Properties

Label 4025.2.a.z.1.2
Level $4025$
Weight $2$
Character 4025.1
Self dual yes
Analytic conductor $32.140$
Analytic rank $1$
Dimension $14$
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] = [4025,2,Mod(1,4025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4025, 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("4025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4025 = 5^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4025.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(32.1397868136\)
Analytic rank: \(1\)
Dimension: \(14\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - 3 x^{13} - 18 x^{12} + 58 x^{11} + 111 x^{10} - 414 x^{9} - 244 x^{8} + 1330 x^{7} - 27 x^{6} - 1853 x^{5} + 539 x^{4} + 891 x^{3} - 218 x^{2} - 133 x - 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.42992\) of defining polynomial
Character \(\chi\) \(=\) 4025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.42992 q^{2} -3.09771 q^{3} +3.90452 q^{4} +7.52721 q^{6} -1.00000 q^{7} -4.62785 q^{8} +6.59584 q^{9} +O(q^{10})\) \(q-2.42992 q^{2} -3.09771 q^{3} +3.90452 q^{4} +7.52721 q^{6} -1.00000 q^{7} -4.62785 q^{8} +6.59584 q^{9} +3.16474 q^{11} -12.0951 q^{12} +6.21716 q^{13} +2.42992 q^{14} +3.43626 q^{16} +2.97980 q^{17} -16.0274 q^{18} -1.94284 q^{19} +3.09771 q^{21} -7.69007 q^{22} -1.00000 q^{23} +14.3357 q^{24} -15.1072 q^{26} -11.1389 q^{27} -3.90452 q^{28} +4.69320 q^{29} +0.0190312 q^{31} +0.905845 q^{32} -9.80346 q^{33} -7.24069 q^{34} +25.7536 q^{36} -5.79370 q^{37} +4.72094 q^{38} -19.2590 q^{39} -10.8089 q^{41} -7.52721 q^{42} -1.89992 q^{43} +12.3568 q^{44} +2.42992 q^{46} +3.77308 q^{47} -10.6446 q^{48} +1.00000 q^{49} -9.23057 q^{51} +24.2750 q^{52} -10.7735 q^{53} +27.0666 q^{54} +4.62785 q^{56} +6.01835 q^{57} -11.4041 q^{58} +2.73236 q^{59} -7.62617 q^{61} -0.0462443 q^{62} -6.59584 q^{63} -9.07366 q^{64} +23.8216 q^{66} -4.77968 q^{67} +11.6347 q^{68} +3.09771 q^{69} -1.11980 q^{71} -30.5245 q^{72} +13.4453 q^{73} +14.0783 q^{74} -7.58585 q^{76} -3.16474 q^{77} +46.7978 q^{78} -14.6291 q^{79} +14.7175 q^{81} +26.2647 q^{82} -2.38154 q^{83} +12.0951 q^{84} +4.61667 q^{86} -14.5382 q^{87} -14.6459 q^{88} +1.55142 q^{89} -6.21716 q^{91} -3.90452 q^{92} -0.0589531 q^{93} -9.16830 q^{94} -2.80605 q^{96} -9.22472 q^{97} -2.42992 q^{98} +20.8741 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q - 3 q^{2} - 4 q^{3} + 17 q^{4} - 4 q^{6} - 14 q^{7} - 3 q^{8} + 18 q^{9} + 5 q^{11} - 17 q^{12} - 11 q^{13} + 3 q^{14} + 23 q^{16} - 3 q^{17} - 15 q^{18} - 2 q^{19} + 4 q^{21} - 23 q^{22} - 14 q^{23} - 12 q^{24} - 9 q^{26} - 25 q^{27} - 17 q^{28} + 7 q^{29} - 3 q^{31} - 24 q^{32} - 6 q^{33} - 14 q^{34} + 13 q^{36} - 22 q^{37} - 20 q^{38} - 10 q^{39} - 17 q^{41} + 4 q^{42} - 18 q^{43} + 28 q^{44} + 3 q^{46} - 30 q^{47} - 8 q^{48} + 14 q^{49} + 4 q^{51} - 8 q^{52} - 11 q^{53} + 20 q^{54} + 3 q^{56} - 18 q^{57} - 38 q^{58} - 22 q^{59} - 8 q^{61} + 22 q^{62} - 18 q^{63} + 29 q^{64} - 9 q^{66} - 39 q^{67} - q^{68} + 4 q^{69} - 5 q^{71} + 24 q^{72} - 18 q^{73} + 35 q^{74} - 41 q^{76} - 5 q^{77} + 22 q^{78} + 10 q^{79} + 2 q^{81} + 8 q^{82} - 24 q^{83} + 17 q^{84} - 26 q^{86} - 5 q^{87} - 58 q^{88} + 25 q^{89} + 11 q^{91} - 17 q^{92} - 47 q^{93} - 2 q^{94} - 117 q^{96} - 43 q^{97} - 3 q^{98} + 55 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.42992 −1.71821 −0.859107 0.511795i \(-0.828981\pi\)
−0.859107 + 0.511795i \(0.828981\pi\)
\(3\) −3.09771 −1.78847 −0.894233 0.447601i \(-0.852278\pi\)
−0.894233 + 0.447601i \(0.852278\pi\)
\(4\) 3.90452 1.95226
\(5\) 0 0
\(6\) 7.52721 3.07297
\(7\) −1.00000 −0.377964
\(8\) −4.62785 −1.63619
\(9\) 6.59584 2.19861
\(10\) 0 0
\(11\) 3.16474 0.954205 0.477102 0.878848i \(-0.341687\pi\)
0.477102 + 0.878848i \(0.341687\pi\)
\(12\) −12.0951 −3.49156
\(13\) 6.21716 1.72433 0.862164 0.506629i \(-0.169108\pi\)
0.862164 + 0.506629i \(0.169108\pi\)
\(14\) 2.42992 0.649424
\(15\) 0 0
\(16\) 3.43626 0.859065
\(17\) 2.97980 0.722708 0.361354 0.932429i \(-0.382315\pi\)
0.361354 + 0.932429i \(0.382315\pi\)
\(18\) −16.0274 −3.77769
\(19\) −1.94284 −0.445717 −0.222859 0.974851i \(-0.571539\pi\)
−0.222859 + 0.974851i \(0.571539\pi\)
\(20\) 0 0
\(21\) 3.09771 0.675977
\(22\) −7.69007 −1.63953
\(23\) −1.00000 −0.208514
\(24\) 14.3357 2.92627
\(25\) 0 0
\(26\) −15.1072 −2.96277
\(27\) −11.1389 −2.14368
\(28\) −3.90452 −0.737886
\(29\) 4.69320 0.871506 0.435753 0.900066i \(-0.356482\pi\)
0.435753 + 0.900066i \(0.356482\pi\)
\(30\) 0 0
\(31\) 0.0190312 0.00341810 0.00170905 0.999999i \(-0.499456\pi\)
0.00170905 + 0.999999i \(0.499456\pi\)
\(32\) 0.905845 0.160132
\(33\) −9.80346 −1.70656
\(34\) −7.24069 −1.24177
\(35\) 0 0
\(36\) 25.7536 4.29227
\(37\) −5.79370 −0.952479 −0.476239 0.879316i \(-0.658000\pi\)
−0.476239 + 0.879316i \(0.658000\pi\)
\(38\) 4.72094 0.765838
\(39\) −19.2590 −3.08390
\(40\) 0 0
