Properties

Label 6003.2.a.l.1.4
Level $6003$
Weight $2$
Character 6003.1
Self dual yes
Analytic conductor $47.934$
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] = [6003,2,Mod(1,6003)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6003, 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("6003.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6003.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: \(47.9341963334\)
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: \( x^{10} - 3x^{9} - 10x^{8} + 32x^{7} + 32x^{6} - 118x^{5} - 29x^{4} + 182x^{3} - 28x^{2} - 101x + 43 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 667)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.4
Root \(-1.31926\) of defining polynomial
Character \(\chi\) \(=\) 6003.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.31926 q^{2} -0.259562 q^{4} +4.11119 q^{5} -2.74867 q^{7} +2.98094 q^{8} +O(q^{10})\) \(q-1.31926 q^{2} -0.259562 q^{4} +4.11119 q^{5} -2.74867 q^{7} +2.98094 q^{8} -5.42371 q^{10} -4.56858 q^{11} -6.36237 q^{13} +3.62620 q^{14} -3.41350 q^{16} +3.25232 q^{17} +6.59861 q^{19} -1.06711 q^{20} +6.02713 q^{22} -1.00000 q^{23} +11.9019 q^{25} +8.39360 q^{26} +0.713450 q^{28} -1.00000 q^{29} -9.08138 q^{31} -1.45860 q^{32} -4.29064 q^{34} -11.3003 q^{35} +6.61278 q^{37} -8.70526 q^{38} +12.2552 q^{40} +2.61975 q^{41} -8.65344 q^{43} +1.18583 q^{44} +1.31926 q^{46} +5.78296 q^{47} +0.555185 q^{49} -15.7016 q^{50} +1.65143 q^{52} -1.33533 q^{53} -18.7823 q^{55} -8.19363 q^{56} +1.31926 q^{58} -7.66955 q^{59} +5.22375 q^{61} +11.9807 q^{62} +8.75127 q^{64} -26.1569 q^{65} +1.97447 q^{67} -0.844178 q^{68} +14.9080 q^{70} +4.65159 q^{71} -6.95340 q^{73} -8.72396 q^{74} -1.71275 q^{76} +12.5575 q^{77} +9.90285 q^{79} -14.0336 q^{80} -3.45613 q^{82} +11.5122 q^{83} +13.3709 q^{85} +11.4161 q^{86} -13.6187 q^{88} +2.94778 q^{89} +17.4881 q^{91} +0.259562 q^{92} -7.62921 q^{94} +27.1281 q^{95} +2.26492 q^{97} -0.732432 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q + 3 q^{2} + 9 q^{4} + 10 q^{5} + q^{7} + 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 10 q + 3 q^{2} + 9 q^{4} + 10 q^{5} + q^{7} + 9 q^{8} - 6 q^{10} - 13 q^{13} + 12 q^{14} - 5 q^{16} + 22 q^{17} - 2 q^{19} - 3 q^{20} + 3 q^{22} - 10 q^{23} + 10 q^{25} + 25 q^{26} + 19 q^{28} - 10 q^{29} - 22 q^{31} + 31 q^{32} + 13 q^{34} + 15 q^{35} - 9 q^{37} + 10 q^{38} - 6 q^{40} + 25 q^{41} + 3 q^{43} + 27 q^{44} - 3 q^{46} + 17 q^{47} + 17 q^{49} - 2 q^{50} - 18 q^{52} + 43 q^{53} - 11 q^{55} + 7 q^{56} - 3 q^{58} + 7 q^{59} - 6 q^{61} - 3 q^{62} + 33 q^{64} - 11 q^{65} + 11 q^{67} + 51 q^{68} + 34 q^{70} + 17 q^{71} - 44 q^{73} - 9 q^{74} + 24 q^{76} + 71 q^{77} + 5 q^{79} - 38 q^{80} + 33 q^{82} + 32 q^{83} + 16 q^{85} + 9 q^{86} + 18 q^{88} + 10 q^{89} - 3 q^{91} - 9 q^{92} + 47 q^{94} + 8 q^{95} + 6 q^{97} + 73 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31926 −0.932855 −0.466428 0.884559i \(-0.654459\pi\)
−0.466428 + 0.884559i \(0.654459\pi\)
\(3\) 0 0
\(4\) −0.259562 −0.129781
\(5\) 4.11119 1.83858 0.919289 0.393582i \(-0.128764\pi\)
0.919289 + 0.393582i \(0.128764\pi\)
\(6\) 0 0
\(7\) −2.74867 −1.03890 −0.519450 0.854501i \(-0.673863\pi\)
−0.519450 + 0.854501i \(0.673863\pi\)
\(8\) 2.98094 1.05392
\(9\) 0 0
\(10\) −5.42371 −1.71513
\(11\) −4.56858 −1.37748 −0.688740 0.725009i \(-0.741836\pi\)
−0.688740 + 0.725009i \(0.741836\pi\)
\(12\) 0 0
\(13\) −6.36237 −1.76460 −0.882302 0.470683i \(-0.844007\pi\)
−0.882302 + 0.470683i \(0.844007\pi\)
\(14\) 3.62620 0.969143
\(15\) 0 0
\(16\) −3.41350 −0.853376
\(17\) 3.25232 0.788803 0.394402 0.918938i \(-0.370952\pi\)
0.394402 + 0.918938i \(0.370952\pi\)
\(18\) 0 0
\(19\) 6.59861 1.51383 0.756913 0.653516i \(-0.226707\pi\)
0.756913 + 0.653516i \(0.226707\pi\)
\(20\) −1.06711 −0.238613
\(21\) 0 0
\(22\) 6.02713 1.28499
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 11.9019 2.38037
\(26\) 8.39360 1.64612
\(27\) 0 0
\(28\) 0.713450 0.134829
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −9.08138 −1.63106 −0.815532 0.578712i \(-0.803556\pi\)
−0.815532 + 0.578712i \(0.803556\pi\)
\(32\) −1.45860 −0.257846
\(33\) 0 0
\(34\) −4.29064 −0.735839
\(35\) −11.3003 −1.91010
\(36\) 0 0
\(37\) 6.61278 1.08714 0.543568 0.839365i \(-0.317073\pi\)
0.543568 + 0.839365i \(0.317073\pi\)
\(38\) −8.70526 −1.41218
\(39\) 0 0
\(40\) 12.2552 1.93772
\(41\) 2.61975 0.409137 0.204568 0.978852i \(-0.434421\pi\)
0.204568 + 0.978852i \(0.434421\pi\)
\(42\) 0 0
\(43\) −8.65344 −1.31964 −0.659819 0.751425i \(-0.729367\pi\)
−0.659819 + 0.751425i \(0.729367\pi\)
