Properties

Label 5929.2.a.p.1.2
Level $5929$
Weight $2$
Character 5929.1
Self dual yes
Analytic conductor $47.343$
Analytic rank $1$
Dimension $2$
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] = [5929,2,Mod(1,5929)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5929, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("5929.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5929 = 7^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5929.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: \(47.3433033584\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 847)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.30278\) of defining polynomial
Character \(\chi\) \(=\) 5929.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.30278 q^{2} +2.30278 q^{3} +3.30278 q^{4} -3.60555 q^{5} +5.30278 q^{6} +3.00000 q^{8} +2.30278 q^{9} +O(q^{10})\) \(q+2.30278 q^{2} +2.30278 q^{3} +3.30278 q^{4} -3.60555 q^{5} +5.30278 q^{6} +3.00000 q^{8} +2.30278 q^{9} -8.30278 q^{10} +7.60555 q^{12} -6.60555 q^{13} -8.30278 q^{15} +0.302776 q^{16} -2.69722 q^{17} +5.30278 q^{18} +3.00000 q^{19} -11.9083 q^{20} -2.69722 q^{23} +6.90833 q^{24} +8.00000 q^{25} -15.2111 q^{26} -1.60555 q^{27} +4.69722 q^{29} -19.1194 q^{30} -1.00000 q^{31} -5.30278 q^{32} -6.21110 q^{34} +7.60555 q^{36} -5.21110 q^{37} +6.90833 q^{38} -15.2111 q^{39} -10.8167 q^{40} -7.00000 q^{41} +1.69722 q^{43} -8.30278 q^{45} -6.21110 q^{46} +1.90833 q^{47} +0.697224 q^{48} +18.4222 q^{50} -6.21110 q^{51} -21.8167 q^{52} -12.9083 q^{53} -3.69722 q^{54} +6.90833 q^{57} +10.8167 q^{58} -6.69722 q^{59} -27.4222 q^{60} +4.30278 q^{61} -2.30278 q^{62} -12.8167 q^{64} +23.8167 q^{65} +8.51388 q^{67} -8.90833 q^{68} -6.21110 q^{69} -4.30278 q^{71} +6.90833 q^{72} +5.00000 q^{73} -12.0000 q^{74} +18.4222 q^{75} +9.90833 q^{76} -35.0278 q^{78} -8.30278 q^{79} -1.09167 q^{80} -10.6056 q^{81} -16.1194 q^{82} -3.00000 q^{83} +9.72498 q^{85} +3.90833 q^{86} +10.8167 q^{87} +14.7250 q^{89} -19.1194 q^{90} -8.90833 q^{92} -2.30278 q^{93} +4.39445 q^{94} -10.8167 q^{95} -12.2111 q^{96} +3.60555 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{2} + q^{3} + 3 q^{4} + 7 q^{6} + 6 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{2} + q^{3} + 3 q^{4} + 7 q^{6} + 6 q^{8} + q^{9} - 13 q^{10} + 8 q^{12} - 6 q^{13} - 13 q^{15} - 3 q^{16} - 9 q^{17} + 7 q^{18} + 6 q^{19} - 13 q^{20} - 9 q^{23} + 3 q^{24} + 16 q^{25} - 16 q^{26} + 4 q^{27} + 13 q^{29} - 13 q^{30} - 2 q^{31} - 7 q^{32} + 2 q^{34} + 8 q^{36} + 4 q^{37} + 3 q^{38} - 16 q^{39} - 14 q^{41} + 7 q^{43} - 13 q^{45} + 2 q^{46} - 7 q^{47} + 5 q^{48} + 8 q^{50} + 2 q^{51} - 22 q^{52} - 15 q^{53} - 11 q^{54} + 3 q^{57} - 17 q^{59} - 26 q^{60} + 5 q^{61} - q^{62} - 4 q^{64} + 26 q^{65} - q^{67} - 7 q^{68} + 2 q^{69} - 5 q^{71} + 3 q^{72} + 10 q^{73} - 24 q^{74} + 8 q^{75} + 9 q^{76} - 34 q^{78} - 13 q^{79} - 13 q^{80} - 14 q^{81} - 7 q^{82} - 6 q^{83} - 13 q^{85} - 3 q^{86} - 3 q^{89} - 13 q^{90} - 7 q^{92} - q^{93} + 16 q^{94} - 10 q^{96}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.30278 1.62831 0.814154 0.580649i \(-0.197201\pi\)
0.814154 + 0.580649i \(0.197201\pi\)
\(3\) 2.30278 1.32951 0.664754 0.747062i \(-0.268536\pi\)
0.664754 + 0.747062i \(0.268536\pi\)
\(4\) 3.30278 1.65139
\(5\) −3.60555 −1.61245 −0.806226 0.591608i \(-0.798493\pi\)
−0.806226 + 0.591608i \(0.798493\pi\)
\(6\) 5.30278 2.16485
\(7\) 0 0
\(8\) 3.00000 1.06066
\(9\) 2.30278 0.767592
\(10\) −8.30278 −2.62557
\(11\) 0 0
\(12\) 7.60555 2.19553
\(13\) −6.60555 −1.83205 −0.916025 0.401121i \(-0.868621\pi\)
−0.916025 + 0.401121i \(0.868621\pi\)
\(14\) 0 0
\(15\) −8.30278 −2.14377
\(16\) 0.302776 0.0756939
\(17\) −2.69722 −0.654173 −0.327086 0.944994i \(-0.606067\pi\)
−0.327086 + 0.944994i \(0.606067\pi\)
\(18\) 5.30278 1.24988
\(19\) 3.00000 0.688247 0.344124 0.938924i \(-0.388176\pi\)
0.344124 + 0.938924i \(0.388176\pi\)
\(20\) −11.9083 −2.66278
\(21\) 0 0
\(22\) 0 0
\(23\) −2.69722 −0.562410 −0.281205 0.959648i \(-0.590734\pi\)
−0.281205 + 0.959648i \(0.590734\pi\)
\(24\) 6.90833 1.41016
\(25\) 8.00000 1.60000
\(26\) −15.2111 −2.98314
\(27\) −1.60555 −0.308988
\(28\) 0 0
\(29\) 4.69722 0.872253 0.436126 0.899885i \(-0.356350\pi\)
0.436126 + 0.899885i \(0.356350\pi\)
\(30\) −19.1194 −3.49071
\(31\) −1.00000 −0.179605 −0.0898027 0.995960i \(-0.528624\pi\)
−0.0898027 + 0.995960i \(0.528624\pi\)
\(32\) −5.30278 −0.937407
\(33\) 0 0
\(34\) −6.21110 −1.06520
\(35\) 0 0
\(36\) 7.60555 1.26759
\(37\) −5.21110 −0.856700 −0.428350 0.903613i \(-0.640905\pi\)
−0.428350 + 0.903613i \(0.640905\pi\)
\(38\) 6.90833 1.12068
\(39\) −15.2111 −2.43573
\(40\) −10.8167 −1.71026
\(41\) −7.00000 −1.09322 −0.546608 0.837389i \(-0.684081\pi\)
−0.546608 + 0.837389i \(0.684081\pi\)
\(42\) 0 0
\(43\) 1.69722 0.258824 0.129412 0.991591i \(-0.458691\pi\)
0.129412 + 0.991591i \(0.458691\pi\)
