Properties

Label 6025.2.a.p.1.45
Level $6025$
Weight $2$
Character 6025.1
Self dual yes
Analytic conductor $48.110$
Analytic rank $1$
Dimension $46$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6025,2,Mod(1,6025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6025, 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("6025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6025 = 5^{2} \cdot 241 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6025.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: \(48.1098672178\)
Analytic rank: \(1\)
Dimension: \(46\)
Twist minimal: no (minimal twist has level 1205)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.45
Character \(\chi\) \(=\) 6025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.67602 q^{2} +0.199289 q^{3} +5.16108 q^{4} +0.533301 q^{6} -2.87374 q^{7} +8.45912 q^{8} -2.96028 q^{9} +O(q^{10})\) \(q+2.67602 q^{2} +0.199289 q^{3} +5.16108 q^{4} +0.533301 q^{6} -2.87374 q^{7} +8.45912 q^{8} -2.96028 q^{9} -0.806904 q^{11} +1.02855 q^{12} -5.09752 q^{13} -7.69018 q^{14} +12.3146 q^{16} -0.390647 q^{17} -7.92178 q^{18} +0.489734 q^{19} -0.572704 q^{21} -2.15929 q^{22} -1.83958 q^{23} +1.68581 q^{24} -13.6411 q^{26} -1.18782 q^{27} -14.8316 q^{28} -8.05368 q^{29} -5.55127 q^{31} +16.0359 q^{32} -0.160807 q^{33} -1.04538 q^{34} -15.2783 q^{36} -2.20153 q^{37} +1.31054 q^{38} -1.01588 q^{39} -3.59719 q^{41} -1.53257 q^{42} -9.27459 q^{43} -4.16450 q^{44} -4.92275 q^{46} +10.9779 q^{47} +2.45416 q^{48} +1.25837 q^{49} -0.0778515 q^{51} -26.3087 q^{52} -1.68955 q^{53} -3.17863 q^{54} -24.3093 q^{56} +0.0975985 q^{57} -21.5518 q^{58} -5.02546 q^{59} +3.39923 q^{61} -14.8553 q^{62} +8.50708 q^{63} +18.2832 q^{64} -0.430323 q^{66} +12.9814 q^{67} -2.01616 q^{68} -0.366608 q^{69} +8.48671 q^{71} -25.0414 q^{72} +13.1818 q^{73} -5.89135 q^{74} +2.52756 q^{76} +2.31883 q^{77} -2.71851 q^{78} +8.08502 q^{79} +8.64413 q^{81} -9.62615 q^{82} +0.366678 q^{83} -2.95577 q^{84} -24.8190 q^{86} -1.60501 q^{87} -6.82569 q^{88} -2.24259 q^{89} +14.6489 q^{91} -9.49422 q^{92} -1.10631 q^{93} +29.3772 q^{94} +3.19578 q^{96} +7.32434 q^{97} +3.36741 q^{98} +2.38866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46 q + 34 q^{4} - 4 q^{6} + 34 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 46 q + 34 q^{4} - 4 q^{6} + 34 q^{9} - 64 q^{11} - 66 q^{14} + 22 q^{16} - 14 q^{21} - 50 q^{24} - 60 q^{26} - 36 q^{29} - 36 q^{31} + 12 q^{34} - 34 q^{36} - 88 q^{39} - 76 q^{41} - 100 q^{44} - 12 q^{46} + 22 q^{49} - 112 q^{51} - 26 q^{54} - 120 q^{56} - 84 q^{59} - 78 q^{61} + 28 q^{64} - 2 q^{66} - 24 q^{69} - 172 q^{71} - 16 q^{74} - 18 q^{76} - 54 q^{79} - 42 q^{81} + 44 q^{84} - 80 q^{86} - 86 q^{89} - 88 q^{91} + 4 q^{94} - 122 q^{96} - 148 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.67602 1.89223 0.946116 0.323828i \(-0.104970\pi\)
0.946116 + 0.323828i \(0.104970\pi\)
\(3\) 0.199289 0.115060 0.0575298 0.998344i \(-0.481678\pi\)
0.0575298 + 0.998344i \(0.481678\pi\)
\(4\) 5.16108 2.58054
\(5\) 0 0
\(6\) 0.533301 0.217719
\(7\) −2.87374 −1.08617 −0.543085 0.839678i \(-0.682744\pi\)
−0.543085 + 0.839678i \(0.682744\pi\)
\(8\) 8.45912 2.99075
\(9\) −2.96028 −0.986761
\(10\) 0 0
\(11\) −0.806904 −0.243291 −0.121645 0.992574i \(-0.538817\pi\)
−0.121645 + 0.992574i \(0.538817\pi\)
\(12\) 1.02855 0.296916
\(13\) −5.09752 −1.41380 −0.706899 0.707315i \(-0.749906\pi\)
−0.706899 + 0.707315i \(0.749906\pi\)
\(14\) −7.69018 −2.05529
\(15\) 0 0
\(16\) 12.3146 3.07865
\(17\) −0.390647 −0.0947457 −0.0473729 0.998877i \(-0.515085\pi\)
−0.0473729 + 0.998877i \(0.515085\pi\)
\(18\) −7.92178 −1.86718
\(19\) 0.489734 0.112353 0.0561763 0.998421i \(-0.482109\pi\)
0.0561763 + 0.998421i \(0.482109\pi\)
\(20\) 0 0
\(21\) −0.572704 −0.124974
\(22\) −2.15929 −0.460362
\(23\) −1.83958 −0.383579 −0.191789 0.981436i \(-0.561429\pi\)
−0.191789 + 0.981436i \(0.561429\pi\)
\(24\) 1.68581 0.344114
\(25\) 0 0
\(26\) −13.6411 −2.67523
\(27\) −1.18782 −0.228596
\(28\) −14.8316 −2.80291
\(29\) −8.05368 −1.49553 −0.747765 0.663963i \(-0.768873\pi\)
−0.747765 + 0.663963i \(0.768873\pi\)
\(30\) 0 0
\(31\) −5.55127 −0.997038 −0.498519 0.866879i \(-0.666123\pi\)
−0.498519 + 0.866879i \(0.666123\pi\)
\(32\) 16.0359 2.83477
\(33\) −0.160807 −0.0279929
\(34\) −1.04538 −0.179281
\(35\) 0 0
\(36\) −15.2783 −2.54638
\(37\) −2.20153 −0.361930 −0.180965 0.983490i \(-0.557922\pi\)
−0.180965 + 0.983490i \(0.557922\pi\)
\(38\) 1.31054 0.212597
\(39\) −1.01588 −0.162671
\(40\) 0 0
\(41\) −3.59719 −0.561787 −0.280893 0.959739i \(-0.590631\pi\)
−0.280893 + 0.959739i \(0.590631\pi\)
\(42\) −1.53257 −0.236480
\(43\) −9.27459 −1.41436 −0.707181 0.707033i \(-0.750033\pi\)
−0.707181 + 0.707033i \(0.750033\pi\)
\(44\) −4.16450 −0.627821
\(45\) 0 0
\(46\) −4.92275 −0.725820
\(47\) 10.9779 1.60130 0.800649 0.599134i \(-0.204488\pi\)
