Properties

Label 8023.2.a.b.1.7
Level $8023$
Weight $2$
Character 8023.1
Self dual yes
Analytic conductor $64.064$
Analytic rank $1$
Dimension $155$
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] = [8023,2,Mod(1,8023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8023, 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("8023.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8023 = 71 \cdot 113 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8023.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: \(64.0639775417\)
Analytic rank: \(1\)
Dimension: \(155\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Character \(\chi\) \(=\) 8023.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.73747 q^{2} +2.98404 q^{3} +5.49374 q^{4} -2.59125 q^{5} -8.16872 q^{6} +4.93159 q^{7} -9.56402 q^{8} +5.90448 q^{9} +O(q^{10})\) \(q-2.73747 q^{2} +2.98404 q^{3} +5.49374 q^{4} -2.59125 q^{5} -8.16872 q^{6} +4.93159 q^{7} -9.56402 q^{8} +5.90448 q^{9} +7.09348 q^{10} -2.39467 q^{11} +16.3935 q^{12} -1.38236 q^{13} -13.5001 q^{14} -7.73240 q^{15} +15.1937 q^{16} -3.63322 q^{17} -16.1633 q^{18} -4.88146 q^{19} -14.2357 q^{20} +14.7160 q^{21} +6.55533 q^{22} +5.06391 q^{23} -28.5394 q^{24} +1.71459 q^{25} +3.78418 q^{26} +8.66709 q^{27} +27.0929 q^{28} -2.15653 q^{29} +21.1672 q^{30} -10.6464 q^{31} -22.4643 q^{32} -7.14578 q^{33} +9.94583 q^{34} -12.7790 q^{35} +32.4377 q^{36} +0.572133 q^{37} +13.3629 q^{38} -4.12503 q^{39} +24.7828 q^{40} -6.06996 q^{41} -40.2847 q^{42} +4.28416 q^{43} -13.1557 q^{44} -15.3000 q^{45} -13.8623 q^{46} -0.417951 q^{47} +45.3386 q^{48} +17.3206 q^{49} -4.69364 q^{50} -10.8417 q^{51} -7.59436 q^{52} +5.93722 q^{53} -23.7259 q^{54} +6.20519 q^{55} -47.1658 q^{56} -14.5665 q^{57} +5.90344 q^{58} +1.38009 q^{59} -42.4798 q^{60} -6.76971 q^{61} +29.1441 q^{62} +29.1185 q^{63} +31.1080 q^{64} +3.58206 q^{65} +19.5614 q^{66} +13.3582 q^{67} -19.9600 q^{68} +15.1109 q^{69} +34.9821 q^{70} +1.00000 q^{71} -56.4706 q^{72} +10.5857 q^{73} -1.56620 q^{74} +5.11640 q^{75} -26.8175 q^{76} -11.8095 q^{77} +11.2921 q^{78} -16.0351 q^{79} -39.3708 q^{80} +8.14947 q^{81} +16.6163 q^{82} -18.0283 q^{83} +80.8462 q^{84} +9.41458 q^{85} -11.7278 q^{86} -6.43517 q^{87} +22.9026 q^{88} -14.8914 q^{89} +41.8833 q^{90} -6.81725 q^{91} +27.8198 q^{92} -31.7691 q^{93} +1.14413 q^{94} +12.6491 q^{95} -67.0344 q^{96} +8.29927 q^{97} -47.4145 q^{98} -14.1393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.73747 −1.93568 −0.967842 0.251559i \(-0.919057\pi\)
−0.967842 + 0.251559i \(0.919057\pi\)
\(3\) 2.98404 1.72284 0.861418 0.507897i \(-0.169577\pi\)
0.861418 + 0.507897i \(0.169577\pi\)
\(4\) 5.49374 2.74687
\(5\) −2.59125 −1.15884 −0.579422 0.815028i \(-0.696722\pi\)
−0.579422 + 0.815028i \(0.696722\pi\)
\(6\) −8.16872 −3.33486
\(7\) 4.93159 1.86397 0.931983 0.362503i \(-0.118078\pi\)
0.931983 + 0.362503i \(0.118078\pi\)
\(8\) −9.56402 −3.38139
\(9\) 5.90448 1.96816
\(10\) 7.09348 2.24315
\(11\) −2.39467 −0.722019 −0.361010 0.932562i \(-0.617568\pi\)
−0.361010 + 0.932562i \(0.617568\pi\)
\(12\) 16.3935 4.73241
\(13\) −1.38236 −0.383399 −0.191700 0.981454i \(-0.561400\pi\)
−0.191700 + 0.981454i \(0.561400\pi\)
\(14\) −13.5001 −3.60805
\(15\) −7.73240 −1.99650
\(16\) 15.1937 3.79843
\(17\) −3.63322 −0.881185 −0.440592 0.897707i \(-0.645232\pi\)
−0.440592 + 0.897707i \(0.645232\pi\)
\(18\) −16.1633 −3.80974
\(19\) −4.88146 −1.11988 −0.559942 0.828532i \(-0.689177\pi\)
−0.559942 + 0.828532i \(0.689177\pi\)
\(20\) −14.2357 −3.18319
\(21\) 14.7160 3.21131
\(22\) 6.55533 1.39760
\(23\) 5.06391 1.05590 0.527949 0.849276i \(-0.322961\pi\)
0.527949 + 0.849276i \(0.322961\pi\)
\(24\) −28.5394 −5.82558
\(25\) 1.71459 0.342918
\(26\) 3.78418 0.742139
\(27\) 8.66709 1.66798
\(28\) 27.0929 5.12007
\(29\) −2.15653 −0.400458 −0.200229 0.979749i \(-0.564169\pi\)
−0.200229 + 0.979749i \(0.564169\pi\)
\(30\) 21.1672 3.86458
\(31\) −10.6464 −1.91214 −0.956071 0.293134i \(-0.905302\pi\)
−0.956071 + 0.293134i \(0.905302\pi\)
\(32\) −22.4643 −3.97117
\(33\) −7.14578 −1.24392
\(34\) 9.94583 1.70569
\(35\) −12.7790 −2.16004
\(36\) 32.4377 5.40629
\(37\) 0.572133 0.0940580 0.0470290 0.998894i \(-0.485025\pi\)
0.0470290 + 0.998894i \(0.485025\pi\)
\(38\) 13.3629 2.16774
\(39\) −4.12503 −0.660533
\(40\) 24.7828 3.91850
\(41\) −6.06996 −0.947968 −0.473984 0.880533i \(-0.657185\pi\)
−0.473984 + 0.880533i \(0.657185\pi\)
\(42\) −40.2847 −6.21607
\(43\) 4.28416 0.653328 0.326664 0.945141i \(-0.394075\pi\)
0.326664 + 0.945141i \(0.394075\pi\)
\(44\) −13.1557 −1.98329
\(45\) −15.3000 −2.28079
\(46\) −13.8623 −2.04389
\(47\) −0.417951 −0.0609644 −0.0304822 0.999535i \(-0.509704\pi\)
−0.0304822 + 0.999535i \(0.509704\pi\)
\(48\) 45.3386 6.54407
\(49\) 17.3206 2.47437
\(50\) −4.69364 −0.663780
\(51\) −10.8417 −1.51814
\(52\) −7.59436 −1.05315
\(53\) 5.93722 0.815540 0.407770 0.913085i \(-0.366306\pi\)
0.407770 + 0.913085i \(0.366306\pi\)
\(54\) −23.7259 −3.22869
\(55\) 6.20519 0.836707
\(56\) −47.1658 −6.30279
\(57\) −14.5665 −1.92937
\(58\) 5.90344 0.775159
