Properties

Label 5225.2.a.n.1.2
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: \( x^{7} - x^{6} - 14x^{5} + 10x^{4} + 59x^{3} - 27x^{2} - 66x + 30 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 209)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-2.03821\) 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)
 
\(f(q)\) \(=\) \(q-2.03821 q^{2} -1.87275 q^{3} +2.15429 q^{4} +3.81704 q^{6} -1.92338 q^{7} -0.314472 q^{8} +0.507178 q^{9} +O(q^{10})\) \(q-2.03821 q^{2} -1.87275 q^{3} +2.15429 q^{4} +3.81704 q^{6} -1.92338 q^{7} -0.314472 q^{8} +0.507178 q^{9} -1.00000 q^{11} -4.03444 q^{12} -2.85122 q^{13} +3.92024 q^{14} -3.66762 q^{16} +2.33033 q^{17} -1.03373 q^{18} +1.00000 q^{19} +3.60199 q^{21} +2.03821 q^{22} +2.74653 q^{23} +0.588926 q^{24} +5.81138 q^{26} +4.66842 q^{27} -4.14350 q^{28} -0.972965 q^{29} -0.00551178 q^{31} +8.10431 q^{32} +1.87275 q^{33} -4.74970 q^{34} +1.09261 q^{36} -9.67124 q^{37} -2.03821 q^{38} +5.33962 q^{39} +6.65137 q^{41} -7.34161 q^{42} -7.99413 q^{43} -2.15429 q^{44} -5.59800 q^{46} -3.46982 q^{47} +6.86852 q^{48} -3.30063 q^{49} -4.36412 q^{51} -6.14236 q^{52} -10.5493 q^{53} -9.51521 q^{54} +0.604847 q^{56} -1.87275 q^{57} +1.98311 q^{58} -13.7814 q^{59} +3.74608 q^{61} +0.0112342 q^{62} -0.975494 q^{63} -9.18303 q^{64} -3.81704 q^{66} +3.97172 q^{67} +5.02021 q^{68} -5.14356 q^{69} +14.2688 q^{71} -0.159493 q^{72} +13.2263 q^{73} +19.7120 q^{74} +2.15429 q^{76} +1.92338 q^{77} -10.8832 q^{78} -1.87656 q^{79} -10.2643 q^{81} -13.5569 q^{82} +10.9619 q^{83} +7.75973 q^{84} +16.2937 q^{86} +1.82212 q^{87} +0.314472 q^{88} +15.0195 q^{89} +5.48397 q^{91} +5.91682 q^{92} +0.0103222 q^{93} +7.07220 q^{94} -15.1773 q^{96} +7.57248 q^{97} +6.72736 q^{98} -0.507178 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + q^{2} - 2 q^{3} + 15 q^{4} - 2 q^{6} - 10 q^{7} + 9 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + q^{2} - 2 q^{3} + 15 q^{4} - 2 q^{6} - 10 q^{7} + 9 q^{8} + 11 q^{9} - 7 q^{11} + 16 q^{12} + 4 q^{13} + 6 q^{14} + 27 q^{16} - 2 q^{17} - 9 q^{18} + 7 q^{19} - 14 q^{21} - q^{22} - 10 q^{23} - 2 q^{24} - 8 q^{26} + 4 q^{27} - 26 q^{28} - 18 q^{29} + 24 q^{31} + 49 q^{32} + 2 q^{33} - 6 q^{34} + 29 q^{36} + q^{38} + 24 q^{39} - 12 q^{41} + 44 q^{42} - 2 q^{43} - 15 q^{44} - 4 q^{46} - 8 q^{47} + 72 q^{48} + 17 q^{49} - 24 q^{51} + 60 q^{52} - 2 q^{53} - 52 q^{54} + 26 q^{56} - 2 q^{57} + 8 q^{58} - 10 q^{59} + 14 q^{61} - 14 q^{62} + 55 q^{64} + 2 q^{66} - 8 q^{67} + 18 q^{68} - 6 q^{69} + 10 q^{71} - 53 q^{72} + 6 q^{73} + 26 q^{74} + 15 q^{76} + 10 q^{77} - 22 q^{78} + 52 q^{79} - q^{81} - 24 q^{82} + 10 q^{83} - 6 q^{84} + 8 q^{86} - 6 q^{87} - 9 q^{88} + 12 q^{91} - 2 q^{93} + 24 q^{94} + 6 q^{96} + 24 q^{97} - 19 q^{98} - 11 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.03821 −1.44123 −0.720615 0.693335i \(-0.756140\pi\)
−0.720615 + 0.693335i \(0.756140\pi\)
\(3\) −1.87275 −1.08123 −0.540615 0.841270i \(-0.681809\pi\)
−0.540615 + 0.841270i \(0.681809\pi\)
\(4\) 2.15429 1.07714
\(5\) 0 0
\(6\) 3.81704 1.55830
\(7\) −1.92338 −0.726967 −0.363484 0.931601i \(-0.618413\pi\)
−0.363484 + 0.931601i \(0.618413\pi\)
\(8\) −0.314472 −0.111183
\(9\) 0.507178 0.169059
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) −4.03444 −1.16464
\(13\) −2.85122 −0.790787 −0.395394 0.918512i \(-0.629392\pi\)
−0.395394 + 0.918512i \(0.629392\pi\)
\(14\) 3.92024 1.04773
\(15\) 0 0
\(16\) −3.66762 −0.916905
\(17\) 2.33033 0.565189 0.282594 0.959239i \(-0.408805\pi\)
0.282594 + 0.959239i \(0.408805\pi\)
\(18\) −1.03373 −0.243653
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 3.60199 0.786019
\(22\) 2.03821 0.434547
\(23\) 2.74653 0.572691 0.286346 0.958126i \(-0.407559\pi\)
0.286346 + 0.958126i \(0.407559\pi\)
\(24\) 0.588926 0.120214
\(25\) 0 0
\(26\) 5.81138 1.13971
\(27\) 4.66842 0.898438
\(28\) −4.14350 −0.783049
\(29\) −0.972965 −0.180675 −0.0903376 0.995911i \(-0.528795\pi\)
−0.0903376 + 0.995911i \(0.528795\pi\)
\(30\) 0 0
\(31\) −0.00551178 −0.000989945 0 −0.000494973 1.00000i \(-0.500158\pi\)
−0.000494973 1.00000i \(0.500158\pi\)
\(32\) 8.10431 1.43265
\(33\) 1.87275 0.326003
\(34\) −4.74970 −0.814567
\(35\) 0 0
\(36\) 1.09261 0.182101
\(37\) −9.67124 −1.58994 −0.794971 0.606647i \(-0.792514\pi\)
−0.794971 + 0.606647i \(0.792514\pi\)
\(38\) −2.03821 −0.330641
\(39\) 5.33962 0.855023
\(40\) 0 0
\(41\) 6.65137 1.03877 0.519385 0.854540i \(-0.326161\pi\)
0.519385 + 0.854540i \(0.326161\pi\)
\(42\) −7.34161 −1.13283
\(43\) −7.99413 −1.21909 −0.609547 0.792750i \(-0.708648\pi\)
−0.609547 + 0.792750i \(0.708648\pi\)
\(44\) −2.15429 −0.324771
\(45\) 0 0
\(46\) −5.59800 −0.825380
\(47\) −3.46982 −0.506125 −0.253062 0.967450i \(-0.581438\pi\)
−0.253062 + 0.967450i \(0.581438\pi\)
\(48\) 6.86852 0.991385
\(49\) −3.30063 −0.471518
\(50\) 0 0
\(51\) −4.36412 −0.611100