\(41\) −10.8089 −1.68806 −0.844030 0.536296i \(-0.819823\pi\)
−0.844030 + 0.536296i \(0.819823\pi\)
\(42\) −7.52721 −1.16147
\(43\) −1.89992 −0.289736 −0.144868 0.989451i \(-0.546276\pi\)
−0.144868 + 0.989451i \(0.546276\pi\)
\(44\) 12.3568 1.86286
\(45\) 0 0
\(46\) 2.42992 0.358273
\(47\) 3.77308 0.550361 0.275180 0.961393i \(-0.411262\pi\)
0.275180 + 0.961393i \(0.411262\pi\)
\(48\) −10.6446 −1.53641
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) −9.23057 −1.29254
\(52\) 24.2750 3.36634
\(53\) −10.7735 −1.47986 −0.739930 0.672684i \(-0.765142\pi\)
−0.739930 + 0.672684i \(0.765142\pi\)
\(54\) 27.0666 3.68330
\(55\) 0 0
\(56\) 4.62785 0.618422
\(57\) 6.01835 0.797151
\(58\) −11.4041 −1.49743
\(59\) 2.73236 0.355724 0.177862 0.984055i \(-0.443082\pi\)
0.177862 + 0.984055i \(0.443082\pi\)
\(60\) 0 0
\(61\) −7.62617 −0.976431 −0.488215 0.872723i \(-0.662352\pi\)
−0.488215 + 0.872723i \(0.662352\pi\)
\(62\) −0.0462443 −0.00587303
\(63\) −6.59584 −0.830997
\(64\) −9.07366 −1.13421
\(65\) 0 0
\(66\) 23.8216 2.93224
\(67\) −4.77968 −0.583931 −0.291966 0.956429i \(-0.594309\pi\)
−0.291966 + 0.956429i \(0.594309\pi\)
\(68\) 11.6347 1.41092
\(69\) 3.09771 0.372921
\(70\) 0 0
\(71\) −1.11980 −0.132896 −0.0664479 0.997790i \(-0.521167\pi\)
−0.0664479 + 0.997790i \(0.521167\pi\)
\(72\) −30.5245 −3.59735
\(73\) 13.4453 1.57366 0.786829 0.617171i \(-0.211721\pi\)
0.786829 + 0.617171i \(0.211721\pi\)
\(74\) 14.0783 1.63656
\(75\) 0 0
\(76\) −7.58585 −0.870157
\(77\) −3.16474 −0.360655
\(78\) 46.7978 5.29881
\(79\) −14.6291 −1.64590 −0.822949 0.568115i \(-0.807673\pi\)
−0.822949 + 0.568115i \(0.807673\pi\)
\(80\) 0 0
\(81\) 14.7175 1.63528
\(82\) 26.2647 2.90045
\(83\) −2.38154 −0.261408 −0.130704 0.991421i \(-0.541724\pi\)
−0.130704 + 0.991421i \(0.541724\pi\)
\(84\) 12.0951 1.31968
\(85\) 0 0
\(86\) 4.61667 0.497828
\(87\) −14.5382 −1.55866
\(88\) −14.6459 −1.56126
\(89\) 1.55142 0.164450 0.0822252 0.996614i \(-0.473797\pi\)
0.0822252 + 0.996614i \(0.473797\pi\)
\(90\) 0 0
\(91\) −6.21716 −0.651735
\(92\) −3.90452 −0.407075
\(93\) −0.0589531 −0.00611315
\(94\) −9.16830 −0.945638
\(95\) 0 0
\(96\) −2.80605 −0.286391
\(97\) −9.22472 −0.936628 −0.468314 0.883562i \(-0.655138\pi\)
−0.468314 + 0.883562i \(0.655138\pi\)
\(98\) −2.42992 −0.245459
\(99\) 20.8741 2.09793
\(100\) 0 0
\(101\) −13.1201 −1.30550 −0.652752 0.757572i \(-0.726385\pi\)
−0.652752 + 0.757572i \(0.726385\pi\)
\(102\) 22.4296 2.22086
\(103\) −20.0577 −1.97634 −0.988171 0.153355i \(-0.950992\pi\)
−0.988171 + 0.153355i \(0.950992\pi\)
\(104\) −28.7720 −2.82133
\(105\) 0 0
\(106\) 26.1789 2.54272
\(107\) −0.297274 −0.0287386 −0.0143693 0.999897i \(-0.504574\pi\)
−0.0143693 + 0.999897i \(0.504574\pi\)
\(108\) −43.4920 −4.18502
\(109\) 12.0661 1.15573 0.577863 0.816134i \(-0.303887\pi\)
0.577863 + 0.816134i \(0.303887\pi\)
\(110\) 0 0
\(111\) 17.9472 1.70348
\(112\) −3.43626 −0.324696
\(113\) 18.9079 1.77870 0.889352 0.457223i \(-0.151156\pi\)
0.889352 + 0.457223i \(0.151156\pi\)
\(114\) −14.6241 −1.36968
\(115\) 0 0
\(116\) 18.3247 1.70141
\(117\) 41.0073 3.79113
\(118\) −6.63943 −0.611209
\(119\) −2.97980 −0.273158
\(120\) 0 0
\(121\) −0.984428 −0.0894935
\(122\) 18.5310 1.67772
\(123\) 33.4828 3.01904
\(124\) 0.0743076 0.00667302
\(125\) 0 0
\(126\) 16.0274 1.42783
\(127\) −6.89872 −0.612162 −0.306081 0.952005i \(-0.599018\pi\)
−0.306081 + 0.952005i \(0.599018\pi\)
\(128\) 20.2366 1.78868
\(129\) 5.88542 0.518183
\(130\) 0 0
\(131\) 1.82144 0.159140 0.0795701 0.996829i \(-0.474645\pi\)
0.0795701 + 0.996829i \(0.474645\pi\)
\(132\) −38.2778 −3.33166
\(133\) 1.94284 0.168465
\(134\) 11.6143 1.00332
\(135\) 0 0
\(136\) −13.7901 −1.18249
\(137\) 15.1089 1.29084 0.645418 0.763829i \(-0.276683\pi\)
0.645418 + 0.763829i \(0.276683\pi\)
\(138\) −7.52721 −0.640758
\(139\) −9.71464 −0.823985 −0.411993 0.911187i \(-0.635167\pi\)
−0.411993 + 0.911187i \(0.635167\pi\)
\(140\) 0 0
\(141\) −11.6879 −0.984301
\(142\) 2.72103 0.228343
\(143\) 19.6757 1.64536
\(144\) 22.6650 1.88875
\(145\) 0 0
\(146\) −32.6711 −2.70388
\(147\) −3.09771 −0.255495
\(148\) −22.6217 −1.85949
\(149\) 17.4977 1.43346 0.716732 0.697349i \(-0.245637\pi\)
0.716732 + 0.697349i \(0.245637\pi\)
\(150\) 0 0
\(151\) −15.6454 −1.27321 −0.636603 0.771191i \(-0.719661\pi\)
−0.636603 + 0.771191i \(0.719661\pi\)
\(152\) 8.99115 0.729279
\(153\) 19.6543 1.58895
\(154\) 7.69007 0.619684
\(155\) 0 0
\(156\) −75.1971 −6.02059
\(157\) −2.79894 −0.223380 −0.111690 0.993743i \(-0.535626\pi\)
−0.111690 + 0.993743i \(0.535626\pi\)
\(158\) 35.5475 2.82801
\(159\) 33.3734 2.64668
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) −35.7625 −2.80977
\(163\) 12.0150 0.941085 0.470543 0.882377i \(-0.344058\pi\)
0.470543 + 0.882377i \(0.344058\pi\)
\(164\) −42.2035 −3.29554
\(165\) 0 0
\(166\) 5.78697 0.449156
\(167\) −15.7187 −1.21635 −0.608175 0.793803i \(-0.708098\pi\)
