(52\) 3.47687 0.482156
\(53\) −11.9870 −1.64654 −0.823271 0.567649i \(-0.807853\pi\)
−0.823271 + 0.567649i \(0.807853\pi\)
\(54\) 11.1744 1.52065
\(55\) −0.389789 −0.0525592
\(56\) 2.12795 0.284359
\(57\) −17.2480 −2.28456
\(58\) 5.49729 0.721830
\(59\) 13.4011 1.74468 0.872340 0.488900i \(-0.162602\pi\)
0.872340 + 0.488900i \(0.162602\pi\)
\(60\) 8.11917 1.04818
\(61\) −2.74011 −0.350835 −0.175418 0.984494i \(-0.556128\pi\)
−0.175418 + 0.984494i \(0.556128\pi\)
\(62\) −3.00511 −0.381650
\(63\) −14.0562 −1.77091
\(64\) 1.00000 0.125000
\(65\) −9.10837 −1.12975
\(66\) 0.461146 0.0567631
\(67\) −14.1888 −1.73344 −0.866718 0.498798i \(-0.833775\pi\)
−0.866718 + 0.498798i \(0.833775\pi\)
\(68\) −5.38312 −0.652799
\(69\) −11.9492 −1.43852
\(70\) −5.57459 −0.666291
\(71\) −5.84157 −0.693267 −0.346633 0.938001i \(-0.612675\pi\)
−0.346633 + 0.938001i \(0.612675\pi\)
\(72\) −6.60550 −0.778466
\(73\) 8.90902 1.04272 0.521361 0.853336i \(-0.325425\pi\)
0.521361 + 0.853336i \(0.325425\pi\)
\(74\) −9.30172 −1.08130
\(75\) −5.77343 −0.666658
\(76\) 5.56518 0.638370
\(77\) −0.316621 −0.0360823
\(78\) 10.7758 1.22012
\(79\) −5.50715 −0.619602 −0.309801 0.950801i \(-0.600262\pi\)
−0.309801 + 0.950801i \(0.600262\pi\)
\(80\) −2.61970 −0.292891
\(81\) 14.8162 1.64624
\(82\) −4.64584 −0.513048
\(83\) −9.90711 −1.08745 −0.543723 0.839265i \(-0.682986\pi\)
−0.543723 + 0.839265i \(0.682986\pi\)
\(84\) 6.59510 0.719584
\(85\) 14.1022 1.52959
\(86\) 3.45167 0.372203
\(87\) 17.0376 1.82662
\(88\) −0.148791 −0.0158612
\(89\) 2.44980 0.259678 0.129839 0.991535i \(-0.458554\pi\)
0.129839 + 0.991535i \(0.458554\pi\)
\(90\) 17.3044 1.82405
\(91\) −7.39861 −0.775585
\(92\) 3.85549 0.401963
\(93\) −9.31367 −0.965782
\(94\) 4.44000 0.457951
\(95\) −14.5791 −1.49578
\(96\) 3.09927 0.316318
\(97\) −5.79639 −0.588534 −0.294267 0.955723i \(-0.595076\pi\)
−0.294267 + 0.955723i \(0.595076\pi\)
\(98\) 2.47184 0.249693
\(99\) 0.982843 0.0987794
\(100\) 1.86283 0.186283
\(101\) −14.8569 −1.47832 −0.739160 0.673529i \(-0.764777\pi\)
−0.739160 + 0.673529i \(0.764777\pi\)
\(102\) −16.6838 −1.65194
\(103\) −2.39252 −0.235742 −0.117871 0.993029i \(-0.537607\pi\)
−0.117871 + 0.993029i \(0.537607\pi\)
\(104\) −3.47687 −0.340936
\(105\) −17.2772 −1.68608
\(106\) 11.9870 1.16428
\(107\) 3.31461 0.320436 0.160218 0.987082i \(-0.448780\pi\)
0.160218 + 0.987082i \(0.448780\pi\)
\(108\) −11.1744 −1.07526
\(109\) 5.94762 0.569678 0.284839 0.958575i \(-0.408060\pi\)
0.284839 + 0.958575i \(0.408060\pi\)
\(110\) 0.389789 0.0371649
\(111\) −28.8286 −2.73629
\(112\) −2.12795 −0.201072
\(113\) −6.35860 −0.598167 −0.299083 0.954227i \(-0.596681\pi\)
−0.299083 + 0.954227i \(0.596681\pi\)
\(114\) 17.2480 1.61543
\(115\) −10.1002 −0.941851
\(116\) −5.49729 −0.510411
\(117\) 22.9665 2.12325
\(118\) −13.4011 −1.23367
\(119\) 11.4550 1.05008
\(120\) −8.11917 −0.741176
\(121\) −10.9779 −0.997987
\(122\) 2.74011 0.248078
\(123\) −14.3987 −1.29829
\(124\) 3.00511 0.269867
\(125\) 8.21844 0.735080
\(126\) 14.0562 1.25222
\(127\) 14.2280 1.26253 0.631266 0.775566i \(-0.282536\pi\)
0.631266 + 0.775566i \(0.282536\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 10.6977 0.941877
\(130\) 9.10837 0.798857
\(131\) −8.78974 −0.767963 −0.383982 0.923341i \(-0.625447\pi\)
−0.383982 + 0.923341i \(0.625447\pi\)
\(132\) −0.461146 −0.0401376
\(133\) −11.8424 −1.02687
\(134\) 14.1888 1.22573
\(135\) 29.2737 2.51948
\(136\) 5.38312 0.461599
\(137\) −2.13472 −0.182382 −0.0911909 0.995833i \(-0.529067\pi\)
−0.0911909 + 0.995833i \(0.529067\pi\)
\(138\) 11.9492 1.01719
\(139\) 21.7640 1.84600 0.923001 0.384798i \(-0.125729\pi\)
0.923001 + 0.384798i \(0.125729\pi\)
\(140\) 5.57459 0.471139
\(141\) 13.7608 1.15887
\(142\) 5.84157 0.490214
\(143\) 0.517329 0.0432613
\(144\) 6.60550 0.550459
\(145\) 14.4013 1.19596
\(146\) −8.90902 −0.737315
\(147\) 7.66090 0.631860
\(148\) 9.30172 0.764597
\(149\) 9.16194 0.750575 0.375288 0.926908i \(-0.377544\pi\)
0.375288 + 0.926908i \(0.377544\pi\)
\(150\) 5.77343 0.471398
\(151\) 8.39943 0.683536 0.341768 0.939784i \(-0.388974\pi\)
0.341768 + 0.939784i \(0.388974\pi\)
\(152\) −5.56518 −0.451396
\(153\) −35.5582 −2.87471
\(154\) 0.316621 0.0255140
\(155\) −7.87249 −0.632334
\(156\) −10.7758 −0.862754
\(157\) −7.42604 −0.592662 −0.296331 0.955085i \(-0.595763\pi\)
−0.296331 + 0.955085i \(0.595763\pi\)
\(158\) 5.50715 0.438125
\(159\) 37.1510 2.94627
\(160\) 2.61970 0.207106
\(161\) −8.20428 −0.646588
\(162\) −14.8162 −1.16407
\(163\) 11.6891 0.915559 0.457779 0.889066i \(-0.348645\pi\)