0.800649 + 0.599134i \(0.204488\pi\)
\(48\) 2.45416 0.354228
\(49\) 1.25837 0.179767
\(50\) 0 0
\(51\) −0.0778515 −0.0109014
\(52\) −26.3087 −3.64836
\(53\) −1.68955 −0.232077 −0.116039 0.993245i \(-0.537020\pi\)
−0.116039 + 0.993245i \(0.537020\pi\)
\(54\) −3.17863 −0.432556
\(55\) 0 0
\(56\) −24.3093 −3.24847
\(57\) 0.0975985 0.0129272
\(58\) −21.5518 −2.82989
\(59\) −5.02546 −0.654259 −0.327130 0.944979i \(-0.606081\pi\)
−0.327130 + 0.944979i \(0.606081\pi\)
\(60\) 0 0
\(61\) 3.39923 0.435227 0.217613 0.976035i \(-0.430173\pi\)
0.217613 + 0.976035i \(0.430173\pi\)
\(62\) −14.8553 −1.88663
\(63\) 8.50708 1.07179
\(64\) 18.2832 2.28539
\(65\) 0 0
\(66\) −0.430323 −0.0529690
\(67\) 12.9814 1.58594 0.792968 0.609263i \(-0.208535\pi\)
0.792968 + 0.609263i \(0.208535\pi\)
\(68\) −2.01616 −0.244495
\(69\) −0.366608 −0.0441344
\(70\) 0 0
\(71\) 8.48671 1.00719 0.503594 0.863941i \(-0.332011\pi\)
0.503594 + 0.863941i \(0.332011\pi\)
\(72\) −25.0414 −2.95116
\(73\) 13.1818 1.54281 0.771404 0.636346i \(-0.219555\pi\)
0.771404 + 0.636346i \(0.219555\pi\)
\(74\) −5.89135 −0.684855
\(75\) 0 0
\(76\) 2.52756 0.289931
\(77\) 2.31883 0.264255
\(78\) −2.71851 −0.307811
\(79\) 8.08502 0.909636 0.454818 0.890584i \(-0.349704\pi\)
0.454818 + 0.890584i \(0.349704\pi\)
\(80\) 0 0
\(81\) 8.64413 0.960459
\(82\) −9.62615 −1.06303
\(83\) 0.366678 0.0402481 0.0201240 0.999797i \(-0.493594\pi\)
0.0201240 + 0.999797i \(0.493594\pi\)
\(84\) −2.95577 −0.322501
\(85\) 0 0
\(86\) −24.8190 −2.67630
\(87\) −1.60501 −0.172075
\(88\) −6.82569 −0.727621
\(89\) −2.24259 −0.237715 −0.118857 0.992911i \(-0.537923\pi\)
−0.118857 + 0.992911i \(0.537923\pi\)
\(90\) 0 0
\(91\) 14.6489 1.53563
\(92\) −9.49422 −0.989841
\(93\) −1.10631 −0.114719
\(94\) 29.3772 3.03003
\(95\) 0 0
\(96\) 3.19578 0.326168
\(97\) 7.32434 0.743674 0.371837 0.928298i \(-0.378728\pi\)
0.371837 + 0.928298i \(0.378728\pi\)
\(98\) 3.36741 0.340160
\(99\) 2.38866 0.240070
\(100\) 0 0
\(101\) 3.65598 0.363783 0.181892 0.983319i \(-0.441778\pi\)
0.181892 + 0.983319i \(0.441778\pi\)
\(102\) −0.208332 −0.0206280
\(103\) −19.1218 −1.88413 −0.942064 0.335434i \(-0.891117\pi\)
−0.942064 + 0.335434i \(0.891117\pi\)
\(104\) −43.1205 −4.22832
\(105\) 0 0
\(106\) −4.52127 −0.439144
\(107\) 6.56240 0.634411 0.317205 0.948357i \(-0.397256\pi\)
0.317205 + 0.948357i \(0.397256\pi\)
\(108\) −6.13043 −0.589901
\(109\) −15.2722 −1.46282 −0.731408 0.681940i \(-0.761136\pi\)
−0.731408 + 0.681940i \(0.761136\pi\)
\(110\) 0 0
\(111\) −0.438741 −0.0416435
\(112\) −35.3889 −3.34394
\(113\) 0.183036 0.0172186 0.00860929 0.999963i \(-0.497260\pi\)
0.00860929 + 0.999963i \(0.497260\pi\)
\(114\) 0.261176 0.0244613
\(115\) 0 0
\(116\) −41.5657 −3.85928
\(117\) 15.0901 1.39508
\(118\) −13.4482 −1.23801
\(119\) 1.12262 0.102910
\(120\) 0 0
\(121\) −10.3489 −0.940810
\(122\) 9.09640 0.823550
\(123\) −0.716880 −0.0646389
\(124\) −28.6506 −2.57290
\(125\) 0 0
\(126\) 22.7651 2.02808
\(127\) 15.1585 1.34510 0.672551 0.740051i \(-0.265199\pi\)
0.672551 + 0.740051i \(0.265199\pi\)
\(128\) 16.8543 1.48972
\(129\) −1.84832 −0.162736
\(130\) 0 0
\(131\) 7.10114 0.620430 0.310215 0.950667i \(-0.399599\pi\)
0.310215 + 0.950667i \(0.399599\pi\)
\(132\) −0.829938 −0.0722368
\(133\) −1.40737 −0.122034
\(134\) 34.7386 3.00096
\(135\) 0 0
\(136\) −3.30453 −0.283361
\(137\) −7.60403 −0.649656 −0.324828 0.945773i \(-0.605306\pi\)
−0.324828 + 0.945773i \(0.605306\pi\)
\(138\) −0.981050 −0.0835125
\(139\) −21.2414 −1.80167 −0.900835 0.434161i \(-0.857045\pi\)
−0.900835 + 0.434161i \(0.857045\pi\)
\(140\) 0 0
\(141\) 2.18778 0.184245
\(142\) 22.7106 1.90583
\(143\) 4.11321 0.343964
\(144\) −36.4547 −3.03789
\(145\) 0 0
\(146\) 35.2746 2.91935
\(147\) 0.250778 0.0206839
\(148\) −11.3623 −0.933975
\(149\) −16.0916 −1.31827 −0.659137 0.752023i \(-0.729078\pi\)
−0.659137 + 0.752023i \(0.729078\pi\)
\(150\) 0 0
\(151\) −10.5518 −0.858695 −0.429348 0.903139i \(-0.641256\pi\)
−0.429348 + 0.903139i \(0.641256\pi\)
\(152\) 4.14272 0.336019
\(153\) 1.15642 0.0934914
\(154\) 6.20523 0.500032
\(155\) 0 0
\(156\) −5.24304 −0.419779
\(157\) 0.254366 0.0203006 0.0101503 0.999948i \(-0.496769\pi\)
0.0101503 + 0.999948i \(0.496769\pi\)
\(158\) 21.6357 1.72124
\(159\) −0.336708 −0.0267027
\(160\) 0 0
\(161\) 5.28647 0.416632
\(162\) 23.1319 1.81741
\(163\) 8.82845 0.691497 0.345749 0.938327i \(-0.387625\pi\)
0.345749 + 0.938327i \(0.387625\pi\)
\(164\) −18.5654 −1.44971
\(165\) 0 0
\(166\) 0.981236 0.0761587
\(167\) −3.04162 −0.235367 −0.117684 0.993051i \(-0.537547\pi\)
−0.117684 + 0.993051i \(0.537547\pi\)
\(168\) −4.84457 −0.373767
\(169\) 12.9847 0.998824
\(170\) 0 0
\(171\) −1.44975 −0.110865
\(172\) −47.8669 −3.64982
\(173\) 6.02560 0.458118 0.229059 0.973413i \(-0.426435\pi\)
0.229059 + 0.973413i \(0.426435\pi\)
\(174\) −4.29504 −0.325606