−0.608175 + 0.793803i \(0.708098\pi\)
\(168\) −14.3357 −1.10603
\(169\) 25.6530 1.97331
\(170\) 0 0
\(171\) −12.8146 −0.979960
\(172\) −7.41830 −0.565640
\(173\) −12.9561 −0.985037 −0.492519 0.870302i \(-0.663924\pi\)
−0.492519 + 0.870302i \(0.663924\pi\)
\(174\) 35.3267 2.67811
\(175\) 0 0
\(176\) 10.8749 0.819724
\(177\) −8.46409 −0.636200
\(178\) −3.76983 −0.282561
\(179\) 10.6322 0.794690 0.397345 0.917669i \(-0.369932\pi\)
0.397345 + 0.917669i \(0.369932\pi\)
\(180\) 0 0
\(181\) −21.5172 −1.59936 −0.799679 0.600427i \(-0.794997\pi\)
−0.799679 + 0.600427i \(0.794997\pi\)
\(182\) 15.1072 1.11982
\(183\) 23.6237 1.74631
\(184\) 4.62785 0.341169
\(185\) 0 0
\(186\) 0.143252 0.0105037
\(187\) 9.43029 0.689611
\(188\) 14.7321 1.07445
\(189\) 11.1389 0.810234
\(190\) 0 0
\(191\) −19.9054 −1.44030 −0.720151 0.693817i \(-0.755927\pi\)
−0.720151 + 0.693817i \(0.755927\pi\)
\(192\) 28.1076 2.02849
\(193\) 26.1721 1.88391 0.941955 0.335740i \(-0.108986\pi\)
0.941955 + 0.335740i \(0.108986\pi\)
\(194\) 22.4153 1.60933
\(195\) 0 0
\(196\) 3.90452 0.278895
\(197\) −23.2832 −1.65886 −0.829428 0.558613i \(-0.811334\pi\)
−0.829428 + 0.558613i \(0.811334\pi\)
\(198\) −50.7224 −3.60469
\(199\) −2.31819 −0.164332 −0.0821660 0.996619i \(-0.526184\pi\)
−0.0821660 + 0.996619i \(0.526184\pi\)
\(200\) 0 0
\(201\) 14.8061 1.04434
\(202\) 31.8809 2.24313
\(203\) −4.69320 −0.329398
\(204\) −36.0410 −2.52337
\(205\) 0 0
\(206\) 48.7386 3.39578
\(207\) −6.59584 −0.458442
\(208\) 21.3638 1.48131
\(209\) −6.14857 −0.425306
\(210\) 0 0
\(211\) 8.55629 0.589039 0.294520 0.955645i \(-0.404840\pi\)
0.294520 + 0.955645i \(0.404840\pi\)
\(212\) −42.0656 −2.88908
\(213\) 3.46882 0.237680
\(214\) 0.722354 0.0493791
\(215\) 0 0
\(216\) 51.5490 3.50746
\(217\) −0.0190312 −0.00129192
\(218\) −29.3198 −1.98579
\(219\) −41.6498 −2.81444
\(220\) 0 0
\(221\) 18.5259 1.24619
\(222\) −43.6104 −2.92694
\(223\) −1.46265 −0.0979463 −0.0489732 0.998800i \(-0.515595\pi\)
−0.0489732 + 0.998800i \(0.515595\pi\)
\(224\) −0.905845 −0.0605243
\(225\) 0 0
\(226\) −45.9447 −3.05620
\(227\) 11.0295 0.732055 0.366027 0.930604i \(-0.380718\pi\)
0.366027 + 0.930604i \(0.380718\pi\)
\(228\) 23.4988 1.55625
\(229\) 18.1813 1.20145 0.600726 0.799455i \(-0.294878\pi\)
0.600726 + 0.799455i \(0.294878\pi\)
\(230\) 0 0
\(231\) 9.80346 0.645020
\(232\) −21.7194 −1.42595
\(233\) 14.6633 0.960625 0.480312 0.877097i \(-0.340523\pi\)
0.480312 + 0.877097i \(0.340523\pi\)
\(234\) −99.6447 −6.51398
\(235\) 0 0
\(236\) 10.6686 0.694466
\(237\) 45.3167 2.94363
\(238\) 7.24069 0.469344
\(239\) 22.9003 1.48130 0.740648 0.671893i \(-0.234519\pi\)
0.740648 + 0.671893i \(0.234519\pi\)
\(240\) 0 0
\(241\) 4.07771 0.262668 0.131334 0.991338i \(-0.458074\pi\)
0.131334 + 0.991338i \(0.458074\pi\)
\(242\) 2.39208 0.153769
\(243\) −12.1741 −0.780971
\(244\) −29.7766 −1.90625
\(245\) 0 0
\(246\) −81.3605 −5.18736
\(247\) −12.0789 −0.768563
\(248\) −0.0880733 −0.00559266
\(249\) 7.37734 0.467520
\(250\) 0 0
\(251\) 20.6618 1.30416 0.652081 0.758149i \(-0.273896\pi\)
0.652081 + 0.758149i \(0.273896\pi\)
\(252\) −25.7536 −1.62232
\(253\) −3.16474 −0.198965
\(254\) 16.7634 1.05183
\(255\) 0 0
\(256\) −31.0260 −1.93913
\(257\) −19.9061 −1.24171 −0.620855 0.783926i \(-0.713214\pi\)
−0.620855 + 0.783926i \(0.713214\pi\)
\(258\) −14.3011 −0.890349
\(259\) 5.79370 0.360003
\(260\) 0 0
\(261\) 30.9556 1.91610
\(262\) −4.42596 −0.273437
\(263\) −6.87878 −0.424164 −0.212082 0.977252i \(-0.568024\pi\)
−0.212082 + 0.977252i \(0.568024\pi\)
\(264\) 45.3689 2.79226
\(265\) 0 0
\(266\) −4.72094 −0.289460
\(267\) −4.80586 −0.294114
\(268\) −18.6624 −1.13999
\(269\) 19.6883 1.20041 0.600207 0.799845i \(-0.295085\pi\)
0.600207 + 0.799845i \(0.295085\pi\)
\(270\) 0 0
\(271\) −30.0104 −1.82300 −0.911502 0.411296i \(-0.865076\pi\)
−0.911502 + 0.411296i \(0.865076\pi\)
\(272\) 10.2394 0.620853
\(273\) 19.2590 1.16561
\(274\) −36.7134 −2.21793
\(275\) 0 0
\(276\) 12.0951 0.728040
\(277\) −23.6208 −1.41924 −0.709619 0.704585i \(-0.751133\pi\)
−0.709619 + 0.704585i \(0.751133\pi\)
\(278\) 23.6058 1.41578
\(279\) 0.125526 0.00751507
\(280\) 0 0
\(281\) 14.5328 0.866957 0.433478 0.901164i \(-0.357286\pi\)
0.433478 + 0.901164i \(0.357286\pi\)
\(282\) 28.4008 1.69124
\(283\) −28.5671 −1.69814 −0.849068 0.528284i \(-0.822836\pi\)
−0.849068 + 0.528284i \(0.822836\pi\)
\(284\) −4.37228 −0.259447
\(285\) 0 0
\(286\) −47.8104 −2.82709
\(287\) 10.8089 0.638027
\(288\) 5.97481 0.352069
\(289\) −8.12078 −0.477693
\(290\) 0 0
\(291\) 28.5755 1.67513
\(292\) 52.4977 3.07219
\(293\) −23.8859 −1.39543 −0.697713 0.716377i \(-0.745799\pi\)
−0.697713 + 0.716377i \(0.745799\pi\)
\(294\) 7.52721 0.438996
\(295\) 0 0
\(296\) 26.8124 1.55844
\(297\) −35.2516 −2.04551
\(298\) −42.5179 −2.46300
\(299\) −6.21716 −0.359547
\(300\) 0 0
\(301\) 1.89992 0.109510