0.457779 + 0.889066i \(0.348645\pi\)
\(164\) 4.64584 0.362779
\(165\) 1.20806 0.0940476
\(166\) 9.90711 0.768941
\(167\) 17.5163 1.35545 0.677725 0.735315i \(-0.262966\pi\)
0.677725 + 0.735315i \(0.262966\pi\)
\(168\) −6.59510 −0.508823
\(169\) −0.911340 −0.0701031
\(170\) −14.1022 −1.08159
\(171\) 36.7608 2.81117
\(172\) −3.45167 −0.263187
\(173\) −18.4618 −1.40362 −0.701812 0.712362i \(-0.747625\pi\)
−0.701812 + 0.712362i \(0.747625\pi\)
\(174\) −17.0376 −1.29162
\(175\) −3.96401 −0.299651
\(176\) 0.148791 0.0112156
\(177\) −41.5338 −3.12187
\(178\) −2.44980 −0.183620
\(179\) −24.4519 −1.82762 −0.913809 0.406144i \(-0.866873\pi\)
−0.913809 + 0.406144i \(0.866873\pi\)
\(180\) −17.3044 −1.28980
\(181\) −19.7749 −1.46985 −0.734927 0.678147i \(-0.762783\pi\)
−0.734927 + 0.678147i \(0.762783\pi\)
\(182\) 7.39861 0.548421
\(183\) 8.49235 0.627773
\(184\) −3.85549 −0.284230
\(185\) −24.3677 −1.79155
\(186\) 9.31367 0.682911
\(187\) −0.800962 −0.0585722
\(188\) −4.44000 −0.323820
\(189\) 23.7786 1.72964
\(190\) 14.5791 1.05768
\(191\) 15.3198 1.10850 0.554252 0.832349i \(-0.313005\pi\)
0.554252 + 0.832349i \(0.313005\pi\)
\(192\) −3.09927 −0.223671
\(193\) −6.32568 −0.455333 −0.227666 0.973739i \(-0.573110\pi\)
−0.227666 + 0.973739i \(0.573110\pi\)
\(194\) 5.79639 0.416157
\(195\) 28.2293 2.02155
\(196\) −2.47184 −0.176560
\(197\) −1.16579 −0.0830594 −0.0415297 0.999137i \(-0.513223\pi\)
−0.0415297 + 0.999137i \(0.513223\pi\)
\(198\) −0.982843 −0.0698476
\(199\) −2.03661 −0.144372 −0.0721858 0.997391i \(-0.522997\pi\)
−0.0721858 + 0.997391i \(0.522997\pi\)
\(200\) −1.86283 −0.131722
\(201\) 43.9750 3.10176
\(202\) 14.8569 1.04533
\(203\) 11.6980 0.821035
\(204\) 16.6838 1.16810
\(205\) −12.1707 −0.850040
\(206\) 2.39252 0.166694
\(207\) 25.4675 1.77011
\(208\) 3.47687 0.241078
\(209\) 0.828051 0.0572775
\(210\) 17.2772 1.19224
\(211\) −12.2799 −0.845385 −0.422692 0.906273i \(-0.638915\pi\)
−0.422692 + 0.906273i \(0.638915\pi\)
\(212\) −11.9870 −0.823271
\(213\) 18.1046 1.24051
\(214\) −3.31461 −0.226582
\(215\) 9.04234 0.616682
\(216\) 11.1744 0.760325
\(217\) −6.39472 −0.434102
\(218\) −5.94762 −0.402824
\(219\) −27.6115 −1.86581
\(220\) −0.389789 −0.0262796
\(221\) −18.7164 −1.25900
\(222\) 28.8286 1.93485
\(223\) −0.298598 −0.0199956 −0.00999779 0.999950i \(-0.503182\pi\)
−0.00999779 + 0.999950i \(0.503182\pi\)
\(224\) 2.12795 0.142180
\(225\) 12.3049 0.820330
\(226\) 6.35860 0.422968
\(227\) 13.7237 0.910876 0.455438 0.890267i \(-0.349483\pi\)
0.455438 + 0.890267i \(0.349483\pi\)
\(228\) −17.2480 −1.14228
\(229\) 6.54010 0.432182 0.216091 0.976373i \(-0.430669\pi\)
0.216091 + 0.976373i \(0.430669\pi\)
\(230\) 10.1002 0.665989
\(231\) 0.981294 0.0645644
\(232\) 5.49729 0.360915
\(233\) 15.0625 0.986775 0.493388 0.869810i \(-0.335758\pi\)
0.493388 + 0.869810i \(0.335758\pi\)
\(234\) −22.9665 −1.50137
\(235\) 11.6315 0.758753
\(236\) 13.4011 0.872340
\(237\) 17.0682 1.10870
\(238\) −11.4550 −0.742517
\(239\) 23.0423 1.49048 0.745241 0.666795i \(-0.232334\pi\)
0.745241 + 0.666795i \(0.232334\pi\)
\(240\) 8.11917 0.524090
\(241\) 16.4598 1.06027 0.530135 0.847913i \(-0.322141\pi\)
0.530135 + 0.847913i \(0.322141\pi\)
\(242\) 10.9779 0.705684
\(243\) −12.3960 −0.795206
\(244\) −2.74011 −0.175418
\(245\) 6.47547 0.413703
\(246\) 14.3987 0.918031
\(247\) 19.3494 1.23118
\(248\) −3.00511 −0.190825
\(249\) 30.7049 1.94584
\(250\) −8.21844 −0.519780
\(251\) 14.2485 0.899356 0.449678 0.893191i \(-0.351539\pi\)
0.449678 + 0.893191i \(0.351539\pi\)
\(252\) −14.0562 −0.885455
\(253\) 0.573664 0.0360660
\(254\) −14.2280 −0.892745
\(255\) −43.7065 −2.73701
\(256\) 1.00000 0.0625000
\(257\) −23.4295 −1.46149 −0.730746 0.682650i \(-0.760828\pi\)
−0.730746 + 0.682650i \(0.760828\pi\)
\(258\) −10.6977 −0.666008
\(259\) −19.7936 −1.22991
\(260\) −9.10837 −0.564877
\(261\) −36.3124 −2.24768
\(262\) 8.78974 0.543032
\(263\) −14.7623 −0.910280 −0.455140 0.890420i \(-0.650411\pi\)
−0.455140 + 0.890420i \(0.650411\pi\)
\(264\) 0.461146 0.0283816
\(265\) 31.4024 1.92903
\(266\) 11.8424 0.726105
\(267\) −7.59260 −0.464659
\(268\) −14.1888 −0.866718
\(269\) 12.8535 0.783691 0.391846 0.920031i \(-0.371837\pi\)
0.391846 + 0.920031i \(0.371837\pi\)
\(270\) −29.2737 −1.78154
\(271\) 17.6066 1.06952 0.534761 0.845003i \(-0.320402\pi\)
0.534761 + 0.845003i \(0.320402\pi\)
\(272\) −5.38312 −0.326400
\(273\) 22.9303 1.38781
\(274\) 2.13472 0.128963
\(275\) 0.277174 0.0167142
\(276\) −11.9492 −0.719259
\(277\) −24.0872 −1.44726 −0.723630 0.690188i \(-0.757528\pi\)