\(175\) 0 0
\(176\) −9.93670 −0.749007
\(177\) −1.00152 −0.0752787
\(178\) −6.00123 −0.449811
\(179\) 7.72419 0.577333 0.288667 0.957430i \(-0.406788\pi\)
0.288667 + 0.957430i \(0.406788\pi\)
\(180\) 0 0
\(181\) −10.3144 −0.766662 −0.383331 0.923611i \(-0.625223\pi\)
−0.383331 + 0.923611i \(0.625223\pi\)
\(182\) 39.2008 2.90576
\(183\) 0.677429 0.0500770
\(184\) −15.5612 −1.14719
\(185\) 0 0
\(186\) −2.96050 −0.217074
\(187\) 0.315214 0.0230507
\(188\) 56.6581 4.13221
\(189\) 3.41348 0.248294
\(190\) 0 0
\(191\) −16.6263 −1.20304 −0.601519 0.798858i \(-0.705438\pi\)
−0.601519 + 0.798858i \(0.705438\pi\)
\(192\) 3.64363 0.262956
\(193\) −26.5699 −1.91254 −0.956271 0.292481i \(-0.905519\pi\)
−0.956271 + 0.292481i \(0.905519\pi\)
\(194\) 19.6001 1.40720
\(195\) 0 0
\(196\) 6.49453 0.463895
\(197\) −4.42875 −0.315536 −0.157768 0.987476i \(-0.550430\pi\)
−0.157768 + 0.987476i \(0.550430\pi\)
\(198\) 6.39211 0.454268
\(199\) 3.44630 0.244302 0.122151 0.992512i \(-0.461021\pi\)
0.122151 + 0.992512i \(0.461021\pi\)
\(200\) 0 0
\(201\) 2.58706 0.182477
\(202\) 9.78347 0.688362
\(203\) 23.1442 1.62440
\(204\) −0.401798 −0.0281315
\(205\) 0 0
\(206\) −51.1703 −3.56521
\(207\) 5.44568 0.378501
\(208\) −62.7740 −4.35259
\(209\) −0.395168 −0.0273343
\(210\) 0 0
\(211\) −0.758471 −0.0522153 −0.0261076 0.999659i \(-0.508311\pi\)
−0.0261076 + 0.999659i \(0.508311\pi\)
\(212\) −8.71990 −0.598885
\(213\) 1.69131 0.115886
\(214\) 17.5611 1.20045
\(215\) 0 0
\(216\) −10.0479 −0.683673
\(217\) 15.9529 1.08295
\(218\) −40.8688 −2.76799
\(219\) 2.62698 0.177515
\(220\) 0 0
\(221\) 1.99133 0.133951
\(222\) −1.17408 −0.0787991
\(223\) −0.994567 −0.0666011 −0.0333006 0.999445i \(-0.510602\pi\)
−0.0333006 + 0.999445i \(0.510602\pi\)
\(224\) −46.0830 −3.07905
\(225\) 0 0
\(226\) 0.489808 0.0325815
\(227\) −9.15012 −0.607315 −0.303657 0.952781i \(-0.598208\pi\)
−0.303657 + 0.952781i \(0.598208\pi\)
\(228\) 0.503714 0.0333593
\(229\) 24.8061 1.63924 0.819618 0.572910i \(-0.194186\pi\)
0.819618 + 0.572910i \(0.194186\pi\)
\(230\) 0 0
\(231\) 0.462117 0.0304051
\(232\) −68.1270 −4.47276
\(233\) 20.8307 1.36466 0.682332 0.731042i \(-0.260966\pi\)
0.682332 + 0.731042i \(0.260966\pi\)
\(234\) 40.3814 2.63982
\(235\) 0 0
\(236\) −25.9368 −1.68834
\(237\) 1.61126 0.104662
\(238\) 3.00414 0.194730
\(239\) −27.2186 −1.76062 −0.880311 0.474397i \(-0.842666\pi\)
−0.880311 + 0.474397i \(0.842666\pi\)
\(240\) 0 0
\(241\) 1.00000 0.0644157
\(242\) −27.6939 −1.78023
\(243\) 5.28614 0.339106
\(244\) 17.5437 1.12312
\(245\) 0 0
\(246\) −1.91839 −0.122312
\(247\) −2.49643 −0.158844
\(248\) −46.9589 −2.98189
\(249\) 0.0730748 0.00463093
\(250\) 0 0
\(251\) 17.6839 1.11620 0.558100 0.829774i \(-0.311531\pi\)
0.558100 + 0.829774i \(0.311531\pi\)
\(252\) 43.9057 2.76580
\(253\) 1.48436 0.0933211
\(254\) 40.5645 2.54524
\(255\) 0 0
\(256\) 8.53615 0.533509
\(257\) −24.6433 −1.53721 −0.768604 0.639725i \(-0.779048\pi\)
−0.768604 + 0.639725i \(0.779048\pi\)
\(258\) −4.94615 −0.307934
\(259\) 6.32663 0.393118
\(260\) 0 0
\(261\) 23.8412 1.47573
\(262\) 19.0028 1.17400
\(263\) −21.3217 −1.31475 −0.657376 0.753563i \(-0.728334\pi\)
−0.657376 + 0.753563i \(0.728334\pi\)
\(264\) −1.36029 −0.0837198
\(265\) 0 0
\(266\) −3.76614 −0.230917
\(267\) −0.446924 −0.0273513
\(268\) 66.9983 4.09257
\(269\) 21.8448 1.33190 0.665951 0.745996i \(-0.268026\pi\)
0.665951 + 0.745996i \(0.268026\pi\)
\(270\) 0 0
\(271\) 1.65986 0.100830 0.0504148 0.998728i \(-0.483946\pi\)
0.0504148 + 0.998728i \(0.483946\pi\)
\(272\) −4.81066 −0.291689
\(273\) 2.91937 0.176688
\(274\) −20.3485 −1.22930
\(275\) 0 0
\(276\) −1.89209 −0.113891
\(277\) 17.1120 1.02816 0.514080 0.857742i \(-0.328134\pi\)
0.514080 + 0.857742i \(0.328134\pi\)
\(278\) −56.8424 −3.40918
\(279\) 16.4333 0.983839
\(280\) 0 0
\(281\) 26.8613 1.60241 0.801205 0.598390i \(-0.204193\pi\)
0.801205 + 0.598390i \(0.204193\pi\)
\(282\) 5.85455 0.348633
\(283\) −4.41536 −0.262466 −0.131233 0.991352i \(-0.541894\pi\)
−0.131233 + 0.991352i \(0.541894\pi\)
\(284\) 43.8006 2.59909
\(285\) 0 0
\(286\) 11.0070 0.650859
\(287\) 10.3374 0.610196
\(288\) −47.4708 −2.79724
\(289\) −16.8474 −0.991023
\(290\) 0 0
\(291\) 1.45966 0.0855668
\(292\) 68.0321 3.98128
\(293\) 27.4208 1.60194 0.800971 0.598703i \(-0.204317\pi\)
0.800971 + 0.598703i \(0.204317\pi\)
\(294\) 0.671088 0.0391387
\(295\) 0 0
\(296\) −18.6230 −1.08244
\(297\) 0.958455 0.0556152
\(298\) −43.0614 −2.49448
\(299\) 9.37730 0.542303
\(300\) 0 0
\(301\) 26.6527 1.53624
\(302\) −28.2369 −1.62485
\(303\) 0.728596 0.0418567
\(304\) 6.03088 0.345895
\(305\) 0 0
\(306\) 3.09462 0.176907
\(307\) 22.4558 1.28162 0.640809 0.767700i \(-0.278599\pi\)
0.640809 + 0.767700i \(0.278599\pi\)
\(308\) 11.9677 0.681921
\(309\) −3.81076 −0.216787
\(310\) 0 0
\(311\) −17.0158 −0.964880 −0.482440 0.875929i \(-0.660249\pi\)