\(44\) 0 0
\(45\) −8.30278 −1.23770
\(46\) −6.21110 −0.915777
\(47\) 1.90833 0.278358 0.139179 0.990267i \(-0.455554\pi\)
0.139179 + 0.990267i \(0.455554\pi\)
\(48\) 0.697224 0.100636
\(49\) 0 0
\(50\) 18.4222 2.60529
\(51\) −6.21110 −0.869728
\(52\) −21.8167 −3.02543
\(53\) −12.9083 −1.77310 −0.886548 0.462638i \(-0.846903\pi\)
−0.886548 + 0.462638i \(0.846903\pi\)
\(54\) −3.69722 −0.503129
\(55\) 0 0
\(56\) 0 0
\(57\) 6.90833 0.915030
\(58\) 10.8167 1.42030
\(59\) −6.69722 −0.871904 −0.435952 0.899970i \(-0.643588\pi\)
−0.435952 + 0.899970i \(0.643588\pi\)
\(60\) −27.4222 −3.54019
\(61\) 4.30278 0.550914 0.275457 0.961313i \(-0.411171\pi\)
0.275457 + 0.961313i \(0.411171\pi\)
\(62\) −2.30278 −0.292453
\(63\) 0 0
\(64\) −12.8167 −1.60208
\(65\) 23.8167 2.95409
\(66\) 0 0
\(67\) 8.51388 1.04014 0.520068 0.854125i \(-0.325907\pi\)
0.520068 + 0.854125i \(0.325907\pi\)
\(68\) −8.90833 −1.08029
\(69\) −6.21110 −0.747729
\(70\) 0 0
\(71\) −4.30278 −0.510646 −0.255323 0.966856i \(-0.582182\pi\)
−0.255323 + 0.966856i \(0.582182\pi\)
\(72\) 6.90833 0.814154
\(73\) 5.00000 0.585206 0.292603 0.956234i \(-0.405479\pi\)
0.292603 + 0.956234i \(0.405479\pi\)
\(74\) −12.0000 −1.39497
\(75\) 18.4222 2.12721
\(76\) 9.90833 1.13656
\(77\) 0 0
\(78\) −35.0278 −3.96611
\(79\) −8.30278 −0.934135 −0.467068 0.884222i \(-0.654690\pi\)
−0.467068 + 0.884222i \(0.654690\pi\)
\(80\) −1.09167 −0.122053
\(81\) −10.6056 −1.17839
\(82\) −16.1194 −1.78009
\(83\) −3.00000 −0.329293 −0.164646 0.986353i \(-0.552648\pi\)
−0.164646 + 0.986353i \(0.552648\pi\)
\(84\) 0 0
\(85\) 9.72498 1.05482
\(86\) 3.90833 0.421446
\(87\) 10.8167 1.15967
\(88\) 0 0
\(89\) 14.7250 1.56084 0.780422 0.625253i \(-0.215004\pi\)
0.780422 + 0.625253i \(0.215004\pi\)
\(90\) −19.1194 −2.01536
\(91\) 0 0
\(92\) −8.90833 −0.928757
\(93\) −2.30278 −0.238787
\(94\) 4.39445 0.453253
\(95\) −10.8167 −1.10977
\(96\) −12.2111 −1.24629
\(97\) 3.60555 0.366088 0.183044 0.983105i \(-0.441405\pi\)
0.183044 + 0.983105i \(0.441405\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 26.4222 2.64222
\(101\) 5.30278 0.527646 0.263823 0.964571i \(-0.415017\pi\)
0.263823 + 0.964571i \(0.415017\pi\)
\(102\) −14.3028 −1.41619
\(103\) 14.3028 1.40929 0.704647 0.709558i \(-0.251105\pi\)
0.704647 + 0.709558i \(0.251105\pi\)
\(104\) −19.8167 −1.94318
\(105\) 0 0
\(106\) −29.7250 −2.88715
\(107\) 12.3944 1.19822 0.599108 0.800668i \(-0.295522\pi\)
0.599108 + 0.800668i \(0.295522\pi\)
\(108\) −5.30278 −0.510260
\(109\) −8.00000 −0.766261 −0.383131 0.923694i \(-0.625154\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(110\) 0 0
\(111\) −12.0000 −1.13899
\(112\) 0 0
\(113\) −10.6972 −1.00631 −0.503155 0.864196i \(-0.667828\pi\)
−0.503155 + 0.864196i \(0.667828\pi\)
\(114\) 15.9083 1.48995
\(115\) 9.72498 0.906859
\(116\) 15.5139 1.44043
\(117\) −15.2111 −1.40627
\(118\) −15.4222 −1.41973
\(119\) 0 0
\(120\) −24.9083 −2.27381
\(121\) 0 0
\(122\) 9.90833 0.897058
\(123\) −16.1194 −1.45344
\(124\) −3.30278 −0.296598
\(125\) −10.8167 −0.967471
\(126\) 0 0
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) −18.9083 −1.67128
\(129\) 3.90833 0.344109
\(130\) 54.8444 4.81017
\(131\) 6.00000 0.524222 0.262111 0.965038i \(-0.415581\pi\)
0.262111 + 0.965038i \(0.415581\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 19.6056 1.69366
\(135\) 5.78890 0.498229
\(136\) −8.09167 −0.693855
\(137\) −10.1194 −0.864561 −0.432281 0.901739i \(-0.642291\pi\)
−0.432281 + 0.901739i \(0.642291\pi\)
\(138\) −14.3028 −1.21753
\(139\) −21.6056 −1.83256 −0.916279 0.400540i \(-0.868823\pi\)
−0.916279 + 0.400540i \(0.868823\pi\)
\(140\) 0 0
\(141\) 4.39445 0.370079
\(142\) −9.90833 −0.831488
\(143\) 0 0
\(144\) 0.697224 0.0581020
\(145\) −16.9361 −1.40647
\(146\) 11.5139 0.952895
\(147\) 0 0
\(148\) −17.2111 −1.41474
\(149\) −4.90833 −0.402106 −0.201053 0.979580i \(-0.564436\pi\)
−0.201053 + 0.979580i \(0.564436\pi\)
\(150\) 42.4222 3.46376
\(151\) −0.211103 −0.0171793 −0.00858964 0.999963i \(-0.502734\pi\)
−0.00858964 + 0.999963i \(0.502734\pi\)
\(152\) 9.00000 0.729996
\(153\) −6.21110 −0.502138
\(154\) 0 0
\(155\) 3.60555 0.289605
\(156\) −50.2389 −4.02233
\(157\) −7.21110 −0.575509 −0.287754 0.957704i \(-0.592909\pi\)
−0.287754 + 0.957704i \(0.592909\pi\)
\(158\) −19.1194 −1.52106
\(159\) −29.7250 −2.35734
\(160\) 19.1194 1.51152
\(161\) 0 0
\(162\) −24.4222 −1.91879
\(163\) 2.81665 0.220617 0.110309 0.993897i \(-0.464816\pi\)
0.110309 + 0.993897i \(0.464816\pi\)
\(164\) −23.1194 −1.80532
\(165\) 0 0
\(166\) −6.90833 −0.536190
\(167\) 5.21110 0.403247 0.201624 0.979463i \(-0.435378\pi\)
0.201624 + 0.979463i \(0.435378\pi\)
\(168\) 0 0
\(169\) 30.6333 2.35641
\(170\) 22.3944 1.71758
\(171\) 6.90833 0.528293
\(172\) 5.60555 0.427419
\(173\) 1.30278 0.0990482 0.0495241 0.998773i \(-0.484230\pi\)
0.0495241 + 0.998773i \(0.484230\pi\)
\(174\) 24.9083 1.88830