−0.723630 + 0.690188i \(0.757528\pi\)
\(278\) −21.7640 −1.30532
\(279\) 19.8503 1.18841
\(280\) −5.57459 −0.333145
\(281\) 22.4219 1.33758 0.668791 0.743451i \(-0.266812\pi\)
0.668791 + 0.743451i \(0.266812\pi\)
\(282\) −13.7608 −0.819442
\(283\) 6.38848 0.379756 0.189878 0.981808i \(-0.439191\pi\)
0.189878 + 0.981808i \(0.439191\pi\)
\(284\) −5.84157 −0.346633
\(285\) 45.1847 2.67651
\(286\) −0.517329 −0.0305903
\(287\) −9.88611 −0.583559
\(288\) −6.60550 −0.389233
\(289\) 11.9780 0.704587
\(290\) −14.4013 −0.845671
\(291\) 17.9646 1.05310
\(292\) 8.90902 0.521361
\(293\) −25.6763 −1.50003 −0.750014 0.661422i \(-0.769953\pi\)
−0.750014 + 0.661422i \(0.769953\pi\)
\(294\) −7.66090 −0.446793
\(295\) −35.1070 −2.04401
\(296\) −9.30172 −0.540651
\(297\) −1.66266 −0.0964775
\(298\) −9.16194 −0.530737
\(299\) 13.4051 0.775234
\(300\) −5.77343 −0.333329
\(301\) 7.34497 0.423357
\(302\) −8.39943 −0.483333
\(303\) 46.0457 2.64526
\(304\) 5.56518 0.319185
\(305\) 7.17827 0.411026
\(306\) 35.5582 2.03273
\(307\) −9.42016 −0.537637 −0.268818 0.963191i \(-0.586633\pi\)
−0.268818 + 0.963191i \(0.586633\pi\)
\(308\) −0.316621 −0.0180411
\(309\) 7.41506 0.421828
\(310\) 7.87249 0.447128
\(311\) 18.4008 1.04342 0.521708 0.853124i \(-0.325295\pi\)
0.521708 + 0.853124i \(0.325295\pi\)
\(312\) 10.7758 0.610059
\(313\) 2.65401 0.150014 0.0750068 0.997183i \(-0.476102\pi\)
0.0750068 + 0.997183i \(0.476102\pi\)
\(314\) 7.42604 0.419075
\(315\) 36.8230 2.07474
\(316\) −5.50715 −0.309801
\(317\) −4.05309 −0.227644 −0.113822 0.993501i \(-0.536309\pi\)
−0.113822 + 0.993501i \(0.536309\pi\)
\(318\) −37.1510 −2.08333
\(319\) −0.817950 −0.0457964
\(320\) −2.61970 −0.146446
\(321\) −10.2729 −0.573377
\(322\) 8.20428 0.457207
\(323\) −29.9580 −1.66691
\(324\) 14.8162 0.823120
\(325\) 6.47683 0.359270
\(326\) −11.6891 −0.647398
\(327\) −18.4333 −1.01936
\(328\) −4.64584 −0.256524
\(329\) 9.44808 0.520890
\(330\) −1.20806 −0.0665017
\(331\) −24.7302 −1.35929 −0.679646 0.733540i \(-0.737867\pi\)
−0.679646 + 0.733540i \(0.737867\pi\)
\(332\) −9.90711 −0.543723
\(333\) 61.4425 3.36703
\(334\) −17.5163 −0.958448
\(335\) 37.1704 2.03084
\(336\) 6.59510 0.359792
\(337\) 16.6246 0.905597 0.452799 0.891613i \(-0.350426\pi\)
0.452799 + 0.891613i \(0.350426\pi\)
\(338\) 0.911340 0.0495704
\(339\) 19.7070 1.07034
\(340\) 14.1022 0.764797
\(341\) 0.447135 0.0242137
\(342\) −36.7608 −1.98780
\(343\) 20.1556 1.08830
\(344\) 3.45167 0.186101
\(345\) 31.3034 1.68532
\(346\) 18.4618 0.992512
\(347\) 14.3029 0.767819 0.383909 0.923371i \(-0.374577\pi\)
0.383909 + 0.923371i \(0.374577\pi\)
\(348\) 17.0376 0.913312
\(349\) 12.6510 0.677191 0.338596 0.940932i \(-0.390048\pi\)
0.338596 + 0.940932i \(0.390048\pi\)
\(350\) 3.96401 0.211885
\(351\) −38.8522 −2.07377
\(352\) −0.148791 −0.00793061
\(353\) −19.6704 −1.04695 −0.523474 0.852041i \(-0.675364\pi\)
−0.523474 + 0.852041i \(0.675364\pi\)
\(354\) 41.5338 2.20750
\(355\) 15.3032 0.812208
\(356\) 2.44980 0.129839
\(357\) −35.5022 −1.87898
\(358\) 24.4519 1.29232
\(359\) 7.69351 0.406048 0.203024 0.979174i \(-0.434923\pi\)
0.203024 + 0.979174i \(0.434923\pi\)
\(360\) 17.3044 0.912024
\(361\) 11.9712 0.630065
\(362\) 19.7749 1.03934
\(363\) 34.0234 1.78577
\(364\) −7.39861 −0.387793
\(365\) −23.3390 −1.22162
\(366\) −8.49235 −0.443902
\(367\) 1.40887 0.0735427 0.0367713 0.999324i \(-0.488293\pi\)
0.0367713 + 0.999324i \(0.488293\pi\)
\(368\) 3.85549 0.200981
\(369\) 30.6881 1.59756
\(370\) 24.3677 1.26682
\(371\) 25.5077 1.32430
\(372\) −9.31367 −0.482891
\(373\) 32.5569 1.68573 0.842866 0.538123i \(-0.180866\pi\)
0.842866 + 0.538123i \(0.180866\pi\)
\(374\) 0.800962 0.0414168
\(375\) −25.4712 −1.31533
\(376\) 4.44000 0.228975
\(377\) −19.1134 −0.984390
\(378\) −23.7786 −1.22304
\(379\) −1.90954 −0.0980867 −0.0490434 0.998797i \(-0.515617\pi\)
−0.0490434 + 0.998797i \(0.515617\pi\)
\(380\) −14.5791 −0.747892
\(381\) −44.0965 −2.25913
\(382\) −15.3198 −0.783830
\(383\) 38.2354 1.95374 0.976869 0.213837i \(-0.0685961\pi\)
0.976869 + 0.213837i \(0.0685961\pi\)
\(384\) 3.09927 0.158159
\(385\) 0.829451 0.0422727
\(386\) 6.32568 0.321969
\(387\) −22.8000 −1.15899
\(388\) −5.79639 −0.294267
\(389\) −7.12094 −0.361046 −0.180523 0.983571i \(-0.557779\pi\)
−0.180523 + 0.983571i \(0.557779\pi\)
\(390\) −28.2293 −1.42945
\(391\) −20.7546 −1.04960
\(392\) 2.47184 0.124847
\(393\) 27.2418 1.37417
\(394\) 1.16579 0.0587318
\(395\) 14.4271 0.725905
\(396\) 0.982843 0.0493897
\(397\) −0.699225 −0.0350931 −0.0175465 0.999846i \(-0.505586\pi\)