−0.482440 + 0.875929i \(0.660249\pi\)
\(312\) −8.59344 −0.486508
\(313\) −30.6076 −1.73004 −0.865022 0.501734i \(-0.832696\pi\)
−0.865022 + 0.501734i \(0.832696\pi\)
\(314\) 0.680689 0.0384135
\(315\) 0 0
\(316\) 41.7275 2.34735
\(317\) −13.1196 −0.736869 −0.368434 0.929654i \(-0.620106\pi\)
−0.368434 + 0.929654i \(0.620106\pi\)
\(318\) −0.901039 −0.0505277
\(319\) 6.49854 0.363848
\(320\) 0 0
\(321\) 1.30781 0.0729950
\(322\) 14.1467 0.788365
\(323\) −0.191313 −0.0106449
\(324\) 44.6131 2.47850
\(325\) 0 0
\(326\) 23.6251 1.30847
\(327\) −3.04359 −0.168311
\(328\) −30.4291 −1.68016
\(329\) −31.5477 −1.73928
\(330\) 0 0
\(331\) 20.2977 1.11566 0.557832 0.829954i \(-0.311633\pi\)
0.557832 + 0.829954i \(0.311633\pi\)
\(332\) 1.89245 0.103862
\(333\) 6.51716 0.357138
\(334\) −8.13942 −0.445369
\(335\) 0 0
\(336\) −7.05262 −0.384752
\(337\) −10.6212 −0.578575 −0.289287 0.957242i \(-0.593418\pi\)
−0.289287 + 0.957242i \(0.593418\pi\)
\(338\) 34.7473 1.89001
\(339\) 0.0364771 0.00198116
\(340\) 0 0
\(341\) 4.47934 0.242570
\(342\) −3.87956 −0.209783
\(343\) 16.4999 0.890913
\(344\) −78.4549 −4.23000
\(345\) 0 0
\(346\) 16.1246 0.866865
\(347\) 1.73240 0.0930001 0.0465001 0.998918i \(-0.485193\pi\)
0.0465001 + 0.998918i \(0.485193\pi\)
\(348\) −8.28358 −0.444047
\(349\) −31.0836 −1.66387 −0.831933 0.554876i \(-0.812766\pi\)
−0.831933 + 0.554876i \(0.812766\pi\)
\(350\) 0 0
\(351\) 6.05493 0.323188
\(352\) −12.9394 −0.689673
\(353\) 33.0003 1.75643 0.878214 0.478268i \(-0.158735\pi\)
0.878214 + 0.478268i \(0.158735\pi\)
\(354\) −2.68008 −0.142445
\(355\) 0 0
\(356\) −11.5742 −0.613432
\(357\) 0.223725 0.0118408
\(358\) 20.6701 1.09245
\(359\) 32.1190 1.69518 0.847589 0.530654i \(-0.178054\pi\)
0.847589 + 0.530654i \(0.178054\pi\)
\(360\) 0 0
\(361\) −18.7602 −0.987377
\(362\) −27.6015 −1.45070
\(363\) −2.06242 −0.108249
\(364\) 75.6044 3.96275
\(365\) 0 0
\(366\) 1.81281 0.0947572
\(367\) 1.93764 0.101144 0.0505719 0.998720i \(-0.483896\pi\)
0.0505719 + 0.998720i \(0.483896\pi\)
\(368\) −22.6537 −1.18091
\(369\) 10.6487 0.554349
\(370\) 0 0
\(371\) 4.85532 0.252076
\(372\) −5.70974 −0.296036
\(373\) −8.78738 −0.454993 −0.227497 0.973779i \(-0.573054\pi\)
−0.227497 + 0.973779i \(0.573054\pi\)
\(374\) 0.843519 0.0436173
\(375\) 0 0
\(376\) 92.8637 4.78908
\(377\) 41.0538 2.11438
\(378\) 9.13454 0.469830
\(379\) 15.6012 0.801378 0.400689 0.916214i \(-0.368771\pi\)
0.400689 + 0.916214i \(0.368771\pi\)
\(380\) 0 0
\(381\) 3.02093 0.154767
\(382\) −44.4924 −2.27643
\(383\) −3.43332 −0.175435 −0.0877173 0.996145i \(-0.527957\pi\)
−0.0877173 + 0.996145i \(0.527957\pi\)
\(384\) 3.35888 0.171407
\(385\) 0 0
\(386\) −71.1016 −3.61897
\(387\) 27.4554 1.39564
\(388\) 37.8015 1.91908
\(389\) −16.1302 −0.817836 −0.408918 0.912571i \(-0.634094\pi\)
−0.408918 + 0.912571i \(0.634094\pi\)
\(390\) 0 0
\(391\) 0.718626 0.0363425
\(392\) 10.6447 0.537637
\(393\) 1.41518 0.0713863
\(394\) −11.8514 −0.597067
\(395\) 0 0
\(396\) 12.3281 0.619510
\(397\) −4.27325 −0.214468 −0.107234 0.994234i \(-0.534199\pi\)
−0.107234 + 0.994234i \(0.534199\pi\)
\(398\) 9.22236 0.462275
\(399\) −0.280472 −0.0140412
\(400\) 0 0
\(401\) −0.0337541 −0.00168560 −0.000842800 1.00000i \(-0.500268\pi\)
−0.000842800 1.00000i \(0.500268\pi\)
\(402\) 6.92302 0.345289
\(403\) 28.2977 1.40961
\(404\) 18.8688 0.938758
\(405\) 0 0
\(406\) 61.9342 3.07374
\(407\) 1.77642 0.0880541
\(408\) −0.658555 −0.0326034
\(409\) 12.7748 0.631672 0.315836 0.948814i \(-0.397715\pi\)
0.315836 + 0.948814i \(0.397715\pi\)
\(410\) 0 0
\(411\) −1.51540 −0.0747491
\(412\) −98.6892 −4.86207
\(413\) 14.4419 0.710637
\(414\) 14.5727 0.716211
\(415\) 0 0
\(416\) −81.7433 −4.00780
\(417\) −4.23317 −0.207299
\(418\) −1.05748 −0.0517229
\(419\) −37.5266 −1.83329 −0.916646 0.399699i \(-0.869115\pi\)
−0.916646 + 0.399699i \(0.869115\pi\)
\(420\) 0 0
\(421\) −9.23835 −0.450250 −0.225125 0.974330i \(-0.572279\pi\)
−0.225125 + 0.974330i \(0.572279\pi\)
\(422\) −2.02968 −0.0988034
\(423\) −32.4978 −1.58010
\(424\) −14.2921 −0.694086
\(425\) 0 0
\(426\) 4.52597 0.219284
\(427\) −9.76849 −0.472730
\(428\) 33.8691 1.63712
\(429\) 0.819717 0.0395763
\(430\) 0 0
\(431\) −28.2694 −1.36169 −0.680845 0.732427i \(-0.738387\pi\)
−0.680845 + 0.732427i \(0.738387\pi\)
\(432\) −14.6275 −0.703767
\(433\) −2.19007 −0.105248 −0.0526239 0.998614i \(-0.516758\pi\)
−0.0526239 + 0.998614i \(0.516758\pi\)
\(434\) 42.6903 2.04920
\(435\) 0 0
\(436\) −78.8213 −3.77486
\(437\) −0.900904 −0.0430961
\(438\) 7.02984 0.335899
\(439\) 16.6956 0.796839 0.398419 0.917203i \(-0.369559\pi\)
0.398419 + 0.917203i \(0.369559\pi\)
\(440\) 0 0
\(441\) −3.72512 −0.177387
\(442\) 5.32884 0.253467
\(443\) −10.7664 −0.511529 −0.255764 0.966739i \(-0.582327\pi\)
−0.255764 + 0.966739i \(0.582327\pi\)
\(444\) −2.26438 −0.107463
\(445\) 0 0
\(446\) −2.66148 −0.126025