\(175\) 0 0
\(176\) 0 0
\(177\) −15.4222 −1.15920
\(178\) 33.9083 2.54154
\(179\) −6.39445 −0.477944 −0.238972 0.971027i \(-0.576810\pi\)
−0.238972 + 0.971027i \(0.576810\pi\)
\(180\) −27.4222 −2.04393
\(181\) 25.2111 1.87393 0.936963 0.349428i \(-0.113624\pi\)
0.936963 + 0.349428i \(0.113624\pi\)
\(182\) 0 0
\(183\) 9.90833 0.732445
\(184\) −8.09167 −0.596526
\(185\) 18.7889 1.38139
\(186\) −5.30278 −0.388818
\(187\) 0 0
\(188\) 6.30278 0.459677
\(189\) 0 0
\(190\) −24.9083 −1.80704
\(191\) −26.8167 −1.94038 −0.970192 0.242336i \(-0.922086\pi\)
−0.970192 + 0.242336i \(0.922086\pi\)
\(192\) −29.5139 −2.12998
\(193\) −2.11943 −0.152560 −0.0762799 0.997086i \(-0.524304\pi\)
−0.0762799 + 0.997086i \(0.524304\pi\)
\(194\) 8.30278 0.596105
\(195\) 54.8444 3.92749
\(196\) 0 0
\(197\) −10.6056 −0.755614 −0.377807 0.925884i \(-0.623322\pi\)
−0.377807 + 0.925884i \(0.623322\pi\)
\(198\) 0 0
\(199\) −19.4222 −1.37680 −0.688402 0.725330i \(-0.741687\pi\)
−0.688402 + 0.725330i \(0.741687\pi\)
\(200\) 24.0000 1.69706
\(201\) 19.6056 1.38287
\(202\) 12.2111 0.859170
\(203\) 0 0
\(204\) −20.5139 −1.43626
\(205\) 25.2389 1.76276
\(206\) 32.9361 2.29477
\(207\) −6.21110 −0.431701
\(208\) −2.00000 −0.138675
\(209\) 0 0
\(210\) 0 0
\(211\) 15.5139 1.06802 0.534010 0.845478i \(-0.320685\pi\)
0.534010 + 0.845478i \(0.320685\pi\)
\(212\) −42.6333 −2.92807
\(213\) −9.90833 −0.678907
\(214\) 28.5416 1.95107
\(215\) −6.11943 −0.417342
\(216\) −4.81665 −0.327732
\(217\) 0 0
\(218\) −18.4222 −1.24771
\(219\) 11.5139 0.778036
\(220\) 0 0
\(221\) 17.8167 1.19848
\(222\) −27.6333 −1.85463
\(223\) −13.9083 −0.931370 −0.465685 0.884950i \(-0.654192\pi\)
−0.465685 + 0.884950i \(0.654192\pi\)
\(224\) 0 0
\(225\) 18.4222 1.22815
\(226\) −24.6333 −1.63858
\(227\) −6.51388 −0.432341 −0.216171 0.976356i \(-0.569357\pi\)
−0.216171 + 0.976356i \(0.569357\pi\)
\(228\) 22.8167 1.51107
\(229\) 2.60555 0.172180 0.0860898 0.996287i \(-0.472563\pi\)
0.0860898 + 0.996287i \(0.472563\pi\)
\(230\) 22.3944 1.47665
\(231\) 0 0
\(232\) 14.0917 0.925164
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) −35.0278 −2.28984
\(235\) −6.88057 −0.448839
\(236\) −22.1194 −1.43985
\(237\) −19.1194 −1.24194
\(238\) 0 0
\(239\) 26.3305 1.70318 0.851590 0.524208i \(-0.175639\pi\)
0.851590 + 0.524208i \(0.175639\pi\)
\(240\) −2.51388 −0.162270
\(241\) −0.486122 −0.0313139 −0.0156569 0.999877i \(-0.504984\pi\)
−0.0156569 + 0.999877i \(0.504984\pi\)
\(242\) 0 0
\(243\) −19.6056 −1.25770
\(244\) 14.2111 0.909773
\(245\) 0 0
\(246\) −37.1194 −2.36665
\(247\) −19.8167 −1.26090
\(248\) −3.00000 −0.190500
\(249\) −6.90833 −0.437797
\(250\) −24.9083 −1.57534
\(251\) −4.39445 −0.277375 −0.138688 0.990336i \(-0.544288\pi\)
−0.138688 + 0.990336i \(0.544288\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 4.60555 0.288978
\(255\) 22.3944 1.40239
\(256\) −17.9083 −1.11927
\(257\) −6.48612 −0.404593 −0.202297 0.979324i \(-0.564840\pi\)
−0.202297 + 0.979324i \(0.564840\pi\)
\(258\) 9.00000 0.560316
\(259\) 0 0
\(260\) 78.6611 4.87835
\(261\) 10.8167 0.669534
\(262\) 13.8167 0.853596
\(263\) 20.2389 1.24798 0.623991 0.781432i \(-0.285510\pi\)
0.623991 + 0.781432i \(0.285510\pi\)
\(264\) 0 0
\(265\) 46.5416 2.85903
\(266\) 0 0
\(267\) 33.9083 2.07516
\(268\) 28.1194 1.71767
\(269\) −16.1194 −0.982819 −0.491409 0.870929i \(-0.663518\pi\)
−0.491409 + 0.870929i \(0.663518\pi\)
\(270\) 13.3305 0.811270
\(271\) 28.5139 1.73209 0.866047 0.499962i \(-0.166653\pi\)
0.866047 + 0.499962i \(0.166653\pi\)
\(272\) −0.816654 −0.0495169
\(273\) 0 0
\(274\) −23.3028 −1.40777
\(275\) 0 0
\(276\) −20.5139 −1.23479
\(277\) 29.9361 1.79868 0.899342 0.437245i \(-0.144046\pi\)
0.899342 + 0.437245i \(0.144046\pi\)
\(278\) −49.7527 −2.98397
\(279\) −2.30278 −0.137864
\(280\) 0 0
\(281\) 6.39445 0.381461 0.190730 0.981642i \(-0.438914\pi\)
0.190730 + 0.981642i \(0.438914\pi\)
\(282\) 10.1194 0.602603
\(283\) −4.39445 −0.261223 −0.130611 0.991434i \(-0.541694\pi\)
−0.130611 + 0.991434i \(0.541694\pi\)
\(284\) −14.2111 −0.843274
\(285\) −24.9083 −1.47544
\(286\) 0 0
\(287\) 0 0
\(288\) −12.2111 −0.719546
\(289\) −9.72498 −0.572058
\(290\) −39.0000 −2.29016
\(291\) 8.30278 0.486717
\(292\) 16.5139 0.966402
\(293\) −4.81665 −0.281392 −0.140696 0.990053i \(-0.544934\pi\)
−0.140696 + 0.990053i \(0.544934\pi\)
\(294\) 0 0
\(295\) 24.1472 1.40590
\(296\) −15.6333 −0.908668
\(297\) 0 0
\(298\) −11.3028 −0.654752
\(299\) 17.8167 1.03036
\(300\) 60.8444 3.51285
\(301\) 0 0
\(302\) −0.486122 −0.0279732
\(303\) 12.2111 0.701510
\(304\) 0.908327 0.0520961
\(305\) −15.5139 −0.888322
\(306\) −14.3028 −0.817635
\(307\) 16.6333 0.949313 0.474657 0.880171i \(-0.342572\pi\)
0.474657 + 0.880171i \(0.342572\pi\)
\(308\) 0 0
\(309\) 32.9361 1.87367
\(310\) 8.30278 0.471566
\(311\) −6.39445 −0.362596 −0.181298 0.983428i \(-0.558030\pi\)
−0.181298 + 0.983428i \(0.558030\pi\)
