Properties

Label 2695.2.a.y.1.1
Level $2695$
Weight $2$
Character 2695.1
Self dual yes
Analytic conductor $21.520$
Analytic rank $0$
Dimension $10$
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] = [2695,2,Mod(1,2695)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2695, 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("2695.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2695 = 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2695.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: \(21.5196833447\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 51x^{6} - 184x^{5} - 45x^{4} + 297x^{3} - 59x^{2} - 109x + 21 \) 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 385)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.47520\) of defining polynomial
Character \(\chi\) \(=\) 2695.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.47520 q^{2} -3.19739 q^{3} +4.12660 q^{4} -1.00000 q^{5} +7.91417 q^{6} -5.26377 q^{8} +7.22329 q^{9} +O(q^{10})\) \(q-2.47520 q^{2} -3.19739 q^{3} +4.12660 q^{4} -1.00000 q^{5} +7.91417 q^{6} -5.26377 q^{8} +7.22329 q^{9} +2.47520 q^{10} +1.00000 q^{11} -13.1944 q^{12} -1.36166 q^{13} +3.19739 q^{15} +4.77565 q^{16} +2.83708 q^{17} -17.8791 q^{18} -2.20953 q^{19} -4.12660 q^{20} -2.47520 q^{22} +6.51211 q^{23} +16.8303 q^{24} +1.00000 q^{25} +3.37039 q^{26} -13.5035 q^{27} +6.29233 q^{29} -7.91417 q^{30} +10.3303 q^{31} -1.29316 q^{32} -3.19739 q^{33} -7.02233 q^{34} +29.8077 q^{36} +7.81172 q^{37} +5.46902 q^{38} +4.35377 q^{39} +5.26377 q^{40} +3.91618 q^{41} -9.47126 q^{43} +4.12660 q^{44} -7.22329 q^{45} -16.1188 q^{46} -1.14620 q^{47} -15.2696 q^{48} -2.47520 q^{50} -9.07124 q^{51} -5.61905 q^{52} +8.33037 q^{53} +33.4239 q^{54} -1.00000 q^{55} +7.06472 q^{57} -15.5748 q^{58} +2.25466 q^{59} +13.1944 q^{60} +6.02240 q^{61} -25.5695 q^{62} -6.35049 q^{64} +1.36166 q^{65} +7.91417 q^{66} -8.71012 q^{67} +11.7075 q^{68} -20.8218 q^{69} -2.86988 q^{71} -38.0217 q^{72} -11.7962 q^{73} -19.3355 q^{74} -3.19739 q^{75} -9.11784 q^{76} -10.7764 q^{78} +8.75950 q^{79} -4.77565 q^{80} +21.5061 q^{81} -9.69331 q^{82} +8.61026 q^{83} -2.83708 q^{85} +23.4432 q^{86} -20.1190 q^{87} -5.26377 q^{88} -10.4755 q^{89} +17.8791 q^{90} +26.8729 q^{92} -33.0300 q^{93} +2.83708 q^{94} +2.20953 q^{95} +4.13472 q^{96} +2.85280 q^{97} +7.22329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 3 q^{2} - 3 q^{3} + 15 q^{4} - 10 q^{5} + 5 q^{6} + 9 q^{8} + 19 q^{9} - 3 q^{10} + 10 q^{11} - 3 q^{12} - 6 q^{13} + 3 q^{15} + 21 q^{16} - 5 q^{17} + q^{18} + q^{19} - 15 q^{20} + 3 q^{22} + 18 q^{23} + 10 q^{24} + 10 q^{25} + 13 q^{26} - 15 q^{27} + 14 q^{29} - 5 q^{30} + 10 q^{31} + 46 q^{32} - 3 q^{33} - 2 q^{34} + 26 q^{36} + 13 q^{37} + 9 q^{38} + 3 q^{39} - 9 q^{40} - 7 q^{41} + 6 q^{43} + 15 q^{44} - 19 q^{45} + 10 q^{46} + q^{47} - 35 q^{48} + 3 q^{50} + 9 q^{51} - 17 q^{52} + 16 q^{53} + 73 q^{54} - 10 q^{55} + 12 q^{57} - 9 q^{58} + 13 q^{59} + 3 q^{60} + 18 q^{61} + 14 q^{62} + 43 q^{64} + 6 q^{65} + 5 q^{66} + 29 q^{67} + 13 q^{68} + 19 q^{71} - 48 q^{72} - 31 q^{73} - 8 q^{74} - 3 q^{75} - 8 q^{76} + 3 q^{78} - 21 q^{80} + 42 q^{81} + q^{82} - 2 q^{83} + 5 q^{85} + 10 q^{86} - 50 q^{87} + 9 q^{88} + 23 q^{89} - q^{90} + 14 q^{92} + 4 q^{93} - 5 q^{94} - q^{95} + 39 q^{96} - 43 q^{97} + 19 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.47520 −1.75023 −0.875115 0.483916i \(-0.839214\pi\)
−0.875115 + 0.483916i \(0.839214\pi\)
\(3\) −3.19739 −1.84601 −0.923007 0.384784i \(-0.874276\pi\)
−0.923007 + 0.384784i \(0.874276\pi\)
\(4\) 4.12660 2.06330
\(5\) −1.00000 −0.447214
\(6\) 7.91417 3.23095
\(7\) 0 0
\(8\) −5.26377 −1.86102
\(9\) 7.22329 2.40776
\(10\) 2.47520 0.782726
\(11\) 1.00000 0.301511
\(12\) −13.1944 −3.80888
\(13\) −1.36166 −0.377658 −0.188829 0.982010i \(-0.560469\pi\)
−0.188829 + 0.982010i \(0.560469\pi\)
\(14\) 0 0
\(15\) 3.19739 0.825562
\(16\) 4.77565 1.19391
\(17\) 2.83708 0.688092 0.344046 0.938953i \(-0.388202\pi\)
0.344046 + 0.938953i \(0.388202\pi\)
\(18\) −17.8791 −4.21414
\(19\) −2.20953 −0.506900 −0.253450 0.967348i \(-0.581565\pi\)
−0.253450 + 0.967348i \(0.581565\pi\)
\(20\) −4.12660 −0.922737
\(21\) 0 0
\(22\) −2.47520 −0.527714
\(23\) 6.51211 1.35787 0.678935 0.734199i \(-0.262442\pi\)
0.678935 + 0.734199i \(0.262442\pi\)
\(24\) 16.8303 3.43547
\(25\) 1.00000 0.200000
\(26\) 3.37039 0.660988
\(27\) −13.5035 −2.59875
\(28\) 0 0
\(29\) 6.29233 1.16846 0.584228 0.811590i \(-0.301397\pi\)
0.584228 + 0.811590i \(0.301397\pi\)
\(30\) −7.91417 −1.44492
\(31\) 10.3303 1.85538 0.927688 0.373355i \(-0.121793\pi\)
0.927688 + 0.373355i \(0.121793\pi\)
\(32\) −1.29316 −0.228600
\(33\) −3.19739 −0.556594
\(34\) −7.02233 −1.20432
\(35\) 0 0
\(36\) 29.8077 4.96795
\(37\) 7.81172 1.28424 0.642119 0.766605i \(-0.278055\pi\)
0.642119 + 0.766605i \(0.278055\pi\)
\(38\) 5.46902 0.887192
\(39\) 4.35377 0.697162
\(40\) 5.26377 0.832274
\(41\) 3.91618 0.611604 0.305802 0.952095i \(-0.401075\pi\)