\(302\) 38.0172 2.18764
\(303\) 40.6425 2.33485
\(304\) −6.67609 −0.382900
\(305\) 0 0
\(306\) −47.7584 −2.73017
\(307\) −21.8334 −1.24610 −0.623048 0.782184i \(-0.714106\pi\)
−0.623048 + 0.782184i \(0.714106\pi\)
\(308\) −12.3568 −0.704094
\(309\) 62.1330 3.53462
\(310\) 0 0
\(311\) 2.50116 0.141828 0.0709139 0.997482i \(-0.477408\pi\)
0.0709139 + 0.997482i \(0.477408\pi\)
\(312\) 89.1276 5.04586
\(313\) −19.9519 −1.12775 −0.563873 0.825862i \(-0.690689\pi\)
−0.563873 + 0.825862i \(0.690689\pi\)
\(314\) 6.80121 0.383815
\(315\) 0 0
\(316\) −57.1195 −3.21323
\(317\) −1.30854 −0.0734952 −0.0367476 0.999325i \(-0.511700\pi\)
−0.0367476 + 0.999325i \(0.511700\pi\)
\(318\) −81.0947 −4.54757
\(319\) 14.8528 0.831595
\(320\) 0 0
\(321\) 0.920871 0.0513980
\(322\) −2.42992 −0.135414
\(323\) −5.78927 −0.322124
\(324\) 57.4650 3.19250
\(325\) 0 0
\(326\) −29.1955 −1.61699
\(327\) −37.3775 −2.06698
\(328\) 50.0217 2.76199
\(329\) −3.77308 −0.208017
\(330\) 0 0
\(331\) −22.5899 −1.24165 −0.620826 0.783948i \(-0.713203\pi\)
−0.620826 + 0.783948i \(0.713203\pi\)
\(332\) −9.29880 −0.510338
\(333\) −38.2143 −2.09413
\(334\) 38.1952 2.08995
\(335\) 0 0
\(336\) 10.6446 0.580708
\(337\) 25.4899 1.38852 0.694261 0.719724i \(-0.255731\pi\)
0.694261 + 0.719724i \(0.255731\pi\)
\(338\) −62.3349 −3.39057
\(339\) −58.5712 −3.18115
\(340\) 0 0
\(341\) 0.0602287 0.00326157
\(342\) 31.1386 1.68378
\(343\) −1.00000 −0.0539949
\(344\) 8.79256 0.474063
\(345\) 0 0
\(346\) 31.4824 1.69251
\(347\) −2.20649 −0.118451 −0.0592254 0.998245i \(-0.518863\pi\)
−0.0592254 + 0.998245i \(0.518863\pi\)
\(348\) −56.7648 −3.04291
\(349\) −19.5526 −1.04663 −0.523314 0.852140i \(-0.675305\pi\)
−0.523314 + 0.852140i \(0.675305\pi\)
\(350\) 0 0
\(351\) −69.2521 −3.69640
\(352\) 2.86676 0.152799
\(353\) −22.4360 −1.19415 −0.597074 0.802186i \(-0.703670\pi\)
−0.597074 + 0.802186i \(0.703670\pi\)
\(354\) 20.5671 1.09313
\(355\) 0 0
\(356\) 6.05756 0.321050
\(357\) 9.23057 0.488534
\(358\) −25.8355 −1.36545
\(359\) −31.0915 −1.64095 −0.820474 0.571684i \(-0.806290\pi\)
−0.820474 + 0.571684i \(0.806290\pi\)
\(360\) 0 0
\(361\) −15.2254 −0.801336
\(362\) 52.2851 2.74804
\(363\) 3.04948 0.160056
\(364\) −24.2750 −1.27236
\(365\) 0 0
\(366\) −57.4037 −3.00054
\(367\) −0.365949 −0.0191024 −0.00955119 0.999954i \(-0.503040\pi\)
−0.00955119 + 0.999954i \(0.503040\pi\)
\(368\) −3.43626 −0.179127
\(369\) −71.2935 −3.71139
\(370\) 0 0
\(371\) 10.7735 0.559335
\(372\) −0.230184 −0.0119345
\(373\) −2.18350 −0.113058 −0.0565288 0.998401i \(-0.518003\pi\)
−0.0565288 + 0.998401i \(0.518003\pi\)
\(374\) −22.9149 −1.18490
\(375\) 0 0
\(376\) −17.4612 −0.900495
\(377\) 29.1784 1.50276
\(378\) −27.0666 −1.39216
\(379\) −13.9764 −0.717918 −0.358959 0.933353i \(-0.616868\pi\)
−0.358959 + 0.933353i \(0.616868\pi\)
\(380\) 0 0
\(381\) 21.3703 1.09483
\(382\) 48.3685 2.47475
\(383\) 15.8694 0.810889 0.405445 0.914120i \(-0.367117\pi\)
0.405445 + 0.914120i \(0.367117\pi\)
\(384\) −62.6872 −3.19899
\(385\) 0 0
\(386\) −63.5962 −3.23696
\(387\) −12.5316 −0.637016
\(388\) −36.0181 −1.82854
\(389\) 9.38084 0.475627 0.237814 0.971311i \(-0.423569\pi\)
0.237814 + 0.971311i \(0.423569\pi\)
\(390\) 0 0
\(391\) −2.97980 −0.150695
\(392\) −4.62785 −0.233742
\(393\) −5.64231 −0.284617
\(394\) 56.5763 2.85027
\(395\) 0 0
\(396\) 81.5034 4.09570
\(397\) −23.0501 −1.15685 −0.578424 0.815736i \(-0.696332\pi\)
−0.578424 + 0.815736i \(0.696332\pi\)
\(398\) 5.63301 0.282358
\(399\) −6.01835 −0.301295
\(400\) 0 0
\(401\) 14.9886 0.748495 0.374248 0.927329i \(-0.377901\pi\)
0.374248 + 0.927329i \(0.377901\pi\)
\(402\) −35.9777 −1.79440
\(403\) 0.118320 0.00589392
\(404\) −51.2279 −2.54868
\(405\) 0 0
\(406\) 11.4041 0.565977
\(407\) −18.3356 −0.908860
\(408\) 42.7177 2.11484
\(409\) 2.73183 0.135080 0.0675402 0.997717i \(-0.478485\pi\)
0.0675402 + 0.997717i \(0.478485\pi\)
\(410\) 0 0
\(411\) −46.8029 −2.30862
\(412\) −78.3157 −3.85834
\(413\) −2.73236 −0.134451
\(414\) 16.0274 0.787702
\(415\) 0 0
\(416\) 5.63178 0.276121
\(417\) 30.0932 1.47367
\(418\) 14.9406 0.730766
\(419\) 10.8024 0.527734 0.263867 0.964559i \(-0.415002\pi\)
0.263867 + 0.964559i \(0.415002\pi\)
\(420\) 0 0
\(421\) 29.8658 1.45557 0.727786 0.685805i \(-0.240550\pi\)
0.727786 + 0.685805i \(0.240550\pi\)
\(422\) −20.7911 −1.01210
\(423\) 24.8866 1.21003
\(424\) 49.8583 2.42133
\(425\) 0 0
\(426\) −8.42896 −0.408384
\(427\) 7.62617 0.369056
\(428\) −1.16072 −0.0561053
\(429\) −60.9496 −2.94268
\(430\) 0 0
\(431\) −27.2852 −1.31428 −0.657142 0.753767i \(-0.728235\pi\)
−0.657142 + 0.753767i \(0.728235\pi\)
\(432\) −38.2761 −1.84156
\(433\) −2.14596 −0.103128 −0.0515642 0.998670i \(-0.516421\pi\)
−0.0515642 + 0.998670i \(0.516421\pi\)
\(434\) 0.0462443 0.00221980
\(435\) 0 0
\(436\) 47.1125 2.25628
\(437\) 1.94284 0.0929385
\(438\) 101.206 4.83580