\(312\) −45.6333 −2.58348
\(313\) −15.3028 −0.864964 −0.432482 0.901643i \(-0.642362\pi\)
−0.432482 + 0.901643i \(0.642362\pi\)
\(314\) −16.6056 −0.937105
\(315\) 0 0
\(316\) −27.4222 −1.54262
\(317\) 17.3028 0.971821 0.485910 0.874009i \(-0.338488\pi\)
0.485910 + 0.874009i \(0.338488\pi\)
\(318\) −68.4500 −3.83848
\(319\) 0 0
\(320\) 46.2111 2.58328
\(321\) 28.5416 1.59304
\(322\) 0 0
\(323\) −8.09167 −0.450233
\(324\) −35.0278 −1.94599
\(325\) −52.8444 −2.93128
\(326\) 6.48612 0.359233
\(327\) −18.4222 −1.01875
\(328\) −21.0000 −1.15953
\(329\) 0 0
\(330\) 0 0
\(331\) 23.8167 1.30908 0.654541 0.756027i \(-0.272862\pi\)
0.654541 + 0.756027i \(0.272862\pi\)
\(332\) −9.90833 −0.543790
\(333\) −12.0000 −0.657596
\(334\) 12.0000 0.656611
\(335\) −30.6972 −1.67717
\(336\) 0 0
\(337\) 11.7889 0.642182 0.321091 0.947048i \(-0.395950\pi\)
0.321091 + 0.947048i \(0.395950\pi\)
\(338\) 70.5416 3.83696
\(339\) −24.6333 −1.33790
\(340\) 32.1194 1.74192
\(341\) 0 0
\(342\) 15.9083 0.860224
\(343\) 0 0
\(344\) 5.09167 0.274525
\(345\) 22.3944 1.20568
\(346\) 3.00000 0.161281
\(347\) 9.60555 0.515653 0.257827 0.966191i \(-0.416994\pi\)
0.257827 + 0.966191i \(0.416994\pi\)
\(348\) 35.7250 1.91506
\(349\) 4.69722 0.251437 0.125718 0.992066i \(-0.459876\pi\)
0.125718 + 0.992066i \(0.459876\pi\)
\(350\) 0 0
\(351\) 10.6056 0.566082
\(352\) 0 0
\(353\) −5.09167 −0.271002 −0.135501 0.990777i \(-0.543264\pi\)
−0.135501 + 0.990777i \(0.543264\pi\)
\(354\) −35.5139 −1.88754
\(355\) 15.5139 0.823391
\(356\) 48.6333 2.57756
\(357\) 0 0
\(358\) −14.7250 −0.778239
\(359\) −33.9361 −1.79108 −0.895539 0.444983i \(-0.853210\pi\)
−0.895539 + 0.444983i \(0.853210\pi\)
\(360\) −24.9083 −1.31278
\(361\) −10.0000 −0.526316
\(362\) 58.0555 3.05133
\(363\) 0 0
\(364\) 0 0
\(365\) −18.0278 −0.943616
\(366\) 22.8167 1.19265
\(367\) 17.6333 0.920451 0.460226 0.887802i \(-0.347769\pi\)
0.460226 + 0.887802i \(0.347769\pi\)
\(368\) −0.816654 −0.0425710
\(369\) −16.1194 −0.839144
\(370\) 43.2666 2.24932
\(371\) 0 0
\(372\) −7.60555 −0.394329
\(373\) −20.1194 −1.04174 −0.520872 0.853635i \(-0.674393\pi\)
−0.520872 + 0.853635i \(0.674393\pi\)
\(374\) 0 0
\(375\) −24.9083 −1.28626
\(376\) 5.72498 0.295243
\(377\) −31.0278 −1.59801
\(378\) 0 0
\(379\) −15.8167 −0.812447 −0.406223 0.913774i \(-0.633155\pi\)
−0.406223 + 0.913774i \(0.633155\pi\)
\(380\) −35.7250 −1.83265
\(381\) 4.60555 0.235950
\(382\) −61.7527 −3.15954
\(383\) −38.6333 −1.97407 −0.987035 0.160506i \(-0.948687\pi\)
−0.987035 + 0.160506i \(0.948687\pi\)
\(384\) −43.5416 −2.22197
\(385\) 0 0
\(386\) −4.88057 −0.248414
\(387\) 3.90833 0.198671
\(388\) 11.9083 0.604554
\(389\) −7.81665 −0.396320 −0.198160 0.980170i \(-0.563497\pi\)
−0.198160 + 0.980170i \(0.563497\pi\)
\(390\) 126.294 6.39516
\(391\) 7.27502 0.367914
\(392\) 0 0
\(393\) 13.8167 0.696958
\(394\) −24.4222 −1.23037
\(395\) 29.9361 1.50625
\(396\) 0 0
\(397\) −30.2111 −1.51625 −0.758126 0.652108i \(-0.773885\pi\)
−0.758126 + 0.652108i \(0.773885\pi\)
\(398\) −44.7250 −2.24186
\(399\) 0 0
\(400\) 2.42221 0.121110
\(401\) −21.2111 −1.05923 −0.529616 0.848238i \(-0.677664\pi\)
−0.529616 + 0.848238i \(0.677664\pi\)
\(402\) 45.1472 2.25174
\(403\) 6.60555 0.329046
\(404\) 17.5139 0.871348
\(405\) 38.2389 1.90010
\(406\) 0 0
\(407\) 0 0
\(408\) −18.6333 −0.922486
\(409\) −20.6056 −1.01888 −0.509439 0.860506i \(-0.670147\pi\)
−0.509439 + 0.860506i \(0.670147\pi\)
\(410\) 58.1194 2.87031
\(411\) −23.3028 −1.14944
\(412\) 47.2389 2.32729
\(413\) 0 0
\(414\) −14.3028 −0.702943
\(415\) 10.8167 0.530969
\(416\) 35.0278 1.71738
\(417\) −49.7527 −2.43640
\(418\) 0 0
\(419\) 38.4222 1.87705 0.938524 0.345215i \(-0.112194\pi\)
0.938524 + 0.345215i \(0.112194\pi\)
\(420\) 0 0
\(421\) −21.8167 −1.06328 −0.531639 0.846971i \(-0.678424\pi\)
−0.531639 + 0.846971i \(0.678424\pi\)
\(422\) 35.7250 1.73906
\(423\) 4.39445 0.213665
\(424\) −38.7250 −1.88065
\(425\) −21.5778 −1.04668
\(426\) −22.8167 −1.10547
\(427\) 0 0
\(428\) 40.9361 1.97872
\(429\) 0 0
\(430\) −14.0917 −0.679561
\(431\) −3.11943 −0.150258 −0.0751288 0.997174i \(-0.523937\pi\)
−0.0751288 + 0.997174i \(0.523937\pi\)
\(432\) −0.486122 −0.0233885
\(433\) −29.1472 −1.40072 −0.700362 0.713788i \(-0.746978\pi\)
−0.700362 + 0.713788i \(0.746978\pi\)
\(434\) 0 0
\(435\) −39.0000 −1.86991
\(436\) −26.4222 −1.26539
\(437\) −8.09167 −0.387077
\(438\) 26.5139 1.26688
\(439\) −27.7250 −1.32324 −0.661621 0.749839i \(-0.730131\pi\)
−0.661621 + 0.749839i \(0.730131\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 41.0278 1.95149
\(443\) 26.9361 1.27977 0.639886 0.768470i \(-0.278982\pi\)
0.639886 + 0.768470i \(0.278982\pi\)
\(444\) −39.6333 −1.88091
\(445\) −53.0917 −2.51679
\(446\) −32.0278 −1.51656
\(447\) −11.3028 −0.534603
\(448\) 0 0
\(449\) 40.3305 1.90332 0.951658 0.307160i \(-0.0993788\pi\)
0.951658 + 0.307160i \(0.0993788\pi\)