\(59\) 1.38009 0.179673 0.0898365 0.995957i \(-0.471366\pi\)
0.0898365 + 0.995957i \(0.471366\pi\)
\(60\) −42.4798 −5.48412
\(61\) −6.76971 −0.866772 −0.433386 0.901208i \(-0.642681\pi\)
−0.433386 + 0.901208i \(0.642681\pi\)
\(62\) 29.1441 3.70130
\(63\) 29.1185 3.66858
\(64\) 31.1080 3.88850
\(65\) 3.58206 0.444299
\(66\) 19.5614 2.40784
\(67\) 13.3582 1.63197 0.815985 0.578074i \(-0.196195\pi\)
0.815985 + 0.578074i \(0.196195\pi\)
\(68\) −19.9600 −2.42050
\(69\) 15.1109 1.81914
\(70\) 34.9821 4.18116
\(71\) 1.00000 0.118678
\(72\) −56.4706 −6.65512
\(73\) 10.5857 1.23896 0.619480 0.785012i \(-0.287343\pi\)
0.619480 + 0.785012i \(0.287343\pi\)
\(74\) −1.56620 −0.182067
\(75\) 5.11640 0.590791
\(76\) −26.8175 −3.07618
\(77\) −11.8095 −1.34582
\(78\) 11.2921 1.27858
\(79\) −16.0351 −1.80409 −0.902043 0.431646i \(-0.857933\pi\)
−0.902043 + 0.431646i \(0.857933\pi\)
\(80\) −39.3708 −4.40179
\(81\) 8.14947 0.905497
\(82\) 16.6163 1.83497
\(83\) −18.0283 −1.97886 −0.989431 0.145005i \(-0.953680\pi\)
−0.989431 + 0.145005i \(0.953680\pi\)
\(84\) 80.8462 8.82104
\(85\) 9.41458 1.02116
\(86\) −11.7278 −1.26464
\(87\) −6.43517 −0.689922
\(88\) 22.9026 2.44143
\(89\) −14.8914 −1.57848 −0.789241 0.614084i \(-0.789526\pi\)
−0.789241 + 0.614084i \(0.789526\pi\)
\(90\) 41.8833 4.41489
\(91\) −6.81725 −0.714642
\(92\) 27.8198 2.90042
\(93\) −31.7691 −3.29431
\(94\) 1.14413 0.118008
\(95\) 12.6491 1.29777
\(96\) −67.0344 −6.84167
\(97\) 8.29927 0.842663 0.421331 0.906907i \(-0.361563\pi\)
0.421331 + 0.906907i \(0.361563\pi\)
\(98\) −47.4145 −4.78959
\(99\) −14.1393 −1.42105
\(100\) 9.41951 0.941951
\(101\) 6.46752 0.643542 0.321771 0.946818i \(-0.395722\pi\)
0.321771 + 0.946818i \(0.395722\pi\)
\(102\) 29.6787 2.93863
\(103\) 3.63991 0.358651 0.179325 0.983790i \(-0.442609\pi\)
0.179325 + 0.983790i \(0.442609\pi\)
\(104\) 13.2210 1.29642
\(105\) −38.1330 −3.72140
\(106\) −16.2530 −1.57863
\(107\) −0.213079 −0.0205991 −0.0102996 0.999947i \(-0.503279\pi\)
−0.0102996 + 0.999947i \(0.503279\pi\)
\(108\) 47.6148 4.58173
\(109\) −15.8856 −1.52157 −0.760783 0.649006i \(-0.775185\pi\)
−0.760783 + 0.649006i \(0.775185\pi\)
\(110\) −16.9865 −1.61960
\(111\) 1.70727 0.162046
\(112\) 74.9292 7.08014
\(113\) 1.00000 0.0940721
\(114\) 39.8753 3.73466
\(115\) −13.1219 −1.22362
\(116\) −11.8474 −1.10001
\(117\) −8.16215 −0.754591
\(118\) −3.77797 −0.347790
\(119\) −17.9175 −1.64250
\(120\) 73.9528 6.75093
\(121\) −5.26557 −0.478688
\(122\) 18.5319 1.67780
\(123\) −18.1130 −1.63319
\(124\) −58.4884 −5.25241
\(125\) 8.51333 0.761455
\(126\) −79.7110 −7.10122
\(127\) 13.5246 1.20011 0.600057 0.799957i \(-0.295145\pi\)
0.600057 + 0.799957i \(0.295145\pi\)
\(128\) −40.2285 −3.55573
\(129\) 12.7841 1.12558
\(130\) −9.80577 −0.860023
\(131\) −11.2403 −0.982073 −0.491036 0.871139i \(-0.663382\pi\)
−0.491036 + 0.871139i \(0.663382\pi\)
\(132\) −39.2571 −3.41689
\(133\) −24.0734 −2.08742
\(134\) −36.5678 −3.15898
\(135\) −22.4586 −1.93293
\(136\) 34.7482 2.97963
\(137\) −6.13584 −0.524220 −0.262110 0.965038i \(-0.584418\pi\)
−0.262110 + 0.965038i \(0.584418\pi\)
\(138\) −41.3657 −3.52128
\(139\) −15.2371 −1.29239 −0.646196 0.763172i \(-0.723641\pi\)
−0.646196 + 0.763172i \(0.723641\pi\)
\(140\) −70.2045 −5.93336
\(141\) −1.24718 −0.105032
\(142\) −2.73747 −0.229723
\(143\) 3.31030 0.276822
\(144\) 89.7111 7.47592
\(145\) 5.58811 0.464068
\(146\) −28.9780 −2.39824
\(147\) 51.6852 4.26293
\(148\) 3.14315 0.258365
\(149\) 19.5160 1.59881 0.799406 0.600791i \(-0.205148\pi\)
0.799406 + 0.600791i \(0.205148\pi\)
\(150\) −14.0060 −1.14358
\(151\) −16.3064 −1.32699 −0.663497 0.748179i \(-0.730928\pi\)
−0.663497 + 0.748179i \(0.730928\pi\)
\(152\) 46.6864 3.78676
\(153\) −21.4523 −1.73431
\(154\) 32.3282 2.60508
\(155\) 27.5874 2.21587
\(156\) −22.6618 −1.81440
\(157\) −18.7400 −1.49561 −0.747807 0.663916i \(-0.768893\pi\)
−0.747807 + 0.663916i \(0.768893\pi\)
\(158\) 43.8955 3.49214
\(159\) 17.7169 1.40504
\(160\) 58.2108 4.60196
\(161\) 24.9731 1.96816
\(162\) −22.3089 −1.75276
\(163\) 10.3827 0.813236 0.406618 0.913598i \(-0.366708\pi\)
0.406618 + 0.913598i \(0.366708\pi\)
\(164\) −33.3468 −2.60395
\(165\) 18.5165 1.44151
\(166\) 49.3519 3.83045
\(167\) −11.6344 −0.900298 −0.450149 0.892953i \(-0.648629\pi\)
−0.450149 + 0.892953i \(0.648629\pi\)
\(168\) −140.745 −10.8587
\(169\) −11.0891 −0.853005
\(170\) −25.7721 −1.97663
\(171\) −28.8225 −2.20411
\(172\) 23.5361 1.79461
\(173\) −0.422922 −0.0321541 −0.0160771 0.999871i \(-0.505118\pi\)
−0.0160771 + 0.999871i \(0.505118\pi\)
\(174\) 17.6161 1.33547
\(175\) 8.45565 0.639187
\(176\) −36.3839 −2.74254
\(177\) 4.11825 0.309547
\(178\) 40.7647 3.05544
\(179\) 4.49068 0.335649 0.167825 0.985817i \(-0.446326\pi\)
0.167825 + 0.985817i \(0.446326\pi\)
\(180\) −84.0543 −6.26504
\(181\) −10.2264 −0.760122 −0.380061 0.924961i \(-0.624097\pi\)
−0.380061 + 0.924961i \(0.624097\pi\)
\(182\) 18.6620 1.38332
\(183\) −20.2011 −1.49331
\(184\) −48.4313 −3.57041
\(185\) −1.48254 −0.108999
\(186\) 86.9671 6.37674
\(187\) 8.70035 0.636232