\(52\) −6.14236 −0.851792
\(53\) −10.5493 −1.44905 −0.724526 0.689247i \(-0.757942\pi\)
−0.724526 + 0.689247i \(0.757942\pi\)
\(54\) −9.51521 −1.29486
\(55\) 0 0
\(56\) 0.604847 0.0808261
\(57\) −1.87275 −0.248051
\(58\) 1.98311 0.260394
\(59\) −13.7814 −1.79419 −0.897096 0.441836i \(-0.854327\pi\)
−0.897096 + 0.441836i \(0.854327\pi\)
\(60\) 0 0
\(61\) 3.74608 0.479636 0.239818 0.970818i \(-0.422912\pi\)
0.239818 + 0.970818i \(0.422912\pi\)
\(62\) 0.0112342 0.00142674
\(63\) −0.975494 −0.122901
\(64\) −9.18303 −1.14788
\(65\) 0 0
\(66\) −3.81704 −0.469846
\(67\) 3.97172 0.485223 0.242612 0.970124i \(-0.421996\pi\)
0.242612 + 0.970124i \(0.421996\pi\)
\(68\) 5.02021 0.608790
\(69\) −5.14356 −0.619211
\(70\) 0 0
\(71\) 14.2688 1.69339 0.846695 0.532078i \(-0.178589\pi\)
0.846695 + 0.532078i \(0.178589\pi\)
\(72\) −0.159493 −0.0187965
\(73\) 13.2263 1.54803 0.774013 0.633170i \(-0.218247\pi\)
0.774013 + 0.633170i \(0.218247\pi\)
\(74\) 19.7120 2.29147
\(75\) 0 0
\(76\) 2.15429 0.247114
\(77\) 1.92338 0.219189
\(78\) −10.8832 −1.23229
\(79\) −1.87656 −0.211130 −0.105565 0.994412i \(-0.533665\pi\)
−0.105565 + 0.994412i \(0.533665\pi\)
\(80\) 0 0
\(81\) −10.2643 −1.14048
\(82\) −13.5569 −1.49711
\(83\) 10.9619 1.20322 0.601612 0.798789i \(-0.294526\pi\)
0.601612 + 0.798789i \(0.294526\pi\)
\(84\) 7.75973 0.846656
\(85\) 0 0
\(86\) 16.2937 1.75699
\(87\) 1.82212 0.195351
\(88\) 0.314472 0.0335228
\(89\) 15.0195 1.59207 0.796034 0.605253i \(-0.206928\pi\)
0.796034 + 0.605253i \(0.206928\pi\)
\(90\) 0 0
\(91\) 5.48397 0.574876
\(92\) 5.91682 0.616871
\(93\) 0.0103222 0.00107036
\(94\) 7.07220 0.729442
\(95\) 0 0
\(96\) −15.1773 −1.54903
\(97\) 7.57248 0.768869 0.384434 0.923152i \(-0.374396\pi\)
0.384434 + 0.923152i \(0.374396\pi\)
\(98\) 6.72736 0.679566
\(99\) −0.507178 −0.0509733
\(100\) 0 0
\(101\) −15.0513 −1.49766 −0.748831 0.662761i \(-0.769385\pi\)
−0.748831 + 0.662761i \(0.769385\pi\)
\(102\) 8.89499 0.880735
\(103\) 0.543451 0.0535478 0.0267739 0.999642i \(-0.491477\pi\)
0.0267739 + 0.999642i \(0.491477\pi\)
\(104\) 0.896629 0.0879218
\(105\) 0 0
\(106\) 21.5016 2.08842
\(107\) −14.7371 −1.42469 −0.712344 0.701831i \(-0.752366\pi\)
−0.712344 + 0.701831i \(0.752366\pi\)
\(108\) 10.0571 0.967748
\(109\) −17.3711 −1.66385 −0.831925 0.554888i \(-0.812761\pi\)
−0.831925 + 0.554888i \(0.812761\pi\)
\(110\) 0 0
\(111\) 18.1118 1.71909
\(112\) 7.05421 0.666560
\(113\) −12.8865 −1.21226 −0.606132 0.795364i \(-0.707280\pi\)
−0.606132 + 0.795364i \(0.707280\pi\)
\(114\) 3.81704 0.357499
\(115\) 0 0
\(116\) −2.09605 −0.194613
\(117\) −1.44608 −0.133690
\(118\) 28.0894 2.58584
\(119\) −4.48211 −0.410874
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −7.63529 −0.691266
\(123\) −12.4563 −1.12315
\(124\) −0.0118740 −0.00106631
\(125\) 0 0
\(126\) 1.98826 0.177128
\(127\) −15.4342 −1.36957 −0.684784 0.728746i \(-0.740103\pi\)
−0.684784 + 0.728746i \(0.740103\pi\)
\(128\) 2.50829 0.221704
\(129\) 14.9710 1.31812
\(130\) 0 0
\(131\) −12.0655 −1.05417 −0.527083 0.849814i \(-0.676714\pi\)
−0.527083 + 0.849814i \(0.676714\pi\)
\(132\) 4.03444 0.351153
\(133\) −1.92338 −0.166778
\(134\) −8.09519 −0.699318
\(135\) 0 0
\(136\) −0.732824 −0.0628392
\(137\) 5.53253 0.472676 0.236338 0.971671i \(-0.424053\pi\)
0.236338 + 0.971671i \(0.424053\pi\)
\(138\) 10.4836 0.892426
\(139\) −8.66764 −0.735180 −0.367590 0.929988i \(-0.619817\pi\)
−0.367590 + 0.929988i \(0.619817\pi\)
\(140\) 0 0
\(141\) 6.49808 0.547237
\(142\) −29.0827 −2.44057
\(143\) 2.85122 0.238431
\(144\) −1.86014 −0.155011
\(145\) 0 0
\(146\) −26.9580 −2.23106
\(147\) 6.18124 0.509820
\(148\) −20.8346 −1.71260
\(149\) −19.3027 −1.58134 −0.790671 0.612241i \(-0.790268\pi\)
−0.790671 + 0.612241i \(0.790268\pi\)
\(150\) 0 0
\(151\) 8.71384 0.709122 0.354561 0.935033i \(-0.384630\pi\)
0.354561 + 0.935033i \(0.384630\pi\)
\(152\) −0.314472 −0.0255070
\(153\) 1.18189 0.0955505
\(154\) −3.92024 −0.315902
\(155\) 0 0
\(156\) 11.5031 0.920983
\(157\) 5.86640 0.468189 0.234095 0.972214i \(-0.424787\pi\)
0.234095 + 0.972214i \(0.424787\pi\)
\(158\) 3.82483 0.304287
\(159\) 19.7561 1.56676
\(160\) 0 0
\(161\) −5.28261 −0.416328
\(162\) 20.9208 1.64369
\(163\) −14.8802 −1.16551 −0.582753 0.812649i \(-0.698025\pi\)
−0.582753 + 0.812649i \(0.698025\pi\)
\(164\) 14.3290 1.11891
\(165\) 0 0
\(166\) −22.3426 −1.73412
\(167\) −4.18971 −0.324209 −0.162105 0.986774i \(-0.551828\pi\)
−0.162105 + 0.986774i \(0.551828\pi\)
\(168\) −1.13273 −0.0873917
\(169\) −4.87053 −0.374656
\(170\) 0 0
\(171\) 0.507178 0.0387849
\(172\) −17.2217 −1.31314
\(173\) −0.707136 −0.0537626 −0.0268813 0.999639i \(-0.508558\pi\)
−0.0268813 + 0.999639i \(0.508558\pi\)
\(174\) −3.71385 −0.281546
\(175\) 0 0
\(176\) 3.66762 0.276457
\(177\) 25.8091 1.93993
\(178\) −30.6129 −2.29454
\(179\) −21.7962 −1.62913 −0.814563 0.580076i \(-0.803023\pi\)