\(439\) −17.9322 −0.855857 −0.427928 0.903813i \(-0.640756\pi\)
−0.427928 + 0.903813i \(0.640756\pi\)
\(440\) 0 0
\(441\) 6.59584 0.314087
\(442\) −45.0165 −2.14122
\(443\) 0.703849 0.0334409 0.0167204 0.999860i \(-0.494677\pi\)
0.0167204 + 0.999860i \(0.494677\pi\)
\(444\) 70.0754 3.32563
\(445\) 0 0
\(446\) 3.55413 0.168293
\(447\) −54.2027 −2.56370
\(448\) 9.07366 0.428690
\(449\) 2.27750 0.107482 0.0537410 0.998555i \(-0.482885\pi\)
0.0537410 + 0.998555i \(0.482885\pi\)
\(450\) 0 0
\(451\) −34.2072 −1.61075
\(452\) 73.8263 3.47250
\(453\) 48.4651 2.27709
\(454\) −26.8009 −1.25783
\(455\) 0 0
\(456\) −27.8520 −1.30429
\(457\) 17.6083 0.823684 0.411842 0.911255i \(-0.364886\pi\)
0.411842 + 0.911255i \(0.364886\pi\)
\(458\) −44.1791 −2.06435
\(459\) −33.1916 −1.54925
\(460\) 0 0
\(461\) 29.1980 1.35989 0.679943 0.733265i \(-0.262005\pi\)
0.679943 + 0.733265i \(0.262005\pi\)
\(462\) −23.8216 −1.10828
\(463\) −9.77411 −0.454241 −0.227121 0.973867i \(-0.572931\pi\)
−0.227121 + 0.973867i \(0.572931\pi\)
\(464\) 16.1271 0.748680
\(465\) 0 0
\(466\) −35.6307 −1.65056
\(467\) −14.3400 −0.663578 −0.331789 0.943354i \(-0.607652\pi\)
−0.331789 + 0.943354i \(0.607652\pi\)
\(468\) 160.114 7.40128
\(469\) 4.77968 0.220705
\(470\) 0 0
\(471\) 8.67032 0.399507
\(472\) −12.6450 −0.582032
\(473\) −6.01276 −0.276467
\(474\) −110.116 −5.05780
\(475\) 0 0
\(476\) −11.6347 −0.533276
\(477\) −71.0605 −3.25364
\(478\) −55.6459 −2.54519
\(479\) 3.59305 0.164171 0.0820853 0.996625i \(-0.473842\pi\)
0.0820853 + 0.996625i \(0.473842\pi\)
\(480\) 0 0
\(481\) −36.0204 −1.64239
\(482\) −9.90851 −0.451320
\(483\) −3.09771 −0.140951
\(484\) −3.84372 −0.174715
\(485\) 0 0
\(486\) 29.5822 1.34188
\(487\) −13.7061 −0.621081 −0.310540 0.950560i \(-0.600510\pi\)
−0.310540 + 0.950560i \(0.600510\pi\)
\(488\) 35.2927 1.59763
\(489\) −37.2190 −1.68310
\(490\) 0 0
\(491\) −7.45921 −0.336629 −0.168315 0.985733i \(-0.553832\pi\)
−0.168315 + 0.985733i \(0.553832\pi\)
\(492\) 130.734 5.89396
\(493\) 13.9848 0.629844
\(494\) 29.3508 1.32056
\(495\) 0 0
\(496\) 0.0653960 0.00293637
\(497\) 1.11980 0.0502299
\(498\) −17.9264 −0.803300
\(499\) −26.5609 −1.18903 −0.594515 0.804085i \(-0.702656\pi\)
−0.594515 + 0.804085i \(0.702656\pi\)
\(500\) 0 0
\(501\) 48.6921 2.17540
\(502\) −50.2066 −2.24083
\(503\) 16.6429 0.742072 0.371036 0.928618i \(-0.379003\pi\)
0.371036 + 0.928618i \(0.379003\pi\)
\(504\) 30.5245 1.35967
\(505\) 0 0
\(506\) 7.69007 0.341865
\(507\) −79.4657 −3.52920
\(508\) −26.9362 −1.19510
\(509\) −28.9693 −1.28404 −0.642020 0.766688i \(-0.721904\pi\)
−0.642020 + 0.766688i \(0.721904\pi\)
\(510\) 0 0
\(511\) −13.4453 −0.594787
\(512\) 34.9177 1.54316
\(513\) 21.6410 0.955474
\(514\) 48.3703 2.13352
\(515\) 0 0
\(516\) 22.9798 1.01163
\(517\) 11.9408 0.525157
\(518\) −14.0783 −0.618563
\(519\) 40.1344 1.76171
\(520\) 0 0
\(521\) −26.7916 −1.17376 −0.586881 0.809673i \(-0.699644\pi\)
−0.586881 + 0.809673i \(0.699644\pi\)
\(522\) −75.2197 −3.29228
\(523\) −5.81521 −0.254281 −0.127141 0.991885i \(-0.540580\pi\)
−0.127141 + 0.991885i \(0.540580\pi\)
\(524\) 7.11186 0.310683
\(525\) 0 0
\(526\) 16.7149 0.728805
\(527\) 0.0567091 0.00247029
\(528\) −33.6872 −1.46605
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 18.0222 0.782098
\(532\) 7.58585 0.328888
\(533\) −67.2004 −2.91077
\(534\) 11.6779 0.505351
\(535\) 0 0
\(536\) 22.1196 0.955423
\(537\) −32.9356 −1.42128
\(538\) −47.8409 −2.06257
\(539\) 3.16474 0.136315
\(540\) 0 0
\(541\) −4.58459 −0.197107 −0.0985535 0.995132i \(-0.531422\pi\)
−0.0985535 + 0.995132i \(0.531422\pi\)
\(542\) 72.9230 3.13231
\(543\) 66.6540 2.86040
\(544\) 2.69924 0.115729
\(545\) 0 0
\(546\) −46.7978 −2.00276
\(547\) 18.9427 0.809933 0.404967 0.914331i \(-0.367283\pi\)
0.404967 + 0.914331i \(0.367283\pi\)
\(548\) 58.9929 2.52005
\(549\) −50.3009 −2.14679
\(550\) 0 0
\(551\) −9.11813 −0.388445
\(552\) −14.3357 −0.610170
\(553\) 14.6291 0.622091
\(554\) 57.3968 2.43856
\(555\) 0 0
\(556\) −37.9311 −1.60864
\(557\) 0.0110934 0.000470043 0 0.000235022 1.00000i \(-0.499925\pi\)
0.000235022 1.00000i \(0.499925\pi\)
\(558\) −0.305020 −0.0129125
\(559\) −11.8121 −0.499600
\(560\) 0 0
\(561\) −29.2124 −1.23335
\(562\) −35.3137 −1.48962
\(563\) 3.35339 0.141329 0.0706643 0.997500i \(-0.477488\pi\)
0.0706643 + 0.997500i \(0.477488\pi\)
\(564\) −45.6358 −1.92161
\(565\) 0 0
\(566\) 69.4158 2.91776
\(567\) −14.7175 −0.618079
\(568\) 5.18226 0.217443
\(569\) −17.9798 −0.753753 −0.376876 0.926264i \(-0.623002\pi\)
−0.376876 + 0.926264i \(0.623002\pi\)
\(570\) 0 0
\(571\) 34.8932 1.46023 0.730117 0.683322i \(-0.239466\pi\)
0.730117 + 0.683322i \(0.239466\pi\)
\(572\) 76.8241 3.21218
\(573\) 61.6612 2.57593
\(574\) −26.2647 −1.09627
\(575\) 0 0
\(576\) −59.8483 −2.49368
\(577\) 3.05779 0.127298 0.0636488 0.997972i \(-0.479726\pi\)
0.0636488 + 0.997972i \(0.479726\pi\)
\(578\) 19.7329 0.820779
