Properties

Label 5225.2.a.m.1.1
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
Analytic rank $0$
Dimension $7$
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] = [5225,2,Mod(1,5225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5225, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("5225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.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: \(41.7218350561\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - x^{6} - 10x^{5} + 8x^{4} + 27x^{3} - 16x^{2} - 18x + 11 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1045)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.58611\) of defining polynomial
Character \(\chi\) \(=\) 5225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.58611 q^{2} -1.69436 q^{3} +4.68797 q^{4} +4.38180 q^{6} -2.28823 q^{7} -6.95140 q^{8} -0.129144 q^{9} +O(q^{10})\) \(q-2.58611 q^{2} -1.69436 q^{3} +4.68797 q^{4} +4.38180 q^{6} -2.28823 q^{7} -6.95140 q^{8} -0.129144 q^{9} +1.00000 q^{11} -7.94312 q^{12} +1.76398 q^{13} +5.91761 q^{14} +8.60115 q^{16} +7.54854 q^{17} +0.333980 q^{18} -1.00000 q^{19} +3.87708 q^{21} -2.58611 q^{22} +6.89418 q^{23} +11.7782 q^{24} -4.56184 q^{26} +5.30190 q^{27} -10.7271 q^{28} +6.12329 q^{29} +8.39796 q^{31} -8.34073 q^{32} -1.69436 q^{33} -19.5214 q^{34} -0.605423 q^{36} +10.1774 q^{37} +2.58611 q^{38} -2.98881 q^{39} +4.07706 q^{41} -10.0266 q^{42} +5.51693 q^{43} +4.68797 q^{44} -17.8291 q^{46} -11.6612 q^{47} -14.5734 q^{48} -1.76402 q^{49} -12.7899 q^{51} +8.26948 q^{52} -12.7919 q^{53} -13.7113 q^{54} +15.9064 q^{56} +1.69436 q^{57} -15.8355 q^{58} +13.5651 q^{59} +5.89246 q^{61} -21.7180 q^{62} +0.295510 q^{63} +4.36777 q^{64} +4.38180 q^{66} +8.79079 q^{67} +35.3873 q^{68} -11.6812 q^{69} -9.61429 q^{71} +0.897730 q^{72} -8.70551 q^{73} -26.3199 q^{74} -4.68797 q^{76} -2.28823 q^{77} +7.72940 q^{78} +4.40940 q^{79} -8.59589 q^{81} -10.5437 q^{82} -0.146311 q^{83} +18.1757 q^{84} -14.2674 q^{86} -10.3751 q^{87} -6.95140 q^{88} -1.54279 q^{89} -4.03638 q^{91} +32.3197 q^{92} -14.2292 q^{93} +30.1572 q^{94} +14.1322 q^{96} +7.32786 q^{97} +4.56195 q^{98} -0.129144 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + q^{7} - 3 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - q^{2} - 3 q^{3} + 7 q^{4} + 8 q^{6} + q^{7} - 3 q^{8} + 2 q^{9} + 7 q^{11} - 13 q^{12} - q^{13} + 12 q^{14} + 3 q^{16} - q^{17} - 7 q^{18} - 7 q^{19} + 5 q^{21} - q^{22} + 8 q^{23} + 25 q^{24} - 12 q^{27} - 4 q^{28} + 11 q^{29} + 7 q^{31} - 12 q^{32} - 3 q^{33} - 14 q^{34} + 7 q^{36} + 17 q^{37} + q^{38} + 30 q^{39} + 17 q^{41} - 33 q^{42} + 3 q^{43} + 7 q^{44} + 18 q^{46} - 14 q^{47} + 12 q^{48} + 6 q^{49} + 8 q^{51} + 17 q^{52} - 7 q^{53} - 27 q^{54} + 36 q^{56} + 3 q^{57} + 15 q^{58} + 35 q^{59} + 17 q^{61} - 46 q^{62} + 22 q^{63} + 5 q^{64} + 8 q^{66} - 4 q^{67} + 35 q^{68} - 4 q^{69} + 10 q^{71} - 12 q^{72} - 22 q^{73} - 11 q^{74} - 7 q^{76} + q^{77} + 41 q^{78} + 11 q^{79} - 21 q^{81} + 14 q^{82} - 39 q^{83} + 21 q^{84} - 24 q^{86} + 2 q^{87} - 3 q^{88} + 18 q^{89} - 22 q^{91} + 51 q^{92} - 10 q^{93} + 14 q^{94} - 11 q^{96} + 4 q^{97} + 26 q^{98} + 2 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.58611 −1.82866 −0.914329 0.404973i \(-0.867281\pi\)
−0.914329 + 0.404973i \(0.867281\pi\)
\(3\) −1.69436 −0.978239 −0.489120 0.872217i \(-0.662682\pi\)
−0.489120 + 0.872217i \(0.662682\pi\)
\(4\) 4.68797 2.34399
\(5\) 0 0
\(6\) 4.38180 1.78886
\(7\) −2.28823 −0.864869 −0.432434 0.901665i \(-0.642345\pi\)
−0.432434 + 0.901665i \(0.642345\pi\)
\(8\) −6.95140 −2.45769
\(9\) −0.129144 −0.0430479
\(10\) 0 0
\(11\) 1.00000 0.301511
\(12\) −7.94312 −2.29298
\(13\) 1.76398 0.489239 0.244620 0.969619i \(-0.421337\pi\)
0.244620 + 0.969619i \(0.421337\pi\)
\(14\) 5.91761 1.58155
\(15\) 0 0
\(16\) 8.60115 2.15029
\(17\) 7.54854 1.83079 0.915395 0.402557i \(-0.131879\pi\)
0.915395 + 0.402557i \(0.131879\pi\)
\(18\) 0.333980 0.0787199
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 3.87708 0.846048
\(22\) −2.58611 −0.551361
\(23\) 6.89418 1.43754 0.718768 0.695250i \(-0.244706\pi\)
0.718768 + 0.695250i \(0.244706\pi\)
\(24\) 11.7782 2.40421
\(25\) 0 0
\(26\) −4.56184 −0.894651
\(27\) 5.30190 1.02035
\(28\) −10.7271 −2.02724
\(29\) 6.12329 1.13707 0.568533 0.822661i \(-0.307511\pi\)
0.568533 + 0.822661i \(0.307511\pi\)
\(30\) 0 0
\(31\) 8.39796 1.50832 0.754159 0.656692i \(-0.228045\pi\)
0.754159 + 0.656692i \(0.228045\pi\)
\(32\) −8.34073 −1.47445
\(33\) −1.69436 −0.294950
\(34\) −19.5214 −3.34789
\(35\) 0 0
\(36\) −0.605423 −0.100904
\(37\) 10.1774 1.67315 0.836577 0.547850i \(-0.184554\pi\)
0.836577 + 0.547850i \(0.184554\pi\)
\(38\) 2.58611 0.419523
\(39\) −2.98881 −0.478593
\(40\) 0 0
\(41\) 4.07706 0.636730 0.318365 0.947968i \(-0.396866\pi\)
0.318365 + 0.947968i \(0.396866\pi\)
\(42\) −10.0266 −1.54713