\(188\) −2.29611 −0.167461
\(189\) 42.7425 3.10906
\(190\) −34.6265 −2.51207
\(191\) 8.31718 0.601810 0.300905 0.953654i \(-0.402711\pi\)
0.300905 + 0.953654i \(0.402711\pi\)
\(192\) 92.8274 6.69924
\(193\) −0.777393 −0.0559579 −0.0279790 0.999609i \(-0.508907\pi\)
−0.0279790 + 0.999609i \(0.508907\pi\)
\(194\) −22.7190 −1.63113
\(195\) 10.6890 0.765455
\(196\) 95.1547 6.79677
\(197\) −9.79939 −0.698177 −0.349089 0.937090i \(-0.613509\pi\)
−0.349089 + 0.937090i \(0.613509\pi\)
\(198\) 38.7058 2.75070
\(199\) 6.87902 0.487641 0.243820 0.969820i \(-0.421599\pi\)
0.243820 + 0.969820i \(0.421599\pi\)
\(200\) −16.3984 −1.15954
\(201\) 39.8615 2.81161
\(202\) −17.7046 −1.24569
\(203\) −10.6351 −0.746439
\(204\) −59.5613 −4.17012
\(205\) 15.7288 1.09855
\(206\) −9.96414 −0.694234
\(207\) 29.8998 2.07818
\(208\) −21.0033 −1.45631
\(209\) 11.6895 0.808578
\(210\) 104.388 7.20345
\(211\) 17.6853 1.21751 0.608753 0.793360i \(-0.291670\pi\)
0.608753 + 0.793360i \(0.291670\pi\)
\(212\) 32.6176 2.24018
\(213\) 2.98404 0.204463
\(214\) 0.583298 0.0398734
\(215\) −11.1013 −0.757105
\(216\) −82.8922 −5.64010
\(217\) −52.5035 −3.56417
\(218\) 43.4864 2.94527
\(219\) 31.5881 2.13452
\(220\) 34.0897 2.29833
\(221\) 5.02243 0.337845
\(222\) −4.67359 −0.313671
\(223\) −14.9901 −1.00381 −0.501906 0.864922i \(-0.667368\pi\)
−0.501906 + 0.864922i \(0.667368\pi\)
\(224\) −110.785 −7.40212
\(225\) 10.1238 0.674918
\(226\) −2.73747 −0.182094
\(227\) 7.60669 0.504874 0.252437 0.967613i \(-0.418768\pi\)
0.252437 + 0.967613i \(0.418768\pi\)
\(228\) −80.0244 −5.29974
\(229\) −28.7613 −1.90060 −0.950300 0.311335i \(-0.899224\pi\)
−0.950300 + 0.311335i \(0.899224\pi\)
\(230\) 35.9207 2.36854
\(231\) −35.2400 −2.31862
\(232\) 20.6251 1.35410
\(233\) −15.2594 −0.999677 −0.499838 0.866119i \(-0.666607\pi\)
−0.499838 + 0.866119i \(0.666607\pi\)
\(234\) 22.3436 1.46065
\(235\) 1.08302 0.0706482
\(236\) 7.58188 0.493538
\(237\) −47.8493 −3.10814
\(238\) 49.0487 3.17936
\(239\) 6.00454 0.388401 0.194201 0.980962i \(-0.437789\pi\)
0.194201 + 0.980962i \(0.437789\pi\)
\(240\) −117.484 −7.58355
\(241\) 11.4386 0.736826 0.368413 0.929662i \(-0.379901\pi\)
0.368413 + 0.929662i \(0.379901\pi\)
\(242\) 14.4143 0.926589
\(243\) −1.68293 −0.107960
\(244\) −37.1910 −2.38091
\(245\) −44.8820 −2.86740
\(246\) 49.5838 3.16134
\(247\) 6.74796 0.429362
\(248\) 101.822 6.46570
\(249\) −53.7971 −3.40925
\(250\) −23.3050 −1.47394
\(251\) −22.3153 −1.40853 −0.704264 0.709939i \(-0.748723\pi\)
−0.704264 + 0.709939i \(0.748723\pi\)
\(252\) 159.969 10.0771
\(253\) −12.1264 −0.762379
\(254\) −37.0232 −2.32304
\(255\) 28.0935 1.75928
\(256\) 47.9084 2.99428
\(257\) −3.63304 −0.226623 −0.113311 0.993560i \(-0.536146\pi\)
−0.113311 + 0.993560i \(0.536146\pi\)
\(258\) −34.9961 −2.17876
\(259\) 2.82152 0.175321
\(260\) 19.6789 1.22043
\(261\) −12.7332 −0.788165
\(262\) 30.7701 1.90098
\(263\) −14.8817 −0.917646 −0.458823 0.888528i \(-0.651729\pi\)
−0.458823 + 0.888528i \(0.651729\pi\)
\(264\) 68.3423 4.20618
\(265\) −15.3848 −0.945083
\(266\) 65.9001 4.04059
\(267\) −44.4364 −2.71946
\(268\) 73.3868 4.48281
\(269\) 6.60815 0.402906 0.201453 0.979498i \(-0.435434\pi\)
0.201453 + 0.979498i \(0.435434\pi\)
\(270\) 61.4798 3.74154
\(271\) 1.06822 0.0648896 0.0324448 0.999474i \(-0.489671\pi\)
0.0324448 + 0.999474i \(0.489671\pi\)
\(272\) −55.2021 −3.34712
\(273\) −20.3429 −1.23121
\(274\) 16.7967 1.01472
\(275\) −4.10587 −0.247593
\(276\) 83.0154 4.99694
\(277\) 26.9706 1.62051 0.810254 0.586079i \(-0.199329\pi\)
0.810254 + 0.586079i \(0.199329\pi\)
\(278\) 41.7110 2.50166
\(279\) −62.8613 −3.76341
\(280\) 122.218 7.30395
\(281\) −6.16900 −0.368012 −0.184006 0.982925i \(-0.558907\pi\)
−0.184006 + 0.982925i \(0.558907\pi\)
\(282\) 3.41412 0.203308
\(283\) 8.61856 0.512320 0.256160 0.966634i \(-0.417543\pi\)
0.256160 + 0.966634i \(0.417543\pi\)
\(284\) 5.49374 0.325994
\(285\) 37.7454 2.23584
\(286\) −9.06186 −0.535839
\(287\) −29.9345 −1.76698
\(288\) −132.640 −7.81590
\(289\) −3.79973 −0.223513
\(290\) −15.2973 −0.898288
\(291\) 24.7653 1.45177
\(292\) 58.1550 3.40327
\(293\) −17.6806 −1.03291 −0.516457 0.856313i \(-0.672749\pi\)
−0.516457 + 0.856313i \(0.672749\pi\)
\(294\) −141.487 −8.25168
\(295\) −3.57617 −0.208213
\(296\) −5.47189 −0.318047
\(297\) −20.7548 −1.20432
\(298\) −53.4244 −3.09479
\(299\) −7.00017 −0.404831
\(300\) 28.1082 1.62283
\(301\) 21.1277 1.21778
\(302\) 44.6382 2.56864
\(303\) 19.2993 1.10872
\(304\) −74.1675 −4.25380
\(305\) 17.5420 1.00445
\(306\) 58.7250 3.35708
\(307\) −22.2929 −1.27232 −0.636161 0.771557i \(-0.719478\pi\)
−0.636161 + 0.771557i \(0.719478\pi\)
\(308\) −64.8784 −3.69679
\(309\) 10.8616 0.617896
\(310\) −75.5197 −4.28923
\(311\) −22.5361 −1.27791 −0.638953 0.769246i \(-0.720632\pi\)
−0.638953 + 0.769246i \(0.720632\pi\)
\(312\) 39.4518 2.23352
\(313\) −12.9239 −0.730501 −0.365251 0.930909i \(-0.619017\pi\)
−0.365251 + 0.930909i \(0.619017\pi\)
\(314\) 51.3001 2.89503
\(315\) −75.4533 −4.25131
\(316\) −88.0925 −4.95559
\(317\) −2.07544 −0.116568 −0.0582841 0.998300i \(-0.518563\pi\)