−0.0175465 + 0.999846i \(0.505586\pi\)
\(398\) 2.03661 0.102086
\(399\) 36.7029 1.83744
\(400\) 1.86283 0.0931416
\(401\) −5.06910 −0.253139 −0.126569 0.991958i \(-0.540397\pi\)
−0.126569 + 0.991958i \(0.540397\pi\)
\(402\) −43.9750 −2.19327
\(403\) 10.4484 0.520472
\(404\) −14.8569 −0.739160
\(405\) −38.8139 −1.92868
\(406\) −11.6980 −0.580560
\(407\) 1.38402 0.0686032
\(408\) −16.6838 −0.825970
\(409\) −31.8131 −1.57306 −0.786528 0.617555i \(-0.788123\pi\)
−0.786528 + 0.617555i \(0.788123\pi\)
\(410\) 12.1707 0.601069
\(411\) 6.61609 0.326348
\(412\) −2.39252 −0.117871
\(413\) −28.5169 −1.40323
\(414\) −25.4675 −1.25166
\(415\) 25.9537 1.27402
\(416\) −3.47687 −0.170468
\(417\) −67.4527 −3.30317
\(418\) −0.828051 −0.0405013
\(419\) −10.6895 −0.522217 −0.261109 0.965309i \(-0.584088\pi\)
−0.261109 + 0.965309i \(0.584088\pi\)
\(420\) −17.2772 −0.843040
\(421\) −33.9650 −1.65535 −0.827676 0.561206i \(-0.810337\pi\)
−0.827676 + 0.561206i \(0.810337\pi\)
\(422\) 12.2799 0.597777
\(423\) −29.3284 −1.42600
\(424\) 11.9870 0.582140
\(425\) −10.0278 −0.486422
\(426\) −18.1046 −0.877172
\(427\) 5.83081 0.282173
\(428\) 3.31461 0.160218
\(429\) −1.60335 −0.0774103
\(430\) −9.04234 −0.436060
\(431\) −6.40630 −0.308581 −0.154290 0.988026i \(-0.549309\pi\)
−0.154290 + 0.988026i \(0.549309\pi\)
\(432\) −11.1744 −0.537631
\(433\) 3.40899 0.163826 0.0819128 0.996639i \(-0.473897\pi\)
0.0819128 + 0.996639i \(0.473897\pi\)
\(434\) 6.39472 0.306956
\(435\) −44.6335 −2.14001
\(436\) 5.94762 0.284839
\(437\) 21.4565 1.02640
\(438\) 27.6115 1.31933
\(439\) 0.867169 0.0413877 0.0206938 0.999786i \(-0.493412\pi\)
0.0206938 + 0.999786i \(0.493412\pi\)
\(440\) 0.389789 0.0185825
\(441\) −16.3277 −0.777511
\(442\) 18.7164 0.890250
\(443\) 25.6977 1.22093 0.610467 0.792042i \(-0.290982\pi\)
0.610467 + 0.792042i \(0.290982\pi\)
\(444\) −28.8286 −1.36814
\(445\) −6.41774 −0.304230
\(446\) 0.298598 0.0141390
\(447\) −28.3954 −1.34305
\(448\) −2.12795 −0.100536
\(449\) 34.1999 1.61399 0.806996 0.590557i \(-0.201092\pi\)
0.806996 + 0.590557i \(0.201092\pi\)
\(450\) −12.3049 −0.580061
\(451\) 0.691262 0.0325503
\(452\) −6.35860 −0.299083
\(453\) −26.0321 −1.22310
\(454\) −13.7237 −0.644087
\(455\) 19.3821 0.908649
\(456\) 17.2480 0.807713
\(457\) 34.9056 1.63281 0.816407 0.577477i \(-0.195963\pi\)
0.816407 + 0.577477i \(0.195963\pi\)
\(458\) −6.54010 −0.305599
\(459\) 60.1534 2.80772
\(460\) −10.1002 −0.470926
\(461\) −38.9820 −1.81557 −0.907787 0.419432i \(-0.862229\pi\)
−0.907787 + 0.419432i \(0.862229\pi\)
\(462\) −0.981294 −0.0456539
\(463\) −20.1468 −0.936299 −0.468150 0.883649i \(-0.655079\pi\)
−0.468150 + 0.883649i \(0.655079\pi\)
\(464\) −5.49729 −0.255205
\(465\) 24.3990 1.13148
\(466\) −15.0625 −0.697756
\(467\) 9.59834 0.444158 0.222079 0.975029i \(-0.428716\pi\)
0.222079 + 0.975029i \(0.428716\pi\)
\(468\) 22.9665 1.06163
\(469\) 30.1930 1.39418
\(470\) −11.6315 −0.536519
\(471\) 23.0153 1.06049
\(472\) −13.4011 −0.616837
\(473\) −0.513579 −0.0236144
\(474\) −17.0682 −0.783966
\(475\) 10.3670 0.475670
\(476\) 11.4550 0.525039
\(477\) −79.1802 −3.62541
\(478\) −23.0423 −1.05393
\(479\) 31.5889 1.44334 0.721668 0.692240i \(-0.243376\pi\)
0.721668 + 0.692240i \(0.243376\pi\)
\(480\) −8.11917 −0.370588
\(481\) 32.3409 1.47462
\(482\) −16.4598 −0.749725
\(483\) 25.4273 1.15698
\(484\) −10.9779 −0.498994
\(485\) 15.1848 0.689507
\(486\) 12.3960 0.562295
\(487\) 8.47054 0.383837 0.191918 0.981411i \(-0.438529\pi\)
0.191918 + 0.981411i \(0.438529\pi\)
\(488\) 2.74011 0.124039
\(489\) −36.2276 −1.63827
\(490\) −6.47547 −0.292532
\(491\) −10.3954 −0.469136 −0.234568 0.972100i \(-0.575368\pi\)
−0.234568 + 0.972100i \(0.575368\pi\)
\(492\) −14.3987 −0.649146
\(493\) 29.5926 1.33278
\(494\) −19.3494 −0.870572
\(495\) −2.57475 −0.115727
\(496\) 3.00511 0.134934
\(497\) 12.4306 0.557587
\(498\) −30.7049 −1.37592
\(499\) −11.1163 −0.497635 −0.248818 0.968550i \(-0.580042\pi\)
−0.248818 + 0.968550i \(0.580042\pi\)
\(500\) 8.21844 0.367540
\(501\) −54.2878 −2.42540
\(502\) −14.2485 −0.635941
\(503\) −2.28972 −0.102093 −0.0510467 0.998696i \(-0.516256\pi\)
−0.0510467 + 0.998696i \(0.516256\pi\)
\(504\) 14.0562 0.626112
\(505\) 38.9207 1.73195
\(506\) −0.573664 −0.0255025
\(507\) 2.82449 0.125440
\(508\) 14.2280 0.631266
\(509\) −3.54828 −0.157275 −0.0786374 0.996903i \(-0.525057\pi\)
−0.0786374 + 0.996903i \(0.525057\pi\)
\(510\) 43.7065 1.93536
\(511\) −18.9579 −0.838649
\(512\) −1.00000 −0.0441942
\(513\) −62.1878 −2.74566
\(514\) 23.4295 1.03343