−0.814563 + 0.580076i \(0.803023\pi\)
\(180\) 0 0
\(181\) −2.93416 −0.218094 −0.109047 0.994037i \(-0.534780\pi\)
−0.109047 + 0.994037i \(0.534780\pi\)
\(182\) −11.1775 −0.828529
\(183\) −7.01546 −0.518598
\(184\) −0.863707 −0.0636733
\(185\) 0 0
\(186\) −0.0210387 −0.00154263
\(187\) −2.33033 −0.170411
\(188\) −7.47498 −0.545169
\(189\) −8.97913 −0.653135
\(190\) 0 0
\(191\) 22.4018 1.62094 0.810468 0.585783i \(-0.199213\pi\)
0.810468 + 0.585783i \(0.199213\pi\)
\(192\) 17.1975 1.24112
\(193\) −2.55447 −0.183875 −0.0919375 0.995765i \(-0.529306\pi\)
−0.0919375 + 0.995765i \(0.529306\pi\)
\(194\) −15.4343 −1.10812
\(195\) 0 0
\(196\) −7.11051 −0.507893
\(197\) 12.6968 0.904607 0.452303 0.891864i \(-0.350602\pi\)
0.452303 + 0.891864i \(0.350602\pi\)
\(198\) 1.03373 0.0734643
\(199\) 10.1553 0.719892 0.359946 0.932973i \(-0.382795\pi\)
0.359946 + 0.932973i \(0.382795\pi\)
\(200\) 0 0
\(201\) −7.43803 −0.524638
\(202\) 30.6777 2.15848
\(203\) 1.87138 0.131345
\(204\) −9.40158 −0.658242
\(205\) 0 0
\(206\) −1.10767 −0.0771747
\(207\) 1.39298 0.0968188
\(208\) 10.4572 0.725076
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) −8.25858 −0.568544 −0.284272 0.958744i \(-0.591752\pi\)
−0.284272 + 0.958744i \(0.591752\pi\)
\(212\) −22.7262 −1.56084
\(213\) −26.7218 −1.83095
\(214\) 30.0372 2.05330
\(215\) 0 0
\(216\) −1.46809 −0.0998907
\(217\) 0.0106012 0.000719658 0
\(218\) 35.4059 2.39799
\(219\) −24.7696 −1.67377
\(220\) 0 0
\(221\) −6.64430 −0.446944
\(222\) −36.9156 −2.47761
\(223\) 21.2289 1.42159 0.710797 0.703398i \(-0.248335\pi\)
0.710797 + 0.703398i \(0.248335\pi\)
\(224\) −15.5876 −1.04149
\(225\) 0 0
\(226\) 26.2655 1.74715
\(227\) 9.06652 0.601766 0.300883 0.953661i \(-0.402719\pi\)
0.300883 + 0.953661i \(0.402719\pi\)
\(228\) −4.03444 −0.267187
\(229\) −5.25556 −0.347297 −0.173649 0.984808i \(-0.555556\pi\)
−0.173649 + 0.984808i \(0.555556\pi\)
\(230\) 0 0
\(231\) −3.60199 −0.236994
\(232\) 0.305970 0.0200879
\(233\) 5.68870 0.372679 0.186340 0.982485i \(-0.440338\pi\)
0.186340 + 0.982485i \(0.440338\pi\)
\(234\) 2.94741 0.192678
\(235\) 0 0
\(236\) −29.6892 −1.93260
\(237\) 3.51433 0.228280
\(238\) 9.13546 0.592164
\(239\) −20.3787 −1.31819 −0.659094 0.752060i \(-0.729060\pi\)
−0.659094 + 0.752060i \(0.729060\pi\)
\(240\) 0 0
\(241\) 17.6930 1.13971 0.569854 0.821746i \(-0.307000\pi\)
0.569854 + 0.821746i \(0.307000\pi\)
\(242\) −2.03821 −0.131021
\(243\) 5.21717 0.334682
\(244\) 8.07014 0.516638
\(245\) 0 0
\(246\) 25.3886 1.61872
\(247\) −2.85122 −0.181419
\(248\) 0.00173330 0.000110065 0
\(249\) −20.5288 −1.30096
\(250\) 0 0
\(251\) −0.776543 −0.0490149 −0.0245075 0.999700i \(-0.507802\pi\)
−0.0245075 + 0.999700i \(0.507802\pi\)
\(252\) −2.10149 −0.132382
\(253\) −2.74653 −0.172673
\(254\) 31.4582 1.97386
\(255\) 0 0
\(256\) 13.2536 0.828352
\(257\) −29.2762 −1.82620 −0.913100 0.407736i \(-0.866318\pi\)
−0.913100 + 0.407736i \(0.866318\pi\)
\(258\) −30.5139 −1.89972
\(259\) 18.6014 1.15584
\(260\) 0 0
\(261\) −0.493467 −0.0305448
\(262\) 24.5919 1.51929
\(263\) 5.90041 0.363835 0.181918 0.983314i \(-0.441770\pi\)
0.181918 + 0.983314i \(0.441770\pi\)
\(264\) −0.588926 −0.0362459
\(265\) 0 0
\(266\) 3.92024 0.240365
\(267\) −28.1278 −1.72139
\(268\) 8.55623 0.522655
\(269\) −10.7278 −0.654087 −0.327044 0.945009i \(-0.606052\pi\)
−0.327044 + 0.945009i \(0.606052\pi\)
\(270\) 0 0
\(271\) 16.2707 0.988375 0.494188 0.869355i \(-0.335466\pi\)
0.494188 + 0.869355i \(0.335466\pi\)
\(272\) −8.54677 −0.518224
\(273\) −10.2701 −0.621574
\(274\) −11.2765 −0.681235
\(275\) 0 0
\(276\) −11.0807 −0.666980
\(277\) −6.77040 −0.406794 −0.203397 0.979096i \(-0.565198\pi\)
−0.203397 + 0.979096i \(0.565198\pi\)
\(278\) 17.6664 1.05956
\(279\) −0.00279545 −0.000167359 0
\(280\) 0 0
\(281\) −17.1455 −1.02281 −0.511407 0.859339i \(-0.670876\pi\)
−0.511407 + 0.859339i \(0.670876\pi\)
\(282\) −13.2444 −0.788695
\(283\) 2.94787 0.175232 0.0876162 0.996154i \(-0.472075\pi\)
0.0876162 + 0.996154i \(0.472075\pi\)
\(284\) 30.7390 1.82403
\(285\) 0 0
\(286\) −5.81138 −0.343634
\(287\) −12.7931 −0.755152
\(288\) 4.11033 0.242203
\(289\) −11.5695 −0.680561
\(290\) 0 0
\(291\) −14.1813 −0.831325
\(292\) 28.4933 1.66745
\(293\) −2.57851 −0.150638 −0.0753192 0.997159i \(-0.523998\pi\)
−0.0753192 + 0.997159i \(0.523998\pi\)
\(294\) −12.5986 −0.734768
\(295\) 0 0
\(296\) 3.04133 0.176774
\(297\) −4.66842 −0.270889
\(298\) 39.3430 2.27908
\(299\) −7.83097 −0.452877
\(300\) 0 0
\(301\) 15.3757 0.886241
\(302\) −17.7606 −1.02201
\(303\) 28.1873 1.61932
\(304\) −3.66762 −0.210352
\(305\) 0 0
\(306\) −2.40895 −0.137710
\(307\) 19.7888 1.12941 0.564704 0.825293i \(-0.308990\pi\)
0.564704 + 0.825293i \(0.308990\pi\)
\(308\) 4.14350 0.236098
\(309\) −1.01775 −0.0578975
\(310\) 0 0
\(311\) 19.7979 1.12264 0.561319 0.827599i \(-0.310294\pi\)
0.561319 + 0.827599i \(0.310294\pi\)