0.305802 + 0.952095i \(0.401075\pi\)
\(42\) 0 0
\(43\) −9.47126 −1.44435 −0.722176 0.691709i \(-0.756858\pi\)
−0.722176 + 0.691709i \(0.756858\pi\)
\(44\) 4.12660 0.622109
\(45\) −7.22329 −1.07679
\(46\) −16.1188 −2.37658
\(47\) −1.14620 −0.167191 −0.0835954 0.996500i \(-0.526640\pi\)
−0.0835954 + 0.996500i \(0.526640\pi\)
\(48\) −15.2696 −2.20398
\(49\) 0 0
\(50\) −2.47520 −0.350046
\(51\) −9.07124 −1.27023
\(52\) −5.61905 −0.779222
\(53\) 8.33037 1.14426 0.572132 0.820161i \(-0.306116\pi\)
0.572132 + 0.820161i \(0.306116\pi\)
\(54\) 33.4239 4.54841
\(55\) −1.00000 −0.134840
\(56\) 0 0
\(57\) 7.06472 0.935745
\(58\) −15.5748 −2.04507
\(59\) 2.25466 0.293532 0.146766 0.989171i \(-0.453114\pi\)
0.146766 + 0.989171i \(0.453114\pi\)
\(60\) 13.1944 1.70338
\(61\) 6.02240 0.771089 0.385545 0.922689i \(-0.374014\pi\)
0.385545 + 0.922689i \(0.374014\pi\)
\(62\) −25.5695 −3.24733
\(63\) 0 0
\(64\) −6.35049 −0.793811
\(65\) 1.36166 0.168894
\(66\) 7.91417 0.974167
\(67\) −8.71012 −1.06411 −0.532055 0.846710i \(-0.678580\pi\)
−0.532055 + 0.846710i \(0.678580\pi\)
\(68\) 11.7075 1.41974
\(69\) −20.8218 −2.50664
\(70\) 0 0
\(71\) −2.86988 −0.340592 −0.170296 0.985393i \(-0.554472\pi\)
−0.170296 + 0.985393i \(0.554472\pi\)
\(72\) −38.0217 −4.48090
\(73\) −11.7962 −1.38064 −0.690322 0.723503i \(-0.742531\pi\)
−0.690322 + 0.723503i \(0.742531\pi\)
\(74\) −19.3355 −2.24771
\(75\) −3.19739 −0.369203
\(76\) −9.11784 −1.04589
\(77\) 0 0
\(78\) −10.7764 −1.22019
\(79\) 8.75950 0.985520 0.492760 0.870165i \(-0.335988\pi\)
0.492760 + 0.870165i \(0.335988\pi\)
\(80\) −4.77565 −0.533934
\(81\) 21.5061 2.38957
\(82\) −9.69331 −1.07045
\(83\) 8.61026 0.945099 0.472549 0.881304i \(-0.343334\pi\)
0.472549 + 0.881304i \(0.343334\pi\)
\(84\) 0 0
\(85\) −2.83708 −0.307724
\(86\) 23.4432 2.52795
\(87\) −20.1190 −2.15698
\(88\) −5.26377 −0.561119
\(89\) −10.4755 −1.11040 −0.555200 0.831717i \(-0.687358\pi\)
−0.555200 + 0.831717i \(0.687358\pi\)
\(90\) 17.8791 1.88462
\(91\) 0 0
\(92\) 26.8729 2.80169
\(93\) −33.0300 −3.42505
\(94\) 2.83708 0.292622
\(95\) 2.20953 0.226693
\(96\) 4.13472 0.421998
\(97\) 2.85280 0.289658 0.144829 0.989457i \(-0.453737\pi\)
0.144829 + 0.989457i \(0.453737\pi\)
\(98\) 0 0
\(99\) 7.22329 0.725968
\(100\) 4.12660 0.412660
\(101\) −1.89945 −0.189002 −0.0945010 0.995525i \(-0.530126\pi\)
−0.0945010 + 0.995525i \(0.530126\pi\)
\(102\) 22.4531 2.22319
\(103\) −8.56203 −0.843642 −0.421821 0.906679i \(-0.638609\pi\)
−0.421821 + 0.906679i \(0.638609\pi\)
\(104\) 7.16749 0.702830
\(105\) 0 0
\(106\) −20.6193 −2.00272
\(107\) 5.61803 0.543116 0.271558 0.962422i \(-0.412461\pi\)
0.271558 + 0.962422i \(0.412461\pi\)
\(108\) −55.7237 −5.36201
\(109\) −9.65700 −0.924972 −0.462486 0.886626i \(-0.653043\pi\)
−0.462486 + 0.886626i \(0.653043\pi\)
\(110\) 2.47520 0.236001
\(111\) −24.9771 −2.37072
\(112\) 0 0
\(113\) 14.0674 1.32335 0.661676 0.749790i \(-0.269846\pi\)
0.661676 + 0.749790i \(0.269846\pi\)
\(114\) −17.4866 −1.63777
\(115\) −6.51211 −0.607258
\(116\) 25.9659 2.41088
\(117\) −9.83571 −0.909311
\(118\) −5.58073 −0.513748
\(119\) 0 0
\(120\) −16.8303 −1.53639
\(121\) 1.00000 0.0909091
\(122\) −14.9066 −1.34958
\(123\) −12.5215 −1.12903
\(124\) 42.6291 3.82820
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −9.30320 −0.825526 −0.412763 0.910839i \(-0.635436\pi\)
−0.412763 + 0.910839i \(0.635436\pi\)
\(128\) 18.3050 1.61795
\(129\) 30.2833 2.66629
\(130\) −3.37039 −0.295603
\(131\) −15.7807 −1.37876 −0.689381 0.724399i \(-0.742118\pi\)
−0.689381 + 0.724399i \(0.742118\pi\)
\(132\) −13.1944 −1.14842
\(133\) 0 0
\(134\) 21.5593 1.86244
\(135\) 13.5035 1.16220
\(136\) −14.9337 −1.28056
\(137\) 6.69088 0.571641 0.285820 0.958283i \(-0.407734\pi\)
0.285820 + 0.958283i \(0.407734\pi\)
\(138\) 51.5380 4.38720
\(139\) −3.57182 −0.302958 −0.151479 0.988461i \(-0.548404\pi\)
−0.151479 + 0.988461i \(0.548404\pi\)
\(140\) 0 0
\(141\) 3.66485 0.308636
\(142\) 7.10353 0.596115
\(143\) −1.36166 −0.113868
\(144\) 34.4960 2.87466
\(145\) −6.29233 −0.522549
\(146\) 29.1980 2.41644
\(147\) 0 0
\(148\) 32.2359 2.64977
\(149\) −23.5761 −1.93143 −0.965717 0.259598i \(-0.916410\pi\)
−0.965717 + 0.259598i \(0.916410\pi\)
\(150\) 7.91417 0.646189
\(151\) 5.39014 0.438644 0.219322 0.975653i \(-0.429616\pi\)
0.219322 + 0.975653i \(0.429616\pi\)
\(152\) 11.6304 0.943353
\(153\) 20.4930 1.65676
\(154\) 0 0
\(155\) −10.3303 −0.829750
\(156\) 17.9663 1.43845
\(157\) 5.95318 0.475115 0.237558 0.971373i \(-0.423653\pi\)
0.237558 + 0.971373i \(0.423653\pi\)
\(158\) −21.6815 −1.72489
\(159\) −26.6354 −2.11233
\(160\) 1.29316 0.102233
\(161\) 0 0
\(162\) −53.2318 −4.18229
\(163\) −12.4822 −0.977679 −0.488840 0.872374i \(-0.662580\pi\)
−0.488840 + 0.872374i \(0.662580\pi\)
\(164\) 16.1605 1.26192
\(165\) 3.19739 0.248916
\(166\) −21.3121 −1.65414
\(167\) 17.6601 1.36658 0.683291 0.730146i \(-0.260548\pi\)
0.683291 + 0.730146i \(0.260548\pi\)
\(168\) 0 0
\(169\) −11.1459 −0.857374