−0.0582841 + 0.998300i \(0.518563\pi\)
\(318\) −48.4995 −2.71972
\(319\) 5.16417 0.289138
\(320\) −80.6087 −4.50616
\(321\) −0.635836 −0.0354889
\(322\) −68.3632 −3.80973
\(323\) 17.7354 0.986824
\(324\) 44.7711 2.48728
\(325\) −2.37019 −0.131474
\(326\) −28.4223 −1.57417
\(327\) −47.4033 −2.62141
\(328\) 58.0532 3.20545
\(329\) −2.06116 −0.113636
\(330\) −50.6884 −2.79031
\(331\) 19.0950 1.04955 0.524777 0.851240i \(-0.324149\pi\)
0.524777 + 0.851240i \(0.324149\pi\)
\(332\) −99.0428 −5.43568
\(333\) 3.37815 0.185121
\(334\) 31.8489 1.74269
\(335\) −34.6146 −1.89120
\(336\) 223.592 12.1979
\(337\) −26.1758 −1.42588 −0.712942 0.701223i \(-0.752638\pi\)
−0.712942 + 0.701223i \(0.752638\pi\)
\(338\) 30.3560 1.65115
\(339\) 2.98404 0.162071
\(340\) 51.7213 2.80498
\(341\) 25.4945 1.38060
\(342\) 78.9007 4.26646
\(343\) 50.8968 2.74817
\(344\) −40.9737 −2.20916
\(345\) −39.1562 −2.10810
\(346\) 1.15774 0.0622402
\(347\) 16.6279 0.892631 0.446316 0.894876i \(-0.352736\pi\)
0.446316 + 0.894876i \(0.352736\pi\)
\(348\) −35.3532 −1.89513
\(349\) −24.3400 −1.30289 −0.651444 0.758697i \(-0.725836\pi\)
−0.651444 + 0.758697i \(0.725836\pi\)
\(350\) −23.1471 −1.23726
\(351\) −11.9811 −0.639503
\(352\) 53.7946 2.86726
\(353\) −7.44748 −0.396389 −0.198195 0.980163i \(-0.563508\pi\)
−0.198195 + 0.980163i \(0.563508\pi\)
\(354\) −11.2736 −0.599185
\(355\) −2.59125 −0.137529
\(356\) −81.8093 −4.33588
\(357\) −53.4666 −2.82975
\(358\) −12.2931 −0.649711
\(359\) −8.37028 −0.441767 −0.220883 0.975300i \(-0.570894\pi\)
−0.220883 + 0.975300i \(0.570894\pi\)
\(360\) 146.330 7.71224
\(361\) 4.82865 0.254139
\(362\) 27.9945 1.47136
\(363\) −15.7127 −0.824701
\(364\) −37.4522 −1.96303
\(365\) −27.4302 −1.43576
\(366\) 55.2998 2.89057
\(367\) 26.8316 1.40060 0.700300 0.713849i \(-0.253050\pi\)
0.700300 + 0.713849i \(0.253050\pi\)
\(368\) 76.9397 4.01076
\(369\) −35.8400 −1.86575
\(370\) 4.05841 0.210987
\(371\) 29.2799 1.52014
\(372\) −174.532 −9.04904
\(373\) 26.2719 1.36031 0.680153 0.733070i \(-0.261913\pi\)
0.680153 + 0.733070i \(0.261913\pi\)
\(374\) −23.8169 −1.23154
\(375\) 25.4041 1.31186
\(376\) 3.99729 0.206144
\(377\) 2.98111 0.153535
\(378\) −117.006 −6.01816
\(379\) −11.3835 −0.584729 −0.292364 0.956307i \(-0.594442\pi\)
−0.292364 + 0.956307i \(0.594442\pi\)
\(380\) 69.4909 3.56481
\(381\) 40.3579 2.06760
\(382\) −22.7680 −1.16491
\(383\) −22.3877 −1.14396 −0.571979 0.820268i \(-0.693824\pi\)
−0.571979 + 0.820268i \(0.693824\pi\)
\(384\) −120.043 −6.12594
\(385\) 30.6014 1.55959
\(386\) 2.12809 0.108317
\(387\) 25.2957 1.28585
\(388\) 45.5940 2.31469
\(389\) −12.8779 −0.652937 −0.326469 0.945208i \(-0.605859\pi\)
−0.326469 + 0.945208i \(0.605859\pi\)
\(390\) −29.2608 −1.48168
\(391\) −18.3983 −0.930442
\(392\) −165.654 −8.36680
\(393\) −33.5416 −1.69195
\(394\) 26.8255 1.35145
\(395\) 41.5509 2.09065
\(396\) −77.6775 −3.90344
\(397\) −32.6367 −1.63799 −0.818995 0.573801i \(-0.805468\pi\)
−0.818995 + 0.573801i \(0.805468\pi\)
\(398\) −18.8311 −0.943918
\(399\) −71.8358 −3.59629
\(400\) 26.0510 1.30255
\(401\) 11.6239 0.580472 0.290236 0.956955i \(-0.406266\pi\)
0.290236 + 0.956955i \(0.406266\pi\)
\(402\) −109.120 −5.44240
\(403\) 14.7172 0.733114
\(404\) 35.5309 1.76773
\(405\) −21.1173 −1.04933
\(406\) 29.1133 1.44487
\(407\) −1.37007 −0.0679117
\(408\) 103.690 5.13341
\(409\) −9.19206 −0.454518 −0.227259 0.973834i \(-0.572976\pi\)
−0.227259 + 0.973834i \(0.572976\pi\)
\(410\) −43.0571 −2.12644
\(411\) −18.3096 −0.903145
\(412\) 19.9967 0.985167
\(413\) 6.80605 0.334904
\(414\) −81.8498 −4.02270
\(415\) 46.7158 2.29319
\(416\) 31.0539 1.52254
\(417\) −45.4680 −2.22658
\(418\) −31.9996 −1.56515
\(419\) 36.7387 1.79480 0.897402 0.441214i \(-0.145452\pi\)
0.897402 + 0.441214i \(0.145452\pi\)
\(420\) −209.493 −10.2222
\(421\) 28.3554 1.38196 0.690980 0.722874i \(-0.257179\pi\)
0.690980 + 0.722874i \(0.257179\pi\)
\(422\) −48.4130 −2.35671
\(423\) −2.46778 −0.119988
\(424\) −56.7837 −2.75766
\(425\) −6.22948 −0.302174
\(426\) −8.16872 −0.395776
\(427\) −33.3854 −1.61563
\(428\) −1.17060 −0.0565832
\(429\) 9.87807 0.476918
\(430\) 30.3896 1.46552
\(431\) −15.0428 −0.724587 −0.362294 0.932064i \(-0.618006\pi\)
−0.362294 + 0.932064i \(0.618006\pi\)
\(432\) 131.685 6.33571
\(433\) 21.8847 1.05171 0.525856 0.850574i \(-0.323745\pi\)
0.525856 + 0.850574i \(0.323745\pi\)
\(434\) 143.727 6.89910
\(435\) 16.6751 0.799512
\(436\) −87.2715 −4.17955
\(437\) −24.7193 −1.18248
\(438\) −86.4714 −4.13176
\(439\) −0.573806 −0.0273862 −0.0136931 0.999906i \(-0.504359\pi\)
−0.0136931 + 0.999906i \(0.504359\pi\)
\(440\) −59.3465 −2.82923
\(441\) 102.269 4.86995
\(442\) −13.7488 −0.653962
\(443\) 26.0554 1.23793 0.618965 0.785419i \(-0.287552\pi\)
0.618965 + 0.785419i \(0.287552\pi\)
\(444\) 9.37928 0.445121
\(445\) 38.5873 1.82921
\(446\) 41.0350 1.94306
\(447\) 58.2364 2.75449
\(448\) 153.412 7.24803
\(449\) 20.9311 0.987800 0.493900 0.869519i \(-0.335571\pi\)
0.493900 + 0.869519i \(0.335571\pi\)
\(450\) −27.7135 −1.30643
\(451\) 14.5355 0.684451