\(43\) 5.51693 0.841323 0.420662 0.907218i \(-0.361798\pi\)
0.420662 + 0.907218i \(0.361798\pi\)
\(44\) 4.68797 0.706739
\(45\) 0 0
\(46\) −17.8291 −2.62876
\(47\) −11.6612 −1.70096 −0.850481 0.526006i \(-0.823689\pi\)
−0.850481 + 0.526006i \(0.823689\pi\)
\(48\) −14.5734 −2.10350
\(49\) −1.76402 −0.252002
\(50\) 0 0
\(51\) −12.7899 −1.79095
\(52\) 8.26948 1.14677
\(53\) −12.7919 −1.75710 −0.878551 0.477649i \(-0.841489\pi\)
−0.878551 + 0.477649i \(0.841489\pi\)
\(54\) −13.7113 −1.86587
\(55\) 0 0
\(56\) 15.9064 2.12558
\(57\) 1.69436 0.224423
\(58\) −15.8355 −2.07930
\(59\) 13.5651 1.76603 0.883013 0.469348i \(-0.155511\pi\)
0.883013 + 0.469348i \(0.155511\pi\)
\(60\) 0 0
\(61\) 5.89246 0.754452 0.377226 0.926121i \(-0.376878\pi\)
0.377226 + 0.926121i \(0.376878\pi\)
\(62\) −21.7180 −2.75820
\(63\) 0.295510 0.0372308
\(64\) 4.36777 0.545971
\(65\) 0 0
\(66\) 4.38180 0.539363
\(67\) 8.79079 1.07397 0.536983 0.843593i \(-0.319564\pi\)
0.536983 + 0.843593i \(0.319564\pi\)
\(68\) 35.3873 4.29135
\(69\) −11.6812 −1.40625
\(70\) 0 0
\(71\) −9.61429 −1.14101 −0.570503 0.821295i \(-0.693252\pi\)
−0.570503 + 0.821295i \(0.693252\pi\)
\(72\) 0.897730 0.105798
\(73\) −8.70551 −1.01890 −0.509451 0.860499i \(-0.670152\pi\)
−0.509451 + 0.860499i \(0.670152\pi\)
\(74\) −26.3199 −3.05962
\(75\) 0 0
\(76\) −4.68797 −0.537747
\(77\) −2.28823 −0.260768
\(78\) 7.72940 0.875182
\(79\) 4.40940 0.496096 0.248048 0.968748i \(-0.420211\pi\)
0.248048 + 0.968748i \(0.420211\pi\)
\(80\) 0 0
\(81\) −8.59589 −0.955099
\(82\) −10.5437 −1.16436
\(83\) −0.146311 −0.0160597 −0.00802984 0.999968i \(-0.502556\pi\)
−0.00802984 + 0.999968i \(0.502556\pi\)
\(84\) 18.1757 1.98313
\(85\) 0 0
\(86\) −14.2674 −1.53849
\(87\) −10.3751 −1.11232
\(88\) −6.95140 −0.741022
\(89\) −1.54279 −0.163535 −0.0817677 0.996651i \(-0.526057\pi\)
−0.0817677 + 0.996651i \(0.526057\pi\)
\(90\) 0 0
\(91\) −4.03638 −0.423127
\(92\) 32.3197 3.36956
\(93\) −14.2292 −1.47550
\(94\) 30.1572 3.11048
\(95\) 0 0
\(96\) 14.1322 1.44236
\(97\) 7.32786 0.744032 0.372016 0.928226i \(-0.378667\pi\)
0.372016 + 0.928226i \(0.378667\pi\)
\(98\) 4.56195 0.460826
\(99\) −0.129144 −0.0129794
\(100\) 0 0
\(101\) 10.5365 1.04843 0.524213 0.851587i \(-0.324360\pi\)
0.524213 + 0.851587i \(0.324360\pi\)
\(102\) 33.0762 3.27503
\(103\) 11.4973 1.13286 0.566430 0.824110i \(-0.308324\pi\)
0.566430 + 0.824110i \(0.308324\pi\)
\(104\) −12.2621 −1.20240
\(105\) 0 0
\(106\) 33.0813 3.21314
\(107\) 9.18318 0.887772 0.443886 0.896083i \(-0.353600\pi\)
0.443886 + 0.896083i \(0.353600\pi\)
\(108\) 24.8552 2.39169
\(109\) −18.0299 −1.72696 −0.863478 0.504387i \(-0.831718\pi\)
−0.863478 + 0.504387i \(0.831718\pi\)
\(110\) 0 0
\(111\) −17.2442 −1.63674
\(112\) −19.6814 −1.85972
\(113\) −10.1400 −0.953888 −0.476944 0.878934i \(-0.658255\pi\)
−0.476944 + 0.878934i \(0.658255\pi\)
\(114\) −4.38180 −0.410394
\(115\) 0 0
\(116\) 28.7058 2.66527
\(117\) −0.227807 −0.0210607
\(118\) −35.0809 −3.22946
\(119\) −17.2728 −1.58339
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −15.2385 −1.37963
\(123\) −6.90801 −0.622874
\(124\) 39.3694 3.53548
\(125\) 0 0
\(126\) −0.764223 −0.0680824
\(127\) 14.3078 1.26961 0.634806 0.772672i \(-0.281080\pi\)
0.634806 + 0.772672i \(0.281080\pi\)
\(128\) 5.38593 0.476053
\(129\) −9.34766 −0.823016
\(130\) 0 0
\(131\) 9.36028 0.817811 0.408906 0.912577i \(-0.365911\pi\)
0.408906 + 0.912577i \(0.365911\pi\)
\(132\) −7.94312 −0.691359
\(133\) 2.28823 0.198414
\(134\) −22.7340 −1.96391
\(135\) 0 0
\(136\) −52.4729 −4.49951
\(137\) −20.7172 −1.76999 −0.884995 0.465601i \(-0.845838\pi\)
−0.884995 + 0.465601i \(0.845838\pi\)
\(138\) 30.2089 2.57156
\(139\) 4.10420 0.348113 0.174057 0.984736i \(-0.444312\pi\)
0.174057 + 0.984736i \(0.444312\pi\)
\(140\) 0 0
\(141\) 19.7583 1.66395
\(142\) 24.8636 2.08651
\(143\) 1.76398 0.147511
\(144\) −1.11078 −0.0925654
\(145\) 0 0
\(146\) 22.5134 1.86322
\(147\) 2.98888 0.246519
\(148\) 47.7113 3.92185
\(149\) −4.70130 −0.385146 −0.192573 0.981283i \(-0.561683\pi\)
−0.192573 + 0.981283i \(0.561683\pi\)
\(150\) 0 0
\(151\) 0.894112 0.0727618 0.0363809 0.999338i \(-0.488417\pi\)
0.0363809 + 0.999338i \(0.488417\pi\)
\(152\) 6.95140 0.563833
\(153\) −0.974847 −0.0788117
\(154\) 5.91761 0.476855
\(155\) 0 0
\(156\) −14.0115 −1.12182
\(157\) −4.74289 −0.378524 −0.189262 0.981927i \(-0.560610\pi\)
−0.189262 + 0.981927i \(0.560610\pi\)
\(158\) −11.4032 −0.907190
\(159\) 21.6741 1.71887
\(160\) 0 0
\(161\) −15.7754 −1.24328
\(162\) 22.2299 1.74655
\(163\) 14.8395 1.16232 0.581159 0.813790i \(-0.302599\pi\)
0.581159 + 0.813790i \(0.302599\pi\)
\(164\) 19.1132 1.49249
\(165\) 0 0
\(166\) 0.378376 0.0293676
\(167\) 7.69641 0.595566 0.297783 0.954634i \(-0.403753\pi\)
0.297783 + 0.954634i \(0.403753\pi\)
\(168\) −26.9511 −2.07933
\(169\) −9.88839 −0.760645
\(170\) 0 0