\(170\) 7.02233 0.538588
\(171\) −15.9601 −1.22050
\(172\) −39.0841 −2.98014
\(173\) 2.91898 0.221926 0.110963 0.993825i \(-0.464606\pi\)
0.110963 + 0.993825i \(0.464606\pi\)
\(174\) 49.7985 3.77522
\(175\) 0 0
\(176\) 4.77565 0.359978
\(177\) −7.20903 −0.541864
\(178\) 25.9289 1.94346
\(179\) −17.9474 −1.34145 −0.670725 0.741706i \(-0.734017\pi\)
−0.670725 + 0.741706i \(0.734017\pi\)
\(180\) −29.8077 −2.22173
\(181\) 11.9052 0.884906 0.442453 0.896792i \(-0.354108\pi\)
0.442453 + 0.896792i \(0.354108\pi\)
\(182\) 0 0
\(183\) −19.2559 −1.42344
\(184\) −34.2782 −2.52703
\(185\) −7.81172 −0.574329
\(186\) 81.7557 5.99462
\(187\) 2.83708 0.207468
\(188\) −4.72992 −0.344965
\(189\) 0 0
\(190\) −5.46902 −0.396764
\(191\) 6.88513 0.498190 0.249095 0.968479i \(-0.419867\pi\)
0.249095 + 0.968479i \(0.419867\pi\)
\(192\) 20.3050 1.46539
\(193\) 1.65966 0.119465 0.0597323 0.998214i \(-0.480975\pi\)
0.0597323 + 0.998214i \(0.480975\pi\)
\(194\) −7.06125 −0.506968
\(195\) −4.35377 −0.311780
\(196\) 0 0
\(197\) 18.7161 1.33347 0.666735 0.745295i \(-0.267691\pi\)
0.666735 + 0.745295i \(0.267691\pi\)
\(198\) −17.8791 −1.27061
\(199\) 19.4444 1.37838 0.689189 0.724582i \(-0.257967\pi\)
0.689189 + 0.724582i \(0.257967\pi\)
\(200\) −5.26377 −0.372204
\(201\) 27.8496 1.96436
\(202\) 4.70151 0.330797
\(203\) 0 0
\(204\) −37.4334 −2.62086
\(205\) −3.91618 −0.273518
\(206\) 21.1927 1.47657
\(207\) 47.0389 3.26943
\(208\) −6.50284 −0.450891
\(209\) −2.20953 −0.152836
\(210\) 0 0
\(211\) −7.35680 −0.506463 −0.253232 0.967406i \(-0.581493\pi\)
−0.253232 + 0.967406i \(0.581493\pi\)
\(212\) 34.3761 2.36096
\(213\) 9.17613 0.628738
\(214\) −13.9057 −0.950577
\(215\) 9.47126 0.645934
\(216\) 71.0793 4.83634
\(217\) 0 0
\(218\) 23.9030 1.61891
\(219\) 37.7171 2.54869
\(220\) −4.12660 −0.278216
\(221\) −3.86315 −0.259864
\(222\) 61.8233 4.14931
\(223\) −1.41504 −0.0947583 −0.0473792 0.998877i \(-0.515087\pi\)
−0.0473792 + 0.998877i \(0.515087\pi\)
\(224\) 0 0
\(225\) 7.22329 0.481553
\(226\) −34.8196 −2.31617
\(227\) 0.192342 0.0127662 0.00638309 0.999980i \(-0.497968\pi\)
0.00638309 + 0.999980i \(0.497968\pi\)
\(228\) 29.1533 1.93072
\(229\) 1.82401 0.120534 0.0602668 0.998182i \(-0.480805\pi\)
0.0602668 + 0.998182i \(0.480805\pi\)
\(230\) 16.1188 1.06284
\(231\) 0 0
\(232\) −33.1213 −2.17452
\(233\) 20.1979 1.32321 0.661604 0.749853i \(-0.269876\pi\)
0.661604 + 0.749853i \(0.269876\pi\)
\(234\) 24.3453 1.59150
\(235\) 1.14620 0.0747700
\(236\) 9.30410 0.605645
\(237\) −28.0075 −1.81928
\(238\) 0 0
\(239\) 13.5674 0.877603 0.438802 0.898584i \(-0.355403\pi\)
0.438802 + 0.898584i \(0.355403\pi\)
\(240\) 15.2696 0.985650
\(241\) −16.0107 −1.03134 −0.515670 0.856788i \(-0.672457\pi\)
−0.515670 + 0.856788i \(0.672457\pi\)
\(242\) −2.47520 −0.159112
\(243\) −28.2528 −1.81242
\(244\) 24.8521 1.59099
\(245\) 0 0
\(246\) 30.9933 1.97606
\(247\) 3.00864 0.191435
\(248\) −54.3763 −3.45290
\(249\) −27.5303 −1.74466
\(250\) 2.47520 0.156545
\(251\) −7.97654 −0.503475 −0.251737 0.967796i \(-0.581002\pi\)
−0.251737 + 0.967796i \(0.581002\pi\)
\(252\) 0 0
\(253\) 6.51211 0.409413
\(254\) 23.0273 1.44486
\(255\) 9.07124 0.568063
\(256\) −32.6076 −2.03797
\(257\) 8.10095 0.505323 0.252662 0.967555i \(-0.418694\pi\)
0.252662 + 0.967555i \(0.418694\pi\)
\(258\) −74.9571 −4.66663
\(259\) 0 0
\(260\) 5.61905 0.348479
\(261\) 45.4513 2.81337
\(262\) 39.0603 2.41315
\(263\) −6.09902 −0.376082 −0.188041 0.982161i \(-0.560214\pi\)
−0.188041 + 0.982161i \(0.560214\pi\)
\(264\) 16.8303 1.03583
\(265\) −8.33037 −0.511731
\(266\) 0 0
\(267\) 33.4942 2.04981
\(268\) −35.9432 −2.19558
\(269\) 27.7349 1.69103 0.845515 0.533952i \(-0.179294\pi\)
0.845515 + 0.533952i \(0.179294\pi\)
\(270\) −33.4239 −2.03411
\(271\) 17.0261 1.03426 0.517132 0.855906i \(-0.327000\pi\)
0.517132 + 0.855906i \(0.327000\pi\)
\(272\) 13.5489 0.821523
\(273\) 0 0
\(274\) −16.5613 −1.00050
\(275\) 1.00000 0.0603023
\(276\) −85.9231 −5.17197
\(277\) 14.7376 0.885498 0.442749 0.896645i \(-0.354003\pi\)
0.442749 + 0.896645i \(0.354003\pi\)
\(278\) 8.84096 0.530245
\(279\) 74.6188 4.46731
\(280\) 0 0
\(281\) −3.54498 −0.211476 −0.105738 0.994394i \(-0.533720\pi\)
−0.105738 + 0.994394i \(0.533720\pi\)
\(282\) −9.07124 −0.540184
\(283\) −22.6670 −1.34741 −0.673707 0.738999i \(-0.735299\pi\)
−0.673707 + 0.738999i \(0.735299\pi\)
\(284\) −11.8429 −0.702745
\(285\) −7.06472 −0.418478
\(286\) 3.37039 0.199295
\(287\) 0 0
\(288\) −9.34085 −0.550415
\(289\) −8.95099 −0.526529
\(290\) 15.5748 0.914581
\(291\) −9.12152 −0.534713
\(292\) −48.6783 −2.84868
\(293\) 5.90965 0.345245 0.172623 0.984988i \(-0.444776\pi\)
0.172623 + 0.984988i \(0.444776\pi\)
\(294\) 0 0
\(295\) −2.25466 −0.131271
\(296\) −41.1191 −2.39000
\(297\) −13.5035 −0.783553
\(298\) 58.3556 3.38045
\(299\) −8.86732 −0.512810
\(300\) −13.1944 −0.761777
\(301\) 0 0
\(302\) −13.3417 −0.767727
\(303\) 6.07327 0.348900
\(304\) −10.5519 −0.605195
\(305\) −6.02240 −0.344841