\(447\) −3.20688 −0.151680
\(448\) −52.5410 −2.48233
\(449\) −32.2748 −1.52314 −0.761571 0.648082i \(-0.775571\pi\)
−0.761571 + 0.648082i \(0.775571\pi\)
\(450\) 0 0
\(451\) 2.90259 0.136677
\(452\) 0.944664 0.0444333
\(453\) −2.10286 −0.0988011
\(454\) −24.4859 −1.14918
\(455\) 0 0
\(456\) 0.825597 0.0386621
\(457\) 19.5040 0.912358 0.456179 0.889888i \(-0.349218\pi\)
0.456179 + 0.889888i \(0.349218\pi\)
\(458\) 66.3817 3.10181
\(459\) 0.464017 0.0216585
\(460\) 0 0
\(461\) −7.59585 −0.353774 −0.176887 0.984231i \(-0.556603\pi\)
−0.176887 + 0.984231i \(0.556603\pi\)
\(462\) 1.23663 0.0575334
\(463\) 12.5155 0.581644 0.290822 0.956777i \(-0.406071\pi\)
0.290822 + 0.956777i \(0.406071\pi\)
\(464\) −99.1779 −4.60422
\(465\) 0 0
\(466\) 55.7433 2.58226
\(467\) 11.4282 0.528833 0.264416 0.964409i \(-0.414821\pi\)
0.264416 + 0.964409i \(0.414821\pi\)
\(468\) 77.8813 3.60006
\(469\) −37.3053 −1.72260
\(470\) 0 0
\(471\) 0.0506924 0.00233578
\(472\) −42.5110 −1.95673
\(473\) 7.48370 0.344101
\(474\) 4.31175 0.198045
\(475\) 0 0
\(476\) 5.79391 0.265564
\(477\) 5.00155 0.229005
\(478\) −72.8374 −3.33150
\(479\) 24.3966 1.11471 0.557354 0.830275i \(-0.311817\pi\)
0.557354 + 0.830275i \(0.311817\pi\)
\(480\) 0 0
\(481\) 11.2224 0.511696
\(482\) 2.67602 0.121889
\(483\) 1.05353 0.0479375
\(484\) −53.4116 −2.42780
\(485\) 0 0
\(486\) 14.1458 0.641667
\(487\) −32.5012 −1.47277 −0.736385 0.676563i \(-0.763469\pi\)
−0.736385 + 0.676563i \(0.763469\pi\)
\(488\) 28.7545 1.30165
\(489\) 1.75941 0.0795633
\(490\) 0 0
\(491\) 15.3890 0.694498 0.347249 0.937773i \(-0.387116\pi\)
0.347249 + 0.937773i \(0.387116\pi\)
\(492\) −3.69988 −0.166803
\(493\) 3.14614 0.141695
\(494\) −6.68049 −0.300569
\(495\) 0 0
\(496\) −68.3618 −3.06953
\(497\) −24.3886 −1.09398
\(498\) 0.195550 0.00876278
\(499\) −33.4862 −1.49905 −0.749525 0.661976i \(-0.769718\pi\)
−0.749525 + 0.661976i \(0.769718\pi\)
\(500\) 0 0
\(501\) −0.606160 −0.0270812
\(502\) 47.3225 2.11211
\(503\) −38.0060 −1.69460 −0.847302 0.531111i \(-0.821775\pi\)
−0.847302 + 0.531111i \(0.821775\pi\)
\(504\) 71.9624 3.20546
\(505\) 0 0
\(506\) 3.97219 0.176585
\(507\) 2.58771 0.114924
\(508\) 78.2344 3.47109
\(509\) 28.9990 1.28536 0.642679 0.766136i \(-0.277823\pi\)
0.642679 + 0.766136i \(0.277823\pi\)
\(510\) 0 0
\(511\) −37.8809 −1.67575
\(512\) −10.8657 −0.480202
\(513\) −0.581715 −0.0256833
\(514\) −65.9460 −2.90875
\(515\) 0 0
\(516\) −9.53935 −0.419946
\(517\) −8.85814 −0.389581
\(518\) 16.9302 0.743870
\(519\) 1.20083 0.0527108
\(520\) 0 0
\(521\) −8.52198 −0.373355 −0.186677 0.982421i \(-0.559772\pi\)
−0.186677 + 0.982421i \(0.559772\pi\)
\(522\) 63.7995 2.79243
\(523\) −6.18981 −0.270662 −0.135331 0.990800i \(-0.543210\pi\)
−0.135331 + 0.990800i \(0.543210\pi\)
\(524\) 36.6496 1.60104
\(525\) 0 0
\(526\) −57.0573 −2.48782
\(527\) 2.16859 0.0944651
\(528\) −1.98027 −0.0861804
\(529\) −19.6159 −0.852867
\(530\) 0 0
\(531\) 14.8768 0.645598
\(532\) −7.26353 −0.314914
\(533\) 18.3367 0.794253
\(534\) −1.19598 −0.0517550
\(535\) 0 0
\(536\) 109.812 4.74314
\(537\) 1.53935 0.0664277
\(538\) 58.4572 2.52027
\(539\) −1.01538 −0.0437355
\(540\) 0 0
\(541\) 23.0092 0.989244 0.494622 0.869108i \(-0.335306\pi\)
0.494622 + 0.869108i \(0.335306\pi\)
\(542\) 4.44183 0.190793
\(543\) −2.05554 −0.0882117
\(544\) −6.26437 −0.268583
\(545\) 0 0
\(546\) 7.81229 0.334335
\(547\) −34.2241 −1.46332 −0.731658 0.681672i \(-0.761253\pi\)
−0.731658 + 0.681672i \(0.761253\pi\)
\(548\) −39.2450 −1.67646
\(549\) −10.0627 −0.429465
\(550\) 0 0
\(551\) −3.94416 −0.168027
\(552\) −3.10118 −0.131995
\(553\) −23.2342 −0.988020
\(554\) 45.7920 1.94552
\(555\) 0 0
\(556\) −109.629 −4.64929
\(557\) 8.34480 0.353580 0.176790 0.984249i \(-0.443429\pi\)
0.176790 + 0.984249i \(0.443429\pi\)
\(558\) 43.9760 1.86165
\(559\) 47.2774 1.99962
\(560\) 0 0
\(561\) 0.0628187 0.00265221
\(562\) 71.8813 3.03213
\(563\) 21.1210 0.890146 0.445073 0.895494i \(-0.353178\pi\)
0.445073 + 0.895494i \(0.353178\pi\)
\(564\) 11.2913 0.475451
\(565\) 0 0
\(566\) −11.8156 −0.496647
\(567\) −24.8410 −1.04322
\(568\) 71.7901 3.01225
\(569\) 38.2880 1.60512 0.802559 0.596573i \(-0.203471\pi\)
0.802559 + 0.596573i \(0.203471\pi\)
\(570\) 0 0
\(571\) 4.36826 0.182806 0.0914031 0.995814i \(-0.470865\pi\)
0.0914031 + 0.995814i \(0.470865\pi\)
\(572\) 21.2286 0.887612
\(573\) −3.31344 −0.138421
\(574\) 27.6630 1.15463
\(575\) 0 0
\(576\) −54.1233 −2.25514
\(577\) −9.27981 −0.386324 −0.193162 0.981167i \(-0.561874\pi\)
−0.193162 + 0.981167i \(0.561874\pi\)
\(578\) −45.0840 −1.87525
\(579\) −5.29508 −0.220056
\(580\) 0 0
\(581\) −1.05373 −0.0437163
\(582\) 3.90608 0.161912
\(583\) 1.36330 0.0564623
\(584\) 111.506 4.61415
\(585\) 0 0
\(586\) 73.3787 3.03125
\(587\) 12.4373 0.513342 0.256671 0.966499i \(-0.417374\pi\)
0.256671 + 0.966499i \(0.417374\pi\)