\(171\) 0.129144 0.00987587
\(172\) 25.8632 1.97205
\(173\) −4.96012 −0.377111 −0.188555 0.982063i \(-0.560381\pi\)
−0.188555 + 0.982063i \(0.560381\pi\)
\(174\) 26.8310 2.03406
\(175\) 0 0
\(176\) 8.60115 0.648336
\(177\) −22.9842 −1.72760
\(178\) 3.98983 0.299050
\(179\) −15.6163 −1.16722 −0.583610 0.812034i \(-0.698360\pi\)
−0.583610 + 0.812034i \(0.698360\pi\)
\(180\) 0 0
\(181\) 11.4001 0.847364 0.423682 0.905811i \(-0.360737\pi\)
0.423682 + 0.905811i \(0.360737\pi\)
\(182\) 10.4385 0.773755
\(183\) −9.98394 −0.738034
\(184\) −47.9242 −3.53302
\(185\) 0 0
\(186\) 36.7982 2.69817
\(187\) 7.54854 0.552004
\(188\) −54.6674 −3.98703
\(189\) −12.1319 −0.882469
\(190\) 0 0
\(191\) 19.0989 1.38195 0.690974 0.722880i \(-0.257182\pi\)
0.690974 + 0.722880i \(0.257182\pi\)
\(192\) −7.40057 −0.534090
\(193\) 3.00325 0.216179 0.108089 0.994141i \(-0.465527\pi\)
0.108089 + 0.994141i \(0.465527\pi\)
\(194\) −18.9507 −1.36058
\(195\) 0 0
\(196\) −8.26967 −0.590690
\(197\) −7.23568 −0.515521 −0.257761 0.966209i \(-0.582985\pi\)
−0.257761 + 0.966209i \(0.582985\pi\)
\(198\) 0.333980 0.0237349
\(199\) −7.80636 −0.553378 −0.276689 0.960960i \(-0.589237\pi\)
−0.276689 + 0.960960i \(0.589237\pi\)
\(200\) 0 0
\(201\) −14.8948 −1.05060
\(202\) −27.2487 −1.91721
\(203\) −14.0115 −0.983412
\(204\) −59.9589 −4.19796
\(205\) 0 0
\(206\) −29.7332 −2.07161
\(207\) −0.890340 −0.0618829
\(208\) 15.1722 1.05200
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) 26.6833 1.83696 0.918478 0.395472i \(-0.129419\pi\)
0.918478 + 0.395472i \(0.129419\pi\)
\(212\) −59.9681 −4.11862
\(213\) 16.2901 1.11618
\(214\) −23.7487 −1.62343
\(215\) 0 0
\(216\) −36.8556 −2.50771
\(217\) −19.2164 −1.30450
\(218\) 46.6274 3.15801
\(219\) 14.7503 0.996731
\(220\) 0 0
\(221\) 13.3154 0.895694
\(222\) 44.5953 2.99304
\(223\) −5.24587 −0.351289 −0.175645 0.984454i \(-0.556201\pi\)
−0.175645 + 0.984454i \(0.556201\pi\)
\(224\) 19.0855 1.27520
\(225\) 0 0
\(226\) 26.2231 1.74433
\(227\) −6.00645 −0.398662 −0.199331 0.979932i \(-0.563877\pi\)
−0.199331 + 0.979932i \(0.563877\pi\)
\(228\) 7.94312 0.526046
\(229\) 10.4545 0.690853 0.345427 0.938446i \(-0.387734\pi\)
0.345427 + 0.938446i \(0.387734\pi\)
\(230\) 0 0
\(231\) 3.87708 0.255093
\(232\) −42.5654 −2.79456
\(233\) −23.3656 −1.53073 −0.765365 0.643597i \(-0.777441\pi\)
−0.765365 + 0.643597i \(0.777441\pi\)
\(234\) 0.589133 0.0385128
\(235\) 0 0
\(236\) 63.5929 4.13954
\(237\) −7.47111 −0.485301
\(238\) 44.6693 2.89548
\(239\) −10.1351 −0.655583 −0.327791 0.944750i \(-0.606304\pi\)
−0.327791 + 0.944750i \(0.606304\pi\)
\(240\) 0 0
\(241\) 10.6219 0.684218 0.342109 0.939660i \(-0.388859\pi\)
0.342109 + 0.939660i \(0.388859\pi\)
\(242\) −2.58611 −0.166242
\(243\) −1.34116 −0.0860351
\(244\) 27.6237 1.76842
\(245\) 0 0
\(246\) 17.8649 1.13902
\(247\) −1.76398 −0.112239
\(248\) −58.3775 −3.70698
\(249\) 0.247903 0.0157102
\(250\) 0 0
\(251\) 4.01095 0.253169 0.126584 0.991956i \(-0.459599\pi\)
0.126584 + 0.991956i \(0.459599\pi\)
\(252\) 1.38534 0.0872685
\(253\) 6.89418 0.433433
\(254\) −37.0015 −2.32168
\(255\) 0 0
\(256\) −22.6641 −1.41651
\(257\) 0.550435 0.0343352 0.0171676 0.999853i \(-0.494535\pi\)
0.0171676 + 0.999853i \(0.494535\pi\)
\(258\) 24.1741 1.50501
\(259\) −23.2882 −1.44706
\(260\) 0 0
\(261\) −0.790784 −0.0489483
\(262\) −24.2067 −1.49550
\(263\) −9.07131 −0.559361 −0.279681 0.960093i \(-0.590229\pi\)
−0.279681 + 0.960093i \(0.590229\pi\)
\(264\) 11.7782 0.724897
\(265\) 0 0
\(266\) −5.91761 −0.362832
\(267\) 2.61404 0.159977
\(268\) 41.2110 2.51736
\(269\) −25.8765 −1.57772 −0.788858 0.614576i \(-0.789327\pi\)
−0.788858 + 0.614576i \(0.789327\pi\)
\(270\) 0 0
\(271\) −6.26185 −0.380380 −0.190190 0.981747i \(-0.560910\pi\)
−0.190190 + 0.981747i \(0.560910\pi\)
\(272\) 64.9261 3.93672
\(273\) 6.83908 0.413920
\(274\) 53.5770 3.23670
\(275\) 0 0
\(276\) −54.7613 −3.29624
\(277\) 16.5892 0.996749 0.498374 0.866962i \(-0.333930\pi\)
0.498374 + 0.866962i \(0.333930\pi\)
\(278\) −10.6139 −0.636580
\(279\) −1.08454 −0.0649299
\(280\) 0 0
\(281\) −1.60057 −0.0954817 −0.0477409 0.998860i \(-0.515202\pi\)
−0.0477409 + 0.998860i \(0.515202\pi\)
\(282\) −51.0971 −3.04279
\(283\) −15.1474 −0.900420 −0.450210 0.892923i \(-0.648651\pi\)
−0.450210 + 0.892923i \(0.648651\pi\)
\(284\) −45.0715 −2.67450
\(285\) 0 0
\(286\) −4.56184 −0.269747
\(287\) −9.32924 −0.550688
\(288\) 1.07715 0.0634719
\(289\) 39.9804 2.35179
\(290\) 0 0
\(291\) −12.4160 −0.727841
\(292\) −40.8112 −2.38829
\(293\) 24.1930 1.41337 0.706686 0.707528i \(-0.250190\pi\)
0.706686 + 0.707528i \(0.250190\pi\)
\(294\) −7.72958 −0.450798
\(295\) 0 0
\(296\) −70.7471 −4.11209
\(297\) 5.30190 0.307647
\(298\) 12.1581 0.704300
\(299\) 12.1612 0.703299
\(300\) 0 0
\(301\) −12.6240 −0.727634
\(302\) −2.31227 −0.133056
\(303\) −17.8527 −1.02561
\(304\) −8.60115 −0.493310
\(305\) 0 0