\(452\) 5.49374 0.258404
\(453\) −48.6588 −2.28619
\(454\) −20.8231 −0.977276
\(455\) 17.6652 0.828159
\(456\) 139.314 6.52397
\(457\) −9.02122 −0.421995 −0.210997 0.977487i \(-0.567671\pi\)
−0.210997 + 0.977487i \(0.567671\pi\)
\(458\) 78.7332 3.67896
\(459\) −31.4894 −1.46980
\(460\) −72.0882 −3.36113
\(461\) 26.4397 1.23142 0.615711 0.787972i \(-0.288869\pi\)
0.615711 + 0.787972i \(0.288869\pi\)
\(462\) 96.4686 4.48812
\(463\) 9.01568 0.418994 0.209497 0.977809i \(-0.432817\pi\)
0.209497 + 0.977809i \(0.432817\pi\)
\(464\) −32.7657 −1.52111
\(465\) 82.3219 3.81759
\(466\) 41.7722 1.93506
\(467\) 14.7630 0.683149 0.341574 0.939855i \(-0.389040\pi\)
0.341574 + 0.939855i \(0.389040\pi\)
\(468\) −44.8408 −2.07276
\(469\) 65.8774 3.04193
\(470\) −2.96472 −0.136753
\(471\) −55.9208 −2.57670
\(472\) −13.1992 −0.607544
\(473\) −10.2591 −0.471715
\(474\) 130.986 6.01638
\(475\) −8.36970 −0.384028
\(476\) −98.4343 −4.51173
\(477\) 35.0562 1.60511
\(478\) −16.4372 −0.751822
\(479\) −10.7631 −0.491781 −0.245890 0.969298i \(-0.579080\pi\)
−0.245890 + 0.969298i \(0.579080\pi\)
\(480\) 173.703 7.92843
\(481\) −0.790896 −0.0360618
\(482\) −31.3129 −1.42626
\(483\) 74.5208 3.39081
\(484\) −28.9277 −1.31489
\(485\) −21.5055 −0.976514
\(486\) 4.60696 0.208976
\(487\) 0.892579 0.0404466 0.0202233 0.999795i \(-0.493562\pi\)
0.0202233 + 0.999795i \(0.493562\pi\)
\(488\) 64.7456 2.93089
\(489\) 30.9824 1.40107
\(490\) 122.863 5.55039
\(491\) −24.5933 −1.10988 −0.554941 0.831890i \(-0.687259\pi\)
−0.554941 + 0.831890i \(0.687259\pi\)
\(492\) −99.5081 −4.48617
\(493\) 7.83514 0.352877
\(494\) −18.4723 −0.831110
\(495\) 36.6384 1.64677
\(496\) −161.758 −7.26314
\(497\) 4.93159 0.221212
\(498\) 147.268 6.59923
\(499\) 4.19706 0.187886 0.0939430 0.995578i \(-0.470053\pi\)
0.0939430 + 0.995578i \(0.470053\pi\)
\(500\) 46.7700 2.09162
\(501\) −34.7175 −1.55107
\(502\) 61.0874 2.72646
\(503\) 15.7243 0.701110 0.350555 0.936542i \(-0.385993\pi\)
0.350555 + 0.936542i \(0.385993\pi\)
\(504\) −278.490 −12.4049
\(505\) −16.7590 −0.745764
\(506\) 33.1956 1.47573
\(507\) −33.0902 −1.46959
\(508\) 74.3007 3.29656
\(509\) −27.9802 −1.24020 −0.620099 0.784523i \(-0.712908\pi\)
−0.620099 + 0.784523i \(0.712908\pi\)
\(510\) −76.9051 −3.40541
\(511\) 52.2042 2.30938
\(512\) −50.6908 −2.24024
\(513\) −42.3080 −1.86795
\(514\) 9.94534 0.438670
\(515\) −9.43192 −0.415620
\(516\) 70.2325 3.09181
\(517\) 1.00085 0.0440175
\(518\) −7.72383 −0.339366
\(519\) −1.26201 −0.0553963
\(520\) −34.2588 −1.50235
\(521\) −23.8689 −1.04571 −0.522857 0.852421i \(-0.675134\pi\)
−0.522857 + 0.852421i \(0.675134\pi\)
\(522\) 34.8567 1.52564
\(523\) −5.58185 −0.244077 −0.122039 0.992525i \(-0.538943\pi\)
−0.122039 + 0.992525i \(0.538943\pi\)
\(524\) −61.7515 −2.69763
\(525\) 25.2320 1.10121
\(526\) 40.7382 1.77627
\(527\) 38.6805 1.68495
\(528\) −108.571 −4.72495
\(529\) 2.64321 0.114922
\(530\) 42.1155 1.82938
\(531\) 8.14874 0.353625
\(532\) −132.253 −5.73389
\(533\) 8.39090 0.363450
\(534\) 121.643 5.26402
\(535\) 0.552142 0.0238712
\(536\) −127.758 −5.51832
\(537\) 13.4004 0.578269
\(538\) −18.0896 −0.779899
\(539\) −41.4770 −1.78654
\(540\) −123.382 −5.30951
\(541\) 9.68449 0.416369 0.208184 0.978090i \(-0.433245\pi\)
0.208184 + 0.978090i \(0.433245\pi\)
\(542\) −2.92421 −0.125606
\(543\) −30.5160 −1.30957
\(544\) 81.6178 3.49933
\(545\) 41.1637 1.76326
\(546\) 55.6882 2.38324
\(547\) −4.04586 −0.172988 −0.0864942 0.996252i \(-0.527566\pi\)
−0.0864942 + 0.996252i \(0.527566\pi\)
\(548\) −33.7087 −1.43997
\(549\) −39.9716 −1.70595
\(550\) 11.2397 0.479262
\(551\) 10.5270 0.448466
\(552\) −144.521 −6.15122
\(553\) −79.0784 −3.36275
\(554\) −73.8313 −3.13679
\(555\) −4.42396 −0.187786
\(556\) −83.7085 −3.55003
\(557\) 20.4738 0.867503 0.433751 0.901033i \(-0.357190\pi\)
0.433751 + 0.901033i \(0.357190\pi\)
\(558\) 172.081 7.28476
\(559\) −5.92227 −0.250485
\(560\) −194.160 −8.20478
\(561\) 25.9622 1.09612
\(562\) 16.8875 0.712354
\(563\) 32.7454 1.38005 0.690027 0.723784i \(-0.257599\pi\)
0.690027 + 0.723784i \(0.257599\pi\)
\(564\) −6.85169 −0.288508
\(565\) −2.59125 −0.109015
\(566\) −23.5931 −0.991690
\(567\) 40.1899 1.68782
\(568\) −9.56402 −0.401297
\(569\) 17.3002 0.725264 0.362632 0.931932i \(-0.381878\pi\)
0.362632 + 0.931932i \(0.381878\pi\)
\(570\) −103.327 −4.32789
\(571\) 21.8202 0.913148 0.456574 0.889686i \(-0.349076\pi\)
0.456574 + 0.889686i \(0.349076\pi\)
\(572\) 18.1860 0.760393
\(573\) 24.8188 1.03682
\(574\) 81.9449 3.42031
\(575\) 8.68253 0.362087
\(576\) 183.677 7.65319
\(577\) −4.93026 −0.205249 −0.102625 0.994720i \(-0.532724\pi\)
−0.102625 + 0.994720i \(0.532724\pi\)
\(578\) 10.4016 0.432651
\(579\) −2.31977 −0.0964063
\(580\) 30.6997 1.27473
\(581\) −88.9081 −3.68853
\(582\) −67.7944 −2.81017
\(583\) −14.2177 −0.588836
\(584\) −101.242 −4.18941
\(585\) 21.1502 0.874453
\(586\) 48.4002 1.99939
\(587\) 35.4082 1.46145 0.730725 0.682672i \(-0.239182\pi\)
0.730725 + 0.682672i \(0.239182\pi\)
\(588\) 283.945 11.7097
\(589\) 51.9698 2.14138
\(590\) 9.78966 0.403034
\(591\) −29.2417 −1.20284