\(588\) 1.29429 0.0533755
\(589\) −2.71865 −0.112020
\(590\) 0 0
\(591\) −0.882602 −0.0363054
\(592\) −27.1110 −1.11426
\(593\) 37.5611 1.54245 0.771225 0.636563i \(-0.219644\pi\)
0.771225 + 0.636563i \(0.219644\pi\)
\(594\) 2.56484 0.105237
\(595\) 0 0
\(596\) −83.0500 −3.40186
\(597\) 0.686809 0.0281092
\(598\) 25.0938 1.02616
\(599\) −22.2278 −0.908204 −0.454102 0.890950i \(-0.650040\pi\)
−0.454102 + 0.890950i \(0.650040\pi\)
\(600\) 0 0
\(601\) −46.9863 −1.91661 −0.958305 0.285747i \(-0.907758\pi\)
−0.958305 + 0.285747i \(0.907758\pi\)
\(602\) 71.3233 2.90692
\(603\) −38.4288 −1.56494
\(604\) −54.4588 −2.21590
\(605\) 0 0
\(606\) 1.94974 0.0792026
\(607\) −0.527341 −0.0214041 −0.0107021 0.999943i \(-0.503407\pi\)
−0.0107021 + 0.999943i \(0.503407\pi\)
\(608\) 7.85332 0.318494
\(609\) 4.61237 0.186903
\(610\) 0 0
\(611\) −55.9603 −2.26391
\(612\) 5.96840 0.241258
\(613\) −9.71818 −0.392514 −0.196257 0.980553i \(-0.562879\pi\)
−0.196257 + 0.980553i \(0.562879\pi\)
\(614\) 60.0921 2.42512
\(615\) 0 0
\(616\) 19.6153 0.790321
\(617\) 2.81867 0.113476 0.0567378 0.998389i \(-0.481930\pi\)
0.0567378 + 0.998389i \(0.481930\pi\)
\(618\) −10.1977 −0.410211
\(619\) −2.75560 −0.110757 −0.0553785 0.998465i \(-0.517637\pi\)
−0.0553785 + 0.998465i \(0.517637\pi\)
\(620\) 0 0
\(621\) 2.18509 0.0876845
\(622\) −45.5347 −1.82578
\(623\) 6.44463 0.258199
\(624\) −12.5102 −0.500807
\(625\) 0 0
\(626\) −81.9065 −3.27364
\(627\) −0.0787526 −0.00314507
\(628\) 1.31281 0.0523866
\(629\) 0.860022 0.0342913
\(630\) 0 0
\(631\) −21.5819 −0.859161 −0.429580 0.903029i \(-0.641338\pi\)
−0.429580 + 0.903029i \(0.641338\pi\)
\(632\) 68.3922 2.72050
\(633\) −0.151155 −0.00600787
\(634\) −35.1083 −1.39433
\(635\) 0 0
\(636\) −1.73778 −0.0689075
\(637\) −6.41455 −0.254154
\(638\) 17.3902 0.688486
\(639\) −25.1231 −0.993853
\(640\) 0 0
\(641\) −21.4224 −0.846135 −0.423068 0.906098i \(-0.639047\pi\)
−0.423068 + 0.906098i \(0.639047\pi\)
\(642\) 3.49973 0.138123
\(643\) 29.1001 1.14760 0.573798 0.818997i \(-0.305469\pi\)
0.573798 + 0.818997i \(0.305469\pi\)
\(644\) 27.2839 1.07514
\(645\) 0 0
\(646\) −0.511957 −0.0201427
\(647\) −8.60753 −0.338397 −0.169198 0.985582i \(-0.554118\pi\)
−0.169198 + 0.985582i \(0.554118\pi\)
\(648\) 73.1218 2.87249
\(649\) 4.05506 0.159175
\(650\) 0 0
\(651\) 3.17924 0.124604
\(652\) 45.5643 1.78444
\(653\) −10.3765 −0.406062 −0.203031 0.979172i \(-0.565079\pi\)
−0.203031 + 0.979172i \(0.565079\pi\)
\(654\) −8.14470 −0.318483
\(655\) 0 0
\(656\) −44.2980 −1.72955
\(657\) −39.0217 −1.52238
\(658\) −84.4223 −3.29113
\(659\) −39.6868 −1.54598 −0.772990 0.634418i \(-0.781240\pi\)
−0.772990 + 0.634418i \(0.781240\pi\)
\(660\) 0 0
\(661\) −37.6874 −1.46587 −0.732934 0.680300i \(-0.761850\pi\)
−0.732934 + 0.680300i \(0.761850\pi\)
\(662\) 54.3171 2.11109
\(663\) 0.396850 0.0154124
\(664\) 3.10177 0.120372
\(665\) 0 0
\(666\) 17.4401 0.675789
\(667\) 14.8154 0.573654
\(668\) −15.6980 −0.607375
\(669\) −0.198206 −0.00766309
\(670\) 0 0
\(671\) −2.74285 −0.105887
\(672\) −9.18382 −0.354274
\(673\) 31.7217 1.22278 0.611390 0.791329i \(-0.290610\pi\)
0.611390 + 0.791329i \(0.290610\pi\)
\(674\) −28.4226 −1.09480
\(675\) 0 0
\(676\) 67.0152 2.57751
\(677\) 45.3409 1.74259 0.871297 0.490757i \(-0.163280\pi\)
0.871297 + 0.490757i \(0.163280\pi\)
\(678\) 0.0976133 0.00374882
\(679\) −21.0482 −0.807757
\(680\) 0 0
\(681\) −1.82352 −0.0698773
\(682\) 11.9868 0.458999
\(683\) 7.82593 0.299451 0.149726 0.988728i \(-0.452161\pi\)
0.149726 + 0.988728i \(0.452161\pi\)
\(684\) −7.48228 −0.286092
\(685\) 0 0
\(686\) 44.1542 1.68581
\(687\) 4.94359 0.188610
\(688\) −114.213 −4.35433
\(689\) 8.61251 0.328111
\(690\) 0 0
\(691\) −35.0023 −1.33155 −0.665775 0.746152i \(-0.731899\pi\)
−0.665775 + 0.746152i \(0.731899\pi\)
\(692\) 31.0986 1.18219
\(693\) −6.86439 −0.260757
\(694\) 4.63594 0.175978
\(695\) 0 0
\(696\) −13.5770 −0.514633
\(697\) 1.40523 0.0532269
\(698\) −83.1803 −3.14842
\(699\) 4.15133 0.157018
\(700\) 0 0
\(701\) −8.28122 −0.312778 −0.156389 0.987696i \(-0.549985\pi\)
−0.156389 + 0.987696i \(0.549985\pi\)
\(702\) 16.2031 0.611547
\(703\) −1.07816 −0.0406638
\(704\) −14.7527 −0.556015
\(705\) 0 0
\(706\) 88.3094 3.32357
\(707\) −10.5063 −0.395131
\(708\) −5.16892 −0.194260
\(709\) −23.7901 −0.893458 −0.446729 0.894669i \(-0.647411\pi\)
−0.446729 + 0.894669i \(0.647411\pi\)
\(710\) 0 0
\(711\) −23.9340 −0.897594
\(712\) −18.9704 −0.710945
\(713\) 10.2120 0.382443
\(714\) 0.598692 0.0224055
\(715\) 0 0
\(716\) 39.8652 1.48983
\(717\) −5.42436 −0.202576
\(718\) 85.9512 3.20767
\(719\) 33.8950 1.26407 0.632035 0.774940i \(-0.282220\pi\)
0.632035 + 0.774940i \(0.282220\pi\)
\(720\) 0 0
\(721\) 54.9510 2.04648
\(722\) −50.2026 −1.86835
\(723\) 0.199289 0.00741163
\(724\) −53.2334 −1.97840
\(725\) 0 0
\(726\) −5.51908 −0.204832