\(306\) 2.52106 0.144120
\(307\) −10.5674 −0.603115 −0.301557 0.953448i \(-0.597506\pi\)
−0.301557 + 0.953448i \(0.597506\pi\)
\(308\) −10.7271 −0.611236
\(309\) −19.4805 −1.10821
\(310\) 0 0
\(311\) −10.0555 −0.570194 −0.285097 0.958499i \(-0.592026\pi\)
−0.285097 + 0.958499i \(0.592026\pi\)
\(312\) 20.7764 1.17623
\(313\) −7.08386 −0.400403 −0.200202 0.979755i \(-0.564160\pi\)
−0.200202 + 0.979755i \(0.564160\pi\)
\(314\) 12.2656 0.692190
\(315\) 0 0
\(316\) 20.6712 1.16284
\(317\) −22.1335 −1.24314 −0.621572 0.783357i \(-0.713506\pi\)
−0.621572 + 0.783357i \(0.713506\pi\)
\(318\) −56.0516 −3.14322
\(319\) 6.12329 0.342838
\(320\) 0 0
\(321\) −15.5596 −0.868453
\(322\) 40.7971 2.27353
\(323\) −7.54854 −0.420012
\(324\) −40.2973 −2.23874
\(325\) 0 0
\(326\) −38.3766 −2.12548
\(327\) 30.5492 1.68938
\(328\) −28.3413 −1.56489
\(329\) 26.6835 1.47111
\(330\) 0 0
\(331\) −16.1808 −0.889377 −0.444689 0.895685i \(-0.646686\pi\)
−0.444689 + 0.895685i \(0.646686\pi\)
\(332\) −0.685900 −0.0376437
\(333\) −1.31435 −0.0720258
\(334\) −19.9038 −1.08909
\(335\) 0 0
\(336\) 33.3474 1.81925
\(337\) −3.94070 −0.214664 −0.107332 0.994223i \(-0.534231\pi\)
−0.107332 + 0.994223i \(0.534231\pi\)
\(338\) 25.5725 1.39096
\(339\) 17.1808 0.933130
\(340\) 0 0
\(341\) 8.39796 0.454775
\(342\) −0.333980 −0.0180596
\(343\) 20.0541 1.08282
\(344\) −38.3504 −2.06771
\(345\) 0 0
\(346\) 12.8274 0.689606
\(347\) −10.5072 −0.564056 −0.282028 0.959406i \(-0.591007\pi\)
−0.282028 + 0.959406i \(0.591007\pi\)
\(348\) −48.6380 −2.60727
\(349\) −28.5144 −1.52634 −0.763170 0.646198i \(-0.776358\pi\)
−0.763170 + 0.646198i \(0.776358\pi\)
\(350\) 0 0
\(351\) 9.35242 0.499195
\(352\) −8.34073 −0.444563
\(353\) 1.73131 0.0921485 0.0460742 0.998938i \(-0.485329\pi\)
0.0460742 + 0.998938i \(0.485329\pi\)
\(354\) 59.4396 3.15918
\(355\) 0 0
\(356\) −7.23256 −0.383325
\(357\) 29.2663 1.54894
\(358\) 40.3856 2.13444
\(359\) 9.07665 0.479047 0.239524 0.970891i \(-0.423009\pi\)
0.239524 + 0.970891i \(0.423009\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −29.4820 −1.54954
\(363\) −1.69436 −0.0889308
\(364\) −18.9224 −0.991805
\(365\) 0 0
\(366\) 25.8196 1.34961
\(367\) −2.85316 −0.148934 −0.0744668 0.997223i \(-0.523725\pi\)
−0.0744668 + 0.997223i \(0.523725\pi\)
\(368\) 59.2979 3.09111
\(369\) −0.526527 −0.0274099
\(370\) 0 0
\(371\) 29.2708 1.51966
\(372\) −66.7059 −3.45854
\(373\) 8.36241 0.432989 0.216494 0.976284i \(-0.430538\pi\)
0.216494 + 0.976284i \(0.430538\pi\)
\(374\) −19.5214 −1.00943
\(375\) 0 0
\(376\) 81.0617 4.18044
\(377\) 10.8013 0.556297
\(378\) 31.3746 1.61373
\(379\) −4.08929 −0.210052 −0.105026 0.994469i \(-0.533493\pi\)
−0.105026 + 0.994469i \(0.533493\pi\)
\(380\) 0 0
\(381\) −24.2425 −1.24198
\(382\) −49.3919 −2.52711
\(383\) 4.95123 0.252996 0.126498 0.991967i \(-0.459626\pi\)
0.126498 + 0.991967i \(0.459626\pi\)
\(384\) −9.12570 −0.465694
\(385\) 0 0
\(386\) −7.76675 −0.395317
\(387\) −0.712477 −0.0362172
\(388\) 34.3528 1.74400
\(389\) −3.51207 −0.178069 −0.0890344 0.996029i \(-0.528378\pi\)
−0.0890344 + 0.996029i \(0.528378\pi\)
\(390\) 0 0
\(391\) 52.0410 2.63183
\(392\) 12.2624 0.619344
\(393\) −15.8597 −0.800015
\(394\) 18.7123 0.942711
\(395\) 0 0
\(396\) −0.605423 −0.0304236
\(397\) 14.2944 0.717414 0.358707 0.933450i \(-0.383218\pi\)
0.358707 + 0.933450i \(0.383218\pi\)
\(398\) 20.1881 1.01194
\(399\) −3.87708 −0.194097
\(400\) 0 0
\(401\) 2.09312 0.104526 0.0522628 0.998633i \(-0.483357\pi\)
0.0522628 + 0.998633i \(0.483357\pi\)
\(402\) 38.5195 1.92118
\(403\) 14.8138 0.737928
\(404\) 49.3951 2.45750
\(405\) 0 0
\(406\) 36.2352 1.79832
\(407\) 10.1774 0.504475
\(408\) 88.9080 4.40160
\(409\) 30.9423 1.53000 0.764998 0.644032i \(-0.222740\pi\)
0.764998 + 0.644032i \(0.222740\pi\)
\(410\) 0 0
\(411\) 35.1024 1.73147
\(412\) 53.8989 2.65541
\(413\) −31.0400 −1.52738
\(414\) 2.30252 0.113163
\(415\) 0 0
\(416\) −14.7129 −0.721357
\(417\) −6.95399 −0.340538
\(418\) 2.58611 0.126491
\(419\) −14.5113 −0.708923 −0.354461 0.935071i \(-0.615336\pi\)
−0.354461 + 0.935071i \(0.615336\pi\)
\(420\) 0 0
\(421\) 18.1495 0.884553 0.442276 0.896879i \(-0.354171\pi\)
0.442276 + 0.896879i \(0.354171\pi\)
\(422\) −69.0061 −3.35916
\(423\) 1.50597 0.0732229
\(424\) 88.9216 4.31841
\(425\) 0 0
\(426\) −42.1279 −2.04111
\(427\) −13.4833 −0.652502
\(428\) 43.0505 2.08093
\(429\) −2.98881 −0.144301
\(430\) 0 0
\(431\) 17.5233 0.844068 0.422034 0.906580i \(-0.361316\pi\)
0.422034 + 0.906580i \(0.361316\pi\)
\(432\) 45.6024 2.19405
\(433\) 25.5188 1.22636 0.613178 0.789944i \(-0.289891\pi\)
0.613178 + 0.789944i \(0.289891\pi\)
\(434\) 49.6958 2.38548
\(435\) 0 0
\(436\) −84.5239 −4.04796
\(437\) −6.89418 −0.329793
\(438\) −38.1458 −1.82268
\(439\) 23.5383 1.12342 0.561711 0.827334i \(-0.310143\pi\)
0.561711 + 0.827334i \(0.310143\pi\)
\(440\) 0 0