\(306\) −50.7243 −2.89972
\(307\) −2.99704 −0.171050 −0.0855249 0.996336i \(-0.527257\pi\)
−0.0855249 + 0.996336i \(0.527257\pi\)
\(308\) 0 0
\(309\) 27.3761 1.55737
\(310\) 25.5695 1.45225
\(311\) 0.595775 0.0337833 0.0168917 0.999857i \(-0.494623\pi\)
0.0168917 + 0.999857i \(0.494623\pi\)
\(312\) −22.9172 −1.29743
\(313\) 7.15763 0.404573 0.202287 0.979326i \(-0.435163\pi\)
0.202287 + 0.979326i \(0.435163\pi\)
\(314\) −14.7353 −0.831561
\(315\) 0 0
\(316\) 36.1470 2.03343
\(317\) 12.1246 0.680987 0.340494 0.940247i \(-0.389406\pi\)
0.340494 + 0.940247i \(0.389406\pi\)
\(318\) 65.9280 3.69706
\(319\) 6.29233 0.352303
\(320\) 6.35049 0.355003
\(321\) −17.9630 −1.00260
\(322\) 0 0
\(323\) −6.26860 −0.348794
\(324\) 88.7472 4.93040
\(325\) −1.36166 −0.0755316
\(326\) 30.8958 1.71116
\(327\) 30.8772 1.70751
\(328\) −20.6138 −1.13821
\(329\) 0 0
\(330\) −7.91417 −0.435661
\(331\) 11.8650 0.652159 0.326079 0.945342i \(-0.394272\pi\)
0.326079 + 0.945342i \(0.394272\pi\)
\(332\) 35.5311 1.95002
\(333\) 56.4263 3.09214
\(334\) −43.7123 −2.39183
\(335\) 8.71012 0.475885
\(336\) 0 0
\(337\) 23.7226 1.29225 0.646125 0.763231i \(-0.276388\pi\)
0.646125 + 0.763231i \(0.276388\pi\)
\(338\) 27.5882 1.50060
\(339\) −44.9790 −2.44292
\(340\) −11.7075 −0.634928
\(341\) 10.3303 0.559417
\(342\) 39.5043 2.13615
\(343\) 0 0
\(344\) 49.8545 2.68797
\(345\) 20.8218 1.12101
\(346\) −7.22506 −0.388422
\(347\) 0.619487 0.0332558 0.0166279 0.999862i \(-0.494707\pi\)
0.0166279 + 0.999862i \(0.494707\pi\)
\(348\) −83.0232 −4.45051
\(349\) −14.0299 −0.751005 −0.375503 0.926821i \(-0.622530\pi\)
−0.375503 + 0.926821i \(0.622530\pi\)
\(350\) 0 0
\(351\) 18.3873 0.981439
\(352\) −1.29316 −0.0689254
\(353\) −25.3392 −1.34867 −0.674334 0.738427i \(-0.735569\pi\)
−0.674334 + 0.738427i \(0.735569\pi\)
\(354\) 17.8438 0.948386
\(355\) 2.86988 0.152318
\(356\) −43.2282 −2.29109
\(357\) 0 0
\(358\) 44.4233 2.34784
\(359\) −11.5719 −0.610743 −0.305371 0.952233i \(-0.598781\pi\)
−0.305371 + 0.952233i \(0.598781\pi\)
\(360\) 38.0217 2.00392
\(361\) −14.1180 −0.743052
\(362\) −29.4677 −1.54879
\(363\) −3.19739 −0.167819
\(364\) 0 0
\(365\) 11.7962 0.617442
\(366\) 47.6623 2.49135
\(367\) 7.05527 0.368282 0.184141 0.982900i \(-0.441050\pi\)
0.184141 + 0.982900i \(0.441050\pi\)
\(368\) 31.0996 1.62118
\(369\) 28.2877 1.47260
\(370\) 19.3355 1.00521
\(371\) 0 0
\(372\) −136.302 −7.06691
\(373\) 2.22163 0.115032 0.0575158 0.998345i \(-0.481682\pi\)
0.0575158 + 0.998345i \(0.481682\pi\)
\(374\) −7.02233 −0.363116
\(375\) 3.19739 0.165112
\(376\) 6.03334 0.311146
\(377\) −8.56804 −0.441277
\(378\) 0 0
\(379\) 0.105060 0.00539655 0.00269828 0.999996i \(-0.499141\pi\)
0.00269828 + 0.999996i \(0.499141\pi\)
\(380\) 9.11784 0.467736
\(381\) 29.7460 1.52393
\(382\) −17.0421 −0.871947
\(383\) 17.4751 0.892937 0.446469 0.894799i \(-0.352681\pi\)
0.446469 + 0.894799i \(0.352681\pi\)
\(384\) −58.5283 −2.98676
\(385\) 0 0
\(386\) −4.10798 −0.209090
\(387\) −68.4137 −3.47766
\(388\) 11.7724 0.597653
\(389\) 26.2774 1.33231 0.666157 0.745811i \(-0.267938\pi\)
0.666157 + 0.745811i \(0.267938\pi\)
\(390\) 10.7764 0.545687
\(391\) 18.4754 0.934340
\(392\) 0 0
\(393\) 50.4569 2.54521
\(394\) −46.3261 −2.33388
\(395\) −8.75950 −0.440738
\(396\) 29.8077 1.49789
\(397\) 19.8732 0.997407 0.498703 0.866773i \(-0.333810\pi\)
0.498703 + 0.866773i \(0.333810\pi\)
\(398\) −48.1288 −2.41248
\(399\) 0 0
\(400\) 4.77565 0.238783
\(401\) −20.1601 −1.00675 −0.503373 0.864069i \(-0.667908\pi\)
−0.503373 + 0.864069i \(0.667908\pi\)
\(402\) −68.9333 −3.43808
\(403\) −14.0664 −0.700698
\(404\) −7.83826 −0.389968
\(405\) −21.5061 −1.06865
\(406\) 0 0
\(407\) 7.81172 0.387213
\(408\) 47.7489 2.36392
\(409\) 20.3956 1.00850 0.504249 0.863558i \(-0.331769\pi\)
0.504249 + 0.863558i \(0.331769\pi\)
\(410\) 9.69331 0.478718
\(411\) −21.3934 −1.05526
\(412\) −35.3321 −1.74069
\(413\) 0 0
\(414\) −116.431 −5.72225
\(415\) −8.61026 −0.422661
\(416\) 1.76085 0.0863325
\(417\) 11.4205 0.559264
\(418\) 5.46902 0.267498
\(419\) 1.96618 0.0960541 0.0480270 0.998846i \(-0.484707\pi\)
0.0480270 + 0.998846i \(0.484707\pi\)
\(420\) 0 0
\(421\) −19.9021 −0.969969 −0.484984 0.874523i \(-0.661175\pi\)
−0.484984 + 0.874523i \(0.661175\pi\)
\(422\) 18.2095 0.886427
\(423\) −8.27936 −0.402556
\(424\) −43.8491 −2.12950
\(425\) 2.83708 0.137618
\(426\) −22.7127 −1.10044
\(427\) 0 0
\(428\) 23.1834 1.12061
\(429\) 4.35377 0.210202
\(430\) −23.4432 −1.13053
\(431\) −25.5183 −1.22918 −0.614588 0.788849i \(-0.710678\pi\)
−0.614588 + 0.788849i \(0.710678\pi\)
\(432\) −64.4881 −3.10269
\(433\) 21.5876 1.03743 0.518717 0.854946i \(-0.326410\pi\)
0.518717 + 0.854946i \(0.326410\pi\)
\(434\) 0 0
\(435\) 20.1190 0.964633
\(436\) −39.8506 −1.90850
\(437\) −14.3887 −0.688304
\(438\) −93.3573 −4.46078
\(439\) −29.2530 −1.39617 −0.698086 0.716014i \(-0.745965\pi\)
−0.698086 + 0.716014i \(0.745965\pi\)
\(440\) 5.26377 0.250940
\(441\) 0 0
\(442\) 9.56206 0.454821