\(727\) 26.5707 0.985451 0.492725 0.870185i \(-0.336001\pi\)
0.492725 + 0.870185i \(0.336001\pi\)
\(728\) 123.917 4.59267
\(729\) −24.8789 −0.921442
\(730\) 0 0
\(731\) 3.62309 0.134005
\(732\) 3.49627 0.129226
\(733\) 50.9266 1.88102 0.940509 0.339768i \(-0.110349\pi\)
0.940509 + 0.339768i \(0.110349\pi\)
\(734\) 5.18516 0.191388
\(735\) 0 0
\(736\) −29.4993 −1.08736
\(737\) −10.4748 −0.385843
\(738\) 28.4961 1.04896
\(739\) 37.8448 1.39214 0.696071 0.717973i \(-0.254930\pi\)
0.696071 + 0.717973i \(0.254930\pi\)
\(740\) 0 0
\(741\) −0.497510 −0.0182765
\(742\) 12.9929 0.476986
\(743\) 18.8351 0.690992 0.345496 0.938420i \(-0.387711\pi\)
0.345496 + 0.938420i \(0.387711\pi\)
\(744\) −9.35839 −0.343095
\(745\) 0 0
\(746\) −23.5152 −0.860953
\(747\) −1.08547 −0.0397153
\(748\) 1.62685 0.0594834
\(749\) −18.8586 −0.689079
\(750\) 0 0
\(751\) 40.1498 1.46509 0.732544 0.680720i \(-0.238333\pi\)
0.732544 + 0.680720i \(0.238333\pi\)
\(752\) 135.189 4.92984
\(753\) 3.52421 0.128429
\(754\) 109.861 4.00089
\(755\) 0 0
\(756\) 17.6172 0.640733
\(757\) 11.3231 0.411546 0.205773 0.978600i \(-0.434029\pi\)
0.205773 + 0.978600i \(0.434029\pi\)
\(758\) 41.7490 1.51639
\(759\) 0.295817 0.0107375
\(760\) 0 0
\(761\) 27.9931 1.01475 0.507374 0.861726i \(-0.330616\pi\)
0.507374 + 0.861726i \(0.330616\pi\)
\(762\) 8.08406 0.292855
\(763\) 43.8884 1.58887
\(764\) −85.8098 −3.10449
\(765\) 0 0
\(766\) −9.18764 −0.331963
\(767\) 25.6174 0.924990
\(768\) 1.70116 0.0613853
\(769\) −8.32041 −0.300042 −0.150021 0.988683i \(-0.547934\pi\)
−0.150021 + 0.988683i \(0.547934\pi\)
\(770\) 0 0
\(771\) −4.91114 −0.176870
\(772\) −137.129 −4.93539
\(773\) −11.4321 −0.411183 −0.205591 0.978638i \(-0.565912\pi\)
−0.205591 + 0.978638i \(0.565912\pi\)
\(774\) 73.4713 2.64087
\(775\) 0 0
\(776\) 61.9575 2.22414
\(777\) 1.26083 0.0452319
\(778\) −43.1649 −1.54754
\(779\) −1.76167 −0.0631182
\(780\) 0 0
\(781\) −6.84796 −0.245039
\(782\) 1.92306 0.0687684
\(783\) 9.56631 0.341872
\(784\) 15.4963 0.553439
\(785\) 0 0
\(786\) 3.78705 0.135079
\(787\) 11.5127 0.410384 0.205192 0.978722i \(-0.434218\pi\)
0.205192 + 0.978722i \(0.434218\pi\)
\(788\) −22.8572 −0.814253
\(789\) −4.24918 −0.151275
\(790\) 0 0
\(791\) −0.525997 −0.0187023
\(792\) 20.2060 0.717989
\(793\) −17.3276 −0.615323
\(794\) −11.4353 −0.405824
\(795\) 0 0
\(796\) 17.7866 0.630430
\(797\) 8.19431 0.290257 0.145129 0.989413i \(-0.453640\pi\)
0.145129 + 0.989413i \(0.453640\pi\)
\(798\) −0.750550 −0.0265692
\(799\) −4.28850 −0.151716
\(800\) 0 0
\(801\) 6.63872 0.234568
\(802\) −0.0903266 −0.00318954
\(803\) −10.6364 −0.375351
\(804\) 13.3520 0.470889
\(805\) 0 0
\(806\) 75.7253 2.66731
\(807\) 4.35343 0.153248
\(808\) 30.9263 1.08799
\(809\) 9.19094 0.323136 0.161568 0.986862i \(-0.448345\pi\)
0.161568 + 0.986862i \(0.448345\pi\)
\(810\) 0 0
\(811\) −23.9711 −0.841740 −0.420870 0.907121i \(-0.638275\pi\)
−0.420870 + 0.907121i \(0.638275\pi\)
\(812\) 119.449 4.19183
\(813\) 0.330793 0.0116014
\(814\) 4.75375 0.166619
\(815\) 0 0
\(816\) −0.958711 −0.0335616
\(817\) −4.54208 −0.158907
\(818\) 34.1856 1.19527
\(819\) −43.3650 −1.51530
\(820\) 0 0
\(821\) −5.58377 −0.194875 −0.0974375 0.995242i \(-0.531065\pi\)
−0.0974375 + 0.995242i \(0.531065\pi\)
\(822\) −4.05524 −0.141443
\(823\) 2.02001 0.0704131 0.0352066 0.999380i \(-0.488791\pi\)
0.0352066 + 0.999380i \(0.488791\pi\)
\(824\) −161.754 −5.63495
\(825\) 0 0
\(826\) 38.6467 1.34469
\(827\) 24.2638 0.843735 0.421867 0.906658i \(-0.361375\pi\)
0.421867 + 0.906658i \(0.361375\pi\)
\(828\) 28.1056 0.976737
\(829\) 0.464596 0.0161361 0.00806805 0.999967i \(-0.497432\pi\)
0.00806805 + 0.999967i \(0.497432\pi\)
\(830\) 0 0
\(831\) 3.41023 0.118299
\(832\) −93.1988 −3.23109
\(833\) −0.491577 −0.0170321
\(834\) −11.3281 −0.392258
\(835\) 0 0
\(836\) −2.03949 −0.0705374
\(837\) 6.59391 0.227919
\(838\) −100.422 −3.46901
\(839\) 11.0915 0.382921 0.191461 0.981500i \(-0.438678\pi\)
0.191461 + 0.981500i \(0.438678\pi\)
\(840\) 0 0
\(841\) 35.8617 1.23661
\(842\) −24.7220 −0.851977
\(843\) 5.35316 0.184372
\(844\) −3.91453 −0.134744
\(845\) 0 0
\(846\) −86.9648 −2.98991
\(847\) 29.7400 1.02188
\(848\) −20.8061 −0.714486
\(849\) −0.879933 −0.0301992
\(850\) 0 0
\(851\) 4.04990 0.138829
\(852\) 8.72897 0.299050
\(853\) −38.1172 −1.30511 −0.652553 0.757743i \(-0.726302\pi\)
−0.652553 + 0.757743i \(0.726302\pi\)
\(854\) −26.1407 −0.894516
\(855\) 0 0
\(856\) 55.5121 1.89736
\(857\) −17.6418 −0.602634 −0.301317 0.953524i \(-0.597426\pi\)
−0.301317 + 0.953524i \(0.597426\pi\)
\(858\) 2.19358 0.0748875
\(859\) −27.4875 −0.937862 −0.468931 0.883235i \(-0.655361\pi\)
−0.468931 + 0.883235i \(0.655361\pi\)
\(860\) 0 0
\(861\) 2.06013 0.0702089
\(862\) −75.6495 −2.57663
\(863\) −19.2496 −0.655263 −0.327632 0.944806i \(-0.606250\pi\)
−0.327632 + 0.944806i \(0.606250\pi\)
\(864\) −19.0477 −0.648017
\(865\) 0 0