\(592\) 8.69283 0.357273
\(593\) 2.30812 0.0947830 0.0473915 0.998876i \(-0.484909\pi\)
0.0473915 + 0.998876i \(0.484909\pi\)
\(594\) 56.8156 2.33117
\(595\) 46.4289 1.90340
\(596\) 107.216 4.39173
\(597\) 20.5273 0.840125
\(598\) 19.1628 0.783624
\(599\) 17.3387 0.708441 0.354220 0.935162i \(-0.384746\pi\)
0.354220 + 0.935162i \(0.384746\pi\)
\(600\) −48.9333 −1.99769
\(601\) −26.6565 −1.08734 −0.543672 0.839298i \(-0.682966\pi\)
−0.543672 + 0.839298i \(0.682966\pi\)
\(602\) −57.8365 −2.35724
\(603\) 78.8735 3.21198
\(604\) −89.5830 −3.64508
\(605\) 13.6444 0.554724
\(606\) −52.8313 −2.14612
\(607\) −21.7413 −0.882453 −0.441227 0.897396i \(-0.645457\pi\)
−0.441227 + 0.897396i \(0.645457\pi\)
\(608\) 109.659 4.44725
\(609\) −31.7356 −1.28599
\(610\) −48.0207 −1.94430
\(611\) 0.577760 0.0233737
\(612\) −117.853 −4.76394
\(613\) 13.4888 0.544809 0.272404 0.962183i \(-0.412181\pi\)
0.272404 + 0.962183i \(0.412181\pi\)
\(614\) 61.0261 2.46281
\(615\) 46.9353 1.89261
\(616\) 112.946 4.55074
\(617\) −30.6207 −1.23274 −0.616371 0.787456i \(-0.711398\pi\)
−0.616371 + 0.787456i \(0.711398\pi\)
\(618\) −29.7334 −1.19605
\(619\) 28.0471 1.12731 0.563654 0.826011i \(-0.309395\pi\)
0.563654 + 0.826011i \(0.309395\pi\)
\(620\) 151.558 6.08672
\(621\) 43.8894 1.76122
\(622\) 61.6919 2.47362
\(623\) −73.4381 −2.94223
\(624\) −62.6746 −2.50899
\(625\) −30.6331 −1.22533
\(626\) 35.3788 1.41402
\(627\) 34.8818 1.39305
\(628\) −102.953 −4.10826
\(629\) −2.07868 −0.0828825
\(630\) 206.551 8.22920
\(631\) −23.1214 −0.920447 −0.460223 0.887803i \(-0.652231\pi\)
−0.460223 + 0.887803i \(0.652231\pi\)
\(632\) 153.360 6.10032
\(633\) 52.7736 2.09756
\(634\) 5.68144 0.225639
\(635\) −35.0456 −1.39074
\(636\) 97.3321 3.85947
\(637\) −23.9433 −0.948670
\(638\) −14.1368 −0.559680
\(639\) 5.90448 0.233578
\(640\) 104.242 4.12054
\(641\) −25.8997 −1.02298 −0.511488 0.859291i \(-0.670905\pi\)
−0.511488 + 0.859291i \(0.670905\pi\)
\(642\) 1.74058 0.0686953
\(643\) 15.8598 0.625451 0.312726 0.949844i \(-0.398758\pi\)
0.312726 + 0.949844i \(0.398758\pi\)
\(644\) 137.196 5.40628
\(645\) −33.1268 −1.30437
\(646\) −48.5501 −1.91018
\(647\) 23.2124 0.912574 0.456287 0.889833i \(-0.349179\pi\)
0.456287 + 0.889833i \(0.349179\pi\)
\(648\) −77.9417 −3.06184
\(649\) −3.30487 −0.129727
\(650\) 6.48832 0.254493
\(651\) −156.672 −6.14047
\(652\) 57.0399 2.23385
\(653\) 20.1594 0.788900 0.394450 0.918917i \(-0.370935\pi\)
0.394450 + 0.918917i \(0.370935\pi\)
\(654\) 129.765 5.07422
\(655\) 29.1265 1.13807
\(656\) −92.2253 −3.60079
\(657\) 62.5030 2.43847
\(658\) 5.64237 0.219962
\(659\) 15.8697 0.618196 0.309098 0.951030i \(-0.399973\pi\)
0.309098 + 0.951030i \(0.399973\pi\)
\(660\) 101.725 3.95964
\(661\) 35.7403 1.39014 0.695068 0.718944i \(-0.255374\pi\)
0.695068 + 0.718944i \(0.255374\pi\)
\(662\) −52.2719 −2.03161
\(663\) 14.9871 0.582052
\(664\) 172.423 6.69130
\(665\) 62.3801 2.41900
\(666\) −9.24758 −0.358336
\(667\) −10.9205 −0.422843
\(668\) −63.9165 −2.47300
\(669\) −44.7310 −1.72940
\(670\) 94.7564 3.66076
\(671\) 16.2112 0.625826
\(672\) −330.586 −12.7526
\(673\) 40.3804 1.55655 0.778276 0.627923i \(-0.216095\pi\)
0.778276 + 0.627923i \(0.216095\pi\)
\(674\) 71.6554 2.76006
\(675\) 14.8605 0.571981
\(676\) −60.9205 −2.34310
\(677\) 36.8301 1.41550 0.707748 0.706465i \(-0.249711\pi\)
0.707748 + 0.706465i \(0.249711\pi\)
\(678\) −8.16872 −0.313718
\(679\) 40.9286 1.57069
\(680\) −90.0412 −3.45292
\(681\) 22.6986 0.869814
\(682\) −69.7904 −2.67241
\(683\) 3.99781 0.152972 0.0764860 0.997071i \(-0.475630\pi\)
0.0764860 + 0.997071i \(0.475630\pi\)
\(684\) −158.343 −6.05441
\(685\) 15.8995 0.607489
\(686\) −139.328 −5.31959
\(687\) −85.8248 −3.27442
\(688\) 65.0923 2.48162
\(689\) −8.20741 −0.312677
\(690\) 107.189 4.08061
\(691\) 1.66405 0.0633035 0.0316517 0.999499i \(-0.489923\pi\)
0.0316517 + 0.999499i \(0.489923\pi\)
\(692\) −2.32342 −0.0883233
\(693\) −69.7291 −2.64879
\(694\) −45.5183 −1.72785
\(695\) 39.4831 1.49768
\(696\) 61.5460 2.33290
\(697\) 22.0535 0.835335
\(698\) 66.6299 2.52198
\(699\) −45.5347 −1.72228
\(700\) 46.4532 1.75576
\(701\) −46.8137 −1.76813 −0.884065 0.467364i \(-0.845204\pi\)
−0.884065 + 0.467364i \(0.845204\pi\)
\(702\) 32.7978 1.23787
\(703\) −2.79284 −0.105334
\(704\) −74.4933 −2.80757
\(705\) 3.23176 0.121715
\(706\) 20.3872 0.767284
\(707\) 31.8951 1.19954
\(708\) 22.6246 0.850285
\(709\) −30.5970 −1.14909 −0.574547 0.818471i \(-0.694822\pi\)
−0.574547 + 0.818471i \(0.694822\pi\)
\(710\) 7.09348 0.266213
\(711\) −94.6788 −3.55073
\(712\) 142.421 5.33746
\(713\) −53.9122 −2.01903
\(714\) 146.363 5.47751
\(715\) −8.57783 −0.320793
\(716\) 24.6707 0.921986
\(717\) 17.9178 0.669152
\(718\) 22.9134 0.855120
\(719\) 32.6023 1.21586 0.607930 0.793991i \(-0.292000\pi\)
0.607930 + 0.793991i \(0.292000\pi\)
\(720\) −232.464 −8.66342
\(721\) 17.9505 0.668513
\(722\) −13.2183 −0.491933
\(723\) 34.1333 1.26943
\(724\) −56.1812 −2.08796
\(725\) −3.69756 −0.137324
\(726\) 43.0129 1.59636
\(727\) 2.54601 0.0944265 0.0472132 0.998885i \(-0.484966\pi\)