\(515\) 6.26768 0.276187
\(516\) 10.6977 0.470938
\(517\) −0.660634 −0.0290546
\(518\) 19.7936 0.869680
\(519\) 57.2182 2.51160
\(520\) 9.10837 0.399429
\(521\) 45.1801 1.97938 0.989689 0.143232i \(-0.0457495\pi\)
0.989689 + 0.143232i \(0.0457495\pi\)
\(522\) 36.3124 1.58935
\(523\) −7.05363 −0.308434 −0.154217 0.988037i \(-0.549285\pi\)
−0.154217 + 0.988037i \(0.549285\pi\)
\(524\) −8.78974 −0.383982
\(525\) 12.2856 0.536186
\(526\) 14.7623 0.643665
\(527\) −16.1769 −0.704676
\(528\) −0.461146 −0.0200688
\(529\) −8.13520 −0.353704
\(530\) −31.4024 −1.36403
\(531\) 88.5213 3.84150
\(532\) −11.8424 −0.513434
\(533\) 16.1530 0.699665
\(534\) 7.59260 0.328564
\(535\) −8.68329 −0.375411
\(536\) 14.1888 0.612863
\(537\) 75.7830 3.27028
\(538\) −12.8535 −0.554153
\(539\) −0.367788 −0.0158418
\(540\) 29.2737 1.25974
\(541\) 27.5940 1.18636 0.593179 0.805071i \(-0.297873\pi\)
0.593179 + 0.805071i \(0.297873\pi\)
\(542\) −17.6066 −0.756266
\(543\) 61.2877 2.63011
\(544\) 5.38312 0.230799
\(545\) −15.5810 −0.667416
\(546\) −22.9303 −0.981327
\(547\) −39.2307 −1.67738 −0.838692 0.544607i \(-0.816679\pi\)
−0.838692 + 0.544607i \(0.816679\pi\)
\(548\) −2.13472 −0.0911909
\(549\) −18.0998 −0.772481
\(550\) −0.277174 −0.0118187
\(551\) −30.5934 −1.30332
\(552\) 11.9492 0.508593
\(553\) 11.7189 0.498339
\(554\) 24.0872 1.02337
\(555\) 75.5223 3.20574
\(556\) 21.7640 0.923001
\(557\) −4.43919 −0.188095 −0.0940473 0.995568i \(-0.529980\pi\)
−0.0940473 + 0.995568i \(0.529980\pi\)
\(558\) −19.8503 −0.840329
\(559\) −12.0010 −0.507589
\(560\) 5.57459 0.235569
\(561\) 2.48240 0.104807
\(562\) −22.4219 −0.945813
\(563\) 36.4136 1.53465 0.767326 0.641257i \(-0.221587\pi\)
0.767326 + 0.641257i \(0.221587\pi\)
\(564\) 13.7608 0.579433
\(565\) 16.6576 0.700791
\(566\) −6.38848 −0.268528
\(567\) −31.5280 −1.32405
\(568\) 5.84157 0.245107
\(569\) −34.0600 −1.42787 −0.713935 0.700212i \(-0.753089\pi\)
−0.713935 + 0.700212i \(0.753089\pi\)
\(570\) −45.1847 −1.89258
\(571\) 38.4969 1.61104 0.805522 0.592566i \(-0.201885\pi\)
0.805522 + 0.592566i \(0.201885\pi\)
\(572\) 0.517329 0.0216306
\(573\) −47.4803 −1.98352
\(574\) 9.88611 0.412638
\(575\) 7.18213 0.299516
\(576\) 6.60550 0.275229
\(577\) 27.7448 1.15503 0.577517 0.816379i \(-0.304022\pi\)
0.577517 + 0.816379i \(0.304022\pi\)
\(578\) −11.9780 −0.498218
\(579\) 19.6050 0.814757
\(580\) 14.4013 0.597980
\(581\) 21.0818 0.874621
\(582\) −17.9646 −0.744657
\(583\) −1.78356 −0.0738677
\(584\) −8.90902 −0.368658
\(585\) −60.1654 −2.48753
\(586\) 25.6763 1.06068
\(587\) −35.4020 −1.46120 −0.730598 0.682808i \(-0.760759\pi\)
−0.730598 + 0.682808i \(0.760759\pi\)
\(588\) 7.66090 0.315930
\(589\) 16.7240 0.689100
\(590\) 35.1070 1.44533
\(591\) 3.61312 0.148624
\(592\) 9.30172 0.382298
\(593\) 5.05182 0.207453 0.103727 0.994606i \(-0.466923\pi\)
0.103727 + 0.994606i \(0.466923\pi\)
\(594\) 1.66266 0.0682199
\(595\) −30.0087 −1.23024
\(596\) 9.16194 0.375288
\(597\) 6.31202 0.258334
\(598\) −13.4051 −0.548174
\(599\) −40.5567 −1.65710 −0.828551 0.559913i \(-0.810834\pi\)
−0.828551 + 0.559913i \(0.810834\pi\)
\(600\) 5.77343 0.235699
\(601\) 10.0840 0.411336 0.205668 0.978622i \(-0.434063\pi\)
0.205668 + 0.978622i \(0.434063\pi\)
\(602\) −7.34497 −0.299359
\(603\) −93.7241 −3.81674
\(604\) 8.39943 0.341768
\(605\) 28.7587 1.16921
\(606\) −46.0457 −1.87048
\(607\) 5.53065 0.224482 0.112241 0.993681i \(-0.464197\pi\)
0.112241 + 0.993681i \(0.464197\pi\)
\(608\) −5.56518 −0.225698
\(609\) −36.2552 −1.46913
\(610\) −7.17827 −0.290640
\(611\) −15.4373 −0.624527
\(612\) −35.5582 −1.43736
\(613\) −37.5472 −1.51652 −0.758258 0.651955i \(-0.773949\pi\)
−0.758258 + 0.651955i \(0.773949\pi\)
\(614\) 9.42016 0.380167
\(615\) 37.7204 1.52103
\(616\) 0.316621 0.0127570
\(617\) 19.6377 0.790585 0.395293 0.918555i \(-0.370643\pi\)
0.395293 + 0.918555i \(0.370643\pi\)
\(618\) −7.41506 −0.298278
\(619\) 13.9631 0.561225 0.280612 0.959821i \(-0.409462\pi\)
0.280612 + 0.959821i \(0.409462\pi\)
\(620\) −7.87249 −0.316167
\(621\) −43.0830 −1.72886
\(622\) −18.4008 −0.737807
\(623\) −5.21304 −0.208856
\(624\) −10.7758 −0.431377
\(625\) −30.8440 −1.23376
\(626\) −2.65401 −0.106076
\(627\) −2.56636 −0.102491
\(628\) −7.42604 −0.296331
\(629\) −50.0723 −1.99651
\(630\) −36.8230 −1.46706
\(631\) 23.4992 0.935488 0.467744 0.883864i \(-0.345067\pi\)
0.467744 + 0.883864i \(0.345067\pi\)
\(632\) 5.50715 0.219063
\(633\) 38.0588 1.51270
\(634\) 4.05309 0.160969
\(635\) −37.2731 −1.47914
\(636\) 37.1510 1.47313
\(637\) −8.59427 −0.340517