\(450\) 42.4222 1.99980
\(451\) 0 0
\(452\) −35.3305 −1.66181
\(453\) −0.486122 −0.0228400
\(454\) −15.0000 −0.703985
\(455\) 0 0
\(456\) 20.7250 0.970536
\(457\) 21.1194 0.987925 0.493963 0.869483i \(-0.335548\pi\)
0.493963 + 0.869483i \(0.335548\pi\)
\(458\) 6.00000 0.280362
\(459\) 4.33053 0.202132
\(460\) 32.1194 1.49758
\(461\) −8.09167 −0.376867 −0.188433 0.982086i \(-0.560341\pi\)
−0.188433 + 0.982086i \(0.560341\pi\)
\(462\) 0 0
\(463\) −30.8167 −1.43217 −0.716086 0.698012i \(-0.754068\pi\)
−0.716086 + 0.698012i \(0.754068\pi\)
\(464\) 1.42221 0.0660242
\(465\) 8.30278 0.385032
\(466\) 41.4500 1.92013
\(467\) 13.5416 0.626632 0.313316 0.949649i \(-0.398560\pi\)
0.313316 + 0.949649i \(0.398560\pi\)
\(468\) −50.2389 −2.32229
\(469\) 0 0
\(470\) −15.8444 −0.730848
\(471\) −16.6056 −0.765143
\(472\) −20.0917 −0.924794
\(473\) 0 0
\(474\) −44.0278 −2.02226
\(475\) 24.0000 1.10120
\(476\) 0 0
\(477\) −29.7250 −1.36101
\(478\) 60.6333 2.77330
\(479\) 28.6333 1.30829 0.654145 0.756370i \(-0.273029\pi\)
0.654145 + 0.756370i \(0.273029\pi\)
\(480\) 44.0278 2.00958
\(481\) 34.4222 1.56952
\(482\) −1.11943 −0.0509886
\(483\) 0 0
\(484\) 0 0
\(485\) −13.0000 −0.590300
\(486\) −45.1472 −2.04792
\(487\) −2.81665 −0.127635 −0.0638174 0.997962i \(-0.520328\pi\)
−0.0638174 + 0.997962i \(0.520328\pi\)
\(488\) 12.9083 0.584333
\(489\) 6.48612 0.293313
\(490\) 0 0
\(491\) −12.6972 −0.573018 −0.286509 0.958078i \(-0.592495\pi\)
−0.286509 + 0.958078i \(0.592495\pi\)
\(492\) −53.2389 −2.40019
\(493\) −12.6695 −0.570604
\(494\) −45.6333 −2.05314
\(495\) 0 0
\(496\) −0.302776 −0.0135950
\(497\) 0 0
\(498\) −15.9083 −0.712869
\(499\) 2.90833 0.130195 0.0650973 0.997879i \(-0.479264\pi\)
0.0650973 + 0.997879i \(0.479264\pi\)
\(500\) −35.7250 −1.59767
\(501\) 12.0000 0.536120
\(502\) −10.1194 −0.451652
\(503\) −5.57779 −0.248702 −0.124351 0.992238i \(-0.539685\pi\)
−0.124351 + 0.992238i \(0.539685\pi\)
\(504\) 0 0
\(505\) −19.1194 −0.850803
\(506\) 0 0
\(507\) 70.5416 3.13286
\(508\) 6.60555 0.293074
\(509\) −22.3028 −0.988553 −0.494277 0.869305i \(-0.664567\pi\)
−0.494277 + 0.869305i \(0.664567\pi\)
\(510\) 51.5694 2.28353
\(511\) 0 0
\(512\) −3.42221 −0.151242
\(513\) −4.81665 −0.212660
\(514\) −14.9361 −0.658802
\(515\) −51.5694 −2.27242
\(516\) 12.9083 0.568257
\(517\) 0 0
\(518\) 0 0
\(519\) 3.00000 0.131685
\(520\) 71.4500 3.13329
\(521\) −7.42221 −0.325173 −0.162586 0.986694i \(-0.551984\pi\)
−0.162586 + 0.986694i \(0.551984\pi\)
\(522\) 24.9083 1.09021
\(523\) 44.5416 1.94767 0.973835 0.227257i \(-0.0729757\pi\)
0.973835 + 0.227257i \(0.0729757\pi\)
\(524\) 19.8167 0.865695
\(525\) 0 0
\(526\) 46.6056 2.03210
\(527\) 2.69722 0.117493
\(528\) 0 0
\(529\) −15.7250 −0.683695
\(530\) 107.175 4.65538
\(531\) −15.4222 −0.669267
\(532\) 0 0
\(533\) 46.2389 2.00283
\(534\) 78.0833 3.37899
\(535\) −44.6888 −1.93207
\(536\) 25.5416 1.10323
\(537\) −14.7250 −0.635430
\(538\) −37.1194 −1.60033
\(539\) 0 0
\(540\) 19.1194 0.822769
\(541\) −32.3944 −1.39275 −0.696373 0.717680i \(-0.745204\pi\)
−0.696373 + 0.717680i \(0.745204\pi\)
\(542\) 65.6611 2.82038
\(543\) 58.0555 2.49140
\(544\) 14.3028 0.613226
\(545\) 28.8444 1.23556
\(546\) 0 0
\(547\) −29.9361 −1.27997 −0.639987 0.768386i \(-0.721060\pi\)
−0.639987 + 0.768386i \(0.721060\pi\)
\(548\) −33.4222 −1.42773
\(549\) 9.90833 0.422877
\(550\) 0 0
\(551\) 14.0917 0.600325
\(552\) −18.6333 −0.793086
\(553\) 0 0
\(554\) 68.9361 2.92881
\(555\) 43.2666 1.83657
\(556\) −71.3583 −3.02627
\(557\) 7.23886 0.306720 0.153360 0.988170i \(-0.450991\pi\)
0.153360 + 0.988170i \(0.450991\pi\)
\(558\) −5.30278 −0.224484
\(559\) −11.2111 −0.474179
\(560\) 0 0
\(561\) 0 0
\(562\) 14.7250 0.621136
\(563\) 0.302776 0.0127605 0.00638024 0.999980i \(-0.497969\pi\)
0.00638024 + 0.999980i \(0.497969\pi\)
\(564\) 14.5139 0.611145
\(565\) 38.5694 1.62263
\(566\) −10.1194 −0.425351
\(567\) 0 0
\(568\) −12.9083 −0.541621
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) −57.3583 −2.40247
\(571\) 25.8444 1.08155 0.540777 0.841166i \(-0.318130\pi\)
0.540777 + 0.841166i \(0.318130\pi\)
\(572\) 0 0
\(573\) −61.7527 −2.57976
\(574\) 0 0
\(575\) −21.5778 −0.899856
\(576\) −29.5139 −1.22974
\(577\) −2.21110 −0.0920494 −0.0460247 0.998940i \(-0.514655\pi\)
−0.0460247 + 0.998940i \(0.514655\pi\)
\(578\) −22.3944 −0.931486
\(579\) −4.88057 −0.202830
\(580\) −55.9361 −2.32262
\(581\) 0 0
\(582\) 19.1194 0.792526
\(583\) 0 0
\(584\) 15.0000 0.620704
\(585\) 54.8444 2.26754
\(586\) −11.0917 −0.458193
\(587\) 13.6056 0.561561 0.280781 0.959772i \(-0.409407\pi\)
0.280781 + 0.959772i \(0.409407\pi\)
\(588\) 0 0
\(589\) −3.00000 −0.123613
\(590\) 55.6056 2.28924
\(591\) −24.4222 −1.00460
\(592\) −1.57779 −0.0648470
\(593\) −22.6056 −0.928299 −0.464149 0.885757i \(-0.653640\pi\)
−0.464149 + 0.885757i \(0.653640\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −16.2111 −0.664033