\(312\) −1.67916 −0.0950637
\(313\) −10.9847 −0.620890 −0.310445 0.950591i \(-0.600478\pi\)
−0.310445 + 0.950591i \(0.600478\pi\)
\(314\) −11.9569 −0.674769
\(315\) 0 0
\(316\) −4.04266 −0.227417
\(317\) −9.88351 −0.555113 −0.277557 0.960709i \(-0.589525\pi\)
−0.277557 + 0.960709i \(0.589525\pi\)
\(318\) −40.2670 −2.25806
\(319\) 0.972965 0.0544756
\(320\) 0 0
\(321\) 27.5988 1.54042
\(322\) 10.7671 0.600024
\(323\) 2.33033 0.129663
\(324\) −22.1123 −1.22846
\(325\) 0 0
\(326\) 30.3289 1.67976
\(327\) 32.5317 1.79901
\(328\) −2.09167 −0.115493
\(329\) 6.67376 0.367936
\(330\) 0 0
\(331\) 25.7597 1.41588 0.707942 0.706271i \(-0.249624\pi\)
0.707942 + 0.706271i \(0.249624\pi\)
\(332\) 23.6151 1.29604
\(333\) −4.90504 −0.268795
\(334\) 8.53949 0.467260
\(335\) 0 0
\(336\) −13.2107 −0.720705
\(337\) −21.8924 −1.19256 −0.596278 0.802778i \(-0.703354\pi\)
−0.596278 + 0.802778i \(0.703354\pi\)
\(338\) 9.92714 0.539965
\(339\) 24.1332 1.31074
\(340\) 0 0
\(341\) 0.00551178 0.000298480 0
\(342\) −1.03373 −0.0558979
\(343\) 19.8120 1.06975
\(344\) 2.51393 0.135542
\(345\) 0 0
\(346\) 1.44129 0.0774842
\(347\) −19.2857 −1.03531 −0.517656 0.855589i \(-0.673195\pi\)
−0.517656 + 0.855589i \(0.673195\pi\)
\(348\) 3.92537 0.210422
\(349\) 15.5220 0.830872 0.415436 0.909622i \(-0.363629\pi\)
0.415436 + 0.909622i \(0.363629\pi\)
\(350\) 0 0
\(351\) −13.3107 −0.710473
\(352\) −8.10431 −0.431961
\(353\) 8.92859 0.475221 0.237610 0.971361i \(-0.423636\pi\)
0.237610 + 0.971361i \(0.423636\pi\)
\(354\) −52.6044 −2.79589
\(355\) 0 0
\(356\) 32.3564 1.71489
\(357\) 8.39385 0.444249
\(358\) 44.4252 2.34794
\(359\) 26.2672 1.38633 0.693165 0.720779i \(-0.256216\pi\)
0.693165 + 0.720779i \(0.256216\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 5.98042 0.314324
\(363\) −1.87275 −0.0982937
\(364\) 11.8141 0.619225
\(365\) 0 0
\(366\) 14.2990 0.747418
\(367\) −10.2560 −0.535358 −0.267679 0.963508i \(-0.586257\pi\)
−0.267679 + 0.963508i \(0.586257\pi\)
\(368\) −10.0732 −0.525103
\(369\) 3.37343 0.175614
\(370\) 0 0
\(371\) 20.2902 1.05341
\(372\) 0.0222369 0.00115293
\(373\) 20.2242 1.04717 0.523584 0.851974i \(-0.324595\pi\)
0.523584 + 0.851974i \(0.324595\pi\)
\(374\) 4.74970 0.245601
\(375\) 0 0
\(376\) 1.09116 0.0562722
\(377\) 2.77414 0.142876
\(378\) 18.3013 0.941318
\(379\) 14.1534 0.727011 0.363505 0.931592i \(-0.381580\pi\)
0.363505 + 0.931592i \(0.381580\pi\)
\(380\) 0 0
\(381\) 28.9044 1.48082
\(382\) −45.6595 −2.33614
\(383\) −12.3217 −0.629611 −0.314806 0.949156i \(-0.601939\pi\)
−0.314806 + 0.949156i \(0.601939\pi\)
\(384\) −4.69739 −0.239713
\(385\) 0 0
\(386\) 5.20655 0.265006
\(387\) −4.05445 −0.206099
\(388\) 16.3133 0.828183
\(389\) 33.9248 1.72006 0.860029 0.510245i \(-0.170445\pi\)
0.860029 + 0.510245i \(0.170445\pi\)
\(390\) 0 0
\(391\) 6.40033 0.323679
\(392\) 1.03795 0.0524246
\(393\) 22.5956 1.13980
\(394\) −25.8786 −1.30375
\(395\) 0 0
\(396\) −1.09261 −0.0549056
\(397\) 20.3357 1.02062 0.510309 0.859991i \(-0.329531\pi\)
0.510309 + 0.859991i \(0.329531\pi\)
\(398\) −20.6987 −1.03753
\(399\) 3.60199 0.180325
\(400\) 0 0
\(401\) −30.6815 −1.53216 −0.766080 0.642746i \(-0.777795\pi\)
−0.766080 + 0.642746i \(0.777795\pi\)
\(402\) 15.1602 0.756124
\(403\) 0.0157153 0.000782836 0
\(404\) −32.4249 −1.61320
\(405\) 0 0
\(406\) −3.81425 −0.189298
\(407\) 9.67124 0.479386
\(408\) 1.37239 0.0679436
\(409\) −34.8086 −1.72117 −0.860586 0.509305i \(-0.829903\pi\)
−0.860586 + 0.509305i \(0.829903\pi\)
\(410\) 0 0
\(411\) −10.3610 −0.511072
\(412\) 1.17075 0.0576787
\(413\) 26.5069 1.30432
\(414\) −2.83918 −0.139538
\(415\) 0 0
\(416\) −23.1072 −1.13292
\(417\) 16.2323 0.794899
\(418\) 2.03821 0.0996920
\(419\) 9.04478 0.441866 0.220933 0.975289i \(-0.429090\pi\)
0.220933 + 0.975289i \(0.429090\pi\)
\(420\) 0 0
\(421\) 29.9089 1.45767 0.728836 0.684688i \(-0.240062\pi\)
0.728836 + 0.684688i \(0.240062\pi\)
\(422\) 16.8327 0.819402
\(423\) −1.75981 −0.0855651
\(424\) 3.31745 0.161109
\(425\) 0 0
\(426\) 54.4645 2.63881
\(427\) −7.20512 −0.348680
\(428\) −31.7479 −1.53459
\(429\) −5.33962 −0.257799
\(430\) 0 0
\(431\) −13.7402 −0.661840 −0.330920 0.943659i \(-0.607359\pi\)
−0.330920 + 0.943659i \(0.607359\pi\)
\(432\) −17.1220 −0.823782
\(433\) −3.28875 −0.158047 −0.0790236 0.996873i \(-0.525180\pi\)
−0.0790236 + 0.996873i \(0.525180\pi\)
\(434\) −0.0216075 −0.00103719
\(435\) 0 0
\(436\) −37.4224 −1.79221
\(437\) 2.74653 0.131384
\(438\) 50.4855 2.41229
\(439\) 13.1729 0.628707 0.314353 0.949306i \(-0.398212\pi\)
0.314353 + 0.949306i \(0.398212\pi\)
\(440\) 0 0
\(441\) −1.67401 −0.0797146
\(442\) 13.5425 0.644149
\(443\) 24.9484 1.18533 0.592666 0.805448i \(-0.298075\pi\)
0.592666 + 0.805448i \(0.298075\pi\)
\(444\) 39.0180 1.85171
\(445\) 0 0
\(446\) −43.2689 −2.04884
\(447\) 36.1491 1.70980
\(448\) 17.6624 0.834470