\(866\) −5.86066 −0.199153
\(867\) −3.35750 −0.114027
\(868\) 82.3342 2.79461
\(869\) −6.52383 −0.221306
\(870\) 0 0
\(871\) −66.1732 −2.24219
\(872\) −129.190 −4.37492
\(873\) −21.6821 −0.733829
\(874\) −2.41084 −0.0815478
\(875\) 0 0
\(876\) 13.5580 0.458084
\(877\) −41.2611 −1.39329 −0.696644 0.717417i \(-0.745324\pi\)
−0.696644 + 0.717417i \(0.745324\pi\)
\(878\) 44.6778 1.50780
\(879\) 5.46467 0.184319
\(880\) 0 0
\(881\) 32.1377 1.08275 0.541373 0.840783i \(-0.317905\pi\)
0.541373 + 0.840783i \(0.317905\pi\)
\(882\) −9.96850 −0.335657
\(883\) 9.13498 0.307416 0.153708 0.988116i \(-0.450878\pi\)
0.153708 + 0.988116i \(0.450878\pi\)
\(884\) 10.2774 0.345667
\(885\) 0 0
\(886\) −28.8112 −0.967931
\(887\) 13.8765 0.465928 0.232964 0.972485i \(-0.425158\pi\)
0.232964 + 0.972485i \(0.425158\pi\)
\(888\) −3.71136 −0.124545
\(889\) −43.5616 −1.46101
\(890\) 0 0
\(891\) −6.97498 −0.233671
\(892\) −5.13304 −0.171867
\(893\) 5.37627 0.179910
\(894\) −8.58167 −0.287014
\(895\) 0 0
\(896\) −48.4349 −1.61809
\(897\) 1.86879 0.0623971
\(898\) −86.3680 −2.88214
\(899\) 44.7082 1.49110
\(900\) 0 0
\(901\) 0.660017 0.0219883
\(902\) 7.76738 0.258625
\(903\) 5.31160 0.176759
\(904\) 1.54832 0.0514965
\(905\) 0 0
\(906\) −5.62730 −0.186954
\(907\) −20.5930 −0.683778 −0.341889 0.939740i \(-0.611067\pi\)
−0.341889 + 0.939740i \(0.611067\pi\)
\(908\) −47.2245 −1.56720
\(909\) −10.8227 −0.358967
\(910\) 0 0
\(911\) −29.8513 −0.989018 −0.494509 0.869173i \(-0.664652\pi\)
−0.494509 + 0.869173i \(0.664652\pi\)
\(912\) 1.20189 0.0397985
\(913\) −0.295873 −0.00979198
\(914\) 52.1931 1.72639
\(915\) 0 0
\(916\) 128.027 4.23012
\(917\) −20.4068 −0.673892
\(918\) 1.24172 0.0409828
\(919\) −44.8288 −1.47877 −0.739383 0.673285i \(-0.764883\pi\)
−0.739383 + 0.673285i \(0.764883\pi\)
\(920\) 0 0
\(921\) 4.47519 0.147462
\(922\) −20.3266 −0.669422
\(923\) −43.2612 −1.42396
\(924\) 2.38502 0.0784615
\(925\) 0 0
\(926\) 33.4917 1.10061
\(927\) 56.6060 1.85918
\(928\) −129.148 −4.23949
\(929\) −53.9902 −1.77136 −0.885681 0.464294i \(-0.846308\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(930\) 0 0
\(931\) 0.616264 0.0201972
\(932\) 107.509 3.52157
\(933\) −3.39107 −0.111019
\(934\) 30.5820 1.00067
\(935\) 0 0
\(936\) 127.649 4.17234
\(937\) 41.8090 1.36584 0.682920 0.730493i \(-0.260710\pi\)
0.682920 + 0.730493i \(0.260710\pi\)
\(938\) −99.8296 −3.25955
\(939\) −6.09975 −0.199058
\(940\) 0 0
\(941\) 17.5326 0.571548 0.285774 0.958297i \(-0.407749\pi\)
0.285774 + 0.958297i \(0.407749\pi\)
\(942\) 0.135654 0.00441984
\(943\) 6.61732 0.215490
\(944\) −61.8866 −2.01424
\(945\) 0 0
\(946\) 20.0265 0.651119
\(947\) 60.8556 1.97754 0.988770 0.149444i \(-0.0477483\pi\)
0.988770 + 0.149444i \(0.0477483\pi\)
\(948\) 8.31582 0.270085
\(949\) −67.1943 −2.18122
\(950\) 0 0
\(951\) −2.61459 −0.0847838
\(952\) 9.49634 0.307778
\(953\) 47.7538 1.54690 0.773449 0.633859i \(-0.218530\pi\)
0.773449 + 0.633859i \(0.218530\pi\)
\(954\) 13.3842 0.433331
\(955\) 0 0
\(956\) −140.477 −4.54336
\(957\) 1.29509 0.0418642
\(958\) 65.2857 2.10928
\(959\) 21.8520 0.705637
\(960\) 0 0
\(961\) −0.183358 −0.00591476
\(962\) 30.0313 0.968247
\(963\) −19.4266 −0.626012
\(964\) 5.16108 0.166227
\(965\) 0 0
\(966\) 2.81928 0.0907088
\(967\) 10.5625 0.339666 0.169833 0.985473i \(-0.445677\pi\)
0.169833 + 0.985473i \(0.445677\pi\)
\(968\) −87.5426 −2.81373
\(969\) −0.0381265 −0.00122480
\(970\) 0 0
\(971\) −42.2601 −1.35619 −0.678096 0.734973i \(-0.737195\pi\)
−0.678096 + 0.734973i \(0.737195\pi\)
\(972\) 27.2822 0.875076
\(973\) 61.0422 1.95692
\(974\) −86.9739 −2.78682
\(975\) 0 0
\(976\) 41.8602 1.33991
\(977\) −0.878630 −0.0281099 −0.0140549 0.999901i \(-0.504474\pi\)
−0.0140549 + 0.999901i \(0.504474\pi\)
\(978\) 4.70822 0.150552
\(979\) 1.80956 0.0578337
\(980\) 0 0
\(981\) 45.2102 1.44345
\(982\) 41.1814 1.31415
\(983\) −20.9666 −0.668731 −0.334365 0.942444i \(-0.608522\pi\)
−0.334365 + 0.942444i \(0.608522\pi\)
\(984\) −6.06417 −0.193319
\(985\) 0 0
\(986\) 8.41914 0.268120
\(987\) −6.28711 −0.200121
\(988\) −12.8843 −0.409903
\(989\) 17.0614 0.542519
\(990\) 0 0
\(991\) 3.56254 0.113168 0.0565840 0.998398i \(-0.481979\pi\)
0.0565840 + 0.998398i \(0.481979\pi\)
\(992\) −89.0196 −2.82638
\(993\) 4.04511 0.128368
\(994\) −65.2643 −2.07006
\(995\) 0 0
\(996\) 0.377145 0.0119503
\(997\) −5.26746 −0.166822 −0.0834111 0.996515i \(-0.526581\pi\)
−0.0834111 + 0.996515i \(0.526581\pi\)
\(998\) −89.6098 −2.83655
\(999\) 2.61502 0.0827356
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 6025.2.a.p.1.45 46
5.2 odd 4 1205.2.b.c.724.45 yes 46
5.3 odd 4 1205.2.b.c.724.2 46
5.4 even 2 inner 6025.2.a.p.1.2 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1205.2.b.c.724.2 46 5.3 odd 4
1205.2.b.c.724.45 yes 46 5.2 odd 4
6025.2.a.p.1.2 46 5.4 even 2 inner
6025.2.a.p.1.45 46 1.1 even 1 trivial