\(44\) 1.18583 0.178771
\(45\) 0 0
\(46\) 1.31926 0.194514
\(47\) 5.78296 0.843531 0.421766 0.906705i \(-0.361410\pi\)
0.421766 + 0.906705i \(0.361410\pi\)
\(48\) 0 0
\(49\) 0.555185 0.0793122
\(50\) −15.7016 −2.22054
\(51\) 0 0
\(52\) 1.65143 0.229012
\(53\) −1.33533 −0.183422 −0.0917111 0.995786i \(-0.529234\pi\)
−0.0917111 + 0.995786i \(0.529234\pi\)
\(54\) 0 0
\(55\) −18.7823 −2.53260
\(56\) −8.19363 −1.09492
\(57\) 0 0
\(58\) 1.31926 0.173227
\(59\) −7.66955 −0.998491 −0.499245 0.866461i \(-0.666389\pi\)
−0.499245 + 0.866461i \(0.666389\pi\)
\(60\) 0 0
\(61\) 5.22375 0.668833 0.334416 0.942425i \(-0.391461\pi\)
0.334416 + 0.942425i \(0.391461\pi\)
\(62\) 11.9807 1.52155
\(63\) 0 0
\(64\) 8.75127 1.09391
\(65\) −26.1569 −3.24436
\(66\) 0 0
\(67\) 1.97447 0.241219 0.120610 0.992700i \(-0.461515\pi\)
0.120610 + 0.992700i \(0.461515\pi\)
\(68\) −0.844178 −0.102372
\(69\) 0 0
\(70\) 14.9080 1.78185
\(71\) 4.65159 0.552042 0.276021 0.961152i \(-0.410984\pi\)
0.276021 + 0.961152i \(0.410984\pi\)
\(72\) 0 0
\(73\) −6.95340 −0.813834 −0.406917 0.913465i \(-0.633396\pi\)
−0.406917 + 0.913465i \(0.633396\pi\)
\(74\) −8.72396 −1.01414
\(75\) 0 0
\(76\) −1.71275 −0.196466
\(77\) 12.5575 1.43106
\(78\) 0 0
\(79\) 9.90285 1.11416 0.557079 0.830460i \(-0.311922\pi\)
0.557079 + 0.830460i \(0.311922\pi\)
\(80\) −14.0336 −1.56900
\(81\) 0 0
\(82\) −3.45613 −0.381665
\(83\) 11.5122 1.26363 0.631816 0.775119i \(-0.282310\pi\)
0.631816 + 0.775119i \(0.282310\pi\)
\(84\) 0 0
\(85\) 13.3709 1.45028
\(86\) 11.4161 1.23103
\(87\) 0 0
\(88\) −13.6187 −1.45176
\(89\) 2.94778 0.312464 0.156232 0.987720i \(-0.450065\pi\)
0.156232 + 0.987720i \(0.450065\pi\)
\(90\) 0 0
\(91\) 17.4881 1.83325
\(92\) 0.259562 0.0270612
\(93\) 0 0
\(94\) −7.62921 −0.786893
\(95\) 27.1281 2.78329
\(96\) 0 0
\(97\) 2.26492 0.229968 0.114984 0.993367i \(-0.463318\pi\)
0.114984 + 0.993367i \(0.463318\pi\)
\(98\) −0.732432 −0.0739868
\(99\) 0 0
\(100\) −3.08927 −0.308927
\(101\) 0.171130 0.0170281 0.00851403 0.999964i \(-0.497290\pi\)
0.00851403 + 0.999964i \(0.497290\pi\)
\(102\) 0 0
\(103\) −14.1919 −1.39837 −0.699187 0.714939i \(-0.746454\pi\)
−0.699187 + 0.714939i \(0.746454\pi\)
\(104\) −18.9659 −1.85976
\(105\) 0 0
\(106\) 1.76165 0.171106
\(107\) 4.01155 0.387811 0.193906 0.981020i \(-0.437884\pi\)
0.193906 + 0.981020i \(0.437884\pi\)
\(108\) 0 0
\(109\) −1.73215 −0.165910 −0.0829551 0.996553i \(-0.526436\pi\)
−0.0829551 + 0.996553i \(0.526436\pi\)
\(110\) 24.7787 2.36255
\(111\) 0 0
\(112\) 9.38259 0.886572
\(113\) 3.63931 0.342358 0.171179 0.985240i \(-0.445242\pi\)
0.171179 + 0.985240i \(0.445242\pi\)
\(114\) 0 0
\(115\) −4.11119 −0.383370
\(116\) 0.259562 0.0240997
\(117\) 0 0
\(118\) 10.1181 0.931447
\(119\) −8.93955 −0.819487
\(120\) 0 0
\(121\) 9.87194 0.897449
\(122\) −6.89147 −0.623924
\(123\) 0 0
\(124\) 2.35718 0.211681
\(125\) 28.3749 2.53792
\(126\) 0 0
\(127\) 2.40280 0.213214 0.106607 0.994301i \(-0.466001\pi\)
0.106607 + 0.994301i \(0.466001\pi\)
\(128\) −8.62798 −0.762613
\(129\) 0 0
\(130\) 34.5077 3.02652
\(131\) 15.6553 1.36781 0.683907 0.729569i \(-0.260279\pi\)
0.683907 + 0.729569i \(0.260279\pi\)
\(132\) 0 0
\(133\) −18.1374 −1.57271
\(134\) −2.60483 −0.225023
\(135\) 0 0
\(136\) 9.69497 0.831337
\(137\) 20.2050 1.72623 0.863113 0.505010i \(-0.168511\pi\)
0.863113 + 0.505010i \(0.168511\pi\)
\(138\) 0 0
\(139\) 8.94680 0.758857 0.379429 0.925221i \(-0.376121\pi\)
0.379429 + 0.925221i \(0.376121\pi\)
\(140\) 2.93313 0.247894
\(141\) 0 0
\(142\) −6.13664 −0.514976
\(143\) 29.0670 2.43071
\(144\) 0 0
\(145\) −4.11119 −0.341416
\(146\) 9.17332 0.759189
\(147\) 0 0
\(148\) −1.71643 −0.141089
\(149\) −8.40338 −0.688432 −0.344216 0.938890i \(-0.611855\pi\)
−0.344216 + 0.938890i \(0.611855\pi\)
\(150\) 0 0
\(151\) 0.901268 0.0733442 0.0366721 0.999327i \(-0.488324\pi\)
0.0366721 + 0.999327i \(0.488324\pi\)
\(152\) 19.6701 1.59545
\(153\) 0 0
\(154\) −16.5666 −1.33497
\(155\) −37.3353 −2.99884
\(156\) 0 0
\(157\) 22.4829 1.79433 0.897164 0.441697i \(-0.145623\pi\)
0.897164 + 0.441697i \(0.145623\pi\)
\(158\) −13.0644 −1.03935
\(159\) 0 0
\(160\) −5.99656 −0.474070
\(161\) 2.74867 0.216626
\(162\) 0 0
\(163\) −7.39140 −0.578939 −0.289470 0.957187i \(-0.593479\pi\)
−0.289470 + 0.957187i \(0.593479\pi\)
\(164\) −0.679988 −0.0530981
\(165\) 0 0
\(166\) −15.1876 −1.17878
\(167\) 1.89972 0.147004 0.0735022 0.997295i \(-0.476582\pi\)
0.0735022 + 0.997295i \(0.476582\pi\)
\(168\) 0 0
\(169\) 27.4798 2.11383
\(170\) −17.6396 −1.35290
\(171\) 0 0
\(172\) 2.24610 0.171264