\(449\) 15.5530 0.733993 0.366996 0.930222i \(-0.380386\pi\)
0.366996 + 0.930222i \(0.380386\pi\)
\(450\) 0 0
\(451\) −6.65137 −0.313201
\(452\) −27.7613 −1.30578
\(453\) −16.3188 −0.766724
\(454\) −18.4794 −0.867283
\(455\) 0 0
\(456\) 0.588926 0.0275790
\(457\) 19.1451 0.895571 0.447786 0.894141i \(-0.352213\pi\)
0.447786 + 0.894141i \(0.352213\pi\)
\(458\) 10.7119 0.500535
\(459\) 10.8790 0.507787
\(460\) 0 0
\(461\) 33.5045 1.56046 0.780229 0.625493i \(-0.215102\pi\)
0.780229 + 0.625493i \(0.215102\pi\)
\(462\) 7.34161 0.341563
\(463\) −2.83101 −0.131568 −0.0657842 0.997834i \(-0.520955\pi\)
−0.0657842 + 0.997834i \(0.520955\pi\)
\(464\) 3.56847 0.165662
\(465\) 0 0
\(466\) −11.5948 −0.537117
\(467\) 20.3717 0.942689 0.471344 0.881949i \(-0.343769\pi\)
0.471344 + 0.881949i \(0.343769\pi\)
\(468\) −3.11527 −0.144003
\(469\) −7.63911 −0.352741
\(470\) 0 0
\(471\) −10.9863 −0.506221
\(472\) 4.33388 0.199483
\(473\) 7.99413 0.367570
\(474\) −7.16293 −0.329004
\(475\) 0 0
\(476\) −9.65575 −0.442571
\(477\) −5.35036 −0.244976
\(478\) 41.5360 1.89981
\(479\) −7.81572 −0.357109 −0.178555 0.983930i \(-0.557142\pi\)
−0.178555 + 0.983930i \(0.557142\pi\)
\(480\) 0 0
\(481\) 27.5749 1.25731
\(482\) −36.0621 −1.64258
\(483\) 9.89299 0.450146
\(484\) 2.15429 0.0979222
\(485\) 0 0
\(486\) −10.6337 −0.482353
\(487\) 9.10523 0.412597 0.206299 0.978489i \(-0.433858\pi\)
0.206299 + 0.978489i \(0.433858\pi\)
\(488\) −1.17804 −0.0533272
\(489\) 27.8668 1.26018
\(490\) 0 0
\(491\) 34.4175 1.55324 0.776619 0.629970i \(-0.216933\pi\)
0.776619 + 0.629970i \(0.216933\pi\)
\(492\) −26.8345 −1.20979
\(493\) −2.26733 −0.102116
\(494\) 5.81138 0.261467
\(495\) 0 0
\(496\) 0.0202151 0.000907685 0
\(497\) −27.4442 −1.23104
\(498\) 41.8420 1.87498
\(499\) 7.80798 0.349533 0.174767 0.984610i \(-0.444083\pi\)
0.174767 + 0.984610i \(0.444083\pi\)
\(500\) 0 0
\(501\) 7.84625 0.350545
\(502\) 1.58275 0.0706418
\(503\) −34.9580 −1.55870 −0.779350 0.626589i \(-0.784450\pi\)
−0.779350 + 0.626589i \(0.784450\pi\)
\(504\) 0.306765 0.0136644
\(505\) 0 0
\(506\) 5.59800 0.248861
\(507\) 9.12126 0.405089
\(508\) −33.2498 −1.47522
\(509\) −11.3952 −0.505082 −0.252541 0.967586i \(-0.581266\pi\)
−0.252541 + 0.967586i \(0.581266\pi\)
\(510\) 0 0
\(511\) −25.4392 −1.12536
\(512\) −32.0302 −1.41555
\(513\) 4.66842 0.206116
\(514\) 59.6710 2.63197
\(515\) 0 0
\(516\) 32.2518 1.41981
\(517\) 3.46982 0.152602
\(518\) −37.9136 −1.66583
\(519\) 1.32429 0.0581297
\(520\) 0 0
\(521\) −28.0648 −1.22954 −0.614770 0.788707i \(-0.710751\pi\)
−0.614770 + 0.788707i \(0.710751\pi\)
\(522\) 1.00579 0.0440221
\(523\) −20.5683 −0.899389 −0.449694 0.893182i \(-0.648467\pi\)
−0.449694 + 0.893182i \(0.648467\pi\)
\(524\) −25.9925 −1.13549
\(525\) 0 0
\(526\) −12.0263 −0.524370
\(527\) −0.0128443 −0.000559506 0
\(528\) −6.86852 −0.298914
\(529\) −15.4566 −0.672025
\(530\) 0 0
\(531\) −6.98965 −0.303325
\(532\) −4.14350 −0.179644
\(533\) −18.9645 −0.821446
\(534\) 57.3302 2.48092
\(535\) 0 0
\(536\) −1.24899 −0.0539484
\(537\) 40.8188 1.76146
\(538\) 21.8655 0.942690
\(539\) 3.30063 0.142168
\(540\) 0 0
\(541\) −4.13908 −0.177953 −0.0889766 0.996034i \(-0.528360\pi\)
−0.0889766 + 0.996034i \(0.528360\pi\)
\(542\) −33.1631 −1.42448
\(543\) 5.49493 0.235810
\(544\) 18.8857 0.809720
\(545\) 0 0
\(546\) 20.9326 0.895831
\(547\) 30.7624 1.31530 0.657652 0.753322i \(-0.271550\pi\)
0.657652 + 0.753322i \(0.271550\pi\)
\(548\) 11.9187 0.509141
\(549\) 1.89993 0.0810870
\(550\) 0 0
\(551\) −0.972965 −0.0414497
\(552\) 1.61750 0.0688455
\(553\) 3.60934 0.153485
\(554\) 13.7995 0.586284
\(555\) 0 0
\(556\) −18.6726 −0.791895
\(557\) −8.84004 −0.374565 −0.187282 0.982306i \(-0.559968\pi\)
−0.187282 + 0.982306i \(0.559968\pi\)
\(558\) 0.00569772 0.000241204 0
\(559\) 22.7930 0.964043
\(560\) 0 0
\(561\) 4.36412 0.184253
\(562\) 34.9461 1.47411
\(563\) 3.15807 0.133097 0.0665484 0.997783i \(-0.478801\pi\)
0.0665484 + 0.997783i \(0.478801\pi\)
\(564\) 13.9987 0.589454
\(565\) 0 0
\(566\) −6.00836 −0.252550
\(567\) 19.7421 0.829091
\(568\) −4.48712 −0.188276
\(569\) 18.7192 0.784749 0.392375 0.919806i \(-0.371654\pi\)
0.392375 + 0.919806i \(0.371654\pi\)
\(570\) 0 0
\(571\) 37.6834 1.57700 0.788500 0.615034i \(-0.210858\pi\)
0.788500 + 0.615034i \(0.210858\pi\)
\(572\) 6.14236 0.256825
\(573\) −41.9529 −1.75261
\(574\) 26.0750 1.08835
\(575\) 0 0
\(576\) −4.65743 −0.194060
\(577\) −1.77272 −0.0737993 −0.0368997 0.999319i \(-0.511748\pi\)
−0.0368997 + 0.999319i \(0.511748\pi\)
\(578\) 23.5811 0.980846
\(579\) 4.78388 0.198811
\(580\) 0 0
\(581\) −21.0838 −0.874704
\(582\) 28.9045 1.19813
\(583\) 10.5493 0.436906
\(584\) −4.15931 −0.172113
\(585\) 0 0
\(586\) 5.25554 0.217105
\(587\) 32.1703 1.32781 0.663906 0.747816i \(-0.268897\pi\)
0.663906 + 0.747816i \(0.268897\pi\)
\(588\) 13.3162 0.549150
\(589\) −0.00551178 −0.000227109 0
\(590\) 0 0