\(443\) 6.49028 0.308363 0.154181 0.988043i \(-0.450726\pi\)
0.154181 + 0.988043i \(0.450726\pi\)
\(444\) −103.071 −4.89151
\(445\) 10.4755 0.496586
\(446\) 3.50251 0.165849
\(447\) 75.3821 3.56545
\(448\) 0 0
\(449\) 14.1900 0.669668 0.334834 0.942277i \(-0.391320\pi\)
0.334834 + 0.942277i \(0.391320\pi\)
\(450\) −17.8791 −0.842828
\(451\) 3.91618 0.184406
\(452\) 58.0507 2.73047
\(453\) −17.2344 −0.809742
\(454\) −0.476084 −0.0223437
\(455\) 0 0
\(456\) −37.1870 −1.74144
\(457\) 16.8076 0.786224 0.393112 0.919491i \(-0.371398\pi\)
0.393112 + 0.919491i \(0.371398\pi\)
\(458\) −4.51477 −0.210962
\(459\) −38.3105 −1.78818
\(460\) −26.8729 −1.25296
\(461\) −11.8158 −0.550318 −0.275159 0.961399i \(-0.588730\pi\)
−0.275159 + 0.961399i \(0.588730\pi\)
\(462\) 0 0
\(463\) −18.7986 −0.873644 −0.436822 0.899548i \(-0.643896\pi\)
−0.436822 + 0.899548i \(0.643896\pi\)
\(464\) 30.0500 1.39503
\(465\) 33.0300 1.53173
\(466\) −49.9938 −2.31592
\(467\) −18.0434 −0.834950 −0.417475 0.908689i \(-0.637085\pi\)
−0.417475 + 0.908689i \(0.637085\pi\)
\(468\) −40.5881 −1.87618
\(469\) 0 0
\(470\) −2.83708 −0.130865
\(471\) −19.0346 −0.877069
\(472\) −11.8680 −0.546269
\(473\) −9.47126 −0.435489
\(474\) 69.3241 3.18416
\(475\) −2.20953 −0.101380
\(476\) 0 0
\(477\) 60.1727 2.75512
\(478\) −33.5821 −1.53601
\(479\) 16.2747 0.743611 0.371806 0.928311i \(-0.378739\pi\)
0.371806 + 0.928311i \(0.378739\pi\)
\(480\) −4.13472 −0.188723
\(481\) −10.6369 −0.485003
\(482\) 39.6296 1.80508
\(483\) 0 0
\(484\) 4.12660 0.187573
\(485\) −2.85280 −0.129539
\(486\) 69.9313 3.17215
\(487\) 7.72075 0.349861 0.174930 0.984581i \(-0.444030\pi\)
0.174930 + 0.984581i \(0.444030\pi\)
\(488\) −31.7005 −1.43501
\(489\) 39.9104 1.80481
\(490\) 0 0
\(491\) −38.6547 −1.74446 −0.872231 0.489095i \(-0.837327\pi\)
−0.872231 + 0.489095i \(0.837327\pi\)
\(492\) −51.6714 −2.32953
\(493\) 17.8518 0.804005
\(494\) −7.44697 −0.335055
\(495\) −7.22329 −0.324663
\(496\) 49.3339 2.21516
\(497\) 0 0
\(498\) 68.1431 3.05356
\(499\) 40.1599 1.79780 0.898901 0.438151i \(-0.144366\pi\)
0.898901 + 0.438151i \(0.144366\pi\)
\(500\) −4.12660 −0.184547
\(501\) −56.4663 −2.52273
\(502\) 19.7435 0.881196
\(503\) −6.75989 −0.301408 −0.150704 0.988579i \(-0.548154\pi\)
−0.150704 + 0.988579i \(0.548154\pi\)
\(504\) 0 0
\(505\) 1.89945 0.0845243
\(506\) −16.1188 −0.716567
\(507\) 35.6377 1.58272
\(508\) −38.3906 −1.70331
\(509\) 34.5690 1.53224 0.766121 0.642696i \(-0.222184\pi\)
0.766121 + 0.642696i \(0.222184\pi\)
\(510\) −22.4531 −0.994240
\(511\) 0 0
\(512\) 44.1002 1.94897
\(513\) 29.8364 1.31731
\(514\) −20.0515 −0.884432
\(515\) 8.56203 0.377288
\(516\) 124.967 5.50137
\(517\) −1.14620 −0.0504099
\(518\) 0 0
\(519\) −9.33313 −0.409679
\(520\) −7.16749 −0.314315
\(521\) −23.3899 −1.02473 −0.512365 0.858768i \(-0.671231\pi\)
−0.512365 + 0.858768i \(0.671231\pi\)
\(522\) −112.501 −4.92404
\(523\) −1.82225 −0.0796815 −0.0398407 0.999206i \(-0.512685\pi\)
−0.0398407 + 0.999206i \(0.512685\pi\)
\(524\) −65.1205 −2.84480
\(525\) 0 0
\(526\) 15.0963 0.658229
\(527\) 29.3079 1.27667
\(528\) −15.2696 −0.664525
\(529\) 19.4076 0.843809
\(530\) 20.6193 0.895646
\(531\) 16.2861 0.706756
\(532\) 0 0
\(533\) −5.33252 −0.230977
\(534\) −82.9049 −3.58765
\(535\) −5.61803 −0.242889
\(536\) 45.8480 1.98033
\(537\) 57.3847 2.47633
\(538\) −68.6495 −2.95969
\(539\) 0 0
\(540\) 55.7237 2.39796
\(541\) −18.3946 −0.790847 −0.395424 0.918499i \(-0.629402\pi\)
−0.395424 + 0.918499i \(0.629402\pi\)
\(542\) −42.1431 −1.81020
\(543\) −38.0655 −1.63355
\(544\) −3.66878 −0.157298
\(545\) 9.65700 0.413660
\(546\) 0 0
\(547\) 3.98726 0.170483 0.0852414 0.996360i \(-0.472834\pi\)
0.0852414 + 0.996360i \(0.472834\pi\)
\(548\) 27.6106 1.17947
\(549\) 43.5016 1.85660
\(550\) −2.47520 −0.105543
\(551\) −13.9031 −0.592290
\(552\) 109.601 4.66492
\(553\) 0 0
\(554\) −36.4786 −1.54983
\(555\) 24.9771 1.06022
\(556\) −14.7395 −0.625093
\(557\) 26.1553 1.10824 0.554119 0.832438i \(-0.313055\pi\)
0.554119 + 0.832438i \(0.313055\pi\)
\(558\) −184.696 −7.81882
\(559\) 12.8967 0.545471
\(560\) 0 0
\(561\) −9.07124 −0.382988
\(562\) 8.77453 0.370131
\(563\) −0.770882 −0.0324888 −0.0162444 0.999868i \(-0.505171\pi\)
−0.0162444 + 0.999868i \(0.505171\pi\)
\(564\) 15.1234 0.636810
\(565\) −14.0674 −0.591821
\(566\) 56.1053 2.35828
\(567\) 0 0
\(568\) 15.1064 0.633850
\(569\) 20.0061 0.838700 0.419350 0.907825i \(-0.362258\pi\)
0.419350 + 0.907825i \(0.362258\pi\)
\(570\) 17.4866 0.732432
\(571\) −4.52174 −0.189229 −0.0946145 0.995514i \(-0.530162\pi\)
−0.0946145 + 0.995514i \(0.530162\pi\)
\(572\) −5.61905 −0.234944
\(573\) −22.0144 −0.919666
\(574\) 0 0
\(575\) 6.51211 0.271574
\(576\) −45.8715 −1.91131
\(577\) 27.6112 1.14947 0.574734 0.818340i \(-0.305105\pi\)
0.574734 + 0.818340i \(0.305105\pi\)
\(578\) 22.1555 0.921546
\(579\) −5.30656 −0.220533
\(580\) −25.9659 −1.07818
\(581\) 0 0
\(582\) 22.5776 0.935870
\(583\) 8.33037 0.345009
\(584\) 62.0925 2.56941