\(173\) 0.795280 0.0604641 0.0302320 0.999543i \(-0.490375\pi\)
0.0302320 + 0.999543i \(0.490375\pi\)
\(174\) 0 0
\(175\) −32.7143 −2.47297
\(176\) 15.5949 1.17551
\(177\) 0 0
\(178\) −3.88888 −0.291484
\(179\) 6.16453 0.460759 0.230379 0.973101i \(-0.426003\pi\)
0.230379 + 0.973101i \(0.426003\pi\)
\(180\) 0 0
\(181\) −17.0943 −1.27061 −0.635304 0.772262i \(-0.719125\pi\)
−0.635304 + 0.772262i \(0.719125\pi\)
\(182\) −23.0712 −1.71015
\(183\) 0 0
\(184\) −2.98094 −0.219758
\(185\) 27.1864 1.99878
\(186\) 0 0
\(187\) −14.8585 −1.08656
\(188\) −1.50104 −0.109474
\(189\) 0 0
\(190\) −35.7890 −2.59640
\(191\) −4.58496 −0.331756 −0.165878 0.986146i \(-0.553046\pi\)
−0.165878 + 0.986146i \(0.553046\pi\)
\(192\) 0 0
\(193\) 14.8598 1.06963 0.534817 0.844968i \(-0.320381\pi\)
0.534817 + 0.844968i \(0.320381\pi\)
\(194\) −2.98801 −0.214527
\(195\) 0 0
\(196\) −0.144105 −0.0102932
\(197\) 16.8176 1.19820 0.599101 0.800674i \(-0.295525\pi\)
0.599101 + 0.800674i \(0.295525\pi\)
\(198\) 0 0
\(199\) 10.6701 0.756386 0.378193 0.925727i \(-0.376546\pi\)
0.378193 + 0.925727i \(0.376546\pi\)
\(200\) 35.4788 2.50873
\(201\) 0 0
\(202\) −0.225764 −0.0158847
\(203\) 2.74867 0.192919
\(204\) 0 0
\(205\) 10.7703 0.752230
\(206\) 18.7228 1.30448
\(207\) 0 0
\(208\) 21.7180 1.50587
\(209\) −30.1463 −2.08526
\(210\) 0 0
\(211\) −24.1044 −1.65942 −0.829709 0.558197i \(-0.811493\pi\)
−0.829709 + 0.558197i \(0.811493\pi\)
\(212\) 0.346602 0.0238047
\(213\) 0 0
\(214\) −5.29226 −0.361772
\(215\) −35.5759 −2.42626
\(216\) 0 0
\(217\) 24.9617 1.69451
\(218\) 2.28516 0.154770
\(219\) 0 0
\(220\) 4.87517 0.328684
\(221\) −20.6925 −1.39193
\(222\) 0 0
\(223\) 0.944548 0.0632516 0.0316258 0.999500i \(-0.489932\pi\)
0.0316258 + 0.999500i \(0.489932\pi\)
\(224\) 4.00920 0.267876
\(225\) 0 0
\(226\) −4.80119 −0.319370
\(227\) −20.3135 −1.34825 −0.674126 0.738617i \(-0.735479\pi\)
−0.674126 + 0.738617i \(0.735479\pi\)
\(228\) 0 0
\(229\) 6.86545 0.453682 0.226841 0.973932i \(-0.427160\pi\)
0.226841 + 0.973932i \(0.427160\pi\)
\(230\) 5.42371 0.357629
\(231\) 0 0
\(232\) −2.98094 −0.195708
\(233\) 9.87907 0.647199 0.323600 0.946194i \(-0.395107\pi\)
0.323600 + 0.946194i \(0.395107\pi\)
\(234\) 0 0
\(235\) 23.7748 1.55090
\(236\) 1.99072 0.129585
\(237\) 0 0
\(238\) 11.7936 0.764463
\(239\) −9.96016 −0.644269 −0.322134 0.946694i \(-0.604400\pi\)
−0.322134 + 0.946694i \(0.604400\pi\)
\(240\) 0 0
\(241\) 6.96142 0.448425 0.224212 0.974540i \(-0.428019\pi\)
0.224212 + 0.974540i \(0.428019\pi\)
\(242\) −13.0236 −0.837190
\(243\) 0 0
\(244\) −1.35589 −0.0868018
\(245\) 2.28247 0.145822
\(246\) 0 0
\(247\) −41.9828 −2.67130
\(248\) −27.0711 −1.71901
\(249\) 0 0
\(250\) −37.4337 −2.36752
\(251\) −10.0183 −0.632352 −0.316176 0.948701i \(-0.602399\pi\)
−0.316176 + 0.948701i \(0.602399\pi\)
\(252\) 0 0
\(253\) 4.56858 0.287224
\(254\) −3.16991 −0.198898
\(255\) 0 0
\(256\) −6.12002 −0.382501
\(257\) 4.87303 0.303971 0.151986 0.988383i \(-0.451433\pi\)
0.151986 + 0.988383i \(0.451433\pi\)
\(258\) 0 0
\(259\) −18.1764 −1.12942
\(260\) 6.78934 0.421057
\(261\) 0 0
\(262\) −20.6534 −1.27597
\(263\) −5.63631 −0.347549 −0.173775 0.984785i \(-0.555596\pi\)
−0.173775 + 0.984785i \(0.555596\pi\)
\(264\) 0 0
\(265\) −5.48981 −0.337236
\(266\) 23.9279 1.46711
\(267\) 0 0
\(268\) −0.512496 −0.0313057
\(269\) 20.0520 1.22259 0.611296 0.791402i \(-0.290648\pi\)
0.611296 + 0.791402i \(0.290648\pi\)
\(270\) 0 0
\(271\) 12.8081 0.778039 0.389020 0.921229i \(-0.372814\pi\)
0.389020 + 0.921229i \(0.372814\pi\)
\(272\) −11.1018 −0.673146
\(273\) 0 0
\(274\) −26.6555 −1.61032
\(275\) −54.3746 −3.27891
\(276\) 0 0
\(277\) 13.1150 0.788002 0.394001 0.919110i \(-0.371091\pi\)
0.394001 + 0.919110i \(0.371091\pi\)
\(278\) −11.8031 −0.707904
\(279\) 0 0
\(280\) −33.6855 −2.01310
\(281\) −3.97492 −0.237124 −0.118562 0.992947i \(-0.537828\pi\)
−0.118562 + 0.992947i \(0.537828\pi\)
\(282\) 0 0
\(283\) −4.04216 −0.240281 −0.120141 0.992757i \(-0.538335\pi\)
−0.120141 + 0.992757i \(0.538335\pi\)
\(284\) −1.20738 −0.0716446
\(285\) 0 0
\(286\) −38.3469 −2.26750
\(287\) −7.20083 −0.425052
\(288\) 0 0
\(289\) −6.42243 −0.377790
\(290\) 5.42371 0.318491
\(291\) 0 0
\(292\) 1.80484 0.105620
\(293\) −8.95096 −0.522921 −0.261460 0.965214i \(-0.584204\pi\)
−0.261460 + 0.965214i \(0.584204\pi\)
\(294\) 0 0
\(295\) −31.5310 −1.83580
\(296\) 19.7123 1.14576
\(297\) 0 0
\(298\) 11.0862 0.642207
\(299\) 6.36237 0.367945
\(300\) 0 0
\(301\) 23.7855 1.37097
\(302\) −1.18900 −0.0684195
\(303\) 0 0
\(304\) −22.5244 −1.29186
\(305\) 21.4758 1.22970
\(306\) 0 0
\(307\) 3.10039 0.176949 0.0884743 0.996078i \(-0.471801\pi\)