\(579\) −81.0737 −3.36931
\(580\) 0 0
\(581\) 2.38154 0.0988031
\(582\) −69.4363 −2.87823
\(583\) −34.0955 −1.41209
\(584\) −62.2230 −2.57481
\(585\) 0 0
\(586\) 58.0408 2.39764
\(587\) 1.13533 0.0468600 0.0234300 0.999725i \(-0.492541\pi\)
0.0234300 + 0.999725i \(0.492541\pi\)
\(588\) −12.0951 −0.498794
\(589\) −0.0369745 −0.00152351
\(590\) 0 0
\(591\) 72.1246 2.96681
\(592\) −19.9087 −0.818241
\(593\) −33.4469 −1.37350 −0.686749 0.726895i \(-0.740963\pi\)
−0.686749 + 0.726895i \(0.740963\pi\)
\(594\) 85.6587 3.51462
\(595\) 0 0
\(596\) 68.3200 2.79850
\(597\) 7.18108 0.293902
\(598\) 15.1072 0.617780
\(599\) 13.7401 0.561405 0.280702 0.959795i \(-0.409433\pi\)
0.280702 + 0.959795i \(0.409433\pi\)
\(600\) 0 0
\(601\) 18.5817 0.757963 0.378982 0.925404i \(-0.376274\pi\)
0.378982 + 0.925404i \(0.376274\pi\)
\(602\) −4.61667 −0.188161
\(603\) −31.5260 −1.28384
\(604\) −61.0879 −2.48563
\(605\) 0 0
\(606\) −98.7580 −4.01177
\(607\) 19.3287 0.784528 0.392264 0.919853i \(-0.371692\pi\)
0.392264 + 0.919853i \(0.371692\pi\)
\(608\) −1.75991 −0.0713738
\(609\) 14.5382 0.589118
\(610\) 0 0
\(611\) 23.4578 0.949002
\(612\) 76.7406 3.10206
\(613\) 11.4780 0.463591 0.231796 0.972764i \(-0.425540\pi\)
0.231796 + 0.972764i \(0.425540\pi\)
\(614\) 53.0534 2.14106
\(615\) 0 0
\(616\) 14.6459 0.590101
\(617\) −0.0442936 −0.00178319 −0.000891596 1.00000i \(-0.500284\pi\)
−0.000891596 1.00000i \(0.500284\pi\)
\(618\) −150.978 −6.07324
\(619\) 44.4063 1.78484 0.892419 0.451207i \(-0.149006\pi\)
0.892419 + 0.451207i \(0.149006\pi\)
\(620\) 0 0
\(621\) 11.1389 0.446988
\(622\) −6.07762 −0.243690
\(623\) −1.55142 −0.0621564
\(624\) −66.1789 −2.64927
\(625\) 0 0
\(626\) 48.4815 1.93771
\(627\) 19.0465 0.760645
\(628\) −10.9285 −0.436096
\(629\) −17.2641 −0.688364
\(630\) 0 0
\(631\) 37.3090 1.48525 0.742623 0.669709i \(-0.233581\pi\)
0.742623 + 0.669709i \(0.233581\pi\)
\(632\) 67.7011 2.69300
\(633\) −26.5049 −1.05348
\(634\) 3.17966 0.126280
\(635\) 0 0
\(636\) 130.307 5.16701
\(637\) 6.21716 0.246333
\(638\) −36.0911 −1.42886
\(639\) −7.38601 −0.292186
\(640\) 0 0
\(641\) −7.27191 −0.287223 −0.143612 0.989634i \(-0.545872\pi\)
−0.143612 + 0.989634i \(0.545872\pi\)
\(642\) −2.23765 −0.0883128
\(643\) 48.9722 1.93128 0.965638 0.259889i \(-0.0836860\pi\)
0.965638 + 0.259889i \(0.0836860\pi\)
\(644\) 3.90452 0.153860
\(645\) 0 0
\(646\) 14.0675 0.553477
\(647\) 38.8836 1.52867 0.764337 0.644817i \(-0.223066\pi\)
0.764337 + 0.644817i \(0.223066\pi\)
\(648\) −68.1105 −2.67563
\(649\) 8.64722 0.339433
\(650\) 0 0
\(651\) 0.0589531 0.00231055
\(652\) 46.9127 1.83724
\(653\) 46.8454 1.83320 0.916600 0.399804i \(-0.130922\pi\)
0.916600 + 0.399804i \(0.130922\pi\)
\(654\) 90.8243 3.55151
\(655\) 0 0
\(656\) −37.1421 −1.45015
\(657\) 88.6833 3.45986
\(658\) 9.16830 0.357417
\(659\) 1.86648 0.0727077 0.0363538 0.999339i \(-0.488426\pi\)
0.0363538 + 0.999339i \(0.488426\pi\)
\(660\) 0 0
\(661\) −1.20431 −0.0468421 −0.0234211 0.999726i \(-0.507456\pi\)
−0.0234211 + 0.999726i \(0.507456\pi\)
\(662\) 54.8917 2.13343
\(663\) −57.3879 −2.22876
\(664\) 11.0214 0.427714
\(665\) 0 0
\(666\) 92.8578 3.59817
\(667\) −4.69320 −0.181722
\(668\) −61.3740 −2.37463
\(669\) 4.53087 0.175174
\(670\) 0 0
\(671\) −24.1348 −0.931715
\(672\) 2.80605 0.108246
\(673\) −4.62815 −0.178402 −0.0892011 0.996014i \(-0.528431\pi\)
−0.0892011 + 0.996014i \(0.528431\pi\)
\(674\) −61.9384 −2.38578
\(675\) 0 0
\(676\) 100.163 3.85242
\(677\) 24.6057 0.945672 0.472836 0.881150i \(-0.343230\pi\)
0.472836 + 0.881150i \(0.343230\pi\)
\(678\) 142.324 5.46590
\(679\) 9.22472 0.354012
\(680\) 0 0
\(681\) −34.1663 −1.30925
\(682\) −0.146351 −0.00560407
\(683\) −8.48187 −0.324550 −0.162275 0.986746i \(-0.551883\pi\)
−0.162275 + 0.986746i \(0.551883\pi\)
\(684\) −50.0350 −1.91314
\(685\) 0 0
\(686\) 2.42992 0.0927749
\(687\) −56.3204 −2.14876
\(688\) −6.52863 −0.248902
\(689\) −66.9808 −2.55177
\(690\) 0 0
\(691\) 24.0039 0.913150 0.456575 0.889685i \(-0.349076\pi\)
0.456575 + 0.889685i \(0.349076\pi\)
\(692\) −50.5876 −1.92305
\(693\) −20.8741 −0.792941
\(694\) 5.36161 0.203524
\(695\) 0 0
\(696\) 67.2806 2.55026
\(697\) −32.2083 −1.21997
\(698\) 47.5114 1.79833
\(699\) −45.4227 −1.71805
\(700\) 0 0
\(701\) 40.6324 1.53467 0.767333 0.641249i \(-0.221583\pi\)
0.767333 + 0.641249i \(0.221583\pi\)
\(702\) 168.277 6.35122
\(703\) 11.2562 0.424536
\(704\) −28.7157 −1.08227
\(705\) 0 0
\(706\) 54.5177 2.05180
\(707\) 13.1201 0.493434
\(708\) −33.0482 −1.24203
\(709\) 40.4391 1.51872 0.759361 0.650670i \(-0.225512\pi\)
0.759361 + 0.650670i \(0.225512\pi\)
\(710\) 0 0
\(711\) −96.4909 −3.61869
\(712\) −7.17974 −0.269072
\(713\) −0.0190312 −0.000712723 0
\(714\) −22.4296 −0.839406
\(715\) 0 0
\(716\) 41.5138 1.55144
\(717\) −70.9386 −2.64925
\(718\) 75.5500 2.81950
\(719\) 34.7435 1.29572 0.647858 0.761761i \(-0.275665\pi\)