\(585\) 9.83571 0.406656
\(586\) −14.6276 −0.604259
\(587\) −41.0780 −1.69547 −0.847734 0.530421i \(-0.822034\pi\)
−0.847734 + 0.530421i \(0.822034\pi\)
\(588\) 0 0
\(589\) −22.8251 −0.940491
\(590\) 5.58073 0.229755
\(591\) −59.8428 −2.46160
\(592\) 37.3061 1.53327
\(593\) −38.7082 −1.58955 −0.794777 0.606902i \(-0.792412\pi\)
−0.794777 + 0.606902i \(0.792412\pi\)
\(594\) 33.4239 1.37140
\(595\) 0 0
\(596\) −97.2894 −3.98513
\(597\) −62.1713 −2.54450
\(598\) 21.9484 0.897535
\(599\) 1.50522 0.0615017 0.0307509 0.999527i \(-0.490210\pi\)
0.0307509 + 0.999527i \(0.490210\pi\)
\(600\) 16.8303 0.687094
\(601\) 31.9404 1.30287 0.651437 0.758702i \(-0.274166\pi\)
0.651437 + 0.758702i \(0.274166\pi\)
\(602\) 0 0
\(603\) −62.9157 −2.56213
\(604\) 22.2430 0.905054
\(605\) −1.00000 −0.0406558
\(606\) −15.0325 −0.610655
\(607\) −33.7368 −1.36933 −0.684667 0.728856i \(-0.740053\pi\)
−0.684667 + 0.728856i \(0.740053\pi\)
\(608\) 2.85726 0.115877
\(609\) 0 0
\(610\) 14.9066 0.603552
\(611\) 1.56074 0.0631409
\(612\) 84.5667 3.41841
\(613\) −35.6784 −1.44104 −0.720519 0.693435i \(-0.756096\pi\)
−0.720519 + 0.693435i \(0.756096\pi\)
\(614\) 7.41825 0.299376
\(615\) 12.5215 0.504917
\(616\) 0 0
\(617\) −0.170005 −0.00684413 −0.00342207 0.999994i \(-0.501089\pi\)
−0.00342207 + 0.999994i \(0.501089\pi\)
\(618\) −67.7613 −2.72576
\(619\) 14.2539 0.572912 0.286456 0.958093i \(-0.407523\pi\)
0.286456 + 0.958093i \(0.407523\pi\)
\(620\) −42.6291 −1.71202
\(621\) −87.9364 −3.52877
\(622\) −1.47466 −0.0591285
\(623\) 0 0
\(624\) 20.7921 0.832351
\(625\) 1.00000 0.0400000
\(626\) −17.7165 −0.708095
\(627\) 7.06472 0.282138
\(628\) 24.5664 0.980307
\(629\) 22.1625 0.883675
\(630\) 0 0
\(631\) −17.5090 −0.697022 −0.348511 0.937305i \(-0.613313\pi\)
−0.348511 + 0.937305i \(0.613313\pi\)
\(632\) −46.1079 −1.83408
\(633\) 23.5226 0.934938
\(634\) −30.0109 −1.19188
\(635\) 9.30320 0.369186
\(636\) −109.914 −4.35837
\(637\) 0 0
\(638\) −15.5748 −0.616610
\(639\) −20.7300 −0.820067
\(640\) −18.3050 −0.723570
\(641\) 38.5729 1.52354 0.761769 0.647849i \(-0.224331\pi\)
0.761769 + 0.647849i \(0.224331\pi\)
\(642\) 44.4621 1.75478
\(643\) −37.7939 −1.49045 −0.745223 0.666815i \(-0.767657\pi\)
−0.745223 + 0.666815i \(0.767657\pi\)
\(644\) 0 0
\(645\) −30.2833 −1.19240
\(646\) 15.5160 0.610470
\(647\) 17.6687 0.694630 0.347315 0.937749i \(-0.387093\pi\)
0.347315 + 0.937749i \(0.387093\pi\)
\(648\) −113.203 −4.44704
\(649\) 2.25466 0.0885032
\(650\) 3.37039 0.132198
\(651\) 0 0
\(652\) −51.5090 −2.01725
\(653\) −38.2713 −1.49767 −0.748837 0.662754i \(-0.769387\pi\)
−0.748837 + 0.662754i \(0.769387\pi\)
\(654\) −76.4271 −2.98854
\(655\) 15.7807 0.616601
\(656\) 18.7023 0.730202
\(657\) −85.2076 −3.32426
\(658\) 0 0
\(659\) −12.2280 −0.476336 −0.238168 0.971224i \(-0.576547\pi\)
−0.238168 + 0.971224i \(0.576547\pi\)
\(660\) 13.1944 0.513590
\(661\) 49.9188 1.94162 0.970808 0.239857i \(-0.0771005\pi\)
0.970808 + 0.239857i \(0.0771005\pi\)
\(662\) −29.3682 −1.14143
\(663\) 12.3520 0.479711
\(664\) −45.3224 −1.75885
\(665\) 0 0
\(666\) −139.666 −5.41196
\(667\) 40.9763 1.58661
\(668\) 72.8763 2.81967
\(669\) 4.52444 0.174925
\(670\) −21.5593 −0.832907
\(671\) 6.02240 0.232492
\(672\) 0 0
\(673\) −13.6846 −0.527502 −0.263751 0.964591i \(-0.584960\pi\)
−0.263751 + 0.964591i \(0.584960\pi\)
\(674\) −58.7181 −2.26173
\(675\) −13.5035 −0.519750
\(676\) −45.9946 −1.76902
\(677\) 8.96977 0.344736 0.172368 0.985033i \(-0.444858\pi\)
0.172368 + 0.985033i \(0.444858\pi\)
\(678\) 111.332 4.27568
\(679\) 0 0
\(680\) 14.9337 0.572682
\(681\) −0.614992 −0.0235665
\(682\) −25.5695 −0.979108
\(683\) −26.3119 −1.00680 −0.503399 0.864054i \(-0.667917\pi\)
−0.503399 + 0.864054i \(0.667917\pi\)
\(684\) −65.8609 −2.51825
\(685\) −6.69088 −0.255646
\(686\) 0 0
\(687\) −5.83205 −0.222507
\(688\) −45.2314 −1.72443
\(689\) −11.3432 −0.432141
\(690\) −51.5380 −1.96202
\(691\) 23.6024 0.897876 0.448938 0.893563i \(-0.351802\pi\)
0.448938 + 0.893563i \(0.351802\pi\)
\(692\) 12.0455 0.457901
\(693\) 0 0
\(694\) −1.53335 −0.0582053
\(695\) 3.57182 0.135487
\(696\) 105.902 4.01420
\(697\) 11.1105 0.420840
\(698\) 34.7269 1.31443
\(699\) −64.5805 −2.44266
\(700\) 0 0
\(701\) 18.1198 0.684374 0.342187 0.939632i \(-0.388832\pi\)
0.342187 + 0.939632i \(0.388832\pi\)
\(702\) −45.5121 −1.71774
\(703\) −17.2602 −0.650981
\(704\) −6.35049 −0.239343
\(705\) −3.66485 −0.138026
\(706\) 62.7195 2.36048
\(707\) 0 0
\(708\) −29.7488 −1.11803
\(709\) 43.5486 1.63550 0.817752 0.575571i \(-0.195220\pi\)
0.817752 + 0.575571i \(0.195220\pi\)
\(710\) −7.10353 −0.266591
\(711\) 63.2724 2.37290
\(712\) 55.1406 2.06648
\(713\) 67.2721 2.51936
\(714\) 0 0
\(715\) 1.36166 0.0509234
\(716\) −74.0617 −2.76782
\(717\) −43.3803 −1.62007
\(718\) 28.6428 1.06894
\(719\) 45.1976 1.68559 0.842794 0.538237i \(-0.180909\pi\)
0.842794 + 0.538237i \(0.180909\pi\)
\(720\) −34.4960 −1.28559
\(721\) 0 0
\(722\) 34.9448 1.30051
\(723\) 51.1924 1.90387