\(591\) −23.7778 −0.978088
\(592\) 35.4704 1.45783
\(593\) −12.2719 −0.503946 −0.251973 0.967734i \(-0.581079\pi\)
−0.251973 + 0.967734i \(0.581079\pi\)
\(594\) 9.51521 0.390414
\(595\) 0 0
\(596\) −41.5837 −1.70333
\(597\) −19.0183 −0.778369
\(598\) 15.9611 0.652700
\(599\) 16.7005 0.682366 0.341183 0.939997i \(-0.389172\pi\)
0.341183 + 0.939997i \(0.389172\pi\)
\(600\) 0 0
\(601\) 14.3030 0.583432 0.291716 0.956505i \(-0.405774\pi\)
0.291716 + 0.956505i \(0.405774\pi\)
\(602\) −31.3389 −1.27728
\(603\) 2.01437 0.0820315
\(604\) 18.7721 0.763827
\(605\) 0 0
\(606\) −57.4516 −2.33381
\(607\) 9.04370 0.367073 0.183536 0.983013i \(-0.441246\pi\)
0.183536 + 0.983013i \(0.441246\pi\)
\(608\) 8.10431 0.328673
\(609\) −3.50461 −0.142014
\(610\) 0 0
\(611\) 9.89322 0.400237
\(612\) 2.54614 0.102922
\(613\) 24.0096 0.969738 0.484869 0.874587i \(-0.338867\pi\)
0.484869 + 0.874587i \(0.338867\pi\)
\(614\) −40.3337 −1.62774
\(615\) 0 0
\(616\) −0.604847 −0.0243700
\(617\) −1.30852 −0.0526791 −0.0263395 0.999653i \(-0.508385\pi\)
−0.0263395 + 0.999653i \(0.508385\pi\)
\(618\) 2.07438 0.0834436
\(619\) 32.2747 1.29723 0.648616 0.761116i \(-0.275348\pi\)
0.648616 + 0.761116i \(0.275348\pi\)
\(620\) 0 0
\(621\) 12.8220 0.514528
\(622\) −40.3523 −1.61798
\(623\) −28.8882 −1.15738
\(624\) −19.5837 −0.783975
\(625\) 0 0
\(626\) 22.3890 0.894845
\(627\) 1.87275 0.0747903
\(628\) 12.6379 0.504308
\(629\) −22.5372 −0.898618
\(630\) 0 0
\(631\) 29.6689 1.18110 0.590551 0.807000i \(-0.298911\pi\)
0.590551 + 0.807000i \(0.298911\pi\)
\(632\) 0.590127 0.0234740
\(633\) 15.4662 0.614727
\(634\) 20.1446 0.800046
\(635\) 0 0
\(636\) 42.5603 1.68763
\(637\) 9.41083 0.372871
\(638\) −1.98311 −0.0785119
\(639\) 7.23680 0.286283
\(640\) 0 0
\(641\) 22.2716 0.879675 0.439838 0.898077i \(-0.355036\pi\)
0.439838 + 0.898077i \(0.355036\pi\)
\(642\) −56.2521 −2.22009
\(643\) 16.6461 0.656456 0.328228 0.944599i \(-0.393549\pi\)
0.328228 + 0.944599i \(0.393549\pi\)
\(644\) −11.3803 −0.448445
\(645\) 0 0
\(646\) −4.74970 −0.186875
\(647\) 15.9531 0.627180 0.313590 0.949559i \(-0.398468\pi\)
0.313590 + 0.949559i \(0.398468\pi\)
\(648\) 3.22783 0.126801
\(649\) 13.7814 0.540969
\(650\) 0 0
\(651\) −0.0198534 −0.000778116 0
\(652\) −32.0562 −1.25542
\(653\) −14.7613 −0.577655 −0.288828 0.957381i \(-0.593265\pi\)
−0.288828 + 0.957381i \(0.593265\pi\)
\(654\) −66.3063 −2.59278
\(655\) 0 0
\(656\) −24.3947 −0.952453
\(657\) 6.70811 0.261708
\(658\) −13.6025 −0.530281
\(659\) −19.6143 −0.764065 −0.382032 0.924149i \(-0.624776\pi\)
−0.382032 + 0.924149i \(0.624776\pi\)
\(660\) 0 0
\(661\) −31.5523 −1.22724 −0.613621 0.789601i \(-0.710288\pi\)
−0.613621 + 0.789601i \(0.710288\pi\)
\(662\) −52.5037 −2.04061
\(663\) 12.4431 0.483250
\(664\) −3.44720 −0.133777
\(665\) 0 0
\(666\) 9.99749 0.387395
\(667\) −2.67228 −0.103471
\(668\) −9.02583 −0.349220
\(669\) −39.7564 −1.53707
\(670\) 0 0
\(671\) −3.74608 −0.144616
\(672\) 29.1917 1.12609
\(673\) −41.3876 −1.59537 −0.797687 0.603071i \(-0.793943\pi\)
−0.797687 + 0.603071i \(0.793943\pi\)
\(674\) 44.6213 1.71875
\(675\) 0 0
\(676\) −10.4925 −0.403558
\(677\) 20.6981 0.795491 0.397746 0.917496i \(-0.369793\pi\)
0.397746 + 0.917496i \(0.369793\pi\)
\(678\) −49.1885 −1.88907
\(679\) −14.5647 −0.558943
\(680\) 0 0
\(681\) −16.9793 −0.650647
\(682\) −0.0112342 −0.000430178 0
\(683\) 0.658543 0.0251985 0.0125992 0.999921i \(-0.495989\pi\)
0.0125992 + 0.999921i \(0.495989\pi\)
\(684\) 1.09261 0.0417769
\(685\) 0 0
\(686\) −40.3809 −1.54175
\(687\) 9.84233 0.375508
\(688\) 29.3194 1.11779
\(689\) 30.0783 1.14589
\(690\) 0 0
\(691\) 34.2462 1.30279 0.651393 0.758741i \(-0.274185\pi\)
0.651393 + 0.758741i \(0.274185\pi\)
\(692\) −1.52338 −0.0579100
\(693\) 0.975494 0.0370559
\(694\) 39.3083 1.49212
\(695\) 0 0
\(696\) −0.573005 −0.0217197
\(697\) 15.4999 0.587101
\(698\) −31.6370 −1.19748
\(699\) −10.6535 −0.402952
\(700\) 0 0
\(701\) 22.4638 0.848445 0.424223 0.905558i \(-0.360547\pi\)
0.424223 + 0.905558i \(0.360547\pi\)
\(702\) 27.1300 1.02396
\(703\) −9.67124 −0.364758
\(704\) 9.18303 0.346098
\(705\) 0 0
\(706\) −18.1983 −0.684902
\(707\) 28.9493 1.08875
\(708\) 55.6003 2.08959
\(709\) −0.410520 −0.0154174 −0.00770870 0.999970i \(-0.502454\pi\)
−0.00770870 + 0.999970i \(0.502454\pi\)
\(710\) 0 0
\(711\) −0.951752 −0.0356935
\(712\) −4.72322 −0.177010
\(713\) −0.0151383 −0.000566933 0
\(714\) −17.1084 −0.640266
\(715\) 0 0
\(716\) −46.9553 −1.75480
\(717\) 38.1641 1.42527
\(718\) −53.5380 −1.99802
\(719\) 36.5145 1.36176 0.680880 0.732395i \(-0.261598\pi\)
0.680880 + 0.732395i \(0.261598\pi\)
\(720\) 0 0
\(721\) −1.04526 −0.0389275
\(722\) −2.03821 −0.0758542
\(723\) −33.1346 −1.23229
\(724\) −6.32102 −0.234919
\(725\) 0 0
\(726\) 3.81704 0.141664
\(727\) 39.2587 1.45602 0.728012 0.685564i \(-0.240444\pi\)
0.728012 + 0.685564i \(0.240444\pi\)