\(597\) −44.7250 −1.83047
\(598\) 41.0278 1.67775
\(599\) −14.7889 −0.604258 −0.302129 0.953267i \(-0.597697\pi\)
−0.302129 + 0.953267i \(0.597697\pi\)
\(600\) 55.2666 2.25625
\(601\) 5.81665 0.237266 0.118633 0.992938i \(-0.462149\pi\)
0.118633 + 0.992938i \(0.462149\pi\)
\(602\) 0 0
\(603\) 19.6056 0.798400
\(604\) −0.697224 −0.0283697
\(605\) 0 0
\(606\) 28.1194 1.14227
\(607\) 20.5416 0.833759 0.416880 0.908962i \(-0.363124\pi\)
0.416880 + 0.908962i \(0.363124\pi\)
\(608\) −15.9083 −0.645168
\(609\) 0 0
\(610\) −35.7250 −1.44646
\(611\) −12.6056 −0.509966
\(612\) −20.5139 −0.829224
\(613\) −33.0555 −1.33510 −0.667550 0.744565i \(-0.732657\pi\)
−0.667550 + 0.744565i \(0.732657\pi\)
\(614\) 38.3028 1.54577
\(615\) 58.1194 2.34360
\(616\) 0 0
\(617\) 21.6333 0.870924 0.435462 0.900207i \(-0.356585\pi\)
0.435462 + 0.900207i \(0.356585\pi\)
\(618\) 75.8444 3.05091
\(619\) −39.8167 −1.60037 −0.800183 0.599756i \(-0.795264\pi\)
−0.800183 + 0.599756i \(0.795264\pi\)
\(620\) 11.9083 0.478250
\(621\) 4.33053 0.173778
\(622\) −14.7250 −0.590418
\(623\) 0 0
\(624\) −4.60555 −0.184370
\(625\) −1.00000 −0.0400000
\(626\) −35.2389 −1.40843
\(627\) 0 0
\(628\) −23.8167 −0.950388
\(629\) 14.0555 0.560430
\(630\) 0 0
\(631\) −31.0555 −1.23630 −0.618150 0.786060i \(-0.712118\pi\)
−0.618150 + 0.786060i \(0.712118\pi\)
\(632\) −24.9083 −0.990800
\(633\) 35.7250 1.41994
\(634\) 39.8444 1.58242
\(635\) −7.21110 −0.286164
\(636\) −98.1749 −3.89289
\(637\) 0 0
\(638\) 0 0
\(639\) −9.90833 −0.391967
\(640\) 68.1749 2.69485
\(641\) −28.8167 −1.13819 −0.569095 0.822272i \(-0.692706\pi\)
−0.569095 + 0.822272i \(0.692706\pi\)
\(642\) 65.7250 2.59396
\(643\) 1.23886 0.0488558 0.0244279 0.999702i \(-0.492224\pi\)
0.0244279 + 0.999702i \(0.492224\pi\)
\(644\) 0 0
\(645\) −14.0917 −0.554859
\(646\) −18.6333 −0.733118
\(647\) −10.6056 −0.416947 −0.208474 0.978028i \(-0.566850\pi\)
−0.208474 + 0.978028i \(0.566850\pi\)
\(648\) −31.8167 −1.24988
\(649\) 0 0
\(650\) −121.689 −4.77303
\(651\) 0 0
\(652\) 9.30278 0.364325
\(653\) −6.81665 −0.266756 −0.133378 0.991065i \(-0.542582\pi\)
−0.133378 + 0.991065i \(0.542582\pi\)
\(654\) −42.4222 −1.65884
\(655\) −21.6333 −0.845283
\(656\) −2.11943 −0.0827498
\(657\) 11.5139 0.449199
\(658\) 0 0
\(659\) 4.63331 0.180488 0.0902440 0.995920i \(-0.471235\pi\)
0.0902440 + 0.995920i \(0.471235\pi\)
\(660\) 0 0
\(661\) 18.3028 0.711895 0.355948 0.934506i \(-0.384158\pi\)
0.355948 + 0.934506i \(0.384158\pi\)
\(662\) 54.8444 2.13159
\(663\) 41.0278 1.59339
\(664\) −9.00000 −0.349268
\(665\) 0 0
\(666\) −27.6333 −1.07077
\(667\) −12.6695 −0.490564
\(668\) 17.2111 0.665918
\(669\) −32.0278 −1.23826
\(670\) −70.6888 −2.73095
\(671\) 0 0
\(672\) 0 0
\(673\) −8.42221 −0.324652 −0.162326 0.986737i \(-0.551900\pi\)
−0.162326 + 0.986737i \(0.551900\pi\)
\(674\) 27.1472 1.04567
\(675\) −12.8444 −0.494382
\(676\) 101.175 3.89134
\(677\) −10.3028 −0.395968 −0.197984 0.980205i \(-0.563439\pi\)
−0.197984 + 0.980205i \(0.563439\pi\)
\(678\) −56.7250 −2.17851
\(679\) 0 0
\(680\) 29.1749 1.11881
\(681\) −15.0000 −0.574801
\(682\) 0 0
\(683\) 15.6972 0.600638 0.300319 0.953839i \(-0.402907\pi\)
0.300319 + 0.953839i \(0.402907\pi\)
\(684\) 22.8167 0.872417
\(685\) 36.4861 1.39406
\(686\) 0 0
\(687\) 6.00000 0.228914
\(688\) 0.513878 0.0195914
\(689\) 85.2666 3.24840
\(690\) 51.5694 1.96321
\(691\) 17.0278 0.647766 0.323883 0.946097i \(-0.395012\pi\)
0.323883 + 0.946097i \(0.395012\pi\)
\(692\) 4.30278 0.163567
\(693\) 0 0
\(694\) 22.1194 0.839642
\(695\) 77.8999 2.95491
\(696\) 32.4500 1.23001
\(697\) 18.8806 0.715153
\(698\) 10.8167 0.409416
\(699\) 41.4500 1.56778
\(700\) 0 0
\(701\) −31.1194 −1.17536 −0.587682 0.809092i \(-0.699960\pi\)
−0.587682 + 0.809092i \(0.699960\pi\)
\(702\) 24.4222 0.921757
\(703\) −15.6333 −0.589621
\(704\) 0 0
\(705\) −15.8444 −0.596735
\(706\) −11.7250 −0.441275
\(707\) 0 0
\(708\) −50.9361 −1.91430
\(709\) 25.3305 0.951308 0.475654 0.879632i \(-0.342211\pi\)
0.475654 + 0.879632i \(0.342211\pi\)
\(710\) 35.7250 1.34073
\(711\) −19.1194 −0.717035
\(712\) 44.1749 1.65553
\(713\) 2.69722 0.101012
\(714\) 0 0
\(715\) 0 0
\(716\) −21.1194 −0.789270
\(717\) 60.6333 2.26439
\(718\) −78.1472 −2.91643
\(719\) −21.2389 −0.792076 −0.396038 0.918234i \(-0.629615\pi\)
−0.396038 + 0.918234i \(0.629615\pi\)
\(720\) −2.51388 −0.0936867
\(721\) 0 0
\(722\) −23.0278 −0.857004
\(723\) −1.11943 −0.0416320
\(724\) 83.2666 3.09458
\(725\) 37.5778 1.39560
\(726\) 0 0
\(727\) −24.1194 −0.894540 −0.447270 0.894399i \(-0.647604\pi\)
−0.447270 + 0.894399i \(0.647604\pi\)
\(728\) 0 0
\(729\) −13.3305 −0.493723
\(730\) −41.5139 −1.53650
\(731\) −4.57779 −0.169316
\(732\) 32.7250 1.20955
\(733\) 6.78890 0.250754 0.125377 0.992109i \(-0.459986\pi\)
0.125377 + 0.992109i \(0.459986\pi\)
\(734\) 40.6056 1.49878
\(735\) 0 0