0.647858 + 0.761761i \(0.275665\pi\)
\(720\) 0 0
\(721\) 20.0577 0.746987
\(722\) 36.9965 1.37687
\(723\) −12.6316 −0.469773
\(724\) −84.0143 −3.12237
\(725\) 0 0
\(726\) −7.40999 −0.275011
\(727\) −33.7465 −1.25159 −0.625794 0.779988i \(-0.715225\pi\)
−0.625794 + 0.779988i \(0.715225\pi\)
\(728\) 28.7720 1.06636
\(729\) −6.44065 −0.238543
\(730\) 0 0
\(731\) −5.66140 −0.209394
\(732\) 92.2393 3.40926
\(733\) −25.1115 −0.927516 −0.463758 0.885962i \(-0.653499\pi\)
−0.463758 + 0.885962i \(0.653499\pi\)
\(734\) 0.889228 0.0328220
\(735\) 0 0
\(736\) −0.905845 −0.0333899
\(737\) −15.1264 −0.557190
\(738\) 173.238 6.37696
\(739\) −27.9564 −1.02839 −0.514196 0.857673i \(-0.671910\pi\)
−0.514196 + 0.857673i \(0.671910\pi\)
\(740\) 0 0
\(741\) 37.4170 1.37455
\(742\) −26.1789 −0.961057
\(743\) −25.4587 −0.933989 −0.466995 0.884260i \(-0.654663\pi\)
−0.466995 + 0.884260i \(0.654663\pi\)
\(744\) 0.272826 0.0100023
\(745\) 0 0
\(746\) 5.30575 0.194257
\(747\) −15.7083 −0.574736
\(748\) 36.8208 1.34630
\(749\) 0.297274 0.0108622
\(750\) 0 0
\(751\) 16.2105 0.591528 0.295764 0.955261i \(-0.404426\pi\)
0.295764 + 0.955261i \(0.404426\pi\)
\(752\) 12.9653 0.472796
\(753\) −64.0044 −2.33245
\(754\) −70.9012 −2.58207
\(755\) 0 0
\(756\) 43.4920 1.58179
\(757\) −9.54004 −0.346739 −0.173369 0.984857i \(-0.555465\pi\)
−0.173369 + 0.984857i \(0.555465\pi\)
\(758\) 33.9615 1.23354
\(759\) 9.80346 0.355843
\(760\) 0 0
\(761\) −41.8640 −1.51757 −0.758784 0.651342i \(-0.774206\pi\)
−0.758784 + 0.651342i \(0.774206\pi\)
\(762\) −51.9281 −1.88116
\(763\) −12.0661 −0.436824
\(764\) −77.7210 −2.81185
\(765\) 0 0
\(766\) −38.5614 −1.39328
\(767\) 16.9875 0.613384
\(768\) 96.1098 3.46806
\(769\) −4.24418 −0.153049 −0.0765244 0.997068i \(-0.524382\pi\)
−0.0765244 + 0.997068i \(0.524382\pi\)
\(770\) 0 0
\(771\) 61.6635 2.22076
\(772\) 102.190 3.67789
\(773\) −36.4215 −1.30999 −0.654994 0.755634i \(-0.727329\pi\)
−0.654994 + 0.755634i \(0.727329\pi\)
\(774\) 30.4508 1.09453
\(775\) 0 0
\(776\) 42.6906 1.53250
\(777\) −17.9472 −0.643854
\(778\) −22.7947 −0.817230
\(779\) 20.9999 0.752398
\(780\) 0 0
\(781\) −3.54387 −0.126810
\(782\) 7.24069 0.258926
\(783\) −52.2770 −1.86823
\(784\) 3.43626 0.122724
\(785\) 0 0
\(786\) 13.7104 0.489033
\(787\) 42.4245 1.51227 0.756135 0.654415i \(-0.227085\pi\)
0.756135 + 0.654415i \(0.227085\pi\)
\(788\) −90.9097 −3.23852
\(789\) 21.3085 0.758603
\(790\) 0 0
\(791\) −18.9079 −0.672287
\(792\) −96.6021 −3.43261
\(793\) −47.4131 −1.68369
\(794\) 56.0098 1.98772
\(795\) 0 0
\(796\) −9.05142 −0.320819
\(797\) 49.6964 1.76034 0.880169 0.474660i \(-0.157429\pi\)
0.880169 + 0.474660i \(0.157429\pi\)
\(798\) 14.6241 0.517689
\(799\) 11.2430 0.397750
\(800\) 0 0
\(801\) 10.2329 0.361562
\(802\) −36.4212 −1.28608
\(803\) 42.5510 1.50159
\(804\) 57.8108 2.03883
\(805\) 0 0
\(806\) −0.287508 −0.0101270
\(807\) −60.9886 −2.14690
\(808\) 60.7180 2.13605
\(809\) 44.5145 1.56505 0.782524 0.622621i \(-0.213932\pi\)
0.782524 + 0.622621i \(0.213932\pi\)
\(810\) 0 0
\(811\) −30.3020 −1.06405 −0.532023 0.846730i \(-0.678568\pi\)
−0.532023 + 0.846730i \(0.678568\pi\)
\(812\) −18.3247 −0.643072
\(813\) 92.9637 3.26038
\(814\) 44.5540 1.56162
\(815\) 0 0
\(816\) −31.7187 −1.11038
\(817\) 3.69124 0.129140
\(818\) −6.63814 −0.232097
\(819\) −41.0073 −1.43291
\(820\) 0 0
\(821\) −0.318150 −0.0111035 −0.00555176 0.999985i \(-0.501767\pi\)
−0.00555176 + 0.999985i \(0.501767\pi\)
\(822\) 113.727 3.96670
\(823\) 12.0689 0.420695 0.210348 0.977627i \(-0.432540\pi\)
0.210348 + 0.977627i \(0.432540\pi\)
\(824\) 92.8239 3.23367
\(825\) 0 0
\(826\) 6.63943 0.231015
\(827\) −14.4275 −0.501692 −0.250846 0.968027i \(-0.580709\pi\)
−0.250846 + 0.968027i \(0.580709\pi\)
\(828\) −25.7536 −0.894999
\(829\) 29.7311 1.03260 0.516301 0.856407i \(-0.327308\pi\)
0.516301 + 0.856407i \(0.327308\pi\)
\(830\) 0 0
\(831\) 73.1706 2.53826
\(832\) −56.4123 −1.95575
\(833\) 2.97980 0.103244
\(834\) −73.1241 −2.53208
\(835\) 0 0
\(836\) −24.0072 −0.830308
\(837\) −0.211986 −0.00732730
\(838\) −26.2491 −0.906760
\(839\) −31.1191 −1.07435 −0.537176 0.843470i \(-0.680509\pi\)
−0.537176 + 0.843470i \(0.680509\pi\)
\(840\) 0 0
\(841\) −6.97385 −0.240478
\(842\) −72.5717 −2.50098
\(843\) −45.0186 −1.55052
\(844\) 33.4082 1.14996
\(845\) 0 0
\(846\) −60.4726 −2.07909
\(847\) 0.984428 0.0338253
\(848\) −37.0207 −1.27130
\(849\) 88.4926 3.03706
\(850\) 0 0
\(851\) 5.79370 0.198606
\(852\) 13.5441 0.464013
\(853\) −28.9135 −0.989980 −0.494990 0.868899i \(-0.664828\pi\)
−0.494990 + 0.868899i \(0.664828\pi\)
\(854\) −18.5310 −0.634118
\(855\) 0 0
\(856\) 1.37574 0.0470218
\(857\) −5.51431 −0.188365 −0.0941827 0.995555i \(-0.530024\pi\)
−0.0941827 + 0.995555i \(0.530024\pi\)
\(858\) 148.103 5.05615
\(859\) −25.5513 −0.871798 −0.435899 0.899995i \(-0.643570\pi\)
−0.435899 + 0.899995i \(0.643570\pi\)
\(860\) 0 0