\(441\) 0.227812 0.0108482
\(442\) −34.4352 −1.63792
\(443\) 26.3065 1.24986 0.624929 0.780682i \(-0.285128\pi\)
0.624929 + 0.780682i \(0.285128\pi\)
\(444\) −80.8402 −3.83651
\(445\) 0 0
\(446\) 13.5664 0.642387
\(447\) 7.96570 0.376765
\(448\) −9.99445 −0.472193
\(449\) −28.8800 −1.36293 −0.681465 0.731851i \(-0.738657\pi\)
−0.681465 + 0.731851i \(0.738657\pi\)
\(450\) 0 0
\(451\) 4.07706 0.191981
\(452\) −47.5359 −2.23590
\(453\) −1.51495 −0.0711785
\(454\) 15.5334 0.729017
\(455\) 0 0
\(456\) −11.7782 −0.551564
\(457\) 14.8718 0.695675 0.347838 0.937555i \(-0.386916\pi\)
0.347838 + 0.937555i \(0.386916\pi\)
\(458\) −27.0365 −1.26333
\(459\) 40.0216 1.86805
\(460\) 0 0
\(461\) −8.11094 −0.377764 −0.188882 0.982000i \(-0.560486\pi\)
−0.188882 + 0.982000i \(0.560486\pi\)
\(462\) −10.0266 −0.466478
\(463\) 2.42168 0.112545 0.0562725 0.998415i \(-0.482078\pi\)
0.0562725 + 0.998415i \(0.482078\pi\)
\(464\) 52.6673 2.44502
\(465\) 0 0
\(466\) 60.4260 2.79918
\(467\) −1.70942 −0.0791026 −0.0395513 0.999218i \(-0.512593\pi\)
−0.0395513 + 0.999218i \(0.512593\pi\)
\(468\) −1.06795 −0.0493661
\(469\) −20.1153 −0.928839
\(470\) 0 0
\(471\) 8.03616 0.370287
\(472\) −94.2965 −4.34035
\(473\) 5.51693 0.253669
\(474\) 19.3211 0.887449
\(475\) 0 0
\(476\) −80.9743 −3.71145
\(477\) 1.65199 0.0756396
\(478\) 26.2104 1.19884
\(479\) −4.20304 −0.192042 −0.0960208 0.995379i \(-0.530612\pi\)
−0.0960208 + 0.995379i \(0.530612\pi\)
\(480\) 0 0
\(481\) 17.9527 0.818572
\(482\) −27.4695 −1.25120
\(483\) 26.7293 1.21622
\(484\) 4.68797 0.213090
\(485\) 0 0
\(486\) 3.46838 0.157329
\(487\) 4.04855 0.183458 0.0917288 0.995784i \(-0.470761\pi\)
0.0917288 + 0.995784i \(0.470761\pi\)
\(488\) −40.9608 −1.85421
\(489\) −25.1434 −1.13703
\(490\) 0 0
\(491\) 18.3438 0.827844 0.413922 0.910312i \(-0.364159\pi\)
0.413922 + 0.910312i \(0.364159\pi\)
\(492\) −32.3846 −1.46001
\(493\) 46.2219 2.08173
\(494\) 4.56184 0.205247
\(495\) 0 0
\(496\) 72.2321 3.24332
\(497\) 21.9997 0.986820
\(498\) −0.641105 −0.0287286
\(499\) −28.2235 −1.26346 −0.631728 0.775190i \(-0.717654\pi\)
−0.631728 + 0.775190i \(0.717654\pi\)
\(500\) 0 0
\(501\) −13.0405 −0.582606
\(502\) −10.3728 −0.462959
\(503\) 44.2412 1.97262 0.986309 0.164910i \(-0.0527335\pi\)
0.986309 + 0.164910i \(0.0527335\pi\)
\(504\) −2.05421 −0.0915018
\(505\) 0 0
\(506\) −17.8291 −0.792601
\(507\) 16.7545 0.744093
\(508\) 67.0745 2.97595
\(509\) 12.9450 0.573776 0.286888 0.957964i \(-0.407379\pi\)
0.286888 + 0.957964i \(0.407379\pi\)
\(510\) 0 0
\(511\) 19.9202 0.881217
\(512\) 47.8402 2.11426
\(513\) −5.30190 −0.234084
\(514\) −1.42349 −0.0627873
\(515\) 0 0
\(516\) −43.8216 −1.92914
\(517\) −11.6612 −0.512859
\(518\) 60.2258 2.64617
\(519\) 8.40423 0.368905
\(520\) 0 0
\(521\) −33.8184 −1.48161 −0.740806 0.671719i \(-0.765556\pi\)
−0.740806 + 0.671719i \(0.765556\pi\)
\(522\) 2.04506 0.0895097
\(523\) −17.1148 −0.748380 −0.374190 0.927352i \(-0.622079\pi\)
−0.374190 + 0.927352i \(0.622079\pi\)
\(524\) 43.8807 1.91694
\(525\) 0 0
\(526\) 23.4594 1.02288
\(527\) 63.3923 2.76141
\(528\) −14.5734 −0.634228
\(529\) 24.5297 1.06651
\(530\) 0 0
\(531\) −1.75185 −0.0760238
\(532\) 10.7271 0.465081
\(533\) 7.19184 0.311513
\(534\) −6.76021 −0.292543
\(535\) 0 0
\(536\) −61.1083 −2.63948
\(537\) 26.4597 1.14182
\(538\) 66.9194 2.88510
\(539\) −1.76402 −0.0759816
\(540\) 0 0
\(541\) 38.6274 1.66072 0.830361 0.557225i \(-0.188134\pi\)
0.830361 + 0.557225i \(0.188134\pi\)
\(542\) 16.1938 0.695585
\(543\) −19.3159 −0.828925
\(544\) −62.9603 −2.69940
\(545\) 0 0
\(546\) −17.6866 −0.756918
\(547\) −21.0804 −0.901333 −0.450667 0.892692i \(-0.648814\pi\)
−0.450667 + 0.892692i \(0.648814\pi\)
\(548\) −97.1217 −4.14883
\(549\) −0.760974 −0.0324776
\(550\) 0 0
\(551\) −6.12329 −0.260861
\(552\) 81.2008 3.45614
\(553\) −10.0897 −0.429058
\(554\) −42.9015 −1.82271
\(555\) 0 0
\(556\) 19.2404 0.815973
\(557\) 41.4863 1.75783 0.878915 0.476978i \(-0.158268\pi\)
0.878915 + 0.476978i \(0.158268\pi\)
\(558\) 2.80475 0.118735
\(559\) 9.73173 0.411608
\(560\) 0 0
\(561\) −12.7899 −0.539992
\(562\) 4.13924 0.174603
\(563\) −22.1691 −0.934317 −0.467159 0.884174i \(-0.654722\pi\)
−0.467159 + 0.884174i \(0.654722\pi\)
\(564\) 92.6263 3.90027
\(565\) 0 0
\(566\) 39.1729 1.64656
\(567\) 19.6693 0.826035
\(568\) 66.8328 2.80424
\(569\) 26.7108 1.11977 0.559887 0.828569i \(-0.310844\pi\)
0.559887 + 0.828569i \(0.310844\pi\)
\(570\) 0 0
\(571\) −5.12388 −0.214428 −0.107214 0.994236i \(-0.534193\pi\)
−0.107214 + 0.994236i \(0.534193\pi\)
\(572\) 8.26948 0.345764
\(573\) −32.3604 −1.35188
\(574\) 24.1265 1.00702
\(575\) 0 0
\(576\) −0.564070 −0.0235029
\(577\) 31.2035 1.29902 0.649510 0.760353i \(-0.274974\pi\)
0.649510 + 0.760353i \(0.274974\pi\)
\(578\) −103.394 −4.30062
\(579\) −5.08859 −0.211475
\(580\) 0 0
\(581\) 0.334792 0.0138895
\(582\) 32.1093 1.33097