\(724\) 49.1280 1.82583
\(725\) 6.29233 0.233691
\(726\) 7.91417 0.293722
\(727\) 37.1901 1.37930 0.689652 0.724141i \(-0.257763\pi\)
0.689652 + 0.724141i \(0.257763\pi\)
\(728\) 0 0
\(729\) 25.8169 0.956183
\(730\) −29.1980 −1.08067
\(731\) −26.8707 −0.993848
\(732\) −79.4617 −2.93699
\(733\) −7.32991 −0.270736 −0.135368 0.990795i \(-0.543222\pi\)
−0.135368 + 0.990795i \(0.543222\pi\)
\(734\) −17.4632 −0.644579
\(735\) 0 0
\(736\) −8.42118 −0.310409
\(737\) −8.71012 −0.320841
\(738\) −70.0176 −2.57738
\(739\) 7.06120 0.259750 0.129875 0.991530i \(-0.458542\pi\)
0.129875 + 0.991530i \(0.458542\pi\)
\(740\) −32.2359 −1.18501
\(741\) −9.61978 −0.353391
\(742\) 0 0
\(743\) −27.2615 −1.00013 −0.500064 0.865988i \(-0.666690\pi\)
−0.500064 + 0.865988i \(0.666690\pi\)
\(744\) 173.862 6.37409
\(745\) 23.5761 0.863763
\(746\) −5.49897 −0.201332
\(747\) 62.1944 2.27558
\(748\) 11.7075 0.428068
\(749\) 0 0
\(750\) −7.91417 −0.288985
\(751\) 46.2169 1.68648 0.843239 0.537538i \(-0.180646\pi\)
0.843239 + 0.537538i \(0.180646\pi\)
\(752\) −5.47387 −0.199611
\(753\) 25.5041 0.929421
\(754\) 21.2076 0.772335
\(755\) −5.39014 −0.196167
\(756\) 0 0
\(757\) −18.0891 −0.657458 −0.328729 0.944424i \(-0.606620\pi\)
−0.328729 + 0.944424i \(0.606620\pi\)
\(758\) −0.260043 −0.00944520
\(759\) −20.8218 −0.755782
\(760\) −11.6304 −0.421880
\(761\) −11.8172 −0.428374 −0.214187 0.976793i \(-0.568710\pi\)
−0.214187 + 0.976793i \(0.568710\pi\)
\(762\) −73.6271 −2.66723
\(763\) 0 0
\(764\) 28.4122 1.02792
\(765\) −20.4930 −0.740928
\(766\) −43.2544 −1.56284
\(767\) −3.07009 −0.110855
\(768\) 104.259 3.76213
\(769\) 42.9075 1.54728 0.773642 0.633623i \(-0.218433\pi\)
0.773642 + 0.633623i \(0.218433\pi\)
\(770\) 0 0
\(771\) −25.9019 −0.932834
\(772\) 6.84874 0.246492
\(773\) 17.9460 0.645473 0.322736 0.946489i \(-0.395397\pi\)
0.322736 + 0.946489i \(0.395397\pi\)
\(774\) 169.337 6.08671
\(775\) 10.3303 0.371075
\(776\) −15.0165 −0.539061
\(777\) 0 0
\(778\) −65.0416 −2.33186
\(779\) −8.65290 −0.310022
\(780\) −17.9663 −0.643297
\(781\) −2.86988 −0.102692
\(782\) −45.7302 −1.63531
\(783\) −84.9685 −3.03653
\(784\) 0 0
\(785\) −5.95318 −0.212478
\(786\) −124.891 −4.45471
\(787\) 8.84623 0.315334 0.157667 0.987492i \(-0.449603\pi\)
0.157667 + 0.987492i \(0.449603\pi\)
\(788\) 77.2341 2.75135
\(789\) 19.5009 0.694252
\(790\) 21.6815 0.771393
\(791\) 0 0
\(792\) −38.0217 −1.35104
\(793\) −8.20049 −0.291208
\(794\) −49.1901 −1.74569
\(795\) 26.6354 0.944661
\(796\) 80.2394 2.84401
\(797\) −23.9643 −0.848859 −0.424429 0.905461i \(-0.639525\pi\)
−0.424429 + 0.905461i \(0.639525\pi\)
\(798\) 0 0
\(799\) −3.25186 −0.115043
\(800\) −1.29316 −0.0457200
\(801\) −75.6676 −2.67358
\(802\) 49.9001 1.76204
\(803\) −11.7962 −0.416280
\(804\) 114.924 4.05307
\(805\) 0 0
\(806\) 34.8171 1.22638
\(807\) −88.6794 −3.12166
\(808\) 9.99824 0.351737
\(809\) 12.0434 0.423423 0.211712 0.977332i \(-0.432096\pi\)
0.211712 + 0.977332i \(0.432096\pi\)
\(810\) 53.2318 1.87038
\(811\) −2.30398 −0.0809035 −0.0404518 0.999181i \(-0.512880\pi\)
−0.0404518 + 0.999181i \(0.512880\pi\)
\(812\) 0 0
\(813\) −54.4392 −1.90927
\(814\) −19.3355 −0.677711
\(815\) 12.4822 0.437231
\(816\) −43.3211 −1.51654
\(817\) 20.9270 0.732143
\(818\) −50.4832 −1.76510
\(819\) 0 0
\(820\) −16.1605 −0.564349
\(821\) 0.964222 0.0336516 0.0168258 0.999858i \(-0.494644\pi\)
0.0168258 + 0.999858i \(0.494644\pi\)
\(822\) 52.9528 1.84694
\(823\) 0.751163 0.0261839 0.0130919 0.999914i \(-0.495833\pi\)
0.0130919 + 0.999914i \(0.495833\pi\)
\(824\) 45.0685 1.57004
\(825\) −3.19739 −0.111319
\(826\) 0 0
\(827\) −2.31121 −0.0803685 −0.0401843 0.999192i \(-0.512794\pi\)
−0.0401843 + 0.999192i \(0.512794\pi\)
\(828\) 194.111 6.74582
\(829\) 46.2419 1.60605 0.803024 0.595947i \(-0.203223\pi\)
0.803024 + 0.595947i \(0.203223\pi\)
\(830\) 21.3121 0.739754
\(831\) −47.1219 −1.63464
\(832\) 8.64724 0.299789
\(833\) 0 0
\(834\) −28.2680 −0.978840
\(835\) −17.6601 −0.611154
\(836\) −9.11784 −0.315347
\(837\) −139.495 −4.82166
\(838\) −4.86668 −0.168117
\(839\) 33.6375 1.16130 0.580648 0.814155i \(-0.302799\pi\)
0.580648 + 0.814155i \(0.302799\pi\)
\(840\) 0 0
\(841\) 10.5934 0.365289
\(842\) 49.2616 1.69767
\(843\) 11.3347 0.390387
\(844\) −30.3586 −1.04499
\(845\) 11.1459 0.383430
\(846\) 20.4930 0.704565
\(847\) 0 0
\(848\) 39.7830 1.36615
\(849\) 72.4752 2.48734
\(850\) −7.02233 −0.240864
\(851\) 50.8708 1.74383
\(852\) 37.8663 1.29728
\(853\) 44.7072 1.53075 0.765373 0.643587i \(-0.222554\pi\)
0.765373 + 0.643587i \(0.222554\pi\)
\(854\) 0 0
\(855\) 15.9601 0.545823
\(856\) −29.5720 −1.01075
\(857\) 20.3336 0.694583 0.347292 0.937757i \(-0.387101\pi\)
0.347292 + 0.937757i \(0.387101\pi\)
\(858\) −10.7764 −0.367902
\(859\) −38.0627 −1.29868 −0.649341 0.760498i \(-0.724955\pi\)
−0.649341 + 0.760498i \(0.724955\pi\)
\(860\) 39.0841 1.33276
\(861\) 0 0
\(862\) 63.1629 2.15134
\(863\) −34.0330 −1.15850 −0.579248 0.815152i \(-0.696654\pi\)