\(728\) −1.72455 −0.0639163
\(729\) 21.0225 0.778610
\(730\) 0 0
\(731\) −18.6290 −0.689018
\(732\) −15.1133 −0.558604
\(733\) 34.3259 1.26786 0.633928 0.773392i \(-0.281442\pi\)
0.633928 + 0.773392i \(0.281442\pi\)
\(734\) 20.9038 0.771575
\(735\) 0 0
\(736\) 22.2587 0.820468
\(737\) −3.97172 −0.146300
\(738\) −6.87575 −0.253100
\(739\) −26.7732 −0.984870 −0.492435 0.870349i \(-0.663893\pi\)
−0.492435 + 0.870349i \(0.663893\pi\)
\(740\) 0 0
\(741\) 5.33962 0.196156
\(742\) −41.3556 −1.51821
\(743\) 9.38431 0.344277 0.172139 0.985073i \(-0.444932\pi\)
0.172139 + 0.985073i \(0.444932\pi\)
\(744\) −0.00324603 −0.000119005 0
\(745\) 0 0
\(746\) −41.2210 −1.50921
\(747\) 5.55963 0.203416
\(748\) −5.02021 −0.183557
\(749\) 28.3449 1.03570
\(750\) 0 0
\(751\) 7.66846 0.279826 0.139913 0.990164i \(-0.455318\pi\)
0.139913 + 0.990164i \(0.455318\pi\)
\(752\) 12.7260 0.464068
\(753\) 1.45427 0.0529965
\(754\) −5.65428 −0.205917
\(755\) 0 0
\(756\) −19.3436 −0.703521
\(757\) 6.75931 0.245671 0.122836 0.992427i \(-0.460801\pi\)
0.122836 + 0.992427i \(0.460801\pi\)
\(758\) −28.8475 −1.04779
\(759\) 5.14356 0.186699
\(760\) 0 0
\(761\) −34.8774 −1.26430 −0.632152 0.774844i \(-0.717828\pi\)
−0.632152 + 0.774844i \(0.717828\pi\)
\(762\) −58.9132 −2.13420
\(763\) 33.4111 1.20956
\(764\) 48.2599 1.74598
\(765\) 0 0
\(766\) 25.1142 0.907415
\(767\) 39.2940 1.41882
\(768\) −24.8207 −0.895640
\(769\) −0.00622027 −0.000224309 0 −0.000112154 1.00000i \(-0.500036\pi\)
−0.000112154 1.00000i \(0.500036\pi\)
\(770\) 0 0
\(771\) 54.8269 1.97454
\(772\) −5.50307 −0.198060
\(773\) −10.8548 −0.390418 −0.195209 0.980762i \(-0.562539\pi\)
−0.195209 + 0.980762i \(0.562539\pi\)
\(774\) 8.26380 0.297036
\(775\) 0 0
\(776\) −2.38133 −0.0854848
\(777\) −34.8357 −1.24973
\(778\) −69.1459 −2.47900
\(779\) 6.65137 0.238310
\(780\) 0 0
\(781\) −14.2688 −0.510576
\(782\) −13.0452 −0.466496
\(783\) −4.54221 −0.162325
\(784\) 12.1054 0.432337
\(785\) 0 0
\(786\) −46.0544 −1.64271
\(787\) −37.8221 −1.34821 −0.674106 0.738635i \(-0.735471\pi\)
−0.674106 + 0.738635i \(0.735471\pi\)
\(788\) 27.3525 0.974392
\(789\) −11.0500 −0.393390
\(790\) 0 0
\(791\) 24.7857 0.881277
\(792\) 0.159493 0.00566735
\(793\) −10.6809 −0.379290
\(794\) −41.4483 −1.47095
\(795\) 0 0
\(796\) 21.8775 0.775428
\(797\) 49.2853 1.74577 0.872887 0.487922i \(-0.162245\pi\)
0.872887 + 0.487922i \(0.162245\pi\)
\(798\) −7.34161 −0.259890
\(799\) −8.08583 −0.286056
\(800\) 0 0
\(801\) 7.61758 0.269154
\(802\) 62.5352 2.20819
\(803\) −13.2263 −0.466747
\(804\) −16.0237 −0.565111
\(805\) 0 0
\(806\) −0.0320311 −0.00112825
\(807\) 20.0905 0.707219
\(808\) 4.73322 0.166514
\(809\) 34.0416 1.19684 0.598420 0.801183i \(-0.295796\pi\)
0.598420 + 0.801183i \(0.295796\pi\)
\(810\) 0 0
\(811\) −44.7037 −1.56976 −0.784880 0.619648i \(-0.787275\pi\)
−0.784880 + 0.619648i \(0.787275\pi\)
\(812\) 4.03149 0.141477
\(813\) −30.4709 −1.06866
\(814\) −19.7120 −0.690905
\(815\) 0 0
\(816\) 16.0059 0.560320
\(817\) −7.99413 −0.279679
\(818\) 70.9470 2.48061
\(819\) 2.78135 0.0971882
\(820\) 0 0
\(821\) −48.0778 −1.67793 −0.838963 0.544188i \(-0.816838\pi\)
−0.838963 + 0.544188i \(0.816838\pi\)
\(822\) 21.1179 0.736572
\(823\) −18.6246 −0.649211 −0.324606 0.945849i \(-0.605232\pi\)
−0.324606 + 0.945849i \(0.605232\pi\)
\(824\) −0.170900 −0.00595358
\(825\) 0 0
\(826\) −54.0265 −1.87982
\(827\) −6.99744 −0.243325 −0.121662 0.992572i \(-0.538823\pi\)
−0.121662 + 0.992572i \(0.538823\pi\)
\(828\) 3.00088 0.104288
\(829\) 24.9441 0.866344 0.433172 0.901311i \(-0.357394\pi\)
0.433172 + 0.901311i \(0.357394\pi\)
\(830\) 0 0
\(831\) 12.6792 0.439838
\(832\) 26.1829 0.907727
\(833\) −7.69157 −0.266497
\(834\) −33.0848 −1.14563
\(835\) 0 0
\(836\) −2.15429 −0.0745076
\(837\) −0.0257313 −0.000889405 0
\(838\) −18.4351 −0.636831
\(839\) 10.2122 0.352566 0.176283 0.984340i \(-0.443593\pi\)
0.176283 + 0.984340i \(0.443593\pi\)
\(840\) 0 0
\(841\) −28.0533 −0.967356
\(842\) −60.9606 −2.10084
\(843\) 32.1091 1.10590
\(844\) −17.7914 −0.612404
\(845\) 0 0
\(846\) 3.58687 0.123319
\(847\) −1.92338 −0.0660879
\(848\) 38.6907 1.32864
\(849\) −5.52060 −0.189467
\(850\) 0 0
\(851\) −26.5624 −0.910546
\(852\) −57.5664 −1.97219
\(853\) −33.5562 −1.14894 −0.574472 0.818524i \(-0.694793\pi\)
−0.574472 + 0.818524i \(0.694793\pi\)
\(854\) 14.6855 0.502528
\(855\) 0 0
\(856\) 4.63440 0.158400
\(857\) −34.8775 −1.19139 −0.595696 0.803210i \(-0.703124\pi\)
−0.595696 + 0.803210i \(0.703124\pi\)
\(858\) 10.8832 0.371548
\(859\) 13.1320 0.448059 0.224029 0.974582i \(-0.428079\pi\)
0.224029 + 0.974582i \(0.428079\pi\)
\(860\) 0 0
\(861\) 23.9582 0.816493
\(862\) 28.0053 0.953863
\(863\) 27.5223 0.936871 0.468435 0.883498i \(-0.344818\pi\)
0.468435 + 0.883498i \(0.344818\pi\)
\(864\) 37.8343 1.28715
\(865\) 0 0
\(866\) 6.70315 0.227782
\(867\) 21.6668 0.735844
\(868\) 0.0228381 0.000775175 0