\(583\) −12.7919 −0.529786
\(584\) 60.5155 2.50415
\(585\) 0 0
\(586\) −62.5659 −2.58457
\(587\) −18.0911 −0.746698 −0.373349 0.927691i \(-0.621791\pi\)
−0.373349 + 0.927691i \(0.621791\pi\)
\(588\) 14.0118 0.577837
\(589\) −8.39796 −0.346032
\(590\) 0 0
\(591\) 12.2599 0.504303
\(592\) 87.5373 3.59776
\(593\) −17.3157 −0.711072 −0.355536 0.934663i \(-0.615702\pi\)
−0.355536 + 0.934663i \(0.615702\pi\)
\(594\) −13.7113 −0.562581
\(595\) 0 0
\(596\) −22.0396 −0.902777
\(597\) 13.2268 0.541336
\(598\) −31.4501 −1.28609
\(599\) −10.4764 −0.428054 −0.214027 0.976828i \(-0.568658\pi\)
−0.214027 + 0.976828i \(0.568658\pi\)
\(600\) 0 0
\(601\) 6.37465 0.260027 0.130014 0.991512i \(-0.458498\pi\)
0.130014 + 0.991512i \(0.458498\pi\)
\(602\) 32.6470 1.33059
\(603\) −1.13528 −0.0462320
\(604\) 4.19158 0.170553
\(605\) 0 0
\(606\) 46.1691 1.87549
\(607\) 22.0826 0.896306 0.448153 0.893957i \(-0.352082\pi\)
0.448153 + 0.893957i \(0.352082\pi\)
\(608\) 8.34073 0.338261
\(609\) 23.7405 0.962013
\(610\) 0 0
\(611\) −20.5701 −0.832177
\(612\) −4.57006 −0.184734
\(613\) −33.9519 −1.37130 −0.685651 0.727930i \(-0.740483\pi\)
−0.685651 + 0.727930i \(0.740483\pi\)
\(614\) 27.3285 1.10289
\(615\) 0 0
\(616\) 15.9064 0.640886
\(617\) −8.00878 −0.322422 −0.161211 0.986920i \(-0.551540\pi\)
−0.161211 + 0.986920i \(0.551540\pi\)
\(618\) 50.3788 2.02653
\(619\) 2.72497 0.109526 0.0547628 0.998499i \(-0.482560\pi\)
0.0547628 + 0.998499i \(0.482560\pi\)
\(620\) 0 0
\(621\) 36.5522 1.46679
\(622\) 26.0046 1.04269
\(623\) 3.53025 0.141437
\(624\) −25.7072 −1.02911
\(625\) 0 0
\(626\) 18.3196 0.732200
\(627\) 1.69436 0.0676662
\(628\) −22.2345 −0.887255
\(629\) 76.8244 3.06319
\(630\) 0 0
\(631\) −28.2517 −1.12468 −0.562342 0.826905i \(-0.690100\pi\)
−0.562342 + 0.826905i \(0.690100\pi\)
\(632\) −30.6515 −1.21925
\(633\) −45.2112 −1.79698
\(634\) 57.2398 2.27328
\(635\) 0 0
\(636\) 101.607 4.02900
\(637\) −3.11168 −0.123289
\(638\) −15.8355 −0.626934
\(639\) 1.24163 0.0491180
\(640\) 0 0
\(641\) −12.7920 −0.505255 −0.252627 0.967564i \(-0.581295\pi\)
−0.252627 + 0.967564i \(0.581295\pi\)
\(642\) 40.2389 1.58810
\(643\) −10.3456 −0.407991 −0.203996 0.978972i \(-0.565393\pi\)
−0.203996 + 0.978972i \(0.565393\pi\)
\(644\) −73.9549 −2.91423
\(645\) 0 0
\(646\) 19.5214 0.768058
\(647\) −13.6757 −0.537647 −0.268824 0.963189i \(-0.586635\pi\)
−0.268824 + 0.963189i \(0.586635\pi\)
\(648\) 59.7535 2.34734
\(649\) 13.5651 0.532477
\(650\) 0 0
\(651\) 32.5595 1.27611
\(652\) 69.5672 2.72446
\(653\) −4.65063 −0.181993 −0.0909966 0.995851i \(-0.529005\pi\)
−0.0909966 + 0.995851i \(0.529005\pi\)
\(654\) −79.0037 −3.08929
\(655\) 0 0
\(656\) 35.0674 1.36915
\(657\) 1.12426 0.0438616
\(658\) −69.0065 −2.69015
\(659\) 14.0335 0.546667 0.273333 0.961919i \(-0.411874\pi\)
0.273333 + 0.961919i \(0.411874\pi\)
\(660\) 0 0
\(661\) −19.7867 −0.769615 −0.384807 0.922997i \(-0.625732\pi\)
−0.384807 + 0.922997i \(0.625732\pi\)
\(662\) 41.8454 1.62637
\(663\) −22.5612 −0.876203
\(664\) 1.01706 0.0394697
\(665\) 0 0
\(666\) 3.39905 0.131710
\(667\) 42.2150 1.63457
\(668\) 36.0805 1.39600
\(669\) 8.88839 0.343645
\(670\) 0 0
\(671\) 5.89246 0.227476
\(672\) −32.3377 −1.24745
\(673\) −34.9325 −1.34655 −0.673274 0.739393i \(-0.735113\pi\)
−0.673274 + 0.739393i \(0.735113\pi\)
\(674\) 10.1911 0.392546
\(675\) 0 0
\(676\) −46.3565 −1.78294
\(677\) −9.72087 −0.373603 −0.186802 0.982398i \(-0.559812\pi\)
−0.186802 + 0.982398i \(0.559812\pi\)
\(678\) −44.4313 −1.70638
\(679\) −16.7678 −0.643490
\(680\) 0 0
\(681\) 10.1771 0.389987
\(682\) −21.7180 −0.831627
\(683\) −25.5204 −0.976511 −0.488255 0.872701i \(-0.662367\pi\)
−0.488255 + 0.872701i \(0.662367\pi\)
\(684\) 0.605423 0.0231489
\(685\) 0 0
\(686\) −51.8620 −1.98010
\(687\) −17.7137 −0.675820
\(688\) 47.4519 1.80909
\(689\) −22.5646 −0.859643
\(690\) 0 0
\(691\) 2.08781 0.0794241 0.0397120 0.999211i \(-0.487356\pi\)
0.0397120 + 0.999211i \(0.487356\pi\)
\(692\) −23.2529 −0.883943
\(693\) 0.295510 0.0112255
\(694\) 27.1728 1.03146
\(695\) 0 0
\(696\) 72.1211 2.73374
\(697\) 30.7759 1.16572
\(698\) 73.7414 2.79115
\(699\) 39.5897 1.49742
\(700\) 0 0
\(701\) 20.5119 0.774724 0.387362 0.921928i \(-0.373386\pi\)
0.387362 + 0.921928i \(0.373386\pi\)
\(702\) −24.1864 −0.912857
\(703\) −10.1774 −0.383848
\(704\) 4.36777 0.164617
\(705\) 0 0
\(706\) −4.47737 −0.168508
\(707\) −24.1100 −0.906750
\(708\) −107.749 −4.04946
\(709\) −51.7570 −1.94377 −0.971887 0.235447i \(-0.924345\pi\)
−0.971887 + 0.235447i \(0.924345\pi\)
\(710\) 0 0
\(711\) −0.569447 −0.0213559
\(712\) 10.7246 0.401920
\(713\) 57.8970 2.16826
\(714\) −75.6859 −2.83247
\(715\) 0 0
\(716\) −73.2090 −2.73595
\(717\) 17.1725 0.641317
\(718\) −23.4732 −0.876013
\(719\) 8.16836 0.304629 0.152314 0.988332i \(-0.451327\pi\)
0.152314 + 0.988332i \(0.451327\pi\)
\(720\) 0 0
\(721\) −26.3084 −0.979774