0.0472132 + 0.998885i \(0.484966\pi\)
\(728\) 65.2003 2.41649
\(729\) −29.4703 −1.09149
\(730\) 75.0893 2.77918
\(731\) −15.5653 −0.575703
\(732\) −110.979 −4.10192
\(733\) −3.88191 −0.143382 −0.0716908 0.997427i \(-0.522839\pi\)
−0.0716908 + 0.997427i \(0.522839\pi\)
\(734\) −73.4508 −2.71112
\(735\) −133.929 −4.94006
\(736\) −113.757 −4.19315
\(737\) −31.9885 −1.17831
\(738\) 98.1108 3.61151
\(739\) −50.3887 −1.85358 −0.926789 0.375583i \(-0.877443\pi\)
−0.926789 + 0.375583i \(0.877443\pi\)
\(740\) −8.14469 −0.299405
\(741\) 20.1362 0.739720
\(742\) −80.1529 −2.94251
\(743\) 2.79949 0.102703 0.0513517 0.998681i \(-0.483647\pi\)
0.0513517 + 0.998681i \(0.483647\pi\)
\(744\) 303.841 11.1393
\(745\) −50.5708 −1.85277
\(746\) −71.9185 −2.63312
\(747\) −106.448 −3.89472
\(748\) 47.7975 1.74765
\(749\) −1.05082 −0.0383961
\(750\) −69.5430 −2.53935
\(751\) −42.3467 −1.54525 −0.772626 0.634861i \(-0.781057\pi\)
−0.772626 + 0.634861i \(0.781057\pi\)
\(752\) −6.35023 −0.231569
\(753\) −66.5896 −2.42666
\(754\) −8.16070 −0.297195
\(755\) 42.2539 1.53778
\(756\) 234.816 8.54019
\(757\) 30.1004 1.09402 0.547008 0.837127i \(-0.315767\pi\)
0.547008 + 0.837127i \(0.315767\pi\)
\(758\) 31.1619 1.13185
\(759\) −36.1856 −1.31345
\(760\) −120.976 −4.38827
\(761\) 41.5038 1.50451 0.752255 0.658872i \(-0.228966\pi\)
0.752255 + 0.658872i \(0.228966\pi\)
\(762\) −110.479 −4.00222
\(763\) −78.3413 −2.83615
\(764\) 45.6924 1.65309
\(765\) 55.5883 2.00980
\(766\) 61.2857 2.21434
\(767\) −1.90779 −0.0688864
\(768\) 142.961 5.15864
\(769\) −38.2825 −1.38050 −0.690251 0.723570i \(-0.742500\pi\)
−0.690251 + 0.723570i \(0.742500\pi\)
\(770\) −83.7705 −3.01888
\(771\) −10.8411 −0.390434
\(772\) −4.27079 −0.153709
\(773\) 25.5431 0.918720 0.459360 0.888250i \(-0.348079\pi\)
0.459360 + 0.888250i \(0.348079\pi\)
\(774\) −69.2463 −2.48901
\(775\) −18.2541 −0.655708
\(776\) −79.3743 −2.84937
\(777\) 8.41953 0.302049
\(778\) 35.2530 1.26388
\(779\) 29.6303 1.06161
\(780\) 58.7226 2.10261
\(781\) −2.39467 −0.0856879
\(782\) 50.3648 1.80104
\(783\) −18.6908 −0.667956
\(784\) 263.164 9.39871
\(785\) 48.5600 1.73318
\(786\) 91.8191 3.27508
\(787\) −22.5144 −0.802550 −0.401275 0.915958i \(-0.631433\pi\)
−0.401275 + 0.915958i \(0.631433\pi\)
\(788\) −53.8353 −1.91780
\(789\) −44.4076 −1.58095
\(790\) −113.744 −4.04684
\(791\) 4.93159 0.175347
\(792\) 135.228 4.80513
\(793\) 9.35820 0.332320
\(794\) 89.3420 3.17063
\(795\) −45.9089 −1.62822
\(796\) 37.7916 1.33949
\(797\) −1.66553 −0.0589962 −0.0294981 0.999565i \(-0.509391\pi\)
−0.0294981 + 0.999565i \(0.509391\pi\)
\(798\) 196.648 6.96128
\(799\) 1.51851 0.0537209
\(800\) −38.5171 −1.36179
\(801\) −87.9258 −3.10671
\(802\) −31.8202 −1.12361
\(803\) −25.3492 −0.894553
\(804\) 218.989 7.72314
\(805\) −64.7117 −2.28079
\(806\) −40.2878 −1.41908
\(807\) 19.7190 0.694141
\(808\) −61.8554 −2.17607
\(809\) −6.44632 −0.226641 −0.113320 0.993559i \(-0.536149\pi\)
−0.113320 + 0.993559i \(0.536149\pi\)
\(810\) 57.8081 2.03117
\(811\) −15.4750 −0.543402 −0.271701 0.962382i \(-0.587586\pi\)
−0.271701 + 0.962382i \(0.587586\pi\)
\(812\) −58.4266 −2.05037
\(813\) 3.18760 0.111794
\(814\) 3.75052 0.131456
\(815\) −26.9042 −0.942413
\(816\) −164.725 −5.76654
\(817\) −20.9129 −0.731651
\(818\) 25.1630 0.879804
\(819\) −40.2524 −1.40653
\(820\) 86.4099 3.01757
\(821\) 50.0046 1.74517 0.872586 0.488461i \(-0.162442\pi\)
0.872586 + 0.488461i \(0.162442\pi\)
\(822\) 50.1219 1.74820
\(823\) −28.9017 −1.00745 −0.503725 0.863864i \(-0.668037\pi\)
−0.503725 + 0.863864i \(0.668037\pi\)
\(824\) −34.8121 −1.21274
\(825\) −12.2521 −0.426562
\(826\) −18.6314 −0.648268
\(827\) 19.1100 0.664519 0.332260 0.943188i \(-0.392189\pi\)
0.332260 + 0.943188i \(0.392189\pi\)
\(828\) 164.262 5.70849
\(829\) −12.6353 −0.438841 −0.219420 0.975630i \(-0.570417\pi\)
−0.219420 + 0.975630i \(0.570417\pi\)
\(830\) −127.883 −4.43889
\(831\) 80.4814 2.79187
\(832\) −43.0026 −1.49085
\(833\) −62.9294 −2.18037
\(834\) 124.467 4.30995
\(835\) 30.1477 1.04330
\(836\) 64.2190 2.22106
\(837\) −92.2730 −3.18942
\(838\) −100.571 −3.47417
\(839\) −6.60303 −0.227962 −0.113981 0.993483i \(-0.536360\pi\)
−0.113981 + 0.993483i \(0.536360\pi\)
\(840\) 364.705 12.5835
\(841\) −24.3494 −0.839634
\(842\) −77.6221 −2.67504
\(843\) −18.4085 −0.634024
\(844\) 97.1585 3.34433
\(845\) 28.7346 0.988499
\(846\) 6.75548 0.232258
\(847\) −25.9676 −0.892258
\(848\) 90.2085 3.09777
\(849\) 25.7181 0.882643
\(850\) 17.0530 0.584913
\(851\) 2.89723 0.0993158
\(852\) 16.3935 0.561633
\(853\) 26.0052 0.890400 0.445200 0.895431i \(-0.353133\pi\)
0.445200 + 0.895431i \(0.353133\pi\)
\(854\) 91.3916 3.12735
\(855\) 74.6864 2.55422
\(856\) 2.03789 0.0696537
\(857\) −4.31988 −0.147564 −0.0737822 0.997274i \(-0.523507\pi\)
−0.0737822 + 0.997274i \(0.523507\pi\)
\(858\) −27.0409 −0.923162
\(859\) 48.0163 1.63830 0.819148 0.573583i \(-0.194447\pi\)
0.819148 + 0.573583i \(0.194447\pi\)
\(860\) −60.9879 −2.07967
\(861\) −89.3258 −3.04421
\(862\) 41.1793 1.40257
\(863\) 22.9002 0.779531 0.389765 0.920914i \(-0.372556\pi\)