\(869\) 1.87656 0.0636581
\(870\) 0 0
\(871\) −11.3243 −0.383708
\(872\) 5.46272 0.184991
\(873\) 3.84060 0.129985
\(874\) −5.59800 −0.189355
\(875\) 0 0
\(876\) −53.3608 −1.80289
\(877\) 18.2679 0.616865 0.308432 0.951246i \(-0.400196\pi\)
0.308432 + 0.951246i \(0.400196\pi\)
\(878\) −26.8490 −0.906111
\(879\) 4.82890 0.162875
\(880\) 0 0
\(881\) −47.0363 −1.58469 −0.792346 0.610072i \(-0.791141\pi\)
−0.792346 + 0.610072i \(0.791141\pi\)
\(882\) 3.41197 0.114887
\(883\) 24.7005 0.831238 0.415619 0.909539i \(-0.363565\pi\)
0.415619 + 0.909539i \(0.363565\pi\)
\(884\) −14.3137 −0.481423
\(885\) 0 0
\(886\) −50.8500 −1.70834
\(887\) −23.3946 −0.785515 −0.392758 0.919642i \(-0.628479\pi\)
−0.392758 + 0.919642i \(0.628479\pi\)
\(888\) −5.69564 −0.191133
\(889\) 29.6858 0.995631
\(890\) 0 0
\(891\) 10.2643 0.343867
\(892\) 45.7332 1.53126
\(893\) −3.46982 −0.116113
\(894\) −73.6794 −2.46421
\(895\) 0 0
\(896\) −4.82438 −0.161171
\(897\) 14.6654 0.489664
\(898\) −31.7003 −1.05785
\(899\) 0.00536277 0.000178858 0
\(900\) 0 0
\(901\) −24.5833 −0.818989
\(902\) 13.5569 0.451395
\(903\) −28.7948 −0.958231
\(904\) 4.05246 0.134783
\(905\) 0 0
\(906\) 33.2611 1.10503
\(907\) −19.2411 −0.638892 −0.319446 0.947605i \(-0.603497\pi\)
−0.319446 + 0.947605i \(0.603497\pi\)
\(908\) 19.5319 0.648189
\(909\) −7.63370 −0.253194
\(910\) 0 0
\(911\) 48.5854 1.60971 0.804853 0.593475i \(-0.202244\pi\)
0.804853 + 0.593475i \(0.202244\pi\)
\(912\) 6.86852 0.227439
\(913\) −10.9619 −0.362785
\(914\) −39.0217 −1.29072
\(915\) 0 0
\(916\) −11.3220 −0.374089
\(917\) 23.2064 0.766344
\(918\) −22.1736 −0.731839
\(919\) 21.2754 0.701812 0.350906 0.936411i \(-0.385874\pi\)
0.350906 + 0.936411i \(0.385874\pi\)
\(920\) 0 0
\(921\) −37.0595 −1.22115
\(922\) −68.2891 −2.24898
\(923\) −40.6834 −1.33911
\(924\) −7.75973 −0.255276
\(925\) 0 0
\(926\) 5.77019 0.189620
\(927\) 0.275626 0.00905276
\(928\) −7.88521 −0.258845
\(929\) 49.9319 1.63821 0.819106 0.573643i \(-0.194470\pi\)
0.819106 + 0.573643i \(0.194470\pi\)
\(930\) 0 0
\(931\) −3.30063 −0.108174
\(932\) 12.2551 0.401429
\(933\) −37.0765 −1.21383
\(934\) −41.5217 −1.35863
\(935\) 0 0
\(936\) 0.454751 0.0148640
\(937\) −11.2142 −0.366353 −0.183176 0.983080i \(-0.558638\pi\)
−0.183176 + 0.983080i \(0.558638\pi\)
\(938\) 15.5701 0.508381
\(939\) 20.5715 0.671325
\(940\) 0 0
\(941\) −47.9390 −1.56277 −0.781383 0.624052i \(-0.785485\pi\)
−0.781383 + 0.624052i \(0.785485\pi\)
\(942\) 22.3923 0.729580
\(943\) 18.2682 0.594894
\(944\) 50.5451 1.64510
\(945\) 0 0
\(946\) −16.2937 −0.529754
\(947\) −14.4633 −0.469993 −0.234997 0.971996i \(-0.575508\pi\)
−0.234997 + 0.971996i \(0.575508\pi\)
\(948\) 7.57088 0.245891
\(949\) −37.7112 −1.22416
\(950\) 0 0
\(951\) 18.5093 0.600206
\(952\) 1.40950 0.0456820
\(953\) −19.3671 −0.627363 −0.313682 0.949528i \(-0.601562\pi\)
−0.313682 + 0.949528i \(0.601562\pi\)
\(954\) 10.9051 0.353067
\(955\) 0 0
\(956\) −43.9016 −1.41988
\(957\) −1.82212 −0.0589007
\(958\) 15.9300 0.514677
\(959\) −10.6411 −0.343620
\(960\) 0 0
\(961\) −31.0000 −0.999999
\(962\) −56.2033 −1.81207
\(963\) −7.47432 −0.240857
\(964\) 38.1159 1.22763
\(965\) 0 0
\(966\) −20.1640 −0.648765
\(967\) 29.6452 0.953326 0.476663 0.879086i \(-0.341846\pi\)
0.476663 + 0.879086i \(0.341846\pi\)
\(968\) −0.314472 −0.0101075
\(969\) −4.36412 −0.140196
\(970\) 0 0
\(971\) −27.9572 −0.897190 −0.448595 0.893735i \(-0.648075\pi\)
−0.448595 + 0.893735i \(0.648075\pi\)
\(972\) 11.2393 0.360500
\(973\) 16.6711 0.534452
\(974\) −18.5583 −0.594648
\(975\) 0 0
\(976\) −13.7392 −0.439781
\(977\) 25.4860 0.815369 0.407684 0.913123i \(-0.366336\pi\)
0.407684 + 0.913123i \(0.366336\pi\)
\(978\) −56.7983 −1.81621
\(979\) −15.0195 −0.480026
\(980\) 0 0
\(981\) −8.81024 −0.281289
\(982\) −70.1499 −2.23857
\(983\) 23.7523 0.757582 0.378791 0.925482i \(-0.376340\pi\)
0.378791 + 0.925482i \(0.376340\pi\)
\(984\) 3.91717 0.124875
\(985\) 0 0
\(986\) 4.62130 0.147172
\(987\) −12.4983 −0.397824
\(988\) −6.14236 −0.195414
\(989\) −21.9561 −0.698164
\(990\) 0 0
\(991\) 10.8187 0.343668 0.171834 0.985126i \(-0.445031\pi\)
0.171834 + 0.985126i \(0.445031\pi\)
\(992\) −0.0446692 −0.00141825
\(993\) −48.2415 −1.53090
\(994\) 55.9369 1.77421
\(995\) 0 0
\(996\) −44.2250 −1.40132
\(997\) 55.0261 1.74270 0.871348 0.490666i \(-0.163247\pi\)
0.871348 + 0.490666i \(0.163247\pi\)
\(998\) −15.9143 −0.503758
\(999\) −45.1494 −1.42847
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.n.1.2 7
5.4 even 2 209.2.a.d.1.6 7
15.14 odd 2 1881.2.a.p.1.2 7
20.19 odd 2 3344.2.a.ba.1.2 7
55.54 odd 2 2299.2.a.q.1.2 7
95.94 odd 2 3971.2.a.i.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
209.2.a.d.1.6 7 5.4 even 2
1881.2.a.p.1.2 7 15.14 odd 2
2299.2.a.q.1.2 7 55.54 odd 2
3344.2.a.ba.1.2 7 20.19 odd 2
3971.2.a.i.1.2 7 95.94 odd 2
5225.2.a.n.1.2 7 1.1 even 1 trivial