\(638\) 0.817950 0.0323830
\(639\) −38.5865 −1.52646
\(640\) 2.61970 0.103553
\(641\) −22.9605 −0.906887 −0.453443 0.891285i \(-0.649805\pi\)
−0.453443 + 0.891285i \(0.649805\pi\)
\(642\) 10.2729 0.405439
\(643\) −0.803322 −0.0316799 −0.0158400 0.999875i \(-0.505042\pi\)
−0.0158400 + 0.999875i \(0.505042\pi\)
\(644\) −8.20428 −0.323294
\(645\) −28.0247 −1.10347
\(646\) 29.9580 1.17868
\(647\) 25.3992 0.998547 0.499273 0.866445i \(-0.333600\pi\)
0.499273 + 0.866445i \(0.333600\pi\)
\(648\) −14.8162 −0.582034
\(649\) 1.99397 0.0782704
\(650\) −6.47683 −0.254042
\(651\) 19.8190 0.776768
\(652\) 11.6891 0.457779
\(653\) −13.3098 −0.520852 −0.260426 0.965494i \(-0.583863\pi\)
−0.260426 + 0.965494i \(0.583863\pi\)
\(654\) 18.4333 0.720799
\(655\) 23.0265 0.899719
\(656\) 4.64584 0.181390
\(657\) 58.8485 2.29590
\(658\) −9.44808 −0.368325
\(659\) −19.7679 −0.770048 −0.385024 0.922907i \(-0.625807\pi\)
−0.385024 + 0.922907i \(0.625807\pi\)
\(660\) 1.20806 0.0470238
\(661\) 18.7619 0.729752 0.364876 0.931056i \(-0.381111\pi\)
0.364876 + 0.931056i \(0.381111\pi\)
\(662\) 24.7302 0.961165
\(663\) 58.0074 2.25282
\(664\) 9.90711 0.384470
\(665\) 31.0236 1.20304
\(666\) −61.4425 −2.38085
\(667\) −21.1948 −0.820664
\(668\) 17.5163 0.677725
\(669\) 0.925436 0.0357794
\(670\) −37.1704 −1.43602
\(671\) −0.407705 −0.0157393
\(672\) −6.59510 −0.254411
\(673\) −15.8115 −0.609489 −0.304745 0.952434i \(-0.598571\pi\)
−0.304745 + 0.952434i \(0.598571\pi\)
\(674\) −16.6246 −0.640354
\(675\) −20.8161 −0.801213
\(676\) −0.911340 −0.0350516
\(677\) −7.89995 −0.303620 −0.151810 0.988410i \(-0.548510\pi\)
−0.151810 + 0.988410i \(0.548510\pi\)
\(678\) −19.7070 −0.756844
\(679\) 12.3344 0.473351
\(680\) −14.1022 −0.540793
\(681\) −42.5336 −1.62989
\(682\) −0.447135 −0.0171217
\(683\) 20.0291 0.766393 0.383197 0.923667i \(-0.374823\pi\)
0.383197 + 0.923667i \(0.374823\pi\)
\(684\) 36.7608 1.40559
\(685\) 5.59234 0.213672
\(686\) −20.1556 −0.769544
\(687\) −20.2696 −0.773332
\(688\) −3.45167 −0.131594
\(689\) −41.6773 −1.58778
\(690\) −31.3034 −1.19170
\(691\) 32.4113 1.23298 0.616492 0.787361i \(-0.288553\pi\)
0.616492 + 0.787361i \(0.288553\pi\)
\(692\) −18.4618 −0.701812
\(693\) −2.09144 −0.0794472
\(694\) −14.3029 −0.542930
\(695\) −57.0153 −2.16271
\(696\) −17.0376 −0.645809
\(697\) −25.0091 −0.947288
\(698\) −12.6510 −0.478846
\(699\) −46.6827 −1.76570
\(700\) −3.96401 −0.149826
\(701\) −25.8457 −0.976179 −0.488089 0.872794i \(-0.662306\pi\)
−0.488089 + 0.872794i \(0.662306\pi\)
\(702\) 38.8522 1.46638
\(703\) 51.7657 1.95238
\(704\) 0.148791 0.00560779
\(705\) −36.0491 −1.35769
\(706\) 19.6704 0.740304
\(707\) 31.6148 1.18900
\(708\) −41.5338 −1.56094
\(709\) 1.03874 0.0390106 0.0195053 0.999810i \(-0.493791\pi\)
0.0195053 + 0.999810i \(0.493791\pi\)
\(710\) −15.3032 −0.574318
\(711\) −36.3775 −1.36426
\(712\) −2.44980 −0.0918101
\(713\) 11.5862 0.433906
\(714\) 35.5022 1.32864
\(715\) −1.35525 −0.0506834
\(716\) −24.4519 −0.913809
\(717\) −71.4144 −2.66702
\(718\) −7.69351 −0.287119
\(719\) 2.02707 0.0755971 0.0377986 0.999285i \(-0.487965\pi\)
0.0377986 + 0.999285i \(0.487965\pi\)
\(720\) −17.3044 −0.644899
\(721\) 5.09115 0.189604
\(722\) −11.9712 −0.445523
\(723\) −51.0135 −1.89721
\(724\) −19.7749 −0.734927
\(725\) −10.2405 −0.380324
\(726\) −34.0234 −1.26273
\(727\) 41.7019 1.54664 0.773319 0.634017i \(-0.218595\pi\)
0.773319 + 0.634017i \(0.218595\pi\)
\(728\) 7.39861 0.274211
\(729\) −6.02979 −0.223326
\(730\) 23.3390 0.863813
\(731\) 18.5807 0.687233
\(732\) 8.49235 0.313886
\(733\) 25.6182 0.946229 0.473114 0.881001i \(-0.343130\pi\)
0.473114 + 0.881001i \(0.343130\pi\)
\(734\) −1.40887 −0.0520025
\(735\) −20.0693 −0.740266
\(736\) −3.85549 −0.142115
\(737\) −2.11117 −0.0777660
\(738\) −30.6881 −1.12965
\(739\) −7.88359 −0.290003 −0.145001 0.989431i \(-0.546319\pi\)
−0.145001 + 0.989431i \(0.546319\pi\)
\(740\) −24.3677 −0.895775
\(741\) −59.9692 −2.20302
\(742\) −25.5077 −0.936418
\(743\) −26.6017 −0.975921 −0.487961 0.872866i \(-0.662259\pi\)
−0.487961 + 0.872866i \(0.662259\pi\)
\(744\) 9.31367 0.341456
\(745\) −24.0015 −0.879348
\(746\) −32.5569 −1.19199
\(747\) −65.4414 −2.39438
\(748\) −0.800962 −0.0292861
\(749\) −7.05332 −0.257723
\(750\) 25.4712 0.930077
\(751\) −9.52630 −0.347620 −0.173810 0.984779i \(-0.555608\pi\)
−0.173810 + 0.984779i \(0.555608\pi\)
\(752\) −4.44000 −0.161910
\(753\) −44.1599 −1.60928
\(754\) 19.1134 0.696069
\(755\) −22.0040 −0.800807
\(756\) 23.7786 0.864821
\(757\) 20.2695 0.736709 0.368355 0.929685i \(-0.379921\pi\)