\(722\) −2.58611 −0.0962451
\(723\) −17.9974 −0.669329
\(724\) 53.4435 1.98621
\(725\) 0 0
\(726\) 4.38180 0.162624
\(727\) 0.887737 0.0329244 0.0164622 0.999864i \(-0.494760\pi\)
0.0164622 + 0.999864i \(0.494760\pi\)
\(728\) 28.0585 1.03992
\(729\) 28.0601 1.03926
\(730\) 0 0
\(731\) 41.6447 1.54029
\(732\) −46.8045 −1.72994
\(733\) −30.3814 −1.12216 −0.561082 0.827761i \(-0.689615\pi\)
−0.561082 + 0.827761i \(0.689615\pi\)
\(734\) 7.37858 0.272349
\(735\) 0 0
\(736\) −57.5025 −2.11957
\(737\) 8.79079 0.323813
\(738\) 1.36166 0.0501233
\(739\) 26.0766 0.959242 0.479621 0.877476i \(-0.340774\pi\)
0.479621 + 0.877476i \(0.340774\pi\)
\(740\) 0 0
\(741\) 2.98881 0.109797
\(742\) −75.6974 −2.77894
\(743\) −7.70703 −0.282744 −0.141372 0.989957i \(-0.545151\pi\)
−0.141372 + 0.989957i \(0.545151\pi\)
\(744\) 98.9126 3.62631
\(745\) 0 0
\(746\) −21.6261 −0.791788
\(747\) 0.0188951 0.000691336 0
\(748\) 35.3873 1.29389
\(749\) −21.0132 −0.767806
\(750\) 0 0
\(751\) 22.8187 0.832666 0.416333 0.909212i \(-0.363315\pi\)
0.416333 + 0.909212i \(0.363315\pi\)
\(752\) −100.300 −3.65756
\(753\) −6.79599 −0.247660
\(754\) −27.9335 −1.01728
\(755\) 0 0
\(756\) −56.8742 −2.06850
\(757\) 23.9190 0.869350 0.434675 0.900587i \(-0.356863\pi\)
0.434675 + 0.900587i \(0.356863\pi\)
\(758\) 10.5753 0.384114
\(759\) −11.6812 −0.424001
\(760\) 0 0
\(761\) −16.5720 −0.600734 −0.300367 0.953824i \(-0.597109\pi\)
−0.300367 + 0.953824i \(0.597109\pi\)
\(762\) 62.6939 2.27116
\(763\) 41.2566 1.49359
\(764\) 89.5352 3.23927
\(765\) 0 0
\(766\) −12.8044 −0.462643
\(767\) 23.9285 0.864009
\(768\) 38.4012 1.38569
\(769\) 14.7713 0.532668 0.266334 0.963881i \(-0.414188\pi\)
0.266334 + 0.963881i \(0.414188\pi\)
\(770\) 0 0
\(771\) −0.932636 −0.0335881
\(772\) 14.0792 0.506721
\(773\) −24.5744 −0.883879 −0.441939 0.897045i \(-0.645709\pi\)
−0.441939 + 0.897045i \(0.645709\pi\)
\(774\) 1.84254 0.0662289
\(775\) 0 0
\(776\) −50.9389 −1.82860
\(777\) 39.4586 1.41557
\(778\) 9.08259 0.325627
\(779\) −4.07706 −0.146076
\(780\) 0 0
\(781\) −9.61429 −0.344026
\(782\) −134.584 −4.81271
\(783\) 32.4650 1.16021
\(784\) −15.1726 −0.541878
\(785\) 0 0
\(786\) 41.0149 1.46295
\(787\) 42.8976 1.52913 0.764566 0.644545i \(-0.222953\pi\)
0.764566 + 0.644545i \(0.222953\pi\)
\(788\) −33.9207 −1.20837
\(789\) 15.3701 0.547189
\(790\) 0 0
\(791\) 23.2025 0.824987
\(792\) 0.897730 0.0318994
\(793\) 10.3942 0.369107
\(794\) −36.9668 −1.31190
\(795\) 0 0
\(796\) −36.5960 −1.29711
\(797\) 3.74141 0.132528 0.0662638 0.997802i \(-0.478892\pi\)
0.0662638 + 0.997802i \(0.478892\pi\)
\(798\) 10.0266 0.354937
\(799\) −88.0251 −3.11410
\(800\) 0 0
\(801\) 0.199242 0.00703986
\(802\) −5.41305 −0.191141
\(803\) −8.70551 −0.307211
\(804\) −69.8262 −2.46258
\(805\) 0 0
\(806\) −38.3101 −1.34942
\(807\) 43.8440 1.54338
\(808\) −73.2438 −2.57671
\(809\) 35.5668 1.25046 0.625232 0.780439i \(-0.285005\pi\)
0.625232 + 0.780439i \(0.285005\pi\)
\(810\) 0 0
\(811\) 16.5102 0.579753 0.289877 0.957064i \(-0.406386\pi\)
0.289877 + 0.957064i \(0.406386\pi\)
\(812\) −65.6854 −2.30511
\(813\) 10.6098 0.372103
\(814\) −26.3199 −0.922511
\(815\) 0 0
\(816\) −110.008 −3.85106
\(817\) −5.51693 −0.193013
\(818\) −80.0202 −2.79784
\(819\) 0.521273 0.0182148
\(820\) 0 0
\(821\) −38.9813 −1.36046 −0.680228 0.733001i \(-0.738119\pi\)
−0.680228 + 0.733001i \(0.738119\pi\)
\(822\) −90.7787 −3.16627
\(823\) −51.7892 −1.80526 −0.902630 0.430418i \(-0.858366\pi\)
−0.902630 + 0.430418i \(0.858366\pi\)
\(824\) −79.9221 −2.78422
\(825\) 0 0
\(826\) 80.2730 2.79306
\(827\) −1.01711 −0.0353684 −0.0176842 0.999844i \(-0.505629\pi\)
−0.0176842 + 0.999844i \(0.505629\pi\)
\(828\) −4.17389 −0.145053
\(829\) −19.8623 −0.689848 −0.344924 0.938631i \(-0.612095\pi\)
−0.344924 + 0.938631i \(0.612095\pi\)
\(830\) 0 0
\(831\) −28.1081 −0.975059
\(832\) 7.70464 0.267110
\(833\) −13.3158 −0.461363
\(834\) 17.9838 0.622728
\(835\) 0 0
\(836\) −4.68797 −0.162137
\(837\) 44.5251 1.53901
\(838\) 37.5278 1.29638
\(839\) −9.36663 −0.323372 −0.161686 0.986842i \(-0.551693\pi\)
−0.161686 + 0.986842i \(0.551693\pi\)
\(840\) 0 0
\(841\) 8.49464 0.292919
\(842\) −46.9366 −1.61754
\(843\) 2.71193 0.0934040
\(844\) 125.091 4.30580
\(845\) 0 0
\(846\) −3.89461 −0.133900
\(847\) −2.28823 −0.0786244
\(848\) −110.025 −3.77827
\(849\) 25.6652 0.880826
\(850\) 0 0
\(851\) 70.1648 2.40522
\(852\) 76.3674 2.61630
\(853\) −34.7410 −1.18951 −0.594755 0.803907i \(-0.702751\pi\)
−0.594755 + 0.803907i \(0.702751\pi\)
\(854\) 34.8693 1.19320
\(855\) 0 0
\(856\) −63.8360 −2.18187
\(857\) 7.19129 0.245650 0.122825 0.992428i \(-0.460805\pi\)
0.122825 + 0.992428i \(0.460805\pi\)
\(858\) 7.72940 0.263877
\(859\) 13.9328 0.475383 0.237691 0.971341i \(-0.423609\pi\)
0.237691 + 0.971341i \(0.423609\pi\)
\(860\) 0 0
\(861\) 15.8071 0.538704
\(862\) −45.3172 −1.54351