0.0884743 + 0.996078i \(0.471801\pi\)
\(308\) −3.25945 −0.185725
\(309\) 0 0
\(310\) 49.2548 2.79748
\(311\) 4.41722 0.250478 0.125239 0.992127i \(-0.460030\pi\)
0.125239 + 0.992127i \(0.460030\pi\)
\(312\) 0 0
\(313\) 12.0162 0.679194 0.339597 0.940571i \(-0.389709\pi\)
0.339597 + 0.940571i \(0.389709\pi\)
\(314\) −29.6607 −1.67385
\(315\) 0 0
\(316\) −2.57040 −0.144596
\(317\) −28.1477 −1.58093 −0.790466 0.612506i \(-0.790161\pi\)
−0.790466 + 0.612506i \(0.790161\pi\)
\(318\) 0 0
\(319\) 4.56858 0.255791
\(320\) 35.9781 2.01124
\(321\) 0 0
\(322\) −3.62620 −0.202080
\(323\) 21.4608 1.19411
\(324\) 0 0
\(325\) −75.7241 −4.20042
\(326\) 9.75115 0.540066
\(327\) 0 0
\(328\) 7.80933 0.431198
\(329\) −15.8954 −0.876344
\(330\) 0 0
\(331\) 18.5216 1.01804 0.509019 0.860755i \(-0.330008\pi\)
0.509019 + 0.860755i \(0.330008\pi\)
\(332\) −2.98814 −0.163995
\(333\) 0 0
\(334\) −2.50621 −0.137134
\(335\) 8.11740 0.443501
\(336\) 0 0
\(337\) −5.49971 −0.299588 −0.149794 0.988717i \(-0.547861\pi\)
−0.149794 + 0.988717i \(0.547861\pi\)
\(338\) −36.2529 −1.97190
\(339\) 0 0
\(340\) −3.47057 −0.188218
\(341\) 41.4890 2.24676
\(342\) 0 0
\(343\) 17.7147 0.956502
\(344\) −25.7954 −1.39080
\(345\) 0 0
\(346\) −1.04918 −0.0564042
\(347\) 21.8641 1.17373 0.586863 0.809686i \(-0.300363\pi\)
0.586863 + 0.809686i \(0.300363\pi\)
\(348\) 0 0
\(349\) 20.1439 1.07828 0.539138 0.842217i \(-0.318750\pi\)
0.539138 + 0.842217i \(0.318750\pi\)
\(350\) 43.1585 2.30692
\(351\) 0 0
\(352\) 6.66372 0.355177
\(353\) 11.2359 0.598029 0.299014 0.954249i \(-0.403342\pi\)
0.299014 + 0.954249i \(0.403342\pi\)
\(354\) 0 0
\(355\) 19.1236 1.01497
\(356\) −0.765132 −0.0405519
\(357\) 0 0
\(358\) −8.13260 −0.429821
\(359\) 30.9360 1.63274 0.816369 0.577531i \(-0.195984\pi\)
0.816369 + 0.577531i \(0.195984\pi\)
\(360\) 0 0
\(361\) 24.5417 1.29167
\(362\) 22.5517 1.18529
\(363\) 0 0
\(364\) −4.53923 −0.237921
\(365\) −28.5867 −1.49630
\(366\) 0 0
\(367\) −22.8506 −1.19279 −0.596396 0.802691i \(-0.703401\pi\)
−0.596396 + 0.802691i \(0.703401\pi\)
\(368\) 3.41350 0.177941
\(369\) 0 0
\(370\) −35.8658 −1.86458
\(371\) 3.67039 0.190557
\(372\) 0 0
\(373\) −7.59121 −0.393058 −0.196529 0.980498i \(-0.562967\pi\)
−0.196529 + 0.980498i \(0.562967\pi\)
\(374\) 19.6021 1.01360
\(375\) 0 0
\(376\) 17.2387 0.889016
\(377\) 6.36237 0.327679
\(378\) 0 0
\(379\) −14.5273 −0.746216 −0.373108 0.927788i \(-0.621708\pi\)
−0.373108 + 0.927788i \(0.621708\pi\)
\(380\) −7.04143 −0.361218
\(381\) 0 0
\(382\) 6.04874 0.309481
\(383\) 32.5891 1.66523 0.832614 0.553854i \(-0.186843\pi\)
0.832614 + 0.553854i \(0.186843\pi\)
\(384\) 0 0
\(385\) 51.6263 2.63112
\(386\) −19.6039 −0.997814
\(387\) 0 0
\(388\) −0.587887 −0.0298454
\(389\) 29.9827 1.52018 0.760092 0.649816i \(-0.225154\pi\)
0.760092 + 0.649816i \(0.225154\pi\)
\(390\) 0 0
\(391\) −3.25232 −0.164477
\(392\) 1.65498 0.0835889
\(393\) 0 0
\(394\) −22.1867 −1.11775
\(395\) 40.7125 2.04847
\(396\) 0 0
\(397\) 2.70605 0.135813 0.0679063 0.997692i \(-0.478368\pi\)
0.0679063 + 0.997692i \(0.478368\pi\)
\(398\) −14.0767 −0.705599
\(399\) 0 0
\(400\) −40.6271 −2.03135
\(401\) −20.8363 −1.04052 −0.520259 0.854009i \(-0.674164\pi\)
−0.520259 + 0.854009i \(0.674164\pi\)
\(402\) 0 0
\(403\) 57.7791 2.87818
\(404\) −0.0444188 −0.00220992
\(405\) 0 0
\(406\) −3.62620 −0.179965
\(407\) −30.2110 −1.49751
\(408\) 0 0
\(409\) −8.56957 −0.423738 −0.211869 0.977298i \(-0.567955\pi\)
−0.211869 + 0.977298i \(0.567955\pi\)
\(410\) −14.2088 −0.701722
\(411\) 0 0
\(412\) 3.68369 0.181482
\(413\) 21.0811 1.03733
\(414\) 0 0
\(415\) 47.3289 2.32329
\(416\) 9.28013 0.454996
\(417\) 0 0
\(418\) 39.7707 1.94525
\(419\) −13.0013 −0.635157 −0.317578 0.948232i \(-0.602870\pi\)
−0.317578 + 0.948232i \(0.602870\pi\)
\(420\) 0 0
\(421\) 22.6385 1.10333 0.551667 0.834064i \(-0.313992\pi\)
0.551667 + 0.834064i \(0.313992\pi\)
\(422\) 31.7999 1.54800
\(423\) 0 0
\(424\) −3.98055 −0.193313
\(425\) 38.7086 1.87764
\(426\) 0 0
\(427\) −14.3584 −0.694850
\(428\) −1.04125 −0.0503305
\(429\) 0 0
\(430\) 46.9338 2.26335
\(431\) 31.8549 1.53439 0.767197 0.641411i \(-0.221651\pi\)
0.767197 + 0.641411i \(0.221651\pi\)
\(432\) 0 0
\(433\) −14.0708 −0.676200 −0.338100 0.941110i \(-0.609784\pi\)
−0.338100 + 0.941110i \(0.609784\pi\)
\(434\) −32.9309 −1.58073
\(435\) 0 0
\(436\) 0.449601 0.0215320
\(437\) −6.59861 −0.315654
\(438\) 0 0
\(439\) 8.82152 0.421028 0.210514 0.977591i \(-0.432486\pi\)
0.210514 + 0.977591i \(0.432486\pi\)
\(440\) −55.9889 −2.66917
\(441\) 0 0
\(442\) 27.2987 1.29847