\(861\) −33.4828 −1.14109
\(862\) 66.3010 2.25822
\(863\) −35.9398 −1.22341 −0.611703 0.791087i \(-0.709515\pi\)
−0.611703 + 0.791087i \(0.709515\pi\)
\(864\) −10.0901 −0.343272
\(865\) 0 0
\(866\) 5.21452 0.177197
\(867\) 25.1559 0.854338
\(868\) −0.0743076 −0.00252217
\(869\) −46.2972 −1.57052
\(870\) 0 0
\(871\) −29.7160 −1.00689
\(872\) −55.8402 −1.89099
\(873\) −60.8447 −2.05928
\(874\) −4.72094 −0.159688
\(875\) 0 0
\(876\) −162.623 −5.49452
\(877\) −18.3007 −0.617971 −0.308986 0.951067i \(-0.599990\pi\)
−0.308986 + 0.951067i \(0.599990\pi\)
\(878\) 43.5738 1.47055
\(879\) 73.9916 2.49567
\(880\) 0 0
\(881\) 29.8245 1.00481 0.502407 0.864631i \(-0.332448\pi\)
0.502407 + 0.864631i \(0.332448\pi\)
\(882\) −16.0274 −0.539670
\(883\) 14.2733 0.480336 0.240168 0.970731i \(-0.422797\pi\)
0.240168 + 0.970731i \(0.422797\pi\)
\(884\) 72.3348 2.43288
\(885\) 0 0
\(886\) −1.71030 −0.0574586
\(887\) 45.0595 1.51295 0.756475 0.654023i \(-0.226920\pi\)
0.756475 + 0.654023i \(0.226920\pi\)
\(888\) −83.0571 −2.78721
\(889\) 6.89872 0.231376
\(890\) 0 0
\(891\) 46.5772 1.56039
\(892\) −5.71095 −0.191217
\(893\) −7.33048 −0.245305
\(894\) 131.708 4.40499
\(895\) 0 0
\(896\) −20.2366 −0.676057
\(897\) 19.2590 0.643038
\(898\) −5.53415 −0.184677
\(899\) 0.0893171 0.00297889
\(900\) 0 0
\(901\) −32.1030 −1.06951
\(902\) 83.1209 2.76762
\(903\) −5.88542 −0.195855
\(904\) −87.5028 −2.91030
\(905\) 0 0
\(906\) −117.766 −3.91252
\(907\) 4.89799 0.162635 0.0813175 0.996688i \(-0.474087\pi\)
0.0813175 + 0.996688i \(0.474087\pi\)
\(908\) 43.0650 1.42916
\(909\) −86.5383 −2.87030
\(910\) 0 0
\(911\) −38.6033 −1.27899 −0.639493 0.768797i \(-0.720855\pi\)
−0.639493 + 0.768797i \(0.720855\pi\)
\(912\) 20.6806 0.684804
\(913\) −7.53696 −0.249437
\(914\) −42.7869 −1.41527
\(915\) 0 0
\(916\) 70.9892 2.34555
\(917\) −1.82144 −0.0601493
\(918\) 80.6531 2.66195
\(919\) 18.2605 0.602358 0.301179 0.953568i \(-0.402620\pi\)
0.301179 + 0.953568i \(0.402620\pi\)
\(920\) 0 0
\(921\) 67.6335 2.22860
\(922\) −70.9488 −2.33657
\(923\) −6.96197 −0.229156
\(924\) 38.2778 1.25925
\(925\) 0 0
\(926\) 23.7503 0.780484
\(927\) −132.297 −4.34521
\(928\) 4.25131 0.139556
\(929\) −36.0755 −1.18360 −0.591799 0.806086i \(-0.701582\pi\)
−0.591799 + 0.806086i \(0.701582\pi\)
\(930\) 0 0
\(931\) −1.94284 −0.0636739
\(932\) 57.2532 1.87539
\(933\) −7.74788 −0.253654
\(934\) 34.8452 1.14017
\(935\) 0 0
\(936\) −189.776 −6.20301
\(937\) −48.0248 −1.56890 −0.784451 0.620190i \(-0.787055\pi\)
−0.784451 + 0.620190i \(0.787055\pi\)
\(938\) −11.6143 −0.379219
\(939\) 61.8052 2.01694
\(940\) 0 0
\(941\) −6.23415 −0.203227 −0.101614 0.994824i \(-0.532401\pi\)
−0.101614 + 0.994824i \(0.532401\pi\)
\(942\) −21.0682 −0.686440
\(943\) 10.8089 0.351985
\(944\) 9.38912 0.305590
\(945\) 0 0
\(946\) 14.6106 0.475030
\(947\) 21.9266 0.712519 0.356260 0.934387i \(-0.384052\pi\)
0.356260 + 0.934387i \(0.384052\pi\)
\(948\) 176.940 5.74674
\(949\) 83.5918 2.71350
\(950\) 0 0
\(951\) 4.05350 0.131444
\(952\) 13.7901 0.446939
\(953\) 46.6376 1.51074 0.755371 0.655298i \(-0.227457\pi\)
0.755371 + 0.655298i \(0.227457\pi\)
\(954\) 172.672 5.59045
\(955\) 0 0
\(956\) 89.4147 2.89188
\(957\) −46.0096 −1.48728
\(958\) −8.73083 −0.282080
\(959\) −15.1089 −0.487890
\(960\) 0 0
\(961\) −30.9996 −0.999988
\(962\) 87.5267 2.82197
\(963\) −1.96077 −0.0631850
\(964\) 15.9215 0.512797
\(965\) 0 0
\(966\) 7.52721 0.242184
\(967\) −38.2271 −1.22930 −0.614650 0.788800i \(-0.710703\pi\)
−0.614650 + 0.788800i \(0.710703\pi\)
\(968\) 4.55578 0.146428
\(969\) 17.9335 0.576107
\(970\) 0 0
\(971\) 3.22879 0.103617 0.0518084 0.998657i \(-0.483501\pi\)
0.0518084 + 0.998657i \(0.483501\pi\)
\(972\) −47.5342 −1.52466
\(973\) 9.71464 0.311437
\(974\) 33.3047 1.06715
\(975\) 0 0
\(976\) −26.2055 −0.838818
\(977\) −49.3683 −1.57943 −0.789716 0.613472i \(-0.789772\pi\)
−0.789716 + 0.613472i \(0.789772\pi\)
\(978\) 90.4392 2.89193
\(979\) 4.90984 0.156919
\(980\) 0 0
\(981\) 79.5863 2.54099
\(982\) 18.1253 0.578402
\(983\) 24.6436 0.786010 0.393005 0.919536i \(-0.371435\pi\)
0.393005 + 0.919536i \(0.371435\pi\)
\(984\) −154.953 −4.93972
\(985\) 0 0
\(986\) −33.9820 −1.08221
\(987\) 11.6879 0.372031
\(988\) −47.1624 −1.50044
\(989\) 1.89992 0.0604141
\(990\) 0 0
\(991\) 28.7831 0.914324 0.457162 0.889384i \(-0.348866\pi\)
0.457162 + 0.889384i \(0.348866\pi\)
\(992\) 0.0172393 0.000547348 0
\(993\) 69.9770 2.22065
\(994\) −2.72103 −0.0863057
\(995\) 0 0
\(996\) 28.8050 0.912722
\(997\) −17.1504 −0.543159 −0.271579 0.962416i \(-0.587546\pi\)
−0.271579 + 0.962416i \(0.587546\pi\)
\(998\) 64.5410 2.04301
\(999\) 64.5353 2.04181
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 4025.2.a.z.1.2 14
5.4 even 2 4025.2.a.bc.1.13 yes 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4025.2.a.z.1.2 14 1.1 even 1 trivial
4025.2.a.bc.1.13 yes 14 5.4 even 2