\(863\) 38.8902 1.32384 0.661918 0.749576i \(-0.269743\pi\)
0.661918 + 0.749576i \(0.269743\pi\)
\(864\) −44.2217 −1.50445
\(865\) 0 0
\(866\) −65.9945 −2.24259
\(867\) −67.7412 −2.30061
\(868\) −90.0861 −3.05772
\(869\) 4.40940 0.149579
\(870\) 0 0
\(871\) 15.5067 0.525426
\(872\) 125.333 4.24432
\(873\) −0.946348 −0.0320290
\(874\) 17.8291 0.603079
\(875\) 0 0
\(876\) 69.1489 2.33632
\(877\) 40.2540 1.35928 0.679640 0.733546i \(-0.262136\pi\)
0.679640 + 0.733546i \(0.262136\pi\)
\(878\) −60.8726 −2.05435
\(879\) −40.9917 −1.38262
\(880\) 0 0
\(881\) −38.5849 −1.29996 −0.649978 0.759953i \(-0.725222\pi\)
−0.649978 + 0.759953i \(0.725222\pi\)
\(882\) −0.589147 −0.0198376
\(883\) 41.6274 1.40087 0.700437 0.713714i \(-0.252989\pi\)
0.700437 + 0.713714i \(0.252989\pi\)
\(884\) 62.4225 2.09949
\(885\) 0 0
\(886\) −68.0314 −2.28556
\(887\) 12.8070 0.430018 0.215009 0.976612i \(-0.431022\pi\)
0.215009 + 0.976612i \(0.431022\pi\)
\(888\) 119.871 4.02261
\(889\) −32.7395 −1.09805
\(890\) 0 0
\(891\) −8.59589 −0.287973
\(892\) −24.5925 −0.823417
\(893\) 11.6612 0.390227
\(894\) −20.6002 −0.688974
\(895\) 0 0
\(896\) −12.3242 −0.411723
\(897\) −20.6054 −0.687994
\(898\) 74.6868 2.49233
\(899\) 51.4231 1.71506
\(900\) 0 0
\(901\) −96.5601 −3.21688
\(902\) −10.5437 −0.351068
\(903\) 21.3896 0.711800
\(904\) 70.4870 2.34436
\(905\) 0 0
\(906\) 3.91783 0.130161
\(907\) −28.3828 −0.942436 −0.471218 0.882017i \(-0.656185\pi\)
−0.471218 + 0.882017i \(0.656185\pi\)
\(908\) −28.1581 −0.934459
\(909\) −1.36073 −0.0451325
\(910\) 0 0
\(911\) −11.6094 −0.384637 −0.192319 0.981333i \(-0.561601\pi\)
−0.192319 + 0.981333i \(0.561601\pi\)
\(912\) 14.5734 0.482575
\(913\) −0.146311 −0.00484218
\(914\) −38.4602 −1.27215
\(915\) 0 0
\(916\) 49.0104 1.61935
\(917\) −21.4184 −0.707299
\(918\) −103.500 −3.41602
\(919\) 12.1480 0.400726 0.200363 0.979722i \(-0.435788\pi\)
0.200363 + 0.979722i \(0.435788\pi\)
\(920\) 0 0
\(921\) 17.9050 0.589991
\(922\) 20.9758 0.690801
\(923\) −16.9594 −0.558225
\(924\) 18.1757 0.597935
\(925\) 0 0
\(926\) −6.26274 −0.205806
\(927\) −1.48480 −0.0487672
\(928\) −51.0727 −1.67654
\(929\) −30.4949 −1.00051 −0.500253 0.865879i \(-0.666760\pi\)
−0.500253 + 0.865879i \(0.666760\pi\)
\(930\) 0 0
\(931\) 1.76402 0.0578133
\(932\) −109.537 −3.58801
\(933\) 17.0376 0.557786
\(934\) 4.42076 0.144652
\(935\) 0 0
\(936\) 1.58357 0.0517608
\(937\) −10.8722 −0.355179 −0.177589 0.984105i \(-0.556830\pi\)
−0.177589 + 0.984105i \(0.556830\pi\)
\(938\) 52.0204 1.69853
\(939\) 12.0026 0.391690
\(940\) 0 0
\(941\) −33.5654 −1.09420 −0.547100 0.837067i \(-0.684268\pi\)
−0.547100 + 0.837067i \(0.684268\pi\)
\(942\) −20.7824 −0.677128
\(943\) 28.1080 0.915322
\(944\) 116.676 3.79746
\(945\) 0 0
\(946\) −14.2674 −0.463873
\(947\) 19.9608 0.648639 0.324319 0.945948i \(-0.394865\pi\)
0.324319 + 0.945948i \(0.394865\pi\)
\(948\) −35.0244 −1.13754
\(949\) −15.3563 −0.498487
\(950\) 0 0
\(951\) 37.5022 1.21609
\(952\) 120.070 3.89149
\(953\) 51.9269 1.68208 0.841039 0.540975i \(-0.181945\pi\)
0.841039 + 0.540975i \(0.181945\pi\)
\(954\) −4.27224 −0.138319
\(955\) 0 0
\(956\) −47.5129 −1.53668
\(957\) −10.3751 −0.335378
\(958\) 10.8695 0.351178
\(959\) 47.4056 1.53081
\(960\) 0 0
\(961\) 39.5257 1.27502
\(962\) −46.4276 −1.49689
\(963\) −1.18595 −0.0382167
\(964\) 49.7953 1.60380
\(965\) 0 0
\(966\) −69.1249 −2.22406
\(967\) −32.5944 −1.04817 −0.524083 0.851667i \(-0.675592\pi\)
−0.524083 + 0.851667i \(0.675592\pi\)
\(968\) −6.95140 −0.223426
\(969\) 12.7899 0.410872
\(970\) 0 0
\(971\) 45.4145 1.45742 0.728710 0.684823i \(-0.240120\pi\)
0.728710 + 0.684823i \(0.240120\pi\)
\(972\) −6.28730 −0.201665
\(973\) −9.39133 −0.301072
\(974\) −10.4700 −0.335481
\(975\) 0 0
\(976\) 50.6819 1.62229
\(977\) 29.4277 0.941475 0.470737 0.882273i \(-0.343988\pi\)
0.470737 + 0.882273i \(0.343988\pi\)
\(978\) 65.0238 2.07923
\(979\) −1.54279 −0.0493078
\(980\) 0 0
\(981\) 2.32845 0.0743418
\(982\) −47.4391 −1.51384
\(983\) −37.4646 −1.19494 −0.597468 0.801893i \(-0.703826\pi\)
−0.597468 + 0.801893i \(0.703826\pi\)
\(984\) 48.0203 1.53083
\(985\) 0 0
\(986\) −119.535 −3.80677
\(987\) −45.2114 −1.43910
\(988\) −8.26948 −0.263087
\(989\) 38.0347 1.20943
\(990\) 0 0
\(991\) −49.2749 −1.56527 −0.782634 0.622482i \(-0.786124\pi\)
−0.782634 + 0.622482i \(0.786124\pi\)
\(992\) −70.0451 −2.22393
\(993\) 27.4161 0.870024
\(994\) −56.8936 −1.80456
\(995\) 0 0
\(996\) 1.16216 0.0368245
\(997\) −25.3145 −0.801719 −0.400859 0.916140i \(-0.631288\pi\)
−0.400859 + 0.916140i \(0.631288\pi\)
\(998\) 72.9890 2.31043
\(999\) 53.9595 1.70720
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 5225.2.a.m.1.1 7
5.4 even 2 1045.2.a.h.1.7 7
15.14 odd 2 9405.2.a.bd.1.1 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1045.2.a.h.1.7 7 5.4 even 2
5225.2.a.m.1.1 7 1.1 even 1 trivial
9405.2.a.bd.1.1 7 15.14 odd 2