\(443\) 33.8771 1.60955 0.804776 0.593579i \(-0.202285\pi\)
0.804776 + 0.593579i \(0.202285\pi\)
\(444\) 0 0
\(445\) 12.1189 0.574491
\(446\) −1.24610 −0.0590046
\(447\) 0 0
\(448\) −24.0544 −1.13646
\(449\) −3.91466 −0.184744 −0.0923721 0.995725i \(-0.529445\pi\)
−0.0923721 + 0.995725i \(0.529445\pi\)
\(450\) 0 0
\(451\) −11.9686 −0.563577
\(452\) −0.944627 −0.0444315
\(453\) 0 0
\(454\) 26.7987 1.25772
\(455\) 71.8967 3.37057
\(456\) 0 0
\(457\) −19.8594 −0.928985 −0.464493 0.885577i \(-0.653763\pi\)
−0.464493 + 0.885577i \(0.653763\pi\)
\(458\) −9.05729 −0.423219
\(459\) 0 0
\(460\) 1.06711 0.0497542
\(461\) 16.4586 0.766553 0.383277 0.923634i \(-0.374796\pi\)
0.383277 + 0.923634i \(0.374796\pi\)
\(462\) 0 0
\(463\) 25.4972 1.18496 0.592478 0.805587i \(-0.298150\pi\)
0.592478 + 0.805587i \(0.298150\pi\)
\(464\) 3.41350 0.158468
\(465\) 0 0
\(466\) −13.0330 −0.603743
\(467\) 22.8174 1.05586 0.527931 0.849287i \(-0.322968\pi\)
0.527931 + 0.849287i \(0.322968\pi\)
\(468\) 0 0
\(469\) −5.42715 −0.250603
\(470\) −31.3651 −1.44676
\(471\) 0 0
\(472\) −22.8625 −1.05233
\(473\) 39.5340 1.81777
\(474\) 0 0
\(475\) 78.5358 3.60347
\(476\) 2.32037 0.106354
\(477\) 0 0
\(478\) 13.1400 0.601010
\(479\) −43.4778 −1.98655 −0.993276 0.115770i \(-0.963067\pi\)
−0.993276 + 0.115770i \(0.963067\pi\)
\(480\) 0 0
\(481\) −42.0730 −1.91836
\(482\) −9.18390 −0.418315
\(483\) 0 0
\(484\) −2.56238 −0.116472
\(485\) 9.31151 0.422814
\(486\) 0 0
\(487\) −1.07464 −0.0486965 −0.0243482 0.999704i \(-0.507751\pi\)
−0.0243482 + 0.999704i \(0.507751\pi\)
\(488\) 15.5717 0.704898
\(489\) 0 0
\(490\) −3.01117 −0.136031
\(491\) −12.4335 −0.561117 −0.280558 0.959837i \(-0.590520\pi\)
−0.280558 + 0.959837i \(0.590520\pi\)
\(492\) 0 0
\(493\) −3.25232 −0.146477
\(494\) 55.3861 2.49194
\(495\) 0 0
\(496\) 30.9993 1.39191
\(497\) −12.7857 −0.573517
\(498\) 0 0
\(499\) −7.45558 −0.333758 −0.166879 0.985977i \(-0.553369\pi\)
−0.166879 + 0.985977i \(0.553369\pi\)
\(500\) −7.36503 −0.329374
\(501\) 0 0
\(502\) 13.2168 0.589893
\(503\) −39.4744 −1.76008 −0.880039 0.474901i \(-0.842484\pi\)
−0.880039 + 0.474901i \(0.842484\pi\)
\(504\) 0 0
\(505\) 0.703547 0.0313074
\(506\) −6.02713 −0.267939
\(507\) 0 0
\(508\) −0.623676 −0.0276711
\(509\) 43.4583 1.92625 0.963127 0.269047i \(-0.0867085\pi\)
0.963127 + 0.269047i \(0.0867085\pi\)
\(510\) 0 0
\(511\) 19.1126 0.845491
\(512\) 25.3298 1.11943
\(513\) 0 0
\(514\) −6.42878 −0.283561
\(515\) −58.3457 −2.57102
\(516\) 0 0
\(517\) −26.4199 −1.16195
\(518\) 23.9793 1.05359
\(519\) 0 0
\(520\) −77.9722 −3.41931
\(521\) 34.6729 1.51905 0.759525 0.650478i \(-0.225432\pi\)
0.759525 + 0.650478i \(0.225432\pi\)
\(522\) 0 0
\(523\) 0.0232653 0.00101732 0.000508660 1.00000i \(-0.499838\pi\)
0.000508660 1.00000i \(0.499838\pi\)
\(524\) −4.06353 −0.177516
\(525\) 0 0
\(526\) 7.43573 0.324213
\(527\) −29.5355 −1.28659
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 7.24247 0.314593
\(531\) 0 0
\(532\) 4.70778 0.204108
\(533\) −16.6678 −0.721964
\(534\) 0 0
\(535\) 16.4922 0.713022
\(536\) 5.88577 0.254226
\(537\) 0 0
\(538\) −26.4537 −1.14050
\(539\) −2.53641 −0.109251
\(540\) 0 0
\(541\) 34.9131 1.50103 0.750515 0.660853i \(-0.229806\pi\)
0.750515 + 0.660853i \(0.229806\pi\)
\(542\) −16.8972 −0.725798
\(543\) 0 0
\(544\) −4.74382 −0.203390
\(545\) −7.12121 −0.305039
\(546\) 0 0
\(547\) −10.1866 −0.435547 −0.217774 0.975999i \(-0.569879\pi\)
−0.217774 + 0.975999i \(0.569879\pi\)
\(548\) −5.24444 −0.224031
\(549\) 0 0
\(550\) 71.7341 3.05875
\(551\) −6.59861 −0.281110
\(552\) 0 0
\(553\) −27.2197 −1.15750
\(554\) −17.3020 −0.735092
\(555\) 0 0
\(556\) −2.32225 −0.0984852
\(557\) −11.2100 −0.474985 −0.237492 0.971389i \(-0.576326\pi\)
−0.237492 + 0.971389i \(0.576326\pi\)
\(558\) 0 0
\(559\) 55.0564 2.32864
\(560\) 38.5736 1.63003
\(561\) 0 0
\(562\) 5.24394 0.221202
\(563\) 8.18989 0.345163 0.172581 0.984995i \(-0.444789\pi\)
0.172581 + 0.984995i \(0.444789\pi\)
\(564\) 0 0
\(565\) 14.9619 0.629451
\(566\) 5.33264 0.224148
\(567\) 0 0
\(568\) 13.8661 0.581810
\(569\) −40.6958 −1.70606 −0.853028 0.521865i \(-0.825237\pi\)
−0.853028 + 0.521865i \(0.825237\pi\)
\(570\) 0 0
\(571\) −39.4479 −1.65084 −0.825422 0.564516i \(-0.809063\pi\)
−0.825422 + 0.564516i \(0.809063\pi\)
\(572\) −7.54469 −0.315459
\(573\) 0 0
\(574\) 9.49975 0.396512
\(575\) −11.9019 −0.496342
\(576\) 0 0
\(577\) 36.5420 1.52126 0.760632 0.649183i \(-0.224889\pi\)
0.760632 + 0.649183i \(0.224889\pi\)
\(578\) 8.47283 0.352423
\(579\) 0 0
\(580\) 1.06711 0.0443092
\(581\) −31.6433 −1.31279
\(582\) 0 0
\(583\) 6.10058 0.252660