0.389765 + 0.920914i \(0.372556\pi\)
\(864\) −194.700 −6.62384
\(865\) 1.09590 0.0372616
\(866\) −59.9087 −2.03578
\(867\) −11.3385 −0.385077
\(868\) −288.441 −9.79031
\(869\) 38.3987 1.30259
\(870\) −45.6477 −1.54760
\(871\) −18.4660 −0.625695
\(872\) 151.930 5.14501
\(873\) 49.0029 1.65850
\(874\) 67.6683 2.28891
\(875\) 41.9842 1.41933
\(876\) 173.537 5.86326
\(877\) 52.6044 1.77632 0.888161 0.459532i \(-0.151983\pi\)
0.888161 + 0.459532i \(0.151983\pi\)
\(878\) 1.57078 0.0530111
\(879\) −52.7597 −1.77954
\(880\) 94.2799 3.17817
\(881\) 18.4839 0.622740 0.311370 0.950289i \(-0.399212\pi\)
0.311370 + 0.950289i \(0.399212\pi\)
\(882\) −279.958 −9.42669
\(883\) −12.6002 −0.424030 −0.212015 0.977266i \(-0.568003\pi\)
−0.212015 + 0.977266i \(0.568003\pi\)
\(884\) 27.5920 0.928018
\(885\) −10.6714 −0.358716
\(886\) −71.3259 −2.39624
\(887\) −41.5176 −1.39402 −0.697012 0.717060i \(-0.745488\pi\)
−0.697012 + 0.717060i \(0.745488\pi\)
\(888\) −16.3283 −0.547942
\(889\) 66.6978 2.23697
\(890\) −105.632 −3.54078
\(891\) −19.5153 −0.653786
\(892\) −82.3518 −2.75734
\(893\) 2.04021 0.0682730
\(894\) −159.421 −5.33182
\(895\) −11.6365 −0.388965
\(896\) −198.391 −6.62776
\(897\) −20.8888 −0.697456
\(898\) −57.2983 −1.91207
\(899\) 22.9592 0.765732
\(900\) 55.6173 1.85391
\(901\) −21.5712 −0.718642
\(902\) −39.7906 −1.32488
\(903\) 63.0459 2.09804
\(904\) −9.56402 −0.318094
\(905\) 26.4992 0.880862
\(906\) 133.202 4.42534
\(907\) −54.3138 −1.80346 −0.901730 0.432299i \(-0.857702\pi\)
−0.901730 + 0.432299i \(0.857702\pi\)
\(908\) 41.7892 1.38682
\(909\) 38.1873 1.26659
\(910\) −48.3580 −1.60305
\(911\) 21.2259 0.703246 0.351623 0.936142i \(-0.385630\pi\)
0.351623 + 0.936142i \(0.385630\pi\)
\(912\) −221.319 −7.32860
\(913\) 43.1718 1.42878
\(914\) 24.6953 0.816848
\(915\) 52.3460 1.73051
\(916\) −158.007 −5.22070
\(917\) −55.4327 −1.83055
\(918\) 86.2014 2.84507
\(919\) −21.0346 −0.693869 −0.346934 0.937889i \(-0.612777\pi\)
−0.346934 + 0.937889i \(0.612777\pi\)
\(920\) 125.498 4.13754
\(921\) −66.5228 −2.19200
\(922\) −72.3780 −2.38364
\(923\) −1.38236 −0.0455011
\(924\) −193.600 −6.36896
\(925\) 0.980972 0.0322542
\(926\) −24.6802 −0.811040
\(927\) 21.4918 0.705882
\(928\) 48.4450 1.59029
\(929\) 0.664410 0.0217986 0.0108993 0.999941i \(-0.496531\pi\)
0.0108993 + 0.999941i \(0.496531\pi\)
\(930\) −225.354 −7.38964
\(931\) −84.5497 −2.77100
\(932\) −83.8313 −2.74598
\(933\) −67.2486 −2.20162
\(934\) −40.4132 −1.32236
\(935\) −22.5448 −0.737294
\(936\) 78.0629 2.55157
\(937\) 24.5068 0.800602 0.400301 0.916384i \(-0.368906\pi\)
0.400301 + 0.916384i \(0.368906\pi\)
\(938\) −180.337 −5.88822
\(939\) −38.5654 −1.25853
\(940\) 5.94981 0.194061
\(941\) 33.4968 1.09196 0.545982 0.837797i \(-0.316157\pi\)
0.545982 + 0.837797i \(0.316157\pi\)
\(942\) 153.082 4.98767
\(943\) −30.7377 −1.00096
\(944\) 20.9688 0.682475
\(945\) −110.757 −3.60291
\(946\) 28.0841 0.913092
\(947\) −29.2233 −0.949629 −0.474814 0.880086i \(-0.657485\pi\)
−0.474814 + 0.880086i \(0.657485\pi\)
\(948\) −262.872 −8.53767
\(949\) −14.6333 −0.475016
\(950\) 22.9118 0.743357
\(951\) −6.19318 −0.200828
\(952\) 171.364 5.55393
\(953\) 11.4667 0.371442 0.185721 0.982603i \(-0.440538\pi\)
0.185721 + 0.982603i \(0.440538\pi\)
\(954\) −95.9654 −3.10699
\(955\) −21.5519 −0.697403
\(956\) 32.9874 1.06689
\(957\) 15.4101 0.498137
\(958\) 29.4638 0.951932
\(959\) −30.2594 −0.977128
\(960\) −240.539 −7.76337
\(961\) 82.3450 2.65629
\(962\) 2.16505 0.0698041
\(963\) −1.25812 −0.0405424
\(964\) 62.8408 2.02397
\(965\) 2.01442 0.0648465
\(966\) −203.998 −6.56354
\(967\) −35.1574 −1.13058 −0.565292 0.824891i \(-0.691237\pi\)
−0.565292 + 0.824891i \(0.691237\pi\)
\(968\) 50.3600 1.61863
\(969\) 52.9231 1.70014
\(970\) 58.8707 1.89022
\(971\) −4.14659 −0.133070 −0.0665352 0.997784i \(-0.521194\pi\)
−0.0665352 + 0.997784i \(0.521194\pi\)
\(972\) −9.24557 −0.296552
\(973\) −75.1429 −2.40897
\(974\) −2.44341 −0.0782919
\(975\) −7.07273 −0.226509
\(976\) −102.857 −3.29237
\(977\) 2.91792 0.0933526 0.0466763 0.998910i \(-0.485137\pi\)
0.0466763 + 0.998910i \(0.485137\pi\)
\(978\) −84.8133 −2.71203
\(979\) 35.6599 1.13969
\(980\) −246.570 −7.87639
\(981\) −93.7964 −2.99469
\(982\) 67.3235 2.14838
\(983\) 42.1455 1.34423 0.672117 0.740445i \(-0.265385\pi\)
0.672117 + 0.740445i \(0.265385\pi\)
\(984\) 173.233 5.52246
\(985\) 25.3927 0.809078
\(986\) −21.4485 −0.683058
\(987\) −6.15058 −0.195775
\(988\) 37.0715 1.17940
\(989\) 21.6946 0.689848
\(990\) −100.297 −3.18764
\(991\) −24.7112 −0.784977 −0.392488 0.919757i \(-0.628386\pi\)
−0.392488 + 0.919757i \(0.628386\pi\)
\(992\) 239.163 7.59345
\(993\) 56.9801 1.80821
\(994\) −13.5001 −0.428196
\(995\) −17.8253 −0.565099
\(996\) −295.547 −9.36478
\(997\) −43.0949 −1.36483 −0.682414 0.730965i \(-0.739070\pi\)
−0.682414 + 0.730965i \(0.739070\pi\)
\(998\) −11.4893 −0.363688
\(999\) 4.95872 0.156887
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 8023.2.a.b.1.7 155
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8023.2.a.b.1.7 155 1.1 even 1 trivial