\(736\) 14.3028 0.527207
\(737\) 0 0
\(738\) −37.1194 −1.36639
\(739\) −43.1194 −1.58617 −0.793087 0.609108i \(-0.791527\pi\)
−0.793087 + 0.609108i \(0.791527\pi\)
\(740\) 62.0555 2.28121
\(741\) −45.6333 −1.67638
\(742\) 0 0
\(743\) 44.9361 1.64855 0.824273 0.566193i \(-0.191584\pi\)
0.824273 + 0.566193i \(0.191584\pi\)
\(744\) −6.90833 −0.253272
\(745\) 17.6972 0.648376
\(746\) −46.3305 −1.69628
\(747\) −6.90833 −0.252762
\(748\) 0 0
\(749\) 0 0
\(750\) −57.3583 −2.09443
\(751\) 7.63331 0.278543 0.139272 0.990254i \(-0.455524\pi\)
0.139272 + 0.990254i \(0.455524\pi\)
\(752\) 0.577795 0.0210700
\(753\) −10.1194 −0.368773
\(754\) −71.4500 −2.60205
\(755\) 0.761141 0.0277008
\(756\) 0 0
\(757\) −23.8167 −0.865631 −0.432816 0.901483i \(-0.642480\pi\)
−0.432816 + 0.901483i \(0.642480\pi\)
\(758\) −36.4222 −1.32291
\(759\) 0 0
\(760\) −32.4500 −1.17708
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 10.6056 0.384199
\(763\) 0 0
\(764\) −88.5694 −3.20433
\(765\) 22.3944 0.809673
\(766\) −88.9638 −3.21439
\(767\) 44.2389 1.59737
\(768\) −41.2389 −1.48808
\(769\) 39.3305 1.41830 0.709148 0.705060i \(-0.249080\pi\)
0.709148 + 0.705060i \(0.249080\pi\)
\(770\) 0 0
\(771\) −14.9361 −0.537910
\(772\) −7.00000 −0.251936
\(773\) −30.6333 −1.10180 −0.550902 0.834570i \(-0.685716\pi\)
−0.550902 + 0.834570i \(0.685716\pi\)
\(774\) 9.00000 0.323498
\(775\) −8.00000 −0.287368
\(776\) 10.8167 0.388295
\(777\) 0 0
\(778\) −18.0000 −0.645331
\(779\) −21.0000 −0.752403
\(780\) 181.139 6.48581
\(781\) 0 0
\(782\) 16.7527 0.599077
\(783\) −7.54163 −0.269516
\(784\) 0 0
\(785\) 26.0000 0.927980
\(786\) 31.8167 1.13486
\(787\) 22.4861 0.801544 0.400772 0.916178i \(-0.368742\pi\)
0.400772 + 0.916178i \(0.368742\pi\)
\(788\) −35.0278 −1.24781
\(789\) 46.6056 1.65920
\(790\) 68.9361 2.45264
\(791\) 0 0
\(792\) 0 0
\(793\) −28.4222 −1.00930
\(794\) −69.5694 −2.46893
\(795\) 107.175 3.80110
\(796\) −64.1472 −2.27364
\(797\) 28.6333 1.01424 0.507122 0.861874i \(-0.330709\pi\)
0.507122 + 0.861874i \(0.330709\pi\)
\(798\) 0 0
\(799\) −5.14719 −0.182094
\(800\) −42.4222 −1.49985
\(801\) 33.9083 1.19809
\(802\) −48.8444 −1.72476
\(803\) 0 0
\(804\) 64.7527 2.28365
\(805\) 0 0
\(806\) 15.2111 0.535788
\(807\) −37.1194 −1.30667
\(808\) 15.9083 0.559653
\(809\) 8.09167 0.284488 0.142244 0.989832i \(-0.454568\pi\)
0.142244 + 0.989832i \(0.454568\pi\)
\(810\) 88.0555 3.09396
\(811\) 40.8444 1.43424 0.717121 0.696949i \(-0.245460\pi\)
0.717121 + 0.696949i \(0.245460\pi\)
\(812\) 0 0
\(813\) 65.6611 2.30283
\(814\) 0 0
\(815\) −10.1556 −0.355735
\(816\) −1.88057 −0.0658331
\(817\) 5.09167 0.178135
\(818\) −47.4500 −1.65905
\(819\) 0 0
\(820\) 83.3583 2.91100
\(821\) −27.4222 −0.957042 −0.478521 0.878076i \(-0.658827\pi\)
−0.478521 + 0.878076i \(0.658827\pi\)
\(822\) −53.6611 −1.87164
\(823\) 35.2111 1.22738 0.613691 0.789546i \(-0.289684\pi\)
0.613691 + 0.789546i \(0.289684\pi\)
\(824\) 42.9083 1.49478
\(825\) 0 0
\(826\) 0 0
\(827\) −14.1833 −0.493203 −0.246602 0.969117i \(-0.579314\pi\)
−0.246602 + 0.969117i \(0.579314\pi\)
\(828\) −20.5139 −0.712907
\(829\) −13.2750 −0.461060 −0.230530 0.973065i \(-0.574046\pi\)
−0.230530 + 0.973065i \(0.574046\pi\)
\(830\) 24.9083 0.864581
\(831\) 68.9361 2.39137
\(832\) 84.6611 2.93509
\(833\) 0 0
\(834\) −114.569 −3.96721
\(835\) −18.7889 −0.650217
\(836\) 0 0
\(837\) 1.60555 0.0554960
\(838\) 88.4777 3.05641
\(839\) −42.2111 −1.45729 −0.728645 0.684892i \(-0.759849\pi\)
−0.728645 + 0.684892i \(0.759849\pi\)
\(840\) 0 0
\(841\) −6.93608 −0.239175
\(842\) −50.2389 −1.73135
\(843\) 14.7250 0.507155
\(844\) 51.2389 1.76371
\(845\) −110.450 −3.79959
\(846\) 10.1194 0.347913
\(847\) 0 0
\(848\) −3.90833 −0.134212
\(849\) −10.1194 −0.347298
\(850\) −49.6888 −1.70431
\(851\) 14.0555 0.481817
\(852\) −32.7250 −1.12114
\(853\) 45.7250 1.56559 0.782797 0.622277i \(-0.213792\pi\)
0.782797 + 0.622277i \(0.213792\pi\)
\(854\) 0 0
\(855\) −24.9083 −0.851847
\(856\) 37.1833 1.27090
\(857\) −35.3583 −1.20782 −0.603908 0.797054i \(-0.706391\pi\)
−0.603908 + 0.797054i \(0.706391\pi\)
\(858\) 0 0
\(859\) 25.3028 0.863320 0.431660 0.902036i \(-0.357928\pi\)
0.431660 + 0.902036i \(0.357928\pi\)
\(860\) −20.2111 −0.689193
\(861\) 0 0
\(862\) −7.18335 −0.244666
\(863\) 31.4222 1.06962 0.534812 0.844971i \(-0.320382\pi\)
0.534812 + 0.844971i \(0.320382\pi\)
\(864\) 8.51388 0.289648
\(865\) −4.69722 −0.159710
\(866\) −67.1194 −2.28081
\(867\) −22.3944 −0.760555
\(868\) 0 0
\(869\) 0 0
\(870\) −89.8082 −3.04478
\(871\) −56.2389 −1.90558
\(872\) −24.0000 −0.812743
\(873\) 8.30278 0.281006
\(874\) −18.6333 −0.630281
\(875\) 0 0
\(876\) 38.0278 1.28484
\(877\) 47.0555 1.58895 0.794476 0.607296i \(-0.207746\pi\)
0.794476 + 0.607296i \(0.207746\pi\)
\(878\) −63.8444 −2.15464
\(879\) −11.0917 −0.374113
\(880\) 0 0
\(881\) −34.3305 −1.15663 −0.578313 0.815815i \(-0.696289\pi\)