\(584\) −20.7277 −0.857717
\(585\) 0 0
\(586\) 11.8086 0.487810
\(587\) −6.69668 −0.276402 −0.138201 0.990404i \(-0.544132\pi\)
−0.138201 + 0.990404i \(0.544132\pi\)
\(588\) 0 0
\(589\) −59.9245 −2.46915
\(590\) 41.5974 1.71254
\(591\) 0 0
\(592\) −22.5728 −0.927735
\(593\) −39.0591 −1.60397 −0.801983 0.597347i \(-0.796222\pi\)
−0.801983 + 0.597347i \(0.796222\pi\)
\(594\) 0 0
\(595\) −36.7522 −1.50669
\(596\) 2.18120 0.0893454
\(597\) 0 0
\(598\) −8.39360 −0.343240
\(599\) 3.20208 0.130834 0.0654168 0.997858i \(-0.479162\pi\)
0.0654168 + 0.997858i \(0.479162\pi\)
\(600\) 0 0
\(601\) −27.6424 −1.12756 −0.563778 0.825927i \(-0.690653\pi\)
−0.563778 + 0.825927i \(0.690653\pi\)
\(602\) −31.3791 −1.27892
\(603\) 0 0
\(604\) −0.233935 −0.00951868
\(605\) 40.5854 1.65003
\(606\) 0 0
\(607\) 33.4334 1.35702 0.678510 0.734591i \(-0.262626\pi\)
0.678510 + 0.734591i \(0.262626\pi\)
\(608\) −9.62471 −0.390334
\(609\) 0 0
\(610\) −28.3321 −1.14713
\(611\) −36.7933 −1.48850
\(612\) 0 0
\(613\) −14.7380 −0.595263 −0.297631 0.954681i \(-0.596197\pi\)
−0.297631 + 0.954681i \(0.596197\pi\)
\(614\) −4.09021 −0.165067
\(615\) 0 0
\(616\) 37.4332 1.50823
\(617\) 21.9315 0.882927 0.441464 0.897279i \(-0.354459\pi\)
0.441464 + 0.897279i \(0.354459\pi\)
\(618\) 0 0
\(619\) 31.7740 1.27710 0.638552 0.769578i \(-0.279534\pi\)
0.638552 + 0.769578i \(0.279534\pi\)
\(620\) 9.69081 0.389192
\(621\) 0 0
\(622\) −5.82745 −0.233660
\(623\) −8.10248 −0.324619
\(624\) 0 0
\(625\) 57.1450 2.28580
\(626\) −15.8524 −0.633590
\(627\) 0 0
\(628\) −5.83570 −0.232870
\(629\) 21.5069 0.857535
\(630\) 0 0
\(631\) −17.8173 −0.709297 −0.354649 0.935000i \(-0.615400\pi\)
−0.354649 + 0.935000i \(0.615400\pi\)
\(632\) 29.5198 1.17424
\(633\) 0 0
\(634\) 37.1340 1.47478
\(635\) 9.87836 0.392011
\(636\) 0 0
\(637\) −3.53230 −0.139955
\(638\) −6.02713 −0.238616
\(639\) 0 0
\(640\) −35.4712 −1.40212
\(641\) 18.3619 0.725253 0.362627 0.931935i \(-0.381880\pi\)
0.362627 + 0.931935i \(0.381880\pi\)
\(642\) 0 0
\(643\) 33.5879 1.32458 0.662289 0.749248i \(-0.269585\pi\)
0.662289 + 0.749248i \(0.269585\pi\)
\(644\) −0.713450 −0.0281139
\(645\) 0 0
\(646\) −28.3123 −1.11393
\(647\) 32.8327 1.29079 0.645394 0.763850i \(-0.276693\pi\)
0.645394 + 0.763850i \(0.276693\pi\)
\(648\) 0 0
\(649\) 35.0390 1.37540
\(650\) 99.8995 3.91838
\(651\) 0 0
\(652\) 1.91853 0.0751353
\(653\) 11.6542 0.456064 0.228032 0.973654i \(-0.426771\pi\)
0.228032 + 0.973654i \(0.426771\pi\)
\(654\) 0 0
\(655\) 64.3621 2.51483
\(656\) −8.94253 −0.349147
\(657\) 0 0
\(658\) 20.9702 0.817502
\(659\) −15.2217 −0.592952 −0.296476 0.955040i \(-0.595811\pi\)
−0.296476 + 0.955040i \(0.595811\pi\)
\(660\) 0 0
\(661\) 13.6959 0.532708 0.266354 0.963875i \(-0.414181\pi\)
0.266354 + 0.963875i \(0.414181\pi\)
\(662\) −24.4347 −0.949682
\(663\) 0 0
\(664\) 34.3173 1.33177
\(665\) −74.5663 −2.89156
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −0.493094 −0.0190784
\(669\) 0 0
\(670\) −10.7089 −0.413722
\(671\) −23.8651 −0.921303
\(672\) 0 0
\(673\) 3.63456 0.140102 0.0700510 0.997543i \(-0.477684\pi\)
0.0700510 + 0.997543i \(0.477684\pi\)
\(674\) 7.25553 0.279472
\(675\) 0 0
\(676\) −7.13270 −0.274335
\(677\) 25.3809 0.975467 0.487734 0.872993i \(-0.337824\pi\)
0.487734 + 0.872993i \(0.337824\pi\)
\(678\) 0 0
\(679\) −6.22552 −0.238913
\(680\) 39.8578 1.52848
\(681\) 0 0
\(682\) −54.7347 −2.09590
\(683\) 3.84356 0.147070 0.0735349 0.997293i \(-0.476572\pi\)
0.0735349 + 0.997293i \(0.476572\pi\)
\(684\) 0 0
\(685\) 83.0664 3.17380
\(686\) −23.3702 −0.892278
\(687\) 0 0
\(688\) 29.5386 1.12615
\(689\) 8.49589 0.323668
\(690\) 0 0
\(691\) −40.4972 −1.54058 −0.770292 0.637691i \(-0.779890\pi\)
−0.770292 + 0.637691i \(0.779890\pi\)
\(692\) −0.206424 −0.00784708
\(693\) 0 0
\(694\) −28.8444 −1.09492
\(695\) 36.7820 1.39522
\(696\) 0 0
\(697\) 8.52027 0.322728
\(698\) −26.5749 −1.00588
\(699\) 0 0
\(700\) 8.49138 0.320944
\(701\) 16.8344 0.635827 0.317913 0.948120i \(-0.397018\pi\)
0.317913 + 0.948120i \(0.397018\pi\)
\(702\) 0 0
\(703\) 43.6352 1.64573
\(704\) −39.9809 −1.50684
\(705\) 0 0
\(706\) −14.8231 −0.557874
\(707\) −0.470380 −0.0176904
\(708\) 0 0
\(709\) −1.94456 −0.0730294 −0.0365147 0.999333i \(-0.511626\pi\)
−0.0365147 + 0.999333i \(0.511626\pi\)
\(710\) −25.2289 −0.946824
\(711\) 0 0
\(712\) 8.78717 0.329313
\(713\) 9.08138 0.340100
\(714\) 0 0
\(715\) 119.500 4.46905
\(716\) −1.60008 −0.0597977
\(717\) 0 0
\(718\) −40.8125 −1.52311
\(719\) −13.5879 −0.506742 −0.253371 0.967369i \(-0.581539\pi\)
−0.253371 + 0.967369i \(0.581539\pi\)
\(720\) 0 0