−0.579248 + 0.815152i \(0.696654\pi\)
\(864\) 17.4621 0.594074
\(865\) −2.91898 −0.0992484
\(866\) −53.4336 −1.81575
\(867\) 28.6198 0.971979
\(868\) 0 0
\(869\) 8.75950 0.297146
\(870\) −49.7985 −1.68833
\(871\) 11.8603 0.401870
\(872\) 50.8322 1.72139
\(873\) 20.6066 0.697429
\(874\) 35.6149 1.20469
\(875\) 0 0
\(876\) 155.644 5.25871
\(877\) 4.57143 0.154366 0.0771831 0.997017i \(-0.475407\pi\)
0.0771831 + 0.997017i \(0.475407\pi\)
\(878\) 72.4071 2.44362
\(879\) −18.8954 −0.637328
\(880\) −4.77565 −0.160987
\(881\) 21.3685 0.719922 0.359961 0.932967i \(-0.382790\pi\)
0.359961 + 0.932967i \(0.382790\pi\)
\(882\) 0 0
\(883\) 17.7488 0.597294 0.298647 0.954364i \(-0.403465\pi\)
0.298647 + 0.954364i \(0.403465\pi\)
\(884\) −15.9417 −0.536177
\(885\) 7.20903 0.242329
\(886\) −16.0647 −0.539705
\(887\) 50.7758 1.70489 0.852443 0.522820i \(-0.175120\pi\)
0.852443 + 0.522820i \(0.175120\pi\)
\(888\) 131.474 4.41197
\(889\) 0 0
\(890\) −25.9289 −0.869140
\(891\) 21.5061 0.720481
\(892\) −5.83932 −0.195515
\(893\) 2.53256 0.0847491
\(894\) −186.586 −6.24036
\(895\) 17.9474 0.599914
\(896\) 0 0
\(897\) 28.3523 0.946654
\(898\) −35.1231 −1.17207
\(899\) 65.0016 2.16793
\(900\) 29.8077 0.993589
\(901\) 23.6339 0.787360
\(902\) −9.69331 −0.322752
\(903\) 0 0
\(904\) −74.0476 −2.46279
\(905\) −11.9052 −0.395742
\(906\) 42.6585 1.41723
\(907\) 30.3479 1.00769 0.503843 0.863795i \(-0.331919\pi\)
0.503843 + 0.863795i \(0.331919\pi\)
\(908\) 0.793719 0.0263405
\(909\) −13.7203 −0.455072
\(910\) 0 0
\(911\) 34.0080 1.12673 0.563367 0.826207i \(-0.309506\pi\)
0.563367 + 0.826207i \(0.309506\pi\)
\(912\) 33.7386 1.11720
\(913\) 8.61026 0.284958
\(914\) −41.6020 −1.37607
\(915\) 19.2559 0.636582
\(916\) 7.52695 0.248697
\(917\) 0 0
\(918\) 94.8261 3.12973
\(919\) −31.0756 −1.02509 −0.512545 0.858660i \(-0.671297\pi\)
−0.512545 + 0.858660i \(0.671297\pi\)
\(920\) 34.2782 1.13012
\(921\) 9.58269 0.315760
\(922\) 29.2465 0.963182
\(923\) 3.90782 0.128627
\(924\) 0 0
\(925\) 7.81172 0.256848
\(926\) 46.5302 1.52908
\(927\) −61.8460 −2.03129
\(928\) −8.13696 −0.267109
\(929\) −32.5075 −1.06654 −0.533268 0.845947i \(-0.679036\pi\)
−0.533268 + 0.845947i \(0.679036\pi\)
\(930\) −81.7557 −2.68088
\(931\) 0 0
\(932\) 83.3487 2.73018
\(933\) −1.90492 −0.0623644
\(934\) 44.6610 1.46135
\(935\) −2.83708 −0.0927824
\(936\) 51.7729 1.69225
\(937\) 19.7428 0.644968 0.322484 0.946575i \(-0.395482\pi\)
0.322484 + 0.946575i \(0.395482\pi\)
\(938\) 0 0
\(939\) −22.8857 −0.746847
\(940\) 4.72992 0.154273
\(941\) 36.4351 1.18775 0.593875 0.804557i \(-0.297597\pi\)
0.593875 + 0.804557i \(0.297597\pi\)
\(942\) 47.1145 1.53507
\(943\) 25.5026 0.830478
\(944\) 10.7675 0.350452
\(945\) 0 0
\(946\) 23.4432 0.762205
\(947\) 33.1578 1.07749 0.538743 0.842470i \(-0.318900\pi\)
0.538743 + 0.842470i \(0.318900\pi\)
\(948\) −115.576 −3.75373
\(949\) 16.0625 0.521411
\(950\) 5.46902 0.177438
\(951\) −38.7672 −1.25711
\(952\) 0 0
\(953\) 33.3590 1.08060 0.540302 0.841471i \(-0.318310\pi\)
0.540302 + 0.841471i \(0.318310\pi\)
\(954\) −148.939 −4.82209
\(955\) −6.88513 −0.222797
\(956\) 55.9874 1.81076
\(957\) −20.1190 −0.650355
\(958\) −40.2832 −1.30149
\(959\) 0 0
\(960\) −20.3050 −0.655341
\(961\) 75.7151 2.44242
\(962\) 26.3285 0.848866
\(963\) 40.5807 1.30769
\(964\) −66.0698 −2.12796
\(965\) −1.65966 −0.0534262
\(966\) 0 0
\(967\) −32.1532 −1.03398 −0.516989 0.855992i \(-0.672947\pi\)
−0.516989 + 0.855992i \(0.672947\pi\)
\(968\) −5.26377 −0.169184
\(969\) 20.0431 0.643879
\(970\) 7.06125 0.226723
\(971\) 11.2955 0.362489 0.181244 0.983438i \(-0.441988\pi\)
0.181244 + 0.983438i \(0.441988\pi\)
\(972\) −116.588 −3.73957
\(973\) 0 0
\(974\) −19.1104 −0.612336
\(975\) 4.35377 0.139432
\(976\) 28.7609 0.920614
\(977\) −45.9622 −1.47046 −0.735230 0.677818i \(-0.762926\pi\)
−0.735230 + 0.677818i \(0.762926\pi\)
\(978\) −98.7860 −3.15883
\(979\) −10.4755 −0.334798
\(980\) 0 0
\(981\) −69.7553 −2.22712
\(982\) 95.6780 3.05321
\(983\) −9.75209 −0.311043 −0.155522 0.987832i \(-0.549706\pi\)
−0.155522 + 0.987832i \(0.549706\pi\)
\(984\) 65.9104 2.10115
\(985\) −18.7161 −0.596346
\(986\) −44.1868 −1.40719
\(987\) 0 0
\(988\) 12.4154 0.394988
\(989\) −61.6779 −1.96124
\(990\) 17.8791 0.568235
\(991\) −3.15511 −0.100225 −0.0501127 0.998744i \(-0.515958\pi\)
−0.0501127 + 0.998744i \(0.515958\pi\)
\(992\) −13.3587 −0.424139
\(993\) −37.9370 −1.20389
\(994\) 0 0
\(995\) −19.4444 −0.616429
\(996\) −113.607 −3.59977
\(997\) −45.0881 −1.42796 −0.713978 0.700168i \(-0.753108\pi\)
−0.713978 + 0.700168i \(0.753108\pi\)
\(998\) −99.4036 −3.14657
\(999\) −105.486 −3.33742
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 2695.2.a.y.1.1 10
7.2 even 3 385.2.i.d.221.10 20
7.4 even 3 385.2.i.d.331.10 yes 20
7.6 odd 2 2695.2.a.z.1.1 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
385.2.i.d.221.10 20 7.2 even 3
385.2.i.d.331.10 yes 20 7.4 even 3
2695.2.a.y.1.1 10 1.1 even 1 trivial
2695.2.a.z.1.1 10 7.6 odd 2