−0.578313 + 0.815815i \(0.696289\pi\)
\(882\) 0 0
\(883\) −7.72498 −0.259966 −0.129983 0.991516i \(-0.541492\pi\)
−0.129983 + 0.991516i \(0.541492\pi\)
\(884\) 58.8444 1.97915
\(885\) 55.6056 1.86916
\(886\) 62.0278 2.08386
\(887\) −44.1194 −1.48139 −0.740693 0.671844i \(-0.765503\pi\)
−0.740693 + 0.671844i \(0.765503\pi\)
\(888\) −36.0000 −1.20808
\(889\) 0 0
\(890\) −122.258 −4.09810
\(891\) 0 0
\(892\) −45.9361 −1.53805
\(893\) 5.72498 0.191579
\(894\) −26.0278 −0.870498
\(895\) 23.0555 0.770661
\(896\) 0 0
\(897\) 41.0278 1.36988
\(898\) 92.8722 3.09918
\(899\) −4.69722 −0.156661
\(900\) 60.8444 2.02815
\(901\) 34.8167 1.15991
\(902\) 0 0
\(903\) 0 0
\(904\) −32.0917 −1.06735
\(905\) −90.8999 −3.02162
\(906\) −1.11943 −0.0371906
\(907\) 0.394449 0.0130975 0.00654873 0.999979i \(-0.497915\pi\)
0.00654873 + 0.999979i \(0.497915\pi\)
\(908\) −21.5139 −0.713963
\(909\) 12.2111 0.405017
\(910\) 0 0
\(911\) −50.4500 −1.67148 −0.835741 0.549124i \(-0.814961\pi\)
−0.835741 + 0.549124i \(0.814961\pi\)
\(912\) 2.09167 0.0692622
\(913\) 0 0
\(914\) 48.6333 1.60865
\(915\) −35.7250 −1.18103
\(916\) 8.60555 0.284335
\(917\) 0 0
\(918\) 9.97224 0.329133
\(919\) 55.4777 1.83004 0.915021 0.403407i \(-0.132174\pi\)
0.915021 + 0.403407i \(0.132174\pi\)
\(920\) 29.1749 0.961869
\(921\) 38.3028 1.26212
\(922\) −18.6333 −0.613655
\(923\) 28.4222 0.935528
\(924\) 0 0
\(925\) −41.6888 −1.37072
\(926\) −70.9638 −2.33202
\(927\) 32.9361 1.08176
\(928\) −24.9083 −0.817656
\(929\) 27.6333 0.906619 0.453310 0.891353i \(-0.350243\pi\)
0.453310 + 0.891353i \(0.350243\pi\)
\(930\) 19.1194 0.626951
\(931\) 0 0
\(932\) 59.4500 1.94735
\(933\) −14.7250 −0.482074
\(934\) 31.1833 1.02035
\(935\) 0 0
\(936\) −45.6333 −1.49157
\(937\) −31.6056 −1.03251 −0.516254 0.856435i \(-0.672674\pi\)
−0.516254 + 0.856435i \(0.672674\pi\)
\(938\) 0 0
\(939\) −35.2389 −1.14998
\(940\) −22.7250 −0.741207
\(941\) −37.4222 −1.21993 −0.609965 0.792429i \(-0.708816\pi\)
−0.609965 + 0.792429i \(0.708816\pi\)
\(942\) −38.2389 −1.24589
\(943\) 18.8806 0.614836
\(944\) −2.02776 −0.0659978
\(945\) 0 0
\(946\) 0 0
\(947\) 46.6611 1.51628 0.758140 0.652091i \(-0.226108\pi\)
0.758140 + 0.652091i \(0.226108\pi\)
\(948\) −63.1472 −2.05093
\(949\) −33.0278 −1.07213
\(950\) 55.2666 1.79309
\(951\) 39.8444 1.29204
\(952\) 0 0
\(953\) −6.02776 −0.195258 −0.0976291 0.995223i \(-0.531126\pi\)
−0.0976291 + 0.995223i \(0.531126\pi\)
\(954\) −68.4500 −2.21615
\(955\) 96.6888 3.12878
\(956\) 86.9638 2.81261
\(957\) 0 0
\(958\) 65.9361 2.13030
\(959\) 0 0
\(960\) 106.414 3.43449
\(961\) −30.0000 −0.967742
\(962\) 79.2666 2.55566
\(963\) 28.5416 0.919741
\(964\) −1.60555 −0.0517113
\(965\) 7.64171 0.245995
\(966\) 0 0
\(967\) 40.5139 1.30284 0.651419 0.758718i \(-0.274174\pi\)
0.651419 + 0.758718i \(0.274174\pi\)
\(968\) 0 0
\(969\) −18.6333 −0.598588
\(970\) −29.9361 −0.961190
\(971\) 6.36669 0.204317 0.102158 0.994768i \(-0.467425\pi\)
0.102158 + 0.994768i \(0.467425\pi\)
\(972\) −64.7527 −2.07695
\(973\) 0 0
\(974\) −6.48612 −0.207829
\(975\) −121.689 −3.89716
\(976\) 1.30278 0.0417008
\(977\) 40.0278 1.28060 0.640301 0.768124i \(-0.278810\pi\)
0.640301 + 0.768124i \(0.278810\pi\)
\(978\) 14.9361 0.477603
\(979\) 0 0
\(980\) 0 0
\(981\) −18.4222 −0.588176
\(982\) −29.2389 −0.933049
\(983\) 9.27502 0.295827 0.147914 0.989000i \(-0.452744\pi\)
0.147914 + 0.989000i \(0.452744\pi\)
\(984\) −48.3583 −1.54161
\(985\) 38.2389 1.21839
\(986\) −29.1749 −0.929119
\(987\) 0 0
\(988\) −65.4500 −2.08224
\(989\) −4.57779 −0.145565
\(990\) 0 0
\(991\) −43.7250 −1.38897 −0.694485 0.719507i \(-0.744368\pi\)
−0.694485 + 0.719507i \(0.744368\pi\)
\(992\) 5.30278 0.168363
\(993\) 54.8444 1.74043
\(994\) 0 0
\(995\) 70.0278 2.22003
\(996\) −22.8167 −0.722973
\(997\) −45.6972 −1.44725 −0.723623 0.690196i \(-0.757524\pi\)
−0.723623 + 0.690196i \(0.757524\pi\)
\(998\) 6.69722 0.211997
\(999\) 8.36669 0.264710
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 5929.2.a.p.1.2 2
7.6 odd 2 847.2.a.g.1.2 yes 2
11.10 odd 2 5929.2.a.k.1.1 2
21.20 even 2 7623.2.a.bc.1.1 2
77.6 even 10 847.2.f.r.729.2 8
77.13 even 10 847.2.f.r.323.2 8
77.20 odd 10 847.2.f.o.323.1 8
77.27 odd 10 847.2.f.o.729.1 8
77.41 even 10 847.2.f.r.372.1 8
77.48 odd 10 847.2.f.o.148.2 8
77.62 even 10 847.2.f.r.148.1 8
77.69 odd 10 847.2.f.o.372.2 8
77.76 even 2 847.2.a.e.1.1 2
231.230 odd 2 7623.2.a.bs.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
847.2.a.e.1.1 2 77.76 even 2
847.2.a.g.1.2 yes 2 7.6 odd 2
847.2.f.o.148.2 8 77.48 odd 10
847.2.f.o.323.1 8 77.20 odd 10
847.2.f.o.372.2 8 77.69 odd 10
847.2.f.o.729.1 8 77.27 odd 10
847.2.f.r.148.1 8 77.62 even 10
847.2.f.r.323.2 8 77.13 even 10
847.2.f.r.372.1 8 77.41 even 10
847.2.f.r.729.2 8 77.6 even 10
5929.2.a.k.1.1 2 11.10 odd 2
5929.2.a.p.1.2 2 1.1 even 1 trivial
7623.2.a.bc.1.1 2 21.20 even 2
7623.2.a.bs.1.2 2 231.230 odd 2