\(721\) 39.0089 1.45277
\(722\) −32.3768 −1.20494
\(723\) 0 0
\(724\) 4.43702 0.164901
\(725\) −11.9019 −0.442024
\(726\) 0 0
\(727\) 37.3198 1.38412 0.692058 0.721842i \(-0.256704\pi\)
0.692058 + 0.721842i \(0.256704\pi\)
\(728\) 52.1309 1.93210
\(729\) 0 0
\(730\) 37.7132 1.39583
\(731\) −28.1437 −1.04093
\(732\) 0 0
\(733\) −16.8847 −0.623650 −0.311825 0.950139i \(-0.600940\pi\)
−0.311825 + 0.950139i \(0.600940\pi\)
\(734\) 30.1458 1.11270
\(735\) 0 0
\(736\) 1.45860 0.0537646
\(737\) −9.02051 −0.332275
\(738\) 0 0
\(739\) −22.1714 −0.815588 −0.407794 0.913074i \(-0.633702\pi\)
−0.407794 + 0.913074i \(0.633702\pi\)
\(740\) −7.05655 −0.259404
\(741\) 0 0
\(742\) −4.84219 −0.177762
\(743\) 1.45976 0.0535535 0.0267767 0.999641i \(-0.491476\pi\)
0.0267767 + 0.999641i \(0.491476\pi\)
\(744\) 0 0
\(745\) −34.5479 −1.26574
\(746\) 10.0148 0.366666
\(747\) 0 0
\(748\) 3.85670 0.141015
\(749\) −11.0264 −0.402897
\(750\) 0 0
\(751\) −16.9248 −0.617596 −0.308798 0.951128i \(-0.599927\pi\)
−0.308798 + 0.951128i \(0.599927\pi\)
\(752\) −19.7402 −0.719849
\(753\) 0 0
\(754\) −8.39360 −0.305677
\(755\) 3.70528 0.134849
\(756\) 0 0
\(757\) 23.6215 0.858539 0.429270 0.903176i \(-0.358771\pi\)
0.429270 + 0.903176i \(0.358771\pi\)
\(758\) 19.1652 0.696112
\(759\) 0 0
\(760\) 80.8674 2.93337
\(761\) 15.3396 0.556059 0.278029 0.960573i \(-0.410319\pi\)
0.278029 + 0.960573i \(0.410319\pi\)
\(762\) 0 0
\(763\) 4.76112 0.172364
\(764\) 1.19008 0.0430556
\(765\) 0 0
\(766\) −42.9935 −1.55342
\(767\) 48.7965 1.76194
\(768\) 0 0
\(769\) −32.1320 −1.15871 −0.579355 0.815075i \(-0.696696\pi\)
−0.579355 + 0.815075i \(0.696696\pi\)
\(770\) −68.1084 −2.45446
\(771\) 0 0
\(772\) −3.85705 −0.138818
\(773\) 0.152416 0.00548201 0.00274101 0.999996i \(-0.499128\pi\)
0.00274101 + 0.999996i \(0.499128\pi\)
\(774\) 0 0
\(775\) −108.085 −3.88254
\(776\) 6.75159 0.242368
\(777\) 0 0
\(778\) −39.5549 −1.41811
\(779\) 17.2867 0.619361
\(780\) 0 0
\(781\) −21.2512 −0.760427
\(782\) 4.29064 0.153433
\(783\) 0 0
\(784\) −1.89513 −0.0676831
\(785\) 92.4313 3.29901
\(786\) 0 0
\(787\) 45.3720 1.61734 0.808669 0.588264i \(-0.200189\pi\)
0.808669 + 0.588264i \(0.200189\pi\)
\(788\) −4.36520 −0.155504
\(789\) 0 0
\(790\) −53.7102 −1.91092
\(791\) −10.0033 −0.355675
\(792\) 0 0
\(793\) −33.2354 −1.18023
\(794\) −3.56997 −0.126693
\(795\) 0 0
\(796\) −2.76956 −0.0981645
\(797\) 43.4238 1.53815 0.769076 0.639158i \(-0.220717\pi\)
0.769076 + 0.639158i \(0.220717\pi\)
\(798\) 0 0
\(799\) 18.8080 0.665380
\(800\) −17.3600 −0.613769
\(801\) 0 0
\(802\) 27.4885 0.970652
\(803\) 31.7672 1.12104
\(804\) 0 0
\(805\) 11.3003 0.398283
\(806\) −76.2255 −2.68493
\(807\) 0 0
\(808\) 0.510128 0.0179463
\(809\) 9.14016 0.321351 0.160675 0.987007i \(-0.448633\pi\)
0.160675 + 0.987007i \(0.448633\pi\)
\(810\) 0 0
\(811\) −26.0277 −0.913957 −0.456979 0.889478i \(-0.651068\pi\)
−0.456979 + 0.889478i \(0.651068\pi\)
\(812\) −0.713450 −0.0250372
\(813\) 0 0
\(814\) 39.8561 1.39696
\(815\) −30.3874 −1.06443
\(816\) 0 0
\(817\) −57.1007 −1.99770
\(818\) 11.3055 0.395286
\(819\) 0 0
\(820\) −2.79556 −0.0976251
\(821\) 2.03323 0.0709603 0.0354802 0.999370i \(-0.488704\pi\)
0.0354802 + 0.999370i \(0.488704\pi\)
\(822\) 0 0
\(823\) −5.62311 −0.196009 −0.0980047 0.995186i \(-0.531246\pi\)
−0.0980047 + 0.995186i \(0.531246\pi\)
\(824\) −42.3053 −1.47378
\(825\) 0 0
\(826\) −27.8113 −0.967680
\(827\) −16.9600 −0.589757 −0.294878 0.955535i \(-0.595279\pi\)
−0.294878 + 0.955535i \(0.595279\pi\)
\(828\) 0 0
\(829\) −29.3835 −1.02053 −0.510265 0.860017i \(-0.670453\pi\)
−0.510265 + 0.860017i \(0.670453\pi\)
\(830\) −62.4390 −2.16729
\(831\) 0 0
\(832\) −55.6788 −1.93032
\(833\) 1.80564 0.0625617
\(834\) 0 0
\(835\) 7.81009 0.270279
\(836\) 7.82483 0.270627
\(837\) 0 0
\(838\) 17.1521 0.592509
\(839\) −22.6490 −0.781931 −0.390966 0.920405i \(-0.627859\pi\)
−0.390966 + 0.920405i \(0.627859\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) −29.8660 −1.02925
\(843\) 0 0
\(844\) 6.25659 0.215361
\(845\) 112.975 3.88644
\(846\) 0 0
\(847\) −27.1347 −0.932359
\(848\) 4.55817 0.156528
\(849\) 0 0
\(850\) −51.0666 −1.75157
\(851\) −6.61278 −0.226683
\(852\) 0 0
\(853\) −3.58645 −0.122798 −0.0613988 0.998113i \(-0.519556\pi\)
−0.0613988 + 0.998113i \(0.519556\pi\)
\(854\) 18.9424 0.648195
\(855\) 0 0
\(856\) 11.9582 0.408723
\(857\) −35.4173 −1.20983 −0.604916 0.796290i \(-0.706793\pi\)
−0.604916 + 0.796290i \(0.706793\pi\)
\(858\) 0 0
\(859\) −45.0733 −1.53788 −0.768941 0.639320i \(-0.779216\pi\)
−0.768941 + 0.639320i \(0.779216\pi\)
\(860\) 9.23415 0.314882