0.368355 + 0.929685i \(0.379921\pi\)
\(758\) 1.90954 0.0693578
\(759\) −1.77794 −0.0645352
\(760\) 14.5791 0.528840
\(761\) 10.4288 0.378042 0.189021 0.981973i \(-0.439469\pi\)
0.189021 + 0.981973i \(0.439469\pi\)
\(762\) 44.0965 1.59745
\(763\) −12.6562 −0.458186
\(764\) 15.3198 0.554252
\(765\) 93.1519 3.36791
\(766\) −38.2354 −1.38150
\(767\) 46.5941 1.68241
\(768\) −3.09927 −0.111835
\(769\) 5.13971 0.185343 0.0926714 0.995697i \(-0.470459\pi\)
0.0926714 + 0.995697i \(0.470459\pi\)
\(770\) −0.829451 −0.0298913
\(771\) 72.6144 2.61515
\(772\) −6.32568 −0.227666
\(773\) −14.7193 −0.529416 −0.264708 0.964329i \(-0.585276\pi\)
−0.264708 + 0.964329i \(0.585276\pi\)
\(774\) 22.8000 0.819529
\(775\) 5.59802 0.201087
\(776\) 5.79639 0.208078
\(777\) 61.3457 2.20077
\(778\) 7.12094 0.255298
\(779\) 25.8550 0.926350
\(780\) 28.2293 1.01077
\(781\) −0.869176 −0.0311016
\(782\) 20.7546 0.742182
\(783\) 61.4292 2.19530
\(784\) −2.47184 −0.0882799
\(785\) 19.4540 0.694343
\(786\) −27.2418 −0.971683
\(787\) 15.5990 0.556043 0.278021 0.960575i \(-0.410321\pi\)
0.278021 + 0.960575i \(0.410321\pi\)
\(788\) −1.16579 −0.0415297
\(789\) 45.7523 1.62882
\(790\) −14.4271 −0.513292
\(791\) 13.5308 0.481099
\(792\) −0.982843 −0.0349238
\(793\) −9.52702 −0.338314
\(794\) 0.699225 0.0248146
\(795\) −97.3246 −3.45175
\(796\) −2.03661 −0.0721858
\(797\) 15.5039 0.549176 0.274588 0.961562i \(-0.411458\pi\)
0.274588 + 0.961562i \(0.411458\pi\)
\(798\) −36.7029 −1.29927
\(799\) 23.9010 0.845558
\(800\) −1.86283 −0.0658611
\(801\) 16.1821 0.571768
\(802\) 5.06910 0.178996
\(803\) 1.32559 0.0467789
\(804\) 43.9750 1.55088
\(805\) 21.4928 0.757520
\(806\) −10.4484 −0.368029
\(807\) −39.8365 −1.40231
\(808\) 14.8569 0.522665
\(809\) 15.4307 0.542514 0.271257 0.962507i \(-0.412561\pi\)
0.271257 + 0.962507i \(0.412561\pi\)
\(810\) 38.8139 1.36378
\(811\) −1.78281 −0.0626030 −0.0313015 0.999510i \(-0.509965\pi\)
−0.0313015 + 0.999510i \(0.509965\pi\)
\(812\) 11.6980 0.410518
\(813\) −54.5676 −1.91377
\(814\) −1.38402 −0.0485098
\(815\) −30.6219 −1.07264
\(816\) 16.6838 0.584049
\(817\) −19.2092 −0.672043
\(818\) 31.8131 1.11232
\(819\) −48.8715 −1.70771
\(820\) −12.1707 −0.425020
\(821\) −13.8490 −0.483335 −0.241667 0.970359i \(-0.577694\pi\)
−0.241667 + 0.970359i \(0.577694\pi\)
\(822\) −6.61609 −0.230763
\(823\) −52.5376 −1.83135 −0.915673 0.401924i \(-0.868341\pi\)
−0.915673 + 0.401924i \(0.868341\pi\)
\(824\) 2.39252 0.0833472
\(825\) −0.859037 −0.0299078
\(826\) 28.5169 0.992231
\(827\) −40.6068 −1.41204 −0.706019 0.708193i \(-0.749511\pi\)
−0.706019 + 0.708193i \(0.749511\pi\)
\(828\) 25.4675 0.885055
\(829\) 2.05702 0.0714431 0.0357216 0.999362i \(-0.488627\pi\)
0.0357216 + 0.999362i \(0.488627\pi\)
\(830\) −25.9537 −0.900865
\(831\) 74.6529 2.58968
\(832\) 3.47687 0.120539
\(833\) 13.3062 0.461032
\(834\) 67.4527 2.33570
\(835\) −45.8874 −1.58800
\(836\) 0.828051 0.0286388
\(837\) −33.5805 −1.16071
\(838\) 10.6895 0.369263
\(839\) −12.4582 −0.430105 −0.215053 0.976602i \(-0.568992\pi\)
−0.215053 + 0.976602i \(0.568992\pi\)
\(840\) 17.2772 0.596119
\(841\) 1.22022 0.0420764
\(842\) 33.9650 1.17051
\(843\) −69.4918 −2.39342
\(844\) −12.2799 −0.422692
\(845\) 2.38744 0.0821304
\(846\) 29.3284 1.00833
\(847\) 23.3603 0.802670
\(848\) −11.9870 −0.411635
\(849\) −19.7997 −0.679523
\(850\) 10.0278 0.343952
\(851\) 35.8627 1.22936
\(852\) 18.1046 0.620254
\(853\) 21.6514 0.741330 0.370665 0.928767i \(-0.379130\pi\)
0.370665 + 0.928767i \(0.379130\pi\)
\(854\) −5.83081 −0.199526
\(855\) −96.3023 −3.29347
\(856\) −3.31461 −0.113291
\(857\) 45.0521 1.53895 0.769475 0.638677i \(-0.220518\pi\)
0.769475 + 0.638677i \(0.220518\pi\)
\(858\) 1.60335 0.0547373
\(859\) −33.3169 −1.13676 −0.568379 0.822767i \(-0.692429\pi\)
−0.568379 + 0.822767i \(0.692429\pi\)
\(860\) 9.04234 0.308341
\(861\) 30.6398 1.04420
\(862\) 6.40630 0.218199
\(863\) −16.4424 −0.559704 −0.279852 0.960043i \(-0.590285\pi\)
−0.279852 + 0.960043i \(0.590285\pi\)
\(864\) 11.1744 0.380162
\(865\) 48.3644 1.64444
\(866\) −3.40899 −0.115842
\(867\) −37.1230 −1.26076
\(868\) −6.39472 −0.217051
\(869\) −0.819416 −0.0277968
\(870\) 44.6335 1.51322
\(871\) −49.3327 −1.67157
\(872\) −5.94762 −0.201412
\(873\) −38.2881 −1.29585
\(874\) −21.4565 −0.725777
\(875\) −17.4884 −0.591216
\(876\) −27.6115 −0.932906
\(877\) 7.83338 0.264515 0.132257 0.991215i \(-0.457777\pi\)
0.132257 + 0.991215i \(0.457777\pi\)
\(878\) −0.867169 −0.0292655
\(879\) 79.5780 2.68410
\(880\) −0.389789 −0.0131398
\(881\) −20.3218 −0.684659 −0.342329 0.939580i \(-0.611216\pi\)
−0.342329 + 0.939580i \(0.611216\pi\)
\(882\) 16.3277 0.549783
\(883\) −27.0014 −0.908668 −0.454334 0.890831i \(-0.650123\pi\)
−0.454334 + 0.890831i \(0.650123\pi\)
\(884\) −18.7164 −0.629502
\(885\) 108.806 3.65748
\(886\) −25.6977 −0.863331
\(887\) −17.1338 −0.575297 −0.287648 0.957736i \(-0.592873\pi\)
−0.287648 + 0.957736i \(0.592873\pi\)
\(888\) 28.8286 0.967424
\(889\) −30.2765 −1.01544
\(890\) 6.41774 0.215123
\(891\) 2.20452 0.0738542
\(892\) −0.298598 −0.00999779
\(893\) −24.7094 −0.826868
\(894\) 28.3954 0.949683
\(895\) 64.0566 2.14117
\(896\) 2.12795 0.0710898
\(897\) −41.5460 −1.38718
\(898\) −34.1999 −1.14126
\(899\) −16.5200 −0.550972
\(900\) 12.3049 0.410165
\(901\) 64.5275 2.14972
\(902\) −0.691262 −0.0230165
\(903\) −22.7641 −0.757541
\(904\) 6.35860 0.211484
\(905\) 51.8042 1.72203
\(906\) 26.0321 0.864860
\(907\) −3.25252 −0.107998 −0.0539991 0.998541i \(-0.517197\pi\)
−0.0539991 + 0.998541i \(0.517197\pi\)
\(908\) 13.7237 0.455438
\(909\) −98.1376 −3.25502
\(910\) −19.3821 −0.642512
\(911\) 17.4018 0.576546 0.288273 0.957548i \(-0.406919\pi\)
0.288273 + 0.957548i \(0.406919\pi\)
\(912\) −17.2480 −0.571139
\(913\) −1.47409 −0.0487854
\(914\) −34.9056 −1.15457
\(915\) −22.2474 −0.735477
\(916\) 6.54010 0.216091
\(917\) 18.7041 0.617664
\(918\) −60.1534 −1.98536
\(919\) 33.9574 1.12015 0.560076 0.828441i \(-0.310772\pi\)
0.560076 + 0.828441i \(0.310772\pi\)
\(920\) 10.1002 0.332995
\(921\) 29.1957 0.962030
\(922\) 38.9820 1.28380
\(923\) −20.3104 −0.668525
\(924\) 0.981294 0.0322822
\(925\) 17.3275 0.569726
\(926\) 20.1468 0.662063
\(927\) −15.8038 −0.519064
\(928\) 5.49729 0.180457
\(929\) 48.4272 1.58885 0.794423 0.607365i \(-0.207773\pi\)
0.794423 + 0.607365i \(0.207773\pi\)
\(930\) −24.3990 −0.800075
\(931\) −13.7562 −0.450842
\(932\) 15.0625 0.493388
\(933\) −57.0293 −1.86706
\(934\) −9.59834 −0.314067
\(935\) 2.09828 0.0686212
\(936\) −22.9665 −0.750684
\(937\) −23.8542 −0.779282 −0.389641 0.920967i \(-0.627401\pi\)
−0.389641 + 0.920967i \(0.627401\pi\)
\(938\) −30.1930 −0.985837
\(939\) −8.22551 −0.268429
\(940\) 11.6315 0.379376
\(941\) 7.04030 0.229507 0.114754 0.993394i \(-0.463392\pi\)
0.114754 + 0.993394i \(0.463392\pi\)
\(942\) −23.0153 −0.749880
\(943\) 17.9120 0.583295
\(944\) 13.4011 0.436170
\(945\) −62.2929 −2.02639
\(946\) 0.513579 0.0166979
\(947\) −39.3170 −1.27763 −0.638815 0.769360i \(-0.720575\pi\)
−0.638815 + 0.769360i \(0.720575\pi\)
\(948\) 17.0682 0.554348
\(949\) 30.9755 1.00551
\(950\) −10.3670 −0.336350
\(951\) 12.5616 0.407339
\(952\) −11.4550 −0.371259
\(953\) −16.5384 −0.535731 −0.267866 0.963456i \(-0.586318\pi\)
−0.267866 + 0.963456i \(0.586318\pi\)
\(954\) 79.1802 2.56355
\(955\) −40.1333 −1.29868
\(956\) 23.0423 0.745241
\(957\) 2.53505 0.0819466
\(958\) −31.5889 −1.02059
\(959\) 4.54258 0.146688
\(960\) 8.11917 0.262045
\(961\) −21.9693 −0.708687
\(962\) −32.3409 −1.04271
\(963\) 21.8947 0.705546
\(964\) 16.4598 0.530135
\(965\) 16.5714 0.533452
\(966\) −25.4273 −0.818111
\(967\) −35.4268 −1.13925 −0.569625 0.821905i \(-0.692912\pi\)
−0.569625 + 0.821905i \(0.692912\pi\)
\(968\) 10.9779 0.352842
\(969\) 92.8482 2.98271
\(970\) −15.1848 −0.487555
\(971\) −7.58846 −0.243525 −0.121763 0.992559i \(-0.538855\pi\)
−0.121763 + 0.992559i \(0.538855\pi\)
\(972\) −12.3960 −0.397603
\(973\) −46.3127 −1.48472
\(974\) −8.47054 −0.271414
\(975\) −20.0735 −0.642866
\(976\) −2.74011 −0.0877088
\(977\) −52.4573 −1.67826 −0.839129 0.543932i \(-0.816935\pi\)
−0.839129 + 0.543932i \(0.816935\pi\)
\(978\) 36.2276 1.15843
\(979\) 0.364509 0.0116498
\(980\) 6.47547 0.206851
\(981\) 39.2870 1.25434
\(982\) 10.3954 0.331729
\(983\) −1.20544 −0.0384476 −0.0192238 0.999815i \(-0.506119\pi\)
−0.0192238 + 0.999815i \(0.506119\pi\)
\(984\) 14.3987 0.459015
\(985\) 3.05403 0.0973095
\(986\) −29.5926 −0.942420
\(987\) −29.2822 −0.932063
\(988\) 19.3494 0.615588
\(989\) −13.3079 −0.423166
\(990\) 2.57475 0.0818310
\(991\) 33.3344 1.05890 0.529450 0.848341i \(-0.322398\pi\)
0.529450 + 0.848341i \(0.322398\pi\)
\(992\) −3.00511 −0.0954124
\(993\) 76.6456 2.43227
\(994\) −12.4306 −0.394273
\(995\) 5.33531 0.169141
\(996\) 30.7049 0.972920
\(997\) 38.2398 1.21107 0.605534 0.795819i \(-0.292960\pi\)
0.605534 + 0.795819i \(0.292960\pi\)
\(998\) 11.1163 0.351881
\(999\) −103.942 −3.28857
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 4034.2.a.c.1.2 49
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4034.2.a.c.1.2 49 1.1 even 1 trivial