\(861\) 0 0
\(862\) −42.0247 −1.43137
\(863\) 31.8710 1.08490 0.542451 0.840087i \(-0.317496\pi\)
0.542451 + 0.840087i \(0.317496\pi\)
\(864\) 0 0
\(865\) 3.26955 0.111168
\(866\) 18.5630 0.630797
\(867\) 0 0
\(868\) −6.47911 −0.219915
\(869\) −45.2420 −1.53473
\(870\) 0 0
\(871\) −12.5623 −0.425657
\(872\) −5.16345 −0.174856
\(873\) 0 0
\(874\) 8.70526 0.294460
\(875\) −77.9931 −2.63665
\(876\) 0 0
\(877\) 46.5013 1.57024 0.785119 0.619345i \(-0.212602\pi\)
0.785119 + 0.619345i \(0.212602\pi\)
\(878\) −11.6378 −0.392758
\(879\) 0 0
\(880\) 64.1134 2.16126
\(881\) −46.8173 −1.57731 −0.788657 0.614834i \(-0.789223\pi\)
−0.788657 + 0.614834i \(0.789223\pi\)
\(882\) 0 0
\(883\) 19.4950 0.656059 0.328030 0.944667i \(-0.393615\pi\)
0.328030 + 0.944667i \(0.393615\pi\)
\(884\) 5.37097 0.180645
\(885\) 0 0
\(886\) −44.6927 −1.50148
\(887\) −30.4696 −1.02307 −0.511534 0.859263i \(-0.670923\pi\)
−0.511534 + 0.859263i \(0.670923\pi\)
\(888\) 0 0
\(889\) −6.60451 −0.221508
\(890\) −15.9879 −0.535917
\(891\) 0 0
\(892\) −0.245169 −0.00820885
\(893\) 38.1595 1.27696
\(894\) 0 0
\(895\) 25.3435 0.847141
\(896\) 23.7155 0.792278
\(897\) 0 0
\(898\) 5.16444 0.172340
\(899\) 9.08138 0.302881
\(900\) 0 0
\(901\) −4.34293 −0.144684
\(902\) 15.7896 0.525736
\(903\) 0 0
\(904\) 10.8486 0.360818
\(905\) −70.2778 −2.33611
\(906\) 0 0
\(907\) 30.3091 1.00640 0.503199 0.864171i \(-0.332156\pi\)
0.503199 + 0.864171i \(0.332156\pi\)
\(908\) 5.27260 0.174977
\(909\) 0 0
\(910\) −94.8502 −3.14425
\(911\) 5.21341 0.172728 0.0863639 0.996264i \(-0.472475\pi\)
0.0863639 + 0.996264i \(0.472475\pi\)
\(912\) 0 0
\(913\) −52.5945 −1.74063
\(914\) 26.1997 0.866609
\(915\) 0 0
\(916\) −1.78201 −0.0588792
\(917\) −43.0314 −1.42102
\(918\) 0 0
\(919\) 25.4577 0.839774 0.419887 0.907577i \(-0.362070\pi\)
0.419887 + 0.907577i \(0.362070\pi\)
\(920\) −12.2552 −0.404042
\(921\) 0 0
\(922\) −21.7131 −0.715083
\(923\) −29.5952 −0.974137
\(924\) 0 0
\(925\) 78.7045 2.58779
\(926\) −33.6373 −1.10539
\(927\) 0 0
\(928\) 1.45860 0.0478808
\(929\) 25.6824 0.842614 0.421307 0.906918i \(-0.361572\pi\)
0.421307 + 0.906918i \(0.361572\pi\)
\(930\) 0 0
\(931\) 3.66345 0.120065
\(932\) −2.56423 −0.0839941
\(933\) 0 0
\(934\) −30.1020 −0.984967
\(935\) −61.0860 −1.99773
\(936\) 0 0
\(937\) 31.5910 1.03203 0.516017 0.856579i \(-0.327414\pi\)
0.516017 + 0.856579i \(0.327414\pi\)
\(938\) 7.15981 0.233776
\(939\) 0 0
\(940\) −6.17104 −0.201277
\(941\) 11.2334 0.366197 0.183099 0.983095i \(-0.441387\pi\)
0.183099 + 0.983095i \(0.441387\pi\)
\(942\) 0 0
\(943\) −2.61975 −0.0853109
\(944\) 26.1800 0.852088
\(945\) 0 0
\(946\) −52.1554 −1.69572
\(947\) −3.53968 −0.115024 −0.0575120 0.998345i \(-0.518317\pi\)
−0.0575120 + 0.998345i \(0.518317\pi\)
\(948\) 0 0
\(949\) 44.2401 1.43609
\(950\) −103.609 −3.36152
\(951\) 0 0
\(952\) −26.6483 −0.863676
\(953\) 19.3911 0.628139 0.314070 0.949400i \(-0.398307\pi\)
0.314070 + 0.949400i \(0.398307\pi\)
\(954\) 0 0
\(955\) −18.8496 −0.609960
\(956\) 2.58528 0.0836138
\(957\) 0 0
\(958\) 57.3584 1.85317
\(959\) −55.5368 −1.79338
\(960\) 0 0
\(961\) 51.4715 1.66037
\(962\) 55.5051 1.78956
\(963\) 0 0
\(964\) −1.80692 −0.0581970
\(965\) 61.0916 1.96661
\(966\) 0 0
\(967\) −25.7607 −0.828409 −0.414204 0.910184i \(-0.635940\pi\)
−0.414204 + 0.910184i \(0.635940\pi\)
\(968\) 29.4277 0.945841
\(969\) 0 0
\(970\) −12.2843 −0.394424
\(971\) 1.98623 0.0637411 0.0318706 0.999492i \(-0.489854\pi\)
0.0318706 + 0.999492i \(0.489854\pi\)
\(972\) 0 0
\(973\) −24.5918 −0.788377
\(974\) 1.41772 0.0454268
\(975\) 0 0
\(976\) −17.8313 −0.570766
\(977\) −62.0767 −1.98601 −0.993004 0.118080i \(-0.962326\pi\)
−0.993004 + 0.118080i \(0.962326\pi\)
\(978\) 0 0
\(979\) −13.4672 −0.430413
\(980\) −0.592443 −0.0189249
\(981\) 0 0
\(982\) 16.4030 0.523441
\(983\) −10.1811 −0.324726 −0.162363 0.986731i \(-0.551912\pi\)
−0.162363 + 0.986731i \(0.551912\pi\)
\(984\) 0 0
\(985\) 69.1401 2.20299
\(986\) 4.29064 0.136642
\(987\) 0 0
\(988\) 10.8971 0.346684
\(989\) 8.65344 0.275163
\(990\) 0 0
\(991\) 37.7804 1.20013 0.600067 0.799950i \(-0.295141\pi\)
0.600067 + 0.799950i \(0.295141\pi\)
\(992\) 13.2461 0.420563
\(993\) 0 0
\(994\) 16.8676 0.535008
\(995\) 43.8670 1.39068
\(996\) 0 0
\(997\) −58.3762 −1.84879 −0.924396 0.381435i \(-0.875430\pi\)
−0.924396 + 0.381435i \(0.875430\pi\)
\(998\) 9.83583 0.311348
\(999\) 0 0
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 6003.2.a.l.1.4 10
3.2 odd 2 667.2.a.a.1.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
667.2.a.a.1.7 10 3.2 odd 2
6003.2.a.l.1.4 10 1.1 even 1 trivial